0
A345206-A343330-A342676-A337917-A337196-A336355-A335520-A335462-A335453-A334740-A332671-A330735-A326688-A326687-A326686-A326685-A326684-A326683-A326682-A326681-A326680-A326679-A326678-A326549-A326548-A326547-A326546-A326545-A326544-A326543-A326542-A326541-A326540-A326463-A326462-A326461-A326460-A326459-A326458-A326457-A326456-A326455-A326292-A326291-A326075-A325720-A325650-A325318-A324870-A324803-A324802-A324731-A324179-A322438-A322437-A320742-A320647-A308583-A307721-A307343-A305892-A305821-A304572-A304571-A304570-A302907-A297247-A297244-A297046-A297045-A294929-A294889-A285007-A285006-A285005-A284978-A284974-A282289-A280815-A280617-A280492-A277165-A277164-A276653-A276570-A276183-A272624-A264668-A264009-A263787-A263014-A260502-A256974-A250002-A248805-A246580-A246578-A244606-A243836-A243835-A243834-A243833-A243832-A243831-A243199-A242435-A241690-A238403-A237123-A236460-A236417-A236374-A236265-A236241-A235358-A235145-A235044-A230915-A230686-A230571-A230533-A230398-A228953-A220441-A220093-A217156-A217155-A217151-A217149-A217148-A212619-A210718-A210633-A210632-A206499-A200214-A198255-A197629-A192541-A191928-A189973-A185715-A185709-A185294-A185284-A185264-A185255-A185246-A185245-A185244-A185238-A185237-A185229-A185228-A185203-A185044-A185037-A184946-A184945-A181838-A181735-A181340-A181009-A180995-A180989-A180601-A180472-A178798-A178780-A167263-A165878-A165766-A161280-A161279-A161278-A161277-A161276-A161275-A160990-A160989-A160988-A160987-A159708-A141097-A137579-A129947-A127937-A122180-A112802-A111899-A111898-A111895-A111859-A111855-A108322-A105519-A105517-A105514-A094382-A093392-A090318-A089458-A089457-A089456-A086015-A086007-A085982-A085980-A085974-A083344-A082998-A076142-A072769-A072325-A071839-A070206-A070205-A070204-A070202-A070141-A070097-A067169-A067168-A067159-A067157-A066035-A065687-A065685-A061858-A055967-A055965-A054900-A054439-A053473-A052375-A048037-A048026-A047752-A036877-A036861-A034582-A034581-A034580-A034579-A034578-A034577-A034576-A034575-A034574-A034573-A034572-A034571-A034570-A034569-A034568-A034567-A034566-A034565-A034564-A034563-A034562-A034561-A034560-A034559-A034558-A034557-A034556-A034555-A034554-A034553-A034552-A034551-A034550-A034549-A034548-A034547-A034546-A034545-A034544-A034543-A034542-A034541-A034540-A034539-A034538-A034537-A034536-A034535-A034534-A034533-A034532-A034531-A034530-A034529-A034528-A034527-A034526-A034525-A034523-A034522-A034521-A034520-A034519-A034518-A034516-A034515-A034514-A034512-A034511-A034510-A034509-A034508-A034507-A034506-A034505-A034504-A034503-A034502-A034501-A034500-A034499-A034498-A034497-A034495-A034493-A034492-A034490-A034489-A034487-A034486-A034485-A034484-A034483-A034482-A034481-A034480-A034479-A034477-A034476-A034475-A034473-A034471-A034469-A034468-A034467-A034466-A034465-A034464-A034462-A034461-A034459-A034458-A034457-A034456-A034455-A034454-A034453-A034452-A034451-A034450-A034449-A034447-A034446-A034445-A034443-A034441-A034440-A034439-A034438-A034437-A034435-A034434-A034432-A034431-A034429-A034427-A034426-A034425-A034424-A034423-A034422-A034421-A034420-A034419-A034417-A025469-A025466-A025444-A025443-A025439-A025438-A024682-A024681-A023976-A023975-A023974-A020740-A011745-A011744-A011743-A011742-A011741-A011740-A011739-A011738-A011737-A011736-A011735-A011734-A011733-A011732-A011731-A011730-A007394-A006983-A000004: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1
A346418-A339235-A336697-A336468-A335078-A330098-A326307-A322674-A319150-A319101-A318809-A318671-A316439-A309913-A307156-A305195-A304042-A296077-A291168-A291149-A290105-A289014-A288120-A287091-A284562-A280865-A279759-A279185-A278657-A275216-A274196-A272901-A272038-A271955-A271954-A271839-A271838-A271837-A269301-A266227-A262681-A262438-A262079-A260897-A254730-A254609-A249770-A242718-A240228-A239700-A236861-A231072-A215788-A214956-A213982-A195061-A194333-A194293-A194285-A193518-A193179-A184348-A184303-A180466-A179742-A178688-A177849-A175782-A172369-A172368-A172363-A172098-A167966-A167965-A167964-A161996-A161618-A160338-A153683-A153675-A152907-A152851-A152849-A152848-A152847-A152846-A152845-A152844-A152831-A141605-A139553-A139551-A139039-A137979-A136640-A135362-A133707-A127836-A125891-A121657-A119849-A119335-A117456-A113515-A111024-A103159-A102609-A101598-A098190-A097876-A097031-A096811-A091717-A085685-A082586-A079724-A076498-A074481-A070672-A066701-A064284-A063435-A062513-A061653-A061494-A059197-A059196-A053878-A049107-A049100-A043568-A043290-A036225-A035115-A032548-A032545-A030599-A016300-A016288-A016272-A016266-A016240-A016236-A016210-A016192-A016182-A016168-A016156-A016126-A016086-A016080-A016068-A016056-A016042-A016030-A015970-A015966-A015952-A015936-A015930-A015928-A015918-A015900-A015862-A015852-A015838-A015828-A015826-A015778-A015772-A015760-A015748-A015726-A015720-A015700-A015688-A015658-A015652-A015642-A015600-A015586-A015550-A015546-A015526-A015522-A015510-A015466-A015420-A015412-A015396-A015372-A015366-A015358-A015352-A015342-A015282-A015280-A015256-A015250-A015228-A015216-A015198-A015168-A015156-A015148-A015130-A015090-A015082-A015046-A015016-A015012-A014998-A014952-A014910-A014908-A014902-A014860-A014826-A014808-A014788-A014740-A014722-A014712-A014706-A014676-A014638-A014598-A014560-A014536-A014502-A014446-A014400-A014332-A000012: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2
A296076-A242259-A239374-A194338-A194334-A176170-A076303-A007395: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
x
A103303: 0 1 2 3 4 5 6 7 8 9
A345201-A341936-A341709-A335525-A335524-A335469-A331172-A328447-A326880-A326872-A323048-A322463-A298639-A292579-A291179-A277112-A275993-A274846-A274399-A273888-A273887-A273886-A273885-A273884-A273883-A273882-A273881-A273880-A272813-A272554-A272443-A272437-A272325-A272323-A272322-A272302-A272284-A272269-A272159-A272118-A272076-A272074-A271980-A271143-A268200-A267086-A267069-A266279-A262545-A262437-A262065-A261924-A260255-A258071-A258070-A258069-A258068-A258009-A256577-A254109-A250395-A250394-A247759-A247756-A247752-A247751-A247163-A247151-A239427-A236851-A236850-A236841-A236674-A229621-A214922-A203565-A191932-A191853-A188459-A182049-A179239-A175427-A171829-A167129-A160700-A154470-A138234-A136602-A135383-A135382-A135381-A130909-A130734-A130696-A128829-A124695-A123719-A123068-A118760-A118759-A115847-A114086-A113221-A113219-A108192-A106620-A106618-A090273-A089870-A089869-A089868-A089867-A084688-A081331-A078453-A076121-A071670-A071669-A066566-A059962-A057946-A057605-A056963-A056962-A056561-A055645-A055644-A055643-A053836-A052060-A052057-A051108-A051107-A050723-A050608-A048340-A048327-A048313-A046510-A043275-A039691-A036218-A033619-A032521-A032520-A032517-A032513-A032512-A030066-A029730-A028823-A025484-A025483-A023810-A023809-A023797-A023796-A023784-A023771-A023770-A023769-A023757-A008554-A004830-A002837-A001477: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
3
A157831-A053444-A010701: 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
(x + 1)
A342591-A342523-A341749-A338555-A338497-A338331-A338265-A336358-A335376-A335282-A335280-A330232-A328617-A326200-A325400-A325383-A325360-A324720-A323404-A323368-A323366-A322554-A321993-A321293-A320249-A320113-A318893-A318892-A318535-A317945-A317257-A316530-A308702-A303502-A302026-A302025-A301274-A300473-A298359-A296906-A296903-A296900-A296897-A296894-A296891-A296888-A296885-A296882-A296879-A296876-A296873-A296870-A296867-A296864-A296765-A296762-A296089-A296088-A295886-A295020-A291769-A289555-A287478-A285054-A281873-A276568-A276347-A275776-A275164-A275156-A274055-A273058-A272215-A269396-A269395-A269394-A269393-A269331-A269172-A269171-A265711-A263314-A263028-A262530-A260424-A260423-A258266-A255422-A255421-A255408-A255407-A250251-A250250-A250249-A250248-A250247-A250246-A250245-A250244-A250243-A249830-A249818-A249817-A249816-A249815-A247064-A246103-A246102-A246101-A246100-A246099-A246098-A246097-A246095-A246094-A246093-A246091-A246090-A246089-A246087-A246086-A246083-A246082-A246079-A246076-A243903-A242474-A242031-A241989-A241673-A230034-A227981-A226537-A214701-A212554-A204315-A197640-A194967-A194966-A194907-A194906-A194417-A193989-A192438-A188462-A180925-A180493-A179978-A179797-A178772-A178157-A174670-A174228-A167976-A167975-A167974-A167662-A166719-A166718-A164710-A160547-A160546-A160544-A160543-A153679-A153671-A151764-A144972-A137317-A135579-A133137-A132264-A132263-A132086-A132033-A132016-A130446-A124231-A122937-A122079-A121761-A120951-A110548-A110303-A107602-A102800-A098452-A098451-A096105-A094759-A093618-A093616-A092629-A090322-A090111-A090110-A090109-A090108-A090107-A090106-A089247-A088480-A088382-A087143-A085736-A085735-A084981-A083243-A080686-A080685-A080684-A080683-A080682-A080681-A080197-A077342-A076499-A076084-A074805-A072676-A070915-A069782-A067080-A064598-A062996-A060340-A056064-A052425-A048266-A048242-A044923-A044922-A044921-A038770-A034837-A032966-A032951-A022465-A008684-A005555-A004441-A004438-A000027: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
(x + ~1)
A023443: ~1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
4
A010709: 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
(x + 2)
A309810-A309066-A292740-A276181-A261906-A257333-A230308-A228144-A193176-A192218-A162421-A146297-A146296-A146295-A132145-A114142-A109427-A109425-A104661-A085380-A081330-A058321-A030545-A030542-A020725: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
(x + ~2)
A023444: ~2 ~1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
2x
A055966-A055964-A005843: 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
(x div 2)
A331163-A330027-A330015-A327036-A274618-A111660-A021895-A004526: 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7
(x mod 2)
A339933-A216188-A125122-A000035: 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
~x
A001489: 0 ~1 ~2 ~3 ~4 ~5 ~6 ~7 ~8 ~9 ~10 ~11 ~12 ~13 ~14 ~15
(~x + 1)
A024000: 1 0 ~1 ~2 ~3 ~4 ~5 ~6 ~7 ~8 ~9 ~10 ~11 ~12 ~13 ~14
(~x + 2)
A022958: 2 1 0 ~1 ~2 ~3 ~4 ~5 ~6 ~7 ~8 ~9 ~10 ~11 ~12 ~13
x2
A174452-A000290: 0 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225
(if x <= 0 then 1 else 0)
A341882-A341881-A341001-A341000-A340999-A325742-A323538-A319330-A318715-A307382-A285698-A284757-A278297-A249832-A240351-A226120-A210709-A181154-A172542-A151935-A151934-A151933-A151909-A151878-A151838-A151818-A151815-A151813-A151812-A151811-A151810-A151722-A151721-A151713-A151660-A151623-A151622-A151621-A151620-A147531-A146888-A134975-A112316-A112315-A112314-A111332-A097479-A091536-A088157-A088156-A088155-A080953-A076710-A072189-A067158-A067156-A058348-A058343-A023935-A023933-A023931-A023929-A018895-A018843-A015161-A015070-A014041-A010894-A010893-A000007: 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(if x <= 0 then 2 else 0)
A000038: 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(if x <= 0 then 0 else 1)
A328672-A324872-A323022-A319689-A319679-A309026-A304118-A267084-A265404-A255270-A231560-A213004-A211666-A178489-A178487-A178334-A139128-A057427: 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(if x <= 0 then 2 else 1)
A058665-A054977: 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(if x <= 0 then 1 else 2)
A343356-A292563-A242253-A177830-A108248-A087104-A040000-A036453-A036452: 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
(if x <= 0 then 1 else x)
A028310: 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
5
A010716: 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
(x + ~3)
A023445: ~3 ~2 ~1 0 1 2 3 4 5 6 7 8 9 10 11 12
(x div 3)
A172474-A113675-A002264: 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4 5
(x mod 3)
A010872: 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
(x + 3)
A154660: 3 4 5 6 7 8
A141213-A081311-A062983-A053233-A030544-A009056: 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
(2x + 1)
A326835-A317439-A317107-A294748-A283002-A247328-A176271-A105356-A089684-A053229-A033041-A005408: 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
(2x + ~1)
A060747: ~1 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
(1 + (x div 2))
A320467-A242681-A157271-A135020-A086388-A008619: 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8
(1 + (x mod 2))
A322357-A184319-A000034: 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
(~x + ~1)
A001478: ~1 ~2 ~3 ~4 ~5 ~6 ~7 ~8 ~9 ~10 ~11 ~12 ~13 ~14 ~15 ~16
(~x + 3)
A022959: 3 2 1 0 ~1 ~2 ~3 ~4 ~5 ~6 ~7 ~8 ~9 ~10 ~11 ~12
(2 div (x + 1))
A033322: 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(x2 + 1)
A172411: 1 2 5 10
A217990-A002522: 1 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226
(x mod ~2)
A293704-A262352: 0 ~1 0 ~1 0 ~1 0 ~1 0 ~1 0 ~1 0 ~1 0 ~1
6
A010722: 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
(2x + 2)
A317440-A317108-A306720-A299174-A141098-A122080-A119432-A087113-A084564-A084563-A053228: 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
((x + 1) div 2)
A110654-A076938: 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8
((x + 1) mod 2)
A331218-A250299-A196563-A102818-A079806-A059841: 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
8
A010731: 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
(x + ~4)
A023446: ~4 ~3 ~2 ~1 0 1 2 3 4 5 6 7 8 9 10 11
(x div 4)
A090617-A054893-A002265: 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3
(x mod 4)
A189480-A010873: 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
(x + 4)
A227983-A114143-A081333-A081313-A030543-A020705: 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
(2x + 4)
A193175-A063127: 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34
4x
A189917-A172326-A008586: 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60
(2 * (x div 2))
A052928: 0 0 2 2 4 4 6 6 8 8 10 10 12 12 14 14
((x div 2) mod 2)
A285501-A188257-A021913: 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
(2 + (x mod 2))
A010693: 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3
(2 * (x mod 2))
A010673: 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2
(~2x + 2)
A239229: 2 0 ~2 ~4 ~6 ~8 ~10 ~12 ~14 ~16 ~18 ~20 ~22 ~24 ~26 ~28
(~x + 4)
A022960: 4 3 2 1 0 ~1 ~2 ~3 ~4 ~5 ~6 ~7 ~8 ~9 ~10 ~11
(~2x + 1)
A165747: 1 ~1 ~3 ~5 ~7 ~9 ~11 ~13 ~15 ~17 ~19 ~21 ~23 ~25 ~27 ~29
(x2 + 2)
A157656: 2 3 6 11 18 27
A059100: 2 3 6 11 18 27 38 51 66 83 102 123 146 171 198 227
2x2
A001105: 0 2 8 18 32 50 72 98 128 162 200 242 288 338 392 450
(x2 div 2)
A007590: 0 0 2 4 8 12 18 24 32 40 50 60 72 84 98 112
3x
A008585: 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45
(x2 + x)
A002378: 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240
(x2 + ~x)
A279019: 0 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210
(x2 + 2x)
A005563: 0 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255
(x2 + ~2x)
A067998: 0 ~1 0 3 8 15 24 35 48 63 80 99 120 143 168 195
(x + (x div 2))
A275672: 0 1 3 4 6 7 9
A258574-A032766: 0 1 3 4 6 7 9 10 12 13 15 16 18 19 21 22
(x * (x mod 2))
A167465: 0 1 0 3 0 5 0 7 0 9 0 11 0 13 0 15
(~x2 + 1)
A258837: 1 0 ~3 ~8 ~15 ~24 ~35 ~48 ~63 ~80 ~99 ~120 ~143 ~168 ~195 ~224
x3
A000578: 0 1 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375
(if x <= 0 then ~1 else 0)
A328959: ~1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (x + ~1) <= 0 then 1 else 0)
A322308-A322281-A298859-A292547-A256433-A240357-A205987-A179961-A019590-A014071-A014067-A014055-A014047-A014043: 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(if x <= 0 then 3 else 0)
A307802: 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (x + ~2) <= 0 then 1 else 0)
A130716-A094497-A094496-A014102-A014096-A014078-A014066-A014060: 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (~x + 2) <= 0 then 1 else 0)
A274070-A225654-A157928-A077433: 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(1 - (if x <= 0 then 2 else 0))
A158388: ~1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(if (x + ~1) <= 0 then x else 0)
A326168-A216284-A178333-A084928-A074038-A063524-A033683: 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (x mod 2) <= 0 then x else 0)
A237420: 0 0 2 0 4 0 6 0 8 0 10 0 12 0 14 0
(if (~x + 2) <= 0 then x else 0)
A199969: 0 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15
(~1 + (if x <= 0 then 1 else 0))
A057428: 0 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1
(if (x + ~2) <= 0 then 0 else 1)
A065686-A000520: 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1
(~1 + (if x <= 0 then 2 else 0))
A153881: 1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1
(x - (if x <= 0 then 0 else 1))
A172275-A139179: 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
(1 + (if x <= 0 then 2 else 1))
A178815: 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
(1 + (if x <= 0 then 0 else 2))
A122916: 1 3 3 3 3
A122553-A087717: 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
(if (x + ~1) <= 0 then 2 else 1)
A141044: 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(1 + (if x <= 0 then 1 else 2))
A244919-A157532: 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
(if (~x + 2) <= 0 then 2 else 1)
A341422-A211661-A087103-A053230: 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
(if (x + ~2) <= 0 then x else 1)
A294619: 0 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1
loop(\(x,i).2x,x,1)
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A123464: 1 2 4 8 16 32 64 128 256 512
A323830-A320487-A260814-A247208-A118655-A050732-A000079: 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768
(if x <= 0 then 0 else (x + 1))
A191882-A173474-A158377-A087156: 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
loop(\(x,i).(x * i),x,1)
A000142: 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000
(if (x + ~2) <= 0 then 1 else 2)
A329683-A204560-A086858: 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2
(2 + (if x <= 0 then 0 else 2))
A040002: 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
(2 + (if x <= 0 then 1 else 2))
A255176: 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
(if x <= 0 then 1 else 4)
A141248-A123932: 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
(if (x + ~1) <= 0 then x else 2)
A130130: 0 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
(2 * (if x <= 0 then 1 else x))
A202102: 2 2 4 6 8 10
((if x <= 0 then 1 else x) mod 2)
A135528-A098800: 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
loop(\(x,i).2x,x,2)
A025489: 2 4 8 16 32 64
((if x <= 0 then 2 else x) div 2)
A123108: 1 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7
(if x <= 0 then 0 else (x + 2))
A114637-A029674: 0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
(if x <= 0 then 1 else (x + 2))
A121818-A065475-A026505: 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
(if x <= 0 then 1 else 2x)
A241071: 1 2 4 6 8 10 12
A271907: 1 2 4 6 8 10 12 14 16 18
A338922-A105360-A076032-A004277: 1 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
(if x <= 0 then 2 else (x mod 2))
A215036: 2 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
(if (~x + 2) <= 0 then x else 2)
A233583: 2 2 2 3 4 5 6 7 8 9 10 11 12 13 14 15
loop(\(x,i).x2,x,2)
A001146: 2 4 16 256 65536 4294967296 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),x,2)
A208529: 2 2 4 12 48 240 1440 10080 80640 725760 7257600 79833600 958003200 12454041600 174356582400 2615348736000
(if (x mod 2) <= 0 then 1 else x)
A093178: 1 1 1 3 1 5 1 7 1 9 1 11 1 13 1 15
(1 mod (if x <= 0 then 2 else x))
A339221-A060576: 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(2 div (if x <= 0 then 2 else x))
A130713: 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0
loop(\(x,i).2x,x,x)
A036289: 0 2 8 24 64 160 384 896 2048 4608 10240 22528 49152 106496 229376 491520
(if x <= 0 then 1 else x2)
A253909: 1 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225
loop(\(x,i).x2,x,x)
A097547: 0 1 16 6561 4294967296 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),x,x)
A001563: 0 1 4 18 96 600 4320 35280 322560 3265920 36288000 439084800 5748019200 80951270400 1220496076800 19615115520000
(1 + (x div 3))
A296357-A127757-A008620: 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6
(1 + (x mod 3))
A010882: 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1
(~1 + (2 mod (x + 1)))
A299912: ~1 ~1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
7
A010727: 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
(2x + 3)
A144396-A082453-A081874: 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33
(1 + ((x + 1) div 2))
A330878-A109728-A080513: 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9
9
A292864-A181693-A099646-A010734: 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
(x + ~5)
A023447: ~5 ~4 ~3 ~2 ~1 0 1 2 3 4 5 6 7 8 9 10
(x div 5)
A301506-A108611-A027868-A002266: 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3
(x mod 5)
A278182-A010874: 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0
(1 + (x div 4))
A328301-A235492-A226762-A008652-A008621: 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4
(1 + (x mod 4))
A010883: 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
(x + 5)
A030541-A020710: 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(2x + 5)
A333038-A049013-A020735: 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35
(4x + 1)
A016813: 1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61
(1 + (2 * (x div 2)))
A293701-A109613: 1 1 3 3 5 5 7 7 9 9 11 11 13 13 15 15
(1 + ((x div 2) mod 2))
A130658: 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2
(3 + (x mod 2))
A010702: 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4
(1 + (2 * (x mod 2)))
A010684: 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3
(3x + 3)
A337244-A194416-A135943-A031193: 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48
((x + 1) div 3)
A157685-A062299: 0 0 1 1 1 2 2 2 3 3 3 4 4 4 5 5
12
A010851: 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
((x + 2) div 3)
A261916: 0 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5
6x
A008588: 0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90
(2x div 3)
A121930-A004523: 0 0 1 2 2 3 4 4 5 6 6 7 8 8 9 10
(2x mod 3)
A080425: 0 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0
(3 * (x div 2))
A168237: 0 0 3 3 6 6 9 9 12 12 15 15 18 18 21 21
((x div 2) div 3)
A340763-A152467-A111856-A054895: 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2
((x div 2) mod 3)
A131555: 0 0 1 1 2 2 0 0 1 1 2 2 0 0 1 1
(3 * (x mod 2))
A021037-A010674: 0 3 0 3 0 3 0 3 0 3 0 3 0 3 0 3
(~x + 5)
A022961: 5 4 3 2 1 0 ~1 ~2 ~3 ~4 ~5 ~6 ~7 ~8 ~9 ~10
(x - (x div 3))
A322042-A032509: 0 1 2 2 3 4 4 5 6 6 7 8 8 9 10 10
(1 - (x mod 3))
A057078: 1 0 ~1 1 0 ~1 1 0 ~1 1 0 ~1 1 0 ~1 1
(x2 + 3)
A117950: 3 4 7 12 19 28 39 52 67 84 103 124 147 172 199 228
3x2
A033428: 0 3 12 27 48 75 108 147 192 243 300 363 432 507 588 675
(x2 div 3)
A000212: 0 0 1 3 5 8 12 16 21 27 33 40 48 56 65 75
(x2 mod 3)
A022928-A011655: 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0
(x mod (1 + (x div 2)))
A140106: 0 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7
(3 - (x mod 2))
A176059: 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2
(x div (1 + (x mod 2)))
A065423: 0 0 2 1 4 2 6 3 8 4 10 5 12 6 14 7
(2x2 + 1)
A058331: 1 3 9 19 33 51 73 99 129 163 201 243 289 339 393 451
(2x2 + ~1)
A056220: ~1 1 7 17 31 49 71 97 127 161 199 241 287 337 391 449
(1 + (x2 div 2))
A099392: 1 1 3 5 9 13 19 25 33 41 51 61 73 85 99 113
(3x + 1)
A145289-A016777: 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46
(x2 + x + 1)
A169627: 1 3 7 13 21 31
A247890: 1 3 7 13 21 31 43 57 73 91 111 133 157 183 211 241
(x2 + ~x + 1)
A084537-A002061: 1 1 3 7 13 21 31 43 57 73 91 111 133 157 183 211
(x2 + ~x + ~1)
A165900: ~1 ~1 1 5 11 19 29 41 55 71 89 109 131 155 181 209
(x2 + 2x + 1)
A221222: 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256
(x2 + 2x + ~1)
A008865: ~1 2 7 14 23 34 47 62 79 98 119 142 167 194 223 254
(x2 + ~2x + 1)
A174902: 1 0 1 4 9 16 25 36 49 64 81 100 121 144 169 196
((x + 1) + (x div 2))
A329925-A329843-A292640-A274384-A248607-A224999-A191266-A127450-A059564-A054386-A001651: 1 2 4 5 7 8 10 11 13 14 16 17 19 20 22 23
(3 div (x + 1))
A278105: 3 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
(4x + 4)
A337080-A059558: 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64
(4 div (x + 1))
A033324: 4 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0
(1 - (2 div (x + 1)))
A261012: ~1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(2x2 + 2x)
A046092: 0 4 12 24 40 60 84 112 144 180 220 264 312 364 420 480
(x3 + x2)
A011379: 0 2 12 36 80 150 252 392 576 810 1100 1452 1872 2366 2940 3600
(x3 + ~x2)
A045991: 0 0 4 18 48 100 180 294 448 648 900 1210 1584 2028 2548 3150
(2 - (x div ~2))
A177876: 2 3 3 4
(x - (x div ~2))
A258575-A007494: 0 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23
10
A010692: 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
(x + ~6)
A023448: ~6 ~5 ~4 ~3 ~2 ~1 0 1 2 3 4 5 6 7 8 9
(x mod 6)
A010875: 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3
(2 + (x div 3))
A079001: 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7
((x mod 3) div 2)
A286747-A285936-A212663-A144604-A022926-A022003: 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0
(2x + 6)
A064466-A020739: 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
(4x + 2)
A122905-A016825: 2 6 10 14 18 22 26 30 34 38 42 46 50 54 58 62
((1 + (x div 2)) div 2)
A326032: 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4
((1 + (x div 2)) mod 2)
A320006-A133872: 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0
(2 * (1 + (x mod 2)))
A010694: 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4
(2 + (2 mod (x + 1)))
A267649: 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4
(2x2 + 2)
A271624: 2 4 10 20 34 52 74 100 130 164 202 244 290 340 394 452
((x2 + 1) div 2)
A192225: 0 1 2 5
A000982: 0 1 2 5 8 13 18 25 32 41 50 61 72 85 98 113
((x div ~2) mod 2)
A269927: 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0
(((x + 1) div 2) div 2)
A129253: 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4
16
A010855: 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
(x + ~8)
A023450: ~8 ~7 ~6 ~5 ~4 ~3 ~2 ~1 0 1 2 3 4 5 6 7
(x div 8)
A303119-A297037-A294234-A277158-A161314-A161300-A161287-A161262-A161248-A161234-A161110-A161097-A161084-A161071-A161058-A161045-A161033-A160979-A132292-A054897-A035672-A033112: 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
(x mod 8)
A309959-A010877: 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
(2 * (x div 4))
A122461: 0 0 0 0 2 2 2 2 4 4 4 4 6 6 6 6
(2 + (x mod 4))
A328943: 2 3 4 5 2 3 4 5 2 3 4 5 2 3 4 5
(2 * (x mod 4))
A131806: 0 2 4 6 0 2 4 6 0 2 4 6 0 2 4 6
(x + 6)
A030546-A020715: 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
(2x + 8)
A020744: 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38
(4x + 8)
A192544: 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68
8x
A008590: 0 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120
(4 + (x mod 2))
A010710: 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5
(2 * (2 + (x mod 2)))
A010711: 4 6 4 6 4 6 4 6 4 6 4 6 4 6 4 6
(4 * (x mod 2))
A010675: 0 4 0 4 0 4 0 4 0 4 0 4 0 4 0 4
(~x mod 4)
A158459: 0 3 2 1 0 3 2 1 0 3 2 1 0 3 2 1
(~x + 6)
A022962: 6 5 4 3 2 1 0 ~1 ~2 ~3 ~4 ~5 ~6 ~7 ~8 ~9
(x - (x div 4))
A215090-A093700-A076539: 0 1 2 3 3 4 5 6 6 7 8 9 9 10 11 12
(x2 + 4)
A087475: 4 5 8 13 20 29 40 53 68 85 104 125 148 173 200 229
4x2
A016742: 0 4 16 36 64 100 144 196 256 324 400 484 576 676 784 900
(x2 div 4)
A002620: 0 0 1 2 4 6 9 12 16 20 25 30 36 42 49 56
(2 * (2 - (x mod 2)))
A105397: 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2
(x mod (2 + (x mod 2)))
A110270: 0 1 0 0 0 2 0 1 0 0 0 2 0 1 0 0
(1 - (2 * (x mod 2)))
A033999-A016327-A016303-A016287-A016251-A016171-A016155-A016083-A016023-A016015-A015987-A015895-A015811-A015807-A015795-A015711-A015643-A015607-A015567-A015471-A015435-A015415-A015403-A015343-A015267-A015187-A015111-A015063-A014995-A014883-A014791-A014655: 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1
(2x2 + 4)
A255843: 4 6 12 22 36 54 76 102 132 166 204 246 292 342 396 454
(3x + 2)
A292661-A190082-A016789: 2 5 8 11 14 17 20 23 26 29 32 35 38 41 44 47
(x2 + x + 2)
A014206: 2 4 8 14 22 32 44 58 74 92 112 134 158 184 212 242
((x2 + x) div 2)
A130910-A109811-A105340-A105339-A105338-A105337-A105336-A078256-A077367-A000217: 0 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120
((x2 + ~x) div 2)
A161680: 0 0 1 3 6 10 15 21 28 36 45 55 66 78 91 105
(x2 + 2x + ~2)
A123968: ~2 1 6 13 22 33 46 61 78 97 118 141 166 193 222 253
(2x2 + 4x)
A054000: 0 6 16 30 48 70 96 126 160 198 240 286 336 390 448 510
(x2 + ~2x + 2)
A160457: 2 1 2 5 10 17 26 37 50 65 82 101 122 145 170 197
((x + 2) + (x div 2))
A052490: 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24
(2 * (x + (x div 2)))
A047238: 0 2 6 8 12 14 18 20 24 26 30 32 36 38 42 44
((x + (x div 2)) div 2)
A187329-A057353: 0 0 1 2 3 3 4 5 6 6 7 8 9 9 10 11
((x * (x div 2)) mod 2)
A342024-A342023-A331282-A331169-A285464-A276077-A188221-A129251-A011765: 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
(2 * (x + (x mod 2)))
A168273: 0 4 4 8 8 12 12 16 16 20 20 24 24 28 28 32
((x * (x mod 2)) div 2)
A234585-A234584-A234583-A034948: 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7
(2x + (x div 2))
A047215-A038126: 0 2 5 7 10 12 15 17 20 22 25 27 30 32 35 37
(2x + (x mod 2))
A014601: 0 3 4 7 8 11 12 15 16 19 20 23 24 27 28 31
2x3
A033431: 0 2 16 54 128 250 432 686 1024 1458 2000 2662 3456 4394 5488 6750
((x div 2) * (x div 2))
A008794: 0 0 1 1 4 4 9 9 16 16 25 25 36 36 49 49
(x2 + (x div 2))
A035608: 0 1 5 10 18 27 39 52 68 85 105 126 150 175 203 232
(x2 - (x div 2))
A014848: 0 1 3 8 14 23 33 46 60 77 95 116 138 163 189 218
(x2 * (x div 2))
A265645: 0 0 4 9 32 50 108 147 256 324 500 605 864 1014 1372 1575
(x div (2 - (x mod 2)))
A026741: 0 1 1 3 2 5 3 7 4 9 5 11 6 13 7 15
(2x - (x mod 2))
A126001-A042948: 0 1 4 5 8 9 12 13 16 17 20 21 24 25 28 29
(x3 + 2)
A084380: 2 3 10 29 66 127 218 345 514 731 1002 1333 1730 2199 2746 3377
(x3 div 2)
A036487: 0 0 4 13 32 62 108 171 256 364 500 665 864 1098 1372 1687
5x
A172336-A172328-A008587: 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
(x + (x div 3))
A138083: 0 1 2 4 5 6
A317551-A104401-A039070-A004773: 0 1 2 4 5 6 8 9 10 12 13 14 16 17 18 20
(x * (x div 3))
A242669: 0 0 0 3 4 5 12 14 16 27 30 33 48 52 56 75
(x2 + 3x)
A028552: 0 4 10 18 28 40 54 70 88 108 130 154 180 208 238 270
(2x2 + x)
A014105: 0 3 10 21 36 55 78 105 136 171 210 253 300 351 406 465
(2x2 + ~x)
A000384: 0 1 6 15 28 45 66 91 120 153 190 231 276 325 378 435
(x * (1 + (x mod 2)))
A109043: 0 2 2 6 4 10 6 14 8 18 10 22 12 26 14 30
(x + (2 mod (x + 1)))
A214084: 0 1 4 5 6 7 8 9 10 11 12 13 14 15 16 17
(~x2 + ~x + 1)
A110331: 1 ~1 ~5 ~11 ~19 ~29 ~41 ~55 ~71 ~89 ~109 ~131 ~155 ~181 ~209 ~239
(x3 + x)
A034262: 0 2 10 30 68 130 222 350 520 738 1010 1342 1740 2210 2758 3390
(x * ((x + ~1) div 2))
A050187: 0 0 0 3 4 10 12 21 24 36 40 55 60 78 84 105
(x + 8)
A020722: 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
(~x + 8)
A022964: 8 7 6 5 4 3 2 1 0 ~1 ~2 ~3 ~4 ~5 ~6 ~7
(x + (x div 4))
A087069-A039145-A038129-A023737-A020654-A001068: 0 1 2 3 5 6 7 8 10 11 12 13 15 16 17 18
(x + (x mod 4))
A083220: 0 2 4 6 4 6 8 10 8 10 12 14 12 14 16 18
(x2 + 4x)
A028347: 0 5 12 21 32 45 60 77 96 117 140 165 192 221 252 285
(3x + 4)
A070300: 4 7 10 13 16 19 22
(x * (2 - (x div 2)))
A079243: 0 2 2 3
(x * (2 - (x mod 2)))
A022998: 0 1 4 3 8 5 12 7 16 9 20 11 24 13 28 15
(x3 + 2x)
A054602: 0 3 12 33 72 135 228 357 528 747 1020 1353 1752 2223 2772 3405
(x3 + ~2x)
A242135: 0 ~1 4 21 56 115 204 329 496 711 980 1309 1704 2171 2716 3345
(x * (x + (x div 2)))
A249127: 0 1 6 12 24 35 54 70 96 117 150 176 216 247 294 330
(1 div (~x2 + 2))
A134824: 0 1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1
x4
A000583: 0 1 16 81 256 625 1296 2401 4096 6561 10000 14641 20736 28561 38416 50625
(~x3 + 1)
A024001: 1 0 ~7 ~26 ~63 ~124 ~215 ~342 ~511 ~728 ~999 ~1330 ~1727 ~2196 ~2743 ~3374
(if (x + ~3) <= 0 then 1 else 0)
A329678: 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
(if (x mod 3) <= 0 then 1 else 0)
A079978: 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1
(if x <= 0 then 5 else 0)
A236239-A020761: 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (x + ~4) <= 0 then 1 else 0)
A014194-A014164-A014154-A014124-A014104-A014094: 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0
(if (x mod 4) <= 0 then 1 else 0)
A265260-A121262-A059484: 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
(if (~x + 4) <= 0 then 1 else 0)
A297033-A175801-A161093-A130543-A111852-A071701: 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1
(if (x + ~1) <= 0 then (x + 1) else 0)
A072507: 1 2 0 0 0 0 0 0 0 0 0
A130706: 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (x + ~2) <= 0 then (x + 1) else 0)
A173012: 1 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (x mod 2) <= 0 then (x + 1) else 0)
A193356: 1 0 3 0 5 0 7 0 9 0 11 0 13 0 15 0
(if (~x + 2) <= 0 then (x + ~2) else 0)
A289207: 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13
(if (x + ~2) <= 0 then (x div 2) else 0)
A343957-A328794-A185012-A181837: 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (x mod 2) <= 0 then (x div 2) else 0)
A326834-A309261-A276457-A257770-A171181-A142150-A135472: 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0
(if (x + ~1) <= 0 then ~x else 0)
A159075: 0 ~1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
loop(\(x,i).(2x + 1),x,0)
A222010: 0 1 3 7
A000225: 0 1 3 7 15 31 63 127 255 511 1023 2047 4095 8191 16383 32767
loop(\(x,i).(x2 + 1),x,0)
A192225: 0 1 2 5
A003095: 0 1 2 5 26 677 458330 210066388901 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (x * i)),x,0)
A002627: 0 1 3 10 41 206 1237 8660 69281 623530 6235301 68588312 823059745 10699776686 149796873605 2246953104076
loop(\(x,i).(2x + 4),x,0)
A028399: 0 4 12 28 60 124 252 508 1020 2044 4092 8188 16380 32764 65532 131068
loop(\(x,i).(x2 + 2),x,0)
A072191: 0 2 6 38 1446 2090918 4371938082726 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (x + i)),x,0)
A145654: 0 2 8 22 52 114 240 494 1004 2026 4072 8166 16356 32738 65504 131038
loop(\(x,i).(x + (i * i)),x,0)
A000330: 0 1 5 14 30 55 91 140 204 285 385 506 650 819 1015 1240
loop(\(x,i).((x + 1) * i),x,0)
A007526: 0 1 4 15 64 325 1956 13699 109600 986409 9864100 108505111 1302061344 16926797485 236975164804 3554627472075
loop(\(x,i).(x2 + i),x,0)
A098152: 0 1 3 12 148 21909 480004287 230404115538378376 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 - i),x,0)
A153059: 0 ~1 ~1 ~2 0 ~5 19 354 125308 15702094855 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + i) * i),x,0)
A030297: 0 1 6 27 124 645 3906 27391 219192 1972809 19728190 217010211 2604122676 33853594957 473950329594 7109254944135
(if (x + ~4) <= 0 then 0 else 1)
A297034-A235043-A161107-A161094-A161068-A161042: 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1
(if (x mod 4) <= 0 then 0 else 1)
A341625-A188260-A166486-A144609: 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1
(if (~2 + (x div 2)) <= 0 then 0 else 1)
A297035-A230493-A185714-A163858-A161108-A161095-A161069-A161043-A121902-A071842: 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1
(1 + (if (x mod 2) <= 0 then 2 else 0))
A176040: 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1
(if (x mod 2) <= 0 then 2 else ~1)
A168361: 2 ~1 2 ~1 2 ~1 2 ~1 2 ~1 2 ~1 2 ~1 2 ~1
(1 + (if (x + ~1) <= 0 then x else 0))
A087102: 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(2x - (if x <= 0 then 0 else 1))
A004273: 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
(1 + (if (~x + 2) <= 0 then 2 else 1))
A326166-A165024: 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3
loop(\(x,i).i,(~1 + (x div 2)),1)
A025159: 1 1 1 1 1 1 2 2 3 3 4 4 5 5 6 6
(1 + loop(\(x,i).2x,x,1))
A000051: 2 3 5 9 17 33 65 129 257 513 1025 2049 4097 8193 16385 32769
(1 + (if (x mod 2) <= 0 then x else 1))
A141310: 1 2 3 2 5 2 7 2 9 2 11 2 13 2 15 2
loop(\(x,i).2x,(x + ~1),1)
A274867-A274866-A274865-A249169-A220493-A011782: 1 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384
(1 + loop(\(x,i).(x * i),x,1))
A038507: 2 2 3 7 25 121 721 5041 40321 362881 3628801 39916801 479001601 6227020801 87178291201 1307674368001
(~1 + loop(\(x,i).(x * i),x,1))
A033312: 0 0 1 5 23 119 719 5039 40319 362879 3628799 39916799 479001599 6227020799 87178291199 1307674367999
(if x <= 0 then 6 else 1)
A257936: 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(1 + (if (x + ~2) <= 0 then 1 else 2))
A345073: 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3
(if x <= 0 then 0 else 5)
A021022: 0 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
loop(\(x,i).i,(x div 4),1)
A097913: 1 1 1 1 1 1 1 1 2 2 2 2 3 3 3 3
(if (~x + 4) <= 0 then 2 else 1)
A214455-A110591-A097944: 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2
loop(\(x,i).i,(~2 + (x div 2)),1)
A122522-A025161: 1 1 1 1 1 1 1 1 2 2 3 3 4 4 5 5
(3 * (if x <= 0 then 0 else 2))
A021019: 0 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
(3 * (if x <= 0 then 1 else 2))
A040006: 3 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
(3 + (if x <= 0 then 1 else x))
A243427: 4 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
loop(\(x,i).2x,x,3)
A007283: 3 6 12 24 48 96 192 384 768 1536 3072 6144 12288 24576 49152 98304
loop(\(x,i).x2,x,3)
A011764: 3 9 81 6561 43046721 1853020188851841 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),x,3)
A052560: 3 3 6 18 72 360 2160 15120 120960 1088640 10886400 119750400 1437004800 18681062400 261534873600 3923023104000
(1 + (if (x + ~1) <= 0 then x else 2))
A185436-A158799: 1 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3
(1 + loop(\(x,i).2x,x,2))
A048578: 3 5 9 17 33 65 129 257 513 1025 2049 4097 8193 16385 32769 65537
(~1 + loop(\(x,i).2x,x,2))
A168604-A126646: 1 3 7 15 31 63 127 255 511 1023 2047 4095 8191 16383 32767 65535
(1 + (if x <= 0 then 0 else (x + 2)))
A171463-A026434-A026419: 1 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
(1 + (if x <= 0 then 1 else (x + 2)))
A162880: 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
loop(\(x,i).(x * i),2x,1)
A279309-A010050: 1 2 24 720 40320 3628800 479001600 87178291200 20922789888000 6402373705728000 2432902008176640000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(x div 2),1)
A076939-A016116: 1 1 2 2 4 4 8 8 16 16 32 32 64 64 128 128
loop(\(x,i).(x * i),(x div 2),1)
A081123: 1 1 1 1 2 2 6 6 24 24 120 120 720 720 5040 5040
(1 + loop(\(x,i).x2,x,2))
A164307-A019434: 3 5 17 257 65537
A262534: 3 5 17 257 65537 4294967297
A000215: 3 5 17 257 65537 4294967297 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).x2,x,2))
A250405: 1 3 15 255 65535
A051179: 1 3 15 255 65535 4294967295 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * i),x,2))
A052898: 3 3 5 13 49 241 1441 10081 80641 725761 7257601 79833601 958003201 12454041601 174356582401 2615348736001
(~1 + loop(\(x,i).(x * i),x,2))
A020543: 1 1 3 11 47 239 1439 10079 80639 725759 7257599 79833599 958003199 12454041599 174356582399 2615348735999
(1 + (if (x + ~2) <= 0 then 0 else x))
A171526: 1 1 1 4 5 6 7 8 9 10 11 12 13 14 15 16
(if (x mod 3) <= 0 then x else 1)
A088439: 0 1 1 3 1 1 6 1 1 9 1 1 12 1 1 15
(1 + (if (x mod 2) <= 0 then 1 else x))
A133265: 2 2 2 4 2 6 2 8 2 10 2 12 2 14 2 16
(1 + (2 div (if x <= 0 then 1 else x)))
A261143: 3 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1
loop(\(x,i).(1 + (x * i)),x,1)
A309115: 1 2 5 16
A000522: 1 2 5 16 65 326 1957 13700 109601 986410 9864101 108505112 1302061345 16926797486 236975164805 3554627472076
loop(\(x,i).(2x + 2),x,1)
A099018-A033484: 1 4 10 22 46 94 190 382 766 1534 3070 6142 12286 24574 49150 98302
(if (x mod 4) <= 0 then x else 1)
A088440: 0 1 1 1 4 1 1 1 8 1 1 1 12 1 1 1
(1 + (if x <= 0 then 4 else x))
A031285: 5 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
loop(\(x,i).(2x + 4),x,1)
A048487: 1 6 16 36 76 156 316 636 1276 2556 5116 10236 20476 40956 81916 163836
loop(\(x,i).(2x + ~4),x,1)
A165751: 1 ~2 ~8 ~20 ~44 ~92 ~188 ~380 ~764 ~1532 ~3068 ~6140 ~12284 ~24572 ~49148 ~98300
loop(\(x,i).4x,x,1)
A000302: 1 4 16 64 256 1024 4096 16384 65536 262144 1048576 4194304 16777216 67108864 268435456 1073741824
(~1 + (if (x mod 2) <= 0 then 2 else x))
A124625: 1 0 1 2 1 4 1 6 1 8 1 10 1 12 1 14
loop(\(x,i).~2x,x,1)
A122803: 1 ~2 4 ~8 16 ~32 64 ~128 256 ~512 1024 ~2048 4096 ~8192 16384 ~32768
loop(\(x,i).(~2x + 2),x,1)
A151575: 1 0 2 ~2 6 ~10 22 ~42 86 ~170 342 ~682 1366 ~2730 5462 ~10922
loop(\(x,i).(~2x + 4),x,1)
A084247: 1 2 0 4 ~4 12 ~20 44 ~84 172 ~340 684 ~1364 2732 ~5460 10924
loop(\(x,i).(~2x + 1),x,1)
A077925: 1 ~1 3 ~5 11 ~21 43 ~85 171 ~341 683 ~1365 2731 ~5461 10923 ~21845
loop(\(x,i).(x2 + 2),x,1)
A102847: 1 3 11 123 15131 228947163 52416803445748571 4611686018427387903 4611686018427387903
loop(\(x,i).2x2,x,1)
A058891: 1 2 8 128 32768 2147483648 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (x + i)),x,1)
A097809: 1 4 12 30 68 146 304 622 1260 2538 5096 10214 20452 40930 81888 163806
loop(\(x,i).(2x * i),x,1)
A000165: 1 2 8 48 384 3840 46080 645120 10321920 185794560 3715891200 81749606400 1961990553600 51011754393600 1428329123020800 42849873690624000
((x + 1) * (if x <= 0 then 0 else 2))
A163300: 0 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
((x + 1) * (if x <= 0 then 1 else 2))
A231407: 1 4 6
A272651-A103517: 1 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
(if (x + ~1) <= 0 then x else (x + 1))
A184985-A179005: 0 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16
(if (x + ~2) <= 0 then x else (x + 1))
A138083: 0 1 2 4 5 6
A326178: 0 1 2 4 5 6 7 8 9 10 11 12 13 14 15 16
loop(\(x,i).(~x + i),x,(x + 1))
A319556: 1 ~1 4 ~2 7 ~3 10 ~4 13 ~5 16 ~6 19 ~7 22 ~8
loop(\(x,i).3x,x,1)
A000244: 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907
loop(\(x,i).(x2 + x),x,1)
A242927-A014117: 1 2 6 42 1806
A007018: 1 2 6 42 1806 3263442 10650056950806 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).2x,x,x))
A002064: 1 3 9 25 65 161 385 897 2049 4609 10241 22529 49153 106497 229377 491521
loop(\(x,i).2x,x2,1)
A002416: 1 2 16 512 65536 33554432 68719476736 562949953421312 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),x2,1)
A088020: 1 1 24 362880 20922789888000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x + i),x,1)
A079583: 1 3 8 19 42 89 184 375 758 1525 3060 6131 12274 24561 49136 98287
loop(\(x,i).(x * (x + i)),x,1)
A110384: 1 2 8 88 8096 65585696 4301483913318592 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * i),x,1)
A052129: 1 1 2 12 576 1658880 16511297126400 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (0 - i)),x,1)
A133942: 1 ~1 2 ~6 24 ~120 720 ~5040 40320 ~362880 3628800 ~39916800 479001600 ~6227020800 87178291200 ~1307674368000
loop(\(x,i).(1 - (x * i)),x,1)
A182386: 1 0 1 ~2 9 ~44 265 ~1854 14833 ~133496 1334961 ~14684570 176214841 ~2290792932 32071101049 ~481066515734
loop(\(x,i).(x + (i * i)),x,1)
A056520: 1 2 6 15 31 56 92 141 205 286 386 507 651 820 1016 1241
loop(\(x,i).(~x + (i * i)),x,1)
A125577: 1 0 4 5 11 14 22 27 37 44 56 65 79 90 106 119
loop(\(x,i).(x * (i * i)),x,1)
A001044: 1 1 4 36 576 14400 518400 25401600 1625702400 131681894400 13168189440000 1593350922240000 229442532802560000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) * i),x,1)
A033540: 1 2 6 21 88 445 2676 18739 149920 1349289 13492900 148421911 1781062944 23153818285 324153456004 4862301840075
loop(\(x,i).((x + ~1) * i),x,1)
A166554: 1 0 ~2 ~9 ~40 ~205 ~1236 ~8659 ~69280 ~623529 ~6235300 ~68588311 ~823059744 ~10699776685 ~149796873604 ~2246953104075
loop(\(x,i).((x + 2) * i),x,1)
A188545: 1 3 10
A165792: 1 3 10 36 152 770 4632 32438 259520 2335698 23357000 256927022 3083124288 40080615770 561128620808 8416929312150
loop(\(x,i).((x + ~2) * i),x,1)
A165793: 1 ~1 ~6 ~24 ~104 ~530 ~3192 ~22358 ~178880 ~1609938 ~16099400 ~177093422 ~2125121088 ~27626574170 ~386772038408 ~5801580576150
loop(\(x,i).(x2 + i),x,1)
A028300: 1 2 6 39 1525 2325630 5408554896906 4611686018427387903 4611686018427387903
loop(\(x,i).((x + i) * i),x,1)
A053817: 1 2 8 33 148 765 4626 32431 259512 2335689 23356990 256927011 3083124276 40080615757 561128620794 8416929312135
(if (x mod 4) <= 0 then 0 else 2)
A277024: 0 2 2 2 0 2 2 2 0 2 2 2 0 2 2 2
(if (x mod 2) <= 0 then 1 else ~2)
A327767: 1 ~2 1 ~2 1 ~2 1 ~2 1 ~2 1 ~2 1 ~2 1 ~2
loop(\(x,i).(~x + i),x,~2)
A152832: ~2 3 ~1 4 0 5 1 6 2 7 3 8 4 9 5 10
((x - (if x <= 0 then 0 else 1)) mod 2)
A144608: 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0
(if (x mod 3) <= 0 then 1 else 2)
A130196: 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1
(if (x + ~4) <= 0 then 1 else 2)
A339276-A217693-A168353-A110592-A069926-A060417: 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2
(if (~2 + (x div 2)) <= 0 then 1 else 2)
A204553-A085576-A032550: 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2
(if x <= 0 then 1 else 6)
A020793: 1 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
((1 + (if x <= 0 then 1 else x)) div 2)
A248180-A088461-A065033-A034888: 1 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8
(2 + loop(\(x,i).2x,x,1))
A052548: 3 4 6 10 18 34 66 130 258 514 1026 2050 4098 8194 16386 32770
(~2 + loop(\(x,i).2x,x,1))
A000918: ~1 0 2 6 14 30 62 126 254 510 1022 2046 4094 8190 16382 32766
(loop(\(x,i).2x,x,1) div 2)
A131577: 0 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384
(2 * (if (x mod 2) <= 0 then x else 1))
A266073: 0 2 4 2 8 2 12 2 16 2 20 2 24 2 28 2
(~2 + loop(\(x,i).(x * i),x,1))
A261193: ~1 ~1 0 4 22 118 718 5038 40318 362878 3628798 39916798 479001598 6227020798 87178291198 1307674367998
(2 * (2 + (if x <= 0 then 2 else 0)))
A131921: 8 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
(2 * (2 + (if x <= 0 then 0 else 2)))
A040012: 4 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
(2 * (2 + (if x <= 0 then 1 else 2)))
A049110: 6 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
(if (x mod 2) <= 0 then 1 else 4)
A010685: 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4
loop(\(x,i).2x,x,4)
A020707: 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072
(2 + (if x <= 0 then 1 else (x + 2)))
A285173-A009005: 3 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
(2 + (if x <= 0 then 1 else 2x))
A051755: 3 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
(if x <= 0 then 1 else 4x)
A295774-A008574: 1 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60
(if x <= 0 then 1 else (2 + (x div 2)))
A266977-A091374-A005410: 1 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9
(~2 + loop(\(x,i).x2,x,2))
A070813: 0 2 14 254 65534
loop(\(x,i).(2x + 1),x,2)
A192580: 2 5 11 23 47
A153893: 2 5 11 23 47 95 191 383 767 1535 3071 6143 12287 24575 49151 98303
(2 - ((if x <= 0 then 1 else x) mod 2))
A066788-A040001: 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
loop(\(x,i).(x2 + ~1),x,2)
A003096: 2 3 8 63 3968 15745023 247905749270528 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (x * i)),x,2)
A201363: 2 3 7
A038159: 2 3 7 22 89 446 2677 18740 149921 1349290 13492901 148421912 1781062945 23153818286 324153456005 4862301840076
loop(\(x,i).(2x + 2),x,2)
A228038: 2 6 14 30 62
loop(\(x,i).4x,x,2)
A004171: 2 8 32 128 512 2048 8192 32768 131072 524288 2097152 8388608 33554432 134217728 536870912 2147483648
((if (x mod 2) <= 0 then 2 else x) div 2)
A057979: 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7
((2 div (if x <= 0 then 2 else x)) mod 2)
A240465-A240353-A186719-A154272-A014061-A014053: 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
loop(\(x,i).(2x * i),x,2)
A066318: 2 4 16 96 768 7680 92160 1290240 20643840 371589120 7431782400 163499212800 3923981107200 102023508787200 2856658246041600 85699747381248000
loop(\(x,i).(x * i),x,(x + 2))
A001048: 2 3 8 30 144 840 5760 45360 403200 3991680 43545600 518918400 6706022400 93405312000 1394852659200 22230464256000
(if (x mod 2) <= 0 then 1 else 2x)
A266303: 1 2 1 6 1 10 1 14 1 18 1 22 1 26 1 30
loop(\(x,i).x2,2,2x)
A016744: 0 16 256 1296 4096 10000 20736 38416 65536 104976 160000 234256 331776 456976 614656 810000
(2x + (if x <= 0 then 1 else x))
A008486: 1 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45
loop(\(x,i).2x,x,2x)
A058922: 0 4 16 48 128 320 768 1792 4096 9216 20480 45056 98304 212992 458752 983040
(if (~x + 2) <= 0 then x else 2x)
A079243: 0 2 2 3
A254667: 0 2 2 3 4 5 6 7 8 9 10 11 12 13 14 15
loop(\(x,i).(x * i),x,2x)
A052582: 0 2 8 36 192 1200 8640 70560 645120 6531840 72576000 878169600 11496038400 161902540800 2440992153600 39230231040000
((if x <= 0 then 1 else x) + (x div 2))
A049624: 1 1 3 4 6 7 9 10 12 13 15 16 18 19 21 22
loop(\(x,i).(x * i),x,(x div 2))
A052657: 0 0 2 6 48 240 2160 15120 161280 1451520 18144000 199584000 2874009600 37362124800 610248038400 9153720576000
((if x <= 0 then 0 else 2) - (x mod 2))
A329129-A134451: 0 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
((if x <= 0 then 1 else x) + (x mod 2))
A131055: 1 2 2 4 4 6 6 8 8 10 10 12 12 14 14 16
loop(\(x,i).(x * i),x,(x mod 2))
A005212: 0 1 0 6 0 120 0 5040 0 362880 0 39916800 0 6227020800 0 1307674368000
loop(\(x,i).3x,x,2)
A008776: 2 6 18 54 162 486 1458 4374 13122 39366 118098 354294 1062882 3188646 9565938 28697814
loop(\(x,i).(x + (x div 2)),x,2)
A061418: 2 3 4 6 9 13 19 28 42 63 94 141 211 316 474 711
(if x <= 0 then 1 else (x2 + 2))
A083462: 1 3 6 11
A010000: 1 3 6 11 18 27 38 51 66 83 102 123 146 171 198 227
loop(\(x,i).x3,x,2)
A023365: 2 8 512 134217728 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (i * i)),x,2)
A201363: 2 3 7
A153056: 2 3 7 16 32 57 93 142 206 287 387 508 652 821 1017 1242
loop(\(x,i).(x * (i * i)),x,2)
A048617: 2 2 8 72 1152 28800 1036800 50803200 3251404800 263363788800 26336378880000 3186701844480000 458885065605120000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 - i),x,2)
A201363: 2 3 7
A198959: 2 3 7 46 2112 4460539 19896408170515 4611686018427387903 4611686018427387903
(if (x mod 3) <= 0 then 0 else x)
A091684: 0 1 2 0 4 5 0 7 8 0 10 11 0 13 14 0
(if (x mod 4) <= 0 then 0 else x)
A190621: 0 1 2 3 0 5 6 7 0 9 10 11 0 13 14 15
(x + (if (x mod 2) <= 0 then 2 else 0))
A137805-A103889: 2 1 4 3 6 5 8 7 10 9 12 11 14 13 16 15
(if (x mod 2) <= 0 then x else ~x)
A038608: 0 ~1 2 ~3 4 ~5 6 ~7 8 ~9 10 ~11 12 ~13 14 ~15
(1 div (if (x mod 2) <= 0 then 1 else x))
A335909-A266591: 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0
loop(\(x,i).2x,x,(~x + 1))
A159964: 1 0 ~4 ~16 ~48 ~128 ~320 ~768 ~1792 ~4096 ~9216 ~20480 ~45056 ~98304 ~212992 ~458752
(if (x mod 2) <= 0 then x else (~x + 1))
A137501: 0 0 2 ~2 4 ~4 6 ~6 8 ~8 10 ~10 12 ~12 14 ~14
(x + loop(\(x,i).2x,x,1))
A083462: 1 3 6 11
A006127: 1 3 6 11 20 37 70 135 264 521 1034 2059 4108 8205 16398 32783
(~x + loop(\(x,i).2x,x,1))
A000325: 1 1 2 5 12 27 58 121 248 503 1014 2037 4084 8179 16370 32753
(x * (if (x mod 2) <= 0 then x else 1))
A065679: 0 1 4 3 16 5 36 7 64 9 100 11 144 13 196 15
loop(\(x,i).2x,(x + ~1),x)
A001787: 0 1 4 12 32 80 192 448 1024 2304 5120 11264 24576 53248 114688 245760
(x + loop(\(x,i).(x * i),x,1))
A005095: 1 2 4 9 28 125 726 5047 40328 362889 3628810 39916811 479001612 6227020813 87178291214 1307674368015
(~x + loop(\(x,i).(x * i),x,1))
A160540: 1 0 0 3
A005096: 1 0 0 3 20 115 714 5033 40312 362871 3628790 39916789 479001588 6227020787 87178291186 1307674367985
(x + (if (x + ~2) <= 0 then 1 else 2))
A293754-A242410: 1 2 3 5 6 7 8 9 10 11 12 13 14 15 16 17
loop(\(x,i).i,(x div 4),x)
A276333: 0 1 2 3 1 1 1 1 2 2 2 2 3 3 3 3
loop(\(x,i).x2,4,x)
A010804: 0 1 65536 43046721 4294967296 152587890625 2821109907456 33232930569601 281474976710656 1853020188851841 10000000000000000 45949729863572161 184884258895036416 665416609183179841 2177953337809371136 4611686018427387903
loop(\(x,i).(x2 div 2),2,x)
A212892: 0 0 2 8 32 72 162 288 512 800 1250 1800 2592 3528 4802 6272
loop(\(x,i).(x2 + 2x),2,x)
A123865: 0 15 80 255 624 1295 2400 4095 6560 9999 14640 20735 28560 38415 50624 65535
loop(\(x,i).2x,(x + ~2),x)
A057711: 0 1 2 6 16 40 96 224 512 1152 2560 5632 12288 26624 57344 122880
loop(\(x,i).2x,(x div 2),x)
A132344: 0 1 4 6 16 20 48 56 128 144 320 352 768 832 1792 1920
loop(\(x,i).x3,2,x)
A001017: 0 1 512 19683 262144 1953125 10077696 40353607 134217728 387420489 1000000000 2357947691 5159780352 10604499373 20661046784 38443359375
(if (x mod 2) <= 0 then ~x else x)
A181983: 0 1 ~2 3 ~4 5 ~6 7 ~8 9 ~10 11 ~12 13 ~14 15
(x + (if (x + ~2) <= 0 then 1 else x))
A316571: 1 2 3 6 8 10 12 14 16 18 20 22 24 26 28 30
loop(\(x,i).(2x + 1),x,x)
A087323: 0 3 11 31 79 191 447 1023 2303 5119 11263 24575 53247 114687 245759 524287
loop(\(x,i).(2x + ~1),x,x)
A092679: 0 1 5 17
A082753: 0 1 5 17 49 129 321 769 1793 4097 9217 20481 45057 98305 212993
A000337: 0 1 5 17 49 129 321 769 1793 4097 9217 20481 45057 98305 212993 458753
(x + (if (x mod 2) <= 0 then 1 else x))
A043547: 1 2 3 6 5 10 7 14 9 18 11 22 13 26 15 30
(x * (if (x mod 2) <= 0 then 1 else x))
A065599: 0 1 2 9 4 25 6 49 8 81 10 121 12 169 14 225
loop(\(x,i).4x,x,x)
A018215: 0 4 32 192 1024 5120 24576 114688 524288 2359296 10485760 46137344 201326592 872415232 3758096384 16106127360
loop(\(x,i).x2,2,x2)
A001016: 0 1 256 6561 65536 390625 1679616 5764801 16777216 43046721 100000000 214358881 429981696 815730721 1475789056 2562890625
loop(\(x,i).2x,x,x2)
A007758: 0 2 16 72 256 800 2304 6272 16384 41472 102400 247808 589824 1384448 3211264 7372800
loop(\(x,i).(x * i),x,x2)
A002775: 0 1 8 54 384 3000 25920 246960 2580480 29393280 362880000 4829932800 68976230400 1052366515200 17086945075200 294226732800000
loop(\(x,i).3x,x,x)
A036290: 0 3 18 81 324 1215 4374 15309 52488 177147 590490 1948617 6377292 20726199 66961566 215233605
loop(\(x,i).(x * (1 + i)),x,x)
A062119: 0 2 12 72 480 3600 30240 282240 2903040 32659200 399168000 5269017600 74724249600 1133317785600 18307441152000 313841848320000
(x + loop(\(x,i).2x,x,x))
A069229: 0 3 10 27 68 165 390 903 2056 4617 10250 22539 49164 106509 229390 491535
(~x + loop(\(x,i).2x,x,x))
A066524: 0 1 6 21 60 155 378 889 2040 4599 10230 22517 49140 106483 229362 491505
loop(\(x,i).2x,x2,x)
A280211: 0 2 32 1536 262144 167772160 412316860416 3940649673949184 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x + i),x,x)
A260006: 0 3 12 35 90 217 504 1143 2550 5621 12276 26611 57330 122865 262128 557039
loop(\(x,i).(x * (i * i)),x,x)
A084915: 0 1 8 108 2304 72000 3110400 177811200 13005619200 1185137049600 131681894400000 17526860144640000 2753310393630720000 4611686018427387903
(1 + (x mod ~3))
A049347-A016202-A016148-A016118-A016100-A016010-A015896-A015776-A015662-A015590-A015488-A015320-A015182-A014978-A011646: 1 ~1 0 1 ~1 0 1 ~1 0 1 ~1 0 1 ~1 0 1
(1 + (x div 5))
A241766-A187183-A133875-A008648: 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4
(1 + (x mod 5))
A010884: 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1
(1 + ((x + 1) div 3))
A194990-A086161: 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6
(~1 + ((x + 1) mod 3))
A102283: 0 1 ~1 0 1 ~1 0 1 ~1 0 1 ~1 0 1 ~1 0
13
A010852: 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13
11
A010850: 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
(3x + 7)
A112414: 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52
(3x + 5)
A180486: 5 8 11 14 17 20 23 26 29 32 35 38 41 44 47 50
(6x + 1)
A225227: 1 7 13
A016921: 1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91
(1 + (2x mod 3))
A130784: 1 3 2 1 3 2 1 3 2 1 3 2 1 3 2 1
(1 + ((x div 2) div 3))
A290792-A280952-A279757-A279221-A133876-A097992: 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3
(1 + ((x div 2) mod 3))
A105899: 1 1 2 2 3 3 1 1 2 2 3 3 1 1 2 2
((x + 1) - (x div 3))
A248103: 1 2 3 3 4 5 5 6 7 7 8 9 9 10 11 11
(3x2 + 1)
A056107: 1 4 13 28 49 76 109 148 193 244 301 364 433 508 589 676
(1 + (2 mod (1 + (x div 2))))
A290858: 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3
(1 + (x div (1 + (x mod 2))))
A323462: 1 1 3 2 5 3 7 4 9 5 11 6 13 7 15 8
(4x + 5)
A004766: 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65
(4x + 3)
A189787-A004767: 3 7 11 15 19 23 27 31 35 39 43 47 51 55 59 63
(x2 + 3x + 1)
A088059-A028387: 1 5 11 19 29 41 55 71 89 109 131 155 181 209 239 271
(2x2 + 2x + 1)
A001844: 1 5 13 25 41 61 85 113 145 181 221 265 313 365 421 481
(2x2 + 2x + ~1)
A142463: ~1 3 11 23 39 59 83 111 143 179 219 263 311 363 419 479
(x3 + x2 + 1)
A318165: 1 3 13
A098547: 1 3 13 37 81 151 253 393 577 811 1101 1453 1873 2367 2941 3601
(x3 + ~x2 + 1)
A100104: 1 1 5 19 49 101 181 295 449 649 901 1211 1585 2029 2549 3151
(x - (x div ~3))
A004772: 0 2 3 4 6 7 8 10 11 12 14 15 16 18 19 20
((x + 1) - (x div ~2))
A225647: 1 3 4 6 7
A329987-A329962-A189935: 1 3 4 6 7 9 10 12 13 15 16 18 19 21 22 24
(x + ~7)
A023449: ~7 ~6 ~5 ~4 ~3 ~2 ~1 0 1 2 3 4 5 6 7 8
(x div 7)
A132270-A111858-A054896: 0 0 0 0 0 0 0 1 1 1 1 1 1 1 2 2
(x mod 7)
A010876: 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1
(1 + (x mod 6))
A010885: 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4
(1 + (2 * (x div 3)))
A130823: 1 1 1 3 3 3 5 5 5 7 7 7 9 9 9 11
(1 + ((x div 3) mod 2))
A135265: 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2
(1 + (2 * (x mod 3)))
A130793: 1 3 5 1 3 5 1 3 5 1 3 5 1 3 5 1
(1 + ((x mod 3) div 2))
A177702: 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1
(1 + ((x mod 3) mod 2))
A131534: 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1
(2x + 7)
A020742: 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37
(1 + ((1 + (x div 2)) div 2))
A128929: 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5
(1 + (2 * (1 + (x mod 2))))
A010703: 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5
(2x2 + 3)
A093328: 3 5 11 21 35 53 75 101 131 165 203 245 291 341 395 453
(1 + ((x2 + 1) div 2))
A074150-A061925: 1 2 3 6 9 14 19 26 33 42 51 62 73 86 99 114
(1 + ((x div ~2) mod 2))
A014695: 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1
(1 + (((x + 1) div 2) div 2))
A144075: 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5
(1 + (((x + ~1) div 2) div 2))
A300763-A285881-A110655: 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4
17
A010856: 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17
15
A010854: 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
(x + ~9)
A023451: ~9 ~8 ~7 ~6 ~5 ~4 ~3 ~2 ~1 0 1 2 3 4 5 6
(x div 9)
A343609-A325955-A297038-A277162-A230257-A173667-A161315-A161301-A161288-A161263-A161249-A161235-A161111-A161098-A161085-A161072-A161059-A161046-A161034-A160980-A135661-A133144-A111851-A102684-A087472-A061217-A054898-A037816-A027197-A004216: 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1
(x mod 9)
A326746-A309788-A010878: 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6
(1 + (x div 8))
A279223-A279041-A214081-A133878-A003108: 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
(1 + (x mod 8))
A338496-A101412-A010887: 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
(1 + (2 * (x div 4)))
A129756: 1 1 1 1 3 3 3 3 5 5 5 5 7 7 7 7
(x + 7)
A020719: 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
(8x + 1)
A017077: 1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121
(1 + (4 * (x div 2)))
A168277: 1 1 5 5 9 9 13 13 17 17 21 21 25 25 29 29
(5 + (x mod 2))
A010717: 5 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6
(1 + (2 * (2 + (x mod 2))))
A010718: 5 7 5 7 5 7 5 7 5 7 5 7 5 7 5 7
(1 + (4 * (x mod 2)))
A010686: 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5
((x + 1) div 5)
A105513-A104355: 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3
((x + 2) div 5)
A105512: 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3
(2x div 5)
A172476-A172267-A097508-A057354: 0 0 0 1 1 2 2 2 3 3 4 4 4 5 5 6
(2x mod 5)
A257164: 0 2 4 1 3 0 2 4 1 3 0 2 4 1 3 0
((x div 2) div 5)
A338505-A335808-A297039-A226135-A185711-A175424-A175402-A161316-A161302-A161289-A161264-A161250-A161236-A161112-A161099-A161086-A161073-A161060-A161047-A161035-A160981-A138471-A133501-A111853-A081503-A076489-A062329-A059995-A054899-A037817-A037807-A031346-A031286: 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1
((x div 2) mod 5)
A106747: 0 0 1 1 2 2 3 3 4 4 0 0 1 1 2 2
(~x + 7)
A022963: 7 6 5 4 3 2 1 0 ~1 ~2 ~3 ~4 ~5 ~6 ~7 ~8
(x - (x div 5))
A303787: 0 1 2 3 4 4 5 6 7 8 8 9 10 11 12 12
(x2 + ~5)
A028875: ~5 ~4 ~1 4 11 20 31 44 59 76 95 116 139 164 191 220
(x2 div 5)
A118015: 0 0 0 1 3 5 7 9 12 16 20 24 28 33 39 45
(x2 mod 5)
A070430: 0 1 4 4 1 0 1 4 4 1 0 1 4 4 1 0
(2 mod (1 + (x div 4)))
A307987: 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2
(x2 + 5)
A117951: 5 6 9 14 21 30 41 54 69 86 105 126 149 174 201 230
(4x2 + 1)
A053755: 1 5 17 37 65 101 145 197 257 325 401 485 577 677 785 901
(4x2 + ~1)
A000466: ~1 3 15 35 63 99 143 195 255 323 399 483 575 675 783 899
(1 + (x2 div 4))
A033638: 1 1 2 3 5 7 10 13 17 21 26 31 37 43 50 57
(~1 + (x2 div 4))
A078126: ~1 ~1 0 1 3 5 8 11 15 19 24 29 35 41 48 55
((x + 1) - ((x div 2) mod 2))
A098180: 1 2 2 3 5 6 6 7 9 10 10 11 13 14 14 15
(1 + (x div (2 + (x mod 2))))
A242112: 1 1 2 2 3 2 4 3 5 4 6 4 7 5 8 6
((x + 1) - (2 * (x mod 2)))
A004442: 1 0 3 2 5 4 7 6 9 8 11 10 13 12 15 14
((x div 3) mod 3)
A163326: 0 0 0 1 1 1 2 2 2 0 0 0 1 1 1 2
(6x + 3)
A016945: 3 9 15 21 27 33 39 45 51 57 63 69 75 81 87 93
((2x + 1) div 3)
A004396: 0 1 1 2 3 3 4 5 5 6 7 7 8 9 9 10
((1 + (x div 2)) div 3)
A163857-A156877-A067100: 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2
(3 * (1 + (x mod 2)))
A010704: 3 6 3 6 3 6 3 6 3 6 3 6 3 6 3 6
18
A010857: 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18
(6x + 6)
A175130: 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96
(((x + 1) div 2) div 3)
A194699-A179528: 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2
24
A010863: 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24
(x + ~12)
A023454: ~12 ~11 ~10 ~9 ~8 ~7 ~6 ~5 ~4 ~3 ~2 ~1 0 1 2 3
(x div 12)
A342696-A297041-A210716-A194698-A161318-A161304-A161291-A161266-A161252-A161238-A161114-A161101-A161088-A161075-A161062-A161049-A161037-A160983-A156878-A064459: 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1
(x mod 12)
A103303: 0 1 2 3 4 5 6 7 8 9
A010881: 0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3
((2x + 4) div 3)
A038372: 1 2 2 3 4 4 5 6 6 7 8 8 9 10 10 11
12x
A008594: 0 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180
((2 * (x div 2)) div 3)
A098428-A098424: 0 0 0 0 1 1 2 2 2 2 3 3 4 4 4 4
(3 * ((x div 2) mod 2))
A021307: 0 0 3 3 0 0 3 3 0 0 3 3 0 0 3 3
(3 * (2 + (x mod 2)))
A010725: 6 9 6 9 6 9 6 9 6 9 6 9 6 9 6 9
(6 * (x mod 2))
A010677: 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6
(x - ((x div 2) div 3))
A303788: 0 1 2 3 4 5 5 6 7 8 9 10 10 11 12 13
((x2 + 2) div 3)
A008810: 0 1 2 3 6 9 12 17 22 27 34 41 48 57 66 75
6x2
A033581: 0 6 24 54 96 150 216 294 384 486 600 726 864 1014 1176 1350
(3 * (x2 div 2))
A319127: 0 0 6 12 24 36 54 72 96 120 150 180 216 252 294 336
((x2 div 2) div 3)
A056827: 0 0 0 1 2 4 6 8 10 13 16 20 24 28 32 37
9x
A008591: 0 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135
(x - ((~x + 1) div 3))
A042965: 0 1 3 4 5 7 8 9 11 12 13 15 16 17 19 20
(x2 + x + 3)
A027688: 3 5 9 15 23 33 45 59 75 93 113 135 159 185 213 243
(3x2 + 3x)
A028896: 0 6 18 36 60 90 126 168 216 270 330 396 468 546 630 720
((x2 + ~x) div 3)
A128422: 0 0 0 2 4 6 10 14 18 24 30 36 44 52 60 70
(x2 + 2x + 3)
A183199: 3 6 11 18 27 38 51 66 83 102 123 146 171 198 227 258
(3x2 + 6x)
A097658-A067725: 0 9 24 45 72 105 144 189 240 297 360 429 504 585 672 765
((x2 + 2x) div 3)
A192225: 0 1 2 5
A032765: 0 1 2 5 8 11 16 21 26 33 40 47 56 65 74 85
(3 * (x + (x mod 2)))
A168328: 0 6 6 12 12 18 18 24 24 30 30 36 36 42 42 48
(2x - (x div 3))
A047212: 0 2 4 5 7 9 10 12 14 15 17 19 20 22 24 25
((x div 2) - (x div 3))
A008615: 0 0 1 0 1 1 1 1 2 1 2 2 2 2 3 2
(4 - (x mod 3))
A244951: 4 3 2 4 3
(2x - (x mod 3))
A047240: 0 1 2 6 7 8 12 13 14 18 19 20 24 25 26 30
(x3 + 3)
A084378: 3 4 11 30 67 128 219 346 515 732 1003 1334 1731 2200 2747 3378
3x3
A117642: 0 3 24 81 192 375 648 1029 1536 2187 3000 3993 5184 6591 8232 10125
(x3 div 3)
A131476: 0 0 2 9 21 41 72 114 170 243 333 443 576 732 914 1125
(1 + ((x2 + x) div 2))
A025739-A025732-A025725-A000124: 1 2 4 7 11 16 22 29 37 46 56 67 79 92 106 121
(1 + ((x2 + ~x) div 2))
A152947: 1 1 2 4 7 11 16 22 29 37 46 56 67 79 92 106
(1 + (2 * (x + (x div 2))))
A086515-A047241: 1 3 7 9 13 15 19 21 25 27 31 33 37 39 43 45
(1 + ((x + (x div 2)) div 2))
A069210-A037915: 1 1 2 3 4 4 5 6 7 7 8 9 10 10 11 12
(1 + ((x * (x div 2)) div 2))
A000403: 1 1 2 2 5 6
(1 + ((x * (x div 2)) mod 2))
A327936-A276329-A177704-A129252-A081117-A022929: 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2
(1 + (2 * (x + (x mod 2))))
A163980: 1 5 5 9 9 13 13 17 17 21 21 25 25 29 29 33
(1 + ((x * (x mod 2)) div 2))
A162520-A152271-A007879: 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8
(1 + ((x + 2) * (x mod 2)))
A210491: 1 4 1 6
((2x + 1) + (x div 2))
A047219: 1 3 6 8 11 13 16 18 21 23 26 28 31 33 36 38
((2x + 1) + (x mod 2))
A338062: 1 4 5 8 9 12 13 16 17 20 21 24 25 28 29 32
(x2 mod (2x + 1))
A225126: 0 1 4 2 7 3 10 4 13 5 16 6 19 7 22 8
(0 - (1 div (2x + ~1)))
A279485-A240356-A240354-A240352-A240350-A240349-A240348-A240331-A240330-A240329-A240328-A154955-A016422-A016411-A016399-A016383-A014040-A014038-A014032-A014028-A014026: 1 ~1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(2x3 + 1)
A033562: 1 3 17 55 129 251 433 687 1025 1459 2001 2663 3457 4395 5489 6751
(~2 mod (1 + (x div 2)))
A244325: 0 0 0 0 1 1 2 2 3 3 4 4 5 5 6 6
(2 - (2 div (1 + (x div 2))))
A111893: 0 0 1 1 2 2 2 2 2 2 2 2 2 2 2 2
(x2 div (1 + (x div 2)))
A233524: 0 1 2 4 5 8
((x2 + 1) + (x div 2))
A317186: 1 2 6 11 19 28 40 53 69 86 106 127 151 176 204 233
((2x + 1) - (x mod 2))
A042963: 1 2 5 6 9 10 13 14 17 18 21 22 25 26 29 30
(1 + (x div 2) - (x mod 2))
A028242: 1 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7
(1 + ((~x2 + x) div 2))
A080956: 1 1 0 ~2 ~5 ~9 ~14 ~20 ~27 ~35 ~44 ~54 ~65 ~77 ~90 ~104
(1 + (x div (x2 + ~2)))
A194337: 1 0 2 1 1 1 1 1 1 1 1 1 1 1 1 1
(~2x2 + x + 1)
A110325: 1 0 ~5 ~14 ~27 ~44 ~65 ~90 ~119 ~152 ~189 ~230 ~275 ~324 ~377 ~434
(1 + (x3 div 2))
A274324: 1 1 5 14 33 63 109 172 257 365 501 666 865 1099 1373 1688
(5x + 1)
A145287-A016861: 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76
((x + 1) + (x div 3))
A337037-A329974-A285465-A276078-A195291-A193303-A187386-A164087-A109237-A059557-A059531-A048103-A042968-A039053: 1 2 3 5 6 7 9 10 11 13 14 15 17 18 19 21
(x2 + 3x + ~1)
A014209: ~1 3 9 17 27 39 53 69 87 107 129 153 179 207 237 269
(2x2 + x + 1)
A084849: 1 4 11 22 37 56 79 106 137 172 211 254 301 352 407 466
(2x2 + ~x + 1)
A130883: 1 2 7 16 29 46 67 92 121 154 191 232 277 326 379 436
(1 + (x * (1 + (x mod 2))))
A114753: 1 3 3 7 5 11 7 15 9 19 11 23 13 27 15 31
(1 + (x * (2 mod (x + 1))))
A267872: 1 1 5 7 9 11 13 15 17 19 21 23 25 27 29 31
(x3 + x + 1)
A071568: 1 3 11 31 69 131 223 351 521 739 1011 1343 1741 2211 2759 3391
(x3 + ~x + 1)
A061600: 1 1 7 25 61 121 211 337 505 721 991 1321 1717 2185 2731 3361
(1 + (x * ((x + 1) div 2)))
A075855: 1 2 3 7 9 16 19 29 33
(x + 9)
A020723-A004498: 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
(~x + 9)
A022965: 9 8 7 6 5 4 3 2 1 0 ~1 ~2 ~3 ~4 ~5 ~6
((x + 1) + (x div 4))
A330002-A261189-A225859-A225496-A190241-A120518-A115180-A101888-A047201-A039116-A023721-A020655-A001961: 1 2 3 4 6 7 8 9 11 12 13 14 16 17 18 19
(x2 + 4x + 1)
A028872: 1 6 13 22 33 46 61 78 97 118 141 166 193 222 253 286
((x + 1) + ((x div 2) mod 2))
A341744: 1 2 4 5 5 6 8 9 9 10 12 13 13 14 16 17
(1 + (x * (2 - (x mod 2))))
A114752: 1 2 5 4 9 6 13 8 17 10 21 12 25 14 29 16
(x3 + 2x + 1)
A135859: 1 4 13 34 73 136 229 358 529 748 1021 1354 1753 2224 2773 3406
(x3 + ~2x + 1)
A033445: 1 0 5 22 57 116 205 330 497 712 981 1310 1705 2172 2717 3346
(5x + 5)
A330003-A140233: 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
(5 div (x + 1))
A033325: 5 2 1 1 1 0 0 0 0 0 0 0 0 0 0 0
((x + 1) * (1 + (x div 2)))
A093005: 1 2 6 8 15 18 28 32 45 50 66 72 91 98 120 128
(x3 + x2 + x + 1)
A053698: 1 4 15 40 85 156 259 400 585 820 1111 1464 1885 2380 2955 3616
(6 div (x + 1))
A033326: 6 3 2 1 1 1 0 0 0 0 0 0 0 0 0 0
(8 div (x + 1))
A033328: 8 4 2 2 1 1 1 1 0 0 0 0 0 0 0 0
(4x2 + 4x)
A033996: 0 8 24 48 80 120 168 224 288 360 440 528 624 728 840 960
((x + 1) * (2 + (x mod 2)))
A106832: 2 6 6 12 10 18 14 24 18 30 22 36 26 42 30 48
((2 + (x mod 2)) mod (x + 1))
A158478: 0 1 2 3 2 3 2 3 2 3 2 3 2 3 2 3
((x + 1) * (2 - (x mod 2)))
A204904: 2 2 6 4 10 6 14 8 18 10 22 12 26 14 30 16
(x3 + x2 + ~2x + ~2)
A214446: ~2 ~2 6 28 70 138 238 376 558 790 1078 1428 1846 2338 2910 3568
(2x3 + 2x2)
A181617: 0 4 24 72 160 300 504 784 1152 1620 2200 2904 3744 4732 5880 7200
(2x2 div (x + 1))
A004275: 0 1 2 4 6 8 10 12 14 16 18 20 22 24 26 28
((x + 1) * (x + (x mod 2)))
A238411: 0 4 6 16 20 36 42 64 72 100 110 144 156 196 210 256
(x3 + ~x2 + x + ~1)
A062158: ~1 0 5 20 51 104 185 300 455 656 909 1220 1595 2040 2561 3164
(x3 + ~x2 + ~x + 1)
A152618: 1 0 3 16 45 96 175 288 441 640 891 1200 1573 2016 2535 3136
(x3 + ~3x2 + 2x)
A007531: 0 0 0 6 24 60 120 210 336 504 720 990 1320 1716 2184 2730
(x4 + ~x3)
A085537: 0 0 8 54 192 500 1080 2058 3584 5832 9000 13310 19008 26364 35672 47250
(~x mod (x2 + 1))
A222010: 0 1 3 7
(x4 + 1)
A002523: 1 2 17 82 257 626 1297 2402 4097 6562 10001 14642 20737 28562 38417 50626
(x - ((x div 2) div ~2))
A047207-A039132: 0 1 3 4 5 6 8 9 10 11 13 14 15 16 18 19
(2x - (x div ~2))
A047218: 0 3 5 8 10 13 15 18 20 23 25 28 30 33 35 38
((x mod 2) - (x div ~2))
A030451: 0 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9
(2 - (x2 div ~2))
A330357: 2 3 4 7 10 15 20 27 34 43 52 63 74 87 100 115
((1 + (x div 3)) mod 2)
A088911: 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0
((1 + (x mod 3)) mod 2)
A204418: 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1
14
A010853: 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
(4x + 6)
A073760: 6 10 14 18 22 26 30 34 38 42 46 50 54 58 62 66
(x + ~10)
A023452: ~10 ~9 ~8 ~7 ~6 ~5 ~4 ~3 ~2 ~1 0 1 2 3 4 5
(x mod 10)
A103303: 0 1 2 3 4 5 6 7 8 9
A175423-A175422-A175421-A175420-A175419-A079475-A031347-A010879-A007954: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
(2 * (x div 5))
A130496: 0 0 0 0 0 2 2 2 2 2 4 4 4 4 4 6
((x div 5) mod 2)
A102675: 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1
((x mod 5) mod 2)
A303591-A285686-A145573: 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0
((1 + (x div 4)) div 2)
A156685-A095861-A071841-A066339: 0 0 0 0 1 1 1 1 1 1 1 1 2 2 2 2
((1 + (x div 4)) mod 2)
A131078: 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0
((1 + (x mod 4)) div 2)
A140081: 0 1 1 2 0 1 1 2 0 1 1 2 0 1 1 2
(8x + 2)
A017089: 2 10 18 26 34 42 50 58 66 74 82 90 98 106 114 122
(2 * (1 + (2 * (x div 2))))
A168276: 2 2 6 6 10 10 14 14 18 18 22 22 26 26 30 30
(2 * (1 + ((x div 2) mod 2)))
A165207: 2 2 4 4 2 2 4 4 2 2 4 4 2 2 4 4
(2 * (3 + (x mod 2)))
A010724: 6 8 6 8 6 8 6 8 6 8 6 8 6 8 6 8
(2 * (1 + (2 * (x mod 2))))
A010696: 2 6 2 6 2 6 2 6 2 6 2 6 2 6 2 6
(2 * ((x + 2) div 3))
A302402: 0 2 2 2 4 4 4 6 6 6 8 8 8 10 10 10
(6x + 2)
A016933: 2 8 14 20 26 32 38 44 50 56 62 68 74 80 86 92
(2 + (3 * (x div 2)))
A168236: 2 2 5 5 8 8 11 11 14 14 17 17 20 20 23 23
((3 * (x div 2)) div 2)
A187321: 0 0 1 1 3 3 4 4 6 6 7 7 9 9 10 10
(((x div 2) mod 3) div 2)
A131532: 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0
(2 + (3 * (x mod 2)))
A010695: 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5
(x2 mod 6)
A070511-A070431: 0 1 4 3 4 1 0 1 4 3 4 1 0 1 4 3
(2 - ((x div 3) mod 2))
A144110: 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1
(2 * (x - (x div 3)))
A063224: 0 2 4 4 6 8 8 10 12 12 14 16 16 18 20 20
(1 - ((x mod 3) div 2))
A198890: 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1
(2x2 + 6)
A255844: 6 8 14 24 38 56 78 104 134 168 206 248 294 344 398 456
(3x2 + 2)
A120328: 2 5 14 29 50 77 110 149 194 245 302 365 434 509 590 677
(3x2 div 2)
A032528: 0 1 6 13 24 37 54 73 96 121 150 181 216 253 294 337
(2 + (1 div (2x + ~1)))
A104435: 1 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2
(2 + (2 mod (1 + (x div 2))))
A335855: 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4
((x mod (1 + (x div 2))) div 2)
A072750: 0 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3
((x mod (1 + (x div 2))) mod 2)
A327219: 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1
(x - ((~1 + (x div 2)) div 2))
A105235-A066530: 1 2 2 3 4 5 5 6 7 8 8 9 10 11 11 12
(2 * (3 - (x mod 2)))
A226294: 6 4 6 4 6 4 6 4 6 4 6 4 6 4 6 4
(x mod (2 * (1 + (x mod 2))))
A109718: 0 1 0 3 0 1 0 3 0 1 0 3 0 1 0 3
(2 * (1 + (x2 div 2)))
A248800: 2 2 6 10 18 26 38 50 66 82 102 122 146 170 198 226
(2x2 + ~2x + 2)
A051890: 2 2 6 14 26 42 62 86 114 146 182 222 266 314 366 422
(2 * ((x + 1) + (x div 2)))
A328588-A047235: 2 4 8 10 14 16 20 22 26 28 32 34 38 40 44 46
(((x + 1) + (x div 2)) div 2)
A249243: 0 1 2 2 3 4 5 5 6 7 8 8 9 10 11 11
((1 + (x * (x div 2))) div 2)
A211521: 0 0 1 2 4 5 9 11 16 18 25 28 36 39 49 53
(2 + (3 div (x + 1)))
A094284: 5 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2
(2 + (4 div (x + 1)))
A343461: 6 4 3 3 2 2 2 2 2 2 2 2 2 2 2 2
((x2 + 3x + 2) div 2)
A176659-A025747-A025738: 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136
(((x + 1) * (x div 2)) mod 2)
A285495: 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0
((x3 + x2) div 2)
A002411: 0 1 6 18 40 75 126 196 288 405 550 726 936 1183 1470 1800
(x2 - ((x + ~1) div 2))
A267682: 1 1 4 8 15 23 34 46 61 77 96 116 139 163 190 218
((x3 + 1) div 2)
A036486: 0 1 4 14 32 63 108 172 256 365 500 666 864 1099 1372 1688
(1 - (x div ~4))
A075245: 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5
(x - (x div ~4))
A047203: 0 2 3 4 5 7 8 9 10 12 13 14 15 17 18 19
(2 * (x - (x div ~2)))
A047233: 0 4 6 10 12 16 18 22 24 28 30 34 36 40 42 46
20
A081245-A010859: 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
(8x + 4)
A017113: 4 12 20 28 36 44 52 60 68 76 84 92 100 108 116 124
(4 * (1 + (x mod 2)))
A105398-A010713: 4 8 4 8 4 8 4 8 4 8 4 8 4 8 4 8
(2 + (((x + 1) div 2) div 2))
A050500: 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6
((((x + 1) div 2) div 2) div 2)
A161313-A161299-A161286-A161261-A161247-A161233-A161083-A161057-A161032-A160978-A104407-A027196-A013941: 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 2
((((x + 1) div 2) div 2) mod 2)
A072626: 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0
32
A010871: 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32
(x + ~16)
A023458: ~16 ~15 ~14 ~13 ~12 ~11 ~10 ~9 ~8 ~7 ~6 ~5 ~4 ~3 ~2 ~1
(2 + (x div 8))
A082896-A079416: 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3
16x
A217558-A008598: 0 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240
(6 + (x mod 2))
A010723: 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7
(2 * (4 + (x mod 2)))
A010733: 8 10 8 10 8 10 8 10 8 10 8 10 8 10 8 10
(8 * (x mod 2))
A010679: 0 8 0 8 0 8 0 8 0 8 0 8 0 8 0 8
(~x + 10)
A022966: 10 9 8 7 6 5 4 3 2 1 0 ~1 ~2 ~3 ~4 ~5
(x - (x div 8))
A245336: 0 1 2 3 4 5 6 7 7 8 9 10 11 12 13 14
(x2 mod 8)
A070432: 0 1 4 1 0 1 4 1 0 1 4 1 0 1 4 1
(x - (2 * (x div 4)))
A083219: 0 1 2 3 2 3 4 5 4 5 6 7 6 7 8 9
((x - (x div 4)) mod 2)
A341389-A188027-A165211-A089809: 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0
((2 - (x mod 4)) div 2)
A102560: 1 0 0 ~1 1 0 0 ~1 1 0 0 ~1 1 0 0 ~1
(x2 + 6)
A114949: 6 7 10 15 22 31 42 55 70 87 106 127 150 175 202 231
(2x2 + 8)
A155966: 8 10 16 26 40 58 80 106 136 170 208 250 296 346 400 458
8x2
A139098: 0 8 32 72 128 200 288 392 512 648 800 968 1152 1352 1568 1800
(x div (4 + (x div 2)))
A297036-A161109-A161096-A161070-A161044-A111892-A033110-A023972: 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1
(1 - (2 * ((x div 2) mod 2)))
A057077: 1 1 ~1 ~1 1 1 ~1 ~1 1 1 ~1 ~1 1 1 ~1 ~1
((x - ((x div 2) mod 2)) div 2)
A004524: 0 0 0 1 2 2 2 3 4 4 4 5 6 6 6 7
((x mod (2 + (x mod 2))) div 2)
A341618-A337690-A336835-A302110-A294936-A286925-A210455-A179527-A172051-A122841-A097796-A093958-A083206-A080225-A044936: 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0
((x mod (2 + (x mod 2))) mod 2)
A300477-A124300-A047764: 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
(((~x + 2) div 2) mod 4)
A160540: 1 0 0 3
(x2 + x + 4)
A027689: 4 6 10 16 24 34 46 60 76 94 114 136 160 186 214 244
((x2 + x) div 4)
A194170-A194166: 0 0 1 3 5 7 10 14 18 22 27 33 39 45 52 60
((x2 + ~x) div 4)
A011848: 0 0 0 1 3 5 7 10 14 18 22 27 33 39 45 52
(x - ((~x + 2) div 4))
A138083: 0 1 2 4 5 6
A039139-A032769: 0 1 2 4 5 6 7 9 10 11 12 14 15 16 17 19
(4x2 + 8x)
A134582: 0 12 32 60 96 140 192 252 320 396 480 572 672 780 896 1020
((x2 + 2x) div 4)
A198442: 0 0 2 3 6 8 12 15 20 24 30 35 42 48 56 63
((x + 4) + (x div 2))
A146968: 4 5 7
((x + (x div 2)) div 4)
A060144-A057364-A057360: 0 0 0 1 1 1 2 2 3 3 3 4 4 4 5 5
(4 * (x + (x mod 2)))
A168397: 0 8 8 16 16 24 24 32 32 40 40 48 48 56 56 64
(2x - (x div 4))
A047293: 0 2 4 6 7 9 11 13 14 16 18 20 21 23 25 27
(2x - (x mod 4))
A047476-A037462: 0 1 2 3 8 9 10 11 16 17 18 19 24 25 26 27
(x3 + 4)
A274077: 4 5 12 31 68 129 220 347 516 733 1004 1335 1732 2201 2748 3379
4x3
A033430: 0 4 32 108 256 500 864 1372 2048 2916 4000 5324 6912 8788 10976 13500
(6x + 4)
A016957: 4 10 16 22 28 34 40 46 52 58 64 70 76 82 88 94
(2x2 + 2x + 4)
A271649: 4 8 16 28 44 64 88 116 148 184 224 268 316 368 424 484
(2 + ((x2 + ~x) div 2))
A152948: 2 2 3 5 8 12 17 23 30 38 47 57 68 80 93 107
(2 * ((x2 + 2x) div 2))
A120413: 0 2 8 14 24 34 48 62 80 98 120 142 168 194 224 254
((4 div (x + 2)) mod 2)
A171386-A093313: 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
(x2 + 4x + 6)
A102305: 6 11 18 27 38 51 66 83 102 123 146 171 198 227 258 291
(((~x + 2) div (x + 2)) mod 2)
A179184: 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1
((2x + 2) + (x div 2))
A329991-A329846-A225000-A067839-A047211: 2 4 7 9 12 14 17 19 22 24 27 29 32 34 37 39
(2 * (2x + (x div 2)))
A146763: 0 4 10 14 20 24 30 34 40 44 50 54 60 64 70 74
(2 * (2x + (x mod 2)))
A047451: 0 6 8 14 16 22 24 30 32 38 40 46 48 54 56 62
(2x - ((x div 2) mod 2))
A047605: 0 2 3 5 8 10 11 13 16 18 19 21 24 26 27 29
((x2 + 2) + (x div 2))
A201363: 2 3 7
(2 * (x2 + (x div 2)))
A139592: 0 2 10 20 36 54 78 104 136 170 210 252 300 350 406 464
((x2 + (x div 2)) div 2)
A038707: 0 0 2 5 9 13 19 26 34 42 52 63 75 87 101 116
(x div (2 * (2 - (x mod 2))))
A130722: 0 0 0 1 1 2 1 3 2 4 2 5 3 6 3 7
(x mod (2 * (2 - (x mod 2))))
A007877: 0 1 2 1 0 1 2 1 0 1 2 1 0 1 2 1
((2x + 2) - (x mod 2))
A338064-A042964: 2 3 6 7 10 11 14 15 18 19 22 23 26 27 30 31
(2 * (2x - (x mod 2)))
A126002-A079599-A047467: 0 2 8 10 16 18 24 26 32 34 40 42 48 50 56 58
((x div 2) mod (2 + (x mod 2)))
A269518: 0 0 1 1 0 2 1 0 0 1 1 2 0 0 1 1
((~x + 1) - (2 * (x mod 2)))
A114285: 1 ~2 ~1 ~4 ~3 ~6 ~5 ~8 ~7 ~10 ~9 ~12 ~11 ~14 ~13 ~16
(5x + 2)
A016873: 2 7 12 17 22 27 32 37 42 47 52 57 62 67 72 77
10x
A008592: 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
((x + 2) + (x div 3))
A230319: 2 3 4 6 7 8 10 11 12 14 15 16 18 19 20 22
(2 * (x + (x div 3)))
A047464: 0 2 4 8 10 12 16 18 20 24 26 28 32 34 36 40
(2x2 + 6x)
A158865: 0 8 20 36 56 80 108 140
A139570: 0 8 20 36 56 80 108 140 176 216 260 308 360 416 476 540
((x2 + 3x) div 2)
A272370-A132337-A132336-A079509-A000096: 0 2 5 9 14 20 27 35 44 54 65 77 90 104 119 135
(2x2 + x + 2)
A096376: 2 5 12 23 38 57 80 107 138 173 212 255 302 353 408 467
(4x2 + 2x)
A002943: 0 6 20 42 72 110 156 210 272 342 420 506 600 702 812 930
(4x2 + ~2x)
A002939: 0 2 12 30 56 90 132 182 240 306 380 462 552 650 756 870
((x3 + x) div 2)
A006003: 0 1 5 15 34 65 111 175 260 369 505 671 870 1105 1379 1695
((x3 + ~x) div 2)
A135503: 0 0 3 12 30 60 105 168 252 360 495 660 858 1092 1365 1680
(x + 10)
A328075-A308407-A102494-A088475-A001637: 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
((x + (x div 4)) div 2)
A136409-A057361: 0 0 1 1 2 3 3 4 5 5 6 6 7 8 8 9
((x + ((x div 2) mod 2)) div 2)
A194169-A194165: 0 0 1 2 2 2 3 4 4 4 5 6 6 6 7 8
(x - (2 * (~x + (x mod 2))))
A047225: 0 1 6 7 12 13 18 19 24 25 30 31 36 37 42 43
((x + 2) * (1 + (x div 2)))
A093353: 2 3 8 10 18 21 32 36 50 55 72 78 98 105 128 136
(2 - (4 div (x + 2)))
A211670-A046698: 0 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2
(4x div (x + 2))
A235224-A186313-A092139-A084558: 0 1 2 2 2 2 3 3 3 3 3 3 3 3 3 3
(3x div (x + 2))
A258198: 0 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2
(x3 + 4x2 + 4x)
A152619: 0 9 32 75 144 245 384 567 800 1089 1440 1859 2352 2925 3584 4335
(2x + (x div 3))
A047349: 0 2 4 7 9 11 14 16 18 21 23 25 28 30 32 35
(x - (2 mod (~2x + 1)))
A214813: 0 1 3 6 9 12 15 18 21
(2x + ((x div 2) mod 2))
A047481: 0 2 5 7 8 10 13 15 16 18 21 23 24 26 29 31
(2x2 + ~3x)
A014107: 0 ~1 2 9 20 35 54 77 104 135 170 209 252 299 350 405
(3x + (x div 2))
A047355: 0 3 7 10 14 17 21 24 28 31 35 38 42 45 49 52
2x4
A244730: 0 2 32 162 512 1250 2592 4802 8192 13122 20000 29282 41472 57122 76832 101250
((1 + (x div 2)) * (x div 2))
A110660: 0 0 2 2 6 6 12 12 20 20 30 30 42 42 56 56
((1 + (x mod 2)) * (x div 2))
A029578: 0 0 1 2 2 4 3 6 4 8 5 10 6 12 7 14
(4x - (x div 2))
A047345: 0 4 7 11 14 18 21 25 28 32 35 39 42 46 49 53
((x2 div 2) * (x div 2))
A131475: 0 0 2 4 16 24 54 72 128 160 250 300 432 504 686 784
(x - ((~x + 1) * (x div 2)))
A031878: 0 1 3 5 10 13 21 25 36 41 55 61 78 85 105 113
((x2 + 2x) - (x div 2))
A156859: 0 3 7 14 22 33 45 60 76 95 115 138 162 189 217 248
(x * ((x div 2) * (x div 2)))
A122656: 0 0 2 3 16 20 54 63 128 144 250 275 432 468 686 735
((x * (x mod 2)) - (x div 2))
A001057: 0 1 ~1 2 ~2 3 ~3 4 ~4 5 ~5 6 ~6 7 ~7 8
(5 * (x mod 2))
A010676: 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5
((x mod 3) + (x mod 2))
A110269: 0 2 2 1 1 3 0 2 2 1 1 3 0 2 2 1
(8 + (x mod 2))
A010732: 8 9 8 9 8 9 8 9 8 9 8 9 8 9 8 9
((x div 4) + (x mod 2))
A026922: 0 1 0 1 1 2 1 2 2 3 2 3 3 4 3 4
(4x + (x mod 2))
A047615: 0 5 8 13 16 21 24 29 32 37 40 45 48 53 56 61
(4x - (x mod 2))
A047470: 0 3 8 11 16 19 24 27 32 35 40 43 48 51 56 59
(((x div 2) mod 2) - (x mod 2))
A291197: 0 ~1 1 0 0 ~1 1 0 0 ~1 1 0 0 ~1 1 0
((x + 2) div (2 - (x mod 2)))
A145051: 1 3 2 5 3 7 4 9 5 11 6 13 7 15 8 17
(x2 div (2 - (x mod 2)))
A129194: 0 1 2 9 8 25 18 49 32 81 50 121 72 169 98 225
(2x2 - (x mod 2))
A077221: 0 1 8 17 32 49 72 97 128 161 200 241 288 337 392 449
((x2 + ~2x) + (x mod 2))
A137932: 0 0 0 4 8 16 24 36 48 64 80 100 120 144 168 196
(1 - (x div (x2 + ~2)))
A171905: 1 2 0 1 1 1 1 1 1 1 1 1 1 1 1 1
(2 - (x div (x2 + ~2)))
A194298: 2 3 1 2 2 2 2 2 2 2 2 2 2 2 2 2
7x
A008589: 0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105
(2x2 + 3x)
A014106: 0 5 14 27 44 65 90 119 152 189 230 275 324 377 434 495
(x * (1 + ((x + 1) div 2)))
A092530: 0 2 4 9 12 20 24 35 40 54 60 77 84 104 112 135
(x + (x div 5))
A191610-A047226-A039259-A037465: 0 1 2 3 4 6 7 8 9 10 12 13 14 15 16 18
(x2 + 5x)
A028557: 0 6 14 24 36 50 66 84 104 126 150 176 204 234 266 300
(2x2 + 5x)
A033537: 0 7 18 33 52 75 102 133 168 207 250 297 348 403 462 525
(4x2 + x)
A007742: 0 5 18 39 68 105 150 203 264 333 410 495 588 689 798 915
(4x2 + ~x)
A033991: 0 3 14 33 60 95 138 189 248 315 390 473 564 663 770 885
(x * (1 + ((x div 2) mod 2)))
A266491: 0 1 4 6 4 5 12 14 8 9 20 22 12 13 28 30
(x + ((x + 1) mod 3))
A080782: 1 3 2 4 6 5 7 9 8 10 12 11 13 15 14 16
(~x + 12)
A109065: 12 11 10 9 8 7 6 5 4 3 2 1
A022968: 12 11 10 9 8 7 6 5 4 3 2 1 0 ~1 ~2 ~3
(x + (2x div 3))
A244644-A047220: 0 1 3 5 6 8 10 11 13 15 16 18 20 21 23 25
(x + (3 * (x div 2)))
A008851: 0 1 5 6 10 11 15 16 20 21 25 26 30 31 35 36
(x + ((x div 2) div 3))
A067570: 0 1 2 3 4 5 7
A267304-A047368-A037470-A020657: 0 1 2 3 4 5 7 8 9 10 11 12 14 15 16 17
(x3 + ~3x)
A136434: 0 ~2 2 18 52 110 198 322 488 702 970 1298 1692 2158
A121670: 0 ~2 2 18 52 110 198 322 488 702 970 1298 1692 2158 2702 3330
(3x2 + x)
A049451: 0 4 14 30 52 80 114 154 200 252 310 374 444 520 602 690
(3x2 + ~x)
A330280: 0 2 10 24
A049450: 0 2 10 24 44 70 102 140 184 234 290 352 420 494 574 660
(2x3 + x)
A061317: 0 3 18 57 132 255 438 693 1032 1467 2010 2673 3468 4407 5502 6765
(2x3 + ~x)
A007588: 0 1 14 51 124 245 426 679 1016 1449 1990 2651 3444 4381 5474 6735
(x3 + x2 + x)
A027444: 0 3 14 39 84 155 258 399 584 819 1110 1463 1884 2379 2954 3615
(x3 + x2 + ~x)
A085490: 0 1 10 33 76 145 246 385 568 801 1090 1441 1860 2353 2926 3585
(x3 + ~x2 + ~x)
A152015: 0 ~1 2 15 44 95 174 287 440 639 890 1199 1572 2015 2534 3135
(5x + 4)
A016897: 4 9 14 19 24 29 34 39 44 49 54 59 64 69 74 79
(x + ((x + 1) * (x div 2)))
A105638: 0 1 5 7 14 17 27 31 44 49 65 71 90 97 119 127
(x + ((x + 1) * (x mod 2)))
A059029: 0 3 2 7 4 11 6 15 8 19 10 23 12 27 14 31
(x4 + x)
A091940: 0 2 18 84 260 630 1302 2408 4104 6570 10010 14652 20748 28574 38430 50640
(x4 + ~x)
A058895: 0 0 14 78 252 620 1290 2394 4088 6552 9990 14630 20724 28548 38402 50610
(x + (2 * (x div 3)))
A192225: 0 1 2 5
A047217: 0 1 2 5 6 7 10 11 12 15 16 17 20 21 22 25
(x + ((x mod 3) div 2))
A130481: 0 1 3 3 4 6 6 7 9 9 10 12 12 13 15 15
(x * ((x div ~2) mod 2))
A078112: 0 1 2 0 0 5 6 0 0 9 10 0 0 13 14 0
(x + 16)
A115420-A004457: 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
(~x + 16)
A022972: 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
(x + (x div 8))
A084689: 0 1 2 3 4 5 6 7 9
A277050-A248375-A052421-A037477-A020661-A013937-A004727: 0 1 2 3 4 5 6 7 9 10 11 12 13 14 15 16
(x + (2 * (x div 4)))
A047246-A039029-A037460: 0 1 2 3 6 7 8 9 12 13 14 15 18 19 20 21
(~x + (2 * (x mod 4)))
A073791: 0 1 2 3 ~4 ~3 ~2 ~1 ~8 ~7 ~6 ~5 ~12 ~11 ~10 ~9
(x2 + 6x)
A028560: 0 7 16 27 40 55 72 91 112 135 160 187 216 247 280 315
(x3 + 4x)
A155965: 0 5 16 39 80 145 240 371 544 765 1040 1375 1776 2249 2800 3435
(x + (x2 div 4))
A024206: 0 1 3 5 8 11 15 19 24 29 35 41 48 55 63 71
(x * (2 - ((x div 2) mod 2)))
A079243: 0 2 2 3
A227380: 0 2 2 3 8 10 6 7 16 18 10 11 24 26 14 15
(3x2 + 2x)
A045944: 0 5 16 33 56 85 120 161 208 261 320 385 456 533 616 705
(3x2 + ~2x)
A000567: 0 1 8 21 40 65 96 133 176 225 280 341 408 481 560 645
(x * (x - ((~x + 2) div 2)))
A191967: 0 1 4 12 20 35 48 70 88 117 140 176 204 247 280 330
(x + ((x + (x div 2)) div 2))
A187330-A047392: 0 1 3 5 7 8 10 12 14 15 17 19 21 22 24 26
(x + ((x * (x div 2)) mod 2))
A140201: 0 1 2 4 4 5 6 8 8 9 10 12 12 13 14 16
(x + (2 * (x + (x mod 2))))
A047264: 0 5 6 11 12 17 18 23 24 29 30 35 36 41 42 47
(x + ((x + 2) * (x mod 2)))
A066104: 0 4 2 8 4 12 6 16 8 20 10 24 12 28 14 32
(x + (x2 div (x + 2)))
A135251: 0 1 3 4 6 8 10
A058992: 0 1 3 4 6 8 10 12 14 16 18 20 22 24 26 28
(x + ((x div 2) * (x div 2)))
A135276: 0 1 3 4 8 9 15 16 24 25 35 36 48 49 63 64
((x div 2) - (x * (x mod 2)))
A130472: 0 ~1 1 ~2 2 ~3 3 ~4 4 ~5 5 ~6 6 ~7 7 ~8
(x4 + 2x)
A185065: 0 3 20 87 264 635 1308 2415 4112 6579 10020 14663 20760 28587 38444 50655
(x4 + ~2x)
A246767: 0 ~1 12 75 248 615 1284 2387 4080 6543 9980 14619 20712 28535 38388 50595
5x2
A033429: 0 5 20 45 80 125 180 245 320 405 500 605 720 845 980 1125
(2x3 + x2)
A099721: 0 3 20 63 144 275 468 735 1088 1539 2100 2783 3600 4563 5684 6975
(2x3 + ~x2)
A015237: 0 1 12 45 112 225 396 637 960 1377 1900 2541 3312 4225 5292 6525
(x4 + x2)
A071253: 0 2 20 90 272 650 1332 2450 4160 6642 10100 14762 20880 28730 38612 50850
(x2 + 8x)
A028566: 0 9 20 33 48 65 84 105 128 153 180 209 240 273 308 345
(3x2 + 4x)
A140676: 0 7 20 39 64 95 132 175 224 279 340 407 480 559 644 735
(x2 * (2 - (x mod 2)))
A181900: 0 1 8 9 32 25 72 49 128 81 200 121 288 169 392 225
(x4 + ~2x2)
A178392: 0 ~1 8 63 224 575 1224 2303 3968 6399 9800 14399 20448 28223 38024 50175
(x2 + (2 mod (x + 1)))
A160842: 0 1 6 11 18 27 38 51 66 83 102 123 146 171 198 227
(x2 + 8)
A189833: 8 9 12 17 24 33 44 57 72 89 108 129 152 177 204 233
(x2 + (x div 4))
A173562: 0 1 4 9 17 26 37 50 66 83 102 123 147 172 199 228
(x2 + (2 * (x mod 2)))
A248825: 0 3 4 11 16 27 36 51 64 83 100 123 144 171 196 227
(2 - (1 mod (~x2 + 2)))
A131959: 1 2 3 8
(~x4 + 1)
A024002: 1 0 ~15 ~80 ~255 ~624 ~1295 ~2400 ~4095 ~6560 ~9999 ~14640 ~20735 ~28560 ~38415 ~50624
x5
A000584: 0 1 32 243 1024 3125 7776 16807 32768 59049 100000 161051 248832 371293 537824 759375
(if (x mod 2) <= 0 then (if x <= 0 then 0 else 2) else 0)
A021499: 0 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0
(if (x + ~2) <= 0 then (if x <= 0 then 1 else 2) else 0)
A180215: 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (x + ~2) <= 0 then (if x <= 0 then 1 else x) else 0)
A130779: 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0
loop(\(x,i).(2 * (if x <= 0 then 1 else x)),x,0)
A155559: 0 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768
loop(\(x,i).(if x <= 0 then i else (x + ~1)),x,1)
A261301: 1 0 2 1 0 5 4 3 2 1 0 11 10 9 8 7
(if (x + ~2) <= 0 then (if x <= 0 then 1 else x) else 1)
A329684: 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1
loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,1)
A035327: 1 0 1 0 3 2 1 0 7 6 5 4 3 2 1 0
loop(\(x,i).loop(\(x,i).(x * i),x,2),x,1)
A181179: 1 2 4 48 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * i),i,x),x,1)
A000178: 1 1 2 12 288 34560 24883200 125411328000 5056584744960000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,(if x <= 0 then 1 else 2))
A151821-A046055: 1 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536
loop(\(x,i).(x * i),x,(if x <= 0 then 1 else 2))
A098558: 1 2 4 12 48 240 1440 10080 80640 725760 7257600 79833600 958003200 12454041600 174356582400 2615348736000
loop(\(x,i).loop(\(x,i).2x,i,x),x,2)
A217994: 2 4 16 128 2048 65536 4194304 536870912 137438953472 70368744177664 72057594037927936 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,(if x <= 0 then 1 else x))
A134401: 1 2 8 24 64 160 384 896 2048 4608 10240 22528 49152 106496 229376 491520
loop(\(x,i).(x * i),x,(if x <= 0 then 1 else x))
A094258: 1 1 4 18 96 600 4320 35280 322560 3265920 36288000 439084800 5748019200 80951270400 1220496076800 19615115520000
loop(\(x,i).(~x + (if x <= 0 then i else 2)),x,x)
A188652: 0 1 2 ~1 6 ~5 12 ~11 20 ~19 30 ~29 42 ~41 56 ~55
(if (x mod 5) <= 0 then 1 else 0)
A079998-A014184: 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
(if (4 mod (x + 1)) <= 0 then 1 else 0)
A329670-A067109: 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
(if (x + ~6) <= 0 then 1 else 0)
A014590-A014562-A014520-A014506-A014478-A014436-A014422-A014380-A014338-A014310-A014296-A014268-A014226-A014212-A014170-A014142-A014128: 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0
(if (x mod 6) <= 0 then 1 else 0)
A319691-A288711-A234954-A079979: 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0
(if (x mod 8) <= 0 then 1 else 0)
A326499-A320319-A304002-A288324-A280130-A279760-A278929-A270599-A253513-A245039-A244171-A126811-A104124-A052434-A015689-A014057: 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
(if (~2 + (x div 4)) <= 0 then 1 else 0)
A118626: 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0
(if (~4 + (x div 2)) <= 0 then 1 else 0)
A247889: 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
(if ((x div 2) mod 4) <= 0 then 1 else 0)
A304021-A279329-A279281: 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0
(if (x mod 2) <= 0 then 5 else 0)
A071873: 5 0 5 0 5 0 5 0 5 0 5 0 5 0 5 0
(if (x mod (2 + (x div 2))) <= 0 then 1 else 0)
A306862: 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0
(if (x + ~1) <= 0 then (2x + 1) else 0)
A169585: 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (x mod 2) <= 0 then (1 + (x div 2)) else 0)
A027656: 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0
(if (2 div (x2 + ~2)) <= 0 then 1 else 0)
A267936-A266678: 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1
(x2 - (if (~x + 2) <= 0 then 1 else 0))
A132411: 0 1 3 8 15 24 35 48 63 80 99 120 143 168 195 224
(if (~x2 + 4x) <= 0 then 1 else 0)
A185114: 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1
loop(\(x,i).(x + (i * i)),(x + 1),0)
A109678: 1 5 14 30 55 91 140 204 285 385 506 650 819 1015 1240 1496
loop(\(x,i).(2x + i),(x + ~1),0)
A000295: 0 0 1 4 11 26 57 120 247 502 1013 2036 4083 8178 16369 32752
(if (x + ~2) <= 0 then (x2 + 1) else 0)
A020821: 1 2 5 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (x + ~1) <= 0 then (2x + 2) else 0)
A266296: 2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
loop(\(x,i).i,(~4 + (x div 2)),0)
A211020: 0 0 0 0 0 0 0 0 0 0 1 1 2 2 3 3
loop(\(x,i).(x + i),(x div 4),0)
A268443: 0 0 0 0 1 1 1 1 3 3 3 3 6 6 6 6
loop(\(x,i).(x + (i * i)),2x,0)
A258582: 0 5 30 91 204 385 650 1015 1496 2109 2870 3795 4900 6201 7714 9455
loop(\(x,i).(2x + 2),(x div 2),0)
A056453: 0 0 2 2 6 6 14 14 30 30 62 62 126 126 254 254
loop(\(x,i).(4x + 1),x,0)
A002450: 0 1 5 21 85 341 1365 5461 21845 87381 349525 1398101 5592405 22369621 89478485 357913941
loop(\(x,i).(3x + 3),x,0)
A029858: 0 3 12 39 120 363 1092 3279 9840 29523 88572 265719 797160 2391483 7174452 21523359
(x - loop(\(x,i).(2x + ~1),x,0))
A052944: 0 2 5 10 19 36 69 134 263 520 1033 2058 4107 8204 16397 32782
loop(\(x,i).(~1 + (2 * (x + i))),x,0)
A050488: 0 1 5 15 37 83 177 367 749 1515 3049 6119 12261 24547 49121 98271
loop(\(x,i).(1 + (2x * i)),x,0)
A056541: 0 1 5 31 249 2491 29893 418503 6696049 120528883 2410577661 53032708543 1272785005033 33092410130859 926587483664053 27797624509921591
loop(\(x,i).(3x + 1),x,0)
A003462: 0 1 4 13 40 121 364 1093 3280 9841 29524 88573 265720 797161 2391484 7174453
loop(\(x,i).(x2 + x + 1),x,0)
A002065: 0 1 3 13 183 33673 1133904603 1285739649838492213 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (x * (1 + i))),x,0)
A056542: 0 1 4 17 86 517 3620 28961 260650 2606501 28671512 344058145 4472755886 62618582405 939278736076 15028459777217
loop(\(x,i).(x2 + 2x + 1),x,0)
A004019: 0 1 4 25 676 458329 210066388900 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + (x div 2)),x,0)
A006999: 0 1 2 4 7 11 17 26 40 61 92 139 209 314 472 709
loop(\(x,i).(1 + (x * (2 + i))),x,0)
A185108: 0 1 5 26 157 1100 8801 79210 792101 8713112 104557345 1359245486 19029436805 285441552076 4567064833217 77640102164690
loop(\(x,i).(4x + 4),x,0)
A080674: 0 4 20 84 340 1364 5460 21844 87380 349524 1398100 5592404 22369620 89478484 357913940 1431655764
loop(\(x,i).((2x + 1) + i),x,0)
A095151: 0 2 7 18 41 88 183 374 757 1524 3059 6130 12273 24560 49135 98286
loop(\(x,i).((x + 1) * (i * i)),x,0)
A193563: 0 1 8 81 1312 32825 1181736 57905113 3705927296 300180111057 30018011105800 3632179343801921 523033825507476768 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + ~1) + (i * i)),x,0)
A051925: 0 0 3 11 26 50 85 133 196 276 375 495 638 806 1001 1225
loop(\(x,i).(x3 + 1),x,0)
A135361: 0 1 2 9 730 389017001 4611686018427387903 4611686018427387903
(1 - loop(\(x,i).(~1 + (x * i)),x,0))
A213937: 1 2 4 11 42 207 1238 8661 69282 623531 6235302 68588313 823059746 10699776687 149796873606 2246953104077
loop(\(x,i).(1 + (x * (i * i))),x,0)
A066998: 0 1 5 46 737 18426 663337 32503514 2080224897 168498216658 16849821665801 2038828421561922 293591292704916769 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x2 + 1) + i),x,0)
A168558: 0 2 7 53 2814 7918602 62704257634411 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + 2),x,0)
A084180: 0 2 10 42 170 682 2730 10922 43690 174762 699050 2796202 11184810
A020988: 0 2 10 42 170 682 2730 10922 43690 174762 699050 2796202 11184810 44739242 178956970 715827882
(if (x mod 8) <= 0 then x else 0)
A127886: 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0
loop(\(x,i).(3x + 2),x,0)
A024023: 0 2 8 26 80 242 728 2186 6560 19682 59048 177146 531440 1594322 4782968 14348906
loop(\(x,i).((x + 2) + (x div 2)),x,0)
A134342: 0 2 5 9 15 24 38 59 90 137 207 312 470 707 1062 1595
loop(\(x,i).(2 * (x + (i div 2))),x,0)
A257198: 0 0 2 6 16 36 78 162 332 672 1354 2718 5448 10908 21830 43674
loop(\(x,i).((2x + 2) + i),x,0)
A000247: 0 3 10 25 56 119 246 501 1012 2035 4082 8177 16368 32751 65518 131053
loop(\(x,i).((x + 2) + (i * i)),x,0)
A145068: 0 3 9 20 38 65 103 154 220 303 405 528 674 845 1043 1270
loop(\(x,i).((x + ~2) + (i * i)),x,0)
A145067: 0 ~1 1 8 22 45 79 126 188 267 365 484 626 793 987 1210
(2 - loop(\(x,i).(~2x + 1),x,0))
A140966: 2 1 3 ~1 7 ~9 23 ~41 87 ~169 343 ~681 1367 ~2729 5463 ~10921
loop(\(x,i).(2x + (i mod 2)),x,0)
A192225: 0 1 2 5
A000975: 0 1 2 5 10 21 42 85 170 341 682 1365 2730 5461 10922 21845
loop(\(x,i).(~3x + 1),x,0)
A014983: 0 1 ~2 7 ~20 61 ~182 547 ~1640 4921 ~14762 44287 ~132860 398581 ~1195742 3587227
loop(\(x,i).(2x + (i * i)),x,0)
A047520: 0 1 6 21 58 141 318 685 1434 2949 5998 12117 24378 48925 98046 196317
(1 div (1 - (if (x mod 2) <= 0 then x else 0)))
A165326: 1 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1
loop(\(x,i).(2 * (2x + i)),x,0)
A145766: 0 2 12 54 224 906 3636 14558 58248 233010 932060 3728262 14913072 59652314 238609284 954437166
loop(\(x,i).(1 - (2 * (x + i))),x,0)
A140962: 0 ~1 ~1 ~3 ~1 ~7 3 ~19 23 ~63 107 ~235 447 ~919 1811 ~3651
loop(\(x,i).((x * i) + (i mod 2)),x,0)
A186763: 0 1 2 7 28 141 846 5923 47384 426457 4264570 46910271 562923252 7318002277 102452031878 1536780478171
loop(\(x,i).(3x + 4),x,0)
A100774: 0 4 16 52 160 484 1456 4372 13120 39364 118096 354292 1062880 3188644 9565936 28697812
loop(\(x,i).((x - i) * (x + i)),x,0)
A143779: 0 ~1 ~3 0 ~16 231 53325 2843555576 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((i mod 2) - (x * i)),x,0)
A009628: 0 1 ~2 7 ~28 141 ~846 5923 ~47384 426457 ~4264570 46910271 ~562923252 7318002277 ~102452031878 1536780478171
(2 - loop(\(x,i).(i - (x * i)),x,0))
A179508: 2 1 2 ~1 10 ~43 266 ~1853 14834 ~133495 1334962 ~14684569 176214842 ~2290792931 32071101050 ~481066515733
loop(\(x,i).(x + ((x + i) * i)),x,0)
A319013: 0 1 7 37 201 1231 8653 69273 623521 6235291 68588301 823059733 10699776673 149796873591 2246953104061 35951249665201
loop(\(x,i).((2x + 1) * i),x,0)
A067273: 0 1 6 39 316 3165 37986 531811 8508984 153161721 3063234430 67391157471 1617387779316 42052082262229 1177458303342426 35323749100272795
(2 - loop(\(x,i).((x + ~1) * i),x,0))
A073591: 2 3 6 17 66 327 1958 13701 109602 986411 9864102 108505113 1302061346 16926797487 236975164806 3554627472077
loop(\(x,i).(((~x + 1) + i) * i),x,0)
A054516: 0 2 2 6 ~4 50 ~258 1862 ~14824 133506 ~1334950 14684582 ~176214828 2290792946 ~32071101034 481066515750
loop(\(x,i).(((x + ~1) + i) * i),x,0)
A038154: 0 0 2 12 60 320 1950 13692 109592 986400 9864090 108505100 1302061332 16926797472 236975164790 3554627472060
loop(\(x,i).((1 + (x * i)) * i),x,0)
A180255: 0 1 6 57 916 22905 824586 40404721 2585902152 209458074321 20945807432110 2534442699285321 364959748697086236 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + (i * i)) * i),x,0)
A337001: 0 1 10 57 292 1585 9726 68425 547912 4931937 49320370 542525401 6510306540 84633987217 1184875823782 17773137360105
(if (x mod 5) <= 0 then 0 else 1)
A011558: 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0
(if ((x div 2) mod 3) <= 0 then 0 else 1)
A131735: 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1 1
(if (x mod 6) <= 0 then 0 else 1)
A097325: 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1
(1 + (if (x mod 3) <= 0 then 2 else 0))
A109007: 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3
(if (x mod 8) <= 0 then 0 else 1)
A324732-A168181: 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1
(if ((x + ~1) mod 4) <= 0 then 0 else 1)
A284677: 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1
(if ((x + 2) mod 4) <= 0 then 0 else 1)
A152822-A105234: 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1
(1 + (if (x mod 2) <= 0 then 4 else 0))
A176260: 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1
(x - (if (~2 + (x div 2)) <= 0 then 0 else 1))
A029915: 0 1 2 3 4 5 5 6 7 8 9 10 11 12 13 14
(1 + (if (x mod 2) <= 0 then (x div 2) else 0))
A336514-A335497-A322182-A318225-A309872-A158416: 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1
(1 + loop(\(x,i).(~2x + 4),x,0))
A083594: 1 5 ~3 13 ~19 45 ~83 173 ~339 685 ~1363 2733 ~5459 10925 ~21843 43693
((x div 3) + (if x <= 0 then 0 else 1))
A261231-A220658: 0 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6
(4x - (if x <= 0 then 0 else 1))
A172338: 0 3 7 11 15 19 23 27 31 35 39 43 47 51 55 59
((2 * (x div 2)) + (if x <= 0 then 0 else 1))
A063196: 0 1 3 3 5 5 7 7 9 9 11 11 13 13 15 15
((2 * (x mod 2)) - (if x <= 0 then 0 else 1))
A062157: 0 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1
(x + ((x div 2) + (if x <= 0 then 0 else 1)))
A195175: 0 2 4 5 7 8 10 11 13 14 16 17 19 20 22 23
(1 + (if (x mod 3) <= 0 then 2 else 1))
A052901: 3 2 2 3 2 2 3 2 2 3 2 2 3 2 2 3
loop(\(x,i).i,(~1 + ((x + ~1) div 2)),1)
A025160: 1 1 1 1 1 1 1 2 2 3 3 4 4 5 5 6
loop(\(x,i).i,(x + ~5),1)
A049812: 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9 10
loop(\(x,i).i,(x div 5),1)
A187188-A120202: 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 3
(1 + (if (~x + 4) <= 0 then 2 else 1))
A165020: 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3
(1 + (3 * (if x <= 0 then 0 else 2)))
A255910: 1 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
(1 + (if (x + ~1) <= 0 then x else 3))
A151798: 1 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4
(1 + loop(\(x,i).2x,x,3))
A181565: 4 7 13 25 49 97 193 385 769 1537 3073 6145 12289 24577 49153 98305
loop(\(x,i).2x,(x div 3),1)
A173862: 1 1 1 2 2 2 4 4 4 8 8 8 16 16 16 32
(1 + loop(\(x,i).x2,x,3))
A059919: 4 10 82 6562 43046722 1853020188851842 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * i),x,3))
A173324: 4 4 7 19 73 361 2161 15121 120961 1088641 10886401 119750401 1437004801 18681062401 261534873601 3923023104001
(~1 + loop(\(x,i).(x * i),x,3))
A173323: 2 2 5 17 71 359 2159 15119 120959 1088639 10886399 119750399 1437004799 18681062399 261534873599 3923023103999
(1 + (x div (if (~x + 2) <= 0 then 2 else 1)))
A263997-A078452: 1 2 2 2 3 3 4 4 5 5 6 6 7 7 8 8
loop(\(x,i).2x,(2x + ~1),1)
A081294: 1 2 8 32 128 512 2048 8192 32768 131072 524288 2097152 8388608 33554432 134217728 536870912
(1 + loop(\(x,i).(x * i),2x,1))
A127231: 2 3 25 721 40321 3628801 479001601 87178291201 20922789888001 6402373705728001 2432902008176640001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).4x,x,1))
A052539: 2 5 17 65 257 1025 4097 16385 65537 262145 1048577 4194305 16777217 67108865 268435457 1073741825
(~1 + loop(\(x,i).4x,x,1))
A024036: 0 3 15 63 255 1023 4095 16383 65535 262143 1048575 4194303 16777215 67108863 268435455 1073741823
(1 + loop(\(x,i).2x2,x,1))
A332203: 2 3 9 129 32769 2147483649 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).2x2,x,1))
A077585: 0 1 7 127 32767 2147483647 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((x + 1) * (if x <= 0 then 1 else x)))
A201363: 2 3 7
A003509: 2 3 7 13 21 31
loop(\(x,i).(2x + 1),(x + ~1),1)
A255047: 1 1 3 7 15 31 63 127 255 511 1023 2047 4095 8191 16383 32767
loop(\(x,i).(2x + ~2),(x + ~1),1)
A122958: 1 1 0 ~2 ~6 ~14 ~30 ~62 ~126 ~254 ~510 ~1022 ~2046 ~4094 ~8190 ~16382
loop(\(x,i).4x,(x + ~1),1)
A265032: 1 1 4 16 64
loop(\(x,i).~2x,(x + ~1),1)
A123344: 1 1 ~2 4 ~8 16 ~32 64 ~128 256 ~512 1024 ~2048 4096 ~8192 16384
loop(\(x,i).3x,(x + ~1),1)
A133494: 1 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969
loop(\(x,i).(x2 - i),(x + ~1),1)
A086851: 1 1 0 ~2 1 ~3 4 10 93 8641 74666872 5575141774264374 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).3x,x,1))
A034472: 2 4 10 28 82 244 730 2188 6562 19684 59050 177148 531442 1594324 4782970 14348908
(1 + loop(\(x,i).(x2 + x),x,1))
A201363: 2 3 7
A000058: 2 3 7 43 1807 3263443 10650056950807 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(x2 + x),x,1))
A065035: 0 1 5 41 1805 3263441 10650056950805 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * (2 + i)),x,1))
A139149: 2 4 13 61 361 2521 20161 181441 1814401 19958401 239500801 3113510401 43589145601 653837184001 10461394944001 177843714048001
(~1 + loop(\(x,i).(x * (2 + i)),x,1))
A139172: 0 2 11 59 359 2519 20159 181439 1814399 19958399 239500799 3113510399 43589145599 653837183999 10461394943999 177843714047999
(~1 + loop(\(x,i).2x,x2,1))
A212739: 0 1 15 511 65535 33554431 68719476735 562949953421311 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(2x + i),x,1))
A123720: 2 4 9 20 43 90 185 376 759 1526 3061 6132 12275 24562 49137 98288
(1 + loop(\(x,i).(x * (i * i)),x,1))
A020549: 2 2 5 37 577 14401 518401 25401601 1625702401 131681894401 13168189440001 1593350922240001 229442532802560001 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if (x mod 3) <= 0 then 0 else 2))
A169609: 1 3 3 1 3 3 1 3 3 1 3 3 1 3 3 1
(1 + (if (x mod 4) <= 0 then 0 else 2))
A167817-A153401: 1 3 3 3 1 3 3 3 1 3 3 3 1 3 3 3
(x - (if (x mod 2) <= 0 then ~2 else 1))
A168232: 2 0 4 2 6 4 8 6 10 8 12 10 14 12 16 14
(x div (if (x mod 2) <= 0 then ~2 else 1))
A176447: 0 1 ~1 3 ~2 5 ~3 7 ~4 9 ~5 11 ~6 13 ~7 15
loop(\(x,i).(~x + i),x,~3)
A152833: ~3 4 ~2 5 ~1 6 0 7 1 8 2 9 3 10 4 11
(1 + (if (x + ~4) <= 0 then 1 else 2))
A068549: 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3
(if (x mod 2) <= 0 then 6 else 1)
A176355: 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1
(if (~x + 2) <= 0 then 6 else 1)
A177057: 1 1 6 6 6 6 6 6 6 6 6 6 6 6 6 6
loop(\(x,i).i,(x + ~6),1)
A322855-A322803-A322800-A049813-A023358-A005711-A005710: 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9
(1 + (x div (if (x + ~2) <= 0 then 1 else 2)))
A137467: 1 2 3 2 3 3 4
(3 + loop(\(x,i).2x,x,1))
A146968: 4 5 7
A062709: 4 5 7 11 19 35 67 131 259 515 1027 2051 4099 8195 16387 32771
(~3 + loop(\(x,i).2x,x,1))
A036563: ~2 ~1 1 5 13 29 61 125 253 509 1021 2045 4093 8189 16381 32765
(1 + (loop(\(x,i).2x,x,1) div 2))
A094373: 1 2 3 5 9 17 33 65 129 257 513 1025 2049 4097 8193 16385
(if x <= 0 then 0 else (2x + 3))
A062545: 0 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33
loop(\(x,i).2x,((x + 1) div 2),1)
A163403-A060546: 1 2 2 4 4 8 8 16 16 32 32 64 64 128 128 256
((x + 2) div (1 + (if x <= 0 then 1 else 2)))
A231153-A020912: 1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5
loop(\(x,i).i,(~2 + ((x + ~1) div 2)),1)
A025162: 1 1 1 1 1 1 1 1 1 2 2 3 3 4 4 5
loop(\(x,i).i,(((x + ~1) div 2) div 2),1)
A120194: 1 1 1 1 1 1 1 1 1 2 2 2 2 3 3 3
(1 + (4 * (if x <= 0 then 0 else 2)))
A291092-A271880: 1 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
(if (x mod 8) <= 0 then 2 else 1)
A160322: 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1
(if ((x + ~1) mod 4) <= 0 then 2 else 1)
A138191: 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1
(if ((x + 2) mod 4) <= 0 then 2 else 1)
A236398: 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1
(if x <= 0 then 0 else 9)
A180599: 0 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
(if (~x + 2) <= 0 then 8 else 1)
A195139: 1 1 8 8 8 8 8 8 8 8 8 8 8 8 8 8
loop(\(x,i).i,(x + ~8),1)
A289410-A274842-A273737-A179622-A175740-A171890-A067453: 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7
loop(\(x,i).2x,x,5)
A323831-A020714: 5 10 20 40 80 160 320 640 1280 2560 5120 10240 20480 40960 81920 163840
loop(\(x,i).x2,x,5)
A176594: 5 25 625 390625 152587890625 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).2x,x,4))
A020737: 5 9 17 33 65 129 257 513 1025 2049 4097 8193 16385 32769 65537 131073
loop(\(x,i).2x,(x div 4),1)
A200675: 1 1 1 1 2 2 2 2 4 4 4 4 8 8 8 8
loop(\(x,i).(2 * i),(x div 4),1)
A092533-A092532: 1 1 1 1 2 2 2 2 4 4 4 4 6 6 6 6
loop(\(x,i).(x + i),(x div 4),1)
A092508: 1 1 1 1 2 2 2 2 4 4 4 4 7 7 7 7
loop(\(x,i).(x * i),(x div 4),1)
A139554: 1 1 1 1 1 1 1 1 2 2 2 2 6 6 6 6
loop(\(x,i).2x,(x mod 4),1)
A222011: 1 2 4 8
A133145: 1 2 4 8 1 2 4 8 1 2 4 8 1 2 4 8
(1 + loop(\(x,i).x2,x,4))
A222008: 5 17 257 65537
(1 + loop(\(x,i).(x * i),x,4))
A173322: 5 5 9 25 97 481 2881 20161 161281 1451521 14515201 159667201 1916006401 24908083201 348713164801 5230697472001
(~1 + loop(\(x,i).(x * i),x,4))
A173321: 3 3 7 23 95 479 2879 20159 161279 1451519 14515199 159667199 1916006399 24908083199 348713164799 5230697471999
(1 + (2 * (if x <= 0 then 1 else (x + 2))))
A005818: 3 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35
((x + 2) div (if (x + ~2) <= 0 then 2 else 1))
A057544: 1 1 2 5 6 7 8 9 10 11 12 13 14 15 16 17
(~1 + (2 * (if x <= 0 then 1 else 2x)))
A131098: 1 3 7 11 15 19 23 27 31 35 39 43 47 51 55 59
loop(\(x,i).(x * i),4x,1)
A100733: 1 24 40320 479001600 20922789888000 2432902008176640000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).2x,(x div 2),2))
A052551: 1 1 3 3 7 7 15 15 31 31 63 63 127 127 255 255
loop(\(x,i).(x * i),(2 * (x div 2)),1)
A248812: 1 1 2 2 24 24 720 720 40320 40320 3628800 3628800 479001600 479001600 87178291200 87178291200
(1 + (if x <= 0 then 0 else (2 + (x mod 2))))
A103947: 1 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4
(3 + loop(\(x,i).x2,x,2))
A130729: 5 7 19 259 65539 4294967299 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * loop(\(x,i).x2,x,2)))
A070969: 5 9 33 513 131073 8589934593 4611686018427387903 4611686018427387903 4611686018427387903
((x - (if x <= 0 then 0 else 1)) div 3)
A172264-A032615: 0 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4
(3 * (if x <= 0 then 4 else 1))
A113923: 12 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
(if x <= 0 then 1 else ((x + ~1) div 3))
A192262: 1 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4
(3 * (2 + (if x <= 0 then 0 else 2)))
A040030: 6 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12
(3 * loop(\(x,i).2x,x,2))
A091629: 6 12 24 48 96 192 384 768 1536 3072 6144 12288 24576 49152 98304 196608
((2 * (if x <= 0 then 2 else x)) mod 3)
A228817: 1 2 1 0 2
loop(\(x,i).2x,(x + 2),3)
A081808: 12 24 48 96 192 384 768 1536 3072 6144 12288 24576 49152 98304 196608 393216
(if (x mod 2) <= 0 then 2x else 3)
A265723: 0 3 4 3 8 3 12 3 16 3 20 3 24 3 28 3
(if x <= 0 then 1 else 6x)
A008458: 1 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90
((if (x mod 2) <= 0 then 1 else x) mod 3)
A093718: 1 1 1 0 1 2 1 1 1 0 1 2 1 1 1 0
(1 - (if (x + ~1) <= 0 then x else 3))
A113679: 1 0 ~2 ~2 ~2 ~2 ~2 ~2 ~2 ~2 ~2 ~2 ~2 ~2 ~2 ~2
loop(\(x,i).(x2 + 1),x,3)
A062013: 3 10 101 10202 104080805 10832813969448026 4611686018427387903 4611686018427387903
loop(\(x,i).(2x + 2),x,3)
A051633: 3 8 18 38 78 158 318 638 1278 2558 5118 10238 20478 40958 81918 163838
loop(\(x,i).4x,x,3)
A164346: 3 12 48 192 768 3072 12288 49152 196608 786432 3145728 12582912 50331648 201326592 805306368 3221225472
loop(\(x,i).(x2 + ~2),x,3)
A001566: 3 7 47 2207 4870847 23725150497407 4611686018427387903 4611686018427387903
A331038: 3 7 47 2207 4870847 23725150497407 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((if x <= 0 then 1 else x) - (x div 3))
A020909: 1 1 2 2 3 4 4 5 6 6 7 8 8 9 10 10
loop(\(x,i).(x2 + x),x,3)
A004168: 3 12 156 24492 599882556 359859081592975692 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + ~x),x,3)
A117805: 3 6 30 870 756030 571580604870 4611686018427387903 4611686018427387903 4611686018427387903
((if x <= 0 then 1 else x2) mod 3)
A267208: 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0
loop(\(x,i).x3,x,3)
A055777: 3 27 19683 7625597484987 4611686018427387903
(3 * loop(\(x,i).(x * i),x,x))
A052673: 0 3 12 54 288 1800 12960 105840 967680 9797760 108864000 1317254400 17244057600 242853811200 3661488230400 58845346560000
loop(\(x,i).(x + (i * i)),x,3)
A153057: 3 4 8 17 33 58 94 143 207 288 388 509 653 822 1018 1243
loop(\(x,i).((x + ~1) * i),x,3)
A117643: 3 2 2 3 8 35 204 1421 11360 102231 1022300 11245289 134943456 1754264915 24559708796 368395631925
(~1 + (2 * (if (x mod 2) <= 0 then 1 else x)))
A266072: 1 1 1 5 1 9 1 13 1 17 1 21 1 25 1 29
(1 + loop(\(x,i).(x2 + ~1),x,2))
A073015: 3 4 9 64 3969 15745024 247905749270529 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(x2 + ~1),x,2))
A100523: 1 2 7 62 3967 15745022 247905749270527 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(2x + 4),x,2))
A048488: 1 7 19 43 91 187 379 763 1531 3067 6139 12283 24571 49147 98299 196603
(1 + loop(\(x,i).4x,x,2))
A087289: 3 9 33 129 513 2049 8193 32769 131073 524289 2097153 8388609 33554433 134217729 536870913 2147483649
(~1 + loop(\(x,i).4x,x,2))
A083420: 1 7 31 127 511 2047 8191 32767 131071 524287 2097151 8388607 33554431 134217727 536870911 2147483647
(if (~x + 2) <= 0 then ((~x + 2) div 2) else 1)
A168050: 1 1 0 ~1 ~1 ~2 ~2 ~3 ~3 ~4 ~4 ~5 ~5 ~6 ~6 ~7
(~1 + loop(\(x,i).(2 * (x + i)),x,2))
A142964: 1 5 15 37 83 177 367 749 1515 3049 6119 12261 24547 49121 98271 196573
(~1 + loop(\(x,i).2x,x,(x + 2)))
A099035: 1 5 15 39 95 223 511 1151 2559 5631 12287 26623 57343 122879 262143 557055
loop(\(x,i).~2x,(x + ~2),1)
A141531: 1 1 1 ~2 4 ~8 16 ~32 64 ~128 256 ~512 1024 ~2048 4096 ~8192
loop(\(x,i).(x * (2 + i)),(x + ~2),1)
A077134: 1 1 1 3 12 60 360 2520 20160 181440 1814400 19958400 239500800
A001710: 1 1 1 3 12 60 360 2520 20160 181440 1814400 19958400 239500800 3113510400 43589145600 653837184000
loop(\(x,i).(2x + 2),2x,1)
A096045: 1 10 46 190 766 3070 12286 49150 196606 786430 3145726 12582910 50331646 201326590 805306366 3221225470
loop(\(x,i).4x,2x,1)
A001025: 1 16 256 4096 65536 1048576 16777216 268435456 4294967296 68719476736 1099511627776 17592186044416 281474976710656 4503599627370496 72057594037927936 1152921504606846976
loop(\(x,i).(2x * i),2x,1)
A067624: 1 8 384 46080 10321920 3715891200 1961990553600 1428329123020800 1371195958099968000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,2,(2x + 1))
A016756: 1 81 625 2401 6561 14641 28561 50625 83521 130321 194481 279841 390625 531441 707281 923521
loop(\(x,i).2x,x,(2x + 1))
A014480: 1 6 20 56 144 352 832 1920 4352 9728 21504 47104 102400 221184 475136 1015808
loop(\(x,i).(x * i),x,(2x + 1))
A188545: 1 3 10
A007680: 1 3 10 42 216 1320 9360 75600 685440 6894720 76204800 918086400 11975040000 168129561600 2528170444800 40537905408000
(if (x + ~2) <= 0 then x else (2x + ~1))
A192225: 0 1 2 5
A163985: 0 1 2 5 7 9 11 13 15 17 19 21 23 25 27 29
loop(\(x,i).3x,2x,1)
A001019: 1 9 81 729 6561 59049 531441 4782969 43046721 387420489 3486784401 31381059609 282429536481 2541865828329 22876792454961 205891132094649
(1 + (if (x + ~1) <= 0 then x else 2x))
A140139: 1 2 5 7 9 11 13 15 17 19 21 23 25 27 29 31
loop(\(x,i).(x * (1 + i)),2x,1)
A009445: 1 6 120 5040 362880 39916800 6227020800 1307674368000 355687428096000 121645100408832000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).2x,x,2x))
A163383: ~1 3 15 47 127 319 767 1791 4095 9215 20479 45055 98303 212991 458751 983039
loop(\(x,i).(x * (2 + i)),2x,1)
A002674: 1 12 360 20160 1814400 239500800 43589145600 10461394944000 3201186852864000 1216451004088320000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if (~x + 2) <= 0 then x else 2x))
A003860: 1 3 3 4 5
(1 + loop(\(x,i).(x * i),x,2x))
A155159: 1 3 9 37 193 1201 8641 70561 645121 6531841 72576001 878169601 11496038401 161902540801 2440992153601 39230231040001
loop(\(x,i).(1 - (x * i)),2x,1)
A306535: 1 1 9 265 14833 1334961 176214841 32071101049 7697064251745 2355301661033953 895014631192902121 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (i * i)),2x,1)
A134372: 1 4 576 518400 1625702400 13168189440000 229442532802560000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).4x,(x div 2),1)
A213173: 1 1 4 4 16 16 64 64 256 256 1024 1024 4096 4096 16384 16384
loop(\(x,i).(~2x + 1),(x div 2),1)
A077953: 1 1 ~1 ~1 3 3 ~5 ~5 11 11 ~21 ~21 43 43 ~85 ~85
loop(\(x,i).(2x * i),(x div 2),1)
A037223: 1 1 2 2 8 8 48 48 384 384 3840 3840 46080 46080 645120 645120
loop(\(x,i).2x,x,(1 + (x div 2)))
A134353: 1 2 8 16 48 96 256 512 1280 2560 6144 12288 28672 57344 131072 262144
loop(\(x,i).(x * i),x,(1 + (x div 2)))
A052558: 1 1 4 12 72 360 2880 20160 201600 1814400 21772800 239500800 3353011200 43589145600 697426329600 10461394944000
loop(\(x,i).3x,(x div 2),1)
A108411: 1 1 3 3 9 9 27 27 81 81 243 243 729 729 2187 2187
loop(\(x,i).(x * (i * i)),(x div 2),1)
A180064: 1 1 1 1 4 4 36 36 576 576 14400 14400 518400 518400 25401600 25401600
loop(\(x,i).2x,x,(1 + (x mod 2)))
A164906-A056450: 1 4 4 16 16 64 64 256 256 1024 1024 4096 4096 16384 16384 65536
(~1 + loop(\(x,i).3x,x,2))
A048473: 1 5 17 53 161 485 1457 4373 13121 39365 118097 354293 1062881 3188645 9565937 28697813
(1 + loop(\(x,i).(x + (x div 2)),x,2))
A003312: 3 4 5 7 10 14 20 29 43 64 95 142 212 317 475 712
(~1 + loop(\(x,i).(x + (x div 2)),x,2))
A156623-A061419: 1 2 3 5 8 12 18 27 41 62 93 140 210 315 473 710
loop(\(x,i).2x,(x2 div 2),1)
A099202: 1 1 4 16 256 4096 262144 16777216 4294967296 1099511627776 1125899906842624 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(2x + i),x,2))
A095768: 3 6 13 28 59 122 249 504 1015 2038 4085 8180 16371 32754 65521 131056
(~1 + loop(\(x,i).(2x + i),x,2))
A125128: 1 4 11 26 57 120 247 502 1013 2036 4083 8178 16369 32752 65519 131054
(1 + (if (x mod 4) <= 0 then 0 else x))
A001438: 1 2 3 4 1 6 7 8
loop(\(x,i).(4x + ~1),x,1)
A007583: 1 3 11 43 171 683 2731 10923 43691 174763 699051 2796203 11184811 44739243 178956971 715827883
loop(\(x,i).(3x + 3),x,1)
A134931: 1 6 21 66 201 606 1821 5466 16401 49206 147621 442866 1328601 3985806 11957421 35872266
loop(\(x,i).(3x + 6),x,1)
A036543: 1 9 33 105 321 969 2913 8745 26241 78729 236193 708585 2125761 6377289 19131873 57395625
loop(\(x,i).(3x + ~6),x,1)
A165746: 1 ~3 ~15 ~51 ~159 ~483 ~1455 ~4371 ~13119 ~39363 ~118095 ~354291 ~1062879 ~3188643 ~9565935 ~28697811
loop(\(x,i).6x,x,1)
A000400: 1 6 36 216 1296 7776 46656 279936 1679616 10077696 60466176 362797056 2176782336 13060694016 78364164096 470184984576
loop(\(x,i).(x * i),3x,1)
A100732: 1 6 720 362880 479001600 1307674368000 6402373705728000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~3x + 3),x,1)
A084567: 1 0 3 ~6 21 ~60 183 ~546 1641 ~4920 14763 ~44286 132861 ~398580 1195743 ~3587226
loop(\(x,i).(~3x + 6),x,1)
A165553: 1 3 ~3 15 ~39 123 ~363 1095 ~3279 9843 ~29523 88575 ~265719 797163 ~2391483 7174455
loop(\(x,i).(3x * i),x,1)
A032031: 1 3 18 162 1944 29160 524880 11022480 264539520 7142567040 214277011200 7071141369600 254561089305600 9927882482918400 416971064282572800 4611686018427387903
loop(\(x,i).(1 + (i div (x + 2))),x,1)
A257212: 1 1 1 2 2 2 2 2 3 2 3 3 3 3 3 4
loop(\(x,i).((~2x + 1) + i),x,1)
A077898: 1 0 3 ~2 9 ~12 31 ~54 117 ~224 459 ~906 1825 ~3636 7287 ~14558
loop(\(x,i).(1 + (2x * i)),x,1)
A318165: 1 3 13
A010844: 1 3 13 79 633 6331 75973 1063623 17017969 306323443 6126468861 134782314943 3234775558633 84104164524459 2354916606684853 70647498200545591
loop(\(x,i).(~1 + (2x * i)),x,1)
A055214: 1 1 3 17 135 1349 16187 226617 3625871 65265677 1305313539 28716897857 689205548567 17919344262741 501741639356747 15052249180702409
(1 + (if (~x + 2) <= 0 then x else (~x + 1)))
A181440: 2 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16
loop(\(x,i).(3x + ~1),x,1)
A007051: 1 2 5 14 41 122 365 1094 3281 9842 29525 88574 265721 797162 2391485 7174454
loop(\(x,i).(~1 + (x * (1 + i))),x,1)
A056543: 1 1 2 7 34 203 1420 11359 102230 1022299 11245288 134943455 1754264914 24559708795 368395631924 5894330110783
((x + 1) + loop(\(x,i).2x,x,1))
A005126: 2 4 7 12 21 38 71 136 265 522 1035 2060 4109 8206 16399 32784
loop(\(x,i).(4x + 4),x,1)
A083597: 1 8 36 148 596 2388 9556 38228 152916 611668 2446676 9786708 39146836 156587348 626349396 2505397588
loop(\(x,i).(2x2 + 2x),x,1)
A059918: 1 4 40 3280 21523360 926510094425920 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + x2),x,1)
A125295: 1 2 12 1872 6563711232 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + (i * i)),x,1)
A081489: 1 3 8 18 35 61 98 148 213 295 396 518 663 833 1030 1256
(1 + loop(\(x,i).2x,(x + ~1),x))
A005183: 1 2 5 13 33 81 193 449 1025 2305 5121 11265 24577 53249 114689 245761
loop(\(x,i).2x,(x2 + ~x),1)
A053773: 1 1 4 64 4096 1048576 1073741824 4398046511104 72057594037927936 4611686018427387903 4611686018427387903 4611686018427387903
A053763: 1 1 4 64 4096 1048576 1073741824 4398046511104 72057594037927936 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (~x + 2) <= 0 then (x2 + ~x) else 1)
A103505: 1 1 2 6 12 20 30 42 56 72 90 110 132 156 182 210
((x + 1) + loop(\(x,i).(x * i),x,1))
A213169: 2 3 5 10 29 126 727 5048 40329 362890 3628811 39916812 479001613 6227020814 87178291215 1307674368016
loop(\(x,i).(1 + (x * (i * i))),x,1)
A006040: 1 2 9 82 1313 32826 1181737 57905114 3705927297 300180111058 30018011105801 3632179343801922 523033825507476769 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (i * (1 + i))),x,1)
A010790: 1 2 12 144 2880 86400 3628800 203212800 14631321600 1316818944000 144850083840000 19120211066880000 2982752926433280000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).~4x,x,1)
A262710: 1 ~4 16 ~64 256 ~1024 4096 ~16384 65536 ~262144 1048576 ~4194304 16777216 ~67108864 268435456 ~1073741824
loop(\(x,i).(2x + 6),x,1)
A048489: 1 8 22 50 106 218 442 890 1786 3578 7162 14330 28666 57338 114682 229370
loop(\(x,i).(4x + 2),x,1)
A020989: 1 6 26 106 426 1706 6826 27306 109226 436906 1747626 6990506 27962026 111848106 447392426 1789569706
loop(\(x,i).(4x + ~2),x,1)
A047849: 1 2 6 22 86 342 1366 5462 21846 87382 349526 1398102 5592406 22369622 89478486 357913942
loop(\(x,i).(2 * ((x + ~1) + i)),x,1)
A097813: 1 2 6 16 38 84 178 368 750 1516 3050 6120 12262 24548 49122 98272
loop(\(x,i).(2x + 8),x,1)
A048491: 1 10 28 64 136 280 568 1144 2296 4600 9208 18424 36856 73720 147448 294904
loop(\(x,i).(4x + ~8),x,1)
A165752: 1 ~4 ~24 ~104 ~424 ~1704 ~6824 ~27304 ~109224 ~436904 ~1747624 ~6990504 ~27962024 ~111848104 ~447392424 ~1789569704
loop(\(x,i).8x,x,1)
A001018: 1 8 64 512 4096 32768 262144 2097152 16777216 134217728 1073741824 8589934592 68719476736 549755813888 4398046511104 35184372088832
(if (~4 + (x div 2)) <= 0 then x else 1)
A103303: 0 1 2 3 4 5 6 7 8 9
A175401-A175400-A175399-A175398-A133500-A000030: 0 1 2 3 4 5 6 7 8 9 1 1 1 1 1 1
loop(\(x,i).(~4x + 8),x,1)
A165622: 1 4 ~8 40 ~152 616 ~2456 9832 ~39320 157288 ~629144 2516584 ~10066328 40265320 ~161061272 644245096
loop(\(x,i).4x2,x,1)
A051191: 1 4 64 16384 1073741824 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).x2,4,x))
A060895: 1 2 65537 43046722 4294967297 152587890626 2821109907457 33232930569602 281474976710657 1853020188851842 10000000000000001 45949729863572162 184884258895036417 665416609183179842 2177953337809371137 4611686018427387903
loop(\(x,i).(4x * i),x,1)
A047053: 1 4 32 384 6144 122880 2949120 82575360 2642411520 95126814720 3805072588800 167423193907200 8036313307545600 417888291992371200 4611686018427387903 4611686018427387903
loop(\(x,i).(~2x + 8),x,1)
A083581: 1 6 ~4 16 ~24 56 ~104 216 ~424 856 ~1704 3416 ~6824 13656 ~27304 54616
loop(\(x,i).(~4x + 1),x,1)
A014985: 1 ~3 13 ~51 205 ~819 3277 ~13107 52429 ~209715 838861 ~3355443 13421773 ~53687091 214748365 ~858993459
loop(\(x,i).(2 * ((x + 2) + i)),x,1)
A099041: 1 8 24 58 128 270 556 1130 2280 4582 9188 18402 36832 73694 147420 294874
loop(\(x,i).(2 * ((x + ~2) + i)),x,1)
A005803: 1 0 0 2 8 22 52 114 240 494 1004 2026 4072 8166 16356 32738
loop(\(x,i).(2 * ((x + 2) - i)),x,1)
A131831-A100314: 1 4 8 14 24 42 76 142 272 530 1044 2070 4120 8218 16412 32798
(1 + (if (x mod 2) <= 0 then x else (~x + 2)))
A057174: 1 2 3 0 5 ~2 7 ~4 9 ~6 11 ~8 13 ~10 15 ~12
loop(\(x,i).(x2 + ~x + 2),x,1)
A166105: 1 2 4 14 184 33674 1133904604 1285739649838492214 4611686018427387903 4611686018427387903
loop(\(x,i).(2 + (x * (~1 + i))),x,1)
A054091: 1 2 4 10 32 130 652 3914 27400 219202 1972820 19728202 217010224 2604122690 33853594972 473950329610
((x + ~1) + loop(\(x,i).2x,x,2))
A122039-A083706: 1 4 9 18 35 68 133 262 519 1032 2057 4106 8203 16396 32781 65550
((~x + 1) + loop(\(x,i).2x,x,2))
A132753: 3 4 7 14 29 60 123 250 505 1016 2039 4086 8181 16372 32755 65522
loop(\(x,i).(2 * (x + (x div 2))),x,1)
A181490: 1 2 6 18
A025192: 1 2 6 18 54 162 486 1458 4374 13122 39366 118098 354294 1062882 3188646 9565938
loop(\(x,i).(2x * (2 + i)),x,1)
A051578: 1 6 48 480 5760 80640 1290240 23224320 464486400 10218700800 245248819200 6376469299200 178541140377600 5356234211328000 171399494762496000 4611686018427387903
loop(\(x,i).(2 * (x + (2 * i))),x,1)
A027178: 1 6 20 52 120 260 544 1116 2264 4564 9168 18380 36808 73668 147392 294844
loop(\(x,i).(2 * (~x + (i mod 2))),x,1)
A167193: 1 0 0 2 ~4 10 ~20 42 ~84 170 ~340 682 ~1364 2730 ~5460 10922
(1 + loop(\(x,i).2x,(x + 2),x))
A048479: 1 9 33 97 257 641 1537 3585 8193 18433 40961 90113 196609 425985 917505 1966081
loop(\(x,i).2x,(x2 + 2x),1)
A103488: 1 8 256 32768 16777216 34359738368 281474976710656 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),(x2 + 2x),1)
A256511: 1 6 40320 1307674368000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((2x + 2) + i),x,1)
A094002: 1 5 14 33 72 151 310 629 1268 2547 5106 10225 20464 40943 81902 163821
loop(\(x,i).((x + 2) + (i * i)),x,1)
A049480: 1 4 10 21 39 66 104 155 221 304 406 529 675 846 1044 1271
loop(\(x,i).(2x + (x div 2)),x,1)
A076883: 1 2 5 12 30 75 187 467 1167 2917 7292 18230 45575 113937 284842 712105
loop(\(x,i).(2x + (i mod 2)),x,1)
A081254: 1 3 6 13 26 53 106 213 426 853 1706 3413 6826 13653 27306 54613
loop(\(x,i).(3x + i),x,1)
A108765: 1 4 14 45 139 422 1272 3823 11477 34440 103330 310001 930015 2790058 8370188 25110579
loop(\(x,i).(3x - i),x,1)
A164039: 1 2 4 9 23 64 186 551 1645 4926 14768 44293 132867 398588 1195750 3587235
loop(\(x,i).(x * i),(x * (x div 2)),1)
A005607: 1 1 2 6 40320
(if (~x + 2) <= 0 then (x + (x mod 2)) else 1)
A085914: 1 1 2 4 4 6 6 8 8 10 10 12 12 14 14 16
loop(\(x,i).2x,(x * (x mod 2)),1)
A066532: 1 2 1 8 1 32 1 128 1 512 1 2048 1 8192 1 32768
((x + ~1) + (if (~x + 2) <= 0 then x else 2))
A053224-A004280: 1 2 3 5 7 9 11 13 15 17 19 21 23 25 27 29
loop(\(x,i).(x * (i * (2 + i))),x,1)
A010791: 1 3 24 360 8640 302400 14515200 914457600 73156608000 7242504192000 869100503040000 124281371934720000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + (2 * i)),x,1)
A318165: 1 3 13
A114317: 1 3 13 175 30633 938380699 880558336255728613 4611686018427387903 4611686018427387903
loop(\(x,i).(2x - (i mod 2)),x,1)
A005578: 1 1 2 3 6 11 22 43 86 171 342 683 1366 2731 5462 10923
(loop(\(x,i).2x,x,1) div (x + 1))
A074099-A006788: 1 1 1 2 3 5 9 16 28 51 93 170 315 585 1092 2048
(loop(\(x,i).2x,x,1) mod (x + 1))
A229878: 0 0 1 0 1 2
A062173: 0 0 1 0 1 2 1 0 4 2 1 8 1 2 4 0
(loop(\(x,i).(x * i),x,1) div (x + 1))
A226198: 1 0 0 1 4 20 102 630 4480 36288 329890 3326400 36846276 444787200 5811886080 81729648000
(loop(\(x,i).(x * i),x,1) mod (x + 1))
A061006: 0 1 2 2 4 0 6 0 0 0 10 0 12 0 0 0
loop(\(x,i).(x2 + x),2,(x + 1))
A176780-A082986: 6 42 156 420 930 1806 3192 5256 8190 12210 17556 24492 33306 44310 57840 74256
(loop(\(x,i).2x,x,2) div (x + 1))
A000799: 2 2 2 4 6 10 18 32 56 102 186 341 630 1170 2184 4096
(loop(\(x,i).2x,x,2) mod (x + 1))
A015910: 0 0 2 0 2 4 2 0 8 4 2 4 2 4 8 0
loop(\(x,i).(x + (x div 2)),2,(x + 1))
A231407: 1 4 6
A330186-A330182: 1 4 6 9 10 13 15 18 19 22 24 27 28 31 33 36
((2x + 2) * (if x <= 0 then 2 else x))
A106232: 4 4 12 24 40 60 84 112 144 180 220 264 312 364 420 480
((x + 1) * (if x <= 0 then 1 else (x + 2)))
A180291: 1 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272
((x + 1) * (if (~x + 2) <= 0 then x else 2))
A060798: 2 4 6 12 20 30 42 56 72 90 110 132 156 182 210 240
loop(\(x,i).(x * (x + i)),2,(x + 1))
A247727: 8 48 168 440 960 1848 3248 5328 8280 12320 17688 24648 33488 44520 58080 74528
((x + 1) + (if (x mod 2) <= 0 then 1 else x))
A321220: 2 3 4 7 6 11 8 15 10 19 12 23 14 27 16 31
loop(\(x,i).(1 + (x * i)),x,(x + 1))
A084756: 1 3 9 34 161 926 6277 48980 432161 4252330 46152101 547589912 7050080545 97878067886 1457471241605 23169742992076
loop(\(x,i).(2x + 2),x,(x + 1))
A328890: 1 6 18 46 110 254 574 1278 2814 6142 13310 28670 61438 131070 278526 589822
loop(\(x,i).(2x + ~2),x,(x + 1))
A181490: 1 2 6 18
A048495: 1 2 6 18 50 130 322 770 1794 4098 9218 20482 45058 98306 212994 458754
(if (x + ~4) <= 0 then x else (x + 1))
A340288-A231237: 0 1 2 3 4 6 7 8 9 10 11 12 13 14 15 16
(if (~2 + (x div 2)) <= 0 then x else (x + 1))
A067570: 0 1 2 3 4 5 7
A103679-A029916: 0 1 2 3 4 5 7 8 9 10 11 12 13 14 15 16
loop(\(x,i).(2 * (x + i)),x,(x + 1))
A027993: 1 6 20 54 132 306 688 1518 3308 7146 15336 32742 69604 147426 311264 655326
loop(\(x,i).(x * (2 + i)),x,(x + 1))
A001286: 1 6 36 240 1800 15120 141120 1451520 16329600 199584000 2634508800 37362124800 566658892800 9153720576000 156920924160000 2845499424768000
loop(\(x,i).(2x + i),x,(x + 1))
A053221: 1 5 16 43 106 249 568 1271 2806 6133 13300 28659 61426 131057 278512 589807
(loop(\(x,i).(x * i),x,x) mod (x + 1))
A061007: 0 1 1 2 1 0 1 0 0 0 1 0 1 0 0 0
loop(\(x,i).(x * (x - i)),2,(x + ~1))
A052762: 0 0 0 0 24 120 360 840 1680 3024 5040 7920 11880 17160 24024 32760
((x + ~1) * loop(\(x,i).2x,x,x))
A128796: 0 0 8 48 192 640 1920 5376 14336 36864 92160 225280 540672 1277952 2981888 6881280
loop(\(x,i).5x,x,1)
A000351: 1 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125 6103515625 30517578125
loop(\(x,i).(x * (3 + i)),x,1)
A001715: 1 4 20 120 840 6720 60480 604800 6652800 79833600 1037836800 14529715200 217945728000 3487131648000 59281238016000 1067062284288000
loop(\(x,i).(x * (~1 + (2 * i))),x,1)
A001147: 1 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 213458046676875 6190283353629375
loop(\(x,i).(x3 + x),x,1)
A074333: 1 2 10 1010 1030302010 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (x * i))),x,1)
A275611: 1 2 10 310 384710 740009305210 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (i * i))),x,1)
A101686: 1 2 10 100 1700 44200 1635400 81770000 5315050000 435834100000 44019244100000 5370347780200000 778700428129000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((1 + i) div 2)),x,1)
A010551: 1 1 1 2 4 12 36 144 576 2880 14400 86400 518400 3628800 25401600 203212800
loop(\(x,i).(3x + 4),x,1)
A058481: 1 7 25 79 241 727 2185 6559 19681 59047 177145 531439 1594321 4782967 14348905 43046719
(1 + loop(\(x,i).4x,x,x))
A050915: 1 5 33 193 1025 5121 24577 114689 524289 2359297 10485761 46137345 201326593 872415233 3758096385 16106127361
loop(\(x,i).(x * (4 + i)),x,1)
A001720: 1 5 30 210 1680 15120 151200 1663200 19958400 259459200 3632428800 54486432000 871782912000 14820309504000 266765571072000 5068545850368000
loop(\(x,i).(x * (2 + (i mod 2))),x,1)
A026532: 1 3 6 18 36 108 216 648 1296 3888 7776 23328 46656 139968 279936 839808
loop(\(x,i).(x * (~2 + (i * i))),x,1)
A263766: 1 ~1 ~2 ~14 ~196 ~4508 ~153272 ~7203784 ~446634608 ~35284134032 ~3457845135136 ~411483571081184 ~58430667093528128 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (2 * (i * i))),x,1)
A188475: 1 3 11 29 61 111 183 281 409 571 771 1013 1301 1639 2031 2481
loop(\(x,i).(1 + (x * i)),x2,1)
A326253: 1 2 65 986410 56874039553217 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).4x,x2,1)
A060757: 1 4 256 262144 4294967296 1125899906842624 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).x2,2,x2))
A060890: 1 2 257 6562 65537 390626 1679617 5764802 16777217 43046722 100000001 214358882 429981697 815730722 1475789057 2562890626
loop(\(x,i).(x * i),x,(x2 + 1))
A082042: 1 2 10 60 408 3120 26640 252000 2620800 29756160 366508800 4869849600 69455232000 1058593536000 17174123366400 295534407168000
loop(\(x,i).3x,x2,1)
A060722: 1 3 81 19683 43046721 847288609443 150094635296999121 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).2x,x,x2))
A248917: 1 3 17 73 257 801 2305 6273 16385 41473 102401 247809 589825 1384449 3211265 7372801
(1 + loop(\(x,i).3x,x,x))
A050914: 1 4 19 82 325 1216 4375 15310 52489 177148 590491 1948618 6377293 20726200 66961567 215233606
loop(\(x,i).(x * (x + (2 * i))),x,1)
A145386: 1 3 21 567 326025 106295560875 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x3,1)
A190539: 1 2 256 134217728 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),x3,1)
A255358: 1 1 40320 4611686018427387903
loop(\(x,i).(x3 * i),x,1)
A054909: 1 1 2 24
A123851: 1 1 2 24 55296 845378412871680 4611686018427387903
loop(\(x,i).(x2 + (i * i)),x,1)
A143760: 1 2 8 73 5345 28569050 816190617902536 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * (i * i)),x,1)
A030450: 1 1 4 144 331776 2751882854400 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(2x + i),x,x))
A221882: 1 4 13 36 91 218 505 1144 2551 5622 12277 26612 57331 122866 262129 557040
loop(\(x,i).(i - (x * (1 - i))),x,1)
A111063: 1 1 3 9 31 129 651 3913 27399 219201 1972819 19728201 217010223 2604122689 33853594971 473950329609
loop(\(x,i).(x + ((2 + i) * i)),x,1)
A047732: 1 4 12 27 51 86 134 197 277 376 496 639 807 1002 1226 1481
loop(\(x,i).(x * ((i mod 2) + i)),x,1)
A001900: 1 2 4 16 64 384 2304 18432 147456 1474560 14745600 176947200 2123366400 29727129600 416179814400 6658877030400
loop(\(x,i).((x + i) * (x + i)),x,1)
A143764: 1 4 36 1521 2325625 5408554896900 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x - i) * (x + i)),x,1)
A153062: 1 0 ~4 7 33 1064 1132060 1281559843551 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((~x + i) * (~x + i)),x,1)
A143763: 1 0 4 1 9 16 100 8649 74666881 5575141774264384 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (i * i * i)),x,1)
A000442: 1 1 8 216 13824 1728000 373248000 128024064000 65548320768000 47784725839872000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (i * i * i)),x,1)
A154323: 1 2 10 37 101 226 442 785 1297 2026 3026 4357 6085 8282 11026 14401
loop(\(x,i).((x + ~3) * i),x,1)
A165814: 1 ~2 ~10 ~39 ~168 ~855 ~5148 ~36057 ~288480 ~2596347 ~25963500 ~285598533 ~3427182432 ~44553371655 ~623747203212 ~9356208048225
loop(\(x,i).((x + 3) * i),x,1)
A165813: 1 4 14 51 216 1095 6588 46137 369120 3322107 33221100 365432133 4385185632 57007413255 798103785612 11971556784225
loop(\(x,i).(((x + ~1) + i) * i),x,1)
A085923: 1 1 4 18 84 440 2670 18732 149912 1349280 13492890 148421900 1781062932 23153818272 324153455990 4862301840060
loop(\(x,i).((1 + (x * i)) * i),x,1)
A026025: 1 2 10 93 1492 37305 1342986 65806321 4211604552 341139968721 34113996872110 4127793621525321 594402281499646236 4611686018427387903 4611686018427387903
loop(\(x,i).((x + ~4) * i),x,1)
A166680: 1 ~3 ~14 ~54 ~232 ~1180 ~7104 ~49756 ~398080 ~3582756 ~35827600 ~394103644 ~4729243776 ~61480169140 ~860722368016 ~12910835520300
loop(\(x,i).((x mod 4) * i),x,1)
A300659: 1 1 2 6 8 0 0 0 0 0 0 0 0 0 0 0
loop(\(x,i).((x + 4) * i),x,1)
A166677: 1 5 18 66 280 1420 8544 59836 478720 4308516 43085200 473937244 5687246976 73934210740 1035078950416 15526184256300
loop(\(x,i).(4x - i),x,1)
A188545: 1 3 10
A164044: 1 3 10 37 144 571 2278 9105 36412 145639 582546 2330173 9320680 37282707 149130814 596523241
loop(\(x,i).((2 * (x + i)) + i),x,1)
A097810: 1 5 16 41 94 203 424 869 1762 3551 7132 14297 28630 57299 114640 229325
((x - (if (x + ~1) <= 0 then 1 else 0)) mod 2)
A266070: 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1
((x - (if (x + ~2) <= 0 then 1 else 0)) mod 2)
A266719: 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1
((x - (if (~x + 2) <= 0 then 1 else 0)) mod 2)
A296066: 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0
(if (x mod 2) <= 0 then 3 else ~2)
A168330: 3 ~2 3 ~2 3 ~2 3 ~2 3 ~2 3 ~2 3 ~2 3 ~2
(x - ((if x <= 0 then 1 else x) div ~2))
A294732: 1 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23
(x - (if x <= 0 then 1 else (x div ~2)))
A045506: ~1 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23
((2x + ~1) * (if x <= 0 then 0 else 2))
A130824: 0 2 6 10 14 18 22 26 30 34 38 42 46 50 54 58
(loop(\(x,i).(2x + i),x,0) div 2)
A320933: 0 0 2 5 13 28 60 123 251 506 1018 2041 4089 8184 16376 32759
(x - (if (x mod 2) <= 0 then ~1 else 2))
A097062: 1 ~1 3 1 5 3 7 5 9 7 11 9 13 11 15 13
(if (x + ~6) <= 0 then 1 else 2)
A300287-A226764-A171622: 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2
(if (~2 + (x div 3)) <= 0 then 1 else 2)
A329624-A282622-A279951-A279224-A277090-A276502-A254524-A248777-A211665-A187187-A167661-A133879-A116371-A103376-A032574-A032572-A032556: 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2
(2 + (if (x mod 3) <= 0 then 2 else 1))
A129344: 4 3 3 4 3 3 4 3 3 4 3 3 4 3 3 4
(if (~2 + (x div 4)) <= 0 then 1 else 2)
A285481-A279758-A145884-A103379: 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2
(if (~4 + (x div 2)) <= 0 then 1 else 2)
A324160-A262190-A226233-A204551-A179051-A160093-A140438-A138902-A133880-A133502-A132272-A108622-A103377-A098378-A055642: 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2
(if ((x + ~1) mod 4) <= 0 then 1 else 2)
A214860: 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2
(if (x mod (2 + (x mod 2))) <= 0 then 1 else 2)
A213636: 1 2 1 1 1 2 1 2 1 1 1 2 1 2 1 1
(if (x mod 2) <= 0 then 1 else 6)
A010687: 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1 6
(2 + (if (x + ~2) <= 0 then x else 3))
A168092: 2 3 4 5 5 5 5 5 5 5 5 5 5 5 5 5
(2 + loop(\(x,i).2x,x,3))
A164094: 5 8 14 26 50 98 194 386 770 1538 3074 6146 12290 24578 49154 98306
(loop(\(x,i).2x,x,3) div 2)
A170684-A170636-A170588-A170540-A170492-A170444-A170396-A170348-A170300-A170252-A170204-A170156-A170108-A170060-A170012-A169544-A169496-A169448-A169400-A169352-A169304-A169256-A169208-A169160-A169112-A169064-A169016-A168968-A168920-A168872-A168824-A168776-A168728-A168680-A167881-A003945: 1 3 6 12 24 48 96 192 384 768 1536 3072 6144 12288 24576 49152
(((if x <= 0 then 2 else x) mod 3) div 2)
A173857: 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0
(if x <= 0 then 1 else (2 + (x div 3)))
A053620: 1 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7
loop(\(x,i).(~x + i),(x mod 3),2)
A131756: 2 ~1 3 2 ~1 3 2 ~1 3 2 ~1 3 2 ~1 3 2
(2 + loop(\(x,i).x2,x,3))
A057726: 5 11 83 6563
A057727: 5 11 83 6563 43046723 1853020188851843 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (4x + 2))
A133653: 1 6 10 14 18 22 26 30 34 38 42 46 50 54 58 62
loop(\(x,i).2x,(2x + ~1),2)
A155543: 2 4 16 64 256 1024 4096 16384 65536 262144 1048576 4194304 16777216 67108864 268435456 1073741824
(if x <= 0 then 1 else (4x + ~2))
A111284: 1 2 6 10 14 18 22 26 30 34 38 42 46 50 54 58
(2 * (~1 + loop(\(x,i).x2,x,2)))
A074777: 2 6 30 510 131070 8589934590
(loop(\(x,i).(2x + 2),x,1) div 2)
A086219-A060153-A055010: 0 2 5 11 23 47 95 191 383 767 1535 3071 6143 12287 24575 49151
(2 + loop(\(x,i).4x,x,1))
A178789: 3 6 18 66 258 1026 4098 16386 65538 262146 1048578 4194306 16777218 67108866 268435458 1073741826
(if (~x2 + 4x) <= 0 then 1 else 2)
A171624: 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1
(loop(\(x,i).x2,2,(x + 1)) div 2)
A191903: 0 8 40 128 312 648 1200 2048 3280 5000 7320 10368 14280 19208 25312 32768
loop(\(x,i).(2x * i),(x + 1),2)
A130683: 4 16 96 768 7680 92160 1290240 20643840 371589120 7431782400 163499212800 3923981107200 102023508787200 2856658246041600 85699747381248000 2742391916199936000
loop(\(x,i).(x * i),x,((x + 1) div 2))
A052591: 0 1 2 12 48 360 2160 20160 161280 1814400 18144000 239500800 2874009600 43589145600 610248038400 10461394944000
loop(\(x,i).2x,x,((x + 1) mod 2))
A199572: 1 0 4 0 16 0 64 0 256 0 1024 0 4096 0 16384 0
loop(\(x,i).(x * i),x,((x + 1) mod 2))
A005359: 1 0 2 0 24 0 720 0 40320 0 3628800 0 479001600 0 87178291200 0
(((x + 1) * (if x <= 0 then 2 else x)) div 2)
A179865: 1 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120
(if (x mod 2) <= 0 then 1 else (2x + ~2))
A265722: 1 0 1 4 1 8 1 12 1 16 1 20 1 24 1 28
(2 + ((x + ~1) * (if x <= 0 then 1 else x)))
A222011: 1 2 4 8
(1 mod loop(\(x,i).x2,(x + ~1),2))
A144616-A068214: 1 1 1 1 1 1 1 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(5 * (if x <= 0 then 1 else 2))
A040020: 5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
((x2 + 1) * (if x <= 0 then 1 else 2))
A005893: 1 4 10 20 34 52 74 100 130 164 202 244 290 340 394 452
(8 * (if x <= 0 then 1 else 2))
A040056: 8 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16
((x div 4) + (if x <= 0 then 1 else 2))
A226763: 1 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5
((x + 4) + (if x <= 0 then 1 else 2))
A242963: 5 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
((2x + 4) + (if x <= 0 then 1 else 2))
A115401: 5 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
((2 - (x mod 2)) * (if x <= 0 then 1 else 2))
A040003: 2 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2
((x2 div 2) + (if x <= 0 then 1 else 2))
A333574: 1 2 4 6 10 14 20 26 34 42 52 62 74 86 100 114
((x2 + x) + (if x <= 0 then 1 else 2))
A003682: 1 4 8 14 22 32 44 58 74 92 112 134 158 184 212 242
(x + ((x div 2) + (if x <= 0 then 1 else 2)))
A114119: 1 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24
(x3 + (if x <= 0 then 1 else 2))
A188545: 1 3 10
(2 + loop(\(x,i).3x,x,1))
A168607: 3 5 11 29 83 245 731 2189 6563 19685 59051 177149 531443 1594325 4782971 14348909
(2 * loop(\(x,i).(x2 + x),x,1))
A053631: 2 4 12 84 3612 6526884 21300113901612 4611686018427387903 4611686018427387903 4611686018427387903
(4 + loop(\(x,i).2x,x,1))
A140504: 5 6 8 12 20 36 68 132 260 516 1028 2052 4100 8196 16388 32772
(2 + (loop(\(x,i).2x,x,1) div 2))
A056469: 2 3 4 6 10 18 34 66 130 258 514 1026 2050 4098 8194 16386
(2 * (loop(\(x,i).(x * i),x,1) div 2))
A124355: 0 0 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000
(2 * (if (x mod 2) <= 0 then 1 else 4))
A010698: 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2 8
(if (x mod 2) <= 0 then 1 else 8)
A010689: 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8
(if x <= 0 then 1 else (x div 8))
A339109-A288684-A264595-A245793-A245148-A185328-A185118-A025153-A017902-A017876-A017875-A017874-A017873: 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
loop(\(x,i).x3,4,2)
A144134-A118329-A115453-A072288-A058446: 4611686018427387903
A291353-A280419-A257374-A217419-A210704-A130682-A008870-A008869: 4611686018427387903 4611686018427387903
A338966-A328860-A291354-A246291-A169667-A160678-A155960-A141756-A135956-A135386-A120335-A115556-A115503-A105300-A033290-A010034-A008868-A003944-A003937-A003854-A003847: 4611686018427387903 4611686018427387903 4611686018427387903
A338958-A338954-A292993-A292992-A292858-A292857-A292856-A292846-A261700-A257376-A246290-A234594-A219283-A217416-A194216-A181789-A171265-A120318-A115555-A115548-A115547-A115542-A115532-A115531-A114993-A105301-A105299-A104300-A008916-A008915-A008872-A008871-A003943-A003942-A003936-A003935-A003846-A003845: 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A332605-A306797-A292635-A291042-A280350-A280349-A280347-A280346-A280301-A280299-A280298-A272522-A246289-A217431-A217428-A217425-A217422-A217413-A217410-A181309-A174817-A174671-A173907-A162033-A135955-A115541-A115540-A104319-A104304-A104283-A009190-A003853-A003852-A003813-A003812-A003806: 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A292859-A272521-A247262-A219323-A217404-A175274-A105298-A104322-A104267-A083104-A083103-A046061-A003805: 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A343266-A341116-A291215-A265913-A246288-A246255-A239924-A181791-A181790-A132902-A120317-A115530-A105303: 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A281907-A272520-A246254-A219322-A217407-A215403-A146561-A121977-A104263-A092118: 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A338609-A246253-A238360-A216854-A187716-A187714-A180247-A175273-A132185-A076335-A037017: 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A343357-A340397-A326414-A324208-A304373-A290156-A252504-A238359-A219321-A215876-A116356: 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A321136-A316155-A288290-A257307-A231562: 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A266961: 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A257370: 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * loop(\(x,i).x2,(x + 2),2))
A109384: 32 512 131072 8589934592 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else 8x)
A022144: 1 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120
(2 + (if (x + ~2) <= 0 then (x div 2) else 2))
A300404: 2 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4
(x - loop(\(x,i).(x2 + 2),2,2))
A023480: ~38 ~37 ~36 ~35 ~34 ~33 ~32 ~31 ~30 ~29 ~28 ~27 ~26 ~25 ~24 ~23
loop(\(x,i).x2,2x,4)
A137840: 4 256 4294967296 4611686018427387903 4611686018427387903
(if (x + ~3) <= 0 then x else 4)
A158411: 0 1 2 3 4 4 4 4 4 4 4 4 4 4 4 4
loop(\(x,i).(2x + 1),x,4)
A153894: 4 9 19 39 79 159 319 639 1279 2559 5119 10239 20479 40959 81919 163839
((if (x mod 2) <= 0 then 1 else x) mod 4)
A093148: 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3
loop(\(x,i).(x2 + ~1),x,4)
A139244: 4 15 224 50175 2517530624 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + ~2),x,4)
A003010: 4 14 194 37634 1416317954 2005956546822746114 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),x,(x + ~4))
A282822: ~4 ~3 ~4 ~6 0 120 1440 15120 161280 1814400 21772800 279417600 3832012800 56043187200 871782912000 14384418048000
((if x <= 0 then 1 else x) - (x div 4))
A213854-A074184: 1 1 2 3 3 4 5 6 6 7 8 9 9 10 11 12
loop(\(x,i).(x2 + ~x),x,4)
A204321: 4 12 132 17292 298995972 89398590973228812 4611686018427387903 4611686018427387903
(4 * loop(\(x,i).(x * i),x,x))
A208528: 0 4 16 72 384 2400 17280 141120 1290240 13063680 145152000 1756339200 22992076800 323805081600 4881984307200 78460462080000
loop(\(x,i).(x + (i * i)),x,4)
A153058: 4 5 9 18 34 59 95 144 208 289 389 510 654 823 1019 1244
loop(\(x,i).(x2 + i),x,4)
A153061: 4 17 291 84684 7171379860 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 - i),x,4)
A153060: 4 15 223 49726 2472675072 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(2x + 1),x,2) div 2)
A083329: 1 2 5 11 23 47 95 191 383 767 1535 3071 6143 12287 24575 49151
(2 + loop(\(x,i).4x,x,2))
A283070: 4 10 34 130 514 2050 8194 32770 131074 524290 2097154 8388610 33554434 134217730 536870914 2147483650
(~2 + loop(\(x,i).4x,x,2))
A002446: 0 6 30 126 510 2046 8190 32766 131070 524286 2097150 8388606 33554430 134217726 536870910 2147483646
loop(\(x,i).2x,x,(x + 4))
A079859: 4 10 24 56 128 288 640 1408 3072 6656 14336 30720 65536 139264 294912 622592
(((x + 2) * (if x <= 0 then 1 else x)) div 2)
A178939: 1 1 4 7 12
(loop(\(x,i).2x,x,(x + 2)) div 2)
A001792: 1 3 8 20 48 112 256 576 1280 2816 6144 13312 28672 61440 131072 278528
loop(\(x,i).(x * (2 + i)),(x + 2),2)
A124657: 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000 20922789888000 355687428096000 6402373705728000 121645100408832000
loop(\(x,i).(2x + 1),2x,2)
A198693: 2 11 47 191 767 3071 12287 49151 196607 786431 3145727 12582911 50331647 201326591 805306367 3221225471
loop(\(x,i).4x,2x,2)
A013776: 2 32 512 8192 131072 2097152 33554432 536870912 8589934592 137438953472 2199023255552 35184372088832 562949953421312 9007199254740992 144115188075855872 2305843009213693952
loop(\(x,i).x2,2,4x)
A016804: 0 256 4096 20736 65536 160000 331776 614656 1048576 1679616 2560000 3748096 5308416 7311616 9834496 12960000
(if (x mod 2) <= 0 then 1 else (2 + (x div 2)))
A342703-A133622: 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9
loop(\(x,i).3x,(x div 2),2)
A117855: 2 2 6 6 18 18 54 54 162 162 486 486 1458 1458 4374 4374
(1 mod (if (~x + 2) <= 0 then (x div 2) else 2))
A267537: 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1
(2 + ((if x <= 0 then 1 else x) + (x mod 2)))
A213222: 3 4 4 6 6 8 8 10 10 12 12 14 14 16 16 18
(2 + loop(\(x,i).3x,x,2))
A115099: 4 8 20 56 164 488 1460 4376 13124 39368 118100 354296 1062884 3188648 9565940 28697816
(loop(\(x,i).(x + (x div 2)),x,2) div 2)
A005428: 1 1 2 3 4 6 9 14 21 31 47 70 105 158 237 355
loop(\(x,i).(x * (2x + i)),2,2)
A157645: 220 220 220 220 220 220 220 220 220 220 220 220 220 220 220 220
((if (x mod 3) <= 0 then 1 else x) mod 2)
A065535: 1 1 0 1 0 1 1 1 0 1 0
A285518-A093719: 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1
loop(\(x,i).(4x + 1),x,2)
A206374: 2 9 37 149 597 2389 9557 38229 152917 611669 2446677 9786709 39146837 156587349 626349397 2505397589
loop(\(x,i).(4x + ~1),x,2)
A136412: 2 7 27 107 427 1707 6827 27307 109227 436907 1747627 6990507 27962027 111848107 447392427 1789569707
loop(\(x,i).(3x + ~3),x,2)
A115098: 2 3 6 15 42 123 366 1095 3282 9843 29526 88575 265722 797163 2391486 7174455
loop(\(x,i).(2x2 + ~1),x,2)
A002812: 2 7 97 18817 708158977 1002978273411373057 4611686018427387903 4611686018427387903
(if (x mod 2) <= 0 then 2 else ((~x + 1) div 2))
A174007: 2 0 2 ~1 2 ~2 2 ~3 2 ~4 2 ~5 2 ~6 2 ~7
loop(\(x,i).(x2 + x + 1),x,2)
A105183: 2 7 57 3307 10939557 119673918295807 4611686018427387903 4611686018427387903 4611686018427387903
(2 * (x + loop(\(x,i).2x,x,1)))
A131520: 2 6 12 22 40 74 140 270 528 1042 2068 4118 8216 16410 32796 65566
loop(\(x,i).(1 + (x * (2 + i))),x,2)
A185109: 2 7 29 146 877 6140 49121 442090 4420901 48629912 583558945 7586266286 106207728005 1593115920076 25489854721217 433327530260690
loop(\(x,i).(4x + 4),x,2)
A080675: 2 12 52 212 852 3412 13652 54612 218452 873812 3495252 13981012 55924052 223696212 894784852 3579139412
(2 * loop(\(x,i).(x * i),(x + ~1),x))
A052849: 0 2 4 12 48 240 1440 10080 80640 725760 7257600 79833600 958003200 12454041600 174356582400 2615348736000
((4 mod (if x <= 0 then 1 else x)) mod 2)
A343958-A193243-A185013-A045840: 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
loop(\(x,i).(x * (i * (1 + i))),x,2)
A047677: 2 4 24 288 5760 172800 7257600 406425600 29262643200 2633637888000 289700167680000 38240422133760000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 2) + (if (x + ~2) <= 0 then 1 else 2))
A063992-A055495: 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18 19
(2 * (x + (if (x + ~2) <= 0 then 1 else 2)))
A309374: 2 4 6 10 12
loop(\(x,i).8x,x,2)
A013730: 2 16 128 1024 8192 65536 524288 4194304 33554432 268435456 2147483648 17179869184 137438953472 1099511627776 8796093022208 70368744177664
(if (~4 + (x div 2)) <= 0 then x else 2)
A103303: 0 1 2 3 4 5 6 7 8 9
A177895: 0 1 2 3 4 5 6 7 8 9 2 2 2 2 2 2
(2 - loop(\(x,i).(~2 + (x div 2)),x,2))
A267884: 0 3 5 6 6 6 6 6 6 6 6 6 6 6 6 6
(loop(\(x,i).(x2 div 2),2,x) div 2)
A030179: 0 0 1 4 16 36 81 144 256 400 625 900 1296 1764 2401 3136
loop(\(x,i).(2 * (x - (i mod 2))),x,2)
A052953: 2 2 4 6 12 22 44 86 172 342 684 1366 2732 5462 10924 21846
loop(\(x,i).((x2 + x) div 2),x,2)
A007501: 2 3 6 21 231 26796 359026206 64449908476890321 4611686018427387903 4611686018427387903
(loop(\(x,i).(x2 + x),2,x) div 2)
A110450: 0 3 21 78 210 465 903 1596 2628 4095 6105 8778 12246 16653 22155 28920
loop(\(x,i).(x2 + 2x + ~2),x,2)
A145502: 2 6 46 2206 4870846 23725150497406 4611686018427387903 4611686018427387903
((~x + loop(\(x,i).2x,x,2)) div 2)
A084174: 1 1 3 6 14 29 61 124 252 507 1019 2042 4090 8185 16377 32760
loop(\(x,i).(2x * (2 + i)),x,2)
A014297: 2 12 96 960 11520 161280 2580480 46448640 928972800 20437401600 490497638400 12752938598400 357082280755200 10712468422656000 342798989524992000 4611686018427387903
(2 * loop(\(x,i).2x,(x + 2),x))
A059165: 0 16 64 192 512 1280 3072 7168 16384 36864 81920 180224 393216 851968 1835008 3932160
loop(\(x,i).2x,(x2 + 2x),2)
A063391: 2 16 512 65536 33554432 68719476736 562949953421312 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,(x + ~2),x) div 2)
A049610: 0 0 1 3 8 20 48 112 256 576 1280 2816 6144 13312 28672 61440
(2 * loop(\(x,i).(x * i),2x,x))
A062779: 0 4 96 4320 322560 36288000 5748019200 1220496076800 334764638208000 115242726703104000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,(x + (x div 2)),2)
A173566: 2 4 256
(if x <= 0 then 1 else (2 * (x + (x mod 2))))
A146890: 1 4 4 8 8 12 12 16 16
((3 mod (if x <= 0 then 2 else x)) mod 2)
A267878-A267870: 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1
loop(\(x,i).(2 + (x2 * i)),x,2)
A065410: 2 6 74 16430 1079779602 4611686018427387903 4611686018427387903 4611686018427387903
((x + 2) + loop(\(x,i).(x * i),x,2))
A275929: 4 5 8 17 54 247 1448 10089 80650 725771 7257612 79833613 958003214 12454041615 174356582416 2615348736017
loop(\(x,i).(x * (i * (2 + i))),x,2)
A175430: 2 6 48 720 17280 604800 29030400 1828915200 146313216000 14485008384000 1738201006080000 248562743869440000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 + ((x + i) * i)),x,2)
A107283: 2 5 16 59 254 1297 7820 54791 438394 3945629 39456392 434020435 5208245366 67707189929 947900659204 14218509888287
loop(\(x,i).((x + 2) - (i * i)),x,2)
A058372: 2 3 1 ~6 ~20 ~43 ~77 ~124 ~186 ~265 ~363 ~482 ~624 ~791 ~985 ~1208
(loop(\(x,i).2x,x,1) mod (x + 2))
A213859: 1 2 0 3 4 4 0 2 6 6 4 7 8 2 0 9
loop(\(x,i).(x2 + ~2),2,(x + 2))
A304725: 2 47 194 527 1154 2207 3842 6239 9602 14159 20162 27887 37634 49727 64514 82367
(loop(\(x,i).(x * i),x,2) div (x + 2))
A061370: 1 0 1 2 8 34 180 1120 8064 65978 604800 6141046 68428800 830269440 10897286400 153844043294
(if (~2 + (x div 2)) <= 0 then x else (x + 2))
A039260: 0 1 2 3 4 5 8 9 10 11 12 13 14 15 16 17
loop(\(x,i).3x,x,(x + 2))
A288834: 2 9 36 135 486 1701 5832 19683 65610 216513 708588 2302911 7440174 23914845 76527504 243931419
(if x <= 0 then 1 else (x3 + 2x2))
A216149: 1 3 16
((x + 2) * loop(\(x,i).(x * i),x,x))
A130744: 0 3 16 90 576 4200 34560 317520 3225600 35925120 435456000 5708102400 80472268800 1214269056000 19527937228800 333456963840000
loop(\(x,i).(x * (i * i)),x,(x + 2))
A179442: 2 3 16 180 3456 100800 4147200 228614400 16257024000 1448500838400 158018273280000 20713561989120000 3212195459235840000 4611686018427387903 4611686018427387903
(if (x + ~4) <= 0 then 1 else (x + ~2))
A171604: 1 1 1 1 1 3 4
(1 mod (if (x + ~2) <= 0 then 2 else (x + ~2)))
A267871: 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
(2 div (if (x + ~2) <= 0 then 2 else (x + ~2)))
A329679: 1 1 1 2 1 0 0 0 0 0 0 0 0 0 0 0
(2x + (if (x + ~1) <= 0 then 1 else 0))
A027440: 1 3 4 6 8 10 12
(2x + (if (~x + 2) <= 0 then 1 else 0))
A130773: 0 2 5 7 9 11 13 15 17 19 21 23 25 27 29 31
loop(\(x,i).x2,3,2x)
A016748: 0 256 65536 1679616 16777216 100000000 429981696 1475789056 4294967296 11019960576 25600000000 54875873536 110075314176 208827064576 377801998336 656100000000
loop(\(x,i).2x,x,(~2x + 1))
A143126: 1 ~2 ~12 ~40 ~112 ~288 ~704 ~1664 ~3840 ~8704 ~19456 ~43008 ~94208 ~204800 ~442368 ~950272
((~x + 2) - (if x <= 0 then 1 else 2x))
A112335: 1 ~1 ~4 ~7 ~10 ~13 ~16 ~19 ~22 ~25 ~28 ~31 ~34 ~37 ~40 ~43
(2x + (if (x + ~2) <= 0 then 1 else 2))
A097911: 1 3 5 8
A073608: 1 3 5 8 10 12
(if (x mod 2) <= 0 then (x div 2) else 2x)
A064680: 0 2 1 6 2 10 3 14 4 18 5 22 6 26 7 30
loop(\(x,i).x3,2,2x)
A016749: 0 512 262144 10077696 134217728 1000000000 5159780352 20661046784 68719476736 198359290368 512000000000 1207269217792 2641807540224 5429503678976 10578455953408 19683000000000
loop(\(x,i).(2x + ~2),x,2x)
A036799: 0 2 10 34 98 258 642 1538 3586 8194 18434 40962 90114 196610 425986 917506
loop(\(x,i).(2x + ~4),x,2x)
A291526: 0 0 4 20 68 196 516 1284 3076 7172 16388 36868 81924 180228 393220 851972
((if (x mod 2) <= 0 then 2 else 0) + (x div 2))
A084964: 2 0 3 1 4 2 5 3 6 4 7 5 8 6 9 7
((if (x mod 2) <= 0 then x else 0) + (x div 2))
A071045: 0 0 3 1 6 2 9 3 12 4 15 5 18 6 21 7
((if (x mod 2) <= 0 then x else 1) - (x div 2))
A097140: 0 1 1 0 2 ~1 3 ~2 4 ~3 5 ~4 6 ~5 7 ~6
(if (x mod 2) <= 0 then (x + 1) else (x div 2))
A174239: 1 0 3 1 5 2 7 3 9 4 11 5 13 6 15 7
loop(\(x,i).2x,(x + ~1),(x div 2))
A274497: 0 0 2 4 16 32 96 192 512 1024 2560 5120 12288 24576 57344 114688
((if (x mod 2) <= 0 then x else 2) + (x div 2))
A266286: 0 2 3 3 6 4 9 5 12 6 15 7 18 8 21 9
((if (x mod 2) <= 0 then 1 else x) + (x div 2))
A266285: 1 1 2 4 3 7 4 10 5 13 6 16 7 19 8 22
((if (~x + 2) <= 0 then 2 else 1) + (x mod 2))
A174296: 1 2 2 3 2 3 2 3 2 3 2 3 2 3 2 3
(loop(\(x,i).2x,x,1) - (x mod 2))
A051049: 1 1 4 7 16 31 64 127 256 511 1024 2047 4096 8191 16384 32767
loop(\(x,i).(x * i),x,(2 - (x mod 2)))
A052566: 2 1 4 6 48 120 1440 5040 80640 362880 7257600 39916800 958003200 6227020800 174356582400 1307674368000
loop(\(x,i).5x,x,2)
A020729: 2 10 50 250 1250 6250 31250 156250 781250 3906250 19531250 97656250 488281250 2441406250 12207031250 61035156250
loop(\(x,i).(2x2 + ~x),x,2)
A097419: 2 6 66 8646 149497986 44699295486614406 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (3 + i)),x,2)
A002301: 2 8 40 240 1680 13440 120960 1209600 13305600 159667200 2075673600 29059430400 435891456000 6974263296000 118562476032000 2134124568576000
loop(\(x,i).(x * (~1 + (2 * i))),x,2)
A097801: 2 2 6 30 210 1890 20790 270270 4054050 68918850 1309458150 27498621150 632468286450 15811707161250 426916093353750 12380566707258750
(loop(\(x,i).(2x + 2),x,x) div 2)
A006589: 0 2 7 19 47 111 255 575 1279 2815 6143 13311 28671 61439 131071 278527
(loop(\(x,i).4x,x,x) div 2)
A002699: 0 2 16 96 512 2560 12288 57344 262144 1179648 5242880 23068672 100663296 436207616 1879048192 8053063680
((x + (if (x mod 2) <= 0 then 2 else x)) div 2)
A029579: 1 1 2 3 3 5 4 7 5 9 6 11 7 13 8 15
(loop(\(x,i).~2x,x,x) div 2)
A085750: 0 ~1 4 ~12 32 ~80 192 ~448 1024 ~2304 5120 ~11264 24576 ~53248 114688 ~245760
loop(\(x,i).2x,x,(x2 + 2))
A217527: 2 6 24 88 288 864 2432 6528 16896 42496 104448 251904 598016 1400832 3244032 7438336
(if x <= 0 then 1 else (x div (x2 + ~2)))
A263013-A014195-A014183-A014147-A014123-A014111: 1 ~1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
loop(\(x,i).x3,x2,2)
A260548-A124075: 2 8 4611686018427387903
(x + (if (x mod 3) <= 0 then 1 else 0))
A147534: 1 1 2 4 4 5 7 7 8 10 10 11 13 13 14 16
(if (x mod 5) <= 0 then 0 else x)
A091703: 0 1 2 3 4 0 6 7 8 9 0 11 12 13 14 0
(x + (if (x + ~4) <= 0 then 1 else 0))
A108141-A072932: 1 2 3 4 5 5 6 7 8 9 10 11 12 13 14 15
(x + (if (x mod 2) <= 0 then (x + 1) else 0))
A133090: 1 1 5 3 9 5 13 7 17 9 21 11 25 13 29 15
(if (~2 + (x div 3)) <= 0 then 0 else x)
A095777: 0 0 0 0 0 0 0 0 0 9 10 11 12 13 14 15
(if (x mod 8) <= 0 then 0 else x)
A004183: 0 1 2 3 4 5 6 7 0 9 10 11 12 13 14 15
(x + (if ((x div 2) mod 2) <= 0 then 2 else 0))
A174091: 2 3 2 3 6 7 6 7 10 11 10 11 14 15 14 15
(if (x mod (2 + (x mod 2))) <= 0 then 0 else x)
A091685: 0 1 0 0 0 5 0 7 0 0 0 11 0 13 0 0
(if (x mod 2) <= 0 then (x + 1) else ~x)
A296063: 1 ~1 3 ~3 5 ~5 7 ~7 9 ~9 11 ~11 13 ~13 15 ~15
(1 div (if (x mod 3) <= 0 then 1 else x))
A329680: 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1
(x + loop(\(x,i).i,(~1 + (x div 2)),1))
A308017: 1 2 3 4 5 6 8 9 11 12 14 15 17 18 20 21
(x + loop(\(x,i).2x,(x + ~1),1))
A288133: 1 2 4 7 12 21 38 71 136 265 522 1035 2060 4109 8206 16399
(x + (if (x + ~4) <= 0 then 2 else 1))
A121604: 2 3 4 5 6 6 7 8 9
(x * (if (x mod 2) <= 0 then 4 else 1))
A195161: 0 1 8 3 16 5 24 7 32 9 40 11 48 13 56 15
(if x <= 0 then 1 else 5x)
A008706: 1 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
(x + (if (~x + 4) <= 0 then 2 else 1))
A099260-A053241: 1 2 3 4 6 7 8 9 10 11 12 13 14 15 16 17
(x + loop(\(x,i).i,(~2 + (x div 2)),1))
A342081: 1 2 3 4 5 6 7 8 10 11 13 14 16 17 19 20
loop(\(x,i).x2,2,3x)
A016768: 0 81 1296 6561 20736 50625 104976 194481 331776 531441 810000 1185921 1679616 2313441 3111696 4100625
(x + ((if x <= 0 then 1 else x) mod 3))
A143097: 1 2 4 3 5 7 6 8 10 9 11 13 12 14 16 15
loop(\(x,i).(x2 + 2x),3,x)
A258809: 0 255 6560 65535 390624 1679615 5764800 16777215 43046720 99999999 214358880 429981695 815730720 1475789055 2562890624 4294967295
loop(\(x,i).x3,3,x)
A122968: 0 1 134217728 7625597484987 18014398509481984 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x * (~1 + loop(\(x,i).2x,x,2)))
A059672: 0 3 14 45 124 315 762 1785 4088 9207 20470 45045 98292 212979 458738 983025
(x * (if (x mod 2) <= 0 then (x + 2) else 1))
A065530-A037206: 0 1 8 3 24 5 48 7 80 9 120 11 168 13 224 15
(if x <= 0 then 1 else (x2 + 3x))
A217748: 1 4 10 18 28 40 54 70 88 108 130 154 180 208 238 270
(x + loop(\(x,i).2x,(x + ~2),1))
A288382: 1 2 3 5 8 13 22 39 72 137 266 523 1036 2061 4110 8207
(x + (if (~x + 2) <= 0 then (x + ~2) else 1))
A300576: 1 2 2 4 6 8 10 12 14 16 18 20 22 24 26 28
(x2 - (if (x mod 2) <= 0 then 1 else x))
A289296: ~1 0 3 6 15 20 35 42 63 72 99 110 143 156 195 210
(~x + loop(\(x,i).(1 + (x * i)),x,1))
A243014: 1 1 3 13 61 321 1951 13693 109593 986401 9864091 108505101 1302061333 16926797473 236975164791 3554627472061
(x * loop(\(x,i).(1 + (x * i)),x,1))
A036918: 0 2 10 48 260 1630 11742 95900 876808 8877690 98641010 1193556232 15624736140 220048367318 3317652307270 53319412081140
(x + loop(\(x,i).4x,x,1))
A158879: 1 5 18 67 260 1029 4102 16391 65544 262153 1048586 4194315 16777228 67108877 268435470 1073741839
(~x + loop(\(x,i).4x,x,1))
A024037: 1 3 14 61 252 1019 4090 16377 65528 262135 1048566 4194293 16777204 67108851 268435442 1073741809
loop(\(x,i).(2x + 1),(x + 1),x)
A003261: 1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575
(~x + loop(\(x,i).x2,2,(x + 1)))
A269657: 1 15 79 253 621 1291 2395 4089 6553 9991 14631 20725 28549 38403 50611 65521
loop(\(x,i).x2,2,(x2 + x))
A248619: 0 16 1296 20736 160000 810000 3111696 9834496 26873856 65610000 146410000 303595776 592240896 1097199376 1944810000 3317760000
(~x + loop(\(x,i).2x,x,(x + 1)))
A188545: 1 3 10
A048493: 1 3 10 29 76 187 442 1017 2296 5111 11254 24565 53236 114675 245746 524273
loop(\(x,i).x3,(x + 1),x)
A323662: 0 1 134217728 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x + loop(\(x,i).(x * i),x,(x + 1)))
A030495: 1 3 8 27 124 725 5046 40327 362888 3628809 39916810 479001611 6227020812 87178291213 1307674368014 20922789888015
loop(\(x,i).(x + (i * i)),(x + 1),x)
A131820: 1 6 16 33 59 96 146 211 293 394 516 661 831 1028 1254 1511
loop(\(x,i).4x,(x + ~1),x)
A002697: 0 1 8 48 256 1280 6144 28672 131072 589824 2621440 11534336 50331648 218103808 939524096 4026531840
loop(\(x,i).3x,(x + ~1),x)
A027471: 0 1 6 27 108 405 1458 5103 17496 59049 196830 649539 2125764 6908733 22320522 71744535
loop(\(x,i).(x * (2 + i)),(x + ~1),x)
A180119: 0 1 6 36 240 1800 15120 141120 1451520 16329600 199584000 2634508800 37362124800 566658892800 9153720576000 156920924160000
(~3 mod (if x <= 0 then 1 else x))
A229878: 0 0 1 0 1 2
(5 * (if x <= 0 then 1 else x))
A242895: 5 5 10 15 20 25 30
((x mod 4) mod (if x <= 0 then 1 else x))
A276335: 0 0 0 0 0 1 2 3 0 1 2 3 0 1 2 3
((2 * (x mod 2)) + (if x <= 0 then 1 else x))
A065190: 1 3 2 5 4 7 6 9 8 11 10 13 12 15 14 17
(x + loop(\(x,i).3x,x,1))
A104743: 1 4 11 30 85 248 735 2194 6569 19692 59059 177158 531453 1594336 4782983 14348922
(~x + loop(\(x,i).3x,x,1))
A024024: 1 2 7 24 77 238 723 2180 6553 19674 59039 177136 531429 1594310 4782955 14348892
loop(\(x,i).2x,(x2 + ~1),x)
A134183: 0 1 16 768 131072 83886080 206158430208 1970324836974592 4611686018427387903 4611686018427387903 4611686018427387903
(x + (if (x + ~4) <= 0 then 1 else 2))
A272978-A132999-A129657-A129487-A097010-A080907: 1 2 3 4 5 7 8 9 10 11 12 13 14 15 16 17
(x + (if (~2 + (x div 2)) <= 0 then 1 else 2))
A327105-A298747-A129618-A049533-A038673: 1 2 3 4 5 6 8 9 10 11 12 13 14 15 16 17
loop(\(x,i).(2x2 + ~1),2,x)
A144130: 1 1 97 577 1921 4801 10081 18817 32257 51841 79201 116161 164737 227137 305761 403201
loop(\(x,i).2x,((x + 1) div 2),x)
A132314: 0 2 4 12 16 40 48 112 128 288 320 704 768 1664 1792 3840
loop(\(x,i).2x,((x + ~1) div 2),x)
A093968: 0 1 2 6 8 20 24 56 64 144 160 352 384 832 896 1920
loop(\(x,i).(x3 + ~1),2,x)
A178393: ~2 ~1 342 17575 250046 1906623 9938374 40001687 133432830 385828351 997002998 2352636999 5150827582 10590025535 20638466406 38409197623
(if ((x + 2) mod 4) <= 0 then 2 else x)
A216972: 0 1 2 3 4 5 2 7 8 9 2 11 12 13 2 15
loop(\(x,i).i,(x + ~8),x)
A053844-A053830-A025482: 0 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7
loop(\(x,i).(x2 div 4),2,x)
A059403: 0 0 0 1 4 9 20 36 64 100 156 225 324 441 600 784
loop(\(x,i).i,(~4 + (x div 2)),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A257295-A113230-A004427: 0 1 2 3 4 5 6 7 8 9 1 1 2 2 3 3
(x + loop(\(x,i).(x2 + 2),2,2))
A341708: 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
(~x + loop(\(x,i).(x2 + 2),2,2))
A022994: 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23
loop(\(x,i).(x - i),(x div 4),x)
A244041: 0 1 2 3 3 4 5 6 5 6 7 8 6 7 8 9
loop(\(x,i).((x2 + x) div 2),2,x)
A002817: 0 1 6 21 55 120 231 406 666 1035 1540 2211 3081 4186 5565 7260
loop(\(x,i).((x2 + ~x) div 2),2,x)
A050534: 0 0 0 3 15 45 105 210 378 630 990 1485 2145 3003 4095 5460
loop(\(x,i).(2x + (x div 2)),2,x)
A214067: 0 5 12 17 25 30 37 42 50 55 62 67 75 80 87 92
(x + loop(\(x,i).(2x + 1),x,2))
A275970: 2 6 13 26 51 100 197 390 775 1544 3081 6154 12299 24588 49165 98318
loop(\(x,i).(2x2 + ~x),2,x)
A063249: 0 1 66 435 1540 4005 8646 16471 28680 46665 72010 106491 152076 210925 285390 378015
loop(\(x,i).(x + ((x + i) div 2)),2,x)
A174396: 1 4 5 8 10 13 14 17 19 22 23 26 28 31 32 35
loop(\(x,i).(x * (2 + i)),(x + 2),x)
A034865: 0 60 720 7560 80640 907200 10886400 139708800 1916006400 28021593600 435891456000 7192209024000 125536739328000 2311968282624000 44816615940096000 912338253066240000
(x + (if (x + ~2) <= 0 then 1 else (x + ~2)))
A333183-A004278: 1 2 3 4 6 8 10 12 14 16 18 20 22 24 26 28
(x + (if (x mod 2) <= 0 then 1 else 2x))
A294178: 1 3 3 9 5 15 7 21 9 27 11 33 13 39 15 45
loop(\(x,i).4x,2x,x)
A268147: 0 16 512 12288 262144 5242880 100663296 1879048192 34359738368 618475290624 10995116277760 193514046488576 3377699720527872 58546795155816448 1008806316530991104 4611686018427387903
loop(\(x,i).3x,2x,x)
A158749: 0 9 162 2187 26244 295245 3188646 33480783 344373768 3486784401 34867844010 345191655699 3389154437772 33044255768277 320275094369454 3088366981419735
(if x <= 0 then 1 else (x * (2 - (x mod 2))))
A257088: 1 1 4 3 8 5 12 7 16 9 20 11 24 13 28 15
loop(\(x,i).2x,x,(x + (x mod 2)))
A291938: 0 4 8 32 64 192 384 1024 2048 5120 10240 24576 49152 114688 229376 524288
((~1 + (x div 2)) mod (if x <= 0 then 2 else x))
A286041: 1 0 0 0 1 1 2 2 3 3 4 4 5 5 6 6
(1 - loop(\(x,i).x3,2,x))
A024007: 1 0 ~511 ~19682 ~262143 ~1953124 ~10077695 ~40353606 ~134217727 ~387420488 ~999999999 ~2357947690 ~5159780351 ~10604499372 ~20661046783 ~38443359374
(1 - loop(\(x,i).(x * (~x + i)),2,x))
A058031: 1 1 9 49 169 441 961 1849 3249 5329 8281 12321 17689 24649 33489 44521
(x + (if (x + ~2) <= 0 then 3 else x))
A299114: 3 4 5 6 8 10
loop(\(x,i).6x,x,x)
A036292: 0 6 72 648 5184 38880 279936 1959552 13436928 90699264 604661760 3990767616 26121388032 169789022208 1097098297344 7052774768640
loop(\(x,i).(x div (1 + (x mod 2))),x,x)
A153733: 0 0 2 0 4 2 6 0 8 4 10 2 12 6 14 0
(x + loop(\(x,i).2x,(x + ~1),x))
A215149: 0 2 6 15 36 85 198 455 1032 2313 5130 11275 24588 53261 114702 245775
loop(\(x,i).((2x + ~1) + i),x,x)
A058877: 0 2 9 28 75 186 441 1016 2295 5110 11253 24564 53235 114674 245745 524272
loop(\(x,i).8x,x,x)
A036294: 0 8 128 1536 16384 163840 1572864 14680064 134217728 1207959552 10737418240 94489280512 824633720832 7146825580544 61572651155456 527765581332480
(x * loop(\(x,i).x2,4,x))
A010805: 0 1 131072 129140163 17179869184 762939453125 16926659444736 232630513987207 2251799813685248 16677181699666569 100000000000000000 505447028499293771 2218611106740436992 4611686018427387903
loop(\(x,i).((x2 + x) div 2),x,x)
A309009: 0 1 6 231
loop(\(x,i).(x div (2 - (x mod 2))),x,x)
A327539-A227140-A106617-A106609: 0 1 1 3 1 5 3 7 1 9 5 11 3 13 7 15
(x + loop(\(x,i).x3,2,x))
A196290: 0 2 514 19686 262148 1953130 10077702 40353614 134217736 387420498 1000000010 2357947702 5159780364 10604499386 20661046798 38443359390
(~x + loop(\(x,i).x3,2,x))
A196289: 0 0 510 19680 262140 1953120 10077690 40353600 134217720 387420480 999999990 2357947680 5159780340 10604499360 20661046770 38443359360
(x * loop(\(x,i).x3,2,x))
A008454: 0 1 1024 59049 1048576 9765625 60466176 282475249 1073741824 3486784401 10000000000 25937424601 61917364224 137858491849 289254654976 576650390625
(x2 + loop(\(x,i).2x,x,1))
A001580: 1 3 8 17 32 57 100 177 320 593 1124 2169 4240 8361 16580 32993
(~x2 + loop(\(x,i).2x,x,1))
A024012: 1 1 0 ~1 0 7 28 79 192 431 924 1927 3952 8023 16188 32543
(x2 + loop(\(x,i).(x * i),x,1))
A004664: 1 2 6 15 40 145 756 5089 40384 362961 3628900 39916921 479001744 6227020969 87178291396 1307674368225
(~x2 + loop(\(x,i).(x * i),x,1))
A005008: 1 0 ~2 ~3 8 95 684 4991 40256 362799 3628700 39916679 479001456 6227020631 87178291004 1307674367775
loop(\(x,i).(x + (x div 2)),2,x2)
A195042: 0 1 9 19 36 55 81 109 144 181 225 271 324 379 441 505
(1 - loop(\(x,i).x2,2,x2))
A024006: 1 0 ~255 ~6560 ~65535 ~390624 ~1679615 ~5764800 ~16777215 ~43046720 ~99999999 ~214358880 ~429981695 ~815730720 ~1475789055 ~2562890624
loop(\(x,i).x3,2,x2)
A010806: 0 1 262144 387420489 68719476736 3814697265625 101559956668416 1628413597910449 18014398509481984 150094635296999121 1000000000000000000 4611686018427387903 4611686018427387903
loop(\(x,i).4x,x,x2)
A128782: 0 4 64 576 4096 25600 147456 802816 4194304 21233664 104857600 507510784 2415919104 11341398016 52613349376 241591910400
(1 - loop(\(x,i).2x,x,x2))
A168298: 1 ~1 ~15 ~71 ~255 ~799 ~2303 ~6271 ~16383 ~41471 ~102399 ~247807 ~589823 ~1384447 ~3211263 ~7372799
loop(\(x,i).3x,x,x2)
A127960: 0 3 36 243 1296 6075 26244 107163 419904 1594323 5904900 21434787 76527504 269440587 937461924 3228504075
(x2 * loop(\(x,i).2x,x,x))
A128789: 0 2 32 216 1024 4000 13824 43904 131072 373248 1024000 2725888 7077888 17997824 44957696 110592000
(x2 * loop(\(x,i).(x * i),x,x))
A091363: 0 1 16 162 1536 15000 155520 1728720 20643840 264539520 3628800000 53129260800 827714764800 13680764697600 239217231052800 4413400992000000
loop(\(x,i).(x + (i * i)),x,x2)
A101986: 0 2 9 23 46 80 127 189 268 366 485 627 794 988 1211 1465
loop(\(x,i).5x,x,x)
A036291: 0 5 50 375 2500 15625 93750 546875 3125000 17578125 97656250 537109375 2929687500 15869140625 85449218750 457763671875
(x + loop(\(x,i).x2,2,x2))
A196288: 0 2 258 6564 65540 390630 1679622 5764808 16777224 43046730 100000010 214358892 429981708 815730734 1475789070 2562890640
(~x + loop(\(x,i).x2,2,x2))
A195859: 0 0 254 6558 65532 390620 1679610 5764794 16777208 43046712 99999990 214358870 429981684 815730708 1475789042 2562890610
loop(\(x,i).x2,2,x3)
A008456: 0 1 4096 531441 16777216 244140625 2176782336 13841287201 68719476736 282429536481 1000000000000 3138428376721 8916100448256 23298085122481 56693912375296 129746337890625
loop(\(x,i).x3,x2,x)
A276972-A250494-A250493-A030198: 0 1 4611686018427387903
A345296: 0 1 4611686018427387903 4611686018427387903
A338981-A338980: 0 1 4611686018427387903 4611686018427387903 4611686018427387903
A338983: 0 1 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A074194: 0 1 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + ((2 + i) * i)),x,x)
A168559: 0 4 13 29 54 90 139 203 284 384 505 649 818 1014 1239 1495
(1 + (x div (1 + (x div 3))))
A346153: 1 2 3 2 3 3 3 3 3 3 3 3 3 3 3 3
(1 + ((x div 2) mod ~3))
A103368: 1 1 ~1 ~1 0 0 1 1 ~1 ~1 0 0 1 1 ~1 ~1
((x + 1) - (x div ~3))
A260003-A183147-A122906-A074227-A005848: 1 3 4 5 7 8 9 11 12 13 15 16 17 19 20 21
(1 + (x div 7))
A280953-A279222-A279012-A187185-A133877: 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3
(1 + (x mod 7))
A010886: 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2
(1 + (x mod 9))
A342829-A177274-A131650-A128244-A114570: 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7
(1 + ((x + 1) div 5))
A235402-A184349: 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4
(1 + (2x div 5))
A302128-A173276: 1 1 1 2 2 3 3 3 4 4 5 5 5 6 6 7
((x + 1) - (x div 5))
A003005: 1 2 3 4 5 5 6 7 8 9 9 10 11 12 13 13
(1 + (2 mod (1 + (x div 4))))
A303168-A032552: 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3
(1 + (3 * (x mod 3)))
A100402: 1 4 7 1 4 7 1 4 7 1 4 7 1 4 7 1
(1 + ((1 + (x div 2)) div 3))
A240567-A185679-A151982-A132085-A111654: 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3
(1 + (3 * (1 + (x mod 2))))
A010712: 4 7 4 7 4 7 4 7 4 7 4 7 4 7 4 7
(x mod (1 + ((x + 1) mod 3)))
A286685: 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1
19
A057430-A010858: 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19
(6x + 5)
A059538-A016969: 5 11 17 23 29 35 41 47 53 59 65 71 77 83 89 95
(1 + (3 * ((x + 1) div 2)))
A168233: 1 4 4 7 7 10 10 13 13 16 16 19 19 22 22 25
(1 + (((x + 1) div 2) div 3))
A147583: 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3
25
A010864: 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25
23
A010862: 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23
(x + ~13)
A023455: ~13 ~12 ~11 ~10 ~9 ~8 ~7 ~6 ~5 ~4 ~3 ~2 ~1 0 1 2
(x div 13)
A297042-A283763-A162781-A161319-A161305-A161292-A161267-A161253-A161239-A161115-A161102-A161089-A161076-A161063-A161050-A161038-A160984-A090620-A011727: 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1
(x + ~11)
A023453: ~11 ~10 ~9 ~8 ~7 ~6 ~5 ~4 ~3 ~2 ~1 0 1 2 3 4
(x div 11)
A344420-A328499-A297040-A250100-A161317-A161303-A161290-A161265-A161251-A161237-A161113-A161100-A161087-A161074-A161061-A161048-A161036-A160982-A131981-A105390-A091195-A091194-A072375-A064458-A037808-A027198-A023973: 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1
(x mod 11)
A103303: 0 1 2 3 4 5 6 7 8 9
A010880: 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4
(1 + (x mod 12))
A034326: 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4
(1 + ((2x + 4) div 3))
A177876: 2 3 3 4
A066481: 2 3 3 4 5 5 6 7 7 8 9 9 10 11 11 12
(12x + 1)
A017533: 1 13 25 37 49 61 73 85 97 109 121 133 145 157 169 181
(1 + (3 * (2 + (x mod 2))))
A010730: 7 10 7 10 7 10 7 10 7 10 7 10 7 10 7 10
(~1 + (3 * (2 + (x mod 2))))
A010719: 5 8 5 8 5 8 5 8 5 8 5 8 5 8 5 8
(1 + (6 * (x mod 2)))
A010688: 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7
((x + 1) - (2x mod 3))
A236348: 1 0 2 4 3 5 7 6 8 10 9 11 13 12 14 16
((x + 1) - ((x div 2) div 3))
A248148: 1 2 3 4 5 6 6 7 8 9 10 11 11 12 13 14
(6x2 + ~1)
A140811: ~1 5 23 53 95 149 215 293 383 485 599 725 863 1013 1175 1349
(9x + 1)
A326833-A017173: 1 10 19 28 37 46 55 64 73 82 91 100 109 118 127 136
((x + 1) - ((~x + 1) div 3))
A329978-A329839-A249245-A184421-A059553: 1 2 4 5 6 8 9 10 12 13 14 16 17 18 20 21
((x + 1) - ((~x + 1) mod 3))
A064429: 0 2 1 3 5 4 6 8 7 9 11 10 12 14 13 15
(3x2 + 3x + 1)
A073859: 1 7 19 37 61
A003215: 1 7 19 37 61 91 127 169 217 271 331 397 469 547 631 721
(3x2 + 3x + ~1)
A004538: ~1 5 17 35 59 89 125 167 215 269 329 395 467 545 629 719
(1 + ((x2 + x) div 3))
A208994: 1 1 3 5 7 11 15 19 25 31 37 45 53 61 71 81
(3x2 + 6x + 1)
A100536: 1 10 25 46 73 106 145 190 241 298 361 430 505 586 673 766
(1 + (3 * (x + (x div 2))))
A087444: 1 4 10 13 19 22 28 31 37 40 46 49 55 58 64 67
(1 + (3 * (x + (x mod 2))))
A168301: 1 7 7 13 13 19 19 25 25 31 31 37 37 43 43 49
(1 + ((x + (x mod 2)) div 3))
A281687: 1 1 1 2 2 3 3 3 3 4 4 5 5 5 5 6
(1 + ((x * (x mod 2)) div 3))
A243554-A243546: 1 1 1 2 1 2 1 3 1 4
((2x + 1) - (x div 3))
A329993-A329845-A064994: 1 3 5 6 8 10 11 13 15 16 18 20 21 23 25 26
(5 - (x mod 3))
A164360: 5 4 3 5 4 3 5 4 3 5 4 3 5 4 3 5
((2x + 1) - (x mod 3))
A194381-A047245: 1 2 3 7 8 9 13 14 15 19 20 21 25 26 27 31
((x + 1) mod (1 + (x mod 3)))
A286688-A285125: 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0
((x + ~1) mod (1 + (x mod 3)))
A214090: 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0
(1 - (2 mod (1 + (x mod 3))))
A131561: 1 1 ~1 1 1 ~1 1 1 ~1 1 1 ~1 1 1 ~1 1
(3x3 + ~1)
A345701: ~1 2 23 80 191 374 647 1028 1535 2186 2999 3992 5183 6590 8231 10124
(~1 - (2 div (2x + ~1)))
A260196: 1 ~3 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1
(3 - (2 div (1 + (x div 2))))
A300402-A214454: 1 1 2 2 3 3 3 3 3 3 3 3 3 3 3 3
(1 + ((x div 2) div (1 + (x mod 2))))
A106466: 1 1 2 1 3 2 4 2 5 3 6 3 7 4 8 4
(1 + (x2 div (1 + (x mod 2))))
A228564: 1 1 5 5 17 13 37 25 65 41 101 61 145 85 197 113
(5x + 6)
A140232: 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81
(x3 + x2 + x + 2)
A188947: 2 5 16 41 86 157 260 401 586 821 1112 1465 1886 2381 2956 3617
(x3 + x2 + ~x + ~2)
A214731: ~2 ~1 8 31 74 143 244 383 566 799 1088 1439 1858 2351 2924 3583
(8x + 9)
A004768: 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129
(8x + 7)
A017149-A004771: 7 15 23 31 39 47 55 63 71 79 87 95 103 111 119 127
(2x2 + 6x + 5)
A099776: 5 13 25 41 61 85 113 145 181 221 265 313 365 421 481 545
(4x2 + 4x + 1)
A016754: 1 9 25 49 81 121 169 225 289 361 441 529 625 729 841 961
(x3 + x2 + 2x + 1)
A100705: 1 5 17 43 89 161 265 407 593 829 1121 1475 1897 2393 2969 3631
(x3 + 2x2 + x + ~1)
A087908: ~1 3 17 47 99 179 293 447 647 899 1209 1583 2027 2547 3149 3839
(x3 + 3x2 + 2x + ~1)
A126420: ~1 5 23 59 119 209 335 503 719 989 1319 1715 2183 2729 3359 4079
(x3 + ~x2 + ~2x + 1)
A123972: 1 ~1 1 13 41 91 169 281 433 631 881 1189 1561 2003 2521 3121
(x3 + ~x2 + ~2x + ~1)
A153257: ~1 ~3 ~1 11 39 89 167 279 431 629 879 1187 1559 2001 2519 3119
(2x2 + 2x + ~5)
A222182: ~5 ~1 7 19 35 55 79 107 139 175 215 259 307 359 415 475
(x div (x2 + ~3x + 3))
A236619: 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0
(~2x2 + 3x + 1)
A168244: 1 2 ~1 ~8 ~19 ~34 ~53 ~76 ~103 ~134 ~169 ~208 ~251 ~298 ~349 ~404
(x3 + x2 + ~2x + 1)
A168297: 1 1 9 31 73 141 241 379 561 793 1081 1431 1849 2341 2913 3571
((x + 1) - ((x div 2) div ~2))
A184738: 1 2 4 5 6 7 9 10 11 12 14 15 16 17 19 20
(x - ((x div 2) div ~3))
A047310: 0 1 3 4 5 6 7 8 10 11 12 13 14 15 17 18
((x + 2) - (x div ~3))
A277676: 2 4 5 6 8 9 10 12 13 14 16 17 18 20 21 22
(2x - (x div ~3))
A047390: 0 3 5 7 10 12 14 17 19 21 24 26 28 31 33 35
((x div 2) - (x div ~3))
A090168: 0 1 2 2 4 4 5 6 7 7 9 9 10 11 12 12
(2x - (x mod ~3))
A047258: 0 4 5 6 10 11 12 16 17 18 22 23 24 28 29 30
((2x + 1) - (x div ~2))
A231407: 1 4 6
A047209: 1 4 6 9 11 14 16 19 21 24 26 29 31 34 36 39
(1 + (x mod 2) - (x div ~2))
A052938: 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 10
(1 - (x div (~1 + (x div ~2))))
A156752: 1 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3
((x2 + 1) - (x div ~2))
A263511: 1 3 6 12 19 29 40 54 69 87 106 128 151 177 204 234
((x + 1) - (x2 div ~2))
A080827: 1 3 5 9 13 19 25 33 41 51 61 73 85 99 113 129
(1 + ((1 + (x div 3)) div 2))
A138194: 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4
(1 + (x mod 10))
A274206-A263131-A010889: 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6
(1 + (2 * (x div 5)))
A130497: 1 1 1 1 1 3 3 3 3 3 5 5 5 5 5 7
(1 + (2 * (x mod 5)))
A141518: 1 3 5 7 9 1 3 5 7 9 1 3 5 7 9 1
(2x + 11)
A277268-A171491: 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
(8x + 3)
A252802: 3 11 19
A017101: 3 11 19 27 35 43 51 59 67 75 83 91 99 107 115 123
(1 + (2 * (1 + (2 * (x div 2)))))
A168269: 3 3 7 7 11 11 15 15 19 19 23 23 27 27 31 31
(1 + (2 * (3 + (x mod 2))))
A010729: 7 9 7 9 7 9 7 9 7 9 7 9 7 9 7 9
(1 + (2 * (1 + (2 * (x mod 2)))))
A010705: 3 7 3 7 3 7 3 7 3 7 3 7 3 7 3 7
(1 + (2 * (2x div 3)))
A168056: 1 1 3 5 5 7 9 9 11 13 13 15 17 17 19 21
(1 + (2 * (2x mod 3)))
A130794: 1 5 3 1 5 3 1 5 3 1 5 3 1 5 3 1
(1 + (((x div 2) mod 3) mod 2))
A096285: 1 1 2 2 1 1 1 1 2 2 1 1 1 1 2 2
(2x div 7)
A172274-A060971-A057356: 0 0 0 0 1 1 1 2 2 2 2 3 3 3 4 4
((x div 2) div 7)
A297043-A216038-A210717-A185274-A185236-A185227-A185063-A185036-A165656-A160985-A157242-A146167-A135297-A122669-A111897-A046786-A034412-A011728: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
(x - (x div 7))
A303789-A171970-A145569: 0 1 2 3 4 5 6 6 7 8 9 10 11 12 12 13
(x2 div 7)
A183140-A056834: 0 0 0 1 2 3 5 7 9 11 14 17 20 24 28 32
(x2 mod 7)
A053879: 0 1 4 2 2 4 1 0 1 4 2 2 4 1 0 1
(x div (3 + (x div 3)))
A338732-A161106-A161067-A161041: 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 1
((x + 1) - (2 * (x div 3)))
A194960: 1 2 3 2 3 4 3 4 5 4 5 6 5 6 7 6
((x + 1) - ((x mod 3) mod 2))
A117571: 1 1 3 4 4 6 7 7 9 10 10 12 13 13 15 16
(4x2 + 3)
A222465: 3 7 19 39 67 103 147 199 259 327 403 487 579 679 787 903
(2x2 + 2x + 3)
A301894: 3 7 15 27
A097080: 3 7 15 27 43 63 87 115 147 183 223 267 315 367 423 483
(1 + (2 * ((x + 1) + (x div 2))))
A047270: 3 5 9 11 15 17 21 23 27 29 33 35 39 41 45 47
(1 + (((x + 1) + (x div 2)) div 2))
A083544: 1 2 3 3 4 5 6 6 7 8 9 9 10 11 12 12
(1 + ((x3 + x2) div 2))
A100119: 1 2 7 19 41 76 127 197 289 406 551 727 937 1184 1471 1801
(1 - (x div ~5))
A154099: 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4
(x - (x div ~5))
A195122-A114024-A047248: 0 2 3 4 5 6 8 9 10 11 12 14 15 16 17 18
(1 + (2 * (x - (x div ~2))))
A322271: 1 5 7 11 13 17 19 23
A070191-A069040-A007310: 1 5 7 11 13 17 19 23 25 29 31 35 37 41 43 47
21
A010860: 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21
(1 + (2 * ((x div 3) mod 2)))
A130974: 1 1 1 3 3 3 1 1 1 3 3 3 1 1 1 3
(8x + 5)
A004770: 5 13 21 29 37 45 53 61 69 77 85 93 101 109 117 125
(1 + (((~1 + (x div 2)) div 2) div 2))
A071840-A071702: 0 0 1 1 1 1 1 1 1 1 2 2 2 2 2 2
(1 + (4 * (1 + (x mod 2))))
A010720: 5 9 5 9 5 9 5 9 5 9 5 9 5 9 5 9
(1 + (((x2 + ~1) div 2) div 2))
A004652: 0 1 1 3 4 7 9 13 16 21 25 31 36 43 49 57
(1 + ((x mod ~4) div 2))
A219977: 1 ~1 0 0 1 ~1 0 0 1 ~1 0 0 1 ~1 0 0
(1 + (2 * ((x div ~2) mod 2)))
A084101: 1 3 3 1 1 3 3 1 1 3 3 1 1 3 3 1
(3 + (((x + 1) div 2) div 2))
A096056-A050501: 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7
(1 + ((((x + 1) div 2) div 2) div 2))
A318585: 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3
(1 + ((((x + ~1) div 2) div 2) div 2))
A236362-A190311-A135660-A115338-A110656: 0 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2
(~1 + (2 * (((x + ~1) div 2) mod 2)))
A319117-A262725-A087960: 1 ~1 ~1 1 1 ~1 ~1 1 1 ~1 ~1 1 1 ~1 ~1 1
31
A010870-A009734: 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31
(x + ~17)
A023459: ~17 ~16 ~15 ~14 ~13 ~12 ~11 ~10 ~9 ~8 ~7 ~6 ~5 ~4 ~3 ~2
(x + ~15)
A023457: ~15 ~14 ~13 ~12 ~11 ~10 ~9 ~8 ~7 ~6 ~5 ~4 ~3 ~2 ~1 0
(x div 15)
A337380-A324326-A321379-A297248-A297246-A297241-A297044-A295884-A284977-A280830-A236344-A236074-A219055-A216602-A216601-A167688-A160986-A157237-A111253-A105516-A101638-A101637-A085860-A082996-A070208-A070140-A070139-A065718-A036665-A034418-A034416-A034413-A014083-A011729: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
(x mod 15)
A103303: 0 1 2 3 4 5 6 7 8 9
A167463: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0
(3 + (x div 8))
A053388: 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4
(1 + (4 * (x mod 4)))
A070370: 1 5 9 13 1 5 9 13 1 5 9 13 1 5 9 13
(16x + 1)
A158057: 1 17 33 49 65 81 97 113 129 145 161 177 193 209 225 241
(1 + (4 * ((x div 2) mod 2)))
A100285: 1 1 5 5 1 1 5 5 1 1 5 5 1 1 5 5
(7 + (x mod 2))
A010728: 7 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8
(1 + (8 * (x mod 2)))
A010690: 1 9 1 9 1 9 1 9 1 9 1 9 1 9 1 9
(~x + 11)
A022967: 11 10 9 8 7 6 5 4 3 2 1 0 ~1 ~2 ~3 ~4
(x - (x div 9))
A245338: 0 1 2 3 4 5 6 7 8 8 9 10 11 12 13 14
(x2 div 9)
A056838: 0 0 0 1 1 2 4 5 7 9 11 13 16 18 21 25
(x2 mod 9)
A070433: 0 1 4 0 7 7 0 4 1 0 1 4 0 7 7 0
(x mod (1 + (x div 8)))
A053472-A035673: 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1
((x + 1) - (x div 8))
A160755: 1 2 3 4 5 6 7 8 8 9 10 11 12 13 14 15
((x + 1) - (x mod 8))
A291720-A290546: 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9
(x div (3 + (x div 4)))
A067099: 0 0 0 1 1 1 1 1 1 1 2 2 2 2 2 2
(1 + (x div (2 + (x div 4))))
A212625: 1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 4
((x + 1) - (2 * (x div 4)))
A235121: 1 2 3 4 3 4 5 6 5 6 7 8 7 8 9 10
(1 + (2 * (1 - (x mod 4))))
A132429: 3 1 ~1 ~3 3 1 ~1 ~3 3 1 ~1 ~3 3 1 ~1 ~3
((x + 3) - (x mod 4))
A244584: 3 3 3 3 7 7 7 7 11 11 11 11 15 15 15 15
(x2 + 7)
A117619: 7 8 11 16 23 32 43 56 71 88 107 128 151 176 203 232
(2x2 + 9)
A339048: 9 11 17 27 41 59 81 107 137 171 209 251 297 347 401 459
(8x2 + 1)
A081585: 1 9 33 73 129 201 289 393 513 649 801 969 1153 1353 1569 1801
(1 + ((x mod (2 + (x mod 2))) div 2))
A334926-A334924-A325469-A300826-A245477-A226957-A108775-A106751-A074971-A050433-A043279: 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1
(1 + ((x mod (2 + (x mod 2))) mod 2))
A031263: 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1
(1 + (x mod (2 * (~2 + (x mod 2)))))
A011632: 1 0 ~1 0 1 0 ~1 0 1 0 ~1 0 1
A101455-A056594-A016245-A016213-A016141-A016117-A016077-A015981-A015933-A015901-A015813-A015757-A015637-A015621-A015573-A015517-A015373-A015301-A015285-A015205-A015021-A014997-A014893-A014845-A014757-A014581: 1 0 ~1 0 1 0 ~1 0 1 0 ~1 0 1 0 ~1 0
(1 + (4 * (x2 div 2)))
A275543: 1 1 9 17 33 49 73 97 129 161 201 241 289 337 393 449
(10x + 5)
A068528-A017329: 5 15 25 35 45 55 65 75 85 95 105 115 125 135 145 155
((2x + 1) div 5)
A288156: 0 0 1 1 1 2 2 3 3 3 4 4 5 5 5 6
(5 * (1 + (x div 2)))
A166598: 5 5 10 10 15 15 20 20 25 25 30 30 35 35 40 40
((1 + (x div 2)) mod 5)
A084054: 1 1 2 2 3 3 4 4 0 0 1 1 2 2 3 3
(5 * (1 + (x mod 2)))
A010721: 5 10 5 10 5 10 5 10 5 10 5 10 5 10 5 10
((x2 + 1) div 5)
A008738: 0 0 1 2 3 5 7 10 13 16 20 24 29 34 39 45
30
A056958-A010869: 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30
(10x + 10)
A158814: 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160
((2x + 2) div 5)
A029920: 0 0 1 1 2 2 2 3 3 4 4 4 5 5 6 6
(5 * ((x + 1) div 2))
A168284: 0 5 5 10 10 15 15 20 20 25 25 30 30 35 35 40
20x
A008602: 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300
(4x div 5)
A090223: 0 0 1 2 3 4 4 5 6 7 8 8 9 10 11 12
((2 * (x div 2)) div 5)
A093354-A090621: 0 0 0 0 0 0 1 1 1 1 2 2 2 2 2 2
(10 * (x mod 2))
A010681: 0 10 0 10 0 10 0 10 0 10 0 10 0 10 0 10
(x - (2x div 5))
A195119-A098294: 0 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9
(x - ((x div 2) div 5))
A103303: 0 1 2 3 4 5 6 7 8 9
A324161-A245339-A081600-A028904: 0 1 2 3 4 5 6 7 8 9 9 10 11 12 13 14
10x2
A033583: 0 10 40 90 160 250 360 490 640 810 1000 1210 1440 1690 1960 2250
(2x2 div 5)
A033437: 0 0 1 3 6 10 14 19 25 32 40 48 57 67 78 90
((x2 div 2) div 5)
A056865: 0 0 0 0 1 2 3 4 6 8 10 12 14 16 19 22
15x
A008597: 0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225
(3x div 5)
A057355: 0 0 1 1 2 3 3 4 4 5 6 6 7 7 8 9
(1 - ((~x + 1) div 5))
A075249: 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4
(x - ((~x + 1) div 5))
A047252-A039235: 0 1 3 4 5 6 7 9 10 11 12 13 15 16 17 18
(x2 + x + 5)
A027690: 5 7 11 17 25 35 47 61 77 95 115 137 161 187 215 245
(5x2 + 5x)
A124080: 0 10 30 60 100 150 210 280 360 450 550 660 780 910 1050 1200
((x2 + x) mod 5)
A053796: 0 2 1 2 0 0 2 1 2 0 0 2 1 2 0 0
((x2 + ~x) div 5)
A011858: 0 0 0 1 2 4 6 8 11 14 18 22 26 31 36 42
(x - ((~x + 2) div 5))
A138083: 0 1 2 4 5 6
A160044-A047263-A039244: 0 1 2 4 5 6 7 8 10 11 12 13 14 16 17 18
(2 - ((~x + 2) mod 5))
A117444: 0 1 2 ~2 ~1 0 1 2 ~2 ~1 0 1 2 ~2 ~1 0
((x + (x div 2)) div 5)
A327440: 0 0 0 0 1 1 1 2 2 2 3 3 3 3 4 4
(5 * (x + (x mod 2)))
A168461: 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80
(2x - (x mod 5))
A293292-A007091: 0 1 2 3 4 10 11 12 13 14 20 21 22 23 24 30
(x3 + 5)
A084381: 5 6 13 32 69 130 221 348 517 734 1005 1336 1733 2202 2749 3380
5x3
A244725: 0 5 40 135 320 625 1080 1715 2560 3645 5000 6655 8640 10985 13720 16875
(x3 mod 5)
A070690-A070471: 0 1 3 2 4 0 1 3 2 4 0 1 3 2 4 0
(2 div (1 + ((~x + 1) mod 4)))
A130731: 1 2 0 0 1 2 0 0 1 2 0 0 1 2 0 0
((x + 1) - ((~x + 2) div 4))
A242491-A062071: 1 2 3 5 6 7 8 10 11 12 13 15 16 17 18 20
(4x2 + 8x + 1)
A082109: 1 13 33 61 97 141 193 253 321 397 481 573 673 781 897 1021
(~1 + ((x2 + ~2x) div 4))
A179272: ~1 ~2 ~1 ~1 1 2 5 7 11 14 19 23 29 34 41 47
(1 + (4 * (x + (x div 2))))
A087445: 1 5 13 17 25 29 37 41 49 53 61 65 73 77 85 89
(1 + ((x + (x div 2)) div 4))
A341440: 1 1 1 2 2 2 3 3 4 4 4 5 5 5 6 6
(1 + (4 * (x + (x mod 2))))
A168390: 1 9 9 17 17 25 25 33 33 41 41 49 49 57 57 65
(1 + ((x * (x mod 2)) div 4))
A340830: 1 1 1 1 1 2 1 2 1 3 1 3 1 4 1 4
((2x + 1) - (x div 4))
A330117-A292648-A284366-A059546: 1 3 5 7 8 10 12 14 15 17 19 21 22 24 26 28
(~2 mod (1 + (x div 4)))
A208246-A072114: 0 0 0 0 0 0 0 0 1 1 1 1 2 2 2 2
(1 - (2 mod (1 + (x div 4))))
A143622: 1 1 1 1 1 1 1 1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1
((2x + 1) - (x mod 4))
A047454: 1 2 3 4 9 10 11 12 17 18 19 20 25 26 27 28
(2x2 + 2x + 5)
A294774: 5 9 17 29 45 65 89 117 149 185 225 269 317 369 425 485
(3 + ((x2 + x) div 2))
A152950: 3 4 6 9 13 18 24 31 39 48 58 69 81 94 108 123
(~3 + ((x2 + x) div 2))
A307681: ~3 ~2 0 3 7 12 18 25 33 42 52 63 75 88 102 117
(3 + ((x2 + ~x) div 2))
A152949: 3 3 4 6 9 13 18 24 31 39 48 58 69 81 94 108
(1 + (2 * ((x2 + 2x) div 2)))
A085046: 1 3 9 15 25 35 49 63 81 99 121 143 169 195 225 255
(~1 + ((x2 + 4x + 4) div 2))
A047838: 1 3 7 11 17 23 31 39 49 59 71 83 97 111 127 143
(x2 div (x + 5))
A127035: 0 0 0 1 1 2 3 4 4 5 6 7 8 9 10 11
((2x + 3) + (x div 2))
A332102: 3 5 8 10 13 15 18 20 23 25 28 30 33 35 38 40
(1 + (2 * (2x + (x div 2))))
A137002: 1 5 11 15
A187715: 1 5 11 15 21 25 31 35 41 45 51 55 61 65 71 75
(1 + (2 * (2x + (x mod 2))))
A047522: 1 7 9 15 17 23 25 31 33 39 41 47 49 55 57 63
(1 + ((x + ~1) div (2 + (x div 2))))
A111972: 0 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2
(1 + ((x + ~2) div (2 + (x div 2))))
A000195: 0 0 1 1 1 1 1 2 2 2 2 2 2 2 2 2
((2x + 1) - ((x div 2) mod 2))
A047415: 1 3 4 6 9 11 12 14 17 19 20 22 25 27 28 30
(1 + (2 * (x2 + (x div 2))))
A317298: 1 3 11 21 37 55 79 105 137 171 211 253 301 351 407 465
(~1 + ((x2 + (x div 2)) div 2))
A082645: ~1 ~1 1 4 8 12 18 25 33 41 51 62 74 86 100 115
(1 + (x div (2 * (2 - (x mod 2)))))
A178804: 1 1 1 2 2 3 2 4 3 5 3 6 4 7 4 8
(1 + (x mod (2 * (2 - (x mod 2)))))
A068073: 1 2 3 2 1 2 3 2 1 2 3 2 1 2 3 2
((2x + 3) - (x mod 2))
A154708: 3 4 7 8 11 12 15 16 19 20 23 24 27 28 31 32
(1 + (2 * (2x - (x mod 2))))
A047471: 1 3 9 11 17 19 25 27 33 35 41 43 49 51 57 59
(1 + (((x div 2) - (x mod 2)) div 2))
A008624: 1 0 1 1 2 1 2 2 3 2 3 3 4 3 4 4
(~1 + ((x + 1) mod (2 + (x mod 2))))
A134667: 0 1 0 0 0 ~1 0 1 0 0 0 ~1 0 1 0 0
(1 + (x div 2) - (2 * (x mod 2)))
A097065: 1 ~1 2 0 3 1 4 2 5 3 6 4 7 5 8 6
(1 + (2 * (x3 div 2)))
A129957: 1 1 9 27 65 125 217 343 513 729 1001 1331 1729 2197 2745 3375
((1 + (x div 3)) div 3)
A135663: 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2
((1 + (x div 3)) mod 3)
A133873: 1 1 1 2 2 2 0 0 0 1 1 1 2 2 2 0
27
A010866: 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27
((x mod 5) div 3)
A011658: 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0
((x mod 5) mod 3)
A119346: 0 1 2 0 1 0 1 2 0 1 0 1 2 0 1 0
(12x + 3)
A017557: 3 15 27 39 51 63 75 87 99 111 123 135 147 159 171 183
(3 * (1 + (2 * (x div 2))))
A168329: 3 3 9 9 15 15 21 21 27 27 33 33 39 39 45 45
((1 + (2 * (x div 2))) div 3)
A266193: 0 0 1 1 1 1 2 2 3 3 3 3 4 4 5 5
(3 * (1 + (2 * (x mod 2))))
A010707: 3 9 3 9 3 9 3 9 3 9 3 9 3 9 3 9
18x
A008600-A004961: 0 18 36 54 72 90 108 126 144 162 180 198 216 234 252 270
(9 * (x mod 2))
A021015-A010680: 0 9 0 9 0 9 0 9 0 9 0 9 0 9 0 9
((x - (x div 3)) mod 3)
A270740: 0 1 2 2 0 1 1 2 0 0 1 2 2 0 1 1
9x2
A016766: 0 9 36 81 144 225 324 441 576 729 900 1089 1296 1521 1764 2025
(x - ((~1 + (x div 2)) div 3))
A157282: 1 2 2 3 4 5 6 7 7 8 9 10 11 12 12 13
(6x2 + 3)
A097803: 3 9 27 57 99 153 219 297 387 489 603 729 867 1017 1179 1353
((2x2 + 1) div 3)
A071619: 0 1 3 6 11 17 24 33 43 54 67 81 96 113 131 150
(9x + 3)
A017197: 3 12 21 30 39 48 57 66 75 84 93 102 111 120 129 138
(3 * ((x + 1) + (x div 2)))
A070790-A016051: 3 6 12 15 21 24 30 33 39 42 48 51 57 60 66 69
(6x2 + 6x)
A049598: 0 12 36 72 120 180 252 336 432 540 660 792 936 1092 1260 1440
(((x + 1) * (x div 2)) mod 3)
A285133: 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1
(2x - ((x + 1) div 3))
A047222: 0 2 3 5 7 8 10 12 13 15 17 18 20 22 23 25
((x div 2) - ((x + 1) div 3))
A338336-A298783: 0 0 0 0 1 0 1 1 1 1 2 1 2 2 2 2
(2x - ((x + ~1) div 3))
A032793: 1 2 4 6 7 9 11 12 14 16 17 19 21 22 24 26
((x div 2) - ((x + ~1) div 3))
A103221: 1 0 1 1 1 1 2 1 2 2 2 2 3 2 3 3
(x - (x div ~6))
A047306: 0 2 3 4 5 6 7 9 10 11 12 13 14 16 17 18
(2 - (3 * (x div ~2)))
A168199: 2 5 5 8 8 11 11 14 14 17 17 20 20 23 23 26
(x - (3 * (x div ~2)))
A047208: 0 4 5 9 10 14 15 19 20 24 25 29 30 34 35 39
(x + ~18)
A023460: ~18 ~17 ~16 ~15 ~14 ~13 ~12 ~11 ~10 ~9 ~8 ~7 ~6 ~5 ~4 ~3
((2 + (x div 3)) div 3)
A097430: 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2
((2 * (x div 3)) div 3)
A090618: 0 0 0 0 0 0 1 1 1 2 2 2 2 2 2 3
(3 * ((x mod 3) div 2))
A021337: 0 0 3 0 0 3 0 0 3 0 0 3 0 0 3 0
(12x + 6)
A017593: 6 18 30 42 54 66 78 90 102 114 126 138 150 162 174 186
(1 - (((x + 1) div 2) div 3))
A014064: 1 1 1 1 1 0 0 0 0 0 0 ~1 ~1 ~1 ~1 ~1
(x - (((x + ~1) div 2) div 3))
A210062: 1 1 2 3 4 5 6 6 7 8 9 10 11 11 12 13
(x + ~24)
A023466: ~24 ~23 ~22 ~21 ~20 ~19 ~18 ~17 ~16 ~15 ~14 ~13 ~12 ~11 ~10 ~9
24x
A008606: 0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360
(8x div 3)
A047618: 0 2 5 8 10 13 16 18 21 24 26 29 32 34 37 40
((2 * (2 + (x div 2))) div 3)
A109497: 1 1 2 2 2 2 3 3 4 4 4 4 5 5 6 6
(x + 11)
A178405: 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
(x + ~14)
A023456: ~14 ~13 ~12 ~11 ~10 ~9 ~8 ~7 ~6 ~5 ~4 ~3 ~2 ~1 0 1
(~x + 13)
A022969: 13 12 11 10 9 8 7 6 5 4 3 2 1 0 ~1 ~2
(~x + 14)
A022970: 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 ~1
(x - (x div 12))
A103303: 0 1 2 3 4 5 6 7 8 9
A180613: 0 1 2 3 4 5 6 7 8 9 10 11 11 12 13 14
(x2 div 12)
A274039-A008724-A005377: 0 0 0 0 1 2 3 4 5 6 8 10 12 14 16 18
(x2 mod 12)
A070516-A070435: 0 1 4 9 4 1 0 1 4 9 4 1 0 1 4 9
(x - (3 * (x div 4)))
A276332-A276328-A053737: 0 1 2 3 1 2 3 4 2 3 4 5 3 4 5 6
(1 - ((x mod 4) mod 3))
A131379: 1 0 ~1 1 1 0 ~1 1 1 0 ~1 1 1 0 ~1 1
12x2
A135453: 0 12 48 108 192 300 432 588 768 972 1200 1452 1728 2028 2352 2700
(4x2 div 3)
A256320: 0 1 5 12 21 33 48 65 85 108 133 161 192 225 261 300
(3 * (x2 div 4))
A242477: 0 0 3 6 12 18 27 36 48 60 75 90 108 126 147 168
(3 * (1 - (2 * (x mod 2))))
A174971: 3 ~3 3 ~3 3 ~3 3 ~3 3 ~3 3 ~3 3 ~3 3 ~3
((2x2 + 4) div 3)
A084672: 1 2 4 7 12 18 25 34 44 55 68 82 97 114 132 151
((2 + (x2 div 2)) div 3)
A056829: 0 0 1 2 3 4 6 8 11 14 17 20 24 28 33 38
(9x + 6)
A017233: 6 15 24 33 42 51 60 69 78 87 96 105 114 123 132 141
(3 * ((x2 + x) div 2))
A045943: 0 3 9 18 30 45 63 84 108 135 165 198 234 273 315 360
(((x2 + ~x) div 2) div 3)
A130518-A062781: 0 0 0 1 2 3 5 7 9 12 15 18 22 26 30 35
(x - (((~x + 2) div 2) div 3))
A138083: 0 1 2 4 5 6
A308065-A047318: 0 1 2 4 5 6 7 8 9 11 12 13 14 15 16 18
(((x2 + 2x) div 2) mod 3)
A171182: 0 1 1 1 0 2 0 1 1 1 0 2 0 1 1 1
(((x + 2) + (x mod 2)) div 3)
A123919: 0 1 1 2 2 2 2 3 3 4 4 4 4 5 5 6
(2x - ((x + ~2) div 3))
A330066-A059535-A047206: 1 3 4 6 8 9 11 13 14 16 18 19 21 23 24 26
((x div 2) - ((x + ~2) div 3))
A320536: 1 1 1 1 2 1 2 2 2 2 3 2 3 3 3 3
6x3
A244726: 0 6 48 162 384 750 1296 2058 3072 4374 6000 7986 10368 13182 16464 20250
(x - ((1 - (x div 2)) div 3))
A047334-A032775-A029927: 0 1 2 3 5 6 7 8 9 10 12 13 14 15 16 17
(2x - ((x div 2) div 3))
A214671: 0 2 4 6 8 10 11 13 15 17 19 21 22 24 26 28
((x2 + (x div 2)) div 3)
A171662: 0 0 1 3 6 9 13 17 22 28 35 42 50 58 67 77
(3 * (x div (2 - (x mod 2))))
A165351: 0 3 3 9 6 15 9 21 12 27 15 33 18 39 21 45
((x div (2 - (x mod 2))) mod 3)
A088689: 0 1 1 0 2 2 0 1 1 0 2 2 0 1 1 0
(((~x2 + 2x) div 2) mod 3)
A300069: 0 0 0 1 2 1 0 0 0 1 2 1 0 0 0 1
((1 - (x2 div 2)) mod 3)
A117447: 1 1 2 0 2 1 1 1 2 0 2 1 1 1 2 0
((x3 + 2) div 3)
A088110: 0 1 3 9
A131477: 0 1 3 9 22 42 72 115 171 243 334 444 576 733 915 1125
(5x + 3)
A016885: 3 8 13 18 23 28 33 38 43 48 53 58 63 68 73 78
(3 * (x + (x div 3)))
A319451: 0 3 6 12 15 18 24 27 30 36 39 42 48 51 54 60
((x + (x div 3)) mod 3)
A327306-A159955: 0 1 2 1 2 0 2 0 1 0 1 2 1 2 0 2
(3x2 + 9x)
A277978: 0 12 30 54 84 120 162 210 264 324 390 462 540 624 714 810
(6x2 + 3x)
A195319: 0 9 30 63 108 165 234 315 408 513 630 759 900 1053 1218 1395
(6x2 + ~3x)
A094159: 0 3 18 45 84 135 198 273 360 459 570 693 828 975 1134 1305
((x * (1 + (x div 2))) mod 3)
A095130: 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0
(2x - ((~x + 1) div 3))
A047386: 0 2 5 7 9 12 14 16 19 21 23 26 28 30 33 35
(1 - ((x2 + x) mod 3))
A257075: 1 ~1 1 1 ~1 1 1 ~1 1 1 ~1 1 1 ~1 1 1
(3x3 + 3x)
A119536: 0 6 30 90 204 390 666 1050 1560 2214 3030 4026 5220 6630 8274 10170
((x * ((x + ~1) div 2)) div 3)
A182079: 0 0 0 1 1 3 4 7 8 12 13 18 20 26 28 35
((x + (x div 4)) div 3)
A336861-A121830-A114540: 0 0 0 1 1 2 2 2 3 3 4 4 5 5 5 6
((x2 + 4x) div 3)
A071408: 0 1 4 7 10 15 20 25 32 39 46 55 64 73 84 95
(3x * (2 - (x mod 2)))
A165988: 0 3 12 9 24 15 36 21 48 27 60 33 72 39 84 45
(x - (3 * (~x + (x mod 2))))
A047393: 0 1 8 9 16 17 24 25 32 33 40 41 48 49 56 57
(1 - ((~x + (x mod 2)) div 3))
A285507: 1 1 2 2 3 3 3 3 4 4 5 5 5 5 6 6
(x - ((~x + (x mod 2)) div 3))
A047517: 0 1 3 4 6 7 8 9 11 12 14 15 16 17 19 20
((x3 + 2x) div 3)
A006527: 0 1 4 11 24 45 76 119 176 249 340 451 584 741 924 1135
((x div 3) * (x div 3))
A211547: 0 0 0 1 1 1 4 4 4 9 9 9 16 16 16 25
((x mod 3) * (x div 3))
A115273: 0 0 0 0 1 2 0 2 4 0 3 6 0 4 8 0
((2x + 1) + (x div 3))
A097911: 1 3 5 8
A073608: 1 3 5 8 10 12
A047391: 1 3 5 8 10 12 15 17 19 22 24 26 29 31 33 36
(1 + ((x div 2) + (x div 3)))
A063208: 1 1 2 3 4 4 6 6 7 8 9 9 11 11 12 13
((2x + 2) + (x div 3))
A184978: 2 4 6 9 11
A330118-A292649-A189930-A061785-A047292: 2 4 6 9 11 13 16 18 20 23 25 27 30 32 34 37
(((x + 1) div 2) + (x div 3))
A063197: 0 1 1 3 3 4 5 6 6 8 8 9 10 11 11 13
(((x + 1) div 2) - (x div 3))
A011960: 0 1 1 1 1 2 1 2 2 2 2 3 2 3 3 3
(((x + 1) mod 2) + (x div 3))
A051274: 1 0 1 1 2 1 3 2 3 3 4 3 5 4 5 5
(2 + ((x div 2) + (x div 3)))
A242774: 2 2 3 4 5 5 7 7 8 9 10 10 12 12 13 14
(3x - (x div 3))
A198084-A047399: 0 3 6 8 11 14 16 19 22 24 27 30 32 35 38 40
(x * ((x div 2) * (x div 3)))
A213033: 0 0 0 3 8 10 36 42 64 108 150 165 288 312 392 525
(x3 - (x div 3))
A002901: 0 1 8 26 63 124 214 341 510 726 997 1328 1724 2193 2740 3370
((2x + 2) - (x mod 3))
A047228: 2 3 4 8 9 10 14 15 16 20 21 22 26 27 28 32
(3x + (x mod 3))
A140282: 0 4 8 9 13 17 18 22 26 27 31 35 36 40 44 45
((x2 + ~x) + (x mod 3))
A028444: 0 1 4 6 13
(3x2 + ~3x + 2)
A242658: 2 2 8 20 38 62 92 128 170 218 272 332 398 470 548 632
((2 mod (~x2 + 2)) mod 3)
A163581-A144603-A100283: 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1
(3x2 + ~x + 1)
A056106: 1 3 11 25 45 71 103 141 185 235 291 353 421 495 575 661
(2x - (x2 mod 3))
A047242: 0 1 3 6 7 9 12 13 15 18 19 21 24 25 27 30
3x4
A219056: 0 3 48 243 768 1875 3888 7203 12288 19683 30000 43923 62208 85683 115248 151875
(10x + 1)
A017281: 1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151
(1 + (2 * (x + (x div 3))))
A047623: 1 3 5 9 11 13 17 19 21 25 27 29 33 35 37 41
(2x2 + 6x + 1)
A059993: 1 9 21 37 57 81 109 141 177 217 261 309 361 417 477 541
(4x2 + 2x + 1)
A054569: 1 7 21 43 73 111 157 211 273 343 421 507 601 703 813 931
(4x2 + 2x + ~1)
A125202: ~1 5 19 41 71 109 155 209 271 341 419 505 599 701 811 929
(4x2 + ~2x + 1)
A318165: 1 3 13
A054554: 1 3 13 31 57 91 133 183 241 307 381 463 553 651 757 871
(x - (x mod (~2x + 3)))
A338923-A004274: 0 1 2 3 5 7 9 11 13 15 17 19 21 23 25 27
(x - (x div (~1 + ((~x + 1) div 2))))
A258022: 0 2 3 5 6 7 8 9 10 11 12 13 14 15 16 17
(1 + ((x + (x div 4)) div 2))
A020915: 1 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10
(1 + ((x * (x div 4)) mod 2))
A227195: 1 1 1 1 1 2 1 2 1 1 1 1 1 2 1 2
(2x2 + 8x + 1)
A161532: 1 11 25 43 65 91 121 155 193 235 281 331 385 443 505 571
(1 + ((x * (2 + (x mod 2))) div 2))
A063914: 1 2 3 5 5 8 7 11 9 14 11 17 13 20 15 23
(1 + (2x * (2 - (x mod 2))))
A178414: 1 3 9 7 17 11 25 15 33 19 41 23 49 27 57 31
((x + 1) - (2 * (~x + (x mod 2))))
A047239: 1 2 7 8 13 14 19 20 25 26 31 32 37 38 43 44
(~1 + ((x + 2) * (1 + (x div 2))))
A079326: 1 2 7 9 17 20 31 35 49 54 71 77 97 104 127 135
(1 + ((2 - (x div 2)) div (x + 2)))
A218245: 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
(2x2 + 7x + 3)
A071355: 3 12 25 42 63 88 117 150 187 228 273 322 375 432 493 558
(4x2 + 12x)
A332519: 0 16 40 72 112 160 216 280 352 432 520 616 720 832 952 1080
(4x div (x + 3))
A286103-A080342: 0 1 1 2 2 2 2 2 2 3 3 3 3 3 3 3
(3x div (x + 3))
A098391: 0 0 1 1 1 1 2 2 2 2 2 2 2 2 2 2
(x3 + 4x2 + 3x)
A317637: 0 8 30 72 140 240 378 560 792 1080 1430 1848 2340 2912 3570 4320
(x - (x2 div (x + 3)))
A004233: 0 1 2 2 2 2 2 3 3 3 3 3 3 3 3 3
(x3 + 4x2 + 4x + 1)
A081437: 1 10 33 76 145 246 385 568 801 1090 1441 1860 2353 2926 3585 4336
((x + 1) - (2 mod (~2x + 1)))
A033627: 1 2 4 7 10 13 16 19 22 25 28 31 34 37 40 43
((2x + 1) + (x div 4))
A190511: 1 3 5 7 10 12 14 16 19 21 23 25 28 30 32 34
((2x + 1) * (1 + (x div 2)))
A188545: 1 3 10
A245524: 1 3 10 14 27 33 52 60 85 95 126 138 175 189 232 248
((2x + 1) * ((x + 1) div 2))
A074378: 0 3 5 14 18 33 39 60 68 95 105 138 150 189 203 248
(16x + 8)
A051062: 8 24 40 56 72 88 104 120 136 152 168 184 200 216 232 248
(8x2 + 4x)
A033586: 0 12 40 84 144 220 312 420 544 684 840 1012 1200 1404 1624 1860
((2x + 1) * (2 - (x mod 2)))
A123167: 2 3 10 7 18 11 26 15 34 19 42 23 50 27 58 31
(2x3 + 3x2 + x)
A055112: 0 6 30 84 180 330 546 840 1224 1710 2310 3036 3900 4914 6090 7440
((x2 + x) mod (2x + 1))
A076937-A014682: 0 2 1 5 2 8 3 11 4 14 5 17 6 20 7 23
((3x + 1) + (x div 2))
A047346: 1 4 8 11 15 18 22 25 29 32 36 39 43 46 50 53
((2x + 1) * (x + (x mod 2)))
A014494: 0 6 10 28 36 66 78 120 136 190 210 276 300 378 406 496
(x3 div (2x + 1))
A082644: 0 0 1 3 7 11 16 22 30 38 47 57 69 81 94 108
(8x2 + ~4x)
A085250: 0 4 24 60 112 180 264 364 480 612 760 924 1104 1300 1512 1740
(1 + ((2 mod (x + 1)) + (x div 2)))
A003869: 1 1 4 4 5 5 6
((4x + 1) - (x div 2))
A047383: 1 5 8 12 15 19 22 26 29 33 36 40 43 47 50 54
(1 + ((x2 div 2) + (x div 2)))
A084263: 1 1 4 6 11 15 22 28 37 45 56 66 79 91 106 120
((2 + (x mod 2)) * (1 + (x div 2)))
A195013: 2 3 4 6 6 9 8 12 10 15 12 18 14 21 16 24
((x + 2) - (2 div (1 + (x div 2))))
A078923: 0 1 3 4 6 7 8 9 10 11 12 13 14 15 16 17
(2 - ((~x + 1) div (1 + (x div 2))))
A130193-A084526-A084516: 1 2 3 3 3 4 4 4 4 4 4 4 4 4 4 4
((x2 + 2x + 1) + (x div 2))
A213398: 1 4 10 17 27 38 52 67 85 104 126 149 175 202 232 263
(1 + ((x * (x mod 2)) + (x div 2)))
A266981: 1 2 2 5 3 8 4 11 5 14 6 17 7 20 8 23
(9 + (x mod 2))
A010735: 9 10 9 10 9 10 9 10 9 10 9 10 9 10 9 10
((4x + 1) + (x mod 2))
A047452: 1 6 9 14 17 22 25 30 33 38 41 46 49 54 57 62
((4x + 1) - (x mod 2))
A047461: 1 4 9 12 17 20 25 28 33 36 41 44 49 52 57 60
(1 + (x2 div 2) - (x mod 2))
A097063: 1 0 3 4 9 12 19 24 33 40 51 60 73 84 99 112
((x2 + 2x + 1) + (x mod 2))
A080335: 1 5 9 17 25 37 49 65 81 101 121 145 169 197 225 257
((x2 + x + 1) - (x mod 2))
A213041: 1 2 7 12 21 30 43 56 73 90 111 132 157 182 211 240
((x2 + 2x + ~1) + (x mod 2))
A181106: ~1 3 7 15 23 35 47 63 79 99 119 143 167 195 223 255
(2x2 + x + ~5)
A100040: ~5 ~2 5 16 31 50 73 100 131 166 205 248 295 346 401 460
(1 + (x4 div 2))
A274323: 1 1 9 41 129 313 649 1201 2049 3281 5001 7321 10369 14281 19209 25313
(7x + 1)
A079043-A016993: 1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106
((x + 1) + (x div 5))
A320340-A248910-A232741-A228869-A204878-A194386-A187390-A184522-A136447-A108586-A108120-A098901-A098767-A094520-A088725-A051772-A049093-A047253-A039215-A037918-A031943-A005100: 1 2 3 4 5 7 8 9 10 11 13 14 15 16 17 19
(x2 + 5x + 1)
A082111: 1 7 15 25 37 51 67 85 105 127 151 177 205 235 267 301
(4x2 + x + 1)
A054567: 1 6 19 40 69 106 151 204 265 334 411 496 589 690 799 916
(4x2 + x + ~1)
A182868: ~1 4 17 38 67 104 149 202 263 332 409 494 587 688 797 914
(4x2 + ~x + 1)
A054556: 1 4 15 34 61 96 139 190 249 316 391 474 565 664 771 886
(4x2 + ~x + ~1)
A185950: ~1 2 13 32 59 94 137 188 247 314 389 472 563 662 769 884
((x + 1) + (3 * (x div 2)))
A047216: 1 2 6 7 11 12 16 17 21 22 26 27 31 32 36 37
((x + 1) + ((x div 2) div 3))
A332107-A302478-A286997-A267305-A187396-A047304-A020658: 1 2 3 4 5 6 8 9 10 11 12 13 15 16 17 18
(x3 + 3x + 1)
A005491: 1 5 15 37 77 141 235 365 537 757 1031 1365 1765 2237 2787 3421
(3x2 + x + 1)
A056108: 1 5 15 31 53 81 115 155 201 253 311 375 445 521 603 691
((x + 1) + (x2 div 3))
A022339-A007980: 1 2 4 7 10 14 19 24 30 37 44 52 61 70 80 91
(x3 + x2 + ~x + 1)
A100109: 1 2 11 34 77 146 247 386 569 802 1091 1442 1861 2354 2927 3586
(x3 + ~x2 + ~x + ~1)
A083074: ~1 ~2 1 14 43 94 173 286 439 638 889 1198 1571 2014 2533 3134
((x + 1) + (2 * (x div 3)))
A047223: 1 2 3 6 7 8 11 12 13 16 17 18 21 22 23 26
((x + 1) + ((x mod 3) mod 2))
A092200: 1 3 3 4 6 6 7 9 9 10 12 12 13 15 15 16
(1 + (x * (2 + (2 div (x + 1)))))
A223134: 1 4 5 7 9 11 13 15 17 19 21 23 25 27 29 31
(1 + (x * ((x2 + 1) div 2)))
A309115: 1 2 5 16
((x + 1) + ((x div ~2) mod 2))
A098181: 1 3 4 4 5 7 8 8 9 11 12 12 13 15 16 16
(~x + 17)
A022973: 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2
(~x + 15)
A022971-A004456: 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
((x + 1) + (x div 8))
A331682-A328335-A327534-A325389-A317492-A316502-A316495-A306202-A265999-A255808-A194151-A168183-A122132-A107037-A088481-A037479-A036741-A032897-A032856-A031980-A020662: 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 17
((x + 1) + (2 * (x div 4)))
A047227-A031477: 1 2 3 4 7 8 9 10 13 14 15 16 19 20 21 22
(x2 + 6x + 1)
A028884: 1 8 17 28 41 56 73 92 113 136 161 188 217 248 281 316
((x + 1) + (x2 div 4))
A231408: 1 2 4 6 9
A087811-A025699: 1 2 4 6 9 12 16 20 25 30 36 42 49 56 64 72
(3x2 + 2x + 1)
A056109: 1 6 17 34 57 86 121 162 209 262 321 386 457 534 617 706
(3x2 + 2x + ~1)
A270710: ~1 4 15 32 55 84 119 160 207 260 319 384 455 532 615 704
(3x2 + ~2x + 1)
A056105: 1 2 9 22 41 66 97 134 177 226 281 342 409 482 561 646
(x3 + 2x2 + 2x + 1)
A069778: 1 6 21 52 105 186 301 456 657 910 1221 1596 2041 2562 3165 3856
((x + 1) + ((x + (x div 2)) div 2))
A184638-A047294: 1 2 4 6 8 9 11 13 15 16 18 20 22 23 25 27
((x + 1) + (2 * (x + (x mod 2))))
A011990: 1 6 7 12
(~x mod (1 + (x * (x div 2))))
A334320: 0 0 1 1 5 6 13 15 25 28 41 45 61 66 85 91
(1 + (x * (2x - (x mod 2))))
A083783: 1 2 9 16
(1 - (1 mod ((~x + 1) + (x mod 2))))
A267458: 1 1 1 1 3 3 5 5 7 7 9 9 11 11 13 13
((x div ~3) mod (x + 1))
A121928: 0 1 2 3 3 4 5 5 6 7 7 8 9 9 10 11
(7x + 7)
A182341: 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112
(7 div (x + 1))
A033327: 7 3 2 1 1 1 1 0 0 0 0 0 0 0 0 0
((x + 1) * (1 + ((x + 1) div 2)))
A231407: 1 4 6
A265225: 1 4 6 12 15 24 28 40 45 60 66 84 91 112 120 144
(9 div (x + 1))
A033329: 9 4 3 2 1 1 1 1 1 0 0 0 0 0 0 0
((x + 1) * (x div 5))
A108613: 0 0 0 0 0 6 7 8 9 10 22 24 26 28 30 48
((x + 1) * (1 + (2 * (x div 2))))
A183207: 1 2 9 12 25 30 49 56 81 90 121 132 169 182 225 240
((x + 1) * (1 + (2 * (x mod 2))))
A165998: 1 6 3 12 5 18 7 24 9 30 11 36 13 42 15 48
(12 div (x + 1))
A033332: 12 6 4 3 2 2 1 1 1 1 1 1 0 0 0 0
((x + 1) * ((x + 2) div 3))
A229593: 0 2 3 4 10 12 14 24 27 30 44 48 52 70 75 80
((x + 1) * (3 - (x mod 2)))
A106833: 3 4 9 8 15 12 21 16 27 20 33 24 39 28 45 32
((2x2 + 1) div (x + 1))
A092535: 1 1 3 4 6 8 10 12 14 16 18 20 22 24 26 28
((x + 1) * ((x + 1) + (x div 2)))
A319259: 1 4 12 20
((x + 1) * ((x + 1) + (x mod 2)))
A011988: 1 6 9 20
((x + 1) * ((x + ~1) + (x mod 2)))
A289870: ~1 2 3 12 15 30 35 56 63 90 99 132 143 182 195 240
(2x3 + 4x2 + 2x)
A035006: 0 8 36 96 200 360 588 896 1296 1800 2420 3168 4056 5096 6300 7680
((x2 + 2x + 1) * (x div 2))
A303692: 0 0 9 16 50 72 147 192 324 400 605 720 1014 1176 1575 1792
(x4 + 2x3 + x2)
A035287: 0 4 36 144 400 900 1764 3136 5184 8100 12100 17424 24336 33124 44100 57600
(10 div (x + 1))
A033330: 10 5 3 2 2 1 1 1 1 1 0 0 0 0 0 0
(10 mod (x + 1))
A324471: 0 0 1 2 0 4 3 2 1 0 10 10 10 10 10 10
((x div ~4) mod (x + 1))
A195180-A195172: 0 1 2 3 4 4 5 6 7 7 8 9 10 10 11 12
((x + 1) * (((x + 1) div 2) div 2))
A233035: 0 0 0 4 5 6 7 16 18 20 22 36 39 42 45 64
(16x + 16)
A044061: 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 256
(16 div (x + 1))
A033336: 16 8 5 4 3 2 2 2 1 1 1 1 1 1 1 1
(x2 + 7x + 6)
A104675: 6 14 24 36 50 66 84 104 126 150 176 204 234 266 300 336
((4x + 8) div (x + 1))
A202258: 8 6 5 5 4
(8x2 + 8x)
A035008: 0 16 48 96 160 240 336 448 576 720 880 1056 1248 1456 1680 1920
(((x + 1) mod 4) mod (x + 1))
A049804: 0 0 0 0 1 2 3 0 1 2 3 0 1 2 3 0
(~4x2 + ~4x + 1)
A184882: 1 ~7 ~23 ~47 ~79 ~119 ~167 ~223 ~287 ~359 ~439 ~527 ~623 ~727 ~839 ~959
(2 - ((~2 + (x div 2)) div (x + 1)))
A171627: 4 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2
(x + ((x mod 2) + (2 mod (x + 1))))
A267460: 0 2 4 6 6 8 8 10 10 12 12 14 14 16 16 18
((x + 1) * ((x2 + x) div 2))
A006002: 0 2 9 24 50 90 147 224 324 450 605 792 1014 1274 1575 1920
((x + 1) * ((x + 2) + (x mod 2)))
A013654: 2 8 12 24 30 48 56 80 90 120 132 168 182 224 240 288
(x3 + 5x2 + 8x + 4)
A114364: 4 18 48 100 180 294 448 648 900 1210 1584 2028 2548 3150 3840 4624
(x4 + 3x3 + 2x2)
A047927: 0 6 48 180 480 1050 2016 3528 5760 8910 13200 18876 26208 35490 47040 61200
(x4 + x3 + x2 + x)
A027445: 0 4 30 120 340 780 1554 2800 4680 7380 11110 16104 22620 30940 41370 54240
((x2 + x) * (2 - (x mod 2)))
A045895: 0 2 12 12 40 30 84 56 144 90 220 132 312 182 420 240
(x5 + x4)
A101362: 0 2 48 324 1280 3750 9072 19208 36864 65610 110000 175692 269568 399854 576240 810000
(x4 + ~x3 + ~x + 1)
A138849: 1 0 7 52 189 496 1075 2052 3577 5824 8991 13300 18997 26352 35659 47236
(x - ((x + ~1) * (x div ~2)))
A222010: 0 1 3 7
A128223: 0 1 3 7 10 17 21 31 36 49 55 71 78 97 105 127
(2x3 + ~6x2 + 4x)
A280058: 0 0 0 12 48 120 240 420 672 1008 1440 1980 2640 3432 4368 5460
(x2 - ((x + ~1) * (x mod 2)))
A325657: 0 1 4 7 16 21 36 43 64 73 100 111 144 157 196 211
(x3 + ~3x2 + 3x)
A001093: 0 1 2 9 28 65 126 217 344 513 730 1001 1332 1729 2198 2745
(x5 + ~x4)
A085538: 0 0 16 162 768 2500 6480 14406 28672 52488 90000 146410 228096 342732 499408 708750
(5x2 + 1)
A212656: 1 6 21 46 81 126 181 246 321 406 501 606 721 846 981 1126
(1 - (2 mod (~x2 + x + 1)))
A276272: 1 1 1 4 10
(x4 + x2 + 1)
A059826: 1 3 21 91 273 651 1333 2451 4161 6643 10101 14763 20881 28731 38613 50851
(x4 + ~x2 + 1)
A060886: 1 1 13 73 241 601 1261 2353 4033 6481 9901 14521 20593 28393 38221 50401
(1 + (x * (x + (2 * (x mod 2)))))
A081345: 1 4 5 16 17 36 37 64 65 100 101 144 145 196 197 256
(x4 + 2x2 + 1)
A082044: 1 4 25 100 289 676 1369 2500 4225 6724 10201 14884 21025 28900 38809 51076
(x2 + 9)
A189834: 9 10 13 18 25 34 45 58 73 90 109 130 153 178 205 234
(4x3 + 4x)
A105374: 0 8 40 120 272 520 888 1400 2080 2952 4040 5368 6960 8840 11032 13560
(x4 + 3x2 + 2)
A304579: 2 6 30 110 306 702 1406 2550 4290 6806 10302 15006 21170 29070 39006 51302
(x5 + x3)
A155977: 0 2 40 270 1088 3250 7992 17150 33280 59778 101000 162382 250560 373490 540568 762750
(4x3 + ~4x)
A272871: 0 0 24 96 240 480 840 1344 2016 2880 3960 5280 6864 8736 10920 13440
(x5 + ~x3)
A133754: 0 0 24 216 960 3000 7560 16464 32256 58320 99000 159720 247104 369096 535080 756000
((x div ~4) div ~2)
A135665: 0 0 0 0 0 1 1 1 1 1 1 1 1 2 2 2
(1 - (x div ~8))
A108582: 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3
(x - (x div ~8))
A057717: 0 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17
(x div (2 - ((x div 2) div ~2)))
A333525-A262303-A056811: 0 0 0 1 1 1 1 1 2 2 2 2 2 2 2 2
((x mod 2) - ((x div 2) div ~2))
A319688: 0 1 1 2 1 2 2 3 2 3 3 4 3 4 4 5
(x - ((x2 + 2x) div ~2))
A116940: 0 3 6 11 16 23 30 39 48 59 70 83 96 111 126 143
(x - ((x + (x div 2)) div ~2))
A047379: 0 2 4 5 7 9 11 12 14 16 18 19 21 23 25 26
((2x + 2) - (x div ~2))
A330067-A075328: 2 5 7 10 12 15 17 20 22 25 27 30 32 35 37 40
(4x - (x div ~2))
A130877: 0 5 9 14 18 23 27 32 36 41 45 50 54 59 63 68
(2 + (x mod 2) - (x div ~2))
A060762: 2 4 3 5 4 6 5 7 6 8 7 9 8 10 9 11
(x2 - (x2 div ~2))
A238410: 0 2 6 14 24 38 54 74 96 122 150 182 216 254 294 338
(2 * (1 + (x div 5)))
A105674: 2 2 2 2 2 4 4 4 4 4 6 6 6 6 6 8
((1 + (x div 5)) mod 2)
A084052: 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0
((1 + (x mod 5)) mod 2)
A188044: 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1
(2 * (1 + ((x + 1) div 3)))
A110870: 2 2 4 4 4 6 6 6 8 8 8
26
A010865: 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26
22
A010861: 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22
(12x + 2)
A017545: 2 14 26 38 50 62 74 86 98 110 122 134 146 158 170 182
((x mod (1 + (x div 3))) div 2)
A024160: 0 0 0 0 0 0 0 0 1 0 1 1 1 1 2 1
(2 * ((x + 1) - (x div 3)))
A082990: 2 4 6 6 8 10 10 12 14 14 16 18 18 20 22 22
(x - (2 * (~1 + (x mod 3))))
A330396: 2 1 0 5 4 3 8 7 6 11 10 9 14 13 12 17
(8x + 6)
A189785-A017137: 6 14 22 30 38 46 54 62 70 78 86 94 102 110 118 126
(2x2 + 6x + 2)
A090288: 2 10 22 38 58 82 110 142 178 218 262 310 362 418 478 542
(4x2 + 4x + 2)
A069894: 2 10 26 50 82 122 170 226 290 362 442 530 626 730 842 962
(x - (2 * (x div ~3)))
A047205: 0 3 4 5 8 9 10 13 14 15 18 19 20 23 24 25
(2 * (x - (x div ~3)))
A047407: 0 4 6 8 12 14 16 20 22 24 28 30 32 36 38 40
(2 * ((x + 1) - (x div ~2)))
A189933: 2 6 8 12 14 18 20 24 26 30 32 36 38 42 44 48
(x mod 14)
A103303: 0 1 2 3 4 5 6 7 8 9
A070696: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0 1
((x div 7) mod 2)
A135500: 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0
(2 * (1 + (2 * (1 + (x mod 2)))))
A010726: 6 10 6 10 6 10 6 10 6 10 6 10 6 10 6 10
((x div ~5) mod 2)
A112713: 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1
((x mod ~5) mod 2)
A188037: 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0
((1 + (((x + 1) div 2) div 2)) div 2)
A067441: 0 0 0 1 1 1 1 1 1 1 1 2 2 2 2 2
((x mod 9) div 2)
A014589: 0 0 1 1 2 2 3 3 4 0 0 1 1 2 2 3
((x mod 9) mod 2)
A287773-A285685: 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0
(2 * (1 + (x div 8)))
A064128: 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4
(2 * (1 + (4 * (x mod 2))))
A010700: 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2 10
(2 * ((x + 1) mod 5))
A135033: 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2
(((x + 1) mod 5) mod 2)
A281274-A198517-A190227: 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1
(((x + 2) mod 5) mod 2)
A085242: 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0
(((x + ~2) mod 5) mod 2)
A285076-A232990: 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1
((x + 1) mod 10)
A179636-A128212-A118943-A087471-A062078: 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6
(x - (x mod 10))
A169932-A070565: 0 0 0 0 0 0 0 0 0 0 10 10 10 10 10 10
(x2 mod 10)
A008959: 0 1 4 9 6 5 6 9 4 1 0 1 4 9 6 5
(2 * (~x mod 5))
A177154: 0 8 6 4 2 0 8 6 4 2 0 8 6 4 2 0
(x - (2 * (x div 5)))
A255938-A081748: 0 1 2 3 4 3 4 5 6 7 6 7 8 9 10 9
((2 div (1 + (x div 4))) mod 2)
A327051: 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0
(x - ((1 + (x div 4)) div 2))
A257682-A029928: 0 1 2 3 3 4 5 6 7 8 9 10 10 11 12 13
(((x + ~1) - (x div 4)) mod 2)
A188467-A187950-A112539-A104104: 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1
((x mod (1 + (x div 4))) div 2)
A255361-A210703: 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1
(x - ((~1 + (x div 4)) div 2))
A105598: 1 2 3 4 4 5 6 7 8 9 10 11 11 12 13 14
((x div (1 + (x mod 4))) mod 2)
A216511: 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1
(2x2 + 10)
A255845: 10 12 18 28 42 60 82 108 138 172 210 252 298 348 402 460
(8x2 + 2)
A108100: 2 10 34 74 130 202 290 394 514 650 802 970 1154 1354 1570 1802
((1 + (x2 div 4)) div 2)
A056837-A001971: 0 0 1 1 2 3 5 6 8 10 13 15 18 21 25 28
(((x + 1) - ((x div 2) mod 2)) div 2)
A194247-A004525: 0 1 1 1 2 3 3 3 4 5 5 5 6 7 7 7
((x mod (3 + (x mod 2))) mod 2)
A276950: 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1
(2 + (3 * (x mod 3)))
A131598: 2 5 8 2 5 8 2 5 8 2 5 8 2 5 8 2
((3 * (x mod 3)) div 2)
A101000: 0 1 3 0 1 3 0 1 3 0 1 3 0 1 3 0
(2 * ((1 + (x div 2)) div 3))
A100825: 0 0 0 0 2 2 2 2 2 2 4 4 4 4 4 4
(2 + (((x + 1) div 2) div 3))
A085290: 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4
(1 - (2 * (2x div 3)))
A168053: 1 1 ~1 ~3 ~3 ~5 ~7 ~7 ~9 ~11 ~11 ~13 ~15 ~15 ~17 ~19
(x - (2 * ((x div 2) div 3)))
A325631-A309064-A276073: 0 1 2 3 4 5 4 5 6 7 8 9 8 9 10 11
((x - ((x div 2) div 3)) div 2)
A183142: 0 0 1 1 2 2 2 3 3 4 4 5 5 5 6 6
(((x2 div 2) mod 3) div 2)
A282778-A120325: 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0
(x2 + x + 6)
A027691: 6 8 12 18 26 36 48 62 78 96 116 138 162 188 216 246
(x3 + 6)
A084382: 6 7 14 33 70 131 222 349 518 735 1006 1337 1734 2203 2750 3381
(9x + 2)
A017185: 2 11 20 29 38 47 56 65 74 83 92 101 110 119 128 137
(x - (2 * ((~x + 1) div 3)))
A008854: 0 1 4 5 6 9 10 11 14 15 16 19 20 21 24 25
(2 * (x - ((~x + 1) div 3)))
A047395: 0 2 6 8 10 14 16 18 22 24 26 30 32 34 38 40
(3x2 + 6x + 2)
A080663: 2 11 26 47 74 107 146 191 242 299 362 431 506 587 674 767
((3 * (x + (x div 2))) div 2)
A010378: 0 1 4 6 9 10
A214068: 0 1 4 6 9 10 13 15 18 19 22 24 27 28 31 33
(2 + (3 * (x + (x mod 2))))
A168286: 2 8 8 14 14 20 20 26 26 32 32 38 38 44 44 50
(x mod (2 - ((x mod 3) div 2)))
A286907-A284851: 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1
(2x - ((x mod 3) div 2))
A047244: 0 2 3 6 8 9 12 14 15 18 20 21 24 26 27 30
((x div 2) - ((x mod 3) div 2))
A174257: 0 0 0 1 2 1 3 3 3 4 5 4 6 6 6 7
(2x - ((x mod 3) mod 2))
A047234: 0 1 4 6 7 10 12 13 16 18 19 22 24 25 28 30
((1 + ((x2 + x) div 2)) div 2)
A194248: 0 1 2 3 5 8 11 14 18 23 28 33 39 46 53 60
((1 + ((x2 + ~x) div 2)) div 2)
A054925: 0 0 1 2 3 5 8 11 14 18 23 28 33 39 46 53
(4x2 + 8x + 2)
A060626: 2 14 34 62 98 142 194 254 322 398 482 574 674 782 898 1022
(2 * (1 + ((x2 + 2x) div 2)))
A137928: 2 4 10 16 26 36 50 64 82 100 122 144 170 196 226 256
((1 + ((x + (x div 2)) div 2)) div 2)
A334415: 0 0 1 1 2 2 2 3 3 3 4 4 5 5 5 6
(2 * (1 + (2 * (x + (x mod 2)))))
A168381: 2 10 10 18 18 26 26 34 34 42 42 50 50 58 58 66
((x2 + 4x + 3) div 2)
A074148: 1 4 7 12 17 24 31 40 49 60 71 84 97 112 127 144
((x2 mod (x + 3)) mod 2)
A339369: 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1
(4x3 + 2)
A278611: 2 6 34
(((x + ~1) mod (1 + (x div 2))) div 2)
A333535-A091372: 0 0 0 0 0 0 0 1 1 1 1 2 2 2 2 3
((4 mod (1 + (x div 2))) mod 2)
A343959: 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0
(2x - ((1 + (x div 2)) div 2))
A047371-A022847: 0 2 3 5 7 9 10 12 14 16 17 19 21 23 24 26
(2x - ((~1 + (x div 2)) div 2))
A184748-A047298: 1 3 4 6 8 10 11 13 15 17 18 20 22 24 25 27
(2 * ((2x + 1) - (x mod 2)))
A047463: 2 4 10 12 18 20 26 28 34 36 42 44 50 52 58 60
((1 + (x div 2) - (x mod 2)) div 2)
A059169: 0 0 1 0 1 1 2 1 2 2 3 2 3 3 4 3
(10x + 2)
A017293: 2 12 22 32 42 52 62 72 82 92 102 112 122 132 142 152
(2 * ((x + 1) + (x div 3)))
A309374: 2 4 6 10 12
A047410: 2 4 6 10 12 14 18 20 22 26 28 30 34 36 38 42
((1 + (x * (1 + (x div 2)))) div 2)
A088414: 0 1 2 3 6 8
(2x + 18)
A088383: 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
(2 * ((x + 1) + (x div 4)))
A217562: 2 4 6 8 12 14 16 18 22 24 26 28 32 34 36 38
(((x + 1) + (x div 4)) div 2)
A090638-A073869-A055930-A005206: 0 1 1 2 3 3 4 4 5 6 6 7 8 8 9 9
(2x2 + 8x + 2)
A152811: 2 12 26 44 66 92 122 156 194 236 282 332 386 444 506 572
(2 * ((x + 1) + (2 * (x mod 2))))
A124356: 2 8 6 12 10 16 14 20 18 24 22 28 26 32 30 36
(x - (2 * ((~x + ~1) + (x mod 2))))
A047243: 2 3 8 9 14 15 20 21 26 27 32 33 38 39 44 45
(2x2 + 3x + 3)
A033816: 3 8 17 30 47 68 93 122 155 192 233 278 327 380 437 498
((6 mod (x + 1)) mod 2)
A185014: 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
((8 mod (x + 1)) mod 2)
A269246: 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0
((x2 + ~3x + ~4) div 2)
A167544: ~2 ~3 ~3 ~2 0 3 7 12 18 25 33 42 52 63 75 88
(((x + 1) * (2 + (x mod 2))) div 2)
A080512: 1 3 3 6 5 9 7 12 9 15 11 18 13 21 15 24
((((~x + 1) div 2) mod (x + 1)) div 2)
A055679: 0 0 1 1 1 2 2 2 2 3 3 3 3 4 4 4
((x3 + x2 + 2x + 2) div 2)
A064808: 1 3 9 22 45 81 133 204 297 415 561 738 949 1197 1485 1816
(((x2 div 2) mod (x + 1)) div 2)
A322996: 0 0 1 0 1 0 2 0 2 0 3 0 3 0 4 0
(((x2 div 2) mod (x + 1)) mod 2)
A292370-A188187-A160380: 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
((2x + 2) + (x div 4))
A193766-A022839: 2 4 6 8 11 13 15 17 20 22 24 26 29 31 33 35
((3x + 2) + (x div 2))
A047385: 2 5 9 12 16 19 23 26 30 33 37 40 44 47 51 54
((x + (x mod 2)) * ((x + 1) div 2))
A079242: 0 2 2 8
((x3 + 3x2 + 2x) div 2)
A027480: 0 3 12 30 60 105 168 252 360 495 660 858 1092 1365 1680 2040
((~x3 + ~x2 + 2x + 2) div 2)
A110427: 1 1 ~3 ~14 ~35 ~69 ~119 ~188 ~279 ~395 ~539 ~714 ~923 ~1169 ~1455 ~1784
(2 + ((x + ~1) * (2 + (x div 2))))
A266287: 0 2 5 8 14 18 27 32 44 50 65 72 90 98 119 128
(((x + ~1) * ((x div 2) mod 2)) div 2)
A131360: 0 0 0 1 0 0 2 3 0 0 4 5 0 0 6 7
(~2x2 + 8x + ~4)
A147973: ~4 2 4 2 ~4 ~14 ~28 ~46 ~68 ~94 ~124 ~158 ~196 ~238 ~284 ~334
(x - (2 * ((x div 2) div ~2)))
A047260: 0 1 4 5 6 7 10 11 12 13 16 17 18 19 22 23
(1 - (((x div 2) div ~2) div 2))
A344517-A058318: 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3
(2x - (x div ~4))
A198082: 0 3 5 7 9 12 14 16 18 21 23 25 27 30 32 34
(2x - (x mod ~4))
A047575: 0 5 6 7 8 13 14 15 16 21 22 23 24 29 30 31
(((x + (x div 2)) div ~2) mod 2)
A130198: 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1
(2 * (2x - (x div ~2)))
A146951: 0 6 10 16 20 26 30 36 40 46 50 56 60 66 70 76
(0 - (x div (~2 + (x div ~2))))
A243113-A135662-A121900-A076620: 0 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2
(1 - (x div (~2 + (x div ~2))))
A125269: 1 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3
(2x - ((x div ~2) mod 2))
A047401: 0 1 3 6 8 9 11 14 16 17 19 22 24 25 27 30
28
A010867: 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28
(x + ~20)
A023462: ~20 ~19 ~18 ~17 ~16 ~15 ~14 ~13 ~12 ~11 ~10 ~9 ~8 ~7 ~6 ~5
(((x mod 5) div 2) div 2)
A305802-A283317-A276206-A248640-A188041-A112765-A093957: 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0
(16x + 4)
A085805: 4 20 36 52 68
A119413: 4 20 36 52 68 84 100 116 132 148 164 180 196 212 228 244
(4 * (1 + (2 * (x div 2))))
A168398: 4 4 12 12 20 20 28 28 36 36 44 44 52 52 60 60
(12x + 4)
A017569: 4 16 28 40 52 64 76 88 100 112 124 136 148 160 172 184
(2 * (2 + (3 * (x div 2))))
A168326: 4 4 10 10 16 16 22 22 28 28 34 34 40 40 46 46
(2 * (2 + (3 * (x mod 2))))
A010715: 4 10 4 10 4 10 4 10 4 10 4 10 4 10 4 10
(1 - (2 * ((x div 3) mod 2)))
A130151: 1 1 1 ~1 ~1 ~1 1 1 1 ~1 ~1 ~1 1 1 1 ~1
((x - ((x div 3) mod 2)) div 2)
A300293: 0 0 1 1 1 2 3 3 4 4 4 5 6 6 7 7
((x - ((x mod 3) div 2)) div 2)
A300068: 0 0 0 1 2 2 3 3 3 4 5 5 6 6 6 7
(((x - (x mod 3)) div 2) div 2)
A166872-A089051: 0 0 0 0 0 0 1 1 1 2 2 2 3 3 3 3
(x - (((1 + (x div 2)) div 2) div 2))
A332613: 0 1 2 3 4 5 5 6 7 8 9 10 11 12 12 13
(2 + ((x mod (1 + (x div 2))) div 2))
A090663: 2 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5
(4x2 + 4x + 4)
A112087: 4 12 28 52 84 124 172 228 292 364 444 532 628 732 844 964
(4 * ((x + 1) + (x div 2)))
A092259: 4 8 16 20 28 32 40 44 52 56 64 68 76 80 88 92
(2 + ((x2 + 3x + 2) div 2))
A255981: 3 5 8 12 17
(2 + (((x + 1) * (x div 2)) mod 2))
A214861-A037914: 2 2 3 2 2 2 3 2 2 2 3 2 2 2 3 2
(4x3 + 4)
A100214: 4 8 36 112 260 504 868 1376 2052 2920 4004 5328 6916 8792 10980 13504
(x - (2 * (x div ~4)))
A047250: 0 3 4 5 6 9 10 11 12 15 16 17 18 21 22 23
((x - (x div ~4)) div 2)
A101803-A029922: 0 1 1 2 2 3 4 4 5 6 6 7 7 8 9 9
(x - (2 * (x mod ~4)))
A120634: 0 7 6 5 4 11 10 9 8 15 14 13 12 19 18 17
(x - (2 * (((x + 1) div 2) div 2)))
A285869: 0 1 2 1 2 3 4 3 4 5 6 5 6 7 8 7
((2 - (((x + ~1) div 2) div 2)) div 2)
A014074: 1 1 1 1 1 0 0 0 0 0 0 0 0 ~1 ~1 ~1
(x - (2 * (((x + ~1) div 2) div 2)))
A162330: 2 1 2 3 4 3 4 5 6 5 6 7 8 7 8 9
(((((x + ~1) div 2) div 2) div 2) mod 2)
A339110-A288685-A245794-A245149-A185329-A185119-A025154-A017903-A017886-A017885-A017884-A017883-A017882: 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1
(x + ~32)
A023474: ~32 ~31 ~30 ~29 ~28 ~27 ~26 ~25 ~24 ~23 ~22 ~21 ~20 ~19 ~18 ~17
32x
A174312: 0 32 64 96 128 160 192 224 256 288 320 352 384 416 448 480
((x mod ~7) mod 2)
A327211-A022925: 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 0
(~x mod 16)
A055126: 0 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
(~x + 18)
A022974: 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3
(x2 mod 16)
A070439: 0 1 4 9 0 9 4 1 0 1 4 9 0 9 4 1
(((~x + 2) div 8) mod 2)
A072609: 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0
(2 * (2 - ((x div 4) mod 2)))
A074803: 4 4 4 4 2 2 2 2 4 4 4 4 2 2 2 2
(1 - (2 * ((x div 4) mod 2)))
A143621: 1 1 1 1 ~1 ~1 ~1 ~1 1 1 1 1 ~1 ~1 ~1 ~1
(x - (2 * (~2 + (x mod 4))))
A113778: 4 3 2 1 8 7 6 5 12 11 10 9 16 15 14 13
(2x2 + 12)
A255842: 12 14 20 30 44 62 84 110 140 174 212 254 300 350 404 462
16x2
A016802: 0 16 64 144 256 400 576 784 1024 1296 1600 1936 2304 2704 3136 3600
(x div (4 * (2 + (x mod 2))))
A072931: 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1
((x div (2 * (~2 + (x mod 2)))) mod 2)
A217207: 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0
((x - ((x div 2) mod 4)) div 2)
A082871: 0 0 0 1 1 1 1 2 4
(x - (x div ~7))
A274375-A047594: 0 2 3 4 5 6 7 8 10 11 12 13 14 15 16 18
((x mod ~2) mod 8)
A010678: 0 7 0 7 0 7 0 7 0 7 0 7 0 7 0 7
(x2 + x + 8)
A027693: 8 10 14 20 28 38 50 64 80 98 118 140 164 190 218 248
((x2 + x) mod 8)
A053794: 0 2 6 4 4 6 2 0 0 2 6 4 4 6 2 0
((x2 + ~x) div 8)
A011861: 0 0 0 0 1 2 3 5 7 9 11 13 16 19 22 26
((x + (x div 2)) div 8)
A105518: 0 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2
((x * (x mod 2)) mod 8)
A109753: 0 1 0 3 0 5 0 7 0 1 0 3 0 5 0 7
(2x - (x div 8))
A316837: 0 2 4 6 8 10 12 14 15 17 19 21 23 25 27 29
((x div 2) - (x div 8))
A073642: 0 0 1 1 2 2 3 3 3 3 4 4 5 5 6 6
(2x - (x mod 8))
A161673: 0 1 2 3 4 5 6 7 16 17 18 19 20 21 22 23
(x3 + ~8)
A259348: ~8 ~7 0 19 56 117 208 335 504 721 992 1323 1720 2189 2736 3367
8x3
A016743: 0 8 64 216 512 1000 1728 2744 4096 5832 8000 10648 13824 17576 21952 27000
(x3 div 8)
A081276: 0 0 1 3 8 15 27 42 64 91 125 166 216 274 343 421
(x - (2 * ((~x + 2) div 4)))
A192225: 0 1 2 5
A047269: 0 1 2 5 6 7 8 11 12 13 14 17 18 19 20 23
(x mod (2 - ((x div 4) mod 2)))
A288223: 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0
((x mod 2) - ((x div 4) mod 2))
A131851: 0 1 0 1 ~1 0 ~1 0 0 1 0 1 ~1 0 ~1 0
((2x + 2) - (x mod 4))
A047596: 2 3 4 5 10 11 12 13 18 19 20 21 26 27 28 29
(12x + 8)
A017617: 8 20 32 44 56 68 80 92 104 116 128 140 152 164 176 188
(4 + ((x2 + x) div 2))
A146968: 4 5 7
A145018: 4 5 7 10 14 19 25 32 40 49 59 70 82 95 109 124
(x2 div (2x + 8))
A233795-A155213: 0 0 0 0 1 1 1 2 2 3 3 4 4 4 5 5
((x2 mod (x + 4)) mod 2)
A219097: 0 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0
(4x3 + 8x2)
A258617: 0 12 64 180 384 700 1152 1764 2560 3564 4800 6292 8064 10140 12544 15300
(7x + 2)
A017005: 2 9 16 23 30 37 44 51 58 65 72 79 86 93 100 107
(2 + ((x + ~1) div (2 + (x div 2))))
A320065: 1 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3
(((x + ~1) div (2 + (x div 2))) mod 2)
A185115: 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1
(2 + ((x + ~2) div (2 + (x div 2))))
A077430: 1 1 2 2 2 2 2 3 3 3 3 3 3 3 3 3
((2x mod (2 + (x div 2))) mod 2)
A308074: 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1
(x - (x div (4 + (x div 2))))
A076946: 0 1 2 3 4 5 6 6 7 8 9 10 11 12 13 14
((2x + 2) - ((x div 2) mod 2))
A047495: 2 4 5 7 10 12 13 15 18 20 21 23 26 28 29 31
(((x2 + (x div 2)) div 2) div 2)
A038709: 0 0 1 2 4 6 9 13 17 21 26 31 37 43 50 58
(2 * ((2x + 2) - (x mod 2)))
A047406: 4 6 12 14 20 22 28 30 36 38 44 46 52 54 60 62
(4 * (2x - (x mod 2)))
A326781: 0 4 16 20 32 36 48 52 64 68 80 84 96 100 112 116
(((x + ~1) mod (2 + (x mod 2))) mod 2)
A285625-A283966: 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0
((1 - (x mod (2 + (x mod 2)))) div 2)
A133944: 0 0 0 0 0 ~1 0 0 0 0 0 ~1 0 0 0 0
(1 - ((x mod (2 + (x mod 2))) div 2))
A294934: 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1
((1 + (x div 4)) mod 4)
A133874: 1 1 1 1 2 2 2 2 3 3 3 3 0 0 0 0
(((x2 + x) div 2) mod 4)
A105198: 0 1 3 2 2 3 1 0 0 1 3 2 2 3 1 0
(4 * (x + (x div 3)))
A104235: 0 4 8 16 20 24 32 36 40 48 52 56 64 68 72 80
((x + (x div 4)) mod 4)
A159956-A053839: 0 1 2 3 1 2 3 0 2 3 0 1 3 0 1 2
((~x + (x div 4)) mod 4)
A287576: 0 3 2 1 1 0 3 2 2 1 0 3 3 2 1 0
(2x - ((~x + 2) div 4))
A022848: 0 2 4 7 9 11 13 16 18 20 22 25 27 29 31 34
(x - (4 * (~x + (x mod 2))))
A197652: 0 1 10 11 20 21 30 31 40 41 50 51 60 61 70 71
((x * (x2 div 2)) div 4)
A034828: 0 0 1 3 8 15 27 42 64 90 125 165 216 273 343 420
((x div 4) * (x div 4))
A295643: 0 0 0 0 1 1 1 1 4 4 4 4 9 9 9 9
((x mod 4) * (x div 4))
A257844: 0 0 0 0 0 1 2 3 0 2 4 6 0 3 6 9
(2x2 - (x div 4))
A293296: 0 2 8 18 31 49 71 97 126 160 198 240 285 335 389 447
(x + ((x div 2) + (x div 4)))
A047344: 0 1 3 4 7 8 10 11 14 15 17 18 21 22 24 25
((2x + 4) - (x mod 4))
A047566: 4 5 6 7 12 13 14 15 20 21 22 23 28 29 30 31
(4x2 + ~3x)
A001107: 0 1 10 27 52 85 126 175 232 297 370 451 540 637 742 855
(x2 - (x2 div 4))
A222010: 0 1 3 7
A077043: 0 1 3 7 12 19 27 37 48 61 75 91 108 127 147 169
(x4 + 4)
A057781: 4 5 20 85 260 629 1300 2405 4100 6565 10004 14645 20740 28565 38420 50629
4x4
A141046: 0 4 64 324 1024 2500 5184 9604 16384 26244 40000 58564 82944 114244 153664 202500
(x4 div 4)
A131479: 0 0 4 20 64 156 324 600 1024 1640 2500 3660 5184 7140 9604 12656
(10x + 4)
A017317: 4 14 24 34 44 54 64 74 84 94 104 114 124 134 144 154
(((~x + (2 mod (x + 1))) div 2) mod 2)
A296028: 0 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1
(2 * ((x + ((x div 2) mod 2)) div 2))
A201629: 0 0 2 4 4 4 6 8 8 8 10 12 12 12 14 16
((2 div ((x + ~2) + (x div 2))) mod 2)
A154281: 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
((x mod ((x + ~2) + (x div 2))) mod 2)
A160351: 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1
(x - (2 * ((~x + ~2) + (x mod 2))))
A047257: 4 5 10 11 16 17 22 23 28 29 34 35 40 41 46 47
(((~1 + (x div 2)) mod (x + 2)) mod 2)
A188189: 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0
(((2x + ~4) mod (x + 2)) mod 2)
A284683: 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 1
((((~x + 1) div 2) mod (x + 2)) div 2)
A257839: 0 0 1 2 2 2 2 3 3 3 3 4 4 4 4 5
(((2 - (x div 2)) div (x + 2)) mod 2)
A185116-A060287: 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1
(((x2 div 2) mod (x + 2)) mod 2)
A231600: 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0
(4x div (x + 4))
A072746: 0 0 1 1 2 2 2 2 2 2 2 2 3 3 3 3
(3x div (x + 4))
A339183-A287272-A211668-A062153: 0 0 1 1 1 1 1 1 2 2 2 2 2 2 2 2
(x - (x2 div (x + 4)))
A244317: 0 1 2 2 2 3 3 3 3 3 3 3 3 4 4 4
(2 * (2x + (x div 4)))
A276340: 0 4 8 12 18 22 26 30 36 40 44 48 54 58 62 66
((4x + 2) + (x div 2))
A193910: 2 6 11 15 20 24 29 33 38 42 47 51 56 60 65 69
((4x + 2) + (x mod 2))
A047524: 2 7 10 15 18 23 26 31 34 39 42 47 50 55 58 63
((4x + 2) - (x div 2))
A047276: 2 6 9 13 16 20 23 27 30 34 37 41 44 48 51 55
((4x + 2) - (x mod 2))
A047617: 2 5 10 13 18 21 26 29 34 37 42 45 50 53 58 61
(4x + (x2 div 2))
A271911: 0 4 10 16 24 32 42 52 64 76 90 104 120 136 154 172
(((x mod 3) * (x div 2)) mod 2)
A277148: 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0
((((x + ~1) div 2) * (x div 2)) div 2)
A130519: 0 0 0 0 1 2 3 4 6 8 10 12 15 18 21 24
(((x mod 4) + (x div 2)) div 2)
A246552: 0 0 1 2 1 1 2 3 2 2 3 4 3 3 4 5
(2 * (4x - (x div 2)))
A238290: 0 8 14 22 28 36 42 50 56 64 70 78 84 92 98 106
(((2 + (x mod 2)) * (x div 2)) div 2)
A226107: 0 0 1 1 2 3 3 4 4 6 5 7 6 9 7 10
(x - (((x mod 2) - (x div 2)) div 2))
A265430: 0 1 3 3 5 6 8 8 10 11 13 13 15 16 18 18
(2 - ((~x + 2) div (2 + (x div 2))))
A084506: 1 2 2 3 3 3 3 3 3 4 4 4 4 4 4 4
((x2 + 2x + 2) + (x div 2))
A171769: 2 5 11 18 28 39 53 68 86 105 127 150 176 203 233 264
(2 + ((x div 2) mod 2) - (x mod 2))
A157810: 2 1 3 2 2 1 3 2 2 1 3 2 2 1 3 2
(3x + ((x div 2) mod 2))
A319279: 0 3 7 10 12 15 19 22 24 27 31 34 36 39 43 46
(x + (x mod 2) - ((x div 2) mod 2))
A080412: 0 2 1 3 4 6 5 7 8 10 9 11 12 14 13 15
(((x2 + x) + (x div 2)) div 2)
A181947: 0 1 3 6 11 16
(2 * ((x2 + 2x) - (x div 2)))
A139596: 0 6 14 28 44 66 90 120 152 190 230 276 324 378 434 496
(2 + (5 * (x mod 2)))
A181284-A010697: 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7
(((x + 1) div (2 - (x mod 2))) div 2)
A124072: 0 1 0 2 1 3 1 4 2 5 2 6 3 7 3 8
(x - ((x + ~1) div (2 + (x mod 2))))
A226142: 1 1 2 3 3 4 4
((x div 4) mod (2 + (x mod 2)))
A277144: 0 0 0 0 1 1 1 1 0 2 0 2 1 0 1 0
((2 + (x mod 2)) * (2 + (x mod 2)))
A071793-A010714: 4 9 4 9 4 9 4 9 4 9 4 9 4 9 4 9
(x - (x2 mod (2 + (x mod 2))))
A213635: 0 0 2 3 4 4 6 6 8 9 10 10 12 12 14 15
(2 * ((x2 + 2x) + (x mod 2)))
A139598: 0 8 16 32 48 72 96 128 160 200 240 288 336 392 448 512
(x - (2 * (x div (x2 + ~2))))
A060858: 0 3 0 3 4 5 6
((x * (1 + (x mod 3))) div 2)
A119719: 0 1 3 1 4
14x
A008596: 0 14 28 42 56 70 84 98 112 126 140 154 168 182 196 210
((x2 + 5x) div 2)
A055998: 0 3 7 12 18 25 33 42 52 63 75 88 102 117 133 150
(8x2 + 2x)
A033585: 0 10 36 78 136 210 300 406 528 666 820 990 1176 1378 1596 1830
(8x2 + ~2x)
A033588-A014635: 0 6 28 66 120 190 276 378 496 630 780 946 1128 1326 1540 1770
((x + ((x + ~1) mod 3)) div 2)
A106251: 1 0 1 2 2 3 4 3 4 5 5 6 7 6 7 8
((x + 2) + (2x div 3))
A028738: 2 3 5 7 8 10 12 13 15 17 18 20 22 23
((x + 2) + (3 * (x div 2)))
A201363: 2 3 7
A233998-A047221: 2 3 7 8 12 13 17 18 22 23 27 28 32 33 37 38
((x + (3 * (x div 2))) div 2)
A187322: 0 0 2 3 5 5 7 8 10 10 12 13 15 15 17 18
((x + 2) + ((x div 2) div 3))
A316228: 2 3 4 5 6 7 9 10 11 12 13 14 16 17 18 19
((x + 2) + ((~x + 1) mod 3))
A105676: 3 3 6 6 6 9 9 9 12 12 12 15 15 15 18 18
((x + ((~x + 1) mod 3)) div 2)
A035307: 0 0 2 2 2 3
(x - (2 * (~x + (x div 3))))
A047281: 0 3 6 7 10 13 14 17 20 21 24 27 28 31 34 35
(x - (2 * (~x + (x mod 3))))
A281899: 0 1 2 9 10 11 18 19 20 27 28 29 36 37 38 45
((x * (x - (x mod 3))) div 2)
A213034: 0 0 0 4 6 7 18 21 24 40 45 49 72 78 84 112
((x3 + 3x) div 2)
A229183: 0 2 7 18 38 70 117 182 268 378 515 682 882 1118 1393 1710
(6x2 + 2x)
A033580: 0 8 28 60 104 160 228 308 400 504 620 748 888 1040 1204 1380
((3x2 + x) div 2)
A005449: 0 2 7 15 26 40 57 77 100 126 155 187 222 260 301 345
(6x2 + ~2x)
A033579: 0 4 20 48 88 140 204 280 368 468 580 704 840 988 1148 1320
((3x2 + ~x) div 2)
A000326: 0 1 5 12 22 35 51 70 92 117 145 176 210 247 287 330
((x + (x2 div 3)) div 2)
A301654: 0 0 1 3 4 6 9 11 14 18 21 25 30 34 39 45
((x + (x mod (1 + (x div 2)))) div 2)
A073719: 0 0 1 2 2 3 4 5 5 6 7 8 8 9 10 11
(4x3 + 2x)
A061804: 0 6 36 114 264 510 876 1386 2064 2934 4020 5346 6936 8814 11004 13530
(2x3 + ~2x2 + x)
A059722: 0 1 10 39 100 205 366 595 904 1305 1810 2431 3180 4069 5110 6315
(10x + 8)
A017365: 8 18 28 38 48 58 68 78 88 98 108 118 128 138 148 158
((x4 + x) div 2)
A027441: 0 1 9 42 130 315 651 1204 2052 3285 5005 7326 10374 14287 19215 25320
((x + 2) + (2 * (x div 3)))
A047202: 2 3 4 7 8 9 12 13 14 17 18 19 22 23 24 27
(2x * (~2 + (2 mod (x + 1))))
A124856: 0 ~4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
((x * ((x div ~2) mod 2)) div 2)
A338780: 0 0 1 0 0 2 3 0 0 4 5 0 0 6 7 0
((x + 2) + (x div 8))
A121603: 2 3 4 5 6 7 8 9 11
A183222-A014089: 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18
((x + (x div 8)) div 2)
A214656-A085268: 0 0 1 1 2 2 3 3 4 5 5 6 6 7 7 8
((x + 2) + (2 * (x div 4)))
A047247: 2 3 4 5 8 9 10 11 14 15 16 17 20 21 22 23
(x2 + 6x + 2)
A028881: 2 9 18 29 42 57 74 93 114 137 162 189 218 249 282 317
((x + ((x + ~1) mod 4)) div 2)
A106249: 1 0 1 2 3 2 3 4 5 4 5 6 7 6 7 8
(x - ((~x + ((x div 2) mod 2)) div 2))
A047229: 0 2 3 4 6 8 9 10 12 14 15 16 18 20 21 22
(x2 div (x - ((~x + 2) div 2)))
A330560: 0 1 2 2 3 3 4 4 5 6 7 7 8 8 9 10
(x - ((~x3 + 2x2) div 2))
A057566: 0 1 2 8 20 43 78 130 200 293 410 556 732 943 1190 1478
(3x2 + 2x + 2)
A141631: 2 7 18 35 58 87 122 163 210 263 322 387 458 535 618 707
(6x2 + 4x)
A202804: 0 10 32 66 112 170 240 322 416 522 640 770 912 1066 1232 1410
(3x2 + ~2x + 2)
A271740: 2 3 10 23 42 67 98 135 178 227 282 343 410 483 562 647
(6x2 + ~4x)
A139267: 0 2 16 42 80 130 192 266 352 450 560 682 816 962 1120 1290
(2x3 + 4x2 + 4x)
A071233: 0 10 40 102 208 370 600 910 1312 1818 2440 3190 4080 5122 6328 7710
(2 * (x + ((x div 2) * (x div 2))))
A266074: 0 2 6 8 16 18 30 32 48 50 70 72 96 98 126 128
(2x - ((x * (x div 2)) mod 2))
A047612: 0 2 4 5 8 10 12 13 16 18 20 21 24 26 28 29
(x3 + 3x2 + x + ~2)
A318765: ~2 3 20 55 114 203 328 495 710 979 1308 1703 2170 2715 3344 4063
(((x2 + x) div 2) mod (x + 2))
A119719: 0 1 3 1 4
A179820: 0 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1
(x4 + 4x3 + 4x2)
A099761: 0 9 64 225 576 1225 2304 3969 6400 9801 14400 20449 28224 38025 50176 65025
((x + 2) * (x div (2 - (x mod 2))))
A066830: 0 3 4 15 12 35 24 63 40 99 60 143 84 195 112 255
(2x - ((x + ~2) * (x div 2)))
A230564: 0 2 4 5 4
(2x + (3 * (x div 2)))
A047352: 0 2 7 9 14 16 21 23 28 30 35 37 42 44 49 51
(2x + ((~x + 1) mod 3))
A327258: 1 2 6 7 8 12 13 14 18 19 20 24 25 26 30 31
(2x + (x2 mod 3))
A047271: 0 3 5 6 9 11 12 15 17 18 21 23 24 27 29 30
((x mod 2) - (1 mod (~2x + 1)))
A192225: 0 1 2 5
A264120: 0 1 2 5 6 9 10 13 14 17 18 21 22 25 26 29
(2 - (2 div (2 div (~2x + 1))))
A113311: 1 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4
(2x + ((x mod 3) div 2))
A047267: 0 2 5 6 8 11 12 14 17 18 20 23 24 26 29 30
(2x + ((x mod 3) mod 2))
A047231: 0 3 4 6 9 10 12 15 16 18 21 22 24 27 28 30
(2x + ((x div ~2) mod 2))
A047444: 0 3 5 6 8 11 13 14 16 19 21 22 24 27 29 30
(2x + (((x + ~1) div 2) mod 2))
A047541: 1 2 4 7 9 10 12 15 17 18 20 23 25 26 28 31
(2x + ((x * (x div 2)) mod 2))
A047540: 0 2 4 7 8 10 12 15 16 18 20 23 24 26 28 31
((2x2 + ~2x) + (x mod 2))
A255840: 0 1 4 13 24 41 60 85 112 145 180 221 264 313 364 421
(x - (2x * (~x + (x mod 2))))
A276914: 0 1 10 15 36 45 78 91 136 153 210 231 300 325 406 435
((x div 5) + (x div 2))
A110532: 0 0 1 1 2 3 4 4 5 5 7 7 8 8 9 10
((x div 5) * (x div 2))
A110533: 0 0 0 0 0 2 3 3 4 4 10 10 12 12 14 21
((3x + 3) + (x div 2))
A047280: 3 6 10 13 17 20 24 27 31 34 38 41 45 48 52 55
((x2 mod 3) + (x div 2))
A105637: 0 1 2 1 3 3 3 4 5 4 6 6 6 7 8 7
((x - (x div ~2)) * (x div 2))
A032438: 0 0 3 5 12 16 27 33 48 56 75 85 108 120 147 161
((((x + 1) div 2) div 2) * (x div 2))
A159915: 0 0 0 1 2 2 3 6 8 8 10 15 18 18 21 28
(1 mod (8 - (x div 2)))
A296079-A228594: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0
(2 div (8 - (x div 2)))
A258186-A185226-A035587: 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 2
((4 * (x mod 2)) + (x div 2))
A168230: 0 4 1 5 2 6 3 7 4 8 5 9 6 10 7 11
(4x2 + (x div 2))
A173511: 0 4 17 37 66 102 147 199 260 328 405 489 582 682 791 907
((2x2 + x) + (x div 2))
A139593: 0 3 11 22 38 57 81 108 140 175 215 258 306 357 413 472
(x - ((~x + (x mod 2)) * (x div 2)))
A266725: 0 1 4 5 12 13 24 25 40 41 60 61 84 85 112 113
((1 + ((x div 2) mod 2)) * (x mod 2))
A131743: 0 1 0 2 0 1 0 2 0 1 0 2 0 1 0 2
(6x + (x mod 2))
A272975: 0 7 12 19 24 31 36 43 48 55 60 67 72 79 84 91
(3x2 + (x mod 2))
A278211: 0 4 12 28 48 76
((4x + 4) - (x mod 2))
A047535: 4 7 12 15 20 23 28 31 36 39 44 47 52 55 60 63
((2 * (x div 4)) - (x mod 2))
A226279: 0 ~1 0 ~1 2 1 2 1 4 3 4 3 6 5 6 5
(((x div 4) mod 2) + (x mod 2))
A345021-A215604-A139351: 0 1 0 1 1 2 1 2 0 1 0 1 1 2 1 2
((x + 3) div (2 - (x mod 2)))
A097362: 1 4 2 6 3 8 4 10 5 12 6 14 7 16 8 18
(((x div 2) * (x div 2)) - (x mod 2))
A131805: 0 ~1 1 0 4 3 9 8 16 15 25 24 36 35 49 48
(1 - (2 mod ((~x + 1) - (x mod 2))))
A140839: 1 1 1 2 2 4
((~x2 + ~2x + 1) - (x mod 2))
A141354: 1 ~3 ~7 ~15 ~23 ~35 ~47 ~63 ~79 ~99 ~119 ~143 ~167 ~195 ~223 ~255
(5x2 div 2)
A032526: 0 2 10 22 40 62 90 122 160 202 250 302 360 422 490 562
((x4 + x2) div 2)
A037270: 0 1 10 45 136 325 666 1225 2080 3321 5050 7381 10440 14365 19306 25425
((x * (x + (2 * (x mod 2)))) div 2)
A213037: 0 1 2 7 8 17 18 31 32 49 50 71 72 97 98 127
(x4 + 2x2 + 2)
A178390: 2 5 26 101 290 677 1370 2501 4226 6725 10202 14885 21026 28901 38810 51077
(2x2 + 16)
A255847: 16 18 24 34 48 66 88 114 144 178 216 258 304 354 408 466
(1 - (2 mod (~2x2 + 1)))
A068941: 1 1 6 16
(x - (x mod (1 - (x2 div 2))))
A295484: 0 1 2 3 7
13x
A008595: 0 13 26 39 52 65 78 91 104 117 130 143 156 169 182 195
11x
A059632-A008593: 0 11 22 33 44 55 66 77 88 99 110 121 132 143 154 165
(6x2 + x)
A049453: 0 7 26 57 100 155 222 301 392 495 610 737 876 1027 1190 1365
(6x2 + ~x)
A049452: 0 5 22 51 92 145 210 287 376 477 590 715 852 1001 1162 1335
(4x2 + 3x)
A033954: 0 7 22 45 76 115 162 217 280 351 430 517 612 715 826 945
(x3 + 3x2 + 3x)
A068601: 0 7 26 63 124 215 342 511 728 999 1330 1727 2196 2743 3374 4095
(2x3 + 2x2 + x)
A048395: 0 5 26 75 164 305 510 791 1160 1629 2210 2915 3756 4745 5894 7215
(x4 + x3 + x)
A100606: 0 3 26 111 324 755 1518 2751 4616 7299 11010 15983 22476 30771 41174 54015
(x + (x div 7))
A335513-A047421-A037474-A022551-A004777-A000378: 0 1 2 3 4 5 6 8 9 10 11 12 13 14 16 17
(2x2 + 7x)
A130861: 0 9 22 39 60 85 114 147 184 225 270 319 372 429 490 555
17x
A161440-A008599: 0 17 34 51 68 85 102 119 136 153 170 187 204 221 238 255
(x + (x div 9))
A235034-A191845-A043094-A031994-A023803-A023751-A020663-A007095-A004774-A004745-A004728: 0 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16
(x2 + 7x)
A028563: 0 8 18 30 44 60 78 98 120 144 170 198 228 260 294 330
(2x2 + 9x)
A139576: 0 11 26 45 68 95 126 161 200 243 290 341 396 455 518 585
(8x2 + x)
A139275: 0 9 34 75 132 205 294 399 520 657 810 979 1164 1365 1582 1815
(8x2 + ~x)
A139274: 0 7 30 69 124 195 282 385 504 639 790 957 1140 1339 1554 1785
(x + ((x + 1) div 5))
A047256-A039252: 0 1 2 3 5 6 7 8 9 11 12 13 14 15 17 18
(x + (2x div 5))
A097506-A047381-A001951: 0 1 2 4 5 7 8 9 11 12 14 15 16 18 19 21
(x + ((x div 2) div 5))
A103303: 0 1 2 3 4 5 6 7 8 9
A342851-A328781-A239016-A226134-A171397-A132781-A131058-A118764-A072544-A065039-A063742-A055572-A055571-A055570-A043095-A023804-A009994-A004746: 0 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16
(x + (2 mod (1 + (x div 4))))
A084690: 0 1 2 3 4 5 6 7 10
A272576-A039269-A039207-A039155-A007094-A000433: 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17
(4x3 + x)
A317297: 0 5 34 111 260 505 870 1379 2056 2925 4010 5335 6924 8801 10990 13515
(4x3 + ~x)
A035328: 0 3 30 105 252 495 858 1365 2040 2907 3990 5313 6900 8775 10962 13485
(7x + 3)
A017017: 3 10 17 24 31 38 45 52 59 66 73 80 87 94 101 108
(x + (3 * (1 + (x div 2))))
A047204: 3 4 8 9 13 14 18 19 23 24 28 29 33 34 38 39
(3x2 + x + 3)
A295089: 3 7 17 33 55 83 117 157 203 255 313 377 447 523 605 693
(7x + 6)
A017053: 6 13 20 27 34 41 48 55 62 69 76 83 90 97 104 111
(x + (((x + 1) div 2) div 3))
A047303: 0 1 2 3 4 6 7 8 9 10 11 13 14 15 16 17
(~x + 24)
A022980: 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9
(x + (x div 12))
A103303: 0 1 2 3 4 5 6 7 8 9
A343268-A325202-A247762-A130572-A107909-A084176-A031996-A023805-A023753: 0 1 2 3 4 5 6 7 8 9 10 11 13 14 15 16
(x + (3 * (x div 4)))
A295484: 0 1 2 3 7
A047361: 0 1 2 3 7 8 9 10 14 15 16 17 21 22 23 24
(x + ((2 * (x div 2)) div 3))
A047450-A039073: 0 1 2 3 5 6 8 9 10 11 13 14 16 17 18 19
(x + (3 * (x + (x mod 2))))
A047521: 0 7 8 15 16 23 24 31 32 39 40 47 48 55 56 63
(x + ((x + (x mod 2)) div 3))
A047498-A039069: 0 1 2 4 5 7 8 9 10 12 13 15 16 17 18 20
(x * (1 + ((x2 + ~2x) div 2)))
A323724: 0 0 2 6 20 40 78 126 200 288 410 550 732 936 1190 1470
(5x2 + x)
A202803: 0 6 22 48 84 130 186 252 328 414 510 616 732 858 994 1140
(x3 + 3x2 + ~x)
A064043: 0 3 18 51 108 195 318 483 696 963 1290 1683 2148 2691 3318 4035
(x2 + 9x)
A028569: 0 10 22 36 52 70 90 112 136 162 190 220 252 286 322 360
(x + (x mod (~1 + (x * (x div 2)))))
A294369: 0 1 2 4 8 10
(x + ((x + 1) * (2 mod (x + 1))))
A061570: 0 1 8 11 14 17 20 23 26 29 32 35 38 41 44 47
(9x + 8)
A017257: 8 17 26 35 44 53 62 71 80 89 98 107 116 125 134 143
(2x2 + 7x + 4)
A091823: 4 13 26 43 64 89 118 151 188 229 274 323 376 433 494 559
(x3 + x2 + 3x + 2)
A270109: 2 7 20 47 94 167 272 415 602 839 1132 1487 1910 2407 2984 3647
(x3 + ~3x2 + 4x)
A242659: 0 2 4 12 32 70 132 224 352 522 740 1012 1344 1742 2212 2760
(x5 + x)
A131471: 0 2 34 246 1028 3130 7782 16814 32776 59058 100010 161062 248844 371306 537838 759390
(x5 + ~x)
A061167: 0 0 30 240 1020 3120 7770 16800 32760 59040 99990 161040 248820 371280 537810 759360
(x + (x mod 10))
A230099: 0 2 4 6 8 10 12 14 16 18 10 12 14 16 18 20
(x * (x mod 10))
A098736-A063462: 0 1 4 9 16 25 36 49 64 81 0 11 24 39 56 75
(x + (2 * (x div 5)))
A047337-A039049-A037466: 0 1 2 3 4 7 8 9 10 11 14 15 16 17 18 21
(~x + (2 * (x mod 5)))
A073792: 0 1 2 3 4 ~5 ~4 ~3 ~2 ~1 ~10 ~9 ~8 ~7 ~6 ~15
(3x2 + 8x)
A140677: 0 11 28 51 80 115 156 203 256 315 380 451 528 611 700 795
(x + (2 * (2x div 3)))
A047347: 0 1 4 7 8 11 14 15 18 21 22 25 28 29 32 35
(x + (2 * ((x div 2) div 3)))
A047602-A039076-A037471: 0 1 2 3 4 5 8 9 10 11 12 13 16 17 18 19
(x + (2 * (2 mod (1 + (x div 2)))))
A161641: 0 1 2 3 8 9 10 11 12 13 14 15 16 17 18 19
(x + ((x mod (1 + (x div 2))) div 2))
A172269-A087066-A045774-A045681-A020656: 0 1 2 3 4 6 7 8 9 11 12 13 14 16 17 18
(x + ((x2 + 3x + 2) div 2))
A058759: 1 4 8 13
A034856: 1 4 8 13 19 26 34 43 53 64 76 89 103 118 134 151
(x + 20)
A008553: 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
(~x + 20)
A022976: 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5
(~x + (2 * (x mod 6)))
A073793: 0 1 2 3 4 5 ~6 ~5 ~4 ~3 ~2 ~1 ~12 ~11 ~10 ~9
(x + (4 * (x div 3)))
A047354: 0 1 2 7 8 9 14 15 16 21 22 23 28 29 30 35
(9x + 4)
A017209: 4 13 22 31 40 49 58 67 76 85 94 103 112 121 130 139
(7x + 4)
A017029: 4 11 18 25 32 39 46 53 60 67 74 81 88 95 102 109
(x + (2 * (2 + (2 mod (x + 1)))))
A177711-A115945: 4 5 10 11 12 13 14 15 16 17 18 19 20 21 22 23
(x + 32)
A115421: 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
(~x + 32)
A022988: 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17
(1 mod (~x + 16))
A340369-A307430-A194325-A025451: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
(2 div (~x + 16))
A332640-A325719-A325649-A297238: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2
(~x + (2 * (x mod 8)))
A073795: 0 1 2 3 4 5 6 7 ~8 ~7 ~6 ~5 ~4 ~3 ~2 ~1
(x + (4 * (2 + (x div 2))))
A174041: 8 9 14 15 20 21 26 27 32 33 38 39 44 45 50 51
(x + (x div ~7))
A172475: 0 0 1 2 3 4 5 6 6 7 8 9 10 11 12 12
(x + ((x - (x div 4)) div 2))
A063732: 0 1 3 4 5 7 8 10 11 12 14 15 16 18 19 21
(x + (x div (4 + (x div 2))))
A052419-A004726: 0 1 2 3 4 5 6 8 9 10 11 12 13 14 15 16
(x + ((x - ((x div 2) mod 2)) div 2))
A047237: 0 1 2 4 6 7 8 10 12 13 14 16 18 19 20 22
(5x2 + ~4x)
A051624: 0 1 12 33 64 105 156 217 288 369 460 561 672 793 924 1065
(x + ((x2 + 2x) div 4))
A079524: 0 1 4 6 10 13 18 22 28 33 40 46 54 61 70 78
(x4 + 4x)
A180354: 0 5 24 93 272 645 1320 2429 4128 6597 10040 14685 20784 28613 38472 50685
(2x2 + 3x + 4)
A100037: 4 9 18 31 48 69 94 123 156 193 234 279 328 381 438 499
(x * (~2 + ((x2 + ~x) div 2)))
A341768: 0 ~2 ~2 3 16 40 78 133 208 306 430 583 768 988 1246 1545
(x + ((x2 + 4x + 4) div 2))
A125622: 2 5 10 15 22
(5x2 + ~2x)
A147874: 0 3 16 39 72 115 168 231 304 387 480 583 696 819 952 1095
(x * ((x2 + 2) + (x mod 2)))
A020875: 0 4 12 36 72 140 228 364 528 756 1020 1364 1752 2236 2772 3420
(5x2 + 2x)
A168668: 0 7 24 51 88 135 192 259 336 423 520 627 744 871 1008 1155
(x4 + x2 + 2x)
A054603: 0 4 24 96 280 660 1344 2464 4176 6660 10120 14784 20904 28756 38640 50880
(x2 + 10x)
A098603: 0 11 24 39 56 75 96 119 144 171 200 231 264 299 336 375
(x + (2 * (x + ((x div 2) mod 2))))
A108752: 0 3 8 11 12 15 20 23 24 27 32 35 36 39 44 47
(x + ((x + ((x div 2) mod 2)) div 2))
A047273: 0 1 3 5 6 7 9 11 12 13 15 17 18 19 21 23
(2 - (1 mod (~3x + 4)))
A145441: 1 2 3 6 9 12 15 18 21 24
(x + (4x div (x + 2)))
A139283: 0 2 4 5 6 7 9 10 11 12 13 14 15 16 17 18
(2x3 + ~3x2)
A015238: 0 ~1 4 27 80 175 324 539 832 1215 1700 2299 3024 3887 4900 6075
(x + (5 * (x div 2)))
A047274: 0 1 7 8 14 15 21 22 28 29 35 36 42 43 49 50
(x + ((2x + 1) * (x div 2)))
A074377: 0 1 7 10 22 27 45 52 76 85 115 126 162 175 217 232
(x5 + ~2x)
A242436: 0 ~1 28 237 1016 3115 7764 16793 32752 59031 99980 161029 248808 371267 537796 759345
7x2
A033582: 0 7 28 63 112 175 252 343 448 567 700 847 1008 1183 1372 1575
(2x3 + 3x2)
A275709: 0 5 28 81 176 325 540 833 1216 1701 2300 3025 3888 4901 6076 7425
(2x3 + 5x2)
A163683: 0 7 36 99 208 375 612 931 1344 1863 2500 3267 4176 5239 6468 7875
(2x3 + ~5x2)
A015240: 0 ~3 ~4 9 48 125 252 441 704 1053 1500 2057 2736 3549 4508 5625
(x2 + 12x)
A098847: 0 13 28 45 64 85 108 133 160 189 220 253 288 325 364 405
(~x2 + 12x)
A257401: 0 11 20
(3x3 + x2)
A294315: 0 4 28 90 208 400 684 1078 1600 2268 3100 4114 5328 6760 8428 10350
(2x4 + ~x2)
A002593: 0 1 28 153 496 1225 2556 4753 8128 13041 19900 29161 41328 56953 76636 101025
(x4 + ~x3 + x2)
A309372: 0 1 12 63 208 525 1116 2107 3648 5913 9100 13431 19152 26533 35868 47475
(x4 + x3 + x2)
A100019: 0 3 28 117 336 775 1548 2793 4672 7371 11100 16093 22608 30927 41356 54225
(x4 + ~x3 + ~x2)
A132998: 0 ~1 4 45 176 475 1044 2009 3520 5751 8900 13189 18864 26195 35476 47025
(5x2 + 4x)
A135705: 0 9 28 57 96 145 204 273 352 441 540 649 768 897 1036 1185
(x5 + ~x2)
A135497: 0 0 28 234 1008 3100 7740 16758 32704 58968 99900 160930 248688 371124 537628 759150
(x2 + 16x)
A098849: 0 17 36 57 80 105 132 161 192 225 260 297 336 377 420 465
(x3 + 6x2)
A126562: 0 7 32 81 160 275 432 637 896 1215 1600 2057 2592 3211 3920 4725
(x2 + 12)
A241748: 12 13 16 21 28 37 48 61 76 93 112 133 156 181 208 237
(x2 + (2x div 3))
A240438: 0 1 5 11 18 28 40 53 69 87 106 128 152 177 205 235
(x2 + 16)
A241751: 16 17 20 25 32 41 52 65 80 97 116 137 160 185 212 241
(x2 + (x2 div 4))
A032527: 0 1 5 11 20 31 45 61 80 101 125 151 180 211 245 281
(1 - (4 mod (~x2 + 2)))
A048873: 1 1 1 4 11
x6
A001014: 0 1 64 729 4096 15625 46656 117649 262144 531441 1000000 1771561 2985984 4826809 7529536 11390625
(~x5 + 1)
A024003: 1 0 ~31 ~242 ~1023 ~3124 ~7775 ~16806 ~32767 ~59048 ~99999 ~161050 ~248831 ~371292 ~537823 ~759374
(if (if (x mod 4) <= 0 then x else 0) <= 0 then 1 else 0)
A345008: 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1
(if (if (x + ~2) <= 0 then x else (x mod 2)) <= 0 then 1 else 0)
A267043: 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0
(loop(\(x,i).2x,x,2) + (if x <= 0 then 1 else 0))
A198633: 3 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536
loop(\(x,i).(2x + 2),x,(if x <= 0 then 1 else 0))
A095121: 1 2 6 14 30 62 126 254 510 1022 2046 4094 8190 16382 32766 65534
loop(\(x,i).(2x + 4),x,(if x <= 0 then 1 else 0))
A269712-A173033: 1 4 12 28 60 124 252 508 1020 2044 4092 8188 16380 32764 65532 131068
(if x <= 0 then 1 else (if (x + ~1) <= 0 then 4 else 0))
A274981: 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (x + ~2) <= 0 then (if x <= 0 then 1 else 4) else 0)
A175372: 1 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (x + ~2) <= 0 then (if x <= 0 then 1 else 2x) else 0)
A166926: 1 2 4 0 0 0 0 0 0 0 0 0 0 0 0 0
loop(\(x,i).(~1 + (if x <= 0 then i else x)),2x,0)
A261693: 0 1 3 1 7 5 3 1 15 13 11 9 7 5 3 1
loop(\(x,i).2x,x,(1 - (if x <= 0 then 2 else 0)))
A171449: ~1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768
(loop(\(x,i).2x,x,1) + (if x <= 0 then 2 else 0))
A171559: 3 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768
loop(\(x,i).loop(\(x,i).4x,x,1),x,0)
A114561: 0 1 4 256 4611686018427387903
loop(\(x,i).((x + 1) * (if x <= 0 then 1 else 2)),x,0)
A296953: 0 1 4 10 22 46 94 190 382 766 1534 3070 6142 12286 24574 49150
loop(\(x,i).(if (x + ~1) <= 0 then i else (x + ~1)),x,0)
A341707: 0 1 2 1 4 3 2 1 8 7 6 5 4 3 2 1
loop(\(x,i).(1 + loop(\(x,i).2x,i,x)),x,0)
A076131: 0 1 5 41 657 21025 1345601 172236929 44092653825 22575438758401 23117249288602625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x - loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0))
A006257: 0 1 1 3 1 3 5 7 1 3 5 7 9 11 13 15
loop(\(x,i).(2x + (if x <= 0 then 1 else x)),x,0)
A088110: 0 1 3 9
A140429: 0 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969
loop(\(x,i).(if x <= 0 then 1 else (2 + (x * i))),x,0)
A296943: 0 1 4 14 58 292 1754 12280 98242 884180 8841802 97259824 1167117890 15172532572 212415456010 3186231840152
loop(\(x,i).(x + loop(\(x,i).2x,x,1)),x,0)
A034797: 0 1 3 11 2059
loop(\(x,i).(x + loop(\(x,i).(x * i),i,1)),x,0)
A088110: 0 1 3 9
A180632: 0 1 3 9 33 153
A007489: 0 1 3 9 33 153 873 5913 46233 409113 4037913 43954713 522956313 6749977113 93928268313 1401602636313
loop(\(x,i).(~x + loop(\(x,i).(x * i),i,1)),x,0)
A005165: 0 1 1 5 19 101 619 4421 35899 326981 3301819 36614981 442386619 5784634181 81393657019 1226280710981
loop(\(x,i).(x + (if (~x + i) <= 0 then 0 else i)),x,0)
A003817: 0 1 3 3 7 7 7 7 15 15 15 15 15 15 15 15
(1 + (if (x mod 2) <= 0 then (if x <= 0 then 0 else 2) else 0))
A153284: 1 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1
(if (x mod 2) <= 0 then (if x <= 0 then 1 else 2) else ~1)
A280193: 1 ~1 2 ~1 2 ~1 2 ~1 2 ~1 2 ~1 2 ~1 2 ~1
(1 + loop(\(x,i).(if x <= 0 then i else (x + ~1)),x,0))
A080079: 1 2 1 4 3 2 1 8 7 6 5 4 3 2 1 16
(1 + loop(\(x,i).(2 * (if x <= 0 then 1 else x)),x,0))
A083318: 1 3 5 9 17 33 65 129 257 513 1025 2049 4097 8193 16385 32769
loop(\(x,i).2x,(if (x mod 2) <= 0 then x else 0),1)
A059222: 1 1 4 1 16 1 64 1 256 1 1024 1 4096 1 16384 1
((if (x mod 2) <= 0 then x else 1) + (if x <= 0 then 0 else 1))
A007389: 0 2 3 2 5 2 7 2 9 2 11 2 13 2 15 2
loop(\(x,i).(x * i),(x + ~1),(if x <= 0 then 0 else 1))
A104150: 0 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200
loop(\(x,i).2x,(x + ~2),(if x <= 0 then 0 else 1))
A166444: 0 1 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192
loop(\(x,i).2x,(x div 2),(if x <= 0 then 0 else 1))
A131572: 0 1 2 2 4 4 8 8 16 16 32 32 64 64 128 128
(loop(\(x,i).x2,x,2) + (if x <= 0 then 0 else 1))
A290200-A269834: 2 5 17 257 65537
loop(\(x,i).(x * i),loop(\(x,i).2x,x,1),1)
A000722: 1 2 24 40320 20922789888000 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).loop(\(x,i).2x,i,x),x,1))
A126884: 2 3 9 65 1025 32769 2097153 268435457 68719476737 35184372088833 36028797018963969 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).loop(\(x,i).2x,i,x),x,1))
A126883: 0 1 7 63 1023 32767 2097151 268435455 68719476735 35184372088831 36028797018963967 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).loop(\(x,i).(x * i),i,x),x,1))
A019515: 2 2 3 13 289 34561 24883201 125411328001 5056584744960001 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).loop(\(x,i).(x * i),i,x),x,1))
A030428: 0 0 1 11 287 34559 24883199 125411327999 5056584744959999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if ((if x <= 0 then 1 else x) mod 3) <= 0 then 2 else 1)
A100063: 1 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2
(if (x mod 4) <= 0 then (if x <= 0 then 1 else 2) else 1)
A277872-A164115-A107453: 1 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1
(if (x mod 2) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1)
A040005: 2 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1
loop(\(x,i).loop(\(x,i).2x,x,1),x,3)
A162185: 3 8 256 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,i,x),x,3)
A060377: 3 9 6561 4611686018427387903
(if (x mod 2) <= 0 then ((if x <= 0 then 2 else x) div 2) else 1)
A177815: 1 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1
(1 + loop(\(x,i).loop(\(x,i).x2,i,x),x,2))
A101331: 3 5 257 4611686018427387903
(if x <= 0 then 0 else (1 + (if (x mod 2) <= 0 then 1 else x)))
A275365: 0 2 2 4 2 6 2 8 2 10 2 12 2 14 2 16
loop(\(x,i).(1 + loop(\(x,i).2x,i,x)),x,1)
A318165: 1 3 13
A182104: 1 3 13 105 1681 53793 3442753 440672385 112812130561
A073587: 1 3 13 105 1681 53793 3442753 440672385 112812130561 57759810847233 59146046307566593 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * i),(x * i),1),x,1)
A000197: 1 1 2 720 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,(x div 2),2),x,1)
A271552: 1 2 4 16 4611686018427387903
loop(\(x,i).(2 + (if (~x + i) <= 0 then 0 else x)),x,1)
A152423: 1 2 2 4 2 4 6 8 2 4 6 8 10 12 14 16
loop(\(x,i).(if (~x + i) <= 0 then 1 else (x + 2)),x,1)
A323555-A323553: 1 1 3 1 3 5 7 1 3 5 7 9 11 13 15 1
loop(\(x,i).x2,x,loop(\(x,i).2x,x,1))
A057156: 1 4 256 16777216 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + i),x,loop(\(x,i).2x,x,1))
A132109: 1 3 7 14 26 47 85 156 292 557 1079 2114 4174 8283 16489 32888
loop(\(x,i).(x - i),x,loop(\(x,i).2x,x,1))
A014833: 1 1 1 2 6 17 43 100 220 467 969 1982 4018 8101 16279 32648
loop(\(x,i).(if (~x + i) <= 0 then x else 2x),x,1)
A098820: 1 1 2 4 4 8 8 8 8 16 16 16 16 16 16 16
loop(\(x,i).(if (x + ~2) <= 0 then i else 2x),x,1)
A098011: 1 1 2 3 6 12 24 48 96 192 384 768 1536 3072 6144 12288
loop(\(x,i).loop(\(x,i).2x,i,2x),x,1)
A036442: 1 4 32 512 16384 1048576 134217728 34359738368 17592186044416 18014398509481984 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,i,2x),x,1)
A079682: 1 4 4096 4611686018427387903
loop(\(x,i).loop(\(x,i).((x + 1) * i),x,2),x,1)
A071107: 1 3 27 4611686018427387903
loop(\(x,i).loop(\(x,i).2x,i,x),x,(x + 1))
A095340: 1 4 24 256 5120 196608 14680064 2147483648 618475290624 351843720888320 396316767208603648 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * i),i,x),x,(x + 1))
A096313: 1 2 6 48 1440 207360 174182400 1003290624000 45509262704640000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (x - i) <= 0 then x else 0)),x,1)
A296613-A062383: 1 2 4 4 8 8 8 8 16 16 16 16 16 16 16 16
loop(\(x,i).(x + (if (i mod 2) <= 0 then x else 1)),x,1)
A083416: 1 2 4 5 10 11 22 23 46 47 94 95 190 191 382 383
loop(\(x,i).(x + loop(\(x,i).(x * i),x,1)),x,1)
A329063: 1 2 4 28 4611686018427387903
loop(\(x,i).(x + (if (i mod 2) <= 0 then x else 2)),x,1)
A123208: 1 3 6 8 16 18 36 38 76 78 156 158 316 318 636 638
loop(\(x,i).(x * (if (i mod 2) <= 0 then i else 2)),x,1)
A222011: 1 2 4 8
A307611: 1 2 4 8 32
A271216: 1 2 4 8 32 64 384 768 6144 12288 122880 245760 2949120 5898240 82575360 165150720
loop(\(x,i).loop(\(x,i).(x * i),(2 * i),x),x,1)
A137592-A098694: 1 2 48 34560 1393459200 5056584744960000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(x * i),i,2)),x,1)
A066237: 1 3 7 19 67 307 1747 11827 92467 818227 8075827 87909427 1045912627 13499954227 187856536627 2803205272627
loop(\(x,i).(~1 + (if x <= 0 then i else x)),x2,1)
A334042: 1 0 3 6 15 6 27 14 63 46 27 6 111 86 59 30
loop(\(x,i).(x + (if (x mod 2) <= 0 then 1 else x)),x,1)
A075427: 1 2 3 6 7 14 15 30 31 62 63 126 127 254 255 510
loop(\(x,i).(x + (if (i mod 2) <= 0 then 2 else x)),x,1)
A222011: 1 2 4 8
A099942: 1 2 4 8 10 20 22 44 46 92 94 188 190 380 382 764
loop(\(x,i).(x + loop(\(x,i).2x,i,x)),x,1)
A028362: 1 3 15 135 2295 75735 4922775 635037975 163204759575 83724041661975 85817142703524375 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + loop(\(x,i).2x,i,x)),x,1)
A005329: 1 1 3 21 315 9765 615195 78129765 19923090075 10180699028325 10414855105976475 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (if (i mod 2) <= 0 then 2 else i)),x,1)
A081125: 1 1 2 6 12 60 120 840 1680 15120 30240 332640 665280 8648640 17297280 259459200
loop(\(x,i).loop(\(x,i).(2x * i),i,x),x,1)
A108400: 1 2 16 768 294912 1132462080 52183852646400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((if x <= 0 then 1 else 0) - (x * i)),x,1)
A009179: 1 ~1 3 ~9 37 ~185 1111 ~7777 62217 ~559953 5599531 ~61594841 739138093 ~9608795209 134523132927 ~2017846993905
loop(\(x,i).(x + i),x,loop(\(x,i).(x * i),x,1))
A101292: 1 2 5 12 34 135 741 5068 40356 362925 3628855 39916866 479001678 6227020891 87178291305 1307674368120
loop(\(x,i).loop(\(x,i).(x * i),i,(x * i)),x,1)
A152653: 1 1 4 72 6912 4147200 17915904000 632073093120000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * (i * i)),i,x),x,1)
A055209: 1 1 4 144 82944 1194393600 619173642240000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).2x,(i * i),x),x,1)
A185995: 1 2 32 16384 1073741824 36028797018963968 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * i),(i * i),x),x,1)
A255322: 1 1 24 8709120 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(loop(\(x,i).(x * i),x,1) + i),x,1)
A189896: 1 2 4 27
A264930: 1 2 4 27 4611686018427387903
loop(\(x,i).(loop(\(x,i).2x,i,x) + i),x,1)
A180435: 1 3 14 115 1844 59013 3776838 483435271 123759429384 63364827844617 64885583712887818 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 2) <= 0 then (if x <= 0 then 1 else 2) else ~2)
A280560: 1 ~2 2 ~2 2 ~2 2 ~2 2 ~2 2 ~2 2 ~2 2 ~2
(2 + loop(\(x,i).(2 * (if x <= 0 then 1 else x)),x,0))
A133140: 2 4 6 10 18 34 66 130 258 514 1026 2050 4098 8194 16386 32770
(2 + loop(\(x,i).loop(\(x,i).x2,x,2),x,0))
A275000: 2 4 18 4611686018427387903
loop(\(x,i).x2,(x + ~2),(if x <= 0 then 0 else 2))
A171163: 0 2 2 4 16 256 65536 4294967296 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,(if (x + ~2) <= 0 then 1 else 2))
A171381: 1 2 4 16 32 64
(if x <= 0 then 1 else (2 * (if (x + ~2) <= 0 then x else 1)))
A077748: 1 2 4 2 2
loop(\(x,i).2x,(x + ~2),(if x <= 0 then 1 else 2))
A090129: 1 2 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384
loop(\(x,i).x2,(x + ~2),(if x <= 0 then 1 else 2))
A165420: 1 2 2 4 16 256 65536 4294967296 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x + 1),x,(if x <= 0 then 1 else 2))
A052940: 1 5 11 23 47 95 191 383 767 1535 3071 6143 12287 24575 49151 98303
((if (x mod 2) <= 0 then 1 else x) * (if x <= 0 then 1 else 2))
A266722: 1 2 2 6 2 10 2 14 2 18 2 22 2 26 2 30
loop(\(x,i).(2x + 2),x,(if x <= 0 then 1 else 2))
A134067: 1 6 14 30 62 126 254 510 1022 2046 4094 8190 16382 32766 65534 131070
loop(\(x,i).4x,x,(if x <= 0 then 1 else 2))
A081654: 1 8 32 128 512 2048 8192 32768 131072 524288 2097152 8388608 33554432 134217728 536870912 2147483648
loop(\(x,i).(2x * i),x,(if x <= 0 then 1 else 2))
A032184: 1 4 16 96 768 7680 92160 1290240 20643840 371589120 7431782400 163499212800 3923981107200 102023508787200 2856658246041600 85699747381248000
loop(\(x,i).3x,x,(if x <= 0 then 1 else 2))
A099856: 1 6 18 54 162 486 1458 4374 13122 39366 118098 354294 1062882 3188646 9565938 28697814
loop(\(x,i).(x + (i * i)),x,(if x <= 0 then 1 else 2))
A179904: 1 3 7 16 32 57 93 142 206 287 387 508 652 821 1017 1242
loop(\(x,i).2x,x,(2 + (if x <= 0 then 1 else 2)))
A171497: 3 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072
loop(\(x,i).2x,x,(if x <= 0 then 1 else 4))
A146541: 1 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072
(if x <= 0 then 1 else (2 + loop(\(x,i).2x,x,2)))
A134351: 1 6 10 18 34 66 130 258 514 1026 2050 4098 8194 16386 32770 65538
loop(\(x,i).loop(\(x,i).(2x + 1),x,0),x,2)
A201363: 2 3 7
A007013: 2 3 7 127 4611686018427387903
loop(\(x,i).(~1 + (if x <= 0 then (2 * i) else x)),x,2)
A171960: 2 1 0 5 4 3 2 1 0 17 16 15 14 13 12 11
(if x <= 0 then 1 else (2 * (2 div (if x <= 0 then 1 else x))))
A167891: 1 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0
loop(\(x,i).2x,x,((if x <= 0 then 1 else x) mod 2))
A103424: 1 2 0 8 0 32 0 128 0 512 0 2048 0 8192 0 32768
loop(\(x,i).(x + (if (i mod 2) <= 0 then x else 1)),x,2)
A066880: 2 3 6 7 14 15 30 31 62 63 126 127 254 255 510 511
loop(\(x,i).(x + (if (2 - i) <= 0 then x else 1)),x,2)
A042950: 2 3 6 12 24 48 96 192 384 768 1536 3072 6144 12288 24576 49152
loop(\(x,i).(x + loop(\(x,i).x2,i,2)),x,2)
A060803: 2 6 22 278 65814 4295033110 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + loop(\(x,i).x2,i,2)),x,2)
A325912: 2 2 14 242 65294 4294902002 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (~2 + i) <= 0 then 2 else x)),x,2)
A058764: 2 4 6 12 24 48 96 192 384 768 1536 3072 6144 12288 24576 49152
loop(\(x,i).2x,x,loop(\(x,i).x2,x,2))
A073113: 2 8 64 2048 1048576 137438953472 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (~2 + i) <= 0 then i else x)),x,2)
A257113: 2 3 5 10 20 40 80 160 320 640 1280 2560 5120 10240 20480 40960
loop(\(x,i).(x + loop(\(x,i).(x * i),i,x)),x,2)
A217757: 2 4 12 84 2100 254100 183206100 923541950100 37238134969982100 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 2) <= 0 then (if x <= 0 then 1 else x) else ~x)
A274922: 1 ~1 2 ~3 4 ~5 6 ~7 8 ~9 10 ~11 12 ~13 14 ~15
loop(\(x,i).loop(\(x,i).x2,x,2),x,(~x + 1))
A114560: 1 2 16 4611686018427387903
loop(\(x,i).2x,(x + ~2),(if x <= 0 then 1 else x))
A129952: 1 1 2 6 16 40 96 224 512 1152 2560 5632 12288 26624 57344 122880
(if loop(\(x,i).x2,x2,x) <= 0 then 1 else x)
A273400: 1 1 2 4611686018427387903
loop(\(x,i).loop(\(x,i).(x + (i * i)),x,0),2,x)
A329753: 0 1 55 1015 9455 56980 255346 924490 2850730 7757035 19096385 43312841 91753025 183453270 349074740 636310340
(if x <= 0 then 1 else loop(\(x,i).2x,(x + 2),x))
A241204: 1 8 32 96 256 640 1536 3584 8192 18432 40960 90112 196608 425984 917504 1966080
loop(\(x,i).loop(\(x,i).2x,i,x),(x + ~2),x)
A123903: 0 1 2 6 32 320 6144 229376 16777216 2415919104 687194767360 387028092977152 432345564227567616 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,(1 mod (if x <= 0 then 2 else x)))
A186949: 1 0 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768
loop(\(x,i).loop(\(x,i).((~x + i) div 2),x,x),2,x)
A143996: 0 0 0 0 1 0 1 1 1 1 1 2 2 2 1 1
loop(\(x,i).(x * loop(\(x,i).x2,i,x)),2,x)
A010803: 0 1 32768 14348907 1073741824 30517578125 470184984576 4747561509943 35184372088832 205891132094649 1000000000000000 4177248169415651 15407021574586368 51185893014090757 155568095557812224
loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)
A229878: 0 0 1 0 1 2
A298486-A189768-A166352-A163351-A025691-A025690-A025689-A025682-A025681-A025680-A025675-A025674-A025668-A025667-A025659-A025650-A002262: 0 0 1 0 1 2 0 1 2 3 0 1 2 3 4 0
loop(\(x,i).(x + loop(\(x,i).(x * i),i,1)),x,x)
A036782: 0 2 5 12 37 158 879 5920 46241 409122 4037923 43954724 522956325 6749977126 93928268327 1401602636328
loop(\(x,i).loop(\(x,i).(~1 + i),(x - i),x),x,x)
A048151: 0 1 0 1 2 0 1 2 3 0 1 2 3 4 0 1
(1 - loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x))
A200443-A200370-A200329-A200272: 1 1 2 1 3 2 1 4 3 2 1 5 4 3 2 1
(if (x mod 7) <= 0 then 1 else 0)
A286935-A082784-A014646-A014548: 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0
(if (x mod 9) <= 0 then 1 else 0)
A341025-A320320-A288325-A267142-A245040-A244172-A127843-A114099-A015899-A014063: 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
(if ((x + 2) mod 5) <= 0 then 1 else 0)
A085856: 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0
(if (x div (2x + ~5)) <= 0 then 1 else 0)
A204443: 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1
(if (x mod (2x + ~5)) <= 0 then 1 else 0)
A183918: 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0
(if (x + ~12) <= 0 then 1 else 0)
A016258-A016180-A016128-A016050-A015972-A015946-A015816-A015790-A015712-A015660-A015478-A015426-A015400-A015348-A015322-A015270-A015166-A015088-A015036-A014958-A014932-A014880-A014802-A014776-A014698-A014620-A014568-A014542-A014490-A014412-A014386-A014308-A014256-A014230: 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0
(if (x mod 12) <= 0 then 1 else 0)
A321936-A293814-A282568-A240355-A181004-A155797-A097798-A056620: 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
(if (x2 mod (x + 3)) <= 0 then 1 else 0)
A267417-A016347-A015989-A015269-A014045: 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
(if (3 mod (1 + (x div 2))) <= 0 then 1 else 0)
A151666: 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0
(if ((x + ~1) mod (1 + (x div 2))) <= 0 then 1 else 0)
A329677: 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0
(if (5 mod (x + 1)) <= 0 then 1 else 0)
A254211-A240467-A047751-A016371-A014065-A014049: 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
(if (x + ~10) <= 0 then 1 else 0)
A016176-A016132-A016110-A016000-A015978-A015912-A015846-A015802-A015736-A015670-A015648-A015538-A015516-A015450-A015406-A015252-A015208-A015186-A015142-A015120-A015076-A014988-A014922-A014878-A014812-A014790-A014746-A014680-A014658-A014592-A014526-A014482-A014460-A014416-A014350-A014328-A014262-A014218-A014196: 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0
(if (x mod 10) <= 0 then 1 else 0)
A341026-A320321-A316898-A316897-A316893-A288326-A245041-A244173-A217096-A216809-A127844-A055641-A051907-A010109: 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
(if (~2 + (x mod 5)) <= 0 then 1 else 0)
A230412: 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1
(if (x + ~1) <= 0 then (2x + 3) else 0)
A152624: 3 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(if ((x + 1) mod 8) <= 0 then 1 else 0)
A342019-A335510-A324832-A323510-A295659-A244413-A188436-A116378-A104488-A083918-A083895-A078128-A072401-A064873-A056626-A044938-A037823-A026828-A026801: 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1
(if ((x + ~1) mod 8) <= 0 then 1 else 0)
A098108: 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
(if ((x + 2) mod 8) <= 0 then 1 else 0)
A186746: 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0
(if (x mod (4 + (x div 2))) <= 0 then 1 else 0)
A297199: 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0
loop(\(x,i).(x + i),(x div 5),0)
A270774: 0 0 0 0 0 1 1 1 1 1 3 3 3 3 3 6
(if ((x + (x div 2)) mod 4) <= 0 then 1 else 0)
A326072: 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0
(if ((x * (x div 2)) mod 4) <= 0 then 1 else 0)
A087049: 1 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0
(if (~2 + ((x * (x mod 2)) div 2)) <= 0 then 1 else 0)
A179775: 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0
(if (x2 mod (x + 4)) <= 0 then 1 else 0)
A181000-A126010-A003982: 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0
(if (x + ~1) <= 0 then (4x + 1) else 0)
A152623: 1 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (2x mod (2 + (x div 2))) <= 0 then 1 else 0)
A195198: 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 0
loop(\(x,i).(~x + (i mod 2)),(x div 3),0)
A242602: 0 0 0 1 1 1 ~1 ~1 ~1 2 2 2 ~2 ~2 ~2 3
(if (x mod 4) <= 0 then (x mod 3) else 0)
A182660: 0 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0
(if (x + ~2) <= 0 then 3x2 else 0)
A181405: 0 3 12 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (6 mod (x + 2)) <= 0 then 1 else 0)
A204843: 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0
(if (8 mod (x + 2)) <= 0 then 1 else 0)
A069845: 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0
(if (x2 + ~6x + 8) <= 0 then 1 else 0)
A093314: 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0
(if ((x + ~2) * (x mod 4)) <= 0 then 1 else 0)
A036297: 1 1 1 0 1 0 0 0 1 0 0 0 1 0 0 0
loop(\(x,i).(x + (i * i)),(2x + 1),0)
A100157: 1 14 55 140 285 506 819 1240 1785 2470 3311 4324 5525 6930 8555 10416
loop(\(x,i).(3 * (x + i)),(x + 1),0)
A290764: 3 15 54 174 537 1629 4908 14748 44271 132843 398562 1195722 3587205 10761657 32285016 96855096
loop(\(x,i).(4 * (x + i)),(x + 1),0)
A145655: 4 24 108 448 1812 7272 29116 116496 466020 1864120 7456524 29826144 119304628 477218568 1908874332 7635497392
loop(\(x,i).(i * i * (x + i)),(x + 1),0)
A288035: 1 12 135 2224 55725 2006316 98309827 6291829440 509638185369 50963818537900 6166622043087231 887993574204562992 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x + 6),(x + ~1),0)
A058809: 0 0 6 24 78 240 726 2184 6558 19680 59046 177144 531438 1594320 4782966 14348904
loop(\(x,i).((x + 1) * (1 + i)),(x + ~1),0)
A038156: 0 0 2 9 40 205 1236 8659 69280 623529 6235300 68588311 823059744 10699776685 149796873604 2246953104075
(1 - loop(\(x,i).(2 * (x - i)),(x + ~1),0))
A183155: 1 1 3 9 23 53 115 241 495 1005 2027 4073 8167 16357 32739 65505
loop(\(x,i).(x + ((i * i) div 2)),(x + ~1),0)
A212964: 0 0 0 2 6 14 26 44 68 100 140 190 250 322 406 504
loop(\(x,i).(x + ((~2 + i) * i)),(x + ~1),0)
A058373: 0 0 ~1 ~1 2 10 25 49 84 132 195 275 374 494 637 805
((2 * (2 + (x div 2))) - (if x <= 0 then 1 else 0))
A263842: 3 4 6 6 8 8
(1 - (if (~x + 2) <= 0 then (x div ~2) else 0))
A226142: 1 1 2 3 3 4 4
A120835: 1 1 2 3 3 4 4 5 5 6 6 7 7 8 8 9
(2 - (if (~x + 2) <= 0 then (x div ~2) else 0))
A321667: 2 2 3 4 4 5 5 6 6 7 7 8 8 9 9 10
(if (~1 + (x mod (2 + (x mod 2)))) <= 0 then 2 else 0)
A137934: 2 2 2 2 2 0 2 2 2 2 2 0 2 2 2 2
(if (x mod 2) <= 0 then (x div 8) else 0)
A277153: 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0
((x + ~1) + (if (x mod 2) <= 0 then 4 else 0))
A165754: 3 0 5 2 7 4 9 6 11 8 13 10 15 12 17 14
(if (5 mod (x + 2)) <= 0 then 2 else 0)
A005926: 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0
(if (x + ~1) <= 0 then (3x + 2) else 0)
A020773: 2 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (~x + 2) <= 0 then ((x2 + x) div 2) else 0)
A057241: 0 0 3 6 10
loop(\(x,i).(2 * (x + (2 * i))),(x + 2),0)
A258547: 16 44 104 228 480 988 2008 4052 8144 16332 32712 65476 131008 262076 524216 1048500
loop(\(x,i).(x + ((i div 2) * i)),(x + 2),0)
A049779: 2 5 13 23 41 62 94 130 180 235 307 385 483 588 716 852
(3 - (if (~x + 2) <= 0 then (x + ~2) else 0))
A215409: 3 3 3 2 1 0
loop(\(x,i).(4x + 1),2x,0)
A195156: 0 5 85 1365 21845 349525 5592405 89478485 1431655765 22906492245 366503875925 5864062014805 93824992236885 1501199875790165 24019198012642645 384307168202282325
loop(\(x,i).(3x + 1),2x,0)
A191681: 0 4 40 364 3280 29524 265720 2391484 21523360 193710244 1743392200 15690529804 141214768240 1270932914164 11438396227480 102945566047324
loop(\(x,i).(~1 + (x * (0 - i))),2x,0)
A306675: 0 1 15 455 25487 2293839 302786759 55107190151 13225725636255 4047072044694047 1537887376983737879 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x + 2),2x,0)
A024101: 0 8 80 728 6560 59048 531440 4782968 43046720 387420488 3486784400 31381059608 282429536480 2541865828328 22876792454960 205891132094648
(x - loop(\(x,i).(2 * (x - i)),2x,0))
A289254: 0 9 54 243 1008 4077 16362 65511 262116 1048545 4194270 16777179 67108824 268435413 1073741778 4294967247
(if (x mod 5) <= 0 then (x mod 2) else 0)
A316866-A086013: 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1
(1 - (if (~2 + (x div 2)) <= 0 then (x mod 2) else 0))
A097456: 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1
(2 - (if (~2 + (x div 2)) <= 0 then (x mod 2) else 0))
A127267: 2 1 2 1 2 1 2 2 2 2 2 2 2 2 2 2
(if (~x + 4) <= 0 then (x2 + ~2) else 0)
A184220: 0 0 0 0 14 23 34 47 62 79 98 119 142 167 194 223
loop(\(x,i).(6x + 1),x,0)
A003464: 0 1 7 43 259 1555 9331 55987 335923 2015539 12093235 72559411 435356467 2612138803 15672832819 94036996915
loop(\(x,i).(~1 + ((x + 2) * (1 + i))),x,0)
A026243: 0 3 14 63 324 1955 13698 109599 986408 9864099 108505110 1302061343 16926797484 236975164803 3554627472074 56874039553215
loop(\(x,i).(1 + (2 * ((x + 1) + i))),x,0)
A168617: 0 5 17 43 97 207 429 875 1769 3559 7141 14307 28641 57311 114653 229339
loop(\(x,i).(8x + 1),x,0)
A023001: 0 1 9 73 585 4681 37449 299593 2396745 19173961 153391689 1227133513 9817068105 78536544841 628292358729 5026338869833
(2 - loop(\(x,i).(4x + ~1),x,0))
A201363: 2 3 7
A163834: 2 3 7 23 87 343 1367 5463 21847 87383 349527 1398103 5592407 22369623 89478487 357913943
loop(\(x,i).(1 + (2 * ((x + 2) - i))),x,0)
A061761: 0 3 7 13 23 41 75 141 271 529 1043 2069 4119 8217 16411 32797
loop(\(x,i).(3x + 9),x,0)
A168569: 0 9 36 117 360 1089 3276 9837 29520 88569 265716 797157 2391480 7174449 21523356 64570077
loop(\(x,i).(6x + 6),x,0)
A105281: 0 6 42 258 1554 9330 55986 335922 2015538 12093234 72559410 435356466 2612138802 15672832818 94036996914 564221981490
loop(\(x,i).(~1 + (2 * (x + (i mod 2)))),x,0)
A154917: 0 1 1 3 5 11 21 43 85 171 341 683 1365 2731 5461
A001045: 0 1 1 3 5 11 21 43 85 171 341 683 1365 2731 5461 10923
loop(\(x,i).(~1 + (2 * (~x + (i mod 2)))),x,0)
A225883: 0 1 ~3 7 ~15 31 ~63 127 ~255 511 ~1023 2047 ~4095 8191 ~16383 32767
loop(\(x,i).((2x + 1) + (x mod 2)),x,0)
A084639: 0 1 4 9 20 41 84 169 340 681 1364 2729 5460 10921 21844 43689
(if (x + ~2) <= 0 then (2x2 + ~x) else 0)
A186685: 0 1 6 0 0 0 0 0 0 0 0 0 0 0 0 0
((x mod 2) - loop(\(x,i).(2x + ~1),x,0))
A166920: 0 2 3 8 15 32 63 128 255 512 1023 2048 4095 8192 16383 32768
loop(\(x,i).(~1 + (2 * (2x + i))),x,0)
A141291: 0 1 7 33 139 565 2271 9097 36403 145629 582535 2330161 9320667 37282693 149130799 596523225
loop(\(x,i).(1 + (x * i) - (i mod 2)),x,0)
A080227: 0 0 1 3 13 65 391 2737 21897 197073 1970731 21678041 260136493 3381774409 47344841727 710172625905
loop(\(x,i).(5x + 1),x,0)
A003463: 0 1 6 31 156 781 3906 19531 97656 488281 2441406 12207031 61035156 305175781 1525878906 7629394531
loop(\(x,i).(1 + (x * (3 + i))),x,0)
A079751: 0 1 6 37 260 2081 18730 187301 2060312 24723745 321408686 4499721605 67495824076 1079933185217 18358864148690 330459554676421
loop(\(x,i).(1 + (x * (~1 + (2 * i)))),x,0)
A286286: 0 1 4 21 148 1333 14664 190633 2859496 48611433 923617228 19395961789 446107121148 11152678028701 301122306774928 8732546896472913
(1 - loop(\(x,i).(~1 + (x * (1 + i))),x,0))
A094294: 1 2 5 18 87 518 3621 28962 260651 2606502 28671513 344058146 4472755887 62618582406 939278736077 15028459777218
loop(\(x,i).(1 + (x * ((1 + i) div 2))),x,0)
A192225: 0 1 2 5
A254342: 0 1 2 5 11 34
loop(\(x,i).((x + 1) + (x div 4)),x,0)
A279075: 0 1 2 3 4 6 8 11 14 18 23 29 37 47 59 74
loop(\(x,i).(5x + 5),x,0)
A104891: 0 5 30 155 780 3905 19530 97655 488280 2441405 12207030 61035155 305175780 1525878905 7629394530 38146972655
loop(\(x,i).((x + 1) * (3 + i)),x,0)
A079750: 0 4 25 156 1099 8800 79209 792100 8713111 104557344 1359245485 19029436804 285441552075 4567064833216 77640102164689 1397521838964420
loop(\(x,i).(x3 + x2 + x + 1),x,0)
A055776: 0 1 4 85 621436 239988219843053389 4611686018427387903
loop(\(x,i).(i - ((1 + i) mod (x + 1))),x,0)
A092323: 0 1 1 3 3 3 3 7 7 7 7 7 7 7 7 15
loop(\(x,i).(~1 + ((2 * (x + i)) + i)),x,0)
A213387: 0 2 9 26 63 140 297 614 1251 2528 5085 10202 20439 40916 81873 163790
loop(\(x,i).((2x + 1) mod (1 + i)),x,0)
A064434: 0 1 0 1 3 1 3 7 6 3 7 3 7 1 3 7
loop(\(x,i).((x2 + 1) mod (1 + i)),x,0)
A330405: 0 1 2 1 2 5 5 2 5 6 4 5 0 1 2 5
loop(\(x,i).(2x - (i div ~2)),x,0)
A178420: 0 1 3 8 18 39 81 166 336 677 1359 2724 5454 10915 21837 43682
loop(\(x,i).(x - ((i * i) div ~2)),x,0)
A131941: 0 1 3 8 16 29 47 72 104 145 195 256 328 413 511 624
loop(\(x,i).(8x + 2),x,0)
A125835: 0 2 18 146 1170 9362 74898 599186 4793490 38347922 306783378 2454267026 19634136210 157073089682 1256584717458 10052677739666
loop(\(x,i).(3x + 8),x,0)
A302507: 0 8 32 104 320 968 2912 8744 26240 78728 236192 708584 2125760 6377288 19131872 57395624
loop(\(x,i).(2 * ((x + ~1) + (2 * i))),x,0)
A051667: 0 2 10 30 74 166 354 734 1498 3030 6098 12238 24522 49094 98242 196542
loop(\(x,i).((x2 + 3x + 2) div 2),x,0)
A072638: 0 1 3 10 66 2278 2598060 3374961778891 4611686018427387903 4611686018427387903
loop(\(x,i).(8x + 4),x,0)
A108019: 0 4 36 292 2340 18724 149796 1198372 9586980 76695844 613566756 4908534052 39268272420 314146179364 2513169434916 20105355479332
loop(\(x,i).(4x + 16),x,0)
A247817: 0 16 80 336 1360 5456 21840 87376 349520 1398096 5592400 22369616 89478480 357913936 1431655760 5726623056
(1 - loop(\(x,i).(2x + ~8),x,0))
A048490: 1 9 25 57 121 249 505 1017 2041 4089 8185 16377 32761 65529 131065 262137
loop(\(x,i).(8 * (x + i)),x,0)
A145729: 0 8 80 664 5344 42792 342384 2739128 21913088 175304776 1402438288 11219506392 89756051232 718048409960 5744387279792 45955098238456
(1 - loop(\(x,i).(4x + ~8),x,0))
A083584: 1 9 41 169 681 2729 10921 43689 174761 699049 2796201 11184809 44739241 178956969 715827881 2863311529
loop(\(x,i).(x + i - (x div 4)),x,0)
A220657: 0 1 3 6 9 12 15 19 23 27 31 35 39 43 47 51
loop(\(x,i).(4 * (2x + i)),x,0)
A145730: 0 4 40 332 2672 21396 171192 1369564 10956544 87652388 701219144 5609753196 44878025616 359024204980 2872193639896 22977549119228
loop(\(x,i).(2 + ((x2 + ~x) div 2)),x,0)
A108225: 0 2 3 5 12 68 2280 2598062 3374961778893 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (2x + (i mod 2))),x,0)
A117616: 0 2 8 34 136 546 2184 8738 34952 139810 559240 2236962 8947848 35791394 143165576 572662306
loop(\(x,i).(i - (x div (~2 + (x mod 2)))),x,0)
A138037: 0 1 3 6 7 12 12 13 21 30 25 36 30 28 28 29
(1 - loop(\(x,i).(2 * (x - (2 * i))),x,0))
A247618: 1 5 17 45 105 229 481 989 2009 4053 8145 16333 32713 65477 131009 262077
(1 - loop(\(x,i).(2 * (x - (i mod 2))),x,0))
A283642: 1 3 5 11 21 43 85 171 341 683 1365 2731 5461 10923 21845 43691
loop(\(x,i).(5x + 2),x,0)
A125831-A121177: 0 2 12 62 312 1562 7812 39062 195312 976562 4882812 24414062 122070312 610351562 3051757812 15258789062
loop(\(x,i).(2x + 16),x,0)
A175164: 0 16 48 112 240 496 1008 2032 4080 8176 16368 32752 65520 131056 262128 524272
loop(\(x,i).((i * i) - ((~x + 2) div 2)),x,0)
A208951: 0 0 3 10 20 34 52 74
loop(\(x,i).(x + (i * i)),(x2 + 2x),0)
A109764: 0 14 204 1240 4900 14910 38024 85344 173880 328350 583220 984984 1594684 2490670 3771600 5559680
(1 - loop(\(x,i).((2x + ~4) * i),x,0))
A085644: 1 5 25 157 1265 12661 151945 2127245 34035937 612646885 12252937721 269564629885 6469551117265 168208329048917 4709833213369705 141294996401091181
loop(\(x,i).(2x + (i div 3)),x,0)
A178455: 0 0 0 1 3 7 16 34 70 143 289 581 1166 2336 4676 9357
loop(\(x,i).(~2x + (2 div (1 + i))),x,0)
A325744: 0 1 ~2 4 ~8 16 ~32 64 ~128 256 ~512 1024 ~2048 4096 ~8192 16384
loop(\(x,i).(3x + (i div 2)),x,0)
A097137: 0 0 1 4 14 44 135 408 1228 3688 11069 33212 99642 298932 896803 2690416
loop(\(x,i).((2x + 4) - (x div 2)),x,0)
A140260: 0 4 10 19 33 54 85 132 202 307 465 702 1057 1590 2389 3588
(1 - (if (x + ~2) <= 0 then (~x + (x mod 2)) else 0))
A103755: 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1
((~x + 1) + loop(\(x,i).(2 * (x + i)),x,0))
A123203: 1 2 7 20 49 110 235 488 997 2018 4063 8156 16345 32726 65491 131024
(1 - loop(\(x,i).(2 * (2x - i)),x,0))
A318165: 1 3 13
A302757: 1 3 13 55 225 907 3637 14559 58249 233011 932061 3728263 14913073 59652315 238609285 954437167
((~x + 1) + loop(\(x,i).(2 + (x * i)),x,0))
A286282: 1 2 5 18 79 408 2469 17314 138555 1247052 12470593 137176614 1646119479 21399553360 299593747197 4493906208138
loop(\(x,i).(4x + (i div 2)),x,0)
A097138: 0 0 1 5 22 90 363 1455 5824 23300 93205 372825 1491306 5965230 23860927 95443715
loop(\(x,i).(x + ((i * i) + (i mod 2))),x,0)
A171218: 0 2 6 16 32 58 94 144 208 290 390 512 656 826 1022 1248
loop(\(x,i).(x + (2 * (i * i)) - i),x,0)
A002412: 0 1 7 22 50 95 161 252 372 525 715 946 1222 1547 1925 2360
loop(\(x,i).(x + (3 * (x + i))),x,0)
A078904: 0 3 18 81 336 1359 5454 21837 87372 349515 1398090 5592393 22369608 89478471 357913926 1431655749
loop(\(x,i).(x + ((i * i) div 3)),x,0)
A181286: 0 0 1 4 9 17 29 45 66 93 126 166 214 270 335 410
loop(\(x,i).(~x + (i div (1 + (i mod 2)))),x,0)
A131119: 0 0 2 ~1 5 ~3 9 ~6 14 ~10 20 ~15 27 ~21 35 ~28
loop(\(x,i).(5x + 4),x,0)
A024049: 0 4 24 124 624 3124 15624 78124 390624 1953124 9765624 48828124 244140624 1220703124 6103515624 30517578124
loop(\(x,i).(x + ((x + 1) * (2 + i))),x,0)
A139176: 0 3 19 119 839 6719 60479 604799 6652799 79833599 1037836799 14529715199 217945727999 3487131647999 59281238015999 1067062284287999
loop(\(x,i).(~x + ((2x + 2) * i)),x,0)
A093303: 0 2 10 56 400 3610 39722 516400 7746016 131682290 2501963530 52541234152 1208448385520 30211209638026 815702660226730 23655377146575200
loop(\(x,i).(x + (i * i * (1 + i))),x,0)
A153978: 0 2 14 50 130 280 532 924 1500 2310 3410 4862 6734 9100 12040 15640
loop(\(x,i).(~x + ((i div 2) * (~1 + i))),x,0)
A245288: 0 0 1 1 5 3 12 6 22 10 35 15 51 21 70 28
loop(\(x,i).(x + ((i * i) div 4)),x,0)
A173196: 0 0 1 3 7 13 22 34 50 70 95 125 161 203 252 308
loop(\(x,i).(x + (2 * (2 + (i * i)))),x,0)
A059834: 0 6 18 40 76 130 206 308 440 606 810 1056 1348 1690 2086 2540
loop(\(x,i).(x + ((i * i * i) div 2)),x,0)
A198297: 0 0 4 17
A173704: 0 0 4 17 49 111 219 390 646 1010 1510 2175 3039 4137 5509 7196
(0 * loop(\(x,i).x3,x2,x))
A338982: 0 0 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + ((2x + 1) * i)),x,0)
A249349: 0 1 7 52 472 5197 67567 1013512 17229712 327364537 6874655287 158117071612 3952926790312 106729023338437 3095141676814687 95949391981255312
loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0)
A016061: 0 3 13 34 70 125 203 308 444 615 825 1078 1378 1729 2135 2600
loop(\(x,i).((2 * (i mod 2)) + (x * i)),x,0)
A306150: 0 2 4 14 56 282 1692 11846 94768 852914 8529140 93820542 1125846504 14636004554 204904063756 3073560956342
(1 - loop(\(x,i).(2x - (i * i)),x,0))
A183156: 1 2 7 22 59 142 319 686 1435 2950 5999 12118 24379 48926 98047 196318
loop(\(x,i).(x + (i * i * i * i)),x,0)
A000538: 0 1 17 98 354 979 2275 4676 8772 15333 25333 39974 60710 89271 127687 178312
(1 - loop(\(x,i).((2x + ~1) * i),x,0))
A308876: 1 2 7 40 317 3166 37987 531812 8508985 153161722 3063234431 67391157472 1617387779317 42052082262230 1177458303342427 35323749100272796
(1 - loop(\(x,i).((2x + ~4) - i),x,0))
A101945: 1 6 17 40 87 182 373 756 1523 3058 6129 12272 24559 49134 98285 196588
loop(\(x,i).((x2 + 4x + 4) - i),x,0)
A143985: 0 3 23 622 389372 151612111871 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x2 + ~4x + 4) - i),x,0)
A143984: 0 3 ~1 6 12 95 8643 74666874 5575141774264376 4611686018427387903 4611686018427387903
(1 - loop(\(x,i).((2 * (x - i)) - i),x,0))
A101946: 1 4 13 34 79 172 361 742 1507 3040 6109 12250 24535 49108 98257 196558
loop(\(x,i).((x + (i * i * i)) * i),x,0)
A337002: 0 1 18 135 796 4605 28926 204883 1643160 14795001 147960010 1627574751 19530917748 253901959285 3554627468406 53319412076715
(if (x mod 7) <= 0 then 0 else 1)
A109720: 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1
(if (x mod 9) <= 0 then 0 else 1)
A168182: 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1
(if ((x + 1) mod 5) <= 0 then 0 else 1)
A190239-A120529: 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1
(if ((x + ~1) mod 5) <= 0 then 0 else 1)
A188038: 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1
(if ((x + ~2) mod 5) <= 0 then 0 else 1)
A179850: 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1
(if ((x div 2) mod 5) <= 0 then 0 else 1)
A102669: 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1
(if ((x div ~2) mod 3) <= 0 then 0 else 1)
A131719: 0 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1
(if (x mod 12) <= 0 then 0 else 1)
A168185: 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1
(if (2x mod (1 + (x div 2))) <= 0 then 0 else 1)
A087101: 0 0 0 0 1 1 0 1 1
(if (x2 mod (1 + (x div 2))) <= 0 then 0 else 1)
A272817: 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1
(if (5 mod (x + 1)) <= 0 then 0 else 1)
A132312: 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1
(1 + (if (~1 + (x mod 3)) <= 0 then 2 else 0))
A144437: 3 3 1 3 3 1 3 3 1 3 3 1 3 3 1 3
(if (x mod 10) <= 0 then 0 else 1)
A336682-A168184-A168046: 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1
(if ((x + ~2) mod 6) <= 0 then 0 else 1)
A127254: 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1
(1 + (if (x mod 2) <= 0 then 6 else 0))
A176415: 7 1 7 1 7 1 7 1 7 1 7 1 7 1 7 1
(x div (1 + (if (x mod 3) <= 0 then 2 else 0)))
A051176: 0 1 2 1 4 5 2 7 8 3 10 11 4 13 14 5
(1 + (if ((x + ~1) mod 4) <= 0 then 2 else 0))
A007362: 1 3 1 1 1 3 1 1
(if ((x + 1) mod 8) <= 0 then 0 else 1)
A212793-A071374: 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0
(if ((x + 2) mod 8) <= 0 then 0 else 1)
A157972: 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1
(if ((x + (x div 2)) mod 4) <= 0 then 0 else 1)
A285418: 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1
(2x - (if (x + ~4) <= 0 then 0 else 1))
A345436: 0 2 4 6 8 9 11 13 15 17 19 21 23 25 27 29
(2x - (if (x mod 4) <= 0 then 0 else 1))
A047624: 0 1 3 5 8 9 11 13 16 17 19 21 24 25 27 29
(if (x2 mod (x + 4)) <= 0 then 0 else 1)
A257680: 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1
(if ((x + ~2) * (x mod 4)) <= 0 then 0 else 1)
A252743: 0 0 0 1 0 1 1 1 0 1 1 1 0 1 1 1
loop(\(x,i).(x * (0 - i)),(x + ~1),~1)
A155456: ~1 ~1 1 ~2 6 ~24 120 ~720 5040 ~40320 362880 ~3628800 39916800 ~479001600 6227020800 ~87178291200
loop(\(x,i).((x + 1) * (1 + i)),x,~1)
A224869: ~1 0 3 16 85 516 3619 28960 260649 2606500 28671511 344058144 4472755885 62618582404 939278736075 15028459777216
loop(\(x,i).(2 * (x + (i mod 2))),x,~1)
A167030: ~1 0 0 2 4 10 20 42 84 170 340 682 1364 2730 5460 10922
(1 - (x mod loop(\(x,i).2x,x,~1)))
A132045: 1 2 3 6 13 28 59 122 249 504 1015 2038 4085 8180 16371 32754
(1 + (if (~1 + (x div 4)) <= 0 then x else 0))
A255829: 1 2 3 4 5 6 7 8 1 1 1 1 1 1 1 1
(1 + (if (~2 + (x div 3)) <= 0 then x else 0))
A306354-A287877-A256229-A179635-A126616-A121042-A075877-A052423: 1 2 3 4 5 6 7 8 9 1 1 1 1 1 1 1
(1 + (if (x mod 8) <= 0 then x else 0))
A264981: 1 1 1 1 1 1 1 1 9 1 1 1 1 1 1 1
(~1 + loop(\(x,i).(2x + 8),x,0))
A172252: ~1 7 23 55 119 247 503 1015 2039 4087 8183 16375 32759 65527 131063 262135
(if (x * ((x + 2) mod 4)) <= 0 then 0 else 1)
A277674-A047988: 0 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1
(1 + loop(\(x,i).(~4x + 1),x,0))
A166114: 1 2 ~2 14 ~50 206 ~818 3278 ~13106 52430 ~209714 838862 ~3355442 13421774 ~53687090 214748366
(1 + loop(\(x,i).((x + 2) + (x div 2)),x,0))
A152009: 1 3 6 10 16 25 39 60 91 138 208 313 471 708 1063 1596
(1 + loop(\(x,i).(~3x + 1),x,0))
A084222: 1 2 ~1 8 ~19 62 ~181 548 ~1639 4922 ~14761 44288 ~132859 398582 ~1195741 3587228
(1 + (if (~x + 2) <= 0 then (x + (x div 2)) else 0))
A097482: 1 1 4 5 7 8 10 11 13 14 16 17 19 20 22 23
(((x + 1) mod 3) - (if x <= 0 then 0 else 1))
A106510: 1 1 ~1 0 1 ~1 0 1 ~1 0 1 ~1 0 1 ~1 0
(6x - (if x <= 0 then 0 else 1))
A172337: 0 5 11 17 23 29 35 41 47 53 59 65 71 77 83 89
(((x div 2) div 3) + (if x <= 0 then 0 else 1))
A264749-A195177-A137588: 0 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3
(((~x + 1) mod 3) - (if x <= 0 then 0 else 1))
A163804: 1 ~1 1 0 ~1 1 0 ~1 1 0 ~1 1 0 ~1 1 0
((x2 div 3) + (if x <= 0 then 0 else 1))
A154255: 0 1 2 4 6 9 13 17 22 28 34 41 49 57 66 76
((2x2 + 2x) - (if x <= 0 then 0 else 1))
A132209: 0 3 11 23 39 59 83 111 143 179 219 263 311 363 419 479
(((x mod 3) div 2) + (if x <= 0 then 0 else 1))
A101825: 0 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1
((x div 8) + (if x <= 0 then 0 else 1))
A261226-A211662-A067394-A048766: 0 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
((x + 6) + (if x <= 0 then 0 else 1))
A135558: 6 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
((2x + 8) - (if x <= 0 then 0 else 1))
A308602: 8 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37
(((x * (x mod 2)) div 2) + (if x <= 0 then 0 else 1))
A249068-A249009-A248034: 0 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8
(2x + (x div 2) - (if x <= 0 then 0 else 1))
A010387: 0 1 4 6 9 11 14 16 19 21 24
(x + (2 * (x mod 2)) - (if x <= 0 then 0 else 1))
A014681: 0 2 1 4 3 6 5 8 7 10 9 12 11 14 13 16
(1 + loop(\(x,i).(~3x + 4),x,0))
A081630: 1 5 ~7 29 ~79 245 ~727 2189 ~6559 19685 ~59047 177149 ~531439 1594325 ~4782967 14348909
(1 + (2 mod (~1 + (if (x mod 2) <= 0 then x else 0))))
A125768: 1 1 1 1 3 1 3 1 3 1 3 1 3 1 3 1
loop(\(x,i).i,(~1 + ((x + ~2) div 3)),1)
A140437: 1 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3
(~1 + loop(\(x,i).(x * i),(x div 3),1))
A241471: 0 0 0 0 0 0 1 1 1 5
(~1 + loop(\(x,i).(x * (0 - i)),(x + 1),1))
A235378: ~2 1 ~7 23 ~121 719 ~5041 40319 ~362881 3628799 ~39916801 479001599 ~6227020801 87178291199 ~1307674368001 20922789887999
(~1 + loop(\(x,i).(x * (i * i)),(x + 1),1))
A046032: 0 3 35 575 14399 518399 25401599 1625702399 131681894399 13168189439999 1593350922239999 229442532802559999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).2x,((x + 1) div 2),1))
A051032: 2 3 3 5 5 9 9 17 17 33 33 65 65 129 129 257
(1 + ((x + 2) div (1 + (if x <= 0 then 1 else 2))))
A231152: 2 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6
loop(\(x,i).i,(x + ~9),1)
A274843-A273738-A271949-A213652-A067032: 1 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6
(1 + (if (x + ~1) <= 0 then x else 5))
A134201: 1 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6
(1 + loop(\(x,i).2x,x,5))
A083575: 6 11 21 41 81 161 321 641 1281 2561 5121 10241 20481 40961 81921 163841
loop(\(x,i).2x,(x div 5),1)
A108105: 1 1 1 1 1 2 2 2 2 2 4 4 4 4 4 8
loop(\(x,i).2x,(x mod 5),1)
A222011: 1 2 4 8
A269266: 1 2 4 8 16 1 2 4 8 16 1 2 4 8 16 1
(1 + loop(\(x,i).x2,x,5))
A199591: 6 26 626 390626 152587890626 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * i),x,5))
A173319: 6 6 11 31 121 601 3601 25201 201601 1814401 18144001 199584001 2395008001 31135104001 435891456001 6538371840001
(~1 + loop(\(x,i).(x * i),x,5))
A173317: 4 4 9 29 119 599 3599 25199 201599 1814399 18143999 199583999 2395007999 31135103999 435891455999 6538371839999
(if (x + ~1) <= 0 then (3x + 3) else 1)
A142464: 3 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(if (~x + 2) <= 0 then ((x + ~1) mod 3) else 1)
A308009: 1 1 1 2 0 1 2 0 1 2 0 1 2 0 1 2
(1 + (if (x + ~2) <= 0 then 2x else 3))
A000655: 1 3 5 4 4 4 4 4 4 4 4 4 4 4 4 4
(1 + (if x <= 0 then 1 else 6x))
A271114: 2 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91
(~1 + (if x <= 0 then 2 else 6x))
A101328: 1 5 11 17 23 29 35 41 47 53 59 65 71 77 83 89
loop(\(x,i).(x * i),6x,1)
A195390: 1 720 479001600 6402373705728000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(2x div 3),1)
A291778: 1 1 2 4 4 8 16 16 32 64 64 128 256 256 512 1024
(1 + (3 * loop(\(x,i).(x * i),x,2)))
A173314: 7 7 13 37 145 721 4321 30241 241921 2177281 21772801 239500801 2874009601 37362124801 523069747201 7846046208001
(~1 + (3 * loop(\(x,i).(x * i),x,2)))
A173316: 5 5 11 35 143 719 4319 30239 241919 2177279 21772799 239500799 2874009599 37362124799 523069747199 7846046207999
(1 + loop(\(x,i).(2x + 4),x,3))
A156127: 4 11 25 53 109 221 445 893 1789 3581 7165 14333 28669 57341 114685 229373
(1 + loop(\(x,i).4x,x,3))
A140660: 4 13 49 193 769 3073 12289 49153 196609 786433 3145729 12582913 50331649 201326593 805306369 3221225473
loop(\(x,i).(2x + 1),(x div 3),1)
A077885: 1 1 1 3 3 3 7 7 7 15 15 15 31 31 31 63
loop(\(x,i).(~2x + 1),(x div 3),1)
A077886: 1 1 1 ~1 ~1 ~1 3 3 3 ~5 ~5 ~5 11 11 11 ~21
loop(\(x,i).(x * i),x,(1 + (x div 3)))
A052569: 1 1 2 12 48 240 2160 15120 120960 1451520 14515200 159667200 2395008000 31135104000 435891456000 7846046208000
loop(\(x,i).3x,(x div 3),1)
A127975: 1 1 1 3 3 3 9 9 9 27 27 27 81 81 81 243
(1 + (3 * loop(\(x,i).2x,x,x)))
A048477: 1 7 25 73 193 481 1153 2689 6145 13825 30721 67585 147457 319489 688129 1474561
(1 + (if (~x2 + 2x) <= 0 then x else 3))
A132293: 1 4 3 4 5 6
(1 + loop(\(x,i).x3,x,3))
A129290: 4 28 19684 7625597484988 4611686018427387903 4611686018427387903
(1 + (x2 div (if (~x + 2) <= 0 then 2 else 1)))
A085913: 1 2 3 5 9 13 19 25 33 41 51 61 73 85 99 113
loop(\(x,i).(x * (i * i)),(2x + 1),1)
A134374: 1 36 14400 25401600 131681894400 1593350922240000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x + 1),(2x + ~1),1)
A103454: 1 3 15 63 255 1023 4095 16383 65535 262143 1048575 4194303 16777215 67108863 268435455 1073741823
loop(\(x,i).(~2x + 4),(2x + ~1),1)
A039301: 1 2 4 12 44 172 684 2732 10924 43692 174764 699052 2796204 11184812 44739244 178956972
loop(\(x,i).3x,(2x + ~1),1)
A102518: 1 3 27 243 2187 19683 177147 1594323 14348907 129140163 1162261467 10460353203 94143178827 847288609443 7625597484987 68630377364883
(1 + loop(\(x,i).3x,2x,1))
A062396: 2 10 82 730 6562 59050 531442 4782970 43046722 387420490 3486784402 31381059610 282429536482 2541865828330 22876792454962 205891132094650
(1 + loop(\(x,i).(x2 + x),2x,1))
A123180: 2 7 1807 10650056950807 4611686018427387903
(1 + loop(\(x,i).6x,x,1))
A062394: 2 7 37 217 1297 7777 46657 279937 1679617 10077697 60466177 362797057 2176782337 13060694017 78364164097 470184984577
(~1 + loop(\(x,i).6x,x,1))
A024062: 0 5 35 215 1295 7775 46655 279935 1679615 10077695 60466175 362797055 2176782335 13060694015 78364164095 470184984575
(1 + loop(\(x,i).(2x2 + 2x),x,1))
A059917: 2 5 41 3281 21523361 926510094425921 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(x3 + 1),x,1))
A115590: 0 1 8 729 389017000 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).8x,x,1))
A062395: 2 9 65 513 4097 32769 262145 2097153 16777217 134217729 1073741825 8589934593 68719476737 549755813889 4398046511105 35184372088833
(~1 + loop(\(x,i).8x,x,1))
A024088: 0 7 63 511 4095 32767 262143 2097151 16777215 134217727 1073741823 8589934591 68719476735 549755813887 4398046511103 35184372088831
(1 + loop(\(x,i).(2 * ((x + 2) - i)),x,1))
A176691: 2 5 9 15 25 43 77 143 273 531 1045 2071 4121 8219 16413 32799
(1 + loop(\(x,i).(2 * (x + (x div 2))),x,1))
A201363: 2 3 7
A052919: 2 3 7 19 55 163 487 1459 4375 13123 39367 118099 354295 1062883 3188647 9565939
(1 + loop(\(x,i).(2 * (x + (i mod 2))),x,1))
A062092: 2 5 9 19 37 75 149 299 597 1195 2389 4779 9557 19115 38229 76459
(1 + loop(\(x,i).(2x + (i mod 2)),x,1))
A171231: 2 4 7 14 27 54 107 214 427 854 1707 3414 6827 13654 27307 54614
(if (~x + 2) <= 0 then ((x + ~1) + (x div 2)) else 1)
A267528: 1 1 2 3 5 6 8 9 11 12 14 15 17 18 20 21
(1 + loop(\(x,i).(x2 + (x mod 2)),x,1))
A092506: 2 3 5 17 257 65537
(~1 + loop(\(x,i).x3,2,(x + 1)))
A258810: 0 511 19682 262143 1953124 10077695 40353606 134217727 387420488 999999999 2357947690 5159780351 10604499372 20661046783 38443359374 68719476735
(1 + loop(\(x,i).(x * (1 + i)),x,(x + 1)))
A188914: 2 5 19 97 601 4321 35281 322561 3265921 36288001 439084801 5748019201 80951270401 1220496076801 19615115520001 334764638208001
(~1 + loop(\(x,i).(x * (2 + i)),x,(x + 1)))
A305739: 0 5 35 239 1799 15119 141119 1451519 16329599 199583999 2634508799 37362124799 566658892799 9153720575999 156920924159999 2845499424767999
loop(\(x,i).(x * ((i div 2) + i)),(x + 1),1)
A319948: 1 3 12 72 504 4536 45360 544320 7076160 106142400 1698278400 30569011200 580811212800 12197035468800 268334780313600 6440034727526400
loop(\(x,i).(~x + (i * i * i)),(x + 1),1)
A153026: 0 8 19 45 80 136 207 305 424 576 755 973 1224 1520 1855 2241
loop(\(x,i).(2x2 + 1),(x + ~1),1)
A329470: 1 1 3 19 723 1045459 2185969041363 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x + 1),(x + ~1),1)
A261547: 1 1 4 13 40 121 364 1093 3280 9841 29524 88573 265720 797161 2391484 7174453
loop(\(x,i).(3x + ~1),(x + ~1),1)
A124302: 1 1 2 5 14 41 122 365 1094 3281 9842 29525 88574 265721 797162 2391485
loop(\(x,i).(2x * (1 + i)),(x + ~1),1)
A002866: 1 1 4 24 192 1920 23040 322560 5160960 92897280 1857945600 40874803200 980995276800 25505877196800 714164561510400 21424936845312000
loop(\(x,i).((2x + 2) + i),(x + ~1),1)
A188589: 1 1 5 14 33 72 151 310 629 1268 2547 5106 10225 20464 40943 81902
loop(\(x,i).(x - (2x * i)),(x + ~1),1)
A330797: 1 1 ~1 3 ~15 105 ~945 10395 ~135135 2027025 ~34459425 654729075 ~13749310575 316234143225 ~7905853580625 213458046676875
loop(\(x,i).(2x - (i mod 2)),(x + ~1),1)
A247968: 1 1 1 2 3 6 11 22 43 86 171 342 683 1366 2731 5462
loop(\(x,i).(x + (x mod (1 + i))),(x + ~1),1)
A073117: 1 1 2 4 4 8 10 13 18 18 26 30 36 46 50 55
(1 + loop(\(x,i).5x,x,1))
A034474: 2 6 26 126 626 3126 15626 78126 390626 1953126 9765626 48828126 244140626 1220703126 6103515626 30517578126
(1 + loop(\(x,i).(x * (3 + i)),x,1))
A139153: 2 5 21 121 841 6721 60481 604801 6652801 79833601 1037836801 14529715201 217945728001 3487131648001 59281238016001 1067062284288001
((~x + 1) mod (1 + loop(\(x,i).(x * i),x,1)))
A066305: 1 0 2 5 22 117
(1 + loop(\(x,i).(x * (i * i * i)),x,1))
A019514: 2 2 9 217 13825 1728001 373248001 128024064001 65548320768001 47784725839872001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if (~2 + (x div 3)) <= 0 then 0 else 2))
A032568: 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3
(if ((x + 1) mod 3) <= 0 then ~2 else 1)
A061347: 1 1 ~2 1 1 ~2 1 1 ~2 1 1 ~2 1 1 ~2 1
(if ((x + ~1) mod 3) <= 0 then ~2 else 1)
A131713: 1 ~2 1 1 ~2 1 1 ~2 1 1 ~2 1 1 ~2 1 1
(x - (if (x mod 3) <= 0 then ~2 else 1))
A004483: 2 0 1 5 3 4 8 6 7 11 9 10 14 12 13 17
(if (((x + ~1) div 2) mod 2) <= 0 then ~2 else 1)
A134430: 1 ~2 ~2 1 1 ~2 ~2 1 1 ~2 ~2 1 1 ~2 ~2 1
(if (x mod 2) <= 0 then ((x div 2) mod ~2) else 1)
A131729: 0 1 ~1 1 0 1 ~1 1 0 1 ~1 1 0 1 ~1 1
(if (x mod 2) <= 0 then 4 else ~3)
A168309: 4 ~3 4 ~3 4 ~3 4 ~3 4 ~3 4 ~3 4 ~3 4 ~3
(x - ((if x <= 0 then 1 else x) div ~3))
A319371-A188188-A187572-A184478: 1 2 3 4 6 7 8 10 11 12 14 15 16 18 19 20
((2 - (x div 2)) mod (1 + (if x <= 0 then 0 else 2)))
A327310: 0 2 1 1 0 0 2 2 1 1 0 0 2 2 1 1
(2 - ((~x + 1) div (1 + (if x <= 0 then 0 else 2))))
A285761-A196176-A121536: 1 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7
(1 + (if (x mod 5) <= 0 then 1 else 2))
A022923: 2 3 3 3 3 2 3 3 3 3 2 3 3 3 3 2
(if ((x + 1) mod 5) <= 0 then 2 else 1)
A177706-A107038-A055457-A032542: 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1
(if ((x + ~2) mod 5) <= 0 then 2 else 1)
A130782: 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1
loop(\(x,i).i,(x + ~10),1)
A271835-A213651: 1 1 1 1 1 1 1 1 1 1 1 1 2 3 4 5
(1 + (x mod (if (~2 + (x div 2)) <= 0 then 1 else 2)))
A334948-A167968: 1 1 1 1 1 1 1 2 1 2 1 2 1 2 1 2
loop(\(x,i).(3x2 + 3),2,1)
A107844: 111 111 111 111 111 111 111 111 111 111 111 111 111 111 111 111
(if ((x div ~2) mod 3) <= 0 then 2 else 1)
A096284: 2 1 1 1 1 2 2 1 1 1 1 2 2 1 1 1
(if (x + ~1) <= 0 then x else 7)
A186684: 0 1 7 7 7 7 7 7 7 7 7 7 7 7 7 7
loop(\(x,i).2x,x,7)
A005009: 7 14 28 56 112 224 448 896 1792 3584 7168 14336 28672 57344 114688 229376
(if x <= 0 then 1 else (x div 7))
A185327-A017863: 1 0 0 0 0 0 0 1 1 1 1 1 1 1 2 2
(1 + loop(\(x,i).x2,x,6))
A078303: 7 37 1297 1679617 2821109907457 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).2x,x,3) div 2))
A103204: 2 4 7 13 25 49 97 193 385 769 1537 3073 6145 12289 24577 49153
loop(\(x,i).(x + i),(2 + (x mod 3)),1)
A175833: 4 7 11 4 7 11 4 7 11 4 7 11 4 7 11 4
(~1 + (2 * loop(\(x,i).(2x + 4),x,1)))
A139634: 1 11 31 71 151 311 631 1271 2551 5111 10231 20471 40951 81911 163831 327671
(1 + (loop(\(x,i).(2x + 4),x,1) div 2))
A052549: 1 4 9 19 39 79 159 319 639 1279 2559 5119 10239 20479 40959 81919
(3 + loop(\(x,i).4x,x,1))
A253208: 4 7 19 67 259 1027 4099 16387 65539 262147 1048579 4194307 16777219 67108867 268435459 1073741827
(3 + loop(\(x,i).(~2x + 4),x,1))
A268741: 4 5 3 7 ~1 15 ~17 47 ~81 175 ~337 687 ~1361 2735 ~5457 10927
(~1 + (2 * loop(\(x,i).(2 * (x + i)),x,1)))
A126284: 1 7 23 59 135 291 607 1243 2519 5075 10191 20427 40903 81859 163775 327611
(1 + (loop(\(x,i).(2 * (x + i)),x,1) div 2))
A133124: 1 3 7 16 35 74 153 312 631 1270 2549 5108 10227 20466 40945 81904
(if (5 mod (x + 1)) <= 0 then 2 else 1)
A214710: 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
loop(\(x,i).(2x2 + 3x + 1),2,1)
A103847: 91 91 91 91 91 91 91 91 91 91 91 91 91 91 91 91
loop(\(x,i).(x * i),x,(2x + 3))
A129326: 3 5 14 54 264 1560 10800 85680 766080 7620480 83462400 997920000 12933043200 180583603200 2702527027200 43153254144000
loop(\(x,i).3x,(2x + 2),1)
A100062: 9 81 729 6561 59049 531441 4782969 43046721 387420489 3486784401 31381059609 282429536481 2541865828329 22876792454961 205891132094649 1853020188851841
loop(\(x,i).(x * i),x,(1 + ((x + 1) div 2)))
A052689: 1 2 4 18 72 480 2880 25200 201600 2177280 21772800 279417600 3353011200 49816166400 697426329600 11769069312000
loop(\(x,i).3x,((x + 1) div 2),1)
A162436-A056449: 1 3 3 9 9 27 27 81 81 243 243 729 729 2187 2187 6561
(1 + (loop(\(x,i).2x,x,(x + 1)) div 2))
A131056: 1 3 7 17 41 97 225 513 1153 2561 5633 12289 26625 57345 122881 262145
(3 + loop(\(x,i).3x,x,1))
A178674: 4 6 12 30 84 246 732 2190 6564 19686 59052 177150 531444 1594326 4782972 14348910
(1 + (2 * loop(\(x,i).(x2 + x),x,1)))
A053630: 3 5 13 85 3613 6526885 21300113901613 4611686018427387903 4611686018427387903
loop(\(x,i).2x,((x2 + 1) div 2),1)
A247014: 1 2 4 32 256 8192 262144 33554432 4294967296 2199023255552 1125899906842624 2305843009213693952 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 10) <= 0 then 2 else 1)
A250209: 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
(if (~2 + (x div 5)) <= 0 then 2 else 1)
A194302-A194294-A074264: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
(if ((x + 2) mod 6) <= 0 then 2 else 1)
A305936: 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1
(if ((x + ~2) mod 6) <= 0 then 2 else 1)
A107577: 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1
(5 + loop(\(x,i).2x,x,1))
A168614: 6 7 9 13 21 37 69 133 261 517 1029 2053 4101 8197 16389 32773
(~5 + loop(\(x,i).2x,x,1))
A168616: ~4 ~3 ~1 3 11 27 59 123 251 507 1019 2043 4091 8187 16379 32763
(if ((x + 1) mod 8) <= 0 then 2 else 1)
A328856-A325988-A325837-A304327-A295657-A107039-A072911-A061704-A053150-A050361-A043281: 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2
(x div (if ((x + 2) mod 4) <= 0 then 2 else 1))
A283971: 0 1 1 3 4 5 3 7 8 9 5 11 12 13 7 15
(1 + (if (x mod 2) <= 0 then 1 else 8))
A010699: 2 9 2 9 2 9 2 9 2 9 2 9 2 9 2 9
loop(\(x,i).2x,x,9)
A005010: 9 18 36 72 144 288 576 1152 2304 4608 9216 18432 36864 73728 147456 294912
loop(\(x,i).2x,(x + ~8),1)
A275075-A275063: 1 1 1 1 1 1 1 1 1 2 4 8 16 32 64 128
loop(\(x,i).(x + i),(x + ~8),1)
A212367: 1 1 1 1 1 1 1 1 1 2 4 7 11 16 22 29
(1 + loop(\(x,i).x2,x,8))
A152581: 9 65 4097 16777217 281474976710657 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).x2,x,8))
A036287: 7 63 4095 16777215 281474976710655 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * (if (x + ~1) <= 0 then x else 4)))
A100401: 1 3 9 9 9 9 9 9 9 9 9 9 9 9 9 9
(if (~x + 2) <= 0 then (2 + (x div 4)) else 1)
A103128: 1 1 2 2 3 3 3 3 4 4 4 4 5 5 5 5
(if (x mod 2) <= 0 then ((x div 4) mod 2) else 1)
A320007-A115971: 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1
(1 + (4 * (if (x + ~1) <= 0 then x else 2)))
A175373: 1 5 9 9 9 9 9 9 9 9 9 9 9 9 9 9
(~1 + (2 * (if x <= 0 then 1 else 4x)))
A133655: 1 7 15 23 31 39 47 55 63 71 79 87 95 103 111 119
loop(\(x,i).(x * i),8x,1)
A195392: 1 40320 20922789888000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (2 + (x mod 2) - (x div 2)) <= 0 then 2 else 1)
A163376: 1 1 1 1 2 1 2 2 2 2 2 2 2 2 2 2
(5 + loop(\(x,i).x2,x,2))
A063486: 7 9 21 261 65541 4294967301 4611686018427387903 4611686018427387903 4611686018427387903
(~5 + loop(\(x,i).x2,x,2))
A232460: ~3 ~1 11 251 65531 4294967291 4611686018427387903 4611686018427387903 4611686018427387903
(if ((x + ~1) mod 3) <= 0 then 4 else 1)
A146325: 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1
(if ((x mod 3) mod 2) <= 0 then 4 else 1)
A173259: 4 1 4 4 1 4 4 1 4 4 1 4 4 1 4 4
(x div (if (x mod 4) <= 0 then 4 else 1))
A214392: 0 1 2 3 1 5 6 7 2 9 10 11 3 13 14 15
(x2 div (if (x mod 2) <= 0 then 4 else 1))
A168077: 0 1 1 9 4 25 9 49 16 81 25 121 36 169 49 225
(5 * (2 + (if x <= 0 then 0 else 2)))
A040090: 10 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
(if x <= 0 then 1 else ((x div 2) div 5))
A288686-A245795-A245150-A083850-A025155-A017904-A017896-A017895-A017894-A017893-A017892-A017891: 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1
loop(\(x,i).(2x + 2),x,5)
A176448: 5 12 26 54 110 222 446 894 1790 3582 7166 14334 28670 57342 114686 229374
loop(\(x,i).(x2 + ~2),x,5)
A003487: 5 23 527 277727 77132286527 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).3x,x,5)
A005030: 5 15 45 135 405 1215 3645 10935 32805 98415 295245 885735 2657205 7971615 23914845 71744535
(1 + (if (x + ~3) <= 0 then x else 4))
A210032: 1 2 3 4 5 5 5 5 5 5 5 5 5 5 5 5
(~1 + loop(\(x,i).(x2 + ~2),x,4))
A145503: 3 13 193 37633 1416317953 2005956546822746113 4611686018427387903
loop(\(x,i).4x,(x div 4),1)
A242954: 1 1 1 1 4 4 4 4 16 16 16 16 64 64 64 64
loop(\(x,i).(x * i),x,(1 + (x div 4)))
A052614: 1 1 2 6 48 240 1440 10080 120960 1088640 10886400 119750400 1916006400 24908083200 348713164800 5230697472000
loop(\(x,i).3x,(x div 4),1)
A111575: 1 1 1 1 3 3 3 3 9 9 9 9 27 27 27 27
(1 + (if (x mod 2) <= 0 then x else (x mod 4)))
A230089: 1 2 3 4 5 2 7 4 9 2 11 4 13 2 15 4
(1 + loop(\(x,i).3x,x,4))
A199108: 5 13 37 109 325 973 2917 8749 26245 78733 236197 708589 2125765 6377293 19131877 57395629
(~1 + loop(\(x,i).3x,x,4))
A171498: 3 11 35 107 323 971 2915 8747 26243 78731 236195 708587 2125763 6377291 19131875 57395627
(1 + loop(\(x,i).(x2 + x),x,4))
A144779: 5 21 421 176821 31265489221 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(x2 div 4),1)
A060656: 1 1 2 4 16 64 512 4096 65536 1048576 33554432 1073741824 68719476736 4398046511104 562949953421312 72057594037927936
(3 + loop(\(x,i).4x,x,2))
A188161: 5 11 35 131 515 2051 8195 32771 131075 524291 2097155 8388611 33554435 134217731 536870915 2147483651
(3 + loop(\(x,i).(~2x + 1),x,2))
A156550: 5 0 10 ~10 30 ~50 110 ~210 430 ~850 1710 ~3410 6830 ~13650 27310 ~54610
(if (5 mod (x + 2)) <= 0 then 2 else 1)
A078315: 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1
loop(\(x,i).2x,x,(x + 5))
A196410: 5 12 28 64 144 320 704 1536 3328 7168 15360 32768 69632 147456 311296 655360
loop(\(x,i).(x * i),x,(x + 5))
A282466: 5 6 14 48 216 1200 7920 60480 524160 5080320 54432000 638668800 8143027200 112086374400 1656387532800 26153487360000
((x mod 3) div (if (x + ~2) <= 0 then 2 else 1))
A229878: 0 0 1 0 1 2
A220659: 0 0 1 0 1 2 0 1 2 0 1 2 0 1 2 0
(~1 + loop(\(x,i).4x,2x,2))
A241888: 1 31 511 8191 131071 2097151 33554431 536870911 8589934591 137438953471 2199023255551 35184372088831 562949953421311 9007199254740991 144115188075855871 2305843009213693951
loop(\(x,i).4x,4x,1)
A133752: 1 256 65536 16777216 4294967296 1099511627776 281474976710656 72057594037927936 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,2,(4x + 1))
A016816: 1 625 6561 28561 83521 194481 390625 707281 1185921 1874161 2825761 4100625 5764801 7890481 10556001 13845841
loop(\(x,i).2x,x,(4x + 1))
A118415: 1 10 36 104 272 672 1600 3712 8448 18944 41984 92160 200704 434176 933888 1998848
loop(\(x,i).(x * i),x,(4x + 1))
A082034: 1 5 18 78 408 2520 18000 146160 1330560 13426560 148780800 1796256000 23471078400 330032102400 4969162598400 79768136448000
(1 + loop(\(x,i).3x,2x,2))
A199559: 3 19 163 1459 13123 118099 1062883 9565939 86093443 774840979 6973568803 62762119219 564859072963 5083731656659 45753584909923 411782264189299
(~1 + loop(\(x,i).3x,2x,2))
A198859: 1 17 161 1457 13121 118097 1062881 9565937 86093441 774840977 6973568801 62762119217 564859072961 5083731656657 45753584909921 411782264189297
(~1 + loop(\(x,i).(x * (2 + i)),2x,2))
A127230: 1 23 719 40319 3628799 479001599 87178291199 20922789887999 6402373705727999 2432902008176639999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(2x + i),2x,2))
A289255: 1 11 57 247 1013 4083 16369 65519 262125 1048555 4194281 16777191 67108837 268435427 1073741793 4294967263
(1 + (if (x + ~2) <= 0 then x else (2 + (x div 2))))
A309250: 1 2 3 4 5 5 6 6 7 7 8 8 9 9 10 10
loop(\(x,i).((x mod 2) + i),(~2 + (x div 2)),1)
A005858: 1 1 1 1 1 1 2 2 2 2 3 3 5 5 6 6
((x + 2) - loop(\(x,i).i,(~2 + (x div 2)),1))
A327708-A079631: 1 2 3 4 5 6 7 8 8 9 9 10 10 11 11 12
(if (~x + 2) <= 0 then (2 - ((x div 2) mod 2)) else 1)
A303827: 1 1 1 1 2 2 1 1 2 2 1 1 2 2 1 1
(if x <= 0 then 0 else (5 - (x mod 2)))
A021026: 0 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4
loop(\(x,i).2x,x,(1 + (2 * (x mod 2))))
A081631: 1 6 4 24 16 96 64 384 256 1536 1024 6144 4096 24576 16384 98304
(1 + (if (~x2 + 2x) <= 0 then (x mod 2) else 2))
A084642: 1 3 1 2 1 2 1 2 1 2 1 2 1 2 1 2
(1 + loop(\(x,i).x2,2x2,2))
A161473: 3 17 4611686018427387903
A162713: 3 17 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).x3,x,2) div 2))
A121270: 2 5 257
(1 + (loop(\(x,i).(2x + i),x,2) div 2))
A201363: 2 3 7
A112884: 2 3 7 14 30 61 125 252 508 1019 2043 4090 8186 16377 32761 65528
(~1 + loop(\(x,i).(x * (x2 + i)),2,2))
A245206: 1019
(9 * (if x <= 0 then 1 else 2))
A040072: 9 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18
(if x <= 0 then 1 else (3 * (~1 + (x mod 2))))
A115634: 1 0 ~3 0 ~3 0 ~3 0 ~3 0 ~3 0 ~3 0 ~3 0
((1 + (if (x + ~2) <= 0 then 0 else x)) div 3)
A062276: 0 0 0 1 1 2 2 2 3 3 3 4 4 4 5 5
(3 * loop(\(x,i).(2x + 2),x,1))
A089143: 3 12 30 66 138 282 570 1146 2298 4602 9210 18426 36858 73722 147450 294906
(((x + ~1) * (if x <= 0 then 0 else 2)) div 3)
A135672: 0 0 0 1 2 2 3 4 4 5 6 6 7 8 8 9
(3 * (if (x mod 3) <= 0 then 1 else 2))
A105396: 3 6 6 3 6 6 3 6 6 3 6 6 3 6 6 3
(3 * (2 + loop(\(x,i).2x,x,1)))
A153973: 9 12 18 30 54 102 198 390 774 1542 3078 6150 12294 24582 49158 98310
(if x <= 0 then 1 else (((x + 1) div 2) div 3))
A114968: 1 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2
(6 * (2 + (if x <= 0 then 0 else 2)))
A040132: 12 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24
(if x <= 0 then 1 else (x div 12))
A017906: 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1
(3 * (2 - ((if x <= 0 then 1 else x) mod 2)))
A040007: 3 3 6 3 6 3 6 3 6 3 6 3 6 3 6 3
(3 * loop(\(x,i).4x,x,2))
A002023: 6 24 96 384 1536 6144 24576 98304 393216 1572864 6291456 25165824 100663296 402653184 1610612736 6442450944
loop(\(x,i).(x * i),x,((x + 2) div 3))
A052688: 0 1 2 6 48 240 1440 15120 120960 1088640 14515200 159667200 1916006400 31135104000 435891456000 6538371840000
loop(\(x,i).(x2 + ~2),2x,3)
A219162: 3 47 4870847 4611686018427387903
loop(\(x,i).x2,2,6x)
A016912: 0 1296 20736 104976 331776 810000 1679616 3111696 5308416 8503056 12960000 18974736 26873856 37015056 49787136 65610000
loop(\(x,i).3x,2x,3)
A013708: 3 27 243 2187 19683 177147 1594323 14348907 129140163 1162261467 10460353203 94143178827 847288609443 7625597484987 68630377364883 617673396283947
loop(\(x,i).4x,(x div 2),3)
A117856: 3 3 12 12 48 48 192 192 768 768 3072 3072 12288 12288 49152 49152
((x + (if (x mod 2) <= 0 then 2 else 0)) div 3)
A285870: 0 0 1 1 2 1 2 2 3 3 4 3 4 4 5 5
loop(\(x,i).(4x + 1),x,3)
A072197: 3 13 53 213 853 3413 13653 54613 218453 873813 3495253 13981013 55924053 223696213 894784853 3579139413
loop(\(x,i).(3x + ~3),x,3)
A067771: 3 6 15 42 123 366 1095 3282 9843 29526 88575 265722 797163 2391486 7174455 21523362
loop(\(x,i).6x,x,3)
A169604: 3 18 108 648 3888 23328 139968 839808 5038848 30233088 181398528 1088391168 6530347008 39182082048 235092492288 1410554953728
loop(\(x,i).(x2 + ~3),x,3)
A186750: 3 6 33 1086 1179393 1390967848446 4611686018427387903 4611686018427387903
loop(\(x,i).(3x * i),x,3)
A032179: 3 9 54 486 5832 87480 1574640 33067440 793618560 21427701120 642831033600 21213424108800 763683267916800 29783647448755200 1250913192847718400 4611686018427387903
loop(\(x,i).(2x2 + ~1),x,3)
A292082: 3 17 577 665857
loop(\(x,i).(3x + 1),x,3)
A237930: 3 10 31 94 283 850 2551 7654 22963 68890 206671 620014 1860043 5580130 16740391 50221174
loop(\(x,i).(3x + ~1),x,3)
A057198: 3 8 23 68 203 608 1823 5468 16403 49208 147623 442868 1328603 3985808 11957423 35872268
loop(\(x,i).(x2 + ~x + ~1),x,3)
A144743: 3 5 19 341 115939 13441735781 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + ~4),x,3)
A135583: 3 8 28 108 428 1708 6828 27308 109228 436908 1747628 6990508 27962028 111848108 447392428 1789569708
((x + 3) - (2 div (if x <= 0 then 1 else x)))
A228728-A174416: 1 2 4 6 7 8 9 10 11 12 13 14 15 16 17 18
loop(\(x,i).(4x + ~2),x,3)
A308124: 3 10 38 150 598 2390 9558 38230 152918 611670 2446678 9786710 39146838 156587350 626349398 2505397590
loop(\(x,i).(4x + ~8),x,3)
A155701: 3 4 8 24 88 344 1368 5464 21848 87384 349528 1398104 5592408 22369624 89478488 357913944
loop(\(x,i).(x2 + ~4),x,3)
A186751: 3 5 21 437 190965 36467631221 4611686018427387903 4611686018427387903
loop(\(x,i).((x2 + x) div 2),x,3)
A096662: 3 6 21 231 26796 359026206 64449908476890321 4611686018427387903 4611686018427387903
((x + 3) + (if (x + ~1) <= 0 then x else 2))
A102890: 3 5 7 8 9 10 11 12 13 14 15 16 17 18 19 20
((x + (if (x mod 2) <= 0 then x else 2)) mod 3)
A021823: 0 0 1 2 2 1 0 0 1 2 2 1 0 0 1 2
(3 + (if x <= 0 then 1 else (x2 + 2x)))
A197985: 4 6 11 18 27 38 51 66 83 102 123 146 171 198 227 258
(loop(\(x,i).(x * i),(x + 2),x) div 3)
A090672: 0 2 16 120 960 8400 80640 846720 9676800 119750400 1596672000 22832409600 348713164800 5666588928000 97639686144000 1778437140480000
(if x <= 0 then 1 else (3 * (x + (x div 2))))
A261953: 1 3 9 12 18 21 27 30 36 39 45 48 54 57 63 66
loop(\(x,i).2x,x,(1 - (x mod 3)))
A104538: 1 0 ~4 8 0 ~32 64 0 ~256 512 0 ~2048 4096 0 ~16384 32768
loop(\(x,i).(x + (x div 3)),x,3)
A299114: 3 4 5 6 8 10
A100585: 3 4 5 6 8 10 13 17 22 29 38 50 66 88 117 156
loop(\(x,i).(2x2 + x),x,3)
A176430: 3 21 903 1631721 5325028475403 4611686018427387903 4611686018427387903
((if (x mod 2) <= 0 then (~x + 1) else x) mod 3)
A100286: 1 1 2 0 0 2 1 1 2 0 0 2 1 1 2 0
((x + (if (x mod 2) <= 0 then 2 else x)) mod 3)
A131026: 2 2 1 0 0 1 2 2 1 0 0 1 2 2 1 0
loop(\(x,i).x3,x2,3)
A162414: 3 27 4611686018427387903
(3 * (~x + loop(\(x,i).2x,x,x)))
A317404: 0 3 18 63 180 465 1134 2667 6120 13797 30690 67551 147420 319449 688086 1474515
loop(\(x,i).((x - i) * (x + i)),x,3)
A110385: 3 8 60 3591 12895265 166287859420200 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (2 * (x + (if (x mod 2) <= 0 then 2 else 0))))
A166519: 3 1 7 5 11 9 15 13 19 17 23 21 27 25 31 29
(~1 + loop(\(x,i).(3x + 3),x,2))
A116952: 1 8 29 92 281 848 2549 7652 22961 68888 206669 620012 1860041 5580128 16740389 50221172
(1 + loop(\(x,i).6x,x,2))
A199317: 3 13 73 433 2593 15553 93313 559873 3359233 20155393 120932353 725594113 4353564673 26121388033 156728328193 940369969153
(~1 + loop(\(x,i).6x,x,2))
A164559: 1 11 71 431 2591 15551 93311 559871 3359231 20155391 120932351 725594111 4353564671 26121388031 156728328191 940369969151
(1 + loop(\(x,i).(1 + (x * (1 + i))),x,2))
A274103: 3 6 17 66 327
(~1 + (2 * (x + loop(\(x,i).2x,x,1))))
A131898: 1 5 11 21 39 73 139 269 527 1041 2067 4117 8215 16409 32795 65565
(~1 + loop(\(x,i).(4x + 4),x,2))
A321421: 1 11 51 211 851 3411 13651 54611 218451 873811 3495251 13981011 55924051 223696211 894784851 3579139411
loop(\(x,i).(x * i),((x2 + x) div 2),1)
A052295: 1 1 6 720 3628800 1307674368000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(4x + ~4),x,2))
A321358: 3 5 13 45 173 685 2733 10925 43693 174765 699053 2796205 11184813 44739245 178956973 715827885
loop(\(x,i).2x,((x2 + ~x) div 2),1)
A006125: 1 1 2 8 64 1024 32768 2097152 268435456 68719476736 35184372088832 36028797018963968 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(2 * (1 + (x * i))),x,2))
A161370: 3 7 27 159 1267 12663 151947 2127247 34035939 612646887 12252937723 269564629887 6469551117267 168208329048919 4709833213369707 141294996401091183
(1 + loop(\(x,i).8x,x,2))
A199493: 3 17 129 1025 8193 65537 524289 4194305 33554433 268435457 2147483649 17179869185 137438953473 1099511627777 8796093022209 70368744177665
(~1 + loop(\(x,i).8x,x,2))
A198850: 1 15 127 1023 8191 65535 524287 4194303 33554431 268435455 2147483647 17179869183 137438953471 1099511627775 8796093022207 70368744177663
(~1 + loop(\(x,i).(4 * (x - i)),x,2))
A210985: 1 3 7 19 63 235 919 3651 14575
(1 + (2 * loop(\(x,i).i,(~2 + (x div 2)),x)))
A103701: 1 3 5 7 9 11 3 3 5 5 7 7 9 9 11 11
(~1 + loop(\(x,i).((x2 + x) div 2),x,2))
A006893: 1 2 5 20 230 26795 359026205 64449908476890320 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).(x2 + 2x),2,x) div 2))
A171714: 1 8 41 128 313 648 1201 2048 3281 5000 7321 10368 14281 19208 25313 32768
(~1 + loop(\(x,i).(2x + (i div 2)),x,2))
A011377: 1 3 8 18 39 81 166 336 677 1359 2724 5454 10915 21837 43682 87372
(~x mod (~1 + loop(\(x,i).2x,x,2)))
A076878: 0 2 5 12 27 58 121 248 503 1014 2037 4084 8179 16370 32753 65520
(~1 + loop(\(x,i).(3x - i),x,2))
A090328: 1 4 12 35 103 306 914 2737 8205 24608 73816 221439 664307 1992910 5978718 17936141
(1 + (2 * loop(\(x,i).(x * (x + i)),2,x)))
A008514: 1 17 97 337 881 1921 3697 6497 10657 16561 24641 35377 49297 66977 89041 116161
(~1 + loop(\(x,i).(x - (2 * (~x + i))),x,2))
A233656: 1 3 7 17 45 127 371 1101 3289 9851 29535 88585 265733 797175 2391499 7174469
(~1 + (loop(\(x,i).(x * i),x,1) mod (x + 2)))
A056051: 0 0 1 0 ~1 0 ~1 ~1 ~1 0 ~1 0 ~1 ~1 ~1 0
(if (2 - (x div 4)) <= 0 then (x + 2) else 1)
A058364: 1 1 1 1 1 1 1 1 10 11 12 13 14 15 16 17
(1 + loop(\(x,i).(x * (x - i)),2,(x + 2)))
A062938: 1 25 121 361 841 1681 3025 5041 7921 11881 17161 24025 32761 43681 57121 73441
(loop(\(x,i).2x,x,1) mod (x + 3))
A077748: 1 2 4 2 2
A294389: 1 2 4 2 2 0 1 8 3 8 10 4 1 0 13 8
(loop(\(x,i).(x * i),x,1) mod (x + 3))
A285982: 1 1 2 0 3 0 0 0 5 0 6 0 0 0 8 0
loop(\(x,i).2x,(x div 2),(x + 3))
A092434: 3 4 10 12 28 32 72 80 176 192 416 448 960 1024
(if (x mod 2) <= 0 then (~x + 1) else (x + 3))
A227832: 1 4 ~1 6 ~3 8 ~5 10 ~7 12 ~9 14 ~11 16 ~13 18
(1 + ((x + 2) * (if (x + ~2) <= 0 then 1 else x)))
A290014: 3 4 5 16 25
(1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2)))
A073599: 1 2 3 4 5 6 9 10 11 12 13 14 15 16 17 18
loop(\(x,i).(4x + 1),2x,1)
A144864: 1 21 341 5461 87381 1398101 22369621 357913941 5726623061 91625968981 1466015503701 23456248059221 375299968947541 6004799503160661 96076792050570581 1537228672809129301
loop(\(x,i).(4x + ~1),2x,1)
A139792: 1 11 171 2731 43691 699051 11184811 178956971 2863311531 45812984491 733007751851 11728124029611 187649984473771 3002399751580331 48038396025285291 768614336404564651
(if ((x + ~1) mod 3) <= 0 then 2x else 1)
A078689: 1 2 1 1 8 1 1 14 1 1 20 1 1 26 1 1
loop(\(x,i).6x,2x,1)
A009980: 1 36 1296 46656 1679616 60466176 2176782336 78364164096 2821109907456 101559956668416 3656158440062976 131621703842267136 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~3x + 3),2x,1)
A054879: 1 3 21 183 1641 14763 132861 1195743 10761681 96855123 871696101 7845264903 70607384121 635466457083 5719198113741 51472783023663
loop(\(x,i).(3x * i),2x,1)
A068181: 1 18 1944 524880 264539520 214277011200 254561089305600 416971064282572800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x + 1),2x,1)
A096053: 1 13 121 1093 9841 88573 797161 7174453 64570081 581130733 5230176601 47071589413 423644304721 3812798742493 34315188682441 308836698141973
loop(\(x,i).(3x + ~1),2x,1)
A083884: 1 5 41 365 3281 29525 265721 2391485 21523361 193710245 1743392201 15690529805 141214768241 1270932914165 11438396227481 102945566047325
loop(\(x,i).(2x * (1 + i)),2x,1)
A002671: 1 24 1920 322560 92897280 40874803200 25505877196800 21424936845312000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + ~2),2x,1)
A091881: 1 6 86 1366 21846 349526 5592406 89478486 1431655766 22906492246 366503875926 5864062014806 93824992236886 1501199875790166 24019198012642646 384307168202282326
(1 + loop(\(x,i).(x2 + ~1),2,2x))
A069075: 1 9 225 1225 3969 9801 20449 38025 65025 104329 159201 233289 330625 455625 613089 808201
loop(\(x,i).8x,2x,1)
A089357: 1 64 4096 262144 16777216 1073741824 68719476736 4398046511104 281474976710656 18014398509481984 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~4x + 2),2x,1)
A061654: 1 10 154 2458 39322 629146 10066330 161061274 2576980378 41231686042 659706976666 10555311626650 168884986026394 2702159776422298 43234556422756762 691752902764108186
loop(\(x,i).(~4x + 1),2x,1)
A299960: 1 13 205 3277 52429 838861 13421773 214748365 3435973837 54975581389 879609302221 14073748835533 225179981368525 3602879701896397 57646075230342349 922337203685477581
loop(\(x,i).(2 * ((x + ~2) + i)),2x,1)
A107584: 1 0 8 52 240 1004 4072 16356 65504 262108 1048536 4194260 16777168 67108812 268435400 1073741764
loop(\(x,i).(2 * ((x + 2) - i)),2x,1)
A221906: 1 8 24 76 272 1044 4120 16412 65568 262180 1048616 4194348 16777264 67108916 268435512 1073741884
loop(\(x,i).(2 * (x + (x div 2))),2x,1)
A092810: 1 6 54 486 4374 39366 354294 3188646 28697814 258280326 2324522934 20920706406 188286357654 1694577218886 15251194969974 137260754729766
loop(\(x,i).(~3x + 1),2x,1)
A066443: 1 7 61 547 4921 44287 398581 3587227 32285041 290565367 2615088301 23535794707 211822152361 1906399371247 17157594341221 154418349070987
((2x + ~1) + (if x <= 0 then 2 else (x mod 2)))
A263881: 1 2 3 6 7 10 11
A053438: 1 2 3 6 7 10 11 14 15 18 19 22 23 26 27 30
loop(\(x,i).(x - (2x * i)),2x,1)
A101485: 1 3 105 10395 2027025 654729075 316234143225 213458046676875 191898783962510625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,3,(2x + 1))
A016760: 1 6561 390625 5764801 43046721 214358881 815730721 2562890625 6975757441 16983563041 37822859361 78310985281 152587890625 282429536481 500246412961 852891037441
loop(\(x,i).2x,(x + ~1),(2x + 1))
A188545: 1 3 10
A128135: 1 3 10 28 72 176 416 960 2176 4864 10752 23552 51200 110592 237568 507904
loop(\(x,i).x3,1,(2x + 1))
A016755: 1 27 125 343 729 1331 2197 3375 4913 6859 9261 12167 15625 19683 24389 29791
((2x + 1) * (2 + (if x <= 0 then 1 else 2)))
A281813: 3 12 20 28 36 44 52 60 68 76 84 92 100 108 116 124
((2x + 1) * ((if x <= 0 then 1 else x) mod 2))
A266437: 1 3 0 7 0 11 0 15 0 19 0 23 0 27 0 31
((2x + 1) * loop(\(x,i).2x,x,2))
A118417: 2 12 40 112 288 704 1664 3840 8704 19456 43008 94208 204800 442368 950272 2031616
(loop(\(x,i).2x,x,2) div (2x + 1))
A191631: 2 1 1 2 3 5 9 17 30 53 97 178 327 606 1129 2114
((2x + 1) * (if x <= 0 then 1 else 2x))
A068377: 1 6 20 42 72 110 156 210 272 342 420 506 600 702 812 930
loop(\(x,i).x3,2,(2x + 1))
A016761: 1 19683 1953125 40353607 387420489 2357947691 10604499373 38443359375 118587876497 322687697779 794280046581 1801152661463 3814697265625 7625597484987 14507145975869 26439622160671
loop(\(x,i).(2x + ~4),x,(2x + 1))
A048497: 1 2 8 28 84 228 580 1412 3332 7684 17412 38916 86020 188420 409604 884740
loop(\(x,i).4x,x,(2x + 1))
A058962: 1 12 80 448 2304 11264 53248 245760 1114112 4980736 22020096 96468992 419430400 1811939328 7784628224 33285996544
loop(\(x,i).(2x * i),x,(2x + 1))
A014481: 1 6 40 336 3456 42240 599040 9676800 175472640 3530096640 78033715200 1880240947200 49049763840000 1377317368627200 41421544567603200 1328346084409344000
loop(\(x,i).3x,x,(2x + 1))
A124647: 1 9 45 189 729 2673 9477 32805 111537 373977 1240029 4074381 13286025 43046721 138706101 444816117
loop(\(x,i).(x * (1 + i)),x,(2x + 1))
A175925: 1 6 30 168 1080 7920 65520 604800 6168960 68947200 838252800 11017036800 155675520000 2353813862400 37922556672000 648606486528000
(if x <= 0 then 1 else (x2 mod (2x + 1)))
A123684: 1 1 4 2 7 3 10 4 13 5 16 6 19 7 22 8
loop(\(x,i).5x,2x,1)
A009969: 1 25 625 15625 390625 9765625 244140625 6103515625 152587890625 3814697265625 95367431640625 2384185791015625 59604644775390625 1490116119384765625 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (2 * i))),2x,1)
A103639: 1 15 945 135135 34459425 13749310575 7905853580625 6190283353629375 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(2x + ~2),x,2x))
A088578: 1 3 11 35 99 259 643 1539 3587 8195 18435 40963 90115 196611 425987 917507
(1 + loop(\(x,i).(2 * (x + i)),x,2x))
A213569: 1 7 25 71 181 435 1009 2287 5101 11243 24553 53223 114661 245731 524257 1114079
(1 + loop(\(x,i).(2 * (x - i)),x,2x))
A048481: 1 3 9 27 77 207 529 1299 3093 7191 16409 36891 81949 180255 393249 852003
(1 + loop(\(x,i).(2x - i),x,2x))
A181527: 1 4 13 38 103 264 649 1546 3595 8204 18445 40974 90127 196624 426001 917522
loop(\(x,i).(x * (i * i * i)),2x,1)
A134373: 1 8 13824 373248000 65548320768000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + 1),(x div 2),1)
A052992: 1 1 5 5 21 21 85 85 341 341 1365 1365 5461 5461 21845 21845
loop(\(x,i).(3x + 1),(x div 2),1)
A052993: 1 1 4 4 13 13 40 40 121 121 364 364 1093 1093 3280 3280
(~1 + loop(\(x,i).2x,x,1) - (x div 2))
A173009: 0 1 2 6 13 29 60 124 251 507 1018 2042 4089 8185 16376 32760
(1 + (if (x mod 2) <= 0 then 2x else (x div 2)))
A112871: 1 1 5 2
A065262: 1 1 5 2 9 3 13 4 17 5 21 6 25 7 29 8
(loop(\(x,i).(x * i),x,1) div (1 + (x div 2)))
A107991: 1 1 1 3 8 40 180 1260 8064 72576 604800 6652800 68428800 889574400 10897286400 163459296000
loop(\(x,i).(x * i),x,(2 mod (1 + (x div 2))))
A052683: 0 0 0 0 48 240 1440 10080 80640 725760 7257600 79833600 958003200 12454041600 174356582400 2615348736000
loop(\(x,i).5x,(x div 2),1)
A074872: 1 1 5 5 25 25 125 125 625 625 3125 3125 15625 15625 78125 78125
loop(\(x,i).(x * (~1 + (2 * i))),(x div 2),1)
A133221: 1 1 1 1 3 3 15 15 105 105 945 945 10395 10395 135135 135135
(1 + (loop(\(x,i).2x,x,1) + (x mod 2)))
A049332: 2 4 5 10 17 34 65 130 257 514 1025 2050 4097 8194 16385 32770
(1 + loop(\(x,i).2x,x,1) - (x mod 2))
A052531: 2 2 5 8 17 32 65 128 257 512 1025 2048 4097 8192 16385 32768
(~1 + loop(\(x,i).2x,x,1) - (x mod 2))
A141023: 0 0 3 6 15 30 63 126 255 510 1023 2046 4095 8190 16383 32766
(if (~2 + (x div 3)) <= 0 then (x mod 2) else 1)
A116372: 0 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1
(if (2 - (x div 4)) <= 0 then (x mod 2) else 1)
A267256: 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1
loop(\(x,i).(x * i),x,(3 - (x mod 2)))
A052616: 3 2 6 12 72 240 2160 10080 120960 725760 10886400 79833600 1437004800 12454041600 261534873600 2615348736000
((if (~x + 2) <= 0 then 2 else 1) * (1 + (x mod 2)))
A106469-A082508: 1 2 2 4 2 4 2 4 2 4 2 4 2 4 2 4
loop(\(x,i).2x,(x + ~1),(1 + (x mod 2)))
A158302: 1 2 2 8 8 32 32 128 128 512 512 2048 2048 8192 8192 32768
loop(\(x,i).4x,x,(1 + (x mod 2)))
A107906: 1 8 16 128 256 2048 4096 32768 65536 524288 1048576 8388608 16777216 134217728 268435456 2147483648
((x * (x + (x mod 2))) + (if x <= 0 then 2 else 1))
A193064: 2 3 5 13
(1 + loop(\(x,i).5x,x,2))
A199212: 3 11 51 251 1251 6251 31251 156251 781251 3906251 19531251 97656251 488281251 2441406251 12207031251 61035156251
(~1 + loop(\(x,i).5x,x,2))
A081655: 1 9 49 249 1249 6249 31249 156249 781249 3906249 19531249 97656249 488281249 2441406249 12207031249 61035156249
(1 + ((x * (if (x + ~2) <= 0 then 1 else x)) div 2))
A323457: 1 1 2 5 9
(1 + loop(\(x,i).(x * (3 + i)),x,2))
A139150: 3 9 41 241 1681 13441 120961 1209601 13305601 159667201 2075673601 29059430401 435891456001 6974263296001 118562476032001 2134124568576001
(~1 + loop(\(x,i).(x * (3 + i)),x,2))
A139173: 1 7 39 239 1679 13439 120959 1209599 13305599 159667199 2075673599 29059430399 435891455999 6974263295999 118562476031999 2134124568575999
(1 + (loop(\(x,i).(2x + 4),x,x) div 2))
A047859: 1 4 11 27 63 143 319 703 1535 3327 7167 15359 32767 69631 147455 311295
(~1 + loop(\(x,i).(x * (2 + (i mod 2))),x,2))
A164560: 1 5 11 35 71 215 431 1295 2591 7775 15551 46655 93311 279935 559871 1679615
(1 + (loop(\(x,i).(2 * (x - i)),x,x) div 2))
A112089: 1 1 1 2 7 24
loop(\(x,i).4x,2x2,1)
A078186: 1 16 65536 68719476736 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).3x,2x2,1)
A060761: 1 9 6561 387420489 1853020188851841 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + x),2x2,1)
A079683: 1 6 4611686018427387903
loop(\(x,i).3x,(x2 div 2),1)
A168493: 1 1 9 81 6561 531441 387420489 282429536481 1853020188851841 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).x2,x3,2))
A058473: 1 3 4611686018427387903
(1 + (2 * loop(\(x,i).(x + (i * i)),x,x)))
A005894: 1 5 15 35 69 121 195 295 425 589 791 1035 1325 1665 2059 2511
(~1 + loop(\(x,i).((2 * (x + i)) + i),x,2))
A095264: 1 6 19 48 109 234 487 996 2017 4062 8155 16344 32725 65490 131023 262092
(1 + (x * loop(\(x,i).(1 + (x * i)),x,0)))
A193657: 1 2 7 31 165 1031 7423 60621 554249 5611771 62353011 754471433 9876716941 139097096919 2097156230471 33704296561141
((~x + ~1) + loop(\(x,i).(2 * (x + i)),x,0))
A109363: ~1 0 5 18 47 108 233 486 995 2016 4061 8154 16343 32724 65489 131022
((x + 1) + (if (x mod 2) <= 0 then x2 else 0))
A190716: 1 2 7 4 21 6 43 8 73 10 111 12 157 14 211 16
loop(\(x,i).(3x + 7),x,1)
A116970: 1 10 37 118 361 1090 3277 9838 29521 88570 265717 797158 2391481 7174450 21523357 64570078
loop(\(x,i).(6x + ~1),x,1)
A083066: 1 5 29 173 1037 6221 37325 223949 1343693 8062157 48372941 290237645 1741425869 10448555213 62691331277 376147987661
loop(\(x,i).(1 + (3x * i)),x,1)
A010845: 1 4 25 226 2713 40696 732529 15383110 369194641 9968255308 299047659241 9868572754954 355268619178345 13855476147955456 581929998214129153 4611686018427387903
loop(\(x,i).(1 + (x mod (1 + (i div 2)))),x,1)
A062050: 1 1 2 1 2 3 4 1 2 3 4 5 6 7 8 1
((x + 1) + loop(\(x,i).2x,(x + ~1),1))
A052968: 2 3 5 8 13 22 39 72 137 266 523 1036 2061 4110 8207 16400
loop(\(x,i).(1 + ((x + 2) mod (1 + i))),x,1)
A054995: 1 2 2 1 4 1 4 7 1 4 7 10 13 2 5 8
loop(\(x,i).(1 + (x * (i * (1 + i)))),x,1)
A228229: 1 3 19 229 4581 137431 5772103 323237769 23273119369 2094580743211 230403881753211 30413312391423853 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x - (x div ~3)),x,1)
A087192: 1 2 3 4 6 8 11 15 20 27 36 48 64 86 115 154
loop(\(x,i).(4x + 9),x,1)
A141725: 1 13 61 253 1021 4093 16381 65533 262141 1048573 4194301 16777213 67108861 268435453 1073741821 4294967293
loop(\(x,i).(8x + ~1),x,1)
A083068: 1 7 55 439 3511 28087 224695 1797559 14380471 115043767 920350135 7362801079 58902408631 471219269047 3769754152375 30158033218999
loop(\(x,i).(x * i),5x,1)
A100734: 1 120 3628800 1307674368000 2432902008176640000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (4x * i)),x,1)
A056545: 1 5 41 493 7889 157781 3786745 106028861 3392923553 122145247909 4885809916361 214975636319885 10318830543354481 536579188254433013 4611686018427387903 4611686018427387903
((x + 1) + (if (~x + 4) <= 0 then 2 else 1))
A249407-A127161-A054027: 2 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18
loop(\(x,i).(6x + ~3),x,1)
A152596: 1 3 15 87 519 3111 18663 111975 671847 4031079 24186471 145118823 870712935 5224277607 31345665639 188073993831
(1 div (if ((x + ~1) mod 3) <= 0 then x else 1))
A329682: 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1
loop(\(x,i).(3 * ((x + 1) div 2)),x,1)
A070885: 1 3 6 9 15 24 36 54 81 123 186 279 420 630 945 1419
loop(\(x,i).(6x + ~12),x,1)
A165758: 1 ~6 ~48 ~300 ~1812 ~10884 ~65316 ~391908 ~2351460 ~14108772 ~84652644 ~507915876 ~3047495268 ~18284971620 ~109709829732 ~658258978404
loop(\(x,i).12x,x,1)
A001021: 1 12 144 1728 20736 248832 2985984 35831808 429981696 5159780352 61917364224 743008370688 8916100448256 106993205379072 1283918464548864 15407021574586368
loop(\(x,i).(~6x + 12),x,1)
A165638: 1 6 ~24 156 ~924 5556 ~33324 199956 ~1199724 7198356 ~43190124 259140756 ~1554844524 9329067156 ~55974402924 335846417556
loop(\(x,i).(~6x + 1),x,1)
A014987: 1 ~5 31 ~185 1111 ~6665 39991 ~239945 1439671 ~8638025 51828151 ~310968905 1865813431 ~11194880585 67169283511 ~403015701065
loop(\(x,i).(6x * i),x,1)
A047058: 1 6 72 1296 31104 933120 33592320 1410877440 67722117120 3656994324480 219419659468800 14481697524940800 1042682221795737600 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,2,(3x + 1))
A016780: 1 256 2401 10000 28561 65536 130321 234256 390625 614656 923521 1336336 1874161 2560000 3418801 4477456
loop(\(x,i).2x,x,(3x + 1))
A130129: 1 8 28 80 208 512 1216 2816 6400 14336 31744 69632 151552 327680 704512 1507328
loop(\(x,i).(x * i),x,(3x + 1))
A082033: 1 4 14 60 312 1920 13680 110880 1008000 10160640 112492800 1357171200 17723059200 249080832000 3748666521600 60153020928000
loop(\(x,i).3x,3x,1)
A009971: 1 27 729 19683 531441 14348907 387420489 10460353203 282429536481 7625597484987 205891132094649 5559060566555523 150094635296999121 4052555153018976267 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + i)),3x,1)
A100089: 1 24 5040 3628800 6227020800 20922789888000 121645100408832000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((3x + ~3) + i),x,1)
A111277: 1 1 2 6 19 59 180 544 1637 4917 14758 44282 132855 398575 1195736 3587220
loop(\(x,i).(3x * (1 + i)),x,1)
A034001: 1 6 54 648 9720 174960 3674160 88179840 2380855680 71425670400 2357047123200 84853696435200 3309294160972800 138990354760857600 4611686018427387903 4611686018427387903
loop(\(x,i).(3x * (2 + i)),x,1)
A051606: 1 9 108 1620 29160 612360 14696640 396809280 11904278400 392841187200 14142282739200 551549026828800 23165059126809600 1042427660706432000 4611686018427387903 4611686018427387903
loop(\(x,i).(x + i - (x div 3)),x,1)
A129896: 1 2 4 6 8 11 14 17 20 23 26 29 32 35 38 41
(1 + loop(\(x,i).(x + i),(x div 3),x))
A101882: 1 2 3 5 6 7 10 11 12 16 17 18 23 24 25 31
loop(\(x,i).3x3,x,1)
A134799: 1 3 81 1594323 4611686018427387903
loop(\(x,i).(x - (3x * i)),x,1)
A133480: 1 ~2 10 ~80 880 ~12320 209440 ~4188800 96342400 ~2504902400 72642169600 ~2324549427200 81359229952000 ~3091650738176000 126757680265216000 4611686018427387903
loop(\(x,i).(1 + ((x2 + x) div 2)),x,1)
A006894: 1 2 4 11 67 2279 2598061 3374961778892 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(2x2 + x),1)
A122067: 1 8 1024 2097152 68719476736 36028797018963968 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((3x + 1) - i),x,1)
A047926: 1 3 8 22 63 185 550 1644 4925 14767 44292 132866 398587 1195749 3587234 10761688
loop(\(x,i).((3x + 1) + i),x,1)
A000340: 1 5 18 58 179 543 1636 4916 14757 44281 132854 398574 1195735 3587219 10761672 32285032
loop(\(x,i).((3x + ~1) + i),x,1)
A188545: 1 3 10
A244762: 1 3 10 32 99 301 908 2730 8197 24599 73806 221428 664295 1992897 5978704 17936126
loop(\(x,i).(1 + (2x * (i * i))),x,1)
A336804: 1 3 25 451 14433 721651 51958873 5091969555 651772103041 105587080692643 21117416138528601 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) + (if (x mod 2) <= 0 then (x div 2) else 1))
A071054: 1 3 4 5 7 7 10 9 13 11 16 13 19 15 22 17
((x + 1) + (if (~x + 2) <= 0 then (x div 2) else 1))
A133223: 2 3 4 5 7 8 10 11 13 14 16 17 19 20 22 23
loop(\(x,i).(1 + (2 * (2x - i))),x,1)
A073724: 1 3 9 31 117 459 1825 7287 29133 116515 466041 1864143 7456549 29826171 119304657 477218599
loop(\(x,i).(2x mod (1 + (2 * i))),x,1)
A035492: 1 2 4 1 2 4 8 1 2 4 8 16 7 14 28 25
loop(\(x,i).(5x + ~1),x,1)
A083065: 1 4 19 94 469 2344 11719 58594 292969 1464844 7324219 36621094 183105469 915527344 4577636719 22888183594
loop(\(x,i).((x + 1) + (x div 3)),x,1)
A193622: 1 2 3 5 7 10
A155167: 1 2 3 5 7 10 14 19 26 35 47 63 85 114 153 205
loop(\(x,i).(1 + (x * (~1 + (2 * i)))),x,1)
A112293: 1 2 7 36 253 2278 25059 325768 4886521 83070858 1578346303 33145272364 762341264373 19058531609326 514580353451803 14922830250102288
(1 + (x * loop(\(x,i).(1 + (x * i)),x,1)))
A001339: 1 3 11 49 261 1631 11743 95901 876809 8877691 98641011 1193556233 15624736141 220048367319 3317652307271 53319412081141
((x + 1) + (if (x mod 4) <= 0 then x else 1))
A095028: 1 3 4 5 9
loop(\(x,i).((x + 1) + (2 * (x + i))),x,1)
A060188: 1 6 23 76 237 722 2179 6552 19673 59038 177135 531428 1594309 4782954 14348891 43046704
loop(\(x,i).((x + ~1) + (2 * (x + i))),x,1)
A132308: 1 4 15 50 157 480 1451 4366 13113 39356 118087 354282 1062869 3188632 9565923 28697798
loop(\(x,i).(4x2 + 4x),x,1)
A190840: 1 8 288 332928 443365544448 4611686018427387903 4611686018427387903
loop(\(x,i).4x,(x2 + x),1)
A053863: 1 16 4096 16777216 1099511627776 1152921504606846976 4611686018427387903
loop(\(x,i).2x,x,(x2 + x + 1))
A276041: 1 6 28 104 336 992 2752 7296 18688 46592 113664 272384 643072 1499136 3457024 7897088
loop(\(x,i).(x * i),x,(x2 + x + 1))
A001564: 1 3 14 78 504 3720 30960 287280 2943360 33022080 402796800 5308934400 75203251200 1139544806400 18394619443200 315149522688000
loop(\(x,i).3x,(x2 + x),1)
A053854: 1 9 729 531441 3486784401 205891132094649 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + i)),(x2 + x),1)
A066061: 1 6 5040 6227020800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 - ((x + 1) * (1 - i))),x,1)
A143918: 1 2 5 14 47 194 977 5870 41099 328802 2959229 29592302 325515335 3906184034 50780392457 710925494414
loop(\(x,i).((x + 1) + ((2 - i) * i)),x,1)
A179297: 1 3 4 2 ~5 ~19 ~42 ~76 ~123 ~185 ~264 ~362 ~481 ~623 ~790 ~984
(1 + loop(\(x,i).(x2 + ~1),(x + ~1),x))
A275203: 1 2 4 64
loop(\(x,i).4x,(x2 + ~x),1)
A053765: 1 1 16 4096 16777216 1099511627776 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).3x,(x2 + ~x),1)
A053764: 1 1 9 729 531441 3486784401 205891132094649 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * (2 + i)),(x + ~1),x))
A300559: 1 2 7 37 241 1801 15121 141121 1451521 16329601 199584001 2634508801 37362124801 566658892801 9153720576001 156920924160001
(1 + loop(\(x,i).(2x - i),(x + ~1),x))
A057580: 1 2 4 9 22
A343291: 1 2 4 9 22 55 136 329 778 1803 4108 9229 20494 45071 98320 213009
(1 + loop(\(x,i).(x + (i * i)),(x + ~1),x))
A081490: 1 2 4 9 19 36 62 99 149 214 296 397 519 664 834 1031
loop(\(x,i).(1 + (x * (i * i * i))),x,1)
A217284: 1 2 17 460 29441 3680126 794907217 272653175432 139598425821185 101767252423643866 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((4x + 1) + i),x,1)
A014825: 1 6 27 112 453 1818 7279 29124 116505 466030 1864131 7456536 29826157 119304642 477218583 1908874348
loop(\(x,i).((4x + ~1) + i),x,1)
A172447: 1 4 17 70 283 1136 4549 18202 72815 291268 1165081 4660334 18641347 74565400 298261613 1193046466
loop(\(x,i).((4x + 1) - i),x,1)
A160156: 1 4 15 58 229 912 3643 14566 58257 233020 932071 3728274 14913085 59652328 238609299 954437182
loop(\(x,i).((x + 4) mod (1 + i)),x,1)
A088333: 1 1 2 2 1 5 2 6 1 5 9 1 5 9 13 1
loop(\(x,i).(4x * (1 + i)),x,1)
A034177: 1 8 96 1536 30720 737280 20643840 660602880 23781703680 951268147200 41855798476800 2009078326886400 104472072998092800 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((2 + i) * (1 + i))),x,1)
A010796: 1 6 72 1440 43200 1814400 101606400 7315660800 658409472000 72425041920000 9560105533440000 1491376463216640000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (i * i * (1 + i))),x,1)
A172492: 1 2 24 864 69120 10368000 2612736000 1024192512000 589934886912000 477847258398720000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x - (x * (i * (~1 + i)))),x,1)
A130031: 1 1 ~1 5 ~55 1045 ~30305 1242505 ~68337775 4851982025 ~431826400225 47069077624525 ~6166049168812775 955737621165980125 4611686018427387903 4611686018427387903
(if (~2 + (x div 5)) <= 0 then x else 1)
A103303: 0 1 2 3 4 5 6 7 8 9
A053835: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1
loop(\(x,i).(2 * (x mod 5)),x,1)
A222011: 1 2 4 8
A000689: 1 2 4 8 6 2 4 8 6 2 4 8 6 2 4 8
loop(\(x,i).(2x + 10),x,1)
A139635: 1 12 34 78 166 342 694 1398 2806 5622 11254 22518 45046 90102 180214 360438
loop(\(x,i).(8x + 2),x,1)
A238276: 1 10 82 658 5266 42130 337042 2696338 21570706 172565650 1380525202 11044201618 88353612946 706828903570 5654631228562 45237049828498
((x + 1) + (if (~2 + (x div 2)) <= 0 then 1 else 2))
A270420-A248182-A183220-A102352-A096432-A007412: 2 3 4 5 6 7 9 10 11 12 13 14 15 16 17 18
loop(\(x,i).(6x + 2),x,1)
A061801: 1 8 50 302 1814 10886 65318 391910 2351462 14108774 84652646 507915878 3047495270 18284971622 109709829734 658258978406
loop(\(x,i).(6x + ~2),x,1)
A261399: 1 4 22 130 778 4666 27994 167962 1007770 6046618 36279706 217678234 1306069402 7836416410 47018498458 282110990746
loop(\(x,i).(2 * ((x + 1) - (i mod 2))),x,1)
A084170: 1 2 6 12 26 52 106 212 426 852 1706 3412 6826 13652 27306 54612
loop(\(x,i).(2 * (1 + (x * (~1 + i)))),x,1)
A099758: 1 2 6 26 158 1266 12662 151946 2127246 34035938 612646886 12252937722
A099760: 1 2 6 26 158 1266 12662 151946 2127246 34035938 612646886 12252937722 269564629886 6469551117266 168208329048918 4709833213369706
loop(\(x,i).(2 * ((x + 1) + (2 * i))),x,1)
A051669: 1 8 26 66 150 322 670 1370 2774 5586 11214 22474 44998 90050 180158 360378
loop(\(x,i).(2 * ((x + ~1) + (i mod 2))),x,1)
A128209: 1 2 2 4 6 12 22 44 86 172 342 684 1366 2732 5462 10924
(1 + loop(\(x,i).(2x2 + 2x),2,x))
A175110: 1 41 313 1201 3281 7321 14281 25313 41761 65161 97241 139921 195313 265721 353641 461761
(~1 + loop(\(x,i).((x + 1) * (x + i)),2,x))
A085151: 5 29 109 305 701 1405 2549 4289 6805 10301 15005 21169 29069 39005 51301 66305
((x + ~1) + loop(\(x,i).2x,(x + ~1),2))
A172411: 1 2 5 10
A132736: 1 2 5 10 19 36 69 134 263 520 1033 2058 4107 8204 16397 32782
((x mod 2) - loop(\(x,i).(2x + ~2),x,1))
A140253: ~1 1 2 7 14 31 62 127 254 511 1022 2047 4094 8191 16382 32767
(1 + loop(\(x,i).(x + i),((x + ~1) div 2),x))
A117142: 1 2 3 5 6 9 10 14 15 20 21 27 28 35 36 44
loop(\(x,i).(2 + ((x + ~1) * (x + i))),x,1)
A274702: 1 2 6 47
loop(\(x,i).((x + ~1) mod (2 * (1 + i))),x,1)
A261302: 1 0 5 4 3 2 1 0 17 16 15 14 13 12 11 10
loop(\(x,i).((x * (i * (1 + i))) div 2),x,1)
A006472: 1 1 3 18 180 2700 56700 1587600 57153600 2571912000 141455160000 9336040560000 728211163680000 66267215894880000 4611686018427387903 4611686018427387903
loop(\(x,i).(2x - ((~1 + i) div 2)),x,1)
A086445: 1 2 4 7 13 24 46 89 175 346 688 1371 2737 5468 10930 21853
loop(\(x,i).(2 * (x - (x div ~2))),x,1)
A170685-A170637-A170589-A170541-A170493-A170445-A170397-A170349-A170301-A170253-A170205-A170157-A170109-A170061-A170013-A169545-A169497-A169449-A169401-A169353-A169305-A169257-A169209-A169161-A169113-A169065-A169017-A168969-A168921-A168873-A168825-A168777-A168729-A168681-A167882-A003946: 1 4 12 36 108 324 972 2916 8748 26244 78732 236196 708588 2125764 6377292 19131876
loop(\(x,i).(2 * (x - ((~1 + i) div 2))),x,1)
A052185: 1 2 4 6 10 16 28
((x + 1) + (4 * (if x <= 0 then 0 else 2)))
A171891: 1 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
loop(\(x,i).(8x + ~16),x,1)
A165760: 1 ~8 ~80 ~656 ~5264 ~42128 ~337040 ~2696336 ~21570704 ~172565648 ~1380525200 ~11044201616 ~88353612944 ~706828903568 ~5654631228560 ~45237049828496
(if ((x + 1) mod 8) <= 0 then x else 1)
A055061: 1 1 1 1 1 1 1 7 1 1 1 1 1 1 1 15
(if x <= 0 then 0 else (x + 9))
A117884: 0 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
loop(\(x,i).(~8x + 16),x,1)
A165748: 1 8 ~48 400 ~3184 25488 ~203888 1631120 ~13048944 104391568 ~835132528 6681060240 ~53448481904 427587855248 ~3420702841968 27365622735760
loop(\(x,i).(8x * i),x,1)
A051189: 1 8 128 3072 98304 3932160 188743680 10569646080 676457349120 48704929136640 3896394330931200 342882701121945600 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~8x + 1),x,1)
A014990: 1 ~7 57 ~455 3641 ~29127 233017 ~1864135 14913081 ~119304647 954437177 ~7635497415 61083979321 ~488671834567 3909374676537 ~31274997412295
loop(\(x,i).(i div (4 + (x mod 2))),x,1)
A029326: 1 0 0 0 1 1 1 1 1 1 2 2 3 2 3 3
loop(\(x,i).(2 * (x div (~2 + (i mod 2)))),x,1)
A152166: 1 ~2 2 ~4 4 ~8 8 ~16 16 ~32 32 ~64 64 ~128 128 ~256
(1 + loop(\(x,i).(2x * i),4,x))
A229853: 1 385 769 1153 1537 1921 2305 2689 3073 3457 3841 4225 4609 4993 5377 5761
((x + ~1) + loop(\(x,i).2x,x,4))
A145071: 3 8 17 34 67 132 261 518 1031 2056 4105 8202 16395 32780 65549 131086
loop(\(x,i).(4 * (x + (x div 2))),x,1)
A067411: 1 4 24 144 864 5184 31104 186624 1119744 6718464 40310784 241864704 1451188224 8707129344 52242776064 313456656384
loop(\(x,i).(4x * (2 + i)),x,1)
A051620: 1 12 192 3840 92160 2580480 82575360 2972712960 118908518400 5231974809600 251134790860800 13059009124761600 731304510986649600 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x + i),(x div 4),x))
A101883: 1 2 3 4 6 7 8 9 12 13 14 15 19 20 21 22
loop(\(x,i).(4x * (i * i)),x,1)
A002454: 1 4 64 2304 147456 14745600 2123366400 416179814400 106542032486400 34519618525593600 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(6x + ~4),x,1)
A047851: 1 2 8 44 260 1556 9332 55988 335924 2015540 12093236 72559412 435356468 2612138804 15672832820 94036996916
loop(\(x,i).(2 * (x - ((~x + 2) div 2))),x,1)
A094388: 1 2 4 10 28 82 244 730 2188 6562 19684 59050 177148 531442 1594324 4782970
loop(\(x,i).(2 * ((x + ~2) + (2 * i))),x,1)
A131064: 1 2 8 24 60 136 292 608 1244 2520 5076 10192 20428 40904 81860 163776
(1 - (1 mod loop(\(x,i).(2x + ~4),x,1)))
A131128: 1 2 8 20 44 92 188 380 764 1532 3068 6140 12284 24572 49148 98300
(1 - (x mod loop(\(x,i).(2x + ~4),x,1)))
A077802: 1 2 7 18 41 88 183 374 757 1524 3059 6130 12273 24560 49135 98286
loop(\(x,i).(5x + ~2),x,1)
A318165: 1 3 13
A034478: 1 3 13 63 313 1563 7813 39063 195313 976563 4882813 24414063 122070313 610351563 3051757813 15258789063
loop(\(x,i).(2 * (2x + (x div 2))),x,1)
A005054: 1 4 20 100 500 2500 12500 62500 312500 1562500 7812500 39062500 195312500 976562500 4882812500 24414062500
loop(\(x,i).(2 * (2x + (x mod 2))),x,1)
A164908: 1 6 24 96 384 1536 6144 24576 98304 393216 1572864 6291456 25165824 100663296 402653184 1610612736
loop(\(x,i).(2 * (~2x + (x mod 2))),x,1)
A009117: 1 ~2 8 ~32 128 ~512 2048 ~8192 32768 ~131072 524288 ~2097152 8388608 ~33554432 134217728 ~536870912
loop(\(x,i).(2 * (2x + (i mod 2))),x,1)
A117614: 1 6 24 98 392 1570 6280 25122 100488 401954 1607816 6431266 25725064 102900258 411601032 1646404130
loop(\(x,i).(~5x + 1),x,1)
A014986: 1 ~4 21 ~104 521 ~2604 13021 ~65104 325521 ~1627604 8138021 ~40690104 203450521 ~1017252604 5086263021 ~25431315104
loop(\(x,i).(5x - i),x,1)
A164045: 1 4 18 87 431 2150 10744 53713 268557 1342776 6713870 33569339 167846683 839233402 4196166996 20980834965
loop(\(x,i).(x - (2 * (~2x + i))),x,1)
A268414: 1 3 11 49 237 1175 5863 29301 146489 732427 3662115 18310553 91552741 457763679 2288818367 11444091805
loop(\(x,i).(2x - ((x div 2) mod 2)),x,1)
A046630: 1 2 3 5 10 19 37 74 147 293 586 1171 2341 4682 9363 18725
((x + 1) + (if (x + ~2) <= 0 then (x mod 2) else 2))
A003879: 1 3 3 6 7 8
loop(\(x,i).(x - (x div (~2 + (x mod 2)))),x,1)
A018251: 1 2 3 6 9 18
A018264: 1 2 3 6 9 18 27 54
A018311: 1 2 3 6 9 18 27 54 81 162
A018481: 1 2 3 6 9 18 27 54 81 162 243 486
A038754: 1 2 3 6 9 18 27 54 81 162 243 486 729 1458 2187 4374
(1 + (x * loop(\(x,i).x3,2,2)))
A076338: 1 513 1025 1537 2049 2561 3073 3585 4097 4609 5121 5633 6145 6657 7169 7681
loop(\(x,i).(2 * (x - ((x + i) mod 2))),x,1)
A135231: 1 2 4 6 12 22 44 86 172 342 684 1366 2732 5462 10924 21846
loop(\(x,i).(2 * (x - (2x * i))),x,1)
A097388: 1 ~2 12 ~120 1680 ~30240 665280 ~17297280 518918400 ~17643225600 670442572800 ~28158588057600 1295295050649600 ~64764752532480000 3497296636753920000 4611686018427387903
loop(\(x,i).(5x + 2),x,1)
A057651: 1 7 37 187 937 4687 23437 117187 585937 2929687 14648437 73242187 366210937 1831054687 9155273437 45776367187
loop(\(x,i).10x,x,1)
A011557: 1 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000 10000000000 100000000000 1000000000000 10000000000000 100000000000000 1000000000000000
loop(\(x,i).(2x * (3 + i)),x,1)
A051580: 1 8 80 960 13440 215040 3870720 77414400 1703116800 40874803200 1062744883200 29756856729600 892705701888000 28566582460416000 971263803654144000 4611686018427387903
loop(\(x,i).(2x * (1 + (2 * i))),x,1)
A000407: 1 6 60 840 15120 332640 8648640 259459200 8821612800 335221286400 14079294028800 647647525324800 32382376266240000 1748648318376960000 4611686018427387903 4611686018427387903
loop(\(x,i).(2x * (~1 + (2 * i))),x,1)
A001813: 1 2 12 120 1680 30240 665280 17297280 518918400 17643225600 670442572800 28158588057600 1295295050649600 64764752532480000 3497296636753920000 4611686018427387903
loop(\(x,i).(2x * (1 + (i mod 2))),x,1)
A094015: 1 4 8 32 64 256 512 2048 4096 16384 32768 131072 262144 1048576 2097152 8388608
(1 + loop(\(x,i).(x + (x div 4)),2,x))
A074215-A022164: 1 2 3 4 7 8 9 11 13 14 16 17 19 21 22 23
((x + 1) + loop(\(x,i).4x,x,2))
A221130: 3 10 35 132 517 2054 8199 32776 131081 524298 2097163 8388620 33554445 134217742 536870927 2147483664
loop(\(x,i).(2x * (4 + i)),x,1)
A051582: 1 10 120 1680 26880 483840 9676800 212889600 5109350400 132843110400 3719607091200 111588212736000 3570822807552000 121407975456768000 4370687116443648000 4611686018427387903
loop(\(x,i).(2x * (~2 + (i mod 2))),x,1)
A094014: 1 ~2 8 ~16 64 ~128 512 ~1024 4096 ~8192 32768 ~65536 262144 ~524288 2097152 ~4194304
((x + 1) + (if (~x + 4) <= 0 then x else 2))
A104373: 3 4 5 6 9 11
loop(\(x,i).(2 * (x + ((x + i) mod 2))),x,1)
A026644: 1 2 4 10 20 42 84 170 340 682 1364 2730 5460 10922 21844 43690
loop(\(x,i).(x - (2 * (~x + (i div 2)))),x,1)
A104522: 1 3 7 19 53 155 459 1371 4105 12307 36911 110723 332157 996459 2989363 8968075
loop(\(x,i).(x - (2 * (~x + (i mod 2)))),x,1)
A122983: 1 1 3 7 21 61 183 547 1641 4921 14763 44287 132861 398581 1195743 3587227
loop(\(x,i).2x,x,(x2 + 2x + 1))
A014477: 1 8 36 128 400 1152 3136 8192 20736 51200 123904 294912 692224 1605632 3686400 8388608
((x + ~1) + loop(\(x,i).(x * i),x,(x + 2)))
A341302: 1 3 9 32 147 844 5765 45366 403207 3991688 43545609 518918410 6706022411 93405312012 1394852659213 22230464256014
loop(\(x,i).(5x + ~10),x,1)
A165755: 1 ~5 ~35 ~185 ~935 ~4685 ~23435 ~117185 ~585935 ~2929685 ~14648435 ~73242185 ~366210935 ~1831054685 ~9155273435 ~45776367185
loop(\(x,i).(2x + ((~1 + i) div 2)),x,1)
A084172: 1 2 4 9 19 40 82 167 337 678 1360 2725 5455 10916 21838 43683
loop(\(x,i).(2x + ((x + i) mod 2)),x,1)
A262864: 1 2 4 9 19 38 76 153 307 614 1228 2457 4915 9830 19660 39321
loop(\(x,i).(3x - (i mod 2)),x,1)
A139629: 1 2 6 17
A153773: 1 2 6 17 51 152 456 1367 4101 12302 36906 110717 332151 996452 2989356 8968067
(x + loop(\(x,i).2x,x,1) - (x div 2))
A134522: 1 3 5 10 18 35 67 132 260 517 1029 2054 4102 8199 16391 32776
(x - (2 mod (x - loop(\(x,i).2x,x,1))))
A296965: 0 1 2 6 14 30 62 126 254 510 1022 2046 4094 8190 16382 32766
((~x2 + 1) + loop(\(x,i).2x,x,1))
A030110: 2 2 1 0 1 8 29 80 193 432 925 1928 3953 8024 16189 32544
((~x2 + x) + loop(\(x,i).2x,x,1))
A142974: 1 2 2 2 4 12 34 86 200 440 934 1938 3964 8036 16202 32558
(1 + loop(\(x,i).3x,2x,x))
A064747: 1 10 163 2188 26245 295246 3188647 33480784 344373769 3486784402 34867844011 345191655700 3389154437773 33044255768278 320275094369455 3088366981419736
(1 + loop(\(x,i).(x + (i * i)),2x,x))
A168574: 1 7 33 95 209 391 657 1023 1505 2119 2881 3807 4913 6215 7729 9471
loop(\(x,i).(2x + ((x mod 2) * i)),x,1)
A077552: 1 3 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536
loop(\(x,i).(2x * (i * i * i)),x,1)
A088386: 1 2 32 1728 221184 55296000 23887872000 16387080192000 16780370116608000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * (x + (i * i))),2,x))
A047673: 1 13 61 193 481 1021 1933 3361 5473 8461 12541 17953 24961 33853 44941 58561
loop(\(x,i).(x + (2x * i) - i),x,1)
A193651: 1 2 8 53 473 5198 67568 1013513 17229713 327364538 6874655288 158117071613 3952926790313 106729023338438 3095141676814688 95949391981255313
loop(\(x,i).(2 + ((2 * (x + i)) + i)),x,1)
A308579: 1 7 22 55 124 265 550 1123 2272 4573 9178 18391 36820 73681 147406 294859
loop(\(x,i).(2 * ((x + (x div 2)) * i)),x,1)
A052563: 1 2 12 108 1296 19440 349920 7348320 176359680 4761711360 142851340800 4714094246400 169707392870400 6618588321945600 277980709521715200 4611686018427387903
loop(\(x,i).((~x + (i * i)) * (i div 2)),x,1)
A091130: 1 0 4 5 22
loop(\(x,i).((x * i) div (2 - (i mod 2))),x,1)
A090932: 1 1 1 3 6 30 90 630 2520 22680 113400 1247400 7484400 97297200 681080400 10216206000
(if (~2 + (x div 3)) <= 0 then 0 else (x + 1))
A256556: 0 0 0 0 0 0 0 0 0 10 11 12 13 14 15 16
(loop(\(x,i).(2x + 1),x,0) mod (x + 1))
A128311: 0 1 0 3 0 1 0 7 3 1 0 7 0 1 3 15
(loop(\(x,i).(2x + i),x,0) mod (x + 1))
A082495: 0 1 1 3 1 3 1 7 7 3 1 3 1 3 7 15
(loop(\(x,i).(x + (i * i)),x,0) mod (x + 1))
A215573: 0 1 2 2 0 1 0 4 6 5 0 2 0 7 10 8
((1 + loop(\(x,i).(x * i),x,1)) mod (x + 1))
A055976: 0 0 0 3 0 1 0 1 1 1 0 1 0 1 1 1
((x + 1) * loop(\(x,i).x2,2,3))
A044251: 81 162 243 324 405 486 567 648 729 810 891 972 1053 1134 1215 1296
(loop(\(x,i).x2,2,3) div (x + 1))
A033401: 81 40 27 20 16 13 11 10 9 8 7 6 6 5 5 5
((1 + loop(\(x,i).2x,x,2)) mod (x + 1))
A096196: 0 1 0 1 3 5 3 1 0 5 3 5 3 5 9 1
((~1 + loop(\(x,i).2x,x,2)) div (x + 1))
A082482: 1 1 2 3 6 10 18 31 56 102 186 341 630 1170 2184 4095
(loop(\(x,i).(x * i),2x,1) div (x + 1))
A060593: 1 1 8 180 8064 604800 68428800 10897286400 2324754432000 640237370572800 221172909834240000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(~1 + (x div 2)),(x + 1))
A005456: 1 2 3 4 10 12 28
(loop(\(x,i).(1 + (x * i)),x,1) mod (x + 1))
A176787: 0 0 2 0 0 2 4 4 8 0 5 8 0 4 5 12
(loop(\(x,i).4x,x,1) mod (x + 1))
A062175: 0 0 1 0 1 4 1 0 7 4 1 4 1 4 1 0
(loop(\(x,i).2x,x,(x + ~1)) mod (x + 1))
A082493: 0 0 1 0 3 2 5 0 1 6 9 8 11 10 7 0
loop(\(x,i).(x * (2 + i)),(x + ~1),(x + 1))
A074143: 1 2 9 48 300 2160 17640 161280 1632960 18144000 219542400 2874009600 40475635200 610248038400 9807557760000 167382319104000
loop(\(x,i).(2x + i),(x + ~1),(x + 1))
A134311: 1 2 7 20 51 122 281 632 1399 3062 6645 14324 30707 65522 139249 294896
(loop(\(x,i).3x,x,1) mod (x + 1))
A062174: 0 1 0 3 1 3 1 3 0 3 1 3 1 3 9 11
(loop(\(x,i).(1 - (x * i)),x,1) mod (x + 1))
A049782: 0 0 1 2 4 4 6 2 1 4 1 10 10 6 4 10
(loop(\(x,i).(x - (i * i)),x,1) mod (x + 1))
A133623: 0 0 2 3 1 0 1 5 4 6 1 11 1 8 6 9
((2x + 2) * (1 + (if x <= 0 then 1 else 2)))
A230628: 4 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96
((x + 1) * (~2 + loop(\(x,i).(x * i),x,1)))
A242569: ~1 ~2 0 16 110 708 5026 40304 362862 3628780 39916778 479001576 6227020774 87178291172 1307674367970 20922789887968
loop(\(x,i).(x - (x div 4)),2,(x + 1))
A304110: 1 2 3 3 3 4 5 5 6 6 7 7 8 9 9 9
(loop(\(x,i).x2,4,2) mod (x + 1))
A245970: 0 0 1 0 1 4 2 0 7 6 9 4 3 2 1 0
(loop(\(x,i).(x2 + 2),2,2) div (x + 1))
A033358: 38 19 12 9 7 6 5 4 4 3 3 3 2 2 2 2
((x + 1) * loop(\(x,i).x2,2,4))
A309092: 256 512 768 1024 1280 1536 1792 2048 2304 2560 2816 3072 3328 3584 3840 4096
(loop(\(x,i).x2,2,4) div (x + 1))
A057066: 256 128 85 64 51 42 36 32 28 25 23 21 19 18 17 16
(loop(\(x,i).x2,2,4) mod (x + 1))
A337398: 0 0 1 0 1 4 4 0 4 6 3 4 9 4 1 0
(loop(\(x,i).2x,x,4) div (x + 1))
A281375: 4 4 5 8 12 21 36 64 113 204 372 682 1260 2340 4369 8192
(loop(\(x,i).2x,x,4) mod (x + 1))
A112983: 0 0 1 0 4 2 4 0 7 8 4 8 4 8 1 0
(1 div loop(\(x,i).x2,4,(x + 1)))
A323535: 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4611686018427387903 4611686018427387903
loop(\(x,i).x3,4,(x + 1))
A309113: 1 4611686018427387903
A338965-A338964-A338952-A194566-A173471-A115543: 1 4611686018427387903 4611686018427387903 4611686018427387903
A338967-A338957-A338956-A338953: 1 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A020476: 1 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A214266: 1 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x2 + x),2,2) div (x + 1))
A033362: 42 21 14 10 8 7 6 5 4 4 3 3 3 3 2 2
(loop(\(x,i).(x2 + 2x),2,2) div (x + 1))
A033400: 80 40 26 20 16 13 11 10 8 8 7 6 6 5 5 5
(loop(\(x,i).2x,(x + 2),2) mod (x + 1))
A212844: 0 0 2 0 3 4 1 0 5 6 8 4 8 2 2 0
loop(\(x,i).x2,(x + 4),(x + 1))
A255344: 1 4294967296
((x + 1) * (2 + (if x <= 0 then 1 else 2x)))
A184636: 3 8 18 32 50 72 98 128 162 200 242 288 338 392 450 512
((x + 1) * (if x <= 0 then 1 else 4x))
A333714: 1 8 24 48 80 120 168 224 288 360 440 528 624 728 840 960
loop(\(x,i).x2,4x,(x + 1))
A255323: 1 65536 4611686018427387903
(loop(\(x,i).2x,x,2) + (2 div (x + 1)))
A258935: 4 5 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536
((if x <= 0 then 1 else 4) + (2 mod (x + 1)))
A231407: 1 4 6
A329502: 1 4 6 6 6 6 6 6 6 6 6 6 6 6 6 6
((x + 1) * (2 - ((if x <= 0 then 1 else x) mod 2)))
A066043: 1 2 6 4 10 6 14 8 18 10 22 12 26 14 30 16
loop(\(x,i).(x * (2 + i)),(x + ~2),(x + 1))
A188588: 1 2 3 12 60 360 2520 20160 181440 1814400 19958400 239500800 3113510400 43589145600 653837184000 10461394944000
loop(\(x,i).3x,2x,(x + 1))
A053540: 1 18 243 2916 32805 354294 3720087 38263752 387420489 3874204890 38354628411 376572715308 3671583974253 35586121596606 343151886824415 3294258113514384
((x + 1) * loop(\(x,i).3x,x,2))
A212697: 2 12 54 216 810 2916 10206 34992 118098 393660 1299078 4251528 13817466 44641044 143489070 459165024
loop(\(x,i).6x,x,(x + 1))
A053469: 1 12 108 864 6480 46656 326592 2239488 15116544 100776960 665127936 4353564672 28298170368 182849716224 1175462461440 7522959753216
((x + loop(\(x,i).2x,x,1)) div (x + 1))
A053637: 1 1 2 2 4 6 10 16 29 52 94 171 316 586 1093 2048
(if (4 mod (x + 1)) <= 0 then x else (x + 1))
A131209: 0 1 3 3 5 6 7 8 9 10 11 12 13 14 15 16
loop(\(x,i).2x,(x2 + x),(x + 1))
A128406: 1 8 192 16384 5242880 6442450944 30786325577728 576460752303423488 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) + loop(\(x,i).2x,(x + ~1),x))
A188626: 1 3 7 16 37 86 199 456 1033 2314 5131 11276 24589 53262 114703 245776
((x + loop(\(x,i).(x * i),x,1)) div (x + 1))
A261779: 1 1 1 2 5 20 103 630 4480 36288 329891 3326400 36846277 444787200 5811886080 81729648000
loop(\(x,i).(2x * (1 + i)),x,(x + 1))
A014479: 1 8 72 768 9600 138240 2257920 41287680 836075520 18579456000 449622835200 11771943321600 331576403558400 9998303861145600 321374052679680000 4611686018427387903
(loop(\(x,i).(x2 div 2),2,x) mod (x + 1))
A226786: 0 0 2 0 2 0 1 0 8 0 7 0 5 0 2 0
loop(\(x,i).((2x + ~4) + i),x,(x + 1))
A188716: 1 1 4 15 46 125 316 763 1786 4089 9208 20471 45046 98293 212980 458739
((~x + ~1) + loop(\(x,i).(x2 + 2x),2,x))
A126423: ~1 13 77 251 619 1289 2393 4087 6551 9989 14629 20723 28547 38401 50609 65519
((x + loop(\(x,i).2x,x,2)) div (x + 1))
A053638: 2 2 3 4 7 11 19 32 57 103 187 342 631 1171 2185 4096
(if (~x + 2) <= 0 then (x2 + 2x) else (x + 1))
A272930: 1 2 8 15
loop(\(x,i).(2x + (i mod 2)),x,(x + 1))
A127980: 1 5 14 37 90 213 490 1109 2474 5461 11946 25941 55978 120149 256682 546133
loop(\(x,i).((x * i) + (x div 2)),x,(x + 1))
A188545: 1 3 10
A309885: 1 3 10 52
loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))
A276234-A161955-A072963-A000265: 1 1 3 1 5 3 7 1 9 5 11 3 13 7 15 1
((x + 1) * (x + (if (~x + 2) <= 0 then x else 2)))
A257479: 2 6 12 24
loop(\(x,i).(x * (1 + (2 * i))),x,(x + 1))
A001879: 1 6 45 420 4725 62370 945945 16216200 310134825 6547290750 151242416325 3794809718700 102776096548125 2988412653476250 92854250304440625 3070380543400170000
loop(\(x,i).(x * (~1 + (2 * i))),x,(x + 1))
A001193: 1 2 9 60 525 5670 72765 1081080 18243225 344594250 7202019825 164991726900 4111043861925 110681950128750 3201870700153125 99044533658070000
((x + 1) * loop(\(x,i).4x,x,x))
A116144: 0 8 96 768 5120 30720 172032 917504 4718592 23592960 115343360 553648128 2617245696 12213813248 56371445760 257698037760
loop(\(x,i).(x * (4 + i)),x,(x + 1))
A061206: 1 10 90 840 8400 90720 1058400 13305600 179625600 2594592000 39956716800 653837184000 11333177856000 207484333056000 4001483566080000 81096733605888000
loop(\(x,i).(x * (2 + (i mod 2))),x,(x + 1))
A027266: 1 6 18 72 180 648 1512 5184 11664 38880 85536 279936 606528 1959552 4199040 13436928
((x + 1) * loop(\(x,i).3x,x,x))
A116138: 0 6 54 324 1620 7290 30618 122472 472392 1771470 6495390 23383404 82904796 290166786 1004423490 3443737680
((x + 1) * loop(\(x,i).(x * (1 + i)),x,x))
A098916: 0 4 36 288 2400 21600 211680 2257920 26127360 326592000 4390848000 63228211200 971415244800 15866448998400 274611617280000 5021469573120000
loop(\(x,i).(x3 + 1),2,(x + ~1))
A178391: 1 2 9 730 21953 274626 2000377 10218314 40707585 135005698 389017001 1003003002 2363266369 5168743490 10618986393 20683643626
(if x <= 0 then 1 else (8x + ~8))
A181390: 1 0 8 16 24 32 40 48 56 64 72 80 88 96 104 112
(if (x mod 2) <= 0 then ((x div 2) mod 2) else (x + ~1))
A338824: 0 0 1 2 0 4 1 6 0 8 1 10 0 12 1 14
((x + ~1) * loop(\(x,i).2x,(x + ~1),x))
A100381: 0 0 4 24 96 320 960 2688 7168 18432 46080 112640 270336 638976 1490944 3440640
((x + ~1) * loop(\(x,i).2x,(x + ~2),x))
A001815: 0 0 2 12 48 160 480 1344 3584 9216 23040 56320 135168 319488 745472 1720320
((x + ~1) * loop(\(x,i).x3,2,x))
A240933: 0 0 512 39366 786432 7812500 50388480 242121642 939524096 3099363912 9000000000 23579476910 56757583872 127253992476 268593608192 538207031250
((x + ~1) * loop(\(x,i).4x,x,x))
A128798: 0 0 32 384 3072 20480 122880 688128 3670016 18874368 94371840 461373440 2214592512 10468982784 48855252992 225485783040
((x + ~1) + (if (x + ~2) <= 0 then 2 else x2))
A111802: 1 2 3 11 19 29 41 55 71 89 109 131 155 181 209 239
((x + ~1) * loop(\(x,i).x2,2,x2))
A240932: 0 0 256 13122 196608 1562500 8398080 34588806 117440512 344373768 900000000 2143588810 4729798656 9788768652 19185257728 35880468750
((x + ~1) * loop(\(x,i).3x,x,x))
A128797: 0 0 18 162 972 4860 21870 91854 367416 1417176 5314410 19486170 70150212 248714388 870500358 3013270470
(1 + (x * (x + (if (x mod 2) <= 0 then 2 else 0))))
A081346: 1 2 9 10 25 26 49 50 81 82 121 122 169 170 225 226
loop(\(x,i).(x * (1 + (i div 3))),x,1)
A264557: 1 1 1 2 4 8 24 72 216 864 3456 13824 69120 345600 1728000 10368000
loop(\(x,i).7x,x,1)
A000420: 1 7 49 343 2401 16807 117649 823543 5764801 40353607 282475249 1977326743 13841287201 96889010407 678223072849 4747561509943
loop(\(x,i).(x * (1 + (2 * (1 + i)))),x,1)
A051577: 1 5 35 315 3465 45045 675675 11486475 218243025 4583103525 105411381075 2635284526875 71152682225625 2063427784543125 63966261320836875 2110886623587616875
loop(\(x,i).(x + (x mod 5)),x,1)
A222011: 1 2 4 8
A235700: 1 2 4 8 11 12 14 18 21 22 24 28 31 32 34 38
loop(\(x,i).(4x2 + ~x),x,1)
A204687: 1 3 33 4323 74748993 22349647743307203 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (5 + i)),x,1)
A001725: 1 6 42 336 3024 30240 332640 3991680 51891840 726485760 10897286400 174356582400 2964061900800 53353114214400 1013709170073600 20274183401472000
loop(\(x,i).(x * (1 + (2 * (2 + i)))),x,1)
A051579: 1 7 63 693 9009 135135 2297295 43648605 916620705 21082276215 527056905375 14230536445125 412685556908625 12793252264167375 422177324717523375 4611686018427387903
loop(\(x,i).(x * (~1 + (4 * i))),x,1)
A008545: 1 3 21 231 3465 65835 1514205 40883535 1267389585 44358635475 1729986783525 74389431691575 3496303289504025 178311467764705275 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (3 + (i mod 2))),x,1)
A282023: 1 4 12 48 144 576 1728 6912 20736 82944 248832 995328 2985984 11943936 35831808 143327232
(1 + loop(\(x,i).6x,x,x))
A050917: 1 7 73 649 5185 38881 279937 1959553 13436929 90699265 604661761 3990767617 26121388033 169789022209 1097098297345 7052774768641
loop(\(x,i).(x3 + 3x),x,1)
A006267: 1 4 76 439204 84722519070079276 4611686018427387903
loop(\(x,i).(3x2 + ~x),x,1)
A161181: 1 2 10 290 252010 190526868290 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + (3x * i)),x,1)
A008544: 1 2 10 80 880 12320 209440 4188800 96342400 2504902400 72642169600 2324549427200 81359229952000 3091650738176000 126757680265216000 4611686018427387903
loop(\(x,i).(x * (i - (i div 3))),x,1)
A004527: 1 1 2 4 12 48 192 960 5760 34560 241920 1935360 15482880 139345920 1393459200 13934592000
loop(\(x,i).(x * (3 - (i mod 2))),x,1)
A026549: 1 2 6 12 36 72 216 432 1296 2592 7776 15552 46656 93312 279936 559872
loop(\(x,i).(x + (x div (1 + (i mod 2)))),x,1)
A182522: 1 1 2 3 6 9 18 27 54 81 162 243 486 729 1458 2187
loop(\(x,i).(x * (1 + (2 * (i * i)))),x,1)
A277352: 1 3 27 513 16929 863379 63026667 6239640033 804913564257 131200910973891 26371383105752091 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + x2 + x),x,1)
A166999: 1 3 39 60879 225636660844959 4611686018427387903
loop(\(x,i).(x * (1 + ((~1 + i) * i))),x,1)
A130032: 1 1 3 21 273 5733 177723 7642089 435599073 31798732329 2893684641939 321198995255229 42719466368945457 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + ((i div 2) + i))),x,1)
A111394: 1 2 8 40 280 2240 22400 246400 3203200 44844800 717516800 12197785600 231757926400 4635158528000 101973487616000 2345390215168000
loop(\(x,i).(x * (~1 + ((i mod 2) + i))),x,1)
A247006-A000246: 1 1 1 3 9 45 225 1575 11025 99225 893025 9823275 108056025 1404728325 18261468225 273922023375
loop(\(x,i).(x * (1 + (i * i * i))),x,1)
A255433: 1 2 18 504 32760 4127760 895723920 308129028480 158070191610240 115391239875475200 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (i - (i div ~2))),x,1)
A293653: 1 2 6 30 180 1440 12960 142560 1710720 23950080 359251200 6107270400 109930867200 2198617344000 46170964224000 1061932177152000
loop(\(x,i).(x * (2 + (i mod 3))),x,1)
A076506: 1 3 12 24 72 288 576 1728 6912 13824 41472 165888 331776 995328 3981312 7962624
loop(\(x,i).(x * (2 + (x mod 4))),x,1)
A005053: 1 3 15 75 375 1875 9375 46875 234375 1171875 5859375 29296875 146484375 732421875 3662109375 18310546875
(1 + loop(\(x,i).8x,x,x))
A064746: 1 9 129 1537 16385 163841 1572865 14680065 134217729 1207959553 10737418241 94489280513 824633720833 7146825580545 61572651155457 527765581332481
loop(\(x,i).(x * (6 + i)),x,1)
A001730: 1 7 56 504 5040 55440 665280 8648640 121080960 1816214400 29059430400 494010316800 8892185702400 168951528345600 3379030566912000 70959641905152000
loop(\(x,i).(~5x + 4),x,1)
A083085: 1 ~1 9 ~41 209 ~1041 5209 ~26041 130209 ~651041 3255209 ~16276041 81380209 ~406901041 2034505209 ~10172526041
loop(\(x,i).(x + (4 * (i * i))),x,1)
A166464: 1 5 21 57 121 221 365 561 817 1141 1541 2025 2601 3277 4061 4961
loop(\(x,i).(x + (2 * ((x + i) div 2))),x,1)
A026646: 1 3 7 17 37 79 163 333 673 1355 2719 5449 10909 21831 43675 87365
loop(\(x,i).(x * (4 - (i mod 2))),x,1)
A282022: 1 3 12 36 144 432 1728 5184 20736 62208 248832 746496 2985984 8957952 35831808 107495424
loop(\(x,i).(x * (2 + ((x - i) div 2))),x,1)
A222011: 1 2 4 8
A307611: 1 2 4 8 32
loop(\(x,i).(~5x + 10),x,1)
A165625: 1 5 ~15 85 ~415 2085 ~10415 52085 ~260415 1302085 ~6510415 32552085 ~162760415 813802085 ~4069010415 20345052085
loop(\(x,i).(x + ((i * i) div (x + 2))),x,1)
A325544-A118103: 1 1 2 4 6 9 12 15 18 22 26 30 34 38 42 47
(1 + loop(\(x,i).(2x * (x + i)),x,x))
A029495: 1 5 337
loop(\(x,i).(x * (2 + (3 * i))),x,1)
A034000: 1 5 40 440 6160 104720 2094400 48171200 1252451200 36321084800 1162274713600 40679614976000 1545825369088000 63378840132608000 2788668965834752000 4611686018427387903
loop(\(x,i).(x * (~2 + (3 * i))),x,1)
A007559: 1 1 4 28 280 3640 58240 1106560 24344320 608608000 17041024000 528271744000 17961239296000 664565853952000 26582634158080000 1143053268797440000
loop(\(x,i).6x,x2,1)
A076781: 1 6 1296 10077696 2821109907456 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x2 + 1) + loop(\(x,i).(x * i),x,1))
A201363: 2 3 7
A227546: 2 3 7 16 41 146 757 5090 40385 362962 3628901 39916922 479001745 6227020970 87178291397 1307674368226
loop(\(x,i).8x,x2,1)
A060760: 1 8 4096 134217728 281474976710656 4611686018427387903 4611686018427387903 4611686018427387903
((x2 + 1) + (if (x + ~1) <= 0 then x else 2))
A062714: 1 3 7 12 19 28 39
((x2 + ~1) + loop(\(x,i).2x,x,2))
A290707: 1 4 11 24 47 88 163 304 575 1104 2147 4216 8335 16552 32963 65760
loop(\(x,i).3x,x,(x2 + 1))
A003486: 1 6 45 270 1377 6318 26973 109350 426465 1614006 5963949 21611934 77058945 271034910 942244893 3242852982
loop(\(x,i).(x * (x - i)),2,(x2 + ~1))
A217574: 0 0 24 3024 43680 303600 1413720 5085024 15249024 39929760 94109400 203889840 412293024 787083024 1431033240 2495102400
loop(\(x,i).5x,x2,1)
A060758: 1 5 625 1953125 152587890625 298023223876953125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x2 + ~1) + (2 div (if x <= 0 then 1 else x)))
A222011: 1 2 4 8
A082562: 1 2 4 8 15 24 35 48 63 80 99 120 143 168 195 224
loop(\(x,i).((x2 + ~x) + i),x2,1)
A068741: 1 1 24 4611686018427387903
loop(\(x,i).(x * i),x4,1)
A255359: 1 1 20922789888000
(1 + loop(\(x,i).5x,x,x))
A050916: 1 6 51 376 2501 15626 93751 546876 3125001 17578126 97656251 537109376 2929687501 15869140626 85449218751 457763671876
(1 + (x * (if (x + ~2) <= 0 then 1 else x2)))
A098812: 1 2 3 28
loop(\(x,i).3x,x3,1)
A187879: 1 3 6561 7625597484987 4611686018427387903 4611686018427387903
loop(\(x,i).(x4 * i),x,1)
A164334: 1 1 2 48 21233664 4611686018427387903
loop(\(x,i).(x2 + ((x + i) * i)),x,1)
A143762: 1 3 19 427 184053 33876427099 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + ((~x + i) * i)),x,1)
A143761: 1 1 3 9 61 3441 11819871 139709267717593 4611686018427387903 4611686018427387903
loop(\(x,i).(5x * i),x,1)
A047054: 1 5 50 750 15000 375000 11250000 393750000 15750000000 708750000000
A052562: 1 5 50 750 15000 375000 11250000 393750000 15750000000 708750000000 35437500000000 1949062500000000 116943750000000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((3 + i) * i)),x,1)
A010792: 1 4 40 720 20160 806400 43545600 3048192000 268240896000 28970016768000 3766102179840000 579979735695360000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((1 + (2 * i)) * i)),x,1)
A007019: 1 3 30 630 22680 1247400 97297200 10216206000 1389404016000 237588086736000 49893498214560000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((~1 + (2 * i)) * i)),x,1)
A000680: 1 1 6 90 2520 113400 7484400 681080400 81729648000 12504636144000 2375880867360000 548828480360160000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((1 + (i mod 2)) * i)),x,1)
A232205: 1 2 4 24 96 960 5760 80640 645120 11612160 116121600 2554675200 30656102400 797058662400 11158821273600 334764638208000
loop(\(x,i).(x * (8 + i)),x,1)
A049389: 1 9 90 990 11880 154440 2162160 32432400 518918400 8821612800 158789030400 3016991577600 60339831552000 1267136462592000 27877002177024000 641171050071552000
loop(\(x,i).(x * ((4 + i) * i)),x,1)
A010793: 1 5 60 1260 40320 1814400 108864000 8382528000 804722688000 94152554496000 13181357629440000 2174924008857600000 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((2 * (2 + i)) + i)),x,1)
A051604: 1 7 70 910 14560 276640 6086080 152152000 4260256000 132067936000 4490309824000 166141463488000 6645658539520000 285763317199360000 4611686018427387903 4611686018427387903
loop(\(x,i).(x + ((2 + (i mod 2)) * i)),x,1)
A298950: 1 4 8 17 25 40 52 73 89 116 136 169 193 232 260 305
loop(\(x,i).(x * ((2 - (i mod 2)) * i)),x,1)
A268363: 1 1 4 12 96 480 5760 40320 645120 5806080 116121600 1277337600 30656102400 398529331200 11158821273600 167382319104000
loop(\(x,i).(x * (i * i * i * i)),x,1)
A134375: 1 1 16 1296 331776 207360000 268738560000 645241282560000 2642908293365760000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(((x + 2) + (i mod 2)) * i),x,1)
A105344: 1 4 12 45
((x - (if (x + ~3) <= 0 then 1 else 0)) mod 2)
A266611: 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1
((x - (if (x + ~4) <= 0 then 1 else 0)) mod 2)
A266246: 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1
(if (~2 + (x div 5)) <= 0 then 0 else 2)
A261596-A161274-A158465: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
(if (~6 + (x div 2)) <= 0 then 0 else 2)
A308979-A308978-A308977-A308976-A308975-A307637: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2
(x - (if (~2 + (x div 3)) <= 0 then 0 else 2))
A245353: 0 1 2 3 4 5 6 7 8 7 8 9 10 11 12 13
(x - (if (~4 + (x div 2)) <= 0 then 0 else 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A309166-A081599-A028903: 0 1 2 3 4 5 6 7 8 9 8 9 10 11 12 13
(if ((x + ~2) mod (2 + (x mod 2))) <= 0 then 0 else 2)
A290542: 0 2 0 2 0 0 0 2 0 2 0 0 0 2 0 2
(2 + (if (~1 + (x div 2)) <= 0 then (x mod 2) else 0))
A159580: 2 3 2 3 2 2 2 2 2 2 2 2 2 2 2 2
loop(\(x,i).(~2x + (x div 2)),x,~2)
A333588: ~2 3 ~5 7 ~11 16 ~24 36 ~54 81 ~122 183 ~275 412 ~618 927
((if (x + ~1) <= 0 then x else 2) - (x div ~2))
A267530: 0 2 3 4 4 5 5 6 6 7 7 8 8 9 9 10
(x - ((if x <= 0 then 1 else x2) div ~2))
A222011: 1 2 4 8
A080476: 1 2 4 8 12 18 24 32 40 50 60 72 84 98 112 128
(2 - (if x <= 0 then 1 else (x2 div ~2)))
A105343: 1 3 4 7 10 15 20 27 34 43 52 63 74 87 100 115
(loop(\(x,i).(3x + 3),x,0) div 2)
A080926: 0 1 6 19 60 181 546 1639 4920 14761 44286 132859 398580 1195741 3587226 10761679
(loop(\(x,i).((x + 2) + (x div 2)),x,0) div 2)
A079719: 0 1 2 4 7 12 19 29 45 68 103 156 235 353 531 797
((2x + 8) + (if x <= 0 then 0 else 2))
A048868: 8 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
(loop(\(x,i).(((~x + 1) + i) * i),x,0) div 2)
A009574: 0 1 1 3 ~2 25 ~129 931 ~7412 66753 ~667475 7342291 ~88107414 1145396473 ~16035550517 240533257875
(loop(\(x,i).(((x + ~1) + i) * i),x,0) div 2)
A038155: 0 0 1 6 30 160 975 6846 54796 493200 4932045 54252550 651030666 8463398736 118487582395 1777313736030
((x - (if (~2 + (x div 2)) <= 0 then 0 else 1)) mod 2)
A082446: 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0
(((x div 3) + (if x <= 0 then 0 else 1)) mod 2)
A327256: 0 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0
(if (x + ~12) <= 0 then 1 else 2)
A103380: 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2
((1 + loop(\(x,i).(2x + 4),x,1)) div 2)
A131051: 1 3 8 18 38 78 158 318 638 1278 2558 5118 10238 20478 40958 81918
(loop(\(x,i).(2 + (x * i)),(x + 1),1) div 2)
A082570: 1 4 13 53 266 1597 11180 89441 804970 8049701 88546712 1062560545 13813287086 193386019205 2900790288076 46412644609217
((1 + loop(\(x,i).(x * (0 - i)),x,1)) div 2)
A105752: 1 0 1 ~3 12 ~60 360 ~2520 20160 ~181440 1814400 ~19958400 239500800 ~3113510400 43589145600 ~653837184000
((x mod (1 + (if (x + ~2) <= 0 then 0 else 2))) div 2)
A320003: 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0
(((if x <= 0 then 1 else x) div ~3) mod 2)
A302203: 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1
(if (x + ~10) <= 0 then 1 else 2)
A292027-A263109-A261585-A214564-A206245-A206244-A112348-A103378-A083311-A055098: 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2
(if (x mod 10) <= 0 then 1 else 2)
A259143: 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2
(if (~2 + (x div 5)) <= 0 then 1 else 2)
A342227-A333748-A320267-A297784-A295658-A287656-A271952-A263110-A262432-A258257-A239526-A238015-A209869-A203640-A163379-A117358-A114295-A069291-A063775-A062379-A053164-A046042-A043567-A043543-A043289: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
(if (~6 + (x div 2)) <= 0 then 1 else 2)
A316089-A072344-A066422: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2
(loop(\(x,i).i,((~1 + (x div 2)) div 2),1) mod 2)
A105586: 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1
(if (~2 + (x mod 8)) <= 0 then 1 else 2)
A038082: 1 1 1 2 2 2 2 2 1 1 1
(2 + (if ((x + 2) mod 4) <= 0 then 2 else 1))
A172515: 3 3 4 3 3 3 4 3 3 3 4 3 3 3 4 3
(x mod (if (~2 + (x div 4)) <= 0 then 1 else 2))
A297242-A230224-A178101-A112801-A046785: 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
(x mod (if (~4 + (x div 2)) <= 0 then 1 else 2))
A308069: 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1
(if (~2 + (x div (2 + (x mod 2)))) <= 0 then 1 else 2)
A237684: 1 1 1 1 1 1 2 1 2 2 2 2 2 2 2 2
(if (x mod 2) <= 0 then 1 else 10)
A010691: 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10
loop(\(x,i).x2,x,10)
A220812: 10 100 10000 100000000 10000000000000000 4611686018427387903 4611686018427387903
(2 + loop(\(x,i).x2,x,5))
A152578: 7 27 627 390627 152587890627 4611686018427387903 4611686018427387903
(x div (2 + (if (~x + 4) <= 0 then 2 else 1)))
A289133: 0 0 0 1 1 1 1 1 2 2 2 2 3 3 3 3
(if (x2 mod (x + 4)) <= 0 then 1 else 2)
A140685: 1 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2
((x mod loop(\(x,i).i,(~2 + (x div 2)),1)) div 2)
A114699-A024157: 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 0
(if x <= 0 then 1 else (2 * (1 + (2 * (x div 2)))))
A063210: 1 2 6 6 10 10 14 14 18 18 22 22 26 26 30 30
(2 + loop(\(x,i).x2,(x + 1),3))
A152582: 11 83 6563 43046723 1853020188851843 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,(x + ~2),3) div 2)
A122391: 1 1 1 3 6 12 24 48 96 192 384 768 1536 3072 6144 12288
(6 + loop(\(x,i).2x,x,1))
A153972: 7 8 10 14 22 38 70 134 262 518 1030 2054 4102 8198 16390 32774
loop(\(x,i).(2x + 1),x,6)
A086224: 6 13 27 55 111 223 447 895 1791 3583 7167 14335 28671 57343 114687 229375
loop(\(x,i).(x2 + ~2),x,6)
A003423: 6 34 1154 1331714 1773462177794 4611686018427387903 4611686018427387903
loop(\(x,i).((x - i) * i),x,6)
A101634: 6 5 6 9 20 75 414 2849 22728 204471 2044610 22490589 269886924 3508529843 49119417606 736791263865
(2 * loop(\(x,i).(x2 + ~2),x,3))
A213681: 6 14 94 4414 9741694 47450300994814 4611686018427387903 4611686018427387903
(1 mod loop(\(x,i).x2,(x + ~3),2))
A053776: 1 1 1 1 1 1 1 1 1 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 * (x - (x div 3))))
A063200: 1 2 4 4 6 8 8 10 12 12 14 16 16 18 20 20
(loop(\(x,i).(x * (1 + i)),x,3) div 2)
A070960: 1 3 9 36 180 1080 7560 60480 544320 5443200 59875200 718502400 9340531200 130767436800 1961511552000 31384184832000
(if x <= 0 then 1 else (3x2 + 2))
A005918: 1 5 14 29 50 77 110 149 194 245 302 365 434 509 590 677
(if x <= 0 then 1 else (2 + (x2 div 3)))
A193622: 1 2 3 5 7 10
(if x <= 0 then 1 else (2 + (x2 mod 3)))
A164359: 1 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2
(loop(\(x,i).x3,x,3) div 2)
A173506: 1 13 9841 3812798742493 4611686018427387903
loop(\(x,i).(2x + 1),(2x + 1),2)
A140529: 5 23 95 383 1535 6143 24575 98303 393215 1572863 6291455 25165823 100663295 402653183 1610612735 6442450943
loop(\(x,i).(2x + 4),(2x + 1),2)
A181358: 8 44 188 764 3068 12284 49148 196604 786428 3145724 12582908 50331644 201326588 805306364 3221225468 12884901884
loop(\(x,i).4x,(2x + 1),2)
A013777: 8 128 2048 32768 524288 8388608 134217728 2147483648 34359738368 549755813888 8796093022208 140737488355328 2251799813685248 36028797018963968 576460752303423488 4611686018427387903
loop(\(x,i).x2,2,(4x + 2))
A016828: 16 1296 10000 38416 104976 234256 456976 810000 1336336 2085136 3111696 4477456 6250000 8503056 11316496 14776336
loop(\(x,i).(2x + i),(2x + 1),2)
A069993: 5 27 121 503 2037 8179 32753 131055 524269 2097131 8388585 33554407 134217701 536870883 2147483617 8589934559
loop(\(x,i).2x2,(2x + ~1),2)
A046967: 2 8 32768 4611686018427387903
(loop(\(x,i).(x * (1 + i)),2x,1) div 2)
A085990: 0 3 60 2520 181440 19958400 3113510400 653837184000 177843714048000 60822550204416000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 + (2 mod (1 + (x div 2)))))
A217871: 1 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4
loop(\(x,i).2x,x,((1 + (x div 2)) mod 2))
A108474: 1 2 0 0 16 32 0 0 256 512 0 0 4096 8192 0 0
(if x <= 0 then 1 else (2 * (3 - (x mod 2))))
A231407: 1 4 6
A168428: 1 4 6 4 6 4 6 4 6 4 6 4 6 4 6 4
((if x <= 0 then 1 else x) mod (2 * (1 + (x mod 2))))
A204689: 1 1 0 3 0 1 0 3 0 1 0 3 0 1 0 3
(2 * (~1 + loop(\(x,i).(x + (x div 2)),x,2)))
A305498: 2 4 6 10 16 24 36 54 82 124 186 280 420 630 946 1420
(if x <= 0 then 1 else (4x2 + 2))
A005899: 1 6 18 38 66 102 146 198 258 326 402 486 578 678 786 902
(loop(\(x,i).(3x + ~1),x,1) div 2)
A015518: 0 1 2 7 20 61 182 547 1640 4921 14762 44287 132860 398581 1195742 3587227
(2 * loop(\(x,i).((x + 1) + (x div 2)),x,1))
A305497: 2 4 8 14 22 34 52 80 122 184 278 418 628 944 1418 2128
(2 * loop(\(x,i).((x + 1) + (i * i)),x,1))
A159938: 2 6 16 36 70 122 196 296 426 590 792 1036 1326 1666 2060 2512
(2 * loop(\(x,i).(2 * ((x + ~2) + i)),x,1))
A302689: 2 0 0 4 16 44 104 228 480 988 2008 4052 8144 16332 32712 65476
(2 * ((x + 1) + (if (x + ~1) <= 0 then x else 2)))
A214586: 2 6 10 12 14 16 18 20 22 24 26 28 30 32 34 36
(loop(\(x,i).(((x + ~1) * i) div 2),x,1) mod 2)
A117944: 1 0 1 1 0 1 0 0 0 1 0 0 0 0 1 0
(loop(\(x,i).x2,3,(x + 1)) div 2)
A191899: 0 128 3280 32768 195312 839808 2882400 8388608 21523360 50000000 107179440 214990848 407865360 737894528 1281445312 2147483648
loop(\(x,i).(x2 + 2x + ~2),(x + 1),2)
A145506: 6 46 2206 4870846 23725150497406 4611686018427387903 4611686018427387903
(((x + 1) * (if x <= 0 then 0 else (x + 2))) div 2)
A253145: 0 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136
loop(\(x,i).x2,(x2 + 3x + 2),2)
A341689: 16 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,(x div 2),(x + 1)) div 2)
A239632: 0 1 3 4 10 12 28 32 72 80 176 192 416 448 960 1024
(loop(\(x,i).x3,2,(x + 1)) div 2)
A191680: 0 256 9841 131072 976562 5038848 20176803 67108864 193710244 500000000 1178973845 2579890176 5302249686 10330523392 19221679687 34359738368
(2 + (loop(\(x,i).(x * i),x,2) mod (x + 1)))
A118136: 2 2 3 2 5 2 7 2 2 2 11 2 13 2 2 2
loop(\(x,i).((x * (i * i)) div 2),(x + 1),2)
A184358: 1 2 9 72 900 16200 396900 12700800 514382400 25719120000 1556006760000 112032486720000 9466745127840000 927741022528320000 4611686018427387903 4611686018427387903
(if (x mod 2) <= 0 then (x div 2) else (2x + 2))
A271478: 0 4 1 8 2 12 3 16 4 20 5 24 6 28 7 32
(x div (if (x + ~2) <= 0 then 2 else ((x + 1) div 2)))
A185219-A185218: 0 0 1 1 2 1 2 1 2 1 2 1 2 1 2 1
loop(\(x,i).2x,(x + ~1),((x + 1) mod 2))
A199573: 1 0 2 0 8 0 32 0 128 0 512 0 2048 0 8192 0
loop(\(x,i).2x,(x div 2),((x + 1) mod 2))
A077957: 1 0 2 0 4 0 8 0 16 0 32 0 64 0 128 0
loop(\(x,i).(~2x + i),x,((x + 1) mod 2))
A082383: 1 1 4 3 14 9 52 31 202 117 800 459 3190 1825 12748 7287
loop(\(x,i).(2 * (~x + i)),x,((x + 1) mod 2))
A068018: 1 2 4 6 12 18 40 62 148 234 576 918 2284 3650 9112 14574
((if (~2 + (x div 2)) <= 0 then x else (x + 1)) div 2)
A194212: 0 0 1 1 2 2 3 4 4 5 5 6 6 7 7 8
((loop(\(x,i).(x * i),x,x) mod (x + 1)) mod 2)
A288818-A283991-A252233-A010051: 0 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0
(2 + loop(\(x,i).(x * i),(x + 2),(x + ~1)))
A280556: 0 2 26 242 2162 20162 201602 2177282 25401602 319334402 4311014402 62270208002 958961203202 15692092416002 271996268544002 4979623993344002
(7 * (if x <= 0 then 1 else 2))
A040042: 7 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
(16 * (if x <= 0 then 1 else 2))
A040240: 16 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32
((x div 8) + (if x <= 0 then 1 else 2))
A134914-A082528: 1 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3
(2 * ((2 - (x mod 2)) * (if x <= 0 then 1 else 2)))
A040013: 4 4 8 4 8 4 8 4 8 4 8 4 8 4 8 4
((x2 + x + 2) * (if x <= 0 then 1 else 2))
A137882: 2 8 16 28 44 64 88 116 148 184 224 268 316 368 424 484
(((x2 + x) div 2) + (if x <= 0 then 1 else 2))
A097911: 1 3 5 8
A133263: 1 3 5 8 12 17 23 30 38 47 57 68 80 93 107 122
(((x2 + ~x) div 2) + (if x <= 0 then 1 else 2))
A089071: 1 2 3 5 8 12 17 23 30 38 47 57 68 80 93 107
(((x2 + ~2x) div 2) + (if x <= 0 then 1 else 2))
A261243: 1 1 2 3 6 9 14 19 26 33 42 51 62 73 86 99
((x + 8) + (if x <= 0 then 1 else 2))
A263772: 9 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
((x * (x + (x mod 2))) + (if x <= 0 then 1 else 2))
A231407: 1 4 6
A157616: 1 4 6 14 18 32 38 58 66 92 102 134
(2 + loop(\(x,i).5x,x,1))
A242328: 3 7 27 127 627 3127 15627 78127 390627 1953127 9765627 48828127 244140627 1220703127 6103515627 30517578127
loop(\(x,i).x3,(x2 + 1),2)
A173058: 8 512 4611686018427387903
(loop(\(x,i).(((x - i) div 2) * i),x,1) mod 2)
A217586: 1 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1
(2 + (if (x mod 5) <= 0 then 0 else 2))
A345438: 2 4 4 4 4 2 4 4
(2 + (if (x + ~6) <= 0 then 0 else 2))
A166594: 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4
(2 * (2 + (if (x mod 4) <= 0 then 2 else 0)))
A226276: 8 4 4 4 8 4 4 4 8 4 4 4 8 4 4 4
(x - (if ((x div 2) mod 2) <= 0 then ~2 else 2))
A004443: 2 3 0 1 6 7 4 5 10 11 8 9 14 15 12 13
(2 - ((if x <= 0 then 1 else x) div ~4))
A050499: 3 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6
(x - ((if x <= 0 then 1 else x) div ~4))
A226066-A184486-A005838: 1 2 3 4 5 7 8 9 10 12 13 14 15 17 18 19
(2 * (~2 + loop(\(x,i).(i - (x * i)),x,0)))
A056158: ~4 ~2 ~4 2 ~20 86 ~532 3706 ~29668 266990 ~2669924 29369138 ~352429684 4581585862 ~64142202100 962133031466
(2 + (if (x mod 2) <= 0 then 1 else 6))
A309345: 3 8 3 8 3 8
A010706: 3 8 3 8 3 8 3 8 3 8 3 8 3 8 3 8
((if x <= 0 then 2 else ((1 + (x div 2)) div 2)) div 2)
A264593: 1 0 0 0 0 0 1 1 1 1 1 1 1 1 2 2
(4 + loop(\(x,i).4x,x,1))
A178675: 5 8 20 68 260 1028 4100 16388 65540 262148 1048580 4194308 16777220 67108868 268435460 1073741828
(~4 + loop(\(x,i).4x,x,1))
A058896: ~3 0 12 60 252 1020 4092 16380 65532 262140 1048572 4194300 16777212 67108860 268435452 1073741820
(~2 + loop(\(x,i).(x2 + 1),(x + 1),2))
A056207: 3 24 675 458328 210066388899 4611686018427387903 4611686018427387903 4611686018427387903
(2 * loop(\(x,i).(2x + 4),(x + 1),2))
A182461: 16 40 88 184 376 760 1528 3064 6136 12280 24568 49144 98296 196600 393208 786424
(2 * loop(\(x,i).(x2 + x),(x + 1),2))
A118017: 12 84 3612 6526884 21300113901612
(loop(\(x,i).(2x + 1),(x + ~1),2) div 2)
A266550: 1 1 2 5 11 23 47 95 191 383 767 1535 3071 6143 12287 24575
(loop(\(x,i).(x + (x div 2)),(x + ~1),2) div 2)
A073941: 1 1 1 2 3 4 6 9 14 21 31 47 70 105 158 237
(4 + loop(\(x,i).3x,x,1))
A178648: 5 7 13 31
A168609: 5 7 13 31 85 247 733 2191 6565 19687 59053 177151 531445 1594327 4782973 14348911
(~4 + loop(\(x,i).3x,x,1))
A168611: ~3 ~1 5 23 77 239 725 2183 6557 19679 59045 177143 531437 1594319 4782965 14348903
(2 * (2 + (loop(\(x,i).2x,x,1) div 2)))
A078785-A053016: 4 6 8 12 20
A146528: 4 6 8 12 20 36 68 132 260 516 1028 2052 4100 8196 16388 32772
((if x <= 0 then 2 else (((x + 1) div 2) div 2)) div 2)
A025152-A017862: 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 2
(2 + (if (x mod 2) <= 0 then 1 else 8))
A010708: 3 10 3 10 3 10 3 10 3 10 3 10 3 10 3 10
((x div loop(\(x,i).i,(x div 4),2)) mod 2)
A181712: 0 0 1 1 0 1 0 1 0 0 1 1 0 0 0 1
(4 * (2 + loop(\(x,i).2x,x,2)))
A175161: 16 24 40 72 136 264 520 1032 2056 4104 8200 16392 32776 65544 131080 262152
(2 + loop(\(x,i).x2,(x + ~1),4))
A073096: 6 6 18 258 65538 4294967298 4611686018427387903 4611686018427387903 4611686018427387903
(8 + loop(\(x,i).2x,x,1))
A242475: 9 10 12 16 24 40 72 136 264 520 1032 2056 4104 8200 16392 32776
loop(\(x,i).(2x + ~1),x,8)
A083686: 8 15 29 57 113 225 449 897 1793 3585 7169 14337 28673 57345 114689 229377
((~x + (if x <= 0 then 2 else 1)) mod 8)
A228819: 2 0 7 6
(if (x + ~2) <= 0 then 1 else (x div 8))
A186728: 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1
(if (x mod 2) <= 0 then 1 else (x div 8))
A339368-A109704-A008618: 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1
loop(\(x,i).3x,x,8)
A005051: 8 24 72 216 648 1944 5832 17496 52488 157464 472392 1417176 4251528 12754584 38263752 114791256
loop(\(x,i).(x * (1 + i)),x,8)
A159038: 8 16 48 192 960 5760 40320 322560 2903040 29030400 319334400 3832012800 49816166400 697426329600 10461394944000 167382319104000
(loop(\(x,i).(2x + 1),x,4) div 2)
A054135: 2 4 9 19 39 79 159 319 639 1279 2559 5119 10239 20479 40959 81919
(2 * loop(\(x,i).(2x + 4),x,4))
A159741: 8 24 56 120 248 504 1016 2040 4088 8184 16376 32760 65528 131064 262136 524280
((if (x mod 2) <= 0 then 1 else (x div 4)) mod 2)
A274828: 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1
((if x <= 0 then 1 else x) - (2 * (x div 4)))
A187180: 1 1 2 3 2 3 4 5 4 5 6 7 6 7 8 9
loop(\(x,i).2x,x,(x + 6))
A078836: 6 14 32 72 160 352 768 1664 3584 7680 16384 34816 73728 155648 327680 688128
loop(\(x,i).x2,x,(4x + 8))
A235383: 8 144
((loop(\(x,i).2x,x,(x + 2)) div 2) div 2)
A129953: 0 1 4 10 24 56 128 288 640 1408 3072 6656 14336 30720 65536 139264
(4 + loop(\(x,i).x2,2,2x))
A222655: 4 20 260 1300 4100 10004 20740 38420 65540 104980 160004 234260 331780 456980 614660 810004
loop(\(x,i).x2,2,8x)
A017068: 0 4096 65536 331776 1048576 2560000 5308416 9834496 16777216 26873856 40960000 59969536 84934656 116985856 157351936 207360000
loop(\(x,i).(x * (1 + i)),4x,2)
A006523: 2 240 725760 12454041600 711374856192000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x3,4x,2)
A176935-A118019: 2 4611686018427387903
A257228: 2 4611686018427387903 4611686018427387903
A100267: 2 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A154424: 2 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A082566: 2 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A309966: 2 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).x3,2x,2) div 2)
A195529-A004217: 1 256 4611686018427387903
(2 + (if (x mod 2) <= 0 then 1 else (2 + (x div 2))))
A244055: 3 4 3 5 3
(if (x mod 2) <= 0 then 1 else (4 + (x div 2)))
A019303: 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 11
(if x <= 0 then 1 else (x div (4 + (x div 2))))
A264594-A185117: 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1
loop(\(x,i).2x,x,(4 + (x mod 2)))
A056486: 4 10 16 40 64 160 256 640 1024 2560 4096 10240 16384 40960 65536 163840
(((if x <= 0 then 1 else x) mod (2 + (x mod 2))) mod 2)
A060396: 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
(loop(\(x,i).2x,x,(2 + (x mod 2))) div 2)
A084221: 1 3 4 12 16 48 64 192 256 768 1024 3072 4096 12288 16384 49152
(((if x <= 0 then 2 else x) div (2 + (x mod 2))) mod 2)
A115604: 1 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1
((if x <= 0 then 2 else (x mod (2 + (x mod 2)))) div 2)
A339089-A327153-A281244-A133943: 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0
(x2 mod loop(\(x,i).(x2 + 2),2,2))
A070460: 0 1 4 9 16 25 36 11 26 5 24 7 30 17 6 35
(x - loop(\(x,i).(~2x2 + 1),2,2))
A130765: 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112
(if (~2 + (x div 3)) <= 0 then 1 else 4)
A032564: 1 1 1 1 1 1 1 1 1 4 4 4 4 4 4 4
(if (~4 + (x div 2)) <= 0 then 1 else 4)
A138908: 1 1 1 1 1 1 1 1 1 1 4 4 4 4 4 4
loop(\(x,i).(2x + 1),2x,4)
A156760: 4 19 79 319 1279 5119 20479 81919 327679 1310719 5242879 20971519 83886079 335544319 1342177279 5368709119
loop(\(x,i).4x,2x,4)
A013709: 4 64 1024 16384 262144 4194304 67108864 1073741824 17179869184 274877906944 4398046511104 70368744177664 1125899906842624 18014398509481984 288230376151711744 4611686018427387903
loop(\(x,i).(x2 + ~2),2x,4)
A219163: 4 194 1416317954 4611686018427387903
loop(\(x,i).(2x * i),2x,4)
A257583: 4 32 1536 184320 41287680 14863564800 7847962214400 5713316492083200 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + 1),x,4)
A330246: 4 17 69 277 1109 4437 17749 70997 283989 1135957 4543829 18175317 72701269 290805077 1163220309 4652881237
loop(\(x,i).(4x + ~1),x,4)
A199210: 4 15 59 235 939 3755 15019 60075 240299 961195 3844779 15379115 61516459 246065835 984263339 3937053355
loop(\(x,i).(2x2 + ~1),x,4)
A005828: 4 31 1921 7380481 108942999582721 4611686018427387903 4611686018427387903
loop(\(x,i).(3x + ~1),x,4)
A199109: 4 11 32 95 284 851 2552 7655 22964 68891 206672 620015 1860044 5580131 16740392 50221175
loop(\(x,i).(x2 + ~x + ~1),x,4)
A144744: 4 11 109 11771 138544669 19194625169774891 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + 4),x,4)
A155721: 4 20 84 340 1364 5460 21844 87380 349524 1398100 5592404 22369620 89478484 357913940 1431655764 5726623060
(4 * loop(\(x,i).(x * i),(x + ~1),x))
A052578: 0 4 8 24 96 480 2880 20160 161280 1451520 14515200 159667200 1916006400 24908083200 348713164800 5230697472000
loop(\(x,i).8x,x,4)
A013731: 4 32 256 2048 16384 131072 1048576 8388608 67108864 536870912 4294967296 34359738368 274877906944 2199023255552 17592186044416 140737488355328
loop(\(x,i).(3x + 2),x,4)
A198643: 4 14 44 134 404 1214 3644 10934 32804 98414 295244 885734 2657204 7971614 23914844 71744534
loop(\(x,i).((x2 + x) div 2),x,4)
A013589: 4 10 55 1540 1186570 703974775735 4611686018427387903 4611686018427387903 4611686018427387903
(4 * loop(\(x,i).(x2 + x),2,x))
A288486: 0 24 168 624 1680 3720 7224 12768 21024 32760 48840 70224 97968 133224 177240 231360
loop(\(x,i).((x2 + ~x) div 2),x,4)
A086714: 4 6 15 105 5460 14903070 111050740260915 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + 2x + ~2),x,4)
A145504: 4 22 526 277726 77132286526 4611686018427387903 4611686018427387903 4611686018427387903
((~x + loop(\(x,i).2x,x,2)) div 4)
A173010: 0 0 1 3 7 14 30 62 126 253 509 1021 2045 4092 8188 16380
(loop(\(x,i).(x * (x + i)),2,x) div 4)
A001621: 0 2 12 42 110 240 462 812 1332 2070 3080 4422 6162 8372 11130 14520
loop(\(x,i).i,(x mod 4),(x div 4))
A276327: 0 1 2 3 1 1 2 3 2 1 2 3 3 1 2 3
((if x <= 0 then 1 else 2x) - (x div 4))
A184654: 1 2 4 6 7 9 11 13 14 16 18 20 21 23 25 27
(4 * (x + (if (x mod 2) <= 0 then 1 else x)))
A272708: 4 8 12 24 20 40 28 56 36 72 44 88 52 104 60 120
loop(\(x,i).(x + (x div 4)),x,4)
A182305: 4 5 6 7 8 10 12 15 18 22 27 33 41 51 63 78
((x * (if (x mod 2) <= 0 then 2 else x)) div 4)
A129889: 0 0 1 2 2 6 3 12 4 20 5 30 6 42 7 56
loop(\(x,i).(x * i),x,(x2 div 4))
A306258: 0 0 2 12 96 720 6480 60480 645120 7257600 90720000 1197504000 17244057600 261534873600 4271736268800 73229764608000
loop(\(x,i).((2x + 4) + i),x,4)
A208638: 4 13 32 71 150 309 628 1267 2546 5105 10224 20463 40942 81901 163820 327659
(loop(\(x,i).(4x + 1),x,2) div 2)
A266753: 1 4 18 74 298 1194 4778 19114 76458 305834 1223338 4893354 19573418 78293674 313174698 1252698794
(loop(\(x,i).(3x + 1),x,2) div 2)
A081250: 1 3 11 33 101 303 911 2733 8201 24603 73811 221433 664301 1992903 5978711 17936133
(2 + loop(\(x,i).(3x + ~1),x,2))
A289521: 4 7 16 43 124 367 1096 3283 9844 29527 88576 265723 797164 2391487 7174456 21523363
(loop(\(x,i).(~1 + (x * (2 + i))),x,2) div 2)
A002395: 1 2 9 47
(x2 mod loop(\(x,i).(x2 + x),2,2))
A070464: 0 1 4 9 16 25 36 7 22 39 16 37 18 1 28 15
loop(\(x,i).x2,(x - ((~x + 2) div 2)),2)
A249760: 2 4 16 65536
(loop(\(x,i).2x,(x + ~1),(x + 2)) div 2)
A087447: 1 1 4 10 24 56 128 288 640 1408 3072 6656 14336 30720 65536 139264
(loop(\(x,i).(x2 + ~x),2,(x + 2)) div 2)
A088058: 1 15 66 190 435 861 1540 2556 4005 5995 8646 12090 16471 21945
loop(\(x,i).((x + 2) + (i * i)),(x + 2),2)
A026037: 11 22 40 67 105 156 222 305 407 530 676 847 1045 1272 1530 1821
(loop(\(x,i).(x * (x - i)),2,(x + 2)) div 2)
A033486: 0 12 60 180 420 840 1512 2520 3960 5940 8580 12012 16380 21840 28560 36720
(loop(\(x,i).2x,x,1) mod (x + 4))
A294390: 1 2 4 1 0 5 4 7 4 5 2 8 0 15 4 12
loop(\(x,i).(x * (2 + i)),x,(x + 4))
A171005: 4 15 72 420 2880 22680 201600 1995840 21772800 259459200 3353011200 46702656000 697426329600 11115232128000 188305108992000 3379030566912000
(if (x mod 2) <= 0 then (x + 1) else (2x + 4))
A066070: 1 6 3 10 5 14 7 18 9 22 11 26 13 30 15 34
((2x + 4) + (if (~x + 2) <= 0 then x else 2))
A086822: 6 8 10 13 16 19 22 25 28 31 34 37 40 43 46 49
loop(\(x,i).3x,x,(2x + 4))
A159715: 4 18 72 270 972 3402 11664 39366 131220 433026 1417176 4605822 14880348 47829690 153055008 487862838
(2 + (if (x + ~4) <= 0 then x else (x + 2)))
A319824: 2 3 4 5 6 9 10 11 12 13 14 15 16 17 18 19
(loop(\(x,i).(2x + 4),x,(x + 2)) div 2)
A047860: 1 5 14 34 78 174 382 830 1790 3838 8190 17406 36862 77822 163838 344062
(2 + (if (~2 + (x div 2)) <= 0 then x else (x + 2)))
A336064-A336063-A279486-A001476: 2 3 4 5 6 7 10 11 12 13 14 15 16 17 18 19
(loop(\(x,i).(2 * (x + i)),x,(x + 2)) div 2)
A133546: 1 4 12 31 74 169 376 823 1782 3829 8180 17395 36850 77809 163824 344047
(loop(\(x,i).(2x * i),x,(x + 2)) div 2)
A216149: 1 3 16
A187735: 1 3 16 120 1152 13440 184320 2903040 51609600 1021870080 22295347200 531372441600 13733933875200 382588157952000 11426632984166400 364223926370304000
(if (x + ~3) <= 0 then x else (2x + ~4))
A068670-A004271: 0 1 2 3 4 6 8 10 12 14 16 18 20 22 24 26
loop(\(x,i).(~3x + 3),2x,2)
A137483: 2 12 102 912 8202 73812 664302 5978712 53808402 484275612 4358480502 39226324512 353036920602 3177332285412 28595990568702 257363915118312
loop(\(x,i).(3x + 1),2x,2)
A255043: 2 22 202 1822 16402 147622 1328602 11957422 107616802 968551222 8716961002 78452649022 706073841202 6354664570822 57191981137402 514727830236622
loop(\(x,i).(3x + ~1),2x,2)
A199560: 2 14 122 1094 9842 88574 797162 7174454 64570082 581130734 5230176602 47071589414 423644304722 3812798742494 34315188682442 308836698141974
loop(\(x,i).(1 + (x * (1 + i))),2x,2)
A294039: 2 16 326 13700 986410 108505112 16926797486 3554627472076 966858672404690 330665665962404000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x * (1 + i)),2x,2)
A067626: 2 48 3840 645120 185794560 81749606400 51011754393600 42849873690624000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).8x,2x,2)
A277757: 2 128 8192 524288 33554432 2147483648 137438953472 8796093022208 562949953421312 36028797018963968 2305843009213693952 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x + 2),2x,2)
A198960: 2 26 242 2186 19682 177146 1594322 14348906 129140162 1162261466 10460353202 94143178826 847288609442 7625597484986 68630377364882 617673396283946
loop(\(x,i).(~3x + 1),2x,2)
A199565: 2 16 142 1276 11482 103336 930022 8370196 75331762 677985856 6101872702 54916854316 494251688842 4448265199576 40034386796182 360309481165636
loop(\(x,i).x2,3,4x)
A016808: 0 65536 16777216 429981696 4294967296 25600000000 110075314176 377801998336 1099511627776 2821109907456 6553600000000 14048223625216 28179280429056 53459728531456 96717311574016 167961600000000
loop(\(x,i).x3,1,4x)
A016803: 0 64 512 1728 4096 8000 13824 21952 32768 46656 64000 85184 110592 140608 175616 216000
loop(\(x,i).x3,2,4x)
A016809: 0 262144 134217728 5159780352 68719476736 512000000000 2641807540224 10578455953408 35184372088832 101559956668416 262144000000000 618121839509504 1352605460594688 2779905883635712
loop(\(x,i).(4x + 2),(x div 2),2)
A263053: 2 2 10 10 42 42 170 170 682 682 2730 2730 10922 10922 43690 43690
loop(\(x,i).(~4x + 8),(x div 2),2)
A167291: 2 2 0 0 8 8 ~24 ~24 104 104 ~408 ~408 1640 1640 ~6552 ~6552
((2 * (if x <= 0 then 1 else x)) div (2 + (x div 2)))
A332025: 1 1 1 2 2 2 2 2 2 3 2 3 3 3 3 3
(x mod loop(\(x,i).x3,(x div 2),2))
A308071: 0 1 2 3 4 5 6 7 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x + ~2) <= 0 then x else (4 - (x mod 2)))
A158515: 0 1 2 3 4 3 4 3 4 3 4 3 4 3 4 3
(~2 + loop(\(x,i).2x,x,2) - (x mod 2))
A101622: 0 1 6 13 30 61 126 253 510 1021 2046 4093 8190 16381 32766 65533
(loop(\(x,i).2x,x,2) div (2 + (x mod 2)))
A092809: 1 1 4 5 16 21 64 85 256 341 1024 1365 4096 5461 16384 21845
loop(\(x,i).2x,(x div 2),(2 + (x mod 2)))
A164090: 2 3 4 6 8 12 16 24 32 48 64 96 128 192 256 384
(loop(\(x,i).2x,x,1) - (2 * (x mod 2)))
A099430: 1 0 4 6 16 30 64 126 256 510 1024 2046 4096 8190 16384 32766
(2 - (loop(\(x,i).(x + (x div 2)),x,2) mod 2))
A304274: 2 1 2 2 1 1 1 2 2 1 2 1 1 2 2 1
(loop(\(x,i).(((x + ~1) + i) * i),x,2) div 2)
A266083: 1 1 3 12 54 280 1695 11886 95116 856080 8560845 94169350 1130032266 14690419536 205665873595 3084988104030
((~x + loop(\(x,i).(1 + (x * i)),x,0)) div 2)
A038158: 0 0 0 3 18 100 615 4326 34636 311760 3117645 34294150 411529866 5349888336 74898436795 1123476552030
loop(\(x,i).(6x + 1),x,2)
A198849: 2 13 79 475 2851 17107 102643 615859 3695155 22170931 133025587 798153523 4788921139 28733526835 172401161011 1034406966067
loop(\(x,i).(6x + ~1),x,2)
A199412: 2 11 65 389 2333 13997 83981 503885 3023309 18139853 108839117 653034701 3918208205 23509249229 141055495373 846332972237
(2 - ((if (x mod 3) <= 0 then 1 else x) mod 2))
A244227-A131718: 1 1 2 1 2 1 1 1 2 1 2 1 1 1 2 1
((x + (if (x + ~4) <= 0 then 2 else 1)) div 2)
A229803: 1 1 2 2 3 3 3 4 4 5 5 6 6 7 7 8
loop(\(x,i).(8x + 1),x,2)
A132433: 2 17 137 1097 8777 70217 561737 4493897 35951177 287609417 2300875337 18407002697 147256021577 1178048172617 9424385380937 75395083047497
(2 - ((if (x + ~4) <= 0 then 1 else x) mod 2))
A334541: 1 1 1 1 1 1 2 1 2 1 2 1 2 1 2 1
loop(\(x,i).(1 + (2 * (x - (i mod 2)))),x,2)
A201363: 2 3 7
A048573: 2 3 7 13 27 53 107 213 427 853 1707 3413 6827 13653 27307 54613
loop(\(x,i).x2,2,(3x + 2))
A016792: 16 625 4096 14641 38416 83521 160000 279841 456976 707281 1048576 1500625 2085136 2825761 3748096 4879681
loop(\(x,i).(x * (2 + i)),3x,2)
A100043: 2 120 40320 39916800 87178291200 355687428096000 2432902008176640000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x * (2 + i)),x,2)
A153647: 2 18 216 3240 58320 1224720 29393280 793618560 23808556800 785682374400 28284565478400 1103098053657600 46330118253619200 2084855321412864000 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (4x2 + ~2x))
A118239: 1 2 12 30 56 90 132 182 240 306 380 462 552 650 756 870
loop(\(x,i).((2x + 1) - (i mod 2)),x,2)
A081253: 2 4 9 18 37 74 149 298 597 1194 2389 4778 9557 19114 38229 76458
((if ((x div 2) mod 2) <= 0 then x else (~x + 1)) div 2)
A127365: 0 0 ~1 ~1 2 2 ~3 ~3 4 4 ~5 ~5 6 6 ~7 ~7
loop(\(x,i).(5x + 1),x,2)
A198769: 2 11 56 281 1406 7031 35156 175781 878906 4394531 21972656 109863281 549316406 2746582031 13732910156 68664550781
loop(\(x,i).(5x + ~1),x,2)
A199308: 2 9 44 219 1094 5469 27344 136719 683594 3417969 17089844 85449219 427246094 2136230469 10681152344 53405761719
((x * (1 + (if (x + ~2) <= 0 then 1 else x))) div 2)
A186783: 0 1 2 6 10 15 21 28 36 45 55 66 78
loop(\(x,i).(x3 + ~x + 1),x,2)
A144787: 2 7 337 38272417 4611686018427387903 4611686018427387903
((x * loop(\(x,i).(1 + (x * i)),x,1)) div 2)
A036919: 0 1 5 24 130 815 5871 47950 438404 4438845 49320505 596778116 7812368070 110024183659 1658826153635 26659706040570
(loop(\(x,i).(x * (2 + i)),(x + 1),x) div 2)
A213269: 0 6 60 540 5040 50400 544320 6350400 79833600 1077753600 15567552000 239740300800 3923023104000 67999067136000 1244905998336000 24008901396480000
(loop(\(x,i).(2x + ~1),(x + ~1),x) div 2)
A139756: 0 0 1 4 12 32 80 192 448 1024 2304 5120 11264 24576 53248 114688
((x * loop(\(x,i).x2,2,(x + ~1))) div 2)
A019583: 0 0 1 24 162 640 1875 4536 9604 18432 32805 55000 87846 134784 199927 288120
((6 mod (if x <= 0 then 1 else x)) mod 2)
A341619-A327159-A318880-A196272-A185015-A177063-A061853-A027192: 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
((x2 + 2) div (2 + (if x <= 0 then 1 else x)))
A101788: 0 1 1 2 3 3 4 5 6 7 8 9 10 11 12 13
loop(\(x,i).((2x * i) div (1 + i)),x,2)
A339711: 2 2 2 3 4 6 10 17 30 54 98 179 330 612 1142 2141
((x * (2 + (if (x mod 2) <= 0 then x else 0))) div 2)
A240134: 0 1 4 3 12 5 24 7 40 9 60 11 84 13 112 15
(if (~2 + (x div 5)) <= 0 then x else 2)
A103303: 0 1 2 3 4 5 6 7 8 9
A043274: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 2
(2 * (x + (if (x + ~4) <= 0 then 1 else 2)))
A260391: 2 4 6 8 10 14 16 18 20 22 24 26 28 30 32 34
((x + 2) + (if (~2 + (x div 2)) <= 0 then 1 else 2))
A154660: 3 4 5 6 7 8
A138928: 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18 19
loop(\(x,i).(6x + 2),x,2)
A005610: 2 14 86 518 3110 18662 111974 671846 4031078 24186470 145118822 870712934 5224277606 31345665638 188073993830 1128443962982
loop(\(x,i).(2 + (3 * (x div 2))),x,2)
A304025: 2 5 8 14 23 35 53 80 122 185 278 419 629 944 1418 2129
((2 div (if (x mod 3) <= 0 then 2 else x)) mod 2)
A227998: 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1
(~2 + loop(\(x,i).(x2 + x + 1),2,x))
A072025: 1 11 55 181 461 991 1891 3305 5401 8371 12431 17821 24805 33671 44731 58321
(loop(\(x,i).(x2 + x + 1),2,x) div 2)
A336535: 1 6 28 91 231 496 946 1653 2701 4186 6216 8911 12403 16836 22366 29161
(2 * loop(\(x,i).((x + 1) * (x + i)),2,x))
A120571: 12 60 220 612 1404 2812 5100 8580 13612 20604 30012 42340 58140 78012 102604 132612
(if (x mod 2) <= 0 then (~x + 8) else 2)
A228818: 8 2 6 2
(x mod ((if ((x div 2) mod 2) <= 0 then 2 else x) div 2))
A122179-A101606-A048622: 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1
(2x * loop(\(x,i).(x2 + 2),2,2))
A004944-A004924: 0 76 152 228 304 380 456 532 608 684 760 836 912 988 1064 1140
(2 * (x + (if (x mod 2) <= 0 then 1 else 4)))
A142954: 2 10 6 14 10 18 14 22 18 26 22 30 26 34 30 38
(2 div (if ((x + 2) mod 4) <= 0 then x else 2))
A303300: 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1
loop(\(x,i).(2 + ((x2 + x) div 2)),x,2)
A067339: 2 5 17 155 12092 73114280 2672849006516342 4611686018427387903 4611686018427387903
loop(\(x,i).(5x + ~2),x,2)
A199213: 2 8 38 188 938 4688 23438 117188 585938 2929688 14648438 73242188 366210938 1831054688 9155273438 45776367188
loop(\(x,i).(2 * (x - ((2 - i) div 2))),x,2)
A288206: 2 4 8 18 38 80 164 334 674 1356 2720 5450 10910 21832 43676 87366
loop(\(x,i).(2x - ((i div 2) mod 2)),x,2)
A262267: 2 4 7 13 26 52 103 205 410 820 1639 3277 6554 13108 26215 52429
((x + 2) + ((if (x + ~2) <= 0 then 1 else x) mod 2))
A320727: 3 4 5 6 6 8
loop(\(x,i).(2x * (~1 + (2 * i))),x,2)
A151817: 2 4 24 240 3360 60480 1330560 34594560 1037836800 35286451200 1340885145600 56317176115200 2590590101299200 129529505064960000 4611686018427387903 4611686018427387903
(loop(\(x,i).(x * (1 + (x * i))),2,x) div 2)
A219086: 0 5 39 150 410 915 1785 3164 5220 8145 12155 17490 24414 33215 44205 57720
((~x + ~2) + loop(\(x,i).4x,x,2))
A124133: 0 5 28 123 506 2041 8184 32759 131062 524277 2097140 8388595 33554418 134217713 536870896 2147483631
loop(\(x,i).((x + 2) + ((2 + i) * i)),x,2)
A145066: 2 7 17 34 60 97 147 212 294 395 517 662 832 1029 1255 1512
(2 * (x + (if (x + ~2) <= 0 then 1 else (x + ~2))))
A050622: 2 4 6 8 12 16 20 24 28 32 36 40 44 48 52 56
(if (x + ~2) <= 0 then 1 else (x2 + ~2x + 2))
A098749: 1 1 1 5 10 17 26 37 50 65 82 101 122 145 170 197
(2x * loop(\(x,i).x2,2,2x))
A016745: 0 32 1024 7776 32768 100000 248832 537824 1048576 1889568 3200000 5153632 7962624 11881376 17210368 24300000
((~1 + (x mod 2)) mod loop(\(x,i).2x,x,2))
A279872: 1 0 7 0 31 0 127 0 511 0 2047 0 8191 0 32767 0
loop(\(x,i).(x3 * (x div 2)),x,2)
A174736: 2 8 2048 8796093022208 4611686018427387903
(2 * (1 - loop(\(x,i).(x * (~x + i)),2,x)))
A173785: 2 2 18 98 338 882 1922 3698 6498 10658 16562 24642 35378 49298 66978 89042
loop(\(x,i).(x * ((2 + i) * (2 + i))),x,2)
A123385: 2 18 288 7200 259200 12700800 812851200 65840947200 6584094720000 796675461120000 114721266401280000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 div (2 - (i mod 2))),x,2)
A068994: 2 4 8 64 2048
((x + 2) * loop(\(x,i).(x + (i * i)),x,0))
A289643: 0 3 20 70 180 385 728 1260 2040 3135 4620 6578 9100 12285 16240 21080
((x + 2) * (if (x mod 2) <= 0 then 4 else 1))
A144433: 8 3 16 5 24 7 32 9 40 11 48 13 56 15 64 17
((1 + loop(\(x,i).(x * i),x,2)) div (x + 2))
A126328: 1 1 1 2 8 34 180 1120 8064 65978 604800 6141046 68428800 830269440 10897286400 153844043294
(loop(\(x,i).~2x,x,1) mod (x + 2))
A213381: 1 1 0 2 4 3 0 7 6 5 4 6 8 13 0 8
((2 + loop(\(x,i).(x * i),x,1)) mod (x + 2))
A160540: 1 0 0 3
A249355: 1 0 0 3 2 3 2 2 2 3 2 3 2 2 2 3
((2 * (if x <= 0 then 1 else 2x)) div (x + 2))
A163291: 1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 3
loop(\(x,i).(x + (x div 4)),2,(x + 2))
A296350: 2 3 6 7 8 10 12 13 15 16 18 20 21 22 25 26
(if (x + ~6) <= 0 then x else (x + 2))
A103681-A039265-A039204: 0 1 2 3 4 5 6 9 10 11 12 13 14 15 16 17
(if (~2 + (x div 3)) <= 0 then x else (x + 2))
A329299-A039272-A039209-A023778: 0 1 2 3 4 5 6 7 8 11 12 13 14 15 16 17
(if (~2 + (x div 4)) <= 0 then x else (x + 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A130574-A113191-A035064-A023780: 0 1 2 3 4 5 6 7 8 9 10 11 14 15 16 17
(if (~4 + (x div 2)) <= 0 then x else (x + 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A343951-A118766-A102487-A055569-A050759-A039274-A009993: 0 1 2 3 4 5 6 7 8 9 12 13 14 15 16 17
(loop(\(x,i).~2x,x,x) mod (x + 2))
A110146: 0 1 0 1 4 1 0 4 8 1 4 1 12 4 0 1
(loop(\(x,i).(2x * i),x,x) mod (x + 2))
A119690: 0 2 0 4 0 6 0 0 0 10 0 12 0 0 0 16
loop(\(x,i).((x mod 4) * i),x,(x + 2))
A115562: 2 3 0 6 0 0 0 0 0 0
(2x + (if (x mod 3) <= 0 then 1 else 0))
A047236: 1 2 4 7 8 10 13 14 16 19 20 22 25 26 28 31
(2x + (if (x mod 4) <= 0 then 1 else 0))
A231408: 1 2 4 6 9
A047411: 1 2 4 6 9 10 12 14 17 18 20 22 25 26 28 30
(2x + (if (~2 + (x div 2)) <= 0 then 1 else 0))
A246407: 1 3 5 7 9 11 12 14 16 18 20 22 24 26 28 30
(2x + (if (x mod 4) <= 0 then 0 else 1))
A047485: 0 3 5 7 8 11 13 15 16 19 21 23 24 27 29 31
(2x + (if (~2 + (x div 2)) <= 0 then 0 else 1))
A246408-A246404: 0 2 4 6 8 10 13 15 17 19 21 23 25 27 29 31
(2x + (if (x mod 3) <= 0 then 2 else 1))
A047254: 2 3 5 8 9 11 14 15 17 20 21 23 26 27 29 32
(2x + (if (x mod 4) <= 0 then 2 else 1))
A047487: 2 3 5 7 10 11 13 15 18 19 21 23 26 27 29 31
(2x + (if (~2 + (x div 2)) <= 0 then 2 else 1))
A285591: 2 4 6 8 10 12 13 15 17 19 21 23 25 27 29 31
(2x + (if (~x + 2) <= 0 then (x + ~2) else 1))
A026488: 1 3 4 7 10 13 16 19 22 25 28 31 34 37 40 43
loop(\(x,i).4x,x,(~2x + 1))
A144704: 1 ~4 ~48 ~320 ~1792 ~9216 ~45056 ~212992 ~983040 ~4456448 ~19922944 ~88080384 ~385875968 ~1677721600 ~7247757312 ~31138512896
(~2x + loop(\(x,i).4x,x,1))
A100103: 1 2 12 58 248 1014 4084 16370 65520 262126 1048556 4194282 16777192 67108838 268435428 1073741794
(~2x + loop(\(x,i).3x,x,1))
A186948: 1 1 5 21 73 233 717 2173 6545 19665 59029 177125 531417 1594297 4782941 14348877
(2x + (if (x + ~4) <= 0 then 1 else 2))
A246405: 1 3 5 7 9 12 14 16 18 20 22 24 26 28 30 32
(2x + (if (~2 + (x div 2)) <= 0 then 1 else 2))
A285590: 1 3 5 7 9 11 14 16 18 20 22 24 26 28 30 32
loop(\(x,i).x3,4,2x)
A330009-A127352: 0 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x + ~1) <= 0 then x else (2x + (x div 2)))
A256680: 0 1 5 7 10 12 15 17 20 22 25 27 30 32 35 37
(2x + (if (x mod 2) <= 0 then x2 else 2))
A066106: 0 4 8 8 24 12 48 16 80 20 120 24 168 28 224 32
loop(\(x,i).(4x + 1),x,2x)
A072258: 0 9 69 405 2133 10581 50517 234837 1070421 4805973 21321045 93672789 408245589 1767200085 7605671253 32570168661
loop(\(x,i).((2x + ~1) + i),x,2x)
A208658: 0 4 17 52 139 346 825 1912 4343 9718 21493 47092 102387 221170 475121 1015792
((if (~2 + (x div 2)) <= 0 then 1 else 2) + (x div 2))
A038810: 1 1 2 2 3 3 5 5 6 6 7 7 8 8 9 9
(loop(\(x,i).(~x + i),(x + ~1),2) * (x div 2))
A174474: 0 0 ~1 3 0 8 3 15 8 24 15 35 24 48 35 63
loop(\(x,i).(x - (x div (2 + i))),2,(x div 2))
A023967: 0 0 1 1 2 2 2 2 3 3 3 3 3 3 4 4
((if (x mod 2) <= 0 then 1 else (x + 2)) + (x div 2))
A064455: 1 3 2 6 3 9 4 12 5 15 6 18 7 21 8 24
((if (x mod 2) <= 0 then 1 else (x + 2)) - (x div 2))
A195084: 1 3 0 4 ~1 5 ~2 6 ~3 7 ~4 8 ~5 9 ~6 10
(x + ((if (x mod 2) <= 0 then 2 else 0) + (x div 2)))
A166517: 2 1 5 4 8 7 11 10 14 13 17 16 20 19 23 22
loop(\(x,i).2x,x,((~x + 1) - (x div 2)))
A179609: 1 0 ~8 ~24 ~80 ~192 ~512 ~1152 ~2816 ~6144 ~14336 ~30720 ~69632 ~147456 ~327680 ~688128
((if (x + ~3) <= 0 then 2 else 1) - (x mod 2))
A275346: 2 1 2 1 1 0 1 0 1 0 1 0 1 0 1 0
(loop(\(x,i).2x,x,3) + (x mod 2))
A280345: 3 7 12 25 48 97 192 385 768 1537 3072 6145 12288 24577 49152 98305
(loop(\(x,i).2x,(x div 2),1) - (x mod 2))
A106624: 1 0 2 1 4 3 8 7 16 15 32 31 64 63 128 127
(loop(\(x,i).4x,x,1) - (x mod 2))
A216149: 1 3 16
A267036: 1 3 16 63 256 1023 4096 16383 65536 262143 1048576 4194303 16777216 67108863 268435456 1073741823
loop(\(x,i).(2x + 1),(x + ~1),(x mod 2))
A140252: 0 1 1 7 7 31 31 127 127 511 511 2047 2047 8191 8191 32767
(2 - (if (x mod 3) <= 0 then 2 else (x mod 2)))
A193680: 0 1 2 0 2 1 0 1 2 0 2 1 0 1 2 0
((if x <= 0 then 1 else (2x + 4)) - (x mod 2))
A100832: 1 5 8 9 12 13 16 17 20 21 24 25 28 29 32 33
loop(\(x,i).2x,(x div 2),(2 - (x mod 2)))
A135530: 2 1 4 2 8 4 16 8 32 16 64 32 128 64 256 128
(loop(\(x,i).x2,x,2) div (2 - (x mod 2)))
A074073: 1 4 8 256 32768 4294967296 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + 2),(x div 2),(x mod 2))
A065653: 0 1 2 3 6 11 38 123 1446 15131 2090918 228947163 4371938082726 52416803445748571 4611686018427387903 4611686018427387903
(x + ((if (~x + 2) <= 0 then 2 else 1) + (x mod 2)))
A265283: 1 3 4 6 6 8 8 10 10 12 12 14 14 16 16 18
loop(\(x,i).7x,x,2)
A109808: 2 14 98 686 4802 33614 235298 1647086 11529602 80707214 564950498 3954653486 27682574402 193778020814 1356446145698 9495123019886
loop(\(x,i).(x * (1 + ((1 + i) div 2))),x,2)
A152875: 2 4 8 24 72 288 1152 5760 28800 172800 1036800 7257600 50803200 406425600 3251404800 29262643200
loop(\(x,i).(x3 + 3x),x,2)
A006266: 2 14 2786 21624372014 4611686018427387903 4611686018427387903
(loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2)
A108202-A025480: 0 0 1 0 2 1 3 0 4 2 5 1 6 3 7 0
loop(\(x,i).(2x3 + ~x),x,2)
A106484: 2 14 5474 328053267374 4611686018427387903 4611686018427387903
loop(\(x,i).(5x + 4),x,2)
A198762: 2 14 74 374 1874 9374 46874 234374 1171874 5859374 29296874 146484374 732421874 3662109374 18310546874 91552734374
(2 * (~x + loop(\(x,i).2x,(x + ~2),x)))
A052749: 0 0 0 6 24 70 180 434 1008 2286 5100 11242 24552 53222 114660 245730
(loop(\(x,i).((~x + 1) * (x div 2)),x,x) mod 2)
A227768: 0 0 0 0 1 0 4611686018427387903
((x + loop(\(x,i).(x * i),(x div 2),x)) div 2)
A023785: 0 1 2 3 6 7 21
((x + loop(\(x,i).x3,2,x)) div 2)
A168116: 0 1 257 9843 131074 976565 5038851 20176807 67108868 193710249 500000005 1178973851 2579890182 5302249693 10330523399 19221679695
(loop(\(x,i).((x * (~x + i)) div 2),x,x) mod 2)
A172577: 0 0 0 0 0 1 4611686018427387903 4611686018427387903 4611686018427387903
(2x2 + (2 div (if x <= 0 then 2 else x)))
A127081: 1 4 9 18 32
(1 mod loop(\(x,i).x3,x2,2))
A255360: 1 1 4611686018427387903
(loop(\(x,i).(x * (~2 + (x div 2))),x,x) mod 2)
A172564: 0 0 0 0 0 0 0 1 4611686018427387903 4611686018427387903 4611686018427387903
((x + loop(\(x,i).x2,2,x2)) div 2)
A168067: 0 1 129 3282 32770 195315 839811 2882404 8388612 21523365 50000005 107179446 214990854 407865367 737894535 1281445320
((~x + loop(\(x,i).(x + (x div 2)),x,x)) div 2)
A339655: 0 0 1 3 7 14 28
(loop(\(x,i).(x + ((x + ~1) * i)),x,x) div 2)
A317527: 0 0 3 24 180 1440 12600 120960 1270080 14515200 179625600 2395008000 34248614400 523069747200 8499883392000 146459529216000
(loop(\(x,i).(x + ((x + ~2) * i)),x,x) div 2)
A317483: 0 0 1 13 121 1081 10081 100801 1088641 12700801 159667201 2155507201 31135104001 479480601601 7846046208001 135998134272001
(x + (if (x + ~6) <= 0 then 1 else 0))
A124808: 1 2 3 4 5 6 7 7 8 9 10 11 12 13 14 15
(if (x mod 9) <= 0 then 0 else x)
A004184: 0 1 2 3 4 5 6 7 8 0 10 11 12 13 14 15
(x + (if (~2 + (x div 4)) <= 0 then 1 else 0))
A071523: 1 2 3 4 5 6 7 8 9 10 11 12 12 13 14 15
(x + (if (~4 + (x div 2)) <= 0 then 1 else 0))
A122262-A122256: 1 2 3 4 5 6 7 8 9 10 10 11 12 13 14 15
(x + (if (x mod 3) <= 0 then 3 else 0))
A130509: 3 1 2 6 4 5 9 7 8 12 10 11 15 13 14 18
(if (x2 mod (x + 3)) <= 0 then 0 else x)
A004181: 0 1 2 3 4 5 0 7 8 9 10 11 12 13 14 15
(~x + loop(\(x,i).(2x + i),(x + ~1),0))
A070313: 0 ~1 ~1 1 7 21 51 113 239 493 1003 2025 4071 8165 16355 32737
(if (~6 + (x div 2)) <= 0 then 0 else x)
A308974: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14 15
(x + (if (x mod 2) <= 0 then 4x else 0))
A195817: 0 1 10 3 20 5 30 7 40 9 50 11 60 13 70 15
(~x + loop(\(x,i).(2x + (i * i)),x,0))
A229788: 0 0 4 18 54 136 312 678 1426 2940 5988 12106 24366 48912 98032 196302
(x + (if (x mod 2) <= 0 then (x + (x div 2)) else 0))
A195140: 0 1 5 3 10 5 15 7 20 9 25 11 30 13 35 15
(x + loop(\(x,i).i,(~1 + (x div 3)),1))
A133812: 1 2 3 4 5 6 7 8 9 11 12 13 15 16 17 19
(x + loop(\(x,i).i,(x + ~5),1))
A292621-A280693-A033059: 1 2 3 4 5 6 7 9 11 13 15 17 19 21 23 25
(x + loop(\(x,i).i,(x div 5),1))
A247397: 1 2 3 4 5 6 7 8 9 10 12 13
A245028-A233264-A198343-A074402: 1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 18
(x + loop(\(x,i).i,(~3 + (x div 2)),1))
A247397: 1 2 3 4 5 6 7 8 9 10 12 13
A309129-A307345: 1 2 3 4 5 6 7 8 9 10 12 13 15 16 18 19
(x + loop(\(x,i).i,((x + ~1) div 3),1))
A082463: 1 2 3 4 5 6 7 9 10
A342525-A325457: 1 2 3 4 5 6 7 9 10 11 13 14 15 17 18 19
((x mod 2) mod (if (x mod 3) <= 0 then 1 else x))
A059781: 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0
(x + loop(\(x,i).(x * (x + i)),(x + ~1),1))
A198864: 1 2 4 11 92 8101 65585702 4301483913318599 4611686018427387903 4611686018427387903
(x * loop(\(x,i).(x2 * i),(x + ~1),1))
A088679: 0 1 2 6 48 2880 9953280 115579079884800 4611686018427387903 4611686018427387903
(x * (1 + (if (x mod 3) <= 0 then 0 else 2)))
A109044: 0 3 6 3 12 15 6 21 24 9 30 33 12 39 42 15
(x * (1 + (if (x + ~4) <= 0 then 0 else 2)))
A102483: 0 1 2 3 4 15
(x * (if (x mod 2) <= 0 then 6 else 1))
A317312: 0 1 12 3 24 5 36 7 48 9 60 11 72 13 84 15
(x + loop(\(x,i).i,(x + ~6),1))
A330729-A316115-A316114-A302834-A122936-A113768-A080750-A079645-A032958-A008726: 1 2 3 4 5 6 7 8 10 12 14 16 18 20 22 24
(x + loop(\(x,i).i,(~2 + (x div 3)),1))
A290492: 1 2 3 4 5 6 7 8 9 10 11 12 14
A338883-A327749-A194424-A155182-A147820-A108864-A096076-A055722-A051038-A033892-A033637-A033620-A028830: 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 18
(x + loop(\(x,i).i,(((x + ~1) div 2) div 2),1))
A336547-A325097-A219361-A122156-A122154: 1 2 3 4 5 6 7 8 9 11 12 13 14 16 17 18
(if ((x + ~1) mod 8) <= 0 then 1 else x)
A319657: 0 1 2 3 4 5 6 7 8 1 10 11 12 13 14 15
(x * (if (x mod 2) <= 0 then 8 else 1))
A317316: 0 1 16 3 32 5 48 7 64 9 80 11 96 13 112 15
loop(\(x,i).i,(x + ~9),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A247796-A209685-A080463-A076314-A053837-A010888-A007953: 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6
(x + (if (~x + 2) <= 0 then 8 else 1))
A171893: 1 2 10 11 12 13 14 15 16 17 18 19 20 21 22 23
(x + loop(\(x,i).i,(x + ~8),1))
A179052-A122618-A117804-A064223-A032960-A008728: 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22
(1 div (if (x mod 8) <= 0 then 1 else x))
A010057: 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
(1 mod (if (x mod 8) <= 0 then 1 else x))
A104121: 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1
(x * (~1 + loop(\(x,i).2x2,2,2)))
A138127: 0 127 254 381 508 635 762 889 1016 1143 1270 1397 1524 1651 1778 1905
loop(\(x,i).x2,2,5x)
A016852: 0 625 10000 50625 160000 390625 810000 1500625 2560000 4100625 6250000 9150625 12960000 17850625 24010000 31640625
loop(\(x,i).(x + i),(x + ~5),x)
A067570: 0 1 2 3 4 5 7
A272072: 0 1 2 3 4 5 7 10
A195944: 0 1 2 3 4 5 7 10 14
loop(\(x,i).(x - i),(x div 5),x)
A245335: 0 1 2 3 4 4 5 6 7 8 7 8 9 10 11 9
(1 div (if (x mod (2 + (x mod 2))) <= 0 then 1 else x))
A071036: 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1
(x * (3 + (if (~x + 2) <= 0 then x else 2)))
A164004: 0 5 10 18 28 40 54 70 88 108 130 154 180 208 238 270
loop(\(x,i).(2x2 + ~1),3,x)
A243134: 1 1 18817 665857 7380481 46099201 203253121 708158977 2081028097 5374978561 12545596801 26986755841 54276558337 103182433537 186979578241 325142092801
(x + (loop(\(x,i).2x,x,1) div 3))
A340849: 0 1 3 5 9 15 27 49 93 179 351 693 1377 2743 5475 10937
(x * loop(\(x,i).(x2 + 2),2,3))
A004965-A004945: 0 123 246 369 492 615 738 861 984 1107 1230 1353 1476 1599 1722 1845
loop(\(x,i).((x2 + x) div 2),3,x)
A064322: 0 1 21 231 1540 7260 26796 82621 222111 536130 1186570 2445366 4747821 8763391 15487395 26357430
(x + (if x <= 0 then 1 else ((x div 2) div 3)))
A247832: 1 1 2 3 4 5 7 8 9 10 11 12 14 15 16 17
loop(\(x,i).x2,3,3x)
A016772: 0 6561 1679616 43046721 429981696 2562890625 11019960576 37822859361 110075314176 282429536481 656100000000 1406408618241 2821109907456 5352009260481 9682651996416 16815125390625
loop(\(x,i).x3,1,3x)
A016767: 0 27 216 729 1728 3375 5832 9261 13824 19683 27000 35937 46656 59319 74088 91125
loop(\(x,i).x3,2,3x)
A016773: 0 19683 10077696 387420489 5159780352 38443359375 198359290368 794280046581 2641807540224 7625597484987 19683000000000 46411484401953 101559956668416 208728361158759 406671383849472
(x + (if (x + ~2) <= 0 then 1 else (x div 3)))
A071959: 1 2 3 4 5 6 8 9 10 12 13 14 16 17 18 20
(if x <= 0 then 1 else (x3 + 3x))
A079908: 1 4 14 36 76 140 234 364 536 756 1030 1364 1764 2236 2786 3420
loop(\(x,i).4x,(2x + 1),x)
A239739: 0 64 2048 49152 1048576 20971520 402653184 7516192768 137438953472 2473901162496 43980465111040 774056185954304 13510798882111488 234187180623265792 4035225266123964416 4611686018427387903
(~x + loop(\(x,i).2x,x,(2x + 1)))
A271771: 1 5 18 53 140 347 826 1913 4344 9719 21494 47093 102388 221171 475122 1015793
(x + loop(\(x,i).3x,2x,1))
A226202: 1 10 83 732 6565 59054 531447 4782976 43046729 387420498 3486784411 31381059620 282429536493 2541865828342 22876792454975 205891132094664
(~x + loop(\(x,i).3x,2x,1))
A024102: 1 8 79 726 6557 59044 531435 4782962 43046713 387420480 3486784391 31381059598 282429536469 2541865828316 22876792454947 205891132094634
(x + loop(\(x,i).(x * i),2x2,1))
A140656: 1 3 40322 6402373705728003 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 + ((x * i) div 2)),x,(~x + 1))
A243299: 1 2 3 6 12 32
(x + loop(\(x,i).6x,x,1))
A226200: 1 7 38 219 1300 7781 46662 279943 1679624 10077705 60466186 362797067 2176782348 13060694029 78364164110 470184984591
(~x + loop(\(x,i).6x,x,1))
A024063: 1 5 34 213 1292 7771 46650 279929 1679608 10077687 60466166 362797045 2176782324 13060694003 78364164082 470184984561
(1 - (x * loop(\(x,i).(~1 + (x * i)),x,1)))
A007808: 1 1 3 13 69 431 3103 25341 231689 2345851 26065011 315386633 4128697741 58145826519 876660153671 14089181041141
(x + loop(\(x,i).8x,x,1))
A226201: 1 9 66 515 4100 32773 262150 2097159 16777224 134217737 1073741834 8589934603 68719476748 549755813901 4398046511118 35184372088847
(~x + loop(\(x,i).8x,x,1))
A024089: 1 7 62 509 4092 32763 262138 2097145 16777208 134217719 1073741814 8589934581 68719476724 549755813875 4398046511090 35184372088817
(x + (if (~4 + (x div 2)) <= 0 then x else 1))
A182324: 0 2 4 6 8 10 12 14 16 18 11 12 13 14 15 16
loop(\(x,i).2x,(x2 + ~2x + 1),x)
A197927: 0 1 4 48 2048 327680 201326592 481036337152 4503599627370496 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x * (1 + loop(\(x,i).x3,2,x)))
A196292: 0 2 1026 59052 1048580 9765630 60466182 282475256 1073741832 3486784410 10000000010 25937424612 61917364236 137858491862 289254654990 576650390640
(x * (~1 + loop(\(x,i).x3,2,x)))
A196291: 0 0 1022 59046 1048572 9765620 60466170 282475242 1073741816 3486784392 9999999990 25937424590 61917364212 137858491836 289254654962 576650390610
loop(\(x,i).(3x + 2),(x + 1),x)
A060352: 2 17 80 323 1214 4373 15308 52487 177146 590489 1948616 6377291 20726198 66961565 215233604 688747535
(x + (loop(\(x,i).x2,x,2) div (x + 1)))
A201363: 2 3 7
A057736: 2 3 7 67
((x2 + x) + loop(\(x,i).2x,x,1))
A131924: 1 4 10 20 36 62 106 184 328 602 1134 2180 4252 8374 16594 33008
((~x2 + ~x) + loop(\(x,i).2x,x,1))
A220588: 1 0 ~2 ~4 ~4 2 22 72 184 422 914 1916 3940 8010 16174 32528
loop(\(x,i).x3,1,(x2 + x))
A060459: 0 8 216 1728 8000 27000 74088 175616 373248 729000 1331000 2299968 3796416 6028568 9261000 13824000
((x2 + x) + loop(\(x,i).(x * i),x,1))
A066143: 1 3 8 18 44 150 762 5096 40392 362970 3628910 39916932 479001756 6227020982 87178291410 1307674368240
(x + (if (x mod 2) <= 0 then x2 else (x + 1)))
A103831: 0 3 6 7 20 11 42 15 72 19 110 23 156 27 210 31
loop(\(x,i).(i - ((x + ~1) div 2)),(x + ~1),x)
A154392: 0 1 1 3 2 4 4 5 5 6 7 7 8 9 9 10
loop(\(x,i).8x,(x + ~1),x)
A053539: 0 1 16 192 2048 20480 196608 1835008 16777216 150994944 1342177280 11811160064 103079215104 893353197568 7696581394432 65970697666560
loop(\(x,i).(4x * i),(x + ~1),x)
A052570: 0 1 8 96 1536 30720 737280 20643840 660602880 23781703680 951268147200 41855798476800 2009078326886400 104472072998092800 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(x2 + ~3x + 2),x)
A217652: 0 1 2 12 256 20480 6291456 7516192768 35184372088832 648518346341351424 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),((x + ~1) * (x div 2)),x)
A114045: 0 1 2 6 2880
loop(\(x,i).(2x - (x mod 2)),(x + ~1),x)
A005985: 0 1 4 9 32 65 192 385 1024 2049 5120 10241 24576 49153 114688 229377
(x + loop(\(x,i).(x * (x - i)),2,(x + ~1)))
A001094: 0 1 2 3 28 125 366 847 1688 3033 5050 7931 11892 17173 24038 32775
loop(\(x,i).(2x + 4),x,(x2 + ~x))
A196508: 0 4 20 76 252 764 2172 5884 15356 38908 96252 233468 557052 1310716 3047420 7012348
loop(\(x,i).5x,(x + ~1),x)
A053464: 0 1 10 75 500 3125 18750 109375 625000 3515625 19531250 107421875 585937500 3173828125 17089843750 91552734375
loop(\(x,i).(x * (3 + i)),(x + ~1),x)
A005990: 0 1 8 60 480 4200 40320 423360 4838400 59875200 798336000 11416204800 174356582400 2833294464000 48819843072000 889218570240000
((x div 8) + (if x <= 0 then 1 else x))
A118065: 1 1 2 3 4 5 6 7 9 10 11 12 13 14 15 16
((x mod 8) mod (if x <= 0 then 1 else x))
A257848-A218470-A143287: 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7
(x - ((x mod 4) mod (if x <= 0 then 1 else x)))
A276334: 0 1 2 3 4 4 4 4 8 8 8 8 12 12 12 12
(2 - ((2 + (x div 2)) div (if x <= 0 then 1 else x)))
A300403-A179076: 0 0 1 1 1 2 2 2 2 2 2 2 2 2 2 2
(x + loop(\(x,i).5x,x,1))
A104745: 1 6 27 128 629 3130 15631 78132 390633 1953134 9765635 48828136 244140637 1220703138 6103515639 30517578140
(~x + loop(\(x,i).5x,x,1))
A024050: 1 4 23 122 621 3120 15619 78118 390617 1953116 9765615 48828114 244140613 1220703112 6103515611 30517578110
(x + loop(\(x,i).(x * (x + (i mod 2))),x,1))
A117850: 1 3 6 23
(x + (if (x + ~6) <= 0 then 1 else 2))
A082463: 1 2 3 4 5 6 7 9 10
A337052-A336592-A335275-A270428-A242094-A220218-A219227-A187947-A138302: 1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 17
(x + (if (~2 + (x div 3)) <= 0 then 1 else 2))
A336557-A335235-A318275-A279367-A277061-A274125-A254621-A243079-A239215-A229301-A229300-A227510-A209931-A190221-A173646-A167619-A129350-A102827-A090274-A083114-A070698-A069570-A067251-A052382-A052040-A032898-A032857-A020731-A020664: 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17
(x + (if (~2 + (x div 4)) <= 0 then 1 else 2))
A290492: 1 2 3 4 5 6 7 8 9 10 11 12 14
A322847-A302492-A256474-A252474-A180004-A113763-A088185-A085824-A011760: 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17
(x + (if (~4 + (x div 2)) <= 0 then 1 else 2))
A247397: 1 2 3 4 5 6 7 8 9 10 12 13
A337843-A333501-A332111-A328869-A179308-A171987-A167520-A160542-A136002-A122260-A122254-A101947-A059543-A048737-A020753: 1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17
loop(\(x,i).i,(x + ~10),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A053831: 0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5
(~x + (loop(\(x,i).2x,x,3) div 2))
A179744: 1 2 4 9 20 43 90 185 376 759 1526 3061 6132 12275 24562 49137
loop(\(x,i).(1 + (x * (4 + i))),2,x)
A128471: 7 37 67 97 127 157 187 217 247 277 307 337 367 397 427 457
loop(\(x,i).(8x + 8),2,x)
A157336: 72 136 200 264 328 392 456 520 584 648 712 776 840 904 968 1032
loop(\(x,i).(8 div (x + 1)),2,x)
A053644: 0 1 2 2 4 4 4 4 8 8 8 8 8 8 8 8
loop(\(x,i).(4x2 + 4x),2,x)
A322677: 0 288 2400 9408 25920 58080 113568 201600 332928 519840 776160 1117248 1560000 2122848 2825760 3690240
(x + (if (x + ~2) <= 0 then 1 else (2x + ~2)))
A051637: 1 2 3 7 10
loop(\(x,i).((x * (x + i)) div (1 + i)),2,x)
A006007: 0 1 5 16 40 85 161 280 456 705 1045 1496 2080 2821 3745 4880
(x + (4 * (1 + (if x <= 0 then 1 else 2))))
A124159: 8 13 14 15
(x + loop(\(x,i).(x2 + 2x + 1),2,2))
A135600: 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115
(~x + loop(\(x,i).(x2 + 2x + 1),2,2))
A096582: 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85
loop(\(x,i).((x3 + x2) div 2),2,x)
A329754: 0 1 126 3078 32800 213750 1008126 3783976 11985408 33297075 83338750 191592126 410450976 828497488 1589341950 2917620000
loop(\(x,i).(~2 + (x div (~2 + (x mod 2)))),2,x)
A225058: ~1 1 1 3 0 5 3 7 1 9 5 11 2 13 7 15
(2 div (if ((x div 2) mod 4) <= 0 then 2 else x))
A025446: 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0
loop(\(x,i).(1 + i),(x + ~8),x)
A245345: 0 1 2 3 4 5 6 7 8 2 3 4 5 6 7 8
loop(\(x,i).(x + ~2),(x + ~8),x)
A287793-A279319: 0 1 2 3 4 5 6 7 8 7 6 5 4 3 2 1
loop(\(x,i).(2 * i),(x + ~8),x)
A043268: 0 1 2 3 4 5 6 7 8 2 4 6 8 10 12 14
(x + loop(\(x,i).(x * (1 + i)),4,2))
A121378: 240 241 242 243 244 245 246 247 248 249
(x + loop(\(x,i).x2,4x,2))
A272137: 2 65537 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x + 2),4,x)
A044712: 80 161 242 323 404 485 566 647 728 809 890 971 1052 1133 1214 1295
loop(\(x,i).((x2 + x) div 2),4,x)
A066370: 0 1 231 26796 1186570 26357430 359026206 3413156131 24666759216 143717956515 703974775735 2989908659661 11270904497931 38398515291136 119929709686710 347357071281165
(x * loop(\(x,i).(x2 + x),2,4))
A169825: 0 420 840 1260 1680 2100 2520 2940 3360 3780 4200 4620 5040 5460 5880 6300
loop(\(x,i).(x * (3 + i)),4,x)
A169827: 0 840 1680 2520 3360 4200 5040 5880 6720 7560 8400 9240 10080 10920 11760 12600
(x + (if (~x + 4) <= 0 then (x + ~2) else 2))
A120370: 2 3 4 5 6 8 10 12 14 16 18 20 22 24 26 28
(~x + loop(\(x,i).(2x + 2),2x,2))
A290721: 2 13 60 251 1018 4089 16376 65527 262134 1048565 4194292 16777203 67108850 268435441 1073741808 4294967279
(x - loop(\(x,i).((~x2 + x) div 2),2,x))
A088110: 0 1 3 9
A101357: 0 1 3 9 25 60 126 238 414 675 1045 1551 2223 3094 4200 5580
(x + loop(\(x,i).x2,2x2,2))
A279883: 2 17 4611686018427387903
(if x <= 0 then 1 else (x * (2 + (x2 div 2))))
A064705: 1 2 8 18 40
(x + loop(\(x,i).(~x3 + 2),2,2))
A121379: 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233
loop(\(x,i).(x2 div ((x + 2) + i)),2,x)
A309689: 0 0 0 0 0 1 2 2 2 3 4 5 6 7 8 9
loop(\(x,i).((x * ((x + i) * i)) div 2),2,x)
A061316: 0 3 15 48 120 255 483 840 1368 2115 3135 4488 6240 8463 11235 14640
loop(\(x,i).(x3 + 3x),2,x)
A261574: 0 76 2786 46764 439204 2744420 12813606 48229636 153992264 432083484 1092730090 2537720636 5489037036 11179326964 21624372014 40001698260
loop(\(x,i).(x * ((~x2 + ~1) + i)),2,x)
A218132: 0 0 504 19656 262080 1953000 10077480 40353264 134217216 387419760 999999000 2357946360 5159778624 10604497176 20661044040 38443356000
loop(\(x,i).(~x + ((x - i) div 4)),2,x)
A340205: 0 0 1 1 2 2 3 4 4 4 5 6 7 7 7 8
loop(\(x,i).(x + (x div (2 * (2 + i)))),2,x)
A067570: 0 1 2 3 4 5 7
A191919: 0 1 2 3 4 5 7 9 10 11 12 13 15 16 18 19
loop(\(x,i).(3x2 + ~2x),2,x)
A264892: 0 1 176 1281 4720 12545 27456 52801 92576 151425 234640 348161 498576 693121 939680 1246785
(~x + loop(\(x,i).(x2 + ~1),2,(x + 2)))
A269607: 8 62 222 572 1220 2298 3962 6392 9792 14390 20438 28212 38012 50162 65010 82928
(x * loop(\(x,i).(x2 + ~x),2,(x + 2)))
A214944: 0 30 264 1140 3480 8610 18480 35784 64080 107910 172920 265980 395304 570570 803040 1105680
(x + (if (x + ~2) <= 0 then (x div 2) else (x + 2)))
A067569: 0 1 3 8 10
((x2 + 2x) + loop(\(x,i).2x,x,1))
A220425: 1 5 12 23 40 67 112 191 336 611 1144 2191 4264 8387 16608 33023
((~x2 + ~2x) + loop(\(x,i).2x,x,1))
A176778: 1 ~1 ~4 ~7 ~8 ~3 16 65 176 413 904 1905 3928 7997 16160 32513
loop(\(x,i).(2x * (1 + i)),(x + ~2),x)
A052564: 0 1 2 12 96 960 11520 161280 2580480 46448640 928972800 20437401600 490497638400 12752938598400 357082280755200 10712468422656000
loop(\(x,i).(2 * ((x * i) div 2)),(x + ~2),x)
A098557: 0 1 2 2 8 24 144 720 5760 40320 403200 3628800 43545600 479001600 6706022400 87178291200
(x * loop(\(x,i).(x * (x - i)),2,(x + ~2)))
A052787: 0 0 0 0 0 120 720 2520 6720 15120 30240 55440 95040 154440 240240 360360
((~x2 + 2x) + loop(\(x,i).2x,x,1))
A176776: 1 3 4 5 8 17 40 93 208 449 944 1949 3976 8049 16216 32573
(~x + loop(\(x,i).(2x + ~1),x,2x))
A059673: 0 2 11 38 109 284 699 1658 3833 8696 19447 42998 94197 204788 442355 950258
loop(\(x,i).(((x div 2) + i) div 2),(x div 2),x)
A265370: 0 1 1 1 1 1 1 1 2 2 3 3 3 3 4 4
loop(\(x,i).x5,2,x)
A010813: 0 1 33554432 847288609443 1125899906842624 298023223876953125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x - ((x div (1 + i)) * i)),2,x)
A332380: 0 1 1 2 2 1 1 2 2 3 3 2 2 3 3 4
(x * (if (~4 + (x div 2)) <= 0 then 1 else x))
A103303: 0 1 2 3 4 5 6 7 8 9
A135295: 0 1 2 3 4 5 6 7 8 9 100 121 144 169 196 225
(x2 * (if (x mod 2) <= 0 then 4 else 1))
A154615: 0 1 16 9 64 25 144 49 256 81 400 121 576 169 784 225
(x + (if (~2 + (x div 2)) <= 0 then 3 else x))
A154660: 3 4 5 6 7 8
A277641: 3 4 5 6 7 8 12
(x2 * loop(\(x,i).x2,2,3))
A017162: 0 81 324 729 1296 2025 2916 3969 5184 6561 8100 9801 11664 13689 15876 18225
(x * loop(\(x,i).x3,3,x))
A122969: 0 1 268435456 22876792454961 72057594037927936 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x - loop(\(x,i).(x div (1 + (x mod 2))),x,x))
A331739: 0 1 0 3 0 3 0 7 0 5 0 9 0 7 0 15
loop(\(x,i).(x - (x div (1 + (2 * i)))),x,x)
A089576: 0 1 2 2 3 4 4 4 5 5 6 6 6 7 7 7
(x * loop(\(x,i).4x,(x + ~1),x))
A086952: 0 1 16 144 1024 6400 36864 200704 1048576 5308416 26214400 126877696 603979776 2835349504 13153337344 60397977600
(~x + loop(\(x,i).(x * (2 + i)),(x + ~1),x))
A213168: 0 0 4 33 236 1795 15114 141113 1451512 16329591 199583990 2634508789 37362124788 566658892787 9153720575986 156920924159985
(x * loop(\(x,i).(x * (i * i)),4,x))
A325475: 0 576 2304 5184 9216 14400 20736 28224 36864 46656 57600 69696 82944 97344 112896 129600
loop(\(x,i).10x,x,x)
A126431: 0 10 200 3000 40000 500000 6000000 70000000 800000000 9000000000 100000000000 1100000000000 12000000000000 130000000000000 1400000000000000 15000000000000000
(x * loop(\(x,i).3x,2x,x))
A128788: 0 9 324 6561 104976 1476225 19131876 234365481 2754990144 31381059609 348678440100 3797108212689 40669853253264 429575324987601 4483851321172356 46325504721296025
(1 - (x * loop(\(x,i).x3,2,x)))
A024008: 1 0 ~1023 ~59048 ~1048575 ~9765624 ~60466175 ~282475248 ~1073741823 ~3486784400 ~9999999999 ~25937424600 ~61917364223 ~137858491848 ~289254654975 ~576650390624
(~x2 + loop(\(x,i).4x,x,1))
A024038: 1 3 12 55 240 999 4060 16335 65472 262063 1048476 4194183 16777072 67108695 268435260 1073741599
(~x2 + loop(\(x,i).x2,2,(x + 1)))
A257925: 1 15 77 247 609 1271 2365 4047 6497 9919 14541 20615 28417 38247 50429 65311
(x2 + loop(\(x,i).3x,x,1))
A251701: 1 4 13 36 97 268 765 2236 6625 19764 59149 177268 531585 1594492 4783165 14349132
(~x2 + loop(\(x,i).3x,x,1))
A024025: 1 2 5 18 65 218 693 2138 6497 19602 58949 177026 531297 1594154 4782773 14348682
loop(\(x,i).2x,(x2 + ~1),x2)
A185968: 0 1 32 2304 524288 419430400 1236950581248 13792273858822144 4611686018427387903 4611686018427387903 4611686018427387903
(x2 + (if (x mod 4) <= 0 then 0 else 2))
A277023: 0 3 6 11 16 27 38 51 64 83 102 123 144 171 198 227
(if x <= 0 then 1 else (x3 + 4x2))
A112613: 1 5 24
loop(\(x,i).(x * ((x + 1) - i)),2,x2)
A218131: 0 0 240 6480 65280 390000 1678320 5762400 16773120 43040160 99990000 214344240 429960960 815702160 1475750640 2562840000
loop(\(x,i).6x,x,x2)
A128785: 0 6 144 1944 20736 194400 1679616 13716864 107495424 816293376 6046617600 43898443776 313456656384 2207257288704 15359376162816 105791621529600
loop(\(x,i).8x,x,x2)
A128787: 0 8 256 4608 65536 819200 9437184 102760448 1073741824 10871635968 107374182400 1039382085632 9895604649984 92908732547072 862017116176384 7916483719987200
loop(\(x,i).(x div (2 - (x mod 2))),x,x2)
A191871: 0 1 1 9 1 25 9 49 1 81 25 121 9 169 49 225
(x2 * loop(\(x,i).x3,2,x))
A008455: 0 1 2048 177147 4194304 48828125 362797056 1977326743 8589934592 31381059609 100000000000 285311670611 743008370688 1792160394037 4049565169664 8649755859375
loop(\(x,i).5x,x,x2)
A128784: 0 5 100 1125 10000 78125 562500 3828125 25000000 158203125 976562500 5908203125 35156250000 206298828125 1196289062500 6866455078125
loop(\(x,i).(x * (~1 + (2 * i))),x,x2)
A161124: 0 1 12 135 1680 23625 374220 6621615 129729600 2791213425 65472907500 1663666579575 45537716624400 1336089255125625 41837777148667500 1392813754566609375
(x2 + (if (x mod 2) <= 0 then (~x + 1) else x))
A081347: 1 2 3 12 13 30 31 56 57 90 91 132 133 182 183 240
(x2 * loop(\(x,i).4x,x,x))
A128790: 0 4 128 1728 16384 128000 884736 5619712 33554432 191102976 1048576000 5582618624 28991029248 147438174208 736586891264 3623878656000
loop(\(x,i).(x * i),x,x4)
A091364: 0 1 32 486 6144 75000 933120 12101040 165150720 2380855680 36288000000 584421868800 9932577177600 177849941068800 3349041234739200 66201014880000000
(x2 * loop(\(x,i).3x,x,x))
A062074: 0 3 72 729 5184 30375 157464 750141 3359232 14348907 59049000 235782657 918330048 3502727631 13124466936 48427561125
loop(\(x,i).(x + (i * i * i)),x,x2)
A117717: 0 2 13 45 116 250 477 833 1360 2106 3125 4477 6228 8450 11221 14625
loop(\(x,i).7x,x,x)
A036293: 0 7 98 1029 9604 84035 705894 5764801 46118408 363182463 2824752490 21750594173 166095446412 1259557135291 9495123019886 71213422649145
loop(\(x,i).(x + (4 * (i * i))),x,x)
A050533: 0 5 22 59 124 225 370 567 824 1149 1550 2035 2612 3289 4074 4975
(x * loop(\(x,i).x2,(x2 + ~2x),x))
A053015: 0 1 4 19683 4611686018427387903
(x + (if (x mod 2) <= 0 then (x + 1) else x2))
A103832: 1 2 5 12 9 30 13 56 17 90 21 132 25 182 29 240
(x * loop(\(x,i).x3,2,x2))
A010807: 0 1 524288 1162261467 274877906944 19073486328125 609359740010496 11398895185373143 144115188075855872 1350851717672992089 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,3,x3)
A010812: 0 1 16777216 282429536481 281474976710656 59604644775390625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x3 + loop(\(x,i).2x,x,1))
A097339: 1 3 12 35 80 157 280 471 768 1241 2024 3379 5824 10389 19128 36143
(~x3 + loop(\(x,i).2x,x,1))
A024013: 1 1 ~4 ~19 ~48 ~93 ~152 ~215 ~256 ~217 24 717 2368 5995 13640 29393
(~x3 + loop(\(x,i).(x * i),x,1))
A007339: 1 0 ~6 ~21 ~40 ~5 504 4697 39808 362151 3627800 39915469 478999872 6227018603 87178288456 1307674364625
(1 - loop(\(x,i).x2,2,x3))
A024010: 1 0 ~4095 ~531440 ~16777215 ~244140624 ~2176782335 ~13841287200 ~68719476735 ~282429536480 ~999999999999 ~3138428376720 ~8916100448255 ~23298085122480 ~56693912375295 ~129746337890624
(x * loop(\(x,i).x2,2,x3))
A010801: 0 1 8192 1594323 67108864 1220703125 13060694016 96889010407 549755813888 2541865828329 10000000000000 34522712143931 106993205379072 302875106592253 793714773254144 1946195068359375
loop(\(x,i).x5,x,x)
A323661: 0 1 33554432 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + ((2 + (i * i)) * i)),x,x)
A334694: 0 4 17 51 124 260 489 847 1376 2124 3145 4499 6252 8476 11249 14655
(1 + (x div (1 + ((x + 2) div 3))))
A272314: 1 1 2 2 2 2 3 2 3 3 3 3 3 3 3 3
((x + 1) - ((x div 2) div ~3))
A188397-A057904: 1 2 4 5 6 7 8 9 11 12 13 14 15 16 18 19
((x + 3) - (x div ~3))
A335740: 3 5 6 7 9 10 11 13 14 15 17 18 19 21 22 23
((2x + 1) - (x div ~3))
A231407: 1 4 6
A225002-A047290: 1 4 6 8 11 13 15 18 20 22 25 27 29 32 34 36
((x + 1) - (x div (~1 + (x div ~2))))
A072442: 1 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18
(1 + ((x + 1) div 7))
A295866: 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3
(1 + ((x + ~2) div 7))
A003074: 0 0 1 1 1 1 1 1 1 2 2 2 2 2 2 2
(~1 + ((x div 2) div 7))
A286707: ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 0 0
(1 + (x mod 15))
A053165-A002377: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1
(1 + ((x + ~1) div 9))
A191228-A111891-A004218: 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2
(1 + (2x mod 9))
A131669: 1 3 5 7 9 2 4 6 8 1 3 5 7 9 2 4
(1 + (x mod (1 + (x div 8))))
A338652-A140195: 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 2
(1 + (x div (3 + (x div 4))))
A204164-A055980-A052374-A052364: 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3
(1 + (x mod (1 + ((x + ~1) mod 4))))
A085476: 1 1 1 1 1 1 1 2 1 1 1 3 1 1 1 1
(10x + 6)
A017341: 6 16 26 36 46 56 66 76 86 96 106 116 126 136 146 156
(1 + ((2x + 1) div 5))
A100719: 1 1 2 2 2 3 3 4 4 4 5 5 6 6 6 7
(~1 + (5 * (1 + (x div 2))))
A168280: 4 4 9 9 14 14 19 19 24 24 29 29 34 34 39 39
(1 + ((~1 + (x div 2)) div 5))
A185712: 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2
((x + 1) - ((x + 1) div 5))
A120507-A003004: 1 2 3 4 4 5 6 7 8 8 9 10 11 12 12 13
(~1 + ((x2 + 1) mod 5))
A080891: 0 1 ~1 ~1 1 0 1 ~1 ~1 1 0 1 ~1 ~1 1 0
(1 + ((x2 + ~1) div 5))
A036404: 0 1 1 2 4 5 8 10 13 17 20 25 29 34 40 45
29
A010868: 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29
(10x + 9)
A017377: 9 19 29 39 49 59 69 79 89 99 109 119 129 139 149 159
(1 + ((2x + 2) div 5))
A248515-A194986-A054071: 1 1 2 2 3 3 3 4 4 5 5 5 6 6 7 7
(1 + (5 * ((x + 1) div 2)))
A168282: 1 6 6 11 11 16 16 21 21 26 26 31 31 36 36 41
(1 + ((2x + ~2) div 5))
A029865: 0 1 1 1 2 2 3 3 3 4 4
(1 + (((x + ~1) div 2) div 5))
A330634-A055640-A035931: 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2
(1 + ((2x + 4) div 5))
A214046: 1 2 2 3 3 3 4 4 5 5 5 6 6 7 7 7
(20x + 1)
A215145: 1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301
(1 + (10 * (x mod 2)))
A266327: 1 11 1 11 1 11 1 11 1 11 1 11 1 11 1 11
(1 + (((~x + 2) div 2) div 5))
A014048: 1 1 1 0 0 0 0 0 0 0 0 0 0 ~1 ~1 ~1
(x mod (1 + ((x + 2) div 5)))
A055087-A025685-A022333: 0 0 0 1 0 1 0 1 2 0 1 2 0 1 2 3
((x + 1) - ((x + 2) div 5))
A138467: 1 2 3 3 4 5 6 7 7 8 9 10 11 11 12 13
(10x2 + 1)
A158187: 1 11 41 91 161 251 361 491 641 811 1001 1211 1441 1691 1961 2251
(1 + (3x div 5))
A256502-A210434-A064542: 1 1 2 2 3 4 4 5 5 6 7 7 8 8 9 10
((x + 1) - ((~x + 1) div 5))
A180917: 1 2 4 5 6 7 8 10 11 12 13 14 16 17 18 19
(5x2 + 5x + 1)
A062786: 1 11 31 61 101 151 211 281 361 451 551 661 781 911 1051 1201
((x + 1) - ((~x + 2) div 5))
A184526: 1 2 3 5 6 7 8 9 11 12 13 14 15 17 18 19
(5x2 + 10x + 1)
A134593: 1 16 41 76 121 176 241 316 401 496 601 716 841 976 1121 1276
(1 + (5 * (x + (x div 2))))
A087446: 1 6 16 21 31 36 46 51 61 66 76 81 91 96 106 111
(1 + ((x + (x div 2)) div 5))
A137214-A034887: 1 1 1 1 2 2 2 3 3 3 4 4 4 4 5 5
(1 + (5 * (x + (x mod 2))))
A168459: 1 11 11 21 21 31 31 41 41 51 51 61 61 71 71 81
((2x + 1) - (x div 5))
A108598: 1 3 5 7 9 10 12 14 16 18 19 21 23 25 27 28
(~2 mod (1 + (x div 5)))
A210715: 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 2
(2 - (2 div (1 + (x div 5))))
A105515: 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 2
((2x + 1) - (x mod 5))
A084545: 1 2 3 4 5 11 12 13 14 15 21 22 23 24 25 31
(~2 mod (1 + (x mod 5)))
A021817: 0 0 1 2 3 0 0 1 2 3 0 0 1 2 3 0
(1 + ((x + 1) mod (1 + (x div 4))))
A266476: 1 1 1 1 2 1 2 1 1 2 3 1 2 3 4 1
(3 - (2 div (1 + (x div 4))))
A124156: 1 1 1 1 2 2 2 2 3 3 3 3 3 3 3 3
(1 + (x2 div (x + 5)))
A182220: 1 1 1 2 2 3 4 5 5 6 7 8 9 10 11 12
(1 + ((x + ~1) div (3 + (x div 2))))
A211669: 0 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2
(1 + (2 mod (1 + (x mod (2 + (x mod 2))))))
A272334-A014491: 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1
(18x + 1)
A161705: 1 19 37 55 73 91 109 127 145 163 181 199 217 235 253 271
(1 + (3 * (2x div 3)))
A168074-A061891: 1 1 4 7 7 10 13 13 16 19 19 22 25 25 28 31
(1 + (3 * (2x mod 3)))
A070403: 1 7 4 1 7 4 1 7 4 1 7 4 1 7 4 1
(9x2 + 1)
A247792: 1 10 37 82 145 226 325 442 577 730 901 1090 1297 1522 1765 2026
(1 + ((x mod (1 + (x div 2))) div 3))
A004052: 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3
(1 + ((x2 + x + 1) div 3))
A096777: 1 2 3 5 8 11 15 20 25 31 38 45 53 62 71 81
(1 + ((x2 + 2x + 1) div 3))
A231408: 1 2 4 6 9
A087483: 1 2 4 6 9 13 17 22 28 34 41 49 57 66 76 86
(1 + (3 * ((x + 1) + (x div 2))))
A125758: 4 7 13 16 22 25 31 34 40 43 49 52 58 61 67 70
(12x + 11)
A017653: 11 23 35 47 59 71 83 95 107 119 131 143 155 167 179 191
(6x2 + 6x + 1)
A003154: 1 13 37 73 121 181 253 337 433 541 661 793 937 1093 1261 1441
((2x + 1) - ((x + 1) mod 3))
A047266: 0 1 5 6 7 11 12 13 17 18 19 23 24 25 29 30
(1 - (x mod (1 + ((x + 1) mod 3))))
A286726: 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0
(6x2 + ~6x + ~1)
A103115: ~1 ~1 11 35 71 119 179 251 335 431 539 659 791 935 1091 1259
((x + 1) mod (1 + ((x + ~1) mod 3)))
A082960: 1 0 1 1 0 0 1 0 1
A141212: 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1
(4 div (1 + ((x + ~1) mod 3)))
A153727: 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1
((x + ~2) mod (1 + ((x + ~1) mod 3)))
A317961: 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1
((x div 2) mod (1 + ((x + ~1) mod 3)))
A287382: 0 0 1 1 0 0 0 0 0 1 0 1 0 0 1 1
((x + 1) - (x div ~6))
A057903: 1 3 4 5 6 7 8 10 11 12 13 14 15 17 18 19
(1 + (3 * (x - (x div ~2))))
A301451: 1 7 10 16 19 25 28 34 37 43 46 52 55 61 64 70
(x + ~19)
A023461: ~19 ~18 ~17 ~16 ~15 ~14 ~13 ~12 ~11 ~10 ~9 ~8 ~7 ~6 ~5 ~4
(12x + 7)
A017605: 7 19 31 43 55 67 79 91 103 115 127 139 151 163 175 187
(12x + 5)
A017581: 5 17 29 41 53 65 77 89 101 113 125 137 149 161 173 185
(~1 + (6 * (1 + (x div 2))))
A168300: 5 5 11 11 17 17 23 23 29 29 35 35 41 41 47 47
(x mod (1 + (((x + 1) div 2) div 3)))
A334872-A322823: 0 0 0 0 0 1 0 1 0 1 0 2 0 1 2 0
((x + 1) - (((x + 1) div 2) div 3))
A256562-A228297: 1 2 3 4 5 5 6 7 8 9 10 10 11 12 13 14
(1 + ((((x + ~1) div 2) div 2) div 3))
A074802: 0 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2
(x + ~25)
A023467: ~25 ~24 ~23 ~22 ~21 ~20 ~19 ~18 ~17 ~16 ~15 ~14 ~13 ~12 ~11 ~10
(x + ~23)
A023465: ~23 ~22 ~21 ~20 ~19 ~18 ~17 ~16 ~15 ~14 ~13 ~12 ~11 ~10 ~9 ~8
(24x + 1)
A216869: 1 25 49
A103214: 1 25 49 73 97 121 145 169 193 217 241 265 289 313 337 361
(24x + ~1)
A183010: ~1 23 47 71 95 119 143 167 191 215 239 263 287 311 335 359
(1 + (8x div 3))
A047400: 1 3 6 9 11 14 17 19 22 25 27 30 33 35 38 41
(x2 div 13)
A011865: 0 0 0 0 1 1 2 3 4 6 7 9 11 13 15 17
(x2 mod 13)
A070436: 0 1 4 9 3 12 10 10 12 3 9 4 1 0 1 4
((x + 1) mod 11)
A275010-A090175: 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5
(x2 mod 11)
A070434: 0 1 4 9 5 3 3 5 9 4 1 0 1 4 9 5
((x + 1) - (3 * (x div 4)))
A173524: 1 2 3 4 2 3 4 5 3 4 5 6 4 5 6 7
(12x2 + 1)
A158480: 1 13 49 109 193 301 433 589 769 973 1201 1453 1729 2029 2353 2701
(12x2 + ~1)
A158463: ~1 11 47 107 191 299 431 587 767 971 1199 1451 1727 2027 2351 2699
(1 + ((x - (2 * (x mod 2))) div 3))
A341307: 1 0 1 1 2 2 3 2 3 3 4 4 5 4 5 5
(9x + 7)
A017245: 7 16 25 34 43 52 61 70 79 88 97 106 115 124 133 142
(9x + 5)
A017221: 5 14 23 32 41 50 59 68 77 86 95 104 113 122 131 140
(1 + (3 * ((x2 + x) div 2)))
A005448: 1 4 10 19 31 46 64 85 109 136 166 199 235 274 316 361
(1 + (((x2 + x) div 2) div 3))
A008748: 1 1 2 3 4 6 8 10 13 16 19 23 27 31 36 41
((x + 1) - (((~x + 2) div 2) div 3))
A057905: 1 2 3 5 6 7 8 9 10 12 13 14 15 16 17 19
(1 + (((x2 + 2x) div 2) div 3))
A008747: 1 1 2 3 5 6 9 11 14 17 21 24 29 33 38 43
(1 + (((x2 + 2x) div 2) mod 3))
A083039: 1 2 2 2 1 3 1 2 2 2 1 3 1 2 2 2
(~1 + (3 * ((x + 2) + (x div 2))))
A253195: 5 8 14 17 23 26 32 35 41 44 50 53 59 62 68 71
((x + 1) - ((1 - (x div 2)) div 3))
A057906: 1 2 3 4 6 7 8 9 10 11 13 14 15 16 17 18
((2x + 1) - ((x div 2) div 3))
A094391: 1 3 5 7 9 11 12 14 16 18 20 22 23 25 27 29
(1 + (3 * (2x - (x mod 2))))
A228137: 1 4 13 16 25 28 37 40 49 52 61 64 73 76 85 88
(1 + ((x * (x mod 3)) div 3))
A270743: 1 1 2 1 2 4 1 3 6 1 4 8 1 5 10 1
(3x2 + 9x + 1)
A166143: 1 13 31 55 85 121 163 211 265 325 391 463 541 625 715 811
(6x2 + 3x + 1)
A085473: 1 10 31 64 109 166 235 316 409 514 631 760 901 1054 1219 1396
((2x + 1) - ((~x + 1) div 3))
A304497-A047282: 1 3 6 8 10 13 15 17 20 22 24 27 29 31 34 36
(1 + ((x + (2 mod (x + 1))) div 3))
A110867: 1 1 2 2 3 3 3 4 4 4 5 5 5
((x + 1) - ((x2 + x) mod 3))
A061800: 1 0 3 4 3 6 7 6 9 10 9 12 13 12 15 16
(1 + ((x + (x div 4)) div 3))
A231149: 1 1 1 2 2 3 3 3 4 4 5 5 6 6 6 7
(x - (2 mod (~1 + ((~x + 2) div 3))))
A067570: 0 1 2 3 4 5 7
A107750: 0 1 2 3 4 5 7 8 9 11 12 13 15 16 17 19
(4 div (1 + ((~x + 2) mod 3)))
A069705: 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1
((x + 1) - ((x + (x mod 2)) div 3))
A257063: 1 2 3 3 4 4 5 6 7 7 8 8 9 10 11 11
((x + 1) - (3 * (~x + (x mod 2))))
A047468: 1 2 9 10 17 18 25 26 33 34 41 42 49 50 57 58
((x + 1) - ((~x + (x mod 2)) div 3))
A026367: 1 2 4 5 7 8 9 10 12 13 15 16 17 18 20 21
(1 + ((x3 + 2x) div 3))
A116731: 1 2 5 12 25 46 77 120 177 250 341 452 585 742 925 1136
((3x + 1) - (x div 3))
A047537: 1 4 7 9 12 15 17 20 23 25 28 31 33 36 39 41
((3x + 1) + (x div 3))
A078309: 1 4 7 11 14 17 21 24 27 31 34 37 41 44 47 51
(1 + (x div 3) - (x mod 3))
A063942: 1 0 ~1 2 1 0 3 2 1 4 3 2 5 4 3 6
((2x + 3) - (x mod 3))
A327257-A047249: 3 4 5 9 10 11 15 16 17 21 22 23 27 28 29 33
((x + 3) div (1 + (x mod 3)))
A323417: 3 2 1 6 3 2
(1 + (x div (1 + ((x * (x div 2)) mod 2))))
A186646: 1 2 3 2 5 6 7 4 9 10 11 6 13 14 15 8
(2x2 + 8x + 5)
A268581: 5 15 29 47 69 95 125 159 197 239 285 335 389 447 509 575
(4x2 + 12x + 1)
A152817: 1 17 41
A166147: 1 17 41 73 113 161 217 281 353 433 521 617 721 833 953 1081
(1 + ((x + 3) * (2 + (x div 2))))
A249333: 7 9 16 19 29 33 46 51 67 73 92 99 121 129 154 163
(4x2 + 6x + 1)
A082108: 1 11 29 55 89 131 181 239 305 379 461 551 649 755 869 991
(1 + ((2x + 1) * ((x + 1) div 2)))
A231407: 1 4 6
A266883: 1 4 6 15 19 34 40 61 69 96 106 139 151 190 204 249
(8x2 + 4x + 1)
A102083: 1 13 41 85 145 221 313 421 545 685 841 1013 1201 1405 1625 1861
(1 + ((~x + 4) mod (2x + 1)))
A077756: 1 1 3 2 1 11
(1 + ((2x + 1) * (x + (x mod 2))))
A193867: 1 7 11 29 37 67 79 121 137 191 211 277 301 379 407 497
(8x2 + ~4x + 1)
A080856: 1 5 25 61 113 181 265 365 481 613 761 925 1105 1301 1513 1741
(1 + (((x + 1) div 2) * (1 + (x div 2))))
A193622: 1 2 3 5 7 10
A025700: 1 2 3 5 7 10 13 17 21 26 31 37 43 50 57 65
(~1 + (8 * (1 + (x div 2))))
A168379: 7 7 15 15 23 23 31 31 39 39 47 47 55 55 63 63
(1 + ((x + 1) mod (3 - (x mod 2))))
A175307: 2 1 1 1 3 1 2 1 1 1 3 1 2 1 1 1
(x mod (1 + (x mod (3 - (x mod 2)))))
A159195: 0 1 2 1 0 1 0 1 2 1 0 1 0 1 2 1
(1 + (3x div (1 + (x mod 2))))
A165355: 1 2 7 5 13 8 19 11 25 14 31 17 37 20 43 23
(1 + ((x2 + 2x) * (1 + (x mod 2))))
A309199: 1 7 9 31 25 71 49 127 81 199 121 287 169 391 225 511
(1 + ((x + (x div 2)) * (1 + (x mod 2))))
A285265: 1 3 4 9 7
(1 + (x2 div ((x + 1) + (x div 2))))
A096607: 1 1 2 2 3 4 4 5 5 6 7 8 8 9 9 10
(x3 + 4x2 + 5x + 1)
A003777: 1 11 35 79 149 251 391 575 809 1099 1451 1871 2365 2939 3599 4351
(1 + ((2x2 + ~2x) div (x + 1)))
A075692: 1 1 2 4 5 7 9 11 13 15
(1 + (((x2 + 1) div 2) mod (x + 1)))
A319702: 1 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2
(16x + 15)
A125169: 15 31 47 63 79 95 111 127 143 159 175 191 207 223 239 255
(x2 + 7x + 5)
A108195: 5 13 23 35 49 65 83 103 125 149 175 203 233 265 299 335
(1 + ((2x + 8) div (x + 1)))
A343947: 9 6 5 4 4 4 3 3 3 3 3 3 3 3 3 3
(4x2 + 12x + 7)
A073577: 7 23 47 79 119 167 223 287 359 439 527 623 727 839 959 1087
(8x2 + 8x + 1)
A069129: 1 17 49 97 161 241 337 449 577 721 881 1057 1249 1457 1681 1921
(3 mod (1 + (4 div (x + 1))))
A307808: 3 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0
(4 div (1 + (4 div (x + 1))))
A071805: 0 1 2 2 4 4 4 4 4 4 4 4 4 4 4 4
((1 + (x div 2)) div (1 + (2 mod (x + 1))))
A226749: 1 1 0 0 1 1 1 1 1 1 2 2 2 2 2 2
(3x2 + 5x + 1)
A144390: 1 9 23 43 69 101 139 183 233 289 351 419 493 573 659 751
(x3 + 2x2 + 3x + 1)
A261893: 1 7 23 55 109 191 307 463 665 919 1231 1607 2053 2575 3179 3871
(x3 + ~3x2 + 3)
A177058: 3 1 ~1 3 19 53 111 199 323 489 703 971 1299 1693 2159 2703
(x4 + x3 + x2 + x + 1)
A053699: 1 5 31 121 341 781 1555 2801 4681 7381 11111 16105 22621 30941 41371 54241
(3x2 + 7x + 3)
A144391: 3 13 29 51 79 113 153 199 251 309 373 443 519 601 689 783
((x + 3) - ((~x + 2) div (x + 1)))
A257542: 1 4 5 7 8 9 10 11 12 13 14 15 16 17 18 19
((x + 1) - ((x + ~1) * (x div ~2)))
A222011: 1 2 4 8
A053439: 1 2 4 8 11 18 22 32 37 50 56 72 79 98 106 128
(x4 + ~x3 + x2 + ~x + 1)
A060884: 1 1 11 61 205 521 1111 2101 3641 5905 9091 13421 19141 26521 35855 47461
(x3 + 3x2 + ~4x + 1)
A106734: 1 1 13 43 97 181 301 463 673 937 1261 1651 2113 2653 3277 3991
(x3 + ~3x2 + 3x + 1)
A034324: 1 2 3 10 29 66 127 218 345 514 731 1002 1333 1730 2199 2746
((~x + 1) mod (x3 + ~x2 + 1))
A198297: 0 0 4 17
(x4 + 3x2 + 1)
A057721: 1 5 29 109 305 701 1405 2549 4289 6805 10301 15005 21169 29069 39005 51301
(x4 + 2x3 + x2 + 2x + 1)
A165563: 1 7 41 151 409 911 1777 3151 5201 8119 12121 17447 24361 33151 44129 57631
(x4 + ~3x2 + 1)
A057722: 1 ~1 5 55 209 551 1189 2255 3905 6319 9701 14279 20305 28055 37829 49951
(1 + (x mod (~2 * (1 + (x mod 2)))))
A230074: 1 ~2 1 0 1 ~2 1 0 1 ~2 1 0 1 ~2 1 0
(x - (x div ~9))
A231239-A231238: 0 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17
((x + 1) - (x div ~8))
A304812: 1 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18
((x + 1) - ((x div 4) div ~2))
A183302-A076216-A003247: 1 2 3 4 6 7 8 9 10 11 12 13 15 16 17 18
(1 + (x div (2 - ((x div 2) div ~2))))
A056813: 1 1 1 2 2 2 2 2 3 3 3 3 3 3 3 3
(1 - (x div (~1 + ((x div 2) div ~2))))
A105096: 1 2 2 3 3 4 3 4 4
(x - ((x div 3) div ~3))
A138083: 0 1 2 4 5 6
A235498-A052405: 0 1 2 4 5 6 7 8 9 10 11 12 14 15 16 17
(x - (2x2 div ~3))
A320259: 0 2 5 9 15 22 30 40 51 63 77 92 108 126 145 165
(x - ((x + (x mod 2)) div ~3))
A047587: 0 2 3 5 6 7 8 10 11 13 14 15 16 18 19 21
(((x + 1) mod 2) - (x div ~3))
A267806: 1 1 2 1 3 2 3 3 4 3 5 4 5 5 6 5
((x div 2) div (2 - (x div ~3)))
A184964-A054908-A034402: 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1
(3x - (x div ~3))
A198266-A067497: 0 4 7 10 14 17 20 24 27 30 34 37 40 44 47 50
((~2x + 1) - (x mod ~3))
A168071: 1 1 ~2 ~5 ~5 ~8 ~11 ~11 ~14 ~17 ~17 ~20 ~23 ~23 ~26 ~29
(x2 - (x2 div ~3))
A147623: 0 2 6 12 22 34 48 66 86 108 134 162 192 226 262 300
((x + 1) - ((x + (x div 2)) div ~2))
A329841-A047329: 1 3 5 6 8 10 12 13 15 17 19 20 22 24 26 27
(1 + ((x div (1 + (x mod 3))) mod 2))
A214074: 1 1 1 2 1 2 1 2 1 2 2 2 1 1 1 2
((x + 1) - (2 * (~1 + (x mod 3))))
A113655: 3 2 1 6 5 4 9 8 7 12 11 10 15 14 13 18
(8x + 11)
A004769: 11 19 27 35 43 51 59 67 75 83 91 99 107 115 123 131
(4x2 + 4x + 3)
A164897: 3 11 27 51 83 123 171 227 291 363 443 531 627 731 843 963
(1 + (2 * (x - (x div ~3))))
A047478: 1 5 7 9 13 15 17 21 23 25 29 31 33 37 39 41
(1 + ((x div (1 + (x mod 4))) mod 2))
A322480-A251683: 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 2
((x + 1) - (2 * (~1 + (x mod 4))))
A004444: 3 2 1 0 7 6 5 4 11 10 9 8 15 14 13 12
(x div (1 + (2 * (3 + (x mod 2)))))
A230198: 0 0 0 0 0 0 0 0 1 1 1 1 1 1 2 1
(1 + (2 * ((2x + 1) div 3)))
A222657: 1 3 3 5 7 7 9 11 11 13 15 15 17 19 19 21
((x + ~1) - (2 * ((x + ~1) div 3)))
A008611: 1 0 1 2 1 2 3 2 3 4 3 4 5 4 5 6
(1 + ((3 * ((x + 1) div 2)) div 2))
A265428: 1 2 2 4 4 5 5 7 7 8 8 10 10 11 11 13
(x div (3 + ((x div 2) div 3)))
A071804: 0 0 0 1 1 1 1 1 2 2 2 2 2 2 2 3
(1 + (x div (2 + ((x div 2) div 3))))
A111393: 1 1 2 2 3 3 3 3 3 4 4 4 4 4 4 4
(1 + ((x - ((x div 2) div 3)) div 2))
A195072-A121828: 1 1 2 2 3 3 3 4 4 5 5 6 6 6 7 7
(x - ((x + ~1) div 7))
A227394-A209900-A097043: 1 1 2 3 4 5 6 7 7 8 9 10 11 12 13 13
((2x + 2) div 7)
A183138-A060065: 0 0 0 1 1 1 2 2 2 2 3 3 3 4 4 4
(4x div 7)
A263574-A194208-A057358-A038128: 0 0 1 1 2 2 3 4 4 5 5 6 6 7 8 8
((2 * (x div 2)) div 7)
A165927: 0 0 0 0 0 0 0 0 1 1 1 1 1 1 2 2
(x - (2x div 7))
A049474: 0 1 2 3 3 4 5 5 6 7 8 8 9 10 10 11
(3x div 7)
A308358-A057357: 0 0 0 1 1 2 2 3 3 3 4 4 5 5 6 6
(3x mod 7)
A111952: 0 3 6 2 5 1 4 0 3 6 2 5 1 4 0 3
(x - ((~x + 1) div 7))
A047565: 0 1 3 4 5 6 7 8 9 11 12 13 14 15 16 17
((x2 + x) mod 7)
A053793: 0 2 6 5 6 2 0 0 2 6 5 6 2 0 0 2
((x2 + ~x) div 7)
A011860: 0 0 0 0 1 2 4 6 8 10 12 15 18 22 26 30
(2 - ((~x + 2) div 7))
A210568-A132944: 2 2 2 3 3 3 3 3 3 3 4 4 4 4 4 4
(x - ((~x + 2) div 7))
A138083: 0 1 2 4 5 6
A047573: 0 1 2 4 5 6 7 8 9 10 12 13 14 15 16 17
(x3 mod 7)
A070472: 0 1 1 6 1 6 6 0 1 1 6 1 6 6 0 1
(x2 + x + 7)
A027692: 7 9 13 19 27 37 49 63 79 97 117 139 163 189 217 247
(1 + ((x2 + 2x) mod 6))
A284517: 1 4 3 4 1 6 1 4 3 4 1 6 1 4 3 4
(x3 + 7)
A084377: 7 8 15 34 71 132 223 350 519 736 1007 1338 1735 2204 2751 3382
(1 + (2 * (x - ((~x + 1) div 3))))
A047529: 1 3 7 9 11 15 17 19 23 25 27 31 33 35 39 41
(1 + (2 * (2x - (x div 3))))
A063213: 1 5 9 11 15 19 21 25 29 31 35 39 41 45 49 51
(1 + (((x div 2) - (x div 3)) div 2))
A297777-A043560-A043536: 1 1 1 1 1 1 1 1 2 1 2 2 2 2 2 2
((x div 2) div (3 + (x div 3)))
A342721-A342720-A340370-A331302-A327932-A326033-A326016-A322358-A297245-A297243-A296213-A292149-A277161-A261488-A235919-A180834-A180649-A159451-A151795-A127686-A127683-A125005-A123546-A098854-A098852-A098851-A070105-A070096-A070090-A036876-A036860-A035678-A034409-A025442-A025437-A024154: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
((2x + 1) - ((x div 3) mod 2))
A187977-A120243: 1 3 5 6 8 10 13 15 17 18 20 22 25 27 29 30
((2x + 1) - ((x mod 3) div 2))
A029739: 1 3 4 7 9 10 13 15 16 19 21 22 25 27 28 31
((2x + 1) - ((x mod 3) mod 2))
A047268: 1 2 5 7 8 11 13 14 17 19 20 23 25 26 29 31
(1 + (2 * (1 + ((x2 + 2x) div 2))))
A286264: 3 5 11 17 27 37 51 65 83 101 123 145 171 197 227 257
(1 + (2 * (1 + (2 * (x + (x mod 2))))))
A168378: 3 11 11 19 19 27 27 35 35 43 43 51 51 59 59 67
(1 + (2 * ((2x + 1) + (x div 2))))
A063239-A063226: 3 7 13 17 23 27 33 37 43 47 53 57 63 67 73 77
(1 + (2 * ((2x + 1) - (x mod 2))))
A066587-A047621: 3 5 11 13 19 21 27 29 35 37 43 45 51 53 59 61
((x div 2) div (1 + (2 * (1 + (x mod 2)))))
A254436: 0 0 0 0 0 0 1 0 1 0 1 1 2 1 2 1
(10x + 3)
A017305: 3 13 23 33 43 53 63 73 83 93 103 113 123 133 143 153
(1 + (2 * ((x + 1) + (x div 3))))
A047484: 3 5 7 11 13 15 19 21 23 27 29 31 35 37 39 43
(1 + (2 * ((x + 1) + (x div 4))))
A261033: 3 5 7 9 13
(1 + (((x + 1) + (x div 4)) div 2))
A097369-A019446: 1 2 2 3 4 4 5 5 6 7 7 8 9 9 10 10
(2x2 + 8x + 3)
A271625: 3 13 27 45 67 93 123 157 195 237 283 333 387 445 507 573
((x + 1) - (2 * ((~x + ~1) + (x mod 2))))
A047230: 3 4 9 10 15 16 21 22 27 28 33 34 39 40 45 46
(1 + (((x + 1) * (1 + (x div 2))) div 2))
A191535-A100598: 1 2 4 5 8 10
(1 + ((x3 + x2 + ~x + ~1) div 2))
A092679: 0 1 5 17
(1 + ((6 mod (x + 1)) mod 2))
A307608: 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
(1 + ((8 mod (x + 1)) mod 2))
A077619: 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1
(1 + (((x + 1) * (x div 4)) mod 2))
A111628-A111620: 1 1 1 1 2 1 2 1 1 1 1 1 2 1 2 1
(1 + (((x + 1) * (2 + (x div 2))) div 2))
A193063-A165132: 2 3 5 7 11 13
(1 + ((x3 + x2 + 2x + 2) div 2))
A189890: 2 4 10 23 46 82 134 205 298 416 562 739 950 1198 1486 1817
(1 + (2 * (2x2 div (x + 1))))
A342474: 1 3 5 9 13 17
(1 + (((x2 div 2) mod (x + 1)) div 2))
A224876: 1 1 2 1 2 1 3 1 3 1 4 1 4 1 5 1
(1 + ((x3 + 3x2 + 2x) div 2))
A158842: 1 4 13 31 61 106 169 253 361 496 661 859 1093 1366 1681 2041
(3 + ((x + ~1) * (2 + (x div 2))))
A031940: 1 3 6 9 15 19 28 33 45 51 66 73 91 99 120 129
(1 + (2 * (1 + (x * (x + (x div 2))))))
A301524: 3 5 15 27
(1 + (((~x + 1) mod (x2 + 1)) div 2))
A238531: 1 1 3 5 8 12 17 23 30 38 47 57 68 80 93 107
(2x2 + x + ~7)
A100041: ~7 ~4 3 14 29 48 71 98 129 164 203 246 293 344 399 458
(1 + (2 * (x - ((x div 2) div ~2))))
A085820-A045572: 1 3 7 9 11 13 17 19 21 23 27 29 31 33 37 39
(x - ((x + 2) div ~5))
A285126-A232012-A187388-A184524-A157846-A059537: 1 2 3 4 6 7 8 9 10 12 13 14 15 16 18 19
(x - (2x div ~5))
A047332: 0 2 3 5 6 7 9 10 12 13 14 16 17 19 20 21
(2x - (x div ~5))
A195167: 0 3 5 7 9 11 14 16 18 20 22 25 27 29 31 33
(1 + (x div (2 - (x div ~4))))
A286888: 1 1 1 2 2 2 2 2 3 2 3 3 3 3 3 3
(x mod ((x + ~1) - (x mod ~4)))
A338774: 0 1 2 0 1 5 6 0 1 9 10 0 1 13 14 0
(1 + (2 * (2x - (x div ~2))))
A131229: 1 7 11 17 21 27 31 37 41 47 51 57 61 67 71 77
((x + 1) - (x div (~2 + (x div ~2))))
A184336: 1 3 4 5 6 7 9 10 11 12 13 14 15 16 17 18
(1 + (((~1 + (x div 3)) div 2) div 2))
A297032-A225541-A161092-A102572: 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 2
(x + ~21)
A023463: ~21 ~20 ~19 ~18 ~17 ~16 ~15 ~14 ~13 ~12 ~11 ~10 ~9 ~8 ~7 ~6
(1 + (4 * (1 + (2 * (x div 2)))))
A168392: 5 5 13 13 21 21 29 29 37 37 45 45 53 53 61 61
((x + 1) - (((1 + (x div 2)) div 2) div 2))
A071377: 1 2 3 4 5 6 6 7 8 9 10 11 12 13 13 14
(1 + (2 * (x - ((1 + (x div 2)) div 2))))
A293990: 1 3 3 5 7 9 9 11 13 15 15 17 19 21 21 23
(1 + (2 * (x mod (2 * (1 + (x mod 2))))))
A112132: 1 3 1 7 1 3 1 7 1 3 1 7 1 3 1 7
(4x2 + 4x + 5)
A078370: 5 13 29 53 85 125 173 229 293 365 445 533 629 733 845 965
(1 + ((((x + ~1) + (x div 2)) div 2) div 2))
A029865: 0 1 1 1 2 2 3 3 3 4 4
A225593: 0 1 1 1 2 2 3 3 3 4 4 4 5 5 6 6
(1 + (((x2 + 3x + 2) div 2) div 2))
A039823: 1 2 4 6 8 11 15 19 23 28 34 40 46 53 61 69
(1 + ((x - (x div ~4)) div 2))
A319433: 1 2 2 3 3 4 5 5 6 7 7 8 8 9 10 10
(1 + (2 * (2 + ((x mod 3) div 2))))
A122273: 5 5 7 5 5 7
((x + 1) - ((((x + 1) div 2) div 2) div 2))
A309082-A228298-A060431: 1 2 3 4 5 6 7 7 8 9 10 11 12 13 14 14
(1 + ((((x2 + ~1) div 2) div 2) div 2))
A036406: 0 1 1 2 2 4 5 7 8 11 13 16 18 22 25 29
(x + ~33)
A023475: ~33 ~32 ~31 ~30 ~29 ~28 ~27 ~26 ~25 ~24 ~23 ~22 ~21 ~20 ~19 ~18
(x + ~31)
A023473: ~31 ~30 ~29 ~28 ~27 ~26 ~25 ~24 ~23 ~22 ~21 ~20 ~19 ~18 ~17 ~16
(~x + 19)
A022975: 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4
(x2 mod 17)
A054580: 0 1 4 9 16 8 2 15 13 13 15 2 8 16 9 4
(2x div 15)
A209899: 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 2
((~x + 1) mod 15)
A261305: 1 0 14 13 12 11 10 9 8 7 6 5 4 3 2 1
(x2 mod 15)
A070638-A070438: 0 1 4 9 1 10 6 4 4 6 10 1 9 4 1 0
(1 + ((x - (x div 8)) div 2))
A104305-A050506: 1 1 2 2 3 3 4 4 4 5 5 6 6 7 7 8
(1 + (x div (4 + (x div 4))))
A245636: 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3
(1 + (4 * (x - (x div 4))))
A080455: 1 5 9 13 13 17 21 25 25 29 33 37 37 41 45 49
((x + 5) - ((x div 2) mod 2))
A335015: 5 6 6 7 9
(1 + (2 * ((x - ((x div 2) mod 2)) div 2)))
A290561: 1 1 1 3 5 5 5 7 9 9 9 11 13 13 13 15
(x mod (1 + (2 * (4 + (x mod 2)))))
A103303: 0 1 2 3 4 5 6 7 8 9
A346511: 0 1 2 3 4 5 6 7 8 9 1 0 3 2 5 4
(x div (1 + (4 * (2 + (x mod 2)))))
A033665-A024163: 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1
(1 + (2 * ((x2 div 2) mod 4)))
A109768: 1 1 5 1 1 1 5 1 1 1 5 1 1 1 5 1
(x2 + 11)
A189836: 11 12 15 20 27 36 47 60 75 92 111 132 155 180 207 236
((~x + ~1) mod 9)
A141726: 8 7 6 5 4 3 2 1 0 8 7 6 5 4 3 2
(x - ((x + 1) mod 9))
A160949: ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 8 8 8 8 8 8 8 8
((2x + 2) mod 9)
A146082: 2 4 6 8 1 3 5 7 0 2 4 6 8 1 3 5
((2x + 4) div 9)
A105564: 0 0 0 1 1 1 1 2 2 2 2 2 3 3 3 3
(x - ((~x + 1) div 9))
A052404: 0 1 3 4 5 6 7 8 9 10 11 13 14 15 16 17
((x2 + ~x) div 9)
A011862: 0 0 0 0 1 2 3 4 6 8 10 12 14 17 20 23
((x2 + 2x) div 9)
A287893: 0 0 0 1 2 3 5 7 8 11 13 15 18 21 24 28
(x3 div 9)
A061263: 0 0 0 3 7 13 24 38 56 81 111 147 192 244 304 375
(x3 mod 9)
A167176: 0 1 8 0 1 8 0 1 8 0 1 8 0 1 8 0
(x2 + x + 9)
A027694: 9 11 15 21 29 39 51 65 81 99 119 141 165 191 219 249
((x + 1) - ((~x + 2) div 8))
A183298: 1 2 3 5 6 7 8 9 10 11 12 14 15 16 17 18
((2x + 1) - (x div 8))
A329938-A329831-A247429-A063460: 1 3 5 7 9 11 13 15 16 18 20 22 24 26 28 30
(1 + (x div 2) - (x div 8))
A285879-A061070: 1 1 2 2 3 3 4 4 4 4 5 5 6 6 7 7
(1 + ((x + ~2) div (2 + (x div 4))))
A284248-A023968: 0 0 1 1 1 2 2 2 2 2 3 3 3 3 3 3
((2x + 1) - ((x div 4) mod 2))
A191230: 1 3 5 7 8 10 12 14 17 19 21 23 24 26 28 30
((2x + 3) - (x mod 4))
A047425: 3 4 5 6 11 12 13 14 19 20 21 22 27 28 29 30
(12x + 9)
A017629: 9 21 33 45 57 69 81 93 105 117 129 141 153 165 177 189
(~1 + (4 * ((x + 2) + (x div 2))))
A168489: 7 11 19 23 31 35 43 47 55 59 67 71 79 83 91 95
((x + 1) - (((2 - (x div 2)) div 2) div 2))
A257458: 1 2 3 4 5 6 8 9 10 11 12 13 14 15 17 18
(1 + (2x div (4 + (x div 2))))
A171626-A069624: 1 1 1 2 2 2 2 3 3 3 3 3 3 3 3 3
(2x div (5 + (x div 2)))
A077429: 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 2
(1 + (2 * (x div (2 * (2 - (x mod 2))))))
A215495: 1 1 1 3 3 5 3 7 5 9 5 11 7 13 7 15
(1 + (2 * (x mod (2 * (2 - (x mod 2))))))
A287765: 1 3 5 3 1 3 5 3 1 3 5 3 1 3 5 3
(1 + (2 * ((2x + 2) - (x mod 2))))
A047550: 5 7 13 15 21 23 29 31 37 39 45 47 53 55 61 63
(1 + (x mod (2 + (x mod (2 + (x mod 2))))))
A131456: 1 2 1 2 1 2 1 2 1 2 1 4 1 2 1 2
(x mod (1 + (2 * (x mod (2 + (x mod 2))))))
A228495: 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0
((x + ~1) - (x mod (2 * (~2 + (x mod 2)))))
A290562: ~1 1 3 3 3 5 7 7 7 9 11 11 11 13 15 15
((2x + 1) - ((x + 1) mod 4))
A047527: 0 1 2 7 8 9 10 15 16 17 18 23 24 25 26 31
(x2 mod (1 + ((x + ~1) mod 4)))
A175854-A101605: 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0
(1 + (((x2 + ~1) div 2) mod 4))
A109008: 4 1 2 1 4 1 2 1 4 1 2 1 4 1 2 1
(1 + (((x2 + x) div 2) mod 4))
A110549: 1 2 4 3 3 4 2 1 1 2 4 3 3 4 2 1
(15x + 15)
A161455: 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240
((3x + 3) div 5)
A171975: 0 1 1 2 3 3 4 4 5 6 6 7 7 8 9 9
30x
A249674: 0 30 60 90 120 150 180 210 240 270 300 330 360 390 420 450
15x2
A064761: 0 15 60 135 240 375 540 735 960 1215 1500 1815 2160 2535 2940 3375
(5 * ((x + 1) + (x div 2)))
A072703: 5 10 20 25 35 40 50 55 65 70 80 85 95 100 110 115
(5 * ((x + 1) + (x mod 2)))
A166621: 5 15 15 25 25 35 35 45 45 55 55 65 65 75 75 85
(10x2 + 10x)
A163761: 0 20 60 120 200 300 420 560 720 900 1100 1320 1560 1820 2100 2400
((x div 2) - ((x + 1) div 5))
A286716: 0 0 1 1 1 1 2 2 3 2 3 3 4 4 4 4
(2 - (5 * (x div ~2)))
A168278: 2 7 7 12 12 17 17 22 22 27 27 32 32 37 37 42
(x - (5 * (x div ~2)))
A047335: 0 6 7 13 14 20 21 27 28 34 35 41 42 48 49 55
(x + ~30)
A023472: ~30 ~29 ~28 ~27 ~26 ~25 ~24 ~23 ~22 ~21 ~20 ~19 ~18 ~17 ~16 ~15
((2 * (1 + (x div 2))) div 5)
A134119: 0 0 0 0 1 1 1 1 2 2 2 2 2 2 3 3
(x - ((2x + 2) div 5))
A098295-A074840: 0 1 1 2 2 3 4 4 5 5 6 7 7 8 8 9
(10x2 + ~10)
A302576: ~10 0 30 80 150 240 350 480 630 800 990 1200 1430 1680 1950 2240
(x + ~40)
A023482: ~40 ~39 ~38 ~37 ~36 ~35 ~34 ~33 ~32 ~31 ~30 ~29 ~28 ~27 ~26 ~25
40x
A317095: 0 40 80 120 160 200 240 280 320 360 400 440 480 520 560 600
(8x div 5)
A085270-A047416: 0 1 3 4 6 8 9 11 12 14 16 17 19 20 22 24
((2 * (2 + (x div 2))) div 5)
A321017-A262694-A259361-A182434-A098429: 0 0 1 1 1 1 2 2 2 2 2 2 3 3 3 3
20x2
A195322: 0 20 80 180 320 500 720 980 1280 1620 2000 2420 2880 3380 3920 4500
(4x2 div 5)
A279169: 0 0 3 7 12 20 28 39 51 64 80 96 115 135 156 180
(x - ((~2x + 2) div 5))
A047299: 0 1 3 4 6 7 8 10 11 13 14 15 17 18 20 21
(5 * ((x2 + x) div 2))
A028895: 0 5 15 30 50 75 105 140 180 225 275 330 390 455 525 600
(((x2 + ~x) div 2) div 5)
A173345: 0 0 0 0 1 2 3 4 5 7 9 11 13 15 18 21
((5x + 10) * (x mod 2))
A187486: 0 15 0 25 0 35 0 45 0 55 0 65 0 75 0 85
((x + ~1) + ((x + 2) mod 5))
A065186: 1 3 5 2 4 6 8 10 7 9 11 13 15 12 14 16
((x + ~2) + ((x + 2) mod 5))
A277618: 0 2 4 1 3 5 7 9 6 8 10 12 14 11 13 15
((x3 + 2x2) mod 5)
A152892: 0 3 1 0 1 0 3 1 0 1 0 3 1 0 1 0
(x - ((~2x + 1) div 5))
A047301: 0 2 3 4 6 7 9 10 11 13 14 16 17 18 20 21
(2x - (2x div 5))
A204399-A195176-A195126-A047496: 0 2 4 5 7 8 10 12 13 15 16 18 20 21 23 24
10x3
A244729: 0 10 80 270 640 1250 2160 3430 5120 7290 10000 13310 17280 21970 27440 33750
((x div 2) - ((x div 2) div 5))
A139789-A117695: 0 0 1 1 2 2 3 3 4 4 4 4 5 5 6 6
25x
A008607: 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375
(10x2 + ~5x)
A152745: 0 5 30 75 140 225 330 455 600 765 950 1155 1380 1625 1890 2175
(1 - ((x2 + x) mod 5))
A105368: 1 ~1 0 ~1 1 1 ~1 0 ~1 1 1 ~1 0 ~1 1 1
((x3 + ~x) mod 5)
A152894: 0 0 1 4 0 0 0 1 4 0 0 0 1 4 0 0
((x + 5) + (x div 4))
A201472: 5 6 7 8 10 11 12 13 15 16 17 18 20 21 22 23
(2x - ((~x + 2) div 5))
A029924: 0 2 4 7 9 11 13 15 18 20 22 24 26 29 31 33
(1 - ((~x + (x mod 2)) div 5))
A260999-A242768-A100617-A090532-A003058: 1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4
(x - ((~x + (x mod 2)) div 5))
A039234: 0 1 3 4 5 6 8 9 10 11 12 13 15 16 17 18
((x div 4) - (x div 5))
A088951: 0 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0
((2x + 4) - (x mod 5))
A059709: 4 5 6 7 8 14 15
(3x - (x mod 5))
A192333: 0 2 4 6 8 15 17 19 21 23 30 32 34 36 38 45
(1 mod ((~x2 + 2) mod 5))
A125144: 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1
5x4
A269792: 0 5 80 405 1280 3125 6480 12005 20480 32805 50000 73205 103680 142805 192080 253125
(2 - (1 mod (~4x + 5)))
A222011: 1 2 4 8
A048166-A019442: 1 2 4 8 12 16 20 24 28 32 36 40 44 48 52 56
(1 + ((x + (x div 4)) mod 4))
A273149: 1 2 3 4 2 3 4 1 3 4 1 2 4 1 2 3
((2x + 1) - ((~x + 2) div 4))
A097911: 1 3 5 8
A073608: 1 3 5 8 10 12
A184584: 1 3 5 8 10 12 14 17 19 21 23 26 28 30 32 35
((x + 1) - ((x + (x div 2)) div 4))
A039729: 1 2 3 3 4 5 5 6 6 7 8 8 9 10 10 11
((x + 1) - (4 * (~x + (x mod 2))))
A136986: 1 2 11 12 21
((4x + 1) + (x div 4))
A081835: 1 5 9 13 18 22 26 30 35 39 43 47 52 56 60 64
(x - (2 mod (~1 - (x div 4))))
A084689: 0 1 2 3 4 5 6 7 9
A249017-A214879-A014133: 0 1 2 3 4 5 6 7 9 10 11 12 14 15 16 17
((x + 2) - (2 div (1 + (x div 4))))
A244218: 0 1 2 3 5 6 7 8 10 11 12 13 14 15 16 17
((x div 2) - (2 mod (1 + (x div 4))))
A290884: 0 0 1 1 2 2 3 3 2 2 3 3 4 4 5 5
(x - ((x div 2) mod (1 + (x div 4))))
A163296: 0 1 2 3 4 5 5 6 7 8 8 9 10 11 11 12
((~x2 + x) mod (1 + (x div 4)))
A035668: 0 0 0 0 0 0 0 0 1 0 0 1 0 0 2 2
((x + 1) + ((x div 2) + (x div 4)))
A047380: 1 2 4 5 8 9 11 12 15 16 18 19 22 23 25 26
((x2 + x) mod (1 + (x mod 4)))
A280799-A218876-A123298: 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0
((~x2 + 1) mod (1 + (x mod 4)))
A330174-A316867-A276306-A185708-A185016-A103674-A096904-A086011-A083928: 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
(4x2 + ~3x + 1)
A054552: 1 2 11 28 53 86 127 176 233 298 371 452 541 638 743 856
((x + 1) mod (1 + (x2 div 4)))
A028253: 0 0 1 1 0 6 7 8 9 10 11 12 13 14 15 16
((x2 + ~1) - (x2 div 4))
A331952: ~1 0 2 6 11 18 26 36 47 60 74 90 107 126 146 168
((x2 + 1) - (x2 div 4))
A222011: 1 2 4 8
A164486-A084684: 1 2 4 8 13 20 28 38 49 62 76 92 109 128 148 170
(1 - (x div (~3 + ((~x + 1) div 2))))
A211664: 1 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3
((x + 1) - (x div (~2 + ((~x + 1) div 2))))
A003619: 1 3 4 5 6 8 9 10 11 12 13 14 15 16 17 18
(1 + (((~x + (2 mod (x + 1))) div 2) mod 2))
A026606: 1 2 1 2 2 1 1 2 2 1 1 2 2 1 1 2
(1 + ((x2 - ((~x + 2) div 2)) div 2))
A082643: 0 1 3 6 9 14 20 27 34 43 53 64 75 88 102 117
(1 + (2 * (x - (2 * (~x + (x mod 2))))))
A318165: 1 3 13
A146512: 1 3 13 15 25 27 37 39 49 51 61 63 73 75 85 87
(x - (x2 div (x + 5)))
A029837-A004258: 0 1 2 2 3 3 3 3 4 4 4 4 4 4 4 4
(1 + (3x div (x + 4)))
A220104-A123119: 1 1 2 2 2 2 2 2 3 3 3 3 3 3 3 3
(1 + ((x * (x div 2)) div (x + 4)))
A280950-A068980: 1 1 1 1 2 2 2 2 3 3 4 4 5 5 6 6
((x2 + ~2) mod (2x + 5))
A279390: 3 6 2 7
(x - (x2 div (2x + 5)))
A065603: 0 1 2 3 3 4 4 5 5 6 6 7 8 8 9
(2x4 + 4x3 + 1)
A274823: 1 7 65
(1 + (((x2 + 2x) * (x mod 2)) div 2))
A176889: 1 2 1 8 1 18 1 32 1 50 1 72 1 98 1 128
(2x2 + ~7x + 9)
A236257: 9 4 3 6 13 24 39 58 81 108 139 174 213 256 303 354
((x + 1) - (2 * (2 mod (~2x + 1))))
A172411: 1 2 5 10
A135042: 1 2 5 10 15 20 25 30 35 40 45 50 55 60 65 70
(1 + (2 * (x - (2 mod (~2x + 1)))))
A144917: 1 3 7 13 19 25 31 37 43 49 55 61 67 73 79 85
((x + 1) - (2 * (~2x + (x mod 2))))
A271508: 1 4 11 14 21 24 31 34 41 44 51 54 61 64 71 74
((4x + 3) - (x div 2))
A248522: 3 7 10 14 17 21 24 28 31 35 38 42 45 49 52 56
((4x + 3) - (x mod 2))
A047398: 3 6 11 14 19 22 27 30 35 38 43 46 51 54 59 62
(3 + (5 * (x div 2)))
A168283: 3 3 8 8 13 13 18 18 23 23 28 28 33 33 38 38
(1 + ((2x + 2) div (2 + (x div 2))))
A288914: 2 3 3 3 3 4 3 4 4 4 4 4 4 4 4 4
(x - ((x + ~1) div (3 + (x div 2))))
A302780: 1 1 2 3 4 5 6 6 7 8 9 10 11 12 13 14
((x + 1) - ((~x + 1) div (2 + (x div 2))))
A212445: 1 2 4 5 6 7 8 10 11 12 13 14 15 16 17 18
((x + 1) - ((~x + 2) div (2 + (x div 2))))
A340745: 0 2 3 5 6 7 8 9 10 12 13 14 15 16 17 18
(1 + ((x + (x mod 2)) * (2 + (x div 2))))
A178218: 1 5 7 13 17 25 31 41 49 61 71 85 97 113 127 145
((x2 + x) div (1 + ((x div 2) mod 2)))
A227316: 0 2 3 6 20 30 21 28 72 90 55 66 156 182 105 120
((x + 1) + (x mod 2) - ((x div 2) mod 2))
A116966: 1 3 2 4 5 7 6 8 9 11 10 12 13 15 14 16
(1 + (((x2 div 2) - (x mod 2)) div 2))
A097066: 1 0 2 2 5 6 10 12 17 20 26 30 37 42 50 56
((x div 4) div (3 + (x mod 2)))
A344446-A337605: 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0
(2 - ((~x + 2) div (3 + (x mod 2))))
A209356: 2 2 2 3 3 3 4 4 4 4 5 5 6
((x + 1) div (1 + (x div (2 + (x mod 2)))))
A257993-A204917-A062356-A055881: 1 2 1 2 1 3 1 2 1 2 1 3 1 2 1 2
((x2 + ~1) div (~1 + (2 * (x mod 2))))
A131386: 1 0 ~3 8 ~15 24 ~35 48 ~63 80 ~99 120 ~143 168 ~195 224
((x + (x div 2)) div (~1 + (2 * (x mod 2))))
A084056: 0 1 ~3 4 ~6 7 ~9 10 ~12 13 ~15 16 ~18 19 ~21 22
((x2 + 2x + 1) + (2 * (x mod 2)))
A086955: 1 6 9 18 25 38 49 66 81 102 121 146 169 198 225 258
((x3 + ~1) + (2 * (x mod 2)))
A123363: ~1 2 7 28 63 126 215 344 511 730 999 1332 1727 2198 2743 3376
(1 + (~x mod (2 + (x2 div 2))))
A267459: 1 2 3 4 7 10 15 20 27 34 43 52 63 74 87 100
(3 * (1 + (2x div 3)))
A136289: 3 3 6 9 9 12 15 15 18 21 21 24 27 27 30 33
(x - ((~1 + (x div ~2)) div 3))
A335137-A187394-A109234-A057907: 1 2 3 4 5 7 8 9 10 11 12 14 15 16 17 18
((x mod 7) div 3)
A307247: 0 0 0 1 1 1 2 0 0 0 1 1 1 2 0 0
((x mod 7) mod 3)
A263844: 0 1 2 0 1 2 0 0 1 2 0 1 2 0 0 1
((1 + (x mod 6)) div 3)
A151899: 0 0 1 1 1 2 0 0 1 1 1 2 0 0 1 1
(x + ~27)
A023469: ~27 ~26 ~25 ~24 ~23 ~22 ~21 ~20 ~19 ~18 ~17 ~16 ~15 ~14 ~13 ~12
((8x + 1) div 3)
A047622: 0 3 5 8 11 13 16 19 21 24 27 29 32 35 37 40
(((x + ~2) mod 5) mod 3)
A014586: 0 1 0 1 2 0 1 0 1 2 0 1 0 1 2 0
(((x div 2) mod 5) div 3)
A102677: 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0
(x - (3 * (x div 5)))
A215088: 0 1 2 3 4 2 3 4 5 6 4 5 6 7 8 6
((1 + (x2 div 4)) div 3)
A328283: 0 0 0 1 1 2 3 4 5 7 8 10 12 14
A069905: 0 0 0 1 1 2 3 4 5 7 8 10 12 14 16 19
(x - ((1 + (2 * (x div 2))) div 3))
A276952: 0 1 1 2 3 4 4 5 5 6 7 8 8 9 9 10
(9 * ((x + 1) div 2))
A168419: 0 9 9 18 18 27 27 36 36 45 45 54 54 63 63 72
(x + ~36)
A023478: ~36 ~35 ~34 ~33 ~32 ~31 ~30 ~29 ~28 ~27 ~26 ~25 ~24 ~23 ~22 ~21
36x
A044102: 0 36 72 108 144 180 216 252 288 324 360 396 432 468 504 540
(3 * ((2 * (x div 2)) mod 3))
A146761: 0 0 6 6 3 3 0 0 6 6 3 3 0 0 6 6
(9 * ((x div 2) mod 2))
A021105: 0 0 9 9 0 0 9 9 0 0 9 9 0 0 9 9
18x2
A195321: 0 18 72 162 288 450 648 882 1152 1458 1800 2178 2592 3042 3528 4050
27x
A305548: 0 27 54 81 108 135 162 189 216 243 270 297 324 351 378 405
(9x2 + 9x)
A163758: 0 18 54 108 180 270 378 504 648 810 990 1188 1404 1638 1890 2160
(9x2 + 18x)
A147651: 0 27 72 135 216 315 432 567 720 891 1080 1287 1512 1755 2016 2295
(x - ((1 - (x div 3)) div 3))
A067570: 0 1 2 3 4 5 7
A052414: 0 1 2 3 4 5 7 8 9 10 11 12 13 14 15 17
((2x - (x div 3)) mod 3)
A060588: 0 2 1 2 1 0 1 0 2 0 2 1 2 1 0 1
9x3
A244728: 0 9 72 243 576 1125 1944 3087 4608 6561 9000 11979 15552 19773 24696 30375
(3 * (1 + ((x2 + x) div 2)))
A290768: 3 6 12 21 33 48 66 87 111 138 168 201 237 276 318 363
(1 - ((x mod (1 + (x div 2))) div 3))
A014100: 1 1 1 1 1 1 1 0 0 0 0 0 0 ~1 ~1 ~1
(2x - ((~1 + (x div 2)) div 3))
A027440: 1 3 4 6 8 10 12
A184736: 1 3 4 6 8 10 12 14 15 17 19 21 23 25 26 28
((1 + (x div (2 - (x mod 2)))) mod 3)
A164965: 1 2 2 1 0 0 1 2 2 1 0 0 1 2 2 1
(((2x + 1) - (x mod 2)) div 3)
A273663-A096386: 0 0 1 2 3 3 4 4 5 6 7 7 8 8 9 10
(((~x + 1) div (1 + (x mod 2))) mod 3)
A110568: 1 0 2 2 0 1 1 0 2 2 0 1 1 0 2 2
(((x + 1) + (x div 4)) mod 3)
A190487: 1 2 0 1 0 1 2 0 2 0 1 2 1 2 0 1
(x - (((~x + 1) + (x mod 2)) div 3))
A047428: 0 1 3 4 5 6 8 9 11 12 13 14 16 17 19 20
(x - (3 * ((~x + ~1) + (x mod 2))))
A047457: 3 4 11 12 19 20 27 28 35 36 43 44 51 52 59 60
(x - (((~x + ~1) + (x mod 2)) div 3))
A047519-A039054: 1 2 3 4 6 7 9 10 11 12 14 15 17 18 19 20
((8x + 8) div 3)
A330094-A236535-A059551: 2 5 8 10 13 16 18 21 24 26 29 32 34 37 40 42
((x2 + 5x + 4) div 3)
A143975: 1 3 6 9 13 18 23 29 36 43 51 60 69 79 90 101
((2x2 + 6x + 4) div 3)
A058759: 1 4 8 13
A143978: 1 4 8 13 20 28 37 48 60 73 88 104 121 140 160 181
(((x2 div 2) mod (x + 1)) div 3)
A260160: 0 0 0 0 1 0 1 0 1 0 2 0 2 0 2 0
(x + ((x + 1) div 3) - (x div 2))
A010761: 0 1 2 3 3 5 5 6 7 8 8 10 10 11 12 13
(1 + ((x + 1) div 3) - (x mod 2))
A051275: 1 0 2 1 2 2 3 2 4 3 4 4 5 4 6 5
(3x3 + 6x2 + 3x)
A059986: 0 12 54 144 300 540 882 1344 1944 2700 3630 4752 6084 7644 9450 11520
(12x2 + ~12x)
A064200: 0 0 24 72 144 240 360 504 672 864 1080 1320 1584 1872 2184 2520
((x2 + 2x) - ((x + ~1) div 3))
A331943: 1 3 8 15 23 34 47 61 78 97 117 140 165 191 220 251
(3x3 + ~6x2 + 3x)
A270205: 0 0 6 36 108 240 450 756 1176 1728 2430 3300 4356 5616 7098 8820
((x3 + ~3x2 + 2x) div 3)
A007290: 0 0 0 2 8 20 40 70 112 168 240 330 440 572 728 910
(x - (3 * ((x div 2) div ~2)))
A047322: 0 1 5 6 7 8 12 13 14 15 19 20 21 22 26 27
(2x - (3 * (x div ~2)))
A047382: 0 5 7 12 14 19 21 26 28 33 35 40 42 47 49 54
(6 * (1 + (x div 3)))
A052380: 6 6 6 12 12 12 18 18 18 24 24 24 30 30 30 36
(24x + 6)
A259752: 6 30 54 78 102 126 150 174 198 222 246 270 294 318 342 366
(3 * (2 + (3 * (x div 2))))
A168414: 6 6 15 15 24 24 33 33 42 42 51 51 60 60 69 69
(x2 mod 18)
A070440: 0 1 4 9 16 7 0 13 10 9 10 13 0 7 16 9
((x mod (2 + (x div 3))) div 3)
A144200-A144198-A085983-A037911: 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0
((x mod (2 + (x mod 3))) div 3)
A341508-A335460-A335446-A333146-A325801-A323547-A321537-A320313-A308424-A297234-A294937-A294930-A294927-A294890-A289110-A282673-A277156-A179801-A179391-A107846-A085863-A085393-A084904-A080224-A070203-A070201-A070109-A065202-A062977-A062535-A045701-A037134-A036875-A035698-A035655-A024155-A024153: 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
(((x2 + 3x + 2) div 2) div 3)
A001840: 0 1 2 3 5 7 9 12 15 18 22 26 30 35 40 45
(7x + 5)
A017041: 5 12 19 26 33 40 47 54 61 68 75 82 89 96 103 110
(x - (3 * (x div ~4)))
A047312: 0 4 5 6 7 11 12 13 14 18 19 20 21 25 26 27
((4 * (x div 3)) div 3)
A054861: 0 0 0 1 1 1 2 2 2 4 4 4 5 5 5 6
(24x + 12)
A073762: 12 36 60 84 108 132 156 180 204 228 252 276 300 324 348 372
((8x + 4) div 3)
A231407: 1 4 6
A047408: 1 4 6 9 12 14 17 20 22 25 28 30 33 36 38 41
(x - (3 * (((x + 1) div 2) div 2)))
A110657: 0 1 2 0 1 2 3 1 2 3 4 2 3 4 5 3
((4 * (x mod 4)) div 3)
A130659: 0 1 2 4 0 1 2 4 0 1 2 4 0 1 2 4
(16x div 3)
A172334: 0 5 10 16 21 26 32 37 42 48 53 58 64 69 74 80
(x + 22)
A296763: 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
(x + ~22)
A023464: ~22 ~21 ~20 ~19 ~18 ~17 ~16 ~15 ~14 ~13 ~12 ~11 ~10 ~9 ~8 ~7
(x + ~26)
A023468: ~26 ~25 ~24 ~23 ~22 ~21 ~20 ~19 ~18 ~17 ~16 ~15 ~14 ~13 ~12 ~11
(~x + 25)
A022981: 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10
(~x + 26)
A022982: 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11
(x2 mod 24)
A070446: 0 1 4 9 16 1 12 1 16 9 4 1 0 1 4 9
(x - (3 * (x div 8)))
A245355: 0 1 2 3 4 5 6 7 5 6 7 8 9 10 11 12
24x2
A195824: 0 24 96 216 384 600 864 1176 1536 1944 2400 2904 3456 4056 4704 5400
(x - ((4 * (x div 2)) div 3))
A337932: 0 1 1 2 2 3 2 3 3 4 4 5 4 5 5 6
((x mod (4 + (x mod 2))) div 3)
A285963: 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0
((((x + 1) div 2) mod 4) div 3)
A288665: 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0
(0 - (x div ~11))
A174631: 0 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2
(1 - ((~x + 2) div 12))
A105209: 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 3
(x3 mod 12)
A070597-A070474: 0 1 8 3 4 5 0 7 8 9 4 11 0 1 8 3
(x - (3 * ((~x + 2) div 4)))
A047279: 0 1 2 6 7 8 9 13 14 15 16 20 21 22 23 27
(((x * (x div 2)) mod 4) div 3)
A340599-A160753: 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0
(2x - (3 * (x div 4)))
A271324-A230631: 0 2 4 6 5 7 9 11 10 12 14 16 15 17 19 21
(2x - ((x mod 4) mod 3))
A047397: 0 1 2 6 8 9 10 14 16 17 18 22 24 25 26 30
((2 + ((x2 + ~x) div 2)) div 3)
A007997: 0 0 1 1 2 4 5 7 10 12 15 19 22 26 31 35
((2x2 + 8x + 8) div 3)
A030511: 2 6 10 16 24 32 42 54 66 80 96 112 130 150 170 192
(11x + 1)
A017401: 1 12 23 34 45 56 67 78 89 100 111 122 133 144 155 166
(11x + 2)
A017413: 2 13 24 35 46 57 68 79 90 101 112 123 134 145 156 167
((((x div 2) * (x div 2)) div 2) div 3)
A319399: 0 0 0 0 0 0 1 1 2 2 4 4 6 6 8 8
((2x div (2 + (x div 2))) div 3)
A219966-A087991: 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1
(15x + 6)
A139606: 6 21 36 51 66 81 96 111 126 141 156 171 186 201 216 231
(3 * ((x2 + 3x) div 2))
A140091: 0 6 15 27 42 60 81 105 132 162 195 231 270 312 357 405
(12x2 + ~6x)
A152746: 0 6 36 90 168 270 396 546 720 918 1140 1386 1656 1950 2268 2610
(((x + 2) + (x div 4)) div 3)
A189574: 0 1 1 1 2 2 3 3 4 4 4 5 5 6 6 6
(1 - (((x2 + ~2x) div 2) mod 3))
A115360: 1 ~1 1 0 0 0 1 ~1 1 0 0 0 1 ~1 1 0
(x - (3 * ((~x + ~2) + (x mod 2))))
A047589: 6 7 14 15 22 23 30 31 38 39 46 47 54 55 62 63
(x - (((~x + ~2) + (x mod 2)) div 3))
A047572-A039052: 1 2 4 5 6 7 9 10 12 13 14 15 17 18 20 21
(4x - ((x + 2) div 3))
A343028: 0 3 7 11 14 18 22 25 29 33 36 40 44 47 51 55
(((x + 1) div 2) - ((x + ~2) div 3))
A026806: 1 2 1 2 2 2 2 3 2 3 3 3 3 4 3 4
(x - ((2 mod (~2x + 1)) div 3))
A061402: 0 1 3 4 6 8 9 11 13 14 16 18 19 21 23 24
((6x + 1) - (x div 2))
A131912: 1 7 12 18 23 29 34 40 45 51 56 62 67 73 78 84
(6x2 + ~5x)
A051866: 0 1 14 39 76 125 186 259 344 441 550 671 804 949 1106 1275
((((x + ~1) div 2) * (x div 2)) div 3)
A011866: 0 0 0 0 0 1 2 3 4 5 6 8 10 12 14 16
(3x - ((x div 2) div 3))
A198263: 0 3 6 9 12 15 17 20 23 26 29 32 34 37 40 43
(x + (x div 2) - ((x div 2) mod 3))
A037472: 0 1 2 3 4 5 9 10 11 12 13 14 18 19 20 21
(x - (((~x + 1) - (x mod 2)) div 3))
A047503: 0 2 3 4 5 7 8 10 11 12 13 15 16 18 19 20
(3 * ((x2 + 2x) + (x mod 2)))
A270257: 0 12 24 48 72 108 144 192 240 300 360 432 504 588 672 768
(3x2 + ~2x + 6)
A047915: 6 7 14 27 46 71 102 139 182 231 286 347 414 487 566 651
((1 - ((~x2 + 2x) div 2)) mod 3)
A115357: 1 1 1 0 2 0 1 1 1 0 2 0 1 1 1 0
21x
A008603: 0 21 42 63 84 105 126 147 168 189 210 231 252 273 294 315
(3 * (x + (x div 5)))
A271449: 0 3 6 9 12 18
(12x2 + 3x)
A063436: 0 15 54 117 204 315 450 609 792 999 1230 1485 1764 2067 2394 2745
(12x2 + ~3x)
A062783: 0 9 42 99 180 285 414 567 744 945 1170 1419 1692 1989 2310 2655
((x + ((x div 2) div 3)) div 3)
A085269-A057362: 0 0 0 1 1 1 2 2 3 3 3 4 4 5 5 5
(1 - ((~x + (x div 3)) div 3))
A108956-A108955: 1 2 2 2 2 3 3 3 3 3 4 4 4 4 5 5
(9x2 + 3x)
A282693: 0 12 42 90 156
A045945: 0 12 42 90 156 240 342 462 600 756 930 1122 1332 1560 1806 2070
(9x2 + ~3x)
A152743: 0 6 30 72 132 210 306 420 552 702 870 1056 1260 1482 1722 1980
((2x3 + x) div 3)
A005900: 0 1 6 19 44 85 146 231 344 489 670 891 1156 1469 1834 2255
((2x + 2) - ((~x + 1) div 3))
A329842: 2 4 7 9 11 14 16 18 21 23 25 28 30 32 35 37
((x2 + x) - ((~x + 1) div 3))
A262523: 0 2 7 13 21 32 44 58 75 93 113 136 160 186 215 245
((x3 + x2 + ~x) div 3)
A212971: 0 0 3 11 25 48 82 128 189 267 363 480 620 784 975 1195
((x + (4 mod (x + 1))) div 3)
A080405: 0 0 1 1 2 3 3 3 4 4 4 5 5 5 6 6
((x * (2 - (x div ~2))) div 3)
A233524: 0 1 2 4 5 8
A095031: 0 1 2 4 5 8 10
((x + 3) + (x div 8))
A154660: 3 4 5 6 7 8
A048135: 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19
(x2 + 6x + 3)
A028878: 3 10 19 30 43 58 75 94 115 138 163 190 219 250 283 318
(3x2 + 18x)
A140681: 0 21 48 81 120 165 216 273 336 405 480 561 648 741 840 945
((x + (2 * (2 + (x mod 2)))) div 3)
A103469: 1 2 2 3 2 3 3 4 4 5 4 5 5 6 6 7
(x - (3 * (~x + (x mod 4))))
A126007: 0 1 2 3 16 17 18 19 32 33 34 35 48 49 50 51
(9x2 + ~6x)
A152751: 0 3 24 63 120 195 288 399 528 675 840 1023 1224 1443 1680 1935
((~x + 1) + (3 * (x + (x div 2))))
A047356: 1 3 8 10 15 17 22 24 29 31 36 38 43 45 50 52
((~x + 2) + (3 * (x + (x div 2))))
A047348: 2 4 9 11 16 18 23 25 30 32 37 39 44 46 51 53
((~x + 2) + (3 * (x + (x mod 2))))
A168205: 2 7 6 11 10 15 14 19 18 23 22 27 26 31 30 35
((x + 2) - (3 * (~x + (x mod 2))))
A047473: 2 3 10 11 18 19 26 27 34 35 42 43 50 51 58 59
((~1 + (x div 3)) * (x div 3))
A241460: 0 0 0 0 0 0 2 2 2 6
((2x + ~3) * (x div 3))
A112986: 0 0 0 3 5 7 18 22 26 45 51 57 84 92 100 135
((3x + 3) + (x div 3))
A171982-A066343: 3 6 9 13 16 19 23 26 29 33 36 39 43 46 49 53
(((x + 1) div 3) * (x div 3))
A008133: 0 0 0 1 1 2 4 4 6 9 9 12 16 16 20 25
(((x + 2) div 3) * (x div 3))
A008130: 0 0 0 1 2 2 4 6 6 9 12 12 16 20 20 25
(((1 + (x div 2)) div 2) + (x div 3))
A187324: 0 0 1 2 2 2 4 4 4 5 6 6 7 7 8 9
((4x + 8) + (x div 3))
A078609: 8 12 16 21 25 29 34 38 42 47 51 55 60 64 68 73
(((x2 + ~x) div 2) + (x div 3))
A171452: 0 0 1 4 7 11 17 23 30 39 48 58 70 82 95 110
((2x2 + ~x) + (x div 3))
A264938: 0 1 6 16 29 46 68 93 122 156 193 234 280 329 382 440
((3x + 4) + (x div 3))
A125620: 4 7 10 14
(x div (6 + (x mod 3)))
A236765: 0 0 0 0 0 0 1 1 1 1 1 1 2 1 1 2
((2 * (x + (x div 2))) - (x mod 3))
A272299: 0 1 4 8 11 12 18 19 22 26 29 30 36 37 40 44
(5x2 div 3)
A222170: 0 1 6 15 26 41 60 81 106 135 166 201 240 281 326 375
((x4 + ~x2) div 3)
A112742: 0 0 4 24 80 200 420 784 1344 2160 3300 4840 6864 9464 12740 16800
(x - ((2 mod (~x2 + 2)) mod 3))
A335129: 0 1 2 2 4 5 5 7 8 8 10 11 11 13 14 14
(2x2 - (x2 div 3))
A113422: 0 2 7 15 27 42 60 82 107 135 167 202 240 282 327 375
(4x - (x2 mod 3))
A083031: 0 3 7 12 15 19 24 27 31 36 39 43 48 51 55 60
(14x + 1)
A131877: 1 15 29 43 57 71 85 99 113 127 141 155 169 183 197 211
(~1 + ((x2 + 5x) div 2))
A046691: ~1 2 6 11 17 24 32 41 51 62 74 87 101 116 132 149
(4x2 + 10x + 1)
A082112: 1 15 37 67 105 151 205 267 337 415 501 595 697 807 925 1051
(8x2 + 2x + 1)
A188135: 1 11 37 79 137 211 301 407 529 667 821 991 1177 1379 1597 1831
(8x2 + 2x + ~1)
A033566: ~1 9 35 77 135 209 299 405 527 665 819 989 1175 1377 1595 1829
(8x2 + ~2x + 1)
A185438: 1 7 29 67 121 191 277 379 497 631 781 947 1129 1327 1541 1771
(1 + ((x * (3 + (x div 2))) div 2))
A013660: 1 2 5 7 11
(1 + ((x + ((x div 2) div 3)) div 2))
A005378: 1 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9
(6x2 + 2x + 1)
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(1 + ((3x2 + x) div 2))
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(1 + ((3x2 + ~x) div 2))
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(1 + ((~x + (x2 div 3)) div 2))
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((x + 1) - ((~x3 + x2) div 2))
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(10x + 7)
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(1 + (2x * (2 + (2 div (x + 1)))))
A222945: 1 7 9 13 17 21 25 29 33 37 41 45 49 53 57 61
(1 + (2 * (x + (x div 8))))
A204458-A192861: 1 3 5 7 9 11 13 15 19 21 23 25 27 29 31 33
(1 + ((x + (x div 8)) div 2))
A226190: 1 1 2 2 3 3 4 4 5 6 6 7 7 8 8 9
(x mod (1 + ((x + (x div 4)) div 2)))
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((x + 1) - (2 * (~x + (x div 4))))
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((x + 1) - ((~x + (x div 4)) div 2))
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A247987: 1 3 4 6 7 8 10 11 12 14 15 17 18 19 21 22
((x + ~1) - (2 * (~x + ((x div 2) mod 2))))
A042944: ~1 2 3 6 11 14 15 18 23 26 27 30 35 38 39 42
((x + 1) - (2 * (~x + ((x div 2) mod 2))))
A174398: 1 4 5 8 13 16 17 20 25 28 29 32 37 40 41 44
((x + 1) - ((~x + ((x div 2) mod 2)) div 2))
A213637-A047251: 1 3 4 5 7 9 10 11 13 15 16 17 19 21 22 23
(6x2 + 4x + 1)
A080859: 1 11 33 67 113 171 241 323 417 523 641 771 913 1067 1233 1411
(1 + (2 * (x + (2 * (x + (x mod 2))))))
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((2x + 1) - ((x * (x div 2)) mod 2))
A047445: 1 3 5 6 9 11 13 14 17 19 21 22 25 27 29 30
(~1 + ((x + 2) * (1 + (x div 3))))
A138984: 1 2 3 9 11 13 23 26 29 43 47 51 69 74 79 101
(~1 + ((x + 2) * (1 + (x div 4))))
A138985: 1 2 3 4 11 13 15 17 29 32 35 38 55 59 63 67
(1 + (3x2 div (x + 2)))
A231408: 1 2 4 6 9
A271906: 1 2 4 6 9 11 14 17 20 23 26
(x3 + 6x2 + 12x + 9)
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(1 + (x mod ((x2 + 2) div (x + 2))))
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((4x + 1) div (x + 3))
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(x4 + 2x3 + ~3x2)
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((2x + 6) * (1 + (x div 2)))
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((x2 div 4) div (x + 3))
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(2 - ((2x + ~4) div (x + 3)))
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((x + 3) * ((x2 + x) div 2))
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((x + 3) * ((x2 + ~x) div 2))
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(2 - ((~2x + 4) div (x + 3)))
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(5x div (x + 3))
A227177: 0 1 2 2 2 3 3 3 3 3 3 3 4 4 4 4
(x - ((x2 + ~x) div (x + 3)))
A331137-A236857-A156874-A084556-A078767-A071578: 0 1 2 2 3 3 3 3 3 3 4 4 4 4 4 4
((2x + 1) + (x2 div 3))
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((2x + 1) - (2 mod (~2x + 1)))
A083505: 1 3 6 10 14
A113127: 1 3 6 10 14 18 22 26 30 34 38 42 46 50 54 58
((x2 + 1) - (2 mod (~2x + 1)))
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((2x + 1) + ((x mod 3) mod 2))
A047259: 1 4 5 7 10 11 13 16 17 19 22 23 25 28 29 31
((2x + 1) + ((x div ~2) mod 2))
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A047508: 1 4 6 7 9 12 14 15 17 20 22 23 25 28 30 31
((2x + 1) + ((x div 4) mod 2))
A225240: 1 3 5 7 10 12 14 16 17 19 21 23 26 28 30 32
((2x + ~1) + ((~x + 1) mod 4))
A047551: 0 1 6 7 8 9 14 15 16 17 22 23 24 25 30 31
((2x + 1) + (x2 div 4))
A004116: 1 3 6 9 13 17 22 27 33 39 46 53 61 69 78 87
(x2 div ((2x + ~1) + (x div 2)))
A283302-A107347: 0 1 1 1 1 2 2 3 3 3 4 4 4 5 5 6
((x div ~3) mod (2x + 1))
A195127: 0 2 4 6 7 9 11 12 14 16 17 19 21 22 24 26
(14x + 7)
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(4x2 + 12x + 5)
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(8x2 + 6x + 1)
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((2x + 1) * (1 + (2 * (x div 2))))
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(6x2 + 5x + 1)
A033570: 1 12 35 70 117 176 247 330 425 532 651 782 925 1080 1247 1426
(2x3 + 3x2 + 3x + 1)
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(2x3 + 7x2 + 7x + 2)
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(4x3 + 6x2 + 2x)
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((x div ~4) mod (2x + 1))
A195173: 0 2 4 6 8 9 11 13 15 16 18 20 22 23 25 27
(2x2 + 13x + 6)
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((2x + 1) * (1 - (2 * (x mod 2))))
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((2x + 1) * ((x2 + x) div 2))
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((2x + 1) * ((x2 + ~x) div 2))
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(2x3 + 5x2 + 6x + 2)
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(4x3 + 4x2 + x)
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((2x2 + x) * (2 - (x mod 2)))
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(8x2 + ~6x + 1)
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(6x2 + ~x + ~1)
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(6x2 + ~5x + 1)
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(16x2 + ~8x)
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(2x3 + ~3x2 + 2x)
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(6x2 + 8x + 1)
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(1 + ((x2 div 3) + (x div 2)))
A281333: 1 1 3 5 8 11 16 20 26 32 39 46 55 63 73 83
(1 + ((x2 + ~x + ~1) * (x div 2)))
A140837: 1 1 2 6 23
((2x2 + 4x + 1) - (x div 2))
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(1 + (((x2 + 2x) div 2) + (x div 2)))
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((2x + 5) * (1 + (x div 2)))
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((3 + (x mod 2)) * (1 + (x div 2)))
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(x mod (2 - (3 mod (1 + (x div 2)))))
A324539-A241666: 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0
(((~x + 1) div 3) mod (1 + (x div 2)))
A261348: 0 0 1 1 2 1 2 2 2 2 3 2 3 3 3 3
((x2 + 2x + 1) * (1 + (x div 2)))
A130656: 1 4 18 32 75 108 196 256 405 500 726 864 1183 1372 1800 2048
(2 - ((x div ~2) * (1 + (x div 2))))
A290743: 2 3 4 6 8 11 14 18 22 27 32 38 44 51 58 66
(2 * ((1 + (x div 2)) * (1 + (x div 2))))
A137583: 2 2 8 8 18 18 32 32
((x - ((x div 2) mod 2)) * (1 + (x div 2)))
A215795: 0 1 2 4 12
(x - ((~x + (x mod 2)) * (~1 + (x div 2))))
A247375: 0 1 2 3 8 9 18 19 32 33 50 51 72 73 98 99
((x + 1) - ((~x2 + 2x) * (x div 2)))
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(1 + ((2 mod (1 + (x div 2))) + (x mod 2)))
A076258: 1 2 1 2 3 4 3 4 3 4 3 4 3 4 3 4
(1 + (x div 8) - (x mod 2))
A025821: 1 0 1 0 1 0 1 0 2 1 2 1 2 1 2 1
(1 + (2 * (x mod 4)) - (x mod 2))
A131800: 1 2 5 6 1 2 5 6 1 2 5 6 1 2 5 6
((x2 + ~2x) mod (3 - (x mod 2)))
A265859: 0 1 0 1 2 1 0 1 0 1 2 1 0 1 0 1
(1 + (((x2 + x) div 2) + (x mod 2)))
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(1 + ((2x + (x div 2)) * (x mod 2)))
A165498: 1 3 1 8 1
((3x + 1) * (1 + (x mod 2)))
A166138: 1 8 7 20 13 32 19 44 25 56 31 68 37 80 43 92
((x2 + 3x + 2) div (1 + (x mod 2)))
A168059: 2 3 12 10 30 21 56 36 90 55 132 78 182 105 240 136
((x - (x div ~2)) div (1 + (x mod 2)))
A006368: 0 1 3 2 6 4 9 5 12 7 15 8 18 10 21 11
((x2 div 4) div (1 + (x mod 2)))
A123596: 0 0 1 1 4 3 9 6 16 10 25 15 36 21 49 28
((x2 + 4x + 1) + (x mod 2))
A225227: 1 7 13
A227786: 1 7 13 23 33 47 61 79 97 119 141 167 193 223 253 287
(1 + (5x2 div 2))
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(2 - (1 mod (~x2 + x + 3)))
A135445: 1 1 2 4 10
(1 + ((3x2 + 4x) div 2))
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(x4 + 4x2 + 3)
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(x4 + ~4x2 + 3)
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(1 + (x5 div 2))
A274325: 1 1 17 122 513 1563 3889 8404 16385 29525 50001 80526 124417 185647 268913 379688
(13x + 1)
A190991: 1 14 27 40 53 66 79 92 105 118 131 144 157 170 183 196
(4x2 + 3x + 1)
A033951: 1 8 23 46 77 116 163 218 281 352 431 518 613 716 827 946
((x + 1) + (x div 7))
A082463: 1 2 3 4 5 6 7 9 10
A344742-A342521-A330977-A329135-A325368-A325251-A255805-A207481-A188437-A182768-A078129-A068937-A048107-A047592-A007915-A004709: 1 2 3 4 5 6 7 9 10 11 12 13 14 15 17 18
(17x + 1)
A215137: 1 18 35 52 69 86 103 120 137 154 171 188 205 222 239 256
(x2 + 7x + 1)
A190576: 1 9 19 31 45 61 79 99 121 145 171 199 229 261 295 331
((x + 1) + (2x div 5))
A047333-A039033-A032796: 1 2 3 5 6 8 9 10 12 13 15 16 17 19 20 22
((x + 1) + (2 mod (1 + (x div 4))))
A214678: 1 2 3 4 5 6 7 8 11 12 13 14 15 16 17 18
(1 + (x * ((x + 1) - ((x div 2) mod 2))))
A076862: 1 3 5 10 21
(~x + 23)
A022979: 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8
((x + 1) + (3 * (x div 4)))
A047338: 1 2 3 4 8 9 10 11 15 16 17 18 22 23 24 25
((x + 1) + (2x2 div 3))
A172411: 1 2 5 10
A008822: 1 2 5 10 15 22 31 40 51 64 77 92 109 126 145 166
((x + 1) + ((x2 + 2x) div 3))
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A183859: 1 3 5 9 13 17 23 29 35 43 51 59 69 79 89 101
((x + 1) + (3 * (x + (x mod 2))))
A241263: 1 8 9 16 17 24 25 32 33 40 41 48 49 56 57 64
((x + 1) + ((x + (x mod 2)) div 3))
A026359: 1 2 3 5 6 8 9 10 11 13 14 16 17 18 19 21
(5x2 + ~x + 1)
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(x2 + 9x + 1)
A275591: 1 11 23 37 53 71 91 113 137 163 191 221 253 287 323 361
((x + 1) + ((x2 div 2) mod (x + 1)))
A187012-A081556: 1 2 5 4 8 6 11 8 14 10 17 12 20 14 23 16
(3x div (x2 + ~x + 1))
A267883: 0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0
(x5 + x + 1)
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(x5 + x + ~1)
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(x5 + ~x + 1)
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((x + 1) + (2 * (x div 5)))
A047369-A031482: 1 2 3 4 5 8 9 10 11 12 15 16 17 18 19 22
((x + 1) + (2 * (2x div 3)))
A047387: 1 2 5 8 9 12 15 16 19 22 23 26 29 30 33 36
((x + 1) + (2 * ((x div 2) div 3)))
A340152-A047422-A031487: 1 2 3 4 5 6 9 10 11 12 13 14 17 18 19 20
((x + 1) + ((x - (x mod 3)) div 2))
A295389: 1 2 3 5 6 7 10 11 12 14 15 16 19 20 21 23
((x + 1) + (2 * (2 mod (1 + (x div 2)))))
A316534: 1 2 3 4 9 10 11 12 13 14 15 16 17 18 19 20
(~x + 21)
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((x + 1) + (4 * (x div 3)))
A131959: 1 2 3 8
A191159-A047360: 1 2 3 8 9 10 15 16 17 22 23 24 29 30 31 36
(1 + (x * (4 + (2 mod (x + 1)))))
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(~x + 33)
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(~x + 31)
A022987: 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16
(1 + (2 div (~x + 16)))
A271831-A036608: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3
(x div ((x + ~1) + (x mod 8)))
A025464: 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0
((x + 1) + ((x - (x div 4)) div 2))
A249115: 1 2 4 5 6 8 9 11 12 13 15 16 17 19 20 22
((x + 1) + ((x - (x div 4)) mod 2))
A078796: 1 3 3 5 6 6 8 8 9 11 11 13 14 14 16 16
((x + 1) + ((x - ((x div 2) mod 2)) div 2))
A047255-A039019: 1 2 3 5 7 8 9 11 13 14 15 17 19 20 21 23
(1 mod (~1 + (x * ((x + 1) mod 4))))
A252744: 0 0 1 0 1 1 1 0 1 1 1 0 1 1 1 0
((x + ~1) + ((2 - (x div 2)) mod 4))
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(5x2 + ~4x + 1)
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(x3 + 2x2 + 4x + 1)
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((x + 1) + ((x2 + 2x) div 4))
A013660: 1 2 5 7 11
A184676: 1 2 5 7 11 14 19 23 29 34 41 47 55 62 71 79
((x + 1) + (4 * (x + (x mod 2))))
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(~x3 + 2x2 + 4x + 1)
A225053: 1 6 9 4
(1 + (x * (2 + ((x2 + x) div 2))))
A006004: 1 4 11 25 49 86 139 211 305 424 571 749 961 1210 1499 1831
(1 + (x2 div (3x + 4)))
A062300: 1 1 1 1 2 2 2 2 3 3 3 4 4 4 5 5
(5x2 + ~2x + 1)
A145995: 1 4 17 40 73 116 169 232 305 388 481 584 697 820 953 1096
((x + 1) + (2 * (2x + (x mod 2))))
A306277-A291663: 1 8 11 18 21 28 31 38 41 48 51 58 61 68 71 78
((~x + 1) + (2 * (x2 + (x mod 2))))
A292850: 1 4 7 18
(5x2 + 2x + 1)
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((x + 1) + (2 * (x + (x div 3))))
A085048: 1 4 7 12 15 18 23
((x + 1) + ((x + (x div 4)) div 2))
A286989-A184656: 1 2 4 5 7 9 10 12 14 15 17 18 20 22 23 25
((x + 1) + ((x + ((x div 2) mod 2)) div 2))
A285520: 1 2 4 6 7 8 10 12 13 14 16 18 19 20 22 24
(2 mod (~1 + (x * ((x * (x div 2)) mod 2))))
A269243: 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 2
(x - (2 mod (~x2 + 3x + ~1)))
A295484: 0 1 2 3 7
A073827: 0 1 2 3 7 14
((x + 1) + (5 * (x div 2)))
A327299-A047353: 1 2 8 9 15 16 22 23 29 30 36 37 43 44 50 51
((x + 1) + ((2x + 1) * (x div 2)))
A174114: 1 2 8 11 23 28 46 53 77 86 116 127 163 176 218 233
((x + 1) + ((1 + (x div 2)) * (x div 2)))
A140144: 1 2 5 6 11 12 19 20 29 30 41 42 55 56 71 72
(x - (x2 div ((x + 1) + (x div 2))))
A227145: 0 1 1 2 2 2 3 3 4 4 4 4 5 5 6 6
((x + 1) * (1 + (x mod ~3)))
A162397: 1 ~2 0 4 ~5 0 7 ~8 0 10 ~11 0 13 ~14 0 16
(13x + 13)
A080196: 13 26 39 52 65 78 91 104 117 130 143 156 169 182 195 208
(13 div (x + 1))
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(11x + 11)
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(11 div (x + 1))
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((x + 1) * (1 + (x2 div 3)))
A192735: 1 2 6 16 30 54 91 136 198 280 374 492 637 798 990 1216
((x + 1) * (1 + (2 mod (1 + (x div 2)))))
A134916: 1 2 3 4 15
((x div ~5) mod (x + 1))
A332204-A195181: 0 1 2 3 4 5 5 6 7 8 9 9 10 11 12 13
(17x + 17)
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(17 div (x + 1))
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(15 div (x + 1))
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((1 + (x mod 8)) mod (x + 1))
A118729: 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8
(((x + 1) mod 5) mod (x + 1))
A330358: 0 0 0 0 0 1 2 3 4 0 1 2 3 4 0 1
((1 + ((~x + 2) mod 4)) div (x + 1))
A307791: 3 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
((x + 1) * (5 - (x mod 2)))
A091574: 5 8 15 16 25 24 35 32 45 40 55 48 65 56 75 64
(18 div (x + 1))
A033338: 18 9 6 4 3 3 2 2 2 1 1 1 1 1 1 1
(24 div (x + 1))
A033344: 24 12 8 6 4 4 3 3 2 2 2 2 1 1 1 1
((x + 1) * (1 + ((x2 + x) div 2)))
A006000: 1 4 12 28 55 96 154 232 333 460 616 804 1027 1288 1590 1936
((x + 1) * (1 + ((x2 + 2x) div 2)))
A317614: 1 4 15 32 65 108 175 256 369 500 671 864 1105 1372 1695 2048
((x + 1) * (1 + (x div (2 - (x mod 2)))))
A231407: 1 4 6
A133092: 1 4 6 16 15 36 28 64 45 100 66 144 91 196 120 256
((x + 1) * ((x + 1) + (2 * (x mod 2))))
A081351: 1 8 9 24 25 48 49 80 81 120 121 168 169 224 225 288
(x4 + 2x3 + 2x2 + 2x + 1)
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((x2 + 2x + 1) * (2 - (x mod 2)))
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(2x4 + 4x3 + 2x2)
A254371: 0 8 72 288 800 1800 3528 6272 10368 16200 24200 34848 48672 66248 88200 115200
(x4 + 3x3 + 3x2 + x)
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(x4 + 4x3 + 5x2 + 2x)
A047928: 0 12 72 240 600 1260 2352 4032 6480 9900 14520 20592 28392 38220 50400 65280
(((x + ~1) * (~1 + (x div 2))) div (x + 1))
A286744: 1 0 0 0 0 0 1 1 2 2 3 3 4 4 5 5
(14 div (x + 1))
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(2x2 + 12x + 10)
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((2x + 2) * (3 - (x mod 2)))
A340519: 6 8 18 16 30 24 42 32 54 40 66 48 78 56 90 64
((x + 1) * ((x3 + x2) div 2))
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((2 * ((x div 2) div ~2)) mod (x + 1))
A330239: 0 0 1 2 3 4 3 4 5 6 5 6 7 8 7 8
(20 div (x + 1))
A033340: 20 10 6 5 4 3 2 2 2 2 1 1 1 1 1 1
((x + 1) * ((((x + 1) div 2) div 2) div 2))
A294238: 0 0 0 0 0 0 0 8 9 10 11 12 13 14 15 32
(32 div (x + 1))
A033352: 32 16 10 8 6 5 4 4 3 3 2 2 2 2 2 2
((x + 1) * (2 + (x div 8)))
A082893: 2 4 6 8 10 12 14 16 27 30 33 36 39 42 45 48
((2 + (x mod 8)) mod (x + 1))
A078510: 0 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9
((x + 1) * (x - (2 * ((x div 2) mod 2))))
A326215: 0 2 0 4 20
(2 - ((2 - (x div 4)) div (x + 1)))
A337637: 0 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3
((x2 - (x div 4)) div (x + 1))
A064524: 0 0 1 2 3 4 5 6 6 7 8 9 10 11 12 13
(4x2 + 3x + 2)
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(2 - ((2 * (1 - (x div 2))) div (x + 1)))
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((1 - (x mod (2 + (x mod 2)))) div (x + 1))
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(((x * (1 + (x div 2))) div 2) mod (x + 1))
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((x + 1) * ((x3 + x) div 2))
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(((~x + (x div 4)) div 2) mod (x + 1))
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((8 mod (x + 2)) div (x + 1))
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(x4 + 5x3 + 8x2 + 4x)
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((2x2 + 3x) - (x div 2))
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((x + 1) * ((x + 2) div (2 - (x mod 2))))
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(((x2 + ~2x) + (x mod 2)) div (x + 1))
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(7x2 + 7x)
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(2x3 + 5x2 + 3x)
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(3x3 + 4x2 + x)
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((x * (((x + ~1) div 2) div 2)) div (x + 1))
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(5x2 + 13x + 8)
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((x + ~1) * (~1 + (2x mod 3)))
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((x + ~1) * ((x3 + x) div 2))
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((x2 + ~3x + 2) * (x2 div 2))
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(x4 + ~2x3 + 2x2 + ~x)
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(3x2 + ~7x + 6)
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(x5 + ~x4 + x3 + ~x2)
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(3x3 + x2 + ~4x)
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(x6 + ~x5)
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(7x2 + 1)
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(5x2 + 4x + 1)
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(x4 + 4x2 + 1)
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(x2 + 13)
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((x2 + 1) + (4 mod (x + 1)))
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(x2 + 17)
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(x2 + 15)
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(8x3 + 8x)
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(x4 + 5x2 + 4)
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(4x4 + 4x2)
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(2x4 + ~3x2 + 1)
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(4x4 + ~4x2)
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(x6 + ~x4)
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(x6 + 1)
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(x - ((3 * (x div 2)) div ~2))
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(x - ((((x + ~1) div 2) div 2) div ~2))
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((x div (~4 + (x mod 2))) div ~2)
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(x - (((x + 1) mod 4) div ~2))
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((x + 2) - ((x div 4) div ~2))
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(x - ((x2 + 4x + 4) div ~2))
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(x - ((x + (x div 4)) div ~2))
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(x - ((x + ((x div 2) mod 2)) div ~2))
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(((~x + 1) div 3) * (x div ~2))
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((x2 div ~2) * (x div ~2))
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(((x mod 3) mod 2) - (x div ~2))
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(~7 * (x div ~2))
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((x div 8) - (x div ~2))
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(2 - ((~x + 2) div (2 - (x div ~2))))
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((2x * (x mod 2)) - (x div ~2))
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((x3 + 2x2) - (x div ~2))
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((2 * (x mod 2)) - (x2 div ~2))
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((1 + (x mod 7)) mod 2)
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((1 + (x2 div 5)) div 2)
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(12x + 10)
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((x mod (1 + ((x + 2) div 3))) mod 2)
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(2 * ((x + 1) - ((~x + 1) div 3)))
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((3 mod (1 + (x div 3))) mod 2)
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(((x + 1) mod (1 + (x div 3))) mod 2)
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((2x mod (1 + (x div 3))) mod 2)
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(2 + (4 div (1 + (x mod 3))))
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((x - (x div (1 + (x mod 3)))) mod 2)
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((1 + (x2 div (1 + (x div 2)))) mod 2)
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((1 + (6 mod (x + 1))) mod 2)
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(2x2 + 10x + 6)
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((1 + ((2 - (x div 2)) mod (x + 1))) mod 2)
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(2x3 + 2x2 + 4x + 2)
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((x div ~9) mod 2)
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((x mod ~9) mod 2)
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(x - (2 * ((x div 2) div ~3)))
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((x mod (2 - (x div ~3))) mod 2)
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(0 - (x div (~2 + (x div ~3))))
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(2 * ((2x + 1) - (x div ~2)))
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(2 * (1 + (2 * (1 + (2 * (x div 2))))))
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(((x + 1) mod 7) mod 2)
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(((x + ~1) div 7) mod 2)
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(((x + 2) mod 7) mod 2)
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(x2 mod 14)
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(((~x + 2) div 7) mod 2)
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(((~x + 2) mod 7) mod 2)
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((x mod (~1 + (2 * (x div 3)))) mod 2)
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(((x + 1) - ((x mod 3) div 2)) div 2)
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(x - (2 * (x div ~5)))
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((x2 div ~5) mod 2)
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(x - (2 * (~1 + (x div ~4))))
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(2 * (1 + (2 * (x - (x div ~2)))))
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((x mod (1 + (((x + 1) div 2) div 2))) div 2)
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(2 + (2 mod (~1 + (2 * ((x + ~1) div 2)))))
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(x + ~34)
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(2 + (x div 15))
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(((x + 2) mod 9) mod 2)
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(((~x + 2) mod 9) mod 2)
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((x div (1 + (x div 8))) mod 2)
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((x div (1 + (x mod 8))) mod 2)
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((1 + (x2 div 8)) div 2)
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((1 + (x div (2 + (x div 4)))) div 2)
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((x mod (~1 + (2 * (x div 4)))) mod 2)
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((1 + ((x - (x div 4)) div 2)) mod 2)
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(2x2 + 14)
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((x mod (~1 + (2 * (~2 + (x mod 2))))) mod 2)
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(2 + (2 div (1 + ((x + 1) mod 4))))
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((x mod (1 + ((x + 1) mod 4))) mod 2)
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((x mod (1 + ((x + ~1) mod 4))) mod 2)
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((x mod (1 + ((x + 2) mod 4))) div 2)
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(2 * ((2x + 1) div 5))
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(((1 + (x div 2)) mod 5) mod 2)
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(x - (2 * ((x + 1) div 5)))
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(((x2 + ~1) div 5) mod 2)
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((((x + ~1) div 2) div 5) mod 2)
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((x - ((x div 2) div 5)) mod 2)
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(x - (2 * ((x div 2) mod 5)))
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(2 * (2x2 mod 5))
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(3x mod 10)
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((x2 + x) mod 10)
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(2x - (x mod 10))
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((~x2 + 1) mod 10)
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(x3 mod 10)
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(x - (2 * ((~x + 1) div 5)))
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(x - (2 * ((~x + 2) div 5)))
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(2 + (5 * (x + (x mod 2))))
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(x2 + ~2x + 10)
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(2 * (2x - (x mod 5)))
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(((x + 1) - ((~x + 2) div 4)) div 2)
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((x mod (~1 + ((~x + 2) div 4))) mod 2)
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((x mod (1 + ((~x + 2) mod 4))) div 2)
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(((x + 1) mod (1 + (x div 4))) div 2)
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(((x + ~1) mod (1 + (x div 4))) div 2)
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((x div 2) - ((1 + (x div 4)) div 2))
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(((x + 1) mod (1 + (x mod 4))) div 2)
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(2x - ((1 + (x mod 4)) div 2))
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(2x - ((~1 + (x mod 4)) div 2))
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((x mod ((x + 1) - (x mod 4))) mod 2)
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(2 * (1 + (2 * ((x + (x div 2)) div 2))))
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(2 * ((2x + 3) + (x div 2)))
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((x2 mod (4x + 1)) mod 2)
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((x2 div (3 + (x div 2))) mod 2)
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((1 + (((~x + 1) * (x div 2)) div 2)) mod 2)
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(((x + 1) mod (3 + (x mod 2))) div 2)
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(2 + (2 mod ((x + ~3) - (x mod 2))))
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(x div (2 + (x div (3 + (x mod 2)))))
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((x - (x mod (~3 + (x mod 2)))) div 2)
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(2 + ((x mod 5) div 3))
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((x - ((x div 3) mod 3)) div 2)
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((x - ((x div 3) mod 3)) mod 2)
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(((x2 div 3) mod 3) mod 2)
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((3 * ((x + 1) + (x div 2))) div 2)
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((x mod 2) - (((x + 1) div 3) mod 2))
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((x mod (x - ((x + 1) mod 3))) div 2)
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(x - (2 * (x div ~6)))
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(x - ((3 * (x div ~2)) div 2))
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(x - (2 * (((x + 1) div 2) div 3)))
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((x - (((x + 1) div 2) div 3)) mod 2)
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(((((x + 1) div 2) div 2) mod 3) mod 2)
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(((((x + ~1) div 2) div 2) div 3) mod 2)
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(((((x + ~1) div 2) div 2) mod 3) div 2)
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(((x mod 8) mod 3) mod 2)
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(2 + (8x div 3))
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((x mod ~11) mod 2)
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((x - (x div 12)) div 2)
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((x - (x div 12)) mod 2)
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(x - ((3 * (x div 4)) div 2))
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((3 * (x2 div 4)) div 2)
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(((x mod (2 + (x div 2))) div 3) mod 2)
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((x - ((~2 + (x div 2)) div 3)) div 2)
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((3 * ((x2 + x) div 2)) div 2)
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(x - (2 * (((~x + 2) div 2) div 3)))
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A047581-A039067: 0 1 2 5 6 7 8 9 10 13 14 15 16 17 18 21
(3x2 + 6x + 8)
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(x - (2 * ((~2x + 1) div 3)))
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((3 * (2x + (x div 2))) div 2)
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(2 * (2 - ((1 - (x div 2)) div 3)))
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(x - (2 * ((1 - (x div 2)) div 3)))
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((x - ((1 - (x div 2)) div 3)) div 2)
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(x - ((x - ((x div 2) div 3)) div 2))
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((x + 2) div (2 + (3 * (x mod 2))))
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(((x2 + x) div 2) mod 6)
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((x + 6) + (x div 4))
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((x * (x + (x div 2))) mod 6)
A076266: 0 1 0 0 0 5 0 4 0 3 0 2 0 1 0 0
(((x * (x div 3)) mod 3) div 2)
A144194: 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0
(((x * (x div 3)) mod 3) mod 2)
A144596: 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0
(x - ((x - ((~x + 1) mod 3)) div 2))
A096445: 1 1 2 2 2 4 4
(2 + ((x + (x div 4)) div 3))
A231151: 2 2 2 3 3 4 4 4 5 5 6 6 7 7 7 8
(2 * ((x + 3) + (2 * (x mod 2))))
A124349: 6 12 10 16 14 20 18 24 22 28 26 32 30 36 34 40
((x mod (~2 - (x div 3))) mod 2)
A260446-A096268: 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0
(x + (x div 2) - (2 * (x div 3)))
A063201: 0 1 3 2 4 5 5 6 8 7 9 10 10 11 13 12
((x * ((x div 2) * (x div 3))) mod 2)
A328981: 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1
(2 + (x div ((x + ~1) + (x mod 3))))
A276857-A244893: 2 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3
((2x + 2) - ((x mod 3) div 2))
A047261: 2 4 5 8 10 11 14 16 17 20 22 23 26 28 29 32
(4x - ((x mod 3) div 2))
A083030: 0 4 7 12 16 19 24 28 31 36 40 43 48 52 55 60
(2 + ((x mod 3) mod 2) - (x mod 2))
A106253: 2 2 2 1 3 1 2 2 2 1 3 1 2 2 2 1
(2 + ((2 mod (~x2 + 2)) mod 3))
A022922: 2 2 2 3 2 2 3 2 2 3 2 2 3 2 2 3
((1 + ((x * (x div 4)) div 2)) div 2)
A161422: 0 0 0 0 1 1 2 2 4 5
((1 + (x mod ((x + ~2) + (x div 2)))) mod 2)
A076213: 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 0
((1 + (8 div (x + 2))) mod 2)
A186727: 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1
(((x * (x div 2)) div (x + 3)) mod 2)
A037828: 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1
(((~x2 + 2x) div (x + 3)) mod 2)
A288508: 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1
(2 + ((~1 + (x div 2)) mod (2x + 1)))
A183193: 2 4 2 2 3 3 4
(2 + ((2x + 1) * (x div 4)))
A112727: 2 2 2 2 11
(((x2 + 1) div (2x + ~1)) mod 2)
A285162: 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 1
(x - (((x + ~1) mod (1 + (x div 2))) div 2))
A176842: 0 1 2 3 4 5 6 6 7 8 9 9 10 11 12 12
(((x2 + 1) mod (1 + (x div 2))) mod 2)
A073059: 0 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0
((6 mod (1 + (x div 2))) mod 2)
A102681-A097470-A065716-A049800-A037832: 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0
(((2x + ~4) mod (1 + (x div 2))) mod 2)
A285931: 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0
((4x mod (1 + (x div 2))) mod 2)
A144601: 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0
(((2 + (x div 2)) * (1 + (x div 2))) div 2)
A008805: 1 1 3 3 6 6 10 10 15 15 21 21 28 28 36 36
(x div (2 + (2x div (1 + (x div 2)))))
A092278: 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 3
((2x2 mod (1 + (x div 2))) mod 2)
A284976-A277149-A011722: 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0
((3x mod (1 + (x div 2))) mod 2)
A116374: 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1
((x * ((x div 2) * (1 + (x div 2)))) div 2)
A290168: 0 0 2 3 12 15 36 42 80 90 150 165 252 273 392 420
(((~x2 + x) mod (1 + (x div 2))) mod 2)
A193139: 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0
((x - (x2 mod (1 + (x div 2)))) mod 2)
A258021-A033684: 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0
(~2 + (x div (~1 + ((~x + 2) * (x div 2)))))
A133852: ~2 ~3 ~4 ~4 ~3
(x div (2 + (x div (3 - (x mod 2)))))
A230773: 0 0 1 1 1 1 1 1 2 1 2 1 2 1 2 1
((1 + (x2 div (2 - (x mod 2)))) div 2)
A147685: 0 1 1 5 4 13 9 25 16 41 25 61 36 85 49 113
(2 * (((x + 1) div 2) div (1 + (x mod 2))))
A240828: 0 0 2 2 4 2 6 4 8 4 10 6 12 6 14 8
(2 * ((x + 1) + (x div 5)))
A225241: 2 4 6 8 10 14 16 18 20 22 26 28 30 32 34 38
(2 * (1 + (x * (1 + (2 * (x div 2))))))
A245764: 2 4 14 20 42 52 86 100 146 164 222 244 314 340 422 452
(2x3 + 2x2 + 2x + ~2)
A155120: ~2 4 26 76 166 308 514 796 1166 1636 2218 2924 3766 4756 5906 7228
(2 * (1 + (x * ((x + ~1) + (x mod 2)))))
A245766: 2 4 6 20 26 52 62 100 114 164 182 244 266 340 366 452
(((x + 1) + (x div 8)) div 2)
A276796: 0 1 1 2 2 3 3 4 5 5 6 6 7 7 8 8
(((x + 1) + ((x div 2) * (x div 2))) div 2)
A166515: 0 1 2 2 4 5 8 8 12 13 18 18 24 25 32 32
(2 + ((x div ~3) mod (x + 1)))
A196165-A020892: 2 3 4 5 5 6 7 7 8 9 9 10 11 11 12 13
(((x + 1) * (x div 5)) mod 2)
A144197: 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0
(2 + ((x + 1) * (1 + (x div 4))))
A154664: 3 4 5 6 12
(((x + 1) * (1 + (x div 4))) mod 2)
A236677-A190236: 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0
(2 - (((x + 1) * (x div ~2)) div 2))
A050679: 2 3 4 6 7 11
((16 mod (x + 1)) mod 2)
A285139: 0 0 1 0 1 0 0 0 1 0 1 0 1 0 1 0
(((2x + ~8) mod (x + 1)) mod 2)
A342845-A180160-A045887-A011724: 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0
((x2 + 7x + 6) div 2)
A141214: 3 7 12 18 25 33 42 52 63 75 88 102 117 133 150 168
(((x2 div 4) mod (x + 1)) mod 2)
A069846-A069843: 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0
(((2 + (x2 div 2)) mod (x + 1)) mod 2)
A288106: 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0
(x - (((x div 2) - (2 div (x + 1))) div 2))
A060151: 1 2 2 3 3 4 5 6 6 7 8 9 9 10 11 12
(x3 + ~x2 + ~4x + ~4)
A153258: ~4 ~8 ~8 2 28 76 152 262 412 608 856 1162 1532 1972 2488 3086
(((x + 1) * ((x + ~2) mod (x + 2))) div 2)
A175631: 0 2 0 2 5 9 14 20 27 35 44 54 65 77 90 104
(2x - (((x + 1) * (x div 2)) mod 2))
A047403: 0 2 3 6 8 10 11 14 16 18 19 22 24 26 27 30
(((x + 1) * (x2 - (x div 2))) div 2)
A220788: 0 1 4 16
((2x + 2) + (x div 5))
A276383-A094390: 2 4 6 8 10 13 15 17 19 21 24 26 28 30 32 35
((2x + 2) + ((x div 2) div 3))
A292651: 2 4 6 8 10 12 15 17 19 21 23 25 28 30 32 34
((2x + 2) + (((x + 1) div 2) div 2))
A184978: 2 4 6 9 11
A252169: 2 4 6 9 11 13 15 18 20 22 24 27 29 31 33 36
((2x + 2) + (x div 8))
A249124-A094041: 2 4 6 8 10 12 14 16 19 21 23 25 27 29 31 33
((3x + 2) - (x div 4))
A330144-A329924-A292988-A187341-A108589: 2 5 8 11 13 16 19 22 24 27 30 33 35 38 41 44
((2x + 2) + (x2 div 4))
A014616: 2 4 7 10 14 18 23 28 34 40 47 54 62 70 79 88
(((x + 1) + (x div 2)) * ((x + 1) div 2))
A152749: 0 2 4 10 14 24 30 44 52 70 80 102 114 140 154 184
(1 - ((~x3 + ~x2 + x) div 2))
A181490: 1 2 6 18
(((x + ~1) * ((x2 + 1) div 2)) div 2)
A212561: 0 0 1 5 12 26 45 75 112 164 225 305 396 510 637 791
((4x + 4) + ((x + ~1) div 2))
A190368: 3 8 12 17 21 26 30 35 39 44 48 53 57 62 66 71
((2 * (x div 3)) - ((x + ~1) div 2))
A008612: 1 0 0 1 1 0 2 1 1 2 2 1 3 2 2 3
(2 div (8 - ((x + ~1) div 2)))
A340001: 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2
(x - ((~x3 + 3x2 + ~2x) div 2))
A060354: 0 1 2 6 16 35 66 112 176 261 370 506 672 871 1106 1380
(1 - (x mod (~2x2 + 2x + ~2)))
A116735: 1 2 5 12 23 38 57 80 107 138 173 212 255 302 353 408
(2x2 + 18)
A255848: 18 20 26 36 50 68 90 116 146 180 218 260 306 356 410 468
(((x2 + 1) + (x div 4)) div 2)
A192225: 0 1 2 5
A120615: 0 1 2 5 9 13 19 25 33 42 51 62 74 86 100 114
(((x2 + 1) + ((x div 2) mod 2)) div 2)
A104563: 0 1 3 5 8 13 19 25 32 41 51 61 72 85 99 113
((x5 + x3) div 2)
A168178: 0 1 20 135 544 1625 3996 8575 16640 29889 50500 81191 125280 186745 270284 381375
((x5 + ~x3) div 2)
A321672: 0 0 12 108 480 1500 3780 8232 16128 29160 49500 79860 123552 184548 267540 378000
(((x div 5) div ~2) mod 2)
A023971: 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0
((x - (x div ~8)) div 2)
A100679: 0 1 1 2 2 3 3 4 4 5 6 6 7 7 8 8
(x - (2 * ((x div 4) div ~2)))
A039141-A008541: 0 1 2 3 6 7 8 9 10 11 12 13 16 17 18 19
((x - ((x div 4) div ~2)) div 2)
A214672: 0 0 1 1 2 3 3 4 4 5 5 6 7 7 8 8
((x + 2) - (((x div 2) div ~2) div 2))
A081023: 2 3 5 6 7 8 9 10 11 12 14 15 16 17 18 19
(4x - (x div ~4))
A004958: 0 5 9 13 17 22 26 30 34 39 43 47 51 56 60 64
(((x + (x div 4)) div ~2) mod 2)
A171587: 0 1 1 0 1 1 0 0 1 0 0 1 0 0 1 1
(((~x + 1) mod (2 - (x div ~2))) mod 2)
A088592: 1 0 0 0 1 1 0 0 1 0 1 0 1 0 1 0
((x + 2) - (x div (~2 + (x div ~2))))
A139143: 2 4 5 6 7 8 10 11 12 13 14 15 16 17 18 19
(4 * (1 + ((x + 1) div 3)))
A105675: 4 4 8 8 8 12 12 12
(16x + 12)
A158953-A098502: 12 28 44 60 76 92 108 124 140 156 172 188 204 220 236 252
(8x2 + 8x + 4)
A108099: 4 20 52 100 164 244 340 452 580 724 884 1060 1252 1460 1684 1924
(x - (4 * (x div ~3)))
A047320: 0 5 6 7 12 13 14 19 20 21 26 27 28 33 34 35
(x + ~28)
A023470: ~28 ~27 ~26 ~25 ~24 ~23 ~22 ~21 ~20 ~19 ~18 ~17 ~16 ~15 ~14 ~13
(~x + 22)
A022978: 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7
(x2 mod 20)
A070643-A070442: 0 1 4 9 16 5 16 9 4 1 0 1 4 9 16 5
(x mod (2 + (x mod 10)))
A103303: 0 1 2 3 4 5 6 7 8 9
A141022: 0 1 2 3 4 5 6 7 8 9 0 2 0 3 2 1
(x - (4 * (x div 5)))
A053824: 0 1 2 3 4 1 2 3 4 5 2 3 4 5 6 3
(2 * (x - (2 * (x div 5))))
A230865: 0 2 4 6 8 6 8 10 12 14 12 14 16 18 20 18
((x div (2 + (x mod 5))) mod 2)
A037814-A011710: 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1
((x - ((~1 + (x div 4)) div 2)) mod 2)
A344649: 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0
(x mod (2 + (((x + ~1) div 3) mod 2)))
A328616-A260736: 0 1 0 1 1 2 0 1 0 1 1 2 0 1 0 1
(((3 * (2 + (x div 2))) div 2) div 2)
A108356: 1 1 2 2 3 3 3 3 4 4 5 5 6 6 6 6
(x mod (2 + (((x + ~2) div 3) mod 2)))
A341514-A276084-A230403-A168570: 0 1 0 1 0 2 0 1 0 1 0 2 0 1 0 1
(x - (4 * ((x div 2) div 3)))
A329243-A215089-A094937: 0 1 2 3 4 5 2 3 4 5 6 7 4 5 6 7
(2 * ((x - ((x div 2) div 3)) div 2))
A202103: 0 0 2 2 4 4 4 6 6 8 8 10
(x - (4 * ((~x + 1) div 3)))
A047275: 0 1 6 7 8 13 14 15 20 21 22 27 28 29 34 35
(4 * (x - ((~x + 1) div 3)))
A267958: 0 4 12 16 20 28 32 36 44 48 52 60 64 68 76 80
((2x mod (2 + (x div 3))) mod 2)
A309163-A104853: 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0
(2x div (4 + (x div 3)))
A099396: 0 0 1 1 1 2 2 2 2 2 2 3 3 3 3 3
((x2 mod (2 + (x div 3))) div 2)
A319687-A085861: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
((x div ((x + ~2) - (x mod 3))) mod 2)
A115517: 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1
(2 + (x mod (2 - ((x mod 3) div 2))))
A244228: 2 3 2 3 2 2 2 3 2 3 2 2 2 3 2 3
(2 * ((1 + ((x2 + x) div 2)) div 2))
A192447: 0 2 4 6 10 16 22 28 36 46 56 66 78 92 106 120
(4x2 + ~16x + 20)
A128445: 20 8 4 8 20 40 68 104 148 200 260 328 404 488 580 680
((((~x + 2) mod (2x + 1)) div 2) div 2)
A091373-A056172: 0 0 0 1 1 2 2 2 2 3 3 3 3 4 4 4
(20x + 4)
A139245: 4 24 44 64 84 104 124 144 164 184 204 224 244 264 284 304
((((x + 1) + (x div 4)) div 2) div 2)
A301461: 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4 4
(2 * ((6 mod (x + 1)) mod 2))
A178926: 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
(((((~x + 1) div 2) mod (x + 1)) div 2) mod 2)
A271591: 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0
(2 + (((x2 div 2) mod (x + 1)) mod 2))
A081147: 2 2 2 2 3 2 2 2 3 2 2 2 3 2 2 2
(2 * ((3x + 2) + (x div 2)))
A113804: 4 10 18 24 32 38 46 52 60 66 74 80 88 94 102 108
(2 + (((x + ~1) * (1 + (x div 2))) div 2))
A323383: 1 2 3 4 6 8 12
((x div 3) - (((x + ~1) div 2) div 2))
A008679: 1 0 0 1 1 0 1 1 1 1 1 1 2 1 1 2
(((x3 + ~3x2 + 2x) div 2) div 2)
A011886: 0 0 0 1 6 15 30 52 84 126 180 247 330 429 546 682
(x - (2 * (((x div 2) div ~2) div 2)))
A039128: 0 1 4 5 6 7 8 9 10 11 14 15 16 17 18 19
(2x - ((x mod ~4) div 2))
A047492: 0 4 5 7 8 12 13 15 16 20 21 23 24 28 29 31
(2 + ((x2 - (x div ~2)) div 2))
A125621: 2 3 4 7 11 16
(2 + (((x mod 5) div 2) div 2))
A217619: 2 2 2 2 3 2 2 2 2 3 2 2 2 2 3 2
(32x + 8)
A305075: 8 40 72 104 136 168 200 232 264 296 328 360 392 424 456 488
(((x mod (2 + (x div 3))) div 2) div 2)
A339172-A323514-A302047-A284261-A278701-A239705-A229660-A188300-A122840-A102683-A086075-A086016-A083910-A056976-A044940-A037878-A037860-A037825-A026830-A026803-A025468-A025465-A025462: 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
(((x - ((x mod 3) div 2)) div 2) div 2)
A294235: 0 0 0 0 1 1 1 1 1 2 2 2 3 3 3 3
(x div (4 + ((x mod 3) mod 2)))
A089050: 0 0 0 0 0 1 1 1 2 2 2 2 3 2 3 3
(8 * ((x + 1) + (x div 2)))
A259751: 8 16 32 40 56 64 80 88 104 112 128 136 152 160 176 184
(2 + (((x2 + 3x + 2) div 2) div 2))
A039825: 2 3 5 7 9 12 16 20 24 29 35 41 47 54 62 70
((x mod (~2 + (x mod ~4))) mod 2)
A037913: 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0
((x - ((((x + 1) div 2) div 2) div 2)) mod 2)
A191152: 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 1
((x mod (2 + (((x + ~1) div 2) mod 2))) mod 2)
A283318: 0 1 0 0 1 1 0 1 0 1 0 0 0 1 0 0
64x
A152691: 0 64 128 192 256 320 384 448 512 576 640 704 768 832 896 960
(((x mod ~7) div 2) mod 2)
A191162: 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 1
(~x + 34)
A022990: 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19
(x2 div 32)
A011881: 0 0 0 0 0 0 1 1 2 2 3 3 4 5 6 7
(x2 mod 32)
A070454: 0 1 4 9 16 25 4 17 0 17 4 25 16 9 4 1
((x div (~2 + (x div 8))) mod 2)
A057215: 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1
((x div (2 + (x mod 8))) mod 2)
A049986: 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1
((x mod (2 + ((x div 4) mod 2))) div 2)
A302049-A078926: 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0
((x div (~2 + ((x div 4) mod 2))) mod 2)
A286049: 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1
(x div (4 * (2 + (x mod 4))))
A035694: 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0
32x2
A244082: 0 32 128 288 512 800 1152 1568 2048 2592 3200 3872 4608 5408 6272 7200
((x mod (6 + (x mod 2))) mod 2)
A268384: 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1
(4 + ((x mod (2 + (x mod 2))) div 2))
A091844: 4 4 4 4 4 5 4 4 4 4 4 5 4 4 4 4
(x - (4 * ((x div 2) mod 4)))
A320283: 0 1 ~2 ~1 ~4 ~3 ~6 ~5 8 9 6 7 4 5 2 3
(1 - (x div ~14))
A204562: 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3
(x2 + 14)
A114962: 14 15 18 23 30 39 50 63 78 95 114 135 158 183 210 239
((x2 + ~x) div 16)
A011869: 0 0 0 0 0 1 1 2 3 4 5 6 8 9 11 13
(x - (2 div (x + ~16)))
A339889-A337379-A337138-A330938-A323035-A297289-A296759-A288139-A253781-A209061-A194897-A178210-A123093-A121684-A121176-A115105-A115063-A097745-A046100-A044965-A044920-A044827-A043719-A037144-A033067-A032965-A022766-A013938: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17
(x3 mod 16)
A070478: 0 1 8 11 0 13 8 7 0 9 8 3 0 5 8 15
(x2 + x + 10)
A187710: 10 12 16 22 30 40 52 66 82 100 120 142 166 192 220 250
((x + 2) - ((~x + 2) div 8))
A302058: 2 3 4 6 7 8 9 10 11 12 13 15 16 17 18 19
(x - (2 * ((~x + 2) div 8)))
A192225: 0 1 2 5
A039135: 0 1 2 5 6 7 8 9 10 11 12 15 16 17 18 19
(16x2 + 32x)
A114444: 0 48 128 240 384 560 768 1008 1280 1584 1920 2288 2688 3120 3584 4080
(((x div 2) - (x div 8)) mod 2)
A284487-A269723: 0 0 1 1 0 0 1 1 1 1 0 0 1 1 0 0
(((x - ((~x + 2) div 4)) div 2) mod 2)
A273129: 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1
(4 + ((x + (x div 2)) div 4))
A134992: 4 4 4 5 5 5 6 6 7 7 7 8 8 8 9 9
(2 + ((x + ~2) div (2 + (x div 4))))
A218461-A186189-A083375: 1 1 2 2 2 3 3 3 3 3 4 4 4 4 4 4
(((x + ~2) div (2 + (x div 4))) mod 2)
A138149: 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0
((2x mod (2 + (x div 4))) mod 2)
A324824: 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0
(2x div (4 + (x div 4)))
A342882-A052146: 0 0 1 1 1 2 2 2 2 3 3 3 3 3 4 4
(((~x + 1) div (2 + (x div 4))) mod 2)
A138150: 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1
((2x + 2) - ((x div 4) mod 2))
A225773: 2 4 6 8 9 11 13 15 18 20 22 24 25 27 29 31
(((x div 2) - ((x div 4) mod 2)) div 2)
A173711: 0 0 0 0 0 0 1 1 2 2 2 2 2 2 3 3
((x mod 2) - (2 * ((x div 4) mod 2)))
A318702: 0 1 0 1 ~2 ~1 ~2 ~1 0 1 0 1 ~2 ~1 ~2 ~1
(1 - (2 * ((x - (x div 4)) mod 2)))
A143431-A112865: 1 ~1 1 ~1 ~1 1 ~1 1 1 ~1 1 ~1 ~1 1 ~1 1
(((x + 1) mod (2 + (x mod 4))) mod 2)
A102863: 1 0 1 0 1 0 1 1 1 1 1 0 1 0 1 1
((x2 div (2x + 8)) mod 2)
A037811: 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1
(x - (2 * (((2 - (x div 2)) div 2) div 2)))
A039150-A008539: 0 1 2 3 4 5 8 9 10 11 12 13 14 15 18 19
(2 + ((x - ((2 - (x div 2)) div 2)) div 2))
A309077-A247908: 1 2 3 3 4 4 5 6 6 7 8 8 9 9 10 11
((((x + ~2) mod (2 + (x div 2))) div 2) div 2)
A027352: 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1
((((x + ~2) mod (2 + (x div 2))) div 2) mod 2)
A174793: 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 0
(2 * (x - (x mod (~2 + ((x div 2) mod 2)))))
A282939: 0 4 4 6 8 12 12 14 16 20 20 22 24 28 28 30
((((x2 + (x div 2)) div 2) div 2) mod 2)
A080887: 0 0 1 0 0 0 1 1 1 1 0 1 1 1 0 0
(2 * (2 + ((x + ~2) mod (2 + (x mod 2)))))
A155874: 4 8 4 6 4 4 4 8 4 6 4 4 4 8 4 6
((x mod (1 - (2 * (2 + (x mod 2))))) mod 2)
A211225: 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0
(1 - ((x + 1) mod ~7))
A309909: 7 6 5 4 3 2 1 7 6 5 4 3 2 1 7 6
(x - ((x + 2) div ~7))
A292638-A059561: 1 2 3 4 5 6 8 9 10 11 12 13 14 16 17 18
(0 - (x2 div ~7))
A036405: 0 1 1 2 3 4 6 7 10 12 15 18 21 25 28 33
(x mod (x - ((x + ~1) mod 8)))
A307629-A257849-A239092-A143288-A138953-A131242-A093882-A088118-A053392-A037886-A037850: 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6
(8 + ((~1 + (x div 2)) div 2))
A108186: 7 7 8 8 8 8 9 9 9 9 10 10 10 10 11 11
(((x2 + x) div 2) mod 8)
A105332: 0 1 3 6 2 7 5 4 4 5 7 2 6 3 1 0
(x - (2 div (~8 + (x div 2))))
A343822-A331995-A324109-A322911-A322901-A321291-A320230-A318991-A317294-A303550-A285801-A247160-A179892-A164563-A080944-A076564-A061773: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 16 17
(((~x + 2) - (x div 2)) mod 8)
A078301: 2 1 7 6 4
((x * (2 + (x div 2))) div 8)
A060407: 0 0 0 1 2 2 3 4 6
(1 - ((x + (x div 2)) div 8))
A343190: 1 1 1 1 1 1 0 0 0 0 0 ~1 ~1 ~1 ~1 ~1
(((x div 2) mod 2) - (x div 8))
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(8x2 + ~7x)
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(x - ((~x2 + x) div 8))
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A024182: 0 1 3 4 6 8 10 13 15 18 22 25 29 33 37 42
(x4 div 8)
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(0 - (x div (~2 + ((~x + 2) div 4))))
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(1 - (x div (~2 + ((~x + 2) div 4))))
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(x - (x div (~2 + ((~x + 2) div 4))))
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((x - ((x + (x div 2)) div 4)) div 2)
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(2 - ((~x + 1) div (2 + (x div 4))))
A182009: 2 2 3 3 3 4 4 4 4 4 5 5 5 5 5 5
(x - ((~x + 1) div (2 + (x div 4))))
A058986: 0 1 3 4 5 7 8 9 10 11 13 14 15 16 17 18
(((x + 1) mod 2) - ((x div 4) mod 2))
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((x + 2) + ((x div 2) + (x div 4)))
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(8x2 + ~6x)
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((x + 2) - (x div (~2 + ((~x + 1) div 2))))
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(x - (4 * ((~x + ~2) + (x mod 2))))
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((x mod (2 + ((x * (x mod 2)) div 2))) div 2)
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(((x2 + 5x + 6) div 2) div 2)
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((((1 - (x div 2)) mod (x + 2)) div 2) div 2)
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(2 + ((x2 + ~2) div (x + 4)))
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(((x2 + ~2) div (x + 4)) mod 2)
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(x3 + 6x2 + 8x + 2)
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((x - (x2 div (x + 4))) div 2)
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(2 + (((x2 + ~x) div (x + 2)) mod 2))
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((x + 4) - ((~x + 2) div (x + 2)))
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(2 * ((x + 2) - ((~x + 2) div (x + 2))))
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((((x + ~2) * (x2 div 2)) div 2) div 2)
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((5x + 2) + (x div 2))
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(2 + (((2 mod (x + 1)) + (x div 2)) div 2))
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(((((x + ~1) div 2) * (x div 2)) div 2) div 2)
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((((2 + (x div 2)) * (x div 2)) div 2) div 2)
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(2 + ((x + ~4) div (2 + (x div 2))))
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(((~x + 4) mod (2 + (x div 2))) mod 2)
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(x mod (2 + ((x + ~2) div (2 + (x div 2)))))
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((2x2 mod (2 + (x div 2))) mod 2)
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(4x div (4 + (x div 2)))
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((x + (x div 2)) div (4 + (x div 2)))
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((3x mod (2 + (x div 2))) div 2)
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((x + 2) - ((~x + 1) div (2 + (x div 2))))
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((x - ((~x + 1) mod (2 + (x div 2)))) mod 2)
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(((x2 + ~x) mod (2 + (x div 2))) mod 2)
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(((~x2 + x) mod (2 + (x div 2))) mod 2)
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(((~x2 + 1) mod (2 + (x div 2))) mod 2)
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(2 * ((x3 + 2) + (x div 2)))
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(2x - (x mod (~2 + ((x div 2) mod 2))))
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(((x2 + x) - ((x div 2) mod 2)) div 2)
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A215098: 0 1 2 5 10 15 20 27 36 45 54 65 78 91 104 119
(((x2 + 2x) + ((x div 2) mod 2)) div 2)
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(((x + (x div 2)) * ((x div 2) mod 2)) div 2)
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(2 * ((x + 2) - ((~x + 2) * (x div 2))))
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(x div (2 + ((x + 1) div (2 + (x mod 2)))))
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(1 - ((~x + 2) div (4 + (x mod 2))))
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(x - ((~x + 2) div (4 + (x mod 2))))
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A039187-A001963: 0 1 2 4 5 6 7 8 10 11 12 13 15 16 17 18
((x + ~1) mod (2 + (x mod (2 + (x mod 2)))))
A331216-A317742: 1 0 1 0 1 0 1 0 1 0 1 2 1 0 1 0
(x + (x div 2) - (2 * (~2 + (x mod 2))))
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(2x - (x mod (2 * (~2 + (x mod 2)))))
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(8x2 + ~3x)
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(((x2 + 2) div 3) mod 4)
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(((~x + 1) + ((~x + 2) div 2)) mod 4)
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(((x2 + x) div ~2) mod 4)
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(((x2 + 3x + 2) div 2) mod 4)
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28x
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(16x2 + ~4x)
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((~x + ((~x + 1) mod 3)) mod 4)
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(x - (4 * (~x + (x mod 3))))
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(1 - ((~x + (x mod 3)) div 4))
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((3x2 + x) div 4)
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(12x2 + ~4x)
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((3x2 + ~x) div 4)
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((x + (x2 mod 3)) div 4)
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(8x3 + ~4x)
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(4x * (1 + (x2 div 2)))
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(x2 - ((x2 + x) div 4))
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(4x - ((~x + 2) div 4))
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((3x2 + 2x) div 4)
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(12x2 + ~8x)
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((3x2 + ~4x) div 4)
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((x * ((x * (x div 2)) mod 2)) div 4)
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(2x - ((x + (x div 2)) div 4))
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((1 + (x div 4)) * (x div 4))
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(6x + (x div 4))
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((4x + 4) + (x div 4))
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((((x + 1) div 2) div 2) * (x div 4))
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(x - compr(\x.((x div 2) mod 2),(x div 4)))
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((1 + (x div 4)) * (x mod 4))
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((x4 + ~x2) div 4)
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((x2 + x) - (x2 div 4))
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(4x3 + ~3x)
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(2 * ((x + 2) + (x div 5)))
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(2 * ((x + 2) + (3 * (x div 2))))
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(2 * ((x + 2) + ((x div 2) div 3)))
A242396: 4 6 8 10 12 14 18 20 22 24 26 28 32 34 36 38
((x2 mod (3x + ~2)) mod 2)
A219558: 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0
(((~x + ((x mod 3) div 2)) div 2) mod 2)
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(2 * ((x * ((x2 + 1) div 2)) div 2))
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((x + 2) - ((~x + ((x div 2) mod 2)) div 2))
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(x - (2 * ((~x + ((x div 2) mod 2)) div 2)))
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(2 * (x - ((~x + ((x div 2) mod 2)) div 2)))
A157932: 0 4 6 8 12 16 18 20 24 28 30 32 36 40 42 44
(((x * (x mod (2 + (x mod 2)))) div 2) mod 2)
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((1 mod (2 + (x * (2 - (x div 2))))) mod 2)
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(x div (2 * (2 - ((x * (x div 2)) mod 2))))
A130845: 0 0 0 1 1 1 1 3 2 2 2 5 3 3 3 7
((2x + 2) - ((x * (x div 2)) mod 2))
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(((~x + 2) div (2 + (x * (x mod 2)))) mod 2)
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(x - ((2 - ((x * (x mod 2)) div 2)) div 2))
A063281: ~1 0 1 3 3 5 5 8 7 10 9 13 11 15 13 18
((x3 + 2x2 + 3x + 6) div 2)
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((3x2 + 7x + 2) div 2)
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(((x div ~4) mod (x + 2)) div 2)
A189663: 0 1 1 2 2 2 3 3 4 4 4 5 5 5 6 6
(((x + 2) * (2 + (x * (x mod 2)))) div 2)
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(x - ((~x2 + ~4x + ~2) div 2))
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((x2 + x + 1) div (x + 4))
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(x - ((x2 + 1) div (x + 4)))
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(3x2 + 16x + 16)
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((2x + 4) + (3 * (x div 2)))
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(((~x2 + (x div 2)) div (x + 2)) mod 2)
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((x3 + ~4x2 + 5x) div 2)
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(x - (2 * (x2 mod (~2x + 1))))
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(4x + (2x div 3))
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(4x + ((x2 + x) div 2))
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(4x + ((x2 + ~x) div 2))
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(((x div 5) * (x div 2)) mod 2)
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((((x + ~2) div 3) * (x div 2)) mod 2)
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(1 - (((x div 3) - (x div 2)) div 2))
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(((((x + 1) div 2) div 2) * (x div 2)) mod 2)
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((2 div (8 - (x div 2))) mod 2)
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((((~x + 2) mod 4) + (x div 2)) div 2)
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((((x + (x div 2)) div 2) * (x div 2)) mod 2)
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((4x + 4) div (2 + (x div 2)))
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((2x * (x div 2)) div (2 + (x div 2)))
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((2x + (x mod 2)) div (2 + (x div 2)))
A078120: 0 1 1 2 2 2 2 3 2 3 2 3 3 3 3 3
(x + (((x div 2) mod 2) + (2 * (x div 2))))
A047439: 0 1 5 6 8 9 13 14 16 17 21 22 24 25 29 30
((x2 mod 3) - ((x div 2) mod 2))
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(((x + 1) * (x mod 2)) + ((x div 2) mod 2))
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((x div 8) + ((x div 2) mod 2))
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(2x - (x mod (2 - ((x div 2) mod 2))))
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(((x * ((x div 2) mod 2)) + (x div 2)) div 2)
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(((x + 1) mod ((~x + 2) - (x div 2))) mod 2)
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((2 - (2 mod ((~x + 2) - (x div 2)))) div 2)
A039960: 1 1 1 1 2 2 3 4 5 5 6 7 8 8 9 10
((((x + 1) mod 3) - (x mod 2)) div 2)
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(2x - (x mod (2 * (2 - (x mod 2)))))
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A047620: 0 1 2 5 8 9 10 13 16 17 18 21 24 25 26 29
((2x2 + 4x + 2) - (x mod 2))
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(((x div 2) div 3) mod (2 + (x mod 2)))
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((~2x + (x div 2)) div (~2 + (x mod 2)))
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(2x - ((x div 2) mod (~2 + (x mod 2))))
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((x2 + ~2x) - (x div (~2 + (x mod 2))))
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(3x2 - (2 * (x mod 2)))
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(((x + 2) - (2 mod (~x2 + 2))) div 2)
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((x3 * (x2 div 2)) div 2)
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(13x + 2)
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26x
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22x
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((3x2 + 7x) div 2)
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((3x2 + 5x) div 2)
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(12x2 + ~2x)
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((3x3 + ~x) div 2)
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(8x2 + 6x)
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((x + 2) + (x div 9))
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((x + 2) + (x mod 9))
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((x + (x mod 9)) div 2)
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(4x2 + 18x)
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((x + 2) + ((x + 1) div 5))
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((x + 2) + (2x div 5))
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((x + (2x div 5)) div 2)
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((x + 2) + ((x div 2) div 5))
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((x + (x2 div 5)) div 2)
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((x + 2) + (2 mod (1 + (x div 4))))
A174908-A136399-A082757-A056167: 2 3 4 5 6 7 8 9 12 13 14 15 16 17 18 19
(x - (2 * (~x + ((x + ~1) div 3))))
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((x + 2) + (x div 12))
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((x + 2) + (3 * (x div 4)))
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(x - (2 * (~x + ((x + ~2) div 3))))
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((x + ((x2 div 2) div 3)) div 2)
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((x + ((x2 + 2x) div 3)) div 2)
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(x2 div ((x + 2) + (x div 3)))
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((2 mod (1 - (x * (x div 3)))) mod 2)
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((x mod (2 - (x * (x div 3)))) mod 2)
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(x - (1 mod (~2 + (x * (x div 3)))))
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((x4 + 2x3 + ~x) div 2)
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(2 - ((~x + (2 div (1 + (x div 2)))) div 2))
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(x - ((~x4 + x3) div 2))
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((5x2 + x) div 2)
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((5x2 + ~x) div 2)
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(x - (x mod (2 - ((x2 + x) div 2))))
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((x5 + x) div 2)
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((x + (x mod 10)) div 2)
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A081596-A028900: 0 1 2 3 4 5 6 7 8 9 5 6 7 8 9 10
((x + 2) + (2 * (x div 5)))
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((x + 2) + (2 * ((x div 2) div 3)))
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((x + ((x mod (1 + (x div 2))) div 2)) div 2)
A060143-A057365-A057363: 0 0 1 1 2 3 3 4 4 5 6 6 7 8 8 9
(x - ((~x + ((~1 + (x div 2)) div 2)) div 2))
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(x - (2 * (~x + ((x div ~2) mod 2))))
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((x + 2) + (4 * (x div 3)))
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((x + 2) + ((((x + 1) div 2) div 2) div 2))
A302569: 2 3 4 5 6 7 8 10 11 12 13 14 15 16 17 19
(~x + 30)
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(18x + 32)
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((x + 2) + (x div ~7))
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(2 - ((~x + (x div 8)) div 2))
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A024745: 2 3 3 4 4 5 5 6 6 6 7 7 8 8 9 9
((x + 2) + (x div (2 + (x div 4))))
A028729: 2 3 5 6 7 8 10 11 12 13 14 15
((x + 2) + (x div (4 + (x div 2))))
A324721-A305732-A183221-A072886: 2 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18
((x * (x mod (4 + (x div 2)))) mod 2)
A288524: 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0
((x + 2) + ((x - ((x div 2) mod 2)) div 2))
A225731-A106577-A068577-A067290-A063450: 2 3 4 6 8 9 10 12 14 15 16 18 20 21 22 24
(10x2 + ~8x)
A152965: 0 2 24 66 128 210 312 434 576 738 920 1122 1344 1586 1848 2130
(x3 + 2x2 + 4x + 2)
A221574: 2 9 26 59 114 197 314 471 674 929 1242 1619 2066 2589 3194 3887
((x + 2) + ((x + (x div 2)) mod 4))
A236629: 2 4 7 5
(5x2 + ~2x + 2)
A295905: 2 5 18 41 74 117 170 233 306 389 482 585 698 821 954 1097
((x + 2) + (2 * (2x + (x mod 2))))
A273669: 2 9 12 19 22 29 32 39 42 49 52 59 62 69 72 79
((x * (x - (x div (~2 + (x mod 2))))) div 2)
A088110: 0 1 3 9
A308422: 0 1 3 9 12 25 27 49 48 81 75 121 108 169 147 225
(x - (x2 div (x - ((~x + 2) div 2))))
A330561: 0 0 0 1 1 2 2 3 3 3 3 4 4 5 5 5
((x3 + 3x2 + ~2x) div 2)
A256857: 0 1 8 24 52 95 156 238 344 477 640 836 1068 1339 1652 2010
((x4 + ~x2 + 2x) div 2)
A101374: 0 1 8 39 124 305 636 1183 2024 3249 4960 7271 10308 14209 19124 25215
((x + 2) + ((x + (x div 4)) div 2))
A186322: 2 3 5 6 8 10 11 13 15 16 18 19 21 23 24 26
((2 - (2 mod (~x + ((~x + 2) div 2)))) div 2)
A074183: 1 1 1 2 2 3 4 5 5 6 7 8 8 9 10 11
((x + 2) + (5 * (x div 2)))
A047358: 2 3 9 10 16 17 23 24 30 31 37 38 44 45 51 52
(2 * (x + (5 * (x div 2))))
A147832: 0 2 14 16 28 30 42 44 56 58 70 72 84 86 98 100
((x div 3) - ((x * (x div 2)) mod 2))
A230128: 0 0 0 0 1 1 2 1 2 3 3 2 4 4 4 4
(11x + 22)
A096768: 22 33 44 55 66 77 88 99 110 121 132 143 154 165 176 187
(3x3 + 6x2 + x + 2)
A179259: 2 12 52 140 294 532 872 1332 1930 2684 3612 4732 6062 7620 9424 11492
((3 + (x2 div 2)) div (x + 2))
A083055: 1 1 1 1 1 2 2 3 3 3 4 4 5 5 6 6
((1 - (x2 div 3)) mod (x + 2))
A092092: 1 1 0 3 2 0 5 3 0 7 4 0 9 5 0 11
(x3 + 6x2 + 9x + 2)
A058794: 2 18 52 110 198 322 488 702 970 1298 1692 2158 2702 3330 4048 4862
(1 - ((1 mod (~2x + 1)) div (x + 2)))
A101787: 1 1 2 2 2 3 3 3 3 3 3 3 3 3 3 3
(x3 + ~3x2 + ~10x)
A126935: 0 ~12 ~24 ~30 ~24 0 48 126 240 396 600 858 1176 1560 2016 2550
(x4 + 3x3 + 3x2 + 2x)
A242604: 0 9 56 195 504 1085 2064 3591 5840 9009 13320 19019 26376 35685 47264 61455
(2x + (x div ~5))
A262770-A187318: 0 1 3 5 7 9 10 12 14 16 18 19 21 23 25 27
(2x + (x div 9))
A058066: 0 2 4 6 8 10 12 14 16 19 21 23 25 27 29 31
(2x + (2x div 5))
A175884: 0 2 4 7 9 12 14 16 19 21 24 26 28 31 33 36
(2x + (x div (1 + (x div 4))))
A133006: 0 3 6 9 10 12 15
(2x + (2 div (1 + (x mod 4))))
A047417: 2 3 4 6 10 11 12 14 18 19 20 22 26 27 28 30
(2x + (3 * (1 + (x div 2))))
A047389: 3 5 10 12 17 19 24 26 31 33 38 40 45 47 52 54
(2x + (x div ~6))
A276384-A272915-A158919: 0 1 3 5 7 9 11 12 14 16 18 20 22 23 25 27
(2x + ((x div 5) mod 2))
A054683: 0 2 4 6 8 11 13 15 17 19 20 22 24 26 28 31
(2x + ((x mod (1 + (x div 2))) div 2))
A262773: 0 2 4 6 8 11 13 15 17 20 22 24 26 29 31 33
(2x + ((x2 + 3x + 2) div 2))
A052905: 1 5 10 16 23 31 40 50 61 73 86 100 115 131 148 166
(2x + (((x mod 2) - (x div 2)) div 2))
A047285: 0 2 3 6 7 9 10 13 14 16 17 20 21 23 24 27
(2x + ((x + 1) mod (2 + (x mod 2))))
A267027: 1 4 5 7 9 10 13 16 17 19 21 22 25 28 29 31
(2x + ((~2 + (x div 2)) * (x div 2)))
A087279: 0 2 3 5 8 10 15 17 24 26 35 37 48 50 63 65
(3x - (2 div (x2 + ~2)))
A011986: 1 5 5 9 12
14x2
A144555: 0 14 56 126 224 350 504 686 896 1134 1400 1694 2016 2366 2744 3150
(3x + ((x * (x div 2)) mod 2))
A319452: 0 3 6 10 12 15 18 22 24 27 30 34 36 39 42 46
((1 + (2 * (1 + (x div 2)))) * (x div 2))
A266440: 0 0 5 5 14 14 27 27 44 44 65 65 90 90 119 119
((2 mod (1 + (x div 4))) + (x div 2))
A147795: 0 0 1 1 2 2 3 3 6 6 7 7 8 8 9 9
((6x + 6) + (x div 2))
A187391: 6 12 19 25 32 38 45 51 58 64 71 77 84 90 97 103
(x - (((~x + 1) + (x mod 2)) * (x div 2)))
A131179: 0 1 3 4 10 11 21 22 36 37 55 56 78 79 105 106
(x - (((~x + ~1) + (x mod 2)) * (x div 2)))
A266304: 0 1 5 6 14 15 27 28 44 45 65 66 90 91 119 120
((((x + 1) div 3) mod 2) - (x div 2))
A176001: 0 0 0 0 ~1 ~2 ~3 ~3 ~3 ~3 ~4 ~5 ~6 ~6 ~6 ~6
((2 * ((x div 2) div 3)) + (x div 2))
A219651: 0 0 1 1 2 2 5 5 6 6 7 7 10 10 11 11
((8 * (x mod 2)) + (x div 2))
A168321: 0 8 1 9 2 10 3 11 4 12 5 13 6 14 7 15
(x - (~7 * (x div 2)))
A090570: 0 1 9 10 18 19 27 28 36 37 45 46 54 55 63 64
((4 * (x + (x mod 2))) + (x div 2))
A274406: 0 8 9 17 18 26 27 35 36 44 45 53 54 62 63 71
(x - ((~2x + (x div 2)) * (x div 2)))
A001082: 0 1 5 8 16 21 33 40 56 65 85 96 120 133 161 176
(2x2 + (x div 2) - (x mod 2))
A139591: 0 1 9 18 34 51 75 100 132 165 205 246 294 343 399 456
((x * (1 + (2 mod (x + 1)))) + (x div 2))
A030123: 0 1 7 10 14 17 21 24 28 31 35 38 42 45 49 52
(x + ((2x div 3) + (x div 2)))
A090169: 0 1 4 6 8 10 13 14 17 19 21 23 26 27 30 32
(x + (((x div 2) div 3) + (x div 2)))
A060832: 0 1 3 4 6 7 10 11 13 14 16 17 20 21 23 24
(x + ((x2 div 3) + (x div 2)))
A236771: 0 1 4 7 11 15 21 26 33 40 48 56 66 75 86 97
(((x div 2) div 5) + (x mod 2))
A196564: 0 1 0 1 0 1 0 1 0 1 1 2 1 2 1 2
(((x div ~3) mod 2) - (x mod 2))
A131531: 0 0 1 0 0 ~1 0 0 1 0 0 ~1 0 0 1 0
((2 * ((x div 2) div 3)) + (x mod 2))
A276090: 0 1 0 1 0 1 2 3 2 3 2 3 4 5 4 5
((8x + 4) + (x mod 2))
A173512: 4 13 20 29 36 45 52 61 68 77 84 93 100 109 116 125
((2 * ((x div 4) mod 2)) + (x mod 2))
A059905: 0 1 0 1 2 3 2 3 0 1 0 1 2 3 2 3
((2 * (2 - (x mod 4))) - (x mod 2))
A216178: 4 1 0 ~3 4 1 0 ~3 4 1 0 ~3 4 1 0 ~3
(((x - ((x div 2) mod 2)) div 2) + (x mod 2))
A291271: 0 1 0 2 2 3 2 4 4 5 4 6 6 7 6 8
((3x + 2) * (2 - (x mod 2)))
A166304: 4 5 16 11 28 17 40 23 52 29 64 35 76 41 88 47
((3x + 2) div (2 - (x mod 2)))
A165367: 1 5 4 11 7 17 10 23 13 29 16 35 19 41 22 47
(((x2 + 3x) div 2) + (x mod 2))
A176222: 0 3 5 10 14 21 27 36 44 55 65 78 90 105 119 136
(2 - ((x + 1) div ((~x + 1) - (x mod 2))))
A329505: 1 4 5 4 4 4 4 4 4 4 4 4 4 4 4 4
(7x2 div 2)
A032525: 0 3 14 31 56 87 126 171 224 283 350 423 504 591 686 787
((x4 + 2x3 + ~x2) div 2)
A255499: 0 1 14 63 184 425 846 1519 2528 3969 5950 8591 12024 16393 21854 28575
((x5 + x2) div 2)
A101378: 0 1 18 126 520 1575 3906 8428 16416 29565 50050 80586 124488 185731 269010 379800
(1 - ((x * (~x + ((~x + 2) div 2))) div 2))
A263465: 1 2 3 7 11
(x2 + 18)
A241848: 18 19 22 27 34 43 54 67 82 99 118 139 162 187 214 243
(1 - ((~x2 + ((x div 2) mod 2)) div 2))
A220315: 1 2 3 5 9 14
(~x * (x2 div ~4))
A213389: 0 1 2 9 16 35 54 91 128 189 250 341 432 559 686 855
(3x2 + 10x)
A140678: 0 13 32 57 88 125 168 217 272 333 400 473 552 637 728 825
19x
A008601: 0 19 38 57 76 95 114 133 152 171 190 209 228 247 266 285
(6x2 + 5x)
A211014: 0 11 34 69 116 175 246 329 424 531 650 781 924 1079 1246 1425
23x
A008605: 0 23 46 69 92 115 138 161 184 207 230 253 276 299 322 345
(x + (x div 13))
A103303: 0 1 2 3 4 5 6 7 8 9
A335467-A334140-A247755-A244511-A172270-A171828-A140332-A084347-A084034-A023806-A023754-A014157: 0 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16
(x + (x div 11))
A103303: 0 1 2 3 4 5 6 7 8 9
A342382-A335523-A331162-A249626-A247809-A247806-A247802-A247801-A241158-A241157-A102823-A052081-A043096-A031995-A023752-A010784-A004775-A004744: 0 1 2 3 4 5 6 7 8 9 10 12 13 14 15 16
(3x3 + 3x2 + x)
A249354: 0 7 38 111 244 455 762 1183 1736 2439 3310 4367 5628 7111 8834 10815
(3x3 + 6x2 + x)
A196507: 0 10 50 138 292 530 870 1330 1928 2682 3610 4730 6060 7618 9422 11490
(8x2 + 7x)
A139278: 0 15 46 93 156 235 330 441 568 711 870 1045 1236 1443 1666 1905
(x4 + x3 + 2x2 + x)
A186636: 0 5 34 129 356 805 1590 2849 4744 7461 11210 16225 22764 31109 41566 54465
(2x2 + 11x)
A139577: 0 13 30 51 76 105 138 175 216 261 310 363 420 481 546 615
(8x2 + 3x)
A139276: 0 11 38 81 140 215 306 413 536 675 830 1001 1188 1391 1610 1845
(x + ((x + 1) div 7))
A067570: 0 1 2 3 4 5 7
A263715-A079298-A047595: 0 1 2 3 4 5 7 8 9 10 11 12 13 15 16 17
(x + ((x + 2) div 7))
A004776: 0 1 2 3 4 6 7 8 9 10 11 12 14 15 16 17
(x + (2x div 7))
A187328-A039105: 0 1 2 3 5 6 7 9 10 11 12 14 15 16 18 19
(x + ((x div 2) div 7))
A103303: 0 1 2 3 4 5 6 7 8 9
A335522-A334966-A120401-A056651-A023807-A023755-A000401: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 15 16
compr(\x.(~1 + (x mod (2 + (x mod 3)))),x)
A039238: 0 1 3 4 5 6 7 8 9 10 12 13 15 16 17 18
(8x2 + 5x)
A139277: 0 13 42 87 148 225 318 427 552 693 850 1023 1212 1417 1638 1875
(8x2 + ~5x)
A139272: 0 3 22 57 108 175 258 357 472 603 750 913 1092 1287 1498 1725
31x
A135631: 0 31 62 93 124 155 186 217 248 279 310 341 372 403 434 465
(x + (x div 15))
A103303: 0 1 2 3 4 5 6 7 8 9
A125007-A095736-A048339-A048326-A048312-A035062-A029960-A023808-A023756-A004829: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 16
(2x2 + 13x)
A139578: 0 15 34 57 84 115 150 189 232 279 330 385 444 507 574 645
(x + (2x div 9))
A039199: 0 1 2 3 4 6 7 8 9 11 12 13 14 15 17 18
(8x3 + x)
A118465: 0 9 66 219 516 1005 1734 2751 4104 5841 8010 10659 13836 17589 21966 27015
(x + (5 * (x div 3)))
A047469: 0 1 2 8 9 10 16 17 18 24 25 26 32 33 34 40
(11x + 5)
A017449: 5 16 27 38 49 60 71 82 93 104 115 126 137 148 159 170
(x + ((2x + 1) div 5))
A047367: 0 1 3 4 5 7 8 10 11 12 14 15 17 18 19 21
(x + (5 * (1 + (x div 2))))
A047319: 5 6 12 13 19 20 26 27 33 34 40 41 47 48 54 55
(11x + 10)
A104341: 10 21 32 43 54 65 76 87 98
A017509: 10 21 32 43 54 65 76 87 98 109 120 131 142 153 164 175
(x + 40)
A082763: 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55
(~x + 40)
A273770-A022996: 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25
(x + (5 * (x div 4)))
A037463: 0 1 2 3 9 10 11 12 18 19 20 21 27 28 29 30
(x + ((2 * (x div 2)) div 5))
A067570: 0 1 2 3 4 5 7
A039264: 0 1 2 3 4 5 7 8 9 10 12 13 14 15 16 17
(x + ((x + (x mod 2)) div 5))
A039258: 0 1 2 3 4 6 7 8 9 11 12 13 14 15 16 18
(5x2 + ~3x)
A135706: 0 2 14 36 68 110 162 224 296 378 470 572 684 806 938 1080
(~x + 27)
A022983: 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12
(x + (3 * (x div 5)))
A047453-A037467: 0 1 2 3 4 8 9 10 11 12 16 17 18 19 20 24
(x + (3 * (1 + (x div 4))))
A047307: 3 4 5 6 10 11 12 13 17 18 19 20 24 25 26 27
(11x + 3)
A017425: 3 14 25 36 47 58 69 80 91 102 113 124 135 146 157 168
(~x + 36)
A022992: 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21
(x + (9 * (x div 2)))
A112651: 0 1 11 12 22 23 33 34 44 45 55 56 66 67 77 78
(x + ((x - (x div 3)) div 3))
A039193: 0 1 2 3 5 6 7 8 10 11 12 13 14 16 17 18
compr(\x.((x2 div 3) mod 3),x)
A265227: 0 1 3 6 8 9 10 12 15 17 18 19 21 24 26 27
(x + (3 * (2 mod (1 + (x div 2)))))
A288657: 0 1 2 3 10 11 12 13 14 15 16 17 18 19 20 21
(x + ((x mod (1 + (x div 2))) div 3))
A043092-A023801-A020659: 0 1 2 3 4 5 6 8 9 10 11 12 13 15 16 17
(11x + 12)
A104340: 12 23 34 45 56 67 78 89
(x - (1 mod (~x + ((x + 1) mod 3))))
A010375: 0 1 3 4 5 9
(x + ((2 * (x div 3)) div 3))
A067570: 0 1 2 3 4 5 7
A039203: 0 1 2 3 4 5 7 8 9 11 12 13 14 15 16 18
(13x + 6)
A186113: 6 19 32 45 58 71 84 97 110 123 136 149 162 175 188 201
(11x + 6)
A017461: 6 17 28 39 50 61 72 83 94 105 116 127 138 149 160 171
(x + 48)
A121377: 48 49 50 51 52 53 54 55 56 57
(x + (6 * (x div 4)))
A276326-A055655-A007090: 0 1 2 3 10 11 12 13 20 21 22 23 30 31 32 33
(x2 + 11x)
A119412: 0 12 26 42 60 80 102 126 152 180 210 242 276 312 350 390
(x + (x div ~11))
A172268: 0 0 1 2 3 4 5 6 7 8 9 10 10 11 12 13
(~x + ((2x2 + 4) div 3))
A076202: 1 1 2 4 8 13
(7x2 + ~6x)
A051868: 0 1 16 45 88 145 216 301 400 513 640 781 936 1105 1288 1485
(7x2 + ~2x)
A135703: 0 5 24 57 104 165 240 329 432 549 680 825 984 1157 1344 1545
(x + ((1 - (x2 div 2)) mod 3))
A235451: 1 2 4 3 6 6 7 8 10 9 12 12 13 14 16 15
(x + ((x + (x div 3)) div 3))
A037087: 0 1 2 4 5 7 8 10 11 13 14 15 17 18 20 21
((x + 1) div (x + ((~x + 1) mod 3)))
A141571: 1 2 0 1 1 0 1 1 0 1 1 0 1 1 0 1
(x + ((x3 + 2x) div 3))
A033547: 0 2 6 14 28 50 82 126 184 258 350 462 596 754 938 1150
(x + ((x div 4) * (x div 3)))
A272341: 0 1 2 3 5 6 8 9 12 15
(1 - (x div ((~x + 1) - (x mod 3))))
A082204: 1 2 2 3 2 2 3 2 2 3 2 2 3 2 2 3
compr(\x.(((x div 2) mod 2) - (x mod 3)),x)
A039241: 0 1 2 4 5 7 8 9 10 11 12 13 14 16 17 19
(4x3 + 2x2 + x)
A110451: 0 7 42 129 292 555 942 1477 2184 3087 4210 5577 7212 9139 11382 13965
(2x2 + 17x)
A139580: 0 19 42 69 100 135 174 217 264 315 370 429 492 559 630 705
(2x2 + 15x)
A139579: 0 17 38 63 92 125 162 203 248 297 350 407 468 533 602 675
(2x3 + 5x2 + x)
A163832: 0 8 38 102 212 380 618 938 1352 1872 2510 3278 4188 5252 6482 7890
(15x + 8)
A164284: 8 23 38 53 68 83 98 113 128 143 158 173 188 203 218 233
(7x2 + x)
A092277: 0 8 30 66 116 180 258 350 456 576 710 858 1020 1196 1386 1590
(x2 + 13x)
A132759: 0 14 30 48 68 90 114 140 168 198 230 264 300 338 378 420
(x4 + ~x3 + ~x2 + ~x)
A152016: 0 ~2 2 42 172 470 1038 2002 3512 5742 8890 13178 18852 26182 35462 47010
(x2 + 17x)
A132761: 0 18 38 60 84 110 138 168 200 234 270 308 348 390 434 480
(x2 + 15x)
A132760: 0 16 34 54 76 100 126 154 184 216 250 286 324 364 406 450
(~x2 + 15x)
A256573: 0 14 26
(3x3 + 2x2 + x)
A067389: 0 6 34 102 228 430 726 1134 1672 2358 3210 4246 5484 6942 8638 10590
(x3 + 3x2 + 5x + 2)
A094792: 2 11 32 71 134 227 356 527 746 1019 1352 1751 2222 2771 3404 4127
((x2 + x) + (x2 div 4))
A249547: 0 2 7 14 24 36 51 68 88 110 135 162 192 224 259 296
(x6 + x)
A131472: 0 2 66 732 4100 15630 46662 117656 262152 531450 1000010 1771572 2985996 4826822 7529550 11390640
(x6 + ~x)
A131473: 0 0 62 726 4092 15620 46650 117642 262136 531432 999990 1771550 2985972 4826796 7529522 11390610
(1 - (x * (x div ~8)))
A092596: 1 2 3 4 5 6 7 8 9 19
(x + (2 * (x div 7)))
A272574-A039111-A037475: 0 1 2 3 4 5 6 9 10 11 12 13 14 15 18 19
(~x + (2 * (x mod 7)))
A073794: 0 1 2 3 4 5 6 ~7 ~6 ~5 ~4 ~3 ~2 ~1 ~14 ~13
(~x + (2 * (x mod 9)))
A073796: 0 1 2 3 4 5 6 7 8 ~9 ~8 ~7 ~6 ~5 ~4 ~3
(x + (2 * ((x + 1) div 5)))
A047287-A039047: 0 1 2 3 6 7 8 9 10 13 14 15 16 17 20 21
(x + ((3 * (1 + (x div 2))) div 2))
A047325: 1 2 5 6 8 9 12 13 15 16 19 20 22 23 26 27
(x + (2 * (((x + 1) div 2) div 3)))
A047549-A039074: 0 1 2 3 4 7 8 9 10 11 12 15 16 17 18 19
(3x2 + 14x)
A140679: 0 17 40 69 104 145 192 245 304 369 440 517 600 689 784 885
(x + ((x - ((x div 2) div 3)) div 2))
A022846: 0 1 3 4 6 7 8 10 11 13 14 16 17 18 20 21
(9x2 + 2x)
A147296: 0 11 40 87 152 235 336 455 592 747 920 1111 1320 1547 1792 2055
(9x2 + ~2x)
A013656: 0 7 32 75 136 215 312 427 560 711 880 1067 1272 1495 1736 1995
(x + (x div (2 + (2 mod (1 + (x div 2))))))
A039236: 0 1 3 4 5 6 7 8 10 11 12 13 15 16 17 18
(x4 + 3x3 + 2x2 + ~2x)
A330651: 0 4 44 174 472 1040 2004 3514 5744 8892 13180 18854 26184 35464 47012 61170
(x + (4 * (1 + (x div 3))))
A047311: 4 5 6 11 12 13 18 19 20 25 26 27 32 33 34 39
(~x + 28)
A022984: 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13
(~x + (2 * (x mod 10)))
A103303: 0 1 2 3 4 5 6 7 8 9
A073835: 0 1 2 3 4 5 6 7 8 9 ~10 ~9 ~8 ~7 ~6 ~5
(x + (2 * (2 + (x div 5))))
A295742: 4 5 6 7 8 11
(x + (4 * (x div 5)))
A037468: 0 1 2 3 4 9 10 11 12 13 18 19 20 21 22 27
(13x + 4)
A127547: 4 17 30 43 56 69 82 95 108 121 134 147 160 173 186 199
(11x + 4)
A017437: 4 15 26 37 48 59 70 81 92 103 114 125 136 147 158 169
(x + (2 * (2 + (3 * (x div 2)))))
A047608: 4 5 12 13 20 21 28 29 36 37 44 45 52 53 60 61
(x + (4 * ((x div 2) div 3)))
A007092: 0 1 2 3 4 5 10 11 12 13 14 15 20 21 22 23
(x + ((x - (x div ~4)) div 2))
A007067: 0 2 3 5 6 8 10 11 13 15 16 18 19 21 23 24
(x + ((((~1 + (x div 2)) div 2) div 2) mod 2))
A118868: 1 2 2 3 4 5 6 7 8 9 11 12 13 14 15 16
(x + (2 * ((((x + 1) div 2) div 2) div 2)))
A039153: 0 1 2 3 4 5 6 9 10 11 12 13 14 15 16 19
(x2 + 14x)
A098848: 0 15 32 51 72 95 120 147 176 207 240 275 312 351 392 435
(3 div (~x + 16))
A034411: 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 3
(4 div (~x + 16))
A168084: 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 4
(x + (x div (4 + (x div 4))))
A276389-A052413: 0 1 2 3 4 6 7 8 9 10 11 12 13 14 16 17
(x + (2x div ~7))
A057359: 0 0 1 2 2 3 4 5 5 6 7 7 8 9 10 10
(x + ((x + (x div 2)) div 8))
A067570: 0 1 2 3 4 5 7
A345913-A043091-A023800: 0 1 2 3 4 5 7 8 9 10 11 13 14 15 16 17
(9x2 + ~8x)
A051872: 0 1 20 57 112 185 276 385 512 657 820 1001 1200 1417 1652 1905
(x + (x div (~2 + ((~x + 2) div 4))))
A028391: 0 0 1 2 2 3 4 5 6 6 7 8 9 10 11 12
(x + ((x - ((~x + 2) div 4)) div 2))
A058065: 0 1 3 5 6 8 9 11 13 14 16 18 19 21 22 24
(11x + 8)
A017485: 8 19 30 41 52 63 74 85 96 107 118 129 140 151 162 173
compr(\x.(((x + 1) div (2 + (x mod 2))) mod 2),x)
A191276: 0 1 4 5 7 8 11 12 13 16 17 19 20 23 24 25
(1 div (1 - (x * ((x + ~1) mod 4))))
A164660: 1 1 ~1 ~1 ~1 1 ~1 ~1 ~1 1 ~1 ~1 ~1 1 ~1 ~1
compr(\x.(1 - ((x * (x div 2)) mod 4)),x)
A047586: 2 3 5 6 7 10 11 13 14 15 18 19 21 22 23 26
(x + ((2 + (x div 2)) * (x div 4)))
A337261: 0 1 2 3 8 9 11 12
(x5 + 4x)
A054604: 0 5 40 255 1040 3145 7800 16835 32800 59085 100040 161095 248880 371345 537880 759435
(x + (2 * ((x + ((x div 2) mod 2)) div 2)))
A047538: 0 1 4 7 8 9 12 15 16 17 20 23 24 25 28 31
compr(\x.(((x mod 3) * (x div 2)) mod 2),x)
A039267-A039206-A000398: 0 1 2 3 4 5 6 8 9 11 12 13 14 15 16 17
(x + (((1 + (x div 2)) * (x div 2)) div 2))
A165157: 0 1 3 4 7 8 12 13 18 19 25 26 33 34 42 43
(x - ((~x + 2) * ((x mod 3) div 2)))
A222256: 0 1 2 3 4 8 6 7 14 9 10 20 12 13 26 15
(x + ((x + ((x div 2) div 3)) div 2))
A275672: 0 1 3 4 6 7 9
A172272-A056576: 0 1 3 4 6 7 9 11 12 14 15 17 19 20 22 23
(x + (2 * (x + ((x div ~2) mod 2))))
A072833: 0 5 8 9 12 17 20 21 24 29 32 33 36 41 44 45
(x + (2 * (x + (((x + ~1) div 2) mod 2))))
A294510: 2 3 6 11 14 15 18 23
A218155: 2 3 6 11 14 15 18 23 26 27 30 35 38 39 42 47
(x2 + 18x)
A098850: 0 19 40 63 88 115 144 175 208 243 280 319 360 403 448 495
(x + ((x + (x div 8)) div 2))
A275672: 0 1 3 4 6 7 9
A140758: 0 1 3 4 6 7 9 10 12 14 15 17 18 20 21 23
(2x3 + ~7x2)
A015242: 0 ~5 ~12 ~9 16 75 180 343 576 891 1300 1815 2448 3211 4116 5175
(x5 + 2x2 + ~2x)
A240129: 0 1 36
(x3 + 6x2 + 11x + 8)
A250352: 8 26 62 122 212 338 506 722 992 1322 1718 2186 2732 3362 4082 4898
((x2 + ~2x) + (x2 mod 3))
A109340: 0 0 1 3 9 16 24 36 49 63 81 100 120 144 169 195
((x + 2) - (2 div (2 div (~2x + 1))))
A231407: 1 4 6
A074764: 1 4 6 7 8 9 10 11 12 13 14 15 16 17 18 19
(x + (1 mod (8 - (x div 2))))
A323372-A322021-A296090-A295888-A295880-A295300: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14 15
(x + (((x * (x mod 2)) div 2) * (x div 2)))
A346004: 0 1 2 4 4 9 6 16 8 25 10 36 12 49 14 64
(((x + 2) + (x div 2)) * (x + (x div 2)))
A057780: 0 3 15 24 48 63 99 120 168 195 255 288 360 399 483 528
((x div (2 + (x mod 2))) + (x * (x div 2)))
A075100: 0 0 3 4 10 11
(((x + 1) + (x div 2)) * (x + (x mod 2)))
A062717: 0 4 8 20 28 48 60 88 104 140 160 204 228 280 308 368
(x * (x2 - ((~x2 + 2x) div 2)))
A212679: 0 1 8 33 80 165 288 469 704 1017 1400 1881 2448 3133 3920 4845
13x2
A152742: 0 13 52 117 208 325 468 637 832 1053 1300 1573 1872 2197 2548 2925
11x2
A033584: 0 11 44 99 176 275 396 539 704 891 1100 1331 1584 1859 2156 2475
(3x3 + 7x2)
A257042: 0 10 52 144 304 550 900 1372 1984 2754 3700 4840 6192 7774 9604 11700
17x2
A244630: 0 17 68 153 272 425 612 833 1088 1377 1700 2057 2448 2873 3332 3825
(2x3 + ~9x2)
A015243: 0 ~7 ~20 ~27 ~16 25 108 245 448 729 1100 1573 2160 2873 3724 4725
(4x3 + 9x2)
A258618: 0 13 68 189 400 725 1188 1813 2624 3645 4900 6413 8208 10309 12740 15525
(x + (2 mod (~x + ((x + ~1) div 3))))
A084520-A084510-A054846: 0 1 2 2 3 3 3 4 4 4 5 5 5 6 6 6
(x2 + 24x)
A132766: 0 25 52 81 112 145 180 217 256 297 340 385 432 481 532 585
(x5 + x3 + x2)
A133073: 0 3 44 279 1104 3275 8028 17199 33344 59859 101100 162503 250704 373659 540764 762975
(x5 + x3 + ~x2)
A240129: 0 1 36
A133072: 0 1 36 261 1072 3225 7956 17101 33216 59697 100900 162261 250416 373321 540372 762525
(x5 + ~x3 + x2)
A133071: 0 1 28 225 976 3025 7596 16513 32320 58401 99100 159841 247248 369265 535276 756225
(x5 + ~x3 + ~x2)
A133070: 0 ~1 20 207 944 2975 7524 16415 32192 58239 98900 159599 246960 368927 534884 755775
(x6 + ~x2)
A136008: 0 0 60 720 4080 15600 46620 117600 262080 531360 999900 1771440 2985840 4826640 7529340 11390400
(x2 + 20x)
A120071: 0 21 44 69 96 125 156 189 224 261 300 341 384 429 476 525
(x + (1 mod (~x + 16)))
A309083: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 15
(3x2 + 16x)
A140680: 0 19 44 75 112 155 204 259 320 387 460 539 624 715 812 915
(x4 + 4x3 + 6x2)
A258402: 0 11 72 243 608 1275 2376 4067 6528 9963 14600 20691 28512 38363 50568 65475
(x2 + 24)
A241890: 24 25 28 33 40 49 60 73 88 105 124 145 168 193 220 249
(x2 + (3 * (x2 div 2)))
A195142: 0 1 10 21 40 61 90 121 160 201 250 301 360 421 490 561
(x2 + 20)
A241850: 20 21 24 29 36 45 56 69 84 101 120 141 164 189 216 245
(x2 + ((1 + (x div 2)) * (x div 2)))
A239767: 0 1 6 11 22 31 48 61 84 101 130 151 186 211 252 281
7x3
A244727: 0 7 56 189 448 875 1512 2401 3584 5103 7000 9317 12096 15379 19208 23625
(x6 + ~x3)
A136006: 0 0 56 702 4032 15500 46440 117306 261632 530712 999000 1770230 2984256 4824612 7526792 11387250
(x2 + (1 mod (~3x + 4)))
A118403: 1 1 3 5 9 15 23 33 45 59 75 93 113 135 159 185
(~x6 + 1)
A024004: 1 0 ~63 ~728 ~4095 ~15624 ~46655 ~117648 ~262143 ~531440 ~999999 ~1771560 ~2985983 ~4826808 ~7529535 ~11390624
x7
A001015: 0 1 128 2187 16384 78125 279936 823543 2097152 4782969 10000000 19487171 35831808 62748517 105413504 170859375
loop(\(x,i).loop(\(x,i).loop(\(x,i).(x * i),i,x),i,x),x,1)
A054909: 1 1 2 24
A055462: 1 1 2 24 6912 238878720 5944066965504000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0),2,x)
A087734: 0 0 0 0 0 1 0 0 0 1 2 3 0 1 0 0
(if (if (x mod 5) <= 0 then x else 0) <= 0 then 1 else 0)
A345009-A236862-A236853-A178666: 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0
(if (if (x mod 6) <= 0 then x else 0) <= 0 then 1 else 0)
A249133-A118102: 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1
(if (if (x mod 8) <= 0 then x else 0) <= 0 then 1 else 0)
A273592-A070887: 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1
(if (x mod 6) <= 0 then (if x <= 0 then 0 else 1) else 0)
A144600-A024943: 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0
(if (x mod 2) <= 0 then (3 * (if x <= 0 then 0 else 2)) else 0)
A021169: 0 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0
(if ((x div 2) mod 2) <= 0 then (if (~x + 2) <= 0 then 2 else 1) else 0)
A143432: 1 1 0 0 2 2 0 0 2 2 0 0 2 2 0 0
(if (x mod 2) <= 0 then (if x <= 0 then 0 else (2x + 1)) else 0)
A266439: 0 0 5 0 9 0 13 0 17 0 21 0 25 0 29 0
loop(\(x,i).i,(~1 + loop(\(x,i).((~x + ~1) + i),x,2)),0)
A008736-A008722: 1 0 2 0 3 0 4 0 5 1 6 2 7 3 8 4
(if (5 mod (if x <= 0 then 1 else x)) <= 0 then 1 else 0)
A094875-A012245: 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0
(if (8 mod (if x <= 0 then 1 else x)) <= 0 then 1 else 0)
A296209-A255738-A076141: 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0
(loop(\(x,i).2x,x,2) + (if (~x + 2) <= 0 then 1 else 0))
A088039: 2 4 9 17 33 65 129 257 513 1025 2049 4097 8193 16385 32769 65537
loop(\(x,i).(x * i),x,(x - (if (~x + 2) <= 0 then 1 else 0)))
A018931: 0 1 2 12 72 480 3600 30240
loop(\(x,i).(2x + 1),(if (x mod 2) <= 0 then x else 1),0)
A080924: 0 1 3 1 15 1 63 1 255 1 1023 1 4095 1 16383 1
(loop(\(x,i).3x,x,2) + (if x <= 0 then 1 else 0))
A110593: 3 6 18 54 162 486 1458 4374 13122 39366 118098 354294 1062882 3188646 9565938 28697814
loop(\(x,i).(2x + 3),x,(if x <= 0 then 1 else 0))
A068156: 1 3 9 21 45 93 189 381 765 1533 3069 6141 12285 24573 49149 98301
loop(\(x,i).(3x + 3),x,(if x <= 0 then 1 else 0))
A123109: 1 3 12 39 120 363 1092 3279 9840 29523 88572 265719 797160 2391483 7174452 21523359
loop(\(x,i).(x2 + 3),x,(if x <= 0 then 1 else 0))
A329471: 1 3 12 147 21612 467078547 218162369067631212 4611686018427387903 4611686018427387903
loop(\(x,i).(2x + 6),x,(if x <= 0 then 1 else 0))
A068293: 1 6 18 42 90 186 378 762 1530 3066 6138 12282 24570 49146 98298 196602
loop(\(x,i).(3x + 2),x,(if x <= 0 then 1 else 0))
A103453: 1 2 8 26 80 242 728 2186 6560 19682 59048 177146 531440 1594322 4782968 14348906
(loop(\(x,i).2x,x,2) + (if (x mod 2) <= 0 then 2 else 0))
A087288: 4 4 10 16 34 64 130 256 514 1024 2050 4096 8194 16384 32770 65536
loop(\(x,i).(2x + 1),x,(if (x mod 2) <= 0 then 2 else 0))
A303611: 2 1 11 7 47 31 191 127 767 511 3071 2047 12287 8191 49151 32767
(1 - (if (x + ~1) <= 0 then x else (if (x mod 2) <= 0 then 2 else 0)))
A105812: 1 0 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1
loop(\(x,i).(~2x + 1),x,(if (x mod 2) <= 0 then 2 else 0))
A255138: 2 1 7 3 27 11 107 43 427 171 1707 683 6827 2731 27307 10923
loop(\(x,i).(x * i),x,(if (~x + 2) <= 0 then (x + ~2) else 0))
A052571: 0 0 0 6 48 360 2880 25200 241920 2540160 29030400 359251200 4790016000 68497228800 1046139494400 16999766784000
(if x <= 0 then 1 else (if (x + ~3) <= 0 then 2x else 0))
A182687: 1 2 4 6 0 0 0 0 0 0 0 0 0 0 0 0
(loop(\(x,i).(x * i),(x + ~2),1) - (if x <= 0 then 2 else 0))
A159333: ~1 1 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800
(2 - loop(\(x,i).(~2x + 1),x,(if x <= 0 then 2 else 0)))
A171501: 0 1 3 ~1 7 ~9 23 ~41 87 ~169 343 ~681 1367 ~2729 5463 ~10921
loop(\(x,i).((2x + 4) - (if x <= 0 then 1 else 0)),x,0)
A053208: 0 3 10 24 52 108 220 444 892 1788 3580 7164 14332 28668 57340 114684
loop(\(x,i).(i - loop(\(x,i).(~2 + (x * i)),x,0)),x,0)
A055591: 0 1 4 85 4611686018427387903
loop(\(x,i).(x - loop(\(x,i).((x + ~1) * i),i,0)),x,0)
A006231: 0 1 5 20 84 409 2365 16064 125664 1112073 10976173 119481284 1421542628 18348340113 255323504917 3809950976992
loop(\(x,i).((2 * (x + i)) + (if x <= 0 then 0 else 1)),x,0)
A116454: 0 2 9 25 59 129 271 557 1131 2281 4583 9189 18403 36833 73695 147421
loop(\(x,i).x2,x,loop(\(x,i).(2x + 1),x,0))
A092258: 0 1 81 5764801 4611686018427387903 4611686018427387903
loop(\(x,i).(x + i),x,loop(\(x,i).(2x + 1),x,0))
A335439: 0 2 6 13 25 46 84 155 291 556 1078 2113 4173 8282 16488 32887
loop(\(x,i).(x * i),x,loop(\(x,i).(2x + 1),x,0))
A052589: 0 1 6 42 360 3720 45360 640080 10281600 185431680 3712262400 81709689600 1961511552000 51005527372800 1428241944729600 42848566016256000
loop(\(x,i).loop(\(x,i).2x,i,(2x + 1)),x,0)
A104462: 0 2 20 328 10512 672800 86118464 22046326912 11287719379200 11558624644301312 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) * (1 + (if x <= 0 then 0 else i))),x,0)
A309490: 0 1 6 28 145 876 6139 49120 442089 4420900 48629911 583558944 7586266285 106207728004 1593115920075 25489854721216
loop(\(x,i).(if x <= 0 then (2 + (i div 2)) else (x + ~1)),x,0)
A092488: 0 2 1 0 4 3 2 1 0 6 5 4 3 2 1 0
loop(\(x,i).((x + 1) - loop(\(x,i).2x,i,x)),x,0)
A176337: 0 1 ~2 15 ~224 6945 ~437534 55566819 ~14169538844 7240634349285 ~7407168939318554 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,1,(1 + (x * i))),x,0)
A303143-A168257: 0 1 9 784
loop(\(x,i).(loop(\(x,i).2x,x,1) mod (1 + i)),x,0)
A131644: 0 1 2 0 1 2 4 0 1 2 4 4 3 8 1 2
(if (x mod 2) <= 0 then 1 else loop(\(x,i).(2x + 2),x,0))
A280412: 1 2 1 14 1 62 1 254 1 1022 1 4094 1 16382 1 65534
loop(\(x,i).((x + 2) + (x div (if i <= 0 then 1 else i))),x,0)
A061717-A003314: 0 2 5 8 12 16 20 24 29 34 39 44 49 54 59 64
(loop(\(x,i).(x * i),x,x) - (if (x + ~2) <= 0 then x else 0))
A052633: 0 0 2 18 96 600 4320 35280 322560 3265920 36288000 439084800 5748019200 80951270400 1220496076800 19615115520000
loop(\(x,i).x2,1,loop(\(x,i).(~2x + 1),x,0))
A139818: 0 1 1 9 25 121 441 1849 7225 29241 116281 466489 1863225 7458361 29822521 119311929
loop(\(x,i).(2x + (if (i mod 2) <= 0 then 1 else x)),x,0)
A329114: 0 0 1 3 7 21 43 129 259 777 1555 4665 9331 27993 55987 167961
loop(\(x,i).loop(\(x,i).(2x + 1),i,2x),x,0)
A215203: 0 1 11 183 5871 375775 48099263 12313411455 6304466665215 6455773865180671 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(x2 + 1),i,0)),x,0)
A125046: 0 1 3 8 34 711 459041 210066847942 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(x * i),(~1 + i),1)),x,0)
A003422: 0 1 2 4 10 34 154 874 5914 46234 409114 4037914 43954714 522956314 6749977114 93928268314
loop(\(x,i).(~x + loop(\(x,i).(x * i),(~1 + i),1)),x,0)
A153229: 0 1 0 2 4 20 100 620 4420 35900 326980 3301820 36614980 442386620 5784634180 81393657020
(if (8 mod (if x <= 0 then 1 else x)) <= 0 then x else 0)
A048298: 0 1 2 0 4 0 0 0 8 0 0 0 0 0 0 0
loop(\(x,i).(x + loop(\(x,i).(2x * i),i,1)),x,0)
A112369: 0 2 10 58 442 4282 50362 695482 11017402 196811962 3912703162 85662309562 2047652863162 53059407256762 1481388530277562 44331262220901562
loop(\(x,i).(5 * (if x <= 0 then 2 else x)),x,0)
A095687: 0 10 50 250 1250 6250 31250 156250 781250 3906250 19531250 97656250 488281250 2441406250 12207031250 61035156250
loop(\(x,i).(x + loop(\(x,i).x2,2,(2 * i))),x,0)
A330151: 0 16 272 1568 5664 15664 36400 74816 140352 245328 405328 639584 971360 1428336 2042992 2852992
loop(\(x,i).x2,1,loop(\(x,i).(2x + i),x,0))
A294140: 0 1 16 121 676 3249 14400 61009 252004 1026169 4145296 16670889 66879684 267944161 1072693504 4292739361
loop(\(x,i).loop(\(x,i).(3x + 2),i,x),x,0)
A206601: 0 2 26 728 59048 14348906 10460353202 22876792454960 150094635296999120 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).x3,2,i)),x,0)
A007487: 0 1 513 20196 282340 2235465 12313161 52666768 186884496 574304985 1574304985 3932252676 9092033028 19696532401 40357579185 78800938560
loop(\(x,i).((if (i mod 2) <= 0 then 2 else 0) + (x * i)),x,0)
A230071: 0 0 2 6 26 130 782 5474 43794 394146 3941462 43356082 520272986 6763548818 94689683454 1420345251810
loop(\(x,i).((if (i mod 2) <= 0 then i else 1) + (x * i)),x,0)
A344418: 0 1 4 13 56 281 1692 11845 94768 852913 8529140 93820541 1125846504 14636004553 204904063756 3073560956341
loop(\(x,i).((if (i mod 2) <= 0 then 1 else i) + (x * i)),x,0)
A344419: 0 1 3 12 49 250 1501 10514 84113 757026 7570261 83272882 999274585 12990569618 181867974653 2728019619810
loop(\(x,i).loop(\(x,i).(x + (i * i * i)),i,x),x,0)
A085437-A024166: 0 1 10 46 146 371 812 1596 2892 4917 7942 12298 18382 26663 37688 52088
loop(\(x,i).(x + loop(\(x,i).x2,2,(i * i))),x,0)
A000542: 0 1 257 6818 72354 462979 2142595 7907396 24684612 67731333 167731333 382090214 812071910 1627802631 3103591687 5666482312
loop(\(x,i).x2,1,loop(\(x,i).(x + (i * i)),x,0))
A271535: 0 1 25 196 900 3025 8281 19600 41616 81225 148225 256036 422500 670761 1030225 1537600
loop(\(x,i).((x + (if (i mod 2) <= 0 then i else 1)) * i),x,0)
A344496: 0 1 6 21 100 505 3066 21469 171816 1546353 15463630 170099941 2041199436 26535592681 371498297730 5572474465965
loop(\(x,i).((if (x mod 2) <= 0 then ~x else x) + i),x,0)
A226940: 0 1 3 6 ~2 7 13 20 ~12 21 31 42 ~30 43 57 72
(if x <= 0 then 0 else (1 + (if (x mod 2) <= 0 then 4 else 0)))
A021070: 0 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1
loop(\(x,i).2x,x,(1 + (if (x mod 2) <= 0 then 2 else 0)))
A098646: 3 2 12 8 48 32 192 128 768 512 3072 2048 12288 8192 49152 32768
(1 + (if (3 mod (if x <= 0 then 2 else x)) <= 0 then 2 else 0))
A121273: 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1
(if (x mod 3) <= 0 then (if x <= 0 then 1 else 2) else ~1)
A099837: 1 ~1 ~1 2 ~1 ~1 2 ~1 ~1 2 ~1 ~1 2 ~1 ~1 2
(1 + loop(\(x,i).(3 * (if x <= 0 then 1 else x)),x,0))
A103457: 1 4 10 28 82 244 730 2188 6562 19684 59050 177148 531442 1594324 4782970 14348908
(1 + loop(\(x,i).((x + 1) * (if x <= 0 then 1 else x)),x,0))
A129871: 1 2 3 7 43 1807 3263443 10650056950807 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(if (x + ~1) <= 0 then i else (x + ~1)),x,0))
A132226: 1 2 3 2 5 4 3 2 9 8 7 6 5 4 3 2
loop(\(x,i).(x * i),loop(\(x,i).(2x + 2),x,0),1)
A028367: 1 2 720 87178291200 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(if x <= 0 then 1 else 4x),x,0))
A123166: 1 2 5 17 65 257 1025 4097 16385 65537 262145 1048577 4194305 16777217 67108865 268435457
(1 + loop(\(x,i).(if x <= 0 then 3 else 2x),x,0))
A004119: 1 4 7 13 25 49 97 193 385 769 1537 3073 6145 12289 24577 49153
(1 + loop(\(x,i).(2x + (if x <= 0 then 2 else x)),x,0))
A100702: 1 3 7 19 55 163 487 1459 4375 13123 39367 118099 354295 1062883 3188647 9565939
(2 div (1 + loop(\(x,i).(if x <= 0 then i else (x div 2)),x,0)))
A135387: 2 1 2 0 1 2 0 0 1 2 0 0 0 1 2 0
loop(\(x,i).(2x + 1),(if (x mod 2) <= 0 then x else 0),1)
A084181: 1 1 7 1 31 1 127 1 511 1 2047 1 8191 1 32767 1
loop(\(x,i).(~2x + 1),(if (x mod 2) <= 0 then x else 0),1)
A166752: 1 1 3 1 11 1 43 1 171 1 683 1 2731 1 10923 1
(loop(\(x,i).(x * i),(x + ~1),1) + (if x <= 0 then 0 else 1))
A185387: 1 2 2 3 7 25 121 721 5041 40321 362881 3628801 39916801 479001601 6227020801 87178291201
loop(\(x,i).2x,(~1 + (x div 2)),(if x <= 0 then 0 else 1))
A158780: 0 1 1 1 2 2 4 4 8 8 16 16 32 32 64 64
(loop(\(x,i).(2x + i),x,1) + (if x <= 0 then 0 else 1))
A133095: 1 4 9 20 43 90 185 376 759 1526 3061 6132 12275 24562 49137 98288
((2 * (if (x mod 2) <= 0 then x else 1)) - (if x <= 0 then 0 else 1))
A266724: 0 1 3 1 7 1 11 1 15 1 19 1 23 1 27 1
(if (~x + 4) <= 0 then 4 else (if x <= 0 then 0 else 1))
A258199: 0 1 1 1 4 4 4 4 4 4 4 4 4 4 4 4
(loop(\(x,i).x2,2x,2) + (if x <= 0 then 0 else 1))
A269836: 2 17 65537
loop(\(x,i).2x,(x - (if (x + ~2) <= 0 then 0 else 1)),1)
A161816: 1 2 4 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384
(1 + (if (x mod 2) <= 0 then (2 * (if x <= 0 then 0 else 2)) else 1))
A059855: 1 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2
(if (x mod 2) <= 0 then (3 * (if x <= 0 then 1 else 2)) else 1)
A040011: 3 1 6 1 6 1 6 1 6 1 6 1 6 1 6 1
loop(\(x,i).x2,1,(1 + loop(\(x,i).2x,x,1)))
A028400: 4 9 25 81 289 1089 4225 16641 66049 263169 1050625 4198401 16785409 67125249 268468225 1073807361
loop(\(x,i).(x * i),x,(1 + loop(\(x,i).2x,x,1)))
A052561: 2 3 10 54 408 3960 46800 650160 10362240 186157440 3719520000 81789523200 1962469555200 51017981414400 1428416301312000 42851181364992000
loop(\(x,i).3x,(~1 + (if x <= 0 then 2 else x)),1)
A155734: 3 1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969
loop(\(x,i).(~x + (if x <= 0 then 1 else (i * i))),(x + 1),1)
A135405: 0 1 8 8 17 19 30 34 47 53 68 76 93 103 122 134
(if (x mod 2) <= 0 then ((x + ~1) * (if x <= 0 then 0 else 2)) else 1)
A267354: 0 1 2 1 6 1 10 1 14 1 18 1 22 1 26 1
loop(\(x,i).loop(\(x,i).2x,i,x2),(x + ~1),1)
A016031: 1 1 2 16 2048 67108864 144115188075855872 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(2x * i),i,x),(x + ~1),1)
A186002: 1 1 2 16 768 294912 1132462080 52183852646400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 8) <= 0 then (if x <= 0 then 0 else 2) else 1)
A327538-A327407: 0 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1
loop(\(x,i).x2,(x + ~2),(1 + (if x <= 0 then 0 else 2)))
A165421: 1 3 3 9 81 6561 43046721 1853020188851841 4611686018427387903 4611686018427387903
loop(\(x,i).(2x + 2),x,(1 + (if x <= 0 then 0 else 2)))
A134062: 1 8 18 38 78 158 318 638 1278 2558 5118 10238 20478 40958 81918 163838
(if ((if x <= 0 then 1 else x) mod 5) <= 0 then 2 else 1)
A277873-A236833: 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2
loop(\(x,i).(x * i),x,(if (x mod 3) <= 0 then 2 else 1))
A052579: 2 1 2 12 24 120 1440 5040 40320 725760 3628800 39916800 958003200 6227020800 87178291200 2615348736000
(if (x mod 6) <= 0 then (if x <= 0 then 1 else 2) else 1)
A303824-A280801-A278567-A204897: 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1
(if (x mod 8) <= 0 then (if x <= 0 then 1 else 2) else 1)
A326297-A325561-A298735-A294335-A294333-A290106-A290104-A198293-A188169-A144871-A066799-A043282-A025452: 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1
(if ((x div 2) mod 4) <= 0 then (if x <= 0 then 1 else 2) else 1)
A174353: 1 2 1 1 1 1 1 1 2 2 1 1 1 1 1 1
(if (x mod 4) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1)
A010121: 2 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1
(if (x mod 4) <= 0 then (2 * (if x <= 0 then 0 else 2)) else 1)
A276330: 0 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1
(if (x mod 2) <= 0 then (2 * (2 + (if x <= 0 then 0 else 2))) else 1)
A040019: 4 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1
(if (x mod 2) <= 0 then (4 * (if x <= 0 then 0 else 2)) else 1)
A021059: 0 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1
loop(\(x,i).(x * i),x,(if (x mod 4) <= 0 then 2 else 1))
A052621: 2 1 2 6 48 120 720 5040 80640 362880 3628800 39916800 958003200 6227020800 87178291200 1307674368000
(if (if (x mod 2) <= 0 then x else (~x + 4)) <= 0 then 2 else 1)
A051700: 2 1 1 1 1 2 1 2 1 2 1 2 1 2 1 2
(if (x mod 2) <= 0 then (~2 + (if x <= 0 then 2 else 0)) else 3)
A049071: 0 3 ~2 3 ~2 3 ~2 3 ~2 3 ~2 3 ~2 3 ~2 3
(if x <= 0 then 1 else (3 * (2 div (if x <= 0 then 1 else x))))
A154738: 1 6 3 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (x + ~2) <= 0 then 0 else loop(\(x,i).(x * i),x,3))
A052619: 0 0 0 18 72 360 2160 15120 120960 1088640 10886400 119750400 1437004800 18681062400 261534873600 3923023104000
loop(\(x,i).2x,(if (x + ~3) <= 0 then x else 2),1)
A222011: 1 2 4 8
A031401: 1 2 4 8 4 4 4 4 4 4 4
loop(\(x,i).2x,x,(1 + (if (x + ~1) <= 0 then x else 2)))
A132477: 1 4 12 24 48 96 192 384 768 1536 3072 6144 12288 24576 49152 98304
(loop(\(x,i).2x,x,1) + (if (~x + 2) <= 0 then 2 else 1))
A089985: 2 3 6 10 18 34 66 130 258 514 1026 2050 4098 8194 16386 32770
((2 * (if x <= 0 then 0 else 2)) + (if (~x + 2) <= 0 then 2 else 1))
A101101: 1 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6
((if x <= 0 then 1 else 4) + (if (~x + 2) <= 0 then 2 else 1))
A113975: 2 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6
(loop(\(x,i).x2,x,2) div (if (~x + 2) <= 0 then 2 else 1))
A200758: 2 4 8 128 32768 2147483648
loop(\(x,i).3x,x,(if (~x + 2) <= 0 then 2 else 1))
A027334: 1 3 18 54 162 486 1458 4374 13122 39366 118098 354294 1062882 3188646 9565938 28697814
loop(\(x,i).x2,1,(~1 + loop(\(x,i).2x,x,2)))
A060867: 1 9 49 225 961 3969 16129 65025 261121 1046529 4190209 16769025 67092481 268402689 1073676289 4294836225
loop(\(x,i).x2,2,(~1 + loop(\(x,i).2x,x,2)))
A128832: 1 81 2401 50625 923521 15752961 260144641 4228250625 68184176641 1095222947841 17557851463681 281200199450625 4501401006735361 72040003462430721 1152780773560811521 4611686018427387903
loop(\(x,i).2x,x,(~1 + loop(\(x,i).2x,x,2)))
A171476: 1 6 28 120 496 2016 8128 32640 130816 523776 2096128 8386560 33550336 134209536 536854528 2147450880
loop(\(x,i).(x + i),x,(~1 + loop(\(x,i).2x,x,2)))
A132925: 1 4 10 21 41 78 148 283 547 1068 2102 4161 8269 16474 32872 65655
loop(\(x,i).(x * (1 + i)),loop(\(x,i).2x,x,2),1)
A317888: 6 120 362880 355687428096000 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),x,(1 + (if x <= 0 then 0 else (x + 2))))
A052572: 1 4 10 36 168 960 6480 50400 443520 4354560 47174400 558835200 7185024000 99632332800 1482030950400 23538138624000
(if (x mod 2) <= 0 then (if x <= 0 then 1 else 2) else (2x + ~1))
A266256: 1 1 2 5 2 9 2 13 2 17 2 21 2 25 2 29
(if (x + ~2) <= 0 then (2x + (if x <= 0 then 1 else x)) else 1)
A177022: 1 3 6 1 1 1 1 1 1 1 1 1 1 1 1 1
loop(\(x,i).(2x * (1 + i)),x,(if x <= 0 then 2 else 1))
A032107: 2 4 24 192 1920 23040 322560 5160960 92897280 1857945600 40874803200 980995276800 25505877196800 714164561510400 21424936845312000 685597979049984000
((x * (if (x mod 2) <= 0 then x else 2)) + (if x <= 0 then 2 else 1))
A215658-A192579: 2 3 5 7 17
loop(\(x,i).2x,loop(\(x,i).(x + (x div 2)),x,2),1)
A023376: 4 8 16 64 512 8192 524288 268435456 4398046511104 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(x + (if (~2 + i) <= 0 then 2 else x)),x,2))
A290114: 1 3 5 11 23 47 95 191 383 767 1535 3071 6143 12287 24575 49151
loop(\(x,i).x2,1,(1 + loop(\(x,i).x2,x,2)))
A330828: 9 25 289 66049 4295098369
(~1 + loop(\(x,i).2x,x,loop(\(x,i).x2,x,2)))
A137810: 1 7 63 2047 1048575 137438953471 4611686018427387903 4611686018427387903 4611686018427387903
(if (if (x mod 8) <= 0 then x else 0) <= 0 then x else 1)
A319656: 0 1 2 3 4 5 6 7 1 9 10 11 12 13 14 15
loop(\(x,i).(x - loop(\(x,i).((x + ~1) * i),i,0)),x,1)
A121726: 1 2 6 21 85 410 2366 16065 125665 1112074 10976174 119481285 1421542629 18348340114 255323504918 3809950976993
loop(\(x,i).loop(\(x,i).2x,i,(2x + 1)),x,1)
A164894: 1 6 52 840 26896 1721376 220336192 56406065280 28879905423616 29573023153783296 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~1 + loop(\(x,i).2x,i,2x)),x,1)
A073588: 1 3 23 367 11743 751551 96198527 24626822911 12608933330431 12911547730361343 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + loop(\(x,i).2x,(~1 + i),x)),x,1)
A117261: 1 2 5 21 169 2705 86561 5539905 709107841 181531607297 92944182936065 95174843326530561 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + loop(\(x,i).(x * i),i,1)),x,1)
A036781: 1 3 6 13 38 159 880 5921 46242 409123 4037924 43954725 522956326 6749977127 93928268328 1401602636329
loop(\(x,i).((x + ~1) + loop(\(x,i).(x * i),i,1)),x,1)
A136574: 1 1 2 7 30 149 868 5907 46226 409105 4037904 43954703 522956302 6749977101 93928268300 1401602636299
loop(\(x,i).(1 + loop(\(x,i).2x,(2 + i),x)),x,1)
A178185: 1 9 145 4641 297025 38019201 9732915457 4983252713985 5102850779120641 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(if (x - i) <= 0 then 2x else (x + ~1)),x,1)
A193298: 1 2 4 3 6 5 10 9 8 16 15 14 13 26 25 24
loop(\(x,i).(~1 + loop(\(x,i).2x,i,x2)),x,1)
A073589: 1 1 3 71 80655 208167328799 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + (if (~2 + i) <= 0 then i else x)),x,1)
A267604: 1 3 6 13 27 55 111 223 447 895 1791 3583 7167 14335 28671 57343
loop(\(x,i).2x,x,loop(\(x,i).(1 + (x * i)),x,1))
A082032: 1 4 20 128 1040 10432 125248 1753600 28057856 505041920 10100839424 222218469376 5333243269120 138664325005312 3882601100165120 116478033004986368
loop(\(x,i).(x + loop(\(x,i).(x * i),i,1) - i),x,1)
A262376: 1 1 1 4 24 139 853 5886 46198 409069 4037859 43954648 522956236 6749977023 93928268209 1401602636194
loop(\(x,i).x2,1,loop(\(x,i).(2x + 2),x,1))
A169721: 1 16 100 484 2116 8836 36100 145924 586756 2353156 9424900 37724164 150945796 603881476 2415722500 9663283204
loop(\(x,i).2x,x,loop(\(x,i).(2x + 2),x,1))
A165665: 1 8 40 176 736 3008 12160 48896 196096 785408 3143680 12578816 50323456 201310208 805273600 3221159936
loop(\(x,i).2x,(if (x mod 2) <= 0 then x else (~x + 2)),1)
A224783: 1 2 4 1 16 1 64 1 256 1 1024 1 4096 1 16384 1
loop(\(x,i).(2 * (~x + (if (~2 + i) <= 0 then 1 else 0))),x,1)
A084633: 1 0 2 ~4 8 ~16 32 ~64 128 ~256 512 ~1024 2048 ~4096 8192 ~16384
loop(\(x,i).2x,x,loop(\(x,i).(~2x + 2),x,1))
A083086: 1 0 8 ~16 96 ~320 1408 ~5376 22016 ~87040 350208 ~1396736 5595136 ~22364160 89489408 ~357892096
loop(\(x,i).((x + 2) + (x div (if i <= 0 then 1 else i))),x,1)
A033156: 1 4 8 12 17 22 27 32 38 44 50 56 62 68 74 80
loop(\(x,i).(2x + (if (~2 + i) <= 0 then 1 else 0)),x,1)
A125176: 1 3 7 14 28 56 112 224 448 896 1792 3584 7168 14336 28672 57344
loop(\(x,i).(~x + 2),x,loop(\(x,i).(~2x + 1),x,1))
A277955: 1 3 3 7 11 23 43 87 171 343 683 1367 2731 5463 10923 21847
loop(\(x,i).(2x + (if (~2 + i) <= 0 then i else 1)),x,1)
A052996: 1 3 8 17 35 71 143 287 575 1151 2303 4607 9215 18431 36863 73727
loop(\(x,i).(2x + loop(\(x,i).(x * i),i,1)),x,1)
A233449: 1 3 8 22 68 256 1232 7504 55328 473536 4575872 49068544 577138688 7381298176 101940887552 1511556143104
loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1))
A161168: 2 6 20 72 272 1056 4160 16512 65792 262656 1049600 4196352 16781312 67117056 268451840 1073774592
loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,x,1))
A020522: 0 2 12 56 240 992 4032 16256 65280 261632 1047552 4192256 16773120 67100672 268419072 1073709056
loop(\(x,i).(x2 + 2x),1,loop(\(x,i).2x,x,1))
A242985: 3 8 24 80 288 1088 4224 16640 66048 263168 1050624 4198400 16785408 67125248 268468224 1073807360
loop(\(x,i).(x - i),(x + 1),loop(\(x,i).2x,x,1))
A014846: 0 ~1 ~2 ~2 1 11 36 92 211 457 958 1970 4005 8087 16264 32632
loop(\(x,i).x2,(x + ~1),loop(\(x,i).2x,x,1))
A088321: 1 2 16 4096 4294967296 4611686018427387903
A061301: 1 2 16 4096 4294967296 4611686018427387903 4611686018427387903
(loop(\(x,i).(x * i),x,1) + loop(\(x,i).2x,x,1))
A007611: 2 3 6 14 40 152 784 5168 40576 363392 3629824 39918848 479005696 6227028992 87178307584 1307674400768
(loop(\(x,i).(x * i),x,1) - loop(\(x,i).2x,x,1))
A123642: 0 ~1 ~2 ~2 8 88 656 4912 40064 362368 3627776 39914752 478997504 6227012608 87178274816 1307674335232
loop(\(x,i).(x2 + ~x),2,loop(\(x,i).2x,x,1))
A020524: 0 2 132 3080 57360 983072 16252992 264241280 4261413120 68451041792 1097364145152 17575006177280 281337537761280 4502500115750912 72048797944922112 1152851135862702080
loop(\(x,i).(2x + 1),x,loop(\(x,i).2x,x,1))
A099393: 1 5 19 71 271 1055 4159 16511 65791 262655 1049599 4196351 16781311 67117055 268451839 1073774591
loop(\(x,i).(2x + ~1),x,loop(\(x,i).2x,x,1))
A318165: 1 3 13
A020515: 1 3 13 57 241 993 4033 16257 65281 261633 1047553 4192257 16773121 67100673 268419073 1073709057
loop(\(x,i).(2x + (if (x + ~2) <= 0 then 0 else x)),x,1)
A025579: 1 2 4 12 36 108 324 972 2916 8748 26244 78732 236196 708588 2125764 6377292
loop(\(x,i).(2x + (if (~2 + i) <= 0 then 1 else x)),x,1)
A141495: 1 3 7 21 63 189 567 1701 5103 15309 45927 137781 413343 1240029 3720087 11160261
loop(\(x,i).(2x + loop(\(x,i).2x,i,x)),x,1)
A006088: 1 4 24 240 4320 146880 9694080 1260230400 325139443200 167121673804800 171466837323724800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x + (if (~2 + i) <= 0 then i else x)),x,1)
A080923: 1 3 8 24 72 216 648 1944 5832 17496 52488 157464 472392 1417176 4251528 12754584
loop(\(x,i).(2x * (if (x + ~2) <= 0 then 1 else i)),x,1)
A121892: 1 2 4 24 192 1920 23040 322560 5160960 92897280 1857945600 40874803200 980995276800
loop(\(x,i).loop(\(x,i).~2x,i,2x),x,1)
A127945: 1 ~4 ~32 512 16384 ~1048576 ~134217728 34359738368 17592186044416 ~18014398509481984 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).~x,x,loop(\(x,i).(~2x + i),x,1))
A006904: 1 1 4 5 14 23 52 97 202 395 800 1589 3190 6367 12748 25481
loop(\(x,i).loop(\(x,i).x2,(x - i),2x),x,1)
A275203: 1 2 4 64
A279969: 1 2 4 64 4611686018427387903
loop(\(x,i).2x,(x + ~1),(~1 + (if x <= 0 then 2 else x)))
A097064: 1 0 2 8 24 64 160 384 896 2048 4608 10240 22528 49152 106496 229376
loop(\(x,i).2x,(x + ~2),(~1 + (if x <= 0 then 2 else x)))
A097067: 1 0 1 4 12 32 80 192 448 1024 2304 5120 11264 24576 53248 114688
loop(\(x,i).(2x + 2),x,(~1 + (if x <= 0 then 2 else x)))
A058966: 1 2 10 30 78 190 446 1022 2302 5118 11262 24574 53246 114686 245758 524286
(~1 + loop(\(x,i).4x,x,(if x <= 0 then 2 else x)))
A060416: 1 3 31 191 1023 5119 24575 114687 524287 2359295 10485759 46137343 201326591 872415231 3758096383 16106127359
(1 + loop(\(x,i).loop(\(x,i).((~x + i) div 2),x,x),2,x))
A143977-A115265: 1 1 1 1 2 1 2 2 2 2 2 3 3 3 2 2
loop(\(x,i).2x,x,loop(\(x,i).2x2,x,1))
A028369: 1 4 32 1024 524288 68719476736 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(loop(\(x,i).(2x * i),i,x) div 2),x,1)
A098695: 1 1 4 96 18432 35389440 815372697600 263006617337856000 4611686018427387903 4611686018427387903 4611686018427387903
(if (4 mod (if x <= 0 then 1 else x)) <= 0 then 0 else (x + 1))
A333479: 0 0 0 4 0 6 7 8 9 10 11 12 13 14 15 16
(if (if (x mod 2) <= 0 then x else (~x + 2)) <= 0 then 0 else (x + 1))
A296065: 0 2 3 0 5 0 7 0 9 0 11 0 13 0 15 0
((x + 1) * loop(\(x,i).loop(\(x,i).(x * i),x,2),x,1))
A175718-A173603: 1 4 12 192 4611686018427387903
loop(\(x,i).loop(\(x,i).2x,x,1),(x mod 2),(x + 1))
A223925: 1 4 3 16 5 64 7 256 9 1024 11 4096 13 16384 15 65536
loop(\(x,i).loop(\(x,i).i,((x + ~1) - i),x),x,(x + 1))
A066041: 1 2 1 2 3 1 2 3 4 1 2 3 4 5 1 2
loop(\(x,i).(x + (if (~2 + i) <= 0 then i else x)),x,(x + 1))
A129954: 1 3 6 14 32 72 160 352 768 1664 3584 7680 16384 34816 73728 155648
((x + 1) + loop(\(x,i).(x - (if x <= 0 then 1 else i)),x,x))
A131818: 1 2 2 3 2 3 4 2 3 4 5 2 3 4 5 6
loop(\(x,i).(if (x mod (1 + i)) <= 0 then i else x),x,(x + 1))
A346466-A187730-A057237-A049559: 1 1 2 1 4 1 6 1 2 1 10 1 12 1 2 1
loop(\(x,i).x2,x,loop(\(x,i).(x * i),x,(x + 1)))
A283260: 1 4 1296 110075314176 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * (i * i)),i,x),x,(x + 1))
A108078: 1 2 12 576 414720 7166361600 4334215495680000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).i,(x - (i * i)),x),x,(x + 1))
A064866: 1 1 2 3 4 1 2 3 4 5 6 7 8 9 1 2
loop(\(x,i).(x + (if (x - i) <= 0 then 2x else 0)),x,1)
A064235: 1 3 3 9 9 9 9 9 9 27 27 27 27 27 27 27
loop(\(x,i).(~x * (if (i mod 2) <= 0 then 1 else i)),x,1)
A055634: 1 ~1 1 ~3 3 ~15 15 ~105 105 ~945 945 ~10395 10395 ~135135 135135 ~2027025
(1 + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x))
A194965-A194905-A133994-A023121-A002260: 1 1 2 1 2 3 1 2 3 4 1 2 3 4 5 1
loop(\(x,i).(x * loop(\(x,i).(x + (i * i)),i,0)),x,1)
A135438: 1 1 5 70 2100 115500 10510500 1471470000 300179880000 85551265800000 32937237333000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (if (x + ~2) <= 0 then x else 1))),x,1)
A111286: 1 2 6 12 24 48 96 192 384 768 1536 3072 6144 12288 24576 49152
loop(\(x,i).(x + loop(\(x,i).(x * i),(~1 + i),1)),x,1)
A067078: 1 2 3 5 11 35 155 875 5915 46235 409115 4037915 43954715 522956315 6749977115 93928268315
loop(\(x,i).(x div 2),x,loop(\(x,i).3x,x,1))
A002379: 1 1 2 3 5 7 11 17 25 38 57 86 129 194 291 437
loop(\(x,i).(x + (if (i mod 2) <= 0 then x else 3)),x,1)
A220753: 1 4 8 11 22 25 50 53 106 109 218 221 442 445 890 893
loop(\(x,i).(~x + loop(\(x,i).(x * i),i,3)),x,1)
A122972: 1 2 4 14 58 302 1858 13262 107698 980942 9905458 109844942 1327159858 17353902542 244180971058 3678842132942
loop(\(x,i).(x + (if (i mod 2) <= 0 then 2x else 1)),x,1)
A220946: 1 2 6 7 21 22 66 67 201 202 606 607 1821 1822 5466 5467
loop(\(x,i).i,loop(\(x,i).(x div (1 + (x mod 2))),x,x),1)
A322250: 1 1 2 1 4 2 6 1 8 4 10 2 12 6 14 1
loop(\(x,i).(x + loop(\(x,i).(x * i),(2 * i),1)),x,1)
A138525: 1 3 27 747 41067 3669867 482671467 87660962667 21010450850667 6423384156578667 2439325392333218667 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(1 + (x * i)),i,1)),x,1)
A294352: 1 2 10 160 10400 3390400 6635012800 90899675360000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(~2x + 1),i,1)),x,1)
A015013: 1 ~1 ~3 15 165 ~3465 ~148995 12664575 2165642325 ~738484032825 ~504384594419475 688484971382583375 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(2x * i),i,1)),x,1)
A112368: 1 3 11 59 443 4283 50363 695483 11017403 196811963 3912703163 85662309563 2047652863163 53059407256763 1481388530277563 44331262220901563
loop(\(x,i).(~x + loop(\(x,i).(2x * i),i,1)),x,1)
A290044: 1 1 7 41 343 3497 42583 602537 9719383 176075177 3539816023 78209790377 1883780763223 49127973630377 1379201149390423 41470672541233577
loop(\(x,i).loop(\(x,i).3x,(1 + i),x),x,1)
A217628: 1 9 243 19683 4782969 3486784401 7625597484987 50031545098999707 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x2,i,(1 + i))),x,1)
A005832: 1 4 324 21233664 3240000000000000000 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(x * i),i,(~1 + i))),x,1)
A132371: 1 1 3 15 87 567 4167 34407 316647 3219687 35878887 435046887 5704064487 80428314087 1213746099687 19521187251687
loop(\(x,i).(x + loop(\(x,i).(x * (2 + i)),i,1)),x,1)
A345889: 1 4 16 76 436 2956 23116 204556 2018956 21977356 261478156 3374988556 46964134156 700801318156 11162196262156 189005910310156
loop(\(x,i).(x + loop(\(x,i).(x * (0 - i)),i,1)),x,1)
A058006: 1 0 2 ~4 20 ~100 620 ~4420 35900 ~326980 3301820 ~36614980 442386620 ~5784634180 81393657020 ~1226280710980
loop(\(x,i).(x + loop(\(x,i).(x * (i * i)),i,1)),x,1)
A061062: 1 2 6 42 618 15018 533418 25935018 1651637418 133333531818 13301522971818 1606652445211818 231049185247771818 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (if (i mod 2) <= 0 then 2 else ~2)),x,1)
A120617: 1 ~2 ~4 8 16 ~32 ~64 128 256 ~512 ~1024 2048 4096 ~8192 ~16384 32768
loop(\(x,i).(x * (2 + (if (~x + 2) <= 0 then 2 else 1))),x,1)
A002001: 1 3 12 48 192 768 3072 12288 49152 196608 786432 3145728 12582912 50331648 201326592 805306368
loop(\(x,i).(x + (2 * (if (i mod 2) <= 0 then x else 1))),x,1)
A220944: 1 3 9 11 33 35 105 107 321 323 969 971 2913 2915 8745 8747
loop(\(x,i).(x * (2 + (if (~2 + i) <= 0 then i else 1))),x,1)
A027327: 1 3 12 36 108 324 972 2916 8748 26244 78732 236196 708588 2125764 6377292 19131876
loop(\(x,i).(x * loop(\(x,i).(x2 + 2),2,2)),x,1)
A009982: 1 38 1444 54872 2085136 79235168 3010936384 114415582592 4347792138496 165216101262848 6278211847988224 238572050223552512 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (i mod 2) <= 0 then x else 4)),x,1)
A224692: 1 5 10 14 28 32 64 68 136 140 280 284 568 572 1144 1148
loop(\(x,i).(x + (if (~x + 2) <= 0 then x else 4)),x,1)
A146523: 1 5 10 20 40 80 160 320 640 1280 2560 5120 10240 20480 40960 81920
loop(\(x,i).(x * (if (x + ~2) <= 0 then i else 4)),x,1)
A084509: 1 1 2 6 24 96 384 1536 6144 24576 98304 393216 1572864 6291456 25165824 100663296
loop(\(x,i).(x * loop(\(x,i).(x2 + x),2,2)),x,1)
A009986: 1 42 1764 74088 3111696 130691232 5489031744 230539333248 9682651996416 406671383849472 17080198121677824 717368321110468608 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(x2 + 2x),2,2)),x,1)
A259076: 1 80 6400 512000 40960000 3276800000 262144000000 20971520000000 1677721600000000 134217728000000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * i),(4 * i),x),x,1)
A268505: 1 24 967680 463520268288000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (i mod 2) <= 0 then 1 else 2x)),x,1)
A094025: 1 3 4 12 13 39 40 120 121 363 364 1092 1093 3279 3280 9840
loop(\(x,i).(x + loop(\(x,i).2x,i,2x)),x,1)
A155104: 1 5 45 765 25245 1640925 211679325 54401586525 27908013887325 28605714234508125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (if ((~x + 2) + i) <= 0 then x else 2)),x,1)
A222011: 1 2 4 8
A167182: 1 2 4 8 64 4096 16777216 281474976710656 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).2x2,i,2)),x,1)
A076688: 1 8 1024 33554432 72057594037927936 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 2),x,loop(\(x,i).(x * (2 + i)),x,1))
A233005: 1 1 3 7 22 78 315 1417 7087 38981 233887 1520268 10641881 79814109 638512875 5427359437
loop(\(x,i).loop(\(x,i).(2x * i),(2 * i),x),x,1)
A137565: 1 8 3072 141557760 1461147874099200 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * (1 + i)),(2 * i),x),x,1)
A168467: 1 6 720 3628800 1316818944000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * (i * i)),(2 * i),x),x,1)
A097476: 1 4 2304 1194393600 1941728542064640000 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (i mod 3) <= 0 then 1 else x)),x,1)
A005018: 1 2 4 5 10 20
loop(\(x,i).(x + (if (x mod 2) <= 0 then 3 else x)),x,1)
A172411: 1 2 5 10
A185647: 1 2 5 10 13 26 29 58 61 122 125 250 253 506 509 1018
loop(\(x,i).(x + loop(\(x,i).2x,(~1 + i),x)),x,1)
A028361: 1 2 6 30 270 4590 151470 9845550 1270075950 326409519150 167448083323950 171634285407048750 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x + (if (2 - i) <= 0 then x else 2)),x,x))
A132750: 1 4 9 21 49 113 257 577 1281 2817 6145 13313 28673 61441 131073 278529
loop(\(x,i).(x2 + loop(\(x,i).2x,i,1)),x,1)
A318165: 1 3 13
A168320: 1 3 13 177 31345 982509057 965324047087029313 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).2x,i,x2)),x,1)
A097421: 1 3 39 12207 2384185791 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + loop(\(x,i).4x,i,x)),x,1)
A027637: 1 3 45 2835 722925 739552275 3028466566125 49615367752825875 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + loop(\(x,i).~2x,i,x)),x,1)
A216206: 1 ~3 ~9 81 1215 ~40095 ~2525985 325852065 83092276575 ~42626337882975 ~43606743654283425 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + loop(\(x,i).3x,i,x)),x,1)
A027871: 1 2 16 416 33280 8053760 5863137280 12816818094080 84078326697164800 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x + loop(\(x,i).(x * i),i,i)),x,1)
A188545: 1 3 10
A140710: 1 3 10 38 172 944 6208 47696 417952 4101824 44491648 528068096 6804155392 94559581184 1409615239168 22434345998336
loop(\(x,i).(x * (if (i mod 3) <= 0 then 1 else i)),x,1)
A232980: 1 1 2 2 8 40 40 280 2240 2240 22400 246400 246400 3203200 44844800 44844800
loop(\(x,i).loop(\(x,i).(x * i),(3 * i),x),x,1)
A268504: 1 6 4320 1567641600 750902834626560000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * i),((~1 + i) * i),x),x,1)
A272168: 1 1 2 1440 689762304000 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(2x * (i * i)),i,x),x,1)
A091804: 1 2 32 9216 84934656 39137889484800 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (x + i)),x,1)
A135287: 1 2 1 4 2 1 7 14 7 16 8 4 2 1 15 30
loop(\(x,i).x2,1,loop(\(x,i).(1 - (x * i)),x,1))
A335691: 1 0 1 4 81 1936 70225 3437316 220017889 17821182016 1782120871521 215636596084900 31051670188655281 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,(x + ~1),(x * i)),x,1)
A073581: 1 1 2 36 4611686018427387903
loop(\(x,i).(loop(\(x,i).2x,i,1) + (x * i)),x,1)
A188545: 1 3 10
A010842: 1 3 10 38 168 872 5296 37200 297856 2681216 26813184 294947072 3539368960 46011804672 644165281792 9662479259648
loop(\(x,i).((if (i mod 2) <= 0 then i else 1) + (x * i)),x,1)
A344317: 1 2 6 19 80 401 2412 16885 135088 1215793 12157940 133737341 1604848104 20863025353 292082354956 4381235324341
loop(\(x,i).loop(\(x,i).2x,(~1 + i),(x * i)),x,1)
A011266: 1 1 4 48 1536 122880 23592960 10569646080 10823317585920 24936923717959680 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + ~x),1,loop(\(x,i).(x * i),x,1))
A020547: 0 0 2 30 552 14280 517680 25396560 1625662080 131681531520 13168185811200 1593350882323200 229442532323558400 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,(x + ~2),loop(\(x,i).(x * i),x,1))
A280420: 1 1 2 36 331776 42998169600000000 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 3),x,loop(\(x,i).(x * i),x,1))
A228448: 1 0 0 0 0 0 0 2 6 18 61 225 901 3905 18226 91134
loop(\(x,i).(x div 4),x,loop(\(x,i).(x * i),x,1))
A228449: 1 0 0 0 0 0 0 0 0 1 3 9 28 92 324 1217
loop(\(x,i).(loop(\(x,i).2x,i,x) + (x * i)),x,1)
A277355: 1 3 18 198 3960 146520 10256400 1384614000 365538096000 190445348016000 196920489848544000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((if (x mod 2) <= 0 then 1 else i) + (x * i)),x,1)
A344262: 1 2 5 18 73 370 2221 15554 124433 1119906 11199061 123189682 1478276185 19217590418 269046265853 4035693987810
loop(\(x,i).loop(\(x,i).(x * (~1 + (2 * i))),i,x),x,1)
A057863: 1 1 3 45 4725 4465125 46414974375 6272287562165625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * (i * i * i)),i,x),x,1)
A061719: 1 1 8 1728 23887872 41278242816000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).~2x,(i * i),x),x,1)
A128146: 1 ~2 ~32 16384 1073741824 ~36028797018963968 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(loop(\(x,i).2x,(x + ~1),1) + i),x,1)
A218129: 1 2 4 11 1028
loop(\(x,i).((x + (if (i mod 2) <= 0 then 1 else i)) * i),x,1)
A344495: 1 2 6 27 112 585 3516 24661 197296 1775745 17757460 195332181 2343986184 30471820561 426605487868 6399082318245
(2 + (if (x mod 2) <= 0 then (if x <= 0 then 1 else 4) else 0))
A040008: 3 2 6 2 6 2 6 2 6 2 6 2 6 2 6 2
(if x <= 0 then 1 else (~2 + loop(\(x,i).(2x + 4),x,0)))
A131130: 1 2 10 26 58 122 250 506 1018 2042 4090 8186 16378 32762 65530 131066
(if (x mod 2) <= 0 then (2x - (if x <= 0 then 0 else 1)) else 2)
A266258: 0 2 3 2 7 2 11 2 15 2 19 2 23 2 27 2
(2 + (if (x mod 4) <= 0 then (if x <= 0 then 1 else 2) else 1))
A276863: 3 3 3 3 4 3 3 3 4 3 3 3 4 3 3 3
(2 * (if (x mod 2) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1))
A040015: 4 2 8 2 8 2 8 2 8 2 8 2 8 2 8 2
loop(\(x,i).loop(\(x,i).x2,x,x),x,6)
A115528: 6 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 + (if (x + ~2) <= 0 then x else 3)))
A128999: 1 3 4 5 5 5 5 5 5 5 5 5 5 5 5 5
(if (x mod 2) <= 0 then (~1 + loop(\(x,i).2x,x,2)) else 2)
A282454: 1 2 7 2 31 2 127 2 511 2 2047 2 8191 2 32767 2
loop(\(x,i).4x,x,(2 + (if x <= 0 then 2 else 1)))
A110594: 4 12 48 192 768 3072 12288 49152 196608 786432 3145728 12582912 50331648 201326592 805306368 3221225472
(2 + loop(\(x,i).3x,x,(if x <= 0 then 2 else 1)))
A259821: 4 5 11 29 83 245 731 2189 6563 19685 59051 177149 531443 1594325 4782971 14348909
(if (5 mod (if x <= 0 then 1 else x)) <= 0 then 1 else 2)
A055666: 1 1 2 2 2 1 2 2 2 2 2 2 2 2 2 2
loop(\(x,i).(x * i),x,(2 + loop(\(x,i).2x,x,1)))
A052626: 3 4 12 60 432 4080 47520 655200 10402560 186520320 3723148800 81829440000 1962948556800 51024208435200 1428503479603200 42852489039360000
(if x <= 0 then 1 else loop(\(x,i).(x * (2 + i)),(x + 1),2))
A342856: 1 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000 20922789888000 355687428096000 6402373705728000
(loop(\(x,i).(x2 + x),x,1) * (if x <= 0 then 1 else 2))
A226960: 1 4 12 84 3612
loop(\(x,i).2x,(x + ~4),(if x <= 0 then 1 else 2))
A171869: 1 2 2 2 2 4 8 16 32 64 128 256 512 1024 2048 4096
loop(\(x,i).(3x * i),x,(if x <= 0 then 1 else 2))
A098559: 1 6 36 324 3888 58320 1049760 22044960 529079040 14285134080 428554022400 14142282739200 509122178611200 19855764965836800 833942128565145600 4611686018427387903
((~x + loop(\(x,i).2x,x,1)) * (if x <= 0 then 1 else 2))
A132732: 1 2 4 10 24 54 116 242 496 1006 2028 4074 8168 16358 32740 65506
loop(\(x,i).(4x * i),x,(if x <= 0 then 1 else 2))
A098560: 1 8 64 768 12288 245760 5898240 165150720 5284823040 190253629440 7610145177600 334846387814400 16072626615091200 835776583984742400 4611686018427387903 4611686018427387903
loop(\(x,i).(2x2 + ~x),x,(if x <= 0 then 1 else 2))
A099147: 1 6 66 8646 149497986 44699295486614406 4611686018427387903 4611686018427387903
(loop(\(x,i).(x + loop(\(x,i).(x * i),i,1)),x,1) div 2)
A192225: 0 1 2 5
A014288: 0 1 2 5 17 77 437 2957 23117 204557 2018957 21977357 261478157 3374988557 46964134157 700801318157
(loop(\(x,i).2x,x,2) * (2 + (if x <= 0 then 1 else 2)))
A171494: 6 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144
loop(\(x,i).x2,(x + ~2),(if x <= 0 then 1 else 4))
A165422: 1 4 4 16 256 65536 4294967296 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,(2 + loop(\(x,i).2x,x,2)))
A028403: 4 12 40 144 544 2112 8320 33024 131584 525312 2099200 8392704 33562624 134234112 536903680 2147549184
loop(\(x,i).(x * i),x,(if x <= 0 then 1 else (x + 4)))
A052644: 1 5 12 42 192 1080 7200 55440 483840 4717440 50803200 598752000 7664025600 105859353600 1569209241600 24845812992000
loop(\(x,i).(x * i),x,(if x <= 0 then 1 else (2 + (x div 2))))
A181490: 1 2 6 18
A052687: 1 2 6 18 96 480 3600 25200 241920 2177280 25401600 279417600 3832012800 49816166400 784604620800 11769069312000
(if x <= 0 then 1 else (2 * loop(\(x,i).x2,x2,2)))
A123276: 1 8 131072 4611686018427387903 4611686018427387903
(2 + (if (x + ~1) <= 0 then x else loop(\(x,i).(~x + i),x,2)))
A297996: 2 3 5 2 6 3 7 4 8 5 9 6 10 7 11 8
(if (if (x mod 8) <= 0 then x else 0) <= 0 then x else 2)
A097449: 0 1 2 3 4 5 6 7 2 9 10 11 12 13 14 15
loop(\(x,i).2x,(~x + loop(\(x,i).2x,x,1)),2)
A118016: 4 4 8 64 8192 268435456 576460752303423488 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(x div 2),((if x <= 0 then 1 else x) mod 2))
A131575: 1 1 0 2 0 4 0 8 0 16 0 32 0 64 0 128
loop(\(x,i).x2,2,loop(\(x,i).4x,x,2))
A013721: 16 4096 1048576 268435456 68719476736 17592186044416 4503599627370496 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 div loop(\(x,i).(if (~x + i) <= 0 then 1 else 2x),x,2))
A228817: 1 2 1 0 2
A156319: 1 2 1 0 2 1 0 0 2 1 0 0 0 2 1 0
loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,2))
A028402: 6 20 72 272 1056 4160 16512 65792 262656 1049600 4196352 16781312 67117056 268451840 1073774592 4295032832
loop(\(x,i).(2x + 1),x,loop(\(x,i).2x,x,2))
A092431: 2 9 35 135 527 2079 8255 32895 131327 524799 2098175 8390655 33558527 134225919 536887295 2147516415
loop(\(x,i).(2x + 2),x,loop(\(x,i).2x,x,2))
A143960: 2 10 38 142 542 2110 8318 33022 131582 525310 2099198 8392702 33562622 134234110 536903678 2147549182
loop(\(x,i).(if (x mod (1 + i)) <= 0 then i else x),x,(x + 2))
A251758: 2 3 1 5 1 7 1 2 1 11 1 13 1 2 1 17
(if (x mod 2) <= 0 then (2 - (if x <= 0 then 1 else x)) else (x + ~2))
A105811: 1 ~1 0 1 ~2 3 ~4 5 ~6 7 ~8 9 ~10 11 ~12 13
(if (x mod 2) <= 0 then (1 + (if x <= 0 then 0 else 2)) else 2x)
A267352: 1 2 3 6 3 10 3 14 3 18 3 22 3 26 3 30
(if x <= 0 then 1 else (if (x + ~3) <= 0 then x else 2x))
A057543: 1 1 2 3 8 10 12 14 16 18 20 22 24 26 28 30
loop(\(x,i).loop(\(x,i).(x * i),x,1),(x mod 2),(x div 2))
A116447: 0 1 1 1 2 2 3 6 4 24 5 120 6 720 7 5040
loop(\(x,i).(if (x + ~1) <= 0 then i else x2),x,(x div 2))
A266198: 0 1 2 4 65536
(if (x mod 4) <= 0 then (if x <= 0 then 1 else 2) else (x mod 2))
A098178: 1 1 0 1 2 1 0 1 2 1 0 1 2 1 0 1
loop(\(x,i).loop(\(x,i).x2,x,2),(x div 2),(x mod 2))
A014221: 0 1 2 4 16 65536
(2 - (if (x + ~2) <= 0 then (if x <= 0 then 1 else x) else (x mod 2)))
A288699: 1 1 0 1 2 1 2 1 2 1 2 1 2 1 2 1
(loop(\(x,i).2x,x,1) - loop(\(x,i).~x,x,2))
A135440: ~1 4 2 10 14 34 62 130 254 514 1022 2050 4094 8194 16382 32770
(loop(\(x,i).2x,x,2) - loop(\(x,i).~x,x,2))
A092297: 0 6 6 18 30 66 126 258 510 1026 2046 4098 8190 16386 32766 65538
loop(\(x,i).(x div 2),x,loop(\(x,i).3x,x,2))
A147788: 2 3 4 6 10 15 22 34 51 76 115 172 259 389 583 875
loop(\(x,i).(x * (2 + loop(\(x,i).x2,i,2))),x,2)
A092124: 2 12 216 55728 3652301664 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + x),1,loop(\(x,i).x2,x,2))
A330825: 6 20 272 65792 4295032832
loop(\(x,i).(x2 + ~x),1,loop(\(x,i).x2,x,2))
A111403: 2 12 240 65280 4294901760 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).3x,i,x)),x,2)
A323716: 2 8 80 2240 183680 44817920 32717081600 71584974540800 469740602936729600 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(x * (i * i)),i,x)),x,2)
A325050: 2 4 20 740 426980 6148938980 3187616116170980 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((1 - loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x)) div 2)
A180918: 0 0 1 0 1 1 0 2 1 1 0 2 2 1 1 0
(x + (if (x + ~1) <= 0 then 1 else (if (x mod 2) <= 0 then 2 else 0)))
A114112-A113981: 1 2 4 3 6 5 8 7 10 9 12 11 14 13 16 15
(x + (if (x mod 2) <= 0 then ((if x <= 0 then 2 else x) div 2) else 0))
A257143: 1 1 3 3 6 5 9 7 12 9 15 11 18 13 21 15
(if (x mod 2) <= 0 then (if x <= 0 then 1 else 2x) else ~x)
A280166: 1 ~1 4 ~3 8 ~5 12 ~7 16 ~9 20 ~11 24 ~13 28 ~15
(x + loop(\(x,i).(~1 + (if x <= 0 then i else x)),2x,1))
A010078: 1 2 5 4 11 10 9 8 23 22 21 20 19 18 17 16
loop(\(x,i).(x + (if x <= 0 then (1 + i) else 0)),x,(~x + 1))
A194908-A167289-A167288-A102482-A023122-A004736: 1 2 1 3 2 1 4 3 2 1 5 4 3 2 1 6
loop(\(x,i).(x + (if (~x + 2) <= 0 then x else 2)),x,(~x + 1))
A323383: 1 2 3 4 6 8 12
A029744-A018635: 1 2 3 4 6 8 12 16 24 32 48 64 96 128 192 256
loop(\(x,i).(x + (if (~2 + i) <= 0 then 2 else x)),x,(~x + 1))
A172160: 1 2 3 4 4 0 ~16 ~64 ~192 ~512 ~1280 ~3072 ~7168 ~16384 ~36864 ~81920
loop(\(x,i).2x,x,(~x + loop(\(x,i).2x,x,1)))
A186947: 1 2 8 40 192 864 3712 15488 63488 257536 1038336 4171776 16728064 67002368 268206080 1073250304
(loop(\(x,i).(2x * i),x,2) div (if x <= 0 then 1 else x))
A064378: 2 4 8 32 192 1536 15360 184320 2580480 41287680 743178240 14863564800 326998425600 7847962214400 204047017574400 5713316492083200
(loop(\(x,i).2x,(x + ~2),x) + (if x <= 0 then 1 else x))
A227978: 1 2 4 9 20 45 102 231 520 1161 2570 5643 12300 26637 57358 122895
(if x <= 0 then 1 else loop(\(x,i).(x * i),(2x + ~2),x))
A327882: 1 1 4 72 2880 201600 21772800 3353011200 697426329600 188305108992000 64023737057280000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 2) <= 0 then (~2 + (if x <= 0 then 2 else x)) else (~x + 2))
A097141: 0 1 0 ~1 2 ~3 4 ~5 6 ~7 8 ~9 10 ~11 12 ~13
loop(\(x,i).(x + (if (x + ~1) <= 0 then i else 4)),2,x)
A169911: 3 6 10 11 12 13 14 15 16 17 18 19 20 21 22 23
loop(\(x,i).(if x <= 0 then 1 else (x * (2 + i))),(x + 2),x)
A034866: 4 60 720 7560 80640 907200 10886400 139708800 1916006400 28021593600 435891456000 7192209024000 125536739328000 2311968282624000 44816615940096000 912338253066240000
loop(\(x,i).loop(\(x,i).3x,i,x),(x + ~2),x)
A219116: 0 1 2 9 108 3645 354294 100442349 83682825624 205891132094649 1500946352969991210 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + (if (~x + i) <= 0 then i else 0)),2x,x)
A053186: 0 0 1 2 0 1 2 3 4 0 1 2 3 4 5 6
loop(\(x,i).loop(\(x,i).2x,(x div 2),2),(x mod 2),x)
A138219: 0 2 2 4 4 8 6 16 8 32 10 64 12 128 14 256
loop(\(x,i).2x,(x + ~2),(1 mod (if x <= 0 then 2 else x)))
A034008: 1 0 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192
(if (x mod 2) <= 0 then (if x <= 0 then 1 else (x2 + ~2)) else x)
A027673: 1 1 2 3 14
loop(\(x,i).(x - (if (~x + i) <= 0 then (2 * i) else 0)),x,x)
A196199: 0 ~1 0 1 ~2 ~1 0 1 2 ~3 ~2 ~1 0 1 2 3
loop(\(x,i).loop(\(x,i).((x + 2) mod (1 + i)),x,0),x,x)
A071055: 0 0 2 0 2 2 6 0 2 2 6 2 6 6 14 0
(x - loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x))
A057944: 0 1 1 3 3 3 6 6 6 6 10 10 10 10 10 15
(x - loop(\(x,i).((x + ~1) - (if x <= 0 then 0 else i)),x,x))
A061885: 0 2 3 6 7 8 12 13 14 15 20 21 22 23 24 30
(0 - loop(\(x,i).((x + ~1) - (if x <= 0 then 1 else i)),x,x))
A138083: 0 1 2 4 5 6
A063656: 0 1 2 4 5 6 9 10 11 12 16 17 18 19 20 25
(0 - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x))
A330238-A122200-A025683-A025677-A025676-A025671-A025670-A025669-A025662-A025661-A025660-A025652-A025651-A025646-A025581: 0 1 0 2 1 0 3 2 1 0 4 3 2 1 0 5
loop(\(x,i).(x - ((if (~x + i) <= 0 then i else 0) div 2)),x,x)
A322832: 0 1 1 2 2 3 2 3 4 3 4 5 3 4 5 6
loop(\(x,i).(2x + (if (2 - i) <= 0 then x else 1)),x,x)
A229277: 0 3 15 63 243 891 3159 10935 37179 124659 413343 1358127 4428675 14348907 46235367 148272039
(x - loop(\(x,i).(x - (2 * (if x <= 0 then 0 else i))),x,x))
A259225: 0 2 2 6 6 6 6 12 12 12 12 12 12 20 20 20
(0 - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * i))),x,x))
A053187: 0 1 1 4 4 4 4 9 9 9 9 9 9 16 16 16
loop(\(x,i).(x - (x div (if i <= 0 then 1 else (2 * i)))),x,x)
A270362: 0 1 1 2 2 3 3 3 3 4 4 5 5 5 5 5
loop(\(x,i).(x * loop(\(x,i).x2,i,x)),2,x2)
A122971: 0 1 1073741824 205891132094649 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x2 + (if (x mod 2) <= 0 then (if x <= 0 then 1 else 2) else x))
A238739: 1 2 6 12 18 30
(x + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 1)),x,x))
A051162: 0 1 2 2 3 4 3 4 5 6 4 5 6 7 8 5
loop(\(x,i).(x * loop(\(x,i).x2,2,(2 * i))),x,x)
A280845: 0 16 8192 15925248 86973087744 1087163596800000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (x * (if (x + ~2) <= 0 then 2 else x2)))
A189896: 1 2 4 27
(if (~1 + (x mod 9)) <= 0 then 1 else 0)
A284095-A167700: 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0
(if (x mod 13) <= 0 then 1 else 0)
A340988-A323402-A294266-A294265-A015868: 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
(if (x mod 11) <= 0 then 1 else 0)
A343380-A341027-A304820-A135767-A100910-A015582-A014856: 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
(if ((x + ~2) mod (1 + (x div 3))) <= 0 then 1 else 0)
A195470: 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0
(if (x2 mod (1 + (x div 3))) <= 0 then 1 else 0)
A336868-A083187: 1 1 1 0 1 0 1 0 0 0 1 0 0 0 0 0
(if (~1 + (x2 mod (x + 3))) <= 0 then 1 else 0)
A241759-A151667: 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0
(if ((x + 1) mod 7) <= 0 then 1 else 0)
A331671-A286996-A214411-A083917-A083894-A079365-A044937-A025459: 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0
(if ((x + 2) mod 7) <= 0 then 1 else 0)
A025458: 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0
(if ((x + ~2) mod 7) <= 0 then 1 else 0)
A025455: 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0
(if (x mod (1 + (x mod 6))) <= 0 then 1 else 0)
A325488-A162289-A089010: 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0
(if (x mod 15) <= 0 then 1 else 0)
A340998-A260813-A085854-A017909-A014376: 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
(if (x mod (1 + ((x + ~1) mod 4))) <= 0 then 1 else 0)
A337263-A214021-A071024: 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1
(if ((x div ~2) mod 5) <= 0 then 1 else 0)
A316896-A017877: 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0
(if (2 - ((x div 2) mod 5)) <= 0 then 1 else 0)
A102673: 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1
(if ((x + 1) mod (1 + (x div 4))) <= 0 then 1 else 0)
A065333: 1 1 1 1 0 1 0 1 1 0 0 1 0 0 0 1
(if ((x + 1) mod (1 + (x mod 4))) <= 0 then 1 else 0)
A317489: 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1
(if (2x mod (x + 5)) <= 0 then 1 else 0)
A016389-A014059: 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
(if (x2 mod (2x + ~5)) <= 0 then 1 else 0)
A245811: 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1
(if (x mod (3 - ((x div 2) mod 2))) <= 0 then 1 else 0)
A285034: 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0
(if x <= 0 then 19 else 0)
A340650: 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(if ((x mod 8) mod 3) <= 0 then 1 else 0)
A289034-A285208-A260444: 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0
(if (~2 + (x div 2) - (x div 3)) <= 0 then 1 else 0)
A340372-A340363-A167851-A167850: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1
(x - (if (~x + 2) <= 0 then (1 + (x div 3)) else 0))
A131737: 0 1 1 1 2 3 3 4 5 5 6 7 7 8 9 9
(if ((x2 div 2) mod (x + 3)) <= 0 then 1 else 0)
A256432-A113052: 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0
(if ((x * (x div 2)) mod (x + 3)) <= 0 then 1 else 0)
A274179: 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0
(if ((2x + ~1) mod (1 + (x div 2))) <= 0 then 1 else 0)
A256574-A089801: 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0
(if ((x + ~4) mod (1 + (x div 2))) <= 0 then 1 else 0)
A266178: 1 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0
(if (2 - ((x + ~2) mod (1 + (x div 2)))) <= 0 then 1 else 0)
A268238: 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1
(if (9 mod (x + 1)) <= 0 then 1 else 0)
A291529-A225569: 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
(if (10 mod (x + 1)) <= 0 then 1 else 0)
A302052-A010052: 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0
(if (16 mod (x + 1)) <= 0 then 1 else 0)
A036987: 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1
(if (x mod (2 - ((x div 2) div ~2))) <= 0 then 1 else 0)
A330682: 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0
(if (x mod (4 - (x div ~2))) <= 0 then 1 else 0)
A085976-A017867: 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0
(if (x mod 14) <= 0 then 1 else 0)
A321448-A320332: 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
(if (~2 + ((x div 2) mod 5)) <= 0 then 1 else 0)
A204441: 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1
(if ((x + ~2) mod 10) <= 0 then 1 else 0)
A316863-A269248-A185706: 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
(if (~2 + (x div (3 + (x mod 2)))) <= 0 then 1 else 0)
A202022-A188641-A136522: 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0
(if (x mod 2) <= 0 then (1 + ((x div 3) mod 2)) else 0)
A239704: 1 0 1 0 2 0 1 0 1 0 2 0 1 0 1 0
(if (x + ~1) <= 0 then (~2x + 7) else 0)
A152627: 7 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(if (x mod (2 * (2 + (x mod 3)))) <= 0 then 1 else 0)
A321375-A321374-A112313: 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0
(if (~2 + (x mod (2 + (x mod 3)))) <= 0 then 1 else 0)
A294935-A242902-A196368-A178788-A168509: 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1
(if (x mod (2 + (x mod 8))) <= 0 then 1 else 0)
A025920: 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0
(if (x mod (4 + (x div 4))) <= 0 then 1 else 0)
A132918: 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0
(if (~2 + (x mod (2 + (x div 4)))) <= 0 then 1 else 0)
A344884: 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1
(if (x mod (6 + (x mod 2))) <= 0 then 1 else 0)
A066288: 1 0 0 0 0 0 1 1 0 0 0 0 1 0
A333818: 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0
(if (~2 + (((x + 1) div 2) mod 4)) <= 0 then 1 else 0)
A262045: 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1
(if ((x + ~4) mod 8) <= 0 then 1 else 0)
A330551-A079260-A024362: 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0
(if (x mod (2 + ((~x + 2) mod 4))) <= 0 then 1 else 0)
A267704: 1 0 1 0 1 0 1 0 1 1 1 0 1 0 1 1
(if (~2 + ((x + (x div 2)) mod 4)) <= 0 then 1 else 0)
A285431-A285421: 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1
(if (x mod ((x + 2) - (x div 4))) <= 0 then 1 else 0)
A029442-A017869: 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0
(if (~4 + ((x * (x mod 2)) div 2)) <= 0 then 1 else 0)
A228710: 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0
(if ((x + ~1) mod (4 + (x div 2))) <= 0 then 1 else 0)
A030583: 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0
(if ((x + ~2) mod (4 + (x div 2))) <= 0 then 1 else 0)
A031234-A030584: 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0
(if ((x div 2) mod (2 + ((x div 2) mod 2))) <= 0 then 1 else 0)
A039963: 1 1 0 0 1 1 1 1 1 1 0 0 1 1 0 0
(if ((x div 2) mod (4 + (x mod 2))) <= 0 then 1 else 0)
A281814: 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0
(if (((x + 2) div 3) mod 4) <= 0 then 1 else 0)
A025926-A017888: 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0
(if ((2 + (x * (x div 2))) mod 4) <= 0 then 1 else 0)
A189624: 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0
(2 - (if (x + ~1) <= 0 then (x + ~5) else 0))
A138096: 7 6 2 2 2 2 2 2 2 2 2 2 2 2 2 2
(if (x mod 4) <= 0 then (x div 5) else 0)
A047753: 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 0
(if ((x * (~1 + (x div 2))) mod 4) <= 0 then 1 else 0)
A104106: 1 0 1 1 1 0 1 0 1 0 1 1 1 0 1 0
(if ((x mod 4) - (x div 4)) <= 0 then 1 else 0)
A165190: 1 0 0 0 1 1 0 0 1 1 1 0 1 1 1 1
(if (x mod (2 + (4 mod (x + 2)))) <= 0 then 1 else 0)
A278169-A267423-A262693-A005369: 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0
(if ((x2 + 1) mod (x + 4)) <= 0 then 1 else 0)
A297240-A292150-A234323-A224772-A162782-A133010-A123545-A086080-A056649-A047766-A036859-A035677: 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
(if ((x2 + ~2) mod (x + 4)) <= 0 then 1 else 0)
A025456: 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0
(if ((x2 + 2) mod (2 + (x div 2))) <= 0 then 1 else 0)
A087032: 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0
(if ((x2 + ~2) mod (2 + (x div 2))) <= 0 then 1 else 0)
A017887: 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0
(if (3 mod (1 + (x div 2))) <= 0 then 3 else 0)
A269707: 3 3 0 0 3 3 0 0 0 0 0 0 0 0 0 0
(x - (if (x mod 3) <= 0 then (x div 3) else 0))
A186101: 0 1 2 2 4 5 4 7 8 6 10 11 8 13 14 10
(if (10 mod (x + 2)) <= 0 then 1 else 0)
A227291: 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0
loop(\(x,i).(x + (i * i * i)),(x + 3),0)
A250813: 36 100 225 441 784 1296 2025 3025 4356 6084 8281 11025 14400 18496 23409 29241
(2x + ((x mod 2) + (if (x + ~2) <= 0 then 1 else 0)))
A005556: 1 4 5 7 8 11
loop(\(x,i).(x + ((2 + i) * i)),(2x + 1),0)
A269342: 3 26 85 196 375 638 1001 1480 2091 2850 3773 4876 6175 7686 9425 11408
loop(\(x,i).((x * i) + (i mod 2)),(2x + ~1),0)
A051397: 0 1 7 141 5923 426457 46910271 7318002277 1536780478171 418004290062513 142957467201379447 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod (8 - (x div 2))) <= 0 then 1 else 0)
A091426-A054907-A014671: 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1
(if ((x + ~1) mod 4) <= 0 then (1 + (x div 2)) else 0)
A195938: 0 1 0 0 0 3 0 0 0 5 0 0 0 7 0 0
(if (x * ((x + 1) mod 8)) <= 0 then 1 else 0)
A284093: 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1
(if (x * ((x + ~1) mod 8)) <= 0 then 1 else 0)
A004530: 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
(if (~x + (8 mod (x + 2))) <= 0 then 1 else 0)
A162519: 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1
(if (~x + ((2x + ~4) mod (x + 2))) <= 0 then 1 else 0)
A307223-A063053: 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1
loop(\(x,i).(x + (i * i)),(x2 + 2x + 1),0)
A113754: 1 30 285 1496 5525 16206 40425 89440 180441 338350 597861 1005720 1623245 2529086 3822225 5625216
loop(\(x,i).((x + 1) + (2 * (i * i))),(x + 1),0)
A037237: 3 12 31 64 115 188 287 416 579 780 1023 1312 1651 2044 2495 3008
loop(\(x,i).(8x + 8),(x + 1),0)
A052379: 8 72 584 4680 37448 299592 2396744 19173960 153391688 1227133512 9817068104 78536544840 628292358728 5026338869832 40210710958664 321685687669320
loop(\(x,i).(2x + (i * i * i)),(x + 1),0)
A213575: 1 10 47 158 441 1098 2539 5590 11909 24818 50967 103662 209521 421786 846947 1697990
loop(\(x,i).(x + (i * i * (i div 2))),(x + 1),0)
A285188: 0 4 13 45 95 203 350 606 930 1430 2035 2899 3913 5285 6860 8908
loop(\(x,i).(x + ((x + (i div 2)) * i)),(x + 1),0)
A080049: 0 2 11 63 388 2734 21893 197069 1970726 21678036 260136487 3381774403 47344841720 710172625898 11362762014473 193166954246169
((x + 1) - loop(\(x,i).(2x + ~4),(x + ~1),0))
A132738: 1 2 7 16 33 66 131 260 517 1030 2055 4104 8201 16394 32779 65548
loop(\(x,i).((2 * (x + i)) - (i mod 2)),(x + ~1),0)
A171507: 0 0 1 6 17 42 93 198 409 834 1685 3390 6801 13626 27277 54582
loop(\(x,i).(~x + (4 * (x + i))),(x + ~1),0)
A061981: 0 0 4 20 72 232 716 2172 6544 19664 59028 177124 531416 1594296 4782940 14348876
loop(\(x,i).(x + (2 * (2x + i))),(x + ~1),0)
A185055: 0 0 2 14 76 388 1950 9762 48824 244136 1220698 6103510 30517572 152587884 762939446 3814697258
((2x2 + 8) + (if x <= 0 then 1 else 0))
A003135: 9 10 16
((x + 16) - (if x <= 0 then 1 else 0))
A043704-A043669: 15 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
(if ((x + 2) mod 9) <= 0 then 2 else 0)
A295663-A138045: 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0
(if (x mod 2) <= 0 then (x mod 10) else 0)
A001613: 0 0 2 0 4 0 6 0 8 0 0 0 2 0 4 0
loop(\(x,i).(x + i),(x mod 10),0)
A107082: 0 1 3 6 10 15 21 28 36 45 0 1 3 6 10 15
(if ((x + 1) mod 12) <= 0 then 2 else 0)
A230730-A230614-A127268-A112053: 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0
(if (~x + 2) <= 0 then (2 + (3 * (x mod 2))) else 0)
A021400: 0 0 2 5 2 5 2 5 2 5 2 5 2 5 2 5
((x + ~1) + (if (x mod 2) <= 0 then 6 else 0))
A168195: 5 0 7 2 9 4 11 6 13 8 15 10 17 12 19 14
(if (x mod 2) <= 0 then ((2 - (x div 3)) div 2) else 0)
A016334-A015829-A015549: 1 0 1 0 0 0 0 0 0 0 ~1 0 ~1 0 ~1 0
((2x + 8) + (if (x + ~1) <= 0 then 2 else 0))
A301860: 10 12 12 14 16
(if (x mod 3) <= 0 then ((x div ~2) mod 2) else 0)
A277145: 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0
(if x <= 0 then 28 else 0)
A243105: 28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(if ((x + 1) mod 10) <= 0 then 2 else 0)
A103270: 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0
(1 - (if ((x + ~1) mod 8) <= 0 then 2 else 0))
A071936: 1 ~1 1 1 1 1 1 1 1 ~1 1 1 1 1 1 1
(if ((x + 1) mod (2 + (x mod 4))) <= 0 then 2 else 0)
A226557: 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
(x - (if (~x + 2) <= 0 then ~7 else 0))
A171892: 0 1 9 10 11 12 13 14 15 16 17 18 19 20 21 22
(x - (if (x mod 2) <= 0 then (2 * (x div 4)) else 0))
A212831: 0 1 2 3 2 5 4 7 4 9 6 11 6 13 8 15
(if (x mod (2 + (4 mod (x + 2)))) <= 0 then 2 else 0)
A089800: 2 0 2 0 0 0 2 0 0 0 0 0 2 0 0 0
(1 - (if ((x + ~1) mod 4) <= 0 then 4 else 0))
A176563: 1 ~3 1 1 1 ~3 1 1 1 ~3 1 1 1 ~3 1 1
((x + ~1) + (if (x mod 4) <= 0 then 4 else 0))
A263313: 3 0 1 2 7 4 5 6 11 8 9 10 15 12 13 14
((x + ~1) + (if ((x div 2) mod 2) <= 0 then 4 else 0))
A256008: 3 4 1 2 7 8 5 6 11 12 9 10 15 16 13 14
(if (x mod 5) <= 0 then (2 * (x mod 2)) else 0)
A241541: 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2
(if (x + ~4) <= 0 then (1 - (2 * (x mod 2))) else 0)
A014379-A014319-A014299-A014239-A014199-A014179: 1 ~1 1 ~1 1 0 0 0 0 0 0 0 0 0 0 0
loop(\(x,i).(1 + ((x2 + 2x) * i)),(x + 2),0)
A010332: 7 190
loop(\(x,i).(2x + 12),(x + 2),0)
A226264: 36 84 180 372 756 1524 3060 6132 12276 24564 49140 98292 196596 393204 786420 1572852
loop(\(x,i).((x * (i div 2)) + (i mod 2)),(x + 2),0)
A007876: 1 2 4 9 27 82 328 1313 6565 32826 196956 1181737 8272159 57905114 463240912 3705927297
loop(\(x,i).(x + ((i * i) div 4)),(x + 2),0)
A002623: 1 3 7 13 22 34 50 70 95 125 161 203 252 308 372 444
loop(\(x,i).(x + (((i * i) div 2) * i)),(x + 2),0)
A006009: 4 16 48 108 216 384 640 1000 1500 2160 3024 4116 5488 7168 9216 11664
(1 - loop(\(x,i).(2 * (x - (i mod 2))),(x + ~2),0))
A152046: 1 1 1 3 5 11 21 43 85 171 341 683 1365 2731 5461 10923
loop(\(x,i).(2x + ((~1 + i) * i)),(x + ~2),0)
A324172: 0 0 0 0 2 10 32 84 198 438 932 1936 3962 8034 16200 32556
loop(\(x,i).(~4x + ~1),2x,0)
A182512: 0 3 51 819 13107 209715 3355443 53687091 858993459 13743895347 219902325555 3518437208883 56294995342131 900719925474099 14411518807585587 230584300921369395
loop(\(x,i).(~4x + ~4),2x,0)
A108020: 0 12 204 3276 52428 838860 13421772 214748364 3435973836 54975581388 879609302220 14073748835532 225179981368524 3602879701896396 57646075230342348 922337203685477580
(1 - loop(\(x,i).(2x + ~8),2x,0))
A141722: 1 25 121 505 2041 8185 32761 131065 524281 2097145 8388601 33554425 134217721 536870905 2147483641 8589934585
loop(\(x,i).(3x + (i div 2)),2x,0)
A004004: 0 1 14 135 1228 11069 99642 896803 8071256 72641337 653772070 5883948671 52955538084 476599842805 4289398585298 38604587267739
(if (x mod 9) <= 0 then (x div 2) else 0)
A236378-A005873: 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
(if ((x + 2) mod (2 + (x mod 2))) <= 0 then (x div 2) else 0)
A046667: 0 0 1 0 2 0 3 3 4 0 5 0 6 6 7 0
(if ((x + 2) mod 5) <= 0 then (x mod 2) else 0)
A316864: 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0
((4x + 16) + (if x <= 0 then 2 else 0))
A295745: 18 20 24
loop(\(x,i).(1 + (x mod (1 + (i mod (x + 1))))),x,0)
A137866: 0 1 1 2 1 2 1 2 3 2 1 2 1 2 3 4
(if (x mod 11) <= 0 then x else 0)
A321803-A321797-A321538: 0 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0
loop(\(x,i).(9x + 1),x,0)
A002452: 0 1 10 91 820 7381 66430 597871 5380840 48427561 435848050 3922632451 35303692060 317733228541 2859599056870 25736391511831
loop(\(x,i).((2x + 1) - (x mod 3)),x,0)
A295484: 0 1 2 3 7
A073827: 0 1 2 3 7 14
A294627: 0 1 2 3 7 14 27 55 110 219 439 878 1755 3511 7022 14043
loop(\(x,i).((x + 1) - (x div (~1 - i))),x,0)
A092757: 0 1 3 5 7 10 13 16 19 22 25 29 33 37 41 45
loop(\(x,i).((x + 1) - ((~x + 1) div (1 + i))),x,0)
A061168: 0 1 2 4 6 8 10 13 16 19 22 25 28 31 34 38
loop(\(x,i).(1 + (x * ((1 + i) * (1 + i)))),x,0)
A074703: 0 1 10 161 4026 144937 7101914 454522497 36816322258 3681632225801 445477499321922 64148759902356769 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (2 * (x mod 5))),x,0)
A222010: 0 1 3 7
A267317: 0 1 3 7 5 1 3 7 5 1 3 7 5 1 3 7
loop(\(x,i).(8x + 3),x,0)
A083713: 0 3 27 219 1755 14043 112347 898779 7190235 57521883 460175067 3681400539 29451204315 235609634523 1884877076187 15079016609499
loop(\(x,i).(1 + (2 * ((x + 1) - (i mod 2)))),x,0)
A084640: 0 1 5 11 25 51 105 211 425 851 1705 3411 6825 13651 27305 54611
loop(\(x,i).(8x + 5),x,0)
A125836: 0 5 45 365 2925 23405 187245 1497965 11983725 95869805 766958445 6135667565 49085340525 392682724205 3141461793645 25131694349165
(1 - loop(\(x,i).(8x + ~1),x,0))
A047853: 1 2 10 74 586 4682 37450 299594 2396746 19173962 153391690 1227133514 9817068106 78536544842 628292358730 5026338869834
loop(\(x,i).(10x + 5),x,0)
A002279: 0 5 55 555 5555 55555 555555 5555555 55555555 555555555 5555555555 55555555555 555555555555 5555555555555 55555555555555 555555555555555
loop(\(x,i).(10x + 10),x,0)
A105279: 0 10 110 1110 11110 111110 1111110 11111110 111111110 1111111110 11111111110 111111111110 1111111111110 11111111111110 111111111111110 1111111111111110
loop(\(x,i).(1 + (x * i) - (x mod 4)),x,0)
A192225: 0 1 2 5
A009551: 0 1 2 5 20 101 606 4241 33928 305353 3053530 33588829 403065948 5239857325 73358002550 1100370038249
loop(\(x,i).(~1 + (2 * (2x + (i mod 2)))),x,0)
A015521: 0 1 3 13 51 205 819 3277 13107 52429 209715 838861 3355443 13421773 53687091 214748365
loop(\(x,i).(~1 + (2 * (~2x + (i mod 2)))),x,0)
A084241: 0 1 ~5 21 ~85 341 ~1365 5461 ~21845 87381 ~349525 1398101 ~5592405 22369621 ~89478485 357913941
(4 - loop(\(x,i).(4x + ~1),x,0))
A163868: 4 5 9 25 89 345 1369 5465 21849 87385 349529 1398105 5592409 22369625 89478489 357913945
(2 - loop(\(x,i).(1 + (2 * (x - (i mod 2)))),x,0))
A153643: 2 3 3 5 7 13 23 45 87 173 343 685 1367 2733 5463 10925
loop(\(x,i).(9x + 9),x,0)
A052386: 0 9 90 819 7380 66429 597870 5380839 48427560 435848049 3922632450 35303692059 317733228540 2859599056869 25736391511830 231627523606479
loop(\(x,i).(3 * (1 + (x2 div 2))),x,0)
A103031: 0 3 15 339
(1 - loop(\(x,i).(3 * ((x + ~1) div 2)),x,0))
A156622: 1 4 7 13 22 34 52 79 121 184 277 418 628 943 1417 2128
(1 - loop(\(x,i).(6x + ~12),x,0))
A233325: 1 13 85 517 3109 18661 111973 671845 4031077 24186469 145118821 870712933 5224277605 31345665637 188073993829 1128443962981
loop(\(x,i).(9x + 6),x,0)
A054880: 0 6 60 546 4920 44286 398580 3587226 32285040 290565366 2615088300 23535794706 211822152360 1906399371246 17157594341220 154418349070986
loop(\(x,i).(5x + 3),x,0)
A125833: 0 3 18 93 468 2343 11718 58593 292968 1464843 7324218 36621093 183105468 915527343 4577636718 22888183593
loop(\(x,i).(10x + 1),x,0)
A002275: 0 1 11 111 1111 11111 111111 1111111 11111111 111111111 1111111111 11111111111 111111111111 1111111111111 11111111111111 111111111111111
((x2 + 2x) - loop(\(x,i).(2x + 1),x,0))
A071099: 0 2 5 8 9 4 ~15 ~64 ~175 ~412 ~903 ~1904 ~3927 ~7996 ~16159 ~32512
(8 - loop(\(x,i).(2x + ~1),x,0))
A168415: 8 9 11 15 23 39 71 135 263 519 1031 2055 4103 8199 16391 32775
((2 * (x mod 2)) - loop(\(x,i).(2x + ~1),x,0))
A062510: 0 3 3 9 15 33 63 129 255 513 1023 2049 4095 8193 16383 32769
loop(\(x,i).((3x + ~1) + (i * i)),x,0)
A061982: 0 0 3 17 66 222 701 2151 6516 19628 58983 177069 531350 1594218 4782849 14348771
loop(\(x,i).((4x + 1) + (x mod 2)),x,0)
A037481: 0 1 6 25 102 409 1638 6553 26214 104857 419430 1677721 6710886 26843545 107374182 429496729
loop(\(x,i).((x + 1) - ((~x + 1) div (2 + i))),x,0)
A130261: 0 1 2 4 6 8 10 12 15 18 21 24 27 30 33 36
loop(\(x,i).(7x + 1),x,0)
A023000: 0 1 8 57 400 2801 19608 137257 960800 6725601 47079208 329554457 2306881200 16148168401 113037178808 791260251657
(1 - loop(\(x,i).(5x + ~1),x,0))
A047850: 1 2 7 32 157 782 3907 19532 97657 488282 2441407 12207032 61035157 305175782 1525878907 7629394532
loop(\(x,i).((x + 1) + (x div 5)),x,0)
A067570: 0 1 2 3 4 5 7
A279076: 0 1 2 3 4 5 7 9 11 14 17 21 26 32 39 47
loop(\(x,i).((x + 1) + ((x div 2) div 3)),x,0)
A279077: 0 1 2 3 4 5 6 8 10 12 15 18 22 26 31 37
loop(\(x,i).((x + ~1) + ((x + 1) * (2 + i))),x,0)
A079752: 0 2 13 82 579 4638 41749 417498 4592487 55109854 716428113 10029993594 150449903923 2407198462782 40922373867309 736602729611578
(1 - loop(\(x,i).((x + ~1) + (x div (1 + i))),x,0))
A092777: 1 2 4 6 8 11 14 17 20 23 26 30 34 38 42 46
loop(\(x,i).((x + 1) + (x div 8)),x,0)
A279079: 0 1 2 3 4 5 6 7 8 10 12 14 16 19 22 25
loop(\(x,i).(7x + 7),x,0)
A104896: 0 7 56 399 2800 19607 137256 960799 6725600 47079207 329554456 2306881199 16148168400 113037178807 791260251656 5538821761599
loop(\(x,i).((x + 2) - (x div (~1 - i))),x,0)
A130235: 0 2 5 9 13 18 23 28 34 40 46 52 58 65 72 79
loop(\(x,i).((1 + (x * (~1 + i))) * (1 + i)),x,0)
A006041: 0 2 9 76 1145 27486 962017 46176824 2909139921 232731193690 23040388175321 2764846581038532 395373061088510089 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(8x + 6),x,0)
A125837: 0 6 54 438 3510 28086 224694 1797558 14380470 115043766 920350134 7362801078 58902408630 471219269046 3769754152374 30158033218998
(if (x mod 14) <= 0 then x else 0)
A243830: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14 0
loop(\(x,i).(9x + 2),x,0)
A125857: 0 2 20 182 1640 14762 132860 1195742 10761680 96855122 871696100 7845264902 70607384120 635466457082 5719198113740 51472783023662
loop(\(x,i).(2 * ((x + ~1) + (i mod 3))),x,0)
A152732: 0 0 2 2 4 10 18 36 74 146 292 586 1170 2340 4682 9362
loop(\(x,i).(x + i - ((1 + (x div 2)) div 2)),x,0)
A001855: 0 1 3 5 8 11 14 17 21 25 29 33 37 41 45 49
loop(\(x,i).(10x + 2),x,0)
A002276: 0 2 22 222 2222 22222 222222 2222222 22222222 222222222 2222222222 22222222222 222222222222 2222222222222 22222222222222 222222222222222
loop(\(x,i).(x - ((i * i) div ~4)),x,0)
A192225: 0 1 2 5
A175287: 0 1 2 5 9 16 25 38 54 75 100 131 167 210 259 316
loop(\(x,i).(2 * (x - ((x + i) div ~2))),x,0)
A178222: 0 2 8 28 88 270 816 2456 7376 22138 66424 199284 597864 1793606 5380832 16142512
loop(\(x,i).(16x + 4),x,0)
A141032: 0 4 68 1092 17476 279620 4473924 71582788 1145324612 18325193796 293203100740 4691249611844 75059993789508 1200959900632132 19215358410114116 307445734561825860
(1 - loop(\(x,i).(2x + ~12),x,0))
A139697: 1 13 37 85 181 373 757 1525 3061 6133 12277 24565 49141 98293 196597 393205
(if (~2 + (x mod (2 + (x mod 3)))) <= 0 then x else 0)
A103303: 0 1 2 3 4 5 6 7 8 9
A321801-A320486: 0 1 2 3 4 5 6 7 8 9 10 0 12 13 14 15
(1 - loop(\(x,i).(8x + ~4),x,0))
A046636: 1 5 37 293 2341 18725 149797 1198373 9586981 76695845 613566757 4908534053 39268272421 314146179365 2513169434917 20105355479333
(1 - loop(\(x,i).(8x + ~16),x,0))
A233328: 1 17 145 1169 9361 74897 599185 4793489 38347921 306783377 2454267025 19634136209 157073089681 1256584717457 10052677739665 80421421917329
loop(\(x,i).(x2 + 10),x,0)
A092500: 0 10 110 12110 146652110 21506841367452110 4611686018427387903 4611686018427387903
loop(\(x,i).(8 + ((x + i) div 2)),x,0)
A328241: 0 8 13 16 18 19 20 21 22 23 24 25 26 27 28 29
((~x + 1) + loop(\(x,i).(4x + 8),x,0))
A144414: 1 8 39 166 677 2724 10915 43682 174753 699040 2796191 11184798 44739229 178956956 715827867 2863311514
loop(\(x,i).(7x + 2),x,0)
A125725: 0 2 16 114 800 5602 39216 274514 1921600 13451202 94158416 659108914 4613762400 32296336802 226074357616 1582520503314
(1 - loop(\(x,i).(2 * (x - ((i div 2) mod 2))),x,0))
A190569: 1 1 3 7 13 25 51 103 205 409 819 1639 3277 6553 13107 26215
loop(\(x,i).(2 * ((2x + 2) - (i mod 2))),x,0)
A115243: 0 2 12 50 204 818 3276 13106 52428 209714 838860 3355442 13421772 53687090 214748364 858993458
loop(\(x,i).(2 * ((x + ~1) + (2 * (i mod 2)))),x,0)
A014113: 0 2 2 6 10 22 42 86 170 342 682 1366 2730 5462 10922 21846
(if (((x + 2) div 3) mod 4) <= 0 then x else 0)
A330024: 0 0 0 0 0 0 0 0 0 0 10 11 12 0 0 0
(1 div (2 - (if ((x + ~1) mod 4) <= 0 then x else 0)))
A292273: 0 1 0 0 0 ~1 0 0 0 ~1 0 0 0 ~1 0 0
loop(\(x,i).(x + (4 * (i * i)) - i),x,0)
A132124: 0 3 17 50 110 205 343 532 780 1095 1485 1958 2522 3185 3955 4840
loop(\(x,i).(10x + 4),x,0)
A002278: 0 4 44 444 4444 44444 444444 4444444 44444444 444444444 4444444444 44444444444 444444444444 4444444444444 44444444444444 444444444444444
((2 * (x mod 2)) - loop(\(x,i).(2x + ~4),x,0))
A014131: 0 6 12 30 60 126 252 510 1020 2046 4092 8190 16380 32766 65532 131070
(2 - loop(\(x,i).(5x + ~2),x,0))
A132079: 2 4 14 64 314 1564 7814 39064 195314 976564 4882814 24414064 122070314 610351564 3051757814 15258789064
loop(\(x,i).(5x + (i div 2)),x,0)
A097139: 0 0 1 6 32 162 813 4068 20344 101724 508625 2543130 12715656 63578286 317891437 1589457192
(1 - loop(\(x,i).(~2 + ((~x + 2) * (x div 2))),x,0))
A232806: 1 3 7 27 367 67347 2267809207 2571479299676984427 4611686018427387903
(x - loop(\(x,i).(2 * (x - ((~x + i) div 2))),x,0))
A183119: 0 1 4 11 32 93 276 823 2464 7385 22148 66435 199296 597877 1793620 5380847
loop(\(x,i).(3x + ((i div 2) mod 2)),x,0)
A177881: 0 0 1 4 12 36 109 328 984 2952 8857 26572 79716 239148 717445 2152336
(1 - loop(\(x,i).(2 * (2x - (i mod 2))),x,0))
A102865: 1 3 9 35 137 547 2185 8739 34953 139811 559241 2236963 8947849 35791395 143165577 572662307
loop(\(x,i).(~1 + ((x * i) + (2 * (i mod 2)))),x,0)
A002467: 0 1 1 4 15 76 455 3186 25487 229384 2293839 25232230 302786759 3936227868 55107190151 826607852266
((x + 1) - loop(\(x,i).(2 * (x - (i mod 2))),x,0))
A094968: 1 4 7 14 25 48 91 178 349 692 1375 2742 5473 10936 21859 43706
((~x + 2) - loop(\(x,i).(2 * (x - (i mod 2))),x,0))
A322783: 2 3 4 9 18 39 80 165 334 675 1356 2721 5450 10911 21832 43677
loop(\(x,i).(10x + 8),x,0)
A002282: 0 8 88 888 8888 88888 888888 8888888 88888888 888888888 8888888888 88888888888 888888888888 8888888888888 88888888888888 888888888888888
loop(\(x,i).(2x + 32),x,0)
A175165: 0 32 96 224 480 992 2016 4064 8160 16352 32736 65504 131040 262112 524256 1048544
loop(\(x,i).((~x + 1) - (2 * (x + (i mod 2)))),x,0)
A076040: 0 ~1 4 ~13 40 ~121 364 ~1093 3280 ~9841 29524 ~88573 265720 ~797161 2391484 ~7174453
loop(\(x,i).(2x + ((~x + i) mod 3)),x,0)
A033129: 0 1 3 6 13 27 54 109 219 438 877 1755 3510 7021 14043 28086
loop(\(x,i).(2x + ((i * i) div 4)),x,0)
A272144: 0 0 1 4 12 30 69 150 316 652 1329 2688 5412 10866 21781 43618
(1 - loop(\(x,i).(3x - (i mod 2)),x,0))
A039300: 1 2 4 11 31 92 274 821 2461 7382 22144 66431 199291 597872 1793614 5380841
loop(\(x,i).(((~1 + i) div 3) - (x mod 2)),x,0)
A035662: 0 0 0 0 1 0 1 1 1 1 2 3 2 4 4 4
loop(\(x,i).(2x + ((i div 2) + (x mod 2))),x,0)
A178452: 0 0 1 4 10 22 47 98 200 404 813 1632 3270 6546 13099 26206
(((x div ~2) mod 2) + (if (x mod 2) <= 0 then x else 0))
A003815: 0 1 3 0 4 1 7 0 8 1 11 0 12 1 15 0
(1 + loop(\(x,i).(2 * (x + i)),x,0) - (x mod 2))
A166754: 1 2 9 22 53 114 241 494 1005 2026 4073 8166 16357 32738 65505 131038
(1 - loop(\(x,i).(2 * (x - (3 * i))),x,0))
A247620: 1 7 25 67 157 343 721 1483 3013 6079 12217 24499 49069 98215 196513 393115
loop(\(x,i).(2 * (((x + ~1) + (2 * i)) * i)),x,0)
A093302: 0 2 20 150 1256 12650 151932 2127230 34035920 612646866 12252937700 269564629862 6469551117240 168208329048890 4709833213369676 141294996401091150
loop(\(x,i).(6x + (i div 2)),x,0)
A178719: 0 0 1 7 44 266 1599 9597 57586 345520 2073125 12438755 74632536 447795222 2686771339 16120628041
((x mod 2) - loop(\(x,i).(2x - (i div 2)),x,0))
A083579: 0 1 1 4 8 19 39 82 166 337 677 1360 2724 5455 10915 21838
loop(\(x,i).(x + ((i * i) div 5)),x,0)
A181640: 0 0 0 1 4 9 16 25 37 53 73 97 125 158 197 242
loop(\(x,i).(7x + 3),x,0)
A120741: 0 3 24 171 1200 8403 58824 411771 2882400 20176803 141237624 988663371 6920643600 48444505203 339111536424 2373780754971
loop(\(x,i).(7x + 6),x,0)
A024075: 0 6 48 342 2400 16806 117648 823542 5764800 40353606 282475248 1977326742 13841287200 96889010406 678223072848 4747561509942
loop(\(x,i).(x + ((i * i * i) div 3)),x,0)
A173707: 0 0 2 11 32 73 145 259 429 672 1005 1448 2024 2756 3670 4795
loop(\(x,i).(x + ((i * i) div (2x + 1))),x,0)
A022554: 0 1 2 3 5 7 9 11 13 16 19 22 25 28 31 34
loop(\(x,i).(x + ((1 + i) * i * (1 + i))),x,0)
A052149: 0 4 22 70 170 350 644 1092 1740 2640 3850 5434 7462 10010 13160 17000
loop(\(x,i).(x + (2 * (i * i * (~1 + i)))),x,0)
A036464: 0 0 8 44 140 340 700 1288 2184 3480 5280 7700 10868 14924 20020 26320
loop(\(x,i).(x + ((i * i) div 6)),x,0)
A171965: 0 0 0 1 3 7 13 21 31 44 60 80 104 132 164 201
loop(\(x,i).(x + ((i * i * (1 + i)) div 2)),x,0)
A001296: 0 1 7 25 65 140 266 462 750 1155 1705 2431 3367 4550 6020 7820
loop(\(x,i).(7x + 4),x,0)
A125823: 0 4 32 228 1600 11204 78432 549028 3843200 26902404 188316832 1318217828 9227524800 64592673604 452148715232 3165041006628
loop(\(x,i).(x + (((x div 2) + i) div 4)),x,0)
A177332: 0 0 0 0 1 2 3 5 7 10 13 17 22 28 35 43
loop(\(x,i).(x + ((x + (i div 2)) * (2 + i))),x,0)
A079756: 0 0 4 29 215 1734 15630 156327 1719637 20635688 268264004 3755696121 56335441899 901367070474 15323240198170 275818323567179
loop(\(x,i).(x + (2 * (i * i * i * i))),x,0)
A259108: 0 2 34 196 708 1958 4550 9352 17544 30666 50666 79948 121420 178542 255374 356624
loop(\(x,i).(x + ((1 + (4 * i)) * i)),x,0)
A331987: 0 5 23 62 130 235 385 588 852 1185 1595 2090 2678 3367 4165 5080
loop(\(x,i).(x + (((x + 1) - (i mod 2)) * i)),x,0)
A014508: 0 0 2 8 44 264 1854 14832 133496 1334960 14684570 176214840 2290792932 32071101048 481066515734 7697064251744
loop(\(x,i).(x + ((1 + ((1 + i) * i)) * i)),x,0)
A152457: 0 3 17 56 140 295 553 952 1536 2355 3465 4928 6812 9191 12145 15760
loop(\(x,i).(x + ((4 + (i mod 2)) * i)),x,0)
A185039: 0 5 13 28 44 69 93 128 160 205 245 300 348 413 469 544
loop(\(x,i).(x + (((i * i) div 4) + i)),x,0)
A005744: 0 1 4 9 17 28 43 62 86 115 150 191 239 294 357 428
(1 + (x mod 2) - loop(\(x,i).(2x - i),x,0))
A084173: 1 3 5 13 27 59 121 249 503 1015 2037 4085 8179 16371 32753 65521
((~2x + 4) - loop(\(x,i).(2x - i),x,0))
A249453: 4 3 4 9 22 51 112 237 490 999 2020 4065 8158 16347 32728 65493
loop(\(x,i).(x + ((~1 + (2 * i)) * i * i)),x,0)
A103220: 0 1 13 58 170 395 791 1428 2388 3765 5665 8206 11518 15743 21035 27560
loop(\(x,i).(x + ((~1 + (i * i)) * i * i)),x,0)
A303916: 0 0 12 84 324 924 2184 4536 8568 15048 24948 39468 60060 88452 126672 177072
loop(\(x,i).(x + (i * i * i * i * i)),x,0)
A000539: 0 1 33 276 1300 4425 12201 29008 61776 120825 220825 381876 630708 1002001 1539825 2299200
loop(\(x,i).(~x + (i * i * i * i * i)),x,0)
A062393: 0 1 31 212 812 2313 5463 11344 21424 37625 62375 98676 150156 221137 316687 442688
loop(\(x,i).(16x + i),x,0)
A014899: 0 1 18 291 4660 74565 1193046 19088743 305419896 4886718345 78187493530 1250999896491 20015998343868 320255973501901 5124095576030430 81985529216486895
(1 - loop(\(x,i).(x - ((x div 4) + i)),x,0))
A332071: 1 2 3 5 8 11 14 17 21 25 29 33 37 41 45 49
loop(\(x,i).(10x + i),x,0)
A014824: 0 1 12 123 1234 12345 123456 1234567 12345678 123456789 1234567900 12345679011 123456790122 1234567901233 12345679012344 123456790123455
(if (x mod 11) <= 0 then 0 else 1)
A322817-A145568: 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1
(if ((x + 2) mod 7) <= 0 then 0 else 1)
A071041: 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1
(if ((x + ~2) mod 7) <= 0 then 0 else 1)
A188395: 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1
(if (x mod (3 + (x mod 3))) <= 0 then 0 else 1)
A288736: 0 1 1 0 0 0 0 1 1 0 1 1 0 1 1 0
(if ((x + 2) mod 9) <= 0 then 0 else 1)
A330548-A136712-A071025: 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1
(if ((x + 1) mod (1 + (x div 4))) <= 0 then 0 else 1)
A333189-A171157-A106799: 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 0
(if ((x + 1) mod (1 + (x mod 4))) <= 0 then 0 else 1)
A341995-A070108: 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0
(if (2x mod (x + 5)) <= 0 then 0 else 1)
A336387-A276398-A086600: 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1
(if ((x + 2) mod (2x + ~5)) <= 0 then 0 else 1)
A039737: 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1
(if ((x - (x div 3)) mod 3) <= 0 then 0 else 1)
A060584: 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1
(x - (if ((x div ~2) mod 3) <= 0 then 0 else 1))
A128054: 0 0 1 2 3 5 6 6 7 8 9 11 12 12 13 14
(if ((x mod 8) mod 3) <= 0 then 0 else 1)
A260394-A189479: 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1
(if ((x + 2) mod 12) <= 0 then 0 else 1)
A228813-A122261-A122255: 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1
(if (~2 + (x div 2) - (x mod 3)) <= 0 then 0 else 1)
A011688: 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1
(if (9 mod (x + 1)) <= 0 then 0 else 1)
A072165: 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1
(if (16 mod (x + 1)) <= 0 then 0 else 1)
A043545: 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0
(~1 + loop(\(x,i).(3x + ~1),(x + ~1),0))
A123183: ~1 ~1 ~2 ~5 ~14 ~41 ~122 ~365 ~1094 ~3281 ~9842 ~29525 ~88574 ~265721 ~797162 ~2391485
(if (~2 + (x mod 7)) <= 0 then 0 else 1)
A191153: 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0
(if ((x + 1) mod 10) <= 0 then 0 else 1)
A336556-A209929: 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1
(if (x mod (2 + ((x div 2) div 3))) <= 0 then 0 else 1)
A105469: 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1
(if (x mod ((x + ~2) - (x mod 3))) <= 0 then 0 else 1)
A239499: 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1
(x2 div (1 + (if (x mod 3) <= 0 then 2 else 0)))
A046162: 0 1 4 3 16 25 12 49 64 27 100 121 48 169 196 75
(if (~2 + (x mod 10)) <= 0 then 0 else 1)
A102671: 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1
(~1 + (if (~2 + (x div 5)) <= 0 then 2 else 0))
A189023-A053981: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ~1
(1 + (if ((x + 1) mod 8) <= 0 then 2 else 0))
A333843-A185358: 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3
(if ((x + 3) mod 8) <= 0 then 0 else 1)
A263000: 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1
(if ((x + ~4) mod 8) <= 0 then 0 else 1)
A330550-A188470-A187944-A105597-A089939: 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1
(if ((2 + (x div 2)) mod 8) <= 0 then 0 else 1)
A131217: 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1
(1 + (if (x mod 2) <= 0 then (x div 8) else 0))
A338651-A247599-A023126: 1 1 1 1 1 1 1 1 2 1 2 1 2 1 2 1
(if ((x div 2) - (x mod 8)) <= 0 then 0 else 1)
A037815: 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0
(if (~2 + (x div 2) - (x mod 4)) <= 0 then 0 else 1)
A338430: 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1
(if ((~1 + (x div 3)) mod 4) <= 0 then 0 else 1)
A204439: 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0
(1 + (if (x mod 5) <= 0 then 4 else 0))
A109009: 5 1 1 1 1 5 1 1 1 1 5 1 1 1 1 5
(if ((2 - (x div 3)) mod 4) <= 0 then 0 else 1)
A285467: 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1
(if (((x + 1) * (x div 2)) mod 4) <= 0 then 0 else 1)
A324908: 0 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0
(if ((x * (x div ~2)) mod 4) <= 0 then 0 else 1)
A224444: 0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0
(x + (x div 2) - (if (x mod 4) <= 0 then 0 else 1))
A187326: 0 0 2 3 6 6 8 9 12 12 14 15 18 18 20 21
(if (~2 + ((2x + ~4) mod (x + 2))) <= 0 then 0 else 1)
A035466: 0 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1
(if ((x2 + 1) mod (x + 4)) <= 0 then 0 else 1)
A133011: 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1
(if ((x + ~2) * (~1 + (x mod 3))) <= 0 then 0 else 1)
A181663: 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0
(x - (if ((x + 1) mod 3) <= 0 then 2 else ~1))
A004482: 1 2 0 4 5 3 7 8 6 10 11 9 13 14 12 16
(if (x mod 2) <= 0 then (x div 8) else ~1)
A270370: 0 ~1 0 ~1 0 ~1 0 ~1 1 ~1 1 ~1 1 ~1 1 ~1
(x - (if (x mod 2) <= 0 then (x mod 4) else ~1))
A291330: 0 2 0 4 4 6 4 8 8 10 8 12 12 14 12 16
(1 - (1 mod loop(\(x,i).(~2x + 1),x,~1)))
A279030: 1 0 5 0 21 0 85 0 341 0 1365 0 5461 0 21845 0
(x2 - (x mod loop(\(x,i).2x,x,~1)))
A290699: 0 2 6 14 28 52 94 170 312 584 1114 2158 4228 8348 16566 32978
(2 - loop(\(x,i).(x + (x div 4)),x,~1))
A100586: 3 4 5 6 7 9 11 14 17 21 26 32 40 50 62 77
(if (x * ((x + 1) mod 5)) <= 0 then 0 else 1)
A022930: 0 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1
(1 + (if (x mod 12) <= 0 then x else 0))
A251072: 1 1 1 1 1 1 1 1 1 1 1 1 13 1 1 1
(1 + loop(\(x,i).(i - ((1 + i) mod (x + 1))),x,0))
A279170: 1 2 2 4 4 4 4 8 8 8 8 8 8 8 8 16
(1 + loop(\(x,i).((2x + 1) mod (1 + i)),x,0))
A079878: 1 2 1 2 4 2 4 8 7 4 8 4 8 2 4 8
(~1 + (if (x + ~10) <= 0 then x else 0))
A216587: ~1 0 1 2 3 4 5 6 7 8 9 ~1 ~1 ~1 ~1 ~1
(1 + (if (x mod 10) <= 0 then x else 0))
A268357: 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1
(if (x * ((x + 1) mod 8)) <= 0 then 0 else 1)
A022932: 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0
(1 + loop(\(x,i).(~5x + 1),x,0))
A166122: 1 2 ~3 22 ~103 522 ~2603 13022 ~65103 325522 ~1627603 8138022 ~40690103 203450522 ~1017252603 5086263022
(~1 + loop(\(x,i).(5x + 2),x,0))
A137410: ~1 1 11 61 311 1561 7811 39061 195311 976561 4882811 24414061 122070311 610351561 3051757811 15258789061
((x div 7) + (if x <= 0 then 0 else 1))
A195174: 0 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3
(((1 + (x div 2)) div 3) + (if x <= 0 then 0 else 1))
A340764-A321018-A056556: 0 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3
((((x + 1) div 2) div 3) + (if x <= 0 then 0 else 1))
A111854: 0 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3
(x - (((x div 2) div 3) + (if x <= 0 then 0 else 1)))
A172266: 0 0 1 2 3 4 4 5 6 7 8 9 9 10 11 12
(((x2 + 2x) div 3) + (if x <= 0 then 0 else 1))
A280984: 0 2 3 6 9 12 17 22 27 34 41 48 57 66 75 86
((x + 2) + (if x <= 0 then 0 else 1) - (x div ~2))
A005781: 2 5 6 8 9 11
A049636: 2 5 6 8 9 11 12 14 15 17 18 20 21 23 24 26
(((x div ~3) mod 2) - (if x <= 0 then 0 else 1))
A000493: 0 0 0 0 ~1 ~1 ~1 0 0 0 ~1 ~1 ~1 0 0 0
((x mod 10) - (if x <= 0 then 0 else 1))
A321999: 0 0 1 2 3 4 5 6 7 8 ~1 0 1 2 3 4
(((1 + (x div 4)) div 2) + (if x <= 0 then 0 else 1))
A000193: 0 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3
((((x div 2) mod 3) div 2) + (if x <= 0 then 0 else 1))
A328483-A321856: 0 1 1 1 2 2 1 1 1 1 2 2 1 1 1 1
(((x2 + 3x + 2) div 2) + (if x <= 0 then 0 else 1))
A134869: 1 4 7 11 16 22 29 37 46 56 67 79 92 106 121 137
(((x - ((x div 2) mod 2)) div 2) + (if x <= 0 then 0 else 1))
A049206: 0 1 1 2 3 3 3 4 5 5 5 6 7 7 7 8
(((x mod (2 + (x mod 2))) div 2) + (if x <= 0 then 0 else 1))
A132126: 0 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1
(((x + 1) mod (2 + (x mod 2))) - (if x <= 0 then 0 else 1))
A163817: 1 1 0 0 0 ~1 0 1 0 0 0 ~1 0 1 0 0
(((~x + 1) mod (2 + (x mod 2))) - (if x <= 0 then 0 else 1))
A163811: 1 ~1 0 0 0 1 0 ~1 0 0 0 1 0 ~1 0 0
(x + (((x div 2) div 3) + (if x <= 0 then 0 else 1)))
A195178: 0 2 3 4 5 6 8 9 10 11 12 13 15 16 17 18
((x + 16) + (if x <= 0 then 0 else 1))
A043705-A043675: 16 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
(1 + loop(\(x,i).((2 * (x + (2 * i))) + i),x,0))
A247904: 1 6 21 56 131 286 601 1236 2511 5066 10181 20416 40891 81846 163761 327596
(~1 + loop(\(x,i).(x * i),(x div 5),1))
A252930: 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 5
loop(\(x,i).i,(~1 + (x div (3 + (x mod 2)))),1)
A329340: 1 1 1 1 1 1 1 1 1 1 2 1 3 2 3 2
loop(\(x,i).(x + i),(~1 + ((x + ~2) div 3)),1)
A001584: 1 1 1 1 1 1 1 1 2 2 2 4 4 4 7 7
(~1 + loop(\(x,i).(x * (i * i * i)),(x + 1),1))
A046033: 0 7 215 13823 1727999 373247999 128024063999 65548320767999 47784725839871999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(2 * (x + (x div 2))),(x + ~1),1))
A154992: 0 0 1 5 17 53 161 485 1457 4373 13121 39365 118097 354293 1062881 3188645
(1 + (x div (1 + (if (x mod 3) <= 0 then 0 else 2))))
A087507: 1 1 1 4 2 2 7 3 3 10 4 4 13 5 5 16
(1 + ((x + 2) div (if (x mod 2) <= 0 then ~2 else 1)))
A174390: 0 4 ~1 6 ~2 8 ~3 10 ~4 12 ~5 14 ~6 16 ~7 18
(~1 + loop(\(x,i).~2x,x,~3))
A140683: ~4 5 ~13 23 ~49 95 ~193 383 ~769 1535 ~3073 6143 ~12289 24575 ~49153 98303
loop(\(x,i).(x * i),x,(1 + (x mod ~3)))
A194770: 1 ~1 0 6 ~24 0 720 ~5040 0 362880 ~3628800 0 479001600 ~6227020800 0 1307674368000
loop(\(x,i).(2 * i),(x + ~7),1)
A322405: 1 1 1 1 1 1 1 1 2 4 6 8 10 12 14 16
(1 + loop(\(x,i).x2,x,7))
A078304: 8 50 2402 5764802 33232930569602 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * i),x,7))
A229554: 8 8 15 43 169 841 5041 35281 282241 2540161 25401601 279417601 3353011201 43589145601 610248038401 9153720576001
(~1 + loop(\(x,i).(x * i),x,7))
A229828: 6 6 13 41 167 839 5039 35279 282239 2540159 25401599 279417599 3353011199 43589145599 610248038399 9153720575999
(1 + ((2 + (x div 2)) div (1 + (if x <= 0 then 1 else 2))))
A060508: 2 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4
(1 + (if (x mod 2) <= 0 then 16 else 1))
A283894: 17 2 17 2 17 2 17 2 17 2 17 2 17 2 17 2
(x mod (1 + (if (x mod 8) <= 0 then 2 else 1)))
A255327: 0 1 0 1 0 1 0 1 2 1 0 1 0 1 0 1
(1 + (x div (if (x mod 8) <= 0 then 2 else 1)))
A234741: 1 2 3 4 5 6 7 8 5 10 11 12 13 14 15 16
(1 + loop(\(x,i).2x,x,9))
A083705: 10 19 37 73 145 289 577 1153 2305 4609 9217 18433 36865 73729 147457 294913
loop(\(x,i).2x,(x + ~9),1)
A275076-A275064-A113019-A113010: 1 1 1 1 1 1 1 1 1 1 2 4 8 16 32 64
loop(\(x,i).(~2 + i),(x + ~9),1)
A307651: 1 1 1 1 1 1 1 1 1 1 ~1 0 1 2 3 4
loop(\(x,i).(x + i),(x + ~9),1)
A212368: 1 1 1 1 1 1 1 1 1 1 2 4 7 11 16 22
(1 + (if (x + ~4) <= 0 then x else 5))
A101272: 1 2 3 4 5 6 6 6 6 6 6 6 6 6 6 6
(1 + loop(\(x,i).4x,x,5))
A199115: 6 21 81 321 1281 5121 20481 81921 327681 1310721 5242881 20971521 83886081 335544321 1342177281 5368709121
(1 + loop(\(x,i).(x2 + x),x,5))
A144780: 6 31 931 865831 749662454731 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x + (x div 2)),x,5))
A183208: 6 8 11 16 23 34 50 74 110 164 245 367 550 824 1235 1852
(if (x mod 2) <= 0 then (2 mod (1 + (x div 4))) else 1)
A221171: 0 1 0 1 0 1 0 1 2 1 2 1 2 1 2 1
(1 + loop(\(x,i).4x,(2x + 4),1))
A209533: 257 4097 65537 1048577 16777217 268435457 4294967297 68719476737 1099511627777 17592186044417 281474976710657 4503599627370497 72057594037927937 1152921504606846977 4611686018427387903
(~1 + loop(\(x,i).4x,4x,1))
A175824: 0 255 65535 16777215 4294967295 1099511627775 281474976710655 72057594037927935 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x + 1),(~3 + (x div 2)),1)
A147096: 1 1 1 1 1 1 1 1 3 3 7 7 15 15 31 31
(~1 + loop(\(x,i).(x * i),(2x2 + 4),1))
A181745: 23 719 479001599 4611686018427387903
loop(\(x,i).(x * i),(~1 + (2 * (x2 div 2))),1)
A028366: 1 1 6 5040 1307674368000 4611686018427387903 4611686018427387903
(1 + (3 * loop(\(x,i).(2x + i),x,1)))
A227712: 4 10 25 58 127 268 553 1126 2275 4576 9181 18394 36823 73684 147409 294862
(1 + (3 * (if (~2 + (x div 2)) <= 0 then 0 else 2)))
A108689: 1 1 1 1 1 1 7 7 7 7 7 7 7 7 7 7
loop(\(x,i).(x + 2),(~3 + ((x + ~1) div 2)),1)
A237718: 1 1 1 1 1 1 1 1 1 3 3 5 5 7 7 9
loop(\(x,i).2x,x,13)
A005029: 13 26 52 104 208 416 832 1664 3328 6656 13312 26624 53248 106496 212992 425984
loop(\(x,i).x2,x,13)
A176596: 13 169 28561 815730721 665416609183179841 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,11)
A005015: 11 22 44 88 176 352 704 1408 2816 5632 11264 22528 45056 90112 180224 360448
loop(\(x,i).x2,x,11)
A176595: 11 121 14641 214358881 45949729863572161 4611686018427387903 4611686018427387903
loop(\(x,i).(x + 2),(x + ~12),1)
A133854: 1 1 1 1 1 1 1 1 1 1 1 1 1 3 5 7
loop(\(x,i).(2 * i),(x + ~12),1)
A224813: 1 1 1 1 1 1 1 1 1 1 1 1 1 2 4 6
(1 + loop(\(x,i).x2,x,12))
A152585: 13 145 20737 429981697 184884258895036417 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),12x,1)
A181728: 1 479001600 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (~x + 2) <= 0 then ((2 + (x div 2)) div 3) else 1)
A122521-A033271: 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3
(1 + (if (x mod 2) <= 0 then ((x div 2) mod 2) else 3))
A176895: 1 4 2 4 1 4 2 4 1 4 2 4 1 4 2 4
(1 + (3 * loop(\(x,i).(2x + 1),x,2)))
A176449: 7 16 34 70 142 286 574 1150 2302 4606 9214 18430 36862 73726 147454 294910
(1 + (3 * loop(\(x,i).4x,x,2)))
A199116: 7 25 97 385 1537 6145 24577 98305 393217 1572865 6291457 25165825 100663297 402653185 1610612737 6442450945
loop(\(x,i).i,(~3 + ((x * (x mod 2)) div 2)),1)
A195843: 1 1 1 1 1 1 1 1 1 1 1 2 1 3 1 4
loop(\(x,i).(x + (i div 2)),((x + 2) div 3),1)
A179269: 1 1 1 1 2 2 2 3 3 3 5 5 5 7 7 7
loop(\(x,i).x2,1,(6x + 1))
A016922: 1 49 169 361 625 961 1369 1849 2401 3025 3721 4489 5329 6241 7225 8281
loop(\(x,i).x2,2,(6x + 1))
A016924: 1 2401 28561 130321 390625 923521 1874161 3418801 5764801 9150625 13845841 20151121 28398241 38950081 52200625 68574961
loop(\(x,i).x2,1,(6x + ~1))
A174371: 1 25 121 289 529 841 1225 1681 2209 2809 3481 4225 5041 5929 6889 7921
(1 + loop(\(x,i).3x,2x,3))
A199561: 4 28 244 2188 19684 177148 1594324 14348908 129140164 1162261468 10460353204 94143178828 847288609444 7625597484988 68630377364884 617673396283948
(1 + (if ((x div 2) mod 2) <= 0 then (x mod 2) else 3))
A094225: 1 2 4 4 1
(1 + loop(\(x,i).6x,x,3))
A199318: 4 19 109 649 3889 23329 139969 839809 5038849 30233089 181398529 1088391169 6530347009 39182082049 235092492289 1410554953729
(~1 + loop(\(x,i).6x,x,3))
A198796: 2 17 107 647 3887 23327 139967 839807 5038847 30233087 181398527 1088391167 6530347007 39182082047 235092492287 1410554953727
loop(\(x,i).(x * i),9x,1)
A195393: 1 362880 6402373705728000 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (3 * loop(\(x,i).2x,(x + ~1),x)))
A048474: 1 4 13 37 97 241 577 1345 3073 6913 15361 33793 73729 159745 344065 737281
(1 + loop(\(x,i).8x,x,3))
A199494: 4 25 193 1537 12289 98305 786433 6291457 50331649 402653185 3221225473 25769803777 206158430209 1649267441665 13194139533313 105553116266497
(~1 + loop(\(x,i).8x,x,3))
A198851: 2 23 191 1535 12287 98303 786431 6291455 50331647 402653183 3221225471 25769803775 206158430207 1649267441663 13194139533311 105553116266495
(if ((x mod 3) mod 2) <= 0 then (x div 3) else 1)
A103627: 0 1 0 1 1 1 2 1 2 3 1 3 4 1 4 5
loop(\(x,i).2x,((x div 2) - (x div 3)),1)
A140426: 1 1 2 1 2 2 2 2 4 2 4 4 4 4 8 4
(if (x mod 3) <= 0 then 0 else (1 + (x div 3)))
A087508: 0 1 1 0 2 2 0 3 3 0 4 4 0 5 5 0
loop(\(x,i).((x + 1) + (i div 2)),(x div 3),1)
A086159: 1 1 1 2 2 2 4 4 4 6 6 6 9 9 9 12
loop(\(x,i).5x,(x mod 3),1)
A271378: 1 5 25 1 5 25 1 5 25 1 5 25 1 5 25 1
(1 + loop(\(x,i).5x,x,3))
A199214: 4 16 76 376 1876 9376 46876 234376 1171876 5859376 29296876 146484376 732421876 3662109376 18310546876 91552734376
(~1 + ((if (x mod 2) <= 0 then (~x + 1) else x) mod 3))
A131736: 0 0 1 ~1 ~1 1 0 0 1 ~1 ~1 1 0 0 1 ~1
(~1 + ((x + (if (x mod 2) <= 0 then 2 else x)) mod 3))
A016350-A016345-A016333-A015947-A011652-A011649-A010892-A000484: 1 1 0 ~1 ~1 0 1 1 0 ~1 ~1 0 1 1 0 ~1
(1 + loop(\(x,i).(x * (4 + i)),x,3))
A139155: 4 16 91 631 5041 45361 453601 4989601 59875201 778377601 10897286401 163459296001 2615348736001 44460928512001 800296713216001 15205637551104001
(~1 + loop(\(x,i).(x * (4 + i)),x,3))
A139183: 2 14 89 629 5039 45359 453599 4989599 59875199 778377599 10897286399 163459295999 2615348735999 44460928511999 800296713215999 15205637551103999
loop(\(x,i).3x,(x2 div 3),1)
A168495: 1 1 3 27 243 6561 531441 43046721 10460353203 7625597484987 5559060566555523 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((x + (x div 2)) div (if (~x + 2) <= 0 then 2 else 1)))
A272206: 1 2 2 3 4 4 5 6 7 7 8 9 10 10 11 12
(~1 + loop(\(x,i).(x * (x - i)),2,(x + 3)))
A069756: 23 119 359 839 1679 3023 5039 7919 11879 17159 24023 32759 43679 57119 73439 93023
(1 + loop(\(x,i).8x,2x,1))
A228081: 2 65 4097 262145 16777217 1073741825 68719476737 4398046511105 281474976710657 18014398509481985 1152921504606846977 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),((2x + ~1) + (x mod 2)),1)
A169661: 1 2 6 720 5040 3628800 39916800
loop(\(x,i).6x,(2x + 1),1)
A013711: 6 216 7776 279936 10077696 362797056 13060694016 470184984576 16926659444736 609359740010496 21936950640377856 789730223053602816 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).8x,(2x + 1),1)
A013713: 8 512 32768 2097152 134217728 8589934592 549755813888 35184372088832 2251799813685248 144115188075855872 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x + 2),(2x + 1),1)
A198963: 5 53 485 4373 39365 354293 3188645 28697813 258280325 2324522933 20920706405 188286357653 1694577218885 15251194969973 137260754729765 1235346792567893
loop(\(x,i).5x,(2x + 1),1)
A013710: 5 125 3125 78125 1953125 48828125 1220703125 30517578125 762939453125 19073486328125 476837158203125 11920928955078125 298023223876953125 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((i div 2) + i)),(2x + 1),1)
A176731: 1 12 504 45360 7076160 1698278400 580811212800 268334780313600 161000868188160000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x * (1 + i)),(2x + ~1),1)
A274304: 1 4 192 23040 5160960 1857945600 980995276800 714164561510400 685597979049984000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (x + (x div 2))),(2x + ~1),1)
A270369: 1 2 18 162 1458 13122 118098 1062882 9565938 86093442 774840978 6973568802 62762119218 564859072962 5083731656658 45753584909922
((2x + 4) - loop(\(x,i).i,(~1 + (x div 2)),1))
A186383: 3 5 7 9 11 13 14 16 17 19 20 22 23 25 26 28
(1 + (2x mod (if (~x + 2) <= 0 then (x div 2) else 1)))
A334949: 1 1 1 1 1 1 1 3 1 3 1 3 1 3 1 3
loop(\(x,i).i,(~1 + (x div 3) - (x mod 2)),1)
A322391: 1 1 1 1 1 1 1 1 1 1 2 1 3 2 3 3
(1 + (if (~2 + (x div 3)) <= 0 then (x mod 2) else 1))
A111627: 1 2 1 2 1 2 1 2 1 2 2 2 2 2 2 2
loop(\(x,i).(2x + 1),(x div (1 + (x mod 2))),1)
A290235: 1 1 7 3 31 7 127 15 511 31 2047 63 8191 127 32767 255
loop(\(x,i).(x * i),x,(1 + (x div (1 + (x mod 2)))))
A191662: 1 1 6 12 120 360 5040 20160 362880 1814400 39916800 239500800 6227020800 43589145600 1307674368000 10461394944000
loop(\(x,i).2x,(x - (x div (1 + (x mod 2)))),1)
A072345: 1 2 1 4 1 8 1 16 1 32 1 64 1 128 1 256
(1 + ((if x <= 0 then 1 else x2) * (1 + (x mod 2))))
A130076: 2 3 5 19
loop(\(x,i).(x * i),(~1 + (x2 * (x mod 2))),1)
A168359: 1 1 1 40320
(1 + loop(\(x,i).12x,x,1))
A178248: 2 13 145 1729 20737 248833 2985985 35831809 429981697 5159780353 61917364225 743008370689 8916100448257 106993205379073 1283918464548865 15407021574586369
(~1 + loop(\(x,i).12x,x,1))
A024140: 0 11 143 1727 20735 248831 2985983 35831807 429981695 5159780351 61917364223 743008370687 8916100448255 106993205379071 1283918464548863 15407021574586367
(2 div (1 + (if ((x div 2) mod 3) <= 0 then x else 1)))
A090405: 2 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1
(1 + (x div loop(\(x,i).(1 + (i div (x + 2))),x,1)))
A137467: 1 2 3 2 3 3 4
A257213: 1 2 3 2 3 3 4 4 3 5 4 4 5 5 5 4
(~1 + loop(\(x,i).4x,(x2 + x),1))
A172322: 0 15 4095 16777215 1099511627775 1152921504606846975 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if (~2 + (x div 5)) <= 0 then x else 1))
A216455: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 2
(1 + loop(\(x,i).10x,x,1))
A062397: 2 11 101 1001 10001 100001 1000001 10000001 100000001 1000000001 10000000001 100000000001 1000000000001 10000000000001 100000000000001 1000000000000001
(~1 + loop(\(x,i).10x,x,1))
A002283: 0 9 99 999 9999 99999 999999 9999999 99999999 999999999 9999999999 99999999999 999999999999 9999999999999 99999999999999 999999999999999
loop(\(x,i).(x * (2 + i)),(x2 + 2x + ~1),1)
A264040: 1 12 181440 10461394944000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((~2x + 1) mod loop(\(x,i).2x,x,1)))
A132824: 1 2 2 4 10 24 54 116 242 496 1006 2028 4074 8168 16358 32740
((x2 + ~x + 1) + loop(\(x,i).2x,x,1))
A201363: 2 3 7
A020873: 2 3 7 15 29 53 95 171 313 585 1115 2159 4229 8349 16567 32979
(((x + 1) div 2) mod (1 + (if (x mod 2) <= 0 then x else 1)))
A166514: 0 1 1 0 2 1 3 0 4 1 5 0 6 1 7 0
(~1 + loop(\(x,i).((x * (1 + i)) + (i mod 2)),x,1))
A001540: 0 2 8 36 184 1110 7776 62216 559952 5599530 61594840 739138092 9608795208 134523132926 2017846993904 32285551902480
(1 + ((x + 1) * loop(\(x,i).x2,2,3)))
A158123: 82 163 244 325 406 487 568 649 730 811 892 973 1054 1135 1216 1297
(~1 + ((x + 1) * loop(\(x,i).x2,2,(x + 1))))
A258807: 0 31 242 1023 3124 7775 16806 32767 59048 99999 161050 248831 371292 537823 759374 1048575
(1 + loop(\(x,i).(x * (x - i)),(x + ~1),(x + 1)))
A201363: 2 3 7
A062935: 2 3 7 121
(1 + loop(\(x,i).(x3 + ~1),2,(x + 1)))
A117197: 0 343 17576 250047 1906624 9938375 40001688 133432831 385828352 997002999 2352637000 5150827583 10590025536 20638466407 38409197624 68669157375
(~1 + ((x + 1) * (2 + loop(\(x,i).(x * i),x,1))))
A139464: 2 5 11 31 129 731 5053 40335 362897 3628819 39916821 479001623 6227020825 87178291227 1307674368029 20922789888031
(1 + ((x + 1) * loop(\(x,i).2x2,2,2)))
A157951: 129 257 385 513 641 769 897 1025 1153 1281 1409 1537 1665 1793 1921 2049
(~1 + ((x + 1) * loop(\(x,i).2x2,2,2)))
A157949: 127 255 383 511 639 767 895 1023 1151 1279 1407 1535 1663 1791 1919 2047
(1 + ((x + 1) * loop(\(x,i).x2,2,4)))
A158231: 257 513 769 1025 1281 1537 1793 2049 2305 2561 2817 3073 3329 3585 3841 4097
(~1 + ((x + 1) * loop(\(x,i).x2,2,4)))
A158250: 255 511 767 1023 1279 1535 1791 2047 2303 2559 2815 3071 3327 3583 3839 4095
loop(\(x,i).x2,2,(4x + 3))
A016840: 81 2401 14641 50625 130321 279841 531441 923521 1500625 2313441 3418801 4879681 6765201 9150625 12117361 15752961
(1 + loop(\(x,i).(x * (i * i)),4,(x + 1)))
A158370: 577 1153 1729 2305 2881 3457 4033 4609 5185 5761 6337 6913 7489 8065 8641 9217
(~1 + loop(\(x,i).(x * (i * i)),4,(x + 1)))
A158372: 575 1151 1727 2303 2879 3455 4031 4607 5183 5759 6335 6911 7487 8063 8639 9215
(~1 + ((x + 1) * loop(\(x,i).(x2 + 2x),2,2)))
A046050: 79 159 239 319 399 479 559
(~1 + ((x + 1) * loop(\(x,i).x3,2,2)))
A158011: 511 1023 1535 2047 2559 3071 3583 4095 4607 5119 5631 6143 6655 7167 7679 8191
(~1 + loop(\(x,i).(2x + 2),x,(2 div (x + 1))))
A290113: 1 3 5 13 29 61 125 253 509 1021 2045 4093 8189 16381 32765 65533
((x + 1) - (loop(\(x,i).2x,x,2) mod (x + 1)))
A082494: 1 2 1 4 3 2 5 8 1 6 9 8 11 10 7 16
loop(\(x,i).(x * i),x,(x2 + 3x + 1))
A213167: 1 5 22 114 696 4920 39600 357840 3588480 39553920 475372800 6187104000 86699289600 1301447347200 20835611596800 354379753728000
loop(\(x,i).x2,1,(2x2 + 2x + 1))
A007204: 1 25 169 625 1681 3721 7225 12769 21025 32761 48841 70225 97969 133225 177241 231361
(1 + (loop(\(x,i).2x,x,2x) div (x + 1)))
A213255: 1 3 6 13 26 54 110 225 456 922 1862 3755 7562 15214 30584 61441
(1 + ((x + 1) * ((if x <= 0 then 1 else x) + (x mod 2))))
A181447: 2 5 7 17
(1 + loop(\(x,i).(x2 * (i * i)),2,(x + 1)))
A211412: 5 65 325 1025 2501 5185 9605 16385 26245 40001 58565 82945 114245 153665 202501 262145
loop(\(x,i).(x * ((2 + i) * (2 + i))),(x + 1),1)
A162993: 9 144 3600 129600 6350400 406425600 32920473600 3292047360000 398337730560000 57360633200640000 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + ((x + 1) * (~x + loop(\(x,i).2x,x,1))))
A092442: 0 1 5 19 59 161 405 967 2231 5029 11153 24443 53091 114505 245549 524047
(1 + ((x + 1) * loop(\(x,i).2x,(x + ~1),x)))
A318165: 1 3 13
A048482: 1 3 13 49 161 481 1345 3585 9217 23041 56321 135169 319489 745473 1720321 3932161
(~1 + ((x + 1) * loop(\(x,i).(x2 + 2x),2,x)))
A126426: ~1 29 239 1019 3119 7769 16799 32759 59039 99989 161039 248819 371279 537809 759359 1048559
loop(\(x,i).(x * ((i div 2) + (2 * i))),(x + 1),1)
A317980: 2 10 70 700 8400 126000 2142000 42840000 942480000 23562000000 636174000000 19085220000000 610727040000000 21375446400000000 790891516800000000 4611686018427387903
loop(\(x,i).(~x + (2 * (i * i * i))),(x + 1),1)
A126950: 1 15 39 89 161 271 415 609 849 1151 1511 1945 2449 3039 3711 4481
loop(\(x,i).(x * (x + ((i mod 2) * i))),(x + 1),1)
A329102: 2 4 28 784
loop(\(x,i).(x * ((i div 3) + i)),(x + 1),1)
A319949: 1 2 8 40 240 1920 17280 172800 2073600 26956800 377395200 6038323200 102651494400 1847726899200 36954537984000 776045297664000
loop(\(x,i).(1 + (x2 mod (1 + i))),(x + ~1),1)
A125678: 1 1 2 2 1 2 5 5 2 5 6 4 5 13 2 5
(1 + ((x + ~1) * loop(\(x,i).(1 + (x * i)),x,1)))
A093964: 0 1 6 33 196 1305 9786 82201 767208 7891281 88776910 1085051121 14322674796 203121569833 3080677142466 49764784609065
(1 + ((x + ~1) * loop(\(x,i).x2,2,(x + ~1))))
A002561: 0 1 2 33 244 1025 3126 7777 16808 32769 59050 100001 161052 248833 371294 537825
loop(\(x,i).(2 * (x - (x div ~2))),(x + ~1),1)
A052156: 1 1 4 12 36 108 324 972 2916 8748 26244 78732 236196 708588 2125764 6377292
loop(\(x,i).(2 * ((x * i) + (x div 2))),(x + ~1),1)
A293962: 1 1 2 10 70 630 6930 90090 1351350 22972950 436486050 9166207050 210822762150 5270569053750 142305364451250 4126855569086250
loop(\(x,i).(x * i),x,(x2 + x + ~3))
A152456: ~3 ~1 6 54 408 3240 28080 267120 2782080 31570560 388281600 5149267200 73287244800 1114636723200 18045906278400 309918825216000
(1 + loop(\(x,i).2x,(x + ~1),1) - (x mod 2))
A052950: 2 1 3 4 9 16 33 64 129 256 513 1024 2049 4096 8193 16384
loop(\(x,i).((2x * i) - (x div 2)),(x + ~1),1)
A119602: 1 1 2 7 39
loop(\(x,i).(x * (1 + (2 * (1 + i)))),(x + ~1),1)
A102147: 1 1 5 35 315 3465 45045 675675 11486475 218243025 4583103525 105411381075 2635284526875 71152682225625 2063427784543125 63966261320836875
loop(\(x,i).(x * (1 + (4 * i))),(x + ~1),1)
A007696: 1 1 5 45 585 9945 208845 5221125 151412625 4996616625 184874815125 7579867420125 341094033905625 16713607661375625 885821206052908125 4611686018427387903
loop(\(x,i).(x * (2 + ((2 + i) * i))),(x + ~1),1)
A051893: 1 1 5 50 850 22100 817700 40885000 2657525000 217917050000 22009622050000 2685173890100000 389350214064500000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((1 + (2 * i)) * i)),(x + ~1),1)
A327021: 1 1 3 30 630 22680 1247400 97297200 10216206000 1389404016000 237588086736000 49893498214560000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + ((x - (i mod 2)) * i)),(x + ~1),1)
A174318: 1 1 1 3 9 45 265 1855 14833 133497 1334961 14684571 176214841 2290792933 32071101049 481066515735
loop(\(x,i).(x + (i * i * i * i)),(x + ~1),1)
A267691: 1 1 2 18 99 355 980 2276 4677 8773 15334 25334 39975 60711 89272 127688
loop(\(x,i).((2 + (x2 div 2)) * i),(x + ~1),1)
A008926: 1 1 2 8 102
(1 + loop(\(x,i).7x,x,1))
A034491: 2 8 50 344 2402 16808 117650 823544 5764802 40353608 282475250 1977326744 13841287202 96889010408 678223072850 4747561509944
(1 + (if (x + ~4) <= 0 then x else (x2 + 1)))
A084853: 1 2 3 4 5 27
(1 + loop(\(x,i).(x * (i * i * i * i)),x,1))
A260478: 2 2 17 1297 331777 207360001 268738560001 645241282560001 2642908293365760001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if (~2 + (x div 5)) <= 0 then 0 else 2))
A339876-A333844-A318497-A317933-A223728-A223726-A069292: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3
(1 + (if (~6 + (x div 2)) <= 0 then 0 else 2))
A147381-A147343-A147072-A146906-A105592-A072917: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3
(x - (if (~1 + (x mod 3)) <= 0 then ~2 else 1))
A130508: 2 3 1 5 6 4 8 9 7 11 12 10 14 15 13 17
(if ((x + 1) mod 5) <= 0 then ~2 else 1)
A140345: 1 1 1 1 ~2 1 1 1 1 ~2 1 1 1 1 ~2 1
((if (x + ~2) <= 0 then 1 else 2) - (x div ~3))
A138161: 1 2 2 3 4 4 4 5 5
loop(\(x,i).(x * i),((x mod 2) - (x div ~2)),1)
A284434: 1 2 1 6 2 24 6
((x + 2) - ((~x + 1) div (1 + (if x <= 0 then 0 else 2))))
A186145: 1 3 5 6 7 9 10 11 13 14 15 17 18 19 21 22
(1 + ((x - loop(\(x,i).(i - (x * i)),x,0)) div 2))
A009281: 1 1 2 1 7 ~19 136 ~923 7421 ~66743 667486 ~7342279 88107427 ~1145396459 16035550532 ~240533257859
(1 + ((x - (if (x + ~4) <= 0 then 0 else 1)) mod 2))
A083921: 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1
(if (~1 + ((x div 2) mod 5)) <= 0 then 2 else 1)
A078786: 2 2 2 2 1 1 1 1 1 1 2 2 2 2 1 1
(1 + ((x mod (1 + (if (x + ~2) <= 0 then 0 else 2))) div 2))
A107751: 1 1 1 1 1 2 1 1 2 1 1 2 1 1 2 1
(if ((x + 1) mod 7) <= 0 then 2 else 1)
A043280-A022931: 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1
loop(\(x,i).i,((x mod 7) div 2),1)
A106797: 1 1 1 1 2 2 3 1 1 1 1 2 2 3 1 1
(if ((x + 2) mod 9) <= 0 then 2 else 1)
A337584-A325989-A325625-A318672-A280940-A270419-A245690-A134870-A091887-A055229: 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1
(if ((x + ~2) mod 9) <= 0 then 2 else 1)
A078379-A031260: 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1
(1 + (x mod (if (~2 + (x div 4)) <= 0 then 1 else 2)))
A297782-A043565-A043541: 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2
(1 + (x mod (if (~4 + (x div 2)) <= 0 then 1 else 2)))
A215745: 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2
(1 + (if (~2 + (x div (2 + (x mod 2)))) <= 0 then 1 else 2))
A212300: 2 2 2 2 2 2 3 2 3 3 3 3 3 3 3 3
(if ((1 + (x div 2)) mod 5) <= 0 then 2 else 1)
A337198-A335208-A030409-A025453: 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1
(if ((2 + (x div 2)) mod 5) <= 0 then 2 else 1)
A030407: 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1
loop(\(x,i).(x + 2),(x + ~10),1)
A133848: 1 1 1 1 1 1 1 1 1 1 1 3 5 7 9 11
loop(\(x,i).2x,(x + ~10),1)
A275077-A275065: 1 1 1 1 1 1 1 1 1 1 1 2 4 8 16 32
loop(\(x,i).(x + i),(x + ~10),1)
A212369: 1 1 1 1 1 1 1 1 1 1 1 2 4 7 11 16
loop(\(x,i).(x * i),(x mod 10),1)
A066459: 1 1 2 6 24 120 720 5040 40320 362880 1 1 2 6 24 120
(1 + loop(\(x,i).x2,x,10))
A080176: 11 101 10001 100000001 10000000000000001 4611686018427387903 4611686018427387903
(if (2x mod (x + 5)) <= 0 then 2 else 1)
A136441: 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
(1 + (loop(\(x,i).(x + i),(~2 + (x div 2)),1) div 2))
A108104: 1 1 1 1 1 1 2 2 3 3 4 4 6 6 9 9
(if x <= 0 then 0 else (1 + (2 * ((x + ~1) mod 3))))
A021078: 0 1 3 5 1 3 5 1 3 5 1 3 5 1 3 5
(if ((x + 1) mod 12) <= 0 then 2 else 1)
A340654-A340596-A338160-A334933-A330461-A327528-A323719-A323163-A322320-A322318-A320105-A309004-A308479-A304779-A285337-A282749-A275215-A274193-A264857-A215870-A213211-A194673-A146291-A107910-A063686-A062760-A043285-A014649-A003652: 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
(if ((x + ~1) mod 12) <= 0 then 2 else 1)
A333254: 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1
(if ((x + 2) mod 12) <= 0 then 2 else 1)
A344008-A286520-A249771-A198067-A124778-A103754-A088530-A083911-A083230-A057523-A053632-A043284: 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
(if (x - (3 * (~2 + (x div 2)))) <= 0 then 2 else 1)
A297781-A043564-A043540: 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2
(7 + loop(\(x,i).x2,x,2))
A130730: 9 11 23 263 65543 4294967303 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,x,1) div 7)
A155803: 0 0 0 1 2 4 9 18 36 73 146 292 585 1170 2340 4681
(if (x + ~1) <= 0 then 2x else 7)
A021040: 0 2 7 7 7 7 7 7 7 7 7 7 7 7 7 7
(if x <= 0 then 1 else ((x div 2) div 7))
A284991-A017908: 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
loop(\(x,i).4x,x,7)
A002042: 7 28 112 448 1792 7168 28672 114688 458752 1835008 7340032 29360128 117440512 469762048 1879048192 7516192768
((if x <= 0 then 1 else x) - (x div 7))
A213851: 1 1 2 3 4 5 6 6 7 8 9 10 11 12 12 13
loop(\(x,i).3x,x,7)
A005032: 7 21 63 189 567 1701 5103 15309 45927 137781 413343 1240029 3720087 11160261 33480783 100442349
loop(\(x,i).(x * (1 + i)),x,7)
A062098: 7 14 42 168 840 5040 35280 282240 2540160 25401600 279417600 3353011200 43589145600 610248038400 9153720576000 146459529216000
(~1 + loop(\(x,i).(x2 + ~2),x,6))
A145505: 5 33 1153 1331713 1773462177793 4611686018427387903 4611686018427387903
loop(\(x,i).i,((x + ~1) mod (2 + (x mod 3))),1)
A331311: 1 1 1 1 1 1 1 1 3 1 1 2 1 1 1 1
(1 + (2 * loop(\(x,i).(x2 + x),x,3)))
A231579: 7 25 313 48985 1199765113 719718163185951385 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).(x * (2 + i)),(x + 2),1) div 2))
A139151: 7 31 181 1261 10081 90721 907201 9979201 119750401 1556755201 21794572801 326918592001 5230697472001 88921857024001 1600593426432001 30411275102208001
(~1 + (loop(\(x,i).(x * (2 + i)),(x + 2),1) div 2))
A139174: 5 29 179 1259 10079 90719 907199 9979199 119750399 1556755199 21794572799 326918591999 5230697471999 88921857023999 1600593426431999 30411275102207999
(~1 + loop(\(x,i).4x,(2x + 1),2))
A241955: 7 127 2047 32767 524287 8388607 134217727 2147483647 34359738367 549755813887 8796093022207 140737488355327 2251799813685247 36028797018963967 576460752303423487 4611686018427387903
loop(\(x,i).3x,(4x + 2),1)
A013714: 9 729 59049 4782969 387420489 31381059609 2541865828329 205891132094649 16677181699666569 1350851717672992089 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).3x,(2x + 1),2))
A199564: 7 55 487 4375 39367 354295 3188647 28697815 258280327 2324522935 20920706407 188286357655 1694577218887 15251194969975 137260754729767 1235346792567895
(1 + (if (x mod 2) <= 0 then x else ((1 + (x div 2)) mod 2)))
A086112: 1 2 3 1 5 2 7 1 9 2 11 1 13 2 15 1
((x + 2) - loop(\(x,i).i,((~1 + (x div 2)) div 2),1))
A061069: 1 2 3 4 5 6 7 8 9 10 10 11 12 13 13 14
(1 + (loop(\(x,i).(3x + 3),x,1) div 2))
A060925: 1 4 11 34 101 304 911 2734 8201 24604 73811 221434 664301 1992904 5978711 17936134
(~1 + (2 * loop(\(x,i).(3x + 6),x,1)))
A036545: 1 17 65 209 641 1937 5825 17489 52481 157457 472385 1417169 4251521 12754577 38263745 114791249
(~1 + (2 * loop(\(x,i).(2x + 6),x,1)))
A173873: 1 15 43 99 211 435 883 1779 3571 7155 14323 28659 57331 114675 229363 458739
(1 + (loop(\(x,i).(2x + (i mod 2)),x,1) div 2))
A107949: 1 2 4 7 14 27 54
(1 + loop(\(x,i).(4x + 4),(x + 1),2))
A206444: 13 53 213 853 3413 13653 54613 218453 873813 3495253
(if (16 mod (x + 1)) <= 0 then 2 else 1)
A297382: 2 2 1 2 1 1 1 2 1 1 1 1 1 1 1 2
(1 + loop(\(x,i).x2,(x2 + 3x + 2),2))
A257377: 17 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A257305: 17 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,x,2) div (2x + 3))
A191630: 0 0 1 1 2 4 8 15 26 48 89 163 303 564 1057 1985
loop(\(x,i).6x,((x + 1) div 2),1)
A056452: 1 6 6 36 36 216 216 1296 1296 7776 7776 46656 46656 279936 279936 1679616
loop(\(x,i).~3x,((x + 1) div 2),1)
A128019: 1 ~3 ~3 9 9 ~27 ~27 81 81 ~243 ~243 729 729 ~2187 ~2187 6561
loop(\(x,i).8x,((x + 1) div 2),1)
A164683: 1 8 8 64 64 512 512 4096 4096 32768 32768 262144 262144 2097152 2097152 16777216
loop(\(x,i).5x,((x + 1) div 2),1)
A162962-A056451: 1 5 5 25 25 125 125 625 625 3125 3125 15625 15625 78125 78125 390625
(if (~4 + (x div 2)) <= 0 then ((x + 1) mod 2) else 1)
A230093: 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 1
(1 + loop(\(x,i).2x,(x div 2),((x + 1) mod 2)))
A052552: 2 1 3 1 5 1 9 1 17 1 33 1 65 1 129 1
(1 + (2 * (if (~2 + (x div 2)) <= 0 then x else (x + 1))))
A204457: 1 3 5 7 9 11 15 17 19 21 23 25 27 29 31 33
(3 - loop(\(x,i).(x * (2 + i)),(x + 1),2))
A092634: ~3 ~21 ~117 ~717 ~5037 ~40317 ~362877 ~3628797 ~39916797 ~479001597 ~6227020797 ~87178291197 ~1307674367997 ~20922789887997 ~355687428095997 ~6402373705727997
(1 + (loop(\(x,i).(x * (1 + i)),x,(x + 1)) div 2))
A188545: 1 3 10
A082426: 1 3 10 49 301 2161 17641 161281 1632961 18144001 219542401 2874009601 40475635201 610248038401 9807557760001 167382319104001
(1 + ((if (x + ~2) <= 0 then x2 else (x + 1)) div 2))
A270059: 1 1 3 3 3 4 4 5 5 6 6 7 7 8 8 9
(1 + (loop(\(x,i).((x + 1) * i),x,(x + 1)) div 2))
A210690: 1 2 6 20 93
(~1 + loop(\(x,i).(x * ((i mod 2) + i)),(x + 1),2))
A103901: 3 7 31 127
loop(\(x,i).4x2,(2x + ~2),1)
A295175: 1 1 64 1073741824 4611686018427387903
(~1 + loop(\(x,i).(x * ((x + i) div 2)),(x + ~1),2))
A120587: 1 1 1 3 11 95
((2 + (x * (x mod 2))) div (1 + (if x <= 0 then 1 else 2)))
A243319: 1 1 0 1 0 2 0 3 0 3
(1 + (2 * (if (x mod 5) <= 0 then 0 else 2)))
A171372: 1 5 5 5 5 1 5 5 5 5 1 5 5 5 5 1
(1 + (2 * (if (~2 + (x div 3)) <= 0 then 0 else 2)))
A032560: 1 1 1 1 1 1 1 1 1 5 5 5 5 5 5 5
(x - ((if x <= 0 then 1 else x) div ~5))
A189891-A184520-A048265-A032798-A030173: 1 2 3 4 5 6 8 9 10 11 12 14 15 16 17 18
loop(\(x,i).x2,1,(x div ~5))
A287392: 0 1 1 1 1 1 4 4 4 4 4 9 9 9 9 9
loop(\(x,i).x2,1,(~1 + (x div ~4)))
A013189: 1 4 4 4 4 9 9 9 9 16 16 16 16 25 25 25
(if (~x + 2) <= 0 then (x - (x div ~4)) else 1)
A118170: 1 1 3 4 5 7 8 9 10 12 13 14 15 17 18 19
(1 + (if x <= 0 then 1 else (2 * (x - (x div ~2)))))
A020581: 2 5 7 11 13 17
((2x + 4) div (3 + (if x <= 0 then 0 else 2)))
A061375: 1 1 1 2 2 2 3 3 4 4 4 5 5 6 6 6
(1 - ((~x + 1) div (1 + (2 * (if x <= 0 then 0 else 2)))))
A105511: 0 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4
(if (x mod 14) <= 0 then 2 else 1)
A345999: 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1
(if ((x + 1) mod 10) <= 0 then 2 else 1)
A329314-A298481-A238900-A191358-A182284-A160094-A147300-A083235-A043283: 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1
(if ((x + ~2) mod 10) <= 0 then 2 else 1)
A280010: 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1
(if ((1 + (x div 2)) mod 6) <= 0 then 2 else 1)
A339047-A309997: 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1
(1 + ((loop(\(x,i).(2x + 4),x,1) div 2) div 2))
A172411: 1 2 5 10
A084215: 1 2 5 10 20 40 80 160 320 640 1280 2560 5120 10240 20480 40960
(~1 + loop(\(x,i).2x2,(2x + 2),2))
A135983: 127 2147483647 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(5 + loop(\(x,i).3x,x,1))
A168610: 6 8 14 32 86 248 734 2192 6566 19688 59054 177152 531446 1594328 4782974 14348912
(~5 + loop(\(x,i).3x,x,1))
A168613: ~4 ~2 4 22 76 238 724 2182 6556 19678 59044 177142 531436 1594318 4782964 14348902
(1 + (4 * (if (x mod 3) <= 0 then 0 else 2)))
A166925: 1 9 9 1 9 9 1 9 9 1 9 9 1 9 9 1
(~1 + (2 * (if x <= 0 then 1 else 16)))
A003892: 1 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31
(if ((x + 2) mod 16) <= 0 then 2 else 1)
A345047-A345045-A334184-A319907-A318829-A297783-A193517-A184340-A167852-A098744-A043566-A043542-A043288: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1
(if ((x + ~4) mod 8) <= 0 then 2 else 1)
A006466: 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1
(if ((2 + (x div 2)) mod 8) <= 0 then 2 else 1)
A184257: 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1
loop(\(x,i).2x,x,17)
A110287: 17 34 68 136 272 544 1088 2176 4352 8704 17408 34816 69632 139264 278528 557056
loop(\(x,i).2x,x,15)
A110286: 15 30 60 120 240 480 960 1920 3840 7680 15360 30720 61440 122880 245760 491520
(if ((x + 1) mod (2 + (x mod 4))) <= 0 then 2 else 1)
A307609-A249622-A030556: 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
(if (x mod 2) <= 0 then (2 * (2 + (x mod 4))) else 1)
A089146: 4 1 8 1 4 1 8 1 4 1 8 1 4 1 8 1
loop(\(x,i).i,(~2 + (x div (2 + (x mod 4)))),1)
A173398: 1 1 1 1 1 1 1 1 2 1 1 1 4 2 1 1
(5 + loop(\(x,i).x2,2x,2))
A130740: 7 21 65541 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).2x,(~4 + (x div 2)),2))
A146450: 1 1 1 1 1 1 1 1 1 1 3 3 7 7 15 15
(~1 + loop(\(x,i).(x * i),(~4 + (x div 2)),2))
A147175-A147159-A147120-A147112-A146828: 1 1 1 1 1 1 1 1 1 1 1 1 3 3 11 11
(1 + (if x <= 0 then 0 else (6 + (x mod 2))))
A327854: 1 8 7 8
(3 + loop(\(x,i).x2,2x,4))
A130741: 7 259 4294967299 4611686018427387903
(1 + ((x - (if x <= 0 then 0 else 1)) mod 8))
A033929: 1 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7
(9 + loop(\(x,i).2x,x,1))
A188165: 10 11 13 17 25 41 73 137 265 521 1033 2057 4105 8201 16393 32777
(~9 + loop(\(x,i).2x,x,1))
A185346: ~8 ~7 ~5 ~1 7 23 55 119 247 503 1015 2039 4087 8183 16375 32759
(loop(\(x,i).2x,x,1) div 9)
A153234: 0 0 0 0 1 3 7 14 28 56 113 227 455 910 1820 3640
(loop(\(x,i).2x,x,1) mod 9)
A222011: 1 2 4 8
A153130: 1 2 4 8 7 5 1 2 4 8 7 5 1 2 4 8
loop(\(x,i).4x,x,9)
A002063: 9 36 144 576 2304 9216 36864 147456 589824 2359296 9437184 37748736 150994944 603979776 2415919104 9663676416
(if (x + ~2) <= 0 then 1 else (x div 9))
A266216-A186729: 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1
(~1 + loop(\(x,i).(x2 + ~2),x,8))
A145507: 7 61 3841 14760961 217885999165441 4611686018427387903 4611686018427387903
loop(\(x,i).(2 + (x div 2)),(x + ~8),1)
A025791: 1 1 1 1 1 1 1 1 1 2 3 3 3 3 3 3
(1 + loop(\(x,i).3x,x,8))
A199111: 9 25 73 217 649 1945 5833 17497 52489 157465 472393 1417177 4251529 12754585 38263753 114791257
(~1 + loop(\(x,i).3x,x,8))
A198644: 7 23 71 215 647 1943 5831 17495 52487 157463 472391 1417175 4251527 12754583 38263751 114791255
(1 + loop(\(x,i).(x2 + x),x,8))
A144782: 9 73 5257 27630793 763460694178057 4611686018427387903 4611686018427387903
(3 + (if (x + ~3) <= 0 then x else 4))
A168093: 3 4 5 6 7 7 7 7 7 7 7 7 7 7 7 7
((x2 + 2) div (if (x + ~4) <= 0 then 2 else 1))
A004044: 1 1 3 5 9 27
(if (x mod 2) <= 0 then x else (1 + (2 * (x div 4))))
A186421: 0 1 2 1 4 3 6 3 8 5 10 5 12 7 14 7
(if ((x2 + 1) mod (x + 4)) <= 0 then 2 else 1)
A332649-A329291-A303929-A303694-A294775-A259094-A210960-A165633-A152830-A118107-A076250-A056059-A055801-A043287: 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1
(if ((x2 + ~2) mod (x + 4)) <= 0 then 2 else 1)
A030379: 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1
(if (x + ~2) <= 0 then x else (x + 7))
A278816: 0 1 2 10 11 12 13 14 15 16 17 18 19 20 21 22
loop(\(x,i).x2,1,(8x + 1))
A017078: 1 81 289 625 1089 1681 2401 3249 4225 5329 6561 7921 9409 11025 12769 14641
loop(\(x,i).x2,2,(8x + 1))
A017080: 1 6561 83521 390625 1185921 2825761 5764801 10556001 17850625 28398241 43046721 62742241 88529281 121550625 163047361 214358881
(1 + loop(\(x,i).x3,4x,2))
A050920: 3 4611686018427387903
A115527: 3 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * loop(\(x,i).3x,2x,2)))
A199562: 5 37 325 2917 26245 236197 2125765 19131877 172186885 1549681957 13947137605 125524238437 1129718145925 10167463313317 91507169819845 823564528378597
(~1 + (2 * loop(\(x,i).3x,2x,2)))
A198961: 3 35 323 2915 26243 236195 2125763 19131875 172186883 1549681955 13947137603 125524238435 1129718145923 10167463313315 91507169819843 823564528378595
(if ((x2 + 1) mod (2 + (x div 2))) <= 0 then 2 else 1)
A031264: 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1
loop(\(x,i).3x,(~4 + (x div 2)),1)
A147244-A146788-A146575: 1 1 1 1 1 1 1 1 1 1 3 3 9 9 27 27
(if (~x + 2) <= 0 then ((x div (2 + (x mod 2))) mod 2) else 1)
A114000: 1 1 1 1 0 1 1 0 0 1 1 1 0 0 1 1
loop(\(x,i).(x * i),(4x2 + 8),1)
A045516: 40320 479001600 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (2 * loop(\(x,i).x2,2x2,2)))
A173649: 3 31 4611686018427387903
(if ((((x + ~1) div 2) div 2) mod 2) <= 0 then 4 else 1)
A071907: 1 4 4 4 4 1 1 1 1 4 4 4 4 1 1 1
(1 + loop(\(x,i).x2,(x + 4),4))
A281576: 4294967297 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).4x,2x,4))
A207262: 5 65 1025 16385 262145 4194305 67108865 1073741825 17179869185 274877906945 4398046511105 70368744177665 1125899906842625 18014398509481985 288230376151711745 4611686018427387903
(if (x mod 4) <= 0 then ((x div 2) mod 4) else 1)
A259042: 0 1 1 1 2 1 1 1 0 1 1 1 2 1 1 1
((x2 + 2x) div (if (x mod 2) <= 0 then 4 else 1))
A142705: 0 3 2 15 6 35 12 63 20 99 30 143 42 195 56 255
(loop(\(x,i).(2x + 2),x,0) div 5)
A140659: 0 0 1 2 6 12 25 50 102 204 409 818 1638 3276 6553 13106
(5 * (1 + loop(\(x,i).2x,x,1)))
A231643: 10 15 25 45 85 165 325 645 1285 2565 5125 10245 20485 40965 81925 163845
(15 * (if x <= 0 then 1 else 2))
A040210: 15 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30
(loop(\(x,i).(x + (i * i)),x,1) div 5)
A173690: 0 0 1 3 6 11 18 28 41 57 77 101 130 164 203 248
(10 * (2 + (if x <= 0 then 0 else 2)))
A040380: 20 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40
(5 * (2 - ((if x <= 0 then 1 else x) mod 2)))
A040021: 5 5 10 5 10 5 10 5 10 5 10 5 10 5 10 5
(5 * loop(\(x,i).4x,x,2))
A002066: 10 40 160 640 2560 10240 40960 163840 655360 2621440 10485760 41943040 167772160 671088640 2684354560 10737418240
(5 * loop(\(x,i).((x + 2) + i),x,2))
A269457: 10 25 45 70 100 135 175 220 270 325 385 450 520 595 675 760
(2 - ((if x <= 0 then 1 else (x + 2)) mod 5))
A257145: 1 ~1 ~2 2 1 0 ~1 ~2 2 1 0 ~1 ~2 2 1 0
(if (x + ~2) <= 0 then 1 else ((x + 2) div 5))
A125893-A094999: 1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 3
loop(\(x,i).(x2 + ~2),2x,5)
A219164: 5 527 77132286527 4611686018427387903
(if (x + ~2) <= 0 then 1 else (2x div 5))
A294622-A025778: 1 1 1 1 1 2 2 2 3 3 4 4 4 5 5 6
(if (x + ~2) <= 0 then 1 else ((x div 2) div 5))
A204269: 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1
(5 * loop(\(x,i).3x,x,2))
A005052: 10 30 90 270 810 2430 7290 21870 65610 196830 590490 1771470 5314410 15943230 47829690 143489070
loop(\(x,i).(4x + ~1),x,5)
A206373: 5 19 75 299 1195 4779 19115 76459 305835 1223339 4893355 19573419 78293675 313174699 1252698795 5010795179
(5 * loop(\(x,i).(x * i),(x + ~1),x))
A052648: 0 5 10 30 120 600 3600 25200 201600 1814400 18144000 199584000 2395008000 31135104000 435891456000 6538371840000
loop(\(x,i).(x2 div 4),x,5)
A014980: 5 6 9 20 100 2500 1562500 610351562500 4611686018427387903 4611686018427387903 4611686018427387903
(x mod (5 * (if (x mod 2) <= 0 then 2 else x)))
A103303: 0 1 2 3 4 5 6 7 8 9
A059707: 0 1 2 3 4 5 6 7 8 9 0 11 2 13 4 15
loop(\(x,i).((x2 + x) div 2),x,5)
A050542: 5 15 120 7260 26357430 347357071281165 4611686018427387903 4611686018427387903
((x + 5) + (if (x + ~1) <= 0 then x else 2))
A194394: 5 7 9 10 11 12 13 14 15 16 17 18 19 20 21 22
(1 + ((if (x + ~4) <= 0 then 1 else x) div 4))
A076885: 1 1 1 1 1 2 2 2 3 3 3 3 4 4 4 4
(1 + loop(\(x,i).6x,x,4))
A199319: 5 25 145 865 5185 31105 186625 1119745 6718465 40310785 241864705 1451188225 8707129345 52242776065 313456656385 1880739938305
(~1 + loop(\(x,i).6x,x,4))
A198797: 3 23 143 863 5183 31103 186623 1119743 6718463 40310783 241864703 1451188223 8707129343 52242776063 313456656383 1880739938303
(1 + loop(\(x,i).(2x2 + 2x),x,4))
A145008: 5 41 3281 21523361 926510094425921 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(4x + 8),x,4))
A146882: 5 25 105 425 1705 6825 27305 109225 436905 1747625 6990505 27962025 111848105 447392425 1789569705 7158278825
(1 + loop(\(x,i).8x,x,4))
A199552: 5 33 257 2049 16385 131073 1048577 8388609 67108865 536870913 4294967297 34359738369 274877906945 2199023255553 17592186044417 140737488355329
(~1 + loop(\(x,i).8x,x,4))
A198852: 3 31 255 2047 16383 131071 1048575 8388607 67108863 536870911 4294967295 34359738367 274877906943 2199023255551 17592186044415 140737488355327
(x mod (1 + (4 * (if (x mod 2) <= 0 then 2 else x))))
A103303: 0 1 2 3 4 5 6 7 8 9
A059717: 0 1 2 3 4 5 6 7 8 9 1 11 3 13 5 15
(~1 - (if (~x + 4) <= 0 then x else 4))
A291497: ~5 ~5 ~5 ~5 ~5 ~6 ~7 ~8 ~9 ~10 ~11 ~12 ~13 ~14 ~15 ~16
((x + 2) mod loop(\(x,i).(x * i),(x div 4),1))
A297330-A165111-A040163-A037904: 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5
(x2 mod loop(\(x,i).(x + i),(x mod 4),1))
A096271: 0 1 0 2 0 1 0 0 0 1 0 2 0 1 0 1
((2x + 4) - loop(\(x,i).i,(x mod 4),1))
A047582: 3 5 6 7 11 13 14 15 19 21 22 23 27 29 30 31
(1 + loop(\(x,i).5x,x,4))
A199215: 5 21 101 501 2501 12501 62501 312501 1562501 7812501 39062501 195312501 976562501 4882812501 24414062501 122070312501
(~1 + loop(\(x,i).5x,x,4))
A198763: 3 19 99 499 2499 12499 62499 312499 1562499 7812499 39062499 195312499 976562499 4882812499 24414062499 122070312499
(1 + (loop(\(x,i).(2x + 4),x,x) div 4))
A131352: 1 2 6 14 32 72 160 352 768 1664 3584 7680 16384 34816 73728 155648
loop(\(x,i).3x,(x2 div 4),1)
A078684: 1 1 3 9 81 729 19683 531441 43046721 3486784401 847288609443 205891132094649 150094635296999121 4611686018427387903 4611686018427387903 4611686018427387903
(x2 mod (1 + loop(\(x,i).(x2 + x),2,2)))
A070465: 0 1 4 9 16 25 36 6 21 38 14 35 15 40 24 10
(~1 + (2 * loop(\(x,i).(2 + (x mod (1 + i))),x,2)))
A172097: 3 3 7 3 7 11 15 3 7 11 15 19 23 27 31 3
((2x + 4) - (if (~x + 4) <= 0 then 2 else 1))
A308412: 3 5 7 9 10 12 14 16 18 20 22 24 26 28 30 32
(1 + loop(\(x,i).x2,(x - ((~x + 2) div 2)),2))
A249759: 3 5 17 65537
(if (~x + 2) <= 0 then (2 + ((x * (x div 2)) mod 2)) else 1)
A185049: 1 1 2 3 2 2 2 3 2 2 2 3 2 2 2 3
loop(\(x,i).i,(x - (2 * (2 + (x * (x mod 2))))),1)
A318775: 1 1 1 1 1 1 2 1 4 1 6 1 8 1 10 1
(~1 + loop(\(x,i).2x,((x * (x mod 2)) div 2),2))
A094024: 1 1 1 3 1 7 1 15 1 31 1 63 1 127 1 255
(if (x + ~4) <= 0 then x else (x + 5))
A119798: 0 1 2 3 4 10 11 12 13 14 15 16 17 18 19 20
(if (x mod 2) <= 0 then (~x + 2) else (x + 5))
A227805: 2 6 0 8 ~2 10 ~4 12 ~6 14 ~8 16 ~10 18 ~12 20
(1 + (if (x + ~4) <= 0 then x else (x + 4)))
A261039: 1 2 3 4 5 10 11
(~1 + loop(\(x,i).(2 + (x2 * i)),(x + ~2),2))
A319767: 1 1 1 5 73
(if (x + ~4) <= 0 then x else (2x + ~5))
A067570: 0 1 2 3 4 5 7
A032515-A004276: 0 1 2 3 4 5 7 9 11 13 15 17 19 21 23 25
(1 + (if (x + ~3) <= 0 then x else (2x + ~4)))
A033057-A004281: 1 2 3 4 5 7 9 11 13 15 17 19 21 23 25 27
(2x + ((x mod 2) + (if (x + ~2) <= 0 then 2 else 1)))
A273867: 2 5 6 8 9 12
(1 + loop(\(x,i).(3x + 3),2x,2))
A198964: 3 31 283 2551 22963 206671 1860043 16740391 150663523 1355971711 12203745403 109833708631 988503377683 8896530399151 80068773592363 720618962331271
(1 + loop(\(x,i).(3x + 1),2x,2))
A135423: 3 23 203 1823 16403 147623 1328603 11957423 107616803 968551223 8716961003 78452649023 706073841203 6354664570823 57191981137403 514727830236623
(1 + (if ((x mod 3) mod 2) <= 0 then 2x else 2))
A130140: 1 3 5 7 3 11 13
(1 + loop(\(x,i).(4x + 2),2x,2))
A141060: 3 43 683 10923 174763 2796203 44739243 715827883 11453246123 183251937963 2932031007403 46912496118443 750599937895083 12009599006321323 192153584101141163 3074457345618258603
(~1 + loop(\(x,i).(~4x + 4),2x,2))
A182460: 1 19 307 4915 78643 1258291 20132659 322122547 5153960755 82463372083 1319413953331 21110623253299 337769972052787 5404319552844595 86469112845513523 1383505805528216371
loop(\(x,i).x2,3,(4x + 1))
A016820: 1 390625 43046721 815730721 6975757441 37822859361 152587890625 500246412961 1406408618241 3512479453921 7984925229121 16815125390625 33232930569601 62259690411361 111429157112001 191707312997281
loop(\(x,i).x3,1,(4x + 1))
A016815: 1 125 729 2197 4913 9261 15625 24389 35937 50653 68921 91125 117649 148877 185193 226981
loop(\(x,i).x3,2,(4x + 1))
A016821: 1 1953125 387420489 10604499373 118587876497 794280046581 3814697265625 14507145975869 46411484401953 129961739795077 327381934393961 756680642578125 1628413597910449 3299763591802133
loop(\(x,i).(x * (x - i)),2,(4x + ~1))
A054777: 0 24 1680 11880 43680 116280 255024 491400 863040 1413720 2193360 3258024 4669920 6497400 8814960 11703240
(1 + loop(\(x,i).(2x + ~2),x,4x))
A339771: 1 7 27 83 227 579 1411 3331 7683 17411 38915 86019 188419 409603 884739 1900547
loop(\(x,i).((x2 + ~2x) * i),4x,1)
A127224: 1 20160 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(2 * (x - (i mod 2))),(x div 2),2))
A077893: 1 1 1 1 3 3 5 5 11 11 21 21 43 43 85 85
(~1 + loop(\(x,i).(2x - (i mod 2)),(x div 2),2))
A287744: 1 1 2 2 5 5 10 10 21 21 42 42 85 85 170 170
(~1 + (2 * (loop(\(x,i).2x,x,1) - (x mod 2))))
A284353: 1 1 7 13 31 61 127 253 511 1021 2047 4093 8191 16381 32767 65533
(1 + (if (x + ~2) <= 0 then x else (4 - (x mod 2))))
A291520: 1 2 3 4 5 4 5 4 5 4 5 4 5 4 5 4
(~1 + loop(\(x,i).2x,(x div (2 - (x mod 2))),2))
A285542: 1 3 3 15 7 63 15 255 31 1023 63 4095 127 16383 255 65535
(1 + loop(\(x,i).2x,(x div 2),(2 + (x mod 2))))
A209721: 3 4 5 7 9 13 17 25 33 49 65 97 129 193 257 385
(~1 + loop(\(x,i).2x,(x div 2),(2 + (x mod 2))))
A052955: 1 2 3 5 7 11 15 23 31 47 63 95 127 191 255 383
loop(\(x,i).2x,(x div 2),(3 + (x mod 2)))
A163978: 3 4 6 8 12 16 24 32 48 64 96 128 192 256 384 512
(1 + loop(\(x,i).2x,x,1) - (2 * (x mod 2)))
A014551: 2 1 5 7 17 31 65 127 257 511 1025 2047 4097 8191 16385 32767
(~1 + loop(\(x,i).2x,x,1) - (2 * (x mod 2)))
A166956: 0 ~1 3 5 15 29 63 125 255 509 1023 2045 4095 8189 16383 32765
(if (x mod 3) <= 0 then 0 else (1 + (2 * (x mod 2))))
A120323: 0 3 1 0 1 3 0 3 1 0 1 3 0 3 1 0
loop(\(x,i).2x,(x div 2),(1 + (2 * (x mod 2))))
A164073: 1 3 2 6 4 12 8 24 16 48 32 96 64 192 128 384
loop(\(x,i).(x * i),2x,(~1 + (2 * (x mod 2))))
A186246: ~1 2 ~24 720 ~40320 3628800 ~479001600 87178291200 ~20922789888000 6402373705728000 ~2432902008176640000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x - (if (~4 + (x div 2)) <= 0 then 0 else 3))
A103303: 0 1 2 3 4 5 6 7 8 9
A245351-A081598-A028902: 0 1 2 3 4 5 6 7 8 9 7 8 9 10 11 12
(loop(\(x,i).(4x + i),x,0) div 3)
A178875: 0 0 2 9 37 151 606 2426 9708 38835 155343 621377 2485512 9942052 39768214 159072861
(loop(\(x,i).(x + (x div 2)),x,~1) mod 3)
A304273: 2 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1
((1 + loop(\(x,i).(~2x + 2),x,0)) div 3)
A135258: 0 1 ~1 2 ~3 7 ~14 29 ~57 114 ~227 455 ~910 1821 ~3641 7282
(3 * ((x2 + x) - (if x <= 0 then 0 else 1)))
A211441: 0 3 15 33 57 87 123 165 213 267 327 393 465 543 627 717
(((x * (x div 2)) + (if x <= 0 then 0 else 1)) mod 3)
A257510: 0 1 0 1 0 2 1 1 0 1 0 2 1 1 0 1
((1 + loop(\(x,i).2x,x,(x + 1))) div 3)
A100335: 0 1 4 11 27 64 149 341 768 1707 3755 8192 17749 38229 81920 174763
(3 * (if (x + ~1) <= 0 then x else 5))
A181404: 0 3 15 15 15 15 15 15 15 15 15 15 15 15 15 15
(9 * (2 + (if x <= 0 then 0 else 2)))
A040306: 18 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36
loop(\(x,i).x2,1,(6x + 3))
A016946: 9 81 225 441 729 1089 1521 2025 2601 3249 3969 4761 5625 6561 7569 8649
loop(\(x,i).x2,2,(6x + 3))
A016948: 81 6561 50625 194481 531441 1185921 2313441 4100625 6765201 10556001 15752961 22667121 31640625 43046721 57289761 74805201
((1 + (if (x mod 3) <= 0 then 0 else x)) div 3)
A229878: 0 0 1 0 1 2
A087509: 0 0 1 0 1 2 0 2 3 0 3 4 0 4 5 0
(if x <= 0 then 1 else (9x + ~3))
A122709: 1 6 15 24 33 42 51 60 69 78 87 96 105 114 123 132
((x mod 2) - (loop(\(x,i).2x,x,1) div 3))
A083943: 0 1 ~1 ~1 ~5 ~9 ~21 ~41 ~85 ~169 ~341 ~681 ~1365 ~2729 ~5461 ~10921
(3 * loop(\(x,i).(x2 + (x mod 2)),x,1))
A085866: 3 6 12 48 768 196608 12884901888 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x2 + 1),2,(x + 1)) div 3)
A014820: 1 8 33 96 225 456 833 1408 2241 3400 4961 7008 9633 12936 17025 22016
(3 * loop(\(x,i).2x,(x + 2),(x + 1)))
A059162: 12 48 144 384 960 2304 5376 12288 27648 61440 135168 294912 638976 1376256 2949120 6291456
(loop(\(x,i).2x,x,2) mod (3x + 3))
A191561: 2 4 8 4 2 10 2 16 26 4 2 28 2 4 8 16
loop(\(x,i).(2x + ~1),x,(3x + 3))
A288038: 3 11 33 89 225 545 1281 2945 6657 14849 32769 71681 155649 335873 720897 1540097
loop(\(x,i).4x,x,(3x + 3))
A212698: 3 24 144 768 3840 18432 86016 393216 1769472 7864320 34603008 150994944 654311424 2818572288 12079595520 51539607552
(3 * (if (~2 + (x div 3)) <= 0 then 0 else 2))
A173068: 0 0 0 0 0 0 0 0 0 6 6 6 6 6 6 6
(x - ((if x <= 0 then 1 else x) div ~6))
A082463: 1 2 3 4 5 6 7 9 10
A332108-A020660: 1 2 3 4 5 6 7 9 10 11 12 13 14 16 17 18
(((x2 - (if x <= 0 then 0 else 1)) div 2) div 3)
A337483: 0 0 0 1 2 4 5 8 10 13 16 20 23 28 32 37
(3 * loop(\(x,i).(2x + 4),(x + 1),2))
A182464: 24 60 132 276 564 1140 2292 4596 9204 18420 36852 73716 147444 294900 589812 1179636
(24 * (if x <= 0 then 1 else 2))
A040552: 24 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48
(3 * ((2 - (x mod 2)) * (if x <= 0 then 1 else 2)))
A040031: 6 6 12 6 12 6 12 6 12 6 12 6 12 6 12 6
(3 * ((x2 + 2x) + (if x <= 0 then 1 else 2)))
A290325: 3 15 30 51 78 111 150 195 246 303 366 435 510 591 678 771
(if (x + ~1) <= 0 then 8x else 3)
A021016: 0 8 3 3 3 3 3 3 3 3 3 3 3 3 3 3
loop(\(x,i).(2x + 1),x,12)
A198274: 12 25 51 103 207 415 831 1663 3327 6655 13311 26623 53247 106495 212991 425983
loop(\(x,i).(2x + ~1),x,12)
A083683: 12 23 45 89 177 353 705 1409 2817 5633 11265 22529 45057 90113 180225 360449
((if x <= 0 then 1 else x) - (3 * (x div 4)))
A033924: 1 1 2 3 1 2 3 4 2 3 4 5 3 4 5 6
loop(\(x,i).x2,1,12x)
A017522: 0 144 576 1296 2304 3600 5184 7056 9216 11664 14400 17424 20736 24336 28224 32400
loop(\(x,i).x2,2,12x)
A017524: 0 20736 331776 1679616 5308416 12960000 26873856 49787136 84934656 136048896 207360000 303595776 429981696 592240896 796594176 1049760000
loop(\(x,i).3x,4x,3)
A013778: 3 243 19683 1594323 129140163 10460353203 847288609443 68630377364883 5559060566555523 450283905890997363 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(3 * loop(\(x,i).(2x + 5),x,2))
A305158: 6 27 69 153 321 657 1329 2673 5361 10737 21489 42993 86001 172017 344049 688113
(3 * loop(\(x,i).(4x + 1),x,2))
A198694: 6 27 111 447 1791 7167 28671 114687 458751 1835007 7340031 29360127 117440511 469762047 1879048191 7516192767
(3 * loop(\(x,i).(2x2 + ~1),x,2))
A213680: 6 21 291 56451 2124476931 3008934820234119171 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (3 * ((x2 + x) div 2)))
A134479: 1 3 9 18 30 45 63 84 108 135 165 198 234 273 315 360
(6 * loop(\(x,i).(x * i),(x + ~1),x))
A298881: 0 6 12 36 144 720 4320 30240 241920 2177280 21772800 239500800 2874009600 37362124800 523069747200 7846046208000
(3 * loop(\(x,i).(2x + 6),x,2))
A305163: 6 30 78 174 366 750 1518 3054 6126 12270 24558 49134 98286 196590 393198 786414
(x - ((1 - loop(\(x,i).2x,x,2)) div 3))
A081660: 1 2 5 8 15 26 49 92 179 350 693 1376 2743 5474 10937 21860
(2 - (((1 - (if x <= 0 then 2 else x)) div 2) div 3))
A065801: 3 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5
(loop(\(x,i).(x * (x - i)),2,(x + 2)) div 3)
A162668: 0 8 40 120 280 560 1008 1680 2640 3960 5720 8008 10920 14560 19040 24480
loop(\(x,i).4x,x,(3x + 6))
A159721: 6 36 192 960 4608 21504 98304 442368 1966080 8650752 37748736 163577856 704643072 3019898880 12884901888 54760833024
(if (x + ~2) <= 0 then (x div 2) else (3x + ~6))
A242088: 0 0 1 3 6 9 12
A296515: 0 0 1 3 6 9 12 15 18 21 24 27 30 33 36 39
loop(\(x,i).(~3x + 1),2x,3)
A199679: 3 25 223 2005 18043 162385 1461463 13153165 118378483 1065406345 9588657103 86297913925 776681225323 6990131027905 62911179251143 566200613260285
(3 * (if (x mod 2) <= 0 then (x div 2) else 2x))
A174012: 0 6 3 18 6 30 9 42 12 54 15 66 18 78 21 90
loop(\(x,i).x2,3,6x)
A016916: 0 1679616 429981696 11019960576 110075314176 656100000000 2821109907456 9682651996416 28179280429056 72301961339136 167961600000000 360040606269696 722204136308736 1370114370683136
loop(\(x,i).x3,1,6x)
A016911: 0 216 1728 5832 13824 27000 46656 74088 110592 157464 216000 287496 373248 474552 592704 729000
loop(\(x,i).x3,2,6x)
A016917: 0 10077696 5159780352 198359290368 2641807540224 19683000000000 101559956668416 406671383849472 1352605460594688 3904305912313344 10077696000000000 23762680013799936 51998697814228992
loop(\(x,i).2x,x,(1 - (2x div 3)))
A171552: 1 2 0 ~8 ~16 ~64 ~192 ~384 ~1024 ~2560 ~5120 ~12288 ~28672 ~57344 ~131072 ~294912
(loop(\(x,i).(x * (1 + i)),x,(x div 2)) div 3)
A259705: 0 0 2 8 80 480 5040 40320
(loop(\(x,i).(2x + 2),x,(x mod 2)) div 3)
A084184: 0 1 2 7 10 31 42 127 170 511 682 2047 2730 8191 10922 32767
((loop(\(x,i).(2x + ~2),x,x) div 2) div 3)
A137221: 0 0 0 1 5 16 43 107 256 597 1365 3072 6827 15019 32768 70997
(3 * (loop(\(x,i).4x,x,x) div 2))
A229504: 0 6 48 288 1536 7680 36864 172032 786432 3538944 15728640 69206016 301989888 1308622848 5637144576 24159191040
(x - ((1 - (if (~x + 2) <= 0 then x else 2)) div 3))
A187681: 1 2 3 4 5 7 8 9 11 12 13 15 16 17 19 20
loop(\(x,i).(x3 + x2 + ~1),x,3)
A231831: 3 35 44099 85762231424099 4611686018427387903
((x + 3) + (if (~2 + (x div 2)) <= 0 then 2 else 1))
A169869: 5 6 7 8 9 10 10 11 12 13 14
loop(\(x,i).(6x + 3),x,3)
A125682: 3 21 129 777 4665 27993 167961 1007769 6046617 36279705 217678233 1306069401 7836416409 47018498457 282110990745 1692665944473
loop(\(x,i).x2,2,9x)
A017164: 0 6561 104976 531441 1679616 4100625 8503056 15752961 26873856 43046721 65610000 96059601 136048896 187388721 252047376 332150625
loop(\(x,i).3x,3x,3)
A013732: 3 81 2187 59049 1594323 43046721 1162261467 31381059609 847288609443 22876792454961 617673396283947 16677181699666569 450283905890997363 4611686018427387903 4611686018427387903 4611686018427387903
((x + 3) + (if (x + ~1) <= 0 then x else 3))
A107820: 3 5 8 9 10 11 12 13 14 15 16 17 18 19 20 21
(if x <= 0 then 1 else (3x * (1 + (x mod 2))))
A298026: 1 6 6 18 12 30 18 42 24 54 30 66 36 78 42 90
loop(\(x,i).(5x + ~1),x,3)
A199314: 3 14 69 344 1719 8594 42969 214844 1074219 5371094 26855469 134277344 671386719 3356933594 16784667969 83923339844
((x + (if (x mod 3) <= 0 then x else 1)) div 3)
A186731: 0 0 1 2 1 2 4 2 3 6 3 4 8 4 5 10
loop(\(x,i).(x3 + ~x + 1),x,3)
A144788: 3 25 15601 3797146111201 4611686018427387903 4611686018427387903
(1 - ((x + (if (x mod 2) <= 0 then x else 1)) mod 3))
A134668: 1 ~1 0 0 ~1 1 1 ~1 0 0 ~1 1 1 ~1 0 0
(3 * loop(\(x,i).(2x * i),(x + ~1),x))
A052676: 0 3 12 72 576 5760 69120 967680 15482880 278691840 5573836800 122624409600 2942985830400 76517631590400 2142493684531200 64274810535936000
((2x + 4) - ((if x <= 0 then 1 else x) mod 3))
A283051: 3 5 6 10
loop(\(x,i).((3x + ~1) - i),x,3)
A103177: 3 7 18 50 145 429 1280 3832 11487 34451 103342 310014 930029 2790073 8370204 25110596
((x + (if (x mod 4) <= 0 then 1 else 2)) div 3)
A189667: 0 1 1 1 1 2 2 3 3 3 4 4 4 5 5 5
loop(\(x,i).(2x2 + ~2x + ~2),x,3)
A308657: 3 10 178
loop(\(x,i).(5x + 2),x,3)
A198766: 3 17 87 437 2187 10937 54687 273437 1367187 6835937 34179687 170898437 854492187 4272460937 21362304687 106811523437
((x2 + ~x) + loop(\(x,i).2x,x,3))
A307457: 3 6 14 30
A308580: 3 6 14 30 60 116 222 426 824 1608 3162 6254 12420 24732 49334 98514
loop(\(x,i).3x,(x + (x div 2)),3)
A055156: 3 9 81 243 2187 6561 59049 177147 1594323 4782969 43046721 129140163 1162261467 3486784401 31381059609 94143178827
(if x <= 0 then 1 else (3x * (2 - (x mod 2))))
A298028: 1 3 12 9 24 15 36 21 48 27 60 33 72 39 84 45
(if (x + ~2) <= 0 then 1 else ((x + (x mod 2)) div 3))
A096605: 1 1 1 1 1 2 2 2 2 3 3 4 4 4 4 5
(2x + ((if x <= 0 then 1 else x) + (x div 3)))
A117549: 1 3 6 10 13 16
((if (x mod 3) <= 0 then 0 else x) - (x div 3))
A166711: 0 1 2 ~1 3 4 ~2 5 6 ~3 7 8 ~4 9 10 ~5
loop(\(x,i).~2x,x,(1 - (x mod 3)))
A120580: 1 0 ~4 ~8 0 32 64 0 ~256 ~512 0 2048 4096 0 ~16384 ~32768
((if x <= 0 then 0 else (x2 + 1)) + (x mod 3))
A098001: 0 3 7 10 18
((if x <= 0 then 1 else 6) - (x mod 3))
A328263: 1 5 4 6 5 4 6 5 4 6 5 4 6 5 4 6
(((x + 2) * (if x <= 0 then 1 else x)) + (x mod 3))
A058201: 2 4 10 15 25
loop(\(x,i).7x,x,3)
A169634: 3 21 147 1029 7203 50421 352947 2470629 17294403 121060821 847425747 5931980229 41523861603 290667031221 2034669218547 14242684529829
loop(\(x,i).(x3 + 3x),x,3)
A006268: 3 36 46764 102266868132036 4611686018427387903
loop(\(x,i).(x3 + ~3x),x,3)
A001999: 3 18 5778 192900153618 4611686018427387903
loop(\(x,i).(x + (x div (1 + (i mod 2)))),x,3)
A153339: 3 4 8 12 24 36 72 108 216 324 648 972 1944 2916 5832 8748
(2 - (if x <= 0 then 1 else (~3x2 + 3x)))
A077588: 1 2 8 20 38 62 92 128 170 218 272 332 398 470 548 632
(loop(\(x,i).(2 * (x + (i mod 2))),x,x) div 3)
A127985: 0 1 4 11 28 67 156 355 796 1763 3868 8419 18204 39139 83740 178403
(if x <= 0 then 1 else (3x * (x + (x div 2))))
A097989: 1 3 18 36
(loop(\(x,i).(2x - (i mod 2)),x,x) div 3)
A140960: 0 0 2 6 18 46 114 270 626 1422 3186 7054 15474 33678 72818 156558
loop(\(x,i).(x3 div 2),x2,3)
A157323: 3 13 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (6 - i)),x,3)
A036750: 3 15 60 180 360 360
loop(\(x,i).(x * (8 - i)),x,3)
A036754: 3 21 126 630 2520 7560 15120 15120
(1 + (2 * (~x + loop(\(x,i).(2 * (x + i)),x,0))))
A318165: 1 3 13
A320661: 1 3 13 39 97 219 469 975 1993 4035 8125 16311 32689 65451 130981 262047
(~1 + (2 * (x + loop(\(x,i).2x,(x + ~1),1))))
A081494: 1 3 7 13 23 41 75 141 271 529 1043 2069 4119 8217 16411 32797
loop(\(x,i).(x * i),10x,1)
A195394: 1 3628800 2432902008176640000 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).12x,x,2))
A199031: 1 23 287 3455 41471 497663 5971967 71663615 859963391 10319560703 123834728447 1486016741375 17832200896511 213986410758143 2567836929097727 30814043149172735
loop(\(x,i).3x,(3x + 2),1)
A013733: 9 243 6561 177147 4782969 129140163 3486784401 94143178827 2541865828329 68630377364883 1853020188851841 50031545098999707 1350851717672992089 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).(x2 + 2x),3,x) div 2))
A191495: 1 128 3281 32768 195313 839808 2882401 8388608 21523361 50000000 107179441 214990848 407865361 737894528 1281445313 2147483648
(1 + (2 * (if x <= 0 then 2 else (x * (x mod 3)))))
A078302: 5 3 9 1
(~1 + loop(\(x,i).(1 + (2 * (x + (x div 2)))),x,2))
A027107: 1 6 20 62 188 566 1700 5102 15308 45926 137780 413342 1240028 3720086 11160260 33480782
(1 + loop(\(x,i).(~1 + (2 * (x + (x div 2)))),x,2))
A079003: 3 6 14 38 110 326 974 2918 8750 26246 78734 236198 708590 2125766 6377294 19131878
(~1 + loop(\(x,i).(5x + ~1),x,2))
A117617: 1 8 43 218 1093 5468 27343 136718 683593 3417968 17089843 85449218 427246093 2136230468 10681152343 53405761718
(~1 + loop(\(x,i).2x,x,(x2 + x + 2)))
A055580: 1 7 31 111 351 1023 2815 7423 18943 47103 114687 274431 647167 1507327 3473407 7929855
loop(\(x,i).x2,1,(1 + ((x2 + x) div 2)))
A086601: 1 4 16 49 121 256 484 841 1369 2116 3136 4489 6241 8464 11236 14641
loop(\(x,i).2x,x,(1 + ((x2 + x) div 2)))
A340257: 1 4 16 56 176 512 1408 3712 9472 23552 57344 137216 323584 753664 1736704 3964928
loop(\(x,i).(1 + (x * i)),((x2 + ~x) div 2),1)
A091479: 1 1 2 16 1957 9864101 3554627472076 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,(1 + ((x2 + ~x) div 2)))
A052481: 1 2 8 32 112 352 1024 2816 7424 18944 47104 114688 274432 647168 1507328 3473408
loop(\(x,i).3x,((x2 + ~x) div 2),1)
A047656: 1 1 3 27 729 59049 14348907 10460353203 22876792454961 150094635296999121 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * loop(\(x,i).3x,(x + ~1),x)))
A318165: 1 3 13
A140320: 1 3 13 55 217 811 2917 10207 34993 118099 393661 1299079 4251529 13817467 44641045 143489071
(~1 + (2 * ((2 * (x mod 2)) + (if x <= 0 then 1 else x))))
A086970: 1 5 3 9 7 13 11 17 15 21 19 25 23 29 27 33
(~1 + (2 * (if (x + ~2) <= 0 then (x2 + 1) else x)))
A285264: 1 3 9 5 7
(1 + loop(\(x,i).((3x + ~1) - i),x,2))
A243513: 3 5 10 24 65 187 552 1646 4927 14769 44294 132868 398589 1195751 3587236 10761690
(1 + loop(\(x,i).(2 * (1 + (2 * (x - i)))),x,2))
A160128: 3 7 19 63 235 919 3651 14575 58267 233031 932083 3728287 14913099 59652343 238609315 954437199
(~1 + loop(\(x,i).(8x + ~4),x,2))
A245599: 1 11 91 731 5851 46811 374491 2995931 23967451 191739611 1533916891 12271335131 98170681051 785365448411 6282923587291 50263388698331
(~1 + loop(\(x,i).8x2,x,2))
A119598: 1 31 8191
(1 + (x mod ((if ((x div 2) mod 2) <= 0 then 2 else x) div 2)))
A318749-A102097-A050330: 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 2
(~1 + loop(\(x,i).(x + i - (x div 4)),x,2))
A231408: 1 2 4 6 9
A083652: 1 2 4 6 9 12 15 18 22 26 30 34 38 42 46 50
(x2 mod (1 + (if (x mod 4) <= 0 then x else 2)))
A194683: 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0
(1 + (2x * (2 + (if (x mod 2) <= 0 then x else 2))))
A271186: 1 9 17 25 49
(1 + (2 * loop(\(x,i).2x,(x + 4),x)))
A115342: 1 65 257 769 2049 5121 12289 28673 65537 147457 327681 720897 1572865 3407873 7340033 15728641
(~1 + loop(\(x,i).(2x - ((x div 2) mod 2)),x,2))
A033138: 1 2 4 9 18 36 73 146 292 585 1170 2340 4681 9362 18724 37449
(~1 + loop(\(x,i).(x - (x div (~2 + (x mod 2)))),x,2))
A112346: 1 2 5 8 17 26 53 80 161 242 485 728 1457 2186 4373 6560
(~1 + loop(\(x,i).(2x - ((i div 2) mod 2)),x,2))
A077854: 1 3 6 12 25 51 102 204 409 819 1638 3276 6553 13107 26214 52428
(~1 + loop(\(x,i).(x - (x div (~2 + (i mod 2)))),x,2))
A060647: 1 3 5 11 17 35 53 107 161 323 485 971 1457 2915 4373 8747
((2 + (x div 4)) * (if (~x + 2) <= 0 then 2 else 1))
A080606: 2 2 4 4 6 6 6 6 8 8 8 8 10 10 10 10
((x2 + 4x) + (if (~x + 2) <= 0 then 2 else 1))
A005281: 1 6 14 23 34
(1 + loop(\(x,i).10x,x,2))
A199682: 3 21 201 2001 20001 200001 2000001 20000001 200000001 2000000001 20000000001 200000000001 2000000000001 20000000000001 200000000000001 2000000000000001
(~1 + loop(\(x,i).10x,x,2))
A067272: 1 19 199 1999 19999 199999 1999999 19999999 199999999 1999999999 19999999999 199999999999 1999999999999 19999999999999 199999999999999 1999999999999999
(~1 + loop(\(x,i).(2x2 + ~x + 2),x,2))
A074487: 1 7 121 29647 1757978161 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).((x3 + x) div 2),x,2))
A296374: 3 6 66 137346 1295413937737986 4611686018427387903
(~1 + loop(\(x,i).((x * (2 + (x div 2))) div 2),x,2))
A006892: 1 2 3 7 23 167 7223 13053767 42600227803223 4611686018427387903 4611686018427387903
(~1 + ((~x + loop(\(x,i).x2,2,(x + 2))) div 2))
A027482: 7 39 126 310 645 1197 2044 3276 4995 7315 10362 14274 19201 25305 32760 41752
loop(\(x,i).x2,1,(1 + ((x2 + 2x) div 2)))
A212893: 1 4 25 64 169 324 625 1024 1681 2500 3721 5184 7225 9604 12769 16384
loop(\(x,i).(x * i),x,(1 + ((x * (x mod 2)) div 2)))
A211374: 1 1 2 12 24 360 720 20160 40320 1814400 3628800 239500800 479001600 43589145600 87178291200 10461394944000
loop(\(x,i).3x,((x * (x mod 2)) div 2),1)
A130599: 1 1 1 3 1 9 1 27 1 81 1 243 1 729 1 2187
loop(\(x,i).2x,(x - ((x * (x mod 2)) div 2)),1)
A079102: 1 2 4 4 16 8 64 16 256 32 1024 64 4096 128 16384 256
(1 - ((~x + 2) div (1 + ((if x <= 0 then 2 else x) div 2))))
A345379: 0 0 1 2 2 2 2 3 3 3 3 3 3 3 3 3
(2 - ((~x + 2) div (1 + ((if x <= 0 then 2 else x) div 2))))
A297212-A090529: 1 1 2 3 3 3 3 4 4 4 4 4 4 4 4 4
(~1 + loop(\(x,i).(2 * (x + ((1 + i) * i))),x,2))
A027180: 1 7 27 79 199 459 1003 2119 4383 8947 18115 36495 73303 146971 294363 589207
(~1 + loop(\(x,i).(2 + ((2 * (x + i)) + i)),x,2))
A169831: 1 8 25 62 139 296 613 1250 2527 5084 10201 20438 40915 81872 163789 327626
(1 + loop(\(x,i).(4 * ((x - i) * i)),x,2))
A056826: 3 5 17 157
(~1 + loop(\(x,i).((2x + 4) - (i mod 2)),x,2))
A085278: 1 6 17 38 81 166 337 678 1361 2726 5457 10918 21841 43686 87377 174758
(1 + ((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)))
A181569: 1 1 2 1 6 1 8 9 10 1 12 1 14 15 16 1
loop(\(x,i).((x + ~1) + ((i * i) div 2)),(x + 2),1)
A213759: 1 4 11 22 39 62 93 132 181 240 311 394 491 602 729 872
(if (~x + 2) <= 0 then ((x2 + 1) div (x + 2)) else 1)
A034138: 1 1 1 2 2 3 4 5 6 7 8 9 10 11 12 13
loop(\(x,i).(x * i),(x2 + 6x + 8),1)
A072269: 40320 1307674368000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x + (x div 4)),2,(x + 2)))
A296352: 3 4 7 8 9 11 13 14 16 17 19 21 22 23 26 27
loop(\(x,i).(2 * (x + i)),(x + 1),(x + 3))
A060602: 8 24 62 148 338 752 1646 3564 7658 16360
((4 * (if x <= 0 then 1 else x)) div (x + 3))
A126235-A111651-A081604: 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 3
loop(\(x,i).(x * (1 + i)),4,(x + 3))
A069478: 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160
((x + 3) * loop(\(x,i).((x + 2) + i),x,2))
A005564: 6 20 45 84 140 216 315 440 594 780 1001 1260 1560 1904 2295 2736
(if (~2 + (x div 3)) <= 0 then x else (x + 3))
A119797: 0 1 2 3 4 5 6 7 8 12 13 14 15 16 17 18
(if (~4 + (x div 2)) <= 0 then x else (x + 3))
A103303: 0 1 2 3 4 5 6 7 8 9
A094823: 0 1 2 3 4 5 6 7 8 9 13 14 15 16 17 18
(1 + (if (x + ~6) <= 0 then x else (x + 2)))
A031981: 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 18
(1 + (if (~2 + (x div 3)) <= 0 then x else (x + 2)))
A344543-A277046-A239216-A239089-A190218-A102234-A032881-A032848: 1 2 3 4 5 6 7 8 9 12 13 14 15 16 17 18
(if x <= 0 then 2 else (~1 + ((x + 2) * (x + (x mod 2)))))
A341322: 2 5 7 19
(~1 + loop(\(x,i).(2x - (i mod 2)),x,(x + 2)))
A127981: 1 4 13 34 85 202 469 1066 2389 5290 11605 25258 54613 117418 251221 535210
loop(\(x,i).(x * (x - (x div ~2))),(x + ~2),1)
A327425: 1 1 1 2 6 54
loop(\(x,i).(~3x + ~5),2x,1)
A211866: 1 19 181 1639 14761 132859 1195741 10761679 96855121 871696099 7845264901 70607384119 635466457081 5719198113739 51472783023661 463255047212959
((~2x + 1) + loop(\(x,i).4x,x,1))
A100102: 2 3 13 59 249 1015 4085 16371 65521 262127 1048557 4194283 16777193 67108839 268435429 1073741795
loop(\(x,i).(x4 + x3),2x,1)
A255403: 1 24 4611686018427387903
loop(\(x,i).((x + 1) + ((1 + i) * i)),2x,1)
A057813: 1 11 45 119 249 451 741 1135 1649 2299 3101 4071 5225 6579 8149 9951
loop(\(x,i).((~x + 1) + (2 * (~x + i))),2x,1)
A325153: 1 5 33 277 2465 22149 199297 1793621 16142529 145282693 1307544161 11767897365 105911076193 953199685637 8578797170625 77209174535509
(1 + loop(\(x,i).((x + 1) * (x - i)),2,2x))
A144139: 1 5 209 1189 3905 9701 20305 37829 64769 104005 158801 232805 330049 454949 612305 807301
loop(\(x,i).~7x,2x,1)
A087752: 1 49 2401 117649 5764801 282475249 13841287201 678223072849 33232930569601 1628413597910449 79792266297612001 3909821048582988049 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x - ((x div 2) mod 2)),2x,1)
A188545: 1 3 10
A046632: 1 3 10 37 147 586 2341 9363 37450 149797 599187 2396746 9586981 38347923 153391690 613566757
loop(\(x,i).(2 * (x - (2x * i))),2x,1)
A009120: 1 12 1680 665280 518918400 670442572800 1295295050649600 3497296636753920000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).10x,2x,1)
A098608: 1 100 10000 1000000 100000000 10000000000 1000000000000 100000000000000 10000000000000000 1000000000000000000 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 2) + (2 * (i * i))),2x,1)
A085474: 1 15 69 195 425 791 1325 2059 3025 4255 5781 7635 9849 12455 15485 18971
loop(\(x,i).4x,(2x + (x div 2)),1)
A067490: 1 16 1024 16384 1048576 16777216 1073741824 17179869184 1099511627776 17592186044416 1125899906842624 18014398509481984 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903
((2x + 1) * loop(\(x,i).(x + (i * i)),x,0))
A180324: 0 3 25 98 270 605 1183 2100 3468 5415 8085 11638 16250 22113 29435 38440
((2x + 1) * (~1 + loop(\(x,i).2x,x,2)))
A118414: 1 9 35 105 279 693 1651 3825 8687 19437 42987 94185 204775 442341 950243 2031585
loop(\(x,i).2x,(2x + ~1),(2x + 1))
A229580: 1 6 40 224 1152 5632 26624 122880 557056 2490368 11010048 48234496 209715200 905969664 3892314112 16642998272
((2x + 1) * loop(\(x,i).2x2,x,1))
A001367: 1 6 40 896 294912 23622320128 4611686018427387903 4611686018427387903 4611686018427387903
((2x2 + 3x + 1) * (if x <= 0 then 0 else 2))
A280344: 0 12 30 56 90 132 182 240 306 380 462 552 650 756 870 992
loop(\(x,i).(x * (2 + i)),(x + 1),(2x + 1))
A034860: 3 36 300 2520 22680 221760 2358720 27216000 339292800 4550515200 65383718400 1002550348800 16345929600000 282457663488000 5157467707392000 99236792438784000
loop(\(x,i).2x,((x + 1) div 2),(2x + 1))
A097578: 1 6 10 28 36 88 104 240 272 608 672 1472 1600 3456 3712 7936
loop(\(x,i).(x * (2 + i)),4,(2x + 1))
A140801: 360 1080 1800 2520 3240 3960 4680 5400 6120 6840 7560 8280 9000 9720 10440 11160
((2x + 1) * loop(\(x,i).4x,x,2))
A288443: 2 24 160 896 4608 22528 106496 491520 2228224 9961472 44040192 192937984 838860800 3623878656 15569256448 66571993088
(loop(\(x,i).4x,x,2) mod (2x + 1))
A179976: 0 2 2 2 8 2 2 8 2 2 8 2 7 26 2 2
((2x + 1) * loop(\(x,i).((x + 2) + i),x,2))
A162256: 2 15 45 98 180 297 455 660 918 1235 1617 2070 2600 3213 3915 4712
loop(\(x,i).(x * (2 + i)),(x + ~2),(2x + 1))
A084253: 1 3 5 21 108 660 4680 37800 342720 3447360 38102400 459043200 5987520000 84064780800 1264085222400 20268952704000
loop(\(x,i).4x,2x,(2x + 1))
A165283: 1 48 1280 28672 589824 11534336 218103808 4026531840 73014444032 1305670057984 23089744183296 404620279021568 7036874417766400 121597189939003392 2089670227099910144 4611686018427387903
loop(\(x,i).3x,2x,(2x + 1))
A155988: 1 27 405 5103 59049 649539 6908733 71744535 731794257 7360989291 73222472421 721764371007 7060738412025 68630377364883 663426981193869 6382625094934119
loop(\(x,i).(x * (1 + i)),2x,(2x + 1))
A061079: 1 18 600 35280 3265920 439084800 80951270400 19615115520000 6046686277632000 2311256907767808000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (x + (2 * i))),2,(2x + 1))
A176711: 21 285 1365 4221 10197 21021 38805 66045 105621 160797 235221 332925 458325 616221 811797 1050621
loop(\(x,i).6x,x,(2x + 1))
A199299: 1 18 180 1512 11664 85536 606528 4199040 28553472 191476224 1269789696 8344332288 54419558400 352638738432 2272560758784 14575734521856
((3x + 1) + loop(\(x,i).2x,x,1))
A194455: 2 6 11 18 29 48 83 150 281 540 1055 2082 4133 8232 16427 32814
loop(\(x,i).8x,x,(2x + 1))
A199301: 1 24 320 3584 36864 360448 3407872 31457280 285212672 2550136832 22548578304 197568495616 1717986918400 14843406974976 127543348822016 1090715534753792
loop(\(x,i).(4x * i),x,(2x + 1))
A167558: 1 12 160 2688 55296 1351680 38338560 1238630400 44920995840 1807409479680 79906524364800 3850733459865600 200907832688640000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (x - (i mod 2))),x,(2x + 1))
A174836: 1 4 16 46 124 310 748 1750 4012 9046 20140 44374 96940 210262 453292 972118
loop(\(x,i).5x,x,(2x + 1))
A171220: 1 15 125 875 5625 34375 203125 1171875 6640625 37109375 205078125 1123046875 6103515625 32958984375 177001953125 946044921875
((2x2 + x + ~1) * (if x <= 0 then 0 else 2))
A187297: 0 4 18 40 70 108 154 208 270 340 418 504 598 700 810 928
((2x + ~1) * loop(\(x,i).2x,(x + ~1),x))
A086950: 0 1 12 60 224 720 2112 5824 15360 39168 97280 236544 565248 1331200 3096576 7127040
((3x + ~1) + loop(\(x,i).2x,x,2))
A131833: 1 6 13 24 43 78 145 276 535 1050 2077 4128 8227 16422 32809 65580
loop(\(x,i).(x * (~1 + (2 * i))),x,(2x + ~1))
A126965: ~1 1 9 75 735 8505 114345 1756755 30405375 585810225 12439852425 288735522075 7273385294175 197646339515625 5763367260275625 179518217255251875
loop(\(x,i).(x * (1 + ((i div 2) + i))),2x,1)
A079929: 1 8 280 22400 3203200 717516800 231757926400 101973487616000 58634755379200000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + ((i mod 2) + i))),2x,1)
A001818: 1 1 9 225 11025 893025 108056025 18261468225 4108830350625 1187451971330625 428670161650355625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (i - (i div ~2))),2x,1)
A176730: 1 6 180 12960 1710720 359251200 109930867200 46170964224000 25486372251648000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(2x + (i div 2)),x,2x))
A127983: 1 5 18 52 137 339 808 1874 4263 9553 21158 46416 101029 218447 469668 1004878
loop(\(x,i).(x * (i - ((2 - i) div 2))),2x,1)
A060079: 1 2 40 2240 246400 44844800 12197785600 4635158528000 2345390215168000
A052502: 1 2 40 2240 246400 44844800 12197785600 4635158528000 2345390215168000 1524503639859200000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (i - (2 * (i * i)))),2x,1)
A067630: 1 6 2520 7484400 81729648000 2375880867360000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).x3,x2,2x))
A058474: 1 9 4611686018427387903
(if x <= 0 then 2 else (2x4 + 1))
A066269: 2 3 33
loop(\(x,i).(x * ((1 + (i mod 2)) * i)),2x,1)
A065140: 1 4 96 5760 645120 116121600 30656102400 11158821273600 5356234211328000 3278015337332736000 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).((2 * (x + i)) + i),x,2x))
A131438: 1 8 29 82 207 492 1129 2534 5603 12256 26589 57306 122839 262100 557009 1179598
(1 + (if (x mod 2) <= 0 then (2x + 2) else (x div 2)))
A235800: 3 1 7 2 11 3 15 4 19 5 23 6 27 7 31 8
(if ((x + ~2) mod 8) <= 0 then (x div 2) else 1)
A344757-A319099: 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 1
loop(\(x,i).10x,(x div 2),1)
A286507: 1 1 10 10 100 100 1000 1000 10000 10000 100000 100000 1000000 1000000 10000000 10000000
(loop(\(x,i).(x * i),x,(x + 1)) div (1 + (x div 2)))
A256881: 1 2 3 12 40 240 1260 10080 72576 725760 6652800 79833600 889574400 12454041600 163459296000 2615348736000
(((1 + (if x <= 0 then 1 else x)) div 2) * (1 + (x div 2)))
A076921: 1 1 2 4 6 9 12 16 20 25 30 36 42 49 56 64
loop(\(x,i).2x,((x + 1) div 2),(1 + (x div 2)))
A222011: 1 2 4 8
A171647: 1 2 4 8 12 24 32 64 80 160 192 384 448 896 1024 2048
(loop(\(x,i).(x * i),x,(x div 2)) * (1 + (x div 2)))
A077611: 0 0 4 12 144 720 8640 60480 806400 7257600 108864000 1197504000 20118067200 261534873600 4881984307200 73229764608000
loop(\(x,i).x3,(x mod 2),(1 + (x div 2)))
A126951: 1 1 2 8 3 27 4 64 5 125 6 216 7 343 8 512
((x + 1) + ((if (x mod 2) <= 0 then x else 1) + (x div 2)))
A113497: 1 3 6 6 11 9 16 12 21 15 26 18 31 21 36 24
((x * (if (x mod 2) <= 0 then 1 else x)) div (1 + (x div 2)))
A019425: 0 1 1 4 1 8 1 12 1 16 1 20 1 24 1 28
loop(\(x,i).(x + ((2 + i) * i)),x,(1 + (x div 2)))
A087035: 1 4 13 28 53 88 137 200 281 380 501 644 813 1008 1233 1488
((x + ~1) + ((if (~x + 2) <= 0 then x else 2) + (x div 2)))
A231408: 1 2 4 6 9
A265286: 1 2 4 6 9 11 14 16 19
loop(\(x,i).(x + ((x mod 4) * i)),(x div 2),1)
A051548: 1 1 2 2 6 6 12 12 12 12 12 12 12 12 12 12
(if ((x + ~1) mod 5) <= 0 then (x mod 2) else 1)
A249351-A071035: 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1
(if (2 - (x mod 5)) <= 0 then (x mod 2) else 1)
A039982: 1 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1
(if (x + ~12) <= 0 then (x mod 2) else 1)
A327532-A327515: 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1
(if ((x div 4) mod 3) <= 0 then (x mod 2) else 1)
A072608: 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1
(1 + (if (x + ~3) <= 0 then x else 1) - (x mod 2))
A186144: 1 1 3 3 2 1 2 1 2 1 2 1 2
(1 + loop(\(x,i).3x,x,1) - (x mod 2))
A052929: 2 3 10 27 82 243 730 2187 6562 19683 59050 177147 531442 1594323 4782970 14348907
(3 - (if (x mod 3) <= 0 then 2 else (x mod 2)))
A135511: 1 2 3 1 3 2 1 2 3 1 3 2 1 2 3 1
(if (x mod (2 + (x div 4))) <= 0 then (x mod 2) else 1)
A316829: 0 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1
(~1 + (loop(\(x,i).2x,(x div 2),2) + (x mod 2)))
A097110: 1 2 3 4 7 8 15 16 31 32 63 64 127 128 255 256
(~1 + loop(\(x,i).2x,(x div 2),(2 - (x mod 2))))
A316742: 1 0 3 1 7 3 15 7 31 15 63 31 127 63 255 127
loop(\(x,i).2x,(x div 2),(3 - (x mod 2)))
A162255: 3 2 6 4 12 8 24 16 48 32 96 64 192 128 384 256
loop(\(x,i).(2x + 2),x,(3 - (x mod 2)))
A117863: 3 6 18 30 78 126 318 510 1278 2046 5118 8190 20478 32766 81918 131070
(if (x + ~2) <= 0 then x else ((2x + 1) - (x mod 2)))
A121248: 0 1 2 6 9 10
((if (x + ~1) <= 0 then x else (x + 1)) * (1 + (x mod 2)))
A296070: 0 2 3 8 5 12 7 16 9 20 11 24 13 28 15 32
loop(\(x,i).(x * (2 + i)),(x + 1),(1 + (x mod 2)))
A070734: 3 24 60 720 2520 40320 181440 3628800 19958400 479001600 3113510400 87178291200 653837184000 20922789888000 177843714048000 6402373705728000
loop(\(x,i).2x,((x + 1) div 2),(1 + (x mod 2)))
A143095: 1 4 2 8 4 16 8 32 16 64 32 128 64 256 128 512
loop(\(x,i).(2x + 2),(x div 2),(1 + (x mod 2)))
A027383: 1 2 4 6 10 14 22 30 46 62 94 126 190 254 382 510
loop(\(x,i).(2x + 4),(x div 2),(1 + (x mod 2)))
A238549: 1 2 6 8 16 20 36 44 76 92 156 188 316 380 636 764
(loop(\(x,i).(x * i),(x + ~1),x) * (1 + (x mod 2)))
A052612: 0 2 2 12 24 240 720 10080 40320 725760 3628800 79833600 479001600 12454041600 87178291200 2615348736000
(if (x * (4 - (x div 2))) <= 0 then (x mod 2) else 1)
A079421: 0 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1
((5x + 8) - (if x <= 0 then 2 else 1))
A248149: 6 12 17 22 27 32 37 42 47 52 57 62 67 72 77 82
(1 + loop(\(x,i).7x,x,2))
A199416: 3 15 99 687 4803 33615 235299 1647087 11529603 80707215 564950499 3954653487 27682574403 193778020815 1356446145699 9495123019887
(~1 + loop(\(x,i).7x,x,2))
A198480: 1 13 97 685 4801 33613 235297 1647085 11529601 80707213 564950497 3954653485 27682574401 193778020813 1356446145697 9495123019885
(1 + ((x * (x + (if (x + ~2) <= 0 then 2 else 1))) div 2))
A013660: 1 2 5 7 11
A342939: 1 2 5 7 11 16 22 29 37 46 56 67 79 92 106 121
(1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2))
A336936-A336935-A336934-A336460-A336392-A336162-A108712-A003602: 1 1 2 1 3 2 4 1 5 3 6 2 7 4 8 1
(1 + loop(\(x,i).(x + (x2 div (1 + i))),x,2))
A003186: 3 5 10 30 198
(1 + (loop(\(x,i).(2x + 8),x,x) div 2))
A047861: 1 6 17 41 93 205 445 957 2045 4349 9213 19453 40957 86013 180221 376829
(1 + loop(\(x,i).(x * ((x + 2) + (x div 2))),x,2))
A006485: 3 11 171 43691 2863311531 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * (2 - (x div (2 + i)))),x,2))
A076877: 3 5 5 9 9 9 9 17 17 17 17 17 17 17 17 33
(1 + (if (~2 + (x div 2)) <= 0 then x else (x2 + 2)))
A173575: 1 2 3 4 5 6 39
((2x2 + 1) + loop(\(x,i).2x,x,1))
A322593: 2 5 13 27 49 83 137 227 385 675 1225 2291 4385 8531 16777 33219
((2x2 + 1) + loop(\(x,i).2x,x,x))
A046916: 1 5 17 43 97 211 457 995 2177 4771 10441 22771 49441 106835 229769 491971
(1 + (2 * loop(\(x,i).(x + (2 * (i * i))),x,x)))
A001845: 1 7 25 63 129 231 377 575 833 1159 1561 2047 2625 3303 4089 4991
(~1 + loop(\(x,i).((2x + 8) + i),x,2))
A058968: 1 12 35 82 177 368 751 1518 3053 6124 12267 24554 49129 98280 196583 393190
(1 + loop(\(x,i).((2 * (x + (2 * i))) + i),x,2))
A114958: 3 10 29 72 163 350 729 1492 3023 6090 12229 24512 49083 98230 196529 393132
(1 + (if (x mod 9) <= 0 then 0 else x))
A328131-A068636-A004719-A004151: 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 16
(1 + (if (x mod 10) <= 0 then 0 else x))
A180409: 1 2 3 4 5 6 7 8 9 10 1 12 13 14 15 16
(1 + (if (~2 + (x div 5)) <= 0 then 0 else x))
A008835: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 16
((x + 1) + (if (x mod 8) <= 0 then x else 0))
A269358-A269356: 1 2 3 4 5 6 7 8 17 10 11 12 13 14 15 16
loop(\(x,i).(1 + (x mod (1 + (i div 3)))),x,1)
A256553-A212721: 1 1 1 2 1 2 3 1 2 3 4 1 2 3 4 5
loop(\(x,i).(12x + 1),x,1)
A016125: 1 13 157 1885 22621 271453 3257437 39089245 469070941 5628851293 67546215517 810554586205 9726655034461 116719860413533 1400638324962397 16807659899548765
loop(\(x,i).(1 + (6x * i)),x,1)
A056547: 1 7 85 1531 36745 1102351 39684637 1666754755 80004228241 4320228325015 259213699500901 17108104167059467 1231783500028281625 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (3 * (x - (i mod 2)))),x,1)
A006342: 1 1 4 10 31 91 274 820 2461 7381 22144 66430 199291 597871 1793614 5380840
loop(\(x,i).(9x + ~1),x,1)
A187709: 1 8 71 638 5741 51668 465011 4185098 37665881 338992928 3050936351 27458427158 247125844421 2224132599788 20017193398091 180154740582818
loop(\(x,i).(3x2 + 3x + 1),x,1)
A172027: 1 7 169 86191 22286924017 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (3x * (1 + i))),x,1)
A173516: 1 7 64 769 11536 207649 4360630 104655121 2825688268 84770648041 2797431385354 100707529872745 3927593665037056 164958933931556353 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (3 * (x + (i mod 2)))),x,1)
A085287: 1 7 22 70 211 637 1912 5740 17221 51667 155002 465010 1395031 4185097 12555292 37665880
loop(\(x,i).(1 + (3x * (i * i))),x,1)
A336805: 1 4 49 1324 63553 4766476 514779409 75672573124 14529134039809 3530579571673588 1059173871502076401 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + ((x + 4) mod (1 + i))),x,1)
A181281: 1 2 1 2 2 1 6 3 8 3 8 1 6 11 1 6
loop(\(x,i).(x - (x div (~1 + (i mod ~2)))),x,1)
A068911: 1 2 4 6 12 18 36 54 108 162 324 486 972 1458 2916 4374
loop(\(x,i).(x * i),7x,1)
A195391: 1 5040 87178291200 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(2x2 + 3x),1)
A121913: 1 32 16384 134217728 17592186044416 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + ((x * (i * (1 + i))) div 2)),x,1)
A228230: 1 2 7 43 431 6466 135787 3802037 136873333 6159299986 338761499231 22358258949247 1743944198041267 158698922021755298 4611686018427387903 4611686018427387903
loop(\(x,i).(16x + 1),x,1)
A131865: 1 17 273 4369 69905 1118481 17895697 286331153 4581298449 73300775185 1172812402961 18764998447377 300239975158033 4803839602528529 76861433640456465 1229782938247303441
(1 + (if ((x + ~1) mod 8) <= 0 then 1 else x))
A318492: 1 2 3 4 5 6 7 8 9 2 11 12 13 14 15 16
loop(\(x,i).(~7x + 1),x,1)
A014989: 1 ~6 43 ~300 2101 ~14706 102943 ~720600 5044201 ~35309406 247165843 ~1730160900 12111126301 ~84777884106 593445188743 ~4154116321200
((x + 1) + (x div (if (~2 + (x div 2)) <= 0 then 2 else 1)))
A232832: 1 2 4 5 7 8 13 15
loop(\(x,i).(1 + (4 * ((x * i) div 2))),x,1)
A000354: 1 1 5 29 233 2329 27949 391285 6260561 112690097 2253801941 49583642701 1190007424825 30940193045449 866325405272573 25989762158177189
loop(\(x,i).(10x + 5),x,1)
A099915: 1 15 155 1555 15555 155555 1555555 15555555 155555555 1555555555 15555555555 155555555555 1555555555555 15555555555555 155555555555555 1555555555555555
loop(\(x,i).(10x + ~5),x,1)
A093140: 1 5 45 445 4445 44445 444445 4444445 44444445 444444445 4444444445 44444444445 444444444445 4444444444445 44444444444445 444444444444445
(1 div (if ((x + ~1) mod 5) <= 0 then x else 1))
A336676: 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1
(1 mod (if ((x + ~1) mod 5) <= 0 then x else 1))
A085862: 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0
loop(\(x,i).20x,x,1)
A009964: 1 20 400 8000 160000 3200000 64000000 1280000000 25600000000 512000000000 10240000000000 204800000000000 4096000000000000 81920000000000000 1638400000000000000 4611686018427387903
loop(\(x,i).(~10x + 20),x,1)
A165750: 1 10 ~80 820 ~8180 81820 ~818180 8181820 ~81818180 818181820 ~8181818180 81818181820 ~818181818180 8181818181820 ~81818181818180 818181818181820
loop(\(x,i).(10x * i),x,1)
A051262: 1 10 200 6000 240000 12000000 720000000 50400000000 4032000000000 362880000000000 36288000000000000 3991680000000000000 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(5x + 1))
A016862: 1 36 121 256 441 676 961 1296 1681 2116 2601 3136 3721 4356 5041 5776
loop(\(x,i).x2,2,(5x + 1))
A016864: 1 1296 14641 65536 194481 456976 923521 1679616 2825761 4477456 6765201 9834496 13845841 18974736 25411681 33362176
loop(\(x,i).15x,x,1)
A001024: 1 15 225 3375 50625 759375 11390625 170859375 2562890625 38443359375 576650390625 8649755859375 129746337890625 1946195068359375 29192926025390625 437893890380859375
loop(\(x,i).(5x * (1 + i)),x,1)
A034325: 1 10 150 3000 75000 2250000 78750000 3150000000 141750000000 7087500000000 389812500000000 23388750000000000 1520268750000000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(5x * (2 + i)),x,1)
A051691: 1 15 300 7500 225000 7875000 315000000 14175000000 708750000000 38981250000000 2338875000000000 152026875000000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + i - (x div 5)),x,1)
A130243: 1 2 4 7 10 13 17 21 25 29 34 39 44 49 54 59
loop(\(x,i).(1 + (4x * (i * i))),x,1)
A336807: 1 5 81 2917 186689 18668901 2688321745 526911062021 134889231877377 43704111128270149 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (2 * (2x + (i mod 2)))),x,1)
A037576: 1 7 29 119 477 1911 7645 30583 122333 489335 1957341 7829367 31317469 125269879 501079517 2004318071
loop(\(x,i).(~1 + (2 * (2x + (i mod 2)))),x,1)
A108981: 1 5 19 77 307 1229 4915 19661 78643 314573 1258291 5033165 20132659 80530637 322122547 1288490189
loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),x,1)
A260216-A260115-A260091-A257953-A000166: 1 0 1 2 9 44 265 1854 14833 133496 1334961 14684570 176214841 2290792932 32071101049 481066515734
loop(\(x,i).(1 + (2 * (x - (2 * (~x + i))))),x,1)
A094259: 1 3 11 55 315 1871 11203 67191 403115 2418655 14511891 87071303 522427771 3134566575 18807399395 112844396311
loop(\(x,i).(3 * (x mod 5)),x,1)
A168400: 1 3 9 12 6 3 9 12 6 3 9 12 6 3 9 12
loop(\(x,i).18x,x,1)
A001027: 1 18 324 5832 104976 1889568 34012224 612220032 11019960576 198359290368 3570467226624 64268410079232 1156831381426176 20822964865671168 374813367582081024 4611686018427387903
loop(\(x,i).(~9x + 18),x,1)
A165749: 1 9 ~63 585 ~5247 47241 ~425151 3826377 ~34437375 309936393 ~2789427519 25104847689 ~225943629183 2033492662665 ~18301433963967 164712905675721
loop(\(x,i).(9x * i),x,1)
A051232: 1 9 162 4374 157464 7085880 382637520 24106163760 1735643790720 140587147048320 12652843234348800 1252631480200531200 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(6x * (1 + i)),x,1)
A034788: 1 12 216 5184 155520 5598720 235146240 11287019520 609499054080 36569943244800 2413616254156800 173780370299289600 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x - ((1 + i) div 3)),x,1)
A136169: 1 2 3 5 9 16 30 58 113 223 443 882 1760 3516 7027 14049
loop(\(x,i).(12x + ~6),x,1)
A173535: 1 6 66 786 9426 113106 1357266 16287186 195446226 2345354706 28144256466 337731077586 4052772931026 48633275172306 583599302067666 7003191624811986
(1 + (x * loop(\(x,i).(x2 + 1),2,3)))
A078787: 1 102 203 304 405 506 607 708 809 910 1011 1112 1213 1314 1415 1516
loop(\(x,i).24x,x,1)
A009968: 1 24 576 13824 331776 7962624 191102976 4586471424 110075314176 2641807540224 63403380965376 1521681143169024 36520347436056576 876488338465357824 4611686018427387903 4611686018427387903
loop(\(x,i).(12x * i),x,1)
A145448: 1 12 288 10368 497664 29859840 2149908480 180592312320 17336861982720 1872381094133760 224685731296051200 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~12x + 1),x,1)
A014994: 1 ~11 133 ~1595 19141 ~229691 2756293 ~33075515 396906181 ~4762874171 57154490053 ~685853880635 8230246567621 ~98762958811451 1185155505737413 ~14221866068848955
loop(\(x,i).(9x + 6),x,1)
A096046: 1 15 141 1275 11481 103335 930021 8370195 75331761 677985855 6101872701 54916854315 494251688841 4448265199575 40034386796181 360309481165635
loop(\(x,i).(3 * ((x2 + x) div 2)),x,1)
A304780: 1 3 18 513 395523 234658258578 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(7x + ~3),x,1)
A034494: 1 4 25 172 1201 8404 58825 411772 2882401 20176804 141237625 988663372 6920643601 48444505204 339111536425 2373780754972
loop(\(x,i).(7x + ~1),x,1)
A083067: 1 6 41 286 2001 14006 98041 686286 4804001 33628006 235396041 1647772286 11534406001 80740842006 565185894041 3956301258286
loop(\(x,i).(7x + ~2),x,1)
A083076: 1 5 33 229 1601 11205 78433 549029 3843201 26902405 188316833 1318217829 9227524801 64592673605 452148715233 3165041006629
loop(\(x,i).(7x - i),x,1)
A122471: 1 6 40 277 1935 13540 94774 663411 4643869 32507074 227549508 1592846545 11149925803 78049480608 546346364242 3824424549679
loop(\(x,i).((2 * i) - (2x div 3)),x,1)
A034298: 1 2 3 4 6 6 8 9 10 12 12 14 15 16 18 18
loop(\(x,i).(x + i - ((x div 2) div 3)),x,1)
A256967: 1 2 4 7 10 14 18 22 27 32 37 42 47 53 59 65
(~1 + loop(\(x,i).(2 * (2x + i)),3,x))
A239124: 53 117 181 245 309 373 437 501 565 629 693 757 821 885 949 1013
loop(\(x,i).(3x * (i * (2 + i))),x,1)
A064633: 1 9 216 9720 699840 73483200 10581580800 1999918771200 479980505088000 142554210011136000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,3,(3x + 1))
A016784: 1 65536 5764801 100000000 815730721 4294967296 16983563041 54875873536 152587890625 377801998336 852891037441 1785793904896 3512479453921 6553600000000 11688200277601 20047612231936
loop(\(x,i).x3,1,(3x + 1))
A061102-A016779: 1 64 343 1000 2197 4096 6859 10648 15625 21952 29791 39304 50653 64000 79507 97336
(if (x mod 2) <= 0 then (x div 2) else (3x + 1))
A006370: 0 4 1 10 2 16 3 22 4 28 5 34 6 40 7 46
loop(\(x,i).x3,2,(3x + 1))
A016785: 1 262144 40353607 1000000000 10604499373 68719476736 322687697779 1207269217792 3814697265625 10578455953408 26439622160671 60716992766464 129961739795077 262144000000000 502592611936843
loop(\(x,i).(2x + ~2),x,(3x + 1))
A027992: 1 6 22 66 178 450 1090 2562 5890 13314 29698 65538 143362 311298 671746 1441794
(if (x mod 2) <= 0 then (x div 2) else (3x + ~1))
A001281: 0 2 1 8 2 14 3 20 4 26 5 32 6 38 7 44
loop(\(x,i).(x * (3 + i)),3x,1)
A065961: 1 120 60480 79833600 217945728000 1067062284288000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~9x + 1),x,1)
A014991: 1 ~8 73 ~656 5905 ~53144 478297 ~4304672 38742049 ~348678440 3138105961 ~28242953648 254186582833 ~2287679245496 20589113209465 ~185302018885184
loop(\(x,i).(3x * (3 + i)),x,1)
A051609: 1 12 180 3240 68040 1632960 44089920 1322697600 43649020800 1571364748800 61283225203200 2573895458534400 115825295634048000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x * (1 + (2 * i))),x,1)
A034723: 1 9 135 2835 76545 2525985 98513415 4433103675 226088287425 12887032383225 811883040143175 56019929769879075 4201494732740930625 4611686018427387903 4611686018427387903
loop(\(x,i).(3x * (~1 + (2 * i))),x,1)
A011781: 1 3 27 405 8505 229635 7577955 295540245 13299311025 678264862275 38661097149675 2435649120429525 168059789309637225 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3 * (x + (x div (1 + i)))),x,1)
A064017: 1 3 12 45 162 567 1944 6561 21870 72171 236196 767637 2480058 7971615 25509168 81310473
loop(\(x,i).(3x * (2 - (i mod 2))),x,1)
A130505: 1 3 18 54 324 972 5832 17496 104976 314928 1889568 5668704 34012224 102036672 612220032 1836660096
(1 + loop(\(x,i).(2 * (x - i)),(x div 3),x))
A280429: 1 2 3 5 7 9 17 21 25 51 59 67 141 157 173 367
loop(\(x,i).((2x + 2) + (x mod 3)),x,1)
A053209: 1 5 14 32 68 140 284 572 1148 2300 4604 9212 18428 36860 73724 147452
loop(\(x,i).(2x - ((x - i) mod 3)),x,1)
A018254: 1 2 4 7 14 28
A057744: 1 2 4 7 14 28 55 110 220 439 878 1756 3511 7022 14044 28087
loop(\(x,i).(10x + 1),x,1)
A135463-A000042: 1 11 111 1111 11111 111111 1111111 11111111 111111111 1111111111 11111111111 111111111111 1111111111111 11111111111111 111111111111111 1111111111111111
loop(\(x,i).(10x + ~1),x,1)
A059482: 1 9 89 889 8889 88889 888889 8888889 88888889 888888889 8888888889 88888888889 888888888889 8888888888889 88888888888889 888888888888889
(if ((x2 + ~1) mod (x + 3)) <= 0 then x else 1)
A326073: 1 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1
loop(\(x,i).(1 + ((x2 + 2x) * (x + i))),x,1)
A308582: 1 7 568
loop(\(x,i).((3x + 1) - (i mod 2)),x,1)
A188545: 1 3 10
A033113: 1 3 10 30 91 273 820 2460 7381 22143 66430 199290 597871 1793613 5380840 16142520
loop(\(x,i).x2,1,(2x2 + x + ~1))
A123198: 1 4 81 400 1225 2916 5929 10816 18225 28900 43681 63504 89401 122500 164025 215296
loop(\(x,i).((3x + 1) + (i mod 2)),x,1)
A037480: 1 5 16 50 151 455 1366 4100 12301 36905 110716 332150 996451 2989355 8968066 26904200
loop(\(x,i).((3x + ~1) + (i mod 2)),x,1)
A153774: 1 3 8 24 71 213 638 1914 5741 17223 51668 155004 465011 1395033 4185098 12555294
(1 + loop(\(x,i).(x + (i * i)),(2x + ~1),x))
A168547: 1 3 17 59 145 291 513 827 1249 1795 2481 3323 4337 5539 6945 8571
((~x + ~1) + loop(\(x,i).(x * (2 + i)),2x,1))
A016101: 0 10 357 20156 1814395 239500794 43589145593 10461394943992 3201186852863991 1216451004088319990 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((4x + 1) - (x mod 2)),x,1)
A033114: 1 4 17 68 273 1092 4369 17476 69905 279620 1118481 4473924 17895697 71582788 286331153 1145324612
loop(\(x,i).(4x * (1 + (2 * i))),x,1)
A034910: 1 12 240 6720 241920 10644480 553512960 33210777600 2258332876800 171633298636800 14417197085491200 1326382131865190400 4611686018427387903 4611686018427387903
loop(\(x,i).(4x * (~1 + (2 * i))),x,1)
A144828: 1 4 48 960 26880 967680 42577920 2214051840 132843110400 9033331507200 686533194547200 57668788341964800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((1 + i) * (~1 + (2 * i)))),x,1)
A132911: 1 2 18 360 12600 680400 52390800 5448643200 735566832000 125046361440000 26134689540960000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((2 + i) * (~1 + (2 * i)))),x,1)
A132912: 1 3 36 900 37800 2381400 209563200 24518894400 3677834160000 687754987920000 156808137245760000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x * (2 + i)) div (1 + (i div 2))),x,1)
A242172: 1 3 6 15 30 70 140 315 630 1386 2772 6006 12012 25740 51480 109395
(1 + (x * loop(\(x,i).(1 + (x * (1 + i))),x,1)))
A093965: 1 4 21 124 825 6186 51961 484968 4988241 56117710 685883121 9053657196 128397320233 1947359356866 31457343457065 539268744978256
loop(\(x,i).(5x + 7),x,1)
A117088: 1 12 67 342 1717 8592 42967 214842 1074217 5371092 26855467 134277342 671386717 3356933592 16784667967 83923339842
((x + ~1) + loop(\(x,i).(2 * (2x - i)),x,1))
A323397: 0 2 5 12 35 122 465 1832 7295 29142 116525 466052 1864155 7456562 29826185 119304672
(1 + loop(\(x,i).(3x + 3),(x + 1),x))
A079272: 4 22 94 364 1336 4738 16402 55768 186988 620014 2037190 6643012 21523360 69353050 222408058 710270896
loop(\(x,i).2x,(5x + 4),1)
A013825: 16 512 16384 524288 16777216 536870912 17179869184 549755813888 17592186044416 562949953421312 18014398509481984 576460752303423488 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + (2 div (x + 1))),x,1)
A269696-A170686-A170638-A170590-A170542-A170494-A170446-A170398-A170350-A170302-A170254-A170206-A170158-A170110-A170062-A170014-A169546-A169498-A169450-A169402-A169354-A169306-A169258-A169210-A169162-A169114-A169066-A169018-A168970-A168922-A168874-A168826-A168778-A168730-A168682-A167896-A003947: 1 5 20 80 320 1280 5120 20480 81920 327680 1310720 5242880 20971520 83886080 335544320 1342177280
(1 + loop(\(x,i).(2 * (x + (i mod 2))),(x + 1),x))
A191007: 3 9 27 69 171 405 939 2133 4779 10581 23211 50517 109227 234837 502443 1070421
(1 + loop(\(x,i).(2x + (i div 2)),(x + 1),x))
A127982: 1 6 20 57 147 360 850 1959 4433 9894 21840 47781 103759 223908 480590 1026723
(1 + loop(\(x,i).(x + (x div 2)),2,(x2 + x)))
A301294: 1 5 14 28 46 68 95 127 163 203 248 298 352 410 473 541
loop(\(x,i).(x * (i * (2 + i))),(x2 + x),1)
A319900: 1 24 14515200 4611686018427387903
loop(\(x,i).(x + (x div 2)),2,(x2 + x + 1))
A301292: 1 6 15 28 46 69 96 127 163 204 249 298 352 411 474 541
loop(\(x,i).(x * (1 + i)),x,(x2 + x + 1))
A162968: 1 6 42 312 2520 22320 216720 2298240 26490240 330220800 4430764800 63707212800 977642265600 15953627289600 275919291648000 5042392363008000
loop(\(x,i).((x + 1) + ((1 + (2 * i)) * i)),x,1)
A174723: 1 5 16 38 75 131 210 316 453 625 836 1090 1391 1743 2150 2616
(1 + loop(\(x,i).(~1 + (x * (1 + i))),(x + ~1),x))
A140836: 1 2 4 15 80
loop(\(x,i).(x * i),(x + ~2),(x2 + ~x + 1))
A108217: 1 1 3 7 26 126 744 5160 41040 367920 3669120 40279680 482630400 6266937600 87657292800 1313901388800
loop(\(x,i).5x,(x2 + ~x),1)
A053766: 1 1 25 15625 244140625 95367431640625 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (2 + (i mod 2))),(x2 + ~x),1)
A109354: 1 1 6 216 46656 60466176 470184984576 21936950640377856 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (i - (x div 2))),(x2 + ~x),1)
A275588: 1 1 2 16 4611686018427387903
(1 + ((x mod 5) mod (if x <= 0 then 1 else x)))
A339146: 1 1 1 1 1 1 2 3 4 5 1 2 3 4 5 1
(1 + ((x mod 8) mod (if x <= 0 then 1 else x)))
A322856-A291146-A280863-A274841-A273736-A175772-A049814: 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8
((x2 + 2x + 1) * (1 + (if x <= 0 then 1 else x)))
A184628: 2 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096
loop(\(x,i).((x2 + ~1) + (2 * (x mod 2))),x,1)
A229220: 1 2 3 10 99 9802 96079203 9231213249115210 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (5x * i)),x,1)
A056546: 1 6 61 916 18321 458026 13740781 480927336 19237093441 865669204846 43283460242301 2380590313326556 142835418799593361 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + ((x div (1 + i)) + i)),x,1)
A062714: 1 3 7 12 19 28 39
A337300: 1 3 7 12 19 28 39 51 65 81 99 119 141 165 191 218
loop(\(x,i).(~1 + ((2 * (x mod 2)) + (x * i))),x,1)
A003048: 1 2 3 10 39 196 1175 8226 65807 592264 5922639 65149030 781788359 10163248668 142285481351 2134282220266
loop(\(x,i).((6x + 1) + i),x,1)
A014829: 1 8 51 310 1865 11196 67183 403106 2418645 14511880 87071291 522427758 3134566561 18807399380 112844396295 677066377786
loop(\(x,i).((8x + 1) + i),x,1)
A014831: 1 10 83 668 5349 42798 342391 2739136 21913097 175304786 1402438299 11219506404 89756051245 718048409974 5744387279807 45955098238472
loop(\(x,i).((1 + (2 * (x + i))) * (1 + i)),x,1)
A271476: 1 10 75 628 6325 75966 1063615 17017960 306323433 6126468850 134782314931 3234775558620 84104164524445 2354916606684838 70647498200545575 2260719942417458896
loop(\(x,i).(x * (i * (1 + i) * (1 + i))),x,1)
A224900: 1 4 72 3456 345600 62208000 18289152000 8193540096000 5309413982208000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + ~1) mod (4 * (1 + i))),x,1)
A261304: 1 0 11 10 9 8 7 6 5 4 3 2 1 0 59 58
loop(\(x,i).(x * (i * (2 + i) * (1 + i))),x,1)
A090443: 1 6 144 8640 1036800 217728000 73156608000 36870930432000 26547069911040000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((5x + 1) + i),x,1)
A014827: 1 7 38 194 975 4881 24412 122068 610349 3051755 15258786 76293942 381469723 1907348629 9536743160 47683715816
(0 - loop(\(x,i).(~2x * (i * i)),x,1))
A055546: ~1 2 ~16 288 ~9216 460800 ~33177600 3251404800 ~416179814400 67421129932800 ~13484225986560000 3263182688747520000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) + (loop(\(x,i).2x,(x + ~1),1) div 2))
A231408: 1 2 4 6 9
A323227: 1 2 4 6 9 14 23 40 73 138 267 524 1037 2062 4111 8208
loop(\(x,i).(2x + 14),x,1)
A099003: 1 16 46 106 226 466 946 1906 3826 7666 15346 30706 61426 122866 245746 491506
loop(\(x,i).(2 * (~x mod 5)),x,1)
A014391: 1 8 4 2 6 8 4 2 6 8 4 2 6 8 4 2
loop(\(x,i).(2 * ((x + 1) - (2 * (i mod 2)))),x,1)
A078008: 1 0 2 2 6 10 22 42 86 170 342 682 1366 2730 5462 10922
loop(\(x,i).(2 * (1 + (2 * (x - (i mod 2))))),x,1)
A122117: 1 2 10 38 154 614 2458 9830 39322 157286 629146 2516582 10066330 40265318 161061274 644245094
(1 + loop(\(x,i).(x + 2),(x + ~6),x))
A308019: 1 2 3 4 5 6 7 10 13 16 19 22 25 28 31 34
loop(\(x,i).(9x + 2),x,1)
A138894: 1 11 101 911 8201 73811 664301 5978711 53808401 484275611 4358480501 39226324511 353036920601 3177332285411 28595990568701 257363915118311
loop(\(x,i).(2 * (x - (3 * (1 - i)))),x,1)
A131068: 1 2 10 32 82 188 406 848 1738 3524 7102 14264 28594 57260 114598 229280
(~1 + loop(\(x,i).(1 + ((x2 + x) div 2)),2,x))
A188545: 1 3 10
A267707: 1 3 10 28 66 136 253 435 703 1081 1596 2278 3160 4278 5671 7381
loop(\(x,i).(2 * (~1 + (2 * (x + (i mod 2))))),x,1)
A255465: 1 6 22 90 358 1434 5734 22938 91750 367002 1468006 5872026 23488102 93952410 375809638 1503238554
loop(\(x,i).(10x + 2),x,1)
A090843: 1 12 122 1222 12222 122222 1222222 12222222 122222222 1222222222 12222222222 122222222222 1222222222222 12222222222222 122222222222222 1222222222222222
(1 + (x * loop(\(x,i).(2x + 1),(x + ~1),2)))
A036542: 1 3 11 34 93 236 571 1338 3065 6904 15351 33782 73717 159732 344051 737266
loop(\(x,i).((x * (i * i * (1 + i))) div 2),x,1)
A167484: 1 1 6 108 4320 324000 40824000 8001504000 2304433152000 933295426560000 513312484608000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (2x - (x div ~2))),x,1)
A170687-A170639-A170591-A170543-A170495-A170447-A170399-A170351-A170303-A170255-A170207-A170159-A170111-A170063-A170015-A169547-A169499-A169451-A169403-A169355-A169307-A169259-A169211-A169163-A169115-A169067-A169019-A168971-A168923-A168875-A168827-A168779-A168731-A168683-A167897-A003948: 1 6 30 150 750 3750 18750 93750 468750 2343750 11718750 58593750 292968750 1464843750 7324218750 36621093750
loop(\(x,i).(x - (x div (~2 + (x mod ~2)))),x,1)
A018752: 1 2 3 4 6 9 12 18 27 36 54 81 108 162 243 324
loop(\(x,i).(2 * (x mod 10)),x,1)
A222011: 1 2 4 8
A095915: 1 2 4 8 16 12 4 8 16 12 4 8 16 12 4 8
(if (~2 + (x mod (2 + (x mod 3)))) <= 0 then x else 1)
A103303: 0 1 2 3 4 5 6 7 8 9
A337864-A137564-A106612-A084905: 0 1 2 3 4 5 6 7 8 9 10 1 12 13 14 15
(~1 + loop(\(x,i).((x2 + 3x + 2) div 2),2,x))
A153977: 2 9 27 65 135 252 434 702 1080 1595 2277 3159 4277 5670 7380 9452
((x + 1) + loop(\(x,i).(x3 + ~1),2,2))
A112821: 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358
loop(\(x,i).(2 + (((x div 2) * (1 + i)) div 2)),x,1)
A107481: 1 2 3 4 7 11 19 38
loop(\(x,i).(4 * (x - (x div ~2))),x,1)
A270576: 1 8 48 288 1728 10368 62208 373248 2239488 13436928 80621568 483729408 2902376448 17414258688 104485552128 626913312768
loop(\(x,i).32x,x,1)
A009976: 1 32 1024 32768 1048576 33554432 1073741824 34359738368 1099511627776 35184372088832 1125899906842624 36028797018963968 1152921504606846976 4611686018427387903 4611686018427387903
((x + ~1) + (2 * (if x <= 0 then 1 else 8)))
A250038-A248501: 1 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
(1 + loop(\(x,i).(1 + i),(x + ~8),x))
A178051: 1 2 3 4 5 6 7 8 9 3 4 5 6 7 8 9
(1 + loop(\(x,i).(x + 2),(x + ~8),x))
A008816: 1 2 3 4 5 6 7 8 9 12 15 18 21 24 27 30
(1 + loop(\(x,i).(x + ~2),(x + ~8),x))
A262734-A179987: 1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2
(1 + loop(\(x,i).(1 - i),(x + ~8),x))
A274580: 1 2 3 4 5 6 7 8 9 1 0 ~1 ~2 ~3 ~4 ~5
loop(\(x,i).(10x + ~8),x,1)
A047855: 1 2 12 112 1112 11112 111112 1111112 11111112 111111112 1111111112 11111111112 111111111112 1111111111112 11111111111112 111111111111112
(if (x mod (2 + ((~x + 2) mod 4))) <= 0 then x else 1)
A131516: 0 1 2 1 4 1 6 1 8 9 10 1 12 1 14 15
(1 + loop(\(x,i).(x + i),(2 * (x mod 4)),x))
A121511: 1 5 13 25 5 9 17 29 9 13 21 33 13 17 25 37
(1 + loop(\(x,i).(6x + 4),2,x))
A044131: 29 65 101 137 173 209 245 281 317 353 389 425 461 497 533 569
loop(\(x,i).(10x + ~4),x,1)
A093142: 1 6 56 556 5556 55556 555556 5555556 55555556 555555556 5555555556 55555555556 555555555556 5555555555556 55555555555556 555555555555556
loop(\(x,i).(4 * (2x + (x div 2))),x,1)
A346178: 1 8 80 800 8000 80000 800000 8000000 80000000 800000000 8000000000 80000000000 800000000000 8000000000000 80000000000000 800000000000000
loop(\(x,i).(4 * (2x + (x mod 2))),x,1)
A270568: 1 12 96 768 6144 49152 393216 3145728 25165824 201326592 1610612736 12884901888 103079215104 824633720832 6597069766656 52776558133248
loop(\(x,i).(7x + 2),x,1)
A238275: 1 9 65 457 3201 22409 156865 1098057 7686401 53804809 376633665 2636435657 18455049601 129185347209 904297430465 6330082013257
loop(\(x,i).(4 * (2x - (x mod 2))),x,1)
A092811: 1 4 32 256 2048 16384 131072 1048576 8388608 67108864 536870912 4294967296 34359738368 274877906944 2199023255552 17592186044416
(if x <= 0 then 2 else ((x + ~1) + (4 * (x mod 2))))
A065164: 2 4 1 6 3 8 5 10 7 12 9 14 11 16 13 18
((x + 1) + (2 * (2 + loop(\(x,i).(x * i),x,2))))
A073829: 9 10 15 32 105 490 2891 20172 161293 1451534 14515215 159667216 1916006417 24908083218 348713164819 5230697472020
loop(\(x,i).(2 * (x - ((x div (2 + i)) mod 2))),x,1)
A222011: 1 2 4 8
A004651: 1 2 4 8 14 28 54
(1 + loop(\(x,i).(3x + i),4,x))
A156796: 59 140 221 302 383 464 545 626 707 788 869 950 1031 1112 1193 1274
loop(\(x,i).(x - (4 * (~x + (i mod 2)))),x,1)
A100284: 1 1 5 21 105 521 2605 13021 65105 325521 1627605 8138021 40690105 203450521 1017252605 5086263021
(1 + loop(\(x,i).(x + 3),(x + ~4),x))
A026484: 1 2 3 4 5 9 13 17 21 25 29 33 37 41 45 49
(1 + loop(\(x,i).(x * i),x,(x + (x div 4))))
A322011: 1 2 5 19 121
(1 - (x mod loop(\(x,i).(~4 + (x * i)),x,1)))
A210689: 1 3 9 32 137
loop(\(x,i).(10x + 4),x,1)
A099914: 1 14 144 1444 14444 144444 1444444 14444444 144444444 1444444444 14444444444 144444444444 1444444444444 14444444444444 144444444444444 1444444444444444
loop(\(x,i).(2 * (x - (2 * (~x + (x mod 2))))),x,1)
A167747: 1 2 12 72 432 2592 15552 93312 559872 3359232 20155392 120932352 725594112 4353564672 26121388032 156728328192
loop(\(x,i).(2 * (3x + (x div 2))),x,1)
A055272: 1 6 42 294 2058 14406 100842 705894 4941258 34588806 242121642 1694851494 11863960458 83047723206 581334062442 4069338437094
loop(\(x,i).(2 * (4x + (x div 2))),x,1)
A055275: 1 8 72 648 5832 52488 472392 4251528 38263752 344373768 3099363912 27894275208 251048476872 2259436291848 20334926626632 183014339639688
loop(\(x,i).(2 * (4x - (x div 2))),x,1)
A170689-A170641-A170593-A170545-A170497-A170449-A170401-A170353-A170305-A170257-A170209-A170161-A170113-A170065-A170017-A169549-A169501-A169453-A169405-A169357-A169309-A169261-A169213-A169165-A169117-A169069-A169021-A168973-A168925-A168877-A168829-A168781-A168733-A168685-A167899-A003950: 1 8 56 392 2744 19208 134456 941192 6588344 46118408 322828856 2259801992 15818613944 110730297608 775112083256 5425784582792
((x + 1) + (if (~x + 4) <= 0 then (x div 2) else 2))
A154660: 3 4 5 6 7 8
A298003: 3 4 5 6 7 8 10 11 13 14 16 17 19 20 22 23
((x + 1) + loop(\(x,i).(2 * (x + i)),(x div 2),2))
A126269: 3 4 9 10 21 22 45 46 93 94 189 190 381 382 765 766
loop(\(x,i).((~2x + 1) - ((x div 2) mod 2)),x,1)
A077931: 1 ~1 2 ~4 9 ~17 34 ~68 137 ~273 546 ~1092 2185 ~4369 8738 ~17476
loop(\(x,i).(2 * (4x - (x mod 2))),x,1)
A083233: 1 6 48 384 3072 24576 196608 1572864 12582912 100663296 805306368 6442450944 51539607552 412316860416 3298534883328 26388279066624
loop(\(x,i).(2 * ((2x * i) - (x mod 2))),x,1)
A274448-A051711: 1 2 16 192 3072 61440 1474560 41287680 1321205760 47563407360 1902536294400 83711596953600 4018156653772800 208944145996185600 4611686018427387903 4611686018427387903
loop(\(x,i).(2 + ((x * (~1 + i)) + (x mod 2))),x,1)
A054099: 1 3 6 14 44 178 892 5354 37480 299842 2698580 26985802 296843824 3562125890 46307636572 648306912010
loop(\(x,i).(x - ((x + 2) div (~2 + (x mod 2)))),x,1)
A164123: 1 4 7 16 25 52 79 160 241 484 727 1456 2185 4372 6559 13120
((x + 1) + (if (x + ~2) <= 0 then 1 else (2 * (x mod 2))))
A104650: 2 3 4 6 5 8 7
loop(\(x,i).(2 * ((x2 + ~x) + (x mod 2))),x,1)
A001510: 1 2 4 24 1104 2435424 11862575248704 4611686018427387903 4611686018427387903
loop(\(x,i).(x + i - (x div (2 * (2 + i)))),x,1)
A025708: 1 2 4 7 11 16 21 27 34 42 51 61 71 82 94 107
loop(\(x,i).((x + 2) - ((~x + 2) div (2 + i))),x,1)
A256966: 1 3 6 9 13 17 21 26 31 36 41 46 52 58 64 70
loop(\(x,i).14x,x,1)
A001023: 1 14 196 2744 38416 537824 7529536 105413504 1475789056 20661046784 289254654976 4049565169664 56693912375296 793714773254144 11112006825558016 155568095557812224
loop(\(x,i).(2x * (1 + (2 * (1 + i)))),x,1)
A051618: 1 10 140 2520 55440 1441440 43243200 1470268800 55870214400 2346549004800 107941254220800 5397062711040000 291441386396160000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~10x + 1),x,1)
A014992: 1 ~9 91 ~909 9091 ~90909 909091 ~9090909 90909091 ~909090909 9090909091 ~90909090909 909090909091 ~9090909090909 90909090909091 ~909090909090909
loop(\(x,i).(2x * (1 + (2 * (2 + i)))),x,1)
A051622: 1 14 252 5544 144144 4324320 147026880 5587021440 234654900480 10794125422080 539706271104000 29144138639616000 1690360041097728000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x * (1 + (4 * i))),x,1)
A034908: 1 10 180 4680 159120 6683040 334152000 19380816000 1279133856000 94655905344000 7761784238208000 698560581438720000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x * (~1 + (4 * i))),x,1)
A147626: 1 6 84 1848 55440 2106720 96909120 5233092480 324451733760 22711621363200 1771506466329600 152349556104345600 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x * (1 + (2 * (i div 2)))),x,1)
A002867: 1 2 12 72 720 7200 100800 1411200 25401600 457228800 10059033600 221298739200 5753767219200 149597947699200 4487938430976000 134638152929280000
loop(\(x,i).(2x * (1 + (2 * (i mod 2)))),x,1)
A107904: 1 6 12 72 144 864 1728 10368 20736 124416 248832 1492992 2985984 17915904 35831808 214990848
((x + ~1) + (if ((x + 1) mod 3) <= 0 then x else 2))
A222257: 1 2 3 4 5 9 7 8 15 10 11 21 13 14 27 16
loop(\(x,i).(2x + 24),x,1)
A139698: 1 26 76 176 376 776 1576 3176 6376 12776 25576 51176 102376 204776 409576 819176
loop(\(x,i).(2 * (x + (3 * (x div 2)))),x,1)
A020699: 1 2 10 50 250 1250 6250 31250 156250 781250 3906250 19531250 97656250 488281250 2441406250 12207031250
loop(\(x,i).((3x2 + x) div 2),x,1)
A059406: 1 2 7 77 8932 119675402 21483302825630107 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (x + (3x * i))),x,1)
A034689: 1 8 112 2240 58240 1863680 70819840 3116072960 155803648000 8725004288000 540950265856000 36784618078208000 2722061737787392000 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (~x + (3x * i))),x,1)
A049308: 1 4 40 640 14080 394240 13404160 536166400 24663654400 1282510028800 74385581670400 4760677226905600 333247405883392000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * ((~x + 1) - (i mod 3))),x,1)
A131562: 1 ~2 2 ~2 4 ~10 22 ~44 86 ~170 340 ~682 1366 ~2732 5462 ~10922
loop(\(x,i).(10x + 8),x,1)
A246059: 1 18 188 1888 18888 188888 1888888 18888888 188888888 1888888888 18888888888 188888888888 1888888888888 18888888888888 188888888888888 1888888888888888
(1 + loop(\(x,i).(x * ((2x + 1) + i)),2,x))
A272850: 1 45 325 1225 3321 7381 14365 25425 41905 65341 97461 140185 195625 266085 354061 462241
((x + 1) + loop(\(x,i).((x + 1) * (x + i)),x,2))
A275338: 3 11 113
loop(\(x,i).(2x * (~1 + ((i mod 2) + i))),x,1)
A110491: 1 2 4 24 144 1440 14400 201600 2822400 50803200 914457600 20118067200 442597478400 11507534438400 299195895398400 8975876861952000
(1 + loop(\(x,i).(x + (x div 8)),2,x))
A259178: 1 2 3 4 5 6 7 8 11 12 13 14 15 16 17 19
loop(\(x,i).((x * (4 + (i mod 2))) div 2),x,1)
A026395: 1 2 4 10 20 50 100 250 500 1250 2500 6250 12500 31250 62500 156250
loop(\(x,i).(x - ((~x + ((x div 2) mod 2)) div 2)),x,1)
A328262: 1 2 3 4 6 9 14 21 32 48 72 108 162 243 364 546
loop(\(x,i).(x - (2x * (~2 + (i mod 2)))),x,1)
A100747: 1 3 15 45 225 675 3375 10125 50625 151875 759375 2278125 11390625 34171875 170859375 512578125
loop(\(x,i).(2x * (2 + (3 * i))),x,1)
A034724: 1 10 160 3520 98560 3351040 134041600 6165913600 320627507200 18596395417600 1190169306726400 83311851470848000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x * (~2 + (3 * i))),x,1)
A047657: 1 2 16 224 4480 116480 3727360 141639680 6232145920 311607296000 17450008576000 1081900531712000 73569236156416000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x * (2 + ((1 + i) * i))) div 2),x,1)
A128814: 1 2 8 56 616 9856 216832 6288128 232660736 10702393856 599334055936 40155381747712 3172275158069248 291849314542370816 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 2) + (((2 + i) * i) div 2)),x,1)
A173154: 1 4 10 19 33 52 78 111 153 204 266 339 425 524 638 767
loop(\(x,i).((2 + (x * (x + i))) div (x + 2)),x,1)
A022856: 1 1 1 2 3 5 8 12 17 23 30 38 47 57 68 80
(loop(\(x,i).2x,x,1) mod (x2 + 2x + 1))
A220105: 0 2 4 8 16 32 15 0 13 12 56 32 40 156 184 0
(loop(\(x,i).(x * i),x,1) div (x2 + 2x + 1))
A242426: 1 0 0 0 0 3 14 78 497 3628 29990 277200 2834328 31770514 387459072 5108103000
(loop(\(x,i).2x,x,2) div (x2 + 2x + 1))
A060505: 2 1 0 1 1 1 2 4 6 10 16 28 48 83 145 256
(loop(\(x,i).2x,x,2) mod (x2 + 2x + 1))
A066606: 0 0 8 0 7 28 30 0 26 24 112 64 80 116 143 0
loop(\(x,i).3x,x,(x2 + 2x + 1))
A069996: 1 12 81 432 2025 8748 35721 139968 531441 1968300 7144929 25509168 89813529 312487308 1076168025 3673320192
loop(\(x,i).(x * (2 + i)),x,(x2 + 2x + 1))
A055533: 1 12 108 960 9000 90720 987840 11612160 146966400 1995840000 28979596800 448345497600 7366565606400 128152088064000 2353813862400000 45527990796288000
loop(\(x,i).(x * i),(x * (x2 div (x + 2))),1)
A005607: 1 1 2 6 40320
A161563: 1 1 2 6 40320 1307674368000 4611686018427387903
loop(\(x,i).(7x + ~14),x,1)
A165759: 1 ~7 ~63 ~455 ~3199 ~22407 ~156863 ~1098055 ~7686399 ~53804807 ~376633663 ~2636435655 ~18455049599 ~129185347207 ~904297430463 ~6330082013255
(1 + loop(\(x,i).(1 + (x2 div 2)),(x + ~2),x))
A124045: 1 2 3 6 42
loop(\(x,i).(~7x + 14),x,1)
A165639: 1 7 ~35 259 ~1799 12607 ~88235 617659 ~4323599 30265207 ~211856435 1482995059 ~10380965399 72666757807 ~508667304635 3560671132459
((x + 1) + (x div (if (x + ~2) <= 0 then 2 else (x + ~2))))
A161211: 1 2 4 7 7 7
((~x2 + 2x + ~1) + loop(\(x,i).2x,x,2))
A243860: 1 4 7 12 23 48 103 220 463 960 1967 3996 8071 16240 32599 65340
loop(\(x,i).(x * i),(x + ~2),(x2 + ~2x + 1))
A094304: 1 0 1 4 18 96 600 4320 35280 322560 3265920 36288000 439084800 5748019200 80951270400 1220496076800
(((x2 + 1) div 2) * (if (x + ~2) <= 0 then x else 1))
A030978: 0 1 4 5 8 13 18 25 32 41 50 61 72 85 98 113
loop(\(x,i).(2x + ((i * i) mod 3)),x,1)
A267210: 1 3 7 14 29 59 118 237 475 950 1901 3803 7606 15213 30427 60854
loop(\(x,i).(2x + ((2 + i) * (1 + i))),x,1)
A134638: 1 8 28 76 182 406 868 1808 3706 7522 15176 30508 61198 122606 245452 491176
loop(\(x,i).(2x + ((i div ~2) mod 2)),x,1)
A151754: 1 3 7 14 28 57 115 230 460 921 1843 3686 7372 14745 29491 58982
loop(\(x,i).(2x + (((~1 + i) * i) div 2)),x,1)
A116702: 1 2 5 13 32 74 163 347 722 1480 3005 6065 12196 24470 49031 98167
loop(\(x,i).(2x + (((x div 2) + i) mod 2)),x,1)
A265381: 1 3 7 14 29 59 119 238 477 955 1911 3822 7645 15291 30583 61166
((2x2 + 2x) + loop(\(x,i).2x,x,1))
A131949: 1 6 16 32 56 92 148 240 400 692 1244 2312 4408 8556 16804 33248
(10 + loop(\(x,i).2x,x,1))
A246139: 11 12 14 18 26 42 74 138 266 522 1034 2058 4106 8202 16394 32778
(((~x2 + x) div 2) + loop(\(x,i).2x,x,1))
A014844: 1 2 3 5 10 22 49 107 228 476 979 1993 4030 8114 16293 32663
(5x + loop(\(x,i).2x,x,1))
A297663: 1 7 14 23 36 57 94 163 296 557 1074 2103 4156 8257 16454 32843
((x2 + 3x) + loop(\(x,i).2x,x,1))
A131951: 1 6 14 26 44 72 118 198 344 620 1154 2202 4276 8400 16622 33038
((~x2 + 3x) + loop(\(x,i).2x,x,1))
A231407: 1 4 6
A176777: 1 4 6 8 12 22 46 100 216 458 954 1960 3988 8062 16230 32588
((x mod 2) - loop(\(x,i).(~3x + 2),x,1))
A341463: ~1 2 ~5 14 ~41 122 ~365 1094 ~3281 9842 ~29525 88574 ~265721 797162 ~2391485 7174454
(1 + loop(\(x,i).(x + ((1 + i) * i)),2x,x))
A336288: 1 10 43 116 245 446 735 1128 1641 2290 3091 4060 5213 6566 8135 9936
loop(\(x,i).(2x * ((2 * (2 + i)) + i)),x,1)
A053101: 1 14 280 7280 232960 8852480 389509120 19475456000 1090625536000 67618783232000 4598077259776000 340257717223424000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((i div (1 + (x div 2))) + (x div 2)),x,1)
A321578: 1 1 2 2 3 3 4 4 4 5 5 5 6 6 6 6
loop(\(x,i).((x * (2 + (x mod 2))) - (x div 2)),x,1)
A086813: 1 3 8 12 18 27 68 102 153 383 958 1437 3593 8983 22458 33687
(((x2 + x) div 2) + (if (x mod 2) <= 0 then x else 1))
A266259: 0 2 5 7 14 16 27 29 44 46 65 67 90 92 119 121
((x2 + 2x + 1) * (1 + (if x <= 0 then 2 else x)))
A066023: 3 8 27 64 125 216 343 512 729 1000 1331 1728 2197 2744 3375 4096
((x + 1) + loop(\(x,i).5x,x,2))
A060460: 3 12 53 254 1255 6256 31257 156258 781259 3906260 19531261 97656262 488281263 2441406264 12207031265 61035156266
loop(\(x,i).(x - (((x div 3) - i) div 2)),x,1)
A126794: 1 2 3 4 6 8 10 12 14 17 20 23 26 29 32 35
loop(\(x,i).(2 * ((2x + (x div 2)) * i)),x,1)
A052675: 1 4 40 600 12000 300000 9000000 315000000 12600000000 567000000000 28350000000000 1559250000000000 93555000000000000 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) * loop(\(x,i).(x + (i * i)),(x + 1),0))
A108678: 1 10 42 120 275 546 980 1632 2565 3850 5566 7800 10647 14210 18600 23936
(if (x + ~10) <= 0 then 0 else (x + 1))
A071955: 0 0 0 0 0 0 0 0 0 0 0 12 13 14 15 16
(loop(\(x,i).((x + 1) * (1 - i)),x,0) mod (x + 1))
A226570: 0 0 2 0 2 2 4 0 8 2 10 8 8 4 2 8
((1 - (2 * (x mod 2))) * (if x <= 0 then 0 else (x + 1)))
A131738: 0 ~2 3 ~4 5 ~6 7 ~8 9 ~10 11 ~12 13 ~14 15 ~16
(loop(\(x,i).(x + (2 * (x + i))),x,0) mod (x + 1))
A094918: 0 0 1 0 1 4 1 0 4 4 1 4 1 4 13 0
((1 + loop(\(x,i).x2,2,3)) div (x + 1))
A033402: 82 41 27 20 16 13 11 10 9 8 7 6 6 5 5 5
(loop(\(x,i).(1 - (x * i)),(x + ~1),1) mod (x + 1))
A067462: 0 1 0 1 3 3 5 1 0 3 0 9 9 5 3 9
(loop(\(x,i).(2x2 + 4),2,1) div (x + 1))
A033396: 76 38 25 19 15 12 10 9 8 7 6 6 5 5 5 4
((~1 + loop(\(x,i).2x2,2,2)) mod (x + 1))
A254410: 0 1 1 3 2 1 1 7 1 7 6 7 10 1 7 15
((1 + loop(\(x,i).(x2 + x),2,2)) div (x + 1))
A033363: 43 21 14 10 8 7 6 5 4 4 3 3 3 3 2 2
((~1 + loop(\(x,i).(x2 + 2x),2,2)) div (x + 1))
A033399: 79 39 26 19 15 13 11 9 8 7 7 6 6 5 5 4
(loop(\(x,i).3x,x,3) div (x + 1))
A092763: 3 4 9 20 48 121 312 820 2187 5904 16104 44286 122640 341640 956593 2690420
(loop(\(x,i).3x,x,3) mod (x + 1))
A066601: 0 1 0 1 3 3 3 1 0 9 3 9 3 9 12 1
(if x <= 0 then 1 else ((x2 div 3) mod (x + 1)))
A089598: 1 0 1 3 0 2 5 0 3 7 0 4 9 0 5 11
((x + 1) * (~1 + loop(\(x,i).4x,x,2)))
A224328: 1 14 93 508 2555 12282 57337 262136 1179639 5242870 23068661 100663284 436207603 1879048178 8053063665 34359738352
loop(\(x,i).4x,(2x + 1),(x + 1))
A267796: 4 128 3072 65536 1310720 25165824 469762048 8589934592 154618822656 2748779069440 48378511622144 844424930131968 14636698788954112 252201579132747776 4323455642275676160 4611686018427387903
(loop(\(x,i).(x * (1 + i)),2x,1) div (x + 1))
A110468: 1 3 40 1260 72576 6652800 889574400 163459296000 39520825344000 12164510040883200 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x + (i * i)),(x div 2),1) mod (x + 1))
A133624: 0 1 2 2 1 0 1 7 4 1 1 8 1 8 6 13
((x + 1) * (~1 + loop(\(x,i).3x,x,2)))
A224327: 1 10 51 212 805 2910 10199 34984 118089 393650 1299067 4251516 13817453 44641030 143489055 459165008
(loop(\(x,i).(4x + 1),x,1) mod (x + 1))
A094919: 0 1 0 1 1 3 1 5 0 5 1 9 1 5 6 5
((x + 1) * loop(\(x,i).(1 + (x * (1 + i))),x,1))
A345887: 1 6 30 164 1030 7422 60620 554248 5611770 62353010 754471432 9876716940 139097096918 2097156230470 33704296561140 575219994643472
((x + 1) * loop(\(x,i).(2 * (x + (x div 2))),x,1))
A027261: 1 4 18 72 270 972 3402 11664 39366 131220 433026 1417176 4605822 14880348 47829690 153055008
((x + 1) * (loop(\(x,i).2x,x,1) div (x + 1)))
A131959: 1 2 3 8
A011946: 1 2 3 8 15 30 63 128 252 510 1023 2040
((x + 1) * (loop(\(x,i).(x * i),x,1) mod (x + 1)))
A072230: 0 2 6 8 20 0 42 0 0 0 110 0 156 0 0 0
loop(\(x,i).((x2 + x) div 2),(x + 1),(x + 1))
A099129: 1 6 231 1186570 347357071281165 4611686018427387903 4611686018427387903
((x + 1) * (loop(\(x,i).2x,x,2) div (x + 1)))
A128092: 2 4 6 16 30 60 126 256 504 1020 2046 4092 8190 16380 32760 65536
loop(\(x,i).(2x * (i * i)),(x + 1),(x + 1))
A333772: 2 32 864 36864 2304000 199065600 22759833600 3329438515200 606790169395200 134842259865600000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (2 * i))),(x + 1),(x + 1))
A200142: 3 30 315 3780 51975 810810 14189175 275675400 5892561675 137493105750 3478575575475 94870242967500 2774954606799375 86663966950811250 2878481759437659375 4611686018427387903
(loop(\(x,i).~2x,x,(x + ~1)) mod (x + 1))
A215747: 0 0 1 0 3 4 5 0 1 4 9 4 11 4 7 0
(loop(\(x,i).5x,x,1) mod (x + 1))
A062176: 0 1 1 1 0 5 1 5 7 5 1 5 1 5 10 13
((x + 1) * (if (x + ~2) <= 0 then 2 else (x2 + ~1)))
A100838: 2 4 6 32
((x + 1) * (if (~2 + (x div 3)) <= 0 then 1 else 2))
A110803-A109795: 1 2 3 4 5 6 7 8 9 20 22 24 26 28 30 32
loop(\(x,i).(8x + ~1),2,(x + 1))
A044242: 55 119 183 247 311 375 439 503 567 631 695 759 823 887 951 1015
((x + 1) * (if (~4 + (x div 2)) <= 0 then 1 else 2))
A132271: 1 2 3 4 5 6 7 8 9 10 22 24 26 28 30 32
loop(\(x,i).12x,2,(x + 1))
A134341: 144 288 432 576 720 864 1008 1152 1296 1440 1584 1728 1872 2016 2160 2304
((2 + loop(\(x,i).x2,2,3)) div (x + 1))
A033403: 83 41 27 20 16 13 11 10 9 8 7 6 6 5 5 5
((x + 1) * (loop(\(x,i).2x,x,3) div 2))
A128543: 1 6 18 48 120 288 672 1536 3456 7680 16896 36864 79872 172032 368640 786432
loop(\(x,i).(x - ((x div 2) div (1 + i))),2,(x + 1))
A324477: 1 2 3 3 4 5 5 5 6 7 8 8 9 10 10 10
(loop(\(x,i).(2x2 + ~1),2,2) div (x + 1))
A033417: 97 48 32 24 19 16 13 12 10 9 8 8 7 6 6 6
(loop(\(x,i).(x2 + x + 1),2,2) div (x + 1))
A033377: 57 28 19 14 11 9 8 7 6 5 5 4 4 4 3 3
((x + 1) * loop(\(x,i).(x2 + 2x + 1),2,2))
A166731-A044332: 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600
(loop(\(x,i).(x2 + 2x + 1),2,2) div (x + 1))
A033420: 100 50 33 25 20 16 14 12 11 10 9 8 7 7 6 6
(loop(\(x,i).(x2 + 2x + 1),2,2) mod (x + 1))
A090976: 0 0 1 0 0 4 2 4 1 0 1 4 9 2 10 4
(loop(\(x,i).((x2 + x) * i),2,2) div (x + 1))
A033404: 84 42 28 21 16 14 12 10 9 8 7 7 6 6 5 5
(loop(\(x,i).(2x2 + ~2),2,2) div (x + 1))
A033390: 70 35 23 17 14 11 10 8 7 7 6 5 5 5 4 4
(loop(\(x,i).(1 + (x * i)),4,2) div (x + 1))
A033409: 89 44 29 22 17 14 12 11 9 8 8 7 6 6 5 5
loop(\(x,i).(2 * i),(x + ~8),(x + 1))
A110805: 1 2 3 4 5 6 7 8 9 2 4 6 8 10 12 14
(loop(\(x,i).(x2 + x + 2),2,2) div (x + 1))
A033394: 74 37 24 18 14 12 10 9 8 7 6 6 5 5 4 4
((2x + 2) * (2 + (if (x + ~1) <= 0 then x else 2)))
A273315: 4 12 24 32 40 48 56 64 72 80 88 96 104 112 120 128
((~2 + loop(\(x,i).(x2 + 2x),2,2)) div (x + 1))
A033398: 78 39 26 19 15 13 11 9 8 7 7 6 6 5 5 4
(loop(\(x,i).((x2 + 2) + i),2,2) div (x + 1))
A033373: 53 26 17 13 10 8 7 6 5 5 4 4 4 3 3 3
(loop(\(x,i).x2,4,4) mod (x + 1))
A245971: 0 0 1 0 1 4 4 0 4 6 4 4 9 4 1 0
loop(\(x,i).2x3,4,(x + 1))
A139573: 1099511627776 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).4x,x,4) div (x + 1))
A129794: 4 8 21 64 204 682 2340 8192 29127 104857 381300 1398101 5162220 19173961 71582788 268435456
(loop(\(x,i).4x,x,4) mod (x + 1))
A066602: 0 0 1 0 4 4 4 0 1 6 4 4 4 2 4 0
(loop(\(x,i).(x * ((x + 1) + i)),2,2) div (x + 1))
A033408: 88 44 29 22 17 14 12 11 9 8 8 7 6 6 5 5
(if (x mod 2) <= 0 then 1 else (4x2 + 4x))
A271060: 1 8 1 48 1 120 1 224 1 360 1 528 1 728 1 960
(loop(\(x,i).((x2 + x) + i),2,2) div (x + 1))
A033378: 58 29 19 14 11 9 8 7 6 5 5 4 4 4 3 3
loop(\(x,i).(~x + (2 * (x div 3))),2,(x + 1))
A194513: ~1 0 ~1 0 1 0 1 0 1 0 1 0 1 2 1 2
(1 - ((if x <= 0 then 1 else (~2x + 4)) div (x + 1)))
A343607: 0 0 1 2 2 2 3 3 3 3 3 3 3 3 3 3
(loop(\(x,i).(3x + 2),x,2) div (x + 1))
A225585: 2 4 8 20 48 121 312 820 2186 5904 16104 44286 122640 341640 956593 2690420
(((x + loop(\(x,i).2x,x,2)) div 2) div (x + 1))
A054650: 1 1 1 2 3 5 9 16 28 51 93 171 315 585 1092 2048
loop(\(x,i).(x * ((~x + 2) + (2 * i))),2,(x + 1))
A157371: 9 8 9 0 ~55 ~216 ~567 ~1216 ~2295 ~3960 ~6391 ~9792 ~14391 ~20440 ~28215 ~38016
((loop(\(x,i).(x * i),x,1) div (x + 2)) div (x + 1))
A143357: 0 0 0 0 0 2 12 70 448 3298 27490 255876 2631876 29652480 363242880 4807626352
loop(\(x,i).(x2 div 2),2,(x2 + 3x + 2))
A202107: 2 162 2592 20000 101250 388962 1229312 3359232 8201250 18301250 37949472 74030112 137149922 243101250 414720000 684204032
loop(\(x,i).3x,x,(x2 + 3x + 2))
A006043: 2 18 108 540 2430 10206 40824 157464 590490 2165130 7794468 27634932 96722262 334807830 1147912560 3902902704
loop(\(x,i).(x * (2 + i)),x,(x2 + 3x + 2))
A001804: 2 18 144 1200 10800 105840 1128960 13063680 163296000 2195424000 31614105600 485707622400 7933224499200 137305808640000 2510734786560000 48373490221056000
loop(\(x,i).(x * (4 + i)),2x,(x + 1))
A091032: 1 60 5040 604800 99792000 21794572800 6102480384000 2134124568576000 912338253066240000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).2x,x,2) + (x div 2)) div (x + 1))
A065482: 2 2 3 4 6 11 18 32 57 102 186 341 630 1170 2185 4096
loop(\(x,i).(x * (x + (2 * (2 + i)))),2,(x + 1))
A190577: 105 384 945 1920 3465 5760 9009 13440 19305 26880 36465 48384 62985 80640 101745 126720
(loop(\(x,i).(x2 + 2x),3,x) div (x + 1))
A258808: 0 127 2186 16383 78124 279935 823542 2097151 4782968 9999999 19487170 35831807 62748516 105413503 170859374 268435455
((2x + 1) - (2 div (if x <= 0 then 3 else x)))
A267873: 1 1 4 7 9 11 13 15 17 19 21 23 25 27 29 31
((x + 1) * loop(\(x,i).((x + 1) * (x + i)),2,x))
A120573: 6 60 330 1224 3510 8436 17850 34320 61254 103020 165066 254040 377910 546084 769530 1060896
loop(\(x,i).(8x * i),x,(x + 1))
A034976: 1 16 384 12288 491520 23592960 1321205760 84557168640 6088116142080 487049291366400 42860337640243200 4114592413463347200 4611686018427387903 4611686018427387903
((x + loop(\(x,i).2x,x,4)) div (x + 1))
A053639: 4 4 6 8 13 22 37 64 114 205 373 683 1261 2341 4370 8192
((x + 1) + loop(\(x,i).((x2 + x) div 2),2,x))
A004255: 1 3 9 25 60 126 238 414 675 1045 1551 2223 3094 4200 5580 7276
loop(\(x,i).10x,x,(x + 1))
A053541: 1 20 300 4000 50000 600000 7000000 80000000 900000000 10000000000 110000000000 1200000000000 13000000000000 140000000000000 1500000000000000 16000000000000000
loop(\(x,i).(2x * (1 + (2 * i))),x,(x + 1))
A001814: 1 12 180 3360 75600 1995840 60540480 2075673600 79394515200 3352212864000 154872234316800 7771770303897600 420970891461120000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x * (~1 + (2 * i))),x,(x + 1))
A002690: 1 4 36 480 8400 181440 4656960 138378240 4670265600 176432256000 7374868300800 337903056691200 16838835658444800 906706535454720000 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(x3 + 3x2 + 2x))
A099764: 0 36 576 3600 14400 44100 112896 254016 518400 980100 1742400 2944656 4769856 7452900 11289600 16646400
loop(\(x,i).(2x + (2 div (1 + i))),x,(x + 1))
A052951: 1 5 14 36 88 208 480 1088 2432 5376 11776 25600 55296 118784 253952 540672
((x + 1) * loop(\(x,i).3x,2x,x))
A116176: 0 18 486 8748 131220 1771470 22320522 267846264 3099363912 34867844010 383546284110 4142299868388 44059007691036 462619580755878 4804126415541810 49413871702715760
(x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))
A135481: 0 1 0 3 0 1 0 7 0 1 0 3 0 1 0 15
loop(\(x,i).3x,(x + (x mod 2)),(x + 1))
A154920: 1 18 27 324 405 4374 5103 52488 59049 590490 649539 6377292 6908733 66961566 71744535 688747536
loop(\(x,i).7x,x,(x + 1))
A027473: 1 14 147 1372 12005 100842 823543 6588344 51883209 403536070 3107227739 23727920916 179936733613 1356446145698 10173346092735 75960984159088
loop(\(x,i).(x * (1 + (2 * (1 + i)))),x,(x + 1))
A000457: 1 10 105 1260 17325 270270 4729725 91891800 1964187225 45831035250 1159525191825 31623414322500 924984868933125 28887988983603750 959493919812553125 4611686018427387903
loop(\(x,i).(x * (5 + i)),x,(x + 1))
A062199: 1 12 126 1344 15120 181440 2328480 31933440 467026560 7264857600 119870150400 2092278988800 38532804710400 746943599001600 15205637551104000 324386934423552000
loop(\(x,i).(x * (1 + (2 * (i div 2)))),x,(x + 1))
A111601: 1 2 9 36 225 1350 11025 88200 893025 8930250 108056025 1296672300 18261468225 255660555150 4108830350625 65741285610000
((x + 1) * loop(\(x,i).6x,x,x))
A116164: 0 12 216 2592 25920 233280 1959552 15676416 120932352 906992640 6651279360 47889211392 339578044416 2377046310912 16456474460160 112844396298240
loop(\(x,i).(x * (3 - (i mod 2))),x,(x + 1))
A027271: 1 4 18 48 180 432 1512 3456 11664 25920 85536 186624 606528 1306368 4199040 8957952
loop(\(x,i).(x * (1 + ((~1 + i) * i))),x,(x + 1))
A262011: 1 2 9 84 1365 34398 1244061 61136712 3920391657 317987323290 31830531061329 3854387943062748 555353062796290941 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) * loop(\(x,i).8x,x,x))
A116166: 0 16 384 6144 81920 983040 11010048 117440512 1207959552 12079595520 118111600640 1133871366144 10720238370816 100055558127616 923589767331840 8444249301319680
loop(\(x,i).(x * (6 + i)),x,(x + 1))
A062148: 1 14 168 2016 25200 332640 4656960 69189120 1089728640 18162144000 319653734400 5928123801600 115598414131200 2365321396838400 50685458503680000 1135354270482432000
((x + 1) * loop(\(x,i).5x,x,x))
A116156: 0 10 150 1500 12500 93750 656250 4375000 28125000 175781250 1074218750 6445312500 38085937500 222167968750 1281738281250 7324218750000
(if (x mod 3) <= 0 then (x div 3) else (x + ~1))
A260316: 0 0 1 1 3 4 2 6 7 3 9 10 4 12 13 5
(x mod (if (~1 + (x mod 3)) <= 0 then 2 else (x + ~1)))
A285515: 0 1 0 1 0 1 0 1 1 1 0 1 0 1 1 1
loop(\(x,i).((x2 + ~x) div (1 + i)),2,(x + ~1))
A034827: 0 0 0 0 2 10 30 70 140 252 420 660 990 1430 2002 2730
loop(\(x,i).(x - (2 * (x div 3))),2,(x + ~1))
A076622: 1 0 1 2 1 2 1 2 1 2 1 2 3 2 3 2
((2x + ~2) * loop(\(x,i).(x * i),(x + ~1),x))
A052609: 0 0 4 24 144 960 7200 60480 564480 5806080 65318400 798336000 10538035200 149448499200 2266635571200 36614882304000
loop(\(x,i).(2x + 4),x,(2x2 + ~2x))
A196514: 0 4 28 124 444 1404 4092 11260 29692 75772 188412 458748 1097724 2588668 6029308 13893628
((~x + 1) + loop(\(x,i).(2x + i),(x + ~1),x))
A066368: 1 1 4 14 40 102 244 562 1264 2798 6124 13290 28648 61414 131044 278498
((x + ~1) + (if (x + ~2) <= 0 then 2 else (x2 + 2x)))
A029876: 1 2 3 17 27
((x + ~1) * loop(\(x,i).4x,(x + ~2),x))
A052780: 0 0 2 24 192 1280 7680 43008 229376 1179648 5898240 28835840 138412032 654311424 3053453312 14092861440
((x2 + ~x) * loop(\(x,i).x2,2,(x + ~2)))
A182788: 0 0 0 6 192 1620 7680 26250 72576 172872 368640 721710 1320000 2283996 3773952 5997810
((x + ~1) * loop(\(x,i).3x,2x,x))
A128803: 0 0 162 4374 78732 1180980 15943230 200884698 2410616376 27894275208 313810596090 3451916556990 37280698815492 396531069219324 4163576226802902 43237137739876290
((x + ~1) * loop(\(x,i).6x,x,x))
A128800: 0 0 72 1296 15552 155520 1399680 11757312 94058496 725594112 5441955840 39907676160 287335268352 2037468266496 14262277865472 98738846760960
((x + ~1) * loop(\(x,i).8x,x,x))
A128802: 0 0 128 3072 49152 655360 7864320 88080384 939524096 9663676416 96636764160 944892805120 9070970929152 85761906966528 800444465020928 7388718138654720
((x + ~1) * loop(\(x,i).5x,x,x))
A128799: 0 0 50 750 7500 62500 468750 3281250 21875000 140625000 878906250 5371093750 32226562500 190429687500 1110839843750 6408691406250
((~x + 1) + loop(\(x,i).(x3 + 2x),x,x))
A262500: 1 3 1751
((x + ~1) + (if (x mod 2) <= 0 then 2 else x3))
A096621: 1 1 3 29
loop(\(x,i).13x,x,1)
A001022: 1 13 169 2197 28561 371293 4826809 62748517 815730721 10604499373 137858491849 1792160394037 23298085122481 302875106592253 3937376385699289 51185893014090757
loop(\(x,i).11x,x,1)
A001020: 1 11 121 1331 14641 161051 1771561 19487171 214358881 2357947691 25937424601 285311670611 3138428376721 34522712143931 379749833583241 4177248169415651
loop(\(x,i).(x * (1 + (3 * (2 + i)))),x,1)
A051607: 1 10 130 2080 39520 869440 21736000 608608000 18866848000 641472832000 23734494784000 949379791360000 40823331028480000 1877873227310080000 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + (3 * (2 + i)))),x,1)
A051605: 1 8 88 1232 20944 418880 9634240 250490240 7264216960 232454942720 8135922995200 309165073817600 12675768026521600 557733793166950400 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + (6 * i))),x,1)
A008543: 1 5 55 935 21505 623645 21827575 894930575 42061737025 2229272062325 131527051677175 8549258359016375 606997343490162625 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + i - (x mod 3))),x,1)
A247007-A102736: 1 1 2 4 16 80 400 2800 22400 179200 1792000 19712000 216832000 2818816000 39463424000 552487936000
loop(\(x,i).(x * (1 + (3 * (i * i)))),x,1)
A277353: 1 4 52 1456 71344 5422144 591013696 87470027008 16881715212544 4119138511860736 1239860692070081536 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (4 * (1 + i)))),x,1)
A051617: 1 9 117 1989 41769 1044225 30282525 999323325 36974963025 1515973484025 68218806781125 3342721532275125 177164241210581625 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + (4 * (1 + i)))),x,1)
A034176: 1 7 77 1155 21945 504735 13627845 422463195 14786211825 576662261175 24796477230525 1165434429834675 59437155921568425 3269043575686263375 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (2 * (i * (1 + i))))),x,1)
A277347: 1 5 65 1625 66625 4064125 345450625 39035920625 5660208490625 1024497736803125 226413999833490625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (2 * (3 + i)))),x,1)
A051581: 1 9 99 1287 19305 328185 6235515 130945815 3011753745 75293843625 2032933777875 58955079558375 1827607466309625 60311046388217625 2110886623587616875 4611686018427387903
loop(\(x,i).(x * (1 + (2 * (1 + (i mod 2))))),x,1)
A101553: 1 5 15 75 225 1125 3375 16875 50625 253125 759375 3796875 11390625 56953125 170859375 854296875
loop(\(x,i).(2x3 + 3x),x,1)
A238799: 1 5 265 37220045 4611686018427387903 4611686018427387903
loop(\(x,i).17x,x,1)
A001026: 1 17 289 4913 83521 1419857 24137569 410338673 6975757441 118587876497 2015993900449 34271896307633 582622237229761 9904578032905937 168377826559400929 2862423051509815793
loop(\(x,i).(x + (x mod 9)),x,1)
A222011: 1 2 4 8
A007612: 1 2 4 8 16 23 28 29 31 35 43 50 55 56 58 62
loop(\(x,i).(x * (7 + i)),x,1)
A049388: 1 8 72 720 7920 95040 1235520 17297280 259459200 4151347200 70572902400 1270312243200 24135932620800 482718652416000 10137091700736000 223016017416192000
loop(\(x,i).(x * (1 + (2 * (4 + i)))),x,1)
A051583: 1 11 143 2145 36465 692835 14549535 334639305 8365982625 225881530875 6550564395375 203067496256625 6701227376468625 234542958176401875 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (4 * (2 + i)))),x,1)
A051621: 1 13 221 4641 116025 3364725 111035925 4108329225 168441498225 7579867420125 371413503586125 19684915690064625 1122040194333683625 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + (4 * (2 + i)))),x,1)
A051619: 1 11 165 3135 72105 1946835 60351885 2112315975 82380323025 3542353890075 166490632833525 8491022274509775 467006225098037625 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + (8 * i))),x,1)
A049210: 1 7 105 2415 74865 2919735 137227545 7547514975 475493443425 33760034483175 2667042724170825 232032717002861775 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x div (1 + (x mod 4))),x,x))
A140210: 1 1 1 1 5 1 1 1 9 5 1 1 13 1 5 1
loop(\(x,i).(x * (1 + (4 * (i * i)))),x,1)
A277354: 1 5 85 3145 204425 20646925 2993804125 589779412625 151573309044625 49261325439503125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + (4 * (i * i)))),x,1)
A079484: 1 3 45 1575 99225 9823275 1404728325 273922023375 69850115960625 22561587455281875 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).12x,x,x))
A064750: 1 13 289 5185 82945 1244161 17915905 250822657 3439853569 46438023169 619173642241 8173092077569 106993205379073 1390911669927937 17974858503684097 231105323618795521
loop(\(x,i).(x * (2x div (1 + (x div 2)))),x,1)
A222011: 1 2 4 8
A026097: 1 2 4 8 24 72 216 648 1944 5832 17496 52488 157464 472392 1417176 4251528
loop(\(x,i).(7x + 8),x,1)
A233326: 1 15 113 799 5601 39215 274513 1921599 13451201 94158415 659108913 4613762399 32296336801 226074357615 1582520503313 11077643523199
(1 + (x * loop(\(x,i).(2x + ~1),(x + ~1),x)))
A048504: 1 2 7 28 101 326 967 2696 7177 18442 46091 112652 270349 638990 1490959 3440656
(1 + loop(\(x,i).(x2 * i),(x2 + ~x),x))
A109336: 1 2 33 4611686018427387903
(1 + (x * (if (x + ~2) <= 0 then (x2 + ~1) else x)))
A098748: 1 1 7 10 17 26 37 50 65 82 101 122 145 170 197 226
loop(\(x,i).(x * (~1 + (5 * i))),x,1)
A008546: 1 4 36 504 9576 229824 6664896 226606464 8837652096 388856692224 19053977918976 1028914807624704 60705973649857536 3885182313590882304 4611686018427387903 4611686018427387903
loop(\(x,i).(x + ((1 + (i div 2)) * (1 + i))),x,1)
A049778: 1 3 9 17 32 50 78 110 155 205 271 343 434 532 652 780
loop(\(x,i).(x * (9 + i)),x,1)
A049398: 1 10 110 1320 17160 240240 3603600 57657600 980179200 17643225600 335221286400 6704425728000 140792940288000 3097444686336000 71241227785728000 1709789466857472000
loop(\(x,i).(x * (8 div (1 + i))),x,1)
A045534: 1 4 8 16 16 16 16 16 0 0 0 0 0 0 0 0
loop(\(x,i).(x * (1 + (i * i * i * i))),x,1)
A255434: 1 2 34 2788 716516 448539016 581755103752 1397375759212304 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (x mod 10)),x,1)
A222011: 1 2 4 8
A102039: 1 2 4 8 16 22 24 28 36 42 44 48 56 62 64 68
loop(\(x,i).(x * (2 + (3 * (2 + i)))),x,1)
A051608: 1 11 154 2618 52360 1204280 31311280 908027120 29056867840 1016990374400 38645634227200 1584471003315200 69716724145868800 3276686034855833600 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (2 + (3 * (i mod 2)))),x,1)
A268100: 1 5 10 50 100 500 1000 5000 10000 50000 100000 500000 1000000 5000000 10000000 50000000
loop(\(x,i).(x * ((2 * i) - ((1 + i) mod 2))),x,1)
A177373: 1 2 6 36 252 2520 27720 388080 5821200 104781600 1990850400 43798708800 1007370302400 26191627862400 707173952284800 21215218568544000
loop(\(x,i).(5x + 16),x,1)
A164785: 1 21 121 621 3121 15621 78121 390621 1953121 9765621 48828121 244140621 1220703121 6103515621 30517578121 152587890621
loop(\(x,i).(~9x + 8),x,1)
A083294: 1 ~1 17 ~145 1313 ~11809 106289 ~956593 8609345 ~77484097 697356881 ~6276211921 56485907297 ~508373165665 4575358490993 ~41178226418929
(1 + (x2 * loop(\(x,i).(x2 + 2),2,2)))
A158593: 1 39 153 343 609 951 1369 1863 2433 3079 3801 4599 5473 6423 7449 8551
loop(\(x,i).(x * (i - (4 * (1 - i)))),x,1)
A008548: 1 1 6 66 1056 22176 576576 17873856 643458816 26381811456 1213563326976 61891729675776 3465936861843456 211422148572450816 4611686018427387903 4611686018427387903
(1 + (x2 * loop(\(x,i).(x2 + x),2,2)))
A158604: 1 43 169 379 673 1051 1513 2059 2689 3403 4201 5083 6049 7099 8233 9451
(1 + (x2 * loop(\(x,i).(x2 + 2x),2,2)))
A158776: 1 81 321 721 1281 2001 2881 3921 5121 6481 8001 9681 11521 13521 15681 18001
loop(\(x,i).(x * (2 + (4 mod (x + 2)))),x,1)
A081341: 1 3 18 108 648 3888 23328 139968 839808 5038848 30233088 181398528 1088391168 6530347008 39182082048 235092492288
loop(\(x,i).(x * (i - (2 * (1 - (2 * i))))),x,1)
A047056: 1 3 24 312 5616 129168 3616704 119351232 4535346816 195019913088 9360955828224 496130658895872 28775578215960576 1812861427605516288 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).10x,x,x))
A064748: 1 11 201 3001 40001 500001 6000001 70000001 800000001 9000000001 100000000001 1100000000001 12000000000001 130000000000001 1400000000000001 15000000000000001
(1 + (x * (x + (if (x + ~2) <= 0 then 1 else 2x))))
A281701: 1 3 7 28
loop(\(x,i).(x * (2 + (5 * i))),x,1)
A034323: 1 7 84 1428 31416 848232 27143424 1004306688 42180880896 1982501402112 103090072909824 5876134155859968 364320317663318016 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (((3 + i) * i) div 2)),x,1)
A067550: 1 2 10 90 1260 25200 680400 23814000 1047816000 56582064000 3677834160000 283193230320000 25487390728800000 2650688635795200000 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (2 * ((1 + (2 * i)) * i))),x,1)
A098931: 1 7 27 69 141 251 407 617 889 1231 1651 2157 2757 3459 4271 5201
loop(\(x,i).(x * (10 + i)),x,1)
A051431: 1 11 132 1716 24024 360360 5765760 98017920 1764322560 33522128640 670442572800 14079294028800 309744468633600 7124122778572800 170978946685747200 4274473667143680000
loop(\(x,i).(x + ((2 + (i div 2)) * (i div 2))),x,1)
A109622: 1 1 4 7 15 23 38 53 77 101 136 171 219 267 330 393
loop(\(x,i).12x,x2,1)
A076807: 1 12 20736 5159780352 184884258895036416 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).10x,x2,1)
A076782: 1 10 10000 1000000000 10000000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * ((x + 1) - i)),2,x2))
A060893: 1 1 241 6481 65281 390001 1678321 5762401 16773121 43040161 99990001 214344241 429960961 815702161 1475750641 2562840001
loop(\(x,i).7x,x2,1)
A060759: 1 7 2401 40353607 33232930569601 4611686018427387903 4611686018427387903 4611686018427387903
(2 - loop(\(x,i).(~x2 + (x div 2)),x2,1))
A059232: 1 3 30 4611686018427387903
(1 + (x2 * loop(\(x,i).3x,x,x)))
A168299: 1 4 73 730 5185 30376 157465 750142 3359233 14348908 59049001 235782658 918330049 3502727632 13124466937 48427561126
(1 + loop(\(x,i).7x,x,x))
A050919: 1 8 99 1030 9605 84036 705895 5764802 46118409 363182464 2824752491 21750594174 166095446413 1259557135292 9495123019887 71213422649146
(1 + (if (x + ~2) <= 0 then (x + 1) else x3))
A100604: 2 3 4 28
loop(\(x,i).(x5 * i),x,1)
A164335: 1 1 2 96 32614907904 4611686018427387903
loop(\(x,i).(x * (x + ((3 + i) * i))),x,1)
A051481: 1 5 75 6975 48845925 2385926342942625 4611686018427387903 4611686018427387903
loop(\(x,i).(7x * i),x,1)
A051188: 1 7 98 2058 57624 2016840 84707280 4150656720 232436776320 14643516908160 1025046183571200 78928556134982400 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((1 + (2 * (1 + i))) * i)),x,1)
A302910: 1 5 70 1890 83160 5405400 486486000 57891834000 8799558768000 1663116607152000 382516819644960000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((5 + i) * i)),x,1)
A010794: 1 6 84 2016 72576 3628800 239500800 20118067200 2092278988800 263627152588800 39544072888320000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((~1 + (2 * (i mod 2))) * i)),x,1)
A165233: 1 1 ~2 ~6 24 120 ~720 ~5040 40320 362880 ~3628800 ~39916800 479001600 6227020800 ~87178291200 ~1307674368000
loop(\(x,i).(x * ((4 * (1 + i)) + i)),x,1)
A034301: 1 9 126 2394 57456 1666224 56651616 2209413024 97214173056 4763494479744 257228701906176 15176493412464384 971295578397720576 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((6 + i) * i)),x,1)
A010795: 1 7 112 3024 120960 6652800 479001600 43589145600 4881984307200 659067881472000 105450861035520000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((4 * (2 + i)) + i)),x,1)
A051689: 1 13 234 5382 150696 4972968 188972784 8125829712 390039826176 20672110787328 1198982425665024 75535892816896512 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((~2 + (3 * i)) * i)),x,1)
A084941: 1 1 8 168 6720 436800 41932800 5577062400 981562982400 220851671040000 61838467891200000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + ((2 + ((~2 + i) * i)) * i)),x,1)
A228394: 1 2 6 21 61 146 302 561 961 1546 2366 3477 4941 6826 9206 12161
(((~x2 + x) div 2) + loop(\(x,i).(x * i),x,1))
A114311: 1 1 1 3 18 110 705 5019 40292 362844 3628755 39916745 479001534 6227020722 87178291109 1307674367895
loop(\(x,i).(x * (((2 * (2 + i)) + i) * i)),x,1)
A302912: 1 7 140 5460 349440 33196800 4381977600 766846080000 171773521920000 47924812615680000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(0 - loop(\(x,i).(2x - ((i mod 2) * i)),x,1))
A106157: ~1 ~1 ~2 ~1 ~2 1 2 11 22 53 106 223 446 905 1810 3635
((x - (if (x + ~6) <= 0 then 1 else 0)) mod 2)
A285592-A276793: 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1
(2x - (if (x mod 5) <= 0 then 0 else 2))
A187333: 0 0 2 4 6 10 10 12 14 16 20 20 22 24 26 30
(2 + (x mod (x - (if (x mod 4) <= 0 then 2 else 0))))
A045818: 2 2 2 2 2 2 2 2 4 2 2 2 4 2 2 2
((x2 + ~x) + (if (x mod 4) <= 0 then 0 else 2))
A330022: 0 2 4 8 12 22 32
(2 + (if (4 mod (x + 2)) <= 0 then (x + 2) else 0))
A236213: 4 2 6 2 2 2 2 2 2 2 2 2 2 2 2 2
(x - (if (~2 + (x div 4)) <= 0 then 1 else ~2))
A108155: ~1 0 1 2 3 4 5 6 7 8 9 10 14 15 16 17
(x mod (if (~1 + (x mod 3)) <= 0 then 2 else ~2))
A131734: 0 1 0 1 0 ~1 0 1 0 1 0 ~1 0 1 0 1
(x mod (if ((x div 4) mod 2) <= 0 then 2 else ~2))
A188510: 0 1 0 1 0 ~1 0 ~1 0 1 0 1 0 ~1 0 ~1
(2 - (if x <= 0 then 1 else ((x div 4) div ~2)))
A130255-A082527: 1 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4
(if x <= 0 then 1 else ((x mod 2) - ((x div 2) div ~2)))
A033922: 1 1 1 2 1 2 2 3 2 3 3 4 3 4 4 5
((if (x + ~2) <= 0 then 1 else x) - ((x div 2) div ~2))
A064318: 1 1 2 4 5 6 8 9 10 11 13 14 15 16 18 19
loop(\(x,i).(x * i),x,(x - (x2 div ~2)))
A152661: 0 2 8 48 288 2160 17280 161280 1612800 18144000 217728000 2874009600 40236134400 610248038400 9763968614400 167382319104000
(2 - (loop(\(x,i).((x + ~2) + (x div 2)),x,0) div 2))
A112088: 2 3 5 7 11 16 24 36 54 81 122 183 274 411 617 925
(6x2 - (if x <= 0 then 0 else 2))
A163433: 0 4 22 52 94 148 214 292 382 484 598 724 862 1012 1174 1348
((x2 + x) + (if x <= 0 then 0 else 2) - (x mod 2))
A335048: 0 3 8 13 22 31 44 57 74 91 112 133 158 183 212 241
(loop(\(x,i).(x + ((x + i) * (1 + i))),x,0) div 2)
A080047: 0 1 7 41 256 1807 14477 130321 1303246 14335751 172029067 2236377937 31309291196 469639368031 7514229888601 127741908106337
(2 * ((((x + 1) div 2) div 2) + (if x <= 0 then 0 else 1)))
A177692: 0 2 2 4 4 4 4 6 6 6 6 8 8 8 8 10
(2 * ((2x + 8) - (if x <= 0 then 0 else 1)))
A308607: 16 18 22 26 30 34 38 42 46 50 54 58 62 66 70 74
(2 * (1 + loop(\(x,i).(((~x + 1) + i) * i),x,0)))
A051398: 2 6 6 14 ~6 102 ~514 3726 ~29646 267014 ~2669898 29369166 ~352429654 4581585894 ~64142202066 962133031502
(if (x mod (1 + (4 mod (x + 1)))) <= 0 then 1 else 2)
A043556: 1 1 1 1 2 1 2 2 2 2 1 2 2 2 2 1
(if (x mod (3 - (x div ~2))) <= 0 then 1 else 2)
A174664: 1 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2
(x mod (if (x mod 9) <= 0 then 1 else 2))
A323239: 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1
(if (x mod (1 + ((x + ~1) mod 4))) <= 0 then 1 else 2)
A331284-A327924-A214575-A177991-A120888: 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1
(if (x mod (1 + ((x + 2) mod 4))) <= 0 then 1 else 2)
A233138: 1 2 1 2 2 2 1 2 2 2 1 2 1 2 1 2
(if ((2 + (x div 2)) mod 5) <= 0 then 1 else 2)
A179529: 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2
(x mod (if ((x + 2) mod 5) <= 0 then 1 else 2))
A284751: 0 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1
(if ((x + 1) mod (1 + (x div 4))) <= 0 then 1 else 2)
A277070-A237442-A094840-A035218: 1 1 1 1 2 1 2 1 1 2 2 1 2 2 2 1
(if ((x + ~1) mod (1 + (x div 4))) <= 0 then 1 else 2)
A270641: 1 1 1 1 2 1 2 1 2 2 1 2 2 1 2 2
(if ((x * (x div ~2)) mod 3) <= 0 then 1 else 2)
A317960: 1 2 2 1 2 1 1 2 2 1 2 1 1 2 2 1
(2 * (1 + loop(\(x,i).4x,x,3)))
A140788: 8 26 98 386 1538 6146 24578 98306 393218 1572866 6291458 25165826 100663298 402653186 1610612738 6442450946
(if (~2 + ((x mod 2) + (x div 3))) <= 0 then 1 else 2)
A297776-A043559-A043535: 1 1 1 1 1 1 1 2 1 2 2 2 2 2 2 2
(if ((x + ~4) * (x mod 3)) <= 0 then 1 else 2)
A274353: 1 1 1 1 1 2 1 2 2 1 2 2 1 2 2 1
(if x <= 0 then 1 else (6x2 + 2))
A005897: 1 8 26 56 98 152 218 296 386 488 602 728 866 1016 1178 1352
(if x <= 0 then 1 else (2 * (1 + (x2 div 3))))
A222011: 1 2 4 8
A053799: 1 2 4 8 12 18 26 34 44 56 68 82 98 114 132 152
(2 * loop(\(x,i).(2 + (x div 2)),(~1 + (x div 2)),1))
A071809: 2 2 2 2 4 4 6 6 6 6 6 6 6 6 6 6
(if (9 mod (x + 1)) <= 0 then 1 else 2)
A055027: 1 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2
(if (12 mod (x + 1)) <= 0 then 1 else 2)
A297773-A043532: 1 1 1 1 2 1 2 2 2 2 2 1 2 2 2 2
(if (10 mod (x + 1)) <= 0 then 1 else 2)
A169695: 1 1 2 2 1 2 2 2 2 1 2 2 2 2 2 2
(if (16 mod (x + 1)) <= 0 then 1 else 2)
A043529: 1 1 2 1 2 2 2 1 2 2 2 2 2 2 2 1
(loop(\(x,i).2x,x,(1 + (2 mod (x + 1)))) div 2)
A082505: 0 1 6 12 24 48 96 192 384 768 1536 3072 6144 12288 24576 49152
((1 + loop(\(x,i).x3,2,(x + 1))) div 2)
A191496: 1 256 9842 131072 976563 5038848 20176804 67108864 193710245 500000000 1178973846 2579890176 5302249687 10330523392 19221679688 34359738368
(loop(\(x,i).(x * (2 + (i mod 2))),(x + 1),1) div 2)
A026565: 1 3 9 18 54 108 324 648 1944 3888 11664 23328 69984 139968 419904 839808
((1 + loop(\(x,i).(x2 * i),x2,1)) div 2)
A107739: 1 1 288 4611686018427387903
((x mod (1 + (if (x mod 4) <= 0 then 0 else 2))) div 2)
A182581: 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0
(if (x + ~2) <= 0 then 0 else ((x div ~3) mod 2))
A341613: 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1
(((1 + (x div 2)) div (1 + (if x <= 0 then 0 else 2))) mod 2)
A138711: 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0
(if (~2 + (x mod (1 + (x div 3)))) <= 0 then 1 else 2)
A297780-A043563-A043539: 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2
(2 + (if ((x + 1) mod 5) <= 0 then 2 else 1))
A091799: 3 3 3 3 4 3 3 3 3 4 3 3 3 3 4 3
(if (~2 + (x div (3 + (x mod 2)))) <= 0 then 1 else 2)
A297779-A261913-A261675-A146879-A094876-A080462-A043562-A043538-A036485: 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2 2
(if (x mod 2) <= 0 then 1 else 14)
A002393: 1 14 1
(2 + loop(\(x,i).x2,x,7))
A152580: 9 51 2403 5764803 33232930569603 4611686018427387903
(if (~2 + (2x mod (1 + (x div 2)))) <= 0 then 1 else 2)
A297778-A088601-A047726-A043561-A043537-A030547: 1 1 1 1 1 1 1 1 1 2 1 2 2 2 2 2
(((x + 1) mod (1 + (2 * (if x <= 0 then 0 else 2)))) mod 2)
A212126-A144605: 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1
(((x + ~2) mod (1 + (2 * (if x <= 0 then 0 else 2)))) mod 2)
A037907: 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1
(x div (2 + (if (~4 + (x div 2)) <= 0 then 2 else 1)))
A176044: 0 0 0 0 1 1 1 1 2 2 3 3 4 4 4 5
(if (~2 + (x mod (4 + (x mod 2)))) <= 0 then 1 else 2)
A235748: 1 1 1 2 1 1 1 1 1 2 1 1 1 2 1 1
(if (~2 + (x div (2 * (2 + (x mod 2))))) <= 0 then 1 else 2)
A337144-A288739-A184240-A167967: 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1
(if (~4 + (x div (2 + (x mod 2)))) <= 0 then 1 else 2)
A049099: 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 2
(loop(\(x,i).2x,(x + ~8),1) div 2)
A009714: 0 0 0 0 0 0 0 0 0 1 2 4 8 16 32 64
(if ((x + 2) mod (2 + (x div 4))) <= 0 then 1 else 2)
A076371: 1 2 1 2 1 2 2 1 2 2 1 2 2 1 2 2
(if ((x + ~2) mod (2 + (x mod 4))) <= 0 then 1 else 2)
A161974: 1 2 1 2 1 1 1 1 1 2 1 2 1 2 1 2
(x - (x mod (if (~4 + (x div 2)) <= 0 then 1 else 2)))
A103303: 0 1 2 3 4 5 6 7 8 9
A228722: 0 1 2 3 4 5 6 7 8 9 10 10 12 12 14 14
((x div (if (x mod 4) <= 0 then 4 else 1)) mod 2)
A285383-A259044: 0 1 0 1 1 1 0 1 0 1 0 1 1 1 0 1
(if x <= 0 then 1 else (2 + ((x + 1) div 5)))
A247189: 1 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5
(~10 + loop(\(x,i).2x,x,1))
A246168: ~9 ~8 ~6 ~2 6 22 54 118 246 502 1014 2038 4086 8182 16374 32758
loop(\(x,i).(2x + 1),x,10)
A086225: 10 21 43 87 175 351 703 1407 2815 5631 11263 22527 45055 90111 180223 360447
loop(\(x,i).(x2 + ~2),x,10)
A135927: 10 98 9602 92198402 8500545331353602 4611686018427387903 4611686018427387903
(if ((x * (1 + (x div 2))) mod 4) <= 0 then 1 else 2)
A103587: 1 2 1 2 1 2 1 1 1 2 1 2 1 2 1 1
((1 + (if x <= 0 then 1 else x) - (x div 4)) div 2)
A026405: 1 1 1 2 2 2 3 3 3 4 4 5 5 5 6 6
(2 * (~1 + loop(\(x,i).3x,x,4)))
A171495: 6 22 70 214 646 1942 5830 17494 52486 157462 472390 1417174 4251526 12754582 38263750 114791254
(if x <= 0 then 1 else (8x2 + 2))
A008527: 1 10 34 74 130 202 290 394 514 650 802 970 1154 1354 1570 1802
(if (x mod (2 + (4 mod (x + 2)))) <= 0 then 1 else 2)
A160242: 1 2 1 2 2 2 1 2 2 2 2 2 1 2 2 2
(if ((x2 + ~2) mod (x + 4)) <= 0 then 1 else 2)
A276788: 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2
loop(\(x,i).x2,1,(8x + 2))
A017090: 4 100 324 676 1156 1764 2500 3364 4356 5476 6724 8100 9604 11236 12996 14884
loop(\(x,i).x2,2,(8x + 2))
A017092: 16 10000 104976 456976 1336336 3111696 6250000 11316496 18974736 29986576 45212176 65610000 92236816 126247696 168896016 221533456
((x + 2) - (2 div loop(\(x,i).i,(~2 + (x div 2)),1)))
A084689: 0 1 2 3 4 5 6 7 9
A039271: 0 1 2 3 4 5 6 7 9 10 12 13 14 15 16 17
(loop(\(x,i).2x,x,(3 + (x mod 2))) div 2)
A231407: 1 4 6
A133572: 1 4 6 16 24 64 96 256 384 1024 1536 4096 6144 16384 24576 65536
(2 + loop(\(x,i).4x,(x + 1),3))
A205354: 14 50 194 770 3074 12290 49154 196610 786434 3145730 12582914 50331650 201326594 805306370 3221225474 12884901890
loop(\(x,i).x2,((x2 + ~1) div 3),2)
A079556: 2 2 4 16 4294967296
((((x div 2) - (if x <= 0 then 0 else 2)) div 3) mod 2)
A138712: 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1
((if x <= 0 then 1 else (((x + 1) div 2) div 3)) mod 2)
A138885: 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0
(if x <= 0 then 1 else (2 + (((x + 1) div 2) div 3)))
A168255: 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4
((3 * (2 + (if x <= 0 then 0 else (x + 2)))) div 2)
A063551: 3 7 9 10 12 13 15
(2 * ((2 * (if x <= 0 then 0 else (x + 2))) div 3))
A273308: 0 4 4 6 8 8 10 12 12 14 16 16 18 20 20 22
(2 + (if x <= 0 then 1 else 12x))
A063098: 3 14 26 38 50 62 74 86 98 110 122 134 146 158 170 182
(2 * (if (x + ~2) <= 0 then x else ((x + 2) div 3)))
A018838: 0 2 4 2 4 4 4 6 6 6 8 8 8 10 10 10
loop(\(x,i).x2,1,(6x + 2))
A016934: 4 64 196 400 676 1024 1444 1936 2500 3136 3844 4624 5476 6400 7396 8464
loop(\(x,i).x2,2,(6x + 2))
A016936: 16 4096 38416 160000 456976 1048576 2085136 3748096 6250000 9834496 14776336 21381376 29986576 40960000 54700816 71639296
(2 + loop(\(x,i).3x,2x,3))
A134752: 5 29 245 2189 19685 177149 1594325 14348909 129140165 1162261469 10460353205 94143178829 847288609445 7625597484989 68630377364885 617673396283949
(if (x + ~1) <= 0 then x else (2 + ((x div 2) div 3)))
A064601-A064557: 0 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4
(if (x + ~1) <= 0 then x else (((x div 2) mod 3) div 2))
A071986: 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0
(2 + (if x <= 0 then 1 else (3 * (2 - (x mod 2)))))
A136188: 3 5 8 5 8 5 8 5 8 5 8 5 8 5 8 5
loop(\(x,i).(x2 + ~2),2x,6)
A219165: 6 1154 1773462177794 4611686018427387903
loop(\(x,i).(4x + 1),x,6)
A323824: 6 25 101 405 1621 6485 25941 103765 415061 1660245 6640981 26563925 106255701 425022805 1700091221 6800364885
loop(\(x,i).(2x2 + ~1),x,6)
A242232: 6 71 10081 203253121 82623662392481281 4611686018427387903 4611686018427387903
loop(\(x,i).(3x + 1),x,6)
A238055: 6 19 58 175 526 1579 4738 14215 42646 127939 383818 1151455 3454366 10363099 31089298 93267895
loop(\(x,i).(3x + ~1),x,6)
A199113: 6 17 50 149 446 1337 4010 12029 36086 108257 324770 974309 2922926 8768777 26306330 78918989
loop(\(x,i).(x2 + ~x + ~1),x,6)
A144746: 6 29 811 656909 431528777371 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + (x div 2)),x,6)
A302748: 6 10 16 25 38 58 88 133 200 301 452 679 1019 1529 2294 3442
(2 * loop(\(x,i).(2 * ((x + 1) - i)),x,3))
A295904: 6 12 20 32 52 88 156 288 548 1064 2092 4144 8244 16440 32828 65600
(loop(\(x,i).(2x + (i mod 2)),x,3) div 2)
A052997: 1 3 7 14 29 58 117 234 469 938 1877 3754 7509 15018 30037 60074
(if (~2 + (x div 2)) <= 0 then x else (2x + ~6))
A004272: 0 1 2 3 4 5 6 8 10 12 14 16 18 20 22 24
((if (x mod 4) <= 0 then 1 else (x div 3)) mod 2)
A267776: 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1
((if ((x div 2) mod 2) <= 0 then 1 else (x div 3)) mod 2)
A298941-A295281-A267778: 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1
((x mod (if (x + ~2) <= 0 then 1 else (x div 3))) div 2)
A193095-A036874: 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0
(if x <= 0 then 1 else (2 * (2x - (x div 3))))
A063087: 1 4 8 10 14 18 20 24 28 30 34 38 40 44 48 50
((if (x mod 2) <= 0 then 1 else x) mod (2 + (x mod 3)))
A133721-A124389-A066636-A061680: 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1
loop(\(x,i).(~2x + 1),x,((x mod 3) div 2))
A157241: 0 1 3 3 ~5 ~21 ~21 43 171 171 ~341 ~1365 ~1365 2731 10923 10923
(2 + loop(\(x,i).x3,x2,3))
A187605: 5 29 4611686018427387903 4611686018427387903
(2 * (~1 + loop(\(x,i).((x2 + x) div 2),x,2)))
A159860: 2 4 10 40 460 53590 718052410 128899816953780640 4611686018427387903 4611686018427387903
(if (12 mod (x + 2)) <= 0 then 1 else 2)
A214574: 1 1 1 2 1 2 2 2 2 2 1 2 2 2 2 2
(if ((2 + (x2 div 2)) mod (x + 2)) <= 0 then 1 else 2)
A118916: 1 2 1 2 2 1 2 2 2 2 2 2 2 2 2 2
(loop(\(x,i).2x,(x + ~1),(x + 3)) div 2)
A045623: 1 2 5 12 28 64 144 320 704 1536 3328 7168 15360 32768 69632 147456
(loop(\(x,i).(x * (x - i)),2,(x + 3)) div 2)
A112415: 12 60 180 420 840 1512 2520 3960 5940 8580 12012 16380 21840 28560 36720 46512
((1 mod (if (x mod 3) <= 0 then (x + ~2) else 1)) mod 2)
A214772: 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1
(loop(\(x,i).(2 * ((x + 1) + i)),(x + ~2),1) div 2)
A247188: 0 0 0 3 9 22 49 104 215 438 885 1780 3571 7154 14321 28656
(((x mod 3) div 2) + (if (x + ~2) <= 0 then 1 else 2))
A239141: 1 1 2 2 2 3 2 2 3 2 2 3 2 2 3 2
loop(\(x,i).(4x + 2),(2x + 1),2)
A325911: 10 170 2730 43690 699050 11184810 178956970 2863311530 45812984490 733007751850 11728124029610 187649984473770 3002399751580330 48038396025285290 768614336404564650 4611686018427387903
loop(\(x,i).8x,(2x + 1),2)
A013735: 16 1024 65536 4194304 268435456 17179869184 1099511627776 70368744177664 4503599627370496 288230376151711744 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,3,(4x + 2))
A016832: 256 1679616 100000000 1475789056 11019960576 54875873536 208827064576 656100000000 1785793904896 4347792138496 9682651996416 20047612231936 39062500000000 72301961339136
loop(\(x,i).x3,1,(4x + 2))
A016827: 8 216 1000 2744 5832 10648 17576 27000 39304 54872 74088 97336 125000 157464 195112 238328
loop(\(x,i).x3,2,(4x + 2))
A016833: 512 10077696 1000000000 20661046784 198359290368 1207269217792 5429503678976 19683000000000 60716992766464 165216101262848 406671383849472 922190162669056 1953125000000000 3904305912313344
loop(\(x,i).((x2 + x) - i),(2x + ~1),2)
A176117: 2 5 809
(x - (if (~2 + (x div 2)) <= 0 then (~1 + (x div 2)) else 2))
A079685: 1 2 2 3 3 4 4 5 6
((1 + ((if (x + ~2) <= 0 then 1 else x) * (x div 2))) mod 2)
A188192: 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0
(loop(\(x,i).2x,x,(3 - (x mod 2))) div 2)
A122756: 1 2 6 8 24 32 96 128 384 512 1536 2048 6144 8192 24576 32768
(2 * (~1 + (loop(\(x,i).2x,x,2) + (x mod 2))))
A250554: 2 8 14 32 62 128 254 512 1022 2048 4094 8192 16382 32768 65534 131072
(2 + loop(\(x,i).(1 + (x * ((1 + i) div 2))),x,1))
A215176: 3 4 5 9 17 48 141 559 2231 11148 55733 334389 2006325 14044264 98309837 786478683
(2 * loop(\(x,i).((x + 1) + (2 * (x + i))),x,1))
A003993: 2 12 46 152 474 1444 4358 13104 39346 118076 354270 1062856 3188618 9565908 28697782 86093408
(2 * loop(\(x,i).((x + 1) + (2 * (i * i))),x,1))
A100504: 2 8 26 64 130 232 378 576 834 1160 1562 2048 2626 3304 4090 4992
((1 + (8 div (if x <= 0 then 1 else x))) mod 2)
A330985: 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1
((1 + (8 mod (if x <= 0 then 1 else x))) mod 2)
A071038: 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1
((~1 + ((x + 4) * (if x <= 0 then 1 else x))) div 2)
A172411: 1 2 5 10
A179207: 1 2 5 10 15 22 29 38 47 58 69 82 95 110 125 142
(2 + ((~x + 1) mod loop(\(x,i).(1 + (x * i)),x,1)))
A303150: 2 2 6 16 64
(2 * ((x + 1) + (if (x + ~4) <= 0 then 1 else 2)))
A051756: 4 6 8 10 12 16 18 20
A053226: 4 6 8 10 12 16 18 20 22 24 26 28 30 32 34 36
(loop(\(x,i).(2x + 12),x,1) div 2)
A100206: 0 7 20 46 98 202 410 826 1658 3322 6650 13306 26618 53242 106490 212986
(loop(\(x,i).(x - (x div (~2 + (x mod 2)))),x,1) div 2)
A232801: 0 1 1 3 4 9 13 27 40 81 121 243 364 729 1093 2187
(loop(\(x,i).(2 + ((x2 + i) div 2)),x,1) div 2)
A327230: 0 1 3 14 198
(2 + loop(\(x,i).(2 * (x + (2 * (i mod 2)))),x,1))
A340627: 3 8 14 30 58 118 234 470 938 1878 3754 7510 15018 30038 60074 120150
(1 - (x mod (2 * (x - loop(\(x,i).2x,x,1)))))
A131959: 1 2 3 8
A132730: 1 2 3 8 21 50 111 236 489 998 2019 4064 8157 16346 32727 65492
((1 + (if x <= 0 then 1 else (x3 + 2x))) div 2)
A139629: 1 2 6 17
loop(\(x,i).(x3 + ~x2 + 1),(x + 1),2)
A231830: 5 101 1020101 1061522231810040101 4611686018427387903
((loop(\(x,i).(2 * (~x + i)),x,1) div (x + 1)) mod 2)
A175192: 1 0 1 1 0 1 1 1 0 0 0 1 1 1 1 0
(((x + 1) * loop(\(x,i).x2,2,(x + 1))) div 2)
A191902: 0 16 121 512 1562 3888 8403 16384 29524 50000 80525 124416 185646 268912 379687 524288
(loop(\(x,i).4x,(x + ~1),(x + 1)) div 2)
A292044: 0 1 6 32 160 768 3584 16384 73728 327680 1441792 6291456 27262976 117440512 503316480 2147483648
(((x + 1) * (if x <= 0 then 2 else ((x + 1) div 2))) div 2)
A189889: 1 1 1 4 5 9 10 16 18 25 27 36 39 49 52 64
(loop(\(x,i).(x * (2 + i)),4,(x + 1)) div 2)
A066164: 180 360 540 720 900 1080 1260 1440 1620 1800 1980 2160 2340 2520 2700 2880
(if x <= 0 then 1 else (2 * (2x - (2 mod (x + 1)))))
A003829: 1 4 4 8 12 16
loop(\(x,i).x2,2,((x2 + 3x + 2) div 2))
A059977: 1 81 1296 10000 50625 194481 614656 1679616 4100625 9150625 18974736 37015056 68574961 121550625 207360000 342102016
loop(\(x,i).(x2 * i),(x2 + 3x + 2),2)
A123238: 32 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + ~x),1,(2x + 2))
A069072: 6 60 210 504 990 1716 2730 4080 5814 7980 10626 13800 17550 21924 26970 32736
loop(\(x,i).((x * (x div 2)) div 2),2,(2x + 2))
A212766: 0 4 18 64 150 324 588 1024 1620 2500 3630 5184 7098 9604 12600 16384
((~2x + ~2) + loop(\(x,i).x2,2,(x + 2)))
A269495: 14 77 250 617 1286 2389 4082 6545 9982 14621 20714 28537 38390 50597 65506 83489
(if x <= 0 then 1 else ((2 + (x div 2)) * ((x + 1) div 2)))
A035106: 1 2 3 6 8 12 15 20 24 30 35 42 48 56 63 72
loop(\(x,i).(x * ((i mod 2) + i)),x,((x + 1) div 2))
A122693: 0 2 4 32 128 1152 6912 73728 589824 7372800 73728000 1061683200 12740198400 208089907200 2913258700800 53271016243200
loop(\(x,i).i,(x div 5),((x + 1) mod 2))
A025811: 1 0 1 0 1 1 1 1 1 1 2 2 2 2 2 3
(if (~1 + (x mod 3)) <= 0 then 2 else ((x + 1) mod 2))
A285930: 2 2 1 2 2 0 2 2 1 2 2 0 2 2 1 2
loop(\(x,i).~2x,(x div 2),((x + 1) mod 2))
A077966: 1 0 ~2 0 4 0 ~8 0 16 0 ~32 0 64 0 ~128 0
loop(\(x,i).3x,(x div 2),((x + 1) mod 2))
A254006: 1 0 3 0 9 0 27 0 81 0 243 0 729 0 2187 0
loop(\(x,i).(x3 + 3x),(x + 1),2)
A145188: 14 2786 21624372014 4611686018427387903 4611686018427387903
(((x + 1) * loop(\(x,i).2x,(x + ~1),x)) div 2)
A001788: 0 1 6 24 80 240 672 1792 4608 11520 28160 67584 159744 372736 860160 1966080
(((x + 1) * (~x + loop(\(x,i).2x,x,2))) div 2)
A048470: 1 3 9 26 70 177 427 996 2268 5075 11209 24510 53170 114597 245655 524168
(((x + 1) * loop(\(x,i).x3,2,x)) div 2)
A170783: 0 1 768 39366 655360 5859375 35271936 161414428 603979776 1937102445 5500000000 14147686146 33538572288 74231495611 154957850880 307546875000
(((x + 1) * loop(\(x,i).x2,2,x2)) div 2)
A168675: 0 1 384 13122 163840 1171875 5878656 23059204 75497472 215233605 550000000 1286153286 2794881024 5710115047 11068417920 20503125000
(loop(\(x,i).((x2 + ~x) div 2),2,(x + ~1)) div 2)
A011926: 0 0 0 0 1 7 22 52 105 189 315 495 742 1072 1501 2047
(if x <= 0 then 1 else (2 + ((x + ~1) * (x2 div 2))))
A100605: 1 2 4 10 26
(((x + ~1) * (loop(\(x,i).(x * i),x,x) div 2)) div 2)
A001809: 0 0 1 9 72 600 5400 52920 564480 6531840 81648000 1097712000 15807052800 242853811200 3966612249600 68652904320000
((2 * ((if x <= 0 then 1 else x) mod 2)) + ((x + ~1) div 2))
A267182: 1 2 0 3 1 4 2 5 3 6 4 7 5 8 6 9
(2 + loop(\(x,i).((x * (2 + i)) div 2),x,(x + ~1)))
A096122: 1 2 4 17 62
(~x mod loop(\(x,i).(2x + i),(x + ~1),2))
A088110: 0 1 3 9
A244331: 0 1 3 9 23 53 115 241 495 1005 2027 4073 8167 16357 32739 65505
(13 * (if x <= 0 then 1 else 2))
A040156: 13 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26
(11 * (if x <= 0 then 1 else 2))
A040110: 11 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22
(17 * (if x <= 0 then 1 else 2))
A040272: 17 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34
(14 * (if x <= 0 then 1 else 2))
A040182: 14 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28
(((x2 + 3x + 2) div 2) + (if x <= 0 then 1 else 2))
A272719: 2 5 8 12 17
((((x + 1) * (x div 2)) mod 2) + (if x <= 0 then 1 else 2))
A186181: 1 2 3 2 2 2 3 2 2 2 3 2 2 2 3 2
(((x - ((x div 2) mod 2)) div 2) + (if x <= 0 then 1 else 2))
A092038: 1 2 2 3 4 4 4 5 6 6 6 7 8 8 8 9
(4 * ((2 - (x mod 2)) * (if x <= 0 then 1 else 2)))
A040057: 8 8 16 8 16 8 16 8 16 8 16 8 16 8 16 8
(((x + (x div 2)) div 4) + (if x <= 0 then 1 else 2))
A245473: 1 2 2 3 3 3 4 4 5 5 5 6 6 6 7 7
(((x3 + 2x2) div 2) + (if x <= 0 then 1 else 2))
A188545: 1 3 10
A231116: 1 3 10 24
(((x2 * (x div 2)) div 2) + (if x <= 0 then 1 else 2))
A192335: 1 2 4 6 18
((x mod (2 * (2 - (x mod 2)))) + (if x <= 0 then 1 else 2))
A164358: 1 3 4 3 2 3 4 3 2 3 4 3 2 3 4 3
(((x * (x div 4)) div 2) + (if x <= 0 then 1 else 2))
A096323: 1 2 2 2 4 4 5
((x div 2) - ((~2x + 1) * (if x <= 0 then 1 else 2)))
A063289: ~1 2 7 11 16 20 25 29 34 38 43 47 52 56 61 65
(5x2 + (if x <= 0 then 1 else 2))
A010001: 1 7 22 47 82 127 182 247 322 407 502 607 722 847 982 1127
(2 * loop(\(x,i).(x + (x mod 5)),x,1))
A002081: 2 4 8 16 22 24 28 36 42 44 48 56 62 64 68 76
(loop(\(x,i).(~x + i - ((x div 2) mod 2)),x,1) div 2)
A162350: 0 0 1 0 2 0 2 1 2 2 3 2 4 2 4 3
(loop(\(x,i).(x + ((x + i) * (2 + i))),x,1) div 2)
A079753: 0 3 21 136 967 7757 69841 698446 7682951 92195467 1198541137 16779575996 251693640031 4027098240601 68460670090337 1232292061626202
(loop(\(x,i).(((x + 1) + (x div 2)) * i),x,1) mod 2)
A327166: 1 0 0 1 0 1 0 0 0 1 0 1 0 1 0 0
(2 * (if (~2 + (x div 5)) <= 0 then 0 else 2))
A184955: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
(2 + (if (~6 + (x div 2)) <= 0 then 0 else 2))
A296078-A137325: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4
(x - (2 * (if (~2 + (x div 3)) <= 0 then 0 else 2)))
A245354: 0 1 2 3 4 5 6 7 8 5 6 7 8 9 10 11
(x - (2 * (if (~4 + (x div 2)) <= 0 then 0 else 2)))
A103303: 0 1 2 3 4 5 6 7 8 9
A081597-A028901: 0 1 2 3 4 5 6 7 8 9 6 7 8 9 10 11
(4 + (if (x + ~2) <= 0 then (2 + (x div 2)) else 0))
A070058: 6 6 7 4
(x mod (if (x mod 5) <= 0 then ~2 else 2))
A134452: 0 1 0 1 0 ~1 0 1 0 1 0 1 0 1 0 ~1
((if (x + ~2) <= 0 then 1 else 2) - (x div ~4))
A066063-A062571: 1 2 2 3 3 4 4 4 4 5 5 5 5 6 6 6
(if x <= 0 then 4 else (x - (x div ~4)))
A225001: 4 2 3 4 5 7 8 9 10 12 13 14 15 17 18 19
(((if (x mod 3) <= 0 then 1 else x) div ~2) mod 2)
A140865: 1 1 1 1 0 1 1 0 0 1 1 0 1 1 1 1
((2 div (~2 + (if (x mod 4) <= 0 then x else 0))) mod 2)
A334460-A063050: 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1
((x mod (~2 + (if (x mod 4) <= 0 then x else 0))) div 2)
A305053: 0 ~1 0 ~1 0 ~1 0 ~1 1 ~1 0 ~1 1 ~1 0 ~1
(x div (2 + (if (~2 + (x div 4)) <= 0 then 1 else 2)))
A330558: 0 0 0 1 1 1 2 2 2 3 3 3 3 3 3 3
(2 + (x mod (if (~4 + (x div 2)) <= 0 then 1 else 2)))
A100961: 2 2 2 2 2 2 2 2 2 2 2 3 2 3 2 3
(2 div loop(\(x,i).i,(x + ~10),2))
A178401: 1 1 1 1 1 1 1 1 1 1 1 2 1 0 0 0
(((~x + 2) div (if (~2 + (x div 2)) <= 0 then 1 else 2)) mod 2)
A189219-A189008: 0 1 0 1 0 1 0 1 1 0 0 1 1 0 0 1
(2 + ((x mod loop(\(x,i).i,(~2 + (x div 2)),1)) div 2))
A076925: 2 2 2 2 2 2 2 2 2 2 2 3 2 2 4 2
(2 div loop(\(x,i).i,(~2 + ((x + ~2) div 3)),2))
A295555-A246465-A211226-A172497-A172356-A172353-A157343-A141604-A085684: 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1
((if x <= 0 then 2 else (x mod (2 + (x mod 3)))) div 2)
A186716: 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0
(2 * (2 + (if (x + ~1) <= 0 then (~2x + 4) else 1)))
A071279: 12 8 6 6 6 6 6 6 6 6 6 6 6 6 6 6
loop(\(x,i).x2,1,(8x + 4))
A017114: 16 144 400 784 1296 1936 2704 3600 4624 5776 7056 8464 10000 11664 13456 15376
loop(\(x,i).x2,2,(8x + 4))
A017116: 256 20736 160000 614656 1679616 3748096 7311616 12960000 21381376 33362176 49787136 71639296 100000000 136048896 181063936 236421376
(2 + loop(\(x,i).3x,(2x + 1),2))
A087290: 8 56 488 4376 39368 354296 3188648 28697816 258280328 2324522936 20920706408 188286357656 1694577218888 15251194969976 137260754729768 1235346792567896
(x2 mod loop(\(x,i).(x2 + 2x + 1),2,2))
A002015: 0 1 4 9 16 25 36 49 64 81 0 21 44 69 96 25
((((x div 2) - (if (x + ~2) <= 0 then x else 1)) div 2) mod 2)
A023959: 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1
(2 * loop(\(x,i).(x * (i * (1 + i))),(x + 1),2))
A108214: 8 48 576 11520 345600 14515200 812851200 58525286400 5267275776000 579400335360000 76480844267520000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + x),(2x + 2),2)
A317526: 1010 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((~2 + (x mod 3)) mod (2 + (if x <= 0 then 1 else 2)))
A224317: 1 3 0 2 3 0 2 3 0 2 3 0 2 3 0 2
(4 + loop(\(x,i).5x,x,1))
A242329: 5 9 29 129 629 3129 15629 78129 390629 1953129 9765629 48828129 244140629 1220703129 6103515629 30517578129
((2 - (if x <= 0 then 1 else (x div ~4))) div 2)
A135664: 0 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3
(4 * loop(\(x,i).(2x + 4),(x + 1),2))
A182466: 32 80 176 368 752 1520 3056 6128 12272 24560 49136 98288 196592 393200 786416 1572848
(2 * (2 + loop(\(x,i).3x,(x + 1),2)))
A205248: 16 40 112 328 976 2920 8752 26248 78736 236200 708592 2125768 6377296 19131880 57395632 172186888
(4 + (loop(\(x,i).(x * i),x,(x + ~1)) div 2))
A133320: 3 4 5 10 40
(8 * (2 + loop(\(x,i).2x,x,2)))
A175162: 32 48 80 144 272 528 1040 2064 4112 8208 16400 32784 65552 131088 262160 524304
(2 + (if x <= 0 then 1 else 16x))
A063116: 3 18 34 50 66 82 98 114 130 146 162 178 194 210 226 242
(if x <= 0 then 1 else (2 + ((x + ~1) mod 8)))
A189506-A173529-A156230-A038506: 1 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8
loop(\(x,i).(2x + 1),x,16)
A198275: 16 33 67 135 271 543 1087 2175 4351 8703 17407 34815 69631 139263 278527 557055
(if (x + ~2) <= 0 then x2 else 16)
A220788: 0 1 4 16
A170836: 0 1 4 16 16 16 16 16 16 16 16 16 16 16 16 16
(2 + loop(\(x,i).(2x + ~1),x,8))
A164285: 10 17 31 59 115 227 451 899 1795 3587 7171 14339 28675 57347 114691 229379
(loop(\(x,i).(x + (x div 2)),x,8) div 2)
A120134: 4 6 9 13 20 30 45 67 101 151 227 340 510 765 1148 1722
((if x <= 0 then 1 else (x2 div 8)) mod 2)
A173858: 1 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0
(((if x <= 0 then 1 else x) mod (2 + (x div 4))) mod 2)
A141727: 1 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0
(2 + loop(\(x,i).x3,4x,2))
A066546: 4 4611686018427387903 4611686018427387903
A132653-A115544: 4 4611686018427387903 4611686018427387903 4611686018427387903
(2 + (if x <= 0 then 2 else (x mod (~2 + ((x div 2) mod 2)))))
A106437: 4 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2
(2 * loop(\(x,i).x2,4x,4))
A067486: 8 8589934592 4611686018427387903 4611686018427387903 4611686018427387903
(0 - ((if x <= 0 then 1 else x) div ~7))
A278950-A109703-A103375: 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3
loop(\(x,i).(2x + 1),2x,8)
A114569: 8 35 143 575 2303 9215 36863 147455 589823 2359295 9437183 37748735 150994943 603979775 2415919103 9663676415
loop(\(x,i).(2x + ~1),2x,8)
A199207: 8 29 113 449 1793 7169 28673 114689 458753 1835009 7340033 29360129 117440513 469762049 1879048193 7516192769
loop(\(x,i).(2x + 3),x,8)
A156198: 8 19 41 85 173 349 701 1405 2813 5629 11261 22525 45053 90109 180221 360445
loop(\(x,i).(3x + 1),x,8)
A295911: 8 25 76 229 688 2065 6196 18589 55768 167305 501916 1505749 4517248 13551745 40655236 121965709
loop(\(x,i).(x2 + ~x + 1),x,8)
A144781: 8 57 3193 10192057 103878015699193 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + ~x + ~1),x,8)
A144748: 8 55 2969 8811991 77651176572089 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x + ~2),x,8)
A199110: 8 22 64 190 568 1702 5104 15310 45928 137782 413344 1240030 3720088 11160262 33480784 100442350
loop(\(x,i).((x2 + x) div 2),x,8)
A050536: 8 36 666 222111 24666759216 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + 2x + ~2),x,8)
A145508: 8 78 6238 38925118 1515164889164158 4611686018427387903 4611686018427387903
(if (x mod 3) <= 0 then 1 else (x div 8))
A025851: 1 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1
(if (x mod 4) <= 0 then 1 else (x div 8))
A029374: 1 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1
(loop(\(x,i).(1 + (2 * (x + i))),x,4) div 2)
A054127: 2 5 13 30 65 136 279 566 1141 2292 4595 9202 18417 36848 73711 147438
(loop(\(x,i).(3x + 1),x,4) div 2)
A081251: 2 6 20 60 182 546 1640 4920 14762 44286 132860 398580 1195742 3587226 10761680 32285040
(if (x + ~2) <= 0 then 1 else ((x + ~2) - (x div 4)))
A051898: 1 1 1 1 1 2 3 4 4 5 6
((x mod (2 + ((if (x + ~2) <= 0 then 1 else x) mod 2))) div 2)
A099395: 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0
(4 * loop(\(x,i).(x2 + ~x),2,(x + 2)))
A086302: 8 120 528 1520 3480 6888 12320 20448 32040 47960 69168 96720 131768 175560 229440 294848
(loop(\(x,i).((x + 2) + (i * i)),(x + 2),2) div 2)
A026038: 5 11 20 33 52 78 111 152 203 265 338 423 522 636 765 910
((loop(\(x,i).(x * (x - i)),2,(x + 2)) div 2) div 2)
A033487: 0 6 30 90 210 420 756 1260 1980 2970 4290 6006 8190 10920 14280 18360
loop(\(x,i).4x2,(x + 4),2)
A139575: 70368744177664 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x * (1 + i)),x,(x + 4)) div 2)
A038720: 2 5 18 84 480 3240 25200 221760 2177280 23587200 279417600 3592512000 49816166400 741015475200 11769069312000 198766503936000
loop(\(x,i).(2x2 + ~1),(2x + 4),2)
A219279: 708158977 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * ((2x + 4) + (2 div (if x <= 0 then 1 else x))))
A272861: 12 16 18 20 24 28 32 36 40 44 48 52 56 60 64 68
(2 + loop(\(x,i).(3x + 3),2x,2))
A199566: 4 32 284 2552 22964 206672 1860044 16740392 150663524 1355971712 12203745404 109833708632 988503377684 8896530399152 80068773592364 720618962331272
(2 + loop(\(x,i).(3x + 6),2x,2))
A198962: 4 44 404 3644 32804 295244 2657204 23914844 215233604 1937102444 17433922004 156905298044 1412147682404 12709329141644 114383962274804 1029455660473244
(loop(\(x,i).2x3,2x,2) div 2)
A309112: 1 4096 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,3,8x)
A017072: 0 16777216 4294967296 110075314176 1099511627776 6553600000000 28179280429056 96717311574016 281474976710656 722204136308736 1677721600000000 3596345248055296 7213895789838336 13685690504052736
loop(\(x,i).x3,1,8x)
A017067: 0 512 4096 13824 32768 64000 110592 175616 262144 373248 512000 681472 884736 1124864 1404928 1728000
loop(\(x,i).x3,2,8x)
A017073: 0 134217728 68719476736 2641807540224 35184372088832 262144000000000 1352605460594688 5416169448144896 18014398509481984 51998697814228992 134217728000000000 316478381828866048 692533995824480256
loop(\(x,i).x2,2,~7x)
A016984: 0 2401 38416 194481 614656 1500625 3111696 5764801 9834496 15752961 24010000 35153041 49787136 68574961 92236816 121550625
(~8x + loop(\(x,i).2x,x,x))
A083727: 0 ~6 ~8 0 32 120 336 840 1984 4536 10160 22440 49056 106392 229264 491400
(2 * loop(\(x,i).(2x2 + i),2x,2))
A135442: 4 328
(x div (if (x + ~2) <= 0 then 1 else (2 + ((x div 2) mod 2))))
A029550: 0 1 2 1 2 2 2 2 4
(2 * loop(\(x,i).5x,(x div 2),2))
A117857: 4 4 20 20 100 100 500 500 2500 2500 12500 12500 62500 62500 312500 312500
(2 + loop(\(x,i).2x,(x div 2),(2 + (x mod 2))))
A209722: 4 5 6 8 10 14 18 26 34 50 66 98 130 194 258 386
(2 * loop(\(x,i).2x,(x div 2),(2 + (x mod 2))))
A090989: 4 6 8 12 16 24 32 48 64 96 128 192 256 384 512 768
(loop(\(x,i).(2x + 1),x,(2 + (x mod 2))) div 2)
A290662: 1 3 5 15 23 63 95 255 383 1023 1535 4095 6143 16383 24575 65535
(loop(\(x,i).4x,x,(2 + (x mod 2))) div 2)
A266180: 1 6 16 96 256 1536 4096 24576 65536 393216 1048576 6291456 16777216 100663296 268435456 1610612736
(4 + (loop(\(x,i).(2x + ~2),x,x) div 2))
A098821: 4 4 5 9 21 53 133 325 773 1797 4101 9221 20485 45061 98309 212997
(x3 mod loop(\(x,i).(x2 + 2),2,2))
A070500: 0 1 8 27 26 11 26 1 18 7 12 1 18 31 8 31
(x mod (if (~2 + (x div 4)) <= 0 then 1 else 4))
A297235-A269445-A093391: 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3
loop(\(x,i).4x,4x,4)
A013780: 4 1024 262144 67108864 17179869184 4398046511104 1125899906842624 288230376151711744 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).8x,2x,4)
A013734: 4 256 16384 1048576 67108864 4294967296 274877906944 17592186044416 1125899906842624 72057594037927936 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x - loop(\(x,i).(x * ((~x + ~1) + i)),2,4))
A112820: 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287
((if (x mod (2 + (x mod 2))) <= 0 then 1 else x) mod 4)
A339877: 1 1 1 1 1 1 1 3 1 1 1 3 1 1 1 1
(4 * loop(\(x,i).3x,(x + ~1),x))
A120908: 0 4 24 108 432 1620 5832 20412 69984 236196 787320 2598156 8503056 27634932 89282088 286978140
loop(\(x,i).((x + ~1) + ((2 + i) * i)),x,4)
A160805: 4 6 13 27 50 84 131 193 272 370 489 631 798 992 1215 1469
((x + (if (x mod 3) <= 0 then 1 else 2)) div 4)
A333348: 0 0 1 1 1 1 1 2 2 2 3 3 3 3 4 4
(loop(\(x,i).((x + 1) * (x + i)),2,x) div 4)
A039623: 1 7 27 76 175 351 637 1072 1701 2575 3751 5292 7267 9751 12825 16576
loop(\(x,i).(8x * i),x,4)
A153511: 4 32 512 12288 393216 15728640 754974720 42278584320 2705829396480 194819716546560 15585577323724800 1371530804487782400 4611686018427387903 4611686018427387903
loop(\(x,i).(6x + 4),x,4)
A125687: 4 28 172 1036 6220 37324 223948 1343692 8062156 48372940 290237644 1741425868 10448555212 62691331276 376147987660 2256887925964
loop(\(x,i).(6x + ~8),x,4)
A005618: 4 16 88 520 3112 18664 111976 671848 4031080 24186472 145118824 870712936 5224277608 31345665640 188073993832 1128443962984
loop(\(x,i).(5x + ~2),x,4)
A199309: 4 18 88 438 2188 10938 54688 273438 1367188 6835938 34179688 170898438 854492188 4272460938 21362304688 106811523438
(loop(\(x,i).(x * ((x + 2) + i)),2,x) div 4)
A168566: 0 8 35 99 224 440 783 1295 2024 3024 4355 6083 8280 11024 14399 18495
((if x <= 0 then 1 else x) - ((x + (x div 2)) div 4))
A177151-A076935: 1 1 2 2 3 4 4 5 5 6 7 7 8 9 9 10
(4 * loop(\(x,i).x2,(x2 + ~2),x))
A171959: 0 4 64 4611686018427387903
((if (x mod 4) <= 0 then 2 else 0) + (x div 4))
A082507: 2 0 0 0 3 1 1 1 4 2 2 2 5 3 3 3
(if (4 mod (x + 1)) <= 0 then 1 else (x div 4))
A272187-A169990: 1 1 0 1 1 1 1 1 2 2 2 2 3 3 3 3
((if x <= 0 then 1 else 4x) + (x div 4))
A311435: 1 4 8 12 17 21 25 29 34 38 42 46 51 55 59 63
(loop(\(x,i).i,(x div 4),1) * (x mod 4))
A309954: 0 1 2 3 0 1 2 3 0 2 4 6 0 3 6 9
loop(\(x,i).7x,x,4)
A208704: 4 28 196 1372 9604 67228 470596 3294172 23059204 161414428 1129900996 7909306972 55365148804 387556041628 2712892291396 18990246039772
loop(\(x,i).(x3 + ~3x),x,4)
A219160: 4 52 140452 2770663499604052 4611686018427387903
loop(\(x,i).(x + (x div (2 + (x mod 2)))),x,4)
A165897: 4 6 9 12 18 27 36 54 81 108 162 243 324 486 729 972
(x - ((if (x mod 2) <= 0 then (~x + 2) else x) div 4))
A265888: 0 1 2 3 5 4 7 6 10 7 12 9 15 10 17 12
loop(\(x,i).x3,1,4x2)
A016746: 0 64 4096 46656 262144 1000000 2985984 7529536 16777216 34012224 64000000 113379904 191102976 308915776 481890304 729000000
loop(\(x,i).((2 * ((x + 2) + i)) + i),x,4)
A059140: 4 15 40 93 202 423 868 1761 3550 7131 14296 28629 57298 114639 229324
(((~x + (if (x + ~4) <= 0 then 2 else 0)) div 2) mod 2)
A284369: 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0
(loop(\(x,i).(1 + ((2 * i) div (x + 1))),x,2) mod 2)
A284792: 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 0
(2 * loop(\(x,i).(2x2 + ~5),x,2))
A099941: 4 6 26 666 443546 196733054106 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).4x,(3x + 2),2)
A277426: 32 2048 131072 8388608 536870912 34359738368 2199023255552 140737488355328 9007199254740992 576460752303423488 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(6x + 4))
A016958: 16 100 256 484 784 1156 1600 2116 2704 3364 4096 4900 5776 6724 7744 8836
loop(\(x,i).x2,2,(6x + 4))
A016960: 256 10000 65536 234256 614656 1336336 2560000 4477456 7311616 11316496 16777216 24010000 33362176 45212176 59969536 78074896
(loop(\(x,i).2x,x,(3x + 2)) div 2)
A053220: 1 5 16 44 112 272 640 1472 3328 7424 16384 35840 77824 167936 360448 770048
(loop(\(x,i).x3,3x,2) div 2)
A161774: 1 67108864 4611686018427387903
(x3 mod loop(\(x,i).(x2 + x),2,2))
A070504: 0 1 8 27 22 41 6 7 8 15 34 29 6 13 14 15
(loop(\(x,i).(((x + 2) + i) * (1 + i)),x,2) div 2)
A103519: 1 5 21 94 485 2931 20545 164396 1479609 14796145 162757661 1953092010 25390196221 355462747199 5331941208105 85311059329816
(((~x + (if (~2 + (x div 2)) <= 0 then 0 else 2)) div 2) mod 2)
A287657: 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1
(((if ((x div 2) mod 3) <= 0 then 2 else x) div 2) mod 2)
A285504: 1 1 1 1 0 0 1 1 0 0 1 1 1 1 1 1
(loop(\(x,i).(2x - ((x div 2) mod 2)),x,2) div 2)
A323457: 1 1 2 5 9
A077947: 1 1 2 5 9 18 37 73 146 293 585 1170 2341 4681 9362 18725
(loop(\(x,i).(2x - ((i div 2) mod 2)),x,2) div 2)
A007910: 1 2 3 6 13 26 51 102 205 410 819 1638 3277 6554 13107 26214
(loop(\(x,i).2x,x,(3x + ~4)) div 2)
A053565: ~2 ~1 4 20 64 176 448 1088 2560 5888 13312 29696 65536 143360 311296 671744
(~2 + loop(\(x,i).10x,x,2))
A086573: 0 18 198 1998 19998 199998 1999998 19999998 199999998 1999999998 19999999998 199999999998 1999999999998 19999999999998 199999999999998 1999999999999998
(loop(\(x,i).2x,x,(x2 + 2x + 2)) div 2)
A084850: 1 5 20 68 208 592 1600 4160 10496 25856 62464 148480 348160 806912 1851392 4210688
(loop(\(x,i).2x,x,((x + 2) + (x div 2))) div 2)
A188545: 1 3 10
A231116: 1 3 10 24
A179608: 1 3 10 24 64 144 352 768 1792 3840 8704 18432 40960 86016 188416 393216
(2 - ((~x + 2) div (2 + ((if x <= 0 then 2 else x) div 2))))
A346425: 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 4
(loop(\(x,i).(2x - ((x + i) mod 2)),x,2) div 2)
A016029: 1 1 2 5 10 19 38 77 154 307 614 1229 2458 4915 9830 19661
(2 * loop(\(x,i).(2 + ((2 * (x + i)) + i)),x,2))
A059133: 4 18 52 126 280 594 1228 2502 5056 10170 20404 40878 81832 163746 327580 655254
((2x + 4) * (3 + (if x <= 0 then 0 else 2)))
A307348: 12 30 40
((2 - ((x + 2) * (if (x mod 2) <= 0 then x else 1))) div 2)
A110326: 1 ~1 ~3 ~2 ~11 ~3 ~23 ~4 ~39 ~5 ~59 ~6 ~83 ~7 ~111 ~8
(((x + 2) * (if (x mod 2) <= 0 then 1 else (x + 2))) div 2)
A226725: 1 4 2 12 3 24 4 40 5 60 6 84 7 112 8 144
((x + 2) - loop(\(x,i).(~x2 + 1),2,(x + 2)))
A269468: 10 66 228 580 1230 2310 3976 6408 9810 14410 20460 28236 38038 50190 65040 82960
(if (~2 + (x div 4)) <= 0 then x else (x + 4))
A103303: 0 1 2 3 4 5 6 7 8 9
A004840: 0 1 2 3 4 5 6 7 8 9 10 11 16 17 18 19
(if (~4 + (x div 2)) <= 0 then x else (x + 4))
A103303: 0 1 2 3 4 5 6 7 8 9
A335134-A244155: 0 1 2 3 4 5 6 7 8 9 14 15 16 17 18 19
loop(\(x,i).(x * ((x + ~1) - i)),2,(2x + 4))
A069079: 40 504 2160 6160 14040 27720 49504 82080 128520 192280 277200 387504 527800 703080 918720 1180480
loop(\(x,i).(2x * (2 + i)),x,(2x + 4))
A019999: 4 36 384 4800 69120 1128960 20643840 418037760 9289728000 224811417600 5885971660800 165788201779200 4999151930572800 160687026339840000 4611686018427387903 4611686018427387903
(2 + (if (x + ~6) <= 0 then x else (x + 2)))
A227691-A167703: 2 3 4 5 6 7 8 11 12 13 14 15 16 17 18 19
(2 + (if (~2 + (x div 4)) <= 0 then x else (x + 2)))
A114522: 2 3 4 5 6 7 8 9 10 11 12 13 16 17 18 19
(loop(\(x,i).(2x + 8),x,(x + 2)) div 2)
A047862: 1 7 20 48 108 236 508 1084 2300 4860 10236 21500 45052 94204 196604 409596
loop(\(x,i).(x + (((1 + i) * i) div 2)),(x + 2),2)
A222001: 6 12 22 37 58 86 122 167 222 288 366 457 562 682 818 971
(x mod (if (x mod 6) <= 0 then (x + ~2) else 2))
A257260: 0 1 0 1 0 1 2 1 0 1 0 1 2 1 0 1
(x - (x mod (1 - loop(\(x,i).2x,(x + ~2),2))))
A295484: 0 1 2 3 7
A153010: 0 1 2 3 7 15 31 63 127 255 511 1023 2047 4095 8191 16383
(if (x + ~4) <= 0 then (x + 1) else (2x + ~4))
A067319: 1 2 3 4 5 6 8 10 12
A032956-A004279: 1 2 3 4 5 6 8 10 12 14 16 18 20 22 24 26
loop(\(x,i).(~1 + (2 * (x2 div 2))),2x,2)
A144836: 2 7 2207 23725150497407 4611686018427387903
(2 * loop(\(x,i).(x2 + 2x + 1),2,2x))
A020329: 8 200
loop(\(x,i).~7x,2x,2)
A324266: 2 98 4802 235298 11529602 564950498 27682574402 1356446145698 66465861139202 3256827195820898 159584532595224002 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 - (2 mod loop(\(x,i).(2x + ~4),2x,2)))
A267924: 1 3 27 123 507 2043 8187 32763 131067 524283 2097147 8388603 33554427 134217723 536870907 2147483643
loop(\(x,i).(x - (2 * ((~x + ~1) + i))),2x,2)
A338186: 2 16 126 1100 9850 88584 797174 7174468 64570098 581130752 5230176622 47071589436 423644304746 3812798742520 34315188682470 308836698142004
loop(\(x,i).(2x * ((i mod 2) + i)),2x,2)
A329928: 2 32 2048 294912 75497472 30198988800 17394617548800 13637380158259200 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + ~x),1,4x)
A069140: 0 60 504 1716 4080 7980 13800 21924 32736 46620 63960 85140 110544 140556 175560 215940
(2 * loop(\(x,i).3x,(x + ~1),(x div 2)))
A274499: 0 0 6 18 108 324 1458 4374 17496 52488 196830 590490 2125764 6377292 22320522 66961566
((loop(\(x,i).(x2 + 1),x,2) - (x div 2)) div 2)
A060596: 1 2 12 338
((~1 + (x mod 2)) mod loop(\(x,i).2x,(x div 2),2))
A077896: 1 0 3 0 7 0 15 0 31 0 63 0 127 0 255 0
(2 + loop(\(x,i).2x,(x div 2),2) - (x mod 2))
A261723: 4 3 6 5 10 9 18 17 34 33 66 65 130 129 258 257
(if (x + ~2) <= 0 then 2 else (2x div (2 + (x div 2))))
A328680: 2 2 2 2 2 2 2 2 2 3 2 3 3 3 3 3
(2x - (if ((x div 2) mod 2) <= 0 then (x mod 2) else 2))
A047466: 0 1 2 4 8 9 10 12 16 17 18 20 24 25 26 28
(if (x mod 4) <= 0 then 1 else (2 * (2 - (x mod 2))))
A177002: 1 2 4 2 1 2 4 2 1 2 4 2 1 2 4 2
(if (x + ~2) <= 0 then 1 else (x div (2 * (2 - (x mod 2)))))
A243561: 1 1 1 1 1 2 1 3 2 4
(loop(\(x,i).(2x + 2),x,(2 - (x mod 2))) div 2)
A284354: 1 2 7 11 31 47 127 191 511 767 2047 3071 8191 12287 32767 49151
(loop(\(x,i).3x,x,2) div (2 + (x mod 2)))
A083423: 1 2 9 18 81 162 729 1458 6561 13122 59049 118098 531441 1062882 4782969 9565938
((if (x + ~2) <= 0 then (x + 1) else 0) + (2 * (x mod 2)))
A067018: 1 4 3 2 0 2 0 2 0 2 0 2 0 2 0 2
((if (~x + 2) <= 0 then 4 else 1) + (2 * (x mod 2)))
A101432: 1 3 4 6 4 6 4 6 4 6 4 6 4 6 4 6
(loop(\(x,i).(2x + 1),x,2) + (2 * (x mod 2)))
A201630: 2 7 11 25 47 97 191 385 767 1537 3071 6145 12287 24577 49151 98305
(0 - loop(\(x,i).(~2x + 1),x,(2 * (x mod 2))))
A096773: 0 3 1 13 5 53 21 213 85 853 341 3413 1365 13653 5461 54613
(loop(\(x,i).(x3 + 3x),x,2) div 2)
A145451: 1 7 1393 10812186007 4611686018427387903 4611686018427387903
(2 * loop(\(x,i).(x3 + x2),x2,2))
A162187: 4 24 4611686018427387903
(2 + loop(\(x,i).(x * ((x - i) * (x + i))),x,2))
A120822: 4 8 194
((x + (if (~2 + (x div 4)) <= 0 then 1 else 0)) div 2)
A062108: 0 1 1 2 2 3 3 4 4 5 5 6 6 6 7 7
((x + (if (~4 + (x div 2)) <= 0 then 1 else 0)) div 2)
A186704: 0 1 1 2 2 3 3 4 4 5 5 5 6
(2 * (~x + loop(\(x,i).(2 * (x + (2 * i))),x,0)))
A308585: 0 6 28 82 200 446 948 1962 4000 8086 16268 32642 65400 130926 261988 524122
((x + 2) + loop(\(x,i).((x + ~1) mod (2 + i)),x,0))
A256302: 2 5 5 5 11 11 11 11 11 11 23 23 23 23 23 23
(2 * (x + loop(\(x,i).i,(x div 5),1)))
A240171: 2 4 6 8 10 12 14 16 18 20 24 26 28 30 32 36
((x + 2) + loop(\(x,i).i,(~3 + (x div 2)),1))
A154660: 3 4 5 6 7 8
A298296: 3 4 5 6 7 8 9 10 11 12 14 15 17 18 20 21
((x + 2) + loop(\(x,i).i,((x + ~2) div 3),1))
A154660: 3 4 5 6 7 8
A298004: 3 4 5 6 7 8 9 10 12 13 14 16 17 18 20 21
loop(\(x,i).(3x2 + 3x + 1),x,2)
A172028: 2 19 1141 3909067 45842426158669 4611686018427387903 4611686018427387903
((if (~2 + (x mod 5)) <= 0 then 1 else x) mod 2)
A185305: 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1
(2 - ((if (~2 + (x div 3)) <= 0 then 1 else x) mod 2))
A338653: 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1
(2 * (x + loop(\(x,i).i,(~2 + (x div 3)),1)))
A147819: 2 4 6 8 10 12 14 16 18 20 22 24 28 30 32 36
((x + 2) + loop(\(x,i).i,((~1 + (x div 2)) div 2),1))
A154660: 3 4 5 6 7 8
A298005: 3 4 5 6 7 8 9 10 11 12 14 15 16 17 19 20
((x + (if (~2 + (x div 3)) <= 0 then 2 else 1)) div 2)
A194964: 1 1 2 2 3 3 4 4 5 5 5 6 6 7 7 8
((x + (if (~2 + (x div 4)) <= 0 then 2 else 1)) div 2)
A075355: 1 1 2 2 3 3 4 4 5 5 6 6 6 7 7 8
(2 * loop(\(x,i).i,(x + ~9),x))
A245627-A169805-A136614-A097586: 0 2 4 6 8 10 12 14 16 18 2 4 6 8 10 12
loop(\(x,i).(1 + (4 * (x2 div 2))),x,2)
A081459: 2 9 161 51841 5374978561 4611686018427387903 4611686018427387903 4611686018427387903
(2 div (if ((x + ~2) mod 5) <= 0 then x else 2))
A118111-A071039: 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1
loop(\(x,i).x2,1,(5x + 2))
A016874: 4 49 144 289 484 729 1024 1369 1764 2209 2704 3249 3844 4489 5184 5929
loop(\(x,i).x2,2,(5x + 2))
A016876: 16 2401 20736 83521 234256 531441 1048576 1874161 3111696 4879681 7311616 10556001 14776336 20151121 26873856 35153041
loop(\(x,i).x2,1,10x)
A017270: 0 100 400 900 1600 2500 3600 4900 6400 8100 10000 12100 14400 16900 19600 22500
loop(\(x,i).x2,2,10x)
A017272: 0 10000 160000 810000 2560000 6250000 12960000 24010000 40960000 65610000 100000000 146410000 207360000 285610000 384160000 506250000
((if x <= 0 then 2 else (x2 + 5x)) div 2)
A027379: 1 3 7 12 18 25 33 42 52 63 75 88 102 117 133 150
((if (x2 mod (x + 4)) <= 0 then 1 else x) mod 2)
A285384: 1 1 0 1 1 1 0 1 0 1 0 1 1 1 0 1
(1 - ((~x + loop(\(x,i).i,(~2 + (x div 2)),1)) div 2))
A232753-A067085: 1 1 2 2 3 3 4 4 4 5 5 5 5 6 6 6
loop(\(x,i).(1 + (x * i) - (2 * (i mod 2))),x,2)
A236438: 2 1 3 8 33 164 985 6894 55153 496376 4963761 54601370 655216441 8517813732 119249392249 1788740883734
loop(\(x,i).(7x + ~3),x,2)
A199417: 2 11 74 515 3602 25211 176474 1235315 8647202 60530411 423712874 2965990115 20761930802 145333515611 1017334609274 7121342264915
loop(\(x,i).(7x + ~1),x,2)
A199489: 2 13 90 629 4402 30813 215690 1509829 10568802 73981613 517871290 3625099029 25375693202 177629852413 1243408966890 8703862768229
loop(\(x,i).(7x + ~2),x,2)
A199420: 2 12 82 572 4002 28012 196082 1372572 9608002 67256012 470792082 3295544572 23068812002 161481684012 1130371788082 7912602516572
loop(\(x,i).x2,3,(3x + 2))
A016796: 256 390625 16777216 214358881 1475789056 6975757441 25600000000 78310985281 208827064576 500246412961 1099511627776 2251875390625 4347792138496 7984925229121 14048223625216 23811286661761
loop(\(x,i).x3,1,(3x + 2))
A061103-A016791: 8 125 512 1331 2744 4913 8000 12167 17576 24389 32768 42875 54872 68921 85184 103823
(loop(\(x,i).2x,x,2) div (3x + 2))
A191629: 1 0 1 1 2 3 6 11 19 35 64 117 215 399 744 1394
loop(\(x,i).x3,2,(3x + 2))
A016797: 512 1953125 134217728 2357947691 20661046784 118587876497 512000000000 1801152661463 5429503678976 14507145975869 35184372088832 78815638671875 165216101262848 327381934393961
loop(\(x,i).2x,(x + (x2 mod 3)),2)
A080095: 2 8 16 16 64 128 128 512 1024 1024 4096 8192 8192 32768 65536 65536
(if ((2x + ~1) mod (x + 3)) <= 0 then x else 2)
A053238: 2 2 2 2 4 2 2 2 2 2 2 2 2 2 2 2
(2 * loop(\(x,i).3x,(2x + ~1),x))
A230540: 0 6 108 1458 17496 196830 2125764 22320522 229582512 2324522934 23245229340 230127770466 2259436291848 22029503845518 213516729579636 2058911320946490
((x + loop(\(x,i).((i div 2) * i),(x div 2),1)) mod 2)
A076404: 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0
loop(\(x,i).((4x + 1) + (x mod 2)),x,2)
A037489: 2 9 38 153 614 2457 9830 39321 157286 629145 2516582 10066329 40265318 161061273 644245094 2576980377
((x3 + 2) - (if (x mod 2) <= 0 then 1 else x))
A085070: 1 2 9 26
((x * (~1 + loop(\(x,i).(2x + i),x,2))) div 2)
A276659: 0 2 11 39 114 300 741 1757 4052 9162 20415 44979 98214 212888 458633 982905
loop(\(x,i).(1 + ((x2 div 2) + (2 * i))),x,2)
A123374: 2 5 17 151
((x + loop(\(x,i).((2 * i) div (x + 2)),x,1)) mod 2)
A332479: 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0
((x * (1 + loop(\(x,i).x3,2,x))) div 2)
A168118: 0 1 513 29526 524290 4882815 30233091 141237628 536870916 1743392205 5000000005 12968712306 30958682118 68929245931 144627327495 288325195320
((x + loop(\(x,i).((x * i) div 2),x,(x + 1))) mod 2)
A337165-A243148: 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0
((x - (5 mod (if x <= 0 then 1 else x))) mod 2)
A275606: 0 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0
(x - (((x div 4) - (if x <= 0 then 1 else x)) div 2))
A305847: 1 2 3 5 6 7 9 10 11 13 14 16 17 18 20 21
(x - ((((x div 2) mod 2) - (if x <= 0 then 1 else x)) div 2))
A171581-A094229: 1 2 3 4 6 8 9 10 12 14 15 16 18 20 21 22
((2x2 + 4) div (2 + (if x <= 0 then 1 else x)))
A187102: 1 2 3 4 6 7 9 11
((x3 + 2x) + ((if x <= 0 then 1 else x) mod 2))
A119683: 1 4 12 34
loop(\(x,i).x2,1,((x3 + x) div 2))
A135509: 0 1 25 225 1156 4225 12321 30625 67600 136161 255025 450241 756900 1221025 1901641 2873025
loop(\(x,i).((2x div (1 + i)) * (1 + i)),x,2)
A178901: 2 4 6 12 20 36 70 136 270 540 1078 2148 4290 8568 17130 34256
loop(\(x,i).(4x * (i * (1 + i))),x,2)
A002474: 2 16 384 18432 1474560 176947200 29727129600 6658877030400 1917756584755200 690392370511872000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (i * (2 + i) * (1 + i))),x,2)
A176037: 2 12 288 17280 2073600 435456000 146313216000 73741860864000 53094139822080000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 2) + (if (x + ~6) <= 0 then 1 else 2))
A154660: 3 4 5 6 7 8
A297468: 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19
loop(\(x,i).(16x + 2),x,2)
A098704: 2 34 546 8738 139810 2236962 35791394 572662306 9162596898 146601550370 2345624805922 37529996894754 600479950316066 9607679205057058 153722867280912930 2459565876494606882
(2 div (if ((x + ~2) mod 6) <= 0 then x else 2))
A340374-A340371: 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1
(loop(\(x,i).(1 + ((x2 + ~2x) div 2)),2,x) div 2)
A307182: 0 0 0 0 4 12 36 72 144 240 400 600 900 1260 1764 2352
(if x <= 0 then 1 else (2x * (2 + (2 mod (x + 1)))))
A234275: 1 4 16 24 32 40 48 56 64 72 80 88 96 104 112 120
loop(\(x,i).((3x + 2) - (i mod 2)),x,2)
A037488: 2 7 23 70 212 637 1913 5740 17222 51667 155003 465010 1395032 4185097 12555293 37665880
((if (~2 + (x div 5)) <= 0 then 2 else x) div 2)
A096194: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7
loop(\(x,i).32x,x,2)
A013822: 2 64 2048 65536 2097152 67108864 2147483648 68719476736 2199023255552 70368744177664 2251799813685248 72057594037927936 2305843009213693952 4611686018427387903 4611686018427387903
((x + loop(\(x,i).i,(x + ~8),2)) div 2)
A025766: 1 1 2 2 3 3 4 4 5 5 6 7 8 9 10 11
(2x * (~2 + loop(\(x,i).2x2,2,2)))
A242570: 0 252 504 756 1008 1260 1512 1764 2016 2268 2520 2772 3024 3276 3528 3780
((x + loop(\(x,i).i,((x div 2) mod 4),2)) div 2)
A140858: 1 1 1 2 3 3 4 5 5 5 5 6 7
loop(\(x,i).2x,x,(x + 10))
A079861: 10 22 48 104 224 480 1024 2176 4608 9728 20480 43008 90112 188416 393216 819200
(loop(\(x,i).(2 + (x div (2 - (x mod 2)))),2,x) div 2)
A331745-A331743-A286378-A103391: 1 2 2 3 2 4 3 5 2 6 4 7 3 8 5 9
((x * loop(\(x,i).(x3 + ~2),2,2)) div 2)
A134297: 0 107 214 321 428 535 642 749 856 963 1070 1177 1284 1391 1498 1605
(2 - (2 div (if ((x + 2) mod 4) <= 0 then x else 2)))
A333915: 1 1 1 1 1 1 2 1 1 1 2 1 1 1 2 1
(loop(\(x,i).2x,x,(3x + 4)) div 2)
A066373: 2 7 20 52 128 304 704 1600 3584 7936 17408 37888 81920 176128 376832 802816
loop(\(x,i).(2 + ((x + 2) * (x + (x div 2)))),x,2)
A101524: 2 14 338
(loop(\(x,i).(2x * (1 + (x * i))),2,x) div 2)
A185096: 0 36 300 1176 3240 7260 14196 25200 41616 64980 97020 139656 195000 265356 353220 461280
(~3 mod loop(\(x,i).4x,x,2))
A267921: 1 5 29 125 509 2045 8189 32765 131069 524285 2097149 8388605 33554429 134217725 536870909 2147483645
loop(\(x,i).((x * (1 + i)) - ((x div 2) mod 2)),x,2)
A082569: 2 3 8 32 160 960 6720 53760 483840 4838400 53222400 638668800 8302694400 116237721600 1743565824000 27897053184000
(2 * (x - loop(\(x,i).((~x2 + x) div 2),2,x)))
A062026: 0 2 6 18 50 120 252 476 828 1350 2090 3102 4446 6188 8400 11160
loop(\(x,i).(2x - (((x * i) div 2) mod 2)),x,2)
A262450: 2 3 5 9 18 35 69 137 274 547 1093 2185 4370 8739 17477 34953
loop(\(x,i).i,((x + 1) mod 3),(~x + 4))
A087775: 1 2 2 1 2 ~1 1 2 ~4 1 2 ~7 1 2 ~10 1
((x + 2) + (if (~1 + (x mod 3)) <= 0 then x else 2))
A079431: 2 4 6 8 10 9 14 16 12 20 22 15 26 28 18 32
loop(\(x,i).((3x2 + ~x) div 2),x,2)
A099137: 2 5 35 1820 4967690 37016913420305 4611686018427387903 4611686018427387903
(loop(\(x,i).(x * (1 + (x * (i * i)))),2,x) div 2)
A339483: 0 9 75 294 810 1815 3549 6300 10404 16245 24255 34914 48750 66339 88305 115320
loop(\(x,i).((x * (4 + (i mod 2))) div 2),x,2)
A162963: 2 5 10 25 50 125 250 625 1250 3125 6250 15625 31250 78125 156250 390625
((x + loop(\(x,i).(2x + (i * i)),x,2)) div 2)
A048492: 1 3 8 20 47 105 226 474 977 1991 4028 8112 16291 32661 65414 130934
loop(\(x,i).((x + 2) + (((1 + i) * i) div 2)),x,2)
A177787: 2 5 10 18 30 47 70 100 138 185 242 310 390 483 590 712
(2 + loop(\(x,i).((2x + 1) - i),(x + 2),x))
A045618: 1 6 23 72 201 522 1291 3084 7181 16398 36879 81936 180241 393234 851987 1835028
(2 + loop(\(x,i).(x3 + 1),2x,x))
A079331: 2 11 4611686018427387903
(2x * loop(\(x,i).x3,2,2x))
A016750: 0 1024 1048576 60466176 1073741824 10000000000 61917364224 289254654976 1099511627776 3570467226624 10240000000000 26559922791424 63403380965376 141167095653376 296196766695424 590490000000000
((3x + 3) + loop(\(x,i).2x,x,2))
A086653: 5 10 17 28 47 82 149 280 539 1054 2081 4132 8231 16426 32813 65584
((~x + 2) + loop(\(x,i).x3,x,2x))
A103562: 2 9 262144 4611686018427387903
loop(\(x,i).(x * i),x,(2 + (x * (2 - (x mod 2)))))
A256031: 2 3 12 30 240 840 10080 45360 725760 3991680 79833600 518918400 12454041600 93405312000 2615348736000 22230464256000
((4x + 4) + ((if x <= 0 then 2 else x) div 2))
A210240: 5 8 13 17 22
(loop(\(x,i).(x2 * ((x + ~1) + i)),2,x) div 2)
A168555: 0 1 288 10206 133120 984375 5062176 20235628 67239936 193975965 500500000 1179859626 2581383168 5304663091 10334288160 19227375000
loop(\(x,i).(2x - (((x div 2) + i) mod 2)),x,2)
A262333: 2 4 8 15 29 57 114 228 456 911 1821 3641 7282 14564 29128 58255
(if (~2 + (x div 5)) <= 0 then 1 else (x + 2))
A300909: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17
(loop(\(x,i).2x,((x + ~1) div 2),1) div (x + 2))
A338333: 0 0 0 0 0 0 0 0 0 1 1 2 2 4 4 7
(if ((x + 2) mod (2 + (x mod 2))) <= 0 then 1 else (x + 2))
A308090: 1 1 1 5 1 7 1 1 1 11 1 13 1 1 1 17
(loop(\(x,i).(x + (x div 2)),x,3) div (x + 2))
A067859: 1 1 1 1 2 2 3 4 6 8 11 16 22 31 44 62
((if x <= 0 then 0 else (4x + ~4)) div (x + 2))
A132090-A071538: 0 0 1 1 2 2 2 2 2 2 3 3 3 3 3 3
loop(\(x,i).((x2 + ~1) + (x mod 2)),2,(x + 2))
A208114: 9 81 225 625 1225 2401 3969 6561 9801 14641 20449 28561 38025 50625 65025 83521
((x + 2) * loop(\(x,i).(x * (i * i)),x,(x + 2)))
A162991: 4 9 64 900 20736 705600 33177600 2057529600 162570240000 15933509222400 1896219279360000 269276305858560000 4611686018427387903 4611686018427387903 4611686018427387903
(if (x + ~12) <= 0 then x else (x + 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A050607-A023781: 0 1 2 3 4 5 6 7 8 9 10 11 12 15 16 17
((x + 2) * loop(\(x,i).3x,(x + ~1),x))
A069515: 0 3 24 135 648 2835 11664 45927 174960 649539 2361960 8444007 29760696 103630995 357128352 1219657095
(if (x + ~10) <= 0 then x else (x + 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A336813-A247812-A209860-A050724-A023779: 0 1 2 3 4 5 6 7 8 9 10 13 14 15 16 17
(if (~2 + (x div 5)) <= 0 then x else (x + 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A344022-A247764-A023783: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 17
(if (~6 + (x div 2)) <= 0 then x else (x + 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A283657-A053432-A023782: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 16 17
(2 div (if ((x div 4) mod 2) <= 0 then 2 else (x + ~2)))
A025448: 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0
(2x + (if (~2 + (x div 3)) <= 0 then 1 else 0))
A249123-A094042: 1 3 5 7 9 11 13 15 17 18 20 22 24 26 28 30
(2x + (if (~4 + (x div 2)) <= 0 then 1 else 0))
A329835-A038124: 1 3 5 7 9 11 13 15 17 19 20 22 24 26 28 30
(2x + (if (~x2 + 4x) <= 0 then 1 else 0))
A231408: 1 2 4 6 9
A326494: 1 2 4 6 9 11 13 15 17 19 21 23 25 27 29 31
(2x + (if ((x + ~1) mod 4) <= 0 then 0 else 1))
A047482: 1 2 5 7 9 10 13 15 17 18 21 23 25 26 29 31
(2x + (if ((x + 2) mod 4) <= 0 then 0 else 1))
A047544: 1 3 4 7 9 11 12 15 17 19 20 23 25 27 28 31
(2x + loop(\(x,i).i,(x + ~6),1))
A005842: 1 3 5 7 9 11 13 15 18 21 24 27 30 33 36 39
(2x + (if (x + ~6) <= 0 then 2 else 1))
A247427: 2 4 6 8 10 12 14 15 17 19 21 23 25 27 29 31
(2x + loop(\(x,i).i,(((x + ~1) div 2) div 2),1))
A248608: 1 3 5 7 9 11 13 15 17 20 22 24 26 29 31 33
(2x + (if ((x + ~1) mod 4) <= 0 then 2 else 1))
A047493: 1 4 5 7 9 12 13 15 17 20 21 23 25 28 29 31
(2x + (if ((x + 2) mod 4) <= 0 then 2 else 1))
A047558: 1 3 6 7 9 11 14 15 17 19 22 23 25 27 30 31
loop(\(x,i).(4x + 1),3,2x)
A239123: 21 149 277 405 533 661 789 917 1045 1173 1301 1429 1557 1685 1813 1941
loop(\(x,i).(2x + 1),(2x + 1),2x)
A098713: 1 23 159 895 4607 22527 106495 491519 2228223 9961471 44040191 192937983 838860799 3623878655 15569256447 66571993087
(2x + (if (x mod 4) <= 0 then x else (x + 1)))
A083032: 0 4 7 10 12 16 19 22 24 28 31 34 36 40 43 46
((2x + 3) * (if x <= 0 then 1 else 2x))
A059193: 3 10 28 54 88 130 180 238 304 378 460 550 648 754 868 990
(2x + (if (x + ~6) <= 0 then 1 else 2))
A247428: 1 3 5 7 9 11 13 16 18 20 22 24 26 28 30 32
(2x + (if (x mod 2) <= 0 then 1 else 6))
A168204: 1 8 5 12 9 16 13 20 17 24 21 28 25 32 29 36
loop(\(x,i).(x * (1 + (2 * (x + i)))),2,2x)
A101734: 0 462
(if ((x + 2) mod 4) <= 0 then (x div 2) else 2x)
A188167: 0 2 1 6 8 10 3 14 16 18 5 22 24 26 7 30
(2x + (if (x mod 4) <= 0 then 2 else (x mod 2)))
A047546: 2 3 4 7 10 11 12 15 18 19 20 23 26 27 28 31
loop(\(x,i).(x - (x div (3 + i))),x,2x)
A121856: 0 2 3 4 5 6 6 7 7 8 8 9 9 9 10 10
(3x + loop(\(x,i).3x,x,1))
A221905: 1 6 15 36 93 258 747 2208 6585 19710 59079 177180 531477 1594362 4783011 14348952
(~3x + loop(\(x,i).3x,x,1))
A107583: 1 0 3 18 69 228 711 2166 6537 19656 59019 177114 531405 1594284 4782927 14348862
(2x * loop(\(x,i).(x * (2 + (x * i))),2,x))
A192832: 0 48 576 2880 9600 25200 56448 112896 207360 356400 580800 906048 1362816 1987440 2822400 3916800
loop(\(x,i).(x + (x div (1 + (i mod 2)))),x,2x)
A187273: 0 3 12 27 72 135 324 567 1296 2187 4860 8019 17496 28431 61236 98415
loop(\(x,i).x2,1,(~2x3 + x))
A277792: 0 1 196 2601 15376 60025 181476 461041 1032256 2099601 3960100 7027801 11861136 19193161 29964676 45360225
(2x + (if (x + ~2) <= 0 then 2 else x3))
A175877: 2 4 6 33
((if (x mod 2) <= 0 then 6 else 1) + (x div 2))
A137235: 6 1 7 2 8 3 9 4 10 5 11 6 12 7 13 8
(loop(\(x,i).i,(x + ~6),1) + (x div 2))
A029025: 1 1 2 2 3 3 4 4 6 7 9 10 12 13 15 16
(loop(\(x,i).i,(~2 + ((x + ~1) div 2)),1) + (x div 2))
A025765: 1 1 2 2 3 3 4 4 5 6 7 8 9 10 11 12
(loop(\(x,i).i,(x + ~8),1) + (x div 2))
A029030: 1 1 2 2 3 3 4 4 5 5 7 8 10 11 13 14
(1 + loop(\(x,i).x2,(x + 2),x) - (x div 2))
A213619: 1 2 65536
(x mod ((if (x + ~4) <= 0 then 1 else 2) + (x div 2)))
A210609-A210608: 0 0 0 1 1 1 1 2 2 3 3 4 4 5 5 6
loop(\(x,i).(x - (x div (1 + (2 * i)))),2,(x div 2))
A048273: 0 0 1 1 2 2 2 2 3 3 4 4 4 4 4 4
loop(\(x,i).(x + 2),(~4 + (x div 2)),(x div 2))
A035679: 0 0 1 1 2 2 3 3 4 4 7 7 10 10 13 13
(loop(\(x,i).(x2 - (x div 2)),x,2) - (x div 2))
A201363: 2 3 7
A156585: 2 3 7 59
((if (x mod 4) <= 0 then x else (x + 2)) + (x div 2))
A244953: 0 3 5 6 6 9 11 12 12 15 17 18 18 21 23 24
(x + ((if (~2 + (x div 2)) <= 0 then 1 else 0) + (x div 2)))
A285423: 1 2 4 5 7 8 9 10 12 13 15 16 18 19 21 22
(x + ((if (x mod 4) <= 0 then 1 else 2) + (x div 2)))
A342051: 1 3 5 6 7 9 11 12 13 15 17 18 19 21 23 24
(x + ((if (~2 + (x div 2)) <= 0 then 1 else 2) + (x div 2)))
A187576: 1 2 4 5 7 8 11 12 14 15 17 18 20 21 23 24
((if (x mod 3) <= 0 then 4 else 1) * (x mod 2))
A120324: 0 1 0 4 0 1 0 1 0 4 0 1 0 1 0 4
(loop(\(x,i).4x,(x div 2),1) - (x mod 2))
A277800: 1 0 4 3 16 15 64 63 256 255 1024 1023 4096 4095 16384 16383
loop(\(x,i).(x + (i * i)),(1 + (x div 2)),(x mod 2))
A215147: 1 2 5 6 14 15 30 31 55 56 91 92 140 141 204 205
(loop(\(x,i).2x,x,(1 + (x mod 2))) - (x mod 2))
A285475: 1 3 4 15 16 63 64 255 256 1023 1024 4095 4096 16383 16384 65535
(loop(\(x,i).(4x + ~1),x,1) - (x mod 2))
A140322: 1 2 11 42 171 682 2731 10922 43691 174762 699051 2796202 11184811 44739242 178956971 715827882
(loop(\(x,i).(3x + 1),x,1) + (x mod 2))
A164907: 1 5 13 41 121 365 1093 3281 9841 29525 88573 265721 797161 2391485 7174453 21523361
(loop(\(x,i).(3x + ~1),x,1) + (x mod 2))
A103425: 1 3 5 15 41 123 365 1095 3281 9843 29525 88575 265721 797163 2391485 7174455
(loop(\(x,i).(3x + ~1),x,1) - (x mod 2))
A046717: 1 1 5 13 41 121 365 1093 3281 9841 29525 88573 265721 797161 2391485 7174453
loop(\(x,i).(~2x + (i mod 2)),(x + ~1),(x mod 2))
A136324: 0 1 1 2 5 6 21 22 85 86 341 342 1365 1366 5461 5462
((if (4 mod (x + 1)) <= 0 then 0 else 2) + (x mod 2))
A321861: 0 1 2 1 2 3 2 3 2 3 2 3 2 3 2 3
((if (~2 + (x div 3)) <= 0 then 1 else 2) - (x mod 2))
A025823: 1 0 1 0 1 0 1 0 1 1 2 1 2 1 2 1
((if (~4 + (x div 2)) <= 0 then 1 else 2) - (x mod 2))
A025826: 1 0 1 0 1 0 1 0 1 0 2 1 2 1 2 1
(if ((x + 1) mod 8) <= 0 then 2 else (x mod 2))
A244415: 0 1 0 1 0 1 0 2 0 1 0 1 0 1 0 2
(if x <= 0 then 1 else ((~2 + (x mod 4)) * (x mod 2)))
A163805: 1 ~1 0 1 0 ~1 0 1 0 ~1 0 1 0 ~1 0 1
(if x <= 0 then 1 else ((2 - (x mod 4)) * (x mod 2)))
A117569: 1 1 0 ~1 0 1 0 ~1 0 1 0 ~1 0 1 0 ~1
loop(\(x,i).4x,(x div 2),(2 - (x mod 2)))
A135520: 2 1 8 4 32 16 128 64 512 256 2048 1024 8192 4096 32768 16384
loop(\(x,i).(x * ((1 + i) div 2)),x,(2 - (x mod 2)))
A092186: 2 1 2 2 8 12 72 144 1152 2880 28800 86400 1036800 3628800 50803200 203212800
((if x <= 0 then 2 else x3) div (2 - (x mod 2)))
A129204: 1 1 4 27 32 125 108 343 256 729 500 1331 864 2197 1372 3375
(loop(\(x,i).(2x2 + 4x),x,2) + (x mod 2))
A007759: 2 17 576 665857 886731088896 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),(x + ~1),(2x - (x mod 2)))
A335873: 0 1 4 10 48 216 1440 9360 80640 685440 7257600 76204800 958003200 11975040000 174356582400 2528170444800
loop(\(x,i).(4x + 2),(x div 2),(x mod 2))
A061547: 0 1 2 6 10 26 42 106 170 426 682 1706 2730 6826 10922 27306
loop(\(x,i).(3x + 2),(x div 2),(x mod 2))
A192225: 0 1 2 5
A062318: 0 1 2 5 8 17 26 53 80 161 242 485 728 1457 2186 4373
loop(\(x,i).(~x + 1),(x div 2),(~x * (x mod 2)))
A309215: 0 ~1 1 4 0 ~5 1 8 0 ~9 1 12 0 ~13 1 16
(1 - loop(\(x,i).(~4x + 2),x,(x mod 2)))
A113870: 1 3 7 39 103 615 1639 9831 26215 157287 419431 2516583 6710887 40265319 107374183 644245095
((x mod 2) - loop(\(x,i).(~2x + 2),x,(x mod 2)))
A193652: 0 1 2 3 10 11 42 43 170 171 682 683 2730 2731 10922 10923
loop(\(x,i).11x,x,2)
A334603: 2 22 242 2662 29282 322102 3543122 38974342 428717762 4715895382 51874849202 570623341222 6276856753442 69045424287862 759499667166482 8354496338831302
loop(\(x,i).(x * (x mod 9)),x,2)
A110365: 2 4 16 112 448 3136 12544 87808 351232 2458624 9834496 68841472 275365888 1927561216 7710244864 53971714048
loop(\(x,i).(7x + 6),x,2)
A198647: 2 20 146 1028 7202 50420 352946 2470628 17294402 121060820 847425746 5931980228 41523861602 290667031220 2034669218546 14242684529828
loop(\(x,i).(x + ((x + 2) div (1 + (i mod 2)))),x,2)
A117862: 2 4 10 16 34 52 106 160 322 484 970 1456 2914 4372 8746 13120
((if (x mod 2) <= 0 then 1 else x) - ((~x2 + x) div 2))
A128918: 1 1 2 6 7 15 16 28 29 45 46 66 67 91 92 120
(2 * (x + loop(\(x,i).4x,(x + ~1),x)))
A229135: 0 4 20 102 520 2570 12300 57358 262160 1179666 5242900 23068694 100663320 436207642 1879048220 8053063710
((x + loop(\(x,i).3x,(x + ~1),x)) div 2)
A082133: 0 1 4 15 56 205 732 2555 8752 29529 98420 324775 1062888 3454373 11160268 35872275
loop(\(x,i).(x + ((1 + i) * i * (1 + i))),x,2)
A087645: 2 6 24 72 172 352 646 1094 1742 2642 3852 5436 7464 10012 13162 17002
loop(\(x,i).(x * (2 + ((1 + i) mod 3))),x,2)
A076508: 2 8 16 48 192 384 1152 4608 9216 27648 110592 221184 663552 2654208 5308416 15925248
(loop(\(x,i).(2 + ((x + 1) * (x div 2))),x,x) div 2)
A051832: 0 1 7 133
((x + loop(\(x,i).3x,(x + ~2),x)) div 2)
A229472: 0 1 2 6 20 70 246 854 2920 9846 32810 108262 354300 1151462 3720094 11957430
((~x2 + loop(\(x,i).(2x + i),x,0)) div 2)
A002662: 0 0 0 1 5 16 42 99 219 466 968 1981 4017 8100 16278 32647
((x2 + (x div (if (x + ~2) <= 0 then 1 else 2))) div 2)
A118026: 0 1 3 5 9 13 19 26 34 42 52 63 75 87 101 116
(loop(\(x,i).(x * ((x + ~1) + i)),2,x2) div 2)
A071231: 0 1 136 3321 32896 195625 840456 2883601 8390656 21526641 50005000 107186761 215001216 407879641 737913736 1281470625
((~x2 + loop(\(x,i).(2x + i),x,2)) div 2)
A084634: 1 2 4 9 21 48 106 227 475 978 1992 4029 8113 16292 32662 65415
loop(\(x,i).(1 + (x2 div 2)),x,(x2 + 2))
A124275: 2 5 181
(2x2 + (if (x + ~2) <= 0 then 1 else ~x))
A056287: 1 3 9 15 28
((if (x mod 4) <= 0 then x else 2) + (x2 div 2))
A161337: 0 2 4 6 12 14 20 26
((x2 + loop(\(x,i).x3,2,x)) div 2)
A168125: 0 1 258 9846 131080 976575 5038866 20176828 67108896 193710285 500000050 1178973906 2579890248 5302249771 10330523490 19221679800
((x2 + loop(\(x,i).x2,2,x2)) div 2)
A168124: 0 1 130 3285 32776 195325 839826 2882425 8388640 21523401 50000050 107179501 214990920 407865445 737894626 1281445425
((x * (x + loop(\(x,i).x3,2,x))) div 2)
A168126: 0 1 514 29529 524296 4882825 30233106 141237649 536870944 1743392241 5000000050 12968712361 30958682184 68929246009 144627327586 288325195425
(x + (if (x + ~10) <= 0 then 1 else 0))
A178787-A072778: 1 2 3 4 5 6 7 8 9 10 11 11 12 13 14 15
(if ((x + 2) mod 9) <= 0 then 0 else x)
A004182: 0 1 2 3 4 5 6 0 8 9 10 11 12 13 14 15
(~x + (if (x mod 2) <= 0 then (2x + 5) else 0))
A158552: 5 ~1 7 ~3 9 ~5 11 ~7 13 ~9 15 ~11 17 ~13 19 ~15
(x + (if (x mod 2) <= 0 then 6x else 0))
A317314: 0 1 14 3 28 5 42 7 56 9 70 11 84 13 98 15
(x + (if (x mod 2) <= 0 then 8x else 0))
A317318: 0 1 18 3 36 5 54 7 72 9 90 11 108 13 126 15
(x + (if ((x div 4) mod 2) <= 0 then 4 else 0))
A244586: 4 5 6 7 4 5 6 7 12 13 14 15 12 13 14 15
(x * loop(\(x,i).((x + 1) * (1 + i)),(x + ~2),0))
A038157: 0 0 0 6 36 200 1230 8652 69272 623520 6235290 68588300 823059732 10699776672 149796873590 2246953104060
(x + loop(\(x,i).((2x + 4) + i),(x + ~2),0))
A296954: 0 1 2 8 20 44 92 188 380 764 1532 3068 6140 12284 24572 49148
(x + (if (x mod 2) <= 0 then (2x + (x div 2)) else 0))
A195159: 0 1 7 3 14 5 21 7 28 9 35 11 42 13 49 15
(x * loop(\(x,i).(~1 + (2 * (x + (i mod 2)))),x,0))
A093835: 0 1 2 9 20 55 126 301 680 1539 3410 7513 16380 35503 76454 163845
(x * loop(\(x,i).(x - ((i * i) div ~2)),x,0))
A325517: 0 1 6 24 64 145 282 504 832 1305 1950 2816 3936 5369 7154 9360
(x * loop(\(x,i).(x + (i * i) - (i div 2)),x,0))
A325656: 0 1 8 36 104 245 492 896 1504 2385 3600 5236 7368 10101 13524 17760
(x * loop(\(x,i).(x + ((i div 2) * (i div 2))),x,0))
A289161: 0 0 2 6 24 50 114 196 352 540 850 1210 1752 2366 3234 4200
(~x + loop(\(x,i).((x mod (~1 + (2 * i))) + i),x,0))
A091068: 0 0 1 3 6 1 6 12 4 12 2 12 0 12 25 10
(x + loop(\(x,i).i,(~1 + ((x + ~2) div 3)),1))
A317468-A064683: 1 2 3 4 5 6 7 8 9 10 11 13 14 15 17 18
(x + loop(\(x,i).i,(~1 + (((x + 1) div 2) div 2)),1))
A338973-A191328: 1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 18
(if ((x + ~1) mod 9) <= 0 then 1 else x)
A103303: 0 1 2 3 4 5 6 7 8 9
A004185: 0 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15
(x + loop(\(x,i).i,(x + ~9),1))
A033063-A032961-A008729: 1 2 3 4 5 6 7 8 9 10 11 13 15 17 19 21
(x + loop(\(x,i).i,((x + 1) div 5),1))
A253643-A052044: 1 2 3 4 5 6 7 8 9 11 12 13 14 15 17 18
(if ((x + ~1) mod 12) <= 0 then 1 else x)
A103303: 0 1 2 3 4 5 6 7 8 9
A106614: 0 1 2 3 4 5 6 7 8 9 10 11 12 1 14 15
(x * (if (x mod 2) <= 0 then 12 else 1))
A317324: 0 1 24 3 48 5 72 7 96 9 120 11 144 13 168 15
(1 div (if (x mod 12) <= 0 then 1 else x))
A256434: 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0
(x + loop(\(x,i).(2 + i),((x + ~2) div 3),1))
A260113: 1 2 3 4 5 8 9 10 12 13 14 16 17 18 20 21
(x + (if (~x + 4) <= 0 then (x mod 3) else 1))
A318936-A088750: 1 2 3 4 5 7 6 8 10 9 11 13 12 14 16 15
(x + loop(\(x,i).(2 + (x * i)),(x mod 3),1))
A121512: 1 4 10 4 7 13 7 10 16 10 13 19 13 16 22 16
(if x <= 0 then 1 else (x3 + 3x2 + 3x))
A135300: 1 7 26 63 124 215 342 511 728 999 1330 1727 2196 2743 3374 4095
(x + loop(\(x,i).((2x + 2) + i),(x + ~1),1))
A154117: 1 2 7 17 37 77 157 317 637 1277 2557 5117 10237 20477 40957 81917
(x + ((~x + 1) mod loop(\(x,i).2x,(x + ~1),1)))
A127904: 0 1 3 5 9 17 33 65 129 257 513 1025 2049 4097 8193 16385
(x + loop(\(x,i).(x + (2 * (x + i))),(x + ~1),1))
A060816: 1 2 7 22 67 202 607 1822 5467 16402 49207 147622 442867 1328602 3985807 11957422
(x + (if (~x + 2) <= 0 then (x3 + ~x2) else 1))
A228398: 1 2 6 21 52 105 186 301 456 657 910 1221 1596 2041 2562 3165
(x + loop(\(x,i).((2x + 4) + i),(x + ~1),1))
A154118: 1 2 9 23 51 107 219 443 891 1787 3579 7163 14331 28667 57339 114683
(x * (if (x mod 2) <= 0 then 10 else 1))
A317320: 0 1 20 3 40 5 60 7 80 9 100 11 120 13 140 15
(x + loop(\(x,i).i,(x + ~10),1))
A290492: 1 2 3 4 5 6 7 8 9 10 11 12 14
A294358-A262358-A246074-A033064-A032962-A008730: 1 2 3 4 5 6 7 8 9 10 11 12 14 16 18 20
(if x <= 0 then 1 else (2x3 + 3x))
A288534: 1 5 22 63 140 265 450 707 1048 1485 2030 2695 3492 4433 5530 6795
(x + (if (~2 + (x div 5)) <= 0 then 2 else 1))
A159062: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 16
(x + loop(\(x,i).(2 * i),(((x + ~1) div 2) div 2),1))
A230999: 1 2 3 4 5 7 8 9 10 13 14 15 16 19 20 21
(if x <= 0 then 1 else 17x)
A048843: 1 17 34 51 68 85 102 119 136 153 170 187 204 221 238 255
loop(\(x,i).(2 - i),(x + ~9),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A225693: 0 1 2 3 4 5 6 7 8 9 1 0 ~1 ~2 ~3 ~4
loop(\(x,i).(i * i),(x + ~9),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A113018-A113009-A112875: 0 1 2 3 4 5 6 7 8 9 1 4 9 16 25 36
(1 div (if (x mod (2 + (x mod 4))) <= 0 then 1 else x))
A064391: 1 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1
(1 mod (if (x mod (2 + (x mod 4))) <= 0 then 1 else x))
A165560: 0 0 1 1 0 1 1 1 0 0 1 1 0 1 1 0
(1 div (if (x mod (4 + (x div 2))) <= 0 then 1 else x))
A291748-A281084-A279280: 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0
(1 div (if (x mod (4 + (x mod 2))) <= 0 then 1 else x))
A178725: 1 1 0 0 1 1 0 0 1 0 0 0 1 0 0 1
loop(\(x,i).(x + i),((x + ~1) div 5),x)
A067570: 0 1 2 3 4 5 7
A004764: 0 1 2 3 4 5 7 8 9 10 11 14 15 16 17 18
loop(\(x,i).(x2 div (x + 2)),5,x)
A340184: 0 0 0 0 0 0 0 0 0 0 1 1 2 3 4 5
loop(\(x,i).x2,3,5x)
A016856: 0 390625 100000000 2562890625 25600000000 152587890625 656100000000 2251875390625 6553600000000 16815125390625 39062500000000 83733937890625 167961600000000 318644812890625 576480100000000 1001129150390625
loop(\(x,i).x3,1,5x)
A016851: 0 125 1000 3375 8000 15625 27000 42875 64000 91125 125000 166375 216000 274625 343000 421875
loop(\(x,i).x3,2,5x)
A016857: 0 1953125 1000000000 38443359375 512000000000 3814697265625 19683000000000 78815638671875 262144000000000 756680642578125 1953125000000000 4605366583984375 10077696000000000 20711912837890625
(x + (if (~x + 4) <= 0 then (2x + ~4) else 1))
A275646: 1 2 3 4 8 11
(1 mod (if (x mod (4 - (x mod 2))) <= 0 then 1 else x))
A059125: 0 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0
(x * loop(\(x,i).(x2 + ~2),3,3))
A004971-A004951: 0 2207 4414 6621 8828 11035 13242 15449 17656 19863 22070 24277 26484 28691 30898 33105
(x * ((1 + loop(\(x,i).2x,x,2)) div 3))
A193449: 0 1 6 15 44 105 258 595 1368 3069 6830 15015 32772 70993 152922 327675
(if (x mod 2) <= 0 then (6x + 3) else x)
A261671: 3 1 15 3 27 5 39 7 51 9 63 11 75 13 87 15
loop(\(x,i).((x * (x + i)) div (1 + i)),3,x)
A061319: 0 1 10 76 430 1870 6601 19810 52326 124785 273790 560626 1083160 1991626 3509065 5957260
loop(\(x,i).(x + i),(((x + ~1) div 2) div 3),x)
A337582-A031992-A023749-A022556-A004828-A004765-A003726: 0 1 2 3 4 5 6 8 9 10 11 12 13 16 17 18
loop(\(x,i).(2 * i),(x + ~12),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A043272: 0 1 2 3 4 5 6 7 8 9 10 11 12 2 4 6
loop(\(x,i).(2 * (x + (2 * (x + i)))),3,x)
A154518: 204 420 636 852 1068 1284 1500 1716 1932 2148 2364 2580 2796 3012 3228 3444
loop(\(x,i).(4 + i),((x div 2) div 3),x)
A194259: 0 1 2 3 4 5 5 5 5 5 5 5 6 6 6 6
(x + (if (x mod 2) <= 0 then x else ((~x + 1) div 3)))
A198473-A026185: 0 1 4 2 8 3 12 5 16 6 20 7 24 9 28 10
loop(\(x,i).(x + ((x + 1) * (i * i))),3,x)
A044812: 99 199 299 399 499 599 699 799 899 999 1099 1199 1299 1399 1499 1599
loop(\(x,i).(x + ((x div 2) div (1 + i))),3,x)
A201804: 0 1 2 3 5 7 9 10 12 13 15 16 19 20 21 23
(if (x mod 2) <= 0 then (3 * (x + (x div 2))) else x)
A195312: 0 1 9 3 18 5 27 7 36 9 45 11 54 13 63 15
(x2 div (x + (if x <= 0 then 1 else (x div 3))))
A265133-A064506: 0 1 2 2 3 4 4 5 6 6 7 8 9 9 10 11
(x * loop(\(x,i).(1 + (x * (1 + i))),(x + ~2),1))
A296964: 0 1 2 9 40 205 1236 8659 69280 623529 6235300 68588311 823059744 10699776685 149796873604 2246953104075
(x + (if ((x + 1) mod 4) <= 0 then (x + ~2) else 1))
A222259: 1 2 3 4 5 6 7 12 9 10 11 20 13 14 15 28
(x * loop(\(x,i).(2 + (x * (1 + i))),(x + ~2),1))
A296944: 0 1 2 12 56 290 1752 12278 98240 884178 8841800 97259822 1167117888 15172532570 212415456008 3186231840150
(x * (1 + loop(\(x,i).(x * (x - i)),2,(x + ~2))))
A001095: 0 1 2 3 4 125 726 2527 6728 15129 30250 55451 95052 154453 240254 360375
(x * (1 + loop(\(x,i).(x2 + ~1),2,2x)))
A069073: 0 9 450 3675 15876 49005 122694 266175 520200 938961 1592010 2566179 3967500 5923125 8583246 12123015
(x + (if ((x + 2) mod 4) <= 0 then (x div 2) else 1))
A279407-A068384: 1 2 3 4 5 6 9 8
(~x + loop(\(x,i).(x + (x div 2)),2,(1 + (x div 2))))
A274009: 1 0 2 1 2 1 3 2 2 1 3 2 3 2 4 3
(~x + ((if x <= 0 then 1 else 4) * (1 + (x mod 2))))
A113959: 1 7 2 5
(((x2 + x) div 2) + (if (x mod 2) <= 0 then 1 else x))
A266257: 1 2 4 9 11 20 22 35 37 54 56 77 79 104 106 135
loop(\(x,i).(x4 + 1),x,(~x + 1))
A246649: 1 1 17 4611686018427387903 4611686018427387903
loop(\(x,i).(2x * (~1 + (2 * i))),x,(~x + 1))
A119837: 1 0 ~12 ~240 ~5040 ~120960 ~3326400 ~103783680 ~3632428800 ~141145804800 ~6033983155200 ~281585880576000 ~14248245557145600 ~777177030389760000 4611686018427387903 4611686018427387903
(~x + loop(\(x,i).12x,x,1))
A024141: 1 11 142 1725 20732 248827 2985978 35831801 429981688 5159780343 61917364214 743008370677 8916100448244 106993205379059 1283918464548850 15407021574586353
(x + (if ((x + ~1) mod 8) <= 0 then x else 1))
A199343: 1 2 3 4 5 6 7 8 9 18 11 12 13 14 15 16
(x + loop(\(x,i).(2 + (x * i) - (i div 2)),x,1))
A220444: 1 4 9 25 92
(x + loop(\(x,i).10x,x,1))
A081552: 1 11 102 1003 10004 100005 1000006 10000007 100000008 1000000009 10000000010 100000000011 1000000000012 10000000000013 100000000000014 1000000000000015
(~x + loop(\(x,i).10x,x,1))
A024115: 1 9 98 997 9996 99995 999994 9999993 99999992 999999991 9999999990 99999999989 999999999988 9999999999987 99999999999986 999999999999985
((~x + ~2) mod (~x + loop(\(x,i).2x,x,1)))
A052515: 0 0 0 0 6 20 50 112 238 492 1002 2024 4070 8164 16354 32736
(~x + loop(\(x,i).((x2 + x) - (i mod 2)),x,1))
A141415: 1 0 0 2 26
(1 div loop(\(x,i).(~x2 + x + 1),(x + 1),x))
A071759: 1 1 ~1 ~1 ~1 4611686018427387903 4611686018427387903
loop(\(x,i).(x4 + 1),(x + 1),x)
A128398: 1 17 4611686018427387903
loop(\(x,i).x2,1,(5x + 4))
A016898: 16 81 196 361 576 841 1156 1521 1936 2401 2916 3481 4096 4761 5476 6241
loop(\(x,i).x2,2,(5x + 4))
A016900: 256 6561 38416 130321 331776 707281 1336336 2313441 3748096 5764801 8503056 12117361 16777216 22667121 29986576 38950081
(x + loop(\(x,i).(x * (1 + i)),4,(x + 1)))
A158130: 120 241 362 483 604 725 846 967 1088 1209 1330 1451 1572 1693 1814 1935
(x + loop(\(x,i).(x * (2 + i)),4,(x + 1)))
A158308: 360 721 1082 1443 1804 2165 2526 2887 3248 3609 3970 4331 4692 5053 5414 5775
(x + loop(\(x,i).((x2 + ~x) div 2),2,(x + 1)))
A176145: 0 1 5 18 49 110 216 385 638 999 1495 2156 3015 4108 5474 7155
(~x + ((x + 1) * loop(\(x,i).(2x + i),x,2)))
A288958: 2 9 34 105 286 721 1730 4017 9118 20361 44914 98137 212798 458529 982786 2096865
loop(\(x,i).(x3 + ~x),1,(x2 + x))
A120436: 0 6 210
((~x2 + ~x) + loop(\(x,i).x2,2,(x + 2)))
A269584: 16 79 250 613 1276 2371 4054 6505 9928 14551 20626 28429 38260 50443 65326 83281
loop(\(x,i).(5x + 4),(x + 1),x)
A064751: 4 49 374 2499 15624 93749 546874 3124999 17578124 97656249 537109374 2929687499 15869140624 85449218749 457763671874 2441406249999
loop(\(x,i).(x + (((1 + i) * i) div 2)),(x + 1),x)
A341209: 1 5 12 23 39 61 90 127 173 229 296 375 467 573 694 831
loop(\(x,i).(1 + (i div (2x + 1))),(x + ~1),x)
A307707: 0 1 1 1 2 1 2 2 2 2 2 3 2 3 2 3
loop(\(x,i).12x,(x + ~1),x)
A081128: 0 1 24 432 6912 103680 1492992 20901888 286654464 3869835264 51597803520 681091006464 8916100448256 115909305827328 1497904875307008 19258776968232960
loop(\(x,i).(2x * (3 + i)),(x + ~1),x)
A058667: 0 1 16 240 3840 67200 1290240 27095040 619315200 15328051200 408748032000 11690193715200 357082280755200 11605174124544000 399932154445824000 4611686018427387903
((8 mod (x + 1)) div (if x <= 0 then 1 else x))
A275451-A086074: 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
((x mod 10) mod (if x <= 0 then 1 else x))
A343608-A330633-A257850-A257297-A218530-A217657-A207505-A171765-A143289-A088117-A056967-A037887-A037851-A035930: 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5
(((x + ((x div 2) mod 2)) div 2) + (if x <= 0 then 1 else x))
A301729: 1 1 3 5 6 7 9 11 12 13 15 17 18 19 21 23
(x + loop(\(x,i).7x,x,1))
A226199: 1 8 51 346 2405 16812 117655 823550 5764809 40353616 282475259 1977326754 13841287213 96889010420 678223072863 4747561509958
(~x + loop(\(x,i).7x,x,1))
A024076: 1 6 47 340 2397 16802 117643 823536 5764793 40353598 282475239 1977326732 13841287189 96889010394 678223072835 4747561509928
loop(\(x,i).(x + (i * i)),x,(x3 + ~x))
A007585: 0 1 11 38 90 175 301 476 708 1005 1375 1826 2366 3003 3745 4600
(x + (if (x + ~12) <= 0 then 1 else 2))
A298534-A291442-A285356-A272477-A122526-A114886-A095392-A026495-A022772-A004440-A004437: 1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17
(x + (if (x + ~10) <= 0 then 1 else 2))
A342526-A342522-A338190-A334969-A325778-A325397-A325369-A325361-A325328-A322547-A321292-A318536-A317710-A317101-A316529-A316521-A304678-A304449-A303554-A299702-A289812-A285100-A283550-A271113-A263837-A255724-A242414-A236510-A206551-A168186-A160453-A131881-A098240-A085924-A085156-A072774-A065200-A053460-A048991-A035332: 1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 17
(x + loop(\(x,i).i,(x + ~7),2))
A122638: 2 3 4 5 6 7 8 9 9 11 13 15 17 19 21 23
(x + (x mod (if (~4 + (x div 2)) <= 0 then 1 else 2)))
A103303: 0 1 2 3 4 5 6 7 8 9
A228723: 0 1 2 3 4 5 6 7 8 9 10 12 12 14 14 16
loop(\(x,i).(x + ~2),(x + ~10),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A334387-A287796: 0 1 2 3 4 5 6 7 8 9 10 9 8 7 6 5
loop(\(x,i).(1 + (x2 div (x + 4))),2,x)
A116572: 1 1 1 1 2 2 3 3 4 5 6 7 8 8 9 10
loop(\(x,i).(x + i),(~2 + ((x + ~2) div 3)),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A247814: 0 1 2 3 4 5 6 7 8 9 10 12 13 14 17 18
(x + (if (x + ~4) <= 0 then 1 else 6))
A316538: 1 2 3 4 5 11 12 13 14 15 16 17 18 19 20 21
loop(\(x,i).(3x + 2),6,x)
A158395: 728 1457 2186 2915 3644 4373 5102 5831 6560 7289 8018 8747 9476 10205 10934 11663
(~x + (loop(\(x,i).(2 * (x + i)),x,3) div 2))
A026624: 1 3 8 20 46 100 210 432 878 1772 3562 7144 14310 28644 57314 114656
(if x <= 0 then 1 else (x * (2 + (x2 mod 3))))
A066393: 1 3 6 6 12 15 12 21 24 18 30 33 24 39 42 30
(x - loop(\(x,i).(x - (x mod (3 + i))),2,x))
A066323: 0 1 2 3 4 5 6 7 3 4 5 6 2 3 4 5
loop(\(x,i).(1 + ((x2 + 2x) div (2 + i))),2,x)
A151521: 1 3 4 13 25
loop(\(x,i).(x2 + 5x + 1),2,x)
A058795: 7 85 301 751 1555 2857 4825 7651 11551 16765 23557 32215 43051 56401 72625 92107
(x * (loop(\(x,i).(2x - (i mod 2)),x,1) div 2))
A099429: 0 0 2 3 12 25 66 147 344 765 1710 3751 8196 17745 38234 81915
loop(\(x,i).(12 div (x + 1)),2,x)
A265533: 0 1 2 3 4 4 6 6 6 6 6 6 12 12 12 12
(x * loop(\(x,i).x3,1,(2x + 2)))
A188785: 0 64 432 1536 4000 8640 16464 28672 46656 72000 106480 152064 210912 285376 378000 491520
loop(\(x,i).(3x + 2),(2x + 2),x)
A064755: 8 161 2186 26243 295244 3188645 33480782 344373767 3486784400 34867844009 345191655698 3389154437771 33044255768276 320275094369453 3088366981419734 29648323021629455
(x + ((loop(\(x,i).(x * i),x,x) mod (x + 1)) mod 2))
A113637: 0 2 3 3 5 5 7 7 8 9 11 11 13 13 14 15
loop(\(x,i).(x2 div 3),((x + ~1) div 2),x)
A291673: 0 1 2 3 5 21
loop(\(x,i).((x * ((x + 2) + i)) div (1 + i)),2,x)
A014629: 0 4 15 39 84 160 279 455 704 1044 1495 2079 2820 3744 4879 6255
(x + (2 mod ((if x <= 0 then 1 else x) div ~4)))
A252373: 0 1 2 3 4 5 6 7 8 8 9 10 11 11 12 13
(if ((x + ~2) mod 10) <= 0 then 2 else x)
A103303: 0 1 2 3 4 5 6 7 8 9
A333921: 0 1 2 3 4 5 6 7 8 9 10 11 2 13 14 15
(x + ((if (x + ~2) <= 0 then 2 else ((x + 1) div 2)) div 2))
A082463: 1 2 3 4 5 6 7 9 10
A187226: 1 2 3 4 5 6 7 9 10 11 12 14 15 16 17 19
loop(\(x,i).(((x + ~1) * ((x div 2) mod 2)) div 2),2,x)
A292256: 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 3
(x * loop(\(x,i).(1 + ((x2 + 2x) * i)),2,2))
A004946-A004926: 0 199 398 597 796 995 1194 1393 1592 1791 1990 2189 2388 2587 2786 2985
(x * (~2 + loop(\(x,i).(x2 + 4x + 4),2,2)))
A004967-A004947: 0 322 644 966 1288 1610 1932 2254 2576 2898 3220 3542 3864 4186 4508 4830
(x * loop(\(x,i).(4x + 2),4,2))
A200860: 0 682 1364 2046 2728 3410 4092 4774 5456 6138 6820 7502 8184 8866 9548 10230
((x mod 3) div (if (x mod 4) <= 0 then 2 else x))
A342000: 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0
loop(\(x,i).(4x2 + ~3x),2,x)
A264895: 0 1 370 2835 10660 28645 63126 121975 214600 351945 546490 812251 1164780 1621165 2200030 2921535
loop(\(x,i).(10x + 4),2,x)
A102438: 44 144 244 344 444 544 644 744 844 944 1044 1144 1244 1344 1444 1544
(x - loop(\(x,i).(~2 + ((x2 + x) div 2)),2,x))
A110426: 1 3 3 ~5 ~30 ~84 ~182 ~342 ~585 ~935 ~1419 ~2067 ~2912 ~3990 ~5340 ~7004
(x - loop(\(x,i).((~x2 + ~x + 2) div 2),2,x))
A086602: 0 0 2 12 39 95 195 357 602 954 1440 2090 2937 4017 5369 7035
loop(\(x,i).(2 + ((x * (x - i)) div (x + 2))),2,x)
A173777: 2 2 2 2 3 3 4 5 5 6 7 8 9 10 11 12
(x + loop(\(x,i).(2x + i),(2 * (x div 2)),2))
A281500: 2 3 14 15 62 63 254 255 1022 1023 4094 4095 16382 16383 65534 65535
(x - loop(\(x,i).(((x * i) + (x div 2)) div 2),2,x))
A334440: 0 1 1 1 1 2 1 1 1 2 2 1 1 2 2 2
loop(\(x,i).(x + i - (x div (2 * (2 + i)))),2,x)
A154660: 3 4 5 6 7 8
A196033: 3 4 5 6 7 8 8 9 9 10 11 12 12 13 14 15
(x + (if (~2 + (x div 3)) <= 0 then 1 else 4))
A092598-A032973: 1 2 3 4 5 6 7 8 9 13 14 15 16 17 18 19
loop(\(x,i).(1 + ((x + 3) * i)),4,x)
A126979: 233 257 281 305 329 353 377 401 425 449 473 497 521 545 569 593
loop(\(x,i).((x * (x + i)) div (1 + i)),4,x)
A061321: 0 1 28 1216 37324 700876 8719921 78503068 547643916 3114359073 14992411852 62860750876 234647983648 793316418076
(x * (4 + (if (x + ~2) <= 0 then 3 else x)))
A164005: 0 7 14 21 32 45 60 77 96 117 140 165 192 221 252 285
loop(\(x,i).(5x + 4),4,x)
A158374: 624 1249 1874 2499 3124 3749 4374 4999 5624 6249 6874 7499 8124 8749 9374 9999
(~x + (4 * loop(\(x,i).(x2 + x),2,x)))
A248698: 0 23 166 621 1676 3715 7218 12761 21016 32751 48830 70213 97956 133211 177226 231345
(x + loop(\(x,i).5x,x,4))
A113022: 4 21 102 503 2504 12505 62506 312507 1562508 7812509 39062510 195312511 976562512 4882812513 24414062514 122070312515
loop(\(x,i).(x - ((~x2 * i) div 2)),2,x)
A235367: 0 6 20 72 156 342 600 1056 1640 2550 3660 5256 7140 9702 12656 16512
loop(\(x,i).((3x2 + ~x) div 2),2,x)
A232713: 0 1 35 210 715 1820 3876 7315 12650 20475 31465 46376 66045 91390 123410 163185
loop(\(x,i).(12 div (x + 2)),2,x)
A070319-A068509-A057142: 1 2 2 3 3 4 4 4 4 4 4 6 6 6 6 6
loop(\(x,i).(10 div (x + 2)),2,x)
A048689: 1 2 2 2 3 3 3 3 3 5 5 5 5 5 5 5
((2x mod 3) mod (if (x mod 2) <= 0 then 2 else x))
A056560: 0 0 1 0 0 1 0 2 1 0 0 1 0 2 1 0
(~x + (2 * (2 + loop(\(x,i).(2x + i),x,x))))
A291064: 4 9 26 71 180 433 1006 2283 5096 11237 24546 53215 114652 245721 524246 1114067
(x + (loop(\(x,i).((x * (x - i)) + i),x,2) div 2))
A271553: 1 2 4 9 64
loop(\(x,i).(x + ((x div 2) div (3 + i))),2,x)
A084689: 0 1 2 3 4 5 6 7 9
A039270-A039208: 0 1 2 3 4 5 6 7 9 11 12 13 14 15 16 17
(x + loop(\(x,i).((~1 + (x * i)) * (1 + i)),x,2))
A300898: 2 3 11 107
loop(\(x,i).(x + ((2 + (x div 2)) div (1 + i))),2,x)
A187911: 1 3 4 5 7 8 10 11 13 14 15 17 19 20 21 22
loop(\(x,i).(x + (x div ((2 + i) * (1 + i)))),2,x)
A067570: 0 1 2 3 4 5 7
A218444-A172152: 0 1 2 3 4 5 7 8 9 10 11 13 15 16 17 18
(x - loop(\(x,i).(~x + ((x - i) div 4)),2,x))
A344497: 0 1 1 2 2 3 3 3 4 5 5 5 5 6 7 7
loop(\(x,i).(~x - (x div (4 + i))),2,x)
A047363: 0 2 3 4 5 7 9 10 11 12 14 16 17 18 19 21
loop(\(x,i).(x + (x div (2 + (i + (x div 2))))),2,x)
A333841-A231236: 0 1 2 3 4 6 8 9 10 11 12 13 14 15 16 17
(x + loop(\(x,i).((x + 2) + ((i div 2) * i)),x,2))
A027613: 2 5 10 16 27 40
loop(\(x,i).(x + (2 * (4x + i))),2,x)
A156795: 22 103 184 265 346 427 508 589 670 751 832 913 994 1075 1156 1237
compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)
A268174: 1 3 5 9 11 15 17 21 27 29 35 39 41 45 51 57
compr(\x.(loop(\(x,i).(x * i),(x div 2),1) mod (x + 2)),x)
A061837: 10 13 14 16 18 19 22 23 25 26 28 30 31 33 34 37
compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)
A249426-A040976: 0 1 3 5 9 11 15 17 21 27 29 35 39 41 45 51
loop(\(x,i).(x2 div (1 + (x mod 2))),(x + ~2),x)
A271551: 0 1 2 4 256
loop(\(x,i).(2x + 3),x,(x2 + ~2x))
A036826: 0 1 9 45 173 573 1725 4861 13053 33789 84989 208893 503805 1196029 2801661 6488061
(x * loop(\(x,i).4x2,2,2x))
A016805: 0 1024 32768 248832 1048576 3200000 7962624 17210368 33554432 60466176 102400000 164916224 254803968 380204032 550731776 777600000
(x + loop(\(x,i).(1 + (x * i)),4,2x))
A044179: 41 90 139 188 237 286 335 384 433 482 531 580 629 678 727 776
(x * loop(\(x,i).(~2 + (x2 * i)),2,2x))
A242850: 0 6 780 6930 30744 96030 241956 526890 1032240 1866294 3168060 5111106 7907400 11811150 17122644 24192090
compr(\x.loop(\(x,i).((~x + 1) div 2),(x div 2),2x),x)
A335033: 0 2 3 6 7 10 11 14 15 16 17 18 19 20 21 22
loop(\(x,i).(x2 mod 5),(x div 2),x)
A185057: 0 1 4 4 1 0 1 1 1 1 0 1 1 1 1 0
(x + (if (~2 + (x div 2)) <= 0 then 3 else (x div 2)))
A154660: 3 4 5 6 7 8
A299532: 3 4 5 6 7 8 9 10 12 13 15 16 18 19 21 22
(x + (if (x mod 2) <= 0 then 1 else ((x div 2) * (x div 2))))
A079097: 1 1 3 4 5 9 7 16 9 25 11 36 13 49 15 64
loop(\(x,i).(2x - (x mod 2)),2,(x + (x div 2)))
A151973: 0 1 9 16 24 25 33 40 48 49 57 64 72 73 81 88
(if x <= 0 then 1 else (x * ((x2 + 2x) - (x div 2))))
A104905: 1 3 14 42
loop(\(x,i).(~x + ~1),(x div 2),(x * (x mod 2)))
A309214: 0 1 ~1 ~4 0 5 ~1 ~8 0 9 ~1 ~12 0 13 ~1 ~16
(((~1 + (x div 2)) div 3) mod (if x <= 0 then 2 else x))
A226982: 1 0 0 0 0 0 0 0 1 1 1 1 1 1 2 2
(x * loop(\(x,i).(x + (x div (2 + (i mod 2)))),x,2))
A187272: 0 2 6 12 24 40 72 112 192 288 480 704 1152 1664 2688 3840
(x + loop(\(x,i).(x * (2 - (x div (2 + i)))),x,2))
A206332: 2 5 6 11 12 13 14 23 24 25 26 27 28 29 30 47
loop(\(x,i).(~x mod (8 + i)),2,x)
A004720: 0 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7
loop(\(x,i).(10x + i),2,x)
A265948: 12 112 212 312 412 512 612 712 812 912 1012 1112 1212 1312 1412 1512
(x + (if (~2 + (x div 5)) <= 0 then 1 else x))
A032950: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 30
(x + loop(\(x,i).i,(x + ~9),x))
A062028: 0 2 4 6 8 10 12 14 16 18 11 13 15 17 19 21
(x2 * loop(\(x,i).(x2 + 4x + 4),2,1))
A017390: 0 121 484 1089 1936 3025 4356 5929 7744 9801 12100 14641 17424 20449 23716 27225
(x + (if (x mod 2) <= 0 then ((~x + 1) div 3) else x))
A338206: 0 2 1 6 3 10 4 14 5 18 7 22 8 26 9 30
loop(\(x,i).(10x + ~1),x,x)
A033713: 0 9 189 2889 38889 488889 5888889 68888889 788888889 8888888889 98888888889 1088888888889 11888888888889 128888888888889 1388888888888889 14888888888888889
(x2 * loop(\(x,i).(2x2 + ~1),2,2))
A174338: 0 97 388 873 1552 2425 3492 4753 6208 7857 9700 11737 13968 16393 19012 21825
(x + loop(\(x,i).((x2 + ~2x + ~1) div 2),2,x))
A133568: 1 2 3 2 5 22
(x * loop(\(x,i).(~8x + 4),2,x))
A304378: 0 36 200 492 912 1460 2136 2940 3872 4932 6120 7436 8880 10452 12152 13980
loop(\(x,i).x2,(x2 + ~8x),x)
A308072-A228052: 0 1 2 3 4 5 6 7 8 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~x + loop(\(x,i).(x * (3 + i)),4,x))
A135639: 0 839 1678 2517 3356 4195 5034 5873 6712 7551 8390 9229 10068 10907 11746 12585
(x - loop(\(x,i).(~2 + ((~x + 2) * (x div 2))),x,x))
A079657: 0 3 8 89
loop(\(x,i).(2 + ((x2 + ~2) div (2 + i))),x,x)
A262279: 0 1 2 6 75
loop(\(x,i).(10x + 8),x,x)
A294327: 0 18 288 3888 48888 588888 6888888 78888888 888888888 9888888888 108888888888 1188888888888 12888888888888 138888888888888 1488888888888888 15888888888888888
(x + loop(\(x,i).(3x + ~6),(x + ~2),x))
A261864: 0 2 4 6 16 62
(x * loop(\(x,i).(x * (1 + (2 * i))),(x + ~2),x))
A161120: 0 1 4 27 240 2625 34020 509355 8648640 164189025 3445942500 79222218075 1979900722800 53443570205025 1549547301802500 48028060502296875
(x * loop(\(x,i).(x * (2 - (x mod 2))),(x + ~2),x))
A168251: 0 1 4 9 64 25 576 49 4096 81 25600 121 147456 169 802816 225
(2x - loop(\(x,i).(x div (2 - (x mod 2))),x,x))
A129527: 0 1 3 3 7 5 9 7 15 9 15 11 21 13 21 15
(x * loop(\(x,i).x5,2,x))
A089081: 0 1 67108864 2541865828329 4503599627370496 1490116119384765625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x2 + loop(\(x,i).(3 * i),(x + ~2),1))
A116729-A048840: 1 2 5 12 22 34 48 64 82 102 124 148 174 202 232 264
(~x2 + loop(\(x,i).3x,2x,1))
A024103: 1 8 77 720 6545 59024 531405 4782920 43046657 387420408 3486784301 31381059488 282429536337 2541865828160 22876792454765 205891132094424
(~x2 + loop(\(x,i).6x,x,1))
A024064: 1 5 32 207 1280 7751 46620 279887 1679552 10077615 60466076 362796935 2176782192 13060693847 78364163900 470184984351
(~x2 + loop(\(x,i).8x,x,1))
A024090: 1 7 60 503 4080 32743 262108 2097103 16777152 134217647 1073741724 8589934471 68719476592 549755813719 4398046510908 35184372088607
(~x2 + loop(\(x,i).5x,x,1))
A024051: 1 4 21 116 609 3100 15589 78076 390561 1953044 9765525 48828004 244140481 1220702956 6103515429 30517577900
loop(\(x,i).(x div (~2 + (x mod 2))),4,x2)
A181318: 0 1 1 9 1 25 9 49 4 81 25 121 9 169 49 225
(x2 * loop(\(x,i).x3,3,x))
A122970: 0 1 536870912 68630377364883 288230376151711744 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x2 * loop(\(x,i).3x,(x + ~1),x))
A086603: 0 1 24 243 1728 10125 52488 250047 1119744 4782969 19683000 78594219 306110016 1167575877 4374822312 16142520375
(~x2 + loop(\(x,i).(2x + i),(x + ~1),x))
A338230: 0 0 1 7 27 81 213 519 1207 2725 6033 13179 28515 61257 130861 278287
(x2 + loop(\(x,i).((x2 + ~x) div 2),2,x))
A037255: 0 1 4 12 31 70 141 259 442 711 1090 1606 2289 3172 4291 5685
(x2 * loop(\(x,i).(x * (2 + (x * i))),2,x))
A292282: 0 24 576 4320 19200 63000 169344 395136 829440 1603800 2904000 4983264 8176896 12918360 19756800 29376000
(x2 * loop(\(x,i).3x,2x,x))
A128795: 0 9 648 19683 419904 7381125 114791256 1640558367 22039921152 282429536481 3486784401000 41768190339579 488038239039168 5584479224838813 62773918496412984 694882570819440375
(1 - (x2 * loop(\(x,i).x3,2,x)))
A024009: 1 0 ~2047 ~177146 ~4194303 ~48828124 ~362797055 ~1977326742 ~8589934591 ~31381059608 ~99999999999 ~285311670610 ~743008370687 ~1792160394036 ~4049565169663 ~8649755859374
loop(\(x,i).7x,x,x2)
A128786: 0 7 196 3087 38416 420175 4235364 40353607 368947264 3268642167 28247524900 239256535903 1993145356944 16374242758783 132931722278404 1068201339737175
(x2 * loop(\(x,i).6x,x,x))
A128792: 0 6 288 5832 82944 972000 10077696 96018048 859963392 7346640384 60466176000 482882881536 3761479876608 28694344753152 215031266279424 1586874322944000
(x2 * loop(\(x,i).8x,x,x))
A128794: 0 8 512 13824 262144 4096000 56623104 719323136 8589934592 97844723712 1073741824000 11433202941952 118747255799808 1207813523111936 12068239626469376 118747255799808000
(~x4 + loop(\(x,i).2x,x,1))
A024014: 1 1 ~12 ~73 ~240 ~593 ~1232 ~2273 ~3840 ~6049 ~8976 ~12593 ~16640 ~20369 ~22032 ~17857
(~x4 + loop(\(x,i).(x * i),x,1))
A196411: 1 0 ~14 ~75 ~232 ~505 ~576 2639 36224 356319 3618800 39902159 478980864 6226992239 87178252784 1307674317375
loop(\(x,i).4x,x,x4)
A062075: 0 4 256 5184 65536 640000 5308416 39337984 268435456 1719926784 10485760000 61408804864 347892350976 1916696264704 10312216477696 54358179840000
(x2 * loop(\(x,i).5x,x,x))
A128791: 0 5 200 3375 40000 390625 3375000 26796875 200000000 1423828125 9765625000 64990234375 421875000000 2681884765625 16748046875000 102996826171875
(x2 * loop(\(x,i).x2,2,x3))
A010802: 0 1 16384 4782969 268435456 6103515625 78364164096 678223072849 4398046511104 22876792454961 100000000000000 379749833583241 1283918464548864 3937376385699289 11112006825558016 29192926025390625
loop(\(x,i).x2,2,x5)
A010808: 0 1 1048576 3486784401 1099511627776 95367431640625 3656158440062976 79792266297612001 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + ((~1 + i) mod 8)),x,x)
A231684: 0 1 3 6 10 15 21 28 36 37 39 42 46 51 57 64
(~x + loop(\(x,i).10x,x,x))
A110807: 0 9 198 2997 39996 499995 5999994 69999993 799999992 8999999991 99999999990 1099999999989 11999999999988 129999999999987 1399999999999986 14999999999999985
(~x3 + loop(\(x,i).4x,x,1))
A024039: 1 3 8 37 192 899 3880 16041 65024 261415 1047576 4192973 16775488 67106667 268432712 1073738449
(x3 + loop(\(x,i).3x,x,1))
A001585: 1 4 17 54 145 368 945 2530 7073 20412 60049 178478 533169 1596520 4785713 14352282
(~x3 + loop(\(x,i).3x,x,1))
A024026: 1 2 1 0 17 118 513 1844 6049 18954 58049 175816 529713 1592126 4780225 14345532
(x3 + (if (x + ~2) <= 0 then 1 else 2x))
A139628: 1 2 9 33
loop(\(x,i).(x + (x div (~1 + (2 * i)))),x2,x)
A278484: 0 2 6 12 18 26 38 48 62 78 90 108 132 146 180 206
loop(\(x,i).(x + ((1 + (4 * i)) * i)),x,x)
A332698: 0 6 25 65 134 240 391 595 860 1194 1605 2101 2690 3380 4179 5095
(~1 + (2 mod (1 + ((x + ~1) mod 5))))
A210247: 1 ~1 ~1 1 1 1 ~1 ~1 1 1 1 ~1 ~1 1 1 1
(1 + (x mod (1 + ((x + 2) div 5))))
A249727-A122197-A030718-A023118: 1 1 1 2 1 2 1 2 3 1 2 3 1 2 3 4
(1 + (x mod (1 + (((x + 1) div 2) div 3))))
A346089-A302789-A302776: 1 1 1 1 1 2 1 2 1 2 1 3 1 2 3 1
(1 + ((x + ~1) div 13))
A287866-A226046-A167383: 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2
(~1 + ((x + 1) mod 11))
A103303: 0 1 2 3 4 5 6 7 8 9
A055017: 0 1 2 3 4 5 6 7 8 9 ~1 0 1 2 3 4
(1 + (2x mod (1 + ((x div 2) div 3))))
A344879: 1 1 1 1 1 1 1 1 1 1 1 1 1 3 2 1
(1 + ((x + ~1) mod (1 + ((~x + 2) mod 3))))
A176514: 3 1 1 3 2 1 3 1 1 3 2 1 3 1 1 3
(2x div (1 + (2 mod (1 + (x mod 3)))))
A342369: 0 2 1 6 8 3 12 14 5 18 20 7 24 26 9 30
(1 + (x mod (1 + (8 mod (x + 1)))))
A139378: 1 1 3 1 1 3 1 1 9
(1 + (x2 div (4x + 5)))
A204591: 1 1 1 1 1 2 2 2 2 2 3 3 3 3 4 4
((x + 1) - (x div ~9))
A304814: 1 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18
((x + 1) - ((x mod 4) mod ~3))
A127932: 1 4 4 4 5 8 8 8 9 12 12 12 13 16 16 16
((x2 + 2x + 1) - (x div ~3))
A080341: 1 5 10 17 27 38 51 67 84 103 125 148 173 201 230 261
(~1 + (2 div (x + 1)) - (x mod ~3))
A122434: 1 2 0 ~1 1 0 ~1 1 0 ~1 1 0 ~1 1 0 ~1
(1 + (x2 div ((x + 1) - (x div ~2))))
A248610-A209081: 1 1 2 2 3 3 4 5 5 6 7 7 8 9 9 10
((x + 3) - (x div (~1 + (x div ~2))))
A229858: 3 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20
(1 + (x mod (1 + ((1 + (x div 4)) div 2))))
A167969: 1 1 1 1 1 2 1 2 1 2 1 2 1 2 3 1
(1 + (x div (3 + ((x div 2) div 3))))
A111850: 1 1 1 2 2 2 2 2 3 3 3 3 3 3 3 4
(1 + ((x + 3) div 7))
A276798-A257639-A076080: 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3
(1 + ((2x + 2) div 7))
A194920-A072912: 1 1 1 2 2 2 3 3 3 3 4 4 4 5 5 5
(1 + ((2x + ~2) div 7))
A086707: 0 1 1 1 1 2 2 2 3 3 3 3 4 4 4 5
(1 + ((2x + 4) div 7))
A217538: 1 1 2 2 2 3 3 3 3 4 4 4 5 5 5 5
((x + 1) - (2x div 7))
A080820: 1 2 3 4 4 5 6 6 7 8 9 9 10 11 11 12
(1 + (3x div 7))
A254528: 1 1 1 2 2 3 3 4 4 4 5 5 6 6 7 7
((x + 1) - ((~x + 1) div 7))
A183297: 1 2 4 5 6 7 8 9 10 12 13 14 15 16 17 18
((x + 1) - ((~x + 2) div 7))
A213257-A171521-A092784: 1 2 3 5 6 7 8 9 10 11 13 14 15 16 17 18
((2x + 1) - (x div 7))
A292650: 1 3 5 7 9 11 13 14 16 18 20 22 24 26 27 29
(1 + ((x + 1) div (3 + (x div 3))))
A256707: 1 1 2 2 2 2 2 2 2 2 2 3 2 3 3 3
(1 + (x div (1 + (x mod (2 * (1 + (x mod 2)))))))
A060819: 1 1 3 1 5 3 7 2 9 5 11 3 13 7 15 4
((x + 1) - (1 mod (~2x + 7)))
A233524: 0 1 2 4 5 8
A322125: 0 1 2 4 5 8 11
((x + 1) - ((x div 2) div ~5))
A133016: 1 2 4 5 6 7 8 9 10 11 12 13 15 16 17 18
(1 + (x div (5 + (x mod 3))))
A278949: 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 4
(1 + (x div (3 + ((x mod 3) div 2))))
A122651: 1 1 1 2 2 2 3 3 3 4 4 3 5 5 4 6
(1 + (x div (1 + (2 * (2 + (x mod 4))))))
A187186: 1 1 1 1 1 1 1 1 2 2 2 2 3 2 2 2
(1 + (x div (1 + (2 * (2 + ((x div 2) mod 2))))))
A105223: 1 1 1 1 1 2 1 2 2 2 2 2 3 3 3 3
(1 + ((2x + 1) div 9))
A104277: 1 1 1 1 2 2 2 2 2 3 3 3 3 4 4 4
(1 + ((~x + ~1) mod 9))
A138531: 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3
(1 + ((x2 + ~1) div 9))
A036407: 0 1 1 1 2 3 4 6 8 9 12 14 16 19 22 25
((x + 1) - (2x div 9))
A247971: 1 2 3 4 5 5 6 7 8 8 9 10 11 12 12 13
(1 + ((x2 + x) mod 9))
A256676: 1 3 7 4 3 4 7 3 1 1 3 7 4 3 4 7
(1 + ((x2 + 2x) mod 9))
A056992: 1 4 9 7 7 9 4 1 9 1 4 9 7 7 9 4
(1 + ((x + (x div 2)) mod 9))
A141425: 1 2 4 5 7 8 1 2 4 5 7 8 1 2 4 5
((x + 1) div (1 + (x mod 9)))
A080461-A066578: 1 1 1 1 1 1 1 1 1 10 5 4 3 2 2 2
((x + 1) mod (1 + (x mod 9)))
A070635: 0 0 0 0 0 0 0 0 0 0 1 0 1 4 3 2
(1 + (~x2 mod 9))
A194825: 1 9 6 1 3 3 1 6 9 1 9 6 1 3 3 1
(1 + ((x + ~2) div (3 + (x div 4))))
A059939: 0 0 1 1 1 1 2 2 2 2 2 2 2 2 3 3
(1 + (2x div (3 + (x div 4))))
A106742-A106733-A087839-A087838: 1 1 2 3 3 3 4 4 4 4 5 5 5 5 5 6
(1 + (x div (1 + ((x mod (2 + (x mod 2))) div 2))))
A125746: 1 2 3 4 5 3 7 8 9 10 11 6 13 14 15 16
(1 + (2x mod (1 + ((x + ~1) mod 4))))
A337820-A322127: 1 1 1 1 1 1 1 3 1 1 1 2 1 1 1 1
(1 + (3 mod (1 + ((x div 2) mod 4))))
A053390: 1 1 2 2 1 1 4 4 1 1 2 2 1 1 4 4
(1 + (5 * (x mod 5)))
A070397: 1 6 11 16 21 1 6 11 16 21 1 6 11 16 21 1
(1 + (5 * (1 + (2 * (x div 2)))))
A168460: 6 6 16 16 26 26 36 36 46 46 56 56 66 66 76 76
(15x + 14)
A257645: 14 29 44 59 74 89 104 119 134 149 164 179 194 209 224 239
(30x + 1)
A128470: 1 31 61 91 121 151 181 211 241 271 301 331 361 391 421 451
(1 + (5 * ((x div 2) div 3)))
A241155: 1 1 1 1 1 1 6 6 6 6 6 6 11 11 11 11
(1 + (5 * (2 mod (1 + (x div 2)))))
A290856: 1 1 1 1 11 11 11 11 11 11 11 11 11 11 11 11
(5x2 + 10x + 4)
A134538: 4 19 44 79 124 179 244 319 404 499 604 719 844 979 1124 1279
(~1 + (5 * ((x + 1) + (x mod 2))))
A168420: 4 14 14 24 24 34 34 44 44 54 54 64 64 74 74 84
(1 + (((x + 1) + (x mod 2)) div 5))
A051742: 1 1 1 2 2 2 2 2 2 3 3 3 3 4 4 4
(1 + ((x - (2 mod (x + 1))) div 5))
A060384: 1 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3
(1 + ((x2 + 3x + 2) div 5))
A025692: 1 2 3 5 7 9 12 15 19 23 27 32 37 43 49 55
(10x2 + 10x + 1)
A069133: 1 21 61 121 201 301 421 561 721 901 1101 1321 1561 1821 2101 2401
((2x + 1) - ((x + 1) div 5))
A253301-A187841: 1 3 5 7 8 10 12 14 16 17 19 21 23 25 26 28
(1 + (x div 2) - ((x + 1) div 5))
A105588: 1 1 2 2 2 2 3 3 4 3 4 4 5 5 5 5
(~2 mod (1 + ((x + 1) div 5)))
A091048: 0 0 0 0 0 0 0 0 0 1 1 1 1 1 2 2
((x div 2) div (1 + ((x + 1) div 5)))
A319661: 0 0 1 1 1 1 1 1 2 1 1 1 2 2 1 1
(x - (x mod (1 + ((x + 1) div 5))))
A081328: 0 1 2 3 4 4 6 6 8 9 9 9 12 12 12 12
((2x + 1) - ((x + 1) mod 5))
A235499: 0 1 2 3 9 10 11 12 13 19 20 21 22 23 29 30
((2x + 1) - ((x + ~1) div 5))
A186290: 2 3 5 7 9 11 12 14 16 18 20 21 23 25 27 29
(3 - (5 * (x div ~2)))
A168209: 3 8 8 13 13 18 18 23 23 28 28 33 33 38 38 43
((x + 1) - ((x div ~2) div 5))
A304816: 1 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18
(x + ~29)
A023471: ~29 ~28 ~27 ~26 ~25 ~24 ~23 ~22 ~21 ~20 ~19 ~18 ~17 ~16 ~15 ~14
(~1 + (10 * (1 + (x div 2))))
A161365: 9 9 19 19 29 29 39 39 49 49 59 59 69 69 79 79
((x + 1) - ((2x + 2) div 5))
A077467: 1 2 2 3 3 4 5 5 6 6 7 8 8 9 9 10
(1 + (((x2 + ~1) div 2) div 5))
A036408: 0 1 1 1 2 3 4 5 7 9 10 13 15 17 20 23
(x + ~39)
A023481: ~39 ~38 ~37 ~36 ~35 ~34 ~33 ~32 ~31 ~30 ~29 ~28 ~27 ~26 ~25 ~24
(1 + ((x mod 8) mod 5))
A276757: 1 2 3 4 5 1 2 3 1 2 3 4 5 1 2 3
(1 + (8x div 5))
A047497: 1 2 4 5 7 9 10 12 13 15 17 18 20 21 23 25
(20x2 + 1)
A158493: 1 21 81 181 321 501 721 981 1281 1621 2001 2421 2881 3381 3921 4501
((x + 1) - ((2 * (x div 2)) div 5))
A319681: 1 2 3 4 5 6 6 7 8 9 9 10 11 12 13 14
((x + 1) - ((~2x + 2) div 5))
A329996-A286428-A258833-A189794: 1 2 4 5 7 8 9 11 12 14 15 16 18 19 21 22
(1 + (5 * ((x2 + x) div 2)))
A005891: 1 6 16 31 51 76 106 141 181 226 276 331 391 456 526 601
(1 + ((2 * (x + (x div 2))) div 5))
A280814: 1 1 2 2 3 3 4 5 5 6 7 7 8 8 9 9
(4 mod (1 + ((x + 2) div 5)))
A037805: 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0
((x + 2) mod (1 + ((x + 2) div 5)))
A037281: 0 0 0 1 0 1 0 1 1 2 0
(4 mod (1 + ((x + 2) mod 5)))
A152889: 1 0 4 0 0 1 0 4 0 0 1 0 4 0 0 1
((x + 1) - ((1 - (x div 2)) div 5))
A132329: 1 2 3 4 6 7 8 9 10 11 12 13 14 15 17 18
(5x2 + 15x + 1)
A166150: 1 21 51 91 141 201 271 351 441 541 651 771 901 1041 1191 1351
(10x2 + 5x + 1)
A080860: 1 16 51 106 181 276 391 526 681 856 1051 1266 1501 1756 2031 2326
((2x + 1) - ((~x + 1) div 5))
A189467: 1 3 6 8 10 12 14 17 19 21 23 25 28 30 32 34
(x - (x mod (~1 + ((~x + 1) div 5))))
A232091: 0 1 2 4 4 6 6 9 9 9 12 12 12 16 16 16
(5x2 + 20x + 1)
A162316: 1 26 61 106 161 226 301 386 481 586 701 826 961 1106 1261 1426
(1 + ((x2 + 4x) div 5))
A193622: 1 2 3 5 7 10
A022790: 1 2 3 5 7 10 13 16 20 24 29 34 39 45 51 58
((x + 1) - ((x + (x div 2)) div 5))
A094500: 1 2 3 4 4 5 6 6 7 8 8 9 10 11 11 12
((x + 1) - ((~x + (x mod 2)) div 5))
A282532-A183299: 1 2 4 5 6 7 9 10 11 12 13 14 16 17 18 19
(x - (2 mod (~1 - (x div 5))))
A103303: 0 1 2 3 4 5 6 7 8 9
A050743: 0 1 2 3 4 5 6 7 8 9 11 12 13 14 15 17
(~4 mod (1 + (x div 5)))
A240713: 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0
((x + ~2) + (2 div (1 + (x div 5))))
A171974: 0 1 2 3 4 4 5 6 7 8 8 9 10 11 12 13
((x + 2) - (2 div (1 + (x div 5))))
A278373: 0 1 2 3 4 6 7 8 9 10 12 13 14 15 16 17
((~x2 + 1) mod (1 + (x div 5)))
A343023: 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0
((2x + 5) - (x mod 5))
A293481: 5 6 7 8 9 15 16 17 18 19 25 26 27 28 29 35
((x + 1) - ((x + 1) mod (1 + (x div 4))))
A179276: 1 2 3 4 4 6 6 8 9 9 9 12 12 12 12 16
((x + 1) - ((x div 2) mod (1 + (x div 4))))
A278055: 1 2 3 4 5 6 6 7 8 9 9 10 11 12 12 13
((x + 2) mod (1 + (x mod (1 + (x div 4)))))
A337383-A276479: 0 0 0 0 0 1 0 1 1 0 0 1 0 1 1 1
(1 + ((x2 + ~1) mod (1 + (x mod 4))))
A093818-A030559: 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1
(1 + ((x2 + x) mod (1 + (x mod 4))))
A326538-A070670: 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1
(1 + ((~x2 + 1) mod (1 + (x mod 4))))
A300362-A156264-A030575: 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1
((x + 1) - (x div (~3 + ((~x + 1) div 2))))
A183296: 1 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18
(1 + (x mod (~3 + ((x * (x div 2)) mod 2))))
A319448: 1 ~1 0 0 ~1 0 1 0 0 1 ~1 0 1 ~1 0 0
((x + 1) - (x2 div (x + 5)))
A070941: 1 2 3 3 4 4 4 4 5 5 5 5 5 5 5 5
(1 + (3x div (3 + (x div 2))))
A261100: 1 2 2 3 3 4 4 4 4 4 4 5 5 5 5 5
(1 + (~x2 mod (3 + (x mod 2))))
A106055: 1 4 3 4 3 4 1 4 3 4 3 4 1 4 3 4
(1 - (x mod (~1 + (x mod (~3 + (x mod 2))))))
A286281: 1 2 1 2 3 2 1 2 1 2 3 2 1 2 1 2
(1 + ((x mod 7) mod 3))
A294180: 1 2 3 1 2 3 1 1 2 3 1 2 3 1 1 2
(1 + ((x mod ~5) div 3))
A016349-A016339-A016336-A016194-A015964-A015624-A011653-A011647-A011644-A010891: 1 ~1 0 0 0 1 ~1 0 0 0 1 ~1 0 0 0 1
(1 + ((~x mod 5) mod 3))
A193865: 1 2 1 3 2 1 2 1 3 2 1 2 1 3 2 1
(1 + ((x - (x mod 5)) div 3))
A187243-A169718-A001306-A001300-A001299: 1 1 1 1 1 2 2 2 2 2 4 4 4 4 4 6
(1 + ((1 + (x2 div 4)) div 3))
A014591: 1 1 1 2 2 3 4 5 6 8 9 11 13 15 17 20
(18x + 10)
A082286: 10 28 46 64 82 100 118 136 154 172 190 208 226 244 262 280
(~1 + (9 * (1 + (x div 2))))
A168409: 8 8 17 17 26 26 35 35 44 44 53 53 62 62 71 71
(18x + 17)
A239129: 17 35 53 71 89 107 125 143 161 179 197 215 233 251 269 287
(1 + (9 * ((x + 1) div 2)))
A168416: 1 10 10 19 19 28 28 37 37 46 46 55 55 64 64 73
(x + ~37)
A023479: ~37 ~36 ~35 ~34 ~33 ~32 ~31 ~30 ~29 ~28 ~27 ~26 ~25 ~24 ~23 ~22
(x + ~35)
A023477: ~35 ~34 ~33 ~32 ~31 ~30 ~29 ~28 ~27 ~26 ~25 ~24 ~23 ~22 ~21 ~20
(1 + ((x - ((~x + 1) div 3)) div 3))
A112995: 1 1 2 2 2 3 3 4 4 5 5 6 6 6 7 7
(9x2 + 9x + 1)
A069131: 1 19 55 109 181 271 379 505 649 811 991 1189 1405 1639 1891 2161
(~1 + ((1 + ((x2 + 2x) div 2)) mod 3))
A278718: 0 1 1 1 0 ~1 0 1 1 1 0 ~1 0 1 1 1
(~1 + ((1 + (x div (2 - (x mod 2)))) mod 3))
A128834: 0 1 1 0 ~1 ~1 0 1 1 0 ~1 ~1 0 1 1 0
((x div 2) div (1 + (3 * (1 + (x mod 2)))))
A035689: 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1
(1 + (((~x + 1) div (1 + (x mod 2))) mod 3))
A110569: 2 1 3 3 1 2 2 1 3 3 1 2 2 1 3 3
(1 + (((x + 1) + ((x div 2) mod 2)) div 3))
A085182: 1 1 2 2 2 3 3 4 4 4 5 5 5 5 6 6
(6x2 + 12x + 7)
A227776: 7 25 55 97 151 217 295 385 487 601 727 865 1015 1177 1351 1537
(1 + ((2x2 + 4x + 2) div 3))
A194069: 1 3 7 11 17 25 33 43 55 67 81 97 113 131 151 171
(3x2 + 15x + 11)
A236485: 11 29 53
(12x2 + 12x + 1)
A069190: 1 25 73 145 241 361 505 673 865 1081 1321 1585 1873 2185 2521 2881
(1 + (x3 mod (3x + 3)))
A203648: 1 2 9 4 5 18 7 8 27 10 11 36 13 14 45 16
((x + 1) + ((x + 1) div 3) - (x div 2))
A337125: 1 2 3 4 4 6 6 7 8 9 9 11 11 12 13 14
(1 + ((x3 + 3x2 + 2x) div 3))
A064999: 1 3 9 21 41 71 113 169 241 331 441 573 729 911 1121 1361
(~1 + ((x3 + 3x2 + 2x) div 3))
A108766: ~1 1 7 19 39 69 111 167 239 329 439 571 727 909 1119 1359
(2 div (5 - ((x + ~1) div 3)))
A319922: 0 0 0 0 0 0 0 0 0 0 1 1 1 2 2 2
((2x + 1) - (x div ~6))
A231407: 1 4 6
A186331: 1 4 6 8 10 12 14 17 19 21 23 25 27 30 32 34
((2x + 1) - (3 * (x div ~2)))
A047336: 1 6 8 13 15 20 22 27 29 34 36 41 43 48 50 55
(24x + 7)
A135659: 7 31 55 79 103 127 151 175 199 223 247 271 295 319 343 367
(18x + 5)
A242215: 5 23 41 59 77 95 113 131 149 167 185 203 221 239 257 275
(1 + ((2 * (2x div 3)) div 3))
A226222: 1 1 1 2 2 3 3 3 4 5 5 5 6 6 7 7
(1 + (3 * (2 + (3 * (x div 2)))))
A168411: 7 7 16 16 25 25 34 34 43 43 52 52 61 61 70 70
(~1 + (3 * (2 + (3 * (x div 2)))))
A168418: 5 5 14 14 23 23 32 32 41 41 50 50 59 59 68 68
(2x mod 19)
A076312-A061762: 0 2 4 6 8 10 12 14 16 18 1 3 5 7 9 11
(x2 div 19)
A011871: 0 0 0 0 0 1 1 2 3 4 5 6 7 8 10 11
(x2 mod 19)
A070441: 0 1 4 9 16 6 17 11 7 5 5 7 11 17 6 16
(1 + (3 * (x - ((x mod 3) div 2))))
A180964: 1 4 4 10 13 13 19 22 22 28 31 31 37 40 40 46
(6x2 + 17)
A151953: 17 23 41 71 113 167 233 311 401 503 617 743 881 1031 1193 1367
(6x2 + 6x + 5)
A260981: 5 17 41
(1 + (((x2 + 3x + 2) div 2) div 3))
A025694-A022796: 1 2 3 4 6 8 10 13 16 19 23 27 31 36 41 46
((2x + 1) - (((x + 1) div 2) div 3))
A329837-A249098: 1 3 5 7 9 10 12 14 16 18 20 21 23 25 27 29
(x2 mod (1 + (((x + 1) div 2) div 3)))
A133008: 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 0
(~6x2 + 12x + 7)
A157517: 7 13 7 ~11 ~41 ~83 ~137 ~203 ~281 ~371 ~473 ~587 ~713 ~851 ~1001 ~1163
((x + 1) - (x div ~12))
A333214: 1 3 4 5 6 7 8 9 10 11 12 13 14 16 17 18
(1 + (6 * (x mod 6)))
A225227: 1 7 13
A070419: 1 7 13 19 25 31 1 7 13 19 25 31 1 7 13 19
(1 + ((8x + 4) div 3))
A047480-A022841: 2 5 7 10 13 15 18 21 23 26 29 31 34 37 39 42
(x2 mod 25)
A070447: 0 1 4 9 16 0 11 24 14 6 0 21 19 19 21 0
(x2 mod 23)
A070445: 0 1 4 9 16 2 13 3 18 12 8 6 6 8 12 18
(24x2 + 1)
A158547: 1 25 97 217 385 601 865 1177 1537 1945 2401 2905 3457 4057 4705 5401
(x - ((x + ~1) div 13))
A274933: 1 1 2 3 4 5 6 7 8 9 10 11 12 13 13 14
((x2 div 2) div 13)
A091848-A011877: 0 0 0 0 0 0 1 1 2 3 3 4 5 6 7 8
(1 - ((~x + 1) div 13))
A211663: 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 3
((x2 + x) mod 13)
A111658: 0 2 6 12 7 4 3
((x * (x div 2)) div 13)
A011879-A011878: 0 0 0 0 0 0 1 1 2 2 3 4 5 6 7 8
(2x - (x div 13))
A195169: 0 2 4 6 8 10 12 14 16 18 20 22 24 25 27 29
(x3 mod 13)
A070475: 0 1 8 1 12 8 8 5 5 1 12 5 12 0 1 8
(1 - ((x + 1) mod 11))
A076313: 0 ~1 ~2 ~3 ~4 ~5 ~6 ~7 ~8 ~9 1 0 ~1 ~2 ~3 ~4
(3x mod 11)
A183033: 0 3 6 9 1 4 7 10 2 5 8
((x2 + ~x) div 11)
A011864: 0 0 0 0 1 1 2 3 5 6 8 10 12 14 16 19
(1 - ((~x + 2) div 11))
A230501: 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3
((x * (x div 2)) div 11)
A011875: 0 0 0 0 0 0 1 1 2 3 4 5 6 7 8 9
(2x - (x div 11))
A214673: 0 2 4 6 8 10 12 14 16 18 20 21 23 25 27 29
(x3 mod 11)
A070473: 0 1 8 5 9 4 7 2 6 3 10 0 1 8 5 9
(1 + ((x2 + 2x) div 12))
A036410: 1 1 1 2 3 3 5 6 7 9 11 12 15 17 19 22
(x mod ((x + ~1) - (x mod 12)))
A297232-A283001-A221912-A143290-A097462: 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4
(1 + ((x - ((~x + 2) div 4)) div 3))
A088462: 1 1 1 2 2 3 3 4 4 4 5 5 6 6 6 7
((2x + 1) - ((x mod 4) mod 3))
A047533: 1 2 3 7 9 10 11 15 17 18 19 23 25 26 27 31
(~1 + (3 * (2 + ((x2 + x) div 2))))
A124011: 5 8 14 23 35 50 68 89 113 140 170 203 239 278 320 365
(1 + ((2 + ((x + 2) * (x div 2))) div 3))
A187679: 1 1 3 3 5 6 9
((x + 1) - ((x - ((x div 2) mod 2)) div 3))
A303735: 1 2 3 4 4 5 6 6 7 7
A187103: 1 2 3 4 4 5 6 6 7 7 8
(~1 + (3 * (2 + (x div 2) - (x mod 2))))
A168202: 5 2 8 5 11 8 14 11 17 14 20 17 23 20 26 23
((x div 2) mod (1 + (6 * (x mod 2))))
A234582: 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 0
(6x2 + 18x + 1)
A166873: 1 25 61 109 169 241 325 421 529 649 781 925 1081 1249 1429 1621
(1 + (3 * ((x2 + 3x) div 2)))
A133694: 1 7 16 28 43 61 82 106 133 163 196 232 271 313 358 406
(1 + (6 * (x + (x div 4))))
A225227: 1 7 13
A004611: 1 7 13 19 31 37 43 49 61 67 73 79 91 97 103 109
(1 + (((x2 + 4x) div 2) div 3))
A156040: 1 1 3 4 6 8 11 13 17 20 24 28 33 37 43 48
(x div (3 - (((~x + 2) div 2) div 3)))
A323015: 0 0 0 0 1 1 1 1 2 1 2 2 2 2 2 2
((x + ~1) - (3 * ((~x + ~2) + (x mod 2))))
A047436: 5 6 13 14 21 22 29 30 37 38 45 46 53 54 61 62
((x + 1) - (((~x + ~2) + (x mod 2)) div 3))
A285420: 2 3 5 6 7 8 10 11 13 14 15 16 18 19 21 22
((x + 1) - ((2 * (~x + (x mod 2))) div 3))
A045573: 1 2 5 6 8 9 11 12 15 16 18 19 21 22 25 26
(2 div (5 - ((x + ~2) div 3)))
A035586: 0 0 0 0 0 0 0 0 0 0 0 1 1 1 2 2
(1 + ((2x + (x div 3)) div 3))
A210436: 1 1 2 3 4 4 5 6 7 8 8 9 10 11 11 12
((x + 1) - (3 * (~2x + (x div 2))))
A168670: 1 8 12 19 23 30 34 41 45 52 56 63 67 74 78 85
((~2x + 4) mod (1 + ((x div 2) div 3)))
A060277: 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 1
((x2 + ~2) mod (1 + ((x div 2) mod 3)))
A300067: 0 0 0 1 2 2 0 0 0 1 2 2 0 0 0 1
((x div 2) div (1 + (3 * (2 - (x mod 2)))))
A125688: 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1
(3x2 + ~2x + 7)
A191413: 7 8 15 28 47 72 103 140 183 232 287 348 415 488 567 652
(1 + (((~x + 1) mod (x2 + 2)) div 3))
A097921: 1 1 2 4 6 8 12 16 20 26 32 38 46 54 62 72
(21x + 1)
A215146: 1 22 43 64 85 106 127 148 169 190 211 232 253 274 295 316
(1 + ((2x2 + 5x) div 3))
A000969: 1 3 7 12 18 26 35 45 57 70 84 100 117 135 155 176
(12x2 + 3x + 1)
A244805: 1 16 55 118 205 316 451 610 793 1000 1231 1486 1765 2068 2395 2746
(12x2 + ~3x + 1)
A244802: 1 10 43 100 181 286 415 568 745 946 1171 1420 1693 1990 2311 2656
(1 + (3 * (x + (3 * (x div 2)))))
A146510: 1 4 16 19 31 34 46 49 61 64 76 79 91 94 106 109
(9x2 + 3x + 1)
A082040: 1 13 43 91 157 241 343 463 601 757 931 1123 1333 1561 1807 2071
((3x + 1) - ((~x + 1) div 3))
A297464: 1 4 8 11 14 18 21 24 28 31 34 38 41 44 48 51
((x + 2) div (1 + ((x2 + x) mod 3)))
A145064: 2 1 4 5 2 7 8 3 10 11 4 13 14 5 16 17
((x + 1) - (3 * (~x + ((x div 2) mod 2))))
A011985: 1 5 6 10 17
((x + 2) - (1 mod (~3x + 7)))
A139544: 1 2 4 6 10 14 18 22 26 30 34 38 42 46 50 54
(9x2 + 6x + 1)
A016778: 1 16 49 100 169 256 361 484 625 784 961 1156 1369 1600 1849 2116
(9x2 + ~6x + 1)
A016790: 1 4 25 64 121 196 289 400 529 676 841 1024 1225 1444 1681 1936
(1 + ((x + ((x * (x div 2)) mod 2)) div 3))
A026414: 1 1 1 2 2 2 3 3 3 4 4 5 5 5 5 6
((2x + 1) - ((~x + (x mod 2)) div 3))
A244223: 1 3 6 8 11 13 15 17 20 22 25 27 29 31 34 36
(1 + (3x * (x2 + (x mod 2))))
A261722: 1 7 25 91
((4x + 3) - (x div 3))
A260484: 3 7 11 14 18 22 25 29 33 36 40 44 47 51 55 58
(1 + ((2 + (x div 3)) * (x div 3)))
A075561: 1 1 1 4 4 4 9 9 9 16 16 16 25 25 25 36
((x2 + 5) - (x div 3))
A341301: 5 6 9 13 20 29 39 52 67 83 102 123 145 170 197 225
((1 + ((x + 1) div 2)) mod (1 + (x div 3)))
A010764: 0 0 0 1 1 0 1 2 2 2 2 3 2 3 3 3
((x mod 6) mod (1 + (x div 3)))
A064722: 0 0 0 1 0 1 0 1 2 3 0 1 0 1 2 3
(((x mod 3) div 2) * (1 + (x div 3)))
A175676: 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0
(((x + 2) mod 4) mod (1 + (x div 3)))
A277904: 0 0 0 1 0 1 0 1 2 3 0 1 2 3 0 1
((1 - (2 * (x mod 2))) * (1 + (x div 3)))
A104581: 1 ~1 1 ~2 2 ~2 3 ~3 3 ~4 4 ~4 5 ~5 5 ~6
(1 + (2 * ((x mod 3) * (x mod 3))))
A168399: 1 3 9 1 3 9 1 3 9 1 3 9 1 3 9 1
((x mod 2) - ((x + ~1) mod (1 + (x mod 3))))
A131720: 0 1 ~1 1 ~1 0 0 1 ~1 1 ~1 0 0 1 ~1 1
(((x div 2) - (x mod 2)) mod (1 + (x mod 3)))
A189706: 0 1 1 0 0 1 0 0 1 0 1 1 0 1 1 0
(1 + ((1 + (x2 div 2)) div (x + 3)))
A093337: 1 1 1 1 2 2 3 3 4 4 4 5 5 6 6 7
(1 + ((x2 div 4) div (x + 3)))
A005857: 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 4
(1 + ((2 + (x2 div 2)) div (x + 3)))
A020911: 1 1 1 2 2 2 3 3 4 4 5 5 5 6 6 7
(1 + (5x div (x + 3)))
A335741-A103586: 1 2 3 3 3 4 4 4 4 4 4 4 5 5 5 5
((x + 1) - ((x * (x div 2)) div (x + 3)))
A039733: 1 2 3 4 4 5 5 6 7 7 8 9 9 10 10 11
((2x + 1) - (x2 div (x + 3)))
A212450: 1 3 5 6 7 8 9 11 12 13 14 15 16 17 18 19
(1 + ((2x + 1) * (1 + (2 * (x div 2)))))
A193868: 2 4 16 22 46 56 92 106 154 172 232 254 326 352 436 466
(8x2 + 12x + 5)
A060820: 5 25 61 113 181 265 365 481 613 761 925 1105 1301 1513 1741 1985
((x + 1) - ((2x + 1) * (x div ~2)))
A245534: 1 5 8 18 23 39 46 68 77 105 116 150 163 203 218 264
(8x2 + 20x + 9)
A273220: 9 37 81 141 217 309 417 541 681 837 1009 1197 1401 1621 1857 2109
(16x2 + 8x + 1)
A016814: 1 25 81 169 289 441 625 841 1089 1369 1681 2025 2401 2809 3249 3721
(1 + ((2x + 1) * ((x2 + ~x) div 2)))
A081441: 1 1 6 22 55 111 196 316 477 685 946 1266 1651 2107 2640 3256
(1 + ((2x2 + ~3x + ~2) * (x div 2)))
A110215: 1 1 1 8 37
(~1 + (7 * (1 + (x div 2))))
A168332: 6 6 13 13 20 20 27 27 34 34 41 41 48 48 55 55
(1 + (((~x + 1) div 3) mod (1 + (x div 2))))
A026834: 1 1 2 2 3 2 3 3 3 3 4 3 4 4 4 4
((~x + 1) mod (1 + (2x mod (1 + (x div 2)))))
A237049: 0 0 0 0 0 0 0 0 1 0 0 0 1 0 2 0
(1 + ((~1 + (x mod 4)) * (1 + (x mod 2))))
A192225: 0 1 2 5
A091086: 0 1 2 5 0 1 2 5 0 1 2 5 0 1 2 5
(1 + ((x2 + 2x + 2) div (1 + (x mod 2))))
A164900: 3 3 11 9 27 19 51 33 83 51 123 73 171 99 227 129
((x + 1) - (x mod (~1 + ((~x2 + 2x) div 2))))
A094859: 1 2 3 4 6 10
(1 + (x2 div ((x + 1) + (x div 4))))
A066508: 1 1 2 3 3 4 5 6 6 7 8 9 10 10 11 12
(1 + ((x + 1) * (1 + ((x + ~1) mod 3))))
A228949: 4 3 7 13 6 13 22 9 19 31 12 25 40 15 31 49
(8x2 + 9x + 2)
A125201: 2 19 52 101 166 247 344 457 586 731 892 1069 1262 1471 1696 1937
(8x2 + 16x + 7)
A157914: 7 31 71 127 199 287 391 511 647 799 967 1151 1351 1567 1799 2047
(2x4 + 4x3 + 2x2 + 1)
A096129: 1 9 73 289 801 1801 3529 6273 10369 16201 24201 34849 48673 66249 88201 115201
(8x2 + 10x + 1)
A194431: 1 19 53 103 169 251 349 463 593 739 901 1079 1273 1483 1709 1951
(6x2 + 8x + 3)
A126587: 3 17 43 81 131 193 267 353 451 561 683 817 963 1121 1291 1473
(1 + ((2x + 2) * (3 - (x div 2))))
A229831: 7 13 13 17
(x4 + 2x3 + x2 + ~2x + ~1)
A165568: ~1 1 31 137 391 889 1751 3121 5167 8081 12079 17401 24311 33097 44071 57569
(32x + 31)
A239128: 31 63 95 127 159 191 223 255 287 319 351 383 415 447 479 511
(1 + ((2 + (x mod 8)) mod (x + 1)))
A285758: 1 2 2 2 2 2 2 2 3 4 5 6 7 8 9 10
(16x2 + 16x + 1)
A195315: 1 33 97 193 321 481 673 897 1153 1441 1761 2113 2497 2913 3361 3841
(1 + (((x + ~2) mod 8) mod (x + 1)))
A137846-A080915: 1 2 1 2 3 4 5 6 7 8 1 2 3 4 5 6
(x - (x mod (~1 - (4 mod (x + 1)))))
A265562: 0 1 2 3 5 5 10 10 10 10 10 15 15 15 15 15
(6x2 + 10x + 5)
A201279: 5 21 49 89 141 205 281 369 469 581 705 841 989 1149 1321 1505
(2 - ((1 - (x div 2)) div (1 + (2 mod (x + 1)))))
A157791: 1 1 2 2 3 3 3 3 3 3 4 4 4 4 4 4
((x + 4) - (x div (1 + (2 mod (x + 1)))))
A196594: 4 4 6 6 7 8 8 9 10 10
(x4 + ~x3 + ~x2 + ~x + ~1)
A125082: ~1 ~3 1 41 171 469 1037 2001 3511 5741 8889 13177 18851 26181 35461 47009
(7x2 + 7x + 1)
A069127: 1 15 43 85 141 211 295 393 505 631 771 925 1093 1275 1471 1681
(1 + ((x * ((x + ~2) div 3)) div (x + 1)))
A053264: 1 0 1 1 1 1 1 1 2 2 2 3 3 3 4 4
(1 + ((x2 + x) * (2 + (2 mod (x + 1)))))
A273789: 1 5 25 49 81 121 169 225 289 361 441 529 625 729 841 961
(1 + ((x * (x mod 8)) div (x + 1)))
A338881: 1 1 2 3 4 5 6 7 1 1 2 3 4 5 6 7
(x3 + 4x2 + ~5x + 1)
A241577: 1 1 15 49 109 201 331 505 729 1009 1351 1761 2245 2809 3459 4201
(4x4 + ~4x2 + 1)
A239607: 1 1 49 289 961 2401 5041 9409 16129 25921 39601 58081 82369 113569 152881 201601
(x5 + ~x3 + ~2x2 + 1)
A177075: 1 ~1 17 199 929 2951 7489 16367 32129 58159 98801 159479 246817 368759 534689 755551
(x div ((x + ~1) - (x mod ~8)))
A329343-A309395-A167262-A037831: 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1
((x + 1) - (x div (2 - ((x div 2) div ~2))))
A230490: 1 2 3 3 4 5 6 7 7 8 9 10 11 12 13 14
(x2 div ((x + 1) - ((x div 2) div ~2)))
A056847: 0 0 1 1 2 3 4 4 5 6 7 8 9 9 10 11
(x - ((2 * (x div 3)) div ~3))
A138083: 0 1 2 4 5 6
A039185: 0 1 2 4 5 6 8 9 10 11 12 13 15 16 17 19
(2x - ((x mod 4) mod ~3))
A047430: 0 4 5 6 8 12 13 14 16 20 21 22 24 28 29 30
((x2 + 2x) - ((x div 2) div ~3))
A024385: 0 3 9 16 25 36 49 64 82 101 122 145 170 197 227 258
(x - ((x + (x div 4)) div ~3))
A001953: 0 2 3 4 6 7 9 10 12 13 14 16 17 19 20 21
(((x div 2) div ~2) * (x div ~3))
A062722: 0 0 1 1 2 2 4 6 6 6 12 12 12 15 20 20
((x2 div 4) - (x div ~3))
A088414: 0 1 2 3 6 8
A211519: 0 1 2 3 6 8 11 15 19 23 29 34 40 47 54 61
(x2 div ((x + 2) - (x div ~3)))
A309945: 0 0 0 1 2 2 3 4 4 5 6 7 8 8 9 10
((2 * (x div 3)) - (x mod ~3))
A131380: 0 2 1 2 4 3 4 6 5 6 8 7 8 10 9 10
((x + 1) - ((x + (x div 4)) div ~2))
A330063-A292644-A188035-A090908-A000202-A000201: 1 3 4 6 8 9 11 12 14 16 17 19 21 22 24 25
(1 + (x mod 2) - ((x2 + 2x) div ~2))
A236283: 1 4 5 10 13 20 25 34 41 52 61 74 85 100 113 130
(1 + (~7 * (x div ~2)))
A168337: 1 8 8 15 15 22 22 29 29 36 36 43 43 50 50 57
(1 + (x div 8) - (x div ~2))
A079685: 1 2 2 3 3 4 4 5 6
A329547: 1 2 2 3 3 4 4 5 6 7 7 8 8 9 9 10
((x + 1) - ((~x + 1) div (2 - (x div ~2))))
A183301: 1 2 4 5 6 7 8 9 11 12 13 14 15 16 17 18
(3 - ((~x + 2) div (2 - (x div ~2))))
A177876: 2 3 3 4
A132983: 2 3 3 4 4 4 4 4 4 4 5 5 5 5 5 5
(1 + ((2 div (1 + (x div 5))) mod 2))
A063059: 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 1
(1 + (2 * (x div (1 + ((x + 1) div 3)))))
A132424: 1 3 3 3 5 3 5 5 5 5 5 5 5 5 5 5
(1 + ((x - (x mod (1 + (x div 3)))) div 2))
A024417-A005041: 1 1 2 2 3 3 4 4 4 5 5 5 6 6 6 7
(16x + 13)
A082285: 13 29 45 61 77 93 109 125 141 157 173 189 205 221 237 253
(1 + ((x mod (2 - (x div ~3))) mod 2))
A293811-A106035: 1 2 1 1 1 2 1 1 2 1 1 2 1 1 1 2
(3 - (x div (~2 + (x div ~3))))
A194882: 3 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6
(1 + (2 * ((2x + 1) - (x div ~2))))
A268044: 3 9 13 19 23 29 33 39 43 49 53 59 63 69 73 79
(1 + (((x + 1) mod 7) mod 2))
A188512: 2 1 2 1 2 1 1 2 1 2 1 2 1 1 2 1
(1 + (((x + 2) mod 7) mod 2))
A214848: 1 2 1 2 1 1 2 1 2 1 2 1 1 2 1 2
(1 + (((x + ~2) mod 7) mod 2))
A071709: 2 1 1 2 1 2 1 2 1 1 2 1 2 1 2 1
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(1 + ((x mod (~1 + (2 * (x div 3)))) mod 2))
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(16x + 11)
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(1 + ((x mod (1 + (((x + 1) div 2) div 2))) div 2))
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(1 + ((x div (1 + (x mod 8))) mod 2))
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(1 + (2 * ((~x + ~1) mod 5)))
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(1 + (((2 + (x div 2)) mod 5) mod 2))
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(1 + (2 * (~2x mod 5)))
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(1 + ((x - ((x div 2) mod 5)) mod 2))
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(1 + (((x2 div 2) div 5) mod 2))
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(2 div (1 + ((x + 2) mod 10)))
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(1 + ((x2 + ~x) mod 10))
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((2x + 1) - (x mod 10))
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(~2 mod (1 + (x mod 10)))
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(x div ((x + 1) - (x mod 10)))
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(1 div (~1 + (2 * ((~x + 2) mod 5))))
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(3 + (5 * (x + (x mod 2))))
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(x2 mod (~1 + (2 * (x div 5))))
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((2x + 1) - ((x div 5) mod 2))
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(1 + (2 * (2x - (x mod 5))))
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(1 + (((~x2 + x) mod 5) div 2))
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(1 + ((x2 div (3 + (x div 2))) mod 2))
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((x + ~1) - (2 * (((x + ~1) div 2) div 3)))
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(1 + ((x - (((x + ~1) div 2) div 3)) div 2))
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((x + 1) - (2 * ((~2x + 1) div 3)))
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(1 + ((x - ((1 - (x div 2)) div 3)) div 2))
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(4 mod (1 + (2 * ((x div 2) div 3))))
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((x + 1) - ((x - ((x div 2) div 3)) div 2))
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((x2 + 3) div 7)
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21x2
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(3x2 div 7)
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(x - ((2x + 1) div 7))
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(x - ((2x + ~1) div 7))
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(21x + 7)
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(2 - ((~x + 3) div 7))
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(x - ((~x + 3) div 7))
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(7 * ((x + 1) + (x div 2)))
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(((x + ~1) * (x mod 2)) div 7)
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(x - ((2x + 2) div 7))
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(x - ((2x + ~2) div 7))
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(7 * (x div 8))
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(7x2 + 28)
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28x2
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(x - ((2x + ~4) div 7))
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(7 * ((x2 + x) div 2))
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(((x2 + ~x) div 2) div 7)
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(x - ((~2x + 4) div 7))
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(((x * (x div 2)) div 2) div 7)
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(2x - (2x div 7))
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((x div 2) - ((x div 2) div 7))
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((x2 - (x div 2)) div 7)
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(x - (3x div 7))
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(14x2 + 7x)
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(14x2 + ~7x)
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((x * ((x div 2) mod 2)) div 7)
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(x4 mod 7)
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(1 + (((x + (x div 4)) mod 3) mod 2))
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((x + 1) - (2 * ((~x + (x mod 2)) div 3)))
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(1 + ((x mod (~2 - (x div 3))) mod 2))
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(1 + (2 * (((x + 1) div 2) + (x div 3))))
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(1 + (((x div 4) * (x mod 3)) mod 2))
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((x div 4) div (3 + (x mod 3)))
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(1 - (2 mod (1 + (x mod (2 + (x mod 3))))))
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(1 + (2 * (2x - (x2 mod 3))))
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(1 + ((1 + ((x + (x div 4)) div 2)) div 2))
A081832: 1 1 2 2 2 3 3 3 4 4 4 4 5 5 5 6
(1 + (2 * ((x2 + 1) div (x + 3))))
A050824: 1 1 3 3 5 7 9 11 11 13 15 17 19 21 23 25
(1 + ((x3 + 5x2 + 6x) div 2))
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(1 + (2 * ((4x + 1) - (x div 2))))
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((x + 1) - (((x + ~1) mod (1 + (x div 2))) div 2))
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(1 + (((x + ~4) div (1 + (x div 2))) mod 2))
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(1 + (((2x + ~4) mod (1 + (x div 2))) mod 2))
A031226: 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1
((x + 1) div (1 + (2 * (2 mod (1 + (x div 2))))))
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(1 + (((~2x + 4) mod (1 + (x div 2))) mod 2))
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(1 + ((2x2 mod (1 + (x div 2))) mod 2))
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(1 + (2 * ((x2 + 2x + 1) + (x div 2))))
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(1 + (((~x2 + 1) mod (1 + (x div 2))) div 2))
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((x + 1) - (2 * (x div (3 - (x mod 2)))))
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(1 + ((x + ~2) div (2 + (x div (1 + (x mod 2))))))
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(2x2 + 10x + 3)
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(1 + (2 * ((x + 1) + (2 * (x div 3)))))
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(1 + (2 * ((x + 1) + (x div 8))))
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(1 + (((x + 1) + ((x div 4) mod 2)) div 2))
A227737: 1 2 2 3 4 4 5 5 5 6 6 7 8 8 9 9
(1 + (((x + 1) + (x2 div 4)) div 2))
A089651: 1 2 3 4 5 7 9 11 13 16 19 22 25 29 33 37
(1 + (((x + 1) * (x div 5)) mod 2))
A079700: 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1
(1 + ((((x div 2) div ~2) mod (x + 1)) div 2))
A306904: 1 1 2 2 3 3 3 4 4 5 5 5 6 6 6 7
(4x div (3 + (2 mod (x + 1))))
A232748: 0 1 1 2 3 4 4 5 6 7 8 8 9 10 11 12
((x3 + 3) + (2 mod (x + 1)))
A174684: 3 4 13 32
((2x + 3) + (3 mod (x + 1)))
A095029: 3 6 7 12 14
((2x + 3) + ((x + 1) mod 4))
A282848: 4 7 10 9 12 15 18 17 20 23 26 25 28 31 34 33
(12x2 + 18x)
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(2x3 + 9x2 + 9x)
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(x - ((~x2 + 2x) div (2x + 3)))
A307913-A155902: 0 1 2 4 5 7 8 10 11 12 14 15 17 18 20 21
(1 + ((x - (x div 3)) * ((x + 1) div 2)))
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(1 + (((x + ~1) + (x div 2)) * ((x + 1) div 2)))
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(1 + (((x + 1) + (x mod 2)) * ((x + 1) div 2)))
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((x + 1) - (((~x + 2) div 2) * ((x + 1) div 2)))
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(((x + 2) + (x mod 2)) * (1 + ((x + 1) div 2)))
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A093907: 2 8 8 18 18 32 32 50 50 72 72 98 98 128 128 162
((x * (x + (x mod 2))) div (1 + ((x + 1) div 2)))
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((x + 1) - ((~x3 + 3x2 + ~2x) div 2))
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(1 + (2 * (x - ((x div 4) div ~2))))
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(x - ((2x + 2) div ~5))
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(x - ((x + (x div 2)) div ~5))
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((2x + 2) - (x div ~5))
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((x + 1) - ((x + (x div 2)) div ~4))
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((3x + 1) - (x div ~4))
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(x div (5 - (x mod ~4)))
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((x + 3) - (x div (~2 + (x div ~2))))
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(x div (2 - (x div (~1 + (2 * (x mod ~2))))))
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(1 + (2 * (x - (2 * (x div ~3)))))
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(3 + ((x mod ~5) mod 2))
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(1 + (4 * (1 + ((x div ~2) mod 2))))
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(32x + 5)
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(1 + (2 * (2 + ((x + 2) mod 5))))
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((~x + 1) mod 21)
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(x2 mod 21)
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((x + 1) - (4 * (x div 5)))
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((x + 1) - (2 * (~2 + (x mod 5))))
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(1 + (2 * ((3 * (x mod 4)) div 2)))
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(1 + ((x mod (~2 + (3 * (x div 2)))) mod 2))
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(x - (1 div (2x + ~13)))
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(1 + ((2x div (2 + (x div 3))) mod 2))
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(1 + ((2x mod (2 + (x div 3))) mod 2))
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(1 + (2x div (4 + (x div 3))))
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(~2 mod (1 + (4 * (x mod 3))))
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(8x2 + 16x + 5)
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(4x2 + 16x + 21)
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(1 + (2 * (x - (2 * ((~x + ~1) + (x mod 2))))))
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(1 + (2 * ((6 mod (x + 1)) mod 2)))
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(1 + (2 * (((2x + ~4) mod (x + 1)) mod 2)))
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(2 div (5 - (((x + 1) div 2) div 2)))
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((x + ~5) + (((x + ~1) div 2) div 2))
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(1 + (((x + (x div 2)) * ((x + ~1) div 2)) div 2))
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(1 + (((x4 + ~1) div 2) div 2))
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((x + 1) - (2 * (((x div 2) div ~2) div 2)))
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(1 - (x div (~3 + (x div ~4))))
A227581-A204166: 1 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4
(1 + ((x div (2 + (x mod 6))) mod 2))
A223708: 1 1 1 1 1 1 2 1 1 2 2 2 1 1 2 2
(~1 + (4 * (x - ((~1 + (x div 2)) div 2))))
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(~1 + (2 * ((x - ((~1 + (x div 2)) div 2)) mod 2)))
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(5 + ((x2 + 3x + 2) div 2))
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(~1 + ((x + 2) div (2 + (((x + 1) div 2) div 2))))
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((2x + 1) - ((((x + 1) div 2) div 2) div 2))
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(1 + (4 * (x - (x div ~4))))
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(1 + (((x - (x div ~4)) div 2) div 2))
A285524-A284726: 1 1 1 2 2 2 3 3 3 4 4 4 4 5 5 5
(1 + ((x mod (~2 + (x mod ~4))) mod 2))
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((x + ~1) - (2 * ((((x + ~1) div 2) div 2) div 2)))
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(1 + ((x - ((((x + ~1) div 2) div 2) div 2)) mod 2))
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(x div (5 + (((x + ~1) div 2) mod 2)))
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(~x + 35)
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(x2 mod 33)
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(x2 mod 31)
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(1 + ((x mod (2 + (x div 8))) mod 2))
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(1 + ((x div (~2 + (x div 8))) mod 2))
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(1 + ((x div (4 + (x div 4))) mod 2))
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(1 + ((x mod (2 + ((x div 4) mod 2))) div 2))
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(1 + (x div (4 * (2 + (x mod 4)))))
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(32x2 + 1)
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(1 + ((x - (x div ~7)) div 2))
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A225875: 1 2 2 3 3 4 4 5 6 6 7 7 8 8 9 10
((x + 1) - (2 * (~8 + (x mod 2))))
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(2 div (1 + ((x + 1) mod 16)))
A343905: 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
((x2 + x) mod 17)
A054579: 0 2 6 12 3 13 8 5 4 5 8 13 3 12 6 2
(x div (~x + 19))
A259195: 0 0 0 0 0 0 0 0 0 0 1 1 1 2 2 3
(x3 mod 17)
A070479: 0 1 8 10 13 6 12 3 2 15 14 5 11 4 7 9
((x2 div 2) div 15)
A011880: 0 0 0 0 0 0 1 1 2 2 3 4 4 5 6 7
((x2 + ~x) div 15)
A011868: 0 0 0 0 0 1 2 2 3 4 6 7 8 10 12 14
(x3 mod 15)
A070697-A070477: 0 1 8 12 4 5 6 13 2 9 10 11 3 7 14 0
((x + 1) - (2 div (x + ~16)))
A247250-A235986: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18
(x2 + x + 11)
A048058: 11 13 17 23 31 41 53 67 83 101 121 143 167 193 221 251
(2x2 + 2x + 17)
A259555: 17 21 29 41 57 77 101 129 161 197 237 281 329 381 437 497
(1 + (((x2 + ~x) div 8) mod 2))
A096993: 1 1 1 1 2 1 2 2 2 2 2 2 1 2 1 1
(x2 + 2x + 11)
A114948: 11 14 19 26 35 46 59 74 91 110 131 154 179 206 235 266
((2x + 3) - (x div 8))
A248196: 3 5 7 9 11 13 15 17 18 20 22 24 26 28 30 32
((2x + 3) - (x mod 8))
A154660: 3 4 5 6 7 8
A137913: 3 4 5 6 7 8 9 10 19 20 21 22 23 24 25 26
((x div 2) div (3 + (x mod 8)))
A283655: 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0
(4x2 + 4x + 15)
A242412: 15 23 39 63 95 135 183 239 303 375 455 543 639 743 855 975
(1 + (2x div (4 + (x div 4))))
A087834: 1 1 2 2 2 3 3 3 3 4 4 4 4 4 5 5
(1 + ((x mod (1 - (2 * (x div 4)))) mod 2))
A183953: 1 1 1 1 1 1 1 1 2 1 1 2 2 1 2 1
((x + ~1) - (2 * ((x - (x div 4)) div 2)))
A339765: ~1 0 ~1 0 1 0 1 0 1 2 1 2 3 2 3 2
((x div 2) div (5 + (x mod 4)))
A085978-A011726: 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0
((x div 2) div (1 + (2 * (2 + (x mod 4)))))
A327450-A309785-A309528-A297237-A293496-A281155-A279948-A277163-A277160-A277157-A225413-A167265-A088918-A088183-A086078-A079302-A049825-A047758-A035699-A035676-A035656: 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
(1 + (2 * (x - (((2 - (x div 2)) div 2) div 2))))
A283800-A043325-A023692: 1 3 5 7 9 11 15 17 19 21 23 25 27 29 33 35
(1 + (((x - ((2 - (x div 2)) div 2)) div 2) div 2))
A192543-A082964: 0 1 1 1 2 2 2 3 3 3 4 4 4 4 5 5
(x div (1 + (2 * (4 - ((x div 2) mod 2)))))
A174847: 0 0 0 0 0 0 0 1 0 1 1 1 1 1 2 2
((x + 1) div (5 + ((x div 2) mod 2)))
A339931: 0 0 0 0 1 1 1 1 1 2 1 2 2 2 2 2
(1 + (4 * (x mod (2 * (2 - (x mod 2))))))
A135169: 1 5 9 5 1 5 9 5 1 5 9 5 1 5 9 5
(x div (3 + (x mod (2 * (2 + (x mod 2))))))
A177236: 0 0 0 0 1 0 1 1 2 1 2 1 4 3 2 2
((x div 2) div (3 + ((x + 2) mod 4)))
A226517: 0 0 0 0 0 0 1 0 0 0 1 1 1 1 2 1
(x - (2 mod (~1 + (x div ~7))))
A084689: 0 1 2 3 4 5 6 7 9
A285316-A187320-A043093-A023802: 0 1 2 3 4 5 6 7 9 10 11 12 13 14 15 17
(1 + (x div (10 - (x div 2))))
A120178: 1 1 1 1 1 1 1 2 2 2 3 3 4 4 5 6
((x + 1) - (2 div (~8 + (x div 2))))
A249611-A140823-A119675-A028261: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18
(9x + 45)
A242267-A242226: 45 54 63 72 81 90 99 108 117 126 135 144 153 162 171 180
(36x + 9)
A139609: 9 45 81 117 153 189 225 261 297 333 369 405 441 477 513 549
27x2
A244634: 0 27 108 243 432 675 972 1323 1728 2187 2700 3267 3888 4563 5292 6075
(x - ((~x + 3) div 9))
A089590-A052406: 0 1 2 3 5 6 7 8 9 10 11 12 13 15 16 17
((x2 + 2x + ~1) mod 9)
A152179: 8 2 7 5 5 7 2 8 7 8 2 7 5 5 7 2
(9 * ((x + 1) + (x div 2)))
A051063: 9 18 36 45 63 72 90 99 117 126 144 153 171 180 198 207
(18x2 + 18x)
A162940: 0 36 108 216 360 540 756 1008 1296 1620 1980 2376 2808 3276 3780 4320
(9 * ((x mod 3) div 2))
A021115: 0 0 9 0 0 9 0 0 9 0 0 9 0 0 9 0
36x2
A016910: 0 36 144 324 576 900 1296 1764 2304 2916 3600 4356 5184 6084 7056 8100
(x - ((2x + 4) div 9))
A105566: 0 1 2 2 3 4 5 5 6 7 8 9 9 10 11 12
(27x + 18)
A124388: 18 45 72 99 126 153 180 207 234 261 288 315 342 369 396 423
(x - ((~2x + 2) div 9))
A039178-A001965: 0 1 3 4 5 6 8 9 10 11 12 14 15 16 17 19
((x2 + x + 2) mod 9)
A146079: 2 4 8 5 4 5 8 4 2 2 4 8 5 4 5 8
(9 * ((x2 + x) div 2))
A027468: 0 9 27 54 90 135 189 252 324 405 495 594 702 819 945 1080
(((x2 + x) div 2) mod 9)
A134804: 0 1 3 6 1 6 3 1 0 0 1 3 6 1 6 3
(x - ((~2x + 4) div 9))
A138083: 0 1 2 4 5 6
A265187-A039186: 0 1 2 4 5 6 7 9 10 11 12 13 15 16 17 18
(2x3 mod 9)
A021041: 0 2 7 0 2 7 0 2 7 0 2 7 0 2 7 0
(18x2 + ~9x)
A152994: 0 9 54 135 252 405 594 819 1080 1377 1710 2079 2484 2925 3402 3915
((~x2 + ~x + 1) mod 9)
A254375: 1 8 4 7 8 7 4 8 1 1 8 4 7 8 7 4
(9x3 + ~9x)
A124007: 0 0 54 216 540 1080 1890 3024 4536 6480 8910 11880 15444 19656 24570
(x4 mod 9)
A070513: 0 1 7 0 4 4 0 7 1 0 1 7 0 4 4 0
(x - (x mod ((x + 1) - (x mod 8))))
A265521: 0 1 2 3 4 5 6 7 0 9 9 9 9 9 9 9
(1 + (x div ((~x + 1) - (x mod 8))))
A015241-A014025: 1 0 0 0 0 0 0 0 ~1 0 0 0 0 0 0 0
((x + 1) - (x div (~2 + ((~x + 2) div 4))))
A184431-A078358: 1 3 4 5 7 8 9 10 11 13 14 15 16 17 18 19
(1 + ((x - ((x + (x div 2)) div 4)) div 2))
A285588: 1 1 2 2 2 3 3 3 3 4 4 4 5 5 5 6
(1 + ((x + 1) div (4 - (x div 4))))
A275378: 1 1 1 2 2 3 3 3 5
(1 + ((2x + ~1) div (2 + (x div 4))))
A061339: 0 1 2 3 3 4 4 5 4 5 5 6 5 6 6 6
((2x + 1) div (3 + (x div 4)))
A169894-A163352-A117707-A083291-A003056: 0 1 1 2 2 2 3 3 3 3 4 4 4 4 4 5
((x + (x div 2)) div (3 + (x div 4)))
A066490: 0 0 1 1 1 1 2 2 2 2 3 3 3 3 3 3
(x2 mod (1 + (x div (2 + (x div 4)))))
A111700-A106002: 0 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1
(1 - ((x + ~2) div (1 + (2 * (x div 4)))))
A242928: 3 2 1 0 1 0 0 0 0 0 0 0 0 0 0 0
(1 + (2 * ((2x + 4) - (x mod 4))))
A214865: 9 11 13 15 25 27 29 31 41 43 45 47 57 59 61 63
(1 + (2 * ((2 - (x mod 2)) * (x mod 4))))
A001148: 1 3 9 7 1 3 9 7 1 3 9 7 1 3 9 7
(3 + ((x2 + 5x + 6) div 2))
A167614: 6 9 13 18 24 31 39 48 58 69 81 94 108 123 139 156
(1 + ((((1 - (x div 2)) mod (x + 2)) div 2) div 2))
A343265-A263846-A230774-A132173: 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3 3
(1 + ((2x2 mod (x + 4)) mod 2))
A031279: 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 2
(1 + (((x2 div 2) mod (x + 4)) mod 2))
A003649: 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 2
((x2 + 1) div (x + 7))
A127037: 0 0 0 1 1 2 2 3 4 5 5 6 7 8 9 10
(x - (x2 div (x + 7)))
A327008: 0 1 2 3 3 3 4 4 4 4 5 5 5 5 5 5
(1 + (2 * (x - (1 mod (~4x + 1)))))
A160912: 1 7 17 27 37 47 57 67 77 87 97 107 117 127 137 147
(1 + (2 * ((4x + 2) + (x div 2))))
A143988: 5 13 23 31 41 49 59 67 77 85 95 103 113 121 131 139
((5x + 3) + (x div 2))
A299647: 3 8 14 19 25 30 36 41 47 52 58 63 69 74 80 85
(1 + (x mod (2 + ((x + ~2) div (2 + (x div 2))))))
A136314-A023128: 1 1 1 2 1 2 1 2 3 1 2 3 1 2 3 1
(x mod (1 + (((x + ~2) mod (2 + (x div 2))) div 2)))
A341519: 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0
(1 + ((2x2 mod (2 + (x div 2))) mod 2))
A303825-A246588-A026492: 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1
(x mod (1 + ((x + ~1) mod (4 + (x div 2)))))
A297236: 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3
(4x div (5 + (x div 2)))
A210533: 0 0 1 2 2 2 3 3 3 4 4 4 4 4 4 5
(1 + (((x2 + ~x) mod (2 + (x div 2))) mod 2))
A330665-A317145-A003650: 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2
(~1 + ((2 + (x div 2)) div (2 + ((x div 2) mod 2))))
A308068: 0 0 0 0 1 1 0 0 2 2 1 1 3 3 2 2
(1 + (2 * (((x * (x mod 2)) - (x div 2)) div 2)))
A186422: 1 1 ~1 3 ~1 3 ~3 5 ~3 5 ~5 7 ~5 7 ~7 9
(x div (3 + (x div (4 - (x mod 2)))))
A081757: 0 0 0 0 1 1 1 1 1 1 2 1 2 1 2 1
(1 + ((x - ((x + ~2) mod (2 + (x mod 2)))) div 2))
A291268: 1 0 2 2 3 3 4 3 5 5 6 6 7 6 8 8
((x div 2) div (1 + (x div (4 + (x mod 2)))))
A307706: 0 0 1 1 1 1 1 1 1 2 1 1 1 2 1 1
((x + 2) div (3 + (x div (2 + (x mod 2)))))
A322401: 0 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2
(1 - (x mod (1 + (2 * (x mod (2 + (x mod 2)))))))
A254377: 1 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1
((2x + 1) - (x mod (2 * (~2 + (x mod 2)))))
A074231: 1 4 7 8 9 12 15 16 17 20 23 24 25 28 31 32
(1 + (((x2 + 2) div 3) mod 4))
A232244-A028356: 1 2 3 4 3 2 1 2 3 4 3 2 1 2 3 4
(x div ((x + 1) - ((~1 + (x div 2)) mod 4)))
A321859: 0 ~1 0 0 1 1 1 1 1 1 0 0 1 1 1 1
(2 div (1 + ((~1 + (x * (x div 2))) mod 4)))
A330005: 0 0 1 0 0 1 1 2 0 0 1 0 0 1 1 2
(1 + ((2x - ((x div 2) mod 2)) mod 4))
A070352: 1 3 4 2 1 3 4 2 1 3 4 2 1 3 4 2
((x + 1) - (((~x + 2) - (x div 2)) div 4))
A260483-A247778-A059567-A006594-A003511: 1 2 4 5 6 8 9 10 12 13 15 16 17 19 20 21
(20x + 15)
A290781: 15 35 55 75 95 115 135 155 175 195 215 235 255 275 295 315
(x - (5 * (x div ~3)))
A047590: 0 6 7 8 14 15 16 22 23 24 30 31 32 38 39 40
((8x + 1) div 5)
A047446: 0 1 3 5 6 8 9 11 13 14 16 17 19 21 22 24
((3x2 + 3) div 5)
A288425: 0 1 3 6 10 15 22 30 39
(30x + 30)
A050519: 30 60 90 120 150 180 210 240 270 300 330 360 390 420 450 480
60x
A169823: 0 60 120 180 240 300 360 420 480 540 600 660 720 780 840 900
(x - (5 * ((x div 2) div 3)))
A283370-A053827: 0 1 2 3 4 5 1 2 3 4 5 6 2 3 4 5
((x - ((x div 2) mod 3)) mod 5)
A341513-A276150-A275729-A034968: 0 1 1 2 2 3 1 2 2 3 3 4 2 3 3 4
30x2
A244636: 0 30 120 270 480 750 1080 1470 1920 2430 3000 3630 4320 5070 5880 6750
(x - (5 * ((~x + 1) div 3)))
A047523: 0 1 7 8 9 15 16 17 23 24 25 31 32 33 39 40
(5 * (1 + ((x2 + ~x) div 2)))
A082450: 5 5 10 20 35 55 80 110 145 185 230 280 335 395 460 530
(5x2 + 20x + 15)
A067724: 15 40 75 120 175 240 315 400 495 600 715 840 975 1120 1275 1440
(2x - ((2x + 1) div 5))
A047488: 0 2 3 5 7 8 10 11 13 15 16 18 19 21 23 24
((x div 2) - ((2x + ~1) div 5))
A008616: 1 0 1 0 1 1 1 1 1 1 2 1 2 1 2 2
((x2 mod (2x + ~1)) div 5)
A302642: 0 0 0 0 0 1 0 2 0 2 1 3 1 3 1 4
((x + ~1) + (5 * (1 + (x div 2))))
A047374: 4 5 11 12 18 19 25 26 32 33 39 40 46 47 53 54
((x + ~2) + (5 * (1 + (x div 2))))
A047341: 3 4 10 11 17 18 24 25 31 32 38 39 45 46 52 53
(((2x + 1) - (x mod 2)) div 5)
A225370: 0 0 1 1 1 2 2 2 3 3 4 4 5 5 5 6
(1 div ((~1 + (x2 div 2)) mod 5))
A289035-A276397: 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1
(1 mod ((~1 + (x2 div 2)) mod 5))
A276395: 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0
(x - (((x + ~1) + (x div 2)) div 5))
A248227-A086525-A061288: 1 1 2 3 3 4 5 6 6 7 8 8 9 10 10 11
(2 - (5 * ((~x + ~1) + (x mod 2))))
A168458: 7 7 17 17 27 27 37 37 47 47 57 57 67 67 77 77
(x - (((~x + ~1) + (x mod 2)) div 5))
A336109-A039216: 1 2 3 4 5 6 8 9 10 11 13 14 15 16 17 18
(25x + 25)
A044077: 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400
((x3 + x2 + x + 1) mod 5)
A152898: 1 4 0 0 0 1 4 0 0 0 1 4 0 0 0 1
((8x + 8) div 5)
A285676-A064724: 1 3 4 6 8 9 11 12 14 16 17 19 20 22 24 25
((4x2 + 4x) div 5)
A281151: 0 1 4 9 16 24 33 44 57 72 88 105 124 145 168 192
(5 * (x2 - (2 mod (x + 1))))
A032772: 0 5 10 35
((2x + 2) - ((x + 1) mod 5))
A037469: 1 2 3 4 10 11 12 13 14 20 21 22 23 24 30 31
(3x - ((x + ~1) div 5))
A191405: 1 3 6 9 12 15 17 20 23 26 29 31 34 37 40 43
((x3 + ~3x2 + 2x) div 5)
A011887: 0 0 0 1 4 12 24 42 67 100 144 198 264 343 436 546
(x + ~50)
A256958: ~50 ~49 ~48 ~47 ~46 ~45 ~44 ~43 ~42 ~41 ~40 ~39 ~38 ~37 ~36 ~35
((8x + 2) div 5)
A047448: 0 2 3 5 6 8 10 11 13 14 16 18 19 21 22 24
(x2 mod 30)
A070653-A070452: 0 1 4 9 16 25 6 19 4 21 10 1 24 19 16 15
(11x + 9)
A017497: 9 20 31 42 53 64 75 86 97 108 119 130 141 152 163 174
((x + ~1) + ((2x + 2) mod 5))
A065187: 1 4 2 5 3 6 9 7 10 8 11 14 12 15 13 16
(((x2 + ~3x + 2) div 2) div 5)
A130520: 0 0 0 0 0 1 2 3 4 5 7 9 11 13 15 18
(2x - ((2x + ~2) div 5))
A047512: 1 2 4 6 7 9 10 12 14 15 17 18 20 22 23 25
(1 - ((2 * (x div ~2)) div 5))
A339391: 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 5
(((x + 1) mod 8) div 5)
A319510: 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0
(x2 mod 40)
A070462: 0 1 4 9 16 25 36 9 24 1 20 1 24 9 36 25
(x - (5 * (x div 8)))
A245347: 0 1 2 3 4 5 6 7 3 4 5 6 7 8 9 10
(x - ((2 * (~2 + (x div 2))) div 5))
A307294: 1 2 3 4 4 5 6 7 8 9 9 10 11 12 12 13
(x div (5 * (2 + ((x div 2) mod 2))))
A055639-A048142: 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1
(((x2 + ~x) div 4) div 5)
A011873: 0 0 0 0 0 1 1 2 2 3 4 5 6 7 9 10
(x - ((2 * ((~x + 2) div 2)) div 5))
A138083: 0 1 2 4 5 6
A039243: 0 1 2 4 5 6 7 9 10 11 12 13 14 16 17 18
(5x2 + 20x + 30)
A027578: 30 55 90 135 190 255 330 415 510 615 730 855 990 1135 1290 1455
(19x + 1)
A215144: 1 20 39 58 77 96 115 134 153 172 191 210 229 248 267 286
(x - ((2 * (1 - (x div 2))) div 5))
A039251: 0 1 2 3 5 6 7 8 10 11 12 13 14 15 17 18
(2x - ((~2 + (x div 2)) div 5))
A285594-A191251: 1 3 5 7 8 10 12 14 16 18 20 22 24 26 27 29
((2x2 + 6x) div 5)
A269132: 0 1 4 7 11 16 21 28 35 43 52 61 72 83 95 108
(20x2 + ~10x)
A144560: 0 10 60 150 280 450 660 910 1200 1530 1900 2310 2760 3250 3780 4350
((x + 2) - ((~2x + 2) div 5))
A087057: 2 3 5 6 8 9 10 12 13 15 16 17 19 20 22 23
(x - (((x + 2) + (x div 2)) div 5))
A049473: 0 1 1 2 3 4 4 5 6 6 7 8 8 9 10 11
(x - (5 * ((~x + ~2) + (x mod 2))))
A102488: 10 11 22 23 34 35 46 47 58 59 70 71 82 83 94 95
(x - (((~x + ~2) + (x mod 2)) div 5))
A039214: 1 2 3 4 6 7 8 9 10 11 13 14 15 16 18 19
(((2x + ~4) mod (x + 2)) div 5)
A026826: 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1
((2x + 2) - ((x + 2) div 5))
A184585: 2 4 6 7 9 11 13 15 16 18 20 22 24 25 27 29
((2x + 2) - ((x + 2) mod 5))
A237415: 0 1 2 8 9 10 11 12 18 19 20 21 22 28 29 30
((x3 + ~2x2 + x + ~2) mod 5)
A152893: 3 3 0 0 4 3 3 0 0 4 3 3 0 0 4 3
(1 - ((~2x + (x div 2)) div 5))
A222642: 1 2 2 2 3 3 3 4 4 4 4 5 5 5 6 6
(x - ((~2x + (x div 2)) div 5))
A195128: 0 2 3 4 6 7 8 10 11 12 13 15 16 17 19 20
(x div ((x + ~2) + (2x mod 5)))
A144611: 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1
(10x2 + ~9x)
A051874: 0 1 22 63 124 205 306 427 568 729 910 1111 1332 1573 1834 2115
(x - ((~2x2 + 2x) div 5))
A005488: 0 1 3 6 9 13 18 24
(((1 + (x div 2)) * (x div 2)) div 5)
A308767: 0 0 0 0 1 1 2 2 4 4 6 6 8 8 11 11
((x + 2) - ((1 - (x div 2)) div 5))
A175407: 2 3 4 5 7 8 9 10 11 12 13 14 15 16 18 19
(x - (((~x + 2) - (x div 2)) div 5))
A001957: 0 1 3 4 5 6 8 9 10 12 13 14 16 17 18 19
(x - (5 * ((~x2 + x) div 2)))
A000566: 0 1 7 18 34 55 81 112 148 189 235 286 342 403 469 540
((x + (x div 5)) mod 5)
A159957-A053840: 0 1 2 3 4 1 2 3 4 0 2 3 4 0 1 3
(x - ((x + (x div 3)) div 5))
A215781: 0 1 2 3 3 4 5 6 6 7 8 9 9 10 11 11
(15x2 + ~5x)
A153780: 0 10 50 120 220 350 510 700 920 1170 1450 1760 2100 2470 2870 3300
((x + 1) div (2 - ((~x + 1) div 5)))
A122921: 0 1 1 1 1 2 2 2 2 2 2 3 2 2 3 3
(1 - ((~x3 + x2) mod 5))
A138019: 1 1 0 ~1 ~1 1 1 0 ~1 ~1 1 1 0 ~1 ~1 1
(1 - ((~x + (2 div (x + 1))) div 5))
A232746: 1 1 2 2 2 2 3 3 3 3 3 4 4 4 4 4
(2 - ((~x + (2 div (x + 1))) div 5))
A182008: 2 2 3 3 3 3 4 4 4 4 4 5 5 5 5 5
((2x + ~1) + ((~x + 2) mod 5))
A242590: 1 2 3 9 10 11 12 13 19 20 21 22 23 29 30 31
((3x2 + 2x) div 5)
A332410: 0 1 3 6 11 17 24 32 41 52 64 77 91 106 123 141
(15x2 + ~10x)
A153795: 0 5 40 105 200 325 480 665 880 1125 1400 1705 2040 2405 2800 3225
((x + 2) - ((~x + (x mod 2)) div 5))
A028729: 2 3 5 6 7 8 10 11 12 13 14 15
A167759-A028813-A028812-A028809-A028797-A028785-A028773-A028761-A000037: 2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20
((x mod 5) * (x div 5))
A257845: 0 0 0 0 0 0 1 2 3 4 0 2 4 6 8 0
((4x + 4) + (x div 5))
A164086-A109238: 4 8 12 16 20 25 29 33 37 41 46 50 54 58 62 67
((x2 + 3x + 2) + (x div 5))
A005991: 2 6 12 20 30 43
((x2 + 3x + 2) - (x div 5))
A034110: 2 6 12 20 30 41 55 71 89 109 130 154 180 208 238 269
((3x + 2) - (x div 5))
A329848: 2 5 8 11 14 16 19 22 25 28 30 33 36 39 42 44
(x * ((x mod 3) * (x mod 5)))
A255680: 0 1 8 0 16 0 0 14 48 0 0 22 0 39 112 0
25x2
A016850: 0 25 100 225 400 625 900 1225 1600 2025 2500 3025 3600 4225 4900 5625
(4 - (2 mod (x2 + ~5)))
A134982: 7 6 4 2 2 2 2 2 2 2 2 2 2 2 2 2
(28x + 1)
A161714: 1 29 57 85 113 141 169 197 225 253 281 309 337 365 393 421
(8x2 + 12x + 1)
A118057: 1 21 57 109 177 261 361 477 609 757 921 1101 1297 1509 1737 1981
(8x2 + 20x + 1)
A161617: 1 29 73 133 209 301 409 533 673 829 1001 1189 1393 1613 1849 2101
(16x2 + 4x + 1)
A082041: 1 21 73 157 273 421 601 813 1057 1333 1641 1981 2353 2757 3193 3661
(1 + (4 * (x + (3 * (x div 2)))))
A228141: 1 5 21 25 41 45 61 65 81 85 101 105 121 125 141 145
(1 + ((~x + ((~x + 1) mod 3)) mod 4))
A190555: 2 4 1 3 1 2 4 2 3 1 3 4 2 4 1 3
((x + 1) - ((~x + (x mod 3)) div 4))
A287527-A187570: 1 2 3 5 6 7 9 10 11 13 14 15 16 17 18 20
(12x2 + 4x + ~1)
A179741: ~1 15 55 119 207 319 455 615 799 1007 1239 1495 1775 2079 2407 2759
(1 + ((x + (x2 div 3)) div 4))
A253012: 1 1 1 2 3 4 5 6 8 10 11 13 16 18 20 23
(1 + ((x + (x2 mod 3)) div 4))
A337635: 1 1 1 1 2 2 2 3 3 3 3 4 4 4 4 4
(1 + ((x + (x div 8)) div 4))
A020913: 1 1 1 1 2 2 2 2 3 3 3 4 4 4 4 5
(1 + ((x + ((x div 2) mod 4)) div 4))
A175018: 1 1 1 2 2 2 3 3 3 3 3 4 4 4 5 5
((3x + 1) - ((~x + 2) div 4))
A172513: 1 4 7 11 14 17 20 24 27 30 33 37 40 43 46 50
(12x2 + 8x + 1)
A014641: 1 21 65 133 225 341 481 645 833 1045 1281 1541 1825 2133 2465 2821
(12x2 + ~8x + 1)
A185212: 1 5 33 85 161 261 385 533 705 901 1121 1365 1633 1925 2241 2581
((x + 1) - ((~x + ((~x + 2) div 2)) div 4))
A247786: 1 3 4 5 7 8 9 11 12 14 15 16 18 19 20 22
(1 + ((x * ((x * (x div 2)) mod 2)) div 4))
A054576-A001492: 1 1 1 1 1 1 1 2 1 1 1 3 1 1 1 4
(1 + ((x * (2 + (x * (x mod 2)))) div 4))
A000463: 1 1 2 4 3 9 4 16 5 25 6 36 7 49 8 64
((2x + 1) - ((x + (x div 2)) div 4))
A247913-A189662-A186320: 1 3 5 6 8 10 11 13 14 16 18 19 21 23 24 26
((x + 1) mod (1 + ((x * (x mod 2)) div 4)))
A252459-A117371-A117370: 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0
(~2 mod (1 + ((x * (x mod 2)) div 4)))
A237184: 0 0 0 0 0 0 0 0 0 1 0 1 0 2 0 2
(2 - (2 div (1 + ((x * (x mod 2)) div 4))))
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((x + 1) mod ((x + 1) div (1 + (x div 4))))
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((x + 4) - (2 div (1 + (x div 4))))
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(((x + 1) div 2) - (2 mod (1 + (x div 4))))
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((2x + ~1) + (2 div (1 + (x mod 4))))
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((x + 2) mod ((x + 2) div (1 + (x mod 4))))
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((2x + 1) - ((~x2 + x) div 4))
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(1 + ((3x2 + 4x) div 4))
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(1 - (x div (~1 + ((~x2 + 2x) div 4))))
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((x2 + x + 1) - (x2 div 4))
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(4x3 + ~3x + 1)
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((x + 1) - (2 * ((~x + ((x div 2) mod 2)) div 2)))
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((4x + 1) + (x2 div 3))
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((4x + 1) + ((x2 + x) div 2))
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(12x2 + 7x + 1)
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(4x3 + 9x2 + 6x + 1)
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(12x2 + ~7x + 1)
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(1 + (((x * (x div 2)) mod 2) * (2 + (x div 2))))
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((x + 1) + (((x div 2) mod 2) + (2 * (x div 2))))
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(x4 div (1 + (2 * (x div 2))))
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((8x + 3) + (x mod 2))
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((2x + 1) - (x mod (2 * (2 - (x mod 2)))))
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((2x + 1) - ((x + 2) div (~2 + (x mod 2))))
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(1 + (x div (2 - ((x div 2) div (~2 + (x mod 2))))))
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((x2 + 3x + 3) - (2 * (x mod 2)))
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((~1 + ((x + 2) mod 5)) mod 3)
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((1 + ((x + ~2) mod (1 + (x div 2)))) div 3)
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((4x2 + 4x + 1) div 3)
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((~1 + ((x + 1) mod 8)) mod 3)
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((x mod (1 + (2 * (x mod 4)))) div 3)
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(x - (3 * ((~x + 1) div 5)))
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(x - (3 * ((~x + 2) div 5)))
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(6x2 + 24x + 21)
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(x2 mod 36)
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((2 * ((x mod 2) * (x div 3))) div 3)
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((2x2 + 7x + 3) div 3)
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((6x + 3) * ((x + 1) div 2))
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((2x3 + 3x2 + x) div 3)
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((2x3 + ~3x2 + ~2x) div 3)
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(24x2 + ~12x)
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((1 + ((~x2 + x) * (x div 2))) mod 3)
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(3 * ((x2 + x + 1) - (x mod 2)))
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(x - ((~1 + ((~x2 + x) div 2)) div 3))
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(x - (((~x + ~1) + (x div 3)) div 3))
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(((~x + ~1) + (x div 8)) mod 3)
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(3 * ((x + 1) + (2 * (x div 4))))
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(((x + 1) + ((x * (x div 2)) mod 2)) div 3)
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((1 + (x * (2x + (x mod 2)))) div 3)
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(6x3 + 12x2 + 6x)
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(((x + 1) * (x - (x div ~2))) div 3)
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((2x3 + 6x2 + 4x) div 3)
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((3x + 3) + ((x + ~2) div 3))
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((3x + 3) + ((x div 2) div 3))
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((3x + 3) + ((x div ~2) mod 2))
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((3x + 3) + (((x + 1) div 2) div 2))
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((3x + 3) + ((x + 1) mod 4))
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((3x + 3) + (x2 div 4))
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((3x + 3) + (2 * (x + (x mod 2))))
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((x4 + x3 + ~x2 + ~x) div 3)
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((2x + 8) - ((x + ~1) div 3))
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((2x4 + ~2x2) div 3)
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((x mod 2) - ((x div 2) div ~6))
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(6 * (1 + (4 * (x mod 2))))
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(x3 mod 18)
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(6 * (2x - (x div 3)))
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((2x mod (2 + (x div 3))) div 3)
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(x - ((x mod (2 + (x mod 3))) div 3))
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(11x + 7)
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((2 + ((x + 2) div (1 + (x mod 2)))) div 3)
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((2 * ((x + 2) mod 8)) mod 3)
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(x2 mod 48)
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((x mod (4 + ((x div 2) mod 2))) div 3)
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(x2 + 21)
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(x3 mod 24)
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(2x - ((x mod 8) div 3))
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((x mod (2 + ((~x + 1) mod 4))) div 3)
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((x + ~2) + (3 * (2 + (x div 4))))
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(x - ((2 * (x - (x mod 4))) div 3))
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(23x + 1)
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(x div (x - (3 * (~4 + (x div 2)))))
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((x mod (x - ((x + 1) mod 4))) div 3)
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(((x mod (2 + (x div 2))) mod 4) div 3)
A037833: 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0
((((x * (x div 2)) div 2) mod 4) div 3)
A306488-A167264: 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0
(0 - (x2 div ~11))
A036409: 0 1 1 1 2 3 4 5 6 8 10 11 14 16 18 21
(x - ((x - ((~x + 2) div 4)) div 3))
A189688: 0 1 2 2 3 3 4 4 5 6 6 7 7 8 9 9
(((~x + ((~x + 2) div 2)) mod 4) div 3)
A068716: 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0
((4x3 + 8x) div 3)
A217873: 0 4 16 44 96 180 304 476 704 996 1360 1804 2336 2964 3696 4540
(((2 * (x div 2)) + (x div 4)) div 3)
A090616: 0 0 0 0 1 1 2 2 3 3 4 4 5 5 5 5
(((x2 + x) + (x mod 4)) div 3)
A192225: 0 1 2 5
A115200: 0 1 2 5 6 10 14
(12x2 + ~11x)
A255185: 0 1 26 75 148 245 366 511 680 873 1090 1331 1596 1885 2198 2535
(12x2 + ~9x)
A152767: 0 3 30 81 156 255 378 525 696 891 1110 1353 1620 1911 2226 2565
(12x2 + ~x + 1)
A244803: 1 12 47 106 189 296 427 582 761 964 1191 1442 1717 2016 2339 2686
(((~x + 2) + (x2 div 4)) div 3)
A211540: 0 0 0 0 0 1 1 2 3 4 5 7 8 10 12 14
(((x + 2) - ((x * (x div 2)) mod 2)) div 3)
A339332: 0 1 1 1 2 2 2 2 3 3 4 4 4 5 5 5
((x3 + 6x2 + 8x) div 3)
A077415: 0 5 16 35 64 105 160 231 320 429 560 715 896 1105 1344 1615
(x - (2x mod ((2x + 4) div 3)))
A307531: 0 1 2 3 4 3 4 5 4 5 6 5 6 7 6 7
((2 * ((x2 + ~x) div (x + 2))) div 3)
A248333: 0 0 0 0 1 1 2 2 3 4 4 5 6 6 7 8
(((x2 + ~5x + 6) div 2) div 3)
A058937: 1 0 0 0 0 1 2 3 5 7 9 12 15 18 22 26
((2 * ((2x + 4) + (x div 2))) div 3)
A288475: 2 4 6 7 9 10 12 14 16 17 19 20 22 24 26 27
(((2x + ~2) div (2 + (x div 2))) div 3)
A287867: ~1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
(((x2 + ~2x) mod (2 + (x div 2))) mod 3)
A187969: 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0
(3 * ((x2 + 5x) div 2))
A140673: 0 9 21 36 54 75 99 126 156 189 225 264 306 351 399 450
(18x2 + 6x)
A045946: 0 24 84 180 312 480 684 924 1200 1512 1860 2244 2664 3120 3612 4140
(3 * ((3x2 + x) div 2))
A081266: 0 6 21 45 78 120 171 231 300 378 465 561 666 780 903 1035
(18x2 + ~6x)
A153792: 0 12 60 144 264 420 612 840 1104 1404 1740 2112 2520 2964 3444 3960
(3 * ((3x2 + ~x) div 2))
A062741: 0 3 15 36 66 105 153 210 276 351 435 528 630 741 861 990
((4x3 + 2x) div 3)
A035597: 0 2 12 38 88 170 292 462 688 978 1340 1782 2312 2938 3668 4510
((x + 3) - ((~x + (2 div (x + 1))) div 2))
A186149: 2 4 6 8 9 11 12 14 15 17 18 20 21 23 24 26
(((x * ((x mod 3) div 2)) div 2) div 3)
A336757-A141100-A035692-A024164-A024159: 0 0 0 0 0 0 0 0 1 0 0 1 0 0 2 0
((x3 + 4x + 2) div 3)
A124677: 0 2 6 13 27
(18x2 + ~12x)
A153796: 0 6 48 126 240 390 576 798 1056 1350 1680 2046 2448 2886 3360 3870
(((x * ((x * (x div 2)) mod 2)) div 2) div 3)
A343222: 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 2
((x3 + 3x2 + 3x + 2) div 3)
A213396: 0 3 9 21 42 72 114 171 243 333 444 576 732 915 1125 1365
((4x2 div (x + 2)) div 3)
A263135: 0 0 1 2 3 4 6 7 8 9 11 12 13 15 16 17
(((x + 2) * ((x + 2) + (x div 2))) div 3)
A264041: 1 3 6 10 16 21 29 36 46 55 68 78 93 105 122 136
(3x4 + ~12x2)
A339488: 0 ~9 0 135 576 1575 3456 6615 11520 18711 28800 42471 60480 83655 112896 149175
(~2x2 mod (3x + 6))
A138339: 0 7 4 12
((x3 + ~3x2 + x + 2) div 3)
A152728: 0 0 0 1 7 19 38 68 110 165 237 327 436 568 724 905
(2x - ((2 mod (~2x + 1)) div 3))
A038127: 0 2 5 7 10 13 15 18 21 23 26 29 31 34 37 39
((x mod 2) - (x mod (~6x + 1)))
A063093: 0 5 9 15 19 25 29 35 39 45 49 55 59 65 69 75
(6x + ((x2 + x) div 2))
A056119: 0 7 15 24 34 45 57 70 84 99 115 132 150 169 189 210
(6x + ((x2 + ~x) div 2))
A056115: 0 6 13 21 30 40 51 63 76 90 105 121 138 156 175 195
((2x4 + 4x2) div 3)
A035598: 0 2 16 66 192 450 912 1666 2816 4482 6800 9922 14016 19266 25872 34050
((x + ~1) div (2 - ((1 - (x div 2)) div 3)))
A064661: ~1 0 0 1 1 1 1 2 2 2 2 2 2 3 3 3
(3x - ((1 - (x div 2)) div 3))
A198264: 0 3 6 9 13 16 19 22 25 28 32 35 38 41 44 47
(((x mod ~4) * (x div 2)) mod 3)
A186034: 0 0 1 2 0 0 0 0 0 0 2 1 0 0 1 2
(x div (3 * (8 - (x div 2))))
A326632-A326631-A326630-A326629-A326628-A326626: 0 0 0 0 0 0 0 0 0 0 1 1 2 2 4 5
(x2 - (3 * ((x div 2) * (x div 2))))
A213038: 0 1 1 6 4 13 9 22 16 33 25 46 36 61 49 78
((x div 5) - ((x div 2) div 3))
A011673: 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1
((x mod 6) * ((x div 2) div 3))
A257846: 0 0 0 0 0 0 0 1 2 3 4 5 0 2 4 6
((3x + 2) - ((x div 2) div 3))
A276385-A140099-A109232: 2 5 8 11 14 17 19 22 25 28 31 34 36 39 42 45
((x + 2) + (x div 2) - ((x div 2) mod 3))
A275910: 2 3 4 5 6 7 11 12 13 14 15 16 20 21 22 23
(2x - (((x div 2) mod 3) + (x mod 2)))
A153883: 0 1 3 4 6 7 12 13 15 16 18 19 24 25 27 28
(4x2 - (3 * (x mod 2)))
A195146: 0 1 16 33 64 97 144 193 256 321 400 481 576 673 784 897
((2x2 + 4x) - (3 * (x mod 2)))
A258717: 0 3 16 27 48 67 96 123 160 195 240 283 336 387 448 507
((x + 2) - (((~x2 + x) div 2) div 3))
A266542: 2 3 5 6 8 11 13 16 20 23 27 32 36 41 47 52
(((x4 + ~x2) div 2) div 3)
A008911: 0 0 2 12 40 100 210 392 672 1080 1650 2420 3432 4732 6370 8400
(x - (((~x3 + x) div 2) div 3))
A222010: 0 1 3 7
A004006: 0 1 3 7 14 25 41 63 92 129 175 231 298 377 469 575
(2 - (4x div (~x + ~3)))
A060197: 2 3 4 4 5 5 5 5 5 5 6 6 6 6 6 6
(18x2 + 3x)
A144314: 0 21 78 171 300 465 666 903 1176 1485 1830 2211 2628 3081 3570 4095
((x * ((x + 1) - (x div ~2))) div 3)
A260699: 0 1 2 6 9 15 20 28 34 45 53 66 76 91 102 120
((x * (x2 div 5)) mod 3)
A085859: 0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 0
((4x3 + ~x) div 3)
A000447: 0 1 10 35 84 165 286 455 680 969 1330 1771 2300 2925 3654 4495
(x - ((~x + ((x + ~1) div 3)) div 3))
A231004-A039161-A032797: 1 2 3 4 5 7 8 9 10 12 13 14 15 16 18 19
(x - ((~x + ((x + ~2) div 3)) div 3))
A175439-A039160: 1 2 3 4 6 7 8 9 10 12 13 14 15 17 18 19
(1 - ((~x + ((x div 2) mod 3)) div 3))
A099480: 1 2 2 2 2 2 3 4 4 4 4 4 5 6 6 6
(x - ((~x + ((x div 2) mod 3)) div 3))
A047424: 0 2 3 4 5 6 8 10 11 12 13 14 16 18 19 20
(x2 div ((x + 3) + (x div 3)))
A125229: 0 0 0 1 2 2 3 4 4 5 6 7 7 8 9 9
(15x2 + ~3x)
A060785: 0 12 54 126 228 360 522 714 936 1188 1470 1782 2124 2496 2898 3330
((x3 + 3x2 + ~x) div 3)
A084990: 0 1 6 17 36 65 106 161 232 321 430 561 716 897 1106 1345
((3x2 + 3x + 1) - (x mod 2))
A090381: 1 6 19 36 61 90 127 168 217 270 331 396 469 546 631 720
((x * (2 - ((x mod 3) mod 2))) div 3)
A009947: 0 0 1 2 1 3 4 2 5 6 3 7 8 4 9 10
(3x3 + 9x2 + 12x)
A280304: 0 24 84 198 384 660 1044 1554 2208 3024 4020 5214 6624 8268 10164 12330
(3 * (x + ((x2 + 3x + 2) div 2)))
A297675: 3 12 24 39 57 78 102 129 159 192 228 267 309 354 402 453
(1 - ((~x + ((x div ~2) mod 2)) div 3))
A058032: 1 1 2 2 3 3 3 4 4 4 4 5 5 5 6 6
((x + 3) + (4 * (x div 3)))
A047364: 3 4 5 10 11 12 17 18 19 24 25 26 31 32 33 38
(27x + 12)
A154266: 12 39 66 93 120 147 174 201 228 255 282 309 336 363 390 417
((x * (((x2 + ~1) div 2) div 2)) div 3)
A006584: 0 0 0 2 4 10 16 28 40 60 80 110 140 182 224 280
((x + ((x div ~4) mod 2)) div 3)
A094708: 0 0 1 1 1 1 2 2 2 3 3 4 4 4 4 5
((x * ((x mod (2 + (x mod 2))) div 2)) div 3)
A094518: 0 0 0 0 0 1 0 0 0 0 0 3 0 0 0 0
(1 - ((~x + ((x div 2) mod 4)) div 3))
A208251: 1 2 2 2 2 2 2 3 4 4 4 5 5 5 5 5
(15x2 + ~12x)
A153448: 0 3 36 99 192 315 468 651 864 1107 1380 1683 2016 2379 2772 3195
(2 + (3 * (x + (x mod 2))) - (x div 2))
A166539: 2 8 7 13 12 18 17 23 22 28 27 33 32 38 37 43
((2x + 2) - ((~x + (x mod 2)) div 3))
A283964: 2 4 7 9 12 14 16 18 21 23 26 28 30 32 35 37
((x + 1) mod (2 - ((~x + (x mod 2)) div 3)))
A122059: 1 0 0 1 1 2 3 0 4
((x div (1 + (x div 3))) + (x div 3))
A276581-A084557-A084500-A030530: 0 1 2 2 3 3 4 4 4 5 5 5 6 6 6 7
(x - ((1 - (x div 3)) * (x div 3)))
A087278: 0 1 2 3 4 5 8 9 10 15 16 17 24 25 26 35
(x2 - ((x div 3) * (x div 3)))
A213035: 0 1 4 8 15 24 32 45 60 72 91 112 128 153 180 200
((2 * (x div 5)) + (x div 3))
A268395: 0 0 0 1 1 3 4 4 4 5 7 7 8 8 8 11
(((3 * (x div 2)) div 2) + (x div 3))
A187323: 0 0 1 2 4 4 6 6 8 9 10 10 13 13 14 15
(((x2 + 3x + 2) div 2) + (x div 3))
A083462: 1 3 6 11
A024401: 1 3 6 11 16 22 30 38 47 58 69 81 95 109 124 141
((x + 2) div (2 + (x div 2) - (x div 3)))
A086833-A054725: 1 1 1 2 2 2 2 3 2 3 3 3 3 3 3 4
((2x2 + 5x + 2) - (x div 3))
A248121: 2 9 20 34 53 76 102 133 168 206 249 296 346 401 460 522
(1 - ((~x + 2) div ((x + 2) - (x div 3))))
A211667-A001069: 0 1 1 2 2 2 2 2 2 2 2 2 2 2 2 3
(2 - ((~x + 2) div ((x + 2) - (x div 3))))
A063510-A010096: 1 2 2 3 3 3 3 3 3 3 3 3 3 3 3 4
(3x + (x div 2) - (x div 3))
A063204: 0 3 7 9 13 16 19 22 26 28 32 35 38 41 45 47
((((x + ~1) div 2) * (x div 2)) - (x div 3))
A108579: 0 0 0 0 1 3 4 7 10 13 17 22 26 32 38 44
((5x + 4) - (x div 3))
A214989-A038123: 4 9 14 18 23 28 32 37 42 46 51 56 60 65 70 74
(x + ((4 mod (x + 1)) + (x div 3)))
A010376: 0 1 3 4 9 10 12
(((1 - (x div 2)) mod 3) - (x mod 3))
A117188: 1 0 ~2 0 1 0 1 0 ~2 0 1 0 1 0 ~2 0
(x2 mod (2 + ((x mod 2) + (x mod 3))))
A125203: 0 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0
(9x3 + 3x2)
A085409: 0 12 84 270 624 1200 2052 3234 4800 6804 9300 12342 15984 20280 25284 31050
((2x4 + x2) div 3)
A071270: 0 1 12 57 176 425 876 1617 2752 4401 6700 9801 13872 19097 25676 33825
(x2 + 19)
A241849: 19 20 23 28 35 44 55 68 83 100 119 140 163 188 215 244
((x2 + (x2 div 4)) div 3)
A033438: 0 0 1 3 6 10 15 20 26 33 41 50 60 70 81 93
(x5 + 4x3 + 3x)
A124152: 0 8 70 360 1292 3640 8658 18200 34840 61992 104030 166408 255780 380120 548842 772920
(3x2 + (x2 div 4))
A227541: 0 3 13 29 52 81 117 159 208 263 325 393 468 549 637 731
((3x2 + x) - (2 * (x mod 2)))
A200039: 0 2 14 28 52 78 114 152 200 250 310 372 444 518 602 688
(3x2 + ((x2 + x) div 2))
A022265: 0 4 15 33 58 90 129 175 228 288 355 429 510 598 693 795
(3x2 + ((x2 + ~x) div 2))
A022264: 0 3 13 30 54 85 123 168 220 279 345 418 498 585 679 780
((x2 + 2x + 1) + (x2 div 3))
A238705: 1 4 10 19 30 44 61 80 102 127 154 184 217 252 290 331
(2 - ((~x3 + (x div 2)) div 3))
A118332: 2 3 5 11 23
(22x + 1)
A161709: 1 23 45 67 89 111 133 155 177 199 221 243 265 287 309 331
(12x2 + 2x + 1)
A194454: 1 15 53 115 201 311 445 603 785 991 1221 1475 1753 2055 2381 2731
(12x2 + ~2x + ~1)
A185918: ~1 9 43 101 183 289 419 573 751 953 1179 1429 1703 2001 2323 2669
(1 + ((x + (x mod (1 + (x div 3)))) div 2))
A226142: 1 1 2 3 3 4 4
A014245: 1 1 2 3 3 4 4 5 6 6 7 8 8 9 10 10
(2x2 + 14x + 1)
A161549: 1 17 37 61 89 121 157 197 241 289 341 397 457 521 589 661
(16x2 + 2x + 1)
A204675: 1 19 69 151 265 411 589 799 1041 1315 1621 1959 2329 2731 3165 3631
(1 + (2 * (x + ((x div 2) div 5))))
A338316-A193414-A138217: 1 3 5 7 9 11 13 15 17 19 23 25 27 29 31 33
(1 + ((x * ((x div 2) mod 5)) mod 2))
A338274: 1 1 1 2 1 1 1 2 1 1 1 1 1 2 1 1
(1 + ((x + (x2 div 5)) div 2))
A249020: 1 1 2 3 4 6 7 9 11 13 16 18 21 24 27 31
(1 + ((x3 + 5x) div 2))
A006001: 1 4 10 22 43 76 124 190 277 388 526 694 895 1132 1408 1726
(8x3 + 2x + ~1)
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(1 + ((x * (3 + (x2 div 2))) div 2))
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(1 + ((x + ((1 + (x div 2)) mod 3)) div 2))
A194272: 1 2 3 3 3 3 4 5 6 6 6 6 7 8 9 9
((x + 1) - ((~x + ((x div 2) mod 3)) div 2))
A092253: 1 3 4 5 6 8 10 12
(1 + ((x + ((x2 div 2) div 3)) div 2))
A242678-A008761-A008760-A008759-A001399: 1 1 2 3 4 5 7 8 10 12 14 16 19 21 24 27
(~1 + ((2 mod (2 - (x * (x div 3)))) mod 2))
A142720: ~1 ~1 ~1 ~1 ~1 0 ~1 ~1 ~1 0 ~1 0 ~1 ~1 ~1 0
(1 + ((x * ((2x + 1) + (x div 2))) div 2))
A237443: 1 2 7 13 23
(1 + ((5x2 + x) div 2))
A116668: 1 4 12 25 43 66 94 127 165 208 256 309 367 430 498 571
(1 + ((5x2 + ~x) div 2))
A188545: 1 3 10
A140066: 1 3 10 22 39 61 88 120 157 199 246 298 355 417 484 556
(1 + ((2x3 + x2 + x) div 2))
A081423: 1 3 12 34 75 141 238 372 549 775 1056 1398 1807 2289 2850 3496
(1 + (2 * (x + (x mod (~1 + (x * (x div 2)))))))
A143106: 1 3 5 9 17 21
(1 + ((x + ((x + 1) mod 6)) div 2))
A215092: 1 2 3 4 5 3 4 5 6 7 8 6 7 8 9 10
(1 + ((x * (~2 + ((x + 1) * (x div 2)))) div 2))
A105510: 1 0 2 4 17
(1 + (x2 div (x + 10)))
A113865: 1 1 1 1 2 2 3 3 4 5 6 6 7 8 9 10
((x + 1) - ((~x + (x div 8)) div 2))
A225647: 1 3 4 6 7
A258048-A186227-A184746: 1 3 4 6 7 9 10 12 13 14 16 17 19 20 22 23
(1 + (2 * (x + (x div (4 + (x div 2))))))
A324846-A324761-A324760-A265166-A244579-A151991-A084820: 1 3 5 7 9 11 13 17 19 21 23 25 27 29 31 33
((x + 1) - ((~x + ((~x + 2) div 4)) div 2))
A292663-A206805-A182774-A182772-A109259: 1 3 4 6 8 9 11 13 14 16 17 19 21 22 24 26
((2x + 1) - ((~x + (x div 4)) div 2))
A231407: 1 4 6
A190348: 1 4 6 9 11 13 16 18 20 23 25 28 30 32 35 37
(4x2 + 14x + 15)
A228318: 15 33 59 93 135 185 243 309 383 465 555 653 759 873 995 1125
((x + 1) - ((~x + ((2 - (x div 2)) div 2)) div 2))
A184732: 1 2 4 6 7 9 11 12 14 15 17 19 20 22 24 25
(1 + ((x + (((x div 2) * (x div 2)) div 2)) div 2))
A008642: 1 1 2 2 4 4 6 6 9 9 12 12 16 16 20 20
(1 + ((x + (2x div (2 + (x div 2)))) div 2))
A259549: 1 2 2 3 4 4 5 5 6 7 7 8 8 9 9 10
(x2 div ((2x + ~1) - ((~x + 2) div 2)))
A226033-A054404: 0 1 1 1 2 2 2 3 3 3 4 4 5 5 5 6
(10x2 + 4x + 1)
A272039: 1 15 49 103 177 271 385 519 673 847 1041 1255 1489 1743 2017 2311
(1 + (2 * (x + ((x + ((x div 2) mod 2)) div 2))))
A276283: 1 3 7 11 13 15 19 23 25 27 31 35 37 39 43 47
(1 + ((x * ((x + 2) + (2 * (x mod 2)))) div 2))
A266723: 1 3 5 11 13 23 25 39 41 59 61 83 85 111 113 143
(1 + ((x + (4x div (x + 2))) div 2))
A139338: 1 2 3 3 4 4 5 6 6 7 7 8 8 9 9 10
(4x3 + ~6x2 + 1)
A141530: 1 ~1 9 55 161 351 649 1079 1665 2431 3401 4599 6049 7775 9801 12151
(~1 + ((x + 2) * (1 + (x div 5))))
A138986: 1 2 3 4 5 13 15 17 19 21 35 38 41 44 47 67
(~1 + ((x + 2) * (1 + ((x div 2) div 3))))
A138987: 1 2 3 4 5 6 15 17 19 21 23 25 41 44 47 50
(x3 + 5x2 + 9x + 7)
A188377: 7 22 53 106 187 302 457 658 911 1222 1597 2042 2563 3166 3857 4642
(~1 + ((x + 2) * (1 + (x div 8))))
A173577: 1 2 3 4 5 6 7 8 19
(x3 + 2x2 + 5x + 11)
A271779: 11 19 37 71 127 211 329 487 691 947 1261 1639 2087 2611 3217 3911
(5x2 + 11x + 1)
A172044: 1 17 43 79 125 181 247 323 409 505 611 727 853 989 1135 1291
((x + 1) - (((x + ~1) * (x div 2)) div (x + 2)))
A340792-A112232: 1 2 3 4 4 5 6 6 7 8 8 9 9 10 10 11
(1 + ((x div ~8) mod (x + 2)))
A118716: 1 3 4 5 6 7 8 9 10 10 11 12 13 14 15 16
((x + 1) - ((1 mod (~2x + 1)) div (x + 2)))
A175431-A138836-A133398: 1 2 4 5 6 8 9 10 11 12 13 14 15 16 17 18
((~1 + (2 * (x mod 3))) mod (x + 3))
A284429: 2 1 3 5 1 3 8 1 3 11 1 3 14 1 3 17
(4x2 + 19x + 21)
A180863: 21 44 75 114 161 216 279 350 429 516 611 714 825 944 1071 1206
(x3 + 7x2 + 15x + 9)
A027620: 9 32 75 144 245 384 567 800 1089 1440 1859 2352 2925 3584 4335 5184
((x2 + 4x + 3) * (2 - (x mod 2)))
A039720: 6 8 30 24 70 48 126 80 198 120 286 168 390 224 510 288
(((x2 + ~3x + 2) div 2) div (x + 3))
A257481: 0 0 0 0 0 0 1 1 1 2 2 3 3 4
(x - ((x2 div 4) div (x + 3)))
A123731: 0 1 2 3 4 5 5 6 7 8 9 9 10 11 12 12
((2x + 6) * ((x + 2) + (x mod 2)))
A242371: 12 32 40 72 84 128 144 200 220 288 312 392 420 512 544 648
((x + 2) - ((~2x + 2) div (x + 3)))
A028729: 2 3 5 6 7 8 10 11 12 13 14 15
A171519: 2 3 5 6 7 8 10 11 12 13 14 15 16 17 18 19
(x - ((x * ((x + 1) div 2)) div (x + 3)))
A339187: 0 1 2 2 3 4 4 5 6 6 7 7 8 8 9 9
((2x + 2) - (x2 div (x + 3)))
A147613: 2 4 6 7 8 9 10 12 13 14 15 16 17 18 19 20
(x2 - (x3 div (x + 3)))
A335408: 0 1 3 5 7 10 12 15 18 21
(2x3 + 7x2 + 6x + 1)
A187277: 1 16 57 136 265 456 721 1072 1521 2080 2761 3576 4537 5656 6945 8416
(1 + ((x + 2) * (x + ((x + 1) * (x div 2)))))
A204557: 1 4 21 36 85 120 217 280 441 540 781 924 1261 1456 1905 2160
(1 + ((x * (4 + (x mod 2))) div (x + 2)))
A108414: 1 2 3 4 3 4 4 4 4 5 4 5 4 5 4 5
(1 + ((x + 2) * (2 - (1 mod (~x2 + 2)))))
A062605: 3 7 13 41
((x + 1) - ((x + ~2) * ((~x + 1) div 3)))
A309370: 1 2 3 5 7 12 15
((2x + 1) + (x div 7))
A184591: 1 3 5 7 9 11 13 16 18 20 22 24 26 28 31 33
((2x + 1) + (x mod (1 + (x div 4))))
A131628: 1 3 5 7 9 12 13
((2x + 1) + (2 div (1 + (x mod 4))))
A047499: 3 4 5 7 11 12 13 15 19 20 21 23 27 28 29 31
((2x + 5) - (2 mod (~2x + 1)))
A190035: 5 7 10 14 18 22 26 30 34 38 42 46 50 54 58 62
((2x + 1) + ((~1 + (x div 2)) * (x div 2)))
A264754: 1 3 5 7 11 13 19 21 29 31 41 43 55 57 71 73
(x - (x2 div ((2x + ~1) + (x div 2))))
A079952: 0 0 1 2 3 3 4 4 5 6 6 7 8 8 9 9
(8x2 + 14x + 5)
A181890: 5 27 65 119 189 275 377 495 629 779 945 1127 1325 1539 1769 2015
(4x3 + 6x2 + 4x + 1)
A005917: 1 15 65 175 369 671 1105 1695 2465 3439 4641 6095 7825 9855 12209 14911
(4x2 + 20x + 9)
A145923: 9 33 65 105 153 209 273 345 425 513 609 713 825 945 1073 1209
(16x2 + 10x + 1)
A028993: 1 27 85 175 297 451 637 855 1105 1387 1701 2047 2425 2835 3277 3751
((2x + 1) * (1 + ((x2 + x) div 2)))
A063488: 1 6 20 49 99 176 286 435 629 874 1176 1541 1975 2484 3074 3751
(10x2 + 7x + 1)
A033571: 1 18 55 112 189 286 403 540 697 874 1071 1288 1525 1782 2059 2356
(4x3 + 8x2 + 5x + 1)
A139757: 1 18 75 196 405 726 1183 1800 2601 3610 4851 6348 8125 10206 12615 15376
(((x + 1) * (x2 div 2)) div (2x + 1))
A194250: 0 0 1 2 4 6 9 12 16 21 26 31 37 43 50 57
((2x + 1) * ((x2 + 3x + 2) div 2))
A002414: 1 9 30 70 135 231 364 540 765 1045 1386 1794 2275 2835 3480 4216
(16x2 + 16x + 4)
A016826: 4 36 100 196 324 484 676 900 1156 1444 1764 2116 2500 2916 3364 3844
((x div ~7) mod (2x + 1))
A228295-A195125: 0 2 4 6 8 10 12 14 15 17 19 21 23 25 27 28
(17x + 7)
A154612: 7 24 41 58 75 92 109 126 143 160 177 194 211 228 245 262
((2x + 1) * (2 + ((x2 + x) div 2)))
A173965: 2 9 25 56 108 187 299 450 646 893 1197 1564 2000 2511 3103 3782
(8x2 + 3x + 1)
A236267: 1 12 39 82 141 216 307 414 537 676 831 1002 1189 1392 1611 1846
(((~x + ((x div 2) mod 2)) div 2) mod (2x + 1))
A227187: 0 2 4 6 7 8 10 12 13 14 16 18 19 20 22 24
(10x2 + ~7x + 1)
A158186: 1 4 27 70 133 216 319 442 585 748 931 1134 1357 1600 1863 2146
(((x3 + 2x) div 2) div (2x + ~1))
A194205: 0 1 2 3 5 7 10 13 17 21 26 32 38 44 51 58
(x - (2x mod (~2x2 + 4x + ~1)))
A224886: 0 1 2 4 13
(1 + (x div (12 - (x div 2))))
A091946: 1 1 1 1 1 1 1 1 2 2 2 2 3 3 3 4
((x + 1) - (((~x + 1) div 3) * (x div 2)))
A123120: 1 2 4 5 7 10 13
(1 + (((x + (x mod 3)) div 2) + (x div 2)))
A274631-A131042: 1 2 4 3 5 6 7 8 10 9 11 12 13 14 16 15
((x + 1) - ((~2x + (x div 2)) * (x div 2)))
A257083: 1 2 6 9 17 22 34 41 57 66 86 97 121 134 162 177
(13 * (1 + (x div 2)))
A166545: 13 13 26 26 39 39 52 52 65 65 78 78 91 91 104 104
(((x div 2) div ~3) mod (1 + (x div 2)))
A329242-A033270: 0 0 1 1 2 2 3 3 3 3 4 4 5 5 5 5
(((x + 1) - (x div ~2)) * (1 + (x div 2)))
A014255: 1 3 8 12 21 27 40 48 65 75 96 108 133 147 176 192
(((x2 + 3x + 2) div 2) * (1 + (x div 2)))
A212760: 1 3 12 20 45 63 112 144 225 275 396 468 637 735 960 1088
((x + (2 * (x mod 2))) * (2 div (1 + (x div 2))))
A021020: 0 6 2 5 0 0 0 0 0 0 0 0 0 0 0 0
((x div 2) - (~2x div (1 + (x div 2))))
A216522-A086419: 0 2 3 4 5 6 6 7 8 8 9 9 10 10 11 11
((x + (x div 5)) div (1 + (x div 2)))
A084359: 0 1 1 1 1 2 1 2 1 2 2 2 2 2 2 2
((x + 4) - ((~x + 1) div (1 + (x div 2))))
A336867: 3 5 7 8 9 11 12 13 14 15 16 17 18 19 20 21
((x + 1) + ((3 mod (x + 1)) + (x div 2)))
A152520: 1 3 4 8 10 11
((x + 1) + (((x div 3) mod 2) + (x div 2)))
A263800: 1 2 4 6 8 9 10
((x + (x div 8)) div (1 + (x div 2)))
A309025: 0 1 1 1 1 1 1 1 1 2 1 2 1 2 1 2
((x + 1) + (((x div 4) mod 2) + (x div 2)))
A286031: 1 2 4 5 8 9 11 12 13 14 16 17 20 21 23 24
((x + 1) + ((4 * (x mod 2)) + (x div 2)))
A177898-A168198: 1 6 4 9 7 12 10 15 13 18 16 21 19 24 22 27
(((x div 2) - (x * (x mod 2))) * (1 + (x div 2)))
A083392: 0 ~1 2 ~4 6 ~9 12 ~16 20 ~25 30 ~36 42 ~49 56 ~64
(5x + (x mod (1 + (x div 2))))
A178181: 0 5 10 16 21 27 32 38 43 49 54
(1 + (x * (2 + (x * (x mod 2)))) - (x div 2))
A174406: 1 4 4 15
(1 + ((3 * (x mod 3)) + (x mod 2)))
A153110: 1 5 7 2 4 8 1 5 7 2 4 8 1 5 7 2
((2x + 4) - (x mod (3 - (x mod 2))))
A334457: 4 5 6 9 11 13 16
((1 + (x mod ~3)) * (1 + (x mod 2)))
A112300: 1 ~2 0 2 ~1 0 1 ~2 0 2 ~1 0 1 ~2 0 2
((x3 + x2 + x + 1) div (1 + (x mod 2)))
A281660: 1 2 15 20 85 78 259 200 585 410 1111 732 1885 1190 2955 1808
(x div (1 - ((x div ~2) div (1 + (x mod 2)))))
A338731: 0 0 1 1 1 1 1 2 1 2 1 2 1 2 1 3
((x mod 10) div (1 + (x mod 2)))
A107130: 0 0 2 1 4 2 6 3 8 4 0 0 2 1 4 2
(((1 + (x div 2)) * (x div 2)) div (1 + (x mod 2)))
A131174: 0 0 2 1 6 3 12 6 20 10 30 15 42 21 56 28
((2x + 1) - (2 mod ((~x + 1) - (x mod 2))))
A097911: 1 3 5 8
A005004: 1 3 5 8 10 14 16 20 22 26 28 32 34 38 40 44
((2x2 + 1) - ((~x2 + 2x) div 2))
A128127: 1 3 9 21 37 59
(x4 + x3 + 3x2 + 2x + 1)
A304160: 1 8 41 142 377 836 1633 2906 4817 7552 11321 16358 22921 31292 41777 54706
(1 - ((~x2 + 2x) div (1 + (x2 div 2))))
A140474: 1 0 1 2 2 3 3 3 3 3 3 3 3 3 3 3
((x2 div 4) * (~1 + (x2 div 2)))
A227970: 0 0 1 6 28 66 153 276 496 780 1225 1770 2556 3486 4753 6216
((~x + ~1) * (((x mod 2) - (x div 2)) div 2))
A308123: 0 0 3 0 5 6 14 8 18 20 33 24 39 42 60 48
(x - ((2 * (x + (x div 2))) div (~x + ~1)))
A274333: 0 2 4 5 7 8 9 10 11 12 13 14 15 16 17 18
(12x2 + x + 1)
A244804: 1 14 51 112 197 306 439 596 777 982 1211 1464 1741 2042 2367 2716
(8x2 + 7x + 1)
A194268: 1 16 47 94 157 236 331 442 569 712 871 1046 1237 1444 1667 1906
((x + 1) + ((x + 2) div 7))
A023055: 1 2 3 4 5 7 8 9 10 11 12 13 15 16 17 18
((x + 1) + (2x div 7))
A039081: 1 2 3 4 6 7 8 10 11 12 13 15 16 17 19 20
(1 + compr(\x.(~1 + (x mod (2 + (x mod 3)))),x))
A039212: 1 2 4 5 6 7 8 9 10 11 13 14 16 17 18 19
(16x2 + x + 1)
A143859: 1 18 67 148 261 406 583 792 1033 1306 1611 1948 2317 2718 3151 3616
(16x2 + ~x + 1)
A143860: 1 16 63 142 253 396 571 778 1017 1288 1591 1926 2293 2692 3123 3586
(x div (~1 + (x * (1 + (x mod 8)))))
A318584: 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
((x + 1) + (5 * (x div 3)))
A047475: 1 2 3 9 10 11 17 18 19 25 26 27 33 34 35 41
(~x + 39)
A022995: 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24
((x + 1) + (2x2 div 5))
A025718-A022783: 1 2 4 7 11 16 21 27 34 42 51 60 70 81 93 106
((x + 1) + ((x2 + 2x) div 5))
A183873: 1 2 4 7 9 13 16 20 25 29 35 40 46 53 59 67
((x + 1) + (2x div (3 + (x div 2))))
A059921: 1 2 4 5 6 8 9 10 11 12 13 14 15 16 17 19
((x + 1) + (3 * (x div 5)))
A194398-A047603: 1 2 3 4 5 9 10 11 12 13 17 18 19 20 21 25
((x + 1) + (9 * (x div 2)))
A143795: 1 2 12 13 23 24 34 35 45 46 56 57 67 68 78 79
((x + 1) + ((2 * (x div 3)) div 3))
A039162: 1 2 3 4 5 6 8 9 10 12 13 14 15 16 17 19
(13x + 7)
A269044: 7 20 33 46 59 72 85 98 111 124 137 150 163 176 189 202
((x + 1) + (6 * (x div 4)))
A084544: 1 2 3 4 11 12 13 14 21 22 23 24 31 32 33 34
((x + 1) + (x2 div 12))
A113769: 1 2 3 4 6 8 10 12 14 16 19 22 25 28 31 34
((x + 1) + ((x mod (2 + (x div 2))) div 3))
A332110-A188301: 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 18
((x + 1) + ((x2 + (x div 2)) div 3))
A078617: 1 2 4 7 11 15 20 25 31 38 46 54 63 72 82 93
(3x3 + 7x2 + 5x + 1)
A100176: 1 16 63 160 325 576 931 1408 2025 2800 3751 4896 6253 7840 9675 11776
(9x2 + 9x + 2)
A001504: 2 20 56 110 182 272 380 506 650 812 992 1190 1406 1640 1892 2162
(9x2 + 15x + 4)
A085024-A085001: 4 28 70 130 208 304 418 550 700 868 1054 1258 1480 1720 1978 2254
((x + 1) + ((x + (x div 4)) div 3))
A184622-A184580: 1 2 3 5 6 8 9 10 12 13 15 16 18 19 20 22
(1 - (x2 mod (~x3 + x2 + 1)))
A039749: 1 1 3 9 32
(3x3 + 2x2 + x + 1)
A130884: 1 7 35 103 229 431 727 1135 1673 2359 3211 4247 5485 6943 8639 10591
((x + 1) + ((x mod ~3) mod (x + 1)))
A080031: 1 2 5 4 8 11 7 14 17 10 20 23 13 26 29 16
(x2 + x + 17)
A007635: 17 19 23 29 37 47 59 73 89 107 127 149 173 199 227 257
(x5 + ~x4 + x3 + ~x2 + x + ~1)
A062159: ~1 0 21 182 819 2604 6665 14706 29127 53144 90909 147630 229691 344772 501969 711914
((x + 1) + (2 * (x div 7)))
A031492: 1 2 3 4 5 6 7 10 11 12 13 14 15 16 19 20
((x + 1) + (2 * ((x + 1) div 5)))
A285405: 1 2 3 4 7 8 9 10 11 14 15 16 17 18 21 22
(x div ((x + ~1) + (x mod 10)))
A030564: 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0
(1 + compr(\x.((x div (~3 + (x mod 2))) mod 2),x))
A005556: 1 4 5 7 8 11
A228919: 1 4 5 7 8 11 12 13 16 17 19 20 23 24 25 28
((x + 1) + ((3 * (1 + (x div 2))) div 2))
A191215: 2 3 6 7 9 10 13 14 16 17 20 21 23 24 27 28
((x + 1) + (2 * (((x + 1) div 2) div 3)))
A080401: 1 2 3 4 5 8 9 10 11 12 13 16 17 18 19 20
(1 mod (~1 + (x * ((x + 1) mod 6))))
A086597: 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1
((x + 1) + (x div (2 + (2 mod (1 + (x div 2))))))
A247419: 1 2 4 5 6 7 8 9 11 12 13 14 16 17 18 19
((x + 1) + (4 * ((x div 2) div 3)))
A057436: 1 2 3 4 5 6 11 12 13 14 15 16 21 22 23 24
((x + 1) + (2 * ((x mod (1 + (x div 2))) div 2)))
A276878: 1 2 3 4 5 8 9 10 11 14 15 16 17 20 21 22
(1 + (x * (2 + ((x2 + 3x + 2) div 2))))
A132127: 1 6 17 37 69 116 181 267 377 514 681 881 1117 1392 1709 2071
((x + 1) + (2 * (((x + ~1) * (x div 2)) div 2)))
A337172: 1 2 3 6 11 14
((x + 1) + ((x - (x div ~4)) div 2))
A225647: 1 3 4 6 7
A247425: 1 3 4 6 7 9 11 12 14 16 17 19 20 22 24 25
(x + 65)
A130764: 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
((x div 2) div (~x + 17))
A034407: 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 3
((x + 1) + ((x - (x div 8)) div 2))
A307513-A186515-A059539: 1 2 4 5 7 8 10 11 12 14 15 17 18 20 21 23
((x + 1) + (2 * (x2 div 8)))
A302488: 1 2 3 6 9 12 15 20 25 30 35 42 49 56 63 72
((x + 1) + (2 * ((x - (x div 4)) div 2)))
A286751: 1 2 5 6 7 10 11 14 15 16 19 20 21 24 25 28
(x - (x2 div (x + 9)))
A061420: 0 1 2 3 3 4 4 4 5 5 5 5 6 6 6 6
((x + 1) + ((x2 + 2x) div 8))
A191535-A100598: 1 2 4 5 8 10
A186349: 1 2 4 5 8 10 13 15 19 22 26 29 34 38 43 47
((x + 1) + (8 * (x + (x mod 2))))
A118510: 1 18 19 36 37 54 55 72 73
(x - (2 mod ((~x + ~1) + (x div 8))))
A172277: 0 1 3 5 7 9 11 13 14 16 18 20 22 24 26 28
(x - (x mod ((~x + ~1) + (x mod 8))))
A084689: 0 1 2 3 4 5 6 7 9
A265570: 0 1 2 3 4 5 6 7 9 9 18 18 18 18 18 18
((x + 1) + (x div (~2 + ((~x + 2) div 4))))
A247983: 1 1 2 3 3 4 5 6 7 7 8 9 10 11 12 13
((x + 1) + ((x - ((~x + 2) div 4)) div 2))
A247910-A184658-A026273: 1 2 4 6 7 9 10 12 14 15 17 19 20 22 23 25
((x + 1) + (2 * ((x + (x div 2)) div 4)))
A276887: 1 2 3 6 7 8 11 12 15 16 17 20 21 22 25 26
((x + 1) + (2x div (4 + (x div 2))))
A213367-A175084-A072099: 1 2 3 5 6 7 8 10 11 12 13 14 15 16 17 18
((x + 1) + ((x3 + x) div 4))
A292528: 1 2 5 11 22
(1 + compr(\x.(x mod (2 + ((x * (x div 2)) mod 2))),x))
A128201: 1 3 4 5 7 9 11 13 15 16 17 19 21 23 25 27
(x3 + 6x2 + 6x + 1)
A090197: 1 14 45 100 185 306 469 680 945 1270 1661 2124 2665 3290 4005 4816
((x + 1) + (((1 + (x div 2)) * (x div 2)) div 2))
A101881: 1 2 4 5 8 9 13 14 19 20 26 27 34 35 43 44
((x + 1) + (((x2 + ~1) * (x div 2)) div 2))
A222011: 1 2 4 8
A014225: 1 2 4 8 20
((x + 1) + ((((x + ~1) div 2) * (x div 2)) div 2))
A328325-A005705-A001972: 1 2 3 4 6 8 10 12 15 18 21 24 28 32 36 40
((2x + 4) div (1 + (x * (2 + (x mod 2)))))
A110916: 4 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0
((x + 1) + (2 * (x + (x div 5))))
A276874: 1 4 7 10 13 18 21 24 27 30 35 38 41 44 47 52
((x + 1) + ((x + ((x div 2) div 3)) div 2))
A020914: 1 2 4 5 7 8 10 12 13 15 16 18 20 21 23 24
((x + 1) + (x2 div (3x + ~2)))
A285659: 1 3 4 5 6 7 9 10 11 13 14 15 17 18 19 21
((x + 1) + ((x + (x2 div 3)) div 2))
A186357: 1 2 4 7 9 12 16 19 23 28 32 37 43 48 54 61
((x + 1) + (2 * (x + ((x mod 3) div 2))))
A028837: 1 4 9 10 13 18 19 22 27 28 31 36 37 40 45 46
((x + 1) + ((x + (x div 8)) div 2))
A226896: 1 2 4 5 7 8 10 11 13 15 16 18 19 21 22 24
(x4 + 5x3 + 9x2 + 7x + 2)
A179824: 2 24 108 320 750 1512 2744 4608 7290 11000 15972 22464 30758 41160 54000 69632
(x5 + 3x4 + 3x3 + x2)
A099762: 0 8 108 576 2000 5400 12348 25088 46656 81000 133100 209088 316368 463736 661500 921600
((x2 + 2x + 1) * ((x2 + 1) div 2))
A177755: 0 4 18 80 200 468 882 1600 2592 4100 6050 8784 12168 16660 22050 28928
(4x4 + 8x3 + 4x2)
A060300: 0 16 144 576 1600 3600 7056 12544 20736 32400 48400 69696 97344 132496 176400 230400
((x2 + 2x + 1) * (1 - (2 * (x mod 2))))
A162395: 1 ~4 9 ~16 25 ~36 49 ~64 81 ~100 121 ~144 169 ~196 225 ~256
((x2 + 2x + 1) * ((x2 + x) div 2))
A092364: 0 4 27 96 250 540 1029 1792 2916 4500 6655 9504 13182 17836 23625 30720
(x4 + ~6x2 + 1)
A272870: 1 ~4 ~7 28 161 476 1081 2108 3713 6076 9401 13916 19873 27548 37241 49276
((x2 + ~2x + 1) * ((x2 + ~x) div 2))
A019582: 0 0 1 12 54 160 375 756 1372 2304 3645 5500 7986 11232 15379 20580
((x + 1) + (2 div (8 - (x div 2))))
A290492: 1 2 3 4 5 6 7 8 9 10 11 12 14
A246450: 1 2 3 4 5 6 7 8 9 10 11 12 14 15 17 18
(1 + (((x + 2) + (x div 2)) * (x + (x div 2))))
A135556: 1 4 16 25 49 64 100 121 169 196 256 289 361 400 484 529
(1 + (((x + 1) + (x div 2)) * (x + (x mod 2))))
A319384: 1 5 9 21 29 49 61 89 105 141 161 205 229 281 309 369
(4x - (1 div ((x + ~1) + (x mod 2))))
A336705: 1 3 7 12 16 20 24 28 32 36 40 44 48 52 56 60
((x + 1) * (1 + (x mod 9)))
A213630: 1 4 9 16 25 36 49 64 81 10 22 36 52 70 90 112
(19 div (x + 1))
A033339: 19 9 6 4 3 3 2 2 2 1 1 1 1 1 1 1
(25 div (x + 1))
A033345: 25 12 8 6 5 4 3 3 2 2 2 2 1 1 1 1
(23 div (x + 1))
A033343: 23 11 7 5 4 3 3 2 2 2 2 1 1 1 1 1
(3x3 + 6x2 + 4x + 1)
A005915: 1 14 57 148 305 546 889 1352 1953 2710 3641 4764 6097 7658 9465 11536
(((x + 2) div (1 + (x div 3))) mod (x + 1))
A131294: 0 1 1 2 3 3 2 3 3 2 3 3 2 3 3 2
((x + 1) * ((x + 1) - (x2 div ~2)))
A074149: 1 6 15 36 65 114 175 264 369 510 671 876 1105 1386 1695 2064
((1 + ((~x + 2) mod 6)) div (x + 1))
A307753: 3 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0
(21 div (x + 1))
A033341: 21 10 7 5 4 3 3 2 2 2 1 1 1 1 1 1
(33 div (x + 1))
A033353: 33 16 11 8 6 5 4 4 3 3 3 2 2 2 2 2
(31 div (x + 1))
A033351: 31 15 10 7 6 5 4 3 3 3 2 2 2 2 2 1
(8x2 + 25x + 17)
A005570: 17 50 99 164 245 342 455 584 729 890 1067 1260 1469 1694 1935 2192
(30 div (x + 1))
A033350: 30 15 10 7 6 5 4 3 3 3 2 2 2 2 2 1
(40 div (x + 1))
A033360: 40 20 13 10 8 6 5 5 4 4 3 3 3 2 2 2
((~1 + ((x2 + ~x) div 4)) mod (x + 1))
A194765: 0 1 2 0 2 4 6 1 4 7 10 2 6 10 14 3
((x + 1) * (~1 + ((x2 + 4x + 4) div 2)))
A180857: 1 6 21 44 85 138 217 312 441 590 781 996 1261 1554 1905 2288
((2x mod (x + 5)) mod (x + 1))
A212598: 0 0 1 2 3 0 1 2 3 4 5 6 7 8 9 10
((2x div (~3 + (x mod 2))) mod (x + 1))
A082460: 0 1 1 1 2 1 3 1 3 1 4 1 5 1 5 1
(27 div (x + 1))
A033347: 27 13 9 6 5 4 3 3 3 2 2 2 2 1 1 1
(36 div (x + 1))
A033356: 36 18 12 9 7 6 5 4 4 3 3 3 2 2 2 2
(48 div (x + 1))
A033368: 48 24 16 12 9 8 6 6 5 4 4 4 3 3 3 3
(~x2 + 12x + 13)
A136316: 13 24 33 40 45 48 49 48 45 40 33 24 13 0 ~15 ~32
compr(\x.((x * (x div 3)) mod 3),(x + 1))
A344208: 1 2 3 6 9 10 11 12 15 18 19 20 21 24 27 28
(4x3 + 6x2 + 3x + 1)
A050492: 1 14 63 172 365 666 1099 1688 2457 3430 4631 6084 7813 9842 12195 14896
((x + 1) * (1 + ((x3 + x) div 2)))
A100177: 1 4 18 64 175 396 784 1408 2349 3700 5566 8064 11323 15484 20700 27136
((x + 1) * (1 + (x3 div (x + 2))))
A274543: 1 2 9 24 55
(((x2 div 2) * (1 + (x div 2))) mod (x + 1))
A226782: 0 0 1 0 4 0 2 0 7 0 3 0 10 0 4 0
((x + 1) * ((x + 1) + (x div 5)))
A108612: 1 4 9 16 25 42 56 72 90 110 143 168 195 224 255 304
(4x3 + 5x2 + 2x + 1)
A204674: 1 12 57 160 345 636 1057 1632 2385 3340 4521 5952 7657 9660 11985 14656
((1 + (x * ((x + ~1) div 3))) div (x + 1))
A247049: 1 0 0 0 1 1 1 1 1 1 2 2 2 3 3 3
((x + 1) * ((x + 1) + (x2 div 3)))
A192736: 1 4 12 28 50 84 133 192 270 370 484 624 793 980 1200 1456
(2 - ((x + 1) * ((~x + ~1) + (x mod 4))))
A083400: 3 4 5 6 27
((x + 1) * ((x + 1) + (x2 div 4)))
A128624: 1 4 12 24 45 72 112 160 225 300 396 504 637 784 960 1152
(x5 + x4 + 2x3 + 2x2 + x + 1)
A288487: 1 8 75 400 1445 4056 9583 20000 38025 67240 112211 178608 273325 404600 582135 817216
(26 div (x + 1))
A033346: 26 13 8 6 5 4 3 3 2 2 2 2 2 1 1 1
(22 div (x + 1))
A033342: 22 11 7 5 4 3 3 2 2 2 2 1 1 1 1 1
(34 div (x + 1))
A033354: 34 17 11 8 6 5 4 4 3 3 3 2 2 2 2 2
((x + 1) * ((x2 + 4x + 3) div 2))
A138179: 1 8 21 48 85 144 217 320 441 600 781 1008 1261 1568 1905 2304
((x + 1) * ((x + 1) mod (2 * (1 + (x mod 2)))))
A251610: 1 4 3 0 5 12 7 0 9 20 11 0 13 28 15 0
(((1 + ((~x2 + x) div 2)) div 2) mod (x + 1))
A194763: 0 0 0 3 2 1 0 6 4 2 0 9 6 3 0 12
((x + 1) * (((x + 1) + (x div 4)) div 2))
A293688: 0 2 3 8 15 18 28 32 45 60 66 84 104 112 135 144
((x + 1) * (2 + ((1 + (x mod 2)) mod (x + 1))))
A014290: 2 4 9 16 15
((x + 1) * ((x3 + 3x2 + 2x) div 2))
A083374: 0 6 36 120 300 630 1176 2016 3240 4950 7260 10296 14196 19110 25200 32640
(28 div (x + 1))
A033348: 28 14 9 7 5 4 4 3 3 2 2 2 2 2 1 1
((2 + (((1 + (x div 2)) div 2) div 2)) mod (x + 1))
A345376: 0 0 2 2 2 2 3 3 3 3 3 3 3 3 4 4
(64x + 64)
A044187: 64 128 192 256 320 384 448 512 576 640 704 768 832 896 960 1024
(64 div (x + 1))
A033384: 64 32 21 16 12 10 9 8 7 6 5 5 4 4 4 4
(4x2 + 28x + 24)
A277108: 24 56 96 144 200 264 336 416 504 600 704 816 936 1064 1200 1344
((2 + ((x + ~2) mod 8)) mod (x + 1))
A103303: 0 1 2 3 4 5 6 7 8 9
A322001-A273005-A244158-A093017-A081594-A028897: 0 1 2 3 4 5 6 7 8 9 2 3 4 5 6 7
((2 + ((x - ((x div 2) mod 2)) div 2)) mod (x + 1))
A173073: 0 0 2 3 4 4 4 5 6 6 6 7 8 8 8 9
(2x3 + 6x2 + 12x + 8)
A153976: 8 28 72 152 280 468 728 1072 1512 2060 2728 3528 4472 5572 6840 8288
((x + 1) * ((2x mod (2 + (x div 2))) mod 2))
A308229: 0 0 3 0 0 0 0 0 0 0 0 12 0 0 15 16
(x mod ((4 + (x2 div 2)) div (x + 1)))
A175835: 0 1 0 1 0 1 0 1 0 1 2 1 2 1 2 1
((4x + 4) + ((1 + (x div 2)) div 2))
A299641: 4 8 13 17 21 25 30 34 38 42 47 51 55 59 64 68
((4x + 4) + ((~1 + (x div 2)) div 2))
A299638: 3 7 12 16 20 24 29 33 37 41 46 50 54 58 63 67
((4x + 4) + (x div 8))
A171984: 4 8 12 16 20 24 28 32 37 41 45 49 53 57 61 65
(((~x2 + 3x) div 4) mod (x + 1))
A194743: 0 0 0 0 4 3 2 1 8 6 4 2 12 9 6 3
(2 - ((2 - (x2 div 4)) div (x + 1)))
A103298: 0 1 2 2 3 3 3 4 4 4 5 5 5 5 6 6
compr(\x.(x mod (2 + ((x * (x div 2)) mod 2))),(x + 1))
A336367: 2 3 4 6 8 10 12 14 15 16 18 20 22 24 26 27
((8 mod (x + 4)) div (x + 1))
A258825: 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0
((2x2 + 6x + 6) - (x mod 2))
A343007: 6 13 26 41 62 85 114 145 182 221 266 313 366 421 482 545
(1 - (2 mod (~4x2 + ~4x + 2)))
A265056: 1 5 21 45 77 117 165 221 285 357 437 525 621 725 837 957
(((~x + ((x div 4) mod 2)) div 2) mod (x + 1))
A089575: 0 1 2 2 3 4 4 5 5 5 6 6 7 8 8 9
((x2 mod (x - ((~x + 2) div 2))) div (x + 1))
A175861: 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0
(x3 + 4x2 + 8x + 4)
A166781: 4 17 44 91 164 269 412 599 836 1129 1484 1907 2404 2981 3644 4399
(((x2 - (x div 2)) mod (x + 2)) div (x + 1))
A031250: 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0
((x2 + 3x + 2) + (x2 div 4))
A226292: 2 6 13 22 34 48 65 84 106 130 157 186 218 252 289 328
((1 - (4 mod (~2x + 1))) div (x + 1))
A267587: 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1
((2x2 + 2x) + ((x2 + ~x) div 2))
A147875: 0 4 13 27 46 70 99 133 172 216 265 319 378 442 511 585
(13x2 + 13x)
A173307: 0 26 78 156 260 390 546 728 936 1170 1430 1716 2028 2366 2730 3120
(11x2 + 11x)
A164136: 0 22 66 132 220 330 462 616 792 990 1210 1452 1716 2002 2310 2640
(2 - ((x2 + x) * (~1 + (x div ~2))))
A071636: 2 6 14 38 62
(17x2 + 17x)
A173308: 0 34 102 204 340 510 714 952 1224 1530 1870 2244 2652 3094 3570 4080
(9x2 + 17x + 8)
A154516: 8 34 78 140 220 318 434 568 720 890 1078 1284 1508 1750 2010 2288
((x + 1) + (2 div (~x + 16)))
A290748-A246085-A246078-A246075-A033066-A032964: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 16 18
((x * (2 + (x mod 8))) div (x + 1))
A055401-A053829: 0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8
((x * (4 + (x div 4))) div (x + 1))
A079243: 0 2 2 3
A270826: 0 2 2 3 4 4 4 4 5 5 5 5 6 6 6 6
((2x mod (x + 8)) mod (x + 1))
A055400: 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7
((x + 1) + ((x + (x mod 2)) * (x + (x mod 2))))
A081348: 1 6 7 20 21 42 43 72 73 110 111 156 157 210 211 272
((x + 1) * (x2 + ((x + 2) mod 4)))
A135443: 2 8 12 40
(x5 + x4 + ~3x3 + ~x2 + 2x)
A192849: 0 0 24 240 1080 3360 8400 18144 35280 63360 106920 171600 264264 393120 567840 799680
((x + ~1) * (x - ((~x3 + x2) div 2)))
A212135: 0 0 4 24 84 220 480 924 1624 2664 4140 6160 8844 12324 16744 22260
(3x3 + ~5x2 + 3x)
A226450: 0 1 10 45 124 265 486 805 1240 1809 2530 3421 4500 5785 7294 9045
(x7 + ~x6)
A240930: 0 0 64 1458 12288 62500 233280 705894 1835008 4251528 9000000 17715610 32845824 57921708 97883968 159468750
(17x2 + ~1)
A321180: ~1 16 67 152 271 424 611 832 1087 1376 1699 2056 2447 2872 3331 3824
(x4 + 5x2 + 1)
A082113: 1 7 37 127 337 751 1477 2647 4417 6967 10501 15247 21457 29407 39397 51751
(7x2 + 4x + 1)
A005892: 1 12 37 76 129 196 277 372 481 604 741 892 1057 1236 1429 1636
(2x3 + 3x2 + 4x + 1)
A047672: 1 10 37 94 193 346 565 862 1249 1738 2341 3070 3937 4954 6133 7486
(1 + (x2 * (2 + ((x2 + ~x) div 2))))
A318165: 1 3 13
A239592: 1 3 13 46 129 301 613 1128 1921 3079 4701 6898 9793 13521 18229 24076
(1 + (x * (2 - (1 mod (~3x + 4)))))
A298125: 1 3 7 19 37 61 91 127 169 217 271 331 397 469 547 631
((x2 + 1) + (2 mod (1 + (x mod 3))))
A105770: 1 2 7 10 17 28 37 50 67 82 101 124 145 170 199 226
(2x4 + 2x3 + 3x2 + 2x + 1)
A058920: 1 10 65 250 697 1586 3145 5650 9425 14842 22321 32330 45385 62050 82937 108706
(x6 + x4 + x2 + 1)
A059830: 1 4 85 820 4369 16276 47989 120100 266305 538084 1010101 1786324 3006865 4855540 7568149 11441476
(x - ((x2 + 1) * ((~x2 + x) div 2)))
A100855: 0 1 7 33 106 265 561 1057 1828 2961 4555 6721 9582 13273 17941 23745
(x5 + ~x4 + x3 + ~x2 + x)
A191012: 0 1 22 183 820 2605 6666 14707 29128 53145 90910 147631 229692 344773 501970 711915
(x6 + x3 + 1)
A060883: 1 3 73 757 4161 15751 46873 117993 262657 532171 1001001 1772893 2987713 4829007 7532281 11394001
(x6 + ~x3 + 1)
A060891: 1 1 57 703 4033 15501 46441 117307 261633 530713 999001 1770231 2984257 4824613 7526793 11387251
(x7 + 1)
A258806: 1 2 129 2188 16385 78126 279937 823544 2097153 4782970 10000001 19487172 35831809 62748518 105413505 170859376
(x3 + 17)
A084379: 17 18 25 44 81 142 233 360 529 746 1017 1348 1745 2214 2761 3392
((x + 2) - ((x div 5) div ~2))
A183219: 2 3 4 5 6 8 9 10 11 12 13 14 15 16 17 19
(~2 * ((x - (x2 div 4)) div 2))
A182568: 0 0 0 0 0 2 4 6 8 12 16 20 24 30 36 42
(((x + 1) mod 2) - (x div ~8))
A185319: 1 1 2 1 2 1 2 1 2 2 3 2 3 2 3 2
((x div 4) - (x div ~8))
A260731-A119026: 0 1 1 1 2 2 2 2 3 4 4 4 5 5 5 5
(4x - (x div ~8))
A198395: 0 5 9 13 17 21 25 29 33 38 42 46 50 54 58 62
(((x + 1) div 2) - ((x div 4) div ~2))
A050292: 0 1 1 2 3 4 4 5 5 6 6 7 8 9 9 10
((x mod 4) - ((x div 4) div ~2))
A339822: 0 1 2 3 1 2 3 4 1 2 3 4 2 3 4 5
(3x - ((x mod 4) div ~2))
A319280: 0 4 7 11 12 16 19 23 24 28 31 35 36 40 43 47
(((~x + ((x div 4) mod 2)) div 2) div ~2)
A192002-A074795-A072358: 0 0 0 1 1 1 1 1 2 2 2 3 3 3 3 3
((2x + 2) - ((x + (x div 2)) div ~2))
A248520: 2 5 8 10 13 16 19 21 24 27 30 32 35 38 41 43
(2 - (7 * (x div ~2)))
A168333: 2 9 9 16 16 23 23 30 30 37 37 44 44 51 51 58
((8x + 4) - (x div ~2))
A155095: 4 13 21 30 38 47 55 64 72 81 89 98 106 115 123 132
(x - ((~x2 + 2x) div (2 - (x div ~2))))
A004401: 0 1 2 4 6 8 11 13 16 18
(2 - ((x2 + 2x + 2) * (x div ~2)))
A092831: 2 7 12 36
(2 - (((x + 2) + (x div 2)) * (x div ~2)))
A133146: 2 5 7 14 18 29 35 50 58 77 87 110 122 149 163 194
((1 + (x div (1 + (x div 5)))) mod 2)
A325616-A101688-A026836: 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0
((x div (1 + (x mod (1 + (x div 3))))) mod 2)
A279863: 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 1
((1 + (x mod (2 - (x div ~3)))) mod 2)
A104521: 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0
(((x + ~1) mod (~1 + (x div ~3))) mod 2)
A328979: 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0
((4 mod (~1 + (x div ~3))) mod 2)
A224782-A027870: 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0
((2x div (~1 + (x div ~3))) mod 2)
A341684: 0 1 0 1 1 0 0 0 0 1 0 1 1 1 1 1
((2x mod (~1 + (x div ~3))) mod 2)
A319581: 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0
((1 + (2x mod (~1 + (x div ~2)))) mod 2)
A318997: 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1
((1 + ((x + 1) mod 7)) mod 2)
A191156: 0 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1
((1 + ((x + 2) mod 7)) mod 2)
A341150-A298426-A113704: 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 0
((1 + ((x + ~2) mod 7)) mod 2)
A073070: 0 1 1 0 1 0 1 0 1 1 0 1 0 1 0 1
((1 + (2x div 7)) mod 2)
A130657: 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1
((1 + ((~x + 2) mod 7)) mod 2)
A128174-A097304-A096055: 1 0 1 1 0 1 0 1 0 1 1 0 1 0 1 0
((1 + (x mod (~1 + (2 * (x div 3))))) mod 2)
A214088-A141646-A129573: 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1
(2 * ((x + 1) - (x div ~5)))
A005795: 2 6 8 10 12 14 18
((1 + (x mod (~1 + (x mod ~4)))) mod 2)
A089011: 1 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0
((1 + (x mod (1 + (((x + 1) div 2) div 2)))) mod 2)
A132194: 1 1 1 0 1 0 1 0 1 1 0 0 1 0 1 1
((1 + (2x div 9)) mod 2)
A130630: 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0
((1 + ((~x + 2) mod 9)) mod 2)
A286990: 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0
((1 + (x div (2x + ~9))) mod 2)
A168553: 1 0 0 0 1 0 1 0 0 0 1 1
(20x + 12)
A305074: 12 32 52 72 92 112 132 152 172 192 212 232 252 272 292 312
(2 * (~1 + (5 * (1 + (x div 2)))))
A168456: 8 8 18 18 28 28 38 38 48 48 58 58 68 68 78 78
(((x + ~1) - ((x div 2) mod 5)) mod 2)
A285258: 1 0 0 1 1 0 0 1 1 0 1 0 0 1 1 0
(10x2 + 10x + 2)
A273366: 2 22 62 122 202 302 422 562 722 902 1102 1322 1562 1822 2102 2402
((x mod (~1 + ((~x + 2) div 5))) mod 2)
A324883: 0 0 0 1 0 1 0 1 1 0 0 1 0 1 0 1
((x mod (1 + ((~x + 2) mod 5))) div 2)
A288377: 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0
(2 * (1 + ((x + (x div 2)) div 5)))
A214628: 2 2 2 2 4 4 4 6 6 6 8 8 8 8 10 10
((x - (2 div (1 + (x div 5)))) mod 2)
A244221-A159684: 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1
((x - (x mod (1 + (x div 5)))) mod 2)
A179829: 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0
(((x + ~1) div (1 + (x mod 5))) mod 2)
A017871: 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0
(18x + 20)
A345339: 20 38 56 74 92 110 128 146 164 182 200 218 236 254 272 290
((1 + ((x2 div 3) mod 3)) mod 2)
A305387: 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1
(24x + 14)
A142241: 14 38 62 86 110 134 158 182 206 230 254 278 302 326 350 374
((x mod ~13) mod 2)
A144599: 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1
((1 + ((x mod 8) mod 3)) mod 2)
A144612: 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0
(((x + ~2) div 13) mod 2)
A216280: 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
(x2 mod 26)
A070448: 0 1 4 9 16 25 10 23 12 3 22 17 14 13 14 17
(x mod (2 + (x mod 13)))
A103303: 0 1 2 3 4 5 6 7 8 9
A053833: 0 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3
(x2 mod 22)
A070444: 0 1 4 9 16 3 14 5 20 15 12 11 12 15 20 5
(((x + 1) div (1 + (2x mod 3))) mod 2)
A245837: 1 0 1 0 1 1 1 0 0 0 1 0 1 0 1 0
((x div (1 + (3 * (2 - (x div 2))))) mod 2)
A144195: 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0
(((x + 1) mod (~1 + (3 * (x div 2)))) mod 2)
A106138: 0 0 1 0 0 1 1 0 1 0 1 0 1 0 1 0
((2x mod (~1 + (3 * (x div 2)))) mod 2)
A340006: 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0
(((x + ~1) div (1 + ((x div 2) div 3))) mod 2)
A320179: 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 0
(((x + ~1) mod (1 + ((x div 2) div 3))) mod 2)
A277147: 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0
(((~x + 1) div (1 + ((x div 2) mod 3))) mod 2)
A322980: 1 0 1 1 1 0 1 0 0 0 1 0 1 0 1 1
((1 + ((~x + (x div 3)) div 3)) mod 2)
A027354: 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1
((1 + ((x * (1 + (x div 2))) div 3)) mod 2)
A089885: 1 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1
((1 + ((x + (x mod 4)) div 3)) mod 2)
A187972: 1 1 0 1 0 1 1 0 1 0 1 1 1 1 0 1
((2x mod (~1 + ((~x + 2) div 3))) mod 2)
A086079: 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0
(2 * ((x + 1) - ((~x + (x mod 2)) div 3)))
A284853: 2 4 8 10 14 16 18 20 24 26 30 32 34 36 40 42
((1 + (x mod (~2 - (x div 3)))) mod 2)
A259599-A141260-A035263: 1 0 1 1 1 0 1 0 1 0 1 1 1 0 1 1
(2 - (((x + 1) mod (1 + (x div 3))) mod 2))
A248380: 2 2 2 2 1 2 1 2 2 2 1 2 1 2 2
((x - (4 mod (1 + (x div 3)))) mod 2)
A288473: 0 1 0 1 0 1 1 0 1 1 0 1 0 1 0 1
(((x + 4) mod (1 + (x div 3))) div 2)
A250214: 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0
(((~2x + 4) mod (1 + (x div 3))) mod 2)
A188172-A037822: 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0
(3x - ((1 + (x div 3)) div 2))
A022851: 0 3 6 8 11 14 17 20 23 25 28 31 34 37 40 42
(3x - ((~1 + (x div 3)) div 2))
A342281: 1 4 7 9 12 15 18 21 24 26 29 32 35 38 41 43
((((~x + 2) div 2) div (1 + (x mod 3))) mod 2)
A106665: 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 1
((~x2 + 2x) mod (2 * (1 + (x mod 3))))
A323878: 0 1 0 1 0 3 0 1 0 1 0 3 0 1 0 1
(((x + 2) div ((x + ~1) - (x mod 3))) mod 2)
A309262: 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1
(1 - ((x mod ((x + ~1) - (x mod 3))) div 2))
A308016: 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1
((x mod (~1 + (x mod (~1 + ((~x + 1) div 2))))) mod 2)
A252742-A066247: 0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1
((1 + ((x2 + 2) mod (x + 3))) mod 2)
A309850-A262448: 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0
((1 + ((~x2 + 2x) div (x + 3))) mod 2)
A331509-A331039: 1 1 1 0 1 1 0 1 0 1 0 1 1 0 1 0
((x div (1 + (x2 mod (x + 3)))) mod 2)
A033103: 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1
(8x2 + 12x + 6)
A254527: 6 26 62 114 182 266 366 482 614 762 926 1106 1302 1514 1742 1986
((1 + ((2x + ~4) mod (1 + (x div 2)))) mod 2)
A333922-A071026: 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1
(((x div 2) mod (1 + (2 mod (1 + (x div 2))))) mod 2)
A323162: 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1
((1 + ((~x + 4) mod (1 + (x div 2)))) mod 2)
A130047: 1 1 1 0 1 1 1 0 0 1 1 0 1 0 1 0
((1 + ((x2 + 2) mod (1 + (x div 2)))) mod 2)
A192280: 1 1 1 0 1 1 1 0 0 0 1 0 1 0 1 0
((1 + (x div (2 - (4 mod (x + 1))))) mod 2)
A341941: 1 1 1 0 1 0 0 1 1 0 0 1 1 0 0 1
(2x3 + 2x2 + 8x + 6)
A304161: 6 18 46 102 198 346 558 846 1222 1698 2286 2998 3846 4842 5998 7326
((x mod (1 + ((~2 + (x div 2)) mod (x + 1)))) mod 2)
A083914-A083891: 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 1
((1 + ((x2 + ~4x + 4) div (x + 1))) mod 2)
A140653: 1 1 1 1 1 0 1 0 1 1 0 1 0 1 0 1
((2 - (x div (~1 + ((x div 2) div ~2)))) div 2)
A238418-A235125-A235124: 1 1 1 2 2 2 2 2 2 2 2 2 2 3 2 2
(x - (2 * ((x div 3) div ~3)))
A192225: 0 1 2 5
A039182: 0 1 2 5 6 7 8 9 10 11 12 13 16 17 18 19
((2x mod (2 - (x div ~3))) mod 2)
A103589: 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0
(0 - (2x div (~2 + (x div ~3))))
A329194: 0 1 2 2 2 3 3 3 4 4 4 4 4 4 4 5
((8 mod (~1 + (x div ~2))) mod 2)
A132726: 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1
((2x2 mod (~1 + (x div ~2))) mod 2)
A025457: 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0
((3x mod (~1 + (x div ~2))) mod 2)
A328891-A276935: 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0
(((x * (x div 2)) div (~1 + (x div ~2))) mod 2)
A179770: 0 0 1 1 1 1 1 1 1 0 1 0 1 0 1 0
((x mod (1 - (x mod (~1 + (x div ~2))))) div 2)
A339895: 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1
((x div (1 + (2 * (1 + (x mod 3))))) mod 2)
A275949: 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1
(4x2 + 12x + 14)
A027575: 14 30 54 86 126 174 230 294 366 446 534 630 734 846 966 1094
((1 + ((x mod 9) div 2)) mod 2)
A286903: 1 1 0 0 1 1 0 0 1 1 1 0 0 1 1 0
((x mod (1 + (2 * (x div 5)))) mod 2)
A304095: 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1
((x mod (1 + ((x mod 5) div 2))) mod 2)
A135461: 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0
((x mod (~1 + (2 * (~1 + (x mod 4))))) mod 2)
A144201-A144199-A103675: 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0
(x - (2 * (~1 + (2 * (~3 + (x div 2))))))
A004455: 14 15 12 13 10 11 8 9 6 7 4 5 2 3 0 1
((x mod (3 + ((x + 1) mod 3))) mod 2)
A172486: 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 1
((x mod (~1 + (2 * ((x + ~1) div 3)))) div 2)
A081130-A035630: 0 0 0 0 0 0 0 0 1 0 0 0 1 3 0 0
(2 + (2 mod (~1 + (2 * ((x + ~2) div 3)))))
A216452: 1 1 2 2 2 2 2 2 4 4 4 4 4 4 4 4
((x mod (~1 + (2 * ((x + ~2) div 3)))) mod 2)
A219157: 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1
(x - ((~1 + ((3 * (x div 2)) div 2)) div 2))
A321695: 1 2 2 3 3 4 5 6 6 7 7 8 8 9 10 11
((x div (3 + ((x div 2) mod 3))) mod 2)
A065714: 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1
(((x + 3) mod 7) mod 2)
A342770-A319797-A152140-A129569: 1 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0
(((2x + 1) mod 7) div 2)
A014587: 0 1 2 0 1 2 3 0 1 2 0 1 2 3 0 1
(x - (2 * ((x + 2) div 7)))
A309241: 0 1 2 3 4 3 4 5 6 7 8 9 8 9 10 11
(2 * (x - (2x div 7)))
A099188: 0 2 4 6 6 8 10 10 12 14 16 16 18 20 20 22
(x3 mod 14)
A070476: 0 1 8 13 8 13 6 7 8 1 6 1 6 13 0 1
(x - (2 * ((~x + 2) div 7)))
A192225: 0 1 2 5
A039097: 0 1 2 5 6 7 8 9 10 11 14 15 16 17 18 19
(((~x2 + x) div 7) mod 2)
A335617: 0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 0
(((x + ~1) mod (1 + (x mod 6))) mod 2)
A254379: 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0
((x mod ((x + 1) - (x mod 6))) mod 2)
A098357: 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0
((x mod (1 + (2 * (2 - (x div 3))))) mod 2)
A080885: 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0
((1 + (2x div (2 + (x div 3)))) mod 2)
A293164-A280711: 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1
((1 + (2x mod (2 + (x div 3)))) mod 2)
A344880: 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1
(2 + ((x div 2) div (3 + (x div 3))))
A107609: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2
(((~x + 2) mod (3 + (x div 3))) mod 2)
A189028: 0 1 0 1 0 1 1 0 0 1 0 1 0 1 0 1
((x - (x mod (3 + (x div 3)))) mod 2)
A037803: 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0
((x div (1 + (x div (2 + (x div 3))))) mod 2)
A284935: 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1
((1 + (x mod (1 - (2 * (x div 3))))) mod 2)
A248863: 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0
(((x div 2) mod (~1 + (2 * (x div 3)))) mod 2)
A169674-A025461: 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
((x2 mod (~1 + (2 * (x div 3)))) div 2)
A299905-A283666: 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
((1 + (x div ((x + ~2) - (x mod 3)))) mod 2)
A121505: 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0
(((x + 2) mod (1 + ((1 + (x div 2)) div 2))) div 2)
A011690: 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1
(((~x + 1) div (1 + ((1 + (x div 2)) div 2))) mod 2)
A275973: 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1
(((x2 + 1) div (1 + ((x + 1) div 2))) mod 2)
A071028: 1 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1
((2x2 mod (1 + ((x + 1) div 2))) mod 2)
A243759-A011692: 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0
((1 + (((x + ~1) * (x + (x div 2))) div 2)) div 2)
A006066: 0 0 1 2 5 7 11 15 21
(x - (2 * ((x div 2) div ~5)))
A039230: 0 1 4 5 6 7 8 9 10 11 12 13 16 17 18 19
(((x mod 2) - (x div ~5)) div 2)
A097471: 0 1 0 1 0 1 1 1 1 1 1 2 1 2 1 2
((x - (x mod (~1 + (x div ~4)))) mod 2)
A011701: 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1
(((x div 2) div (1 + ((x div ~2) mod 2))) mod 2)
A169675: 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1
((1 + ((x - ((x mod 3) div 2)) div 2)) div 2)
A176146: 0 0 0 1 1 1 2 2 2 2 3 3 3 3 3 4
(((~x + 2) mod (1 + (((x + 1) div 2) div 2))) div 2)
A320312: 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1
(2x - ((~1 + (((x + ~1) div 2) div 2)) div 2))
A287774: 1 3 5 7 9 10 12 14 16 18 20 22 24 25 27 29
((x div (~3 + (x div ~4))) mod 2)
A204549: 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1
((x mod (~1 + (2 * (((x + 1) div 2) div 2)))) div 2)
A221836-A035788: 0 0 0 0 0 0 0 0 1 0 0 0 1 1 2 0
(((x + ~1) - ((((x + 1) div 2) div 2) div 2)) mod 2)
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((1 + ((x - (x div 8)) div 2)) mod 2)
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((x div (1 + (2 * ((~x + 1) mod 4)))) mod 2)
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((1 + ((x2 mod (x + 4)) div 2)) mod 2)
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(10x2 + 7)
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(((x - (2 mod (x + 1))) mod 5) mod 2)
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((5 * ((x2 + x) div 2)) div 2)
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(2 * ((x2 + ~x + 2) mod 5))
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(((x + (x div 3)) mod 5) mod 2)
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((x div ((x + ~5) + (x div 2))) mod 2)
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(1 - (2 * ((~x + (x mod 2)) div 5)))
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(1 - (1 mod (1 - (2 * (x div 5)))))
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(2 - (2 mod (1 - (2 * (x div 5)))))
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((1 + (x div 2)) div (2 + (x mod 5)))
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(((x div 2) mod (1 + (~x mod 4))) div 2)
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(1 - ((x mod (1 + ((~x + 2) mod 4))) div 2))
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((1 + ((x div 4) * (x div 4))) div 2)
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(((x + 1) mod (~1 - (x div 4))) mod 2)
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(x + (x div 2) - ((1 + (x div 4)) div 2))
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(x + (x div 2) - ((~1 + (x div 4)) div 2))
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(((x2 + x + 1) - (x div 4)) div 2)
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(((x div 3) div (1 + (x mod 4))) mod 2)
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((x - ((~x + 1) div (1 + (x mod 4)))) mod 2)
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(2 + ((~x2 + 1) mod (1 + (x mod 4))))
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((2x + 2) - ((~1 + (x mod 4)) div 2))
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((1 + (((2x + ~4) mod (x + 2)) div 2)) mod 2)
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((1 + (2x2 mod (x + 4))) mod 2)
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(((x2 + ~1) mod (2x + ~5)) mod 2)
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((x + 2) - ((x div 2) div (2x + ~5)))
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(x - (2 * (~1 + (2 * (~2x + (x div 2))))))
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(((x2 + ~2) mod (4x + ~1)) mod 2)
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((2x div (~1 + (2 * (2 - (x div 2))))) mod 2)
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((1 + ((x2 + 1) div (2 + (x div 2)))) mod 2)
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((1 + (2x2 mod (2 + (x div 2)))) mod 2)
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((2x2 div (3 + (x div 2))) mod 2)
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(((x2 + ~x) div (3 + (x div 2))) mod 2)
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(((~x2 + x) mod (3 + (x div 2))) mod 2)
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(((~x2 + 2) mod (3 + (x div 2))) mod 2)
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((1 + ((x2 + ~x) mod (2 + (x div 2)))) mod 2)
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((x3 div (~1 + (2 * (x div 2)))) mod 2)
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(((x div 4) div (1 + ((x div 2) mod 2))) mod 2)
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((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2)
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(x - (2 * (~1 + (x mod (2 * (2 - (x mod 2)))))))
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(((x + 1) - (((x div 2) - (x mod 2)) div 2)) div 2)
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((x mod (1 - (x div (~3 + (x mod 2))))) div 2)
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((x mod (2 - (x mod (~3 + (x mod 2))))) div 2)
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(4 - ((x mod (~3 + (x mod 2))) mod 2))
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(x - (2 * ((1 + (x div 3)) div 3)))
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(((x - (x div 5)) mod 3) div 2)
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((x mod (3 * (1 + (x mod 4)))) mod 2)
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((((2x + ~2) div 3) mod 3) div 2)
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(x - ((3 * ((x div 2) div 3)) div 2))
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(27x + 2)
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((((x2 + ~x) div 3) mod 3) div 2)
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(x - (2 * ((1 - (x div 3)) div 3)))
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((((x + ~1) + (x div 3)) div 3) mod 2)
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((((x + ~1) mod (1 + (x div 2))) mod 3) mod 2)
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((((x + ~2) mod (1 + (x div 2))) mod 3) mod 2)
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(((~1 + (x * (x div 4))) div 3) mod 2)
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((x mod (((~x + ~1) + (x mod 2)) div 3)) mod 2)
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((((x + 1) * (x div 4)) div 3) mod 2)
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(((x + 1) mod (x - ((x + 1) mod 3))) div 2)
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(2 * (x - (3 * ((x div 3) mod 2))))
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((x - (((~1 + (x div 2)) div 2) div 3)) div 2)
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((x - (x div ~12)) mod 2)
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(2 * ((4 * (x div 3)) div 3))
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((3 * ((((x + 1) div 2) div 2) div 2)) div 2)
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((((x + ~1) mod 8) mod 3) mod 2)
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((((x + 2) mod 8) mod 3) mod 2)
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(((x mod (2 + (x div 4))) mod 3) div 2)
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(((x div (~2 + ((x div 2) mod 2))) mod 3) mod 2)
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((x2 div ~11) mod 2)
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((x2 mod ~11) mod 2)
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((x mod (~12 + (x div 2))) mod 2)
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(((2x - (x div 4)) div 3) mod 2)
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(((2x mod (2 + (x div 2))) mod 3) div 2)
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(((((~x + 1) * (x div 2)) div 2) div 3) mod 2)
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((((x * (x div 3)) div 2) div 3) mod 2)
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(((2 + (x * (x div 4))) div 3) mod 2)
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(x - (2 * (((~x + ~2) + (x mod 2)) div 3)))
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((((1 - (x div 2)) mod (x + 2)) mod 3) mod 2)
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((((2 - (x div 2)) mod (x + 2)) mod 3) mod 2)
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(((x3 div (x + 2)) mod 3) div 2)
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(((~2x + (x div 3)) div 3) mod 2)
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(1 - (x div (~2 + ((1 - (x div 2)) div 3))))
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(((x + 1) mod (2 - (3 * (x div 2)))) mod 2)
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(1 - ((~x + 2) div (2 + ((x div 2) div 3))))
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((x + ~2) mod (2 + ((x2 div 2) mod 3)))
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((x2 + 6) - (x div ~2))
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((x + ((x div 2) div 3)) mod 6)
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(2 + ((2x2 + 5x) div 3))
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(x - (2 * ((~x + ~3) + (x mod 3))))
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((x - (x div (2 - ((~x + 1) div 3)))) mod 2)
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(((x * ((1 + (x div 2)) div 2)) mod 3) div 2)
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(((x + (((x + ~1) div 2) div 2)) mod 3) div 2)
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((3 * (x + (4 * (x mod 2)))) div 2)
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(((~x + ((~x + 1) mod 4)) div 3) mod 2)
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(2 + (3 * (x + (x2 div 4))))
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(((x * (x mod (2 + (x div 2)))) div 3) mod 2)
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((x + 2) mod (2 + ((x + (x mod 2)) div 3)))
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(((~1 + (x div 3)) * (x div 3)) div 2)
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(((1 + (x div 4)) * (x div 3)) mod 2)
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(2 * (2 div (6 - (x div 3))))
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((((x div 4) mod 2) + (x div 3)) div 2)
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((((x2 + x) div 2) + (x div 3)) div 2)
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(((~x + 2) div ((x + 2) - (x div 3))) mod 2)
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(((x2 + 3x + 2) + (x mod 3)) div 2)
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((((x div 2) div ~2) * (x mod 3)) mod 2)
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((x mod (((~x + 2) div 2) - (x mod 3))) mod 2)
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((((x * (x div 2)) mod 2) + (x mod 3)) div 2)
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(((x + 1) mod 4) div (2 + (x mod 3)))
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(((x div 2) mod 4) div (2 + (x mod 3)))
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(x mod (4 - (x mod (2 + (x mod 3)))))
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((((x + ~1) div 2) div 2) * ((x mod 3) div 2))
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(((x + 1) div ((~x + 2) + (x mod 3))) mod 2)
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((1 + ((x * ((x + ~2) div 3)) div 2)) mod 2)
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((1 + ((x * ((~x + 1) div 3)) div 2)) mod 2)
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(x - ((~1 + ((~x + (x mod 3)) div 2)) div 2))
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((1 + (((~x + 1) * (x div 3)) div 2)) mod 2)
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((1 + ((~x + ((~x + 2) div 4)) div 2)) mod 2)
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(x - (2 * (~1 + ((~x + ((x div 2) mod 2)) div 2))))
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((x3 mod (~2x + 5)) mod 2)
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((1 + (((x2 + 1) div 2) mod (x + 2))) mod 2)
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((1 + ((x2 div 4) mod (x + 2))) mod 2)
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(((x3 + x2) div (x + 3)) mod 2)
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(((4x + ~4) mod (x + 3)) mod 2)
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(((x3 + ~1) mod (x + 3)) mod 2)
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(((2x2 + 4) mod (x + 3)) mod 2)
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(((~x2 + 4x + ~4) div (x + 3)) mod 2)
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(((1 - (x2 div 2)) mod (x + 3)) mod 2)
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((1 + ((~x2 + (x div 2)) div (x + 2))) mod 2)
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((2x3 + 3x2 + 3x + 1) div 2)
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((4x + 2) + ((2 - (x div 2)) div 2))
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((4x + 2) + ((x2 + x) div 2))
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((x4 div (2x + ~1)) mod 2)
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((1 + (((x + ~2) div 3) * (x div 2))) mod 2)
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((x mod (~1 + ((x div 4) * (x div 2)))) mod 2)
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((1 + (((x + (x div 2)) div 2) * (x div 2))) mod 2)
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(2 * (1 + (2 * (x + (x mod 2))) - (x div 2)))
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((2x mod (1 + ((x div 2) * (x div 2)))) mod 2)
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(~2 + (7 * (1 + (x div 2))))
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((6x mod (1 + (x div 2))) mod 2)
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(((x3 + ~1) div (1 + (x div 2))) mod 2)
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(((~2x + 6) mod (1 + (x div 2))) mod 2)
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(((x2 + 4) mod (1 + (x div 2))) mod 2)
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((((x + 1) div 2) div 2) * ((1 + (x div 2)) div 2))
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(((2x2 + ~x) mod (1 + (x div 2))) div 2)
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((x div 2) div (2 + (x2 mod (1 + (x div 2)))))
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(((x2 div 4) * (~1 + (x div 2))) div 2)
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((((x + ~1) div 2) div 2) * ((~1 + (x div 2)) div 2))
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((1 + (x * ((x div 2) mod 2)) - (x div 2)) div 2)
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((x mod (1 + ((x div 4) + (x mod 2)))) div 2)
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((2x div 3) mod (2 * (1 + (x mod 2))))
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((1 + ((x2 + (x mod 4)) div 2)) div 2)
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(((x + 1) - ((~x2 + (x div 2)) div 2)) div 2)
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((x3 div (3x + 1)) mod 2)
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(((~x2 + 2) div (3x + ~1)) mod 2)
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(2 * ((x + 1) + (1 mod (~2x + 5))))
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((1 + (x * (x div (2 + (x mod 3))))) mod 2)
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(((x + 1) + ((x - (x div 4)) div 2)) div 2)
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((2 mod ((~x + ~1) + (x mod (2 + (x mod 2))))) mod 2)
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(10x2 + 4x + 2)
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(2 * ((x + 1) + ((x + ((x div 2) mod 2)) div 2)))
A118286: 2 4 8 12 14 16 20 24 26 28 32 36 38 40 44 48
((x - (~2 mod (1 + (x * (x div 2))))) mod 2)
A284944-A284674: 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1
((x div 2) div (2 + (5 mod (x + 1))))
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(((4 - (x div 3)) div (x + 1)) mod 2)
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((2x3 + 3x2 + 2x + 1) div 2)
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(((x + 1) * ((x mod (1 + (x div 2))) div 2)) mod 2)
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(((x + 1) * (2 + (x div (1 + (x mod 2))))) div 2)
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(((x + 1) * ((x3 + x2) div 2)) div 2)
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(((x + 1) * (((1 + (x div 2)) div 2) div 2)) mod 2)
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(((1 - (x2 div 4)) div (x + 1)) mod 2)
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(((x + 1) * (2 + ((x2 + 2x) div 2))) div 2)
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((x3 + 5x2 + 10x + 6) div 2)
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(((x + 2) + (x div 2)) div (2 + (2 mod (x + 1))))
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((2x3 + 3x2 + 3x + 2) div 2)
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((~2 + (x mod 2)) mod ((x2 + 3x + 2) div 2))
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(((x + 1) * (((x + ~1) div 2) * (x div 2))) div 2)
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(((x + 1) * ((x mod 4) + (x div 2))) div 2)
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((((~2 + (x div 2)) * (x div 2)) mod (x + 1)) mod 2)
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(((2 + (x * (x + (x div 2)))) div (x + 1)) mod 2)
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((2x + 2) + (x div 9))
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((2x + 2) + ((x + 1) div 5))
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((2x + 2) + (2x div 5))
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A285075-A186220: 2 4 6 9 11 14 16 18 21 23 26 28 30 33 35 38
((2x + 2) + ((x div 2) div 5))
A246414-A137804-A064720-A059548-A059534-A054965: 2 4 6 8 10 12 14 16 18 20 23 25 27 29 31 33
((2 div (2x + ~5)) mod (2x + 2))
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((2x + 2) + (((x + 1) div 2) div 3))
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((2x + 2) + (x div 12))
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((2x + 2) + ((x mod 5) mod 2))
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((2x + 2) + (((x + 1) div 3) mod 2))
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((2x + 2) + (((x div 2) mod 3) mod 2))
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((2x + 2) + ((((x + 1) div 2) div 2) div 2))
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((2x + 2) + ((((x + 1) div 2) div 2) mod 2))
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A191231: 2 4 6 9 11 13 15 16 18 20 22 25 27 29 31 32
((2x + 2) + (x div ~7))
A186330: 2 3 5 7 9 11 13 15 16 18 20 22 24 26 28 29
((3x + 2) - (x div 8))
A329988-A329961-A078608: 2 5 8 11 14 17 20 23 25 28 31 34 37 40 43 46
((2x + 2) + ((x - (x div 4)) div 2))
A190004-A182761: 2 4 7 9 11 14 16 19 21 23 26 28 30 33 35 38
((2x + 2) + (x div (4 + (x div 2))))
A247430: 2 4 6 8 10 12 14 17 19 21 23 25 27 29 31 33
((2x + 2) + ((x2 + ~x) div 4))
A186351: 2 4 6 9 13 17 21 26 32 38 44 51 59 67 75 84
((2x + 2) + ((x + (x div 4)) div 2))
A189379-A184735-A184583: 2 4 7 9 12 15 17 20 23 25 28 30 33 36 38 41
((2x + 2) + ((~1 + (x div 2)) * (x div 2)))
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(((x2 + 2) div (x + 2)) + ((x + 1) div 2))
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(((x2 + 2x) + (x mod 2)) * ((x + 1) div 2))
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((x + (x div (1 + (x mod 2)))) * ((x + 1) div 2))
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((x - ((x * (~2 + (x div 2))) div (x + 1))) div 2)
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((3x3 + x2 + ~2x) div 2)
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((x6 + x5) div 2)
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(3 div (8 - ((x + ~1) div 2)))
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((x3 + 4x2) - ((x + ~1) div 2))
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A205669: 1 5 24 62
((~x + 1) mod (2 - ((~x2 + 3x + ~2) div 2)))
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(2x2 - ((~x2 + 3x + ~2) div 2))
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(((x2 + 1) + (x2 div 4)) div 2)
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((x4 + ~2x3 + 3x2 + ~2x + 2) div 2)
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(((x2 + 1) * (2x - (x mod 2))) div 2)
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((x6 + x4) div 2)
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(x - (2 * ((x div 5) div ~2)))
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(x - (2 * ((((x + ~1) div 2) div 2) div ~2)))
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(((x2 + x) div ~8) mod 2)
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(((x div 2) - (x div ~8)) mod 2)
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(0 - (x div (~2 + (x div ~8))))
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(2 * ((x + 2) - ((x div 4) div ~2)))
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(((x div 2) - ((x div 4) div ~2)) mod 2)
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((x mod 2) - (2 * ((x div 4) div ~2)))
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(((x2 mod (x + 4)) div ~2) mod 2)
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(((2x mod (2 + (x div 2))) div ~2) mod 2)
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(((x div (2 - ((x div 2) mod 2))) div ~2) mod 2)
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((((x + (x mod 3)) div 2) div ~2) mod 2)
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((((~x + (x mod 3)) div 2) div ~2) mod 2)
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((0 - (x div 4)) * (x div ~4))
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(1 - ((~x + 2) div (2 - (x div ~4))))
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(2 - ((~x + 2) div (2 - (x div ~4))))
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(x - ((x mod ~4) + (x mod 4)))
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((((x + ~1) div 3) * (x div ~2)) mod 2)
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(((~x + 3) mod (2 - (x div ~2))) mod 2)
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((8 mod (2 - (x div ~2))) mod 2)
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(((~x2 + 1) mod (2 - (x div ~2))) mod 2)
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(1 - (3x div (~2 + (x div ~2))))
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((x + 1) mod (1 - (x div (~2 + (x div ~2)))))
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(((x div 2) * (x div 2)) + ((x div ~2) mod 2))
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(4 - ((x + 2) mod (~2 + (x mod ~2))))
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(4 + (2 mod (1 + (x mod 5))))
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(((~1 + (x div (1 + (x mod 4)))) div 2) mod 2)
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((((x + 1) - ((x + 1) mod 3)) div 2) div 2)
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(2 + ((2x mod (1 + (x div 3))) mod 2))
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((x mod (2 + (x mod (1 + (x div 3))))) div 2)
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(2 + ((x mod ~9) mod 2))
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(x - (2 * (~2 + (x div (~1 + (x div ~2))))))
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(x2 + ~28)
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(x2 mod 28)
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((((~x + 2) mod 7) div 2) mod 2)
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(x - (4 * (x div 7)))
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(((x mod (1 + (x mod 6))) div 2) div 2)
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(1 - (2 * ((x mod ~5) mod 2)))
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(4 * (1 + (2 * (x - (x div ~2)))))
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(2 * ((x mod (1 + (((x + 1) div 2) div 2))) mod 2))
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(2 * (2 + (x div 15)))
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(((x mod (5 + (x mod 2))) div 2) div 2)
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(2 + ((5 * (x mod 4)) div 2))
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(x3 mod 20)
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((((x + (x div 2)) mod 5) div 2) mod 2)
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(((~x + 2) mod (2 + (x div 5))) div 2)
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(2 + ((x mod (1 + ((~x + 2) mod 4))) div 2))
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((x div 2) - (2 * ((1 + (x div 4)) div 2)))
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(((x div 2) - ((~1 + (x div 4)) div 2)) mod 2)
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(2 + (((x + 1) mod (1 + (x mod 4))) div 2))
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(((~1 + (2x mod (2 + (x div 2)))) div 2) mod 2)
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(((2x mod (3 + (x div 2))) div 2) mod 2)
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((((x div 2) - ((x + 1) mod 3)) div 2) mod 2)
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(((x + ~1) div (2 + ((x + ~1) mod 3))) mod 2)
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(x - (2 * ((3 * (x div 4)) div 2)))
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(2 * ((3 * ((x2 + x) div 2)) div 2))
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((x2 mod (3x + ~8)) mod 2)
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((((x + ~1) + ((x div 2) div 3)) div 2) mod 2)
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(2 - (4 div (2 + (x mod 6))))
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(((x + 1) mod (~2 + ((~x + 1) div 3))) mod 2)
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(((((x + ~1) div 2) - (x div 3)) div 2) mod 2)
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((x - ((x + ~1) div (2 + (x div 3)))) mod 2)
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(((x2 + ~1) div (2 + (x div 3))) mod 2)
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(((x + ~4) mod (2 + (x div 3))) mod 2)
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(2 - ((2x div (2 + (x div 3))) mod 2))
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(((((x + 1) div 2) + (x mod 3)) div 2) mod 2)
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(((((~x + 2) div 2) * (x mod 3)) div 2) mod 2)
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((((x + ~1) div 2) mod (2 + (x mod 3))) div 2)
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((x div 2) - (x div (2 + ((x mod 3) div 2))))
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(((~1 + ((x div 4) * (x div 2))) div 2) mod 2)
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(x - (2 * ((4 mod (1 + (x div 2))) mod 2)))
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((((x + ~4) mod (1 + (x div 2))) div 2) mod 2)
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((((x mod 3) mod (~x + ~1)) div 2) mod 2)
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((((x + 1) * (~1 + (x mod 3))) div 2) mod 2)
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((((x + 1) * (x div ~3)) div 2) mod 2)
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(2 * (2 + ((x div ~3) mod (x + 1))))
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((((x + 1) * (x div 5)) div 2) mod 2)
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(2 * ((x3 + 3x2 + 3x + 1) div 2))
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(((x3 + 5x2 + 8x + 4) div 2) div 2)
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((((x + 1) + (x div 2)) * ((x + 1) div 2)) div 2)
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A001318: 0 1 2 5 7 12 15 22 26 35 40 51 57 70 77 92
((x div 8) + (((x + 1) div 2) div 2))
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(((x div ~3) * ((x + ~1) div 2)) mod 2)
A336356-A319988-A268340: 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1
((((x div 2) mod 3) * ((x + ~1) div 2)) mod 2)
A295308: 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1
((x mod (~2 + (x div ~8))) mod 2)
A272664: 0 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1
(x - (2 * ((1 + (x div 2)) mod ~4)))
A244588: 6 7 6 7 6 7 6 7 14 15 14 15 14 15 14 15
(((x * (x div 4)) div ~4) mod 2)
A336921-A325122-A324930: 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0
(((~x + 2) div (2 - (x div ~4))) mod 2)
A030300: 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1
(0 - (2x div (~2 + (x div ~4))))
A253272-A123578-A023965: 0 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5
((x + 2) - (x div (~2 + (x div ~4))))
A172284-A062289: 2 4 5 6 8 9 10 11 12 13 14 16 17 18 19 20
((2x div (2 - (x mod ~4))) mod 2)
A309061: 0 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0
(2 + (x2 div ((x + 2) - (x div ~2))))
A303003: 2 2 2 3 4 4 5 5 6 7 7 8 9 9 10
((x div (2 + ((x div ~3) mod 2))) mod 2)
A134391: 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 1
(2 + (((x - (x mod ~3)) div 2) div 2))
A057810: 2 2 2 2 3 3 3 4 4 4 5 5 5 5 5 5
(4 * (x - (2 * (x div 5))))
A081747: 0 4 8 12 16 12 16 20 24 28 24 28 32 36 40 36
((x div (4 + ((x + ~1) mod 3))) mod 2)
A194670: 0 0 0 0 1 1 1 1 1 1 0 0 0 1 0 0
((2 div (~2 + ((3 * (x div 2)) div 2))) mod 2)
A281083-A117964-A074079: 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0
(x - (8 * ((~x + 1) div 3)))
A112654: 0 1 10 11 12 21 22 23 32 33 34 43 44 45 54 55
((((x + ~1) mod (2 + (x div 3))) div 2) div 2)
A055240: 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0
((2 - (x mod (~4 + (x mod 3)))) div 2)
A006928: 1 2 1 1 2 1 2 2 1 2 2 1 1 2 1 1
((((x - (x2 mod 3)) div 2) div 2) mod 2)
A325954: 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1
((((~1 + ((x2 + x) div 2)) div 2) div 2) mod 2)
A143580-A010059: 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1
(4 * ((x2 + 4x + 3) div 2))
A332044: 4 16 28 48 68 96 124 160 196 240 284 336 388 448 508 576
(40x + 8)
A139279: 8 48 88 128 168 208 248 288 328 368 408 448 488 528 568 608
(4 + (((x2 div 2) mod (x + 1)) mod 2))
A276866: 4 4 4 4 5 4 4 4 5 4 4 4 5 4 4 4
((2x + 2) - ((((x + 1) div 2) div 2) div 2))
A184592: 2 4 6 8 10 12 14 15 17 19 21 23 25 27 29 30
(((((x + ~1) * (x div 3)) div 2) div 2) mod 2)
A070100-A070095: 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1
((((x3 + ~3x2 + 2x) div 2) div 2) div 2)
A011890: 0 0 0 0 3 7 15 26 42 63 90 123 165 214 273 341
(((x mod (2 - ((x2 + ~1) div 2))) div 2) mod 2)
A276630: 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0
((x mod (~2 + (((x div 2) div ~2) div 2))) mod 2)
A288752: 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0 1
(2 * (4 + ((x + ~1) mod 6)))
A104218: 18 8 10 12 14 16 18 8 10 12 14 16 18
(2 + ((x - (((~1 + (x div 2)) div 2) mod 2)) div 2))
A110862: 1 2 3 3 4 4 4 5 5 6 7 7
((((((x + ~1) * (x div 2)) div 2) div 2) div 2) div 2)
A011885: 0 0 0 0 0 0 0 1 1 2 2 3 4 4 5 6
((x mod (2 + ((((x + 1) div 2) div 2) mod 2))) mod 2)
A174998: 0 1 0 0 1 0 0 1 0 1 0 0 0 1 0 1
(x + 60)
A266916: 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
(x + 62)
A296766: 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77
(4 + ((x - (x div 8)) mod 2))
A126128: 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4
((x mod (4 + ((x div 4) mod 2))) mod 2)
A285966: 0 1 0 1 0 0 1 0 0 1 0 1 0 1 0 0
(2 * (x - (4 * ((x div 4) mod 2))))
A004518: 0 2 4 6 0 2 4 6 16 18 20 22 16 18 20 22
64x2
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((x div (2 * (2 + ((x + 1) mod 4)))) mod 2)
A011716: 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1
((x div (4 + ((x + ~1) mod 4))) mod 2)
A037812: 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0
(2 + ((x mod (~8 + (x mod 2))) mod 2))
A307713: 2 2 2 2 2 2 2 2 2 3 2 3 2 3 2 2
(x2 + 30)
A114964: 30 31 34 39 46 55 66 79 94 111 130 151 174 199 226 255
(x3 mod 32)
A070494: 0 1 8 27 0 29 24 23 0 25 8 19 0 21 24 15
(2 * (x - (2 div (x + ~16))))
A194396: 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 34
(2 + ((x + ~2) div (2 + (x div 8))))
A157792: 1 1 2 2 3 3 4 4 4 4 4 5 5 5 6 6
(((x mod (~2 + ((~x + 2) div 4))) div 2) mod 2)
A082401-A080846: 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0
((((x + 2) mod (2 + (x div 4))) div 2) mod 2)
A011684: 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1
(((2x mod (2 + (x div 4))) div 2) mod 2)
A084143: 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0
(((x + ~1) div (4 + (x div 4))) mod 2)
A204545: 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0
(2 * ((x div 2) - (2 * ((x div 4) mod 2))))
A063695: 0 0 2 2 0 0 2 2 8 8 10 10 8 8 10 10
((x - (((x - (x div 4)) div 2) mod 2)) div 2)
A245710: 0 0 0 1 1 2 3 3 3 4 5 5 6 6 6 7
(8 * (2x - (x mod 4)))
A125991: 0 8 16 24 64 72 80 88 128 136 144 152 192 200 208 216
(((x div 2) mod (4 + (x mod 4))) mod 2)
A288551: 0 0 1 1 0 0 1 1 0 0 1 1 0 1 1 0
(((x - (x mod (2 + (x mod 4)))) div 2) mod 2)
A083916-A083893: 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1
(28x + 8)
A139608: 8 36 64 92 120 148 176 204 232 260 288 316 344 372 400 428
29x
A248786-A195819-A004922: 0 29 58 87 116 145 174 203 232 261 290 319 348 377 406 435
(2 * ((x mod (1 - (2 * (2 + (x mod 2))))) mod 2))
A110177: 0 0 2 0 0 0 0 2 2 2 0 0 0 0 2 0
((x div (2 * (x - ((x + 1) mod 4)))) mod 2)
A316341: 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0
(((x + 2) mod (2 + ((x + ~1) mod 4))) div 2)
A069847: 1 0 0 0 0 0 1 0 0 0 0 0 2 0 0 0
((x mod (2 + (((x + ~1) div 2) mod 4))) div 2)
A340007: 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0
(((x + ~1) div (2 + ((x + 2) mod 4))) mod 2)
A025919: 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0
(((~x + 2) div (2 + ((x div 2) mod 4))) mod 2)
A027360: 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1
((x - (x div (2 + ((x div 2) mod 4)))) mod 2)
A284468: 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0
(((x2 + x) div ~7) mod 2)
A288478: 0 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1
((2 - (x2 div ~7)) div 2)
A029040: 1 1 1 2 2 3 4 4 6 7 8 10 11 13 15 17
((2x + 2) - ((x + 1) mod 8))
A309126: 1 2 3 4 5 6 7 16 17 18 19 20 21 22 23 32
((x + 2) - (2 div (~8 + (x div 2))))
A154660: 3 4 5 6 7 8
A192452-A132147: 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19
(x - (2 * (2 div (~8 + (x div 2)))))
A279487-A046039: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 18 19
(2 * (x - (2 div (~8 + (x div 2)))))
A321193-A284788: 2 4 6 8 10 12 14 16 18 20 22 24 26 28 32 34
((x + ~8) mod 16)
A004449: 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7
(((x2 + x) div 2) mod 16)
A105333: 0 1 3 6 10 15 5 12 4 13 7 2 14 11 9 8
((x2 * (x mod 2)) mod 16)
A167545: 0 1 0 9 0 9 0 1 0 1 0 9 0 9 0 1
(2 div (1 - (2 mod (x + ~16))))
A034410: 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2
(x4 div 16)
A011863: 0 0 1 5 16 39 81 150 256 410 625 915 1296 1785 2401 3164
((4x + 2) - (x div 8))
A251538: 2 6 10 14 18 22 26 30 33 37 41 45 49 53 57 61
((x mod 4) div (2 + (x div 8)))
A339824: 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1
(16x2 + ~15x)
A282854: 0 1 34 99 196 325 486 679 904 1161 1450 1771 2124 2509 2926 3375
(((x + 1) mod (~2 + ((~x + 2) div 4))) mod 2)
A309848: 1 0 1 0 1 0 0 0 1 0 1 1 0 1 0 0
(2 * (1 - (x div (~2 + ((~x + 2) div 4)))))
A130819: 2 4 4 4 6 6 6 6 6 8 8 8 8 8 8 8
((x + 2) - (x div (~2 + ((~x + 2) div 4))))
A345443-A135668: 2 4 5 6 8 9 10 11 12 14 15 16 17 18 19 20
(1 - (2 * (x div (~2 + ((~x + 2) div 4)))))
A130175-A001650: 1 3 3 3 5 5 5 5 5 7 7 7 7 7 7 7
(x - (2 * (x div (~2 + ((~x + 2) div 4)))))
A112594: 0 3 4 5 8 9 10 11 12 15 16 17 18 19 20 21
((x - (((x + (x div 2)) div 4) mod 2)) div 2)
A267097: 0 0 1 1 1 2 3 3 3 4 4 5 6 6 6 7
(((x + ~1) mod (4 - (x div 4))) div 2)
A014108-A014072: 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0
(((2x + 1) mod (2 + (x div 4))) div 2)
A101257-A069859: 0 0 0 0 0 1 0 0 0 1 0 1 0 1 2 0
(((2x + 2) mod (2 + (x div 4))) mod 2)
A092573: 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0
(((2x + ~2) mod (2 + (x div 4))) mod 2)
A033107: 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1
((x - (2x div (2 + (x div 4)))) mod 2)
A011697: 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1
((2x + 2) div (4 + (x div 4)))
A261104: 0 1 1 2 2 2 2 3 3 3 3 4 3 4 4 4
((x + (x div 2)) div (2 * (2 + (x div 4))))
A161105-A161066-A161040: 0 0 0 1 1 1 1 1 1 1 1 2 1 1 2 2
((x + 2) - ((~x + 1) div (2 + (x div 4))))
A183874-A175140: 2 3 5 6 7 9 10 11 12 13 15 16 17 18 19 20
(x - (4 div (~4 + (x div 4))))
A101771: 1 2 3 4 6 7 8 9 10 11 12 13 16 17 18 19
(((x + ~1) mod (4 - (x mod 4))) div 2)
A103840: 1 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0
(((~x + 4) div (2 + (x mod 4))) mod 2)
A106701: 0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1
(2 - (((x + 2) div (2 + (x mod 4))) mod 2))
A337565: 1 1 1 1 1 2 2 1 1 1 1 2 1 1 2 1
(((x2 + 2) div (2 + (x mod 4))) mod 2)
A285671-A230901: 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1
(((x2 + 2) mod (2 + (x mod 4))) mod 2)
A287372-A188291: 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0
(x - ((x + ~1) div (4 + (x mod 4))))
A093697: 1 1 2 3 4 5 6 7 7 8 9 10 10 11 12 13
((x * (x mod 2)) div (2 * (2 + (x mod 4))))
A283929: 0 0 0 0 0 0 0 0 0 1 0 1 0 2 0 1
((2 - (x mod (1 - (2 * (x mod 4))))) div 2)
A337260-A296772-A228525: 1 1 1 2 1 1 1 2 1 1 2 3 1 1 1 1
((2 mod ((x + 2) - (x2 div 4))) mod 2)
A011704: 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1
((1 - ((x - (x2 div 4)) div 2)) div 2)
A011872: 0 0 0 0 0 1 1 2 2 3 4 5 6 8 9 11
(2 + ((((1 - (x div 2)) mod (x + 2)) div 2) div 2))
A104147: 2 2 2 2 3 3 3 3 3 4 4 4 4 4 4 4
(((x2 + ~2x) div (x + 6)) mod 2)
A085977: 0 1 0 0 0 1 0 0 1 0 1 1 0 1 0 1
((x - (x2 div (x + 6))) mod 2)
A086072: 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 1
((((~x2 + 2) mod (x + 4)) div 2) mod 2)
A141738: 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0
(x - (((x - ((2 - (x div 2)) div 2)) div 2) div 2))
A210435-A175406: 1 1 2 3 3 4 5 5 6 7 7 8 9 10 10 11
((((x2 + ~1) mod (2 + (x div 2))) div 2) div 2)
A297239-A034408: 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2
((((2x + 2) mod (2 + (x div 2))) div 2) div 2)
A116377: 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1
((((x2 + ~2) mod (2 + (x div 2))) div 2) div 2)
A026799: 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1
(((x - ((~x + 2) mod (2 + (x div 2)))) div 2) mod 2)
A289074: 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1
((((~x2 + x) mod (2 + (x div 2))) div 2) mod 2)
A280164: 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1
(((~1 + (x div 2)) mod (2 + ((x div 2) mod 2))) mod 2)
A285661: 1 1 0 0 1 1 0 0 1 1 1 1 1 1 0 0
((((~x + 2) div 2) mod (2 + ((x div 2) mod 2))) mod 2)
A141737-A141728: 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0
(((x mod (2 + ((~x + 2) * (x div 2)))) div 2) mod 2)
A011718: 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1
((x - ((~x + 2) div (4 + (x mod 2)))) mod 2)
A188014: 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 0
((((x div 2) - (x mod (2 + (x mod 2)))) div 2) mod 2)
A282244: 0 1 0 0 1 0 1 1 0 0 0 1 1 0 1 1
(x div (2 + (x mod (2 + (x mod (2 + (x mod 2)))))))
A213633: 0 0 1 1 2 1 3 2 4 3 5 2 6 4 7 5
(((x + ~1) mod (~2 + (x div (~2 + (x mod 2))))) mod 2)
A267927: 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1
(((x + ~2) div (~2 + (x div (~2 + (x mod 2))))) mod 2)
A267155: 1 0 0 1 1 1 1 1 1 1 0 1 0 1 0 1
(16x2 + ~6x)
A028994: 0 10 52 126 232 370 540 742 976 1242 1540 1870 2232 2626 3052 3510
(((x + ~1) div (x - ((x + ~1) mod 4))) mod 2)
A024359: 0 0 1 0 1 0 1 1 1 0 1 1 1 0 1 1
(((x + 2) div (x - ((x + ~1) mod 4))) mod 2)
A267579: 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1
((x mod 2) - ((0 - ((x div 2) mod 4)) div 2))
A140085: 0 1 1 2 1 2 2 3 0 1 1 2 1 2 2 3
((x + 2) - (((~x + 2) - (x div 2)) div 4))
A188070: 2 3 5 6 7 9 10 11 13 14 16 17 18 20 21 22
(x - ((2x + 2) div ~7))
A287770-A039080: 1 2 3 5 6 7 8 10 11 12 14 15 16 17 19 20
(1 - (3x div ~7))
A120397: 1 2 2 3 3 4 4 4 5 5 6 6 7 7 7 8
(x - (3x div ~7))
A195129: 0 2 3 5 6 8 9 10 12 13 15 16 18 19 20 22
(3x - (x div ~7))
A121381: 0 4 7 10 13 16 19 22 26 29 32 35 38 41 44 48
(~x mod (x - ((x + ~1) mod 8)))
A138472: 0 0 0 0 0 0 0 0 0 0 8 7 6 5 4 3
(x - (x mod (x - ((x + ~1) mod 8))))
A103303: 0 1 2 3 4 5 6 7 8 9
A329623-A257779: 0 1 2 3 4 5 6 7 8 9 9 9 9 9 9 9
((x - (2 * ((x div 2) mod 2))) mod 8)
A063694: 0 1 0 1 4 5 4 5 0 1 0 1 4 5 4 5
(8 + ((x2 + 3x) div 2))
A167487: 8 10 13 17 22 28 35 43 52 62 73 85 98 112 127 143
(1 - (((~x + 2) - (x div 2)) div 8))
A247781: 1 1 2 2 2 2 2 2 3 3 3 3 3 4 4 4
(((x2 + x) + (x mod 2)) mod 8)
A159058: 0 3 6 5 4 7 2 1 0 3 6 5 4 7 2 1
((x + (x div 8)) mod 8)
A053843: 0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 0
(24x2 + ~16x)
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((x mod 2) - (8 * (~x + (x mod 2))))
A151977: 0 1 16 17 32 33 48 49 64 65 80 81 96 97 112 113
((3x + 3) - (x div 8))
A342831: 3 6 9 12 15 18 21 24 26 29 32 35 38 41 44 47
((2x + 8) - (x mod 8))
A115419: 8 9 10 11 12 13 14 15 24 25 26 27 28 29 30 31
((x2 + (x mod 4)) mod 8)
A077750: 0 2 6 4 0 2 6 4 0 2 6 4 0 2 6 4
((x + 2) - ((~x + (2 div (x + 1))) div 4))
A136432: 2 3 5 6 7 9 10 11 12 14 15 16 17 19 20 21
((x - ((~x + (2 div (x + 1))) div 4)) div 2)
A194179-A005379: 0 0 1 2 2 3 4 4 5 6 6 7 7 8 9 9
(((~x + ((x + 1) * (x div 2))) div 4) mod 2)
A255817: 0 1 0 0 1 1 1 0 1 1 1 0 0 1 0 0
(((x * (~2 + (x div 3))) div 4) mod 2)
A161382: 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1
(2 + ((x * (2 - ((x div 2) mod 2))) mod 4))
A182215: 2 4 4 5 2 4 4 5 2 4 4 5 2 4 4 5
(((x div 5) * (x div 4)) div 2)
A211190: 0 0 0 0 0 0 0 0 1 1 2 2 3 3 3 4
((x div (8 - (x div 4))) mod 2)
A011713: 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1
(((~x + 2) mod 4) div (2 + (x div 4)))
A205633: 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0
(2x - ((x + ~2) div (2 + (x div 4))))
A193732: 1 3 4 6 8 9 11 13 15 17 18 20 22 24 26 28
(x - ((~x + (x mod 2)) div (2 + (x div 4))))
A066533: 0 1 3 4 6 7 8 9 10 11 13 14 15
(2x + ((x div 4) mod 2) - (x mod 2))
A003995: 0 1 4 5 9 10 13 14 16 17 20 21 25 26 29 30
(3x div ((x + 2) - (x div 4)))
A029835: 0 1 1 1 2 2 2 2 3 3 3 3 3 3 3 3
(x + ((x - (x div 4)) mod 2) - (x mod 2))
A340477-A340401: 0 1 2 3 5 4 7 6 8 9 10 11 13 12 15 14
((x mod (~2 + ((x * (2 - (x div 2))) div 2))) mod 2)
A086483: 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1
(1 - (2 * ((x mod ((x + ~2) + (x div 2))) mod 2)))
A276438: 1 1 1 ~1 1 1 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1
(2 - ((x div (2 + ((x * (x div 2)) mod 2))) mod 2))
A320473: 2 2 1 1 2 2 1 2 2 2 1 1 2 2 1 1
((((x + 2) * (~1 + (x div 3))) div 2) mod 2)
A029444: 1 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0
((((x + 2) * (~1 + (x mod 3))) div 2) mod 2)
A262805: 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1
(((3x2 div (x + 2)) div 2) mod 2)
A074937: 0 0 1 0 0 1 0 0 1 1 0 1 1 0 0 1
(((3x2 + 7x + 2) div 2) div 2)
A024219: 0 3 7 12 19 28 38 49 62 77 93 110 129 150 172 195
(2 * ((x3 + 3x2 + 3x + 2) div 2))
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(x3 + 6x2 + 12x + 4)
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(((1 + (x2 div 2)) mod (x + 4)) mod 2)
A237048: 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0
(x2 + 10x + 26)
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((x2 + ~3x + 2) div (x + 6))
A319413: 0 0 0 0 0 1 1 2 3 3 4 5 6 6 7 8
(8x div (x + 6))
A156876: 0 1 2 2 3 3 4 4 4 4 5 5 5 5 5 5
(x - ((x2 + ~2) div (x + 6)))
A201052: 1 2 2 3 3 3 4 4 4 4 4 4 5 5 5 5
(x - ((x2 + x) div (x + 6)))
A135034: 0 1 2 2 2 3 3 3 3 3 4 4 4 4 4 4
(1 - ((~x2 + 2) div (x + 6)))
A103354: 1 1 2 2 3 4 4 5 6 7 8 8 9 10 11 12
(2 div ((x2 + ~2) mod (2x + 8)))
A280618: 0 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0
(x - (2 * ((x * (x div 2)) div (x + 4))))
A276439-A064289: 0 1 2 3 2 3 4 5 4 5 4 5 4 5 4 5
((x + 2) - ((x2 + ~x) div (2x + 4)))
A198292: 2 3 4 5 5 6 7 7 8 8 9 9 10 10 11 11
(x2 + ~10x + 12)
A127146: 12 3 ~4 ~9 ~12 ~13 ~12 ~9 ~4 3 12 23 36 51 68 87
(8x + ((x2 + x) div 2))
A056126: 0 9 19 30 42 55 69 84 100 117 135 154 174 195 217 240
(8x + ((x2 + ~x) div 2))
A056121: 0 8 17 27 38 50 63 77 92 108 125 143 162 182 203 225
(8x3 + ~12x)
A163322: 0 ~4 40 180 464 940 1656 2660 4000 5724 7880 10516 13680 17420 21784 26820
(8x3 + ~3x)
A173202: 0 5 58 207 500 985 1710 2723 4072 5805 7970 10615 13788 17537 21910 26955
(4 + (7 * (x div 2)))
A168373: 4 4 11 11 18 18 25 25 32 32 39 39 46 46 53 53
(2 + ((((x + ~2) div 3) * (x div 2)) mod 2))
A273165: 2 2 2 2 2 2 3 3 2 2 2 3 2 2 2 2
((2 - (((x mod 3) - (x div 2)) div 2)) div 2)
A053261: 1 1 1 1 1 1 2 1 1 2 2 2 2 2 2 3
((((x2 + 3x + 2) + (x div 2)) div 2) div 2)
A261223: 0 1 3 5 8 11 14 18 23 28 34 40 47 54 61 69
(x - ((((2 - (x div 2)) * (x div 2)) div 2) div 2))
A067570: 0 1 2 3 4 5 7
A274337: 0 1 2 3 4 5 7 8 10 11 14
((x mod (2 - (((x mod 2) - (x div 2)) div 2))) div 2)
A345375: 0 0 1 0 0 1 1 0 0 0 0 1 1 1 1 0
(((x2 + ~x + ~1) mod (2 + (x div 2))) mod 2)
A285960: 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0
(((2x2 + 2) div (2 + (x div 2))) mod 2)
A333437-A308264-A186518: 1 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0
(2 + ((3x + ~4) div (2 + (x div 2))))
A130245: 0 1 2 3 4 4 4 5 5 5 5 6 6 6 6 6
((~x + 2) mod (2 + ((x + ~2) div (2 + (x div 2)))))
A025664-A025656: 0 0 0 1 0 1 0 1 0 2 1 0 2 1 0 2
(((~2x2 + 2x) div (2 + (x div 2))) mod 2)
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(((~2x2 + 2x) mod (2 + (x div 2))) mod 2)
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(((x3 + 2) div (2 + (x div 2))) mod 2)
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((2x + ~6) div (4 + (x div 2)))
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(1 - ((x - (x2 div (2 + (x div 2)))) div 2))
A279135: 1 1 1 1 1 2 2 2 2 3 3 4 4 5 5 6
(((~x3 + x) div (2 + (x div 2))) mod 2)
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((x * (x mod 3)) mod (2 + ((x div 2) mod 2)))
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((x * ((x + 1) div 2)) mod (2 + ((x div 2) mod 2)))
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(x - ((x div 4) div (~2 + ((x div 2) mod 2))))
A039253: 0 1 2 3 5 6 7 8 9 10 12 13 14 15 17 18
((2x + 4) - ((x - ((x div 2) mod 2)) div 2))
A192506-A175526-A091212: 4 6 8 9 10 12 14 15 16 18 20 21 22 24 26 27
((2x mod (2 + (x div 2) - (x mod 2))) mod 2)
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((x div 2) - (((x + 1) div (2 + (x mod 2))) div 2))
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(((x - ((x div 2) mod 2)) div (2 + (x mod 2))) mod 2)
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((x + 1) mod (2 + ((x + 2) mod (2 + (x mod 2)))))
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((x + (x mod 3)) div (4 + (x mod 2)))
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(2 - ((x + 1) mod (2 + (x mod (2 + (x mod 2))))))
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(((2 - (x div 3)) div (~2 + (x mod 2))) mod 2)
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(2 + ((~x mod 4) * (~2 + (x mod 2))))
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(x - (((~2 + (x mod (~x2 + 2))) div 2) div 2))
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A019529: 1 2 3 5 7 10 14 18 22 27 33 39 45 52 60 68
((x div (~1 + (2 * (x mod 3)))) mod 4)
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((x - (((~x + 2) div 2) div 3)) mod 4)
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((x - ((x + (x mod 2)) div 3)) mod 4)
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((1 + (x * (1 + (x div 4)))) mod 4)
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(1 - ((5 mod (x + 1)) mod 4))
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(x + ((x + 1) mod 4) - ((x div 2) mod 2))
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((~2x + 1) mod (x - ((x + 1) mod 4)))
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(x + ((x + ~1) mod 4) - ((x div 2) mod 2))
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(2 - (2x div (~4 + (x div ~2))))
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(2x - (x mod (6 + (x div 2))))
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A276392: 0 1 2 3 4 5 6 7 8 9 10 22 24 25 27 28
((x - (2x * (x div 4))) mod 4)
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((x3 + 3x2 + x) div 4)
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(4 * (x + (x div 7)))
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(16x3 + 4x)
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(x - ((~x + (x2 mod 3)) div 4))
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(2x + ((x div 2) + ((~x + 1) mod 4)))
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(x - ((x + ((x div 3) mod 2)) div 4))
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(x - (4 * (~x + (x mod 8))))
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((x + 4) + (x div (4 + (x div 2))))
A162706-A088331: 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19 20
((x + (x div (4 + (x div 2)))) mod 4)
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((x * ((x mod (2 + (x mod 2))) div 2)) div 4)
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(x - ((x + ((x div 2) mod 4)) div 4))
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(1 - ((~x + ((x div 2) mod 4)) div 4))
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(20x2 + ~8x)
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((x4 + x2 + 2x) div 4)
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(3x - ((x + (x div 2)) div 4))
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((1 - (x mod (2 - (x * (x mod 2))))) mod 4)
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((1 + (((x + 1) div 2) div 2)) * (x div 4))
A038715: 0 0 0 0 2 2 2 3 6 6 6 8 12 12 12 15
((x div (1 + (x div 4))) + (x div 4))
A202304: 0 1 2 3 3 3 4 4 4 5 5 5 6 6 6 6
((5x + 5) + (x div 4))
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((4 * (x mod 4)) + (x div 4))
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((4x div (x + 2)) + (x div 4))
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((x * ((x + (x div 2)) div 2)) + (x mod 4))
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(7x2 div 4)
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((2x3 + 3x2) div 4)
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((x * (x + (x div 5))) div 4)
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((x2 + x) - ((~x2 + x) div 4))
A249852: 0 2 7 14 23 35 50 67 86 108 133 160 189 221 256 293
((x2 + 2x) - ((~x2 + 2x) div 4))
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(4x2 + ((x2 + x) div 2))
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(4x2 + ((x2 + ~x) div 2))
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(2 + ((x + ((x div 2) div 5)) div 2))
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((2 - ((~x + (x mod 5)) div 2)) div 2)
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(2 * ((x mod ((~x + 1) + (x mod 4))) mod 2))
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(2 * ((x + 2) + (x div 12)))
A284665-A111305: 4 6 8 10 12 14 16 18 20 22 24 26 30 32 34 36
(((x * (((~x + 2) div 2) mod 3)) div 2) mod 2)
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(((~x2 + 1) mod (3x + 2)) mod 2)
A267814-A191232: 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1
((2 - ((~x + (x2 mod 3)) div 2)) div 2)
A111890: 1 1 1 2 2 2 2 2 3 3 3 3 4 4 4 5
(x - (((x + (2 mod (1 + (x div 2)))) div 2) div 2))
A282029-A079420: 0 1 2 3 3 4 4 5 6 7 7 8 9 10 10 11
(((x * ((~1 + (x div 4)) div 2)) div 2) mod 2)
A232442: 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1
((x div (~2x + 32)) mod 2)
A249856-A118135: 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1
((x + 2) - ((~x + ((~x + 2) div 4)) div 2))
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(((x mod (2 - (x * (x div 4)))) div 2) mod 2)
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(((x * ((~x + 1) div (2 + (x div 2)))) div 2) mod 2)
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(((x * ((~x + 1) mod (2 + (x div 2)))) div 2) mod 2)
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((x div (~2 + (x * (x mod (2 + (x mod 2)))))) mod 2)
A288694: 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0
((x - (x2 mod (x - ((~x + 2) div 2)))) mod 2)
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(((x2 + ~1) mod ((x + ~2) + (x div 2))) mod 2)
A109700: 1 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0
(((x2 div 2) div ((x + ~2) + (x div 2))) mod 2)
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(((x + 1) div (2 - ((x * (x div 2)) mod 2))) div 2)
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((x div 2) - (x div (2 + ((x * (x div 2)) mod 2))))
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(((1 + ((x2 + 1) div 2)) mod (x + 2)) mod 2)
A285341: 1 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0
((((~x + 1) div 5) mod (x + 2)) mod 2)
A138328-A095907: 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0
(2 + ((4x2 + ~1) div (x + 2)))
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(((x + 2) * (1 + ((x2 + 2x) div 2))) div 2)
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A005997: 1 3 10 20 39 63 100 144 205 275 366 468 595 735 904 1088
((5x2 + 11x + 2) div 2)
A131895: 1 9 22 40 63 91 124 162 205 253 306 364 427 495 568 646
((x3 + 6x2 + 9x + 2) div 2)
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(((6 - (x div 2)) div (x + 2)) mod 2)
A099200: 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1
(((2 - (x2 div 4)) div (x + 2)) mod 2)
A120532: 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0
(((x + 2) * ((x2 + 4x + 4) div 2)) div 2)
A005996: 2 6 16 30 54 84 128 180 250 330 432 546 686 840 1024 1224
(((((~x + 2) - (x div 2)) div 2) mod (x + 2)) div 2)
A345378: 0 0 1 2 2 2 2 2 2 2 2 3 3 3 3 3
((2x2 + 8x + 4) + (x mod 2))
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(((x3 + ~4x2 + 4x) div (x + 2)) mod 2)
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(((x + 2) * ((x + 2) div (2 - (x mod 2)))) div 2)
A241496: 1 4 4 12 9 24 16 40 25 60 36 84 49 112 64 144
(((2 + (x * (x + (x div 2)))) div (x + 2)) div 2)
A082774: 0 0 1 1 2 2 3 4 4 5 6 6 7 8 9 9
((x div 2) - (((x2 div 2) mod (x + 2)) mod 2))
A173989: 0 0 1 1 2 1 3 3 4 3 5 5 6 5 7 7
((2x + 4) - (x2 div (x + 4)))
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((2x + 4) + (3 * (x + (x div 2))))
A092464: 4 9 17 22 30 35 43 48 56 61 69 74 82 87 95 100
((((~x + 1) * (2 + (x mod 2))) div (x + 2)) mod 2)
A284957: 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1
(x - ((x + 2) div (~2 + ((~x + 1) div (x + 2)))))
A184484: 1 3 4 5 6 8 9 10 12 13 14 16 17 18 20 21
(2 + ((x * (x - (x div 4))) div (x + 2)))
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(((x + 2) * (x + ((x * (x div 2)) mod 2))) div 2)
A079283: 0 1 4 10 12 17
((x + 2) - ((x2 div 2) div (~2x + 1)))
A183572: 2 3 5 6 8 9 10 11 13 14 15 16 18 19 20 21
((x div 2) - (2 * (~2x + (2 mod (x + 1)))))
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(4x + ((x mod (1 + (x div 2))) div 2))
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(4x + ((x2 + 3x + 2) div 2))
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(4x + ((x + (x div 2)) div 4))
A172325: 0 4 8 13 17 21 26 30 35 39 43 48 52 56 61 65
((((x + 1) - (x div ~2)) * (x div 2)) div 2)
A211539: 0 0 2 3 7 9 15 18 26 30 40 45 57 63 77 84
(x - ((((x + ~2) div 3) + (x div 2)) div 2))
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((x + 2) - (((~x + 1) div 3) * (x div 2)))
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((x mod 2) - (((x div 3) - (x div 2)) div 2))
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(((((x div 2) div 3) mod 2) + (x div 2)) div 2)
A307726-A156875: 0 0 0 0 1 1 2 2 2 2 3 3 3 3 3 3
(((((x div 2) mod 3) mod 2) + (x div 2)) div 2)
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(1 - ((((x div 4) mod 2) - (x div 2)) div 2))
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(x - ((((x div 4) mod 2) - (x div 2)) div 2))
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(2x - (((x mod 4) + (x div 2)) div 2))
A047340: 0 2 3 4 7 9 10 11 14 16 17 18 21 23 24 25
((((x + ~2) - ((~x + 2) div 2)) * (x div 2)) div 2)
A211538: 0 0 0 1 3 5 9 12 18 22 30 35 45 51 63 70
(((x2 div (2 + (x div 2))) - (x div 2)) div 2)
A181972: 0 0 0 1 1 2 2 3 3 4 4 6 6 7 7 9
(x - (2 * ((x div (2 + (x mod 2))) - (x div 2))))
A265228: 0 1 2 3 4 7 6 9 8 11 10 15 12 17 14 19
((x + 2) - ((~2x + (x div 2)) * (x div 2)))
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A271713: 2 3 7 10 18 23 35 42 58 67 87 98 122 135 163 178
(2x3 * ((x div 2) * (x div 2)))
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((x - (1 mod (~2x + 1))) div (2 + (x div 2)))
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(((x * (x mod 2)) - (x div 2)) * (2 + (x div 2)))
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((2 - ((x div 2) mod 4)) * ((x div 2) mod 2))
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(2x - ((~2 + (x mod 2)) * ((x div 2) mod 2)))
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((x2 + 3x + 2) div (2 - ((x div 2) mod 2)))
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(x + (((x + (x div 2)) div 2) + ((x div 2) mod 2)))
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(x + ((x + (x div 2)) div 2) - ((x div 2) mod 2))
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A047351: 0 1 2 4 7 8 9 11 14 15 16 18 21 22 23 25
(30 - (x mod 2))
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(2 + (2x div (8 - (x mod 2))))
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(((2 + (x div 4)) div (2 - (x mod 2))) mod 2)
A267129: 1 0 1 0 1 1 1 1 0 0 0 0 0 1 0 1
((x div 7) mod (2 + (x mod 2)))
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((~3x + 2) * (x div (~2 + (x mod 2))))
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((3x2 + 3x) + (2 * (x mod 2)))
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(x2 - (4 * (~x2 + (x mod 2))))
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((x4 + ~2x3 + ~2x2 + 5x) div 2)
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((x + 2) + (x div 13))
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((x + 2) + (x div 11))
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(2 * (x + (x div 11)))
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((3x2 + 13x) div 2)
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((3x2 + 11x) div 2)
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(1 - ((~x + (x mod (1 + (x div 3)))) div 2))
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(2 + (x * (1 + ((x3 + 1) div 2))))
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((x + 2) + ((x + 1) mod 9))
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((x + 2) + (5 * (x div 3)))
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((x + 2) + ((2x + 1) div 5))
A248233-A097432: 2 3 5 6 7 9 10 12 13 14 16 17 19 20 21 23
((5x2 + 11x) div 2)
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((x + 2) + ((x2 + 2x) div 5))
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((x + 2) + ((x + (x div 2)) div 5))
A284676-A247915: 2 3 4 5 7 8 9 11 12 13 15 16 17 18 20 21
(10x2 + ~6x)
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((5x2 + ~7x) div 2)
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((x + (x div (~1 - (x div 4)))) div 2)
A218447: 0 0 0 0 1 1 1 1 2 3 3 3 4 4 5 5
(2 * compr(\x.(1 - (x mod (1 + (x mod 4)))),x))
A345211: 2 4 6 10 14 18 20 22 26 28 30 34 38 42 44 46
((x * (1 + (x mod (2 * (2 - (x mod 2)))))) div 2)
A186813: 0 1 3 3 2 5 9 7 4 9 15 11 6 13 21 15
((x + 2) + (3 * (x div 5)))
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((x + 2) + ((x mod (1 + (x div 2))) div 3))
A307646-A287519: 2 3 4 5 6 7 8 10 11 12 13 14 15 17 18 19
(x - ((~x + ((~1 + (x div 2)) div 3)) div 2))
A184624-A184117: 1 2 3 5 6 8 9 11 12 13 15 16 18 19 20 22
(22x + 12)
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(x - ((~x + (x div 12)) div 2))
A195123-A061054: 0 2 3 5 6 8 9 11 12 14 15 17 18 19 21 22
(x - ((~x + (x mod 12)) div 2))
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A289234: 0 1 2 3 4 5 6 7 8 9 10 11 18 19 20 21
((x + 2) + ((x mod (2 + (x div 2))) div 3))
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(2 * (x + (3 * ((x + 2) + (x div 2)))))
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(14x2 + ~6x)
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((7x2 + ~3x) div 2)
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((x + 2) + (3 * (2x + (x mod 2))))
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(14x2 + ~4x)
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(9x2 + 18x + 8)
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(3x5 + 2x4)
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((x + 2) + ((x + (x div 3)) div 3))
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((x * ((x + 1) - (2 * (~x + (x mod 2))))) div 2)
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((x4 + ~x3 + ~x2 + ~x) div 2)
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((x * ((x + ~1) + (2 * (x + (x mod 2))))) div 2)
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(((x + 2) * (x mod 2)) + ((x2 + x) div 2))
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((x6 + x) div 2)
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(x - ((~x + ((~1 + (x div 3)) div 2)) div 2))
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((x + ((x div (1 + (2 mod (x + 1)))) mod 2)) div 2)
A194202: 0 1 1 2 2 3 3 3 4 5 5 6 6 6 7 8
(x - (2 * (~x + (x mod 10))))
A103303: 0 1 2 3 4 5 6 7 8 9
A024658: 0 1 2 3 4 5 6 7 8 9 30 31 32 33 34 35
((x + (((1 + (x div 2)) div 3) mod 2)) div 2)
A194243: 0 0 1 1 2 3 3 4 4 5 5 5 6 6 7 7
((x + (((~2 + (x div 2)) div 3) mod 2)) div 2)
A194161: 0 1 1 2 2 2 3 3 4 4 5 6 6 7 7 8
(x - ((~x + ((x mod (1 + (x div 2))) div 2)) div 2))
A195121: 0 2 3 5 6 7 9 10 12 13 14 16 17 18 20 21
((x + (((x mod 5) div 2) div 2)) div 2)
A194249: 0 0 1 1 2 2 3 3 4 5 5 5 6 6 7 7
((x + (((1 + (x div 4)) div 2) mod 2)) div 2)
A217713: 0 0 1 1 2 3 3 4 4 5 5 6 6 6 7 7
((x + 2) + ((x - (x div 8)) div 2))
A246046-A224996: 2 3 5 6 8 9 11 12 13 15 16 18 19 21 22 24
((x div (~x + (2 * (~2 + (x mod 4))))) mod 2)
A341591-A101040: 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0
((x2 + 2) div (x + 10))
A127039: 0 0 0 0 1 1 2 3 3 4 5 5 6 7 8 9
(9x2 + ~8x + 2)
A154254: 2 3 22 59 114 187 278 387 514 659 822 1003 1202 1419 1654 1907
(1 - ((~x + (((2 - (x div 2)) div 2) div 2)) div 2))
A309093: 1 2 2 3 3 4 5 5 6 6 7 7 8 8 9 10
((x * ((2x mod (2 + (x div 2))) mod 2)) div 2)
A308224: 0 0 1 0 0 0 0 0 0 0 0 5 0 0 7 7
(1 - ((~x + ((x mod (2 + (x div 2))) div 2)) div 2))
A248170: 1 2 2 3 3 4 4 4 5 5 6 6 6 7 7 7
(2 - ((~x + ((x mod (2 + (x div 2))) div 2)) div 2))
A177876: 2 3 3 4
A134995-A070984: 2 3 3 4 4 5 5 5 6 6 7 7 7 8 8 8
((x + (x div (4 - ((x div 2) mod 2)))) div 2)
A257808: 0 0 1 2 2 3 4 4 5 5 6 7 7 8 9 10
((x + ((x + ~2) mod (2 + ((x div 2) mod 2)))) div 2)
A256991: 0 1 1 2 2 3 3 4 4 5 6 5 6 7 7 8
(1 - ((x * (x div (2 * (~2 + (x mod 2))))) div 2))
A140860: 1 2 2 4 3 9
(5x + 34)
A295750: 34 39
(2x - ((~x + ((~x + 2) div 4)) div 2))
A022850: 0 3 5 8 11 13 16 19 21 24 26 29 32 34 37 40
(2x - (((~x + 2) - (x div 4)) div 2))
A057843: ~1 2 4 7 10 12 15 17 20 23 25 28 31 33 36 38
(x - (x2 div ((x + 2) + (x div 4))))
A227568-A097882: 0 1 1 2 2 2 2 3 3 3 3 3 4 4 4 4
(x3 + 6x2 + 6x + 2)
A229013: 2 15 46 101 186 307 470 681 946 1271 1662 2125 2666 3291 4006 4817
(2 + compr(\x.(((x mod 3) * (x div 2)) mod 2),x))
A131565: 2 3 4 5 6 7 8 10 11 13 14 15 16 17 18 19
((x + (((x mod 4) + (x div 2)) div 2)) div 2)
A072490: 0 0 1 2 2 3 4 5 5 5 6 7 7 8 9 10
((x + (3x div (2 + (x div 2)))) div 2)
A317596: 0 1 2 3 3 4 4 5 6 6 7 7 8 8 9 10
(x - ((2 mod ((~x + 2) - ((x div 2) mod 2))) div 2))
A173905: 0 1 2 3 4 6 8 9 10 12 14 15 16 18 20 21
((x + 2) + ((x + (x2 div 3)) div 2))
A186498: 2 3 5 8 10 13 17 20 24 29 33 38 44 49 55 62
(2x - ((2 mod (~x2 + ~2x + 2)) div 2))
A267461: 0 2 6 12 18 26 34 44 54 66 78 92 106 122 138 156
((2x2 + 4x) + (x mod 2) - (x div 2))
A139597: 0 7 15 30 46 69 93 124 156 195 235 282 330 385 441 504
((x + (2 div (8 - (x div 2)))) div 2)
A180639: 0 0 1 1 2 2 3 3 4 4 5 5 6 7 8 8
((x2 + x + 1) div ((x + 2) + (x div 2)))
A283371: 0 1 1 2 2 3 3 4 5 6 6 7 7 8 9 10
(2 div (8 - ((x * (x mod 2)) div 2)))
A236138: 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2
((3 + (x2 div 3)) div (x + 2))
A025786: 1 1 1 1 1 1 1 2 2 2 3 3 3 3 4 4
((1 + ((x2 + ~3x + 2) div 2)) mod (x + 2))
A175630: 0 1 1 2 4 0 3 7 2 7 1 7 0 7 15 7
compr(\x.(1 - (x mod (1 + (x mod 4)))),(x + 2))
A325798-A238524-A237287-A237046-A067715: 3 5 7 9 10 11 13 14 15 17 19 21 22 23 25 26
((3 * ((x mod 2) - (x div 2))) mod (x + 2))
A336764: 0 0 1 0 0 4 7
((2 + (x div 3) - (x div 2)) div (x + 2))
A321447: 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ~1 0
((2 - (x mod (2 + (x mod 3)))) div (x + 2))
A304819-A015824-A015703: 1 0 0 0 0 0 0 0 0 0 0 ~1 0 0 0 0
((2 * (x div ~7)) mod (x + 2))
A005599: 0 1 2 3 4 5 6 7 6 7 8 9 10 11 12 11
compr(\x.(((x + 1) * (x div 2)) mod 4),(x + 2))
A229838: 3 5 7 8 9 11 13 15 16 17 19 21 23 24 25 27
((1 mod (~x2 + 2x + 4)) mod (x + 2))
A171950: 1 1 1 0 3 4 5 6 7 8 9 10 11 12 13 14
((2 * ((~x + (x div 4)) div 2)) mod (x + 2))
A116939: 0 1 2 1 2 3 2 3 4 3 4 3 4 5 4 5
((x2 mod (x - ((~x + 2) div 2))) div (x + 2))
A269166-A169673: 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0
((2 * (x div 2)) mod ((x2 + 2) div (x + 2)))
A184221: 0 0 0 0 1 1 2 1 2 1 2 1 2 1 2 1
(x - ((x * (x - (x div 3))) div (x + 2)))
A186704: 0 1 1 2 2 3 3 4 4 5 5 5 6
A320297: 0 1 1 2 2 3 3 4 4 5 5 5 6 6 6 7
(2x4 + 8x3 + 7x2 + ~2x)
A196506: 0 15 120 435 1128 2415 4560 7875 12720 19503 28680 40755 56280 75855 100128 129795
((x * (((x + 1) + (x div 2)) div 2)) div (x + 2))
A285902: 0 0 1 1 2 2 3 3 4 5 6 6 7 8 9 9
((x * (4 + (x div 4))) div (x + 2))
A342678: 0 1 2 2 3 3 3 3 4 4 5 5 6 6 6 6
((x + ~2) * ((2x + 1) mod (1 + (x div 2))))
A325689: 0 0 0 1 0 6 4 15 12 28 24 45 40 66 60 91
(2x + (2 div (1 + ((x + 1) mod 4))))
A222011: 1 2 4 8
A003485: 1 2 4 8 9 10 12 16 17 18 20 24 25 26 28 32
(2x + ((x div ~2) div 5))
A172273: 0 1 3 5 7 9 11 13 15 17 19 20 22 24 26 28
(2x + (x div ~11))
A214657: 0 1 3 5 7 9 11 13 15 17 19 21 22 24 26 28
((3x + 3) - (2 mod (~2x + 1)))
A168101: 3 6 10 15 20 25 30 35 40 45 50 55 60 65 70 75
(2x + (4 div (2 + (x div 3))))
A287113: 2 4 6 7 9 11 13 15 17 18 20 22 24 26 28 30
(2x + (((x + 1) * (2 - (x div 2))) div 2))
A292192: 1 4 5 8 8 10
(2x + ((x - (x div ~4)) div 2))
A004937: 0 3 5 8 10 13 16 18 21 24 26 29 31 34 37 39
(2x + (((((x + ~1) div 2) div 2) div 2) mod 2))
A241071: 1 2 4 6 8 10 12
A248195: 1 2 4 6 8 10 12 14 16 19 21 23 25 27 29 31
(2x + (2x div ~7))
A083042-A082977: 0 1 3 5 6 8 10 12 13 15 17 18 20 22 24 25
(2x + ((x mod ~2) mod 8))
A168203: 0 9 4 13 8 17 12 21 16 25 20 29 24 33 28 37
(2x + ((x + (x div 2)) div 8))
A172278: 0 2 4 6 8 10 13 15 17 19 21 24 26 28 30 32
(10x2 + ~3x)
A195018: 0 7 34 81 148 235 342 469 616 783 970 1177 1404 1651 1918 2205
(2x + (((x mod 4) + (x div 2)) div 2))
A174438: 0 2 5 8 9 11 14 17 18 20 23 26 27 29 32 35
(1 - (x2 div ((~2x + 1) - (x div 2))))
A165906: 1 2 2 3 3 4 4 5 5 5 6 6 6 7 7 8
26x2
A244633: 0 26 104 234 416 650 936 1274 1664 2106 2600 3146 3744 4394 5096 5850
22x2
A195323: 0 22 88 198 352 550 792 1078 1408 1782 2200 2662 3168 3718 4312 4950
34x2
A303302: 0 34 136 306 544 850 1224 1666 2176 2754 3400 4114 4896 5746 6664 7650
(3x + ((x mod (1 + (x div 2))) div 2))
A276854: 0 3 6 9 12 16 19 22 25 29 32 35 38 42 45 48
(3x + ((x + (x div 2)) div 4))
A277722: 0 3 6 10 13 16 20 23 27 30 33 37 40 43 47 50
((10 * (x mod 2)) + (x div 2))
A340138-A332177-A317330-A238880-A130858-A107408-A098760: 0 10 1 11 2 12 3 13 4 14 5 15 6 16 7 17
compr(\x.((x + 1) mod (1 + (x div 4))),(x div 2))
A121261: 0 0 1 1 2 2 3 3 5 5 7 7 8 8 11 11
((9x + 9) + (x div 2))
A194152: 9 18 28 37 47 56 66 75 85 94 104 113 123 132 142 151
(x - (~11 * (x div 2)))
A112653: 0 1 13 14 26 27 39 40 52 53 65 66 78 79 91 92
((3x * (x + (x mod 2))) - (x div 2))
A193866: 0 6 11 35 46 88 105 165 188 266 295 391 426 540 581 713
(((1 - (x div 2)) mod (2x + 1)) + (x div 2))
A163750: 0 1 1 1 10 12 14 16 18 20 22 24 26 28 30 32
(((x + 1) * (x2 + (x mod 2))) + (x div 2))
A213496: 0 4 13 41 82 158 255 403 580 824 1105 1469 1878 2386 2947 3623
((2 + (x mod 2) - (x div ~2)) * (x div 2))
A236203: 0 0 3 5 8 12 15 21 24 32 35 45 48 60 63 77
(((3 * (x div 4)) div 2) + (x div 2))
A011371: 0 0 1 1 3 3 4 4 7 7 8 8 10 10 11 11
(((x + 1) mod (2 * (1 + (x mod 2)))) + (x div 2))
A121496: 1 2 2 1 3 4 4 3 5 6 6 5 7 8 8 7
(x mod (20 - (x div 2)))
A103303: 0 1 2 3 4 5 6 7 8 9
A053834: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2
((4 * (x - (x div ~2))) - (x div 2))
A243520: 0 8 11 19 22 30 33 41 44 52 55 63 66 74 77 85
(x - (~15 * (x div 2)))
A151978: 0 1 17 18 34 35 51 52 68 69 85 86 102 103 119 120
((2 * (x + ((x * (x div 2)) mod 2))) + (x div 2))
A100530: 0 2 5 9 10 12 15 19 20 22 25 29 30 32 35 39
((1 mod (8 - (x div 2))) + (x div 2))
A238263: 1 1 2 2 3 3 4 4 5 5 6 6 7 7 7 7
((x * ((2x + 2) + (x mod 2))) - (x div 2))
A274681: 0 5 11 26 38 63 81 116 140 185 215 270 306 371 413 488
((x * ((2x + 2) - (x mod 2))) + (x div 2))
A299645: 0 3 13 22 42 57 87 108 148 175 225 258 318 357 427 472
((3 + (x div 8)) * (x mod 2))
A053387: 0 3 0 3 0 3 0 3 0 4 0 4 0 4 0 4
((3 * (x + ((x div 2) mod 2))) - (x mod 2))
A072065: 0 2 9 11 12 14 21 23 24 26 33 35 36 38 45 47
((4x2 + 12x + 8) + (x mod 2))
A188819: 8 25 48 81 120 169 224 289 360 441 528 625 728 841 960 1089
((2 * (x + ((x div 4) mod 2))) - (x mod 2))
A131855: 0 1 4 5 10 11 14 15 16 17 20 21 26 27 30 31
((3x4 + ~x2) div 2)
A260810: 0 1 22 117 376 925 1926 3577 6112 9801 14950 21901 31032 42757 57526 75825
((7x2 + 3x) div 2)
A186029: 0 5 17 36 62 95 135 182 236 297 365 440 522 611 707 810
((x6 + x2) div 2)
A168122: 0 1 34 369 2056 7825 23346 58849 131104 265761 500050 885841 1493064 2413489 3764866 5695425
((x2 * (x - (x div (~2 + (x mod 2))))) div 2)
A309337: 0 1 6 27 48 125 162 343 384 729 750 1331 1296 2197 2058 3375
((x5 + ~x3 + 2x2) div 2)
A101377: 0 1 16 117 496 1525 3816 8281 16192 29241 49600 79981 123696 184717 267736 378225
((x3 + 7x2 + 8x) div 2)
A111694: 0 8 26 57 104 170 258 371 512 684 890 1133 1416 1742 2114 2535
(2 * (x2 + ((x2 + 2x) div 4)))
A195015: 0 2 12 24 44 66 96 128 168 210 260 312 372 434 504 576
(2x2 + ((x2 + 3x + 2) div 2))
A134238: 1 5 14 28 47 71 100 134 173 217 266 320 379 443 512 586
((x2 mod (2x + 1)) + (x2 div 2))
A266223: 0 1 6 6 15 15 28 28 45 45 66 66 91 91 120 120
((x6 + x3) div 2)
A240129: 0 1 36
A071232: 0 1 36 378 2080 7875 23436 58996 131328 266085 500500 886446 1493856 2414503 3766140 5697000
((x6 + ~x3) div 2)
A085744: 0 0 28 351 2016 7750 23220 58653 130816 265356 499500 885115 1492128 2412306 3763396 5693625
(2 - (4x div (x3 + ~2)))
A246505: 2 6 1 2 2
compr(\x.(~1 + (x mod (1 + (x div 5)))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A053433: 0 1 2 3 4 5 6 7 8 9 10 12 13 16 17 20
(x * (1 + ((x + ~1) mod 9)))
A057147: 0 1 4 9 16 25 36 49 64 81 10 22 36 52 70 90
compr(\x.(1 + (x mod (~1 + (2 * (~2 + (x mod 2)))))),x)
A324583: 1 2 4 5 6 7 8 11 12 13 14 16 17 18 19 22
compr(\x.(~1 + (x mod (3 - ((x div 2) mod 2)))),x)
A039256: 0 1 2 3 4 6 7 9 10 11 12 13 14 15 16 18
37x
A085959: 0 37 74 111 148 185 222 259 296 333 370 407 444 481 518 555
47x
A004963-A004943: 0 47 94 141 188 235 282 329 376 423 470 517 564 611 658 705
(9x2 + ~7x)
A152995: 0 2 22 60 116 190 282 392 520 666 830 1012 1212 1430 1666 1920
(7x2 + ~5x)
A139268: 0 2 18 48 92 150 222 308 408 522 650 792 948 1118 1302 1500
(3x2 + 23x)
A277976: 0 26 58 96 140 190 246 308 376 450 530 616 708 806 910 1020
(4x3 + 6x2 + 3x)
A268201: 0 13 62 171 364 665 1098 1687 2456 3429 4630 6083 7812 9841 12194 14895
(x + ((2 - (x div 2)) div (1 + (2 mod (x + 1)))))
A134986: 2 3 2 3 4 5 5 6 7 8 9 10 10 11 12 13
(x5 + x4 + x3 + x2 + x)
A152031: 0 5 62 363 1364 3905 9330 19607 37448 66429 111110 177155 271452 402233 579194 813615
compr(\x.(1 - (x mod (2 - (x mod ~3)))),x)
A153088: 1 2 3 5 7 8 9 10 11 13 14 15 17 19 20 21
(8x3 + 3x)
A173200: 0 11 70 225 524 1015 1746 2765 4120 5859 8030 10681 13860 17615 21994 27045
(x + ((2x + 1) div 7))
A138083: 0 1 2 4 5 6
A140102-A039101: 0 1 2 4 5 6 7 9 10 11 13 14 15 16 18 19
compr(\x.(1 - (x mod (1 + (x mod 6)))),x)
A141819: 1 2 3 4 5 7 8 9 11 13 14 15 16 17 19 20
(2x2 + 19x)
A139581: 0 21 46 75 108 145 186 231 280 333 390 451 516 585 658 735
(x + ((x + ~1) div (~1 + (x mod ~4))))
A008741: 1 1 1 2 1 4 4 4 1
(x + (x div (5 + (x mod 3))))
A067570: 0 1 2 3 4 5 7
A002855: 0 1 2 3 4 5 7 8 9 10 11 12 14 15 16 18
(x + ((2x + 1) div 9))
A039194: 0 1 2 3 5 6 7 8 9 11 12 13 14 16 17 18
(x + ((x2 + ~x) div 9))
A023535: 0 1 2 3 5 7 9 11 14 17 20 23 26 30 34 38
(x + (2 div (1 + (x div (4 + (x mod 2))))))
A317334: 2 3 4 5 5 6 7 8 8 10 10 11 12 13 14 15
compr(\x.(1 + (x mod 2) - ((x div 2) mod 4)),x)
A047570: 2 4 5 6 7 10 12 13 14 15 18 20 21 22 23 26
(x + (5 * (1 + (x div 3))))
A047574: 5 6 7 13 14 15 21 22 23 29 30 31 37 38 39 45
(x + (((x + 1) + (x mod 2)) div 5))
A138083: 0 1 2 4 5 6
A039245: 0 1 2 4 5 6 7 8 9 11 12 13 14 16 17 18
(11x2 + ~10x)
A051876: 0 1 24 69 136 225 336 469 624 801 1000 1221 1464 1729 2016 2325
compr(\x.((x * (x mod 3)) mod 5),x)
A281746: 0 3 5 6 9 10 12 15 18 20 21 24 25 27 30 33
(x + compr(\x.((x div 2) mod 2),(x div 5)))
A166274: 0 1 2 3 4 6 7 8 9 10 14 15 16 17 18 20
compr(\x.((x mod 3) - (x mod 5)),x)
A004763: 0 1 2 3 4 6 7 8 9 12 13 14 15 16 17 18
(x5 + 5x)
A180355: 0 6 42 258 1044 3150 7806 16842 32808 59094 100050 161106 248892 371358 537894 759450
(x + ((~x + 2) mod ((x + 1) - (x mod 4))))
A295484: 0 1 2 3 7
A171464: 0 1 2 3 7 7 7 7 11 11 11 11 15 15 15 15
(4x5 + x)
A069078: 0 5 130 975 4100 12505 31110 67235 131080 236205 400010 644215 995340 1485185 2151310 3037515
(x + ((x2 + 1) div (2x + 5)))
A061723: 0 1 2 3 5 6 8 9 11 12 14 15 17 18 19 21
compr(\x.(1 - (2x mod (3 + (x div 2)))),x)
A193406: 1 3 4 7 8 9 10 11 12 13 14 16 17 19 20 21
(x + (3 * (1 + (x div 5))))
A047562: 3 4 5 6 7 11 12 13 14 15 19 20 21 22 23 27
(x + ((~1 + (x mod 5)) mod 3))
A113790: 2 1 3 5 4 7 6 8 10 9 12 11 13 15 14 17
(x + (3 * (x div 7)))
A007093: 0 1 2 3 4 5 6 10 11 12 13 14 15 16 20 21
(x + (3 * ((x + 1) div 5)))
A295484: 0 1 2 3 7
A047534: 0 1 2 3 7 8 9 10 11 15 16 17 18 19 23 24
(x + ((1 + (x div (~2 + (x mod 2)))) mod 3))
A030118: 1 1 2 4 6 7 7 7 8 10 12 13 13 13 14 16
(x + ((x - ((x div 2) mod 3)) div 3))
A047420-A039075: 0 1 2 3 4 6 8 9 10 11 12 14 16 17 18 19
(25x + 24)
A044482: 24 49 74 99 124 149 174 199 224 249 274 299 324 349 374 399
(x + (((1 - (x div 2)) mod (x + 1)) div 3))
A039192: 0 1 2 3 5 6 7 9 10 11 12 13 14 16 17 18
(x + ((x3 + 3x2 + 2x) div 3))
A145069: 0 3 10 23 44 75 118 175 248 339 450 583 740 923 1134 1375
(x + ((2 * ((x + 1) div 3)) div 3))
A039198: 0 1 2 3 4 6 7 8 10 11 12 13 14 15 17 18
(x + ((2 * (2 + (x div 3))) div 3))
A039159-A003251: 1 2 3 5 6 7 8 9 10 12 13 14 16 17 18 19
(x + ((4 * (x div 3)) div 3))
A138083: 0 1 2 4 5 6
A004128: 0 1 2 4 5 6 8 9 10 13 14 15 17 18 19 21
(x2 + 21x)
A132763: 0 22 46 72 100 130 162 196 232 270 310 352 396 442 490 540
(x2 + 23x)
A132765: 0 24 50 78 108 140 174 210 248 288 330 374 420 468 518 570
(x2 + 22x)
A132764: 0 23 48 75 104 135 168 203 240 279 320 363 408 455 504 555
(13x2 + ~12x)
A161935: 0 1 28 81 160 265 396 553 736 945 1180 1441 1728 2041 2380 2745
(x + ((((x + ~2) * (x div 2)) div 2) div 3))
A010385: 0 1 2 3 4 6 8 9 12 13 16 18
(~x + (3 * ((x + ((x div 2) mod 2)) div 2)))
A215415: 0 ~1 1 3 2 1 3 5 4 3 5 7 6 5 7 9
(x + ((2x * (x2 div 2)) div 3))
A181946: 0 1 4 11 25 45
(x + ((x + ((x div 2) div 3)) div 3))
A138083: 0 1 2 4 5 6
A247964: 0 1 2 4 5 6 8 9 11 12 13 15 16 18 19 20
(x2 + 19x)
A132762: 0 20 42 66 92 120 150 182 216 252 290 330 372 416 462 510
(x + (2 div (6 - (x div 3))))
A103303: 0 1 2 3 4 5 6 7 8 9
A329481: 0 1 2 3 4 5 6 7 8 9 10 11 13 14 15 17
(x * (2 div (6 - (x div 3))))
A308919: 0 0 0 0 0 0 0 0 0 0 0 0 12 13 14 30
(14x2 + ~x)
A195024: 0 13 54 123 220 345 498 679 888 1125 1390 1683 2004 2353 2730 3135
(x + (x mod (1 + ((x + (x div 4)) div 2))))
A138083: 0 1 2 4 5 6
A172276: 0 1 2 4 5 6 8 9 10 12 13 15 16 17 19 20
(2x4 + ~3x3 + 2x2)
A344866: 0 1 16 99 352 925 2016 3871 6784 11097 17200 25531 36576 50869 68992 91575
(x2 + 25x)
A132767: 0 26 54 84 116 150 186 224 264 306 350 396 444 494 546 600
(x2 + 31x)
A132773: 0 32 66 102 140 180 222 266 312 360 410 462 516 572 630 690
((x + 1) - (x mod (~x2 + 3x + ~1)))
A185092: 1 2 3 4 6 12
(x + ((1 + (x mod 8)) mod (x + 1)))
A084689: 0 1 2 3 4 5 6 7 9
A031876: 0 1 2 3 4 5 6 7 9 11 13 15 17 19 21 23
(x + ((1 - ((x * (x div 2)) div 2)) div (x + 1)))
A226142: 1 1 2 3 3 4 4
A076895: 1 1 2 3 3 4 4 5 6 7 7 8 9 10 10 11
(x * (2 - ((x + ~1) * ((~x2 + x) div 2))))
A117665: 0 2 6 24 80 210 462 896 1584 2610 4070 6072 8736 12194 16590 22080
(x * ((x2 + ~3x + 2) + (x2 div 2)))
A212680: 0 0 4 18 56 120 228 378 592 864 1220 1650 2184 2808 3556 4410
(x7 + x)
A190578: 0 2 130 2190 16388 78130 279942 823550 2097160 4782978 10000010 19487182 35831820 62748530 105413518 170859390
(x7 + ~x)
A133499: 0 0 126 2184 16380 78120 279930 823536 2097144 4782960 9999990 19487160 35831796 62748504 105413490 170859360
(x + (2 * ((x + 1) div 7)))
A039109: 0 1 2 3 4 5 8 9 10 11 12 13 14 17 18 19
(x + (2 * ((x + 2) div 7)))
A039106: 0 1 2 3 4 7 8 9 10 11 12 13 16 17 18 19
compr(\x.(~2 + (x mod (1 + ((1 + (x div 2)) div 2)))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A193096: 0 1 2 3 4 5 6 7 8 9 10 12 13 15 16 17
(3x2 + 20x)
A140689: 0 23 52 87 128 175 228 287 352 423 500 583 672 767 868 975
(x + (((x + 2) + (x div 2)) * ((x + 1) div 2)))
A271675: 0 4 7 15 20 32 39 55 64 84 95 119 132 160 175 207
(x + (((x - (x mod ~3)) div 2) div 2))
A171948-A045749: 0 1 2 3 5 6 7 9 10 11 13 14 15 16 17 18
(x + (4 * (((x + 1) div 2) div 3)))
A135210: 0 1 2 3 4 9 10 11 12 13 14 19 20 21 22 23
(~x + (2 * (6 + (x mod 4))))
A004453: 12 13 14 15 8 9 10 11 4 5 6 7 0 1 2 3
(x + ((~x + 1) div (4 + (x mod 3))))
A109401: 0 1 1 2 3 4 4 5 6 7 8 9 9 10 11 11
(x + ((((2 - (x div 2)) mod (x + 1)) div 2) div 2))
A067570: 0 1 2 3 4 5 7
A039263: 0 1 2 3 4 5 7 8 9 11 12 13 14 15 16 17
(x + (((x - ((x mod 3) div 2)) div 2) div 2))
A099354: 0 1 2 3 5 6 7 8 9 11 12 13 15 16 17 18
(x2 + 28x)
A132770: 0 29 60 93 128 165 204 245 288 333 380 429 480 533 588 645
(x2 + 30x)
A132772: 0 31 64 99 136 175 216 259 304 351 400 451 504 559 616 675
(x2 div (~x + 32))
A257594: 0 0 0 0 0 0 1 1 2 3 4 5 7 8 10
(x + (2 * (x div (4 + (x div 4)))))
A039195: 0 1 2 3 4 7 8 9 10 11 12 13 14 15 18 19
(x + (x div (4 + ((x div 4) mod 2))))
A039257: 0 1 2 3 4 6 7 8 10 11 12 13 14 15 16 18
(x + (x div (2 * (2 + ((x div 4) mod 2)))))
A067570: 0 1 2 3 4 5 7
A039262: 0 1 2 3 4 5 7 8 10 11 12 13 14 15 16 17
(x + (((x - ((x div 4) mod 2)) div 2) div 2))
A039149: 0 1 2 3 4 6 7 8 10 11 12 13 14 16 17 18
(x + (x div (4 + ((x div 2) mod 4))))
A039266-A039205: 0 1 2 3 4 5 6 8 10 11 12 13 14 15 16 17
(x + (((x - ((x div 2) mod 4)) div 2) div 2))
A039154: 0 1 2 3 4 5 6 8 10 11 12 13 14 15 16 18
(17x2 + ~16x)
A240129: 0 1 36
A282853: 0 1 36 105 208 345 516 721 960 1233 1540 1881 2256 2665 3108 3585
(x + (2x div (4 + (x div 4))))
A081688: 0 1 3 4 5 7 8 9 10 12 13 14 15 16 18 19
(x + (((x div 2) - ((x div 4) mod 2)) div 2))
A067570: 0 1 2 3 4 5 7
A039152: 0 1 2 3 4 5 7 8 10 11 12 13 14 15 17 18
compr(\x.(~4 + (x2 mod (2 + (x div 2)))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A159452: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 15 20
(x + (2 * (2 + ((x + ~2) mod (2 + (x mod 2))))))
A155875: 4 9 6 9 8 9 10 15 12 15 14 15 16 21 18 21
(x + (x mod (x - ((x + ~1) mod 8))))
A103303: 0 1 2 3 4 5 6 7 8 9
A071980: 0 1 2 3 4 5 6 7 8 9 11 13 15 17 19 21
compr(\x.(x mod (x - ((x + ~1) mod 8))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A319725: 0 1 2 3 4 5 6 7 8 9 17 25 33 41 49 57
compr(\x.(((x + ~2) * (x div 2)) mod 8),x)
A329952: 0 1 2 8 10 16 17 18 24 26 32 33 34 40 42 48
((x2 + x + 1) div (x + 8))
A127036: 0 0 0 1 1 2 3 3 4 5 6 7 7 8 9 10
(2 div ((x2 + ~2) mod (x + 8)))
A243827: 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0
(19x + 8)
A144619: 8 27 46 65 84 103 122 141 160 179 198 217 236 255 274 293
(x + ((((2 - (x div 2)) mod (x + 2)) div 2) div 2))
A067570: 0 1 2 3 4 5 7
A039201: 0 1 2 3 4 5 7 9 10 11 12 13 14 15 16 18
(x * (2 + ((x2 + ~2) div (x + 4))))
A119640: 0 1 4 9 12 20 30 42 56 72 90 99 120 143 168 195
(x + ((~x2 + 2) div (x + 6)))
A325678: 0 1 1 2 2 2 3 3 3 3 3 4 4 4 4 4
(x + ((x + ((x div 4) mod 2)) div 4))
A039144: 0 1 2 3 5 6 7 9 10 11 12 13 15 16 17 19
(x + ((x + ((x div 2) mod 4)) div 4))
A138083: 0 1 2 4 5 6
A039138: 0 1 2 4 5 6 8 9 10 11 12 14 15 16 18 19
(~x + (2 * (x2 div (x - ((~x + 2) div 2)))))
A330559: 0 1 2 1 2 1 2 1 2 3 4 3 4 3 4 5
(x + (((~x + 2) * (x div 2)) div (x + 4)))
A195124: 0 1 2 2 3 4 4 5 6 6 7 8 8 9 9 10
(x + ((((x div 4) mod 2) + (x div 2)) div 2))
A039143: 0 1 2 3 5 6 8 9 10 11 12 13 15 16 18 19
(x2 + 26x)
A132768: 0 27 56 87 120 155 192 231 272 315 360 407 456 507 560 615
(x + (2 * (x + ((x + (x mod 2)) div 3))))
A246976: 0 3 6 11 14 19 22 25 28 33 36 41 44 47 50 55
(x + ((x + ((x mod (1 + (x div 2))) div 2)) div 2))
A066096: 0 1 3 4 6 8 9 11 12 14 16 17 19 21 22 24
(x + (2 * (2 div (~x + 16))))
A103303: 0 1 2 3 4 5 6 7 8 9
A154125: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 16 19
(~2x3 + 17x2)
A015234: 0 15 52 99 144 175 180 147 64 ~81 ~300 ~605 ~1008 ~1521 ~2156 ~2925
(2x3 + ~11x2)
A015245: 0 ~9 ~28 ~45 ~48 ~25 36 147 320 567 900 1331 1872 2535 3332 4275
(x + (2 * (x + (5 * (x mod 2)))))
A168210: 0 13 6 19 12 25 18 31 24 37 30 43 36 49 42 55
(x + (1 mod (3 - (2x * (x mod 2)))))
A118402: 1 1 3 1 5 ~1 7 ~3 9 ~5 11 ~7 13 ~9 15 ~11
(x + ((1 + (x mod ~3)) mod (x + 2)))
A325909: 1 3 2 4 9 5 7 15 8 10 21 11 13 27 14 16
(x + (17 * (x div 2)))
A151979: 0 1 19 20 38 39 57 58 76 77 95 96 114 115 133 134
(x + (x2 div (8 + (x div 2))))
A047893: 0 1 2 4 5 7 9 11 13 15 17 20 22 25 27 30
(x + (3 div (8 - (x div 2))))
A103303: 0 1 2 3 4 5 6 7 8 9
A333126: 0 1 2 3 4 5 6 7 8 9 11 12 13 14 17 18
(x + (((2x + 2) + (x div 2)) * (x div 2)))
A195162: 0 1 9 12 28 33 57 64 96 105 145 156 204 217 273 288
((x + 1) div (2 - (x mod (2 - (x * (x mod 2))))))
A273943: 0 1 1 2 2 2 3 1 4 1 5 1 6 1 7 1
(2x3 + ~15x2)
A015247: 0 ~13 ~44 ~81 ~112 ~125 ~108 ~49 64 243 500 847 1296 1859 2548 3375
19x2
A244631: 0 19 76 171 304 475 684 931 1216 1539 1900 2299 2736 3211 3724 4275
23x2
A244632: 0 23 92 207 368 575 828 1127 1472 1863 2300 2783 3312 3887 4508 5175
(2x3 + ~13x2)
A015246: 0 ~11 ~36 ~63 ~80 ~75 ~36 49 192 405 700 1089 1584 2197 2940 3825
(x2 * (1 + (4 * (x2 div 2))))
A240129: 0 1 36
A275496: 0 1 36 153 528 1225 2628 4753 8256 13041 20100 29161 41616 56953 77028 101025
(x2 + 27x)
A132769: 0 28 58 90 124 160 198 238 280 324 370 418 468 520 574 630
(x * (x + ((x - (x div ~4)) div 2)))
A050508: 0 2 6 15 24 40 60 77 104 135 160 198 228 273 322 360
(x + (x mod (~x + ((x + ~1) mod 8))))
A103303: 0 1 2 3 4 5 6 7 8 9
A122481-A043269: 0 1 2 3 4 5 6 7 8 9 2 4 6 8 10 12
(x + ((~x2 + 1) div (x + 8)))
A034463: 0 1 1 2 2 3 3 3 4 4 4 4 4 5 5 5
(x5 + ~4x4 + 5x3)
A079503: 0 2 8 54 320 1250 3672 8918 18944 36450 65000 109142 174528 268034 397880 573750
(x2 + 10x + 5)
A134594: 5 16 29 44 61 80 101 124 149 176 205 236 269 304 341 380
(x2 + (5 * (x2 div 2)))
A195145: 0 1 14 29 56 85 126 169 224 281 350 421 504 589 686 785
(x2 + ((2x + 1) * (1 + (x div 2))))
A213399: 1 4 14 23 43 58 88 109 149 176 226 259 319 358 428 473
(~x7 + 1)
A024005: 1 0 ~127 ~2186 ~16383 ~78124 ~279935 ~823542 ~2097151 ~4782968 ~9999999 ~19487170 ~35831807 ~62748516 ~105413503 ~170859374
loop(\(x,i).loop(\(x,i).loop(\(x,i).2x,i,x),i,x),(x + ~1),1)
A125791: 1 1 2 16 1024 1048576 34359738368 72057594037927936 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(loop(\(x,i).(x * i),i,1) div (if x <= 0 then 1 else x)),x,1)
A006882: 1 1 2 3 8 15 48 105 384 945 3840 10395 46080 135135 645120 2027025
loop(\(x,i).loop(\(x,i).(x * i),loop(\(x,i).2x,i,1),x),x,1)
A261125: 1 2 48 1935360 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).(x * i),i,x),i,1)),x,1)
A152690: 1 2 4 16 304 34864 24918064 125436246064 5056710181206064 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).loop(\(x,i).(x * i),i,x),(2 * i),x),x,1)
A306635: 1 2 576 14332723200 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * (x div (if i <= 0 then 1 else i))),x,i),x,1)
A046882: 1 1 4 46656 4611686018427387903
loop(\(x,i).(x - i),x,loop(\(x,i).2x,x,(if x <= 0 then 1 else 2)))
A080522: 1 3 5 10 22 49 107 228 476 979 1993 4030 8114 16293 32663 65416
(x - loop(\(x,i).loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0),2,x))
A342126: 0 1 2 3 4 4 6 7 8 8 8 8 12 12 14 15
loop(\(x,i).(1 + loop(\(x,i).(if x <= 0 then i else (x + ~1)),x,0)),x,x)
A065176: 0 2 2 4 4 2 2 8 8 2 2 4 4 2 2 16
compr(\x.loop(\(x,i).loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0),2,x),x)
A077436-A023758: 0 1 2 3 4 6 7 8 12 14 15 16 24 28 30 31
(if (if (x mod 12) <= 0 then x else 0) <= 0 then 1 else 0)
A307090-A267959-A214020-A155454-A114213-A108358-A065413: 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1
(if (if ((x + (x div 2)) mod 4) <= 0 then x else 0) <= 0 then 1 else 0)
A307421: 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1
(if (x mod (2 + (x mod 4))) <= 0 then (if x <= 0 then 0 else 1) else 0)
A220400: 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1
(if ((x * (x div 2)) mod 4) <= 0 then (if x <= 0 then 0 else 1) else 0)
A118605: 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0
(if (x mod 8) <= 0 then (if x <= 0 then 0 else 3) else 0)
A171063: 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0
(if (x mod 2) <= 0 then (if x <= 0 then 1 else ((x div 2) div 3)) else 0)
A341981-A219203: 1 0 0 0 0 0 1 0 1 0 1 0 2 0 2 0
(if (x + ~1) <= 0 then x else (if (x mod 2) <= 0 then (2x + 1) else 0))
A266222: 0 1 5 0 9 0 13 0 17 0 21 0 25 0 29 0
(loop(\(x,i).(2x + 2),x,0) - (if (~x + 2) <= 0 then 1 else 0))
A091270: 0 2 5 13 29 61 125 253 509 1021 2045 4093 8189 16381 32765 65533
loop(\(x,i).(x + (if (x mod 2) <= 0 then (i * i) else 1)),(x + 1),0)
A140148: 1 2 11 12 37 38 87 88 169 170 291 292 461 462 687 688
loop(\(x,i).loop(\(x,i).(x + ((2 + i) * i)),i,x),(x + 1),0)
A005701: 3 14 40 90 175 308 504 780 1155 1650 2288 3094 4095 5320 6800 8568
loop(\(x,i).(x + ((if (i mod 2) <= 0 then 1 else i) * i)),(x + 1),0)
A136047: 1 3 12 16 41 47 96 104 185 195 316 328 497 511 736 752
loop(\(x,i).2x,x,loop(\(x,i).(x + (i * i)),(x + 1),0))
A014483: 1 10 56 240 880 2912 8960 26112 72960 197120 518144 1331200 3354624 8314880 20316160 49020928
loop(\(x,i).(x + loop(\(x,i).(x * i),i,(i * i))),(x + 1),0)
A206816: 1 9 63 447 3447 29367 276327 2856807 32250087 395130087 5225062887 74201293287 1126567808487 18213512883687 312440245683687 5668674457011687
loop(\(x,i).(x * i),x,loop(\(x,i).(2x + 1),(x + ~1),0))
A052665: 0 0 2 18 168 1800 22320 317520 5120640 92534400 1854316800 40834886400 980516275200 25499650176000 714077383219200 21423629170944000
(if (x mod 2) <= 0 then 1 else loop(\(x,i).(2x + 4),(x + ~1),0))
A277799: 1 0 1 12 1 60 1 252 1 1020 1 4092 1 16380 1 65532
loop(\(x,i).(~2x + 5),(x + ~1),(if x <= 0 then 1 else 0))
A140360: 1 0 5 ~5 15 ~25 55 ~105 215 ~425 855 ~1705 3415 ~6825 13655 ~27305
((2 * loop(\(x,i).(x2 + x),x,1)) + (if x <= 0 then 1 else 0))
A127690: 3 4 12 84 3612 6526884 21300113901612 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).3x,(x div 2),2) + (if x <= 0 then 1 else 0))
A225367: 3 2 6 6 18 18 54 54 162 162 486 486 1458 1458 4374 4374
(2 + (loop(\(x,i).3x,x,2) + (if x <= 0 then 1 else 0)))
A198635: 5 8 20 56 164 488 1460 4376 13124 39368 118100 354296 1062884 3188648 9565940 28697816
loop(\(x,i).(4x + 10),x,(if x <= 0 then 1 else 0))
A086462: 1 10 50 210 850 3410 13650 54610 218450 873810 3495250 13981010 55924050 223696210 894784850 3579139410
(1 - (1 mod loop(\(x,i).(~2x + 4),x,(if x <= 0 then 1 else 0))))
A282579: 1 0 4 0 20 0 84 0 340 0 1364 0 5460 0 21844 0
loop(\(x,i).(5x + 4),x,(if x <= 0 then 1 else 0))
A103455: 1 4 24 124 624 3124 15624 78124 390624 1953124 9765624 48828124 244140624 1220703124 6103515624 30517578124
(if (x mod 2) <= 0 then (if (~2 + (x div 3)) <= 0 then 1 else 2) else 0)
A230103-A045843: 1 0 1 0 1 0 1 0 1 0 2 0 2 0 2 0
(if x <= 0 then 1 else (if (x + ~1) <= 0 then 10 else 0))
A285476: 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(if x <= 0 then 1 else (if (x mod 12) <= 0 then 2 else 0))
A029696: 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
(if x <= 0 then 1 else (if (5 mod (x + 1)) <= 0 then 2 else 0))
A071164-A028718-A028714-A028710-A028706-A028661-A028653-A028645-A028637-A028629: 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
(if (x mod 10) <= 0 then (if x <= 0 then 1 else 2) else 0)
A086008-A067898: 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0
(if (x mod (2 + (x mod 3))) <= 0 then (if x <= 0 then 1 else 2) else 0)
A160498: 1 0 0 0 0 0 2 0 2 0 0 0 2 0 0 0
(if ((x - (if (x + ~2) <= 0 then 2 else 0)) mod 4) <= 0 then 2 else 0)
A262682: 0 0 2 0 2 0 0 0 2 0 0 0 2 0 0 0
(if (~x + 2) <= 0 then (if (x mod 2) <= 0 then 1 else 8) else 0)
A021554: 0 0 1 8 1 8 1 8 1 8 1 8 1 8 1 8
(if (x mod 8) <= 0 then (if x <= 0 then 1 else 4) else 0)
A341880: 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
(if (x mod 4) <= 0 then (if x <= 0 then 1 else (x div 4)) else 0)
A035444: 1 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0
(if (x mod 8) <= 0 then (if x <= 0 then 0 else (x + 2)) else 0)
A270035: 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0
(if ((if x <= 0 then 1 else x) mod 8) <= 0 then (x + ~2) else 0)
A173453: 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0
loop(\(x,i).(x + i),((if (x mod 2) <= 0 then 2 else 0) + (x div 2)),0)
A111074: 3 0 6 1 10 3 15 6 21 10 28 15 36 21 45 28
loop(\(x,i).((x * i) - loop(\(x,i).(~1 + (x * i)),i,0)),x,0)
A114870: 0 1 5 25 141 911 6703 55581 513929 5248891 58724211 714554633 9397715341 132870076119 2009977939271 32396622193141
loop(\(x,i).(x - loop(\(x,i).(((x + 1) - i) * i),i,0)),x,0)
A119913: 0 0 2 14 74 394 2344 16036 125628 1112028 10976118 119481218 1421542550 18348340022 255323504812 3809950976872
loop(\(x,i).(10 * (if x <= 0 then 1 else x)),x,0)
A178500: 0 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000 10000000000 100000000000 1000000000000 10000000000000 100000000000000 1000000000000000
(if (x + ~2) <= 0 then (if (x mod 2) <= 0 then (x + 3) else x) else 0)
A318382: 3 1 5 0 0 0 0 0 0 0 0 0 0 0 0 0
loop(\(x,i).2x2,1,loop(\(x,i).(2x + 1),x,0))
A087291: 0 2 18 98 450 1922 7938 32258 130050 522242 2093058 8380418 33538050 134184962 536805378 2147352578
loop(\(x,i).(x * (x div 2)),1,loop(\(x,i).(2x + 1),x,0))
A134057: 0 0 3 21 105 465 1953 8001 32385 130305 522753 2094081 8382465 33542145 134193153 536821761
loop(\(x,i).(x * i),(x + ~1),loop(\(x,i).(2x + 1),x,0))
A029767: 0 1 3 14 90 744 7560 91440 1285200 20603520 371226240 7428153600 163459296000 3923502105600 102017281766400 2856571067750400
(loop(\(x,i).x2,x,2) - loop(\(x,i).(2x + 1),x,0))
A119564: 2 3 13 249 65521 4294967265 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).3x,x,loop(\(x,i).(2x + 1),x,0))
A248225: 0 3 27 189 1215 7533 45927 277749 1673055 10058013 60407127 362619909 2176250895 13059099693 78359381127 470170635669
loop(\(x,i).(x * (x div 2)),1,loop(\(x,i).(2x + ~1),x,0))
A006516: 0 1 6 28 120 496 2016 8128 32640 130816 523776 2096128 8386560 33550336 134209536 536854528
(loop(\(x,i).(x * i),x,1) - loop(\(x,i).(2x + ~1),x,0))
A127986: 1 2 5 13 39 151 783 5167 40575 363391 3629823 39918847 479005695 6227028991 87178307583 1307674400767
(loop(\(x,i).x2,x,2) - loop(\(x,i).(2x + ~1),x,0))
A119550: 2 5 19 263 65551
A119563: 2 5 19 263 65551 4294967327 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,loop(\(x,i).(3x + 1),x,0))
A238976: 0 1 16 169 1600 14641 132496 1194649 10758400 96845281 871666576 7845176329 70607118400 635465659921 5719195722256 51472775849209
loop(\(x,i).(x * i),x,loop(\(x,i).(3x + 1),x,0))
A052698: 0 1 8 78 960 14520 262080 5508720 132249600 3571102080 107136691200 3535550726400 127280305152000 4963938127948800 208485488552140800 4611686018427387903
loop(\(x,i).(1 + (x * loop(\(x,i).(x2 + 2),2,2))),x,0)
A218741: 0 1 39 1483 56355 2141491 81376659 3092313043 117507895635 4465300034131 169681401296979 6447893249285203 245019943472837715 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (x * loop(\(x,i).x2,2,4))),x,0)
A218723: 0 1 257 65793 16843009 4311810305 1103823438081 282578800148737 72340172838076673 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (x * loop(\(x,i).(x2 + x),2,2))),x,0)
A218745: 0 1 43 1807 75895 3187591 133878823 5622910567 236162243815 9918814240231 416590198089703 17496788319767527 734865109430236135 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((~1 + loop(\(x,i).(x * i),i,1)) div (x + 1)),x,0)
A128882: 0 0 1 2 7 14 47 104 383 944 3839 10394 46079 135134 645119 2027024
loop(\(x,i).loop(\(x,i).((x + (i * i)) * i),x,(x + 1)),x,0)
A055590: 0 1 3 81 4611686018427387903
(loop(\(x,i).(x * i),x,(x + 1)) + (if (x + ~1) <= 0 then x else 0))
A338112: 1 3 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000 20922789888000
loop(\(x,i).x2,(x + ~1),loop(\(x,i).(1 + (x * i)),x,0))
A321618: 0 1 9 10000
loop(\(x,i).((x + 1) - loop(\(x,i).3x,i,x)),x,0)
A176338: 0 1 ~7 183 ~14639 3542639 ~2579041191 5637784043527 ~36983863325537119 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((if x <= 0 then 1 else (x + 2)) + (x div (1 + i))),x,0)
A130262: 0 1 3 5 8 11 14 17 20 24 28 32 36 40 44 48
loop(\(x,i).(x2 + 1),1,loop(\(x,i).(2x + 2),x,0))
A273539: 1 5 37 197 901 3845 15877 64517 260101 1044485 4186117 16760837 67076101 268369925 1073610757 4294705157
loop(\(x,i).(2x + 1),x,loop(\(x,i).(2x + 2),x,0))
A129868: 0 5 27 119 495 2015 8127 32639 130815 523775 2096127 8386559 33550335 134209535 536854527 2147450879
(1 - loop(\(x,i).2x,x,loop(\(x,i).(2x + ~2),x,0)))
A092440: 1 5 25 113 481 1985 8065 32513 130561 523265 2095105 8384513 33546241 134201345 536838145 2147418113
loop(\(x,i).((2x + (i mod 2)) * (if x <= 0 then 1 else 2)),x,0)
A117615: 0 1 4 18 72 290 1160 4642 18568 74274 297096 1188386 4753544 19014178 76056712 304226850
loop(\(x,i).(if x <= 0 then 1 else (4x2 + 8x)),x,0)
A060612: 0 1 12 672
loop(\(x,i).(if x <= 0 then 1 else 10x),x,0)
A178501: 0 1 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000 10000000000 100000000000 1000000000000 10000000000000 100000000000000
loop(\(x,i).2x,x,loop(\(x,i).(3x + 2),x,0))
A248216: 0 4 32 208 1280 7744 46592 279808 1679360 10077184 60465152 362795008 2176778240 13060685824 78364147712 470184951808
loop(\(x,i).((x + 2) + loop(\(x,i).(x * i),(x + ~2),1)),x,0)
A274999: 0 3 6 32 4611686018427387903
loop(\(x,i).(x + i),(x + (if (x + ~2) <= 0 then 1 else (x + ~2))),0)
A299017: 1 3 6 10 21 36 55 78 105 136 171 210 253 300 351
loop(\(x,i).(x * (x div 2)),1,loop(\(x,i).(~2x + 1),x,0))
A084152: 0 0 1 3 15 55 231 903 3655 14535 58311 232903 932295 3727815 14913991 59650503
loop(\(x,i).(if (x div 4) <= 0 then (1 + i) else 2x),x,0)
A244750: 0 2 3 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384
loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),x,0)
A210448: 0 3 15 57 195 633 1995 6177 18915 57513 174075 525297 1582035 4758393 14299755 42948417
loop(\(x,i).(~2x - (if (~2 + i) <= 0 then 1 else x)),x,0)
A141413: 0 ~1 1 ~3 9 ~27 81 ~243 729 ~2187 6561 ~19683 59049 ~177147 531441 ~1594323
loop(\(x,i).~x,x,(1 - loop(\(x,i).(~2x + i),x,0)))
A113954: 1 0 1 2 3 8 13 30 55 116 225 458 907 1824 3637 7286
loop(\(x,i).~x,x,loop(\(x,i).(~2x + (i * i)),x,0))
A232603: 0 ~1 2 ~5 6 ~13 10 ~29 6 ~69 ~38 ~197 ~250 ~669 ~1142 ~2509
loop(\(x,i).(x + i - (if (~x + i) <= 0 then (2 * i) else 0)),x,0)
A008344: 0 1 3 0 4 9 3 10 2 11 1 12 0 13 27 12
loop(\(x,i).(x + loop(\(x,i).2x2,(~1 + i),1)),x,0)
A072639: 0 1 3 11 139 32907 2147516555 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (i mod 2) <= 0 then x else (1 + (x div 2)))),x,0)
A048328: 0 1 2 4 8 13 26 40 80 121 242 364 728 1093 2186 3280
loop(\(x,i).(loop(\(x,i).(x * i),i,1) + (x * (1 + i))),x,0)
A001705: 0 1 5 26 154 1044 8028 69264 663696 6999840 80627040 1007441280 13575738240 196287356160 3031488633600 49811492505600
loop(\(x,i).(x + loop(\(x,i).(x * (~1 + (2 * i))),i,1)),x,0)
A099953: 0 1 4 19 124 1069 11464 146599 2173624 36633049 691362124 14440672699 330674815924 8236528396549 221694575073424 6411977928702799
loop(\(x,i).(~x + loop(\(x,i).(x * (1 + (i div 2))),i,1)),x,0)
A121746: 0 1 1 3 9 27 117 459 2421 11979 74421 443979 3184821 22216779 180996021 1444706379
loop(\(x,i).(x + (if x <= 0 then 2 else (x div (2 + (x mod 2))))),x,0)
A171826: 0 2 3 4 6 9 12 18 27
loop(\(x,i).(x + (if x <= 0 then 1 else ((x + (i mod 2)) div 2))),x,0)
A117792: 0 1 1 2 3 5 7 11 16 24 36 54 81 122 183 275
loop(\(x,i).(x + (loop(\(x,i).(x + (i * i)),i,0) * i)),x,0)
A207361: 0 1 11 53 173 448 994 1974 3606 6171 10021 15587 23387 34034 48244 66844
loop(\(x,i).2x,x,(1 - loop(\(x,i).(2x - i),x,0)))
A008353: 1 4 20 96 432 1856 7744 31744 128768 519168 2085888 8364032 33501184 134103040 536625152 2146959360
(x - loop(\(x,i).2x,x,loop(\(x,i).(2x - i),x,0)))
A064671: 0 3 18 91 420 1829 7686 31623 128520 518665 2084874 8361995 33497100 134094861 536608782 2146926607
loop(\(x,i).(loop(\(x,i).(x * i),(~1 + i),1) + (x * i)),x,0)
A000254: 0 1 3 11 50 274 1764 13068 109584 1026576 10628640 120543840 1486442880 19802759040 283465647360 4339163001600
loop(\(x,i).(loop(\(x,i).2x,(~2 + i),1) + (x * i)),x,0)
A187249: 0 1 3 11 48 248 1504 10560 84544 761024 7610496 83715968 1004592640 13059706368 182835893248 2742538406912
loop(\(x,i).(loop(\(x,i).(x * (i * i)),i,1) + (x * i)),x,0)
A217238: 0 1 6 54 792 18360 628560 29801520 1864114560 148458925440 14652778694400 1754531487878400 250496910657100800 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(loop(\(x,i).2x,(~1 + i),i) + (x * i)),x,0)
A066534: 0 1 6 30 152 840 5232 37072 297600 2680704 26812160 294945024 3539364864 46011796480 644165265408 9662479226880
loop(\(x,i).(x + ((x + loop(\(x,i).(x * i),i,1)) * i)),x,0)
A067318: 0 1 7 46 326 2556 22212 212976 2239344 25659360 318540960 4261576320 61148511360 937030429440 15275952518400 264030355814400
loop(\(x,i).loop(\(x,i).(x + ((2 + (i mod 2)) * i)),i,x),x,0)
A212967: 0 3 10 26 50 89 140 212 300 415 550 718 910 1141 1400 1704
loop(\(x,i).(x + (loop(\(x,i).x3,2,i) * i)),x,0)
A023002: 0 1 1025 60074 1108650 10874275 71340451 353815700 1427557524 4914341925 14914341925 40851766526 102769130750 240627622599 529882277575 1106532668200
loop(\(x,i).2x,(x + ~1),loop(\(x,i).(x + (i * i)),x,0))
A087076: 0 1 10 56 240 880 2912 8960 26112 72960 197120 518144 1331200 3354624 8314880 20316160
loop(\(x,i).(x + (loop(\(x,i).2x,i,i) * i * i)),x,0)
A036827: 0 2 34 250 1274 5274 19098 63002 194074 567322 1591322 4317210 11395098 29392922 74350618 184942618
loop(\(x,i).(x + (loop(\(x,i).~2x,i,i) * i)),x,0)
A232601: 0 ~2 14 ~58 198 ~602 1702 ~4570 11814 ~29658 72742 ~175066 414758 ~969690 2241574 ~5131226
loop(\(x,i).(x + loop(\(x,i).x2,2,(i * i * i))),x,0)
A123094: 0 1 4097 535538 17312754 261453379 2438235715 16279522916 84998999652 367428536133 1367428536133 4505856912854 13421957361110 36720042483591 93413954858887 223160292749512
(1 + (if (~x + 2) <= 0 then (if (x mod 2) <= 0 then 4 else 1) else 0))
A112871: 1 1 5 2
A072996: 1 1 5 2 5 2 5 2 5 2 5 2 5 2 5 2
(1 + loop(\(x,i).(4 * (if x <= 0 then 1 else x)),(x + ~1),0))
A092896: 1 1 5 17 65 257 1025 4097 16385 65537 262145 1048577 4194305 16777217 67108865 268435457
(1 + (if (x mod 8) <= 0 then (if x <= 0 then 0 else 2) else 0))
A342466-A336651-A327537-A327401-A318449-A049586-A030560: 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1
(if ((x + 2) mod (2 + (if (x + ~2) <= 0 then 1 else 2))) <= 0 then 0 else 1)
A284368: 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1
loop(\(x,i).i,(if (x mod 2) <= 0 then (~2 + ((x + ~1) div 2)) else 0),1)
A195842: 1 1 1 1 1 1 1 1 1 1 2 1 3 1 4 1
(1 + loop(\(x,i).2x,x,(if (x mod 4) <= 0 then 2 else 0)))
A066827: 3 1 1 1 33 1 1 1 513 1 1 1 8193 1 1 1
(if ((x - (if (x + ~2) <= 0 then 0 else 2)) mod 4) <= 0 then 0 else 1)
A185207-A185206-A185205: 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1
loop(\(x,i).2x,((x div 2) - (if (x mod 2) <= 0 then 2 else 0)),1)
A076736: 1 1 1 2 1 4 2 8 4 16 8 32 16 64 32 128
((if x <= 0 then 1 else (x + 4)) + (if (x + ~2) <= 0 then 0 else 1))
A270653: 1 5 6 8 9 10 11 12 13 14 15 16 17 18 19 20
(1 + loop(\(x,i).(3 * (if x <= 0 then 1 else x)),2x,0))
A103460: 1 10 82 730 6562 59050 531442 4782970 43046722 387420490 3486784402 31381059610 282429536482 2541865828330 22876792454962 205891132094650
(if (~1 + (x mod 3)) <= 0 then (if x <= 0 then 1 else 2) else ~1)
A143098: 1 2 ~1 2 2 ~1 2 2 ~1 2 2 ~1 2 2 ~1 2
loop(\(x,i).(2 * (x + (if (i mod 2) <= 0 then 2 else 0))),x,~1)
A153772: ~1 ~2 0 0 4 8 20 40 84 168 340 680 1364 2728 5460 10920
(1 + loop(\(x,i).((x + 1) * (2 + (if x <= 0 then 2 else 1))),x,0))
A052909: 1 5 16 49 148 445 1336 4009 12028 36085 108256 324769 974308 2922925 8768776 26306329
(1 + loop(\(x,i).(if x <= 0 then (2 + (i div 2)) else (x + ~1)),x,0))
A080883: 1 3 2 1 5 4 3 2 1 7 6 5 4 3 2 1
(1 + loop(\(x,i).(loop(\(x,i).2x,x,2) mod (1 + i)),x,0))
A119979: 1 1 3 1 3 3 2 5 6 5 11 9 6 9 3 9
(1 + loop(\(x,i).(8 * (if x <= 0 then 1 else x)),x,0))
A103459: 1 9 65 513 4097 32769 262145 2097153 16777217 134217729 1073741825 8589934593 68719476737 549755813889 4398046511105 35184372088833
(1 + loop(\(x,i).(if x <= 0 then 1 else (2x + 8)),x,0))
A154251: 1 2 11 29 65 137 281 569 1145 2297 4601 9209 18425 36857 73721 147449
(1 + loop(\(x,i).((2x + 4) * (if x <= 0 then 1 else x)),x,0))
A084765: 1 5 49 4801 46099201 4250272665676801 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(2 * (if x <= 0 then 1 else (x2 + 2x))),x,0))
A001601: 1 3 17 577 665857 886731088897 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).((x + 2) + (x div (if i <= 0 then 1 else i))),x,0))
A123753: 1 3 6 9 13 17 21 25 30 35 40 45 50 55 60 65
((if (x mod 6) <= 0 then 2 else 1) + (if x <= 0 then 0 else 1))
A096917: 2 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2
loop(\(x,i).(x * i),x,((2x + 2) + (if x <= 0 then 0 else 1)))
A052649: 2 5 14 54 264 1560 10800 85680 766080 7620480 83462400 997920000 12933043200 180583603200 2702527027200 43153254144000
(if ((x + 1) mod 8) <= 0 then 2 else (if x <= 0 then 0 else 1))
A341644: 0 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2
(if ((x + 2) mod 8) <= 0 then 2 else (if x <= 0 then 0 else 1))
A158819: 0 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1
(loop(\(x,i).(1 + (x2 div 2)),x,2) + (if x <= 0 then 0 else 1))
A275664: 2 4 6 14 86 3614 6526886 21300113901614 4611686018427387903 4611686018427387903
(x + (loop(\(x,i).2x,x,(x + 1)) + (if x <= 0 then 0 else 1)))
A135854: 1 6 15 36 85 198 455 1032 2313 5130 11275 24588 53261 114702 245775 524304
(~x + (loop(\(x,i).x2,2,(x + 2)) + (if x <= 0 then 0 else 1)))
A250362: 16 81 255 623 1293 2397 4091 6555 9993 14633 20727 28551 38405 50613 65523 83507
(1 + loop(\(x,i).(if x <= 0 then 3 else (x2 + ~x)),x,0))
A000289: 1 4 7 31 871 756031 571580604871 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),(x + ~1),(1 + (if (~x + 2) <= 0 then x else 0)))
A059171: 1 1 3 8 30 144 840 5760 45360 403200 3991680 43545600 518918400 6706022400 93405312000 1394852659200
(1 + loop(\(x,i).(if x <= 0 then 4 else (x2 + ~2x)),x,0))
A000324: 1 5 9 49 2209 4870849 23725150497409 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),x,(1 + loop(\(x,i).2x,(x + ~1),1)))
A052584: 2 2 6 30 216 2040 23760 327600 5201280 93260160 1861574400 40914720000 981474278400 25512104217600 714251739801600 21426244519680000
(if (~x + 2) <= 0 then (if ((x div 2) mod 3) <= 0 then 2 else 1) else 1)
A099384: 1 1 1 1 1 1 2 2 1 1 1 1 2 2 1 1
(1 + (if (x + ~2) <= 0 then x else (if (x mod 2) <= 0 then 4 else 1)))
A328317: 1 2 3 2 5 2 5 2 5 2 5 2 5 2
(if (x mod 2) <= 0 then (3 * (2 + (if x <= 0 then 0 else 2))) else 1)
A040041: 6 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1
loop(\(x,i).(x * (if (i mod 2) <= 0 then 2 else i)),(x div 3),1)
A139552: 1 1 1 1 1 1 2 2 2 6 6 6 12 12 12 60
(~1 + loop(\(x,i).(2 + (if (~x + i) <= 0 then 0 else x)),(x div 2),1))
A266539-A266529-A266509: 0 0 1 1 1 1 3 3 1 1 3 3 5 5 7 7
(if x <= 0 then 2 else (if (x + ~2) <= 0 then (2x2 + ~1) else 1))
A116891: 2 1 7 1 1 1 1 1 1 1 1 1 1 1 1 1
(1 + loop(\(x,i).((x + 1) * (if (~2 + i) <= 0 then 2 else x)),x,1))
A239900: 2 5 11 111 12211 149096311 22229709804712411 4611686018427387903
loop(\(x,i).(x * i),x,(1 + loop(\(x,i).4x,x,1)))
A052695: 2 5 34 390 6168 123000 2949840 82580400 2642451840 95127177600 3805076217600 167423233824000 8036313786547200 417888298219392000 4611686018427387903 4611686018427387903
loop(\(x,i).2x,loop(\(x,i).(2 * ((x + ~2) + i)),x,1),1)
A165623: 2 1 1 4 256 4194304 4503599627370496 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(if x <= 0 then 1 else 2x),x,(~x + 3)))
A088041: 2 3 3 3 7 15 31 63 127 255 511 1023 2047 4095 8191 16383
(1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1)))
A001576: 3 7 21 73 273 1057 4161 16513 65793 262657 1049601 4196353 16781313 67117057 268451841 1073774593
(~1 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,x,1)))
A156589: ~1 1 11 55 239 991 4031 16255 65279 261631 1047551 4192255 16773119 67100671 268419071 1073709055
(~1 + loop(\(x,i).(x2 + 2x),1,loop(\(x,i).2x,x,1)))
A130567: 2 7 23 79 287 1087 4223 16639 66047 263167 1050623 4198399 16785407 67125247 268468223 1073807359
(~1 + loop(\(x,i).(x2 + 2x),2,loop(\(x,i).2x,x,1)))
A099360: 14 79 623 6559 83519 1185919 17850623 276922879 4362470399 69257922559 1103812890623 17626570956799 281749955297279 4505799053311999 72075187834650623 1153062248537784319
(1 + (loop(\(x,i).x2,x,2) + loop(\(x,i).2x,x,1)))
A119561: 4 7 21 265 65553 4294967329 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x3,1,(1 + loop(\(x,i).2x,x,1)))
A343318: 8 27 125 729 4913 35937 274625 2146689 16974593 135005697 1076890625 8602523649 68769820673 549957165057 4398851866625 35187593412609
loop(\(x,i).3x,x,(1 + loop(\(x,i).2x,x,1)))
A074607: 2 9 45 243 1377 8019 47385 282123 1686177 10097379 60525225 362974203 2177313777 13062288339 78368947065 470199333483
(1 + (if (x mod 3) <= 0 then 0 else (if (x mod 2) <= 0 then x else 1)))
A214055: 1 2 3 1 5 2 1 2 9 1 11 2 1 2 15 1
loop(\(x,i).loop(\(x,i).(x * (1 + i)),(2 * i),x),(x + 1),1)
A169668: 6 720 3628800 1316818944000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * (2 + i)),(2 * i),x),(x + 1),1)
A169657: 12 4320 87091200 158018273280000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).4x,i,x)),(x + 1),1)
A018925: 5 85 5525 1419925
loop(\(x,i).(2x - loop(\(x,i).(x * i),i,1)),(x + ~1),1)
A106539: 1 1 1 0 ~6 ~36 ~192 ~1104 ~7248 ~54816 ~472512 ~4573824 ~49064448 ~577130496 ~7381281792 ~101940854784
(if ((if x <= 0 then 1 else x) mod 6) <= 0 then (x + ~1) else 1)
A282304: 1 1 1 1 1 1 5 1 1 1 1 1 11 1 1 1
(if ((if x <= 0 then 1 else x) mod 8) <= 0 then (x + ~1) else 1)
A336699: 1 1 1 1 1 1 1 1 7 1 1 1 1 1 1 1
loop(\(x,i).loop(\(x,i).x2,(x + ~2),2x),(x + ~1),1)
A048829: 1 1 2 4 4096
(if x <= 0 then 4 else (0 - loop(\(x,i).2x,(x + ~1),1)))
A154589: 4 ~1 ~2 ~4 ~8 ~16 ~32 ~64 ~128 ~256 ~512 ~1024 ~2048 ~4096 ~8192 ~16384
(loop(\(x,i).(x * i),x,1) - loop(\(x,i).2x,(x + ~1),1))
A059204: 0 0 0 2 16 104 688 4976 40192 362624 3628288 39915776 478999552 6227016704 87178283008 1307674351616
loop(\(x,i).(2x + loop(\(x,i).2x,i,x)),(x + ~1),1)
A126391: 1 1 4 24 240 4320 146880 9694080 1260230400 325139443200 167121673804800 171466837323724800 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (i mod 2) <= 0 then (x + ~2) else 1)),(x + ~1),1)
A228693: 1 1 2 2 3 4 5 8 9 16 17 32 33 64 65 128
loop(\(x,i).x2,1,loop(\(x,i).(x2 + x),(x + ~1),1))
A174864: 1 1 4 36 1764 3261636 10650053687364 4611686018427387903 4611686018427387903
(if x <= 0 then 0 else loop(\(x,i).(x * (i div ~2)),(x + ~1),1))
A111942: 0 1 ~1 1 ~2 4 ~12 36 ~144 576 ~2880 14400 ~86400 518400 ~3628800 25401600
loop(\(x,i).(x * (~x + loop(\(x,i).x2,i,2))),(x + ~1),1)
A076628: 1 1 3 39 8463 483008799 1841209495473815103 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).4x,i,x)),(x + ~1),1)
A309327: 1 1 5 85 5525 1419925 1455423125 5962868543125 97701601079103125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).3x,i,x)),(x + ~1),1)
A290000: 1 1 4 40 1120 91840 22408960 16358540800 35792487270400 234870301468364800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * (i * (1 + i))),i,x),(x + ~1),1)
A054909: 1 1 2 24
A059332: 1 1 2 24 3456 9953280 859963392000 3120635156889600000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).x2,2,loop(\(x,i).3x,x,1)))
A063270: 2 82 6562 531442 43046722 3486784402 282429536482 22876792454962 1853020188851842 150094635296999122 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,(1 + loop(\(x,i).3x,x,1)))
A074601: 2 8 40 224 1312 7808 46720 280064 1679872 10078208 60467200 362799104 2176786432 13060702208 78364180480 470185017344
loop(\(x,i).(x * i),x,(1 + loop(\(x,i).3x,x,1)))
A052573: 2 4 20 168 1968 29280 525600 11027520 264579840 7142929920 214280640000 7071181286400 254561568307200 9927888709939200 416971151460864000 4611686018427387903
(~x mod (1 + loop(\(x,i).loop(\(x,i).2x,x,x),x,1)))
A320505: 0 2 7 2046
(1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).(x * i),x,1)))
A066142: 3 3 7 43 601 14521 519121 25406641 1625742721 131682257281 13168193068801 1593350962156801 229442533281561601 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).(x * i),x,1)))
A261471: 1 1 3 31 553 14281 517681 25396561 1625662081 131681531521 13168185811201 1593350882323201 229442532323558401 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).(if x <= 0 then i else (x div 2)),(x + ~1),0) div 2))
A089688: 1 1 1 1 2 1 1 4 2 1 1 6 3 2 1 1
(loop(\(x,i).2x,x,1) - (if (x mod 2) <= 0 then ~2 else 1))
A280293: 3 1 6 7 18 31 66 127 258 511 1026 2047 4098 8191 16386 32767
(if (x mod 12) <= 0 then (if x <= 0 then 0 else 2) else 1)
A049704: 0 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1
(if (x mod 10) <= 0 then (if x <= 0 then 0 else 2) else 1)
A303837-A193582-A095827-A085021: 0 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1
(if (x mod 4) <= 0 then (if (x mod 3) <= 0 then 1 else 2) else 1)
A244226: 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1
(if (~2 + (x div 2)) <= 0 then (if (x mod 3) <= 0 then 1 else 2) else 1)
A100244: 1 2 2 1 2 2 1 1 1 1 1 1 1 1 1 1
(1 + (loop(\(x,i).(if x <= 0 then i else (x div 2)),(x + ~1),1) div 2))
A104762: 1 1 1 2 1 1 3 2 1 1 5 3 2 1 1 8
(if ((if x <= 0 then 1 else x) mod 12) <= 0 then 2 else 1)
A333737-A333733-A333159-A332770-A322494-A306741-A296554-A284582-A284558-A273975-A257463-A257462-A245013-A242784-A238384-A227690-A226444-A224697-A220122-A219924-A212177-A204162-A196929-A196017-A189006-A171398-A155050-A143654-A140356-A139549-A139147-A139040-A139038-A133687-A129192-A119963-A119326-A109035-A108465-A067059-A057790-A052307-A047996-A043286-A008327: 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1
(1 + (2 * loop(\(x,i).loop(\(x,i).(x2 + ~1),x,2),x,1)))
A005844: 3 7 127 4611686018427387903
(1 + (2 * loop(\(x,i).loop(\(x,i).(2 + (x * i)),x,2),x,1)))
A318970: 3 9 261 4611686018427387903
(if (x mod 2) <= 0 then (5 * (if x <= 0 then 1 else 2)) else 1)
A040029: 5 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1
(if (x mod 2) <= 0 then (8 * (if x <= 0 then 1 else 2)) else 1)
A040071: 8 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1
(if (x mod (4 + (x div 2))) <= 0 then (if x <= 0 then 1 else 2) else 1)
A204014: 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1
(if ((x div ~2) mod 4) <= 0 then (if x <= 0 then 1 else 2) else 1)
A329040: 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 2
(if ((x + (x div 2)) mod 4) <= 0 then (if x <= 0 then 1 else 2) else 1)
A294932: 1 1 1 2 1 1 1 1 2 1 1 2 1 1 1 1
(~1 + loop(\(x,i).(2x + i),(x + ~2),(if x <= 0 then 1 else 2)))
A130103: 0 1 1 4 11 26 57 120 247 502 1013 2036 4083 8178 16369 32752
((2 + (if (x + ~1) <= 0 then x else 0)) * (1 + (if x <= 0 then 1 else 2)))
A168608: 4 9 6 6 6 6 6 6 6 6 6 6 6 6 6 6
(x - (if (x mod 4) <= 0 then (2 * (if x <= 0 then 0 else 2)) else 1))
A276331: 0 0 1 2 0 4 5 6 4 8 9 10 8 12 13 14
loop(\(x,i).x2,(x + ~2),(1 + (2 * (if x <= 0 then 0 else 2))))
A165423: 1 5 5 25 625 390625 152587890625 4611686018427387903 4611686018427387903
loop(\(x,i).i,((x - (if (x mod 3) <= 0 then 1 else 2)) div 2),1)
A029111: 1 1 1 1 1 1 2 2 3 4 4 4 5 5 6 7
loop(\(x,i).4x,x,(3 + (if x <= 0 then 1 else 2)))
A292540: 4 20 80 320 1280 5120 20480 81920 327680 1310720 5242880 20971520 83886080 335544320 1342177280 5368709120
(if x <= 0 then 0 else (if (x2 mod (x + 4)) <= 0 then 2 else 1))
A257679: 0 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1
(if (x mod 8) <= 0 then (if x <= 0 then 1 else 4) else 1)
A336649: 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1
loop(\(x,i).2x,(x div 2),(if (x mod 2) <= 0 then 4 else 1))
A112032: 4 1 8 2 16 4 32 8 64 16 128 32 256 64 512 128
(if x <= 0 then 1 else (5 * loop(\(x,i).(x * i),x,2)))
A174183: 1 10 20 60 240 1200 7200 50400 403200 3628800 36288000 399168000 4790016000 62270208000 871782912000 13076743680000
loop(\(x,i).x2,1,loop(\(x,i).2x,x,5))
A309779: 25 100 400 1600 6400 25600 102400 409600 1638400 6553600 26214400 104857600 419430400 1677721600 6710886400 26843545600
(if (x mod 4) <= 0 then (if x <= 0 then 1 else (x div 4)) else 1)
A260534-A178239: 1 1 1 1 1 1 1 1 2 1 1 1 3 1 1 1
loop(\(x,i).x2,1,(~1 + loop(\(x,i).x2,x,4)))
A330830: 9 225 65025 4294836225 4611686018427387903
(if (x mod 4) <= 0 then 0 else (if (~x + 4) <= 0 then 2 else 1))
A215883: 0 1 1 1 0 2 2 2 0 2 2 2 0 2 2 2
(1 + loop(\(x,i).2x,x,(2 + loop(\(x,i).2x,x,2))))
A085601: 5 13 41 145 545 2113 8321 33025 131585 525313 2099201 8392705 33562625 134234113 536903681 2147549185
(~1 + loop(\(x,i).2x,x,(2 + loop(\(x,i).2x,x,2))))
A281482: 3 11 39 143 543 2111 8319 33023 131583 525311 2099199 8392703 33562623 134234111 536903679 2147549183
loop(\(x,i).2x,x,(~1 + loop(\(x,i).2x,(x + 2),2)))
A171472: 7 30 124 504 2032 8160 32704 130944 524032 2096640 8387584 33552384 134213632 536862720 2147467264 8589901824
(~1 + loop(\(x,i).2x2,(if x <= 0 then 1 else 2x),2))
A277634-A077586: 7 127 2147483647 4611686018427387903
loop(\(x,i).(x * i),x,(~1 + loop(\(x,i).2x,(x div 2),2)))
A052634: 1 1 6 18 168 840 10800 75600 1249920 11249280 228614400 2514758400 60833203200 790831641600 22230464256000 333456963840000
(1 + loop(\(x,i).2x,x,(2 * loop(\(x,i).x2,x,2))))
A076448: 5 17 129 4097 2097153 274877906945 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (3 * (1 + (if (~x + 2) <= 0 then 2 else 1))))
A100403: 1 6 9 9 9 9 9 9 9 9 9 9 9 9 9 9
(3 * (if (x mod 2) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1))
A040033: 6 3 12 3 12 3 12 3 12 3 12 3 12 3 12 3
(loop(\(x,i).(if (~x + i) <= 0 then 1 else (x + 2)),x,1) mod 3)
A065252: 1 1 0 1 0 2 1 1 0 2 1 0 2 1 0 1
loop(\(x,i).(x * i),x,(3 * (if (x + ~2) <= 0 then x else 1)))
A052637: 0 3 12 18 72 360 2160 15120 120960 1088640 10886400 119750400 1437004800 18681062400 261534873600 3923023104000
(loop(\(x,i).(~1 + (if x <= 0 then i else x)),x2,1) mod 3)
A123635: 1 0 0 0 0 0 0 2 0 1 0 0 0 2 2 0
(loop(\(x,i).2x,x,1) - loop(\(x,i).x2,2,3))
A220088: ~80 ~79 ~77 ~73 ~65 ~49 ~17 47 175 431 943 1967 4015 8111 16303 32687
(if x <= 0 then 2 else (3 * (if (~x + 2) <= 0 then x2 else 2)))
A289443: 2 6 12 27 48 75 108 147 192 243 300 363 432 507 588 675
((if x <= 0 then 1 else (x * (if (x mod 2) <= 0 then x else 1))) mod 3)
A204688: 1 1 1 0 1 2 0 1 1 0 1 2 0 1 1 0
(if x <= 0 then 1 else (3 * loop(\(x,i).2x,(x + ~1),x)))
A167667: 1 3 12 36 96 240 576 1344 3072 6912 15360 33792 73728 159744 344064 737280
(if x <= 0 then 1 else loop(\(x,i).(2 * (x + (x div 2))),x,3))
A083583: 1 8 24 72 216 648 1944 5832 17496 52488 157464 472392 1417176 4251528 12754584 38263752
loop(\(x,i).x3,1,loop(\(x,i).2x,x,3))
A272342: 27 216 1728 13824 110592 884736 7077888 56623104 452984832 3623878656 28991029248 231928233984 1855425871872 14843406974976 118747255799808 949978046398464
(if x <= 0 then 2 else (if (x + ~3) <= 0 then x else (x + ~3)))
A329794: 2 1 2 3 1 2 3 4 5 6 7 8 9 10 11 12
loop(\(x,i).(~x + loop(\(x,i).2x,(~1 + i),1)),x,3)
A154879: 3 ~2 4 0 8 8 24 40 88 168 344 680 1368 2728 5464 10920
loop(\(x,i).x2,2,loop(\(x,i).3x,x,3))
A089683: 81 6561 531441 43046721 3486784401 282429536481 22876792454961 1853020188851841 150094635296999121 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).x2,i,3)),x,3)
A115245: 3 12 93 6654 43053375 1853020231905216 4611686018427387903 4611686018427387903
loop(\(x,i).x2,(x div 2),(if (~x + 2) <= 0 then x else 3))
A175796: 3 3 4 9 256
loop(\(x,i).x2,1,(3 * loop(\(x,i).(x * i),x,x)))
A069134: 0 9 144 2916 82944 3240000 167961600 11202105600 936404582400 95996101017600 11851370496000000 1735159154319360000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if (if (x mod 8) <= 0 then x else 0) <= 0 then x else 2))
A327535-A327389-A282779: 1 2 3 4 5 6 7 8 3 10 11 12 13 14 15 16
loop(\(x,i).3x,x,(1 + (if (x + ~1) <= 0 then x else 2)))
A027313: 1 6 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721
loop(\(x,i).2x,x,(1 + loop(\(x,i).(2x + 4),x,2)))
A103897: 3 18 84 360 1488 6048 24384 97920 392448 1571328 6288384 25159680 100651008 402628608 1610563584 6442352640
loop(\(x,i).2x,x,(~1 + loop(\(x,i).4x,x,2)))
A147590: 1 14 124 1016 8176 65504 524224 4194176 33554176 268434944 2147482624 17179867136 137438949376 1099511619584 8796093005824 70368744144896
loop(\(x,i).(x * i),x,(~1 + loop(\(x,i).4x,x,2)))
A167550: 1 7 62 762 12264 245640 5897520 165145680 5284782720 190253266560 7610141548800 334846347897600 16072626136089600 835776577757721600 4611686018427387903 4611686018427387903
(loop(\(x,i).(x * (2 + i)),x,1) div (if (~x + 2) <= 0 then 2 else 1))
A133799: 1 3 6 30 180 1260 10080 90720 907200 9979200 119750400 1556755200 21794572800 326918592000 5230697472000 88921857024000
(~1 + loop(\(x,i).4x,x,loop(\(x,i).i,(~x + 2),2)))
A267941: 1 3 31 127 511 2047 8191 32767 131071 524287 2097151 8388607 33554431 134217727 536870911 2147483647
(1 + loop(\(x,i).(2 * (x + (if (i mod 2) <= 0 then 2 else 0))),x,2))
A159290: 3 5 13 25 53 105 213 425 853 1705 3413 6825 13653 27305 54613 109225
(~1 + loop(\(x,i).(2 * (x + (if (i mod 2) <= 0 then 2 else 0))),x,2))
A173078: 1 3 11 23 51 103 211 423 851 1703 3411 6823 13651 27303 54611 109223
loop(\(x,i).x2,1,(~1 + loop(\(x,i).~2x,x,2)))
A216869: 1 25 49
A171590: 1 25 49 289 961 4225 16129 66049 261121 1050625 4190209 16785409 67092481 268468225 1073676289 4295098369
loop(\(x,i).~x,x,(1 + loop(\(x,i).(~2x + 4),x,2)))
A171382: 3 ~1 5 3 13 19 45 83 173 339 685 1363 2733 5459 10925 21843
(~1 + loop(\(x,i).(2x + (if (~2 + i) <= 0 then 2 else 1)),x,2))
A060182: 1 5 13 28 58 118 238 478 958 1918 3838 7678 15358 30718 61438 122878
(~1 + loop(\(x,i).(x2 + 2x),1,loop(\(x,i).2x,x,2)))
A093069: 7 23 79 287 1087 4223 16639 66047 263167 1050623 4198399 16785407 67125247 268468223 1073807359 4295098367
(~1 + loop(\(x,i).(x2 + ~2x),1,loop(\(x,i).2x,x,2)))
A093112: ~1 7 47 223 959 3967 16127 65023 261119 1046527 4190207 16769023 67092479 268402687 1073676287 4294836223
loop(\(x,i).(x2 + 2),1,(~1 + loop(\(x,i).2x,x,2)))
A191341: 3 11 51 227 963 3971 16131 65027 261123 1046531 4190211 16769027 67092483 268402691 1073676291 4294836227
loop(\(x,i).x3,1,(~1 + loop(\(x,i).2x,x,2)))
A128831: 1 27 343 3375 29791 250047 2048383 16581375 133432831 1070599167 8577357823 68669157375 549554511871 4397241253887 35181150961663 281462092005375
loop(\(x,i).3x,x,(~1 + loop(\(x,i).2x,x,2)))
A016137: 1 9 63 405 2511 15309 92583 557685 3352671 20135709 120873303 725416965 4353033231 26119793709 156723545223 940355620245
loop(\(x,i).2x,x2,(~1 + loop(\(x,i).2x,x,2)))
A088668: 1 6 112 7680 2031616 2113929216 8727373545472 143552238122434560 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (i * i)),x,(~1 + loop(\(x,i).2x,x,2)))
A174121: 1 4 12 29 61 118 218 395 715 1308 2432 4601 8841 17202 33782 66775
loop(\(x,i).(x - (i * i)),x,(~1 + loop(\(x,i).2x,x,2)))
A174120: 1 2 2 1 1 8 36 115 307 738 1662 3589 7541 15564 31752 64295
(if (x mod 8) <= 0 then (if x <= 0 then 1 else (x + 2)) else 1)
A284100: 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1
loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),x,(x + 3))
A309391: 3 1 5 1 7 1 1 1 11 1 13 1 1 1 17 1
loop(\(x,i).(x * i),x,(~1 + (if (x + ~2) <= 0 then 1 else (x + ~2))))
A052520: 0 0 0 0 24 240 2160 20160 201600 2177280 25401600 319334400 4311014400 62270208000 958961203200 15692092416000
(if (x + ~2) <= 0 then x else loop(\(x,i).(2x + 4),(x + ~2),1))
A270810: 0 1 2 6 16 36 76 156 316 636 1276 2556 5116 10236 20476 40956
loop(\(x,i).(if ((x + 1) mod 3) <= 0 then i else 2),(x + ~2),1)
A275382: 1 1 1 2 2 3 2 5 6
loop(\(x,i).x2,1,loop(\(x,i).2x,x,(2x + 1)))
A164583: 1 36 400 3136 20736 123904 692224 3686400 18939904 94633984 462422016 2218786816 10485760000 48922361856 225754218496 1031865892864
loop(\(x,i).(x * (if (~1 + i) <= 0 then x else i)),x,(2x + 1))
A007681: 1 9 50 294 1944 14520 121680 1134000 11652480 130999680 1600300800 21115987200 299376000000 4539498163200 73316942899200 1256675067648000
(1 + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,2x))
A057036: 1 2 2 1 3 1 3 5 2 4 6 2 4 6 1 3
loop(\(x,i).(x div 2),x,loop(\(x,i).3x,2x,1))
A094971: 1 4 20 91 410 1845 8303 37366 168151 756680 3405062 15322783 68952523 310286355 1396288601 6283298708
loop(\(x,i).(x * (2 + (if (~2 + i) <= 0 then x else 2))),2x,1)
A090411: 1 15 240 3840 61440 983040 15728640 251658240 4026531840 64424509440 1030792151040 16492674416640 263882790666240 4222124650659840 67553994410557440 1080863910568919040
loop(\(x,i).loop(\(x,i).(x * (1 + (2 * i))),i,x),2x,1)
A089626: 1 45 4465125 6272287562165625 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((if (i mod 2) <= 0 then 2 else i) + i)),2x,1)
A065141: 1 8 288 23040 3225600 696729600 214592716800 89270570188800 48206107901952000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 2),x,loop(\(x,i).(x * (i * i)),2x,1))
A264153: 1 2 144 64800 101606400 411505920000 3585039575040000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (if (~x + i) <= 0 then 0 else i))),(x div 2),1)
A286865: 1 1 1 1 3 3 3 3 15 15 15 15 15 15 15 15
loop(\(x,i).(x * (if (i mod 2) <= 0 then ~2 else 2)),(x div 2),1)
A320770: 1 1 2 2 ~4 ~4 ~8 ~8 16 16 32 32 ~64 ~64 ~128 ~128
(1 + loop(\(x,i).(if (~x + 2) <= 0 then x2 else 2),x,(x div 2)))
A007516: 1 3 5 17 65537
loop(\(x,i).(~2 + loop(\(x,i).x2,2,4)),(x mod 2),1)
A110827: 1 254 1
(1 + loop(\(x,i).x2,x,((if x <= 0 then 1 else x) + (x mod 2))))
A258429: 2 5 17 65537
(1 - loop(\(x,i).(2 * (x - (i mod 2))),x,(if x <= 0 then 2 else 1)))
A167167: ~1 1 1 3 5 11 21 43 85 171 341 683 1365 2731 5461 10923
(1 + (2 * loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)))
A158405: 1 1 3 1 3 5 1 3 5 7 1 3 5 7 9 1
loop(\(x,i).x2,1,(1 + loop(\(x,i).3x,x,2)))
A169724: 9 49 361 3025 26569 237169 2128681 19140625 172213129 1549760689 13947373801 125524947025 1129720271689 10167469690609 91507188951721 823564585774225
loop(\(x,i).2x,x,(~1 + loop(\(x,i).3x,x,2)))
A081656: 1 10 68 424 2576 15520 93248 559744 3358976 20154880 120931328 725592064 4353560576 26121379840 156728311808 940369936384
(~1 + loop(\(x,i).(x + (if (2 - (i div 2)) <= 0 then x else 2)),x,2))
A334084: 1 3 5 7 15 31 63 127 255 511 1023
(1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).x2,x,2)))
A220161: 7 21 273 65793 4295032833 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).x2,x,2)))
A220294: 3 13 241 65281 4294901761 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (x div 2)),1,(1 + loop(\(x,i).x2,x,2)))
A191363: 3 10 136 32896 2147516416
loop(\(x,i).(x * i),x,(~1 + loop(\(x,i).(2x + i),x,2)))
A052650: 1 4 22 156 1368 14400 177840 2530080 40844160 738823680 14816390400 326439590400 7840777190400 203947385241600 5711834461132800 171375956623872000
(if (if (x mod 12) <= 0 then x else 0) <= 0 then x else 1)
A103303: 0 1 2 3 4 5 6 7 8 9
A345672: 0 1 2 3 4 5 6 7 8 9 10 11 1 13 14 15
((x + 1) + loop(\(x,i).(if x <= 0 then (2 * i) else (x + ~1)),x,0))
A179526: 1 4 4 4 13 13 13 13 13 13 13 13 13 40 40 40
loop(\(x,i).(x + i - (if (x - (2 * i)) <= 0 then 0 else 1)),x,1)
A077169: 1 2 4 7 11 15 20 26 33 41 50 60 71 83 96 110
(if (x mod 2) <= 0 then (2 mod (if (x mod 3) <= 0 then 1 else x)) else 1)
A038698: 0 1 0 1 2 1 0 1 2 1 2 1 0 1 2 1
loop(\(x,i).loop(\(x,i).2x,(i div (2x + 1)),1),x,1)
A113793: 1 1 1 2 1 2 2 2 2 2 4 2 4 2 4 2
loop(\(x,i).((x * i) - loop(\(x,i).(x * i),(~1 + i),1)),x,1)
A081047: 1 0 ~1 ~5 ~26 ~154 ~1044 ~8028 ~69264 ~663696 ~6999840 ~80627040 ~1007441280 ~13575738240 ~196287356160 ~3031488633600
loop(\(x,i).(if (~x + i) <= 0 then 10 else 1),x,1)
A269352: 1 10 10 10 10 10 10 10 10 10 10 1 1 1 1 1
loop(\(x,i).2x,x,loop(\(x,i).(4x + 1),x,1))
A016131: 1 10 84 680 5456 43680 349504 2796160 22369536 178956800 1431655424 11453245440 91625967616 733007749120 5864062009344 46912496107520
loop(\(x,i).(x * i),x,loop(\(x,i).(4x + 1),x,1))
A052654: 1 5 42 510 8184 163800 3931920 110098800 3523201920 126835632000 5073428908800 223230911904000 10715084250393600 557184387247488000 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,loop(\(x,i).(4x + ~1),x,1))
A082412: 1 6 44 344 2736 21856 174784 1398144 11184896 89478656 715828224 5726623744 45812985856 366503878656 2932031012864 23456248070144
loop(\(x,i).(3 * (~x + loop(\(x,i).2x,i,1))),x,1)
A165405: 1 3 3 15 3 87 ~69 591 ~1005 4551 ~10581 37887 ~101373 328695 ~936933 2909103
loop(\(x,i).~x,x,loop(\(x,i).((~2x + 1) + i),x,1))
A053088: 1 0 3 2 9 12 31 54 117 224 459 906 1825 3636 7287 14558
loop(\(x,i).(~x + 2),x,loop(\(x,i).((~2x + 1) + i),x,1))
A133993: 1 2 3 4 9 14 31 56 117 226 459 908 1825 3638 7287 14560
loop(\(x,i).2x,x,loop(\(x,i).(1 + (2x * i)),x,1))
A097820: 1 6 52 632 10128 202592 4862272 136143744 4356600064 156837602816 6273504113664 276034181003264 13249640688160768 688981315784368128 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (x * loop(\(x,i).x2,2,3))),x,1)
A239670: 1 82 6643 538084 43584805 3530369206 285959905687 23162752360648 1876182941212489 151970818238211610 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,loop(\(x,i).(3x + 1),x,1))
A016129: 1 8 52 320 1936 11648 69952 419840 2519296 15116288 90698752 544194560 3265171456 19591036928 117546237952 705277460480
loop(\(x,i).(x * i),x,loop(\(x,i).(3x + 1),x,1))
A052577: 1 4 26 240 2904 43680 786960 16531200 396789120 10713669120 321413702400 10606692096000 381841394457600 14891820610867200 625456552834713600 4611686018427387903
loop(\(x,i).x2,1,loop(\(x,i).(3x + ~1),x,1))
A051500: 1 4 25 196 1681 14884 133225 1196836 10764961 96864964 871725625 7845353476 70607649841 635467254244 5719200505225 51472790198116
loop(\(x,i).2x,x,loop(\(x,i).(3x + ~1),x,1))
A081335: 1 4 20 112 656 3904 23360 140032 839936 5039104 30233600 181399552 1088393216 6530351104 39182090240 235092508672
loop(\(x,i).(1 + loop(\(x,i).4x,(1 + i),x)),x,1)
A130449: 1 17 1089 278785 285475841 1169309044737 19157959388971009 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + loop(\(x,i).3x,(~1 + i),x)),x,1)
A117263: 1 2 7 64 1729 140050 34032151 24809438080 54258241080961 355988319732185122 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (x * loop(\(x,i).x2,(~1 + i),2))),x,1)
A318165: 1 3 13
A085010: 1 3 13 209 53505 3506503681 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + loop(\(x,i).(x * (1 + i)),4,x)),x,1)
A178512: 1 121 14521 1742521 209102521 25092302521 3011076302521 361329156302521 43359498756302521 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (x * loop(\(x,i).(x2 + 2x),2,2))),x,1)
A178513: 1 81 6481 518481 41478481 3318278481 265462278481 21236982278481 1698958582278481 135916686582278481 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + loop(\(x,i).3x,(2 + i),x)),x,1)
A178187: 1 28 2269 551368 401947273 879058686052 5767504039187173 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 2),x,loop(\(x,i).(2x2 + 2x),x,1))
A059723: 1 2 10 410 1345210 28953440450810 4611686018427387903 4611686018427387903
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else ((~x + 1) + i)),x,1)
A345877: 1 1 2 1 4 2 1 7 2 1 10 5 8 4 2 1
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else ((x + 1) + i)),x,1)
A090895: 1 3 6 3 8 4 2 1 10 5 16 8 4 2 1 17
loop(\(x,i).4x,x,loop(\(x,i).(1 + (x * i)),x,1))
A097815: 1 8 80 1024 16640 333824 8015872 224460800 7182811136 258581463040 10343259570176 455103425282048 21844964430315520 1135938150443515904 4611686018427387903 4611686018427387903
loop(\(x,i).3x,x,loop(\(x,i).(1 + (x * i)),x,1))
A097814: 1 6 45 432 5265 79218 1426653 29961900 719092161 19415508030 582465299949 19221355075464 691968783248145 26986782548271978 1133444867032206045 4611686018427387903
loop(\(x,i).((~2x + 1) - (if (~2 + i) <= 0 then i else 1)),x,1)
A110164: 1 ~2 3 ~6 12 ~24 48 ~96 192 ~384 768 ~1536 3072 ~6144 12288 ~24576
loop(\(x,i).(1 + ((if (x mod (1 + i)) <= 0 then 0 else x) + i)),x,1)
A343752: 1 3 3 7 12 6 13 21 30 10 21 33 46 60 15 31
loop(\(x,i).((if (x mod 4) <= 0 then x else i) * (1 + i)),x,1)
A160274-A072938: 1 2 6 12 60 360 2520
loop(\(x,i).~x,x,loop(\(x,i).((x + 1) - (i * i)),x,1))
A167386: 1 ~1 ~2 10 ~25 49 ~84 132 ~195 275 ~374 494 ~637 805 ~1000 1224
loop(\(x,i).(2x + ~1),x,loop(\(x,i).(2x + 2),x,1))
A169726: 1 7 37 169 721 2977 12097 48769 195841 784897 3142657 12576769 50319361 201302017 805257217 3221127169
loop(\(x,i).3x,x,loop(\(x,i).(2x + 2),x,1))
A093801: 1 12 90 594 3726 22842 138510 835434 5025726 30193722 181280430 1088036874 6529284126 39178893402 235082926350 1410526255914
loop(\(x,i).(2 * (x - (if (i mod 2) <= 0 then 2 else ~2))),x,1)
A083595: 1 6 8 20 36 76 148 300 596 1196 2388 4780 9556 19116 38228 76460
(1 + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),4,x))
A222417-A194896: 1 1 2 1 2 3 1 2 3 4 1 2 3 4 5 6
loop(\(x,i).2x,x,loop(\(x,i).(~4x + 4),x,1))
A083295: 1 0 16 ~96 832 ~6528 52480 ~419328 3355648 ~26843136 214749184 ~1717985280 13743898624 ~109951156224 879609315328 ~7036874391552
loop(\(x,i).(2 * (if (~1 + (i mod 3)) <= 0 then x else 2)),x,1)
A222011: 1 2 4 8
A167426: 1 2 4 8 16 4 8 16 4 8 16 4 8 16 4 8
(loop(\(x,i).(x * i),x,1) mod loop(\(x,i).4x,x,1))
A212310: 0 1 2 6 24 120 720 5040 40320 100736 483072 2168064 9239552 53005312 205203456 930568192
loop(\(x,i).(x div 3),x,loop(\(x,i).4x,x,1))
A064628: 1 1 1 2 3 4 5 7 9 13 17 23 31 42 56 74
loop(\(x,i).(2x + 1),x,loop(\(x,i).4x,x,1))
A155592: 1 9 67 519 4111 32799 262207 2097279 16777471 134218239 1073742847 8589936639 68719480831 549755822079 4398046527487 35184372121599
loop(\(x,i).(2x + ~1),x,loop(\(x,i).4x,x,1))
A155599: 1 7 61 505 4081 32737 262081 2097025 16776961 134217217 1073740801 8589932545 68719472641 549755805697 4398046494721 35184372056065
loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,1)
A002457: 1 6 30 140 630 2772 12012 51480 218790 923780 3879876 16224936 67603900 280816200 1163381400 4808643120
loop(\(x,i).(2 * (x + (if (i mod 2) <= 0 then 2x else 0))),x,1)
A176710: 1 2 12 24 144 288 1728 3456 20736 41472 248832 497664 2985984 5971968 35831808 71663616
loop(\(x,i).(x2 + ~x),1,loop(\(x,i).~2x,x,1))
A071930: 0 6 12 72 240 1056 4032 16512 65280 262656 1047552 4196352 16773120 67117056 268419072 1073774592
loop(\(x,i).(~2x + 1),x,loop(\(x,i).(~2x + 2),x,1))
A245489: 1 1 7 19 91 331 1387 5419 21931 87211 349867 1397419 5593771 22366891 89483947 357903019
loop(\(x,i).~x,x,loop(\(x,i).(3x + ~4),x,1))
A168589: 1 1 ~7 25 ~79 241 ~727 2185 ~6559 19681 ~59047 177145 ~531439 1594321 ~4782967 14348905
loop(\(x,i).x2,1,loop(\(x,i).(2 * (x + (x div 2))),x,1))
A270473: 1 4 36 324 2916 26244 236196 2125764 19131876 172186884 1549681956 13947137604 125524238436 1129718145924 10167463313316 91507169819844
((2 * (2 + (if x <= 0 then 0 else 2))) - (if (x + ~2) <= 0 then x else 1))
A292510: 4 7 6 7 7 7 7 7 7 7 7 7 7 7 7 7
loop(\(x,i).(2x + (if (i mod 4) <= 0 then 1 else 0)),x,1)
A222011: 1 2 4 8
A018299: 1 2 4 8 17 34 68 136
A083593: 1 2 4 8 17 34 68 136 273 546 1092 2184 4369 8738 17476 34952
loop(\(x,i).(x * (x div 2)),1,loop(\(x,i).(~2x + 1),x,1))
A084175: 0 1 3 15 55 231 903 3655 14535 58311 232903 932295 3727815 14913991 59650503 238612935
loop(\(x,i).(x * (0 - i)),x,loop(\(x,i).(~2x + 1),x,1))
A052585: 1 1 6 30 264 2520 30960 428400 6894720 123742080 2478470400 54486432000 1308153369600 34005760588800 952248474777600 28566146568960000
loop(\(x,i).loop(\(x,i).3x,(~1 + i),2x),x,1)
A083667: 1 2 12 216 11664 1889568 918330048 1338925209984 5856458868470016 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,((x + ~2) - i),2x),x,1)
A222011: 1 2 4 8
A071071: 1 2 4 8 65536
((if (x mod 3) <= 0 then 1 else 0) + loop(\(x,i).2x,x,1))
A052935: 2 2 4 9 16 32 65 128 256 513 1024 2048 4097 8192 16384 32769
((if (x + ~2) <= 0 then (x div 2) else 0) + loop(\(x,i).2x,x,1))
A240951: 1 2 5 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768
loop(\(x,i).(x3 + x2),1,loop(\(x,i).2x,x,1))
A063481: 2 12 80 576 4352 33792 266240 2113536 16842752 134479872 1074790400 8594128896 68736253952 549822922752 4398314946560 35185445830656
loop(\(x,i).(x3 + ~x2),1,loop(\(x,i).2x,x,1))
A059409: 0 4 48 448 3840 31744 258048 2080768 16711680 133955584 1072693248 8585740288 68702699520 549688705024 4397778075648 35183298347008
loop(\(x,i).(x2 + x + 2),1,loop(\(x,i).2x,x,1))
A170938: 4 8 22 74 274 1058 4162 16514 65794 262658 1049602 4196354 16781314 67117058 268451842 1073774594
loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).2x,x,1))
A188545: 1 3 10
A007582: 1 3 10 36 136 528 2080 8256 32896 131328 524800 2098176 8390656 33558528 134225920 536887296
loop(\(x,i).(x2 + ~x + 2),1,loop(\(x,i).2x,x,1))
A170939: 2 4 14 58 242 994 4034 16258 65282 261634 1047554 4192258 16773122 67100674 268419074 1073709058
((if (x + ~1) <= 0 then 2x else 1) + loop(\(x,i).2x,x,1))
A143096: 1 4 5 9 17 33 65 129 257 513 1025 2049 4097 8193 16385 32769
loop(\(x,i).(x2 - (x div 2)),1,loop(\(x,i).2x,x,1))
A131262: 1 3 14 60 248 1008
loop(\(x,i).(x3 + x),1,loop(\(x,i).2x,x,1))
A074603: 2 10 68 520 4112 32800 262208 2097280 16777472 134218240 1073742848 8589936640 68719480832 549755822080 4398046527488 35184372121600
loop(\(x,i).(x3 + ~x),1,loop(\(x,i).2x,x,1))
A248217: 0 6 60 504 4080 32736 262080 2097024 16776960 134217216 1073740800 8589932544 68719472640 549755805696 4398046494720 35184372056064
(loop(\(x,i).(1 + (x * i)),x,1) + loop(\(x,i).2x,x,1))
A097656: 2 4 9 24 81 358 2021 13828 109857 986922 9865125 108507160 1302065441 16926805678 236975181189 3554627504844
(loop(\(x,i).(1 + (x * i)),x,1) - loop(\(x,i).2x,x,1))
A097204: 0 0 1 8 49 294 1893 13572 109345 985898 9863077 108503064 1302057249 16926789294 236975148421 3554627439308
loop(\(x,i).(x3 + 2x),1,loop(\(x,i).2x,x,1))
A020530: 3 12 72 528 4128 32832 262272 2097408 16777728 134218752 1073743872 8589938688 68719484928 549755830272 4398046543872 35184372154368
loop(\(x,i).(2x + ~1),(x + ~1),loop(\(x,i).2x,x,1))
A134169: 1 2 7 29 121 497 2017 8129 32641 130817 523777 2096129 8386561 33550337 134209537 536854529
(loop(\(x,i).3x,x,1) + loop(\(x,i).2x,x,1))
A007689: 2 5 13 35 97 275 793 2315 6817 20195 60073 179195 535537 1602515 4799353 14381675
(loop(\(x,i).3x,x,1) - loop(\(x,i).2x,x,1))
A001047: 0 1 5 19 65 211 665 2059 6305 19171 58025 175099 527345 1586131 4766585 14316139
(loop(\(x,i).3x,x,1) mod loop(\(x,i).2x,x,1))
A002380: 0 1 1 3 1 19 25 11 161 227 681 1019 3057 5075 15225 29291
loop(\(x,i).(2x2 + ~1),2,loop(\(x,i).2x,x,1))
A020538: 1 97 1921 32257 522241 8380417 134184961 2147352577 34359214081 549753716737 8796084633601 140737454800897 2251799679467521 36028796482093057 576460750155939841 4611686018427387903
(loop(\(x,i).(x * i),(x + 2),2) + loop(\(x,i).2x,x,1))
A133751: 5 14 52 248 1456 10112 80704 725888 7257856 79834112 958004224 12454043648 174356586496 2615348744192 41845579792384 711374856224768
loop(\(x,i).(2x + 1),2x,loop(\(x,i).2x,x,1))
A155619: 1 11 79 575 4351 33791 266239 2113535 16842751 134479871 1074790399 8594128895 68736253951 549822922751 4398314946559 35185445830655
loop(\(x,i).(2x + ~1),2x,loop(\(x,i).2x,x,1))
A155629: 1 5 49 449 3841 31745 258049 2080769 16711681 133955585 1072693249 8585740289 68702699521 549688705025 4397778075649 35183298347009
(loop(\(x,i).3x,x,2) - loop(\(x,i).2x,x,1))
A027649: 1 4 14 46 146 454 1394 4246 12866 38854 117074 352246 1058786 3180454 9549554 28665046
loop(\(x,i).(3x + 2),x,loop(\(x,i).2x,x,1))
A155604: 1 8 44 242 1376 8018 47384 282122 1686176 10097378 60525224 362974202 2177313776 13062288338 78368947064 470199333482
loop(\(x,i).(3x + ~2),x,loop(\(x,i).2x,x,1))
A155611: 1 4 28 190 1216 7534 45928 277750 1673056 10058014 60407128 362619910 2176250896 13059099694 78359381128 470170635670
(loop(\(x,i).3x,x,x) + loop(\(x,i).2x,x,1))
A086090: 1 5 22 89 340 1247 4438 15437 52744 177659 591514 1950665 6381388 20734391 66977950 215266373
(~2 mod loop(\(x,i).(x - i),x,loop(\(x,i).2x,x,1)))
A342352: 0 0 0 0 4 15 41 98 218 465 967 1980 4016 8099 16277 32646
loop(\(x,i).(2x + (if (i mod 3) <= 0 then 1 else x)),x,1)
A018316: 1 3 9 19 57 171
loop(\(x,i).(2x * (if (x + ~4) <= 0 then 1 else x)),x,1)
A222011: 1 2 4 8
A130693: 1 2 4 8 128
loop(\(x,i).(2x + loop(\(x,i).2x,(~1 + i),x)),x,1)
A139486: 1 3 12 72 720 12960 440640 29082240 3780691200 975418329600 501365021414400 514400511971174400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x + loop(\(x,i).2x,i,2)),x,1)
A102485: 1 7 29 103 341 1087 3389 10423 31781 96367 291149 877543 2640821 7938847 23849309 71613463
loop(\(x,i).loop(\(x,i).~3x,i,2x),x,1)
A127946: 1 ~6 ~108 5832 944784 ~459165024 ~669462604992 2928229434235008 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).~x,x,loop(\(x,i).((~2x + 1) - i),x,1))
A131959: 1 2 3 8
A103196: 1 2 3 8 13 30 55 116 225 458 907 1824 3637 7286 14559 29132
loop(\(x,i).loop(\(x,i).8x,i,2x),x,1)
A121366: 1 16 2048 2097152 17179869184 1125899906842624 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).5x,i,2x),x,1)
A127947: 1 10 500 125000 156250000 976562500000 30517578125000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * (~1 - i)),i,2x),x,1)
A112693: 1 ~4 ~48 2304 552960 ~796262400 ~8026324992000 647242847354880000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(0 - loop(\(x,i).(x * (0 - i)),i,2x)),x,1)
A156926: 1 2 ~8 ~96 4608 1105920 ~1592524800 ~16052649984000 1294485694709760000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).2x,x,1) div 2) - (if (x mod 2) <= 0 then x else 1))
A293047: 0 0 0 3 4 15 26 63 120 255 502 1023 2036 4095 8178 16383
loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x2,x,1))
A002542: 0 2 56 16256 1073709056 4611686016279904256 4611686018427387903 4611686018427387903
loop(\(x,i).((x + loop(\(x,i).3x,i,x)) div 2),x,1)
A156296: 1 2 10 140 5740 700280 255602200 279628806800 917462115110800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(loop(\(x,i).6x,i,x) div 2),x,1)
A171739: 1 3 54 5832 3779136 14693280768 342764853755904 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x - (loop(\(x,i).4x,i,x) div 2)),x,1)
A290974: 1 ~1 7 ~217 27559 ~14082649 28827182503 ~236123451882073 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1)
A000984: 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520
loop(\(x,i).(3x mod loop(\(x,i).2x,i,2)),x,1)
A058842: 1 3 1 3 9 27 81 243 217 651 1953 1763 5289 15867 14833 44499
loop(\(x,i).((loop(\(x,i).(x2 + ~2x),2,x) * i) div 2),x,1)
A297119: 1 1 3 4 96
loop(\(x,i).(x2 div 2),(x div 2),(if x <= 0 then 0 else (x + 1)))
A261714: 0 2 4 8 72
loop(\(x,i).(x * (1 + i)),(2 + (if x <= 0 then 1 else 2)),(x + 1))
A247825: 24 240 360
loop(\(x,i).(2x + (if (2 - i) <= 0 then x else 1)),x,(x + 1))
A081038: 1 5 21 81 297 1053 3645 12393 41553 137781 452709 1476225 4782969 15411789 49424013 157837977
loop(\(x,i).(if (x mod 4) <= 0 then x else 2x),x,(x + 1))
A084351: 1 4 12 4 20 12 28 8 36 20 44 12 52 28 60 16
((x + 1) + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x))
A132118: 1 2 4 4 6 8 7 9 11 13 11 13 15 17 19 16
((x + 1) + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 1)),x,x))
A094727: 1 2 3 3 4 5 4 5 6 7 5 6 7 8 9 6
loop(\(x,i).(x + (2 * (if (2 - i) <= 0 then x else 1))),x,(x + 1))
A006234: 1 4 15 54 189 648 2187 7290 24057 78732 255879 826686 2657205 8503056 27103491 86093442
loop(\(x,i).(if (x mod 4) <= 0 then (x div 2) else x),x,(x + 1))
A327937-A259445: 1 2 3 2 5 6 7 2 9 10 11 6 13 14 15 2
loop(\(x,i).(x * loop(\(x,i).x2,2,(2 * i))),x,(x + 1))
A280100: 1 32 12288 21233664 108716359680 1304596316160000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((2x + 1) - loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x))
A136272: 1 3 6 7 11 12 13 18 19 20 21 27 28 29 30 31
loop(\(x,i).x2,(x + ~1),loop(\(x,i).(x * i),x,(x + 1)))
A283261: 1 2 36 331776 42998169600000000 4611686018427387903 4611686018427387903
loop(\(x,i).x2,(x div 2),loop(\(x,i).(x * i),x,(x + 1)))
A064030: 1 2 36 576 207360000 268738560000 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x))
A035031: 1 2 2 3 3 5 5 7 7 7 7 11 11 13 13 13
loop(\(x,i).(x + i - (if (~x + i) <= 0 then (2 * i) else 0)),x,1)
A008343: 1 0 2 5 1 6 0 7 15 6 16 5 17 4 18 3
loop(\(x,i).(x * (if (i mod 2) <= 0 then 4 else ~1)),x,1)
A164111: 1 ~1 ~4 4 16 ~16 ~64 64 256 ~256 ~1024 1024 4096 ~4096 ~16384 16384
loop(\(x,i).(x * (1 + (if (i mod 2) <= 0 then 4 else 1))),x,1)
A004643: 1 2 10 20 100 200 1000 2000 10000 20000 100000 200000 1000000 2000000 10000000 20000000
loop(\(x,i).(x + loop(\(x,i).(x * (i * i)),(1 + i),1)),x,1)
A104344: 1 5 41 617 15017 533417 25935017 1651637417 133333531817 13301522971817 1606652445211817 231049185247771817 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + loop(\(x,i).(x * (i * i)),(1 + i),1)),x,1)
A092170: 1 3 33 543 13857 504543 24897057 1600805343 130081089057 13038108350943 1580312813889057 227862219988670943 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(2x * i),(~1 + i),1)),x,1)
A004400: 1 2 4 12 60 444 4284 50364 695484 11017404 196811964 3912703164 85662309564 2047652863164 53059407256764 1481388530277564
loop(\(x,i).(x * (~1 + loop(\(x,i).2x2,2,2))),x,1)
A138128: 1 127 16129 2048383 260144641 33038369407 4195872914689 532875860165503 67675234241018881 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 2),x,loop(\(x,i).5x,x,1))
A094969: 1 2 6 15 39 97 244 610 1525 3814 9536 23841 59604 149011 372529 931322
loop(\(x,i).(x * (1 + loop(\(x,i).(x2 + x),2,2))),x,1)
A009987: 1 43 1849 79507 3418801 147008443 6321363049 271818611107 11688200277601 502592611936843 21611482313284249 929293739471222707 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(x2 + 1),2,3)),x,1)
A096884: 1 101 10201 1030301 104060401 10510100501 1061520150601 107213535210701 10828567056280801 1093685272684360901 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (i mod 2) <= 0 then 2x else 3)),x,1)
A224785: 1 4 12 15 45 48 144 147 441 444 1332 1335 4005 4008 12024 12027
loop(\(x,i).loop(\(x,i).(x * i),(6 * i),x),x,1)
A271946: 1 720 344881152000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).2x,(~1 + i),3x),x,1)
A132727: 1 3 18 216 5184 248832 23887872 4586471424 1761205026816 1352605460594688 2077601987473440768 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + x),1,loop(\(x,i).3x,x,1))
A074610: 2 12 90 756 6642 59292 532170 4785156 43053282 387440172 3486843450 31381236756 282430067922 2541867422652 22876797237930 205891146443556
loop(\(x,i).(x2 + ~x),1,loop(\(x,i).3x,x,1))
A059410: 0 6 72 702 6480 58806 530712 4780782 43040160 387400806 3486725352 31380882462 282429005040 2541864234006 22876787671992 205891117745742
loop(\(x,i).(x * (x div 2)),1,loop(\(x,i).3x,x,1))
A026121: 0 3 36 351 3240 29403 265356 2390391 21520080 193700403 1743362676 15690441231 141214502520 1270932117003 11438393835996 102945558872871
(loop(\(x,i).(x * i),x,1) mod loop(\(x,i).3x,x,1))
A212309: 0 1 2 6 24 120 720 666 954 8586 26811 58725 173259 1189485 3898206 1077462
loop(\(x,i).(2x + 1),x,loop(\(x,i).3x,x,1))
A155589: 1 7 39 223 1311 7807 46719 280063 1679871 10078207 60467199 362799103 2176786431 13060702207 78364180479 470185017343
loop(\(x,i).(2x + ~1),x,loop(\(x,i).3x,x,1))
A155597: 1 5 33 209 1281 7745 46593 279809 1679361 10077185 60465153 362795009 2176778241 13060685825 78364147713 470184951809
loop(\(x,i).2x,x2,loop(\(x,i).3x,x,1))
A133460: 1 6 144 13824 5308416 8153726976 50096498540544 1231171548132409344 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (x + ~2) <= 0 then 1 else (x div 3))),x,1)
A054961: 1 2 3 4 5 6 8 10 13 17
loop(\(x,i).loop(\(x,i).~2x,(i mod 3),x),x,1)
A128018: 1 ~2 ~8 ~8 16 64 64 ~128 ~512 ~512 1024 4096 4096 ~8192 ~32768 ~32768
loop(\(x,i).((~x + 1) + loop(\(x,i).2x,i,2x)),x,1)
A277357: 1 4 29 436 13517 851572 108149645 27578159476 14092439492237 14416565600558452 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (i mod 2) <= 0 then x else (1 + (x div 2)))),x,1)
A181655: 1 2 4 7 14 22 44 67 134 202 404 607 1214 1822 3644 5467
loop(\(x,i).(x + loop(\(x,i).(x * (2 + i)),(~2 + i),1)),x,1)
A093468: 1 2 3 6 18 78 438 2958 23118 204558 2018958 21977358 261478158 3374988558 46964134158 700801318158
loop(\(x,i).(x + loop(\(x,i).x2,2,(1 + (2 * i)))),x,1)
A002309: 1 82 707 3108 9669 24310 52871 103496 187017 317338 511819 791660 1182285 1713726 2421007 3344528
loop(\(x,i).loop(\(x,i).(2x * i),(~1 + (2 * i)),x),x,1)
A168442: 1 2 96 368640 237817036800 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 2),x,loop(\(x,i).(x * (~1 + (2 * i))),x,1))
A020090: 1 0 0 1 6 29 162 1055 7918 67303 639383 6713530 77205601 965070017 13028445231 188912455860
loop(\(x,i).(x + loop(\(x,i).(x * (1 + i)),(2 * i),1)),x,1)
A138523: 1 7 127 5167 368047 40284847 6267305647 1313941673647 357001369769647 122002101778601647 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(~2x + 1),(i div 2),1)),x,1)
A077874: 1 2 1 0 3 6 1 ~4 7 18 ~3 ~24 19 62 ~23 ~108
loop(\(x,i).(x * (1 + (if (i mod 3) <= 0 then 0 else i))),x,1)
A123144: 1 2 6 6 30 180 180 1440 12960 12960 142560 1710720 1710720 23950080 359251200 359251200
loop(\(x,i).(x * (1 + (if (x mod (1 + i)) <= 0 then 0 else i))),x,1)
A066616: 1 2 6 24 120 120 840 840 7560 7560 83160 83160 1081080 1081080 1081080 17297280
((x + 1) - loop(\(x,i).((x + ~1) - (if x <= 0 then 0 else i)),x,x))
A004201: 1 3 4 7 8 9 13 14 15 16 21 22 23 24 25 31
loop(\(x,i).(x * loop(\(x,i).(4x + 1),i,1)),x,1)
A015002: 1 5 105 8925 3043425 4154275125 22686496457625 495586515116818125 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(3x * i),i,1)),x,1)
A112370: 1 4 22 184 2128 31288 556168 11578648 276118168 7418685208 221695696408 7292837066008 261853926371608 10189736409290008 427160800691862808 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(3x + 1),i,1)),x,1)
A015001: 1 4 52 2080 251680 91611520 100131391360 328430963660800 3232089113385932800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(x * (i * (1 + i))),i,1)),x,1)
A016065: 1 3 15 159 3039 89439 3718239 206931039 14838252639 1331657196639 146181741036639 19266392807916639 3002019319241196639 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(~4x + 1),i,1)),x,1)
A015017: 1 ~3 ~39 1989 407745 ~333943155 ~1094331718935 14343405840081045 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(~3x + 1),i,1)),x,1)
A015015: 1 ~2 ~14 280 17080 ~3108560 ~1700382320 2788627004800 13722833490620800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(x - (2x * i)),i,1)),x,1)
A263801: 1 0 3 ~12 93 ~852 9543 ~125592 1901433 ~32557992 622171083 ~13127139492 303107003733 ~7602746576892 205855300099983 ~5984428053529392
((x + 1) - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x))
A127739: 1 3 3 6 6 6 10 10 10 10 15 15 15 15 15 21
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (x * (1 + i))),x,1)
A290650: 1 2 1 4 2 1 7 56 28 14 7 84 42 21 315 5040
loop(\(x,i).(~x + loop(\(x,i).4x,i,(1 + i))),x,1)
A191010: 1 7 41 215 1065 5079 23593 107479 482345 2139095 9395241 40936407 177167401 762356695 3264175145 13915694039
loop(\(x,i).(~x + loop(\(x,i).3x,i,(1 + i))),x,1)
A191008: 1 5 22 86 319 1139 3964 13532 45517 151313 498226 1627538 5281195 17039327 54705208 174877304
loop(\(x,i).(loop(\(x,i).2x,i,1) + (x * (~1 + i))),x,1)
A195254: 1 2 6 20 76 336 1744 10592 74400 595712 5362432 53626368 589894144 7078737920 92023609344 1288330563584
loop(\(x,i).(x + loop(\(x,i).(i - (x * (1 - i))),i,1)),x,1)
A285201: 1 2 5 14 45 174 825 4738 32137 251338 2224157 21952358 238962581 2843085270 36696680241 510647009850
loop(\(x,i).(x + loop(\(x,i).(x * (i * i * i)),i,1)),x,1)
A289948: 1 2 10 226 14050 1742050 374990050 128399054050 65676719822050 47850402559694050 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + loop(\(x,i).~x,x,(i * i)))),x,1)
A129464: 1 ~2 ~6 ~48 ~720 ~17280 ~604800 ~29030400 ~1828915200 ~146313216000 ~14485008384000 ~1738201006080000 ~248562743869440000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (2 * (if (~x + 2) <= 0 then x else 3))),x,1)
A083596: 1 7 21 63 189 567 1701 5103 15309 45927 137781 413343 1240029 3720087
A082541: 1 7 21 63 189 567 1701 5103 15309 45927 137781 413343 1240029 3720087 11160261 33480783
loop(\(x,i).(x + (2 * (if (i mod 2) <= 0 then (x + ~2) else 1))),x,1)
A062547: 1 3 5 7 17 19 53 55 161 163 485 487 1457 1459 4373 4375
loop(\(x,i).(x * (2 + (if (~x + 4) <= 0 then x else 1))),x,1)
A078221: 1 3 9 99 9999 99999999 9999999999999999 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (4 + (if (~x + 2) <= 0 then 2 else 1))),x,1)
A052934: 1 5 30 180 1080 6480 38880 233280 1399680 8398080 50388480 302330880 1813985280 10883911680 65303470080 391820820480
loop(\(x,i).(x + (4 * (if (~x + 2) <= 0 then x else 2))),x,1)
A270567-A189274: 1 9 45 225 1125 5625 28125 140625 703125 3515625 17578125 87890625 439453125 2197265625 10986328125 54931640625
loop(\(x,i).(x * (if (i mod 2) <= 0 then ~1 else 4)),x,1)
A141125: 1 4 ~4 ~16 16 64 ~64 ~256 256 1024 ~1024 ~4096 4096 16384 ~16384 ~65536
loop(\(x,i).(x + (if (~x + 2) <= 0 then x else (2x + 4))),x,1)
A135092: 1 7 14 28 56 112 224 448 896 1792 3584 7168 14336 28672 57344 114688
loop(\(x,i).(x + (2 * (if (~2 + i) <= 0 then 1 else 2x))),x,1)
A074701: 1 3 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125 6103515625
loop(\(x,i).loop(\(x,i).(x * (1 + i)),(4 * i),x),x,1)
A294320: 1 120 43545600 271159356948480000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (2 * (if (i mod 3) <= 0 then 1 else x))),x,1)
A057245-A018282: 1 3 9 11 33 99
loop(\(x,i).(x + (2 * (if (i mod 4) <= 0 then 1 else x))),x,1)
A018644: 1 3 9 27 29 87 261 783
loop(\(x,i).(x + (2 * (if (i mod 3) <= 0 then 2 else x))),x,1)
A018292: 1 3 9 13 39 117
loop(\(x,i).(x + (2 * (if (i mod 4) <= 0 then 2 else x))),x,1)
A018675: 1 3 9 27 31 93 279 837
loop(\(x,i).(if (x + ~2) <= 0 then (x + 1) else (x2 + 2x)),x,1)
A250404: 1 2 3 15 255 65535
(1 + loop(\(x,i).((if (x mod 2) <= 0 then 2 else 0) + (x div 2)),x,x))
A172984: 1 1 2 3 5 3 3 1 4 5 4 4 3 2 5 2
loop(\(x,i).(x + ((x + (if (i mod 2) <= 0 then 2 else x)) div 2)),x,1)
A222011: 1 2 4 8
A043816-A043807-A043799: 1 2 4 8 13 26 40 80 121 242 364 728 1093 2186 3280 6560
loop(\(x,i).(x + loop(\(x,i).2x,i,2x2)),x,1)
A068531: 1 5 205 672605 14476720225405 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (loop(\(x,i).4x,i,x) div 2)),x,1)
A085521: 1 3 27 891 114939 58963707 120816635643 989850695823099 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(x * (x - i)),2,(2 + i))),x,1)
A090444: 1 24 2880 1036800 870912000 1463132160000 4424511651840000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).2x,(~1 + i),(x * (2 + i))),x,1)
A185970: 1 3 24 480 23040 2580480 660602880 380507258880 487049291366400 1371530804487782400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(x * i),(~1 + i),(~2 + i))),x,1)
A065355: 1 0 0 2 14 86 566 4166 34406 316646 3219686 35878886 435046886 5704064486 80428314086 1213746099686
loop(\(x,i).loop(\(x,i).(x - (2x * i)),(2 * i),x),x,1)
A168440: 1 3 315 3274425 6637341335625 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else loop(\(x,i).(x * i),(x + ~2),(x2 + ~1)))
A261766: 1 0 3 8 30 144 840 5760 45360 403200 3991680 43545600 518918400 6706022400 93405312000 1394852659200
loop(\(x,i).2x,x,loop(\(x,i).3x,x2,1))
A135397: 1 6 324 157464 688747536 27113235502176 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (x mod (3 + i)) <= 0 then 1 else x)),x,1)
A222011: 1 2 4 8
A018366: 1 2 4 8 16 17 34 68 136 272
loop(\(x,i).(x + (if (i mod 4) <= 0 then 3 else x)),x,1)
A222011: 1 2 4 8
A018277: 1 2 4 8 11 22 44 88
loop(\(x,i).(x * (~x + loop(\(x,i).x2,i,3))),x,1)
A225168: 1 8 584 3490568 138073441864904 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).i,loop(\(x,i).(x div (1 + (x mod 2))),x,x),x))
A274346: 1 2 3 4 5 3 7 8 9 5 11 3 13 7 15 16
loop(\(x,i).(x + (if (i mod 4) <= 0 then (1 + i) else x)),x,1)
A222011: 1 2 4 8
A018285: 1 2 4 8 13 26 52 104
loop(\(x,i).(x + loop(\(x,i).(x + (i * i)),(1 + i),x)),x,1)
A156928: 1 7 28 86 227 545 1230 2664 5613 11611 23728 48106 97031 195077 391394 784284
loop(\(x,i).(x + loop(\(x,i).2x,(i - (x mod 2)),x)),x,1)
A082472: 1 2 10 90 1530 50490 3281850 423358650 108803173050 55816027774650 57211428469016250 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + loop(\(x,i).3x,(2 * i),x)),x,1)
A027877: 1 8 640 465920 3056435200 180476385689600 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(0 - loop(\(x,i).(~x2 + loop(\(x,i).2x,i,1)),x,1))
A168319: ~1 ~1 ~3 1 ~15 193 37185 1382724097 1911925928424465153 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + loop(\(x,i).6x,i,x)),x,1)
A027873: 1 5 175 37625 48724375 378832015625 17674407688984375 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + loop(\(x,i).8x,i,x)),x,1)
A027876: 1 7 441 225351 922812345 30237792108615 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (0 - loop(\(x,i).~2x,i,x))),x,1)
A331691: 1 2 ~16 2048 ~67108864 144115188075855872 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + loop(\(x,i).5x,i,x)),x,1)
A027872: 1 4 96 11904 7428096 23205371904 362560730628096 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 - (2 mod (~1 + loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x))))
A193592: 1 1 1 1 2 1 1 3 2 1 1 4 3 2 1 1
(2x mod loop(\(x,i).(x + (if (~x + i) <= 0 then 0 else i)),x,1))
A336018: 0 0 1 0 1 3 5 0 1 3 5 7 9 11 13 0
loop(\(x,i).(x * ((1 + (if (i mod 2) <= 0 then 2 else 0)) * i)),x,1)
A059944: 1 1 6 18 216 1080 19440 136080 3265920 29393280 881798400 9699782400 349192166400 4539498163200 190658922854400 2859883842816000
loop(\(x,i).loop(\(x,i).(x * i),(5 * i),x),x,1)
A268506: 1 120 435456000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * (1 + i)),(3 * i),x),x,1)
A294318: 1 24 120960 438939648000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(2x * (i * (1 + i))),i,x),x,1)
A159783: 1 4 192 221184 10192158720 28179280429056000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((2 + (if (~x + 2) <= 0 then 2 else 1)) * i)),x,1)
A052592: 1 3 24 288 4608 92160 2211840 61931520 1981808640 71345111040 2853804441600 125567395430400 6027234980659200 313416218994278400 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(4x * (i * i)),i,x),x,1)
A136807: 1 4 256 589824 86973087744 1282470362637926400 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(2x * (~1 + (2 * i))),i,x),x,1)
A110131: 1 2 24 2880 4838400 146313216000 97339256340480000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(loop(\(x,i).(x * i),(~1 + i),1) + (x * i)),x,1)
A000774: 1 2 5 17 74 394 2484 18108 149904 1389456 14257440 160460640 1965444480 26029779840 370643938560 5646837369600
loop(\(x,i).(loop(\(x,i).~x,(~2 + i),1) + (x * i)),x,1)
A110043: 1 2 5 14 57 284 1705 11934 95473 859256 8592561 94518170 1134218041 14744834532 206427683449 3096415251734
loop(\(x,i).(loop(\(x,i).(1 + (x * i)),i,1) - (x * i)),x,1)
A087208: 1 1 3 7 37 141 1111 5923 62217 426457 5599531 46910271 739138093 7318002277 134523132927 1536780478171
loop(\(x,i).(loop(\(x,i).4x,i,1) + (x * i)),x,1)
A053487: 1 5 26 142 824 5144 34960 261104 2154368 19651456 197563136 2177388800 26145442816 339957865472 4759678552064 71396252022784
loop(\(x,i).(loop(\(x,i).~2x,i,1) + (x * i)),x,1)
A000023: 1 ~1 2 ~2 8 8 112 656 5504 49024 491264 5401856 64826368 842734592 11798300672 176974477312
loop(\(x,i).(loop(\(x,i).(2 + (x * i)),i,1) + (x * i)),x,1)
A306495: 1 4 16 74 402 2542 18446 151482 1390738 14126582 157365222 1908110866 25022451482 352918443438 5327630246542 85716034274282
loop(\(x,i).(loop(\(x,i).3x,i,1) + (x * i)),x,1)
A053486: 1 4 17 78 393 2208 13977 100026 806769 7280604 72865089 801693126 9620848953 125072630712 1751021612937 26265338542962
loop(\(x,i).(loop(\(x,i).(x * (i * i)),i,1) + (x * i)),x,1)
A143217: 1 2 8 60 816 18480 629280 29806560 1864154880 148459288320 14652782323200 1754531527795200 250496911136102400 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(loop(\(x,i).(x * i),(~1 + i),2) + (x * i)),x,1)
A000776: 1 3 8 28 124 668 4248 31176 259488 2416032 24886080 281004480 3451887360 45832538880 654109585920 9986000371200
loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).(x * i),x,1))
A055555: 1 1 3 21 300 7260 259560 12703320 812871360 65841128640 6584096534400 796675481078400 114721266640780800 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + 2x),1,loop(\(x,i).(x * i),x,1))
A020550: 3 3 12 228 13872 1728240 373249440 128024074080 65548320848640 47784725840597760 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).3x,x,1) + loop(\(x,i).(x * i),x,1))
A249945: 2 4 11 33 105 363 1449 7227 46881 382563 3687849 40093947 479533041 6228615123 87183074169 1307688716907
((loop(\(x,i).2x,x,1) div 2) + loop(\(x,i).(x * i),x,1))
A089476: 1 2 4 10 32 136
loop(\(x,i).(x div (1 + i)),(x div 2),loop(\(x,i).(x * i),x,1))
A262033: 1 1 1 3 4 20 30 210 336 3024 5040 55440 95040 1235520 2162160 32432400
loop(\(x,i).(x div (2 - (x mod 2))),x,loop(\(x,i).(x * i),x,1))
A160624-A049606: 1 1 1 3 3 15 45 315 315 2835 14175 155925 467775 6081075 42567525 638512875
loop(\(x,i).((if (i mod 4) <= 0 then 1 else i) + (x * i)),x,1)
A344229: 1 2 6 21 85 430 2586 18109 144873 1303866 13038670 143425381 1721104573 22374359462 313241032482 4698615487245
loop(\(x,i).loop(\(x,i).(~x + (3x * i)),i,x),x,1)
A263417: 1 2 20 1600 1408000 17346560000 3633063526400000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + ((x + loop(\(x,i).(x * i),i,1)) * i)),x,1)
A318165: 1 3 13
A121586: 1 3 13 70 446 3276 27252 253296 2602224 29288160 358457760 4740577920 67375532160 1024208720640 16583626886400 284953145702400
loop(\(x,i).loop(\(x,i).(x * (~2 + (3 * i))),i,x),x,1)
A263416: 1 1 4 112 31360 114150400 6648119296000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * ((~1 + (2 * i)) * i)),i,x),x,1)
A121835: 1 1 6 540 1360800 154314720000 1154953090368000000 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * (i * i * i * i)),i,x),x,1)
A168488: 1 1 16 20736 6879707136 1426576071720960000 4611686018427387903 4611686018427387903
loop(\(x,i).(loop(\(x,i).2x,i,1) + (x * (i * i))),x,1)
A216149: 1 3 16
A228513: 1 3 16 152 2448 61232 2204416 108016512 6913057024 559957619456 55995761946624 6775487195543552 975670156158275584 4611686018427387903 4611686018427387903 4611686018427387903
((if x <= 0 then 2 else (x - (if (x mod 3) <= 0 then 1 else 0))) div 2)
A243322: 1 0 1 1 2 2 2 3 4 4
(if x <= 0 then 1 else (2 + (if (x mod 5) <= 0 then 2 else 0)))
A227783: 1 2 2 2 2 4 2 2 2 2 4 2 2 2 2 4
(if (x + ~1) <= 0 then x else (2 + (if (x mod 2) <= 0 then 4 else 0)))
A126664: 0 1 6 2 6 2 6 2 6 2 6 2 6 2 6 2
loop(\(x,i).(x2 + x + 1),(if (x mod 2) <= 0 then 2 else 0),2)
A278068: 57 2 57 2 57 2 57 2 57 2 57 2 57 2 57 2
(loop(\(x,i).(2x + 1),x,(if (x mod 2) <= 0 then 2 else 0)) div 2)
A283507: 1 0 5 3 23 15 95 63 383 255 1535 1023 6143 4095 24575 16383
(if x <= 0 then (x + ~1) else (2 + loop(\(x,i).(i * i),(x + ~2),0)))
A102762: ~1 2 2 3 6 11 18 27 38 51 66 83 102 123 146 171
(if (x + ~1) <= 0 then 1 else (if ((x div 2) mod 2) <= 0 then 2 else ~2))
A084100: 1 1 ~2 ~2 2 2 ~2 ~2 2 2 ~2 ~2 2 2 ~2 ~2
(if (x mod 4) <= 0 then (if x <= 0 then 1 else 2) else (x mod ~2))
A323202: 1 ~1 0 ~1 2 ~1 0 ~1 2 ~1 0 ~1 2 ~1 0 ~1
(loop(\(x,i).(2 - loop(\(x,i).(2 * (x - i)),x,0)),x,0) div 2)
A105035: 0 1 5 2037
(~2 + loop(\(x,i).x2,2,loop(\(x,i).(2x + 1),x,0)))
A118558: ~2 ~1 79 2399 50623 923519 15752959 260144639 4228250623 68184176639 1095222947839 17557851463679 281200199450623 4501401006735359 72040003462430719 1152780773560811519
(2 * loop(\(x,i).(loop(\(x,i).2x,x,3) div 2),x,0))
A173609: 0 2 6 24 12288
(2 * loop(\(x,i).(x + ((i * i) + (if x <= 0 then 1 else 2))),x,0))
A121318: 0 4 16 38 74 128 204 306 438 604 808 1054 1346 1688 2084 2538
(2 + loop(\(x,i).(2 * ((if x <= 0 then 1 else x) + (i div 2))),x,0))
A288170: 2 4 8 16 34 70 144 292 590 1186 2380 4768 9546 19102 38216 76444
(x + ((if (~2 + (x div 2)) <= 0 then 1 else 2) + (if x <= 0 then 0 else 2)))
A231369: 1 4 5 6 7 8 10 11 12 13 14 15 16 17 18 19
(loop(\(x,i).(x + loop(\(x,i).(x2 div 2),2,i)),x,0) div 2)
A059859: 0 0 1 5 21 57 138 282 538 938 1563 2463 3759 5523 7924 11060
(2 + loop(\(x,i).((if (x + ~2) <= 0 then 2 else (x + ~2)) * i),x,0))
A152491: 2 4 6 8 18 72
(2 * (if (x mod 2) <= 0 then (3 * (if x <= 0 then 1 else 2)) else 1))
A040035: 6 2 12 2 12 2 12 2 12 2 12 2 12 2 12 2
(loop(\(x,i).(2x * i),loop(\(x,i).2x,x,1),1) div 2)
A028370: 1 4 192 5160960 685597979049984000 4611686018427387903
(if x <= 0 then 1 else (2 * (1 + loop(\(x,i).(x2 + 2),x,1))))
A002268: 1 8 24 248
(if x <= 0 then 1 else (2 * loop(\(x,i).(2x + 4),(x + ~1),1)))
A154252: 1 2 12 32 72 152 312 632 1272 2552 5112 10232 20472 40952 81912 163832
(if x <= 0 then 1 else (2 * (1 + (if (x + ~4) <= 0 then 0 else 2))))
A260188-A048764: 1 2 2 2 2 6 6 6 6 6 6 6 6 6 6 6
(2 + (if (x mod 6) <= 0 then (if x <= 0 then 1 else 2) else 1))
A081168: 3 3 3 3 3 3 4 3 3 3 3 3 4 3 3 3
(2 * (if (x mod 2) <= 0 then (2 * (2 + (if x <= 0 then 0 else 2))) else 1))
A040063: 8 2 16 2 16 2 16 2 16 2 16 2 16 2 16 2
(if x <= 0 then 1 else (2 + (if (x mod 2) <= 0 then 8 else 1)))
A188545: 1 3 10
A072988: 1 3 10 3 10 3 10 3 10 3 10 3 10 3 10 3
(2 + (if (if (x mod 3) <= 0 then x else (x mod 2)) <= 0 then 2 else 1))
A171783: 4 3 4 3 4 3 3 3 4 3 4 3 3 3 4 3
(if x <= 0 then 1 else (2 * (if (x + ~2) <= 0 then 2x else 3)))
A063808: 1 4 8 6 6 6 6 6 6 6 6 6 6 6 6 6
(if x <= 0 then 1 else loop(\(x,i).2x,(2x div 3),2))
A222011: 1 2 4 8
A132720: 1 2 4 8 8 16 32 32 64 128 128 256 512 512 1024 2048
loop(\(x,i).x2,(x + ~2),(if x <= 0 then 1 else 6))
A165424: 1 6 6 36 1296 1679616 2821109907456 4611686018427387903 4611686018427387903
(if (x mod 2) <= 0 then (if (x + ~2) <= 0 then 1 else 2) else 6)
A078300: 1 6 1 6 2
((if x <= 0 then 2 else (if (x + ~4) <= 0 then (x + ~2) else 1)) div 2)
A204853: 1 ~1 0 0 1 0 0 0 0 0 0 0 0 0 0 0
(if (x + ~1) <= 0 then x else (if (x mod 2) <= 0 then (2x + ~1) else 2))
A266664: 0 1 3 2 7 2 11 2 15 2 19 2 23 2 27 2
loop(\(x,i).~3x,x,(2 + (if x <= 0 then 2 else 1)))
A256096: 4 ~9 27 ~81 243 ~729 2187 ~6561 19683 ~59049 177147 ~531441 1594323 ~4782969 14348907 ~43046721
(if (12 mod (if x <= 0 then 1 else x)) <= 0 then 1 else 2)
A342510-A043557: 1 1 1 1 1 2 1 2 2 2 2 2 1 2 2 2
loop(\(x,i).2x,x,(loop(\(x,i).(2x + 2),x,1) div 2))
A093357: 0 4 20 88 368 1504 6080 24448 98048 392704 1571840 6289408 25161728 100655104 402636800 1610579968
(2 + loop(\(x,i).(2 * (x + (if (i mod 2) <= 0 then 2 else 0))),x,1))
A171160: 3 4 10 18 38 74 150 298 598 1194 2390 4778 9558 19114 38230 76458
loop(\(x,i).(2x + 2),x,(2 + loop(\(x,i).2x,x,1)))
A290718: 3 10 30 94 318 1150 4350 16894 66558 264190 1052670 4202494 16793598 67141630 268500990 1073872894
loop(\(x,i).(2 + loop(\(x,i).(x2 + ~1),i,x)),(x + 1),2)
A072952: 5 577 4611686018427387903
loop(\(x,i).(x + (if (~2 + i) <= 0 then 2 else x)),x,((x + 1) mod 2))
A104721: 1 2 5 8 20 32 80 128 320 512 1280 2048 5120 8192 20480 32768
loop(\(x,i).(x div 2),x,(loop(\(x,i).(x * i),x,(x + 1)) div 2))
A066979: 0 0 0 1 3 11 39 157 708 3543 19490 116943 760134 5320940 39907054 319256437
loop(\(x,i).(x2 + ~2x),1,loop(\(x,i).2x,(x + ~1),2))
A211012: 0 0 8 48 224 960 3968 16128 65024 261120 1046528 4190208 16769024 67092480 268402688 1073676288
(loop(\(x,i).(x div 2),x,loop(\(x,i).x2,2,(x + ~1))) div 2)
A036443: 0 0 0 1 2 4 4 5 4 4 3 2 1 1
(if x <= 0 then 1 else (if (x div 4) <= 0 then x else (2x + ~2)))
A089422: 1 1 2 3 6 8 10 12 14 16 18 20 22 24 26 28
loop(\(x,i).(x * loop(\(x,i).2x,(~1 + i),x)),(x + ~1),2)
A300361: 2 2 4 32 4096 134217728 288230376151711744 4611686018427387903 4611686018427387903
((1 + (if (x mod 2) <= 0 then 4 else 0)) * (if x <= 0 then 1 else 2))
A040024: 5 2 10 2 10 2 10 2 10 2 10 2 10 2 10 2
((2 + (if (x mod 2) <= 0 then 4 else 0)) * (if x <= 0 then 1 else 2))
A040032: 6 4 12 4 12 4 12 4 12 4 12 4 12 4 12 4
(2 * ((if (x mod 2) <= 0 then 4 else 1) * (if x <= 0 then 1 else 2)))
A040059: 8 4 16 4 16 4 16 4 16 4 16 4 16 4 16 4
loop(\(x,i).x2,((x2 + ~1) div 2),(if x <= 0 then 1 else 2))
A006263: 1 2 4 65536
(loop(\(x,i).(2x * i),(x + ~2),2) - (if x <= 0 then 1 else 2))
A033169: 1 0 0 2 14 94
(loop(\(x,i).8x,x,2) + (if x <= 0 then 1 else 2))
A291775: 3 18 130 1026
(if (2 - (x * (x mod 2))) <= 0 then (x div 2) else (if x <= 0 then 1 else 2))
A168208: 1 2 2 1 2 2 2 3 2 4 2 5 2 6 2 7
loop(\(x,i).(2 * ((2x + ~1) - i)),x,(if x <= 0 then 1 else 2))
A151746: 1 4 10 32 118 460 1826 7288 29134 116516 466042 1864144 7456550 29826172 119304658 477218600
loop(\(x,i).(x - (x div (~2 + (x mod 2)))),x,(if x <= 0 then 1 else 2))
A182751: 1 3 6 9 18 27 54 81 162 243 486 729 1458 2187 4374 6561
loop(\(x,i).(3x2 + ~2x),x,(if x <= 0 then 1 else 2))
A099175: 1 8 176 92576 25710762176 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x + (i * i)),x,x2) + (if x <= 0 then 1 else 2))
A110610: 1 4 11 25 48 82 129 191 270 368 487 629 796 990 1213 1467
(x - (2 * (loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0) div 2)))
A339132: 0 1 2 3 2 3 6 7 2 3 6 7 10 11 14 15
(4 + loop(\(x,i).(if x <= 0 then 3 else 2x),x,0))
A003461: 4 7 10 16 28 52 100 196 388 772 1540 3076 6148 12292 24580 49156
(if x <= 0 then 1 else (2 * (~2 + loop(\(x,i).(2x + 4),x,1))))
A321237: 1 8 28 68 148 308 628 1268 2548 5108 10228 20468 40948 81908 163828 327668
(if x <= 0 then 1 else (4 * loop(\(x,i).(x2 + x),x,1)))
A226962: 1 8 24 168 7224
(if (x + ~2) <= 0 then (if x <= 0 then 1 else 8x) else 2)
A073926: 1 8 16 2
(if (x + ~4) <= 0 then (if x <= 0 then 0 else 1) else 8)
A201053: 0 1 1 1 1 8 8 8 8 8 8 8 8 8 8 8
loop(\(x,i).x2,(x + ~2),(if x <= 0 then 1 else 8))
A165426: 1 8 8 64 4096 16777216 281474976710656 4611686018427387903 4611686018427387903
(if (x mod 8) <= 0 then (if x <= 0 then 1 else x) else 4)
A113472: 1 4 4 4 4 4 4 4 8 4 4 4 4 4 4 4
(if x <= 0 then 1 else (4 * loop(\(x,i).3x,x,x)))
A236967: 1 12 72 324 1296 4860 17496 61236 209952 708588 2361960 7794468 25509168 82904796 267846264 860934420
(loop(\(x,i).2x,x,loop(\(x,i).(2x + 1),x,2)) div 2)
A010036: 1 5 22 92 376 1520 6112 24512 98176 392960 1572352 6290432 25163776 100659200 402644992 1610596352
(2 * ((x + 2) + (if x <= 0 then 2 else (if (x + ~2) <= 0 then x else 1))))
A329822: 8 8 12 12 14 16 18 20 22 24 26 28 30 32 34 36
(loop(\(x,i).2x,x,loop(\(x,i).((x + 1) + i),x,2)) div 2)
A007466: 1 4 14 44 128 352 928 2368 5888 14336 34304 80896 188416 434176 991232 2244608
(loop(\(x,i).(x * i),x,loop(\(x,i).((x + 1) + i),x,2)) div 2)
A006595: 1 2 7 33 192 1320 10440 93240 927360 10160640 121564800 1576713600 22034073600 330032102400 5274286617600 89575694208000
(if (x mod 2) <= 0 then 1 else (~2 + loop(\(x,i).4x,x,2)))
A266302: 1 6 1 126 1 2046 1 32766 1 524286 1 8388606 1 134217726 1 2147483646
(loop(\(x,i).(2x + (if (i mod 2) <= 0 then i else 1)),x,2) div 2)
A091919: 1 2 6 12 27 54 112 224 453 906 1818 3636 7279 14558 29124 58248
(~2 + loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,2)))
A005367: 4 18 70 270 1054 4158 16510 65790 262654 1049598 4196350 16781310 67117054 268451838 1073774590 4295032830
(~2 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,x,2)))
A170940: 0 10 54 238 990 4030 16254 65278 261630 1047550 4192254 16773118 67100670 268419070 1073709054 4294901758
(2 * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,x,2)))
A059153: 4 24 112 480 1984 8064 32512 130560 523264 2095104 8384512 33546240 134201344 536838144 2147418112 8589803520
loop(\(x,i).(2x + 1),x,(2 + loop(\(x,i).2x,x,2)))
A297928: 4 13 43 151 559 2143 8383 33151 131839 525823 2100223 8394751 33566719 134242303 536920063 2147581951
(loop(\(x,i).(if (x mod 2) <= 0 then (~x + 1) else 2x),x,2) div 2)
A077980: 1 ~1 ~1 1 3 ~3 ~5 5 11 ~11 ~21 21 43 ~43 ~85 85
(loop(\(x,i).2x,x,loop(\(x,i).((x + 2) + i),x,2)) div 2)
A001793: 1 5 18 56 160 432 1120 2816 6912 16640 39424 92160 212992 487424 1105920 2490368
loop(\(x,i).x2,(x + ~2),loop(\(x,i).2x,(x + 2),2))
A239280: 8 16 32 4096
(loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,(x + 2)) div 2)
A333361: 1 1 0 1 0 0 1 1 0 0 1 1 2 0 0 1
(loop(\(x,i).(x + (if (~2 + i) <= 0 then 2 else x)),x,(x + 2)) div 2)
A109975: 1 2 4 9 20 44 96 208 448 960 2048 4352 9216 19456 40960 86016
(if x <= 0 then 1 else (if (x mod 8) <= 0 then (x + ~2) else 2))
A063790: 1 2 2 2 2 2 2 2 6 2 2 2 2 2 2 2
loop(\(x,i).2x,x,loop(\(x,i).(2x + 2),2x,2))
A147537: 2 28 248 2032 16352 131008 1048448 8388352 67108352 536869888 4294965248 34359734272 274877898752 2199023239168 17592186011648 140737488289792
loop(\(x,i).x2,2,loop(\(x,i).4x,2x,2))
A013804: 16 1048576 68719476736 4503599627370496 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * (2x + loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,2)))
A079250: 4 6 8 16 18 20 34 36 38 40 42 44 70 72 74 76
loop(\(x,i).x2,2x,(if x <= 0 then 1 else 4x))
A185981: 1 256 281474976710656 4611686018427387903
loop(\(x,i).2x,(x div 2),(if x <= 0 then 1 else (2 + (x mod 2))))
A145751-A063759: 1 3 4 6 8 12 16 24 32 48 64 96 128 192 256 384
(2 * loop(\(x,i).(x2 + x),1,loop(\(x,i).x2,x,2)))
A330826: 12 40 544 131584 8590065664
(loop(\(x,i).(x2 + ~x),1,loop(\(x,i).x2,x,2)) div 2)
A040996: 1 6 120 32640 2147450880 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,x,loop(\(x,i).(2x + i),x,2)) div 2)
A112613: 1 5 24
A008464: 1 5 24 108 464 1936 7936 32192 129792 521472 2091008 8375296 33525760 134156288 536739840 2147205120
(if x <= 0 then 1 else (2 * (x + (if (x mod 2) <= 0 then 2x else 0))))
A035877: 1 2 12 6 24 10 36 14 48 18 60 22 72 26 84 30
(2 * loop(\(x,i).(x + (if (~x + 2) <= 0 then x else 2)),x,~x))
A131117: 0 2 4 6 8 12 16 24 32 48 64 96 128 192 256 384
(2 * loop(\(x,i).(x + (if x <= 0 then (1 + i) else 0)),x,(~x + 1)))
A212012: 2 4 2 6 4 2 8 6 4 2 10 8 6 4 2 12
(loop(\(x,i).(x + (if x <= 0 then (1 + i) else 0)),x,(~x + 1)) div 2)
A060450: 0 1 0 1 1 0 2 1 1 0 2 2 1 1 0 3
((loop(\(x,i).2x,(x div 2),1) div (if x <= 0 then 1 else x)) div 2)
A206559-A034397: 0 0 0 0 0 0 0 0 1 0 1 1 2 2 4 4
((if x <= 0 then 1 else (8 mod (if x <= 0 then 1 else x))) mod 2)
A186741-A173864: 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0
((~1 + loop(\(x,i).2x,x,2)) * ((if x <= 0 then 1 else x) mod 2))
A277936: 1 3 0 15 0 63 0 255 0 1023 0 4095 0 16383 0 65535
loop(\(x,i).(~1 + (x * (x + (if (2 - i) <= 0 then x else 1)))),x,2)
A244014: 2 5 49 4801 46099201 4250272665676801 4611686018427387903 4611686018427387903
loop(\(x,i).(~1 + loop(\(x,i).(x2 + ~1),2,x2)),x,2)
A242835: 2 223 4611686018427387903
(if x <= 0 then 0 else loop(\(x,i).(x * ((2 + i) * (1 + i))),x,2))
A143248: 0 12 144 2880 86400 3628800 203212800 14631321600 1316818944000 144850083840000 19120211066880000 2982752926433280000 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,loop(\(x,i).(4x + 2),x,2))
A115489: 2 20 168 1360 10912 87360 699008 5592320 44739072 357913600 2863310848 22906490880 183251935232 1466015498240 11728124018688 93824992215040
loop(\(x,i).(x + i),(x + 1),loop(\(x,i).(2x + 2),x,2))
A145070: 3 9 20 40 77 147 282 546 1067 2101 4160 8268 16473 32871 65654 131206
loop(\(x,i).(2x + 1),x,loop(\(x,i).(2x + 2),x,2))
A187560: 2 13 59 247 1007 4063 16319 65407 261887 1048063 4193279 16775167 67104767 268427263 1073725439 4294934527
loop(\(x,i).4x,x,loop(\(x,i).(2x + 2),x,2))
A147538: 2 24 224 1920 15872 129024 1040384 8355840 66977792 536346624 4292870144 34351349760 274844352512 2198889037824 17591649173504 140735340871680
(if x <= 0 then 1 else (2 * loop(\(x,i).(x * i),(2x + ~2),x)))
A166356: 1 2 8 144 5760 403200 43545600 6706022400 1394852659200 376610217984000 128047474114560000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (x - (if (i mod 2) <= 0 then 2 else ~2))),x,2)
A115102: 2 8 12 28 52 108 212 428 852 1708 3412 6828 13652 27308 54612 109228
loop(\(x,i).x2,2,loop(\(x,i).8x,x,2))
A013758: 16 65536 268435456 1099511627776 4503599627370496 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + ~x),1,loop(\(x,i).4x,x,2))
A193475: 2 56 992 16256 261632 4192256 67100672 1073709056 17179738112 274877382656 4398044413952 70368735789056 1125899873288192 18014398375264256 288230375614840832 4611686016279904256
(loop(\(x,i).(x + (if x <= 0 then (1 + i) else 0)),x,(~x + 2)) div 2)
A152146: 1 0 1 0 1 1 0 2 1 1 0 2 2 1 1 0
loop(\(x,i).(2 * (x + loop(\(x,i).3x,i,1))),x,2)
A081956: 2 10 38 130 422 1330 4118 12610 38342 116050 350198 1054690 3172262 9533170 28632278 85962370
loop(\(x,i).(2x + (if (~1 + (i div 2)) <= 0 then 1 else 0)),x,2)
A248646: 2 5 11 23 46 92 184 368 736 1472 2944 5888 11776 23552 47104 94208
loop(\(x,i).x2,1,loop(\(x,i).(~2x + (i mod 2)),x,2))
A262473: 4 9 36 121 484 1849 7396 29241 116964 466489 1865956 7458361 29833444 119311929 477247716 1908903481
(loop(\(x,i).2x,(x div 2),1) + loop(\(x,i).2x,x,2))
A001445: 3 5 10 18 36 68 136 264 528 1040 2080 4128 8256 16448 32896 65664
loop(\(x,i).(x2 + (x div 2)),1,loop(\(x,i).2x,x,2))
A164051: 5 18 68 264 1040 4128 16448 65664 262400 1049088 4195328 16779264 67112960 268443648 1073758208 4295000064
loop(\(x,i).(x2 - (x div 2)),1,loop(\(x,i).2x,x,2))
A171499: 3 14 60 248 1008 4064 16320 65408 261888 1048064 4193280 16775168 67104768 268427264 1073725440 4294934528
loop(\(x,i).(2x2 + ~x),1,loop(\(x,i).2x,x,2))
A171496: 6 28 120 496 2016 8128 32640 130816 523776 2096128 8386560 33550336 134209536 536854528 2147450880 8589869056
loop(\(x,i).(x3 + ~2x),1,loop(\(x,i).2x,x,2))
A020540: 4 56 496 4064 32704 262016 2096896 16776704 134216704 1073739776 8589930496 68719468544 549755797504 4398046478336 35184372023296 281474976579584
(loop(\(x,i).(x * i),x,(x + 1)) mod loop(\(x,i).2x,x,2))
A068496: 1 2 6 8 24 16 48 128 384 768 1280 3072 3072 10240 22528 32768
(loop(\(x,i).3x,x,1) - loop(\(x,i).2x,x,2))
A003063: ~1 ~1 1 11 49 179 601 1931 6049 18659 57001 173051 523249 1577939 4750201 14283371
loop(\(x,i).(2 + (x * (2 + i))),2,loop(\(x,i).2x,x,2))
A211715: 34 58 106 202 394 778 1546 3082 6154 12298 24586 49162 98314 196618 393226 786442
loop(\(x,i).(x + (2 * (x + i))),2,loop(\(x,i).2x,x,2))
A305060: 28 46 82 154 298 586 1162 2314 4618 9226 18442 36874 73738 147466 294922 589834
(loop(\(x,i).3x,x,2) - loop(\(x,i).2x,x,2))
A056182: 0 2 10 38 130 422 1330 4118 12610 38342 116050 350198 1054690 3172262 9533170 28632278
loop(\(x,i).((x + (if (x + ~2) <= 0 then 1 else x)) * (x div 2)),x,2)
A173501: 2 3 6 36 1296 1679616 2821109907456 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x3,1,2x2),x,2)
A139302: 2 512 144115188075855872
loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,2)
A028329: 2 4 12 40 140 504 1848 6864 25740 97240 369512 1410864 5408312 20801200 80233200 310235040
loop(\(x,i).x2,1,loop(\(x,i).(x * (i * (2 + i))),x,2))
A179870: 4 36 2304 518400 298598400 365783040000 842764124160000 3344930808791040000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + 1),(x div 2),(if (x mod 2) <= 0 then 1 else (x + 2)))
A077140: 1 3 0 ~4 1 7 0 ~8 1 11 0 ~12 1 15 0 ~16
loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 1 else 0)),x,(x + 2))
A305430-A268101-A123318: 2 3 5 5 7 7 11 11 11 11 13 13 17 17 17 17
((x + 2) + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 1)),x,x))
A248110-A108872: 2 3 4 4 5 6 5 6 7 8 6 7 8 9 10 7
loop(\(x,i).(x + (if (x + ~2) <= 0 then 1 else 2)),3,(x + ~2))
A089743: 1 2 3 5 7 9 10 11 12 13 14 15 16 17 18 19
(2x + (if (x mod 2) <= 0 then ((if x <= 0 then 2 else x) div 2) else 0))
A184418: 1 2 5 6 10 10 15 14 20 18 25 22 30 26 35 30
loop(\(x,i).(x + (if x <= 0 then (1 + i) else 0)),x,(~2x + 1))
A057037: 1 1 2 4 2 5 3 1 5 3 1 6 4 2 8 6
(if x <= 0 then 1 else loop(\(x,i).((x + ~2) * (x - i)),2,2x))
A095956: 1 4 16 324
(2x + loop(\(x,i).(x + (if (x - i) <= 0 then x else 0)),x,2))
A171757: 2 4 8 10 16 18 20 22 32 34 36 38 40 42 44 46
loop(\(x,i).(x * i),(x + ~1),loop(\(x,i).x2,2,2x))
A174335: 0 16 256 2592 24576 240000 2488320 27659520 330301440 4232632320 58060800000 850068172800 13243436236800 218892235161600 3827475696844800 70614415872000000
(x - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * i))),x,2x))
A168038: 0 1 4 4 9 9 9 16 16 16 16 25 25 25 25 25
(2x + (if ((if x <= 0 then 1 else x) mod 2) <= 0 then 2 else x2))
A066107: 0 3 6 15 10 35 14 63 18 99 22 143 26 195 30 255
((if (4 mod (if x <= 0 then 1 else x)) <= 0 then 2 else 1) + (x div 2))
A162897: 2 2 3 2 4 3 4 4 5 5 6 6 7 7 8 8
(1 - loop(\(x,i).(~2x + (if x <= 0 then 2 else 0)),x,(x mod 2)))
A086893: 1 3 5 13 21 53 85 213 341 853 1365 3413 5461 13653 21845 54613
loop(\(x,i).(x + (if (x2 mod (2 + i)) <= 0 then 2 else 0)),x,2)
A309195: 2 2 4 4 4 4 6 8 8 8 8 8 8 8 10 10
loop(\(x,i).((x + 1) div 2),x,loop(\(x,i).3x,x,2))
A117590: 2 3 5 7 11 16 23 35 52 77 116 173 260 390 584 876
loop(\(x,i).2x,loop(\(x,i).(x div (1 + (x mod 2))),x,x),2)
A274139: 2 2 8 2 32 8 128 2 512 32 2048 8 8192 128 32768 2
loop(\(x,i).(x * loop(\(x,i).x2,i,(1 + (2 * i)))),x,2)
A191554: 2 18 11250 64854011250 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,loop(\(x,i).(~x2 + ~x + 1),x,2))
A093959: 4 25 361 116281 13441851721 4611686018427387903 4611686018427387903
((x + 2) - loop(\(x,i).((x + ~1) - (if x <= 0 then 0 else i)),x,x))
A166021: 2 4 5 8 9 10 14 15 16 17 22 23 24 25 26 32
(1 - (2 * loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)))
A099375: 1 3 1 5 3 1 7 5 3 1 9 7 5 3 1 11
loop(\(x,i).(x + (loop(\(x,i).2x,i,2) div (1 + i))),x,2)
A000801: 2 4 6 10 16 26 44 76 132 234 420 761 1391 2561 4745 8841
loop(\(x,i).(x * loop(\(x,i).((~x + 3) + i),i,1)),x,2)
A152873: 2 6 12 48 144 720 2880 17280 86400 604800 3628800 29030400 203212800 1828915200 14631321600 146313216000
(2 + loop(\(x,i).(x - ((if (~x + i) <= 0 then i else 0) div 2)),x,x))
A177876: 2 3 3 4
A336751: 2 3 3 4 4 5 4 5 6 5 6 7 5 6 7 8
loop(\(x,i).loop(\(x,i).(x * i),(2 * (1 + (2 * i))),x),x,2)
A294321: 2 1440 5225472000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(x * (2 + i)),(2 * i),2)),x,2)
A138524: 2 26 746 41066 3669866 482671466 87660962666 21010450850666 6423384156578666 2439325392333218666 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * i),(2 + (3 * i)),x),x,2)
A294319: 2 240 9676800 386266890240000 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else ((x2 + 2) + (if (x mod 2) <= 0 then 1 else x)))
A157615: 1 4 7 14 19 32 39 58 67 92 103 134 147 184 199 242
loop(\(x,i).(x * (if (~2 + (x div 3)) <= 0 then 2 else x)),x,2)
A281291: 2 4 8 16 256 65536
((if (x + ~1) <= 0 then 4 else 0) + loop(\(x,i).x2,x,2))
A299030: 6 8 16 256
(loop(\(x,i).x2,x,3) - loop(\(x,i).x2,x,2))
A167536: 1 5 65 6305 42981185 1853015893884545 4611686018427387903 4611686018427387903
(loop(\(x,i).(x * i),x2,2) div loop(\(x,i).(x * i),x,2))
A127223: 1 1 12 60480 871782912000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (x2 div (if i <= 0 then 1 else (i * i)))),x,2)
A061322: 2 6 15 40 140 924 24640 12415040 2408343949440 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(((x + i) * i) div (x + 1)),x,i),x,2)
A000381: 2 3 4 6 9 14 22 35 56 90 145 234 378 611 988 1598
(x * loop(\(x,i).(x + loop(\(x,i).(x * i),i,1)),(x + ~1),0))
A288780: 0 0 2 9 36 165 918 6111 47304 416097 4091130 44417043 527456556 6798432069 94499679582 1408924024695
(x + loop(\(x,i).(x + (if (~x + i) <= 0 then 0 else i)),(x + ~1),0))
A004760: 0 1 3 6 7 12 13 14 15 24 25 26 27 28 29 30
loop(\(x,i).(if x <= 0 then (x + (i * i)) else x),(x + 1),~x)
A253902: 1 4 3 2 1 9 8 7 6 5 4 3 2 1 16 15
loop(\(x,i).(x + (if x <= 0 then 1 else (i * i))),2x,~x)
A172076: 0 1 17 62 150 295 511 812 1212 1725 2365 3146 4082 5187 6475 7960
(if (x mod 2) <= 0 then ((if x <= 0 then 1 else x) + (x div 2)) else ~x)
A280167: 1 ~1 3 ~3 6 ~5 9 ~7 12 ~9 15 ~11 18 ~13 21 ~15
(x + loop(\(x,i).(3 * (if x <= 0 then 3 else x)),x,0))
A301571: 0 10 29 84 247 734 2193 6568 19691 59058 177157 531452 1594335 4782982 14348921 43046736
compr(\x.(x - loop(\(x,i).(~1 + (if x <= 0 then (2 * i) else x)),x,0)),x)
A134025: 0 1 3 4 9 10 11 12 13 27 28 29 30 31 32 33
(x + loop(\(x,i).loop(\(x,i).(2 + (x * i)),x,2),(x + ~1),1))
A274695: 1 2 6 133 4611686018427387903
loop(\(x,i).i,(if (x mod 2) <= 0 then (x mod 6) else 1),x)
A276094: 0 1 2 1 4 1 6 1 2 1 4 1 12 1 2 1
(if x <= 0 then 1 else (x * loop(\(x,i).i,(x + ~8),1)))
A114800: 1 1 2 3 4 5 6 7 8 9 20 33 48 65 84 105
(loop(\(x,i).2x,(x + ~1),1) - (if (x mod 2) <= 0 then 1 else x))
A293046: 0 0 1 1 7 11 31 57 127 247 511 1013 2047 4083 8191 16369
loop(\(x,i).((x + i) div (x + 1)),loop(\(x,i).2x,x,1),x)
A017910: 1 1 2 2 4 5 8 11 16 22 32 45 64 90 128 181
(~x + loop(\(x,i).(2 + (x * loop(\(x,i).x2,i,x))),x,1))
A049333: 1 2 243 4611686018427387903
loop(\(x,i).((if (~2 + i) <= 0 then 1 else x) + (x * i)),(x + 1),x)
A006157: 1 5 28 180 1320 10920 100800 1028160 11491200 139708800 1836172800 25945920000 392302310400 6320426112000 108101081088000 1956280854528000
loop(\(x,i).(x - loop(\(x,i).((x + ~1) * i),i,0)),(x + ~1),x)
A002104: 0 1 3 8 24 89 415 2372 16072 125673 1112083 10976184 119481296 1421542641 18348340127 255323504932
loop(\(x,i).(2x * (if (x + ~2) <= 0 then 2 else i)),(x + ~1),x)
A052656: 0 1 8 24 192 1920 23040 322560 5160960 92897280 1857945600 40874803200 980995276800 25505877196800 714164561510400 21424936845312000
loop(\(x,i).(x * (1 + (if (x + ~2) <= 0 then 2 else i))),(x + ~1),x)
A052655: 0 1 6 18 96 600 4320 35280 322560 3265920 36288000 439084800 5748019200 80951270400 1220496076800 19615115520000
loop(\(x,i).(x * (if (i mod 2) <= 0 then 2 else ~2)),(x + ~1),x)
A118442: 0 1 ~4 ~12 32 80 ~192 ~448 1024 2304 ~5120 ~11264 24576 53248 ~114688 ~245760
(loop(\(x,i).(1 + i - (x * i)),x,0) div (if x <= 0 then 1 else x))
A302190: 0 2 ~1 2 ~6 24 ~120 720 ~5040 40320 ~362880 3628800 ~39916800 479001600 ~6227020800 87178291200
(if x <= 0 then 1 else ((x mod 8) mod (if x <= 0 then 1 else x)))
A263364: 1 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7
(loop(\(x,i).(2x + ~1),(x + ~2),x) + (if x <= 0 then 1 else x))
A222011: 1 2 4 8
A154222: 1 2 4 8 17 38 87 200 457 1034 2315 5132 11277 24590 53263 114704
(loop(\(x,i).(2x + 3),x,x) + (if x <= 0 then 1 else x))
A269059: 1 6 19 48 113 258 579 1284 2821 6150 13319 28680 61449 131082 278539 589836
(x + loop(\(x,i).(x2 + x),1,loop(\(x,i).(x * i),x,1)))
A066084: 2 3 8 45 604 14525 519126 25406647 1625742728 131682257289 13168193068810 1593350962156811 229442533281561612 4611686018427387903 4611686018427387903 4611686018427387903
(x + loop(\(x,i).(x + loop(\(x,i).(2x - i),i,i)),x,1))
A048503: 1 3 8 22 61 165 430 1080 2627 6223 14428 32874 73849 163977 360602 786604
loop(\(x,i).loop(\(x,i).(x + (2 * (i * i)) - i),x,0),2,x)
A329755: 0 1 252 7337 84575 576080 2795121 10700382 34388362 96606475 243939410 564840991 1217275137 2469392562 4757404575 8765621740
loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,x)
A329424-A106610: 0 1 2 1 4 5 2 7 8 1 10 11 4 13 14 5
loop(\(x,i).(if (x mod 2) <= 0 then (x div 4) else (x + ~1)),2,x)
A035663: 0 0 0 0 0 1 0 1 0 2 0 2 2 3 2 3
compr(\x.((1 + loop(\(x,i).loop(\(x,i).(~x + i),x,x),x,x)) mod 2),x)
A201363: 2 3 7
A338691: 2 3 7 8 10 11 12 15 18 19 23 26 27 28 31 32
loop(\(x,i).((~x + 2) + (if x <= 0 then 1 else 2)),8,x)
A275974: 1 1 2 3 3 3 3 3 4 5 6 7 8 9 10 11
loop(\(x,i).x2,1,(x + (if (x + ~2) <= 0 then 1 else 4)))
A164839: 1 4 9 49 64 81
(x + (if x <= 0 then 0 else (if (x + ~2) <= 0 then 1 else (2x + ~4))))
A271876: 0 2 3 5 8 11 14 17 20
loop(\(x,i).(i - (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),2,x)
A195508: 1 2 3 1 5 6 1 8 9 1 11 2 1 14 15 1
loop(\(x,i).(x + (if ((x div 4) - i) <= 0 then 1 else 2)),2,x)
A121603: 2 3 4 5 6 7 8 9 11
A099649: 2 3 4 5 6 7 8 9 11 12 14 15 16 17 18 19
loop(\(x,i).loop(\(x,i).(x - ((x div 2) div (1 + i))),2,x),2,x)
A189721: 0 1 2 3 3 3 4 4 4 5 5 5 5 6 7 7
compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x + 2)),x)
A153167: 2 4 6 7 8 10 12 13 14 16 18 19 20 22 23 24
(if x <= 0 then 1 else loop(\(x,i).(2 * (i * i * i)),(x + ~2),x))
A001119: 1 1 2 2 16 54
loop(\(x,i).(x2 * (if (x mod 2) <= 0 then x else 1)),(x + ~2),x)
A132859: 0 1 2 9 262144
loop(\(x,i).(if (x mod 2) <= 0 then (x + (2 * i)) else 2),(x div 2),x)
A193422: 0 1 4 2 10 6 18 12 28 20 40 30 54 42 70 56
((if (~2 + (x div 4)) <= 0 then 1 else 2) mod (if x <= 0 then 2 else x))
A109038: 1 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2
loop(\(x,i).(x2 * loop(\(x,i).x2,(1 + i),x)),2,x)
A276377: 0 1 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,x,1) - loop(\(x,i).x3,2,x))
A024019: 1 1 ~508 ~19675 ~262128 ~1953093 ~10077632 ~40353479 ~134217472 ~387419977 ~999998976 ~2357945643 ~5159776256 ~10604491181 ~20661030400 ~38443326607
(loop(\(x,i).(x * i),x,1) - loop(\(x,i).x3,2,x))
A144768: 1 0 ~510 ~19677 ~262120 ~1953005 ~10076976 ~40348567 ~134177408 ~387057609 ~996371200 ~2318030891 ~4680778752 ~4377478573 66517244416 1269231008625
(2 - loop(\(x,i).loop(\(x,i).((x + 2) mod (1 + i)),x,0),x,x))
A142242: 2 2 0 2 0 0 ~4 2 0 0 ~4 0 ~4 ~4 ~12 2
loop(\(x,i).2x,(x + ~1),loop(\(x,i).(2x + ~1),x,x))
A192021: 0 1 10 68 392 2064 10272 49216 229504 1048832 4719104 20972544 92276736 402657280 1744838656 7516209152
(x - loop(\(x,i).((x + ~1) - (2 * (if x <= 0 then 0 else i))),x,x))
A161983: 0 3 4 5 10 11 12 13 14 21 22 23 24 25 26 27
(1 - loop(\(x,i).(x - (if (~x + 2) <= 0 then (2 + i) else 1)),x,x))
A171601: 1 1 3 3 3 6 6 6 6 10 10 10 10 10 15 15
(x - loop(\(x,i).((x + 1) - (if x <= 0 then 1 else (2 * i))),x,x))
A048761: 0 1 4 4 4 9 9 9 9 9 16 16 16 16 16 16
compr(\x.(~x + loop(\(x,i).(~1 + (if x <= 0 then (2 * i) else x)),x,1)),x)
A095028: 1 3 4 5 9
A132141: 1 3 4 5 9 10 11 12 13 14 15 16 17 27 28 29
compr(\x.(loop(\(x,i).(2x + ~2),x,1) mod (if x <= 0 then 1 else x)),x)
A158611: 0 1 2 3 5 7 11 13 17 19 23 29 31 37 41 43
compr(\x.(loop(\(x,i).(~2x + 4),x,2) mod (if x <= 0 then 1 else x)),x)
A335402: 0 1 2 4 5 7 11 13 17 19 23 29 31 37 41 43
(if x <= 0 then 1 else (x * loop(\(x,i).(2x + ~1),(x + ~2),x)))
A003013: 1 1 4 15 52 165 486 1351 3592 9225 23050 56331 135180 319501 745486 1720335
(x * loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),(x + ~2),x))
A103164: 0 1 4 9 4 25 6 49 8 9 10 121 12 169 14 15
(loop(\(x,i).3x,x,x) - loop(\(x,i).2x,x,x))
A004142: 0 1 10 57 260 1055 3990 14413 50440 172539 580250 1926089 6328140 20619703 66732190 214742085
(x + loop(\(x,i).(~x + (if (~x + i) <= 0 then i else 0)),2x,x))
A094761: 0 1 3 5 4 6 8 10 12 9 11 13 15 17 19 21
loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,x)
A005430: 0 2 12 60 280 1260 5544 24024 102960 437580 1847560 7759752 32449872 135207800 561632400 2326762800
loop(\(x,i).(x - (x div (2 + (if (x mod 2) <= 0 then 2 else i)))),x,x)
A331135: 0 1 2 2 3 3 3 3 3 3 5 5 5 5 5 5
loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),2x,x2)
A076816: 0 0 1 3 1 4 0 4 9 3 9 1 8 16 6 15
(loop(\(x,i).2x,x,1) - loop(\(x,i).x2,2,x2))
A024018: 1 1 ~252 ~6553 ~65520 ~390593 ~1679552 ~5764673 ~16776960 ~43046209 ~99998976 ~214356833 ~429977600 ~815722529 ~1475772672 ~2562857857
(loop(\(x,i).(x * i),x,1) - loop(\(x,i).x2,2,x2))
A196738: 1 0 ~254 ~6555 ~65512 ~390505 ~1678896 ~5759761 ~16736896 ~42683841 ~96371200 ~174442081 49019904 5411290079 85702502144 1305111477375
compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,x),x)
A005823: 0 2 6 8 18 20 24 26 54 56 60 62 72 74 78 80
loop(\(x,i).(x + (2 * (x + (if (2 - i) <= 0 then x else 1)))),x,x)
A229279: 0 5 40 275 1750 10625 62500 359375 2031250 11328125 62500000 341796875 1855468750 10009765625 53710937500 286865234375
compr(\x.loop(\(x,i).(if (x mod 4) <= 0 then x else (x div 2)),x,x),x)
A003754: 0 1 2 3 5 6 7 10 11 13 14 15 21 22 23 26
loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,x)
A174002: 0 5 30 105 280 630 1260 2310 3960 6435 10010 15015 21840 30940 42840 58140
(if (~1 + (x mod 11)) <= 0 then 1 else 0)
A339627: 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0
(if (~1 + (x mod (3 + (x div 3)))) <= 0 then 1 else 0)
A068434: 1 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0
(if (x mod (1 + (x mod 9))) <= 0 then 1 else 0)
A025924: 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0
(if (x mod (1 + ((x + 2) div 5))) <= 0 then 1 else 0)
A240025: 1 1 1 0 1 0 1 0 0 1 0 0 1 0 0 0
(if ((x + 1) mod (1 + (x div 5))) <= 0 then 1 else 0)
A336477: 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1
(if (x mod (1 + (2 mod (1 + (x div 4))))) <= 0 then 1 else 0)
A328306: 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1
(if (x mod (1 + (((x + 1) div 2) div 3))) <= 0 then 1 else 0)
A345950-A122895: 1 1 1 1 1 0 1 0 1 0 1 0 1 0 0 1
(if ((x * (x div 2)) mod (1 + (x mod 3))) <= 0 then 1 else 0)
A136442: 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0 1
(if (~1 + ((3x + ~6) mod (x + 1))) <= 0 then 1 else 0)
A093709: 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0
(if ((x + ~1) mod (1 + (4 mod (x + 1)))) <= 0 then 1 else 0)
A155972: 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0
(if (x mod (3 + ((x + ~1) mod 3))) <= 0 then 1 else 0)
A341024-A287457-A127842: 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
(if (x mod (1 + (2 * (2x mod 3)))) <= 0 then 1 else 0)
A164704: 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1
(if (x mod (3 + ((x div 2) div 3))) <= 0 then 1 else 0)
A318983-A318982-A102448-A065803-A035153: 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1
(if (x mod (1 + (2 * ((x div 2) mod 3)))) <= 0 then 1 else 0)
A153778: 1 1 0 1 0 1 1 1 0 1 1 0 1 1 0 1
(if (2 - (2x mod 7)) <= 0 then 1 else 0)
A095770: 0 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1
(if ((x + 1) mod (1 + (x mod 6))) <= 0 then 1 else 0)
A279693-A225542: 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1
(if (x mod (3 + ((~x + 1) mod 3))) <= 0 then 1 else 0)
A338211-A281455: 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0
(if (x mod (2 - (x mod ~5))) <= 0 then 1 else 0)
A266243: 1 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0
(if (x mod (1 + (2 * (x mod 6)))) <= 0 then 1 else 0)
A277264-A127840: 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0
(if (~1 + (x mod (4 + (x div 4)))) <= 0 then 1 else 0)
A298246: 1 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1
(if ((x2 + ~2x) mod 9) <= 0 then 1 else 0)
A281458: 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0
(if (x mod (~1 + (2 * (~x mod 4)))) <= 0 then 1 else 0)
A285621: 1 0 0 1 1 1 1 1 1 0 0 1 1 0 0 1
(if ((x + ~2) mod (~1 + (2 * (x mod 4)))) <= 0 then 1 else 0)
A261092-A145362: 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0
(if (2x mod (x + 7)) <= 0 then 1 else 0)
A156297: 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
(if (~1 + (2x mod (4 + (x div 2)))) <= 0 then 1 else 0)
A293449: 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0
(if ((x div 2) mod (5 + (x mod 2))) <= 0 then 1 else 0)
A281815: 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0
(if ((x + ~1) mod (1 + (2 * (2 + (x mod 2))))) <= 0 then 1 else 0)
A288673: 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1
(if ((x + ~2) mod (1 + (2 * (2 + (x mod 2))))) <= 0 then 1 else 0)
A188371: 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0
(if ((x + 1) mod (1 + ((x div 2) mod 4))) <= 0 then 1 else 0)
A087429: 1 1 0 1 0 1 0 1 1 1 0 1 0 0 0 1
(if (((x + 1) * (x div 2)) mod 5) <= 0 then 1 else 0)
A216577: 1 1 0 0 1 0 0 0 0 1 1 1 0 0 1 0
(if ((x - (x div ~2)) mod 5) <= 0 then 1 else 0)
A281457: 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0
(if ((x - (x div 4)) mod 5) <= 0 then 1 else 0)
A281245: 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0
(if (((x + ~2) + (x div 2)) mod 5) <= 0 then 1 else 0)
A269245: 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1
(if (~1 + ((x mod 2) + (x mod 5))) <= 0 then 1 else 0)
A333817: 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1
(if (x mod ((x + 1) div (1 + (x div 4)))) <= 0 then 1 else 0)
A206567-A203945: 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0
(if (x - (x2 mod (x + 5))) <= 0 then 1 else 0)
A085357: 1 1 1 0 1 1 0 0 1 1 1 0 0 0 0 0
(if (~1 + ((2x + ~2) mod (2 + (x div 2)))) <= 0 then 1 else 0)
A254634-A108336: 1 1 0 1 0 1 1 0 0 0 0 0 0 1 0 1
(if ((x + 2) mod (1 + (x mod (2 + (x div 2))))) <= 0 then 1 else 0)
A089012: 1 0 0 1 1 0 1 1 0 0 1 0 0 0 0 0
(if ((x + 1) mod (1 + (x div (2 + (x mod 2))))) <= 0 then 1 else 0)
A322586-A147612: 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0
(if (x mod (3 * (1 + (x div 4)))) <= 0 then 1 else 0)
A024692: 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0
(if (x mod ((x + 3) - (x div 3))) <= 0 then 1 else 0)
A025923-A017878: 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0
(if ((x - (2 mod (1 + (x div 2)))) mod 3) <= 0 then 1 else 0)
A299196: 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0
(if (((x + ~1) * (x mod 4)) mod 3) <= 0 then 1 else 0)
A285568: 1 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1
(if ((x mod 10) mod 3) <= 0 then 1 else 0)
A306383: 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0
(if (((x + 2) mod 8) mod 3) <= 0 then 1 else 0)
A286654-A285205-A188034-A003849: 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0
(if (x mod (3 * (2 - ((x div 2) mod 2)))) <= 0 then 1 else 0)
A070563-A037011: 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1
(if (((x * (~1 + (x div 2))) div 2) mod 3) <= 0 then 1 else 0)
A082960: 1 0 1 1 0 0 1 0 1
A266502: 1 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1
(if ((x mod 4) - (2x mod 3)) <= 0 then 1 else 0)
A285345: 1 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0
(if (x - (((x div 2) * (x div 2)) div 3)) <= 0 then 1 else 0)
A185364-A058276: 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1
(if ((x + ((x div 2) div 3)) mod 3) <= 0 then 1 else 0)
A281271: 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0
(if (x mod (8 - (x div 3))) <= 0 then 1 else 0)
A307897-A008651: 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1
(if ((x mod 8) - (x div 3)) <= 0 then 1 else 0)
A017870: 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0
(if (x mod 5) <= 0 then (~1 + (x mod 3)) else 0)
A095408: ~1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ~1
(if ((x + ~5) mod (1 + (x div 2))) <= 0 then 1 else 0)
A197183: 1 1 0 1 0 1 0 0 0 0 0 1 1 0 0 0
(if ((2x + ~5) mod (1 + (x div 2))) <= 0 then 1 else 0)
A113047: 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0
(if ((4x + 1) mod (1 + (x div 2))) <= 0 then 1 else 0)
A255849: 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0
(if ((2 - ((~1 + (x div 2)) div 2)) mod (x + 1)) <= 0 then 1 else 0)
A017889: 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0
(if (2 - (16 mod (x + 1))) <= 0 then 1 else 0)
A236192: 0 0 0 0 0 1 1 0 1 1 1 1 1 1 0 0
(if (x + ~2) <= 0 then (4x2 + ~4x + 1) else 0)
A226121: 1 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0
((x + 12) - (if (x + ~1) <= 0 then 1 else 0))
A247849: 11 12 14 15 16 17
(if ((x + ~1) mod (2 - ((x div 2) div ~2))) <= 0 then 1 else 0)
A179828: 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0
(if ((x + ~2) mod (4 - (x div ~2))) <= 0 then 1 else 0)
A030565: 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0
(if ((~x + 4) mod (2 - (x div ~2))) <= 0 then 1 else 0)
A127692: 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0
(if (~2 + (x2 mod 7)) <= 0 then 1 else 0)
A080764: 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1
(if (x mod (2 + ((x + 1) mod 5))) <= 0 then 1 else 0)
A086071: 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1
(if ((x + 2) mod (2 + (x div 5))) <= 0 then 1 else 0)
A088517: 1 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0
(if (x mod ((x + 2) - (x div 5))) <= 0 then 1 else 0)
A017890: 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0
(if (x2 mod (2 + (x mod 5))) <= 0 then 1 else 0)
A108340: 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0
(if ((x + ~2) mod (2 * (1 + (x div 4)))) <= 0 then 1 else 0)
A088917: 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0
(if (((x + ~1) mod (3 + (x div 2))) div 2) <= 0 then 1 else 0)
A270803: 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0
(if ((x - ((x div 2) mod 2)) mod 6) <= 0 then 1 else 0)
A059117: 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0
(if ((2x + 2) mod (2 + (x div 3))) <= 0 then 1 else 0)
A115356: 1 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0
(if (x mod 4) <= 0 then (1 + ((x div 3) mod 2)) else 0)
A258059: 1 0 0 0 2 0 0 0 1 0 0 0 1 0 0 0
(if (~x + 2) <= 0 then (1 + (2 * (3 - (x mod 2)))) else 0)
A021136: 0 0 7 5 7 5 7 5 7 5 7 5 7 5 7 5
(if (((2x + ~8) mod (x + 1)) div 2) <= 0 then 1 else 0)
A324822-A220945-A062892: 1 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0
(if ((x mod 3) - ((x div ~2) mod 2)) <= 0 then 1 else 0)
A055088: 1 1 0 1 0 0 1 0 0 1 1 0 1 1 0 1
(if (~2 + ((x + 2) mod 10)) <= 0 then 1 else 0)
A025918-A017868: 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0
(if (2x mod (2 + (x mod 6))) <= 0 then 1 else 0)
A267525: 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 1
(if (~2 + (2x mod (2 + (x div 3)))) <= 0 then 1 else 0)
A336546: 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1
(if (~2 + (x mod (2 - (x mod ~4)))) <= 0 then 1 else 0)
A334465-A137794: 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1
(if (2 + ((x + 2) mod ~7)) <= 0 then 1 else 0)
A285403: 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1
(if (2 + (2x mod ~7)) <= 0 then 1 else 0)
A286746: 0 1 1 0 1 1 1 0 1 1 0 1 1 1 0 1
(if (x mod (2 + ((x + 2) mod 8))) <= 0 then 1 else 0)
A267463: 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1
(if (~2 + ((x + (x div 2)) mod 8)) <= 0 then 1 else 0)
A280454: 1 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0
(if (2x mod (4 + (x div 4))) <= 0 then 1 else 0)
A320841-A261477-A023531: 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0
(if (x mod (2 + (x mod (2 * (2 + (x mod 2)))))) <= 0 then 1 else 0)
A181923: 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1
(if (~2 + (x mod (x - ((x + 1) mod 4)))) <= 0 then 1 else 0)
A334946-A225595: 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1
(if ((x * (2 + (x div 2))) mod 8) <= 0 then 1 else 0)
A343870-A339070-A091006: 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0
(if (x mod 3) <= 0 then (1 + (x div 8)) else 0)
A341793-A341792-A341791-A341778-A341777-A341776-A341773: 1 0 0 1 0 0 1 0 0 2 0 0 2 0 0 2
(if (~2 + ((~x + ((~x + 2) div 2)) mod 4)) <= 0 then 1 else 0)
A188433: 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1
(if (x mod 4) <= 0 then (1 + ((x div 4) mod 2)) else 0)
A126812-A008442: 1 0 0 0 2 0 0 0 1 0 0 0 2 0 0 0
(if (x mod (2 + (x2 mod (x + 4)))) <= 0 then 1 else 0)
A116857: 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0
(if ((x + ~3) mod (4 + (x div 2))) <= 0 then 1 else 0)
A030585: 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0
(if ((((~x + 1) div 2) mod (x + 1)) mod 4) <= 0 then 1 else 0)
A281082: 1 1 0 0 0 1 1 0 0 0 0 0 0 1 1 0
(if ((x mod 3) - ((x + 1) mod 4)) <= 0 then 1 else 0)
A143104: 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1
(if ((x - (x div 8)) mod 4) <= 0 then 1 else 0)
A303947-A280129-A111900: 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0
(if (((x2 div 2) mod (x + 2)) mod 4) <= 0 then 1 else 0)
A183919: 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0
(x - (if (x mod 2) <= 0 then ((x div 2) mod 5) else 0))
A107128: 0 1 1 3 2 5 3 7 4 9 10 11 11 13 12 15
(if (x mod 4) <= 0 then (1 - (x div 5)) else 0)
A016343-A016328-A016289-A016193-A016049-A015857-A015569-A015329-A014849-A014033: 1 0 0 0 1 0 0 0 0 0 0 0 ~1 0 0 0
(if ((x + (x div 8)) mod 4) <= 0 then 1 else 0)
A281456: 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1
(if ((x div 4) - ((~x + 2) mod 4)) <= 0 then 1 else 0)
A190230: 1 1 1 1 1 1 0 1 1 0 0 1 0 0 0 1
loop(\(x,i).(x + i),(1 + ((x * (x mod 2)) div 4)),0)
A236939-A236936-A236915-A236865: 1 1 1 1 1 3 1 3 1 6 1 6 1 10 1 10
(if (x mod 2) <= 0 then ((x + ~2) mod (1 + (x div 4))) else 0)
A342121: 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0
(if (x mod 2) <= 0 then ((~x + 2) mod (1 + (x div 4))) else 0)
A100951: 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0
(if ((2x mod 3) - (x mod 4)) <= 0 then 1 else 0)
A239302-A105806: 1 0 1 1 0 1 1 1 0 1 1 1 1 0 1 1
(if ((x2 mod ((x + 2) + (x div 2))) div 2) <= 0 then 1 else 0)
A133100: 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0
(if ((x + 1) mod (2 + (3 mod (x + 2)))) <= 0 then 1 else 0)
A339367: 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0
(if (x mod (2 * (8 - (x div 2)))) <= 0 then 1 else 0)
A324917: 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0
(if ((x2 + 2x + 1) mod (2 + (x div 2))) <= 0 then 1 else 0)
A010058: 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0
(if ((4x + 2) mod (2 + (x div 2))) <= 0 then 1 else 0)
A214263: 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0
(if ((x2 + (x mod 2)) mod (2 + (x div 2))) <= 0 then 1 else 0)
A216230: 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0
(if (x mod 5) <= 0 then (1 + ((x div 2) mod 2)) else 0)
A001343: 1 0 0 0 0 1 0 0 0 0 2 0 0 0 0 2
(if ((x + 2) mod 9) <= 0 then 3 else 0)
A280051: 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0
loop(\(x,i).(x + i),((x div 2) - ((x + ~1) div 3)),0)
A025796: 1 0 1 1 1 1 3 1 3 3 3 3 6 3 6 6
(if ((x + 1) mod 5) <= 0 then (x div 3) else 0)
A097017: 0 0 0 0 1 0 0 0 0 3 0 0 0 0 4 0
(if (x mod 5) <= 0 then (1 - (x mod 3)) else 0)
A015284-A014984-A014834-A014534: 1 0 0 0 0 ~1 0 0 0 0 0 0 0 0 0 1
loop(\(x,i).(x + (((1 + i) div 2) * i)),(2x + 1),0)
A051662: 1 9 32 78 155 271 434 652 933 1285 1716 2234 2847 3563 4390 5336
(if (((x + 2) mod 6) * (x div 2)) <= 0 then 1 else 0)
A023533-A014305: 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0
(if (x2 mod (8 + (x div 2))) <= 0 then 1 else 0)
A340851-A178665: 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1
(if ((x + 1) mod 8) <= 0 then (~1 + (x div 2)) else 0)
A282530: 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 6
(if (~x + (2 * (2 + ((x + 2) mod 4)))) <= 0 then 1 else 0)
A218754: 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1
(if (x * ((x + 3) mod 8)) <= 0 then 1 else 0)
A205809-A024941: 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0
(if (x - (x2 mod (x + 8))) <= 0 then 1 else 0)
A229429-A166360: 1 1 1 1 1 1 1 0 0 1 1 0 0 0 1 1
(if (~x + (x2 mod (x - ((~x + 2) div 2)))) <= 0 then 1 else 0)
A175860: 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1
loop(\(x,i).(6x + 7),(x + 1),0)
A146884: 7 49 301 1813 10885 65317 391909 2351461 14108773 84652645 507915877 3047495269 18284971621 109709829733 658258978405 3949553870437
loop(\(x,i).(5 * (2x + i)),(x + 1),0)
A099672: 5 60 615 6170 61725 617280 6172835 61728390 617283945 6172839500 61728395055 617283950610 6172839506165 61728395061720 617283950617275 6172839506172830
(if ((x + 1) mod (1 + (x div 4))) <= 0 then (x + 1) else 0)
A065332: 1 2 3 4 0 6 0 8 9 0 0 12 0 0 0 16
(if ((x + 1) mod 12) <= 0 then (x + 1) else 0)
A308425-A187795: 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0
loop(\(x,i).((x + ~1) + (4 * (i * i))),(x + 1),0)
A268484: 3 18 53 116 215 358 553 808 1131 1530 2013 2588 3263 4046 4945 5968
(if (16 mod (x + 1)) <= 0 then (x + 1) else 0)
A099894: 1 2 0 4 0 0 0 8 0 0 0 0 0 0 0 16
loop(\(x,i).(2 * (x + (4 * (x + i)))),(x + 1),0)
A099675: 8 96 984 9872 98760 987648 9876536 98765424 987654312 9876543200 98765432088 987654320976 9876543209864 98765432098752 987654320987640 9876543209876528
loop(\(x,i).(2 * (x + (2 * (2x + i)))),(x + 1),0)
A099671: 4 48 492 4936 49380 493824 4938268 49382712 493827156 4938271600 49382716044 493827160488 4938271604932 49382716049376 493827160493820 4938271604938264
loop(\(x,i).(3x + (i * i * i)),(x + 1),0)
A066999: 1 11 60 244 857 2787 8704 26624 80601 242803 729740 2190948 6575041 19727867 59186976 177565024
loop(\(x,i).(x + (3 * (x + (i mod 2)))),(x + 1),0)
A043291: 3 12 51 204 819 3276 13107 52428 209715 838860 3355443 13421772 53687091 214748364 858993459 3435973836
loop(\(x,i).(7x + 8),(x + 1),0)
A146885: 8 64 456 3200 22408 156864 1098056 7686400 53804808 376633664 2636435656 18455049600 129185347208 904297430464 6330082013256 44310574092800
loop(\(x,i).(x + ((~1 + i) mod 6)),(x + 1),0)
A130484: 0 1 3 6 10 15 15 16 18 21 25 30 30 31 33 36
loop(\(x,i).(x + (((2 + i) * (1 + i)) div 2)),(x + 1),0)
A062748: 3 9 19 34 55 83 119 164 219 285 363 454 559 679 815 968
loop(\(x,i).(x + ((~1 + i) mod 8)),(x + 1),0)
A130486: 0 1 3 6 10 15 21 28 28 29 31 34 38 43 49 56
loop(\(x,i).(x + ((1 + (2 * i)) * i * i)),(x + 1),0)
A024196: 3 23 86 230 505 973 1708 2796 4335 6435 9218 12818 17381 23065 30040 38488
((x mod 2) - loop(\(x,i).(2x + ~3),(x + ~1),0))
A192033: 0 1 3 10 21 46 93 190 381 766 1533 3070 6141 12286 24573 49150
(if ((x + ~1) mod 9) <= 0 then (x + ~1) else 0)
A193581: 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0
(if ((x + 2) mod 9) <= 0 then (x + ~1) else 0)
A331428: 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0
(1 - loop(\(x,i).(2 * (x - ((i div 2) mod 2))),(x + ~1),0))
A078000-A007909: 1 1 1 3 7 13 25 51 103 205 409 819 1639 3277 6553 13107
(1 - loop(\(x,i).(2 * (x - (2 * (i mod 2)))),(x + ~1),0))
A097074: 1 1 5 9 21 41 85 169 341 681 1365 2729 5461 10921 21845 43689
(1 + loop(\(x,i).(2x + 4),(x + ~1),0) - (x mod 2))
A283506: 1 0 5 12 29 60 125 252 509 1020 2045 4092 8189 16380 32765 65532
((x mod 2) - loop(\(x,i).(2 * (x + (i mod 2))),(x + ~1),0))
A083944: 0 1 ~2 ~3 ~10 ~19 ~42 ~83 ~170 ~339 ~682 ~1363 ~2730 ~5459 ~10922 ~21843
loop(\(x,i).(2x + ((x + 1) * (i mod 2))),(x + ~1),0)
A329115: 0 0 1 2 7 14 43 86 259 518 1555 3110 9331 18662 55987 111974
loop(\(x,i).(x + (4 * (2x + i))),(x + ~1),0)
A002754: 0 0 4 44 408 3688 33212 298932 2690416 24213776 217924020 1961316220 17651846024 158866614264 1429799528428 12868195755908
((4x2 + 8x + 4) + (if x <= 0 then 1 else 0))
A184635: 5 16 36 64 100 144 196 256 324 400 484 576 676 784 900 1024
((16x + 4) + (if x <= 0 then 1 else 0))
A063110: 5 20 36 52 68 84 100 116 132 148 164 180 196 212 228 244
((4x2 + 8x + 8) - (if x <= 0 then 1 else 0))
A162024: 7 20 40 68 104 148 200 260 328 404 488 580 680 788 904 1028
(x + (2 * (2 + (x div 4))) - (if x <= 0 then 1 else 0))
A154663: 3 5 6 7 10 11
(x - (if ((x + 2) mod 9) <= 0 then 2 else 0))
A331173: 0 1 2 3 4 5 6 5 8 9 10 11 12 13 14 15
(x - (if (x mod 2) <= 0 then (x mod 10) else 0))
A210524: 0 1 0 3 0 5 0 7 0 9 10 11 10 13 10 15
(if ((x + 2) mod 8) <= 0 then 6 else 0)
A323487: 0 0 0 0 0 0 6 0 0 0 0 0 0 0 6 0
loop(\(x,i).(3x + 8),(2x + 2),0)
A173952: 32 320 2912 26240 236192 2125760 19131872 172186880 1549681952 13947137600 125524238432 1129718145920 10167463313312 91507169819840 823564528378592 7412080755407360
(x - loop(\(x,i).i,(~2 + (x mod 10)),0))
A171818: 0 1 2 2 2 2 2 2 2 2 10 11 12 12 12 12
(2 - (if (x mod 2) <= 0 then (~2 + ((x mod 3) div 2)) else 0))
A291357: 4 2 3 2 4 2 4 2 3 2 4 2 4 2 3 2
(if (x mod 3) <= 0 then ((x div ~4) mod 2) else 0)
A024889: 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0
(1 - (if ((x + ~4) mod 8) <= 0 then 2 else 0))
A156608: 1 1 1 1 ~1 1 1 1 1 1 1 1 ~1 1 1 1
(1 - (if ((x + 1) mod (4 + (x div 2))) <= 0 then 2 else 0))
A157895: 1 1 1 1 1 ~1 ~1 1 1 1 1 1 1 1 1 1
(if (x mod 4) <= 0 then (x mod (2 + (x div 4))) else 0)
A334348-A331902-A257685: 0 0 0 0 1 0 0 0 0 0 0 0 2 0 0 0
(x - (if ((x2 + 1) mod (x + 4)) <= 0 then 2 else 0))
A103303: 0 1 2 3 4 5 6 7 8 9
A331166: 0 1 2 3 4 5 6 7 8 9 10 11 12 11 14 15
(1 - (if ((x + 1) mod 5) <= 0 then 4 else 0))
A291568: 1 1 1 1 ~3 1 1 1 1 ~3 1 1 1 1 ~3 1
(if ((x + 1) mod 12) <= 0 then 4 else 0)
A318679-A308429-A308428-A308426-A089371: 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
loop(\(x,i).(5x + 1),(2x + 4),0)
A275766: 156 3906 97656 2441406 61035156 1525878906 38146972656 953674316406 23841857910156 596046447753906 14901161193847656 372529029846191406 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if ((x + 1) mod 8) <= 0 then (~2 + (x div 2)) else 0)
A068385: 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 5
(if ((x + 2) mod (2 + (x mod 2))) <= 0 then (2 * (x div 2)) else 0)
A046666: 0 0 2 0 4 0 6 6 8 0 10 0 12 12 14 0
(if (x mod 5) <= 0 then (1 - (2 * (x mod 2))) else 0)
A014359: 1 0 0 0 0 ~1 0 0 0 0 1 0 0 0 0 ~1
(if (~1 + (x div 4)) <= 0 then (1 - (2 * (x mod 2))) else 0)
A292560: 1 ~1 1 ~1 1 ~1 1 ~1 0 0 0 0 0 0 0 0
(if (x + ~6) <= 0 then (1 - (2 * (x mod 2))) else 0)
A015171-A015115-A015031-A015003-A014947-A014863-A014835-A014751-A014667-A014611-A014583-A014527-A014443-A014415-A014331-A014275-A014247: 1 ~1 1 ~1 1 ~1 1 0 0 0 0 0 0 0 0 0
((3x2 + 3x) + (if (x mod 2) <= 0 then 2 else 0))
A202963: 2 6 20 36 62 90 128 168 218 270 332 396 470 546 632 720
((2x2 + 3x + 1) + (if (x mod 2) <= 0 then 2 else 0))
A235088: 3 6 17 28 47 66 93 120 155 190 233 276 327 378 437 496
(if (x * (((~1 + (x div 2)) div 3) mod 2)) <= 0 then 2 else 0)
A089582: 2 0 2 2 2 2 2 2 0 0 0 0 0 0 2 2
(if ((x + 2) mod 9) <= 0 then (x + 2) else 0)
A270034: 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0
loop(\(x,i).((x + 2) + (((1 + i) * i) div 2)),(x + 2),0)
A255993: 8 16 28 45 68 98 136 183 240 308 388 481 588 710 848 1003
(if (x mod 4) <= 0 then ((2 - (x div 2)) div (x + 2)) else 0)
A321376: 1 0 0 0 0 0 0 0 ~1 0 0 0 ~1 0 0 0
(if ((x + ~2) mod 12) <= 0 then (x + ~2) else 0)
A340362: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0
loop(\(x,i).((x + 1) mod (2 + (i div 3))),(x + ~2),0)
A255120: 0 0 0 1 0 1 2 0 1 2 3 4 0 1 2 3
(1 - loop(\(x,i).(2 * (x + (2 * (i mod 2)))),(x + ~2),0))
A173114: 1 1 1 ~3 ~7 ~19 ~39 ~83 ~167 ~339 ~679 ~1363 ~2727 ~5459 ~10919 ~21843
loop(\(x,i).(10x + 1),2x,0)
A099814: 0 11 1111 111111 11111111 1111111111 111111111111 11111111111111 1111111111111111 111111111111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 11) <= 0 then (x div 2) else 0)
A048894: 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0
((x mod 2) - loop(\(x,i).(4x + ~4),(x div 2),0))
A080610: 0 1 4 5 20 21 84 85 340 341 1364 1365 5460 5461 21844 21845
(0 - (x mod (1 - (if (x mod 4) <= 0 then (x div 2) else 0))))
A160086: 0 0 0 0 0 0 0 0 1 0 0 0 3 0 0 0
((x mod 2) - loop(\(x,i).(3x + ~2),(x div 2),0))
A030439: 0 1 2 3 8 9 26 27 80 81 242 243 728 729 2186 2187
(if ((2x div 3) mod 3) <= 0 then (x mod 2) else 0)
A324964: 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0
((2x + 17) - (if x <= 0 then 2 else 0))
A224535: 15 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47
loop(\(x,i).(10x + 6),x,0)
A073549-A002280: 0 6 66 666 6666 66666 666666 6666666 66666666 666666666 6666666666 66666666666 666666666666 6666666666666 66666666666666 666666666666666
loop(\(x,i).(20x + 1),x,0)
A064108: 0 1 21 421 8421 168421 3368421 67368421 1347368421 26947368421 538947368421 10778947368421 215578947368421 4311578947368421 86231578947368421 1724631578947368421
loop(\(x,i).(18x + 1),x,0)
A218721: 0 1 19 343 6175 111151 2000719 36012943 648232975 11668193551 210027483919 3780494710543 68048904789775 1224880286215951 22047845151887119 396861212733968143
loop(\(x,i).(24x + 1),x,0)
A218727: 0 1 25 601 14425 346201 8308825 199411801 4785883225 114861197401 2756668737625 66160049703001 1587841192872025 38108188628928601 914596527094286425 4611686018427387903
(1 - loop(\(x,i).(12x + ~1),x,0))
A196791: 1 2 14 158 1886 22622 271454 3257438 39089246 469070942 5628851294 67546215518 810554586206 9726655034462 116719860413534 1400638324962398
loop(\(x,i).(9x + 5),x,0)
A125962: 0 5 50 455 4100 36905 332150 2989355 26904200 242137805 2179240250 19613162255 176518460300 1588666142705 14297995284350 128681957559155
(1 - loop(\(x,i).(9x + ~1),x,0))
A047854: 1 2 11 92 821 7382 66431 597872 5380841 48427562 435848051 3922632452 35303692061 317733228542 2859599056871 25736391511832
loop(\(x,i).((x + 1) - (x div (~3 - i))),x,0)
A279539: 0 1 3 5 7 9 11 14 17 20 23 26 29 32 35 38
loop(\(x,i).((~2x + 2) mod 7),x,0)
A021043: 0 2 5 6 4 1 0 2 5 6 4 1 0 2 5 6
loop(\(x,i).(1 + (2 * (x2 div (1 + (x div 2))))),x,0)
A088110: 0 1 3 9
A084508: 0 1 3 9 33 129 513 2049 8193 32769 131073 524289 2097153 8388609 33554433 134217729
loop(\(x,i).(10x + 3),x,0)
A002277: 0 3 33 333 3333 33333 333333 3333333 33333333 333333333 3333333333 33333333333 333333333333 3333333333333 33333333333333 333333333333333
loop(\(x,i).(32x + 1),x,0)
A132469: 0 1 33 1057 33825 1082401 34636833 1108378657 35468117025 1134979744801 36319351833633 1162219258676257 37191016277640225 1190112520884487201 4611686018427387903 4611686018427387903
loop(\(x,i).(x + i - (x mod 9)),x,0)
A103303: 0 1 2 3 4 5 6 7 8 9
A340254-A317110-A227378-A226637-A051885: 0 1 2 3 4 5 6 7 8 9 19 29 39 49 59 69
loop(\(x,i).(5x + 25),x,0)
A168571: 0 25 150 775 3900 19525 97650 488275 2441400 12207025 61035150 305175775 1525878900 7629394525 38146972650 190734863275
(2 - loop(\(x,i).(10x + ~5),x,0))
A178769: 2 7 57 557 5557 55557 555557 5555557 55555557 555555557 5555555557 55555555557 555555555557 5555555555557 55555555555557 555555555555557
(1 div (2 - (if ((x + ~1) mod 5) <= 0 then x else 0)))
A030213: 0 1 0 0 0 0 ~1 0 0 0 0 ~1 0 0 0 0
(1 - loop(\(x,i).(10x + ~20),x,0))
A165402: 1 21 221 2221 22221 222221 2222221 22222221 222222221 2222222221 22222222221 222222222221 2222222222221 22222222222221 222222222222221 2222222222222221
(if ((x * (x mod 3)) mod 5) <= 0 then x else 0)
A102391: 0 0 0 3 0 5 6 0 0 9 10 0 12 0 0 15
loop(\(x,i).((x + 1) - (2 * (~2x + (x mod 2)))),x,0)
A015531: 0 1 4 21 104 521 2604 13021 65104 325521 1627604 8138021 40690104 203450521 1017252604 5086263021
loop(\(x,i).(~1 + (2 * (3x + (i mod 2)))),x,0)
A015540: 0 1 5 31 185 1111 6665 39991 239945 1439671 8638025 51828151 310968905 1865813431 11194880585 67169283511
loop(\(x,i).(~1 + (2 * (4x + (i mod 2)))),x,0)
A082310: 0 1 7 57 455 3641 29127 233017 1864135 14913081 119304647 954437177
A015565: 0 1 7 57 455 3641 29127 233017 1864135 14913081 119304647 954437177 7635497415 61083979321 488671834567 3909374676537
((x mod 2) - loop(\(x,i).(1 + (2 * (x - (i mod 2)))),x,0))
A155944: 0 2 1 4 5 12 21 44 85 172 341 684 1365 2732 5461 10924
loop(\(x,i).(3 * ((x + ~1) + (i mod 3))),x,0)
A152733: 0 0 3 6 18 57 168 504 1515 4542 13626 40881 122640 367920 1103763 3311286
(if (x + ~2) <= 0 then (x + (3 * (1 + (x mod 2)))) else 0)
A301755: 3 7 5 0 0 0 0 0 0 0 0 0 0 0 0 0
(1 - loop(\(x,i).(9x + ~3),x,0))
A039306: 1 4 31 274 2461 22144 199291 1793614 16142521 145282684 1307544151 11767897354 105911076181 953199685624 8578797170611 77209174535494
loop(\(x,i).(6x + 30),x,0)
A178672: 0 30 210 1290 7770 46650 279930 1679610 10077690 60466170 362797050 2176782330 13060694010 78364164090 470184984570 2821109907450
loop(\(x,i).(7x + 5),x,0)
A125729: 0 5 40 285 2000 14005 98040 686285 4804000 33628005 235396040 1647772285 11534406000 80740842005 565185894040 3956301258285
loop(\(x,i).(6x + 36),x,0)
A247840: 0 36 252 1548 9324 55980 335916 2015532 12093228 72559404 435356460 2612138796 15672832812 94036996908 564221981484 3385331888940
(1 - loop(\(x,i).(7x + ~1),x,0))
A047852: 1 2 9 58 401 2802 19609 137258 960801 6725602 47079209 329554458 2306881201 16148168402 113037178809 791260251658
(1 - loop(\(x,i).(3 * ((x * i) - (i div 2))),x,0))
A266757: 1 1 4 31 367
(1 - (if (x mod 3) <= 0 then (~x + (x div 3)) else 0))
A101443: 1 1 1 3 1 1 5 1 1 7 1 1 9 1 1 11
(2 - loop(\(x,i).(10x + ~1),x,0))
A098406: 2 3 13 113 1113 11113 111113 1111113 11111113 111111113 1111111113 11111111113 111111111113 1111111111113 11111111111113 111111111111113
loop(\(x,i).(10x + 7),x,0)
A002281: 0 7 77 777 7777 77777 777777 7777777 77777777 777777777 7777777777 77777777777 777777777777 7777777777777 77777777777777 777777777777777
(1 - loop(\(x,i).(16x + ~8),x,0))
A139760: 1 9 137 2185 34953 559241 8947849 143165577 2290649225 36650387593 586406201481 9382499223689 150119987579017 2401919801264265 38430716820228233 614891469123651721
(12 - loop(\(x,i).(2x + ~1),x,0))
A267615: 12 13 15 19 27 43 75 139 267 523 1035 2059 4107 8203 16395 32779
((2x2 + ~2x) - loop(\(x,i).(2x + ~1),x,0))
A295077: 0 1 7 19 39 71 123 211 367 655 1203 2267 4359 8503 16747 33187
loop(\(x,i).((x + 1) + (x div (1 + (x mod 3)))),x,0)
A295484: 0 1 2 3 7
A180516: 0 1 2 3 7 11 15 31 47 63 127 191 255 511 767 1023
loop(\(x,i).((x + 1) + (x div 7)),x,0)
A084689: 0 1 2 3 4 5 6 7 9
A279078: 0 1 2 3 4 5 6 7 9 11 13 15 18 21 25 29
loop(\(x,i).((x + 1) + (x div (1 + (x mod 4)))),x,0)
A181287: 0 1 2 3 4 9 14 19 24 49 74 99 124 249 374 499
loop(\(x,i).((x + 1) + (x mod 10)),x,0)
A222010: 0 1 3 7
A235699: 0 1 3 7 15 21 23 27 35 41 43 47 55 61 63 67
loop(\(x,i).((x + 1) + (4 * (x + (x div 2)))),x,0)
A015552: 0 1 6 43 300 2101 14706 102943 720600 5044201 35309406 247165843 1730160900 12111126301 84777884106 593445188743
loop(\(x,i).(11x + 11),x,0)
A105280: 0 11 132 1463 16104 177155 1948716 21435887 235794768 2593742459 28531167060 313842837671 3452271214392 37974983358323 417724816941564 4594972986357215
loop(\(x,i).(~1 + (x * ((1 - (2 * (i mod 2))) * i))),x,0)
A176304: 0 ~1 ~3 8 31 ~156 ~937 6558 52463 ~472168 ~4721681 51938490 623261879 ~8102404428 ~113433661993 1701504929894
loop(\(x,i).(8x - (i div ~2)),x,0)
A178827: 0 1 9 74 594 4755 38043 304348 2434788 19478309 155826477 1246611822 9972894582 79783156663 638265253311 5106122026496
loop(\(x,i).(x + i - (x mod 10)),x,0)
A103303: 0 1 2 3 4 5 6 7 8 9
A247107-A158699-A138142-A061511: 0 1 2 3 4 5 6 7 8 9 10 21 32 43 54 65
((2 div (x + 1)) - loop(\(x,i).(2x + ~6),x,0))
A037294: 2 7 18 42 90 186
(8 - (if (~2 + (x div 3)) <= 0 then x else 0))
A307339: 8 7 6 5 4 3 2 1 0 8 8 8 8 8 8 8
loop(\(x,i).(x + i - ((x mod (1 + (x div 2))) div 2)),x,0)
A084525-A084515: 0 1 3 6 9 12 16 20 24 28 32 36 40 44 48 52
((~x + 1) - loop(\(x,i).(2 * ((x + 1) - (2 * i))),x,0))
A131066: 1 2 9 28 71 162 349 728 1491 3022 6089 12228 24511 49082 98229 196528
(1 - loop(\(x,i).(10x + ~2),x,0))
A093135: 1 3 23 223 2223 22223 222223 2222223 22222223 222222223 2222222223 22222222223 222222222223 2222222222223 22222222222223 222222222222223
loop(\(x,i).(2 * ((2x + 2) - (x div (1 + i)))),x,0)
A115112: 0 4 18 68 250 922 3430 12868 48618 184754 705430 2704154 10400598 40116598 155117518 601080388
loop(\(x,i).(x - ((i * i) div ~7)),x,0)
A175822: 0 1 2 4 7 11 17 24 34 46 61 79 100 125 153 186
loop(\(x,i).(8x + 64),x,0)
A247841: 0 64 576 4672 37440 299584 2396736 19173952 153391680 1227133504 9817068096 78536544832 628292358720 5026338869824 40210710958656 321685687669312
(1 - loop(\(x,i).(10x + ~16),x,0))
A246058: 1 17 177 1777 17777 177777 1777777 17777777 177777777 1777777777 17777777777 177777777777 1777777777777 17777777777777 177777777777777 1777777777777777
(if ((~x + 4) mod (4 + (x mod 2))) <= 0 then x else 0)
A105570: 0 0 0 0 4 0 0 0 8 9 0 0 12 0 0 0
(x - loop(\(x,i).(x - (((x div 2) + i) div 4)),x,0))
A092919: 0 1 2 3 5 7 9 11 13 15 17 19 22 25 28 31
loop(\(x,i).(x - (2 * (1 - (2 * (x + (i mod 2)))))),x,0)
A231103: 0 2 8 42 208 1042 5208 26042 130208 651042 3255208 16276042 81380208 406901042 2034505208 10172526042
(1 - loop(\(x,i).(x - (2 * (~2x + (i mod 2)))),x,0))
A039302: 1 3 11 53 261 1303 6511 32553 162761 813803 4069011 20345053 101725261 508626303 2543131511 12715657553
((x + 1) - loop(\(x,i).(5x - i),x,0))
A188545: 1 3 10
A094195: 1 3 10 42 199 981 4888 24420 122077 610359 3051766 15258798 76293955 381469737 1907348644 9536743176
loop(\(x,i).(~1 + ((x * (2 + i)) + (2 * (i mod 2)))),x,0)
A006347: 0 1 3 16 95 666 5327 47944 479439 5273830 63285959 822717468 11518044551 172770668266 2764330692255 46993621768336
loop(\(x,i).(~1 + ((x * (i * i)) + (2 * (i mod 2)))),x,0)
A340789: 0 1 3 28 447 11176 402335 19714416 1261722623 102199532464 10219953246399 1236614342814280 178072465365256319 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 2) + (x div (1 + (2 * (i div 2))))),x,0)
A130251: 0 2 4 7 10 14 18 22 26 30 34 39 44 49 54 59
((2 * (x mod 2)) - loop(\(x,i).(3x + ~2),x,0))
A105723: 0 4 8 28 80 244 728 2188 6560 19684 59048 177148 531440 1594324 4782968 14348908
loop(\(x,i).(2x + 64),x,0)
A175166: 0 64 192 448 960 1984 4032 8128 16320 32704 65472 131008 262080 524224 1048512 2097088
loop(\(x,i).((x + 2) + (x div (2 + i - (x mod 2)))),x,0)
A130240: 0 2 4 6 9 12 15 18 21 25 29 33 37 41 45 49
(2 - loop(\(x,i).((x + ~2) + (x div (4 + i))),x,0))
A003067: 2 4 7 10 13 17 21 25 29 34 39 44 49 54 59 64
loop(\(x,i).(2x + ((i div ~4) mod 2)),x,0)
A222010: 0 1 3 7
A224520: 0 1 3 7 15 30 60 120 240 481 963 1927 3855 7710 15420 30840
loop(\(x,i).(3x + (((x + ~1) div 2) mod 2)),x,0)
A062107: 0 1 3 10 30 90 270 810 2430 7290 21870 65610 196830 590490 1771470 5314410
(1 - loop(\(x,i).(2 * (((x + 1) - (2 * i)) * i)),x,0))
A007566: 1 3 21 151 1257 12651 151933 2127231 34035921 612646867 12252937701 269564629863 6469551117241 168208329048891 4709833213369677 141294996401091151
((x + 1) - loop(\(x,i).(2 * (x - ((2 + i) * i))),x,0))
A213764: 1 8 31 90 225 516 1123 2366 4885 9960 20151 40578 81481 163340 327115 654726
loop(\(x,i).((8x + 4) - (i mod 2)),x,0)
A172241: 0 3 28 227 1820 14563 116508 932067 7456540 59652323 477218588 3817748707 30541989660 244335917283 1954687338268 15637498706147
loop(\(x,i).(10x + (i mod 2)),x,0)
A056830: 0 1 10 101 1010 10101 101010 1010101 10101010 101010101 1010101010 10101010101 101010101010 1010101010101 10101010101010 101010101010101
loop(\(x,i).(11x + 10),x,0)
A024127: 0 10 120 1330 14640 161050 1771560 19487170 214358880 2357947690 25937424600 285311670610 3138428376720 34522712143930 379749833583240 4177248169415650
loop(\(x,i).(x + ((((1 + i) * i) div 2) * (1 + i))),x,0)
A000914: 0 2 11 35 85 175 322 546 870 1320 1925 2717 3731 5005 6580 8500
loop(\(x,i).(x + ((1 + (2 * (2 + i))) * (~1 + i))),x,0)
A266397: 0 0 9 31 70 130 215 329 476 660 885 1155 1474 1846 2275 2765
loop(\(x,i).(x + i - ((~1 + (x div 4)) div 2)),x,0)
A219657: 0 2 5 8 12 16 21 26 32 38 44 50 57 64 71 78
loop(\(x,i).(x + (((1 + (i * i)) * i * i) div 2)),x,0)
A079547: 0 1 11 56 192 517 1183 2408 4488 7809 12859 20240 30680 45045 64351 89776
loop(\(x,i).(x + ((1 + ((1 + (2 * i)) * i)) * i)),x,0)
A172123: 0 4 26 92 240 520 994 1736 2832 4380 6490 9284 12896 17472 23170 30160
loop(\(x,i).(x + ((1 + ((4 + i) * i)) * i)),x,0)
A296196: 0 6 32 98 230 460 826 1372 2148 3210 4620 6446 8762 11648 15190 19480
loop(\(x,i).(x + ((i - (4 * (1 - i))) * i)),x,0)
A007587: 0 1 13 46 110 215 371 588 876 1245 1705 2266 2938 3731 4655 5720
loop(\(x,i).(x + (((x + ~1) + (2 * (i mod 2))) * i)),x,0)
A155521: 0 1 1 7 31 191 1331 10655 95887 958879 10547659 126571919 1645434935 23036089103 345541336531 5528661384511
loop(\(x,i).(x + (7 * (i * i))),x,0)
A169607: 0 7 35 98 210 385 637 980 1428 1995 2695 3542 4550 5733 7105 8680
loop(\(x,i).(x + ((~2 + (3 * i)) * i * i)),x,0)
A172045: 0 1 17 80 240 565 1141 2072 3480 5505 8305 12056 16952 23205 31045 40720
loop(\(x,i).(x + (i * i * i * i * i * i)),x,0)
A000540: 0 1 65 794 4890 20515 67171 184820 446964 978405 1978405 3749966 6735950 11562759 19092295 30482920
loop(\(x,i).(((x2 + 2x) div (x + 4)) + i),x,0)
A024536: 0 1 2 4 7 10 14 19 25 32 40 49 59 70 82 95
loop(\(x,i).(10x + (i * i)),x,0)
A032343: 0 1 14 149 1506 15085 150886 1508909 15089154 150891621 1508916310 15089163221 150891632354 1508916323709 15089163237286 150891632373085
(if (x mod (1 + ((x + ~1) mod 5))) <= 0 then 0 else 1)
A011714: 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0
(if ((x + 1) mod (1 + (x div 5))) <= 0 then 0 else 1)
A336469-A295297: 0 0 0 0 0 0 1 0 1 0 1 0 1 1 0 0
(if ((x + ~1) mod 13) <= 0 then 0 else 1)
A131695: 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1
(if (x mod (1 + (3 * (x mod 4)))) <= 0 then 0 else 1)
A284939-A098725: 0 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1
(if ((x + ~1) mod (1 + (4 mod (x + 1)))) <= 0 then 0 else 1)
A335106-A288132-A070200: 0 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1
(if (x mod (3 + ((x div 2) div 3))) <= 0 then 0 else 1)
A049240: 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0
(if ((x + 3) mod 7) <= 0 then 0 else 1)
A071027: 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1
(if (x mod (3 + (2 mod (1 + (x div 2))))) <= 0 then 0 else 1)
A080886: 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0
(if (x mod ((x + 1) - ((~1 + (x div 2)) div 2))) <= 0 then 0 else 1)
A204437: 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1
(if ((x + 2) mod (3 + (2 mod (x + 1)))) <= 0 then 0 else 1)
A230632: 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1
(if ((x + ~1) mod (5 + (x div 2))) <= 0 then 0 else 1)
A341167: 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1
(if (x mod (1 + (x div (2 * (2 + (x mod 2)))))) <= 0 then 0 else 1)
A011699: 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0
(if (x mod (1 + (((x + 1) div 2) mod 4))) <= 0 then 0 else 1)
A060952: 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0
(if (((x + 1) + (x div 2)) mod 5) <= 0 then 0 else 1)
A188318: 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1
(if ((x - (x div ~2)) mod 5) <= 0 then 0 else 1)
A285978: 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1
(if ((x2 div ~2) mod 5) <= 0 then 0 else 1)
A284929: 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1
(if ((x div 2) - ((x + 2) mod 5)) <= 0 then 0 else 1)
A237657: 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1
(if ((x2 div (x + 2)) mod 5) <= 0 then 0 else 1)
A288226: 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1
(if ((x + (x mod 2)) mod (1 + (x div 4))) <= 0 then 0 else 1)
A294233: 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0
(if (~1 + ((~x2 + x) mod (2 + (x div 2)))) <= 0 then 0 else 1)
A011708: 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1
(if ((x - (x2 div 3)) mod 3) <= 0 then 0 else 1)
A284622: 0 1 1 0 1 0 0 0 1 0 1 1 0 1 0 0
(if ((x mod ~8) mod 3) <= 0 then 0 else 1)
A022924: 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1
(if ((x - (((x + ~1) div 2) mod 2)) mod 3) <= 0 then 0 else 1)
A283437: 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1
(if (((x + 1) mod 8) mod 3) <= 0 then 0 else 1)
A114986: 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0
(if (((x + 2) mod 8) mod 3) <= 0 then 0 else 1)
A005614: 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1
(if (((~x + 1) mod 8) mod 3) <= 0 then 0 else 1)
A334413-A114483: 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1
(if ((x - (x div 8)) mod 3) <= 0 then 0 else 1)
A188295: 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1
(if ((x mod (4 + (x mod 2))) mod 3) <= 0 then 0 else 1)
A292077: 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 0
(if (x mod (3 * (2 - ((x div 2) mod 2)))) <= 0 then 0 else 1)
A014578: 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0
(1 + (if ((x div 2) mod 3) <= 0 then (x div 3) else 0))
A014421: 1 1 1 1 1 1 3 3 1 1 1 1 5 5 1 1
(if (x mod (8 - (x div 3))) <= 0 then 0 else 1)
A182067: 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0
((x + 2) div (1 + (if (x mod 2) <= 0 then (x div 3) else 0)))
A088492: 2 3 4 5 3 7 2 9 3 11 3 13 2 15 3 17
(1 + (if (x mod 5) <= 0 then (x mod 3) else 0))
A023593: 1 1 1 1 1 3 1 1 1 1 2 1 1 1 1 1
(if ((x + ~2) mod (4 - (x mod 3))) <= 0 then 0 else 1)
A165728: 1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1
(if (20 mod (x + 1)) <= 0 then 0 else 1)
A339184: 0 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1
(~1 + loop(\(x,i).(5x + 8),(x + 1),0))
A064385: 7 47 247 1247 6247 31247 156247 781247 3906247 19531247 97656247 488281247 2441406247 12207031247 61035156247 305175781247
(1 + loop(\(x,i).(2 * (x + (2 * (i div 2)))),(x + ~1),0))
A141025: 1 1 1 5 13 33 73 157 325 665 1345 2709 5437 10897 21817 43661
(1 + (if ((x + 2) mod 9) <= 0 then 2 else 0))
A094404-A066715-A031246-A030579: 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1
(if (x - (2 * ((~x + 2) mod 5))) <= 0 then 0 else 1)
A308243: 0 0 1 0 0 1 1 1 0 1 1 1 1 1 1 1
(if (x mod ((x + 2) - (x div 5))) <= 0 then 0 else 1)
A204447: 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1
(if (x mod (4 - ((x div 2) div 3))) <= 0 then 0 else 1)
A280379-A217564: 0 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1
(if (2x mod (2 + ((x div 2) div 3))) <= 0 then 0 else 1)
A011709: 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 1
(if ((x div 4) - (x mod 6)) <= 0 then 0 else 1)
A124760: 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0
(if ((2x + 2) mod (2 + (x div 3))) <= 0 then 0 else 1)
A238451: 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 1
(1 + (if ((x + 1) mod 10) <= 0 then 2 else 0))
A030580: 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1
(1 + (if ((1 + (x div 2)) mod 6) <= 0 then 2 else 0))
A186028: 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1
(if (2x mod (4 + (x div 4))) <= 0 then 0 else 1)
A090477-A023532: 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0 1
(1 + (if ((x + 1) mod (2 + (x mod 4))) <= 0 then 2 else 0))
A250208-A120263-A083202-A030578: 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1
(1 + (if ((1 + ((x + 1) div 2)) mod 4) <= 0 then 2 else 0))
A059790: 1 1 1 1 1 3 3 1 1 1 1 1 1 3 3 1
(if ((x + 1) mod (2 + ((~x + 1) mod 4))) <= 0 then 0 else 1)
A080545: 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 0
(if ((x + ~2) mod (2 + ((~x + 2) mod 4))) <= 0 then 0 else 1)
A262808: 1 1 0 1 1 0 0 0 1 1 0 1 1 1 0 1
(1 + (if ((x2 + 1) mod (x + 4)) <= 0 then 2 else 0))
A340085-A214268-A214249-A195768: 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1
(if (x mod (2 + (x2 mod (x + 4)))) <= 0 then 0 else 1)
A285972-A275510: 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1
(2 - ((~x + 1) div (1 + (if (~2 + (x div 2)) <= 0 then 2 else 0))))
A160642: 2 2 3 3 3 4 7 8 9 10 11 12 13 14 15 16
(1 + (if ((x + 1) mod 5) <= 0 then 4 else 0))
A060904: 1 1 1 1 5 1 1 1 1 5 1 1 1 1 5 1
(if (((x + 1) * ((x + 1) div 2)) mod 4) <= 0 then 0 else 1)
A341642-A296211: 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0
(if (((x + 1) * (2 + (x div 2))) mod 4) <= 0 then 0 else 1)
A284948: 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0
(x div (1 + (if (x mod 6) <= 0 then 4 else 0)))
A214394: 0 1 2 3 4 5 1 7 8 9 10 11 2 13 14 15
(if ((x - ((2 - (x div 2)) div 2)) mod 4) <= 0 then 0 else 1)
A334377: 1 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1
(if (x2 + ~12x + 32) <= 0 then 0 else 1)
A266434: 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1
(1 + (if (~2 + (x div 3)) <= 0 then (x div 4) else 0))
A225538: 1 1 1 1 2 2 2 2 3 1 1 1 1 1 1 1
(if ((2x mod 3) - (x mod 4)) <= 0 then 0 else 1)
A129185-A129184: 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0
(if ((x3 + ~1) mod (2 + (x div 2))) <= 0 then 0 else 1)
A120530: 1 0 1 1 1 0 0 1 1 1 1 0 1 1 1 1
(1 + (if (x mod 12) <= 0 then (x div 2) else 0))
A174544: 1 1 1 1 1 1 1 1 1 1 1 1 7 1 1 1
(if (((x + 2) mod 6) * (x div 2)) <= 0 then 0 else 1)
A014306: 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1
(1 + (if (x mod (2 + (x mod 4))) <= 0 then (x mod 2) else 0))
A124148: 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2
((x + 1) div (1 + (if (~x + 4) <= 0 then (x mod 2) else 0)))
A275823: 1 2 3 4 5 3 7 4 9 5 11 6 13 7 15 8
(x - (x div (if ((x + 1) mod 3) <= 0 then 2 else ~1)))
A138750: 0 2 1 6 8 3 12 14 4 18 20 6 24 26 7 30
(2x - (if ((x div 2) mod 2) <= 0 then (x mod 2) else ~1))
A047479: 0 1 5 7 8 9 13 15 16 17 21 23 24 25 29 31
(if ((x + 1) mod 12) <= 0 then x else ~1)
A321804-A321800: ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 11 ~1 ~1 ~1 ~1
(if (~2 + (x mod (2 + (x mod 3)))) <= 0 then x else ~1)
A103303: 0 1 2 3 4 5 6 7 8 9
A321802-A320485: 0 1 2 3 4 5 6 7 8 9 10 ~1 12 13 14 15
(1 + loop(\(x,i).(1 + (x mod (1 + (i mod (x + 1))))),x,0))
A099427: 1 2 2 3 2 3 2 3 4 3 2 3 2 3 4 5
(1 + (if ((x + 2) mod 9) <= 0 then x else 0))
A056191: 1 1 1 1 1 1 1 8 1 1 1 1 1 1 1 1
(1 + (if (x mod (3 + (x mod 4))) <= 0 then x else 0))
A280506: 1 1 1 1 1 1 1 1 1 1 11 1 13 1 1 1
(1 + loop(\(x,i).(1 + (x * (2 + (x * (i * i))))),x,0))
A035129: 1 2 8 457
(1 + loop(\(x,i).((x + 8) mod (1 + i)),x,0))
A109630: 1 1 3 3 1 3 4 4 3 1 9 5 13 7 15 7
(1 + loop(\(x,i).((x + 1) mod (2 + (i div 3))),x,0))
A037125: 1 2 1 2 3 1 2 3 4 5 1 2 3 4 5 6
(1 + (if (~2 + (x mod (2 + (x mod 3)))) <= 0 then x else 0))
A322094: 1 2 3 4 5 6 7 8 9 10 11 1 13 14 15 16
(((x + 2) div 7) + (if x <= 0 then 0 else 1))
A180447: 0 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3
((2x div (3 + (x div 2))) + (if x <= 0 then 0 else 1))
A269024: 0 1 2 2 2 3 3 3 3 3 3 3 3 3 3 4
(18x - (if x <= 0 then 0 else 1))
A004921: 0 17 35 53 71 89 107 125 143 161 179 197 215 233 251 269
(((1 + (x * (x div 2))) mod 3) + (if x <= 0 then 0 else 1))
A204893: 1 2 1 2 1 3 2 2 1 2 1 3 2 2 1 2
(((x - ((x div 2) mod 2)) div 3) + (if x <= 0 then 0 else 1))
A257807-A211339-A152595: 0 1 1 1 2 2 2 3 3 4 4 4 5 5 5 5
(2x - ((if x <= 0 then 0 else 1) + ((x div 2) div 3)))
A214315: 0 1 3 5 7 9 10 12 14 16 18 20 21 23 25 27
((x + 2) + (if x <= 0 then 0 else 1) - ((~x + 1) div 3))
A135673: 2 4 6 7 8 10 11 12 14 15 16 18 19 20 22 23
(4x - ((if x <= 0 then 0 else 1) + (x div 3)))
A172323: 0 3 7 10 14 18 21 25 29 32 36 40 43 47 51 54
(x + (if x <= 0 then 0 else 1) - (2 * (x div 5)))
A326167: 0 2 3 4 5 4 5 6 7 8 7 8 9 10 11 10
(2 + ((((x + 1) div 2) div 3) + (if x <= 0 then 0 else 1)))
A155934: 2 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5
((2 * ((2x + 1) + (x div 2))) + (if x <= 0 then 0 else 1))
A063206: 2 7 13 17 23 27 33 37 43 47 53 57 63 67 73 77
((2 * ((1 + (x div 4)) div 2)) + (if x <= 0 then 0 else 1))
A331134: 0 1 1 1 3 3 3 3 3 3 3 3 5 5 5 5
((2 * (x - (2 * (x div 3)))) - (if x <= 0 then 0 else 1))
A063198: 0 1 3 1 3 5 3 5 7 5 7 9 7 9 11 9
(2 + (if x <= 0 then 0 else 1) - ((x mod (2 + (x mod 2))) div 2))
A276858: 2 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3
((((x * (x div 4)) div 2) mod 2) + (if x <= 0 then 0 else 1))
A344339: 0 1 1 1 1 1 2 2 1 2 1 2 1 2 2 1
((((x mod 3) * (x div 2)) mod 2) + (if x <= 0 then 0 else 1))
A120891-A092523: 0 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1
(x div ((x + 2) div (2 + (if x <= 0 then 0 else 1) - (x mod 2))))
A332202: 0 1 2 1 2 1 3 1 2 1 2 1 3 1 2 1
((2x2 + x + 8) + (if x <= 0 then 0 else 1))
A232867: 8 12 19 30 45 64 87 114 145 180 219 262 309 360 415 474
(x + ((4x div (x + 2)) + (if x <= 0 then 0 else 1)))
A138891: 0 3 5 6 7 8 10 11 12 13 14 15 16 17 18 19
(2x + (((x div 2) div 3) + (if x <= 0 then 0 else 1)))
A195179: 0 3 5 7 9 11 14 16 18 20 22 24 27 29 31 33
((x3 + 6x2) - (if x <= 0 then 0 else 1))
A087725: 0 6 31 80
(~1 + loop(\(x,i).(x + ((4 + (i mod 2)) * i)),x,0))
A266958: ~1 4 12 27 43 68 92 127 159 204 244 299 347 412 468 543
(1 + loop(\(x,i).(((x * (i * i)) div (2 + i)) + i),x,0))
A004252: 1 2 4 9 26 95
(1 + loop(\(x,i).2x,x,13))
A168596: 14 27 53 105 209 417 833 1665 3329 6657 13313 26625 53249 106497 212993 425985
(1 + loop(\(x,i).x2,x,11))
A199592: 12 122 14642 214358882 45949729863572162 4611686018427387903 4611686018427387903
(1 + (x mod (1 + (if (x mod 5) <= 0 then 0 else 2))))
A106038: 1 2 3 1 2 1 1 2 3 1 1 3 1 2 3 1
(1 + (if (x mod 15) <= 0 then 2 else 1))
A248743: 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3
(1 + (if (x mod (1 + (x mod 8))) <= 0 then 2 else 1))
A270003: 3 2 2 2 2 2 2 2 3 2 2 2 2 2 3 2
(if (~2 + (x div 2)) <= 0 then (1 + ((x mod 3) div 2)) else 1)
A283149-A183017: 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1
(1 + (x mod (if (x mod 3) <= 0 then ((x + ~1) div 2) else 1)))
A337798: 1 1 1 1 1 1 1 1 1 2 1 1 3 1 1 2
loop(\(x,i).i,(~1 + ((x - ((x mod 3) div 2)) div 2)),1)
A029113: 1 1 1 1 1 1 2 2 2 3 4 4 5 5 5 6
(1 + ((x + ~1) mod (1 + (4 * (if x <= 0 then 0 else 2)))))
A033930: 1 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6
(~1 + loop(\(x,i).2x,x,15))
A196305: 14 29 59 119 239 479 959 1919 3839 7679 15359 30719 61439 122879 245759 491519
((~x + 1) mod (1 + (if (x mod 8) <= 0 then 2 else 1)))
A179010: 1 0 1 0 1 0 1 0 2 0 1 0 1 0 1 0
(1 + loop(\(x,i).(2x + 4),x,9))
A156202: 10 23 49 101 205 413 829 1661 3325 6653 13309 26621 53245 106493 212989 425981
(1 + loop(\(x,i).4x,x,9))
A199208: 10 37 145 577 2305 9217 36865 147457 589825 2359297 9437185 37748737 150994945 603979777 2415919105 9663676417
loop(\(x,i).x2,1,(1 + (x mod 9)))
A153211: 1 4 9 16 25 36 49 64 81 1 4 9 16 25 36 49
(1 + loop(\(x,i).(x2 + x),x,9))
A144783: 10 91 8191 67084291 4500302031888391 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if ((x2 + 1) mod (x + 4)) <= 0 then 2 else 1))
A180258: 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2
(1 + (if ((x mod 5) mod 2) <= 0 then 4 else 1))
A244892: 5 2 5 2 5 5 2 5 2 5 5 2 5 2 5 5
(1 + ((x - (if (x mod 2) <= 0 then 2 else 0)) div 5))
A240874: 0 1 1 1 1 2 1 2 2 2 2 3 3 3 3 4
loop(\(x,i).((~x + ~1) + i),((x + 1) div 5),1)
A037869: 1 1 1 1 ~1 ~1 ~1 ~1 ~1 2 2 2 2 2 0 0
(1 + ((~2 + loop(\(x,i).2x,x,1)) div 5))
A256494: 0 1 1 2 3 7 13 26 51 103 205 410 819 1639 3277 6554
(~1 + (if x <= 0 then 1 else (10x + 10)))
A038364: 0 19 29 39 49 59 69 79 89 99
(1 + (if x <= 0 then 1 else ((2x + ~2) div 5)))
A127950: 2 1 1 1 2 2 3 3 3 4 4 5 5 5 6 6
(1 + (5 * loop(\(x,i).4x,x,2)))
A199209: 11 41 161 641 2561 10241 40961 163841 655361 2621441 10485761 41943041 167772161 671088641 2684354561 10737418241
(if (x mod 4) <= 0 then ((x + 2) div 5) else 1)
A076398: 0 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1
(1 + loop(\(x,i).3x,2x,5))
A199563: 6 46 406 3646 32806 295246 2657206 23914846 215233606 1937102446 17433922006 156905298046 1412147682406 12709329141646 114383962274806 1029455660473246
loop(\(x,i).3x,(~5 + (x div 2)),1)
A147510-A147502-A147433-A147128-A146607: 1 1 1 1 1 1 1 1 1 1 1 1 3 3 9 9
(1 + (5 * loop(\(x,i).3x,x,2)))
A199112: 11 31 91 271 811 2431 7291 21871 65611 196831 590491 1771471 5314411 15943231 47829691 143489071
(~1 + (5 * loop(\(x,i).3x,x,2)))
A198645: 9 29 89 269 809 2429 7289 21869 65609 196829 590489 1771469 5314409 15943229 47829689 143489069
(1 + loop(\(x,i).6x,x,5))
A199320: 6 31 181 1081 6481 38881 233281 1399681 8398081 50388481 302330881 1813985281 10883911681 65303470081 391820820481 2350924922881
(~1 + loop(\(x,i).6x,x,5))
A198794: 4 29 179 1079 6479 38879 233279 1399679 8398079 50388479 302330879 1813985279 10883911679 65303470079 391820820479 2350924922879
(1 + (5 * loop(\(x,i).2x,(x + ~1),x)))
A048476: 1 6 21 61 161 401 961 2241 5121 11521 25601 56321 122881 266241 573441 1228801
(1 + loop(\(x,i).8x,x,5))
A199553: 6 41 321 2561 20481 163841 1310721 10485761 83886081 671088641 5368709121 42949672961 343597383681 2748779069441 21990232555521 175921860444161
(~1 + loop(\(x,i).8x,x,5))
A198853: 4 39 319 2559 20479 163839 1310719 10485759 83886079 671088639 5368709119 42949672959 343597383679 2748779069439 21990232555519 175921860444159
loop(\(x,i).2x,(x - ((~x + 2) div 5)),1)
A171381: 1 2 4 16 32 64
A334083: 1 2 4 16 32 64 128 256 1024
(1 + (5 * loop(\(x,i).(x2 + x),2,x)))
A022521: 1 31 211 781 2101 4651 9031 15961 26281 40951 61051 87781 122461 166531 221551 289201
loop(\(x,i).5x,(x div 5),1)
A243757: 1 1 1 1 1 5 5 5 5 5 25 25 25 25 25 125
(1 + loop(\(x,i).(x * i),((x + 4) + (x div 2)),1))
A087399-A085692: 25 121 5041
(1 + loop(\(x,i).(x2 + x),x,(1 + (x div 4))))
A201363: 2 3 7
A014546: 2 3 7 43 3263443
(1 + ((~x + 3) mod loop(\(x,i).i,(x div 4),1)))
A228570: 1 1 1 1 1 1 1 1 2 1 2 1 1 3 2 1
(1 + (x2 mod loop(\(x,i).(x + i),(x mod 4),1)))
A078734: 1 2 1 3 1 2 1 1 1 2 1 3 1 2 1 2
loop(\(x,i).(x * i),(2x2 + 8x + 7),1)
A072242: 5040 355687428096000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(x2 div (x + 5)),1)
A140839: 1 1 1 2 2 4
A054243: 1 1 1 2 2 4 8 16 16 32 64 128 256 512 1024 2048
loop(\(x,i).6x,(4x + 1),1)
A013784: 6 7776 10077696 13060694016 16926659444736 21936950640377856 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).8x,(4x + 1),1)
A013788: 8 32768 134217728 549755813888 2251799813685248 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).5x,(4x + 1),1)
A013782: 5 3125 1953125 1220703125 762939453125 476837158203125 298023223876953125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x - i),(1 + (x div 2) - (2 * (x mod 2))),1)
A317301: 0 1 ~2 1 ~5 0 ~9 ~2 ~14 ~5 ~20 ~9 ~27 ~14 ~35 ~20
(~1 + (loop(\(x,i).2x,x,2) div (1 + (2 * (x mod 2)))))
A282798: 1 0 7 4 31 20 127 84 511 340 2047 1364 8191 5460 32767 21844
(1 + (3 * loop(\(x,i).((x + 2) mod (1 + i)),x,0)))
A256255: 1 1 7 1 7 13 19 1 7 13 19 25 31 37 43 1
loop(\(x,i).(x * i),(12x + 3),1)
A072240: 6 1307674368000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (3 * loop(\(x,i).(~1 + (x * i)),x,3)))
A068444: 10 7 10 25 94 463 2770 19381 155038 1395331 13953298 153486265 1841835166 23943857143 335213999986 5028209999773
loop(\(x,i).2x,((x - (x div 3)) div 3),1)
A113452: 1 1 1 1 2 2 2 2 4 4 4 4 4 8 8 8
(1 + (((x + 2) div (if (~x + 2) <= 0 then 2 else 1)) div 3))
A082892: 1 2 1 1 2 2 2 2 2 2 3 3 3 3 3 3
(1 + (loop(\(x,i).(~1 + (x * (1 + i))),x,1) div 3))
A039750: 1 1 1 3 12 68
loop(\(x,i).2x,((x2 + x + 1) div 3),1)
A179532: 1 2 4 16 128 1024 16384 524288 16777216 1073741824 137438953472 17592186044416 4503599627370496 2305843009213693952 4611686018427387903 4611686018427387903
(4 div (1 + ((1 + (if x <= 0 then 1 else x)) mod 3)))
A136619: 1 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2
loop(\(x,i).2x,((x2 + 2x + 1) div 3),1)
A134751: 1 2 8 32 256 4096 65536 2097152 134217728 8589934592 1099511627776 281474976710656 72057594037927936 4611686018427387903 4611686018427387903 4611686018427387903
(if (~x + 2) <= 0 then ((x2 + 2x + ~1) div 3) else 1)
A199085: 1 1 2 4 7 11 15 20 26 32 39 47 55 64 74 84
(~1 + (3 * loop(\(x,i).2x,(x + ~1),(x + 1))))
A074494: 2 5 17 47 119 287 671 1535 3455 7679 16895 36863 79871 172031 368639 786431
(if ((x + 2) mod 4) <= 0 then ((x + 1) div 3) else 1)
A292505-A281119: 1 1 1 1 1 1 2 1 1 1 3 1 1 1 5 1
(if (~x + 2) <= 0 then ((x div 2) - ((x + 1) div 3)) else 1)
A112220: 1 1 0 0 1 0 1 1 1 1 2 1 2 2 2 2
loop(\(x,i).(4 - (x div 2)),((x + ~1) div 3),1)
A109610: 1 1 1 1 4 4 4 2 2 2 3 3 3 3 3 3
loop(\(x,i).2x,((x div 2) - ((x + ~1) div 3)),1)
A060548: 2 1 2 2 2 2 4 2 4 4 4 4 8 4 8 8
(1 + (x mod (3 * (if (~2 + (x div 2)) <= 0 then 1 else 2))))
A194074: 1 2 3 1 2 3 1 2 3 4 5 6 1 2 3 4
loop(\(x,i).2x,x,19)
A110288: 19 38 76 152 304 608 1216 2432 4864 9728 19456 38912 77824 155648 311296 622592
(~1 + loop(\(x,i).x2,1,(6x + 6)))
A136017: 35 143 323 575 899 1295 1763 2303 2915 3599 4355 5183 6083 7055 8099 9215
loop(\(x,i).x2,1,(6x + 5))
A016970: 25 121 289 529 841 1225 1681 2209 2809 3481 4225 5041 5929 6889 7921 9025
loop(\(x,i).x2,2,(6x + 5))
A016972: 625 14641 83521 279841 707281 1500625 2825761 4879681 7890481 12117361 17850625 25411681 35153041 47458321 62742241 81450625
(loop(\(x,i).2x,x,1) mod 13)
A222011: 1 2 4 8
A036118: 1 2 4 8 3 6 12 11 9 5 10 7 1 2 4 8
loop(\(x,i).3x,x,13)
A258597: 13 39 117 351 1053 3159 9477 28431 85293 255879 767637 2302911 6908733 20726199 62178597 186535791
(loop(\(x,i).2x,x,1) mod 11)
A222011: 1 2 4 8
A036117: 1 2 4 8 5 10 9 7 3 6 1 2 4 8 5 10
loop(\(x,i).4x,x,11)
A002089: 11 44 176 704 2816 11264 45056 180224 720896 2883584 11534336 46137344 184549376 738197504 2952790016 11811160064
loop(\(x,i).3x,x,11)
A120354: 11 33 99 297 891 2673 8019 24057 72171 216513 649539 1948617 5845851 17537553 52612659 157837977
(~1 + (3 * ((if (x mod 2) <= 0 then 2 else x) mod 4)))
A142702: 5 2 5 8 5 2 5 8 5 2 5 8 5 2 5 8
loop(\(x,i).(x * i),(x - (3 * (x div 4))),1)
A269224: 1 1 2 6 1 2 6 24 2 6 24 120 6 24 120 720
(1 + (if (x + ~2) <= 0 then x else (6x + ~12)))
A100764: 1 2 3 7 13 19 25 31 37 43 49 55 61 67 73 79
loop(\(x,i).x2,1,(12x + 1))
A017534: 1 169 625 1369 2401 3721 5329 7225 9409 11881 14641 17689 21025 24649 28561 32761
loop(\(x,i).x2,2,(12x + 1))
A017536: 1 28561 390625 1874161 5764801 13845841 28398241 52200625 88529281 141158161 214358881 312900721 442050625 607573201 815730721 1073283121
loop(\(x,i).(x * (1 + i)),12x,1)
A198807: 1 6227020800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (3 * ((if x <= 0 then 2 else (x2 + ~x)) div 2)))
A143208: 2 ~1 2 8 17 29 44 62 83 107 134 164 197 233 272 314
(~1 + (loop(\(x,i).(2 + (x mod (1 + i))),x,2) mod 3))
A065251: 1 1 0 1 0 ~1 1 1 0 ~1 1 0 ~1 1 0 1
(1 + (3 * loop(\(x,i).8x,x,2)))
A199554: 7 49 385 3073 24577 196609 1572865 12582913 100663297 805306369 6442450945 51539607553 412316860417 3298534883329 26388279066625 211106232532993
(~1 + (3 * loop(\(x,i).8x,x,2)))
A198854: 5 47 383 3071 24575 196607 1572863 12582911 100663295 805306367 6442450943 51539607551 412316860415 3298534883327 26388279066623 211106232532991
(1 + (3 * (loop(\(x,i).(x * (x + i)),2,x) div 2)))
A143008: 1 13 73 253 661 1441 2773 4873 7993 12421 18481 26533 36973 50233 66781 87121
(1 + (loop(\(x,i).2x,(x + ~1),(x + 2)) div 3))
A145230: 1 2 3 7 17 38
(if (x mod 2) <= 0 then (x div 2) else (3x + 5))
A181762: 0 8 1 14 2 20 3 26 4 32 5 38 6 44 7 50
(1 + (loop(\(x,i).(2x + ~4),x,(x + 2)) div 3))
A318234: 1 1 2 5 13 34 87
loop(\(x,i).x2,3,(6x + 1))
A016928: 1 5764801 815730721 16983563041 152587890625 852891037441 3512479453921 11688200277601 33232930569601 83733937890625 191707312997281 406067677556641 806460091894081 1517108809906561
loop(\(x,i).x3,1,(6x + 1))
A016923: 1 343 2197 6859 15625 29791 50653 79507 117649 166375 226981 300763 389017 493039 614125 753571
loop(\(x,i).x3,2,(6x + 1))
A016929: 1 40353607 10604499373 322687697779 3814697265625 26439622160671 129961739795077 502592611936843 1628413597910449 4605366583984375 11694146092834141 27206534396294947 58871586708267913
loop(\(x,i).(2x + ~4),x,(6x + 1))
A027981: 1 10 40 124 340 868 2116 4996 11524 26116 58372 129028 282628 614404 1327108 2850820
(if ((x + ~1) mod 3) <= 0 then (2x div 3) else 1)
A005131: 1 0 1 1 2 1 1 4 1 1 6 1 1 8 1 1
loop(\(x,i).6x,((x div 2) div 3),1)
A243758: 1 1 1 1 1 1 6 6 6 6 6 6 36 36 36 36
(x mod (1 + (if (x + ~2) <= 0 then 2 else ((x div 2) div 3))))
A101668: 0 1 2 0 0 0 0 1 0 1 0 1 0 1 2 0
(1 + (3 * loop(\(x,i).5x,x,2)))
A199216: 7 31 151 751 3751 18751 93751 468751 2343751 11718751 58593751 292968751 1464843751 7324218751 36621093751 183105468751
(~1 + (3 * loop(\(x,i).5x,x,2)))
A198764: 5 29 149 749 3749 18749 93749 468749 2343749 11718749 58593749 292968749 1464843749 7324218749 36621093749 183105468749
(~1 + (3 * loop(\(x,i).x3,x2,2)))
A200822: 5 23 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).12x,x,3))
A199032: 2 35 431 5183 62207 746495 8957951 107495423 1289945087 15479341055 185752092671 2229025112063 26748301344767 320979616137215 3851755393646591 46221064723759103
loop(\(x,i).x2,1,(9x + 1))
A017174: 1 100 361 784 1369 2116 3025 4096 5329 6724 8281 10000 11881 13924 16129 18496
loop(\(x,i).x2,2,(9x + 1))
A017176: 1 10000 130321 614656 1874161 4477456 9150625 16777216 28398241 45212176 68574961 100000000 141158161 193877776 260144641 342102016
loop(\(x,i).(x * i),x,(3x2 + 3x + 1))
A056197: 1 7 38 222 1464 10920 91440 851760 8749440 98340480 1201132800 15846969600 224651750400 3406180377600 55009501747200 942833219328000
(1 + (if (~2 + (x div 5)) <= 0 then x else 3))
A338782: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 4
(1 + ((x + (if (x mod 4) <= 0 then 1 else 2)) div 3))
A090701: 1 2 2 2 2 3 3 4 4 4 5 5 5 6 6 6
(1 + loop(\(x,i).10x,x,3))
A199683: 4 31 301 3001 30001 300001 3000001 30000001 300000001 3000000001 30000000001 300000000001 3000000000001 30000000000001 300000000000001 3000000000000001
(~1 + loop(\(x,i).10x,x,3))
A198698: 2 29 299 2999 29999 299999 2999999 29999999 299999999 2999999999 29999999999 299999999999 2999999999999 29999999999999 299999999999999 2999999999999999
((x + 1) + loop(\(x,i).2x,x,3) - (x mod 2))
A116969: 4 7 15 27 53 101 199 391 777 1545 3083 6155 12301 24589 49167 98319
(if ((x + 1) mod 6) <= 0 then (x + ~3) else 1)
A327156: 1 1 1 1 1 2 1 1 1 1 1 8 1 1 1 1
(if (x mod 10) <= 0 then (x div 3) else 1)
A326029: 0 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1
(if (x mod 3) <= 0 then ((x + 2) - (x div 3)) else 1)
A208648: 2 1 1 4 1 1 6 1 1 8 1 1 10 1 1 12
(1 + ((if x <= 0 then 1 else x) + (x div 2) + (x div 3)))
A049625: 2 2 4 6 8 9 12 13 15 17 19 20 23 24 26 28
((if (x mod 3) <= 0 then 1 else 2) * (1 + (x div 3)))
A087627: 1 2 2 2 4 4 3 6 6 4 8 8 5 10 10 6
(if (x * ((x + 1) mod 4)) <= 0 then (x div 3) else 1)
A316767-A316695: 0 1 1 1 1 1 1 2 1 1 1 3 1 1 1 5
(if (~1 + (x mod 3)) <= 0 then (x - (x div 3)) else 1)
A092942: 0 1 1 2 3 1 4 5 1 6 7 1 8 9 1 10
(if ((x mod 3) mod 2) <= 0 then (x - (x div 3)) else 1)
A110090: 0 1 2 2 1 4 4 1 6 6 1 8 8 1 10 10
(if (x mod 7) <= 0 then (x mod 3) else 1)
A331596: 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1
(if ((x div 2) mod 5) <= 0 then (x mod 3) else 1)
A343639-A331592-A211111-A071625-A058060: 0 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1
(~1 + (loop(\(x,i).4x,x,1) + (x mod 3)))
A191272: 0 4 17 63 256 1025 4095 16384 65537 262143 1048576 4194305 16777215 67108864 268435457 1073741823
(if (x mod (2 + ((x div 2) mod 2))) <= 0 then (x mod 3) else 1)
A261029: 0 1 1 0 1 1 0 1 2 1 1 1 0 1 1 0
loop(\(x,i).10x,(x mod 3),1)
A145644: 1 10 100 1 10 100 1 10 100 1 10 100 1 10 100 1
loop(\(x,i).x2,(x div 3),(1 + (x mod 3)))
A121340: 1 2 3 1 4 9 1 16 81 1 256 6561 1 65536 43046721 1
((x + (if (x + ~2) <= 0 then x else 1)) mod (1 + (x mod 3)))
A111406: 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0
(1 + (if ((x * (x div 2)) mod 2) <= 0 then x else (x mod 3)))
A327938-A065883: 1 2 3 1 5 6 7 2 9 10 11 3 13 14 15 1
(1 + loop(\(x,i).7x,x,3))
A199418: 4 22 148 1030 7204 50422 352948 2470630 17294404 121060822 847425748 5931980230 41523861604 290667031222 2034669218548 14242684529830
(1 + loop(\(x,i).(x3 + ~3x),x,3))
A002813: 4 19 5779 192900153619 4611686018427387903 4611686018427387903
(if (~x + 2) <= 0 then (2 - ((~x2 + x) div 3)) else 1)
A097922: 1 1 3 4 6 9 12 16 21 26 32 39 46 54 63 72
(~1 + ((if ((x div 2) mod 2) <= 0 then (~x + 2) else x) mod 3))
A260192: 1 0 1 ~1 0 ~1 ~1 0 ~1 1 0 1 1 0 1 ~1
(1 + (if (~2 + (x div 2)) <= 0 then x else (x2 div 3)))
A057224: 1 2 3 4 5 6 13 17
(~1 + (if (~x + 4) <= 0 then ((x2 + x) div 2) else 1))
A184218: 0 0 0 0 9 14 20 27 35 44 54 65 77 90 104 119
loop(\(x,i).(x * i),(1 + (4x div (x + 2))),1)
A048765: 1 2 6 6 6 6 24 24 24 24 24 24 24 24 24 24
loop(\(x,i).(x * i),(x - (x2 div (x + 3))),1)
A343122-A338869: 1 1 2 2 2 2 2 6 6 6 6 6 6 6 6 6
(1 + ((x + 1) div loop(\(x,i).(2 + (x div 2)),(x + ~2),1)))
A343435: 2 3 4 3 2 3 3 3 4 4 4 5 5 5 6 6
(1 + loop(\(x,i).((x2 + 2) * (~1 + i)),2x,1))
A071219: 2 3 439
(~1 + loop(\(x,i).10x,2x,1))
A098609: 0 99 9999 999999 99999999 9999999999 999999999999 99999999999999 9999999999999999 999999999999999999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).~2x,((2x + ~1) + (x mod 2)),1)
A091095: 1 4 ~8 64 ~128 1024 ~2048 16384 ~32768 262144 ~524288 4194304 ~8388608 67108864 ~134217728 1073741824
loop(\(x,i).12x,(2x + 1),1)
A013717: 12 1728 248832 35831808 5159780352 743008370688 106993205379072 15407021574586368 2218611106740436992 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + ((2x + 1) * loop(\(x,i).2x2,2,2)))
A143034: 127 383 639 895 1151 1407 1663 1919 2175 2431 2687 2943 3199 3455 3711 3967
(~1 + ((2x + 1) * loop(\(x,i).x2,2,4)))
A143035: 255 767 1279 1791 2303 2815 3327 3839 4351 4863 5375 5887 6399 6911 7423 7935
(~1 + ((2x + 1) * loop(\(x,i).x3,2,2)))
A143036: 511 1535 2559 3583 4607 5631 6655 7679 8703 9727 10751 11775 12799 13823 14847 15871
loop(\(x,i).10x,(2x + 1),1)
A013715: 10 1000 100000 10000000 1000000000 100000000000 10000000000000 1000000000000000 100000000000000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).7x,(2x + 1),1)
A013712: 7 343 16807 823543 40353607 1977326743 96889010407 4747561509943 232630513987207 11398895185373143 558545864083284007 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,((x2 + x) mod (2x + 1)),1)
A076936: 1 4 2 32 4 256 8 2048 16 16384 32 131072 64 1048576 128 8388608
(1 + ((x * (if (x mod 2) <= 0 then 1 else x)) div (1 + (x div 2))))
A266662: 1 2 2 5 2 9 2 13 2 17 2 21 2 25 2 29
loop(\(x,i).i,(x4 mod (1 + (x div 2))),1)
A153094: 1 1 1 1 1 1 1 1 1 1 4 1 2 1 1 1
(if ((x + 2) mod 6) <= 0 then (~1 + (x div 2)) else 1)
A336870: 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1
(1 + (if (x + ~12) <= 0 then (x mod 2) else 1))
A082898: 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 2
(1 + (if ((x div 4) mod 3) <= 0 then (x mod 2) else 1))
A111626: 1 2 1 2 2 2 2 2 2 2 2 2 1 2 1 2
(1 + ((x + ~1) mod (1 + (if x <= 0 then 0 else 2) - (x mod 2))))
A205794: 1 1 2 1 1 1 3 1 2 1 1 1 3 1 2 1
(3 - (if (~2 + (x div 3)) <= 0 then (x mod 2) else 1))
A308006: 3 2 3 2 3 2 3 2 3 2 2 2 2 2 2 2
(1 + (if (x mod (2 + (x div 4))) <= 0 then (x mod 2) else 1))
A105220: 1 2 1 2 2 2 1 2 1 2 2 2 2 2 2 2
(1 + (loop(\(x,i).2x,x,1) div (3 - (x mod 2))))
A080880: 1 2 2 5 6 17 22 65 86 257 342 1025 1366 4097 5462 16385
(~1 + ((if (x + ~2) <= 0 then 1 else x) mod (3 - (x mod 2))))
A063933: 0 0 0 0 0 0 ~1 0 1 0 0 0 ~1 0 1 0
loop(\(x,i).4x,(1 + (x div 2) - (x mod 2)),1)
A094361: 4 1 16 4 64 16 256 64 1024 256 4096 1024 16384 4096 65536 16384
((x + 1) - loop(\(x,i).2x,(x div 2),(~1 + (x mod 2))))
A016724: 2 2 5 4 9 6 15 8 25 10 43 12 77 14 143 16
loop(\(x,i).(x * i),((x3 + 1) + (x mod 2)),1)
A079288: 1 6 362880 4611686018427387903
(1 + (1 mod (if ((x + ~1) mod 5) <= 0 then x else 1)))
A074064: 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1
loop(\(x,i).6x,(3x + 1),1)
A013738: 6 1296 279936 60466176 13060694016 2821109907456 609359740010496 131621703842267136 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).8x,(3x + 1),1)
A013742: 8 4096 2097152 1073741824 549755813888 281474976710656 144115188075855872 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).5x,(3x + 1),1)
A013736: 5 625 78125 9765625 1220703125 152587890625 19073486328125 2384185791015625 298023223876953125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).((x2 + x) div (1 + (x div 2))),x,1))
A256994: 2 3 4 7 11 19 35 67 131 259 515 1027 2051 4099 8195 16387
(1 + loop(\(x,i).(x * ((1 + i) * (1 + (i mod 2)))),x,1))
A082101: 2 5 13 97
(1 + (2 mod (if ((x + ~2) mod 6) <= 0 then x else 1)))
A262619-A166123: 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 1
((~x + 1) mod (1 + (if (x mod 6) <= 0 then x else 1)))
A340928: 0 0 1 0 1 0 2 0 1 0 1 0 2 0 1 0
(1 + loop(\(x,i).((x * ((2 + i) * (1 + i))) div 2),x,1))
A061213: 2 4 19 181 2701 56701 1587601 57153601 2571912001 141455160001 9336040560001 728211163680001 66267215894880001 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).x3,1,(x2 + 2x + 1)))
A123866: 0 63 728 4095 15624 46655 117648 262143 531440 999999 1771560 2985983 4826808 7529535 11390624 16777215
((2x2 + 2x + 1) + loop(\(x,i).2x,x,1))
A321123: 2 7 17 33 57 93 149 241 401 693 1245 2313 4409 8557 16805 33249
loop(\(x,i).(2x + 3),(~1 + (x * (x mod 2))),1)
A277866: 1 1 1 13 1 61 1 253 1 1021 1 4093 1 16381 1 65533
(1 + ((if x <= 0 then 0 else 9) div (x + 1)))
A317173-A190302: 1 5 4 3 2 2 2 2 2 1 1 1 1 1 1 1
(1 + ((x + 1) * loop(\(x,i).x2,2,5)))
A158383: 626 1251 1876 2501 3126 3751 4376 5001 5626 6251 6876 7501 8126 8751 9376 10001
(~1 + loop(\(x,i).(x * (2 + i)),5,(x + 1)))
A166931: 2519 5039 7559 10079 12599 15119 17639 20159 22679 25199 27719 30239 32759 35279 37799 40319
(1 + ((x + 1) * loop(\(x,i).(x2 + 4x + 4),2,1)))
A158131: 122 243 364 485 606 727 848 969 1090 1211 1332 1453 1574 1695 1816 1937
loop(\(x,i).(12x + ~6),(x + 1),1)
A127858: 6 66 786 9426 113106 1357266 16287186 195446226 2345354706 28144256466 337731077586 4052772931026 48633275172306 583599302067666 7003191624811986 84038299497743826
(1 + loop(\(x,i).(2x * (i * i)),3,(x + 1)))
A157990: 289 577 865 1153 1441 1729 2017 2305 2593 2881 3169 3457 3745 4033 4321 4609
(~1 + loop(\(x,i).(2x * (i * i)),3,(x + 1)))
A157997: 287 575 863 1151 1439 1727 2015 2303 2591 2879 3167 3455 3743 4031 4319 4607
(1 + ((x + 1) * loop(\(x,i).(x2 * i),2,3)))
A157952: 163 325 487 649 811 973 1135 1297 1459 1621 1783 1945 2107 2269 2431 2593
(~1 + ((x + 1) * loop(\(x,i).(x2 * i),2,3)))
A157954: 161 323 485 647 809 971 1133 1295 1457 1619 1781 1943 2105 2267 2429 2591
loop(\(x,i).((x + 1) + (4 * (i * i))),(x + 1),1)
A208598: 6 23 60 125 226 371 568 825 1150 1551 2036 2613 3290 4075 4976 6001
(~1 + loop(\(x,i).6x,(x + 1),(x + 1)))
A064752: 5 71 647 5183 38879 279935 1959551 13436927 90699263 604661759 3990767615 26121388031 169789022207 1097098297343 7052774768639 45137758519295
(~1 + loop(\(x,i).8x,(x + 1),(x + 1)))
A064754: 7 127 1535 16383 163839 1572863 14680063 134217727 1207959551 10737418239 94489280511 824633720831 7146825580543 61572651155455 527765581332479 4503599627370495
(~1 + ((x + 1) * loop(\(x,i).x3,2,(x + 1))))
A123867: 0 1023 59048 1048575 9765624 60466175 282475248 1073741823 3486784400 9999999999 25937424600 61917364223 137858491848 289254654975 576650390624 1099511627775
(1 + ((x + 1) * loop(\(x,i).(x * (1 + (x * i))),x,1)))
A295391: 2 5 31 1241 1923551 4440055831261 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).12x,2,(x + 1)))
A158133: 145 289 433 577 721 865 1009 1153 1297 1441 1585 1729 1873 2017 2161 2305
(~1 + loop(\(x,i).12x,2,(x + 1)))
A158136: 143 287 431 575 719 863 1007 1151 1295 1439 1583 1727 1871 2015 2159 2303
(1 + ((x + 1) * loop(\(x,i).x2,(x2 + ~1),2)))
A119497: 3 5 769 4611686018427387903
(1 + ((x + 1) * loop(\(x,i).(x2 + 2x + 1),2,2)))
A158128: 101 201 301 401 501 601 701 801 901 1001 1101 1201 1301 1401 1501 1601
(1 + ((x + 1) * (2 + loop(\(x,i).2x,(x + ~1),2))))
A292773: 5 9 19 41 91
(~1 + ((x + 1) * loop(\(x,i).4x2,2,2)))
A158421: 1023 2047 3071 4095 5119 6143 7167 8191 9215 10239 11263 12287 13311 14335 15359 16383
(~1 + loop(\(x,i).x2,1,(8x + 8)))
A158684: 63 255 575 1023 1599 2303 3135 4095 5183 6399 7743 9215 10815 12543 14399 16383
loop(\(x,i).x2,1,(8x + 7))
A017150: 49 225 529 961 1521 2209 3025 3969 5041 6241 7569 9025 10609 12321 14161 16129
loop(\(x,i).x2,2,(8x + 7))
A017152: 2401 50625 279841 923521 2313441 4879681 9150625 15752961 25411681 38950081 57289761 81450625 112550881 151807041 200533921 260144641
(1 + ((x + 1) * loop(\(x,i).(x2 + 4x + 4),2,2)))
A158272: 325 649 973 1297 1621 1945 2269 2593 2917 3241 3565 3889 4213 4537 4861 5185
(~1 + ((x + 1) * loop(\(x,i).(x2 + 4x + 4),2,2)))
A158306: 323 647 971 1295 1619 1943 2267 2591 2915 3239 3563 3887 4211 4535 4859 5183
(1 + ((x + 1) * loop(\(x,i).((x + 2) * (x + i)),2,2)))
A158223: 197 393 589 785 981 1177 1373 1569 1765 1961 2157 2353 2549 2745 2941 3137
(~1 + ((x + 1) * loop(\(x,i).((x + 2) * (x + i)),2,2)))
A158225: 195 391 587 783 979 1175 1371 1567 1763 1959 2155 2351 2547 2743 2939 3135
loop(\(x,i).(2x * i),x,(4x + 5))
A158455: 5 18 104 816 8064 96000 1336320 21288960 381911040 7617576960 167215104000 4005730713600 103985499340800 2907670000435200 87128076504268800 2785241789890560000
loop(\(x,i).x2,3,(4x + 3))
A016844: 6561 5764801 214358881 2562890625 16983563041 78310985281 282429536481 852891037441 2251875390625 5352009260481 11688200277601 23811286661761 45767944570401 83733937890625
loop(\(x,i).x3,1,(4x + 3))
A016839: 27 343 1331 3375 6859 12167 19683 29791 42875 59319 79507 103823 132651 166375 205379 250047
loop(\(x,i).x3,2,(4x + 3))
A016845: 19683 40353607 2357947691 38443359375 322687697779 1801152661463 7625597484987 26439622160671 78815638671875 208728361158759 502592611936843 1119130473102767 2334165173090451 4605366583984375
loop(\(x,i).(2x + 20),(x + 1),1)
A305064: 22 64 148 316 652 1324 2668 5356 10732 21484 42988 85996 172012 344044 688108 1376236
loop(\(x,i).x2,1,(x2 + 5x + 3))
A207399: 9 81 289 729 1521 2809 4761 7569 11449 16641 23409 32041 42849 56169 72361 91809
loop(\(x,i).((x + 2) - ((~x + 2) div (2 + i))),(x + 1),1)
A280944: 3 6 9 13 17 21 26 31 36 41 46 52 58 64 70 76
(1 + (loop(\(x,i).(3x + 2),x,2) div (x + 1)))
A129787: 3 5 9 21 49 122 313 821 2187 5905 16105 44287 122641 341641 956594 2690421
(1 + ((x + 1) * (if ((x * (x mod 2)) div 2) <= 0 then x else 2)))
A096102: 1 3 7 9 21 13
loop(\(x,i).(2x2 + 2x),(x2 + 3x + 2),1)
A116101: 40 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x2 + 4),(x2 + 3x + 2),1)
A116246: 76 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + x + 2),(x2 + 3x + 2),1)
A119566: 22 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x2 + x),(x2 + 3x + 2),1)
A062012: 21 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),x,(x3 + x2 + 2x + 1))
A002776: 1 5 34 258 2136 19320 190800 2051280 23909760 300827520 4067884800 58877280000 908666035200 14901260774400 258832346572800 4748165630208000
(1 + ((x + 1) * (if (x + ~2) <= 0 then x else (x2 + 2x))))
A046859: 1 3 7 61
(1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))
A006519: 1 2 1 4 1 2 1 8 1 2 1 4 1 2 1 16
loop(\(x,i).(1 + (x mod (1 + (i div 3)))),(x + ~1),1)
A243712: 1 1 1 1 2 1 2 3 1 2 3 4 1 2 3 4
loop(\(x,i).(2x mod 9),(x + ~1),1)
A029898: 1 1 2 4 8 7 5 1 2 4 8 7 5 1 2 4
loop(\(x,i).((x - (2 * i)) * (1 + (2 * i))),(x + ~1),1)
A339516: 1 1 ~3 ~35 ~287 ~2655 ~29315 ~381251 ~5718975 ~97222847 ~1847234435 ~38791923555 ~892214242271 ~22305356057375 ~602244613549827 ~17465093792945795
loop(\(x,i).((x * (1 + i)) div (1 + (i div 2))),(x + ~1),1)
A001405: 1 1 2 3 6 10 20 35 70 126 252 462 924 1716 3432 6435
loop(\(x,i).(1 + (x * ((i * i) + (x div 2)))),(x + ~1),1)
A287149: 1 1 2 11 155
loop(\(x,i).(x - (x div (~2 + (x mod ~2)))),(x + ~1),1)
A000792: 1 1 2 3 4 6 9 12 18 27 36 54 81 108 162 243
loop(\(x,i).(2 * ((x + ~1) + (2 * (i mod 2)))),(x + ~1),1)
A084214: 1 1 4 6 14 26 54 106 214 426 854 1706 3414 6826 13654 27306
loop(\(x,i).(x + ((i mod 2) + (2 * (x div 2)))),(x + ~1),1)
A115451: 1 1 2 4 9 17 34 68 137 273 546 1092 2185 4369 8738 17476
loop(\(x,i).(x * (1 + (6 * i))),(x + ~1),1)
A008542: 1 1 7 91 1729 43225 1339975 49579075 2131900225 104463111025 5745471106375 350473737488875 23481740411754625 1714167050058087625 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + ((2 * i) div 3))),(x + ~1),1)
A004395: 1 1 1 2 6 18 72 360 1800 10800 75600 529200 4233600 38102400 342921600 3429216000
loop(\(x,i).(x + (x mod 9)),(x + ~1),1)
A130917: 1 1 2 4 8 16 23 28 29 31 35 43 50 55 56 58
loop(\(x,i).(x * (1 + (8 * i))),(x + ~1),1)
A045755: 1 1 9 153 3825 126225 5175225 253586025 14454403425 939536222625 68586144251625 5555477684381625 494437513909964625 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (2 - (3 * (i mod 2)))),(x + ~1),1)
A117575: 1 1 ~1 ~2 2 4 ~4 ~8 8 16 ~16 ~32 32 64 ~64 ~128
loop(\(x,i).(x * (x + ((x + 2) * (i mod 2)))),(x + ~1),1)
A262546: 1 1 4 16 544
loop(\(x,i).(x + (i * i * i * i * i)),(x + ~1),1)
A263689: 1 1 2 34 277 1301 4426 12202 29009 61777 120826 220826 381877 630709 1002002 1539826
(1 + loop(\(x,i).11x,x,1))
A034524: 2 12 122 1332 14642 161052 1771562 19487172 214358882 2357947692 25937424602 285311670612 3138428376722 34522712143932 379749833583242 4177248169415652
(1 + loop(\(x,i).17x,x,1))
A224384: 2 18 290 4914 83522 1419858 24137570 410338674 6975757442 118587876498 2015993900450 34271896307634 582622237229762 9904578032905938 168377826559400930 2862423051509815794
(~1 + loop(\(x,i).(x + ((x + (i div 2)) * (2 + i))),x,1))
A079755: 0 3 23 148 1054 8453 76109 761126 8372436 100469287 1306100803 18285411320 274281169898 4388498718473 74604478214169 1342880607855178
((x2 + ~x + 1) + (if (x mod 3) <= 0 then 0 else 2))
A163979: 1 3 5 7 15 23 31 45 59 73 93 113 133 159 185 211
(x div (3 + (if (~2 + (x div 4)) <= 0 then 2 else 0)))
A035660: 0 0 0 0 0 1 1 1 1 1 2 2 4 4 4 5
(1 + (if ((x div 2) - (x mod 8)) <= 0 then 0 else 2))
A324497: 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 1
loop(\(x,i).i,(x mod (2 - ((x div 4) div ~2))),1)
A341674: 1 1 1 1 1 2 1 1 2 1 1 2 1 1 2 3
(if (x mod 2) <= 0 then (2 + (x mod 4)) else ~3)
A131731: 2 ~3 4 ~3 2 ~3 4 ~3 2 ~3 4 ~3 2 ~3 4 ~3
(if x <= 0 then 1 else (x - ((x2 + 2x) div ~3)))
A183861: 1 2 5 8 12 17 22 28 35 42 50 59 68 78 89 100
((if (x mod 3) <= 0 then 0 else 2) - (x div ~3))
A226576: 0 3 3 1 4 4 2 5 5 3 6 6 4 7 7 5
(if (x mod 2) <= 0 then 1 else (x div (2 - (x div ~3))))
A122402: 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2
(if x <= 0 then 1 else (3x - (x div ~3)))
A123384: 1 4 7 10 14 17 20 24 27 30 34 37 40 44 47 50
loop(\(x,i).2x,(x div 2),((x + 1) - (x div ~2)))
A058582: 1 3 8 12 28 36 80 96 208 240 512 576 1216 1344 2816 3072
(1 + (loop(\(x,i).(1 + (x * i) - (i div 2)),x,0) div 2))
A177921: 1 1 2 4 12 58
((8x + 1) div (1 + (if x <= 0 then 0 else 2)))
A097911: 1 3 5 8
A008576: 1 3 5 8 11 13 16 19 21 24 27 29 32 35 37 40
((x + 4) - ((~x + 1) div (1 + (if x <= 0 then 0 else 2))))
A024352: 3 5 7 8 9 11 12 13 15 16 17 19 20 21 23 24
(if ((x + ~1) mod 11) <= 0 then 2 else 1)
A131789: 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1
(if x <= 0 then 1 else ((x + ~1) - (2 * (x mod ~3))))
A074066: 1 4 3 2 7 6 5 10 9 8 13 12 11 16 15 14
(1 + (x div (if (~2 + (x div 5)) <= 0 then 1 else 2)))
A291581-A291580-A058035: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 8
(if ((x + 3) mod 7) <= 0 then 2 else 1)
A120336-A030392: 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1
(if (2 - ((x + 2) mod 7)) <= 0 then 2 else 1)
A083534: 2 2 2 2 2 1 1 2 2 2 2 2 1 1 2 2
(1 + loop(\(x,i).x2,x,14))
A152587: 15 197 38417 1475789057 2177953337809371137 4611686018427387903 4611686018427387903
(if (~x + 2) <= 0 then ((x div 7) mod 2) else 1)
A266253: 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0
(1 + ((x + 1) div (if (~2 + (x div 3)) <= 0 then 1 else 2)))
A254596: 2 3 4 5 6 7 8 9 10 6 6 7 7 8 8 9
(1 + (2 * (3 + loop(\(x,i).4x,x,1))))
A193579: 9 15 39 135 519 2055 8199 32775 131079 524295 2097159 8388615 33554439 134217735 536870919 2147483655
(if (~x + 2) <= 0 then (2 * (1 + (((x + ~1) div 2) div 2))) else 1)
A096445: 1 1 2 2 2 4 4
A007614: 1 1 2 2 2 4 4 4 4 6 6 6 6 8 8 8
(if (x mod (1 + (2 * (2 + (x div 4))))) <= 0 then 2 else 1)
A078572: 2 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1
(1 + (x div (2 + (if (~4 + (x div 2)) <= 0 then 2 else 1))))
A185322: 1 1 1 1 2 2 2 2 3 3 4 4 5 5 5 6
(if (x mod (1 + (8 * (x mod 2)))) <= 0 then 2 else 1)
A214715: 2 1 2 1 2 1 2 1 2 2 2 1 2 1 2 1
(if ((x + ~1) div (~1 + (2 * (x mod 4)))) <= 0 then 2 else 1)
A106825: 1 2 2 2 2 1 1 1 2 1 1 1 2 1 1 1
loop(\(x,i).(x * i),(8x + 14),1)
A045519: 87178291200 4611686018427387903 4611686018427387903 4611686018427387903
(if ((1 + (x div 3)) mod 5) <= 0 then 2 else 1)
A152906-A109037-A030597: 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1
loop(\(x,i).i,(~2 + ((2x + ~1) div 5)),1)
A103264: 1 1 1 1 1 1 1 1 1 1 1 2 2 3 3 3
(if (x mod 2) <= 0 then (((x + ~1) div 5) mod 2) else 1)
A137161: 1 1 0 1 0 1 1 1 1 1 1 1 0 1 0 1
(~1 + loop(\(x,i).(x2 + ~2),x,10))
A145509: 9 97 9601 92198401 8500545331353601 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x2 + x),x,10))
A144784: 11 111 12211 149096311 22229709804712411 4611686018427387903 4611686018427387903
loop(\(x,i).i,((x + 1) mod (2 + (x div 5))),1)
A285851: 1 1 1 1 1 1 1 2 1 1 3 1 1 2 3 1
(1 + (2 * (3 + loop(\(x,i).4x,x,2))))
A195463: 11 23 71 263 1031 4103 16391 65543 262151 1048583 4194311 16777223 67108871 268435463 1073741831 4294967303
(if ((x + 3) mod (2x + ~5)) <= 0 then 2 else 1)
A258383: 2 2 2 2 1 1 1 1 2 1 1 1 1 1 1 1
loop(\(x,i).x2,1,(8x + 3))
A017102: 9 121 361 729 1225 1849 2601 3481 4489 5625 6889 8281 9801 11449 13225 15129
loop(\(x,i).x2,2,(8x + 3))
A017104: 81 14641 130321 531441 1500625 3418801 6765201 12117361 20151121 31640625 47458321 68574961 96059601 131079601 174900625 228886641
loop(\(x,i).3x,(8x + 2),1)
A013790: 9 59049 387420489 2541865828329 16677181699666569 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if ((x2 + x) mod (2 + (x div 2))) <= 0 then 1 else 2))
A281855: 2 2 2 2 2 3 3 3 2 2 3 3 3 3 3 3
(1 + ((x div 4) mod (if (~2 + (x div 2)) <= 0 then 1 else 2)))
A342461: 1 1 1 1 1 1 2 2 1 1 1 1 2 2 2 2
(if (x mod (3 * (1 + (x div 4)))) <= 0 then 2 else 1)
A205375: 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 1
(if x <= 0 then 1 else ((x + ~1) - (2 * ((x + 1) div 3))))
A253174: 1 0 ~1 0 1 0 1 2 1 2 3 2 3 4 3 4
loop(\(x,i).(i div 3),(2 * ((x + ~1) div 3)),1)
A262742: 1 1 1 1 0 0 0 1 1 1 2 2 2 2 2 2
(if ((x mod ~8) mod 3) <= 0 then 2 else 1)
A245222: 2 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1
(if (((x + 2) mod 8) mod 3) <= 0 then 2 else 1)
A055443-A003842: 1 2 1 1 2 1 2 1 1 2 1 1 2 1 2 1
loop(\(x,i).i,(x mod (2 + ((x div 4) mod 3))),1)
A321744: 1 1 1 1 1 2 1 1 1 1 2 3 1 1 1 1
(if ((x + ~2) mod (3 * (2 + (x mod 2)))) <= 0 then 2 else 1)
A085006: 1 1 2 1 1 1 1 1 2 1 1 2 1 1 2 1
loop(\(x,i).(~x + 4),(~2 + ((x + ~2) div 3)),1)
A172364-A172358: 1 1 1 1 1 1 1 1 1 1 1 3 3 3 1 1
loop(\(x,i).3x,(6x + 2),1)
A013744: 9 6561 4782969 3486784401 2541865828329 1853020188851841 1350851717672992089 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 2) - loop(\(x,i).i,(~2 + (2x div 3)),1))
A091987: 1 2 3 4 5 6 6 7 7 7 8 8 8 9 9 9
loop(\(x,i).2x,x,(1 + (2 * (2x div 3))))
A168057: 1 2 12 40 80 224 576 1152 2816 6656 13312 30720 69632 139264 311296 688128
(x div (3 + (if (x mod 2) <= 0 then (x div 2) else 3)))
A161312-A161298-A161285-A161260-A161246-A161232-A161082-A161056-A161031-A160977: 0 0 0 0 0 0 1 1 1 1 1 1 1 2 1 2
(if (~x + 4) <= 0 then (2 + ((x div 2) div 3)) else 1)
A156081: 1 1 1 1 2 2 3 3 3 3 3 3 4 4 4 4
(if (x + ~2) <= 0 then x else (3 + ((x div 2) div 3)))
A262070: 0 1 2 3 3 3 4 4 4 4 4 4 5 5 5 5
(if ((x + 1) mod 5) <= 0 then 6 else 1)
A339747: 1 1 1 1 6 1 1 1 1 6 1 1 1 1 6 1
(if ((x + 1) mod 6) <= 0 then 6 else 1)
A325471-A234959: 1 1 1 1 1 6 1 1 1 1 1 6 1 1 1 1
(21 * (if x <= 0 then 1 else 2))
A040420: 21 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42
(7 * loop(\(x,i).2x,x,3))
A175805: 21 42 84 168 336 672 1344 2688 5376 10752 21504 43008 86016 172032 344064 688128
(loop(\(x,i).~2x,x,1) mod 7)
A070365: 1 5 4 6 2 3 1 5 4 6 2 3 1 5 4 6
((if x <= 0 then 1 else x) - ((x + 1) div 7))
A106744: 1 1 2 3 4 5 5 6 7 8 9 10 11 11 12 13
(loop(\(x,i).3x,x,1) mod 7)
A033940: 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6
(14 * (2 + (if x <= 0 then 0 else 2)))
A040756: 28 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56
(7 * (2 - ((if x <= 0 then 1 else x) mod 2)))
A040043: 7 7 14 7 14 7 14 7 14 7 14 7 14 7 14 7
(loop(\(x,i).(x + (i * i)),x,2) div 7)
A173721: 0 0 1 2 4 8 13 20 29 41 55 72 93 117 145 177
(loop(\(x,i).(x * (i * i)),x,2) div 7)
A285995: 0 0 1 10 164
loop(\(x,i).(4x + 1),x,7)
A072261: 7 29 117 469 1877 7509 30037 120149 480597 1922389 7689557 30758229 123032917 492131669 1968526677 7874106709
loop(\(x,i).(x2 + ~x + ~1),x,7)
A144747: 7 41 1639 2684681 7207509387079 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x2 + x) div 2),x,7)
A050548: 7 28 406 82621 3413156131 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(x + (x div 2)),7)
A135536: 7 14 56 112 448 896 3584 7168 28672 57344 229376 458752 1835008 3670016 14680064 29360128
loop(\(x,i).5x,x,7)
A005055: 7 35 175 875 4375 21875 109375 546875 2734375 13671875 68359375 341796875 1708984375 8544921875 42724609375 213623046875
(1 + ((x + (if (x mod 2) <= 0 then x else 1)) mod 6))
A110551: 1 3 5 5 3 1 1 3 5 5 3 1 1 3 5 5
((~x + 3) mod loop(\(x,i).i,(x + ~6),1))
A165091-A037903-A037895-A037841: 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6
(x + loop(\(x,i).i,(x + ~6),1) - (x div 2))
A079685: 1 2 2 3 3 4 4 5 6
A035448: 1 2 2 3 3 4 4 5 6 8 9 11 12 14 15 17
(x mod (1 + (2 * ((if (x mod 2) <= 0 then 1 else x) mod 3))))
A078979: 0 1 2 0 1 0 0 1 2 0 1 1 0 1 2 0
((x + 8) - (if (x + ~3) <= 0 then 2 else 1))
A143616: 6 7 8 9 11 12 13 14 15 16 17 18 19 20 21 22
(if (~x + 2) <= 0 then (x - ((2 - (x div 3)) div 2)) else 1)
A247833: 1 1 1 3 4 5 6 7 8 10 11 12 13 14 15 17
(if (x + ~2) <= 0 then 1 else (x div (3 + (x div 3))))
A086257: 1 1 1 0 1 1 1 1 1 1 1 1 1 1 2 1
(if (x mod 3) <= 0 then (x div (2 + (x div 3))) else 1)
A286334: 0 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2
(if (x mod 3) <= 0 then 0 else (1 + (2 * (x div 3))))
A102899: 0 1 1 0 3 3 0 5 5 0 7 7 0 9 9 0
(if (~2 + (x div 4)) <= 0 then ((x mod 3) div 2) else 1)
A285177: 0 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1
(1 + (loop(\(x,i).(x * (i * (1 + i))),(x + ~2),1) div 2))
A319621: 1 1 1 2 7 73
(1 + (((x2 + ~1) div 2) div (if (x + ~2) <= 0 then 1 else 2)))
A181385: 0 1 2 3 4 7 9 13 16 21 25 31 36 43 49 57
(if (2 - (5 mod (1 + (x div 2)))) <= 0 then 2 else 1)
A343504-A328582-A328581-A227153: 1 1 1 1 2 2 1 1 1 1 2 2 2 2 2 2
(~1 + loop(\(x,i).x3,x,(2 * (1 + (x mod 2)))))
A283931: 1 63 511
(1 + loop(\(x,i).x2,((x + 1) + (x div 4)),2))
A222008: 5 17 257 65537
A286678: 5 17 257 65537 4611686018427387903 4611686018427387903
(~1 + (2 * loop(\(x,i).(2 * (x - ((x + i) mod 2))),x,1)))
A267052: 1 3 7 11 23 43 87 171 343 683 1367 2731 5463 10923 21847 43691
(1 + (loop(\(x,i).((2 * (x + i)) + (i mod 2)),x,1) div 2))
A026635: 1 3 8 18 40 84 174 354 716 1440 2890 5790 11592 23196 46406 92826
(~1 + (loop(\(x,i).(2x2 + 4x),2,(x + 1)) div 2))
A069760: 47 287 959 2399 5039 9407 16127 25919 39599 58079 82367 113567 152879 201599 261119 332927
(~1 + loop(\(x,i).(x2 + 2x),(x2 + 3x + 2),2))
A243432: 79 4611686018427387903
A093404: 79 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(x2 * i),(x2 + 3x + 2),2))
A091308: 31 4611686018427387903 4611686018427387903
((1 + loop(\(x,i).2x,x,2)) div (2x + 3))
A191633: 1 1 1 1 3 5 8 15 27 48 89 163 303 565 1057 1985
loop(\(x,i).((x2 + ~x) div 2),2,(2x + 3))
A062346: 3 45 210 630 1485 3003 5460 9180 14535 21945 31878 44850 61425 82215 107880 139128
(loop(\(x,i).4x,x,2) mod (2x + 3))
A178970: 2 3 4 2 6 7 2 9 10 2 12 8 20 15 16 2
loop(\(x,i).(x * (1 + i)),2x,(2x + 3))
A174549: 3 30 840 45360 3991680 518918400 93405312000 22230464256000 6758061133824000 2554547108585472000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,((2 * (x mod 2)) + ((x + 1) div 2)),1)
A164587: 1 8 2 16 4 32 8 64 16 128 32 256 64 512 128 1024
loop(\(x,i).10x,((x + 1) div 2),1)
A286508: 1 10 10 100 100 1000 1000 10000 10000 100000 100000 1000000 1000000 10000000 10000000 100000000
(1 + (((x + 1) * loop(\(x,i).2x,(x + ~1),x)) div 2))
A048506: 1 2 7 25 81 241 673 1793 4609 11521 28161 67585 159745 372737 860161 1966081
(~1 + loop(\(x,i).(x4 + 1),(x + ~1),2))
A144830: 1 1 16 83521 4611686018427387903
loop(\(x,i).(~x2 + 2x + 3),((x + ~1) div 2),1)
A239351: 1 1 1 4 4 ~5
((x + 2) - loop(\(x,i).(2 * (x - i)),((x + ~1) div 2),1))
A081026: 1 2 3 5 6 11 12 23 24 47 48 95 96 191 192 383
(1 div ((x + 1) - (2 * (if (x mod 3) <= 0 then 0 else 2))))
A185906: 1 ~1 ~1 0 1 0 0 0 0 0 0 0 0 0 0 0
(1 + (2 * (if (~2 + (x div 5)) <= 0 then 0 else 2)))
A333751-A269626-A069293: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5
(1 + (2 * (if (~6 + (x div 2)) <= 0 then 0 else 2)))
A147494-A147016: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 5
(~1 - (x mod (2 * (if (x div 2) <= 0 then 2 else ~2))))
A194525: ~1 ~2 1 0 ~1 2 1 0 ~1 2 1 0 ~1 2 1 0
(3 + (if x <= 0 then 1 else x) - ((x div 2) div ~2))
A006672: 4 4 6 7 8 9 11 12 13 14
((x + 2) - (if x <= 0 then 1 else (x div ~5)))
A251392: 1 4 5 6 7 8 10 11 12 13 14 16 17 18 19 20
((if (x + ~2) <= 0 then 1 else 2) - (x div ~5))
A162988: 1 2 2 3 3 3 4 4 4 4 4 5 5 5 5 5
(if (x + ~2) <= 0 then x else (x - (x div ~5)))
A138083: 0 1 2 4 5 6
A080240: 0 1 2 4 5 6 8 9 10 11 12 14 15 16 17 18
(if x <= 0 then 1 else (x div (3 - (x div ~4))))
A058776: 1 0 0 0 1 1 1 1 1 1 1 1 2 1 2 2
(1 + (if x <= 0 then 1 else (2 * (2x - (x div ~2)))))
A063097: 2 7 11 17 21 27 31 37 41 47 51 57 61 67 71 77
loop(\(x,i).x2,1,(1 + (2 * (x - (x div ~2)))))
A216869: 1 25 49
A104777: 1 25 49 121 169 289 361 529 625 841 961 1225 1369 1681 1849 2209
(if ((x + 1) mod (2 * (1 + (2 mod (x + 1))))) <= 0 then 2 else 1)
A062557: 1 2 1 1 1 2 1 1 1 1 1 2 1 1 1 1
(if x <= 0 then 0 else (~1 + (2 * ((x div ~3) mod 2))))
A070747: 0 1 1 1 ~1 ~1 ~1 1 1 1 ~1 ~1 ~1 1 1 1
(1 + (x div (2 + (if ((x div 2) mod 4) <= 0 then 1 else 2))))
A025424: 1 1 1 1 2 2 2 2 3 4 3 3 4 4 4 4
(if (x mod 2) <= 0 then (2 * ((x div 5) mod 2)) else 1)
A175799: 0 1 0 1 0 1 2 1 2 1 0 1 0 1 0 1
(1 + ((x div (if (x mod (2 + (x mod 2))) <= 0 then 1 else 2)) mod 2))
A300409-A279495: 1 1 1 2 1 1 1 2 1 2 1 2 1 1 1 2
(1 + (if (x mod 2) <= 0 then (((x + ~1) div 3) mod 2) else 2))
A071282: 2 3 1 3 2 3 2 3 1 3 2 3 2 3 1 3
(if (x mod 2) <= 0 then (2 * (((x div 2) div 3) mod 2)) else 1)
A221169: 0 1 0 1 0 1 2 1 2 1 2 1 0 1 0 1
(1 + (4 * (loop(\(x,i).x2,x,2) div 3)))
A101694: 1 5 21 341 87381 5726623061 4611686018427387903 4611686018427387903 4611686018427387903
(if ((1 + ((x + 1) div 2)) mod 6) <= 0 then 2 else 1)
A083888: 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1
(1 + (4 * loop(\(x,i).(2x + 4),x,3)))
A305155: 13 41 97 209 433 881 1777 3569 7153 14321 28657 57329 114673 229361 458737 917489
(if (~x + 4) <= 0 then (2 + ((x mod 3) div 2)) else 1)
A166497: 1 1 1 1 2 3 2 2 3 2 2 3 2 2 3 2
((x + 1) - ((0 - (x div (if (x + ~2) <= 0 then 1 else 2))) div 2))
A247914-A184518: 1 3 4 5 6 7 9 10 11 12 14 15 16 17 19 20
(~1 + loop(\(x,i).x2,1,(8x + 4)))
A177065: 15 143 399 783 1295 1935 2703 3599 4623 5775 7055 8463 9999 11663 13455 15375
loop(\(x,i).x2,1,(8x + 5))
A017126: 25 169 441 841 1369 2025 2809 3721 4761 5929 7225 8649 10201 11881 13689 15625
loop(\(x,i).x2,2,(8x + 5))
A017128: 625 28561 194481 707281 1874161 4100625 7890481 13845841 22667121 35153041 52200625 74805201 104060401 141158161 187388721 244140625
(5 + loop(\(x,i).6x,x,1))
A253209: 6 11 41 221 1301 7781 46661 279941 1679621 10077701 60466181 362797061 2176782341 13060694021 78364164101 470184984581
(3 + (loop(\(x,i).(4x + 2),x,1) div 2))
A340498: 3 6 16 56 216 856 3416 13656 54616 218456 873816 3495256 13981016 55924056 223696216 894784856
(1 + (((0 - (if (~2 + (x div 2)) <= 0 then x else 1)) div 2) div 2))
A016346-A016284-A015934-A014034: 1 0 0 0 0 ~1 0 0 0 0 0 0 0 0 0 0
(if x <= 0 then 1 else (2x2 + ~4x + 7))
A207079: 1 5 7 13 23
(1 + (2 * loop(\(x,i).(2x + 6),(x + 1),2)))
A304517: 21 53 117 245 501 1013 2037 4085 8181 16373 32757 65525 131061 262133 524277 1048565
(1 + (2 * loop(\(x,i).(x2 + ~2),x,(2x + 2))))
A057706: 5 29 2309
loop(\(x,i).((x mod 4) * i),(((x + 1) div 2) div 2),1)
A248782: 1 1 1 1 1 1 1 2 2 2 2 6 6 6 6 8
(5 + loop(\(x,i).5x,x,1))
A178676: 6 10 30 130 630 3130 15630 78130 390630 1953130 9765630 48828130 244140630 1220703130 6103515630 30517578130
(~5 + loop(\(x,i).5x,x,1))
A178671: ~4 0 20 120 620 3120 15620 78120 390620 1953120 9765620 48828120 244140620 1220703120 6103515620 30517578120
(x mod (1 + (4 * (if (x mod 3) <= 0 then 0 else 2))))
A070692: 0 1 2 0 4 5 0 7 8 0 1 2 0 4 5 0
(1 + ((if (x mod 2) <= 0 then x else (x mod ~4)) div 2))
A110514: 1 ~1 2 0 3 ~1 4 0 5 ~1 6 0 7 ~1 8 0
(if (2x mod (2 + (x mod 6))) <= 0 then 2 else 1)
A214713: 2 1 2 1 1 1 2 1 2 1 1 1 2 1 2 2
(~1 + (4 * (4 + loop(\(x,i).2x,x,1))))
A168144: 19 23 31 47 79
(if (4 + (x div (2 * (~2 + (x mod 2))))) <= 0 then 2 else 1)
A338650: 1 1 1 1 1 1 1 2 1 2 1 2 1 2 2 2
(if ((1 + ((x + 1) div 2)) mod 8) <= 0 then 2 else 1)
A184318: 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1
(if ((2 - (x div ~2)) mod 8) <= 0 then 2 else 1)
A318191-A208183: 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1
(if (((x + ~2) + (x div 2)) mod 8) <= 0 then 2 else 1)
A249545-A122934-A072170: 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1
(loop(\(x,i).2x,x,1) mod 17)
A222011: 1 2 4 8
A062116: 1 2 4 8 16 15 13 9 1 2 4 8 16 15 13 9
loop(\(x,i).3x,x,17)
A258598: 17 51 153 459 1377 4131 12393 37179 111537 334611 1003833 3011499 9034497 27103491 81310473 243931419
loop(\(x,i).(x * i),x,(x div 15))
A061126: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1307674368000
(1 + loop(\(x,i).(x2 + x),x,16))
A179093: 17 273 74257 5514027793 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).(2x + 1),x,8) div 2))
A116453: 5 9 18 36 72 144 288 576 1152 2304 4608 9216 18432 36864 73728 147456
(~1 + (4 * loop(\(x,i).(2x + 4),x,4)))
A166118: 15 47 111 239 495 1007 2031 4079 8175 16367 32751 65519 131055 262127 524271 1048559
(if ((x2 + 1) mod (2 + (x mod 4))) <= 0 then 2 else 1)
A031230: 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1
(1 + (loop(\(x,i).2x,x,(x + 6)) div 2))
A115618: 4 8 17 37 81 177 385 833 1793 3841 8193 17409 36865 77825 163841 344065
loop(\(x,i).(x * (1 + i)),16x,1)
A198803: 1 355687428096000 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (4 * loop(\(x,i).3x,2x,2)))
A199677: 9 73 649 5833 52489 472393 4251529 38263753 344373769 3099363913 27894275209 251048476873 2259436291849 20334926626633 183014339639689 1647129056757193
(~1 + (4 * loop(\(x,i).3x,2x,2)))
A198966: 7 71 647 5831 52487 472391 4251527 38263751 344373767 3099363911 27894275207 251048476871 2259436291847 20334926626631 183014339639687 1647129056757191
(if ((x2 + 2x) mod (4 + (x div 2))) <= 0 then 2 else 1)
A276948: 2 1 1 2 2 1 1 2 2 1 1 1 1 1 1 1
(if ((2 + (x div 2)) mod (2 * (2 + (x mod 2)))) <= 0 then 2 else 1)
A263723: 1 1 1 1 2 1 1 1 1 2 1 1 2 1 1 1
(if ((1 + ((x + 1) div 3)) mod 4) <= 0 then 2 else 1)
A025454: 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1
(if (x - (4 * (~1 + (x div 3)))) <= 0 then 2 else 1)
A115579-A115573: 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2
(if ((1 + ((x * (x div 2)) div 2)) mod 4) <= 0 then 2 else 1)
A298917: 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1
(~1 + (2 * loop(\(x,i).x2,(2x + ~1),4)))
A101329: 7 31 131071 4611686018427387903
((x + ~1) - (2 * ((x + ~2) div (if x <= 0 then 1 else 4))))
A183041: 3 2 1 2 3 4 3 4 5 6 5 6 7 8 7 8
(3 + loop(\(x,i).x2,(2x + 2),4))
A063485: 259 4294967299 4611686018427387903 4611686018427387903 4611686018427387903
(if (((x + ~2) - (x div 4)) mod 4) <= 0 then 2 else 1)
A030419: 1 1 2 1 1 1 1 2 2 1 1 1 1 2 1 1
(if ((2 + ((~x + 1) * (x div 2))) mod 4) <= 0 then 2 else 1)
A264119: 1 1 1 2 2 1 1 2 1 1 1 2 2 1 1 2
(if (((2x + ~4) mod (x + 2)) mod 4) <= 0 then 2 else 1)
A111621: 2 1 2 1 2 1 2 1 1 1 2 1 1 1 2 1
(if ((x + 1) mod 8) <= 0 then 8 else 1)
A268355-A008834: 1 1 1 1 1 1 1 8 1 1 1 1 1 1 1 8
((x2 + 2x) div (if (x mod 2) <= 0 then 8 else 1))
A198148: 0 3 1 15 3 35 6 63 10 99 15 143 21 195 28 255
(if (~4 + (x div 2)) <= 0 then 0 else 9)
A270172-A066568: 0 0 0 0 0 0 0 0 0 0 9 9 9 9 9 9
(27 * (if x <= 0 then 1 else 2))
A040702: 27 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54
(9 * loop(\(x,i).2x,x,3))
A175806: 27 54 108 216 432 864 1728 3456 6912 13824 27648 55296 110592 221184 442368 884736
(if x <= 0 then 1 else (x - ((x + ~1) mod 9)))
A160941: 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10
(loop(\(x,i).2x,x,4) mod 9)
A146501: 4 8 7 5 1 2 4 8 7 5 1 2 4 8 7 5
(9 * (2 - ((if x <= 0 then 1 else x) mod 2)))
A040073: 9 9 18 9 18 9 18 9 18 9 18 9 18 9 18 9
loop(\(x,i).x3,2x,9)
A154110: 9 387420489
loop(\(x,i).(x2 + ~x + ~1),x,9)
A144745: 9 71 4969 24685991 609398126966089 4611686018427387903 4611686018427387903
(9 * loop(\(x,i).(x * i),(x + ~1),x))
A295473: 0 9 18 54 216 1080 6480 45360 362880 3265920 32659200 359251200 4311014400 56043187200 784604620800 11769069312000
loop(\(x,i).((x2 + x) div 2),x,9)
A050909: 9 45 1035 536130 143717956515 4611686018427387903 4611686018427387903
((x + (if (x mod 2) <= 0 then x else 2)) div 9)
A072527: 0 0 0 0 0 0 1 1 1 1 2 1 2 1 3 1
(if (x mod 3) <= 0 then 1 else (x div 9))
A025856: 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1
(1 + (if (~1 + (x div 4)) <= 0 then x else 8))
A328865: 1 2 3 4 5 6 7 8 9 9 9 9 9 9 9 9
(1 + loop(\(x,i).6x,x,8))
A199411: 9 49 289 1729 10369 62209 373249 2239489 13436929 80621569 483729409 2902376449 17414258689 104485552129 626913312769 3761479876609
(~1 + loop(\(x,i).6x,x,8))
A198845: 7 47 287 1727 10367 62207 373247 2239487 13436927 80621567 483729407 2902376447 17414258687 104485552127 626913312767 3761479876607
((x + 2) - loop(\(x,i).(2 * i),(x + ~8),1))
A289642: 1 2 3 4 5 6 7 8 9 9 8 7 6 5 4 3
(1 + loop(\(x,i).5x,x,8))
A199311: 9 41 201 1001 5001 25001 125001 625001 3125001 15625001 78125001 390625001 1953125001 9765625001 48828125001 244140625001
(~1 + loop(\(x,i).5x,x,8))
A198767: 7 39 199 999 4999 24999 124999 624999 3124999 15624999 78124999 390624999 1953124999 9765624999 48828124999 244140624999
(if (~x + 2) <= 0 then (2 + ((x + (x div 2)) div 4)) else 1)
A087823: 1 1 2 3 3 3 4 4 5 5 5 6 6 6 7 7
(if (x2 + ~12x + 32) <= 0 then 2 else 1)
A345112-A016016: 1 1 1 1 2 2 2 2 2 1 1 1 1 1 1 1
(x2 div (if (x mod 2) <= 0 then (2 + (x mod 4)) else 1))
A251091: 0 1 1 9 8 25 9 49 32 81 25 121 72 169 49 225
(if ((x * (x + (x div 4))) mod 4) <= 0 then 2 else 1)
A104248: 2 1 2 1 2 1 1 2 2 1 2 1 2 2 1 1
(1 + (2 * (loop(\(x,i).(3x + 1),x,2) div 2)))
A096019: 3 7 23 67 203 607 1823 5467 16403 49207 147623 442867 1328603 3985807 11957423 35872267
(~1 + (2 * (if x <= 0 then 1 else (2 * (x - ((~x + 2) div 2))))))
A092899: 1 3 7 15 19 27 31 39 43 51 55 63 67 75 79 87
(3 + loop(\(x,i).x2,(x - ((~x + 2) div 2)),2))
A274022: 5 7 19 65539
(~1 + (2 * loop(\(x,i).x2,(x - ((~x + 2) div 2)),2)))
A249761: 3 7 31 131071
(1 + ((x - ((2 - ((if x <= 0 then 2 else x) div 2)) div 2)) div 2))
A253671: 1 1 2 2 3 3 4 5 5 6 7 7 8 8 9 10
(1 + (2 * (if x <= 0 then 1 else (2 * (2x + (x mod 2))))))
A339329: 3 13 17 29
loop(\(x,i).x2,3,(8x + 1))
A017084: 1 43046721 6975757441 152587890625 1406408618241 7984925229121 33232930569601 111429157112001 318644812890625 806460091894081 1853020188851841 3936588805702081 7837433594376961 14774554437890625
loop(\(x,i).x3,1,(8x + 1))
A017079: 1 729 4913 15625 35937 68921 117649 185193 274625 389017 531441 704969 912673 1157625 1442897 1771561
loop(\(x,i).x3,2,(8x + 1))
A017085: 1 387420489 118587876497 3814697265625 46411484401953 327381934393961 1628413597910449 6351461955384057 20711912837890625 58871586708267913 150094635296999121 350356403707485209
loop(\(x,i).x2,1,(~7x + ~1))
A016994: 1 64 225 484 841 1296 1849 2500 3249 4096 5041 6084 7225 8464 9801 11236
loop(\(x,i).x2,2,(~7x + ~1))
A016996: 1 4096 50625 234256 707281 1679616 3418801 6250000 10556001 16777216 25411681 37015056 52200625 71639296 96059601 126247696
(if (~x + 2) <= 0 then (2 + (((x div 2) * (x div 2)) div 2)) else 1)
A018819-A008645-A008644-A008643: 1 1 2 2 4 4 6 6 10 10 14 14 20 20 26 26
(if (2 - ((2x + ~2) mod (2 + (x div 2)))) <= 0 then 2 else 1)
A110627: 1 1 2 1 2 1 1 2 2 2 2 2 2 1 2 1
loop(\(x,i).2x,(x div 2),(5 + (x mod 2)))
A164095: 5 6 10 12 20 24 40 48 80 96 160 192 320 384 640 768
loop(\(x,i).2x,(x div 2),(1 + (2 * (2 + (x mod 2)))))
A070875: 5 7 10 14 20 28 40 56 80 112 160 224 320 448 640 896
(1 + loop(\(x,i).2x,x,1) - (4 * (x mod 2)))
A269019: 2 ~1 5 5 17 29 65 125 257 509 1025 2045 4097 8189 16385 32765
((x + 1) - (x2 div loop(\(x,i).(x2 + 2),2,2)))
A327707: 1 2 3 4 5 6 7 7 8 8 9 9 10 10 10 11
(1 + (x mod (if (~2 + (x div 4)) <= 0 then 1 else 4)))
A271950: 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 4
((if x <= 0 then 1 else x2) mod (1 + ((x + ~1) mod 4)))
A238897-A205808: 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0
(1 + ((x2 div (if (x + ~2) <= 0 then 1 else 2)) mod 4))
A211005: 1 2 1 1 1 1 3 1 1 1 3 1 1 1 3 1
(1 + loop(\(x,i).(3x + 3),2x,4))
A198969: 5 49 445 4009 36085 324769 2922925 26306329 236756965 2130812689 19177314205 172595827849 1553362450645 13980262055809 125822358502285 1132401226520569
(1 + (if (~1 + (x div 4)) <= 0 then (x div 2) else 4))
A282711: 1 1 2 2 3 3 4 4 5 5 5 5 5 5 5 5
(1 - (if (x mod 4) <= 0 then ((x div 2) mod 4) else 1))
A016033-A015985-A015777-A015681-A015505-A015297-A015153-A015073-A014961-A014737-A014625-A014289-A014017: 1 0 0 0 ~1 0 0 0 1 0 0 0 ~1 0 0 0
((x2 + 4) div (if (x mod 2) <= 0 then 4 else 1))
A261327: 1 5 2 13 5 29 10 53 17 85 26 125 37 173 50 229
((x2 + 4x) div (if (x mod 2) <= 0 then 4 else 1))
A171621: 0 5 3 21 8 45 15 77 24 117 35 165 48 221 63 285
(if (~2 + (x div 5)) <= 0 then 0 else 5)
A281462: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
(15 * (2 + (if x <= 0 then 0 else 2)))
A040870: 30 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
loop(\(x,i).x2,1,(10x + 5))
A017330: 25 225 625 1225 2025 3025 4225 5625 7225 9025 11025 13225 15625 18225 21025 24025
loop(\(x,i).x2,2,(10x + 5))
A017332: 625 50625 390625 1500625 4100625 9150625 17850625 31640625 52200625 81450625 121550625 174900625 244140625 332150625 442050625 577200625
(((x + 1) + (if (x mod 2) <= 0 then 2 else 0)) div 5)
A070098: 0 0 1 0 1 1 1 1 2 2 2 2 3 2 3 3
(loop(\(x,i).(x * (x - i)),2,(x + ~1)) div 5)
A011915: 0 0 0 0 4 24 72 168 336 604 1008 1584 2376 3432 4804 6552
(5 * (if (x mod 6) <= 0 then 0 else 2))
A131722: 0 10 10 10 10 10 0 10 10 10 10 10 0 10 10 10
(25 * (if x <= 0 then 1 else 2))
A040600: 25 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50
(5 * ((2 - (x mod 2)) * (if x <= 0 then 1 else 2)))
A040091: 10 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10
(5 * loop(\(x,i).(2x + 2),x,4))
A182462: 20 50 110 230 470 950 1910 3830 7670 15350 30710 61430 122870 245750 491510 983030
(5 * loop(\(x,i).3x,x,4))
A116530: 20 60 180 540 1620 4860 14580 43740 131220 393660 1180980 3542940 10628820 31886460 95659380 286978140
(x - ((~2 + (if (x + ~2) <= 0 then 0 else x)) div 5))
A214449: 1 2 3 3 4 5 6 6 7 8 9 10 10 11 12 13
(x - ((1 - (2 * (if x <= 0 then 1 else x))) div 5))
A214857: 1 2 3 4 6 7 9 10 11 13 14 16 17 18 20 21
loop(\(x,i).x2,1,(x - ((x + ~2) div 5)))
A226096: 1 4 4 9 16 25 36 36 49 64 81 100 100 121 144 169
loop(\(x,i).(~4x + 1),2x,5)
A318236: 5 77 1229 19661 314573 5033165 80530637 1288490189 20615843021 329853488333 5277655813325 84442493013197 1351079888211149 21617278211378381 345876451382054093 4611686018427387903
(5 * (2x + (if (x + ~1) <= 0 then x else 2)))
A167210: 0 15 30 40
loop(\(x,i).6x,(x div 2),5)
A117858: 5 5 30 30 180 180 1080 1080 6480 6480 38880 38880 233280 233280 1399680 1399680
loop(\(x,i).((x + 1) + (2 * (x + i))),x,5)
A133648: 5 18 59 184 561 1694 5095 15300 45917 137770 413331 1240016 3720073 11160246 33480767 100442332
(5 * loop(\(x,i).4x,(x + ~1),x))
A269822: 0 5 40 240 1280 6400 30720 143360 655360 2949120 13107200 57671680 251658240 1090519040 4697620480 20132659200
(loop(\(x,i).~2x,(x + ~1),x) mod 5)
A082116: 0 1 1 2 3 0 3 3 1 4 0 4 4 3 2 0
(if x <= 0 then 1 else (5x3 + 5x))
A008531: 1 10 50 150 340 650 1110 1750 2600 3690 5050 6710 8700 11050 13790 16950
loop(\(x,i).(5x + ~2),x,5)
A199312: 5 23 113 563 2813 14063 70313 351563 1757813 8789063 43945313 219726563 1098632813 5493164063 27465820313 137329101563
loop(\(x,i).(5x + 2),x,5)
A198771: 5 27 137 687 3437 17187 85937 429687 2148437 10742187 53710937 268554687 1342773437 6713867187 33569335937 167846679687
(x + ((if (~x + 2) <= 0 then 2 else 1) + (x div 5)))
A276216: 1 2 4 5 6 8 9 10 11 12 14 15 16 17 18 20
loop(\(x,i).7x,x,5)
A193577: 5 35 245 1715 12005 84035 588245 4117715 28824005 201768035 1412376245 9886633715 69206436005 484445052035 3391115364245 23737807549715
loop(\(x,i).(x + (x div 5)),x,5)
A182306: 5 6 7 8 9 10 12 14 16 19 22 26 31 37 44 52
loop(\(x,i).(x3 + 3x),x,5)
A006269: 5 140 2744420 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + ~3x),x,5)
A219161: 5 110 1330670 2356194280407770990 4611686018427387903
loop(\(x,i).x5,x,5)
A137841: 5 3125 298023223876953125 4611686018427387903
(~1 + loop(\(x,i).12x,x,4))
A199106: 3 47 575 6911 82943 995327 11943935 143327231 1719926783 20639121407 247669456895 2972033482751 35664401793023 427972821516287 5135673858195455 61628086298345471
(1 + ((if ((x div 2) mod 2) <= 0 then x else (~x + 1)) mod 4))
A070402: 1 2 4 3 1 2 4 3 1 2 4 3 1 2 4 3
loop(\(x,i).~2x,((x2 + x) div 4),1)
A160637: 1 1 ~2 ~8 ~32 ~128 1024 16384 262144 4194304 ~134217728 ~8589934592 ~549755813888 ~35184372088832 4503599627370496 1152921504606846976
(1 + (4x * (if (x + ~2) <= 0 then x else (x + 1))))
A273384: 1 5 17 49 81 121 169 225 289 361 441 529 625 729 841 961
(1 + (loop(\(x,i).(2x + 4),(x + ~1),x) div 4))
A045891: 1 1 3 7 16 36 80 176 384 832 1792 3840 8192 17408 36864 77824
(1 + (4 * loop(\(x,i).(x + (i * i)),(x + ~1),x)))
A321124: 1 5 13 33 73 141 245 393 593 853 1181 1585 2073 2653 3333 4121
(~1 + loop(\(x,i).(2 * (2x - (i mod 2))),x,4))
A037583: 3 13 55 221 887 3549 14199 56797 227191 908765 3635063 14540253 58161015 232644061 930576247 3722304989
(1 + loop(\(x,i).10x,x,4))
A199684: 5 41 401 4001 40001 400001 4000001 40000001 400000001 4000000001 40000000001 400000000001 4000000000001 40000000000001 400000000000001 4000000000000001
(~1 + loop(\(x,i).10x,x,4))
A198970: 3 39 399 3999 39999 399999 3999999 39999999 399999999 3999999999 39999999999 399999999999 3999999999999 39999999999999 399999999999999 3999999999999999
(if ((x + 1) mod 5) <= 0 then (x div 4) else 1)
A250261-A175010: 1 1 1 1 1 1 1 1 1 2 1 1 1 1 3 1
(2 - loop(\(x,i).(~x2 + x + ~1),(x div 4),1))
A339971: 1 1 1 1 3 3 3 3 5 5 5 5 15 15 15 15
(x - ((x + 2) mod loop(\(x,i).(x * i),(x div 4),1)))
A265541: 0 1 2 3 4 5 6 7 8 8 10 10 10 10 10 10
(if ((x + ~1) mod 5) <= 0 then (x mod 4) else 1)
A296240: 1 1 1 1 1 1 2 1 1 1 1 3 1 1 1 1
(1 - (if (x mod 6) <= 0 then (x mod 4) else 1))
A014189: 1 0 0 0 0 0 ~1 0 0 0 0 0 1 0 0 0
loop(\(x,i).(x * i),((x div 4) - (x mod 4)),1)
A331562: 1 1 1 1 1 1 1 1 2 1 1 1 6 2 1 1
((if (~2 + (x div 2)) <= 0 then 1 else 2) div (1 + (x mod 4)))
A280586-A280125-A025872: 1 0 0 0 1 0 0 0 2 1 0 0 2 1 0 0
(1 + loop(\(x,i).7x,x,4))
A199419: 5 29 197 1373 9605 67229 470597 3294173 23059205 161414429 1129900997 7909306973 55365148805 387556041629 2712892291397 18990246039773
(~1 + loop(\(x,i).7x,x,4))
A198686: 3 27 195 1371 9603 67227 470595 3294171 23059203 161414427 1129900995 7909306971 55365148803 387556041627 2712892291395 18990246039771
loop(\(x,i).3x,(6x + 4),1)
A013745: 81 59049 43046721 31381059609 22876792454961 16677181699666569 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x3 mod (1 + loop(\(x,i).(x2 + x),2,2)))
A070505: 0 1 8 27 21 39 1 42 39 41 11 41 8 4 35 21
(~1 + (2 * (if ((x + ~2) mod 8) <= 0 then x else 2)))
A079083: 3 3 3 3 3 3 3 3 3 3 19 3 3 3 3 3
(if (x mod 2) <= 0 then (((x + (x div 4)) div 2) mod 2) else 1)
A285596: 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1
(3 + ((if x <= 0 then 2 else (x * (x div 4))) div 2))
A281705: 4 3 3 3 5 5 6
(3 + loop(\(x,i).10x,x,2))
A173041: 5 23 203 2003 20003 200003 2000003 20000003 200000003 2000000003 20000000003 200000000003 2000000000003 20000000000003 200000000000003 2000000000000003
(1 + (((x + loop(\(x,i).(2x + 1),x,2)) div 2) div 2))
A099155: 1 2 4 7 13 26 50 98
(1 + (2 * (if (x + ~2) <= 0 then x else (2x2 + 4x))))
A273254: 1 3 5 61
(1 + (if (x + ~1) <= 0 then x else (2 + ((x * (x mod 2)) div 2))))
A323238-A323237-A319701: 1 2 3 4 3 5 3 6 3 7 3 8 3 9 3 10
(3 - ((~x + 2) div (2 + ((if x <= 0 then 2 else x) div 2))))
A289189: 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 5
((x + 1) - ((~x + 2) div (2 + ((if x <= 0 then 2 else x) div 2))))
A183295: 1 2 3 5 6 7 8 9 10 12 13 14 15 16 17 18
((x + 3) - loop(\(x,i).(~x2 + 1),2,(x + 2)))
A268458: 11 67 229 581 1231 2311 3977 6409 9811 14411 20461 28237 38039 50191 65041 82961
loop(\(x,i).(2x + ~8),x,(4x + 1))
A048501: 1 2 12 48 152 424 1096 2696 6408 14856 33800 75784 167944 368648 802824 1736712
loop(\(x,i).(x * (~1 + (2 * i))),x,(4x + 1))
A126119: 1 5 27 195 1785 19845 259875 3918915 66891825 1274998725 26843892075 618718975875 15495473018025 419010239773125 12167108660581875 377607284571391875
loop(\(x,i).(x * (((1 + i) div 2) * i)),4x,1)
A163494: 1 96 23224320 248314429440000 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).(3x + 3),x,2x) div 2))
A083877: 1 5 25 101 385 1397 4921 16949 57409 191909 634777 2081477 6775873 21921941 70548793 225995285
(1 + (((if (~2 + (x div 2)) <= 0 then 1 else 2) + (x div 2)) div 2))
A023193: 1 1 2 2 2 2 3 3 4 4 4 4 5 5 5 5
(1 + (if x <= 0 then 1 else (2 * ((2x + 4) + (x div 2)))))
A020585: 2 13 19 23
(1 + (if x <= 0 then 1 else (2 * (4x - (x div 2)))))
A063094: 2 9 15 23 29 37 43 51 57 65 71 79 85 93 99 107
(~1 + (if (x + ~8) <= 0 then 1 else (~2 + (x div 2))))
A238701-A238134: 0 0 0 0 0 0 0 0 0 1 2 2 3 3 4 4
(if ((x + 2) mod 8) <= 0 then (~2 + (x div 2)) else 1)
A340366-A322356-A119788: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1
(x mod (if ((x + 2) mod 4) <= 0 then (~2 + (x div 2)) else 1))
A046782: 0 0 0 0 0 0 0 0 0 0 1 0 0 0 4 0
(if ((x + 1) mod 5) <= 0 then ((x div 2) mod 2) else 1)
A187967-A185304: 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1
(if ((x + 2) mod 5) <= 0 then ((x div 2) mod 2) else 1)
A209349-A203986-A166280-A071023: 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1
(if ((x * (x div 2)) mod 3) <= 0 then ((x div 2) mod 2) else 1)
A189078: 0 0 1 1 1 1 1 1 1 0 1 1 0 0 1 1
(x - loop(\(x,i).(~x + 1),x,((x + ~1) - ((x div 2) mod 2))))
A266614: 1 0 2 3 1 8 2 11 1 16 2 19 1 24 2 27
(~1 + (2 * (x + ((if (x mod 2) <= 0 then 2 else 0) + (x div 2)))))
A136320: 3 1 9 7 15 13 21 19 27 25 33 31 39 37 45 43
(~1 + loop(\(x,i).(x + (x div (2 + (i mod 2)))),(x div 2),2))
A119620: 1 1 1 1 2 2 3 3 5 5 7 7 11 11 15 15
(1 + (loop(\(x,i).(x + ((2 + i) * i)),x,(x div 2)) div 2))
A014112: 1 2 7 14 27 44 69 100 141 190 251 322 407 504 617 744
(~1 + (2 * (loop(\(x,i).2x,(x div 2),1) + (x mod 2))))
A086341: 1 3 3 5 7 9 15 17 31 33 63 65 127 129 255 257
(~1 + (2 * (loop(\(x,i).4x,x,1) + (x mod 2))))
A140323: 1 9 31 129 511 2049 8191 32769 131071 524289 2097151 8388609 33554431 134217729 536870911 2147483649
(~1 + (2 * (((x + 1) * (if x <= 0 then 1 else x)) + (x mod 2))))
A296911: 1 5 11 25 39 61 83 113 143 181 219 265 311 365 419 481
(~1 + (2 * (loop(\(x,i).3x,x,1) + (x mod 2))))
A081632: 1 7 17 55 161 487 1457 4375 13121 39367 118097 354295 1062881 3188647 9565937 28697815
(1 + (2 * (loop(\(x,i).3x,x,1) - (x mod 2))))
A174132: 3 5 19 53 163 485 1459 4373 13123 39365 118099 354293 1062883 3188645 9565939 28697813
(if ((x + 2) mod (8 + (x mod 2))) <= 0 then 2 else 1)
A236000: 1 1 1 1 1 1 2 2 1 1 1 1 1 1 2 1
loop(\(x,i).2x,(x div 2),(5 - (x mod 2)))
A163888: 5 4 10 8 20 16 40 32 80 64 160 128 320 256 640 512
((if x <= 0 then 1 else x) div (1 + (x div (4 - (x mod 2)))))
A323424: 1 1 2 1 2 2 3 2 2 2 3 2 3 2 3 2
(1 + (2 * loop(\(x,i).(2x + 2),(x div 2),(x mod 2))))
A136252: 1 3 5 9 13 21 29 45 61 93 125 189 253 381 509 765
(1 + (loop(\(x,i).(x2 + x),x,1) * (2 + (x mod 2))))
A221211: 3 7 13 127
loop(\(x,i).2x,((x + 1) div 2),(3 + (x mod 2)))
A164654: 3 8 6 16 12 32 24 64 48 128 96 256 192 512 384 1024
(loop(\(x,i).2x,(x + 2),2) div (3 + (x mod 2)))
A238720: 2 4 10 16 42 64 170 256 682 1024 2730 4096 10922 16384 43690 65536
(2x mod (if (~x + 2) <= 0 then (x div (2 + (x mod 2))) else 1))
A262889: 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0
loop(\(x,i).(3x2 + 3x),(2 * (x mod 2)),1)
A110825: 1 126 1
(~1 + (loop(\(x,i).4x,x,1) + (2 * (x mod 2))))
A247281: 0 5 15 65 255 1025 4095 16385 65535 262145 1048575 4194305 16777215 67108865 268435455 1073741825
(1 + loop(\(x,i).4x,x,1) - (2 * (x mod 2)))
A201455: 2 3 17 63 257 1023 4097 16383 65537 262143 1048577 4194303 16777217 67108863 268435457 1073741823
(1 + loop(\(x,i).3x,x,1) - (2 * (x mod 2)))
A102345: 2 2 10 26 82 242 730 2186 6562 19682 59050 177146 531442 1594322 4782970 14348906
(~1 + loop(\(x,i).3x,x,1) - (2 * (x mod 2)))
A141317: 0 0 8 24 80 240 728 2184 6560 19680 59048 177144 531440 1594320 4782968 14348904
((~1 + loop(\(x,i).2x,x,2)) div (1 + (2 * (x mod 2))))
A213243: 1 1 7 5 31 21 127 85 511 341 2047 1365 8191 5461 32767 21845
loop(\(x,i).2x,((x + 1) div 2),(1 + (2 * (x mod 2))))
A163864: 1 6 2 12 4 24 8 48 16 96 32 192 64 384 128 768
((if x <= 0 then 1 else (x div 4)) div (1 + (2 * (x mod 2))))
A319973: 1 0 0 0 1 0 1 0 2 0 2 0 3 1 3 1
loop(\(x,i).2x,(x + (x div 2)),(1 + (2 * (x mod 2))))
A164640: 1 6 8 48 64 384 512 3072 4096 24576 32768 196608 262144 1572864 2097152 12582912
((~x + 2) div (if (x + ~1) <= 0 then 2 else (~1 + (2 * (x mod 2)))))
A099570: 1 0 0 ~1 2 ~3 4 ~5 6 ~7 8 ~9 10 ~11 12 ~13
(1 + ((loop(\(x,i).(4x + 8),x,x) div 2) div 2))
A087449: 1 4 19 91 427 1963 8875 39595 174763 764587 3320491 14330539 61516459 262843051 1118481067 4742359723
(1 + loop(\(x,i).(2x2 + 2x),2x2,2))
A039954: 3 313 4611686018427387903
(loop(\(x,i).(4 * (x + i)),(x + ~1),0) div 3)
A178744: 0 0 1 8 36 149 604 2424 9705 38832 155340 621373 2485508 9942048 39768209 159072856
(loop(\(x,i).((x + 3) mod (1 + i)),x,0) div 3)
A218601-A066628: 0 0 0 0 1 0 1 2 0 1 2 3 4 0 1 2
((1 mod (2 - (if (x mod 4) <= 0 then x else 0))) mod 3)
A176046-A172090: 1 1 1 1 2 1 1 1 1 1 1 1 0 1 1 1
((((~x + 2) div 2) - (if (x + ~2) <= 0 then x else 0)) mod 3)
A175862: 1 2 1 2 2 1 1 0 0 2 2 1 1 0 0 2
((1 + ((x + ~1) mod 3)) * (if x <= 0 then 0 else 3))
A180593: 0 3 6 9 3 6 9 3 6 9 3 6 9 3 6 9
(x - ((x - (if (x mod 4) <= 0 then 0 else 1)) div 3))
A189726: 0 1 2 3 3 4 5 5 6 7 7 8 8 9 10 11
(3 * ((2x + 8) - (if x <= 0 then 0 else 1)))
A308603: 24 27 33 39 45 51 57 63 69 75 81 87 93 99 105 111
(3 * (if x <= 0 then 0 else (1 + ((~x + 2) mod 3))))
A180596: 0 6 3 9 6 3 9 6 3 9 6 3 9 6 3 9
((1 + loop(\(x,i).8x,x,1)) div 3)
A132805: 0 3 21 171 1365 10923 87381 699051 5592405 44739243 357913941 2863311531 22906492245 183251937963 1466015503701 11728124029611
(loop(\(x,i).(4x + 1),(x + 1),1) div 3)
A037597: 1 7 28 113 455 1820 7281 29127 116508 466033 1864135 7456540 29826161 119304647 477218588 1908874353
(loop(\(x,i).(4x + 2),(x + 1),1) div 3)
A037618: 2 8 35 142 568 2275 9102 36408 145635 582542 2330168 9320675 37282702 149130808 596523235 2386092942
((1 + loop(\(x,i).(~x + (i mod 2)),x,4)) div 3)
A014119: 1 ~1 1 ~1 1 0 0 0 0 0 0 1 ~1 1 ~1 1
loop(\(x,i).x2,1,(12x + 3))
A017558: 9 225 729 1521 2601 3969 5625 7569 9801 12321 15129 18225 21609 25281 29241 33489
loop(\(x,i).x2,2,(12x + 3))
A017560: 81 50625 531441 2313441 6765201 15752961 31640625 57289761 96059601 151807041 228886641 332150625 466948881 639128961 855036081 1121513121
(if x <= 0 then 1 else (3 * (x - ((~x + 1) div 3))))
A136290: 1 3 9 12 15 21 24 27 33 36 39 45 48 51 57 60
(3 * ((x + (if (x mod 2) <= 0 then x else 2)) mod 3))
A021277: 0 0 3 6 6 3 0 0 3 6 6 3 0 0 3 6
((1 + loop(\(x,i).8x,x,2)) div 3)
A082311: 1 5 43 341 2731 21845 174763 1398101 11184811 89478485 715827883 5726623061 45812984491 366503875925 2932031007403 23456248059221
((1 + loop(\(x,i).2x,(x2 + 2x),2)) div 3)
A231279: 1 5 171 21845 11184811 22906492245 187649984473771 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((1 + loop(\(x,i).2x,(x + (x div 2)),2)) div 3)
A141355: 1 1 5 11 43 85 341 683 2731 5461 21845 43691 174763 349525 1398101 2796203
(loop(\(x,i).(x2 + 1),2,(2x + 1)) div 3)
A142993: 1 33 225 833 2241 4961 9633 17025 28033 43681 65121 93633 130625 177633 236321 308481
loop(\(x,i).x2,3,(6x + 3))
A016952: 6561 43046721 2562890625 37822859361 282429536481 1406408618241 5352009260481 16815125390625 45767944570401 111429157112001 248155780267521 513798374428641 1001129150390625 1853020188851841
loop(\(x,i).x3,1,(6x + 3))
A016947: 27 729 3375 9261 19683 35937 59319 91125 132651 185193 250047 328509 421875 531441 658503 804357
loop(\(x,i).x3,2,(6x + 3))
A016953: 19683 387420489 38443359375 794280046581 7625597484987 46411484401953 208728361158759 756680642578125 2334165173090451 6351461955384057 15633814156853823 35452087835576229 75084686279296875
loop(\(x,i).4x,x,(6x + 3))
A268898: 3 36 240 1344 6912 33792 159744 737280 3342336 14942208 66060288 289406976 1258291200 5435817984 23353884672 99857989632
loop(\(x,i).x2,1,(~5x + ~3))
A016886: 9 64 169 324 529 784 1089 1444 1849 2304 2809 3364 3969 4624 5329 6084
loop(\(x,i).x2,2,(~5x + ~3))
A016888: 81 4096 28561 104976 279841 614656 1185921 2085136 3418801 5308416 7890481 11316496 15752961 21381376 28398241 37015056
(loop(\(x,i).(~2x + 1),x,(2x + 1)) div 3)
A232600: 0 ~2 6 ~18 46 ~114 270 ~626 1422 ~3186 7054 ~15474 33678 ~72818 156558 ~334962
(x - ((0 - (if (~x + 2) <= 0 then (x div 2) else 1)) div 3))
A332109-A246786-A158037: 1 2 3 4 5 6 7 8 10 11 12 13 14 15 17 18
(3 * (1 + loop(\(x,i).5x,x,2)))
A097804: 9 33 153 753 3753 18753 93753 468753 2343753 11718753 58593753 292968753 1464843753 7324218753 36621093753 183105468753
((1 + loop(\(x,i).5x,x,2)) div 3)
A083217: 1 3 17 83 417 2083 10417 52083 260417 1302083 6510417 32552083 162760417 813802083 4069010417 20345052083
loop(\(x,i).x2,1,(9x + 3))
A017198: 9 144 441 900 1521 2304 3249 4356 5625 7056 8649 10404 12321 14400 16641 19044
loop(\(x,i).x2,2,(9x + 3))
A017200: 81 20736 194481 810000 2313441 5308416 10556001 18974736 31640625 49787136 74805201 108243216 151807041 207360000 276922881 362673936
loop(\(x,i).(x3 + ~x),1,(3x + 3))
A097321: 24 210 720 1716 3360 5814 9240 13800 19656 26970 35904 46620 59280 74046 91080 110544
loop(\(x,i).(x div (2 - (x mod 2))),x,(3x + 3))
A166466: 3 3 9 3 15 9 21 3 27 15 33 9 39 21 45 3
((if x <= 0 then 1 else 4x) + ((x + 1) div 3))
A312901: 1 4 9 13 17 22 26 30 35 39 43 48 52 56 61 65
(2x + ((if x <= 0 then 1 else x) + ((x + 1) div 3)))
A298786: 1 3 7 10 13 17 20 23 27 30 33 37 40 43 47 50
(loop(\(x,i).(2x - (i mod 2)),x,(x + 1)) div 3)
A088110: 0 1 3 9
A045883: 0 1 3 9 23 57 135 313 711 1593 3527 7737 16839 36409 78279 167481
(3 * loop(\(x,i).((x2 + ~x) div 2),2,(x + ~1)))
A060008: 0 0 0 0 9 45 135 315 630 1134 1890 2970 4455 6435 9009 12285
(loop(\(x,i).((x2 + ~x) div 2),2,(x + ~1)) div 3)
A000332: 0 0 0 0 1 5 15 35 70 126 210 330 495 715 1001 1365
((if (x + ~2) <= 0 then 1 else (x + ~2)) + ((x + ~1) div 3))
A253570: 0 1 1 1 3 4 5 7 8 9
(loop(\(x,i).(x + ((i * i) div 3)),x,1) div 3)
A177100: 0 0 0 1 3 6 10 15 22 31 42 55 71 90 112 137
(x - (3 * (if (~4 + (x div 2)) <= 0 then 0 else 2)))
A103303: 0 1 2 3 4 5 6 7 8 9
A081595-A028899: 0 1 2 3 4 5 6 7 8 9 4 5 6 7 8 9
(((x + 2) div (if (~2 + (x div 2)) <= 0 then 1 else 2)) div 3)
A328114-A246359: 0 1 1 1 2 2 1 1 1 1 2 2 2 2 2 2
(if x <= 0 then 1 else (18x + ~6))
A019557: 1 12 30 48 66 84 102 120 138 156 174 192 210 228 246 264
loop(\(x,i).(2x + 1),x,18)
A198276: 18 37 75 151 303 607 1215 2431 4863 9727 19455 38911 77823 155647 311295 622591
((loop(\(x,i).(x + (i * i)),(x + 2),1) div 2) div 3)
A014126: 1 2 5 9 15 23 34 47 64 84 108 136 169 206 249 297
loop(\(x,i).x2,1,(12x + 6))
A017594: 36 324 900 1764 2916 4356 6084 8100 10404 12996 15876 19044 22500 26244 30276 34596
loop(\(x,i).x2,2,(12x + 6))
A017596: 1296 104976 810000 3111696 8503056 18974736 37015056 65610000 108243216 168896016 252047376 362673936 506250000 688747536 916636176 1196883216
(loop(\(x,i).(4x + 1),(x + 1),2) div 3)
A037646: 3 12 49 199 796 3185 12743 50972 203889 815559 3262236 13048945 52195783 208783132 835132529 3340530119
(loop(\(x,i).(4x + 2),(x + 1),2) div 3)
A037667: 3 14 56 227 910 3640 14563 58254 233016 932067 3728270 14913080 59652323 238609294 954437176 3817748707
loop(\(x,i).(x2 + ~x),1,(6x + 6))
A291582: 30 132 306 552 870 1260 1722 2256 2862 3540 4290 5112 6006 6972 8010 9120
(loop(\(x,i).5x,(x + 1),2) div 3)
A037584: 3 16 83 416 2083 10416 52083 260416 1302083 6510416 32552083 162760416 813802083 4069010416 20345052083 101725260416
(loop(\(x,i).(2 * (x - (i mod 2))),(x + ~1),2) div 3)
A113405: 0 0 0 1 2 4 7 14 28 57 114 228 455 910 1820 3641
(6 * ((2 - (x mod 2)) * (if x <= 0 then 1 else 2)))
A040133: 12 12 24 12 24 12 24 12 24 12 24 12 24 12 24 12
((((x2 - (if x <= 0 then 0 else 1)) div 2) div 2) div 3)
A340445-A230059: 0 0 0 0 1 2 2 4 5 6 8 10 11 14 16 18
(3 * (loop(\(x,i).(x + (x div 2)),(x + ~1),2) div 2))
A081848: 3 3 3 6 9 12 18 27 42 63 93 141 210 315 474 711
loop(\(x,i).(~x + i),x,~22)
A152835: ~22 23 ~21 24 ~20 25 ~19 26 ~18 27 ~17 28 ~16 29 ~15 30
(6 * loop(\(x,i).(2x + 4),x,4))
A305065: 24 72 168 360 744 1512 3048 6120 12264 24552 49128 98280 196584 393192 786408 1572840
(3 * (loop(\(x,i).2x,x,(2 + (x mod 2))) div 2))
A137344: 3 9 12 36 48 144 192 576 768 2304 3072 9216 12288 36864 49152 147456
loop(\(x,i).(2x + ~1),(x + 1),12)
A122041: 23 45 89 177 353 705 1409 2817 5633 11265 22529 45057 90113 180225 360449 720897
loop(\(x,i).(x2 + ~x + 1),x,12)
A144785: 12 133 17557 308230693 95006159799029557 4611686018427387903 4611686018427387903
loop(\(x,i).8x,x,12)
A204623: 12 96 768 6144 49152 393216 3145728 25165824 201326592 1610612736 12884901888 103079215104 824633720832 6597069766656 52776558133248 422212465065984
loop(\(x,i).(3x + ~2),x,12)
A199114: 12 34 100 298 892 2674 8020 24058 72172 216514 649540 1948618 5845852 17537554 52612660 157837978
loop(\(x,i).5x,x,12)
A216491: 12 60 300 1500 7500 37500 187500 937500 4687500 23437500 117187500 585937500 2929687500 14648437500 73242187500 366210937500
(3 * loop(\(x,i).(4x + ~1),x,4))
A199211: 12 45 177 705 2817 11265 45057 180225 720897 2883585 11534337 46137345 184549377 738197505 2952790017 11811160065
(if x <= 0 then 1 else (6 * (x - ((~x + 2) div 2))))
A298033: 1 6 12 24 30 42 48 60 66 78 84 96 102 114 120 132
(x - ((x - (((if x <= 0 then 2 else x) div 2) mod 2)) div 3))
A284006: 1 1 2 3 3 4 5 5 6 6 7 8 8 9 10 11
((loop(\(x,i).(x * (x - i)),2,(x + 2)) div 2) div 3)
A033488: 0 4 20 60 140 280 504 840 1320 1980 2860 4004 5460 7280 9520 12240
loop(\(x,i).x2,3,12x)
A017528: 0 429981696 110075314176 2821109907456 28179280429056 167961600000000 722204136308736 2478758911082496 7213895789838336 18509302102818816 42998169600000000 92170395205042176
loop(\(x,i).x3,1,12x)
A017523: 0 1728 13824 46656 110592 216000 373248 592704 884736 1259712 1728000 2299968 2985984 3796416 4741632 5832000
loop(\(x,i).x3,2,12x)
A017529: 0 5159780352 2641807540224 101559956668416 1352605460594688 10077696000000000 51998697814228992 208215748530929664 692533995824480256 1999004627104432128 4611686018427387903
loop(\(x,i).x2,2,~11x)
A017392: 0 14641 234256 1185921 3748096 9150625 18974736 35153041 59969536 96059601 146410000 214358881 303595776 418161601 562448656 741200625
(6 * loop(\(x,i).(3x + 4),x,2))
A277106: 12 60 204 636 1932 5820 17484 52476 157452 472380 1417164 4251516 12754572 38263740 114791244 344373756
loop(\(x,i).x2,1,(9x + 6))
A017234: 36 225 576 1089 1764 2601 3600 4761 6084 7569 9216 11025 12996 15129 17424 19881
loop(\(x,i).x2,2,(9x + 6))
A017236: 1296 50625 331776 1185921 3111696 6765201 12960000 22667121 37015056 57289761 84934656 121550625 168896016 228886641 303595776 395254161
(if x <= 0 then 1 else (6x * (1 + (x mod 2))))
A298036: 1 12 12 36 24 60 36 84 48 108 60 132 72 156 84 180
(x - (((x mod 2) - (2 * (if x <= 0 then 1 else x))) div 3))
A174799: 1 2 4 5 7 8 10 12 14 15 17 18 20 22 24 25
(if x <= 0 then 1 else (6x3 + 6x))
A008530: 1 12 60 180 408 780 1332 2100 3120 4428 6060 8052 10440 13260 16548 20340
(3 * loop(\(x,i).(5x + 2),x,2))
A146883: 6 36 186 936 4686 23436 117186 585936 2929686 14648436 73242186 366210936 1831054686 9155273436 45776367186 228881835936
(if (x + ~2) <= 0 then x else (~3 + (2 * (x + (x div 2)))))
A192225: 0 1 2 5
A067568: 0 1 2 5 9 11 15
(if x <= 0 then 1 else (6x * (2 - (x mod 2))))
A298038: 1 6 24 18 48 30 72 42 96 54 120 66 144 78 168 90
(x - ((loop(\(x,i).(~x2 + x),2,x) div 2) div 3))
A006484: 0 1 3 10 30 75 161 308 540 885 1375 2046 2938 4095 5565 7400
(((x + 2) * (2 + (if (~x + 2) <= 0 then x else 0))) div 3)
A229154: 1 2 5 8 12 16 21 27 33 40 48 56 65 75 85 96
(3 * loop(\(x,i).((x + 2) * (x - i)),2,(x + 2)))
A014136: 36 288
((2x + (if (x mod 4) <= 0 then 0 else 1)) div 3)
A274616: 0 1 1 2 2 3 4 5 5 6 7 7 8 9 9 10
(3 * (2x + (if (x mod 3) <= 0 then 1 else 2)))
A234904: 3 12 18 21 30 36 39 48 54 57 66 72 75 84 90 93
(~3 + loop(\(x,i).((x + 1) * (x + i)),2,2x))
A094200: 3 107 699 2547 6803 15003 29067 51299 84387 131403 195803 281427 392499 533627 709803 926403
((if (~2 + (x div 2)) <= 0 then (x + 2) else (x div 2)) div 3)
A341356-A276153-A099564-A099563: 0 1 1 1 2 2 1 1 1 1 1 1 2 2 2 2
(loop(\(x,i).(2x + 2),x,1) + (3 * (x mod 2)))
A280173: 1 7 10 25 46 97 190 385 766 1537 3070 6145 12286 24577 49150 98305
(3 * loop(\(x,i).7x,x,2))
A216517: 6 42 294 2058
(2 - (if x <= 0 then 1 else (3 * ((~x2 + x) div 2))))
A139482: 1 2 5 11 20 32 47 65 86 110 137 167 200 236 275 317
(3 * (loop(\(x,i).(3x + ~1),x,x) div 2))
A289399: 0 3 21 102 426 1641 6015 21324 73812 250959 841449 2790066 9167358 29893557 96855123 312088728
(3 * (loop(\(x,i).8x,x,x) div 2))
A230539: 0 12 192 2304 24576 245760 2359296 22020096 201326592 1811939328 16106127360 141733920768 1236950581248 10720238370816 92358976733184 791648371998720
((x + 2) - ((1 - (if (~x + 2) <= 0 then x else 2)) div 3))
A113777: 3 4 5 6 7 9 10 11 13 14 15 17 18 19 21 22
(x - (((x mod 2) - (if (~x + 2) <= 0 then x else 2)) div 3))
A188010: 1 2 3 4 6 7 8 9 11 12 14 15 16 17 19 20
((x + (if (~2 + (x div 4)) <= 0 then 2 else 0)) div 3)
A046155: 0 1 1 1 2 2 2 3 3 3 4 4 4 4 4 5
loop(\(x,i).(3x2 + 3x + 1),x,3)
A172029: 3 37 4219 53412541 8558698768467667 4611686018427387903 4611686018427387903
(3 * (x + loop(\(x,i).i,(~2 + (x div 3)),1)))
A194423: 3 6 9 12 15 18 21 24 27 30 33 36 42 45 48 54
((x + 3) + loop(\(x,i).i,((~1 + (x div 2)) div 2),1))
A063713: 4 5 6 7 8 9 10 11 12 13 15 16 17 18 20 21
loop(\(x,i).3x,5x,3)
A013826: 3 729 177147 43046721 10460353203 2541865828329 617673396283947 150094635296999121 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x - (if (x + ~12) <= 0 then x else 3))
A048024: 0 0 0 0 0 0 0 0 0 0 0 0 0 10 11 12
loop(\(x,i).(7x + ~3),x,3)
A199421: 3 18 123 858 6003 42018 294123 2058858 14412003 100884018 706188123 4943316858 34603218003 242222526018 1695557682123 11868903774858
loop(\(x,i).(7x + ~2),x,3)
A199484: 3 19 131 915 6403 44819 313731 2196115 15372803 107609619 753267331 5272871315 36910099203 258370694419 1808594860931 12660164026515
loop(\(x,i).(4x + 1),3x,3)
A072196: 3 213 13653 873813 55924053 3579139413 229064922453 14660155037013 938249922368853 60047995031606613 3843071682022823253 4611686018427387903 4611686018427387903
loop(\(x,i).x2,3,9x)
A017168: 0 43046721 11019960576 282429536481 2821109907456 16815125390625 72301961339136 248155780267521 722204136308736 1853020188851841 4304672100000000 9227446944279201 18509302102818816 35114532758015841
loop(\(x,i).(x2 + ~x),1,9x)
A277991: 0 72 306 702 1260 1980 2862 3906 5112 6480 8010 9702 11556 13572 15750 18090
loop(\(x,i).x3,1,9x)
A017163: 0 729 5832 19683 46656 91125 157464 250047 373248 531441 729000 970299 1259712 1601613 2000376 2460375
loop(\(x,i).x3,2,9x)
A017169: 0 387420489 198359290368 7625597484987 101559956668416 756680642578125 3904305912313344 15633814156853823 51998697814228992 150094635296999121 387420489000000000 913517247483640899
loop(\(x,i).2x,(x div 3),((~x + 1) mod 3))
A168090: 1 0 2 2 0 4 4 0 8 8 0 16 16 0 32 32
(x - ((if (x mod 3) <= 0 then x else (~x + 1)) div 3))
A006369: 0 1 3 2 5 7 4 9 11 6 13 15 8 17 19 10
(1 - ((x + (if (x + ~3) <= 0 then x else 1)) mod 3))
A010890: 1 ~1 0 1 ~1 1 0 ~1 1
loop(\(x,i).x2,1,((x3 + ~x) div 3))
A169801: 0 0 4 64 400 1600 4900 12544 28224 57600 108900 193600 327184 529984 828100 1254400
(x - (if (~6 + (x div 2)) <= 0 then x else 3))
A048035: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11 12
((x + 3) + (8 * (if x <= 0 then 1 else 2)))
A102815: 11 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
(2x - (if (~2 + (x mod 4)) <= 0 then x else 3))
A222258: 0 1 2 3 4 5 6 11 8 9 10 19 12 13 14 27
(loop(\(x,i).(2 + ((x2 + x) div 2)),2,x) div 3)
A027927: 1 2 5 12 26 51 92 155 247 376 551 782 1080 1457 1926 2501
((x + ~3) + loop(\(x,i).(x3 + 2),2,2))
A317594: 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014
(3 + (x * (if (~2 + (x div 2)) <= 0 then 1 else 4)))
A154660: 3 4 5 6 7 8
A082464: 3 4 5 6 7 8 27
loop(\(x,i).(2 * (x + (2x div (1 + i)))),x,3)
A052482: 3 12 40 120 336 896 2304 5760 14080 33792 79872 186368 430080 983040 2228224 5013504
loop(\(x,i).(x - ((~x + ((x div 2) mod 2)) div 2)),x,3)
A147790: 3 4 6 9 14 21 32 48 72 108 162 243 364 546 819 1228
loop(\(x,i).((x + 2) + (((2 + i) * i) div 2)),x,3)
A203292: 3 6 12 21 35 54 80 113 155 206 268 341 427 526 640 769
(if (x + ~2) <= 0 then (3x + 3) else (x div 3))
A094560: 3 6 9 1 1 1 2 2 2 3 3 3 4 4 4 5
(3x mod (if (x + ~2) <= 0 then 1 else (x div 3)))
A269162: 0 0 0 0 0 0 0 1 0 0 0 0 0 3 2 0
(loop(\(x,i).(x3 + 1),x,1) - (x div 3))
A249903: 1 2 9 729
loop(\(x,i).2x,(x + ~1),(2x - (x mod 3)))
A128205: 0 1 4 24 56 128 384 832 1792 4608 9728 20480 49152 102400 212992 491520
loop(\(x,i).(x + (x mod 10)),x,3)
A102040: 3 6 12 14 18 26 32 34 38 46 52 54 58 66 72 74
((x * (~x + (if (x + ~4) <= 0 then 1 else 2))) mod 3)
A286044-A129272: 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0
loop(\(x,i).(x + (4 * (x div 3))),x,3)
A338852: 3 7 15 35 79 183 427 995 2319 5411 12623 29451 68719 160343 374131 872971
(x - (3 * (~x + loop(\(x,i).i,(x div 4),x))))
A048704: 0 1 2 3 13 17 21 25 26 30 34 38 39 43 47 51
(if x <= 0 then 1 else (x3 + 4x2 + 3))
A084825: 1 8 27 66
(3x2 + (if (x mod 4) <= 0 then 1 else 0))
A058034: 1 3 12 27 49 75 108 147 193 243 300 363 433 507 588 675
(if (x div 4) <= 0 then (x + 1) else (x2 div 3))
A254328: 1 2 3 4 5 8 12 16
(3 + (if (x mod 3) <= 0 then 1 else x3))
A161433: 4 4 11 4
((x + 1) - ((~x + (if (~x + 4) <= 0 then 1 else 0)) div 2))
A225647: 1 3 4 6 7
A083922: 1 3 4 6 7 8 10 11 13 14 16 17 19 20 22 23
(1 + ((if (~2 + (x div 5)) <= 0 then 0 else x) div 2))
A322473: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8
loop(\(x,i).4x,(5x + 2),1)
A013831: 16 16384 16777216 17179869184 17592186044416 18014398509481984 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).3x,(5x + 2),1)
A013827: 9 2187 531441 129140163 31381059609 7625597484987 1853020188851841 450283905890997363 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).x2,1,10x))
A323178: 1 101 401 901 1601 2501 3601 4901 6401 8101 10001 12101 14401 16901 19601 22501
loop(\(x,i).x2,1,(10x + 1))
A017282: 1 121 441 961 1681 2601 3721 5041 6561 8281 10201 12321 14641 17161 19881 22801
loop(\(x,i).x2,2,(10x + 1))
A017284: 1 14641 194481 923521 2825761 6765201 13845841 25411681 43046721 68574961 104060401 151807041 214358881 294499921 395254161 519885601
(1 + loop(\(x,i).x2,(x + (x div 5)),2))
A164307-A019434: 3 5 17 257 65537
A123599-A100270: 3 5 17 257 65537 4611686018427387903
(~1 + (2 * (~x + loop(\(x,i).(x2 + 1),2,3))))
A107843: 201 199 197 195 193 191 189 187 185 183 181 179 177 175 173 171
loop(\(x,i).6x,(3x + 2),1)
A013739: 36 7776 1679616 362797056 78364164096 16926659444736 3656158440062976 789730223053602816 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).8x,(3x + 2),1)
A013743: 64 32768 16777216 8589934592 4398046511104 2251799813685248 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).5x,(3x + 2),1)
A013737: 25 3125 390625 48828125 6103515625 762939453125 95367431640625 11920928955078125 1490116119384765625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(x + (x div 2)),x,(3x + 2)))
A083045: 1 6 17 35 68 122 224 383 656 1092 1841 2978 4859 7835 12776 20291
(1 + (loop(\(x,i).(2x + ~4),x,3x) div 2))
A048496: 1 2 7 23 67 179 451 1091 2563 5891 13315 29699 65539 143363 311299 671747
(2 - (if (~x + 2) <= 0 then ((x * (x div 3)) mod 2) else 1))
A051034-A024935: 1 1 2 1 2 1 2 2 2 1 2 1 2 2 2 1
loop(\(x,i).2x,((3x2 + ~x) div 2),1)
A166077: 1 2 32 4096 4194304 34359738368 2251799813685248 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(3 * (x + ((i mod 2) * i))),x,2))
A262251: 3 10 28 91
loop(\(x,i).(x * i),x,(4x2 + 2x + 1))
A082035: 1 7 42 258 1752 13320 113040 1063440 11007360 124467840 1527724800 20237817600 287879961600 4377595622400 70875950745600 1217444836608000
(1 + ((x * ((x + 1) + (if (x + ~2) <= 0 then x else 1))) div 2))
A087327: 1 2 6 8 13 18 25 32 41 50 61 72 85 98 113 128
(1 + (loop(\(x,i).(3x + 1),(x + 1),x) div 2))
A014915: 1 7 34 142 547 2005 7108 24604 83653 280483 930022 3055786 9964519 32285041 104029576 333612088
(1 + loop(\(x,i).((4 * (x + i)) div (x + 1)),x,2))
A205560: 3 5 5 6 7 7 7 8 8 9 9 9 9 10 10 10
loop(\(x,i).2x,(x + ~1),(1 + ((x2 + x) div 2)))
A087431: 1 2 8 28 88 256 704 1856 4736 11776 28672 68608 161792 376832 868352 1982464
(1 + (2 * loop(\(x,i).(3x + ~2),(x + ~1),x)))
A180741: 1 3 9 39 165
loop(\(x,i).8x,((x2 + ~x) div 2),1)
A109966: 1 1 8 512 262144 1073741824 35184372088832 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),(x + ~1),(1 + ((x2 + ~x) div 2)))
A121635: 1 1 2 8 42 264 1920 15840 146160 1491840 16692480 203212800 2674425600 37841126400 572885913600 9240898867200
loop(\(x,i).5x,((x2 + ~x) div 2),1)
A109345: 1 1 5 125 15625 9765625 30517578125 476837158203125 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * (x + (if (~2 + (x div 3)) <= 0 then 1 else 2))))
A288452: 3 5 7 9 11 13 15 17 19 23 25 27 29 31 33 35
(~1 + loop(\(x,i).(2x - ((i mod 3) mod 2)),x,2))
A292528: 1 2 5 11 22
A033120: 1 2 5 11 22 45 91 182 365 731 1462 2925 5851 11702 23405 46811
(1 + (2 * loop(\(x,i).(8 div (x + 1)),2,x)))
A090792: 1 3 5 5 9 9 9 9 17 17 17 17 17 17 17 17
(~1 + loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2))
A030662: 1 5 19 69 251 923 3431 12869 48619 184755 705431 2704155 10400599 40116599 155117519 601080389
(if (~x + (2 * (2 + ((x + 2) mod 4)))) <= 0 then 2 else 1)
A282625: 1 1 1 1 1 1 2 2 2 1 2 2 2 2 2 2
(1 + (2x * loop(\(x,i).((x + 2) * (x + i)),2,2)))
A158002: 1 393 785 1177 1569 1961 2353 2745 3137 3529 3921 4313 4705 5097 5489 5881
(~1 + loop(\(x,i).(2 + ((x2 div 2) + (x div 2))),x,2))
A037447: 1 4 15 137
(~1 + loop(\(x,i).(2 * (2x2 + (i mod 2))),x,2))
A268067: 1 17 1295
((3x2 + 1) * (if (~x + 2) <= 0 then 2 else 1))
A273981: 1 4 26 56 98 152 218 296 386 488 602 728 866 1016 1178 1352
(~1 + (2 * (x + (2 * (x + (if (x mod 2) <= 0 then 2 else 0))))))
A166639: 7 5 19 17 31 29 43 41 55 53 67 65 79 77 91 89
(~1 + loop(\(x,i).(2x3 + ~x + 2),x,2))
A074488: 1 15 8177 1093884103327 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).((x + 2) + (x div (4 + i))),x,2))
A130257: 1 3 5 7 10 13 16 19 22 25 28 31 35 39 43 47
(1 + (2 * loop(\(x,i).(x + ((1 + i) * i)),2x,x)))
A063496: 1 19 85 231 489 891 1469 2255 3281 4579 6181 8119 10425 13131 16269 19871
(if (x + ~1) <= 0 then (x + 2) else (~1 + (2 * (x + (x div 2)))))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A192489-A038179: 2 3 5 7 11 13 17 19 23 25 29 31 35 37 41 43
loop(\(x,i).2x,((x div 2) - ((x * (x div 2)) mod 2)),1)
A300622: 1 1 2 1 4 4 8 4 16 16 32 16 64 64 128 64
(1 + ((x + 2) * (1 - loop(\(x,i).(2x + ~4),x,0))))
A190730: 3 16 53 146 367 876 2025 4582 10211 22496 49117 106458 229335 491476 1048529 2228174
(1 + loop(\(x,i).x2,x,(x3 + 2x2 + x + 2)))
A176245: 3 37 160001
(if ((x + 1) mod 10) <= 0 then (x + 2) else 1)
A337335: 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1
(1 + (((x2 + 1) * (if x <= 0 then 1 else 2)) div (x + 2)))
A080276: 1 2 3 5 6 8 10 12 14 15 17 19 21 23 25 27
loop(\(x,i).(x + 1),(x2 + ~6x + ~16),1)
A250666: 1 1 1 1 1 1 1 1 1 12 25 40 57 76 97 120
(~1 + ((x + 2) * (if (x + ~2) <= 0 then 2 else (x2 div 2))))
A154526: 3 5 7 19 47
((x + 3) * loop(\(x,i).((2x + 2) + i),x,0))
A342482: 0 12 50 150 392 952 2214 5010 11132 24420 53066 114478 245520 524016 1113806 2358954
((x + 3) * (~1 + loop(\(x,i).(2x + i),x,2)))
A027540: 3 16 55 156 399 960 2223 5020 11143 24432 53079 114492 245535 524032 1113823 2358972
loop(\(x,i).(((x2 + ~x) * i) div 2),2,(x + 3))
A107394: 6 30 90 210 420 756 1260 1980 2970 4290
((2x + 6) * (if x <= 0 then 8 else 2))
A124354: 48 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72
(if (x + ~12) <= 0 then x else (x + 3))
A103303: 0 1 2 3 4 5 6 7 8 9
A004841: 0 1 2 3 4 5 6 7 8 9 10 11 12 16 17 18
(if (x + ~2) <= 0 then 1 else ((x2 + ~x) div (x + 3)))
A053758: 1 1 1 1 1 2 3 4 5 6 6 7 8 9 10 11
(if (x + ~10) <= 0 then x else (x + 3))
A103303: 0 1 2 3 4 5 6 7 8 9
A050726: 0 1 2 3 4 5 6 7 8 9 10 14 15 16 17 18
(if (~6 + (x div 2)) <= 0 then x else (x + 3))
A103303: 0 1 2 3 4 5 6 7 8 9
A106039: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 17 18
(1 + (if (~2 + (x div 5)) <= 0 then x else (x + 2)))
A341750-A331026-A258264-A246096-A098312: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 18
(1 + (if (~6 + (x div 2)) <= 0 then x else (x + 2)))
A302140-A166535-A039698: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 17 18
loop(\(x,i).(x + ((4x + 2) * i)),(x + 2),1)
A212557: 67 877
(if ((x + 2) mod 9) <= 0 then (x + ~2) else 1)
A059592: 1 1 1 1 1 1 1 5 1 1 1 1 1 1 1 1
loop(\(x,i).((x * (1 + i)) div (1 + (i div 2))),(x + ~2),1)
A210736: 1 1 1 2 3 6 10 20 35 70 126 252 462 924 1716 3432
(1 - (if ((x + ~1) mod 8) <= 0 then (x + ~2) else 1))
A002483: 0 2 0 0 0 0 0 0 0 ~6 0 0 0 0 0 0
((2 + (x div 2)) mod (if (x mod 4) <= 0 then (x + ~2) else 1))
A334709-A272625: 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0
loop(\(x,i).(2x3 + 4x2 + x),(x + ~2),1)
A330295: 1 1 1 7 889
loop(\(x,i).(7x + ~3),2x,1)
A120694: 1 25 1201 58825 2882401 141237625 6920643601 339111536425 16616465284801 814206798955225 39896133148806001 1954910524291494025 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(10x + 1),2x,1)
A100706: 1 111 11111 1111111 111111111 11111111111 1111111111111 111111111111111 11111111111111111 1111111111111111111 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((1 + i) * (1 + (2 * i)))),2x,1)
A052277: 1 90 113400 681080400 12504636144000 548828480360160000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((2x + 1) + loop(\(x,i).(x * (x - i)),2,(x + ~1)))
A137864: 1 3 5 7 33 131 373 855 1697 3043 5061 7943 11905 17187 24053 32791
loop(\(x,i).(10x + 2),2x,1)
A131970: 1 122 12222 1222222 122222222 12222222222 1222222222222 122222222222222 12222222222222222 1222222222222222222 4611686018427387903 4611686018427387903
loop(\(x,i).((x * (i * i)) div ~4),2x,1)
A171105: 1 1 12 675
loop(\(x,i).32x,2x,1)
A140300: 1 1024 1048576 1073741824 1099511627776 1125899906842624 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (x - (2 * (~x + (x mod 2))))),2x,1)
A067429: 1 12 432 15552 559872 20155392 725594112 26121388032 940369969152 33853318889472 1218719480020992 43873901280755712 1579460446107205632 4611686018427387903 4611686018427387903 4611686018427387903
((2x + ~1) + (if (~x + 4) <= 0 then (x + ~2) else 2))
A080751: 1 3 5 7 9 12 15 18 21 24 27 30 33 36 39 42
loop(\(x,i).(~10x + 1),2x,1)
A095372: 1 91 9091 909091 90909091 9090909091 909090909091 90909090909091 9090909090909091 909090909090909091 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x * (1 + (2 * (i div 2)))),2x,1)
A000909: 1 12 720 100800 25401600 10059033600 5753767219200 4487938430976000 4577697199595520000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * (1 + (2 * (x + i)))),2,2x))
A102997: 1 463
((2x + 1) + ((4 div (if x <= 0 then 1 else x)) mod 2))
A097911: 1 3 5 8
A192881: 1 3 5 8 10 11 13 15 17 19
loop(\(x,i).(1 - (2 * (x + ((i div 2) mod 2)))),2x,1)
A102900: 1 1 7 25 103 409 1639 6553 26215 104857 419431 1677721 6710887 26843545 107374183 429496729
((2x + 1) * loop(\(x,i).(x + (i * i)),(x + 1),0))
A053134: 1 15 70 210 495 1001 1820 3060 4845 7315 10626 14950 20475 27405 35960 46376
(loop(\(x,i).3x,x,3) div (2x + 1))
A191632: 3 3 5 11 27 66 168 437 1157 3107 8435 23106 63772 177147 494789 1388603
loop(\(x,i).3x,(2x + 1),(2x + 1))
A060851: 3 81 1215 15309 177147 1948617 20726199 215233605 2195382771 22082967873 219667417263 2165293113021 21182215236075 205891132094649 1990280943581607 19147875284802357
((2x + 1) * (if (x + ~2) <= 0 then 1 else (x2 + ~1)))
A086340: 1 3 5 56
loop(\(x,i).x5,1,(2x + 1))
A016757: 1 243 3125 16807 59049 161051 371293 759375 1419857 2476099 4084101 6436343 9765625 14348907 20511149 28629151
((2x + 1) * loop(\(x,i).(x2 + 3x + 2),2,2))
A272361: 182 546 910 1274 1638 2002 2366 2730 3094 3458 3822 4186 4550 4914 5278 5642
((4x + 2) * (if x <= 0 then 1 else 4x))
A068379: 2 24 80 168 288 440 624 840 1088 1368 1680 2024 2400 2808 3248 3720
loop(\(x,i).(x * (3 + i)),4,(2x + 1))
A232099: 840 2520 4200 5880 7560 9240 10920 12600 14280 15960 17640 19320 21000 22680 24360 26040
((2x + 1) * loop(\(x,i).(2x2 + x),2,2))
A236432-A235921: 210 630 1050 1470 1890 2310 2730 3150 3570 3990 4410 4830 5250 5670 6090 6510
(if (~x + 4) <= 0 then (2 * (x mod 2)) else (2x + 1))
A173013: 1 3 5 7 0 2 0 2 0 2 0 2 0 2 0 2
loop(\(x,i).5x,2x,(2x + 1))
A166725: 1 75 3125 109375 3515625 107421875 3173828125 91552734375 2593994140625 72479248046875 2002716064453125 54836273193359375 1490116119384765625 4611686018427387903 4611686018427387903
((3x + 1) + loop(\(x,i).3x,x,1))
A176805: 2 7 16 37 94 259 748 2209 6586 19711 59080 177181 531478 1594363 4783012 14348953
loop(\(x,i).7x,x,(2x + 1))
A199300: 1 21 245 2401 21609 184877 1529437 12353145 98001617 766718533 5931980229 45478515089 346032180025 2616003280989 19668469112621 147174406808233
((2x + 1) * loop(\(x,i).(x + (i * i)),x,x2))
A302709: 0 6 45 161 414 880 1651 2835 4556 6954 10185 14421 19850 26676 35119 45415
((4x2 + 2x + ~2) * (if x <= 0 then 0 else 2))
A187287: 0 8 36 80 140 216 308 416 540 680 836 1008 1196 1400 1620 1856
((2x + ~1) * ((1 + (x mod 2)) * (if x <= 0 then 0 else 2)))
A123169: 0 4 6 20 14 36 22 52 30 68 38 84 46 100 54 116
(if x <= 0 then 1 else (8x2 + ~8x + 2))
A077591: 1 2 18 50 98 162 242 338 450 578 722 882 1058 1250 1458 1682
(if x <= 0 then 1 else ((2x + ~1) * (2 + (2 mod (x + 1)))))
A136725: 1 2 12 20 28 36 44 52 60 68 76 84 92 100
(if x <= 0 then 1 else (16x2 + ~8x))
A067239: 1 8 48 120 224 360 528 728 960 1224 1520 1848 2208 2600 3024 3480
((~3x + 1) + loop(\(x,i).4x,x,1))
A175976: 2 2 11 56 245 1010 4079 16364 65513 262118 1048547 4194272 16777181 67108826 268435415 1073741780
((3x + ~1) + loop(\(x,i).2x,(x + ~1),2))
A132074: 1 4 9 16 27 46 81 148 279 538 1053 2080 4131 8230 16425 32812
loop(\(x,i).(x * (1 + (2 * (2 + (i mod 2))))),2x,1)
A009979: 1 35 1225 42875 1500625 52521875 1838265625 64339296875 2251875390625 78815638671875 2758547353515625 96549157373046875 3379220508056640625 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).((2 * (x + i)) div 3),x,2x))
A214585: 1 3 4 5 7 8 9 11 13 15 17 19 21 23 25 27
loop(\(x,i).(3x + 16),2x,1)
A177095: 1 73 721 6553 59041 531433 4782961 43046713 387420481 3486784393 31381059601 282429536473 2541865828321 22876792454953 205891132094641 1853020188851833
(1 + (2x2 * loop(\(x,i).(x2 + 2),2,2)))
A158767: 1 77 305 685 1217 1901 2737 3725 4865 6157 7601 9197 10945 12845 14897 17101
(if (x + ~2) <= 0 then 2x else (2x3 + 1))
A121234: 0 2 4 55
loop(\(x,i).((x + 1) + i - (x div 4)),(x div 2),1)
A290966: 1 1 3 3 6 6 9 9 12 12 15 15 19 19 23 23
(if ((x + ~2) mod 12) <= 0 then (x div 2) else 1)
A101027: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 1
loop(\(x,i).(10x + 1),(x div 2),1)
A289404: 1 1 11 11 111 111 1111 1111 11111 11111 111111 111111 1111111 1111111 11111111 11111111
(if (~1 + (x * (x mod (2 + (x mod 2))))) <= 0 then (x div 2) else 1)
A175126: 0 0 1 1 2 1 3 1 4 4 5 1 6 1 7 7
(if ((x + ~2) mod 10) <= 0 then (x div 2) else 1)
A260340: 1 1 1 1 1 1 1 1 1 1 1 1 6 1 1 1
(1 + loop(\(x,i).(x - (x div (1 + (2 * i)))),2,(x div 2)))
A196383: 1 1 2 2 3 3 3 3 4 4 5 5 5 5 5 5
((if (x mod 4) <= 0 then (x + ~2) else 1) mod (1 + (x div 2)))
A205617: 0 0 1 1 2 1 1 1 1 1 1 1 3 1 1 1
(loop(\(x,i).(x * (1 + i)),x,(x + 1)) div (1 + (x div 2)))
A256880: 1 4 9 48 200 1440 8820 80640 653184 7257600 73180800 958003200 11564467200 174356582400 2451889440000 41845579776000
(if x <= 0 then 1 else (x - ((x div ~2) * (1 + (x div 2)))))
A184674: 1 2 4 7 10 14 18 23 28 34 40 47 54 62 70 79
((if x <= 0 then 0 else (2 * (1 + (x div 2)))) * (1 + (x div 2)))
A116471: 0 2 8 8 18 18 32 32 50 50 72 72 98 98 128 128
loop(\(x,i).(x * i),x,(((x + 1) div 2) * (1 + (x div 2))))
A077613: 0 1 4 24 144 1080 8640 80640 806400 9072000 108864000 1437004800 20118067200 305124019200 4881984307200 83691159552000
((loop(\(x,i).(x * i),x,(x div 2)) div 2) * (1 + (x div 2)))
A152885: 0 0 2 6 72 360 4320 30240 403200 3628800 54432000 598752000 10059033600 130767436800 2440992153600 36614882304000
((2x + (if (~x + 2) <= 0 then x else 2)) * (1 + (x div 2)))
A052289: 2 4 12 18 36
(if (x mod 2) <= 0 then 5x else (1 + (x div 2)))
A319154: 0 1 10 2 20 3 30 4 40 5 50 6 60 7 70 8
((x mod 2) - ((if x <= 0 then 0 else (~x + 1)) * (1 + (x div 2))))
A192225: 0 1 2 5
A109094: 0 1 2 5 9 13 20 25 35 41 54 61 77 85 104 113
loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,(1 + (x div 2)))
A304487: 1 4 15 36 73 128 207 312 449 620 831 1084 1385 1736 2143 2608
loop(\(x,i).(x + (((2 + i) * (1 + i)) div 2)),(x div 2),1)
A058187: 1 1 4 4 10 10 20 20 35 35 56 56 84 84 120 120
(if (~1 + ((x + ~1) mod 5)) <= 0 then (x mod 2) else 1)
A285668-A267813-A117278: 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1
(if (2 - (x mod 7)) <= 0 then (x mod 2) else 1)
A104120: 1 1 0 1 0 1 0 1 1 1 0 1 0 1 1 1
(1 + ((if (~x + 2) <= 0 then (2 + (x div 2)) else 1) * (x mod 2)))
A282738: 1 2 1 4 1 5 1 6 1 7 1 8 1 9 1 10
(1 + ((loop(\(x,i).(2x + 4),x,1) div 2) + (x mod 2)))
A087940: 1 5 9 20 39 80 159 320 639 1280 2559 5120 10239 20480 40959 81920
(1 + loop(\(x,i).4x,(x div 2),(2 - (x mod 2))))
A140590: 3 2 9 5 33 17 129 65 513 257 2049 1025 8193 4097 32769 16385
(1 + ((if (~1 + (x mod 3)) <= 0 then x else 2) * (x mod 2)))
A214057: 1 2 1 4 1 3 1 8 1 10 1 3 1 14 1 16
(~1 + loop(\(x,i).(2 * (x - (i mod 2))),x,2) - (x mod 2))
A097072: 1 0 3 4 11 20 43 84 171 340 683 1364 2731 5460 10923 21844
(1 + loop(\(x,i).(4x + 4),(x div 2),(x mod 2)))
A097163: 1 2 5 9 21 37 85 149 341 597 1365 2389 5461 9557 21845 38229
(if (x + ~12) <= 0 then 0 else (1 + (x mod 2)))
A161273: 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 2
((1 + (if (x mod 3) <= 0 then 2 else 0)) * (1 + (x mod 2)))
A089145: 3 2 1 6 1 2 3 2 1 6 1 2 3 2 1 6
(loop(\(x,i).i,((~1 + (x div 2)) div 2),1) div (1 + (x mod 2)))
A332677: 1 0 1 0 1 0 1 0 1 0 2 1 2 1 3 1
((if (x mod 3) <= 0 then 2x else 1) * (1 + (x mod 2)))
A069566: 0 2 1 12 1 2
(loop(\(x,i).4x,(x div 2),1) div (1 + (x mod 2)))
A154383: 1 0 4 2 16 8 64 32 256 128 1024 512 4096 2048 16384 8192
(loop(\(x,i).(~2x + 1),(x div 2),1) div (1 + (x mod 2)))
A117576: 1 0 ~1 ~1 3 1 ~5 ~3 11 5 ~21 ~11 43 21 ~85 ~43
loop(\(x,i).(x * (i * i)),(1 + (x div 2)),(1 + (x mod 2)))
A222011: 1 2 4 8
A263623: 1 2 4 8 36
(loop(\(x,i).(4x + 1),x,1) div (1 + (x mod 2)))
A266873: 1 2 21 42 341 682 5461 10922 87381 174762 1398101 2796202 22369621 44739242 357913941 715827882
(loop(\(x,i).6x,x,1) div (1 + (x mod 2)))
A156189: 1 3 36 108 1296 3888 46656 139968 1679616 5038848 60466176 181398528 2176782336 6530347008 78364164096 235092492288
(loop(\(x,i).(3x + ~1),x,1) div (1 + (x mod 2)))
A167205: 1 1 5 7 41 61 365 547 3281 4921 29525 44287 265721 398581 2391485 3587227
(loop(\(x,i).(2 * (~x + (i mod 2))),x,1) * (1 + (x mod 2)))
A087213: 1 0 0 4 ~4 20 ~20 84 ~84 340 ~340 1364 ~1364 5460 ~5460 21844
((if (x + ~2) <= 0 then 1 else (x div 4)) div (1 + (x mod 2)))
A029238: 1 0 1 0 1 0 1 0 2 1 2 1 3 1 3 1
((if (x mod 4) <= 0 then x else 2x) * (1 + (x mod 2)))
A109045: 0 4 4 12 4 20 12 28 8 36 20 44 12 52 28 60
loop(\(x,i).(4x + 4),(x div 2),(1 + (x mod 2)))
A176961: 1 2 8 12 36 52 148 212 596 852 2388 3412 9556 13652 38228 54612
loop(\(x,i).5x,(x div 2),(1 + (x mod 2)))
A172411: 1 2 5 10
A018262: 1 2 5 10 25 50
A018356: 1 2 5 10 25 50 125 250
A026383: 1 2 5 10 25 50 125 250 625 1250 3125 6250 15625 31250 78125 156250
loop(\(x,i).(x2 + 3x),(x div 2),(1 + (x mod 2)))
A003223: 1 2 4 10 28 130
loop(\(x,i).(x - (x div (~2 + (i mod 2)))),x,(1 + (x mod 2)))
A166552: 1 4 3 12 9 36 27 108 81 324 243 972 729 2916 2187 8748
loop(\(x,i).(x * (3 + (i mod 2))),x,(1 + (x mod 2)))
A162466: 1 8 12 96 144 1152 1728 13824 20736 165888 248832 1990656 2985984 23887872 35831808 286654464
loop(\(x,i).(x * (1 + (2 * (i mod 2)))),x,(1 + (x mod 2)))
A166450: 1 6 3 18 9 54 27 162 81 486 243 1458 729 4374 2187 13122
loop(\(x,i).(x * (3 - (i mod 2))),x,(1 + (x mod 2)))
A231407: 1 4 6
A164532: 1 4 6 24 36 144 216 864 1296 5184 7776 31104 46656 186624 279936 1119744
(1 + ((if ((x + ~1) mod 3) <= 0 then 1 else x) * (x mod 2)))
A258409-A060680: 1 2 1 4 1 6 1 2 1 10 1 12 1 2 1 16
(1 + loop(\(x,i).11x,x,2))
A199750: 3 23 243 2663 29283 322103 3543123 38974343 428717763 4715895383 51874849203 570623341223 6276856753443 69045424287863 759499667166483 8354496338831303
(~1 + loop(\(x,i).11x,x,2))
A198974: 1 21 241 2661 29281 322101 3543121 38974341 428717761 4715895381 51874849201 570623341221 6276856753441 69045424287861 759499667166481 8354496338831301
((x + 1) - (loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2))
A225381: 1 2 2 4 3 5 4 8 5 8 6 11 7 11 8 16
(~1 + loop(\(x,i).(x + i - (x div (3 + i))),x,2))
A025704-A022776: 1 2 4 7 10 14 19 24 30 37 45 53 62 72 82 93
(1 + (loop(\(x,i).(2x + 12),x,x) div 2))
A048467: 1 8 23 55 123 267 571 1211 2555 5371 11259 23547 49147 102395 212987 442363
(1 + (loop(\(x,i).(2x + 16),x,x) div 2))
A048469: 1 10 29 69 153 329 697 1465 3065 6393 13305 27641 57337 118777 245753 507897
(1 + loop(\(x,i).(2x * (1 + (2 * i))),x2,2))
A112856: 3 13 30241 670442572801 4611686018427387903 4611686018427387903
((2x2 + 1) * (1 + (if (~x + 2) <= 0 then x else 2)))
A135415: 3 9 27 76
(if (x + ~4) <= 0 then (x + 1) else (2x2 + ~1))
A173574: 1 2 3 4 5 49
(if (x + ~4) <= 0 then x2 else (2x2 + ~1))
A291216: 0 1 4 9 16 49
loop(\(x,i).((x + 2) * i),(x + ~1),(1 + (x2 div 2)))
A343165: 1 1 5 18 84
(15 + loop(\(x,i).x2,x,2))
A160027: 17 19 31 271 65551 4294967311
(1 + (2 * loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,x)))
A177342: 1 9 31 75 149 261 419 631 905 1249 1671 2179 2781 3485 4299 5231
(1 + (if ((x + 2) mod 9) <= 0 then 0 else x))
A270418-A056192: 1 2 3 4 5 6 7 1 9 10 11 12 13 14 15 16
(1 + (if (x mod (3 + (x mod 4))) <= 0 then 0 else x))
A280505: 1 2 3 4 5 6 7 8 9 10 1 12 1 14 15 16
(1 + (if ((x div ~2) mod 5) <= 0 then 0 else x))
A180410: 1 2 3 4 5 6 7 8 9 1 1 12 13 14 15 16
((x + 1) + (if ((x + 2) mod 5) <= 0 then 2 else 0))
A093783: 1 2 3 6 5 6 7 8 11 10 11 12 13 16 15 16
(1 + (if (~2 + (2x div (2 + (x div 2)))) <= 0 then 0 else x))
A179937: 1 1 1 1 1 1 1 1 1 10 1 12 13 14 15 16
(1 + (if (((x + 1) * (x div 2)) mod 4) <= 0 then 0 else x))
A147661: 1 1 3 1 5 1 7 1 1 1 11 1 13 1 15 1
(~2x mod ((x + 1) + (if (x mod 2) <= 0 then 2 else 0)))
A021796: 0 0 1 2 6 2 6 2 6 2 6 2 6 2 6 2
(1 + (x * loop(\(x,i).(1 + (x * (2 + i))),(x + ~2),0)))
A131965: 1 1 1 4 21 131 943 7701 70409 712891 7921011 95844233 1254688141 17670191319 266412115271 4281623281141
((x + 1) + (if (x mod 9) <= 0 then x else 0))
A092596: 1 2 3 4 5 6 7 8 9 19
A199344: 1 2 3 4 5 6 7 8 9 19 11 12 13 14 15 16
((x + 1) + loop(\(x,i).(i - ((1 + i) mod (x + 1))),x,0))
A092754: 1 3 4 7 8 9 10 15 16 17 18 19 20 21 22 31
((~x + 1) + loop(\(x,i).((2 * (x + i)) + (i mod 2)),x,0))
A005262: 1 3 9 25 59 131 277 573 1167 2359 4745 9521 19075 38187 76413 152869
loop(\(x,i).(1 + (x mod (1 + (i div (1 + (x mod 2)))))),x,1)
A071797: 1 1 2 3 1 2 3 4 5 1 2 3 4 5 6 7
loop(\(x,i).(10x + 6),x,1)
A246057: 1 16 166 1666 16666 166666 1666666 16666666 166666666 1666666666 16666666666 166666666666 1666666666666 16666666666666 166666666666666 1666666666666666
loop(\(x,i).(10x + ~6),x,1)
A093137: 1 4 34 334 3334 33334 333334 3333334 33333334 333333334 3333333334 33333333334 333333333334 3333333333334 33333333333334 333333333333334
loop(\(x,i).(10x + 21),x,1)
A033175: 1 31 331 3331 33331 333331 3333331 33333331 333333331 3333333331 33333333331 333333333331 3333333333331 33333333333331 333333333333331 3333333333333331
loop(\(x,i).(15x + 1),x,1)
A135518: 1 16 241 3616 54241 813616 12204241 183063616 2745954241 41189313616 617839704241 9267595563616 139013933454241 2085209001813616 31278135027204241 469172025408063616
loop(\(x,i).(1 + (5x * (i * i))),x,1)
A336808: 1 6 121 5446 435681 54460126 9802822681 2401691556846 768541298190721 311259225767242006 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (((x + 1) * (x + i)) div 3)),x,1)
A097980: 1 2 5 17 127
loop(\(x,i).(6x + 25),x,1)
A164784: 1 31 211 1291 7771 46651 279931 1679611 10077691 60466171 362797051 2176782331 13060694011 78364164091 470184984571 2821109907451
(1 + (if ((x + ~1) mod 12) <= 0 then 1 else x))
A268982: 1 2 3 4 5 6 7 8 9 10 11 12 13 2 15 16
loop(\(x,i).(~11x + 1),x,1)
A014993: 1 ~10 111 ~1220 13421 ~147630 1623931 ~17863240 196495641 ~2161452050 23775972551 ~261535698060 2876892678661 ~31645819465270 348104014117971 ~3829144155297680
((x + ~1) + loop(\(x,i).2x2,(x + ~3),1))
A259503: 0 1 2 3 5 12 133
loop(\(x,i).((4x + 1) + (i mod 3)),x,1)
A037604: 1 6 27 109 438 1755 7021 28086 112347 449389 1797558 7190235 28760941 115043766 460175067 1840700269
(1 + (x * loop(\(x,i).(1 + (x * i)),(2x + ~1),1)))
A086894: 1 3 33 979 54801 4932051 651030673 118487582403 28437019776609 8701728051642211 3306656659624040001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.(~1 + (loop(\(x,i).2x,x,1) mod (x + 1))),x))
A174090: 1 2 3 4 5 7 8 11 13 16 17 19 23 29 31 32
(~1 + (if x <= 0 then 2 else (4x2 + 5x)))
A164754: 1 8 25 50 83 124 173 230 295 368 449 538 635 740 853 974
loop(\(x,i).(1 + ((x + 6) mod (1 + i))),x,1)
A178853: 1 2 3 2 4 5 5 4 2 9 5 12 6 13 5 12
loop(\(x,i).(x - (x div ~9)),x,1)
A060472-A033062: 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 23
loop(\(x,i).(1 + (x mod (2 + ((1 + i) div 3)))),x,1)
A194063-A194053: 1 2 3 1 2 3 4 1 2 3 4 5 6 1 2 3
loop(\(x,i).(1 + ((3 * (2x + i)) div 2)),x,1)
A141397: 1 5 19 62 193 587 1771 5324 15985 47969 143923 431786 1295377 3886151 11658475 34975448
loop(\(x,i).(10x + 3),x,1)
A097166: 1 13 133 1333 13333 133333 1333333 13333333 133333333 1333333333 13333333333 133333333333 1333333333333 13333333333333 133333333333333 1333333333333333
loop(\(x,i).(~14x + 1),x,1)
A268413: 1 ~13 183 ~2561 35855 ~501969 7027567 ~98385937 1377403119 ~19283643665 269971011311 ~3779594158353 52914318216943 ~740800455037201 10371206370520815 ~145196889187291409
(1 + loop(\(x,i).(2 * i),(x mod 9),x))
A118137: 1 3 5 7 9 11 13 15 17 10 3 5 7 9 11 13
loop(\(x,i).(1 + (4 * ((x * (i * i)) div 2))),x,1)
A337152: 1 1 9 161 5153 257649 18550729 1817971441 232700344449 37697455800737 7539491160147401 1824556860755671041 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).30x,x,1)
A009974: 1 30 900 27000 810000 24300000 729000000 21870000000 656100000000 19683000000000 590490000000000 17714700000000000 531441000000000000 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x + i),((x + ~1) div 5),x))
A269164: 1 2 3 4 5 6 8 9 10 11 12 15 16 17 18 19
loop(\(x,i).(10x * (1 + i)),x,1)
A035279: 1 20 600 24000 1200000 72000000 5040000000 403200000000 36288000000000 3628800000000000 399168000000000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).40x,x,1)
A009984: 1 40 1600 64000 2560000 102400000 4096000000 163840000000 6553600000000 262144000000000 10485760000000000 419430400000000000 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x2 div (x + 2)),5,x))
A111633: 1 1 1 1 1 1 1 1 1 1 2 2 3 4 5 6
loop(\(x,i).(11x + ~5),x,1)
A034659: 1 6 61 666 7321 80526 885781 9743586 107179441 1178973846 12968712301 142655835306 1569214188361 17261356071966 189874916791621 2088624084707826
loop(\(x,i).x2,3,(5x + 1))
A016868: 1 1679616 214358881 4294967296 37822859361 208827064576 852891037441 2821109907456 7984925229121 20047612231936 45767944570401 96717311574016 191707312997281 360040606269696
loop(\(x,i).x3,1,(5x + 1))
A016863: 1 216 1331 4096 9261 17576 29791 46656 68921 97336 132651 175616 226981 287496 357911 438976
loop(\(x,i).x3,2,(5x + 1))
A016869: 1 10077696 2357947691 68719476736 794280046581 5429503678976 26439622160671 101559956668416 327381934393961 922190162669056 2334165173090451 5416169448144896 11694146092834141 23762680013799936
loop(\(x,i).(5x * (x mod 3)),x,1)
A093143: 1 5 50 500 5000 50000 500000 5000000 50000000 500000000 5000000000 50000000000 500000000000 5000000000000 50000000000000 500000000000000
loop(\(x,i).(5x * (1 + (2 * i))),x,1)
A035274: 1 15 375 13125 590625 32484375 2111484375 158361328125 13460712890625 1278767724609375 134270611083984375 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (x * (1 + loop(\(x,i).(x2 + ~1),x,4))))
A271438: 1 17 451
loop(\(x,i).((x + 1) - (2 * (~2x + (x mod 2)))),x,1)
A083425: 1 4 21 104 521 2604 13021 65104 325521 1627604 8138021 40690104 203450521 1017252604 5086263021 25431315104
loop(\(x,i).((5x + 1) - (i mod 2)),x,1)
A033115: 1 5 26 130 651 3255 16276 81380 406901 2034505 10172526 50862630 254313151 1271565755 6357828776 31789143880
loop(\(x,i).((5x + 1) + (i mod 2)),x,1)
A037482: 1 7 36 182 911 4557 22786 113932 569661 2848307 14241536 71207682 356038411 1780192057 8900960286 44504801432
loop(\(x,i).(1 + (2 * (3x + (i mod 2)))),x,1)
A037578: 1 9 55 333 1999 11997 71983 431901 2591407 15548445 93290671 559744029 3358464175 20150785053 120904710319 725428261917
loop(\(x,i).(~1 + (2 * (3x + (i mod 2)))),x,1)
A108983: 1 7 41 247 1481 8887 53321 319927 1919561 11517367 69104201 414625207 2487751241 14926507447 89559044681 537354268087
(1 + (x2 div (x + loop(\(x,i).i,(~2 + (x div 2)),1))))
A100721: 1 1 2 3 4 5 6 7 7 8 8 9 10 10 11 12
loop(\(x,i).(1 + (x * (i * i)) - (2 * (x mod 2))),x,1)
A073701: 1 0 1 8 129 3224 116065 5687184 363979777 29482361936 2948236193601 356736579425720 51370067437303681 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + i - (x div (1 + (4 * i)))),x,1)
A025726: 1 2 4 7 11 16 22 29 37 45 54 64 75 87 100 114
loop(\(x,i).(1 + (2 * (4x + (i mod 2)))),x,1)
A037580: 1 11 89 715 5721 45771 366169 2929355 23434841 187478731 1499829849 11998638795 95989110361 767912882891 6143303063129 49146424505035
loop(\(x,i).(3 * ((x + 1) - (2 * (x mod 2)))),x,1)
A054878: 1 0 3 6 21 60 183 546 1641 4920 14763 44286 132861 398580 1195743 3587226
loop(\(x,i).(9x * (1 + i)),x,1)
A035023: 1 18 486 17496 787320 42515280 2678462640 192849310080 15620794116480 1405871470483200 139181275577836800 4611686018427387903 4611686018427387903 4611686018427387903
(2 - loop(\(x,i).(((x + ~1) * (1 + i)) div 3),x,1))
A003218: 1 2 3 5 9 18 42
loop(\(x,i).(3x * ((1 + i) * (1 + i))),x,1)
A080141: 1 12 324 15552 1166400 125971200 18517766400 3555411148800 863964909158400 259189472747520000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3 * (x mod 10)),x,1)
A168427: 1 3 9 27 21 3 9 27 21 3 9 27 21 3 9 27
loop(\(x,i).48x,x,1)
A009992: 1 48 2304 110592 5308416 254803968 12230590464 587068342272 28179280429056 1352605460594688 64925062108545024 3116402981210161152 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if ((x + 1) mod 8) <= 0 then 3 else x))
A007948: 1 2 3 4 5 6 7 4 9 10 11 12 13 14 15 4
loop(\(x,i).(24x * i),x,1)
A080775: 1 24 1152 82944 7962624 955514880 137594142720 23115815976960 4438236667576320 958659120196485120 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(13x + ~6),x,1)
A193578: 1 7 85 1099 14281 185647 2413405 31374259 407865361 5302249687 68929245925 896080197019 11649042561241 151437553296127 1968688192849645 25592946507045379
loop(\(x,i).(13x + ~2),x,1)
A083078: 1 11 141 1831 23801 309411 4022341 52290431 679775601 8837082811 114882076541 1493466995031 19415070935401 252395922160211 3281146988082741 42654910845075631
loop(\(x,i).(~13x + 1),x,1)
A015000: 1 ~12 157 ~2040 26521 ~344772 4482037 ~58266480 757464241 ~9847035132 128011456717 ~1664148937320 21633936185161 ~281241170407092 3656135215292197 ~47529757798798560
loop(\(x,i).(11x + 1),x,1)
A016123: 1 12 133 1464 16105 177156 1948717 21435888 235794769 2593742460 28531167061 313842837672 3452271214393 37974983358324 417724816941565 4594972986357216
loop(\(x,i).(11x + 2),x,1)
A199023: 1 13 145 1597 17569 193261 2125873 23384605 257230657 2829537229 31124909521 342374004733 3766114052065 41427254572717 455699800299889 5012697803298781
loop(\(x,i).(6 * (2x - (x mod 2))),x,1)
A067419: 1 6 72 864 10368 124416 1492992 17915904 214990848 2579890176 30958682112 371504185344 4458050224128 53496602689536 641959232274432 7703510787293184
loop(\(x,i).(6x * (1 + (2 * i))),x,1)
A254381: 1 18 540 22680 1224720 80831520 6304858560 567437270400 57878601580800 6598160580211200 831368233106611200 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(6x * (~1 + (2 * i))),x,1)
A221954: 1 6 108 3240 136080 7348320 484989120 37829151360 3404623622400 347271609484800 39588963481267200 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x + 30),x,1)
A036546: 1 33 129 417 1281 3873 11649 34977 104961 314913 944769 2834337 8503041 25509153 76527489 229582497
loop(\(x,i).(x - (3 * (~2x + (x mod 2)))),x,1)
A270471: 1 4 28 196 1372 9604 67228 470596 3294172 23059204 161414428 1129900996 7909306972 55365148804 387556041628 2712892291396
loop(\(x,i).((6x + 1) - (x mod 2)),x,1)
A033116: 1 6 37 222 1333 7998 47989 287934 1727605 10365630 62193781 373162686 2238976117 13433856702 80603140213 483618841278
((x + ~1) + (if (x + ~2) <= 0 then 2 else (2x div 3)))
A032955: 1 2 3 4 5 7 9 10 12 14 15 17 19 20 22 24
loop(\(x,i).(x - ((((~x + 2) - i) div 2) div 3)),x,1)
A007279: 1 1 2 3 4 6 8 11 14 18 23 29 36 44 54 66
loop(\(x,i).10x,3x,1)
A060366: 1 1000 1000000 1000000000 1000000000000 1000000000000000 1000000000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x * (~1 + (2 * i))),3x,1)
A166351: 1 120 665280 17643225600 1295295050649600 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((3x + 1) * loop(\(x,i).(x + (i * i)),x,0))
A011195: 0 4 35 140 390 880 1729 3080 5100 7980 11935 17204 24050 32760 43645 57040
loop(\(x,i).(x div (~2 + (x mod 2))),2,(3x + 1))
A176672: 1 1 7 5 13 4 19 11 25 7 31 17 37 10 43 23
loop(\(x,i).(2x + ~6),x,(3x + 1))
A048499: 1 2 10 38 118 326 838 2054 4870 11270 25606 57350 126982 278534 606214 1310726
loop(\(x,i).(x3 + ~x),1,(3x + ~1))
A054776: 0 6 120 504 1320 2730 4896 7980 12144 17550 24360 32736 42840 54834 68880 85140
loop(\(x,i).21x,x,1)
A009965: 1 21 441 9261 194481 4084101 85766121 1801088541 37822859361 794280046581 16679880978201 350277500542221 7355827511386641 154472377739119461 3243919932521508681 4611686018427387903
loop(\(x,i).(3x * (1 + (2 * (1 + i)))),x,1)
A053102: 1 15 315 8505 280665 10945935 492567075 25120920825 1431892487025 90209226682575 6224436641097675 466832748082325625 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3 * (x + (3x * i))),x,1)
A035013: 1 12 252 7560 294840 14152320 806682240 53241027840 3993077088000 335418475392000 31193918211456000 3181779657568512000 4611686018427387903 4611686018427387903
loop(\(x,i).(3 * (~x + (3x * i))),x,1)
A147630: 1 6 90 2160 71280 2993760 152681760 9160905600 632102486400 49303993939200 4289447472710400 411786957380198400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 3) + ((x * i) div 3)),x,1)
A076861: 1 4 9 21 52
((x + 1) + (if (x mod 2) <= 0 then x else ((~x + 1) div 3)))
A026219-A026201: 1 2 5 3 9 4 13 6 17 7 21 8 25 10 29 11
((2x + 1) - loop(\(x,i).i,((~x + 1) mod 3),x))
A080029: 0 2 3 6 5 9 12 8 15 18 11 21 24 14 27 30
loop(\(x,i).(3 * (x + (2x div (1 + i)))),x,1)
A036068: 1 6 30 135 567 2268 8748 32805 120285 433026 1535274 5373459 18600435 63772920 216827928 731794257
((x + 1) + ((if (x mod 2) <= 0 then x else (~x + 2)) mod 3))
A077859: 1 3 5 6 6 6 7 9 11 12 12 12 13 15 17 18
((x + 1) + (loop(\(x,i).(x * (x div 2)),2,x) div 3))
A072246: 1 2 3 5 15 22
loop(\(x,i).(3x * (2 + (3 * i))),x,1)
A035020: 1 15 360 11880 498960 25446960 1526817600 105350414400 8217332323200 714907912118400 68631159563366400 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x * (~2 + (3 * i))),x,1)
A144758: 1 3 36 756 22680 884520 42456960 2420046720 159723083520 11979231264000 1006255426176000 93581754634368000 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (x2 div (x + (if x <= 0 then 1 else (x div 3)))))
A181534: 1 2 3 3 4 5 5 6 7 7 8 9 10 10 11 12
((x + 1) + (if (~2 + (x div 2)) <= 0 then 2 else (x div 3)))
A154660: 3 4 5 6 7 8
A298112: 3 4 5 6 7 8 9 10 11 13 14 15 17 18 19 21
(if ((x + ~1) mod 3) <= 0 then (x + (x div 3)) else 1)
A058281: 1 1 1 1 5 1 1 9 1 1 13 1 1 17 1 1
loop(\(x,i).(8x + (x mod 3)),x,1)
A170690-A170642-A170594-A170546-A170498-A170450-A170402-A170354-A170306-A170258-A170210-A170162-A170114-A170066-A170018-A169550-A169502-A169454-A169406-A169358-A169310-A169262-A169214-A169166-A169118-A169070-A169022-A168974-A168926-A168878-A168830-A168782-A168734-A168686-A167900-A003951: 1 9 72 576 4608 36864 294912 2359296 18874368 150994944 1207959552 9663676416 77309411328 618475290624 4947802324992 39582418599936
loop(\(x,i).((2 * (~x + (i mod 2))) - (x mod 3)),x,1)
A122959: 1 ~1 0 2 ~6 14 ~30 62 ~126 254 ~510 1022 ~2046 4094 ~8190 16382
loop(\(x,i).(~2x + (i mod 2) - (x mod 3)),x,1)
A248155: 1 ~2 3 ~5 9 ~17 33 ~65 129 ~257 513 ~1025 2049 ~4097 8193 ~16385
loop(\(x,i).(14x + 1),x,1)
A135519: 1 15 211 2955 41371 579195 8108731 113522235 1589311291 22250358075 311505013051 4361070182715 61054982558011 854769755812155 11966776581370171 167534872139182395
loop(\(x,i).((6x + 1) + (x mod 2)),x,1)
A037483: 1 8 49 296 1777 10664 63985 383912 2303473 13820840 82925041 497550248 2985301489 17911808936 107470853617 644825121704
loop(\(x,i).((8x + 1) + (x mod 2)),x,1)
A037485: 1 10 81 650 5201 41610 332881 2663050 21304401 170435210 1363481681 10907853450 87262827601 698102620810 5584820966481 44678567731850
loop(\(x,i).((8x + 1) - (x mod 2)),x,1)
A033118: 1 8 65 520 4161 33288 266305 2130440 17043521 136348168 1090785345 8726282760 69810262081 558482096648 4467856773185 35742854185480
loop(\(x,i).(x * ((1 + (2 * i)) * (3 + i))),x,1)
A014130: 1 12 300 12600 793800 69854400 8172964800 1225944720000 229251662640000 52269379081920000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1)
A188545: 1 3 10
A001700: 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195
loop(\(x,i).(8x * (1 + (2 * i))),x,1)
A254619: 1 24 960 53760 3870720 340623360 35424829440 4250979532800 578133216460800 87876248902041600 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (2 * (5x + i))),x,1)
A179619: 1 13 135 1357 13579 135801 1358023 13580245 135802467 1358024689 13580246911 135802469133 1358024691355 13580246913577 135802469135799 1358024691358021
loop(\(x,i).(13x + 1),x,1)
A091030: 1 14 183 2380 30941 402234 5229043 67977560 883708281 11488207654 149346699503 1941507093540 25239592216021 328114698808274 4265491084507563 55451384098598320
loop(\(x,i).(11x + ~1),x,1)
A199760: 1 10 109 1198 13177 144946 1594405 17538454 192922993 2122152922 23343682141 256780503550 2824585539049 31070440929538 341774850224917 3759523352474086
loop(\(x,i).(17x + 1),x,1)
A091045: 1 18 307 5220 88741 1508598 25646167 435984840 7411742281 125999618778 2141993519227 36413889826860 619036127056621 10523614159962558 178901440719363487 3041324492229179280
(1 + (x * loop(\(x,i).(1 + ((x * (i * i)) + i)),x,1)))
A141827: 1 4 31 418 8917 278656 12037939 688168846 50334635593 4586743668412 509638185379111 67832842473959674 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + ((i * i * (1 + i)) div 2)),x,1)
A188545: 1 3 10
A130218: 1 3 10 29 70 146 273 470 759 1165 1716 2443 3380 4564 6035 7836
loop(\(x,i).((x + 1) + (2 * (2x + (x mod 2)))),x,1)
A037577: 1 8 41 208 1041 5208 26041 130208 651041 3255208 16276041 81380208 406901041 2034505208 10172526041 50862630208
loop(\(x,i).((x + ~1) + (2 * (2x + (x mod 2)))),x,1)
A108982: 1 6 29 146 729 3646 18229 91146 455729 2278646 11393229 56966146 284830729 1424153646 7120768229 35603841146
((x + 1) + loop(\(x,i).(2 + (x * i) - (x div 2)),x,1))
A324149: 2 5 10 24 77
((x + ~1) + loop(\(x,i).10x,x,1))
A123522: 0 10 101 1002 10003 100004 1000005 10000006 100000007 1000000008 10000000009 100000000010 1000000000011 10000000000012 100000000000013 1000000000000014
loop(\(x,i).((x + 1) + (((2 + (i mod 2)) * i) div 2)),x,1)
A083462: 1 3 6 11
A087099: 1 3 6 11 16 24 31 42 51 65 76 93 106 126 141 164
loop(\(x,i).((x + 1) + ((2 + (i div 2)) * (i div 2))),x,1)
A005993: 1 2 6 10 19 28 44 60 85 110 146 182 231 280 344 408
(1 + compr(\x.(loop(\(x,i).(2x + 1),x,0) mod (x + 1)),x))
A176997-A175524-A138980-A074918-A006005: 1 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53
(1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))
A324050-A094742-A064555-A052424-A015919-A008578-A005180: 1 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
(1 + compr(\x.(loop(\(x,i).(~2x + 1),x,0) mod (x + 1)),x))
A322271: 1 5 7 11 13 17 19 23
A271116-A175212-A140475: 1 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59
((x + 1) + (if (x + ~2) <= 0 then 1 else (4x + 4)))
A309789: 2 3 4 20 25
(~1 + loop(\(x,i).x2,1,(5x + 4)))
A180577: 15 80 195 360 575 840 1155 1520 1935 2400 2915 3480 4095 4760 5475 6240
loop(\(x,i).4x,(5x + 4),1)
A013833: 256 262144 268435456 274877906944 281474976710656 288230376151711744 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).3x,(5x + 4),1)
A013829: 81 19683 4782969 1162261467 282429536481 68630377364883 16677181699666569 4052555153018976267 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + ((x + i) div (2 + (x mod 2)))),x,1)
A077866: 1 2 5 8 15 22 37 52 83 114 177 240 367 494 749 1004
loop(\(x,i).(6x + (2 div (x + 1))),x,1)
A170688-A170640-A170592-A170544-A170496-A170448-A170400-A170352-A170304-A170256-A170208-A170160-A170112-A170064-A170016-A169548-A169500-A169452-A169404-A169356-A169308-A169260-A169212-A169164-A169116-A169068-A169020-A168972-A168924-A168876-A168828-A168780-A168732-A168684-A167898-A003949: 1 7 42 252 1512 9072 54432 326592 1959552 11757312 70543872 423263232 2539579392 15237476352 91424858112 548549148672
loop(\(x,i).(8x - (2 div (x + 1))),x,1)
A055274: 1 7 56 448 3584 28672 229376 1835008 14680064 117440512 939524096 7516192768 60129542144 481036337152 3848290697216 30786325577728
((x + ~1) + (if (x mod 2) <= 0 then 4 else (2 div (x + 1))))
A065168: 3 1 5 2 7 4 9 6 11 8 13 10 15 12 17 14
((~x2 + ~x + ~1) + loop(\(x,i).x2,2,(x + 2)))
A269620: 15 78 249 612 1275 2370 4053 6504 9927 14550 20625 28428 38259 50442 65325 83280
(1 + loop(\(x,i).(x + ((x + 4) * i)),(x + 1),x))
A052225: 5 27 141 837 5757 45357 403197 3991677 43545597 518918397 6706022397 93405311997 1394852659197 22230464255997 376610217983997 6758061133823997
loop(\(x,i).((7x + 1) + i),x,1)
A014830: 1 9 66 466 3267 22875 160132 1120932 7846533 54925741 384480198 2691361398 18839529799 131876708607 923136960264 6461958721864
loop(\(x,i).((x + 1) + ((2 + (x div 3)) * i)),x,1)
A096124: 1 4 11 27 72
loop(\(x,i).((x + 1) + ((6 + i) * i)),x,1)
A052153: 1 9 26 54 95 151 224 316 429 565 726 914 1131 1379 1660 1976
(8 - loop(\(x,i).(4x + ~4),x,1))
A156605: 7 8 12 28 92 348 1372 5468 21852 87388 349532 1398108 5592412 22369628 89478492 357913948
(1 + loop(\(x,i).10x,(x + ~1),x))
A094797: 1 2 21 301 4001 50001 600001 7000001 80000001 900000001 10000000001 110000000001 1200000000001 13000000000001 140000000000001 1500000000000001
((x2 + ~x + 1) * (if (x + ~2) <= 0 then 1 else x2))
A135444: 1 1 3 63
loop(\(x,i).(x * (i - (2 * (i * i)))),(x2 + ~x),1)
A273723: 1 1 6 7484400 4611686018427387903
(1 + loop(\(x,i).(x + ((i * i) div 4)),(x + ~1),x))
A088795: 1 2 3 5 8 13 20 30 43 60 81 107 138 175 218 268
loop(\(x,i).((x + ~1) + ((~1 + (2 * i)) * i * i)),x,1)
A046998: 1 1 12 56 167 391 786 1422 2381 3757 5656 8196 11507 15731 21022 27546
(1 + (((~x + (x mod 2)) div 3) mod (if x <= 0 then 1 else x)))
A005229: 1 1 2 3 3 4 5 6 6 7 7 8 9 10 10 11
((1 + (x mod 8)) mod (1 + (if x <= 0 then 1 else x)))
A263363: 1 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8
loop(\(x,i).(x * (2 + i)),(x4 + ~x),1)
A127225: 1 1 10461394944000 4611686018427387903
loop(\(x,i).((9x + 1) + i),x,1)
A014832: 1 11 102 922 8303 74733 672604 6053444 54481005 490329055 4412961506 39716653566 357449882107 3217048938977 28953440450808 260580964057288
loop(\(x,i).(x - (3x div (~1 - i))),x,1)
A083462: 1 3 6 11
A014125: 1 3 6 11 18 27 39 54 72 94 120 150 185 225 270 321
loop(\(x,i).((12x + 1) + i),x,1)
A014882: 1 14 171 2056 24677 296130 3553567 42642812 511713753 6140565046 73686780563 884241366768 10610896401229 127330756814762 1527969081777159 18335628981325924
loop(\(x,i).(1 + (((x + 1) * (x div 4)) + i)),x,1)
A005433: 1 2 3 4 10 28
loop(\(x,i).((1 + (4 * (x div 2))) * (1 + i)),x,1)
A161937: 1 2 15 116 1165 13974 195643 3130280 56345049 1126900970 24791821351 595003712412 15470096522725 433162702636286 12994881079088595 415836194530835024
loop(\(x,i).(((x + 1) - (2 * (x mod 2))) * (1 + i)),x,1)
A000240: 1 0 3 8 45 264 1855 14832 133497 1334960 14684571 176214840 2290792933 32071101048 481066515735 7697064251744
loop(\(x,i).((3x * (2 + i)) div (1 + i)),x,1)
A120926: 1 4 16 60 216 756 2592 8748 29160 96228 314928 1023516 3306744 10628820 34012224 108413964
loop(\(x,i).(((x + ~1) + (2 * (x mod 2))) * (1 + i)),x,1)
A085110: 1 4 9 40 195 1176 8225 65808 592263 5922640 65149029 781788360 10163248667 142285481352 2134282220265 34148515524256
loop(\(x,i).((x * (1 + i)) - ((x + 1) div (1 + i))),x,1)
A000255: 1 1 3 11 53 309 2119 16687 148329 1468457 16019531 190899411 2467007773 34361893981 513137616783 8178130767479
loop(\(x,i).(x * (i * i * (1 + i) * (1 + i))),x,1)
A069135: 1 4 144 20736 8294400 7464960000 13168189440000 41295442083840000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + i - (x div (4 * (1 + i)))),x,1)
A025707: 1 2 4 7 11 16 22 29 37 46 55 65 76 88 101 115
loop(\(x,i).((2 * (x - (2x * i))) div (1 + i)),x,1)
A168491: 1 ~1 2 ~5 14 ~42 132 ~429 1430 ~4862 16796 ~58786 208012 ~742900 2674440 ~9694845
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1)
A000108: 1 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845
loop(\(x,i).((2x * (4 + i)) div (1 + i)),x,1)
A080930: 1 5 20 70 224 672 1920 5280 14080 36608 93184 232960 573440 1392640 3342336 7938048
loop(\(x,i).(7x * (1 + i)),x,1)
A034834: 1 14 294 8232 288120 12101040 592950960 33205253760 2091930986880 146435169081600 11275508019283200 947142673619788800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((2x * (x mod 2)) - (x div ~2)),x,1)
A185453: 1 3 8 4 2 1 3 8 4 2 1 3 8 4 2 1
loop(\(x,i).(2 * (x mod 13)),x,1)
A222011: 1 2 4 8
A167425: 1 2 4 8 16 6 12 24 22 18 10 20 14 2 4 8
loop(\(x,i).(2 * (x mod 11)),x,1)
A222011: 1 2 4 8
A167421: 1 2 4 8 16 10 20 18 14 6 12 2 4 8 16 10
(if x <= 0 then 2 else (~1 + (2x * (1 + (x mod 3)))))
A084743: 2 3 11 5
(1 + loop(\(x,i).(x - (x mod (1 + (x div (1 + i))))),2,x))
A155047: 1 2 3 3 3 3 5 5 5 5 7 7 7 7 7 7
(x mod (1 + (if (x mod 7) <= 0 then 2 else x)))
A106608: 0 1 2 3 4 5 6 1 8 9 10 11 12 13 2 15
(1 + loop(\(x,i).(x div (1 + (x mod 6))),2,x))
A248909-A170824-A140213: 1 1 1 1 1 1 7 1 1 1 1 1 13 7 1 1
loop(\(x,i).((1 + (((x + 1) * (2 + i)) div 2)) div 2),x,1)
A182080: 1 2 3 5 9 18 38
loop(\(x,i).(2 * (1 + (2 * (2x - (i mod 2))))),x,1)
A090409: 1 6 50 398 3186 25486 203890 1631118 13048946 104391566 835132530 6681060238 53448481906 427587855246 3420702841970 27365622735758
loop(\(x,i).(2 * (x - (3 * (x div ~2)))),x,1)
A128625: 1 8 40 200 1000 5000 25000 125000 625000 3125000 15625000 78125000 390625000 1953125000 9765625000 48828125000
(1 + loop(\(x,i).(x - (x div 12)),2,x))
A303219: 1 2 3 4 5 6 7 8 9 10 11 12 12 12 13 14
(1 + loop(\(x,i).(x + i),(~2 + ((x + ~2) div 3)),x))
A135402-A135393: 1 2 3 4 5 6 7 8 9 10 11 13 14 15 18 19
((x + 1) + (if (~2 + (x div 2)) <= 0 then x else 6))
A194391: 1 3 5 7 9 11 13 14 15 16 17 18 19 20 21 22
(1 mod (if ((x + ~1) mod (2 + (x div 3))) <= 0 then x else 1))
A212213-A027351: 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1
loop(\(x,i).((4 * (x mod 2)) + ((x + 1) div 2)),x,1)
A070366: 1 5 7 8 4 2 1 5 7 8 4 2 1 5 7 8
((x + 1) + ((loop(\(x,i).(x * i),x,x) mod (x + 1)) mod 2))
A014683: 1 3 4 4 6 6 8 8 9 10 12 12 14 14 15 16
loop(\(x,i).((x * ((4 + i) * (1 + i))) div 2),x,1)
A085356: 1 5 45 630 12600 340200 11907000 523908000 28291032000 1838917080000 141596615160000 12743695364400000 1325344317897600000 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (x - ((x * (2 - i)) div (1 + i)))),x,1)
A068875: 1 2 4 10 28 84 264 858 2860 9724 33592 117572 416024 1485800 5348880 19389690
loop(\(x,i).(x - (x div (~2 + ((x div 2) mod ~2)))),x,1)
A323383: 1 2 3 4 6 8 12
A319054: 1 2 3 4 6 8 12 18 24 36 54 72 108 162 216 324
((x + 1) + (2 mod ((if x <= 0 then 1 else x) div ~4)))
A137721-A081304: 1 2 3 4 5 6 7 8 9 9 10 11 12 12 13 14
loop(\(x,i).(2 * (4x - (x div ~2))),x,1)
A170691-A170643-A170595-A170547-A170499-A170451-A170403-A170355-A170307-A170259-A170211-A170163-A170115-A170067-A170019-A169551-A169503-A169455-A169407-A169359-A169311-A169263-A169215-A169167-A169119-A169071-A169023-A168975-A168927-A168879-A168831-A168783-A168735-A168687-A167908-A003952: 1 10 90 810 7290 65610 590490 5314410 47829690 430467210 3874204890 34867844010 313810596090 2824295364810 25418658283290 228767924549610
loop(\(x,i).(4 * ((x + 1) - (2 * (i mod 2)))),x,1)
A109499: 1 0 4 12 52 204 820 3276 13108 52428 209716 838860 3355444 13421772 53687092 214748364
((x + 1) + (2 * (2 + (if (x + ~1) <= 0 then x else 3))))
A046038: 5 8 13 14 15 16 17 18 19 20 21 22 23 24 25 26
(1 + loop(\(x,i).i,(x mod (2 + ((x mod 3) div 2))),x))
A109674: 1 2 3 2 5 3 7 2 3 2 11 3 13 2 3 2
loop(\(x,i).((x + ~1) mod (4 + (i div 3))),x,1)
A179753: 1 0 3 2 1 0 5 4 3 2 1 0 7 6 5 4
(2 - loop(\(x,i).(2 * (x - ((i mod 3) mod 2))),x,1))
A063823: 1 2 2 2 4 6 10 20 38 74 148 294 586 1172 2342 4682
loop(\(x,i).(8 * (x - (x div ~2))),x,1)
A338100: 1 16 192 2304 27648 331776 3981312 47775744 573308928 6879707136 82556485632 990677827584 11888133931008 142657607172096 1711891286065152 20542695432781824
loop(\(x,i).(x - (x div (~4 + (x div 4)))),x,1)
A323383: 1 2 3 4 6 8 12
A018253: 1 2 3 4 6 8 12 24
((x + ~1) + loop(\(x,i).(x2 + 4x + 6),2,2))
A296904: 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416
(1 + loop(\(x,i).(((x2 + x) div 2) mod 4),2,x))
A090281: 1 2 3 4 4 3 2 1 1 2 3 4 4 3 2 1
(2 - (2 div (if ((x + ~2) mod 8) <= 0 then x else 1)))
A290081: 0 0 1 0 0 0 0 0 0 0 2 0 0 0 0 0
(1 + (if (x mod 2) <= 0 then (x div 2) else (x + 8)))
A303784: 1 10 2 12 3 14 4 16 5 18 6 20 7 22 8 24
loop(\(x,i).(2 * (x - (4 * (~x + (x mod 2))))),x,1)
A093136: 1 2 20 200 2000 20000 200000 2000000 20000000 200000000 2000000000 20000000000 200000000000 2000000000000 20000000000000 200000000000000
loop(\(x,i).(2 * (x - (4x * (1 - i)))),x,1)
A084948: 1 2 20 360 9360 318240 13366080 668304000 38761632000 2558267712000 189311810688000 15523568476416000 1397121162877440000 4611686018427387903 4611686018427387903
loop(\(x,i).(x - (x div (~2 - (i mod 4)))),x,1)
A245779: 1 2 3 4 6 8 10 12 18 24
A020490: 1 2 3 4 6 8 10 12 18 24 30
(1 + loop(\(x,i).(10x + 4),2,x))
A053743: 45 145 245 345 445 545 645 745 845 945 1045 1145 1245 1345 1445 1545
loop(\(x,i).(2 * (x - (2 * (~2x + (x mod 2))))),x,1)
A090019: 1 6 60 600 6000 60000 600000 6000000 60000000 600000000 6000000000 60000000000 600000000000 6000000000000 60000000000000 600000000000000
loop(\(x,i).(2 * (5x + (x div 2))),x,1)
A055276: 1 10 110 1210 13310 146410 1610510 17715610 194871710 2143588810 23579476910 259374246010 2853116706110 31384283767210 345227121439310 3797498335832410
(2 mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1))
A087893-A079169: 0 0 0 0 0 2 0 0 0 2 0 2 0 2 2 0
loop(\(x,i).(x - (4 * (x - (2x * i)))),x,1)
A147625: 1 5 65 1365 39585 1464645 65909025 3493178325 213083877825 14702787569925 1132114642884225 96229744645159125 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (x * (if (x + ~6) <= 0 then 1 else 4)))
A173576: 1 2 3 4 5 6 7 29
(5 mod (if ((x + ~1) mod 4) <= 0 then x else 1))
A243829: 0 0 0 0 0 0 0 0 0 5 0 0 0 5 0 0
loop(\(x,i).28x,x,1)
A009972: 1 28 784 21952 614656 17210368 481890304 13492928512 377801998336 10578455953408 296196766695424 8293509467471872 232218265089212416 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(4 * ((~x + ~1) + (2 * (i mod 2)))),x,1)
A084240: 1 0 ~4 20 ~84 340 ~1364 5460 ~21844 87380 ~349524 1398100 ~5592404 22369620 ~89478484 357913940
loop(\(x,i).(4 * (x + (3 * (x div 2)))),x,1)
A093141: 1 4 40 400 4000 40000 400000 4000000 40000000 400000000 4000000000 40000000000 400000000000 4000000000000 40000000000000 400000000000000
loop(\(x,i).(x - ((~x + ((~x + 2) div 2)) div 4)),x,1)
A003411: 1 2 3 4 6 8 11 15 21 29 40 55 76 105 145 200
((x + 2) - loop(\(x,i).(x + (x mod 4) - i),x,1))
A222011: 1 2 4 8
A118030: 1 2 4 8 12 16 20 28 36 44 52 64 76 88 100 116
((x + 1) + loop(\(x,i).5x,x,4))
A308807: 5 22 103 504 2505 12506 62507 312508 1562509 7812510 39062511 195312512 976562513 4882812514 24414062515 122070312516
loop(\(x,i).(x * i),x,((x + 1) + (x2 div 4)))
A052618: 1 2 8 36 216 1440 11520 100800 1008000 10886400 130636800 1676505600 23471078400 348713164800 5579410636800 94152554496000
(1 + loop(\(x,i).(10x + 8),2,x))
A044421: 89 189 289 389 489 589 689 789 889 989 1089 1189 1289 1389 1489 1589
(~1 + loop(\(x,i).(10x + 8),2,x))
A067749: 87 187 287 387 487 587 687 787 887 987 1087 1187 1287 1387 1487 1587
((x + 1) + loop(\(x,i).(~2x3 + x2),2,2))
A296907: 3601 3602 3603 3604 3605 3606 3607 3608 3609 3610 3611 3612 3613 3614 3615 3616
loop(\(x,i).(4x + ((1 + i) mod 3)),x,1)
A037505: 1 6 24 97 390 1560 6241 24966 99864 399457 1597830 6391320 25565281 102261126 409044504 1636178017
loop(\(x,i).(4x + ((1 - i) mod 3)),x,1)
A037497: 1 4 18 73 292 1170 4681 18724 74898 299593 1198372 4793490 19173961 76695844 306783378 1227133513
loop(\(x,i).(4x + ((x + 1) mod 4)),x,1)
A037695: 1 6 27 108 433 1734 6939 27756 111025 444102 1776411 7105644 28422577 113690310 454761243 1819044972
loop(\(x,i).(4x + ((x + ~1) mod 4)),x,1)
A037681: 1 4 19 78 313 1252 5011 20046 80185 320740 1282963 5131854 20527417 82109668 328438675 1313754702
loop(\(x,i).(4x + (i * i * (x mod 2))),x,1)
A112613: 1 5 24
A270126: 1 5 24 96 384 1536 6144 24576 98304 393216 1572864 6291456 25165824 100663296 402653184 1610612736
loop(\(x,i).(4x + (2 div (x2 + ~2))),x,1)
A055841: 1 2 9 36 144 576 2304 9216 36864 147456 589824 2359296 9437184 37748736 150994944 603979776
loop(\(x,i).(2 * (6x - (x div 2))),x,1)
A170693-A170645-A170597-A170549-A170501-A170453-A170405-A170357-A170309-A170261-A170213-A170165-A170117-A170069-A170021-A169553-A169505-A169457-A169409-A169361-A169313-A169265-A169217-A169169-A169121-A169073-A169025-A168977-A168929-A168881-A168833-A168785-A168737-A168689-A167916-A003954: 1 12 132 1452 15972 175692 1932612 21258732 233846052 2572306572 28295372292 311249095212 3423740047332 37661140520652 414272545727172 4556998002998892
loop(\(x,i).(2 * (8x - (x div 2))),x,1)
A170735-A170697-A170649-A170601-A170553-A170505-A170457-A170409-A170361-A170313-A170265-A170217-A170169-A170121-A170073-A170025-A169557-A169509-A169461-A169413-A169365-A169317-A169269-A169221-A169173-A169125-A169077-A169029-A168981-A168933-A168885-A168837-A168789-A168741-A168693-A167924: 1 16 240 3600 54000 810000 12150000 182250000 2733750000 41006250000 615093750000 9226406250000 138396093750000 2075941406250000 31139121093750000 467086816406250000
((x + ~1) + (2 * (if (x mod 4) <= 0 then 2 else (x mod 2))))
A092486: 3 2 1 4 7 6 5 8 11 10 9 12 15 14 13 16
loop(\(x,i).((x + 2) - ((~x + 4) div (2 + i))),x,1)
A231408: 1 2 4 6 9
A075349: 1 2 4 6 9 12 15 19 23 27 31 36 41 46 51 56
(if x <= 0 then 1 else ((~x + 3) * (1 - (2 * (x mod 2)))))
A248157: 1 ~2 1 0 ~1 2 ~3 4 ~5 6 ~7 8 ~9 10 ~11 12
loop(\(x,i).26x,x,1)
A009970: 1 26 676 17576 456976 11881376 308915776 8031810176 208827064576 5429503678976 141167095653376 3670344486987776 95428956661682176 2481152873203736576 4611686018427387903 4611686018427387903
loop(\(x,i).(11x + ~2),x,1)
A083077: 1 9 97 1065 11713 128841 1417249 15589737 171487105 1886358153 20749939681 228249336489 2510742701377 27618169715145 303799866866593 3341798535532521
loop(\(x,i).22x,x,1)
A009966: 1 22 484 10648 234256 5153632 113379904 2494357888 54875873536 1207269217792 26559922791424 584318301411328 12855002631049216 282810057883082752 4611686018427387903 4611686018427387903
loop(\(x,i).(2x * (~1 + (3 * (2 + i)))),x,1)
A053103: 1 16 352 9856 335104 13404160 616591360 32062750720 1859639541760 119016930672640 8331185147084800 633170071178444800 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x * (1 + (4 * (1 + i)))),x,1)
A053115: 1 18 468 15912 668304 33415200 1938081600 127913385600 9465590534400 776178423820800 69856058143872000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x * (~1 + (4 * (1 + i)))),x,1)
A034912: 1 14 308 9240 351120 16151520 872182080 54075288960 3785270227200 295251077721600 25391592684057600 2386809712301414400 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x + (x div 7)),2,x))
A231272-A143719-A078779: 1 2 3 4 5 6 7 10 11 12 13 14 15 17 19 20
loop(\(x,i).(2x * (1 + (2 * (1 + (i mod 2))))),x,1)
A281863: 1 10 60 600 3600 36000 216000 2160000 12960000 129600000 777600000 7776000000 46656000000 466560000000 2799360000000 27993600000000
loop(\(x,i).34x,x,1)
A009978: 1 34 1156 39304 1336336 45435424 1544804416 52523350144 1785793904896 60716992766464 2064377754059776 70188843638032384 2386420683693101056 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (x + (12 * i))),x,1)
A026915: 1 26 100 272 640 1400 2944 6056 12304 24824 49888 100040 200368 401048 802432 1605224
loop(\(x,i).(2 * (x + (3 * ((x + i) mod 2)))),x,1)
A283353: 1 2 4 14 28 62 124 254 508 1022 2044 4094 8188 16382 32764 65534
loop(\(x,i).(2x * (1 + (5 * i))),x,1)
A035265: 1 12 264 8448 354816 18450432 1143926784 82362728448 6753743732736 621344423411712 63377131187994624 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x + (x div ((2 + i) * (1 + i)))),2,x))
A163101-A059519: 1 2 3 4 5 6 8 9 10 11 12 14 16 17 18 19
loop(\(x,i).(x - ((~x + ((i mod 3) mod 2)) div 2)),x,1)
A117791: 1 1 2 3 4 6 9 13 20 30 45 68 102 153 230 345
loop(\(x,i).((x * (2 - (i div ~4))) div 2),x,1)
A275071: 1 1 1 1 1 2 4 8 16 40 100 250 625 1875 5625 16875
(1 + loop(\(x,i).(~x - (x div (4 + i))),2,x))
A047309: 1 3 4 5 6 8 10 11 12 13 15 17 18 19 20 22
loop(\(x,i).(x * (1 + i)),(x + ((x + (x div 2)) div 2)),1)
A093459: 1 2 24 720 40320 362880 39916800 6227020800
loop(\(x,i).(2x * (2 + (5 * i))),x,1)
A035273: 1 14 336 11424 502656 27143424 1737179136 128551256064 10798305509376 1015040717881344 105564234659659776 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * ((4x + 2) + i)),2,x))
A014771: 1 225 2025 8281 23409 53361 105625 189225 314721 494209 741321 1071225 1500625 2047761 2732409 3575881
(1 + compr(\x.(loop(\(x,i).(x * i),(x div 2),1) mod (x + 2)),x))
A061743: 11 14 15 17 19 20 23 24 26 27 29 31 32 34 35 38
(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A249427-A146886-A075728-A006093: 1 2 4 6 10 12 16 18 22 28 30 36 40 42 46 52
(~1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A086801: ~1 0 2 4 8 10 14 16 20 26 28 34 38 40 44 50
(1 + compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x))
A231407: 1 4 6
A165972: 1 4 6 10 12 16 18 22 28 30 36 40 42 46 52 58
loop(\(x,i).(4x + 9),(x2 + 2x),1)
A237419: 1 253 262141 4294967293 1125899906842621 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x2 + 2x + ~1) + loop(\(x,i).2x,(x + ~1),2))
A132072: 1 4 11 22 39 66 111 190 335 610 1143 2190 4263 8386 16607 33022
((1 + loop(\(x,i).(x * i),x,1)) mod (x2 + 2x + 1))
A301316: 0 2 3 7 0 13 35 49 64 81 11 1 0 57 1 1
loop(\(x,i).2x3,1,(x2 + 2x + 1))
A106318: 2 128 1458 8192 31250 93312 235298 524288 1062882 2000000 3543122 5971968 9653618 15059072 22781250 33554432
loop(\(x,i).(x3 div 2),1,(x2 + 2x + 1))
A191901: 0 32 364 2048 7812 23328 58824 131072 265720 500000 885780 1492992 2413404 3764768 5695312 8388608
loop(\(x,i).(x * (i * i)),(x + 1),(x2 + 2x + 1))
A176128: 1 16 324 9216 360000 18662400 1244678400 104044953600 10666233446400 1316818944000000 192795461591040000 4611686018427387903 4611686018427387903 4611686018427387903
((x2 + 2x + 1) * loop(\(x,i).2x,x,2x))
A128985: 0 16 144 768 3200 11520 37632 114688 331776 921600 2478080 6488064 16613376 41746432 103219200 251658240
loop(\(x,i).((x + 2) + (5 * (i * i))),x,1)
A063489: 1 8 30 77 159 286 468 715 1037 1444 1946 2553 3275 4122 5104 6231
((~x2 + 2x + ~1) + loop(\(x,i).(x * i),x,(x + 1)))
A127065: 0 2 5 20 111 704 5015 40284 362831 3628736 39916719 479001500 6227020679 87178291056 1307674367831 20922789887804
loop(\(x,i).(2x + (3 * ((x mod 2) * i))),x,1)
A132479: 1 5 16 32 64 128 256 512 1024 2048
loop(\(x,i).(2x + (((1 + i) mod (x + 1)) mod 2)),x,1)
A222011: 1 2 4 8
A267045: 1 2 4 8 17 34 69 138 277 554 1109 2218 4437 8874 17749 35498
loop(\(x,i).(2x + ((x + ((x div 2) mod 2)) div 2)),x,1)
A140832: 1 2 5 12 30 75 188 470 1175 2938 7345 18362 45905 114762 286905 717262
((8 * (x mod 2)) - loop(\(x,i).2x,x,1))
A166978: ~1 6 ~4 0 ~16 ~24 ~64 ~120 ~256 ~504 ~1024 ~2040 ~4096 ~8184 ~16384 ~32760
loop(\(x,i).(3x + ((x + 1) mod 3)),x,1)
A037504: 1 5 15 46 140 420 1261 3785 11355 34066 102200 306600 919801 2759405 8278215 24834646
loop(\(x,i).(3x + ((x + ~1) mod 3)),x,1)
A037496: 1 3 11 34 102 308 925 2775 8327 24982 74946 224840 674521 2023563 6070691 18212074
loop(\(x,i).(3x + ((x + i) mod 3)),x,1)
A037536: 1 5 16 49 149 448 1345 4037 12112 36337 109013 327040 981121 2943365 8830096 26490289
loop(\(x,i).(3x + ((x div 3) mod 2)),x,1)
A188545: 1 3 10
A033121: 1 3 10 31 93 280 841 2523 7570 22711 68133 204400 613201 1839603 5518810 16556431
loop(\(x,i).(2x * ((1 + (2 * (1 + i))) * i)),x,1)
A165457: 1 10 280 15120 1330560 172972800 31135104000 7410154752000 2252687044608000 851515702861824000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x * ((4 * (1 + i)) + i)),x,1)
A035277: 1 18 504 19152 919296 53319168 3625703424 282804867072 24886828302336 2438909173628928 263402190751924224 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((6 * (x mod 2)) + (x div 2)),x,1)
A070392: 1 6 3 7 9 10 5 8 4 2 1 6 3 7 9 10
loop(\(x,i).((5 * (x mod 2)) - (x div 2)),x,1)
A135448: 1 5 3 4 ~2 1 5 3 4 ~2 1 5 3 4 ~2 1
(((x2 + 3x) div 2) + (if (x mod 2) <= 0 then x else 1))
A098001: 0 3 7 10 18
A265724: 0 3 7 10 18 21 33 36 52 55 75 78 102 105 133 136
((x + 1) + loop(\(x,i).(x * (2 - (x div (2 + i)))),x,2))
A141742: 3 6 7 12 13 14 15 24 25 26 27 28 29 30
A004755: 3 6 7 12 13 14 15 24 25 26 27 28 29 30 31 48
loop(\(x,i).(x + (2 * i) - (x div (1 + (2 * i)))),x,1)
A025713: 1 3 7 12 19 28 38 50 64 79 96 114 134 156 179 204
loop(\(x,i).(x + (((x div 2) div 3) + (i div 2))),x,1)
A218507: 1 1 2 3 5 7 11 15 21 28 37 48 62 78 98 121
loop(\(x,i).(10x + (i mod 2)),x,1)
A266219: 1 11 110 1101 11010 110101 1101010 11010101 110101010 1101010101 11010101010 110101010101 1101010101010 11010101010101 110101010101010 1101010101010101
((x + 1) * loop(\(x,i).(x + (2 * (i * i))),(x + 1),0))
A098077: 2 20 84 240 550 1092 1960 3264 5130 7700 11132 15600 21294 28420 37200 47872
((x + 1) * loop(\(x,i).(2x2 + 8x + 8),2,0))
A117412: 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200
(if (~2 + (2x div (2 + (x div 2)))) <= 0 then 0 else (x + 1))
A088001: 0 0 0 0 0 0 0 0 0 10 0 12 13 14 15 16
((x + 1) * ((x + ~1) + (if (x + ~1) <= 0 then 4 else 0)))
A106230: 3 8 3 8 15 24 35 48 63 80 99 120 143 168 195 224
((0 - loop(\(x,i).(x + (i * i)),(x div 2),0)) mod (x + 1))
A259748: 0 0 2 3 0 1 0 2 6 0 0 5 0 7 10 4
(loop(\(x,i).(x - ((~2x + 2) * i)),x,0) mod (x + 1))
A318623: 0 0 1 0 1 4 1 0 1 6 1 4 1 8 1 0
(loop(\(x,i).(x + (4 * (x + i))),x,0) mod (x + 1))
A094920: 0 0 1 0 1 0 1 0 4 6 1 0 1 6 1 0
(loop(\(x,i).(x + ((2x + 1) * i)),x,0) div (x + 1))
A104255: 0 0 2 13 94 866 9652 126689 1914412 32736453 624968662 13176422634 304071291562 7623501667031 206342778454312 5996836998828457
((x + 1) * (1 + (if (x mod 2) <= 0 then 6 else 1)))
A147601: 7 4 21 8 35 12 49 16 63 20 77 24 91 28 105 32
((1 + loop(\(x,i).(2x2 + 4),2,1)) div (x + 1))
A033397: 77 38 25 19 15 12 11 9 8 7 7 6 5 5 5 4
((x + 1) * loop(\(x,i).i,((x + 1) div 5),1))
A132029: 1 2 3 4 5 6 7 8 9 20 22 24 26 28 45 48
((x + 1) * (if (~x + 2) <= 0 then ((x + 1) div 3) else 1))
A132027: 1 2 3 4 5 12 14 16 27 30 33 48 52 56 75 80
(loop(\(x,i).i,((~x + 2) mod (1 + (x div 2))),1) mod (x + 1))
A345439: 0 1 1 1 1 1 1 3 4 3 4 3 4 3 4 3
(loop(\(x,i).6x,(x + 1),1) div (x + 1))
A129796: 6 18 72 324 1555 7776 39990 209952 1119744 6046617 32981550 181398528 1004668770 5597440292 31345665638 176319369216
(loop(\(x,i).6x,(x + 1),1) mod (x + 1))
A066604: 0 0 0 0 1 0 6 0 0 6 6 0 6 8 6 0
(loop(\(x,i).8x,(x + 1),1) div (x + 1))
A129798: 8 32 170 1024 6553 43690 299593 2097152 14913080 107374182 780903144 5726623061 42288908760 314146179364 2345624805922 17592186044416
(loop(\(x,i).8x,(x + 1),1) mod (x + 1))
A066439: 0 0 2 0 3 4 1 0 8 4 8 4 8 8 2 0
(loop(\(x,i).5x,(x + 1),1) div (x + 1))
A129795: 5 12 41 156 625 2604 11160 48828 217013 976562 4438920 20345052 93900240 435965401 2034505208 9536743164
(loop(\(x,i).5x,(x + 1),1) mod (x + 1))
A066603: 0 1 2 1 0 1 5 1 8 5 5 1 5 11 5 1
((x + 1) * (1 + (if (x + ~6) <= 0 then 0 else 2)))
A142594: 1 2 3 4 5 6 7 24 27 30 33 36 39 42 45 48
((x + 1) * (1 + (x mod (if (~2 + (x div 2)) <= 0 then 1 else 2))))
A334953: 1 2 3 4 5 6 7 16 9 20 11 24 13 28 15 32
((x + 1) * loop(\(x,i).(3x2 + 3),2,1))
A177769: 111 222 333 444 555 666 777 888 999 1110 1221 1332 1443 1554 1665 1776
(loop(\(x,i).(2x2 + 3x + 1),2,1) div (x + 1))
A033411: 91 45 30 22 18 15 13 11 10 9 8 7 7 6 6 5
(loop(\(x,i).3x,(2x + 2),1) div (x + 1))
A129799: 9 40 243 1640 11809 88573 683281 5380840 43046721 348678440 2852823600 23535794706 195528140640 1634056603925 13726075472976 115813761803240
(loop(\(x,i).(2x2 + 2x + 2),2,1) div (x + 1))
A033406: 86 43 28 21 17 14 12 10 9 8 7 7 6 6 5 5
((x + 1) * (if ((x + 1) mod 8) <= 0 then 2 else 1))
A065640: 1 2 3 4 5 6 7 16 9 10 11 12 13 14 15 32
((x + 1) * (~1 + loop(\(x,i).(x3 + 2),2,2)))
A153814: 1001 2002 3003 4004 5005 6006 7007 8008 9009 10010 11011 12012 13013 14014 15015 16016
loop(\(x,i).(x + (i * i)),x,(5x + 5))
A080957: 5 11 20 34 55 85 126 180 249 335 440 566 715 889 1090 1320
loop(\(x,i).((x + 1) * i),(x + ~5),(x + 1))
A241947: 1 2 3 4 5 6 8 20
((~1 + loop(\(x,i).(x * ((x + 1) + i)),2,2)) div (x + 1))
A033407: 87 43 29 21 17 14 12 10 9 8 7 7 6 6 5 5
(loop(\(x,i).x3,3,3) mod (x + 1))
A240162: 0 1 0 3 2 3 6 3 0 7 9 3 1 13 12 11
(loop(\(x,i).x2,(1 + (x mod 2)),3) mod (x + 1))
A066440: 0 1 0 1 4 3 2 1 0 1 9 9 9 11 9 1
(loop(\(x,i).(x * (x - i)),4,3) mod (x + 1))
A273650: 0 0 0 0 0 0 0 0 0 0 1 0 8 0 0 0
((x + 1) * (if (x + ~2) <= 0 then 1 else (3x + 6)))
A124083: 1 2 3 60 90
((x + 1) * (~1 + loop(\(x,i).6x,x,2)))
A224330: 1 22 213 1724 12955 93306 653177 4478968 30233079 201553910 1330255861 8707129332 56596340723 365699432434 2350924922865 15045919506416
((x + 1) * (~1 + loop(\(x,i).8x,x,2)))
A224332: 1 30 381 4092 40955 393210 3670009 33554424 301989879 2684354550 23622320117 206158430196 1786706395123 15393162788850 131941395333105 1125899906842608
((x + 1) * (if (2 - (x div 4)) <= 0 then (x + 2) else 1))
A109752: 1 2 3 4 5 6 7 8 90
(loop(\(x,i).(x - (2x * i)),(x div 2),1) mod (x + 1))
A126868: 0 1 2 3 3 3 6 1 6 5 1 3 8 7 0 1
((x + 1) * loop(\(x,i).x3,1,(1 + (x div 2))))
A212759: 1 2 24 32 135 162 448 512 1125 1250 2376 2592 4459 4802 7680 8192
((x + 1) * (~1 + loop(\(x,i).5x,x,2)))
A224329: 1 18 147 996 6245 37494 218743 1249992 7031241 39062490 214843739 1171874988 6347656237 34179687486 183105468735 976562499984
((~1 + loop(\(x,i).(x * (~1 + (2 * i))),x,2)) mod (x + 1))
A058359: 0 1 2 1 4 5 6 5 8 9 10 5 12 13 14 13
(loop(\(x,i).(6x + 1),x,1) mod (x + 1))
A094921: 0 1 1 3 0 1 1 3 7 5 1 7 1 7 10 3
(loop(\(x,i).(8x + 1),x,1) mod (x + 1))
A094923: 0 1 1 1 1 3 0 1 1 9 1 9 1 7 13 9
(loop(\(x,i).(2 * (x - (x div 3))),x,1) div (x + 1))
A274157: 1 1 1 1 1 2 2 2 3 4 4 6 7 9 11 14
(loop(\(x,i).10x,x,1) div (x + 1))
A056159: 1 5 33 250 2000 16666 142857 1250000 11111111 100000000 909090909 8333333333 76923076923 714285714285 6666666666666 62500000000000
(loop(\(x,i).10x,x,1) mod (x + 1))
A056968: 0 0 1 0 0 4 1 0 1 0 1 4 1 10 10 0
(loop(\(x,i).(2x * (~1 + (2 * i))),x,1) div (x + 1))
A001761: 1 1 4 30 336 5040 95040 2162160 57657600 1764322560 60949324800 2346549004800 99638080819200 4626053752320000 233153109116928000 4611686018427387903
((x + 1) * ((~1 + loop(\(x,i).2x,x,2)) div (x + 1)))
A162214: 1 2 6 12 30 60 126 248 504 1020 2046 4092 8190 16380 32760 65520
((x + 1) * loop(\(x,i).x2,(x2 + ~1),(x + 1)))
A089210: 1 4 19683 4611686018427387903
((x + 1) * ((x + loop(\(x,i).2x,x,1)) div (x + 1)))
A162213: 1 2 6 8 20 36 70 128 261 520 1034 2052 4108 8204 16395 32768
((x + 1) * ((x + loop(\(x,i).2x,x,2)) div (x + 1)))
A128093: 2 4 9 16 35 66 133 256 513 1030 2057 4104 8203 16394 32775 65536
(loop(\(x,i).(x * (2 + (x mod 2))),x,(x + 1)) div (x + 1))
A092270: 1 2 9 8 81 32 729 128 6561 512 59049 2048 531441 8192 4782969 32768
(1 - ((1 - loop(\(x,i).(x * (i * i)),x,1)) div (x + 1)))
A131811: 1 1 2 10 116
(2 - ((2 + (if x <= 0 then 0 else 2) - (x div 2)) div (x + 1)))
A303370: 0 0 1 2 2 2 2 2 2 2 3 3 3 3 3 3
((x + 1) * (if (x + ~12) <= 0 then 1 else 2))
A132031: 1 2 3 4 5 6 7 8 9 10 11 12 13 28 30 32
loop(\(x,i).(9x + ~1),2,(x + 1))
A044322: 71 152 233 314 395 476 557 638 719 800 881 962 1043 1124 1205 1286
((x + 1) * (if (x + ~10) <= 0 then 1 else 2))
A132030: 1 2 3 4 5 6 7 8 9 10 11 24 26 28 30 32
((x + 1) * (if (~2 + (x div 5)) <= 0 then 1 else 2))
A309127-A132032: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 32
((x + 1) * loop(\(x,i).x2,2,10))
A168651: 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 110000 120000 130000 140000 150000 160000
(loop(\(x,i).x2,2,10) div (x + 1))
A033422: 10000 5000 3333 2500 2000 1666 1428 1250 1111 1000 909 833 769 714 666 625
(loop(\(x,i).x2,2,10) mod (x + 1))
A067007-A066298: 0 0 1 0 0 4 4 0 1 0 1 4 3 4 10 0
((loop(\(x,i).x2,3,(x + 1)) div 2) div (x + 1))
A191900: 0 64 1093 8192 39062 139968 411771 1048576 2391484 5000000 9743585 17915904 31374258 52706752 85429687 134217728
loop(\(x,i).(x3 + x2),(2x + 2),(x + 1))
A081357: 12 4611686018427387903
loop(\(x,i).(x3 + 1),(2x + 2),(x + 1))
A058472-A058454: 9 4611686018427387903
A058448: 9 4611686018427387903 4611686018427387903
A067487: 9 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + 2x2),(2x + 2),(x + 1))
A110479: 45 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) * loop(\(x,i).(2x + i),x,(2x + 2)))
A068605: 2 18 84 300 930 2646 7112 18360 45990 112530 270204 638820 1490762 3440430 7864080 17825520
((x + 1) * loop(\(x,i).x3,1,((x + 1) div 2)))
A212763: 0 2 3 32 40 162 189 512 576 1250 1375 2592 2808 4802 5145 8192
((x + 1) * ((loop(\(x,i).(x * i),x,x) mod (x + 1)) mod 2))
A061397: 0 2 3 0 5 0 7 0 0 0 11 0 13 0 0 0
loop(\(x,i).(x - (x div (1 + ((2 + i) * i)))),2,(x + 1))
A100618: 1 2 3 3 4 5 6 6 7 8 8 8 9 10 11 11
((x + 1) * ((if (x + ~2) <= 0 then 2 else ((x + 1) div 2)) div 2))
A132028: 1 2 3 4 5 6 7 16 18 20 22 36 39 42 45 64
((x + 1) * (~2 + loop(\(x,i).(x3 + 2),2,2)))
A168650: 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000
((~2 + loop(\(x,i).(x3 + 2),2,2)) div (x + 1))
A033421: 1000 500 333 250 200 166 142 125 111 100 90 83 76 71 66 62
((~2 + loop(\(x,i).(x3 + 2),2,2)) mod (x + 1))
A324472: 0 0 1 0 0 4 6 0 1 0 10 4 12 6 10 8
(loop(\(x,i).x2,3,8) div (x + 1))
A057070: 16777216 8388608 5592405 4194304 3355443 2796202 2396745 2097152 1864135 1677721 1525201 1398101 1290555 1198372 1118481 1048576
(if (2 - (x div 4)) <= 0 then 8 else (x + 1))
A108922: 1 2 3 4 5 6 7 8 8 8 8 8 8 8 8 8
(loop(\(x,i).x2,4,8) mod (x + 1))
A332055: 0 0 1 0 1 4 1 0 1 6 3 4 1 8 1 0
loop(\(x,i).x2,1,(~8x + ~6))
A017138: 36 196 484 900 1444 2116 2916 3844 4900 6084 7396 8836 10404 12100 13924 15876
loop(\(x,i).x2,2,(~8x + ~6))
A017140: 1296 38416 234256 810000 2085136 4477456 8503056 14776336 24010000 37015056 54700816 78074896 108243216 146410000 193877776 252047376
loop(\(x,i).(2x + ~4),(x + ~8),(x + 1))
A322260: 1 2 3 4 5 6 7 8 9 16 32
(x - ((x + 1) * loop(\(x,i).(~2x2 + 1),2,2)))
A157924: 97 195 293 391 489 587 685 783 881 979 1077 1175 1273 1371 1469 1567
(x + ((x + 1) * (if x <= 0 then 1 else 4)) - (x div 2))
A263941: 1 9 13 18 22 27 31 36 40 45 49 54 58 63 67 72
(2 - loop(\(x,i).(x3 + ~1),4,(x + 1)))
A241570: 11 4611686018427387903
A257304: 11 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).x2,(2 - (x mod 2)),4) mod (x + 1))
A155836: 0 0 1 0 1 4 4 0 4 6 3 4 9 2 1 0
((x + (x div 2)) div (if (x mod 2) <= 0 then 4 else (x + 1)))
A084360: 0 0 0 1 1 1 2 1 3 1 3 1 4 1 5 1
(x - ((x + 1) * loop(\(x,i).(~x2 + 1),2,4)))
A158227: 224 449 674 899 1124 1349 1574 1799 2024 2249 2474 2699 2924 3149 3374 3599
(x - ((x + 1) * loop(\(x,i).(x * (~x + i)),2,4)))
A158219: 168 337 506 675 844 1013 1182 1351 1520 1689 1858 2027 2196 2365 2534 2703
loop(\(x,i).5x,x,(4x + 4))
A212699: 4 40 300 2000 12500 75000 437500 2500000 14062500 78125000 429687500 2343750000 12695312500 68359375000 366210937500 1953125000000
((2x + 2) * (2 + (if (x mod 2) <= 0 then x else ~x)))
A270456: 4 4 24 ~8 60 ~36 112 ~80 180 ~140 264 ~216 364 ~308 480 ~416
((x + 1) * loop(\(x,i).(~2x3 + x2),2,2))
A096472: 3600 7200 10800 14400 18000 21600 25200 28800 32400 36000 39600 43200 46800 50400 54000 57600
((x + 1) * (loop(\(x,i).4x,x,(x + 2)) div 2))
A038845: 1 12 96 640 3840 21504 114688 589824 2949120 14417920 69206016 327155712 1526726656 7046430720 32212254720 146028888064
(if x <= 0 then 1 else (x - ((~4x + 2) div (x + 1))))
A053663: 1 2 4 6 7 8 10 11 12 13 14 15 16 17 18 19
((2 + (if (x mod 4) <= 0 then 2 else (x mod 2))) mod (x + 1))
A211010: 0 1 2 3 4 3 2 3 4 3 2 3 4 3 2 3
(x + ((if (x + ~4) <= 0 then 1 else 2) + (2 mod (x + 1))))
A048972: 1 2 5 6 7 9 10 11 12 13 14 15 16
((x + 1) * (2 - ((if (x + ~4) <= 0 then 1 else x) mod 2)))
A334733: 1 2 3 4 5 6 14 8 18 10 22 12 26 14 30 16
loop(\(x,i).(x + (x div (4 * (1 + i)))),2,(x + 1))
A082463: 1 2 3 4 5 6 7 9 10
A239289-A210490-A166155: 1 2 3 4 5 6 7 9 10 11 13 14 15 16 17 19
loop(\(x,i).((~x + 2) - (x div 8)),2,(x + 1))
A285432: 1 2 4 5 6 7 8 10 11 13 14 15 16 17 18 20
loop(\(x,i).(x * ((4x + ~2) + i)),2,(x + 1))
A014772: 36 784 4356 14400 36100 76176 142884 246016 396900 608400 894916 1272384 1758276 2371600 3132900 4064256
((x + 1) * (2 + (x * (if (x mod 2) <= 0 then 1 else (x + 2)))))
A181427: 2 10 12 68 30 222 56 520 90 1010 132 1740 182 2758 240 4112
loop(\(x,i).2x,x,(2x3 + 6x2 + 4x))
A128960: 0 24 192 960 3840 13440 43008 129024 368640 1013760 2703360 7028736 17891328 44728320 110100480 267386880
((x + 1) * loop(\(x,i).(x * (2 + i)),(x + 1),(x + 2)))
A200978: 6 72 720 7200 75600 846720 10160640 130636800 1796256000 26345088000 410983372800 6799906713600 118998367488000 2196892938240000 42682491371520000 870722823979008000
((x + 1) * loop(\(x,i).(x * ((x + 1) - i)),2,(x + 2)))
A208139: 12 144 720 2400 6300 14112 28224 51840 89100 145200 226512 340704 496860 705600 979200 1331712
((~x2 + ~3x + ~2) + loop(\(x,i).(x + (i * i)),x,0))
A167554: ~2 ~5 ~7 ~6 0 13 35 68 114 175 253 350 468 609 775 968
(loop(\(x,i).(x * (1 + (i div 2))),x,2x) div (x + 1))
A118364: 0 1 2 6 19 60
(if x <= 0 then 0 else (2 - (x mod (2 - ((x + 1) * (x div 2))))))
A294524: 0 1 2 3 6 7 15
loop(\(x,i).(10x + ~10),x,(x + 1))
A033714: 1 10 190 2890 38890 488890 5888890 68888890 788888890 8888888890 98888888890 1088888888890 11888888888890 128888888888890 1388888888888890 14888888888888890
loop(\(x,i).20x,x,(x + 1))
A061650: 1 40 1200 32000 800000 19200000 448000000 10240000000 230400000000 5120000000000 112640000000000 2457600000000000 53248000000000000 1146880000000000000 4611686018427387903 4611686018427387903
loop(\(x,i).15x,x,(x + 1))
A027475: 1 30 675 13500 253125 4556250 79734375 1366875000 23066015625 384433593750 6343154296875 103797070312500 1686702392578125 27246730957031250 437893890380859375 4611686018427387903
loop(\(x,i).(1 + (x * i) - (2 * (i mod 2))),x,(x + 1))
A334716: 1 1 5 20 105 644 4585 37134 337393 3399416 37622961 453769370 5924234041 83242063332 1252567177849 20096182035734
((x + 1) + loop(\(x,i).(x - (x div (1 + i))),3,x))
A225647: 1 3 4 6 7
A111909: 1 3 4 6 7 8 9 11 12 13 14 15 16 18 19 21
loop(\(x,i).(x * ((2 + i) * (3 + i))),x,(x + 1))
A105187: 1 24 720 28800 1512000 101606400 8534937600 877879296000 108637562880000 15933509222400000 2734190182563840000 4611686018427387903 4611686018427387903
((x + 1) + loop(\(x,i).(x + (2 * (x + i))),(x + ~1),x))
A086972: 1 3 11 41 149 527 1823 6197 20777 68891 226355 738113 2391485 7705895 24712007 78918989
((x + 1) + loop(\(x,i).(x * (x + (x div 2))),(x + ~1),x))
A091409: 1 3 9 220
((x + 1) + ((x mod 8) mod (if x <= 0 then 1 else x)))
A331009-A322341-A317621-A298297-A225580-A122620-A088450-A088380-A080676-A058183-A033061-A008727: 1 2 3 4 5 6 7 8 9 11 13 15 17 19 21 23
loop(\(x,i).((x * ((1 + i) * (1 + i))) div 2),x,(x + 1))
A203157: 1 4 27 288 4500 97200 2778300 101606400 4629441600 257191200000 17116074360000 1344389840640000 123067686661920000 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) + loop(\(x,i).((x * (x + i)) div (1 + i)),2,x))
A134393: 1 3 8 20 45 91 168 288 465 715 1056 1508 2093 2835 3760 4896
((x + 1) * loop(\(x,i).(3x + 2),4,x))
A157953: 80 322 726 1292 2020 2910 3962 5176 6552 8090 9790 11652 13676 15862 18210 20720
((x + loop(\(x,i).4x,x,4)) div (x + 1))
A129788: 4 8 22 64 205 683 2341 8192 29128 104858 381301 1398102 5162221 19173962 71582789 268435456
((x + 1) div loop(\(x,i).(x div (~2 + (x mod 2))),x,(x + 1)))
A118827: 1 ~2 1 ~4 1 ~2 1 ~8 1 ~2 1 ~4 1 ~2 1 ~16
loop(\(x,i).(x2 div 2),1,(x3 + 3x2 + 2x))
A288959: 0 18 288 1800 7200 22050 56448 127008 259200 490050 871200 1472328 2384928 3726450 5644800 8323200
((x + 1) * ((if (x mod 2) <= 0 then 1 else x) + (x * (x div 2))))
A204556: 1 2 9 24 45 90 133 224 297 450 561 792 949 1274 1485 1920
(x - (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))
A129760: 0 0 2 0 4 4 6 0 8 8 10 8 12 12 14 0
loop(\(x,i).(x * (~1 + (4 * (i * i)))),x,(x + 1))
A013299: 1 6 135 6300 496125 58939650 9833098275 2191376187000 628651043645625 225615874552818750 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.loop(\(x,i).(x div (1 + (2 * (x mod 2)))),x,x),(x + 1))
A191110: 1 3 5 9 11 15 17 27 29 33 35 45 47 51 53 81
loop(\(x,i).(x + ((x div 2) div (3 + i))),x,(x + 1))
A281613: 1 2 3 4 5 6 7 9 11 13 15 17 19 21 23 27
((if x <= 0 then 2 else (x2 + 8x)) div (x + 1))
A189466: 2 4 6 8 9 10 12 13 14 15 16 17 18 19 20 21
(loop(\(x,i).10x,x,x) mod (x + 1))
A066209: 0 0 2 0 0 2 6 0 8 0 10 8 12 4 5 0
loop(\(x,i).5x,x,(x3 + x2))
A129005: 0 10 300 4500 50000 468750 3937500 30625000 225000000 1582031250 10742187500 70898437500 457031250000 2888183593750 17944335937500 109863281250000
((x + 1) * loop(\(x,i).7x,x,x))
A116165: 0 14 294 4116 48020 504210 4941258 46118408 415065672 3631824630 31072277390 261007130076 2159240803356 17633799894074 142426845298290 1139414762386320
loop(\(x,i).(x2 div 2),1,(x4 + x3))
A163276: 0 2 288 5832 51200 281250 1143072 3764768 10616832 26572050 60500000 127552392 252315648 473027282 847072800 1458000000
loop(\(x,i).(x * ((1 + (2 * (1 + i))) * i)),x,(x + 1))
A327411: 1 10 210 7560 415800 32432400 3405402000 463134672000 79196028912000 16631166071520000 4207685016094560000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x + ~1) <= 0 then x else (4x2 + ~8x + 4))
A220788: 0 1 4 16
A055808: 0 1 4 16 36 64 100 144 196 256 324 400 484 576 676 784
(2 div (if (~2 + (x mod 8)) <= 0 then 2 else (x + ~1)))
A025447: 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0
((x + ~1) * loop(\(x,i).(4x * i),(x + ~2),x))
A052670: 0 0 2 24 384 7680 184320 5160960 165150720 5945425920 237817036800 10463949619200 502269581721600 26118018249523200 1462609021973299200 4611686018427387903
(if (x + ~2) <= 0 then (x + 1) else (x3 + ~3x2 + 2x))
A171708: 1 2 3 6 24
((x + ~1) * loop(\(x,i).(x * (1 + (2 * i))),(x + ~2),x))
A161122: 0 0 2 18 180 2100 28350 436590 7567560 145945800 3101348250 72020198250 1814908995900 49332526343100 1438865351673750 44826189802143750
loop(\(x,i).19x,x,1)
A001029: 1 19 361 6859 130321 2476099 47045881 893871739 16983563041 322687697779 6131066257801 116490258898219 2213314919066161 42052983462257059 799006685782884121 4611686018427387903
loop(\(x,i).(x * (1 + (6 * (1 + i)))),x,1)
A053100: 1 13 247 6175 191425 7082725 304557175 14923301575 820781586625 50067676784125 3354534344536375 244881007151155375 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + (6 * (1 + i)))),x,1)
A034787: 1 11 187 4301 124729 4365515 178986115 8412347405 445854412465 26305410335435 1709851671803275 121399468698032525 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).23x,x,1)
A009967: 1 23 529 12167 279841 6436343 148035889 3404825447 78310985281 1801152661463 41426511213649 952809757913927 21914624432020321 504036361936467383 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + (9 * i))),x,1)
A049211: 1 8 136 3536 123760 5445440 288608320 17893715840 1270453824640 101636305971200 9045631231436800 886471860680806400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (2 * i) - (i div 3))),x,1)
A319950: 1 3 15 90 720 7200 79200 1029600 15444000 247104000 4447872000 88957440000 1868106240000 42966443520000 1074161088000000 27928188288000000
loop(\(x,i).(x * (1 + (5 * (1 + i)))),x,1)
A051687: 1 11 176 3696 96096 2978976 107243136 4396968576 202260554496 10315288279296 577656143640576 35237024762075136 2325643634296958976 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (8 * (1 + i)))),x,1)
A053114: 1 17 425 14025 575025 28176225 1606044825 104392913625 7620682694625 617275298264625 54937501545551625 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + (8 * (1 + i)))),x,1)
A034975: 1 15 345 10695 417105 19603935 1078216425 67927634775 4822862069025 381006103452975 33147531000408825 3149015445038838375 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (2 * (1 + (x mod 3))))),x,1)
A196661: 1 5 35 245 1715 12005 84035 588245 4117715 28824005 201768035 1412376245 9886633715 69206436005 484445052035 3391115364245
loop(\(x,i).(x * (1 + (2 * (1 + (4 * i))))),x,1)
A034909: 1 11 209 5643 197505 8492715 433128465 25554579435 1712156822145 128411761660875 10658176217852625 969894035824588875 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (4 * (1 + (2 * i))))),x,1)
A034911: 1 13 273 7917 292929 13181805 698635665 42616775565 2940557513985 226422928576845 19245948929031825 1789873250399959725 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + (4 * (~1 + (2 * i))))),x,1)
A144756: 1 3 33 627 16929 592515 25478145 1299385395 76663738305 5136470466435 385235284982625 31974528653557875 2909682107473766625 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (2 * (2 + (2 mod (x + 1)))))),x,1)
A067403: 1 5 45 405 3645 32805 295245 2657205 23914845 215233605 1937102445 17433922005 156905298045 1412147682405 12709329141645 114383962274805
loop(\(x,i).33x,x,1)
A009977: 1 33 1089 35937 1185921 39135393 1291467969 42618442977 1406408618241 46411484401953 1531578985264449 50542106513726817 1667889514952984961 4611686018427387903 4611686018427387903
loop(\(x,i).31x,x,1)
A009975: 1 31 961 29791 923521 28629151 887503681 27512614111 852891037441 26439622160671 819628286980801 25408476896404831 787662783788549761 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (2 * (4 + (i mod 2))))),x,1)
A090337: 1 11 99 1089 9801 107811 970299 10673289 96059601 1056655611 9509900499 104608905489 941480149401 10356281643411 93206534790699 1025271882697689
loop(\(x,i).(x + (x div (1 + ((x + ~1) mod 4)))),x,1)
A140730: 1 2 3 4 5 10 15 20 25 50 75 100 125 250 375 500
loop(\(x,i).(11x + 5),x,1)
A199018: 1 16 181 1996 21961 241576 2657341 29230756 321538321 3536921536 38906136901 427967505916 4707642565081 51784068215896 569624750374861 6265872254123476
loop(\(x,i).(x + (10x * i)),x,1)
A045757: 1 11 231 7161 293601 14973651 913392711 64850882481 5252921480961 478015854767451 48279601331512551 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + (10x * i)),x,1)
A049212: 1 9 171 4959 193401 9476649 559122291 38579438079 3047775608241 271252029133449 26853950884211451 2927080646379048159 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + (5x * (2 + i))),x,1)
A051690: 1 14 266 6384 185136 6294624 245490336 10801574784 529277164416 28580966878464 1686277045829376 107921730933080064 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) + loop(\(x,i).(x + ~2),(~3 + (x div 2)),x))
A293703: 1 3 5 7 9 11 13 15 15 17 17 19 19 21 21 23
loop(\(x,i).(x * (~1 + i - (2 * (1 - (2 * i))))),x,1)
A084946: 1 2 14 168 2856 62832 1696464 54286848 2008613376 84361761792
A047055: 1 2 14 168 2856 62832 1696464 54286848 2008613376 84361761792 3965002804224 206180145819648 11752268311719936 728640635326636032 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (i - (3 * (1 - (2 * i))))),x,1)
A144827: 1 4 44 792 19800 633600 24710400 1136678400 60243955200 3614637312000 242180699904000 17921371792896000 1451631115224576000 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (i - (3 * (2 - (2 * i))))),x,1)
A045754: 1 1 8 120 2640 76560 2756160 118514880 5925744000 337767408000 21617114112000 1534815101952000 119715577952256000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (3 + (5 * i))),x,1)
A034300: 1 8 104 1872 43056 1205568 39783744 1511782272 65006637696 3120318609408 165376886298624 9591859405320192 604287142535172096 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),x,(x4 + x2 + 1))
A219619: 1 3 42 546 6552 78120 959760 12353040 167771520 2410611840 36654508800 589291718400 10002032409600 178908534604800 3366215358105600 66496549287168000
loop(\(x,i).(x * (~1 + (7 * i))),x,1)
A049209: 1 6 78 1560 42120 1432080 58715280 2818333440 155008339200 9610517030400 663125675097600 50397551307417600 4182996758515660800 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (11 - i)),x,1)
A306957: 1 10 90 720 5040 30240 151200 604800 1814400 3628800 3628800 0 0 0 0 0
loop(\(x,i).(x + ((1 + ((i mod 2) * i)) * (1 + i))),x,1)
A140113: 1 5 8 24 29 65 72 136 145 245 256 400 413 609 624 880
loop(\(x,i).(x * (~1 + ((4 * (2 + i)) + i))),x,1)
A051688: 1 12 204 4488 121176 3877632 143472384 6025840128 283214486016 14727153272832 839447736551424 52045759666188288 3487065897634615296 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (i * i * i * i * i))),x,1)
A255435: 1 2 66 16104 16506600 51599631600 401290334953200 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (6 + (x mod 4))),x,1)
A270472: 1 7 63 567 5103 45927 413343 3720087 33480783 301327047 2711943423 24407490807 219667417263 1977006755367 17793060798303 160137547184727
loop(\(x,i).(9x2 + 2x),x,1)
A136308: 1 11 1111 11111111 1111111111111111 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (2 + (9 * i))),x,1)
A035012: 1 11 220 6380 242440 11394680 638102080 41476635200 3069271004800 254749493398400 23436953392652800 2367132292657932800 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~2 + (9 * i))),x,1)
A147631: 1 7 112 2800 95200 4093600 212867200 12984899200 908942944000 71806492576000 6318971346688000 612940220628736000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (((4 + i) * (1 + i)) div 2)),x,1)
A005286: 1 6 15 29 49 76 111 155 209 274 351 441 545 664 799 951
loop(\(x,i).(x + (((2 + (i mod 2)) * (1 + i)) div 2)),x,1)
A111710: 1 4 7 13 18 27 34 46 55 70 81 99 112 133 148 172
loop(\(x,i).(x * (2 + (((x div 2) div 3) mod 2))),x,1)
A222011: 1 2 4 8
A290859: 1 2 4 8 24 48 96 192 384 768 1536 3072 6144 12288 24576 49152
loop(\(x,i).(x * (2 + (((1 + (x div 2)) div 2) mod 2))),x,1)
A202337: 1 2 6 12 36 108 324 972 2916 8748 26244 78732 236196 708588 2125764 6377292
(1 + (x2 * loop(\(x,i).(2x2 + ~2),2,2)))
A158734: 1 71 281 631 1121 1751 2521 3431 4481 5671 7001 8471 10081 11831 13721 15751
loop(\(x,i).(x * (i - (8 * (1 - i)))),x,1)
A144772-A045756: 1 1 10 190 5320 196840 9054640 498005200 31872332800 2326680294400 190787784140800 17361688356812800 1736168835681280000 4611686018427387903 4611686018427387903
(1 + (x2 * loop(\(x,i).(x2 + x + 2),2,2)))
A158742: 1 75 297 667 1185 1851 2665 3627 4737 5995 7401 8955 10657 12507 14505 16651
(1 + (x2 * (~2 + loop(\(x,i).(x2 + 2x),2,2))))
A158769: 1 79 313 703 1249 1951 2809 3823 4993 6319 7801 9439 11233 13183 15289 17551
loop(\(x,i).(x * (4 + (4 mod (x + 2)))),x,1)
A067412: 1 5 40 320 2560 20480 163840 1310720 10485760 83886080 671088640 5368709120 42949672960 343597383680 2748779069440 21990232555520
loop(\(x,i).(x * (i - (4 * (1 - (2 * i))))),x,1)
A147629: 1 5 70 1610 51520 2112320 105616000 6231344000 423731392000 32627317184000 2805949277824000 266565181393280000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (2 * (x + ((x div (2 + i)) mod 2)))),x,1)
A018361: 1 3 9 29 87 261
loop(\(x,i).(x * (2 + (7 * i))),x,1)
A034829: 1 9 144 3312 99360 3676320 161758080 8249662080 478480400640 31101226041600 2239288274995200 176903773724620800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~2 + (7 * i))),x,1)
A147585: 1 5 60 1140 29640 978120 39124800 1838865600 99298742400 6057223286400 411891183475200 30891838760640000 2533130778372480000 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (i - (2 * (2 - (3 * i))))),x,1)
A144739: 1 3 30 510 12240 379440 14418720 648842400 33739804800 1990648483200 131382799891200 9590944392057600 767275551364608000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (((2 + ((1 + i) * i)) * i) div 2)),x,1)
A144335: 1 3 11 32 76 156 288 491 787 1201 1761 2498 3446 4642 6126 7941
loop(\(x,i).(x + (((2 + ((~1 + i) * i)) * i) div 2)),x,1)
A181490: 1 2 6 18
A308305: 1 2 6 18 46 101 197 351 583 916 1376 1992 2796 3823 5111 6701
loop(\(x,i).(x + i - (2 * ((x div (1 + i)) * i))),x,1)
A085059: 1 2 4 1 5 10 4 11 3 12 2 13 1 14 28 13
loop(\(x,i).(x * (((~1 + ((2 * i) + i)) * i) div 2)),x,1)
A084939: 1 1 5 60 1320 46200 2356200 164934000 15173928000 1775349576000 257425688520000 45306921179520000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).20x,x2,1)
A078354: 1 20 160000 512000000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).15x,x2,1)
A078185: 1 15 50625 38443359375 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).18x,x2,1)
A078352: 1 18 104976 198359290368 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 + (2 * i) - (x div 4)),x2,1)
A008137: 1 4 9 17 28 42 60 81 105 132 162 196 233 273 316 362
loop(\(x,i).14x,x2,1)
A073940: 1 14 38416 20661046784 2177953337809371136 4611686018427387903 4611686018427387903
((~x2 + ~1) + loop(\(x,i).2x,(x + ~1),(x + 2)))
A339032: 1 1 3 10 31 86 219 526 1215 2734 6043 13190 28527 61270 130875 278302
((~x2 + 1) + loop(\(x,i).(x2 + ~1),2,(x + 2)))
A269641: 9 63 221 567 1209 2279 3933 6351 9737 14319 20349 28103 37881 50007 64829 82719
(1 + loop(\(x,i).(2x - (i mod 2)),(x + ~2),x2))
A068000: 1 2 5 18 63
((x2 + 1) * (if (x + ~2) <= 0 then 1 else (2x + 1)))
A175169: 1 2 5 70
(loop(\(x,i).2x,((x + ~1) div 2),x) div (x2 + 1))
A206558: 0 0 0 0 0 0 0 1 0 1 1 2 2 4 4 8
((x2 + 1) * loop(\(x,i).3x,2x,x))
A128074: 0 18 810 21870 446148 7676370 117979902 1674039150 22384294920 285916320882 3521652245010 42113381995278 491427393476940 5617523480607090 63094193590782438 697970937800860110
loop(\(x,i).13x,x2,1)
A076811: 1 13 28561 10604499373 665416609183179841 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).11x,x2,1)
A076783: 1 11 14641 2357947691 45949729863572161 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).17x,x2,1)
A078351: 1 17 83521 118587876497 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (x2 * (if (x + ~2) <= 0 then 1 else x3)))
A175977: 1 2 5 244
(1 + loop(\(x,i).11x,x,x))
A064749: 1 12 243 3994 58565 805256 10629367 136410198 1714871049 21221529220 259374246011 3138428376722 37661140520653 448795257871104 5316497670165375 62658722541234766
loop(\(x,i).(x2 + ((x * (x + i)) div 4)),x,1)
A319640: 1 1 1 2 7 70
(1 + loop(\(x,i).(x * ((x + 1) - i)),2,x3))
A060896: 1 1 4033 530713 16773121 244125001 2176735681 13841169553 68719214593 282429005041 999999000001 3138426605161 8916097462273 23298080295673 56693904845761 129746326500001
(1 + loop(\(x,i).(x + (x div (~1 + (2 * i)))),x2,x))
A000960: 1 3 7 13 19 27 39 49 63 79 91 109 133 147 181 207
loop(\(x,i).(11x * i),x,1)
A196258: 1 11 242 7986 351384 19326120 1275523920 98215341840 8642950081920 855652058110080 94121726392108800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((1 + (4 * (1 + i))) * i)),x,1)
A302914: 1 9 234 11934 1002456 125307000 21803418000 5036589558000 1490830509168000 550116457882992000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((1 + (4 * (~1 + i))) * i)),x,1)
A084943: 1 1 10 270 14040 1193400 150368400 26314470000 6104957040000 1813172240880000 670873729125600000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((3 * (1 + (2 * i))) + i)),x,1)
A034830: 1 10 170 4080 126480 4806240 216280800 11246601600 663549494400 43794266630400 3196981464019200 255758517121536000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((6 * (1 + i)) + i)),x,1)
A034833: 1 13 260 7020 238680 9785880 469722240 25834723200 1601752838400 110520945849600 8399591884569600 697166126419276800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((8 * (1 + i)) + i)),x,1)
A035022: 1 17 442 15470 680680 36076040 2236714480 158806728080 12704538246400 1130703903929600 110808982585100800 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((8 * (1 + i)) - i)),x,1)
A053104: 1 15 330 9570 344520 14814360 740718000 42220926000 2702139264000 191851887744000 14964447244032000 1271978015742720000 4611686018427387903 4611686018427387903
loop(\(x,i).(x + ((((2 + i) * (1 + i)) div 2) + i)),x,1)
A008778: 1 5 13 26 45 71 105 148 201 265 341 430 533 651 785 936
loop(\(x,i).(x * ((4 * (1 + (2 * i))) + i)),x,1)
A035017: 1 13 286 8866 354640 17377360 1007886880 67528420960 5132159992960 436233599401600 41005958343750400 4223613709406291200 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((4 * (1 + (2 * i))) - i)),x,1)
A034831: 1 11 198 4950 158400 6177600 284169600 15060988800 903659328000 60545174976000 4480342948224000 362907778806144000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((i - (4 * (1 - i))) * i)),x,1)
A276482: 1 1 12 396 25344 2661120 415134720 90084234240 25944259461120 9573431741153280 4403778600930508800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) - loop(\(x,i).(~x + (((x div 2) mod 2) + i)),x,1))
A275380: 0 2 1 2 2 3 3 5 3 6
loop(\(x,i).(~x + (i * i * i * i * i * i)),x,1)
A187620: 1 0 64 665 3431 12194 34462 83187 178957 352484 647516 1124045 1861939 2964870 4564666 6825959
loop(\(x,i).((x2 mod (4x + 1)) * i),x,1)
A039748: 1 1 2 12 184
loop(\(x,i).(x - ((~1 + (2 * (x div (2 + i)))) * i)),x,1)
A139696: 1 2 4 7 3 8 2 9 17 8 18 7 19 6 20 5
((x - (if (8 mod (x + 1)) <= 0 then 1 else 0)) mod 2)
A173856: 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 1
((x - (if ((x div 3) mod 4) <= 0 then 1 else 0)) mod 2)
A117195: 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1
((x - (if ((x div ~2) mod 4) <= 0 then 1 else 0)) mod 2)
A141735: 1 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0
(3x - (if (x mod 5) <= 0 then 0 else 2))
A187334: 0 1 4 7 10 15 16 19 22 25 30 31 34 37 40 45
(2 * loop(\(x,i).(~x + ((2 + (i * i)) * i)),(x + 1),0))
A248462: 6 18 48 96 174 282 432 624 870 1170 1536 1968 2478 3066 3744 4512
((x + 2) - loop(\(x,i).((~x + ~1) + (x * i)),(x + ~1),0))
A046689: 2 3 5 7 11 23
(((x + 1) div 2) - (if (x + ~6) <= 0 then 0 else 2))
A332249: 0 1 1 2 2 3 3 2 2 3 3 4 4 5 5 6
(((x + 1) div 2) - (if (~2 + (x div 3)) <= 0 then 0 else 2))
A340320: 0 1 1 2 2 3 3 4 4 3 3 4 4 5 5 6
(2 + (if (x mod 9) <= 0 then (x div 2) else 0))
A250201: 2 2 2 2 2 2 2 2 2 6 2 2 2 2 2 2
(2 + (if (x mod (2 + (x mod 4))) <= 0 then (x mod 2) else 0))
A104230: 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 3
(x - ((if x <= 0 then 1 else 3x2) div ~2))
A227017: 1 3 8 17 28 43 60 81 104 131 160 193 228 267 308 353
(1 - (x div (~2 * (if (x + ~4) <= 0 then 1 else 2))))
A226390: 1 2 2 3 3 3 3 3 3 4 4 4 4 5 5 5
(x mod (if (x mod (2 + (x mod 4))) <= 0 then 2 else ~2))
A228109: 0 ~1 0 ~1 0 ~1 0 ~1 0 1 0 ~1 0 ~1 0 1
((x + 2) - (if x <= 0 then 1 else ((x div 4) div ~2)))
A171520: 1 3 4 5 7 8 9 10 11 12 13 14 16 17 18 19
((if x <= 0 then 1 else 2) - (((x + (x div 2)) div 2) div ~2))
A196376: 1 2 3 3 4 4 4 5 5 5 6 6 7 7 7 8
((if x <= 0 then 1 else 2x) - ((x2 + 2x) div ~2))
A265284: 1 4 8 14 20 28 36 46 56 68 80 94 108 124 140 158
loop(\(x,i).(x * i),x,((x div ~2) * (x div ~2)))
A145889: 0 1 2 24 96 1080 6480 80640 645120 9072000 90720000 1437004800 17244057600 305124019200 4271736268800 83691159552000
((if x <= 0 then 1 else 4x) - (x2 div ~2))
A307028: 1 5 10 17 24 33 42 53
(loop(\(x,i).((x + 3) + (x div (1 + i))),x,0) div 2)
A060606: 0 1 3 5 8 10 13 16 19 22 26 29 33 36 40 44
(x - (2 * ((x div 3) - (if (x + ~1) <= 0 then x else 0))))
A047878: 0 3 2 1 2 3 2 3 4 3 4 5 4 5 6 5
(x - (2 * ((x div 4) - (if (x + ~1) <= 0 then x else 0))))
A018837: 0 3 2 3 2 3 4 5 4 5 6 7 6 7 8 9
(loop(\(x,i).(((x + ~2) + (i * i)) * (1 + i)),x,0) div 2)
A076128: 0 ~1 0 14 105 699 5012 40284 362835 3628745 39916734 479001522 6227020709 87178291095 1307674367880 20922789887864
((x mod (5 - (if (x mod 2) <= 0 then x else 0))) mod 2)
A116865: 0 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0
((((x2 + ~1) div 2) mod 4) + (if x <= 0 then 0 else 2))
A134267: 3 2 3 2 5 2 3 2 5 2 3 2 5 2 3 2
(loop(\(x,i).(x + i - (2 * (~x + (x mod 2)))),x,0) div 2)
A178828: 0 0 1 5 17 53 162 490 1474 4426 13283 39855 119571 358719 1076164 3228500
(loop(\(x,i).(x + ((3 + i) * (2 + i))),x,0) div 2)
A092286: 0 6 16 31 52 80 116 161 216 282 360 451 556 676 812 965
(loop(\(x,i).(2x + ((x + i) * (1 + i))),x,0) div 2)
A079754: 0 1 8 54 388 3119 28092 280948 3090464 37085613 482113024 6749582402 101243736108 1619899777819 27538296223028 495689332014624
((x - (if ((x div 2) mod 5) <= 0 then 0 else 1)) mod 2)
A284912-A192082: 0 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0
((x mod 2) - (if ((x div 3) mod 2) <= 0 then ~1 else 2))
A057079: 1 2 1 ~1 ~2 ~1 1 2 1 ~1 ~2 ~1 1 2 1 ~1
(2 * (1 + loop(\(x,i).((x + ~1) mod (2 * (1 + i))),x,0)))
A028352: 2 8 6 4 2 24 22 20 18 16 14 12 10 8 6 4
(1 - ((2 mod (1 + loop(\(x,i).(~2x + 2),x,0))) div 2))
A282577: 1 0 1 0 5 0 21 0 85 0 341 0 1365 0 5461 0
((((x + 1) mod 5) + (if x <= 0 then 0 else 1)) mod 2)
A286987: 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0
(((((x + 1) div 2) div 3) + (if x <= 0 then 0 else 1)) mod 2)
A138886: 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1
(if (~1 + (x2 mod (1 + (x div 3)))) <= 0 then 1 else 2)
A326952: 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 2
(if (x mod (1 + ((x + 2) div 5))) <= 0 then 1 else 2)
A175044: 1 1 1 2 1 2 1 2 2 1 2 2 1 2 2 2
(if ((x + 1) mod (1 + (x div 5))) <= 0 then 1 else 2)
A295660-A193453-A193169: 1 1 1 1 1 1 2 1 2 1 2 1 2 2 1 1
(if (x mod (1 + (x div (3 + (x mod 2))))) <= 0 then 1 else 2)
A107800: 1 1 1 1 1 2 1 2 2 1 2 2 2 2 2 2
(if (x mod (1 + (((x + 1) div 2) div 3))) <= 0 then 1 else 2)
A345935: 1 1 1 1 1 2 1 2 1 2 1 2 1 2 2 1
(if (x mod (1 + (6 mod (x + 1)))) <= 0 then 1 else 2)
A043558: 1 1 1 1 1 1 2 1 2 2 2 2 2 2 1 2
(x - (2 * (if x <= 0 then 0 else (1 + (x mod ~3)))))
A165958: 0 3 2 1 6 5 4 9 8 7
(if (x mod (~1 + (2 * (x div 5)))) <= 0 then 1 else 2)
A119646: 1 1 1 1 1 1 1 1 1 1 2 2 1 2 2 1
(if (x mod (3 + ((x div 2) div 3))) <= 0 then 1 else 2)
A275437: 1 2 2 1 2 2 2 2 1 2 2 2 2 2 2 1
(loop(\(x,i).2x,(x + ~7),1) div 2)
A009694: 0 0 0 0 0 0 0 0 1 2 4 8 16 32 64 128
((x + 1) mod (if (x mod 7) <= 0 then 1 else 2))
A174275: 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0
(if (x mod ((x + 1) - (x mod 6))) <= 0 then 1 else 2)
A298071: 1 1 1 1 1 1 2 1 2 2 2 2 2 1 2 2
((x + 1) mod (if ((x + ~2) mod 5) <= 0 then 1 else 2))
A285301: 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0
(if ((x * (x mod 3)) mod 5) <= 0 then 1 else 2)
A001285: 1 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1
(((if x <= 0 then 1 else x) div (1 + (x div 5))) mod 2)
A140820: 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 1
(if ((x + ~4) mod (1 + (x div 4))) <= 0 then 1 else 2)
A240471: 1 1 1 1 1 2 1 2 2 2 1 2 1 2 2 2
(if (4x mod (1 + (x div 4))) <= 0 then 1 else 2)
A109672: 1 1 1 1 1 1 1 1 2 1 2 2 1 1 1 1
(if (((x + 2) mod (2x + ~1)) mod 3) <= 0 then 1 else 2)
A074265: 1 1 2 1 1 2 2 1 2 2 1 2 2 1 2 2
(((x + 1) mod (1 + (3 * (if x <= 0 then 0 else 2)))) mod 2)
A144606-A144598: 0 0 1 0 1 0 0 1 0 1 0 1 0 0 1 0
(if x <= 0 then 1 else (2 * (1 + (((x + 1) div 2) div 3))))
A131883: 1 2 2 2 2 4 4 4 4 4 4 6 6 6 6 6
(if (((x + 2) mod 8) mod 3) <= 0 then 1 else 2)
A014675: 2 1 2 2 1 2 1 2 2 1 2 2 1 2 1 2
(if (((~x + 1) mod 8) mod 3) <= 0 then 1 else 2)
A006340: 2 1 2 1 2 2 1 2 2 1 2 1 2 2 1 2
(if (((~x + 2) mod 8) mod 3) <= 0 then 1 else 2)
A246127-A245977: 2 2 1 2 1 2 2 1 2 2 1 2 1 2 2 1
(2 + loop(\(x,i).x2,x,13))
A152586: 15 171 28563 815730723 665416609183179843 4611686018427387903 4611686018427387903
(2 + loop(\(x,i).x2,x,11))
A152583: 13 123 14643 214358883 45949729863572163 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(12x + 2))
A017546: 4 196 676 1444 2500 3844 5476 7396 9604 12100 14884 17956 21316 24964 28900 33124
loop(\(x,i).x2,2,(12x + 2))
A017548: 16 38416 456976 2085136 6250000 14776336 29986576 54700816 92236816 146410000 221533456 322417936 454371856 623201296 835210000 1097199376
(if x <= 0 then 1 else (12x2 + 2))
A005914: 1 14 50 110 194 302 434 590 770 974 1202 1454 1730 2030 2354 2702
(((x + ~2) mod (1 + (if x <= 0 then 2 else (x div 3)))) mod 2)
A285252: 1 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1
((if x <= 0 then 1 else (x2 mod (1 + (x div 3)))) mod 2)
A266344: 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 1
(2 * (~1 + ((x + (if (x mod 2) <= 0 then 2 else x)) mod 3)))
A130772: 2 2 0 ~2 ~2 0 2 2 0 ~2 ~2 0 2 2 0 ~2
(if ((x + 1) mod (1 + (4 mod (x + 2)))) <= 0 then 1 else 2)
A297772-A043531: 1 1 1 2 1 2 2 2 2 1 2 2 2 2 1 2
(if ((2x + ~6) mod (1 + (x div 2))) <= 0 then 1 else 2)
A320107: 1 1 1 1 2 2 2 1 1 2 2 2 2 2 2 1
((1 + loop(\(x,i).(x * i),x,(3x + 1))) div 2)
A066114: 1 2 7 30 156 960 6840 55440 504000 5080320 56246400 678585600 8861529600 124540416000 1874333260800 30076510464000
((1 + loop(\(x,i).(2x + ((1 + i) * i)),x,1)) div 2)
A335927: 1 2 7 20 50 115 251 530 1096 2237 4529 9124 18326 36743 73591 147302
((1 + ((x + 1) * loop(\(x,i).x2,2,(x + 1)))) div 2)
A191484: 1 16 122 512 1563 3888 8404 16384 29525 50000 80526 124416 185647 268912 379688 524288
(2 + loop(\(x,i).10x,(x + 1),1))
A133384: 12 102 1002 10002 100002 1000002 10000002 100000002 1000000002 10000000002 100000000002 1000000000002 10000000000002 100000000000002 1000000000000002 10000000000000002
(~2 + loop(\(x,i).10x,(x + 1),1))
A099150: 8 98 998 9998 99998 999998 9999998 99999998 999999998 9999999998 99999999998 999999999998 9999999999998 99999999999998 999999999999998 9999999999999998
(2 * loop(\(x,i).(2 * (x + ((i div 2) mod 2))),(x + 1),1))
A102653: 4 12 28 56 112 228 460 920 1840 3684 7372 14744 29488 58980 117964 235928
((1 + (loop(\(x,i).2x,(x + ~1),x) div (x + 1))) div 2)
A340163: 0 0 1 2 3 7 14 28 57 115 233 469 945 1902 3823 7680
((1 + loop(\(x,i).(x * (1 + (i * i * i))),x,1)) div 2)
A256019: 1 1 9 252 16380 2063880 447861960 154064514240 79035095805120 57695619937737600 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x mod (1 + (if ((~x + 2) mod 4) <= 0 then 0 else 2))) div 2)
A316359: 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0
((x div (if (x mod 2) <= 0 then 4 else ~3)) mod 2)
A123640: 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1
(if (x mod 3) <= 0 then 1 else (2 * (x div ~3)))
A138189: 1 ~2 ~2 1 ~4 ~4 1 ~6 ~6 1 ~8 ~8 1 ~10 ~10 1
((x mod (~3 + (if (x mod 4) <= 0 then x else 0))) mod 2)
A083913-A083890: 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 0
(if (~2 + (x mod (3 - (x div ~2)))) <= 0 then 1 else 2)
A080586: 1 1 1 2 2 2 1 1 1 1 1 1 2 2 2 2
(2 + (if ((x + 1) mod 7) <= 0 then 2 else 1))
A276870-A063438: 3 3 3 3 3 3 4 3 3 3 3 3 3 4 3 3
(if (~2 + (x mod (1 + (2 * (x mod 3))))) <= 0 then 1 else 2)
A339790-A331295-A325133-A324907-A262618-A257743-A046597-A033272: 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1
(2 * (1 + (2 * (3 + loop(\(x,i).2x,x,1)))))
A250737: 18 22 30 46 78 142 270 526 1038 2062 4110 8206 16398 32782 65550 131086
(if (x2 mod (2 + (x mod 5))) <= 0 then 1 else 2)
A214708-A083952: 1 2 1 2 2 2 1 2 2 2 1 2 1 2 2 2
(if x <= 0 then 1 else (16x + ~6))
A113770: 1 10 26 42 58 74 90 106 122 138 154 170 186 202 218 234
(if x <= 0 then 1 else (2 + ((x + 2) div 7)))
A083277: 1 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4
((if (x + ~2) <= 0 then 1 else (x div 7)) mod 2)
A266659: 1 1 1 0 0 0 0 1 1 1 1 1 1 1 0 0
(if ((x div 4) - (x mod 6)) <= 0 then 1 else 2)
A184167: 1 1 1 1 1 1 2 1 1 1 1 1 2 2 2 1
((1 + loop(\(x,i).(x + (x div 2)),x,6)) div 2)
A140261: 3 5 7 10 14 21 32 47 71 106 158 237 356 533 800 1199
(if (x mod 2) <= 0 then 1 else (2 * (1 + ((x mod 3) div 2))))
A235918-A071222: 1 2 1 2 1 4 1 2 1 2 1 4 1 2 1 2
(((2 + (x div 2)) div (if (x mod 3) <= 0 then 2 else 1)) mod 2)
A068426: 1 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0
((if x <= 0 then 1 else (x mod (1 + ((1 + (x div 2)) div 2)))) mod 2)
A121559: 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0
(2 * (1 + (2 * loop(\(x,i).(2x + 6),x,1))))
A305164: 6 34 90 202 426 874 1770 3562 7146 14314 28650 57322 114666 229354 458730 917482
((1 + ((loop(\(x,i).2x,x,2) mod (x + 1)) div 2)) div 2)
A340831-A334862-A087436: 0 0 1 0 1 1 1 0 2 1 1 1 1 1 2 0
((if ((x div 2) mod 3) <= 0 then ((x + ~1) div 2) else 1) mod 2)
A267922: 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1
((x mod (3 + (if (x + ~4) <= 0 then 0 else 2))) mod 2)
A189572: 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0
(if (~2 + (x mod (2 - ((x div 2) div ~2)))) <= 0 then 1 else 2)
A336137: 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 2
(2 - (if x <= 0 then 1 else ((x mod ~5) mod 2)))
A022921: 1 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2
(2 - (((x + 1) div (1 + (2 * (if x <= 0 then 0 else 2)))) mod 2))
A126061: 1 2 2 2 1 1 1 1 1 2 2 2 2 2 1 1
(x div (2 + (if (x + ~10) <= 0 then 2 else 1)))
A308303: 0 0 0 0 1 1 1 1 2 2 2 3 4 4 4 5
(if (~2 + (2x mod (2 + (x div 3)))) <= 0 then 1 else 2)
A328511-A202053: 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1
(if (~2 + (x mod (2 - (x mod ~4)))) <= 0 then 1 else 2)
A339095-A186006: 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 1
(2 + loop(\(x,i).x2,x,17))
A152591: 19 291 83523 6975757443 4611686018427387903 4611686018427387903 4611686018427387903
(2 + loop(\(x,i).x2,x,15))
A152588: 17 227 50627 2562890627 4611686018427387903 4611686018427387903 4611686018427387903
(if (~2 + ((x + 2) mod (2 + (x div 4)))) <= 0 then 1 else 2)
A097588: 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1
(if (~2 + (x mod (x - ((x + 1) mod 4)))) <= 0 then 1 else 2)
A263025: 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1
(if x <= 0 then 1 else (2 + ((x + ~1) mod 9)))
A117230: 1 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7
((x + 2) - loop(\(x,i).i,(x + ~9),2))
A103303: 0 1 2 3 4 5 6 7 8 9
A262039-A262037: 0 1 2 3 4 5 6 7 8 9 11 11 11 11 11 11
(((if x <= 0 then 1 else x2) mod 9) mod 2)
A142724: 1 1 0 0 1 1 0 0 1 0 1 0 0 1 1 0
(loop(\(x,i).(x + (i div 2)),(x + ~8),1) div 2)
A309831: 0 0 0 0 0 0 0 0 0 0 1 1 2 3 5 6
(if (x + ~2) <= 0 then 1 else (2 * (1 + (x div 8))))
A295101: 1 1 1 2 2 2 2 2 4 4 4 4 4 4 4 4
((x mod 3) div (if (x mod 8) <= 0 then 1 else 2))
A191265-A007949: 0 0 1 0 0 1 0 0 2 0 0 1 0 0 1 0
((1 + ((if x <= 0 then 2 else (x - (x div 4))) div 2)) div 2)
A095139: 1 0 1 1 1 1 1 2 2 2 2 2 2 3 3 3
(((if x <= 0 then 1 else x) div (~1 + (2 * (x mod 4)))) mod 2)
A321081: 1 1 0 0 0 1 0 1 0 1 1 0 0 1 0 1
(if x <= 0 then 1 else (16x2 + 2))
A010006: 1 18 66 146 258 402 578 786 1026 1298 1602 1938 2306 2706 3138 3602
(2 * (~1 + (2 * loop(\(x,i).(2x + i),(x + 2),2))))
A250778: 46 106 230 482 990 2010 4054 8146 16334 32714 65478 131010 262078 524218 1048502 2097074
(((if x <= 0 then 1 else x) mod (3 + ((x div 2) mod 2))) mod 2)
A141736: 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1
((x div (if (~x + 2) <= 0 then (2 * (2 + (x mod 2))) else 1)) mod 2)
A285411: 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0
(if x <= 0 then 1 else (2 * (1 + (x mod (2 * (~2 + (x mod 2)))))))
A176742: 1 0 ~2 0 2 0 ~2 0 2 0 ~2 0 2 0 ~2 0
((if x <= 0 then 1 else (x div (1 + ((x + 2) mod 4)))) mod 2)
A254113: 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1
((x mod (~5 + (if (x mod 2) <= 0 then x else 0))) mod 2)
A059648: 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0
(if x <= 0 then 1 else (20x + ~2))
A114698: 1 18 38 58 78 98 118 138 158 178 198 218 238 258 278 298
((x - (((if x <= 0 then 2 else x) div 2) mod 5)) mod 2)
A230001: 1 1 1 0 0 1 1 0 0 1 0 1 1 0 0 1
(2 + (if (x + ~2) <= 0 then 1 else ((x + 2) div 5)))
A091786: 3 3 3 3 3 3 3 3 4 4 4 4 4 5 5 5
(if (x + ~1) <= 0 then x else (2 + (2x div 5)))
A166724: 0 1 2 3 3 4 4 4 5 5 6 6 6 7 7 8
(if x <= 0 then 1 else (10x2 + 2))
A005901: 1 12 42 92 162 252 362 492 642 812 1002 1212 1442 1692 1962 2252
loop(\(x,i).(2x + 1),2x,10)
A198695: 10 43 175 703 2815 11263 45055 180223 720895 2883583 11534335 46137343 184549375 738197503 2952790015 11811160063
((if (x mod 2) <= 0 then x else ~x) mod 10)
A172423: 0 9 2 7 4 5 6 3 8 1 0 9 2 7 4 5
loop(\(x,i).(3x + 2),x,10)
A198646: 10 32 98 296 890 2672 8018 24056 72170 216512 649538 1948616 5845850 17537552 52612658 157837976
loop(\(x,i).(x2 + 2x + ~2),x,10)
A145510: 10 118 14158 200477278 40191139395243838 4611686018427387903 4611686018427387903
((x + (if (x mod 2) <= 0 then 1 else x)) mod 10)
A136315: 1 2 3 6 5 0 7 4 9 8 1 2 3 6 5 0
(if x <= 0 then 1 else (2 + ((x2 + x) div 5)))
A002984: 1 2 3 4 6 8 10 13 16 20 24 28 33 38 44 50
((if (x mod 3) <= 0 then 1 else (x div 5)) mod 2)
A126999: 1 0 0 1 0 1 1 1 1 1 0 0 1 0 0 1
(((if x <= 0 then 2 else (x div 2)) - (x div 5)) div 2)
A214131-A029348: 1 0 0 0 1 0 1 1 1 1 1 1 2 2 2 2
(if x <= 0 then 1 else (2 * (2x - (x mod 5))))
A341869: 1 2 4 6 8 20 22 24 26 28 40 42 44 46 48 60
((if x <= 0 then 1 else (x mod (~1 + ((~x + 2) div 4)))) mod 2)
A213728: 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0
(if ((2x mod 3) - (x mod 4)) <= 0 then 1 else 2)
A042974: 1 2 1 1 2 1 1 1 2 1 1 1 1 2 1 1
(if ((((x + ~1) div 2) div 2) - (x mod 4)) <= 0 then 1 else 2)
A273866-A182590: 1 1 1 1 1 1 1 1 2 2 1 1 2 2 2 1
(if (x mod (~2 + ((x * ((x div 2) mod 2)) div 2))) <= 0 then 1 else 2)
A330348-A038769: 1 1 1 1 1 1 1 1 1 1 2 2 1 1 2 1
(loop(\(x,i).((x2 + ~2x) * i),(2x + 4),1) div 2)
A217867: 10080 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * (1 + loop(\(x,i).(3x + 3),2x,2)))
A198965: 6 62 566 5102 45926 413342 3720086 33480782 301327046 2711943422 24407490806 219667417262 1977006755366 17793060798302 160137547184726 1441237924662542
loop(\(x,i).x2,3,(8x + 2))
A017096: 256 100000000 11019960576 208827064576 1785793904896 9682651996416 39062500000000 128063081718016 360040606269696 899194740203776 2044140858654976 4304672100000000 8507630225817856 15938480745308416
loop(\(x,i).x3,1,(8x + 2))
A017091: 8 1000 5832 17576 39304 74088 125000 195112 287496 405224 551368 729000 941192 1191016 1481544 1815848
loop(\(x,i).x3,2,(8x + 2))
A017097: 512 1000000000 198359290368 5429503678976 60716992766464 406671383849472 1953125000000000 7427658739644928 23762680013799936 66540410775079424 167619550409708032 387420489000000000
loop(\(x,i).x2,1,(~7x + ~2))
A017006: 4 81 256 529 900 1369 1936 2601 3364 4225 5184 6241 7396 8649 10000 11449
loop(\(x,i).x2,2,(~7x + ~2))
A017008: 16 6561 65536 279841 810000 1874161 3748096 6765201 11316496 17850625 26873856 38950081 54700816 74805201 100000000 131079601
(((x * (x div 2)) div 2) mod (if (~2 + (x div 2)) <= 0 then 1 else 2))
A265757-A059782: 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0
(if x <= 0 then 1 else (2 * (1 + (x mod (2 * (2 - (x mod 2)))))))
A231407: 1 4 6
A164356: 1 4 6 4 2 4 6 4 2 4 6 4 2 4 6 4
(loop(\(x,i).2x,(x + ~1),(3 + (x mod 2))) div 2)
A131959: 1 2 3 8
A134683: 1 2 3 8 12 32 48 128 192 512 768 2048 3072 8192 12288 32768
((if x <= 0 then 0 else 2) - ((x mod (~3 + (x mod 2))) mod 2))
A049046: 0 1 1 1 2 1 2 1 1 1 2 1 2 1 1 1
(((x - (if (x + ~3) <= 0 then 1 else 0)) div 3) mod 2)
A164950: 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 1
(2 + ((x - (if x <= 0 then 1 else (x div 3))) div 3))
A225687: 1 2 2 2 3 3 3 3 4 4 4 4 4 5 5 5
(((x - (if x <= 0 then 2 else (x div 3))) mod 3) mod 2)
A286993: 1 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1
(if (x + ~1) <= 0 then x else (((x div 3) mod 3) div 2))
A122415: 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1
(if x <= 0 then 1 else (9x2 + 2))
A010002: 1 11 38 83 146 227 326 443 578 731 902 1091 1298 1523 1766 2027
(if x <= 0 then 2 else ((3x2 + 6x + 3) div 2))
A184533: 2 6 13 24 37 54 73 96 121 150 181 216 253 294 337 384
((3 * loop(\(x,i).2x,(x + ~1),(x + 1))) div 2)
A084858: 1 3 9 24 60 144 336 768 1728 3840 8448 18432 39936 86016 184320 393216
(if x <= 0 then 1 else (2 * (2x - ((x + 1) div 3))))
A231407: 1 4 6
A298784: 1 4 6 10 14 16 20 24 26 30 34 36 40 44 46 50
(if (x mod 2) <= 0 then (3 * ((x div 3) mod 2)) else 2)
A264940: 0 2 0 2 3 2 0 2 0 2 3 2 0 2 0 2
(if (x + ~1) <= 0 then x else (2 + (((x + 1) div 2) div 3)))
A276611-A004257: 0 1 2 2 2 3 3 3 3 3 3 4 4 4 4 4
(if x <= 0 then 1 else (2 + (4x2 div 3)))
A115285: 1 3 7 14 23 35 50 67 87 110 135 163 194 227 263 302
(((if x <= 0 then 1 else x) - ((~2 + (x div 2)) div 3)) div 2)
A247366: 1 1 1 2 2 2 3 3 4 4 4 5 5 6 6 7
(if (x + ~1) <= 0 then x else (2 + ((2 * (x div 2)) div 3)))
A283992-A070549-A000720: 0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6
(2 * loop(\(x,i).(~3x + 1),2x,3))
A199680: 6 50 446 4010 36086 324770 2922926 26306330 236756966 2130812690 19177314206 172595827850 1553362450646 13980262055810 125822358502286 1132401226520570
(if (x mod 3) <= 0 then 1 else (6x + 2))
A329499: 1 8 14 1
loop(\(x,i).x2,3,(6x + 2))
A016940: 256 16777216 1475789056 25600000000 208827064576 1099511627776 4347792138496 14048223625216 39062500000000 96717311574016 218340105584896 457163239653376 899194740203776 1677721600000000
loop(\(x,i).x3,1,(6x + 2))
A016935: 8 512 2744 8000 17576 32768 54872 85184 125000 175616 238328 314432 405224 512000 636056 778688
loop(\(x,i).x3,2,(6x + 2))
A016941: 512 134217728 20661046784 512000000000 5429503678976 35184372088832 165216101262848 618121839509504 1953125000000000 5416169448144896 13537086546263552 31087100296429568 66540410775079424
loop(\(x,i).2x,x,(1 - (2 * (2x div 3))))
A168054: 1 2 ~4 ~24 ~48 ~160 ~448 ~896 ~2304 ~5632 ~11264 ~26624 ~61440 ~122880 ~278528 ~622592
(((if (x mod 4) <= 0 then 2 else (x div 2)) mod 3) div 2)
A065293: 1 0 0 0 1 1 0 0 1 0 1 1 1 0 0 0
(2 + loop(\(x,i).(~x2 + 1),2x2,3))
A092823: 5 ~61 4611686018427387903
(((x mod 3) - (if x <= 0 then 0 else 1)) mod 6)
A021670: 0 0 1 5 0 1 5 0 1 5 0 1 5 0 1 5
(if ((x + 2) mod 6) <= 0 then 1 else 6)
A080066: 6 6 6 6 1 6 6 6 6 6 1 6 6 6 6 6
((x + 1) div (if (x + ~4) <= 0 then 1 else 6))
A339256: 1 2 3 4 5 1 1 1 1 1 1 2 2 2 2 2
loop(\(x,i).x2,(4x + 1),6)
A058458: 36 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x + 1),(2x + 1),6)
A206372: 13 55 223 895 3583 14335 57343 229375 917503 3670015 14680063 58720255 234881023 939524095 3758096383 15032385535
(6 + loop(\(x,i).6x,x,1))
A178681: 7 12 42 222 1302 7782 46662 279942 1679622 10077702 60466182 362797062 2176782342 13060694022 78364164102 470184984582
(6 + loop(\(x,i).5x,x,1))
A084443: 7 11 31 131
((if (x + ~1) <= 0 then 2 else (x2 + ~1)) mod 6)
A300817: 2 2 3 2 3 0 5 0 3 2 3 0 5 0 3 2
(1 - ((x + (if (x mod 2) <= 0 then x else 1)) mod 6))
A130778: 1 ~1 ~3 ~3 ~1 1 1 ~1 ~3 ~3 ~1 1 1 ~1 ~3 ~3
loop(\(x,i).(5x + ~2),x,6)
A199315: 6 28 138 688 3438 17188 85938 429688 2148438 10742188 53710938 268554688 1342773438 6713867188 33569335938 167846679688
((if (x mod 2) <= 0 then 2 else (x2 + 2x)) mod 6)
A342309-A236454-A112047-A053669: 2 3 2 3 2 5 2 3 2 3 2 5 2 3 2 3
loop(\(x,i).(x + ((x div 2) div 3)),x,6)
A182307: 6 7 8 9 10 11 12 14 16 18 21 24 28 32 37 43
loop(\(x,i).(x3 + 3x),x,6)
A145180: 6 234 12813606 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + ~3x),x,6)
A112845: 6 198 7761798 4611686018427387903 4611686018427387903
loop(\(x,i).(5x + 4),x,6)
A198765: 6 34 174 874 4374 21874 109374 546874 2734374 13671874 68359374 341796874 1708984374 8544921874 42724609374 213623046874
loop(\(x,i).x2,1,(9x + 2))
A017186: 4 121 400 841 1444 2209 3136 4225 5476 6889 8464 10201 12100 14161 16384 18769
loop(\(x,i).x2,2,(9x + 2))
A017188: 16 14641 160000 707281 2085136 4879681 9834496 17850625 29986576 47458321 71639296 104060401 146410000 200533921 268435456 352275361
(((x div 2) - ((if (x + ~2) <= 0 then 1 else x) mod 3)) mod 2)
A342991: 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1
(if x <= 0 then 1 else (2 + (x div (2 - ((~x + 1) div 3)))))
A130147: 1 2 2 3 3 3 3 3 3 3 4 3 4 4 4 4
(if x <= 0 then 1 else (2 * (2x - ((~x + 1) div 3))))
A298024: 1 4 10 14 18 24 28 32 38 42 46 52 56 60 66 70
((((2 - (x div 2)) mod (if x <= 0 then 1 else x)) mod 3) div 2)
A275305-A169671: 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0
(loop(\(x,i).(2 * ((x2 + ~1) div 2)),x,3) div 2)
A084764: 1 4 31 1921 7380481 108942999582721 4611686018427387903 4611686018427387903
(((if x <= 0 then 2 else (x * (x div 4))) mod 3) div 2)
A014084: 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0
loop(\(x,i).(4x + 1),x,(2x + ~6))
A072257: ~6 ~15 ~27 21 597 4437 25941 136533 677205 3233109 15029589 68506965 307582293 1364546901 5995058517 26127717717
(((x + ~3) * loop(\(x,i).2x,(x + ~1),x)) div 2)
A178987: 0 ~1 ~2 0 16 80 288 896 2560 6912 17920 45056 110592 266240 630784 1474560
(if x <= 0 then 1 else (2 * (1 + ((x div 2) + (x div 3)))))
A063199: 1 2 4 6 8 8 12 12 14 16 18 18 22 22 24 26
((if (x mod 2) <= 0 then 1 else ~2) + ((x div 3) mod 2))
A131556: 1 ~2 1 ~1 2 ~1 1 ~2 1 ~1 2 ~1 1 ~2 1 ~1
(if x <= 0 then 1 else (2 * (3x - (x div 3))))
A063089: 1 6 12 16 22 28 32 38 44 48 54 60 64 70 76 80
((3x * (x + (if (x mod 2) <= 0 then 2 else 0))) div 2)
A322462: 0 1 12 13 36 37 72 73 120 121 180 181 252 253 336 337
(if x <= 0 then 1 else (2 * (3 + (x * (x + (x mod 2))))))
A115603: 1 10 14 30
(~2 + loop(\(x,i).(x * i),(x + ~1),(x2 + 3)))
A101206: 1 2 5 22 112
loop(\(x,i).x2,1,((~3x2 + x) div 2))
A100255: 0 1 25 144 484 1225 2601 4900 8464 13689 21025 30976 44100 61009 82369 108900
(if ((x * (2 - (x mod 5))) div 2) <= 0 then 1 else 2)
A303828: 1 1 1 1 1 2 2 1 1 1 2 2 1 1 1 2
(if x <= 0 then 1 else (2 * (x - (2 mod (~2x + 3)))))
A222011: 1 2 4 8
A140164: 1 2 4 8 14 20 26 32 38 44 50 56 62 68 74 80
(((x + ~1) div (1 + (if (~2 + (x div 2)) <= 0 then x else 2))) mod 2)
A025906: 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0
((1 + loop(\(x,i).(x div 2),(x div 3),(x + 2))) mod 2)
A070829: 1 0 1 1 0 0 1 1 1 0 0 0 1 1 0 1
(~2 + loop(\(x,i).10x,(x + 2),1))
A292552: 98 998 9998 99998 999998 9999998 99999998 999999998 9999999998 99999999998 999999999998 9999999999998 99999999999998 999999999999998 9999999999999998 99999999999999998
(if (x - (((x2 + ~x) div 2) mod (x + 2))) <= 0 then 1 else 2)
A102297: 1 2 2 1 2 2 1 2 1 2 2 2 2 2 2 2
(~2 + ((x + 3) * (if (~x + 2) <= 0 then x else (x + 1))))
A011989: 1 6 8 16 26
(~2 + loop(\(x,i).((x + 2) * i),(x + ~1),(x + 3)))
A118814: 1 2 5 18 70
(((x + 3) * (2 + (if x <= 0 then 0 else (x + 2)))) div 2)
A112355: 3 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171
((if x <= 0 then 1 else ((x2 div 2) div (x + 3))) mod 2)
A195376: 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0
loop(\(x,i).2x2,(x div 2),(2x + 6))
A295429: 6 8 200
loop(\(x,i).(4x + 1),x,(2x + 6))
A072260: 6 33 165 789 3669 16725 75093 333141 1463637 6378837 27612501 118838613 508908885 2169853269 9216283989 39012619605
(loop(\(x,i).(x * (1 + (i * i * i))),(x + 2),1) div 2)
A158621: 9 252 16380 2063880 447861960 154064514240 79035095805120 57695619937737600 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * (1 + (if (~2 + (x div 4)) <= 0 then x else (x + 2))))
A230201: 2 4 6 8 10 12 14 16 18 20 22 24 30 32 34 36
(2 - ((x div ~4) * (if (x + ~2) <= 0 then 1 else 2)))
A177876: 2 3 3 4
A105677: 2 3 3 4 4 6 6 6
(2 + loop(\(x,i).(x3 + 4),2x,1))
A048796: 3 131 4611686018427387903
loop(\(x,i).(x4 + x3),(2x + 1),2)
A067669: 24 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + ~x),1,(4x + 2))
A001505: 6 210 990 2730 5814 10626 17550 26970 39270 54834 74046 97290 124950 157410 195054 238266
((4x + 2) + ((if x <= 0 then 1 else x) + (x mod 2)))
A063225: 3 8 12 18 22 28 32 38 42 48 52 58 62 68 72 78
loop(\(x,i).(x * ((1 + (2 * i)) * i)),(2x + 1),2)
A052278: 6 1260 2494800 20432412000 475176173472000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 + ((2x + ~1) * loop(\(x,i).(1 + (x * i)),x,1)))
A082028: 1 4 17 82 457 2936 21529 178102 1644017 16768972 187417921 2278607354 29947410937 423169937152 6398329449737 103084196690206
(loop(\(x,i).2x,(~1 + (x div 2)),(1 + (x div 2))) div 2)
A336102: 0 0 1 1 3 3 8 8 20 20 48 48 112 112 256 256
loop(\(x,i).2x,(x div 4),((1 + (x div 2)) mod 2))
A119332: 1 1 0 0 2 2 0 0 4 4 0 0 8 8 0 0
(loop(\(x,i).2x,(x div 2),(3 - (x mod 2))) div 2)
A074323: 1 1 3 2 6 4 12 8 24 16 48 32 96 64 192 128
((6x + 1) * (2 + (if x <= 0 then 2 else 1)))
A063122: 4 21 39 57 75 93 111 129 147 165 183 201 219 237 255 273
((1 + loop(\(x,i).i,((x + 1) div 5),x)) div 2)
A161606: 0 1 1 2 1 1 1 1 1 1 1 1 1 1 2 2
loop(\(x,i).x2,1,(10x + 2))
A017294: 4 144 484 1024 1764 2704 3844 5184 6724 8464 10404 12544 14884 17424 20164 23104
loop(\(x,i).x2,2,(10x + 2))
A017296: 16 20736 234256 1048576 3111696 7311616 14776336 26873856 45212176 71639296 108243216 157351936 221533456 303595776 406586896 533794816
(loop(\(x,i).(~1 + (2 * ((x * (x + i)) div 2))),x,1) div 2)
A327146: 0 0 0 1 9 227
((1 + (x div (4 - (if (x mod 2) <= 0 then 1 else x)))) mod 2)
A068431: 1 1 1 0 0 0 1 0 1 1 0 1 1 1 1 1
((2 - (if (6 mod (x + 1)) <= 0 then x else 1)) div 2)
A089803: 1 0 0 0 0 ~2 0 0 0 0 0 0 0 0 0 0
((~1 + ((4 + (x mod 2)) * (if x <= 0 then 1 else x))) div 2)
A179894: 1 2 3 7 7 12 11 17 15 22 19 27 23 32 27 37
((1 + (((x div 2) * (x div 2)) mod (if x <= 0 then 1 else x))) mod 2)
A116683: 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0 1
(((~3x + 6) div (1 + (if x <= 0 then 1 else x))) mod 2)
A266155: 1 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1
(((x2 + 2x + 1) * (1 + (if x <= 0 then 1 else x))) div 2)
A184632: 1 4 13 32 62 108 171 256 364 500 665 864 1098 1372 1687 2048
(2 * (1 + (if (~2 + (x div 2)) <= 0 then 6 else x)))
A291510: 14 14 14 14 14 14 14 16 18 20 22 24 26 28 30 32
(((x + 1) + (x2 div (if (x + ~2) <= 0 then 1 else 2))) div 2)
A182531: 0 1 3 4 6 9 12 16 20 25 30 36 42 49 56 64
(if (x - (x2 mod (x + 8))) <= 0 then 1 else 2)
A204260-A109338-A102715-A071202: 1 1 1 1 1 1 1 2 2 1 1 2 2 2 1 1
(2 + loop(\(x,i).(10x + ~8),x,1))
A173735: 3 4 14 114 1114 11114 111114 1111114 11111114 111111114 1111111114 11111111114 111111111114 1111111111114 11111111111114 111111111111114
(2 * loop(\(x,i).(2 * (x - (4 * (~x + i)))),x,1))
A036544: 2 4 8 32 256 2480 24704 246928 2469152 24691376 246913600 2469135824 24691358048 246913580272 2469135802496 24691358024720
((1 + loop(\(x,i).(x - (4 mod (x + 2))),2,x)) div 2)
A262907: 0 0 1 0 0 0 1 0 0 1 1 2 2 3 3 4
(if (~x + ((2x + ~4) mod (x + 4))) <= 0 then 1 else 2)
A122586: 1 2 1 1 1 2 2 2 1 1 1 1 1 1 1 1
(if (x - (x2 mod (3x + 4))) <= 0 then 1 else 2)
A195007: 1 1 1 1 2 1 1 1 1 1 1 2 1 1 2 1
(2 * (1 + (x * loop(\(x,i).x2,(x2 + ~2),2))))
A219037: 2 6 66 4611686018427387903
((1 + (if x <= 0 then 1 else x)) div (2 + (3 mod (x + 1))))
A319816-A025809: 1 0 1 0 1 1 1 1 1 2 2 2 2 2 3 3
(loop(\(x,i).(x * (2 + (i mod 2))),(x + 1),(x + 1)) div 2)
A027276: 1 6 27 72 270 648 2268 5184 17496 38880 128304 279936 909792 1959552 6298560 13436928
loop(\(x,i).((x2 + ~x) * i),(4x + 4),2)
A045517: 5040 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(x div 4),(2 + (2 mod (x + 1))))
A287293: 2 2 4 4 8 8 8 8 16 16 16 16 32 32 32 32
(((x + 1) * (loop(\(x,i).2x,(x + ~2),x) div 2)) div 2)
A309294: 0 0 1 6 20 60 168 448 1152 2880 7040 16896 39936 93184 215040 491520
(((x + 1) * loop(\(x,i).2x,(x + ~1),(x + 2))) div 2)
A080929: 1 3 12 40 120 336 896 2304 5760 14080 33792 79872 186368 430080 983040 2228224
((loop(\(x,i).(x * i),x,2) mod (x2 + 3x + 2)) div 2)
A120387: 0 1 2 6 9 15 20 0 0 45 54 66 77 0 0 120
loop(\(x,i).x2,3,((x2 + 3x + 2) div 2))
A059980: 1 6561 1679616 100000000 2562890625 37822859361 377801998336 2821109907456 16815125390625 83733937890625 360040606269696 1370114370683136 4702525276151521 14774554437890625 42998169600000000
loop(\(x,i).x3,1,((x2 + 3x + 2) div 2))
A059827: 1 27 216 1000 3375 9261 21952 46656 91125 166375 287496 474552 753571 1157625 1728000 2515456
(loop(\(x,i).2x,x,2) mod ((x2 + 3x + 2) div 2))
A289382: 0 1 2 6 2 1 16 4 17 34 2 40 2 4 8 120
loop(\(x,i).3x,x,((x2 + 3x + 2) div 2))
A027472: 1 9 54 270 1215 5103 20412 78732 295245 1082565 3897234 13817466 48361131 167403915 573956280 1951451352
(((x + 1) * (loop(\(x,i).(x * i),x,x) mod (x + 2))) div 2)
A175567: 0 1 0 6 0 15 0 0 0 45 0 66 0 0 0 120
(loop(\(x,i).3x,x,3) mod (2x + 2))
A082511: 1 1 3 1 3 9 3 1 9 9 3 9 3 9 27 1
loop(\(x,i).(2x * (1 + (2 * i))),x,(2x + 2))
A126804: 2 24 360 6720 151200 3991680 121080960 4151347200 158789030400 6704425728000 309744468633600 15543540607795200 841941782922240000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (2 * (1 + i)))),x,(2x + 2))
A000906: 2 20 210 2520 34650 540540 9459450 183783600 3928374450 91662070500 2319050383650 63246828645000 1849969737866250 57775977967207500 1918987839625106250 4611686018427387903
(if x <= 0 then 1 else ((3 + (x div 2)) * ((x + 1) div 2)))
A265611: 1 3 4 8 10 15 18 24 28 35 40 48 54 63 70 80
(if x <= 0 then 1 else (((x + 1) + (x mod 2)) * ((x + 1) div 2)))
A266221: 1 3 3 10 10 21 21 36 36 55 55 78 78 105 105 136
(loop(\(x,i).(x * i),x,((x + ~1) div 2)) * ((x + 1) div 2))
A077612: 0 0 0 12 48 720 4320 60480 483840 7257600 72576000 1197504000 14370048000 261534873600 3661488230400 73229764608000
((2x + 1) mod (if (x + ~1) <= 0 then 2 else ((x + 1) div 2)))
A243334: 1 1 0 1 1 2 1 3 1 4
(2 + ((x + 1) div 2) - loop(\(x,i).i,(x div 4),2))
A327715: 0 1 1 2 3 4 4 5 4 5 5 6 5 6 6 7
loop(\(x,i).(4x + 2),(x div 2),((x + 1) mod 2))
A176965: 1 0 6 2 26 10 106 42 426 170 1706 682 6826 2730 27306 10922
loop(\(x,i).(x * (~1 + (2 * i))),(x div 2),((x + 1) mod 2))
A123023: 1 0 1 0 3 0 15 0 105 0 945 0 10395 0 135135 0
((if (x mod 9) <= 0 then x else (x + 1)) div 2)
A194173: 0 1 1 2 2 3 3 4 4 4 5 6 6 7 7 8
(loop(\(x,i).(x2 + 2x),(x2 + ~x),(x + 1)) div 2)
A101327: 0 1 127 4611686018427387903
(((x + 1) * (~x + loop(\(x,i).2x,(x + 2),x))) div 2)
A059937: 0 7 45 186 630 1905 5355 14308 36828 92115 225225 540606 1277874 2981797 6881175 15728520
((x + 2) div (2 + (loop(\(x,i).2x,x,x) mod (x + 1))))
A160467: 1 1 1 2 1 1 1 4 1 1 1 2 1 1 1 8
(((x2 + x) * loop(\(x,i).x3,2,x)) div 2)
A170793: 0 1 1536 118098 2621440 29296875 211631616 1129900996 4831838208 17433922005 55000000000 155624547606 402462867456 965009442943 2169409912320 4613203125000
((x + 2) - ((loop(\(x,i).(x * i),x,x) mod (x + 1)) mod 2))
A113636: 2 2 3 5 5 7 7 9 10 11 11 13 13 15 16 17
(2 + ((x + ~1) * loop(\(x,i).(2 + (x * (~1 + i))),x,1)))
A054096-A006183: 1 2 6 22 98 522 3262 23486 191802 1753618 17755382 197282022 2387112466 31249472282 440096734638 6635304614542
loop(\(x,i).(2x + 2),x,((x2 + ~3x + 2) div 2))
A217528: 1 2 6 22 78 254 766 2174 5886 15358 38910 96254 233470 557054 1310718 3047422
(if (~2 + (x div 5)) <= 0 then x else (2x + ~2))
A103303: 0 1 2 3 4 5 6 7 8 9
A023795: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 28
(x + ((if (x + ~4) <= 0 then 1 else x) + ((x + ~1) div 2)))
A179333: 0 2 3 5 6 12 14 17
(((x + ~1) * loop(\(x,i).3x,(x + ~1),x)) div 2)
A129530: 0 0 3 27 162 810 3645 15309 61236 236196 885735 3247695 11691702 41452398 145083393 502211745
(2 + loop(\(x,i).2x4,x,(x + ~1)))
A077747-A041012: 1 2 34 4611686018427387903
(19 * (if x <= 0 then 1 else 2))
A040342: 19 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38
(23 * (if x <= 0 then 1 else 2))
A040506: 23 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46
(31 * (if x <= 0 then 1 else 2))
A040930: 31 62 62 62 62 62 62 62 62 62 62 62 62 62 62 62
(((2x + ~2) mod 5) * (if x <= 0 then 1 else 2))
A128178: 3 0 4 8 2 6 0 4 8 2 6 0 4 8 2 6
((16x + 8) - (if x <= 0 then 1 else 2))
A063130: 7 22 38 54 70 86 102 118 134 150 166 182 198 214 230 246
(26 * (if x <= 0 then 1 else 2))
A040650: 26 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52
(22 * (if x <= 0 then 1 else 2))
A040462: 22 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44
(2 * (((x + 1) - (x div ~2)) * (if x <= 0 then 1 else 2)))
A295821: 2 12 16 24 28 36 40 48 52 60 64 72 76 84 88 96
((x div (2 + ((x div 2) div 3))) + (if x <= 0 then 1 else 2))
A230411: 1 2 3 3 4 4 4 4 4 5 5 5 5 5 5 5
((x div (4 + (x div 4))) + (if x <= 0 then 1 else 2))
A309398-A235037-A074279: 1 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4
(8 * ((2 - (x mod 2)) * (if x <= 0 then 1 else 2)))
A040241: 16 16 32 16 32 16 32 16 32 16 32 16 32 16 32 16
(((x div 2) + (if x <= 0 then 1 else 2)) - (x div 8))
A061091: 1 2 3 3 4 4 5 5 5 5 6 6 7 7 8 8
(2 - ((~x + 1) div ((x div 4) + (if x <= 0 then 1 else 2))))
A260998-A085423: 1 2 3 3 3 4 4 4 4 4 5 5 5 5 5 5
(((x2 + 5x + 6) div 2) + (if x <= 0 then 1 else 2))
A340266: 4 8 12 17 23 30 38 47 57 68 80 93 107 122 138 155
((3x2 div (x + 2)) + (if x <= 0 then 1 else 2))
A182136: 1 3 5 7 10 12 15 18 21
(((x2 + 2x) div 2) + (x div 2) + (if x <= 0 then 1 else 2))
A114113: 1 3 7 10 16 21 29 36 46 55 67 78 92 105 121 136
(((x div 8) + (if x <= 0 then 1 else 2)) - (x mod 2))
A185318: 1 1 2 1 2 1 2 1 3 2 3 2 3 2 3 2
((5x2 div 2) + (if x <= 0 then 1 else 2))
A008253: 1 4 12 24 42 64 92 124 162 204 252 304 362 424 492 564
(x + (((x + (x div 2)) div 4) + (if x <= 0 then 1 else 2)))
A225647: 1 3 4 6 7
A276218: 1 3 4 6 7 8 10 11 13 14 15 17 18 19 21 22
(x + (((x + ((x div 2) mod 2)) div 2) + (if x <= 0 then 1 else 2)))
A062958: 1 3 5 7 8 9 11 13 14 15 17 19 20 21 23 25
(7x2 + (if x <= 0 then 1 else 2))
A005919: 1 9 30 65 114 177 254 345 450 569 702 849 1010 1185 1374 1577
(2 + loop(\(x,i).13x,x,1))
A153079: 3 15 171 2199 28563 371295 4826811 62748519 815730723 10604499375 137858491851 1792160394039 23298085122483 302875106592255 3937376385699291 51185893014090759
((1 + loop(\(x,i).((x + i) div (1 + (x div 2))),x,x)) div 2)
A327007: 0 1 2 1 2 2 2 3 2 2 2 3 3 3 3 3
(((x2 + 1) * loop(\(x,i).x3,2,x)) div 2)
A170784: 0 1 1280 98415 2228224 25390625 186437376 1008840175 4362076160 15884240049 50500000000 143834809151 374084075520 901382446705 2035113108224 4344099609375
(((x2 + 1) * loop(\(x,i).x2,2,x2)) div 2)
A170774: 0 1 640 32805 557056 5078125 31072896 144120025 545259520 1764915561 5050000000 13075891741 31173672960 69337111285 145365222016 289606640625
(((x - (if (~2 + (x div 4)) <= 0 then 1 else 0)) div 2) mod 2)
A188083: 1 0 0 1 1 0 0 1 1 0 0 1 0 0 1 1
((x div 2) mod (if ((x div 2) mod 3) <= 0 then ~2 else 2))
A274369: 0 0 1 1 0 0 ~1 ~1 0 0 1 1 0 0 1 1
(x - ((x + 2) div (if ((x div 2) mod 2) <= 0 then ~2 else 2)))
A273155: 1 3 0 1 7
(((if x <= 0 then 2 else x2) div (2 - (x div ~2))) mod 2)
A321740: 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0
((x - (x div (~2 + (if (x mod 3) <= 0 then x else 0)))) mod 2)
A226474: 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 0
((2 - (loop(\(x,i).(~1 + (2x * i)),x,0) div 2)) div 2)
A212413: 1 1 2 9 63
(2 * (6x2 - (if x <= 0 then 0 else 2)))
A188148: 0 8 44 104 188 296 428 584 764 968 1196 1448 1724 2024 2348 2696
((loop(\(x,i).(x + ((i * i) div 3)),x,0) div 2) div 2)
A181120: 0 0 0 1 2 4 7 11 16 23 31 41 53 67 83 102
(2 + (if ((x + 2) mod 9) <= 0 then 1 else 2))
A251539: 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4
(((x + ~1) div (if ((x div 2) mod 3) <= 0 then 1 else 2)) mod 2)
A285305: 1 0 0 1 1 0 1 0 1 0 0 1 1 0 0 1
((((~x + 2) div 2) div (if (x mod 3) <= 0 then 1 else 2)) mod 2)
A266982: 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1
(x - (((x div 2) - (if (x mod 3) <= 0 then 1 else 2)) div 2))
A156562: 1 2 3 3 4 5 5 7 7 8 9 10 10 11 12 12
(2 * ((1 + loop(\(x,i).(2x + (i mod 2)),x,1)) div 2))
A151794: 2 4 6 14 26 54 106 214 426 854 1706 3414 6826 13654 27306 54614
(((~1 + (x div (if (x mod 3) <= 0 then 1 else 2))) div 2) mod 2)
A179416: 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1
(2 + (if x <= 0 then 1 else ((x mod ~5) mod 2)))
A245219-A097509: 3 2 3 2 3 2 2 3 2 3 2 2 3 2 3 2
(((x + 2) mod (2 + (if (~2 + (x div 2)) <= 0 then 2 else 1))) div 2)
A284391: 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 1
(if x <= 0 then 1 else (2 + (((x + 1) mod 5) mod 2)))
A085239: 1 2 3 2 2 3 2 3 2 2 3 2 3 2 2 3
loop(\(x,i).(2x + 1),x,20)
A171389: 20 41 83 167 335 671 1343 2687 5375 10751 21503 43007 86015 172031 344063 688127
(4 + (if (x + ~4) <= 0 then x else 5))
A168094: 4 5 6 7 8 9 9 9 9 9 9 9 9 9 9 9
((if x <= 0 then 1 else x) - (4 * (x div 5)))
A033925: 1 1 2 3 4 1 2 3 4 5 2 3 4 5 6 3
loop(\(x,i).x2,1,(4 * (1 + (2 * (x div 2)))))
A174994: 16 16 144 144 400 400 784 784 1296 1296 1936 1936 2704 2704 3600 3600
(if x <= 0 then 1 else (2 * (2 + (((x + 1) div 2) div 3))))
A175961: 1 4 4 4 4 6 6 6 6 6 6 8 8 8 8 8
(if x <= 0 then 1 else (2 * (2 + ((2 * (x div 2)) div 3))))
A277433: 1 4 4 4 6 6 8 8 8 8
loop(\(x,i).x2,1,(12x + 4))
A017570: 16 256 784 1600 2704 4096 5776 7744 10000 12544 15376 18496 21904 25600 29584 33856
loop(\(x,i).x2,2,(12x + 4))
A017572: 256 65536 614656 2560000 7311616 16777216 33362176 59969536 100000000 157351936 236421376 342102016 479785216 655360000 875213056 1146228736
((if x <= 0 then 1 else (x div (2 + ((x div 2) div 3)))) mod 2)
A266377: 1 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1
(if x <= 0 then 1 else (4 * (x - ((~x + 1) div 3))))
A310565: 1 4 12 16 20 28 32 36 44 48 52 60 64 68 76 80
((if x <= 0 then 2 else (x2 mod (2 + (x div 3)))) div 2)
A318886-A070536: 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
(((if x <= 0 then 2 else x2) div (2 + (x mod 3))) mod 2)
A089806: 1 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0
(4 + ((x + (if (x mod 2) <= 0 then 1 else x)) div 3))
A202151: 4 4 5 6 5 7
((((x + 3) * loop(\(x,i).(x * i),x,x)) div 2) div 2)
A180928: 0 1 5 27
A138772: 0 1 5 27 168 1200 9720 88200 887040 9797760 117936000 1536796800 21555072000 323805081600 5187108326400 88268019840000
loop(\(x,i).x2,3,(8x + 4))
A017120: 65536 429981696 25600000000 377801998336 2821109907456 14048223625216 53459728531456 167961600000000 457163239653376 1113034787454976 2478758911082496 5132188731375616 10000000000000000
loop(\(x,i).x3,1,(8x + 4))
A017115: 64 1728 8000 21952 46656 85184 140608 216000 314432 438976 592704 778688 1000000 1259712 1560896 1906624
loop(\(x,i).x3,2,(8x + 4))
A017121: 262144 5159780352 512000000000 10578455953408 101559956668416 618121839509504 2779905883635712 10077696000000000 31087100296429568 84590643846578176 208215748530929664 472161363286556672
loop(\(x,i).x2,1,(~7x + ~4))
A017030: 16 121 324 625 1024 1521 2116 2809 3600 4489 5476 6561 7744 9025 10404 11881
loop(\(x,i).x2,2,(~7x + ~4))
A017032: 256 14641 104976 390625 1048576 2313441 4477456 7890481 12960000 20151121 29986576 43046721 59969536 81450625 108243216 141158161
((x2 mod (2 + (if (x mod 2) <= 0 then (x div 2) else 1))) mod 2)
A189135: 0 1 1 0 0 1 1 1 0 0 0 1 0 1 1 0
((x mod (if (x + ~1) <= 0 then 1 else ((1 + (x div 2)) div 2))) mod 2)
A011703: 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1
(2 + (if (x * ((x + 1) mod 5)) <= 0 then 1 else 2))
A018244: 3 4 4 4 3 4 4 4 4 3 4 4 4 4 3 4
((loop(\(x,i).(x - ((i * i) div ~2)),x,1) div 2) div 2)
A173722: 0 0 1 2 4 7 12 18 26 36 49 64 82 103 128 156
(loop(\(x,i).((x + 1) + ((i * i) div 2)),(x + 1),2) div 2)
A209008: 1 3 5 10 16 26 38 55 75 101 131 168 210 260 316 381
(~2 + loop(\(x,i).10x,(x + 1),2))
A083812: 18 198 1998 19998 199998 1999998 19999998 199999998 1999999998 19999999998 199999999998 1999999999998 19999999999998 199999999999998 1999999999999998 19999999999999998
(loop(\(x,i).((x + 2) + ((i * i) div 2)),(x + 1),2) div 2)
A266464: 2 4 7 12 19 29 42 59 80 106 137 174 217 267 324 389
loop(\(x,i).(x3 + x2 + ~1),(2x + 2),2)
A122421: 1451 4611686018427387903
(if ((x + 2) mod 5) <= 0 then ((x + 1) div 2) else 2)
A145992: 2 2 2 2 2 2 2 2 4 2 2 2 2 7 2 2
((if (~2 + (x div 3)) <= 0 then 2 else ((x + 1) div 2)) div 2)
A116458: 1 1 1 1 1 1 1 1 1 2 2 3 3 3 3 4
(2 + loop(\(x,i).(x div (2 - (x mod 2))),x,((x + 1) div 2)))
A329245: 2 3 3 3 3 5 5 3 3 7 7 5 5 9 9 3
(2 * loop(\(x,i).(2x3 + ~2x2),(x + ~1),2))
A051460: 4 4 16 1792
((loop(\(x,i).((x2 + ~x) div 2),2,(x + ~1)) div 2) div 2)
A011942: 0 0 0 0 0 3 11 26 52 94 157 247 371 536 750 1023
(if (x mod 5) <= 0 then 1 else (2 * ((x + ~1) div 2)))
A328873: 1 0 0 2 2 1 4 6 6
(((~x + 1) div ((x div 4) + (if x <= 0 then 1 else 2))) mod 2)
A267034: 1 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1
(2 * (((x2 + 2) div (x + 2)) * (if x <= 0 then 1 else 2)))
A076342: 2 4 4 8 12 12 16 20 24 28 32 36 40 44 48 52
(x - (2 * (if ((x div 4) mod 2) <= 0 then ~2 else 2)))
A004445: 4 5 6 7 0 1 2 3 12 13 14 15 8 9 10 11
((if x <= 0 then 2 else 0) - (x div (~2 + (x div ~4))))
A038605: 2 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3
(((x + ~2) div (2 + (if (x mod 3) <= 0 then 1 else 2))) mod 2)
A179771: 1 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0
loop(\(x,i).i,(x div (2 + (x mod 10))),2)
A103663: 2 2 2 2 2 2 2 2 2 2 5 3 3 2 2 2
(((x mod (2 + (if (x mod 2) <= 0 then (x div 2) else 1))) div 2) mod 2)
A216278: 0 0 1 0 0 1 0 0 1 0 1 1 0 0 0 0
(8 * loop(\(x,i).(2 * (x + (x div 2))),x,1))
A188825: 8 16 48 144 432 1296 3888 11664 34992 104976 314928 944784 2834352 8503056 25509168 76527504
loop(\(x,i).~x,x,((2 - (((x + ~1) div 2) div 2)) div 2))
A014139: 1 ~1 1 ~1 1 0 0 0 0 0 0 0 0 1 ~1 1
((if (x mod 3) <= 0 then x else (((x + ~1) div 2) div 2)) mod 2)
A341612: 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1
(2 + (if x <= 0 then 1 else (4 * (x - (x div ~2)))))
A063221: 3 10 14 22 26 34 38 46 50 58 62 70 74 82 86 94
(((if x <= 0 then 1 else x) mod (2 + (((x + ~1) div 2) mod 2))) mod 2)
A265698: 1 1 0 0 1 1 0 1 0 1 0 0 0 1 0 0
(if (x mod 2) <= 0 then 1 else 64)
A174927: 1 64 1 64 1 64 1 64 1 64 1 64 1 64 1 64
(16 * (2 + loop(\(x,i).2x,x,2)))
A175163: 64 96 160 288 544 1056 2080 4128 8224 16416 32800 65568 131104 262176 524320 1048608
loop(\(x,i).(2x + ~1),x,32)
A206371: 32 63 125 249 497 993 1985 3969 7937 15873 31745 63489 126977 253953 507905 1015809
(~2 + loop(\(x,i).(2x + 1),x,16))
A156203: 14 31 65 133 269 541 1085 2173 4349 8701 17405 34813 69629 139261 278525 557053
(if (x mod 2) <= 0 then (((x - (x div 4)) div 2) mod 2) else 2)
A316828: 0 2 1 2 1 2 0 2 1 2 0 2 0 2 1 2
(4 * loop(\(x,i).3x,(2 * (x div 2)),2))
A117861: 8 8 72 72 648 648 5832 5832 52488 52488 472392 472392 4251528 4251528 38263752 38263752
((x div (2 * (if (x mod 3) <= 0 then 1 else 4))) mod 2)
A262588-A193140: 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1
((((x + 1) div (if (x + ~2) <= 0 then 1 else 4)) div 2) mod 2)
A030301: 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0
((x mod (~8 + (if (x + ~2) <= 0 then 2 else 1))) mod 2)
A059620: 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 0
((x + 2) - ((~x + 2) div (if x <= 0 then 1 else 8)))
A092459: 0 3 4 6 7 8 9 10 11 12 13 15 16 17 18 19
loop(\(x,i).(2x + ~1),(x + 1),16)
A195744: 31 61 121 241 481 961 1921 3841 7681 15361 30721 61441 122881 245761 491521 983041
(16 + loop(\(x,i).3x,x,1))
A205646: 17 19 25 43 97 259 745 2203 6577 19699 59065 177163 531457 1594339 4782985 14348923
loop(\(x,i).(x2 + ~x + 1),x,16)
A179092: 16 241 57841 3345523441 4611686018427387903 4611686018427387903 4611686018427387903
(2 - ((x - (if x <= 0 then 1 else (x div 8))) mod 2))
A081129-A022934: 1 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2
(if (~2 + (x div 3)) <= 0 then (x div 8) else 2)
A102682-A008838: 0 0 0 0 0 0 0 0 1 2 2 2 2 2 2 2
((x mod (2 + (if (x mod 2) <= 0 then 1 else (x div 4)))) div 2)
A097795: 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0
(if (x mod 2) <= 0 then ((x + 2) div (2 + (x div 4))) else 2)
A037968: 1 2 2 2 2 2 2 2 2 2 3 2 2 2 3 2
(((if x <= 0 then 2 else x2) div (2 + (x mod 4))) mod 2)
A168002: 1 0 1 1 0 0 1 1 0 1 1 0 0 0 1 1
(2 * loop(\(x,i).(x2 * (x div 2)),(x + 4),2))
A139574: 4398046511104 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(2 * (x + i)),x,(x + 6)) div 2)
A291097: 3 8 20 47 106 233 504 1079 2294 4853 10228 21491 45042 94193 196592 409583
((loop(\(x,i).4x,x,(x + 4)) div 2) div 2)
A112613: 1 5 24
A081104: 1 5 24 112 512 2304 10240 45056 196608 851968 3670016 15728640
A079028: 1 5 24 112 512 2304 10240 45056 196608 851968 3670016 15728640 67108864 285212672 1207959552 5100273664
(2 * (2 + loop(\(x,i).(3x + 3),2x,2)))
A199567: 8 64 568 5104 45928 413344 3720088 33480784 301327048 2711943424 24407490808 219667417264 1977006755368 17793060798304 160137547184728 1441237924662544
(2 * (2 + loop(\(x,i).(3x + ~3),2x,2)))
A062508: 8 16 88 736 6568 59056 531448 4782976 43046728 387420496 3486784408 31381059616 282429536488 2541865828336 22876792454968 205891132094656
(2 * (~2 + loop(\(x,i).(x3 + 1),2x,2)))
A255345: 0 1456 4611686018427387903 4611686018427387903
(((((if (x mod 2) <= 0 then 1 else x) + (x div 2)) div 2) div 2) div 2)
A144765: 0 0 0 0 0 0 0 1 0 1 0 2 0 2 1 2
((x mod (2 + (if (~x + 4) <= 0 then (x mod 2) else 2))) div 2)
A156660: 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0
(4 + loop(\(x,i).2x,(x div 2),(2 + (x mod 2))))
A209723: 6 7 8 10 12 16 20 28 36 52 68 100 132 196 260 388
(if (x + ~1) <= 0 then x else (2 * ((x mod (2 + (x mod 2))) mod 2)))
A045839: 0 1 0 0 0 0 0 2 0 0 0 0 0 2 0 0
(2 + ((loop(\(x,i).(2x + 4),x,(x mod 2)) div 2) div 2))
A014556: 2 3 5 11 17 41
A082605: 2 3 5 11 17 41 65 161 257 641 1025 2561 4097 10241 16385 40961
(if (x mod 2) <= 0 then (1 + ((x div 2) mod 2)) else 8)
A143025: 1 8 2 8 1 8 2 8 1 8 2 8 1 8 2 8
(8 + loop(\(x,i).3x,2x,1))
A253212: 9 17 89 737 6569 59057 531449 4782977 43046729 387420497 3486784409 31381059617 282429536489 2541865828337 22876792454969 205891132094657
(if (x + ~2) <= 0 then (3x + 1) else 8)
A115291: 1 4 7 8 8 8 8 8 8 8 8 8 8 8 8 8
(8 + ((x + loop(\(x,i).x2,x,2)) div 2))
A100595: 9 10 17 137
((x + 8) + loop(\(x,i).i,(~1 + (x div 2)),1))
A121816: 9 10 11 12 13 14 16 17 19 20 22 23 25 26 28 29
loop(\(x,i).(5x + ~4),x,8)
A199310: 8 36 176 876 4376 21876 109376 546876 2734376 13671876 68359376 341796876 1708984376 8544921876 42724609376 213623046876
((if (x mod 3) <= 0 then 1 else 0) + (x div 8))
A029316: 1 0 0 1 0 0 1 0 1 2 1 1 2 1 1 2
loop(\(x,i).(x3 + 3x),x,8)
A145182: 8 536 153992264 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + ~3x),x,8)
A282180: 8 488 116212808 4611686018427387903 4611686018427387903
loop(\(x,i).(5x + 4),x,8)
A198768: 8 44 224 1124 5624 28124 140624 703124 3515624 17578124 87890624 439453124 2197265624 10986328124 54931640624 274658203124
loop(\(x,i).(x + (x div 8)),x,8)
A182361-A023391: 8 9 10 11 12 13 14 15 16 18 20 22 24 27 30 33
(8 * loop(\(x,i).(x div (2 - (x mod 2))),x,x))
A109049: 0 8 8 24 8 40 24 56 8 72 40 88 24 104 56 120
loop(\(x,i).x2,2,8x3)
A016752: 0 4096 16777216 2176782336 68719476736 1000000000000 8916100448256 56693912375296 281474976710656 1156831381426176 4096000000000000 12855002631049216 36520347436056576 95428956661682176 232218265089212416 531441000000000000
(x - ((if x <= 0 then 1 else x) div (~2 + ((~x + 2) div 4))))
A286689: 1 2 3 4 6 7 8 9 10 12 13 14 15 16 17 18
((if x <= 0 then 0 else 1) - (x div (~2 + ((~x + 2) div 4))))
A130239: 0 2 2 2 3 3 3 3 3 4 4 4 4 4 4 4
loop(\(x,i).x2,1,(x div (~2 + ((~x + 2) div 4))))
A048760: 0 1 1 1 4 4 4 4 4 9 9 9 9 9 9 9
(2 * loop(\(x,i).x2,1,(x2 + 2x + 4)))
A190176: 32 98 288 722 1568 3042 5408 8978 14112 21218 30752 43218 59168 79202 103968 134162
(2 * loop(\(x,i).x2,1,((x + 4) + (x div 2))))
A176542: 32 50 98 128 200 242 338 392 512 578 722 800 968 1058 1250 1352
((if ((x div 3) mod 2) <= 0 then 1 else (x div 4)) mod 2)
A318924: 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 1
loop(\(x,i).2x,(x div 2),((2 - (x mod 4)) div 2))
A102561: 1 0 0 ~2 4 0 0 ~8 16 0 0 ~32 64 0 0 ~128
(loop(\(x,i).(x3 + ~3x),x,4) div 2)
A094680: 2 26 70226 1385331749802026 4611686018427387903
loop(\(x,i).4x,(6x + 4),2)
A013789: 512 2097152 8589934592 35184372088832 144115188075855872 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(12x + 8))
A017618: 64 400 1024 1936 3136 4624 6400 8464 10816 13456 16384 19600 23104 26896 30976 35344
loop(\(x,i).x2,2,(12x + 8))
A017620: 4096 160000 1048576 3748096 9834496 21381376 40960000 71639296 116985856 181063936 268435456 384160000 533794816 723394816 959512576 1249198336
(loop(\(x,i).2x,x,(2 + ((x2 + x) div 2))) div 2)
A188545: 1 3 10
A104270: 1 3 10 32 96 272 736 1920 4864 12032 29184 69632 163840 380928 876544 1998848
(loop(\(x,i).2x,x,(2 + ((x2 + ~x) div 2))) div 2)
A053730: 1 2 6 20 64 192 544 1472 3840 9728 24064 58368 139264 327680 761856 1753088
(loop(\(x,i).(x * i),x,(2 + ((x2 + ~x) div 2))) div 2)
A076301: 1 1 3 15 96 720 6120 57960 604800 6894720 85276800 1137628800 16286054400 249080832000 4053790540800 69960578688000
(x - (((x - loop(\(x,i).(x2 + 1),x,2)) div 2) div 2))
A105232: 1 2 8 172
(4 * (2 + (if x <= 0 then 10 else x)))
A087407: 48 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68
(((x + ~1) div (2 + ((if (x mod 2) <= 0 then 2 else x) div 2))) mod 2)
A288855: 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 1
(2 * (~2 + loop(\(x,i).10x,x,2)))
A086575: 0 36 396 3996 39996 399996 3999996 39999996 399999996 3999999996 39999999996 399999999996 3999999999996 39999999999996 399999999999996 3999999999999996
(((2 + (x div 2)) div (2 + (if (x mod 2) <= 0 then x else 2))) mod 2)
A173861: 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0
((x + 2) - ((~x + 2) div (2 + ((if x <= 0 then 2 else x) div 2))))
A183217: 2 3 4 6 7 8 9 10 11 13 14 15 16 17 18 19
((x2 mod (2 + (if (x mod 2) <= 0 then 1 else (x + 2)))) mod 2)
A228039: 0 1 1 0 1 1 0 1 1 1 1 1 0 0 1 0
(if x <= 0 then 1 else (4 * ((x2 + 2) div (x + 2))))
A086663: 1 4 4 8 12 12 16 20 24 28 32 36 40 44 48 52
(loop(\(x,i).x3,3,(x + 4)) div 2)
A320865: 9007199254740992 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (~4 + (x div 2)) <= 0 then x else (x + 6))
A103303: 0 1 2 3 4 5 6 7 8 9
A102489-A004838: 0 1 2 3 4 5 6 7 8 9 16 17 18 19 20 21
loop(\(x,i).5x,x,(x + 6))
A079027: 6 35 200 1125 6250 34375 187500 1015625 5468750 29296875 156250000 830078125 4394531250 23193359375 122070312500 640869140625
((if x <= 0 then 1 else x) - (x2 div (x + 6)))
A278044: 1 1 2 2 3 3 3 4 4 4 4 4 4 5 5 5
loop(\(x,i).5x,x,(4x + 8))
A159727: 8 60 400 2500 15000 87500 500000 2812500 15625000 85937500 468750000 2539062500 13671875000 73242187500 390625000000 2075195312500
(((if ((x div 2) mod 3) <= 0 then x else (x + 2)) div 2) div 2)
A156080: 0 0 1 1 1 1 1 1 2 2 3 3 3 3 4 4
(if x <= 0 then 1 else (2 * (((x2 + ~x) div (x + 2)) mod 2)))
A226914: 1 0 0 2 0 0 2 0 2 0 2 0 2 0 2 0
(2 + loop(\(x,i).(x + (x2 div (1 + i))),(x + 2),2))
A093382: 11 31 199
loop(\(x,i).x2,3,~7x)
A016988: 0 5764801 1475789056 37822859361 377801998336 2251875390625 9682651996416 33232930569601 96717311574016 248155780267521 576480100000000 1235736291547681 2478758911082496 4702525276151521
(8x + loop(\(x,i).x2,2,x2))
A180358: 0 9 272 6585 65568 390665 1679664 5764857 16777280 43046793 100000080 214358969 429981792 815730825 1475789168 2562890745
(2 * loop(\(x,i).(x + ((2 + i) * (1 + i))),2x,2))
A199833: 4 40 140 336 660 1144 1820 2720 3876 5320 7084 9200 11700 14616 17980 21824
(((if x <= 0 then 2 else ((x div 3) * (x div 2))) div 2) mod 2)
A200261: 1 0 0 0 1 1 1 1 0 0 1 1 0 0 0 1
(2 + (if x <= 0 then 1 else (2 * (4x - (x div 2)))))
A063109: 3 10 16 24 30 38 44 52 58 66 72 80 86 94 100 108
(if x <= 0 then 2 else ((x + (x div 2)) div (4 + (x div 2))))
A129753: 2 0 0 0 1 1 1 1 1 1 1 1 1 1 1 2
(((if (x mod 3) <= 0 then 1 else x) mod (2 + (x div 2))) mod 2)
A267269: 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1
(((if (x mod 2) <= 0 then (~x + 1) else x) mod (2 + (x div 2))) mod 2)
A339052: 1 1 0 0 1 1 0 0 1 1 1 0 1 1 1 0
(1 - (if (x mod 3) <= 0 then 1 else (2 * ((x div 2) mod 2))))
A174784: 0 1 ~1 0 1 1 0 ~1 1 0 ~1 ~1 0 1 ~1 0
((if (x mod 2) <= 0 then 1 else x) div (1 - (2 * ((x div 2) mod 2))))
A009001: 1 1 ~1 ~3 1 5 ~1 ~7 1 9 ~1 ~11 1 13 ~1 ~15
((if (x + ~2) <= 0 then x else ((x + 1) mod (2 + (x mod 2)))) mod 2)
A308185: 0 1 0 1 1 0 1 0 1 1 1 0 1 0 1 1
(loop(\(x,i).(x2 + 1),(x div 2),(2 + (x mod 2))) div 2)
A303792: 1 1 2 5 13 50
loop(\(x,i).(2x + 1),(x div 2),(2 * (2 + (x mod 2))))
A010737: 4 6 9 13 19 27 39 55 79 111 159 223 319 447 639 895
(loop(\(x,i).(3x + 1),x,(2 + (x mod 2))) div 2)
A297445: 1 5 11 47 101 425 911 3827 8201 34445 73811 310007 664301 2790065 5978711 25110587
(loop(\(x,i).(2 * (x + (x div 2))),x,(2 + (x mod 2))) div 2)
A133125: 1 4 9 36 81 324 729 2916 6561 26244 59049 236196 531441 2125764 4782969 19131876
(0 - (if (x + ~2) <= 0 then 1 else ((x mod (2 + (x mod 2))) div 2)))
A096606: ~1 ~1 ~1 0 0 ~1 0 0 0 0 0 ~1 0 0 0 0
(loop(\(x,i).(2x + 2),x,1) + (4 * (x mod 2)))
A259713: 1 8 10 26 46 98 190 386 766 1538 3070 6146 12286 24578 49150 98306
((1 - ((loop(\(x,i).~2x,x,x) div 2) div 2)) div 2)
A168150: 0 1 ~1 3 ~8 20 ~48 112 ~256 576 ~1280 2816 ~6144 13312 ~28672 61440
(x4 mod loop(\(x,i).(x2 + 2),2,2))
A070581: 0 1 16 5 28 17 4 7 30 25 6 11 26 23 36 9
((2x - (if (x + ~4) <= 0 then 0 else 1)) mod 4)
A307197: 0 2 0 2 0 1 3 1 3 1 3 1 3 1 3 1
(if (~2 + (x div (3 + (x mod 2)))) <= 0 then 1 else 4)
A196222: 1 1 1 1 1 1 1 1 1 1 4 1 4 4 4 4
(x mod (if (~6 + (x div 2)) <= 0 then 1 else 4))
A308980: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3
loop(\(x,i).(2x + 5),(x + 3),4)
A304383: 67 139 283 571 1147 2299 4603 9211 18427 36859 73723 147451 294907 589819 1179643 2359291
((x2 + 4x + 4) - (if (x mod 2) <= 0 then 1 else 4))
A142717: 3 5 15 21 35 45 63 77 99 117 143 165 195 221 255 285
((if (x mod 2) <= 0 then 2x else 0) + ((x + 1) mod 4))
A199398: 1 2 7 0 9 2 15 0 17 2 23 0 25 2 31 0
loop(\(x,i).4x,(4x + 2),4)
A013781: 64 16384 4194304 1073741824 274877906944 70368744177664 18014398509481984 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if ((x + 2) mod 8) <= 0 then (x + ~2) else 4)
A088899: 4 4 4 4 4 4 4 4 4 4 4 4 4 4 12 4
(x - (if (x + ~12) <= 0 then x else 4))
A048048: 0 0 0 0 0 0 0 0 0 0 0 0 0 9 10 11
((x + 4) + (if (x + ~2) <= 0 then 2x else 3))
A093465: 4 7 10 10 11
loop(\(x,i).(7x + ~2),x,4)
A199490: 4 26 180 1258 8804 61626 431380 3019658 21137604 147963226 1035742580 7250198058 50751386404 355259704826 2486817933780 17407725536458
(loop(\(x,i).(2x + 4),x,(x2 + ~x)) div 4)
A053545: 0 1 5 19 63 191 543 1471 3839 9727 24063 58367 139263 327679 761855 1753087
((x + loop(\(x,i).(((x + ~1) div 2) * i),x,1)) mod 4)
A206705: 1 1 0 1 0 0 0 1 0 0 0 1 0 0 0 3
((x + 4) + (if (~4 + (x div 2)) <= 0 then 1 else 2))
A268541: 5 6 7 8 9 10 11 12 13 14 16 17 18 19 20 21
(x - (if (~2 + (x div 5)) <= 0 then x else 4))
A048015: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
(x - (if (~6 + (x div 2)) <= 0 then x else 4))
A048002: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 11
loop(\(x,i).32x,x,4)
A013823: 4 128 4096 131072 4194304 134217728 4294967296 137438953472 4398046511104 140737488355328 4503599627370496 144115188075855872 4611686018427387903 4611686018427387903 4611686018427387903
(if ((x + ~4) mod 8) <= 0 then x else 4)
A290205: 4 4 4 4 4 4 4 4 4 4 4 4 12 4 4 4
loop(\(x,i).(4 + ((x2 + x) div 2)),x,4)
A283793: 4 14 109 5999 17997004 161946085486514 4611686018427387903 4611686018427387903
loop(\(x,i).(4 + ((x2 + ~x) div 2)),x,4)
A151611: 4 10 49 1180 695614 241939070695 4611686018427387903 4611686018427387903
((if x <= 0 then 1 else 2x) - ((x + (x div 2)) div 4))
A026351: 1 2 4 5 7 9 10 12 13 15 17 18 20 22 23 25
((if (x mod 8) <= 0 then 0 else 1) + (x div 4))
A131849-A090736-A090735: 0 1 1 1 2 2 2 2 2 3 3 3 4 4 4 4
(if (x + ~10) <= 0 then 1 else (x div 4))
A025794: 1 1 1 1 1 1 1 1 1 1 1 2 3 3 3 3
loop(\(x,i).i,((x + 1) mod 5),(x div 4))
A277543: 1 2 3 4 1 1 2 3 4 2 1 2 3 4 3 1
((if x <= 0 then 2 else (3x + 3)) + (x div 4))
A186500: 2 6 9 12 16 19 22 25 29 32 35 38 42 45 48 51
(3 div (if (x + ~4) <= 0 then 2 else (x div 4)))
A110566: 1 1 1 1 1 3 3 3 1 1 1 1 1 1 1 1
((if (~x + 2) <= 0 then 2 else 1) + (x mod 2) + (x div 4))
A105096: 1 2 2 3 3 4 3 4 4
A226164: 1 2 2 3 3 4 3 4 4 5 4 5 5 6 5 6
((if x <= 0 then 1 else (~x mod 4)) - (x mod 4))
A084099: 1 2 0 ~2 0 2 0 ~2 0 2 0 ~2 0 2 0 ~2
loop(\(x,i).13x,x,4)
A222138: 4 52 676 8788 114244 1485172 19307236 250994068 3262922884 42417997492 551433967396 7168641576148 93192340489924 1211500426369012 15749505542797156 204743572056363028
loop(\(x,i).(7x + 6),x,4)
A198687: 4 34 244 1714 12004 84034 588244 4117714 28824004 201768034 1412376244 9886633714 69206436004 484445052034 3391115364244 23737807549714
(~4 + loop(\(x,i).(2x2 + 2),2,x2))
A088256: 6 30 2310
loop(\(x,i).x2,1,(x2 - (x2 div 4)))
A212503: 0 1 9 49 144 361 729 1369 2304 3721 5625 8281 11664 16129 21609 28561
(loop(\(x,i).(1 + (x mod (1 + (i mod (x + 1))))),x,2) div 2)
A167746-A050374-A050370: 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 2
(((x - (2 mod (if (x mod 3) <= 0 then 1 else x))) div 2) mod 2)
A228487: 0 0 1 1 1 1 1 0 1 0 0 0 0 1 0 1
loop(\(x,i).x2,1,(10x + 4))
A017318: 16 196 576 1156 1936 2916 4096 5476 7056 8836 10816 12996 15376 17956 20736 23716
loop(\(x,i).x2,2,(10x + 4))
A017320: 256 38416 331776 1336336 3748096 8503056 16777216 29986576 49787136 78074896 116985856 168896016 236421376 322417936 429981696 562448656
(loop(\(x,i).(7x + ~3),x,2) div 2)
A083232: 1 5 37 257 1801 12605 88237 617657 4323601 30265205 211856437 1482995057 10380965401 72666757805 508667304637 3560671132457
loop(\(x,i).x2,3,(6x + 4))
A016964: 65536 100000000 4294967296 54875873536 377801998336 1785793904896 6553600000000 20047612231936 53459728531456 128063081718016 281474976710656 576480100000000 1113034787454976 2044140858654976
loop(\(x,i).x3,1,(6x + 4))
A016959: 64 1000 4096 10648 21952 39304 64000 97336 140608 195112 262144 343000 438976 551368 681472 830584
loop(\(x,i).x3,2,(6x + 4))
A016965: 262144 1000000000 68719476736 1207269217792 10578455953408 60716992766464 262144000000000 922190162669056 2779905883635712 7427658739644928 18014398509481984 40353607000000000 84590643846578176
(loop(\(x,i).(x * (1 + i)),x,(3x + 2)) div 2)
A112613: 1 5 24
A066118: 1 5 24 132 840 6120 50400 463680 4717440 52617600 638668800 8382528000 118313395200 1787154969600 28768836096000 491685562368000
((if x <= 0 then 1 else ((x * ((~x + 1) div 3)) div 2)) mod 2)
A164364: 1 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0
loop(\(x,i).2x,((x + (x2 div 3)) div 2),2)
A291338: 2 2 4 16 32 128 1024 4096 32768 524288 4194304 67108864 2147483648 34359738368 1099511627776 70368744177664
(loop(\(x,i).((2x + 1) - ((x * i) mod 2)),x,2) div 2)
A292528: 1 2 5 11 22
A266721: 1 2 5 11 22 45 90 181 362 725 1450 2901 5802 11605 23210 46421
(2 + (loop(\(x,i).(3x + ~1),(x + 1),x) div 2))
A088581: 1 4 22 103 427 1642 6016 21325 73813 250960 841450 2790067 9167359 29893558 96855124 312088729
(loop(\(x,i).2x,x,(2 - ((x2 + x) div 2))) div 2)
A127276: 1 1 ~2 ~16 ~64 ~208 ~608 ~1664 ~4352 ~11008 ~27136 ~65536 ~155648 ~364544 ~843776 ~1933312
(x4 mod loop(\(x,i).(x2 + x),2,2))
A070585: 0 1 16 39 4 37 36 7 22 9 4 25 30 1 28 15
(((((x div 2) * (x div 2)) mod (if x <= 0 then 1 else x)) div 2) div 2)
A288166: 0 0 0 0 0 1 0 0 0 1 1 0 0 2 1 1
(2 * (2 + (x * loop(\(x,i).(2x + i),(x + 1),2))))
A058227: 4 28 112 352 972 2484 6040 14200
(loop(\(x,i).(2x - ((~1 + i) div 4)),x,2) div 2)
A222011: 1 2 4 8
A018487: 1 2 4 8 16 31 62 124 248 496
((if x <= 0 then 2 else (x - ((~x + (x div 4)) div 2))) div 2)
A248183: 1 1 1 2 3 3 4 5 5 6 7 8 8 9 10 10
(2 + loop(\(x,i).x2,1,((x mod 2) - ((~x + 2) div 2))))
A267942: 3 3 2 6 3 11 6 18 11 27 18 38 27 51 38 66
(2 + (if (x + ~1) <= 0 then x else (5x + 10)))
A298470: 2 3 22 27 32 37 42 47 52 57 62 67 72 77 82 87
(((x + 2) * (~1 + loop(\(x,i).x2,2,(x + 2)))) div 2)
A027484: 15 120 510 1560 3885 8400 16380 29520 49995 80520 124410 185640 268905 379680 524280 709920
(((x + 2) * (~1 + loop(\(x,i).(2x + i),x,2))) div 2)
A003469: 1 6 22 65 171 420 988 2259 5065 11198 24498 53157 114583 245640 524152 1113959
(((x + 2) * loop(\(x,i).(3x + 1),x,1)) div 2)
A261064: 1 6 26 100 363 1274 4372 14760 49205 162382 531438 1727180 5580127 17936130 57395624 182948560
((x + 2) - (loop(\(x,i).((x + ~1) * i),x,1) div (x + 2)))
A192578-A140768: 2 3 5 7 13 37
((loop(\(x,i).(x + (x div 2)),(x + ~1),2) div (x + 2)) div 2)
A035563: 0 0 0 0 0 0 0 1 1 1 2 3 5 7 9 13
((2 - ((x + 2) * (if (x mod 2) <= 0 then (x div 2) else 2))) div 2)
A110332: 1 ~2 ~1 ~4 ~5 ~6 ~11 ~8 ~19 ~10 ~29 ~12 ~41 ~14 ~55 ~16
((x - loop(\(x,i).(~x2 + (x div 2)),2,(x + 2))) div 2)
A289947: 5 34 102
((x + 4) * (if (~x + 4) <= 0 then (x + ~2) else 0))
A286429: 0 0 0 0 16 27 40 55 72 91 112 135 160 187 216 247
((if x <= 0 then 1 else x) - ((x2 + 1) div (x + 4)))
A134021: 1 1 2 2 2 3 3 3 3 3 3 3 3 3 4 4
loop(\(x,i).(x mod (2 + (x div 4))),2,(x + 4))
A238406: 1 0 0 1 0 1 0 1 0 1 1 0 1 2 0 1
(if (~2 + (x div 5)) <= 0 then x else (x + 4))
A103303: 0 1 2 3 4 5 6 7 8 9
A072089-A072088: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 19
(loop(\(x,i).((x * (2 + i)) div 2),x,x) div (x + 4))
A274326: 0 0 1 2 11 40
((2x + 4) + (if (~1 + (x div 2)) <= 0 then (x mod 2) else 0))
A319926: 4 7 8 11 12 14 16
(loop(\(x,i).(2x + 12),x,(x + 2)) div 2)
A048468: 1 9 26 62 138 298 634 1338 2810 5882 12282 25594 53242 110586 229370 475130
(loop(\(x,i).(2x * (1 + (2 * i))),x,(x + 2)) div 2)
A002691: 1 9 120 2100 45360 1164240 34594560 1167566400 44108064000 1843717075200 84475764172800 4209708914611200 226676633863680000 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(2x + 16),x,(x + 2)) div 2)
A195857: 1 11 32 76 168 360 760 1592 3320 6904 14328 29688 61432 126968 262136 540664
((if (x mod 3) <= 0 then 1 else (x2 div (x + 2))) mod 2)
A307183: 1 0 1 1 0 1 1 1 0 1 0 1 1 1 0 1
(loop(\(x,i).(((x + (x div 2)) div 2) + i),x,(x + 2)) div 2)
A320848: 1 1 2 3 4 5 7 9 10 12 14 16 18 20 22 24
(x mod (if ((x + ~1) mod 8) <= 0 then (x + ~2) else 2))
A280800: 0 0 0 1 0 1 0 1 0 2 0 1 0 1 0 1
(if (~2 + (x div 5)) <= 0 then x else (2x + ~4))
A103303: 0 1 2 3 4 5 6 7 8 9
A023768: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 26
(x2 - (loop(\(x,i).x3,x,(x + ~2)) div 2))
A302349: 1 2 4 9 4611686018427387903
loop(\(x,i).(2 * (2x - (x div (1 + i)))),2x,2)
A099976: 2 20 252 3432 48620 705432 10400600 155117520 2333606220 35345263800 538257874440 8233430727600 126410606437752 1946939425648112 30067266499541040 465428353255261088
(loop(\(x,i).(x3 + ~3x),2,2x) div 2)
A243135: 0 1 70226 3880899 58106404 456335045 2421980406 9863382151 33165873224 96450076809 250283080090 592479412811 1300371936876 2678768828749 5228741809214 9743412645135
loop(\(x,i).(2x + ((i * i) mod 3)),2x,2)
A037639: 2 11 45 182 731 2925 11702 46811 187245 748982 2995931 11983725 47934902 191739611 766958445 3067833782
loop(\(x,i).6x,x,(~4x + 1))
A144708: 1 ~18 ~252 ~2376 ~19440 ~147744 ~1073088 ~7558272 ~52068096 ~352719360 ~2358180864 ~15600273408 ~102308769792 ~666095394816 ~4310029025280 ~27740914089984
(4x + ((if x <= 0 then 2 else (x2 + ~x)) div 2))
A134227: 1 4 9 15 22 30 39 49 60 72 85 99 114 130 147 165
(if ((x + 2) mod 4) <= 0 then (x div 2) else 4x)
A187541: 0 4 1 12 16 20 3 28 32 36 5 44 48 52 7 60
loop(\(x,i).13x,2x,2)
A324272: 2 338 57122 9653618 1631461442 275716983698 46596170244962 7874752771398578 1330833218366359682 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 + loop(\(x,i).(x - (x div (3 + i))),x,2x))
A238461: 2 4 5 6 7 8 8 9 9 10 10 11 11 11 12 12
((if x <= 0 then 1 else ((1 + (x div 3)) * (x div 2))) mod 2)
A228747: 1 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0
((if x <= 0 then 1 else (((x + ~1) div 3) * (x div 2))) mod 2)
A122276: 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0
((if (x mod 2) <= 0 then x else (4x - (x div 2))) div 2)
A318972: 0 2 1 5 2 9 3 12 4 16 5 19 6 23 7 26
((((if (x mod 2) <= 0 then 1 else x) + (x div 2)) * (x div 2)) div 2)
A245467: 0 0 1 2 3 7 6 15 10 26 15 40 21 57 28 77
(((x2 + x) + (if x <= 0 then 1 else 2)) * (2 + (x div 2)))
A171261: 2 8 24 42
((x + 2) + ((if (x mod 4) <= 0 then 1 else 2) + (x div 2)))
A295075: 3 5 7 8 9 11 13 14 15 17 19 20 21 23 25 26
((if (x + ~2) <= 0 then 1 else (2x + ~4)) + ((x div 2) mod 2))
A189887: 1 1 2 3 4 6 9 11 12 14 17 19 20 22 25 27
((if (x mod 2) <= 0 then (x + 3) else x) - ((x div 2) mod 2))
A067060: 3 1 4 2 7 5 8 6 11 9 12 10 15 13 16 14
loop(\(x,i).2x2,(x div 2),(x - ((x div 2) mod 2)))
A054874: 0 1 2 8 2048
(((x2 + ~2) div ((if x <= 0 then 1 else x) + (x div 2))) mod 2)
A288640: 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0
(((~x2 + 1) div ((if x <= 0 then 1 else x) + (x div 2))) mod 2)
A100060: 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1
(2 + (loop(\(x,i).(2x + 4),x,3) + (x mod 2)))
A322417: 5 13 26 55 110 223 446 895 1790 3583 7166 14335 28670 57343 114686 229375
(2 * (loop(\(x,i).(3x + 1),x,1) - (x mod 2)))
A322116: 2 6 26 78 242 726 2186 6558 19682 59046 177146 531438 1594322 4782966 14348906 43046718
(if (16 mod (x + 1)) <= 0 then (x mod 2) else 2)
A201219: 0 1 2 1 2 2 2 1 2 2 2 2 2 2 2 1
loop(\(x,i).2x,((x3 + x2) + (x mod 2)),2)
A092798: 2 16 8192 274877906944 4611686018427387903 4611686018427387903
(if (~2 + (x mod (4 + (x mod 2)))) <= 0 then (x mod 2) else 2)
A267860: 0 1 0 2 0 1 0 1 0 2 0 1 0 2 0 1
((loop(\(x,i).2x,x,(2 + (x mod 2))) - (x mod 2)) div 2)
A277867: 1 2 4 11 16 47 64 191 256 767 1024 3071 4096 12287 16384 49151
loop(\(x,i).3x,(x div 2),(4 - (x mod 2)))
A162766: 4 3 12 9 36 27 108 81 324 243 972 729 2916 2187 8748 6561
(if (x + ~4) <= 0 then 1 else (x mod (2 * (2 - (x mod 2)))))
A334462: 1 1 1 1 1 1 2 1 0 1 2 1 0 1 2 1
(2 + loop(\(x,i).(4x + 4),(x div 2),(x mod 2)))
A137208: 2 3 6 10 22 38 86 150 342 598 1366 2390 5462 9558 21846 38230
(loop(\(x,i).6x,x,2) div (2 + (x mod 2)))
A083223: 1 4 36 144 1296 5184 46656 186624 1679616 6718464 60466176 241864704 2176782336 8707129344 78364164096 313456656384
(if ((x + 1) mod 6) <= 0 then x else (2 + (x mod 2)))
A060395: 2 3 2 3 2 5 2 3 2 3 2 11 2 3 2 3
((if (x mod 3) <= 0 then 1 else 2) * (1 - (2 * (x mod 2))))
A131714: 1 ~2 2 ~1 2 ~2 1 ~2 2 ~1 2 ~2 1 ~2 2 ~1
loop(\(x,i).(~4x + 1),x,(1 - (2 * (x mod 2))))
A113876: 1 5 13 77 205 1229 3277 19661 52429 314573 838861 5033165 13421773 80530637 214748365 1288490189
(loop(\(x,i).(2x + (i mod 2)),x,1) - (2 * (x mod 2)))
A140359: 1 1 6 11 26 51 106 211 426 851 1706 3411 6826 13651 27306 54611
((if (x mod 3) <= 0 then 1 else ~2) + (2 * (x mod 2)))
A079757: 1 0 ~2 3 ~2 0 1 0 ~2 3 ~2 0 1 0 ~2 3
(loop(\(x,i).(2x + 1),x,4) + (2 * (x mod 2)))
A321643: 4 11 19 41 79 161 319 641 1279 2561 5119 10241 20479 40961 81919 163841
(loop(\(x,i).(2x + 1),(x div 2),2) + (2 * (x mod 2)))
A097581: 2 4 5 7 11 13 23 25 47 49 95 97 191 193 383 385
(2 + ((if ((x + ~1) mod 3) <= 0 then 1 else x) * (x mod 2)))
A092067-A092028: 2 3 2 5 2 7 2 3 2 11 2 13 2 3 2 17
(2 + (2 mod (if (x mod 3) <= 0 then 1 else x)) - (x mod 2))
A341827: 2 1 2 1 4 3 2 3 4 1 4 3 2 3 4 1
(loop(\(x,i).(x + ((2 * (i * i)) div (x + 1))),x,2) div 2)
A062427: 1 1 2 3 5 7 9 11 14 16 19 22 25 28 31 34
(((x2 + 2) * (if (x + ~2) <= 0 then 2 else x2)) div 2)
A097350: 2 3 6 49
((x + (if ((x + ~1) mod 5) <= 0 then 1 else 0)) div 2)
A194204: 0 1 1 1 2 2 3 3 4 4 5 6 6 6 7 7
(1 - (x mod (2 * (~x + (if (x mod 4) <= 0 then 2 else 0)))))
A001438: 1 2 3 4 1 6 7 8
A109680: 1 2 3 4 1 6 7 8 5 10 11 12 9 14 15 16
((x + 2) + loop(\(x,i).(i - ((1 + i) mod (x + 1))),x,0))
A004754: 2 4 5 8 9 10 11 16 17 18 19 20 21 22 23 32
((x + 2) + loop(\(x,i).(x + i - (x div 4)),x,0))
A003068: 2 4 7 11 15 19 23 28 33 38 43 48 53 58 63 68
loop(\(x,i).((x + 1) - (x div (~1 + (i div ~2)))),x,2)
A002789: 2 4 7 11 16 21 28 35 43 52 62 72 84 96 109 123
((if (x mod (1 + (x mod 6))) <= 0 then 1 else x) mod 2)
A254651: 1 1 0 1 0 1 1 1 0 1 1 1 1 1 0 1
((x + 2) + loop(\(x,i).i,(~1 + (((x + 1) div 2) div 2)),1))
A154660: 3 4 5 6 7 8
A298113: 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 20
((x + 2) + loop(\(x,i).i,(x + ~9),1))
A154660: 3 4 5 6 7 8
A283810-A130231: 3 4 5 6 7 8 9 10 11 12 13 15 17 19 21 23
loop(\(x,i).(10x + ~6),x,2)
A073553: 2 14 134 1334 13334 133334 1333334 13333334 133333334 1333333334 13333333334 133333333334 1333333333334 13333333333334 133333333333334 1333333333333334
((if ((x + ~2) mod (1 + (x div 4))) <= 0 then 1 else x) mod 2)
A086299: 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1
(2 - ((if (x mod (1 + (x div 4))) <= 0 then 1 else x) mod 2))
A266871: 1 1 1 1 1 1 1 1 2 1 2 1 1 1 2 1
((x + 2) + loop(\(x,i).i,(~3 + ((x + ~1) div 2)),1))
A154660: 3 4 5 6 7 8
A026447: 3 4 5 6 7 8 9 10 11 12 13 15 16 18 19 21
((if (8 mod (1 + (x div 2))) <= 0 then 1 else x) mod 2)
A255339: 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 1
((x + (if (x mod (3 + (x div 2))) <= 0 then 2 else 1)) div 2)
A135304: 1 1 1 2 2 3 4 4 4 5 5 6 6 7 7 8
((x + (if ((x div 4) mod 3) <= 0 then 2 else 1)) div 2)
A135636: 1 1 2 2 2 3 3 4 4 5 5 6 7
loop(\(x,i).(10x + 3),x,2)
A100893: 2 23 233 2333 23333
A198972: 2 23 233 2333 23333 233333 2333333 23333333 233333333 2333333333 23333333333 233333333333 2333333333333 23333333333333 233333333333333 2333333333333333
loop(\(x,i).(10x + ~3),x,2)
A126109: 2 17 167 1667 16667 166667 1666667 16666667 166666667 1666666667 16666666667 166666666667 1666666666667 16666666666667 166666666666667 1666666666666667
(if x <= 0 then 1 else (4x3 + 6x))
A008532: 1 10 44 126 280 530 900 1414 2096 2970 4060 5390 6984 8866 11060 13590
loop(\(x,i).(10x + ~15),x,2)
A133473: 2 5 35 335 3335 33335 333335 3333335 33333335 333333335 3333333335 33333333335 333333333335 3333333333335 33333333333335 333333333333335
loop(\(x,i).(11x + ~5),x,2)
A199751: 2 17 182 1997 21962 241577 2657342 29230757 321538322 3536921537 38906136902 427967505917 4707642565082 51784068215897 569624750374862 6265872254123477
loop(\(x,i).x2,3,(5x + 2))
A016880: 256 5764801 429981696 6975757441 54875873536 282429536481 1099511627776 3512479453921 9682651996416 23811286661761 53459728531456 111429157112001 218340105584896 406067677556641 722204136308736 1235736291547681
loop(\(x,i).(x2 + x),1,(5x + 2))
A177059: 6 56 156 306 506 756 1056 1406 1806 2256 2756 3306 3906 4556 5256 6006
loop(\(x,i).x3,1,(5x + 2))
A016875: 8 343 1728 4913 10648 19683 32768 50653 74088 103823 140608 185193 238328 300763 373248 456533
loop(\(x,i).x3,2,(5x + 2))
A016881: 512 40353607 5159780352 118587876497 1207269217792 7625597484987 35184372088832 129961739795077 406671383849472 1119130473102767 2779905883635712 6351461955384057 13537086546263552 27206534396294947
loop(\(x,i).x2,3,10x)
A017276: 0 100000000 25600000000 656100000000 6553600000000 39062500000000 167961600000000 576480100000000 1677721600000000 4304672100000000 10000000000000000 21435888100000000 42998169600000000
loop(\(x,i).x3,1,10x)
A017271: 0 1000 8000 27000 64000 125000 216000 343000 512000 729000 1000000 1331000 1728000 2197000 2744000 3375000
loop(\(x,i).x3,2,10x)
A017277: 0 1000000000 512000000000 19683000000000 262144000000000 1953125000000000 10077696000000000 40353607000000000 134217728000000000 387420489000000000 1000000000000000000 2357947691000000000
loop(\(x,i).x2,1,((x + 2) + (x div 5)))
A328558: 4 9 16 25 36 64 81 100 121 144 196 225 256 289 324 400
((x * (1 + loop(\(x,i).(2x2 + x),2,2))) div 2)
A242063: 0 105 211 316 422 527 633 738 844 949 1055
(2 + loop(\(x,i).2x,x,(x2 + 5x)))
A096367: 2 14 58 194 578 1602 4226 10754 26626 64514 153602 360450 835586 1916930 4358146 9830402
loop(\(x,i).(3 * ((x + 1) - (2 * (i mod 2)))),x,2)
A135522: 2 3 12 33 102 303 912 2733 8202 24603 73812 221433 664302 1992903 5978712 17936133
(2 + (if ((x + 1) mod 8) <= 0 then 3 else x))
A097377: 2 3 4 5 6 7 8 5 10 11 12 13 14 15 16 5
(loop(\(x,i).2x,x,(x + 12)) div 2)
A159694: 6 13 28 60 128 272 576 1216 2560 5376 11264 23552 49152 102400 212992 442368
loop(\(x,i).((6x + 2) - (i mod 2)),x,2)
A037491: 2 13 80 481 2888 17329 103976 623857 3743144 22458865 134753192 808519153 4851114920 29106689521 174640137128 1047840822769
((x + (loop(\(x,i).(x + (i * i)),x,2) div 3)) div 2)
A175812: 0 1 2 4 7 12 18 27 38 52 69 90 114 143 176 214
loop(\(x,i).(x div (~2 + (x mod 2))),2,(3x + 2))
A302773: 1 5 2 11 7 17 5 23 13 29 8 35 19 41 11 47
loop(\(x,i).((2x3 + x) div 3),x,2)
A099185: 2 6 146 2074806 4611686018427387903 4611686018427387903 4611686018427387903
(2 + (x * (if (x mod 2) <= 0 then 2 else 3x2)))
A244434: 2 5 6 83
loop(\(x,i).x2,1,((3x2 + x) div 2))
A100256: 0 4 49 225 676 1600 3249 5929 10000 15876 24025 34969 49284 67600 90601 119025
loop(\(x,i).((4x + 2) - (i mod 3)),x,2)
A037521: 2 9 36 146 585 2340 9362 37449 149796 599186 2396745 9586980 38347922 153391689 613566756 2454267026
loop(\(x,i).((3x + 2) - (i mod 3)),x,2)
A037520: 2 7 21 65 196 588 1766 5299 15897 47693 143080 429240 1287722 3863167 11589501 34768505
((x * loop(\(x,i).(x * (x - i)),2,(x + 3))) div 2)
A293615: 0 60 360 1260 3360 7560 15120 27720 47520 77220 120120 180180 262080 371280 514080 697680
(2x * loop(\(x,i).(x + ((~1 + i) * i)),(x + ~2),1))
A319575: 0 2 4 6 24 90 252 574 1136 2034 3380 5302 7944 11466 16044 21870
loop(\(x,i).((8x + 1) + (x mod 2)),x,2)
A037493: 2 17 138 1105 8842 70737 565898 4527185 36217482 289739857 2317918858 18543350865 148346806922 1186774455377 9494195643018 75953565144145
loop(\(x,i).(4x * (i * (1 + (2 * i)))),x,2)
A122551: 2 24 960 80640 11612160 2554675200 797058662400 334764638208000 182111963185152000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + ((x - (i mod 4)) div 2)),x,2)
A222431: 2 3 4 5 8 12 18 26 40 60 90 134 202 303 454 680
(2 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))
A028815: 2 3 4 6 8 12 14 18 20 24 30 32 38 42 44 48
loop(\(x,i).((x + 1) * (2 - (x div (1 + (2 * i))))),x,2)
A157671: 2 6 7 8 18 19 20 21 22 23 24 25 26 54 55 56
(loop(\(x,i).(x2 + 1),(4x + 4),x) div 2)
A262298-A102910: 13 4611686018427387903
A322517-A228033: 13 4611686018427387903 4611686018427387903
A257375: 13 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A257369-A257308: 13 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).4x,(5x + 4),2)
A320861: 512 524288 536870912 549755813888 562949953421312 576460752303423488 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(10x + 8))
A017366: 64 324 784 1444 2304 3364 4624 6084 7744 9604 11664 13924 16384 19044 21904 24964
loop(\(x,i).x2,2,(10x + 8))
A017368: 4096 104976 614656 2085136 5308416 11316496 21381376 37015056 59969536 92236816 136048896 193877776 268435456 362673936 479785216 623201296
((x + 2) + loop(\(x,i).(x * (2 + i)),4,(x + 1)))
A158310: 362 723 1084 1445 1806 2167 2528 2889 3250 3611 3972 4333 4694 5055 5416 5777
((x + 2) + (if (x + ~1) <= 0 then x else ((x + 1) * (x mod 2))))
A227906: 2 4 4 9 6 13 8 17 10 21 12 25 14 29 16 33
(((x2 + x) + (if (x + ~4) <= 0 then 2 else 0)) div 2)
A261993: 1 2 4 7 11 15 21 28 36 45 55 66 78 91 105 120
(((~x2 + ~x) + loop(\(x,i).2x,(x div 2),2)) div 2)
A163417: 1 0 ~1 ~4 ~6 ~11 ~13 ~20 ~20 ~29 ~23 ~34 ~14 ~27 23 8
(x + ((if (x mod 2) <= 0 then 1 else x) + ((x2 + x) div 2)))
A267353: 1 3 6 12 15 25 28 42 45 63 66 88 91 117 120 150
(2 + loop(\(x,i).(2x2 + ~x + ~1),(x + ~1),x))
A201363: 2 3 7
A062615: 2 3 7 379
(((~x2 + x) + loop(\(x,i).3x,x,2)) div 2)
A182453: 1 3 8 24 75 233 714 2166 6533 19647 59004 177092 531375 1594245 4782878 14348802
((x * ((~x + 1) + loop(\(x,i).2x,(x + 2),x))) div 2)
A059938: 0 4 31 141 506 1590 4593 12523 32740 82908 204755 495561 1179582 2768818 6422437 14745495
(((~1 + (x mod 5)) mod (if x <= 0 then 1 else x)) mod 2)
A327205: 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0
(2 * ((x mod 10) mod (if x <= 0 then 1 else x)))
A088116-A069816: 0 0 0 0 0 0 0 0 0 0 0 2 4 6 8 10
((x + 2) - (((x + 1) mod 4) mod (if x <= 0 then 1 else x)))
A256405: 2 3 3 5 5 5 5 9 9 9 9 13 13 13 13 17
(2x - (((x div 4) - (if x <= 0 then 1 else x)) div 2))
A097911: 1 3 5 8
A073608: 1 3 5 8 10 12
A090846: 1 3 5 8 10 12 15 17 19 22 24 27 29 31 34 36
(2 + ((4x div (x + 2)) + (if x <= 0 then 1 else x)))
A107907: 3 4 6 7 8 9 11 12 13 14 15 16 17 18 19 20
(2x * loop(\(x,i).(x * (2 + (x mod 4))),x,1))
A269760: 0 6 60 450 3000 18750 112500 656250 3750000 21093750 117187500 644531250 3515625000 19042968750 102539062500 549316406250
((x * (1 + (x * loop(\(x,i).x3,2,x)))) div 2)
A168119: 0 1 1025 88575 2097154 24414065 181398531 988663375 4294967300 15690529809 50000000005 142655835311 371504185350 896080197025 2024782584839 4324877929695
((x2 + ~1) + loop(\(x,i).(~1 + ((x div 2) + i)),x,2))
A267882: 1 1 4 10 19 30 43 58 75 94 115 138 163 190 219 250
((x + 2) + (if (x + ~12) <= 0 then 1 else 2))
A154660: 3 4 5 6 7 8
A191838-A118955: 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19
(loop(\(x,i).(2 - (x div (1 + (x mod 4)))),2,x) div 2)
A335570-A305027-A303912-A293551-A135225-A124445-A099233-A096815-A096751: 1 1 1 1 1 1 1 1 2 1 1 1 3 3 1 1
loop(\(x,i).(2 * ((x + 1) - (2 * (~x + (i mod 2))))),x,2)
A092165: 2 10 62 370 2222 13330 79982 479890 2879342 17276050 103656302 621937810 3731626862 22389761170 134338567022 806031402130
loop(\(x,i).((5x + 2) - (i mod 2)),x,2)
A037490: 2 11 57 286 1432 7161 35807 179036 895182 4475911 22379557 111897786 559488932 2797444661 13987223307 69936116536
loop(\(x,i).(2 * ((5x + 1) + i)),x,2)
A099669: 2 24 246 2468 24690 246912 2469134 24691356 246913578 2469135800 24691358022 246913580244 2469135802466 24691358024688 246913580246910 2469135802469132
(loop(\(x,i).(x2 div 16),2,x) div 2)
A344635: 0 0 0 0 0 0 0 0 0 0 1 1 2 3 4 6
loop(\(x,i).2x,x,(x + 18))
A079862: 18 38 80 168 352 736 1536 3200 6656 13824 28672 59392 122880 253952 524288 1081344
(loop(\(x,i).2x,x,(x + 16)) div 2)
A159696: 8 17 36 76 160 336 704 1472 3072 6400 13312 27648 57344 118784 245760 507904
(2x * loop(\(x,i).(4x + 2),4,2))
A004950-A004930: 0 1364 2728 4092 5456 6820 8184 9548 10912 12276 13640 15004 16368 17732 19096 20460
(((1 + (x div 2)) div (if (x mod 4) <= 0 then 2 else x)) mod 2)
A181011: 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0
loop(\(x,i).(11x + ~4),x,2)
A156341: 2 18 194 2130 23426 257682 2834498 31179474 342974210 3772716306 41499879362 456498672978 5021485402754 55236339430290 607599733733186 6683597071065042
((x + loop(\(x,i).(~1 + (x * (1 + i))),x,4)) div 2)
A067353: 2 4 11 41 199 1184 8273 66163 595439 5954354 65497849 785974133 10217663663 143047291204 2145709367969 34331349887399
((x - (if (x + ~2) <= 0 then 1 else (x * (x div 4)))) mod 2)
A133101: 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0
(2 + loop(\(x,i).(x + ((x div 4) + i)),4,x))
A295744: 13 16 17 19 23
(2 * loop(\(x,i).((x2 + 5x) div 2),2,x))
A168538: 0 24 84 204 414 750 1254 1974 2964 4284 6000 8184 10914 14274 18354 23250
((x + 2) + (((x + ~2) * (if x <= 0 then 1 else x2)) div 2))
A057580: 1 2 4 9 22
loop(\(x,i).2x,(x + (2 * (2x + (x mod 2)))),2)
A067480: 2 256 2048 262144 2097152 268435456 2147483648 274877906944 2199023255552 281474976710656 2251799813685248 288230376151711744 2305843009213693952 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + ((~1 + i) mod 3)),x,2)
A037513: 2 8 33 134 536 2145 8582 34328 137313 549254 2197016 8788065 35152262 140609048 562436193 2249744774
loop(\(x,i).(4x + ((x + 1) mod 4)),x,2)
A037744: 2 11 44 177 710 2843 11372 45489 181958 727835 2911340 11645361 46581446 186325787 745303148 2981212593
loop(\(x,i).(4x + ((x + ~1) mod 4)),x,2)
A037730: 2 9 36 147 590 2361 9444 37779 151118 604473 2417892 9671571 38686286 154745145 618980580 2475922323
(((~x + 2) - (if (x mod 2) <= 0 then (x2 div 2) else 2)) div 2)
A110315: 1 ~1 ~1 ~2 ~5 ~3 ~11 ~4 ~19 ~5 ~29 ~6 ~41 ~7 ~55 ~8
loop(\(x,i).(11x + ~2),x,2)
A199761: 2 20 218 2396 26354 289892 3188810 35076908 385845986 4244305844 46687364282 513561007100 5649171078098 62140881859076 683549700449834 7519046704948172
((x + loop(\(x,i).((x2 * i) div (x + 1)),x,2)) div 2)
A132346: 1 1 1 2 3 5 18
loop(\(x,i).((x + 2) + (((x + i) * i) div (x + 1))),x,2)
A109470: 2 5 9 14 20 27 36 46 57 69 82 96 111 127 144 162
(2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))
A338134-A322184-A245072-A240699-A215697-A211075-A075763-A065380-A065091-A056912-A038134: 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59
(2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x))
A332346-A243292-A240710-A215848-A136207-A115232-A066047-A020626-A020624-A020621: 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61
(~2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x))
A172367: 1 3 7 9 13 15 19 25 27 33 37 39 43 49 55 57
(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A322443-A322394-A316903-A301378-A295425-A242541-A238853-A238852-A234960-A233360-A231588-A229106-A228296-A219697-A216887-A216886-A216885-A216884-A216883-A196230-A176165-A171047-A171041-A171028-A164837-A163849-A137589-A124591-A124590-A118850-A118849-A118848-A110923-A100726-A100725-A095320-A095316-A095313-A095285-A082646-A080191-A079152-A078668-A077390-A077359-A073350-A070159-A069684-A069683-A069682-A069681-A069680-A069679-A069678-A069677-A069676-A069675-A062353-A061022-A058853-A057448-A055398-A052085-A050260-A050246-A049585-A049573-A049569-A049561-A049551-A049549-A038618-A038616-A038614-A030475-A030291-A000040: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53
(2 * compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A140777: 0 2 6 10 18 22 30 34 42 54 58 70 78 82 90 102
(2 + compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x))
A020581: 2 5 7 11 13 17
A045344: 2 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59
(2 + compr(\x.(2 - (loop(\(x,i).2x,x,2) mod (x + 2))),x))
A111774: 6 9 10 12 14 15 18 20 21 22 24 25 26 27 28 30
(loop(\(x,i).(x * i),x,(x + 1)) mod (x2 + 2x + 2))
A177353: 1 2 6 7 16 17 40 20 30 72 108 45 20 188 206 115
(2 + compr(\x.(x - (loop(\(x,i).2x,x,x) mod (x + 2))),x))
A144147: 2 3 5 6 7 10 11 13 14 17 19 22 23 26 29 30
(if x <= 0 then 1 else (2 * (x + ((x + ~2) * (x div 3)))))
A222011: 1 2 4 8
A052184: 1 2 4 8 12 16 28
(2 * loop(\(x,i).(2x + 3),x,(x2 + ~2x)))
A036800: 0 2 18 90 346 1146 3450 9722 26106 67578 169978 417786 1007610 2392058 5603322 12976122
(2 * loop(\(x,i).((x + (x mod 2)) * (1 + i)),2x,x))
A006548: 0 24 480 40320 2903040 479001600 74724249600 20922789888000 5690998849536000 2432902008176640000 4611686018427387903 4611686018427387903 4611686018427387903
(~3 mod loop(\(x,i).(2x + (i mod 2)),x,2))
A054111: 1 2 7 18 39 82 167 338 679 1362 2727 5458 10919 21842 43687 87378
loop(\(x,i).(3x + ((x + 1) mod 3)),x,2)
A037512: 2 6 19 59 177 532 1598 4794 14383 43151 129453 388360 1165082 3495246 10485739 31457219
((x - (if (x mod 3) <= 0 then 1 else (x * (x div 2)))) mod 2)
A218380: 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0
loop(\(x,i).2x,(x div 4),((x * (x div 2)) mod 2))
A236799: 0 0 0 1 0 0 0 2 0 0 0 4 0 0 0 8
(2 + loop(\(x,i).(x + (((1 + i) * i) div 2)),(x div 2),x))
A053436: 2 3 5 6 10 11 18 19 30 31 47 48 70 71 100 101
((x + 2) + (if (~2 + (x div 2)) <= 0 then 1 else 2x2))
A154660: 3 4 5 6 7 8
A144046: 3 4 5 6 7 8 80
(loop(\(x,i).(2x2 + 8x + 8),2,0) div (x + 2))
A180102: 100 66 50 40 33 28 25 22 20 18 16 15 14 13 12 11
(loop(\(x,i).(x + (i * i)),((x + 1) div 2),1) div (x + 2))
A026927: 0 0 0 1 1 2 1 3 3 5 4 7 6 9 8 12
((3 * (if (~x + 2) <= 0 then 2x else 1)) div (x + 2))
A163400: 1 1 3 3 4 4 4 4 4 4 5 5 5 5 5 5
loop(\(x,i).(x2 + ~1),(3x + 3),(x + 2))
A116232: 63 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((3 + loop(\(x,i).i,(x div 4),2)) mod (x + 2))
A109167: 1 2 1 0 4 4 4 4 5 5 5 5 6 6 6 6
(x2 - (loop(\(x,i).(x * i),(x + ~2),1) div (x + 2)))
A010409: 0 1 4 9 16 25 33 36
((x + 2) * ((x + 1) + (2 * ((if x <= 0 then 1 else x) mod 2))))
A063722: 6 12 12 30 30
((x + 2) * (if (~6 + (x div 2)) <= 0 then 1 else 2))
A250039-A248502: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 32 34
(if x <= 0 then 1 else ((x + 2) * (2 + (x div 2) - (x mod 2))))
A182455: 1 3 12 10 24 21 40 36 60 55 84 78 112 105 144 136
loop(\(x,i).x2,1,((x + 2) * (x div (~2 + (x mod 2)))))
A171522: 0 9 16 225 144 1225 576 3969 1600 9801 3600 20449 7056 38025 12544 65025
((2x + (if (x mod 4) <= 0 then 0 else x)) div (x + 2))
A276337-A160385: 0 1 1 1 1 2 2 2 1 2 2 2 1 2 2 2
((loop(\(x,i).(2 + (x * i)),x,2) + (x div 2)) div (x + 2))
A185349: 1 1 2 6 22 93
loop(\(x,i).x6,2,(x + 2))
A139572: 68719476736 150094635296999121 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 2) + ((x mod 8) mod (if x <= 0 then 1 else x)))
A331400-A317622: 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24
(if (~2 + (x mod (2 + (x mod 3)))) <= 0 then x else (x + 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A325402: 0 1 2 3 4 5 6 7 8 9 10 13 12 13 14 15
loop(\(x,i).(x * i),x,(3x2 + 10x + 8))
A225658: 8 21 80 390 2304 15960 126720 1134000 11289600 123742080 1480550400 19199980800 268240896000 4016428416000 64163222323200 1089292748544000
loop(\(x,i).(x - (x div 8)),3,(x + ~2))
A102672: 0 0 0 1 2 3 4 5 6 7 7 7 7 8 9 10
(2x + (if (x + ~12) <= 0 then 1 else 0))
A064679: 1 3 5 7 9 11 13 15 17 19 21 23 25 26 28 30
(2x + (if (x + ~10) <= 0 then 1 else 0))
A137803-A064719-A059547-A059533: 1 3 5 7 9 11 13 15 17 19 21 22 24 26 28 30
(2x + (x div 2) - (if (x mod 4) <= 0 then 0 else 1))
A187331: 0 1 4 6 10 11 14 16 20 21 24 26 30 31 34 36
(2x + (if (x + ~10) <= 0 then 2 else 1))
A246410: 2 4 6 8 10 12 14 16 18 20 22 23 25 27 29 31
(2x + (if x <= 0 then 1 else ((~x + (x mod 2)) div 3)))
A025055: 1 2 3 5 6 8 10 12 13 15 16 18 20 22 23 25
(if x <= 0 then 1 else (4x - (2 mod (~2x + 1))))
A270545: 1 4 9 15 21 27 33 39 45 51 57 63 69 75 81 87
(2x + loop(\(x,i).10x,x,1))
A173835: 1 12 104 1006 10008 100010 1000012 10000014 100000016 1000000018 10000000020 100000000022 1000000000024 10000000000026 100000000000028 1000000000000030
(~2x + loop(\(x,i).10x,x,1))
A173834: 1 8 96 994 9992 99990 999988 9999986 99999984 999999982 9999999980 99999999978 999999999976 9999999999974 99999999999972 999999999999970
(((~1 + (x div 2)) * (x div 2)) + (if x <= 0 then 1 else 2x))
A152919: 1 2 4 6 10 12 18 20 28 30 40 42 54 56 70 72
(2x + (if ((x div 2) mod 2) <= 0 then 1 else (x mod ~2)))
A095028: 1 3 4 5 9
A047600: 1 3 4 5 9 11 12 13 17 19 20 21 25 27 28 29
(2x + (if (x + ~10) <= 0 then 1 else 2))
A293167-A246413-A246411-A158333: 1 3 5 7 9 11 13 15 17 19 21 24 26 28 30 32
(2x + (if ((x div 2) mod 2) <= 0 then 2 else ((x + 1) mod 2)))
A047433: 2 4 5 6 10 12 13 14 18 20 21 22 26 28 29 30
(2x + (if (x + ~4) <= 0 then 1 else (x + ~4)))
A318919: 1 3 5 7 9 11 14 17 20 23 26 29 32 35 38 41
loop(\(x,i).((x div 5) + (x mod 2)),2,2x)
A000999: 0 0 0 1 1 0 0 0 1 1 0 0 0 2 2 1
(2x + (if ((x div ~2) mod 2) <= 0 then (x mod 2) else 2))
A047507: 0 4 6 7 8 12 14 15 16 20 22 23 24 28 30 31
(2x + ((x + (if (~2 + (x div 2)) <= 0 then 2 else 0)) div 2))
A284534: 1 3 6 8 11 13 15 17 20 22 25 27 30 32 35 37
(2x + ((~x + loop(\(x,i).(x * i),x,2)) div (x + 2)))
A280031: 1 2 4 7 15 43
loop(\(x,i).(x + (((1 + i) * i) div 2)),(x + 2),2x)
A010897: 4 12 24 41 64 94
(3x + (if (~4 + (x div 2)) <= 0 then 1 else 0))
A190084: 1 4 7 10 13 16 19 22 25 28 30 33 36 39 42 45
(3x + (x div (1 + (if (x + ~2) <= 0 then 1 else 2))))
A081842: 0 3 7 10 13 16 20 23 26 30 33 36 40 43 46 50
(3x + (if (~2 + (x div 3)) <= 0 then 2 else 1))
A189934: 2 5 8 11 14 17 20 23 26 28 31 34 37 40 43 46
(3x + (if (x mod 2) <= 0 then 1 else 8))
A166521: 1 11 7 17 13 23 19 29 25 35 31 41 37 47 43 53
(2x2 * loop(\(x,i).(x2 * (2 + i)),2,x))
A286930: 0 72 4608 52488 294912 1125000 3359232 8470728 18874368 38263752 72000000 127552392 214990848 347530248 542126592 820125000
(loop(\(x,i).((x + 2) + (x div (1 + i))),x,0) - (x div 2))
A097383: 0 2 3 6 8 11 13 17 20 24 27 31 34 38 41 46
(loop(\(x,i).i,(x + ~9),1) + (x div 2))
A029031: 1 1 2 2 3 3 4 4 5 5 6 7 9 10 12 13
(((x2 - (if x <= 0 then 0 else 1)) div 3) - (x div 2))
A337484: 0 0 0 1 3 6 8 13 17 22 28 35 41 50 58 67
((if (x mod 2) <= 0 then 1 else 10) + (x div 2))
A318486-A303850-A303848: 1 10 2 11 3 12 4 13 5 14 6 15 7 16 8 17
((if (x mod 2) <= 0 then (x div 2) else (2x + ~2)) * (x div 2))
A174595: 0 0 1 4 4 16 9 36 16 64 25 100 36 144 49 196
((if (x mod 2) <= 0 then (x + 1) else 8) - (x div 2))
A317386: 1 8 2 7 3 6 4 5 5 4 6 3 7 2 8 1
loop(\(x,i).((~x + 2) div 2),((x + 1) mod 4),(x div 2))
A066746: 1 0 0 1 0 1 0 3 ~1 1 0
((((if (~2 + (x div 2)) <= 0 then 2 else x) div 2) mod 2) + (x div 2))
A306921: 1 1 2 2 3 3 4 4 4 4 6 6 6 6 8 8
(loop(\(x,i).((x + 2) + ((2 + i) * i)),x,2) - (x div 2))
A208995: 2 7 16 33 58 95 144 209 290 391 512 657 826 1023 1248 1505
((if (x mod 2) <= 0 then 12 else x) - (x div 2))
A059857: 12 1 11 2 10 3 9 4 8 5 7 6 6 7 5 8
(x + ((2 * (if (~x + 2) <= 0 then 4 else 1)) + (x div 2)))
A189818: 2 3 11 12 14 15 17 18 20 21 23 24 26 27 29 30
(x + ((if (x mod 2) <= 0 then 1 else (x div 4)) + (x div 2)))
A107432: 1 1 4 4 7 8 10 11 13
(loop(\(x,i).(x + ((x + (i mod 2)) * i)),x,0) - (x mod 2))
A133798: 0 0 3 14 75 454 3185 25486 229383 2293838 25232229 302786758 3936227867 55107190150 826607852265 13225725636254
((if (~2 + (x mod 8)) <= 0 then 0 else 1) + (x mod 2))
A143668: 0 1 0 2 1 2 1 2 0 1 0 2 1 2 1 2
(loop(\(x,i).(3x + 1),(x + ~1),1) + (x mod 2))
A152011: 1 2 4 14 40 122 364 1094 3280 9842 29524 88574 265720 797162 2391484 7174454
((if ((2 + (x div 2)) mod 4) <= 0 then 2 else 1) * (x mod 2))
A292252: 0 1 0 1 0 2 0 1 0 1 0 1 0 2 0 1
((if (~x + 2) <= 0 then (2x * (x mod 2)) else 1) + (x mod 2))
A266220: 1 2 0 7 0 11 0 15 0 19 0 23 0 27 0 31
(loop(\(x,i).(4x + 4),(x div 2),1) + (x mod 2))
A221049: 1 2 8 9 36 37 148 149 596 597 2388 2389 9556 9557 38228 38229
loop(\(x,i).(x + ((x + 1) * i)),(1 + (x div 2)),(x mod 2))
A030494: 1 3 5 11 23 47 119 239 719 1439 5039 10079 40319 80639 362879 725759
(loop(\(x,i).(5x + 1),x,1) + (x mod 2))
A102239: 1 7 31 157 781 3907 19531 97657 488281 2441407 12207031 61035157 305175781 1525878907 7629394531 38146972657
(loop(\(x,i).(5x + ~2),x,1) - (x mod 2))
A081340: 1 2 13 62 313 1562 7813 39062 195313 976562 4882813 24414062 122070313 610351562 3051757813 15258789062
loop(\(x,i).(~1 + (2 * (x + (i mod 2)))),(x + ~1),(x mod 2))
A084183: 0 1 1 5 3 21 11 85 43 341 171 1365 683 5461 2731 21845
(1 - loop(\(x,i).(2 * (x - (i mod 2))),(x + ~1),(x mod 2)))
A092808: 1 0 3 1 11 5 43 21 171 85 683 341 2731 1365 10923 5461
((if (x + ~10) <= 0 then 1 else 2) - (x mod 2))
A025827: 1 0 1 0 1 0 1 0 1 0 1 1 2 1 2 1
(loop(\(x,i).(4x + ~2),(x + 1),2) - (x mod 2))
A088556: 6 21 86 341 1366 5461 21846 87381 349526 1398101 5592406 22369621 89478486 357913941 1431655766 5726623061
((2 + (loop(\(x,i).2x,x,2) mod (x + 1))) * (x mod 2))
A158327: 0 2 0 2 0 6 0 2 0 6 0 6 0 6 0 2
((if (x mod 3) <= 0 then ((x + 1) mod 2) else 2) - (x mod 2))
A131017: 1 1 2 ~1 2 1 1 1 2 ~1 2 1 1 1 2 ~1
((if (x mod 4) <= 0 then 1 else 8) + (x mod 2))
A269222: 1 9 8 9 1 9 8 9 1 9 8 9 1 9 8 9
loop(\(x,i).(x * (x div 2)),x,(8 - (x mod 2)))
A019281: 8 21 512
((1 + (if (x mod 3) <= 0 then 2 else 0)) * (2 - (x mod 2)))
A089128: 6 1 2 3 2 1 6 1 2 3 2 1 6 1 2 3
(loop(\(x,i).(x * (x + i)),(x div 2),2) div (2 - (x mod 2)))
A171708: 1 2 3 6 24
A160683: 1 2 3 6 24 48
(2x2 + ((if (~x + 2) <= 0 then 2 else 1) + (x mod 2)))
A049486: 1 4 10 21 34 53 74 101 130 165 202 245 290 341 394 453
((x mod 2) - loop(\(x,i).(2 * (x - (i mod 2))),x,(x mod 2)))
A270797: 0 1 4 3 20 11 84 43 340 171 1364 683 5460 2731 21844 10923
((x2 + 2x) + (loop(\(x,i).(x * i),x,2) + (x mod 2)))
A057582: 2 6 12 28 72
loop(\(x,i).(11x + 5),x,2)
A199021: 2 27 302 3327 36602 402627 4428902 48717927 535897202 5894869227 64843561502 713279176527 7846070941802 86306780359827 949374583958102 10443120423539127
loop(\(x,i).(11x + 10),x,2)
A199019: 2 32 362 3992 43922 483152 5314682 58461512 643076642 7073843072 77812273802 855935011832 9415285130162 103568136431792 1139249500749722 12531744508246952
((x2 * (1 + loop(\(x,i).x3,2,x))) div 2)
A168153: 0 1 1026 88578 2097160 24414075 181398546 988663396 4294967328 15690529845 50000000050 142655835366 371504185416 896080197103 2024782584930 4324877929800
loop(\(x,i).(x + ((3x + 6) div (1 + i))),x,2)
A166830: 2 8 18 33 54 82 118 163 218 284 362 453 558 678 814 967
(2 * (x + loop(\(x,i).(6x + ~1),2,x)))
A277986: ~14 60 134 208 282 356 430 504 578 652 726 800 874 948 1022 1096
loop(\(x,i).(x + (x div (2 + ((~1 + i) mod 4)))),x,2)
A133463: 2 3 4 5 6 9 12 15 18 27 36 45 54 81 108 135
((4x + 3) div (if (~x + 2) <= 0 then x else 2))
A329509: 1 3 5 5 4 4 4 4 4 4 4 4 4 4 4 4
((x + (if (~2 + (x div 2)) <= 0 then 1 else (x * (x div 2)))) mod 2)
A154388: 1 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0
((x * loop(\(x,i).(x2 * ((x + ~1) + i)),2,x)) div 2)
A168660: 0 1 576 30618 532480 4921875 30373056 141649396 537919488 1745783685 5005000000 12978455886 30976598016 68960620183 144680034240 288410625000
loop(\(x,i).(x4 + x3 + ~1),x2,2)
A228241: 2 23 4611686018427387903
loop(\(x,i).(x4 + 3),x2,2)
A301637: 2 19 4611686018427387903
(~x mod ((~x2 + ~2) + loop(\(x,i).2x,x,1)))
A052516: 0 0 0 0 0 0 20 70 182 420 912 1914 3938 8008 16172 32526
((x2 * loop(\(x,i).(~x3 + 2),2,2)) div 2)
A174339: 0 109 436 981 1744 2725 3924 5341 6976 8829 10900 13189 15696 18421 21364 24525
(loop(\(x,i).(x * (~2 + (x * (2 + i)))),2,x2) div 2)
A151750: 0 1 3160
((x2 * (x + loop(\(x,i).x3,2,x))) div 2)
A168189: 0 1 1028 88587 2097184 24414125 181398636 988663543 4294967552 15690530169 50000000500 142655835971 371504186208 896080198117 2024782586204 4324877931375
((x2 * (x + loop(\(x,i).x2,2,x2))) div 2)
A168188: 0 1 516 29538 524320 4882875 30233196 141237796 536871168 1743392565 5000000500 12968712966 30958682976 68929247023 144627328860 288325197000
((x2 + loop(\(x,i).x2,2,x3)) div 2)
A168176: 0 1 2050 265725 8388616 122070325 1088391186 6920643625 34359738400 141214768281 500000000050 1569214188421 4458050224200 11649042561325 28346956187746 64873168945425
(loop(\(x,i).(2x - (x div (1 + (x mod 2)))),x,x) div 2)
A085062: 0 1 1 4 2 4 3 13 4 7 5 13 6 10 7 40
((x * loop(\(x,i).(x * ((x + ~1) + i)),2,x2)) div 2)
A168372: 0 1 272 9963 131584 978125 5042736 20185207 67125248 193739769 500050000 1179054371 2580014592 5302435333 10330792304 19222059375
(loop(\(x,i).(x3 + x),1,x3) div 2)
A168187: 0 1 260 9855 131104 976625 5038956 20176975 67109120 193710609 500000500 1178974511 2579891040 5302250785 10330524764 19221681375
(loop(\(x,i).(x * ((x + ~1) + i)),2,x3) div 2)
A071235: 0 1 2080 266085 8390656 122078125 1088414496 6920702425 34359869440 141215033961 500000500000 1569215074141 4458051717120 11649044974645 28346959952416 64873174640625
(if ((x * (x mod 3)) mod 5) <= 0 then 0 else x)
A102392: 0 1 2 0 4 0 0 7 8 0 0 11 0 13 14 0
(x + (if ((x div 2) mod 2) <= 0 then (1 + (2 * (x mod 2))) else 0))
A284307: 1 4 2 3 5 8 6 7 9 12 10 11 13 16 14 15
(x + (if (x mod 2) <= 0 then 12x else 0))
A317326: 0 1 26 3 52 5 78 7 104 9 130 11 156 13 182 15
(x + (if (x mod 2) <= 0 then (3 * (x + (x div 2))) else 0))
A317311: 0 1 11 3 22 5 33 7 44 9 55 11 66 13 77 15
(x + (5x * (if (x mod 2) <= 0 then 2 else 0)))
A317322: 0 1 22 3 44 5 66 7 88 9 110 11 132 13 154 15
(x + loop(\(x,i).(i - ((1 + i) mod (x + 1))),(x + ~2),0))
A233524: 0 1 2 4 5 8
A004761: 0 1 2 4 5 8 9 10 11 16 17 18 19 20 21 22
(x * loop(\(x,i).(10x + 1),x,0))
A053422: 0 1 22 333 4444 55555 666666 7777777 88888888 999999999 11111111110 122222222221 1333333333332 14444444444443 155555555555554 1666666666666665
(x + loop(\(x,i).(1 + (x * (2 + (x div 3)))),x,0))
A214853: 0 2 5 13 55
(~x + loop(\(x,i).(1 + (((x + 1) div 2) * (x + i))),x,0))
A322399: 0 0 2 12 149
(x + loop(\(x,i).(1 + (x * i)),(x + ~5),1))
A019532: 1 2 3 4 5 6 8 12 24
(~2 mod (x + loop(\(x,i).i,(x + ~5),1)))
A092755: 0 0 1 2 3 4 5 7 9 11 13 15 17 19 21 23
(x + loop(\(x,i).(2 + (x div 2)),(~3 + (x div 2)),1))
A039218: 1 2 3 4 5 6 7 8 10 11 13 14 15 16 17 18
(if x <= 0 then 1 else 19x)
A048844: 1 19 38 57 76 95 114 133 152 171 190 209 228 247 266 285
(if x <= 0 then 1 else 23x)
A048845: 1 23 46 69 92 115 138 161 184 207 230 253 276 299 322 345
loop(\(x,i).(x + i),(x + ~11),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A332166: 0 1 2 3 4 5 6 7 8 9 10 11 13 16 20 25
(x + loop(\(x,i).(2 * i),(x + ~12),1))
A246092: 1 2 3 4 5 6 7 8 9 10 11 12 13 15 18 21
(x * (~1 + ((x + (if (x mod 2) <= 0 then 2 else x)) mod 3)))
A110665: 0 1 0 ~3 ~4 0 6 7 0 ~9 ~10 0 12 13 0 ~15
(x + loop(\(x,i).(((x + 1) * i) div 3),(x + ~1),1))
A118987: 1 2 2 3 5 7 11 19
(x + loop(\(x,i).(2 * ((x + ~1) + (i div 2))),(x + ~1),1))
A023105: 1 2 2 3 4 7 12 23 44 87 172 343 684 1367 2732 5463
(x + ((~x + 1) mod loop(\(x,i).4x,(x + ~1),1)))
A092679: 0 1 5 17
A046231: 0 1 5 17 65 257 1025 4097 16385 65537 262145 1048577 4194305 16777217 67108865 268435457
(x * loop(\(x,i).(2 * ((x + (x div 2)) * i)),(x + ~1),1))
A052700: 0 1 4 36 432 6480 116640 2449440 58786560 1587237120 47617113600 1571364748800 56569130956800 2206196107315200 92660236507238400 4169710642825728000
(x * loop(\(x,i).(x * (x - (x div ~2))),(x + ~1),1))
A327335: 0 1 4 18 216
(x + loop(\(x,i).(x * i),((1 + (x div 3)) div 2),1))
A178160: 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 21
(x + (if ((x + 2) mod 9) <= 0 then 2 else 1))
A323785: 1 2 3 4 5 6 7 9 9 10 11 12 13 14 15 16
(1 div (if ((x div (~3 + (x mod 2))) mod 2) <= 0 then 1 else x))
A077605-A070936: 1 1 0 1 1 0 1 1 0 0 1 1 1 0 0 1
loop(\(x,i).x3,1,7x)
A016983: 0 343 2744 9261 21952 42875 74088 117649 175616 250047 343000 456533 592704 753571 941192 1157625
loop(\(x,i).x3,2,7x)
A016989: 0 40353607 20661046784 794280046581 10578455953408 78815638671875 406671383849472 1628413597910449 5416169448144896 15633814156853823 40353607000000000 95151694449171437 208215748530929664
(x + (if ((x div 3) - (x mod 3)) <= 0 then 2 else 1))
A193768: 2 3 4 4 6 7 7 8 10 10 11 12 13 14 15 16
(x * (1 + (2 * (if (x mod 5) <= 0 then 0 else 2))))
A109046: 0 5 10 15 20 5 30 35 40 45 10 55 60 65 70 15
(x + (if ((x + 1) mod 10) <= 0 then 2 else 1))
A033862: 1 2 3 4 5 6 7 8 9 11 11 12 13 14 15 16
(x * (1 + loop(\(x,i).(2x2 + 8),2,2)))
A004948-A004928: 0 521 1042 1563 2084 2605 3126 3647 4168 4689 5210 5731 6252 6773 7294 7815
(1 div (if (x mod (4 + (x div 4))) <= 0 then 1 else x))
A253903: 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0
(x * (1 + loop(\(x,i).(x2 - (x div 2)),4,2)))
A004952-A004932: 0 3571 7142 10713 14284 17855 21426 24997 28568 32139 35710 39281 42852 46423 49994 53565
(x + loop(\(x,i).(2 + (x div 2)),(x + ~8),1))
A039219-A038365: 1 2 3 4 5 6 7 8 9 11 13 14 15 16 17 18
(x + loop(\(x,i).(3 * i),(x + ~8),1))
A079238-A079042: 1 2 3 4 5 6 7 8 9 12 16 20 24 28 32 36
loop(\(x,i).(x + i),(~1 + ((x - ((x div 2) mod 2)) div 2)),x)
A028722: 0 1 2 3 5 6 7 10 14
(~x + loop(\(x,i).(2 * (x - i)),(x + ~1),5))
A270841: 5 4 6 9 14 23 40 73 138 267 524 1037 2062 4111 8208 16401
(x + (if (x + ~2) <= 0 then 1 else ((x + 2) div 5)))
A257500-A210940-A121208: 1 2 3 4 5 6 7 8 10 11 12 13 14 16 17 18
(x - loop(\(x,i).(x2 div (x + 2)),5,x))
A103303: 0 1 2 3 4 5 6 7 8 9
A137180: 0 1 2 3 4 5 6 7 8 9 9 10 10 10 10 10
(if (x mod 2) <= 0 then (5 * (x + (x div 2))) else x)
A317315: 0 1 15 3 30 5 45 7 60 9 75 11 90 13 105 15
(if x <= 0 then 1 else (2x4 + 4x3 + x))
A274822: 1 7 66
(x + (if (x + ~4) <= 0 then x else (2x + ~5)))
A130174: 0 2 4 6 8 10 13 16 19 22 25 28 31 34 37 40
(1 div (if ((x mod 3) - ((x div 2) mod 2)) <= 0 then 1 else x))
A275661: 1 1 0 1 0 0 1 1 0 1 1 0 1 0 0 1
(x + (if ((x div 2) mod 2) <= 0 then 2 else (~1 + (2 * (x mod 2)))))
A298364: 2 3 1 4 6 7 5 8 10 11 9 12 14 15 13 16
(x + (loop(\(x,i).(~1 + ((x + 2) * i)),x,0) div 3))
A088110: 0 1 3 9
A180632: 0 1 3 9 33 153
(x + (3 * loop(\(x,i).i,(x + ~8),1)))
A154660: 3 4 5 6 7 8
A321153: 3 4 5 6 7 8 9 10 11 12 16 20 24
loop(\(x,i).x2,1,(7x + 3))
A017018: 9 100 289 576 961 1444 2025 2704 3481 4356 5329 6400 7569 8836 10201 11664
loop(\(x,i).x2,2,(7x + 3))
A017020: 81 10000 83521 331776 923521 2085136 4100625 7311616 12117361 18974736 28398241 40960000 57289761 78074896 104060401 136048896
loop(\(x,i).(x + (2 * i)),((~1 + (x div 2)) div 3),x)
A084690: 0 1 2 3 4 5 6 7 10
A329298: 0 1 2 3 4 5 6 7 10 11 12 13 14 15 20 21
(x * (loop(\(x,i).(x2 + 1),2,(x + 1)) div 3))
A121782: 0 8 66 288 900 2280 4998 9856 17928 30600 49610 77088 115596 168168 238350 330240
loop(\(x,i).x2,1,(7x + 6))
A017054: 36 169 400 729 1156 1681 2304 3025 3844 4761 5776 6889 8100 9409 10816 12321
loop(\(x,i).x2,2,(7x + 6))
A017056: 1296 28561 160000 531441 1336336 2825761 5308416 9150625 14776336 22667121 33362176 47458321 65610000 88529281 116985856 151807041
(x + (3 * ((x2 + 2) + (if x <= 0 then 1 else 2))))
A257496: 9 16 26 42
(x * loop(\(x,i).(4x2 + 2),2,3))
A004973-A004953: 0 5778 11556 17334 23112 28890 34668 40446 46224 52002 57780 63558 69336 75114 80892 86670
(x * loop(\(x,i).(x2 + 4x + 6),2,3))
A004969-A004949: 0 843 1686 2529 3372 4215 5058 5901 6744 7587 8430 9273 10116 10959 11802 12645
compr(\x.(1 - (loop(\(x,i).(x + (x div 2)),x,2) mod 3)),x)
A087791: 0 2 5 6 7 10 12 13 16 18 20 21 24 26 27 29
compr(\x.((x2 + 2) mod loop(\(x,i).x2,2,3)),x)
A156797: 22 59 103 140 184 221 265 302 346 383 427 464 508 545 589 626
(if (x mod 3) <= 0 then (x div 3) else 3x)
A130724: 0 3 6 1 12 15 2 21 24 3 30 33 4 39 42 5
loop(\(x,i).x5,1,3x)
A016769: 0 243 7776 59049 248832 759375 1889568 4084101 7962624 14348907 24300000 39135393 60466176 90224199 130691232 184528125
(if (x mod 2) <= 0 then (~3x + 1) else 3x)
A084060: 1 3 ~5 9 ~11 15 ~17 21 ~23 27 ~29 33 ~35 39 ~41 45
loop(\(x,i).(x * (1 + (6 * i))),3,x)
A138129: 0 1729 3458 5187 6916 8645 10374 12103 13832 15561 17290 19019 20748 22477 24206 25935
(x - loop(\(x,i).(~x + ((x div 3) mod 2)),3,x))
A154571: 0 3 4 5 7 8 12 15 16 17 19 20 24 27 28 29
(x + (loop(\(x,i).(2x2 + ~1),2,x) div 3))
A058581: 0 1 34 195 644 1605 3366 6279 10760 17289 26410 38731 54924 75725 101934 134415
(x + (3 * loop(\(x,i).((x div 2) + i),4,x)))
A297290-A296760: 18 19 20 21 22 23 24 25 26 27 28 29 30 31 35 36
((x2 + ~x) div (x + (if x <= 0 then 1 else (x div 3))))
A083920: 0 0 1 1 2 3 3 4 5 6 6 7 8 9 10 10
(x + (if (~x + 2) <= 0 then ((x * (x div 3)) mod 2) else 1))
A004079: 1 2 2 4 4 6 6 7 8 10 10 12
(~x + loop(\(x,i).x2,1,(1 + ((x2 + x) div 2))))
A123350: 1 3 14 46 117 251 478 834 1361 2107 3126 4478 6229 8451 11222 14626
(x * loop(\(x,i).((x2 + ~x) div 2),2,(x + 3)))
A151974: 0 15 90 315 840 1890 3780 6930 11880 19305 30030 45045 65520 92820 128520 174420
compr(\x.(loop(\(x,i).(2x + ~1),x,x) mod (x + 3)),x)
A154115: 0 2 4 8 10 14 16 20 26 28 34 38 40 44 50 56
(x + loop(\(x,i).(((x + i) div 2) * (2 + i)),(x + ~2),1))
A337638: 1 2 3 6 12 30 90
(x + loop(\(x,i).(x4 + 2x),(x + ~2),1))
A180445: 1 2 3 6 91
loop(\(x,i).((x + ~1) + (2 * (i * i))),(2x + 1),x)
A024381: 1 26 107 276 565 1006 1631 2472 3561 4930 6611 8636 11037 13846 17095 20816
loop(\(x,i).x3,1,(x + (x mod (1 + (x div 2)))))
A118719: 0 1 8 64 125 343 512 1000 1331 2197 2744 4096 4913 6859 8000 10648
((2x2 + ~x + 1) * (if (x mod 2) <= 0 then 1 else x))
A106159: 1 2 7 48
(~x + loop(\(x,i).(x * (1 + (x * i))),3x,1))
A114484: 1 309 4611686018427387903
(~x + loop(\(x,i).(1 + (x * (2 + (x div 4)))),x,1))
A039719: 1 2 5 19 151
(~x + loop(\(x,i).((x + 1) * (1 + ((x * i) div 2))),x,1))
A058881: 1 1 7 137
(~x + loop(\(x,i).(2 * ((x + 2) - (x div ~2))),x,1))
A027138: 1 7 26 85 264 803 2422 7281 21860 65599 196818 590477 1771456 5314395 15943214 47829673
(x * loop(\(x,i).(2 * (4x - (x div 2))),x,1))
A270111: 0 8 112 1176 10976 96040 806736 6588344 52706752 415065672 3228288560 24857821912 189823367328 1439493868904 10851569165584 81386768741880
(~x + loop(\(x,i).((x + 2) + ((i * i) div (x + 1))),x,1))
A096182: 1 2 4 6 8 10 13 16 19 22 26 30 34 38 42 46
(x + loop(\(x,i).(x * (x + (i mod 2))),(x2 + ~2x),1))
A115031: 1 2 3 23 4611686018427387903
(x + ((((x + ~1) div 2) mod 2) + (if (x mod 2) <= 0 then x else 1)))
A109534: 1 2 4 5 9 6 12 9 17 10 20 13 25 14 28 17
(x + (if (~x + 4) <= 0 then (x3 + 2x) else 1))
A142959: 1 2 3 4 76
(~x + loop(\(x,i).3x,5,(x + 1)))
A157958: 243 485 727 969 1211 1453 1695 1937 2179 2421 2663 2905 3147 3389 3631 3873
(x + ((~1 + loop(\(x,i).2x,(x + ~2),2)) div (x + 1)))
A291298: 1 1 2 3 5 7 10 14 22
loop(\(x,i).(x4 + x3 + x + 1),(x + 1),x)
A274307: 1 325 4611686018427387903
loop(\(x,i).(x4 + x2 + 1),(x + 1),x)
A323060: 1 91 4611686018427387903
compr(\x.(loop(\(x,i).(x * ((1 + i) div 2)),x,1) mod (x + 1)),x)
A118742: 0 5 7 8 9 11 13 14 15 17 19 20 21 23 24 25
(~x + ((x + 1) * loop(\(x,i).(x2 + 1),3,2)))
A158386: 677 1353 2029 2705 3381 4057 4733 5409 6085 6761 7437 8113 8789 9465 10141 10817
(~x + ((x + 1) * loop(\(x,i).(x3 + 1),2,2)))
A158397: 730 1459 2188 2917 3646 4375 5104 5833 6562 7291 8020 8749 9478 10207 10936 11665
loop(\(x,i).x2,1,(9x + 8))
A017258: 64 289 676 1225 1936 2809 3844 5041 6400 7921 9604 11449 13456 15625 17956 20449
loop(\(x,i).x2,2,(9x + 8))
A017260: 4096 83521 456976 1500625 3748096 7890481 14776336 25411681 40960000 62742241 92236816 131079601 181063936 244140625 322417936 418161601
(~x + ((x + 1) * loop(\(x,i).(x2 + 1),2,4)))
A158255: 290 579 868 1157 1446 1735 2024 2313 2602 2891 3180 3469 3758 4047 4336 4625
(x + ((x + 1) * loop(\(x,i).(x * (x + i)),2,4)))
A158319: 440 881 1322 1763 2204 2645 3086 3527 3968 4409 4850 5291 5732 6173 6614 7055
loop(\(x,i).x2,3,(5x + 4))
A016904: 65536 43046721 1475789056 16983563041 110075314176 500246412961 1785793904896 5352009260481 14048223625216 33232930569601 72301961339136 146830437604321 281474976710656 513798374428641
loop(\(x,i).x3,1,(5x + 4))
A016899: 64 729 2744 6859 13824 24389 39304 59319 85184 117649 157464 205379 262144 328509 405224 493039
loop(\(x,i).x3,2,(5x + 4))
A016905: 262144 387420489 20661046784 322687697779 2641807540224 14507145975869 60716992766464 208728361158759 618121839509504 1628413597910449 3904305912313344 8662995818654939 18014398509481984
(x + loop(\(x,i).(x * (3 + i)),4,(x + 1)))
A158402: 840 1681 2522 3363 4204 5045 5886 6727 7568 8409 9250 10091 10932 11773 12614 13455
(x + loop(\(x,i).((x + 2) + (x div 4)),2,(x + 1)))
A280537: 5 8 10 13 16 18 20
(x + ((x + 1) * loop(\(x,i).(x * (x - i)),2,2x)))
A243131: 0 1 362 3363 15124 47525 120126 262087 514088 930249 1580050 2550251 3946812 5896813 8550374 12082575
loop(\(x,i).x5,1,(x2 + x))
A248720: 0 32 7776 248832 3200000 24300000 130691232 550731776 1934917632 5904900000 16105100000 40074642432 92389579776 199690286432 408410100000 796262400000
loop(\(x,i).2x,((x2 + ~x) div 2),(x2 + x))
A095338: 0 2 12 96 1280 30720 1376256 117440512 19327352832 6184752906240 3870280929771520 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(7x + 6),(x + 1),x)
A064753: 6 97 1028 9603 84034 705893 5764800 46118407 363182462 2824752489 21750594172 166095446411 1259557135290 9495123019885 71213422649144 531726889113615
(x * (if (~2 + (x div 5)) <= 0 then 2 else (x + ~1)))
A322131: 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 210
((~x2 + x) + loop(\(x,i).((x2 + x) div 2),2,x))
A294259: 0 1 4 15 43 100 201 364 610 963 1450 2101 2949 4030 5383 7050
loop(\(x,i).11x,(x + ~1),x)
A081127: 0 1 22 363 5324 73205 966306 12400927 155897368 1929229929 23579476910 285311670611 3423740047332 40799568897373 483317970015034 5696247503748615
(x div ((3x + 12) div (if x <= 0 then 1 else x)))
A234537: 0 0 0 0 0 1 1 1 2 2 2 2 3 4 4 5
(x + loop(\(x,i).11x,x,1))
A226737: 1 12 123 1334 14645 161056 1771567 19487178 214358889 2357947700 25937424611 285311670622 3138428376733 34522712143944 379749833583255 4177248169415666
(~x + loop(\(x,i).11x,x,1))
A024128: 1 10 119 1328 14637 161046 1771555 19487164 214358873 2357947682 25937424591 285311670600 3138428376709 34522712143918 379749833583227 4177248169415636
(x + loop(\(x,i).(x + ((i mod 2) * i * (2 + i))),x,1))
A135301: 1 5 6 22 23 59 60 124 125 225 226 370 371 567 568 824
loop(\(x,i).(1 - (x2 mod 7)),2,x)
A234046: 0 1 ~1 0 0 ~1 1 0 1 ~1 0 0 ~1 1 0 1
loop(\(x,i).(8 div (1 + ((x + 1) div 2))),2,x)
A334789-A063511: 1 2 2 4 4 4 4 4 4 4 4 4 4 4 4 8
loop(\(x,i).(~10x + ~4),2,x)
A067865: 36 136 236 336 436 536 636 736 836 936 1036 1136 1236 1336 1436 1536
loop(\(x,i).i,((~x + ~1) mod 10),x)
A030076: 9 8 7 6 5 4 3 2 1 9 9 8 7 6 5 4
loop(\(x,i).((x + 1) - ((~x + 1) div (2 + (x div 2)))),2,x)
A275844: 2 4 6 7 8 10 11 13 14 15 16 17 18 19 20 21
loop(\(x,i).(6 * (2 + (x * (1 + i)))),2,x)
A154519: 228 444 660 876 1092 1308 1524 1740 1956 2172 2388 2604 2820 3036 3252 3468
(x + (loop(\(x,i).(x * (2 + i)),(x + ~2),3) div 2))
A151908: 1 2 3 7 22 95
(x + (if (~2 + (x div 4)) <= 0 then 1 else 6))
A227508: 1 2 3 4 5 6 7 8 9 10 11 12 18 19 20 21
(x + (if (~4 + (x div 2)) <= 0 then 1 else 6))
A032993: 1 2 3 4 5 6 7 8 9 10 16 17 18 19 20 21
(~x mod loop(\(x,i).(~1 + ((x2 + x) div 2)),2,x))
A337130: 0 0 0 11 40 99 203 370 621 980 1474 2133 2990 4081 5445 7124
loop(\(x,i).((2x + ~1) * ((x2 + x) div 2)),2,x)
A329757: 0 1 765 27435 345415 2469420 12352956 48294610 157609530 447989355 1141711615 2663460261 5775482505 11777133550 22789550070 42150245460
loop(\(x,i).((x - (x div ~2)) div (1 + (x mod 2))),2,x)
A168221: 0 1 2 3 9 6 7 4 18 5 11 12 27 15 16 8
loop(\(x,i).(1 + (x * (1 + (6 * i)))),2,x)
A139614: 14 105 196 287 378 469 560 651 742 833 924 1015 1106 1197 1288 1379
loop(\(x,i).(1 + (x * (1 + (8 * i)))),2,x)
A139618: 18 171 324 477 630 783 936 1089 1242 1395 1548 1701 1854 2007 2160 2313
compr(\x.(((x div 2) - (if (x mod 3) <= 0 then x else 1)) mod 2),x)
A140794: 0 2 3 7 10 11 12 14
loop(\(x,i).2x,x,(x + ((x2 + 3x + 2) div 2)))
A100312: 1 8 32 104 304 832 2176 5504 13568 32768 77824 182272 421888 966656 2195456 4947968
loop(\(x,i).(x * i),x,(x + ((x2 + 3x + 2) div 2)))
A000780: 1 4 16 78 456 3120 24480 216720 2136960 23224320 275788800 3552595200 49337164800 734788454400 11681891020800 197458829568000
(x + (if (x + ~4) <= 0 then 3 else ((x + 1) div 2)))
A154660: 3 4 5 6 7 8
A299534-A298111: 3 4 5 6 7 8 9 11 12 14 15 17 18 20 21 23
(x + (if (~1 + (x div 4)) <= 0 then 1 else (2x + ~2)))
A240963: 1 2 3 4 5 6 7 8 22
loop(\(x,i).(16 * (1 + (x * i))),2,x)
A157475: 528 1040 1552 2064 2576 3088 3600 4112 4624 5136 5648 6160 6672 7184 7696 8208
(1 - loop(\(x,i).(1 - ((x * (x + i)) div (1 + i))),2,x))
A299120: 1 0 0 5 21 56 120 225 385 616 936 1365 1925 2640 3536 4641
loop(\(x,i).((1 + (x2 div 8)) div 2),2,x)
A308952: 0 0 0 0 0 0 0 1 1 2 2 4 5 8 9 12
(x + (x div (2 + (if (~2 + (x div 4)) <= 0 then 1 else 2))))
A138083: 0 1 2 4 5 6
A145395: 0 1 2 4 5 6 8 9 10 12 13 14 15 16 17 18
loop(\(x,i).(x - ((x - ((x * i) div 3)) div 2)),2,x)
A189674: 0 1 1 2 3 3 3 4 4 5 6 6 7 8 8 8
loop(\(x,i).(2 * (1 + (2 * (x + (2 * (x + i)))))),2,x)
A187206: 138 282 426 570 714 858 1002 1146 1290 1434 1578 1722 1866 2010 2154 2298
loop(\(x,i).x2,1,(9x + 4))
A017210: 16 169 484 961 1600 2401 3364 4489 5776 7225 8836 10609 12544 14641 16900 19321
loop(\(x,i).x2,2,(9x + 4))
A017212: 256 28561 234256 923521 2560000 5764801 11316496 20151121 33362176 52200625 78074896 112550881 157351936 214358881 285610000 373301041
(x + (2 * ((loop(\(x,i).(x * i),x,x) mod (x + 1)) mod 2)))
A175028: 0 3 4 3 6 5 8 7 8 9 12 11 14 13 14 15
(x + (4 * (if (~2 + (x div 3)) <= 0 then 0 else 2)))
A146029: 0 1 2 3 4 5 6 7 8 17 18
(x + (4 * (if (~2 + (x div 4)) <= 0 then 0 else 2)))
A103303: 0 1 2 3 4 5 6 7 8 9
A273376-A247758-A247757-A247754: 0 1 2 3 4 5 6 7 8 9 10 11 20 21 22 23
loop(\(x,i).(1 - ((x - ((x mod 3) div 2)) div 2)),2,x)
A120502: 1 1 1 1 2 2 2 2 2 3 4 4 4 4 4 4
(x + (2 * ((if (x + ~2) <= 0 then 2 else ((x + 1) div 2)) div 2)))
A093515: 2 3 4 5 6 7 8 11 12 13 14 17 18 19 20 23
(~x + (4 * (2 + (if (x mod 2) <= 0 then (x div 2) else 2))))
A134990: 8 15 10 13 12 11 14 9 16 7 18 5 20 3 22 1
(x + (if (~2 + (x div 3)) <= 0 then 1 else 8))
A326298: 1 2 3 4 5 6 7 8 9 17 18 19 20 21 22 23
loop(\(x,i).(1 - (((x + 2) * (x2 div 2)) div 2)),2,x)
A224707: 1 1 3 141
loop(\(x,i).(1 - ((x * (~x + i)) div (x + 4))),2,x)
A029074-A008906: 1 1 1 1 2 2 2 3 4 5 5 6 7 8 9 10
(x * loop(\(x,i).2x2,2,8x))
A017069: 0 32768 1048576 7962624 33554432 102400000 254803968 550731776 1073741824 1934917632 3276800000 5277319168 8153726976 12166529024 17623416832 24883200000
loop(\(x,i).(x + 8),(~4 + (x div 2)),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A067043: 0 1 2 3 4 5 6 7 8 9 18 19 28 29 38 39
(x + loop(\(x,i).(~x + 2),(x + ~1),(2 + ((x div 2) mod 2))))
A116468: 2 3 1 6 4 7 5 10 8 11 9 14 12 15 13 18
(x * loop(\(x,i).((x2 + x + 1) * (2 + i)),2,2))
A303272: 0 1852 3704 5556 7408 9260 11112 12964 14816 16668 18520 20372 22224 24076 25928 27780
(x + (if (~2 + (x div 5)) <= 0 then 1 else 4))
A098314: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 19
(x + (if (~6 + (x div 2)) <= 0 then 1 else 4))
A078107: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 18 19
(x + (x mod (if (~2 + (x div 4)) <= 0 then 1 else 4)))
A103303: 0 1 2 3 4 5 6 7 8 9
A032519: 0 1 2 3 4 5 6 7 8 9 10 11 12 14 16 18
(x + (if (~1 + (x div 4)) <= 0 then (x div 2) else 4))
A275672: 0 1 3 4 6 7 9
A246443: 0 1 3 4 6 7 9 10 12 13 14 15 16 17 18 19
loop(\(x,i).(2 * (5x + i)),4,x)
A102689: 2468 12468 22468 32468 42468 52468 62468 72468 82468 92468 102468 112468 122468 132468 142468 152468
(x + ((if (~4 + (x div 2)) <= 0 then 1 else x) div 4))
A103303: 0 1 2 3 4 5 6 7 8 9
A048097: 0 1 2 3 4 5 6 7 8 9 12 13 15 16 17 18
(x + (if (~2 + (x div 3)) <= 0 then 1 else (x div 4)))
A342191-A253784-A253567-A193671-A130073-A081306-A074779-A073491-A048197: 1 2 3 4 5 6 7 8 9 11 12 13 15 16 17 18
loop(\(x,i).(x3 + ~x),1,(3x + 4))
A228889: 60 336 990 2184 4080 6840 10626 15600 21924 29760 39270 50616 63960 79464 97290 117600
(if ((x + 1) mod 5) <= 0 then (2x + ~4) else x)
A222260: 0 1 2 3 4 5 6 7 8 14 10 11 12 13 24 15
loop(\(x,i).(2x + ((x div 5) mod 2)),2,x)
A268620: 0 4 8 13 17 22 26 31 35 39 40 44 48 53 57 62
(x + (((if (~2 + (x div 2)) <= 0 then 1 else 2) + (x div 2)) div 2))
A219636: 0 1 3 4 5 6 8 9 11 12 13 14 16 17 18 19
(x + (if (~2 + (x div 3)) <= 0 then 1 else (2 * (x mod 2))))
A183083: 1 2 3 4 5 6 7 8 9 11 10 13 12 15 14 17
loop(\(x,i).(2 * (5x - (i * i))),2,x)
A277987: ~28 72 172 272 372 472 572 672 772 872 972 1072 1172 1272 1372 1472
loop(\(x,i).(1 + ((x * i) mod 4)),(x + ~1),(~x + 2))
A230850: 2 1 1 1 2 1 2 1 4 1 2 1 4 1 2 1
(x + ((x + (if (~2 + (x div 3)) <= 0 then 2 else 1)) div 2))
A330116-A320829-A194145-A189784-A072633: 1 2 4 5 7 8 10 11 13 14 15 17 18 20 21 23
(x + ((x + (if (x mod (2 + (x div 2))) <= 0 then 2 else 1)) div 2))
A186513: 1 2 3 5 7 8 9 11 12 14 15 17 18 20 21 23
loop(\(x,i).(17x + 16),2,x)
A158253: 288 577 866 1155 1444 1733 2022 2311 2600 2889 3178 3467 3756 4045 4334 4623
(~x + (2 * loop(\(x,i).(3x - i),(x + ~1),x)))
A176177: 0 1 8 41 176 689 2552 9113 31712 108257 364136 1210505 3985808 13020305 42249560 136314617
(x * ((if (~2 + (x div 5)) <= 0 then 2 else x) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A330336: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 105
(x + loop(\(x,i).(10x + ~8),x,2))
A110369: 2 13 114 1115 11116 111117 1111118 11111119 111111120 1111111121 11111111122 111111111123 1111111111124 11111111111125 111111111111126 1111111111111127
(~x + (2 * loop(\(x,i).(x - (x div (4 + i))),2,x)))
A165576: 0 1 2 3 4 3 4 3 4 5 4 5 6 7 6 5
(x + ((x + (if (~2 + (x div 2)) <= 0 then 1 else 4)) div 2))
A028966: 0 2 3 5 6 8 11 12 14 15 17 18 20 21 23 24
(x + (if (x + ~2) <= 0 then 2 else ((x + ((x div 2) mod 2)) div 2)))
A063934: 2 3 4 5 6 7 9 11 12 13 15 17 18 19 21 23
(x + ((x + loop(\(x,i).((1 + i) * i),(x div 2),2)) div 2))
A282737: 1 2 4 5 9 10 15 16 22 23 30 31 39 40 49 50
loop(\(x,i).(x + ((1 + (2 * (2 + i))) * (x div 2))),2,x)
A037042: 0 1 45 55 99
loop(\(x,i).(x + ((x mod (1 + (x div 2))) div (2 + i))),2,x)
A034047: 0 1 2 3 4 5 6 8 10 11 12 13 14 16 17 19
loop(\(x,i).(6x + 6),2,(x2 + 2x))
A158479: 42 150 330 582 906 1302 1770 2310 2922 3606 4362 5190 6090 7062 8106 9222
loop(\(x,i).(1 - ((x div 2) div 3)),2,(x2 + 2x))
A342098-A025770: 1 1 1 2 2 2 3 3 3 4 5 5 6 7 7 8
loop(\(x,i).((x div 2) div (1 + (x mod 2))),2,(x2 + 2x))
A115880: 0 0 2 0 6 4 12 3 20 12 30 8 42 24 56 15
loop(\(x,i).(5x + 5),2,(x2 + 2x))
A158445: 30 105 230 405 630 905 1230 1605 2030 2505 3030 3605 4230 4905 5630 6405
loop(\(x,i).(8x + 8),2,(x2 + 2x))
A158488: 72 264 584 1032 1608 2312 3144 4104 5192 6408 7752 9224 10824 12552 14408 16392
loop(\(x,i).(8 * (x + i)),2,(x2 + 2x))
A157912: 80 272 592 1040 1616 2320 3152 4112 5200 6416 7760 9232 10832 12560 14416 16400
loop(\(x,i).(x + ((x + i) * (2 + i))),2,(x2 + 2x))
A167573: 23 83 183 323 503 723 983 1283 1623 2003 2423 2883 3383 3923 4503 5123
((x2 + 2x) + (if (x mod 2) <= 0 then 1 else 2x2))
A270454: 1 5 9 33 25 85 49 161 81 261 121 385 169 533 225 705
(x + loop(\(x,i).(~2 + (x * (1 + (2 * i)))),x,(x + 2)))
A296366: 2 8 50 442
loop(\(x,i).((x * (1 + i)) div (1 + (i div 2))),(x + ~2),x)
A100071: 0 1 2 6 12 30 60 140 280 630 1260 2772 5544 12012 24024 51480
loop(\(x,i).((x2 div 2) * ((x + 1) div 2)),(x + ~2),x)
A322142: 0 1 2 8 1024
((x2 + ~2x + 1) + (if (x mod 4) <= 0 then 0 else 2))
A018251: 1 2 3 6 9 18
(2 - loop(\(x,i).(~2x2 + 4x + 1),2x,x))
A100360-A061421: 2 7 71 4611686018427387903
(if (x mod 2) <= 0 then (6x + (x div 2)) else x)
A317313: 0 1 13 3 26 5 39 7 52 9 65 11 78 13 91 15
loop(\(x,i).(x2 mod 10),(x div 2),x)
A186723: 0 1 4 9 6 5 6 1 6 1 0 1 6 1 6 5
(x + loop(\(x,i).(1 + ((x + (x div 2)) div 2)),2,(x div 2)))
A175320: 1 2 3 4 6 7 9 10 12 13 14 15 16 17 19 20
(~x + loop(\(x,i).(1 + (x * i)),4,2) - (x div 2))
A096400: 89 88 86 85 83 82 80 79 77 76 74 73 71 70 68 67
(if (x mod 2) <= 0 then (8x + (x div 2)) else x)
A317317: 0 1 17 3 34 5 51 7 68 9 85 11 102 13 119 15
(x + loop(\(x,i).(2 + (x div 2)),(x div 4),(x div 2)))
A232779: 0 1 3 4 7 8 9 10 12 13 14 15 16 17 18 19
loop(\(x,i).(~1 + ((i div 3) + (x div 2))),(x div 2),x)
A321860: 0 1 0 0 ~1 ~1 0 0 0 0 0 0 1 1 1 1
(if (x mod 4) <= 0 then (x div 4) else (x * (x mod 2)))
A316631: 0 1 0 3 1 5 0 7 2 9 0 11 3 13 0 15
loop(\(x,i).(1 + (x * (x + (x div 2)))),(x2 + 2),x)
A185120: 2 71 4611686018427387903 4611686018427387903
((x3 + 2x) + loop(\(x,i).(x - (i * i)),x,1))
A139488: 1 3 8 20 43 81 138 218 325 463 636 848 1103 1405 1758 2166
(x + (if ((x + ~1) mod 9) <= 0 then 1 else x))
A070196: 0 2 4 6 8 10 12 14 16 18 11 22 24 26 28 30
(x + (x2 div (x + (if x <= 0 then 1 else (x div 3)))))
A303589: 0 2 4 5 7 9 10 12 14 15 17 19 21 22 24 26
(x * (x + loop(\(x,i).(2x - (i mod 2)),(x + ~2),1)))
A029929: 0 2 6 12 24 40 72 126 240 468 960 2002 4248 9048 19320 41190
(x2 * (if (x + ~2) <= 0 then x else (x2 + 2x + 1)))
A227875: 0 1 8 144
(~x + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))
A162177: 0 0 0 1 2 5 6 9 10 13 18 19 24 27 28 31
(x + ((x mod 10) mod (if x <= 0 then 1 else x)))
A103303: 0 1 2 3 4 5 6 7 8 9
A190760-A172432-A164836-A144688-A130514-A130232-A119823-A102685-A098952-A088235-A083292-A067082-A032518: 0 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20
compr(\x.((x mod 10) mod (if x <= 0 then 1 else x)),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A338829-A244890-A236402-A202272-A201982-A107085-A070958-A052018-A032945: 0 1 2 3 4 5 6 7 8 9 10 20 30 40 50 60
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,x)
A001791: 0 1 4 15 56 210 792 3003 11440 43758 167960 646646 2496144 9657700 37442160 145422675
loop(\(x,i).(x - ((x mod (1 + (x div 3))) div 2)),x,x)
A265539: 0 1 2 3 4 5 6 7 7 9 9 9 9 9 9 9
(x + loop(\(x,i).(1 + ((3 * (x div 2)) div 2)),2,x))
A189633: 1 2 4 5 8 9 10 11 13 14 17 18 20 21 22 23
(x + loop(\(x,i).(10x + 10),2,x))
A032614: 110 211 312 413 514 615 716 817 918 1019 1120 1221 1322 1423 1524 1625
compr(\x.(2 - loop(\(x,i).(x div (1 + (2 * (x mod 2)))),2,x)),x)
A330945: 2 4 6 7 8 10 12 13 14 16 18 19 20 21 22 23
(x * loop(\(x,i).(3 * (~1 + (x * (1 + i)))),2,x))
A277984: 0 24 156 396 744 1200 1764 2436 3216 4104 5100 6204 7416 8736 10164 11700
(x + loop(\(x,i).(x - (x div 12)),2,x))
A337718: 0 2 4 6 8 10 12 14 16 18 20 22 23 24 26 28
(x2 * loop(\(x,i).x2,2,8x))
A016806: 0 4096 262144 2985984 16777216 64000000 191102976 481890304 1073741824 2176782336 4096000000 7256313856 12230590464 19770609664 30840979456 46656000000
(x * loop(\(x,i).2x,(2 * (~2 + (x * (x mod 2)))),x))
A323515: 0 1 4 36 16 1600
(1 div (if (x mod 10) <= 0 then (~x + 2) else x))
A030215: 0 1 0 0 0 0 0 0 0 0 ~1 0 0 0 0 0
(~x + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A065890: 0 0 1 2 5 6 9 10 13 18 19 24 27 28 31 36
(x2 * loop(\(x,i).3x2,2,2x))
A228105: 0 432 27648 314928 1769472 6750000 20155392 50824368 113246208 229582512 432000000 765314352 1289945088 2085181488 3252759552 4920750000
loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,x)
A024483: 0 2 10 42 168 660 2574 10010 38896 151164 587860 2288132 8914800 34767720 135727830 530365050
((x2 + 1) + (2 * loop(\(x,i).(i * i),(x + ~2),0)))
A116720: 1 2 5 12 25 44 69 100 137 180 229 284 345 412 485 564
(if (x mod 2) <= 0 then (1 + ((x2 + 2x) div 2)) else x2)
A271391: 1 1 5 9 13 25 25 49 41 81 61 121 85 169 113 225
(x2 + loop(\(x,i).(2x + (i * i)),(x + ~2),1))
A026622: 1 2 5 12 26 54 110 222 446 894 1790 3582 7166 14334 28670 57342
(~x2 + loop(\(x,i).12x,x,1))
A024142: 1 11 140 1719 20720 248807 2985948 35831759 429981632 5159780271 61917364124 743008370567 8916100448112 106993205378903 1283918464548668 15407021574586143
(~x2 + loop(\(x,i).10x,x,1))
A024116: 1 9 96 991 9984 99975 999964 9999951 99999936 999999919 9999999900 99999999879 999999999856 9999999999831 99999999999804 999999999999775
loop(\(x,i).(2x3 + 1),(x + 1),x2)
A250489: 1 55 4611686018427387903
(~x2 + loop(\(x,i).7x,x,1))
A024077: 1 6 45 334 2385 16782 117613 823494 5764737 40353526 282475149 1977326622 13841287057 96889010238 678223072653 4747561509718
loop(\(x,i).(4x2 + ~4x + 1),2,x2)
A239609: 1 1 9409 332929 3690241 23049601 101626561 354079489 1040514049 2687489281 6272798401 13493377921 27138279169 51591216769 93489789121 162571046401
(x2 * loop(\(x,i).2x2,2,3x))
A185270: 0 648 41472 472392 2654208 10125000 30233088 76236552 169869312 344373768 648000000 1147971528 1934917632 3127772232 4879139328 7381125000
(x3 * loop(\(x,i).2x2,2,2x))
A016747: 0 128 16384 279936 2097152 10000000 35831808 105413504 268435456 612220032 1280000000 2494357888 4586471424 8031810176 13492928512 21870000000
(x4 + loop(\(x,i).4x,x,1))
A001589: 1 5 32 145 512 1649 5392 18785 69632 268705 1058576 4208945 16797952 67137425 268473872 1073792449
(~x4 + loop(\(x,i).4x,x,1))
A024040: 1 3 0 ~17 0 399 2800 13983 61440 255583 1038576 4179663 16756480 67080303 268397040 1073691199
(~x4 + loop(\(x,i).3x,x,1))
A024027: 1 2 ~7 ~54 ~175 ~382 ~567 ~214 2465 13122 49049 162506 510705 1565762 4744553 14298282
(x2 * loop(\(x,i).7x,x,x))
A128793: 0 7 392 9261 153664 2100875 25412184 282475249 2951578112 29417779503 282475249000 2631821894933 23917744283328 212865155864179 1861044111897656 16023020096057625
(~x5 + loop(\(x,i).2x,x,1))
A024015: 1 1 ~28 ~235 ~1008 ~3093 ~7712 ~16679 ~32512 ~58537 ~98976 ~159003 ~244736 ~363101 ~521440 ~726607
(~x5 + loop(\(x,i).(x * i),x,1))
A196412: 1 0 ~30 ~237 ~1000 ~3005 ~7056 ~11767 7552 303831 3528800 39755749 478752768 6226649507 87177753376 1307673608625
loop(\(x,i).(x + ((~1 + i) mod 9)),x,x)
A037123: 0 1 3 6 10 15 21 28 36 45 46 48 51 55 60 66
loop(\(x,i).(x * (6 + (2 div (1 + i)))),x,x)
A269895: 0 7 84 756 6048 45360 326592 2286144 15676416 105815808 705438720 4655895552 30474952704 198087192576 1279948013568 8228237230080
compr(\x.loop(\(x,i).(x div (2 - ((x mod 3) div 2))),x,x),x)
A295897: 0 1 3 6 7 12 13 15 24 25 27 30 31 48 49 51
(x * (x + loop(\(x,i).(x * (3 + i)),4,x)))
A133496: 0 841 3364 7569 13456 21025 30276 41209 53824 68121 84100 101761 121104 142129 164836 189225
compr(\x.loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,x),x)
A233524: 0 1 2 4 5 8
A340956-A003714: 0 1 2 4 5 8 9 10 16 17 18 20 21 32 33 34
(~x3 + loop(\(x,i).3x,2x,1))
A024104: 1 8 73 702 6497 58924 531225 4782626 43046209 387419760 3486783401 31381058278 282429534753 2541865826132 22876792452217 205891132091274
(~x3 + loop(\(x,i).6x,x,1))
A024065: 1 5 28 189 1232 7651 46440 279593 1679104 10076967 60465176 362795725 2176780608 13060691819 78364161352 470184981201
(x3 + loop(\(x,i).(3x + ~1),x,1))
A318165: 1 3 13
A241527: 1 3 13 41 105 247 581 1437 3793 10571 30525 89905 267449 799359 2394229 7177829
(~x3 + loop(\(x,i).8x,x,1))
A024091: 1 7 56 485 4032 32643 261928 2096809 16776704 134216999 1073740824 8589933261 68719475008 549755811691 4398046508360 35184372085457
(~x3 + loop(\(x,i).5x,x,1))
A024052: 1 4 17 98 561 3000 15409 77782 390113 1952396 9764625 48826794 244138897 1220700928 6103512881 30517574750
(x * loop(\(x,i).x2,2,x5))
A010809: 0 1 2097152 10460353203 4398046511104 476837158203125 21936950640377856 558545864083284007 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 div (1 + ((x + 1) mod 9))))
A231071: 2 1 1 1 1 1 1 1 3 2 1 1 1 1 1 1
(1 + (~2 mod (1 + (x mod 9))))
A338882: 1 1 2 3 4 5 6 7 8 1 1 2 3 4 5 6
(1 + (2 mod (1 + (x mod (1 + (4 * (x mod 2)))))))
A095345: 1 1 1 3 1 1 1 3 1 3 1 1 1 3 1 1
(1 + (x2 mod (1 + ((x + 1) div 5))))
A049236: 1 1 1 1 1 2 1 2 1 1 2 2 1 2 1 2
(1 + (x2 mod (1 + ((x + ~1) mod 5))))
A238408: 1 1 1 1 1 1 1 2 2 2 1 1 1 2 1 1
(1 + ((1 + (x div 2)) mod (1 + (x div 5))))
A184848-A184720: 1 1 1 1 1 2 1 1 2 2 1 1 2 2 3 1
((x + 3) - (2 div (1 + (x div 5))))
A286926-A187392-A145198-A121229-A083210: 1 2 3 4 5 7 8 9 10 11 13 14 15 16 17 18
(1 + ((x2 div 2) mod (1 + (x div 5))))
A214709: 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1
(1 + ((x mod 3) div (1 + (x mod 5))))
A023591: 1 1 1 1 1 3 1 1 1 1 2 2 1 1 1 1
(1 + ((x mod 4) mod (1 + (x mod 5))))
A255825: 1 2 3 4 1 1 1 1 1 2 1 2 1 2 3 1
(x mod (3 - (2 div (1 + (x mod 5)))))
A101671: 0 1 2 0 1 0 0 1 2 0 0 1 0 1 2 0
(1 + (2x mod 19))
A245234: 1 3 5 7 9 11 13 15 17 19 2 4 6 8 10 12
(1 + (x mod (1 + ((2 * (x div 3)) div 3))))
A097868: 1 1 1 1 1 1 1 2 1 1 2 3 1 2 3 4
(1 + ((x2 + ~2) div 13))
A082543: 0 0 1 1 2 2 3 4 5 7
((x + 1) - ((~x + 1) div 11))
A083794-A083792: 1 2 4 5 6 7 8 9 10 11 12 13 14 16 17 18
((x + 1) - ((~x + 2) div 11))
A333638: 1 2 3 5 6 7 8 9 10 11 12 13 14 15 17 18
(1 + ((x div 2) mod (1 + ((2 * (x div 2)) mod 3))))
A157129: 1 1 2 2 1 1 1 1 2 2 2 2 1 1 2 2
(1 + ((x div 2) div (1 + (6 * (x mod 2)))))
A308073: 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 2
(1 + (2x2 mod (1 + ((x div 2) div 3))))
A046533-A046532: 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1
(1 + (x mod (~1 + ((~x + (x div 3)) div 3))))
A292049: 1 0 1 0 1 0 1 ~1 0 1 ~1 0 1 ~2 0 1
(1 + (2x div (1 + ((x2 + x) mod 3))))
A146535: 1 1 5 7 3 11 13 5 17 19 7 23 25 9 29 31
(1 + (x div (~1 + ((x div ~2) * (x div 3)))))
A131483: 1 0 ~1 0 ~1 ~1 0 0 0 0 0 0 0 0 0 0
(1 + ((x - (x mod 3)) * (1 + (x div 3))))
A092076: 1 1 1 7 7 7 19 19 19 37 37 37 61 61 61 91
(1 + ((x mod 6) mod (1 + (x div 3))))
A305300-A175851: 1 1 1 2 1 2 1 2 3 4 1 2 1 2 3 4
(1 + ((x + (x div 4)) div (1 + (x div 3))))
A123182: 1 2 3 2 3 4 3 3 4
((2x + 2) div (1 + (2 mod (1 + (x mod 3)))))
A068217: 2 4 2 8 10 4 14 16 6 20 22 8 26 28 10 32
((2x + 4) div (1 + (2 mod (1 + (x mod 3)))))
A059030: 4 6 2 10 12 4 16 18 6 22 24 8 28 30 10 34
(1 + ((~x + 1) mod (1 + (2x mod (1 + (x div 2))))))
A068347: 1 1 1 1 1 1 1 1 2 1 1 1 2 1 3 1
(x mod (1 + (x mod (1 + (~x mod (1 + (x div 2)))))))
A334208-A271420-A099313: 0 0 0 1 0 1 0 1 2 1 0 1 0 1 2 1
((x + 3) - (x div ~9))
A008521: 3 5 6 7 8 9 10 11 12 13 15 16 17 18 19 20
((x + 1) - ((2 * (x div 3)) div ~3))
A188087: 1 2 3 5 6 7 9 10 11 12 13 14 16 17 18 20
((2x + 1) - ((x mod 4) mod ~3))
A047576: 1 5 6 7 9 13 14 15 17 21 22 23 25 29 30 31
((x + 1) - ((x + (x div 4)) div ~3))
A184618-A136119: 1 3 4 5 7 8 10 11 13 14 15 17 18 20 21 22
((2x + 1) + ((x mod 2) + (x mod ~3)))
A222011: 1 2 4 8
A133007: 1 2 4 8 7 11 13 14
(1 + (2 div (1 + ((x + 2) mod 10))))
A337199: 1 1 1 1 1 1 1 1 3 2 1 1 1 1 1 1
(1 + (~2 mod (1 + (x mod 10))))
A214950-A051802-A051801: 1 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5
(1 + (x div (1 + (x div (2 + (x div 5))))))
A087233: 1 2 2 2 2 3 3 3 3 3 4 4 4 4 4 4
(1 + (2x mod (1 + ((x mod 5) div 2))))
A030558: 1 1 1 1 3 1 1 1 1 1 1 1 1 1 2 1
((x + 1) - (x div (3 + ((x div 2) div 3))))
A208746: 1 2 3 3 4 5 6 7 7 8 9 10 11 12 13 13
(14x2 + 14x + 1)
A195314: 1 29 85 169 281 421 589 785 1009 1261 1541 1849 2185 2549 2941 3361
((2x + 1) - ((x + 1) div 7))
A329827-A182765: 1 3 5 7 9 11 12 14 16 18 20 22 24 25 27 29
(~1 + ((x3 + 1) mod 7))
A175629: 0 1 1 ~1 1 ~1 ~1 0 1 1 ~1 1 ~1 ~1 0 1
(28x2 + 1)
A158556: 1 29 113 253 449 701 1009 1373 1793 2269 2801 3389 4033 4733 5489 6301
((x + 1) - ((~2x + 2) div 7))
A286924: 1 2 4 5 6 8 9 10 11 13 14 15 17 18 19 20
(1 + (7 * ((x2 + x) div 2)))
A069099: 1 8 22 43 71 106 148 197 253 316 386 463 547 638 736 841
(1 + (((x2 + 2x) div 2) div 7))
A091581-A088670: 1 1 1 2 2 3 4 5 6 8 9 11 13 14 17 19
((2x + 1) - (2x div 7))
A285074-A213908-A186315-A186219: 1 3 5 7 8 10 12 13 15 17 19 20 22 24 25 27
(1 + ((x * ((x div 2) mod 2)) div 7))
A117147: 1 1 1 1 1 1 1 2 1 1 2 2 1 1 3 3
(1 + (x div (1 + ((x div 2) mod (2 + (x mod 3))))))
A160419: 1 2 2 2 2 2 4 8
(1 + ((x div 3) mod (~1 + (2 * (x mod 3)))))
A331368: 1 1 1 1 1 2 1 1 3 1 1 1 1 1 2 1
(1 + (x div (1 + (x div (2 + (2 mod (1 + (x div 2))))))))
A096036: 1 2 2 2 3 3 4 4 3 4 4 4 4 4 4 4
(6x2 + 21x + 17)
A227721: 17 44 83 134 197 272 359 458 569 692 827 974 1133 1304 1487 1682
((2x + 1) - (2x div ~5))
A231407: 1 4 6
A189926-A060106: 1 4 6 9 11 13 16 18 21 23 25 28 30 33 35 37
((x + 1) - ((x2 + 2x) div ~5))
A184013: 1 3 5 7 10 13 17 21 25 30 35 41 47 53 60 67
((x + 5) - (x div ~5))
A043694-A043602-A031950: 5 7 8 9 10 11 13 14 15 16 17 19 20 21 22 23
(0 - ((x + 1) mod (~1 + (x div ~5))))
A216607-A025672-A025665: 0 0 1 0 1 0 2 1 0 2 1 0 3 2 1 0
(1 - ((x + 1) mod (~1 + (x div ~5))))
A084822-A023116: 1 1 2 1 2 1 3 2 1 3 2 1 4 3 2 1
(1 + (x div (2 - (x div (~1 + (2 * (x mod ~2)))))))
A336312: 1 1 1 2 1 2 1 2 1 2 1 2 1 2 1 3
(1 + (2x mod 21))
A238704: 1 3 5 7 9 11 13 15 17 19 21 2 4 6 8 10
((x + 1) - (x div (~3 + (x div ~4))))
A183300: 1 3 4 5 6 7 9 10 11 12 13 14 15 16 17 19
(1 + (x mod ((x + 1) - ((((x + 1) div 2) div 2) div 2))))
A255828: 1 2 3 4 5 6 7 1 1 1 1 1 1 1 1 2
(1 + (x div (11 - (x div 2))))
A324918-A120186: 1 1 1 1 1 1 1 1 2 2 2 2 3 3 4 4
(1 + ((x mod ~3) mod 9))
A073636: 1 8 9 1 8 9 1 8 9 1 8 9 1 8 9 1
(1 + ((0 - (x mod 3)) mod 9))
A275615: 1 9 8 1 9 8 1 9 8 1 9 8 1 9 8 1
(36x + 37)
A158065: 37 73 109 145 181 217 253 289 325 361 397 433 469 505 541 577
(36x + 35)
A044518: 35 71 107 143 179 215 251 287 323 359 395 431 467 503 539 575
(18x2 + 18x + 1)
A195316: 1 37 109 217 361 541 757 1009 1297 1621 1981 2377 2809 3277 3781 4321
(1 + ((2x2 + 2x) mod 9))
A254373: 1 5 4 7 5 7 4 5 1 1 5 4 7 5 7 4
(36x2 + 1)
A158591: 1 37 145 325 577 901 1297 1765 2305 2917 3601 4357 5185 6085 7057 8101
((x + 1) - ((~2x + 2) div 9))
A184516: 1 2 4 5 6 7 9 10 11 12 13 15 16 17 18 20
(1 + (9 * ((x2 + x) div 2)))
A081273-A060544: 1 10 28 55 91 136 190 253 325 406 496 595 703 820 946 1081
(1 + (((x2 + ~x) div 2) mod 9))
A133292: 1 1 2 4 7 2 7 4 2 1 1 2 4 7 2 7
((x + 1) - ((~2x + 4) div 9))
A183292: 1 2 3 5 6 7 8 10 11 12 13 14 16 17 18 19
((x + 1) - ((~2x + 1) div 9))
A247782: 1 3 4 5 6 7 9 10 11 12 14 15 16 17 18 20
(1 + ((x2 + 3x) mod 9))
A275704: 1 5 2 1 2 5 1 8 8 1 5 2 1 2 5 1
(18x2 + 9x + 1)
A272399: 1 28 91 190 325 496 703 946 1225 1540 1891 2278 2701 3160 3655 4186
(x - (x mod ((x + 1) - (x mod 9))))
A265523: 0 1 2 3 4 5 6 7 8 0 10 10 10 10 10 10
(1 + (((x + 1) div 2) mod (1 + (x div 8))))
A086247: 1 1 1 1 1 1 1 1 1 2 2 1 1 2 2 1
(1 + (2 mod (1 + (x mod (2 + ((~x + 2) mod 4))))))
A154754: 1 1 1 3 1 3 1 3 1 1 1 1 1 1 1 1
(1 + ((2x + 1) div (3 + (x div 4))))
A341510-A196238-A130146-A113764-A002024: 1 2 2 3 3 3 4 4 4 4 5 5 5 5 5 6
((x + 1) - ((~x + 2) div (3 + (x div 4))))
A046841: 1 2 3 5 6 7 8 10 11 12 13 14 15 16 17 19
(~x mod (1 + (x mod (~1 + (2 * (x div 4))))))
A036870: 0 0 0 0 0 0 0 0 1 0 0 1 0 3 1 0
(1 + ((x2 div 2) mod (4x + ~9)))
A010558: 1 1 1 2 2 2 4 6 10
(1 + (2 mod (1 + (((x + ~2) mod (2 + (x div 2))) div 2))))
A082457: 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3
(1 + (x mod (1 + ((x + ~1) mod (4 + (x div 2))))))
A309932: 1 1 1 1 1 1 1 1 1 1 1 2 1 2 3 4
(1 + (((x + ~1) div 2) div (1 + (2 * (2 + (x mod 2))))))
A028950: 0 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2
(1 + (x div 2) - (x div (1 + (2 * (2 + (x mod 2))))))
A156251: 1 1 2 2 3 3 3 3 4 4 4 5 5 6 6 6
(1 + (2 div (1 + ((~1 + (x * (x div 2))) mod 4))))
A092334-A092332: 1 1 2 1 1 2 2 3 1 1 2 1 1 2 2 3
(1 + ((2x + 4) mod (1 + ((x + 1) mod 4))))
A344759: 1 1 1 1 1 3 1 1 1 2 1 1 1 1 1 1
(1 + (x div (5 * (1 + (x mod 4)))))
A333893-A065941: 1 1 1 1 1 1 1 1 2 1 1 1 3 2 1 1
(1 + (((x + 1) - (2 * (x mod 2))) div 5))
A325357: 1 1 1 1 2 1 2 2 2 2 3 3 3 3 4 3
(30x + 29)
A128469: 29 59 89 119 149 179 209 239 269 299 329 359 389 419 449 479
((x + 1) - (5 * ((x div 2) div 3)))
A173526: 1 2 3 4 5 6 2 3 4 5 6 7 3 4 5 6
(30x2 + 1)
A158558: 1 31 121 271 481 751 1081 1471 1921 2431 3001 3631 4321 5071 5881 6751
((x + 1) - (5 * ((~x + 1) div 3)))
A283774: 1 2 8 9 10 16 17 18 24 25 26 32 33 34 40 41
((x + 1) - (((x + 1) + (x mod 2)) div 5))
A091960: 1 2 3 3 4 5 6 7 8 8 9 10 11 11 12 13
(25x + 26)
A158060: 26 51 76 101 126 151 176 201 226 251 276 301 326 351 376 401
(10x2 + 20x + 9)
A158447: 9 39 89 159 249 359 489 639 809 999 1209 1439 1689 1959 2249 2559
(1 + ((2x2 + 4x + 2) div 5))
A025696: 1 2 4 7 11 15 20 26 33 41 49 58 68 79 91 103
(20x2 + 20x + 1)
A195317: 1 41 121 241 401 601 841 1121 1441 1801 2201 2641 3121 3641 4201 4801
((~x2 + x) mod (1 + ((x + 1) div 5)))
A024158: 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 2
(1 + ((2x2 + ~6x + 4) div 5))
A185170: 1 1 1 1 3 5 9 13 17 23 29 37 45 53 63 73
(1 + (5 * ((x mod 2) - (x div ~2))))
A122088: 1 11 6 16 11 21 16 26 21 31 26 36 31 41 36 46
((2x + 1) - (5 * (x div ~2)))
A061908-A056020: 1 8 10 17 19 26 28 35 37 44 46 53 55 62 64 71
(1 + (10 * (x mod 5)))
A108812: 1 11 21 31 41 1 11 21 31 41 1 11 21 31 41 1
(1 + ((8x + 2) div 5))
A225647: 1 3 4 6 7
A330095-A284773-A182770-A059552-A047516: 1 3 4 6 7 9 11 12 14 15 17 19 20 22 23 25
(30x + 11)
A128467: 11 41 71 101 131 161 191 221 251 281 311 341 371 401 431 461
(x2 mod 29)
A070451: 0 1 4 9 16 25 7 20 6 23 13 5 28 24 22 22
((2x + 1) - ((2x + ~2) div 5))
A295282: 2 3 5 7 8 10 11 13 15 16 18 19 21 23 24 26
(40x + 19)
A250024: 19 59 99 139 179 219 259 299 339 379 419 459 499 539 579 619
(1 + ((x mod ~7) div 5))
A016428-A016425-A016417-A016407-A016404-A016393-A016384-A016377-A016374-A016367-A016358-A016355-A016341-A016332-A016270-A014016-A011654: 1 ~1 0 0 0 0 0 1 ~1 0 0 0 0 0 1 ~1
(x2 mod 41)
A070463: 0 1 4 9 16 25 36 8 23 40 18 39 21 5 32 20
(x2 mod 39)
A070461: 0 1 4 9 16 25 36 10 25 3 22 4 27 13 1 30
(40x2 + 1)
A158602: 1 41 161 361 641 1001 1441 1961 2561 3241 4001 4841 5761 6761 7841 9001
(1 + ((x - ((x div 2) mod 4)) div 5))
A025790: 1 1 1 1 1 1 1 1 2 2 2 3 3 3 3 3
(30x + 19)
A156376: 19 49 79 109 139 169 199 229 259 289 319 349 379 409 439 469
(~1 + ((2 + ((x2 + ~x) div 2)) mod 5))
A175922: 1 1 2 ~1 2 1 1 2 ~1 2 1 1 2 ~1 2 1
((x + 1) - ((2 * ((~x + 2) div 2)) div 5))
A337533-A283296-A166546-A164514: 1 2 3 5 6 7 8 10 11 12 13 14 15 17 18 19
((x + 1) - ((2 * (1 - (x div 2))) div 5))
A187968: 1 2 3 4 6 7 8 9 11 12 13 14 15 16 18 19
(1 + (5 * ((x2 + 3x) div 2)))
A166137: 1 11 26 46 71 101 136 176 221 271 326 386 451 521 596 676
((2x + 1) - ((~2x + 2) div 5))
A286666: 1 3 6 8 11 13 15 18 20 23 25 27 30 32 35 37
((2x + 1) - (((~x + 2) div 2) div 5))
A097911: 1 3 5 8
A073608: 1 3 5 8 10 12
A138829: 1 3 5 8 10 12 14 16 18 20 22 24 26 29 31 33
(2 - (3 div (1 + ((x + 2) mod 5))))
A175921: 1 2 2 ~1 1 1 2 2 ~1 1 1 2 2 ~1 1 1
((3x + 1) - (2x div 5))
A186323: 1 4 7 9 12 14 17 20 22 25 27 30 33 35 38 40
(8 mod (1 + (2x mod 5)))
A152857: 0 2 3 0 0 0 2 3 0 0 0 2 3 0 0 0
((x + 1) - (((~x + 1) - (x mod 2)) div 5))
A304808-A077656: 1 3 4 5 6 7 8 10 11 12 13 15 16 17 18 19
(1 + ((2x2 + 3x) div 5))
A008823: 1 2 3 6 9 14 19 24 31 38 47 56 65 76 87 100
((x + 1) - ((x + (x div 3)) div 5))
A328309: 1 2 3 4 4 5 6 7 7 8 9 10 10 11 12 12
(25x + 19)
A044096: 19 44 69 94 119 144 169 194 219 244 269 294 319 344 369 394
((x + 1) - ((~x + ((x div 2) mod 2)) div 5))
A304804-A184530: 1 3 4 5 6 7 8 10 11 12 13 14 16 17 18 19
((2x + 1) - ((x + (x div 2)) div 5))
A186342: 1 3 5 7 8 10 12 13 15 17 18 20 22 24 25 27
((x + ~1) mod (1 + ((x * (x mod 2)) div 5)))
A280683: 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2
(1 + (((x + ~1) div 2) div 2) - (x div 5))
A320015: 0 1 1 1 1 1 1 1 1 2 1 1 1 2 2 1
((x + 2) - (2 mod (~1 - (x div 5))))
A102466-A067340-A062770: 2 3 4 5 6 7 8 9 10 11 13 14 15 16 17 19
((1 - (x div 3)) mod (1 + (x div 5)))
A048485: 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0
((2x + ~1) + (2 div (1 + (x div 5))))
A184808: 1 3 5 7 9 10 12 14 16 18 19 21 23 25 27 29
((x * (1 + (x div 2))) mod (1 + (x div 5)))
A342557-A334621-A289618-A280710-A268374-A071006: 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0
(1 - (5 mod (1 + (x mod 5))))
A131670: 1 0 ~1 0 1 1 0 ~1 0 1 1 0 ~1 0 1 1
((x div 5) div (1 + (x mod 5)))
A036869-A036868: 0 0 0 0 0 1 0 0 0 0 2 1 0 0 0 3
((x mod (2 + (x mod 2))) div (1 + (x mod 5)))
A060862: 0 0 0 0 0 2 0 0 0 0 0 1 0 0 0 0
((2x + ~1) + (2 div (1 + (x mod 5))))
A001742: 1 2 3 5 7 11 12 13 15 17 21 22 23 25 27 31
(2x mod (~1 + ((~x2 + x) mod 5)))
A281154-A279372: 0 0 0 0 0 0 0 0 1 0 0 0 0 2 0 0
(5x4 + ~10x2 + 1)
A121671: 1 ~4 41 316 1121 2876 6121 11516 19841 31996 49001 71996 102241 141116 190121 250876
(1 + ((x + 1) mod (1 + ((x * (x mod 2)) div 4))))
A237513-A069897: 1 1 1 1 1 1 1 1 1 2 1 1 1 3 1 1
(1 + (x2 div ((2x + 1) - (x div 4))))
A225215: 1 1 1 2 3 3 4 4 5 5 6 6 7 8 8 9
((x + 1) - ((x + 1) mod (~1 - (x div 4))))
A134361: 1 2 3 4 6 6 8 8 9 12 12 12 16 16 16 16
(1 + ((x + ~5) mod (1 + (x div 4))))
A205781: 1 1 1 1 2 1 2 1 1 2 3 1 4 1 2 3
((x + 1) mod (1 + ((x + ~1) mod (1 + (x div 4)))))
A100563: 0 0 0 0 1 0 1 0 1 1 0 0 1 0 1 1
(1 + ((2 * (x div 3)) mod (1 + (x div 4))))
A345932: 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 3
(1 + ((2 * (~2 + (x div 2))) mod (1 + (x div 4))))
A152905: 1 1 1 1 1 1 1 1 2 2 1 1 1 1 3 3
((x + 3) - ((x div 2) mod (1 + (x div 4))))
A154660: 3 4 5 6 7 8
A248631: 3 4 5 6 7 8 8 9 10 11 11 12 13 14 14 15
(1 + ((x + (x mod 4)) * (1 + (x div 4))))
A200975: 1 3 5 7 9 13 17 21 25 31 37 43 49 57 65 73
(1 + (((x2 + ~1) div 2) mod (1 + (x mod 4))))
A079229: 1 1 2 1 1 1 3 1 1 1 2 1 1 1 2 1
((x + 1) - (x2 div (~2x + ~5)))
A186499-A110882: 1 3 4 5 7 8 10 11 13 14 15 17 18 20 21 23
((x + 1) - ((x2 + ~1) div (x + 5)))
A137397: 2 2 3 3 4 4 4 4 5 5 5 5 5 5 5 5
(2x2 + 2x + ~41)
A155769: ~41 ~37 ~29 ~17 ~1 19 43 71 103 139 179 223 271 323 379 439
((x + 1) - ((x2 + 2) div (x + 5)))
A316846: 1 2 3 3 3 4 4 4 4 5 5 5 5 5 5 5
(1 + (2 div ((x2 + ~2) mod (x + 5))))
A175432: 1 1 2 1 1 1 3 1 1 1 1 1 1 1 1 1
((x + 1) - ((x2 div 2) div (2x + 5)))
A291764: 1 2 3 4 5 6 6 7 8 9 9 10 11 12 13 13
((x + 1) - ((x2 div 2) div (3 + (x div 2))))
A061775: 1 2 3 3 4 4 4 4 5 5 5 5 5 5 6 5
(~1 + (((x + 1) + (x div 2)) * (1 + (2 * (x div 2)))))
A195818: 0 1 11 14 34 39 69 76 116 125 175 186 246 259 329 344
(1 + ((x + 1) mod (1 + ((x + 1) div (2 + (x mod 2))))))
A290988: 1 1 2 1 3 1 4 3 5 3 6 3 7 5 8 5
(1 + ((2 + (x2 div 2)) * (1 + (2 * (x mod 2)))))
A282598: 3 7 5 19 11
(~1 + ((~1 + ((x + ~2) mod 5)) mod 3))
A156174: 1 ~1 1 ~1 0 1 ~1 1 ~1 0 1 ~1 1 ~1 0 1
(x div (1 + (3 * (1 + ((x + ~1) mod 3)))))
A288165: 0 0 0 0 1 0 0 1 1 0 2 1 1 3 2 1
(1 + (3 * (1 + (3 * ((x + 1) div 2)))))
A168401: 4 13 13 22 22 31 31 40 40 49 49 58 58 67 67 76
(6x2 + 9x + 7)
A129109: 7 22 49 88 139 202 277 364 463 574 697 832 979 1138 1309 1492
(1 + ((1 + (6 mod (x + 1))) mod 3))
A194290: 2 2 2 1 3 2 2 2 2 2 2 2 2 2 2 2
((x div 2) mod (1 + ((1 + ((x + 1) div 2)) mod 3)))
A284817: 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 0
(1 + ((2x mod ~5) div 3))
A105367: 1 0 0 ~1 0 1 0 0 ~1 0 1 0 0 ~1 0 1
(1 + ((0 - (2x mod 5)) div 3))
A105385: 1 0 ~1 0 0 1 0 ~1 0 0 1 0 ~1 0 0 1
(1 + ((5x2 + 5x) div 3))
A298787: 1 4 11 21 34 51 71 94 121 151 184 221 261 304 351 401
(1 + (3 * (2 mod (1 + (x mod (2 + (x mod 2)))))))
A339748-A325470: 1 1 1 1 1 7 1 1 1 1 1 7 1 1 1 1
(~1 + (3 * (2 - (3 * (x div ~2)))))
A168213: 5 14 14 23 23 32 32 41 41 50 50 59 59 68 68 77
((x + 1) - (9 * (x div ~2)))
A101233: 1 11 12 22 23 33 34 44 45 55 56 66 67 77 78 88
(x2 mod 37)
A070459: 0 1 4 9 16 25 36 12 27 7 26 10 33 21 11 3
(x2 mod 35)
A070457: 0 1 4 9 16 25 1 14 29 11 30 16 4 29 21 15
(1 + ((x - ((x div 4) mod 3)) div 3))
A132011: 1 1 1 2 2 2 2 3 3 3 3 4 5 5 5 6
(1 + (((x2 + 2x) - (x mod 3)) div 3))
A212984: 1 1 3 6 8 12 17 21 27 34 40 48 57 65 75 86
(1 + ((x3 + 3x2 + 2x + 6) div 3))
A155753: 3 5 11 23 43 73 115 171 243 333 443 575 731 913 1123 1363
(12x2 + 18x + 7)
A154105: 7 37 91 169 271 397 547 721 919 1141 1387 1657 1951 2269 2611 2977
(1 + ((4x2 + 10x + 4) div 3))
A194111: 2 7 14 24 37 52 70 91 114 140 169 200 234 271 310 352
(1 + (((x + ~3) mod (1 + (x div 2))) div 3))
A031262: 1 1 1 1 1 1 2 1 1 1 1 1 1 2 2 2
(1 + (3 * (((x + 1) div 2) * (1 + (x div 2)))))
A194073: 1 4 7 13 19 28 37 49 61 76 91 109 127 148 169 193
((x + ~3) mod (1 + ((1 + (x div 2)) div 3)))
A215592-A073189-A025684-A025678: 0 0 0 0 1 0 1 0 1 0 1 2 0 1 2 0
((2x + 1) - ((x mod (1 + (x div 2))) div 3))
A286999: 1 3 5 7 9 11 13 14 16 18 20 22 24 25 27 29
(1 + ((1 + (x * (x2 + (x mod 2)))) div 3))
A018259: 1 2 4 11 22 44
(1 + ((4x2 + 5x + 1) div 3))
A022781: 1 4 10 18 29 43 59 78 100 124 151 181 213 248 286 326
(1 + (((x + 1) * (2 - (x div ~2))) div 3))
A225647: 1 3 4 6 7
A011975: 1 3 4 6 7 11 12 17 19 24 26 33 35 43 46 54
(1 + ((4x2 + 12x + 8) div 3))
A202253: 3 9 17 27 41 57 75 97 121 147 177 209 243 281 321 363
(1 + ((8x2 + 8x) div 3))
A301696: 1 6 17 33 54 81 113 150 193 241 294 353 417 486 561 641
(9x2 + 15x + 7)
A304163: 7 31 73 133 211 307 421 553 703 871 1057 1261 1483 1723 1981 2257
((2x + 1) - (((x + 1) * (x div 2)) mod 3))
A327206: 1 3 5 6 8 11 13 15 17 18 20 23 25 27 29 30
(1 + (((x3 + x2) * (x div 2)) div 3))
A089794: 1 1 5 13 54
((x + 1) + ((x + 1) div 3) - (x div ~2))
A106252: 1 3 5 7 8 11 12 14 16 18 19 22 23 25 27 29
(1 + (x div (8 - ((x + 1) div 3))))
A239508: 1 1 1 1 1 1 2 2 2 2 3 3 4 4 5 6
((x + ~1) + ((x div 3) + ((x + 1) mod 3)))
A131452: 0 2 1 4 6 5 8 10 9 12 14 13 16 18 17 20
((4x + 3) + ((x + ~1) mod 3))
A263536: 5 7 12 17 19 24 29 31 36 41 43 48 53 55 60 65
((x + 1) - ((~x3 + 3x2 + ~2x) div 3))
A086514: 1 2 3 6 13 26 47 78 121 178 251 342 453 586 743 926
((x div ~2) div (~1 + (x div ~6)))
A211263: 0 0 0 1 1 1 1 1 1 1 1 2 2 1 1 2
((x + 1) - (((x2 + x) div ~2) div 3))
A243302: 1 3 4 6 9 11 14 18 21 25
(1 - (x2 div (~1 + (3 * (x div ~2)))))
A249036: 1 2 2 3 4 4 5 5 6 7 8 8 9 9 10 10
(1 + (3 * (x2 - (x2 div ~2))))
A298034: 1 7 19 43 73 115 163 223 289 367 451 547 649 763 883 1015
((x + 1) - ((~2 + (x div ~3)) div 3))
A095410: 2 3 4 5 7 8 9 10 11 12 13 14 15 17 18 19
(1 + (6 * (x div 7)))
A240830: 1 1 1 1 1 1 1 7 7 7 7 7 7 7 13 13
(1 + ((2 * (1 + (x mod 6))) div 3))
A131282: 1 2 3 3 4 5 1 2 3 3 4 5 1 2 3 3
(~1 + ((2 * ((x + 2) mod 5)) div 3))
A244895: 0 1 1 ~1 ~1 0 1 1 ~1 ~1 0 1 1 ~1 ~1 0
(1 + ((2 * (2x div 5)) div 3))
A063272: 1 1 1 1 1 2 2 2 3 3 3 3 3 4 4 5
(1 + (6 * (2 mod (1 + (x div 4)))))
A290686: 1 1 1 1 1 1 1 1 13 13 13 13 13 13 13 13
(~1 + (3 * (6 + (x2 div 2))))
A345735: 17 17 23 29 41 53 71 89 113 137 167 197 233 269 311 353
(x - (2x mod 19))
A249121: 0 ~1 ~2 ~3 ~4 ~5 ~6 ~7 ~8 ~9 9 8 7 6 5 4
((x * (x div 2)) div 19)
A015743: 0 0 0 0 0 0 0 1 1 1 2 2 3 4 5 5
(x - (x div (x + ~19)))
A191881: 0 2 3 4 5 6 7 8 9 10 12 13 14 16 17 19
(x3 mod 19)
A070481: 0 1 8 8 7 11 7 1 18 7 12 1 18 12 8 12
(1 + ((2x - (x mod 6)) div 3))
A020917: 1 1 1 2 2 2 5 5 5 6 6 6 9 9 9 10
(9x2 + 18x + 7)
A259055: 7 34 79 142 223 322 439 574 727 898 1087 1294 1519 1762 2023 2302
(1 + ((~x mod (2 + (x div 3))) div 3))
A210721: 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 3
(x div (1 + ((2 * (x - (x div 3))) div 3)))
A231813: 0 1 1 1 1 1 2 1 1 1 2 1 2 1 2 2
(1 + (x div (3 * (2 - ((x mod 3) mod 2)))))
A117910: 1 1 1 1 2 1 2 3 2 2 4 2 3 5 3 3
(1 + (3 * ((1 + ((x2 + x) div 2)) div 2)))
A213484: 1 4 7 10 16 25 34 43 55 70 85 100 118 139 160 181
(1 + (6 * ((2x + 1) + (x mod 2))))
A140716: 7 25 31 49 55 73 79 97 103 121 127 145 151 169 175 193
(1 + ((x - ((x mod (1 + (x div 2))) mod 2)) div 3))
A157684-A087847: 1 1 1 1 2 2 3 3 3 4 4 4 4 5 5 5
((x + ~1) - (3 * ((~2x + ~2) + (x mod 2))))
A113805: 5 9 19 23 33 37 47 51 61 65 75 79 89 93 103 107
((~1 + (x div 2)) mod (1 + (((x + 1) div 2) mod 3)))
A283683: 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0
(1 + (x div (3 * (2 + ((x mod 3) div 2)))))
A197081: 1 1 1 1 1 1 2 2 1 2 2 2 3 3 2 3
(x2 div 49)
A265409: 0 0 0 0 0 0 0 1 1 1 2 2 2 3 4 4
(x2 mod 47)
A070469: 0 1 4 9 16 25 36 2 17 34 6 27 3 28 8 37
(48x2 + 1)
A158638: 1 49 193 433 769 1201 1729 2353 3073 3889 4801 5809 6913 8113 9409 10801
(48x2 + ~1)
A065532: ~1 47 191 431 767 1199 1727 2351 3071 3887 4799 5807 6911 8111 9407 10799
(1 + (((x + 3) mod 8) mod 3))
A270788: 1 2 3 1 2 1 2 3 1 2 3 1 2 1 2 3
(x mod (1 + ((x mod ~7) mod 3)))
A280046: 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0
(x3 mod 25)
A070487: 0 1 8 2 14 0 16 18 12 4 0 6 3 22 19 0
((x2 + ~x) div 23)
A011876: 0 0 0 0 0 0 1 1 2 3 3 4 5 6 7 9
(x3 mod 23)
A070485: 0 1 8 4 18 10 9 21 6 16 11 20 3 12 7 17
(1 + ((x2 + 2x) div 24))
A029071: 1 1 1 1 2 2 3 3 4 5 6 6 8 9 10 11
(3x2 + 3x + 23)
A007637: 23 29 41 59 83 113 149 191 239 293 353 419 491 569 653 743
(1 + (3 * ((~x2 + 2x) mod 8)))
A146160: 1 4 1 16 1 4 1 16 1 4 1 16 1 4 1 16
(1 + ((2 + ((x2 + ~x) div 4)) div 3))
A008673: 1 1 1 2 2 3 4 5 6 7 9 10 12 14 16 19
(1 + ((x - ((2 - (x div 4)) div 2)) mod 3))
A305391: 3 1 2 3 2 3 1 2 3 1 2 3 2 3 1 2
(1 + (((x + 2) div (2 + ((x div 2) mod 2))) div 3))
A261129: 1 1 1 1 2 2 1 2 2 2 2 2 3 3 2 2
(13 + ((x2 + x) div 2))
A173036: 13 14 16 19 23 28 34 41 49 58 68 79 91 104 118 133
((x + 1) div (1 + ((x + 2) mod 12)))
A338920: 0 0 0 0 0 0 0 0 0 0 11 6 4 3 3 2
((x + 1) - (x div (~12 + (x div 2))))
A091213: 1 3 4 5 6 7 8 9 10 12 13 14 15 17 18 19
(x4 mod 13)
A070517: 0 1 3 3 9 1 9 9 1 9 3 3 1 0 1 3
(3x2 div 11)
A194213: 0 0 1 2 4 6 9 13 17 22 27 33 39 46 53 61
(x4 mod 11)
A070515: 0 1 5 4 3 9 9 3 4 5 1 0 1 5 4 3
(1 + (5x mod 12))
A258054: 1 6 11 4 9 2 7 12 5 10 3 8 1 6 11 4
((3x + 1) - (x mod 12))
A033037: 1 3 5 7 9 11 13 15 17 19 21 23 37 39 41 43
(1 + (((x div 4) - (x mod 4)) div 3))
A025864: 1 0 0 0 1 1 0 0 1 1 1 0 2 1 1 1
(30x + 13)
A082369: 13 43 73 103 133 163 193 223 253 283 313 343 373 403 433 463
(~1 + ((x3 + 4x2 + 2x + 8) div 3))
A160860: 1 4 11 24 47 80
((~1 + (x div 2)) mod (1 + ((2 + (x div 2)) div 3)))
A257684: 0 0 0 0 1 1 0 0 0 0 1 1 2 2 2 2
(2 - ((~x + 1) div (1 + ((2 + (x div 2)) div 3))))
A061716: 1 2 3 3 4 4 5 5 5 5 5 6 6 6 6 6
(5 mod (1 + ((2 * (x div 2)) div 3)))
A334235-A321858: 0 0 0 0 1 1 2 2 2 2 1 1 0 0 0 0
((x + 1) - ((~x - ((x div 2) mod 2)) div 3))
A225647: 1 3 4 6 7
A234349: 1 3 4 6 7 8 10 11 12 13 15 16 17 19 20 22
((2x + 4) div (~1 + (3 * (2 + (x mod 2)))))
A302604: 0 0 1 1 2 1 3 2 4 2 4 3 5 3 6 4
(1 + ((x - ((x div 2) mod (~2 + (x mod 2)))) div 3))
A086916: 1 1 2 2 2 2 3 3 3 4 4 4 5 5 6 6
(18x2 + 6x + 1)
A081272: 1 25 85 181 313 481 685 925 1201 1513 1861 2245 2665 3121 3613 4141
(1 + (3 * ((3x2 + x) div 2)))
A081274-A038764: 1 7 22 46 79 121 172 232 301 379 466 562 667 781 904 1036
(18x2 + ~6x + 1)
A081589: 1 13 61 145 265 421 613 841 1105 1405 1741 2113 2521 2965 3445 3961
(1 + (3 * ((3x2 + ~x) div 2)))
A080855: 1 4 16 37 67 106 154 211 277 352 436 529 631 742 862 991
(30x + 23)
A128473: 23 53 83 113 143 173 203 233 263 293 323 353 383 413 443 473
((x + 1) - (((x3 + ~x) div 2) div 3))
A254749: 1 2 2 0 ~5 ~14 ~28 ~48 ~75 ~110 ~154 ~208 ~273 ~350 ~440 ~544
(1 + (6 * (x + (2 * (x div 3)))))
A225227: 1 7 13
A073473: 1 7 13 31 37 43 61 67 73
(1 + (((x + 2) + (x mod (2 + (x mod 2)))) div 3))
A016729: 1 2 2 2 3 4 3 4 4 4 5 6 5 6 6 6
(18x2 + 12x + 1)
A081275: 1 31 97 199 337 511 721 967 1249 1567 1921 2311 2737 3199 3697 4231
((2x + 1) - (((~x + ~2) + (x mod 2)) div 3))
A284589: 2 4 7 9 11 13 16 18 21 23 25 27 30 32 35 37
(1 + (x div (8 - ((x + ~2) div 3))))
A094996-A025787: 1 1 1 1 1 1 1 2 2 2 2 3 3 3 4 4
((x + 1) - ((~2x + (x div 4)) div 3))
A186223: 1 3 5 6 8 9 11 13 14 16 17 19 20 22 24 25
((6x + 1) + ((x2 + x) div 2))
A302537: 1 8 16 25 35 46 58 71 85 100 116 133 151 170 190 211
(1 + ((x2 div 4) + (2x div 3)))
A212986: 1 1 3 5 7 10 14 17 22 27 32 38 45 51 59 67
(2x - (x2 div (1 + (2x div 3))))
A131138: 0 1 2 3 3 4 5 5 6 7 6 7 8 8 9 10
((1 + (2 * (x mod 2))) mod (1 + ((x div 2) div 3)))
A011682: 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0
((~2 + (x mod 3)) mod (1 + ((x div 2) div 3)))
A319854: 0 0 0 0 0 0 0 1 0 0 1 0 1 2 0 1
(1 + (((2 + (x div 2)) div (2 - (x mod 2))) div 3))
A287476: 1 1 1 2 1 2 1 2 2 3 2 3 2 3 2 4
(~2 mod (1 + ((x div (2 - (x mod 2))) div 3)))
A304034: 0 0 0 0 0 0 0 1 0 2 0 2 1 3 1 4
((x2 + 4x + 5) - (3 * (x mod 2)))
A214345: 5 7 17 23 37 47 65 79 101 119 145 167 197 223 257 287
(9x2 + 12x + 5)
A185939: 5 26 65 122 197 290 401 530 677 842 1025 1226 1445 1682 1937 2210
((x + ~1) - (((~x3 + x) div 2) div 3))
A283551: ~1 0 2 6 13 24 40 62 91 128 174 230 297 376 468 574
((x + 1) - (((~x3 + x) div 2) div 3))
A222011: 1 2 4 8
A000125: 1 2 4 8 15 26 42 64 93 130 176 232 299 378 470 576
((x + 1) - (3 * (~x + (x div 5))))
A188261: 1 5 9 13 17 18 22 26 30 34 35 39 43 47 51 52
(1 + ((x + (x2 div 5)) div 3))
A062490: 1 1 1 2 3 4 5 6 7 9 11 12 14 16 18 21
(1 + ((x + (((~x + 2) div 2) mod 3)) div 3))
A058224: 1 1 1 2 3 3 3 3 3 4 5 5 5 5 5 6
((x + 1) - ((~x + ((x div 2) mod 3)) div 3))
A047564: 1 3 4 5 6 7 9 11 12 13 14 15 17 19 20 21
(1 + ((x + ((x + (x mod 2)) div 3)) div 3))
A287864: 1 1 1 2 2 3 3 4 4 5 5 6 6 6 7 7
(0 - (x div (~1 + ((~x + (x div 3)) div 3))))
A235123: 0 1 1 2 2 2 2 3 3 3 3 3 3 4 3 3
(1 + ((x3 + 4x2 + 5x) div 3))
A212973: 1 4 12 27 50 84 131 192 270 367 484 624 789 980 1200 1451
(3x4 + 6x3 + ~3x + 1)
A181475: 1 7 91 397 1141 2611 5167 9241 15337 24031 35971 51877 72541 98827 131671 172081
(~1 + ((x3 + ~3x2 + ~x) div 3))
A109620: ~1 ~2 ~3 ~2 3 14 33 62 103 158 229 318 427 558 713 894
((x + 1) - ((~x + ((x div 2) div ~2)) div 3))
A225647: 1 3 4 6 7
A186159-A184578: 1 3 4 6 7 8 10 11 13 14 16 17 18 20 21 23
((x + ~1) - (3 * (~x + ((~1 + (x div 2)) div 2))))
A088227: 2 6 7 11 15 19 20 24 28 32 33 37 41 45 46 50
(1 + ((x + (x2 div 8)) div 3))
A025767: 1 1 1 2 3 3 4 5 6 7 8 9 11 12 13 15
(1 + ((x + ((x mod (2 + (x div 2))) div 2)) div 3))
A330996: 1 1 2 2 2 2 3 3 4 4 4 5 5 6 6 7
(1 + ((x * ((x mod (2 + (x mod 2))) div 2)) div 3))
A173441-A132068: 1 1 1 1 1 2 1 1 1 1 1 4 1 1 1 1
((2x + 1) - (3 * (~x + (x div 4))))
A305408: 1 6 11 16 18 23 28 33 35 40 45 50 52 57 62 67
((x + 1) - ((~x + ((2 - (x div 2)) div 2)) div 3))
A289036: 1 2 4 5 7 8 10 11 12 14 15 17 18 19 21 22
(1 + ((x * (x div (2 - ((x div 2) mod 2)))) mod 3))
A296976: 1 1 2 1 3 2 1 2 3 1 2 2 1 1 2 1
(1 + ((x + ((x + ~2) mod (2 + (x mod 2)))) div 3))
A123920: 1 2 1 2 2 2 3 4 3 4 4 4 5 6 5 6
((x div 3) - (x div (~1 + ((~x + 2) div 3))))
A073188: 0 1 2 3 3 4 4 5 5 6 6 6 7 7 7 8
(15x2 + 6x + 1)
A080861: 1 22 73 154 265 406 577 778 1009 1270 1561 1882 2233 2614 3025 3466
(1 + ((x2 + 2) div ((x + 3) + (x div 2))))
A092982: 1 1 2 2 3 3 4 4 5 6 6 7 7 8 9 10
(x3 mod (1 + ((x * (x mod 2)) div 3)))
A035464: 0 0 0 1 0 1 0 1 0 1 0 3 0 2 0 3
((6x + 5) - (x div 3))
A187387: 5 11 17 22 28 34 39 45 51 56 62 68 73 79 85 90
((x + 2) div (9 - (x div 3)))
A302931: 0 0 0 0 0 0 1 1 1 1 2 2 2 3 3 4
(2 div (1 + (2 * (2 + (x mod 2))) - (x div 3)))
A337563: 0 0 0 0 0 0 0 0 0 0 1 0 2 0 2 1
((2x + 1) + (x div 3) - (x div 4))
A097911: 1 3 5 8
A190280: 1 3 5 8 9 11 14 16 17 20 22 24 26 28 30 33
(x2 div ((x + 5) + (x div 3)))
A074239: 0 0 0 1 1 2 2 3 4 4 5 6 6 7 8 9
(1 + ((x + ~2) div (2 + (x div 2) - (x div 3))))
A097429: 0 0 1 1 1 2 2 2 2 3 3 3 3 3 3 4
((4x + 1) - ((x div 3) + (x div 2)))
A063247: 1 5 8 11 14 18 20 24 27 30 33 37 39 43 46 49
(3x mod (1 + (x div 2) - (x div 3)))
A057556: 0 0 0 0 0 1 0 1 0 1 0 0 0 0 2 0
((~1 + ((x + 1) mod 3)) * (1 + (x div 3)))
A128615: 0 1 ~1 0 2 ~2 0 3 ~3 0 4 ~4 0 5 ~5 0
((~1 + (x div 2)) mod ((x + 1) div (1 + (x div 3))))
A108736: 0 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0
((x - ((1 + (x div 2)) div 2)) div (1 + (x div 3)))
A305426: 0 1 1 1 1 2 1 1 2 1 1 2 1 2 2 1
(x - (~7 * (1 + (x div 3))))
A285468: 7 8 9 17 18 19 27 28 29 37 38 39 47 48 49 57
(~2 + (((x + 1) div 2) + (2 div (1 + (x div 3)))))
A035454: 0 1 1 1 1 2 1 2 2 3 3 4 4 5 5 6
((x + 1) + ((x div 8) + (x div 3)))
A207672: 1 2 3 5 6 7 9 10 12 14 15 16 18 19 20 22
((x + 2) - ((~x + 2) div ((x + 1) - (x div 3))))
A092460: 0 3 4 6 7 8 9 10 11 12 13 14 16 17 18 19
(1 + ((x mod (1 + (x div 2))) mod 2) - (x mod 3))
A258940: 1 0 ~1 2 1 ~1 1 1 0 1 0 0 2 0 ~1 2
((1 + (x div 8)) div (1 + (x mod 3)))
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((2x2 + 2x + 1) - (x2 div 3))
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(x - (7 * ((~x + 1) div 3)))
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(7x2 + 28x + 21)
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(2x - ((x + 3) div 7))
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(2x - ((2x + 1) div 7))
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((2x2 + ~x + 1) div 7)
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(2x - ((2x + ~2) div 7))
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((x - ((x div 2) mod 4)) mod 7)
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(2x - ((2x + 4) div 7))
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(1 mod ((x2 + ~2x + ~2) mod 7))
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(x - (14 * (~x + (x mod 2))))
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(0 - ((~2x + (x mod 2)) div 7))
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(14x2 + ~13x)
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(x - (7 * ((~x2 + x) div 2)))
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(x - ((~x2 + 2x + ~2) div 7))
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(1 + (((x * (1 - (x div 3))) div 3) mod 2))
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(1 + (x mod (2 + ((~x + (x div 3)) mod 3))))
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(1 + ((9x2 + 6x) div 2))
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(1 + ((x div 2) + ((x mod 3) div 2)) - (x mod 2))
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(1 + ((x3 mod (~2x + 5)) mod 2))
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A088676: 1 2 2 2 3 3 3 3 4 4 5 5 5 5 6 6
(3 + ((x2 div 4) div (x + 3)))
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(1 + ((x4 div (2x + ~1)) mod 2))
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(3 + ((x - ((x div 2) mod 2)) * (1 + (x div 2))))
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(1 + (((x + 1) + (x div (4 + (x mod 2)))) div 2))
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(1 + (2 * ((x + 1) + (2 * (2x + (x mod 2))))))
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(1 + ((((~x + 2) div 5) mod (x + 1)) mod 2))
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((2x + 3) + (x mod (~3 + (x mod 2))))
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((2x + 3) + (x div 2) - (x mod 4))
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(1 + (((~x + ((x div 2) mod 2)) div 2) mod (2x + 2)))
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A205783: 1 4 6 8 9 10 12 14 15 16 18 20 21 22 24 26
(4x3 + 14x2 + 16x + 6)
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((2 * (x mod ~3)) mod (2x + 3))
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(16x2 + 32x + 12)
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(x - ((~x2 + x + ~2) div (2x + 3)))
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((x + 2) - ((~x2 + 2x) div (2x + 3)))
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((2x + 2) - (x2 div (2x + 3)))
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((x + 1) - ((~1 + (x div ~2)) * ((x + 1) div 2)))
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(1 + (((x + 1) * (x + ((x div ~2) mod 2))) div 2))
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(1 + ((x - ((x * (~2 + (x div 2))) div (x + 1))) div 2))
A082429-A047744: 1 2 2 3 3 3 4 4 4 5 5 5 5 6 6 6
(1 + ((x5 + 2x2 + 1) div 2))
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(2x2 + 29)
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(1 + (2 * (x - ((x div 5) div ~2))))
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(1 + (((2x mod (2 + (x div 2))) div ~2) mod 2))
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((2x + 2) - (2x div ~5))
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((x + 1) mod (1 + (x mod (2 - (x div ~4)))))
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((x + 1) - (2 * ((x + (x div 4)) div ~2)))
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(1 + (2 * (x - ((x + (x div 4)) div ~2))))
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(1 + ((x - ((x + ~2) mod (2 - (x div ~2)))) mod 2))
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(1 + (2 * ((2x mod (~1 + (x div ~2))) mod 2)))
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(1 + (2 * ((x mod (~1 + (2 * (x div 3)))) mod 2)))
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(1 + (((x mod (~1 + (2 * (x div 4)))) div 2) mod 2))
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(x3 mod 21)
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((x div 2) mod (1 + (2 * ((x mod 5) mod 2))))
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(1 + (x div (4 - (((x div 2) mod 3) div 2))))
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(1 + (2 * ((x mod (~2 - (x div 3))) mod 2)))
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(1 + (((1 - (x div 2)) div (2 + (x mod 3))) mod 2))
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((x + 3) div (3 + ((x mod 3) div 2)))
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((x + 2) div (1 + ((((x + 1) + (x div 2)) div 2) div 2)))
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(3 + (((x + 1) + (x div 2)) * ((x + 1) div 2)))
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(1 + ((((x + 1) + (x div 2)) * ((x + 1) div 2)) div 2))
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(1 + ((x div 8) + (((x + 1) div 2) div 2)))
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(2x2 + 18x + 21)
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(1 + (((x div ~3) * ((x + ~1) div 2)) mod 2))
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(4x3 + ~12x2 + 12x + 1)
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((x + 1) - (2 * ((x + (x div 2)) div ~4)))
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(1 + (((x + ~1) mod (2 - (x div ~4))) div 2))
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((x + 1) - (2x div (~2 + (x div ~4))))
A080036: 1 3 5 6 8 9 10 12 13 14 15 17 18 19 20 21
((x + 3) - (x div (~2 + (x div ~4))))
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(~1 + (2 * (((~x + 1) mod (2 - (x div ~2))) mod 2)))
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(1 + (4 * ((x div ~5) mod 2)))
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(1 + ((2x mod (2 + (x mod 6))) div 2))
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(~1 + (2 * (x - (2 * ((~2x + ~2) + (x mod 2))))))
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((x + 1) - (1 mod (1 - (2 * (((x + 1) div 2) div 2)))))
A173919: 1 2 3 4 5 6 7 10 11 12 13 16 17 18 19 22
compr(\x.((x div 2) mod 2),(1 + ((((x + 1) div 2) div 2) div 2)))
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(2 div ((x + 2) div (1 + (2 * (((x + ~1) div 2) div 2)))))
A076881: ~1 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1
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(1 + ((x div (4 + ((x div 3) mod 2))) mod 2))
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(5 + ((x mod ~7) mod 2))
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(64x2 + 1)
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(x2 + 29)
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(x3 mod 33)
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((x2 + ~x) div 31)
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(x3 mod 31)
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((x + 3) - (2 div (x + ~16)))
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(1 + ((x + 2) div (4 + (x div 8))))
A274011-A076634: 1 1 2 2 2 2 3 3 3 3 3 3 3 4 4 4
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(1 + ((x - (((x - (x div 4)) div 2) mod 2)) div 2))
A159481: 1 1 1 2 2 3 4 4 4 5 6 6 7 7 7 8
(1 + (x div (2 * (6 - (x mod 4)))))
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(1 + (((x - (x mod (2 + (x mod 4)))) div 2) mod 2))
A204697: 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 2
(29x + 1)
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(2x div (1 + (4 * (2 + ((x div 2) mod 2)))))
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(1 + ((x div (2 + (x mod (2 + ((x div 2) mod 2))))) mod 2))
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((x div 2) div (3 + ((x + 1) mod 8)))
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((2 + (x * (x div 2))) div 17)
A194210: 0 0 0 0 0 0 1 1 2 2 3 3 4 4 5 6
((x + 1) div (~x + 19))
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(x4 mod 17)
A070534: 0 1 16 13 1 13 4 4 16 16 4 4 13 1 13 16
(((x2 + ~x) div 2) div 15)
A011883-A011882: 0 0 0 0 0 0 1 1 1 2 3 3 4 5 6 7
(x4 mod 15)
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(1 + (((x2 + ~3x) div 8) mod 2))
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((x + 1) div (5 + ((~x + 1) mod 4)))
A278341-A276520: 0 0 0 0 0 1 0 1 1 2 1 1 2 2 1 2
(1 + (2 * (1 - (x div (~2 + ((~x + 2) div 4))))))
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(1 + (((2x + 1) mod (2 + (x div 4))) div 2))
A330754-A330753-A330746-A324369-A303759-A293810-A276781-A187279-A082068-A076820: 1 1 1 1 1 2 1 1 1 2 1 2 1 2 3 1
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A156775: 1 1 1 1 1 2 1 1 1 2 1 2 1 3 2 1
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A303979-A094091: 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0
((~x + 1) mod (1 + (x div (4 + (x mod 4)))))
A067432: 0 0 0 0 1 0 1 0 2 0 1 0 1 0 2 1
(1 + ((((x2 + 2x) - (x mod 4)) div 2) div 2))
A212988: 1 1 2 4 7 9 12 16 21 25 30 36 43 49 56 64
(16x2 + ~3x + 1)
A143861: 1 14 59 136 245 386 559 764 1001 1270 1571 1904 2269 2666 3095 3556
(x2 div (5 + (x2 div 4)))
A086673: 0 0 0 1 1 2 2 2 3 3 3 3 3 3 3 3
(1 + (2 * ((x + 2) - (x div (~2 + ((~x + 1) div 2))))))
A257292: 5 9 11 13 15 19 21 23 25 27 29 31 33 35 37 39
(1 + ((x2 + ~2x) div (2x + 12)))
A008671: 1 0 1 1 1 1 2 2 2 3 3 3 4 4 5 5
(1 + (2 * (x - (2 * (2 mod (~4x + 2))))))
A298035: 1 3 21 39 57 75 93 111 129 147 165 183 201 219 237 255
(1 + (2 * (x - (1 mod (~8x + 2)))))
A063305: ~1 13 31 49 67 85 103 121 139 157 175 193 211 229 247 265
((x + 1) - (2 * (~8x + (x mod 2))))
A161441: 1 16 35 50 69 84 103 118 137 152 171 186 205 220 239 254
(1 + ((((x2 + ~1) mod (2 + (x div 2))) div 2) div 2))
A272917: 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 3
(1 + ((((2x + 2) mod (2 + (x div 2))) div 2) div 2))
A030421: 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 2
(x mod (1 + (2 * (2 + (2x div (2 + (x div 2)))))))
A103303: 0 1 2 3 4 5 6 7 8 9
A241494: 0 1 2 3 4 5 6 7 8 9 1 0 1 2 3 4
(3 + ((2x2 mod (2 + (x div 2))) mod 2))
A115787: 3 3 3 3 3 3 3 4 3 3 3 3 3 3 4 3
(1 + (2 * (4x div (4 + (x div 2)))))
A177691: 1 3 3 5 5 7 7 9 9 9 9 9 9 11 11 11
(1 + ((x - (((~x + 1) mod (2 + (x div 2))) mod 2)) div 2))
A113512: 0 1 2 2 2 3 4 4 4 5 5 6 6 7 7 8
(1 + (2 * (((x2 + ~x) mod (2 + (x div 2))) mod 2)))
A060268: 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 3
(1 + ((((~x2 + x) mod (2 + (x div 2))) div 2) mod 2))
A046072-A034380: 1 1 1 1 1 1 1 2 1 1 1 2 1 1 2 2
(1 + (((x - (x2 mod (2 + (x div 2)))) div 2) mod 2))
A307614: 1 1 1 2 1 1 1 2 1 2 1 1 1 1 2 2
(1 + ((((x div 3) - ((x div 2) mod 2)) div 2) div 2))
A081753: 1 1 0 1 1 1 1 1 1 1 1 1 2 2 1 2
(1 + ((((x + 1) div 2) mod (2 + ((x div 2) mod 2))) div 2))
A337473: 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 2
(2 div (1 + ((x + 1) mod (4 + ((x div 2) mod 2)))))
A097516: 1 0 0 0 1 0 0 0 1 0 1 0 1 0 2 1
(2 div (1 + ((~x + 1) mod (2 * (2 + ((x div 2) mod 2))))))
A245187: 1 2 0 0 1 2 1 2 1 2 0 0 1 2 0 0
(1 + (((x mod (2 + ((~x + 2) * (x div 2)))) div 2) mod 2))
A188795: 1 1 1 1 1 1 1 2 2 2 1 1 2 1 1 2
(1 + (x div (2 * (2 + ((x + 1) mod (2 + (x mod 2)))))))
A332086: 1 1 1 1 1 2 2 1 2 2 2 3 3 2 3 3
((2x + 1) - (x div (4 * (2 + (x mod 2)))))
A187907-A187232: 1 3 5 7 9 11 13 15 16 19 20 23 24 26 28 30
((x + 2) mod (~1 + (4 * (x mod (2 + (x mod 2))))))
A294887-A035322: 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0
(16x2 + ~7x + 1)
A143855: 1 10 51 124 229 366 535 736 969 1234 1531 1860 2221 2614 3039 3496
(1 + ((x - ((1 - (x div 3)) mod 4)) div 2))
A335358: 0 1 1 2 3 3 2 3 3 4 5 5 6 7 7 8
((x div 2) div (1 + (x div (2 + ((x + 1) mod 4)))))
A341594: 0 0 1 0 1 1 1 0 1 1 1 0 1 1 2 0
(1 + (2 * ((2x - ((x div 2) mod 2)) mod 4)))
A155158: 1 5 7 3 1 5 7 3 1 5 7 3 1 5 7 3
(1 + ((x mod 9) mod 8))
A277547: 1 2 3 4 5 6 7 8 1 1 2 3 4 5 6 7
((x + 1) - ((2x + 4) div ~7))
A093435-A048964: 2 3 5 6 7 8 10 11 12 14 15 16 17 19 20 21
((x + 1) - (4x div ~7))
A186324: 1 3 5 6 8 9 11 12 14 16 17 19 20 22 23 25
((2x + 1) - ((x + 2) div ~7))
A064997: 2 4 6 8 10 12 15 17 19 21 23 25 27 30 32 34
((x + 1) div (3 - (x div ~7)))
A339930: 0 0 0 1 1 1 1 2 1 2 2 2 2 2 3 2
(2x - (2 mod (~1 + (x div ~7))))
A063459: 0 2 4 6 8 10 12 14 17 19 21 23 25 27 29 32
(x2 div ((x + 1) - (x div ~7)))
A319288: 0 0 1 1 2 3 4 5 5 6 7 8 9 10 11 11
((x + 1) - (((~x + 2) - (x div 2)) div 8))
A027925: 1 2 4 5 6 7 8 9 11 12 13 14 15 17 18 19
((4x + 3) mod 9)
A142069: 3 7 2 6 1 5 0 4 8 3 7 2 6 1 5 0
(((x + 1) * (x div 3)) div 9)
A307727: 0 0 0 0 0 0 1 1 2 3 3 4 5 6 6 8
((~2x2 + ~2x + 1) mod 9)
A254374: 1 6 7 4 6 4 7 6 1 1 6 7 4 6 4 7
((x2 + 3x + ~4) mod 9)
A144483: 5 0 6 5 6 0 5 3 3 5 0 6 5 6 0 5
(1 + ((x + ~1) div 9) - (x mod 2))
A247051: 0 0 1 0 1 0 1 0 1 0 2 1 2 1 2 1
((x3 + ~3x2 + 2x) div 9)
A011891: 0 0 0 0 2 6 13 23 37 56 80 110 146 190 242 303
(54x + 36)
A305068: 36 90 144 198 252 306 360 414 468 522 576 630 684 738 792 846
(36x2 + ~18x)
A060787: 0 18 108 270 504 810 1188 1638 2160 2754 3420 4158 4968 5850 6804 7830
(1 mod ((x2 + 2x + ~2) mod 9))
A287725: 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0
(1 mod ((x2 + ~2x + ~2) mod 9))
A287769: 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1
(x div ((x + ~1) + (2x mod 9)))
A186733-A185643: 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0
(18x2 + ~17x)
A282850: 0 1 38 111 220 365 546 763 1016 1305 1630 1991 2388 2821 3290 3795
((x2 div (2 - (x mod 2))) mod 9)
A168037: 0 1 2 0 8 7 0 4 5 0 5 4 0 7 8 0
((2x2 + (x mod 2)) mod 9)
A086245: 0 3 8 1 5 6
(x - (9 * ((~x2 + x) div 2)))
A051682: 0 1 11 30 58 95 141 196 260 333 415 506 606 715 833 960
((x + (2 * (2 + (x mod 2)))) div 9)
A320278: 0 0 0 1 0 1 1 1 1 1 1 1 1 2 2 2
((3x2 + 2x) mod 9)
A145577: 0 5 7 6 2 4 3 8 1 0 5 7 6 2 4 3
(27x2 + ~18x)
A064201: 0 9 72 189 360 585 864 1197 1584 2025 2520 3069 3672 4329 5040 5805
(((1 + (x div 2)) div 2) - (x div 9))
A037809: 0 0 1 1 1 1 2 2 2 1 2 2 2 2 3 3
(x - ((x div 9) + (x div 4)))
A013928: 0 1 2 3 3 4 5 6 6 6 7 8 8 9 10 11
((x + 2) mod ((x + 2) - (x mod 9)))
A289411: 0 1 0 1 0 1 0 1 0 0 1 2 3 4 5 6
((~3x2 + 4x) mod 9)
A111889: 0 1 5 3 4 8 6 7 2 0 1 5 3 4 8 6
(x5 mod 9)
A070595: 0 1 5 0 7 2 0 4 8 0 1 5 0 7 2 0
((x2 + 2x) mod (1 + ((~x + 1) mod 8)))
A008437: 0 0 0 1 0 0 0 0 0 0 0 3 0 0 0 0
(1 - (x mod (1 + ((x2 + 2x) mod 8))))
A291584: 1 0 1 ~2 1 0 1 ~6 1 0 1 ~2 1 0 1 ~6
(1 div ((x + 1) - ((x2 + ~2x) mod 8)))
A185175: 1 ~1 0 1 0 ~1 0 0 0 0 0 0 0 0 0 0
((2x + 1) + (x div 2) - (x div 8))
A190085: 1 3 6 8 11 13 16 18 20 22 25 27 30 32 35 37
((2x + 1) + (x div 8) - (x mod 2))
A327220: 1 2 5 6 9 10 13 14 18 19 22 23 26 27 30 31
((((x + 1) div 2) div 2) div (1 + (x div 8)))
A147753: 0 0 0 1 1 1 1 2 1 1 1 1 1 1 1 2
(1 + (((x + ((~x + 1) mod 3)) div 4) mod 2))
A085297: 1 1 2 2 2 2 2 2 1 1 1 2 2 2 1 1
(1 + (((x * (~2 + (x div 3))) div 4) mod 2))
A161385: 1 2 2 2 2 1 1 1 1 1 1 1 1 1 2 2
(1 - (2x div (~3 + ((~x + 2) div 4))))
A101776: 1 2 3 3 3 4 4 4 5 5 5 5 5 6 6 6
(2 - (2x div (~3 + ((~x + 2) div 4))))
A132913: 2 3 4 4 4 5 5 5 6 6 6 6 6 7 7 7
((x + 1) - ((0 - ((x2 + 2x) div 4)) div 2))
A186347: 1 2 4 6 8 10 13 16 19 22 26 30 34 38 43 48
((x + ~2) mod (~1 + (2 * ((x * (x mod 2)) div 4))))
A035640: 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 3
(1 + ((((x mod 3) mod 2) + (x div 4)) div 2))
A019556-A008350: 1 1 1 1 2 1 1 2 2 2 2 2 2 3 2 2
(x mod (1 + (2 * (8 - (x div 4)))))
A103303: 0 1 2 3 4 5 6 7 8 9
A053832: 0 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4
(1 + (((x + ~1) + (x mod 2)) div (2 + (x div 4))))
A241216-A125173-A064415: 0 1 1 2 2 2 2 3 2 3 3 3 3 3 3 4
(1 + (~7 mod (2 + (x div 4))))
A053384: 2 2 2 2 3 3 3 3 2 2 2 2 4 4 4 4
((3x + 1) div (3 + (x div 4)))
A023964: 0 1 2 3 3 4 4 5 5 5 6 6 6 6 7 7
(4 - ((~x + 1) div (3 + (x div 4))))
A080800: 4 4 5 5 5 5 6 6 6 6 6 6 6 6 7 7
((x + ~1) mod (1 + (x2 mod (2 + (x div 4)))))
A196096: 0 0 0 0 1 0 0 0 0 0 0 0 1 2 1 0
((x div 2) mod (1 + (x2 mod (2 + (x div 4)))))
A284508-A283316: 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0
((3x + 1) - ((x - (x div 4)) div 2))
A231407: 1 4 6
A066095-A003622: 1 4 6 9 12 14 17 19 22 25 27 30 33 35 38 40
(0 - (x div (~1 + (x div (~2 - (x mod 4))))))
A167439: 0 1 1 2 2 2 2 3 2 3 3 3 2 3 3 4
(3 + (2 * (x + (x div 2))) - (x mod 4))
A112062: 3 4 7 8 15 16 19 20 27 28 31 32 39 40 43 44
(1 + (2 * (2x + (x div 2) - (x mod 4))))
A045797: 1 3 7 9 21 23 27 29 41 43 47 49 61 63 67 69
(1 + (4 * ((4x2 + ~x) div 2)))
A301858: 1 5 29 65
(~1 + (2 * ((x2 div (x - ((~x + 2) div 2))) mod 2)))
A077008: ~1 1 ~1 ~1 1 1 ~1 ~1 1 ~1 1 1 ~1 ~1 1 ~1
(1 + ((((~x + ((x + 2) * (x div 2))) div 2) div 2) div 2))
A008667: 1 0 1 1 2 2 3 3 5 5 7 7 10 10 13 14
(1 + ((x mod (~2 + ((x * (2 - (x div 2))) div 2))) mod 2))
A300983: 1 1 1 1 1 2 1 2 1 1 2 1 1 2 2 2
(1 + (((x + ~2) * (x div 2)) div (x + 6)))
A172033-A094994-A026839: 1 1 1 1 1 1 2 2 2 2 3 3 4 4 5 5
(x - ((x2 + ~1) div (x + 7)))
A130241: 1 1 2 3 3 3 4 4 4 4 5 5 5 5 5 5
((2x + 9) + ((x2 + x) div 2))
A166136: 9 12 16 21 27 34 42 51 61 72 84 97 111 126 142 159
(x - ((~x2 + 1) div (4x + 9)))
A099352: 0 1 3 4 5 6 8 9 10 11 13 14 15 16 17 19
(~1 + (((3x2 + 10x + 8) div 2) div 2))
A184005: 1 4 9 15 23 32 43 55 69 84 101 119 139 160 183 207
((x + 1) - ((0 - ((x3 + 2x2) div 2)) div 2))
A322108: 1 3 7 15 29 50 79 118 169 233 311 405 517 648 799 972
((8x + 1) + ((x + ~2) * (x div 2)))
A342434: 1 9 17 26 37 47
(1 + (4 * (x - (2x * (~x + (x mod 2))))))
A276916: 1 5 41 61 145 181 313 365 545 613 841 925 1201 1301 1625 1741
(1 + (((2x2 + 1) mod (2 + (x div 2))) div 2))
A304041: 1 1 1 1 1 2 2 3 2 1
(1 + ((~x + 2) mod (2 + ((x + ~2) div (2 + (x div 2))))))
A167970-A023132-A023124-A023120: 1 1 1 2 1 2 1 2 1 3 2 1 3 2 1 3
(1 - (x mod (1 + (((x + ~2) mod (2 + (x div 2))) div 2))))
A336834: 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1
(2 - (x mod (1 + (((x + ~2) mod (2 + (x div 2))) div 2))))
A098220: 2 2 2 2 2 1 2 2 2 2 2 1 2 1 2 2
(1 + (((~2x2 + 2x) div (2 + (x div 2))) mod 2))
A105224: 1 1 1 1 1 1 1 2 2 1 1 1 2 2 2 2
(1 + (((~2x2 + 2x) mod (2 + (x div 2))) mod 2))
A206491-A187447-A146292-A122172: 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 2
(1 - (x2 mod (1 + (x mod (4 + (x div 2))))))
A029436: 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1
(x mod (1 + ((3x mod (2 + (x div 2))) div 2)))
A322989: 0 0 0 0 0 1 0 0 0 1 0 2 0 1 2 0
(x mod (1 + ((~x2 mod (2 + (x div 2))) div 2)))
A279210-A232243: 0 0 0 0 0 1 0 0 0 1 1 2 0 1 0 0
(1 + (((~x3 + x) div (2 + (x div 2))) mod 2))
A307433-A245618-A178058-A166279-A077478-A047072: 1 1 1 1 2 1 1 1 1 1 1 2 2 2 1 1
(1 - (x mod (1 + ((x + ~2) mod (2 + ((x div 2) mod 2))))))
A325414: 1 0 1 0 1 0 1 0 1 0 0 1 1 0 1 0
(1 + (2 * ((3x2 + 2) + (x mod 2))))
A020576: 5 13 29 61
(1 + ((x - ((~x + 1) div (4 - (x mod 2)))) div 2))
A317686-A093878: 1 1 2 3 3 4 5 5 6 7 7 8 8 9 10 11
(~1 + ((x + 2) div (2 + (x div (2 * (2 - (x mod 2)))))))
A286351: 0 0 1 0 1 0 1 0 1 0 2 0 1 0 2 0
(x div ((x + ~1) + (x mod (5 + (x mod 2)))))
A153638: 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0
(1 + (((x2 + 2x) div 2) mod (2 * (2 + (x mod 2)))))
A225821-A055770-A053589: 1 2 1 2 1 6 1 2 1 2 1 6 1 2 1 2
((x + 1) div (1 + (x div (2 + (x mod (2 + (x mod 2)))))))
A232098-A195155-A055874: 1 2 1 2 1 3 1 2 1 2 1 4 1 2 1 2
((x + 1) mod (1 + (x div (2 + (x mod (2 + (x mod 2)))))))
A089196: 0 0 1 0 2 0 3 2 4 0 5 0 6 4 7 0
(1 div (2 - (x div (~1 + (2 * (x mod (2 + (x mod 2))))))))
A322796: 0 1 0 0 0 1 0 ~1 0 0 0 ~1 0 ~1 0 0
(x div (4 - (x mod (~1 + (2 * (~2 + (x mod 2)))))))
A189684: 0 0 0 0 0 1 0 1 1 2 2 2 1 2 2 3
((2x + ~1) + (2 div (1 + ((x + 1) mod 4))))
A222010: 0 1 3 7
A047530: 0 1 3 7 8 9 11 15 16 17 19 23 24 25 27 31
((x + ~1) + (5 * (1 + (x div 3))))
A047429: 4 5 6 12 13 14 20 21 22 28 29 30 36 37 38 44
((x + ~2) + (5 * (1 + (x div 3))))
A047598: 3 4 5 11 12 13 19 20 21 27 28 29 35 36 37 43
(x - (5 * (x div 7)))
A245342-A203580: 0 1 2 3 4 5 6 2 3 4 5 6 7 8 4 5
(5 * (1 + (2 * (x - (x div ~2)))))
A084967: 5 25 35 55 65 85 95 115 125 145 155 175 185 205 215 235
(x2 mod 45)
A070467: 0 1 4 9 16 25 36 4 19 36 10 31 9 34 16 0
(50x + 25)
A053742: 25 75 125 175 225 275 325 375 425 475 525 575 625 675 725 775
(x div (5 * (1 + ((~x + 2) mod 4))))
A087773: 0 0 0 0 0 0 1 0 0 0 2 0 0 1 2 0
(5 * (1 + (2 * ((x + 2) + (x div 2)))))
A063149: 25 35 55 65 85 95 115 125 145 155 175 185 205 215 235 245
(2x - ((~1 + (2 * (x div 2))) div 5))
A246705: 1 3 4 6 8 10 11 13 15 17 19 21 22 24 26 28
((12x + 12) div 5)
A003151: 2 4 7 9 12 14 16 19 21 24 26 28 31 33 36 38
(x2 mod 60)
A159852: 0 1 4 9 16 25 36 49 4 21 40 1 24 49 16 45
(15 * ((x2 + x) div 2))
A194715: 0 15 45 90 150 225 315 420 540 675 825 990 1170 1365 1575 1800
((3x2 + 6x + 6) div 5)
A173106-A025723: 1 3 6 10 15 22 30 39 49 60 73 87 102 118 135 154
(x - (15 * (~x + (x mod 2))))
A151983: 0 1 32 33 64 65 96 97 128 129 160 161 192 193 224 225
(x - ((~1 + (2 * (~x + (x mod 2)))) div 5))
A187484: 1 2 3 4 6 7 9 10 12 13 15 16 17 18 20 21
(1 - ((1 + (x mod 2) - (x div 2)) div 5))
A094916: 1 1 1 1 2 1 2 2 2 2 2 2 2 2 3 2
(5 * ((x + 1) + ((x div 2) div 3)))
A067761: 5 10 15 20 25 30 40 45 50 55 60 65 75 80 85 90
(x - (((~x + ~1) + (x mod 3)) div 5))
A113619: 1 2 3 4 5 6 8 9 10 11 12 13 15 16 17 19
((16x + 16) div 5)
A189783: 3 6 9 12 16 19 22 25 28 32 35 38 41 44 48 51
((3x + 2) - ((x + 1) div 5))
A292643: 2 5 8 11 13 16 19 22 25 27 30 33 36 39 41 44
(5x - ((x + 1) div 5))
A081839: 0 5 10 15 19 24 29 34 39 43 48 53 58 63 67 72
((2x3 + ~2x2 + x + ~1) mod 5)
A152856: 4 0 4 3 4 4 0 4 3 4 4 0 4 3 4 4
(((x + 1) div 3) - ((x + ~1) div 5))
A165640: 1 0 1 1 1 2 1 1 2 2 2 2 2 2 3 3
((~x + 1) + (5 * (x - (x div ~2))))
A168671: 1 10 14 23 27 36 40 49 53 62 66 75 79 88 92 101
(x3 mod 30)
A070711-A070492: 0 1 8 27 4 5 6 13 2 9 10 11 18 7 14 15
(45x + 10)
A139610: 10 55 100 145 190 235 280 325 370 415 460 505 550 595 640 685
(x - (10 * ((~x + 1) div 3)))
A112655: 0 1 12 13 14 25 26 27 38 39 40 51 52 53 64 65
(1 div (((x2 + ~2x + ~1) div 2) mod 5))
A320926-A144597-A125117: 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0
(x - (((~2x + ~2) + (x div 2)) div 5))
A184480-A098572-A001955: 1 2 3 5 6 7 9 10 11 13 14 15 16 18 19 20
(4x - ((2x + 2) div 5))
A198271: 0 4 7 11 14 18 22 25 29 32 36 40 43 47 50 54
((((x + ~1) * (x div 3)) div 2) div 5)
A015742: 0 0 0 0 0 0 1 1 1 2 2 3 4 4 5 7
(((x3 + ~3x2 + 2x) div 2) div 5)
A011892: 0 0 0 0 2 6 12 21 33 50 72 99 132 171 218 273
((~x + 2) + (((x2 + ~1) div 2) div 5))
A070178: 1 1 0 ~1 ~1 ~1 ~1 ~1 0 1 1
(x mod (5 * (2 + ((x mod 3) div 2))))
A103303: 0 1 2 3 4 5 6 7 8 9
A139281: 0 1 2 3 4 5 6 7 8 9 0 11 2 3 14 5
(20 * ((x + 1) + (x div 2)))
A270296: 20 40 80 100 140 160 200 220 260 280 320 340 380 400 440 460
(x3 mod 40)
A070721-A070502: 0 1 8 27 24 5 16 23 32 9 0 11 8 37 24 15
(1 - ((x - (x2 div 4)) div 5))
A094988: 1 1 1 1 1 2 2 2 3 4 4 5 6 7 8 10
(50x + 20)
A053741: 20 70 120 170 220 270 320 370 420 470 520 570 620 670 720 770
(1 mod ((2 + ((x2 + 2x) div 2)) mod 5))
A285358: 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1
(((x2 + 5x + 6) div 2) div 5)
A067570: 0 1 2 3 4 5 7
A248421: 0 1 2 3 4 5 7 9 11 13 15 18 21 24 27 30
(x + (5 * ((x div 2) mod 2)) - (x div 2))
A197916: 0 1 6 7 2 3 8 9 4 5 10 11 6 7 12 13
(5 * ((x2 + 5x) div 2))
A212331: 0 15 35 60 90 125 165 210 260 315 375 440 510 585 665 750
(5 * ((x + 2) + (3 * (x div 2))))
A055049: 10 15 35 40 60 65 85 90 110 115 135 140 160 165 185 190
(5 * ((3x2 + ~x) div 2))
A152734: 0 5 25 60 110 175 255 350 460 585 725 880 1050 1235 1435 1650
(x - (((~x + ~2) + ((x div 2) mod 2)) div 5))
A183293: 1 2 3 4 6 7 8 9 10 12 13 14 15 16 17 19
(2x - ((x - ((~x + 2) div 2)) div 5))
A292654-A136617-A083088: 1 2 4 6 7 9 11 12 14 16 18 19 21 23 24 26
(0 - (((x * (1 - (x div 2))) div 2) div 5))
A145816: 0 0 0 0 1 1 2 2 3 3 4 5 6 7 9 9
(x - (((x * (2 - (x div 2))) div 2) div 5))
A067570: 0 1 2 3 4 5 7
A213858: 0 1 2 3 4 5 7 8 10 11 13 15 17 19 21 23
((12 mod (x + 2)) div 5)
A339166: 0 0 0 0 0 1 0 0 0 0 0 2 2 2 2 2
(4 div (4 - ((x + 2) div 5)))
A160675: 1 1 1 1 1 1 1 1 2 2 2 2 2 4 4 4
((2x + ((x + ~1) mod 3)) div 5)
A090702: 0 0 1 1 1 2 2 2 3 4 4 4 5 5 5 6
(1 - (5 * (3 mod (~2x + 1))))
A123849: 1 1 1 11 21 31 41
((x + 2) - (5 * (~2x + (x div 2))))
A168672: 2 13 19 30 36 47 53 64 70 81 87 98 104 115 121 132
((~x + 1) - (5 * (~2x + (x mod 2))))
A146509: 1 5 19 23 37 41 55 59 73 77 91 95 109 113 127 131
((((x + 1) div 2) div 2) - ((x div 2) div 5))
A280534: 0 0 0 1 1 1 1 2 2 2 1 2 2 2 2 3
((x5 div 2) div 5)
A342112: 0 0 3 24 102 312 777 1680 3276 5904 10000 16105 24883 37129 53782 75937
(x - (5 * ((~x3 + x) div 2)))
A063522: 0 1 17 63 154 305 531 847 1268 1809 2485 3311 4302 5473 6839 8415
(x - ((~x + ((x + 1) mod 3)) div 5))
A039180: 0 1 3 4 5 6 7 8 10 11 12 14 15 16 17 18
(5x + 120)
A030501: 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195
(2x - ((x + (x div 3)) div 5))
A198081: 0 2 4 6 7 9 11 13 14 16 18 20 21 23 25 26
((x + 2) - ((~x + (2 div (x + 1))) div 5))
A184004: 2 3 5 6 7 8 10 11 12 13 14 16 17 18 19 20
((x5 + ~x) div 5)
A208536: 0 0 6 48 204 624 1554 3360 6552 11808 19998 32208 49764 74256 107562 151872
((~x + 1) + (5 * (x + (2 * (x mod 2)))))
A166523: 1 15 9 23 17 31 25 39 33 47 41 55 49 63 57 71
(15x2 + ~9x)
A153786: 0 6 42 108 204 330 486 672 888 1134 1410 1716 2052 2418 2814 3240
(2x3 + ~3x2 + 5)
A152064: 5 4 9 32 85 180 329 544 837 1220 1705 2304 3029 3892 4905 6080
(x - (x2 div ((x + 5) + (x div 2))))
A177357: 0 1 2 2 3 3 4 4 5 5 5 6 6 6 7 7
((~2x + 2) + (5 * (x + (x div 2))))
A168486: 2 5 13 16 24 27 35 38 46 49 57 60 68 71 79 82
(((x + 1) div 5) * (x div 5))
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((6x + 6) + (x div 5))
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((2 * (x mod 5)) + (x div 5))
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(((2 - (x div 2)) div (x + 2)) + (x div 5))
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((x div 3) + (x div 2) + (x div 5))
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((x2 + (x mod 5)) div 5)
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(x2 - (5 * (~x2 + (x mod 2))))
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((x + 1) + (~x mod 4) - (x mod 4))
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(1 + (2 * ((2 - (x mod 2)) * (~x mod 4))))
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(4x4 + 8x3 + ~4x + ~1)
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((x + 1) - ((~x + ((x div 3) mod 2)) div 4))
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(1 + ((x + (x2 div 8)) div 4))
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(1 + ((x + (x div (4 + (x div 2)))) mod 4))
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(1 + ((x * ((x mod (2 + (x mod 2))) div 2)) div 4))
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((x + 1) - (((~x + 2) - (x div 4)) div 4))
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(1 - ((x2 + x) mod (~1 + ((~x + 2) div 4))))
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((3x + 1) - ((x + (x div 2)) div 4))
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(1 + ((x div (1 + (x div 4))) + (x div 4)))
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((x div 4) - (x div (~1 - (x div 4))))
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(((x + 2) mod 5) mod (1 + (x div 4)))
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(((x + ~1) * (1 + (x div 2))) mod (1 + (x div 4)))
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((2 * ((x + 1) + (x mod 2))) mod (1 + (x div 4)))
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(x div ((x + 6) div (1 + (x div 4))))
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(1 + (2 * ((x + 2) + (x div 2))) - (x mod 4))
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((4x2 + 1) + ((x2 + x) div 2))
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((4x2 + 1) + ((x2 + ~x) div 2))
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((x2 + 3x + 1) - (x2 div 4))
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(1 + (2 * (2 + (x * ((x2 + ~1) + (x mod 2))))))
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(x - ((x + 2) div (~1 + (x div (~2 + ((~x + 1) div 2))))))
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((x + 1) - (((~x + ((x div 2) div ~2)) div 2) div 2))
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(1 + (((x * ((~x + 1) div (2 + (x div 2)))) div 2) mod 2))
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(1 + (2 * ((x + ((2x + 1) * (x div 2))) div 2)))
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(1 + ((2x2 div ((x + 2) + (x div 2))) mod 2))
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(1 + ((x3 div ((x + 2) + (x mod 2))) mod 2))
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(1 + ((((x + ~1) * (x + (x div 2))) div (x + 2)) div 2))
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(1 + (((x3 + ~4x2 + 4x) div (x + 2)) mod 2))
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(1 + (((2 + (x * (x + (x div 2)))) div (x + 2)) div 2))
A168581-A024699: 1 1 2 2 3 3 4 5 5 6 7 7 8 9 10 10
(1 + (((x + ~1) * (x + (x div 2))) div (x + 4)))
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(1 + ((8x + ~2) div (x + 4)))
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(x - ((x2 + ~x + 2) div (x + 5)))
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(x - ((x2 + ~2x + ~2) div (x + 5)))
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(((x * (x + (x div 2))) div 2) div (x + 5))
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(x4 + 4x3 + ~3x2 + 10x)
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(1 + ((~x + (x2 div 3)) div (x + 4)))
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(x - (((x2 + ~1) div 2) div (2x + 5)))
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(1 + ((2x + 4) * ((x + 1) + (2 mod (x + 1)))))
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(1 + (((x + 2) * (x + ((x * (x div 2)) mod 2))) div 2))
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(1 + (x div 2) - (((~x2 + 2x) div (x + 2)) mod 2))
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(x mod (~1 + (((x + ~2) * ((x div 2) div 3)) div 2)))
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((4x + 1) + ((x2 + ~2x) div 4))
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(16x2 + 24x + 5)
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(48x2 + 12x)
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(8x3 + 14x2 + 7x + 1)
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(~1 + (2 * ((3x + 12) - (x div 2))))
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(1 + (x mod 2) - (((x div 3) - (x div 2)) div 2))
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(1 - (x mod (~1 + (((x div 3) - (x div 2)) div 2))))
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(1 + (((((x div 2) div 3) mod 2) + (x div 2)) div 2))
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((x + 1) - ((((x div 4) mod 2) - (x div 2)) div 2))
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((2x + 1) - (((x mod 4) + (x div 2)) div 2))
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(~1 + (2 * ((x3 + 2x2 + x + 2) + (x div 2))))
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(1 + ((((x2 div 2) mod (x + 2)) * (x div 2)) div 2))
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((x + 3) - ((~2x + (x div 2)) * (x div 2)))
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(1 + (2 * (x - ((~2x + (x div 2)) * (x div 2)))))
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(1 + ((x2 div (2 - ((x div 2) * (x div 2)))) mod 2))
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(1 + ((2 + (x div (1 + (x mod 2)))) * (2 + (x div 2))))
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(2x mod (x - ((x + ~1) mod (3 + (x div 2)))))
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((x + 2) - (3x div (3 + (x div 2))))
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(((x + 2) mod 6) mod (1 + (2 * (x div 2))))
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((1 - (2 * ((x div 2) mod 2))) * (1 + (2 * (x div 2))))
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(x - ((x mod 5) mod (~1 + (2 * (x div 2)))))
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(1 + ((2 + (x div 8)) * ((x div 2) mod 2)))
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((x + 1) + ((x + (x div 2)) div 2) - ((x div 2) mod 2))
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(1 + (((x div 7) - (x mod 2)) div 2))
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((x + 1) - (((2x mod 3) - (x mod 2)) div 2))
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(1 + (2 * ((4 * (x mod 4)) - (x mod 2))))
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((x + 2) mod (1 + ((x div 2) mod (2 * (2 - (x mod 2))))))
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(~1 + ((3 + (x * (x div 2))) * (2 + (x mod 2))))
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((x div 2) div (1 + ((2 + (x div 2)) div (2 + (x mod 2)))))
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(x2 mod (3 - ((x div 2) mod (2 + (x mod 2)))))
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((5 + (x div 2)) div (3 + (x mod 2)))
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((x div 3) mod (1 + ((~x + 2) mod (2 + (x mod 2)))))
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(x div (((x + ~1) div 2) - (x mod (~3 + (x mod 2)))))
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(1 + (x mod 10) - (2 * (x mod 2)))
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(2 - (((~x + 1) mod 3) * (~1 + (2 * (x mod 2)))))
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(((x2 + 2x + ~1) div 2) * (~1 + (2 * (x mod 2))))
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(((x2 + 3x + 2) div 2) * (~1 + (2 * (x mod 2))))
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((~1 + ((x + 1) mod 7)) mod 3)
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((1 + ((x2 + ~1) div 5)) mod 3)
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((x - (x div (1 + (x div 5)))) div 3)
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(3 * (~2 mod (1 + (x mod 5))))
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(27x + 15)
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(3 * (1 + (3 * ((x2 + x) div 2))))
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((x - ((x + ~1) mod (1 + (x div 3)))) div 3)
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((2 - (x div (~1 + ((x div 2) div ~2)))) div 3)
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(x - ((~1 + (2 * ((x + 1) div 3))) div 3))
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((x mod (1 + (2 * ((x + 2) div 3)))) div 3)
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((x mod (1 + ((x + 1) mod 6))) div 3)
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(((x + 1) div (1 + (x mod 6))) mod 3)
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((1 + (2 * ((x + (x mod 2)) div 3))) div 3)
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((x - (x mod (~3 + (x mod ~2)))) div 3)
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(x - (3 * (~1 + (2 * ((x div 3) mod 2)))))
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((1 + (x2 div 16)) div 3)
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(x3 mod 27)
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(((x + ~1) mod (3 + (x div 4))) div 3)
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(x - (((x + 1) - ((x div 4) mod 2)) div 3))
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(x - (x mod (3 * (1 + ((x + 1) mod 4)))))
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((1 + ((2x + (x div 2)) mod 4)) mod 3)
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((5x2 + 5x + 5) div 3)
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(x div (x - (3 * ((x + ~1) div 5))))
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(x - (3 * ((~2x + 2) div 5)))
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((5 * ((x2 + x) div 2)) div 3)
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(x - (3 * ((x + (x div 2)) div 5)))
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((4x div (1 + (x div 4))) mod 3)
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((x - (x2 div (x + 5))) mod 3)
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(x - ((x2 div (3 + (x div 2))) div 3))
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(x - ((x - ((~1 + (x div 2)) mod 3)) div 3))
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(x3 mod 36)
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(x - ((x - ((x * (x div 2)) mod 3)) div 3))
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(((x mod 5) + (x div 3)) mod 3)
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((2x + 2) - ((1 - (x div 3)) div 3))
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((2x + 2) - ((x - (x div 3)) div 3))
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((((x div 2) mod 4) + (x mod 3)) div 3)
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(x - (((x + ~2) - (x2 div 3)) div 3))
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(1 - (((x mod 2) - (x2 div 3)) div 3))
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(((2x + 1) - ((x * (x div 2)) mod 2)) div 3)
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((1 + (((~x + 2) div 3) mod (x + 2))) div 3)
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((2x3 + 5x2 + 4x + 1) div 3)
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((4x3 + 6x2 + 2x) div 3)
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(24x2 + 24x + 6)
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((6x + 3) * ((x2 + x) div 2))
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((8x2 + ~6x + 1) div 3)
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(((~3 + (x mod 2)) mod (2x + ~1)) div 3)
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(x - ((~2x3 + 3x2 + ~x) div 3))
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(((~x + 5) mod (1 + (x div 2))) div 3)
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(((~x2 + 2x + ~1) mod (1 + (x div 2))) div 3)
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(((0 - (x mod 4)) mod (1 + (x div 2))) div 3)
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(((x3 + ~2) mod (1 + (x div 2))) div 3)
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(((~x2 + 3x) mod (1 + (x div 2))) div 3)
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((x2 div (x + 2)) - ((~1 + (x div 2)) div 3))
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(1 - (((x div 3) mod (~x + ~1)) div 3))
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((1 + (x * (1 + ((x mod 3) mod 2)))) div 3)
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(x - (((~x + ~1) + (x div 5)) div 3))
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(x - (((~x + ~1) + ((x div 2) mod 3)) div 3))
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(2x - (((~x + ~1) + (x div 3)) div 3))
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(1 mod (2 div (x - ((x2 + ~x + ~1) div 3))))
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(((x + 1) * ((x + 1) - (x div ~2))) div 3)
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(3x3 + 9x2 + 15x + 9)
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((x3 + 3x2 + 5x + 3) div 3)
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((2x3 + 8x2 + 10x + 4) div 3)
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((3x + 3) * ((x2 + 3x + 2) div 2))
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((3x + 3) + (x div 7))
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((3x + 3) + (x div 9))
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((3x + 3) + (2x div 5))
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((3x + 3) + ((x div 2) div 5))
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((3x + 3) + (x div 12))
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((3x + 3) + ((((x + ~1) div 2) div 2) div 2))
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((((x + 1) div 2) mod 3) + ((x + 1) div 3))
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((x - (x2 mod 3)) * ((x + 1) div 3))
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((x div (4 + (x div 2))) + ((x + 1) div 3))
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((2 * (x + (x div 3))) - ((x + 1) div 3))
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((4x2 + x) + ((x + 1) div 3))
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((4x2 + ~x) - ((x + 1) div 3))
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(2 - ((1 - (2 * (x mod 2))) * ((x + 1) mod 3)))
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((4x3 + 3x2 + ~x) div 3)
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(3x5 + ~6x4 + 3x3)
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(((x + ~1) * ((x2 + ~2x) div 4)) div 3)
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((2x div 5) - ((x + ~1) div 3))
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(((x - ((x div 2) mod 2)) div 2) - ((x + ~1) div 3))
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((2 * (x + (x div 3))) - ((x + ~1) div 3))
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((5x + 4) - ((x + ~1) div 3))
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(2x - ((~x3 + 3x2 + ~2x) div 3))
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(x - ((~2 * (((x + ~1) div 2) div 2)) div 3))
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((x + 6) - (x div ~6))
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((2 + (x div 2)) div (2 - (x div ~6)))
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((x + 2) - (3 * ((x2 + 2x) div ~2)))
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(((x2 + ~1) mod (2 - (x div ~2))) mod 3)
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((~x + 2) + (3 * (2x - (x div ~2))))
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(36x + 30)
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(6 * (1 + ((x2 + 2) div 3)))
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(18x2 + 18x + 6)
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(1 - ((x mod (2 * (1 + (x div 3)))) div 3))
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(2 - ((x mod (2 * (1 + (x div 3)))) div 3))
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(6 * (~x mod (1 + (x div 3))))
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((x + 2) - ((~2 + (x div ~3)) div 3))
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(x - (6 * (x div 7)))
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(((2x mod 9) div 2) mod 3)
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((2 * (1 + (x2 div 8))) div 3)
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A145813: 0 0 0 1 2 2 3 4 6 7 8 10 12 14 16 19
(x div (3 * (2 + ((x + ~1) mod 5))))
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((x mod (2 + (2x mod 5))) div 3)
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(6 * (1 + (2 * ((x + 2) + (x div 2)))))
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(5 + (2 mod ((x + ~3) - (x mod 2))))
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(x - (6 * ((x div 3) mod 3)))
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((2 * (x - (((x + 1) div 2) div 3))) div 3)
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((2 * (x - ((2 + (x div 2)) div 3))) div 3)
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((2 * (x - ((2 * (x div 2)) div 3))) div 3)
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(x4 mod 18)
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((((x2 div 2) - (x div 3)) div 2) div 3)
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((x - (2 mod (1 - (2 * (x div 3))))) div 3)
A218446: 0 0 0 1 1 1 2 2 3 4 4 4 5 6 6 7
(6 * ((x + 1) + (x2 div 3)))
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(3 + ((((x div 2) div ~2) mod (x + 1)) div 2))
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(3 * ((x3 + 5x2 + 8x + 4) div 2))
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(2 - (((~2x + ~2) + ((x div 2) mod 2)) div 3))
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((3x + 2) - (((x + 1) div 2) div 3))
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(((x4 + x3 + 2x2 + 2x) div 2) div 3)
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(((x3 + 3x2 + ~4x) div 2) div 3)
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(((x4 + ~x3 + 2x2 + ~2x) div 2) div 3)
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((2 * (x - (2 * (x div 5)))) div 3)
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((2 * ((x + 2) - (x div 5))) div 3)
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(x mod (3 * (1 - (2 * ((x div 3) mod 2)))))
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(12x2 + 48x + 60)
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((((x3 + ~3x2 + 2x) div 2) div 2) div 3)
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(((x + 2) - ((x mod ~4) div 2)) div 3)
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(6 * (((x - (x mod 3)) div 2) div 2))
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(24 * ((x + 1) + (x div 2)))
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((2 * ((x - (x div ~4)) div 2)) div 3)
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(x div (3 * (2 + ((x + 1) mod 8))))
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(x3 mod 48)
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((x + ~2) + (3 * (2 + (x div 8))))
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(5x mod 24)
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(x4 mod 24)
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(24x2 + ~23x)
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(((~x + 2) + (x2 div 8)) div 3)
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((((x + 1) div 2) - ((x div 4) mod 2)) mod 3)
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((((~x2 + 1) * (x div 4)) div 2) mod 3)
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(60x + 24)
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(x - ((~2 + (x2 div (2 + (x div 2)))) div 3))
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(1 - (((((~x + 2) * (x div 2)) div 2) div 2) div 3))
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(((1 + (x div 2)) mod (2 * (2 + (x mod 2)))) div 3)
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((x div 2) - ((2 + (x div (2 + (x mod 2)))) div 3))
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(((((x + 1) + (x div 2)) div 2) mod 4) div 3)
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((((x2 + ~x) div 4) mod 4) div 3)
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((((x2 + ~2x) div (x + 2)) mod 4) div 3)
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((x2 + 2x) div (x + 11))
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((2x + 2) - ((x + 2) mod 12))
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((2x + 4) - ((x + 2) mod 12))
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(x - ((x + 1) div (~12 + (x div 2))))
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((x4 + ~x2) div 12)
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((4 * (x + (x div 5))) div 3)
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(3 * (1 - ((~x + (x mod 3)) div 4)))
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(1 - ((~4x2 + ~7x) div 3))
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((((~x + 2) mod 4) + (x div 4)) div 3)
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(1 - ((((~x + 2) div 2) * (x div 4)) div 3))
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((~x + 2) + (3 * (2x - (x mod 4))))
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((x2 - ((~x2 + 2x) div 4)) div 3)
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(x - ((2 * ((x + ((x div 2) mod 2)) div 2)) div 3))
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(((x2 mod ((x + ~2) + (x div 2))) div 2) div 3)
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(x - (3 * ((~x + ~4) + (x mod 4))))
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(((3x2 + 8x + 4) div 2) div 3)
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((2 + ((x3 + ~2x2) div (x + 2))) div 3)
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((((x2 - (x div 2)) mod (x + 2)) div 2) div 3)
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(x - ((~2 + (2x2 div (x + 2))) div 3))
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(((x2 + ~3x + 2) div (x + 4)) div 3)
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(x - (((~2x + ~4) + (x div 3)) div 3))
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((2 * (2x + ((x div 3) mod 2))) div 3)
A047513-A039068: 0 1 2 4 6 7 8 9 10 12 14 15 16 17 18 20
(3 * (4x + ((x2 + ~x) div 2)))
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(2x - ((x - ((2 - (x div 2)) div 2)) div 3))
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(((~x2 + 3) mod (2 + (x div 2))) div 3)
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((4x2 mod (2 + (x div 2))) div 3)
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(((x3 + ~2x2) div (2 + (x div 2))) mod 3)
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(((x3 + x) mod (2 + (x div 2))) div 3)
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((x2 + ~x + 2) - (6 * (x div 2)))
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(x - ((x - (2x mod (2 + (x mod 2)))) div 3))
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((2 + (x * (~1 + ((x + 1) mod 3)))) div 3)
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(x - (((~x + ~2) + (x div ~3)) div 3))
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((8x3 + ~2x) div 3)
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(12x2 + 5x + 1)
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((2 * (x + (6 div (x + 1)))) div 3)
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(((x + 2) + ((x mod 5) mod 2)) div 3)
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(x - (((~x + ~2) + (x div ~4)) div 3))
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(x - (((~x + ~2) + (((x + ~1) div 2) mod 2)) div 3))
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(6 * (x + (2 * (2 + (x div 4)))))
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(x - (((~x + ~2) + (x div 8)) div 3))
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(x - (3 * ((~x + (x mod 8)) div 2)))
A024644: 0 1 2 3 4 5 6 7 20 21 22 23 24 25 26 27
(6x * (2 + ((x + 2) * (x div 2))))
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((~x + 2) - (3 * ((~x + ((x div 2) mod 2)) div 2)))
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(3 + ((x div ~6) mod (x + 2)))
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(3x2 + 15x + 26)
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((x + 1) div (8 - ((x + 2) div 3)))
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((x + (2x div 3)) * ((x + 2) div 3))
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((2 * (x + (x div 3))) - ((x + ~2) div 3))
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(((x + (x div 4)) div 2) - ((x + ~2) div 3))
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(1 + (3 * (2x + (x mod 2))) - (x div 2))
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(6x + (x div ~6))
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(6x + (x div ~7))
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(x - (x3 div (~6x + 2)))
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(18x3 + 6x2)
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(2x + (2x div 3) - (x mod 3))
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(2x + ((x mod 3) + (2x div 3)))
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((2 + ((3 mod (x + 1)) + (x div 2))) div 3)
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(((((1 + (x div 2)) div 2) div 2) * (x div 2)) div 3)
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(x - ((((x + 1) mod 4) + (x div 2)) div 3))
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(x mod (1 - (((x mod 4) - (x div 2)) div 3)))
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(x div (2 + ((x div 3) + ((x div 2) mod 3))))
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((x + 3) + ((3 mod (x + 1)) + (x div 2)))
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((2x2 + 6x + 4) - (3 * (x mod 2)))
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((2x2 + 4) - ((x2 + ~2) div 3))
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((x3 + ~x) - (3 * (x2 div 2)))
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(x - (((~x4 + x2) div 2) div 3))
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((x + 2) - (((~x3 + x) div 2) div 3))
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(27x2 + 3x)
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(9x3 + 9x2 + 3x)
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(x - ((~x + ((x div 2) mod ~3)) div 3))
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((x + ((x + 1) mod 7)) mod 3)
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((8x3 + x) div 3)
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(x - (3 * (~x + ((x + ~1) div 5))))
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((x + (x2 div (3 + (x div 2)))) mod 3)
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(3 * (x + ((x mod (1 + (x div 2))) div 3)))
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(x - ((~x + ((2 * (x div 2)) div 3)) div 3))
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(((~x + 1) * (1 + (x2 div 3))) mod 3)
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((x * (x2 div 2)) mod (2 - ((~x + 1) div 3)))
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((2 * (x + (x div 3))) + ((~x + 1) mod 3))
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((x * ((3x + ~6) mod (x + 1))) mod 3)
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((x + 3) + (6x div (x + 1)))
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((x + 3) + ((x - (x mod ~3)) div 2))
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((x * (1 - (x mod 10))) mod 3)
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(x - (3 * (~x + (x mod 10))))
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(1 - ((~x + ((x mod 5) mod 2)) div 3))
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(x - ((~x + ((~1 + (x mod 4)) div 2)) div 3))
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((x + 3) + ((x - ((x div 2) div 3)) div 2))
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((x + (2 * (x mod 10))) div 3)
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((x + (4 * ((x + 1) mod 3))) div 3)
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((x + (4 * ((x div 2) div 3))) div 3)
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(x - (((~x + ~2) + (x mod ~4)) div 3))
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(1 - ((~x + ((x mod ~4) div 2)) div 3))
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(3 + compr(\x.(x mod (4 - (x mod 4))),x))
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((x + 2) - ((~x + ((2 - (x div 2)) div 2)) div 3))
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(9x2 + 5x + 1)
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((~x + 1) + (3 * (x + ((x + (x div 2)) div 2))))
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((5x3 + ~2x) div 3)
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(2x + (x div 3) - (x mod ~3))
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(2 + ((x div (1 + (x div 3))) + (x div 3)))
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((2 * (2 mod (1 + (x mod 3)))) + (x div 3))
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((2 * (x - (x div ~3))) - (x div 3))
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(x - ((2 * (x div 5)) + (x div 3)))
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((((x + 1) - (x div 4)) div 2) - (x div 3))
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((((x + 1) - ((x div 2) mod 2)) div 2) - (x div 3))
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((2 * (x - ((~x + 1) div 3))) - (x div 3))
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(x div (x - (((~1 + (x div 2)) div 2) + (x div 3))))
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((2x + 2) + ((x div 4) + (x div 3)))
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(((x div 4) + (x div 3)) - ((x + ~1) div 2))
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(((2 - (x div ~4)) div 2) + (x div 3))
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(x - ((x + 2) div (8 - (x div 3))))
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(((2x + 2) div (2 + (x div 2))) + (x div 3))
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(2x + (((~x + 1) mod 3) + (x div 3)))
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(x + ((2 * (2x div 3)) + (x div 3)))
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((2 div (~x + 16)) * (x div 3))
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(1 + (((x + ~2) * (x2 div 2)) + (x mod 3)))
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((2 * (x - (x div ~3))) - (x mod 3))
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((4 * (2x div 3)) + (x mod 3))
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(x div (4 + (x div 4) - (x mod 3)))
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(((x + (2 * (x mod 2))) * (x div 2)) + (x mod 3))
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((4x4 + ~x2) div 3)
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(2x mod (2 - ((~x + (x * (x mod 2))) div 3)))
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(3x2 + ((x2 + ~3x + 2) div 2))
A140065: 1 3 12 28 51 81 118 162 213 271 336 408 487 573 666 766
(((x + ~1) mod 8) + (x2 div 3))
A118288: 7 0 2 5 8
((2x5 + x3) div 3)
A272125: 0 1 24 171 704 2125 5256 11319 22016 39609 67000 107811 166464 248261 359464 507375
((~2x + 4) - ((~x3 + x) div 3))
A270809: 4 2 2 6 16 34 62 102 156 226 314 422 552 706 886 1094
(1 + (2 * (x + (x div 11))))
A062505: 1 3 5 7 9 11 13 15 17 19 21 25 27 29 31 33
((x + ~1) - (2 * (~x + ((x + ~1) div 5))))
A276881: 1 2 5 8 11 14 15 18 21 24 27 28 31 34 37 40
(22x + 19)
A248339: 19 41 63 85 107 129 151 173 195 217 239 261 283 305 327 349
(1 + ((x + ((x2 div 2) div 5)) div 2))
A238886: 1 1 2 2 3 4 5 6 8 9 11 12 14 15 17 19
(1 + (2 * (x + ((x div 2) mod (1 + (x div 4))))))
A327260: 1 3 5 7 9 11 15 17 19 21 25 27 29 31 35 37
((x + 1) - ((~x + ((x div 3) mod 3)) div 2))
A330565: 1 3 4 5 7 8 9 11 12 15
(14x + 47)
A126980: 47 61 75 89 103 117 131 145 159 173 187 201 215 229 243 257
(1 + (x2 div (2x + 24)))
A008668: 1 1 1 1 1 1 2 2 2 2 3 3 4 4 4 5
(1 + (2 * (x + ((x - (x mod 4)) div 3))))
A283680: 1 3 5 7 11 13 15 17 21 23 25 27 33 35 37 39
((x + 1) - ((~x + (((~x + 2) div 2) div 3)) div 2))
A285206: 1 3 4 6 8 9 11 12 14 16 17 19 20 22 23 25
((2x + 1) - ((~x + ((x div 2) div 3)) div 2))
A231407: 1 4 6
A285078: 1 4 6 9 11 14 16 18 21 23 26 28 30 33 35 38
(30x + 17)
A128468: 17 47 77 107 137 167 197 227 257 287 317 347 377 407 437 467
(1 + (((x + 2) * (x mod 2)) + ((x2 + x) div 2)))
A316671: 1 5 4 12 11 23 22 38 37 57 56 80 79 107 106 138
((2x + 1) - ((~x + ((x div 2) div ~2)) div 2))
A279054: 1 4 7 9 12 14 17 20 22 25 28 30 33 35 38 41
(1 + (2 * (x + (2 * ((x + 1) div 5)))))
A285130: 1 3 5 7 13 15 17 19 21 27 29 31 33 35 41 43
((x + 1) - ((~x + ((~1 + (x div 4)) div 2)) div 2))
A248229: 2 3 5 6 7 9 10 12 13 15 16 18 19 20 22 23
((x + 1) - ((~x + (x div (~2 + (x div ~2)))) div 2))
A276210: 1 3 5 6 8 9 11 13 14 16 17 19 20 22 23 25
(1 + ((x + ((x mod (2 + (x mod 3))) div 2)) div 2))
A317648-A284007: 1 1 2 2 3 3 4 4 5 5 6 7 7 7 8 8
((x + ~1) - (2 * (~x + ((((x + ~1) div 2) div 2) div 2))))
A276877: 1 2 5 8 11 14 17 20 23 24 27 30 33 36 39 42
(1 + ((2x + 1) mod (x + 10)))
A115299-A088133: 2 4 6 8 10 12 14 16 18 1 2 3 4 5 6 7
(x - (x mod (1 + (2 * (~x + (x mod 8))))))
A171649: 0 1 2 3 4 5 6 7 15 15 15 15 15 15 15 15
(x - (x mod (~1 + (2 * (~x + (x mod 8))))))
A171678: 0 1 2 3 4 5 6 7 17 17 17 17 17 17 17 17
(1 + (2 * (x + (x div (~2 + ((~x + 2) div 4))))))
A122800: 1 1 3 5 5 7 9 11 13 13 15 17 19 21 23 25
(1 + ((x + (x2 div (2x + 8))) div 2))
A213855: 1 1 2 2 3 4 4 5 6 7 7 8 9 9 10 11
((x + 1) - ((~x + (((2 - (x div 2)) div 2) div 2)) div 2))
A225647: 1 3 4 6 7
A247779-A243989: 1 3 4 6 7 9 11 12 14 15 17 18 20 21 23 25
(1 + (2 * (~x + (4 * (x + (2 * (x mod 2)))))))
A166526: 1 23 13 35 25 47 37 59 49 71 61 83 73 95 85 107
((x + 1) - (x2 div ((x + 2) + (x div 4))))
A146323: 1 2 2 3 3 3 3 4 4 4 4 4 5 5 5 5
(1 + ((x + (((x * (x div 3)) div 2) mod 2)) div 2))
A137512: 1 1 2 3 3 3 4 5 5 6 6 6 7 7 8 9
((x + 1) - (x2 div (2x - ((~x + 2) div 2))))
A309430-A076370: 1 2 2 3 4 4 5 6 6 7 7 8 9 9 10 10
((2x + 1) - (x2 div (x - ((~x + 2) div 2))))
A026371: 1 2 3 5 6 8 9 11 12 13 14 16 17 19 20 21
(1 + (2 * (x + ((x + (x div 8)) div 2))))
A132222: 1 3 7 9 13 15 19 21 25 29 31 35 37 41 43 47
(1 + (2 * (((x + 2) + (x div 2)) * (x + (x div 2)))))
A298039: 1 7 31 49 97 127 199 241
((x + 1) - ((x2 + 1) div ((x + 2) + (x div 2))))
A061017: 1 2 2 3 3 4 4 4 5 5 6 6 6 6 7 7
((2x2 + 1) div (1 + (2 * (x + (x div 2)))))
A062298: 1 1 1 2 2 3 3 4 5 6 6 7 7 8 9 10
(((x div 2) mod 3) div (1 + ((x * (x div 2)) mod 2)))
A060571: 0 0 1 0 2 2 0 0 1 1 2 1 0 0 1 0
(~1 + ((x + 2) * (1 + (x div 7))))
A138988: 1 2 3 4 5 6 7 17 19 21 23 25 27 29 47 50
(~x2 + 9x + 23)
A126719: 23 31 37 41 43 43 41 37 31 23 13 1 ~13 ~29 ~47 ~67
(2x3 + 12x2 + 23x + 15)
A193608: 15 52 125 246 427 680 1017 1450 1991 2652 3445 4382 5475 6736 8177 9810
(1 + ((2 * ((~x + (x div 4)) div 2)) mod (x + 2)))
A100795: 1 2 3 2 3 4 3 4 5 4 5 4 5 6 5 6
(x4 + 6x3 + 12x2 + 10x + 3)
A221464: 3 32 135 384 875 1728 3087 5120 8019 12000 17303 24192 32955 43904 57375 73728
(1 + ((x2 mod (x - ((~x + 2) div 2))) div (x + 2)))
A117546: 1 1 1 1 1 1 1 2 1 1 1 1 1 2 2 1
((3 * (2x + (x div 2))) div (x + 3))
A130250: 0 1 3 3 4 4 5 5 5 5 5 5 6 6 6 6
((x + 3) * ((x + 1) + (x2 div 4)))
A143785: 3 8 20 36 63 96 144 200 275 360 468 588 735 896 1088 1296
((x + 3) * (2 + ((x + 2) div (1 + (x mod 2)))))
A048759: 12 12 30 24 56 40 90 60 132 84 182 112 240 144 306 180
((((x + ~1) * (x + (x div 2))) div 2) div (x + 3))
A127041: 0 0 0 0 1 1 2 3 3 4 5 5 6 7 8 8
compr(\x.(x mod (2 + ((x * (x div 2)) mod 2))),(x + 3))
A272601: 4 6 8 10 12 14 15 16 18 20 22 24 26 27 28 30
(5x2 + 14x + ~6)
A239794: ~6 13 42 81 130 189 258 337 426 525 634 753 882 1021 1170 1329
(x - ((x + 3) * ((~x3 + x2) div 2)))
A212134: 0 1 12 57 172 405 816 1477 2472 3897 5860 8481 11892 16237 21672 28365
((x + 2) - (((~x + 2) * (x div 2)) div (x + 3)))
A186511: 2 3 4 6 7 8 10 11 13 14 16 17 18 20 21 23
(2x - (((~x + 2) * (x div 2)) div (x + 3)))
A081841: 0 2 4 7 9 11 14 16 19 21 24 26 28 31 33 36
(2x div (1 + (5x div (x + 2))))
A101402: 0 1 1 1 2 2 3 3 3 3 4 4 4 5 5 6
((2x + 5) - ((x2 + ~x) div (x + 2)))
A160811: 5 7 9 10 11 13 14 15 16 17 18 19 20 21 22 23
((2x + 1) + ((x - ((x div 2) div ~2)) mod 2))
A231407: 1 4 6
A133483: 1 4 6 7 10 11 13 16
((2x + 1) + ((x - ((~1 + (x div 2)) div 2)) mod 2))
A133484: 2 3 5 8 9 12 14 15
((2x + 1) + ((x - (x div ~4)) div 2))
A231407: 1 4 6
A003259: 1 4 6 9 11 14 17 19 22 25 27 30 32 35 38 40
((2x + 1) + (((x - (x div 4)) div 2) mod 2))
A286754: 1 3 6 8 10 11 13 16 18 20 21 23 25 28 30 31
((2x + 1) + (((x div 2) - (x mod 4)) div 2))
A129630: 1 2 4 6 10 11 13 15 19 20 22 24 28 29 31 33
((2x + 1) + ((x + ((x div 2) div 3)) div 2))
A122437: 1 3 6 8 11 13 16 19 21 24 26 29 32 34 37 39
((2x + 1) + (x2 div (3x + ~2)))
A231407: 1 4 6
A286043: 1 4 6 8 10 12 15 17 19 22 24 26 29 31 33 36
(1 - ((x2 + 2x) div ((~2x + ~1) + (x div 2))))
A254828: 1 2 3 4 5 5 6 7 8 8 9 9 10 11 12 12
(24x2 + 14x + 1)
A033576: 1 39 125 259 441 671 949 1275 1649 2071 2541 3059 3625 4239 4901 5611
(18x2 + 11x + 1)
A033573: 1 30 95 196 333 506 715 960 1241 1558 1911 2300 2725 3186 3683 4216
(6x3 + 9x2 + 5x + 1)
A193218: 1 21 95 259 549 1001 1651 2535 3689 5149 6951 9131 11725 14769 18299 22351
(10x2 + 17x + 6)
A153127: 6 33 80 147 234 341 468 615 782 969 1176 1403 1650 1917 2204 2511
((~1 + ((~x + 2) mod 8)) div (2x + 1))
A089805: 1 0 ~1 0 0 0 0 0 0 0 ~1 0 0 0 0 0
compr(\x.((x + 1) mod (3 + (x mod 2))),(2x + 1))
A140492: 3 8 14 19 23 27 32 38 43 47 51 56 62 67 71 75
(20x2 + 12x + 1)
A033574: 1 33 105 217 369 561 793 1065 1377 1729 2121 2553 3025 3537 4089 4681
(14x2 + 9x + 1)
A033572: 1 24 75 154 261 396 559 750 969 1216 1491 1794 2125 2484 2871 3286
((2x + 1) * (1 + (x * (2 + (2 div (x + 1))))))
A280321: 1 12 25 49 81 121 169 225 289 361 441 529 625 729 841 961
(6x3 + 11x2 + 6x + 1)
A011199: 1 24 105 280 585 1056 1729 2640 3825 5320 7161 9384 12025 15120 18705 22816
(8x3 + 20x2 + 16x + 4)
A192418: 4 48 180 448 900 1584 2548 3840 5508 7600 10164 13248 16900 21168 26100 31744
(16x3 + 24x2 + 8x)
A181773: 0 48 240 672 1440 2640 4368 6720 9792 13680 18480 24288 31200 39312 48720 59520
(16x2 + 20x + 6)
A256833: 6 42 110 210 342 506 702 930 1190 1482 1806 2162 2550 2970 3422 3906
(8x3 + 12x2 + 12x + 4)
A173961: 4 36 140 364 756 1364 2236 3420 4964 6916 9324 12236 15700 19764 24476 29884
((15x + 8) + (x div 2))
A164131: 8 23 39 54 70 85 101 116 132 147 163 178 194 209 225 240
(16x2 + 7x + 1)
A143839: 1 24 79 166 285 436 619 834 1081 1360 1671 2014 2389 2796 3235 3706
(((x * (x2 div 3)) div 2) div (2x + 1))
A321195: 0 0 0 0 1 1 2 3 4 6 7 9 11 13 15 18
((3x + 1) + (x div 7))
A327139: 1 4 7 10 13 16 19 23 26 29 32 35 38 41 45 48
((3x + 1) + (2x div 5))
A083051: 1 4 7 11 14 18 21 24 28 31 35 38 41 45 48 52
(14x2 + 13x + 3)
A195029: 3 30 85 168 279 418 585 780 1003 1254 1533 1840 2175 2538 2929 3348
((~x + (2 * (x mod 8))) mod (2x + 1))
A084689: 0 1 2 3 4 5 6 7 9
A245761: 0 1 2 3 4 5 6 7 9 12
((~1 + (x mod 9)) div (2x + ~1))
A015494-A014954-A014036: 1 0 0 0 0 0 0 0 0 ~1 0 0 0 0 0 0
((8x + 8) + (1 div (2x + ~1)))
A273745: 7 17 24 32 40 48 56 64 72 80 88 96 104 112 120 128
(6x3 + ~11x2 + 6x + ~1)
A033594: ~1 0 15 80 231 504 935 1560 2415 3536 4959 6720 8855 11400 14391 17864
(4x4 + 6x3 + ~2x)
A187190: 0 8 108 480 1400 3240 6468 11648 19440 30600 45980 66528 93288 127400 170100 222720
((2x + ~1) * ((3x2 + ~x) div 2))
A005945: 0 1 15 60 154 315 561 910 1380 1989 2755 3696 4830 6175 7749 9570
(7x2 + ~5x + 1)
A239449: 1 3 19 49 93 151 223 309 409 523 651 793 949 1119 1303 1501
(((x4 + ~x2) div 2) div (2x + ~1))
A045947: 0 0 2 7 17 33 57 90 134 190 260 345 447 567 707 868
(26x2 + ~13x)
A194713: 0 13 78 195 364 585 858 1183 1560 1989 2470 3003 3588 4225 4914 5655
(22x2 + ~11x)
A154617: 0 11 66 165 308 495 726 1001 1320 1683 2090 2541 3036 3575 4158 4785
(26x2 + 1)
A158549: 1 27 105 235 417 651 937 1275 1665 2107 2601 3147 3745 4395 5097 5851
(22x2 + 1)
A158537: 1 23 89 199 353 551 793 1079 1409 1783 2201 2663 3169 3719 4313 4951
(34x2 + 1)
A158586: 1 35 137 307 545 851 1225 1667 2177 2755 3401 4115 4897 5747 6665 7651
(1 + ((10 * (x mod 2)) + (x div 2)))
A338191-A330521: 1 11 2 12 3 13 4 14 5 15 6 16 7 17 8 18
(1 + ((x + 2) div (12 - (x div 2))))
A242763-A025788: 1 1 1 1 1 1 1 2 2 2 2 2 3 3 4 4
((x + 1) - (((~2x + ~1) + (x div 2)) * (x div 2)))
A309805: 1 2 7 10 19 24 37 44 61 70 91 102 127 140 169 184
(1 + (2 div ((4 * (2 + (x mod 2))) - (x div 2))))
A210954: 1 1 1 1 1 1 1 1 1 1 1 1 2 1 3 1
(1 + (4 * (x + (2 * (x mod 2)))) - (x div 2))
A166522: 1 13 8 20 15 27 22 34 29 41 36 48 43 55 50 62
(1 + ((2 * (x + (3 * (x mod 2)))) + (x div 2)))
A166520: 1 9 6 14 11 19 16 24 21 29 26 34 31 39 36 44
(1 + ((2 * (x + ((x div 3) mod 2))) + (x div 2)))
A028357: 1 3 6 10 13 15 16 18 21 25 28 30 31 33 36 40
(1 + ((2 * (x + (2 * (x + (x mod 2))))) + (x div 2)))
A106389: 1 11 14 24 27 37 40 50 53 63 66 76 79 89 92 102
(1 + (((2x3 + ~x2) div 2) + (x div 2)))
A129959: 1 1 8 24 59 115 202 322 485 693 956 1276 1663 2119 2654 3270
((1 + (3 * (x + (x mod 2)))) * (1 + (x div 2)))
A095894: 1 7 14 26 39 57 76 100 125 155 186 222 259 301 344 392
((1 + (2 * (((x + 1) div 2) div 2))) * (1 + (x div 2)))
A282079: 1 1 2 6 9 9 12 20 25 25 30 42 49 49 56 72
(((x + 1) div 2) * (1 + (x div 2)) * (1 + (x div 2)))
A210433: 0 1 4 8 18 27 48 64 100 125 180 216 294 343 448 512
((x2 + ~2) div (7 + (x div 2)))
A127565: ~1 ~1 0 0 1 2 3 4 5 7 8 9 10 12 13 15
((2 + ((x + 2) div (1 + (x mod 2)))) * (1 + (x div 2)))
A055523: 4 3 12 8 24 15 40 24 60 35 84 48 112 63 144 80
(x mod ((4x + 16) div (1 + (x div 2))))
A103303: 0 1 2 3 4 5 6 7 8 9
A217928: 0 1 2 3 4 5 6 7 8 9 1 1 3 4 5 6
(((x2 + ~1) mod (2 + (x mod 2))) mod (1 + (x div 2)))
A174695: 0 0 1 0 1 0 1 0 1 2 1 0 1 0 1 2
(~2 + (((x2 + x) div 2) + (2 div (1 + (x div 2)))))
A192225: 0 1 2 5
A054254: 0 1 2 5 8 13 19 26 34 43 53 64 76 89 103 118
(((x + ~2) + ((x div 2) mod 4)) mod (1 + (x div 2)))
A229878: 0 0 1 0 1 2
A053645: 0 0 1 0 1 2 3 0 1 2 3 4 5 6 7 0
((x + 1) + (((2 * (x div 2)) div 3) + (x div 2)))
A286805: 1 2 4 5 8 9 12 13 15 16 19 20 23 24 26 27
((x * (1 + (2x * (x mod 2)))) div (1 + (x div 2)))
A019427: 0 3 1 10 1 18 1 26 1 34 1 42 1 50 1 58
(1 + (x * ((2x + 2) + (x mod 2))) - (x div 2))
A057029: 1 6 12 27 39 64 82 117 141 186 216 271 307 372 414 489
(~1 + ((x mod 4) + (x div 2)) - (x * (x mod 2)))
A134405: ~1 ~1 2 0 1 ~3 4 ~2 3 ~5 6 ~4 5 ~7 8 ~6
(1 + ((x - (x mod 9)) * (x mod 2)))
A343132: 1 1 1 1 1 1 1 1 1 10 1 10 1 10 1 10
(1 + ((3 * ((x + (x div 2)) div 2)) + (x mod 2)))
A222011: 1 2 4 8
A028836: 1 2 4 8 10 11 13 17 19 20 22 26 28 29 31 35
(1 + (((x + 1) * (x2 div (x + 2))) + (x mod 2)))
A002097: 1 2 4 6 11 20 29
(1 - (x mod (~1 + ((x mod 6) + (x mod 2)))))
A321144: 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1
(1 + (((x div 2) - (x div 3)) div 2) - (x mod 2))
A025822: 1 0 1 0 1 0 1 0 2 0 2 1 2 1 2 1
(1 + ((2 * ((x div 5) mod 2)) + (x mod 2)))
A105778: 1 2 1 2 1 4 3 4 3 4 1 2 1 2 1 4
(1 + ((x2 + ~2x) div (8 - (x mod 2))))
A114220: 1 0 1 1 2 3 4 6 7 10 11 15 16 21 22 28
((x + 1) + (x mod 2) - (((x + (x div 2)) div 2) mod 2))
A109451: 1 3 2 5 4 6 7 8 9 11 10 13 12 14 15 16
(1 + ((x - (x div ~4)) * (2 - (x mod 2))))
A328984: 1 3 7 5 11 8 17 10 21 13 27 15 31 18 37 20
((1 + (x2 div 3)) div (3 - (x mod 2)))
A279405: 0 0 0 2 2 4 4 8 7
(1 + ((x + ((x div 2) * (x div 2))) div 2) - (x mod 2))
A008818: 1 0 2 2 5 4 8 8 13 12 18 18 25 24 32 32
((x div 11) * (1 + (x mod 2)))
A161272: 0 0 0 0 0 0 0 0 0 0 0 2 1 2 1 2
((1 + ((~x + 1) mod 8)) div (1 + (x mod 2)))
A252852: 2 0 8 3 6
(x div (x - (((x + ~1) div 3) * (1 + (x mod 2)))))
A293895: 0 1 1 1 1 1 1 2 1 1 1 2 1 2 1 2
(x3 mod (8 * (1 + (x mod 2))))
A167166: 0 1 0 11 0 13 0 7 0 9 0 3 0 5 0 15
((1 + (x div 2)) mod ((2 + (x div 2)) div (1 + (x mod 2))))
A135157: 1 0 2 0 3 1 4 0 5 2 6 0 7 3 8 0
((x4 + ~x2 + x + 1) + (x mod 2))
A125700: 1 3 15 77
((x4 + ~x3 + ~x2 + 1) + (x mod 2))
A307406: 1 1 5 47
((x + 1) - (2 * ((x mod 2) - (x * (x + (x div 2))))))
A175828: 1 2 15 26 53 74 115 146 201 242 311 362 445 506 603 674
((2x2 + 1) + ((x2 + 2x) div 4))
A121471: 1 3 11 22 39 59 85 114 149 187 231 278 331 387 449 514
((x3 + 4x2 + 4x + 1) - (x2 div 2))
A111500: 1 10 31 72 137 234 367 544 769 1050 1391 1800 2281 2842 3487 4224
(((x + 1) div 2) - (4x div (~x + ~1)))
A121854: 0 3 4 5 6 7 7 8 8 9 9 10 10 11 11 12
(1 + (x * ((x + 1) - (x mod 9))))
A066492: 1 2 3 4 5 6 7 8 9 91 101 111 121 131 141 151
(9x2 + 7x + 1)
A214660: 1 17 51 103 173 261 367 491 633 793 971 1167 1381 1613 1863 2131
(4x3 + ~3x2 + ~2x + ~1)
A268644: ~1 ~2 15 74 199 414 743 1210 1839 2654 3679 4938 6455 8254 10359 12794
(16x2 + 3x + 1)
A143854: 1 20 71 154 269 416 595 806 1049 1324 1631 1970 2341 2744 3179 3646
((x + 1) + (x div (3 + ((x div 2) div 3))))
A183570: 1 2 3 5 6 7 8 9 11 12 13 14 15 16 17 19
(16x2 + 5x + 1)
A143838: 1 22 75 160 277 426 607 820 1065 1342 1651 1992 2365 2770 3207 3676
(16x2 + ~5x + 1)
A143856: 1 12 55 130 237 376 547 750 985 1252 1551 1882 2245 2640 3067 3526
((x + 1) + ((x2 + 2x) div 9))
A184017: 1 2 3 5 7 9 12 15 17 21 24 27 31 35 39 44
(x - (x mod ((~x + ~1) + (x mod 9))))
A265572: 0 1 2 3 4 5 6 7 8 10 10 20 20 20 20 20
((x + 1) + (((x2 + x) div 2) div 5))
A248420: 1 2 3 5 7 9 11 13 16 19 22 25 28 32 36 40
((x + 1) + ((2x2 + 4x) div 5))
A083505: 1 3 6 10 14
A183863: 1 3 6 10 14 20 26 33 41 49 59 69 80 92 104 118
((x + 1) + (5 * ((x + 2) + (x mod 2))))
A095779: 11 22 23 34 35 46 47 58 59 70 71 82 83 94 95 106
((x + 1) + compr(\x.((x div 2) mod 2),(x div 5)))
A333943-A333764: 1 2 3 4 5 7 8 9 10 11 15 16 17 18 19 21
((x + 1) + (3 * (x div 7)))
A214677: 1 2 3 4 5 6 7 11 12 13 14 15 16 17 21 22
(1 + compr(\x.(((~x2 + 2x) div 3) mod 3),x))
A028841: 1 2 3 5 8 10 11 12 14 17 19 20 21 23 26 28
((x + 1) + ((2 * (2x div 3)) div 3))
A288373: 1 2 3 5 6 8 9 10 12 14 15 16 18 19 21 22
((x + 1) + (3 * ((x mod (1 + (x div 2))) div 2)))
A032969: 1 2 3 4 5 9 10 11 12 16 17 18 19 23 24 25
((x + 1) + ((4 * (x div 3)) div 3))
A189529-A120514-A101886: 1 2 3 5 6 7 9 10 11 14 15 16 18 19 20 22
(1 + (x2 div (x + 24)))
A029112: 1 1 1 1 1 1 2 2 3 3 3 4 5 5 6 6
(x3 mod (x + 13))
A106670: 0 1 8 11 13 17
((x + 1) + ((2x2 + 8x + 8) div 3))
A317195: 3 8 13 20 29 38
((x + 1) + (3 * ((x + (x div 4)) div 2)))
A286995: 1 2 6 7 11 15 16 20 24 25 29 30 34 38 39 43
((x + 1) + ((2x2 div (x + 2)) div 3))
A026355: 1 2 3 5 6 8 10 11 13 14 16 18 19 21 23 24
((~x2 + 2x) mod ((x + 1) + ((x div 2) div 3)))
A293497: 0 1 0 1 2 3 0 1 2 3 4 5 0 1 2 3
(15x2 + 8x + 1)
A144459: 1 24 77 160 273 416 589 792 1025 1288 1581 1904 2257 2640 3053 3496
(3x4 + ~10x3 + 9x2 + ~2x)
A115056: 0 0 0 48 264 840 2040 4200 7728 13104 20880 31680 46200 65208 89544 120120
(6x3 + ~8x2 + 3x)
A272378: 0 1 22 99 268 565 1026 1687 2584 3753 5230 7051 9252 11869 14938 18495
((x + 1) + ((x * ((x + 1) mod 3)) div 3))
A115274: 1 2 3 5 7 6 9 12 9 13 17 12 17 22 15 21
((x + 1) + (((x + ~2) div 3) * (x div 3)))
A274583: 1 2 3 4 5 7 9 10 13 16 17 21 25 26 31 36
(1 + (x * (16 - (x div 3))))
A340000: 1 17 33 46
((x2 + x + 1) div ((x + 1) + (x div 3)))
A122797: 1 1 2 2 3 4 4 5 6 7 7 8 9 10 11 11
((x + 1) + ((2x + 5) * (1 + (x div 2))))
A165717: 6 9 21 26 44 51 75 84 114 125 161 174 216 231 279 296
(2x3 + 9x2 + x + 1)
A274973: 1 13 55 139 277 481 763 1135 1609 2197 2911 3763 4765 5929 7267 8791
(4 mod (1 + (x * (5 div (x + 1)))))
A178990: 0 1 1 0 4 0 0 0 0 0 0 0 0 0 0 0
(4x3 + 3x2 + 2x + 1)
A056578: 1 10 49 142 313 586 985 1534 2257 3178 4321 5710 7369 9322 11593 14206
((x2 + x + 1) + ((1 + (x div 2)) * (x div 2)))
A247643: 1 3 9 15 27 37 55 69 93 111 141 163 199 225 267 297
(2x4 + 4x3 + 5x2 + 3x + 1)
A237516: 1 15 91 325 861 1891 3655 6441 10585 16471 24531 35245 49141 66795 88831 115921
(x6 + x5 + x4 + x3 + x2 + x)
A228290: 0 6 126 1092 5460 19530 55986 137256 299592 597870 1111110 1948716 3257436 5229042 8108730 12204240
(~2x3 + 12x2 + ~12x + 10)
A147974: 10 8 18 28 26 0 ~62 ~172 ~342 ~584 ~910 ~1332 ~1862 ~2512 ~3294 ~4220
((x + 1) + (2 * (2x div 7)))
A276876: 1 2 3 4 7 8 9 12 13 14 15 18 19 20 23 24
((x + 1) + ((x - (x div 7)) div 2))
A066344-A059549: 1 2 4 5 7 8 10 11 12 14 15 17 18 20 21 22
(x - (x mod ((~x + ~1) + (x mod 10))))
A103303: 0 1 2 3 4 5 6 7 8 9
A262038: 0 1 2 3 4 5 6 7 8 9 11 11 22 22 22 22
((x + 1) + ((3 * ((x div 2) div 3)) div 2))
A343110-A247063-A032895-A032854: 1 2 3 4 5 6 8 9 10 11 12 13 16 17 18 19
((x + 1) + (2 * ((x mod (1 + (x div 2))) div 3)))
A181046: 1 2 3 4 5 6 7 10 11 12 13 14 15 18 19 20
((x + 1) + (2 * ((x + (x div 3)) div 3)))
A263881: 1 2 3 6 7 10 11
A276884: 1 2 3 6 7 10 11 14 15 18 19 20 23 24 27 28
((x + 1) + (2 * ((x div ~3) mod (x + 1))))
A082206: 1 4 7 10 11 14 17 18 21 24 25 28 31 32 35 38
(x4 + ~x3 + ~3x2 + ~3x + ~1)
A178617: ~1 ~7 ~11 17 131 409 953 1889 3367 5561 8669 12913 18539 25817 35041 46529
((x + 1) + ((((x div 2) div ~2) mod (x + 1)) div 2))
A288204-A276220: 1 2 4 5 7 8 9 11 12 14 15 16 18 19 20 22
((x + 1) + ((((~x + 2) div 4) mod (x + 1)) div 2))
A187909: 1 2 3 5 7 8 10 11 12 14 15 16 18 19 21 22
((x + 1) + (2 div (8 - ((x + ~1) div 2))))
A272916-A254075-A232528-A140401: 1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 18
((x + 1) + ((x - (x div ~8)) div 2))
A225647: 1 3 4 6 7
A329847-A286323-A059559: 1 3 4 6 7 9 10 12 13 15 17 18 20 21 23 24
((x + ~1) + ((~x + 2) div (2 - (x div ~4))))
A320847: 0 0 1 1 2 3 4 4 5 6 7 8 9 10 11 11
(1 + (x2 div (x + 20)))
A029099: 1 1 1 1 1 2 2 2 3 3 4 4 5 6 6 7
(2x div (~x + 21))
A135585: 0 0 0 0 0 0 0 1 1 1 1 2 2 3 4 5
((x + 1) + (4 * (((x + 1) div 2) div 3)))
A261039: 1 2 3 4 5 10 11
A241213-A037473: 1 2 3 4 5 10 11 12 13 14 15 20 21 22 23 24
((x + 1) + ((((2 - (x div 2)) mod (x + 1)) div 2) div 2))
A192188: 1 2 3 4 5 6 8 9 10 12 13 14 15 16 17 18
((x + 1) + ((((x2 + 3x + 2) div 2) div 2) div 2))
A186380: 1 2 4 6 8 11 14 17 20 23 27 31 35 40 45 50
((~x + 1) + (4 * (2 + ((x div 2) mod 4))))
A004450: 9 8 11 10 13 12 15 14 1 0 3 2 5 4 7 6
((x + 1) + (x2 div 32))
A184107: 1 2 3 4 5 6 8 9 11 12 14 15 17 19 21 23
((x + 1) + (x div (4 + ((x div 4) mod 2))))
A344881: 1 2 3 4 5 7 8 9 11 12 13 14 15 16 17 19
((x + 1) + (((x - ((x div 4) mod 2)) div 2) div 2))
A039117: 1 2 3 4 5 7 8 9 11 12 13 14 15 17 18 19
((x + 1) + (((x - ((x div 2) mod 4)) div 2) div 2))
A039119: 1 2 3 4 5 6 7 9 11 12 13 14 15 16 17 19
((x + 1) + ((x - (x div ~7)) div 2))
A225647: 1 3 4 6 7
A330143-A330113-A329923-A292987-A206912-A187342: 1 3 4 6 7 9 10 12 14 15 17 18 20 21 23 25
(1 + compr(\x.((x mod (~8 + (x mod 2))) mod 2),x))
A325364-A133810: 1 2 3 4 5 6 7 8 9 11 13 15 16 17 18 19
((2 + (x div 2)) div (~x + 17))
A332579: 0 0 0 0 0 0 0 0 0 0 1 1 1 2 3 4
((x + 1) + ((x2 + 2x) div 16))
A184103: 1 2 3 4 6 8 10 11 14 16 18 20 23 26 29 31
(1 + compr(\x.(~2 + ((x + ~1) mod (2 + (x div 4)))),x))
A193159: 1 2 3 4 5 6 7 8 10 11 12 13 14 20 23 24
((x + 1) + (((x div 2) - ((x div 4) mod 2)) div 2))
A039118: 1 2 3 4 5 6 8 9 11 12 13 14 15 16 18 19
(1 + ((x2 + x + ~1) div (x + 8)))
A248958: 0 1 1 2 2 3 3 4 5 6 7 7 8 9 10 11
(3x2 div (x + 9))
A046654: 0 0 1 2 3 5 7 9 11 13 15 18 20 23 25 28
((x + 2) - (x2 div (x + 9)))
A200311: 2 3 4 5 5 6 6 6 7 7 7 7 8 8 8 8
((x + 1) + ((x2 + 3x) div 8))
A186382: 1 2 4 6 8 11 13 16 20 23 27 31 35 40 44 49
(x - ((x + 1) mod ((~x + ~1) + (x mod 8))))
A171722: 0 1 2 3 4 5 6 7 8 17 17 17 17 17 17 17
((x + 1) + (2 * (x - (4 * (~x + (x mod 2))))))
A293698: 1 4 23 26 45 48 67 70 89 92 111 114 133 136 155 158
((x + 1) + (2 * ((4x + 2) + (x mod 2))))
A225539: 5 16 23 34 41 52 59 70 77 88 95 106 113 124 131 142
((x + 1) + ((x + ((~x + 1) mod 3)) div 4))
A288992-A288168-A085007: 1 2 4 5 6 7 8 9 11 12 13 15 16 17 19 20
((x + 1) + ((x + (x2 div 3)) div 4))
A186390: 1 2 3 5 7 9 11 13 16 19 21 24 28 31 34 38
((x + 1) + (x div (8 - (x div 4))))
A082463: 1 2 3 4 5 6 7 9 10
A331119: 1 2 3 4 5 6 7 9 10 11 12 13 15 16 17 19
(2x2 div ((x + 1) + (x2 div 4)))
A266082-A257569-A213711: 0 1 2 3 3 4 4 4 5 5 5 5 5 6 6 6
((x + 1) + ((((x div 2) div ~2) mod (x + 2)) div 2))
A289072: 1 2 4 6 7 9 10 11 13 14 15 17 18 20 21 22
((x + 1) + (8x div (x + 4)))
A215138: 1 3 5 7 9 10 11 13 14 15 16 17 19 20 21 22
(1 + compr(\x.(2 - (x3 mod (x + 4))),x))
A058654: 3 4 6 7 8 9 11 12 14 15 16 17 18 19 20 21
((x + 1) + ((2x * (x div 2)) div (2 + (x div 2))))
A231408: 1 2 4 6 9
A265286: 1 2 4 6 9 11 14 16 19
A091626: 1 2 4 6 9 11 14 16 19 22 25 27 31 33 36 39
((x + 1) + (((x * (x div 2)) div 2) div (2 + (x div 2))))
A248559: 1 2 3 4 6 7 8 10 11 13 14 15 17 18 20 21
((x + 1) + (((x2 div 3) + (x mod 2)) div 2))
A069813: 1 2 3 6 7 10 13 16 19 24 27 32 37 42 47 54
(~x4 + ~3x3 + 6x2 + 28x + 24)
A301575: 24 54 64
((x + 1) + ((x + (x mod (1 + (x div 3)))) div 2))
A189518-A189407: 1 2 4 6 7 9 10 12 14 15 17 19 20 22 24 25
((x + 1) + (2 * (x + (2x div 5))))
A276888-A237514: 1 4 7 12 15 20 23 26 31 34 39 42 45 50 53 58
((x + 1) + ((x + (x div 12)) div 2))
A213219: 1 2 4 5 7 8 10 11 13 14 16 17 19 21 22 24
((x + ~1) + (2 * (x + ((1 - (x div 2)) mod 3))))
A145265: 1 4 5 8 15 18 19 22 23 26 33 36 37 40 41 44
((x + 1) + (2 * (x + ((x + (x mod 2)) div 3))))
A026360: 1 4 7 12 15 20 23 26 29 34 37 42 45 48 51 56
((x + 1) + (x2 div ((x + 2) + (x div 3))))
A106829: 1 2 4 5 7 9 10 12 14 15 17 19 21 22 24 26
((x + 1) + (x2 div (x + 10)))
A225819: 1 2 3 4 6 7 9 10 12 14 16 17 19 21 23 25
((x + 1) + (x2 div ((x + 2) + (x div 4))))
A093848: 1 2 4 5 7 9 11 12 14 16 18 20 21 23 25 27
((x2 + 2x + 1) * (1 + ((x2 + x) div 2)))
A092365: 1 8 36 112 275 576 1078 1856 2997 4600 6776 9648 13351 18032 23850 30976
((x2 + 2x + 1) * (1 + ((x2 + 2x) div 2)))
A210378: 1 8 45 128 325 648 1225 2048 3321 5000 7381 10368 14365 19208 25425 32768
(4x4 + 12x3 + 12x2 + 4x)
A160538: 0 32 216 768 2000 4320 8232 14336 23328 36000 53240 76032 105456 142688 189000 245760
((x2 + 2x + 1) * (x - (x2 div ~2)))
A210379: 0 8 36 128 300 648 1176 2048 3240 5000 7260 10368 14196 19208 25200 32768
((x2 + 2x + 1) * ((x2 + ~2x + 1) div 2))
A172517: 0 0 0 32 100 288 588 1152 1944 3200 4840 7200 10140 14112 18900 25088
((x + 1) + (((2x + 2) + (x div 2)) * (x div 2)))
A062317: 1 2 10 13 29 34 58 65 97 106 146 157 205 218 274 289
((2x2 + ~x + 1) - ((x div 2) * (x div 2)))
A269706: 1 2 6 15 25 42
(((x + 1) - (x div ~2)) * ((x + 1) + (x div 2)))
A102214: 1 6 16 30 49 72 100 132 169 210 256 306 361 420 484 552
(((x2 + 3x + 2) div 2) * ((x + 1) + (x mod 2)))
A086500: 1 9 18 50 75 147 196 324 405 605 726 1014 1183 1575 1800 2312
((x + 1) div (2 - ((x + ~2) mod ((~x + ~1) + (x mod 2)))))
A161090: 0 1 1 1 1 1 1 2 1 2 2 3 2 3 3 4
((x + 1) * (1 + ((x + 1) mod 9)))
A160938: 2 6 12 20 30 42 56 72 9 20 33 48 65 84 105 128
(29 div (x + 1))
A033349: 29 14 9 7 5 4 4 3 3 2 2 2 2 2 1 1
(10x2 + 21x + 11)
A055437: 11 42 93 164 255 366 497 648 819 1010 1221 1452 1703 1974 2265 2576
(41 div (x + 1))
A033361: 41 20 13 10 8 6 5 5 4 4 3 3 3 2 2 2
(39 div (x + 1))
A033359: 39 19 13 9 7 6 5 4 4 3 3 3 3 2 2 2
((~1 + (2x2 div 5)) mod (x + 1))
A194737: 0 1 0 2 0 3 6 2 6 1 6 11 4 10 2 9
(9x2 + 19x + 10)
A154517: 10 38 84 148 230 330 448 584 738 910 1100 1308 1534 1778 2040 2320
(37 div (x + 1))
A033357: 37 18 12 9 7 6 5 4 4 3 3 3 2 2 2 2
(35 div (x + 1))
A033355: 35 17 11 8 7 5 5 4 3 3 3 2 2 2 2 2
(49x + 49)
A044138: 49 98 147 196 245 294 343 392 441 490 539 588 637 686 735 784
(49 div (x + 1))
A033369: 49 24 16 12 9 8 7 6 5 4 4 4 3 3 3 3
(47 div (x + 1))
A033367: 47 23 15 11 9 7 6 5 5 4 4 3 3 3 3 2
((x + 1) * (1 + (3 * ((x2 + x) div 2))))
A100175: 1 8 30 76 155 276 448 680 981 1360 1826 2388 3055 3836 4740 5776
compr(\x.(2x mod (1 + ((x div 2) div 3))),(x + 1))
A083970: 1 2 3 4 5 6 7 8 9 10 11 12 15 18 20 22
(6x3 + 9x2 + 4x + 1)
A169711: 1 20 93 256 545 996 1645 2528 3681 5140 6941 9120 11713 14756 18285 22336
((1 + ((2 + (x div 2)) * (x div 3))) div (x + 1))
A025832: 1 0 0 1 1 0 1 1 1 1 2 1 2 2 2 2
(x4 + 6x3 + 11x2 + 7x + 1)
A183066: 1 26 123 364 845 1686 3031 5048 7929 11890 17171 24036 32773 43694 57135 73456
(16x2 + 33x + 17)
A157474: 17 66 147 260 405 582 791 1032 1305 1610 1947 2316 2717 3150 3615 4112
(16x2 + 31x + 15)
A157446: 15 62 141 252 395 570 777 1016 1287 1590 1925 2292 2691 3122 3585 4080
(1 - (x2 div ((~x + ~1) + (x div ~3))))
A247784-A138466: 1 2 2 3 4 5 5 6 7 8 8 9 10 10 11 12
((x + 1) * ((x + ~1) - (2 * ((x + ~1) div 3))))
A229598: 1 0 3 8 5 12 21 16 27 40 33 48 65 56 75 96
((1 + (2 * ((~x + (x mod 2)) div 3))) mod (x + 1))
A282701: 0 1 2 3 2 3 4 5 4 5 4 5 6 7 6 7
((x + 1) * (1 + (((x + 1) + (x div 4)) div 2)))
A231407: 1 4 6
A019445: 1 4 6 12 20 24 35 40 54 70 77 96 117 126 150 160
((x + 1) * (1 + (((x + 1) * (x div 4)) mod 2)))
A111619: 1 2 3 4 10 6 14 8 9 10 11 12 26 14 30 16
((1 + (2 * (x mod 10))) mod (x + 1))
A103303: 0 1 2 3 4 5 6 7 8 9
A264600-A259043-A138470-A061486: 0 1 2 3 4 5 6 7 8 9 1 3 5 7 9 11
(65 div (x + 1))
A033385: 65 32 21 16 13 10 9 8 7 6 5 5 5 4 4 4
(63 div (x + 1))
A033383: 63 31 21 15 12 10 9 7 7 6 5 5 4 4 4 3
compr(\x.(x mod (1 + (8 * (x mod 2)))),(x + 1))
A118672: 2 4 6 8 9 10 12 14 16 18 20 22 24 26 27 28
((x + 1) * (1 + (2 * ((x2 + 2x) div 4))))
A212975: 1 2 15 28 65 102 175 248 369 490 671 852 1105 1358 1695 2032
((1 + (4 * ((x * (x div 2)) mod 2))) mod (x + 1))
A293235: 0 1 1 1 1 1 1 5 1 1 1 5 1 1 1 5
((1 + (4 * (x2 - (x div 2)))) div (x + 1))
A222011: 1 2 4 8
A086790: 1 2 4 8 11 15 19 23 26 30 34 38 42 46 50 54
(45 div (x + 1))
A033365: 45 22 15 11 9 7 6 5 5 4 4 3 3 3 3 2
(60 div (x + 1))
A033380: 60 30 20 15 12 10 8 7 6 6 5 5 4 4 4 3
(50 div (x + 1))
A033370: 50 25 16 12 10 8 7 6 5 5 4 4 3 3 3 3
(((~2x2 + 4) div 5) mod (x + 1))
A194735: 0 0 2 1 4 2 0 5 2 8 4 0 8 3 12 6
(((x2 + 1) mod (x + 5)) div (x + 1))
A266298: 1 1 1 0 1 1 0 0 0 1 1 0 0 0 0 0
(((x2 + ~x) mod (x + 5)) div (x + 1))
A092575: 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0
(51 div (x + 1))
A033371: 51 25 17 12 10 8 7 6 5 5 4 4 3 3 3 3
(54 div (x + 1))
A033374: 54 27 18 13 10 9 7 6 6 5 4 4 4 3 3 3
(72 div (x + 1))
A033392: 72 36 24 18 14 12 10 9 8 7 6 6 5 5 4 4
(96 div (x + 1))
A033416: 96 48 32 24 19 16 13 12 10 9 8 8 7 6 6 6
(x3 + 9x2 + 21x + 13)
A226514: 13 44 99 184 305 468 679 944 1269 1660 2123 2664 3289 4004 4815 5728
(5x3 + 9x2 + 5x + 1)
A027849: 1 20 87 232 485 876 1435 2192 3177 4420 5951 7800 9997 12572 15555 18976
(x5 + ~x4 + ~x3 + ~x2 + ~x)
A152017: 0 ~3 2 123 684 2345 6222 14007 28088 51669 88890 144947 226212 340353 496454 705135
((x + 1) * ((x mod 2) - ((x2 + 2x) div ~2)))
A212976: 0 6 12 36 60 114 168 264 360 510 660 876 1092 1386 1680 2064
((x + 1) * ((x + 4) - (x2 div ~2)))
A192797: 4 12 24 48 80 132 196 288 396 540 704 912 1144 1428 1740 2112
(46 div (x + 1))
A033366: 46 23 15 11 9 7 6 5 5 4 4 3 3 3 3 2
((2 + (x mod 11)) mod (x + 1))
A214949: 0 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6
(6x3 + 12x2 + 8x + 2)
A213829: 2 28 114 296 610 1092 1778 2704 3906 5420 7282 9528 12194 15316 18930 23072
(((x mod 2) - (2 * (1 + (x div 3)))) mod (x + 1))
A063195: 0 1 1 1 1 3 1 3 3 3 3 5 3 5 5 5
(16x2 + 34x + 18)
A158056: 18 68 150 264 410 588 798 1040 1314 1620 1958 2328 2730 3164 3630 4128
(16x2 + 30x + 14)
A158058: 14 60 138 248 390 564 770 1008 1278 1580 1914 2280 2678 3108 3570 4064
(2x3 + 12x2 + 16x + 6)
A086113: 6 36 102 216 390 636 966 1392 1926 2580 3366 4296 5382 6636 8070 9696
(66 div (x + 1))
A033386: 66 33 22 16 13 11 9 8 7 6 6 5 5 4 4 4
(62 div (x + 1))
A033382: 62 31 20 15 12 10 8 7 6 6 5 5 4 4 4 3
((2 * ((~2x + 2) div 5)) mod (x + 1))
A086520: 0 0 1 2 1 2 3 2 3 2 3 4 3 4 3 4
(3x3 + 12x2 + 17x + 8)
A143943: 8 40 114 248 460 768 1190 1744 2448 3320 4378 5640 7124 8848 10830 13088
((x + 1) * ((3x2 + 5x + 2) div 2))
A050509: 1 10 36 88 175 306 490 736 1053 1450 1936 2520 3211 4018 4950 6016
((x + 1) * ((x3 + 5x2 + 4x) div 2))
A292058: 0 10 54 168 400 810 1470 2464 3888 5850 8470 11880 16224 21658 28350 36480
((x + 1) * ((3x2 + 7x + 4) div 2))
A036659: 2 14 45 104 200 342 539 800 1134 1550 2057 2664 3380 4214 5175 6272
((x + 1) * ((x5 + x4) div 2))
A163274: 0 2 72 648 3200 11250 31752 76832 165888 328050 605000 1054152 1752192 2798978 4321800 6480000
(52 div (x + 1))
A033372: 52 26 17 13 10 8 7 6 5 5 4 4 4 3 3 3
(52 mod (x + 1))
A050514: 0 0 1 0 2 4 3 4 7 2 8 4 0 10 7 4
(44 div (x + 1))
A033364: 44 22 14 11 8 7 6 5 4 4 4 3 3 3 2 2
(68 div (x + 1))
A033388: 68 34 22 17 13 11 9 8 7 6 6 5 5 4 4 4
(4x3 + 12x2 + 20x + 12)
A292022: 12 48 132 288 540 912 1428 2112 2988 4080 5412 7008 8892 11088 13620 16512
((((~x + 1) div (2 + (x div 3))) div 2) mod (x + 1))
A080331: 0 0 2 3 4 5 6 7 8 9 10 11 12 13 13 15
((1 - (x mod (2 + ((x div ~2) mod 2)))) div (x + 1))
A128407: 1 0 ~1 0 0 ~1 0 0 0 0 0 0 0 0 ~1 0
(56 div (x + 1))
A033376: 56 28 18 14 11 9 8 7 6 5 5 4 4 4 3 3
((x + 1) * (((x - ((x mod 3) div 2)) div 2) div 2))
A294239: 0 0 0 0 5 6 7 8 9 20 22 24 39 42 45 48
(((x2 * (x mod 2)) div 8) mod (x + 1))
A175677: 0 0 0 1 0 3 0 6 0 0 0 3 0 7 0 12
compr(\x.((x mod 4) - (x div 8)),(x + 1))
A078137: 4 8 9 12 13 16 17 18 20 21 22 24 25 26 27 28
((2 * (x - ((x + (x div 2)) div 4))) mod (x + 1))
A229878: 0 0 1 0 1 2
A060145: 0 0 1 0 1 2 1 2 1 2 3 2 3 4 3 4
(((~x2 + 1) mod (x + 6)) div (x + 1))
A296212-A078768: 1 0 1 0 1 1 0 0 0 1 1 1 0 0 0 0
((x + 1) * (((x2 + ~x) mod (2 + (x div 2))) mod 2))
A280832: 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 16
((4x + 4) + (x div 7))
A059532: 4 8 12 16 20 24 28 33 37 41 45 49 53 57 62 66
((4x + 4) + (x div 12))
A329975: 4 8 12 16 20 24 28 32 36 40 44 48 53 57 61 65
((4x + 4) + (((x + ~1) div 2) * (x div 2)))
A036573: 4 8 12 17 22 28 34 41 48 56 64 73 82 92 102 113
(((x4 + x) div 4) mod (x + 1))
A077814: 0 0 1 1 0 1 3 2 0 2 5 3 0 3 7 4
(4 - ((x + 1) * ((~x + 2) + (x div 4))))
A085620-A085619: 2 2 4 8 9 16
compr(\x.(((x + ((x div 2) div 3)) div 2) mod 2),(x + 1))
A005556: 1 4 5 7 8 11
A120753: 1 4 5 7 8 11 14 15 18 21 22 24 25 28 29 31
compr(\x.(((x + (x div 8)) div 2) mod 2),(x + 1))
A190860: 1 4 5 8 11 12 15 18 19 22 23 25 26 29 30 32
compr(\x.(x mod (2 + ((x * (x div 4)) mod 2))),(x + 1))
A280877: 2 4 6 8 10 12 14 15 16 18 20 21 22 24 26 28
(((1 mod (~2x + 1)) mod (x + 4)) div (x + 1))
A174875: 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0
(((x div 2) - (x mod (2 - ((x div 2) mod 2)))) mod (x + 1))
A116921: 0 1 1 1 2 1 3 3 4 3 5 5 6 5 7 7
(4 + (2 div (x + 1)) - (x div 8))
A125089: 6 5 4 4 4 4 4 4 3 3 3 3 3 3 3 3
(x + (((x - ((x div 2) mod 2)) div 2) + (2 mod (x + 1))))
A141468: 0 1 4 6 8 9 10 12 14 15 16 18 20 21 22 24
(8x3 + 14x2 + 6x)
A192796: 0 28 132 360 760 1380 2268 3472 5040 7020 9460 12408 15912 20020 24780 30240
(18x2 + 34x + 16)
A178574: 16 68 156 280 440 636 868 1136 1440 1780 2156 2568 3016 3500 4020 4576
(2 - ((2x2 + 2x) * (~2 + (x div ~2))))
A216528: 2 14 38 98
(x - (((x2 div 2) * ((~x + 2) div 2)) div (x + 1)))
A145801: 0 1 2 4 6 9 12 16 19 25 29 36
(((x2 + ~x) mod (x - ((~x + 2) div 2))) div (x + 1))
A037821: 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0
(((~x2 + 1) div (x - ((~x + 2) div 2))) mod (x + 1))
A091226: 0 0 1 2 2 2 2 3 3 3 3 4 4 5 5 5
((x + 1) * ((x3 + 3x2 + ~2x) div 2))
A172225: 0 2 24 96 260 570 1092 1904 3096 4770 7040 10032 13884 18746 24780 32160
((2x * (2x2 + (x div 2))) div (x + 1))
A211623: 0 2 12 28 54 86 128 176 234 298 372 452 542 638 744 856
(x - (((x3 + ~2x2) div (x + 2)) div (x + 1)))
A079243: 0 2 2 3
A130249: 0 2 2 3 3 4 4 4 4 4 4 5 5 5 5 5
(((x mod 10) - (x div 2)) mod (x + 1))
A279766: 0 1 1 2 2 3 3 4 4 5 6 8 9 11 12 14
(x - (((4 + (x div 2)) * (x div 2)) div (x + 1)))
A211275: 0 1 1 2 2 3 3 5 5 6 6 8 8 9 9 11
(((((~x + 2) div 2) mod 4) - (x mod 2)) div (x + 1))
A291147: 1 ~1 0 0 0 0 0 0 0 ~1 0 0 0 0 0 0
((x2 + 2x + 2) div ((x2 + 2) div (x + 1)))
A003861: 1 5 5 8 8 9 10
(19x2 + 19x)
A173309: 0 38 114 228 380 570 798 1064 1368 1710 2090 2508 2964 3458 3990 4560
(~x3 + 7x2 + ~5x + 1)
A161708: 1 2 11 22 29 26 7 ~34 ~103 ~206 ~349 ~538 ~779 ~1078 ~1441 ~1874
(3x4 + 6x3 + 5x2 + 2x)
A248621: 0 16 120 456 1240 2760 5376 9520 15696 24480 36520 52536 73320 99736 132720 173280
(x - ((2x mod (x + 8)) mod (x + 1)))
A048762: 0 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8
((x2 * (1 + ((x + 2) div 3))) div (x + 1))
A219114: 0 1 2 4 9 12 15 24
((x + ~1) * ((x2 + x) mod (1 + (x mod 4))))
A160145: 0 0 0 0 0 0 0 0 0 0 18 0 0 0 0 0
(9x2 + ~10x + 3)
A154262: 3 2 19 54 107 178 267 374 499 642 803 982 1179 1394 1627 1878
((~x + 1) + (4 * (3 + ((x div 2) mod 2))))
A004454: 13 12 15 14 9 8 11 10 5 4 7 6 1 0 3 2
(x4 + 4x3 + ~3x2 + ~2x)
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(x7 + ~x6 + x4 + ~x3)
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(x8 + ~x7)
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((~2 + ((1 - (x div 2)) div 3)) mod (x2 + 1))
A140479: 0 0 3 8 14 23 34 47 62 79 97 118 141 166 193 222
((x2 + 1) * (~x + (4 * (2 + (x div 2)))))
A218555: 8 14 50 90
(x6 + ~x3 + ~x2 + x)
A218130: 0 0 54 696 4020 15480 46410 117264 261576 530640 998910 1770120 2984124 4824456 7526610 11387040
(4x - ((((x + ~1) div 2) div 2) div ~2))
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(x - (((x - ((x div 4) mod 2)) div 2) div ~2))
A039133: 0 1 3 4 5 6 7 9 10 11 13 14 15 16 17 19
(x - (((x - ((x div 2) mod 4)) div 2) div ~2))
A138083: 0 1 2 4 5 6
A039140: 0 1 2 4 5 6 7 8 10 11 12 14 15 16 17 18
((x + 3) div (2 - (x div ~8)))
A186188: 1 1 1 2 2 2 3 3 3 3 3 3 3 4 4 4
(1 - ((~x + 2) div (2 - (x div ~8))))
A263270: 0 1 1 2 2 2 3 3 3 3 3 4 4 4 4 5
((x + 8) - (x div ~8))
A043697-A043624-A031953: 8 10 11 12 13 14 15 16 17 19 20 21 22 23 24 25
((x mod 2) - ((x div (2 - ((x div 2) mod 2))) div ~2))
A173234: 0 1 1 3 1 2 3 5 2 3 5 7 3 4 7 9
(x - (((x + ((x div 4) mod 2)) div 2) div ~2))
A039131: 0 1 3 4 5 7 8 9 10 11 13 14 15 17 18 19
(x - ((((x div 4) mod 2) + (x div 2)) div ~2))
A039130: 0 1 3 4 6 7 8 9 10 11 13 14 16 17 18 19
((x + 2) - ((~x + 1) div (2 - ((x div 2) div ~2))))
A068938: 2 3 5 6 7 9 10 11 12 13 14 15 17 18 19 20
(2 - ((x + ((x + (x div 4)) div 2)) div ~2))
A280471: 2 3 4 4 5 6 7 8 9 9 10 11 12 13 13 14
(4 - (7 * (x div ~2)))
A168212: 4 11 11 18 18 25 25 32 32 39 39 46 46 53 53 60
((2 * ((x + 1) + (x div 3))) - (x div ~2))
A063217: 2 5 7 12 14 17 21 24 26 31 33 36 40 43 45 50
(4x div (8 - (x div ~2)))
A072749: 0 0 0 1 1 1 2 2 2 2 3 3 3 3 3 3
((2x + 4) - ((~x + 2) div (2 - (x div ~2))))
A212451: 3 6 8 11 13 15 17 19 21 23 26 28 30 32 34 36
((x + 2) + ((x * (x div 2)) mod 2) - (x div ~2))
A085624: 2 4 5 8 8 10 11 14 14 16 17 20 20 22 23 26
((2 * (x + (4 * (x mod 2)))) - (x div ~2))
A168206: 0 11 5 16 10 21 15 26 20 31 25 36 30 41 35 46
((1 + (x mod (~1 + (x div ~5)))) mod 2)
A275714: 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 0
((1 + (x mod (1 + ((~x + 1) mod 5)))) mod 2)
A267253-A261178: 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 0
(((x + 1) - (2 div (1 + (x div 5)))) mod 2)
A283963-A244220: 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0
((1 + (x div (1 + ((x div 3) mod 3)))) mod 2)
A266112: 1 0 1 0 1 1 1 1 1 0 1 0 1 1 0 0
((1 + ((x div 2) div (1 + ((~x + 1) mod 3)))) mod 2)
A127247: 1 1 1 1 1 1 0 0 0 1 0 0 0 1 1 0
((1 + (x2 mod (~3x + 5))) mod 2)
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((1 + ((2x + 2) mod (1 + (x div 3)))) mod 2)
A118172-A071037: 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1
((1 + ((x2 + ~2x) mod (1 + (x div 3)))) mod 2)
A342004: 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0
((1 + (x mod (~1 + (x mod (~1 + ((~x + 1) div 2)))))) mod 2)
A294905-A192490-A080339: 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0
((1 + (x mod (1 + (x2 mod (1 + (x div 2)))))) mod 2)
A297086: 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0
((1 + (2x mod (2 - (x div ~3)))) mod 2)
A103583: 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1
(((x + 1) - (x mod (2 - (x div ~3)))) mod 2)
A342005: 1 1 1 0 1 1 1 0 0 0 1 1 1 0 1 1
((x div (1 + (x mod (3 - (x div ~2))))) mod 2)
A087187: 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1
((1 + (x div (~1 + (2 * (~1 + (x mod 4)))))) mod 2)
A162549: 1 0 1 0 1 0 1 1 0 0 1 0 1 0 1 0
((1 + (x div (3 + ((x div 2) div 3)))) mod 2)
A266300: 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0
((1 + (x div (1 + ((x + ~1) mod 6)))) mod 2)
A029445: 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0
((1 + ((2x + 2) div 7)) mod 2)
A284512: 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1
(((x + 1) div (1 + (x div 7))) mod 2)
A189169: 1 0 1 0 1 0 1 0 0 1 1 0 0 1 1 1
(((x div 2) div (1 + (x mod 7))) mod 2)
A011717: 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 1
((1 + ((x + 1) div (1 + (x mod 6)))) mod 2)
A011705: 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1
((1 + (x mod ((x + 1) - ((~1 + (x div 2)) div 2)))) mod 2)
A179761: 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1
((1 + (2x2 mod (1 + ((x + 1) div 2)))) mod 2)
A127236: 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1
(2 * ((x + 1) - ((x div 2) div ~5)))
A133012: 2 4 8 10 12 14 16 18 20 22 24 26 30 32 34 36
((1 + (x div (~1 + (4 * (~2 + (x mod 2)))))) mod 2)
A029439: 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0
((1 + ((x + 4) mod 9)) mod 2)
A287722-A284588-A177990: 1 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0
((x div (1 + ((~x + 2) mod 9))) mod 2)
A011677: 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0
(((x + ~1) mod (1 + (x mod 9))) mod 2)
A340607: 0 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0
((1 + (x div (1 + (2 * ((~x + 1) mod 4))))) mod 2)
A082960: 1 0 1 1 0 0 1 0 1
A156258: 1 0 1 1 0 0 1 0 1 0 0 1 1 0 1 0
((1 + ((x + 1) mod (1 + (2 * (x mod 4))))) mod 2)
A323000: 1 1 0 1 1 1 1 0 1 0 0 0 1 1 1 1
((1 + (x2 div (~1 + (4 * (x div 2))))) div 2)
A294107: 0 0 1 2 1 2 2 2 2 3 3 3 3 4 4 4
(((x + ~1) - (x div (3 + ((x div 2) mod 2)))) mod 2)
A039983: 1 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1
((1 + (x div (1 + (x mod (4 + (x mod 2)))))) mod 2)
A011750: 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 0
(((x + ~1) - (x div (1 + ((x + 2) mod 4)))) mod 2)
A267635: 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1
((x - (2 div (1 + ((x + 1) div 5)))) mod 2)
A286665-A284533: 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1
((1 + (x div (5 * (~2 + (x mod 2))))) mod 2)
A025914: 1 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0
(2 * ((x + 1) - ((~2x + 2) div 5)))
A286909-A189792: 2 4 8 10 14 16 18 22 24 28 30 32 36 38 42 44
(((x + ~1) mod (1 + ((x + ~2) mod 5))) div 2)
A280912-A280287-A280285: 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1
((x + 2) mod (2 * (1 + (2x div 5))))
A012265: 0 1 0 1 2 1 2 3 2 3 2 3 4 3 4 3
(x - (2 * (2 - (2 div (1 + (x div 5))))))
A322290: 0 1 2 3 4 3 4 5 6 7 6 7 8 9 10 11
(2 - ((x - (2 div (1 + (x div 5)))) mod 2))
A080763: 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 1
(2 * ((2x + 5) - (x mod 5)))
A179083-A007958: 10 12 14 16 18 30 32 34 36 38 50 52 54 56 58 70
(((2x + ~1) mod (1 + (x mod 5))) div 2)
A001899: 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0
((3x mod (1 + (x mod 5))) div 2)
A116375: 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0
((1 + ((x + 1) div (1 + ((~x + 2) mod 4)))) mod 2)
A105165: 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1
((1 + ((~x + ~1) mod (1 + (x div 4)))) div 2)
A019269: 0 0 0 0 1 0 1 0 0 1 1 0 2 1 1 0
((x div (1 + ((~x + 1) mod (1 + (x div 4))))) mod 2)
A115516: 0 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1
((1 + ((x2 + 2) div (x + 5))) mod 2)
A275737: 1 1 1 0 1 1 0 1 0 0 1 0 1 0 1 0
((1 + ((x2 + 2) mod (4x + 1))) mod 2)
A335392: 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1
((1 + (x3 div (~1 + (2 * (x div 2))))) mod 2)
A291904: 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0
((1 + (x mod (2 - (x div (1 + ((x div 2) mod 2)))))) mod 2)
A345064-A344885-A328958-A325964-A324290-A160804-A010055: 1 1 1 1 1 0 1 1 1 0 1 0 1 0 0 1
(((x + 1) - ((~x + 2) div (3 + (x mod 2)))) div 2)
A194640: 0 1 1 2 3 3 4 5 5 6 7 7 8 8 9 10
(((x + 1) div (1 + (x div (3 + (x mod 2))))) mod 2)
A127829-A124788-A089198-A059607: 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0
((1 + ((x div 2) div (1 + (x mod (2 + (x mod 2)))))) mod 2)
A073784: 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0
((x div (1 + ((x div 2) div (1 + (2 * (x mod 2)))))) mod 2)
A252372: 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1
((1 + ((x - (x div ~3)) div 3)) mod 2)
A286749: 1 1 0 0 1 1 1 0 0 1 1 0 0 1 1 1
((x mod (1 + (((x + ~2) div 3) mod 3))) mod 2)
A117943: 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1
(((~x + 1) div (~1 + (3 * (x mod 3)))) mod 2)
A266754: 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0
((1 + (((x + ~1) mod (1 + (x div 2))) mod 3)) mod 2)
A131377: 1 1 0 1 1 0 0 1 1 1 1 0 0 1 1 1
((1 + ((x - (2 mod (1 + (x div 2)))) mod 3)) mod 2)
A285430: 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 0
((1 + (((x + ~2) mod (1 + (x div 2))) mod 3)) mod 2)
A167021: 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1
((1 + (x2 mod (3 * (1 + (x div 2))))) mod 2)
A266282: 1 0 1 0 0 0 1 0 1 1 1 0 1 0 1 0
((x div (~1 - ((1 + (x div 2)) mod 3))) mod 2)
A189723: 0 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1
(2 - ((x - (x div (1 + ((x + 1) mod 3)))) mod 2))
A049710: 2 1 2 2 1 2 1 1 2 1 1 2 2 1 2 2
((x div (~1 + (3 * (((x + ~1) div 2) div 2)))) mod 2)
A309752: 0 1 0 1 0 0 1 1 0 1 0 0 0 1 1 1
(x2 mod 46)
A070468: 0 1 4 9 16 25 36 3 18 35 8 29 6 31 12 41
((~1 + (x div (~3 + (x div 8)))) mod 2)
A303561: 1 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1
((1 + ((x div (~2 + ((x div 2) mod 2))) mod 3)) mod 2)
A285414: 1 1 0 1 0 1 1 1 1 0 1 0 1 1 0 1
((1 + (x div (6 * (~2 + (x mod 2))))) mod 2)
A025913: 1 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0
(x3 mod 26)
A070488: 0 1 8 1 12 21 8 5 18 1 12 5 12 13 14 21
(x3 mod 22)
A070484: 0 1 8 5 20 15 18 13 6 3 10 11 12 19 16 9
(x - (2 * (~1 + ((~x + 2) div 12))))
A241783: 2 3 4 7 8 9 10 11 12 13 14 15 16 17 18 21
(((x + ~2) div (1 + (3 * (x mod 4)))) mod 2)
A031233: 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 1
((1 + (x2 div ((2x + 4) div 3))) mod 2)
A131309: 1 1 1 0 1 1 0 1 1 0 1 0 1 1 0 1
(((x + 1) div (1 + ((2 * (x div 2)) mod 3))) mod 2)
A127245: 1 0 1 1 0 1 1 0 1 1 1 0 1 0 1 1
(((x2 + 1) - (3 * ((x div 2) mod 2))) div 2)
A187093: 0 1 1 3 8 13 17 23 32 41 49 59 72 85 97 111
((1 + (((~x + ((x div 2) mod 2)) div 2) mod 3)) mod 2)
A290808: 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1
((x - ((x + ~1) mod (1 + ((x + 2) div 3)))) mod 2)
A288858: 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1
(((x div 2) - (x mod (1 + ((x + 2) div 3)))) mod 2)
A285255: 0 1 1 0 1 0 1 0 0 1 1 0 0 1 1 0
(((x * (x div 2)) mod (6x + 1)) mod 2)
A275855-A270573-A268310-A144602: 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0
((3x mod (1 + (2x div 3))) mod 2)
A321013: 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1
(((x2 + ~x) div (1 + (2x div 3))) mod 2)
A288520: 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1
((x - (x2 mod (1 + (3 * (x div 2))))) mod 2)
A062103: 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0
(((x2 + 1) div (1 + ((x div 2) div 3))) mod 2)
A004569: 1 0 1 0 1 0 0 1 0 1 0 1 0 0 1 1
(2 * ((x2 div 2) mod (1 + ((x div 2) div 3))))
A224893: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2
((x2 + 2x) mod (2 * (1 + ((x div 2) div 3))))
A221170: 0 1 0 1 0 1 0 3 0 3 0 3 0 3 2 3
((((~x + 2) div 2) div (1 + ((x div 2) mod 3))) mod 2)
A072792: 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 0
((x - ((~x + 1) div (1 + ((x div 2) mod 3)))) mod 2)
A267866: 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0
((x mod (~1 + (((~x + 2) * (x div 2)) div 3))) mod 2)
A337475: 0 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1
((1 + ((~x + (x div 5)) mod 3)) mod 2)
A188090: 1 1 0 1 1 1 0 1 1 0 0 1 1 0 1 1
((1 + ((~x + ((x div 2) div 3)) mod 3)) mod 2)
A175480: 1 1 0 1 1 0 0 1 1 0 1 1 1 0 1 1
(((x + ~1) - (x div (2 - ((~x + 1) div 3)))) mod 2)
A026920: 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 0
((0 - ((x div 2) mod (~1 + ((~x + 1) div 3)))) div 2)
A248327: 0 0 0 0 0 0 0 0 0 0 1 0 2 2 2 2
((2 - ((x div 2) mod (~1 + ((~x + 1) div 3)))) div 2)
A226273: 1 1 1 1 1 1 1 1 1 1 2 1 3 3 3 3
(((x + (x mod 2)) mod (~1 + ((~x + 1) div 3))) mod 2)
A011715: 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0
(((2 + (x div 2)) div (1 + ((~x + 1) mod 3))) mod 2)
A249866: 1 0 1 1 0 1 0 1 0 1 1 0 0 0 1 0
((1 + ((x * ((1 + (x div 2)) div 2)) div 3)) mod 2)
A195053: 1 1 1 0 0 0 1 1 0 1 1 0 1 0 1 1
((x3 mod (~1 + ((~x + 2) div 3))) mod 2)
A174898: 0 0 0 1 0 1 0 0 1 1 0 1 0 1 1 1
(((~x + 2) mod (1 + ((x * (x div 2)) div 3))) div 2)
A257594: 0 0 0 0 0 0 1 1 2 3 4 5 7 8 10
A034154: 0 0 0 0 0 0 1 1 2 3 4 5 7 8 10 11
((x mod ((x + 1) - ((x * (x div 2)) mod 3))) mod 2)
A261013: 0 1 0 1 1 0 0 1 1 1 1 0 0 1 1 1
((2x mod (~1 + ((~x + (x mod 2)) div 3))) mod 2)
A238012-A080343: 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0
(2 * ((x + 1) + (x div 3) - (x div ~2)))
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(((x2 + 4x + 5) + (x div 3)) div 2)
A027916: 2 5 8 13 19 25 33 42 51 62 74 86 100 115 130 147
(((2x + ~5) mod (1 + (x div 3))) div 2)
A144764: 0 0 0 0 0 0 0 0 1 0 1 0 2 0 1 0
(((~x + 1) div ((x + 1) div (1 + (x div 3)))) mod 2)
A179762: 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1
(((2x + ~6) div (1 + (x div 3))) mod 2)
A037879: 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0
(((3x + 2) div (1 + (x div 3))) mod 2)
A316832-A086747: 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1
(((2 + (x * (x div 2))) mod (1 + (x div 3))) mod 2)
A162641: 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1
(((~x + ((~x + 2) div 2)) mod (1 + (x div 3))) div 2)
A011702: 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1
(2 + ((x2 + x) div ((x + 1) - (x div 3))))
A188262: 2 3 4 6 7 8 10 11 12 14 15 16 19 20 21 23
(((x2 + ~x) div ((x + 1) - (x div 3))) mod 2)
A122924: 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1
((x2 mod ((2x + 1) - (x mod 3))) mod 2)
A327974: 0 1 1 0 0 1 0 1 0 1 0 0 1 1 1 0
(((((x + ~1) div 2) div 2) mod (1 + (x mod 3))) mod 2)
A063100: 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0
(((2 + (x div 4)) mod (1 + (x mod 3))) mod 2)
A300372-A102082: 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0
(((~x + (x div 3)) mod (1 + (x mod 3))) mod 2)
A156595: 0 1 1 0 1 0 0 1 0 0 1 1 0 1 0 0
((x - (x2 mod ((x + 1) - (x mod 3)))) div 2)
A194251: 0 0 1 1 2 2 2 3 3 4 5 5 5 6 6 7
((1 + (x mod (~1 - (4 mod (x + 2))))) mod 2)
A166946: 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 1
((1 + ((x * (x mod 4)) div (x + 3))) mod 2)
A128915: 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1
(4x3 + 10x2 + 8x + 4)
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(((x + ~1) - (6 div (1 + (x div 2)))) mod 2)
A190198: 1 0 0 1 1 0 0 1 0 1 0 1 1 0 1 0
((1 + ((2 * (x mod 4)) div (1 + (x div 2)))) mod 2)
A118274: 1 1 1 0 1 1 0 0 1 1 1 0 1 1 1 1
((1 + (8x div (1 + (x div 2)))) mod 2)
A167020: 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0
((x mod (1 + ((~2x + 2) mod (1 + (x div 2))))) mod 2)
A056980: 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0
((2x div (1 + ((x + ~2) mod (1 + (x div 2))))) mod 2)
A065719: 0 0 0 1 0 0 0 1 0 0 0 1 0 1 1 1
((x div (1 + ((~2x + 1) mod (1 + (x div 2))))) mod 2)
A334812: 0 1 1 1 1 1 1 1 0 0 1 0 0 1 0 1
((2 div (1 + ((x2 + 2) mod (1 + (x div 2))))) mod 2)
A101349: 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0
((x + 1) mod (2 * (1 + (x mod (3 - (x mod 2))))))
A292603: 1 2 3 0 1 2 1 0 3 2 3 0 1 2 3 0
((2x div (1 + ((x div 2) div (1 + (x mod 2))))) mod 2)
A070092: 0 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1
((1 + (x div (~1 + (x * ((x + 1) mod 3))))) mod 2)
A286046: 1 0 1 0 1 0 0 1 1 0 1 0 0 1 1 0
((1 + (x3 div (3x + 1))) mod 2)
A217206: 1 1 0 1 1 0 0 0 1 1 1 0 1 1 0 0
((1 + ((~1 + (x mod 5)) mod (x + 1))) mod 2)
A190191: 1 1 0 1 0 0 1 0 1 0 1 1 0 1 0 0
((1 + ((1 + (x2 div 4)) mod (x + 1))) mod 2)
A316533-A085405: 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0
((x div (1 + (16 mod (x + 1)))) mod 2)
A130854: 0 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1
(((2x + 1) div (1 + (4 mod (x + 1)))) mod 2)
A157926: 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 0
(((2x + ~1) div (1 + (4 mod (x + 1)))) mod 2)
A129572: 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1
((x mod (1 + ((2 - (x mod 4)) mod (x + 1)))) div 2)
A318502: 0 0 0 1 0 0 0 3 1 0 0 5 0 0 0 7
((1 + ((x2 + ~6x + 8) div (x + 1))) mod 2)
A341346: 1 0 1 0 1 1 0 0 1 0 1 0 1 0 1 1
((1 + (((~2 + (x div 2)) * (x div 2)) mod (x + 1))) mod 2)
A229062-A000161: 1 1 1 0 1 1 0 0 1 1 1 0 0 1 0 0
((1 + ((2 + (x * (x + (x div 2)))) div (x + 1))) mod 2)
A135022: 1 0 1 0 0 1 1 0 1 0 0 1 1 0 0 1
((1 + ((x * (2 + (x2 div 2))) div (x + 1))) div 2)
A303331: 0 1 1 2 4 6 9 11 15 19
(2 + (x2 div ((x + 1) - ((x div 2) div ~2))))
A086861: 2 2 3 3 4 5 6 6 7 8 9 10 11 11 12 13
(((x + 2) mod (2 - ((x div 2) div ~3))) div 2)
A001878: 0 0 0 1 0 0 1 0 1 1 0 0 1 1 0 1
((x - ((~x + 2) div (2 - (x mod ~3)))) mod 2)
A267418: 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0
(2 * ((x + 1) - ((x + (x div 4)) div ~2)))
A283233: 2 6 8 12 16 18 22 24 28 32 34 38 42 44 48 50
((x mod (1 + ((~x + 2) mod (2 - (x div ~2))))) mod 2)
A090171: 0 1 0 1 1 0 0 1 0 0 1 1 1 1 0 1
(1 - (((x2 + ~2x) mod (~1 + (x div ~2))) mod 2))
A196251: 1 0 1 1 0 0 1 1 1 0 1 1 1 0 1 0
((x mod (1 + (2 * (1 + ((x div 2) mod 4))))) mod 2)
A172303: 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0
((x div (1 + (2 * ((x + ~1) div 5)))) mod 2)
A112416: 0 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1
((1 + ((x + 1) div (2 + (x div 5)))) div 2)
A337788: 0 1 1 1 1 1 1 1 2 2 1 2 2 2 2 2
((x mod (1 + (x div (2 + (x mod 5))))) div 2)
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(((x + ~2) mod (~1 + (2 * (x mod 5)))) div 2)
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((1 + ((x - (3 * (x div 4))) div 2)) div 2)
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((((~x + 1) * (x div 2)) div 7) mod 2)
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((1 + (x div (2 - ((x - (x mod 3)) div 2)))) mod 2)
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(2 * (1 + (2 * (1 + (x * (1 + (2 mod (x + 1))))))))
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((1 + (((x + 1) * (x div ~3)) div 2)) mod 2)
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((1 + (((x mod ~3) mod (x + 1)) div 2)) mod 2)
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(((x + ~2) mod (5 + (x mod 3))) mod 2)
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(((2x + ~2) mod (1 + (((x + 1) div 2) div 2))) div 2)
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(((x2 + x) div (1 + (((x + 1) div 2) div 2))) mod 2)
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((x - (x div (~3 + (x div ~4)))) mod 2)
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(2 + ((x div 2) div (1 + (2 * (2 + (x mod 4))))))
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((x mod ((x + ~1) - ((x + 2) mod 8))) mod 2)
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(((x2 + ~2x + 1) mod 9) mod 2)
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(x - (2 * ((2x + ~2) div 9)))
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(((2 * (x2 div 2)) div 9) mod 2)
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(9x2 + 9x + 20)
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(2 + (9 * ((x2 + x) div 2)))
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(2 + ((2x2 + 4x) mod 9))
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(((x + ~1) - ((x + 2) div (2 + (x div 4)))) mod 2)
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(2 + ((2x + 1) div (3 + (x div 4))))
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(2 * ((2x + 1) div (3 + (x div 4))))
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(((2x + 1) div (3 + (x div 4))) mod 2)
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(((2x + ~4) div (3 + (x div 4))) mod 2)
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((x div (~1 + (2 * ((x div 2) - (x mod 4))))) mod 2)
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((1 + ((~x2 + 2) div (x + 6))) mod 2)
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(((x div 2) div (1 + (x mod (4 + (x div 2))))) mod 2)
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((1 + ((x + (x mod 2)) mod (2 + ((x div 2) mod 2)))) mod 2)
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((1 + ((x - (x div (4 - (x mod 2)))) div 2)) mod 2)
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(2 + (x mod (1 + ((x + ~1) mod (4 + (x mod 2))))))
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((1 + (2x mod (2 + (x div (2 + (x mod 2)))))) mod 2)
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(((x + ~2) mod (1 + ((1 + (x div 2)) mod 4))) div 2)
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(((x div 3) div (1 + ((x + 2) mod 4))) mod 2)
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((x - (x div (1 + ((1 - (x div 2)) mod 4)))) mod 2)
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(1 - ((x mod (1 + ((2 - (x div 2)) mod 4))) div 2))
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((x mod (1 + (((~x2 + x) div 2) mod 4))) div 2)
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(((~1 + ((x + ~2) div 3)) mod 5) mod 2)
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((5x2 + 15x + 5) div 2)
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((5 * (3 - (x mod 4))) div 2)
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((x - ((1 + (2 * (x div 2))) mod 5)) mod 2)
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(((x + ~2) mod (5 + (x div 3))) mod 2)
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((((x + ~2) mod (1 + (x div 2))) mod 5) mod 2)
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(2 * ((x + ~2) + (5 * (1 + (x div 2)))))
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((((x2 + 1) + (x div 2)) mod 5) mod 2)
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(2 * (~1 + ((x mod 2) + ((x + 1) mod 5))))
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(2 * ((2x + 2) - ((x + 1) mod 5)))
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((2x mod (5 + ((x + 1) div 2))) mod 2)
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(((2 + (x div (2 + (x mod 2)))) mod 5) mod 2)
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(((2 + ((~x + 2) * (x div 2))) mod 5) mod 2)
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((((x * (x div 3)) div 2) div 5) mod 2)
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((x - ((~2 + (x * (x div 2))) mod 5)) mod 2)
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(((x * (x div 2)) - (2x div 5)) mod 2)
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(2 * (((x * (x mod 2)) - (x div 2)) mod 5))
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((x mod (0 - ((x2 + 2) mod 5))) mod 2)
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(2 + (x mod (x - ((x2 + 2) mod 5))))
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((2x2 + 3x + 1) mod 10)
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((~2x2 + ~x + 1) mod 10)
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((2x + 2) - ((x + 1) mod 10))
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((2 + ((x2 + x) div 2)) mod 10)
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((x - (2 * (~x + (x mod 2)))) mod 10)
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((~2x2 + ~3x + 2) mod 10)
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((x + (x div 8)) mod 10)
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A021085: 0 1 2 3 4 5 6 7 9 0 1 2 3 4 5 6
(x2 mod (x2 + ~x + 10))
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((2 * (1 + (x div 2))) - (x mod 10))
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(((x * (~1 + (x div 3))) div 5) mod 2)
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(((x * (x div 5)) mod 5) mod 2)
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(((x * (1 + (2 * (x div 2)))) div 5) mod 2)
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(((~x + ((~x + 1) mod 3)) mod 5) mod 2)
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(x - ((5 * (~x + (x div 3))) div 2))
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((((~x + 1) * (x mod 3)) div 5) mod 2)
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(((x * (2 - (x div ~2))) div 5) mod 2)
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(2 * (((~x + 2) * (2 + (x mod 2))) mod 5))
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((x - (x mod ((x + ~5) + (x div 2)))) mod 2)
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((((x + 2) div 3) + (x div 5)) div 2)
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(2 - ((~x + 3) div (2 + (x div 5))))
A259899-A095791: 1 1 2 2 3 3 3 4 4 4 4 4 5 5 5 5
(((x + 2) mod 4) div (2 + (x div 5)))
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((x2 mod ((x + ~1) + (x mod 5))) mod 2)
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(((x * (~x + (x div 3))) div 5) mod 2)
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((x - ((x + 1) div (1 + (~x mod 4)))) mod 2)
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((1 + ((x * (x mod 5)) div 4)) mod 2)
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((1 + ((x * (2 + (x div 3))) div 4)) mod 2)
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(((x2 div 2) div (~1 + ((~x + 2) div 4))) mod 2)
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(x mod (2 * (2 - (x div (~1 + ((~x + 2) div 4))))))
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(((~x + 2) mod (1 + ((x * (x div 2)) div 4))) div 2)
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((x mod 2) - (2 * (~1 + (4 * (~x + (x mod 2))))))
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((x mod (2 - (x mod (~1 - (x div 4))))) mod 2)
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(((~1 + (x div ~2)) mod (1 + (x div 4))) mod 2)
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(((1 + (x mod 4)) div (1 + (x div 4))) mod 2)
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((x - ((~1 + (x div 2)) mod (1 + (x div 4)))) mod 2)
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(((x + ~1) mod ((x + 1) div (1 + (x div 4)))) div 2)
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(((~x2 + 3) div (1 + (x div 4))) mod 2)
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((x - ((2 * (x div 2)) div (1 + (x div 4)))) mod 2)
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(((2x div 3) mod (1 + (x mod 4))) mod 2)
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((1 + ((3x2 + 4x) div 4)) div 2)
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(2 * (3 + ((x + ((x mod 3) div 2)) div 2)))
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((1 + (((~2 + (x mod 3)) mod (x + 2)) div 2)) mod 2)
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(((x + 1) mod (3 + (4 mod (x + 2)))) mod 2)
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((x div (~1 + (2 * ((2x + ~4) mod (x + 2))))) mod 2)
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((1 + ((2x2 + 1) div (x + 4))) mod 2)
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((1 + (4x2 div (x + 4))) mod 2)
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(2 * (x - ((x2 + 1) div (x + 5))))
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((1 + ((x * (x2 div 2)) div (x + 4))) mod 2)
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(((~x + 1) mod (1 + (x2 mod (x + 4)))) mod 2)
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(((2x2 + 4) div (2x + ~5)) mod 2)
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((1 + ((x2 mod (~3x + 2)) div 2)) mod 2)
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((1 + (((x - (x div ~2)) * (x div 2)) div 2)) div 2)
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(2 + (2 mod (1 + (((x mod 4) * (x div 2)) div 2))))
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(((x + 1) div (1 + ((x + ~2) mod (2 + (x div 2))))) mod 2)
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((1 + ((~2x2 + 2x) mod (2 + (x div 2)))) mod 2)
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((1 + (x div 2) - ((~x + 2) div (2 + (x div 2)))) mod 2)
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((1 + ((~x2 + 4x) mod (2 + (x div 2)))) mod 2)
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(((~x + 1) div (2 - (x div (1 + ((x div 2) mod 2))))) mod 2)
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((1 + (x div ((~x + 3) + ((x div 2) mod 2)))) mod 2)
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((1 + (((x * (x mod 3)) + (x div 2)) div 2)) mod 2)
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(((x + 2) mod (~1 + (2 * ((x div 2) - (x mod 2))))) div 2)
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((1 + ((x - ((x div 2) mod 2)) div (2 + (x mod 2)))) mod 2)
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(((~x + 2) div (1 + ((x + 2) div (2 + (x mod 2))))) mod 2)
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(((x2 + ~1) mod ((x + ~3) - (x mod 2))) mod 2)
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(1 - (x mod (1 - (2 * (x div (3 + (x mod 2)))))))
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(1 - ((x mod (~1 - (x div (2 + (x mod 2))))) div 2))
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(2 * ((x div 2) - (2 mod (1 + (x mod (2 + (x mod 2)))))))
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(2 - (((x div 2) div (1 + (x mod (2 + (x mod 2))))) mod 2))
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(((((x + ~1) div 2) div 2) div (1 + (2 * (x mod 2)))) mod 2)
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(x mod (2 + ((x div 4) mod (1 + (2 * (x mod 2))))))
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(2 + ((2 + (x2 div 2)) * (1 + (2 * (x mod 2)))))
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(((x mod 13) mod 3) mod 2)
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(((x mod 11) mod 3) mod 2)
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((x - ((1 + (2x div 3)) mod 3)) mod 2)
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(((~1 + ((x2 div 2) div 3)) div 3) mod 2)
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(((~1 + ((x2 + x) div 3)) div 3) mod 2)
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((((x + 2) div (1 + (x mod 3))) mod 3) div 2)
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(((1 + (x div (3 - (x mod 2)))) div 3) mod 2)
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(2x - ((3 * (~1 + (x div ~2))) div 2))
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(x - ((3 * (x div 7)) div 2))
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(((x2 div 7) mod 3) mod 2)
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(2 + ((x2 mod 7) div 3))
A261865-A157439: 2 2 3 2 2 3 2 2 2 3 2 2 3 2 2 2
((x - ((1 + (((x + 1) div 2) div 2)) mod 3)) mod 2)
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((3 * (x mod (1 + ((x + ~1) mod 4)))) div 2)
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((((2x + 1) div 5) mod 3) mod 2)
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((x div (3 * (~1 + ((~x + 2) div 4)))) mod 2)
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((3 * ((x + 1) - ((~x + 2) div 4))) div 2)
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((((~x + 2) mod (3 + (x div 2))) mod 3) div 2)
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(2 * ((x - ((x div 3) mod 3)) div 3))
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((((x2 + 2x + 1) div 3) mod 3) div 2)
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(((((x + 1) * (x div 2)) div 3) mod 3) div 2)
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(((x - (x div ~6)) mod 3) div 2)
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((x - (((2 * (x div 2)) div 3) mod 3)) mod 2)
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(((x - ((1 - (x div 2)) div 3)) mod 3) div 2)
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(((x2 - ((x div 2) div 3)) mod 3) div 2)
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(((x2 mod (~2x + 5)) div 3) mod 2)
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((x - (((x + 2) mod (2x + ~1)) mod 3)) div 2)
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((x - (((x + ~2) mod (1 + (x div 2))) mod 3)) mod 2)
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(((x2 + ~2x) div (3 * (1 + (x div 2)))) mod 2)
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(((8 mod (~x + ~1)) mod 3) mod 2)
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((3x3 + 9x2 + 9x + 3) div 2)
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((((2 - (x mod 4)) mod (x + 1)) mod 3) div 2)
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((((x2 + ~4x + 4) div (x + 1)) div 3) mod 2)
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(((x2 div 4) mod (3x + 3)) mod 2)
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(2 * (((x mod 3) div 2) + ((x + 1) div 3)))
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(((x + ~1) mod 4) div (2 + ((x + 1) mod 3)))
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(((x2 + 2x) div (x - ((x + 1) mod 3))) mod 2)
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(((~1 + (x * (x div 2))) * ((x + ~1) div 3)) mod 2)
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((((x div 2) div 3) + ((x + ~1) mod 3)) div 2)
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(x - (2 * ((x - ((x div 2) div ~2)) div 3)))
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((1 - (x div (x + ~18))) div 2)
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(1 - ((~x + 1) div (2 + (((x + 1) div 2) div 3))))
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(x - (2 * ((4 * (x div 3)) div 3)))
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(2 * (x - ((4 * (x div 3)) div 3)))
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(((x div (~2 + ((x div 4) mod 2))) mod 3) div 2)
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(x - ((((x + 2) mod 8) mod 3) mod 2))
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((((x + 1) mod (2 + (x div 4))) mod 3) mod 2)
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(2 + (((x + 2) mod (2 + (x div 4))) div 3))
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((x mod (2 - (3 * (2 + (x div 4))))) mod 2)
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((1 - ((x mod (2 + (x div 4))) mod 3)) div 2)
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(((2x - ((x div 4) mod 2)) div 3) mod 2)
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((((x + 1) mod (4 + (x div 2))) mod 3) mod 2)
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((((x + 1) div (2 + ((x div 2) mod 2))) mod 3) mod 2)
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(((x - ((1 + (x div 2)) mod 4)) mod 3) div 2)
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(((x mod (6 + (x div 2))) mod 3) mod 2)
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((x div 2) div (2 + ((x + ~2) mod 12)))
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(((x + 1) div 2) - ((3 * (x div 4)) div 2))
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(((((x2 div 2) mod (x + 2)) div 2) mod 3) mod 2)
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(((x3 div (x + 4)) mod 3) mod 2)
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(((x2 + 1) mod ((2x + 4) div 3)) mod 2)
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((6 div ((2x + 4) div 3)) mod 2)
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(((x2 - ((2 - (x div 2)) div 2)) div 3) mod 2)
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((((x + ~3) mod (2 + (x div 2))) mod 3) mod 2)
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(((x - ((~x + 1) div (2 + (x div 2)))) mod 3) mod 2)
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((((x2 + 2x) div (2 + (x div 2))) mod 3) mod 2)
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((2 - (((~x * (x div 2)) div 2) div 3)) div 2)
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((x - (((x2 * (x div 2)) div 2) div 3)) mod 2)
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(24x2 + ~10x)
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(((2 + (x * (1 + (x div 3)))) div 3) mod 2)
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((((x + (((x + ~1) div 2) div 2)) div 2) mod 3) div 2)
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(x - ((3 * ((~x + ((x div 2) mod 2)) div 2)) div 2))
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((x2 div (x - (3 * ((~x + 2) div 2)))) mod 2)
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((((x + 2) * (2 - (x div 3))) div 3) mod 2)
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(2x2 + 16x + 18)
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(((x - ((x2 div 2) mod (x + 2))) div 3) mod 2)
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(((((x + 1) div 2) div 2) + ((x + ~2) div 3)) mod 2)
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((2x div (2 - ((1 - (x div 2)) div 3))) mod 2)
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((x + 2) - (x div (~2 + ((1 - (x div 2)) div 3))))
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(2 - ((~x + 3) div (2 + ((x div 2) div 3))))
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A342010-A006670: 1 1 2 2 3 3 3 4 4 4 5 5 5 5 5 5
(2 * (2x - (((x div 2) mod 3) + (x mod 2))))
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((x mod 2) - ((~x + 1) div (2 + (3 * (x mod 2)))))
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(x - ((x + ~2) div (~6 + (x div 4))))
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A193928: 0 1 2 4 5 6 7 8 10 11 12 14 16 17 18 20
(((x * (1 + (x mod ~4))) div 3) mod 2)
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((3 * (x + (2x div 5))) div 2)
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(((x * (((x + 1) + (x div 2)) div 2)) div 3) mod 2)
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((3 * (x + ((x - ((x div 2) mod 2)) div 2))) div 2)
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(((x * (((x + 1) div 2) mod 4)) div 3) mod 2)
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((3 * (x + (2 * ((x + (x div 2)) div 2)))) div 2)
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(((x + (((x div 2) * (x div 2)) div 2)) mod 3) mod 2)
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((2x mod (3 + (x * ((x div 2) mod 2)))) mod 2)
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((3 * (x + ((x + ((x div 2) mod 2)) div 2))) div 2)
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A242660: 0 1 4 7 9 10 13 16 18 19 22 25 27 28 31 34
(2 * (1 - ((x * (~2x + (x div 2))) div 3)))
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((9x2 + ~5x) div 2)
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(((x + ~1) mod (2 - ((~x + (x mod 2)) div 3))) mod 2)
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((((x + 2) div (2 - (x * (x mod 2)))) mod 3) mod 2)
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((x - (x2 div (3 + (x * (x mod 2))))) mod 2)
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(((1 + ((x + 1) div 3)) * (x div 3)) div 2)
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((((x + ~2) div 5) * (x div 3)) div 2)
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((x + ~2) div (2 + ((x div 3) * (x div 3))))
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(2 * ((x mod (3 - (x mod 2))) + (x div 3)))
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(x - (2 * ((x div 8) + (x div 3))))
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((x - ((x div 2) div 3)) div (2 + (x div 3)))
A322811-A262885: 0 0 1 1 1 1 1 1 1 1 1 2 1 1 2 1
(x + ((x2 div 4) + ((x div 3) mod 2)))
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((x2 div (~4 - (x mod 3))) mod 2)
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((x div (4 + ((x mod 2) + (x mod 3)))) mod 2)
A011679: 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1
((2 - ((~x + 2) div (4 - (x mod 3)))) div 2)
A320385: 1 1 1 1 1 2 1 2 2 2 2 3 2 3 4 3
((2 + (x div 2) - (x mod 2)) div (2 + (x mod 3)))
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(x div (6 - (x mod (2 + (x mod 3)))))
A079294: 0 0 0 0 0 1 1 1 1 1 2 3 2 2 3 3
((2 * (x + (x div 3))) - ((x mod 3) div 2))
A047474: 0 2 3 8 10 11 16 18 19 24 26 27 32 34 35 40
((x3 div 3) + ((x mod 3) mod 2))
A212069: 0 1 2 9 22 41 72 115 170 243 334 443 576 733 914 1125
(2x + ((x - (x mod 3)) div 2) - (x mod 2))
A010378: 0 1 4 6 9 10
A010462: 0 1 4 6 9 10 15 16 19 21 24 25
(x - ((~x2 + 1) div (2 + (x2 div 3))))
A008520: 0 1 3 5 7 8 9 10 11 12 13 14 15 16 17 18
((2 - (x mod ((~x + 2) + (x2 mod 3)))) div 2)
A029165: 1 0 1 1 1 1 2 1 2 3 3 3 5 4 5 6
((1 + ((x + (x mod (3 + (x mod 2)))) div 2)) div 2)
A262868: 0 1 1 2 1 2 2 3 3 3 3 4 3 4 4 5
((1 + ((x * (~1 + (x mod (2 + (x mod 2))))) div 2)) mod 2)
A030324: 1 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1
((1 + ((~x + ((x2 div 2) div 3)) div 2)) div 2)
A121385: 0 0 0 0 0 0 0 0 1 1 2 2 3 4 5 6
((x2 mod (~1 + ((~x + (x mod 3)) div 2))) mod 2)
A011706: 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0
(x - (((x div 4) mod (~1 + ((~x + 1) div 2))) div 2))
A039249: 0 1 2 3 5 6 8 9 10 11 12 13 14 15 17 18
((1 + ((x * (2 - (((x + 1) div 2) div 2))) div 2)) mod 2)
A004593: 1 0 1 0 1 1 0 1 1 1 1 1 1 0 0 0
((1 + ((x + ((x + 1) mod 8)) div 2)) div 2)
A340327: 0 1 1 2 2 3 3 2 2 3 3 4 4 5 5 4
((1 + (2x mod (x + 10))) div 2)
A103303: 0 1 2 3 4 5 6 7 8 9
A338379-A004426: 0 1 2 3 4 5 6 7 8 9 0 1 1 2 2 3
(x - ((~1 + ((~x + ((x div 4) mod 2)) div 2)) div 2))
A039115: 1 2 3 5 6 7 8 9 11 12 13 15 16 17 18 19
(2x - ((~1 + ((~x + (x div 4)) div 2)) div 2))
A097911: 1 3 5 8
A073608: 1 3 5 8 10 12
A003265: 1 3 5 8 10 12 14 16 18 21 23 25 27 29 32 34
((1 + ((x + (((~x + 1) * (x div 2)) div 2)) div 2)) mod 2)
A127243: 1 1 1 0 1 1 0 0 0 1 0 0 0 1 1 0
((1 + ((x2 + x) div (x - ((~x + 2) div 2)))) div 2)
A305817: 0 1 2 2 2 2 3 3 3 3 4 4 5 5 5 5
((1 + ((x * ((~x + (x mod 3)) div 2)) div 2)) mod 2)
A341540: 1 1 1 0 1 0 0 0 1 0 0 1 1 0 1 1
((1 + ((x2 + ~2x) div ((x + 2) + (x div 2)))) mod 2)
A099075: 1 0 1 1 0 0 1 1 0 1 1 0 1 1 0 1
((1 + ((~x mod 5) mod (x + 2))) mod 2)
A277450: 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1
(((3x2 + 1) div (x + 3)) mod 2)
A286339: 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 1
(((x + 3) * ((x3 + ~x2) div 2)) div 2)
A085740: 0 0 5 27 84 200 405 735 1232 1944 2925 4235 5940 8112 10829 14175
(x - (2 * ((2 + (x2 div 2)) div (x + 3))))
A283431: 0 1 2 1 2 3 2 3 2 3 2 3 4 3 4 3
(2 * ((2x3 + 2x) div (x + 3)))
A278212: 0 2 8 20 38 64
(((x + 3) * (((x + ~1) div 2) * (x div 2))) div 2)
A211379: 0 0 0 3 7 16 27 45 66 96 130 175 225 288 357 441
(2 div (2 + (((~x2 + 2x) div 2) mod (x + 3))))
A105349: 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0
((x - ((x3 + ~2) div (x + 3))) mod 2)
A284656: 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0
(((2x2 + ~5x) div (x + 3)) mod 2)
A083924: 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0
(x mod (~2 + ((2x2 + ~x) mod (x + 3))))
A153587: 0 0 0 0 0 2 0 0 0 2 4 1 0 1 0 0
((1 + ((x2 * (x + (x div 2))) div (x + 2))) mod 2)
A284527: 1 1 0 0 1 0 1 1 1 0 0 1 0 1 0 0
(2 * ((2x + 1) + ((~x + 1) mod 5)))
A125133: 4 6 18 20 22 24 26 38 40 42 44 46 58 60 62 64
((((x3 + ~1) div 2) mod (2x + 1)) mod 2)
A308901-A289007: 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1
((((x * (~1 + (x div 2))) div 2) mod (2x + 1)) mod 2)
A327462: 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0
(2 + (((~x + ((x div 2) mod 2)) div 2) mod (2x + 1)))
A324560: 2 4 6 8 9 10 12 14 15 16 18 20 21 22 24 26
((4x + 2) + (((x + ~1) div 2) * (x div 2)))
A190091: 2 6 10 15 20 26 32 39 46 54 62 71 80 90 100 111
(((~x2 + ~2x + 4) div (2x + 1)) mod 2)
A286059: 0 0 1 0 1 1 0 0 1 1 0 1 1 0 0 1
((x + 1) div (2 + ((x2 + 1) mod (2x + ~1))))
A307196: 0 1 0 2 1 0 1 0 1 0 1 0 1 0 1 0
((((x3 + 2x2) div 2) div (2x + ~1)) mod 2)
A334941-A079101: 0 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1
(2 * ((4x + 4) + (2 div (2x + ~1))))
A273791: 4 20 24 32 40 48 56 64 72 80 88 96 104 112 120 128
((((x + ~2) * (x2 div 2)) div (2x + ~1)) mod 2)
A011696: 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0
((x div (~1 + ((x + ~2) div 3) - (x div 2))) mod 2)
A079336: 0 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0
(((x + 1) - ((~2x + (x div 2)) * (x div 2))) div 2)
A186423: 0 1 3 4 8 11 17 20 28 33 43 48 60 67 81 88
((1 + (x2 div (2 - ((x div 2) * (x div 2))))) mod 2)
A100923: 1 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0
(((8x + 1) div (1 + (x div 2))) mod 2)
A125999: 1 1 0 0 1 1 0 0 1 0 1 0 1 1 0 1
(((3 * (x mod 3)) mod (1 + (x div 2))) div 2)
A074936: 0 0 0 0 0 0 0 1 0 0 1 0 0 1 3 0
(((x3 + 2x + 1) mod (1 + (x div 2))) mod 2)
A295309: 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0
(((x + 1) * (((x + 1) div 2) * (1 + (x div 2)))) div 2)
A109900: 0 1 3 8 15 27 42 64 90 125 165 216 273 343 420 512
((((x + (x div 2)) mod 4) mod (1 + (x div 2))) div 2)
A025428: 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1
(((~5x + 1) div (1 + (x div 2))) mod 2)
A099076: 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 0
((((x2 + (x div 2)) div 2) mod (1 + (x div 2))) div 2)
A235189: 0 0 0 0 0 0 1 1 2 1 2 1 2 1 2 2
(((2 * (~x + ((x div 2) mod 2))) mod (1 + (x div 2))) div 2)
A282459: 0 0 0 0 0 1 1 0 2 1 0 2 2 1 3 2
((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)
A342955-A261684-A082858-A048571-A004197: 0 0 0 0 1 0 0 1 1 0 0 1 2 1 0 0
((x - ((~2x + (x div 2)) * (1 + (x div 2)))) div 2)
A144065: 0 1 4 6 11 14 21 25 34 39 50 56 69 76 91 99
((4x div (x + 1)) + ((1 + (x div 2)) div 2))
A087793: 0 2 3 4 4 4 5 5 5 5 6 6 6 6 7 7
(((x * ((x div 2) mod 4)) div (1 + (x div 2))) mod 2)
A184172: 0 0 1 1 0 1 0 1 0 0 1 1 1 1 1 1
(((~3x2 + 4x) div (1 + (x div 2))) mod 2)
A138710: 0 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1
((((x + ~1) div 2) * (x div 2) * (~1 + (x div 2))) div 2)
A028724: 0 0 0 0 1 2 6 9 18 24 40 50 75 90 126 147
(((x2 + 1) div (x + 2)) - ((~1 + (x div 2)) div 2))
A097330: 1 1 1 2 2 3 3 4 5 6 6 7 8 9 9 10
(4x div ((x + 2) - ((~1 + (x div 2)) div 2)))
A197637: 0 1 2 2 2 2 3 3 3 3 4 4 4 4 4 4
(2 * ((x3 + 3x + 1) + (x mod 2)))
A286230: 2 12 30 76
((1 + ((x2 * (2x + (x mod 2))) div 2)) div 2)
A220788: 0 1 4 16
A296819: 0 1 4 16 32 69 108 184 256 385 500 696 864 1141 1372 1744
((x + 2) - ((~x2 + 2x) div (1 + (x2 div 2))))
A152424: 2 2 4 6 7 9 10 11 12 13 14
(((~x2 + 1) div (5x + 1)) mod 2)
A267272: 1 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1
(2 - (((x2 + 2) mod (3x + 1)) mod 2))
A160198: 2 1 2 1 1 1 2 1 2 1 1 1 1 1 2 1
((9x2 + 15x + 4) div 2)
A145910: 2 14 35 65 104 152 209 275 350 434 527 629 740 860 989 1127
(((x2 + x + 1) + (x2 div 4)) div 2)
A265431: 0 1 4 7 12 18 26 34 44 55 68 81 96 112 130 148
((1 + (x * ((x - ((x div 2) div 3)) div 2))) mod 2)
A285373: 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1
(((x + 1) + (((x - (x div 4)) div 2) mod 2)) div 2)
A115384: 0 1 2 2 3 3 3 4 5 5 5 6 6 7 8 8
(x - ((~1 + (x2 div (x + 8))) div 2))
A168389: 1 2 3 4 4 5 6 6 7 8 8 9 9 10 11 11
(((x + 1) + (((x + (x div 2)) div 4) mod 2)) div 2)
A267098: 0 1 1 2 3 3 3 4 5 5 6 6 6 7 8 8
(((x + 1) + (((x + 1) div 3) mod 4)) div 2)
A335380: 0 1 2 2 3 4 4 5 6 6 7 6 6 7 8 8
(x mod ((2 - (x mod ((~x + ~1) + (x mod 4)))) div 2))
A200221: 0 0 0 0 0 0 0 1 0 0 0 3 0 0 0 3
(2 * ((x + 1) + (((x2 + ~1) * (x div 2)) div 2)))
A028497: 2 4 8 16 40
(2 * (1 + compr(\x.((x * ((x div 2) div 3)) mod 2),x)))
A194372: 2 4 6 8 10 12 14 18 22 26 28 30 32 34 36 38
((1 + ((x2 + ~2x) div (~3x + 4))) mod 2)
A103522: 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0
(((x + 1) + (((x div 2) * (x div 2)) div (x + 2))) mod 2)
A328101: 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 0
(2 div (2 + ((x2 + ~2) mod ((x + 1) + (x div 2)))))
A276791: 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0
(((1 + (x2 div (2 + (x div 2)))) mod (x + 1)) mod 2)
A286052: 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0
((((x * (~1 + (x div 2))) div 3) mod (x + 1)) mod 2)
A279024: 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0
(((x div (~2 - (x div 3))) mod (x + 1)) mod 2)
A048156: 0 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1
(x div (2 + ((4 - (x mod 3)) mod (x + 1))))
A289122: 0 0 0 1 0 1 1 1 2 1 2 2 2 2 3 2
((((x + (x div 2)) * (~1 + (x div 2))) div (x + 1)) mod 2)
A079813: 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 0
(2x - ((((x div 2) div ~2) mod (x + 1)) div 2))
A029921: 0 2 3 5 6 8 10 11 13 14 16 18 19 21 23 24
(((2 + (x mod 7)) mod (x + 1)) mod 2)
A167393: 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1
(((x + 1) * ((x2 + 4x + 5) div 2)) div 2)
A199771: 1 5 12 26 45 75 112 164 225 305 396 510 637 791 960 1160
((((x + 1) mod (2 + (x mod 4))) mod (x + 1)) div 2)
A011689: 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0
(((x div 2) - ((4x + ~8) div (x + 1))) mod 2)
A288622: 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 0
(((2 - (x div (2 * (~2 + (x mod 2))))) mod (x + 1)) mod 2)
A053259: 0 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0
((4x3 + x2 + ~3x) div 2)
A172073: 0 1 15 54 130 255 441 700 1044 1485 2035 2706 3510 4459 5565 6840
((2x3 + 7x2 + 9x + 4) div 2)
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(((2 - (x2 div (2 + (x mod 2)))) div (x + 1)) mod 2)
A189031: 0 1 0 1 0 1 1 0 0 1 1 0 0 0 1 1
(((x + 1) * (x3 + (2 * (x mod 2)))) div 2)
A079245: 0 3 12 58
(((x + 1) * (2 + (x * (1 + (2 * (x mod 2)))))) div 2)
A110344: 1 5 6 22 15 51 28 92 45 145 66 210 91 287 120 376
(((2 + (x * (x div (2 + (x mod 2))))) div (x + 1)) mod 2)
A095076: 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 0
((3x3 + 5x2 + 4x + 2) div 2)
A143690: 1 7 27 70 145 261 427 652 945 1315 1771 2322 2977 3745 4635 5656
((x - ((1 - ((x * (x div 2)) div 2)) div (x + 1))) mod 2)
A298952: 1 1 0 1 1 0 0 1 0 1 1 0 1 0 0 1
((x3 + 7x2 + 10x + 4) div 2)
A162260: 2 11 30 62 110 177 266 380 522 695 902 1146 1430 1757 2130 2552
((((~x2 + 2x + ~2) * (x div 2)) div (x + 1)) mod 2)
A308253: 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1
((3x3 + 7x2 + 6x + 2) div 2)
A005920: 1 9 33 82 165 291 469 708 1017 1405 1881 2454 3133 3927 4845 5896
((2x + 2) + (2x div 9))
A186289: 2 4 6 8 10 13 15 17 19 22 24 26 28 30 33 35
((2x + 2) + ((2x + 1) div 5))
A329830: 2 4 7 9 11 14 16 19 21 23 26 28 31 33 35 38
((2x + 2) + (2 div (1 + (~x mod 4))))
A128037: 4 4 6 9 12 12 14
((2x + 2) + ((x - (x div 3)) div 3))
A184809: 2 4 6 8 11 13 15 17 20 22 24 26 28 31 33 35
((2x + 2) + ((x mod (1 + (x div 2))) div 3))
A186329: 2 4 6 8 10 12 14 17 19 21 23 25 27 30 32 34
((2x + 2) + ((x + (x div 4)) div 3))
A184978: 2 4 6 9 11
A186316: 2 4 6 9 11 14 16 18 21 23 26 28 31 33 35 38
((2x + 2) + (x div (2 - ((x div 2) div ~2))))
A184978: 2 4 6 9 11
A207188: 2 4 6 9 11 13 15 17 20 22 24 26 28 30 32 34
((2x + 2) + (((x + 1) div 5) mod 2))
A327255: 2 4 6 8 11 13 15 17 19 20 22 24 26 28 31 33
((2x + 2) + (((x + 1) + (x div 4)) div 2))
A330064-A292645-A001950: 2 5 7 10 13 15 18 20 23 26 28 31 34 36 39 41
((2x + 2) + ((((x + 1) + (x div 2)) div 2) div 2))
A292647-A054406: 2 4 7 9 11 14 16 18 21 23 26 28 30 33 35 37
((2x + 2) + (x div (~2 + (x mod ~4))))
A028728: 2 3 5 7 8 11 12 13 14
((2x + 2) + ((x - (x div 8)) div 2))
A329834-A189681-A059542: 2 4 7 9 12 14 17 19 21 24 26 29 31 34 36 39
((2x + 2) + (((x div 2) - (x mod 4)) div 2))
A070026-A028835-A028834: 2 3 5 7 11 12 14 16 20 21 23 25 29 30 32 34
((2x + 2) + (x div 4) - ((x div 2) mod 2))
A056527: 2 4 5 7 11 13 14 16 20 22 23 25 29 31 32 34
((3x + 2) + ((x - (x div 4)) div 2))
A108165: 2 5 9 12 15 19 22 26 29 32 36 39 42 46 49 53
(((2x + 1) - (x div ~2)) * ((x + 1) div 2))
A219190: 0 4 6 18 22 42 48 76 84 120 130 174 186 238 252 312
((1 + (2 * (x - (x div ~2)))) * ((x + 1) div 2))
A036498: 0 5 7 22 26 51 57 92 100 145 155 210 222 287 301 376
((1 + (2 * (2x + (x mod 2)))) * ((x + 1) div 2))
A154260: 0 7 9 30 34 69 75 124 132 195 205 282 294 385 399 504
(((3x + 2) + (x div 2)) * ((x + 1) div 2))
A132354: 0 5 9 24 32 57 69 104 120 165 185 240 264 329 357 432
((4 * (1 + (2 * (x div 2)))) + ((x + 1) div 2))
A156638: 4 5 13 14 22 23 31 32 40 41 49 50 58 59 67 68
((4 * ((x + 1) + (x div 2))) - ((x + 1) div 2))
A281445: 4 7 15 18 26 29 37 40 48 51 59 62 70 73 81 84
((((x + 1) div (2 + (x mod 2))) div 2) + ((x + 1) div 2))
A154951: 0 1 1 2 3 4 4 5 6 6 7 8 9 9 10 10
(((x + 2) + (3 * (x div 2))) * ((x + 1) div 2))
A036666: 0 3 7 16 24 39 51 72 88 115 135 168 192 231 259 304
(x + ((x div (4 + (x mod 2))) + ((x + 1) div 2)))
A083033: 0 2 3 5 7 9 10 12 14 15 17 19 21 22 24 26
((13x2 + 13x) div 2)
A152741: 0 13 39 78 130 195 273 364 468 585 715 858 1014 1183 1365 1560
((11x2 + 11x) div 2)
A152740: 0 11 33 66 110 165 231 308 396 495 605 726 858 1001 1155 1320
((4x3 + 9x2 + 5x) div 2)
A281381: 0 9 39 102 210 375 609 924 1332 1845 2475 3234 4134 5187 6405 7800
((4x3 + 7x2 + 3x) div 2)
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((17x2 + 17x) div 2)
A195037: 0 17 51 102 170 255 357 476 612 765 935 1122 1326 1547 1785 2040
((2x3 + 11x2 + 9x) div 2)
A162261: 0 11 39 90 170 285 441 644 900 1215 1595 2046 2574 3185 3885 4680
((((~x + 1) * (1 + (x mod 3))) div (x + 1)) mod 2)
A082960: 1 0 1 1 0 0 1 0 1
A108882: 1 0 1 1 0 0 1 0 1 1 0 1 1 0 1 1
((5x3 + x2 + ~4x) div 2)
A237616: 0 1 18 66 160 315 546 868 1296 1845 2530 3366 4368 5551 6930 8520
((2x3 + 11x2 + 17x + 8) div 2)
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((x7 + x6) div 2)
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(((x2 + ~x) * (~2 + ((x2 + x) div 2))) div 2)
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((7x2 + x + 7) div 2)
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A006124: 3 7 18 36 61 93 132 178 231 291 358 432 513 601 696 798
((x7 + x5) div 2)
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((x7 + x4) div 2)
A168194: 0 1 72 1134 8320 39375 140616 412972 1050624 2394765 5005000 9750906 17926272 31388539 52725960 85455000
((x div (2 - ((x + 2) mod ~8))) mod 2)
A091247: 0 0 0 0 1 1 1 0 1 1 1 0 1 0 1 1
(x - (((x2 + x) div ~8) mod 2))
A161560: 0 0 1 3 3 5 6 6 7 9 10 10 12 12 13 15
((x + 1) div (1 - (x div (~2 + ((x div 2) div ~2)))))
A280253: 1 1 1 2 1 2 2 2 3 2 3 3 3 3 3 4
(x div (2 - (((x div 2) div 3) mod ~4)))
A071838: 0 0 1 1 2 2 1 1 1 1 2 2 3 3 3 3
((2x + 2) - ((x + (x div 2)) div ~4))
A003256: 2 5 7 9 12 14 17 19 21 24 26 28 31 33 36 38
((x + 2) - ((~x + 2) div (2 - (x div ~4))))
A225647: 1 3 4 6 7
A080804: 1 3 4 6 7 8 9 11 12 13 14 15 16 17 18 20
(((x2 + 2) div (4 - (x div ~2))) mod 2)
A152228: 0 0 1 1 1 1 1 0 0 1 1 0 0 1 0 0
(((2x2 + ~1) mod (2 - (x div ~2))) mod 2)
A119842-A091862-A091492: 1 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1
(((x3 + ~2x2) div (2 - (x div ~2))) mod 2)
A285957: 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0
(2x + ((x div ~2) mod 2) - (x div 4))
A047328: 0 3 5 6 7 10 12 13 14 17 19 20 21 24 26 27
(2x - (((x div ~2) mod 2) + (x div 4)))
A047283: 0 1 3 6 7 8 10 13 14 15 17 20 21 22 24 27
(((~1 + ((x + ~1) mod (1 + (x div 3)))) div 2) mod 2)
A117198: 1 1 1 1 0 1 0 1 0 1 0 0 0 0 1 0
((x div (~2 + (x mod (~1 + (x div ~3))))) mod 2)
A053867: 0 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1
(((~1 + (x mod (1 + (((x + 1) div 2) div 2)))) div 2) mod 2)
A050073: 1 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1
(20x2 + 20x + 4)
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(2 + ((x - (2 div (1 + (x div 5)))) mod 2))
A276862: 2 3 2 3 2 2 3 2 3 2 2 3 2 3 2 3
(((~1 + (x div (1 + ((~x + 2) mod 4)))) div 2) mod 2)
A058840: 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1
(((1 + (2x div (1 + (x div 4)))) div 2) div 2)
A157230-A072273: 0 0 1 1 1 1 1 2 1 1 1 2 1 1 2 2
(x2 mod 44)
A070466: 0 1 4 9 16 25 36 5 20 37 12 33 12 37 20 5
((x + 4) - (2 mod (~3x + 7)))
A284743: 2 3 6 7 11 15 19 23
(2 + ((2x mod (~1 + ((~x + 2) div 3))) mod 2))
A147793: 2 2 2 2 2 2 2 3 2 2 2 2 3 2 2 2
(1 - (2 * (((x + ~1) mod (1 + (x div 3))) mod 2)))
A160357: 1 1 1 1 ~1 1 1 1 ~1 1 ~1 1 ~1 1 ~1 1
((((~x2 + 2) mod (1 + (x div 3))) div 2) mod 2)
A336396-A115861-A081227: 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0
(((1 + ((x * (x div 2)) + (x div 3))) div 2) mod 2)
A025075: 0 0 1 0 1 0 0 0 1 0 1 1 0 1 1 1
(16x2 + 32x + 20)
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(2 * ((x mod (~1 + (2 * (2x div 3)))) mod 2))
A093569: 0 0 0 0 2 0 0 0 0 2 0 2 0 2 0 2
(x3 mod 28)
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(1 - (2 * (((~x + 2) mod 7) mod 2)))
A097807: 1 ~1 1 1 ~1 1 ~1 1 ~1 1 1 ~1 1 ~1 1 ~1
(2 + ((x2 mod (~1 + (2 * (x div 3)))) div 2))
A309120: 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2
((x - ((~1 + (x div (2 + (x mod 3)))) div 2)) mod 2)
A088150: 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0
(((~1 + (x div (2 + (x2 mod 3)))) div 2) mod 2)
A127001: 1 1 1 0 0 0 1 0 0 1 1 1 0 1 1 1
(4 * (1 + (2 * (x - ((x div 2) div ~2)))))
A072182: 4 12 28 36 44 52 68 76 84 92 108 116 124 132 148 156
(((x2 mod (~1 + (2 * ((x + ~1) div 2)))) div 2) div 2)
A337621: 0 0 0 0 0 0 0 1 1 1 0 1 0 1 2 1
(((2x mod (1 + (x mod 8))) div 2) div 2)
A011670: 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1
(2 + ((x mod (1 + (2 * (1 - (x div 4))))) mod 2))
A031217: 2 3 2 2 2 2 2 2 2 2 2 2 2 2 3 2
(((~1 + ((~x + 1) mod (2 + (x div 4)))) div 2) mod 2)
A189673: 0 1 0 1 1 0 0 1 0 1 1 0 1 1 0 0
(((x - ((~2x + 2) mod 5)) div 2) mod 2)
A272532: 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0
(((x + ~1) div (2 + ((x + ~2) mod 5))) mod 2)
A029441: 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0
(x - (x div (4 + ((x div 2) mod 5))))
A025548: 0 1 2 3 4 5 6 6 7 8 8 9 10 11 12 13
(x4 mod 20)
A070539: 0 1 16 1 16 5 16 1 16 1 0 1 16 1 16 5
((2 - (x mod (~2 + ((~x + 1) div 5)))) div 2)
A002635: 1 1 1 1 2 1 1 1 1 2 2 1 2 2 1 1
((x - ((~x + 1) div (2 + (x mod 5)))) mod 2)
A181932: 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0
(((x + ~2) div (2 + (x2 mod 5))) mod 2)
A190245: 1 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0
(((1 + ((x * (x div 3)) div 4)) div 2) mod 2)
A085114: 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1
(((x - (3 div (1 + (x div 4)))) div 2) mod 2)
A143222: 0 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1
((x mod (2 + ((~x + 1) mod (1 + (x div 4))))) div 2)
A113263: 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 1
(x - (4 * (~1 + (2 * (~2x + (x div 2))))))
A306285: 4 21 30 47 56 73 82 99 108 125 134 151 160 177 186 203
(2 + (x div (2 + (x2 mod (4x + ~1)))))
A316990: 2 2 2 2 3 2 2 2 4 2 2 2 4 2 2 2
(1 - (2 * ((x2 div (3 + (x div 2))) mod 2)))
A186032-A108784: 1 1 ~1 1 ~1 ~1 1 1 ~1 ~1 1 ~1 1 1 ~1 1
(((1 + (3x mod (2 + (x div 2)))) div 2) div 2)
A333382: 0 0 0 0 0 1 1 0 0 1 0 1 1 2 1 0
(((x + 2) div (x - (2 * (1 + ((x div 2) mod 2))))) mod 2)
A263243: 1 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1
(((~x + 1) mod (2 + (x div (1 + ((x div 2) mod 2))))) div 2)
A230596: 0 0 1 0 1 1 0 2 1 1 2 2 1 1 2 2
((x - ((~1 + ((x2 + (x div 2)) div 2)) div 2)) mod 2)
A104105: 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 0
(2 div (4 - ((~1 + (x div (2 + (x mod 2)))) div 2)))
A034399: 0 0 0 0 0 0 0 0 0 0 1 0 1 0 2 1
(x - (2 * ((3 * (x div 5)) div 2)))
A245343: 0 1 2 3 4 3 4 5 6 7 4 5 6 7 8 7
(2 + ((3 * ((1 + (x div 2)) div 3)) div 2))
A111656: 2 2 2 2 3 3 3 3 3 3 5 5 5 5 5 5
(2x - (((3 * (~1 + (x div 2))) div 2) div 2))
A260479: 1 3 4 6 8 10 11 13 14 16 17 19 21 23 24 26
((((x div 4) - ((x + 1) mod 3)) div 2) mod 2)
A286937: 1 1 0 1 1 0 0 1 1 0 0 1 1 0 1 1
(x div (4 + (((x + ~1) * (x div 2)) mod 3)))
A089216: 0 0 0 0 1 0 1 1 1 1 2 1 3 3 2 2
(((x + 1) div ((x + ~2) - ((x + ~1) mod 3))) mod 2)
A267594: 1 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1
(((3 * (1 - (x div ~4))) div 2) div 2)
A324965: 0 1 1 1 1 2 2 2 2 3 3 3 3 3 3 3
(((~x + 2) div (2 + ((2 * (x div 2)) mod 3))) mod 2)
A200246: 1 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0
((2 - (x div (~2 + (((~x + 2) div 2) div 3)))) div 2)
A309432: 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 2
(2 + ((x2 + x) div (2 + (2x div 3))))
A284946: 2 3 4 5 7 8 9 11 12 13 15 16 17 20 21 22
(2 - (((~x + 2) div (2 + (2x div 3))) mod 2))
A165735: 1 2 2 1 1 1 1 1 1 1 1 1 1 2 2 2
((x - (x mod (1 - (2 * ((x div 2) div 3))))) div 2)
A194255-A194245: 0 0 1 1 2 2 3 3 4 4 5 5 6 7 7 7
(1 - ((~x + 2) div (2 * (2 + ((x div 2) mod 3)))))
A216325: 1 1 1 2 2 2 2 3 2 3 2 3 4 4 3 4
(((x - ((x2 + (x div 2)) div 3)) div 2) mod 2)
A080679: 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1
(x2 - (4 * ((x2 div 2) div 3)))
A267489: 0 1 4 5 8 9 12 17 24 29 36 41 48 57 68 77
(~2 + ((1 - ((x div 2) mod 3)) mod 6))
A135695: ~1 ~1 ~2 ~2 3 3 ~1 ~1 ~2 ~2 3 3 ~1 ~1 ~2 ~2
((x2 mod (x - ((x + 1) mod 6))) mod 2)
A025430: 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 1
(2 * ((x + 6) - (x div ~4)))
A126763: 12 16 18 20 22 26
(x - ((2 - ((2 + (x div 2)) mod 6)) div 2))
A197354: 0 1 3 4 5 6 8 9 7 8 10 11 12 13 15 16
(x div ((x + 2) div (2 + ((x div 2) mod 6))))
A103303: 0 1 2 3 4 5 6 7 8 9
A190600: 0 1 2 3 4 5 6 7 8 9 10 11 1 1 2 3
(((2x + 2) div (~6 + (x mod 2))) mod 2)
A246142: 1 1 1 0 0 1 1 0 1 0 0 1 1 0 1 1
(2 * (2x + (x div 2) - (x mod 6)))
A328770-A276154: 0 2 6 8 12 14 30 32 36 38 42 44 60 62 66 68
(2 + ((3 * (x + (x div 5))) div 2))
A028731: 2 3 5 6 8 11 12 14 15 17
A268226: 2 3 5 6 8 11 12 14 15 17 20 21 23 24 26 29
((x mod (2 + ((x + (x div 3)) mod 3))) div 2)
A049320: 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 1
(((3 * (x + (x div 8))) div 2) div 2)
A180446: 0 0 1 2 3 3 4 5 6 7 8 9 9 10 11 12
(((x - ((x + (x mod 4)) mod 3)) div 2) mod 2)
A165263: 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1
(1 - (2 * ((x mod (~2 - (x div 3))) mod 2)))
A309873: 1 ~1 1 1 1 ~1 1 ~1 1 ~1 1 1 1 ~1 1 1
(((x - (x mod (~2 - (x div 3)))) div 2) div 2)
A177001: 0 0 0 0 1 1 2 2 2 2 2 3 3 4 4 5
((((x - (x div ~2)) * (x div 3)) div 2) mod 2)
A011665: 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 1
((x - ((((x + 1) div 2) * (x div 3)) div 2)) mod 2)
A286691: 0 1 0 0 1 0 1 1 0 0 1 0 0 1 0 1
(((3x + 3) mod (2 + (x div 3))) div 2)
A035652: 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 3
(((x div 2) - ((x + ~1) div (2 + (x div 3)))) mod 2)
A153639: 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1
(((~2x + (x mod 2)) mod (2 + (x div 3))) div 2)
A345039: 0 0 0 0 0 0 0 1 0 1 0 2 0 2 1 3
((~2x2 mod (2 + (x div 3))) div 2)
A035665: 0 0 0 0 0 0 0 1 0 1 0 1 0 2 2 2
((((~x + 2) - (x div 2)) div (2 + (x div 3))) mod 2)
A246260: 1 0 1 1 0 0 0 0 1 1 1 1 1 1 0 1
(((x - (x * ((x div 2) * (x div 3)))) div 2) mod 2)
A189632: 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1
(((x - ((2 + (x div 2)) * (x mod 3))) div 2) mod 2)
A175992-A068933: 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 1
((x - ((x2 + 2) div (2 + (x mod 3)))) mod 2)
A145273: 1 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0
((x + 2) - ((~x + 1) div (4 + (x mod 3))))
A028729: 2 3 5 6 7 8 10 11 12 13 14 15
A158276-A028793-A028753: 2 3 5 6 7 8 10 11 12 13 14 15 17 18 19 21
(((2 + (x div 2)) div (2 - ((x mod 3) mod 2))) mod 2)
A138709: 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 0
(((x + 1) div 2) - (((x - (x mod 3)) div 2) div 2))
A176839: 0 1 1 2 2 3 2 3 3 3 3 4 3 4 4 5
(((6x3 + 3x2) div 2) div 2)
A256328: 0 2 15 47 108 206 351 551 816 1154 1575 2087 2700 3422 4263 5231
(((~1 + (((~x + 1) * (x mod 3)) div 2)) div 2) mod 2)
A230031-A226206-A219946-A154957-A127970: 1 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1
(((~1 + ((x * ((~1 + (x div 2)) div 2)) div 2)) div 2) mod 2)
A131364: 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0
(((1 + ((x * ((x + ~2) + (x div 2))) div 2)) div 2) div 2)
A211520: 0 0 0 1 2 3 5 7 10 12 16 19 24 27 33 37
(((~1 + ((x + 2) * ((x div 2) mod 3))) div 2) mod 2)
A342877: 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0
((((2 + (x * (x div 2))) mod (x + 3)) div 2) mod 2)
A239200: 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0
(2 + (((~x * (x div 2)) div (x + 3)) mod 2))
A071820: 2 2 3 3 2 2 2 3 3 3 2 2 3 3 2 2
(((2x3 + 5x2 + 4x + 1) div 2) div 2)
A182260: 0 3 11 28 56 99 159 240 344 475 635 828 1056 1323 1631 1984
(1 - (2 * (((2x + 1) * (x div ~2)) div 2)))
A058918: 1 5 7 15 19 35
(((2x3 + ~3x2 + 2x + 2) div 2) div 2)
A212683: 0 0 2 8 22 46 84 138 212 308 430 580 762 978 1232 1526
((((x mod ~3) * (1 + (x div 2))) div 2) mod 2)
A295890: 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 0
(1 - (2 * (((x + ~4) div (1 + (x div 2))) mod 2)))
A339265: 1 ~1 ~1 ~1 1 1 1 1 1 ~1 ~1 ~1 ~1 ~1 ~1 ~1
((x mod (2 + ((x + ~4) mod (1 + (x div 2))))) div 2)
A011666: 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0
(2 + ((4x2 div (1 + (x div 2))) mod 2))
A093450: 2 2 2 2 3 3 2 3 3 2 2 2 2 2 2 2
(((x - (4x div (1 + (x div 2)))) div 2) mod 2)
A081371: 0 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0
(x - (3 mod (1 - (2 * ((1 + (x div 2)) div 2)))))
A103303: 0 1 2 3 4 5 6 7 8 9
A305462: 0 1 2 3 4 5 6 7 8 9 12 13 14 15 18 19
(4 div (4 - ((x mod (1 + (x div 2))) div 2)))
A032576: 1 1 1 1 1 1 1 1 1 2 2 2 2 4 4 4
(((((x + 1) mod 3) * (~1 + (x div 2))) div 2) mod 2)
A341754: 1 1 0 0 1 0 1 0 0 1 0 0 0 1 0 1
((((1 - (x mod 3)) * (~1 + (x div 2))) div 2) mod 2)
A287801: 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 1
((x div (~2 - (x mod (3 - (x mod 2))))) mod 2)
A118249: 0 1 1 1 0 0 1 1 0 1 0 0 0 1 0 1
(((~x + 2) div (2 + (x mod (3 - (x mod 2))))) mod 2)
A120531: 1 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1
(((~1 + ((x * (x + (x div 4))) div 2)) div 2) mod 2)
A105470: 1 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1
(2 + ((2 mod ((~x + ~1) + (x mod (2 + (x mod 2))))) mod 2))
A171135: 2 2 3 2 3 2 3 3 3 2 3 2 3 3 3 2
(((2x + 1) div (2 + (3 mod (x + 1)))) mod 2)
A295891: 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 0
((x3 div (2 + (3 mod (x + 1)))) mod 2)
A078646: 0 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1
((x div (2 + ((x2 div 3) mod (x + 1)))) mod 2)
A011667: 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1
((((x + 1) * (1 + (x * ((x + 1) div 2)))) div 2) div 2)
A235355: 0 1 2 7 11 24 33 58 74 115 140 201 237 322 371 484
((x mod (x - (((x + 1) * (~2 + (x div 2))) div 2))) mod 2)
A288512: 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0
(2 + (((x + 1) * (x2 - ((x div 2) mod 2))) div 2))
A057581: 2 3 6 18 42
(2 + ((x - (((x + ~2) * (x div 2)) div (x + 1))) div 2))
A126848: 2 2 3 3 4 4 4 5 5 5 5 6 6 6 6 7
(2 * ((2x + 2) + ((x - (x div 4)) div 2)))
A190002: 4 8 14 18 22 28 32 38 42 46 52 56 60 66 70 76
(((x2 div (2 + (x div 2))) * ((x + 1) div 2)) mod 2)
A289165: 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0
(1 - (((1 - (x2 div 2)) * ((x + 1) div 2)) div 2))
A185178: 1 1 2 4 8 18
((5x + 5) + (((x + 1) div 2) div 2))
A115181: 5 10 15 21 26 31 36 42 47 52 57 63 68 73 78 84
((((x + 1) + (x div 2)) div 2) * (((x + 1) div 2) div 2))
A296160: 0 0 0 2 3 4 5 10 12 14 16 24 27 30 33 44
(x - ((x div 8) + (((x + 1) div 2) div 2)))
A242493: 0 1 2 2 3 4 5 5 5 6 7 7 8 9 10 10
(2x + ((x div 2) mod 2) - (((x + 1) div 2) div 2))
A047324: 0 2 5 6 7 9 12 13 14 16 19 20 21 23 26 27
(x4 + x3 + 3x2 + 3x + 4)
A166115: 4 12 46
(~2 + ((x2 + 17x + 16) div 2))
A051940: 6 15 25 36 48 61 75 90 106 123 141 160 180 201 223 246
(2 + ((x5 + ~x4 + x + ~1) div 2))
A121194: 1 2 10 84
(((2x - (x div ~2)) * ((x + ~1) div 2)) div 2)
A338544: 0 0 0 4 5 13 15 27 30 46 50 70 75 99 105 133
(x2 - (((x + (x div 2)) * ((x + ~1) div 2)) div 2))
A085787: 0 1 4 7 13 18 27 34 46 55 70 81 99 112 133 148
(((x + ~1) mod (2 - (((x div 2) div ~2) div 2))) div 2)
A237584: 0 0 0 1 0 0 1 0 0 1 0 1 1 0 0 1
(((2x + 1) mod (1 - (x div ~4))) div 2)
A325166-A111775-A091979: 0 0 0 0 0 1 0 0 1 1 0 1 0 1 2 0
(((~x + 4) mod (2 - (x div ~4))) div 2)
A085425: 0 0 1 0 0 1 1 0 0 0 2 1 1 1 1 0
(2 * (1 - ((~x + 2) div (2 - (x div ~4)))))
A239896: 0 2 2 4 4 4 4 6 6 6 6 6 6 6 6 8
(2 * (2 - ((~x + 2) div (2 - (x div ~4)))))
A191682: 2 4 4 6 6 6 6 8 8 8 8 8 8 8 8 10
((((x + ~1) div 2) mod (2 - (x mod ~4))) mod 2)
A296338: 1 0 0 1 1 0 0 0 1 0 0 0 1 1 0 1
(2 - (((~x + 2) div (2 - (x mod ~4))) mod 2))
A030614: 1 2 2 1 1 1 1 2 1 2 2 1 1 1 1 1
(1 - ((((x div 4) * (x div ~2)) div 2) div 2))
A029082: 1 1 1 1 2 2 2 2 3 4 4 4 6 7 7 7
((x2 + x) div (2 * (2 - ((x div ~2) mod 2))))
A064038: 0 1 3 3 5 15 21 14 18 45 55 33 39 91 105 60
(64x + 56)
A157330: 56 120 184 248 312 376 440 504 568 632 696 760 824 888 952 1016
(2 + (((~1 + (((x + 1) * (x div 2)) div 2)) div 2) div 2))
A029026: 1 1 2 2 3 3 4 4 6 6 8 9 11 12 14 15
(8 * (1 - (x div ~5)))
A242890: 8 16 16 16 16 16 24
((x div (4 * (1 + (2 * (~2 + (x mod 2)))))) mod 2)
A324828: 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 0
((x + 2) - (4 * (~1 + ((x div 2) mod 4))))
A004447: 6 7 4 5 2 3 0 1 14 15 12 13 10 11 8 9
(((x - (((x + 1) div 5) mod 2)) div 2) mod 2)
A073089: 0 0 1 1 1 0 0 1 1 0 1 1 0 0 0 1
(((x - (((x + 1) mod 5) mod 2)) div 2) mod 2)
A269175-A089013: 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1
(x - (4 * (((x div 2) mod 5) div 2)))
A132387: 0 1 2 3 0 1 2 3 0 1 10 11 12 13 10 11
(((x div 2) div (~2 + ((x div 5) mod 2))) mod 2)
A072126: 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1
(2 + (((~1 + ((x2 + ~x) div 4)) div 2) div 2))
A106244: 1 1 1 2 2 3 3 4 5 6 7 8 10 11 13 14
(((x + 2) div (2 + (((x + ~2) div 3) mod 2))) mod 2)
A341256-A091446-A091445: 0 1 0 0 1 0 0 1 1 1 0 0 0 1 0 0
(((x2 + ~1) div (4 + (x mod 3))) mod 2)
A141095: 1 0 0 0 1 0 0 1 0 0 1 0 1 1 0 0
(((((x * (x div 2)) + (x mod 3)) div 2) div 2) mod 2)
A154103: 0 0 1 0 0 1 0 1 0 1 0 0 0 1 1 0
(2 + ((x - ((2 - (x2 div 3)) div 2)) div 2))
A275673: 1 2 3 4 5 6 7 9 11 13 15 17 19 22 25 28
(2 - ((((x - (x2 div 3)) div 2) div 2) div 2))
A120195: 2 2 2 2 3 3 3 4 4 5 5 6 7 8 9 10
((((x3 + 3x2 + 2x + 6) div 2) div 2) div 2)
A047866: 0 1 3 8 15 27 42 63 90 124 165 215 273 342 420 510
((((2x3 + 5x2 + 2x) div 2) div 2) div 2)
A002717: 0 1 5 13 27 48 78 118 170 235 315 411 525 658 812 988
(((((2x + ~1) * ((~x + 2) div 2)) div 2) div 2) mod 2)
A029411: 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1
((x mod (2 + ((x2 mod (2x + ~1)) div 2))) mod 2)
A285830: 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0
((((~1 + ((x * (x + (x div 2))) div 2)) div 2) div 2) mod 2)
A262683: 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1
((((x2 mod (3x + ~1)) div 2) div 2) mod 2)
A260445: 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1
(8 * (1 + (x * (x - (x div ~2)))))
A302489: 8 24 56 128
(1 - ((~2x + 4) div (2 + (((x + 1) div 2) div 2))))
A301640: ~1 0 1 2 3 3 4 4 4 5 5 5 5 6 6 6
((x + ((x div 2) mod 2) - (((x + 1) div 2) div 2)) div 2)
A194220-A189627: 0 0 1 1 1 2 3 3 3 3 4 4 4 5 6 6
((((1 + (x div 4)) * ((x + ~1) div 2)) div 2) mod 2)
A218218: 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0
(1 - (((x + 1) div 2) div (2 + (((x + ~1) div 2) mod 2))))
A343189: 1 1 1 1 1 0 0 0 0 ~1 ~1 ~1 ~1 ~2 ~2 ~1
(((x + (x div 2)) div (~2 + (x mod ~4))) mod 2)
A100821: 0 1 1 0 1 0 1 0 0 1 0 0 1 0 0 0
(((x2 + x) - ((x mod ~4) div 2)) div 2)
A269403: 0 2 3 6 10 16 21 28 36 46 55 66 78 92 105 120
(2 + ((x - (x2 div (~2 + (x div ~2)))) div 2))
A073571: 2 3 4 5 6 7 9 10 11 12 14 15 17 18 20 21
((x mod (1 - (2 * (2 + (x mod 6))))) mod 2)
A289242: 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 1
(8 * ((x div 2) - ((x mod 3) div 2)))
A174256: 0 0 0 8 16 8 24 24 24 32 40 32 48 48 48 56
((x - (((x - ((x mod 3) div 2)) div 2) div 2)) mod 2)
A096270: 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0
(((2x + ~4) div (2 + (((x + 1) div 2) div 2))) mod 2)
A078359: 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0
(2 - ((~x + 2) div (2 + ((((x + 1) div 2) div 2) div 2))))
A179390: 1 2 2 3 3 4 4 4 4 5 5 5 6 6 6 6
((x + 1) div (2 + (x div (2 + (((x + ~1) div 2) mod 2)))))
A211272: 0 1 1 1 1 1 1 2 2 1 1 2 2 1 1 2
(((((x3 + ~3x2 + 2x) div 2) div 2) div 2) div 2)
A011898: 0 0 0 0 1 3 7 13 21 31 45 61 82 107 136 170
(2 + ((x mod (2 + ((((x + 1) div 2) div 2) mod 2))) mod 2))
A116909: 2 3 2 2 3 2 2 3 2 3 2 2 2 3 2 3
(((2 - (x div (x + ~16))) div 2) div 2)
A178898: 0 0 0 0 0 0 0 0 0 1 1 1 1 1 2 4
(2 + ((x - ((2 - (x mod 8)) div 2)) div 2))
A116549: 1 2 3 4 4 5 6 7 5 6 7 8 8 9 10 11
(2 + (((x - (x mod (2 + (x mod 4)))) div 2) mod 2))
A188794: 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 3
((x2 div (8 * (~2 + (x mod 2)))) mod 2)
A296135-A213729: 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1
((x - (x div (4 + ((x + 2) mod 4)))) mod 2)
A327216: 0 1 0 1 0 1 1 0 1 0 0 1 0 0 1 0
(((x + ~1) div (2 * (2 + ((x + 2) mod 4)))) mod 2)
A025900: 1 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0
(x div (2 * (2 + ((x2 + ~1) mod 8))))
A271484: 0 0 0 0 0 1 0 1 0 2 1 2 0 3 1 3
((x + 4) - (2 div (~8 + (x div 2))))
A296603-A101107: 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21
(2 * (x - (2 * (2 div (~8 + (x div 2))))))
A307782-A093161: 4 6 8 10 12 14 16 18 20 22 24 26 28 30 36 38
(4 div (2 + ((x + 1) mod 16)))
A261517: 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2
(((x2 + x) div 2) mod 32)
A105334: 0 1 3 6 10 15 21 28 4 13 23 2 14 27 9 24
(0 - (x2 div (x + ~32)))
A067659: 0 1 1 1 1 1 2 2 3 4 5 6 8 9 11 14
(1 - ((~x2 + 2x) div 32))
A018118: 1 1 1 2 2 2 2 3 3 3 4 5 5 6 7 8
(x4 mod 32)
A070575: 0 1 16 17 0 17 16 1 0 1 16 17 0 17 16 1
((2 - ((~x2 + x) div 16)) div 2)
A214129-A032739: 1 1 1 1 1 2 2 2 3 3 4 4 5 6 7 8
(((x + 1) div (2 + ((~x + 2) mod 8))) mod 2)
A309768: 0 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1
(2 * (((2x + 1) mod (2 + (x div 4))) div 2))
A345060: 0 0 0 0 0 2 0 0 0 2 0 2 0 2 4 0
((x mod (2 + ((x + 1) div (2 + (x div 4))))) div 2)
A191410: 0 0 1 1 0 0 1 1 0 0 1 0 0 0 2 0
(((2x + ~1) div (4 + (x div 4))) mod 2)
A057211: 1 0 0 1 1 1 0 0 0 0 1 1 1 1 1 0
(2 + ((x - ((~x + 1) div (2 + (x div 4)))) div 2))
A078489: 2 2 3 4 4 5 6 6 7 7 8 9 9 10 10 11
(((x + ~1) mod (2 + (x div (2 + (x div 4))))) div 2)
A078134: 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 2
(((x + ~2) div (2 + (x mod (2 + (x div 4))))) mod 2)
A336040: 1 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0
(((x mod 3) div (~2 + ((x div 4) mod 2))) mod 2)
A284848: 0 1 1 0 1 0 0 1 1 0 1 1 0 1 0 0
((2x + 2) - (((x - (x div 4)) div 2) mod 2))
A286753: 2 4 5 7 9 12 14 15 17 19 22 24 26 27 29 32
((x mod (2 + ((x + 2) div (2 + (x mod 4))))) mod 2)
A288426: 0 1 0 0 0 1 0 1 1 0 0 1 1 0 0 0
((1 - (x div (~2 + (((2 - (x div 2)) div 2) div 2)))) div 2)
A138033: 0 1 1 1 1 2 1 2 2 2 2 2 2 3 2 2
((((2x + ~2) mod (4 + (x div 2))) div 2) div 2)
A023969: 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 1
((((x2 + ~2) div (4 + (x div 2))) div 2) mod 2)
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((x mod (2 + (((~x + 2) mod (2 + (x div 2))) div 2))) div 2)
A157218: 0 0 0 0 0 0 0 0 0 0 0 1 1 0 2 1
(x div (4 + ((x + 1) mod (2 + ((x div 2) mod 2)))))
A158925: 0 0 0 0 0 1 1 1 1 2 1 2 2 3 3 3
((x div (x - (8 * (2 - (x mod 2))))) mod 2)
A225181: 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0
(2 + (x div (2 * (2 + ((x + 1) mod (2 + (x mod 2)))))))
A084294: 2 2 2 2 2 3 3 2 3 3 3 4 4 3 4 4
((x + 4) - ((x div 2) div (~4 + (x mod 2))))
A146968: 4 5 7
A182757: 4 5 7 8 9 10 11 12 13 15 16 17 18 19 20 22
((x mod (2 + (((x + ~1) div 3) mod 4))) div 2)
A144196: 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0
((x mod (2 + ((2 - (x div 3)) mod 4))) div 2)
A318950: 0 0 1 0 0 1 0 0 0 2 0 0 0 0 1 0
(x - (2 * ((2 - ((~1 + (x div 2)) mod 4)) div 2)))
A317613: 2 3 0 1 4 5 6 7 10 11 8 9 12 13 14 15
(((2 - (x div 2)) div (2 + ((x + 1) mod 4))) mod 2)
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(((x + ~2) mod (2 + (((~x + 2) div 2) mod 4))) mod 2)
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(((x div 2) - (x div (2 + ((x + 2) mod 4)))) div 2)
A282192: 0 0 0 0 0 0 0 0 1 1 0 1 1 2 0 1
(((2x + 1) mod (2 + ((x div 2) mod 4))) div 2)
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((x + 1) div (2 + (x div (2 + ((x div 2) mod 4)))))
A190321: 0 1 1 1 1 2 2 2 1 1 2 2 2 2 3 3
((x + 1) div (2 + ((x - ((x div 2) mod 4)) div 2)))
A327104: 0 1 1 1 1 2 2 2 1 1 1 1 1 2 2 2
(0 - ((x2 + 2x) div ~14))
A061052: 0 1 1 2 2 3 4 5 6 8 9 11 12 14 16 19
((2 - ((x * (x div 2)) div ~7)) div 2)
A029080: 1 1 1 1 2 2 2 2 3 4 5 5 6 7 8 8
(((x + 1) mod (1 - (x mod ~7))) mod 2)
A337802-A257531-A164292: 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 0
(x - (2 * (x mod (x - ((x + ~1) mod 8)))))
A103303: 0 1 2 3 4 5 6 7 8 9
A287794-A232360-A158289: 0 1 2 3 4 5 6 7 8 9 8 7 6 5 4 3
(x - ((x mod (x - ((x + ~1) mod 8))) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A100470: 0 1 2 3 4 5 6 7 8 9 10 10 11 11 12 12
(2 * ((x - (2 * ((x div 2) mod 2))) mod 8))
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(16 + ((x + 1) * (1 + (x div 2))))
A295487: 17 18 22 24 31
((3x2 + 2x) div 16)
A183137: 0 0 1 2 3 5 7 10 13 16 20 24 28 33 38 44
((2 * (x div 2)) div (~x + 18))
A185225: 0 0 0 0 0 0 0 0 0 0 1 1 2 2 3 4
((x - ((x * (x div ~2)) div 8)) mod 2)
A262684: 0 0 1 0 1 1 1 1 0 1 1 0 1 1 1 0
((2x + 2) - (x div (~2 + ((~x + 2) div 4))))
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(x - ((x + 2) div (6 - (x div 4))))
A025556: 0 1 2 3 3 4 5 6 6 7 7 8 8 8 9 10
(((3x + ~6) div (2 + (x div 4))) mod 2)
A266441: 1 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1
(((~x2 + x + 1) mod (2 + (x div 4))) mod 2)
A300294: 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1
(((4x + ~2) div (2 + (x div 4))) mod 2)
A328682: 1 1 1 1 0 0 1 0 1 0 1 0 1 0 0 1
(((~2x + 6) div (2 + (x div 4))) mod 2)
A189215: 1 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1
(((2 * (x mod 4)) div (2 + (x div 4))) mod 2)
A135993: 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1
((((x + ~2) + (x div 2)) mod (2 + (x div 4))) mod 2)
A324823: 0 1 1 0 1 0 1 0 0 1 1 0 1 0 0 0
(((~2 + (x * (x div 2))) mod (2 + (x div 4))) div 2)
A309162: 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1
(((x3 + ~2x2) mod (2 + (x div 4))) div 2)
A085857: 0 0 0 0 1 0 0 1 0 1 0 0 0 2 1 0
(1 div ((2x + ~1) mod (4 + (x div 4))))
A073424: 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1
(1 mod ((2x + ~1) mod (4 + (x div 4))))
A326017-A306269-A123110-A114607: 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0
(1 div (1 - (2x mod (4 + (x div 4)))))
A154990: 1 ~1 1 ~1 ~1 1 ~1 ~1 ~1 1 ~1 ~1 ~1 ~1 1 ~1
(((2 - (x * (x div 2))) div (2 + (x div 4))) mod 2)
A178225: 1 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1
(x div (4 - (x mod (1 - (2 * (x div 4))))))
A161283-A161258-A161230-A161054: 0 0 0 0 1 1 1 1 1 2 1 2 1 2 2 3
(x - ((((~x + 2) div 2) - ((x div 4) mod 2)) div 2))
A039137: 0 1 2 4 5 7 8 9 10 11 12 14 15 17 18 19
(((2x + ~1) mod ((x + 2) - (x div 4))) mod 2)
A244528: 1 1 1 0 0 1 0 1 1 0 1 0 1 1 1 1
((4x + 2) - ((x - (x div 4)) div 2))
A054770: 2 6 9 13 17 20 24 27 31 35 38 42 46 49 53 56
((((x + 2) * (x mod 2)) div (2 + (x mod 4))) div 2)
A308066: 0 0 0 0 0 1 0 0 0 1 0 1 0 2 0 1
(((x - ((2 - ((x + (x div 2)) div 2)) div 2)) div 2) mod 2)
A141687: 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0
(1 - ((((2 - ((x * (x div 2)) div 2)) div 2) div 2) div 2))
A029083: 1 1 1 1 2 2 2 2 3 3 4 5 6 6 7 8
((x + 2) - ((((x + 2) * ((~x + 2) div 2)) div 2) div 2))
A240767: 2 3 4 7 8 11 12 16
((((x4 + 4x3 + 4x2) div 2) div 2) div 2)
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(((((x + 2) * (x3 div 2)) div 2) div 2) div 2)
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((((x3 + ~1) mod (x + 4)) div 2) mod 2)
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(((x - ((1 - (x div 2)) mod (x + 4))) div 2) mod 2)
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(((x3 + x2) div (x + 6)) mod 2)
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(2x2 + 20x + 24)
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(2 + (((3x2 + 10x + 8) div 2) div 2))
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((x + 2) + (x div 2) - (((2 - (x div 2)) div 2) div 2))
A280771: 2 3 5 6 8 9 12 13 15 16 18 19 21 22 25 26
(((x2 - (((x mod 2) - (x div 2)) div 2)) div 2) div 2)
A194256-A194246: 0 0 1 2 4 6 9 12 16 20 25 30 36 43 50 57
((x mod (2 + ((2x + 1) mod (2 + (x div 2))))) mod 2)
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(x mod (4 + (4x div (2 + (x div 2)))))
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A133048-A054055: 0 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5
((x - (x div (2 + ((x + ~2) div (2 + (x div 2)))))) mod 2)
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((((~2x2 + x) mod (2 + (x div 2))) div 2) mod 2)
A169672: 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1
(2 + ((x2 + 2x + ~1) div (4 + (x div 2))))
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(((4x + ~4) div (4 + (x div 2))) mod 2)
A303709-A112526-A102354-A075802: 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1
(2 + (((x div 2) - ((~x + 2) div (2 + (x div 2)))) div 2))
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((x + 1) div (2 + (((x + 1) div (2 + (x mod 2))) div 2)))
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(x - ((~x + 1) div (2 + (x div (4 + (x mod 2))))))
A081690: 0 1 3 4 5 7 8 9 10 12 13 14 15 16 17 18
(((x * (x + (x div 2))) div (4 + (x mod 2))) mod 2)
A343219: 0 0 1 0 0 1 1 0 0 1 1 1 0 1 1 0
(((x2 + x) - (x mod (2 * (~2 + (x mod 2))))) div 2)
A116996: 0 1 4 6 10 15 22 28 36 45 56 66 78 91 106 120
((((((x + ~1) div 2) - (x2 div 2)) div 2) div 2) mod 2)
A102511: 1 0 1 1 0 1 0 0 0 1 0 0 1 0 1 1
(x - ((4x + 8) div ~7))
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(1 - ((x * (x div 4)) div ~7))
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((2 + (x mod 2)) div (2 - (x mod ~7)))
A277349-A127841: 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0
((x + 2) div (8 + (x div ~4)))
A072613: 0 0 0 0 0 1 1 1 1 2 2 2 2 3 4 4
(2x - (x mod (8 + (x div 4))))
A103303: 0 1 2 3 4 5 6 7 8 9
A247803: 0 1 2 3 4 5 6 7 8 9 20 21 23 24 25 26
(x - ((x div 4) div (~8 + (x div 2))))
A165332-A031179: 0 1 2 3 5 6 7 8 9 10 11 12 14 15 17 18
((x * (1 + (2x div 3))) div 8)
A051602: 0 0 0 1 1 2 3 4 6 7 8 11
((x + 8) + (x div 9))
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(8 * (x + (x div 12)))
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((x + (2x mod (2 + (x div 2)))) div 8)
A220091: 0 0 0 0 0 0 1 1 1 1 2 1 1 1 1 2
(x - (((2 - (x div 2)) div 2) * (x div 8)))
A084689: 0 1 2 3 4 5 6 7 9
A063949: 0 1 2 3 4 5 6 7 9 10 12 13 14 15 17 18
(((x + ~1) mod 3) div (2 - (x div 8)))
A025850: 1 0 0 1 0 0 1 0 1 2 0 1 2 0 1 2
(((x * ((x + ~2) div 5)) div 4) mod 2)
A330306: 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1
((x - ((x + ((~x + 1) mod 3)) div 4)) mod 2)
A139689: 0 1 1 0 1 0 1 0 0 1 0 0 1 0 0 1
((2x + 2) - ((~x + (x mod 3)) div 4))
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A284365: 2 4 6 9 11 13 16 18 20 23 25 27 29 31 33 36
(((x * (2 + (x div 5))) div 4) mod 2)
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((x + 2) - ((~x + ((x mod 3) div 2)) div 4))
A085302: 2 4 5 6 7 8 10 11 12 14 15 16 17 19 20 21
(x + (x div 4) - (2 * ((~x + 2) div 4)))
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A047388: 0 1 2 5 7 8 9 12 14 15 16 19 21 22 23 26
((2x2 div (~4 + (x * (x div 2)))) mod 2)
A258822: 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0
(x - (2 * ((x div 5) + (x div 4))))
A304111: 0 1 2 3 2 1 2 3 2 3 2 3 2 3 4 3
((x - (x div (8 - (x div 4)))) mod 2)
A288466: 0 1 0 1 0 1 0 0 1 0 1 0 0 1 0 0
(1 - ((((~x + 2) div 4) * (x div 4)) div 2))
A029084: 1 1 1 1 2 2 2 2 3 3 3 4 6 6 6 7
((x + ~1) mod (1 - (((x mod 2) - (x div 4)) div 2)))
A194591: 0 0 0 0 1 0 1 0 1 0 1 0 2 0 1 0
(((x div ~4) mod 2) - ((x div 4) mod 2))
A046978: 0 1 1 1 0 ~1 ~1 ~1 0 1 1 1 0 ~1 ~1 ~1
(((((x + 1) div 2) div 2) mod 2) + ((x div 4) mod 2))
A334889: 0 0 0 1 2 2 2 1 0 0 0 1 2 2 2 1
(2 div (2 - (((x div 4) - (x mod 4)) div 2)))
A025860: 1 0 0 0 1 1 0 0 2 1 1 0 2 2 1 1
(((x2 + 3x + 2) - (x2 div 4)) div 2)
A265429: 1 3 5 9 13 18 23 30 37 45 53 63 73 84 95 108
((x4 div (~2x + ~4)) mod 2)
A130853: 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1
(x mod (2 + (((x * ((x div 2) mod 3)) div 2) mod 2)))
A101670: 0 1 2 0 0 2 0 1 0 1 0 2 0 1 2 0
((((~x2 + 2) mod (3x + 2)) div 2) mod 2)
A289174: 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0
((x + ~1) mod (2 + (((x * (~1 + (x div 2))) div 2) mod 2)))
A179759: 1 0 1 0 1 0 1 0 1 2 1 0 1 0 1 2
((x + 4) - (((~x + 1) * (x div 3)) div 2))
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((x - ((x mod (2 - ((x2 + x) div 2))) div 2)) div 2)
A024174: 0 0 1 2 3 4 6 8 10 13 16 19 22 25 29 33
((2 - (((x * (~2 + (x div ~2))) div 2) div 2)) div 2)
A173151: 1 1 2 2 3 4 5 6 7 9 10 12 13 16 17 20
(~4x3 + 8x2 + 16x + 8)
A202290: 8 28 40 20
(2 * (4 + (x * (2 + (3 mod (x + 2))))))
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(((((~x + 2) * (2 + (x div 4))) div 2) div 2) mod 2)
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(1 - (2 * ((x2 div (x - ((~x + 2) div 2))) mod 2)))
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(1 - ((x mod (~2 + ((x * (2 - (x div 2))) div 2))) mod 2))
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(2 + ((3x2 + 13x + 14) div 2))
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(2 + (((~3 + (x div 3)) mod (x + 2)) mod 2))
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(((2 - ((x3 + ~x2) div (x + 2))) div 2) mod 2)
A100672-A080813: 1 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0
((((x4 + ~1) div (x + 2)) div 2) mod 2)
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((((~4 + (x div 3)) mod (x + 2)) div 2) mod 2)
A295893: 0 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0
(((((x2 + x) div 4) mod (x + 2)) div 2) mod 2)
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(2x2 + 11x + 22)
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((((x + 2) * ((x + 2) + (2 mod (x + 1)))) div 2) div 2)
A064796: 1 2 6 8 12 15 20 24 30 35 42 48 56 63 72 80
((x3 + 8x2 + 21x + 20) div 2)
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(2 + ((8x + ~2) div (x + 4)))
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(1 - (2 * (((~x + 2) * (x div 2)) div (x + 4))))
A101435: 1 1 1 3 3 3 5 5 5 7 7 7 9 9 11 11
(((5x2 + 18x + 16) div 2) div 2)
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(x - (((~x4 + 2x3 + x + ~2) div 2) div 2))
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((x - (x3 div (~4x + 2))) mod 2)
A224326: 0 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0
(8x + ((x2 + 3x) div 2))
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((x - (((x div ~4) * (x div 2)) div 2)) mod 2)
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(x - ((((2 + (x div 4)) * (x div 2)) div 2) div 2))
A056792: 0 1 2 3 3 4 4 5 4 5 5 6 5 6 6 7
((2x + 2) - (((x mod 4) + (x div 2)) div 2))
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((x + 2) - (1 mod (2 * ((~2x + 4) + (x div 2)))))
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(2 + ((x2 div (2 - ((x div 2) * (x div 2)))) mod 2))
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(((x + 1) div (1 - (((x mod 2) - (x div 2)) div 2))) mod 2)
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(((1 + (2 * (x mod 4))) mod (2 + (x div 2))) mod 2)
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((((x + 1) * (x div 3)) div (2 + (x div 2))) mod 2)
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(((x3 + ~x + ~2) div (2 + (x div 2))) mod 2)
A253084-A113998: 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 1
(((x3 + 2x2 + x + 2) div (2 + (x div 2))) mod 2)
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((((x2 + 2) div (x + 2)) mod (2 + (x div 2))) mod 2)
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(((x + 1) div 2) - (2x div (4 + (x div 2))))
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(1 - (((~x + 2) * (x div 2)) div (4 + (x div 2))))
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((3x + 3) - (x div (4 + (x div 2))))
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(((~x + ((x + ~2) div 3)) mod (2 + (x div 2))) mod 2)
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(((~x + (x div 8)) mod (2 + (x div 2))) div 2)
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(x - (((x div 2) - ((~x + 2) div (2 + (x div 2)))) div 2))
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(((3x2 + ~4x) div (2 + (x div 2))) mod 2)
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((x2 + 3x) div (2 * (2 - ((x div 2) mod 2))))
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(2 - (((x + (x div 2)) div 2) mod (2 + ((x div 2) mod 2))))
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((x + 2) + ((x + (x div 2)) div 2) - ((x div 2) mod 2))
A047300: 2 3 4 6 9 10 11 13 16 17 18 20 23 24 25 27
(1 - (x2 mod ((~x + 2) + (2 * ((x div 2) mod 2)))))
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(((x + 1) div 2) - (x div (6 - (x mod 2))))
A189671: 0 1 1 2 2 2 2 3 3 4 4 4 4 5 5 5
(((~2x + 1) mod (2 + (x div 2) - (x mod 2))) mod 2)
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((2 + (x div 2) - (x mod 2)) mod (4 + (x mod 2)))
A190451: 2 1 3 2 0 3 1 4 2 0 3 1 0 2 1 3
(((x + 2) div 3) - (x div (2 * (2 + (x mod 2)))))
A082498: 0 1 1 1 1 2 1 2 1 2 2 3 1 3 2 3
((1 + ((2x + 1) div 5)) mod 4)
A084053: 1 1 2 2 2 3 3 0 0 0 1 1 2 2 2 3
((x - (2 * ((x div 3) mod 3))) mod 4)
A051329: 0 1 2 1 2 3 2 3 0 1 2 3 2 3 0 3
((((2 + (x div 2)) * (1 + (x div 2))) div 2) mod 4)
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(16x3 + 12x)
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(x - ((~x + ((x + 2) mod 5)) div 4))
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A127428: 0 1 2 4 5 6 7 8 10 11 12 13 14 17 18 19
(44x + 24)
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(x - (4 * (~x + (x mod 10))))
A103303: 0 1 2 3 4 5 6 7 8 9
A024660: 0 1 2 3 4 5 6 7 8 9 50 51 52 53 54 55
((x + ((x2 + ~1) mod 6)) div 4)
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(((x + 1) div (~x + 16)) div 4)
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((x + ((~1 + (x div 4)) mod 4)) div 4)
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(2x - ((x + ((x div 2) mod 4)) div 4))
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(x - ((x + ((~x2 + x) div 4)) div 4))
A067570: 0 1 2 3 4 5 7
A135675: 0 1 2 3 4 5 7 8 10 12 14 16 18 20 22 25
(x2 div ((~x + 4) + (x2 div 4)))
A085600: 0 0 1 3 4 5 5 5 5 5 5 5 5 5 5 5
((x3 + 3x2 + 5x + 4) div 4)
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((3x div 5) - (x div 4))
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((x2 + 1) div ((2x + 4) - (x div 4)))
A105098: 0 0 0 1 1 2 2 2 3 4 4 5 5 6 6 7
(2 * ((x + 2) + (x div 13)))
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(~2 + ((x + (x2 div 7)) div 2))
A251418: ~2 ~2 ~1 0 1 2 3 5 6 8 10 12 14 16 19 21
(((x + ((~x + 2) mod (1 + ((x + 1) div 2)))) div 2) div 2)
A327469: 0 0 0 1 1 1 1 1 3 3 3 4 4 4 4 5
(x - (2 * (((~x + ~1) + ((x div 4) mod 2)) div 2)))
A097757-A001422: 2 3 6 7 8 11 12 15 18 19 22 23 24 27 28 31
((x2 mod ((x + ~2) + (2x div 3))) mod 2)
A202238: 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0
(2 * (2 - ((~x2 + 2) div (3x + 2))))
A207540: 2 4 6 6 6 8 8 10 10 10 12 12 12 14 14 14
(((2 - (x mod (2 - (x * (x div 3))))) div 2) mod 2)
A072418: 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 0
(4x2 + 18x + ~20)
A277981: ~20 2 32 70 116 170 232 302 380 466 560 662 772 890 1016 1150
((2x + 2) - ((~x + ((x div 2) div ~2)) div 2))
A247426: 2 5 8 10 13 15 18 21 23 26 29 31 34 36 39 42
(((x + ((x + ~2) mod (2 + (x div 3)))) div 2) mod 2)
A189687: 0 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0
(((x + (x div (2 - (x mod ~4)))) div 2) mod 2)
A011656: 0 0 1 0 1 1 1 0 0 1 0 1 1 1 0 0
(((~x + (x mod (~2 + (x div ~4)))) div 2) mod 2)
A037801: 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1
(4 - ((~x + ((((x + ~1) div 2) div 2) div 2)) div 2))
A092279: 5 5 5 6 6 7 7 8 8 8 9 9 10 10 11 11
((x - (x div (~2x + 32))) div 2)
A337853: 0 0 1 1 2 2 3 3 4 4 5 5 5 5 5 4
((x + 2) - ((~x + ((2 - (x div 4)) div 2)) div 2))
A184590: 2 3 5 6 8 10 11 13 14 16 17 19 21 22 24 25
(((x * (2 - (x div (2 + (x mod 4))))) div 2) mod 2)
A213676: 0 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0
((2 - ((~x + ((~x2 + x) div 4)) div 2)) div 2)
A029021: 1 1 2 2 3 3 4 5 6 8 9 11 12 14 16 18
(((~x + (2x2 div (x + 4))) div 2) mod 2)
A200263: 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 0
((2 - ((~x + (((~x + 1) * (x div 2)) div 2)) div 2)) div 2)
A029022: 1 1 2 2 3 3 4 5 6 7 9 10 12 13 16 17
((((~x + 2) * (1 + ((x div 2) div 3))) div 2) mod 2)
A071004: 1 0 0 1 1 0 0 1 0 1 0 1 1 1 0 0
((x + 2) - ((x2 + 1) div ((x + 2) + (x div 2))))
A177876: 2 3 3 4
A143502: 2 3 3 4 4 5 5 5 6 6 7 7 7 7 8 8
(((x + 2) * (1 + (x mod (2 * (1 + (x mod 2)))))) div 2)
A176743: 1 3 2 10 3 7 4 18 5 11 6 26 7 15 8 34
(((5x * (x div 2)) div (x + 2)) mod 2)
A093385: 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 0
(((x div 2) - ((2x + ~5) div (x + 2))) div 2)
A056970: 1 0 1 0 1 1 1 1 1 1 2 2 2 2 3 3
(((~9x + 18) div (x + 2)) mod 2)
A325896: 1 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1
((((2x2 + 1) div 3) mod (x + 2)) mod 2)
A080110: 0 1 1 1 1 1 0 0 1 0 1 1 0 0 1 0
((((2x2 + ~1) div 3) mod (x + 2)) mod 2)
A080111: 1 0 0 0 0 0 1 1 0 1 0 0 1 1 0 1
(((1 + (x mod 3) - (x div 2)) mod (x + 2)) mod 2)
A029408: 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1
(((~1 + ((x + (x div 4)) div 2)) mod (x + 2)) mod 2)
A092130: 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0
((7x2 + 15x + 2) div 2)
A131874: 1 12 30 55 87 126 172 225 285 352 426 507 595 690 792 901
((~x3 + 4x2 + 13x + 2) div 2)
A028494: 1 9 18 25 27 21 4 ~27 ~75 ~143 ~234 ~351 ~497 ~675 ~888 ~1139
(((1 + (x2 * (2 - (x div 2)))) div (x + 2)) mod 2)
A261185: 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0 1
(((x div (~4 + ((x div 2) mod 2))) mod (x + 2)) div 2)
A100196: 0 1 1 2 2 2 3 3 4 4 4 4 5 5 5 6
((x - ((~4x2 + x) div (x + 2))) div 2)
A047932: 0 1 3 5 7 9 12 14 16 19 21 24 26 29 31 34
((x + 2) - ((2 - (x2 div 4)) div (x + 2)))
A276212: 1 3 4 5 7 8 9 11 12 13 14 16 17 18 19 21
((((2 - ((x + (x div 2)) div 2)) div 2) mod (x + 2)) mod 2)
A157686: 1 1 0 0 1 0 1 1 0 1 1 0 0 1 0 0
(2x2 div (((x + 2) * (2 + (x div 2))) div 2))
A262558: 0 0 1 2 2 3 3 4 4 4 4 5 5 5 5 5
(((2 + ((x + (x div 2)) * (x div 2))) div (x + 2)) mod 2)
A118175: 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 1
(((2 + (x * (x mod 6))) div (x + 2)) mod 2)
A317595: 1 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0
((((~x + ((2 - (x div 2)) div 2)) div 2) mod (x + 2)) div 2)
A059396: 0 0 1 1 2 2 2 2 2 3 3 3 3 3 3 4
((((x + ~2) * ((x + ~1) div 3)) div (x + 2)) mod 2)
A025908: 1 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1
(4 - (((~x + 3) * (x div 2)) div (x + 2)))
A138195: 4 4 4 4 5 5 6 6 6 7 7 8 8 8 9 9
(((x + 2) * (x3 - (x2 div 2))) div 2)
A212682: 0 1 12 57 168 395 792 1435 2400 3789 5700 8261 11592 15847 21168 27735
((1 + (x * (4 + (x mod 2)))) div (x + 4))
A331362: 0 1 1 2 2 2 2 3 2 3 2 3 3 3 3 4
((x2 - (2 * (~2 + (x mod 2)))) div (x + 4))
A083058: 1 0 1 1 2 3 4 4 5 6 7 8 9 10 11 11
((2x + 4) + (x2 mod (1 + (x mod 4))))
A159619: 4 7 9 11 12 15 16 19 20 23 25 27 28 31 33 35
((2x + 4) + ((x + (x div 2)) div 8))
A258036: 4 6 8 10 12 14 17 19 21 23 25 28 30 32 34 36
((2x + 4) + ((x * (2 - (x div 2))) div (x + 2)))
A248419: 4 6 8 10 12 14 15 17 18 20 21 23 24 26 27 29
((2x + 4) + (7 * (x div 2)))
A106387: 4 6 15 17 26 28 37 39 48 50 59 61 70 72 81 83
((3x + 4) + (2x div 5))
A125620: 4 7 10 14
A184625: 4 7 10 14 17 21 24 27 31 34 38 41 44 48 51 55
(2 - (((x * (x - (x div 3))) div (x + 2)) mod 2))
A323116: 2 2 1 1 2 2 1 1 2 2 1 2 2 1 2 2
(((x + 2) * (x + ((~x + 2) mod (1 + (x div 2))))) div 2)
A106668: 0 1 4 10 15 17
(((x * ((x + 2) mod 6)) div (x + 2)) mod 2)
A215530: 0 1 0 1 0 0 1 0 1 0 0 0 1 0 1 0
(2 * ((x * (((x + 1) + (x div 2)) div 2)) div (x + 2)))
A285999: 0 0 2 2 4 4 6 6 8 10 12 12 14 16 18 18
((~6x + 2) * (1 mod (~2x + 1)))
A187156: 0 0 20 64 132 224 340 480 644 832 1044 1280 1540 1824 2132 2464
((1 - ((x3 + x2) div (~2x + 1))) div 2)
A194174: 0 1 2 4 6 9 12 16 20 24 29 35 41 48 55 63
((x + 2) - (x2 div ((~2x + 1) - (x div 2))))
A186157: 2 4 5 7 8 10 11 13 14 15 17 18 19 21 22 24
(4x + ((x2 + 5x + 6) div 2))
A051938: 3 10 18 27 37 48 60 73 87 102 118 135 153 172 192 213
(4x + ((x + ((x + (x div 2)) div 2)) div 2))
A172324: 0 4 9 14 19 24 29 34 39 43 48 53 58 63 68 73
(5x + ((2 - (x div 2)) div (x + 2)))
A313730: 1 5 10 15 20 25 29 34 39 44 49 54 59 64 69 74
((x - (x3 div (~3x + 2))) div 2)
A101433: 0 1 2 3 5 7 10 13 16 19 23 27 31 36 41 47
(2 + ((1 + (x div 2) - (2 * (x mod 2))) * (x div 2)))
A338042: 2 2 4 2 8 4 14 8 22 14 32 22 44 32 58 44
(2 * ((3x * (x + (x mod 2))) - (x div 2)))
A014633: 0 12 22 70 92 176 210 330 376 532 590 782 852 1080 1162 1426
(((2x3 + 3x2 + x) + (x div 2)) div 2)
A219085: 0 3 15 42 91 166 274 421 614 857 1157 1520 1953 2460 3048 3723
((x2 + x) - (((1 + (x div 2)) * (x div 2)) div 2))
A274830: 0 2 5 11 17 27 36 50 62 80 95 117 135 161 182 212
(((16 mod (x + 1)) + (x div 2)) div 2)
A077819: 0 0 1 0 1 3 2 1 5
(((2 + (x div 2)) div (8 - (x div 2))) div 2)
A319403: 0 0 0 0 0 0 0 0 0 0 1 1 2 2 4 4
((((2 - (x div 3)) mod 4) + (x div 2)) div 2)
A195851-A029127: 1 1 1 1 1 1 1 1 2 3 4 4 4 4 4 4
((x + 2) - (x2 div ((2x + 4) - (x div 2))))
A196162: 2 3 4 4 5 5 6 6 6 7 7 8 8 8 9 9
(1 - (x div (~2 + (x div (2 + (x mod 2))) - (x div 2))))
A330393: 1 2 2 3 3 3 4 4 5 4 6 4 7 5 8 5
(((x div 2) div 7) * (2 + (x div 2)))
A305503: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 9
(x div (x - ((x3 + 1) mod (2 + (x div 2)))))
A327103-A060128-A055090: 0 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1
((2 + ((x * (x div 2)) div 3)) div (2 + (x div 2)))
A225956-A169995-A169994-A169993-A169992-A169991-A053693-A032229-A000700: 1 1 0 1 1 1 1 1 2 2 2 2 3 3 3 4
(1 - (x div (0 - ((2x + 2) div (2 + (x div 2))))))
A056155: 1 2 2 3 3 3 4 4 4 4 5 5 5 6 6 6
(((x + 1) div 2) - ((2x + ~2) div (2 + (x div 2))))
A029122: 1 1 1 1 1 1 1 2 2 3 3 4 4 4 5 5
((x div ~14) mod (2 + (x div 2)))
A176841-A176814: 0 1 2 2 3 3 4 4 5 5 6 6 7 7 8 7
((4x3 + ~x2) + (2 * (x div 2)))
A211617: 0 3 30 101 244 479 834 1329 1992 2843 3910 5213 6780 8631 10794 13289
(((x + 2) div (2 + (x div 4))) - ((x div 2) mod 2))
A232551: 1 1 1 1 2 2 1 2 2 2 2 2 2 3 2 2
((((x div 2) - (x * (x mod 2))) div 2) + ((x div 2) mod 2))
A131730: 0 ~1 1 0 1 ~2 2 ~1 2 ~3 3 ~2 3 ~4 4 ~3
(((3 * (x + (x div 4))) + (x mod 2)) div 2)
A327492: 0 2 3 5 7 9 10 12 15 17 18 20 22 24 25 27
(((3 * (x + (x div 4))) - (x mod 2)) div 2)
A005187: 0 1 3 4 7 8 10 11 15 16 18 19 22 23 25 26
((x - (3 * (x div ~2))) div (2 + (x mod 2)))
A340709: 0 1 2 3 5 4 7 6 10 8 12 9 15 11 17 13
((2x mod (2 + (x div 3))) div (2 + (x mod 2)))
A083915-A083892: 0 0 0 0 1 0 0 0 0 1 0 0 0 0 2 0
((3 * ((x mod 3) div 2)) + (2 * (x mod 2)))
A178142: 0 2 3 2 0 5 0 2 3 2 0 5 0 2 3 2
((1 + (2x div 3)) * (1 - (2 * (x mod 2))))
A168052: 1 ~1 2 ~3 3 ~4 5 ~5 6 ~7 7 ~8 9 ~9 10 ~11
(((x3 + 2x2) div 2) * (1 - (2 * (x mod 2))))
A269429: 0 ~1 8 ~22 48 ~87 144 ~220 320 ~445 600 ~786 1008 ~1267 1568 ~1912
((x + (x div (1 + ((x + 1) div 5)))) div 2)
A064474: 0 1 2 3 3 3 4 5 6 6 6 7 8 8 8 9
((15x2 + x) div 2)
A022273: 0 8 31 69 122 190 273 371 484 612 755 913 1086 1274 1477 1695
((15x2 + ~x) div 2)
A022272: 0 7 29 66 118 185 267 364 476 603 745 902 1074 1261 1463 1680
((3x2 + 19x) div 2)
A140675: 0 11 25 42 62 85 111 140 172 207 245 286 330 377 427 480
((3x2 + 17x) div 2)
A140674: 0 10 23 39 58 80 105 133 164 198 235 275 318 364 413 465
((9x2 + 7x) div 2)
A062728: 0 8 25 51 86 130 183 245 316 396 485 583 690 806 931 1065
((9x2 + 5x) div 2)
A062725: 0 7 23 48 82 125 177 238 308 387 475 572 678 793 917 1050
(14x2 + ~10x)
A152760: 0 4 36 96 184 300 444 616 816 1044 1300 1584 1896 2236 2604 3000
((x + (x2 div (1 + (2x div 3)))) div 2)
A052083-A039268: 0 1 2 3 4 5 6 8 9 10 12 13 14 15 16 17
((6x3 + 3x2 + x) div 2)
A115519: 0 5 31 96 218 415 705 1106 1636 2313 3155 4180 5406 6851 8533 10470
((x * (1 + ((x3 + 2x) div 3))) div 2)
A257055: 0 1 5 18 50 115 231 420 708 1125 1705 2486 3510 4823 6475 8520
(2x * ((x + 1) - (x mod 10)))
A169919: 0 2 4 6 8 10 12 14 16 18 220 242 264 286 308 330
((x + 2) + (x div (3 + ((x div 2) div 3))))
A175970: 2 3 4 6 7 8 9 10 12 13 14 15 16 17 18 20
(x - ((~x + ((x div 2) div 7)) div 2))
A248758: 0 2 3 5 6 8 9 11 12 14 15 17 18 20 21 22
(64x2 + 2x)
A158070: 0 66 260 582 1032 1610 2316 3150 4112 5202 6420 7766 9240 10842 12572 14430
(~2x2 + 38x)
A182428: 0 36 68 96 120 140 156 168 176 180 180 176 168 156 140 120
(2 + compr(\x.(~1 + (x mod (2 + ((x div 2) mod 4)))),x))
A028749: 2 3 5 6 7 8 10 11 12 14 15 17 18 19 20 21
((x + 2) + ((x2 + 2x) div 9))
A184109: 2 3 4 6 8 10 13 16 18 22 25 28 32 36 40 45
(14x2 + 3x)
A195025: 0 17 62 135 236 365 522 707 920 1161 1430 1727 2052 2405 2786 3195
(2 * (x + (5 * ((x div 2) div 3))))
A212495: 0 2 4 6 8 10 22 24 26 28 30 32 44 46 48 50
((x + 2) + ((x - (2 mod (x + 1))) div 5))
A106092-A095949: 2 3 4 5 6 7 8 10 11 12 13 14 16 17 18 19
((11x2 + ~5x) div 2)
A226492: 0 3 17 42 78 125 183 252 332 423 525 638 762 897 1043 1200
(2x - ((~x + ((x div 2) div 5)) div 2))
A198083: 0 3 5 8 10 13 15 18 20 23 25 27 30 32 35 37
((x + 2) + ((x - (x div ~3)) div 3))
A167389: 2 3 5 6 8 9 10 12 13 15 16 18 19 21 22 23
((x mod (~x + (3 * (~1 + (x mod 4))))) mod 2)
A341999-A341996-A327928: 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1
((x + 2) + (9 * (1 + (x div 2))))
A118512: 11 12 22 23 33 34 44 45 55 56 66 67 77 78 88 89
((x + 2) mod ((x + ((~1 + (x div 2)) mod 3)) div 2))
A165033: 0 0 0 0 0 1 0 1 2 3 2 1 0 1 2 3
((x + 2) + (3 mod (x - ((x + 1) mod 3))))
A259444: 2 3 5 6 7 10 11 12 13 14 15 16 17 18 19 20
(14x2 + 10x)
A195027: 0 24 76 156 264 400 564 756 976 1224 1500 1804 2136 2496 2884 3300
((7x2 + 5x) div 2)
A179986: 0 6 19 39 66 100 141 189 244 306 375 451 534 624 721 825
(26x + 72)
A099943: 72 98 124 150 176 202 228 254 280 306 332 358 384 410 436 462
((x + ((2 + ((x div 2) mod 4)) mod 3)) div 2)
A034586: 1 1 1 1 2 3 4 4 5 5 5 5 6 7 8 8
((x2 + 21x) div 2)
A101859: 0 11 23 36 50 65 81 98 116 135 155 176 198 221 245 270
((x2 + 23x) div 2)
A132754: 0 12 25 39 54 70 87 105 124 144 165 187 210 234 259 285
((x + (((1 + (x div 2)) mod 4) mod 3)) div 2)
A236916: 0 1 2 2 2 2 3 3 4 5 6 6 6 6 7 7
(2x - ((~x + (x div 12)) div 2))
A195168: 0 3 5 8 10 13 15 18 20 23 25 28 30 32 35 37
((5x2 + 13x) div 2)
A302906: 0 9 23 42 66 95 129 168 212 261 315 374 438 507 581 660
((13x2 + ~3x) div 2)
A186030: 0 5 23 54 98 155 225 308 404 513 635 770 918 1079 1253 1440
((13x2 + ~x) div 2)
A022270: 0 6 25 57 102 160 231 315 412 522 645 781 930 1092 1267 1455
((11x2 + x) div 2)
A022269: 0 6 23 51 90 140 201 273 356 450 555 671 798 936 1085 1245
(2x - ((~x + ((~2 + (x div 2)) div 3)) div 2))
A064437: 1 3 6 8 10 13 15 18 20 23 25 27 30 32 35 37
((3x2 + 19x + 24) div 2)
A341740: 12 23 37 54 74 97 123 152 184 219 257 298 342 389 439 492
((x + 2) + ((x * (x2 div 3)) div 3))
A004045: 2 3 4 8 12 20 32
((x + 2) + ((x + ((x * (x div 2)) mod 2)) div 3))
A099619: 2 3 4 6 7 8 10 11 12 14 15 17 18 19 20 22
((4 mod ((~x + 3) - (x div 3))) mod 2)
A029424: 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1
(x - ((~x2 + x) div ((x + 2) + (x div 3))))
A133280: 0 1 3 4 6 8 9 11 13 15 16 18 20 22 24 25
(2 - ((~3x3 + ~x2 + x) div 2))
A332234: 2 4 15 46
((x * (1 + ((x + 2) * (3 - (x div 2))))) div 2)
A076856: 0 5 9 16 14
(2 * (x + ((x + 3) * (x div 8))))
A140955: 0 2 4 6 8 10 12 14 38
((13x2 + x) div 2)
A022271: 0 7 27 60 106 165 237 322 420 531 655 792 942 1105 1281 1470
((11x2 + ~x) div 2)
A022268: 0 5 21 48 86 135 195 266 348 441 545 660 786 923 1071 1230
((17x2 + x) div 2)
A022275: 0 9 35 78 138 215 309 420 548 693 855 1034 1230 1443 1673 1920
((17x2 + ~x) div 2)
A022274: 0 8 33 75 134 210 303 413 540 684 845 1023 1218 1430 1659 1905
((x2 + 25x) div 2)
A132755: 0 13 27 42 58 75 93 112 132 153 175 198 222 247 273 300
((x2 + 33x) div 2)
A212427: 0 17 35 54 74 95 117 140 164 189 215 242 270 299 329 360
((x2 + 31x) div 2)
A132758: 0 16 33 51 70 90 111 133 156 180 205 231 258 286 315 345
(((x2 + x) + (x2 div (x + 4))) div 2)
A181947: 0 1 3 6 11 16
A333709: 0 1 3 6 11 16 22 30 38 48 58 70 82 95 110 125
(2 * ((x2 + x) + ((1 + (x div 2)) * (x div 2))))
A273368: 0 4 16 28 52 72 108 136 184 220 280 324 396 448 532 592
((x7 + x) div 2)
A168029: 0 1 65 1095 8194 39065 139971 411775 1048580 2391489 5000005 9743591 17915910 31374265 52706759 85429695
((x + 2) + ((x - ((x div 2) div ~3)) div 2))
A184588: 2 3 5 7 8 10 11 13 15 16 18 19 21 22 24 26
((x + 2) + ((x - (x div 7)) div 2))
A226721: 2 3 5 6 8 9 11 12 13 15 16 18 19 21 22 23
((x + 2) + ((x - (x div 9)) div 2))
A332101: 2 3 5 6 8 9 11 12 14 15 16 18 19 21 22 24
((x + ((x div (~1 + (2 * (x div 4)))) mod 2)) div 2)
A194253-A194163: 0 1 1 2 2 3 3 4 4 5 5 6 6 6 7 8
(2x div (2 + (x * (x mod 10))))
A108695: 0 0 0 0 0 0 0 0 0 0 10 1 0 0 0 0
((x + 2) + ((x mod ((x + 1) - (x mod 4))) mod 2))
A179464: 2 3 4 5 6 7 9 9 10 11 13 13 14 15 17 17
(14x2 + ~3x)
A185019: 0 11 50 117 212 335 486 665 872 1107 1370 1661 1980 2327 2702 3105
((x + 2) + (2 * ((x + (x div 3)) div 3)))
A188190: 2 3 4 7 8 11 12 15 16 19 20 21 24 25 28 29
(1 - (x div ((~x + ~2) + (x mod (2 + (x mod 3))))))
A036450: 1 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2
(2x - ((~x + ((x mod (1 + (x div 2))) div 2)) div 2))
A195170: 0 3 5 8 10 12 15 17 20 22 24 27 29 31 34 36
((x + 2) + (((~2 + ((x div 2) mod 2)) mod (x + 1)) div 2))
A143664: 2 3 5 6 7 9 11 12 13 15 17 18 19 21 23 24
((x4 + 4x3 + x2 + 2x) div 2)
A201243: 0 4 28 102 268 580 1104 1918 3112 4788 7060 10054 13908 18772 24808 32190
((x + 2) + ((((2 - (x div 2)) mod (x + 1)) div 2) div 2))
A072497: 2 3 4 5 6 7 9 10 11 13 14 15 16 17 18 19
((x + (((x2 - ((x + ~1) div 2)) div 2) div 2)) div 2)
A065130: 0 0 1 2 3 5 7 9 11 14 17 20 23 26 30 34
(2 + compr(\x.((x2 div ~7) mod 2),x))
A283778: 2 5 7 8 10 11 13 16 19 21 22 24 25 27 30 33
((x2 + 1) div (x + 18))
A302930: 0 0 0 0 0 1 1 2 2 3 3 4 4 5 6 6
((x + 2) + ((x2 + 2x) div 16))
A184112: 2 3 4 5 7 9 11 12 15 17 19 21 24 27 30 32
(x - ((~x + (2 div (x + ~16))) div 2))
A003253: 1 2 4 5 7 8 10 11 13 14 16 17 19 20 22 24
((x + ((~x2 + x) div 16)) div 2)
A163529: 0 0 0 1 1 1 2 2 2 2 2 2 1 1 1 0
((x + 2) + (2x div (4 + (x div 4))))
A183864-A181133: 2 3 5 6 7 9 10 11 12 14 15 16 17 18 20 21
((x + 2) + (((x div 2) - ((x div 4) mod 2)) div 2))
A125299: 2 3 4 5 6 7 9 10 12 13 14 15 16 17 19 20
((x * (2 - ((x div 2) mod ~7))) div 2)
A106669: 0 1 8 12 14 17
(((~x + 1) - (x2 div ~7)) div 2)
A143286: 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 9
(1 - ((x + (x2 div ~7)) div 2))
A173925: 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 10
(1 - ((~x + (x2 div ~7)) div 2))
A022788: 1 2 3 4 5 6 7 8 10 12 14 16 18 20 22 25
((x + 2) - (1 mod (~x + ((x + ~2) mod 8))))
A138100: 1 2 5 6 7 8 9 10 11 12 21 22 23 24 25 26
(x - (((x2 + 1) div (x + 8)) div 2))
A039708: 0 1 2 3 4 4 5 6 6 7 8 8 9 9 10 11
(x mod (2 + ((x2 + ~2) div (x + 8))))
A337636: 0 0 0 1 1 2 2 2 3 3 3 3 3 4 4 4
(((x2 + 3x) div (x + 8)) mod 2)
A286807: 0 0 1 1 0 1 1 0 1 0 1 0 1 1 0 1
((x + 2) - (1 mod (~x + (2 * (2 - (x div 4))))))
A065520: 1 2 3 5 7 9 11 13 17 19 21 23 27 29 31 33
((x + 2) + ((((1 - (x div 2)) mod (x + 2)) div 2) div 2))
A286291: 2 3 4 5 7 8 9 10 11 13 14 15 16 17 18 19
(2 + compr(\x.(((~x2 + x) mod (2 + (x div 2))) mod 2),x))
A109423-A028737: 2 3 5 6 7 8 10 11 13 14 15 17 18 19 20 21
(2 + compr(\x.(2 - ((x2 + 2) mod (x + 4))),x))
A214329: 2 3 5 6 8 9 10 11 12 13 14 17 18 19 20 21
((x + ((x2 + 2x + 2) * (2 + (x mod 2)))) div 2)
A093918: 2 8 11 27 28 58 53 101 86 156 127 223 176 302 233 393
((~x + ((x2 + 2x + 2) * (2 + (x mod 2)))) div 2)
A093916: 2 7 9 24 24 53 47 94 78 147 117 212 164 289 219 378
((x2 + x) div (2 + (x * (x div (2 + (x mod 2))))))
A332581: 0 1 1 2 2 4 2 3 2 3 2 3 2 3 2 3
((x + 2) + ((x + (2x div 5)) div 2))
A285077-A186344-A186317: 2 3 5 7 8 10 12 13 15 17 19 20 22 24 25 27
((x + 2) + ((x + ((x mod (1 + (x div 2))) div 2)) div 2))
A099267: 2 3 5 6 8 10 11 13 14 16 18 19 21 23 24 26
((x + 2) + ((x + ((x - (x div 4)) div 2)) div 2))
A186221: 2 3 5 7 8 10 12 14 15 17 19 20 22 24 25 27
((x2 + 2x + 2) + ((x div 2) div 5))
A322008: 2 5 10 17 26 37 50 65 82 101 123 146 171 198 227 258
(((x2 + 2x + ~1) div 2) * ((x2 + 2x) div 2))
A218832: 0 1 12 49 132 289 552 961 1560 2401 3540 5041 6972 9409 12432 16129
(1 - ((~x + (2 div (8 - (x div 2)))) div 2))
A264810: 1 2 2 3 3 4 4 5 5 6 6 7 7 7 7 8
((1 + ((x div 4) mod 2)) * ((x * (x div 2)) mod 2))
A343221: 0 0 0 1 0 0 0 2 0 0 0 1 0 0 0 2
(((x + ~1) div (6 - (x * (x mod 2)))) mod 2)
A029443: 1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0
((2 - (x mod (2 - (x mod ~3)))) div (x + 2))
A240332-A015920-A015626-A014744: 1 0 0 0 0 0 0 ~1 0 0 0 0 0 0 0 0
(((~x + (2 * (x div 4))) div 3) mod (x + 2))
A238839: 0 2 3 4 5 6 6 7 8 9 10 10 12 12 13 14
((6x - (x div 3)) div (x + 2))
A081288: 0 2 3 3 3 4 4 4 4 4 4 4 4 4 5 5
(x - ((1 + ((x + (x div 2)) * (x div 2))) div (x + 2)))
A137791: 0 1 1 2 2 3 3 4 4 5 4 5 5 6 5 6
((2 * (1 + (x mod 12))) mod (x + 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A043271: 0 1 2 3 4 5 6 7 8 9 10 11 2 4 6 8
((2 - ((x mod 7) div 2)) div (x + 2))
A284504: 1 0 0 0 0 0 ~1 0 0 0 0 0 0 ~1 0 0
((2 * ((x + 1) mod 10)) mod (x + 2))
A190727: 0 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12
((2 - (x mod (4 + ((x div 2) mod 2)))) div (x + 2))
A224877: 1 0 0 ~1 0 0 0 0 0 0 0 0 0 0 ~1 0
(((x div 2) - ((x + 1) mod 8)) mod (x + 2))
A045430: 1 1 2 2 3 3 4 3 3 2 2 1 1
((4x + (x2 div 4)) div (x + 2))
A082462-A055086: 0 1 2 2 3 3 4 4 4 5 5 5 6 6 6 6
(x - ((2 * (~x + (x2 div 3))) div (x + 2)))
A202305: 0 2 3 3 4 5 5 5 6 6 7 7 7 8 8 8
((2 * (x + (2 * (x + (x div 3))))) div (x + 2))
A211675: 0 2 3 4 4 4 5 5 5 6 6 6 6 6 6 6
(1 - ((2 + (x mod 4) - (x div 2)) div (x + 2)))
A122922: 0 0 1 1 1 1 1 1 2 2 2 1 2 2 2 2
(x - ((x - ((~2 + (x div 2)) * (x div 2))) div (x + 2)))
A103303: 0 1 2 3 4 5 6 7 8 9
A191878-A028964: 0 1 2 3 4 5 6 7 8 9 11 12 13 14 16 17
((x * (3 + (((x + 1) div 2) div 2))) div (x + 2))
A176844: 0 1 1 2 2 2 3 3 4 4 4 5 5 5 5 6
(1 - ((x * (~2 + ((~x + 2) div 4))) div (x + 2)))
A228720-A225559-A085089-A069924: 1 2 2 3 3 4 4 5 5 5 5 6 6 6 6 7
(2x + (4 mod (1 + (x div 5))))
A118070: 0 2 4 6 8 10 12 14 16 18 21 23 25 27 29 30
(2x + ((~2x + 1) div 7))
A083034: 0 1 3 5 7 8 10 12 13 15 17 19 20 22 24 25
(2x + (5 * (1 + (x div 4))))
A283771: 5 7 9 11 18 20 22 24 31 33 35 37 44 46 48 50
(2x + ((x2 + 2x + 2) div (1 + (x mod 2))))
A087420: 2 4 14 14 34 28 62 46 98 68 142 94 194 124 254 158
(1 + (((x2 + x) div 2) + (2 mod (~2x + 1))))
A016028: 1 2 3 4 6 9 13 18 24 31 39 48 58 69 81 94
(2x + ((x - (x div 9)) div 2))
A022849: 0 2 5 7 10 12 15 17 20 22 24 27 29 32 34 37
(2x + (((1 + (x div 2)) mod 5) mod 2))
A158705: 1 3 4 6 9 11 12 14 16 18 21 23 24 26 29 31
(2x + ((x - (x div 12)) mod 2))
A227148: 0 3 4 7 8 11 12 15 16 19 20 23 25 26 29 30
(2x + ((~x + 2) div (2 - (x div ~4))))
A049039: 1 2 4 5 7 9 11 12 14 16 18 20 22 24 26 27
(2x + (((x div 2) - (x div 8)) mod 2))
A158704: 0 2 5 7 8 10 13 15 17 19 20 22 25 27 28 30
(2x + (x2 div (~x + ~6)))
A188916: 0 1 3 5 6 7 9 10 11 12 13 14 16 17 18 19
(2x + ((x - ((2 mod (~x2 + 2)) div 2)) div 2))
A267531: 0 2 5 9 13 18 23 29 35 42 49 57 65 74 83 93
(2x + ((x + ((x mod (1 + (x div 2))) div 2)) div 2))
A090909: 0 2 5 7 10 13 15 18 20 23 26 28 31 34 36 39
(2x + ((2x div (1 + (x div 2))) * (x div 2)))
A191873: 0 2 6 9 12 16 21
(3x + (((x * (x div 2)) mod 2) + (x mod 2)))
A180713: 0 4 6 11 12 16 18 23 24 28 30 35 36 40 42 47
(10x3 + ~6x2)
A006592: 0 4 56 216 544 1100 1944 3136 4736 6804 9400 12584 16416 20956 26264 32400
(14x2 + ~11x)
A195021: 0 3 34 93 180 295 438 609 808 1035 1290 1573 1884 2223 2590 2985
(3x + (2x div ~7))
A022843: 0 2 5 8 10 13 16 19 21 24 27 29 32 35 38 40
((6 * (x + (x div 4))) - (x div 2))
A184550: 0 6 11 17 28 34 39 45 56 62 67 73 84 90 95 101
((3 * ((2x + 4) + (x mod 2))) - (x div 2))
A248378: 12 21 23 32 34 43 45 54 56 65 67 76 78 87 89 98
((3 * (x + (4 * (x mod 2)))) + (x div 2))
A168211: 0 15 7 22 14 29 21 36 28 43 35 50 42 57 49 64
(1 + ((x mod ((x2 + 2) div (x + 2))) + (x div 2)))
A317442: 1 1 2 3 4 5 6 6 7 7 8 8 9 9 10 10
(x - (((~3x + ~1) + (x div 2)) * (x div 2)))
A210982: 0 1 8 12 26 33 54 64 92 105 140 156 198 217 266 288
(((x + 1) * (1 + ((x + 2) * (x mod 2)))) - (x div 2))
A308217: 1 8 2 23 3 46 4 77 5 116 6 163 7 218 8 281
(((x * (2 + (x2 div 2))) div (x + 1)) + (x div 2))
A340528: 0 1 3 5 10 13 20 25 34 41 52 61 74 85 100 113
(((x2 div 7) mod 2) + (x div 2))
A194175: 0 0 1 2 2 3 4 4 5 5 5 6 6 6 7 7
((((x + ~2) mod (1 + ((x + 1) div 2))) mod 2) + (x div 2))
A180101: 0 1 1 2 2 3 3 3 5 5 5 5 7 7 7 7
((2 * ((1 - (x div 2)) div 5)) + (x div 2))
A340321-A332250: 0 0 1 1 0 0 1 1 2 2 3 3 4 4 3 3
(((~x + 2) div (2 + (x div 5))) + (x div 2))
A035386: 1 0 1 0 1 1 1 1 2 1 3 2 3 3 4 4
(x - (((x div 4) - ((x + ~1) div 2)) * (x div 2)))
A340448: 0 1 2 4 4 7 9 13 12 17 20 26 24 31 35 43
(x - (x2 div ((2x + 8) - (x div 2))))
A336112: 0 1 2 3 3 4 4 5 5 6 6 7 7 7 8 8
(((1 + ((x + 1) div 2)) * (x div 4)) - (x div 2))
A131804: 0 0 ~1 ~1 1 2 1 2 6 8 7 9 15 18 17 20
(x2 - (((2x + 2) + (x div 2)) * (x div 2)))
A317300: 0 1 ~3 0 ~8 ~3 ~15 ~8 ~24 ~15 ~35 ~24 ~48 ~35 ~63 ~48
(x - ((x2 + ~2) div ((~2x + 4) - (x div 2))))
A285667: 1 2 4 6 7 8 10 11 12 14 15 17 18 19 21 22
(x + (((x2 + 1) div (2 + (x div 2))) + (x div 2)))
A226596: 0 2 4 7 10 13 16 20 22
(x + ((1 mod (8 - (x div 2))) + (x div 2)))
A284602: 1 2 4 5 7 8 10 11 13 14 16 17 19 20 21 22
((1 + ((x div 2) mod (1 + (x mod 4)))) * (x mod 2))
A053389: 0 1 0 2 0 1 0 4 0 1 0 2 0 1 0 4
((1 + ((x div (2 + ((x div 2) mod 2))) mod 2)) * (x mod 2))
A191254: 0 1 0 2 0 1 0 1 0 1 0 2 0 1 0 2
((15x + 5) - (x mod 2))
A255413: 5 19 35 49 65 79 95 109 125 139 155 169 185 199 215 229
((9 * (x2 div 2)) + (x mod 2))
A195147: 0 1 18 37 72 109 162 217 288 361 450 541 648 757 882 1009
((2 * (x div (1 + (2 * (2 + (x mod 2)))))) + (x mod 2))
A156723: 0 1 0 1 0 1 2 3 2 3 4 3 4 3 4 5
((((~x + 1) div (1 + (x mod 4))) mod 2) - (x mod 2))
A260971: 1 ~1 1 0 1 ~1 0 ~1 1 ~1 1 0 1 ~1 1 ~1
(((1 + ((x div 2) + (x mod 3))) div 2) * (x mod 2))
A137899: 0 1 0 1 0 2 0 2 0 2 0 4 0 4 0 4
((4 * ((x div 5) mod 2)) + (x mod 2))
A093348: 0 1 0 1 0 5 4 5 4 5 0 1 0 1 0 5
((8 * ((x div 3) mod 2)) + (x mod 2))
A021095: 0 1 0 9 8 9 0 1 0 9 8 9 0 1 0 9
((2 * (2 - ((x mod (2 + (x mod 2))) div 2))) - (x mod 2))
A231475: 4 3 4 3 4 1 4 3 4 3 4 1 4 3 4 3
(2 div ((2x + 2) mod (8 + (x mod 2))))
A280542-A275001: 1 0 0 0 1 0 0 0 1 1 0 0 1 2 0 0
(1 - ((x mod 2) + (2 * (x div (~2 + ((~x + 1) div 2))))))
A078759: 1 2 3 2 3 4 5 4 5 4 5 4 5 4 5 4
(((x + 2) div 3) - ((x mod 2) + (x div 4)))
A238097-A066955: 0 0 1 0 1 0 1 1 1 0 2 1 1 1 2 1
(x - ((~x + (x mod 10)) * (x mod 2)))
A103303: 0 1 2 3 4 5 6 7 8 9
A341935: 0 1 2 3 4 5 6 7 8 9 10 21 12 23 14 25
((x + compr(\x.(x mod (1 + (x div 8))),x)) div 2)
A103303: 0 1 2 3 4 5 6 7 8 9
A154771: 0 1 2 3 4 5 6 7 8 9 11 12 15 17 19 21
((~x + compr(\x.(x mod (1 + (x div 8))),x)) div 2)
A154781: 0 0 0 0 0 0 0 0 0 0 1 1 3 4 5 6
((5x3 + ~3x2) div 2)
A006597: 0 1 14 54 136 275 486 784 1184 1701 2350 3146 4104 5239 6566 8100
((x2 + 27x) div 2)
A132756: 0 14 29 45 62 80 99 119 140 162 185 209 234 260 287 315
((11x2 + 3x) div 2)
A254963: 0 7 25 54 94 145 207 280 364 459 565 682 810 949 1099 1260
((2x5 + ~x4 + x2) div 2)
A100242: 0 1 26 207 904 2825 7146 15631 30752 55809 95050 153791 238536 357097 518714 734175
((x5 + ~x4 + x3 + x2) div 2)
A101376: 0 1 14 99 424 1325 3366 7399 14624 26649 45550 73931 114984 172549 251174 356175
((x7 + x2) div 2)
A168123: 0 1 66 1098 8200 39075 139986 411796 1048608 2391525 5000050 9743646 17915976 31374343 52706850 85429800
(4x3 + 9x2 + 8x + 2)
A131464: 2 23 86 215 434 767 1238 1871 2690 3719 4982 6503 8306 10415 12854 15647
((x + (((x + 1) + (x div 2)) * (x + (x div 2)))) div 2)
A210981: 0 1 7 11 23 30 48 58 82 95 125 141 177 196 238 260
(((x + 1) * (2x + (x mod 2))) + (x2 div 2))
A273365: 0 6 14 32 48 78 102 144 176 230 270 336 384 462 518 608
((x7 + x3) div 2)
A168179: 0 1 68 1107 8224 39125 140076 411943 1048832 2391849 5000500 9744251 17916768 31375357 52708124 85431375
(~x * (x div (~2 + ((1 - (x div 2)) div 3))))
A166447: 0 1 2 6 8 10 12 21 24 27 30 33 36 52 56 60
compr(\x.(~1 + (x mod (1 + ((x + ~1) mod 8)))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A334967-A333223: 0 1 2 3 4 5 6 7 8 9 10 12 15 16 17 18
(x - (1 mod ((~x + 1) + (x mod 9))))
A004837: 0 1 2 3 4 5 6 7 8 16 17 18 19 20 21 22
(11x2 + ~9x)
A152997: 0 2 26 72 140 230 342 476 632 810 1010 1232 1476 1742 2030 2340
compr(\x.(~1 + ((x2 + ~x) mod (1 + (x div 4)))),x)
A084689: 0 1 2 3 4 5 6 7 9
A254636: 0 1 2 3 4 5 6 7 9 10 12 13 16 18 21 22
(x * (~1 + ((1 + (x div (2 - (x mod 2)))) mod 3)))
A100050: 0 1 2 0 ~4 ~5 0 7 8 0 ~10 ~11 0 13 14 0
(x + (x mod ((x + ~1) - (x mod 12))))
A103303: 0 1 2 3 4 5 6 7 8 9
A032516: 0 1 2 3 4 5 6 7 8 9 10 11 13 15 17 19
(15x2 + ~13x)
A263226: 0 2 34 96 188 310 462 644 856 1098 1370 1672 2004 2366 2758 3180
(x + (2 div (5 - ((x + ~2) div 3))))
A103303: 0 1 2 3 4 5 6 7 8 9
A239348-A154314: 0 1 2 3 4 5 6 7 8 9 10 12 13 14 16 17
compr(\x.(1 + (x mod 4) - ((x div 2) div 3)),x)
A331801: 8 12 13 16 17 18 20 21 22 24 25 26 27 28 29 30
((x + 1) + compr(\x.((x div 4) mod 2),(x div 3)))
A023705: 1 2 3 5 6 7 9 10 11 13 14 15 21 22 23 25
(9x3 + 12x2 + ~x)
A299965: 0 20 118 348 764 1420 2370 3668 5368 7524 10190 13420 17268 21788 27034 33060
(14x2 + 13x)
A195028: 0 27 82 165 276 415 582 777 1000 1251 1530 1837 2172 2535 2926 3345
(x5 + 5x3 + 5x)
A261391: 0 11 82 393 1364 3775 8886 18557 35368 62739 105050 167761 257532 382343 551614 776325
compr(\x.(x mod ((x + 1) - (x mod 10))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A076641: 0 1 2 3 4 5 6 7 8 9 11 21 31 41 51 61
compr(\x.(x mod (1 + (2 * ((x2 div 2) mod 3)))),x)
A254614: 0 1 3 5 6 7 9 10 11 12 13 15 17 18 19 20
compr(\x.((x * (x mod 3)) mod 7),x)
A176409: 0 3 6 7 9 12 14 15 18 21 24 27 28 30 33 35
compr(\x.((x div 4) - (x mod 7)),x)
A329297: 0 1 2 3 4 5 6 9 10 11 12 13 18 19 20 27
compr(\x.(1 - (x mod (1 + (x2 mod 6)))),x)
A097904: 1 2 3 4 5 7 8 9 11 13 14 15 16 17 19 21
(x + (2 div (5 - (((x + 1) div 2) div 2))))
A103303: 0 1 2 3 4 5 6 7 8 9
A125705: 0 1 2 3 4 5 6 7 8 9 10 12 13 14 15 17
(x2 + 29x)
A132771: 0 30 62 96 132 170 210 252 296 342 390 440 492 546 602 660
(x * (x div (~x + 19)))
A308854: 0 0 0 0 0 0 0 0 0 0 10 11 12 26 28 45
compr(\x.((x + ~2) mod (1 + (2 * (x mod (2 + (x mod 2)))))),x)
A153276: 0 2 3 4 6 8 9 10 12 14 15 16 17 18 20 21
compr(\x.(1 + (x mod 2) - ((~1 + (x div 2)) mod 4)),x)
A047509: 0 1 4 6 7 8 9 12 14 15 16 17 20 22 23 24
(x + (x2 mod (x - ((x + ~1) div 5))))
A067570: 0 1 2 3 4 5 7
A334273-A114994-A107686-A004743: 0 1 2 3 4 5 7 8 9 10 11 15 16 17 18 19
(x + ((x - (x2 div ~2)) div 5))
A165453: 0 1 2 4 6 8 10 13 16 19 22 25 28 32 36 40
(x + (5 * (2 + (2 mod (1 + (x div 2))))))
A244156: 10 11 12 13 24 25 26 27 28 29 30 31 32 33 34 35
(x + ((8x + 16) div 5))
A184659: 3 5 8 11 13 16 18 21 24 26 29 31 34 37 39 42
(x * (((1 + (x div 2)) * (x div 2)) div 5))
A308783: 0 0 0 0 4 5 12 14 32 36 60 66 96 104 154 165
compr(\x.(2 - ((x + (x div 3)) mod 5)),x)
A188094: 2 3 6 7 9 10 11 13 14 17 18 21 22 24 25 26
compr(\x.(1 - ((x * (x mod 3)) mod 5)),x)
A229829: 1 2 4 7 8 11 13 14 16 17 19 22 23 26 28 29
compr(\x.((x mod 6) * (x mod 5)),x)
A093509: 0 5 6 10 12 15 18 20 24 25 30 35 36 40 42 45
compr(\x.(3 - ((x2 div 2) mod (x + 4))),x)
A233746: 3 5 6 8 10 12 13 14 15 16 17 18 19 20 21 22
(x + ((~x2 + 2x + 1) div (x + 5)))
A255121-A238965-A143824-A036042: 0 1 2 2 3 3 3 4 4 4 4 4 5 5 5 5
(49x + 12)
A304205: 12 61 110 159 208 257 306 355 404 453 502 551 600 649 698 747
compr(\x.((1 + (x div 3)) mod (1 + (2 * (x mod 2)))),x)
A153282: 0 2 4 6 7 8 10 12 14 15 16 17 18 20 22 24
(x + 99)
A317592: 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114
(x + (3 * (2 mod (1 + (x mod (2 + (x mod 2)))))))
A325692: 0 1 2 3 4 11 6 7 8 9 10 17 12 13 14 15
(x + (x2 mod (9x + 9)))
A160942: 0 2 6 12 20 30 42 56 72 90 11 24 39 56 75 96
(19x2 + ~18x)
A261191: 0 1 40 117 232 385 576 805 1072 1377 1720 2101 2520 2977 3472 4005
(x + ((x2 - ((x + ~2) div 3)) div 3))
A235269: 0 1 3 6 9 13 17 23 28 35 42 50 59 68 78 88
compr(\x.(((~x + (x * (x mod 2))) div 3) mod 3),x)
A153309: 0 1 3 5 7 8 9 11 13 15 16 17 18 19 21 23
((x + 1) - (2 mod (~x + ((~x + 3) div 3))))
A223577: 1 2 3 5 8 10 12 15 17 19 22 24 26 29 31 33
(49x + 48)
A044567: 48 97 146 195 244 293 342 391 440 489 538 587 636 685 734 783
compr(\x.((x mod 2) - (((~1 + (x div 2)) div 2) mod 3)),x)
A039240: 0 1 2 4 6 7 8 9 10 11 12 13 14 16 18 19
(x + (((x + (x div 2)) * ((x + ~1) div 2)) div 3))
A327094: 0 1 2 4 6 9 12 17 20
compr(\x.(x - (6 * (x mod 6))),x)
A023775: 0 1 2 3 4 5 8 9 10 11 15 16 17 22 23 29
(x + ((2 * ((x - (x div 4)) div 2)) div 3))
A039148: 0 1 2 3 4 6 7 9 10 11 12 13 14 16 17 19
(x + ((2 * (x2 - (x mod 4))) div 3))
A222010: 0 1 3 7
A161210: 0 1 3 7 14 21 28
(1 - (x div ((~x + 1) - (x mod 12))))
A337301: 1 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2
(x + ((x3 + 6x2 + 8x) div 3))
A180118: 0 6 18 38 68 110 166 238 328 438 570 726 908 1118 1358 1630
(x + (((~x2 + 2x) div (2 + (x div 2))) div 3))
A176843-A071542: 0 1 2 2 3 3 4 4 5 5 6 6 7 7 7 7
(x + (3 * ((x + 2) + (3 * (x div 2)))))
A212161: 6 10 23 27 40 44 57 61 74 78 91 95 108 112 125 129
compr(\x.(1 - (((x div 3) + (x div 2)) mod 3)),x)
A145266: 2 3 6 7 9 10 11 12 13 14 16 17 20 21 24 25
(x * (x div (3 * (8 - (x div 2)))))
A326627: 0 0 0 0 0 0 0 0 0 0 10 11 24 26 56 75
(x + ((x + ((x + (x mod 2)) div 3)) div 3))
A062005: 0 1 2 4 5 7 8 10 11 13 14 16 17 18 20 21
(x + (x2 div ((2x + 4) + (x mod 3))))
A087067: 0 1 2 3 5 6 8 9 10 12 14 15 17 18 19 21
(2x2 + 19x + 36)
A187989: 36 57 82 111 144 181 222 267 316 369 426 487 552 621 694 771
compr(\x.(~1 + ((1 + (x div 2)) mod 4) - (x mod 2)),x)
A047559: 0 1 3 6 7 8 9 11 14 15 16 17 19 22 23 24
compr(\x.(~1 + (((~x + 2) div 2) mod 4) - (x mod 2)),x)
A192225: 0 1 2 5
A047483: 0 1 2 5 7 8 9 10 13 15 16 17 18 21 23 24
((x + 1) - (x mod ((~x2 + 2x + 1) - (x mod 2))))
A118841: 1 2 3 4 8 16
(x + ((x3 div 2) div (3x + 1)))
A032514: 0 1 2 4 6 8 11 14 18 22 26 30 35 40 45 51
((~x + 1) - (x2 div ((~x + ~1) + (x div 3))))
A105590: 1 1 1 1 1 1 3 3 3 4 4 4 5 5 5 7
(x + (2 div (1 + (x div (~x + 16)))))
A100637: 2 3 4 5 6 7 8 9 9 10 11 11 12 13 14 15
(x * (((x + 2) mod 12) mod (x + 1)))
A103303: 0 1 2 3 4 5 6 7 8 9
A321243-A067079: 0 1 2 3 4 5 6 7 8 9 0 11 24 39 56 75
(x + ((2 + ((x2 div 2) mod 4)) mod (x + 1)))
A124194: 0 1 3 5 6 7 10 9
(x + ((x + 1) * (2 + ((x3 + x) div 2))))
A129669: 2 7 23 71
(x + ((x - (x mod 11)) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A004839: 0 1 2 3 4 5 6 7 8 9 10 16 17 18 19 20
compr(\x.(~2 + ((x div 2) div (1 + (x mod 6)))),x)
A067570: 0 1 2 3 4 5 7
A023748: 0 1 2 3 4 5 7 8 9 10 11 14 15 16 17 21
compr(\x.((x - (x div (1 + ((x + 2) mod 4)))) mod 2),x)
A029598-A028968-A028962: 0 2 3 5 6 7 8 10 11 12 13 14 15 18 19 20
(x + (2 * ((3 * (x div 2)) div 5)))
A161824: 0 1 2 3 6 7 8 9 12 13 16 17 18 19 22 23
(x + (1 mod (1 - (2 * (2x div 5)))))
A325933: 0 1 2 3 4 3 4 5 4 5 4 5 6 5 6 5
compr(\x.(~2 + (x mod (2 - ((~x + 1) div 5)))),x)
A010432: 0 1 2 3 4 5 6 8 9 10 12 15 16 18 19 20
(x + (2x div (~2 + (x div ~6))))
A096336: 0 0 0 1 1 1 2 3 4 4 5 5 6 7 8 9
compr(\x.(1 - (x2 mod (2 + ((x div 2) div 3)))),x)
A071977: 1 3 5 7 8 10 11 13 15 17 18 19 21 22 23 25
compr(\x.(((x + 1) mod 2) - (((x div 2) div 3) mod 2)),x)
A194370: 1 3 5 6 7 8 9 10 11 13 15 17 18 19 20 21
(x6 + 6x)
A180356: 0 7 76 747 4120 15655 46692 117691 262192 531495 1000060 1771627 2986056 4826887 7529620 11390715
((x + 1) - (2 mod (2 - ((x - (x mod 3)) div 2))))
A135578: 1 2 3 4 5 6 7 8 9 10 11 12 15 16 17 19
compr(\x.((1 + ((x + ((x div 2) div 3)) div 2)) mod 2),x)
A120752: 2 3 6 9 10 12 13 16 17 19 20 23 26 27 30 33
compr(\x.((1 + ((x + (x div 8)) div 2)) mod 2),x)
A190847: 2 3 6 7 9 10 13 14 16 17 20 21 24 27 28 31
(x * ((x3 + x2 + ~5x + 3) div 2))
A144298: 0 0 4 36 124 320 672 1260 2152 3456 5260 7700 10884 14976 20104 26460
(x + (((1 - (x div 4)) mod (1 + (x div 2))) div 2))
A084690: 0 1 2 3 4 5 6 7 10
A035060: 0 1 2 3 4 5 6 7 10 11 12 13 14 15 17 18
(x + (((x + 1) * (2 + ((x + (x div 2)) div 2))) div 2))
A083462: 1 3 6 11
A099951: 1 3 6 11 16 20
(x + (((x2 + x) div ~8) mod 2))
A093505: 0 2 3 3 5 5 6 8 9 9 10 12 12 14 15 15
(x + ((((2 - (x div 2)) mod (2x + 1)) div 2) div 2))
A118732: 0 1 2 3 4 5 9 10 11 13 14 16 17 18 20 21
(x * (((~1 + ((x + ~1) div 2)) * ((x + ~1) div 2)) div 2))
A060423: 0 0 0 0 0 5 6 21 24 54 60 110 120 195 210 315
(x + (((x + (x div 2)) div 2) * (((x + ~1) div 2) div 2)))
A296161: 0 1 2 3 4 8 10 12 14 21 24 27 30 40 44 48
compr(\x.(2 + (x mod (~2 + (4 * (~2 + (x mod 2)))))),x)
A330120-A330108-A330104-A330060-A320456: 1 2 3 4 6 7 8 9 12 13 14 15 16 18 19 21
(x + ((~x2 + 1) div 32))
A268680: 0 1 1 2 3 4 4 5 6 6 6 7 7 7 7 8
(x + (((x - (x mod (2 + (x div 4)))) div 2) div 2))
A067570: 0 1 2 3 4 5 7
A039202: 0 1 2 3 4 5 7 8 10 11 12 13 14 15 16 18
29x2
A244635: 0 29 116 261 464 725 1044 1421 1856 2349 2900 3509 4176 4901 5684 6525
(x - ((x2 + ~2) div (x + 16)))
A047783: 1 2 2 3 4 4 5 5 6 6 7 7 7 8 8 8
(x + ((x + 2) div (~x + 18)))
A084689: 0 1 2 3 4 5 6 7 9
A294295: 0 1 2 3 4 5 6 7 9 10 11 12 14 16 18 20
(1 - (1 mod ((~x + 4) + ((~x + 1) mod 4))))
A161838: 0 0 0 0 1 1 1 1 3 5
compr(\x.(1 - (x2 mod (2 * (2 + (x div 4))))),x)
A155935: 1 3 4 5 7 9 10 11 12 13 14 15 16 17 19 20
compr(\x.((x div (2 * (~2 + ((x * (x div 2)) mod 2)))) mod 2),x)
A047583: 0 3 5 6 7 8 11 13 14 15 16 19 21 22 23 24
(x - ((x2 + x + ~1) div (x + 8)))
A098388: 1 1 2 2 3 3 4 4 4 4 4 5 5 5 5 5
(1 - ((~x2 + ~x + 2) div (x + 8)))
A281957: 1 1 2 2 3 4 4 5 6 7 7 8 9 10 11 12
(1 - ((~2x2 + 4x) div (x + 8)))
A067175: 1 1 1 2 3 4 5 6 7 9 10 12 13 15 17 18
(~x2 + ~x + 72)
A110678: 72 70 66 60 52 42 30 16 0 ~18 ~38 ~60 ~84 ~110 ~138 ~168
(x * (1 - ((~x2 + 2) div (x + 6))))
A119638: 0 1 4 6 12 20 24 35 48 63 80 88 108 130 154 180
compr(\x.(x - (2 * ((~x2 + 2x) mod (2x + 4)))),x)
A073849: 0 1 3 4 5 6 8 10 12 13 14 15 16 17 18 19
(6x2 + 19x + 20)
A228319: 20 45 82 131 192 265 350 447 556 677 810 955 1112 1281 1462 1655
(x + ((((x mod 5) + (x div 2)) div 2) div 2))
A140202: 0 1 2 4 5 5 7 8 9 11 11 12 14 15 16 16
(x div ((~x + 2) + ((x2 + 1) div (2 + (x div 2)))))
A319610: 0 0 2 1 2 1 2 1 2 1 1 1 1 1 1 1
(x + (((~x + (x div 3)) mod (2 + (x div 2))) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A247144: 0 1 2 3 4 5 6 7 8 9 10 14 12 16 18 19
(x + ((x + ((1 - (x div 2)) mod 4)) div 4))
A039142: 0 1 2 3 5 7 8 9 10 11 12 13 15 17 18 19
(x + (2 * ((x + 2) + ((x + (x div 4)) div 2))))
A190442: 4 7 12 15 20 25 28 33 38 41 46 49 54 59 62 67
(x * (4 + (x * (2x2 + (x div 2)))))
A258156: 0 6 44 183
(x + (2 * (2x + ((x mod (1 + (x div 2))) div 2))))
A045682: 0 5 10 15 20 27 32 37 42 49 54 59 64 71 76 81
(x + ((x + (x div 2) - (x mod 8)) div 2))
A197433: 0 1 2 3 5 6 7 8 14 15 16 17 19 20 21 22
(1 + (((x + 1) mod 3) + (x * (2 + (x div 2)))))
A134641: 2 5 7 11 19
(x + ((x + (((~x + 2) mod 4) + (x div 2))) div 2))
A047286: 1 2 3 6 8 9 10 13 15 16 17 20 22 23 24 27
(x + ((x + ((x + ~1) mod (1 + (x div 3)))) div 2))
A135215: 0 1 3 4 6 7 10 10 12 13 15
(x + ((x + ((x div 2) div ~6)) div 2))
A240977: 0 1 2 4 5 7 8 10 11 13 14 16 17 19 20 21
(x + ((x + (((x + (x div 2)) div 4) mod 2)) div 2))
A026430: 0 1 3 5 6 8 9 10 12 14 15 16 18 19 21 23
(x6 + x3 + 2x2 + 2x)
A054605: 0 6 84 780 4200 15810 46956 118104 262800 532350 1001220 1773156 2988024 4829370 7532700 11394480
(x + ((((x + 1) div 3) * (x + (x div 2))) div 2))
A070334: 0 1 3 5 7 12 15
(x + ((10x + 10) div (x + 2)))
A165513: 5 7 9 11 12 13 14 15 17 18 19 20 21 22 23 24
(x + ((1 + (x * (4 mod (x + 1)))) div (x + 2)))
A088414: 0 1 2 3 6 8
A321883: 0 1 2 3 6 8 9 10 11 12 13 14 15 16 17 18
(x + ((2 - (x mod (2 + (x mod 3)))) div (x + 2)))
A130024: 1 1 2 3 4 5 6 7 8 9 10 10 12 13 14 15
(x + ((x * (2 + (3 mod (x + 2)))) div (x + 2)))
A138887: 0 1 4 6 7 8 9 10 12 13 14 15 16 17 18 19
compr(\x.(((x mod 9) mod 2) - (x mod 2)),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A191839: 0 1 2 3 4 5 6 7 8 9 11 13 15 17 18 19
(((2x + 1) - (x div ~2)) * (x + (x mod 2)))
A132356: 0 8 12 36 44 84 96 152 168 240 260 348 372 476 504 624
(((x3 + 2x) div 3) - (x * (x mod 2)))
A212686: 0 0 4 8 24 40 76 112 176 240 340 440 584 728 924 1120
49x2
A016982: 0 49 196 441 784 1225 1764 2401 3136 3969 4900 5929 7056 8281 9604 11025
(x + (x mod (~x + ((x + ~1) mod 9))))
A103303: 0 1 2 3 4 5 6 7 8 9
A043270: 0 1 2 3 4 5 6 7 8 9 10 2 4 6 8 10
((x + 1) - (2 mod ((~x + 2) - (2x div 3))))
A193622: 1 2 3 5 7 10
A096221: 1 2 3 5 7 10 13 15 18
(x + ((x2 + x) div (x + 16)))
A218442: 0 1 2 3 5 6 7 9 11 12 14 15 17 19 21 22
(x + ((x2 + 3x + 2) div (x + 8)))
A135251: 0 1 3 4 6 8 10
A300997: 0 1 3 4 6 8 10 11 13 15 17 19 21 23 24 26
(x2 + (x2 div 11))
A152785: 0 1 4 9 17 27 39 53 69 88 109 132 157 184 213 245
(x2 + (9 * (x2 div 2)))
A195149: 0 1 22 45 88 133 198 265 352 441 550 661 792 925 1078 1233
(x2 + (x div (~2 + ((1 - (x div 2)) div 3))))
A213077: 0 0 3 7 14 23 34 46 61 78 97 118 141 165 192 221
loop(\(x,i).loop(\(x,i).loop(\(x,i).loop(\(x,i).(x * i),i,x),i,x),i,x),x,1)
A057527: 1 1 2 48 331776 79254226206720 4611686018427387903 4611686018427387903
(if (x mod 2) <= 0 then (if ((if x <= 0 then 1 else x) mod 3) <= 0 then 2 else 1) else 0)
A133565: 1 0 1 0 1 0 2 0 1 0 1 0 2 0 1 0
loop(\(x,i).(if x <= 0 then 1 else loop(\(x,i).(x * i),i,x)),(x2 + x),0)
A296627: 0 2 24883200 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x + loop(\(x,i).(x * i),i,1)),i,~x),x,0)
A341900: 0 1 2 7 26 127 746 5167 41066 368047 3669866 40284847 482671466 6267305647 87660962666 1313941673647
loop(\(x,i).(x + i),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),0)
A112367: 0 0 1 0 1 3 0 1 3 6 0 1 3 6 10 0
loop(\(x,i).(x + loop(\(x,i).(if (~x + i) <= 0 then x else 2x),i,1)),x,0)
A222010: 0 1 3 7
A181497: 0 1 3 7 11 19 27 35 43 59 75 91 107 123 139 155
(if x <= 0 then 1 else loop(\(x,i).(x + loop(\(x,i).(x * (2 + i)),i,2)),x,0))
A054117: 1 6 30 150 870 5910 46230 409110 4037910 43954710 522956310 6749977110 93928268310 1401602636310 22324392524310 378011820620310
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).i,(x div 4),x),1,i)),x,0)
A073850: 0 1 3 6 7 8 9 10 12 14 16 18 21 24 27 30
loop(\(x,i).(x + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),i,i)),x,0)
A111138: 0 0 1 1 2 4 4 5 7 10 10 11 13 16 20 20
(~1 + loop(\(x,i).2x,x,(if loop(\(x,i).(~x + i),x,2) <= 0 then 1 else 2)))
A290683: 1 1 7 7 31 63 127 255 511 1023 2047 4095 8191 16383 32767 65535
loop(\(x,i).x2,1,loop(\(x,i).2x,x,(1 + (if x <= 0 then 1 else 2))))
A183354: 4 36 144 576 2304 9216 36864 147456 589824 2359296 9437184 37748736 150994944 603979776 2415919104 9663676416
(loop(\(x,i).2x,x,2) - (if loop(\(x,i).(~x + i),x,2) <= 0 then 2 else 1))
A290682: 1 2 7 14 31 63 127 255 511 1023 2047 4095 8191 16383 32767 65535
(~1 + loop(\(x,i).loop(\(x,i).2x,loop(\(x,i).(x * i),i,1),1),x,2))
A135444: 1 1 3 63
A175985: 1 1 3 63 16777215 4611686018427387903
loop(\(x,i).loop(\(x,i).2x,i,x),x,(~1 + loop(\(x,i).2x,x,2)))
A122743: 1 6 56 960 31744 2064384 266338304 68451041280 35115652612096 35993612646875136 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 2 else loop(\(x,i).loop(\(x,i).(x * (1 + i)),i,x),2x,1))
A280734: 2 12 34560 125411328000 4611686018427387903 4611686018427387903
(if loop(\(x,i).x2,x,x) <= 0 then 2 else (1 + loop(\(x,i).x2,x,2)))
A290200-A269834: 2 5 17 257 65537
A111635: 2 5 17 257 65537 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + loop(\(x,i).(if x <= 0 then i else (x + ~1)),i,0)),x,1)
A255748: 1 3 4 8 11 13 14 22 29 35 40 44 47 49 50 66
loop(\(x,i).loop(\(x,i).(x * (x div (if i <= 0 then 1 else i))),x,(1 + i)),x,1)
A165812: 1 4 46656 4611686018427387903
loop(\(x,i).(1 - loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x)),2,(x + 1))
A220465: 1 2 1 1 2 1 3 1 2 1 2 3 1 2 1 1
compr(\x.loop(\(x,i).loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0),2,x),(x + 1))
A300630-A277704-A082752: 1 2 3 4 6 7 8 12 14 15 16 24 28 30 31 32
loop(\(x,i).2x,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1)
A059268: 1 1 2 1 2 4 1 2 4 8 1 2 4 8 16 1
loop(\(x,i).(2 * i),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1)
A168266: 1 1 2 1 2 4 1 2 4 6 1 2 4 6 8 1
loop(\(x,i).(i div 2),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1)
A133734: 1 1 0 1 0 1 1 0 1 1 1 0 1 1 2 1
loop(\(x,i).(x * i),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1)
A233543: 1 1 1 1 1 2 1 1 2 6 1 1 2 6 24 1
loop(\(x,i).loop(\(x,i).(x + loop(\(x,i).(x * i),i,1)),i,(~x + 1)),x,1)
A136580: 1 1 3 7 27 127 747 5167 41067 368047 3669867 40284847 482671467 6267305647 87660962667 1313941673647
loop(\(x,i).(x + loop(\(x,i).x2,1,loop(\(x,i).(~x + i),i,1))),x,1)
A030533: 1 1 5 6 15 19 35 44 69 85 121 146 195 231 295 344
loop(\(x,i).(x - loop(\(x,i).((x + ~1) - (if x <= 0 then 0 else i)),x,x)),x,1)
A060985: 1 2 3 6 12 22 43 79 157 310 610 1205 2381 4727 9383 18699
loop(\(x,i).loop(\(x,i).(x + loop(\(x,i).2x,i,1) - i),i,x),x,1)
A088921: 1 2 5 13 33 80 185 411 885 1862 3853 7881 15993 32284 64945 130359
loop(\(x,i).x2,1,loop(\(x,i).(x * (if (i mod 2) <= 0 then 2 else i)),x,1))
A193282: 1 1 4 36 144 3600 14400 705600 2822400 228614400 914457600 110649369600 442597478400 74798973849600 299195895398400 67319076464640000
loop(\(x,i).loop(\(x,i).(2x + 1),i,loop(\(x,i).2x,i,x)),x,1)
A215172: 1 5 83 5319 1361679 1394359327 5711295803455 93573870443806847 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).2x,i,x),i,1)),x,0) div 2)
A246534: 0 1 5 37 549 16933 1065509 135283237 34495021605 17626681066021 18032025190548005 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else loop(\(x,i).(x2 + ~2x),1,loop(\(x,i).2x,x,2)))
A271061: 1 8 48 224 960 3968 16128 65024 261120 1046528 4190208 16769024 67092480 268402688 1073676288 4294836224
(if loop(\(x,i).x3,x,x) <= 0 then 1 else loop(\(x,i).2x,x,2))
A074025: 1 4 8 16 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).((x + 2) + i),i,x),i,1)),x,2)
A252814: 2 6 17 40 81 147 246 387 580 836 1167 1586 2107 2745 3516 4437
loop(\(x,i).(x - loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0)),3,x)
A038573: 0 1 1 3 1 3 3 7 1 3 3 7 3 7 7 15
loop(\(x,i).(x * i),x,(x + (if (x + ~2) <= 0 then (if x <= 0 then 1 else x) else 1)))
A052624: 1 2 8 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000 20922789888000
loop(\(x,i).loop(\(x,i).(x + loop(\(x,i).(x * i),i,1)),i,x),(x + ~1),x)
A222010: 0 1 3 7
A014144: 0 1 3 7 17 51 205 1079 6993 53227 462341 4500255 48454969 571411283 7321388397 101249656711
(loop(\(x,i).(x - (if (~x + i) <= 0 then i else 1)),x,x) + (if x <= 0 then 1 else x))
A134478: 1 1 2 2 3 4 3 4 5 6 4 5 6 7 8 5
(2 - loop(\(x,i).(2 + loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x)),2,x))
A335964-A055363: 1 1 0 1 0 0 1 1 0 0 1 2 1 0 0 1
loop(\(x,i).loop(\(x,i).(x + (if (~2 + i) <= 0 then 1 else x)),x,2),x,(~x + 2))
A343494: 2 3 4 16 65536
(if x <= 0 then 1 else loop(\(x,i).(if (i mod 2) <= 0 then 1 else 2x),(x + ~2),x))
A289203: 1 1 2 6 1 2 1 2 1 2 1 2 1 2 1 2
(if x <= 0 then 1 else loop(\(x,i).(loop(\(x,i).(x * i),i,x) + i),(x + ~2),x))
A319634: 1 1 2 4 12 87
loop(\(x,i).x2,1,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x))
A143844: 0 0 1 0 1 4 0 1 4 9 0 1 4 9 16 0
loop(\(x,i).x2,1,loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x))
A095831: 0 1 0 4 1 0 9 4 1 0 16 9 4 1 0 25
compr(\x.(1 - loop(\(x,i).loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0),2,x)),x)
A300669-A277706-A166934-A101082: 5 9 10 11 13 17 18 19 20 21 22 23 25 26 27 29
loop(\(x,i).(x + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),i,i)),x,x)
A332023: 0 1 3 4 6 9 10 12 15 19 20 22 25 29 34 35
(if (if ((x * (x div 2)) mod 4) <= 0 then (x + ~1) else 0) <= 0 then 1 else 0)
A264048-A110471: 1 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1
(if x <= 0 then 2 else (if (x mod 10) <= 0 then ~1 else 0))
A010106: 2 0 0 0 0 0 0 0 0 0 ~1 0 0 0 0 0
(if (if ((x mod 8) mod 3) <= 0 then x else 0) <= 0 then 1 else 0)
A050072: 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1
(if (if (x mod (2 - (x mod ~4))) <= 0 then x else 0) <= 0 then 1 else 0)
A117908: 1 1 1 0 0 0 1 1 0 1 1 1 0 1 1 0
(if (if (x mod (2 + ((x div 2) mod 4))) <= 0 then x else 0) <= 0 then 1 else 0)
A240009-A117904: 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0
(if (if (10 mod (x + 2)) <= 0 then x else 0) <= 0 then 1 else 0)
A175087-A050332: 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1
(if ((x + ~2) mod (1 + (x div 3))) <= 0 then (if x <= 0 then 0 else 1) else 0)
A342704: 0 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0
(if x <= 0 then 2 else (if ((x + ~2) mod 9) <= 0 then 1 else 0))
A307832: 2 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
(if (x mod 3) <= 0 then loop(\(x,i).2x,(x div 3),1) else 0)
A077958: 1 0 0 2 0 0 4 0 0 8 0 0 16 0 0 32
((x * loop(\(x,i).(x * i),(x + ~2),x)) + (if (x + ~1) <= 0 then 1 else 0))
A054119: 1 2 4 9 32 150 864 5880 46080 408240 4032000 43908480 522547200 6745939200 93884313600 1401079680000
(if (x mod 2) <= 0 then (if x <= 0 then 1 else (x div 7)) else 0)
A294142: 1 0 0 0 0 0 0 0 1 0 1 0 1 0 2 0
(if (~x + 2) <= 0 then (if (x mod (2 + (x mod 3))) <= 0 then 2 else 1) else 0)
A194636: 0 0 1 1 1 1 2 1 2 1 1 1 2 1 1 1
(if (x mod 3) <= 0 then (if ((x + ~1) mod 4) <= 0 then 2 else 1) else 0)
A341774: 1 0 0 1 0 0 1 0 0 2 0 0 1 0 0 1
(if (~x + 2) <= 0 then (if ((x div ~2) mod 4) <= 0 then 2 else 1) else 0)
A118164: 0 0 1 1 1 1 1 2 2 1 1 1 1 1 1 2
(if (~x + 4) <= 0 then loop(\(x,i).i,(x + ~8),1) else 0)
A033104: 0 0 0 0 1 1 1 1 1 1 2 3 4 5 6 7
(if (x + ~2) <= 0 then (~x + 1) else (if (x mod 8) <= 0 then 1 else 0))
A154271: 1 0 ~1 0 0 0 0 0 1 0 0 0 0 0 0 0
(if (x + ~2) <= 0 then 1 else (if (x mod (2 + (x mod 4))) <= 0 then 1 else 0))
A079295: 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1
loop(\(x,i).((x + 1) * (if x <= 0 then 1 else 2)),(x div 5),0)
A035627: 0 0 0 0 0 1 1 1 1 1 4 4 4 4 4 10
loop(\(x,i).(1 + loop(\(x,i).2x,x,1)),(x mod 5),0)
A254429: 0 2 5 33 8589934593
(if x <= 0 then 1 else (if (x mod 10) <= 0 then 3 else 0))
A269250: 1 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0
(if (x mod 4) <= 0 then ((2 - (if x <= 0 then 1 else x)) mod 3) else 0)
A325194-A073345: 1 0 0 0 1 0 0 0 0 0 0 0 2 0 0 0
loop(\(x,i).(~x + 1),(x div 2),(if (x mod 2) <= 0 then (1 + (x div 2)) else 0))
A166445: 1 0 ~1 1 3 0 ~3 1 5 0 ~5 1 7 0 ~7 1
(if (if (x mod 8) <= 0 then x else 0) <= 0 then (1 + (x mod 2)) else 0)
A078461: 1 2 1 2 1 2 1 2 0 2 1 2 1 2 1 2
loop(\(x,i).(2x + 1),(1 + (if (x mod 2) <= 0 then x else (~x + 1))),0)
A282413: 1 1 7 0 31 0 127 0 511 0 2047 0 8191 0 32767 0
(loop(\(x,i).(2 * (x + (i mod 2))),x,1) + (if (~x + 2) <= 0 then 1 else 0))
A133649: 1 4 9 19 37 75 149 299 597 1195 2389 4779 9557 19115 38229 76459
loop(\(x,i).((x + loop(\(x,i).(x * i),i,1)) * (2 + i)),(x + 1),0)
A000276: 3 20 130 924 7308 64224 623376 6636960 76998240 967524480 13096736640 190060335360 2944310342400 48503818137600 846795372595200 15618926924697600
loop(\(x,i).loop(\(x,i).(x + ((2 + i) * i)),(1 + i),x),(x + 1),0)
A217947: 11 37 87 172 305 501 777 1152 1647 2285 3091 4092 5317 6797 8565 10656
loop(\(x,i).(x + ((if (i mod 2) <= 0 then i else 1) * i * i)),(x + 1),0)
A140149: 1 9 18 82 107 323 372 884 965 1965 2086 3814 3983 6727 6952 11048
loop(\(x,i).(2x * i),x,loop(\(x,i).(x + (i * i)),(x + 1),0))
A014484: 1 10 112 1440 21120 349440 6451200 131604480 2941747200 71530905600 1880240947200 53137244160000 1606870263398400 51776930709504000 1771128112545792000 4611686018427387903
loop(\(x,i).(x + ((if (i mod 2) <= 0 then 1 else i) * i * i)),(x + 1),0)
A140154: 1 5 32 48 173 209 552 616 1345 1445 2776 2920 5117 5313 8688 8944
loop(\(x,i).(x * i),(x + ~1),loop(\(x,i).(2x + 2),(x + ~1),0))
A052867: 0 0 2 12 84 720 7440 90720 1280160 20563200 370863360 7424524800 163419379200 3923023104000 102011054745600 2856483889459200
loop(\(x,i).2x,(x + ~2),loop(\(x,i).(2x + i),(x + ~1),0))
A100575: 0 0 1 8 44 208 912 3840 15808 64256 259328 1042432 4180992 16748544 67047424 268304384
loop(\(x,i).(loop(\(x,i).(x * i),(~1 + i),2) + (x * i)),(x + ~1),0)
A052517: 0 0 2 6 22 100 548 3528 26136 219168 2053152 21257280 241087680 2972885760 39605518080 566931294720
((if (x mod 9) <= 0 then 2 else 0) + (if x <= 0 then 1 else 0))
A063667: 3 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0
(if ((x + 1) mod 12) <= 0 then 2 else (if x <= 0 then 1 else 0))
A110981: 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0
(loop(\(x,i).5x,x,4) + (if x <= 0 then 1 else 0))
A110595: 5 20 100 500 2500 12500 62500 312500 1562500 7812500 39062500 195312500 976562500 4882812500 24414062500 122070312500
(if (x mod 2) <= 0 then loop(\(x,i).(x * (~1 + ((i mod 2) + i))),x,1) else 0)
A177145: 1 0 1 0 9 0 225 0 11025 0 893025 0 108056025 0 18261468225 0
(if (x mod 5) <= 0 then (if (x mod 2) <= 0 then 1 else ~2) else 0)
A089814: 1 0 0 0 0 ~2 0 0 0 0 1 0 0 0 0 ~2
(if (x mod 2) <= 0 then 1 else (if (~1 + (x mod 5)) <= 0 then 2 else 0))
A191329: 1 2 1 0 1 2 1 0 1 0 1 2 1 0 1 2
(if x <= 0 then 1 else (if (x mod 13) <= 0 then 2 else 0))
A300715: 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
(if (x mod 2) <= 0 then (if (4 mod (1 + (x div 2))) <= 0 then 1 else 2) else 0)
A230642: 1 0 1 0 2 0 1 0 2 0 2 0 2 0 2 0
(if (x mod 4) <= 0 then (if (~2 + (x div 3)) <= 0 then 1 else 2) else 0)
A280751: 1 0 0 0 1 0 0 0 1 0 0 0 2 0 0 0
(if ((x div 2) mod 2) <= 0 then (if (~2 + (x div 3)) <= 0 then 1 else 2) else 0)
A137676: 1 1 0 0 1 1 0 0 1 2 0 0 2 2 0 0
(if (x mod 3) <= 0 then (if (~2 + (x div 4)) <= 0 then 1 else 2) else 0)
A079807: 1 0 0 1 0 0 1 0 0 1 0 0 2 0 0 2
(if (x mod 2) <= 0 then (if x <= 0 then 1 else ((1 + (x div 4)) div 2)) else 0)
A008614: 1 0 0 0 1 0 1 0 1 0 1 0 2 0 2 0
(if x <= 0 then 1 else (if (4x mod (x + 3)) <= 0 then 2 else 0))
A335379: 1 2 0 2 0 0 0 0 0 2 0 0 0 0 0 0
(if x <= 0 then 1 else (if (10 mod (x + 1)) <= 0 then 2 else 0))
A329266-A318985-A318984-A260676-A255258-A033759-A033755-A033753-A033749-A033743-A033741-A033735-A033731-A033729-A000122: 1 2 0 0 2 0 0 0 0 2 0 0 0 0 0 0
(if x <= 0 then 1 else (if (16 mod (x + 1)) <= 0 then 2 else 0))
A069517: 1 2 0 2 0 0 0 2 0 0 0 0 0 0 0 2
(if x <= 0 then 1 else (if ((~4 + (x div 2)) mod (x + 1)) <= 0 then 2 else 0))
A214304: 1 2 2 0 0 0 0 0 2 2 0 0 0 0 0 0
(if (x + ~1) <= 0 then 1 else (if (x mod 10) <= 0 then 2 else 0))
A257403: 1 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0
(if x <= 0 then 1 else (x - (if (x + ~2) <= 0 then ~7 else 0)))
A339800: 1 8 9 3
(if x <= 0 then 1 else (if (x mod 9) <= 0 then 4 else 0))
A217511: 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
(if (x mod 10) <= 0 then (if x <= 0 then 1 else 4) else 0)
A307380: 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
(if (x mod 3) <= 0 then (2 - (((if x <= 0 then 2 else x) div 2) mod 2)) else 0)
A341775: 1 0 0 1 0 0 1 0 0 2 0 0 2 0 0 1
(if x <= 0 then 0 else (1 - (if (x mod 3) <= 0 then (~2 + (x mod 2)) else 0)))
A137457: 0 1 1 2 1 1 3 1 1 2 1 1 3 1 1 2
loop(\(x,i).2x,x,(1 - loop(\(x,i).(2x + ~4),(x + ~2),0)))
A187468: 1 2 4 40 208 928 3904 16000 64768 260608 1045504 4188160 16764928 67084288 268386304 1073643520
loop(\(x,i).2x,(x + ~2),loop(\(x,i).(2x + i),(x + ~2),0))
A000431: 0 0 0 2 16 88 416 1824 7680 31616 128512 518656 2084864 8361984 33497088 134094848
(if x <= 0 then 1 else (if (x mod 12) <= 0 then (x div 2) else 0))
A331979: 1 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0
(if (x + ~1) <= 0 then 1 else (if (x mod 5) <= 0 then (x mod 2) else 0))
A256436: 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1
loop(\(x,i).(((x2 + 3x + 2) div 2) + (if x <= 0 then 0 else 1)),x,0)
A220788: 0 1 4 16
A226588: 0 1 4 16 154 12091 73114279 2672849006516341 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (2 * (x - (if (i mod 4) <= 0 then 2 else 0)))),x,0)
A222010: 0 1 3 7
A139814: 0 1 3 7 11 23 47 95 187 375 751 1503 3003 6007 12015 24031
loop(\(x,i).(3 * (x - (if (i mod 2) <= 0 then 2 else ~2))),x,0)
A120471: 0 6 12 42 120 366 1092 3282 9840 29526 88572 265722 797160 2391486 7174452 21523362
loop(\(x,i).2x,x,loop(\(x,i).(3x + 12),x,0))
A066406: 0 24 192 1248 7680 46464 279552 1678848 10076160 60463104 362790912 2176770048 13060669440 78364114944 470184886272 2821109710848
(1 - loop(\(x,i).2x,x,loop(\(x,i).(3x + ~6),x,0)))
A049294: 1 13 97 625 3841 23233 139777 839425 5038081 30231553 181395457 1088385025 6530334721 39182057473 235092443137 1410554855425
loop(\(x,i).x2,1,(1 - loop(\(x,i).(~3x + 6),x,0)))
A120096: 1 25 169 1681 14641 133225 1194649 10764961 96845281 871725625 7845176329 70607649841 635465659921 5719200505225 51472775849209 463255068736321
loop(\(x,i).~x,x,loop(\(x,i).(1 + (2 * (x + (x mod 2)))),x,0))
A344920: 0 ~1 5 ~13 29 ~61 125 ~253 509 ~1021 2045 ~4093 8189 ~16381 32765 ~65533
(loop(\(x,i).((x + 1) * i),x,0) + loop(\(x,i).(2x + 1),x,0))
A097967: 0 2 7 22 79 356 2019 13826 109855 986920 9865123 108507158 1302065439 16926805676 236975181187 3554627504842
(loop(\(x,i).x2,2,3) * loop(\(x,i).(2x + 1),x,0))
A335843: 0 81 243 567 1215 2511 5103 10287 20655 41391 82863 165807 331695 663471 1327023 2654127
loop(\(x,i).(x3 + 2x2),1,loop(\(x,i).(2x + 1),x,0))
A060242: 0 3 45 441 3825 31713 257985 2080641 16711425 133955073 1072692225 8585738241 68702695425 549688696833 4397778059265 35183298314241
loop(\(x,i).(x3 + ~2),1,loop(\(x,i).(2x + 1),x,0))
A098878: ~2 ~1 25 341 3373 29789 250045 2048381 16581373 133432829 1070599165 8577357821 68669157373 549554511869 4397241253885 35181150961661
loop(\(x,i).4x,(x + ~1),loop(\(x,i).(2x + 1),x,0))
A016152: 0 1 12 112 960 7936 64512 520192 4177920 33488896 268173312 2146435072 17175674880 137422176256 1099444518912 8795824586752
(loop(\(x,i).3x,x,1) + loop(\(x,i).(2x + 1),x,0))
A119683: 1 4 12 34
A005056: 1 4 12 34 96 274 792 2314 6816 20194 60072 179194 535536 1602514 4799352 14381674
(loop(\(x,i).3x,x,1) - loop(\(x,i).(2x + 1),x,0))
A083323: 1 2 6 20 66 212 666 2060 6306 19172 58026 175100 527346 1586132 4766586 14316140
(2 + loop(\(x,i).x2,x,2) - loop(\(x,i).(2x + 1),x,0))
A119562: 4 5 15 251 65523 4294967267 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(x2 + ~x),loop(\(x,i).(2x + 1),x,0))
A322556: 0 1 12 448 61440 32505856 67645734912 558551906910208 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).5x,x,loop(\(x,i).(2x + 1),x,0))
A248340: 0 5 75 875 9375 96875 984375 9921875 99609375 998046875 9990234375 99951171875 999755859375 9998779296875 99993896484375 999969482421875
loop(\(x,i).(x * i),(x + ~1),(x - loop(\(x,i).(2x + ~1),x,0)))
A052850: 0 2 5 20 114 864 8280 96480 1325520 20966400 374855040 7468070400 163938297600 3929729126400 102104460057600 2857878742118400
loop(\(x,i).(1 + (x * (1 + loop(\(x,i).(x2 + x),2,2)))),x,0)
A218746: 0 1 44 1893 81400 3500201 150508644 6471871693 278290482800 11966490760401 514559102697244 22126041415981493 951419780887204200 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,x,1) - loop(\(x,i).(3x + ~1),x,0))
A094374: 1 3 8 21 56 153 428 1221 3536 10353 30548 90621 269816 805353 2407868 7207221
loop(\(x,i).(x2 + 1),1,loop(\(x,i).(x2 + x + 1),x,0))
A063573: 1 2 10 170 33490 1133870930 1285739648704587610 4611686018427387903
loop(\(x,i).(~1 + (loop(\(x,i).(x * i),i,1) + (x * (1 + i)))),x,0)
A121633: 0 0 1 9 68 527 4408 40303 403046 4393339 51955528 663383135 9102982354 133668773755 2092209897524 34783032728383
loop(\(x,i).((x + 1) * loop(\(x,i).(x2 + 2x),(~1 + i),1)),x,0)
A048707: 0 1 6 105 27030 1771476585 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).4x,x,2) - (if (x + ~1) <= 0 then x else 0))
A267890: 1 6 31 127 511 2047 8191 32767 131071 524287 2097151 8388607 33554431 134217727 536870911 2147483647
loop(\(x,i).(x2 + x + 1),1,loop(\(x,i).(x2 + 1),x,0))
A213437: 1 3 7 31 703 459007 210066847231 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + ~x + 1),1,loop(\(x,i).(x2 + 1),x,0))
A001699: 1 1 3 21 651 457653 210065930571 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + loop(\(x,i).10x,i,x)),x,0)
A076127: 0 1 101 101001 1010010001 101001000100001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~1 + (loop(\(x,i).2x,(~2 + i),1) + (x * i))),x,0)
A187246: 0 0 0 1 7 42 267 1900 15263 137494 1375195 15127656 181532895 2359929682 33039019643 495585302836
(1 - loop(\(x,i).2x,x,loop(\(x,i).(2x + ~6),x,0)))
A020527: 1 13 73 337 1441 5953 24193 97537 391681 1569793 6285313 25153537 100638721 402604033 1610514433 6442254337
(if (x + ~1) <= 0 then (~x + 1) else loop(\(x,i).(4x + 2),x,0))
A087120: 1 0 10 42 170 682 2730 10922 43690 174762 699050 2796202 11184810 44739242 178956970 715827882
(loop(\(x,i).(i * i),(x + ~1),1) * loop(\(x,i).(2x + 2),x,0))
A213026: 0 2 6 56 270
loop(\(x,i).3x,(x + ~1),loop(\(x,i).(2x + 2),x,0))
A060589: 0 2 18 126 810 5022 30618 185166 1115370 6705342 40271418 241746606 1450833930 8706066462 52239587418 313447090446
(loop(\(x,i).3x,x,1) - loop(\(x,i).(2x + 2),x,0))
A101052: 1 1 3 13 51 181 603 1933 6051 18661 57003 173053 523251 1577941 4750203 14283373
loop(\(x,i).(2 * (if x <= 0 then 1 else (2 * ((x + 1) + (i mod 2))))),x,0)
A122229: 0 2 12 56 228 920 3684 14744 58980 235928 943716 3774872 15099492 60397976 241591908 966367640
loop(\(x,i).(2 * (4x + (if (x + ~2) <= 0 then 1 else x))),x,0)
A337855: 0 2 18 180 1800 18000 180000 1800000 18000000 180000000 1800000000 18000000000 180000000000 1800000000000 18000000000000 180000000000000
loop(\(x,i).2x,x,(1 - loop(\(x,i).(2 * (x - (i mod 2))),x,0)))
A246036: 1 6 20 88 336 1376 5440 21888 87296 349696 1397760 5593088 22368256 89481216 357908480 1431666688
loop(\(x,i).loop(\(x,i).(x + i),i,10x),x,0)
A052262: 0 1 13 136 1370 13715 137171 1371738 13717416 137174205 1371742105 13717421116 137174211238 1371742112471 13717421124815 137174211248270
loop(\(x,i).(~2x + loop(\(x,i).(4x + i),i,0)),x,0)
A096978: 0 1 4 19 74 305 1208 4863 19398 77709 310612 1242907 4970722 19884713 79535216 318148151
loop(\(x,i).(~2x + loop(\(x,i).3x,(~1 + i),1)),x,0)
A015441: 0 1 1 7 13 55 133 463 1261 4039 11605 35839 105469 320503 953317 2876335
loop(\(x,i).~2x,(x + ~1),loop(\(x,i).(~2x + 1),x,0))
A003683: 0 1 2 12 40 176 672 2752 10880 43776 174592 699392 2795520 11186176 44736512 178962432
loop(\(x,i).((if x <= 0 then (1 + (i div 3)) else 0) + (x div 2)),x,0)
A219659: 0 1 0 2 1 0 3 1 0 4 2 1 0 5 2 1
(loop(\(x,i).(2x + (i mod 2)),x,0) - (if (x mod 2) <= 0 then x else 0))
A132796: 0 1 0 5 6 21 36 85 162 341 672 1365 2718 5461 10908 21845
(loop(\(x,i).2x,x,1) - (1 div (1 - (if (x mod 2) <= 0 then x else 0))))
A166977: 0 1 5 7 17 31 65 127 257 511 1025 2047 4097 8191 16385 32767
loop(\(x,i).(if x <= 0 then 1 else (x + (x mod 7))),x,0)
A010459-A010410: 0 1 2 4 8 9 11 15 16 18 22 23 25 29 30 32
loop(\(x,i).(x + loop(\(x,i).2x,(((~1 + i) * i) div 2),1)),x,0)
A181388: 0 1 3 11 75 1099 33867 2131019 270566475 68990043211 35253362132043 36064050381096011 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(x * (1 + (2 * i))),(~2 + i),1)),x,0)
A192225: 0 1 2 5
A076795: 0 1 2 5 20 125 1070 11465 146600 2173625 36633050 691362125 14440672700 330674815925 8236528396550 221694575073425
loop(\(x,i).(x + loop(\(x,i).(x * (x - i)),2,(1 + (2 * i)))),x,0)
A228406: 0 24 384 2064 7104 18984 43008 86688 160128 276408 451968 706992 1065792 1557192 2214912 3077952
loop(\(x,i).(x + loop(\(x,i).((x * (1 + i)) - (x mod 2)),i,1)),x,0)
A056199: 0 1 3 11 51 291 1971 15411 136371 1345971 14651571 174318771 2249992371 31309422771 467200878771 7441464174771
loop(\(x,i).(x + ((x + loop(\(x,i).(x * i),i,1)) * (1 + i))),x,0)
A122057: 0 2 14 94 684 5508 49104 482256 5185440 60668640 767940480 10462227840 152698210560 2377651449600 39350097561600 689874448435200
loop(\(x,i).(if x <= 0 then 2 else (x + ((i * i * (1 + i)) div 2))),x,0)
A211885: 0 2 8 26 66 141 267 463 751
loop(\(x,i).(x + ((if (x mod 2) <= 0 then 1 else x) * (i - (x mod 2)))),x,0)
A192225: 0 1 2 5
A077138: 0 1 2 5 20 25 150 157 1256 1265 12650 12661 151932 151945 2127230 2127245
loop(\(x,i).loop(\(x,i).(10x + i),2,x),x,0)
A177090: 0 12 1212 121212 12121212 1212121212 121212121212 12121212121212 1212121212121212 121212121212121212 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + ((if (i mod 2) <= 0 then 2 else 2x) * (i div 2))),x,0)
A222559: 0 0 2 6 10 50 56 392 400 3600 3610 39710 39722 516386 516400 7746000
loop(\(x,i).(x2 + loop(\(x,i).2x2,(~1 + i),1)),x,0)
A332758: 0 1 3 17 417 206657 44854599297 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(2x - (x mod 2)),(~1 + i),i)),x,0)
A176640: 0 1 5 14 46 111 303 688 1712 3761 8881 19122 43698 92851 207539 436916
loop(\(x,i).(x + loop(\(x,i).((x * (x + i)) div (1 + i)),2,i)),x,0)
A081282: 0 1 6 22 62 147 308 588 1044 1749 2794 4290 6370 9191 12936 17816
loop(\(x,i).(loop(\(x,i).((x * i) + (i mod 2)),i,0) + (x * i)),x,0)
A088129: 0 1 4 19 104 661 4812 39607 364240 3704617 41310740 501328411 6578864184 92843236669 1402257345244 22570640656831
loop(\(x,i).(loop(\(x,i).(1 + (x * i)),(~1 + i),1) + (x * i)),x,0)
A093904: 0 1 4 17 84 485 3236 24609 210572 2004749 21033900 241237001
A093344: 0 1 4 17 84 485 3236 24609 210572 2004749 21033900 241237001 3003349124 40345599957 581765196884 8963453118065
loop(\(x,i).(loop(\(x,i).~2x,(~1 + i),1) + (x * i)),x,0)
A063083: 0 1 0 4 8 56 304 2192 17408 156928 1568768 17257472 207087616 2692143104 37689995264 565349945344
loop(\(x,i).(loop(\(x,i).(2x * i),(~1 + i),1) + (x * i)),x,0)
A126674: 0 1 4 20 128 1024 9984 115968 1572864 24477696 430571520 8452177920 183175741440 4343275192320 111817607086080 3105593229312000
loop(\(x,i).(loop(\(x,i).2x,(~1 + i),(i mod 2)) + (x * i)),x,0)
A080252: 0 1 2 10 40 216 1296 9136 73088 658048 6580480 72386304 868635648 11292267520 158091745280 2371376195584
loop(\(x,i).loop(\(x,i).(x + ((i * i * (1 + i)) div 2)),i,x),x,0)
A051836: 0 1 8 33 98 238 504 966 1716 2871 4576 7007 10374 14924 20944 28764
loop(\(x,i).(x + loop(\(x,i).10x,i,i)),x,0)
A052245: 0 10 210 3210 43210 543210 6543210 76543210 876543210 9876543210 109876543210 1209876543210 13209876543210 143209876543210 1543209876543210 16543209876543210
loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).(x + (i * i)),x,0))
A076767: 0 1 15 105 465 1540 4186 9870 20910 40755 74305 128271 211575 335790 515620 769420
loop(\(x,i).(x + (loop(\(x,i).2x,(~1 + i),i) * i * i)),x,0)
A036828: 0 1 17 125 637 2637 9549 31501 97037 283661 795661 2158605 5697549 14696461 37175309 92471309
loop(\(x,i).(x + (loop(\(x,i).x3,2,i) * i * i)),x,0)
A123095: 0 1 2049 179196 4373500 53201625 415998681 2393325424 10983260016 42364319625 142364319625 427675990236 1170684360924 2962844754961 7012409924625 15662165784000
loop(\(x,i).((x + loop(\(x,i).(x * (i * i)),(~1 + i),1)) * i),x,0)
A061640: 0 1 4 24 240 4080 110880 4404960 238452480 16777393920 1484592883200 161180605555200 21054378333542400 3256459844769331200 4611686018427387903 4611686018427387903
(if ((x + 2) mod (1 + (2 * (if (x mod 2) <= 0 then x else 2)))) <= 0 then 0 else 1)
A100544-A031214: 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1
(1 + (if (x mod 3) <= 0 then (3 * (if x <= 0 then 0 else 2)) else 0))
A105395: 1 1 1 7 1 1 7 1 1 7 1 1 7 1 1 7
(1 + loop(\(x,i).(if x <= 0 then 2 else (3x + ~3)),(x + ~1),0))
A291773: 1 1 3 4 7 16 43 124 367 1096 3283 9844 29527 88576 265723 797164
loop(\(x,i).2x,(x + ~1),(~1 + (if x <= 0 then ~4 else 0)))
A157823: ~5 ~1 ~2 ~4 ~8 ~16 ~32 ~64 ~128 ~256 ~512 ~1024 ~2048 ~4096 ~8192 ~16384
(if ((x + 2) mod (2 + (if (x + ~4) <= 0 then 1 else 2))) <= 0 then 0 else 1)
A317241: 1 0 1 1 0 1 0 1 1 1 0 1 1 1 0 1
(if x <= 0 then 0 else (1 + (if ((x + 1) mod 8) <= 0 then 2 else 0)))
A331273: 0 1 1 1 1 1 1 3 1 1 1 1 1 1 1 3
(if x <= 0 then 0 else (1 + (if (x mod (4 + (x div 2))) <= 0 then 2 else 0)))
A225054: 0 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1
(loop(\(x,i).(2x + 2),x,0) div (1 + (if (x mod 2) <= 0 then 2 else 0)))
A060590: 0 2 2 14 10 62 42 254 170 1022 682 4094 2730 16382 10922 65534
(3 * ((if x <= 0 then 1 else 2) * (1 + (if (x mod 2) <= 0 then 2 else 0))))
A040074: 9 6 18 6 18 6 18 6 18 6 18 6 18 6 18 6
(2 * ((2 + (if x <= 0 then 0 else 2)) * (1 + (if (x mod 2) <= 0 then 2 else 0))))
A040134: 12 8 24 8 24 8 24 8 24 8 24 8 24 8 24 8
loop(\(x,i).2x,x,(1 + loop(\(x,i).(2x + 4),(x + 2),0)))
A086221: 13 58 244 1000 4048 16288 65344 261760 1047808 4192768 16774144 67102720 268423168 1073717248 4294918144 17179770880
(if (x mod 2) <= 0 then (2 - (((if x <= 0 then 2 else x) div 2) mod 2)) else ~1)
A164117: 1 ~1 1 ~1 2 ~1 1 ~1 2 ~1 1 ~1 2 ~1 1 ~1
(1 + loop(\(x,i).(10 * (if x <= 0 then 1 else x)),x,0))
A000533: 1 11 101 1001 10001 100001 1000001 10000001 100000001 1000000001 10000000001 100000000001 1000000000001 10000000000001 100000000000001 1000000000000001
(1 + loop(\(x,i).(x - (if x <= 0 then (x - ((i div 2) + i)) else 1)),x,0))
A280513: 1 2 1 5 4 3 2 1 13 12 11 10 9 8 7 6
(1 + loop(\(x,i).(2 * (if x <= 0 then 2 else ((x + 1) - (i mod 2)))),x,0))
A168642: 1 5 11 21 43 85 171 341 683 1365 2731 5461 10923 21845 43691 87381
loop(\(x,i).(2x * (1 + i)),loop(\(x,i).(2x + 2),x,0),1)
A028371: 1 24 322560 21424936845312000 4611686018427387903
(1 + (if (x + ~2) <= 0 then 2x else loop(\(x,i).(2x + 2),x,0)))
A286521: 1 3 5 15 31 63 127 255 511 1023 2047 4095 8191 16383 32767 65535
(1 + loop(\(x,i).(2x + loop(\(x,i).(x2 + 1),i,2)),x,0))
A285934: 1 6 37 750 459829 210067308558 4611686018427387903 4611686018427387903
(loop(\(x,i).(x2 + ~x),(x + ~1),3) - (if x <= 0 then 0 else 1))
A005267: 3 2 5 29 869 756029 571580604869 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).10x,x,1) - (if x <= 0 then 0 else 1))
A103456: 1 9 99 999 9999 99999 999999 9999999 99999999 999999999 9999999999 99999999999 999999999999 9999999999999 99999999999999 999999999999999
(loop(\(x,i).7x,x,1) + (if x <= 0 then 0 else 1))
A103458: 1 8 50 344 2402 16808 117650 823544 5764802 40353608 282475250 1977326744 13841287202 96889010408 678223072850 4747561509944
(loop(\(x,i).(x2 + ~x),(x + ~1),4) - (if x <= 0 then 0 else 1))
A126604: 4 3 11 131 17291 298995971 89398590973228811 4611686018427387903 4611686018427387903
((if (x mod 2) <= 0 then 4 else 1) * (2x - (if x <= 0 then 0 else 1)))
A110185: 0 1 12 5 28 9 44 13 60 17 76 21 92 25 108 29
((2 * loop(\(x,i).(x div (2 - (x mod 2))),x,x)) - (if x <= 0 then 0 else 1))
A129343: 0 1 1 5 1 9 5 13 1 17 9 21 5 25 13 29
((x * (1 + (if (x + ~2) <= 0 then x else 3))) - (if x <= 0 then 0 else 1))
A217585: 0 1 5 11 15 19 23 27 31 35 39 43 47 51 55 59
((x * loop(\(x,i).(x2 + 2),2,3)) - (if x <= 0 then 0 else 1))
A004925: 0 122 245 368 491 614 737 860 983 1106 1229 1352 1475 1598 1721 1844
(1 + loop(\(x,i).(x + (if (i mod (2 + (x mod 2))) <= 0 then 1 else x)),x,0))
A113050: 1 1 2 3 4 7 8 15 16 17 18 35 36 71 72 73
(1 + loop(\(x,i).(2x + (if (i mod 4) <= 0 then i else 1)),x,0))
A222011: 1 2 4 8
A018306: 1 2 4 8 19 38 76 152
(1 + loop(\(x,i).(x2 + x),1,(1 + loop(\(x,i).2x,x,1))))
A239679: 7 13 31 91 307 1123 4291 16771 66307 263683 1051651 4200451 16789507 67133443 268484611 1073840131
(1 + loop(\(x,i).3x,x,(1 + loop(\(x,i).2x,x,1))))
A074508: 3 10 46 244 1378 8020 47386 282124 1686178 10097380 60525226 362974204 2177313778 13062288340 78368947066 470199333484
(1 + loop(\(x,i).2x,x,(1 + loop(\(x,i).3x,x,1))))
A074502: 3 9 41 225 1313 7809 46721 280065 1679873 10078209 60467201 362799105 2176786433 13060702209 78364180481 470185017345
loop(\(x,i).2x,loop(\(x,i).(x * i),(x mod 8),1),1)
A050923: 2 2 4 64 16777216 4611686018427387903
(if (~x + 2) <= 0 then (if ((x * (x div 2)) mod 4) <= 0 then 2 else 1) else 1)
A085424: 1 1 1 1 2 1 1 1 2 2 1 1 2 1 1 1
loop(\(x,i).2x,(x div 2),(1 + (if (x mod 2) <= 0 then 4 else 1)))
A162396: 5 2 10 4 20 8 40 16 80 32 160 64 320 128 640 256
(if (x mod 2) <= 0 then (5 * (2 + (if x <= 0 then 0 else 2))) else 1)
A040109: 10 1 20 1 20 1 20 1 20 1 20 1 20 1 20 1
(if (x mod 4) <= 0 then (if x <= 0 then 1 else (x div 5)) else 1)
A219866-A156070: 1 1 1 1 0 1 1 1 1 1 1 1 2 1 1 1
loop(\(x,i).(x * i),(1 + (2 * (2x + (if x <= 0 then 2 else x)))),1)
A126245: 120 5040 6227020800 121645100408832000 4611686018427387903 4611686018427387903
(if (x mod 2) <= 0 then (9 * (if x <= 0 then 1 else 2)) else 1)
A010170: 9 1 18 1 18 1 18 1 18 1 18 1 18 1 18 1
loop(\(x,i).x2,(x + ~2),(1 + (3 * (if x <= 0 then 0 else 2))))
A165425: 1 7 7 49 2401 5764801 33232930569601 4611686018427387903 4611686018427387903
(if (x mod 5) <= 0 then (3 * (if x <= 0 then 1 else 2)) else 1)
A010122: 3 1 1 1 1 6 1 1 1 1 6 1 1 1 1 6
(if (x mod 2) <= 0 then (6 * (2 + (if x <= 0 then 0 else 2))) else 1)
A040155: 12 1 24 1 24 1 24 1 24 1 24 1 24 1 24 1
(if ((if x <= 0 then 1 else x) mod 5) <= 0 then (x div 3) else 1)
A111368: 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 5
(2 div (if x <= 0 then 2 else (if (x mod 3) <= 0 then (x div 3) else 1)))
A202146: 1 2 2 2 2 2 1 2 2 0 2 2 0 2 2 0
(1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))
A325643-A272565-A214606-A135679-A079879-A020639: 1 2 3 2 5 2 7 2 3 2 11 2 13 2 3 2
(1 + loop(\(x,i).(x * (x div 2)),1,(1 + loop(\(x,i).x2,x,2))))
A119571: 4 11 137 32897 2147516417 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x2 + ~1),2,(1 + loop(\(x,i).x2,x,2))))
A330831: 64 576 82944 4362338304 4611686018427387903
(1 + loop(\(x,i).(x * i),loop(\(x,i).(x + (i * i * i)),x,2),1))
A103319: 3 7 39916801 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * i),4,loop(\(x,i).(2x + 4),x,1)))
A305269: 25 145 385 865 1825 3745 7585 15265 30625 61345 122785 245665 491425 982945 1965985 3932065
(1 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).4x,x,1)))
A020520: 1 13 241 4033 65281 1047553 16773121 268419073 4294901761 68719214593 1099510579201 17592181850113 281474959933441 4503599560261633 72057593769492481 1152921503533105153
(~1 + (if (x + ~1) <= 0 then (x + 2) else loop(\(x,i).4x,x,1)))
A267596: 1 2 15 63 255 1023 4095 16383 65535 262143 1048575 4194303 16777215 67108863 268435455 1073741823
loop(\(x,i).(2x + ~2),x,(~1 + loop(\(x,i).4x,x,1)))
A302942: 0 4 54 490 4050 32674 261954 2096770 16776450 134216194 1073738754 8589928450 68719464450 549755789314 4398046461954 35184371990530
(1 + loop(\(x,i).(x3 + x2),1,loop(\(x,i).2x,x,1)))
A074514: 3 13 81 577 4353 33793 266241 2113537 16842753 134479873 1074790401 8594128897 68736253953 549822922753 4398314946561 35185445830657
(1 + loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).2x,x,1)))
A281481: 2 4 11 37 137 529 2081 8257 32897 131329 524801 2098177 8390657 33558529 134225921 536887297
(1 + loop(\(x,i).((x2 + 2x) div 2),1,loop(\(x,i).2x,x,1)))
A343175: 2 5 13 41 145 545 2113 8321 33025 131585 525313 2099201 8392705 33562625 134234113 536903681
(1 + loop(\(x,i).(x3 + x),1,loop(\(x,i).2x,x,1)))
A074504: 3 11 69 521 4113 32801 262209 2097281 16777473 134218241 1073742849 8589936641 68719480833 549755822081 4398046527489 35184372121601
(~1 + loop(\(x,i).2x2,x,1) - loop(\(x,i).2x,x,1))
A103743: ~1 ~1 3 119 32751 2147483615 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).3x,x,1) + loop(\(x,i).2x,x,1)))
A001550: 3 6 14 36 98 276 794 2316 6818 20196 60074 179196 535538 1602516 4799354 14381676
loop(\(x,i).(x2 div 4),1,(1 + loop(\(x,i).2x,x,1)))
A063376: 1 2 6 20 72 272 1056 4160 16512 65792 262656 1049600 4196352 16781312 67117056 268451840
loop(\(x,i).((x2 + x) div 2),1,(1 + loop(\(x,i).2x,x,1)))
A028401: 3 6 15 45 153 561 2145 8385 33153 131841 525825 2100225 8394753 33566721 134242305 536920065
loop(\(x,i).(x3 + ~2),1,(1 + loop(\(x,i).2x,x,1)))
A099359: 6 25 123 727 4911 35935 274623 2146687 16974591 135005695 1076890623 8602523647 68769820671 549957165055 4398851866623 35187593412607
(1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).2x2,x,1)))
A119572: 3 7 73 16513 1073774593 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + loop(\(x,i).2x,(1 + (i * i)),x)),(x + 1),1)
A117068: 5 161 164865 21609185281 1450167876173430785 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * i),(~1 + (4 * i)),x),(x + 1),1)
A294322: 6 30240 1207084032000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,loop(\(x,i).(3x + ~1),(x + ~1),1))
A092807: 1 2 8 40 224 1312 7808 46720 280064 1679872 10078208 60467200 362799104 2176786432 13060702208 78364180480
loop(\(x,i).2x,(x + ~1),loop(\(x,i).(~2x + 4),(x + ~1),1))
A123016: 1 1 4 0 32 ~64 384 ~1280 5632 ~21504 88064 ~348160 1400832 ~5586944 22380544 ~89456640
(loop(\(x,i).3x,x,1) - loop(\(x,i).2x,(x + ~1),1))
A064686: 0 2 7 23 73 227 697 2123 6433 19427 58537 176123 529393 1590227 4774777 14332523
(if x <= 0 then 10 else loop(\(x,i).2x,(x + ~1),1))
A090555: 10 1 2 4 8 16
loop(\(x,i).(x * loop(\(x,i).(~3x + 2),i,1)),(x + ~1),1)
A247540: 1 1 ~1 ~5 65 2665 ~322465 ~117699725 128645799425 422086867913425 ~4153756867136015425 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).3x,(x div 2),2)),(x + ~1),1)
A078590: 1 1 3 9 171 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(x2 div 2),2,(x + 2))),(x + ~1),1)
A165429: 1 1 8 10000 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(3x + ~1),i,2)),(x + ~1),1)
A015502: 1 1 5 70 2870 350140 127801100 139814403400 458731057555400 4514831068460246800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(4x + ~2),i,2)),(x + ~1),1)
A015503: 1 1 6 132 11352 3882384 5303336544 28966824203328 632809241545903488 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (x * loop(\(x,i).x2,2,(1 + i)))),(x + ~1),1)
A256020: 1 1 17 1394 358258 224269508 290877551876 698687879606152 2862524242746404744 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(2x * (1 + (2 * i))),i,x),(x + ~1),1)
A086205: 1 1 6 360 302400 4572288000 1520925880320000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(2x * (~1 + (2 * i))),i,x),(x + ~1),1)
A054909: 1 1 2 24
A112332: 1 1 2 24 2880 4838400 146313216000 97339256340480000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * (1 + (4 * i))),i,x),(x + ~1),1)
A263430: 1 1 5 225 131625 1309010625 273380323978125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) - loop(\(x,i).(x - (if x <= 0 then 1 else (i * i))),x,(x + ~1)))
A291621: 2 3 4 8 9 10 11 20 21 22 23 24 25 26 27 28
loop(\(x,i).2x,x,(1 + loop(\(x,i).5x,x,1)))
A050621: 2 12 104 1008 10016 100032 1000064 10000128 100000256 1000000512 10000001024 100000002048 1000000004096 10000000008192 100000000016384 1000000000032768
(1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).3x,x,1)))
A034513: 3 13 91 757 6643 59293 532171 4785157 43053283 387440173 3486843451 31381236757 282430067923 2541867422653 22876797237931 205891146443557
(~1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).3x,x,1)))
A155607: 1 11 89 755 6641 59291 532169 4785155 43053281 387440171 3486843449 31381236755 282430067921 2541867422651 22876797237929 205891146443555
(1 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).3x,x,1)))
A155614: 1 7 73 703 6481 58807 530713 4780783 43040161 387400807 3486725353 31380882463 282429005041 2541864234007 22876787671993 205891117745743
(1 + loop(\(x,i).loop(\(x,i).~2x,(i mod 3),x),x,1))
A157240: 2 ~1 ~7 ~7 17 65 65 ~127 ~511 ~511 1025 4097 4097 ~8191 ~32767 ~32767
(1 + loop(\(x,i).(~x + loop(\(x,i).(2x2 + 2),x,1)),x,1))
A328313: 2 4 2312 4611686018427387903
(1 + loop(\(x,i).(x + (if (x + ~2) <= 0 then x else (x2 + 2x))),x,1))
A110389: 2 3 5 29 869 756029 571580604869 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * i),2x,1) - loop(\(x,i).(x * i),x,1))
A237580: 1 2 23 715 40297 3628681 479000881 87178286161 20922789847681 6402373705365121 2432902008173011201 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(3 + (if (x mod 8) <= 0 then (if x <= 0 then 0 else 2) else 0))
A200811: 3 3 3 3 3 3 3 3 5 3 3 3 3 3 3 3
loop(\(x,i).2x,x,(if ((x + ~1) mod 3) <= 0 then ~2 else 1))
A137717: 1 ~4 4 8 ~32 32 64 ~256 256 512 ~2048 2048 4096 ~16384 16384 32768
loop(\(x,i).x3,(x2 + ~2x),(1 + (if x <= 0 then 0 else 2)))
A264932: 1 3 3 7625597484987
loop(\(x,i).~2x,x,(1 + (2 * (1 + (if x <= 0 then 2 else 0)))))
A176414: 7 ~6 12 ~24 48 ~96 192 ~384 768 ~1536 3072 ~6144 12288 ~24576 49152 ~98304
(1 + (2 * (1 + loop(\(x,i).loop(\(x,i).(2 * (x + i)),x,1),x,1))))
A276511: 5 11 139 4611686018427387903
(if (if x <= 0 then 1 else (x mod (1 + (x mod 6)))) <= 0 then 2 else 1)
A228287: 1 1 1 1 1 1 2 1 1 1 2 1 2 1 1 1
(if x <= 0 then 0 else (if (x mod (1 + (x mod 6))) <= 0 then 2 else 1))
A329443: 0 1 1 1 1 1 2 1 1 1 2 1 2 1 1 1
(1 + loop(\(x,i).x2,(x + ~1),(2 * (1 + (if x <= 0 then 1 else 2)))))
A178428: 5 7 37 1297 1679617 2821109907457 4611686018427387903 4611686018427387903
(if x <= 0 then 0 else (if (x mod (1 + (x mod 8))) <= 0 then 2 else 1))
A324882-A257990-A214566: 0 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1
(if (x mod 3) <= 0 then 0 else (if (x mod 5) <= 0 then 2 else 1))
A140080: 0 1 1 0 1 2 0 1 1 0 2 1 0 1 1 0
(1 + (if x <= 0 then 1 else loop(\(x,i).x2,(x + ~1),6)))
A182331: 2 7 37 1297
(1 - (if x <= 0 then 0 else loop(\(x,i).(~2 + i),(x mod 6),1)))
A193690: 1 2 1 0 ~1 ~2 0 2 1 0 ~1 ~2 0 2 1 0
(if (x mod 5) <= 0 then 0 else (if (x mod 3) <= 0 then 2 else 1))
A330714-A140082: 0 1 1 2 1 0 2 1 1 2 0 1 2 1 1 0
(1 + loop(\(x,i).(x * (if (~2 + i) <= 0 then 2 else x)),(2x + ~1),2))
A261071: 3 5 65 16777217 4611686018427387903
loop(\(x,i).(x * i),x,(1 + (loop(\(x,i).(2x + 4),x,1) div 2)))
A052617: 1 4 18 114 936 9480 114480 1607760 25764480 464123520 9286099200 204334099200 4904497382400 127523158963200 3570735629260800 107123376552192000
(loop(\(x,i).2x,x,1) - loop(\(x,i).2x,((x + 1) div 2),1))
A233411: 0 0 2 4 12 24 56 112 240 480 992 1984 4032 8064 16256 32512
(loop(\(x,i).2x,x,2) - loop(\(x,i).2x,((x + 1) div 2),1))
A122746: 1 2 6 12 28 56 120 240 496 992 2016 4032 8128 16256 32640 65280
(~1 + loop(\(x,i).2x,x,loop(\(x,i).(2x + 2),(x + ~1),2)))
A267816: 1 3 23 111 479 1983 8063 32511 130559 523263 2095103 8384511 33546239 134201343 536838143 2147418111
(if (x mod 2) <= 0 then (7 * (if x <= 0 then 1 else 2)) else 1)
A040055: 7 1 14 1 14 1 14 1 14 1 14 1 14 1 14 1
(if (x mod 4) <= 0 then (5 * (if x <= 0 then 1 else 2)) else 1)
A010130: 5 1 1 1 10 1 1 1 10 1 1 1 10 1 1 1
(if (x mod 2) <= 0 then (16 * (if x <= 0 then 1 else 2)) else 1)
A040271: 16 1 32 1 32 1 32 1 32 1 32 1 32 1 32 1
(if (x mod (2 + ((x div 2) mod 4))) <= 0 then (if x <= 0 then 1 else 2) else 1)
A117898: 1 1 1 2 2 1 1 1 2 1 1 1 2 1 1 2
(if (x mod 4) <= 0 then (8 * (if x <= 0 then 1 else 2)) else 1)
A010153: 8 1 1 1 16 1 1 1 16 1 1 1 16 1 1 1
(1 + (2 * (1 + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x))))
A158894: 3 3 5 3 5 7 3 5 7 9 3 5 7 9 11 3
(1 + (loop(\(x,i).(x + (if (i mod 2) <= 0 then (~1 + i) else x)),x,1) div 2))
A147678: 1 2 2 4 5 10 12 24 27 54 58 116 121 242 248 496
(if x <= 0 then 0 else (if (x mod (2 + ((x + ~1) mod 3))) <= 0 then 2 else 1))
A276088: 0 1 1 1 2 1 1 1 1 1 2 1 2 1 1 1
(1 + (2 * (2 + loop(\(x,i).loop(\(x,i).(x2 + ~1),x,2),x,1))))
A057737: 7 11 131 4611686018427387903
loop(\(x,i).x2,(x + ~2),(1 + (4 * (if x <= 0 then 0 else 2))))
A165427: 1 9 9 81 6561 43046721 1853020188851841 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).x2,(x + ~1),(2 * (2 + (if x <= 0 then 1 else 2)))))
A178427: 7 9 65 4097 16777217 281474976710657 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).2x,x,(~2 + loop(\(x,i).2x2,2,2))))
A196657: 127 253 505 1009 2017 4033 8065 16129 32257 64513 129025 258049 516097 1032193 2064385 4128769
(if (~2 + (x div 3)) <= 0 then (if x <= 0 then 1 else 8) else 1)
A269350: 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1
(if (x + ~1) <= 0 then x else (if ((x * (x div 2)) mod 4) <= 0 then 2 else 1))
A255326: 0 1 1 1 2 1 1 1 2 2 1 1 2 1 1 1
(if ((if x <= 0 then 1 else x) mod 12) <= 0 then 4 else 1)
A196879: 1 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1
(1 + (if x <= 0 then 1 else loop(\(x,i).(x2 + ~x),(x + ~1),4)))
A275698: 2 5 13 133 17293 298995973 89398590973228813 4611686018427387903 4611686018427387903
(3 * ((if x <= 0 then 1 else 2) * (if (x mod 2) <= 0 then 4 else 1)))
A040135: 12 6 24 6 24 6 24 6 24 6 24 6 24 6 24 6
(2 * ((2 + (if x <= 0 then 0 else 2)) * (if (x mod 2) <= 0 then 4 else 1)))
A040243: 16 8 32 8 32 8 32 8 32 8 32 8 32 8 32 8
(5 * (if (x mod 2) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1))
A040093: 10 5 20 5 20 5 20 5 20 5 20 5 20 5 20 5
loop(\(x,i).x2,1,(~1 + loop(\(x,i).~2x,x,4)))
A208556: 9 81 225 1089 3969 16641 65025 263169 1046529 4198401 16769025 67125249 268402689 1073807361 4294836225 17180131329
(loop(\(x,i).i,(x mod 4),1) * loop(\(x,i).i,(x div 4),1))
A338854: 1 1 2 3 1 1 2 3 2 2 4 6 3 3 6 9
(loop(\(x,i).2x,x,2) - loop(\(x,i).2x,(x mod 4),1))
A222011: 1 2 4 8
A018355: 1 2 4 8 31 62 124 248
(1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) mod 4))
A138060: 1 1 2 1 2 3 1 2 3 4 1 2 3 4 1 1
loop(\(x,i).2x,x,(~1 + loop(\(x,i).3x,x,4)))
A321003: 3 22 140 856 5168 31072 186560 1119616 6718208 40310272 241863680 1451186176 8707125248 52242767872 313456640000 1880739905536
(loop(\(x,i).2x,x,1) mod (1 + loop(\(x,i).(x2 + x),2,2)))
A222011: 1 2 4 8
A070349: 1 2 4 8 16 32 21 42 41 39 35 27 11 22 1 2
(1 + (if (x + ~1) <= 0 then x else (~2 + loop(\(x,i).4x,x,2))))
A267888: 1 2 31 127 511 2047 8191 32767 131071 524287 2097151 8388607 33554431 134217727 536870911 2147483647
loop(\(x,i).(x * i),x,(if (5 mod (x + 2)) <= 0 then 2 else 1))
A052565: 1 1 2 12 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000
(if (~x + 2) <= 0 then (2 * (loop(\(x,i).2x,x,1) div (x + 2))) else 1)
A286496: 1 1 2 2 4 8 16 28 50 92 170 314 584 1092 2048 3854
(loop(\(x,i).(x2 + x),(x + ~2),x) * (if (x + ~2) <= 0 then 2 else 1))
A030064: 0 2 4 12 420
(if x <= 0 then 0 else (if (x mod (8 - (x div 2))) <= 0 then 2 else 1))
A005136: 0 1 1 1 1 1 1 1 2 1 1 1 2 1 2 2
(loop(\(x,i).(x + loop(\(x,i).(x * i),i,2)),(x + 2),0) div 3)
A309579: 2 6 22 102 582 3942 30822 272742 2691942 29303142 348637542 4499984742 62618845542 934401757542 14882928349542 252007880413542
(loop(\(x,i).(x + (if (x mod 2) <= 0 then 1 else i)),(x + ~2),0) mod 3)
A056558: 0 0 0 1 0 0 1 0 1 2 0 0 1 0 1 2
(3 * (if (x mod 2) <= 0 then (3 * (if x <= 0 then 1 else 2)) else 1))
A040077: 9 3 18 3 18 3 18 3 18 3 18 3 18 3 18 3
(3 + loop(\(x,i).loop(\(x,i).(x * i),x,(2 + i)),(x + ~1),1))
A261146: 4 4 6 27 4611686018427387903
(3 * (if (x mod 2) <= 0 then (2 * (2 + (if x <= 0 then 0 else 2))) else 1))
A040139: 12 3 24 3 24 3 24 3 24 3 24 3 24 3 24 3
loop(\(x,i).loop(\(x,i).(2x + 1),x,2),(x mod 3),3)
A264929: 3 23 25165823
(loop(\(x,i).2x,x,(1 + loop(\(x,i).2x,x,2))) div 3)
A192467: 1 3 12 45 176 693 2752 10965 43776 174933 699392 2796885 11186176 44741973 178962432 715838805
(3 * loop(\(x,i).x2,1,(~1 + loop(\(x,i).2x,x,2))))
A127509: 3 27 147 675 2883 11907 48387 195075 783363 3139587 12570627 50307075 201277443 805208067 3221028867 12884508675
((1 + loop(\(x,i).loop(\(x,i).2x,i,2x),x,2)) div 3)
A083228: 1 3 21 341 10923 699051 89478485 22906492245 11728124029611 12009599006321323 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 div 2),1,(loop(\(x,i).2x,x,1) div 3))
A241683: 0 0 0 2 12 50 220 882 3612 14450 58140 232562 931612 3726450 14911260 59645042
loop(\(x,i).2x,(x + ~2),(loop(\(x,i).2x,x,1) div 3))
A320934: 0 0 1 4 20 80 336 1344 5440 21760 87296 349184 1397760 5591040 22368256 89473024
(if x <= 0 then 1 else loop(\(x,i).8x,(x + ~1),3))
A103333: 1 3 24 192 1536 12288 98304 786432 6291456 50331648 402653184 3221225472 25769803776 206158430208 1649267441664 13194139533312
(6 * loop(\(x,i).(if (x + ~1) <= 0 then i else (x + ~1)),x,0))
A262617: 0 6 12 6 24 18 12 6 48 42 36 30 24 18 12 6
loop(\(x,i).4x,(x + 1),(3 * (if x <= 0 then 0 else 2)))
A292543: 0 96 384 1536 6144 24576 98304 393216 1572864 6291456 25165824 100663296 402653184 1610612736 6442450944 25769803776
(loop(\(x,i).2x,x,1) mod loop(\(x,i).(x2 + 1),2,3))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A036138: 1 2 4 8 16 32 64 27 54 7 14 28 56 11 22 44
loop(\(x,i).(x * i),x,(loop(\(x,i).2x,x,4) div 3))
A052600: 1 2 10 60 504 5040 61200 856800 13749120 247484160 4953312000 108972864000 2615827737600 68011521177600 1904409771264000 57132293137920000
(loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,2)) div 3)
A192466: 2 6 24 90 352 1386 5504 21930 87552 349866 1398784 5593770 22372352 89483946 357924864 1431677610
(3 * (if x <= 0 then 1 else loop(\(x,i).x3,x,2x)))
A297533: 3 24 786432
loop(\(x,i).2x,((if (x mod 2) <= 0 then 2 else 0) + (x div 2)),3)
A112033: 12 3 24 6 48 12 96 24 192 48 384 96 768 192 1536 384
(3 * loop(\(x,i).(x * (if (~1 + i) <= 0 then 2 else x2)),x,2))
A181493: 6 12 192 786432
loop(\(x,i).((x + 1) * ((if (x mod 2) <= 0 then 2 else x) div 2)),x,3)
A076601: 3 4 5 12 13 84 85 3612 3613 6526884 6526885 21300113901612 21300113901613 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).3x,x,2) + loop(\(x,i).2x,x,3))
A094125: 5 12 30 78 210 582 1650 4758 13890 40902 121170 360438 1075170 3213222 9615090 28796118
(loop(\(x,i).3x,x,2) - loop(\(x,i).2x,x,3))
A245804: ~1 0 6 30 114 390 1266 3990 12354 37830 115026 348150 1050594 3164070 9516786 28599510
loop(\(x,i).loop(\(x,i).(x2 + ~2),2,(x2 + 2)),x,3)
A195834: 3 14159 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 2),(x mod 3),(if x <= 0 then 1 else (x div 3)))
A029293: 1 0 0 1 0 0 2 1 0 3 1 0 4 2 1 5
loop(\(x,i).(if x <= 0 then 1 else (x * (~1 + (i * i)))),x,(x div 3))
A030063: 0 1 3 8 120
loop(\(x,i).(x * (1 + (if (i mod 2) <= 0 then 4 else 1))),x,3)
A125521: 3 6 30 60 300 600 3000 6000 30000 60000 300000 600000 3000000 6000000 30000000 60000000
(1 - (3 * loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)))
A143971: 1 4 1 7 4 1 10 7 4 1 13 10 7 4 1 16
loop(\(x,i).3x,(x div 2),loop(\(x,i).(~x + 2),x,3))
A162852: 3 ~1 9 ~3 27 ~9 81 ~27 243 ~81 729 ~243 2187 ~729 6561 ~2187
(~1 + (2 * (x + (if ((if x <= 0 then 1 else x) mod 2) <= 0 then 2x else 1))))
A153285: 1 3 11 7 23 11 35 15 47 19 59 23 71 27 83 31
(~1 + loop(\(x,i).2x,x,(2 * (~x + loop(\(x,i).2x,x,1)))))
A186942: 1 3 15 79 383 1727 7423 30975 126975 515071 2076671 8343551 33456127 134004735 536412159 2146500607
loop(\(x,i).(x * i),x,loop(\(x,i).(x * i),((x2 + x) div 2),1))
A127233: 1 1 12 4320 87091200 156920924160000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * (x + loop(\(x,i).(x + (if (x - i) <= 0 then x else 0)),x,1))))
A080565: 3 7 13 15 25 27 29 31 49 51 53 55 57 59 61 63
(~1 + loop(\(x,i).(2 * (x - (if (i mod 4) <= 0 then 2 else 0))),x,2))
A139806: 1 3 7 15 27 55 111 223 443 887 1775 3551 7099 14199 28399 56799
(~1 + loop(\(x,i).2x,x,loop(\(x,i).(2x + 6),x,2)))
A195460: 1 19 103 463 1951 7999 32383 130303 522751 2094079 8382463 33542143 134193151 536821759 2147385343 8589737983
(~1 + loop(\(x,i).(x div 2),(x + ~2),loop(\(x,i).(2x + 2),x,2)))
A134202: 1 5 13 14 14 14 14 14 14 14 14 14 14 14 14 14
(if x <= 0 then 0 else (1 + (2x * loop(\(x,i).(x2 + 2),2,2))))
A004964: 0 77 153 229 305 381 457 533 609 685 761 837 913 989 1065 1141
(if ((x + ~1) mod 3) <= 0 then loop(\(x,i).4x,x,2) else 1)
A254460: 1 8 1 1 512 1 1 32768 1 1 2097152 1 1 134217728 1 1
(~1 + loop(\(x,i).2x2,2,loop(\(x,i).4x,x,2)))
A175825: 127 32767 8388607 2147483647 549755813887 140737488355327 36028797018963967 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 div 2),1,(1 + loop(\(x,i).4x,x,2)))
A075878: 4 40 544 8320 131584 2099200 33562624 536903680 8590065664 137439477760 2199025352704 35184380477440
loop(\(x,i).2x,x2,(~1 + loop(\(x,i).4x,x,2)))
A190999: 1 14 496 65024 33488896 68685922304 562881233944576 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).x2,1,loop(\(x,i).(x2 + ~x + 2),x,2)))
A096407: 5 17 197 33857 1133938277 1285739650972396817 4611686018427387903
loop(\(x,i).~2x,x,(~1 + loop(\(x,i).(~2x + 1),x,2)))
A246030: 1 8 24 112 416 1728 6784 27392 109056 437248 1746944 6991872 27959296 111853568 447381504 1789591552
(1 + loop(\(x,i).3x,x,1) - loop(\(x,i).2x,x,2))
A028243: 0 0 2 12 50 180 602 1932 6050 18660 57002 173052 523250 1577940 4750202 14283372
(1 + loop(\(x,i).3x,x,2) - loop(\(x,i).2x,x,2))
A002783: 1 3 11 39 131 423 1331 4119 12611 38343 116051 350199 1054691 3172263 9533171 28632279
loop(\(x,i).(2x2 + ~x),1,(1 + loop(\(x,i).2x,x,2)))
A127069: 15 45 153 561 2145 8385 33153 131841 525825 2100225 8394753 33566721 134242305 536920065 2147581953 8590131201
loop(\(x,i).3x,2x,(~1 + loop(\(x,i).2x,x,2)))
A076008: 1 27 567 10935 203391 3720087 67493007 1219657095 21996874431 396331160247 7137447668847 128505439098855 2313380333315871 41643387865514007 749603858371707087 4611686018427387903
loop(\(x,i).6x,x,(~1 + loop(\(x,i).2x,x,2)))
A016175: 1 18 252 3240 40176 489888 5925312 71383680 858283776 10309483008 123774262272 1485653944320 17830024114176 213973350064128 2567758564933632 30813572964188160
loop(\(x,i).8x,x,(~1 + loop(\(x,i).2x,x,2)))
A060195: 1 24 448 7680 126976 2064384 33292288 534773760 8573157376 137304735744 2197949513728 35175782154240 562881233944576 9006649498927104 144110790029344768 2305807824841605120
loop(\(x,i).5x,x,(~1 + loop(\(x,i).2x,x,2)))
A016164: 1 15 175 1875 19375 196875 1984375 19921875 199609375 1998046875 19990234375 199951171875 1999755859375 19998779296875 199993896484375 1999969482421875
(~1 + loop(\(x,i).loop(\(x,i).x3,1,2x2),x,2))
A139303: 1 511 144115188075855871
(~1 + loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,2))
A134760: 1 3 11 39 139 503 1847 6863 25739 97239 369511 1410863 5408311 20801199 80233199 310235039
(if x <= 0 then 0 else (if (5 mod (x + 1)) <= 0 then (x + 2) else 1))
A143532: 0 1 1 1 6 1 1 1 1 1 1 1 1 1 1 1
loop(\(x,i).2x,x,(if (2 - (x div 4)) <= 0 then 2x else 1))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A079845: 1 2 4 8 16 32 64 128 4096
loop(\(x,i).(4x + (if (~2 + i) <= 0 then 2 else x)),2x,1)
A170745-A170707-A170659-A170611-A170563-A170515-A170467-A170419-A170371-A170323-A170275-A170227-A170179-A170131-A170083-A170035-A169567-A169519-A169471-A169423-A169375-A169327-A169279-A169231-A169183-A169135-A169087-A169039-A168991-A168943-A168895-A168847-A168799-A168751-A168703-A167941-A167697-A167225: 1 26 650 16250 406250 10156250 253906250 6347656250 158691406250 3967285156250 99182128906250 2479553222656250 61988830566406250 1549720764160156250 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (~2x + (x div (if i <= 0 then 1 else i)))),2x,1)
A001448: 1 6 70 924 12870 184756 2704156 40116600 601080390 9075135300 137846528820 2104098963720 32247603683100 495918532948104 7648690600760440 118264581564861424
loop(\(x,i).(2x * (if (i mod 3) <= 0 then 1 else 2)),2x,1)
A067488: 1 16 128 1024 16384 131072 1048576 16777216 134217728 1073741824 17179869184 137438953472 1099511627776 17592186044416 140737488355328 1125899906842624
loop(\(x,i).(~2x + loop(\(x,i).3x,i,1)),2x,1)
A096951: 1 7 55 463 4039 35839 320503 2876335 25854247 232557151 2092490071 18830313487 169464432775 1525146340543 13726182847159 123535108753519
loop(\(x,i).(2x + (if (~2 + i) <= 0 then 1 else 2x)),2x,1)
A067404: 1 7 112 1792 28672 458752 7340032 117440512 1879048192 30064771072 481036337152 7696581394432 123145302310912 1970324836974592 31525197391593472 504403158265495552
loop(\(x,i).loop(\(x,i).(~2x + (i * i)),x,0),1,(2x + 1))
A239367: 1 5 13 29 69 197 669 2509 9813 38965 155501 621565 2485733 9942309 39768509 159073197
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(2x + 1))
A016764: 1 531441 244140625 13841287201 282429536481 3138428376721 23298085122481 129746337890625 582622237229761 2213314919066161 7355827511386641 21914624432020321 59604644775390625 150094635296999121 353814783205469041 787662783788549761
(if (if (x mod 8) <= 0 then x else 0) <= 0 then x else (2x + 1))
A325829: 0 1 2 3 4 5 6 7 17 9 10 11 12 13 14 15
((2x + 1) + (if (x + ~2) <= 0 then (2 + (if x <= 0 then 1 else 2)) else x))
A234429: 4 7 9 10 13 16 19 22 25 28 31 34 37 40 43 46
(x mod loop(\(x,i).(if (x mod (1 + i)) <= 0 then 2 else x),x,(2x + 1)))
A307865: 0 1 2 3 0 5 6 1 8 9 0 11 0 1 14 15
((2x + 1) + loop(\(x,i).((x + ~2) - (if x <= 0 then 0 else i)),x,x))
A213183: 1 1 2 3 2 3 4 5 3 4 5 6 7 4 5 6
((2x + 1) + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 2)),x,x))
A134483: 1 3 4 5 6 7 7 8 9 10 9 10 11 12 13 11
(if x <= 0 then 1 else ((2x + ~1) * loop(\(x,i).(x * (i * i)),x,2)))
A344057: 1 2 24 360 8064 259200 11404800 660441600 48771072000 4477184409600 500391198720000 66920738734080000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 4),x,loop(\(x,i).3x,2x,1))
A094981: 1 2 5 11 25 57 129 291 656 1477 3325 7481 16834 37876 85222 191751
loop(\(x,i).(x * (2 + (if (x + ~4) <= 0 then 1 else 2))),2x,1)
A067415: 1 9 144 2304 36864 589824 9437184 150994944 2415919104 38654705664 618475290624 9895604649984 158329674399744 2533274790395904 40532396646334464 648518346341351424
loop(\(x,i).(x + (2 * (x + (if (~2 + i) <= 0 then 1 else x)))),2x,1)
A196676: 1 17 425 10625 265625 6640625 166015625 4150390625 103759765625 2593994140625 64849853515625 1621246337890625 40531158447265625 1013278961181640625 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,x,1) - loop(\(x,i).(2x + ~2),(x div 2),1))
A056309: 0 1 4 8 18 34 70 134 270 526 1054 2078 4158 8254 16510 32894
loop(\(x,i).(2 * (~2x + (x div (if i <= 0 then 1 else i)))),(x div 2),1)
A128057: 1 1 ~2 ~2 6 6 ~20 ~20 70 70 ~252 ~252 924 924 ~3432 ~3432
(1 + (if (x mod 2) <= 0 then (2x + (if x <= 0 then 1 else x)) else (x div 2)))
A160413: 2 1 7 2 13 3 19 4 25 5 31 6 37 7 43 8
(1 + loop(\(x,i).loop(\(x,i).(2x + 1),x,0),(x mod 2),(x div 2)))
A242971: 1 1 2 2 3 4 4 8 5 16 6 32 7 64 8 128
loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x div 2),1)
A128014: 1 1 2 2 6 6 20 20 70 70 252 252 924 924 3432 3432
loop(\(x,i).(x + ((if (i mod 2) <= 0 then 1 else i) * i)),x,(1 + (x div 2)))
A228958: 1 2 5 14 19 44 51 100 109 190 201 322 335 504 519 744
(loop(\(x,i).2x,x,1) - loop(\(x,i).3x,(x div 2),1))
A167936: 0 1 1 5 7 23 37 101 175 431 781 1805 3367 7463 14197 30581
loop(\(x,i).x2,(x mod 2),loop(\(x,i).(x2 + x),(x div 2),1))
A269265: 1 1 2 4 6 36 42 1764 1806 3261636 3263442 10650053687364 10650056950806 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),(x div 2),1)
A189976: 1 1 5 5 15 15 35 35 70 70 126 126 210 210 330 330
loop(\(x,i).(x div (2 - (x mod 2))),x,loop(\(x,i).(x * i),(x div 2),1))
A095987: 1 1 1 1 1 1 3 3 3 3 15 15 45 45 315 315
(loop(\(x,i).(x * i),x,1) div loop(\(x,i).(x * (i * i)),(x div 2),1))
A056040: 1 1 2 6 6 30 20 140 70 630 252 2772 924 12012 3432 51480
loop(\(x,i).(x * i),x,(1 + loop(\(x,i).2x,x,1) - (x mod 2)))
A052647: 2 2 10 48 408 3840 46800 645120 10362240 185794560 3719520000 81749606400 1962469555200 51011754393600 1428416301312000 42849873690624000
loop(\(x,i).2x,(x div 2),(1 + (if x <= 0 then 0 else 2) - (x mod 2)))
A072946: 1 2 6 4 12 8 24 16 48 32 96 64 192 128 384 256
(1 + (loop(\(x,i).loop(\(x,i).((x + 2) mod (1 + i)),x,0),x,x) div 2))
A048896: 1 1 2 1 2 2 4 1 2 2 4 2 4 4 8 1
(1 + loop(\(x,i).(x + (x div (if (x mod (2 + i)) <= 0 then 2 else 1))),x,2))
A154700: 3 5 7 13 19 37 73 109
loop(\(x,i).(x * (x div 2)),1,(~1 + loop(\(x,i).3x,x,2)))
A240917: 0 10 136 1378 12880 117370 1060696 9559378 86073760 774781930 6973391656 62761587778 564857478640 5083726873690 45753570561016 411782221142578
loop(\(x,i).2x,(loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2),1)
A082392: 1 1 2 1 4 2 8 1 16 4 32 2 64 8 128 1
(1 + (2 * loop(\(x,i).(x - ((if (~x + i) <= 0 then i else 0) div 2)),x,x)))
A261046: 1 3 3 5 5 7 5 7 9 7 9 11 7 9 11 13
(1 + (2 * (x + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 1)),x,x))))
A131421: 1 3 5 5 7 9 7 9 11 13 9 11 13 15 17 11
(1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).x3,x,2)))
A051154: 7 73 262657 18014398643699713 4611686018427387903
(1 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).x3,x,2)))
A198915: 3 57 261633 18014398375264257 4611686018427387903
loop(\(x,i).(x div 3),x,(1 + loop(\(x,i).x3,x,2)))
A066807: 3 3 57 4971027 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x - (if (x mod (2 * (1 + i))) <= 0 then 1 else 0)),x,1)
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A133024: 1 2 4 8 16 32 64 127 254 508 1016 2032 4064 8128
loop(\(x,i).(4x - loop(\(x,i).(~2x + 2),i,0)),x,1)
A108924: 1 2 10 34 146 562 2290 9074 36466 145522 582770 2329714 9321586 37280882 149134450 596515954
loop(\(x,i).2x,x,loop(\(x,i).(6x + 1),x,1))
A016136: 1 14 172 2072 24880 298592 3583168 42998144 515977984 6191736320 74300836864 891610044416 10699320537088 128391846453248 1540702157455360 18488425889497088
loop(\(x,i).loop(\(x,i).2x,((x * (x + i)) div (x + 1)),1),x,1)
A114642: 1 2 4 32 17179869184
loop(\(x,i).((x * i) - loop(\(x,i).~2x,(~1 + i),1)),x,1)
A062282: 1 0 2 2 16 64 416 2848 22912 205952 2060032 22659328 271913984 3534877696 49488295936 742324422656
loop(\(x,i).2x,loop(\(x,i).i,(x + ~9),x),1)
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A123464: 1 2 4 8 16 32 64 128 256 512
A329562: 1 2 4 8 16 32 64 128 256 512 2 4 8 16 32 64
loop(\(x,i).2x,x,loop(\(x,i).(4x + 9),x,1))
A020537: 1 26 244 2024 16336 130976 1048384 8388224 67108096 536869376 4294964224 34359732224 274877894656 2199023230976 17592185995264 140737488257024
loop(\(x,i).4x,x,loop(\(x,i).(4x + 1),x,1))
A166984: 1 20 336 5440 87296 1397760 22368256 357908480 5726601216 91625881600 1466015154176 23456246661120 375299963355136 6004799480791040 96076791961092096 1537228672451215360
loop(\(x,i).3x,x,loop(\(x,i).(4x + 1),x,1))
A016147: 1 15 189 2295 27621 331695 3981069 47775015 573306741 6879700575 82556465949 990677768535 11888133753861 142657606640655 1711891284470829 20542695427998855
loop(\(x,i).2x,x2,loop(\(x,i).(4x + ~1),x,1))
A165928: 1 6 176 22016 11206656 22917677056 187672890966016 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * i),(x + ~1),(1 + (2 * (x mod 2)))),x,1)
A019437: 1 3 6 120 4611686018427387903
loop(\(x,i).(3 * (x - loop(\(x,i).(~2x + 1),i,0))),x,1)
A091000: 1 0 3 0 15 12 99 168 759 1764 6315 16896 54783 156156 484851 1421784
loop(\(x,i).(3 * (x - (if (i mod 2) <= 0 then 2 else ~2))),x,1)
A137340: 1 9 21 69 201 609 1821 5469 16401 49209 147621 442869 1328601 3985809 11957421 35872269
(loop(\(x,i).2x,x,2) - loop(\(x,i).(3x + ~6),x,1))
A134350: 1 7 23 67 191 547 1583 4627 13631 40387 120143 358387 1071071 3205027
loop(\(x,i).(3 * (x + loop(\(x,i).(x2 + x),2,2))),x,1)
A036548: 1 129 513 1665 5121 15489 46593 139905 419841 1259649 3779073 11337345 34012161 102036609 306109953 918329985
loop(\(x,i).((2x + ~1) + (if (i mod 4) <= 0 then x else 1)),x,1)
A222011: 1 2 4 8
A018323: 1 2 4 8 23 46 92 184
loop(\(x,i).2x,x,loop(\(x,i).(x * i),(2x2 + x),1))
A165970: 1 12 14515200 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((3x + 1) + (if (~2 + i) <= 0 then 1 else x)),x,1)
A272743: 1 5 17 69 277 1109 4437 17749 70997 283989 1135957 4543829 18175317 72701269 290805077 1163220309
loop(\(x,i).((x + loop(\(x,i).2x,i,1)) * (1 + (2 * i))),x,1)
A128195: 1 9 65 511 4743 52525 683657 10256775 174369527 3313030741 69573667065 1600194389599 40004859842375 1080131215965309 31323805263469097
loop(\(x,i).(1 + (x * (1 + loop(\(x,i).x2,(~1 + i),2)))),x,1)
A048164: 1 4 21 358 92007 6029862760 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,loop(\(x,i).(5x + 1),x,1))
A016134: 1 12 124 1248 12496 124992 1249984 12499968 124999936 1249999872 12499999744 124999999488 1249999998976 12499999997952 124999999995904 1249999999991808
loop(\(x,i).2x,x,loop(\(x,i).(5x + ~1),x,1))
A083234: 1 8 76 752 7504 75008 750016 7500032 75000064 750000128 7500000256 75000000512 750000001024 7500000002048 75000000004096 750000000008192
loop(\(x,i).2x2,1,loop(\(x,i).(3x + 1),x,1))
A060868: 2 32 338 3200 29282 264992 2389298 21516800 193690562 1743333152 15690352658 141214236800 1270931319842 11438391444512 102945551698418 926510051379200
loop(\(x,i).4x,x,loop(\(x,i).(3x + 1),x,1))
A016159: 1 16 208 2560 30976 372736 4476928 53739520 644939776 7739539456 92875522048 1114510458880 13374142283776 160489774514176 1925877562605568 23110531825008640
loop(\(x,i).4x,x,loop(\(x,i).(3x + ~1),x,1))
A233123: 1 8 80 896 10496 124928 1495040 17924096 215023616 2580021248 30959206400 371506282496 4458058612736 53496636243968 641959366492160 7703511324164096
loop(\(x,i).(1 + (x * loop(\(x,i).(1 + (x * (1 + i))),i,1))),x,1)
A059730: 1 4 41 1682 346493 428611842 3711778551721 257155729841782602 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + i)),x,loop(\(x,i).(1 + (x * (1 + i))),x,1))
A061573: 1 6 60 984 24720 890640 43646400 2793409920 226266566400 22626660268800 2737825932441600 394246934750592000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (x * loop(\(x,i).((x + 1) * (x + i)),2,2))),x,1)
A172175: 1 111 12211 1343211 147753211 16252853211 1787813853211 196659523853211 21632547623853211 2379580238623853211 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + loop(\(x,i).10x,2,x)),x,1)
A094028: 1 101 10101 1010101 101010101 10101010101 1010101010101 101010101010101 10101010101010101 1010101010101010101 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (x * loop(\(x,i).(x3 + x),2,2))),x,1)
A178349: 1 1011 1021111 1031322111 1041635332111 1052051685432111 1062572202286432111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).((x + i) div (x + 1)),loop(\(x,i).2x,x,1),x))
A136417: 2 2 3 3 5 6 9 12 17 23 33 46 65 91 129 182
loop(\(x,i).(1 + loop(\(x,i).5x,(2 + i),x)),x,1)
A178189: 1 126 78751 246096876 3845263687501 300411225586015626 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) * loop(\(x,i).(x2 + 2x),(~1 + i),1)),x,1)
A133468: 1 2 9 150 38505 2523490710 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + ((1 + loop(\(x,i).2x,i,2)) * i)),x,1)
A078501: 1 7 26 78 211 537 1312 3112 7217 16443 36934 82002 180319 393325 852092 1835148
loop(\(x,i).(if (x + ~2) <= 0 then 8x else (x + ~1)),x,1)
A132672: 1 8 7 6 5 4 3 2 16 15 14 13 12 11 10 9
loop(\(x,i).loop(\(x,i).(x div (2 - (x mod 2))),i,((x + 1) + i)),x,1)
A208884: 1 3 3 7 3 9 1 9 9 19 15 27 5 19 17 33
loop(\(x,i).5x,x,loop(\(x,i).(1 + (x * i)),x,1))
A097816: 1 10 125 2000 40625 1018750 30578125 1070312500 42812890625 1926582031250 96329111328125 5298101171875000 317886070556640625 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x * i),x,x2) div loop(\(x,i).(1 + (x * i)),x,1))
A032635: 0 0 1 3 5 9 13 18 23 29 36 44 52 62 72 82
loop(\(x,i).((3x * i) + loop(\(x,i).2x,i,1)),x,1)
A097817: 1 5 34 314 3784 56792 1022320 21468848 515252608 13911820928 417354628864 13772702754560 495817299168256 19336874667570176 812148736037963776 4611686018427387903
loop(\(x,i).(5x + loop(\(x,i).2x,i,1)),x,1)
A016127: 1 7 39 203 1031 5187 25999 130123 650871 3254867 16275359 81378843 406898311 2034499747 10172515119 50862608363
loop(\(x,i).(5x - loop(\(x,i).2x,i,1)),x,1)
A247313: 1 3 11 47 219 1063 5251 26127 130379 651383 3255891 16277407 81382939 406906503 2034516131 10172547887
loop(\(x,i).((x * (~1 + (2 * i))) + loop(\(x,i).2x,i,1)),x,1)
A318165: 1 3 13
A128196: 1 3 13 73 527 4775 52589 683785 10257031 174370039 3313031765 69573669113 1600194393695 40004859850567 1080131215981693
loop(\(x,i).(x div 2),x,loop(\(x,i).((2x + 1) * (1 + i)),x,1))
A030799: 1 3 9 39 197 1187 8309 66476 598287 5982879 65811677 789740126 10266621646 143732703044 2155990545670 34495848730735
loop(\(x,i).loop(\(x,i).4x,i,(2x * (1 + i))),x,1)
A071900: 1 16 1536 786432 2013265920
loop(\(x,i).(2x + loop(\(x,i).3x,i,1) - i),x,1)
A090326: 1 4 15 54 185 608 1939 6058 18669 57012 173063 523262 1577953 4750216 14283387 42915666
(1 + loop(\(x,i).x2,1,(x + (if (~2 + (x div 2)) <= 0 then 1 else 2))))
A069987: 2 5 10 17 26 37 65 82 101 122 145 170 197 226 257 290
loop(\(x,i).x2,1,((x + 1) + (if (~2 + (x div 2)) <= 0 then 1 else 2)))
A179126: 4 9 16 25 36 49 81 100 121 144 169 196 225 256 289 324
loop(\(x,i).(2 * ((if x <= 0 then 1 else x) - ((x * i) mod 3))),x,1)
A087009: 1 0 2 4 6 12 24 48 96 192 384 768 1536 3072 6144 12288
loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).(2x + 2),x,1))
A169720: 1 10 55 253 1081 4465 18145 73153 293761 1177345 4713985 18865153 75479041 301953025 1207885825 4831690753
loop(\(x,i).(4 * (if x <= 0 then 1 else (x - (x mod 3)))),x,1)
A092898: 1 0 4 12 48 192 768 3072 12288 49152 196608 786432 3145728 12582912 50331648 201326592
(if (x mod 2) <= 0 then (if ((x + ~2) mod 8) <= 0 then 2 else x) else 1)
A342242: 0 1 2 1 4 1 6 1 8 1 2 1 12 1 14 1
loop(\(x,i).(x div 3),x,loop(\(x,i).8x,x,1))
A094976: 1 2 7 18 50 134 359 958 2557 6818 18183 48490 129307 344820 919522 2452059
loop(\(x,i).(2 * (4x + (x div (if i <= 0 then 1 else i)))),x,1)
A004985: 1 10 90 780 6630 55692 464100 3845400 31724550 260846300 2138939660 17500415400 142920059100 1165348174200 9489263704200 77179344794160
loop(\(x,i).(4 * (2x + (x div (if i <= 0 then 1 else i)))),x,1)
A115902: 1 12 120 1120 10080 88704 768768 6589440 56010240 472975360 3972993024 33228668928 276905574400 2300446310400 19060840857600 157569617756160
loop(\(x,i).(4 * (~2x + (x div (if i <= 0 then 1 else i)))),x,1)
A343842: 1 ~4 24 ~160 1120 ~8064 59136 ~439296 3294720 ~24893440 189190144 ~1444724736 11076222976 ~85201715200 657270374400 ~5082890895360
loop(\(x,i).(4 * (x - (x div (if i <= 0 then 1 else (2 * i))))),x,1)
A100320: 1 4 12 40 140 504 1848 6864 25740 97240 369512 1410864 5408312 20801200 80233200 310235040
((2 + (if x <= 0 then 1 else 2)) mod (1 + (if (x mod 2) <= 0 then 4 else x)))
A297217: 3 0 4 0 4 4 4 4 4 4 4 4 4 4 4 4
loop(\(x,i).~x,x,loop(\(x,i).(5x + ~8),x,1))
A081628: 1 3 ~23 123 ~623 3123 ~15623 78123 ~390623 1953123 ~9765623 48828123 ~244140623 1220703123 ~6103515623 30517578123
loop(\(x,i).(4 * (2x - (x div (if i <= 0 then 1 else i)))),x,1)
A059304: 1 4 24 160 1120 8064 59136 439296 3294720 24893440 189190144 1444724736 11076222976 85201715200 657270374400 5082890895360
loop(\(x,i).(4x + (if (i mod 3) <= 0 then 1 else 0)),x,1)
A033140: 1 4 16 65 260 1040 4161 16644 66576 266305 1065220 4260880 17043521 68174084 272696336 1090785345
loop(\(x,i).(4x + (if (i mod 4) <= 0 then 1 else 0)),x,1)
A083589: 1 4 16 64 257 1028 4112 16448 65793 263172 1052688 4210752 16843009 67372036 269488144 1077952576
loop(\(x,i).~2x,x,loop(\(x,i).(~4x + 1),x,1))
A083301: 1 6 52 408 3280 26208 209728 1677696 13421824 107374080 858993664 6871947264 54975582208 439804649472 3518437212160 28147497664512
loop(\(x,i).(4x + (if (i mod 3) <= 0 then 1 else 2)),x,1)
A037545: 1 6 26 105 422 1690 6761 27046 108186 432745 1730982 6923930 27695721 110782886 443131546 1772526185
loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).4x,x,1))
A026244: 1 10 136 2080 32896 524800 8390656 134225920 2147516416 34359869440 549756338176 8796095119360 140737496743936 2251799847239680 36028797153181696 576460752840294400
loop(\(x,i).((x2 + ~x) div 2),1,loop(\(x,i).4x,x,1))
A026337: 0 6 120 2016 32640 523776 8386560 134209536 2147450880 34359607296 549755289600 8796090925056 140737479966720 2251799780130816 36028796884746240 576460751766552576
loop(\(x,i).(2x2 + ~x),1,loop(\(x,i).4x,x,1))
A079598: 1 28 496 8128 130816 2096128 33550336 536854528 8589869056 137438691328 2199022206976 35184367894528 562949936644096 9007199187632128 144115187807420416 2305843008139952128
(loop(\(x,i).3x,x,1) + loop(\(x,i).4x,x,1))
A074605: 2 7 25 91 337 1267 4825 18571 72097 281827 1107625 4371451 17308657 68703187 273218425 1088090731
loop(\(x,i).((x + 1) div 3),x,loop(\(x,i).4x,x,1))
A309212: 1 1 2 2 3 4 6 7 10 13 18 24 32 42 56 75
loop(\(x,i).((x + 2) div 3),x,loop(\(x,i).4x,x,1))
A130082: 1 2 2 3 4 5 6 8 10 14 18 24 32 43 57 75
loop(\(x,i).3x,x2,loop(\(x,i).4x,x,1))
A133461: 1 12 1296 1259712 11019960576 867623536069632 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,(if (~x + 2) <= 0 then (x + (2 * (x mod 2))) else 1))
A152458: 1 2 8 40 64
loop(\(x,i).x2,1,loop(\(x,i).(2 * (x - (2x * i))),x,1))
A122747: 1 4 144 14400 2822400 914457600 442597478400 299195895398400 269276305858560000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((2x div (if i <= 0 then 1 else i)) * (4 + i)),x,1)
A003472: 1 10 60 280 1120 4032 13440 42240 126720 366080 1025024 2795520 7454720 19496960 50135040 127008768
loop(\(x,i).(((x + loop(\(x,i).(x * i),i,1)) * (2 + i)) div 2),x,1)
A188545: 1 3 10
A136128: 1 3 10 40 192 1092 7248 55296 478080 4625280 49524480 581368320 7422589440 102372076800 1516402944000 24004657152000
(~1 + loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 2 else 1)),x,(~x + 2)))
A059964: 1 1 2 2 3 2 3 2 3 4 5 2 3 2 3 4
loop(\(x,i).(x - (2 * (~x + (if (i mod 3) <= 0 then 2 else 0)))),x,1)
A018334: 1 3 9 23 69 207
loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).~2x,x,1))
A003665: 1 1 10 28 136 496 2080 8128 32896 130816 524800 2096128 8390656 33550336 134225920 536854528
loop(\(x,i).((x2 + ~x) div 2),1,loop(\(x,i).~2x,x,1))
A003674: 0 3 6 36 120 528 2016 8256 32640 131328 523776 2098176 8386560 33558528 134209536 536887296
loop(\(x,i).(x * (x div 3)),1,loop(\(x,i).~2x,x,1))
A192382: 0 2 4 24 80 352 1344 5504 21760 87552 349184 1398784 5591040 22372352 89473024 357924864
(loop(\(x,i).3x,x,1) + loop(\(x,i).~2x,x,1))
A087451: 2 1 13 19 97 211 793 2059 6817 19171 60073 175099 535537 1586131 4799353 14316139
loop(\(x,i).(2 * (~x + loop(\(x,i).3x,(~1 + i),1))),x,1)
A102901: 1 0 6 6 42 78 330 798 2778 7566 24234 69630 215034 632814 1923018 5719902
loop(\(x,i).(2 * loop(\(x,i).~2x,(i mod 3),x)),x,1)
A138340: 1 ~4 ~32 ~64 256 2048 4096 ~16384 ~131072 ~262144 1048576 8388608 16777216 ~67108864 ~536870912 ~1073741824
(loop(\(x,i).(x * (0 - i)),x,1) * loop(\(x,i).(~2x + 2),x,1))
A052598: 1 0 4 12 144 1200 15840 211680 3467520 61689600 1241049600 27223257600 654316185600 16999766784000 476167826534400 14282419447296000
loop(\(x,i).~4x,x,loop(\(x,i).(~2x + 2),x,1))
A091905: 1 0 32 128 1536 10240 90112 688128 5636096 44564480 358612992 2860515328 22917677056 183207198720 1466194460672 11727408201728
loop(\(x,i).(2 * (~x + (4 * (x div (if i <= 0 then 1 else i))))),x,1)
A175375: 1 6 12 8 0 0 0 0 0 0 0 0 0 0 0 0
loop(\(x,i).(x * (x div 2)),1,loop(\(x,i).(3x + ~4),x,1))
A241038: 0 1 28 325 3160 29161 264628 2388205 21513520 193680721 1743303628 15690264085 141213971080 1270930522681 11438389053028 102945544523965
(if x <= 0 then 1 else (12 - (if (x + ~2) <= 0 then x else 1)))
A217789: 1 11 10 11 11 11 11 11 11 11 11 11 11 11 11 11
(1 + loop(\(x,i).(x * loop(\(x,i).(x2 + x),2,x)),(x + ~2),x))
A128874: 1 2 3 469
loop(\(x,i).(2x + (if (i mod 3) <= 0 then (x div 2) else 0)),x,1)
A004647: 1 2 4 10 20 40 100 200 400 1000 2000 4000 10000 20000 40000 100000
loop(\(x,i).(2x + (if (x mod (3 + i)) <= 0 then i else 0)),x,1)
A222011: 1 2 4 8
A018536: 1 2 4 8 16 37 74 148 296 592
loop(\(x,i).(2x + (x div (1 + (if (i mod 2) <= 0 then 2 else 0)))),x,1)
A018303: 1 3 7 21 49 147
loop(\(x,i).(~2x + loop(\(x,i).3x,(~1 + i),1)),x,1)
A232015: 1 ~1 5 ~1 29 23 197 335 1517 3527 12629 33791 109565 312311 969701 2843567
loop(\(x,i).(2x + loop(\(x,i).2x,((1 + i) div 2),1)),x,1)
A107659: 1 4 10 24 52 112 232 480 976 1984 4000 8064 16192 32512 65152 130560
loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),x,1)
A016133: 1 11 103 935 8431 75911 683263 6149495 55345711 498111911 4483008223 40347076055 363123688591 3268113205511 29413018865983 264717169826615
loop(\(x,i).(2x2 + ~x),1,loop(\(x,i).(~2x + 1),x,1))
A015249: 1 3 15 55 231 903 3655 14535 58311 232903 932295 3727815 14913991 59650503 238612935 954429895
loop(\(x,i).(~2x + ((2 * (if x <= 0 then 1 else x)) div (1 + i))),x,1)
A126930: 1 ~1 2 ~3 6 ~10 20 ~35 70 ~126 252 ~462 924 ~1716 3432 ~6435
loop(\(x,i).loop(\(x,i).6x,(~1 + i),2x),x,1)
A081955: 1 2 24 1728 746496 1934917632 30091839012864 2807929681968365568 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + x2 + x + 1),1,loop(\(x,i).2x,x,1))
A034496: 4 15 85 585 4369 33825 266305 2113665 16843009 134480385 1074791425 8594130945 68736258049 549822930945 4398314962945 35185445863425
loop(\(x,i).((x3 + x2) div 2),1,loop(\(x,i).2x,x,1))
A081337: 1 6 40 288 2176 16896 133120 1056768 8421376 67239936 537395200 4297064448 34368126976 274911461376 2199157473280 17592722915328
loop(\(x,i).((x2 + 3x) div 2),1,loop(\(x,i).2x,x,1))
A257273: 2 5 14 44 152 560 2144 8384 33152 131840 525824 2100224 8394752 33566720 134242304 536920064
loop(\(x,i).((x3 + x) div 2),1,loop(\(x,i).2x,x,1))
A081342: 1 5 34 260 2056 16400 131104 1048640 8388736 67109120 536871424 4294968320 34359740416 274877911040 2199023263744 17592186060800
loop(\(x,i).((x3 + ~x) div 2),1,loop(\(x,i).2x,x,1))
A120689: 0 3 30 252 2040 16368 131040 1048512 8388480 67108608 536870400 4294966272 34359736320 274877902848 2199023247360 17592186028032
(loop(\(x,i).3x,2x,1) + loop(\(x,i).2x,x,1))
A074604: 2 11 85 737 6577 59081 531505 4783097 43046977 387421001 3486785425 31381061657 282429540577 2541865836521 22876792471345 205891132127417
(loop(\(x,i).3x,2x,1) - loop(\(x,i).2x,x,1))
A191465: 0 7 77 721 6545 59017 531377 4782841 43046465 387419977 3486783377 31381057561 282429532385 2541865820137 22876792438577 205891132061881
(loop(\(x,i).3x,2x,1) mod loop(\(x,i).2x,x,1))
A138998: 0 1 1 1 1 9 49 121 65 329 913 25 2273 8169 16177 30905
loop(\(x,i).(x + (x2 div 3)),1,loop(\(x,i).2x,x,1))
A079319: 1 3 9 29 101 373 1429 5589 22101 87893 350549 1400149 5596501 22377813 89494869 357946709
(loop(\(x,i).(3x + 1),x,1) - loop(\(x,i).2x,x,1))
A053152: 0 2 9 32 105 332 1029 3152 9585 29012 87549 263672 793065 2383292 7158069 21490592
(loop(\(x,i).(3x + ~1),x,1) + loop(\(x,i).2x,x,1))
A099754: 2 4 9 22 57 154 429 1222 3537 10354 30549 90622 269817 805354 2407869 7207222
loop(\(x,i).(x3 + x2 + x),1,loop(\(x,i).2x,x,1))
A074535: 3 14 84 584 4368 33824 266304 2113664 16843008 134480384 1074791424 8594130944 68736258048 549822930944 4398314962944 35185445863424
(loop(\(x,i).5x,x,1) + loop(\(x,i).2x,x,1))
A074600: 2 7 29 133 641 3157 15689 78253 390881 1953637 9766649 48830173 244144721 1220711317 6103532009 30517610893
(loop(\(x,i).5x,x,1) - loop(\(x,i).2x,x,1))
A005057: 0 3 21 117 609 3093 15561 77997 390369 1952613 9764601 48826077 244136529 1220694933 6103499241 30517545357
(loop(\(x,i).5x,x,1) mod loop(\(x,i).2x,x,1))
A029757: 0 1 1 5 1 21 9 45 225 357 761 1757 2641 5013 489 18829
(loop(\(x,i).3x,x2,1) + loop(\(x,i).2x,x,1))
A120798: 2 5 85 19691 43046737 847288609475 150094635296999185 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).3x,x2,1) - loop(\(x,i).2x,x,1))
A120799: 0 1 77 19675 43046705 847288609411 150094635296999057 4611686018427387903 4611686018427387903 4611686018427387903
((if x <= 0 then 0 else (4x + 2)) + loop(\(x,i).2x,x,1))
A100315: 1 8 14 22 34 54 90 158 290 550 1066 2094 4146 8246 16442 32830
(loop(\(x,i).3x,(x + 1),2) - loop(\(x,i).2x,x,1))
A304168: 5 16 50 154 470 1426 4310 12994 39110 117586 353270 1060834 3184550 9557746 28681430 86060674
(2 + (loop(\(x,i).3x,x,1) + loop(\(x,i).2x,x,1)))
A173657: 4 7 15 37 99 277 795 2317 6819 20197 60075 179197 535539 1602517 4799355 14381677
(loop(\(x,i).(3x + ~3),x,2) - loop(\(x,i).2x,x,1))
A134063: 1 1 2 7 26 91 302 967 3026 9331 28502 86527 261626 788971 2375102 7141687
(loop(\(x,i).(3x + ~1),x,2) + loop(\(x,i).2x,x,1))
A267799: 3 7 18 49 138 397 1158 3409 10098 30037 89598 267769 801258 2399677 7190838 21556129
(loop(\(x,i).(3x + ~1),x,2) - loop(\(x,i).2x,x,1))
A188545: 1 3 10
A053156: 1 3 10 33 106 333 1030 3153 9586 29013 87550 263673 793066 2383293 7158070 21490593
(loop(\(x,i).2x,(x div 2),(x mod 2)) + loop(\(x,i).2x,x,1))
A051437: 1 3 4 10 16 36 64 136 256 528 1024 2080 4096 8256 16384 32896
(loop(\(x,i).5x,x,2) - loop(\(x,i).2x,x,1))
A083421: 1 8 46 242 1234 6218 31186 156122 780994 3905738 19530226 97654202 488277154 2441398058 12207014866 61035123482
(x + (loop(\(x,i).3x,x,1) + loop(\(x,i).2x,x,1)))
A120846: 2 6 15 38 101 280 799 2322 6825 20204 60083 179206 535549 1602528 4799367 14381690
(~x + (loop(\(x,i).3x,x,1) + loop(\(x,i).2x,x,1)))
A120848: 2 4 11 32 93 270 787 2308 6809 20186 60063 179184 535525 1602502 4799339 14381660
loop(\(x,i).(5x + ~4),x,loop(\(x,i).2x,x,1))
A155643: 1 6 76 876 9376 96876 984376 9921876 99609376 998046876 9990234376 99951171876 999755859376 9998779296876 99993896484376 999969482421876
loop(\(x,i).(5x + 4),x,loop(\(x,i).2x,x,1))
A155637: 1 14 124 1124 10624 103124 1015624 10078124 100390624 1001953124 10009765624 100048828124 1000244140624 10001220703124 100006103515624 1000030517578124
loop(\(x,i).(3x + (if (i mod 3) <= 0 then 1 else 0)),x,1)
A033139: 1 3 9 28 84 252 757 2271 6813 20440 61320 183960 551881 1655643 4966929 14900788
loop(\(x,i).(2x + (if (i mod 3) <= 0 then ~1 else x)),x,1)
A018307: 1 3 9 17 51 153
loop(\(x,i).(~3x + loop(\(x,i).4x,i,1)),x,1)
A053404: 1 1 13 25 181 481 2653 8425 40261 141361 624493 2320825 9814741 37664641 155441533 607417225
loop(\(x,i).(2x + loop(\(x,i).(x + (i * i)),(1 + i),x)),x,1)
A156934: 1 8 38 144 487 1552 4796 14592 44061 132568 398210 1195280 3586659 10760992 32284216 96854144
loop(\(x,i).(2x + loop(\(x,i).3x,(~1 + i),x)),x,1)
A153280: 1 3 15 165 4785 397155 97302975 71128474725 155700231173025 1021860617188563075 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x + (if (i mod 3) <= 0 then 1 else 2)),x,1)
A037544: 1 5 17 52 158 476 1429 4289 12869 38608 115826 347480 1042441 3127325 9381977 28145932
loop(\(x,i).loop(\(x,i).x2,i,2x4),x,1)
A067501: 1 4 68719476736 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (3x + i)),x,1)
A135294: 1 4 2 1 7 26 13 46 23 78 39 128 64 32 16 8
(1 + loop(\(x,i).(if (x mod 2) <= 0 then (x + (2 * i)) else 2),(x div 2),x))
A185061: 1 2 5 3 11 7 19 13 29 21 41 31 55 43 71 57
(loop(\(x,i).x2,x,2) - loop(\(x,i).(x2 + (x mod 2)),x,1))
A087046: 1 2 12 240 65280 4294901760 4611686018427387903 4611686018427387903 4611686018427387903
(3 - loop(\(x,i).(~2x2 + (if x <= 0 then 1 else 0)),x,1))
A277438: 2 5 10 100
(1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).x3,2,x)))
A326618: 1 3 262657 387440173 68719738881 3814699218751 101559966746113 1628413638264057 18014398643699713 150094635684419611 1000000001000000001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (x + (3x div (if i <= 0 then 1 else i)))),x,1)
A001789: 1 8 40 160 560 1792 5376 15360 42240 112640 292864 745472 1863680 4587520 11141120 26738688
loop(\(x,i).(loop(\(x,i).(1 + (x * i)),i,1) + (2x * i)),x,1)
A053482: 1 4 21 142 1201 12336 149989 2113546 33926337 611660476 12243073621 269456124774 6468249055921 168191402251432 4709596238204901 141291441773619106
loop(\(x,i).(loop(\(x,i).3x,i,1) - (2x * i)),x,1)
A343582: 1 1 5 ~3 105 ~807 10413 ~143595 2304081 ~41453775 829134549 ~18240782931 437779321785 ~11382260772087 318703306401405 ~9561099177693243
(loop(\(x,i).(x * i),2x,1) - loop(\(x,i).(2x * i),x,1))
A204841: 0 0 16 672 39936 3624960 478955520 87177646080 20922779566080 6402373519933440 2432902004460748800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (4x - (x div (if i <= 0 then 1 else i)))),x,1)
A004982: 1 6 42 308 2310 17556 134596 1038312 8046918 62587140 488179692 3816677592 29897307804 234578876616 1843119744840 14499208659408
loop(\(x,i).(1 + loop(\(x,i).(2 * (x - i)),(x div 2),x)),1,(x + 1))
A057225: 2 3 5 9 13 27
((x + 1) * loop(\(x,i).loop(\(x,i).(x2 + x),x,x),(x + ~1),1))
A135937: 1 2 6 168 4611686018427387903
((~1 + (2 * loop(\(x,i).(if x <= 0 then i else (x div 2)),x,1))) div (x + 1))
A167374: 1 ~1 1 0 ~1 1 0 0 ~1 1 0 0 0 ~1 1 0
((x + 1) * (if (x mod 6) <= 0 then (if x <= 0 then 1 else 2) else 1))
A204896: 1 2 3 4 5 6 14 8 9 10 11 12 26 14 15 16
((x + 1) * (if (x mod 8) <= 0 then (if x <= 0 then 1 else 2) else 1))
A205406: 1 2 3 4 5 6 7 8 18 10 11 12 13 14 15 16
loop(\(x,i).(x * (1 + (2 * i))),(1 + (if x <= 0 then 1 else 2)),(x + 1))
A019553: 15 210 315 420 525 630 735 840 945 1050 1155 1260 1365 1470 1575 1680
(loop(\(x,i).(if x <= 0 then 2 else (x * (~1 + i))),2x,1) div (x + 1))
A322450: 1 1 4 60 2016 120960 11404800 1556755200 290594304000 71137485619200 22117290983424000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,(0 - (loop(\(x,i).2x,x,1) div (x + 1))))
A119000: ~1 ~2 ~4 ~16 ~48 ~160 ~576
(loop(\(x,i).2x,x,2) - (loop(\(x,i).2x,x,1) mod (x + 1)))
A320465: 2 4 7 16 31 62 127 256 508 1022 2047 4088 8191 16382 32764 65536
(loop(\(x,i).(x * (1 + (if (i mod 2) <= 0 then i else 1))),x,1) div (x + 1))
A205825: 1 1 2 3 12 20 120 210 1680 3024 30240 55440 665280 1235520 17297280 32432400
(loop(\(x,i).(x + loop(\(x,i).(x * i),i,(1 + i))),x,1) div (x + 1))
A078619: 1 1 3 8 30 145 844 5779 45457 403791 3995883 43579692 519229008 6709162022 93440175754 1395274532769
(loop(\(x,i).(~x + loop(\(x,i).(1 - (x * i)),i,1)),x,1) mod (x + 1))
A258817: 0 1 2 0 3 3 0 0 8 5 4 0 9 7 8 0
loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,(x + 1))
A038502: 1 2 1 4 5 2 7 8 1 10 11 4 13 14 5 16
((2 - loop(\(x,i).2x,(if (x mod 2) <= 0 then x else 1),2)) mod (x + 1))
A249744: 0 0 0 2 0 4 0 6 3 8 0 10 0 12 9 14
loop(\(x,i).loop(\(x,i).2x,i,x3),4,(x + 1))
A183062: 288230376151711744 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,loop(\(x,i).(2x + 1),x,(2 div (x + 1))))
A088037: 4 9 9 49 225 961 3969 16129 65025 261121 1046529 4190209 16769025 67092481 268402689 1073676289
loop(\(x,i).(x + (if (~2 + (x div 4)) <= 0 then 1 else 2)),2,(x + 1))
A154660: 3 4 5 6 7 8
A099474: 3 4 5 6 7 8 9 10 11 12 14 16 17 18 19 20
((x + 1) * loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x + 2)))
A243015: 2 6 0 20 0 42 0 0 0 110 0 156 0 0 0 272
loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then i else 0)),(x div 2),(x + 1))
A113459: 1 2 3 5 5 7 7 11 11 11 11 13
A159477: 1 2 3 5 5 7 7 11 11 11 11 13 13 17 17 17
((x + 1) + loop(\(x,i).(x - (if (~2 + (x div 2)) <= 0 then 0 else 1)),2,x))
A260392: 1 3 5 7 9 11 12 13 15 17 19 21 23 25 27 29
loop(\(x,i).(4x + (if (2 - i) <= 0 then x else 1)),x,(x + 1))
A081040: 1 9 65 425 2625 15625 90625 515625 2890625 16015625 87890625 478515625 2587890625 13916015625 74462890625 396728515625
loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,(x + 1))
A002544: 1 12 90 560 3150 16632 84084 411840 1969110 9237800 42678636 194699232 878850700 3931426800 17450721000 76938289920
((x + 1) + (if x <= 0 then 1 else (if (x + ~2) <= 0 then x else (x2 + 2x))))
A130076: 2 3 5 19
A161414: 2 3 5 19 29
loop(\(x,i).(3x + (if (2 - i) <= 0 then x else 1)),x,(x + 1))
A081039: 1 7 40 208 1024 4864 22528 102400 458752 2031616 8912896 38797312 167772160 721420288 3087007744 13153337344
loop(\(x,i).2x,x,loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))
A014964: 1 2 12 8 80 96 448 128 2304 2560 11264 6144 53248 57344 245760 32768
loop(\(x,i).loop(\(x,i).~2x,(i mod 3),x),x,(x + 1))
A176900: 1 ~4 ~24 ~32 80 384 448 ~1024 ~4608 ~5120 11264 49152 53248 ~114688 ~491520 ~524288
((2x + 1) - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x))
A064801: 1 4 5 9 10 11 16 17 18 19 25 26 27 28 29 36
loop(\(x,i).x3,1,loop(\(x,i).(x * (1 + i)),x,(x + 1)))
A321207: 1 64 5832 884736 216000000 80621568000 43912253952000 33560740233216000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.loop(\(x,i).(x div (if (x mod 2) <= 0 then 1 else 4)),x,x),(x + 1))
A032911: 1 3 5 7 13 15 21 23 29 31 53 55 61 63 85 87
((x + 1) + (if x <= 0 then 1 else loop(\(x,i).((x * (x + i)) div 2),x,x)))
A322067: 2 3 10 328
loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,(x + 1))
A027800: 1 10 45 140 350 756 1470 2640 4455 7150 11011 16380 23660 33320 45900 62016
loop(\(x,i).((if (~2 + (x div 2)) <= 0 then 1 else 2) + (x * i)),x,(x + 1))
A005346: 1 3 9 35 178 1132
loop(\(x,i).(loop(\(x,i).(x * i),(~1 + i),2) + (x * i)),x,(x + 1))
A000775: 1 4 12 46 220 1268 8568 66456 582048 5681952 61174080 720089280 9199906560 126783809280 1874605662720 29601115891200
loop(\(x,i).(x * i),(x2 + x),loop(\(x,i).(x * i),x,(x + 1)))
A127235: 1 4 4320 11496038400 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(x div (1 + (x mod 2))),i,i)),x,(x + 1))
A135013: 1 2 5 6 11 14 21 22 31 36 47 50 63 70 85 86
loop(\(x,i).(x * (if (x + ~2) <= 0 then 1 else x2)),(x + ~1),(x + ~1))
A257229: ~1 0 1 2 7625597484987
(if x <= 0 then 2 else loop(\(x,i).(2x2 + ~2),2x,(x + ~1)))
A103527: 2 6 70 4611686018427387903
(if (x + ~4) <= 0 then 0 else loop(\(x,i).(x * (x - i)),2,(x + ~1)))
A052768: 0 0 0 0 0 120 360 840 1680 3024 5040 7920 11880 17160 24024 32760
(2x - loop(\(x,i).(x - (if x <= 0 then 0 else (2 + i))),x,(x + ~1)))
A048859: 1 2 6 7 8 13 14 15 16 22 23 24 25 26 33 34
loop(\(x,i).(x * loop(\(x,i).(x + (2 * (i * i)) - i),i,0)),x,1)
A279662: 1 1 7 154 7700 731500 117771500 29678418000 11040371496000 5796195035400000 4144279450311000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x))
A016014: 1 1 1 2 1 1 2 1 1 2 1 3 2 1 1 3
loop(\(x,i).(x * (1 + loop(\(x,i).(~2x + 2),(~1 + i),1))),x,1)
A247525: 1 2 2 6 ~6 ~42 378 8694 ~356454 ~31011498 5240943162 1797643504566 ~1224195226609446 ~1673474874775112682 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + loop(\(x,i).(x * (x + i)),2,3))),x,1)
A175558: 1 167 27889 4657463 777796321 129891985607 21691961596369 3622557586593623 604967116961135041 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).x2,1,(1 + (i div 3)))),x,1)
A263465: 1 2 3 7 11
A092353: 1 2 3 7 11 15 24 33 42 58 74 90 115 140 165 201
loop(\(x,i).(x + loop(\(x,i).(x * (i * i * i)),(1 + i),1)),x,1)
A138564: 1 9 225 14049 1742049 374990049 128399054049 65676719822049 47850402559694049 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(3x2 + 3),2,1)),x,1)
A225374: 1 111 12321 1367631 151807041 16850581551 1870414552161 207616015289871 23045377697175681 2558036924386500591 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 2),x,loop(\(x,i).7x,x,1))
A094970: 1 3 12 42 150 525 1838 6433 22518 78815 275854 965491 3379220 11827271 41395451 144884079
loop(\(x,i).(x * (~1 + loop(\(x,i).(x3 + 2),2,2))),x,1)
A097659: 1 1001 1002001 1003003001 1004006004001 1005010010005001 1006015020015006001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (x div (if (i mod 3) <= 0 then 4 else 1))),x,1)
A005018: 1 2 4 5 10 20
A018283: 1 2 4 5 10 20 25 50 100
A018489: 1 2 4 5 10 20 25 50 100 125 250 500
A245478: 1 2 4 5 10 20 25 50 100 125 250 500 625 1250 2500 3125
loop(\(x,i).(x + (x div (if (i mod 4) <= 0 then 4 else 1))),x,1)
A222011: 1 2 4 8
A004655: 1 2 4 8 10 20 40 80 100 200 400 800 1000 2000 4000 8000
loop(\(x,i).(x * (x div 2)),1,loop(\(x,i).5x,x,1))
A162729: 0 10 300 7750 195000 4881250 122062500 3051718750 76293750000 1907347656250 47683710937500 1192092871093750 29802322265625000 745058059082031250 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 3),x,loop(\(x,i).5x,x,1))
A094974: 1 1 2 4 7 12 21 35 59 99 165 275 459 765 1276 2126
loop(\(x,i).(2x + 1),x,loop(\(x,i).5x,x,1))
A155594: 1 11 103 1007 10015 100031 1000063 10000127 100000255 1000000511 10000001023 100000002047 1000000004095 10000000008191 100000000016383 1000000000032767
loop(\(x,i).(2x + ~1),x,loop(\(x,i).5x,x,1))
A155601: 1 9 97 993 9985 99969 999937 9999873 99999745 999999489 9999998977 99999997953 999999995905 9999999991809 99999999983617 999999999967233
loop(\(x,i).(x div 4),x,loop(\(x,i).5x,x,1))
A094979-A065565: 1 1 1 1 2 3 3 4 5 7 9 11 14 18 22 28
loop(\(x,i).(x * (x div 2)),1,(0 - loop(\(x,i).3x,x,1)))
A025551: 1 6 45 378 3321 29646 266085 2392578 21526641 193720086 1743421725 15690618378 141215033961 1270933711326 11438398618965 102945573221778
loop(\(x,i).(2x2 + ~x),1,loop(\(x,i).3x,x,1))
A010035: 1 15 153 1431 13041 117855 1062153 9563751 86086881 774821295 6973509753 62761942071 564858541521 5083730062335 45753580126953 411782249840391
(loop(\(x,i).(2x + ~4),x,1) mod loop(\(x,i).3x,x,1))
A094729: 0 1 1 7 37 151 541 1807 5797 18151 55981 171007 519157 1569751 4733821 14250607
(loop(\(x,i).4x,x,1) - loop(\(x,i).3x,x,1))
A005061: 0 1 7 37 175 781 3367 14197 58975 242461 989527 4017157 16245775 65514541 263652487 1059392917
(loop(\(x,i).4x,x,1) mod loop(\(x,i).3x,x,1))
A064629: 0 1 7 10 13 52 451 1075 6487 6265 44743 119923 302545 147298 589192 11922706
loop(\(x,i).(x * (x2 div 2)),1,loop(\(x,i).3x,x,1))
A130213: 0 12 360 9828 265680 7174332 193709880 5230175508 141214764960 3812798732652 102945566017800 2779530283189188 75047317648233840 2026277576508690972 4611686018427387903 4611686018427387903
loop(\(x,i).(2x + ~1),(x + ~1),loop(\(x,i).3x,x,1))
A036551: 1 3 17 105 641 3873 23297 139905 839681 5038593 30232577 181397505 1088389121 6530342913 39182073857 235092475905
loop(\(x,i).(x * (x + (x div 2))),1,loop(\(x,i).3x,x,1))
A016142: 1 12 117 1080 9801 88452 796797 7173360 64566801 581120892 5230147077 47071500840 423644039001 3812797945332 34315186290957 308836690967520
(loop(\(x,i).2x,x2,1) + loop(\(x,i).3x,x,1))
A120767: 2 5 25 539 65617 33554675 68719477465 562949953423499 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,x2,1) - loop(\(x,i).3x,x,1))
A120773: 0 ~1 7 485 65455 33554189 68719476007 562949953419125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).3x2,2,loop(\(x,i).3x,x,1))
A013779: 27 2187 177147 14348907 1162261467 94143178827 7625597484987 617673396283947 50031545098999707 4052555153018976267 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,(2x + ~4),loop(\(x,i).3x,x,1))
A057269: 1 3 9 531441
(loop(\(x,i).4x,x,2) - loop(\(x,i).3x,x,1))
A085350: 1 5 23 101 431 1805 7463 30581 124511 504605 2038103 8211461 33022991 132623405 532087943 2133134741
((x + 1) div loop(\(x,i).i,loop(\(x,i).(x div (1 + (x mod 2))),x,x),1))
A329900: 1 2 1 4 1 3 1 8 1 2 1 6 1 2 1 16
loop(\(x,i).(x + loop(\(x,i).(x * (1 + i)),(i - (x mod 2)),1)),x,1)
A054116: 1 2 8 32 152 872 5912 46232 409112 4037912 43954712 522956312 6749977112 93928268312 1401602636312 22324392524312
((x + 1) - loop(\(x,i).((x + ~1) - (2 * (if x <= 0 then 0 else i))),x,x))
A007606: 1 4 5 6 11 12 13 14 15 22 23 24 25 26 27 28
loop(\(x,i).(x * (1 + loop(\(x,i).(2x2 + 2x),i,2))),x,1)
A068532: 1 13 4069 794728597 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + loop(\(x,i).(2 * (x - (i mod 2))),i,2))),x,1)
A269694: 1 1 3 15 165 3465 148995 12664575 2165642325 738484032825 504384594419475 688484971382583375 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x3,1,loop(\(x,i).(x * (~1 + (2 * i))),x,1))
A166750: 1 1 27 3375 1157625 843908625 1123242379875 2467763508585375 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) div 2),x,loop(\(x,i).(x * (~1 + (2 * i))),x,1))
A020135: 1 1 1 2 7 30 163 1056 7919 67304 639384 6713531 77205602 965070018 13028445232 188912455861
((x + 1) - loop(\(x,i).(x - (if x <= 0 then 1 else (1 + (i div 2)))),x,x))
A274427: 1 2 4 5 7 8 11 12 13 16 17 18 22 23 24 25
loop(\(x,i).(x * (~1 + (loop(\(x,i).2x,i,1) + (i mod 2)))),x,1)
A003053: 1 2 6 48 720 23040 1451520 185794560 47377612800 24257337753600 24815256521932800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((if x <= 0 then 1 else 8) * loop(\(x,i).(x2 + x),x,1))
A226966: 1 16 48 336 14448
loop(\(x,i).(x + (loop(\(x,i).2x,i,1) div (1 + (x * i)))),x,1)
A064324: 1 2 2 3 4 5 7 9 12 16 22 30 41 56 76 104
loop(\(x,i).(x * loop(\(x,i).(6x + 1),i,1)),x,1)
A015005: 1 7 301 77959 121226245 1131162092095 63330372050122765 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(8x + 1),i,1)),x,1)
A015007: 1 9 657 384345 1799118945 67375205371305 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(~6x + 1),i,1)),x,1)
A015019: 1 ~5 ~155 28675 31857925 ~212333070125 ~8491411807368875 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(1 + ((x2 + x) div 2)),i,1)),x,1)
A173449: 1 3 7 18 85 2364 2600425 3374964379317 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(5x + 1),i,1)),x,1)
A015004: 1 6 186 29016 22661496 88515803376 1728802155736656 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).((x * (i * (1 + i))) div 2),i,1)),x,1)
A154604: 1 1 3 54 9720 26244000 1488034800000 2362404048480000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(~8x + 1),i,1)),x,1)
A015022: 1 ~7 ~399 181545 661005345 ~19253102683815 ~4486300228074519855 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(~5x + 1),i,1)),x,1)
A015018: 1 ~4 ~84 8736 4551456 ~11851991424 ~154324780331904 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).4x,(2 * i),(1 + i))),x,1)
A014931: 1 33 801 17185 344865 6636321 124076833 2271560481 40926266145 728121033505 12822748939041 223928981472033 3883103678710561 66933498461897505 1147797409030816545 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).3x,(2 * i),(1 + i))),x,1)
A014923: 1 19 262 3178 35983 390277 4110364 42374116 429794605 4303999495 42658627906 419231343214 4090815317467 39676936914073 382828823738488 3677086937252872
loop(\(x,i).loop(\(x,i).(x + (((1 + i) div 2) * i)),(1 + i),x),x,1)
A206806: 1 4 13 30 62 112 190 300 455 660 931 1274 1708 2240 2892 3672
loop(\(x,i).loop(\(x,i).(x + (i * i * i * i)),(1 + i),x),x,1)
A101089: 1 18 116 470 1449 3724 8400 17172 32505 57838 97812 158522 247793 375480 553792 797640
loop(\(x,i).(x + loop(\(x,i).8x,i,(1 + i))),x,1)
A014921: 1 17 209 2257 22737 219345 2054353 18831569 169826513 1512003793 13323163857 116402378961 1009755576529 8706336970961 74677034637521 637626988058833
loop(\(x,i).(loop(\(x,i).4x,i,1) + (x * (~1 + i))),x,1)
A195256: 1 4 20 104 568 3296 20576 139840 1044416 8617472 78605824 790252544 8709555200 104581771264 1359831461888 19038714208256
loop(\(x,i).(x * loop(\(x,i).(x * (2 + (x mod 4))),i,1)),x,1)
A099168: 1 3 45 3375 1265625 2373046875 22247314453125 1042842864990234375 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(x * (i * i * i * i)),i,1)),x,1)
A289949: 1 2 18 1314 333090 207693090 268946253090 645510228813090 2643553803594573090 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (2 + (if (~x + 2) <= 0 then 8 else 1))),x,1)
A093138: 1 3 30 300 3000 30000 300000 3000000 30000000 300000000 3000000000 30000000000 300000000000 3000000000000 30000000000000 300000000000000
loop(\(x,i).(x mod 2),(x mod 2),loop(\(x,i).(x * ((1 + i) div 2)),x,1))
A110947: 1 1 1 0 4 0 36 0 576 0 14400 0 518400 0 25401600 0
loop(\(x,i).(x * loop(\(x,i).4x,(x div (1 + i)),2)),x,1)
A073888: 1 2 4 32 262144 4611686018427387903
loop(\(x,i).((~x + 1) + (x * loop(\(x,i).x2,(~1 + i),2))),x,1)
A162634: 1 2 7 106 27031 1771476586 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,loop(\(x,i).(x * (2 + (x mod 4))),x,1))
A067405: 1 9 225 5625 140625 3515625 87890625 2197265625 54931640625 1373291015625 34332275390625 858306884765625 21457672119140625 536441802978515625 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (4 * (if (i mod 3) <= 0 then 1 else x))),x,1)
A018612: 1 5 25 29 145 725
loop(\(x,i).(x + (2 * (x + (if (i mod 3) <= 0 then 2 else 0)))),x,1)
A018370: 1 3 9 31 93 279
(1 + loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,x))
A318165: 1 3 13
A319924: 1 3 13 61 281 1261 5545 24025 102961 437581 1847561 7759753 32449873 135207801 561632401 2326762801
loop(\(x,i).(loop(\(x,i).~x,i,3) + (x * (2 + i))),x,1)
A176408: 1 0 3 12 75 522 4179 37608 376083 4136910 49642923 645357996 9035011947 135525179202 2168402867235 36862848742992
loop(\(x,i).(loop(\(x,i).(x * (0 - i)),i,1) + (x * (2 + i))),x,1)
A142983: 1 2 10 44 288 1896 15888 137952 1419840 15255360 186693120 2387093760 33898314240 502247692800 8123141376000 136785729024000
loop(\(x,i).loop(\(x,i).(x * (((1 + i) div 2) * i)),(2 * i),x),x,1)
A174827: 1 2 192 4976640 115579079884800 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + ((if (i mod 2) <= 0 then 2 else 2x) * (i div 2))),x,1)
A047905: 1 1 3 9 13 65 71 497 505 4545 4555 50105 50117 651521 651535 9773025
loop(\(x,i).(x * (loop(\(x,i).(2x + 1),i,1) + (i mod 2))),x,1)
A086812: 1 4 28 448 13888 888832 112881664 28897705984 14766727757824 15121129224011776 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).3x,x,loop(\(x,i).4x,x2,1))
A135398: 1 12 2304 7077888 347892350976 273593677362757632 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x2,1)
A201555: 1 2 70 48620 601080390 126410606437752 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,x),x))
A191106: 1 3 7 9 19 21 25 27 55 57 61 63 73 75 79 81
loop(\(x,i).(x + (if (x mod (3 + i)) <= 0 then 3 else x)),x,1)
A222011: 1 2 4 8
A018383: 1 2 4 8 16 19 38 76 152 304
loop(\(x,i).(x * (if (~2 + (x div 4)) <= 0 then 3 else x)),x,1)
A175129: 1 3 9 27 729 531441 282429536481 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).2x,(~1 + i),3x)),x,1)
A155105: 1 4 28 364 9100 445900 43252300
loop(\(x,i).(x + loop(\(x,i).4x,(~1 + (2 * i)),x)),x,1)
A085523: 1 5 325 333125 5458253125 1430853765453125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).3x,(~1 + (2 * i)),x)),x,1)
A085522: 1 4 112 27328 59793664 1176978482176 208499384160514048 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (i mod 3) <= 0 then (x2 + ~1) else x)),x,1)
A018273: 1 2 4 19 38 76
loop(\(x,i).(x + (if (i mod 3) <= 0 then (1 + (x * i)) else x)),x,1)
A018269: 1 2 4 17 34 68
loop(\(x,i).(x + loop(\(x,i).2x,(4 div (1 + i)),x)),x,1)
A094283: 1 5 15 45 90 180 360 720 1440 2880 5760 11520 23040 46080 92160 184320
loop(\(x,i).(~x + loop(\(x,i).(x * (3 + i)),4,x)),x,1)
A135640: 1 839 703921 590589719 495504774241 415728505588199 348796216188498961 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.loop(\(x,i).(if (x mod 4) <= 0 then x else (x div 2)),x,x),x))
A052499: 1 2 3 4 6 7 8 11 12 14 15 16 22 23 24 27
(1 + loop(\(x,i).(if x <= 0 then 1 else (x * (((~1 + i) * i) div 2))),x,x))
A048774: 1 1 2 4 19 181
loop(\(x,i).(~x + loop(\(x,i).5x,(2 * i),x)),x,1)
A028694: 1 24 14976 233985024 91400166014976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + loop(\(x,i).2x2,(~1 + i),1)),x,1)
A332757: 1 2 6 44 2064 4292864 18430828806144 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).7x,i,x2),x,1)
A067504: 1 7 2401 1977326743
loop(\(x,i).(~x + loop(\(x,i).12x,i,x)),x,1)
A027880: 1 11 1573 2716571 56328099685 14016177372718235 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + loop(\(x,i).10x,i,x)),x,1)
A027878: 1 9 891 890109 8900199891 890011088900109 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + (loop(\(x,i).3x,i,1) + (x * i))),x,1)
A195255: 1 3 12 51 234 1179 6624 41931 300078 2420307 21841812 218595267 2405079378 28862546859 375217892136 5253064838811
loop(\(x,i).(x + (loop(\(x,i).(x * (0 - i)),i,1) + (x * i))),x,1)
A024167: 1 1 5 14 94 444 3828 25584 270576 2342880 29400480 312888960 4546558080 57424792320 948550176000 13869128448000
loop(\(x,i).(~x + loop(\(x,i).7x,i,x)),x,1)
A027875: 1 6 288 98496 236390400 3972777062400 467389275837235200 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * i),(7 * i),x),x,1)
A271947: 1 5040 439378587648000 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * (1 + i)),(5 * i),x),x,1)
A294323: 1 720 28740096000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(4x * (~1 + (2 * i))),i,x),x,1)
A203516: 1 4 192 184320 4954521600 4794391461888000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * (i * i * i * (1 + i))),i,x),x,1)
A091810: 1 2 96 497664 825564856320 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (8x div (if i <= 0 then 1 else i))),x,1)
A000581: 1 9 45 165 495 1287 3003 6435 12870 24310 43758 75582 125970 203490 319770 490314
loop(\(x,i).(~x + loop(\(x,i).3x,6,i)),x,1)
A056084: 1 728 730 1457 1459 2186 2188 2915 2917 3644 3646 4373 4375 5102 5104 5831
loop(\(x,i).(loop(\(x,i).(1 + (x * i)),(~1 + i),1) + (x * i)),x,1)
A093345: 1 2 6 23 108 605 3956 29649 250892 2367629 24662700 281153801 3482350724 46572620757 668943488084 10271127486065
loop(\(x,i).(loop(\(x,i).6x,i,1) + (x * i)),x,1)
A108869: 1 7 50 366 2760 21576 176112 1512720 13781376 134110080 1401566976 15780033792 191537187840 2503044135936 35120982067200 527284915992576
loop(\(x,i).(loop(\(x,i).~3x,i,1) + (x * i)),x,1)
A010843: 1 ~2 5 ~12 33 ~78 261 ~360 3681 13446 193509 1951452 23948865 309740922 4341155877 65102989248
loop(\(x,i).(loop(\(x,i).(1 + (2x * i)),i,1) - (x * i)),x,1)
A110322: 1 2 9 52 425 4206 50737 708464 11350257 204171130 4084757561 89849981772 2156575777369 56068679418662 1569955094823585 47098171778191816
loop(\(x,i).(loop(\(x,i).5x,i,1) + (x * i)),x,1)
A080954: 1 6 37 236 1569 10970 81445 648240 5576545 52142030 531185925 5891873300 70946620225 923526766050 12935478240325 194062691183000
loop(\(x,i).(loop(\(x,i).(x * (~1 + (2 * i))),i,1) + (x * i)),x,1)
A034430: 1 2 7 36 249 2190 23535 299880 4426065 74294010 1397669175 29123671500 665718201225 16560190196550 445300709428575 12869793995058000
loop(\(x,i).(loop(\(x,i).(x * (~1 + (2 * i))),i,1) - (x * i)),x,1)
A331403: 1 0 3 6 81 540 7155 85050 1346625 22339800 431331075 9004668750 208178118225 5199538043700 140664514065075 4080315642653250
loop(\(x,i).(x + (x * i) - (if (i mod 2) <= 0 then ~2 else 2)),x,1)
A055596: 1 0 2 6 32 190 1332 10654 95888 958878 10547660 126571918 1645434936 23036089102 345541336532 5528661384510
(loop(\(x,i).(x * i),4x,1) div loop(\(x,i).(x * i),x,1))
A166338: 1 24 20160 79833600 871782912000 20274183401472000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x * (~1 + (2 * i))),x,1) div loop(\(x,i).(x * i),x,1))
A024502: 1 1 1 2 4 7 14 26 50 94 180 344 660 1269 2448 4733
(loop(\(x,i).4x,x2,1) + loop(\(x,i).(x * i),x,1))
A309675: 2 5 258 262150 4294967320 1125899906842744 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * (~1 + (4 * (i * i)))),i,x),x,1)
A136411: 1 3 135 212625 21097715625 207248662456171875 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x * i),x2,1) div loop(\(x,i).(x * (i * i)),x,1))
A088021: 1 1 6 10080 36324288000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(x + (5 * i)),i,i)),x,1)
A302911: 1 6 102 3366 181764 14541120 1614064320 237267455040 44606281547520 10437869882119680 2974792916404108800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(loop(\(x,i).(2x + (i div 3)),x,1) + i),x,1)
A212814: 1 3 11 2632
(if x <= 0 then 1 else (2 + (if (x mod 10) <= 0 then 2 else 0)))
A103817: 1 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2
(loop(\(x,i).2x,x,1) div (if (x mod 3) <= 0 then 1 else ~2))
A104537: 1 ~1 ~2 8 ~8 ~16 64 ~64 ~128 512 ~512 ~1024 4096 ~4096 ~8192 32768
((if x <= 0 then 1 else x) mod (if ((x div 4) mod 2) <= 0 then 2 else ~2))
A257170: 1 1 0 1 0 ~1 0 ~1 0 1 0 1 0 ~1 0 ~1
((x - (if (x + ~2) <= 0 then 1 else (if (x mod 3) <= 0 then x else 0))) mod 2)
A265245: 1 0 1 0 0 1 0 1 0 0 0 1 0 1 0 0
(if x <= 0 then 1 else (loop(\(x,i).(1 + (x * i) - (x div 2)),x,0) div 2))
A101205: 1 0 1 4 16 75
(if (x mod (1 + ((x + ~1) mod 4))) <= 0 then (if x <= 0 then 0 else 1) else 2)
A331591-A193509: 0 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1
(if ((x + ~2) mod (1 + (x div 4))) <= 0 then (if x <= 0 then 0 else 1) else 2)
A212179: 0 1 1 1 1 2 1 2 1 2 2 1 2 2 1 2
(if x <= 0 then 0 else (if (x mod (~1 + (2 * (x div 4)))) <= 0 then 1 else 2))
A233544: 0 1 1 1 1 1 1 1 2 1 2 2 2 2 2 1
(2 * (if (x mod 3) <= 0 then (3 * (if x <= 0 then 1 else 2)) else 1))
A010133: 6 2 2 12 2 2 12 2 2 12 2 2 12 2 2 12
(2 * (if (x mod 2) <= 0 then (3 * (2 + (if x <= 0 then 0 else 2))) else 1))
A040143: 12 2 24 2 24 2 24 2 24 2 24 2 24 2 24 2
(loop(\(x,i).2x,x,(1 + loop(\(x,i).2x,x,3))) div 2)
A049775: 2 7 26 100 392 1552 6176 24640 98432 393472 1573376 6292480 25167872 100667392 402661376 1610629120
loop(\(x,i).(x * i),x,(loop(\(x,i).2x,(x + ~3),1) div 2))
A052652: 0 0 0 0 24 240 2880 40320 645120 11612160 232243200 5109350400 122624409600 3188234649600 89270570188800 2678117105664000
(loop(\(x,i).2x,x,(1 + loop(\(x,i).(2x + 4),x,1))) div 2)
A080960: 1 7 34 148 616 2512 10144 40768 163456 654592 2619904 10482688 41936896 167759872 671064064 2684305408
(((x + 2) div (if (if (x mod 3) <= 0 then x else 0) <= 0 then 2 else 1)) mod 2)
A051023: 1 1 0 1 1 1 0 0 1 1 0 0 0 1 0 1
(2 * (if (x mod 2) <= 0 then (5 * (if x <= 0 then 1 else 2)) else 1))
A040099: 10 2 20 2 20 2 20 2 20 2 20 2 20 2 20 2
(2 * (if (x mod 2) <= 0 then (8 * (if x <= 0 then 1 else 2)) else 1))
A040255: 16 2 32 2 32 2 32 2 32 2 32 2 32 2 32 2
(if (x + ~1) <= 0 then x else (2 * (if (x mod 2) <= 0 then 8 else 1)))
A144532: 0 1 16 2 16 2 16 2 16 2 16 2 16 2 16 2
((if x <= 0 then 1 else x) mod (if ((2 + (x div 2)) mod 4) <= 0 then 1 else 2))
A321512: 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1
(if x <= 0 then 1 else (2 * (if (x + ~2) <= 0 then 2x else 5)))
A329503: 1 4 8 10 10 10 10 10 10 10 10 10 10 10 10 10
loop(\(x,i).x2,(x + ~2),(if x <= 0 then 1 else 10))
A165428: 1 10 10 100 10000 100000000 10000000000000000 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,loop(\(x,i).3x,5,2))
A249227: 486 972 1944 3888 7776 15552 31104 62208 124416 248832 497664 995328 1990656 3981312 7962624 15925248
(if (x mod 5) <= 0 then 0 else (if (x + ~4) <= 0 then 1 else 2))
A215884: 0 1 1 1 1 0 2 2 2 2 0 2 2 2 2 0
(loop(\(x,i).(x * i),x,(1 + (if x <= 0 then 1 else (x + 4)))) div 2)
A229039: 1 3 7 24 108 600 3960 30240 262080 2540160 27216000 319334400 4071513600 56043187200 828193766400 13076743680000
((if (x mod 3) <= 0 then 1 else x) mod (if (~2 + (x div 2)) <= 0 then 1 else 2))
A011680: 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 1
(if (x + ~1) <= 0 then x else (if ((x + ~2) mod (2 + (x mod 2))) <= 0 then 1 else 2))
A242481: 0 1 1 2 1 1 1 2 1 2 1 1 1 2 1 2
(if (x mod 2) <= 0 then (9 * (if x <= 0 then 1 else 2)) else 2)
A040080: 9 2 18 2 18 2 18 2 18 2 18 2 18 2 18 2
(if x <= 0 then 1 else loop(\(x,i).2x,((1 + (x div 2)) div 3),2))
A306390: 1 2 2 2 4 4 4 4 4 4 8 8 8 8 8 8
(loop(\(x,i).2x,x,1) mod (2 + loop(\(x,i).x2,2,3)))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A036135: 1 2 4 8 16 32 64 45 7 14 28 56 29 58 33 66
((if x <= 0 then 1 else (x * (if (x mod 2) <= 0 then x else 1))) mod 6)
A204671: 1 1 4 3 4 5 0 1 4 3 4 5 0 1 4 3
(if x <= 0 then 1 else (2 * (~1 + (2 * (if (x mod 2) <= 0 then x else (~x + 1))))))
A161718: 1 ~2 6 ~10 14 ~18 22 ~26 30 ~34 38 ~42 46 ~50 54 ~58
loop(\(x,i).x2,2,loop(\(x,i).4x,(2x + 1),2))
A013805: 4096 268435456 17592186044416 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,2,loop(\(x,i).2x2,(2x + ~1),2))
A139296: 16 4096 1152921504606846976 4611686018427387903
(2 * (1 + (2 * loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x))))
A174028: 2 2 6 2 6 10 2 6 10 14 2 6 10 14 18 2
(((if (x + ~2) <= 0 then 1 else 2) - (if (x mod 3) <= 0 then x else 1)) mod 2)
A267810: 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1
(2 + loop(\(x,i).(x div 2),x,loop(\(x,i).(3x + 1),x,1)))
A259796: 3 4 5 7 9 13 19 27 40 59 88 131 196 293 439 658
(if x <= 0 then 1 else (2 * ((x + 1) + (if (~2 + (x div 2)) <= 0 then 1 else 2))))
A303580: 1 6 8 10 12 14 18 20 22 24 26 28 30 32 34 36
(2 * loop(\(x,i).~x,(x + ~1),loop(\(x,i).(~2x + 4),x,1)))
A115341: 2 4 0 8 8 24 40 88 168 344 680 1368 2728 5464 10920 21848
(2 * ((if (x + ~3) <= 0 then 2 else 0) + loop(\(x,i).2x,x,1)))
A212350: 6 8 12 20 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536
(loop(\(x,i).3x,x,1) - (loop(\(x,i).2x,x,1) div 2))
A083313: 1 2 7 23 73 227 697 2123 6433 19427 58537 176123 529393 1590227 4774777 14332523
loop(\(x,i).(x * i),x,loop(\(x,i).(x * (i * (2 + i))),(x + 1),2))
A084259: 6 48 1440 103680 14515200 3483648000 1316818944000 737418608640000 584035538042880000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((2x + 2) + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 2)),x,x))
A182815: 2 4 5 6 7 8 8 9 10 11 10 11 12 13 14 12
loop(\(x,i).(2 + (if (x mod 2) <= 0 then 2x else 1)),x,((x + 1) mod 2))
A282004: 1 2 3 14 3 62 3 254 3 1022 3 4094 3 16382 3 65534
loop(\(x,i).x2,1,loop(\(x,i).(x * (3 + i)),(x + 1),2))
A162994: 64 1600 57600 2822400 180633600 14631321600 1463132160000 177038991360000 25493614755840000 4308420893736960000 4611686018427387903 4611686018427387903
(loop(\(x,i).(if (x mod 2) <= 0 then x else ((~x + 1) div 2)),x,(x + 1)) div 2)
A329480: 0 1 0 2 ~1 3 1 4 ~2 5 0 6 ~3 7 2 8
loop(\(x,i).loop(\(x,i).2x,(x + ~1),x3),(x + ~1),2)
A100680: 2 2 16 134217728 4611686018427387903
((1 + (if (x mod 2) <= 0 then 6 else 0)) * (if x <= 0 then 1 else 2))
A040048: 7 2 14 2 14 2 14 2 14 2 14 2 14 2 14 2
(loop(\(x,i).(3x * i),(x + 1),1) div (if x <= 0 then 1 else 2))
A032108: 3 9 81 972 14580 262440 5511240 132269760 3571283520 107138505600 3535570684800 127280544652800 4963941241459200 208485532141286400 4611686018427387903 4611686018427387903
loop(\(x,i).x2,((x2 div 2) div 3),(if x <= 0 then 1 else 2))
A051285: 1 2 2 4 16 65536 4611686018427387903
((if (~6 + (x div 2)) <= 0 then 0 else 2) + (if x <= 0 then 1 else 2))
A151659: 1 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4
(2 * ((1 + (if (x mod 2) <= 0 then 4 else 0)) * (if x <= 0 then 1 else 2)))
A040094: 10 4 20 4 20 4 20 4 20 4 20 4 20 4 20 4
(2 * ((if (x mod 2) <= 0 then 6 else 1) * (if x <= 0 then 1 else 2)))
A040137: 12 4 24 4 24 4 24 4 24 4 24 4 24 4 24 4
(2 * ((if (x mod 2) <= 0 then 8 else 1) * (if x <= 0 then 1 else 2)))
A040247: 16 4 32 4 32 4 32 4 32 4 32 4 32 4 32 4
loop(\(x,i).5x,(2 - (x mod 2)),(if x <= 0 then 1 else 2))
A040604: 25 10 50 10 50 10 50 10 50 10 50 10 50 10 50 10
((loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2) + (if x <= 0 then 1 else 2))
A331280: 1 2 3 2 4 3 5 2 6 4 7 3 8 5 9 2
((x + (if (~4 + (x div 2)) <= 0 then 1 else 2)) * (if x <= 0 then 1 else 2))
A231407: 1 4 6
A175246: 1 4 6 8 10 12 14 16 18 20 24 26 28 30 32 34
(2 * loop(\(x,i).(x + loop(\(x,i).x2,2,(1 + (2 * i)))),x,1))
A259319: 2 164 1414 6216 19338 48620 105742 206992 374034 634676 1023638 1583320 2364570 3427452 4842014 6689056
(2 * loop(\(x,i).(x * (if (~2 + (x div 3)) <= 0 then 2 else x)),x,1))
A272698: 2 4 8 16 32 512
(if x <= 0 then 1 else (2 * (if (~2 + (x div 5)) <= 0 then 0 else 2)))
A205295: 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
(2 * (3 + loop(\(x,i).(x + (if (x + ~1) <= 0 then i else x)),x,0)))
A146529: 6 8 12 18 30 54 102 198 390 774 1542 3078 6150 12294 24582 49158
(2 * (2 + (if x <= 0 then 1 else (3 * loop(\(x,i).2x,x,2)))))
A091307: 6 28 52 100 196 388 772 1540 3076 6148 12292 24580 49156 98308 196612 393220
(2 + loop(\(x,i).(x + loop(\(x,i).(x * i),i,1)),(x + 3),2))
A147615: 13 37 157 877 5917 46237 409117 4037917 43954717 522956317 6749977117 93928268317 1401602636317 22324392524317 378011820620317 6780385526348317
(loop(\(x,i).2x,x,1) mod loop(\(x,i).(2x2 + 1),2,2))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A036150: 1 2 4 8 16 32 64 128 93 23 46 92 21 42 84 5
(loop(\(x,i).2x,x,1) mod loop(\(x,i).(x2 + 2x + 1),2,2))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A000855: 1 2 4 8 16 32 64 28 56 12 24 48 96 92 84 68
(4 + ((x + 1) * (if (x mod 2) <= 0 then (if x <= 0 then 1 else x) else 2)))
A087280: 5 8 10 12 24
(loop(\(x,i).2x,x,2) - loop(\(x,i).2x,((x + 1) div 2),2))
A208901: 0 0 4 8 24 48 112 224 480 960 1984 3968 8064 16128 32512 65024
(loop(\(x,i).(x + loop(\(x,i).i,(x div 4),1)),(x + ~1),2) div 2)
A125894: 1 1 1 2 2 3 3 4 5 6 7 9 11 13 16 20
(if x <= 0 then 1 else (4 * (if (x + ~4) <= 0 then 1 else 4)))
A132383: 1 4 4 4 4 16 16 16 16 16 16 16 16 16 16 16
(loop(\(x,i).(x + (x div 2)),x,loop(\(x,i).(x2 + 2),2,2)) div 2)
A120144: 19 28 42 63 95 142 213 320 480 720 1080 1620 2430 3645 5467 8201
(loop(\(x,i).(x * i),x,1) mod loop(\(x,i).2x2,4,2))
A289282: 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 1932053504 1278945280 2004310016
((if (x mod 2) <= 0 then loop(\(x,i).2x,x,1) else x) mod 8)
A204694: 1 1 4 3 0 5 0 7 0 1 0 3 0 5 0 7
((if x <= 0 then 1 else (x div ((if (x mod 2) <= 0 then 2 else x) mod 4))) mod 2)
A233320-A131218: 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1 1
(2 * loop(\(x,i).(x + i),(x + 2),loop(\(x,i).2x,x,4)))
A077265: 14 28 52 94 170 312 584 1114 2158 4228 8348 16566 32978 65776 131344 262450
(loop(\(x,i).2x,x,loop(\(x,i).x2,1,(x + ~4))) div 2)
A135466: 8 9 8 4 0 16 128 576 2048 6400 18432 50176 131072 331776 819200 1982464
(2 * (loop(\(x,i).(x * i),x,(if (x + ~3) <= 0 then x else 2)) div 2))
A052642: 0 0 4 18 48 240 1440 10080 80640 725760 7257600 79833600 958003200 12454041600 174356582400 2615348736000
loop(\(x,i).2x,x,(2 + (loop(\(x,i).(2x + 1),x,2) div 2)))
A093356: 3 8 28 104 400 1568 6208 24704 98560 393728 1573888 6293504 25169920 100671488 402669568 1610645504
(4 * loop(\(x,i).(x * (x - i)),(if x <= 0 then 1 else 2),(x + 2)))
A241813: 8 96 480 1440
(2 + (if (x + ~1) <= 0 then x else loop(\(x,i).x2,1,(2x + 4))))
A099080: 2 3 66 102
loop(\(x,i).2x,x,(2 + loop(\(x,i).(x * (2 + i)),(x div 2),2)))
A094867: 4 8 32 64 416 832
(if x <= 0 then 1 else loop(\(x,i).2x,(x + ~1),(4 + (x mod 2))))
A084568: 1 5 8 20 32 80 128 320 512 1280 2048 5120 8192 20480 32768 81920
(loop(\(x,i).3x,x,1) mod loop(\(x,i).(x2 + 2),2,2))
A070360: 1 3 9 27 5 15 7 21 25 37 35 29 11 33 23 31
(loop(\(x,i).(2x + 2),x,2) + loop(\(x,i).2x2,2,2))
A250740: 130 134 142 158 190 254 382 638 1150 2174 4222 8318 16510 32894 65662 131198
(loop(\(x,i).2x,x,1) mod loop(\(x,i).((x2 + 2) + i),2,2))
A222011: 1 2 4 8
A036128: 1 2 4 8 16 32 11 22 44 35 17 34 15 30 7 14
loop(\(x,i).(3x + 1),x,(if (x + ~2) <= 0 then 1 else 4))
A045886: 1 4 13 121 364 1093 3280 9841 29524 88573 265720 797161 2391484 7174453
(loop(\(x,i).(2x + 2),x,2) + loop(\(x,i).x2,2,4))
A250741: 258 262 270 286 318 382 510 766 1278 2302 4350 8446 16638 33022 65790 131326
loop(\(x,i).x2,2,loop(\(x,i).8x,x,4))
A013759: 256 1048576 4294967296 17592186044416 72057594037927936 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,4)
A002011: 4 24 120 560 2520 11088 48048 205920 875160 3695120 15519504 64899744 270415600 1123264800 4653525600 19234572480
(loop(\(x,i).3x,x,1) - loop(\(x,i).2x,x,4))
A214091: ~3 ~5 ~7 ~5 17 115 473 1675 5537 17635 54953 168955 515057 1561555 4717433 14217835
loop(\(x,i).loop(\(x,i).x2,1,(x2 * (x div 2))),x,4)
A139300: 4 1024 288230376151711744
loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,4)
A240530: 4 8 24 80 280 1008 3696 13728 51480 194480 739024 2821728 10816624 41602400 160466400 620470080
((if (4 mod (if x <= 0 then 1 else x)) <= 0 then 1 else 2) + (x div 4))
A087845: 1 1 1 2 2 3 3 3 4 4 4 4 5 5 5 5
((2 - ((~x + loop(\(x,i).(if x <= 0 then i else (x div 2)),x,0)) div 2)) div 2)
A193738: 1 1 1 1 2 2 1 2 3 3 1 2 3 4 4 1
(loop(\(x,i).2x,x,loop(\(x,i).(2x + 5),x,2)) div 2)
A081193: 1 9 46 204 856 3504 14176 57024 228736 916224 3667456 14674944 58710016 234860544 939483136 3758014464
(if x <= 0 then 1 else (2 * loop(\(x,i).(1 + (2 * (x - (i mod 2)))),x,2)))
A168648: 1 6 14 26 54 106 214 426 854 1706 3414 6826 13654 27306 54614 109226
(loop(\(x,i).2x,x,loop(\(x,i).(3x + ~3),x,2)) div 2)
A092803: 1 3 12 60 336 1968 11712 70080 420096 2519808 15117312 90700800 544198656 3265179648 19591053312 117546270720
(loop(\(x,i).4x,x,loop(\(x,i).(2x + 1),x,2)) div 2)
A165148: 1 10 88 736 6016 48640 391168 3137536 25133056 201195520 1610088448 12882804736 103070826496 824600166400 6596935548928 52776021262336
loop(\(x,i).2x,x,(2 + loop(\(x,i).(3x + ~1),x,2)))
A154407: 4 14 64 344 1984 11744 70144 420224 2520064 15117824 90701824 544200704 3265183744 19591061504 117546287104 705277558784
(loop(\(x,i).2x,x,loop(\(x,i).(3x + ~1),x,2)) div 2)
A090040: 1 5 28 164 976 5840 35008 209984 1259776 7558400 45349888 272098304 1632587776 9795522560 58773127168 352638746624
loop(\(x,i).(x * i),x,(2 + ((4 mod (if x <= 0 then 1 else x)) mod 2)))
A052628: 2 2 4 18 48 240 1440 10080 80640 725760 7257600 79833600 958003200 12454041600 174356582400 2615348736000
(loop(\(x,i).2x,(x + ~1),loop(\(x,i).((x + 1) + i),x,2)) div 2)
A084264: 1 2 7 22 64 176 464 1184 2944 7168 17152 40448 94208 217088 495616 1122304
(loop(\(x,i).(x * (1 + i)),x,loop(\(x,i).((x + 1) + i),x,2)) div 2)
A284816: 1 4 21 132 960 7920 73080 745920 8346240 101606400 1337212800 18920563200 286442956800 4620449433600 79114299264000 1433211107328000
(loop(\(x,i).x3,1,loop(\(x,i).(2x + 2),x,2)) div 2)
A128865: 4 108 1372 13500 119164 1000188 8193532 66325500 533731324 4282396668 34309431292 274676629500 2198218047484 17588965015548 140724603846652 1125848368021500
(loop(\(x,i).(2x + 1),x,loop(\(x,i).(2x + 2),x,2)) div 2)
A267774: 1 6 29 123 503 2031 8159 32703 130943 524031 2096639 8387583 33552383 134213631 536862719 2147467263
(2 * loop(\(x,i).(2 * (x - i)),x,loop(\(x,i).(2x + 2),x,2)))
A250162: 4 20 96 436 1880 7836 32032 129572 521256 2091052 8376368 33529908 134168632 536772668 2147287104 8589541444
(if (x + ~1) <= 0 then (x + 1) else (~2 + loop(\(x,i).4x,x,2)))
A267851: 1 2 30 126 510 2046 8190 32766 131070 524286 2097150 8388606 33554430 134217726 536870910 2147483646
(~2 + loop(\(x,i).(~2x + 4),x,loop(\(x,i).(~2x + 2),x,2)))
A279260: 0 6 18 90 330 1386 5418 21930 87210 349866 1397418 5593770 22366890 89483946 357903018 1431677610
(loop(\(x,i).2x,x,loop(\(x,i).((2x + 2) + i),x,2)) div 2)
A085354: 1 7 36 164 704 2928 11968 48448 195072 783104 3138560 12567552 50298880 201256960 805158912 3220914176
(2 * loop(\(x,i).(x3 + ~x),1,loop(\(x,i).2x,x,2)))
A059155: 12 120 1008 8160 65472 524160 4194048 33553920 268434432 2147481600 17179865088 137438945280 1099511611392 8796092989440 70368744112128 562949953290240
(2 * (loop(\(x,i).3x,x,2) - loop(\(x,i).2x,x,2)))
A145563: 0 4 20 76 260 844 2660 8236 25220 76684 232100 700396 2109380 6344524 19066340 57264556
(loop(\(x,i).loop(\(x,i).x3,1,2x2),x,2) div 2)
A139304: 1 256 72057594037927936
loop(\(x,i).2x,((2x + 4) * (if x <= 0 then 1 else 2x)),2)
A139568: 32 8192 8589934592 2305843009213693952 4611686018427387903
loop(\(x,i).(2x + 1),(x + 2),loop(\(x,i).2x,(x + 2),2))
A171473: 35 135 527 2079 8255 32895 131327 524799 2098175 8390655 33558527 134225919 536887295 2147516415 8590000127 34359869439
(if x <= 0 then 0 else ((x + 4) * (2 + (if (~x + 2) <= 0 then 2 else 1))))
A173035: 0 15 24 28 32 36 40 44 48 52 56 60 64 68 72 76
loop(\(x,i).(~x + loop(\(x,i).4x,(~1 + i),1)),(x + 2),2)
A109546: 5 11 53 203 821 3275 13109 52427 209717 838859 3355445 13421771 53687093 214748363 858993461 3435973835
(x - (loop(\(x,i).(x - (if x <= 0 then 1 else (2 * i))),x,(x + ~2)) div 2))
A032953: 1 2 3 5 6 8 9 10 11 15 16 17 18 19 20 24
(if x <= 0 then 1 else (2 * (2x + (if (~2 + (x div 2)) <= 0 then 0 else 1))))
A311225: 1 4 8 12 16 20 26 30 34 38 42 46 50 54 58 62
(2 + (if (x mod 2) <= 0 then (if x <= 0 then 6 else 1) else 2x))
A292529: 8 4 3 8 3
loop(\(x,i).8x2,(if x <= 0 then 1 else 2x),2)
A139294: 32 8192 2305843009213693952 4611686018427387903
loop(\(x,i).(x * i),2x,loop(\(x,i).(2x + 2),2x,2))
A331839: 2 28 1488 182880 41207040 14856307200 7847004211200 5713142135500800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,4x)
A016812: 0 16777216 68719476736 8916100448256 281474976710656 4096000000000000 36520347436056576 232218265089212416 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x + (if (~x + 2) <= 0 then x else 2)),x,(2 - (x div 2))) div 2)
A029867: 1 2 3 6 8 16 24
(if (x + ~2) <= 0 then x else loop(\(x,i).(x * (1 + (2 * i))),(x div 2),2))
A126989: 0 1 2 6 30 30 210
((1 - loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x)) div (2 + (x mod 2)))
A144903: 0 0 1 0 1 0 0 1 1 0 0 1 2 1 1 0
(loop(\(x,i).(3x + 3),(if x <= 0 then 1 else x),(x mod 2)) div 2)
A297444: 1 3 6 33 60 303 546 2733 4920 24603 44286 221433 398580 1992903 3587226 17936133
(2 * loop(\(x,i).(x + (loop(\(x,i).2x,(~1 + i),x) div 2)),x,2))
A060202: 4 6 12 36 180 1620 27540 908820 59073300 7620455700 1958457114900 1004688499943700 1029805712442292500 4611686018427387903 4611686018427387903 4611686018427387903
(2 * loop(\(x,i).x2,(x + ~2),loop(\(x,i).2x,x2,2)))
A285634: 4 8 64 2097152 4611686018427387903
((loop(\(x,i).x2,(x + ~1),2) + loop(\(x,i).x2,x,2)) div 2)
A055708: 2 3 10 136 32896 2147516416
(~2 + loop(\(x,i).(x + loop(\(x,i).~x,(i mod 3),i)),x,2))
A267313: 0 ~1 1 4 0 5 11 4 12 21 11 22 34 21 35 50
loop(\(x,i).(x + (if x <= 0 then (1 + i) else 0)),(x + 1),~2x)
A057039: 2 3 1 3 1 4 2 6 4 2 7 5 3 1 7 5
loop(\(x,i).(1 + (if ((2 + i) mod (2 + (x mod 2))) <= 0 then x else 1)),x,2)
A308050: 2 2 3 2 3 2 3 4 5 2 3 2 3 4 5 2
(if x <= 0 then 1 else ((x + 2) + loop(\(x,i).i,(~2 + (x div 3)),1)))
A026440: 1 4 5 6 7 8 9 10 11 12 13 14 16 17 18 20
(if x <= 0 then 1 else (2 * (x + loop(\(x,i).i,(~2 + (x div 3)),1))))
A231407: 1 4 6
A210939: 1 4 6 8 10 12 14 16 18 20 22 24 28 30 32 36
(loop(\(x,i).2x,x,2) - loop(\(x,i).(3x + ~6),x,2))
A072674: 0 4 14 40 110 304 854 2440 7070 20704 61094 181240 539630 1610704 4815734 14414440
loop(\(x,i).x2,1,loop(\(x,i).(x * (~x + i)),3x,2))
A058460: 4 7744 4611686018427387903 4611686018427387903
(loop(\(x,i).3x,x,2) - loop(\(x,i).(2x + 1),x,2))
A091344: 0 1 7 31 115 391 1267 3991 12355 37831 115027 348151 1050595 3164071 9516787 28599511
((x + 2) + (if (x mod 2) <= 0 then (if x <= 0 then 3 else (x div 2)) else 1))
A069214: 5 4 5 6 8 8 11 10 14 12 17 14 20 16 23 18
(2 + loop(\(x,i).(2 + (if (x + ~1) <= 0 then x else 2x)),x,(~x + 1)))
A228305: 3 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512
loop(\(x,i).3x,x,loop(\(x,i).(3x + ~1),x,2))
A051407: 2 15 126 1107 9882 88695 797526 7175547 64573362 581140575 5230206126 47071677987 423644570442 3812799539655 34315191073926 308836705316427
loop(\(x,i).((x + 1) + loop(\(x,i).(x * (x - i)),2,(2 + i))),x,2)
A166942: 2 27 148 509 1350 3031 6056 11097 19018 30899 48060 72085 104846 148527 205648 279089
loop(\(x,i).loop(\(x,i).2x,(x + ~1),x),1,((x2 + x) div 2))
A095351: 0 1 12 192 5120 245760 22020096 3758096384 1236950581248 791648371998720 990791918021509120 4611686018427387903 4611686018427387903 4611686018427387903
(2 * loop(\(x,i).((if (~2 + i) <= 0 then 1 else x) + (x * i)),(x + 1),x))
A097971: 2 10 56 360 2640 21840 201600 2056320 22982400 279417600 3672345600 51891840000 784604620800 12640852224000 216202162176000 3912561709056000
((~1 + loop(\(x,i).4x,x,2)) * ((if x <= 0 then 1 else x) mod 2))
A266436: 1 7 0 127 0 2047 0 32767 0 524287 0 8388607 0 134217727 0 2147483647
(loop(\(x,i).(3x + ~1),x,1) - ((if x <= 0 then 1 else x) mod 2))
A080925: 0 1 5 13 41 121 365 1093 3281 9841 29525 88573 265721 797161 2391485 7174453
(loop(\(x,i).(~x + 1),x,(x + loop(\(x,i).(1 - (x * i)),x,1))) div 2)
A145221-A000387: 0 0 1 0 6 20 135 924 7420 66744 667485 7342280 88107426 1145396460 16035550531 240533257860
loop(\(x,i).(2x + 1),x,loop(\(x,i).(2x + 6),x,2))
A188530: 2 21 107 471 1967 8031 32447 130431 523007 2094591 8383487 33544191 134197247 536829951 2147401727 8589770751
loop(\(x,i).~2x,x,loop(\(x,i).(~2x + ~2),x,2))
A110953: 2 12 40 176 672 2752 10880 43776 174592 699392 2795520 11186176 44736512 178962432 715816960 2863333376
loop(\(x,i).((x + 2) * i),4,loop(\(x,i).(2x + 2),x,2))
A305062: 176 272 464 848 1616 3152 6224 12368 24656 49232 98384 196688 393296 786512 1572944 3145808
(loop(\(x,i).3x,x,2) - loop(\(x,i).(2x + 2),x,2))
A260217: 0 0 4 24 100 360 1204 3864 12100 37320 114004 346104 1046500 3155880 9500404 28566744
(loop(\(x,i).((x2 + x) * (if (x mod 2) <= 0 then 1 else x)),2,x) div 2)
A171104: 0 3 21 666
(2 * compr(\x.((1 + loop(\(x,i).loop(\(x,i).(~x + i),x,x),x,x)) mod 2),x))
A343501: 4 6 14 16 20 22 24 30 36 38 46 52 54 56 62 64
loop(\(x,i).(4x + (if (i mod 3) <= 0 then 2 else 1)),x,2)
A037553: 2 9 37 150 601 2405 9622 38489 153957 615830 2463321 9853285 39413142 157652569 630610277 2522441110
loop(\(x,i).x2,1,loop(\(x,i).(2x - ((x div 2) mod 2)),x,2))
A262753: 4 9 25 100 361 1369 5476 21609 85849 343396 1371241 5480281 21921124 87665769 350625625 1402502500
loop(\(x,i).x2,1,loop(\(x,i).(2x - ((i div 2) mod 2)),x,2))
A262268: 4 16 49 169 676 2704 10609 42025 168100 672400 2686321 10738729 42954916 171819664 687226225 2748800041
(2 * loop(\(x,i).(i - (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),2,x))
A329726-A260300-A182291-A071294-A060684: 2 4 6 2 10 12 2 16 18 2 22 4 2 28 30 2
loop(\(x,i).x2,1,loop(\(x,i).(5x + 2),x,2))
A060870: 4 144 3844 97344 2439844 61027344 1525839844 38146777344 953673339844 23841853027344 596046423339844 14901161071777344 372529029235839844 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 * (x + ((if (x + ~4) <= 0 then 1 else x) div 2))))
A049015: 1 2 4 6 8 14 18
(2 * loop(\(x,i).loop(\(x,i).(4x + 2),i,1),(x + ~2),x))
A075876: 0 2 4 12 52 212 852 3412 13652 54612 218452 873812 3495252 13981012
loop(\(x,i).(x3 + ~x2 + x + ~1),1,loop(\(x,i).2x,x,2))
A145641: 5 51 455 3855 31775 258111 2080895 16711935 133956095 1072694271 8585742335 68702703615 549688713215 4397778092031 35183298379775 281470681808895
((if (~x + 2) <= 0 then (x mod ~2) else 1) mod loop(\(x,i).2x,x,2))
A277929: 1 1 0 15 0 63 0 255 0 1023 0 4095 0 16383 0 65535
loop(\(x,i).(x * (x - (x mod 3))),1,loop(\(x,i).2x,x,2))
A242026: 0 12 48 240 960 4032 16128 65280 261120 1047552 4190208 16773120 67092480 268419072 1073676288 4294901760
(loop(\(x,i).(3x + 4),x,1) + loop(\(x,i).2x,x,2))
A171270: 3 11 33 95 273 791 2313 6815 20193 60071 179193 535535 1602513 4799351 14381673 43112255
(loop(\(x,i).(4x + ~4),x,2) + loop(\(x,i).2x,x,2))
A060919: 4 8 20 60 204 748 2860 11180 44204 175788 701100 2800300 11193004 44755628 178989740 715893420
loop(\(x,i).(3x + (if (i mod 3) <= 0 then 2 else 1)),x,2)
A037552: 2 7 22 68 205 616 1850 5551 16654 49964 149893 449680 1349042 4047127 12141382 36424148
loop(\(x,i).(3x + loop(\(x,i).2x,(~2 + i),1)),x,2)
A291012: 2 7 22 68 208 632 1912 5768 17368 52232 156952 471368 1415128 4247432 12746392 38247368
(2 - (if (x + ~2) <= 0 then 1 else (loop(\(x,i).(x * (~x + i)),2,x) div 2)))
A138081: 1 1 1 26 86
loop(\(x,i).3x,(x + 1),loop(\(x,i).((x + 2) + i),x,2))
A288835: 6 45 243 1134 4860 19683 76545 288684 1062882 3838185 13640319 47829690 165809592 569173311 1937102445 6543101592
(loop(\(x,i).(if (x div 2) <= 0 then (x + 2) else ~1),x,0) mod (x + 2))
A283878: 0 2 3 1 3 6 1 3 9 1 3 12 1 3 15 1
((x + 2) * loop(\(x,i).loop(\(x,i).2x,x,(2 + (i div 2))),x,0))
A173011: 0 6 48 61440
(if x <= 0 then 1 else ((x + 2) * loop(\(x,i).(2x + (i mod 2)),x,0)))
A026970: 1 3 8 25 60 147 336 765 1700 3751 8184 17745 38220 81915 174752 371365
((x + 2) * ((x + 1) + loop(\(x,i).(if x <= 0 then i else (x + ~1)),x,0)))
A253608: 2 9 12 35 42 49 56 135 150 165 180 195 210 225 240 527
loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 1 else 0)),(x + ~2),(x + 2))
A266620: 2 3 4 5 7 7 11 11 11 11 13 13 17 17 17 17
loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),(x div 2),(x + 2))
A151799-A007917: 2 3 3 5 5 7 7 7 7 11 11 13 13 13 13 17
loop(\(x,i).(2x - (if (x mod (1 + i)) <= 0 then 1 else x)),x,(x + 2))
A201363: 2 3 7
A050921-A034694: 2 3 7 5 11 7 29 17 19 11 23 13 53 29 31 17
(2 - loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else x)),x,(x + 2)))
A161872: 0 2 0 2 2 2 2 2 2 2 2 2 2 2 3 2
((2x + 2) - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x))
A004202: 2 5 6 10 11 12 17 18 19 20 26 27 28 29 30 37
loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,(x + 2))
A006470: 2 15 60 175 420 882 1680 2970 4950 7865 12012 17745 25480 35700 48960 65892
loop(\(x,i).(x - (2 * (if (x + ~1) <= 0 then x else 2))),(x div 2),(x + ~2))
A118825: ~2 ~1 0 ~1 2 1 0 1 ~2 ~1 0 ~1 2 1 0 1
loop(\(x,i).(x + (if (x + ~2) <= 0 then 3 else x)),x,(~2x + 1))
A067319: 1 2 3 4 5 6 8 10 12
A253789-A029747: 1 2 3 4 5 6 8 10 12 16 20 24 32 40 48 64
loop(\(x,i).(x2 - loop(\(x,i).(x * (2 + i)),i,2)),2,2x)
A163323: 12 ~20 76 876 3340 8812 19020 36076 62476 101100 155212 228460 324876 448876 605260 799212
loop(\(x,i).(i - (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),2,2x)
A214062: 1 3 5 1 9 11 1 15 2 1 21 23 1 2 29 1
(2x + (if x <= 0 then 0 else ((x + 2) + loop(\(x,i).(x * i),x,2))))
A076852: 0 7 12 23 62
loop(\(x,i).(x - (if (2x mod (1 + i)) <= 0 then 2 else 1)),x,2x)
A047949: 0 0 1 2 1 4 5 4 7 8 7 10 9 8 13 14
(0 - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * (1 + i)))),x,2x))
A061579: 0 2 1 5 4 3 9 8 7 6 14 13 12 11 10 20
(1 - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * (1 + i)))),x,2x))
A194910-A194909-A038722: 1 3 2 6 5 4 10 9 8 7 15 14 13 12 11 21
(2x + (if x <= 0 then 1 else (if (x + ~2) <= 0 then 2 else (x + (x div 2)))))
A231407: 1 4 6
A058917: 1 4 6 10 14 17
(x - loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else x)),x,2x))
A113523: 0 0 0 4 4 6 6 8 9 10 10 12 12 14 15 16
loop(\(x,i).(if (x + ~2) <= 0 then (x + 1) else x3),x,(x div 2))
A014222: 0 1 3 27 7625597484987
((x - loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0)) div (2 - (x mod 2)))
A115379: 0 1 0 3 0 3 2 7 0 3 2 7 4 11 6 15
loop(\(x,i).(~x + loop(\(x,i).2x,(~1 + i),1)),(x div 2),(x mod 2))
A133684: 0 1 1 0 1 2 3 2 5 6 11 10 21 22 43 42
(loop(\(x,i).4x,x,1) - loop(\(x,i).3x,x,2))
A002250: ~1 ~2 ~2 10 94 538 2638 12010 52414 222778 930478 3840010 15714334 63920218 258869518 1045044010
loop(\(x,i).(x * loop(\(x,i).(x * (2 + (x mod 4))),i,1)),x,2)
A218151: 2 6 90 6750 2531250 4746093750 44494628906250 2085685729980468750 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((~x + 1) + (x * loop(\(x,i).x2,(~1 + i),2))),x,2)
A162647: 2 3 10 151 38506 2523490711 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).4x2,i,4)),x,2)
A209248: 2 128 2097152 2251799813685248 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 + (x2 * loop(\(x,i).(x2 + x),2,2))))
A010023: 1 44 170 380 674 1052 1514 2060 2690 3404 4202 5084 6050 7100 8234 9452
(loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,x) div 2)
A051133: 0 3 30 210 1260 6930 36036 180180 875160 4157010 19399380 89237148 405623400 1825305300 8143669800 36064823400
loop(\(x,i).(x * loop(\(x,i).6x,(2 * i),2)),x,2)
A232998: 2 144 373248 34828517376 116997070082015232 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * i),(2 + (5 * i)),x),x,2)
A294324: 2 10080 4828336128000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(2x * (1 + (2 * i))),i,2)),x,2)
A111424: 2 14 134 1814 32054 697334 17994614 536913014 18180138614 688622711414 28847210769014 1324142261418614 66088894793898614 3563385531547818614 4611686018427387903 4611686018427387903
(2x2 + (if ((if x <= 0 then 1 else x) mod 2) <= 0 then 1 else 4))
A137253: 4 6 9 22 33
(2 * (x - loop(\(x,i).i,loop(\(x,i).(x div (1 + (x mod 2))),x,x),x)))
A318877: 0 0 0 0 0 6 0 0 0 10 0 18 0 14 0 0
((if x <= 0 then 1 else (2 * (x + (x mod 2)))) * loop(\(x,i).x2,x,2))
A094505: 2 16 64 2048
loop(\(x,i).(x2 + loop(\(x,i).3x,(x div 2),i)),x,2)
A122524: 2 7 103 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (x div 2)),(x + 1),loop(\(x,i).x3,x,2))
A131489: 3 18 1728 679477248
loop(\(x,i).(loop(\(x,i).(1 + (x * i)),(1 + i),1) + (x * i)),x,2)
A144495: 2 7 30 155 946 6687 53822 486355 4877250 53759351 646098622 8409146187 117836551730 1768850337295 28318532194206 481652022466307
(loop(\(x,i).(x * (~1 + (2 * i))),x,1) div loop(\(x,i).(x * i),x,2))
A024504: 0 0 0 1 2 3 7 13 25 47 90 172 330 634 1224 2366
((loop(\(x,i).2x,x,1) - (x mod 2)) mod loop(\(x,i).(x * i),x,2))
A286773: 1 1 0 7 16 31 64 127 256 511 1024 2047 4096 8191 16384 32767
(x + (if x <= 0 then 1 else (if (x mod 3) <= 0 then (x div 3) else 0)))
A257174: 1 1 2 4 4 5 8 7 8 12 10 11 16 13 14 20
(x + loop(\(x,i).(x2 + 3),x,(if (x + ~2) <= 0 then 1 else 0)))
A306589: 1 5 21 150
(x + loop(\(x,i).(~1 + (if x <= 0 then (i div (2 - (i mod 2))) else x)),x,0))
A192225: 0 1 2 5
A171438: 0 1 2 5 5 5 8 8 8 17 17 17 17 17 17 17
(~x + loop(\(x,i).loop(\(x,i).(x2 * (1 + (2 * i))),x,2),x,0))
A111416: 0 1 718 4611686018427387903
compr(\x.((x + 1) mod (1 + loop(\(x,i).(if x <= 0 then i else (x + ~1)),x,0))),x)
A089633: 0 1 2 3 5 6 7 11 13 14 15 23 27 29 30 31
(if x <= 0 then 1 else (x * loop(\(x,i).i,(x + ~9),1)))
A114806: 1 1 2 3 4 5 6 7 8 9 10 22 36 52 70 90
((if x <= 0 then 1 else 2) div (if (~1 + (x mod 8)) <= 0 then 1 else x))
A173677: 1 2 1 0 0 0 0 0 2 2 0 0 0 0 0 0
(x + loop(\(x,i).i,((x div 2) - (if (x mod 4) <= 0 then 2 else 1)),1))
A324578-A295585-A286608: 1 2 3 4 5 6 8 9 10 12 14 15 16 18 20 21
(x + loop(\(x,i).(2x + (if (~2 + i) <= 0 then 1 else i)),(x + ~1),1))
A172411: 1 2 5 10
A267880: 1 2 5 10 21 43 87 175 351 703 1407 2815 5631 11263 22527 45055
(if x <= 0 then 1 else (x * loop(\(x,i).i,(x + ~10),1)))
A288327: 1 1 2 3 4 5 6 7 8 9 10 11 24 39 56 75
loop(\(x,i).2x,x,(if x <= 0 then 1 else 7x))
A281200: 1 14 56 168 448 1120 2688 6272 14336 32256 71680 157696 344064 745472 1605632 3440640
loop(\(x,i).x2,1,loop(\(x,i).i,(x + ~9),x))
A118881: 0 1 4 9 16 25 36 49 64 81 1 4 9 16 25 36
(x + (if x <= 0 then 1 else (3 * (2 + (if (~x + 2) <= 0 then x else 0)))))
A131439: 1 7 14 18 22 26 30 34 38 42 46 50 54 58 62 66
loop(\(x,i).loop(\(x,i).x2,2,x3),1,3x)
A016776: 0 531441 2176782336 282429536481 8916100448256 129746337890625 1156831381426176 7355827511386641 36520347436056576 150094635296999121 531441000000000000 1667889514952984961 4611686018427387903
loop(\(x,i).(x + (x2 div (if i <= 0 then 1 else (i * i)))),3,x)
A061318: 0 4 40 304 1720 7480 26404 79240 209304 499140 1095160 2242504 4332640 7966504 14036260 23829040
(x + loop(\(x,i).(2 + loop(\(x,i).(1 + (x * i)),x,1)),(x + ~2),1))
A333132: 1 2 3 7 71 4611686018427387903
(x * loop(\(x,i).(x + loop(\(x,i).x3,i,2)),(x + ~2),1))
A327128: 0 1 2 27 2084
(loop(\(x,i).(x * (i * i)),(x div 2),1) * (if (x mod 2) <= 0 then 1 else x))
A062870: 1 1 1 3 4 20 36 252 576 5184 14400 158400 518400 6739200 25401600 381024000
loop(\(x,i).(~x + loop(\(x,i).3x,i,1)),(x + ~1),(~x + 1))
A092897: 1 0 4 4 24 56 188 540 1648 4912 14772 44276 132872 398568 1195756 3587212
loop(\(x,i).(x + (if (x + ~1) <= 0 then 2 else (2x + ~1))),x,(~x + 1))
A246360: 1 2 3 5 8 14 23 41 68 122 203 365 608 1094 1823 3281
((2x + 1) + loop(\(x,i).(if x <= 0 then i else (x + ~1)),(x + ~2),0))
A097911: 1 3 5 8
A185456: 1 3 5 8 9 14 15 16 17 26 27 28 29 30 31 32
(if x <= 0 then 1 else (x * (1 + loop(\(x,i).(2x + ~1),(x + ~2),x))))
A181490: 1 2 6 18
A002999: 1 2 6 18 56 170 492 1358 3600 9234 23060 56342 135192 319514 745500 1720350
(x + loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1))
A134758: 1 3 8 23 74 257 930 3439 12878 48629 184766 705443 2704168 10400613 40116614 155117535
(~x + loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1))
A045992: 1 1 4 17 66 247 918 3425 12862 48611 184746 705421 2704144 10400587 40116586 155117505
(if x <= 0 then 1 else compr(\x.(loop(\(x,i).(~2x + 2),x,0) mod (x + 1)),x))
A156037: 1 1 4 6 10 12 16 18 22 28 30 36 40 42 46 52
(2 - loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 2 else 1)),(x + 1),x))
A161758: 4 4 5 4 5 4 5 6 7 4 5 4 5 6 7 4
loop(\(x,i).(x + (if (x + ~1) <= 0 then 1 else (3 + i))),(x + 1),x)
A183897: 1 7 17 25 34 44 55 67 80 94 109 125 142 160 179 199
loop(\(x,i).loop(\(x,i).x2,1,((x + 1) * (i * i))),(x + ~1),x)
A323337: 0 1 9 4624
loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x + ~1),x)
A037965: 0 1 4 18 80 350 1512 6468 27456 115830 486200 2032316 8465184 35154028 145608400 601749000
loop(\(x,i).(loop(\(x,i).(x * i),i,1) + (x * (1 + i))),(x + ~1),x)
A121636: 0 1 5 23 122 754 5364 43308 391824 3929616 43287840 519711840 6755460480 94527008640 1416783432960 22646604153600
(x * loop(\(x,i).(2x + (if (~2 + i) <= 0 then 1 else x)),x,(x + ~1)))
A086951: 0 1 14 99 540 2565 11178 45927 180792 688905 2558790 9310059 33303636 117448461 409209570 1410975855
(loop(\(x,i).(x + (3 * i)),(x div 2),1) div (if x <= 0 then 1 else x))
A053277: 1 1 2 1 2 2 3 2 3 3 4 4 5 4 6 5
(loop(\(x,i).3x2,3,x) div (if x <= 0 then 1 else x))
A016771: 0 2187 279936 4782969 35831808 170859375 612220032 1801088541 4586471424 10460353203 21870000000 42618442977 78364164096 137231006679 230539333248 373669453125
(loop(\(x,i).4x2,3,x) div (if x <= 0 then 1 else x))
A016807: 0 16384 2097152 35831808 268435456 1280000000 4586471424 13492928512 34359738368 78364164096 163840000000 319277809664 587068342272 1028071702528 1727094849536 2799360000000
(x * loop(\(x,i).(loop(\(x,i).(x * i),i,1) + (x * (1 + i))),x,1))
A121723: 0 3 22 150 1096 8820 78408 767088 8212608 95657760 1205438400 16350871680 237633108480 3685053415680 60748282022400 1061014235904000
(~x + loop(\(x,i).(x + loop(\(x,i).3x,(x div 2),2)),x,1))
A077746: 1 2 7 168 4611686018427387903
(x + loop(\(x,i).(x + (2 * loop(\(x,i).(x * (x + i)),2,i))),x,1))
A061803: 1 18 115 452 1333 3254 6951 13448 24105 40666 65307 100684 149981 216958 305999 422160
loop(\(x,i).x2,1,(x + (if (~2 + (x div 3)) <= 0 then 1 else 2)))
A052041: 1 4 9 16 25 36 49 64 81 121 144 169 196 225 256 289
loop(\(x,i).(x2 + 2x),1,(x + (if (x + ~4) <= 0 then 1 else 2)))
A066079: 3 8 15 24 35 63 80 99 120 143 168 195 224 255
loop(\(x,i).((4 * (2 + (if x <= 0 then 2 else 0))) div (x + 1)),2,x)
A230875: 0 1 2 2 4 4 4 4 16 16 16 16 16 16 16 16
loop(\(x,i).((x + 1) * (2x + (if (i mod 2) <= 0 then 1 else x))),2,x)
A338795: 1 91 703 2701 7381 16471 32131 56953 93961 146611 218791 314821 439453 597871 795691 1038961
(if (x mod 2) <= 0 then 1 else (if ((x div 2) mod 2) <= 0 then (2x + 2) else x))
A123251: 1 4 1 3 1 12 1 7 1 20 1 11 1 28 1 15
loop(\(x,i).(if (x + ~2) <= 0 then 0 else (x mod 10)),2,x)
A176407: 0 0 0 3 4 5 6 7 8 9 0 0 0 3 4 5
(x - loop(\(x,i).((x - (((if x <= 0 then 2 else x) div 2) mod 2)) div 2),2,x))
A132351: 1 2 3 3 4 5 6 6 6 7 8 9 10 11 12 12
(x - loop(\(x,i).(x - (if (~2 + (x div 2)) <= 0 then 0 else 1)),4,x))
A102678: 0 0 0 0 0 0 1 2 3 4 4 4 4 4 4 4
loop(\(x,i).(x + (x2 div (if i <= 0 then 1 else (i * i)))),4,x)
A061320: 0 5 140 6080 186620 3504380 43599605 392515340 2738219580 15571795365 74962059260 314303754380 1173239918240 3966582090380
loop(\(x,i).(x * i),(x + ~1),loop(\(x,i).((x2 + ~x) div 2),2,x))
A317487: 0 0 0 6 90 1080 12600 151200 1905120 25401600 359251200 5388768000 85621536000 1438441804800 25499650176000 475993469952000
(x + loop(\(x,i).(~1 + loop(\(x,i).(x * (~1 + (2 * i))),x,i)),x,2))
A201363: 2 3 7
A048979: 2 3 7 2837
loop(\(x,i).loop(\(x,i).i,(x mod (2 + ((x div 2) div 3))),x),2,x)
A257022: 0 1 2 1 4 1 6 1 2 9 1 2 12 1 2 1
(if x <= 0 then 1 else (x * (if (x mod 4) <= 0 then (x2 + 2x) else 2)))
A066719: 1 2 4 6 96
(x + (2 * loop(\(x,i).(~x + (if (~x + i) <= 0 then i else 0)),2x,x)))
A094765: 0 1 4 7 4 7 10 13 16 9 12 15 18 21 24 27
loop(\(x,i).(2x - (if (x mod (1 + i)) <= 0 then i else 0)),(x + ~2),x)
A144530: 0 1 2 6 14 37 88
compr(\x.(loop(\(x,i).(~2x + 2),x,1) mod (if x <= 0 then 1 else 2x)),x)
A171577: 0 1 5 7 11 13 17 19 23 29 31 37 41 43 47 53
compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),x)
A010376: 0 1 3 4 9 10 12
A005836: 0 1 3 4 9 10 12 13 27 28 30 31 36 37 39 40
compr(\x.loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,2x),x)
A047845: 0 4 7 10 12 13 16 17 19 22 24 25 27 28 31 32
(x + (if (~2 + (x div 2)) <= 0 then (1 + (if x <= 0 then 1 else 2)) else (x div 2)))
A030771: 2 4 5 6 7 8 9 10 12 13 15 16 18 19 21 22
(~x + (loop(\(x,i).(if (x mod 2) <= 0 then (x + 2) else (x div 2)),x,x) div 2))
A191362: 0 ~1 1 ~2 2 0 3 ~3 4 1 5 ~1 6 2 7 ~4
(loop(\(x,i).4x,x,1) - loop(\(x,i).x3,2,x))
A024045: 1 3 ~496 ~19619 ~261888 ~1952101 ~10073600 ~40337223 ~134152192 ~387158345 ~998951424 ~2353753387 ~5143003136 ~10537390509 ~20392611328 ~37369617551
(loop(\(x,i).3x,x,1) - loop(\(x,i).x3,2,x))
A024032: 1 2 ~503 ~19656 ~262063 ~1952882 ~10076967 ~40351420 ~134211167 ~387400806 ~999940951 ~2357770544 ~5159248911 ~10602905050 ~20656263815 ~38429010468
loop(\(x,i).3x,2x,loop(\(x,i).x3,2,x))
A198478: 0 9 41472 14348907 1719926784 115330078125 5355700839936 193010051319183 5777633090469888 150094635296999121 3486784401000000000 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.loop(\(x,i).(if (x mod 2) <= 0 then (~x + 2) else (x div 2)),3,x),x)
A187905-A187228-A121538: 1 2 4 6 7 8 10 11 12 14 16 18 19 20 22 24
loop(\(x,i).(x + (x div (if i <= 0 then 1 else (2 * i)))),3x,x)
A007952: 0 1 3 5 9 11 17 21 29 33 41 47 57 59 77 81
(1 - loop(\(x,i).(x - (if x <= 0 then 0 else (i - (i div 3)))),x,x))
A205696: 1 1 2 1 2 1 3 2 1 4 3 2 1 4 3 2
(2x - loop(\(x,i).((x + 1) - (if x <= 0 then 1 else (2 * i))),x,x))
A165775: 0 2 6 7 8 14 15 16 17 18 26 27 28 29 30 31
loop(\(x,i).(x - (loop(\(x,i).2x,(x div 2),2) mod (x + 1))),x,x)
A218403: 0 1 1 3 1 3 1 7 3 7 1 7 1 7 7 15
loop(\(x,i).2x,(x + ~2),(~x + loop(\(x,i).2x,(x + ~1),x)))
A308700: 0 0 2 18 112 600 2976 14112 65024 293760 1308160 5761536 25153536 109025280 469704704 2013143040
compr(\x.(loop(\(x,i).2x,x,1) mod (if (x mod 3) <= 0 then 2 else x)),x)
A231404: 1 2 3 4 6 8 9 12 15 16 18 21 24 27 30 32
(x * loop(\(x,i).(x * (~1 + loop(\(x,i).(i * i),(x + ~2),x))),2,x))
A327113: 0 0 4 0 4752
(x + loop(\(x,i).(x - loop(\(x,i).i,(~4 + (x div 2)),x)),2,x))
A103303: 0 1 2 3 4 5 6 7 8 9
A247808: 0 1 2 3 4 5 6 7 8 9 10 20 21 23 24 25
compr(\x.loop(\(x,i).(0 - (if (x mod (1 + i)) <= 0 then 1 else x)),(x + ~2),x),x)
A160656: 0 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53
(0 - loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,x))
A093049: 0 0 0 2 1 4 4 6 4 8 8 10 9 12 12 14
(loop(\(x,i).2x,x,1) - (x * loop(\(x,i).x3,2,x)))
A024020: 1 1 ~1020 ~59041 ~1048560 ~9765593 ~60466112 ~282475121 ~1073741568 ~3486783889 ~9999998976 ~25937422553 ~61917360128 ~137858483657 ~289254638592 ~576650357857
(loop(\(x,i).(x * i),x,1) - (x * loop(\(x,i).x3,2,x)))
A196739: 1 0 ~1022 ~59043 ~1048552 ~9765505 ~60465456 ~282470209 ~1073701504 ~3486421521 ~9996371200 ~25897507801 ~61438362624 ~131631471049 ~202076363776 731023977375
(x2 + loop(\(x,i).x3,2,(if (x + ~2) <= 0 then 1 else 2)))
A133378: 1 2 5 521
(loop(\(x,i).4x,x,1) - loop(\(x,i).x2,2,x2))
A024044: 1 3 ~240 ~6497 ~65280 ~389601 ~1675520 ~5748417 ~16711680 ~42784577 ~98951424 ~210164577 ~413204480 ~748621857 ~1207353600 ~1489148801
(loop(\(x,i).3x,x,1) - loop(\(x,i).x2,2,x2))
A024031: 1 2 ~247 ~6534 ~65455 ~390382 ~1678887 ~5762614 ~16770655 ~43027038 ~99940951 ~214181734 ~429450255 ~814136398 ~1471006087 ~2548541718
loop(\(x,i).8x,x,loop(\(x,i).x2,2,x2))
A198404: 0 8 16384 3359232 268435456 12800000000 440301256704 12089663946752 281474976710656 5777633090469888 107374182400000000 1841328767004311552 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,x2)
A002736: 0 2 24 180 1120 6300 33264 168168 823680 3938220 18475600 85357272 389398464 1757701400 7862853600 34901442000
compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x)
A067076: 0 1 2 4 5 7 8 10 13 14 17 19 20 22 25 28
compr(\x.loop(\(x,i).(x - (if ((x + 2) mod (2 + i)) <= 0 then 0 else 1)),x,x),x)
A173064: 0 2 6 8 12 14 18 24 26 32 36 38 42 48 54 56
(x + loop(\(x,i).(x - (if x <= 0 then 1 else (1 + (2 * (i div 2))))),x,x))
A141455: 0 1 0 1 2 1 2 3 0 1 2 3 4 1 2 3
loop(\(x,i).(x + (3 * (x + (if (2 - i) <= 0 then x else 1)))),x,x)
A229281: 0 7 77 735 6517 55223 453789 3647119 28824005 224827239 1735205101 13276336703 100843663893 761270796055 5716451614013 42728053589487
loop(\(x,i).(x + (4 * (x + (if (2 - i) <= 0 then x else 1)))),x,x)
A229283: 0 9 126 1539 17496 190269 2007666 20726199 210450636 2109289329 20920706406 205720279659 2008387814976 19487638017189 188098071296346 1807266603941919
(~x + loop(\(x,i).3x,x,x) - loop(\(x,i).2x,x,x))
A152692: 0 0 8 54 256 1050 3984 14406 50432 172530 580240 1926078 6328128 20619690 66732176 214742070
compr(\x.(1 - loop(\(x,i).(if (x mod 4) <= 0 then x else (x div 2)),x,x)),x)
A004753: 4 8 9 12 16 17 18 19 20 24 25 28 32 33 34 35
(x + (x div (if x <= 0 then 1 else loop(\(x,i).(x div (2 - (x mod 2))),x,x))))
A285326: 0 2 4 4 8 6 8 8 16 10 12 12 16 14 16 16
(x * loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),(x + ~2),x2))
A282462: 0 1 8 27 4 125 6 343 8 9 10 1331 12 2197 14 15
(loop(\(x,i).2x,x,1) - loop(\(x,i).x2,2,x3))
A024022: 1 1 ~4092 ~531433 ~16777200 ~244140593 ~2176782272 ~13841287073 ~68719476480 ~282429535969 ~999999998976 ~3138428374673 ~8916100444160 ~23298085114289 ~56693912358912 ~129746337857857
(~x + compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,x),x))
A091311: 0 1 4 5 14 15 18 19 46 47 50 51 60 61 64 65
compr(\x.(x + loop(\(x,i).((x + 1) - (if x <= 0 then 0 else (i * i))),x,x)),x)
A214489: 0 4 8 9 10 11 16 17 18 19 20 21 22 23 24 25
(x + (if (x mod 2) <= 0 then (if (x + ~2) <= 0 then 1 else x3) else x))
A124649: 1 2 3 6 68
(if (~1 + (x mod (1 + (2 * (x div 5))))) <= 0 then 1 else 0)
A221641: 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1
(if (~1 + (x mod (1 + (2 * (2 + (x mod 3)))))) <= 0 then 1 else 0)
A279279: 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1
(if (~1 + (2x mod (5 + (x div 2)))) <= 0 then 1 else 0)
A116860: 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0
(if (x mod (1 + ((1 - (x div 3)) mod 3))) <= 0 then 1 else 0)
A267358: 1 0 1 1 1 1 1 0 0 0 1 0 1 1 1 1
(if (x2 mod (1 + (3 * ((x + 1) div 2)))) <= 0 then 1 else 0)
A186718: 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1
(if ((x + 1) mod (1 + ((2 + (x div 2)) div 3))) <= 0 then 1 else 0)
A331281-A331168: 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1
(if (x mod (1 + (3 * (4 mod (x + 2))))) <= 0 then 1 else 0)
A323513-A186717: 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
(if ((x mod 5) mod (1 + (x div 3))) <= 0 then 1 else 0)
A145361-A011748: 1 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1
(if ((x3 + 2) mod (1 + (x div 3))) <= 0 then 1 else 0)
A192687: 1 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0
(if (x mod (1 + ((2x + ~4) mod (x + 3)))) <= 0 then 1 else 0)
A345197: 1 0 1 1 0 0 0 1 1 1 0 0 1 0 0 0
(if (x mod (1 + ((x + ~4) mod (1 + (x div 2))))) <= 0 then 1 else 0)
A266843: 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 0
(if (x mod (1 + (3x mod (1 + (x div 2))))) <= 0 then 1 else 0)
A321759-A266974-A075437: 1 1 1 0 1 1 1 0 0 1 1 0 1 0 0 0
(if (x mod (1 + ((1 + (x div 2)) div (1 + (x mod 2))))) <= 0 then 1 else 0)
A316480: 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1
(if ((x + 1) mod (1 + ((x div 2) div (1 + (x mod 2))))) <= 0 then 1 else 0)
A344438-A341629-A326956-A322860-A322585-A322583: 1 1 0 1 0 1 0 1 0 0 0 1 0 0 0 1
(if (x mod (1 + ((3 + (x mod 2)) mod (x + 1)))) <= 0 then 1 else 0)
A194679: 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 1
(if (x mod (1 + (2 * (1 + (x div 5))))) <= 0 then 1 else 0)
A214264: 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0
(if ((x + 1) mod (1 + ((x mod 5) div 2))) <= 0 then 1 else 0)
A103842: 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1
(if ((x + ~3) mod (1 + (x mod 6))) <= 0 then 1 else 0)
A295896: 1 1 0 1 0 0 1 1 0 0 0 0 1 1 0 1
(if ((x div 2) mod (1 + (2 * (3 - (x mod 2))))) <= 0 then 1 else 0)
A186742: 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0
(if (2x mod (3 - (x div ~4))) <= 0 then 1 else 0)
A321016-A185907: 1 0 1 0 1 1 0 0 0 1 0 0 1 0 1 0
(if (x mod (1 + (4 * (x mod 5)))) <= 0 then 1 else 0)
A319734-A286934: 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1
(if (x2 mod (1 + (2 * (2 + (x div 3))))) <= 0 then 1 else 0)
A341022: 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1
(if (x mod (1 + (2 * ((x + 1) mod 8)))) <= 0 then 1 else 0)
A341023: 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1
(if (x2 mod (1 + (4 * (2 + (x mod 2))))) <= 0 then 1 else 0)
A109708: 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0
(if (x mod (1 + (2 * (x div (2 * (2 + (x mod 2))))))) <= 0 then 1 else 0)
A233427-A176508-A131219-A103451: 1 1 1 1 0 1 1 0 0 1 1 0 0 0 1 1
(if (x mod (1 + (3 mod (2 + (x div 4))))) <= 0 then 1 else 0)
A267179-A244527: 1 0 1 0 1 1 1 1 1 0 0 0 1 0 0 0
(if (x mod (1 + ((~x + 1) mod (4 + (x div 2))))) <= 0 then 1 else 0)
A260595: 1 1 0 0 1 0 1 0 1 1 1 0 0 0 0 0
(if (x mod (1 + (2 * (2 - (x mod (2 + (x mod 2))))))) <= 0 then 1 else 0)
A109702: 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1
(if (x mod (4 - ((x + 1) div 5))) <= 0 then 1 else 0)
A321665: 1 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1
(if (x mod 2) <= 0 then (1 + (((~x + 2) div 2) div 5)) else 0)
A016419-A016391-A016378-A014037: 1 0 1 0 0 0 0 0 0 0 0 0 0 0 ~1 0
(x - (if (x mod 2) <= 0 then (~1 + ((x div 2) mod 5)) else 0))
A106647: 1 1 2 3 3 5 4 7 5 9 11 11 12 13 13 15
(if ((x + ~2) mod (2 - ((~x + 2) div 5))) <= 0 then 1 else 0)
A134286: 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0
(if (x mod (1 + ((x2 + 1) mod (2 + (x div 2))))) <= 0 then 1 else 0)
A177444: 1 1 0 0 1 0 1 1 0 0 0 0 1 0 0 0
(if (x mod (1 + (2 * ((x div 4) - (x mod 2))))) <= 0 then 1 else 0)
A304569-A174294-A051731: 1 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1
(if ((x div (~1 + (x mod ~4))) mod 3) <= 0 then 1 else 0)
A025925: 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0
(if ((x - (((x + 1) div 2) div 3)) mod 3) <= 0 then 1 else 0)
A170956-A024942: 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0
(if (((x * (2 - (x div 2))) div 3) mod 3) <= 0 then 1 else 0)
A181653: 1 1 1 0 1 1 0 1 1 1 0 0 0 1 1 0
(if (x mod (6 - ((x + ~1) div 3))) <= 0 then 1 else 0)
A344447: 1 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0
(if (x mod (2 - (x mod ~12))) <= 0 then 1 else 0)
A058342: 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0
(if (((~x2 + x) div 8) mod 3) <= 0 then 1 else 0)
A266837: 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 1
(if ((x - ((1 + (x div 2)) mod 4)) mod 3) <= 0 then 1 else 0)
A071981: 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 1
(if (2x mod (3 + ((x + ~1) mod 4))) <= 0 then 1 else 0)
A266174: 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 1
(if ((x3 div (x + 4)) mod 3) <= 0 then 1 else 0)
A068427: 1 1 0 1 0 0 1 0 1 0 0 0 1 1 0 1
(if ((((2x + ~1) * (x div 2)) div 2) mod 3) <= 0 then 1 else 0)
A328802-A257402: 1 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0
(if ((x mod 9) - (x div 3)) <= 0 then 1 else 0)
A017880: 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0
(if ((x + 2) mod 5) <= 0 then (~1 + (x div 3)) else 0)
A036873: 0 0 0 0 0 0 0 0 1 0 0 0 0 3 0 0
(if (~1 + (x mod 3)) <= 0 then ((x + 1) - (x div 3)) else 0)
A117909: 1 2 0 3 4 0 5 6 0 7 8 0 9 10 0 11
(if ((2x mod 5) - (x mod 3)) <= 0 then 1 else 0)
A025889: 1 0 0 0 0 1 0 0 1 0 1 1 0 1 0 1
((x div 7) + (if (x mod 3) <= 0 then 1 else 0))
A029306: 1 0 0 1 0 0 1 1 1 2 1 1 2 1 2 3
((x div 9) + (if (x mod 3) <= 0 then 1 else 0))
A029322: 1 0 0 1 0 0 1 0 0 2 1 1 2 1 1 2
(((x div 2) div 5) + (if (x mod 3) <= 0 then 1 else 0))
A029325: 1 0 0 1 0 0 1 0 0 1 1 1 2 1 1 2
((2 * (x + (x div 3))) + (if (x mod 3) <= 0 then 1 else 0))
A047465: 1 2 4 9 10 12 17 18 20 25 26 28 33 34 36 41
(if ((x + ~1) mod (1 + ((2x + ~4) mod (x + 2)))) <= 0 then 1 else 0)
A143466: 1 1 1 0 0 0 1 1 0 1 0 0 0 0 0 0
(if ((8x + 1) mod (1 + (x div 2))) <= 0 then 1 else 0)
A129186: 1 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0
(if ((4x + 4) mod (2 - (x div ~2))) <= 0 then 1 else 0)
A324252-A307303: 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0
(if (x mod (2 + (2x mod 7))) <= 0 then 1 else 0)
A027356: 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0
(if ((x div 2) mod 2) <= 0 then (1 + ((x div 5) mod 2)) else 0)
A122071: 1 1 0 0 1 2 0 0 2 2 0 0 1 1 0 0
(if (x mod (2 + ((x + 2) mod (1 + (x div 4))))) <= 0 then 1 else 0)
A266840: 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 1
(if (x mod 2) <= 0 then (1 + ((x mod (1 + (x div 4))) div 2)) else 0)
A248908: 1 0 1 0 1 0 1 0 2 0 1 0 1 0 2 0
(if (~2 + (x div (1 + (x2 mod (2 + (x div 2)))))) <= 0 then 1 else 0)
A145379: 1 1 1 0 0 1 0 1 1 1 0 0 0 0 1 0
(if (x mod (2 + ((x mod 8) mod 3))) <= 0 then 1 else 0)
A025902: 1 0 0 0 0 0 1 0 1 1 0 0 1 0 1 1
(if (2x mod (4 - ((x div 2) div 3))) <= 0 then 1 else 0)
A104606: 1 0 1 0 1 0 1 0 0 1 0 0 1 1 1 1
(if (x mod 3) <= 0 then (1 - (x div 7)) else 0)
A016424-A016380-A014054: 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 ~1
(if ((x div 5) - (x mod 6)) <= 0 then 1 else 0)
A264034: 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1
(x + (if (~2 + (x div 3)) <= 0 then 1 else 0) - (x div 4))
A107079: 1 2 3 4 4 5 6 7 7 7 8 9 9 10 11 12
(if (x mod (2 + ((~x2 + 2x) mod (1 + (x div 2))))) <= 0 then 1 else 0)
A082960: 1 0 1 1 0 0 1 0 1
A320815: 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0
(if ((2x + 2) mod (2 - (x div ~4))) <= 0 then 1 else 0)
A178471-A090626: 1 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0
(if (x mod (2 - ((x div 2) div (~2 + (x mod ~2))))) <= 0 then 1 else 0)
A239434: 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1
(if (~x + 2) <= 0 then (5 + ((x + ~1) mod 3)) else 0)
A021152: 0 0 6 7 5 6 7 5 6 7 5 6 7 5 6 7
(if (2 - ((x + ~1) mod (4 + (x div 3)))) <= 0 then 1 else 0)
A027355: 1 0 0 1 1 1 1 0 0 0 1 1 1 1 1 1
(if (x mod 2) <= 0 then (~1 + (2 * (((~1 + (x div 2)) div 2) mod 2))) else 0)
A091337: 1 0 ~1 0 ~1 0 1 0 1 0 ~1 0 ~1 0 1 0
(if ((x mod 3) - ((((x + 1) div 2) div 2) mod 2)) <= 0 then 1 else 0)
A078650: 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 1
(if (2x mod (2 + ((x + 1) mod 8))) <= 0 then 1 else 0)
A252488: 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1
(if (~2 + ((x2 div 2) mod (4 + (x div 2)))) <= 0 then 1 else 0)
A294821-A113706: 1 1 1 0 1 1 0 0 1 1 0 0 1 0 0 1
(if (x mod (2 + (((1 + (x div 2)) div 2) mod 4))) <= 0 then 1 else 0)
A230135: 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0
((x mod 2) - (if ((x + ~4) mod 8) <= 0 then 1 else 0))
A280237: 0 1 0 1 ~1 1 0 1 0 1 0 1 ~1 1 0 1
(if ((x + (2 * (x mod 2))) mod (2 + (x div 4))) <= 0 then 1 else 0)
A179560: 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 0
(if ((x div 4) - (x mod (2 + (x mod 4)))) <= 0 then 1 else 0)
A239681: 1 1 1 1 0 1 1 1 0 0 1 0 0 0 0 0
(if (x mod (2 + (((x2 + 2) div (x + 2)) mod 2))) <= 0 then 1 else 0)
A029423: 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1
(if (x mod (1 - (2 * ((~x + 1) div (2 + (x div 2)))))) <= 0 then 1 else 0)
A287619-A131018-A033806-A033802-A033800-A033796-A033790-A033788-A033782-A033778-A033776-A010054: 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1
(if ((x div (1 + (x div 8))) mod 4) <= 0 then 1 else 0)
A067618: 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0
(if (((x + ~3) mod (1 + (x div 2))) mod 4) <= 0 then 1 else 0)
A053866: 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 1
(if ((x - ((x div 4) div ~2)) mod 4) <= 0 then 1 else 0)
A168201: 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0
(if ((x mod (~2 + ((~x + 2) div 4))) mod 4) <= 0 then 1 else 0)
A082960: 1 0 1 1 0 0 1 0 1
A082596: 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0
(if (((x * (1 + ((x + 1) div 2))) div 2) mod 4) <= 0 then 1 else 0)
A068429: 1 0 0 1 0 0 1 0 1 0 0 0 0 1 1 0
(if (x mod 4) <= 0 then ((x2 + ~x) mod 5) else 0)
A059483: 0 0 0 0 2 0 0 0 1 0 0 0 2 0 0 0
((5x + 2) + (if (x + ~4) <= 0 then 1 else 0))
A282025: 3 8 13 18 23 27 32 37 42 47 52 57 62 67 72 77
(if (((x + (x div 2)) mod 4) - (x div 4)) <= 0 then 1 else 0)
A109699: 1 0 0 1 0 0 1 0 1 1 0 1 1 1 1 1
loop(\(x,i).(2x + 1),((x div 2) - ((x + ~1) div 3)),0)
A042951-A029155: 1 0 1 1 1 1 3 1 3 3 3 3 7 3 7 7
(if ((x + ~2) mod 5) <= 0 then ((x + ~1) mod 3) else 0)
A181502-A083927: 0 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0
(if (x mod 5) <= 0 then (1 - ((x div 2) div 3)) else 0)
A016337-A015959-A015659-A015059: 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 ~1
(if ((x2 + ~2) mod (x + 4)) <= 0 then (x div 3) else 0)
A051344: 0 0 0 1 0 0 0 0 0 0 3 0 0 0 0 0
((5x + 5) + (if (~x + 4) <= 0 then 1 else 0))
A028435: 5 10 15 20 26 31 36 41 46 51 56 61 66 71 76 81
(if (x mod 5) <= 0 then (1 + ((x * (x div 2)) mod 2)) else 0)
A234859: 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 2
(if (((x + 1) mod ~7) mod (x + 2)) <= 0 then 1 else 0)
A102242: 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0
(if ((2x mod 7) - (x div 2)) <= 0 then 1 else 0)
A025868: 1 0 0 0 1 0 0 1 1 1 0 1 1 1 1 1
(if ((x + ~1) mod 10) <= 0 then (1 + (x div 2)) else 0)
A339629: 0 1 0 0 0 0 0 0 0 0 0 6 0 0 0 0
(if ((((x + 2) mod 5) div 2) - (x mod 2)) <= 0 then 1 else 0)
A030308: 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1 1
(if (x mod 10) <= 0 then (x2 + 2x + 1) else 0)
A106544: 1 0 0 0 0 0 0 0 0 0 121 0 0 0 0 0
loop(\(x,i).(10x + 11),(x + 1),0)
A132583: 11 121 1221 12221 122221 1222221 12222221 122222221 1222222221 12222222221 122222222221 1222222222221 12222222222221 122222222222221 1222222222222221 12222222222222221
(if ((x * (x mod 3)) mod 5) <= 0 then (x + 1) else 0)
A102393: 1 0 0 4 0 6 7 0 0 10 11 0 13 0 0 16
loop(\(x,i).(1 + (2 * (3x + (i mod 2)))),(x + 1),0)
A037585: 3 19 117 703 4221 25327 151965 911791 5470749 32824495 196946973 1181681839 7090091037 42540546223 255243277341 1531459664047
loop(\(x,i).(1 + (2 * (4x + (i mod 2)))),(x + 1),0)
A037587: 3 25 203 1625 13003 104025 832203 6657625 53261003 426088025 3408704203 27269633625 218157069003 1745256552025 13962052416203 111696419329625
(1 - loop(\(x,i).(12x + ~6),(x + 1),0))
A127859: 7 79 943 11311 135727 1628719 19544623 234535471 2814425647 33773107759
(if (2x mod (4 + (x div 4))) <= 0 then (x + 1) else 0)
A127773: 1 0 3 0 0 6 0 0 0 10 0 0 0 0 15 0
loop(\(x,i).(4x + (i * i * i * i)),(x + 1),0)
A067534: 1 20 161 900 4225 18196 75185 304836 1225905 4913620 19669121 78697220 314817441 1259308180 5037283345 20149198916
loop(\(x,i).((x + 2) + (((2 + i) * (1 + i)) div 2)),(x + 1),0)
A240001: 5 13 25 42 65 95 133 180 237 305 385 478 585 707 845 1000
((~5x + 1) * (if (x + ~2) <= 0 then (x + 1) else 0))
A119522: 1 ~8 ~27 0 0 0 0 0 0 0 0 0 0 0 0 0
(if ((x mod 10) * (x div 2)) <= 0 then (x + 1) else 0)
A245515: 1 2 0 0 0 0 0 0 0 0 11 0 0 0 0 0
loop(\(x,i).(x + ((~1 + i) mod 9)),(x + 1),0)
A130487: 0 1 3 6 10 15 21 28 36 36 37 39 42 46 51 57
loop(\(x,i).(x + (9 * (x + i))),(x + 1),0)
A099676: 9 108 1107 11106 111105 1111104 11111103 111111102 1111111101 11111111100 111111111099 1111111111098 11111111111097 111111111111096 1111111111111095 11111111111111094
loop(\(x,i).(x + ((~1 + i) mod 12)),(x + 1),0)
A130490: 0 1 3 6 10 15 21 28 36 45 55 66 66 67 69 72
loop(\(x,i).(x + (3 * (3x + i))),(x + 1),0)
A099670: 3 36 369 3702 37035 370368 3703701 37037034 370370367 3703703700 37037037033 370370370366 3703703703699 37037037037032 370370370370365 3703703703703698
loop(\(x,i).(x + (3 * (x + (2 * (x + i))))),(x + 1),0)
A099673: 6 72 738 7404 74070 740736 7407402 74074068 740740734 7407407400 74074074066 740740740732 7407407407398 74074074074064 740740740740730 7407407407407396
loop(\(x,i).(x + (2 * ((1 + i) * (1 + (2 * i))))),(x + 1),0)
A193068: 12 42 98 188 320 502 742 1048 1428 1890 2442 3092 3848 4718 5710 6832
loop(\(x,i).(x + ((~1 + i) mod 10)),(x + 1),0)
A130488: 0 1 3 6 10 15 21 28 36 45 45 46 48 51 55 60
loop(\(x,i).(x + ((i * i * i * (1 + i)) div 2)),(x + 1),0)
A086689: 1 13 67 227 602 1358 2730 5034 8679 14179 22165 33397 48776 69356 96356 131172
loop(\(x,i).(x + ((~1 + (i * i)) * (2 + i) * i)),(x + 1),0)
A158874: 0 24 144 504 1344 3024 6048 11088 19008 30888 48048 72072 104832 148512 205632 279072
loop(\(x,i).((10x + 10) - i),(x + 1),0)
A064617: 9 98 987 9876 98765 987654 9876543 98765432 987654321 9876543210 98765432099 987654320988 9876543209877 98765432098766 987654320987655 9876543209876544
((24x + 6) + (if x <= 0 then 1 else 0))
A063148-A063128: 7 30 54 78 102 126 150 174 198 222 246 270 294 318 342 366
((18x + 6) + (if x <= 0 then 1 else 0))
A063136: 7 24 42 60 78 96 114 132 150 168 186 204 222 240 258 276
((2 * ((2x + ~1) mod 5)) - (if x <= 0 then 1 else 0))
A128475: 7 2 6 0 4 8 2 6 0 4 8 2 6 0 4 8
((24x + 4) + (if x <= 0 then 1 else 0))
A063140: 5 28 52 76 100 124 148 172 196 220 244 268 292 316 340 364
((20x + 4) + (if x <= 0 then 1 else 0))
A063143: 5 24 44 64 84 104 124 144 164 184 204 224 244 264 284 304
((2 * ((3x + 2) + (x div 2))) - (if x <= 0 then 1 else 0))
A063211: 3 10 18 24 32 38 46 52 60 66 74 80 88 94 102 108
((32x + 8) + (if x <= 0 then 1 else 0))
A063164: 9 40 72 104 136 168 200 232 264 296 328 360 392 424 456 488
((24x + 8) + (if x <= 0 then 1 else 0))
A063134: 9 32 56 80 104 128 152 176 200 224 248 272 296 320 344 368
((14x + 4) + (if x <= 0 then 1 else 0))
A063120: 5 18 32 46 60 74 88 102 116 130 144 158 172 186 200 214
((20x + 8) + (if x <= 0 then 1 else 0))
A063155: 9 28 48 68 88 108 128 148 168 188 208 228 248 268 288 308
((14x + 6) + (if x <= 0 then 1 else 0))
A063151: 7 20 34 48 62 76 90 104 118 132 146 160 174 188 202 216
(1 - (if (x mod (3 + ((x div 2) div 3))) <= 0 then 2 else 0))
A158387: ~1 1 1 ~1 1 1 1 1 ~1 1 1 1 1 1 1 ~1
(if (((~x2 + 4x + ~4) div 3) mod 3) <= 0 then 2 else 0)
A273514: 0 0 2 0 0 2 2 2 2 0 0 2 0 0 2 2
((x + ~2) div (x - (if (x mod 12) <= 0 then 2 else 0)))
A034389: 1 ~1 0 0 0 0 0 0 0 0 0 0 1 0 0 0
((3 * (1 + (x div 2))) - (if (x mod 3) <= 0 then 2 else 0))
A321773: 1 3 6 4 9 9 10 12 15 13 18 18 19 21 24 22
(if ((x + ~3) mod 8) <= 0 then (2x + 2) else 0)
A085121: 0 0 0 8 0 0 0 0 0 0 0 24 0 0 0 0
(if ((x + 1) mod 12) <= 0 then (2x + ~2) else 0)
A091234: 0 0 0 0 0 0 0 0 0 0 0 20 0 0 0 0
(x mod (x - (if (2x mod (2 - (x div ~2))) <= 0 then 2 else 0)))
A082523: 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 2
(if ((x + 1) mod (2 + (x2 mod 5))) <= 0 then 2 else 0)
A275962: 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 2
(1 - (if (x mod (2 + (x div 12))) <= 0 then 2 else 0))
A119665: ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 1 ~1
(1 - (2x div (x - (if (x mod 6) <= 0 then 2 else 0))))
A300547: 1 ~1 ~1 ~1 ~1 ~1 ~2 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1
(2x mod ((x div 2) - (if ((x div 3) mod 2) <= 0 then 2 else 0)))
A278922: 0 0 0 0 0 0 0 0 0 2 0 2 0 2 3 2
(if (x mod (2 + (6 mod (1 + (x div 2))))) <= 0 then 2 else 0)
A105118: 2 0 2 0 2 0 0 0 0 2 2 0 0 0 0 0
((x + 1) - (if ((x + 1) mod (2 + (x mod 4))) <= 0 then 2 else 0))
A158366: 1 2 3 4 5 4 7 8 9 10 11 12 13 14 15 16
(if (x mod (1 - (2 * ((~x + 1) div (2 + (x div 2)))))) <= 0 then 2 else 0)
A089799: 2 2 0 2 0 0 2 0 0 0 2 0 0 0 0 2
(x mod (x - (if (x mod 2) <= 0 then ((x + ~1) mod 8) else 0)))
A164736: 0 0 0 0 0 0 0 0 0 0 1 0 3 0 5 0
((x + 1) - (if ((x + 2) mod 5) <= 0 then 4 else 0))
A291305: 1 2 3 0 5 6 7 8 5 10 11 12 13 10 15 16
(if (x mod 7) <= 0 then (1 - (2 * (x mod 2))) else 0)
A015283-A015087: 1 0 0 0 0 0 0 ~1 0 0 0 0 0 0 1 0
((3x2 + 5x + 2) + (if (x mod 2) <= 0 then 2 else 0))
A200455: 4 10 26 44 72 102 142 184 236 290 354 420 496 574 662 752
loop(\(x,i).(x + ((~1 + i) mod 10)),(x + 2),0)
A061076: 1 3 6 10 15 21 28 36 45 45 46 48 51 55 60 66
((2 * (x mod 2)) - loop(\(x,i).(2x - (i mod 2)),(x + ~2),0))
A135351: 0 2 0 3 2 7 10 23 42 87 170 343 682 1367 2730 5463
(x - (if (x mod 11) <= 0 then (x div 2) else 0))
A103303: 0 1 2 3 4 5 6 7 8 9
A048893: 0 1 2 3 4 5 6 7 8 9 10 6 12 13 14 15
loop(\(x,i).((x + 1) + ((x + (x div 4)) div 2)),(x div 2),0)
A131524: 0 0 1 1 2 2 4 4 7 7 12 12 20 20 33 33
(1 - (x2 mod (1 - (if ((x div 2) mod 2) <= 0 then (x div 2) else 0))))
A178252: 1 1 1 1 1 1 1 1 3 1 1 1 2 2 1 1
((x + 1) - loop(\(x,i).(1 + (x mod (1 + (i mod (x + 1))))),x,0))
A124195: 1 1 2 2 4 4 6 6 6 8 10 10 12 12 12 12
loop(\(x,i).(30x + 1),x,0)
A218733: 0 1 31 931 27931 837931 25137931 754137931 22624137931 678724137931 20361724137931 610851724137931 18325551724137931 549766551724137931 4611686018427387903 4611686018427387903
loop(\(x,i).(40x + 1),x,0)
A218743: 0 1 41 1641 65641 2625641 105025641 4201025641 168041025641 6721641025641 268865641025641 10754625641025641 430185025641025641 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (5 * (x - ((x div 2) mod 2)))),x,0)
A046233: 0 1 6 26 126 626 3126 15626 78126 390626 1953126 9765626 48828126 244140626 1220703126 6103515626
loop(\(x,i).(25x + 1),x,0)
A218728: 0 1 26 651 16276 406901 10172526 254313151 6357828776 158945719401 3973642985026 99341074625651 2483526865641276 62088171641031901 1552204291025797526 4611686018427387903
loop(\(x,i).(36x + 1),x,0)
A218739: 0 1 37 1333 47989 1727605 62193781 2238976117 80603140213 2901713047669 104461669716085 3760620109779061 135382323952046197 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(27x + 1),x,0)
A218730: 0 1 28 757 20440 551881 14900788 402321277 10862674480 293292210961 7918889695948 213810021790597 5772870588346120 155867505885345241 4208422658904321508 4611686018427387903
loop(\(x,i).(48x + 1),x,0)
A218751: 0 1 49 2353 112945 5421361 260225329 12490815793 599559158065 28778839587121 1381384300181809 66306446408726833 3182709427618887985 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (12 * (x + (x mod 2)))),x,0)
A240846: 0 1 25 313 3769 45241 542905 6514873 78178489 938141881 11257702585 135092431033 1621109172409 19453310068921 233439720827065 2801276649924793
loop(\(x,i).(21x + 1),x,0)
A218724: 0 1 22 463 9724 204205 4288306 90054427 1891142968 39714002329 833994048910 17513875027111 367791375569332 7723618886955973 162195996626075434 3406115929147584115
(if ((x mod 6) mod (1 + (x div 3))) <= 0 then x else 0)
A166260: 0 1 2 0 4 0 6 0 0 0 10 0 12 0 0 0
(1 div (2 - (if ((x + ~1) mod 7) <= 0 then x else 0)))
A030214: 0 1 0 0 0 0 0 0 ~1 0 0 0 0 0 0 ~1
loop(\(x,i).((2x + 1) - (i mod (2 * (1 + (x mod 2))))),x,0)
A229878: 0 0 1 0 1 2
A181586: 0 0 1 0 1 2 5 8 17 34 69 136 273 546 1093 2184
loop(\(x,i).(64x + 1),x,0)
A133853: 0 1 65 4161 266305 17043521 1090785345 69810262081 4467856773185 285942833483841 18300341342965825 1171221845949812801 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((2x + 1) mod 17),x,0)
A222010: 0 1 3 7
A117589: 0 1 3 7 15 14 12 8 0 1 3 7 15 14 12 8
loop(\(x,i).(1 + (2 * (x - (2 * (~2x + (x mod 2)))))),x,0)
A073552-A067275: 0 1 7 67 667 6667 66667 666667 6666667 66666667 666666667 6666666667 66666666667 666666666667 6666666666667 66666666666667
loop(\(x,i).((x + 1) - (2 * (~4x + (x mod 2)))),x,0)
A015577: 0 1 8 73 656 5905 53144 478297 4304672 38742049 348678440 3138105961 28242953648 254186582833 2287679245496 20589113209465
loop(\(x,i).(~1 + (2 * (5x + (i mod 2)))),x,0)
A015585: 0 1 9 91 909 9091 90909 909091 9090909 90909091 909090909 9090909091 90909090909 909090909091 9090909090909 90909090909091
loop(\(x,i).(10x + 45),x,0)
A086576: 0 45 495 4995 49995 499995 4999995 49999995 499999995 4999999995 49999999995 499999999995 4999999999995 49999999999995 499999999999995 4999999999999995
(1 - loop(\(x,i).(10x + ~40),x,0))
A173768: 1 41 441 4441 44441 444441 4444441 44444441 444444441 4444444441 44444444441 444444444441 4444444444441 44444444444441 444444444444441 4444444444444441
loop(\(x,i).(19x + 1),x,0)
A218722: 0 1 20 381 7240 137561 2613660 49659541 943531280 17927094321 340614792100 6471681049901 122961939948120 2336276859014281 44389260321271340 843395946104155461
(1 - loop(\(x,i).(10 * (x - (i mod 2))),x,0))
A266508: 1 11 101 1011 10101 101011 1010101 10101011 101010101 1010101011 10101010101 101010101011 1010101010101 10101010101011 101010101010101 1010101010101011
loop(\(x,i).(28x + 1),x,0)
A218731: 0 1 29 813 22765 637421 17847789 499738093 13992666605 391794664941 10970250618349 307167017313773 8600676484785645 240818941573998061 4611686018427387903 4611686018427387903
(7 - (if (~1 + (x div 4)) <= 0 then x else 0))
A307338: 7 6 5 4 3 2 1 0 7 7 7 7 7 7 7 7
(((x mod 3) div 2) - loop(\(x,i).(4x + ~1),x,0))
A191597: 0 1 6 21 85 342 1365 5461 21846 87381 349525 1398102 5592405 22369621 89478486 357913941
loop(\(x,i).(~1 + (2 * (6x + (i mod 2)))),x,0)
A015609: 0 1 11 133 1595 19141 229691 2756293 33075515 396906181 4762874171 57154490053 685853880635 8230246567621 98762958811451 1185155505737413
(1 - loop(\(x,i).(3 * (x - (3 * (i mod 2)))),x,0))
A116973: 1 10 28 91 271 820 2458 7381 22141 66430 199288 597871 1793611 5380840 16142518 48427561
loop(\(x,i).(23x + 1),x,0)
A218726: 0 1 24 553 12720 292561 6728904 154764793 3559590240 81870575521 1883023236984 43309534450633 996119292364560 22910743724384881 526947105660852264 4611686018427387903
(1 - loop(\(x,i).(13x + ~1),x,0))
A196792: 1 2 15 184 2381 30942 402235 5229044 67977561 883708282 11488207655 149346699504 1941507093541 25239592216022 328114698808275 4265491084507564
(1 - loop(\(x,i).(x - (3 * (~2x + (i mod 2)))),x,0))
A039304: 1 4 22 151 1051 7354 51472 360301 2522101 17654704 123582922 865080451 6055563151 42388942054 296722594372 2077058160601
loop(\(x,i).(7x - (i div ~2)),x,0)
A178730: 0 1 8 58 408 2859 20016 140116 980816 6865717 48060024 336420174 2354941224 16484588575 115392120032 807744840232
loop(\(x,i).(3x + 96),x,0)
A277107: 0 96 384 1248 3840 11616 34944 104928 314880 944736 2834304 8503008 25509120 76527456 229582464 688747488
(if (x mod 12) <= 0 then (x + (x div 3)) else 0)
A181029: 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0
loop(\(x,i).(26x + 1),x,0)
A218729: 0 1 27 703 18279 475255 12356631 321272407 8353082583 217180147159 5646683826135 146813779479511 3817158266467287 99246114928149463 2580398988131886039 4611686018427387903
loop(\(x,i).(22x + 1),x,0)
A218725: 0 1 23 507 11155 245411 5399043 118778947 2613136835 57489010371 1264758228163 27824681019587 612142982430915 13467145613480131 296277203496562883 4611686018427387903
loop(\(x,i).(34x + 1),x,0)
A218737: 0 1 35 1191 40495 1376831 46812255 1591616671 54114966815 1839908871711 62556901638175 2126934655697951 72315778293730335 2458736461986831391 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (((x + 1) + (i div (2 + (x mod 2)))) div 2)),x,0)
A282692: 0 1 2 3 3 3 4 5 5 5 5 5 6 7 7
loop(\(x,i).((x + 1) + (x div (1 + (x mod 5)))),x,0)
A181288: 0 1 2 3 4 5 11 17 23 29 35 71 107 143 179 215
(1 - loop(\(x,i).(11x + ~1),x,0))
A047856: 1 2 13 134 1465 16106 177157 1948718 21435889 235794770 2593742461 28531167062 313842837673 3452271214394 37974983358325 417724816941566
loop(\(x,i).((x + 1) + (x div (1 + (x mod 6)))),x,0)
A181303: 0 1 2 3 4 5 6 13 20 27 34 41 48 97 146 195
loop(\(x,i).(33x + 1),x,0)
A218736: 0 1 34 1123 37060 1222981 40358374 1331826343 43950269320 1450358887561 47861843289514 1579440828553963 52121547342280780 1720011062295265741 4611686018427387903 4611686018427387903
loop(\(x,i).(31x + 1),x,0)
A218734: 0 1 32 993 30784 954305 29583456 917087137 28429701248 881320738689 27320942899360 846949229880161 26255426126284992 813918209914834753 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + (3 * (x mod 8))),x,0)
A170837: 0 1 5 21 37 53 69 85 101 117 133 149 165 181 197 213
loop(\(x,i).((x + 1) + ((x - ((x mod 3) div 2)) div 2)),x,0)
A327421: 0 1 2 3 5 8 12 19 29 44 66 100 151 227 341 512
loop(\(x,i).((x + 1) + (4 * (2x + (x div 2)))),x,0)
A015592: 0 1 10 111 1220 13421 147630 1623931 17863240 196495641 2161452050 23775972551 261535698060 2876892678661 31645819465270 348104014117971
(1 - loop(\(x,i).((x + ~1) + ((x + (x div 2)) div (2 + i))),x,0))
A231408: 1 2 4 6 9
A095114: 1 2 4 6 9 12 16 20 24 29 34 39 45 51 57 63
((4x2 + 4x + 1) - (if (x + ~1) <= 0 then x else 0))
A273743: 1 8 25 49 81 121 169 225 289 361 441 529 625 729 841 961
loop(\(x,i).(2x - ((1 - (2 * (i mod 2))) * (1 + i))),x,0)
A172285: 0 2 1 6 7 20 33 74 139 288 565 1142 2271 4556 9097 18210
loop(\(x,i).((x + ((~1 + (2 * (i mod 2))) * i)) * (1 + i)),x,0)
A180189: 0 2 0 12 40 270 1848 14840 133488 1334970 14684560 176214852 2290792920 32071101062 481066515720 7697064251760
(1 - loop(\(x,i).(2x + ~30),x,0))
A139700: 1 31 91 211 451 931 1891 3811 7651 15331 30691 61411 122851 245731 491491 983011
(9 - (if (~4 + (x div 2)) <= 0 then x else 0))
A307340: 9 8 7 6 5 4 3 2 1 0 9 9 9 9 9 9
(((x + 1) mod 2) - loop(\(x,i).(2 * (x - ((i div 2) mod 2))),x,0))
A199403: 1 0 3 6 13 24 51 102 205 408 819 1638 3277 6552 13107 26214
((2 * (x mod 2)) - loop(\(x,i).(5x + ~4),x,0))
A274072: 0 6 24 126 624 3126 15624 78126 390624 1953126 9765624 48828126 244140624 1220703126 6103515624 30517578126
(x - (if (x mod 5) <= 0 then (~x + (x div 4)) else 0))
A236852: 0 1 2 3 4 9 6 7 8 9 18 11 12 13 14 27
(1 - (6 mod (2 - (if (x mod 4) <= 0 then x else 0))))
A250662-A220054-A135469: 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1
((~2x + 1) mod ((~x + 2) + loop(\(x,i).(2 * (x + i)),x,0)))
A309115: 1 2 5 16
A132734: 1 2 5 16 43 102 225 476 983 2002 4045 8136 16323 32702 65465 130996
(1 - loop(\(x,i).(4x - (((~1 + i) * i) div 2)),x,0))
A326294: 1 1 2 8 35 147 600 2418
loop(\(x,i).((x + 1) + (x * (2 + i)) - (2 * (x mod 2))),x,0)
A006348: 0 1 4 25 174 1393 12536 125361 1378970 16547641 215119332 3011670649 45175059734 722800955745 12287616247664 221177092457953
loop(\(x,i).(10x + 27),x,0)
A086574: 0 27 297 2997 29997 299997 2999997 29999997 299999997 2999999997 29999999997 299999999997 2999999999997 29999999999997 299999999999997 2999999999999997
loop(\(x,i).(x + ((((3 + i) * i) div 2) * (1 + i))),x,0)
A215862: 0 4 19 55 125 245 434 714 1110 1650 2365 3289 4459 5915 7700 9860
loop(\(x,i).(x + (((4 + i) * i * (1 + i)) div 2)),x,0)
A241765: 0 5 23 65 145 280 490 798 1230 1815 2585 3575 4823 6370 8260 10540
loop(\(x,i).(x + (((2 + i) * i) div (x + 6))),x,0)
A005356: 0 0 1 3 5 8 11 14 18 22 26 30 34 38 43 48
loop(\(x,i).(x + (2 * (i * i * i * i * i * i))),x,0)
A259109: 0 2 130 1588 9780 41030 134342 369640 893928 1956810 3956810 7499932 13471900 23125518 38184590 60965840
loop(\(x,i).(x + ((1 + (8 * (~1 + i))) * i)),x,0)
A172078: 0 1 19 70 170 335 581 924 1380 1965 2695 3586 4654 5915 7385 9080
loop(\(x,i).(x + ((~2 + (7 * i)) * i)),x,0)
A050409: 0 5 29 86 190 355 595 924 1356 1905 2585 3410 4394 5551 6895 8440
loop(\(x,i).(x + ((i - (4 * (1 - i))) * i * i)),x,0)
A172047: 0 1 25 124 380 905 1841 3360 5664 8985 13585 19756 27820 38129 51065 67040
loop(\(x,i).(x + ((1 - (2 * (i mod 2))) * i * i * i)),x,0)
A232599: 0 ~1 7 ~20 44 ~81 135 ~208 304 ~425 575 ~756 972 ~1225 1519 ~1856
loop(\(x,i).(x + (i * i * i * i * i * i * i)),x,0)
A000541: 0 1 129 2316 18700 96825 376761 1200304 3297456 8080425 18080425 37567596 73399404 136147921 241561425 412420800
loop(\(x,i).(~x + (i * i * i * i * i * i * i)),x,0)
A152726: 0 1 127 2060 14324 63801 216135 607408 1489744 3293225 6706775 12780396 23051412 39697105 65716399 105142976
(if (x mod (1 + ((x div 2) div (1 + (x mod 4))))) <= 0 then 0 else 1)
A011661: 0 0 0 0 1 1 0 0 1 0 0 1 1 1 1 1
(if ((x3 + 2) mod (1 + (x div 3))) <= 0 then 0 else 1)
A288381-A095792: 0 0 0 1 0 1 1 0 1 1 1 1 0 1 1 1
(if ((x + 1) mod (1 + ((1 + (x div 3)) div 2))) <= 0 then 0 else 1)
A011662: 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0
(if ((x + ~1) mod (3 + (x div 5))) <= 0 then 0 else 1)
A263804: 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 1
(if (x mod (3 + (x2 mod 5))) <= 0 then 0 else 1)
A286055: 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0
(if ((x2 + x + 1) mod 7) <= 0 then 0 else 1)
A098457: 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1
(if ((x * (x mod 3)) mod 7) <= 0 then 0 else 1)
A284627: 0 1 1 0 1 1 0 0 1 0 1 1 0 1 0 0
(if ((x + ~1) mod (1 + ((~x + 2) mod 6))) <= 0 then 0 else 1)
A333815: 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1
(if (x mod (1 + (2 * (x - (2 * (x div 3)))))) <= 0 then 0 else 1)
A181632: 0 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1
(if (x mod (1 + (2 * ((x + 2) mod 8)))) <= 0 then 0 else 1)
A196147: 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0
(if ((x + 1) mod (1 + (2 * ((~x + 1) mod 4)))) <= 0 then 0 else 1)
A209198: 1 0 1 1 1 0 0 1 0 0 1 1 1 0 1 1
(if ((~x + 3) mod (3 + (x div 4))) <= 0 then 0 else 1)
A294018: 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0
(if ((~1 + (x div 2)) div (~1 + (2 * (x mod 4)))) <= 0 then 0 else 1)
A117957: 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 1
(if (((x + 1) - (x div 4)) mod 5) <= 0 then 0 else 1)
A071040: 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1
(if (((x + ~2) + ((x div 2) mod 2)) mod 5) <= 0 then 0 else 1)
A249865: 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1
(if ((x * (x mod (2 + (x div 2)))) mod 5) <= 0 then 0 else 1)
A076182: 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 0
(1 + (if (x mod 6) <= 0 then (x div 5) else 0))
A319430-A033630: 1 1 1 1 1 1 2 1 1 1 1 1 3 1 1 1
(1 + (if (x mod 2) <= 0 then ((x + ~2) mod (1 + (x div 4))) else 0))
A291634: 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1
(if (((x + ~1) div (1 + (2 * (x mod 2)))) mod 3) <= 0 then 0 else 1)
A273512: 1 0 1 0 0 1 1 1 1 1 0 0 1 1 1 1
(if ((x div (3 * (1 + (x mod 2)))) mod 3) <= 0 then 0 else 1)
A039738: 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1
(if ((x - (x div 12)) mod 3) <= 0 then 0 else 1)
A022933: 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1
(if (((~x2 + 4x + ~4) div 3) mod 3) <= 0 then 0 else 1)
A039966: 1 1 0 1 1 0 0 0 0 1 1 0 1 1 0 0
(if ((x2 mod (~2x + 5)) mod 3) <= 0 then 0 else 1)
A270742: 0 1 0 0 1 0 0 1 1 1 1 0 1 1 1 0
(if (((x + 1) * (~1 + (x mod 4))) mod 3) <= 0 then 0 else 1)
A187074: 1 0 0 1 1 0 1 1 0 0 1 0 1 0 0 1
(if (((x + ~1) mod (2 - (x div ~2))) mod 3) <= 0 then 0 else 1)
A321223: 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1
(if ((2x mod (2 - (x div ~2))) mod 3) <= 0 then 0 else 1)
A174206: 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0
(if ((x - ((x div 5) mod 2)) mod 3) <= 0 then 0 else 1)
A105565: 0 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1
(if ((x mod (~2 + ((~x + 1) div 3))) mod 3) <= 0 then 0 else 1)
A127000: 0 1 1 0 1 0 1 1 1 1 0 1 0 1 0 0
(if ((x + 2) mod (5 - (x div 4))) <= 0 then 0 else 1)
A330667: 1 1 1 0 1 1 0 1 1 1 0 1 0 1 0 1
(if ((2x2 mod (2 + (x div 2))) mod 3) <= 0 then 0 else 1)
A005091: 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 0
(if ((((~x + 2) * (2 + (x div 2))) div 2) mod 3) <= 0 then 0 else 1)
A290307-A055800: 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 1
(if ((x + ((x + ~2) div (2 + (x div 2)))) mod 3) <= 0 then 0 else 1)
A287523: 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1
(1 + (if ((x + ~2) mod 5) <= 0 then (x div 3) else 0))
A131324: 1 1 1 1 1 1 1 3 1 1 1 1 5 1 1 1
(~1 + loop(\(x,i).(10x + 8),(x + 1),0))
A173812: 7 87 887 8887 88887 888887 8888887 88888887 888888887 8888888887 88888888887 888888888887 8888888888887 88888888888887 888888888888887 8888888888888887
(1 + loop(\(x,i).((x + 1) mod (2 + (i div 3))),(x + ~1),0))
A194844-A194055: 1 1 2 1 2 3 1 2 3 4 5 1 2 3 4 5
(1 + (if (x mod 2) <= 0 then (x mod 14) else 0))
A327531-A327514: 1 1 3 1 5 1 7 1 9 1 11 1 13 1 1 1
(~1 + (if ((x * (x mod 3)) mod 5) <= 0 then 2 else 0))
A106400: 1 ~1 ~1 1 ~1 1 1 ~1 ~1 1 1 ~1 1 ~1 ~1 1
(~1 + (if ((x mod (4 + (x mod 2))) mod 3) <= 0 then 2 else 0))
A209615: 1 ~1 ~1 1 1 1 ~1 ~1 1 ~1 ~1 ~1 1 1 ~1 1
(if ((x + ~2) mod (2 + ((2 * (x div 2)) mod 3))) <= 0 then 0 else 1)
A117872: 0 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1
(1 + (if (x mod 7) <= 0 then 6 else 0))
A109010: 7 1 1 1 1 1 1 7 1 1 1 1 1 1 7 1
(if ((x div 3) - (x2 mod 6)) <= 0 then 0 else 1)
A196049: 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1
(4x2 div (1 + (if (x mod 3) <= 0 then 2 else 0)))
A147560: 0 4 16 12 64 100 48 196 256 108 400 484 192 676 784 300
(if (((~3x + 3) mod (1 + (x div 2))) div 2) <= 0 then 0 else 1)
A011698: 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1
(if ((x + ~1) mod (4 + (x div 5))) <= 0 then 0 else 1)
A275694: 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0
(if ((x + 1) mod (4 - (((x + ~1) div 2) div 2))) <= 0 then 0 else 1)
A174897: 1 1 1 0 1 0 1 1 0 0 1 0 1 0 0 0
((x div 2) - (if (~2 + ((x + 1) mod 8)) <= 0 then 0 else 1))
A140427: 0 0 0 0 1 1 2 3 4 4 4 4 5 5 6 7
(if ((2x + 2) mod (4 + (x div 4))) <= 0 then 0 else 1)
A157749: 1 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1
(1 + (if ((1 + ((x * (x div 2)) div 2)) mod 4) <= 0 then 2 else 0))
A063065: 1 1 1 1 1 1 1 1 1 1 1 3 1 3 1 1
(1 + (if ((x + 1) mod 8) <= 0 then 8 else 0))
A113061: 1 1 1 1 1 1 1 9 1 1 1 1 1 1 1 9
(1 + (if (x mod 4) <= 0 then (x mod (2 + (x div 4))) else 0))
A321125-A225174-A204127-A204125-A204112-A059895: 1 1 1 1 2 1 1 1 1 1 1 1 3 1 1 1
((~x + 1) mod (1 + (if (2x mod (2 + (x div 2))) <= 0 then 2 else 0)))
A291749: 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0
(if (x mod (1 - (2 * ((~x + 1) div (2 + (x div 2)))))) <= 0 then 0 else 1)
A316101: 0 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0
((2x + ~1) + (if (~2 + (x div 2)) <= 0 then 2 else 0) - (x mod 2))
A284492: 1 2 5 6 9 10 11 12 15 16 19 20 23 24 27 28
(if ((x mod ~11) mod 4) <= 0 then 0 else 1)
A188068-A144610: 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1
(if ((1 + ((x2 + ~2x) div (x + 2))) mod 4) <= 0 then 0 else 1)
A319102-A103582: 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0
(if ((x - (6 div (x + 1))) mod 4) <= 0 then 0 else 1)
A232750: 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 1
(if (((x + 1) * (2 + (x div 4))) mod 4) <= 0 then 0 else 1)
A094934: 1 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0
(1 + (if ((x2 + 1) mod (x + 4)) <= 0 then 4 else 0))
A337337-A250131: 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1
(if ((x + (x2 div (2 + (x div 2)))) mod 4) <= 0 then 0 else 1)
A189576: 0 1 1 1 0 1 1 0 1 1 0 0 1 1 1 0
((6x + 6) + (if (x + ~4) <= 0 then 0 else 1))
A028436: 6 12 18 24 30 37 43 49 55 61 67 73 79 85 91 97
((5x + 4) - (if (x + ~4) <= 0 then 0 else 1))
A190086: 4 9 14 19 24 28 33 38 43 48 53 58 63 68 73 78
(1 + (if ((x + 1) mod 8) <= 0 then (x div 4) else 0))
A342017-A073753-A062378: 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 4
(1 + (if (x2 mod (x + 4)) <= 0 then (x div 4) else 0))
A204133: 1 1 1 1 2 1 1 1 1 1 1 1 4 1 1 1
(if (x - ((2x2 + ~1) mod (x + 4))) <= 0 then 0 else 1)
A037818: 0 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1
(2x + (if (~2 + (x div 2)) <= 0 then 0 else 1) - (x mod 3))
A026311: 0 1 2 6 7 8 13 14 15 19 20 21 25 26 27 31
((1 - (2 * ((x div 2) mod 2))) * (1 + (if (x mod 2) <= 0 then 2 else 0)))
A112030: 3 1 ~3 ~1 3 1 ~3 ~1 3 1 ~3 ~1 3 1 ~3 ~1
(1 + (if (x mod 13) <= 0 then (x div 2) else 0))
A240831-A074465: 1 1 1 1 1 1 1 1 1 1 1 1 1 7 1 1
(1 + loop(\(x,i).((3x + 1) + (x mod 3)),x,0))
A077834: 1 2 6 19 56 168 505 1514 4542 13627 40880 122640 367921 1103762 3311286 9933859
(~1 + loop(\(x,i).(10x + 3),x,0))
A323639: ~1 2 32 332 3332 33332 333332 3333332 33333332 333333332 3333333332 33333333332 333333333332 3333333333332 33333333333332 333333333333332
(1 + loop(\(x,i).(x + i - (x mod 9)),x,0))
A302768-A223080-A212499-A180480-A166508-A093475-A080459-A071061-A051596-A037124-A032571: 1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70
(1 + loop(\(x,i).((x2 + ~1) mod (2x + 5)),x,0))
A070367: 1 5 3 4 9 1 5 3 4 9 1 5 3 4 9 1
(1 + loop(\(x,i).(~1 + (2 * ((2x div (1 + i)) + i))),x,0))
A222011: 1 2 4 8
A215459: 1 2 4 8 12 16 20 22 24 26 28 30 32 34 36 38
(1 + loop(\(x,i).(2 * ((~x + 2) mod 7)),x,0))
A070369: 1 5 11 13 9 3 1 5 11 13 9 3 1 5 11 13
(1 + loop(\(x,i).(x + i - (x mod 10)),x,0))
A179309-A178354-A032946: 1 2 3 4 5 6 7 8 9 10 11 22 33 44 55 66
(if (~x + ((x2 + 2x) mod 16)) <= 0 then 0 else 1)
A102460: 0 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0
((x mod (1 + ((x + 1) div 5))) + (if x <= 0 then 0 else 1))
A081327: 0 1 1 1 1 2 1 2 1 1 2 3 1 2 3 4
((x div (5 + (x mod 3))) + (if x <= 0 then 0 else 1))
A030603: 0 1 1 1 1 1 2 2 2 2 2 2 3 3 3 4
(((x + 1) mod (1 + ((~x + 2) mod 4))) + (if x <= 0 then 0 else 1))
A031228: 1 1 1 1 3 1 1 1 1 1 1 1 2 1 1 1
(((1 + (x div (~2 + (x mod 2)))) mod 3) - (if x <= 0 then 0 else 1))
A163810: 1 ~1 ~1 0 1 1 0 ~1 ~1 0 1 1 0 ~1 ~1 0
(54 - (if x <= 0 then 0 else 1))
A116386: 54 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53
(((1 + (x div (2 - (x mod 2)))) mod 3) - (if x <= 0 then 0 else 1))
A163806: 1 1 1 0 ~1 ~1 0 1 1 0 ~1 ~1 0 1 1 0
((3 * (2 + ((x2 + ~x) div 2))) + (if x <= 0 then 0 else 1))
A081359: 6 7 10 16 25
(((x mod (1 + ((1 + (x div 2)) div 2))) mod 2) + (if x <= 0 then 0 else 1))
A023520: 0 1 1 2 1 2 1 2 1 1 1 2 1 2 1 1
(((x mod (1 + (x mod (2 + (x div 2))))) div 2) + (if x <= 0 then 0 else 1))
A326775: 0 1 2 1 1 1 1 1 2 1 2 1 2 1 2 1
(((x div 2) + (if x <= 0 then 0 else 1)) - (2 * ((x div 2) div 3)))
A287271: 0 1 2 2 3 3 2 2 3 3 4 4 3 3 4 4
((2 * ((2x + 1) + (x div 3))) + (if x <= 0 then 0 else 1))
A063205: 2 7 11 17 21 25 31 35 39 45 49 53 59 63 67 73
(((x mod (~8 + (x mod 2))) mod 2) + (if x <= 0 then 0 else 1))
A306446: 0 1 1 1 1 1 1 1 1 2 1 2 1 2 1 1
(4 + (if x <= 0 then 0 else 1) - ((x mod (2 + (x mod 2))) div 2))
A018245: 4 5 5 5 5 4 5 5 5 5 5 4 5 5 5 5
(x + (if x <= 0 then 0 else 1) - ((x + 2) div ~7))
A155854: 1 3 4 5 6 7 9 10 11 12 13 14 15 17 18 19
((((x div 2) * (x div 2)) div 8) + (if x <= 0 then 0 else 1))
A237979: 0 1 1 1 1 1 2 2 3 3 4 4 5 5 7 7
((20x + 8) - (if x <= 0 then 0 else 1))
A063144: 8 27 47 67 87 107 127 147 167 187 207 227 247 267 287 307
((2 * (((x2 + ~x) div (x + 2)) mod 2)) - (if x <= 0 then 0 else 1))
A226523: 0 ~1 ~1 1 ~1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1
(((((x div 3) * (x div 2)) div 2) mod 2) + (if x <= 0 then 0 else 1))
A104638: 0 1 1 1 2 2 2 2 1 1 2 2 1 1 1 2
((((2x + ~2) mod (2 + (x div 2))) mod 2) + (if x <= 0 then 0 else 1))
A346087: 0 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2
(((x + (x2 mod 3)) div 4) + (if x <= 0 then 0 else 1))
A172263: 0 1 1 1 2 2 2 3 3 3 3 4 4 4 4 4
(((8x + 1) div (x + 2)) + (if x <= 0 then 0 else 1))
A225491: 0 4 5 6 6 6 7 7 7 7 7 7 7 8 8 8
(((8x + 1) div (x + 2)) - (if x <= 0 then 0 else 1))
A225486: 0 2 3 4 4 4 5 5 5 5 5 5 5 6 6 6
((9x2 + ~2x) - (if x <= 0 then 0 else 1))
A187508: 0 6 31 74 135 214 311 426 559 710 879 1066 1271 1494 1735 1994
(1 + loop(\(x,i).(x + ((1 + ((2 + i) * i)) div (x + 1))),x,0))
A262161: 1 5 6 8 11 14 17 20 24 28 32 36 40 44 49 54
(1 + loop(\(x,i).(~x + (8 * (x + (i mod 2)))),x,0))
A102303: 1 9 57 401 2801 19609 137257 960801 6725601 47079209 329554457 2306881201 16148168401 113037178809 791260251657 5538821761601
(1 + ((x div 2) div (1 + (if ((x mod 3) mod 2) <= 0 then 2 else 0))))
A117905: 1 1 1 1 3 1 2 4 2 2 6 2 3 7 3 3
loop(\(x,i).2x,((x + ~1) - (x mod 9)),1)
A248776: 1 1 1 1 1 1 1 1 1 256 256 256 256 256 256 256
(x div (1 + ((~x + 1) mod (1 + (if (x mod 4) <= 0 then 2 else 1)))))
A168485: 0 1 1 3 4 5 3 7 2 9 5 11 6 13 7 15
(1 + (if (x mod 2) <= 0 then 40 else 1))
A283895: 41 2 41 2 41 2 41 2 41 2 41 2 41 2 41 2
(1 + (if ((x div 3) mod 2) <= 0 then (x div 5) else 1))
A242306: 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 2
loop(\(x,i).2x,(~1 + (x div (1 + ((~x + 2) mod 4)))),1)
A320076: 1 1 2 1 1 2 32 1
(1 + ((x + ~2) mod (1 + (if (x mod 2) <= 0 then (x div 4) else 1))))
A259656-A096370: 1 2 1 2 1 2 1 2 1 2 3 2 3 2 1 2
(1 + (if (x mod 2) <= 0 then 36 else 1))
A278067: 37 2 37 2 37 2 37 2 37 2 37 2 37 2 37 2
(1 + (if (x + ~1) <= 0 then x else (1 + (3 * (x mod 3)))))
A141449: 1 2 8 2 5 8 2 5 8 2 5 8 2 5 8 2
(~1 + loop(\(x,i).2x,x,23))
A291557: 22 45 91 183 367 735 1471 2943 5887 11775 23551 47103 94207 188415 376831 753663
(1 + loop(\(x,i).(x2 + x),x,13))
A179090: 14 183 33307 1109322943 1230597390756858307 4611686018427387903 4611686018427387903
(1 + (x div (1 + (if (x mod 2) <= 0 then ((x div 2) mod 2) else 3))))
A087620: 1 1 2 1 5 2 4 2 9 3 6 3 13 4 8 4
((x + ~1) mod (1 + (if ((x div 2) mod 2) <= 0 then (x div 3) else 1)))
A072927: 0 0 1 0 1 0 1 0 1 0 1 0 1 2 1 0
loop(\(x,i).i,((~x2 + ~1) mod (1 + (x div 3))),1)
A014600: 1 1 1 1 1 1 2 1 1 2 3 2 1 1 3 2
(if ((x + ~2) mod 5) <= 0 then (~1 + (x mod 3)) else 1)
A064334: 1 1 1 1 1 1 1 0 1 1 1 1 ~1 1 1 1
(1 + loop(\(x,i).10x,(2x + 1),1))
A152577: 11 1001 100001 10000001 1000000001 100000000001 10000000000001 1000000000000001 100000000000000001 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (x mod (1 + (loop(\(x,i).2x,x,2) mod (2x + 1)))))
A083346: 1 2 3 1 5 6 7 2 3 10 11 3 13 14 15 1
(1 + (x mod (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))
A327405: 1 2 1 4 1 2 1 8 1 2 1 4 1 2 3 16
(~1 + loop(\(x,i).(4x - (i mod 3)),(x + 1),1))
A037632: 2 9 39 158 633 2535 10142 40569 162279 649118 2596473 10385895 41543582 166174329 664697319 2658789278
(1 + loop(\(x,i).(10x + ~2),(x + 1),1))
A173808: 9 79 779 7779 77779 777779 7777779 77777779 777777779 7777777779 77777777779 777777777779 7777777777779 77777777777779 777777777777779 7777777777777779
(1 + (x mod loop(\(x,i).i,(16 mod (x + 1)),1)))
A297170: 1 1 1 1 1 2 1 1 2 4 1 4 1 2 1 1
loop(\(x,i).6x,(4x + 3),1)
A013785: 216 279936 362797056 470184984576 609359740010496 789730223053602816 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).5x,(4x + 3),1)
A013783: 125 78125 48828125 30517578125 19073486328125 11920928955078125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (x mod (1 + (loop(\(x,i).(x2 + 2x),2,2) mod (x + 1)))))
A278509: 1 1 3 1 1 3 3 1 9 1 3 3 1 3 3 1
(~1 + loop(\(x,i).(x * (2 + (3 * (i mod 2)))),(x + 1),1))
A268099: 4 9 49 99 499 999 4999 9999 49999 99999 499999 999999 4999999 9999999 49999999 99999999
(1 + loop(\(x,i).((x * (1 + i)) div (1 + (i div 2))),(x + ~1),1))
A051920: 2 2 3 4 7 11 21 36 71 127 253 463 925 1717 3433 6436
(~1 + loop(\(x,i).((x * (1 + i)) div (1 + (i div 2))),(x + ~1),1))
A014495: 0 0 1 2 5 9 19 34 69 125 251 461 923 1715 3431 6434
loop(\(x,i).2x,(x - (2x2 div ~3)),1)
A186339: 1 4 32 512 32768 4194304 1073741824 1099511627776 2251799813685248 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + 1),((x + 1) - (x div ~2)),1)
A198586: 5 85 341 5461 21845 349525 1398101 22369621 89478485 1431655765 5726623061 91625968981 366503875925 5864062014805 23456248059221 375299968947541
(1 + (x div (if (x mod 11) <= 0 then 2 else 1)))
A327526-A062759: 1 2 3 4 5 6 7 8 9 10 11 6 13 14 15 16
(1 + (if (x mod 2) <= 0 then (2 * (1 + ((x div 3) mod 2))) else 1))
A116895: 3 2 3 2 5 2 3 2 3 2 5 2 3 2 3 2
((x + 1) - ((~x + 1) div (1 + (if (x + ~4) <= 0 then 1 else 2))))
A187895: 1 2 4 5 7 8 9 10 12 13 14 16 17 18 20 21
loop(\(x,i).i,(~1 + (x div 2) - (((x + 1) div 3) mod 2)),1)
A029115: 1 1 1 1 1 1 2 2 2 2 3 4 5 5 5 5
loop(\(x,i).i,(x mod (~1 + (2 * ((2 * (x div 2)) div 3)))),1)
A090628: 1 1 1 1 1 1 1 1 2 1 1 1 5 6 1 1
(1 + loop(\(x,i).6x,x,7))
A199321: 8 43 253 1513 9073 54433 326593 1959553 11757313 70543873 423263233 2539579393 15237476353 91424858113 548549148673 3291294892033
(~1 + loop(\(x,i).6x,x,7))
A198795: 6 41 251 1511 9071 54431 326591 1959551 11757311 70543871 423263231 2539579391 15237476351 91424858111 548549148671 3291294892031
(1 + (7 * loop(\(x,i).2x,(x + ~1),x)))
A048478: 1 8 29 85 225 561 1345 3137 7169 16129 35841 78849 172033 372737 802817 1720321
(1 + loop(\(x,i).8x,x,7))
A199555: 8 57 449 3585 28673 229377 1835009 14680065 117440513 939524097 7516192769 60129542145 481036337153 3848290697217 30786325577729 246290604621825
(~1 + loop(\(x,i).8x,x,7))
A198855: 6 55 447 3583 28671 229375 1835007 14680063 117440511 939524095 7516192767 60129542143 481036337151 3848290697215 30786325577727 246290604621823
(1 + (x mod (1 + (2 * ((if (x mod 2) <= 0 then 1 else x) mod 3)))))
A078711: 1 2 3 1 2 1 1 2 3 1 2 2 1 2 3 1
(1 + ((2x + 3) * loop(\(x,i).(2x + 2),x,0)))
A213763: 1 11 43 127 331 807 1891 4319 9691 21463 47059 102351 221131 475079 1015747 2162623
(if (x mod 3) <= 0 then (x2 div (2x + 3)) else 1)
A240850: 0 1 1 1 1 1 2 1 1 3 1 1 5 1 1 6
(1 + ((if x <= 0 then 0 else (x + 3)) * (1 + ((x + 1) div 2))))
A329279: 1 9 11 19 22 33 37 51 56 73 79 99 106 129 137 163
(1 + (if (x mod 2) <= 0 then (2 * (2 - ((x mod 3) div 2))) else 1))
A291358: 5 2 3 2 5 2 5 2 3 2 5 2 5 2 3 2
(1 + loop(\(x,i).(x2 + x),x,17))
A179121: 18 307 93943 8825193307 4611686018427387903 4611686018427387903 4611686018427387903
((x * (x div 2)) mod (1 + (if (x mod 8) <= 0 then 2 else 1)))
A334109-A333842-A277885: 0 0 0 1 0 0 0 1 2 0 0 1 0 0 0 1
(1 + ((~1 + loop(\(x,i).(x * i),x,1)) mod 9))
A086358: 1 1 2 6 6 3 9 9 9 9 9 9 9 9 9 9
(if x <= 0 then 0 else (1 + ((2x + ~1) mod 9)))
A180592: 0 2 4 6 8 1 3 5 7 9 2 4 6 8 1 3
(if x <= 0 then 0 else (1 + ((~x + ~1) mod 9)))
A180598: 0 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3
(1 + loop(\(x,i).6x,x,9))
A199413: 10 55 325 1945 11665 69985 419905 2519425 15116545 90699265 544195585 3265173505 19591041025 117546246145 705277476865 4231664861185
(~1 + loop(\(x,i).6x,x,9))
A198846: 8 53 323 1943 11663 69983 419903 2519423 15116543 90699263 544195583 3265173503 19591041023 117546246143 705277476863 4231664861183
(1 + (9 * loop(\(x,i).2x,(x + ~1),x)))
A048480: 1 10 37 109 289 721 1729 4033 9217 20737 46081 101377 221185 479233 1032193 2211841
(1 + loop(\(x,i).8x,x,9))
A199556: 10 73 577 4609 36865 294913 2359297 18874369 150994945 1207959553 9663676417 77309411329 618475290625 4947802324993 39582418599937 316659348799489
(~1 + loop(\(x,i).8x,x,9))
A198856: 8 71 575 4607 36863 294911 2359295 18874367 150994943 1207959551 9663676415 77309411327 618475290623 4947802324991 39582418599935 316659348799487
(1 + (loop(\(x,i).(x2 + 2x),2,x) mod 9))
A303296: 1 7 9 4 4 9 7 1 9 1 7 9 4 4 9 7
loop(\(x,i).(x mod 2),(x mod 2),(1 + (x mod 9)))
A071649: 1 0 3 0 5 0 7 0 9 1 2 1 4 1 6 1
(1 + loop(\(x,i).5x,x,9))
A199313: 10 46 226 1126 5626 28126 140626 703126 3515626 17578126 87890626 439453126 2197265626 10986328126 54931640626 274658203126
loop(\(x,i).i,((~1 + (x div 2)) div (~1 + (2 * (x mod 4)))),1)
A081060: 1 1 1 1 1 1 1 1 1 3 1 1 1 5 2 1
(1 + (x div (if ((x + 1) mod 8) <= 0 then 4 else 1)))
A066990: 1 2 3 4 5 6 7 2 9 10 11 12 13 14 15 4
loop(\(x,i).x2,1,(10x + 6))
A017342: 36 256 676 1296 2116 3136 4356 5776 7396 9216 11236 13456 15876 18496 21316 24336
loop(\(x,i).x2,2,(10x + 6))
A017344: 1296 65536 456976 1679616 4477456 9834496 18974736 33362176 54700816 84934656 126247696 181063936 252047376 342102016 454371856 592240896
loop(\(x,i).x2,1,(10x + 9))
A017378: 81 361 841 1521 2401 3481 4761 6241 7921 9801 11881 14161 16641 19321 22201 25281
loop(\(x,i).x2,2,(10x + 9))
A017380: 6561 130321 707281 2313441 5764801 12117361 22667121 38950081 62742241 96059601 141158161 200533921 276922881 373301041 492884401 639128961
(if x <= 0 then 4 else (1 + ((2x + ~2) div 5)))
A128211: 4 1 1 1 2 2 3 3 3 4 4 5 5 5 6 6
(~1 + ((2 * (if x <= 0 then 1 else (x2 + ~1))) mod 5))
A164116: 1 ~1 0 0 ~1 2 ~1 0 0 ~1 2 ~1 0 0 ~1 2
(1 + (5 * loop(\(x,i).(2x + 1),x,4)))
A250777: 21 46 96 196 396 796 1596 3196 6396 12796 25596 51196 102396 204796 409596 819196
(if (x + ~1) <= 0 then x else (1 + ((2x + 4) div 5)))
A230418: 0 1 2 3 3 3 4 4 5 5 5 6 6 7 7 7
(1 + (5 * loop(\(x,i).3x,2x,2)))
A199678: 11 91 811 7291 65611 590491 5314411 47829691 430467211 3874204891 34867844011 313810596091 2824295364811 25418658283291 228767924549611 2058911320946491
(~1 + (5 * loop(\(x,i).3x,2x,2)))
A198967: 9 89 809 7289 65609 590489 5314409 47829689 430467209 3874204889 34867844009 313810596089 2824295364809 25418658283289 228767924549609 2058911320946489
(1 + (5 * loop(\(x,i).6x,x,2)))
A199414: 11 61 361 2161 12961 77761 466561 2799361 16796161 100776961 604661761 3627970561 21767823361 130606940161 783641640961 4701849845761
(~1 + (5 * loop(\(x,i).6x,x,2)))
A198847: 9 59 359 2159 12959 77759 466559 2799359 16796159 100776959 604661759 3627970559 21767823359 130606940159 783641640959 4701849845759
(1 + (5 * loop(\(x,i).8x,x,2)))
A199557: 11 81 641 5121 40961 327681 2621441 20971521 167772161 1342177281 10737418241 85899345921 687194767361 5497558138881 43980465111041 351843720888321
(~1 + (5 * loop(\(x,i).8x,x,2)))
A198857: 9 79 639 5119 40959 327679 2621439 20971519 167772159 1342177279 10737418239 85899345919 687194767359 5497558138879 43980465111039 351843720888319
loop(\(x,i).~x,x,(1 + (((~x + 2) div 2) div 5)))
A014087: 1 ~1 1 0 0 0 0 0 0 0 0 0 0 1 ~1 1
(if ((x + 1) mod 4) <= 0 then ((x + 2) div 5) else 1)
A280688-A095136: 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 3
loop(\(x,i).(3x + 2),(~5 + (x div 2)),1)
A147206-A147167-A146876-A146860-A146852-A146836-A146796-A146780-A146719-A146647: 1 1 1 1 1 1 1 1 1 1 1 1 5 5 17 17
((x + 1) - (5 * (2 - (if (~x + 2) <= 0 then x else 2))))
A091361: 1 2 3 9 15 21 27 33 39 45 51 57 63 69 75 81
(~1 + loop(\(x,i).12x,x,5))
A199107: 4 59 719 8639 103679 1244159 14929919 179159039 2149908479 25798901759 309586821119 3715041853439 44580502241279 534966026895359 6419592322744319 77035107872931839
(1 + loop(\(x,i).10x,x,5))
A199685: 6 51 501 5001 50001 500001 5000001 50000001 500000001 5000000001 50000000001 500000000001 5000000000001 50000000000001 500000000000001 5000000000000001
(~1 + loop(\(x,i).10x,x,5))
A198971: 4 49 499 4999 49999 499999 4999999 49999999 499999999 4999999999 49999999999 499999999999 4999999999999 49999999999999 499999999999999 4999999999999999
(if ((x + 2) mod 8) <= 0 then (x + ~5) else 1)
A340365: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9 1
(if ((x2 div 2) mod 3) <= 0 then (x div 5) else 1)
A327342: 0 0 1 1 1 1 1 1 1 1 1 2 2 2 1 1
(1 + loop(\(x,i).7x,x,5))
A199422: 6 36 246 1716 12006 84036 588246 4117716 28824006 201768036 1412376246 9886633716 69206436006 484445052036 3391115364246 23737807549716
(1 + loop(\(x,i).(x2 + (x mod 2)),x,(1 + (x div 4))))
A268210-A004249: 2 3 5 17 65537
(if (2 - (x div 4)) <= 0 then (x div (1 + (x div 4))) else 1)
A121242-A065681-A025789: 1 1 1 1 1 1 1 1 2 3 3 3 3 3 3 3
loop(\(x,i).12x,(4x + 1),1)
A013796: 12 248832 5159780352 106993205379072 2218611106740436992 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).10x,(4x + 1),1)
A013792: 10 100000 1000000000 10000000000000 100000000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).7x,(4x + 1),1)
A013786: 7 16807 40353607 96889010407 232630513987207 558545864083284007 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((1 + ((x + ~1) mod 3)) * (if x <= 0 then 0 else 3)))
A118517: 1 4 7 10 4 7 10 4 7 10 4 7 10 4 7 10
(1 + (3 * (1 + loop(\(x,i).(x + (2 * (x + i))),x,1))))
A092359: 7 19 61 193
(1 + (if x <= 0 then 2 else (((x + 2) mod 5) div 3)))
A077450: 3 2 2 1 1 1 2 2 1 1 1 2 2 1 1 1
(if (x mod 2) <= 0 then ((x div (1 + (x mod 4))) mod 3) else 1)
A339455: 0 1 0 1 1 1 2 1 2 1 0 1 0 1 1 1
loop(\(x,i).(x * (1 + i)),18x,1)
A198801: 1 121645100408832000 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (3 * ((x + (if (x mod 2) <= 0 then x else 1)) mod 3)))
A153349: 1 7 4 4 7 1 1 7 4 4 7 1 1 7 4 4
(1 + (3 * ((if (x mod 2) <= 0 then x else (~x + 2)) mod 3)))
A084104: 1 4 7 7 4 1 1 4 7 7 4 1 1 4 7 7
(if (x mod 4) <= 0 then ((1 - (x div 3)) mod 3) else 1)
A257179: 1 1 1 1 0 1 1 1 2 1 1 1 0 1 1 1
(1 + (3 * ((if (x mod 2) <= 0 then (~x + 2) else x) mod 3)))
A131028: 7 4 1 1 4 7 7 4 1 1 4 7 7 4 1 1
(1 + ((1 + (loop(\(x,i).2x,x,2) mod (x + 2))) div 3))
A243928: 1 1 1 1 2 1 1 2 2 1 4 1 2 2 1 1
(1 + loop(\(x,i).(2x + 8),(x + 3),3))
A250655: 81 169 345 697 1401 2809 5625 11257 22521 45049 90105 180217 360441 720889 1441785 2883577
(if x <= 0 then 1 else (x2 mod (1 + ((1 + (x div 2)) div 3))))
A011746: 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0
(1 + (loop(\(x,i).(2x + 2),x,(1 + (x mod 2))) div 3))
A239024: 1 3 4 11 16 43 64 171 256 683 1024 2731 4096 10923 16384 43691
(1 + (loop(\(x,i).(2x + 4),x,(1 + (x mod 2))) div 3))
A282123: 1 3 6 15 26 63 106 255 426 1023 1706 4095 6826 16383 27306 65535
(1 + (loop(\(x,i).((3x + 1) - i),x,1) div 3))
A131959: 1 2 3 8
A006545: 1 2 3 8 22 62
(if (~x + 2) <= 0 then (((x + 1) + ((x div 2) mod 2)) div 3) else 1)
A087831: 1 1 1 1 1 2 2 3 3 3 4 4 4 4 5 5
loop(\(x,i).x2,1,(12x + 11))
A017654: 121 529 1225 2209 3481 5041 6889 9025 11449 14161 17161 20449 24025 27889 32041 36481
loop(\(x,i).x2,2,(12x + 11))
A017656: 14641 279841 1500625 4879681 12117361 25411681 47458321 81450625 131079601 200533921 294499921 418161601 577200625 777796321 1026625681 1330863361
(~1 + ((3x + 3) * (if x <= 0 then 2 else 2x2)))
A216071: 5 11 71
(~1 + loop(\(x,i).2x3,1,(3x + 3)))
A181968: 53 431 1457 3455 6749 11663 18521 27647 39365 53999 71873 93311 118637 148175 182249 221183
loop(\(x,i).10x,(3x + 3),1)
A060365: 1000 1000000 1000000000 1000000000000 1000000000000000 1000000000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (x - (x div 3))),((x + 1) div 3),1)
A096445: 1 1 2 2 2 4 4
A123050-A079438: 1 1 2 2 2 4 4 4 6 6 6 8 8 8 12 12
(if (x + ~3) <= 0 then (x + 1) else (1 + ((x + ~1) mod 3)))
A322424: 1 2 3 4 1 2 3 1 2 3 1 2 3 1 2 3
(1 + (loop(\(x,i).(x + ((x div (2 + i)) + i)),x,1) div 3))
A102424: 1 1 2 3 5 7 9 12 16 20 25 30 36 43 50 58
(1 + ((x - (if (~2 + (x div 4)) <= 0 then 0 else 2)) div 3))
A026819: 1 1 1 2 2 2 3 3 3 4 4 4 4 4 5 5
(loop(\(x,i).2x,x,1) mod 19)
A222011: 1 2 4 8
A036120: 1 2 4 8 16 13 7 14 9 18 17 15 11 3 6 12
loop(\(x,i).3x,x,19)
A176413: 19 57 171 513 1539 4617 13851 41553 124659 373977 1121931 3365793 10097379 30292137 90876411 272629233
loop(\(x,i).x2,1,(12x + 7))
A017606: 49 361 961 1849 3025 4489 6241 8281 10609 13225 16129 19321 22801 26569 30625 34969
loop(\(x,i).x2,2,(12x + 7))
A017608: 2401 130321 923521 3418801 9150625 20151121 38950081 68574961 112550881 174900625 260144641 373301041 519885601 705911761 937890625 1222830961
loop(\(x,i).x2,1,(12x + 5))
A017582: 25 289 841 1681 2809 4225 5929 7921 10201 12769 15625 18769 22201 25921 29929 34225
loop(\(x,i).x2,2,(12x + 5))
A017584: 625 83521 707281 2825761 7890481 17850625 35153041 62742241 104060401 163047361 244140625 352275361 492884401 671898241 895745041 1171350625
loop(\(x,i).2x,(((x2 + 3x + 2) div 2) div 3),1)
A222011: 1 2 4 8
A307611: 1 2 4 8 32
A186340: 1 2 4 8 32 128 512 4096 32768 262144 4194304 67108864 1073741824 34359738368 1099511627776 35184372088832
(~1 + loop(\(x,i).2x2,1,(6x + 6)))
A158738: 71 287 647 1151 1799 2591 3527 4607 5831 7199 8711 10367 12167 14111 16199 18431
loop(\(x,i).x2,3,(6x + 5))
A016976: 390625 214358881 6975757441 78310985281 500246412961 2251875390625 7984925229121 23811286661761 62259690411361 146830437604321 318644812890625 645753531245761 1235736291547681 2252292232139041
loop(\(x,i).x3,1,(6x + 5))
A016971: 125 1331 4913 12167 24389 42875 68921 103823 148877 205379 274625 357911 456533 571787 704969 857375
loop(\(x,i).x3,2,(6x + 5))
A016977: 1953125 2357947691 118587876497 1801152661463 14507145975869 78815638671875 327381934393961 1119130473102767 3299763591802133 8662995818654939 20711912837890625 45848500718449031 95151694449171437
(loop(\(x,i).2x,x,1) mod 25)
A222011: 1 2 4 8
A070336: 1 2 4 8 16 7 14 3 6 12 24 23 21 17 9 18
(loop(\(x,i).2x,x,1) mod 23)
A222011: 1 2 4 8
A070335: 1 2 4 8 16 9 18 13 3 6 12 1 2 4 8 16
(~1 + (6 * loop(\(x,i).(2x + 4),x,4)))
A248877: 23 71 167 359 743 1511 3047 6119 12263 24551 49127 98279 196583 393191 786407 1572839
(if x <= 0 then 1 else (1 + ((~x + 3) mod 12)))
A280512: 1 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1
(loop(\(x,i).4x,x,1) mod 13)
A168430: 1 4 3 12 9 10 1 4 3 12 9 10 1 4 3 12
(loop(\(x,i).4x,x,1) mod 11)
A168429: 1 4 5 9 3 1 4 5 9 3 1 4 5 9 3 1
(loop(\(x,i).~2x,x,1) mod 11)
A187466: 1 9 4 3 5 1 9 4 3 5 1 9 4 3 5 1
(loop(\(x,i).3x,x,1) mod 11)
A070341: 1 3 9 5 4 1 3 9 5 4 1 3 9 5 4 1
loop(\(x,i).(4x + 1),x,11)
A072262: 11 45 181 725 2901 11605 46421 185685 742741 2970965 11883861 47535445 190141781 760567125 3042268501 12169074005
(if x <= 0 then 1 else (~1 + (3 * (x - ((~x + 2) div 4)))))
A251536: 1 2 5 11 14 17 20 26 29 32 35 41 44 47 50 56
(~1 + (if (x mod 2) <= 0 then 2 else (3 * (2 - (x mod 4)))))
A133186: 1 2 1 ~4 1 2 1 ~4 1 2 1 ~4 1 2 1 ~4
loop(\(x,i).x2,3,(12x + 1))
A017540: 1 815730721 152587890625 3512479453921 33232930569601 191707312997281 806460091894081 2724905250390625 7837433594376961 19925626416901921 45949729863572161 97906861202319841
loop(\(x,i).x3,1,(12x + 1))
A017535: 1 2197 15625 50653 117649 226981 389017 614125 912673 1295029 1771561 2352637 3048625 3869893 4826809 5929741
loop(\(x,i).x3,2,(12x + 1))
A017541: 1 10604499373 3814697265625 129961739795077 1628413597910449 11694146092834141 58871586708267913 231616946283203125 760231058654565217 2171893279442309389 4611686018427387903
loop(\(x,i).x2,1,(~11x + ~1))
A017402: 1 144 529 1156 2025 3136 4489 6084 7921 10000 12321 14884 17689 20736 24025 27556
loop(\(x,i).x2,2,(~11x + ~1))
A017404: 1 20736 279841 1336336 4100625 9834496 20151121 37015056 62742241 100000000 151807041 221533456 312900721 429981696 577200625 759333136
((x - (if x <= 0 then 0 else 1)) div (1 + ((2 + (x div 2)) div 3)))
A140361: 0 0 0 1 1 2 2 3 2 2 3 3 3 4 3 3
loop(\(x,i).2x,(x div 2),(~1 + (3 * (2 + (x mod 2)))))
A164682: 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024
(~1 + (3 * (2 + loop(\(x,i).x3,x2,2))))
A057739: 11 29 4611686018427387903
loop(\(x,i).x2,1,(9x + 7))
A017246: 49 256 625 1156 1849 2704 3721 4900 6241 7744 9409 11236 13225 15376 17689 20164
loop(\(x,i).x2,2,(9x + 7))
A017248: 2401 65536 390625 1336336 3418801 7311616 13845841 24010000 38950081 59969536 88529281 126247696 174900625 236421376 312900721 406586896
loop(\(x,i).x2,1,(9x + 5))
A017222: 25 196 529 1024 1681 2500 3481 4624 5929 7396 9025 10816 12769 14884 17161 19600
loop(\(x,i).x2,2,(9x + 5))
A017224: 625 38416 279841 1048576 2825761 6250000 12117361 21381376 35153041 54700816 81450625 116985856 163047361 221533456 294499921 384160000
(~1 + ((2 * loop(\(x,i).(1 + (x * (x + i))),2,x)) div 3))
A001846: 1 9 41 129 321 681 1289 2241 3649 5641 8361 11969 16641 22569 29961 39041
(1 + (3 * loop(\(x,i).10x,x,2)))
A199686: 7 61 601 6001 60001 600001 6000001 60000001 600000001 6000000001 60000000001 600000000001 6000000000001 60000000000001 600000000000001 6000000000000001
(~1 + (3 * loop(\(x,i).10x,x,2)))
A099151: 5 59 599 5999 59999 599999 5999999 59999999 599999999 5999999999 59999999999 599999999999 5999999999999 59999999999999 599999999999999 5999999999999999
(1 + (loop(\(x,i).((x2 + ~x) div 2),2,(x + 2)) div 3))
A145126: 1 2 6 16 36 71 127 211 331 496 716 1002 1366 1821 2381 3061
(1 + (loop(\(x,i).(2 * (x + (i mod 2))),x,(x + 2)) div 3))
A127984: 1 3 7 17 39 89 199 441 967 2105 4551 9785 20935 44601 94663 200249
(2 - loop(\(x,i).(2 * (x - (i mod 2))),((x + ~2) div 3),1))
A307616: 1 1 1 1 1 2 2 2 2 2 2 4 4 4 6 6
((if (x mod 3) <= 0 then 1 else x) mod (1 + ((x div 2) div 3)))
A220136: 0 0 0 0 0 0 1 1 0 1 0 1 1 1 2 1
((x + 1) + ((if (x + ~1) <= 0 then x else 2) + ((x div 2) div 3)))
A163162: 1 3 5 6 7 8 10 11 12 13 14 15 17 18 19 20
(if x <= 0 then 1 else (2x - (x mod (1 + ((x div 2) mod 3)))))
A072920: 1 2 4 5 7 8 12 14 16 17 19 20 24 26 28 29
((x + 1) - (((if (x mod 2) <= 0 then 1 else x) - (x div 2)) div 3))
A260307: 1 2 3 4 6 5 8 7 10 9 13 10 15 12 17 14
(1 + (loop(\(x,i).(2x + 2),(x div 2),(x mod 2)) div 3))
A135318: 1 1 1 2 3 4 5 8 11 16 21 32 43 64 85 128
(1 + (3 * loop(\(x,i).7x,x,2)))
A199483: 7 43 295 2059 14407 100843 705895 4941259 34588807 242121643 1694851495 11863960459 83047723207 581334062443 4069338437095 28485369059659
(~1 + (3 * loop(\(x,i).7x,x,2)))
A198688: 5 41 293 2057 14405 100841 705893 4941257 34588805 242121641 1694851493 11863960457 83047723205 581334062441 4069338437093 28485369059657
(1 + ((2 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 3))
A318509: 1 1 2 1 3 2 3 1 4 3 5 2 5 3 6 1
(if (x mod 5) <= 0 then ((x2 div 2) mod 3) else 1)
A086251: 0 1 1 1 1 0 1 1 1 1 2 1 1 1 1 1
((x + 1) - ((~x + (if (x mod 4) <= 0 then 1 else 0)) div 3))
A304800: 1 3 4 5 6 8 9 11 12 13 15 16 17 19 20 21
(1 + (if x <= 0 then 1 else (3 * (x + ((x div 2) div 3)))))
A137281: 2 4 7 10 13 16 22 25 28 31 34 37 43 46 49 52
loop(\(x,i).x2,3,(9x + 1))
A017180: 1 100000000 16983563041 377801998336 3512479453921 20047612231936 83733937890625 281474976710656 806460091894081 2044140858654976 4702525276151521 10000000000000000 19925626416901921 37588592026706176
loop(\(x,i).x3,1,(9x + 1))
A017175: 1 1000 6859 21952 50653 97336 166375 262144 389017 551368 753571 1000000 1295029 1643032 2048383 2515456
loop(\(x,i).x3,2,(9x + 1))
A017181: 1 1000000000 322687697779 10578455953408 129961739795077 922190162669056 4605366583984375 18014398509481984 58871586708267913 167619550409708032 427929800129788411 1000000000000000000
(1 + (if (x + ~4) <= 0 then x else (2 - ((~x + 1) div 3))))
A180600: 1 2 3 4 5 5 5 5 6 6 6 7 7 7 8 8
(1 + (if (x mod 3) <= 0 then 2 else (x - ((~x + 1) mod 3))))
A244477: 3 2 1 3 5 4 3 8 7 3 11 10 3 14 13 3
(1 + (loop(\(x,i).(4x + 2),(x + 1),x) div 3))
A014916: 1 9 57 313 1593 7737 36409 167481 757305 3378745 14913081 65244729 283348537 1222872633 5249404473 22429273657
loop(\(x,i).(x * (x div 2)),1,(3x2 + 3x + 1))
A241219: 0 21 171 666 1830 4095 8001 14196 23436 36585 54615 78606 109746 149331 198765 259560
loop(\(x,i).x3,1,(3x2 + 3x + 1))
A277636: 1 343 6859 50653 226981 753571 2048383 4826809 10218313 19902511 36264691 62570773 103161709 163667323 251239591 374805361
(1 + ((1 - (6 mod (if x <= 0 then 1 else x))) mod 3))
A194330: 2 2 2 2 3 1 2 2 2 2 2 2 2 2 2 2
(1 + (loop(\(x,i).(x + 2),(x + ~8),x) div 3))
A029060: 1 1 1 2 2 2 3 3 3 4 5 6 7 8 9 10
(if (~x + 2) <= 0 then ((x + ((x div 4) mod 2)) div 3) else 1)
A283422: 1 1 0 1 1 2 2 2 2 3 3 3 4 4 5 5
(~1 + (if ((x div 2) mod 3) <= 0 then 2 else 0) - (x div 3))
A101677: 1 1 ~1 ~2 ~2 ~2 ~1 ~1 ~3 ~4 ~4 ~4 ~3 ~3 ~5 ~6
(if ((1 + (x div 2)) mod 5) <= 0 then (x div 3) else 1)
A337201-A337200: 1 1 1 1 1 1 1 1 2 3 1 1 1 1 1 1
loop(\(x,i).2x,(((x2 + ~x) div 2) + (x div 3)),1)
A171451: 1 1 2 16 128 2048 131072 8388608 1073741824 549755813888 281474976710656 288230376151711744 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 3) + ((if (x + ~1) <= 0 then x else 2) + (x div 3)))
A281005: 3 5 7 9 10 11 13 14 15 17 18 19 21 22 23 25
((if (~2 + (x div 3)) <= 0 then 1 else 2) * (1 + (x div 3)))
A132328: 1 1 1 2 2 2 3 3 3 8 8 8 10 10 10 12
loop(\(x,i).(x + (((2 + i) * (1 + i)) div 2)),(x div 3),1)
A190717: 1 1 1 4 4 4 10 10 10 20 20 20 35 35 35 56
(if ((x + 1) mod 8) <= 0 then (0 - (x mod 3)) else 1)
A189022-A053865: 1 1 1 1 1 1 1 ~1 1 1 1 1 1 1 1 0
(1 + loop(\(x,i).(2x + 4),(x div 3),(x mod 3)))
A200672: 1 2 3 5 7 9 13 17 21 29 37 45 61 77 93 125
(~1 + ((if (x + ~1) <= 0 then 2 else 4x) + (x mod 3)))
A098934: 1 2 9 11 16
loop(\(x,i).4x,(x div 3),(1 + (x mod 3)))
A133464: 1 2 3 4 8 12 16 32 48 64 128 192 256 512 768 1024
((if (~4 + (x div 2)) <= 0 then 1 else 2) div (1 + (x mod 3)))
A025857: 1 0 0 1 0 0 1 0 0 1 1 0 2 1 0 2
(1 + loop(\(x,i).11x,x,3))
A199752: 4 34 364 3994 43924 483154 5314684 58461514 643076644 7073843074 77812273804 855935011834 9415285130164 103568136431794 1139249500749724 12531744508246954
(if x <= 0 then 0 else (1 + ((x * (x + (x mod 3))) div 3)))
A305185: 0 1 3 4 7 12 13 19 27 28 37 48 49 61 75 76
(1 + (loop(\(x,i).(1 + (2 * (x + (i mod 2)))),x,x) div 3))
A059570: 1 2 6 14 34 78 178 398 882 1934 4210 9102 19570 41870 89202 189326
(~1 + ((x + (if ((x div ~2) mod 2) <= 0 then 2 else x)) mod 3))
A117441: 1 1 0 1 ~1 0 ~1 ~1 0 ~1 1 0 1 1 0 1
((x + 3) - ((~x + 2) div (1 + ((if x <= 0 then 2 else x) div 2))))
A180221: 2 3 5 7 8 9 10 12 13 14 15 16 17 18 19 20
(1 + (x div (1 + (loop(\(x,i).(~2x + 1),x,1) mod (x + 2)))))
A255198: 1 1 1 4 1 6 2 2 5
loop(\(x,i).(x2 + x),(4x div (x + 3)),1)
A196872: 1 2 2 6 6 6 6 6 6 42 42 42 42 42 42 42
((x + 1) - loop(\(x,i).((x + ~1) + (x div (1 + i))),(x + ~2),1))
A296349: 0 1 2 4 6 9 12 15 18 22 26 30 34 38 42 46
loop(\(x,i).20x,(2x + 1),1)
A013725: 20 8000 3200000 1280000000 512000000000 204800000000000 81920000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).15x,(2x + 1),1)
A013720: 15 3375 759375 170859375 38443359375 8649755859375 1946195068359375 437893890380859375 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).18x,(2x + 1),1)
A013723: 18 5832 1889568 612220032 198359290368 64268410079232 20822964865671168 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).24x,(2x + 1),1)
A013729: 24 13824 7962624 4586471424 2641807540224 1521681143169024 876488338465357824 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).32x,(2x + 1),1)
A320859: 32 32768 33554432 34359738368 35184372088832 36028797018963968 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).14x,(2x + 1),1)
A013719: 14 2744 537824 105413504 20661046784 4049565169664 793714773254144 155568095557812224 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (x div (1 + ((~x + 4) mod (2x + 1)))))
A089418: 1 1 0 1 4 0 0 0 0 0 0 0 0 0 0 0
loop(\(x,i).((x div (2 - (x mod 2))) * (2 + i)),(2x + 1),1)
A160473: 3 30 315 11340 311850 12162150 638512875 86837751000 7424627710500 779585909602500 98617617564716250 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).13x,(2x + 1),1)
A013718: 13 2197 371293 62748517 10604499373 1792160394037 302875106592253 51185893014090757 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).11x,(2x + 1),1)
A013716: 11 1331 161051 19487171 2357947691 285311670611 34522712143931 4177248169415651 505447028499293771 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).17x,(2x + 1),1)
A013722: 17 4913 1419857 410338673 118587876497 34271896307633 9904578032905937 2862423051509815793 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (2 * ((3 + i) * i))),(2x + 1),1)
A212668: 9 65 201 449 841 1409 2185 3201 4489 6081 8009 10305 13001 16129 19721 23809
loop(\(x,i).(2x * (1 + (2 * (i div 2)))),(2x + ~1),1)
A123072: 1 2 72 7200 1411200 457228800 221298739200 149597947699200 134638152929280000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x4 + 2x3 + x),2x,1))
A176937: 2 389 4611686018427387903
(if x <= 0 then 1 else ((x div 2) mod (1 + (x mod (3 - (x mod 2))))))
A265246: 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1
(1 + (if x <= 0 then 1 else (2x3 * (1 + (x mod 2)))))
A161609: 2 5 17 109
(~1 + loop(\(x,i).(x - (x div ~9)),x,1))
A103303: 0 1 2 3 4 5 6 7 8 9
A279080: 0 1 2 3 4 5 6 7 8 9 11 13 15 17 19 22
(1 + (if ((x + ~1) mod (1 + (4 * (x mod 2)))) <= 0 then x else 1))
A057815: 1 2 3 2 5 2 7 2 9 2 11 12 13 2 15 2
(1 + (if ((~x + 2) mod (1 + ((x + 1) mod 4))) <= 0 then x else 1))
A284255-A284253: 1 2 3 4 5 6 7 8 9 2 11 12 13 2 15 16
loop(\(x,i).6x,(5x + 1),1)
A013838: 6 46656 362797056 2821109907456 21936950640377856 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).8x,(5x + 1),1)
A013846: 8 262144 8589934592 281474976710656 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).5x,(5x + 1),1)
A013834: 5 15625 48828125 152587890625 476837158203125 1490116119384765625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).10x,3x,1))
A271527: 2 1001 1000001 1000000001 1000000000001 1000000000000001 1000000000000000001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).12x,(3x + 1),1)
A013750: 12 20736 35831808 61917364224 106993205379072 184884258895036416 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).10x,(3x + 1),1)
A013746: 10 10000 10000000 10000000000 10000000000000 10000000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).7x,(3x + 1),1)
A013740: 7 2401 823543 282475249 96889010407 33232930569601 11398895185373143 3909821048582988049 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(2x2 + 2x),(x + (x div 3)),1))
A093625: 2 5 41 21523361 926510094425921 4611686018427387903
(1 + loop(\(x,i).(2x2 + 4x),(x + (x div 3)),1))
A277434: 2 7 97 708158977
(~1 + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1))
A010763: 0 2 9 34 125 461 1715 6434 24309 92377 352715 1352077 5200299 20058299 77558759 300540194
(1 + loop(\(x,i).(x - (((2 + i) * i) div (~x + ~1))),x,1))
A003066: 2 4 6 9 12 15 19 23 27 31 35 40 45 50 55 60
(1 + loop(\(x,i).(x3 div 2),1,(x2 + x + ~1)))
A152725: 0 1 63 666 3430 12195 34461 83188 178956 352485 647515 1124046 1861938 2964871 4564665 6825960
(1 + loop(\(x,i).4x2,(x * ((x + 1) div 2)),1))
A268211: 2 5 65 4611686018427387903
(1 + loop(\(x,i).(x - (x div (~2 + ((x div 2) div ~2)))),x,1))
A158923: 2 3 4 5 7 9 11 13 16 19 22 25 28 31 34 38
(1 + loop(\(x,i).(x - (x div (~4 + (x div 4)))),x,1))
A239048: 2 3 4 5 7 9 13 25
(1 + (if (x mod 2) <= 0 then (x div 2) else (x + 9)))
A303785: 1 11 2 13 3 15 4 17 5 19 6 21 7 23 8 25
(1 + (2 mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1)))
A325446: 1 1 1 1 1 3 1 1 1 3 1 3 1 3 3 1
(1 + loop(\(x,i).(x * (1 + i)),(x + ((x * (x div 2)) mod 2)),1))
A201363: 2 3 7
A062935: 2 3 7 121
A083436: 2 3 7 121 121
(1 + loop(\(x,i).((x + 2) * ((x + ~1) + (2 * (i mod 2)))),x,1))
A109172: 2 7 41 1723 2967005 8803121637031 4611686018427387903
(1 + loop(\(x,i).(x3 + x2),1,(x2 + 2x + 1)))
A123656: 3 81 811 4353 16251 47953 120051 266241 538003 1010001 1786203 3006721 4855371 7567953 11441251 16842753
(~1 + ((x2 + 2x + 1) * loop(\(x,i).(x2 + 2),2,2)))
A158596: 37 151 341 607 949 1367 1861 2431 3077 3799 4597 5471 6421 7447 8549 9727
(~1 + ((x2 + 2x + 1) * loop(\(x,i).(x2 + x),2,2)))
A158626: 41 167 377 671 1049 1511 2057 2687 3401 4199 5081 6047 7097 8231 9449 10751
(~1 + ((x2 + 2x + 1) * loop(\(x,i).(x2 + 2x),2,2)))
A158774: 79 319 719 1279 1999 2879 3919 5119 6479 7999 9679 11519 13519 15679 17999 20479
(((x2 + 3x + 2) div 2) * (1 + loop(\(x,i).2x,x,1)))
A273652: 2 9 30 90 255 693 1820 4644 11565 28215 67650 159822 372827 860265 1966200 4456584
(1 + ((x + 1) * loop(\(x,i).(2x2 + 8x + 8),2,0)))
A157956: 201 401 601 801 1001 1201 1401 1601 1801 2001 2201 2401 2601 2801 3001 3201
(~1 + ((x + 1) * loop(\(x,i).(2x2 + 8x + 8),2,0)))
A157955: 199 399 599 799 999 1199 1399 1599 1799 1999 2199 2399 2599 2799 2999 3199
(1 + ((x + 1) * (1 + loop(\(x,i).(x * (x + i)),2,3))))
A158221: 170 339 508 677 846 1015 1184 1353 1522 1691 1860 2029 2198 2367 2536 2705
(if (x mod 2) <= 0 then ((1 + (x mod 8)) mod (x + 1)) else 1)
A339421: 0 1 0 1 0 1 0 1 1 1 3 1 5 1 7 1
(1 + ((x + 1) * (1 + loop(\(x,i).(x2 + ~1),2,4))))
A158229: 226 451 676 901 1126 1351 1576 1801 2026 2251 2476 2701 2926 3151 3376 3601
(1 + ((x + 1) * (1 + loop(\(x,i).(x * (x + i)),2,4))))
A158322: 442 883 1324 1765 2206 2647 3088 3529 3970 4411 4852 5293 5734 6175 6616 7057
(1 + loop(\(x,i).2x2,1,(5x + 5)))
A157916: 51 201 451 801 1251 1801 2451 3201 4051 5001 6051 7201 8451 9801 11251 12801
(~1 + loop(\(x,i).2x2,1,(5x + 5)))
A157919: 49 199 449 799 1249 1799 2449 3199 4049 4999 6049 7199 8449 9799 11249 12799
(1 + ((x + 1) * loop(\(x,i).((x + 2) * (x + i)),2,3)))
A158326: 485 969 1453 1937 2421 2905 3389 3873 4357 4841 5325 5809 6293 6777 7261 7745
(~1 + ((x + 1) * loop(\(x,i).((x + 2) * (x + i)),2,3)))
A158330: 483 967 1451 1935 2419 2903 3387 3871 4355 4839 5323 5807 6291 6775 7259 7743
(1 + ((1 + loop(\(x,i).((x + 1) * (x + i)),2,x)) div (x + 1)))
A197773: 8 16 38 77 141 235 365 537 757 1031 1365 1765 2237 2787 3421 4145
(~1 + loop(\(x,i).x2,2,(x3 + 3x2 + 3x + 1)))
A123868: 0 4095 531440 16777215 244140624 2176782335 13841287200 68719476735 282429536480 999999999999 3138428376720 8916100448255 23298085122480 56693912375295 129746337890624 281474976710655
(~1 + loop(\(x,i).12x,(x + 1),(x + 1)))
A064758: 11 287 5183 82943 1244159 17915903 250822655 3439853567 46438023167 619173642239 8173092077567 106993205379071 1390911669927935 17974858503684095 231105323618795519 2958148142320582655
(~1 + loop(\(x,i).10x,(x + 1),(x + 1)))
A064756: 9 199 2999 39999 499999 5999999 69999999 799999999 8999999999 99999999999 1099999999999 11999999999999 129999999999999 1399999999999999 14999999999999999 159999999999999999
loop(\(x,i).(x - (4x div (~1 - i))),(x + 1),1)
A036830: 3 7 14 26 44 70 105 152 213 291 388 508 654 829 1037 1281
(1 + ((2x + 2) * (6 + (if x <= 0 then 0 else 1))))
A120827: 13 29 43
(1 + loop(\(x,i).20x,2,(x + 1)))
A158313: 401 801 1201 1601 2001 2401 2801 3201 3601 4001 4401 4801 5201 5601 6001 6401
(~1 + loop(\(x,i).20x,2,(x + 1)))
A158317: 399 799 1199 1599 1999 2399 2799 3199 3599 3999 4399 4799 5199 5599 5999 6399
(~1 + loop(\(x,i).(10 div (x + 1)),2,(x + 1)))
A082852: 0 1 2 2 4 4 4 4 4 9 9 9 9 9 9 9
(~1 + ((x + 1) * loop(\(x,i).(x2 + 3x + 4),2,2)))
A157961: 241 483 725 967 1209 1451 1693 1935 2177 2419 2661 2903 3145 3387 3629 3871
loop(\(x,i).x2,3,(8x + 7))
A017156: 5764801 2562890625 78310985281 852891037441 5352009260481 23811286661761 83733937890625 248155780267521 645753531245761 1517108809906561 3282116715437121 6634204312890625 12667700813876161
loop(\(x,i).x3,1,(8x + 7))
A017151: 343 3375 12167 29791 59319 103823 166375 250047 357911 493039 658503 857375 1092727 1367631 1685159 2048383
loop(\(x,i).x3,2,(8x + 7))
A017157: 40353607 38443359375 1801152661463 26439622160671 208728361158759 1119130473102767 4605366583984375 15633814156853823 45848500718449031 119851595982618319 285544154243029527 630249409724609375
(~1 + ((x + 1) * loop(\(x,i).((x + 2) * ((x + i) * i)),2,2)))
A158004: 391 783 1175 1567 1959 2351 2743 3135 3527 3919 4311 4703 5095 5487 5879 6271
(~1 + ((x + 1) * loop(\(x,i).(x2 + 2x + 1),2,4)))
A158393: 675 1351 2027 2703 3379 4055 4731 5407 6083 6759 7435 8111 8787 9463 10139 10815
(~1 + ((4x + 4) * (x + (if (x mod 2) <= 0 then 2 else 0))))
A173294: 7 7 47 47 119 119 223 223 359 359 527 527 727 727 959 959
(~1 + loop(\(x,i).(~x3 + ~x + 2),4,(x + 1)))
A138647: 521 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x3,1,(4x2 + 4x + 1))
A016758: 1 729 15625 117649 531441 1771561 4826809 11390625 24137569 47045881 85766121 148035889 244140625 387420489 594823321 887503681
(~1 + (loop(\(x,i).((x + 2) + (x div 4)),x,2) div (x + 1)))
A210024: 1 1 1 1 1 2 2 3 3 4 5 6 7 9 11 13
loop(\(x,i).2x3,1,(x2 + 3x + 1))
A109118: 2 250 2662 13718 48778 137842 332750 715822 1409938 2590058 4496182 7447750 11859482 18258658 27303838 39805022
(1 + (loop(\(x,i).(x * i),(x + ~2),(2 - (x mod 2))) mod (x + 1)))
A014973: 1 2 3 2 5 1 7 1 1 1 11 1 13 1 1 1
loop(\(x,i).(x + ((~1 + i) mod 10)),(x + 1),1)
A070280: 1 2 4 7 11 16 22 29 37 46 46 47 49 52 56 61
(loop(\(x,i).2x,x,2) div (x3 + 3x2 + 2x + 1))
A233441: 2 0 0 0 0 0 0 0 0 1 1 2 3 5 9 16
(1 + ((x2 * loop(\(x,i).x3,2,x)) div (x + 1)))
A269486: 1 1 683 44287 838861 8138021 51828151 247165843 954437177 3138105961 9090909091 23775972551 57154490053 128011456717 269971011311 540609741211
(1 + ((x * loop(\(x,i).x2,2,x3)) div (x + 1)))
A266229: 1 1 2731 398581 13421773 203450521 1865813431 12111126301 61083979321 254186582833 909090909091 2876892678661 8230246567621 21633936185161 52914318216943 121637191772461
loop(\(x,i).(x * (((2 + i) * i * (1 + i)) + i)),(x + 1),1)
A158620: 7 182 11466 1421784 305683560 104543777520 53421870312720 38891121587660160 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((10x + 1) - i),(x + 1),1)
A179477: 10 99 988 9877 98766 987655 9876544 98765433 987654322 9876543211 98765432100 987654320989 9876543209878 98765432098767 987654320987656 9876543209876545
loop(\(x,i).((x + 1) - ((1 - (x div 2)) div 3)),(x + ~1),1)
A171997: 1 1 2 3 4 6 8 10 13 16 20 24 29 35 42 50
loop(\(x,i).((2x2 + 8x) div 3),(x + ~1),1)
A260995: 1 1 3 14 168
loop(\(x,i).(x + ((i div 3) + (x div 3))),(x + ~1),1)
A007478: 1 1 1 1 2 3 5 8 12 18 27 39 55
loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x + ~1),1)
A088218: 1 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760
(1 + loop(\(x,i).(2x2 + 2x),1,(4x + ~4)))
A272129: 25 1 41 145 313 545 841 1201 1625 2113 2665 3281 3961 4705 5513 6385
loop(\(x,i).(~1 + ((x * (1 + i)) + (2 * (i mod 2)))),(x + ~1),1)
A001120: 1 1 3 8 33 164 985 6894 55153 496376 4963761 54601370 655216441 8517813732 119249392249 1788740883734
loop(\(x,i).(2 * (x + (2 * (x + (2 mod (x + 1)))))),(x + ~1),1)
A309418: 1 1 6 44 272
loop(\(x,i).(x + (10x * i)),(x + ~1),1)
A144773: 1 1 11 231 7161 293601 14973651 913392711 64850882481 5252921480961 478015854767451 48279601331512551 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (((x + 1) - (2 * (i mod 2))) * i)),(x + ~1),1)
A212291: 1 1 1 5 17 89 529 3709 29665 266993 2669921 29369141 352429681 4581585865 64142202097 962133031469
(~1 + loop(\(x,i).(x + ((x2 + 2) div (1 + (x div 2)))),x,1))
A114982: 0 3 9 26 78 234 702 2106 6318 18954 56862 170586 511758 1535274 4605822 13817466
(~1 + (if ((x + ~1) mod 9) <= 0 then x2 else 1))
A097601: 0 0 0 0 0 0 0 0 0 0 99 0 0 0 0 0
loop(\(x,i).2x,(x3 + 8x2 + x + 8),1)
A100636: 256 262144 1125899906842624 4611686018427387903 4611686018427387903
(1 + (if (x mod (3 + ((x div 2) div 3))) <= 0 then 0 else 2))
A171369: 1 3 3 1 3 3 3 3 1 3 3 3 3 3 3 1
(1 + (if (2x mod (x + 7)) <= 0 then 0 else 2))
A122916: 1 3 3 3 3
A135203: 1 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3
(1 + (if ((x * (x mod 3)) mod 5) <= 0 then 0 else 2))
A268676: 1 3 3 1 3 1 1 3 3 1 1 3 1 3 3 1
(1 + (if (((x + 2) mod 8) mod 3) <= 0 then 0 else 2))
A050141: 3 1 3 3 1 3 1 3 3 1 3 3 1 3 1 3
(1 + (2 * (2x + ((x mod 2) + (if (x + ~2) <= 0 then 1 else 0)))))
A106373: 3 9 11 15 17 23
(1 + (loop(\(x,i).(1 + ((x * i) + (i div 2))),(x + ~1),0) div 2))
A066304: 1 1 1 3 8 30 150
(x div (3 + (if (x + ~12) <= 0 then 2 else 0)))
A035682: 0 0 0 0 0 1 1 1 1 1 2 2 2 4 4 5
(1 + ((x div 2) div (2 + (if (~2 + (x div 3)) <= 0 then 2 else 0))))
A029129: 1 1 1 1 1 1 1 1 2 3 3 3 4 4 4 4
(1 + (2 * (x + (x div 2))) - (if (~2 + (x div 2)) <= 0 then 0 else 2))
A285144: 1 3 7 9 13 15 17 19 23 25 29 31 35 37 41 43
((x2 + 1) div (x - ((if x <= 0 then 1 else x) div ~3)))
A064317: 1 1 1 2 2 3 4 5 5 6 7 8 9 9 10 11
((x + 1) - (2 * loop(\(x,i).(3 * (x - (2 * i))),x,0)))
A339136: 1 14 63 220 701 2154 6523 19640 59001 177094 531383 1594260 4782901 14348834 43046643 129140080
(3 + loop(\(x,i).(x4 + x2 + 1),x,0))
A267943: 3 4 6 94
(1 + (if (x - (x2 mod (x + 8))) <= 0 then 0 else 2))
A285116: 1 1 1 1 1 1 1 3 3 1 1 3 3 3 1 1
(1 + (2 * ((x mod 2) - loop(\(x,i).(2 * (x - (i mod 2))),x,0))))
A083582: 1 7 9 23 41 87 169 343 681 1367 2729 5463 10921 21847 43689 87383
((16x + 1) div (1 + (if x <= 0 then 0 else 2)))
A219529: 1 5 11 16 21 27 32 37 43 48 53 59 64 69 75 80
((x + 1) - ((((x div 2) mod 2) - (if (~x + 2) <= 0 then x else 0)) div 2))
A122825: 1 2 4 5 7 9 10 11 13 15 16 17 19 21 22 23
(1 + (2 * loop(\(x,i).(x + (2 * ((x + 4) + i))),x,0)))
A116972: 1 21 85 281 873 2653 7997 24033 72145 216485 649509 1948585 5845817 17537517 52612621 157837937
(~1 + (loop(\(x,i).(x + ((~1 + (i * i)) * (2 + i))),x,0) div 2))
A059302: ~1 ~1 5 25 70 154 294 510 825 1265 1859 2639 3640 4900 6460 8364
(1 + (loop(\(x,i).(x + ((~1 + (i * i)) * (~2 + i))),x,0) div 2))
A226639: 1 1 1 5 20 56 126 246 435 715 1111 1651 2366 3290 4460 5916
(1 + (if ((x + ~1) mod 13) <= 0 then 1 else 2))
A098726: 3 2 3 3 3 3 3 3 3 3 3 3 3 3 2 3
(1 + (((x + ~1) div (1 + (if (x mod 4) <= 0 then 2 else 1))) mod 2))
A264840: 2 1 1 2 2 1 1 2 1 1 1 2 2 1 1 2
(if ((x + ~2) mod (1 + ((x + 2) div 5))) <= 0 then 2 else 1)
A080354: 2 2 2 1 2 1 2 1 2 1 1 2 1 1 2 1
(if (2 - ((x div 2) mod (1 + (x mod 5)))) <= 0 then 2 else 1)
A279496: 1 1 1 1 2 1 1 1 1 2 1 1 1 2 2 1
(1 + (if ((x - ((x div 2) div 3)) mod 3) <= 0 then 1 else 2))
A276859: 2 3 3 2 3 3 3 2 3 3 2 3 3 3 2 3
(1 + (if (((x + 1) mod 8) mod 3) <= 0 then 1 else 2))
A076662: 3 3 2 3 3 2 3 2 3 3 2 3 3 2 3 2
(1 + (if ((x - (x div 8)) mod 3) <= 0 then 1 else 2))
A276869: 2 3 3 2 3 3 2 3 3 3 2 3 3 2 3 3
loop(\(x,i).i,(x div (2 + (x mod 11))),1)
A223475: 1 1 1 1 1 1 1 1 1 1 1 5 4 3 2 2
(if (x mod (2 - (x mod (~1 + ((~x + 2) div 3))))) <= 0 then 2 else 1)
A084989: 2 1 2 2 2 1 2 1 1 1 1 1 1 1 1 2
(~1 + (2 * loop(\(x,i).(3 * (x + (i mod 2))),(x + 1),1)))
A199817: 11 35 113 341
loop(\(x,i).3x,(8x + 6),1)
A013791: 729 4782969 31381059609 205891132094649 1350851717672992089 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(3 + loop(\(x,i).10x,(x + 1),1))
A216179: 13 103 1003 10003 100003 1000003 10000003 100000003 1000000003 10000000003 100000000003 1000000000003 10000000000003 100000000000003 1000000000000003 10000000000000003
(~3 + loop(\(x,i).10x,(x + 1),1))
A173833: 7 97 997 9997 99997 999997 9999997 99999997 999999997 9999999997 99999999997 999999999997 9999999999997 99999999999997 999999999999997 9999999999999997
(~1 + (2 * (~1 + (if (x mod 2) <= 0 then 2 else (2x2 + 2x)))))
A269910: 1 5 1 45 1 117 1 221 1 357 1 525 1 725 1 957
(1 + (2 * (if x <= 0 then 2 else (2x3 + 2x2 + ~1))))
A174267: 5 7 47
(~1 + (2 * loop(\(x,i).(2 * (2x + (x mod 2))),(x + ~1),1)))
A267614: 1 1 11 47 191 767 3071 12287 49151 196607 786431 3145727 12582911 50331647 201326591 805306367
(1 + (loop(\(x,i).(2 * (x + ((x + i) * i))),(x + ~1),1) div 2))
A317967: 1 1 4 23 186
(1 + (2 * ((x + 2) - ((~x + 1) div (1 + (if x <= 0 then 0 else 2))))))
A102213: 3 7 11 13 15 19 21 23 27 29 31 35 37 39 43 45
(if (2 - (x mod (1 + (2 * ((x + ~1) mod 3))))) <= 0 then 2 else 1)
A270642: 1 1 2 2 1 2 1 1 2 2 1 2 2 1 2 1
(if ((x2 + x + 1) mod 7) <= 0 then 2 else 1)
A092400: 1 1 2 1 2 1 1 1 1 2 1 2 1 1 1 1
(1 + loop(\(x,i).(x2 + x),x,14))
A179091: 15 211 44311 1963420411 3855019708367988511 4611686018427387903 4611686018427387903
(if ((x + 1) mod (1 + (2 * ((~x + 2) mod 3)))) <= 0 then 2 else 1)
A175128: 1 1 2 1 1 2 1 1 2 2 1 2 1 1 2 1
(if (2 - ((x + 1) mod (1 + (2 * (x mod 3))))) <= 0 then 2 else 1)
A270643: 1 2 2 1 2 1 1 2 2 1 2 2 1 2 1 1
(if ((x + 2) mod (1 + (2 * (3 - (x mod 2))))) <= 0 then 2 else 1)
A031276: 1 1 1 2 1 1 1 1 1 1 1 1 2 2 1 1
(1 + ((1 + ((loop(\(x,i).2x,x,2) mod (x + 1)) div 2)) div 2))
A327657: 1 1 2 1 2 2 2 1 3 2 2 2 2 2 3 1
(1 + ((x mod (3 + (if (x + ~4) <= 0 then 0 else 2))) mod 2))
A246140: 1 2 1 1 2 1 2 1 2 1 1 2 1 2 1 1
(1 + ((x mod (3 + (if (~2 + (x div 2)) <= 0 then 0 else 2))) div 2))
A340260: 1 1 2 1 1 2 1 2 2 3 1 1 2 2 3 1
(1 + (((x2 + ~1) mod (1 + (2 * (if x <= 0 then 0 else 2)))) div 2))
A135352: 1 1 2 2 1 3 1 2 2 1 3 1 2 2 1 3
(1 + (2 * ((2x + 2) mod (1 + (2 * (if x <= 0 then 0 else 2))))))
A127794: 1 9 3 7 1 5 9 3 7 1 5 9 3 7 1 5
(1 + (x div (2 + (if (x + ~10) <= 0 then 2 else 1))))
A025775: 1 1 1 1 2 2 2 2 3 3 3 4 5 5 5 6
(if (2 - (x mod (~1 + (2 * ((x + ~1) mod 4))))) <= 0 then 2 else 1)
A077479: 1 1 1 1 2 1 1 1 2 1 1 2 2 1 1 1
(if (x mod (3 + (((~x + 1) div 2) mod 4))) <= 0 then 2 else 1)
A205007: 2 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1
(1 + (2 * (loop(\(x,i).2x,x,1) div 9)))
A132780: 1 1 1 1 3 7 15 29 57 113 227 455 911 1821 3641 7281
(1 + ((x mod 3) div (if (x mod 8) <= 0 then 1 else 2)))
A280509-A051064: 1 1 2 1 1 2 1 1 3 1 1 2 1 1 2 1
(2 - ((~x + 2) div (1 + (if (x mod 8) <= 0 then 1 else 2))))
A077113: 1 2 2 3 3 3 4 4 5 5 5 5 6 6 6 7
(1 + ((((x + ~1) div 2) mod (1 + (if x <= 0 then 1 else 4))) mod 2))
A160245: 2 1 1 2 2 1 1 2 2 1 1 1 1 2 2 1
(1 + ((x + ~1) mod (2 * (if (x mod 4) <= 0 then 4 else 1))))
A109011: 8 1 2 1 4 1 2 1 8 1 2 1 4 1 2 1
(if ((1 + ((x + (x div 2)) div 2)) mod 5) <= 0 then 2 else 1)
A082478: 1 1 1 1 1 1 2 1 1 1 1 1 2 2 1 1
(if ((x - ((~1 + (x div 2)) div 2)) mod 5) <= 0 then 2 else 1)
A105551: 1 1 1 1 1 2 2 1 1 1 1 1 2 1 1 1
(1 + (2 * ((2 * (~1 + (if x <= 0 then 2 else x))) mod 5)))
A128359: 5 1 5 9 3 7 1 5 9 3 7 1 5 9 3 7
(if (((x + ~2) + ((x div 2) mod 2)) mod 5) <= 0 then 2 else 1)
A163100: 1 1 1 1 1 1 2 1 1 1 1 2 2 1 1 1
(1 + (((if (x + ~2) <= 0 then x else 2x) mod 5) div 2))
A136109-A080237: 1 1 2 1 2 1 2 3 1 2 1 2 3 1 2 1
(2 div (1 + ((if x <= 0 then 1 else x2) mod 10)))
A219482: 1 1 0 0 0 0 0 0 0 1 2 1 0 0 0 0
(if (~x + 2) <= 0 then (2 + ((x2 + ~x) div 5)) else 1)
A109965: 1 1 2 3 4 6 8 10 13 16 20 24 28 33 38 44
(1 + (2 * ((x + (if (x + ~1) <= 0 then x else 2)) mod 5)))
A127414: 1 5 9 1 3 5 7 9 1 3 5 7 9 1 3 5
(1 + (if x <= 0 then 0 else (2 + ((x2 + 2x) div 5))))
A225647: 1 3 4 6 7
A202169: 1 3 4 6 7 10 12 15 19 22
loop(\(x,i).i,(x mod 3),(1 + ((x div 5) mod 2)))
A025142: 1 1 2 1 1 2 2 1 2 2 1 2 1 1 2 2
(if x <= 0 then 0 else (1 + (2 * (2 div (1 + (~x mod 4))))))
A091084: 0 1 1 3 5 1 1 3 5 1 1 3 5 1 1 3
(1 + (((1 + (x div 2)) div 2) div (if (x + ~4) <= 0 then 1 else 2)))
A129139: 1 1 2 2 2 1 2 2 2 2 2 2 2 2 3 3
(1 + (loop(\(x,i).(2x + 4),x,(x + 5)) div 2))
A267226: 3 9 21 47 103 223 479 1023 2175 4607 9727 20479 43007 90111 188415 393215
loop(\(x,i).x2,3,(8x + 3))
A017108: 6561 214358881 16983563041 282429536481 2251875390625 11688200277601 45767944570401 146830437604321 406067677556641 1001129150390625 2252292232139041 4702525276151521 9227446944279201
loop(\(x,i).x3,1,(8x + 3))
A017103: 27 1331 6859 19683 42875 79507 132651 205379 300763 421875 571787 753571 970299 1225043 1520875 1860867
loop(\(x,i).x3,2,(8x + 3))
A017109: 19683 2357947691 322687697779 7625597484987 78815638671875 502592611936843 2334165173090451 8662995818654939 27206534396294947 75084686279296875 186940255267540403 427929800129788411
loop(\(x,i).5x,(8x + 2),1)
A191559: 25 9765625 3814697265625 1490116119384765625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(3 + (if (x mod 2) <= 0 then (2x - ((x div 2) mod 2)) else 1))
A139186: 3 4 6 4 11 4
(if (~x + 2) <= 0 then ((x div (1 + (x mod (2 + (x mod 2))))) mod 2) else 1)
A264739: 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1
(1 + ((x div (3 * (if (x mod 2) <= 0 then 4 else 1))) mod 2))
A003647: 1 1 1 2 1 2 1 1 1 2 1 2 2 1 2 2
(if (x mod 4) <= 0 then (2 * ((x div 3) mod 3)) else 1)
A345000: 0 1 1 1 2 1 1 1 4 1 1 1 2 1 1 1
(if x <= 0 then 1 else (x mod (~1 + (2 * ((x div 3) mod 3)))))
A281669: 1 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0
(1 + (((x - (if (x mod 4) <= 0 then x else 1)) div 3) mod 2))
A317756-A052494-A039998: 1 1 1 1 1 2 2 1 1 1 2 2 1 1 1 1
loop(\(x,i).x2,1,((x + 1) - (2 * ((x + 1) div 3))))
A007891: 1 4 1 4 9 4 9 16 9 16 25 16 25 36 25 36
(1 + ((3 * (if (x + ~4) <= 0 then x else (x + 1))) div 2))
A182337: 1 2 4 5 7 10 11 13 14 16 17 19 20 22 23 25
(if ((x - ((x div 5) mod 2)) mod 3) <= 0 then 2 else 1)
A056731: 2 1 1 2 1 1 1 2 1 1 1 1 2 1 1 1
(1 + (if (x + ~1) <= 0 then x else (2 + (((x + 1) div 2) div 3))))
A117806: 1 2 3 3 3 4 4 4 4 4 4 5 5 5 5 5
(if (((x + 1) mod 16) mod 3) <= 0 then 2 else 1)
A138742: 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 2
loop(\(x,i).i,(2 * ((x - ((x div 2) mod 4)) div 3)),1)
A248781: 1 1 1 1 1 2 2 2 4 6 6 6 6 6 6 8
(1 + (if (x + ~1) <= 0 then x else (2 + ((2 * (x div 2)) div 3))))
A192512-A185195-A038567-A036234: 1 2 3 3 4 4 5 5 5 5 6 6 7 7 7 7
(if (~x + 2) <= 0 then (2 + (((x2 + ~x) div 2) div 3)) else 1)
A076677-A008750: 1 1 2 3 4 5 7 9 11 14 17 20 24 28 32 37
(1 + (2 * (loop(\(x,i).8x,x,2) div 3)))
A082365: 1 11 85 683 5461 43691 349525 2796203 22369621 178956971 1431655765 11453246123 91625968981 733007751851 5864062014805 46912496118443
(if (((~x2 + 4x + ~4) div (x + 2)) mod 3) <= 0 then 2 else 1)
A157196: 1 1 2 1 1 1 1 2 1 1 2 1 1 2 2 1
(if (((x mod 5) + (x mod 2)) mod 3) <= 0 then 2 else 1)
A030613: 2 1 1 1 1 1 1 2 2 1 2 1 1 1 1 1
(7 + loop(\(x,i).8x,x,1))
A253211: 8 15 71 519 4103 32775 262151 2097159 16777223 134217735 1073741831 8589934599 68719476743 549755813895 4398046511111 35184372088839
(loop(\(x,i).(3x + 1),x,1) div 7)
A178703: 0 0 1 5 17 52 156 468 1405 4217 12653 37960 113880 341640 1024921 3074765
(loop(\(x,i).(x * (x - i)),2,(x + ~1)) div 7)
A011917: 0 0 0 0 3 17 51 120 240 432 720 1131 1697 2451 3432 4680
(7 * ((2 - (x mod 2)) * (if x <= 0 then 1 else 2)))
A040183: 14 14 28 14 28 14 28 14 28 14 28 14 28 14 28 14
(7 * loop(\(x,i).(2x + 2),x,4))
A182465: 28 70 154 322 658 1330 2674 5362 10738 21490 42994 86002 172018 344050 688114 1376242
loop(\(x,i).8x,(x div 2),7)
A117860: 7 7 56 56 448 448 3584 3584 28672 28672 229376 229376 1835008 1835008 14680064 14680064
((x + loop(\(x,i).3x,x,1)) mod 7)
A168455: 1 4 4 2 1 3 0 3 3 1 0 2 6 2 2 0
loop(\(x,i).(x3 + 3x),x,7)
A145181: 7 364 48229636 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + ~3x),x,7)
A002000: 7 322 33385282 4611686018427387903 4611686018427387903
(1 + ((x + 1) mod ((if (x mod 2) <= 0 then 1 else x) mod 6)))
A245548: 1 1 1 2 1 2 1 1 1 2 1 3 1 1 1 2
(1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 6))
A099547: 1 1 3 1 5 3 1 1 3 5 5 3 1 1 3 1
(1 + ((3 * (x + (if (x mod 2) <= 0 then 4 else 0))) div 2))
A147677: 7 2 10 5 13 8 16 11 19 14 22 17 25 20 28 23
(1 + (if x <= 0 then 2 else (((x * (x div 3)) mod 3) mod 2)))
A282496: 3 1 1 1 2 1 1 1 2 1 1 1 1 2 1 1
(1 + (2 * loop(\(x,i).(2x + 10),x,3)))
A275163: 7 33 85 189 397 813 1645 3309 6637 13293 26605 53229 106477 212973 425965 851949
(1 + ((3 * (x + (if (~2 + (x div 2)) <= 0 then 1 else 2))) div 2))
A189303: 2 4 5 7 8 10 13 14 16 17 19 20 22 23 25 26
(1 + (if x <= 0 then 1 else (2 * (3x - (x div 3)))))
A063099: 2 7 13 17 23 29 33 39 45 49 55 61 65 71 77 81
((if x <= 0 then 1 else (x div 3)) div (1 + (2 * (x mod 3))))
A029301: 1 0 0 1 0 0 2 0 0 3 1 0 4 1 0 5
(1 + loop(\(x,i).4x,x,2) - ((x mod 3) div 2))
A183425: 3 9 32 129 513 2048 8193 32769 131072 524289 2097153 8388608 33554433 134217729 536870912 2147483649
(2 + (x mod 2) - (if (~x + 2) <= 0 then ((x mod 3) div 2) else 1))
A033559: 1 2 1 3 2 2 2 3 1 3 2 2 2 3 1 3
(if (~x + 2) <= 0 then (2 + ((x mod 3) mod 2) - (x mod 2)) else 1)
A069929: 1 1 2 1 3 1 2 2 2 1 3 1 2 2 2 1
((2 * (x + (x div 3))) + (if (x mod 3) <= 0 then 2 else 1))
A047604: 2 3 5 10 11 13 18 19 21 26 27 29 34 35 37 42
(~1 + (2 * (~1 + loop(\(x,i).10x,x,2))))
A083818: 1 37 397 3997 39997 399997 3999997 39999997 399999997 3999999997 39999999997 399999999997 3999999999997 39999999999997 399999999999997 3999999999999997
loop(\(x,i).(x * (1 + i)),(2 * (1 + ((x2 + 2x) div 2))),1)
A126244: 6 120 39916800 355687428096000 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) + (if (x + ~2) <= 0 then 1 else 2) - (x div ~4))
A184014: 2 4 5 7 8 10 11 12 13 15 16 17 18 20 21 22
loop(\(x,i).x2,1,(1 + (2 * ((2x + 1) + (x div 2)))))
A273374: 9 49 169 289 529 729 1089 1369 1849 2209 2809 3249 3969 4489 5329 5929
(~1 + loop(\(x,i).(x4 + x3),(2x + 1),2))
A053558: 23 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (2 - ((2x + ~6) mod (1 + (x div 2)))) <= 0 then 2 else 1)
A205107: 1 1 1 1 2 1 2 1 1 2 2 2 2 2 2 1
(if ((x + 2) mod 5) <= 0 then ((1 + (x div 2)) div 2) else 1)
A306489: 1 1 1 1 1 1 1 1 2 1 1 1 1 3 1 1
(if ((x + ~2) mod 5) <= 0 then ((1 + (x div 2)) div 2) else 1)
A134505: 1 1 1 1 1 1 1 2 1 1 1 1 3 1 1 1
(if x <= 0 then 1 else (~1 + (2 * ((x + 1) div (3 - (x mod 2))))))
A344674: 1 1 1 3 1 5 3 7 5 9 5 11
(1 + (2 * (1 + loop(\(x,i).(2x + 4),(x div 2),(x mod 2)))))
A164053: 3 5 11 15 27 35 59 75 123 155 251 315 507 635 1019 1275
((if (x + ~2) <= 0 then 3 else x) div (1 + (2 * (1 + (x mod 2)))))
A025806: 1 0 1 0 1 1 2 1 2 1 3 2 4 2 4 3
loop(\(x,i).x2,1,(10x + 3))
A017306: 9 169 529 1089 1849 2809 3969 5329 6889 8649 10609 12769 15129 17689 20449 23409
loop(\(x,i).x2,2,(10x + 3))
A017308: 81 28561 279841 1185921 3418801 7890481 15752961 28398241 47458321 74805201 112550881 163047361 228886641 312900721 418161601 547981281
loop(\(x,i).3x,(10x + 2),1)
A013850: 9 531441 31381059609 1853020188851841 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).2x,(x + ~1),(3x + 1)) div 2))
A170881: 1 3 8 21 53 129 305 705 1601 3585 7937 17409 37889 81921 176129 376833
(1 + (loop(\(x,i).(2x + i - (x div 3)),x,1) div 2))
A222011: 1 2 4 8
A339656: 1 2 4 8 15 28 49 84
(1 + (if (x - (x2 mod (x + 8))) <= 0 then 1 else 2))
A109829: 2 2 2 2 2 2 2 3 3 2 2 3 3 3 2 2
(1 + (if (x - (x2 mod (3x + 4))) <= 0 then 1 else 2))
A020649: 2 2 2 2 3 2 2 2 2 2 2 3 2 2 3 2
(1 + (2 * loop(\(x,i).(10x + 16),x,1)))
A173802: 3 53 553 5553 55553 555553 5555553 55555553 555555553 5555555553 55555555553 555555555553 5555555555553 55555555555553 555555555555553 5555555555555553
(~1 + (2 * loop(\(x,i).(10x + 16),x,1)))
A173804: 1 51 551 5551 55551 555551 5555551 55555551 555555551 5555555551 55555555551 555555555551 5555555555551 55555555555551 555555555555551 5555555555555551
((x + 1) div (if (10 mod (x + 1)) <= 0 then 2 else 1))
A143052: 0 1 3 4 2 6 7 8 9 5 11 12 13 14 15 16
loop(\(x,i).(x * i),x,(1 + ((6 mod (x + 1)) mod 2)))
A052596: 1 1 2 6 48 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000
(1 + loop(\(x,i).(10x + 2),(x + 1),2))
A091628: 23 223 2223 22223 222223 2222223 22222223 222222223 2222222223 22222222223 222222222223 2222222222223 22222222222223 222222222222223 2222222222222223 22222222222222223
((x + 1) div (if (16 mod (x + 1)) <= 0 then 2 else 1))
A153152: 0 1 3 2 5 6 7 4 9 10 11 12 13 14 15 8
loop(\(x,i).(9x + 1),(2x + 2),1)
A217853: 91 7381 597871 48427561 3922632451 317733228541 25736391511831 2084647712458321 168856464709124011 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((2x + 3) * loop(\(x,i).4x,x,3))
A268965: 9 60 336 1728 8448 39936 184320 835584 3735552 16515072 72351744 314572800 1358954496 5838471168 24964497408 106300440576
((2x + 3) * loop(\(x,i).4x,x,(x + 1)))
A002700: 3 40 336 2304 14080 79872 430080 2228224 11206656 55050240 265289728 1258291200 5888802816 27246198784 124822487040 566935683072
(loop(\(x,i).4x,x,4) div (2x + 3))
A191637: 1 3 9 28 93 315 1092 3855 13797 49932 182361 671088 2485513 9256395 34636833 130150524
(loop(\(x,i).4x,x,4) mod (2x + 3))
A177023: 1 1 1 4 1 1 4 1 1 4 1 16 13 1 1 4
((2x + 3) + loop(\(x,i).(x + (i * i)),(x + ~2),x))
A316531: 3 6 9 13 20 32
(1 + (loop(\(x,i).(x2 + 2x),3,x) div (2x + 2)))
A191494: 1 64 1094 8192 39063 139968 411772 1048576 2391485 5000000 9743586 17915904 31374259 52706752 85429688 134217728
loop(\(x,i).(x + ((x3 + x2) * i)),(2x + 2),1)
A116234: 75 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + (((x div 2) + i) div 2)),((x + 1) div 2),1)
A277133: 1 2 2 4 4 7 7 11 11 17 17 25 25 35 35 48
loop(\(x,i).(2 * ((x + 1) - (2 * (i mod 2)))),((x + 1) div 2),1)
A230096: 1 0 0 2 2 2 2 6 6 10 10 22 22 42 42 86
loop(\(x,i).2x,((2x2 + 4x) - ((x + 1) div 2)),1)
A285389: 1 32 32768 268435456 70368744177664 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (4x div (2 + i))),((x + 1) div 2),1)
A323539: 1 2 2 4 4 7 7 11 11 17 17 25 25 36 36 50
(1 + (2 * (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A038712: 1 3 1 7 1 3 1 15 1 3 1 7 1 3 1 31
(1 + (loop(\(x,i).(x + (2 * (x div 3))),x,(x + 1)) div 2))
A343592: 1 2 4 9 14 36
(1 + (loop(\(x,i).(x div (1 + (2 * (x mod 2)))),2,(x + ~1)) div 2))
A246277: 0 1 1 2 1 3 1 4 2 5 1 6 1 7 3 8
(~1 + (2 * (x - loop(\(x,i).((~x2 + x) div 2),2,(x + ~1)))))
A341703: 1 1 3 7 19 51 121 253 477 829 1351 2091 3103 4447 6189 8401
(1 + (((x + ~1) * loop(\(x,i).(1 + (x * (1 + i))),x,2)) div 2))
A134432: 0 1 9 66 490 3915 34251 328804 3452436 39456405 488273005 6510306726 93097386174 1421850988831 23105078568495 398118276872520
((x + 2) div (1 + ((2x mod 3) + (if x <= 0 then 1 else 2))))
A025798: 1 0 1 1 1 1 2 1 2 3 2 3 4 3 4 5
(~1 + (((4x + 4) + (x mod 2)) * (if x <= 0 then 1 else 2)))
A273407: 3 17 23 33 39 49 55 65 71 81 87 97 103 113 119 129
(1 + (2 * loop(\(x,i).(x + ((x + ~2) mod 5)),x,1)))
A322171: 3 11 17 19 23 31 37 39 43 51 57 59 63 71 77 79
loop(\(x,i).(1 + (x2 div 2)),x,(1 + ((x2 + 1) div 2)))
A318165: 1 3 13
A016104: 1 3 13 16381
(1 + (2 * (if (16 mod (x + 1)) <= 0 then 0 else 2)))
A306577: 1 1 5 1 5 5 5 1 5 5 5 5 5 5 5 1
((x + 1) - (2 * (if (~2 + (x div 5)) <= 0 then 0 else 2)))
A331270-A117657: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 12
(1 + ((loop(\(x,i).(2 + (x2 * i)),(x + ~2),0) div 2) div 2))
A089301: 1 1 1 1 3 76
loop(\(x,i).x2,1,(1 + (2 * (x - ((x div 2) div ~2)))))
A167744-A028375: 1 9 49 81 121 169 289 361 441 529 729 841 961 1089 1369 1521
(if (x + ~2) <= 0 then x else (x - ((x + 2) div ~5)))
A155939: 0 1 2 4 6 7 8 9 10 12 13 14 15 16 18 19
(x + (if (x + ~2) <= 0 then 1 else 2) - (x div ~5))
A225647: 1 3 4 6 7
A143344: 1 3 4 6 7 8 10 11 12 13 14 16 17 18 19 20
(1 - ((x + 1) mod (1 + ((~x + 2) mod (2 + (if x <= 0 then 0 else 2))))))
A105567: 1 1 1 1 ~1 1 1 1 1 1 1 1 0 1 1 1
((x + 4) - ((~x + 1) div (1 + (2 * (if x <= 0 then 0 else 2)))))
A100318: 3 5 7 8 9 10 11 13 14 15 16 17 19 20 21 22
(loop(\(x,i).2x,x,1) mod 21)
A222011: 1 2 4 8
A070347: 1 2 4 8 16 11 1 2 4 8 16 11 1 2 4 8
(1 + (2 * (if (x + ~1) <= 0 then x else (2 + (x div 5)))))
A113722: 1 3 5 5 5 7 7 7 7 7 9 9 9 9 9 11
loop(\(x,i).i,((x + ~4) - (x div 12)),1)
A053759: 1 1 1 1 1 1 2 3 4 5 6 7 7 8 9 10
(2 - ((~x + 1) div (if ((x + ~2) mod 6) <= 0 then 2 else 1)))
A325351: 1 2 3 4 5 6 7 8 6 10 11 12 13 14 9 16
(if (~x + 2) <= 0 then ((x div (2 + ((~x + 1) mod 3))) mod 2) else 1)
A267015: 1 1 0 1 0 1 0 1 0 1 1 0 0 0 1 1
(1 + (2 * ((x mod (if (x + ~2) <= 0 then 1 else (x div 3))) div 2)))
A226306: 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 1
(1 + ((x mod (2 + (if (x mod 2) <= 0 then 1 else (x div 3)))) div 2))
A243987: 1 1 2 1 1 2 1 2 2 3 1 1 1 1 2 1
(((x + ~1) mod 3) div (if (~2 + (x div 3)) <= 0 then 2 else 1))
A025855: 1 0 0 1 0 0 1 0 0 2 0 1 2 0 1 2
(if ((1 + (x div 4)) mod (2 + (x mod 3))) <= 0 then 2 else 1)
A323437: 1 1 1 1 1 1 2 1 1 1 2 1 2 1 2 2
(if ((x + ~1) mod 4) <= 0 then (2 + ((x mod 3) div 2)) else 1)
A263845: 1 2 1 1 1 3 1 1 1 2 1 1 1 2 1 1
loop(\(x,i).x2,3,(8x + 5))
A017132: 390625 815730721 37822859361 500246412961 3512479453921 16815125390625 62259690411361 191707312997281 513798374428641 1235736291547681 2724905250390625 5595818096650401 10828567056280801
loop(\(x,i).x3,1,(8x + 5))
A017127: 125 2197 9261 24389 50653 91125 148877 226981 328509 456533 614125 804357 1030301 1295029 1601613 1953125
loop(\(x,i).x3,2,(8x + 5))
A017133: 1953125 10604499373 794280046581 14507145975869 129961739795077 756680642578125 3299763591802133 11694146092834141 35452087835576229 95151694449171437 231616946283203125 520411082988487293
loop(\(x,i).x2,1,(~7x + ~5))
A017042: 25 144 361 676 1089 1600 2209 2916 3721 4624 5625 6724 7921 9216 10609 12100
loop(\(x,i).x2,2,(~7x + ~5))
A017044: 625 20736 130321 456976 1185921 2560000 4879681 8503056 13845841 21381376 31640625 45212176 62742241 84934656 112550881 146410000
(if (x mod (2 + (5 mod (1 + (x div 2))))) <= 0 then 2 else 1)
A023396: 2 1 1 2 2 1 2 1 2 1 1 1 1 1 2 1
(5 + loop(\(x,i).10x,x,1))
A133472: 6 15 105 1005 10005 100005 1000005 10000005 100000005 1000000005 10000000005 100000000005 1000000000005 10000000000005 100000000000005 1000000000000005
(1 + (2 * ((loop(\(x,i).x2,(x + ~1),2) mod (x + 1)) div 2)))
A231409: 1 1 1 1 1 5 5 4611686018427387903
((2x2 + 1) - loop(\(x,i).(x2 + 3x + 2),2,2))
A218977: ~181 ~179 ~173 ~163 ~149 ~131 ~109 ~83 ~53 ~19 19 61 107 157 211 269
(if (x mod 3) <= 0 then (2 + (((x + 1) * (x div 2)) mod 2)) else 1)
A213852: 2 1 1 2 1 1 3 1 1 2 1 1 2 1 1 2
(1 + (if (x + ~2) <= 0 then x else (2 + (((x + 1) * (x div 2)) mod 2))))
A087162: 1 2 3 3 3 3 4 3 3 3 4 3 3 3 4 3
(~1 + ((if (~2 + (x div 3)) <= 0 then 2 else ((x + 1) div 2)) div 2))
A234451: 0 0 0 0 0 0 0 0 0 1 1 2 2 2 2 3
(1 - (if (~4 + (x div 2)) <= 0 then (((x + 1) div 2) div 2) else 1))
A016421-A016400-A016390-A014030: 1 1 1 0 0 0 0 ~1 ~1 ~1 0 0 0 0 0 0
(1 + (2 * (x - (2 * (if (~4 + (x div 2)) <= 0 then 0 else 2)))))
A240848: 1 3 5 7 9 11 13 15 17 19 13 15 17 19 21 23
((if (x mod 2) <= 0 then x else 1) div (~1 + (2 * ((x div ~2) mod 2))))
A009531: 0 1 2 ~1 ~4 1 6 ~1 ~8 1 10 ~1 ~12 1 14 ~1
(1 + (if (x + ~2) <= 0 then 0 else ((x div (~2 + (x mod ~2))) mod 2)))
A221646: 1 1 1 2 1 1 2 2 1 2 2 1 1 2 2 2
((~1 + (x mod 3)) mod (1 + (4 * (if x <= 0 then 0 else 2))))
A021559: 0 0 1 8 0 1 8 0 1 8 0 1 8 0 1 8
(5 + (if (~2 + (x div 2)) <= 0 then x else 6))
A168095: 5 6 7 8 9 10 11 11 11 11 11 11 11 11 11 11
(if ((x + 2) mod (4 + (3 mod (x + 1)))) <= 0 then 2 else 1)
A030382: 1 1 2 1 1 2 1 1 1 1 1 1 2 1 1 1
(if (x mod 4) <= 0 then 0 else (1 + ((((x + 1) div 2) div 2) mod 2)))
A082115: 0 1 1 2 0 2 2 1 0 1 1 2 0 2 2 1
loop(\(x,i).2x,(x div 2),(1 + (2 * (((x + ~1) div 2) mod 2))))
A308709: 3 1 2 6 12 4 8 24 48 16 32 96 192 64 128 384
(1 + (4 * (x - ((if x <= 0 then 1 else x) div ~4))))
A291180-A057948: 5 9 13 17 21 29 33 37 41 49 53 57 61 69 73 77
(if (x mod 2) <= 0 then (2 * ((((~1 + (x div 2)) div 2) div 2) mod 2)) else 1)
A215030: 2 1 0 1 0 1 0 1 0 1 2 1 2 1 2 1
(if ((x mod 3) - ((((x + 1) div 2) div 2) mod 2)) <= 0 then 2 else 1)
A049705: 2 1 1 2 2 1 2 1 1 2 1 1 2 2 1 2
(1 + ((x div (2 + (if (x mod 2) <= 0 then 1 else 8))) mod 2))
A118383: 1 1 1 1 2 1 1 1 1 1 2 2 1 2 1 2
(if (2 + ((2x + 2) mod ~7)) <= 0 then 2 else 1)
A291454-A105697: 2 2 1 2 2 2 1 2 2 1 2 2 2 1 2 2
(loop(\(x,i).2x,x,1) mod 33)
A222011: 1 2 4 8
A070338: 1 2 4 8 16 32 31 29 25 17 1 2 4 8 16 32
(if (x mod 2) <= 0 then (2 * (((x - (x div 4)) div 2) mod 2)) else 1)
A076826: 0 1 2 1 2 1 0 1 2 1 0 1 0 1 2 1
(if ((x + 2) mod (4 + (x mod (2 + (x mod 2))))) <= 0 then 2 else 1)
A341997: 1 1 2 1 1 1 2 1 1 1 2 1 1 2 2 1
(1 + ((x mod (~8 + (if (x + ~2) <= 0 then 2 else 1))) mod 2))
A245933: 1 2 1 1 2 1 2 1 1 2 1 2 1 2 1 1
(loop(\(x,i).4x,x,1) mod 17)
A266973: 1 4 16 13 1 4 16 13 1 4 16 13 1 4 16 13
(loop(\(x,i).3x,x,1) mod 17)
A036119: 1 3 9 10 13 5 15 11 16 14 8 7 4 12 2 6
loop(\(x,i).(4x + 1),x,15)
A072201: 15 61 245 981 3925 15701 62805 251221 1004885 4019541 16078165 64312661 257250645 1029002581 4116010325 16464041301
(loop(\(x,i).2x,x,1) - (x div 15))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A123464: 1 2 4 8 16 32 64 128 256 512
A220051: 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32767
(if ((x + 1) mod 4) <= 0 then (2 + (x mod 8)) else 1)
A168677: 1 1 1 5 1 1 1 9 1 1 1 5 1 1 1 9
loop(\(x,i).i,(x mod (2 + ((x + 1) mod (2 + (x div 4))))),1)
A212171: 1 1 2 1 1 1 1 3 2 1 1 1 2 1 1 1
loop(\(x,i).(x * i),(2 + ((x + ~2) div (2 + (x div 4)))),1)
A214078: 1 1 2 2 2 6 6 6 6 6 24 24 24 24 24 24
(if ((1 + (x div 4)) mod (2 + (x mod 4))) <= 0 then 2 else 1)
A300410-A286361: 1 1 1 1 2 1 1 1 1 2 1 1 2 1 2 1
(1 + (4 * (~2 + loop(\(x,i).8x,x,2))))
A164786: 1 57 505 4089 32761 262137 2097145 16777209 134217721 1073741817 8589934585 68719476729 549755813881 4398046511097 35184372088825 281474976710649
loop(\(x,i).x2,1,(~14x + ~1))
A134934: 1 225 841 1849 3249 5041 7225 9801 12769 16129 19881 24025 28561 33489 38809 44521
(if (x mod (1 - (2 * ((~x + 1) div (2 + (x div 2)))))) <= 0 then 2 else 1)
A164295-A035214: 2 2 1 2 1 1 2 1 1 1 2 1 1 1 1 2
(1 + ((loop(\(x,i).(x2 div 2),2,(~2 + (x div 2))) div 2) div 2))
A146068: 1 1 1 1 1 1 1 1 1 1 3 3 9 9 19 19
(((x + ~1) mod 3) div (if (~4 + (x div 2)) <= 0 then 2 else 1))
A025858: 1 0 0 1 0 0 1 0 0 1 0 1 2 0 1 2
(if (~2 + (x div 2)) <= 0 then 1 else (1 + (8 * (x mod 2))))
A224835: 1 1 1 1 1 1 1 9 1 9 1 9 1 9 1 9
(1 + (2 * (4 + loop(\(x,i).x2,x3,2))))
A257373: 13 17 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if ((1 + (((x + 1) + (x div 2)) div 2)) mod 4) <= 0 then 2 else 1)
A125238-A050432-A043278: 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 2
(if ((1 + ((x2 + (x div 2)) div 2)) mod 4) <= 0 then 2 else 1)
A008967: 1 1 1 1 1 1 2 1 1 1 1 2 2 2 1 1
(if ((x - ((2 - (x div 2)) div (x + 2))) mod 4) <= 0 then 2 else 1)
A235757: 1 1 1 1 2 1 1 2 1 1 1 2 1 1 1 2
(2 div (1 + ((1 - (if (~x + 2) <= 0 then x else 0)) mod 8)))
A332016-A331845: 1 1 0 0 0 0 0 0 1 2 0 0 0 0 0 0
(if ((x + 1) mod 7) <= 0 then 8 else 1)
A088842: 1 1 1 1 1 1 8 1 1 1 1 1 1 8 1 1
(if ((x2 + 1) mod (x + 4)) <= 0 then 8 else 1)
A056201: 1 1 1 1 1 1 1 1 1 1 1 1 1 8 1 1
(9 * loop(\(x,i).i,(((x + ~1) div 2) div 2),1))
A245400: 9 9 9 9 9 9 9 9 9 18 18 18 18 27 27 27
(9 * (1 + loop(\(x,i).2x,x,4)))
A305154: 45 81 153 297 585 1161 2313 4617 9225 18441 36873 73737 147465 294921 589833 1179657
(9 * (if (x mod 2) <= 0 then (2 + (x div 2)) else 1))
A181761: 18 9 27 9 36 9 45 9 54 9 63 9 72 9 81 9
(loop(\(x,i).(x * (x - i)),2,(x + ~1)) div 9)
A011919: 0 0 0 0 2 13 40 93 186 336 560 880 1320 1906 2669 3640
(9 * ((x + 4) + (if x <= 0 then 1 else 2)))
A242264-A242263: 45 63 72 81 90 99 108 117 126 135 144 153 162 171 180 189
(9 * ((2 - (x mod 2)) * (if x <= 0 then 1 else 2)))
A040307: 18 18 36 18 36 18 36 18 36 18 36 18 36 18 36 18
(9 * loop(\(x,i).(2x + 2),x,4))
A182467: 36 90 198 414 846 1710 3438 6894 13806 27630 55278 110574 221166 442350 884718 1769454
loop(\(x,i).10x,x,9)
A052268: 9 90 900 9000 90000 900000 9000000 90000000 900000000 9000000000 90000000000 900000000000 9000000000000 90000000000000 900000000000000 9000000000000000
loop(\(x,i).(x3 + 3x),x,9)
A145183: 9 756 432083484 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + ~3x),x,9)
A282181: 9 702 345946302 4611686018427387903 4611686018427387903
(9 + (x * loop(\(x,i).x2,4,x)))
A165254: 9 10 131081 129140172 17179869193 762939453134 16926659444745 232630513987216 2251799813685257 16677181699666578 100000000000000009 505447028499293780 2218611106740437001 4611686018427387903
(~1 - (if (2 - (x div 4)) <= 0 then x else 8))
A291514: ~9 ~9 ~9 ~9 ~9 ~9 ~9 ~9 ~9 ~10 ~11 ~12 ~13 ~14 ~15 ~16
(1 + loop(\(x,i).10x,x,8))
A199689: 9 81 801 8001 80001 800001 8000001 80000001 800000001 8000000001 80000000001 800000000001 8000000000001 80000000000001 800000000000001 8000000000000001
(~1 + loop(\(x,i).10x,x,8))
A198973: 7 79 799 7999 79999 799999 7999999 79999999 799999999 7999999999 79999999999 799999999999 7999999999999 79999999999999 799999999999999 7999999999999999
((4x + 2) mod loop(\(x,i).i,(x + ~8),1))
A316945: 0 0 0 0 0 0 0 0 0 0 0 1 2 4 4 6
(1 + loop(\(x,i).7x,x,8))
A199485: 9 57 393 2745 19209 134457 941193 6588345 46118409 322828857 2259801993 15818613945 110730297609 775112083257 5425784582793 37980492079545
(~1 + loop(\(x,i).7x,x,8))
A198689: 7 55 391 2743 19207 134455 941191 6588343 46118407 322828855 2259801991 15818613943 110730297607 775112083255 5425784582791 37980492079543
(1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 8))
A099549: 1 1 3 1 5 3 7 1 1 5 3 3 5 7 7 1
(1 + loop(\(x,i).(x2 + ~6x),x,8))
A110360: 9 17 161 24641 606981761 368426853330807041 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).(2x + 8),x,x) div 8))
A111297: 1 2 5 11 24 52 112 240 512 1088 2304 4864 10240 21504 45056 94208
(1 + (if (~4 + (x div 2)) <= 0 then x else (2x + ~8)))
A151547: 1 2 3 4 5 6 7 8 9 10 13 15 17 19 21 23
(if (x2 mod (x + 4)) <= 0 then (2 + (x div 4)) else 1)
A204118: 2 1 1 1 3 1 1 1 1 1 1 1 5 1 1 1
(if x <= 0 then 1 else (x2 mod (1 + (x div (2 + (x div 4))))))
A242252-A100810: 1 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1
(if ((x + ~1) mod 3) <= 0 then (x mod (2 + (x div 4))) else 1)
A232529: 1 1 1 1 1 1 1 1 1 1 2 1 1 3 1 1
(1 + (if (x + ~2) <= 0 then x else (2 * (2x - (x mod 4)))))
A160513: 1 2 3 7 17 19
((2 * (x + (x div 4))) + (if (x mod 4) <= 0 then 2 else 1))
A260181: 2 3 5 7 12 13 15 17 22 23 25 27 32 33 35 37
loop(\(x,i).x2,1,(12x + 9))
A017630: 81 441 1089 2025 3249 4761 6561 8649 11025 13689 16641 19881 23409 27225 31329 35721
loop(\(x,i).x2,2,(12x + 9))
A017632: 6561 194481 1185921 4100625 10556001 22667121 43046721 74805201 121550625 187388721 276922881 395254161 547981281 741200625 981506241 1275989841
(1 + (loop(\(x,i).(x * i),x,(~2 + ((x2 + ~x) div 2))) div 2))
A173038: 0 0 0 4 49 481 4681 47881 524161 6168961 78019201 1057795201 15328051201 236626790401 3879433958401 67345229952001
(if (x mod 2) <= 0 then (2 * (((x + (x div 4)) div 2) mod 2)) else 1)
A284620: 0 1 2 1 0 1 2 1 2 1 0 1 2 1 0 1
(2 div (1 + ((x + ~1) mod (2 * (2 + (if (x mod 2) <= 0 then x else 2))))))
A295976: 0 2 1 0 0 0 0 0 0 2 0 0 0 0 0 0
(1 + loop(\(x,i).x2,1,(9x + ~4)))
A154277: 17 26 197 530 1025 1682 2501 3482 4625 5930 7397 9026 10817 12770 14885 17162
(~1 + (2 * loop(\(x,i).(~8x + 2),2x,2)))
A228871: 3 227 14563 932067 59652323 3817748707 244335917283 15637498706147 1000799917193443 64051194700380387 4099276460824344803 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x3,2x,(8x + 1))
A276274: 1 387420489 4611686018427387903 4611686018427387903
loop(\(x,i).x2,3,(~7x + ~1))
A017000: 1 16777216 2562890625 54875873536 500246412961 2821109907456 11688200277601 39062500000000 111429157112001 281474976710656 645753531245761 1370114370683136 2724905250390625 5132188731375616
(if (~x + 2) <= 0 then ((((x mod 3) - (x div 2)) div 2) mod 2) else 1)
A189138: 1 1 0 1 1 0 0 1 1 0 0 0 1 1 1 0
(3 + (if x <= 0 then 1 else (2 * (4x - (x div 2)))))
A063237: 4 11 17 25 31 39 45 53 59 67 73 81 87 95 101 109
(~1 + (2 * loop(\(x,i).(2 * (x2 div 2)),x,(2 + (x div 2)))))
A079622: 3 7 127 8191
(if ((x + 1) mod 3) <= 0 then (2 * (2 - ((x div 2) mod 2))) else 1)
A061462: 1 1 2 1 1 4 1 1 4 1 1 2 1 1 2 1
(if ((x + 1) mod 5) <= 0 then (2 + ((x div 2) mod 2)) else 1)
A334925: 1 1 1 1 2 1 1 1 1 2 1 1 1 1 3 1
(1 + (if (x mod 2) <= 0 then x else (x - (x div (~2 + ((x div 2) mod 2))))))
A129266: 1 3 3 7 5 9 7 15 9 15
(if (x mod 2) <= 0 then (x div 2) else (x mod (1 + (2 * ((x div 2) mod 2)))))
A249122: 0 0 1 0 2 0 3 1 4 0 5 2 6 0 7 0
(1 + ((if (x + ~2) <= 0 then x else ((x + 1) mod (2 + (x mod 2)))) mod 2))
A308186-A107362: 1 2 1 2 2 1 2 1 2 2 2 1 2 1 2 2
(1 + (2 * loop(\(x,i).(2x + 4),(x div 2),(2 + (x mod 2)))))
A164120: 5 7 17 21 41 49 89 105 185 217 377 441 761 889 1529 1785
loop(\(x,i).2x,(x + (x div 2)),(5 + (x mod 2)))
A164737: 5 12 40 96 320 768 2560 6144 20480 49152 163840 393216 1310720 3145728 10485760 25165824
loop(\(x,i).3x,(x div 2),(1 + (4 * (x mod 2))))
A166465: 1 5 3 15 9 45 27 135 81 405 243 1215 729 3645 2187 10935
(1 + (4 * loop(\(x,i).(x3 + x2),x2,2)))
A116169: 9 49 4611686018427387903 4611686018427387903 4611686018427387903
((x + ~2) mod (1 + ((1 - (if (~x + 2) <= 0 then x else 0)) mod 4)))
A318655: 0 1 0 1 0 0 0 2 0 0 0 0 0 0 0 1
(if ((x + 1) mod (3 + (x mod 4))) <= 0 then 4 else 1)
A069289: 1 1 1 1 1 1 1 1 4 1 1 4 1 1 4 1
((x + 1) div (if ((x + 1) mod 5) <= 0 then 4 else 1))
A001438: 1 2 3 4 1 6 7 8
A132739-A060791: 1 2 3 4 1 6 7 8 9 2 11 12 13 14 3 16
(1 + ((x2 + 2x + 2) div (if (x mod 2) <= 0 then 1 else 4)))
A065014-A013945: 3 2 11 5 27 10 51 17 83 26 123 37 171 50 227 65
(if (x + ~4) <= 0 then (x + 1) else (1 + ((x + ~1) mod 4)))
A322425: 1 2 3 4 5 1 2 3 4 1 2 3 4 1 2 3
(if ((1 + ((x + 1) div 2)) mod 8) <= 0 then 4 else 1)
A046553-A046552: 1 1 1 1 1 1 1 1 1 1 1 1 1 4 4 1
(if (((x + ~2) - (x div 4)) mod 4) <= 0 then 4 else 1)
A053231: 1 1 4 1 1 1 1 4 4 1 1 1 1 4 1 1
((x + 1) - (((if (x mod 2) <= 0 then x else 2) - (x div 2)) div 4))
A284120: 1 2 3 4 5 6 7 9 8 11 10 13 12 15 14 18
(if (16 mod (x + 1)) <= 0 then 0 else 5)
A238192: 0 0 5 0 5 5 5 0 5 5 5 5 5 5 5 0
(0 - (loop(\(x,i).(3x + ~3),x,0) div 5))
A178543: 0 1 3 8 24 73 219 656 1968 5905 17715 53144 159432 478297 1434891 4304672
(2x - ((~1 + (if (~x + 2) <= 0 then x else 0)) div 5))
A232499: 1 3 4 6 8 10 11 13 15 17 19 20 22 24 26 28
(5 * (~1 + (2 * loop(\(x,i).x2,2,(x + 2)))))
A224336: 155 805 2555 6245 12955 24005 40955 65605 99995 146405 207355 285605 384155 506245 655355 835205
(15 * (2 - ((if x <= 0 then 1 else x) mod 2)))
A040211: 15 15 30 15 30 15 30 15 30 15 30 15 30 15 30 15
((3 * loop(\(x,i).((x + 2) + i),x,2)) div 5)
A097911: 1 3 5 8
A186494: 1 3 5 8 12 16 21 26 32 39 46 54 62 71 81 91
((if x <= 0 then 1 else x) - (5 * ((x div 2) div 3)))
A033926: 1 1 2 3 4 5 1 2 3 4 5 6 2 3 4 5
(if x <= 0 then 1 else (5 * (x - ((x div 2) div 3))))
A007845: 1 5 10 15 20 25 25 30 35 40 45 50 50 55 60 65
loop(\(x,i).x2,3,(10x + 5))
A017336: 390625 2562890625 152587890625 2251875390625 16815125390625 83733937890625 318644812890625 1001129150390625 2724905250390625 6634204312890625 14774554437890625 30590228625390625 59604644775390625
loop(\(x,i).x3,1,(10x + 5))
A017331: 125 3375 15625 42875 91125 166375 274625 421875 614125 857375 1157625 1520875 1953125 2460375 3048625 3723875
loop(\(x,i).x3,2,(10x + 5))
A017337: 1953125 38443359375 3814697265625 78815638671875 756680642578125 4605366583984375 20711912837890625 75084686279296875 231616946283203125 630249409724609375 1551328215978515625 3517876291919921875
(5 * (1 + loop(\(x,i).(2x + ~1),(x div 2),x)))
A236391: 5 10 20 30 70
(5 * loop(\(x,i).6x,x,(x + 1)))
A212700: 5 60 540 4320 32400 233280 1632960 11197440 75582720 503884800 3325639680 21767823360 141490851840 914248581120 5877312307200 37614798766080
(loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) mod 5)
A099546: 1 1 3 1 0 3 2 1 4 0 1 3 3 2 0 1
(5 * loop(\(x,i).((x2 + ~x) div 2),2,(x + ~1)))
A266395: 0 0 0 0 15 75 225 525 1050 1890 3150 4950 7425 10725 15015 20475
(loop(\(x,i).(x * i),(x + ~1),(x2 + 1)) mod 5)
A151669: 1 2 0 0 2 4 0 0 0 0 0 0 0 0 0 0
(10 * loop(\(x,i).i,(x div 5),1))
A245403: 10 10 10 10 10 10 10 10 10 10 20 20 20 20 20 30
(loop(\(x,i).(x * (2 + i)),(x + 3),2) div 5)
A129923: 24 144 1008 8064 72576 725760 7983360 95800320 1245404160 17435658240 261534873600 4184557977600 71137485619200 1280474741145600 24329020081766400 486580401635328000
(10 * ((2 - (x mod 2)) * (if x <= 0 then 1 else 2)))
A040381: 20 20 40 20 40 20 40 20 40 20 40 20 40 20 40 20
(10 * ((x + 4) + (if x <= 0 then 1 else 2)))
A272607: 50 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210
(loop(\(x,i).(2x + 1),x,(x div 4)) mod 5)
A287556: 0 1 3 2 1 3 2 0 2 0 1 3 3 2 0 1
(loop(\(x,i).((x + 2) + (i * i)),(x + 2),2) div 5)
A026039: 2 4 8 13 21 31 44 61 81 106 135 169 209 254 306 364
(if x <= 0 then 6 else ((2x + 4) div 5))
A128423: 6 1 1 2 2 2 3 3 4 4 4 5 5 6 6 6
(if x <= 0 then 8 else ((2x + 4) div 5))
A128881: 8 1 1 2 2 2 3 3 4 4 4 5 5 6 6 6
(5 * loop(\(x,i).(6x + 1),x,2))
A198848: 10 65 395 2375 14255 85535 513215 3079295 18475775 110854655 665127935 3990767615 23944605695 143667634175 862005805055 5172034830335
(5 * loop(\(x,i).6x,x,(x + 2)))
A159733: 10 90 720 5400 38880 272160 1866240 12597120 83980800 554273280 3627970560 23581808640 152374763520 979552051200 6269133127680 39965723688960
(5 * loop(\(x,i).2x,(x div 2),(2 - (x mod 2))))
A147675: 10 5 20 10 40 20 80 40 160 80 320 160 640 320 1280 640
((x + 2) - ((1 - (if (~x + 2) <= 0 then x else 2)) div 5))
A154660: 3 4 5 6 7 8
A258187: 3 4 5 6 7 8 9 11 12 13 14 15 17 18 19 20
((x + 2) - ((~x + (if (x + ~2) <= 0 then x else 0)) div 5))
A249299: 2 3 4 6 7 8 10 11 12 13 14 16 17 18 19 20
((x * (~1 + loop(\(x,i).2x2,2,2))) div 5)
A169860: 0 25 50 76 101 127 152 177 203 228 254 279 304 330 355 381
loop(\(x,i).(7x + ~3),x,5)
A199486: 5 32 221 1544 10805 75632 529421 3705944 25941605 181591232 1271138621 8897970344 62285792405 436000546832 3052003827821 21364026794744
(if x <= 0 then 1 else ((x + (2 * ((x div 2) mod 2))) div 5))
A029280: 1 0 0 1 0 1 1 1 1 1 2 2 2 2 3 3
((if x <= 0 then 1 else 4x) - ((~x + 2) div 5))
A058759: 1 4 8 13
A311807: 1 4 8 13 17 21 25 29 34 38 42 46 50 55 59 63
(if ((x + (x div 2)) mod 4) <= 0 then 1 else (x div 5))
A008677: 1 0 0 1 0 1 1 1 1 1 2 1 2 2 2 3
((x + 4) + ((if x <= 0 then 1 else 2) + (x div 5)))
A038609: 5 7 8 9 10 12 13 14 15 16 18 19 20 21 22 24
((if (~4 + (x div 2)) <= 0 then 1 else 2) * (x mod 5))
A309956: 0 1 2 3 4 0 1 2 3 4 0 2 4 6 8 0
(2 + ((if (x + ~1) <= 0 then x else 3) + (x mod 5)))
A301936: 2 4 7 8 9 5
loop(\(x,i).(x + (x mod 9)),x,5)
A016084: 5 10 11 13 17 25 32 37 38 40 44 52 59 64 65 67
((x2 + ~x) + loop(\(x,i).2x,(~x mod 4),1))
A110214: 1 8 6 8 13
((x + 1) mod (1 + ((if (x mod 3) <= 0 then 1 else x) mod 4)))
A284825-A202523: 1 0 0 0 0 0 1 0 0 0 2 0 1 0 0 0
((x + 1) - ((~x + (if (x mod 3) <= 0 then 2 else 1)) div 4))
A249031: 1 2 4 5 6 7 8 10 11 12 14 15 16 17 19 20
(~1 + loop(\(x,i).(4x - (i mod 4)),x,4))
A037793: 3 14 57 228 915 3662 14649 58596 234387 937550 3750201 15000804 60003219 240012878 960051513 3840206052
(~1 + loop(\(x,i).(10x + 4),x,4))
A173770: 3 43 443 4443 44443 444443 4444443 44444443 444444443 4444444443 44444444443 444444444443 4444444444443 44444444444443 444444444444443 4444444444444443
(x mod (1 + (if (x mod (2 + (x mod 2))) <= 0 then 1 else (x div 4))))
A106404: 0 0 0 1 0 1 0 1 0 1 0 2 0 1 0 1
(if ((x + (x div 3)) mod 3) <= 0 then (x div 4) else 1)
A137773: 0 1 1 1 1 1 1 1 1 2 1 1 1 1 3 1
(if (x mod (2 + (x mod 8))) <= 0 then (x div 4) else 1)
A326644: 0 1 1 1 1 1 1 1 2 2 1 1 3 1 1 1
loop(\(x,i).2x,(x - compr(\x.((x div 2) mod 2),(x div 4))),1)
A222011: 1 2 4 8
A029930: 1 2 4 8 8 16 32 64 16 32 64 128 128 256 512 1024
(if (x mod 2) <= 0 then 1 else ((x2 + 1) mod (1 + (x div 4))))
A025824: 1 0 1 0 1 0 1 0 1 1 1 2 1 2 1 2
(if (x mod 8) <= 0 then 1 else (2 mod (1 + (x div 4))))
A244462: 1 0 0 0 0 0 0 0 1 2 2 2 2 2 2 2
(1 + (if (x mod 8) <= 0 then (x div 2) else (x mod 4)))
A338484: 1 2 3 4 1 2 3 4 5 2 3 4 1 2 3 4
((if (~2 + (x div 3)) <= 0 then 1 else 2) div (1 + (x mod 4)))
A256012-A025874: 1 0 0 0 1 0 0 0 1 1 0 0 2 1 0 0
(1 + loop(\(x,i).11x,x,4))
A199753: 5 45 485 5325 58565 644205 7086245 77948685 857435525 9431790765 103749698405 1141246682445 12553713506885 138090848575725 1518999334332965 16708992677662605
(~1 + loop(\(x,i).11x,x,4))
A199020: 3 43 483 5323 58563 644203 7086243 77948683 857435523 9431790763 103749698403 1141246682443 12553713506883 138090848575723 1518999334332963 16708992677662603
(1 + (((~x + loop(\(x,i).((x2 + x) + i),x,0)) div 2) div 2))
A288557: 1 1 1 6 139
loop(\(x,i).4x,(10x + 4),1)
A013879: 256 268435456 281474976710656 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).3x,(10x + 4),1)
A013851: 81 4782969 282429536481 16677181699666569 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if x <= 0 then 1 else (2 * (x - (2 * (~x + (x div 3)))))))
A063222: 2 7 13 15 21 27 29 35 41 43 49 55 57 63 69 71
(x4 mod (1 + loop(\(x,i).(x2 + x),2,2)))
A070586: 0 1 16 38 41 23 6 36 11 25 24 21 10 9 17 14
(3 + loop(\(x,i).(10x + ~8),x,2))
A173736: 5 15 115 1115 11115 111115 1111115 11111115 111111115 1111111115 11111111115 111111111115 1111111111115 11111111111115 111111111111115 1111111111111115
(1 + (2 * loop(\(x,i).(10x + ~16),x,2)))
A173776: 5 9 49 449 4449 44449 444449 4444449 44444449 444444449 4444444449 44444444449 444444444449 4444444444449 44444444444449 444444444444449
(1 + ((if x <= 0 then 1 else (x2 div (x - ((~x + 2) div 2)))) mod 2))
A270646: 2 2 1 1 2 2 1 1 2 1 2 2 1 1 2 1
(2 div (1 + ((1 + (x div 2)) mod (2 + (if (x mod 2) <= 0 then x else 2)))))
A127282: 1 1 0 0 0 0 0 2 0 1 0 0 0
(~1 + (2 * (x - ((0 - loop(\(x,i).(x * i),x,1)) div (x + 2)))))
A018260: 1 3 5 9 15 45
(~1 + (((x + 2) * (2 + loop(\(x,i).2x,x,3))) div 2))
A340228: 4 11 27 64 149 342 775 1736 3849 8458 18443 39948 86029 184334 393231 835600
(1 + (if (x mod 2) <= 0 then 2 else (((2 - (x div 2)) mod (x + 2)) mod 2)))
A317203: 3 1 3 2 3 1 3 1 3 2 3 1 3 2 3 1
((x + 5) * loop(\(x,i).4x,x,(x + 2)))
A228310: 10 72 448 2560 13824 71680 360448 1769472 8519680 40370176 188743680 872415232 3992977408 18119393280 81604378624 365072220160
(1 + (if (~2 + (x div 5)) <= 0 then x else (x + 4)))
A252493-A005496: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20
((2x + 5) * loop(\(x,i).(x * (2 + i)),4,1))
A069476: 1800 2520 3240 3960 4680 5400 6120 6840 7560 8280 9000 9720 10440 11160 11880 12600
(3 + (if (x + ~10) <= 0 then x else (x + 2)))
A154660: 3 4 5 6 7 8
A333491: 3 4 5 6 7 8 9 10 11 12 13 16 17 18 19 20
loop(\(x,i).(x * (5 + (x mod 2))),(2x + ~4),1)
A259345: 1 1 1 30 750
(1 + (loop(\(x,i).(x2 + ~2x + ~1),(x + ~1),2x) div 2))
A110067: 1 2 4 242
(1 + (2 * (((x div ~2) mod 2) + (if x <= 0 then 1 else 2x))))
A020574: 3 7 11 13 17 23
(~1 + (if x <= 0 then 1 else (2 * (2x + ((x mod 3) mod 2)))))
A168224: 0 5 7 11 17 19 23 29 31 35 41 43 47 53 55 59
(~1 + (if x <= 0 then 2 else (4x + ((x2 + x) div 2))))
A183905: 1 4 10 17 25 34 44 55 67 80 94 109 125 142 160 179
loop(\(x,i).x5,1,(4x + 1))
A016817: 1 3125 59049 371293 1419857 4084101 9765625 20511149 39135393 69343957 115856201 184528125 282475249 418195493 601692057 844596301
(1 + (if x <= 0 then 1 else (2 * (8x - (x div 2)))))
A063118: 2 17 31 47 61 77 91 107 121 137 151 167 181 197 211 227
loop(\(x,i).3x,(0 - ((~x + 2) div (2 + (x div 2)))),1)
A105159: 1 1 1 3 3 3 3 3 3 9 9 9 9 9 9 9
loop(\(x,i).2x,((x div 2) - (x mod (2 - ((x div 2) mod 2)))),1)
A173300: 1 1 2 2 4 2 8 8 16 8 32 32 64 32 128 128
(1 + (if (16 mod (x + 1)) <= 0 then (x mod 2) else 2))
A091935: 1 2 3 2 3 3 3 2 3 3 3 3 3 3 3 2
(1 + (x div (if (x mod 4) <= 0 then 1 else (2 * (2 - (x mod 2))))))
A065261: 1 1 1 2 5 3 2 4 9 5 3 6 13 7 4 8
loop(\(x,i).3x,(x div 2),(1 + (2 * (2 - (x mod 2)))))
A162813: 5 3 15 9 45 27 135 81 405 243 1215 729 3645 2187 10935 6561
(if (x + ~1) <= 0 then x else ((2x2 + 3) - (x mod 2)))
A160843: 0 1 11 20 35 52 75 100 131 164 203 244 291 340 395 452
(if ((x + 2) mod 7) <= 0 then (2 + (x mod 2)) else 1)
A030395: 1 1 1 1 1 3 1 1 1 1 1 1 2 1 1 1
(1 + ((loop(\(x,i).2x,x,1) div 3) * (2 + (x mod 2))))
A131588: 1 1 3 7 11 31 43 127 171 511 683 2047 2731 8191 10923 32767
((x2 + ~1) mod (1 + (if (x + ~2) <= 0 then 1 else (2 + (x mod 2)))))
A000086: 1 0 1 0 0 0 2 0 0 0 0 0 2 0 0 0
(~1 + ((if (~4 + (x div 2)) <= 0 then 1 else 2) * (2 + (x mod 2))))
A323287: 1 2 1 2 1 2 1 2 1 2 3 5 3 5 3 5
(loop(\(x,i).3x,x,4) div (3 + (x mod 2)))
A133647: 1 3 12 27 108 243 972 2187 8748 19683 78732 177147 708588 1594323 6377292 14348907
loop(\(x,i).2x,((x2 + 2x) div 2),(3 + (x mod 2)))
A146161: 3 8 48 512 12288 524288 50331648 8589934592 3298534883328 2251799813685248 3458764513820540928 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (loop(\(x,i).(x * (i * i)),(x + 1),1) + (2 * (x mod 2))))
A089043: 0 5 35 577 14399 518401 25401599 1625702401 131681894399 13168189440001 1593350922239999 229442532802560001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if ((1 + (x div 2)) mod 5) <= 0 then (2 * (x mod 2)) else 1)
A136713: 1 1 1 1 1 1 1 1 0 2 1 1 1 1 1 1
(1 - (if (x + ~12) <= 0 then (2 * (x mod 2)) else 1))
A016323-A016167-A016063-A015907-A015855-A015751-A015595-A015543-A015387-A015231-A015127-A015075-A014971-A014815-A014763-A014607-A014503-A014451: 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 0 0 0
(~1 + (loop(\(x,i).6x,x,1) + (2 * (x mod 2))))
A274073: 0 7 35 217 1295 7777 46655 279937 1679615 10077697 60466175 362797057 2176782335 13060694017 78364164095 470184984577
(1 + loop(\(x,i).6x,x,1) - (2 * (x mod 2)))
A274074: 2 5 37 215 1297 7775 46657 279935 1679617 10077695 60466177 362797055 2176782337 13060694015 78364164097 470184984575
(1 + loop(\(x,i).5x,x,1) - (2 * (x mod 2)))
A087404: 2 4 26 124 626 3124 15626 78124 390626 1953124 9765626 48828124 244140626 1220703124 6103515626 30517578124
(loop(\(x,i).(2 * i),(x div 4),1) div (1 + (2 * (x mod 2))))
A029186: 1 0 1 0 2 0 2 0 4 1 4 1 6 2 6 2
(loop(\(x,i).2x,(x div 2),3) * (1 + (2 * (x mod 2))))
A134693: 3 9 6 18 12 36 24 72 48 144 96 288 192 576 384 1152
(loop(\(x,i).2x2,(x div 2),2) * (1 + (2 * (x mod 2))))
A116083: 2 6 8 24 128 384 32768 98304 2147483648 6442450944
loop(\(x,i).(3x + 3),(x div 2),(1 + (2 * (x mod 2))))
A087503: 1 3 6 12 21 39 66 120 201 363 606 1092 1821 3279 5466 9840
loop(\(x,i).(4x + 2),(x div 2),(1 + (2 * (x mod 2))))
A277954: 1 3 6 14 26 58 106 234 426 938 1706 3754 6826 15018 27306 60074
loop(\(x,i).8x,(x div 2),(1 + (2 * (x mod 2))))
A096886: 1 3 8 24 64 192 512 1536 4096 12288 32768 98304 262144 786432 2097152 6291456
loop(\(x,i).5x,(x div 2),(1 + (2 * (x mod 2))))
A018272: 1 3 5 15 25 75
A018421: 1 3 5 15 25 75 125 375
A111386-A056487: 1 3 5 15 25 75 125 375 625 1875 3125 9375 15625 46875 78125 234375
loop(\(x,i).(2x * (1 + (i mod 2))),x,(1 + (2 * (x mod 2))))
A164675: 1 12 8 96 64 768 512 6144 4096 49152 32768 393216 262144 3145728 2097152 25165824
(if (~4 + (x div 2)) <= 0 then x else ((x + 1) - (2 * (x mod 2))))
A103303: 0 1 2 3 4 5 6 7 8 9
A113220-A113218: 0 1 2 3 4 5 6 7 8 9 11 10 13 12 15 14
(1 + (2 * (2x2 + loop(\(x,i).x2,2,3))))
A057604: 163 167 179 199 227 263 307 359 419 487 563 647 739 839 947 1063
(~1 + (2 * loop(\(x,i).(x * (x + (x2 div (x + 2)))),x,2)))
A319749: 3 11 119 14159 200477279 40191139395243839
(1 + loop(\(x,i).x2,1,(2 * (x - (x3 div 2)))))
A096996: 1 5 17 401
(loop(\(x,i).(x + i),(x + ~7),0) div 3)
A309881: 0 0 0 0 0 0 0 0 0 1 2 3 5 7 9 12
(3 * loop(\(x,i).(2 + ((2 * (x + i)) + i)),(x + 1),0))
A059145: 15 54 141 324 699 1458 2985 6048 12183 24462 49029 98172 196467 393066 786273
(((~x + 1) - loop(\(x,i).(2x - (i div 2)),x,0)) div 3)
A178742: 0 0 0 0 1 4 11 25 53 109 222 449 904 1814 3634 7274
(loop(\(x,i).(x + ((2 + (i * i)) * i * i)),x,0) div 3)
A061927: 0 1 9 42 138 363 819 1652 3060 5301 8701 13662 20670 30303 43239 60264
(3 * (x - (if (x mod 7) <= 0 then 0 else 1)))
A187337: 0 0 3 6 9 12 15 21 21 24 27 30 33 36 42 42
(3 * (1 + loop(\(x,i).(2 + (x * ((x + ~1) + i))),x,0)))
A300981: 3 9 27 249
(loop(\(x,i).i,(x mod (1 + (4 mod (x + 1)))),1) mod 3)
A282714: 1 1 1 1 1 1 1 2 0 1 1 1 2 0 1 1
(3 * (1 + ((x + (if (x mod 2) <= 0 then x else 1)) mod 3)))
A269226: 3 9 6 6 9 3 3 9 6 6 9 3 3 9 6 6
((1 + loop(\(x,i).2x,x,(x2 mod 3))) div 3)
A087463: 0 1 1 0 5 11 0 43 85 0 341 683 0 2731 5461 0
loop(\(x,i).x2,1,(6x2 + 6x + ~3))
A110853: 9 81 1089
(~27 + loop(\(x,i).2x,x,1))
A220087: ~26 ~25 ~23 ~19 ~11 5 37 101 229 485 997 2021 4069 8165 16357 32741
(loop(\(x,i).2x,x,1) mod 27)
A222011: 1 2 4 8
A269305-A070337: 1 2 4 8 16 5 10 20 13 26 25 23 19 11 22 17
(~3 + loop(\(x,i).2x2,x2,5))
A177190: 2 47 4999999999999997 4611686018427387903 4611686018427387903
((1 + ((if (x mod 2) <= 0 then 2 else 0) + (x div 4))) div 3)
A025825: 1 0 1 0 1 0 1 0 1 1 1 1 2 1 2 1
(3 * (~1 + (2 * loop(\(x,i).(x - (2 * (~x + i))),x,2))))
A173391: 9 21 45 105 273 765 2229 6609 19737 59109 177213 531513 1594401 4783053 14348997 43046817
loop(\(x,i).x2,3,(12x + 3))
A017564: 6561 2562890625 282429536481 5352009260481 45767944570401 248155780267521 1001129150390625 3282116715437121 9227446944279201 23045377697175681 52389094428262881 110324037687890625
loop(\(x,i).x3,1,(12x + 3))
A017559: 27 3375 19683 59319 132651 250047 421875 658503 970299 1367631 1860867 2460375 3176523 4019679 5000211 6128487
loop(\(x,i).x3,2,(12x + 3))
A017565: 19683 38443359375 7625597484987 208728361158759 2334165173090451 15633814156853823 75084686279296875 285544154243029527 913517247483640899 2558036924386500591 4611686018427387903
loop(\(x,i).x2,1,(~11x + ~3))
A017426: 9 196 625 1296 2209 3364 4761 6400 8281 10404 12769 15376 18225 21316 24649 28224
loop(\(x,i).x2,2,(~11x + ~3))
A017428: 81 38416 390625 1679616 4879681 11316496 22667121 40960000 68574961 108243216 163047361 236421376 332150625 454371856 607573201 796594176
((1 + ((2 * (if x <= 0 then 1 else x)) + ((x div 2) mod 2))) div 3)
A213856: 1 1 2 2 3 3 4 5 5 6 7 8 8 9 10 10
(loop(\(x,i).2x,x,1) - (3 * (~1 + (2 * (x mod 2)))))
A140657: 4 ~1 7 5 19 29 67 125 259 509 1027 2045 4099 8189 16387 32765
loop(\(x,i).(2x + 1),x,36)
A171390: 36 73 147 295 591 1183 2367 4735 9471 18943 37887 75775 151551 303103 606207 1212415
(loop(\(x,i).(~2x + 4),x,((~x + 1) mod 3)) div 3)
A328824: 0 1 1 1 ~7 ~7 ~7 57 57 57 ~455 ~455 ~455 3641 3641 3641
(if (x div 5) <= 0 then x else (3x + ~9))
A204502: 0 1 2 3 4 6 9 12 15 18 21 24 27 30 33 36
(3 * (if x <= 0 then 0 else (3x2 + ~3x + 2)))
A211615: 0 6 24 60 114 186 276 384 510 654 816 996 1194 1410 1644 1896
loop(\(x,i).x3,1,9x2)
A016770: 0 729 46656 531441 2985984 11390625 34012224 85766121 191102976 387420489 729000000 1291467969 2176782336 3518743761 5489031744 8303765625
(if x <= 0 then 1 else (3 * (x - (1 mod (~2x + 3)))))
A179805: 1 3 6 15 24 33 42 51 60 69 78 87 96 105 114 123
((1 + loop(\(x,i).(x * (~1 + (2 * i))),x,(x + 2))) div 3)
A261898: 1 1 4 25 210 2205 27720 405405 6756750 126351225 2618916300 59580345825 1475759335050 39529267903125 1138442915610000 35078272337233125
(2 - (if x <= 0 then 1 else ((~6x + ~3) + (x div 2))))
A258588: 1 11 16 22 27 33 38 44 49 55 60 66 71 77 82 88
loop(\(x,i).x2,3,(~5x + ~3))
A016892: 6561 16777216 815730721 11019960576 78310985281 377801998336 1406408618241 4347792138496 11688200277601 28179280429056 62259690411361 128063081718016 248155780267521 457163239653376
(loop(\(x,i).(2 * (x - (i mod 2))),x,(2x + 1)) div 3)
A113861: 0 1 5 15 41 103 249 583 1337 3015 6713 14791 32313 70087 151097 324039
loop(\(x,i).~x,x,(1 - ((x mod (1 + (x div 2))) div 3)))
A014191: 1 ~1 1 ~1 1 ~1 1 0 0 0 0 0 0 1 ~1 1
((~1 + (if (~2 + (x div 4)) <= 0 then 2 else (x mod 2))) mod 3)
A264049: 1 1 1 1 1 1 1 1 1 1 1 1 2 0 2 0
(loop(\(x,i).(1 + (4x div (1 + i))),x,1) mod 3)
A194317: 1 0 2 0 2 1 0 2 1 1 1 1 1 1 1 1
loop(\(x,i).x2,3,(9x + 3))
A017204: 6561 429981696 37822859361 656100000000 5352009260481 28179280429056 111429157112001 360040606269696 1001129150390625 2478758911082496 5595818096650401 11716593810022656 23045377697175681
loop(\(x,i).x3,1,(9x + 3))
A017199: 27 1728 9261 27000 59319 110592 185193 287496 421875 592704 804357 1061208 1367631 1728000 2146689 2628072
loop(\(x,i).x3,2,(9x + 3))
A017205: 19683 5159780352 794280046581 19683000000000 208728361158759 1352605460594688 6351461955384057 23762680013799936 75084686279296875 208215748530929664 520411082988487293 1195092568622310912
(3 * loop(\(x,i).(10x + ~1),x,1))
A199688: 3 27 267 2667 26667 266667 2666667 26666667 266666667 2666666667 26666666667 266666666667 2666666666667 26666666666667 266666666666667 2666666666666667
(3 * loop(\(x,i).((2x2 + 1) - (x mod 2)),x,1))
A074894: 3 6 27 486
(loop(\(x,i).(x2 div 2),2,(x2 + ~x + ~1)) div 3)
A179059: 0 0 0 24 600 5400 29400 117600 381024 1058400 2613600 5880600 12269400 24048024 44717400 79497600
(2 - (loop(\(x,i).((x + ~2) + (x div 3)),x,1) div 3))
A120149: 2 3 4 5 7 9 12 16 21 28 38 50 67 89 119 159
((((x div 2) mod 3) + loop(\(x,i).2x,x,1)) div 3)
A024495: 0 0 1 3 6 11 21 42 85 171 342 683 1365 2730 5461 10923
(((x + 1) * (1 + loop(\(x,i).x2,(x + ~1),2))) div 3)
A034384: 1 2 5 22 428
(if x <= 0 then 1 else (((x2 div 3) mod (x + 1)) div 3))
A029318: 1 0 0 1 0 0 1 0 1 2 0 1 3 0 1 3
(loop(\(x,i).(x div (~3 + (x mod 2))),2,(x + 1)) mod 3)
A236831: 0 0 0 0 1 0 1 1 2 1 2 1 0 2 2 2
loop(\(x,i).(x2 + ~2x),1,(12x + 12))
A305072: 120 528 1224 2208 3480 5040 6888 9024 11448 14160 17160 20448 24024 27888 32040 36480
loop(\(x,i).x2,1,(~12x + ~10))
A017642: 100 484 1156 2116 3364 4900 6724 8836 11236 13924 16900 20164 23716 27556 31684 36100
loop(\(x,i).x2,2,(~12x + ~10))
A017644: 10000 234256 1336336 4477456 11316496 24010000 45212176 78074896 126247696 193877776 285610000 406586896 562448656 759333136 1003875856 1303210000
loop(\(x,i).4x,(2x + 1),(3x + 3))
A193132: 12 384 9216 196608 3932160 75497472 1409286144 25769803776 463856467968 8246337208320 145135534866432 2533274790395904 43910096366862336 756604737398243328 4611686018427387903 4611686018427387903
((3x + 3) + loop(\(x,i).4x,x,4))
A286186: 7 22 73 268 1039 4114 16405 65560 262171 1048606 4194337 16777252 67108903 268435498 1073741869 4294967344
((if x <= 0 then 1 else 6x) - ((x + 1) div 3))
A315538: 1 6 11 17 23 28 34 40 45 51 57 62 68 74 79 85
((if x <= 0 then 1 else 5x) - ((x + 1) div 3))
A301298: 1 5 9 14 19 23 28 33 37 42 47 51 56 61 65 70
((loop(\(x,i).(x2 div 3),2,x) div (x + 1)) mod 3)
A132896-A089789-A034852: 0 0 0 0 1 0 0 1 1 0 0 2 2 2 0 0
((3x + ~3) * loop(\(x,i).4x,(x + ~2),x))
A129532: 0 0 6 72 576 3840 23040 129024 688128 3538944 17694720 86507520 415236096 1962934272 9160359936 42278584320
loop(\(x,i).2x,x,((x3 + ~3x2 + 2x) div 3))
A290031: 0 0 0 16 128 640 2560 8960 28672 86016 245760 675840 1802240 4685824 11927552 29818880
(loop(\(x,i).2x,x,1) div (x3 + ~x2 + 3))
A332281: 0 0 0 0 0 0 0 0 0 0 1 1 2 4 6 10
(3 * loop(\(x,i).(x * (2 + ((~1 + i) mod 3))),x,1))
A076510: 3 6 18 72 144 432 1728 3456 10368 41472 82944 248832 995328 1990656 5971968 23887872
(((x2 + ~1) * loop(\(x,i).2x,(x + ~1),x)) div 3)
A290026: 0 0 4 32 160 640 2240 7168 21504 61440 168960 450560 1171456 2981888 7454720 18350080
(6 * (1 + (if x <= 0 then 1 else 6x)))
A270700: 12 42 78 114 150 186 222 258 294 330 366 402 438 474 510 546
((2 + (if x <= 0 then 1 else (x mod (1 + (x div 3))))) div 3)
A035942: 1 0 0 1 0 1 0 1 1 1 1 1 1 1 2 1
((x + ~1) + (3 * (2 + (if (x mod 3) <= 0 then 2 else 1))))
A004500: 11 9 10 14 12 13 17 15 16 20 18 19 23 21 22 26
(if (~2 + (x div 3)) <= 0 then x else 18)
A171723: 0 1 2 3 4 5 6 7 8 18 18 18 18 18 18 18
loop(\(x,i).(3x + 4),x,18)
A155155: 18 58 178 538 1618 4858 14578 43738 131218 393658 1180978 3542938 10628818 31886458 95659378 286978138
((2 * loop(\(x,i).(x * (x - i)),2,(x + 3))) div 3)
A130810: 16 80 240 560 1120 2016 3360 5280 7920 11440 16016 21840 29120 38080 48960 62016
loop(\(x,i).x2,3,(12x + 6))
A017600: 1679616 11019960576 656100000000 9682651996416 72301961339136 360040606269696 1370114370683136 4304672100000000 11716593810022656 28525864220672256 63527879748485376 131532383853732096
loop(\(x,i).x3,1,(12x + 6))
A017595: 216 5832 27000 74088 157464 287496 474552 729000 1061208 1481544 2000376 2628072 3375000 4251528 5268024 6434856
loop(\(x,i).x3,2,(12x + 6))
A017601: 10077696 198359290368 19683000000000 406671383849472 3904305912313344 23762680013799936 106868920913284608 387420489000000000 1195092568622310912 3251948521156637184 4611686018427387903
loop(\(x,i).x2,1,(~11x + ~6))
A017462: 36 289 784 1521 2500 3721 5184 6889 8836 11025 13456 16129 19044 22201 25600 29241
loop(\(x,i).x2,2,(~11x + ~6))
A017464: 1296 83521 614656 2313441 6250000 13845841 26873856 47458321 78074896 121550625 181063936 260144641 362673936 492884401 655360000 855036081
(3 + (if (x * ((x + 1) mod 5)) <= 0 then 1 else 2))
A117768: 4 5 5 5 4 5 5 5 5 4 5 5 5 5 4 5
loop(\(x,i).x2,1,(3 * ((x2 + 3x + 2) div 2)))
A208138: 9 81 324 900 2025 3969 7056 11664 18225 27225 39204 54756 74529 99225 129600 166464
(if x <= 0 then 1 else ((7x + 6) - (x div 2)))
A258589: 1 13 19 26 32 39 45 52 58 65 71 78 84 91 97 104
(12 * ((2 - (x mod 2)) * (if x <= 0 then 1 else 2)))
A040553: 24 24 48 24 48 24 48 24 48 24 48 24 48 24 48 24
((x3 + 2x) div loop(\(x,i).(x2 + 1),2,3))
A177337: 0 0 0 0 0 1 2 3 5 7 10 13 17 22 27 33
((x + 2) - (if x <= 0 then 1 else (x div ~12)))
A026425: 1 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19
((2 * (if (x + ~2) <= 0 then x else (2 - (x div ~2)))) div 3)
A255574-A230980: 0 0 1 2 2 3 3 4 4 4 4 5 5 6 6 6
(3 * loop(\(x,i).2x,((x mod 2) - (x div ~2)),2))
A112034: 6 24 12 48 24 96 48 192 96 384 192 768 384 1536 768 3072
((if x <= 0 then 1 else x) - ((x - ((x div ~2) mod 2)) div 3))
A156351: 1 1 2 2 3 4 5 5 6 7 7 8 8 9 10 10
(12 * loop(\(x,i).(2x + 4),(x + 1),1))
A304376: 72 192 432 912 1872 3792 7632 15312 30672 61392 122832 245712 491472 982992 1966032 3932112
(6 * (2 + loop(\(x,i).2x,x,5)))
A305153: 42 72 132 252 492 972 1932 3852 7692 15372 30732 61452 122892 245772 491532 983052
(((4x2 + 4) * (if x <= 0 then 1 else 2)) div 3)
A299259: 1 5 13 26 45 69 98 133 173 218 269 325 386 453 525 602
(loop(\(x,i).(x + (x div 2)),x,16) div 3)
A120135: 5 8 12 18 27 40 60 90 135 203 304 456 684 1026 1539 2309
(if (x + ~1) <= 0 then x else (((x + 1) mod 8) mod 3))
A242082-A242081: 0 1 0 1 2 0 1 0 1 2 0 1 2 0 1 0
(loop(\(x,i).(x + (x div 3)),(x + ~2),4) div 3)
A072493: 1 1 1 1 2 2 3 4 5 7 9 12 16 22 29 39
loop(\(x,i).(3x + ~2),2x,12)
A199681: 12 100 892 8020 72172 649540 5845852 52612660 473513932 4261625380 38354628412 345191655700 3106724901292 27960524111620 251644717004572 2264802453041140
(((if (x mod 2) <= 0 then x else 0) - (x div 2)) mod 12)
A074335: 0 0 1 11 2 10 3 9 4 8 5 7 6 6
loop(\(x,i).(5x + ~4),x,12)
A199316: 12 56 276 1376 6876 34376 171876 859376 4296876 21484376 107421876 537109376 2685546876 13427734376 67138671876 335693359376
loop(\(x,i).(x3 + 3x),x,12)
A145186: 12 1764 5489037036 4611686018427387903 4611686018427387903
((4 * (x + (if (~x + 4) <= 0 then x else 1))) div 3)
A013578: 1 2 4 5 10 13 16
((4 * (x + (if (~2 + (x div 2)) <= 0 then 1 else 2))) div 3)
A285385-A026437: 1 2 4 5 6 8 10 12 13 14 16 17 18 20 21 22
((4 * (x + (if (~x + 4) <= 0 then x else 2))) div 3)
A240748: 2 4 5 6 10 13
(6 * loop(\(x,i).(3x + 5),x,2))
A277104: 12 66 228 714 2172 6546 19668 59034 177132 531426 1594308 4782954 14348892 43046706 129140148 387420474
(3 * (~2 + loop(\(x,i).10x,x,2)))
A086577: 0 54 594 5994 59994 599994 5999994 59999994 599999994 5999999994 59999999994 599999999994 5999999999994 59999999999994 599999999999994 5999999999999994
((2 * loop(\(x,i).(x - (2 * (~x + (i mod 2)))),x,2)) div 3)
A321573: 1 2 8 22 68 202 608 1822 5468 16402 49208 147622 442868 1328602 3985808 11957422
((2 * loop(\(x,i).3x,(x + ~1),(x + 2))) div 3)
A199923: 1 2 8 30 108 378 1296 4374 14580 48114 157464 511758 1653372 5314410 17006112 54206982
((loop(\(x,i).(x * (~1 + (x * i))),2,(x + 2)) div 2) div 3)
A006324: 1 11 46 130 295 581 1036 1716 2685 4015 5786 8086 11011 14665 19160 24616
(3 * (if (~4 + (x div 2)) <= 0 then x else (x + 4)))
A323422-A071073: 0 3 6 9 12 15 18 21 24 27 42 45 48 51 54 57
(loop(\(x,i).((x2 + ~x) div 2),2,(2x + 4)) div 3)
A053126: 5 35 126 330 715 1365 2380 3876 5985 8855 12650 17550 23751 31465 40920 52360
loop(\(x,i).x2,3,~11x)
A017396: 0 214358881 54875873536 1406408618241 14048223625216 83733937890625 360040606269696 1235736291547681 3596345248055296 9227446944279201 21435888100000000 45949729863572161 92170395205042176
loop(\(x,i).x2,1,(11x + 2))
A017414: 4 169 576 1225 2116 3249 4624 6241 8100 10201 12544 15129 17956 21025 24336 27889
loop(\(x,i).x2,2,(11x + 2))
A017416: 16 28561 331776 1500625 4477456 10556001 21381376 38950081 65610000 104060401 157351936 228886641 322417936 442050625 592240896 777796321
((2 * (if (~2 + (x div 3)) <= 0 then 2 else (x div 2))) div 3)
A029133: 1 1 1 1 1 1 1 1 1 2 3 3 4 4 4 4
(3 * loop(\(x,i).7x,(x div 2),2))
A117859: 6 6 42 42 294 294 2058 2058 14406 14406 100842 100842 705894 705894 4941258 4941258
(3x - ((~2 + (if (x + ~2) <= 0 then 0 else x)) div 3))
A086824: 1 4 7 9 12 14 17 20 22 25 28 30 33 36 38 41
(loop(\(x,i).(1 + (2 * (x - (2 * (i mod 2))))),x,2) div 3)
A131666: 0 0 1 1 2 3 7 14 29 57 114 227 455 910 1821 3641
loop(\(x,i).3x,(5x + 2),3)
A013828: 27 6561 1594323 387420489 94143178827 22876792454961 5559060566555523 1350851717672992089 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(3 + (x mod (2 + (if ((~x + 2) mod 4) <= 0 then 1 else x))))
A154660: 3 4 5 6 7 8
A333914: 3 4 5 6 7 8 3 10 11 12 4 14 15 16 5 18
(3 * loop(\(x,i).(7x + ~1),x,2))
A199491: 6 39 270 1887 13206 92439 647070 4529487 31706406 221944839 1553613870 10875297087 76127079606 532889557239 3730226900670 26111588304687
loop(\(x,i).x2,3,(9x + 6))
A017240: 1679616 2562890625 110075314176 1406408618241 9682651996416 45767944570401 167961600000000 513798374428641 1370114370683136 3282116715437121 7213895789838336 14774554437890625 28525864220672256
loop(\(x,i).x3,1,(9x + 6))
A017235: 216 3375 13824 35937 74088 132651 216000 328509 474552 658503 884736 1157625 1481544 1860867 2299968 2803221
loop(\(x,i).x3,2,(9x + 6))
A017241: 10077696 38443359375 2641807540224 46411484401953 406671383849472 2334165173090451 10077696000000000 35452087835576229 106868920913284608 285544154243029527 692533995824480256 1551328215978515625
(3 + ((x * ((if (x + ~2) <= 0 then 1 else x) mod 3)) div 2))
A254279: 3 3 4 3 5 8 3
((if x <= 0 then 1 else x) - ((2 * (~x + (x div 3))) div 3))
A289026: 1 2 4 5 6 8 9 11 12 13 15 17 18 19 21 22
((x + ~2) + loop(\(x,i).x2,((x2 + ~x) div 2),3))
A175980: 1 2 9 6562 4611686018427387903
((x mod (2 + (if ((~x + 1) mod 3) <= 0 then 2 else x))) div 3)
A249858: 0 0 0 1 0 1 2 1 2 3 0 3 4 0 4 5
(3 * loop(\(x,i).(10x + 2),x,2))
A137120: 6 66 666 6666 66666 666666 6666666 66666666 666666666 6666666666 66666666666 666666666666 6666666666666 66666666666666 666666666666666
((loop(\(x,i).((x + 1) * (x + (i * i))),2,x) div 2) div 3)
A132366: 1 6 21 56 125 246 441 736 1161 1750 2541 3576 4901 6566 8625 11136
((loop(\(x,i).(2 + ((x * (x + i)) div 2)),2,x) div 2) div 3)
A274233: 1 1 3 7 14 27 48 80 127 192 280 397 547 736 972 1261
(if (x mod 2) <= 0 then (x + 2) else (3 * ((x + 2) + (x div 2))))
A228967: 2 9 4 18 6 27 8 36 10 45 12 54 14 63 16 72
(if (x + ~12) <= 0 then 1 else ((x + ~2) div 3))
A078490: 1 1 1 1 1 1 1 1 1 1 1 1 1 3 4 4
loop(\(x,i).~11x,2x,3)
A324269: 3 363 43923 5314683 643076643 77812273803 9415285130163 1139249500749723 137849189590716483 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (3 * (2x - (2 mod (~2x + 1)))))
A316320: 1 6 15 27 39 51 63 75 87 99 111 123 135 147 159 171
(6x + loop(\(x,i).6x,x,1))
A221908: 1 12 48 234 1320 7806 46692 279978 1679664 10077750 60466236 362797122 2176782408 13060694094 78364164180 470184984666
(~6x + loop(\(x,i).6x,x,1))
A198396: 1 0 24 198 1272 7746 46620 279894 1679568 10077642 60466116 362796990 2176782264 13060693938 78364164012 470184984486
loop(\(x,i).x5,1,6x)
A016913: 0 7776 248832 1889568 7962624 24300000 60466176 130691232 254803968 459165024 777600000 1252332576 1934917632 2887174368 4182119424 5904900000
(1 + loop(\(x,i).3x,2x,3) - (x mod 2))
A183430: 4 27 244 2187 19684 177147 1594324 14348907 129140164 1162261467 10460353204 94143178827 847288609444 7625597484987 68630377364884 617673396283947
((x + 4) - (if x <= 0 then 1 else ((1 - (x div 2)) div 3)))
A276278: 3 5 6 7 9 10 11 12 13 14 16 17 18 19 20 21
((2 * (x + (if ((x + ~1) mod 3) <= 0 then 1 else x))) div 3)
A338743-A265667: 0 1 2 4 3 6 8 5 10 12 7 14 16 9 18 20
(loop(\(x,i).(x * (2 + i)),(x + ~1),(x2 div 2)) div 3)
A259706: 0 0 2 16 160 1440 15120
(1 - ((x + (if (~2 + (x div 4)) <= 0 then x else 0)) mod 3))
A016310-A016076-A015842-A015686-A015608-A015452-A015218-A015140-A014906-A014750-A014672: 1 ~1 0 1 ~1 0 1 ~1 0 1 ~1 0 1 0 ~1 1
((if (x mod (2 + ((x div 4) mod 2))) <= 0 then 1 else x) mod 3)
A278287: 1 1 1 0 1 2 1 1 1 0 1 2 1 1 2 1
loop(\(x,i).(11x + ~5),x,3)
A199754: 3 28 303 3328 36603 402628 4428903 48717928 535897203 5894869228 64843561503 713279176528 7846070941803 86306780359828 949374583958103 10443120423539128
loop(\(x,i).x3,1,(5x + 3))
A016887: 27 512 2197 5832 12167 21952 35937 54872 79507 110592 148877 195112 250047 314432 389017 474552
loop(\(x,i).x3,2,(5x + 3))
A016893: 19683 134217728 10604499373 198359290368 1801152661463 10578455953408 46411484401953 165216101262848 502592611936843 1352605460594688 3299763591802133 7427658739644928 15633814156853823
loop(\(x,i).(x * (x - i)),2,(5x + 3))
A001512: 24 3024 24024 93024 255024 570024 1113024 1974024 3258024 5085024 7590024 10923024 15249024 20748024 27615024 36060024
(((x + 1) + (2 * (if (x + ~2) <= 0 then 2 else (x div 2)))) div 3)
A086936: 1 2 2 2 3 3 4 4 5 6 7 7 8 8 9 10
((x + (if (x + ~4) <= 0 then 2 else (x + ~3))) div 3)
A083479: 0 1 1 1 2 2 3 3 4 5 5 6 7 7 8 9
((x + loop(\(x,i).(1 + (x * (i * i))),(x + ~2),1)) div 3)
A327436: 0 0 1 1 4 29
loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,3)
A003409: 3 9 30 105 378 1386 5148 19305 72930 277134 1058148 4056234 15600900 60174900 232676280 901620585
(1 - ((x + (if (~4 + (x div 2)) <= 0 then x else 1)) mod 3))
A016220-A016022-A015956-A015758-A015560-A015428-A015362-A015230-A015032-A014966-A014768-A014636-A014570: 1 ~1 0 1 ~1 0 1 ~1 0 1 ~1 1 0 ~1 1 0
(3 * loop(\(x,i).(1 + ((~x + 2) div (2 + (x div 2)))),2,x))
A073080: 3 3 3 6 6 6 6 6 6 12 12 12 12 12 12 12
((x + (2 * loop(\(x,i).i,(x + ~6),2))) div 3)
A184258: 1 1 2 2 2 3 3 3 4 5 6 7 8 9 10 11
((x + (2 * ((if (x + ~2) <= 0 then 2 else (x + ~2)) div 2))) div 3)
A255573: 0 1 1 1 2 2 3 3 4 5 6 6 7 7 8 9
((~x + (x div ((if (x mod 2) <= 0 then 1 else x) mod 4))) mod 3)
A235127: 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 2
((x + 2) - (if x <= 0 then 1 else ((~x + (x mod 4)) div 3)))
A120519: 1 3 4 5 8 9 10 11 13 14 15 16 18 19 20 21
(~3 + loop(\(x,i).(2x2 + 1),(2x + 4),x))
A282021: 720 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + (2x div (1 + i))),x,3)
A033876: 3 15 70 315 1386 6006 25740 109395 461890 1939938 8112468 33801950 140408100 581690700 2404321560 9917826435
loop(\(x,i).(4x + ((x + 1) mod 4)),x,3)
A037758: 3 12 49 198 795 3180 12721 50886 203547 814188 3256753 13027014 52108059 208432236 833728945 3334915782
loop(\(x,i).((x * ((x + ~1) + (2 * (i mod 2)))) div 2),x,3)
A110809: 3 6 15 120 7140 25493370 324955944231765 4611686018427387903 4611686018427387903 4611686018427387903
(((x2 + 2x) * loop(\(x,i).x2,2,(x + 1))) div 3)
A245828: 0 16 216 1280 5000 15120 38416 86016 174960 330000 585640 988416 1599416 2497040 3780000 5570560
(3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A008864: 3 4 6 8 12 14 18 20 24 30 32 38 42 44 48 54
(3 + compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x))
A135731: 3 6 8 12 14 18 20 24 30 32 38 42 44 48 54 60
(loop(\(x,i).((x2 + ~x) div 2),2,(x2 + 2x)) div 3)
A189345: 0 1 126 1820 12650 58905 211876 635376 1663740 3921225 8495410 17178876 32795126 59626385 103962600 174792640
(loop(\(x,i).(3x * (1 + i)),(x + ~2),x) div 3)
A052678: 0 0 0 6 72 1080 19440 408240 9797760 264539520 7936185600 261894124800 9428188492800 367699351219200 15443372751206400 694951773804288000
(loop(\(x,i).((x + ~1) + (x div 4)),(x div 2),x) div 3)
A241317: 0 0 0 0 1 1 2 2 4 4 6 7 10 11 15 17
loop(\(x,i).((2x * (~1 + (2 * i))) div (2 + i)),x,3)
A007054: 3 2 3 6 14 36 99 286 858 2652 8398 27132 89148 297160 1002915 3421710
loop(\(x,i).((x2 div 2) div 5),2,(x + ~3))
A338335: 0 0 0 0 0 0 0 0 0 0 1 3 6 10 14 19
(loop(\(x,i).~x,x,(~1 + (x mod 3))) * (x div 3))
A160706: 0 0 0 1 0 ~1 ~2 0 2 3 0 ~3 ~4 0 4 5
(if (~2 + ((x div 2) mod 5)) <= 0 then 1 else (x div 3))
A106795: 1 1 1 1 1 1 2 2 2 3 1 1 1 1 1 1
((2x + 2) + (if x <= 0 then 1 else (x div 3)) - (x mod 2))
A049626: 3 3 6 8 11 12 16 17 20 22 25 26 30 31 34 36
(x3 - loop(\(x,i).x3,1,(x div 3)))
A213039: 0 1 8 26 63 124 208 335 504 702 973 1304 1664 2133 2680 3250
(x - ((if (~2 + (x div 3)) <= 0 then 0 else 2) + (x div 3)))
A065361: 0 1 2 2 3 4 4 5 6 4 5 6 6 7 8 8
loop(\(x,i).(x + 2),(~2 + ((x + ~2) div 3)),(x div 3))
A035680: 0 0 0 1 1 1 2 2 2 3 3 5 6 6 8 9
((if x <= 0 then 1 else ((x2 + 3x) div 2)) - (x div 3))
A111097: 1 2 5 8 13 19 25 33 42 51 62 74 86 100 115 130
(2x + ((if (x mod 3) <= 0 then 2 else 1) + (x div 3)))
A047370: 2 3 5 9 10 12 16 17 19 23 24 26 30 31 33 37
(x + ((if ((x div 2) mod 3) <= 0 then 0 else 1) + (x div 3)))
A047585: 0 1 3 5 6 7 8 9 11 13 14 15 16 17 19 21
(x + ((if (x + ~2) <= 0 then 2 else 8) + (x div 3)))
A285618: 2 3 4 12 13 14 16 17 18 20 21 22 24 25 26 28
(x + loop(\(x,i).2x,(x + ~1),(x mod 2)) - (x div 3))
A266479: 0 2 2 6 3 20 4
((if (~2 + (x div 3)) <= 0 then 0 else 3) + (x mod 3))
A163325: 0 1 2 0 1 2 0 1 2 3 4 5 3 4 5 3
(loop(\(x,i).((x2 + x) + (i mod 2)),x,1) + (x mod 3))
A111266: 1 4 14 157
(2x + (if (~2 + (x div 2)) <= 0 then 1 else 2) - (x mod 3))
A246440: 1 2 3 7 8 9 14 15 16 20 21 22 26 27 28 32
loop(\(x,i).(3 * ((x + ~1) mod 4)),x,(x mod 3))
A021147: 0 0 6 9 9 3 0 0 6 9 9 3 0 0 6 9
(if x <= 0 then 1 else (8x * (x - (x mod 3))))
A030025: 1 0 0 72 96
loop(\(x,i).(11x + 5),x,3)
A199025: 3 38 423 4658 51243 563678 6200463 68205098 750256083 8252816918 90780986103 998590847138 10984499318523 120829492503758 1329124417541343 14620368592954778
loop(\(x,i).(x + (2x div (1 + (2 * (i mod 2))))),x,3)
A163114: 3 5 15 25 75 125 375 625 1875 3125 9375 15625 46875 78125 234375 390625
(3x * loop(\(x,i).x3,2,3x))
A016774: 0 59049 60466176 3486784401 61917364224 576650390625 3570467226624 16679880978201 63403380965376 205891132094649 590490000000000 1531578985264449 3656158440062976 8140406085191601 17080198121677824
loop(\(x,i).(x + ((4x + 8) div (1 + i))),x,3)
A166805: 3 13 33 68 124 208 328 493 713 999 1363 1818 2378 3058 3874 4843
((x + 2) - (if (x + ~1) <= 0 then 1 else ((~x2 + 2x) div 3)))
A231408: 1 2 4 6 9
A156022: 1 2 4 6 9 12 16 21 26 32 39 46 54 63 72 82
loop(\(x,i).((2x div (1 + i)) - (x * (2 + i))),x,3)
A238474: 3 ~6 20 ~90 504 ~3360 25920 ~226800 2217600 ~23950080 283046400 ~3632428800 50295168000 ~747242496000 11856247603200 ~200074178304000
(loop(\(x,i).(4x - (x div 2)),2,x2) div 3)
A256322: 0 4 16 37 65 102 147 200 261 331 408 494 588 690 800 919
loop(\(x,i).(x4 + 2x3 + 2x),x2,3)
A255190: 3 141 4611686018427387903
(1 + (2 * (if ((x + ~1) mod 9) <= 0 then 1 else x)))
A160144: 1 3 5 7 9 11 13 15 17 19 3 23 25 27 29 31
(1 + (2 * loop(\(x,i).(x + 3),(~1 + (x div 3)),x)))
A039578-A033032: 1 3 5 7 9 11 19 21 23 31 33 35 43 45 47 55
(~1 + loop(\(x,i).(~1 + (6x div (1 + i))),x,2))
A331052: 1 4 8 11 12 11 8 4 1
(1 + (if x <= 0 then 1 else (2 * (x + ((x div 2) div 5)))))
A324697: 2 3 5 7 9 11 13 15 17 19 23 25 27 29 31 33
loop(\(x,i).6x,(5x + 2),1)
A013839: 36 279936 2176782336 16926659444736 131621703842267136 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).8x,(5x + 2),1)
A013847: 64 2097152 68719476736 2251799813685248 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).5x,(5x + 2),1)
A013835: 25 78125 244140625 762939453125 2384185791015625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,3,(10x + 1))
A017288: 1 214358881 37822859361 852891037441 7984925229121 45767944570401 191707312997281 645753531245761 1853020188851841 4702525276151521 10828567056280801 23045377697175681 45949729863572161
loop(\(x,i).x3,1,(10x + 1))
A017283: 1 1331 9261 29791 68921 132651 226981 357911 531441 753571 1030301 1367631 1771561 2248091 2803221 3442951
loop(\(x,i).x3,2,(10x + 1))
A017289: 1 2357947691 794280046581 26439622160671 327381934393961 2334165173090451 11694146092834141 45848500718449031 150094635296999121 427929800129788411 1093685272684360901 2558036924386500591
(1 + (2 * loop(\(x,i).(2x + ~4),(x + ~5),x)))
A152484: 1 3 5 7 9 11 17 33
(1 + (if x <= 0 then 1 else (8x3 + ~2x)))
A065397: 2 7 61 211
(~1 + loop(\(x,i).(4x - ((~1 + i) mod 3)),x,2))
A037611: 1 7 30 121 487 1950 7801 31207 124830 499321 1997287 7989150 31956601 127826407 511305630 2045222521
loop(\(x,i).12x,(3x + 2),1)
A013751: 144 248832 429981696 743008370688 1283918464548864 2218611106740436992 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((3x + 2) * loop(\(x,i).2x2,2,2)))
A229855: 257 641 1025 1409 1793 2177 2561 2945 3329 3713 4097 4481 4865 5249 5633 6017
loop(\(x,i).10x,(3x + 2),1)
A013747: 100 100000 100000000 100000000000 100000000000000 100000000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).7x,(3x + 2),1)
A013741: 49 16807 5764801 1977326743 678223072849 232630513987207 79792266297612001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(~1 + ((x * (~1 + (2 * i))) + (x div 2))),x,2))
A211179: 1 1 5 31 238
(1 + (2 * compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x)))
A076274: 1 3 5 9 13 21 25 33 37 45 57 61 73 81 85 93
(1 + ((x * loop(\(x,i).x3,(x + 1),(x + 1))) div 2))
A308675-A308672: 1 257 7625597484988 4611686018427387903 4611686018427387903
loop(\(x,i).4x,(10x + 8),1)
A013881: 65536 68719476736 72057594037927936 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(10x + 7))
A017354: 49 289 729 1369 2209 3249 4489 5929 7569 9409 11449 13689 16129 18769 21609 24649
loop(\(x,i).x2,2,(10x + 7))
A017356: 2401 83521 531441 1874161 4879681 10556001 20151121 35153041 57289761 88529281 131079601 187388721 260144641 352275361 466948881 607573201
loop(\(x,i).3x,(10x + 8),1)
A013853: 6561 387420489 22876792454961 1350851717672992089 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div (2 - (x mod 2))),x,(1 + ((x2 + x) div 2)))
A213671: 1 1 1 7 11 1 11 29 37 23 7 67 79 23 53 121
(1 + (loop(\(x,i).(~1 + (x * (2 - (i mod 2)))),(x + ~1),x) div 2))
A330442: 1 1 1 2 3 6 8 18
(1 + (2 * loop(\(x,i).(x + (2 * (i * i)) - i),(x + ~1),x)))
A161707: 1 3 7 21 53 111 203 337 521 763 1071 1453 1917 2471 3123 3881
loop(\(x,i).10x,((x2 + ~x) div 2),1)
A110147: 1 1 10 1000 1000000 10000000000 1000000000000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).7x,((x2 + ~x) div 2),1)
A109493: 1 1 7 343 117649 282475249 4747561509943 558545864083284007 4611686018427387903 4611686018427387903 4611686018427387903
((x + ~1) - (2 * ((x div 8) - (if x <= 0 then 1 else x))))
A276889: 1 2 5 8 11 14 17 20 21 24 27 30 33 36 39 42
((2x + 1) - (((x div 4) - (if x <= 0 then 1 else x)) div 2))
A184978: 2 4 6 9 11
A184627: 2 4 6 9 11 13 16 18 20 23 25 28 30 32 35 37
(1 + ((((x + 2) + (2 * (x mod 2))) * (if x <= 0 then 1 else x)) div 2))
A020607: 2 3 5 11 13 23
(~1 + (2 * (((x + 2) + (x div 3)) * (if x <= 0 then 1 else x))))
A089485: 3 5 15 35 55
(~1 + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,2))
A131428: 1 1 3 9 27 83 263 857 2859 9723 33591 117571 416023 1485799 5348879 19389689
((2x + 1) - ((~x + (if (~2 + (x div 2)) <= 0 then 0 else 2)) div 2))
A231407: 1 4 6
A234373: 1 4 6 9 11 14 15 18 20 23
(1 + (2 * (if ((x + 2) mod 9) <= 0 then 2 else x)))
A056617: 1 3 5 7 9 11 13 5 17 19 21 23 25 27 29 31
((1 + (x div 2)) div (1 + (if (~2 + (x div 3)) <= 0 then x else 2)))
A244463: 1 0 0 0 0 0 0 0 0 1 2 2 2 2 2 2
(1 + ((x * loop(\(x,i).(3x + ~1),(x + 1),2)) div 2))
A212337: 1 8 42 184 731 2736 9844 34448 118101 398584 1328606 4384392 14348911 46633952 150663528 484275616
(~1 + (2 * (x + (if x <= 0 then 1 else 20))))
A073921: 1 41 43 45 47
(~1 + (2 * (x + (if (x + ~3) <= 0 then 1 else 8))))
A269721: 1 3 5 7 23 25
(1 + ((x + (x div (2 + ((if (x mod 2) <= 0 then 2 else x) div 2)))) div 2))
A086335: 1 1 2 3 3 4 5 5 6 6 7 7 9 8 10 9
(x + (((x - ((x div 2) mod 2)) div 2) + (if (~x + 2) <= 0 then 2 else 1)))
A263800: 1 2 4 6 8 9 10
A065090: 1 2 4 6 8 9 10 12 14 15 16 18 20 21 22 24
(1 + ((x + (loop(\(x,i).(x2 + ~1),(x div 2),x) div 2)) div 2))
A242737: 1 1 2 4 59
(1 + (2 * compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A131426: 1 3 7 11 19 23 31 35 43 55 59 71 79 83 91 103
(1 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) div 2))
A130290: 1 1 2 3 5 6 8 9 11 14 15 18 20 21 23 26
(~1 + loop(\(x,i).(2x + (3 * (i * (1 + i)))),x,2))
A257448: 1 9 37 111 283 657 1441 3051 6319 12909 26149 52695 105859 212265 425161 851043
(1 - (3 mod (1 + (x mod 2) - loop(\(x,i).2x,x,2))))
A290073: 1 2 5 12 29 60 125 252 509 1020 2045 4092 8189 16380 32765 65532
(1 + (2 * loop(\(x,i).(x + (2 * (i * (1 + i)))),2x,x)))
A015219: 1 35 165 455 969 1771 2925 4495 6545 9139 12341 16215 20825 26235 32509 39711
(1 + (2 * (if ((x + ~2) mod 5) <= 0 then (x mod 2) else x)))
A033465: 1 3 1 7 9 11 13 3 17 19 21 23 1 27 29 31
(~1 + loop(\(x,i).(x + (2 * i) - (x div (1 + (2 * i)))),x,2))
A283733: 1 3 7 12 19 28 38 50 63 78 95 113 133 155 178 203
(if ((x + 2) mod (2 - (x mod ~4))) <= 0 then (x + 2) else 1)
A088140: 2 1 4 1 6 1 8 9 10 1 12 1 14 15 16 1
loop(\(x,i).2x,x,(x2 + 8x + 13))
A098385: 13 44 132 368 976 2496 6208 15104 36096 84992 197632 454656 1036288 2342912 5259264 11730944
(1 + ((x + 2) * loop(\(x,i).(2x + 1),x,(x + 4))))
A250652: 9 34 109 316 859 2234 5625 13816 33271 78838 184309 425972 974835 2211826 4980721 11141104
loop(\(x,i).2x,((4x - (x div 2)) div (x + 2)),1)
A164632: 1 2 2 4 4 4 4 4 4 4 4 8 8 8 8 8
loop(\(x,i).(x4 + x3 + ~2x2),1,(x + 3))
A027621: 90 288 700 1440 2646 4480 7128 10800 15730 22176 30420 40768 53550 69120 87856 110160
loop(\(x,i).(2x + 8),6,(x + 3))
A157435: 696 760 824 888 952 1016 1080 1144 1208 1272 1336 1400 1464 1528 1592 1656
(if ((x + ~1) mod 8) <= 0 then (x2 div (x + 2)) else 1)
A117825: 1 0 1 1 1 1 1 1 1 7 1 1 1 1 1 1
loop(\(x,i).(x - ((~1 + (x div ~2)) div 3)),(x + ~2),1)
A266744: 1 1 1 2 3 4 5 7 9 11 14 17 21 25 30 36
loop(\(x,i).(2x4 + ~x2 + 2),(x + ~2),1)
A327058: 1 1 1 3 155
loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + ~2),1)
A120588: 1 1 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440
loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),2x,1)
A002458: 1 10 126 1716 24310 352716 5200300 77558760 1166803110 17672631900 269128937220 4116715363800 63205303218876 973469712824056 15033633249770520 232714176627630544
loop(\(x,i).(4x - ((2 * i) div (x + 1))),2x,1)
A196664: 1 11 176 2816 45056 720896 11534336 184549376 2952790016 47244640256 755914244096 12094627905536 193514046488576 3096224743817216 49539595901075456 792633534417207296
loop(\(x,i).((2 * (x - (2x * i))) div (1 + i)),2x,1)
A048990: 1 2 14 132 1430 16796 208012 2674440 35357670 477638700 6564120420 91482563640 1289904147324 18367353072152 263747951750360 3814986502092304
loop(\(x,i).((10x + 1) + i),2x,1)
A095761: 1 123 12345 1234567 123456789 12345679011 1234567901233 123456790123455 12345679012345677 1234567901234567899 4611686018427387903 4611686018427387903
loop(\(x,i).((2x * (4 + i)) div (1 + i)),2x,1)
A054329: 1 20 224 1920 14080 93184 573440 3342336 18677760 100925440 530579456 2726297600 13740539904 68115496960 332859965440 1606317768704
((~2x + ~1) + loop(\(x,i).x3,(x2 + 1),2))
A224469: 7 509 4611686018427387903 4611686018427387903
((2x + 1) + (if (~4 + (x div 2)) <= 0 then 1 else 4))
A251237: 2 4 6 8 10 12 14 16 18 20 25 27 29 31 33 35
loop(\(x,i).((6 * (x mod 2)) - (x div 2)),2x,1)
A117378: 1 ~3 ~4 ~1 3 4 1 ~3 ~4 ~1 3 4 1 ~3 ~4 ~1
loop(\(x,i).3x,(x div 2),((2x + 1) + (x mod 2)))
A203231: 1 4 15 24 81 108 351 432 1377 1620 5103 5832 18225 20412 63423 69984
loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),2x,1)
A024492: 1 5 42 429 4862 58786 742900 9694845 129644790 1767263190 24466267020 343059613650 4861946401452 69533550916004 1002242216651368 14544636039226909
(loop(\(x,i).(x * i),(x - (x div 3)),1) mod (2x + 1))
A283362: 0 1 2 2 6 2 11 0 6 17 0 1 20 0 1 2
((~1 + loop(\(x,i).4x,x,4)) div (2x + 1))
A191636: 3 5 12 36 113 372 1260 4369 15420 55188 199728 729444 2684354 9942053 37025580 138547332
((2x + 1) * loop(\(x,i).(2 * (x + (x div 2))),x,3))
A268633: 3 24 120 504 1944 7128 25272 87480 297432 997272 3306744 10865016 35429400 114791256 369882936 1186176312
(loop(\(x,i).(x - (2x * i)),2x,1) div (2x + 1))
A035319: 1 1 21 1485 225225 59520825 24325703325 14230536445125 11288163762500625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).x2,3,(2x + 1)) div (2x + 1))
A016759: 1 2187 78125 823543 4782969 19487171 62748517 170859375 410338673 893871739 1801088541 3404825447 6103515625 10460353203 17249876309 27512614111
((4x2 + 4x + 1) * ((if x <= 0 then 1 else x) mod 2))
A270010: 1 9 0 49 0 121 0 225 0 361 0 529 0 729 0 961
((2x + 1) * loop(\(x,i).x3,2,(2x + 1)))
A016762: 1 59049 9765625 282475249 3486784401 25937424601 137858491849 576650390625 2015993900449 6131066257801 16679880978201 41426511213649 95367431640625 205891132094649 420707233300201 819628286980801
loop(\(x,i).5x,(2x + 1),(2x + 1))
A072172: 5 375 15625 546875 17578125 537109375 15869140625 457763671875 12969970703125 362396240234375 10013580322265625 274181365966796875 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,((2x + 1) * ((~x + ~1) + (x mod 2))))
A014736: 1 9 225 441 2025 3025 8281 11025 23409 29241 53361 64009 105625 123201 189225 216225
loop(\(x,i).((2x2 + x) div (1 + i)),2,(2x + 1))
A060541: 1 70 495 1820 4845 10626 20475 35960 58905 91390 135751 194580 270725 367290 487635 635376
((4x + 2) * loop(\(x,i).3x,2x,2))
A269270: 4 108 1620 20412 236196 2598156 27634932 286978140 2927177028 29443957164 292889889684 2887057484028 28242953648100 274521509459532 2653707924775476 25530500379736476
((2x + 1) * (loop(\(x,i).4x,x,(x + 2)) div 2))
A002698: 1 18 160 1120 6912 39424 212992 1105920 5570560 27394048 132120576 627048448 2936012800 13589544960 62277025792 282930970624
((2x + 1) * (~2 + loop(\(x,i).(x2 + x + 1),2,x)))
A008515: 1 33 275 1267 4149 10901 24583 49575 91817 159049 261051 409883 620125 909117 1297199 1807951
((2x + 1) + loop(\(x,i).(x - ((x div 2) div (1 + i))),2,x))
A184911: 1 4 7 10 12 15 18 20 22 25 28 31 33 36 39 41
loop(\(x,i).(x + (x2 div (x + 3))),x,(2x + 1))
A306349: 1 4 13 35 99
loop(\(x,i).(x * (1 + (2 * (4 + (i mod 2))))),2x,1)
A327926: 1 99 9801 970299 96059601 9509900499 941480149401 93206534790699 9227446944279201 913517247483640899 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (2 * ((x * i) div 5))),(x div 2),1)
A147236-A146812-A146687-A146655-A146599: 1 1 1 1 1 1 1 1 1 1 3 3 7 7 19 19
loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x div 2),1)
A128015: 1 1 3 3 10 10 35 35 126 126 462 462 1716 1716 6435 6435
(if (x + ~2) <= 0 then (20 - (x div 2)) else 1)
A278831: 20 20 19 1 1 1 1 1 1 1 1 1 1 1 1 1
(if (2 - (x mod (2 + ((~x + 2) mod 4)))) <= 0 then (x div 2) else 1)
A111957: 1 1 1 1 1 2 1 3 1 1 1 1 1 1 1 1
(1 + ((x mod ((if ((x div 2) mod 2) <= 0 then 2 else x) div 2)) * (x div 2)))
A063928: 1 1 1 1 1 1 1 4 1 1 1 6 1 1 1 8
(x div (1 - ((~x2 + x) div loop(\(x,i).2x,(x div 2),1))))
A113788: 0 1 1 0 1 0 1 1 1 1 2 2 3 3 4 5
((1 + (if (x mod 2) <= 0 then (x div 2) else ~2)) * (1 + (x div 2)))
A051494: 1 ~1 4 ~2 9 ~3 16 ~4 25 ~5 36 ~6 49 ~7 64 ~8
loop(\(x,i).x2,1,((2x + 3) * (1 + (x div 2))))
A051515: 9 25 196 324 1089 1521 3600 4624 9025 11025 19044 22500 35721 41209 61504 69696
((if ((x div 2) mod 2) <= 0 then 8 else 1) mod (1 + (x div 2)))
A064894: 0 0 1 1 2 2 1 1 3 3 1 1 1 1 1 1
(loop(\(x,i).(x * i),x,(1 + (2 * (x div 2)))) div (1 + (x div 2)))
A229244: 1 1 3 9 40 200 1260 8820 72576 653184 6652800 73180800 889574400 11564467200 163459296000 2451889440000
((1 + (x * (if (x + ~2) <= 0 then x else (x + 1)))) div (1 + (x div 2)))
A079811: 1 2 2 6 7 10 10
((if (x mod 2) <= 0 then 1 else 10) * (1 + (x div 2)))
A173237: 1 10 2 20 3 30 4 40 5 50 6 60 7 70 8 80
(loop(\(x,i).x3,1,((x + 1) div 2)) * (1 + (x div 2)))
A212765: 0 1 2 16 24 81 108 256 320 625 750 1296 1512 2401 2744 4096
(loop(\(x,i).2x,((x + ~1) div 2),(x div 2)) * (1 + (x div 2)))
A330592: 0 0 2 4 12 24 48 96 160 320 480 960 1344 2688 3584 7168
(1 + (((x mod 8) mod (if x <= 0 then 1 else x)) + (x div 2)))
A029027: 1 1 2 2 3 3 4 4 5 6 8 9 11 12 14 15
(2 - ((if (x mod (2 + (x mod 2))) <= 0 then 2 else x) div (1 + (x div 2))))
A072491: 0 1 1 1 2 1 2 1 2 2 2 1 2 1 2 2
((x + (if (x + ~2) <= 0 then 1 else (x2 div 2))) * (1 + (x div 2)))
A283438: 1 2 6 14 36
loop(\(x,i).(x * (~1 + (i + (2 * (i mod 2))))),x,(1 + (x div 2)))
A155519: 1 2 4 16 72 432 2880 23040 201600 2016000 21772800 261273600 3353011200 46942156800 697426329600 11158821273600
loop(\(x,i).(x * ((2x - (i mod 2)) mod (1 + i))),(x div 2),1)
A139550: 1 1 1 1 2 2 6 6 12 12 60 60 60 60 420 420
(1 + ((2x div (1 + (if (x mod 2) <= 0 then 2 else 0))) + (x mod 2)))
A026209: 1 4 2 8 3 12 5 16 6 20 7 24 9 28 10 32
(1 + ((if (~2 + (x mod 5)) <= 0 then 2 else 1) * (x mod 2)))
A227339: 1 3 1 2 1 3 1 3 1 2 1 3 1 2 1 3
(~1 + (((2x + 1) * (if (x mod 2) <= 0 then 2 else x)) + (x mod 2)))
A330987: 1 3 9 21 17 55 25 105 33 171 41 253 49 351 57 465
(1 + ((if (~1 + (x mod 5)) <= 0 then 1 else 2) * (x mod 2)))
A108103: 1 2 1 3 1 2 1 3 1 3 1 2 1 3 1 2
(~1 + (if (x mod 14) <= 0 then 2 else (x mod 2)))
A318657: 1 0 ~1 0 ~1 0 ~1 0 ~1 0 ~1 0 ~1 0 1 0
(if x <= 0 then 1 else (1 + (2 * ((x + ~1) mod 4)) - (x mod 2)))
A173014: 1 0 3 4 7 0 3 4 7 0 3 4 7 0 3 4
(~1 + (if (((x mod 3) * (x div 2)) mod 2) <= 0 then 2 else (x mod 2)))
A077010: 1 1 1 1 1 1 1 0 1 1 ~1 1 1 1 1 1
(~1 + loop(\(x,i).(2x + 4),((x + 1) div 2),(2 - (x mod 2))))
A058918: 1 5 7 15 19 35
A079360: 1 5 7 15 19 35 43 75 91 155 187 315 379 635 763 1275
(~1 + loop(\(x,i).(4 * (x - (i mod 2))),x,2) - (x mod 2))
A126019: 1 2 15 58 239 954 3823 15290 61167 244666 978671 3914682 15658735 62634938 250539759 1002159034
(1 + loop(\(x,i).(5x + 2),(x div 2),(x mod 2)))
A131959: 1 2 3 8
A294566: 1 2 3 8 13 38 63 188 313 938 1563 4688 7813 23438 39063 117188
loop(\(x,i).i,((x + 1) mod 7),(1 + (x mod 2)))
A277545: 1 2 3 4 5 6 1 1 2 3 4 5 6 2 1 2
(loop(\(x,i).(x * (1 + ((1 + i) div 2))),x,1) div (1 + (x mod 2)))
A092187: 1 1 4 6 36 72 576 1440 14400 43200 518400 1814400 25401600 101606400 1625702400 7315660800
loop(\(x,i).8x,((x + 1) div 2),(1 + (x mod 2)))
A164703: 1 16 8 128 64 1024 512 8192 4096 65536 32768 524288 262144 4194304 2097152 33554432
loop(\(x,i).(5x + 2),(x div 2),(1 + (x mod 2)))
A238366: 1 2 7 12 37 62 187 312 937 1562 4687 7812 23437 39062 117187 195312
loop(\(x,i).7x,(x div 2),(1 + (x mod 2)))
A018281: 1 2 7 14 49 98
A018592: 1 2 7 14 49 98 343 686
A123752: 1 2 7 14 49 98 343 686 2401 4802 16807 33614 117649 235298 823543 1647086
(x * ((1 + (if (x mod 3) <= 0 then 0 else 2)) * (1 + (x mod 2))))
A109047: 0 6 6 6 12 30 6 42 24 18 30 66 12 78 42 30
loop(\(x,i).((2x + 1) * (1 + (x mod 2))),x,(1 + (x mod 2)))
A113835: 1 5 13 45 109 365 877 2925 7021 23405 56173 187245 449389 1497965 3595117 11983725
loop(\(x,i).((x + 1) + (x div (1 + (i mod 2)))),x,(1 + (x mod 2)))
A079362: 1 4 5 14 17 44 53 134 161 404 485 1214 1457 3644 4373 10934
((3 * (1 + (if x <= 0 then 2 else x))) - (x div (1 + (x mod 2))))
A157989: 9 6 7 11 11
loop(\(x,i).(x * (1 + (2 * (2 + (i mod 2))))),x,(1 + (x mod 2)))
A182753: 1 14 35 490 1225 17150 42875 600250 1500625 21008750 52521875 735306250 1838265625 25735718750 64339296875 900750156250
(1 + ((if ((x + ~1) mod 5) <= 0 then 1 else x) * (x mod 2)))
A214060: 1 2 1 4 1 6 1 8 1 10 1 2 1 14 1 16
(1 + loop(\(x,i).((x + 1) + (x div (1 + (i mod 2)))),x,(x mod 2)))
A211221: 1 3 4 9 12 27 36 81 108 243 324 729 972 2187 2916 6561
((9x + 36) + (if x <= 0 then 2 else 1))
A295491: 38 46 55
((24x + 8) + (if x <= 0 then 2 else 1))
A063160: 10 33 57 81 105 129 153 177 201 225 249 273 297 321 345 369
(1 + loop(\(x,i).(x * (~1 + (x * (1 + (2 * (1 + i)))))),x,2))
A120563: 3 19 2251
(1 + (loop(\(x,i).(2x + 20),x,x) div 2))
A195858: 1 12 35 83 183 391 823 1719 3575 7415 15351 31735 65527 135159 278519 573431
loop(\(x,i).(2x + 1),(x + ~1),(1 + (x div (x2 + ~2))))
A283592: 1 0 5 7 15 31 63 127 255 511 1023 2047 4095 8191 16383 32767
((2x2 + 1) * (if x <= 0 then 1 else 8x))
A007900: 1 24 144 456 1056 2040 3504 5544 8256 11736 16080 21384 27744 35256 44016 54120
(33 + loop(\(x,i).x2,x,2))
A160021: 35 37 49 289 65569 4294967329 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * loop(\(x,i).(x + (5 * (i * i))),x,x)))
A005902: 1 13 55 147 309 561 923 1415 2057 2869 3871 5083 6525 8217 10179 12431
(1 + loop(\(x,i).(x + ((((2 + i) * (1 + i)) div 2) + i)),x,2))
A027965: 3 7 15 28 47 73 107 150 203 267 343 432 535 653 787 938
(1 + (if ((x + 1) mod (~1 + (2 * (x div 4)))) <= 0 then 0 else x))
A334676: 1 1 1 1 1 1 1 1 1 10 11 1 13 14 1 16
(1 + (x * loop(\(x,i).(10x + 1),x,0)))
A091693: 1 2 23 334 4445 55556 666667 7777778 88888889 1000000000 11111111111 122222222222 1333333333333 14444444444444 155555555555555 1666666666666666
loop(\(x,i).(1 + (3 * (x - ((i mod 3) mod 2)))),x,1)
A077842: 1 1 4 13 37 112 337 1009 3028 9085 27253 81760 245281 735841 2207524 6622573
(1 + loop(\(x,i).i,(x mod (1 + (((x + 1) div 2) div 3))),x))
A223490: 1 2 3 4 5 2 7 2 9 2 11 3 13 2 3 16
(1 + loop(\(x,i).(x + 4),(~1 + ((x + ~2) div 3)),x))
A032977: 1 2 3 4 5 6 7 8 13 14 15 20 21 22 27 28
loop(\(x,i).((7x + 1) - (i mod 2)),x,1)
A033117: 1 7 50 350 2451 17157 120100 840700 5884901 41194307 288360150 2018521050 14129647351 98907531457 692352720200 4846469041400
loop(\(x,i).(2x - (x div (~1 + (3 * (x div 2))))),x,1)
A288135: 1 3 5 9 18 36 72 144 288 576 1152 2304 4608 9216 18432 36864
loop(\(x,i).((6x + 1) + (x mod 3)),x,1)
A037606: 1 8 51 307 1844 11067 66403 398420 2390523 14343139 86058836 516353019 3098118115 18588708692 111532252155 669193512931
(1 + (((x div ~2) mod 2) mod (if (x mod 3) <= 0 then 1 else x)))
A345287: 1 1 2 1 1 2 1 1 1 1 2 1 1 2 2 1
loop(\(x,i).((8x + 1) + (i mod 3)),x,1)
A037608: 1 10 83 665 5322 42579 340633 2725066 21800531 174404249 1395233994 11161871955 89294975641 714359805130 5714878441043 45719027528345
loop(\(x,i).((5x + 1) + (i mod 3)),x,1)
A037605: 1 7 38 191 957 4788 23941 119707 598538 2992691 14963457 74817288 374086441 1870432207 9352161038 46760805191
loop(\(x,i).((2x + 1) - (4 mod (1 + (x div 2)))),x,1)
A147595: 1 3 7 15 27 51 99 195 387 771 1539 3075 6147 12291 24579 49155
loop(\(x,i).(1 + ((2x div (1 + i)) * (1 + (2 * i)))),x,1)
A112849: 1 4 11 36 127 463 1717 6436 24311 92379 352717 1352079 5200301 20058301 77558761 300540196
(1 + compr(\x.(~1 + (loop(\(x,i).(2x + 2),x,1) mod (x + 1))),x))
A033946: 1 2 3 5 7 9 11 13 17 19 23 29 31 37 41 43
(1 + compr(\x.(~1 + (loop(\(x,i).4x,x,1) mod (x + 1))),x))
A307824-A081730: 1 2 3 4 5 7 8 11 13 15 16 17 19 23 29 31
(1 + compr(\x.(x mod (1 + (loop(\(x,i).2x,x,x) mod (x + 1)))),x))
A242418: 1 2 4 6 8 10 14 16 22 26 30 32 34 36 38 46
loop(\(x,i).(~1 + (2x * ((~1 + (2 * i)) * (1 + i)))),x,1)
A100444: 1 3 53 2119 148329 16019531 2467007773 513137616783 138547156531409 47106033220679059 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x3,1,(7x + 1))
A016995: 1 512 3375 10648 24389 46656 79507 125000 185193 262144 357911 474552 614125 778688 970299 1191016
loop(\(x,i).x3,2,(7x + 1))
A017001: 1 134217728 38443359375 1207269217792 14507145975869 101559956668416 502592611936843 1953125000000000 6351461955384057 18014398509481984 45848500718449031 106868920913284608 231616946283203125
loop(\(x,i).((3x + 1) - ((x div 3) mod 2)),x,1)
A033130: 1 4 12 37 112 336 1009 3028 9084 27253 81760 245280 735841 2207524 6622572 19867717
loop(\(x,i).(1 + (2 * ((x2 + x) - (x mod 3)))),x,1)
A309116: 1 3 25 1299
loop(\(x,i).((4x + 1) - ((i mod 3) div 2)),x,1)
A033131: 1 5 20 81 325 1300 5201 20805 83220 332881 1331525 5326100 21304401 85217605 340870420 1363481681
loop(\(x,i).((4x + 1) - ((i mod 3) mod 2)),x,1)
A033122: 1 4 17 69 276 1105 4421 17684 70737 282949 1131796 4527185 18108741 72434964 289739857 1158959429
loop(\(x,i).((14x + 1) + i),x,1)
A014897: 1 16 227 3182 44553 623748 8732479 122254714 1711566005 23961924080 335466937131 4696537119846 65751519677857 920521275490012 12887297856860183 180422169996042578
(1 div (if (2 - (2x mod 9)) <= 0 then x else 1))
A179776: 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0
loop(\(x,i).45x,x,1)
A009989: 1 45 2025 91125 4100625 184528125 8303765625 373669453125 16815125390625 756680642578125 34050628916015625 1532278301220703125 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) - (4 * (~2x + (x div 2)))),x,1)
A037579: 1 10 71 500 3501 24510 171571 1201000 8407001 58849010 411943071 2883601500 20185210501 141296473510 989075314571 6923527202000
loop(\(x,i).((x + ~1) - (4 * (~2x + (x div 2)))),x,1)
A108984: 1 8 55 386 2701 18908 132355 926486 6485401 45397808 317784655 2224492586 15571448101 109000136708 763000956955 5341006698686
loop(\(x,i).((9x + 1) - (i mod 2)),x,1)
A033119: 1 9 82 738 6643 59787 538084 4842756 43584805 392263245 3530369206 31773322854 285959905687 2573639151183 23162752360648 208464771245832
loop(\(x,i).(1 + (2 * (5x + (i mod 2)))),x,1)
A037582: 1 13 131 1313 13131 131313 1313131 13131313 131313131 1313131313 13131313131 131313131313 1313131313131 13131313131313 131313131313131 1313131313131313
loop(\(x,i).(5 * ((x + 1) - (2 * (x mod 2)))),x,1)
A109500: 1 0 5 20 105 520 2605 13020 65105 325520 1627605 8138020 40690105 203450520 1017252605 5086263020
loop(\(x,i).60x,x,1)
A159991: 1 60 3600 216000 12960000 777600000 46656000000 2799360000000 167961600000000 10077696000000000 604661760000000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).50x,x,1)
A165800: 1 50 2500 125000 6250000 312500000 15625000000 781250000000 39062500000000 1953125000000000 97656250000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(10x * (~1 + (2 * i))),x,1)
A221953: 1 10 300 15000 1050000 94500000 10395000000 1351350000000 202702500000000 34459425000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((2x + ~2) + ((x + 2) mod 5)),x,1)
A100455: 1 3 4 7 16 33 64 127 256 513 1024 2047 4096 8193 16384 32767
loop(\(x,i).(x - (((~x + 2) - (i div 2)) div 5)),x,1)
A280909: 1 1 1 1 2 3 4 5 7 9 12 15 19 24 30 37
loop(\(x,i).((x2 + ~x) div 2),1,(5x + ~1))
A080857: 1 6 36 91 171 276 406 561 741 946 1176 1431 1711 2016 2346 2701
loop(\(x,i).(5x * (1 + (2 mod (x + 1)))),x,1)
A091882: 1 5 75 1125 16875 253125 3796875 56953125 854296875 12814453125 192216796875 2883251953125 43248779296875 648731689453125 9730975341796875 145964630126953125
(1 + loop(\(x,i).(x + 6),(x + ~5),x))
A255261: 1 2 3 4 5 6 13 20 27 34 41 48 55 62 69 76
loop(\(x,i).((4x + 1) + ((i mod 3) div 2)),x,1)
A037529: 1 5 22 89 357 1430 5721 22885 91542 366169 1464677 5858710 23434841 93739365 374957462 1499829849
loop(\(x,i).((4x + 1) + ((i mod 3) mod 2)),x,1)
A037537: 1 6 25 101 406 1625 6501 26006 104025 416101 1664406 6657625 26630501 106522006 426088025 1704352101
loop(\(x,i).((5x + 1) + ((x div 2) mod 2)),x,1)
A037530: 1 6 32 161 806 4032 20161 100806 504032 2520161 12600806 63004032 315020161 1575100806 7875504032 39377520161
loop(\(x,i).((4x + 1) + ((i div 3) + i)),x,1)
A141844: 1 6 27 113 458 1839 7365 29470 117891 471577 1886322 7545303 30181229 120724934 482899755 1931599041
(1 + loop(\(x,i).(x + 5),(~3 + (x div 2)),x))
A208530: 1 2 3 4 5 6 7 8 14 15 21 22 28 29 35 36
loop(\(x,i).((6x + 1) + ((x div 2) mod 2)),x,1)
A037531: 1 7 44 265 1591 9548 57289 343735 2062412 12374473 74246839 445481036 2672886217 16037317303 96223903820 577343422921
loop(\(x,i).(3x - (x mod (~3 + (x mod 2)))),x,1)
A037528: 1 4 14 43 130 392 1177 3532 10598 31795 95386 286160 858481 2575444 7726334 23179003
loop(\(x,i).(1 + (3x * i) - (2 * (x mod 2))),x,1)
A000180: 1 2 13 116 1393 20894 376093 7897952 189550849 5117872922 153536187661 5066694192812 182400990941233 7113638646708086 298772823161739613 4611686018427387903
loop(\(x,i).(12x * (~1 + (2 * i))),x,1)
A221955: 1 12 432 25920 2177280 235146240 31039303680 4842131374080 871583647334400 177803064056217600 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x3 * (~1 + (2 * i))),x,1)
A092799: 1 3 243 215233605 4611686018427387903 4611686018427387903
loop(\(x,i).(6x + ((x + 1) mod 3)),x,1)
A037507: 1 8 48 289 1736 10416 62497 374984 2249904 13499425 80996552 485979312 2915875873 17495255240 104971531440 629829188641
loop(\(x,i).(6x + ((x + ~1) mod 3)),x,1)
A037499: 1 6 38 229 1374 8246 49477 296862 1781174 10687045 64122270 384733622 2308401733 13850410398 83102462390 498614774341
loop(\(x,i).(8x + ((1 + i) mod 3)),x,1)
A037509: 1 10 80 641 5130 41040 328321 2626570 21012560 168100481 1344803850 10758430800 86067446401 688539571210 5508316569680 44066532557441
loop(\(x,i).(5x + ((1 + i) mod 3)),x,1)
A037506: 1 7 35 176 882 4410 22051 110257 551285 2756426 13782132 68910660 344553301 1722766507 8613832535 43069162676
loop(\(x,i).(6 * ((x + 1) - (2 * (i mod 2)))),x,1)
A109501: 1 0 6 30 186 1110 6666 39990 239946 1439670 8638026 51828150 310968906 1865813430 11194880586 67169283510
loop(\(x,i).(x + i - ((~1 + i) mod 12)),x,1)
A032948: 1 2 3 4 5 6 7 8 9 10 11 12 13 26 39 52
(~1 + loop(\(x,i).(4 + (x * (4 + i))),3,x))
A033168: 199 409 619 829 1039 1249 1459 1669 1879 2089
loop(\(x,i).((11x + 1) + i),x,1)
A014881: 1 13 146 1610 17715 194871 2143588 23579476 259374245 2853116705 31384283766 345227121438 3797498335831 41772481694155 459497298635720 5054470284992936
loop(\(x,i).(6 * (3x + (x div 2))),x,1)
A285400: 1 18 378 7938 166698 3500658 73513818 1543790178 32419593738 680811468498 14297040838458 300237857607618 6304995009759978 132404895204959538 2780502799304150298 4611686018427387903
loop(\(x,i).(x + (6 * (x mod 2)) - (x div 2)),x,1)
A070405: 1 7 10 5 9 11 12 6 3 8 4 2 1 7 10 5
loop(\(x,i).(6x + ((x + i) mod 3)),x,1)
A037539: 1 8 49 295 1772 10633 63799 382796 2296777 13780663 82683980 496103881 2976623287 17859739724 107158438345 642950630071
loop(\(x,i).(6x + ((x - i) mod 3)),x,1)
A033124: 1 6 37 223 1338 8029 48175 289050 1734301 10405807 62434842 374609053 2247654319 13485925914 80915555485 485493332911
loop(\(x,i).(6x + ((x div ~2) mod 2)),x,1)
A033133: 1 7 42 253 1519 9114 54685 328111 1968666 11811997 70871983 425231898 2551391389 15308348335 91850090010 551100540061
loop(\(x,i).(6x + (((x + ~1) div 2) mod 2)),x,1)
A033142: 1 6 36 217 1302 7812 46873 281238 1687428 10124569 60747414 364484484 2186906905 13121441430 78728648580 472371891481
loop(\(x,i).(6x + ((1 + i) mod 4)),x,1)
A037697: 1 8 51 306 1837 11024 66147 396882 2381293 14287760 85726563 514359378 3086156269 18516937616 111101625699 666609754194
loop(\(x,i).(6x + ((~x + 1) mod 4)),x,1)
A037683: 1 6 39 236 1417 8502 51015 306092 1836553 11019318 66115911 396695468 2380172809 14281036854 85686221127 514117326764
loop(\(x,i).((6x + 2) - ((x div 2) mod 2)),x,1)
A037547: 1 8 50 301 1808 10850 65101 390608 2343650 14061901 84371408 506228450 3037370701 18224224208 109345345250 656072071501
loop(\(x,i).(x - ((0 - (((x div 2) + i) div 2)) div 3)),x,1)
A029001: 1 1 2 3 4 5 7 9 11 14 17 20 24 28 33 38
(1 + loop(\(x,i).(x div (1 + (x mod 2))),(x + 1),3x))
A067745: 1 1 7 5 13 1 19 11 25 7 31 17 37 5 43 23
(loop(\(x,i).3x,x,3) div (3x + 1))
A191628: 3 2 3 8 18 45 115 298 787 2108 5714 15630 43089 119574 333695 935798
(loop(\(x,i).(2 + (x * (i * i))),x,1) div (3x + 1))
A326222: 1 0 2 12 157
loop(\(x,i).x5,1,(3x + 1))
A016781: 1 1024 16807 100000 371293 1048576 2476099 5153632 9765625 17210368 28629151 45435424 69343957 102400000 147008443 205962976
loop(\(x,i).39x,x,1)
A009983: 1 39 1521 59319 2313441 90224199 3518743761 137231006679 5352009260481 208728361158759 8140406085191601 317475837322472439 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) + (if (x + ~2) <= 0 then x else (2 - ((~x + 1) div 3))))
A186350: 1 3 5 7 8 10 11 12 14 15 16 18 19 20 22 23
loop(\(x,i).(8x + ((~x + 1) mod 3)),x,1)
A037501: 1 8 66 529 4232 33858 270865 2166920 17335362 138682897 1109463176 8875705410 71005643281 568045146248 4544361169986 36354889359889
loop(\(x,i).(5x + ((~x + 1) mod 3)),x,1)
A037498: 1 5 27 136 680 3402 17011 85055 425277 2126386 10631930 53159652 265798261 1328991305 6644956527 33224782636
loop(\(x,i).(3 * (x + ((2x * i) div (1 + i)))),x,1)
A034171: 1 6 42 315 2457 19656 160056 1320462 11003850 92432340 781473420 6642524070 56716936290 486145168200 4180848446520 36059817851235
loop(\(x,i).(x - (3x * (2 - (3 * i)))),x,1)
A144829: 1 4 52 1144 35464 1418560 69509440 4031547520 270113683840 20528639971840 1744934397606400 164023833375001600 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(4 div ((x + 2) div loop(\(x,i).(1 + (i div (x + 2))),x,1)))
A136673: 2 1 1 2 1 1 1 1 1 0 1 1 1 0 0 1
((x + ~1) + loop(\(x,i).(x4 + 2x),(x + ~2),1))
A192225: 0 1 2 5
A215797: 0 1 2 5 90
loop(\(x,i).(1 + (2x * ((1 + (2 * (1 + i))) * i))),x,1)
A100445: 1 11 309 16687 1468457 190899411 34361893981 8178130767479 2486151753313617 939765362752547227 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + ((x * (2 + (x * (x mod 2)))) + (x div 2))),x,1)
A089920: 1 4 11 149
(1 + (x * (if (x + ~12) <= 0 then (x mod 2) else 1)))
A327529-A327512: 1 2 1 4 1 6 1 8 1 10 1 12 1 14 15 16
loop(\(x,i).((10x + 1) + (x mod 2)),x,1)
A037487: 1 12 121 1212 12121 121212 1212121 12121212 121212121 1212121212 12121212121 121212121212 1212121212121 12121212121212 121212121212121 1212121212121212
loop(\(x,i).((4x + 1) - (((~1 + i) * i) div 2)),x,1)
A028814: 1 5 20 78 307 1219 4862 19428 77685 310705 1242776 4971050 19884135 79536463 318145762 1272582944
loop(\(x,i).(x * ((2 + i) * (1 + i) * (3 + i))),x,1)
A010797: 1 24 1440 172800 36288000 12192768000 6145155072000 4424511651840000 4380266535321600000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((4x div (1 + i)) * (1 + (2 * i))),x,1)
A069720: 1 6 40 280 2016 14784 109824 823680 6223360 47297536 361181184 2769055744 21300428800 164317593600 1270722723840 9848101109760
loop(\(x,i).(((x * (i * (1 + i))) div 2) * (~1 + (2 * i))),x,1)
A202689: 1 1 9 270 18900 2551500 589396500 214540326000 115851776040000 88626608670600000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * ((x - (2x * i)) * (~1 + (2 * i)))),x,1)
A126934: 1 ~2 36 ~1800 176400 ~28576800 6915585600 ~2337467932800 1051860569760000 ~607975409321280000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((~1 + (4 * i)) * (~1 + (2 * i)))),x,1)
A159605: 1 3 63 3465 363825 62214075 15740160975 5524796502225 2569030373534625 1528573072253101875 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((10x + 1) + (i div 2)),x,1)
A104720: 1 11 112 1122 11223 112233 1122334 11223344 112233445 1122334455 11223344556 112233445566 1122334455667 11223344556677 112233445566778 1122334455667788
loop(\(x,i).((9x + 1) + (i mod 2)),x,1)
A037486: 1 11 100 902 8119 73073 657658 5918924 53270317 479432855 4314895696 38834061266 349506551395 3145558962557 28310030663014 254790275967128
loop(\(x,i).((7x + 1) + (i mod 2)),x,1)
A037484: 1 9 64 450 3151 22059 154414 1080900 7566301 52964109 370748764 2595241350 18166689451 127166826159 890167783114 6231174481800
loop(\(x,i).((x + 1) + (2 * ((x + (x mod 2)) * (~1 + i)))),x,1)
A277565: 1 2 7 40 281 2538
loop(\(x,i).((x + 1) + (x div (4 * (2 + (x mod 2))))),x,1)
A060471-A033060-A003045: 1 2 3 4 5 6 7 8 10 12 14 16 19 21 23 25
loop(\(x,i).((x + 1) + ((x + (x div (2 + i))) div 4)),x,1)
A100673: 1 2 3 4 6 8 11 15 20 26 34 44 56 71 90 114
loop(\(x,i).((x + 1) + (2 * (4x + (x mod 2)))),x,1)
A037581: 1 12 109 984 8857 79716 717445 6457008 58113073 523017660 4707158941 42364430472 381279874249 3431518868244 30883669814197 277953028327776
((x + 1) + (if (x + ~1) <= 0 then x else (1 + (x * (2 + (x mod 2))))))
A106386: 1 3 8 14 14
loop(\(x,i).((x + 1) + (((x div 5) + i) div 2)),x,1)
A231408: 1 2 4 6 9
A114830: 1 2 4 6 9 13 18 24 31 39 48 59 71 85 101 119
(1 + compr(\x.(loop(\(x,i).(2x * i),4,1) mod (x + 1)),x))
A323383: 1 2 3 4 6 8 12
A018425: 1 2 3 4 6 8 12 16 24 32 48 64 96 128 192 384
(1 + loop(\(x,i).(10x + 10),(x + 1),x))
A075858: 11 211 3111 41111 511111 6111111 71111111 811111111 9111111111 101111111111 1111111111111 12111111111111 131111111111111 1411111111111111 15111111111111111 161111111111111111
(1 + compr(\x.(loop(\(x,i).(x * (2 + i)),4,1) mod (x + 1)),x))
A018412: 1 2 3 4 5 6 8 9 10 12 15 18 20 24 30 36
(1 + compr(\x.(loop(\(x,i).2x2,2,3) mod (x + 1)),x))
A018570: 1 2 3 4 6 8 9 12 18 24 27 36 54 72 81 108
(1 + compr(\x.(loop(\(x,i).(x * (x + i)),2,3) mod (x + 1)),x))
A018314: 1 2 3 4 6 7 8 12 14 21 24 28 42 56 84 168
(1 + compr(\x.(loop(\(x,i).(x * (1 + (i div 2))),x,1) mod (x + 1)),x))
A231407: 1 4 6
A174891-A140209-A077091-A018252: 1 4 6 8 9 10 12 14 15 16 18 20 21 22 24 25
(1 + compr(\x.(loop(\(x,i).(x * ((1 + i) div 2)),x,1) mod (x + 1)),x))
A056653: 1 6 8 9 10 12 14 15 16 18 20 21 22 24 25 26
(1 + compr(\x.(loop(\(x,i).x2,2,6) mod (x + 1)),x))
A018452: 1 2 3 4 6 8 9 12 16 18 24 27 36 48 54 72
(1 + compr(\x.(loop(\(x,i).(x2 + x),3,2) mod (x + 1)),x))
A018258: 1 2 3 6 7 14 21 42
A191614: 1 2 3 6 7 14 21 42 43 86 129 258 301 602 903 1806
(1 + compr(\x.(loop(\(x,i).(2x2 + 2x),2,2) mod (x + 1)),x))
A323383: 1 2 3 4 6 8 12
A018387: 1 2 3 4 6 8 12 13 24 26 39 52 78 104 156 312
(1 + (x * ((x + 1) + loop(\(x,i).(x3 + 1),2,2))))
A180919: 1 733 1467 2203 2941 3681 4423 5167 5913 6661 7411 8163 8917 9673 10431 11191
(1 + compr(\x.((2 + loop(\(x,i).x2,4,2)) mod (x + 1)),x))
A018331: 1 2 3 6 9 11 18 22 33 66 99 198
(1 + compr(\x.(loop(\(x,i).(x * (1 + i)),4,2) mod (x + 1)),x))
A067319: 1 2 3 4 5 6 8 10 12
A018350: 1 2 3 4 5 6 8 10 12 15 16 20 24 30 40 48
(1 + compr(\x.(loop(\(x,i).(x * (2 + i)),4,2) mod (x + 1)),x))
A018609: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30
(1 + compr(\x.(loop(\(x,i).(2x2 + 4x),2,2) mod (x + 1)),x))
A344472-A018528: 1 2 3 4 6 8 9 12 16 18 24 32 36 48 64 72
(1 + compr(\x.(loop(\(x,i).(2x * (x + i)),2,2) mod (x + 1)),x))
A018399: 1 2 3 4 6 7 8 12 14 16 21 24 28 42 48 56
(1 + compr(\x.((~2 + loop(\(x,i).x3,2,2)) mod (x + 1)),x))
A018494: 1 2 3 5 6 10 15 17 30 34 51 85 102 170 255 510
(1 + compr(\x.(loop(\(x,i).(x2 + x),2,4) mod (x + 1)),x))
A018444: 1 2 3 4 5 6 7 10 12 14 15 20 21 28 30 35
(1 + compr(\x.(loop(\(x,i).(x2 + 2x),2,4) mod (x + 1)),x))
A323383: 1 2 3 4 6 8 12
A018556: 1 2 3 4 6 8 12 13 16 24 26 39 48 52 78 104
(1 + compr(\x.(loop(\(x,i).(x * (x + i)),2,4) mod (x + 1)),x))
A191535-A100598: 1 2 4 5 8 10
A018457: 1 2 4 5 8 10 11 20 22 40 44 55 88 110 220 440
(1 + compr(\x.(loop(\(x,i).(x * (x - i)),2,4) mod (x + 1)),x))
A067319: 1 2 3 4 5 6 8 10 12
A018293: 1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120
loop(\(x,i).6x,(5x + 4),1)
A013841: 1296 10077696 78364164096 609359740010496 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).8x,(5x + 4),1)
A013849: 4096 134217728 4398046511104 144115188075855872 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).5x,(5x + 4),1)
A013837: 625 1953125 6103515625 19073486328125 59604644775390625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.(loop(\(x,i).(2x2 + x),2,2) mod (x + 1)),x))
A030050: 1 2 3 5 6 7 10 14 15
A194359-A018336: 1 2 3 5 6 7 10 14 15 21 30 35 42 70 105 210
(1 + compr(\x.(1 - (loop(\(x,i).(x2 + 2x),2,2) mod (x + 1))),x))
A085837-A005767: 3 6 7 9 11 12 13 14 15 17 18 19 21 22 23 24
(1 + compr(\x.(loop(\(x,i).(x2 * (x + i)),2,2) mod (x + 1)),x))
A177500: 1 2 3 4 6 7 8 9 12 14 16 18 21 24 28 32
(1 + compr(\x.(loop(\(x,i).(x * (x2 + i)),2,2) mod (x + 1)),x))
A018779: 1 2 3 4 5 6 10 12 15 17 20 30 34 51 60 68
loop(\(x,i).(12x + (2 div (x + 1))),x,1)
A170732-A170694-A170646-A170598-A170550-A170502-A170454-A170406-A170358-A170310-A170262-A170214-A170166-A170118-A170070-A170022-A169554-A169506-A169458-A169410-A169362-A169314-A169266-A169218-A169170-A169122-A169074-A169026-A168978-A168930-A168882-A168834-A168786-A168738-A168690-A167919: 1 13 156 1872 22464 269568 3234816 38817792 465813504 5589762048 67077144576 804925734912 9659108818944 115909305827328 1390911669927936 16690940039135232
loop(\(x,i).(12x - (2 div (x + 1))),x,1)
A196731: 1 11 132 1584 19008 228096 2737152 32845824 394149888 4729798656 56757583872 681091006464 8173092077568 98077104930816 1176925259169792 14123103110037504
loop(\(x,i).(16x + (2 div (x + 1))),x,1)
A170736-A170698-A170650-A170602-A170554-A170506-A170458-A170410-A170362-A170314-A170266-A170218-A170170-A170122-A170074-A170026-A169558-A169510-A169462-A169414-A169366-A169318-A169270-A169222-A169174-A169126-A169078-A169030-A168982-A168934-A168886-A168838-A168790-A168742-A168694-A167926: 1 17 272 4352 69632 1114112 17825792 285212672 4563402752 73014444032 1168231104512 18691697672192 299067162755072 4785074604081152 76561193665298432 1224979098644774912
loop(\(x,i).(10x + (2 div (x + 1))),x,1)
A170692-A170644-A170596-A170548-A170500-A170452-A170404-A170356-A170308-A170260-A170212-A170164-A170116-A170068-A170020-A169552-A169504-A169456-A169408-A169360-A169312-A169264-A169216-A169168-A169120-A169072-A169024-A168976-A168928-A168880-A168832-A168784-A168736-A168688-A167914-A003953: 1 11 110 1100 11000 110000 1100000 11000000 110000000 1100000000 11000000000 110000000000 1100000000000 11000000000000 110000000000000 1100000000000000
(~1 + loop(\(x,i).(5x + 8),2,(x2 + x)))
A281437: 47 97 197 347 547 797 1097 1447 1847 2297 2797 3347 3947 4597 5297 6047
((x + 1) + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))
A086799: 1 3 3 7 5 7 7 15 9 11 11 15 13 15 15 31
loop(\(x,i).((x + 1) + ((2 + (5 * i)) * i)),x,1)
A100179: 1 9 34 86 175 311 504 764 1101 1525 2046 2674 3419 4291 5300 6456
(1 + (x * loop(\(x,i).(x2 + ~x + ~1),(x + ~2),(x + ~1))))
A111799: 1 1 3 4 77
loop(\(x,i).((x + 1) + ((1 + ((~1 + (2 * i)) * i)) * i)),x,1)
A100185: 1 4 19 68 185 416 819 1464 2433 3820 5731 8284 11609 15848 21155 27696
loop(\(x,i).((13x + 1) + i),x,1)
A014896: 1 15 198 2578 33519 435753 5664796 73642356 957350637 12445558291 161792257794 2103299351334 27342891567355 355457590375629 4620948674883192 60072332773481512
loop(\(x,i).((17x + 1) + i),x,1)
A014900: 1 19 326 5546 94287 1602885 27249052 463233892 7874976173 133874594951 2275868114178 38689757941038 657725884997659 11181340044960217 190082780764323704 3231407272993502984
loop(\(x,i).(x - (5x div (~1 - i))),x,1)
A215052: 1 4 11 25 50 92 158 257 400 600 873 1237 1713 2325 3100 4069
loop(\(x,i).((20x + 1) + i),x,1)
A014904: 1 22 443 8864 177285 3545706 70914127 1418282548 28365650969 567313019390 11346260387811 226925207756232 4538504155124653 90770083102493074 1815401662049861495 4611686018427387903
loop(\(x,i).((15x + 1) + i),x,1)
A014898: 1 17 258 3874 58115 871731 13075972 196139588 2942093829 44131407445 661971111686 9929566675302 148943500129543 2234152501943159 33512287529147400 502684312937211016
loop(\(x,i).((18x + 1) + i),x,1)
A014901: 1 20 363 6538 117689 2118408 38131351 686364326 12354557877 222382041796 4002876752339 72051781542114 1296932067758065 23344777219645184 420205989953613327 4611686018427387903
loop(\(x,i).((24x + 1) + i),x,1)
A014913: 1 26 627 15052 361253 8670078 208081879 4993965104 119855162505 2876523900130 69036573603131 1656877766475156 39765066395403757 954361593489690182 4611686018427387903 4611686018427387903
loop(\(x,i).((4x * (~1 + (2 * i))) div (1 + i)),x,1)
A151374: 1 2 8 40 224 1344 8448 54912 366080 2489344 17199104 120393728 852017152 6085836800 43818024960 317680680960
loop(\(x,i).((2x2 * (~1 + (2 * i))) div (1 + i)),x,1)
A003047: 1 1 2 10 280 235200 173859840000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((1 + i) * (1 + (i div 2)) * (1 + i))),x,1)
A203264: 1 4 72 2304 172800 18662400 3657830400 936404582400 379243855872000 189621927936000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x * (1 + i)) - (((x + ~1) + i) div (1 + i))),x,1)
A052169: 1 2 5 19 91 531 3641 28673 254871 2523223 27526069 328018989 4239014627 59043418019 881715042417 14052333488521
loop(\(x,i).(x - (~7x div (1 + i))),x,1)
A215053: 1 5 17 47 113 245 490 919 1634 2778 4546 7198 11074 16611 24363 35022
loop(\(x,i).((4x * (4 + i)) div (1 + i)),x,1)
A036070: 1 10 80 560 3584 21504 122880 675840 3604480 18743296 95420416 477102080 2348810240 11408506880 54760833024 260113956864
loop(\(x,i).((2x * (~1 + (4 * i))) div (1 + i)),x,1)
A048779: 1 3 14 77 462 2926 19228 129789 894102 6258714 44379972 318056466 2299792908 16755634044 122874649656 906200541213
loop(\(x,i).((4x * ((~x + 1) + i)) div (1 + i)),x,1)
A140357: 1 2 2 4 3 6 3 7 6 9 6 12 3 9 14 7
loop(\(x,i).(x * ((1 + (i * i * i)) * i * (1 + i))),x,1)
A055627: 1 4 216 72576
loop(\(x,i).(3x mod 14),x,1)
A070353: 1 3 9 13 11 5 1 3 9 13 11 5 1 3 9 13
loop(\(x,i).(2 * (x - (1 div (~1 + (2 * (i mod 4)))))),x,1)
A139800: 1 0 0 0 2 2 4 8 18 34 68 136 274 546 1092 2184
(if (((x + ~2) div (1 + ((x + ~1) mod 4))) mod 2) <= 0 then x else 1)
A225650: 1 1 2 3 4 1 6 1 1 1 10 1 12 1 14 15
loop(\(x,i).(2 * ((x + 1) - (i mod (2 * (2 - (i mod 2)))))),x,1)
A100088: 1 2 2 4 10 20 38 76 154 308 614 1228 2458 4916 9830 19660
(1 + loop(\(x,i).(x + 3),(~2 + ((x + ~1) div 3)),x))
A134933: 1 2 3 4 5 6 7 8 9 10 14 15 16 20 21 22
loop(\(x,i).(2 * (x - (3 * (~2x + (x mod 2))))),x,1)
A067414: 1 8 112 1568 21952 307328 4302592 60236288 843308032 11806312448 165288374272 2314037239808 32396521357312 453551299002368 6349718186033152 88896054604464128
loop(\(x,i).(2 * (7x - (x div 2))),x,1)
A170733-A170695-A170647-A170599-A170551-A170503-A170455-A170407-A170359-A170311-A170263-A170215-A170167-A170119-A170071-A170023-A169555-A169507-A169459-A169411-A169363-A169315-A169267-A169219-A169171-A169123-A169075-A169027-A168979-A168931-A168883-A168835-A168787-A168739-A168691-A167922: 1 14 182 2366 30758 399854 5198102 67575326 878479238 11420230094 148462991222 1930018885886 25090245516518 326173191714734 4240251492291542 55123269399790046
(1 + loop(\(x,i).(x + 5),(~2 + (x div 3)),x))
A032978: 1 2 3 4 5 6 7 8 9 15 16 17 23 24 25 31
(1 + loop(\(x,i).(~1 + ((~x + ((~x + 2) div 4)) div 2)),2,x))
A255072: 0 1 1 2 2 2 3 4 4 4 4 5 5 5 6 7
(1 + compr(\x.(~2 + (loop(\(x,i).(~2x + 1),x,0) mod (x + 1))),x))
A193622: 1 2 3 5 7 10
A325460: 1 2 3 5 7 10 11 13 14 17 19 22 23 26 29 31
(2 - loop(\(x,i).((2x + ~2) - (4 mod (x + 1))),x,1))
A222011: 1 2 4 8
A026474: 1 2 4 8 15 22 29 36 43 50 57 64 71 78 85 92
(1 + compr(\x.(~2 + (loop(\(x,i).~2x,x,2) mod (x + 1))),x))
A067133: 1 2 3 4 5 6 7 8 11 13 16 17 19 23 29 31
loop(\(x,i).((2x + 2) + ((x div 3) * (1 + i))),x,1)
A045652: 1 4 13 44 160
((x + 1) + loop(\(x,i).((x2 + ~x) div 2),2,(2x + 2)))
A135400: 1 17 108 382 995 2151 4102 7148 11637 17965 26576 37962 52663 71267 94410 122776
(1 + loop(\(x,i).(x - (x div (1 + (5 * i)))),2,x))
A269169: 1 2 3 4 5 6 6 7 8 9 10 11 11 11 12 13
loop(\(x,i).(2 * (x - ((x mod 8) div (1 + i)))),x,1)
A164143: 1 2 4 6 10 20 40 80 160 320 640 1280 2560 5120 10240 20480
loop(\(x,i).(2 * (8x - (x div ~2))),x,1)
A170737-A170699-A170651-A170603-A170555-A170507-A170459-A170411-A170363-A170315-A170267-A170219-A170171-A170123-A170075-A170027-A169559-A169511-A169463-A169415-A169367-A169319-A169271-A169223-A169175-A169127-A169079-A169031-A168983-A168935-A168887-A168839-A168791-A168743-A168695-A167927: 1 18 306 5202 88434 1503378 25557426 434476242 7386096114 125563633938 2134581776946 36287890208082 616894133537394 10487200270135698 178282404592306866 3030800878069216722
((x + 1) + (x div (2 + (if (~2 + (x div 4)) <= 0 then 1 else 2))))
A188292: 1 2 3 5 6 7 9 10 11 13 14 15 16 17 18 19
(if (x - (2 * (2 + (x div (1 + (x mod 4)))))) <= 0 then x else 1)
A160377: 0 1 2 3 4 5 6 1 8 9 10 1 12 13 1 1
loop(\(x,i).(x * i),(15x + 4),1)
A072244: 24 121645100408832000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(8 * ((x + 1) - (2 * (i mod 2)))),x,1)
A093134: 1 0 8 56 456 3640 29128 233016 1864136 14913080 119304648 954437176 7635497416 61083979320 488671834568 3909374676536
loop(\(x,i).(x - (((x div (~2 + (x mod ~2))) div 2) div 2)),x,1)
A242367: 1 2 3 4 5 6 7 8 9 10 12 14 16 18 21 23
loop(\(x,i).i,(x + ((x + ~32) div 2)),1)
A036606: 1 1 1 1 1 1 1 1 1 1 1 1 2 3 5 6
loop(\(x,i).(3x mod 32),x,1)
A070358: 1 3 9 27 17 19 25 11 1 3 9 27 17 19 25 11
loop(\(x,i).29x,x,1)
A009973: 1 29 841 24389 707281 20511149 594823321 17249876309 500246412961 14507145975869 420707233300201 12200509765705829 353814783205469041 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) + loop(\(x,i).x2,1,(x + ~16)))
A260679: 257 227 199 173 149 127 107 89 73 59 47 37 29 23 19 17
loop(\(x,i).(2 * (x - (4 * (~2x + (x mod 2))))),x,1)
A067416: 1 10 180 3240 58320 1049760 18895680 340122240 6122200320 110199605760 1983592903680 35704672266240 642684100792320 11568313814261760 208229648656711680 3748133675820810240
(1 + (if (x mod 2) <= 0 then ((x2 + 2x) div 8) else x))
A106247: 1 2 2 4 4 6 7 8 11 10 16 12 22 14 29 16
((~x + ~1) + (4 * loop(\(x,i).(2 * ((x + 1) + i)),x,2)))
A339196: 7 30 85 204 451 954 1969 4008 8095 16278 32653 65412 130939 262002 524137 1048416
loop(\(x,i).(8x + ((x + 1) mod 4)),x,1)
A037699: 1 10 83 664 5313 42506 340051 2720408 21763265 174106122 1392848979 11142791832 89142334657 713138677258 5705109418067 45640875344536
loop(\(x,i).(8x + ((x + ~1) mod 4)),x,1)
A037685: 1 8 67 538 4305 34440 275523 2204186 17633489 141067912 1128543299 9028346394 72226771153 577814169224 4622513353795 36980106830362
(1 + loop(\(x,i).(x + 8),(~4 + (x div 2)),x))
A343131: 1 2 3 4 5 6 7 8 9 10 19 20 29 30 39 40
((x + 1) + (if (~2 + (x div 5)) <= 0 then 1 else 4))
A342478: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 20
((x + 1) + (x mod (if (~2 + (x div 4)) <= 0 then 1 else 4)))
A346288-A138389-A033065-A032963: 1 2 3 4 5 6 7 8 9 10 11 12 13 15 17 19
loop(\(x,i).(5x + ((1 + i) mod 4)),x,1)
A037696: 1 7 38 190 951 4757 23788 118940 594701 2973507 14867538 74337690 371688451 1858442257 9292211288 46461056440
loop(\(x,i).44x,x,1)
A009988: 1 44 1936 85184 3748096 164916224 7256313856 319277809664 14048223625216 618121839509504 27197360938418176 1196683881290399744 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(32x2 + 4x),x,1)
A185097: 1 36 41616 55420693056 4611686018427387903 4611686018427387903
((x + 1) + (if (~4 + (x div 2)) <= 0 then 1 else (x div 4)))
A342256: 2 3 4 5 6 7 8 9 10 11 13 14 16 17 18 19
(1 + compr(\x.(loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 4),x))
A091072: 1 2 4 5 8 9 10 13 16 17 18 20 21 25 26 29
loop(\(x,i).(5x + ((1 - i) mod 4)),x,1)
A037682: 1 5 28 142 711 3555 17778 88892 444461 2222305 11111528 55557642 277788211 1388941055 6944705278 34723526392
((x + ~1) + (if ((x + 1) mod 5) <= 0 then (x + ~2) else 2))
A222261: 1 2 3 4 5 6 7 8 9 15 11 12 13 14 25 16
loop(\(x,i).(4x + ((~x + 1) mod 5)),x,1)
A037674: 1 4 18 75 301 1204 4818 19275 77101 308404 1233618 4934475 19737901 78951604 315806418 1263225675
loop(\(x,i).(4x + (((2 + i) * (1 + i)) div 2)),x,1)
A052161: 1 7 34 146 599 2417 9696 38820 155325 621355 2485486 9942022 39768179 159072821 636291404 2545165752
loop(\(x,i).(2 * (12x - (x div 2))),x,1)
A170743-A170705-A170657-A170609-A170561-A170513-A170465-A170417-A170369-A170321-A170273-A170225-A170177-A170129-A170081-A170033-A169565-A169517-A169469-A169421-A169373-A169325-A169277-A169229-A169181-A169133-A169085-A169037-A168989-A168941-A168893-A168845-A168797-A168749-A168701-A167938-A167695-A167183: 1 24 552 12696 292008 6716184 154472232 3552861336 81715810728 1879463646744 43227663875112 994236269127576 22867434189934248 525950986368487704 4611686018427387903 4611686018427387903
((x + 1) + (((if (~2 + (x div 2)) <= 0 then 1 else 2) + (x div 2)) div 2))
A188033-A187485: 1 2 4 5 6 7 9 10 12 13 14 15 17 18 19 20
loop(\(x,i).(2 * (16x - (x div 2))),x,1)
A170751-A170713-A170665-A170617-A170569-A170521-A170473-A170425-A170377-A170329-A170281-A170233-A170185-A170137-A170089-A170041-A169573-A169525-A169477-A169429-A169381-A169333-A169285-A169237-A169189-A169141-A169093-A169045-A168997-A168949-A168901-A168853-A168805-A168757-A168709-A167947-A167757-A167382-A167085-A063818: 1 32 992 30752 953312 29552672 916132832 28400117792 880403651552 27292513198112 846067909141472 26228105183385632 813071260684954592 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (10x - (x div 2))),x,1)
A170739-A170701-A170653-A170605-A170557-A170509-A170461-A170413-A170365-A170317-A170269-A170221-A170173-A170125-A170077-A170029-A169561-A169513-A169465-A169417-A169369-A169321-A169273-A169225-A169177-A169129-A169081-A169033-A168985-A168937-A168889-A168841-A168793-A168745-A168697-A167931-A167680: 1 20 380 7220 137180 2606420 49521980 940917620 17877434780 339671260820 6453753955580 122621325156020 2329805177964380 44266298381323220 841059669245141180 4611686018427387903
(1 + (if ((x + 1) mod 6) <= 0 then ((x div 2) mod 2) else x))
A244414: 1 2 3 4 5 1 7 8 9 10 11 2 13 14 15 16
((x + 1) + (2 * loop(\(x,i).(x * (2 - (x div (2 + i)))),x,2)))
A004757: 5 10 11 20 21 22 23 40 41 42 43 44 45 46 47 80
(if (x + ~2) <= 0 then x else (2x4 + 4x + ~1))
A339641: 0 1 2 173
loop(\(x,i).(2 * ((2x * (1 + (2 * i))) div (2 + i))),x,1)
A003645: 1 4 20 112 672 4224 27456 183040 1244672 8599552 60196864 426008576 3042918400 21909012480 158840340480 1158600130560
((2 * (2 + (x mod 2))) - loop(\(x,i).(2 * (x - (i mod 2))),x,1))
A154890: 3 6 4 8 8 16 24 48 88 176 344 688 1368 2736 5464 10928
((loop(\(x,i).x3,(x + 1),2) div 2) div (~x + 3))
A121702: 1 128 67108864 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).46x,x,1)
A009990: 1 46 2116 97336 4477456 205962976 9474296896 435817657216 20047612231936 922190162669056 42420747482776576 1951354384207722496 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x + ((x - (x div 3)) div 3)),2,x))
A022162: 1 2 3 4 7 8 9 11 13 14 15 17 18 20 22 23
loop(\(x,i).2x,(x + ((x + ((x div 2) div 3)) div 2)),1)
A098232: 1 2 8 16 64 128 512 2048 4096 16384 32768 131072 524288 1048576 4194304 8388608
loop(\(x,i).(2x - ((~x + ((x div 2) div 3)) div 2)),x,1)
A126876: 1 3 8 20 49 119 288
loop(\(x,i).(2x * (3 + (5 * i))),x,1)
A035275: 1 16 416 14976 688896 38578176 2546159616 193508130816 16641699250176 1597603128016896 169345931569790976 4611686018427387903 4611686018427387903 4611686018427387903
((~x + 1) + (2 * loop(\(x,i).(2x + 4),x,(x2 + ~x))))
A055581: 1 8 39 150 501 1524 4339 11762 30705 77808 192495 466926 1114093 2621420 6094827 14024682
((x + 1) + ((x + (if (~2 + (x div 4)) <= 0 then 1 else 2)) div 2))
A225647: 1 3 4 6 7
A140098-A109231-A064717: 1 3 4 6 7 9 10 12 13 15 16 18 20 21 23 24
((x + ~1) + ((if (~6 + (x div 2)) <= 0 then 2 else x) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A173899: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 20 21
((x + 1) + (if (x + ~2) <= 0 then x else ((x + ((x div 2) mod 2)) div 2)))
A093511: 1 3 5 6 7 8 10 12 13 14 16 18 19 20 22 24
loop(\(x,i).(x + i - (((~x + 2) * (x div 3)) div 2)),x,1)
A222011: 1 2 4 8
A007881: 1 2 4 8 18 71
loop(\(x,i).((x + 2) + ((x + (x div 4)) div (2 + i))),x,1)
A097911: 1 3 5 8
A060432: 1 3 5 8 11 14 18 22 26 30 35 40 45 50 55 61
loop(\(x,i).((x + 2) + ((5 * (i * i)) div 2)),x,1)
A007904: 1 5 17 41 83 147 239 363 525 729 981 1285 1647 2071 2563 3127
(1 + (x * (if (~2 + (x div 5)) <= 0 then 1 else (x + 2))))
A044917-A043320: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 256
(~1 + loop(\(x,i).2x,x,(x2 + 7x + 8)))
A107392: 7 31 103 303 831 2175 5503 13567 32767 77823 182271 421887 966655 2195455 4947967 11075583
((x2 + 2x + 1) + loop(\(x,i).(x * (x - i)),2,(x + ~1)))
A027382: 1 4 9 16 49 156 409 904 1761 3124 5161 8064 12049 17356 24249 33016
(if (x mod 10) <= 0 then 0 else (x2 + 2x + 1))
A106545: 0 4 9 16 25 36 49 64 81 100 0 144 169 196 225 256
loop(\(x,i).((x3 + 1) div 2),1,(x2 + 2x + 1))
A191489: 1 32 365 2048 7813 23328 58825 131072 265721 500000 885781 1492992 2413405 3764768 5695313 8388608
(loop(\(x,i).3x,x,3) div (x2 + 2x + 1))
A230664: 3 2 3 5 9 20 44 102 243 590 1464 3690 9433 24402 63772 168151
(loop(\(x,i).3x,x,3) mod (x2 + 2x + 1))
A233471: 0 1 0 1 18 9 31 33 0 49 3 81 146 177 207 65
loop(\(x,i).(x3 + 4x2 + 4x),1,(x2 + 2x + 1))
A325173: 9 144 1089 5184 18225 51984 127449 278784 558009 1040400 1830609 3069504 4941729 7683984 11594025 17040384
((x2 + 2x + 1) * loop(\(x,i).((x2 + x) * i),2,2))
A210645: 84 336 756 1344 2100 3024 4116 5376 6804 8400 10164 12096 14196 16464 18900 21504
((x2 + 2x + 1) * loop(\(x,i).2x,x,(2x + 4)))
A129002: 4 48 288 1280 4800 16128 50176 147456 414720 1126400 2973696 7667712 19382272 48168960 117964800 285212672
((x2 + 2x + 1) * loop(\(x,i).4x,(x + 1),x))
A128987: 0 64 1152 12288 102400 737280 4816896 29360128 169869312 943718400 5075107840 26575110144 136096776192 683973541888 3382286745600 16492674416640
((x2 + 2x + 1) * loop(\(x,i).3x,(x + 1),x))
A128986: 0 36 486 3888 24300 131220 642978 2939328 12754584 53144100 214347870 841802544 3233287044 12187005012 45199057050 165299408640
((x2 + 2x + ~1) * (if (x mod 2) <= 0 then (x div 2) else 2x))
A136276: 0 4 7 84
loop(\(x,i).(5x2 + ~5),(x2 + ~2x),1)
A033187: 1 1 1 120 4611686018427387903
((1 - (4 * (x mod 2))) * loop(\(x,i).(~2x + 1),x,1))
A282124: 1 3 3 15 11 63 43 255 171 1023 683 4095 2731 16383 10923 65535
loop(\(x,i).(2x + (((((x + ~1) div 2) div 2) div 2) mod 2)),x,1)
A222011: 1 2 4 8
A119610: 1 2 4 8 16 33 66 132 264 528 1057 2114 4228 8456 16912 33825
loop(\(x,i).(2x + ((x mod ~7) mod 2)),x,1)
A172411: 1 2 5 10
A267589: 1 2 5 10 20 41 83 167 335 671 1343 2687 5375 10751 21503 43007
loop(\(x,i).(2x + ((i div (2 * (~2 + (x mod 2)))) mod 2)),x,1)
A074988: 1 3 7 14 29 59 119 238 476 953 1907 3814 7629 15259 30519 61038
loop(\(x,i).(2x + ((2x div (2 + (x div 2))) mod 2)),x,1)
A267539: 1 3 6 12 25 51 103 207 415 831 1663 3327 6655 13311 26623 53247
loop(\(x,i).(2x + (((1 - (2 * (i mod 2))) * i) div 2)),x,1)
A172416: 1 1 3 4 10 17 37 70 144 283 571 1136 2278 4549 9105 18202
loop(\(x,i).(3x + (((2 + i) * (1 + i)) div 2)),x,1)
A052150: 1 6 24 82 261 804 2440 7356 22113 66394 199248 597822 1793557 5380776 16142448 48427480
(1 + (x * (if (x mod 2) <= 0 then 3 else 2x3)))
A264931: 1 3 7 163
((x + ~1) + (if (~2 + (x div 5)) <= 0 then 2 else (x div 2)))
A331271-A194898: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 21
(1 + (if ((x + 1) mod 7) <= 0 then (x mod 2) else x))
A328018-A242603: 1 2 3 4 5 6 1 8 9 10 11 12 13 2 15 16
loop(\(x,i).(1 + (x * (2x + (x div 2))) - (x mod 2)),x,1)
A198894: 1 2 11 297
loop(\(x,i).(10x + 1),(x * (x mod 2)),1)
A285473: 1 11 1 1111 1 111111 1 11111111 1 1111111111 1 111111111111 1 11111111111111 1 1111111111111111
((x3 + x2 + 2x + 1) + (if (x mod 2) <= 0 then x else 1))
A272707: 1 6 19 44 93 162 271 408 601 830 1131 1476 1909 2394 2983 3632
(((x + 1) * (x2 div 3)) + (if (x mod 2) <= 0 then x else 1))
A230281: 0 1 5 13 29 49
loop(\(x,i).((x * (2 + (3 mod (x + 2)))) + (x mod 2)),x,1)
A216149: 1 3 16
A055842: 1 3 16 80 400 2000 10000 50000 250000 1250000 6250000 31250000 156250000 781250000 3906250000 19531250000
loop(\(x,i).(10x + ((x + i) mod 2)),x,1)
A262863: 1 10 100 1001 10011 100110 1001100 10011001 100110011 1001100110 10011001100 100110011001 1001100110011 10011001100110 100110011001100 1001100110011001
loop(\(x,i).((x + 2) + (7 * (i * i))),x,1)
A063490: 1 10 40 105 219 396 650 995 1445 2014 2716 3565 4575 5760 7134 8711
loop(\(x,i).(2x - (((1 - (2 * (i mod 2))) * i) div 2)),x,1)
A177143: 1 3 5 12 22 47 91 186 368 741 1477 2960 5914 11835 23663 47334
loop(\(x,i).((4x * (~1 + (2 * i))) div (2 + i)),x,1)
A000257: 1 1 3 12 56 288 1584 9152 54912 339456 2149888 13891584 91287552 608583680 4107939840 28030648320
loop(\(x,i).((2x2 * (1 + (2 * i))) div (2 + i)),x,1)
A028580: 1 2 10 280 235200 173859840000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + ((x div 12) + (i div 2))),x,1)
A008766: 1 1 2 3 5 7 10 13 18 23 29 36 45 54 65 77
(if ((x * (x mod 3)) mod 5) <= 0 then 0 else (x + 1))
A102394: 0 2 3 0 5 0 0 8 9 0 0 12 0 14 15 0
((x + 1) * loop(\(x,i).(x + ((1 + i) * i)),(2x + 2),0))
A100431: 8 80 336 960 2200 4368 7840 13056 20520 30800 44528 62400 85176 113680 148800 191488
(loop(\(x,i).(x + (6 * (x + i))),x,0) mod (x + 1))
A094922: 0 0 0 0 1 0 1 0 0 8 1 0 1 8 12 0
(loop(\(x,i).12x,(x + 1),1) mod (x + 1))
A066442: 0 0 0 0 2 0 5 0 0 4 1 0 12 4 3 0
((x + 1) * (1 + ((x + 1) * loop(\(x,i).x2,2,3))))
A031696: 82 326 732 1300 2030 2922 3976 5192 6570 8110 9812 11676 13702 15890 18240 20752
((x + 1) * ((x + 1) - (loop(\(x,i).(x * i),x,1) mod (x + 1))))
A131959: 1 2 3 8
A170826: 1 2 3 8 5 36 7 64 81 100 11 144 13 196 225 256
((x + 1) * (1 + ((x + 1) * loop(\(x,i).x2,2,4))))
A031710: 257 1026 2307 4100 6405 9222 12551 16392 20745 25610 30987 36876 43277 50190 57615 65552
((x + 1) * (~1 + ((x + 1) * loop(\(x,i).x2,2,4))))
A158010: 255 1022 2301 4092 6395 9210 12537 16376 20727 25590 30965 36852 43251 50162 57585 65520
((x + 1) * (1 + loop(\(x,i).(x * (i * i)),4,(x + 1))))
A031726: 577 2306 5187 9220 14405 20742 28231 36872 46665 57610 69707 82956 97357 112910 129615 147472
(loop(\(x,i).10x,(x + 1),1) div (x + 1))
A060156: 10 50 333 2500 20000 166666 1428571 12500000 111111111 1000000000 9090909090 83333333333 769230769230 7142857142857 66666666666666 625000000000000
(loop(\(x,i).10x,(x + 1),1) mod (x + 1))
A056969: 0 0 1 0 0 4 3 0 1 0 10 4 10 2 10 0
(loop(\(x,i).7x,(x + 1),1) div (x + 1))
A129797: 7 24 114 600 3361 19608 117649 720600 4483734 28247524 179756976 1153440600 7453000800 48444505203 316504100662 2077058160600
(loop(\(x,i).7x,(x + 1),1) mod (x + 1))
A066438: 0 1 1 1 2 1 0 1 1 9 7 1 7 7 13 1
((x + 1) * (1 + ((loop(\(x,i).(x * i),x,x) mod (x + 1)) mod 2)))
A231407: 1 4 6
A143545: 1 4 6 4 10 6 14 8 9 10 22 12 26 14 15 16
((x + 1) * (if ((x + 2) mod 16) <= 0 then 2 else 1))
A060695: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 30 16
((1 + (2 * loop(\(x,i).x2,4,4))) mod (x + 1))
A254411: 0 1 0 1 3 3 2 1 0 3 9 9 6 9 3 1
(loop(\(x,i).x3,2,9) div (x + 1))
A057071: 387420489 193710244 129140163 96855122 77484097 64570081 55345784 48427561 43046721 38742048 35220044 32285040 29801576 27672892 25828032 24213780
(loop(\(x,i).x3,2,9) mod (x + 1))
A332054-A129810: 0 1 0 1 4 3 1 1 0 9 5 9 1 1 9 9
(if (x mod 2) <= 0 then 1 else ((1 + (x mod 8)) mod (x + 1)))
A339420: 1 0 1 0 1 0 1 0 1 2 1 4 1 6 1 8
((1 + loop(\(x,i).x2,(2 - (x mod 2)),4)) mod (x + 1))
A137327: 0 1 2 1 2 5 5 1 5 7 4 5 10 3 2 1
loop(\(x,i).10x,5,(x + 1))
A168652: 100000 200000 300000 400000 500000 600000 700000 800000 900000 1000000 1100000 1200000 1300000 1400000 1500000 1600000
loop(\(x,i).(x + (x div (2 + (i mod 2)))),5,(x + 1))
A247061: 1 8 16 17 24 32 33 40 48 49 56 64 65 72 80 81
(if x <= 0 then 1 else (x - ((~6x + 3) div (x + 1))))
A258432: 1 3 5 7 9 10 11 12 13 15 16 17 18 19 20 21
(x - loop(\(x,i).(~x + 1),(x + ~1),(x - (3 mod (x + 1)))))
A267048: 0 1 3 3 4 3 8 3 12 3 16 3 20 3 24 3
((x + 1) * (if (x mod 2) <= 0 then 2 else (~1 + ((x2 + 2x) div 2))))
A171734: 2 0 6 24 10 96 14 240 18 480 22 840 26 1344 30 2016
compr(\x.((1 + loop(\(x,i).2x,x,1)) mod (2x + 1)),(x + 1))
A224486: 1 2 5 6 9 14 18 21 26 29 30 33 41 50 53 54
(loop(\(x,i).(x * (1 + i)),2x,(2x + 1)) div (x + 1))
A052145: 1 9 200 8820 653184 73180800 11564467200 2451889440000 671854030848000 231125690776780800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.(loop(\(x,i).2x,x,(~x + 2)) mod (1 + (x div 2))),(x + 1))
A019438: 1 2 3 5 6 7 11 14 15 23
((x + 1) * (~1 + loop(\(x,i).7x,x,2)))
A224331: 1 26 291 2740 24005 201678 1647079 13176680 103766409 807072130 6214455467 47455841820 359873467213 2712892291382 20346692185455 151921968318160
((~1 + loop(\(x,i).(x + ((x + i) div 3)),x,2)) div (x + 1))
A127217: 1 1 1 1 1 2 2 3 4 5 6 8 10 13 17 21
((x + 1) * (1 + loop(\(x,i).(x * (2 - (x div (2 + i)))),x,2)))
A020330: 3 10 15 36 45 54 63 136 153 170 187 204 221 238 255 528
(loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),x,1) mod (x + 1))
A216369: 0 0 1 2 4 2 6 6 1 6 1 2 10 8 4 6
(loop(\(x,i).(x * (4 + i)),3x,1) div (x + 1))
A028917: 1 105 50400 64864800 174356582400 844757641728000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(10x + 1),x,1) div (x + 1))
A089303: 1 5 37 277 2222 18518 158730 1388888 12345679 111111111 1010101010 9259259259 85470085470 793650793650 7407407407407 69444444444444
(loop(\(x,i).(10x + 1),x,1) mod (x + 1))
A095250: 0 1 0 3 1 3 1 7 0 1 1 3 1 11 6 7
(loop(\(x,i).((4x + ~1) + (x mod 2)),x,1) div (x + 1))
A013560: 1 2 5 15 47 159
(loop(\(x,i).((x * (1 + i)) div (1 + (i div 2))),x,1) mod (x + 1))
A042970: 0 0 0 2 0 2 0 6 0 2 0 0 0 2 0 6
(loop(\(x,i).(2x * (1 + (2 * (i div 2)))),x,1) div (x + 1))
A059837: 1 1 4 18 144 1200 14400 176400 2822400 45722880 914457600 18441561600 442597478400 10685567692800 299195895398400 8414884558080000
((x + 1) * ((x2 + 2x + 1) + loop(\(x,i).(x * i),x,1)))
A080668: 2 10 33 88 245 936 5383 40832 363609 3629800 39918131 479003328 6227022997 87178293944 1307674371375 20922789892096
(loop(\(x,i).2x,x,2) mod (x3 + 3x2 + 3x + 1))
A233442: 0 4 8 16 32 64 128 256 512 24 717 640 1601 2664 2393 0
(2 - ((1 - (loop(\(x,i).2x,x,1) mod (x + 1))) div (x + 1)))
A327390: 1 2 2 2 2 3 2 2 3 3 2 3 2 3 3 2
((x + 1) * ((loop(\(x,i).2x,x,2) + (x div 2)) div (x + 1)))
A082894: 2 4 9 16 30 66 126 256 513 1020 2046 4092 8190 16380 32775 65536
loop(\(x,i).x3,1,(x4 + 2x3 + x2))
A249076: 0 64 46656 2985984 64000000 729000000 5489031744 30840979456 139314069504 531441000000 1771561000000 5289852801024 14412774445056 36343632130624 85766121000000 191102976000000
compr(\x.(~1 + loop(\(x,i).((x * (x mod 2)) + (x div 2)),x,x)),(x + 1))
A039500: 1 2 3 4 6 8 11 12 15 16 22 24 29 30 32 39
((loop(\(x,i).(x + ((2x + 1) * i)),x,0) div 2) div (x + 1))
A104256: 0 0 1 6 47 433 4826 63344 957206 16368226 312484331 6588211317 152035645781 3811750833515 103171389227156 2998418499414228
loop(\(x,i).(x - (x mod (1 + (x div 5)))),2,(x + 1))
A138768: 1 2 3 4 4 6 6 8 8 8 8 12 12 12 12 16
(loop(\(x,i).x2,3,10) div (x + 1))
A033424: 100000000 50000000 33333333 25000000 20000000 16666666 14285714 12500000 11111111 10000000 9090909 8333333 7692307 7142857 6666666 6250000
(loop(\(x,i).x3,2,10) div (x + 1))
A033423: 1000000000 500000000 333333333 250000000 200000000 166666666 142857142 125000000 111111111 100000000 90909090 83333333 76923076 71428571 66666666 62500000
loop(\(x,i).(3 * ((x2 + 3x) div 2)),2,(x + 1))
A102741: 81 405 1215 2835 5670 10206 17010 26730 40095 57915 81081 110565 147420 192780 247860 313956
(loop(\(x,i).(x2 * (2 + i)),2,6) div (x + 1))
A057068: 46656 23328 15552 11664 9331 7776 6665 5832 5184 4665 4241 3888 3588 3332 3110 2916
(x - ((x + 1) * loop(\(x,i).(x * (~x + i)),2,6)))
A158412: 960 1921 2882 3843 4804 5765 6726 7687 8648 9609 10570 11531 12492 13453 14414 15375
loop(\(x,i).((2 * (x mod 3)) - (x div 3)),2,(x + 1))
A194512: 4 1 5 2 ~1 3 0 4 1 5 2 6 3 0 4 1
((x + 1) * ((if (x mod 2) <= 0 then 1 else x) mod (2 + (x mod 3))))
A285769-A066638: 1 2 3 4 5 6 7 8 9 10 11 36 13 14 15 16
loop(\(x,i).(5x mod (1 + (x div 2))),2,(x + 1))
A036849: 0 0 0 0 0 0 1 0 0 0 0 2 0 2 1 0
((loop(\(x,i).2x2,3,(x + 1)) div 2) div (x + 1))
A291832: 64 8192 139968 1048576 5000000 17915904 52706752 134217728 306110016 640000000 1247178944 2293235712 4015905088 6746464256 10935000000 17179869184
((x + 1) * (2 + ((x + 1) * loop(\(x,i).x2,2,3))))
A177099: 83 328 735 1304 2035 2928 3983 5200 6579 8120 9823 11688 13715 15904 18255 20768
((x + 1) * (~2 + ((x + 1) * loop(\(x,i).x2,2,3))))
A157507: 79 320 723 1288 2015 2904 3955 5168 6543 8080 9779 11640 13663 15848 18195 20704
((x + 1) * (2 + ((x + 1) * loop(\(x,i).x2,2,4))))
A158230: 258 1028 2310 4104 6410 9228 12558 16400 20754 25620 30998 36888 43290 50204 57630 65568
((x + 1) * (~2 + ((x + 1) * loop(\(x,i).x2,2,4))))
A158249: 254 1020 2298 4088 6390 9204 12530 16368 20718 25580 30954 36840 43238 50148 57570 65504
((x + 1) * (2 + loop(\(x,i).(x * (i * i)),4,(x + 1))))
A158369: 578 2308 5190 9224 14410 20748 28238 36880 46674 57620 69718 82968 97370 112924 129630 147488
((x + 1) * (~2 + loop(\(x,i).(x * (i * i)),4,(x + 1))))
A158371: 574 2300 5178 9208 14390 20724 28210 36848 46638 57580 69674 82920 97318 112868 129570 147424
loop(\(x,i).(x3 + 2x + 1),(2x + 2),(x + 1))
A289853: 73 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((~x + 1) + (x div (4 * (1 + i)))),2,(x + 1))
A006164: 1 1 2 3 4 5 6 6 7 8 9 10 11 12 12 12
((x + 1) * (2 + ((loop(\(x,i).(x * i),x,x) mod (x + 1)) mod 2)))
A175030: 2 6 9 8 15 12 21 16 18 20 33 24 39 28 30 32
(x - ((x + 1) * loop(\(x,i).(~4x2 + 1),2,2)))
A158409: 899 1799 2699 3599 4499 5399 6299 7199 8099 8999 9899 10799 11699 12599 13499 14399
((4x + 4) * loop(\(x,i).3x,2x,2))
A235383: 8 144
A212703: 8 144 1944 23328 262440 2834352 29760696 306110016 3099363912 30993639120 306837027288 3012581722464 29372671794024 284688972772848 2745215094595320 26354064908115072
loop(\(x,i).x2,3,(~8x + ~6))
A017144: 1679616 1475789056 54875873536 656100000000 4347792138496 20047612231936 72301961339136 218340105584896 576480100000000 1370114370683136 2992179271065856 6095689385410816 11716593810022656
loop(\(x,i).(((x div 5) * (x div 2)) div 2),2,(x + 1))
A035591: 0 0 0 0 0 0 0 0 0 1 1 1 1 1 5 6
(4 - ((x + 1) * loop(\(x,i).(~2x2 + 1),2,2)))
A100775: 101 198 295 392 489 586 683 780 877 974 1071 1168 1265 1362 1459 1556
loop(\(x,i).16x2,4,(x + 1))
A183085: 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903
(x - ((x + 1) * loop(\(x,i).(~x2 + ~2x),2,4)))
A158365: 528 1057 1586 2115 2644 3173 3702 4231 4760 5289 5818 6347 6876 7405 7934 8463
((4x + 4) + ((x + 2) div (1 + (if x <= 0 then 1 else 2))))
A184479: 5 9 13 17 22 26 30 35 39 43 48 52 56 61 65 69
((x2 + loop(\(x,i).(x * i),x,1)) mod (4x + 4))
A133933: 1 2 6 15 0 1 0 1 28 1 0 25 0 1 16 33
((2 - (if (x mod 3) <= 0 then 1 else (x div 4))) div (x + 1))
A016423-A016412-A014035: 1 1 0 0 0 0 0 0 0 0 0 0 0 ~1 ~1 0
(loop(\(x,i).(5x + 4),x,4) div (x + 1))
A225586: 4 12 41 156 624 2604 11160 48828 217013 976562 4438920 20345052 93900240 435965401 2034505208 9536743164
loop(\(x,i).((x * (~1 + (x * (~1 + (2 * i))))) div 2),2,(x + 1))
A236770: 0 1 12 51 145 330 651 1162 1926 3015 4510 6501 9087 12376 16485 21540
loop(\(x,i).2x,x,(2x3 + 6x2 + 8x + 4))
A119635: 4 40 240 1088 4160 14208 44800 133120 377856 1034240 2748416 7127040 18104320 45187072 111083520 269484032
((x + 1) * (loop(\(x,i).(x * (2 + i)),(x + 1),(x + 2)) div 2))
A055303: 3 36 360 3600 37800 423360 5080320 65318400 898128000 13172544000 205491686400 3399953356800 59499183744000 1098446469120000 21341245685760000 435361411989504000
((x + 1) + (loop(\(x,i).(2 * (x + i)),(x + ~1),(x + 2)) div 2))
A129955: 2 3 8 18 40 88 192 416 896 1920 4096 8704 18432 38912 81920 172032
((x + 1) * (loop(\(x,i).(x * (i * i)),(x + 2),(x + 2)) div 2))
A131092: 4 108 3456 144000 7776000 533433600 45519667200 4740548198400 592568524800000 87634300723200000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) * loop(\(x,i).(x * (4 + i)),x,(2x + 4)))
A055315: 4 60 720 8400 100800 1270080 16934400 239500800 3592512000 57081024000 958961203200 16999766784000 317328979968000 6224529991680000 128047474114560000 2757288942600192000
(if ((x + 1) mod 6) <= 0 then (2x + ~4) else (x + 1))
A295417-A293448-A225891-A105119-A085079-A072356-A069799: 1 2 3 4 5 6 7 8 9 10 11 18 13 14 15 16
(if (x mod 4) <= 0 then 1 else ((2x + 2) * (2 - (x mod 2))))
A331054: 1 4 12 8 1
((x + 1) * (2 + (if (x mod 3) <= 0 then (x + 1) else ~x)))
A321518: 3 2 0 24
((2 + (if (((x + ~1) div 2) mod 3) <= 0 then 1 else x)) div (x + 1))
A278907: 2 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1
(loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2) div (x + 1))
A024498: 2 3 6 17 50 154 490 1608 5402 18475 64130 225346 800046 2865471 10341168 37567524
(loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2) mod (x + 1))
A059288: 0 0 2 2 2 0 2 6 2 6 2 4 2 6 0 6
loop(\(x,i).(x + (i * i)),x,(x3 + 3x2 + 4x + 2))
A205342: 2 11 35 82 160 277 441 660 942 1295 1727 2246 2860 3577 4405 5352
(((x + 2) * loop(\(x,i).(x2 + 2x + 1),2,2)) div (x + 1))
A180104: 200 150 133 125 120 116 114 112 111 110 109 108 107 107 106 106
((x + 1) * (loop(\(x,i).(x * (2 + i)),2x,2) div (x + 2)))
A274136: 1 16 540 32256 3024000 410572800 76281004800 18598035456000 5762136335155200 2211729098342400000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + 2x2 + 2x),1,(x2 + 3x + 2))
A250015: 20 300 2040 8840 28860 77700 182000 383760 745380 1355420 2335080 3845400 6095180 9349620 13939680 20272160
((x2 + 3x + 2) * loop(\(x,i).4x,(x + 1),x))
A128962: 0 96 1536 15360 122880 860160 5505024 33030144 188743680 1038090240 5536481280 28789702656 146565758976 732828794880 3607772528640 17523466567680
((x2 + 3x + 2) * loop(\(x,i).3x,(x + 1),x))
A128961: 0 54 648 4860 29160 153090 734832 3306744 14171760 58458510 233834040 911952756 3482001432 13057505370 48212327520 175630621680
loop(\(x,i).(2x3 + 5x2 + 2x),2x,(x + 1))
A330399: 1 136080 4611686018427387903
(if (x + ~3) <= 0 then (x + 3) else (2x2 + 2x))
A154665: 3 4 5 6 40
(x - ((1 - (2 * (x + (if (x + ~2) <= 0 then 1 else x)))) div (x + 1)))
A225647: 1 3 4 6 7
A233334: 1 3 4 6 7 9 10 11 12 13 14 15 16 17 18 19
((x2 + 6x + 8) * loop(\(x,i).x2,2,(x + 1)))
A221466: 8 240 1944 8960 30000 81648 192080 405504 787320 1430000 2459688 4043520 6397664 9796080 14580000 21168128
((x + loop(\(x,i).6x,(x + 1),1)) div (x + 1))
A129790: 6 18 72 324 1556 7776 39991 209952 1119744 6046618 32981551 181398528 1004668771 5597440293 31345665639 176319369216
((x + loop(\(x,i).8x,(x + 1),1)) div (x + 1))
A129792: 8 32 171 1024 6554 43691 299594 2097152 14913081 107374183 780903145 5726623062 42288908761 314146179365 2345624805923 17592186044416
((x + loop(\(x,i).5x,(x + 1),1)) div (x + 1))
A129789: 5 13 42 157 625 2605 11161 48829 217014 976563 4438921 20345053 93900241 435965402 2034505209 9536743165
((x + loop(\(x,i).3x,(2x + 2),1)) div (x + 1))
A129793: 9 41 243 1641 11810 88574 683282 5380841 43046721 348678441 2852823601 23535794707 195528140641 1634056603926 13726075472977 115813761803241
compr(\x.loop(\(x,i).(x div 2),(x mod 9),x),(x + 1))
A032986: 1 2 3 4 5 6 7 8 13 14 15 16 17 23 24 25
((x + 1) + loop(\(x,i).(x2 div (x + 4)),3,x))
A285710: 1 2 3 4 5 6 7 8 9 11 13 14 16 17 19 21
((x + 1) * loop(\(x,i).(x + ((x + 1) * (i * i))),3,x))
A157659: 99 398 897 1596 2495 3594 4893 6392 8091 9990 12089 14388 16887 19586 22485 25584
loop(\(x,i).(3 * (x + (2x div (1 + i)))),x,(x + 1))
A036216: 1 12 90 540 2835 13608 61236 262440 1082565 4330260 16888014 64481508 241805655 892820880 3252418920 11708708112
((x + 1) + (x2 div (x + (if x <= 0 then 1 else (x div 3)))))
A329833-A189682-A059541: 1 3 5 6 8 10 11 13 15 16 18 20 22 23 25 27
((x + (if (x mod 2) <= 0 then x else 3x2)) div (x + 1))
A019426: 0 2 1 7 1 13 1 19 1 25 1 31 1 37 1 43
((x + loop(\(x,i).10x,x,1)) div (x + 1))
A066559: 1 5 34 250 2000 16667 142858 1250000 11111112 100000000 909090910 8333333334 76923076924 714285714286 6666666666667 62500000000000
(compr(\x.(loop(\(x,i).(2x + 1),x,0) mod (x + 1)),x) mod (x + 1))
A087611: 0 0 1 2 0 0 2 2 4 8 8 0 1 0 1 4
((x + 1) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))
A097911: 1 3 5 8
A167136: 1 3 5 8 11 16 19 24 27 32 39 42 49 54 57 62
((x + 1) * (x + loop(\(x,i).(x * (1 + i)),4,(x + 1))))
A157960: 120 482 1086 1932 3020 4350 5922 7736 9792 12090 14630 17412 20436 23702 27210 30960
((x + 1) * loop(\(x,i).7x,(x + 1),x))
A128801: 0 98 2058 28812 336140 3529470 34588806 322828856 2905459704 25422772410 217505941730 1827049910532 15114685623492 123436599258518 996987917088030 7975903336704240
((4x + 5) * ((x + 1) + (if x <= 0 then 1 else x)))
A220021: 10 27 65 119 189 275 377 495 629 779 945 1127 1325 1539 1769 2015
((x + 1) + loop(\(x,i).(10x + 10),2,x))
A082946: 111 212 313 414 515 616 717 818 919
compr(\x.loop(\(x,i).(x div 2),(x mod 10),x),(x + 1))
A032987: 1 2 3 4 5 6 7 8 9 14 15 16 17 18 19 25
compr(\x.loop(\(x,i).(x - i),(x mod 10),x),(x + 1))
A190298: 1 2 3 4 5 6 7 8 9 15 16 17 18 19 27 28
((x + 1) div (0 - loop(\(x,i).(x div (~2 + (x mod 2))),x,(x + 1))))
A118830: ~1 2 ~1 4 ~1 2 ~1 8 ~1 2 ~1 4 ~1 2 ~1 16
((2x + 2) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))
A171977: 2 4 2 8 2 4 2 16 2 4 2 8 2 4 2 32
((x + 1) + loop(\(x,i).(10x + ~1),x,x))
A072290: 1 11 192 2893 38894 488895 5888896 68888897 788888898 8888888899 98888888900 1088888888901 11888888888902 128888888888903 1388888888888904 14888888888888905
compr(\x.(~x + loop(\(x,i).(x div (2 - (x mod 2))),x,x2)),(x + 1))
A222011: 1 2 4 8
A116882: 1 2 4 8 12 16 24 32 40 48 56 64 80 96 112 128
loop(\(x,i).((1 + (x2 div 8)) div 2),2,(x + ~1))
A326445-A326443: 0 0 0 0 0 0 0 0 1 1 2 2 4 5 8 9
((x + ~1) * (loop(\(x,i).6x,(x + ~2),x) div 2))
A081136: 0 0 1 18 216 2160 19440 163296 1306368 10077696 75582720 554273280 3990767616 28298170368 198087192576 1371372871680
((x + ~1) * (loop(\(x,i).8x,(x + ~2),x) div 2))
A081138: 0 0 1 24 384 5120 61440 688128 7340032 75497472 754974720 7381975040 70866960384 670014898176 6253472382976 57724360458240
((x + ~1) * (loop(\(x,i).2x,(x + ~2),(x2 + ~2x)) div 2))
A052771: 0 0 0 6 48 240 960 3360 10752 32256 92160 253440 675840 1757184 4472832 11182080
((x + ~1) * (loop(\(x,i).(x * (3 + i)),(x + ~2),x) div 2))
A001754: 0 0 1 12 120 1200 12600 141120 1693440 21772800 299376000 4390848000 68497228800 1133317785600 19833061248000 366148823040000
((x2 + ~x) * loop(\(x,i).(x * (x - i)),2,(x + ~3)))
A053625: 0 0 0 0 0 0 720 5040 20160 60480 151200 332640 665280 1235520 2162160 3603600
((x2 + ~x) * loop(\(x,i).(x2 + 2x),1,(~x + 3)))
A062765: 0 0 6 0 ~12 0 90 336 840 1728 3150 5280 8316 12480 18018 25200
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(x + ~1))
A276666: ~1 0 2 10 42 168 660 2574 10010 38896 151164 587860 2288132 8914800 34767720 135727830
((x + ~1) + loop(\(x,i).(x - ((~2 + (x div 2)) div 3)),2,x))
A328585-A277573: 1 3 5 6 7 9 11 13 15 17 18 19 21 23 25 27
((x + ~1) + loop(\(x,i).(x - ((x + ~2) div (2 + (x div 2)))),2,x))
A042996: 1 2 3 5 7 9 11 12 13 15 17 19 21 23 25 27
((~x + 1) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A014689: 1 1 2 3 6 7 10 11 14 19 20 25 28 29 32 37
((~x + 1) + compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x))
A107819: 1 3 4 7 8 11 12 15 20 21 26 29 30 33 38 43
loop(\(x,i).(x * (~1 + (10 * (1 + i)))),x,1)
A035278: 1 19 551 21489 1052961 62124699 4286604231 338641734249 30139114348161 2983772320467939 325231182931005351 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).41x,x,1)
A009985: 1 41 1681 68921 2825761 115856201 4750104241 194754273881 7984925229121 327381934393961 13422659310152401 550329031716248441 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(20x2 + x),x,1)
A176446: 1 21 8841 1563274461 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (9 * (1 + i)))),x,1)
A053116: 1 19 532 19684 905464 49800520 3187233280 232668029440 19078778414080 1736168835681280 173616883568128000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).37x,x,1)
A009981: 1 37 1369 50653 1874161 69343957 2565726409 94931877133 3512479453921 129961739795077 4808584372417849 177917621779460413 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (3 * (1 - (i mod 3))))),x,1)
A138230: 1 1 ~2 ~8 ~8 16 64 64 ~128 ~512 ~512 1024 4096 4096 ~8192 ~32768
loop(\(x,i).47x,x,1)
A009991: 1 47 2209 103823 4879681 229345007 10779215329 506623120463 23811286661761 1119130473102767 52599132235830049 2472159215084012303 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (3 * (2 + (3 * i))))),x,1)
A035021: 1 16 400 13600 584800 30409600 1854985600 129848992000 10258070368000 902710192384000 87562888661248000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + (3 * (2 + (3 * i))))),x,1)
A035018: 1 14 322 10304 422464 21123200 1246268800 84746278400 6525463436800 561189855564800 53313036278656000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + (3 * (~2 + (3 * i))))),x,1)
A084949: 1 2 22 440 12760 484880 22789360 1276204160 82953270400 6138542009600 509498986796800 46873906785305600 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (3 * (((1 + i) * i) div 2)))),x,1)
A140701: 1 4 40 760 23560 1083760 69360640 5895654400 642626329600 87397180825600 14507932017049600 2887078471392870400 4611686018427387903 4611686018427387903
loop(\(x,i).(x + i - (x div (1 + (6 * i)))),x,1)
A025716: 1 2 4 7 11 16 22 29 37 46 56 67 79 91 104 118
loop(\(x,i).(x * (~1 + ((1 - (2 * i)) * (~1 + (2 * i))))),x,1)
A101927: 1 ~2 20 ~520 26000 ~2132000 260104000 ~44217680000 9993195680000 ~2898026747200000 1049085682486400000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (2 * (1 + (5 * i))))),x,1)
A035272: 1 13 299 9867 424281 22486893 1416674259 103417220907 8583629335281 798277528181133 82222585402656699 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + (2 * (4 + (2 mod (x + 1)))))),x,1)
A196663: 1 9 117 1521 19773 257049 3341637 43441281 564736653 7341576489 95440494357 1240726426641 16129443546333 209682766102329 2725875959330277 35436387471293601
loop(\(x,i).(x * (~1 + (4 * (2 + (2 mod (x + 1)))))),x,1)
A067420: 1 7 105 1575 23625 354375 5315625 79734375 1196015625 17940234375 269103515625 4036552734375 60548291015625 908224365234375 13623365478515625 204350482177734375
loop(\(x,i).(x + (5 * ((1 + (i * i)) * i))),x,1)
A222408: 1 11 61 211 551 1201 2311 4061 6661 10351 15401 22111 30811 41861 55651 72601
loop(\(x,i).(x * (1 + (4 * (i * i * i * i)))),x,1)
A274306: 1 5 325 105625 108265625 270772328125 1403954521328125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(7x + 36),x,1)
A164783: 1 43 337 2395 16801 117643 823537 5764795 40353601 282475243 1977326737 13841287195 96889010401 678223072843 4747561509937 33232930569595
loop(\(x,i).(x * (26 - i)),x,1)
A104643: 1 25 600 13800 303600 6375600 127512000 2422728000 43609104000 741354768000 11861676288000 177925144320000 2490952020480000 32382376266240000 388588515194880000 4274473667143680000
((x3 + 3x) + loop(\(x,i).3x,x,1))
A220509: 1 7 23 63 157 383 963 2551 7097 20439 60079 178511 533205 1596559 4785755 14352327
loop(\(x,i).(x + (3 * ((3x + ~4) + i))),x,1)
A133462: 1 1 4 37 370 3703 37036 370369 3703702 37037035 370370368 3703703701 37037037034 370370370367 3703703703700 37037037037033
loop(\(x,i).(5x3 + ~3x),x,1)
A045529: 1 2 34 196418 37889062373143906 4611686018427387903
loop(\(x,i).(x + ((3 * (i * i)) div (2x + 1))),x,1)
A061465: 1 2 4 7 10 13 17 21 25 29 34 39 44 49 54 60
(1 + (x * loop(\(x,i).(2x2 + 2x),(2x + ~1),x)))
A067502: 1 5 390625 4611686018427387903
loop(\(x,i).(x + ((x2 + i) div (3x + ~1))),x,1)
A164001: 1 2 3 4 5 7 9 12 16 21 28 37 49 65 86 114
(2 - loop(\(x,i).((~x2 + ~x) + (x3 div 2)),x,1))
A180745: 1 4 8 140
(1 + compr(\x.((x mod 10) mod (if x <= 0 then 1 else x)),x))
A068637-A034704: 1 2 3 4 5 6 7 8 9 10 11 21 31 41 51 61
loop(\(x,i).(x * (~1 + (11 * i))),x,1)
A254322: 1 10 210 6720 288960 15603840 1014249600 77082969600 6706218355200 657209398809600 71635824470246400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + (4 * ((~1 + i) * (1 - i))))),x,1)
A101928: 1 ~1 5 ~85 3145 ~204425 20646925 ~2993804125 589779412625 ~151573309044625 49261325439503125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + ((~1 + (4 * (i * i))) * (1 + i))),x,1)
A057675: 1 7 52 192 507 1101 2102 3662 5957 9187 13576 19372 26847 36297 48042 62426
loop(\(x,i).(x + ((1 + (2 * (x + (x div 2)))) div (1 + i))),x,1)
A000601: 1 2 4 7 11 16 23 31 41 53 67 83 102 123 147 174
loop(\(x,i).(x + ((1 + (((1 + i) * i) div 2)) * (1 + i))),x,1)
A133252: 1 5 17 45 100 196 350 582 915 1375 1991 2795 3822 5110 6700 8636
loop(\(x,i).(x + ((1 + (((2 + i) * i) div 2)) * (1 + i))),x,1)
A006010: 1 5 20 52 117 225 400 656 1025 1525 2196 3060 4165 5537 7232 9280
loop(\(x,i).(x * (1 + ((6 * (~1 + i)) + i))),x,1)
A084947: 1 2 18 288 6624 198720 7352640 323516160 16499324160 956960801280 62202452083200 4478576549990400 353807547449241600 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x - (x * (i - (8 * (1 + i))))),x,1)
A053105: 1 16 368 11040 408480 17973120 916629120 53164488960 3455691782400 248809808332800 19655974858291200 1690413837813043200 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,x))
A309115: 1 2 5 16
A323229: 1 2 5 16 57 211 793 3004 11441 43759 167961 646647 2496145 9657701 37442161 145422676
loop(\(x,i).(x * (1 + (4 * (1 + (2 * i))) - i)),x,1)
A034832: 1 12 228 5928 195624 7824960 367773120 19859748480 1211444657280 82378236695040 6178367752128000 506626155674496000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (2 * (1 + (2 * (2x - (i mod 2)))))),x,1)
A274823: 1 7 65
A083302: 1 7 65 583 5249 47239 425153 3826375 34437377 309936391 2789427521 25104847687 225943629185 2033492662663 18301433963969 164712905675719
loop(\(x,i).(x + (((6 + i) * (1 + i)) div 2)),x,1)
A006416: 1 8 20 38 63 96 138 190 253 328 416 518 635 768 918 1086
loop(\(x,i).(x * (2 + (x mod (2 + (x div 5))))),x,1)
A067864: 1 3 9 18 90
loop(\(x,i).(x * (6 + (4 mod (x + 2)))),x,1)
A196662: 1 7 70 700 7000 70000 700000 7000000 70000000 700000000 7000000000 70000000000 700000000000 7000000000000 70000000000000 700000000000000
loop(\(x,i).(x + (4 * (2 + ((4 + i) * i)))),x,1)
A323218: 1 29 85 177 313 501 749 1065 1457 1933 2501 3169 3945 4837 5853 7001
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x2,1)
A214441: 1 1 14 4862 35357670 4861946401452 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((1 + (if (x mod 2) <= 0 then 6 else 1)) mod (x2 + 1))
A021444: 0 0 2 2 7 2 7 2 7 2 7 2 7 2 7 2
loop(\(x,i).((x div 2) - ((x + ~1) div 3)),2,(x2 + 1))
A008625: 1 0 0 1 1 1 2 2 2 3 3 4 5 5 6 7
loop(\(x,i).19x,x2,1)
A078353: 1 19 130321 322687697779 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (x2 * loop(\(x,i).2x2,2,3x)))
A345702: ~1 647 41471 472391 2654207 10124999 30233087 76236551 169869311 344373767 647999999 1147971527 1934917631 3127772231 4879139327 7381124999
loop(\(x,i).(x * (27 - i)),x,1)
A106793: 1 26 650 15600 358800 7893600 165765600 3315312000 62990928000 1133836704000 19275223968000 308403583488000 4626053752320000 64764752532480000 841941782922240000 4611686018427387903
loop(\(x,i).(x * ((3 * (((1 + i) * i) div 2)) + i)),x,1)
A302909: 1 4 44 924 31416 1570800 108385200 9863053200 1144114171200 164752440652800 28831677114240000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (((6 * (1 + i)) + i) * i)),x,1)
A299646: 1 14 54 135 271 476 764 1149 1645 2266 3026 3939 5019 6280 7736 9401
loop(\(x,i).(((2x * (1 + (2 * i))) div (2 + i)) * i),x,1)
A121194: 1 2 10 84
A065866: 1 2 10 84 1008 15840 308880 7207200 196035840 6094932480 213322636800 8303173401600 355850288640000 16653793508352000 845180020548864000 4611686018427387903
((x - (if ((x2 + ~x) mod (1 + (x div 2))) <= 0 then 1 else 0)) mod 2)
A288932: 1 0 1 0 1 1 0 1 0 1 1 1 0 1 0 1
(if ((x + 1) mod (1 + ((x div 2) div (1 + (x mod 2))))) <= 0 then 0 else 2)
A281009: 0 0 2 0 2 0 2 0 2 2 2 0 2 2 2 0
((((x + 2) div 3) - (if (~2 + (x div 2)) <= 0 then 1 else 0)) mod 2)
A104107: 1 0 0 0 1 1 0 1 1 1 0 0 0 1 1 1
(2x - (((x div 2) - (if (~2 + (x div 2)) <= 0 then 1 else 0)) div 2))
A285344: 1 3 4 6 8 10 11 13 14 16 18 20 21 23 25 27
(((x div 2) - (if (8 mod (x + 2)) <= 0 then 1 else 0)) mod 2)
A170984-A170983-A170982-A170981-A170965-A170964-A170963-A170962-A170961-A170960-A170959-A170958-A170957-A147599: 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1
((((x * (~1 + (x div 2))) div 2) + (if (x + ~2) <= 0 then 1 else 0)) mod 2)
A296238: 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1
(loop(\(x,i).(x + ((~1 + ((2 + i) * i)) * i)),(x + 1),0) div 2)
A290312: 1 8 29 75 160 301 518 834 1275 1870 2651 3653 4914 6475 8380 10676
(loop(\(x,i).(x + (((i * i) div 2) * i * i)),(x + 1),0) div 2)
A060453: 0 4 22 86 236 560 1148 2172 3792 6292 9922 15106 22204 31808 44408 60792
((if (16 mod (x + 2)) <= 0 then (x + 2) else 0) div 2)
A135416: 1 0 2 0 0 0 4 0 0 0 0 0 0 0 8 0
(loop(\(x,i).(x + ((((i * i) div 2) * i) div 2)),(x + 2),0) div 2)
A007009: 1 4 12 27 54 96 160 250 375 540 756 1029 1372 1792 2304 2916
(if (2x mod (4 + (x div 4))) <= 0 then 1 else ~2)
A114284: 1 ~2 1 ~2 ~2 1 ~2 ~2 ~2 1 ~2 ~2 ~2 ~2 1 ~2
(x div (if (x mod 2) <= 0 then (2 + (x div 2)) else ~8))
A268173: 0 ~1 0 ~1 1 ~1 1 ~1 1 ~2 1 ~2 1 ~2 1 ~2
loop(\(x,i).2x2,1,(4x - (x div ~2)))
A085445: 0 50 162 392 648
(x + (if (x + ~6) <= 0 then 1 else 2) - (x div ~2))
A225647: 1 3 4 6 7
A187580: 1 3 4 6 7 9 10 13 14 16 17 19 20 22 23 25
((1 - loop(\(x,i).(4x - (i mod 3)),x,0)) div 2)
A178872: 0 1 3 12 49 195 780 3121 12483 49932 199729 798915 3195660 12782641 51130563 204522252
(loop(\(x,i).(x + (2 * i) - (((x + ~1) div 2) div 2)),x,0) div 2)
A060293: 0 1 3 6 9 12 15 19 22 26 30 34 38 42 46 50
(loop(\(x,i).(1 + ((i div (2 + (x mod 2))) + (x div 2))),x,0) div 2)
A275891: 0 0 0 1 2 2 2 2 2 3 4 4 5 5 6 6
(2 + loop(\(x,i).((~x + 2) - (2x mod 5)),x,0))
A328985: 2 4 ~2 6 ~3 9 ~7 11 ~8 14 ~12 16 ~13 19 ~17 21
(loop(\(x,i).(x + (i * i * i * (1 + (i * i)))),x,0) div 2)
A331528: 0 1 21 156 700 2325 6321 14896 31536 61425 111925 193116 318396 505141 775425 1156800
(loop(\(x,i).(x + ((~1 + ((2 + i) * i)) * (2 + i))),x,0) div 2)
A163943: 0 3 17 52 121 240 428 707 1102 1641 2355 3278 4447 5902 7686 9845
(loop(\(x,i).(x + ((5 * (i * i)) div 2)),x,0) div 2)
A212980: 0 1 6 17 37 68 113 174 254 355 480 631 811 1022 1267 1548
(loop(\(x,i).(x + ((1 + ((1 + (2 * i)) * i)) * i)),x,0) div 2)
A176060: 0 2 13 46 120 260 497 868 1416 2190 3245 4642 6448 8736 11585 15080
((x - (if (10 mod (x + 1)) <= 0 then 0 else 1)) mod 2)
A254114: 0 1 1 0 0 0 1 0 1 1 1 0 1 0 1 0
((x - (if (~2 + (x mod 10)) <= 0 then 0 else 1)) mod 2)
A260455: 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0
((x - (if ((x div 2) mod (4 + (x mod 2))) <= 0 then 0 else 1)) mod 2)
A131929: 0 1 1 0 1 0 1 0 0 0 1 1 1 0 1 0
((x - (if ((x mod (1 + (x div 2))) mod 4) <= 0 then 0 else 1)) mod 2)
A327202: 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 0
((((x + ~1) div 3) - (if (x + ~4) <= 0 then 0 else 1)) mod 2)
A104108: 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1
(((x + 1) div (1 + (if (~x + 2) <= 0 then (x mod 4) else 0))) mod 2)
A225145-A129565: 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0
((x - (if (x - (x2 mod (x + 4))) <= 0 then 0 else 1)) mod 2)
A244735: 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 1
((((1 - (x div 2)) mod 5) + (if x <= 0 then 0 else 1)) mod 2)
A039984: 1 0 1 1 1 1 0 0 1 1 0 0 1 1 1 1
(((x div (1 + (2 * (2 - (x mod 2))))) + (if x <= 0 then 0 else 1)) mod 2)
A215581: 0 1 1 0 1 0 0 1 0 0 1 0 1 1 1 0
(((3 * ((x2 + x) div 2)) - (if x <= 0 then 0 else 1)) div 2)
A024398: 0 1 4 8 14 22 31 41 53 67 82 98 116 136 157 179
(((((1 + (x * (x div 2))) div 2) div 2) + (if x <= 0 then 0 else 1)) mod 2)
A051105: 0 1 1 0 1 1 1 0 1 0 1 1 1 0 1 1
(if (x mod (1 + (4 mod (1 + (x div 3))))) <= 0 then 1 else 2)
A211355-A211353: 1 1 1 1 1 1 1 2 1 1 1 1 2 2 2 1
(if ((x + ~2) mod (1 + ((~x + 1) mod 5))) <= 0 then 1 else 2)
A091237: 1 1 1 2 2 2 1 1 2 2 1 1 1 2 1 2
(if ((x2 + x) mod (1 + ((x + 2) div 3))) <= 0 then 1 else 2)
A345238: 1 1 1 1 2 1 1 1 1 2 1 2 2 2 1 1
(if (x mod (1 + ((x * (x div 3)) mod 3))) <= 0 then 1 else 2)
A300978: 1 1 1 1 1 2 1 2 1 1 1 1 1 2 2 1
(if (x mod (1 + ((x div 4) * (x div 3)))) <= 0 then 1 else 2)
A297774-A043533: 1 1 1 1 1 2 1 2 2 2 2 2 2 1 2 2
(if ((x3 + 2) mod (1 + (x div 3))) <= 0 then 1 else 2)
A105446-A058978: 1 1 1 2 1 2 2 1 2 2 2 2 1 2 2 2
((if x <= 0 then 2 else (x mod (1 + (x mod (1 + (x div 3)))))) div 2)
A055334: 1 0 0 0 0 0 0 0 1 0 0 1 0 0 2 1
(if (~1 + (2x mod (1 + ((x div 2) * (x div 2))))) <= 0 then 1 else 2)
A254315: 1 1 1 1 2 1 2 2 2 1 2 2 2 2 2 2
(if (x mod (1 + ((~2x + 2) mod (1 + (x div 2))))) <= 0 then 1 else 2)
A290257-A184304: 1 1 1 1 1 2 1 1 1 2 1 2 2 2 1 1
((1 + (x mod (~3 + (if (x mod 4) <= 0 then x else 0)))) mod 2)
A106602: 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1
(if ((x + 1) mod (~1 + (2 * ((x + ~1) div 3)))) <= 0 then 1 else 2)
A338260: 1 1 1 1 1 1 1 2 1 2 2 2 2 1 2 2
((if x <= 0 then 1 else (x mod (1 + (x mod 7)))) mod 2)
A323509: 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 1
(loop(\(x,i).(2x + 2),(~3 + (x div 3)),1) div 2)
A308923: 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 5
(if (3x mod (~1 + (2 * (x div 3)))) <= 0 then 1 else 2)
A180580: 1 1 1 1 1 1 1 1 1 2 1 2 2 2 1 1
(if ((x + 1) mod (1 + ((x - (x mod 3)) div 2))) <= 0 then 1 else 2)
A107459: 1 1 1 1 2 1 2 1 2 1 2 2 2 1 2 1
(if ((3x + 2) mod (1 + ((x + 1) div 2))) <= 0 then 1 else 2)
A229904: 1 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2
(if (x mod (1 + (4 * (x mod 5)))) <= 0 then 1 else 2)
A225180: 1 2 2 2 2 1 2 2 2 2 1 2 2 1 2 1
(if ((x + 2) mod (3 + (x div 8))) <= 0 then 1 else 2)
A225515: 2 1 2 2 1 2 2 1 2 2 1 2 2 2 1 2
(if (x mod (1 + ((x mod (2 + (x div 4))) div 2))) <= 0 then 1 else 2)
A184170: 1 1 1 1 1 2 1 1 1 1 1 2 1 2 2 1
(if (x mod (1 + (2 * (x div (2 * (2 + (x mod 2))))))) <= 0 then 1 else 2)
A163994-A154325-A143187: 1 1 1 1 2 1 1 2 2 1 1 2 2 2 1 1
(if (x mod ((x + 1) - ((x + 2) mod 8))) <= 0 then 1 else 2)
A297775-A043534: 1 1 1 1 1 1 2 1 2 2 2 2 2 2 2 1
(if ((x3 + ~2x2) mod 9) <= 0 then 1 else 2)
A245936: 1 2 1 1 2 2 1 2 2 1 2 1 1 2 2 1
(if x <= 0 then 1 else (20x2 + 2))
A010010: 1 22 82 182 322 502 722 982 1282 1622 2002 2422 2882 3382 3922 4502
(if ((x * (x mod (2 + (x div 2)))) mod 5) <= 0 then 1 else 2)
A006513: 1 2 2 1 1 1 2 2 2 2 1 2 2 1 1 1
(if (x + ~2) <= 0 then 1 else (2 * (1 + (2 mod (1 + (x div 4))))))
A104588: 1 1 1 2 2 2 2 2 6 6 6 6 6 6 6 6
(3 + (if (~4 + (x div 2)) <= 0 then (2 * (x mod 2)) else 1))
A107489: 3 5 3 5 3 5 3 5 3 5 4 4 4 4 4 4
(if ((2x mod (3 + (x div 2))) mod 3) <= 0 then 1 else 2)
A140816: 1 2 1 2 1 1 1 2 2 2 2 1 1 2 2 1
(if (((2 + (x * (x div 2))) div 3) mod 3) <= 0 then 1 else 2)
A119469: 1 1 2 2 1 2 1 2 2 1 2 2 1 2 1 2
(if (2x mod (3 + ((x + 2) div 3))) <= 0 then 1 else 2)
A023575: 1 2 1 2 2 1 2 2 2 1 2 2 2 2 2 2
(if (((x * (2 - (x div 2))) div 3) mod 3) <= 0 then 1 else 2)
A073204-A073203: 1 1 1 2 1 1 2 1 1 1 2 2 2 1 1 2
(if x <= 0 then 1 else (18x2 + 2))
A010008: 1 20 74 164 290 452 650 884 1154 1460 1802 2180 2594 3044 3530 4052
(if (((x2 + 2) mod (1 + (x div 2))) mod 3) <= 0 then 1 else 2)
A078316: 1 1 1 2 1 1 2 1 2 1 1 1 1 1 1 1
(if (((x + 1) * (x div 5)) mod 3) <= 0 then 1 else 2)
A098398: 1 1 1 1 1 1 2 2 1 2 2 1 2 2 1 1
(if ((x - ((x div 4) div ~2)) mod 3) <= 0 then 1 else 2)
A082389-A059426: 1 2 2 1 2 1 2 2 1 2 2 1 2 1 2 2
(if ((x mod (2 + ((x div 2) mod 3))) mod 3) <= 0 then 1 else 2)
A013949: 1 2 2 1 1 2 1 2 2 1 2 1 1 2 2 1
(if x <= 0 then 1 else (24x2 + 2))
A010014: 1 26 98 218 386 602 866 1178 1538 1946 2402 2906 3458 4058 4706 5402
loop(\(x,i).x2,3,(12x + 2))
A017552: 256 1475789056 208827064576 4347792138496 39062500000000 218340105584896 899194740203776 2992179271065856 8507630225817856 21435888100000000 49077072127303936 103953325454500096
loop(\(x,i).x3,1,(12x + 2))
A017547: 8 2744 17576 54872 125000 238328 405224 636056 941192 1331000 1815848 2406104 3112136 3944312 4913000 6028568
loop(\(x,i).x3,2,(12x + 2))
A017553: 512 20661046784 5429503678976 165216101262848 1953125000000000 13537086546263552 66540410775079424 257327417311663616 833747762130149888 2357947691000000000 4611686018427387903
((if (~x + 2) <= 0 then ((x2 - (x div 2)) div 3) else 1) mod 2)
A325898: 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0
(if ((x + (x2 mod 5)) mod 3) <= 0 then 1 else 2)
A098396: 1 2 1 2 2 2 2 2 1 2 2 1 2 2 1 1
(((x + 2) div (1 + ((if (x + ~2) <= 0 then 1 else x) mod 3))) mod 2)
A145099: 1 1 0 1 1 0 0 0 1 1 0 0 0 1 1 1
(((if x <= 0 then 1 else 2x) div (~1 + ((~x + 1) div 3))) mod 2)
A170977: 1 0 0 1 0 0 0 1 0 1 1 1 1 0 1 1
(if (x + ~2) <= 0 then 1 else ((x div (1 + ((~x + 1) mod 3))) mod 2))
A336923: 1 1 1 1 0 1 1 1 0 0 0 1 0 1 0 1
((1 + ((x + (if (~2 + (x div 2)) <= 0 then x else 1)) div 3)) mod 2)
A145575: 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 0
((1 + (3 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 2)
A028731: 2 3 5 6 8 11 12 14 15 17
A028794-A028767-A028740: 2 3 5 6 8 11 12 14 15 17 18 20 21 23 24 26
(if ((x + (x div (2 + (x div 4)))) mod 3) <= 0 then 1 else 2)
A001468: 1 2 1 2 2 1 2 1 2 2 1 2 2 1 2 1
(if ((x + ((x + ~2) div (2 + (x div 2)))) mod 3) <= 0 then 1 else 2)
A245920: 2 1 2 1 2 2 1 2 1 2 2 1 2 2 1 2
(if (x mod 2) <= 0 then 1 else (0 - ((x div (1 + (x mod 3))) mod 2)))
A182394: 1 0 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 0 1 ~1
(((~x * (x div 2)) div 2) mod (if (x mod 3) <= 0 then 1 else 2))
A282317: 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0
(if x <= 0 then 1 else ((x mod (~1 + (x mod (~1 + ((~x + 1) div 2))))) mod 2))
A283265-A174889-A050372-A005171: 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1
(if ((4 * (1 + (x mod 2))) mod (1 + (x div 2))) <= 0 then 1 else 2)
A212632: 1 1 1 1 2 2 1 1 2 2 2 2 2 2 2 1
((1 + loop(\(x,i).(x * (1 + i)),(x div 2),(1 + (x mod 2)))) div 2)
A187741: 1 1 1 2 3 6 12 24 60 120 360 720 2520 5040 20160 40320
((1 + loop(\(x,i).(x * i),(x + ((x div 2) * (x div 2))),1)) div 2)
A239891: 1 1 3 12 20160
((1 + loop(\(x,i).(2x2 + 4),(x + (x div 2)),1)) div 2)
A248506: 1 3 5778
(2 + loop(\(x,i).(10x + ~5),(x + 1),1))
A173772: 7 47 447 4447 44447 444447 4444447 44444447 444444447 4444444447 44444444447 444444444447 4444444444447 44444444444447 444444444444447 4444444444444447
(~2 + loop(\(x,i).(2 * ((2x + 3) + i)),(x + 1),1))
A116971: 10 56 242 988 3974 15920 63706 254852 1019438 4077784 16311170 65244716 260978902 1043915648 4175662634 16702650580
loop(\(x,i).x3,1,(8x + 6))
A017139: 216 2744 10648 27000 54872 97336 157464 238328 343000 474552 636056 830584 1061208 1331000 1643032 2000376
loop(\(x,i).x3,2,(8x + 6))
A017145: 10077696 20661046784 1207269217792 19683000000000 165216101262848 922190162669056 3904305912313344 13537086546263552 40353607000000000 106868920913284608 257327417311663616 572994802228616704
(~2 + loop(\(x,i).((x + 2) + (x div (4 + i))),(x + 1),1))
A213510: 1 3 5 7 10 13 16 19 22 25 28 31 34 38 42 46
(~2 + loop(\(x,i).11x,(x + 1),1))
A130652: 9 119 1329 14639 161049 1771559 19487169 214358879 2357947689 25937424599 285311670609 3138428376719 34522712143929 379749833583239 4177248169415649 45949729863572159
(~2 + loop(\(x,i).((x * (1 + i)) div (1 + (i div 2))),(x + ~1),1))
A201686: ~1 ~1 0 1 4 8 18 33 68 124 250 460 922 1714 3430 6433
(loop(\(x,i).(x + ((2 + ((1 + i) * i)) * i)),(x + ~1),1) div 2)
A090809: 0 0 2 10 31 75 155 287 490 786 1200 1760 2497 3445 4641 6125
(if x <= 0 then 1 else (2 * (1 + (x div (2 - ((x div 2) div ~2))))))
A063095: 1 2 2 4 4 4 4 4 6 6 6 6 6 6 6 6
loop(\(x,i).x2,1,(2 * ((2x + 1) - (x div ~2))))
A273375: 4 64 144 324 484 784 1024 1444 1764 2304 2704 3364 3844 4624 5184 6084
((if x <= 0 then 2 else (x mod (1 - (x mod (~1 + (x div ~2)))))) div 2)
A025910: 1 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1
((1 + (loop(\(x,i).2x,(x + ~6),1) div 2)) div 2)
A079262: 0 0 0 0 0 0 0 1 1 2 4 8 16 32 64 128
((1 + (loop(\(x,i).2x,(x + ~8),1) div 2)) div 2)
A122265: 0 0 0 0 0 0 0 0 0 1 1 2 4 8 16 32
((1 + (loop(\(x,i).(x + i),(x + ~8),1) div 2)) div 2)
A344625: 0 0 0 0 0 0 0 0 0 1 1 2 3 4 6 7
(if (2x mod (2 + ((x + 1) mod 5))) <= 0 then 1 else 2)
A331348: 1 2 2 1 1 2 1 2 2 1 2 2 2 2 1 1
(2 + (if ((~2 + (x2 div 2)) mod 5) <= 0 then 2 else 1))
A188590: 3 3 4 3 3 4 3 3 4 3 3 3 4 3 3 4
(if (~2 + ((x div 2) div (1 + ((~x + 2) mod 4)))) <= 0 then 1 else 2)
A328966: 1 1 1 1 1 1 2 1 1 1 2 1 1 2 2 1
(if ((x + 2) mod (2 + (x mod (1 + (x div 4))))) <= 0 then 1 else 2)
A341765: 1 2 1 2 1 2 1 1 2 2 1 2 1 1 1 2
((if x <= 0 then 1 else (x mod ((x + ~1) - (x mod 6)))) mod 2)
A025903: 1 0 0 0 0 0 1 0 1 0 0 1 1 0 1 0
(((1 + (if x <= 0 then 1 else x)) div (~1 + (2 * (x div 3)))) mod 2)
A285666: 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1
((x div (2 - (if (~x + 2) <= 0 then (~2 + (x mod 3)) else 1))) mod 2)
A074871: 0 1 1 0 1 0 1 0 0 0 1 1 1 0 1 1
((if x <= 0 then 2 else (1 + (x div 2) - ((x mod 3) mod 2))) div 2)
A025800: 1 0 1 1 1 1 2 1 2 2 2 3 3 3 4 4
((x + (if (x mod 3) <= 0 then 2 else 1) - (x div 4)) div 2)
A307152: 1 1 1 2 2 2 3 3 3 4 4 5 5 5 6 7
((1 + (loop(\(x,i).(x + ((x + i) div 2)),(x div 2),1) div 2)) div 2)
A103609: 0 0 1 1 1 1 2 2 3 3 5 5 8 8 13 13
(((if x <= 0 then 1 else x) mod (1 + (2 * (3 - (x mod 2))))) mod 2)
A321083: 1 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0
(2 * (1 + (2 * ((x + 1) + loop(\(x,i).2x,x,3)))))
A250770: 18 34 62 114 214 410 798 1570 3110 6186 12334 24626 49206 98362 196670 393282
loop(\(x,i).((x + 2) * (x + (x div 2))),(2x + 3),2)
A116253: 96012 4611686018427387903 4611686018427387903 4611686018427387903
(2 * (1 + (((x2 + 2) div (x + 2)) * (if x <= 0 then 1 else 2))))
A267573: 4 6 6 10 14 14 18 22 26 30 34 38 42 46 50 54
(2 * loop(\(x,i).x2,1,(~1 + (((x div 2) div ~2) div 2))))
A138102: 2 2 8 8 8 8 8 8 8 8 18 18 18 18 18 18
(if (~2 + (x mod (2 + (2x mod 5)))) <= 0 then 1 else 2)
A279497: 1 1 1 1 2 1 1 1 1 2 1 2 1 1 2 1
(2 + loop(\(x,i).x2,x,21))
A174262: 23 443 194483
((1 + ((if x <= 0 then 2 else (x - ((x div 3) mod 2))) div 2)) div 2)
A244479: 1 0 1 1 1 1 2 2 2 2 2 3 3 3 4 4
((if x <= 0 then 2 else (2x mod (1 + (((x + 1) div 2) div 2)))) div 2)
A209287: 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0
(if ((x mod 3) - ((((x + 1) div 2) div 2) mod 2)) <= 0 then 1 else 2)
A331349-A000002: 1 2 2 1 1 2 1 2 2 1 2 2 1 1 2 1
(if (x mod 2) <= 0 then 1 else 62)
A110823: 1 62 1
(if (~2 + (x mod (2 + ((~x + 2) mod 8)))) <= 0 then 1 else 2)
A025146: 1 1 1 2 2 2 1 1 1 1 1 1 2 2 1 1
((1 + (x div (2 + (if (x mod 2) <= 0 then 1 else 8)))) mod 2)
A106468: 1 1 1 1 0 1 1 1 1 1 0 0 1 0 1 0
(2 * (~1 + (2 * (8 + loop(\(x,i).2x,x,1)))))
A250738: 34 38 46 62 94 158 286 542 1054 2078 4126 8222 16414 32798 65566 131102
(loop(\(x,i).(x + (x div 2)),x,17) div 2)
A120137: 8 12 18 27 41 61 92 138 207 310 465 698 1047 1570 2355 3533
(x - (((x div 2) - (if (~2 + (x div 4)) <= 0 then 2 else 1)) div 2))
A072894: 1 2 3 4 4 5 6 7 7 8 9 10 10 11 11 12
(if x <= 0 then 1 else (32x2 + 2))
A010021: 1 34 130 290 514 802 1154 1570 2050 2594 3202 3874 4610 5410 6274 7202
(if (~2 + ((x2 div 2) mod (4 + (x div 2)))) <= 0 then 1 else 2)
A281007-A023589: 1 1 1 2 1 1 2 2 1 1 2 2 1 2 2 1
(if (~2 + ((~x2 + 1) mod (4 + (x div 2)))) <= 0 then 1 else 2)
A002637: 1 1 1 1 2 1 1 1 1 1 1 2 2 1 2 2
(2 + loop(\(x,i).4x,(x + 1),9))
A164093: 38 146 578 2306 9218 36866 147458 589826 2359298 9437186 37748738 150994946 603979778 2415919106 9663676418 38654705666
(~2 + loop(\(x,i).4x,(x + 1),9))
A153465: 34 142 574 2302 9214 36862 147454 589822 2359294 9437182 37748734 150994942 603979774 2415919102 9663676414 38654705662
(if (x + ~2) <= 0 then 1 else (2 + (2x div 9)))
A061555: 1 1 1 2 2 3 3 3 3 4 4 4 4 4 5 5
((~1 + (x div (~8 + (if (x mod 2) <= 0 then 2 else x)))) mod 2)
A025890: 1 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1
((1 + (if x <= 0 then 1 else ((x2 + 2x) div 8))) div 2)
A062419: 1 0 1 1 2 2 3 4 5 6 8 9 11 12 14 16
(x - ((x - loop(\(x,i).(2 * i),(x + ~8),1)) div 2))
A029028: 1 1 2 2 3 3 4 4 5 6 7 9 10 12 13 15
((if x <= 0 then 1 else x) - ((1 + (x2 div 8)) div 2))
A341155: 1 1 2 2 3 3 4 4 4 4 4 3 3 2 2 1
(if ((x + 3) mod (2 + ((~x + 1) mod 4))) <= 0 then 1 else 2)
A078377: 1 1 1 2 2 1 2 2 2 1 2 2 1 1 2 2
(if x <= 0 then 1 else (2 * (x div (1 + ((x - (x div 4)) div 2)))))
A335901: 1 2 2 2 4 2 4 2 4 4 4 4 4 4 4 4
(if (x mod (1 - (2 * ((~x + 1) div (2 + (x div 2)))))) <= 0 then 1 else 2)
A238303: 1 1 2 1 2 2 1 2 2 2 1 2 2 2 2 1
((x + 2) - ((~x + 1) div (2 + (if (~2 + (x div 2)) <= 0 then 2 else 1))))
A028801: 2 3 5 6 7 8 10 11 13 14 15 17 18 19 21 22
(2 * loop(\(x,i).2x,(x div 2),(1 + (2 * (2 + (x mod 2))))))
A063920: 10 14 20 28 40 56 80 112 160 224 320 448 640 896 1280 1792
(if x <= 0 then 1 else (2 * (1 + ((~1 + (x mod 3)) mod 4))))
A222011: 1 2 4 8
A167420: 1 2 4 8 2 4 8 2 4 8 2 4 8 2 4 8
(if ((x mod ~11) mod 4) <= 0 then 1 else 2)
A080757: 1 2 2 1 2 2 2 1 2 2 2 1 2 2 1 2
(if ((((x + ~1) div 2) * (x mod 3)) mod 4) <= 0 then 1 else 2)
A046219: 1 1 1 1 2 1 1 2 2 1 1 2 1 2 1 1
(if (((x + ~3) mod (1 + (x div 2))) mod 4) <= 0 then 1 else 2)
A082071-A082070-A082065: 1 1 2 1 2 2 2 1 1 2 2 2 2 2 2 1
(2 * (1 + loop(\(x,i).(3x + 3),2x,4)))
A198968: 10 98 890 8018 72170 649538 5845850 52612658 473513930 4261625378 38354628410 345191655698 3106724901290 27960524111618 251644717004570 2264802453041138
(2 * (1 + (if (2 - (x div 4)) <= 0 then (x div 2) else 4)))
A109751: 10 10 10 10 10 10 10 10 10 10 12 12 14 14 16 16
(if x <= 0 then 1 else (15x2 + 2))
A010005: 1 17 62 137 242 377 542 737 962 1217 1502 1817 2162 2537 2942 3377
(((if (~2 + (x div 2)) <= 0 then x else (x + 1)) mod 5) mod 2)
A157687: 0 1 0 1 0 0 0 1 0 0 1 0 1 0 0 1
(if x <= 0 then 1 else (2 + (8x div 5)))
A184734-A184582: 1 3 5 6 8 10 11 13 14 16 18 19 21 22 24 26
(2 * loop(\(x,i).(2x + 6),(x + 2),5))
A099944: 76 164 340 692 1396 2804 5620 11252 22516 45044 90100 180212 360436 720884 1441780 2883572
(if (x + ~1) <= 0 then x else (2 + (2x2 div 5)))
A094913: 0 1 3 5 8 12 16 21 27 34 42 50 59 69 80 92
((if (x mod 2) <= 0 then (~x + 1) else (x + 2)) mod 10)
A285264: 1 3 9 5 7
A106586: 1 3 9 5 7 7 5 9 3 1 1 3 9 5 7 7
(x - loop(\(x,i).(~x2 + x),1,(x mod 10)))
A068522: 0 1 4 9 16 25 36 49 64 81 10 11 14 19 26 35
loop(\(x,i).(x3 + 3x),x,10)
A145184: 10 1030 1092730090 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + ~3x),x,10)
A006242: 10 970 912670090 4611686018427387903 4611686018427387903
loop(\(x,i).(5x + 4),x,10)
A198770: 10 54 274 1374 6874 34374 171874 859374 4296874 21484374 107421874 537109374 2685546874 13427734374 67138671874 335693359374
(((x + (if (~2 + (x div 2)) <= 0 then 1 else 0)) mod 5) mod 2)
A284471: 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0
(if x <= 0 then 1 else (2 + ((x + (x mod 3)) div 5)))
A331255: 1 2 2 2 3 3 3 3 4 3 4 4 4 4 5 5
(x - (2 * (if (~4 + (x div 2)) <= 0 then x else 5)))
A187844: 0 ~1 ~2 ~3 ~4 ~5 ~6 ~7 ~8 ~9 0 1 2 3 4 5
(if x <= 0 then 1 else (2 * (2x - ((~x + 2) div 5))))
A312475: 1 4 8 14 18 22 26 30 36 40 44 48 52 58 62 66
(if x <= 0 then 2 else (x - (2 * ((x + (x mod 2)) div 5))))
A320581: 2 1 2 3 4 3 4 5 6 5 6 7 8 9 10
(((if (x mod 4) <= 0 then 1 else 2) + (x div 5)) div 2)
A339383: 0 1 1 1 0 1 1 1 1 1 2 2 1 2 2 2
(2 * loop(\(x,i).(x + (x div 5)),x,5))
A055983: 10 12 14 16 18 20 24 28 32 38 44 52 62 74 88 104
((if x <= 0 then 2 else ((x div 2) mod (1 + (~x mod 4)))) div 2)
A339366: 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0
((x mod (1 + ((if (x mod 2) <= 0 then 2 else 0) + (x div 4)))) div 2)
A309766: 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1
(if (x + ~1) <= 0 then 2 else (((x + 1) mod (1 + (x div 4))) mod 2))
A316342: 2 2 0 0 1 0 1 0 0 1 0 0 1 0 1 0
((x - (if (x + ~2) <= 0 then 1 else (x mod (1 + (x div 4))))) mod 2)
A258769: 1 0 1 1 0 0 0 0 0 1 1 1 0 0 0 0
((1 + (x mod 5)) * (if (x mod 4) <= 0 then 1 else 2))
A231407: 1 4 6
A331059: 1 4 6 8 5 2
((1 + (((x + ~1) div 2) div 2)) * (if (x mod 4) <= 0 then 1 else 2))
A131308: 0 2 2 2 1 4 4 4 2 6 6 6 3 8 8 8
((if x <= 0 then 1 else (x mod (~3 + ((x * (x div 2)) mod 2)))) mod 2)
A300185: 1 0 1 1 0 1 0 1 1 0 0 1 0 0 1 1
(((x + 5) * loop(\(x,i).2x,(x + ~1),x)) div 2)
A176027: 0 3 14 48 144 400 1056 2688 6656 16128 38400 90112 208896 479232 1089536 2457600
(((x + 5) * loop(\(x,i).(x * (2 + i)),x,x)) div 2)
A272582: 0 9 84 720 6480 63000 665280 7620480 94348800 1257379200 17962560000 273988915200 4446092851200 76498950528000 1391365527552000 26676557107200000
((if (x + ~2) <= 0 then 1 else (x2 div (2x + 5))) mod 2)
A109409-A097806: 1 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0
loop(\(x,i).x2,3,(~7x + ~2))
A017012: 256 43046721 4294967296 78310985281 656100000000 3512479453921 14048223625216 45767944570401 128063081718016 318644812890625 722204136308736 1517108809906561 2992179271065856 5595818096650401
(if x <= 0 then 1 else (2 * (1 + (((x mod 3) * (x div 2)) mod 2))))
A100007: 1 2 2 2 2 2 2 4 2 2 4 2 2 2 2 2
((if x <= 0 then 2 else (1 + (~2x mod (2 + (x div 2))))) mod 2)
A257799: 0 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1
(if x <= 0 then 1 else (2 + (3x div (3 + (x div 2)))))
A130253: 1 3 3 4 4 5 5 5 5 5 5 6 6 6 6 6
(((if x <= 0 then 1 else x) mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2)
A327517-A322452-A318721-A080732: 1 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0
((if x <= 0 then 1 else (x div (2 - (x div (1 + ((x div 2) mod 2)))))) mod 2)
A342025: 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1
(x div (3 + (if (~2 + (x div 3)) <= 0 then (x mod 2) else 2)))
A331973: 0 0 0 0 1 1 2 1 2 1 2 2 2 2 2 3
(2 * (1 + loop(\(x,i).x2,1,((2x + 2) - (x mod 2)))))
A276764: 10 20 74 100 202 244 394 452 650 724 970 1060 1354 1460 1802 1924
(2 * ((1 + loop(\(x,i).8x,x,1)) div 3))
A132804: 0 6 42 342 2730 21846 174762 1398102 11184810 89478486 715827882 5726623062 45812984490 366503875926 2932031007402 23456248059222
((3 * (if x <= 0 then 1 else (x div 7))) div 2)
A245147: 1 0 0 0 0 0 0 1 1 1 1 1 1 1 3 3
(if x <= 0 then 1 else (2 * ((8x + 1) div 3)))
A301694: 1 6 10 16 22 26 32 38 42 48 54 58 64 70 74 80
(loop(\(x,i).(~x + 1),(x + ~1),(3 * (x mod 3))) div 2)
A133513: 0 1 ~3 0 ~1 3 0 1 ~3 0 ~1 3 0 1 ~3 0
(((if x <= 0 then 1 else ((~x2 + 2x) div 3)) mod 3) mod 2)
A027345: 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1
(2 * ((1 + loop(\(x,i).8x,x,2)) div 3))
A132397: 2 10 86 682 5462 43690 349526 2796202 22369622 178956970 1431655766 11453246122 91625968982 733007751850 5864062014806 46912496118442
(((~1 + (if (x mod 4) <= 0 then x else (x div 2))) div 3) mod 2)
A127239: 1 1 0 0 1 0 0 0 0 1 1 1 1 1 0 0
(((if x <= 0 then 1 else (x div 3)) * ((x + ~1) mod 3)) div 2)
A029297: 1 0 0 1 0 0 2 0 1 3 0 1 4 0 2 5
(if (x + ~1) <= 0 then 0 else (2 + (3 * ((x mod 3) mod 2))))
A021448: 0 0 2 2 5 2 2 5 2 2 5 2 2 5 2 2
(2 + (3 * (2 + loop(\(x,i).3x,2x,1))))
A224790: 11 35 251 2195 19691 177155 1594331 14348915 129140171 1162261475 10460353211 94143178835 847288609451 7625597484995 68630377364891 617673396283955
((3 * ((if x <= 0 then 2 else (((x + 1) div 2) div 2)) div 2)) div 2)
A339108: 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 3
(~2 + (3 * loop(\(x,i).(2x + 1),x,8)))
A304387: 22 49 103 211 427 859 1723 3451 6907 13819 27643 55291 110587 221179 442363 884731
(2 * ((2 + (loop(\(x,i).((x + i) * i),x,2) div 2)) mod 3))
A072680: 0 0 2 0 2 0 4 4 4 0 2 0 4 4 4 0
(if (x + ~2) <= 0 then (x + ~2) else (2 + ((2 * (x div 2)) div 3)))
A061009: ~2 ~1 0 2 3 3 4 4 4 4 5 5 6 6 6 6
((3 * (loop(\(x,i).2x,x,2) div (2 + (x mod 2)))) div 2)
A282005: 1 1 6 7 24 31 96 127 384 511 1536 2047 6144 8191 24576 32767
(2 + (((x2 div 2) - ((if x <= 0 then 1 else x) mod 2)) div 3))
A008749: 1 1 2 3 4 5 8 9 12 15 18 21 26 29 34 39
(if x <= 0 then 1 else (2 + ((x - ((x * (x div 2)) mod 2)) div 3)))
A087739: 1 2 2 2 3 3 4 4 4 5 5 5 6 6 6 6
loop(\(x,i).3x,x,(1 - (2 * (2x div 3))))
A171557: 1 3 ~9 ~81 ~243 ~1215 ~5103 ~15309 ~59049 ~216513 ~649539 ~2302911 ~7971615 ~23914845 ~81310473 ~272629233
(if x <= 0 then 0 else (1 - ((~x + 1) div (2 + ((x div 2) div 3)))))
A265340: 0 1 2 2 3 3 3 3 4 4 4 5 4 4 5 5
(if (x mod 3) <= 0 then 2 else ((x - ((x div 2) div 3)) mod 2))
A321102: 2 1 0 2 0 1 2 0 1 2 1 0 2 1 0 2
(2 * (loop(\(x,i).(x + (x div (2 + (x mod 2)))),x,2) div 3))
A091915: 0 2 2 4 6 8 12 18 24 36 54 72 108 162 216 324
(2 - (if x <= 0 then 1 else ((x - (3 * (x2 div 2))) div 2)))
A267529: 1 2 4 7 12 18 26 35 46 58 72 87 104 122 142 163
(((~x + 1) mod (~3 + (if x <= 0 then 2 else 0))) mod 6)
A021189: 0 0 5 4 0 5 4 0 5 4 0 5 4 0 5 4
(((if x <= 0 then 1 else 0) - ((~x + 1) mod 3)) mod 6)
A021226: 0 0 4 5 0 4 5 0 4 5 0 4 5 0 4 5
(if (4 mod (x + 1)) <= 0 then (2x + 1) else 6)
A329516: 1 3 6 7 6 6 6 6 6 6 6 6 6 6 6 6
loop(\(x,i).(x3 + ~3x),(x + 1),6)
A006243: 198 7761798 4611686018427387903 4611686018427387903
(6 + loop(\(x,i).7x,x,1))
A253210: 7 13 55 349 2407 16813 117655 823549 5764807 40353613 282475255 1977326749 13841287207 96889010413 678223072855 4747561509949
loop(\(x,i).(x2 * (2 + i)),(2x + 2),6)
A132642: 46656 4611686018427387903
((x + 6) - (if x <= 0 then 1 else (x div 8)))
A302980: 5 7 8 9 10 11 12 13 13 14
(x - ((if x <= 0 then 1 else x) div (~6 + (x div 4))))
A176845: 1 2 3 4 5 6 8 9 10 12 13 14 16 18 19 20
(6 + loop(\(x,i).2x,(x div 2),(2 + (x mod 2))))
A209724: 8 9 10 12 14 18 22 30 38 54 70 102 134 198 262 390
((if (~2 + (x div 4)) <= 0 then 1 else 2) * (x mod 6))
A309957: 0 1 2 3 4 5 0 1 2 3 4 5 0 2 4 6
loop(\(x,i).(x * (1 + (x div 5))),x,6)
A117596: 6 12 36 288 16704 55808064 622908012647232 4611686018427387903 4611686018427387903 4611686018427387903
(((if ((2 + (x div 2)) mod 4) <= 0 then 1 else x) mod 3) mod 2)
A337546-A157238-A059448: 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0
(((if (2x mod (2 + (x div 2))) <= 0 then 1 else x) mod 3) mod 2)
A286801-A123594: 1 1 0 1 1 0 0 1 0 1 1 0 1 1 0 0
loop(\(x,i).x2,3,(9x + 2))
A017192: 256 214358881 25600000000 500246412961 4347792138496 23811286661761 96717311574016 318644812890625 899194740203776 2252292232139041 5132188731375616 10828567056280801 21435888100000000 40213853471634241
loop(\(x,i).x3,1,(9x + 2))
A017187: 8 1331 8000 24389 54872 103823 175616 274625 405224 571787 778688 1030301 1331000 1685159 2097152 2571353
loop(\(x,i).x3,2,(9x + 2))
A017193: 512 2357947691 512000000000 14507145975869 165216101262848 1119130473102767 5416169448144896 20711912837890625 66540410775079424 186940255267540403 472161363286556672 1093685272684360901
(((x div 4) - ((if (x + ~2) <= 0 then 1 else x) mod 3)) mod 2)
A123272: 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 1
(if x <= 0 then 1 else (2 + ((2x3 + x) div 3)))
A179903: 1 3 8 21 46 87 148 233 346 491 672 893 1158 1471 1836 2257
(2 + (loop(\(x,i).(4x + ~1),(x + 1),x) div 3))
A088582: 1 5 37 229 1253 6373 30949 145637 669925 3029221 13514981 59652325 260978917 1133394149 4891490533 20997617893
((3 * (x + (if (~2 + (x div 3)) <= 0 then 1 else 2))) div 2)
A225647: 1 3 4 6 7
A330176: 1 3 4 6 7 9 10 12 13 16 18 19 21 22 24 25
(2 * (x mod (3 * (if (~2 + (x div 4)) <= 0 then 2 else x))))
A004522: 0 2 4 6 8 10 0 2 4 6 8 10 24 26 28 30
((loop(\(x,i).i,(x div 4),1) * ((~x + 2) mod 3)) div 2)
A029323: 1 0 0 1 0 0 1 0 0 2 1 0 3 1 0 3
(2 * ((x + 3) + (2 * (if (x + ~4) <= 0 then 1 else x))))
A092132: 10 12 14 16 18 36 42
(if x <= 0 then 1 else ((x - (3 * (~x + ((~x + 2) div 2)))) div 2))
A195669: 1 2 4 7 9 13 15 18 20
(loop(\(x,i).(~2x + ((x div 2) mod 3)),x,3) div 2)
A279634: 1 ~3 5 ~9 18 ~36 72 ~144 288 ~576 1152 ~2304 4608 ~9216 18432 ~36864
(if (x + ~1) <= 0 then x else ((x - ((x * (x div 2)) div 3)) div 2))
A292052: 0 1 1 1 1 1 0 0 ~1 ~2 ~3 ~4 ~6 ~7 ~9 ~10
((1 + (if x <= 0 then 1 else x)) mod (2 + ((x + (x mod 2)) div 3)))
A073438: 0 0 1 1 2 2 3 0 1 0 1 0 1 2 3 2
(((x + (if (~x + 8) <= 0 then x else 2)) div 3) mod 2)
A051067: 0 1 1 1 0 0 0 1 1 0 0 1 0 0 1 0
(((if x <= 0 then 2 else (x div (1 + (x mod 2)))) - (x div 3)) div 2)
A029220: 1 0 1 0 1 0 2 0 3 0 3 1 4 1 5 1
(2 - ((~2x + 4) div (2 + (if x <= 0 then 1 else (x div 3)))))
A239683: 1 1 2 3 4 4 4 5 5 5 6 6 6 6 6 6
loop(\(x,i).2x,((3x + 2) + (x div 3)),2)
A074116-A074113: 8 64 512 8192 65536 524288 8388608 67108864 536870912 8589934592 68719476736 549755813888 8796093022208 70368744177664 562949953421312 9007199254740992
(if x <= 0 then 1 else (2 * (2x + (x mod 2) - (x div 3))))
A063207: 1 6 8 12 14 20 20 26 28 32 34 40 40 46 48 52
(((if (x + ~4) <= 0 then 1 else (x div 2)) + (x div 3)) mod 2)
A115361: 1 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0
(((2 * (x + (if (x + ~2) <= 0 then 1 else x))) - (x div 3)) div 2)
A258037: 1 2 3 5 7 9 11 13 15 16 18 20 22 24 26 27
((if (~2 + (x div 2)) <= 0 then 2 else (x + ~2)) div (2 + (x div 3)))
A186726: 1 1 1 0 0 0 1 1 1 1 1 1 1 1 2 1
(if x <= 0 then 1 else (2 * (5x - (x div 3))))
A063117: 1 10 20 28 38 48 56 66 76 84 94 104 112 122 132 140
(((if (x + ~2) <= 0 then 1 else (2 + (x mod 2))) + (x mod 3)) div 2)
A097867: 0 1 1 1 1 2 1 2 2 1 1 2 1 2 2 1
((if (x mod 2) <= 0 then 1 else (x div 3)) * ((x mod 3) div 2))
A233286: 0 0 1 0 0 1 0 0 1 0 0 3 0 0 1 0
((if (~2 + (x div 3)) <= 0 then 1 else 2) * ((x mod 3) div 2))
A116373: 0 0 1 0 0 1 0 0 1 0 0 2 0 0 2 0
(2 + ((x mod 3) div 2) - ((if (x + ~2) <= 0 then 1 else x) mod 2))
A239140: 1 1 2 1 2 2 2 1 3 1 2 2 2 1 3 1
((if (x + ~2) <= 0 then 1 else 2) + (x mod 2) + ((x mod 3) div 2))
A217984: 1 2 2 3 2 4 2 3 3 3 2 4 2 3 3 3
loop(\(x,i).2x,(x div 3),(2 - ((x mod 3) mod 2)))
A060547: 2 1 2 4 2 4 8 4 8 16 8 16 32 16 32 64
(2 * loop(\(x,i).(x * (10 + i)),x,3))
A267141: 6 66 792 10296 144144 2162160 34594560 588107520 10585935360 201132771840 4022655436800 84475764172800 1858466811801600 42744736671436800 1025873680114483200 4611686018427387903
((1 + (if x <= 0 then 1 else ((x * ((~x + 1) div 3)) div 2))) mod 2)
A334820: 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1
(if x <= 0 then 1 else (2 * (~1 + (2 * (x + (x div 8))))))
A182991: 1 2 6 10 14 18 22 26 34 38 42 46 50 54 58 62
((1 + ((if ((x div 2) mod (2 + (x mod 2))) <= 0 then 2 else x) div 2)) div 2)
A060240: 1 1 1 1 1 1 2 1 1 2 3 3 1 1 4 4
((1 + (loop(\(x,i).2x,x,(3x + 4)) div 2)) div 2)
A133086: 1 4 10 26 64 152 352 800 1792 3968 8704 18944 40960 88064 188416 401408
(((x + 3) + ((4 div (if x <= 0 then 1 else x)) mod 2)) div 2)
A138161: 1 2 2 3 4 4 4 5 5
A112325: 1 2 2 3 4 4 4 5 5 6 6 7 7 8 8 9
(2 * loop(\(x,i).(2 * (4x + (x div 2))),(x + 2),1))
A203819: 144 1296 11664 104976 944784 8503056 76527504 688747536 6198727824 55788550416 502096953744 4518872583696 40669853253264 366028679279376 3294258113514384 29648323021629456
(2 * loop(\(x,i).(2 * (4x - (x div 2))),(x + 2),1))
A203789: 112 784 5488 38416 268912 1882384 13176688 92236816 645657712 4519603984 31637227888 221460595216 1550224166512 10851569165584 75960984159088 531726889113616
((if x <= 0 then 1 else ((x3 + x2) div (x + 3))) mod 2)
A339375-A202108: 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0
((x div 2) - (loop(\(x,i).(2 * (x - (i div 2))),(x + ~2),1) div 2))
A328284: 0 0 1 0 1 1 3 5 11 21 43 85 171 341 683 1365
(1 - ((x div ~5) * (if (x + ~2) <= 0 then 1 else 2)))
A175944: 1 2 2 3 3 3 5 5 5 5 5 7 7 7 7 7
((3x + 24) + (if (x + ~2) <= 0 then 1 else 2))
A295748: 25 28 31 35
(x + (if (x + ~2) <= 0 then 1 else 2) - ((~x + ((x div 2) mod 2)) div 2))
A175071: 1 3 4 6 8 10 11 12 14 16 17 18 20 22 23 24
((if x <= 0 then 1 else (x2 mod ((2x + 1) + (x div 2)))) mod 2)
A213719: 1 1 0 1 1 0 0 1 1 0 0 1 0 0 0 1
loop(\(x,i).32x,(2x + 1),2)
A013832: 64 65536 67108864 68719476736 70368744177664 72057594037927936 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x5,1,(4x + 2))
A016829: 32 7776 100000 537824 1889568 5153632 11881376 24300000 45435424 79235168 130691232 205962976 312500000 459165024 656356768 916132832
loop(\(x,i).x2,1,((~4x + ~2) + (x div ~2)))
A061100: 4 49 121 256 400 625 841 1156 1444 1849 2209 2704 3136 3721 4225 4900
((1 + (loop(\(x,i).(x * (1 + (i div 2))),x,1) + (x div 2))) div 2)
A110887: 1 1 2 3 7 19 74
((x + 1) div (2 + (if ((x * (x div 2)) mod 2) <= 0 then (x div 2) else 1)))
A299203: 0 1 1 1 1 1 1 2 1 1 1 4 1 1 1 5
((if x <= 0 then 2 else ((x + 1) - ((1 - (x div 2)) * (x div 2)))) div 2)
A055802: 1 1 1 2 3 4 6 7 10 11 15 16 21 22 28 29
(if x <= 0 then 1 else (2 * ((x2 + 2x + ~1) div (1 + (x div 2)))))
A231407: 1 4 6
A296910: 1 4 6 14 14 22 22 30 30 38 38 46 46 54 54 62
((((if (x mod 2) <= 0 then 2 else 0) + (x div 2)) * (1 + (x div 2))) div 2)
A008795: 1 0 3 1 6 3 10 6 15 10 21 15 28 21 36 28
(x + ((if (x mod 4) <= 0 then 2 else 0) + ((1 + (x div 2)) div 2)))
A160186: 2 1 3 4 7 6 8 9 12 11 13 14 17 16 18 19
(((if (x mod 2) <= 0 then (x div 2) else (~x + 1)) * (1 + (x div 2))) div 2)
A131259: 0 0 1 ~2 3 ~6 6 ~12 10 ~20 15 ~30 21 ~42 28 ~56
(loop(\(x,i).(x + ((i * i) div 3)),x,(1 + (x div 2))) div 2)
A173691: 0 0 1 3 6 10 16 24 35 49 66 86 110 138 171 209
(2 - (if (~2 + (x div 3)) <= 0 then 2 else ((~1 + (x div 2)) div 2)))
A286134: 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ~1 ~1
(if (((x * (x div 3)) mod 3) - (x mod 2)) <= 0 then 1 else 2)
A059689: 1 1 1 1 2 2 1 2 2 1 1 1 1 1 2 1
(if (x + ~1) <= 0 then 1 else (2 * (((x + 1) div 2) div (1 + (x mod 2)))))
A185048: 1 1 2 2 4 2 6 4 8 4 10 6 12 6 14 8
((1 + ((x * (x + (if (x + ~4) <= 0 then 2 else 1))) div 2)) div 2)
A321531: 0 1 2 4 6 8 11 14 18 23
(((x + 1) + loop(\(x,i).(2 + (x * (1 + i))),(x + ~1),1)) div 2)
A089475: 1 1 3 9 31 149
loop(\(x,i).x2,3,(10x + 2))
A017300: 256 429981696 54875873536 1099511627776 9682651996416 53459728531456 218340105584896 722204136308736 2044140858654976 5132188731375616 11716593810022656 24759631762948096 49077072127303936
loop(\(x,i).x3,1,(10x + 2))
A017295: 8 1728 10648 32768 74088 140608 238328 373248 551368 778688 1061208 1404928 1815848 2299968 2863288 3511808
loop(\(x,i).x3,2,(10x + 2))
A017301: 512 5159780352 1207269217792 35184372088832 406671383849472 2779905883635712 13537086546263552 51998697814228992 167619550409708032 472161363286556672 1195092568622310912 2773078757450186752
(loop(\(x,i).(x div (1 + (x mod 2))),x,(3x + 1)) div 2)
A173732: 0 2 0 5 3 8 2 11 6 14 0 17 9 20 5 23
(((3x + ~1) * loop(\(x,i).2x,(x + ~1),x)) div 2)
A084857: 0 1 10 48 176 560 1632 4480 11776 29952 74240 180224 430080 1011712 2351104 5406720
(loop(\(x,i).((2x + ~1) + (x mod 2) - (i mod 2)),x,1) div 2)
A115851: 0 0 1 1 1 2 5 9 17 34 69 137 273 546 1093 2185
(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1) div 2)
A092679: 0 1 5 17
A301560: 0 1 5 17 63 231 858 3217 12155 46189 176358 676039 2600150 10029150 38779380 150270097
(2 * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x)))
A001747: 2 4 6 10 14 22 26 34 38 46 58 62 74 82 86 94
(loop(\(x,i).3x,(x + 1),(x2 + x + 1)) div 2)
A153703: 1 13 94 526 2551 11299 47020 186988 718429 2686729 9831658 35340826 125154355 437641663 1513809688 5187129880
((1 + loop(\(x,i).(x + (2 * (x + (i mod 2)))),(x + ~1),x)) div 2)
A119916: 0 1 4 17 64 233 820 2825 9568 31985 105796 346913 1129312 3653657 11758132 37665881
((1 + (((x + 2) mod 6) mod (if x <= 0 then 1 else x))) div 2)
A139365: 0 0 0 1 0 1 1 2 2 3 0 1 1 2 2 3
(~2 + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1))
A120304: ~1 ~1 0 3 12 40 130 427 1428 4860 16794 58784 208010 742898 2674438 9694843
(2 * (if (x + ~1) <= 0 then 1 else ((x + ~1) + ((x mod 3) div 2))))
A264788: 2 2 4 4 6 10 10 12 16 16 18 22 22 24 28 28
(2 * loop(\(x,i).(2 * ((x + ~1) + (2 * (x + (i mod 2))))),x,1))
A220932: 2 16 92 556 3332 19996 119972 719836 4319012 25914076 155484452 932906716 5597440292 33584641756 201507850532 1209047103196
((1 + loop(\(x,i).i,(x div (2 + ((x mod 3) div 2))),x)) div 2)
A193676: 0 1 1 1 1 1 2 2 1 2 3 2 3 3 2 4
(if (x - (x3 mod (x + 8))) <= 0 then 1 else 2)
A273134: 1 1 1 1 1 1 1 1 2 1 1 2 2 1 1 1
(loop(\(x,i).(2 * (x + (x div (1 + (4 * i))))),x,1) div 2)
A182442: 0 1 2 4 8 16 33 68 140 287 588 1202 2453 4998 10171 20675
(2 * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A037168: 2 4 8 12 20 24 32 36 44 56 60 72 80 84 92 104
(2 * loop(\(x,i).3x2,2,(x2 + 2x + 1)))
A085482: 54 13824 354294 3538944 21093750 90699264 311299254 905969664 2324522934 5400000000 11575379574 23219011584 44049458934 79692609024 138396093750 231928233984
(((x + 1) + (if (x mod 4) <= 0 then 2x else (x div 2))) div 2)
A028390: 0 1 2 2 6 4 5 5 12 7 8 8 18 10 11 11
(2 * ((x + 1) + loop(\(x,i).(x * (2 - (x div (2 + i)))),x,2)))
A079946: 6 12 14 24 26 28 30 48 50 52 54 56 58 60 62 96
loop(\(x,i).(10x + 3),(x + 1),2)
A290425: 23 233 2333 23333
(((x + 1) * (if (x mod 2) <= 0 then (2 + (x mod 4)) else 1)) div 2)
A062828: 1 1 6 2 5 3 14 4 9 5 22 6 13 7 30 8
(2 + compr(\x.(~1 + (loop(\(x,i).2x,x,2) mod (x + 2))),(x + 1)))
A066542: 3 4 5 7 8 11 13 16 17 19 23 29 31 32 37 41
((2x + 2) * loop(\(x,i).(2 * ((x * i) + (x div 2))),x,1))
A208124: 2 8 60 560 6300 83160 1261260 21621600 413513100 8729721000 201656555100 5059746291600 137034795397500 3984550204635000 123805667072587500 4093840724533560000
((x + 2) - ((2 + (if x <= 0 then 0 else 2) - (x div 2)) div (x + 1)))
A048293: 0 1 3 5 6 7 8 9 10 11 13 14 15 16 17 18
(2 * loop(\(x,i).(x3 + 2),(2x + 2),(x + 1)))
A116115-A116103: 58 4611686018427387903 4611686018427387903 4611686018427387903
(((x + 1) * (if (x mod 2) <= 0 then 2 else (x mod ~4))) div 2)
A186111: 1 ~3 3 ~2 5 ~9 7 ~4 9 ~15 11 ~6 13 ~21 15 ~8
(if x <= 0 then 1 else (2 + (2 div (16 div (x + 1)))))
A087181: 1 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4
(((if (x mod 6) <= 0 then (x div 2) else 2) mod (x + 1)) div 2)
A317624: 0 0 1 1 1 1 1 1 1 1 1 1 3 1 1 1
(loop(\(x,i).((x - ((~x + 2) div 2)) * (x div 2)),2,(x + 1)) div 2)
A145920: 0 1 5 35 70 210 330 715 1001 1820 2380 3876 4845 7315 8855 12650
(((x + 1) * ((x + 2) + (if (x mod 2) <= 0 then 2x else 0))) div 2)
A110345: 1 3 12 10 35 21 70 36 117 55 176 78 247 105 330 136
loop(\(x,i).(x3 + ~x2),1,((x2 + 3x + 2) div 2))
A071910: 0 18 180 900 3150 8820 21168 45360 89100 163350 283140 468468 745290 1146600 1713600 2496960
(loop(\(x,i).x2,2,(x + 2)) - ((x2 + 3x + 2) div 2))
A269436: 15 78 250 615 1281 2380 4068 6525 9955 14586 20670 28483 38325 50520 65416 83385
loop(\(x,i).2x,(x2 + ~x),((x2 + 3x + 2) div 2))
A202944: 1 3 24 640 61440 22020096 30064771072 158329674399744 3242591731706757120 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x * (2 + i)),x,((x2 + 3x + 2) div 2))
A286725: 1 18 288 4800 86400 1693440 36126720 836075520 20901888000 562028544000 16186422067200 497364605337600 16247243774361600 562404592189440000 4611686018427387903 4611686018427387903
loop(\(x,i).(x div (2 - (x mod 2))),x,((x2 + 3x + 2) div 2))
A069834: 1 3 3 5 15 21 7 9 45 55 33 39 91 105 15 17
loop(\(x,i).(x * (4 + i)),x,((x2 + 3x + 2) div 2))
A005461: 1 15 180 2100 25200 317520 4233600 59875200 898128000 14270256000 239740300800 4249941696000 79332244992000 1556132497920000 32011868528640000 689322235650048000
(if ((x + 2) mod 9) <= 0 then 1 else (2x + 2))
A274611: 2 4 6 8 10 12 14 1 18 20 22 24 26 28 30 32
(loop(\(x,i).5x,(x + 1),1) mod (2x + 2))
A083528: 1 1 5 1 5 1 5 1 17 5 5 1 5 25 5 1
(loop(\(x,i).(x * (1 + (2 * (i div 2)))),x,1) mod (2x + 2))
A215456: 1 1 3 1 5 9 7 1 9 5 11 9 13 21 15 1
loop(\(x,i).(1 + (x2 div (x + 4))),2,(2x + 2))
A280196: 1 2 3 4 6 8 9 10 12 14 16 18 20 22 24 26
((2x + 2) + ((if (x + ~4) <= 0 then x else (x + 1)) div 2))
A247912: 2 4 7 9 12 15 17 20 22 25 27 30 32 35 37 40
(if x <= 0 then 1 else ((4x + 3) * ((x + 1) div 2)))
A083363: 1 7 11 30 38 69 81 124 140 195 215 282 306 385 413 504
(loop(\(x,i).x3,1,(1 + (x div 2))) * ((x + 1) div 2))
A212764: 0 1 8 16 54 81 192 256 500 625 1080 1296 2058 2401 3584 4096
((loop(\(x,i).(x * i),x,((x + ~1) div 2)) div 2) * ((x + 1) div 2))
A152886: 0 0 0 6 24 360 2160 30240 241920 3628800 36288000 598752000 7185024000 130767436800 1830744115200 36614882304000
(if (x + ~2) <= 0 then (x mod 2) else ((2 * (x mod 2)) + ((x + 1) div 2)))
A267185: 0 1 0 4 2 5 3 6 4 7 5 8 6 9 7 10
loop(\(x,i).(4x + 4),((x + 1) div 2),((x + 1) mod 2))
A133628-A097164: 1 4 8 20 36 84 148 340 596 1364 2388 5460 9556 21844 38228 87380
(((x + 1) * loop(\(x,i).5x,(x + ~1),x)) div 2)
A084902: 0 1 15 150 1250 9375 65625 437500 2812500 17578125 107421875 644531250 3808593750 22216796875 128173828125 732421875000
(loop(\(x,i).(x div (2 - ((x div ~2) mod 2))),x,(x + 1)) div 2)
A163575: 0 1 0 1 2 3 0 1 4 5 2 3 6 7 0 1
(~2 + ((x + 1) * loop(\(x,i).(6x + 4),2,x)))
A304834: 26 126 298 542 858 1246 1706 2238 2842 3518 4266 5086 5978 6942 7978 9086
(1 - (x div (2 * loop(\(x,i).(x div (~2 + (x mod 2))),x,(x + 1)))))
A330569: 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 9
((x * (loop(\(x,i).(x * i),x,2) div (x + 1))) - ((x + ~1) div 2))
A257555: 1 1 2 8 35 198
(((x + ~1) * loop(\(x,i).3x,(2x + ~4),x)) div 2)
A081139: 0 0 1 27 486 7290 98415 1240029 14880348 172186884 1937102445 21308126895 230127770466 2447722649502 25701087819771 266895911974545
(((x + ~1) * loop(\(x,i).5x,(x + ~2),x)) div 2)
A081135: 0 0 1 15 150 1250 9375 65625 437500 2812500 17578125 107421875 644531250 3808593750 22216796875 128173828125
(29 * (if x <= 0 then 1 else 2))
A040812: 29 58 58 58 58 58 58 58 58 58 58 58 58 58 58 58
((24x + 12) - (if x <= 0 then 1 else 2))
A063162: 11 34 58 82 106 130 154 178 202 226 250 274 298 322 346 370
(((x3 * (x div 2)) div 3) + (if x <= 0 then 1 else 2))
A140838: 1 2 4 11 44
((7x2 + 1) * (if x <= 0 then 1 else 2))
A005905: 1 16 58 128 226 352 506 688 898 1136 1402 1696 2018 2368 2746 3152
(((x div (1 + (x mod 8))) mod 2) + (if x <= 0 then 1 else 2))
A226774: 1 2 2 2 2 2 2 2 2 2 3 2 2 2 2 3
(((x - (x2 mod 5)) div 2) + (if x <= 0 then 1 else 2))
A302097: 1 2 1 1 3 4 4 3
(((x mod (1 + ((~x + 2) mod 4))) div 2) + (if x <= 0 then 1 else 2))
A346213: 1 2 2 3 2 2 2 3 3 2 2 3 2 2 2 3
((9x2 div 2) + (if x <= 0 then 1 else 2))
A009946: 1 6 20 42 74 114 164 222 290 366 452 546 650 762 884 1014
((x div (2 * (2 + ((x div 4) mod 2)))) + (if x <= 0 then 1 else 2))
A304884: 1 2 2 2 2 2 3 3 4 4 4 4 4 4 4 4
(x + (if x <= 0 then 1 else 2) - (x div ~14))
A026456: 1 4 5 6 7 8 9 10 11 12 13 14 15 16 17 19
(x + (if x <= 0 then 1 else 2) - ((x + 2) div ~7))
A183571: 2 4 5 6 7 8 10 11 12 13 14 15 16 18 19 20
(((x + ((x div 3) mod 2)) div 4) + (if x <= 0 then 1 else 2))
A262685: 1 2 2 3 3 3 3 3 4 4 4 5 5 5 5 6
(((x + ((x mod (2 + (x div 2))) div 2)) div 2) + (if x <= 0 then 1 else 2))
A160511: 1 2 3 3 4 4 5 6 6 7 7 8 9 9 10 11
(x + (if x <= 0 then 1 else 2) - ((~x + ((2 - (x div 2)) div 2)) div 2))
A276224: 1 3 5 7 8 10 12 13 15 16 18 20 21 23 25 26
(~11 * ((x mod 2) - (if x <= 0 then 1 else 2)))
A040111: 11 11 22 11 22 11 22 11 22 11 22 11 22 11 22 11
(x + (((x + 2) div 7) + (if x <= 0 then 1 else 2)))
A183294: 1 3 4 5 6 8 9 10 11 12 13 14 16 17 18 19
(x + (((x + (x mod 2)) div 5) + (if x <= 0 then 1 else 2)))
A188040: 1 3 4 5 6 8 9 10 11 13 14 15 16 17 18 20
(x + ((2x div (3 + (x div 2))) + (if x <= 0 then 1 else 2)))
A269020: 1 3 5 6 7 9 10 11 12 13 14 15 16 17 18 20
(x + ((((1 + (x div 2)) * (x div 2)) div 2) + (if x <= 0 then 1 else 2)))
A269110: 1 3 5 6 9 10 14 15 20 21
(13x2 + (if x <= 0 then 1 else 2))
A010004: 1 15 54 119 210 327 470 639 834 1055 1302 1575 1874 2199 2550 2927
(11x2 + (if x <= 0 then 1 else 2))
A010003: 1 13 46 101 178 277 398 541 706 893 1102 1333 1586 1861 2158 2477
(17x2 + (if x <= 0 then 1 else 2))
A010007: 1 19 70 155 274 427 614 835 1090 1379 1702 2059 2450 2875 3334 3827
(loop(\(x,i).(x + (3x div (1 + (i mod 2)))),x,1) div 2)
A136859: 0 1 4 10 40 100 400 1000 4000 10000 40000 100000 400000 1000000 4000000 10000000
(2 * ((x + ~1) + loop(\(x,i).(6x + 8),2,x)))
A146081: 110 184 258 332 406 480 554 628 702 776 850 924 998 1072 1146 1220
(((x3 + x) * loop(\(x,i).x3,2,x)) div 2)
A170794: 0 1 2560 295245 8912896 126953125 1118624256 7061881225 34896609280 142958160441 505000000000 1582182900661 4489008906240 11717971807165 28491583515136 65161494140625
(((x3 + 1) * loop(\(x,i).x2,2,x2)) div 2)
A170775: 0 1 1152 91854 2129920 24609375 182238336 991545772 4303355904 15712053165 50050000000 142763014746 371719176192 896488062379 2025520479360 4326159375000
(2 * (1 + loop(\(x,i).(x + (x div (~1 + ((2 * i) + i)))),x,x)))
A060378: 2 4 8 10 16 20 26 32 38 40 52 56 64 68 82 86
(2 - ((~x + 2) div (2 + (if (x + ~6) <= 0 then 0 else 2))))
A061071: 1 2 2 3 3 4 4 4 4 4 4 5 5 5 5 6
(if x <= 0 then 1 else (((2x mod (2 + (x div 2))) div ~2) mod 2))
A120522: 1 0 1 0 0 1 1 0 0 0 1 1 0 1 1 0
((x2 + 1) div (x - ((if x <= 0 then 1 else x) div ~4)))
A118168: 1 1 1 2 3 3 4 5 6 6 7 8 9 10 10 11
(((if (x mod 3) <= 0 then 1 else x) mod (2 - (x div ~2))) mod 2)
A266716: 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1
((if (~2 + (x div 4)) <= 0 then 1 else 2) * ((x div ~2) mod 2))
A257654: 0 1 1 0 0 1 1 0 0 1 1 0 0 2 2 0
(loop(\(x,i).(x3 + x2),1,(x - (x div ~2))) div 2)
A299412: 0 6 18 75 126 288 405 726 936 1470 1800 2601 3078 4200 4851 6348
((loop(\(x,i).(x + ((~1 + (i * i)) * i * i)),x,0) div 2) div 2)
A112851: 0 0 3 21 81 231 546 1134 2142 3762 6237 9867 15015 22113 31668 44268
(4 * ((4x2 + ~x) - (if x <= 0 then 0 else 1)))
A180319: 0 8 52 128 236 376 548 752 988 1256 1556 1888 2252 2648 3076 3536
((loop(\(x,i).2x,x,(3x + 5)) div 2) div 2)
A339252: 1 4 11 28 68 160 368 832 1856 4096 8960 19456 41984 90112 192512 409600
(((x mod (1 + (if (x + ~2) <= 0 then 2 else (x div 3)))) div 2) mod 2)
A147873: 0 0 1 0 0 0 0 0 1 0 1 1 1 1 0 1
(2 + (if ((x mod ~7) mod (x + 1)) <= 0 then 1 else 2))
A216190: 3 3 4 3 4 4 4 3 4 4 4 4 4 4 3 4
(((1 + ((x + 1) * (if x <= 0 then 1 else (x div 4)))) div 2) mod 2)
A266895: 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0
(2 * (~2 + loop(\(x,i).10x,(x + 1),1)))
A086940: 16 196 1996 19996 199996 1999996 19999996 199999996 1999999996 19999999996 199999999996 1999999999996 19999999999996 199999999999996 1999999999999996 19999999999999996
(4 * loop(\(x,i).x2,(x mod 2),7))
A135826: 28 196 28 196
(loop(\(x,i).(x + (x div 2)),x,14) div 2)
A120136: 7 10 15 23 34 51 77 115 173 259 389 583 875 1312 1968 2952
(2 * ((2x + 4) div (2 + (if (x + ~3) <= 0 then 2 else 1))))
A051754: 2 2 4 4 8 8 10 12 12 14
(if x <= 0 then 1 else (2 * ((x mod (1 + ((1 + (x div 2)) div 2))) mod 2)))
A103271: 1 0 0 2 0 2 0 2 0 0 0 2 0 2 0 0
(2 * (loop(\(x,i).(x + (i div 2)),(x + ~8),1) div 2))
A309834: 0 0 0 0 0 0 0 0 0 0 2 2 4 6 10 12
((loop(\(x,i).(x + i),((x - ((x div 2) mod 2)) div 2),1) div 2) div 2)
A035659: 0 0 0 0 1 1 1 1 2 2 2 4 5 5 5 7
(2 * (2 + (5 * (1 + loop(\(x,i).2x,x,2)))))
A305061: 34 54 94 174 334 654 1294 2574 5134 10254 20494 40974 81934 163854 327694 655374
(2 + (((if (x + ~2) <= 0 then x else 2x) mod 5) div 2))
A295568: 2 2 3 2 3 2 3 4 2 3 2 3 4 2 3 2
(((~x + 2) mod (2 + (if x <= 0 then 1 else (x div 5)))) div 2)
A025905: 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1
((x + (if (x + ~4) <= 0 then 1 else 2) - (x div 4)) mod 2)
A257585: 1 0 1 0 0 0 1 0 0 1 0 1 1 0 1 0
(2 * (~2 + loop(\(x,i).(2x + 8),(x + 4),1)))
A304388: 268 556 1132 2284 4588 9196 18412 36844 73708 147436 294892 589804 1179628 2359276 4718572 9437164
(2 + (if (x + ~3) <= 0 then x else (4x + 10)))
A114333: 2 3 4 5 28 32
(2 + (((x * (x div 2)) div 2) mod (if (~2 + (x div 2)) <= 0 then 1 else 2)))
A297850-A171092: 2 2 2 2 2 2 3 2 2 2 3 3 2 3 3 2
(2 + (if x <= 0 then 0 else (2 + ((x3 + ~x2) div 3))))
A114879: 2 4 5 10 20 37
(if (x + ~2) <= 0 then x else (4 + ((2 * (x div 2)) div 3)))
A061008: 0 1 2 4 5 5 6 6 6 6 7 7 8 8 8 8
loop(\(x,i).2x,((x + ~2) - ((2 * (x div 2)) div 3)),2)
A089819: 2 2 2 4 4 8 8 16 32 64 64 128 128 256 512 1024
((loop(\(x,i).2x,(x - ((~x + 2) div 2)),3) div 2) div 2)
A206917: 0 1 3 12 24 96 192 768 1536 6144 12288 49152 98304 393216 786432 3145728
(((3 * loop(\(x,i).2x,(x + ~1),(x + 2))) div 2) div 2)
A084860: 1 2 6 15 36 84 192 432 960 2112 4608 9984 21504 46080 98304 208896
(if x <= 0 then 1 else (2 * (x - (2 * ((~2x + 1) div 3)))))
A315907: 1 6 8 14 20 22 28 34 36 42 48 50 56 62 64 70
loop(\(x,i).x2,3,(12x + 4))
A017576: 65536 4294967296 377801998336 6553600000000 53459728531456 281474976710656 1113034787454976 3596345248055296 10000000000000000 24759631762948096 55895067029733376 117033789351264256
loop(\(x,i).x3,1,(12x + 4))
A017571: 64 4096 21952 64000 140608 262144 438976 681472 1000000 1404928 1906624 2515456 3241792 4096000 5088448 6229504
loop(\(x,i).x3,2,(12x + 4))
A017577: 262144 68719476736 10578455953408 262144000000000 2779905883635712 18014398509481984 84590643846578176 316478381828866048 1000000000000000000 2773078757450186752 4611686018427387903
loop(\(x,i).x2,1,(~11x + ~4))
A017438: 16 225 676 1369 2304 3481 4900 6561 8464 10609 12996 15625 18496 21609 24964 28561
loop(\(x,i).x2,2,(~11x + ~4))
A017440: 256 50625 456976 1874161 5308416 12117361 24010000 43046721 71639296 112550881 168896016 244140625 342102016 466948881 623201296 815730721
(((x + 2) div (~6 + (if (x mod 2) <= 0 then 1 else x))) mod 2)
A090678: 1 1 1 0 0 1 0 1 0 1 1 0 1 0 0 1
(if (x + ~2) <= 0 then 1 else ((x div (2 + ((~x + 1) mod 3))) mod 2))
A174852: 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 1
(2 + (if x <= 0 then 1 else (2 * (4x - (x div 3)))))
A063111: 3 10 18 24 32 40 46 54 62 68 76 84 90 98 106 112
(2 + (if x <= 0 then 1 else (2 * (3x - (x div 3)))))
A063218: 3 8 14 18 24 30 34 40 46 50 56 62 66 72 78 82
(if (~2 + (x div 3)) <= 0 then 1 else (2 + ((x mod 3) div 2)))
A121041: 1 1 1 1 1 1 1 1 1 2 2 3 2 2 3 2
((if x <= 0 then 1 else 2x) - ((x - ((x mod 3) div 2)) div 2))
A004059: 1 2 4 5 6 8 9 11 13 14 15 17 18 20 22 23
((if (x + ~2) <= 0 then 1 else x) - ((x - ((x mod 3) div 2)) div 2))
A285759: 1 1 1 2 2 3 3 4 5 5 5 6 6 7 8 8
loop(\(x,i).x2,1,(~12x2 + 4x))
A014794: 0 64 1600 9216 30976 78400 166464 313600 541696 876096 1345600 1982464 2822400 3904576 5271616 6969600
(4 * (~1 + loop(\(x,i).(2x - ((i div 2) mod 2)),x,2)))
A102652: 4 12 24 48 100 204 408 816 1636 3276 6552 13104 26212 52428 104856 209712
((x + (if (x + ~2) <= 0 then 1 else 2) - ((x div 3) mod 2)) div 2)
A194177: 0 1 1 2 2 3 4 4 5 5 5 6 7 7 8 8
loop(\(x,i).x2,3,(~7x + ~4))
A017036: 65536 214358881 11019960576 152587890625 1099511627776 5352009260481 20047612231936 62259690411361 167961600000000 406067677556641 899194740203776 1853020188851841 3596345248055296
loop(\(x,i).(x2 + x),1,(~7x + ~4))
A177071: 12 110 306 600 992 1482 2070 2756 3540 4422 5402 6480 7656 8930 10302 11772
(((if x <= 0 then 2 else ((x2 + 2) mod (1 + (x div 2)))) div 2) mod 2)
A029418: 1 0 0 0 0 0 1 1 0 1 0 1 1 1 1 1
(x - ((x mod (if (x + ~1) <= 0 then 1 else ((1 + (x div 2)) div 2))) mod 2))
A343779: 0 1 2 3 4 5 6 6 8 8 9 11 12 12 14 14
(((if x <= 0 then 2 else (3x mod (1 + (x div 2)))) div 2) mod 2)
A239199: 1 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0
(if x <= 0 then 1 else (2 - (((x mod 2) - ((~1 + (x div 2)) div 2)) div 2)))
A057525: 1 1 2 2 2 2 3 2 3 2 3 3 3 3 4 3
((loop(\(x,i).((x + 1) - (2 * (~2x + i))),x,1) div 2) div 2)
A178874: 0 1 4 20 98 489 2442 12208 61036 305177 1525880 7629396 38146974 190734865 953674318 4768371584
(4 * (1 + (x * loop(\(x,i).(~x + 2),x,(x + 3)))))
A269913: 4 ~4 44 ~44 116 ~116 220 ~220 356 ~356 524 ~524 724 ~724 956 ~956
(((((x + 1) mod 3) * (1 + (if x <= 0 then 1 else x))) div 2) mod 2)
A267636: 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0
(2 * (2 + loop(\(x,i).(10x + ~4),x,1)))
A173737: 6 16 116 1116 11116 111116 1111116 11111116 111111116 1111111116 11111111116 111111111116 1111111111116 11111111111116 111111111111116 1111111111111116
(4 * loop(\(x,i).(2x + (((x div 2) + i) mod 2)),x,1))
A102650: 4 12 28 56 116 236 476 952 1908 3820 7644 15288 30580 61164 122332 244664
(2 * (loop(\(x,i).((4x * i) + (x div 2)),x,1) div 2))
A309170: 0 4 34 424
(((loop(\(x,i).(~2x + 6),x,1) mod (x + 1)) div 2) div 2)
A219839: 0 0 0 0 0 1 0 0 1 1 0 2 0 1 3 0
(((loop(\(x,i).(~2x + 1),(x div 2),2) mod (x + 1)) div 2) div 2)
A035583: 0 0 0 0 0 0 0 0 0 1 0 1 0 2 3 2
(if (x mod 5) <= 0 then 1 else (2 * (2 + (2 mod (x + 1)))))
A330555: 1 4 8 8 8 1
((~2 + (x div 2)) mod ((if (x + ~2) <= 0 then 2 else ((x + 1) div 2)) div 2))
A035667: 0 0 0 0 0 0 0 1 0 0 1 0 1 1 2 1
(loop(\(x,i).i,((~1 + (x div 2)) div 2),1) + (((x + 1) div 2) div 2))
A325620: 1 1 1 2 2 2 2 3 3 3 4 5 5 5 6 7
(x + ((if (~x + 4) <= 0 then 2 else 1) + (((x + 1) div 2) div 2)))
A228856: 1 2 3 5 7 8 9 11 12 13 14 16 17 18 19 21
(4 + ((x + 1) * (if (x + ~2) <= 0 then x else (x2 + 2x))))
A274991: 4 6 10 64
(loop(\(x,i).(x - (x div ~6)),(x + ~1),2) div 2)
A261770: 1 1 1 2 2 3 3 4 5 6 8 9 11 13 16 19
((if (x + ~2) <= 0 then 1 else (((x + ~1) * (x div 3)) div 2)) mod 2)
A307377: 1 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1
(2 + (loop(\(x,i).(x div (1 + (2 * (x mod 2)))),2,(x + ~1)) div 2))
A305897-A300248-A300247: 1 2 2 3 2 4 2 5 3 6 2 7 2 8 4 9
((((x + 1) + (6 div (if x <= 0 then 1 else x))) div 2) mod 2)
A090971: 1 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0
(4 + loop(\(x,i).(x2 * (1 + i)),2,(x2 + 1)))
A093060: 16 196 7504
(2 * (2 + (if (9 mod (x + 1)) <= 0 then 0 else 2)))
A055026: 4 8 4 8 8 8 8 8 4 8 8 8 8 8 8 8
(((x + ~1) mod (2 - ((if x <= 0 then 1 else x) div ~4))) mod 2)
A284524: 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0
(2 + (if x <= 0 then 1 else (2 * (4x - (x div ~2)))))
A063102: 3 12 20 30 38 48 56 66 74 84 92 102 110 120 128 138
(x div (2 + ((x mod (~2 + (if (x mod 4) <= 0 then x else 0))) div 2)))
A246416: 0 1 1 3 2 5 3 7 2 9 5 11 4 13 7 15
(8 * ((x + 6) + (if x <= 0 then 0 else 1)))
A323610: 48 64 72 80 88 96 104 112 120 128 136 144 152 160 168 176
(((2 - (x div (if ((x div 2) mod 3) <= 0 then 1 else 2))) div 2) mod 2)
A029434: 1 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1
(4 * (if (~2 + (x mod (1 + (x div 3)))) <= 0 then 1 else 2))
A066014: 4 4 4 4 4 4 4 4 4 4 4 8 4 8 8 8
((((1 + (x div (if (x + ~4) <= 0 then 1 else 2))) div 2) div 2) mod 2)
A093384: 0 0 0 1 1 0 1 1 1 1 1 1 1 1 0 0
(loop(\(x,i).(x + (x div 2)),x,20) div 2)
A120138: 10 15 22 33 50 75 112 168 252 378 567 851 1276 1914 2871 4307
(2 + ((((x div 2) - ((if x <= 0 then 1 else x) mod 3)) div 2) mod 2))
A074804: 3 3 3 2 2 2 3 3 3 2 2 3 3 2 2 3
(2 + (if x <= 0 then 1 else (4 * (2x - (x div 3)))))
A063234-A063220: 3 10 18 22 30 38 42 50 58 62 70 78 82 90 98 102
(if (x + ~2) <= 0 then x else (2 + ((x - ((x div 3) mod 2)) div 2)))
A123579: 0 1 2 3 3 4 5 5 6 6 6 7 8 8 9 9
(if x <= 0 then 2 else ((2 - (x mod (~4 + (x mod 3)))) div 2))
A078880: 2 2 1 1 2 1 2 2 1 2 2 1 1 2 1 1
(2 + (loop(\(x,i).(1 + (x * (i * i))),(x + 3),2) div 2))
A138790: 61 946
(2 * (2 + (if (x mod 2) <= 0 then 3 else ((1 + (x div 2)) mod 2))))
A167873: 10 6 10 4 10 6 10 4 10 6 10 4 10 6 10 4
(2 + ((loop(\(x,i).((x + 2) + (x div 4)),x,1) div 2) div 2))
A120161: 2 2 3 4 5 6 7 9 11 14 18 22 28 35 43 54
(2 * ((loop(\(x,i).((1 + (x * i)) * (i div 2)),x,1) div 2) div 2))
A215702: 0 0 0 2 16 170
(if x <= 0 then 0 else (2 + ((((x + 1) * ((x + ~1) div 2)) div 2) mod 2)))
A227196: 0 2 2 2 2 2 3 2 3 2 2 2 2 2 3 2
(4 * (((~x + ~1) + loop(\(x,i).x2,2,4)) div 2))
A152524: 508 508 504 504 500 500 496 496 492 492 488 488 484 484 480 480
(2 * (~2 + loop(\(x,i).10x,(x + 1),2)))
A083811: 36 396 3996 39996 399996 3999996 39999996 399999996 3999999996 39999999996 399999999996 3999999999996
(loop(\(x,i).(x3 + ~3),(2x + 2),2) div 2)
A147667: 61 4611686018427387903 4611686018427387903 4611686018427387903
(x - ((~x + 2) div (2 + (if x <= 0 then 2 else (((x + 1) div 2) div 2)))))
A138083: 0 1 2 4 5 6
A039242: 0 1 2 4 5 6 8 9 10 11 12 13 14 16 17 18
((2x div (2 + (x div (2 + (if (x + ~2) <= 0 then 0 else 2))))) mod 2)
A159637: 0 1 1 1 0 1 0 0 0 0 1 1 0 1 1 0
(~2 + (if (x mod 2) <= 0 then 1 else (2 * (((~1 + (x div 2)) div 2) mod 2))))
A123724: ~1 0 ~1 ~2 ~1 ~2 ~1 0 ~1 0 ~1 ~2 ~1 ~2 ~1 0
(16 * loop(\(x,i).(x * (x - i)),2,(x + ~1)))
A134175: 0 0 0 0 384 1920 5760 13440 26880 48384 80640 126720 190080 274560 384384 524160
(loop(\(x,i).(x + (x div 2)),x,32) div 2)
A120142: 16 24 36 54 81 121 182 273 409 614 921 1381 2072 3108 4662 6993
((((loop(\(x,i).(x + (x div 2)),(x + ~2),2) div 2) div 2) div 2) div 2)
A308994: 0 0 0 0 0 0 0 0 1 1 2 3 5 8 13 19
(loop(\(x,i).2x,x,(x + 14)) div 2)
A159695: 7 15 32 68 144 304 640 1344 2816 5888 12288 25600 53248 110592 229376 475136
(2 + loop(\(x,i).x3,(x + 2),16))
A321284: 68719476738 4611686018427387903 4611686018427387903
((((if x <= 0 then 1 else x) mod (~2 + ((~x + 2) div 4))) div 2) mod 2)
A229541: 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0
(if (x + ~2) <= 0 then x else (2 + ((x - ((x div 4) mod 2)) div 2)))
A219642: 0 1 2 3 3 4 4 5 6 6 7 7 7 8 8 9
(28x + (if x <= 0 then 1 else x))
A048846: 1 29 58 87 116 145 174 203 232 261 290 319 348 377 406 435
(if x <= 0 then 0 else (2 + (x mod (2 + ((x - ((x div 2) mod 2)) div 2)))))
A163751: 0 3 2 2 2 3 4 4 4 5 6 6 6 7 8 8
(2 * (if (x + ~1) <= 0 then x else (2 * ((x mod (2 + (x mod 2))) mod 2))))
A005929: 0 2 0 0 0 0 0 4 0 0 0 0 0 4 0 0
(x2 mod (4 * (if (~2 + (x div 2)) <= 0 then 1 else 4)))
A344851: 0 1 0 1 0 1 4 1 0 1 4 9 0 9 4 1
((loop(\(x,i).(x + (x div 4)),(x + ~1),4) div 2) div 2)
A120160: 1 1 1 1 1 2 2 3 3 4 5 6 8 10 12 15
(2 * loop(\(x,i).(x + (x div (1 + (i mod 2)))),x,8))
A205187: 16 24 48 72 144 216 432 648 1296 1944 3888 5832 11664 17496 34992 52488
(4 - (x mod (2 * (~4 + (if (x mod 2) <= 0 then 1 else x)))))
A199203: 4 9 8 5 6 3
(if (x + ~2) <= 0 then 1 else ((2x div (2 + (x div 4))) mod 2))
A121802: 1 1 1 1 0 1 0 0 0 0 1 1 0 1 1 0
(((if (x mod 3) <= 0 then 2 else x) mod (2 + (x div 4))) div 2)
A073454: 0 0 0 0 0 1 1 0 0 1 1 1 1 1 2 1
((if x <= 0 then 1 else ((x * (x div 2)) div (2 + (x div 4)))) mod 2)
A024711: 1 0 1 1 0 1 0 1 0 1 0 1 0 1 1 1
((if x <= 0 then 1 else 0) - ((x mod (~2 - (x mod 4))) mod 2))
A247223: 1 0 0 0 0 ~1 0 ~1 0 0 0 0 0 0 0 0
((x div (2 * (if (x mod 2) <= 0 then 4 else (x mod 4)))) mod 2)
A011711: 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0
(4 * (~2 + loop(\(x,i).10x,x,2)))
A086579: 0 72 792 7992 79992 799992 7999992 79999992 799999992 7999999992 79999999992 799999999992 7999999999992 79999999999992 799999999999992 7999999999999992
((loop(\(x,i).x3,3,(x + 4)) div 2) div 2)
A173533: 4503599627370496 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).(~2 + (x * (x - i))),2,(x + 4)) div 2) div 2)
A342737: 19 71 181 379 701 1189 1891 2861 4159 5851 8009 10711 14041 18089 22951 28729
((loop(\(x,i).(x * ((x + ~1) - i)),2,(x + 4)) div 2) div 2)
A105938: 10 45 126 280 540 945 1540 2376 3510 5005 6930 9360 12376 16065 20520 25840
loop(\(x,i).(4x + 1),x,(2x + 12))
A072259: 12 57 261 1173 5205 22869 99669 431445 1856853 7951701 33903957 144004437 609572181 2572506453 10826896725 45455070549
(4 * loop(\(x,i).3x,2x,(2x + 4)))
A159739: 16 216 2592 29160 314928 3306744 34012224 344373768 3443737680 34093003032 334731302496 3263630199336 31632108085872 305023899399480 2928229434235008 28001193964872264
(if x <= 0 then 1 else (2 * (2x - (((2 - (x div 2)) div 2) div 2))))
A311226: 1 4 8 12 16 20 26 30 34 38 42 46 50 54 60 64
((loop(\(x,i).x2,1,(~2 + (x mod 2) - (x div 2))) div 2) div 2)
A008733: 1 0 2 1 4 2 6 4 9 6 12 9 16 12 20 16
(((if x <= 0 then 2 else ((x2 + 1) div (2 + (x div 2)))) div 2) mod 2)
A143221: 1 0 0 1 0 1 1 1 1 0 1 0 1 0 0 0
((if x <= 0 then 2 else (((~2x + 2) mod (2 + (x div 2))) div 2)) div 2)
A010108: 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2
(x div (2 + ((((if (x mod 2) <= 0 then 2 else x) + (x div 2)) div 2) div 2)))
A072531: 0 0 1 1 1 1 2 1 2 1 3 1 3 2 3 2
(2 + (if (~1 + (x mod 3)) <= 0 then (1 - (2 * (x mod 2))) else 2))
A278536: 3 1 4 1 3 4 3 1 4 1 3 4 3 1 4 1
(~2 + ((2 - (loop(\(x,i).(x * i),x,2) mod (x + 1))) mod 4))
A151763: 0 0 ~1 0 1 0 ~1 0 0 0 ~1 0 1 0 0 0
((x + 2) - (if x <= 0 then 1 else (8 * ((~x + 2) div 2))))
A109474: 1 3 4 13 14 23 24 33 34 43 44 53 54 63 64 73
(3x - ((if x <= 0 then 1 else x) div ~7))
A004084: 1 4 7 10 13 16 19 22 26 29 32 35 38 41 44 48
((if (~x + 4) <= 0 then 2 else 1) - (x div ~7))
A108229-A088141: 1 2 2 2 3 3 3 3 4 4 4 4 4 4 4 5
(x - (if (~1 + (x div 4)) <= 0 then (x mod 2) else 8))
A330271: 0 0 2 2 4 4 6 6 0 1 2 3 4 5 6 7
((if ((x div 4) mod 2) <= 0 then x else ~x) mod 8)
A266313: 0 1 2 3 4 3 2 1 0 1 2 3 4 3 2 1
loop(\(x,i).(x - ((1 - (x div 2)) div 3)),x,8)
A120184: 8 9 10 12 14 16 19 22 26 30 35 41 48 56 65 76
loop(\(x,i).32x,x,8)
A013824: 8 256 8192 262144 8388608 268435456 8589934592 274877906944 8796093022208 281474976710656 9007199254740992 288230376151711744 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(4x * (i * (2 + i))),x,8)
A002506: 8 96 3072 184320 17694720 2477260800 475634073600 119859786547200 38355131695104000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(7x + 6),x,8)
A198690: 8 62 440 3086 21608 151262 1058840 7411886 51883208 363182462 2542277240 17795940686 124571584808 872001093662 6104007655640 42728053589486
loop(\(x,i).(7x + 16),x,8)
A304826: 8 72 520 3656 25608 179272 1254920 8784456 61491208 430438472 3013069320 21091485256 147640396808 1033482777672 7234379443720 50640656106056
(if x <= 0 then 0 else (1 - (2 * ((~x + (x mod 3)) div 4))))
A101290: 0 1 1 3 3 3 5 5 5 7 7 7 7 7 7 9
(((1 + (x div 2)) div (~4 + (if (x mod 2) <= 0 then 1 else x))) mod 2)
A087755: 1 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0
(((x * (2 + (if (x + ~4) <= 0 then 1 else x))) div 4) mod 2)
A289071: 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1
((x + 2) - (if (~4 + (x div 2)) <= 0 then 1 else (x div 4)))
A071604: 1 2 3 4 5 6 7 8 9 10 10 11 11 12 13 14
(2 * (loop(\(x,i).(x + ((2 + i) * i)),x,1) + (x div 4)))
A152132: 2 8 24 54 104 174 270 396 558 756 996 1282 1620 2010 2458 2968
((if x <= 0 then 2 else (((x div 3) mod 2) + (x div 4))) div 2)
A025863: 1 0 0 0 1 1 0 0 1 1 1 1 1 1 1 2
(((if x <= 0 then 2 else ((x * (~1 + (x mod 3))) div 2)) div 2) mod 2)
A101266: 1 0 0 1 0 1 0 0 0 1 0 0 1 0 1 0
(2 * (2 + loop(\(x,i).2x,x,(5x + 2))))
A195590: 8 32 100 276 708 1732 4100 9476 21508 48132 106500 233476 507908 1097732 2359300 5046276
loop(\(x,i).x2,3,(12x + 8))
A017624: 16777216 25600000000 1099511627776 14048223625216 96717311574016 457163239653376 1677721600000000 5132188731375616 13685690504052736 32784148919812096 72057594037927936 147578905600000000
loop(\(x,i).x3,1,(12x + 8))
A017619: 512 8000 32768 85184 175616 314432 512000 778688 1124864 1560896 2097152 2744000 3511808 4410944 5451776 6644672
loop(\(x,i).x3,2,(12x + 8))
A017625: 134217728 512000000000 35184372088832 618121839509504 5416169448144896 31087100296429568 134217728000000000 472161363286556672 1423311812421484544 3802961274698203136
loop(\(x,i).x2,1,(~11x + ~8))
A017486: 64 361 900 1681 2704 3969 5476 7225 9216 11449 13924 16641 19600 22801 26244 29929
loop(\(x,i).x2,2,(~11x + ~8))
A017488: 4096 130321 810000 2825761 7311616 15752961 29986576 52200625 84934656 131079601 193877776 276922881 384160000 519885601 688747536 895745041
((x + 4) - ((~x + loop(\(x,i).i,(x div 4),2)) div 2))
A186356: 3 5 6 8 10 11 13 14 15 17 18 20 21 22 24 25
(2 + loop(\(x,i).((x + 2) + (((1 + i) * i) div 2)),(x + 2),2))
A026041: 12 20 32 49 72 102 140 187 244 312 392 485 592 714 852 1007
((if x <= 0 then 1 else ((2x2 + 1) div (x + 4))) mod 2)
A189209: 1 0 1 0 0 1 1 1 0 0 0 0 0 1 1 1
(if x <= 0 then 1 else (2 + ((2x2 + 2x) div (x + 4))))
A248566: 1 2 4 5 7 8 10 12 14 15 17 19 21 23 25 27
((if x <= 0 then 1 else (4x2 div (x + 4))) mod 2)
A262855: 1 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1
((8 * (if x <= 0 then 1 else x)) div (x + 6))
A239684: 1 1 2 2 3 3 4 4 4 4 5 5 5 5 5 5
(if (x div 5) <= 0 then (x + 1) else (4x + 8))
A265098: 1 2 3 4 5 28 32
(2 + (((x2 div 2) - (if (x + ~2) <= 0 then 1 else (x + ~2))) div 2))
A028309: 1 1 2 3 5 6 9 11 15 18 23 27 33 38 45 51
(8x + loop(\(x,i).8x,x,1))
A221910: 1 16 80 536 4128 32808 262192 2097208 16777280 134217800 1073741904 8589934680 68719476832 549755813992 4398046511216 35184372088952
(~8x + loop(\(x,i).8x,x,1))
A198398: 1 0 48 488 4064 32728 262096 2097096 16777152 134217656 1073741744 8589934504 68719476640 549755813784 4398046510992 35184372088712
loop(\(x,i).x3,1,(7x + 2))
A017007: 8 729 4096 12167 27000 50653 85184 132651 195112 274625 373248 493039 636056 804357 1000000 1225043
loop(\(x,i).x3,2,(7x + 2))
A017013: 512 387420489 68719476736 1801152661463 19683000000000 129961739795077 618121839509504 2334165173090451 7427658739644928 20711912837890625 51998697814228992 119851595982618319
(9x + loop(\(x,i).x3,2,x))
A180359: 0 10 530 19710 262180 1953170 10077750 40353670 134217800 387420570 1000000090 2357947790 5159780460 10604499490 20661046910 38443359510
((~x + 2) + (loop(\(x,i).(x3 + 2x),2x,2) div 2))
A253578: 3 877
((if x <= 0 then 2 else ((((~x + 1) mod 3) + (x div 2)) div 2)) div 2)
A029383: 1 0 0 0 0 1 1 0 1 1 1 1 1 1 2 2
(if (x + ~1) <= 0 then x else ((((x mod 3) - (x div 2)) div 2) mod 2))
A189132-A189017-A189014: 0 1 0 1 1 0 0 1 1 0 0 0 1 1 1 0
(((x2 + x + 1) div (if x <= 0 then 1 else (2 + (x div 2)))) mod 2)
A267845: 1 1 0 0 1 1 0 1 0 1 1 1 1 0 1 0
(2 - ((if x <= 0 then 2 else (~x2 * (2 + (x div 2)))) div 2))
A337118: 1 3 8 16 34
(((if (x mod 2) <= 0 then 2 else x3) mod (2 + (x div 2))) div 2)
A092111: 0 0 1 0 1 0 1 1 1 1 1 0 1 2 1 0
((x - (((x div 2) mod 2) + (if (~2 + (x div 2)) <= 0 then 0 else 1))) div 2)
A064475: 0 0 0 1 2 2 2 2 3 4 4 4 5 6 6 6
((x + 2) - loop(\(x,i).(~x + 1),x,((~x + 2) + ((x div 2) mod 2))))
A266616: 0 3 3 4 8 3 11 4 16 3 19 4 24 3 27 4
(4 * (loop(\(x,i).(~2x + 2),(x div 2),1) - (x mod 2)))
A096406: 4 0 0 ~4 8 4 ~8 ~12 24 20 ~40 ~44 88 84 ~168 ~172
loop(\(x,i).(3x + 4),x,(4 * (2 - (x mod 2))))
A117868: 8 16 88 160 808 1456 7288 13120 65608 118096 590488 1062880 5314408 9565936 47829688 86093440
(((if x <= 0 then 1 else 2x) mod (2 + (x div 2) - (x mod 2))) mod 2)
A124752-A098173: 1 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0
loop(\(x,i).5x,(x div 2),(4 + (x mod 2)))
A163141: 4 5 20 25 100 125 500 625 2500 3125 12500 15625 62500 78125 312500 390625
(if (~2 + (x div 4)) <= 0 then 1 else (x div (4 + (x mod 2))))
A343886: 1 1 1 1 1 1 1 1 1 1 1 1 3 2 3 3
(2 * ((x mod 2) - loop(\(x,i).(~2x + 2),x,(2 * (x mod 2)))))
A120462: 0 6 4 22 20 86 84 342 340 1366 1364 5462 5460 21846 21844 87382
(x5 mod loop(\(x,i).(x2 + 2),2,2))
A070621: 0 1 32 15 36 9 24 11 12 35 22 7 8 33 10 21
(((x + ~1) div 2) mod (if (~2 + (x div 4)) <= 0 then 1 else 4))
A237817: 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 3
((if ((x + ~2) mod 6) <= 0 then (x + 2) else 1) mod 4)
A169987: 1 1 0 1 1 1 1 1 2 1 1 1 1 1 0 1
(((x2 + 4x + 4) div 2) - (if (x mod 2) <= 0 then 1 else 4))
A326658: 1 0 7 8 17 20 31 36 49 56 71 80 97 108 127 140
((loop(\(x,i).4x,x,4) div (x + 1)) mod 4)
A323592: 0 0 1 0 0 2 0 0 3 1 0 1 0 1 0 0
(((1 + (loop(\(x,i).2x,x,1) mod (x + 1))) div 2) mod 4)
A257988: 0 0 1 0 1 1 1 0 2 1 1 0 1 1 2 0
((x3 + 2x2) div loop(\(x,i).(x2 + 1),2,4))
A309715: 0 0 0 0 0 0 0 1 2 3 4 5 6 8 10 13
loop(\(x,i).32x,2x,4)
A067482-A013830: 4 4096 4194304 4294967296 4398046511104 4503599627370496 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A320860: 4 4096 4194304 4294967296 4398046511104 4503599627370496 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((if ((x div 3) mod 3) <= 0 then x else ~x) mod 4)
A112658: 0 1 2 1 0 3 2 1 0 1 2 3 0 3 2 1
((~x + (if (x + ~12) <= 0 then 2 else 1)) mod 4)
A190693: 2 1 0 3 2 1 0 3 2 1 0 3 2 0 3 2
loop(\(x,i).(10x + ~3),x,4)
A199690: 4 37 367 3667 36667 366667 3666667 36666667 366666667 3666666667 36666666667 366666666667 3666666666667 36666666666667 366666666666667 3666666666666667
(4 * loop(\(x,i).(x + 3),(~1 + ((x + ~1) div 2)),x))
A071072: 0 4 8 12 16 32 36 52 56 72 76 92 96
((if ((x mod (4 + (x div 2))) mod 2) <= 0 then 1 else x) mod 4)
A030394: 1 1 1 3 1 1 1 1 1 1 2 1 1 1 2 1
(if x <= 0 then 2 else (4 * (x + (x div 9))))
A335738: 2 4 8 12 16 20 24 28 32 40 44 48 52 56 60 64
(x - ((1 - (if (~4 + (x div 2)) <= 0 then 1 else x)) div 4))
A103303: 0 1 2 3 4 5 6 7 8 9
A305932-A007377: 0 1 2 3 4 5 6 7 8 9 13 14 15 16 18 19
loop(\(x,i).(11x + ~5),x,4)
A199757: 4 39 424 4659 51244 563679 6200464 68205099 750256084 8252816919 90780986104 998590847139 10984499318524 120829492503759 1329124417541344 14620368592954779
(if x <= 0 then 1 else ((x + 4) + (((x + 1) div 2) div 3)))
A325435: 1 5 6 7 8 10 11 12 13 14 15 17 18 19 20 21
((~x + (loop(\(x,i).(x + (i * i)),x,2) div 3)) div 4)
A175724: 0 0 0 0 1 3 6 10 15 21 29 39 51 65 81 99
(loop(\(x,i).(x * i),x,(3x2 + x)) div 4)
A134437: 0 1 7 45 312 2400 20520 194040 2016000 22861440 281232000 3732220800 53169177600 809512704000 13120332825600 225573828480000
loop(\(x,i).((x - (x div ~2)) div (1 + (x mod 2))),x,4)
A180853: 4 6 9 7 5 4 6 9 7 5 4 6 9 7 5 4
(x - ((((x div 2) mod 4) - (if x <= 0 then 1 else x)) div 4))
A263977-A039164: 1 2 3 4 5 6 7 8 10 12 13 14 15 16 17 18
loop(\(x,i).((10x + ~1) - i),x,4)
A155859: 4 38 377 3766 37655 376544 3765433 37654322 376543211 3765432100 37654320989 376543209878 3765432098767 37654320987656 376543209876545 3765432098765434
(loop(\(x,i).(1 + (x2 div 2) - (x mod 2)),2,x) div 4)
A317714: 0 0 1 2 10 18 45 72 136 200 325 450 666 882 1225 1568
(4x * loop(\(x,i).x3,2,4x))
A016810: 0 1048576 1073741824 61917364224 1099511627776 10240000000000 63403380965376 296196766695424 1125899906842624 3656158440062976 10485760000000000 27197360938418176 64925062108545024 144555105949057024 303305489096114176 604661760000000000
loop(\(x,i).x2,1,((3x2 + 2x) div 4))
A212506: 0 1 16 64 196 441 900 1600 2704 4225 6400 9216 12996 17689 23716 30976
((if x <= 0 then 1 else x) - ((x * ((x * (x div 2)) mod 2)) div 4))
A122168: 1 1 2 3 4 5 6 6 8 9 10 9 12 13 14 12
(4 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))
A048974: 5 7 9 13 15 19 21 25 31 33 39 43 45 49 55 61
(~4 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))
A118538: ~3 ~1 1 5 7 11 13 17 23 25 31 35 37 41 47 53
(4 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A146968: 4 5 7
A052147: 4 5 7 9 13 15 19 21 25 31 33 39 43 45 49 55
((x + 4) + (if (~x + 4) <= 0 then 3 else (x div 2)))
A146968: 4 5 7
A159698: 4 5 7 8 11 12 13 14 15 16 17 18 19 20 21 22
((if x <= 0 then 1 else 4x) - ((x + (x div 2)) div 4))
A214971: 1 4 8 11 15 19 22 26 29 33 37 40 44 48 51 55
(2x + (if x <= 0 then 1 else x) - ((x + (x div 2)) div 4))
A026352: 1 3 6 8 11 14 16 19 21 24 27 29 32 35 37 40
(loop(\(x,i).(2 + (x div 2)),((x + ~1) div 2),0) + (x div 4))
A130242: 0 0 0 2 3 4 4 4 5 5 5 5 6 6 6 6
(if ((((~1 + (x div 2)) div 2) div 2) mod 2) <= 0 then 1 else (x div 4))
A215406: 0 0 1 1 1 1 1 1 1 1 2 2 3 3 3 3
(if ((x + 2) mod (2 + (x mod 4))) <= 0 then 1 else (x div 4))
A003639: 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 3
(((x + 1) * (if (~2 + (x div 2)) <= 0 then 1 else 2)) + (x div 4))
A162570: 1 2 3 4 6 7 15
(loop(\(x,i).(x * (1 + (4 * i))),x,1) - (x div 4))
A243678: 1 5 45 585 9944
((2 * (if (x mod 2) <= 0 then ((x div 2) mod 2) else 2)) + (x div 4))
A226577: 0 4 2 4 1 5 3 5 2 6 4 6 3 7 5 7
((if x <= 0 then 1 else (x div (2 + (x mod 4)))) - (x div 4))
A114374-A029371: 1 0 0 0 1 0 0 0 2 1 0 0 3 1 0 0
loop(\(x,i).(11x + 5),x,4)
A199028: 4 49 544 5989 65884 724729 7972024 87692269 964614964 10610764609 116718410704 1283902517749 14122927695244 155352204647689 1708874251124584 18797616762370429
loop(\(x,i).(11x + 10),x,4)
A199022: 4 54 604 6654 73204 805254 8857804 97435854 1071794404 11789738454 129687123004 1426558353054 15692141883604 172613560719654 1898749167916204 20886240847078254
((x + 4) + ((x mod 8) mod (if x <= 0 then 1 else x)))
A299544: 4 5 6 7 8 9 10 11 12 14 16 18 20 22 24 26
loop(\(x,i).(x + ((4x + 4) div (1 + i))),x,4)
A063258: 4 14 34 69 125 209 329 494 714 1000 1364 1819 2379 3059 3875 4844
(4x2 * loop(\(x,i).x3,2,2x))
A016751: 0 2048 4194304 362797056 8589934592 100000000000 743008370688 4049565169664 17592186044416 64268410079232 204800000000000 584318301411328 1521681143169024 3670344486987776 8293509467471872 17714700000000000
(if (x + ~1) <= 0 then (3x + 4) else 4x2)
A144916: 4 7 16 36 64 100 144 196 256 324 400 484 576 676 784 900
loop(\(x,i).x2,1,(4x3 + ~3x))
A239608: 0 1 676 9801 59536 235225 715716 1825201 4096576 8346321 15760900 27994681 47279376 76545001 119552356 181037025
(loop(\(x,i).((x + 1) - (i div (~2 + (x mod ~2)))),x,2) div 2)
A097602: 1 2 3 4 6 8 10 12 14 16 19 22 25 29 33 37
(loop(\(x,i).((x + 1) - ((~x + 2) div 8)),x,2) div 2)
A008756: 1 1 2 3 4 5 7 8 10 12 14 16 19 22 25 29
(loop(\(x,i).(x2 + x),1,(5x + 2)) div 2)
A061793: 3 28 78 153 253 378 528 703 903 1128 1378 1653 1953 2278 2628 3003
loop(\(x,i).x2,3,(10x + 4))
A017324: 65536 1475789056 110075314176 1785793904896 14048223625216 72301961339136 281474976710656 899194740203776 2478758911082496 6095689385410816 13685690504052736 28525864220672256 55895067029733376
loop(\(x,i).x3,1,(10x + 4))
A017319: 64 2744 13824 39304 85184 157464 262144 405224 592704 830584 1124864 1481544 1906624 2406104 2985984 3652264
loop(\(x,i).x3,2,(10x + 4))
A017325: 262144 20661046784 2641807540224 60716992766464 618121839509504 3904305912313344 18014398509481984 66540410775079424 208215748530929664 572994802228616704 1423311812421484544 3251948521156637184
(2 * loop(\(x,i).(~1 + (2 * (3x + (i mod 2)))),x,2))
A092167: 4 26 154 926 5554 33326 199954 1199726 7198354 43190126 259140754 1554844526 9329067154 55974402926 335846417554 2015078505326
loop(\(x,i).x2,1,(2 * ((x + 2) + (3 * (x div 2)))))
A273373: 16 36 196 256 576 676 1156 1296 1936 2116 2916 3136 4096 4356 5476 5776
(loop(\(x,i).((x + 3) + ((x + 2) div (1 + i))),x,2) div 2)
A060605: 1 3 6 9 13 16 20 24 28 32 37 41 46 50 55 60
(2 + (loop(\(x,i).(x + ((1 + i) * i)),(1 + (x div 2)),x) div 2))
A263794: 3 3 7 7 14 14 25 25 41 41 63 63 92 92 129 129
(2 + ((x2 + x + 2) * loop(\(x,i).(2x + 1),x,0)))
A191821: 2 6 26 100 332 994 2774 7368 18872 47014 114578 274300 647012 1507146 3473198 7929616
(x5 mod loop(\(x,i).(x2 + x),2,2))
A070625: 0 1 32 33 16 17 6 7 8 39 40 23 24 13 14 15
((2x + 2) - (((x div 4) - (if x <= 0 then 1 else x)) div 2))
A184653: 3 5 7 10 12 14 17 19 21 24 26 29 31 33 36 38
((x - ((((2 - (x div 2)) div 2) mod (if x <= 0 then 1 else x)) div 2)) div 2)
A072748: 0 0 1 1 2 2 2 2 2 2 3 3 3 4 4 4
(1 - (((x * loop(\(x,i).((x - (i mod 2)) * i),x,1)) div 2) div 2))
A241905: 1 1 1 4 13 83
(loop(\(x,i).((x * (2 + i)) - (4 div (1 + i))),x,2) div 2)
A245902: 1 2 7 37 222
(if x <= 0 then 1 else ((x + 2) - ((~x + ((x div 2) div ~2)) div 2)))
A231407: 1 4 6
A080746: 1 4 6 7 9 10 12 14 15 17 19 20 22 23 25 27
(loop(\(x,i).2x,x,(x + 18)) div 2)
A159697: 9 19 40 84 176 368 768 1600 3328 6912 14336 29696 61440 126976 262144 540672
(x - ((2 - ((if (~2 + (x div 4)) <= 0 then 2 else x) div 2)) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A191923-A191922: 0 1 2 3 4 5 6 7 8 9 10 11 14 15 17 18
(1 div ((if ((x + 2) mod (4 + (x mod 2))) <= 0 then x else 2) div 2))
A276254: 1 1 1 1 1 1 0 1 1 1 0 1 1 0 0 1
(if x <= 0 then 1 else (2 * (2x - ((~x + ((x div 2) mod 2)) div 2))))
A315211: 1 6 10 14 20 26 30 34 40 46 50 54 60 66 70 74
(2 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A100484: 4 6 10 14 22 26 34 38 46 58 62 74 82 86 94 106
(2 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) div 2))
A130291: 2 2 3 4 6 7 9 10 12 15 16 19 21 22 24 27
(2 * (loop(\(x,i).(2x * (~1 + (2 * i))),(x + ~2),x) div 2))
A052717: 0 0 2 6 48 600 10080 211680 5322240 155675520 5189184000 194075481600 8045310873600 366061644748800 18134130709094400 971471287987200000
(loop(\(x,i).(2x + ((~1 + (2 * (x mod 2))) * i)),x,2) div 2)
A034299: 1 1 4 6 15 27 58 112 229 453 912 1818 3643 7279 14566 29124
(loop(\(x,i).2x,((x + 1) div 2),((x + 2) + (x div 2))) div 2)
A203150: 1 3 5 12 16 36 44 96 112 240 272 576 640 1344 1472 3072
(if (~1 + (x mod 3)) <= 0 then 1 else (2 + ((x * (x div 2)) mod 2)))
A230404: 1 1 2 1 1 2 1 1 2 1 1 3 1 1 2 1
(~2 + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,2))
A128634: 0 2 8 26 82 262 856 2858 9722 33590 117570 416022 1485798 5348878 19389688 70715338
((x + 1) div (2 + (loop(\(x,i).(x + (i * i)),x,0) mod (x + 2))))
A099362: 0 0 1 0 2 0 1 1 1 0 3 0 1 1 1 0
(loop(\(x,i).(x2 + ~x),1,(5x + 10)) div 2)
A331190: 45 105 190 300 435 595 780 990 1225 1485 1770 2080 2415 2775 3160 3570
(((x + 2) * (1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2)))) div 2)
A152899: 1 3 6 10 15 21 36 45 55 66 78 91 105 120 136 153
(((x + 2) * ((2x + ~1) + (if (~x + 2) <= 0 then x else 2))) div 2)
A140229: 1 4 10 20 33 49 68 90 115 143 174 208 245 285 328 374
(((x + 2) * (~1 + loop(\(x,i).((2 * (x + i)) + i),x,2))) div 2)
A213583: 1 9 38 120 327 819 1948 4482 10085 22341 48930 106236 229075 491175 1048184 2227782
loop(\(x,i).((x + 2) + ((x + 1) div 5)),(x + 2),2)
A020752: 7 10 14 19 25 32 40 50 62 76 93 113 137 166 201 243
(loop(\(x,i).(x * i),(x + 2),2) div ((x2 + 4x + 4) div 2))
A277876: 2 3 6 20 80 420 2520 18144 145152 1330560 13305600 148262400 1779148800 23351328000 326918592000 4940103168000
(~2 + loop(\(x,i).(x3 + ~2x),x,(x2 + 4x + 4)))
A062665: 2 709
(((if (x mod 3) <= 0 then 1 else (2 - (x div 2))) mod (x + 2)) mod 2)
A266514: 1 0 1 1 0 0 1 0 0 1 1 0 1 1 1 1
((x + 4) * loop(\(x,i).(2x + i),(x + 1),(x + 1)))
A000554: 12 60 210 630 1736 4536 11430 28050 67452 159588 372554 859950 1965840 4456176 10026702 22412970
((2 * (1 + (4 * (if x <= 0 then 1 else x)))) div (x + 4))
A303594-A035100: 2 2 3 3 4 4 5 5 5 5 5 6 6 6 6 6
((2x + 4) + (if (x mod (1 + (x mod 4))) <= 0 then 1 else 0))
A151976: 5 6 8 10 13 14 17 18 21 22 24 26 29 30 32 34
(if (x div 2) <= 0 then x else ((2x + 4) + (2x mod 3)))
A110095: 0 1 9 10 14 15 16 20 21 22 26 27 28 32 33 34
((if (~2 + ((x + 2) mod 8)) <= 0 then x else (x + 2)) div 2)
A034584: 0 1 2 2 3 3 3 3 4 5 6 6 7 7 7 7
((x + 2) - (4 div (if (~2 + (x div 2)) <= 0 then 2 else (x + ~2))))
A067570: 0 1 2 3 4 5 7
A039261: 0 1 2 3 4 5 7 9 10 11 12 13 14 15 16 17
(loop(\(x,i).(x * i),(x + ~2),((x + ~2) * (x2 div 2))) div 2)
A329550: 0 0 0 2 16 108 864 7200 69120 705600 8064000 97977600 1306368000 18441561600 281652940800 4533271142400
(if x <= 0 then 1 else (2 * (2x + ((x * (x div 2)) div 3))))
A232996: 1 4 8 14 20 26 36
(if x <= 0 then 1 else (2 * (2x + (x div (4 + (x div 2))))))
A311179: 1 4 8 12 16 20 24 30 34 38 42 46 50 54 58 62
(if x <= 0 then 1 else (2 * (2x + ((x + ((x div 2) mod 2)) div 2))))
A310498: 1 4 10 16 20 24 30 36 40 44 50 56 60 64 70 76
(4x + (if (~x + 2) <= 0 then (4x + ~4) else 1))
A086570: 1 5 12 20 28 36 44 52 60 68 76 84 92 100 108 116
(((x + ((x div 2) mod 2)) div 2) + (if x <= 0 then 1 else 4x))
A301293: 1 4 9 14 18 22 27 32 36 40 45 50 54 58 63 68
(~4x + loop(\(x,i).(x2 * i),x,(x2 + 2)))
A082973: 2 5 2584
(5x + loop(\(x,i).5x,x,1))
A221907: 1 10 35 140 645 3150 15655 78160 390665 1953170 9765675 48828180 244140685 1220703190 6103515695 30517578200
(~5x + loop(\(x,i).5x,x,1))
A107585: 1 0 15 110 605 3100 15595 78090 390585 1953080 9765575 48828070 244140565 1220703060 6103515555 30517578050
(2 * (3x + (if (~2 + (x div 3)) <= 0 then 2 else 1)))
A189932: 4 10 16 22 28 34 40 46 52 56 62 68 74 80 86 92
((x + 2) mod (2 + (if (x mod 2) <= 0 then (x mod 3) else (x div 2))))
A318518: 0 1 0 2 0 3 0 4 2 5 0 6 0 7 0 8
(((if (x mod 2) <= 0 then (1 + (x div 2)) else (x + ~1)) * (x div 2)) div 2)
A124093: 0 0 1 1 3 4 6 9 10 16 15 25 21 36 28 49
((if x <= 0 then 2 else ((((x div 2) mod 3) mod 2) + (x div 2))) div 2)
A112217: 1 0 1 1 1 1 1 1 2 2 2 2 3 3 4 4
(~2 + (((if (x + ~2) <= 0 then 2 else (x + ~2)) mod 4) + (x div 2)))
A227542: 0 0 1 0 2 3 1 2 4 5 3 4 6 7 5 6
loop(\(x,i).((x + 2) - (4 * (~x + (i mod 2)))),(x div 2),2)
A230928: 2 2 8 8 42 42 208 208 1042 1042 5208 5208 26042 26042 130208 130208
(if x <= 0 then 1 else ((x2 div (2 - ((x div 2) * (x div 2)))) mod 2))
A267612: 1 0 0 1 0 1 0 1 1 0 1 0 1 1 1 1
(x div (2x - (if x <= 0 then 1 else (((x div 2) * (x div 2)) div 2))))
A024162: 0 0 0 0 0 0 0 0 1 0 1 1 2 1 3 2
(2 * (loop(\(x,i).(x + ((2 + i) * (1 + i))),x,2) - (x div 2)))
A152133: 4 16 38 78 136 220 330 474 652 872 1134 1446 1808 2228 2706 3250
((1 + (if (~x + 2) <= 0 then 3x else 1)) div (2 + (x div 2)))
A213251: 1 1 2 3 3 4 3 4 4 4 4 4 4 5 4 5
((x + (if (~4 + (x div 2)) <= 0 then 1 else x)) div (2 + (x div 2)))
A344511-A065682: 0 1 1 1 1 1 1 1 1 1 2 3 3 3 3 3
((if (x mod 2) <= 0 then 3 else x3) * (2 + (x div 2)))
A055021: 6 2 9 81
((if ((x + 1) mod 5) <= 0 then 2 else 1) * ((x div 2) mod 2))
A107628: 0 0 1 1 0 0 1 1 0 0 1 1 0 0 2 1
(2 + ((1 + (if (~4 + (x div 2)) <= 0 then 2 else 1)) * (x mod 2)))
A073054: 2 5 2 5 2 5 2 5 2 5 2 4 2 4 2 4
(if (x - (x2 mod (x + 5))) <= 0 then (x mod 2) else 2)
A101663: 0 1 0 2 0 1 2 2 0 1 0 2 2 2 2 2
(((loop(\(x,i).2x,(x div 2),1) div (x + 1)) + (x mod 2)) div 2)
A266690: 0 0 0 0 0 0 0 1 0 1 1 1 2 2 4 4
(loop(\(x,i).2x,(~2 + (x div 2)),1) div (4 - (x mod 2)))
A326446: 0 0 0 0 0 0 0 0 1 1 2 2 4 5 8 10
(((~1 + loop(\(x,i).2x,x,2)) div (x + 1)) mod (2 + (x mod 2)))
A327170: 1 1 0 0 0 1 0 1 0 0 0 2 0 0 0 0
loop(\(x,i).(4x + ~2),(2 * (x div 2)),(2 + (x mod 2)))
A268866: 2 3 22 38 342 598 5462 9558 87382 152918 1398102 2446678 22369622 39146838
loop(\(x,i).((2x + 1) + (x mod 2)),(x div 2),(2 + (x mod 2)))
A260795: 2 3 5 8 12 17 25 36 52 73 105 148 212 297 425 596
(if ((x + 1) mod 6) <= 0 then (x div 2) else (2 + (x mod 2)))
A258115: 2 3 2 3 2 2 2 3 2 3 2 5 2 3 2 3
(loop(\(x,i).(5x + ~1),x,0) div (~2 + (x mod 2)))
A152417: 0 1 3 31 78 781 1953 19531 48828 488281 1220703 12207031 30517578 305175781 762939453 7629394531
((if ((x + 1) mod 8) <= 0 then 2 else 1) + (2 * (x mod 2)))
A233269: 1 3 1 3 1 3 1 4 1 3 1 3 1 3 1 4
loop(\(x,i).~2x,(x mod 3),(1 - (2 * (x mod 2))))
A132954: 1 2 4 ~1 ~2 ~4 1 2 4 ~1 ~2 ~4 1 2 4 ~1
loop(\(x,i).(~4x + ~1),x,(1 - (2 * (x mod 2))))
A112627: 1 3 19 51 307 819 4915 13107 78643 209715 1258291 3355443 20132659 53687091 322122547 858993459
(loop(\(x,i).(2 * (x - ((x + i) mod 2))),x,1) - (2 * (x mod 2)))
A097073: 1 0 4 4 12 20 44 84 172 340 684 1364 2732 5460 10924 21844
(loop(\(x,i).(2x + ~1),x,8) - (2 * (x mod 2)))
A321483: 8 13 29 55 113 223 449 895 1793 3583 7169 14335 28673 57343 114689 229375
(loop(\(x,i).((2x + 1) - (i mod 2)),x,2) - (2 * (x mod 2)))
A290604: 2 2 9 16 37 72 149 296 597 1192 2389 4776 9557 19112 38229 76456
loop(\(x,i).((2x + 1) * (1 + (x mod 2))),x,(2 * (x mod 2)))
A273050: 0 5 6 45 54 365 438 2925 3510 23405 28086 187245 224694 1497965 1797558 11983725
loop(\(x,i).(x * (1 + (2 * (1 + (i mod 2))))),x,(2 * (x mod 2)))
A221414: 0 10 0 150 0 2250 0 33750 0 506250 0 7593750 0 113906250 0 1708593750
((x mod 2) - (loop(\(x,i).(2 * (x - (i mod 2))),x,(x mod 2)) div 2))
A094359: 0 1 2 2 10 6 42 22 170 86 682 342 2730 1366 10922 5462
(loop(\(x,i).(3x - (4 div (1 + i))),x,2) div 2)
A309115: 1 2 5 16
A257970: 1 2 5 16 48 144 432 1296 3888 11664 34992 104976 314928 944784 2834352 8503056
loop(\(x,i).2x,x,(((x + 2) - (2 mod (~x2 + 2))) div 2))
A074092: 1 2 8 40 144 448 1280 3456 8960 22528 55296 133120 315392 737280 1703936 3899392
((x + (if ((x + 1) mod (1 + (x div 3))) <= 0 then 1 else 0)) div 2)
A194200: 0 1 1 2 2 3 3 3 4 4 5 6 6 6 7 7
((x * loop(\(x,i).(x + (i * i * (1 + i))),(x + 1),0)) div 2)
A293475: 0 7 50 195 560 1330 2772 5250 9240 15345 24310 37037 54600 78260 109480 149940
((~x + 1) mod ((x + (if ((x div 2) mod 3) <= 0 then 2 else 0)) div 2))
A071960: 0 0 0 0 1 0 3 2 1 0 1 0 3 2 1 0
((x * loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),x,0)) div 2)
A208493: 0 0 1 3 18
A000274: 0 0 1 3 18 110 795 6489 59332 600732 6674805 80765135 1057289046 14890154058 224497707343 3607998868005
((~x + loop(\(x,i).(7x + 3),x,0)) div 2)
A244975: 0 1 11 84 598 4199 29409 205882 1441196 10088397 70618807 494331680 3460321794 24222252595 169555768205 1186890377478
(if x <= 0 then 1 else (2 * (x + (x div 11))))
A241071: 1 2 4 6 8 10 12
A271907: 1 2 4 6 8 10 12 14 16 18
A221284: 1 2 4 6 8 10 12 14 16 18 20 24 26 28 30 32
((if (~4 + (x div 2)) <= 0 then (1 + (x div 3)) else x) mod 2)
A257341: 1 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1
loop(\(x,i).((6x + 1) + (x mod 3)),x,2)
A037641: 2 15 91 548 3291 19747 118484 710907 4265443 25592660 153555963 921335779 5528014676 33168088059 199008528355 1194051170132
(if x <= 0 then 1 else (2 * (x + ((x div 2) div 7))))
A241071: 1 2 4 6 8 10 12
A271907: 1 2 4 6 8 10 12 14 16 18
A209211: 1 2 4 6 8 10 12 14 16 18 20 22 24 26 30 32
(2 + (x2 div (x + (if (~2 + (x div 4)) <= 0 then 2 else 1))))
A062049: 2 2 3 3 4 5 6 7 8 9 10 11 13 14 15 16
(if x <= 0 then 1 else ((x + 2) + ((x + ~1) mod 9)))
A160939: 1 3 5 7 9 11 13 15 17 19 12 14 16 18 20 22
loop(\(x,i).x2,1,((x + 2) + (x div 9)))
A326707: 4 9 16 25 36 49 64 81 100 144 169 196 225 256 289 324
(x div ((x + ((1 + (if x <= 0 then 1 else x)) mod 5)) div 2))
A001179: 0 1 1 1 2 1 1 1 1 2 2 1 1 1 2 1
loop(\(x,i).(x3 + ~x),1,(5x + 2))
A001509: 6 336 1716 4896 10626 19656 32736 50616 74046 103776 140556 185136 238266 300696 373176 456456
loop(\(x,i).(x + i - ((1 + (x div 3)) div 3)),x,2)
A131073: 2 3 5 8 11 15 19 24 29 35 41 48 55 62 69 76
((x + 2) + loop(\(x,i).(x div 2),(~x + 5),3))
A254318: 2 3 4 5 7 10 11 12 13 14 15 16 17 18 19 20
loop(\(x,i).(x + i - ((x - (x div 3)) div 3)),x,2)
A302334: 2 3 5 7 10 13 16 20 24 28 32 36 40 44 48 53
(2 + loop(\(x,i).((x + 2) - (2 div (1 + (x div 2)))),3,x))
A008522: 2 3 8 10 12 13 14 15 16 17 18 19 20 21 22 23
loop(\(x,i).(((x2 + x) * (1 + (x div 2))) div 3),x,2)
A099179: 2 4 20 1540 609896980 4611686018427387903 4611686018427387903
loop(\(x,i).(6x + ((x + 1) mod 3)),x,2)
A037515: 2 12 73 440 2640 15841 95048 570288 3421729 20530376 123182256 739093537 4434561224 26607367344 159644204065 957865224392
loop(\(x,i).(6x + ((x + ~1) mod 3)),x,2)
A037523: 2 13 78 470 2821 16926 101558 609349 3656094 21936566 131619397 789716382 4738298294 28429789765 170578738590 1023472431542
loop(\(x,i).(8x + ((~1 + i) mod 3)),x,2)
A037517: 2 16 129 1034 8272 66177 529418 4235344 33882753 271062026 2168496208 17347969665 138783757322 1110270058576 8882160468609 71057283748874
loop(\(x,i).(5x + ((~1 + i) mod 3)),x,2)
A037514: 2 10 51 257 1285 6426 32132 160660 803301 4016507 20082535 100412676 502063382 2510316910 12551584551 62757922757
loop(\(x,i).(6x + ((2 + i) mod 4)),x,2)
A037746: 2 15 90 541 3248 19491 116946 701677 4210064 25260387 151562322 909373933 5456243600 32737461603 196424769618 1178548617709
loop(\(x,i).((6x + 2) - ((x div 2) mod 2)),x,2)
A037571: 2 13 80 482 2893 17360 104162 624973 3749840 22499042 134994253 809965520 4859793122 29158758733 174952552400 1049715314402
(loop(\(x,i).3x,x,3) div (3x + 2))
A191627: 1 1 3 7 17 42 109 285 757 2036 5535 15184 41955 116657 326111 915887
loop(\(x,i).(x div (2 - (x mod 2))),(x + 1),(3x + 2))
A075677: 1 5 1 11 7 17 5 23 13 29 1 35 19 41 11 47
loop(\(x,i).x5,1,(3x + 2))
A016793: 32 3125 32768 161051 537824 1419857 3200000 6436343 11881376 20511149 33554432 52521875 79235168 115856201 164916224 229345007
((3x + 2) * loop(\(x,i).(x2 + 2x + 1),2,2))
A109632: 200 500 800 1100 1400 1700 2000 2300 2600 2900 3200 3500 3800
loop(\(x,i).((9x + 2) - (i mod 2)),x,2)
A037494: 2 19 173 1558 14024 126217 1135955 10223596 92012366 828111295 7453001657 67077014914 603693134228 5433238208053 48899143872479 440092294852312
loop(\(x,i).((8x + 2) - (i mod 3)),x,2)
A037525: 2 17 136 1090 8721 69768 558146 4465169 35721352 285770818 2286166545 18289332360 146314658882 1170517271057 9364138168456 74913105347650
loop(\(x,i).((5x + 2) - (i mod 3)),x,2)
A037522: 2 11 55 277 1386 6930 34652 173261 866305 4331527 21657636 108288180 541440902 2707204511 13536022555 67680112777
loop(\(x,i).(x div (2 - (x mod 2))),2,((x2 + 3x) div 2))
A125650: 0 1 5 9 7 5 27 35 11 27 65 77 45 26 119 135
((x + (loop(\(x,i).x2,2,2x) div (2x + 1))) div 2)
A211622: 0 3 26 94 229 457 800 1284 1931 2767 3814 5098 6641 8469 10604 13072
((x * loop(\(x,i).4x,2x,(2x + ~1))) div 2)
A268148: 0 8 768 30720 917504 23592960 553648128 12213813248 257698037760 5257039970304 104453604638720 2031897488130048 38843546786070528 731834939447705600 4611686018427387903 4611686018427387903
loop(\(x,i).((10x + 1) + (x mod 2)),x,2)
A037495: 2 21 212 2121 21212 212121 2121212 21212121 212121212 2121212121 21212121212 212121212121 2121212121212 21212121212121 212121212121212 2121212121212121
loop(\(x,i).((10x + 1) + (i div 2)),x,2)
A024763: 2 21 212 2122
(x - (loop(\(x,i).(x3 div 3),x,(~x + 1)) div 2))
A152859: 0 1 3 125 4611686018427387903
loop(\(x,i).(~x + 2),x,((5x2 + x) div 2))
A266088: 0 ~1 11 ~22 42 ~63 93 ~124 164 ~205 255 ~306 366 ~427 497 ~568
((x + loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),x,1)) div 2)
A216779: 0 0 1 2 6 24 135 930 7420 66752 667485 7342290 88107426 1145396472 16035550531 240533257874
((x * ((x + 1) + (2 * (x + (if (x mod 2) <= 0 then x else 1))))) div 2)
A225144: 0 3 11 18 42 45 93 84 164 135 255 198 366 273 497 360
(2 + compr(\x.(loop(\(x,i).(x * (1 + (i div 2))),x,1) mod (x + 1)),x))
A291109: 2 5 7 9 10 11 13 15 16 17 19 21 22 23 25 26
(2 + compr(\x.(loop(\(x,i).(x2 + x),3,2) mod (x + 1)),x))
A227007: 2 3 4 7 8 15 22 43 44 87 130 259 302 603 904 1807
((x + 2) + loop(\(x,i).((x * (x + i)) div (1 + i)),2,(x + 1)))
A014628: 3 8 20 45 91 168 288 465 715 1056 1508 2093 2835 3760 4896 6273
loop(\(x,i).x2,3,(10x + 8))
A017372: 16777216 11019960576 377801998336 4347792138496 28179280429056 128063081718016 457163239653376 1370114370683136 3596345248055296 8507630225817856 18509302102818816 37588592026706176 72057594037927936 131532383853732096 230193853492166656
loop(\(x,i).x3,1,(10x + 8))
A017367: 512 5832 21952 54872 110592 195112 314432 474552 681472 941192 1259712 1643032 2097152 2628072 3241792 3944312
loop(\(x,i).x3,2,(10x + 8))
A017373: 134217728 198359290368 10578455953408 165216101262848 1352605460594688 7427658739644928 31087100296429568 106868920913284608 316478381828866048 833747762130149888 1999004627104432128
((x + 2) + loop(\(x,i).(x * (3 + i)),4,(x + 1)))
A158404: 842 1683 2524 3365 4206 5047 5888 6729 7570 8411 9252 10093 10934 11775 12616 13457
(((x2 + x) + loop(\(x,i).(2x + (i mod 2)),x,2)) div 2)
A081661: 1 3 8 16 31 57 106 198 377 727 1420 2796 5539 11013 21950 43810
(loop(\(x,i).(2 * (x + (2 * i))),x,0) - ((x2 + x) div 2))
A277411: 0 3 13 38 94 213 459 960 1972 4007 8089 16266 32634 65385 130903 261956
((if ((x + 2) mod 4) <= 0 then 2 else 1) + ((x2 + x) div 2))
A013660: 1 2 5 7 11
A089781: 1 2 5 7 11 16 23 29 37 46 57 67 79 92 107 121
((x * loop(\(x,i).x2,1,(x4 + x3))) div 2)
A163277: 0 2 576 17496 204800 1406250 6858432 26353376 84934656 239148450 605000000 1403076312 3027787776 6149354666 11859019200 21870000000
(loop(\(x,i).(x2 + 4x + 4),2,1) - ((x2 + ~x) div 2))
A137517: 121 121 120 118 115 111 106 100 93 85 76 66 55 43 30 16
(((2 + ((x div ~2) mod 3)) mod (if x <= 0 then 1 else x)) div 2)
A308884: 0 0 0 0 1 1 1 2 2 1 1 1 1 2 2 1
(2 + ((2 * (x div (~2 + (x mod ~2)))) mod (if x <= 0 then 1 else x)))
A164024: 2 2 2 3 2 3 2 3 2 5 2 5 2 5 2 7
(x - (((x div (4 + (x mod 2))) - (if x <= 0 then 1 else x)) div 2))
A248565: 1 2 3 5 6 7 9 10 11 13 14 16 17 19 20 21
(4x - ((((x div 2) mod 2) - (if x <= 0 then 1 else x)) div 2))
A301291: 1 5 9 13 18 23 27 31 36 41 45 49 54 59 63 67
((9x + 3) + ((if x <= 0 then 1 else x) mod 2))
A063121: 4 13 21 31 39 49 57 67 75 85 93 103 111 121 129 139
(13 * (2 - ((if x <= 0 then 1 else x) mod 2)))
A040157: 13 13 26 13 26 13 26 13 26 13 26 13 26 13 26 13
(17 * (2 - ((if x <= 0 then 1 else x) mod 2)))
A040273: 17 17 34 17 34 17 34 17 34 17 34 17 34 17 34 17
((if x <= 0 then 1 else 4) - ((~x3 + x2 + ~x) div 2))
A076860: 1 5 7 15 30
loop(\(x,i).((4x * (~1 + (2 * i))) div (1 + i)),x,2)
A025225: 2 4 16 80 448 2688 16896 109824 732160 4978688 34398208 240787456 1704034304 12171673600 87636049920 635361361920
(~2 + loop(\(x,i).(1 + ((x2 + 5x + 6) * i)),2,x))
A062651: 179 479
(2 + loop(\(x,i).((3x + ~1) div 5),2,x))
A087817: 1 1 2 2 3 3 3 4 4 4 4 5 6 6 6 6
(loop(\(x,i).(2 - ((x + ~2) div (1 + (2 * (x mod 2))))),2,x) div 2)
A078898: 0 1 1 1 2 1 3 1 4 2 5 1 6 1 7 3
loop(\(x,i).((7x + 2) - (i mod 2)),x,2)
A037492: 2 15 107 750 5252 36765 257357 1801500 12610502 88273515 617914607 4325402250 30277815752 211944710265 1483612971857 10385290803000
(2 + compr(\x.((1 + (loop(\(x,i).2x,x,1) mod (x + 2))) mod 2),x))
A086807: 2 5 13 17 29 37 41 53 61
loop(\(x,i).((5x + 2) - ((x div 2) mod 2)),x,2)
A037554: 2 11 56 282 1411 7056 35282 176411 882056 4410282 22051411 110257056 551285282 2756426411 13782132056 68910660282
((x * (2 + loop(\(x,i).(3x + (i mod 2)),x,1))) div 2)
A126875: 0 3 14 58 226
loop(\(x,i).(2 * (x - ((3x + ~3) div (1 + i)))),x,2)
A291299: 2 2 2 4 6 8 10 14 20 30
((x + 2) + (((x - (if (~2 + (x div 2)) <= 0 then 1 else 0)) div 2) div 2))
A287727: 1 3 4 5 6 8 9 10 12 13 14 15 17 18 19 20
((~x + 2) div (2 + (if (x mod 10) <= 0 then 2 else x)))
A030621: 0 0 0 ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~2 ~1 ~1 ~1 ~1 ~1
loop(\(x,i).((4x + 2) - ((i mod 3) mod 2)),x,2)
A037569: 2 9 38 154 617 2470 9882 39529 158118 632474 2529897 10119590 40478362 161913449 647653798 2590615194
(loop(\(x,i).(2 + ((~2 + ((x + ~1) div 2)) mod (x + 1))),2,x) div 2)
A140225: 1 1 2 1 1 1 1 2 2 3 3 1 1 1 1 1
(loop(\(x,i).(2 + (x div (2 + (3 * (x mod 2))))),2,x) div 2)
A268057-A107435: 1 1 1 1 2 1 1 1 2 1 1 2 3 2 1 1
loop(\(x,i).2x,x,(x + 34))
A079863: 34 70 144 296 608 1248 2560 5248 10752 22016 45056 92160 188416 385024 786432 1605632
(2 div ((x + 2) div (if ((~x + 1) mod 8) <= 0 then x else 2)))
A231366: 2 0 1 1 0 0 0 0 0 2 0 0 0 0 0 0
loop(\(x,i).(8x + ((x + 1) mod 4)),x,2)
A037748: 2 19 152 1217 9738 77907 623256 4986049 39888394 319107155 2552857240 20422857921 163382863370 1307062906963 10456503255704 83652026045633
loop(\(x,i).(8x + ((x + ~1) mod 4)),x,2)
A037734: 2 17 136 1091 8730 69841 558728 4469827 35758618 286068945 2288551560 18308412483 146467299866 1171738398929 9373907191432 74991257531459
((x + 2) + (if (x + ~2) <= 0 then 1 else ((x - ((x div 2) mod 2)) div 2)))
A253897: 3 4 5 6 8 9 10 12 14 15 16 18 20 21 22 24
loop(\(x,i).x2,1,((x + 2) + ((x - ((x div 2) mod 2)) div 2)))
A106575: 4 9 16 36 64 81 100 144 196 225 256 324 400 441 484 576
loop(\(x,i).(5x + ((2 + i) mod 4)),x,2)
A037745: 2 13 65 326 1632 8163 40815 204076 1020382 5101913 25509565 127547826 637739132 3188695663 15943478315 79717391576
(2 * (x + (if (~2 + (x div 3)) <= 0 then 1 else (x div 4))))
A309239: 2 4 6 8 10 12 14 16 18 22 24 26 30 32 34 36
loop(\(x,i).(4x + ((x + (x div 2)) mod 4)),x,2)
A037625: 2 11 44 178 715 2860 11442 45771 183084 732338 2929355 11717420 46869682 187478731 749914924 2999659698
((x + 2) + (((if (~2 + (x div 2)) <= 0 then 1 else 2) + (x div 2)) div 2))
A307295: 2 3 5 6 7 8 10 11 13 14 15 16 18 19 20 21
(2 * (x + ((x + (if (~2 + (x div 3)) <= 0 then 2 else 1)) div 2)))
A189782: 2 4 8 10 14 16 20 22 26 28 30 34 36 40 42 46
loop(\(x,i).((3x + 2) - ((i mod 3) mod 2)),x,2)
A129669: 2 7 23 71
A037568: 2 7 23 71 214 644 1934 5803 17411 52235 156706 470120 1410362 4231087 12693263 38079791
(2 + compr(\x.((1 + loop(\(x,i).2x,(x div 2),2)) mod (x + 2)),x))
A319041-A175865-A059646-A059644-A059350-A003629: 3 5 11 13 19 29 37 43 53 59 61 67 83 101 107 109
(2 + compr(\x.(1 - (loop(\(x,i).(x * i),(x div 2),1) mod (x + 2))),x))
A178156: 2 3 4 5 6 7 8 9 10 11 13 14 17 19 22 23
loop(\(x,i).((x + 2) + ((1 + (4 * (1 + i))) * i)),x,2)
A219054: 2 13 41 94 180 307 483 716 1014 1385 1837 2378 3016 3759 4615 5592
((x + 2) * ((4x2 + x) + (if x <= 0 then 0 else 1)))
A296363: 0 18 76 200 414 742 1208 1836 2650 3674 4932 6448 8246 10350 12784 15572
(if (x mod (1 + ((x + 2) div 5))) <= 0 then 1 else (x + 2))
A089027: 1 1 1 5 1 7 1 9 10 1 12 13 1 15 16 17
((x + 2) * (~1 + loop(\(x,i).((x + 1) * (1 + i)),(x + 1),1)))
A141834: 6 42 252 1620 11730 95886 876792 8877672 98640990 1193556210 15624736116 220048367292 3317652307242 53319412081110 909984632851440 16436597430879696
((1 + loop(\(x,i).(x + (x mod (1 + i))),(x + ~1),1)) div (x + 2))
A283875-A099773: 1 0 0 1 0 1 1 1 1 1 2 2 2 3 3 3
((if (x mod 4) <= 0 then (2x + ~5) else 1) mod (x + 2))
A204131: 1 1 1 1 3 1 1 1 1 1 1 1 5 1 1 1
((1 + loop(\(x,i).(2x * (1 + (2 * i))),x,1)) div (x + 2))
A262035: 1 2 15 168 2520 47520 1081080 28828800 882161280 30474662400 1173274502400 49819040409600 2313026876160000 116576554558464000 4611686018427387903 4611686018427387903
(if (~2 + (x mod (1 + (2 * (x mod 3))))) <= 0 then 1 else (x + 2))
A279051: 1 1 1 1 1 1 1 1 10 1 1 1 1 1 16 1
(if ((x + 2) mod (2 - (x mod ~4))) <= 0 then 1 else (x + 2))
A090585: 1 3 1 5 1 7 1 1 1 11 1 13 1 1 1 17
(x div (if x <= 0 then 1 else (x2 mod (5x + 10))))
A341743: 0 1 0 0 0 0 0 1 0 0 0 0 3 0 0 0
(((x + ~1) + loop(\(x,i).(x2 + 3x + 2),2,2)) div (x + 2))
A161823: 90 60 45 36 30 26 23 20 18 17 15 14 13 12 12 11
(loop(\(x,i).((2x + 2) - (x div 4)),x,1) div (x + 2))
A202278: 0 1 2 3 5 8 13 21 34 55 89
(((x + 1) * loop(\(x,i).(x2 + 2x + 1),2,2)) div (x + 2))
A180103: 50 66 75 80 83 85 87 88 90 90 91 92 92 93 93 94
loop(\(x,i).(16 * (~1 + (x * i))),2,(x + 2))
A157447: 496 1008 1520 2032 2544 3056 3568 4080 4592 5104 5616 6128 6640 7152 7664 8176
((2 + loop(\(x,i).(2x * (~1 + (2 * i))),x,x)) div (x + 2))
A272688: 1 1 6 72 1120 21600 498960 13453440 415134720 14435366400
((x + 2) * loop(\(x,i).x3,3,(x2 + 2)))
A137492: 268435456 22876792454961 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((if x <= 0 then 2 else 17x) div (x + 2))
A006186: 1 5 8 10 11 12 12 13 13 13
((x + 2) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))
A090178: 2 4 6 9 12 17 20 25 28 33 40 43 50 55 58 63
((4 * (2 + (x mod 2))) + ((x + 2) * (if x <= 0 then 1 else x)))
A076226: 10 15 16 27
((x + 2) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A095116: 2 4 7 10 15 18 23 26 31 38 41 48 53 56 61 68
((x + (2 * (x + (if (x + ~4) <= 0 then 1 else x)))) div (x + 2))
A130535: 1 1 2 2 2 3 3 3 4 4 4 4 4 4 4 4
((x + 2) + loop(\(x,i).(x - (x div (8 - i))),2,x))
A161602: 2 4 6 8 10 12 13 14 16 18 20 22 24 25 26 28
loop(\(x,i).((1 + (x2 div 8)) div 2),2,(x + ~2))
A326526-A326525-A326524-A326522: 0 0 0 0 0 0 0 0 0 1 1 2 2 4 5 8
((x2 + ~2x) * (if (x mod 12) <= 0 then 2 else 0))
A282230: 0 0 0 0 0 0 0 0 0 0 0 0 240 0 0 0
((~x + 2) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A086969-A014692: 2 2 3 4 7 8 11 12 15 20 21 26 29 30 33 38
(2x + (if (~1 + (2x mod (1 + (x div 2)))) <= 0 then 1 else 0))
A190333: 1 3 5 7 8 11 13 14 17 18 20 22 24 26 28 30
(2x + (if (~2 + ((x mod 2) + (x div 3))) <= 0 then 1 else 0))
A187472: 1 3 5 7 9 11 13 14 17 18 20 22 24 26 28 30
(2x + (if (~2 + (x mod (2 + (x mod 3)))) <= 0 then 1 else 0))
A189397: 1 3 5 7 9 11 13 15 17 19 21 22 25 27 29 31
(2x + (if (~2 + (x div (2 * (2 - (x mod 2))))) <= 0 then 1 else 0))
A187411: 1 3 5 7 9 11 13 14 17 18 21 22 24 26 28 30
(2x + (if ((x div 2) - (2 * (2 + (x mod 2)))) <= 0 then 1 else 0))
A187349: 1 3 5 7 9 11 13 15 17 19 20 23 24 27 28 30
(2x + (if ((x + 1) mod 7) <= 0 then 2 else 1))
A190053: 1 3 5 7 9 11 14 15 17 19 21 23 25 28 29 31
(2x + (if x <= 0 then 1 else (x2 div 12)))
A231408: 1 2 4 6 9
A130664: 1 2 4 6 9 12 15 18 21 24 28 32 36 40 44 48
(2x + (if (~x + 2) <= 0 then ((x * (x div 3)) mod 2) else 1))
A295771: 1 3 4 7 8 11 12 14 16 19 20 23 24 26
(2x + loop(\(x,i).(x - (x div (1 + (2 * i)))),2,(x + 1)))
A231407: 1 4 6
A190304: 1 4 6 9 12 14 16 19 21 24 27 29 32 34 36 39
(2x + loop(\(x,i).(x + (x div 4) - i),x,(x + 1)))
A298808: 1 3 4 6 6 3 1
loop(\(x,i).(1 + (2 * ((x + 1) mod 3))),(x + ~1),2x)
A234255: 0 2 5 3 1 1 3 5 5 3 1 1 3 5 5 3
(((((x + ~1) div 2) * (x div 2)) div 2) + (if x <= 0 then 1 else 2x))
A231408: 1 2 4 6 9
A337134: 1 2 4 6 9 12 15 18 22 26 30 34 39 44 49 54
(2x + ((x - (if (~2 + (x div 4)) <= 0 then 1 else 0)) mod 2))
A227149: 1 2 5 6 9 10 13 14 17 18 21 22 24 27 28 31
(2x + (if (x mod 13) <= 0 then 1 else 2))
A231407: 1 4 6
A175074: 1 4 6 8 10 12 14 16 18 20 22 24 26 27 30 32
(2x + (if (x mod (2 + ((x + ~1) mod 3))) <= 0 then 1 else 2))
A231407: 1 4 6
A161576: 1 4 6 8 9 12 14 16 18 20 21 24 25 28 30 32
(~2x + (x * loop(\(x,i).(x2 + 4x + 4),3,1)))
A004975-A004955: 0 15127 30254 45381 60508 75635 90762 105889 121016 136143 151270 166397 181524 196651 211778 226905
(3x + loop(\(x,i).i,(x - (x mod (2 + (x mod 2)))),1))
A321177: 1 4 8 12 16 18 24 27 32 36 40
(~2x + compr(\x.(loop(\(x,i).(2x + 1),x,0) mod (x + 1)),x))
A192326: 0 0 0 0 2 2 4 4 6 10 10 14 16 16 18 22
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,2x)
A162551: 0 2 8 30 112 420 1584 6006 22880 87516 335920 1293292 4992288 19315400 74884320 290845350
loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,2x)
A246574: 0 4 20 84 336 1320 5148 20020 77792 302328 1175720 4576264 17829600 69535440 271455660 1060730100
(2x * (~x + loop(\(x,i).(2x + ~1),(x + ~3),x)))
A052760: 0 0 0 0 24 120 420 1260 3472 9072 22860 56100 134904 319176 745108 1719900
(loop(\(x,i).((x + 1) + ((i * i) div 3)),x,1) + (x div 2))
A007979: 1 2 5 9 16 25 39 56 79 107 142 183 233 290 357 433
(1 + ((x * loop(\(x,i).(1 + (x * (i * i))),x,2)) + (x div 2)))
A309147: 1 4 28 356
(((x + 1) * (if (x mod 2) <= 0 then 1 else 6)) - (x div 2))
A335043: 1 12 2 23 3 34 4 45 5 56 6 67 7 78 8 89
((x + 1) mod ((if (x mod 4) <= 0 then ~1 else 2) + (x div 2)))
A060755: 0 0 0 1 0 2 2 3 0 4 4 5 3 6 6 7
((if (x mod (2 * (2 + (x mod 3)))) <= 0 then 1 else 2) + (x div 2))
A324475: 1 2 3 3 4 4 5 5 5 6 7 7 7 8 9 9
((if (x mod 2) <= 0 then 1 else 20) + (x div 2))
A303849-A303847: 1 20 2 21 3 22 4 23 5 24 6 25 7 26 8 27
((2 * (2x + (if (x mod 2) <= 0 then 1 else 4))) - (x div 2))
A166544: 2 12 9 19 16 26 23 33 30 40 37 47 44 54 51 61
((2 * (x + (if (x mod 2) <= 0 then 1 else 6))) + (x div 2))
A168207: 2 14 7 19 12 24 17 29 22 34 27 39 32 44 37 49
(x + ((if ((x div 2) mod 5) <= 0 then 2 else 1) + (x div 2)))
A189729: 2 3 4 5 7 8 10 11 13 14 17 18 19 20 22 23
(x + ((if (x - (4 mod (x + 2))) <= 0 then 2 else 1) + (x div 2)))
A067118: 2 3 4 6 8 8 10 11 13 14 16 17 19 20 22 23
(((x mod 10) mod (if x <= 0 then 1 else x)) + (x div 2))
A060969: 0 0 1 1 2 2 3 3 4 4 5 6 8 9 11 12
((2x div (2 + (x div 2))) + (if x <= 0 then 1 else x) + (x div 2))
A298861: 1 2 4 6 8 9 11 12 14 16 17 19 21 22 24 25
((if ((x2 + 1) mod (1 + (x div 2))) <= 0 then 0 else 1) + (x mod 2))
A165034: 0 1 1 1 1 2 1 2 0 2 1 2 1 2 1 2
((if (16 mod (x + 1)) <= 0 then 0 else 1) + (x mod 2))
A327403-A124766: 0 1 1 1 1 2 1 1 1 2 1 2 1 2 1 1
((1 + (if (x mod 3) <= 0 then 1 else (x div 3))) * (x mod 2))
A172441: 0 1 0 2 0 2 0 3 0 2 0 4 0 5 0 2
((if ((1 + (x div 3)) mod 4) <= 0 then 2 else 1) + (x mod 2))
A083897: 1 2 1 2 1 2 1 2 1 3 2 3 1 2 1 2
((loop(\(x,i).2x,x,1) div 9) + (x mod 2))
A131090: 0 1 0 1 1 4 7 15 28 57 113 228 455 911 1820 3641
((if ((x2 div 2) mod 3) <= 0 then 4 else 1) - (x mod 2))
A131027: 4 3 1 0 1 3 4 3 1 0 1 3 4 3 1 0
((if (((x + ~1) div 3) mod 2) <= 0 then 4 else 1) - (x mod 2))
A254745: 1 3 4 3 1 0 1 3 4 3 1 0 1 3 4 3
loop(\(x,i).(6x + 3),(1 + (x div 2)),(x mod 2))
A026551: 3 9 21 57 129 345 777 2073 4665 12441 27993 74649 167961 447897 1007769 2687385
(loop(\(x,i).(10x + 1),x,1) - (x mod 2))
A290191: 1 10 111 1110 11111 111110 1111111 11111110 111111111 1111111110 11111111111 111111111110 1111111111111 11111111111110 111111111111111 1111111111111110
(loop(\(x,i).((x2 + x + ~1) + (x mod 2)),x,1) + (x mod 2))
A109173: 1 3 5 31 929 863971 746445024869 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(2 * (x + ((x - (i mod 2)) div 2))),x,1) + (x mod 2))
A307685: 1 3 6 17 48 143 426 1277
((if ((x2 div 2) mod 3) <= 0 then 1 else ~2) - (x mod 2))
A100219: 1 0 ~2 ~3 ~2 0 1 0 ~2 ~3 ~2 0 1 0 ~2 ~3
((if ((x2 + 1) mod (1 + (x div 2))) <= 0 then 1 else 2) + (x mod 2))
A165035: 1 2 2 2 2 3 2 3 1 3 2 3 2 3 2 3
((if (16 mod (x + 1)) <= 0 then 1 else 2) + (x mod 2))
A163671: 1 2 2 2 2 3 2 2 2 3 2 3 2 3 2 2
(loop(\(x,i).(2x + 1),((x div 2) div 3),2) * (x mod 2))
A307692: 0 2 0 2 0 2 0 5 0 5 0 5 0 11 0 11
((((x mod 3) div 2) * (if (x + ~2) <= 0 then 1 else 2)) + (x mod 2))
A339558: 0 1 1 1 0 3 0 1 2 1 0 3 0 1 2 1
(((if x <= 0 then 2 else ((x * (x div 2)) div 4)) div 2) + (x mod 2))
A133564: 1 1 0 1 1 2 2 3 4 5 6 7 9 10 12 14
((4 * (if (x mod 4) <= 0 then x else (x + 1))) - (x mod 2))
A072834: 0 7 12 15 16 23 28 31 32 39 44 47 48 55 60 63
(loop(\(x,i).2x,x,1) - ((2 - (x mod 4)) * (x mod 2)))
A007679: 1 1 4 9 16 31 64 129 256 511 1024 2049 4096 8191 16384 32769
((1 + (if (~1 + (x mod 3)) <= 0 then 2 else 0)) * (2 - (x mod 2)))
A129203: 6 3 2 3 6 1 6 3 2 3 6 1 6 3 2 3
(loop(\(x,i).(x * (2 + i)),(2x + 1),2) * (2 - (x mod 2)))
A301898: 12 120 10080 362880 79833600 6227020800 2615348736000 355687428096000 243290200817664000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).((x + 1) + (((2 + i) * i) div 2)),x,2) - (x mod 2))
A173809: 2 3 9 16 30 47 73 104 146 195 257 328 414 511 625 752
loop(\(x,i).(1 + (2 * (~2x + (x div 2)))),(x div 2),(x mod 2))
A287479: 0 1 1 ~3 ~3 9 9 ~27 ~27 81 81 ~243 ~243 729 729 ~2187
loop(\(x,i).(10x + 2),(x div 2),(x mod 2))
A094626: 0 1 2 12 22 122 222 1222 2222 12222 22222 122222 222222 1222222 2222222 12222222
(loop(\(x,i).(((x2 + 1) div 2) + (x mod 2)),2,x) - (x mod 2))
A212740: 0 1 2 17 32 97 162 337 512 881 1250 1921 2592 3697 4802 6497
(2 * loop(\(x,i).(5 * (1 + (2 * (x - i)))),x,x))
A089906: 0 10 270 4650 66430 864210 10641990 126419770 1464197550 16641975330 186419753110 2064197530890 22641975308670 246419753086450 2664197530864230 28641975308642010
loop(\(x,i).(10x + 27),x,2)
A276509: 2 47 497 4997 49997 499997 4999997 49999997 499999997 4999999997 49999999997 499999999997 4999999999997 49999999999997 499999999999997 4999999999999997
(2 + loop(\(x,i).((2x + ~2) + (2 div (1 + (x div 2)))),x,x))
A260790: 2 4 7 16 36 100
(2 + compr(\x.(2 - loop(\(x,i).(x div (1 + (2 * (x mod 2)))),2,x)),x))
A088224: 4 6 8 9 10 12 14 15 16 18 20 21 22 23 24 25
(loop(\(x,i).(2 + ((x - ((~x + 1) mod 3)) div 2)),x,x) div 2)
A214364: 0 1 1 1 2 1 2 1 1 2 1 2 1 1 1 2
((x + loop(\(x,i).(((x2 + x) div 2) mod 4),2,x)) div 2)
A327041: 0 1 2 3 3 3 3 3 4 5 6 7 7 7 7 7
(2 * (x + loop(\(x,i).((x2 + 2) div (x + 4)),2,x)))
A339331: 0 2 4 6 10 12 14 18 22 24 28 32 36 40 44 46
((x + (if (~2 + (x div 2)) <= 0 then 1 else (x * (x div 4)))) mod 2)
A171894: 1 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0
((x2 + loop(\(x,i).(~1 + (x * (x + i))),(x + ~1),1)) div 2)
A192225: 0 1 2 5
A293023: 0 1 2 5 12 70
(((~x2 + 1) + loop(\(x,i).(x3 + x),x,1)) div 2)
A334304: 1 1 3 501
(loop(\(x,i).(x5 + x3),1,x2) div 2)
A168564: 0 1 544 29889 526336 4890625 30256416 141296449 537001984 1743657921 5000500000 12969598081 30960175104 68931659329 144631092256 288330890625
(loop(\(x,i).(x5 + x2),1,x2) div 2)
A168220: 0 1 520 29565 524416 4883125 30233736 141238825 536872960 1743395481 5000005000 12968719621 30958692480 68929260205 144627346696 288325220625
((x2 + (if ((x div 2) mod 2) <= 0 then 1 else (2x + 2))) div 2)
A335298: 0 1 5 8 8 13 25 32 32 41 61 72 72 85 113 128
((4 * (if (x mod 2) <= 0 then 4 else 1)) mod (x2 + 2))
A177241: 0 1 4 4 16 4 16
((x2 + loop(\(x,i).(x * i),x,3)) div (x2 + 2))
A059687: 1 1 1 2 4 14 57
(2x2 + (if (x + ~3) <= 0 then 2 else (x2 + 2x)))
A090246: 2 4 10 20 56
(2 + ((if (x mod 2) <= 0 then 3x else 1) + (x2 div 2)))
A338043: 2 3 10 7 22 15 38 27 58 43 82 63 110 87 142 115
(loop(\(x,i).(x3 + x2),1,x4) div 2)
A170776: 0 1 2176 269001 8421376 122265625 1089230976 6923526001 34368126976 141236291601 500050000000 1569321367801 4458265214976 11649450426601 28347694082176 64874450390625
(loop(\(x,i).(x3 + x),1,x4) div 2)
A168227: 0 1 2056 265761 8388736 122070625 1088391816 6920644801 34359740416 141214771521 500000005000 1569214195681 4458050234496 11649042575521 28346956206856 64873168970625
((x2 * (x2 + loop(\(x,i).x3,2,x))) div 2)
A168225: 0 1 1032 88614 2097280 24414375 181399176 988664572 4294969344 15690533085 50000005000 142655842626 371504195712 896080211299 2024782604040 4324877955000
(loop(\(x,i).(x2 + x),1,x5) div 2)
A071236: 0 1 528 29646 524800 4884375 30236976 141246028 536887296 1743421725 5000050000 12968792826 30958806528 68929431571 144627596400 288325575000
(2 * loop(\(x,i).x2,(x + ~1),x5))
A275002: 0 2 2048 6973568802 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 - ((x * ((~x + 1) - (if (x + ~4) <= 0 then 1 else x))) div 2))
A111274: 1 2 3 6 9 24
(2 * compr(\x.loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,x),x))
A085406-A022340: 0 2 4 8 10 16 18 20 32 34 36 40 42 64 66 68
(loop(\(x,i).(x4 + x3),1,x3) div 2)
A170785: 0 1 2304 275562 8519680 123046875 1093430016 6940820404 34426847232 141408478485 500500000000 1570393162206 4460630114304 11654344810927 28357286711040 64892390625000
(loop(\(x,i).(x4 + x),1,x3) div 2)
A168190: 0 1 2052 265734 8388640 122070375 1088391276 6920643772 34359738624 141214768605 500000000500 1569214189026 4458050224992 11649042562339 28346956189020 64873168947000
(27 + loop(\(x,i).x2,x,2))
A273547: 29 31 43 283 65563
((x * (x2 + loop(\(x,i).x2,2,x3))) div 2)
A168191: 0 1 4100 797175 33554464 610351625 6530347116 48444505375 274877907200 1270932914529 5000000000500 17261356072631 53496602690400 151437553297225 396857386628444 973097534181375
loop(\(x,i).((~x + 4) + ((x div 4) + (x * i))),x,2)
A324148: 2 4 9 24 82
loop(\(x,i).(((2x * (1 + (2 * i))) div (2 + i)) * i),x,2)
A110371: 2 4 20 168 2016 31680 617760 14414400 392071680 12189864960 426645273600 16606346803200 711700577280000 33307587016704000 1690360041097728000 4611686018427387903
(x + (if ((x + 1) mod 5) <= 0 then 5 else 0))
A325645: 0 1 2 3 9 5 6 7 8 14 10 11 12 13 19 15
compr(\x.(if (x mod 2) <= 0 then ((x2 div 3) mod 3) else 0),x)
A039231: 0 1 3 5 6 7 8 9 10 11 12 13 15 17 18 19
(x + (if ((x + 1) mod 10) <= 0 then (x + 1) else 0))
A103205: 0 1 2 3 4 5 6 7 8 19 10 11 12 13 14 15
(x + (if ((x + 1) mod 8) <= 0 then 8 else 0))
A325805: 0 1 2 3 4 5 6 15 8 9 10 11 12 13 14 23
compr(\x.(if (x mod 2) <= 0 then ((x + 1) mod (2 + (x div 4))) else 0),x)
A081534: 1 3 5 7 9 11 13 14 15 17 19 20 21 23 25 27
compr(\x.(if (x mod 2) <= 0 then ((2 + (x div 4)) mod 4) else 0),x)
A173186: 1 3 5 7 8 9 10 11 13 15 17 19 21 23 24 25
(x + loop(\(x,i).((x + 1) + (x div 8)),(x + ~2),0))
A276128: 0 1 2 4 6 8 10 12 14 16 18 21 24 27 30 34
(x * ((x mod 2) - loop(\(x,i).(2x - (i mod 2)),(x + ~2),0)))
A099431: 0 1 0 6 8 30 60 154 336 774 1700 3762 8184 17758 38220 81930
(x + (if (x mod 13) <= 0 then (x div 2) else 0))
A103303: 0 1 2 3 4 5 6 7 8 9
A246200: 0 1 2 3 4 5 6 7 8 9 10 11 12 19 14 15
(x + (if (x mod 2) <= 0 then (8x + (x div 2)) else 0))
A317319: 0 1 19 3 38 5 57 7 76 9 95 11 114 13 133 15
compr(\x.(if (x mod (4 + (x2 mod 3))) <= 0 then x else 0),x)
A103677: 0 1 2 3 4 6 7 8 9 11 13 14 15 16 17 18
(~x + loop(\(x,i).(x + i - ((~1 + (x div 4)) div 2)),x,0))
A219656: 0 1 3 5 8 11 15 19 24 29 34 39 45 51 57 63
(x * loop(\(x,i).(x + ((~1 + (2 * i)) * (1 + i))),x,~1))
A264851: 0 1 20 90 260 595 1176 2100 3480 5445 8140 11726 16380 22295 29680 38760
((x + 1) + loop(\(x,i).(1 + (x * (1 + (x2 div 2)))),x,0))
A038198: 1 3 5 11 181
compr(\x.(~1 + (x mod (~1 + (loop(\(x,i).2x,x,x) mod (x + 1))))),x)
A226038-A181062: 0 1 2 3 4 6 7 8 10 12 15 16 18 22 24 26
(x + loop(\(x,i).i,(~1 + (x mod (2 - (x mod ~4)))),1))
A143265: 1 2 3 4 5 6 7 8 9 12 11 12 13 15 15 16
(x + loop(\(x,i).i,(5 * (~1 + (x div 3))),1))
A032984: 1 2 3 4 5 6 11 12 13 19 20 21 27 28 29 35
(x + loop(\(x,i).(~x + i),(1 + ((x2 + 2x) div 4)),1))
A231664: 0 1 3 6 7 9 12 16 18 21 25 30 33 37 42 48
(1 div (if (((2x + 1) div 3) mod 3) <= 0 then 1 else x))
A191747: 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1 0
(x + loop(\(x,i).2x,((x - (x div 3)) div 3),1))
A285986: 1 2 3 4 6 7 8 9 12 13 14 15 16 21 22 23
(x + loop(\(x,i).4x,(((x + 1) div 2) div 3),1))
A096304: 1 2 3 4 5 9 10 11 12 13 14 27 28 29 30 31
loop(\(x,i).x3,1,11x)
A017391: 0 1331 10648 35937 85184 166375 287496 456533 681472 970299 1331000 1771561 2299968 2924207 3652264 4492125
loop(\(x,i).x3,2,11x)
A017397: 0 2357947691 1207269217792 46411484401953 618121839509504 4605366583984375 23762680013799936 95151694449171437 316478381828866048 913517247483640899 2357947691000000000 4611686018427387903
(x + (if x <= 0 then 1 else ((x + 2) div (1 + (2x div 3)))))
A102126: 1 4 4 4 6 6 7 8 9 10 11 12 13 14 15 16
(x + (if (~x + 2) <= 0 then ((x + ((x div 2) mod 2)) div 3) else 1))
A168134: 1 2 3 4 5 6 8 9 10 12 13 15 16 17 19 20
((~x + 1) mod (x + loop(\(x,i).(4 * i),(x mod 3),1)))
A021112: 0 0 9 2 5 9 2 5 9 2 5 9 2 5 9 2
compr(\x.(~1 + (loop(\(x,i).4x,x,1) mod (2x + 1))),x)
A102781: 0 1 2 3 5 6 8 9 11 14 15 18 20 21 23 26
compr(\x.(1 div (~1 + (loop(\(x,i).(2 * (x + i)),x,0) mod (x + 1)))),x)
A166460: 0 1 5 7 8 9 11 13 14 15 17 19 20 21 23 24
compr(\x.(~1 + (loop(\(x,i).(2x + 6),x,1) mod (x + 1))),x)
A248614: 0 1 2 4 6 10 12 16 18 20 22 28 30 36 40 42
compr(\x.(2 - (x mod (~1 + (loop(\(x,i).2x,x,x) mod (x + 1))))),x)
A226039-A080765: 5 9 11 13 14 17 19 20 21 23 25 27 29 32 33 34
(x + loop(\(x,i).(3x2 + ~3x + 3),(x + ~1),1))
A326971: 1 2 5 24 1267
(x + loop(\(x,i).(3 * ((x * i) - (x div 2))),(x + ~1),1))
A281532: 1 2 5 18 118
((~2x + 1) mod (x + loop(\(x,i).(~x + (i * i)),(x + ~1),1)))
A107386: 0 1 1 2 2 7 9 16 20 29 35 46 54 67 77 92
(0 - loop(\(x,i).(x - ((x div 4) + i)),(x + ~1),1))
A295513: ~1 ~1 0 2 4 7 10 13 16 20 24 28 32 36 40 44
((~x + 1) + ((1 + loop(\(x,i).((x2 div 2) + i),x,0)) div 2))
A319624: 1 1 0 1 5 63
((x + ~1) + (2 * loop(\(x,i).(2 * (x + (2 * i))),(x + 1),1)))
A059142: 11 40 105 242 523 1092 2237 4534 9135 18344 36769 73626 147347 294796 589701
(1 div (if ((x mod (1 + (2 * (x mod 3)))) mod 2) <= 0 then 1 else x))
A127972: 1 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1
(x + loop(\(x,i).i,(~2 + ((2x + ~1) div 5)),1))
A195044: 1 2 3 4 5 6 7 8 9 10 11 13 14 16 17 18
(1 div (if ((x mod (1 + (2 * (2 - (x mod 2))))) mod 2) <= 0 then 1 else x))
A174856: 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1
loop(\(x,i).x3,1,(x + (x div 7)))
A125084: 0 1 8 27 64 125 216 512 729 1000 1331 1728 2197 2744 4096 4913
(2 - loop(\(x,i).(~x2 + ~x + 2),(2x + 3),x))
A001503: 12 90 4611686018427387903
(x + (x mod (1 + (2 * (if (~4 + (x div 2)) <= 0 then 0 else 2)))))
A103303: 0 1 2 3 4 5 6 7 8 9
A343160: 0 1 2 3 4 5 6 7 8 9 10 12 14 16 18 15
(x + (if (x + ~2) <= 0 then 2 else (1 + (4 * ((x + ~1) div 2)))))
A244151: 2 3 4 8 9 14 15 20 21 26 27 32 33 38 39 44
(1 div (if (x mod (2 + ((((x + ~1) div 2) div 2) mod 2))) <= 0 then 1 else x))
A323519: 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 1
loop(\(x,i).i,((x * (1 + (x mod 2))) mod 9),x)
A092384: 0 2 2 6 4 1 6 5 8 9 1 4 3 8 5 3
(x * (if (~x + 2) <= 0 then (2 + (((x div 2) * (x div 2)) div 2)) else 1))
A304909: 0 1 4 6 16 20 36 42 80 90 140 154 240 260 364 390
(1 div (if (((x2 + ~2x) mod (2 + (x div 2))) mod 2) <= 0 then 1 else x))
A340375: 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1
compr(\x.((x2 + ~2) mod (~1 + loop(\(x,i).2x2,2,2))),x)
A177046: 16 111 143 238 270 365 397 492 524 619 651 746 778 873 905 1000
(x + (x div (if (~1 + (x div 2) - (x mod 2)) <= 0 then 4 else 1)))
A109230: 0 1 2 3 8 6 12 14
loop(\(x,i).x2,1,(11x + 5))
A017450: 25 256 729 1444 2401 3600 5041 6724 8649 10816 13225 15876 18769 21904 25281 28900
loop(\(x,i).x2,2,(11x + 5))
A017452: 625 65536 531441 2085136 5764801 12960000 25411681 45212176 74805201 116985856 174900625 252047376 352275361 479785216 639128961 835210000
loop(\(x,i).x2,1,(11x + 10))
A017510: 100 441 1024 1849 2916 4225 5776 7569 9604 11881 14400 17161 20164 23409 26896 30625
loop(\(x,i).x2,2,(11x + 10))
A017512: 10000 194481 1048576 3418801 8503056 17850625 33362176 57289761 92236816 141158161 207360000 294499921 406586896 547981281 723394816 937890625
loop(\(x,i).i,(10x + ~80),x)
A048334-A048320-A048306-A029955: 0 1 2 3 4 5 6 7 8 10 20 30 40 50 60 70
(if (x mod 2) <= 0 then (5 * (2x + (x div 2))) else x)
A317325: 0 1 25 3 50 5 75 7 100 9 125 11 150 13 175 15
loop(\(x,i).x5,1,5x)
A016853: 0 3125 100000 759375 3200000 9765625 24300000 52521875 102400000 184528125 312500000 503284375 777600000 1160290625 1680700000 2373046875
(x + (if (~4 + (x div 2)) <= 0 then 0 else (1 + (x div 4))))
A103303: 0 1 2 3 4 5 6 7 8 9
A135140-A052061: 0 1 2 3 4 5 6 7 8 9 13 14 16 17 18 19
(x + loop(\(x,i).i,(~2 + ((x + ((x div 2) div 3)) div 2)),1))
A082463: 1 2 3 4 5 6 7 9 10
A190209: 1 2 3 4 5 6 7 9 10 12 13 15 17 18 20 21
compr(\x.((x2 + ~2) mod (~1 + loop(\(x,i).(x2 + 2x),2,2))),x)
A167534: 9 70 88 149 167 228 246 307 325 386 404 465 483 544 562 623
loop(\(x,i).(x div (~2 + (x mod 2))),2,(x2 + 5x))
A178242: 0 3 7 6 9 25 33 21 26 63 75 44 51 117 133 75
((x + ~1) + loop(\(x,i).(2x3 + ~2x2),(x + ~2),2))
A330294: 1 2 3 10 899
(if x <= 0 then 1 else (x + (4x div (3 + (x div 2)))))
A026516: 1 2 4 6 7 9 10 11 12 14 15 16 17 18 19 21
(if x <= 0 then 1 else (x + (3x div (3 + (x div 2)))))
A188320-A049386: 1 2 3 5 6 8 9 10 11 12 13 15 16 17 18 19
(x + loop(\(x,i).(x * i),(2 - ((~x + 2) div (2 + (x div 2)))),1))
A220695: 1 3 4 9 10 11 12 13 14 33 34 35 36 37 38 39
(x * loop(\(x,i).2x,(x + ~1),(5 - (x mod 2))))
A187274: 0 4 20 48 160 320 960 1792 5120 9216 25600 45056 122880 212992 573440 983040
((x mod 8) mod (if (x mod (2 + (x mod 2))) <= 0 then 1 else x))
A154725: 0 0 0 0 0 0 0 0 0 0 0 3 0 5 0 0
compr(\x.(1 - ((x div (if (x mod 2) <= 0 then 4 else 1)) mod 3)),x)
A194414: 1 4 5 6 7 8 10 11 13 16 17 18 19 20 22 23
((x + 2) div (if ((x div 2) mod 5) <= 0 then 3 else x))
A078090: 0 1 2 1 1 1 1 1 1 1 4 4 1 1 1 1
loop(\(x,i).((x + ~1) + (2 * (x mod 2)) - (x div 2)),3,x)
A194516: 2 ~1 1 3 0 2 ~1 1 3 0 2 4 1 3 0 2
(if (x mod 3) <= 0 then (9 * (x mod 2)) else x)
A070700: 0 1 2 9 4 5 0 7 8 9 10 11 0 13 14 9
loop(\(x,i).x2,3,(7x + 3))
A017024: 6561 100000000 6975757441 110075314176 852891037441 4347792138496 16815125390625 53459728531456 146830437604321 360040606269696 806460091894081 1677721600000000 3282116715437121 6095689385410816
loop(\(x,i).x3,1,(7x + 3))
A017019: 27 1000 4913 13824 29791 54872 91125 140608 205379 287496 389017 512000 658503 830584 1030301 1259712
loop(\(x,i).x3,2,(7x + 3))
A017025: 19683 1000000000 118587876497 2641807540224 26439622160671 165216101262848 756680642578125 2779905883635712 8662995818654939 23762680013799936 58871586708267913 134217728000000000
(x + ((1 + (if (~2 + (x div 3)) <= 0 then 0 else x)) mod 3))
A287929-A287928-A085516: 1 2 3 4 5 6 7 8 9 10 12 11 13 15 14 16
(x + ((1 + (if (~2 + (x div 4)) <= 0 then 0 else x)) mod 3))
A195099-A195098: 1 2 3 4 5 6 7 8 9 10 11 12 13 15 14 16
(x + (loop(\(x,i).((x2 + ~x) div 2),2,(x + ~1)) div 3))
A014626: 0 1 2 3 5 10 21 42 78 135 220 341 507 728 1015 1380
(x + (if (~2 + (x div 3)) <= 0 then 1 else ((x + ~1) div 3)))
A129562: 1 2 3 4 5 6 7 8 9 11 13 14 15 17 18 19
loop(\(x,i).x2,3,(7x + 6))
A017060: 1679616 815730721 25600000000 282429536481 1785793904896 7984925229121 28179280429056 83733937890625 218340105584896 513798374428641 1113034787454976 2252292232139041 4304672100000000
loop(\(x,i).x3,1,(7x + 6))
A017055: 216 2197 8000 19683 39304 68921 110592 166375 238328 328509 438976 571787 729000 912673 1124864 1367631
loop(\(x,i).x3,2,(7x + 6))
A017061: 10077696 10604499373 512000000000 7625597484987 60716992766464 327381934393961 1352605460594688 4605366583984375 13537086546263552 35452087835576229 84590643846578176 186940255267540403
loop(\(x,i).(2 * (2x - (x mod 8))),3,x)
A127988: 0 8 32 40 128 136 160 168 512 520 544 552 640 648 672 680
(x + (if (~2 + (x div 3)) <= 0 then 1 else 12))
A069571: 1 2 3 4 5 6 7 8 9 21 22 23 24 25 26 27
(if (x mod 2) <= 0 then (3 * (3x + (x div 2))) else x)
A317321: 0 1 21 3 42 5 63 7 84 9 105 11 126 13 147 15
compr(\x.((loop(\(x,i).(x div (2 - (x mod 2))),x,x) div 2) mod 3),x)
A260488: 0 1 2 4 7 8 13 14 16 19 25 26 28 31 32 37
(x + (if (~1 + (x div 2)) <= 0 then 1 else (3x2 + 6)))
A098811: 1 2 3 4 58
(x + (if (x mod 3) <= 0 then 2 else (x - ((~x + 2) mod 3))))
A080030: 2 1 4 5 7 10 8 13 16 11 19 22 14 25 28 17
(x + (loop(\(x,i).(x + ((2 + i) * i)),(x + 2),x) div 3))
A010896: 3 10 19 32 49 72 100
(x + (if (~2 + (x div 2)) <= 0 then 1 else ((x + (x mod 2)) div 3)))
A225857: 1 2 3 4 5 6 8 9 10 12 13 15 16 17 18 20
(x + (if (~6 + (x div 2)) <= 0 then 2 else (x div 3)))
A074739: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 18 20
(x + ((x * loop(\(x,i).(2x + ~2),(x + ~1),x)) div 3))
A088110: 0 1 3 9
A118365: 0 1 3 9 28 88
((3x2 + x) + (if (x div 2) <= 0 then 4 else 2))
A131649: 4 8 16 32 54 82 116 156 202 254 312 376 446 522 604 692
compr(\x.((x + loop(\(x,i).(x div (2 - (x mod 2))),x,x)) mod 3),x)
A084090: 0 2 3 6 8 9 10 12 14 15 18 21 22 24 26 27
(x * loop(\(x,i).((x2 + ~x) div (1 + i)),2,(x + 3)))
A266732: 0 10 60 210 560 1260 2520 4620 7920 12870 20020 30030 43680 61880 85680 116280
compr(\x.loop(\(x,i).((~x - i) div (x + 4)),2x,1),x)
A048683: 1 2 3 4 5 7 8 9 11 12 13 16 17 18 19 23
(~x + loop(\(x,i).((2 * (x + (2 * i))) + i),x,(2x + 1)))
A027982: 1 10 38 108 270 632 1426 3148 6854 14784 31674 67508 143278 303016 638882 1343388
(x + (if ((x + ~2) mod 9) <= 0 then (x div 2) else 1))
A115060: 1 2 3 4 5 6 7 8 9 10 11 16 13 14 15 16
(((4x + 1) + (x mod 2)) * (if (x mod 2) <= 0 then 1 else x))
A330983: 1 6 9 42 17 110 25 210 33 342 41 506 49 702 57 930
((~x + 1) * loop(\(x,i).(x * (~1 + (2 * (i div 2)))),2x,1))
A013302: 1 0 3 90 4725 396900 49116375 8428369950 1917454163625 558800927685000 203054287097536875 4611686018427387903 4611686018427387903 4611686018427387903
(3 - loop(\(x,i).(2x3 + 2x),x,(~x + 1)))
A057738: 2 3 139
(~x + loop(\(x,i).((x + 1) + i - ((x div 2) div 3)),x,1))
A231408: 1 2 4 6 9
A105434: 1 2 4 6 9 12 16 20 24 28 32 36 41 46 51 56
(x + (loop(\(x,i).3x,x,1) div (3x + 1)))
A134365: 1 1 3 5 10 20 44
(x + (if (~x + 2) <= 0 then (x * (x3 div 3)) else 1))
A099081: 1 2 6 30 88
(x + loop(\(x,i).(1 + ((x3 + ~x2 + x) * i)),x,1))
A290610: 1 3 15 6127
(~x + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1))
A246604: 1 0 0 2 10 37 126 422 1422 4853 16786 58775 208000 742887 2674426 9694830
((~x + 1) - loop(\(x,i).((x + ~2) + (x div (4 + i))),x,1))
A036604: 0 1 3 5 7 10 13 16 19 22 26 30 34 38 42
A327672-A001768: 0 1 3 5 7 10 13 16 19 22 26 30 34 38 42 46
(~x + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,1))
A273526: 1 1 3 11 38 127 423 1423 4854 16787 58776 208001 742888 2674427 9694831 35357655
compr(\x.(loop(\(x,i).4x2,2,3) mod (x + 1)),x)
A069353: 0 1 2 3 5 7 8 11 15 17 23 26 31 35 47 53
(x + (if (x + ~2) <= 0 then 1 else (x4 + x3 + ~x + ~1)))
A097653: 1 2 3 107
(x + ((x + 1) * loop(\(x,i).(x3 + ~x + 1),2,2)))
A157999: 337 675 1013 1351 1689 2027 2365 2703 3041 3379 3717 4055 4393 4731 5069 5407
loop(\(x,i).x2,3,(9x + 8))
A017264: 16777216 6975757441 208827064576 2251875390625 14048223625216 62259690411361 218340105584896 645753531245761 1677721600000000 3936588805702081 8507630225817856 17181861798319201 32784148919812096
loop(\(x,i).x3,1,(9x + 8))
A017259: 512 4913 17576 42875 85184 148877 238328 357911 512000 704969 941192 1225043 1560896 1953125 2406104 2924207
loop(\(x,i).x3,2,(9x + 8))
A017265: 134217728 118587876497 5429503678976 78815638671875 618121839509504 3299763591802133 13537086546263552 45848500718449031 134217728000000000 350356403707485209 833747762130149888 1838459212420154507
(~x + ((x + 1) * loop(\(x,i).(2 + (x * (x + i))),2,4)))
A158368: 530 1059 1588 2117 2646 3175 3704 4233 4762 5291 5820 6349 6878 7407 7936 8465
(~x + ((x + 1) * loop(\(x,i).(~x3 + (x div 2)),2,2)))
A158000: 339 677 1015 1353 1691 2029 2367 2705 3043 3381 3719 4057 4395 4733 5071 5409
loop(\(x,i).(x * i),x,(x3 + 3x2 + 5x + 2))
A001565: 2 11 64 426 3216 27240 256320 2656080 30078720 369774720 4906137600 69894316800 1064341555200 17255074636800 296754903244800 5396772116736000
loop(\(x,i).(~7x + ~1),2,(x2 + x))
A001526: 6 104 300 594 986 1476 2064 2750 3534 4416 5396 6474 7650 8924 10296 11766
((x2 + x) + (2 * (~1 + (if x <= 0 then 2 else (x + (x mod 2))))))
A229718: 2 4 8 18 26 40 52 70 86 108 128 154 178 208
loop(\(x,i).(x - (2 * (4x + i))),2,(x2 + x))
A177060: 10 108 304 598 990 1480 2068 2754 3538 4420 5400 6478 7654 8928 10300 11770
loop(\(x,i).(11x + 10),(x + 1),x)
A064757: 10 241 3992 58563 805254 10629365 136410196 1714871047 21221529218 259374246009 3138428376720 37661140520651 448795257871102 5316497670165373 62658722541234764 735195677817154575
(x + loop(\(x,i).(x - ((~1 + (x div 4)) div 2)),2,(x + ~1)))
A191257: 1 3 5 7 8 9 11 13 15 17 19 21 23 24 25 27
loop(\(x,i).(x + (7 * (i * i))),(x + ~1),x)
A071229: 0 1 9 38 102 215 391 644 988 1437 2005 2706 3554 4563 5747 7120
(((~x2 + ~x) div 5) mod (if x <= 0 then 1 else x))
A249345: 0 0 0 0 0 4 3 2 1 0 8 6 4 2 0 12
(2x - ((x mod 10) mod (if x <= 0 then 1 else x)))
A092451-A007928: 0 2 4 6 8 10 12 14 16 18 20 21 22 23 24 25
(x + loop(\(x,i).(x + (6 div (1 + (x div 2)))),x,1))
A080752: 1 8 10 12 14 16 18 19 20 21 22 23 24 25 26 27
(~x + loop(\(x,i).(x + ((3x + 1) * (1 + i))),x,1))
A234280: 1 8 91 1210
(~x + loop(\(x,i).(x4 + x3 + 3x2),x,1))
A072725: 1 4 823
(x + loop(\(x,i).(x + ((x div (1 + (4 * i))) + i)),x,1))
A025715: 1 3 6 10 15 21 28 36 45 56 68 81 95 110 126 143
(x + ((3 * (x div 4)) + loop(\(x,i).(x * i),x,1)))
A092329: 1 2 4 9 31 128
(x + loop(\(x,i).((x * ((1 + (2 * i)) * (x div 2))) + i),x,1))
A326972: 1 2 4 20 1232
(2 div (if ((x div 2) mod (1 + (2x mod 3))) <= 0 then 2 else x))
A030317: 1 1 1 1 0 1 1 1 1 1 0 0 1 1 0 1
(x * ((1 + (loop(\(x,i).(2x * i),(x + ~1),1) div 2)) div 2))
A052587: 0 0 2 6 48 480 5760 80640 1290240 23224320 464486400 10218700800 245248819200 6376469299200 178541140377600 5356234211328000
(2 div (if ((x div 2) mod (1 + (2 * (1 + (x mod 2))))) <= 0 then 2 else x))
A127693: 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0
loop(\(x,i).((x div 2) div (1 + (x mod (2 * (1 + (x mod 2)))))),2,x)
A110962: 0 0 0 0 1 0 0 0 2 1 1 0 3 0 0 0
(x + (x div (2 + (x div loop(\(x,i).i,(x + ~8),1)))))
A103303: 0 1 2 3 4 5 6 7 8 9
A050741: 0 1 2 3 4 5 6 7 8 9 11 13 14 16 17 18
loop(\(x,i).(x - (5 * ((~x2 + x) div 2))),2,x)
A264891: 0 1 112 783 2839 7480 16281 31192 54538 89019 137710 204061 291897 405418 549199 728190
loop(\(x,i).10x,10,x)
A130427: 0 10000000000 20000000000 30000000000 40000000000
A130431: 0 10000000000 20000000000 30000000000 40000000000 50000000000 60000000000 70000000000 80000000000
(x + loop(\(x,i).(x * ((x + ~1) + i)),2,10))
A213184-A213182: 10100 10101 10102 10103 10104 10105 10106 10107 10108 10109 10110 10111 10112 10113 10114 10115
loop(\(x,i).(x + 8),(x + ~10),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A319726-A264979: 0 1 2 3 4 5 6 7 8 9 10 19 28 37 46 55
compr(\x.((if (x mod 2) <= 0 then 1 else x) - (x mod 10)),x)
A324022: 1 2 3 4 5 6 7 8 9 12 14 16 18 22 24 26
loop(\(x,i).(((x3 + 3x2 + 2x) div 2) div 3),2,x)
A140236: 0 1 20 220 1540 7770 30856 102340 295240 762355 1798940 3939936 8104460 15803060 29426320 52636760
(x + (if (x + ~10) <= 0 then 1 else 6))
A032994: 1 2 3 4 5 6 7 8 9 10 11 17 18 19 20 21
(x + (~x mod (if (x + ~4) <= 0 then 1 else 6)))
A265564: 0 1 2 3 4 6 6 12 12 12 12 12 12 18 18 18
(x + ((3 * (x + loop(\(x,i).x2,(x + ~2),2))) div 2))
A296378: 3 5 8 13 34
(x - loop(\(x,i).(x + (x mod 3) - (2 * (x mod 2))),2,x))
A131193: 0 1 ~3 3 ~1 0 0 1 ~3 3 ~1 0 0 1 ~3 3
(x + ((if (~x + 2) <= 0 then (x + ~1) else 2) + ((x mod 3) div 2)))
A144430: 2 3 4 5 7 10 11 13 16 17 19 22 23 25 28 29
(x - loop(\(x,i).((~2x + 8) div (x + 3)),2,x))
A227179: 0 0 0 1 2 0 1 2 3 4 5 6 0 1 2 3
loop(\(x,i).(1 + (x * (1 + (9 * i)))),2,x)
A139620: 20 210 400 590 780 970 1160 1350 1540 1730 1920 2110 2300 2490 2680 2870
(~x + (if x <= 0 then 1 else (2x5 + 2x3)))
A065993: 1 3 78
(x + (if (x + ~2) <= 0 then 1 else (4 * (1 + (2 * (x div 2))))))
A162890: 1 2 3 15 24 25
loop(\(x,i).x2,3,(9x + 4))
A017216: 65536 815730721 54875873536 852891037441 6553600000000 33232930569601 128063081718016 406067677556641 1113034787454976 2724905250390625 6095689385410816 12667700813876161 24759631762948096
loop(\(x,i).(x2 + x),1,(9x + 4))
A177073: 20 182 506 992 1640 2450 3422 4556 5852 7310 8930 10712 12656 14762 17030 19460
loop(\(x,i).x3,1,(9x + 4))
A017211: 64 2197 10648 29791 64000 117649 195112 300763 438976 614125 830584 1092727 1404928 1771561 2197000 2685619
loop(\(x,i).x3,2,(9x + 4))
A017217: 262144 10604499373 1207269217792 26439622160671 262144000000000 1628413597910449 7427658739644928 27206534396294947 84590643846578176 231616946283203125 572994802228616704 1304773183829244583
loop(\(x,i).x3,1,(7x + 4))
A017031: 64 1331 5832 15625 32768 59319 97336 148877 216000 300763 405224 531441 681472 857375 1061208 1295029
loop(\(x,i).x3,2,(7x + 4))
A017037: 262144 2357947691 198359290368 3814697265625 35184372088832 208728361158759 922190162669056 3299763591802133 10077696000000000 27206534396294947 66540410775079424 150094635296999121
compr(\x.((x2 + ~2) mod loop(\(x,i).(2x2 + ~1),2,2)),x)
A176010: 14 83 111 180 208 277 305 374 402 471 499 568 596 665 693 762
compr(\x.((loop(\(x,i).(x - (x div ~3)),x,1) div 2) mod 2),x)
A087792: 0 3 5 8 10 11 12 21 24 27 33 35 36 37 39 43
compr(\x.((x2 + x) mod loop(\(x,i).(x2 + 2x + 1),2,2)),x)
A265424: 0 24 75 99 100 124 175 199 200 224 275 299 300 324 375 399
compr(\x.((x2 + ~x) mod loop(\(x,i).(x2 + 2x + 1),2,2)),x)
A008852: 0 1 25 76 100 101 125 176 200 201 225 276 300 301 325 376
(x + ((if (~4 + (x div 2)) <= 0 then 2 else ((x + 1) div 2)) div 2))
A243463: 1 2 3 4 5 6 7 8 9 10 12 14 15 16 17 19
(x + (4 * (if (x + ~12) <= 0 then 0 else 2)))
A103303: 0 1 2 3 4 5 6 7 8 9
A178403-A134336-A131207-A130577: 0 1 2 3 4 5 6 7 8 9 10 11 12 21 22 23
loop(\(x,i).(8x + 72),2,x)
A157432: 648 712 776 840 904 968 1032 1096 1160 1224 1288 1352 1416 1480 1544 1608
loop(\(x,i).((~2x + 1) div (4 + (x div 4))),2,x)
A108037: 0 1 1 1 1 1 2 2 2 2 3 3 3 3 3 5
compr(\x.((x2 + 1) mod loop(\(x,i).(1 + (x * i)),4,2)),x)
A241520: 34 55 123 144 212 233 301 322 390 411 479 500 568 589 657 678
compr(\x.((x2 + ~2) mod loop(\(x,i).(1 + (x * i)),4,2)),x)
A159008: 25 64 114 153 203 242 292 331 381 420 470 509 559 598 648 687
(x + loop(\(x,i).x2,1,(x div (~2 + ((~x + 2) div 4)))))
A061887: 0 2 3 4 8 9 10 11 12 18 19 20 21 22 23 24
compr(\x.(1 - (x mod (2 + (if (x mod 2) <= 0 then 2 else (x div 4))))),x)
A074235: 1 2 3 5 6 7 9 10 11 13 14 17 18 19 22 23
loop(\(x,i).((~3x + 5) div (x + 4)),2,x)
A081290: 0 1 2 2 2 5 5 5 5 5 5 5 5 5 14 14
compr(\x.((x2 + ~1) mod loop(\(x,i).(x2 + x),2,4)),x)
A057539: 1 29 41 71 139 169 181 209 211 239 251 281 349 379 391 419
(x + ((if (x + ~10) <= 0 then 1 else x) div 4))
A103303: 0 1 2 3 4 5 6 7 8 9
A247810-A247800: 0 1 2 3 4 5 6 7 8 9 10 13 15 16 17 18
(x + ((x + (if (~2 + (x div 2)) <= 0 then 1 else 4)) div 4))
A138083: 0 1 2 4 5 6
A328594: 0 1 2 4 5 6 8 9 11 12 13 14 16 17 18 19
((x3 + x) + ((if x <= 0 then 1 else 2) + (x mod 4)))
A076858: 1 5 14 35 70
loop(\(x,i).((x * ((~x + 1) + (2x * (i * i)))) div 2),2,x)
A152041: 0 4 33 129 355 795 1554 2758 4554 7110 10615 15279 21333 29029 38640 50460
(x + (if (x + ~1) <= 0 then 1 else (x3 + 4x2 + 2x + 8)))
A173026: 1 2 38 80
(loop(\(x,i).4x,x,4) div (3x + 4))
A191639: 1 2 6 19 64 215 744 2621 9362 33825 123361 453438 1677721 6242685 23342213 87652393
(5x + (if (x + ~2) <= 0 then 3 else 2x))
A317194: 3 8 13 21 28
loop(\(x,i).(2 + ((x div 2) + (x div 4))),(~2 + (x div 2)),x)
A265537: 0 1 2 3 4 5 6 6 8 8 8 8 8 8 8 8
(x + (if x <= 0 then 1 else (x - (1 mod (2 + ((~x2 + x) div 2))))))
A060577: 1 1 4 6 11 17 24 32 41 51 62 74 87 101 116 132
(x + ((x + (if (x mod 7) <= 0 then 2 else 1)) div 2))
A248562: 1 2 3 5 6 8 9 11 12 14 15 17 18 20 22 23
(x + ((x + (if (x mod (1 + (x mod 4))) <= 0 then 2 else 1)) div 2))
A298863: 1 2 3 5 7 8 10 11 13 14 15 17 19 20 21 23
(x + ((x + (if (x + ~12) <= 0 then 2 else 1)) div 2))
A292665-A286355-A138251-A110118: 1 2 4 5 7 8 10 11 13 14 16 17 19 20 21 23
(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x)))
A083726: 0 3 8 18 32 60 84 126 160 216 300 352 456 546 616 720
(x + ((x + (if ((2 + (x div 2)) mod 4) <= 0 then 1 else 2)) div 2))
A284818: 1 2 4 5 6 8 10 11 13 14 16 17 18 20 22 23
(x + (if (x + ~2) <= 0 then 1 else ((x + ~2) + ((x mod 3) div 2))))
A144429: 1 2 3 4 6 9 10 12 15 16 18 21 22 24 27 28
(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A117495: 0 3 10 21 44 65 102 133 184 261 310 407 492 559 658 795
(x + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) div 2))
A080370: 0 1 3 5 8 10 13 15 18 22 24 28 31 33 36 40
(x * (2 + compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x)))
A306192: 0 5 14 33 52 85 114 161 232 279 370 451 516 611 742 885
(~x + (2 * loop(\(x,i).(x - (x div 8)),(x div 2),x)))
A279313: 0 1 2 3 4 5 6 7 6 5 4 3 2 1 0 1
(x + ((x + loop(\(x,i).(x + ((i * i) div (x + 1))),x,2)) div 2))
A031435: 1 2 4 7 9 12 15 18 21 25 28 32 35 39 42 46
(x * (2 + (x * (loop(\(x,i).(2x + (x div 2)),x,x) div 2))))
A160872: 0 3 28 195 1240
compr(\x.(loop(\(x,i).(x * (2 + i)),((x + 1) div 2),1) mod (x + 2)),x)
A175553: 1 4 7 8 10 12 13 14 16 18 19 20 22 23 24 25
(x + ((2 * (x + (if (x + ~4) <= 0 then 1 else x))) div (x + 2)))
A080612: 1 2 3 4 5 7 9 10 11 12 13 14 15 16 17 18
((x2 + 2x) + loop(\(x,i).i,(x + ~9),1))
A025741: 1 4 9 16 25 36 49 64 81 100 121 145 171 199 229 261
((x2 + 2x) + (if (~x + 2) <= 0 then (4x + 4) else 1))
A205670: 1 4 20 31
((x2 + 2x) + (if (x + ~2) <= 0 then 1 else (~3x + 6)))
A181023: 1 4 9 12 18 26 36
loop(\(x,i).(9x + 9),2,(x2 + 2x))
A157888: 90 333 738 1305 2034 2925 3978 5193 6570 8109 9810 11673 13698 15885 18234 20745
loop(\(x,i).(7x + 7),2,(x2 + 2x))
A158481: 56 203 448 791 1232 1771 2408 3143 3976 4907 5936 7063 8288 9611 11032 12551
loop(\(x,i).(~7x + ~7),2,(x2 + 2x))
A158484: 42 189 434 777 1218 1757 2394 3129 3962 4893 5922 7049 8274 9597 11018 12537
(x + (loop(\(x,i).(2x * i),((x + 1) div 2),x) div (x + 2)))
A222010: 0 1 3 7
A100839: 0 1 3 7 9 39
loop(\(x,i).(x6 + ~x2),(x + ~2),x)
A036298: 0 1 2 720 4611686018427387903
(3x + loop(\(x,i).((~x + 1) - i),(x div 3),1))
A190765: 1 4 7 8 11 14 18 21 24 25 28 31 35 38 41 42
loop(\(x,i).(((~2x + 1) + (x div (1 + i))) div 2),2x,x)
A316355: 0 1 1 2 3 3 3 3 4 5 5 5 5 5 5 6
(if (x mod 2) <= 0 then (12x - (x div 2)) else x)
A317323: 0 1 23 3 46 5 69 7 92 9 115 11 138 13 161 15
((if x <= 0 then 1 else (x3 + ~x2 + 2)) + (x * (x mod 2)))
A117850: 1 3 6 23
A176424: 1 3 6 23 50
(x * (loop(\(x,i).(x * ((x + ~1) + i)),2,x3) div 2))
A168663: 0 1 4160 798255 33562624 610390625 6530486976 48444916975 274878955520 1270935305649 5000005000000 17261365815551 53496620605440 151437584670385 396857439333824 973097619609375
(2x - loop(\(x,i).(x - (x div (8 - i))),2,x))
A067570: 0 1 2 3 4 5 7
A039110: 0 1 2 3 4 5 7 9 10 11 12 13 14 16 18 19
(x + (x2 div (x + (if (~2 + (x div 4)) <= 0 then 2 else 1))))
A135251: 0 1 3 4 6 8 10
A215476: 0 1 3 4 6 8 10 12 14 16 18 20 23
loop(\(x,i).i,(x + (3 * (x mod ~5))),x)
A319652: 0 1 2 3 1 5 6 7 2 6 10 11 3 7 11 15
compr(\x.(1 - loop(\(x,i).(x * (x mod (1 + (2 * i)))),3,x)),x)
A222011: 1 2 4 8
A236206: 1 2 4 8 11 13 16 17 19 22 23 26 29 31 32 34
(x + loop(\(x,i).((x + 1) - (((x + 1) div 2) div 3)),2,x))
A325572: 2 4 6 8 9 10 12 14 16 18 20 21 22 24 26 28
(x + loop(\(x,i).((x + 1) - ((x div 4) div ~2)),2,x))
A183422: 2 4 6 9 12 14 16 18 20 22 25 27 30 32 34 36
(x + loop(\(x,i).((x + 1) - ((x - (x div 4)) mod 2)),2,x))
A247062: 1 2 5 6 8 11 12 16 17 18 21 22 24 27 28 32
(x + (if (~4 + (x div 2)) <= 0 then 10 else x))
A182363-A055982: 10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30
(x + loop(\(x,i).(x - ((~1 + (((x + ~1) div 2) div 2)) div 2)),2,x))
A247423-A182339: 2 4 6 8 9 10 12 14 16 18 20 22 24 25 26 28
(x * loop(\(x,i).((1 + (x2 div 8)) div 2),2,x))
A308953: 0 0 0 0 0 0 0 7 8 18 20 44 60 104 126 180
(x + loop(\(x,i).(x - ((2x + ~4) div (x + 4))),2,x))
A064377: 2 3 4 6 8 10 12 14 15 16 18 20 22 24 26 28
(x2 * loop(\(x,i).2x3,2,4x))
A016811: 0 4194304 8589934592 743008370688 17592186044416 204800000000000 1521681143169024 8293509467471872 36028797018963968 131621703842267136 419430400000000000 1196683881290399744 3116402981210161152 4611686018427387903 4611686018427387903
(x * ((~x + ~2) + loop(\(x,i).(1 + ((x2 + x) div 2)),2,x)))
A106845: 0 1 14 72 244 650 1476 2989 5552 9639 15850 24926 37764 55432 79184 110475
loop(\(x,i).(x5 + ~x4 + x3 + ~x2),1,x2)
A064583: 0 0 816 53136 986880 9390000 58831920 276825696 1057222656 3444262560 9900990000 25724822640 61490347776 137047559376 287786357040 574098840000
((~x2 + ~1) + (2 * loop(\(x,i).((x + (i mod 2)) * i),x,1)))
A125763: 1 2 3 20 103
((x2 + ~1) + (2 * (if (x + ~2) <= 0 then 1 else (2x + ~4))))
A116711: 1 2 5 12 23 36 51 68 87 108 131 156 183 212 243 276
(x2 + (loop(\(x,i).(x2 + 1),2,(x + 1)) div 3))
A165394: 1 9 37 105 241 481 869 1457 2305 3481 5061 7129 9777 13105 17221 22241
(x2 + loop(\(x,i).x2,1,(1 + ((x2 + ~x) div 2))))
A066455: 1 2 8 25 65 146 292 533 905 1450 2216 3257 4633 6410 8660 11461
((x2 + ~1) + loop(\(x,i).((x + 2) + i),(1 + (x div 2)),x))
A198392: 2 4 12 18 31 41 59 73 96 114 142 164 197 223 261 291
(~x2 + loop(\(x,i).11x,x,1))
A024129: 1 10 117 1322 14625 161026 1771525 19487122 214358817 2357947610 25937424501 285311670490 3138428376577 34522712143762 379749833583045 4177248169415426
(x2 + ((if x <= 0 then 2 else (5 mod (x + 1))) div 2))
A072174: 1 1 5 9 16 27 38 51
((5x + 4) * loop(\(x,i).x2,2,x2))
A229151: 0 9 3584 124659 1572864 11328125 57106944 224827239 738197504 2109289329 5400000000 12647173979 27518828544 56285419749 109208390144 202468359375
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,x2)
A110609: 0 1 8 45 224 1050 4752 21021 91520 393822 1679600 7113106 29953728 125550100 524190240 2181340125
(~x4 + loop(\(x,i).3x,2x,1))
A024105: 1 8 65 648 6305 58424 530145 4780568 43042625 387413928 3486774401 31381044968 282429515745 2541865799768 22876792416545 205891132044024
(~x4 + loop(\(x,i).6x,x,1))
A024066: 1 5 20 135 1040 7151 45360 277535 1675520 10071135 60456176 362782415 2176761600 13060665455 78364125680 470184933951
(~x4 + loop(\(x,i).8x,x,1))
A024092: 1 7 48 431 3840 32143 260848 2094751 16773120 134211167 1073731824 8589919951 68719456000 549755785327 4398046472688 35184372038207
(~x4 + loop(\(x,i).5x,x,1))
A024053: 1 4 9 44 369 2500 14329 75724 386529 1946564 9755625 48813484 244119889 1220674564 6103477209 30517527500
(x4 + loop(\(x,i).(x2 + 4x + 4),2,2))
A272298: 324 325 340 405 580 949 1620 2725 4420 6885 10324 14965 21060 28885 38740 50949
(x4 * loop(\(x,i).5x,x,x))
A198402: 0 5 800 30375 640000 9765625 121500000 1313046875 12800000000 115330078125 976562500000 7863818359375 60750000000000 453238525390625 3282617187500000 23174285888671875
(~x6 + loop(\(x,i).2x,x,1))
A024016: 1 1 ~60 ~721 ~4080 ~15593 ~46592 ~117521 ~261888 ~530929 ~998976 ~1769513 ~2981888 ~4818617 ~7513152 ~11357857
(~x6 + loop(\(x,i).(x * i),x,1))
A196413: 1 0 ~62 ~723 ~4072 ~15505 ~45936 ~112609 ~221824 ~168561 2628800 38145239 476015616 6222193991 87170761664 1307662977375
(x2 * loop(\(x,i).x2,2,x5))
A010810: 0 1 4194304 31381059609 17592186044416 2384185791015625 131621703842267136 3909821048582988049 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~x5 + loop(\(x,i).4x,x,1))
A024041: 1 3 ~16 ~179 ~768 ~2101 ~3680 ~423 32768 203095 948576 4033253 16528384 66737571 267897632 1072982449
(~x5 + loop(\(x,i).3x,x,1))
A024028: 1 2 ~23 ~216 ~943 ~2882 ~7047 ~14620 ~26207 ~39366 ~40951 16096 282609 1223030 4245145 13589532
loop(\(x,i).(x + ((2x div (1 + i)) div (1 + (2 * i)))),x,x)
A138083: 0 1 2 4 5 6
A069470: 0 1 2 4 5 6 9 10 11 13 15 16 19 20 21 24
compr(\x.(1 - loop(\(x,i).(x div (4 - (x mod 4))),x,x)),x)
A187811: 3 6 7 9 11 12 14 15 18 19 21 22 23 24 27 28
compr(\x.loop(\(x,i).(x div (2 - ((x * (x div 4)) mod 2))),x,x),x)
A048716: 0 1 2 3 4 6 8 9 12 16 17 18 19 24 25 32
compr(\x.(1 - loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,x)),x)
A004780: 3 6 7 11 12 13 14 15 19 22 23 24 25 26 27 28
loop(\(x,i).(x + (((3x + 3) * i) div (2 + i))),x,x)
A322938: 0 3 14 55 209 791 3002 11439 43757 167959 646645 2496143 9657699 37442159 145422674 565722719
(~x3 + loop(\(x,i).12x,x,1))
A024143: 1 11 136 1701 20672 248707 2985768 35831465 429981184 5159779623 61917363224 743008369357 8916100446528 106993205376875 1283918464546120 15407021574582993
(~x3 + loop(\(x,i).10x,x,1))
A024117: 1 9 92 973 9936 99875 999784 9999657 99999488 999999271 9999999000 99999998669 999999998272 9999999997803 99999999997256 999999999996625
(~x3 + loop(\(x,i).7x,x,1))
A024078: 1 6 41 316 2337 16682 117433 823200 5764289 40352878 282474249 1977325412 13841285473 96889008210 678223070105 4747561506568
(~x + loop(\(x,i).(x + (((~1 + (x div 2)) div 3) mod 2)),x,x))
A213014: 0 1 0 0 0 0 0 0 6 5 4 3 2 1 0 0
(1 + (x mod (3 - (2 div (1 + (x mod 5))))))
A127246: 1 2 3 1 2 1 1 2 3 1 1 2 1 2 3 1
(1 + (x div (1 + (x mod (1 + (((x + 1) div 2) div 3))))))
A346088-A223491: 1 2 3 4 5 3 7 4 9 5 11 4 13 7 5 16
(1 + (x mod (1 + (x mod ((x + 1) - ((x div 2) div 3))))))
A255827: 1 2 3 4 5 6 1 1 1 1 1 1 1 2 1 2
(1 + ((x div 2) mod (1 + (4 mod (1 + (x div 3))))))
A140193: 1 1 1 1 1 1 2 2 1 1 1 1 2 2 3 3
(1 + (4x div (1 + (2 mod (1 + (x mod 3))))))
A093544: 1 5 3 13 17 7 25 29 11 37 41 15 49 53 19 61
(1 + (x mod (1 + (x mod (1 + (~x mod (1 + (x div 2))))))))
A322813-A102096-A087039: 1 1 1 2 1 2 1 2 3 2 1 2 1 2 3 2
(1 + (x div (1 + ((2x + 4) div 7))))
A335925: 1 2 2 2 3 2 3 3 3 3 3 3 3 3 3 4
((x + 1) - (x div (~1 + (2x div ~5))))
A324540: 1 3 4 5 7 8 9 10 11 12 13 14 15 16 17 19
(1 + (x mod (1 + (x div (3 + ((x + 1) mod 4))))))
A338669-A257977-A070966-A034880: 1 1 1 2 1 2 1 2 3 2 1 4 1 2 3 4
(x div (1 + (x div (1 + ((x + ~1) mod 9)))))
A335979: 0 0 1 1 2 2 3 3 4 4 0 1 2 3 4 5
(1 + (2 mod (1 + (x2 mod (3 + (x div 4))))))
A046556: 1 1 1 1 1 1 1 1 3 1 1 1 1 1 3 3
(1 + (x mod (1 + ((x + 2) mod (~1 + (2 * (x div 4)))))))
A208879: 1 1 1 1 1 1 1 1 1 1 1 2 3 1 1 1
(1 + ((x + ~2) mod (1 + (x mod (~1 + (2 * (x mod 4)))))))
A137844: 1 1 1 2 1 1 1 3 1 1 1 2 1 1 1 1
(1 + ((x + 1) mod (1 + (x mod (5 + (x div 2))))))
A215561: 1 1 1 1 1 1 1 1 1 1 1 1 2 3 1 1
(1 + (2x mod (1 + (x div (1 + (2 * (2 + (x mod 2))))))))
A249773: 1 1 1 1 1 1 1 1 1 1 3 1 1 1 2 1
(1 + ((x2 + x) mod (1 + ((x + ~1) mod 5))))
A176187: 1 1 1 1 1 1 1 1 1 3 1 1 1 3 3 1
(x mod (1 + ((1 + (x div 2)) mod (1 + (x div 5)))))
A345228: 0 0 0 0 0 1 0 0 0 1 0 0 0 1 2 0
(1 + ((x div ~4) mod (1 + (x div 5))))
A193516: 1 1 1 1 1 1 1 1 1 2 1 1 1 3 3 1
(1 + ((x div (2 + (x mod 2))) mod (1 + (x div 5))))
A279522: 1 1 1 1 1 2 2 1 1 2 3 1 1 2 2 2
(3 mod (1 + ((x div 2) mod (1 + (x div 5)))))
A101856: 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 3
((x div 3) mod (1 + (2 div (1 + (x mod 5)))))
A086010: 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 2
(~1 + (2x mod (~1 + ((~x2 + x) mod 5))))
A144382: ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 0 ~1 ~1 ~1 ~1 1 ~1 ~1
(1 + ((~x + 1) mod (1 + (~x mod (1 + (x div 4))))))
A325355: 1 1 1 1 1 1 1 1 2 1 1 1 1 1 3 1
((x div 2) mod (1 + (x mod (1 + (x mod (1 + (x div 4)))))))
A216599: 0 0 0 0 0 0 0 1 1 0 0 2 0 0 1 3
(1 + ((x div 4) div (1 + (x mod (1 + (x mod 4))))))
A112971-A112970: 1 1 1 1 2 1 2 1 3 2 2 1 4 2 2 1
(1 + ((x + ~1) mod (1 + ((x div 2) mod (3 + (x mod 2))))))
A135062: 1 1 2 1 1 2 1 3 2 1 1 1
(1 + ((x div 2) mod (1 + ((x div 5) mod 3))))
A003638: 1 1 1 1 1 1 2 2 1 1 3 3 1 1 2 1
(1 + (x mod (~1 + (3 * (((x + ~1) div 2) mod 3)))))
A255274-A049847: 1 1 1 2 1 1 2 1 1 2 1 2 3 1 1 2
(1 + ((x + ~3) mod (1 + ((1 + (x div 2)) div 3))))
A023134: 1 1 1 1 2 1 2 1 2 1 2 3 1 2 3 1
(1 + (x div (~1 + (3 * ((1 + (x mod 2)) mod (x + 1))))))
A289440: 1 0 2 1 3 2 4 2 5 2 6 3 7 3 8 4
(4 mod (1 + ((x + 1) mod (1 + ((x + 1) div 3)))))
A035638: 0 0 0 0 0 0 0 1 0 1 0 1 0 4 0 4
((x div 2) mod (1 + (x2 mod (1 + ((x + 1) div 3)))))
A056966: 0 0 0 1 0 0 0 1 0 0 0 1 1 1 2 3
((x + 1) - (2 div (5 - ((x + ~1) div 3))))
A337769: 1 2 3 4 5 6 7 8 9 10 10 11 12 12 13 14
(1 + (((x div 2) div 3) div (1 + ((x + ~1) mod 3))))
A145574: 1 1 1 1 1 1 1 2 1 1 2 1 1 3 2 1
(1 + (x div (1 + ((2 * (2x div 3)) div 3))))
A105528: 1 2 3 2 3 2 3 3 3 2 3 3 3 3 3 3
((x div 2) mod (1 + (x mod (1 + (((x + 1) div 2) div 3)))))
A109527: 0 0 0 0 0 0 0 1 0 0 0 2 0 0 1 0
(1 + ((~1 + (x div 2)) mod (1 + (((x + 1) div 2) mod 3))))
A020906: 1 2 1 1 2 1 1 1 2 1 2 1 1 2 1 1
(1 + (x2 div 49))
A253144: 1 1 1 1 1 1 1 2 2 2 3 3 3 4 5 5
(1 + (x mod (1 + ((x mod ~7) mod 3))))
A088737: 1 1 1 1 1 2 1 1 1 2 2 1 1 2 1 1
(1 mod (~1 + ((x2 + ~1) mod 13)))
A187948: 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 1
((x + 3) - ((~x + 1) div 13))
A165240: 3 4 6 7 8 9 10 11 12 13 14 15 16 17 18 20
(1 + ((x div 3) mod (1 + ((x mod 4) mod 3))))
A139434: 1 1 1 1 1 2 3 1 1 2 1 1 1 1 2 1
(1 + (((x2 + ~1) div 2) mod (1 + ((x div 2) div 3))))
A338649: 1 1 1 1 1 1 2 1 2 1 2 1 3 1 2 2
(1 + ((x * ((x + 1) div 2)) mod (1 + ((x div 2) div 3))))
A340812-A340811: 1 1 1 1 1 1 1 1 1 2 1 1 1 2 3 1
(1 + ((x div 2) mod (1 + ((x * (x div 3)) mod 3))))
A031245: 1 1 1 1 1 3 1 1 1 1 1 1 1 1 2 1
(1 + (x div 4) - (x div (~1 + ((~x + 1) div 3))))
A138161: 1 2 2 3 4 4 4 5 5
A076642: 1 2 2 3 4 4 4 5 5 6 6 6 7 7 7 7
((x + 2) - (x div (~1 + (x div (~1 + ((~x + 1) div 3))))))
A030124: 2 4 5 6 8 9 10 11 13 14 15 16 17 19 20 21
(1 + ((x2 + x) div (1 + ((x2 + x) mod 3))))
A130770: 1 1 7 13 7 31 43 19 73 91 37 133 157 61 211 241
(1 + (x div 3) - (x div (~1 + ((~x + 2) div 3))))
A047741: 1 2 3 4 4 5 5 6 6 7 7 7 8 8 8 9
(1 + (x mod (1 + ((x * ((x * (x div 2)) mod 2)) div 3))))
A165983: 1 1 1 2 1 1 1 2 1 1 1 4 1 1 1 4
(1 + (3x mod (1 + (x div 2) - (x div 3))))
A057557: 1 1 1 1 1 2 1 2 1 2 1 1 1 1 3 1
(1 + ((~3 + (x * (x div 2))) mod (1 + (x div 3))))
A179541: 1 1 1 1 2 2 1 1 3 2 4
((2x + 1) - ((x mod 3) mod (1 + (x div 3))))
A090542: 1 3 5 7 8 11 13 14 15
(x mod (1 + ((4 + (x div 2)) mod (1 + (x div 3)))))
A057918: 0 0 0 1 0 0 0 1 2 0 0 1 0 0 0 3
(~2x mod (1 + (2x mod (1 + (x div 3)))))
A212868: 0 0 0 0 0 0 0 1 0 0 0 2 1 0 0 0
((3x + ~3) mod (1 + (x mod (1 + (x div 3)))))
A158118: 0 0 0 0 0 0 0 0 0 0 0 2 0 0 4 2
(1 + (2x mod (1 + ((2x + ~2) mod (1 + (x div 2))))))
A296072: 1 1 1 1 1 2 1 1 2 1 1 2 1 3 2 1
(1 + ((~x + 1) mod (1 + ((~2x + 4) mod (1 + (x div 2))))))
A306209-A238888-A225631-A205573-A179748-A144406-A130461-A119338-A096670-A054124: 1 1 1 1 1 1 1 1 2 1 1 1 2 3 1 1
(1 + (x mod (1 + ((x3 + ~x) mod (1 + (x div 2))))))
A070010: 1 1 1 1 1 1 1 1 4 1 1 1 1 1 3 1
((x + 1) - ((~x2 + 2x) div (4x + 5)))
A184514-A138309: 1 2 3 5 6 7 8 10 11 12 13 15 16 17 18 19
(1 + ((2x + ~1) div (2 - ((x div 2) div ~3))))
A112778: 0 1 2 2 3 4 4 5 4 5 5 6 6 7 6 6
((2x + 1) - ((x + (x div 4)) div ~3))
A231407: 1 4 6
A086377: 1 4 6 8 11 13 16 18 21 23 25 28 30 33 35 37
((x + 1) - (((x + ~1) div 3) * (x div ~3)))
A050271: 1 2 3 4 7 8 9 14 15 16 23 24 25 34 35 36
((x + 1) - (((x + 2) div 3) * (x div ~3)))
A095028: 1 3 4 5 9
A228941: 1 3 4 5 9 10 11 17 18 19 27 28 29 39 40 41
((x + 17) - (x div ~3))
A130808: 17 19 20 21 23
(1 + (((x + 1) mod 4) div (2 - (x mod ~3))))
A309059: 1 1 2 1 1 1 2 1 1 2 1 1 1 1 2 1
(1 + (2 * (x + (x div 3))) - (x mod ~3))
A047438: 1 5 6 9 13 14 17 21 22 25 29 30 33 37 38 41
(1 + (x div (1 + (2 * (1 + (x mod 9))))))
A117462: 1 1 1 1 1 1 1 1 1 4 3 2 2 2 2 2
(1 + ((x div 2) div (1 + (2 * (1 + ((x + ~1) mod 3))))))
A261036: 1 1 1 1 1 1 1 2 1 1 2 2 1 3 2 2
(1 + ((x + ~1) mod (1 + (x mod (2 + (x div 5))))))
A320010: 1 1 1 1 1 2 1 1 2 1 1 3 1 1 2 1
(1 + ((2x + 2) mod (1 + ((x mod 5) div 2))))
A158464: 1 1 1 1 2 1 1 1 1 3 1 1 1 1 1 1
(~1 + ((1 + (x div 2)) div (1 + ((1 + (x div 4)) div 2))))
A066520: 0 0 1 1 0 0 1 1 1 1 2 2 1 1 1 1
(1 + (x mod (1 + ((x mod ((x + ~1) - (x mod 4))) div 2))))
A327402: 1 1 1 1 1 2 1 1 1 2 1 3 1 2 1 1
((x + 1) div (1 + (x div (3 + ((x div 2) div 3)))))
A079643: 1 2 3 2 2 3 3 4 3 3 3 4 4 4 5 4
(1 + ((x + 1) mod (1 + (x div (2 + (3 * (x mod 2)))))))
A090331: 1 1 2 1 3 1 4 1 5 1 6 1 7 3 8 1
((2x + 1) - ((2x + 1) div 7))
A320997: 1 3 5 6 8 10 12 13 15 17 18
A329829-A182760-A000210: 1 3 5 6 8 10 12 13 15 17 18 20 22 24 25 27
(14x2 + 28x + 15)
A158482: 15 57 127 225 351 505 687 897 1135 1401 1695 2017 2367 2745 3151 3585
(14x2 + 28x + 13)
A158485: 13 55 125 223 349 503 685 895 1133 1399 1693 2015 2365 2743 3149 3583
(1 mod (~1 + ((x3 + ~x2) mod 7)))
A011657: 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0
((2x + 1) - ((2x + 2) div 7))
A325913-A003152: 1 3 5 6 8 10 11 13 15 17 18 20 22 23 25 27
(1 + (14 * (4 + (x mod 2))))
A176636: 57 71 57 71 57 71 57 71 57 71 57 71 57 71 57 71
(56x2 + 1)
A158660: 1 57 225 505 897 1401 2017 2745 3585 4537 5601 6777 8065 9465 10977 12601
((2x + 1) - ((2x + 4) div 7))
A285681-A081031: 1 3 4 6 8 9 11 13 15 16 18 20 21 23 25 27
(1 + (7 * ((x2 + 3x) div 2)))
A166146: 1 15 36 64 99 141 190 246 309 379 456 540 631 729 834 946
(7x2 + 7x + ~43)
A298078: ~43 ~29 ~1 41 97 167 251 349 461 587 727 881 1049 1231 1427 1637
((2x + 1) - ((~2x + 1) div 7))
A231407: 1 4 6
A189383: 1 4 6 8 10 13 15 17 20 22 24 26 29 31 33 36
((3x + 1) - (2x div 7))
A103762: 1 4 7 10 12 15 18 20 23 26 29 31 34 37 39 42
((x + 1) - ((~2x2 + 2x) div 7))
A231408: 1 2 4 6 9
A025698: 1 2 4 6 9 12 16 20 25 31 37 44 51 59 67 76
((3x + 1) - ((~x + 1) div 7))
A327136: 1 4 8 11 14 17 20 23 26 30 33 36 39 42 45 48
(1 + ((x + (((x + ~1) div 2) div 2)) mod 7))
A116369: 7 2 3 4 5 7 1 2 3 5 6 7 1 3 4 5
((4x + 3) - (x div 7))
A329977: 3 7 11 15 19 23 27 30 34 38 42 46 50 54 57 61
(1 + ((0 - (x mod 3)) mod (1 + (x mod 6))))
A158068: 1 2 2 1 5 5 1 2 2 1 5 5 1 2 2 1
(1 + (x div (1 + ((x mod (~2 - (x div 3))) mod 2))))
A214682: 1 1 3 4 5 3 7 4 9 5 11 12 13 7 15 16
(1 + ((x + 1) mod (1 + ((~x + 2) mod (2 + (x div 3))))))
A175025: 1 1 1 2 2 1 1 1 1 3 3 1 2 1 1 1
(12x2 + 30x + 19)
A127854: 19 61 127 217 331 469 631 817 1027 1261 1519 1801 2107 2437 2791 3169
(2 div (1 + ((2x2 + 4) mod (2x + 3))))
A073346: 1 1 0 0 0 0 1 2 0 0 0 0 0 0 0 0
(1 + ((2x + 3) * ((x2 + 3x) div 2)))
A081438: 1 11 36 82 155 261 406 596 837 1135 1496 1926 2431 3017 3690 4456
((2x + 1) - ((x + (x div 2)) div ~5))
A231407: 1 4 6
A189462: 1 4 6 8 11 13 15 17 20 22 24 27 29 31 34 36
(1 + (2x div (5 + (x mod 5))))
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((x + 1) + (x div 5) - ((~x + 1) div 3))
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(1 + (((x3 + x2) div 2) div (1 + ((x div 2) mod 2))))
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((x + 1) - ((x2 div (3 + (x div 2))) div 3))
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((2x + 1) - (9 * (x div ~2)))
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(3x2 + 39x + 37)
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(1 + (2 * (x + (x div 3))) - ((x + 1) mod 3))
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(1 + ((7x2 + 7x) div 3))
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((x + 1) - ((~x3 + 3x2 + ~3x + 1) div 3))
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((x + 1) - (6 * (x div 7)))
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(~1 + (6 * (1 + (2 * ((x + 1) + (x div 2))))))
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(1 + (((2x mod 9) div 2) mod 3))
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(1 + ((2 * ((2x + 2) div 5)) div 3))
A030617: 1 1 1 1 2 2 2 3 3 3 3 3 4 4 5 5
(6x2 + 6x + 31)
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(x2 mod (1 + ((2 * (2x div 3)) mod 3)))
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(2 - ((~x2 + 2x) div 19))
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(x4 mod 19)
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(1 + ((((x div 3) * (x div 3)) div 2) div 3))
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(~1 + (6 * ((2x + 1) + (x div 3))))
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(1 + (((1 + ((x * (x div 4)) div 2)) div 2) div 3))
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(1 + (((x3 + 3x2 + ~x + ~3) div 2) div 3))
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((x + ~1) - (3 * ((~4x + ~2) + (x div 2))))
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(1 + (6 * ((x + 1) + (3 * (x div 2)))))
A267985: 7 13 37 43 67 73 97 103 127 133 157 163 187 193 217 223
(1 + ((((x + 1) * (1 + (x div 3))) div 2) div 3))
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(1 + ((2 * (((~x + 1) div 3) mod (x + 1))) div 3))
A287355: 1 1 2 3 3 3 4 5 5 5 6 6 7 7 7 8
(~1 + (x div 2) - (3 * ((~2x + ~2) + (x mod 2))))
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(1 + (3 * (((x + 1) + (x div 2)) * ((x + 1) div 2))))
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((4x + 3) - (((x + 1) div 2) div 3))
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(1 + ((x div 2) div (4 - (((x + 1) div 2) div 3))))
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(1 - ((~1 + (x div 2)) mod (1 + (((x + 1) div 2) mod 3))))
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(1 + (((x3 + 3x2 + ~4x) div 2) div 3))
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(1 + (((x + 2) div (2 - (x mod ~4))) div 3))
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(1 + (6 * ((1 + (x2 div 4)) div 2)))
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(1 + ((4 * ((2 + (x div 2)) div 3)) div 3))
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(1 + ((2 * ((x - (x div ~4)) div 2)) div 3))
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(1 + (6 * ((x div ~7) mod 2)))
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(1 + (x div (3 * (2 + ((x + 1) mod 8)))))
A326976-A321167-A190867: 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 3
(x3 mod 47)
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(1 + ((x2 + 2x) div 48))
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(1 + ((2 + (x div (2 + ((~x + 2) mod 4)))) div 3))
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(1 + (x div (6 * (4 - (x mod 4)))))
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(1 + ((2 * (x2 div (2x + 8))) div 3))
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(1 + (24 * (2x + (x div 2))))
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(~x mod (48x + ~1))
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(x - (1 div (2x + ~25)))
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(x4 mod 25)
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(x - (1 div (2x + ~23)))
A331746-A319705-A305795: 1 2 3 4 5 6 7 8 9 10 11 12 11 13 14 15
(x4 mod 23)
A070551: 0 1 16 12 3 4 8 9 2 6 18 13 13 18 6 2
((x + 1) - (2x div (x + ~24)))
A258777-A211347: 1 3 4 5 6 7 8 9 10 12 13 14 15 17 18 20
((x div 2) mod (1 + ((~x mod 8) mod 3)))
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A229977: 1 1 1 1 2 2 2 2 3 3 4 4 5 5 6 7
(1 + ((2 + ((x2 + ~1) div (2 + (x div 2)))) div 3))
A094838: 1 1 2 2 2 3 4 4 5 6 6 7 7 8 8 9
(x - ((x + ~1) div (1 + (3 * (2 + ((x div 2) mod 2))))))
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(1 + ((x - ((((~x + 1) * (x div 2)) div 2) div 2)) div 3))
A337766: 1 1 2 2 3 3 4 5 6 6 8 9 10 11 13 14
(1 + ((x mod (2 - (x div (~4 + (x mod 2))))) div 3))
A228572: 1 1 1 1 1 1 1 1 1 2 1 2 1 3 1 1
((2x + 1) - ((x + 1) mod ~10))
A169905-A102492-A007959: 10 11 12 13 14 15 16 17 18 19 30 31 32 33 34 35
(1 - (2x div (~11 + (x div 2))))
A121279: 1 2 2 2 2 3 3 3 4 4 5 5 6 7 8 9
(78x + 13)
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((x3 + ~3x2 + 2x) div 13)
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(x - ((x2 div 4) div 13))
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(x - ((2 + (x2 div 2)) div 13))
A261101: 0 1 2 3 4 4 5 5 6 6 6 7 7 7 7 7
((2x + 4) - ((x + 2) mod 13))
A039210: 2 3 4 5 6 7 8 9 10 11 12 26 27 28 29 30
(1 - ((~x2 + ~x + 2) div 13))
A089197: 1 1 2 2 3 4 5 6 7 8 10 11 13 15 17 20
(x5 mod 13)
A070598: 0 1 6 9 10 5 2 11 8 3 4 7 12 0 1 6
(11x2 + 44x + 33)
A067705: 33 88 165 264 385 528 693 880 1089 1320 1573 1848 2145 2464 2805 3168
(55x + 11)
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((x3 + ~3x2 + 2x) div 11)
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((2x + 2) - ((x + 2) mod 11))
A024650: 0 1 2 3 4 5 6 7 8 20 21 22 23 24 25 26
((2x + 4) - ((x + 2) mod 11))
A039112: 2 3 4 5 6 7 8 9 10 22 23 24 25 26 27 28
((2x + 2) - ((~x + 1) div 11))
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(1 - ((x * (1 - (x div 2))) div 11))
A241826: 1 1 1 1 2 2 3 3 4 4 5 5 7 7 9 10
(x - ((x div 11) + (x div 3)))
A308754: 0 1 2 2 3 4 4 5 6 6 7 7 7 8 9 9
(1 - ((~x2 + 4) div 11))
A029033: 1 1 1 2 3 3 4 6 7 8 10 12 14 16 19 22
(x5 mod 11)
A070596: 0 1 10 1 1 1 10 10 10 1 10 0 1 10 1 1
(1 + (7x mod 12))
A257811: 1 8 3 10 5 12 7 2 9 4 11 6 1 8 3 10
((x + 1) - ((~x3 + 2) div 12))
A084842: 1 2 4 7 11 17 25 37
(1 + ((4 * (x + (x div 5))) div 3))
A047449: 1 2 3 5 6 9 10 11 13 14 17 18 19 21 22 25
(1 + ((4 * (x + ((x div 2) div 3))) div 3))
A336223-A333634-A326535-A325779-A325511-A325467-A325399-A325398-A319315-A301899-A298540-A240370-A193304-A077377-A076786-A064594-A005117: 1 2 3 5 6 7 10 11 13 14 15 17 19 21 22 23
(1 + ((~4x2 + 20x) div 3))
A330564: 1 6 9 9 6 1
(1 + ((8x3 + 4x) div 3))
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(1 + (3 * ((x2 + x) - (x2 div 4))))
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(~1 + (6 * ((x + 2) + (2x div 3))))
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(1 + (3 * ((3x2 + 7x + 2) div 2)))
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(1 + ((((x2 - (x div 2)) mod (x + 2)) div 2) div 3))
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((x + 1) - ((~2 + (2x2 div (x + 2))) div 3))
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A269225: 2 3 3 4 4 5 5 6 6 6 7 7 7 8 8 8
((x + 1) - ((((1 - (x div 2)) * (x div 2)) div 2) div 3))
A028237-A004436: 1 2 3 4 6 7 8 9 11 12 15 16 18 19 22 23
(~1 + (((2 - ((x + ~1) div 2)) * (2 + (x div 2))) div 3))
A060022: 1 0 1 0 0 ~1 ~1 ~3 ~3 ~5 ~6 ~8 ~9 ~12 ~13 ~16
(1 + (3 * ((3x2 + 5x) div 2)))
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(1 + ((2x3 + 6x2 + 6x) div 3))
A213397: 1 5 18 43 83 144 229 341 486 667 887 1152 1465 1829 2250 2731
(~1 + (6 * (x + (3 * (1 + (x div 2))))))
A267984: 17 23 47 53 77 83 107 113 137 143 167 173 197 203 227 233
(1 + ((2x4 + 4x2 + ~2x) div 3))
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((x2 + x + 1) - (((x2 + ~x) div 2) div 3))
A025742-A022791: 1 3 7 12 19 28 38 50 64 79 96 115 135 157 181 206
(1 div (1 + ((x - ((x * (x div ~2)) div 2)) mod 3)))
A267355-A267050: 1 0 1 1 0 0 1 1 1 0 0 0 1 0 1 1
(1 + (3 * ((x * ((x2 + 4x + 4) div 2)) div 2)))
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(1 + ((x3 mod (x - ((~x + 2) div 2))) mod 3))
A309228: 1 1 1 1 2 1 1 1 1 2 1 1 3 1 2 1
(x mod (1 + ((2 * (x + ((x * (x div 2)) mod 2))) div 3)))
A172151: 0 0 0 0 1 1 1 1 2 2 3 2 3 4 4 4
(1 + ((3 * (x mod 3)) + ((x + 2) div 3)))
A227417: 1 5 8 2 6 9 3 7 10 4 8 11 5 9 12 6
(1 + ((x + 1) div (8 - ((x + 2) div 3))))
A300270-A255405: 1 1 1 1 1 2 2 2 2 3 3 4 4 5 6 6
(1 + ((2x3 + 9x2 + 10x) div 3))
A143371-A131423: 1 8 25 56 105 176 273 400 561 760 1001 1288 1625 2016 2465 2976
((x + 1) - (x div (8 - ((x + ~2) div 3))))
A095703: 1 2 3 4 5 6 7 7 8 9 10 10 11 12 12 13
(1 + (2 * (x + (x div 3))) - ((x + ~2) div 3))
A047378: 2 4 5 9 11 12 16 18 19 23 25 26 30 32 33 37
(1 + ((2x + ((((x + 1) div 2) div 2) mod 2)) div 3))
A206767: 1 1 2 3 4 4 5 5 6 7 7 8 9 10 10 11
(1 + (x mod 2) - (3 * (~2x + (x div 4))))
A219721: 1 8 13 20 22 29 34 41 43 50 55 62 64 71 76 83
(x - (x3 div (~5x + ~1)))
A226329: 0 2 3 5 8 10 13 17 21 25 30 35 41 47 53 60
(1 + (((x + ~1) div 5) * ((x div 2) div 3)))
A029116: 1 1 1 1 1 1 2 2 2 2 2 3 5 5 5 5
(1 + ((x + (((x div 2) mod 4) + (x div 2))) div 3))
A069928: 1 1 2 2 3 4 5 5 5 5 6 6 7 8 9 9
(1 - ((x div 2) mod (1 + ((x div (2 - (x mod 2))) div 3))))
A343159: 1 1 1 0 1 1 0 1 1 1 0 0 1 0 0 0
((x + 4) mod (1 + ((2x - (x mod 2)) div 3)))
A073368: 0 0 0 1 2 1 0 1 0 1 0 7 7 8 8 9
(1 + (((x * (x + (x div (2 + (x mod 2))))) div 2) mod 3))
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((2x + 5) - (((~x2 + 2x) div 2) mod 3))
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((2x + 1) - (((~x3 + x) div 2) div 3))
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A180415: 1 3 6 11 19 31 48 71 101 139 186 243 311 391 484 591
((x2 + 1) - (((~x3 + x) div 2) div 3))
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(1 + ((4x3 + 5x) div 3))
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(99x + 1)
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(1 + ((4x3 + ~7x) div 3))
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(1 + ((x * ((x + 1) mod (1 + (x div 4)))) mod 3))
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((x + 1) - ((~x + ((x div 3) mod 3)) div 3))
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(1 + ((x + ((2x2 + 4x) div 3)) div 3))
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A022780: 1 2 3 5 7 10 13 17 21 26 31 36 42 48 55 62
((2x + 1) - ((~x + ((x + ~2) div 3)) div 3))
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(15x2 + 9x + 1)
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((x div 8) - (x div (~1 + ((~x + 1) div 3))))
A061392: 0 1 1 2 2 2 2 3 3 4 4 4 4 4 4 4
(1 + ((2 * (x + (x div 3))) + ((~x + 1) mod 3)))
A201363: 2 3 7
A047531: 2 3 7 10 11 15 18 19 23 26 27 31 34 35 39 42
((x2 + 3x + 2) div (1 + ((x2 + x) mod 3)))
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((2x + 1) - ((~x + ((x div 2) div ~2)) div 3))
A231407: 1 4 6
A186222: 1 4 6 9 11 13 16 18 21 23 26 28 30 33 35 38
((x + 1) - ((~x + (((x + 1) * (x div 2)) mod 2)) div 3))
A285958: 1 3 4 5 7 8 9 11 12 13 14 16 17 19 20 21
((2x + 1) - ((~x + (((x + ~1) div 2) mod 2)) div 3))
A231407: 1 4 6
A287106: 1 4 6 8 10 13 15 17 20 22 25 27 29 32 34 36
((x + 1) - ((x + ((x div ~4) mod 2)) div 3))
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((x + 1) - ((~x + ((x div ~4) mod 2)) div 3))
A288174: 1 2 4 5 6 8 9 11 12 13 14 16 17 19 20 21
(1 + (x2 div (x + 19)))
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((x div 2) mod (1 - (2x mod (~1 + ((~x + 2) div 3)))))
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((x div 2) mod (2 - (2x mod (~1 + ((~x + 2) div 3)))))
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(1 + ((x * ((2x + 8) - (x div 2))) div 3))
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((4x + 3) - ((x * (x div 2)) mod 3))
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(1 + (3 * (((x + 1) + (x div 2)) * (x + (x mod 2)))))
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(x - ((~x2 + 1) mod (1 + ((x * (x mod 2)) div 3))))
A103303: 0 1 2 3 4 5 6 7 8 9
A327886: 0 1 2 3 4 5 6 7 8 9 10 11 12 11 14 11
((2x + 1) + (x div 3) - (x mod ~3))
A047321: 1 5 6 8 12 13 15 19 20 22 26 27 29 33 34 36
((2x + 1) + (x div 3) - ((x + 1) mod 3))
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(1 + (4x div (8 + (x div 3))))
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((x + 1) - (x2 div ((2x + 4) - (x div 3))))
A195778: 1 2 3 3 4 5 5 5 6 6 7 7 7 8 8 9
(1 + ((2 * (x + (x div 8))) + (x div 3)))
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A073608: 1 3 5 8 10 12
A287236: 1 3 5 8 10 12 15 17 21 24 26 28 31 33 35 38
(1 + ((x2 + 2x + 1) div ((x + 2) - (x div 3))))
A092418-A004195: 1 2 3 5 6 7 9 10 11 13 14 15 17 18 19 22
((~1 + ((x + ~1) mod 5)) mod (1 + (x div 3)))
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(3 + (x div 3) - (x div (~1 + (x div ~2))))
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((~4x2 + ~4x + 1) mod (1 + (x div 3)))
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((x + ~1) + ((~x + 1) div ((x + 1) div (1 + (x div 3)))))
A224709: 0 0 0 1 1 2 2 3 4 4 4 6 5 6 8 7
((((x div 2) - (x mod 3)) mod 2) * (1 + (x div 3)))
A101348: 0 1 1 2 2 0 3 0 0 0 0 4 0 5 5 6
((~2 + ((x + ~1) * (1 + (x div 2)))) mod (1 + (x div 3)))
A076472: 0 0 0 0 1 0 0 1 0 2 0 2 0 2 2 2
(((x mod 4) - ((x + ~1) div 2)) mod (1 + (x div 3)))
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(x mod (6 - ((~x + 1) div (1 + (x div 3)))))
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((~3x2 + ~4x) mod (1 + (x div 3)))
A328194: 0 0 0 1 0 1 0 2 1 1 0 1 0 1 1 3
((x + 1) + ((2 * (2x div 3)) + (x div 3)))
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(1 + ((2 div (~x + 16)) * (x div 3)))
A160923: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 11
(1 + (2 * (x - (x div ~3))) - (x mod 3))
A047610: 1 4 5 9 12 13 17 20 21 25 28 29 33 36 37 41
((x + 2) div (1 + ((2 * (1 + (x mod 2))) + (x mod 3))))
A133755: 0 0 0 1 1 1 2 1 2 2 3 1 4 2 3 3
((x + 1) - (x2 div ((2x + 2) + (x mod 3))))
A266350: 1 2 3 3 4 5 5 6 6 6 7 8 8 9 9 9
(1 + ((4 * (2x div 3)) + (x mod 3)))
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((x + 1) + (x mod 3) - (2 * ((x div 3) mod 2)))
A131793: 1 3 5 2 4 6 7 9 11 8 10 12 13 15 17 14
(1 + ((x2 + ~1) div ((2x + 4) + (x mod 3))))
A029865: 0 1 1 1 2 2 3 3 3 4 4
A242736: 0 1 1 1 2 2 3 3 3 4 4 5 6 6 6 7
((2 - ((~x + 1) div 5)) mod (1 + (x mod 3)))
A127324: 0 0 0 0 1 0 0 0 1 0 0 1 0 1 2 0
((2 + (x mod (2 + (x div 3)))) mod (1 + (x mod 3)))
A290825: 0 1 2 0 1 1 0 1 2 0 0 0 0 1 1 0
(x div (x - ((((x + ~1) div 2) div 2) * (1 + (x mod 3)))))
A300820-A284259: 0 1 1 1 1 2 1 1 1 1 1 2 1 1 2 1
((~2 + ((x - ((x div 2) mod 2)) div 2)) mod (1 + (x mod 3)))
A341353: 0 0 1 0 0 0 0 1 2 0 0 0 0 0 1 0
((~1 + (2 * ((x div ~2) mod 2))) * (~1 + (x mod 3)))
A260190: 1 0 1 1 0 1 ~1 0 ~1 ~1 0 ~1 1 0 1 1
((~1 + (x mod (2 * (2 - (x mod 2))))) * (~1 + (x mod 3)))
A016340-A016331-A016253-A015725-A014021: 1 0 1 0 0 0 ~1 0 ~1 0 0 0 1 0 1 0
(21x2 + 9x + 1)
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((2x2 + 8x + 8) mod (3x2 + 1))
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(~1 + (2 div (1 + (x div (~2x + 32)))))
A014152: 1 1 1 1 1 1 1 1 1 1 1 0 0 ~1 ~1 ~1
(2 div (1 + ((x + 1) mod (1 + (((~x + 2) div 2) mod (x + 2))))))
A039972: 1 2 2 0 0 2 2 1 1 0 0 0 0 0 0 0
((x + 3) - ((x2 div 3) div (x + 3)))
A121151: 3 4 5 6 7 7 8 9 10 10 11 12 12 13
(~1 + ((x + 3) * (2 + ((x2 + 3x + 2) div 2))))
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(3 div (1 + ((2 + (x * (x div 2))) mod (x + 3))))
A319625: 1 1 0 0 0 0 1 0 1 1 3
((x + 1) div (1 + (16 mod (2x + 1))))
A001231: 1 1 1 1 0 1 1 4 0
(1 + ((2x div ~7) mod (2x + 1)))
A144077: 1 3 5 7 8 10 12 14 15 17 19 20 22 24 26 27
(x2 mod (1 + ((x + 5) mod (1 + (x div 2)))))
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(~x mod (1 + ((2x div 3) mod (1 + (x div 2)))))
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(1 + ((8 mod (2x + 1)) mod (1 + (x div 2))))
A071434: 1 1 2 2 3 3 1 1 4 4 3 3 2 2 1 1
(1 + (((x + 2) - (x mod ~4)) * (1 + (x div 2))))
A118889: 3 7 13 13 19 31
(~1 + (2 * (((x + 2) - (x div ~2)) * (1 + (x div 2)))))
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(1 + (((x2 + ~1) mod (2 + (x mod 2))) mod (1 + (x div 2))))
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(12x2 + 16x + 13)
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((2x + 1) - ((((x + 1) + (x div 4)) div 2) div 2))
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(x div (~1 + (4 * (2 + (x mod (2 + ((x div 2) mod 2)))))))
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(x4 mod 33)
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(x4 mod 31)
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((x + 1) - ((x div 2) div (~10 + (x div 2))))
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(136x + 17)
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((x3 + ~3x2 + 2x) div 17)
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((x * ((1 + (x div 2)) div 2)) div 15)
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(1 + (x div 3) - (((~x + 2) div 8) mod 2))
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((x + 1) - ((((1 - (x div 2)) * (x div 4)) div 2) div 2))
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((x + 1) - (((2x + 1) mod (2 + (x div 4))) div 2))
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(1 + ((~2x2 + 2x) mod (4 + (x div 4))))
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((x + 1) - (((((x * (2 - (x div 2))) div 2) div 2) div 2) div 2))
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((x + 1) - (x div (2 + (x mod (2 + (x mod (2 + (x mod 2))))))))
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(1 + (((x div 2) - (((x + 1) div 3) mod 4)) div 2))
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((2x + 1) - ((2x + 2) div ~7))
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((2x + 1) - (3x div ~7))
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(1 + ((x + 2) div (8 + (x div ~4))))
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(2 div (1 + (((x + 2) div (2 - (x mod 2))) mod 8)))
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(90x + 9)
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(9x2 + 45x + 63)
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((3x2 + x + ~1) mod 9)
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((3x2 + ~4x + 1) mod 9)
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((9x + 9) * (3 - (x mod 2)))
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(((x + 1) * (3 - (x mod 2))) mod 9)
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(9 * ((3x2 + ~x) div 2))
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((~x + 1) + (9 * ((x2 + x) div 2)))
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((x3 + 3x2 + 3x + 2) div 9)
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(9 * (x + ((x div 2) div 5)))
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(((~x + 1) * (1 + (2 * (x mod 2)))) mod 9)
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(((2 * (x div 2)) div 3) + (x div 9))
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((x + 10) + (x div 9))
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(9x4 + 18x3 + ~9x2)
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(1 + ((x * (x div 2)) mod (1 - ((~x + 2) div 8))))
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(~1 + ((2 * ((x + 1) mod 4)) + (x mod 8)))
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((x + 1) - (2 * ((x + ((x div 3) mod 2)) div 4)))
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(1 + (2 * (3x - ((x + (x div 2)) div 4))))
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(1 + (((1 - (x div ~4)) * (x div 4)) div 2))
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(~1 + (2 * ((2 * ((x + 2) + (x div 2))) - (x mod 4))))
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(x mod (1 + ((4 mod (x + 1)) mod (2 + (x mod 4)))))
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((x2 + 2x + 1) - ((x - (x2 div 4)) div 2))
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(1 + (((x - (((~x + 1) * (x div 3)) div 2)) div 2) div 2))
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(1 + (((x - ((x * (x div ~4)) div 2)) div 2) div 2))
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((x + 1) - (((3x2 div (x + 2)) div 2) div 2))
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(1 + ((2x mod (2 + (4x div (x + 2)))) div 2))
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((3 * (x2 div 2)) div (x + 7))
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(x - ((x2 + ~2x + ~1) div (x + 7)))
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((x * (~2 + ((x + ~1) div 2))) mod (x + 7))
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(2x - ((x2 + ~2) div (4x + 9)))
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(1 + (2 * ((x + 2) - ((x2 div 2) div (~2x + 1)))))
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((x + 3) - ((((~x + 1) div 3) - (x div 2)) div 2))
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((x + 1) - ((((2 + (x div 4)) * (x div 2)) div 2) div 2))
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((2x + 3) - (((x mod 4) + (x div 2)) div 2))
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(~1 + ((x + 2) div (2 + ((2x + ~2) div (2 + (x div 2))))))
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(x - ((x * ((x + ~1) div 2)) div (5 + (x div 2))))
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(1 + (((x3 + ~3x2) mod (2 + (x div 2))) div 2))
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((2x + 4) div (1 + (((x2 + ~1) div 2) mod 4)))
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((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4)))
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(x3 mod 45)
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(50x2 + 50x)
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(((~x + ~2) - (x div 5)) mod 5)
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(15x3 + ~15x2 + 5x)
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((3x2 + 11x + 6) div 5)
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(1 mod ((1 + ((x + ~2) * (2 + (x div 2)))) mod 5))
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(x + (5 * ((x + 1) + (x mod 2))) - (x div 2))
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(1 - ((x + 2) mod (((~x + ~1) + (x mod 2)) div 5)))
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((17x + 17) div 5)
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((20 mod (x + 1)) div 5)
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(x + ((x div 5) + ((x + 1) div 5)))
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(((x2 + x) div 2) - ((x2 + 1) div 5))
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(x - ((~2 * ((x + 1) + (x mod 2))) div 5))
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(5 * (x - (2 * ((x div 2) mod 5))))
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(((x2 + x) div 2) mod 30)
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(x4 mod 30)
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(10x3 + 40x2 + 40x + 10)
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(2x - ((2 * ((x + ~1) + (x div 2))) div 5))
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((3x + 3) - ((2x + 2) div 5))
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(6x - ((2x + 2) div 5))
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((((x + ~1) * (x2 div 4)) div 2) div 5)
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((x div 2) - (((~x2 + 3x + ~2) div 2) div 5))
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((((x3 + ~3x2 + 2x) div 2) div 2) div 5)
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(10 * (x mod (2 + ((~x + 2) mod 4))))
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(x2 + 2x + 35)
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(x4 mod 40)
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(0 - ((2x - (x2 div 4)) div 5))
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(((x2 + ~x) - (x2 div 4)) div 5)
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(x - (((~x2 + ~3x + ~4) div 2) div 5))
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A186384: 1 2 4 6 8 10 12 15 18 21 24 27 31 35 39 43
((2 * (x + ((x + ~1) mod 5))) div 5)
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((4x + 4) - ((~2x + 2) div 5))
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((3x + 2) - ((~2x + 2) div 5))
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(5 * ((5x2 + x) div 2))
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(x - (((~x + ~2) + ((x div 2) mod 4)) div 5))
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(3x - ((x - ((~x + 2) div 2)) div 5))
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((6x + 4) + ((x + 2) div 5))
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((3x + 2) - ((~2x + 1) div 5))
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(2 + (x mod 2) - (5 * (~2x + (x div 2))))
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((2x + 2) - ((~2x + (x div 2)) div 5))
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((x2 + 6x + 8) - (2x div 5))
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((6x + 6) + ((x div 2) div 5))
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((2x + 10) + ((x div 2) div 5))
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(3x - (((~x + 1) - (x div 2)) div 5))
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(((x div 2) div 3) div ((x2 + 2) mod 5))
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((x + 5) + ((x2 div 2) div (x + 3)))
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((x + ~8) mod (2 - ((~x + 1) div 5)))
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((x + 5) + (6x div (x + 1)))
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((x + 1) mod (2 - ((~x2 + ~x) mod 5)))
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(x - (5 * (~x + (x mod 10))))
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(x - ((~x + ((~1 + (x div 2)) mod 4)) div 5))
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((x5 + 4x) div 5)
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(1 - (((~x + 2) * (1 + (x div 3))) div 5))
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(((x + ~1) div 2) mod (2 - ((x2 + 2x) mod 5)))
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((x + 2) - (x2 div ((x + 5) + (x div 2))))
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(1 - ((x div ~5) * (x div 5)))
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(3 div (3 + (x mod 2) - (x div 5)))
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((9x + 9) + (x div 5))
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(((x * (x div 2)) div (x + 4)) - (x div 5))
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(((1 + (x div 5)) div 2) + (x mod 5))
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((x + (x div (~x + 16))) div 5)
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((1 + (x div 8)) div (1 + (~x mod 4)))
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((x + 1) - ((~x + ((x + 2) mod 5)) div 4))
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((x + 1) - ((~x + ((~1 + (x div 2)) mod 3)) div 4))
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((2x + 1) - ((x + ((~x + 1) mod 3)) div 4))
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((x + 1) - (((~x + 2) - (x2 div 3)) div 4))
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((x + 1) - (4 * (~x + (2 * (x div 5)))))
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((2x + 1) - ((x + ((x div 2) mod 4)) div 4))
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((2x + 1) - (((~x + 2) - (x div 4)) div 4))
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A073608: 1 3 5 8 10 12
A189929: 1 3 5 8 10 12 15 17 19 22 24 26 29 31 33 35
((x div 2) mod (1 - ((x + 2) mod (~1 + ((~x + 2) div 4)))))
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(1 - (1 div ((2x + 1) - ((x2 + ~2x) div 4))))
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((x + 1) - ((x + 1) div (8 - (x div 4))))
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((3x2 + 8x + 5) + (x div 4))
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((1 + (x mod (1 + (x div 3)))) div (1 + (x div 4)))
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((3 * (2x div 3)) mod (1 + (x div 4)))
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(x - ((~2 + (3 * (x div 2))) mod (1 + (x div 4))))
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(((x + 1) mod (2 * (1 + (x mod 2)))) * (1 + (x div 4)))
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((~8 + (x2 div 2)) mod (1 + (x div 4)))
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(~2 + ((((x + 1) div 2) div 2) + (2 div (1 + (x div 4)))))
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((1 + ((x mod (1 + (x div 2))) div 2)) div (1 + (x mod 4)))
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(52x2 + 1)
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(44x2 + 1)
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(68x2 + 1)
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((x + 3) - ((~x + (x div 12)) div 2))
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(x - (x div (~1 + (2 * ((x + ((~x + 1) mod 3)) div 2)))))
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(1 + (((x + ((x + ~2) mod (2 + (x div 3)))) div 2) mod 2))
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(x mod (5 - ((~x + ((x mod 3) div 2)) div 2)))
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(1 + (((x + 2) div (~2x + 32)) div 2))
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(1 + (((x + (4x div (x + 4))) div 2) mod 2))
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((x + 1) - (2 mod (1 - (2 * ((x + ((x div 2) mod 2)) div 2)))))
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(1 + (2 * ((x + 2) + ((x + (x2 div 3)) div 2))))
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(2x2 + 22x + 27)
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(~1 + (x mod 2) - (2 * (((x div 2) - (x * (x mod 2))) div 2)))
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(1 + ((((x div 2) div ~5) mod (x + 2)) div 2))
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((x + 1) - ((((~x + (x mod 2)) div 3) mod (x + 2)) mod 2))
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(~1 + ((2x + 4) * ((x + 1) + (4 mod (x + 2)))))
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(x div (1 + (2 * ((2 * (~x + ((x div 2) mod 2))) mod (x + 2)))))
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((x + 1) - (((2 + (x * (x + (x div 2)))) div (x + 2)) div 2))
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(~x2 + 9x + 53)
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(2x3 + 18x2 + 46x + 30)
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(2x - ((2x2 + 2) div (x + 5)))
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((x mod 2) - ((~4x + 4) div (x + 5)))
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((x + 5) * (x - ((~x3 + x2) div 2)))
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((4x + 1) - ((~x2 + 1) div (x + 4)))
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(15x div (2x + 5))
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(4x2 + 27x + 39)
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((x + 1) - (2 * (~2x + ((x - (x div 4)) div 2))))
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((4x + 1) + ((~x + 2) div (2 + (x div 3))))
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(16x3 + 20x2 + 8x + 1)
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((2x div ~5) mod (4x + 1))
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(16x3 + 12x2 + 6x + 1)
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(36x2 + 17x + 2)
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((~x + ((x + (x div 2)) div 4)) mod (4x + 1))
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(~1 + (2 * ((10x + 10) + (x div 2))))
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(1 + (2 * ((3 * (x + (2 * (x mod 2)))) - (x div 2))))
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(1 + (2 * ((2x3 + 3x2 + x) + (x div 2))))
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(1 + ((((x2 + ~x) div 8) + (x div 2)) div 2))
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((2x + 1) - ((0 - ((x div 2) + (x mod 4))) div 2))
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(1 + (((~2 + ((x2 + ~1) * (x div 2))) * (x div 2)) div 2))
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(2 div (1 + ((8x + ~2) mod (2 + (x div 2)))))
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((x + 4) mod (~1 + ((2x + ~4) mod (2 + (x div 2)))))
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((2x + 1) - (((x * (x div 2)) div 2) div (2 + (x div 2))))
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(((x + 1) div 3) - (2x div (3 + (x div 2))))
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((x - (2 * (((x + 1) div 2) div 2))) * (1 + (2 * (x div 2))))
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((4 + (x div 8)) mod (1 + (2 * (x div 2))))
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((1 + (2 mod (1 + (x mod 3)))) * (1 + ((x div 2) mod 2)))
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((2 + ((x + 2) div (1 + (x mod 2)))) div (1 + ((x div 2) mod 2)))
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(1 + (x div (2 + ((1 + ((x + ~1) mod 3)) * (x mod 2)))))
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(1 + (x div (2 + ((1 + ((x div 2) mod 3)) * (x mod 2)))))
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(1 + (((3 * (x + (x div 4))) + (x mod 2)) div 2))
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(1 + (((3 * (x + (x div 4))) - (x mod 2)) div 2))
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(1 + (2 * ((3 * (x + ((x div 2) mod 2))) - (x mod 2))))
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(1 + (x mod (2 + (x mod 2))) - (x mod (3 + (x mod 2))))
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(1 + (((x2 + 4x + 4) div 2) + (x div (2 + (x mod 2)))))
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(((~x + 2) mod (1 + (x div 4))) div (1 + (2 * (x mod 2))))
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(1 + (4 * (x2 + (3 * (x + (x mod 2))))))
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(1 + (2 * (((x + 1) * (2 + (x mod 2))) + (x2 div 2))))
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((1 + ((2x + 2) mod (1 + (x div 3)))) mod 3)
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((x div (1 + ((x + 2) mod (1 + (x div 3))))) mod 3)
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((1 + (3x mod 7)) div 3)
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((1 + (x div (1 + (x div (2 * (2 + (x mod 2))))))) div 3)
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(75x + 3)
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((1 + (4x div (1 + (x div 4)))) mod 3)
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((~1 + (4x div (1 + (x div 4)))) mod 3)
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(((~x2 + 1) mod 11) mod 3)
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(1 - ((2x div (1 + ((~x + 2) mod 3))) mod 3))
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((5x2 + 13x + 9) div 3)
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((x2 - ((x div 3) div ~3)) mod 3)
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((x mod (((x + 1) mod 2) - (x div ~3))) mod 3)
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(((x3 + x2) mod 7) div 3)
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((x - ((2x + 2) div 7)) mod 3)
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(((3x + ~2) mod 7) div 3)
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(((x3 + 2x2) mod 7) div 3)
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(((~x3 + 2x2) mod 7) div 3)
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((2x div (1 + (x div (2 + (x mod 3))))) mod 3)
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(3 * (1 + (4 * ((x + 1) + (x div 4)))))
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(x2 mod 99)
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(x4 mod 27)
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(3 * (x - (5 * ((~x2 + x) div 2))))
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((2x + 2) - ((x - (x div 5)) div 3))
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(1 - (((x mod 2) - (x2 div 5)) div 3))
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((1 + (4 * (x + (x div 5)))) div 3)
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((1 - (4x div (1 + (x div 4)))) mod 3)
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((1 + (x * ((x div 3) * (x div 4)))) mod 3)
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(3 + ((x + 5) * (x2 - (x div 2))))
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((1 + ((x - ((x div 2) mod 2)) mod (2 + (x div 2)))) div 3)
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(x4 mod 36)
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((((4x + 1) mod (x + 2)) div 3) mod 3)
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(1 - ((((~x + 1) div 3) * (x div 3)) div 3))
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(((x + 1) div 3) - ((1 - (x div 3)) div 3))
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((x2 div ((~x + ~1) - (x div 3))) mod 3)
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(((8x + 8) + (x div 3)) div 3)
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((3x + 3) - ((x - (x div 3)) div 3))
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(((x2 div 2) - ((~x2 + 2x) div 3)) div 3)
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(3 * (1 + ((x + ((x2 div 2) div 3)) div 2)))
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(x - ((~1 + (2 * (~x + (x div 8)))) div 3))
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(2x - ((~1 + ((x + ((x div 2) mod 2)) div 2)) div 3))
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((1 + ((x + 2) * (x + ((x + 1) mod 3)))) div 3)
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(3 + ((2x + 1) * (1 div (x2 + ~3))))
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(((3x + 9) mod (1 + (x div 2))) mod 3)
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(((5x + 4) div (1 + (x div 2))) mod 3)
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((1 + ((x2 div 8) + (x mod 2))) div 3)
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(((2x2 + 1) * ((x2 + x) div 2)) div 3)
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(((2x2 + 1) * ((x2 + ~x) div 2)) div 3)
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((1 + (x * ((2x mod (2 + (x div 2))) mod 2))) div 3)
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(24x2 + 39x + 15)
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(((x + 1) * (1 + (((x div 2) * (x div 2)) div 2))) mod 3)
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(((x + 1) * (4 + ((x mod 3) div 2))) div 3)
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(24x3 + 72x2 + 48x)
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((8x3 + 24x2 + 16x) div 3)
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(((x + 1) * (x mod (~2 + ((~x + 2) div 4)))) mod 3)
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(9x2 + 14x + 7)
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((x3 + 9x2 + 20x + 12) div 3)
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((3x2 + 10x + 6) - (x * (x div 2)))
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((3x + 3) + (x div 11))
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((3x + 3) + ((x + 1) div 7))
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((3x + 3) + ((x div 2) mod (1 + (x div 4))))
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((3x + 3) + ((x - (x div 3)) div 3))
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((3x + 3) + ((~x2 + 2x) div (x + 3)))
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((3x + 3) + ((x - ((x div 2) div 3)) div 2))
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((3x + 3) + ((x - ((x div 3) mod 2)) div 2))
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((3x + 3) + ((x3 div (x + 2)) div 2))
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(27x2 + 39x + 12)
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((x + 2) - (((~x + 1) div 3) * ((x + 1) div 3)))
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(x + ((x2 + x) mod 3) - ((x + 1) div 3))
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((4x3 + 9x2 + 5x) div 3)
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((5x3 + 6x2 + x) div 3)
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(~x + ((x mod 2) + ((x3 + 3x2 + 2x) div 3)))
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((5x3 + 9x2 + 4x) div 3)
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(x - (((~x + 1) + ((1 + (x div 2)) mod 3)) div 3))
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(((x + ~1) * (2 + (x div (2 - ((x div 2) mod 2))))) mod 3)
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((3x2 + 6x + 6) + ((x + ~1) div 3))
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((2x + 4) + ((x + ~1) div 3) - (x mod 3))
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((2 * ((x + 1) + (x div 3))) - ((x + ~1) div 3))
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((2 * ((x + 2) + (x div 3))) - ((x + ~1) mod 3))
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(((x2 + ~x) * (2 + ((x2 + ~x) div 2))) div 3)
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((2x + 4) - ((~x3 + 3x2 + ~2x) div 3))
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((3x4 + 2x3 + ~3x2 + ~2x) div 3)
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((2 + (x div 4)) div (2 - (x mod ~6)))
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((2 * ((x + 1) - (x div 7))) div 3)
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(6 * ((2x + 1) - ((x + ~2) div 3)))
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(6 * (1 + (2 * (x - ((x div 2) div ~2)))))
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(1 - ((2 * (2x div ~5)) div 3))
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(x - ((2 * (2x div ~5)) div 3))
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((((x + ~3) mod 9) div 2) mod 3)
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((~x + 1) + (6 * (x - (x div 5))))
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((2 * (1 + ((x * (x div 4)) div 4))) div 3)
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(x - (3 * ((x div 2) - ((1 + (x div 4)) div 2))))
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(x - (6 * (~1 + (2 * (~2x + (x div 2))))))
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(3 * ((3 * (1 + (x * (2 + (x mod 2))))) div 2))
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(66x + 12)
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((x + ~2) + (3 * (2 + (3 * (2 + (x div 2))))))
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((2 + ((2x2 - (x div 2)) div 3)) div 3)
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((2x - (x mod (2 + ((x div 2) mod 3)))) mod 3)
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(x - ((x + ~3) div (x + ~18)))
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((~x4 + 2x2) mod 18)
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(x5 mod 18)
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(((x + 2) div 3) - ((2 * (x div 3)) div 3))
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((2 * (1 + (2 * (x + (x div 5))))) div 3)
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(((x3 + 3x2 + ~4x + ~12) div 2) div 3)
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(x div (3 * (2 + (2x2 mod (1 + (x div 2))))))
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(~x + ((x div 2) + (6 * ((x + 1) + (x div 2)))))
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(3 * (((x + 1) * ((x3 + x2) div 2)) div 2))
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(((x4 + 5x3 + 8x2 + 4x) div 2) div 3)
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(((x5 + 3x4 + 2x3) div 2) div 3)
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((6x + 6) + ((4 div (x + 2)) mod 2))
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((x + 2) + ((2 mod (x + 1)) + (((x + 1) div 2) div 3)))
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((5x + 4) - (((x + 1) div 2) div 3))
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((((x div 2) mod 3) div 2) + (((x + 1) div 2) mod 3))
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(3 * ((5x2 + 9x + 4) div 2))
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((2 * ((x * (4 + (x div 2))) div (x + 1))) div 3)
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(((x3 + 9x2 + 8x) div 2) div 3)
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((((x + ~1) * ((x mod (2 + (x div 2))) div 2)) div 2) mod 3)
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((x2 + 3x + 2) - (((x2 + ~1) div 2) div 3))
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(0 - (x div (3 * (~2 + (x mod ~8)))))
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((x + 1) mod ((2 * (2 - ((x div 2) div ~2))) div 3))
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((1 - ((~x + 2) div (2 - (x div ~4)))) mod 3)
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((4 * (2x - (x mod ~3))) div 3)
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(((x + 2) - (x div (~2 + (x mod ~3)))) div 3)
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((x - (4 * (x div ~5))) div 3)
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((4 * (x - (x div ~5))) div 3)
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((4 * (x - ((~x + 1) div 5))) div 3)
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((4 * (x - ((~x + 2) div 5))) div 3)
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((2 + ((x + ~1) mod (2 * (1 + (x div 4))))) div 3)
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((4 * ((x div 2) - ((x + ~1) div 3))) div 3)
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((x - (x mod (~4 + ((x div 2) div 3)))) div 3)
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((x - (x div (~4 + ((x div 2) mod 3)))) div 3)
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((4 * ((2x + 2) - (x mod 3))) div 3)
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((2 * (2 + (x div (4 - (x mod 3))))) div 3)
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(6 * ((1 + ((x * (x div 4)) div 2)) div 2))
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(((((x + 3) * ((x + 1) div 2)) div 2) div 2) div 3)
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((4 * ((x + 1) + (x div 5))) div 3)
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((~x + 1) + (3 * ((((x + 1) + (x div 2)) div 2) div 2)))
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((2 * (2 + (4x2 div (x + 1)))) div 3)
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(3 * ((((x + 1) + (x div 2)) * ((x + 1) div 2)) div 2))
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((x + ~3) - (2x div (~2 + (x div ~4))))
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(((((x3 + ~3x2 + 2x) div 2) div 2) div 2) div 3)
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((4 * (x - (x div (~2 + (x div ~2))))) div 3)
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((x2 mod (4 + (((x + 1) div 2) div 2))) mod 3)
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(((x + 2) - (2 * ((~x + 2) div 8))) div 3)
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(3 * (2 + ((x2 mod (2 + (x div 4))) div 2)))
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((2 * (((~x + 2) mod (2 + (x mod 4))) div 2)) mod 3)
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(0 - (x2 div ~42))
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(x4 mod 48)
A070591: 0 1 16 33 16 1 0 1 16 33 16 1 0 1 16 33
(x mod (3 * (2 + ((x2 + x) mod 8))))
A337223: 0 1 2 3 4 5 6 1 2 9 10 11 12 13 2 3
(((x - ((x * (x div 2)) mod 8)) div 2) div 3)
A070104-A024156: 0 0 0 0 0 0 0 0 1 0 1 0 2 1 2 2
(((2x + ~1) div (4 + (x div 4))) mod 3)
A204263: 2 0 0 1 1 1 2 2 2 2 0 0 0 0 0 1
(((~2x + 1) div (4 + (x div 4))) mod 3)
A204433: 0 2 2 1 1 1 0 0 0 0 2 2 2 2 2 1
((2 * (2 + (((2 + (x div 2)) * (x div 2)) div 2))) div 3)
A001364: 1 1 2 2 4 4 6 6 9 9 12 12 17 17 22 22
(0 - ((x2 + 2x) div ~21))
A096911: 0 1 1 1 2 2 3 3 4 5 6 7 8 10 11 13
(x div (1 - (x mod (~24 + (x div 2)))))
A345166: 0 0 0 0 0 0 0 0 0 0 1 1 1 2 3 5
(((x * (x2 div 3)) mod 8) div 3)
A244518: 0 0 0 0 1 0 0 0 0 1 0 0 0 0 2 1
(x - ((~8x3 + 8x) div 3))
A063523: 0 1 18 67 164 325 566 903 1352 1929 2650 3531 4588 5837 7294 8975
(1 - (((x - ((x2 + ~x) div 4)) div 2) div 3))
A120170: 1 1 1 1 1 1 2 2 2 3 3 4 5 6 7 8
(((1 + (x div 2)) div 2) - (3 * ((x div 4) mod 2)))
A318439: 0 0 1 1 ~2 ~2 ~1 ~1 2 2 3 3 0 0 1 1
((x - (((~x2 + x) - (x mod 4)) div 2)) div 3)
A087539: 0 0 1 2 3 5 7 10 12 15 18 22 26 30 35 40
((2 - (x div (2 * (~2 + ((x * (x div 2)) mod 2))))) div 3)
A097637: 0 1 1 1 1 1 1 2 1 1 1 2 1 2 2 3
((2 + (((x + 2) * (1 - (2 * (x mod 2)))) div 2)) div 3)
A187035: 1 0 1 ~1 1 ~1 2 ~1 2 ~2 2 ~2 3 ~2 3 ~3
(1 - ((2 * ((((~x + 1) div 2) * (x div 2)) div 2)) div 3))
A040039: 1 1 2 2 3 3 5 5 7 7 10 10 13 13 18 18
((2 - ((~x2 + 2x) div (4 + (x div 2)))) div 3)
A060970: 0 0 0 1 1 1 2 2 2 3 3 4 4 5 6 6
(1 - (((~x2 + 2x) div (4 + (x div 2))) div 3))
A199017: 1 1 1 2 2 2 3 3 3 4 4 5 5 6 7 7
(1 - (((0 - ((x2 + (x div 2)) div 2)) div 2) div 3))
A029015: 1 1 2 2 3 4 5 6 7 8 10 12 14 16 18 21
((x mod (4 * (1 + (x mod 5)))) mod 3)
A101672: 0 1 2 0 1 1 0 1 2 0 2 0 0 1 2 0
((x div 2) - (((~x2 + 2x + ~1) div 4) div 3))
A008806: 1 0 2 2 3 4 6 6 9 10 12 14 17 18 22 24
((2x + 4) - ((x + 3) mod 12))
A062998: 1 2 3 4 5 6 7 8 9 22 23 24 25 26 27 28
(x - ((4x + 4) div ~11))
A292636-A279607: 1 2 4 5 6 8 9 10 12 13 14 16 17 19 20 21
(x - ((x + 2) div (~12 + ((x + ~1) div 2))))
A331914-A328369-A324935-A209638-A207674-A123345-A093641: 1 2 3 4 5 6 7 8 10 11 12 13 14 16 17 19
((2x div (2 + (x div 2))) - (x div 12))
A081326: 0 1 1 2 2 2 2 2 2 3 2 3 2 2 2 2
((4 * (x + ((x + 1) div 5))) div 3)
A047412: 0 1 2 4 6 8 9 10 12 14 16 17 18 20 22 24
((x - (4 * (~x + (x div 5)))) div 3)
A047330: 0 1 3 5 6 7 8 10 12 13 14 15 17 19 20 21
((((x + ~1) mod 5) + (x div 4)) div 3)
A025862: 1 0 0 0 1 1 0 0 1 1 2 0 1 1 2 2
(((1 + ((x * (x div 2)) mod 2)) * (x div 4)) mod 3)
A334222: 0 0 0 0 1 1 1 2 2 2 2 1 0 0 0 0
(3 * (4x2 + ((x2 + ~x) div 2)))
A268351: 0 12 51 117 210 330 477 651 852 1080 1335 1617 1926 2262 2625 3015
(2x2 - ((1 - (x2 div 4)) div 3))
A256321: 0 2 8 19 33 52 75 102 133 169 208 252 300 352 408 469
(0 - (((~x2 + x) - (x2 div 4)) div 3))
A002578: 0 0 1 3 6 9 13 18 24 31 39 47 56 66 77 89
(3 + (((x * ((~1 + (x div 2)) mod 3)) div 2) mod 2))
A322347: 3 4 3 3 3 3 3 4 3 3 4 4 3 4 3 3
(((x3 + 3x2 + 5x + 6) div 2) div 3)
A084570: 1 2 6 12 23 38 60 88 125 170 226 292 371 462 568 688
(((x3 + 6x2 + 14x + 12) div 2) div 3)
A026035: 2 5 12 22 38 59 88 124 170 225 292 370 462 567 688 824
((2 * (2x + (x div ~5))) div 3)
A239492: 0 0 2 3 4 6 6 8 9 10 12 12 14 15 16 18
((~x + 1) + (3 * ((4x + 2) + (x div 2))))
A156619: 7 18 32 43 57 68 82 93 107 118 132 143 157 168 182 193
(1 - ((2 * (((x div 4) mod 2) - (x div 2))) div 3))
A071903: 1 1 2 2 2 2 3 3 4 4 5 5 5 5 5 5
((((x div 2) div 3) mod 2) + ((2 + (x div 2)) div 3))
A266123: 0 0 1 1 1 1 2 2 3 3 3 3 2 2 3 3
(((x - ((x div 2) mod 2)) div 2) - ((2 * (x div 2)) div 3))
A275235: 0 0 0 1 1 1 0 1 2 2 1 2 2 2 2 3
((2 * ((x mod (1 + (x div 4))) + (x mod 2))) div 3)
A337541: 0 0 0 0 0 1 0 1 1 0 0 2 0 1 1 2
((((x2 + x) div 3) * (2 + (x mod 2))) mod 3)
A292251: 0 0 1 0 0 0 1 0 0 0 0 0 2 0 2 0
(3 * (((x + 2) + (x div 2)) * (1 - (2 * (x mod 2)))))
A269416: 6 ~9 15 ~18 24 ~27 33 ~36 42 ~45 51 ~54 60 ~63 69 ~72
(54x2 + 6x)
A277990: 0 60 228 504 888 1380 1980 2688 3504 4428 5460 6600 7848 9204 10668 12240
(2 - ((2 * (~x + (x div 9))) div 3))
A316627: 2 3 4 4 5 6 6 7 8 8 8 9 10 10 11 12
(x - ((2 * (~x + (2x div 5))) div 3))
A047316: 0 2 4 5 6 7 9 11 12 13 14 16 18 19 20 21
(((5x3 + x) div 2) div 3)
A004068: 0 1 7 23 54 105 181 287 428 609 835 1111 1442 1833 2289 2815
(1 - ((x mod (4 - ((x2 + x) div 2))) mod 3))
A112214: 1 0 1 ~1 0 1 0 0 1 0 0 1 0 0 1 0
(x - (6 * (~x + (x mod 10))))
A103303: 0 1 2 3 4 5 6 7 8 9
A024662: 0 1 2 3 4 5 6 7 8 9 70 71 72 73 74 75
(x - (3 * ((~x + (x mod 10)) div 2)))
A103303: 0 1 2 3 4 5 6 7 8 9
A174141: 0 1 2 3 4 5 6 7 8 9 25 26 27 28 29 30
(1 - ((2 * (~x + (2 * ((x div 2) div 3)))) div 3))
A243351: 1 2 3 3 4 5 4 5 5 6 7 7 7 7 8 9
(((x * (((x + 1) + ((x div 2) mod 2)) div 2)) div 2) div 3)
A256984: 0 0 0 1 1 2 4 4 5 7 10
((x + 2) - (3 * ((~x + ~2) + (x mod 8))))
A161639: 8 9 10 11 12 13 14 15 40 41 42 43 44 45 46 47
((x + 2) - (3 * ((~x + (x mod 8)) div 2)))
A037344: 2 3 4 5 6 7 8 9 22 23 24 25 26 27 28 29
(((x * (((1 - (x div 2)) * (x div 2)) div 2)) div 2) mod 3)
A241910: 0 0 0 0 1 0 0 1 0 0 1 2 0 1 0 1
(((x + 1) div 2) - (((x * ((x div 2) mod 2)) div 2) div 3))
A335967: 0 1 1 2 2 3 2 3 4 5 4 5 6 7 5 6
((3x2 + 7x + 6) - (2 * (x mod 2)))
A199705: 6 14 32 52 82 114 156 200 254 310 376 444 522 602 692 784
(12x2 + 10x + ~30)
A277982: ~30 ~8 38 108 202 320 462 628 818 1032 1270 1532 1818 2128 2462 2820
(((x + (x mod 2)) div 5) + ((x + 2) div 3))
A156261: 0 1 1 1 2 3 3 4 4 5 6 6 6 7 7 8
((x div (4 + (x div 4))) + ((x + 2) div 3))
A189672: 0 1 1 1 2 3 3 4 4 4 5 5 5 6 7 7
(x - ((x + 1) div (8 - ((x + 2) div 3))))
A025528: 0 1 2 3 4 4 5 6 7 7 8 8 9 9 9 10
((2x + ((2 + (x div 4)) mod 4)) div 3)
A054633: 0 1 2 2 3 4 5 5 5 6 6 7 8 9 9 10
(x + (3 * (2x + ((x div 2) mod 2))) - (x mod 2))
A184549: 0 6 17 23 28 34 45 51 56 62 73 79 84 90 101 107
(6x + (2x div 7))
A246295: 0 6 12 18 25 31 37 44 50 56 62 69 75 81 88 94
(6x + (2x div 9))
A277723: 0 6 12 18 24 31 37 43 49 56 62 68 74 80 87 93
((6x + 2) - ((~x + 1) div (1 + (x div 2))))
A274290: 1 8 15 21 27 34 40 46
(3x + (2x mod 3) - (x div 3))
A047477: 0 5 7 8 13 15 16 21 23 24 29 31 32 37 39 40
((1 - (2 * ((x div 3) mod 2))) * (2x mod 3))
A132798: 0 2 1 0 ~2 ~1 0 2 1 0 ~2 ~1 0 2 1 0
((6x2 + ~6x) + ((x2 + x) div 2))
A051867: 0 1 15 42 82 135 201 280 372 477 595 726 870 1027 1197 1380
(3 * ((9x + 6) - (x div 2)))
A002798: 18 45 69 96 120 147 171 198 222 249 273 300 324 351 375 402
(x div (2 - ((((~x + 1) mod 4) - (x div 2)) div 3)))
A141070: 0 0 1 1 1 1 3 2 2 2 3 3 3 3 3 3
((1 + (((x + ~1) div 2) div 3)) * ((x div 2) div 3))
A008737: 0 0 0 0 0 0 1 2 2 2 2 2 4 6 6 6
((7x + 7) + ((x div 2) div 3))
A187395: 7 14 21 28 35 42 50 57 64 71 78 85 93 100 107 114
(x - (((x + ~2) div (2 + (x div 2))) + ((x div 2) div 3)))
A261345: 1 2 2 3 4 5 5 5 6 7 8 9 9 10 11 12
((1 - (2 * ((x div 2) mod 2))) * (1 - ((x div 2) mod 3)))
A309970: 1 1 0 0 ~1 ~1 ~1 ~1 0 0 1 1 1 1 0 0
((((x2 + 2x) div 5) + (x mod 2)) mod 3)
A178146: 0 1 1 1 1 2 0 1 1 2 0 2 0 1 2 1
((x2 + 2) - (((~x3 + x) div 2) div 3))
A201363: 2 3 7
A074742: 2 3 7 15 28 47 73 107 150 203 267 343 432 535 653 787
((~x2 + 2x) - (((~x3 + x) div 2) div 3))
A050407: 0 1 1 1 2 5 11 21 36 57 85 121 166 221 287 365
(x3 - (((~x3 + x) div 2) div 3))
A004126: 0 1 9 31 74 145 251 399 596 849 1165 1551 2014 2561 3199 3935
(~3 + compr(\x.(1 - (x mod (1 + (x div 5)))),x))
A183858: 2 4 6 7 8 10 11 12 14 15 16 18 19 20 21 22
((x * (~1 + (x2 div (x + 5)))) mod 3)
A295819: 0 2 1 0 0 2 0 0 0 0 2 0 0 2 0 0
(1 - ((~x + ((x + ~1) mod (1 + (x div 3)))) div 3))
A209082: 1 2 2 2 2 3 3 4 4 4 4 4 5 5 5 6
((x + 3) + (x div (3 + ((x div 2) div 3))))
A175968: 3 4 5 7 8 9 10 11 13 14 15 16 17 18 19 21
(x - (((~x + ~1) + (x mod (~2 + ((x div 2) mod 2)))) div 3))
A285962: 1 2 3 5 6 8 9 10 11 13 14 15 17 18 19 21
((x + ((4 * (x div 3)) div 3)) mod 3)
A053838: 0 1 2 1 2 0 2 0 1 1 2 0 2 0 1 0
(((~x2 + 1) mod (x + 12)) mod 3)
A137993: 1 0 2 1 1 1 1 0 2 1 2 0 1 1 1 1
((2x + 2) - ((~x + ((x + ~2) div 3)) div 3))
A248106: 3 5 7 9 12 14 16 18 20 23 25 27 29 32 34 36
((2x3 + 9x2 + 13x + 4) div 3)
A112524: 1 9 27 59 109 181 279 407 569 769 1011 1299 1637 2029 2479 2991
((x4 + 4x3 + 5x2 + 5x + 4) div 3)
A100188: 1 6 27 84 205 426 791 1352 2169 3310 4851 6876 9477 12754 16815 21776
((2x + 2) - ((~x + ((x div 2) div ~2)) div 3))
A003153: 2 5 7 10 12 14 17 19 22 24 27 29 31 34 36 39
((x + 3) + (((~x + 1) div 9) mod 2))
A243293-A181590: 3 4 6 7 8 9 10 11 12 13 14 14 15 16 17 18
((x + 3) + (2 * (x - ((~x + (x mod 2)) div 3))))
A026368: 3 6 11 14 19 22 25 28 33 36 41 44 47 50 55 58
((x + 3) + (2 * (4 + (x div 8))))
A119247: 11 12 13 14 15 16 17 18 21 22 23 24 25 26 27 28
(3 * (x + (2 * (x2 div 16))))
A161338: 0 3 6 9 18 21 30 39
((x + 3) + (2x div (4 + (x div 4))))
A275481: 3 4 6 7 8 10 11 12 13 15 16 17 18 19 21 22
((x + ((x + (x2 mod 3)) div 4)) mod 3)
A214332: 0 1 2 0 2 0 1 0 1 2 0 2 0 1 2 0
((2x + 2) - ((~x + ((~x + 2) div 4)) div 3))
A082845: 2 5 7 10 12 14 17 19 22 24 26 29 31 34 36 39
((x + ((x3 + 6x2 + 12x + 8) div 2)) div 3)
A110611: 1 4 11 21 37 58 87 123 169 224 291 369 461 566 687 823
(9x2 + 39x + 24)
A304374: 24 72 138 222 324 444 582 738 912 1104 1314 1542 1788 2052 2334 2634
(x - (((~x + 2) * (1 + ((x2 + ~x) div 2))) div 3))
A192225: 0 1 2 5
A290464: 0 1 2 5 9 16 28
((x + 2) - (((~x + 1) - ((x * (x div 2)) mod 2)) div 3))
A135674: 2 3 5 6 7 9 10 12 13 14 15 17 18 19 21 22
((2x + 2) - ((~x + ((x * (x div 2)) mod 2)) div 3))
A304498: 2 5 7 9 12 14 16 18 21 23 26 28 30 33 35 37
(1 + (x2 div (1 + ((x + 1) div 2))) - (x div 3))
A262355: 1 1 3 3 5 6 8 8 11 11 14 15
(4 div (5 + (x mod 2) - (x div 3)))
A035685: 0 0 0 0 1 0 1 1 1 1 2 1 4 2 4 4
(1 + (((~2 + (x mod 3)) mod (x + 2)) + (x div 3)))
A188146: 1 3 1 5 7 2 9 11 3 13 15 4 17 19 5 21
((x + 4) + (x div 3) - ((~x + 2) div (x + 1)))
A224779: 2 5 6 9 10 11 13 14 15 17 18 19 21 22 23 25
(((3 * ((x div 2) div 3)) div 2) + (x div 3))
A073750: 0 0 0 1 1 1 3 3 3 4 4 4 7 7 7 8
(4 + (((x + (x mod 2)) div 3) + (x div 3)))
A116446: 4 4 4 6 6 7 8 8 8
((x + 1) div (2 + (((x div ~2) mod 2) + (x div 3))))
A294602: 0 0 1 1 1 1 1 2 2 1 1 2 2 2 2 2
(x - (4x div (8 + (x div 3))))
A067022: 0 1 1 2 3 3 4 5 5 6 7 7 8 9 10 11
((2 * ((2x + 4) - (x mod 4))) + (x div 3))
A335013: 8 10 12 15 25
((x + 4) - ((x div 3) + ((~x + 2) div (x + 2))))
A196112: 3 5 6 7 8 9 9 10 11 11 12 13 13 14 15 15
(x + (x div 3) - (2 * (~x + ((x + ~1) div 3))))
A047402: 2 3 6 10 11 14 18 19 22 26 27 30 34 35 38 42
(x + (x div 3) - (2 * (~x + ((x + ~2) div 3))))
A047440: 2 5 6 10 13 14 18 21 22 26 29 30 34 37 38 42
((6x + 3) + ((x mod 2) + (x div 3)))
A063231: 3 10 15 23 28 35 41 48 53 61 66 73 79 86 91 99
(((1 + (x div (~2 + (x mod 2)))) mod 3) - (x mod 3))
A101675: 1 ~1 ~2 1 1 0 1 ~1 ~2 1 1 0 1 ~1 ~2 1
((2x + 4) + (2x div 3) - (x mod 3))
A146968: 4 5 7
A047491: 4 5 7 12 13 15 20 21 23 28 29 31 36 37 39 44
((x + 4) - ((x * (~x + (x div 3))) div 3))
A062002: 4 6 8 9 12 16 18
((x + 1) + (((x * (x div 2)) mod 2) + (x2 div 3)))
A222011: 1 2 4 8
A292550: 1 2 4 8 10 14 19
((((~x + 1) * (1 + (x div 2))) div 2) + (x2 div 3))
A325690: 0 0 0 1 0 2 2 4 3 7 6 10 9 14 13 19
((7x + 2) + (x2 mod 3))
A304809: 2 10 17 23 31 38 44 52 59 65 73 80 86 94 101 107
((3x3 + ~3x) + ((x2 + x) div 2))
A172082: 0 1 21 78 190 375 651 1036 1548 2205 3025 4026 5226 6643 8295 10200
((x * ((x + 1) div 2)) - ((~x3 + x) div 3))
A289179: 0 1 4 14 28 55 88 140 200 285 380 506 644 819 1008 1240
((x + 1) - ((~x + (x mod 11)) div 2))
A033000: 1 2 3 4 5 6 7 8 9 10 11 18 19 20 21 22
(1 + ((9x2 + 5x) div 2))
A064225: 1 8 24 49 83 126 178 239 309 388 476 573 679 794 918 1051
(1 + ((x + (x2 div (1 + (2x div 3)))) div 2))
A082463: 1 2 3 4 5 6 7 9 10
A300064-A039217: 1 2 3 4 5 6 7 9 10 11 13 14 15 16 17 18
((x + 1) - ((~x + ((x div 2) div 7)) div 2))
A225647: 1 3 4 6 7
A026322: 1 3 4 6 7 9 10 12 13 15 16 18 19 21 22 23
(1 + ((x + ((x + 2) mod (1 + (x mod 6)))) div 2))
A188666: 1 2 2 3 3 4 4 5 5 7 7 7 7 8 8 9
(1 + ((x + ((x3 div 2) div 5)) div 2))
A094055: 1 1 2 3 6 9 14 21
((x + 1) - ((~x + (((x + 2) div 3) mod 3)) div 2))
A188092: 1 2 4 5 6 8 9 12 13 15 16 17 19 20 21 23
((2x + 1) - ((~x + ((~1 + (x div 2)) div 3)) div 2))
A184978: 2 4 6 9 11
A186343: 2 4 6 9 11 14 16 19 21 23 26 28 31 33 35 38
((x + 1) - (2 * (~x + (((~x + ~2) + (x mod 2)) div 3))))
A285422: 3 6 11 14 17 20 25 28 33 36 39 42 47 50 55 58
(1 + ((x * ((2x + 4) - (2x div 3))) div 2))
A058759: 1 4 8 13
A335445: 1 4 8 13 21 28 37 50
((x + 1) - ((~x2 + x) div ((x + 2) + (x div 3))))
A001614: 1 2 4 5 7 9 10 12 14 16 17 19 21 23 25 26
(1 + (2 * ((x2 + x) + ((1 + (x div 2)) * (x div 2)))))
A220082: 1 5 17 29 53 73 109 137 185 221 281 325 397 449 533 593
(1 + (x mod 2) - (2 * (~x + (x mod 10))))
A167679: 1 2 1 2 1 2 1 2 1 2 21 22 21 22 21 22
(x - (x mod (1 + (2 * (~x + (x mod 10))))))
A103303: 0 1 2 3 4 5 6 7 8 9
A087052: 0 1 2 3 4 5 6 7 8 9 19 19 19 19 19 19
(1 + (2 * (x + (((~2 + ((x div 2) mod 2)) mod (x + 1)) div 2))))
A125667: 1 3 7 9 11 15 19 21 23 27 31 33 35 39 43 45
((x + 1) - ((~x + ((x mod (2 + (x div 3))) mod 2)) div 2))
A287379: 1 2 4 6 7 9 10 11 13 15 16 17 19 20 22 23
(1 + ((x + (((~x + 2) mod (2 + (x div 4))) mod 2)) div 2))
A261224: 1 2 2 3 3 3 4 5 5 6 6 7 7 7 8 8
((x + 1) - ((~x + (((x + (x div 2)) div 4) mod 2)) div 2))
A285950: 1 3 4 5 7 8 10 12 13 14 16 18 19 21 22 23
(1 + ((x + (((~2x + 4) mod (2 + (x div 2))) div 2)) div 2))
A086841-A004001: 1 1 2 2 3 4 4 4 5 6 7 7 8 8 8 8
((x + 1) - ((~x + ((~x + (x mod 3)) div 4)) div 2))
A292652: 1 3 4 6 8 9 11 13 14 16 18 19 21 22 24 26
(1 + ((x * (x div 2)) div ((x + 2) + ((~x + 1) mod 4))))
A280168-A025774-A001156: 1 1 1 1 2 2 2 2 3 4 4 4 5 6 6 6
((2x + 1) - (x2 div ((x + 2) + (x div 4))))
A225647: 1 3 4 6 7
A256827-A184010-A175139: 1 3 4 6 7 8 9 11 12 13 14 15 17 18 19 20
((~x + 2) + (x2 mod (1 + (2 * (x + (x div 4))))))
A248503: 2 2 4 1 3 9
((~2x + 1) mod (1 + ((x + (x2 div 4)) div 2)))
A161834: 0 0 1 1 3 3 5 7 11 13
(1 + ((x + (((x2 div 3) + (x div 2)) div 2)) div 2))
A085680: 1 1 2 3 4 6 7 9 11 13 15 17 20 23 26 29
(1 + (2 * (x + ((((x div 4) mod 2) + (x div 2)) div 2))))
A285516: 1 3 5 7 11 13 17 19 21 23 25 27 31 33 37 39
(1 + ((x + (((2 + (x2 div 2)) * (x div 2)) div 2)) div 2))
A072606: 1 1 3 4 8 10 19 24
(1 + (2 * (x + ((x + ((x mod (1 + (x div 2))) div 2)) div 2))))
A130568: 1 3 7 9 13 17 19 23 25 29 33 35 39 43 45 49
((2x2 + 4x + 1) * ((x2 + 3x + 2) div 2))
A076454: 1 21 102 310 735 1491 2716 4572 7245 10945 15906 22386 30667 41055 53880 69496
(1 + ((x * ((x2 + 5x + 4) - (x div 2))) div 2))
A163983: 1 6 18 41 77
(1 + (2 * (x + (((2x + 2) + (x div 2)) * (x div 2)))))
A273367: 1 3 19 25 57 67 115 129 193 211 291 313 409 435 547 577
(((x2 + 4x + 4) div 2) mod (1 + ((x + (x div 2)) div 2)))
A338227: 0 0 0 0 2 0 2 4 1 4 0 3 8 2 7 0
(((1 + (x div 3)) div 2) div (1 + ((x * (x div 2)) mod 2)))
A338236: 0 0 0 0 1 1 1 0 1 2 2 1 2 2 2 1
(~1 + ((x + 2) * ((x + 1) - (x mod 9))))
A077726: 1 2 3 4 5 6 7 8 9 109 119 129 139 149 159 169
(1 + compr(\x.(1 - (x mod (1 + (x mod 6)))),(x + 2)))
A091242: 4 5 6 8 9 10 12 14 15 16 17 18 20 21 22 23
(1 + ((x + 2) * ((1 + (x mod 8)) mod (x + 1))))
A250665: 1 1 1 1 1 1 1 1 11 23 37 53 71 91 113 137
(1 + ((2 * ((x + 1) mod 10)) mod (x + 2)))
A156207: 1 2 3 4 5 6 7 8 9 1 3 5 7 9 11 13
(1 + ((x + 2) * (x mod (x - ((x + ~1) mod 8)))))
A250667: 1 1 1 1 1 1 1 1 1 1 13 27 43 61 81 103
(2 div (1 + ((2 - ((~x + 1) mod 8)) mod (x + 2))))
A095683: 1 0 0 1 0 0 0 2 1 0 0 0 0 0 0 2
(1 + ((4x + (x2 div 4)) div (x + 2)))
A249728-A000267: 1 2 3 3 4 4 5 5 5 6 6 6 7 7 7 7
(8x3 + 36x2 + 40x + 12)
A192848: 12 96 300 672 1260 2112 3276 4800 6732 9120 12012 15456 19500 24192 29580 35712
((x + 3) * (((x2 + 3x + 2) div 2) div 3))
A050188: 0 4 10 18 35 56 81 120 165 216 286 364 450 560 680 810
(x - (((x + ~2) - (x2 div 3)) div (x + 3)))
A082463: 1 2 3 4 5 6 7 9 10
A070115: 1 2 3 4 5 6 7 9 10 11 12 14 15 16 18 19
((1 + (2x * (1 + (2 mod (x + 1))))) div (x + 3))
A130256: 0 0 2 3 3 3 4 4 4 4 4 4 4 4 5 5
((x + 3) * ((x2 + 3x + 2) div (1 + (x mod 2))))
A033931: 6 12 60 60 210 168 504 360 990 660 1716 1092 2730 1680 4080 2448
((4x + 4) - ((x2 + ~1) div (x + 3)))
A212452: 5 8 12 15 18 21 25 28 31 34 37 40 43 46 49 52
((x + 3) * (((x2 div 3) + (x mod 2)) div 2))
A330197: 0 0 0 12 14 32 54 80 110 168 208 280 360 448 544 684
((3x + 4) - ((~2x + 2) div (x + 3)))
A212447: 4 7 11 14 17 20 24 27 30 33 36 39 42 45 48 51
((x2 + 3x) * ((x2 + ~5x + 6) div 2))
A060784: 0 4 0 0 28 120 324 700 1320 2268 3640 5544 8100 11440 15708 21060
(x4 + 7x3 + 15x2 + 10x + 1)
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(1 + ((x + ((x3 + 2x) div 3)) div (x + 2)))
A062485: 1 1 2 3 5 8 11 15 19 24 30 36 43 51 59 68
(1 + ((x * (6 + (x div 3))) div (x + 2)))
A278375: 1 3 4 5 5 6 7 7 7 8 8 8 9 9
((2x + 1) + (2x2 div 7))
A154287: 1 3 6 9 13 18 23 29 35 42 49 57 66 75 85 95
((2x + 1) + ((x2 + (x mod 2)) div 5))
A233779: 1 3 5 9 12 16
A243205: 1 3 5 9 12 16 20 25 29
(x2 div ((2x + ~1) + ((x div 4) mod 3)))
A029865: 0 1 1 1 2 2 3 3 3 4 4
A194237: 0 1 1 1 2 2 3 3 3 4 4 5 6 6 7 7
((2x + 1) + ((x2 div 4) * (~1 + (x div 2))))
A182981: 1 3 5 7 13 17 31 39
((2x + 1) + (x mod 2) - (x div ~8))
A188191: 1 5 6 9 10 13 14 17 18 22 23 26 27 30 31 34
((2x + 1) + (((x + 1) div 7) mod 2))
A327209: 1 3 5 7 9 11 14 16 18 20 22 24 26 27 29 31
((2x + 1) + ((x - (x div 7)) div 2))
A303590: 1 3 6 8 11 13 16 18 20 23 25 28 30 33 35 37
((2x + 1) + ((2x div 9) mod 2))
A291154: 1 3 5 7 9 12 14 16 18 19 21 23 25 27 30 32
((2x + 1) + ((x2 div 12) mod 2))
A189220: 1 3 5 7 10 11 14 15 18 19 21 23 25 27 29 31
((2x + 1) + (((x - ((x div 2) div ~2)) div 2) mod 2))
A190335: 1 3 6 7 9 12 13 15 18 20 21 24 26 27 30 32
((2x + 1) + (((x + 2) div ~7) mod 2))
A327210: 2 4 6 8 10 12 13 15 17 19 21 23 25 28 30 32
((2x + 1) + ((~x + ((x div 2) mod 4)) div 4))
A241071: 1 2 4 6 8 10 12
A336735: 1 2 4 6 8 10 12 14 15 16 18 20 22 24 26 28
((2x + 1) + ((x + ((x div 2) div 5)) div 2))
A139477: 1 3 6 8 11 13 16 18 21 23 26 29 31 34 36 39
((2x + 1) + ((x + ((x mod (2 + (x div 2))) div 2)) div 2))
A090848: 1 3 6 8 11 13 16 19 21 24 26 29 32 34 37 40
(82x + 41)
A232100: 41 123 205 287 369 451 533 615 697 779 861 943 1025 1107 1189 1271
(10x3 + 15x2 + 7x + 1)
A005904: 1 33 155 427 909 1661 2743 4215 6137 8569 11571 15203 19525 24597 30479 37231
(12x3 + 18x2 + 8x + 1)
A193228: 1 39 185 511 1089 1991 3289 5055 7361 10279 13881 18239 23425 29511 36569 44671
((2x + 1) * (1 + (3 * ((x2 + x) div 2))))
A063491: 1 12 50 133 279 506 832 1275 1853 2584 3486 4577 5875 7398 9164 11191
(4x4 + 12x3 + 9x2 + ~1)
A123197: ~1 24 195 728 1935 4224 8099 14160 23103 35720 52899 75624 104975 142128 188355 245024
(8x3 + 28x2 + 30x + 9)
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(16x3 + 24x2 + 10x + 1)
A193250: 1 51 245 679 1449 2651 4381 6735 9809 13699 18501 24311 31225 39339 48749 59551
((~1 + (2 * (~1 + (4 * (x mod 2))))) mod (2x + 1))
A266595: 0 2 2 5 6 5 10 5 14 5 18 5 22 5 26 5
(22x2 + 13x + 1)
A033575: 1 36 115 238 405 616 871 1170 1513 1900 2331 2806 3325 3888 4495 5146
(16x3 + 12x2 + 4x + 1)
A046142: 1 33 185 553 1233 2321 3913 6105 8993 12673 17241 22793 29425 37233 46313 56761
(4x4 + ~6x3 + 2x2 + 3x)
A344907: 0 3 30 189 684 1815 3978 7665 13464 22059 34230 50853 72900 101439 137634 182745
((2x + 1) + (x2 div (x + 12)))
A175312: 1 3 5 7 10 12 15 17 20 22 25 28 31 33 36 39
((2x + 1) + ((~x2 + x) div (x + 8)))
A317391: 1 3 4 6 8 9 10 12 13 14 16 17 18 19 20 21
((x * (x2 - (x2 div (x + 2)))) div (2x + ~1))
A152125: 0 1 2 4 8 12 17 23 30 39
(46x2 + 1)
A158632: 1 47 185 415 737 1151 1657 2255 2945 3727 4601 5567 6625 7775 9017 10351
(66x2 + 1)
A158689: 1 67 265 595 1057 1651 2377 3235 4225 5347 6601 7987 9505 11155 12937 14851
(62x2 + 1)
A158676: 1 63 249 559 993 1551 2233 3039 3969 5023 6201 7503 8929 10479 12153 13951
((x2 + 2x + 1) - ((1 + (x div 3)) * (x div 2)))
A122224: 1 4 8 14 21 32 40
(1 + (((5x + 5) * (x mod 2)) + (x div 2)))
A176592: 1 11 2 22 3 33 4 44 5 55 6 66 7 77 8 88
(1 + (((6x + 6) * (x mod 2)) + (x div 2)))
A176593: 1 13 2 26 3 39 4 52 5 65 6 78 7 91 8 104
(x div (1 + (x2 mod ((3x + 3) + (x div 2)))))
A328037: 0 0 0 0 0 0 0 0 2 0 0 0 1 0 0 2
(1 + (((x + 1) * (x + (2 * (x + (x mod 2))))) + (x div 2)))
A164576: 1 11 20 46 63 105 130 188 221 295 336 426 475 581 638 760
(1 + ((4x div (4 + (x div 2))) + (x div 2)))
A258632: 1 2 3 4 5 6 7 8 9 9 10 10 11 12 13 13
(1 + ((4 * (x + (3 * (x mod 2)))) + (x div 2)))
A166524: 1 17 10 26 19 35 28 44 37 53 46 62 55 71 64 80
((x2 + 2x + 1) - ((~2x + (x div 2)) * (x div 2)))
A212965: 1 4 12 21 37 52 76 97 129 156 196 229 277 316 372 417
((x - ((x + 1) mod 9)) mod (1 + (x div 2)))
A253315: 0 0 1 1 2 2 3 3 3 3 2 2 1 1 0 0
((x - (x mod (~1 - (x div 4)))) div (1 + (x div 2)))
A139355: 0 1 1 1 1 2 1 2 1 1 2 2 1 2 2 2
((0 - ((x + 1) div (1 + (x div 4)))) mod (1 + (x div 2)))
A308318: 0 0 1 0 1 0 1 0 2 2 3 2 4 4 5 4
((3 + (x2 mod (2x + ~1))) * (1 + (x div 2)))
A055057: 3 3 8 14 15
(2x - (~11 * (1 + (x div 2))))
A295340: 11 13 26 28 41 43 56 58 71 73 86 88 101 103 116 118
((x div (~2 - (x2 mod 3))) mod (1 + (x div 2)))
A156643-A071635: 0 0 1 0 1 1 1 1 2 0 2 2 1 2 3 0
(~1 + ((x + 1) * (2 + ((x2 + 2x) div 2))) - (x div 2))
A246697: 1 5 16 34 67 111 178 260 373 505 676 870 1111 1379 1702 2056
(x + (((x div 2) div 3) + (4 mod (1 + (x div 2)))))
A062877: 0 1 2 3 5 6 7 8 13 14 15 16 18 19 20 21
(((x3 + 2x2 + 4x + 8) div 2) * (1 + (x div 2)))
A271676: 4 7 32 64
((x + 15) - (2 div (1 + (x div 2))))
A060275: 13 14 16 17 19 20 21 22 23 24 25 26 27 28 29 30
((~x2 + 1) + ((2x + (x div 2)) * (1 + (x div 2))))
A338041: 1 2 7 6 15 12 25 20 37 30 51 42 67 56 85 72
((x + ((x mod (2 + (x div 4))) div 2)) div (1 + (x div 2)))
A305501: 0 1 1 1 1 2 1 1 1 1 1 2 1 2 2 1
((x + 1) + ((8 * (x + (x mod 2))) + (x div 2)))
A113541: 1 18 20 37 39 56 58 75 77 94 96 113 115 132 134 151
((5x + 2) mod ((x2 + 1) + (x div 2)))
A039631: 0 1 0 6 3 27
(1 + ((4x2 + 4x + ~5) * (x mod 2)))
A269906: 1 4 1 44 1 116 1 220 1 356 1 524 1 724 1 956
(~1 + (3 * (((x + ~2) div 3) mod 2)) - (x mod 2))
A087204: 2 1 ~1 ~2 ~1 1 2 1 ~1 ~2 ~1 1 2 1 ~1 ~2
(1 + ((x mod (~1 + (x div ~3))) mod 2) - (x mod 2))
A194321-A194309: 1 1 1 1 1 1 1 1 1 1 1 0 2 1 1 1
(1 + (((x mod (1 + (4 mod (x + 1)))) mod 2) + (x mod 2)))
A198333: 1 2 1 2 1 2 2 2 2 2 1 3 1 3 1 2
(1 + (((x mod (~1 + (2 * (x div 4)))) mod 2) + (x mod 2)))
A099305: 1 2 1 2 1 2 1 2 1 2 2 2 1 3 1 2
(~1 + (((x - (x div (1 + (x mod 4)))) mod 2) + (x mod 2)))
A156706: ~1 1 ~1 1 ~1 1 ~1 0 ~1 1 0 1 ~1 1 ~1 0
(x div (3 + (x div (3 + (x mod 2))) - (x mod 2)))
A211262: 0 0 0 1 1 1 1 2 1 2 1 2 1 2 2 3
(1 + ((3 * (x div 5)) div 2) - (x mod 2))
A344245: 1 0 1 0 1 1 2 1 2 1 4 3 4 3 4 4
((3x2 + 12x + 11) div (1 + (x mod 2)))
A188386: 11 13 47 37 107 73 191 121 299 181 431 253 587 337 767 433
((1 + ((x div (~2 + (x mod ~2))) mod 2)) * (1 + (x mod 2)))
A135513: 1 4 2 4 1 2 2 4 1 4 2 2 1 4 2 4
((1 + ((x + ((x div 3) mod 2)) div 2)) div (1 + (x mod 2)))
A290636: 1 0 2 1 3 2 4 2 5 3 6 3 7 3 8 4
(2 div ((2 + ((x + 2) mod 5)) div (1 + (x mod 2))))
A333325: 0 1 0 2 0 1 0 0 1 2 0 1 0 2 0 1
(((x + 2) div (2 + (3 * (x mod 2)))) * (1 + (x mod 2)))
A289435: 1 0 2 2 3 2 4 2 5 4 6 4 7 6 8 6
(((((x + ~1) mod 3) + (x div 2)) div 2) div (1 + (x mod 2)))
A029223: 1 0 1 0 1 0 2 0 2 1 2 1 4 1 4 2
(2x2 + 71)
A127316: 71 73 79 89 103 121 143 169 199 233 271 313 359 409 463 521
(31 div (2x2 + 1))
A145584: 31 10 3 1
(1 + compr(\x.(~1 + (x mod (1 + ((x + ~1) mod 8)))),x))
A344974: 1 2 3 4 5 6 7 8 9 10 11 13 16 17 18 19
(1 + compr(\x.((x + 1) mod (1 + (x mod 9))),x))
A235591-A064807: 1 2 3 4 5 6 7 8 9 10 12 18 19 20 21 24
(5x2 + 31x + 1)
A172193: 1 37 83 139 205 281 367 463 569 685 811 947 1093 1249 1415 1591
(1 + compr(\x.(~1 + (3x mod (1 + (x div 4)))),x))
A261888: 1 2 3 4 5 6 7 8 9 10 11 12 13 16 18 21
(5x3 + 5x2 + 3x + 1)
A064096: 1 14 67 190 413 766 1279 1982 2905 4078 5531 7294 9397 11870 14743 18046
((x + 1) + (3x2 div 7))
A025717-A025702: 1 2 4 7 11 16 22 29 36 44 53 63 74 86 99 112
((x + 1) + ((x2 + (x div 2)) div 7))
A071423: 1 2 3 5 7 9 12 15 18 22 26 30 34 39 44 49
(3x mod ((x + 1) + (x div 7)))
A065651: 0 1 0 1 2 3 4 3 4 5 6 7 8 9 8 9
(1 + compr(\x.(2 - ((x div 2) div (1 + (x mod 6)))),x))
A194408: 7 13 14 15 19 20 21 22 23 25 26 27 28 29 30 31
(1 + (x * ((x + 2) - ((x + 1) mod 9))))
A044910: 1 2 3 4 5 6 7 8 81 91 101 111 121 131 141 151
((x + 1) + (((x2 + 4x + 4) div 2) div 5))
A130798: 1 2 4 6 8 10 13 16 19 22 25 28 32 36 40 44
((5x + 1) + ((1 + (x div 2)) mod 4))
A209886: 2 7 13 18 24 29 31 36 42 47 53 58 64 69 71 76
(25x2 + 25x + 4)
A001545: 4 54 154 304 504 754 1054 1404 1804 2254 2754 3304 3904 4554 5254 6004
((x + 1) + ((x * (x div 8)) div 5))
A317717-A076487: 1 2 3 4 5 6 7 8 10 11 13 14 15 16 17 19
((x + 1) + (x div (2 - (x div (~1 + ((~x + 2) div 4))))))
A187945: 1 2 3 4 6 7 8 9 10 11 12 14 15 16 17 19
((x + 1) + (3 * ((x + 1) div 7)))
A285469-A037476: 1 2 3 4 5 6 10 11 12 13 14 15 16 20 21 22
((x + 1) + (3 * ((x mod (1 + (x div 2))) div 3)))
A032971: 1 2 3 4 5 6 7 11 12 13 14 15 16 20 21 22
(1 + compr(\x.(((~x + (x * (x mod 2))) div 3) mod 3),x))
A263800: 1 2 4 6 8 9 10
A153184: 1 2 4 6 8 9 10 12 14 16 17 18 19 20 22 24
(13x2 + 10x + 1)
A161587: 1 24 73 148 249 376 529 708 913 1144 1401 1684 1993 2328 2689 3076
((x + 1) + (3 * (4 + (x div 8))))
A178402: 13 14 15 16 17 18 19 20 24 25 26 27 28 29 30 31
((x + 1) + (3 * (x div (4 + (x div 4)))))
A069117: 1 2 3 4 5 9 10 11 12 13 14 15 16 17 21 22
((x + 1) + ((2 * ((x - (x div 4)) div 2)) div 3))
A051705: 1 2 3 4 5 7 8 10 11 12 13 14 15 17 18 20
((x + 1) + ((x2 + x) div 24))
A184105: 1 2 3 4 5 7 8 10 12 13 15 17 19 21 23 26
((x + 1) + (3 * ((x + (x div 2)) div 8)))
A032970: 1 2 3 4 5 6 10 11 12 13 14 18 19 20 21 22
((x + 1) + (x2 div (x + 11)))
A248635: 1 2 3 4 6 7 9 10 12 14 15 17 19 21 22 24
(1 + (x * ((x + 2) - ((x + 1) mod 12))))
A044913: 1 2 3 4 5 6 7 8 9 10 11 144 157 170 183 196
(9x3 + 15x2 + 7x + 1)
A100165: 1 32 147 400 845 1536 2527 3872 5625 7840 10571 13872 17797 22400 27735 33856
((2x div ~7) mod (3x + 1))
A121384: 0 3 6 9 11 14 17 20 22 25 28 30 33 36 39 41
(36x2 + 36x + 8)
A144410: 8 80 224 440 728 1088 1520 2024 2600 3248 3968 4760 5624 6560 7568 8648
(36x2 + 60x + 16)
A144449: 16 112 280 520 832 1216 1672 2200 2800 3472 4216 5032 5920 6880 7912 9016
((x + 1) + ((x2 + (x2 div 4)) div 3))
A025727: 1 2 4 7 11 16 22 28 35 43 52 62 73 84 96 109
((x + 1) + ((x * (x2 div 3)) mod (2x + 1)))
A175135: 1 2 5 6 7 13
(x2 + x + 41)
A273756-A202018-A155884-A005846: 41 43 47 53 61 71 83 97 113 131 151 173 197 223 251 281
(3x4 + 6x3 + 7x2 + 4x + 1)
A243201: 1 21 133 481 1281 2821 5461 9633 15841 24661 36741 52801 73633 100101 133141 173761
(x5 + 5x4 + 11x3 + 14x2 + 10x + 4)
A123650: 4 45 280 1105 3276 8029 17200 33345 59860 101101 162504 250705 373660 540765 762976 1052929
((x3 + x + 1) * ((x3 + ~x) div 2))
A085742: 0 0 33 372 2070 7860 23415 58968 131292 266040 500445 886380 1493778 2414412 3766035 5696880
(x mod ((x + ~1) + ((x div (1 + ((~x + 1) mod 3))) mod 2)))
A336922: 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0
(1 + (x * ((x mod (~1 + (x mod (~1 + ((~x + 1) div 2))))) mod 2)))
A135683: 1 1 1 4 1 6 1 8 9 10 1 12 1 14 15 16
((x + 1) + (2 * (4x div 7)))
A276883: 1 2 5 6 9 10 13 16 17 20 21 24 25 28 31 32
(1 + compr(\x.(((x2 + ~2x) div 7) mod 2),x))
A283777: 1 3 4 6 9 12 14 15 17 18 20 23 26 28 29 31
(1 + compr(\x.(~2 + ((x + ~1) mod (1 + (x mod 6)))),x))
A332485: 1 2 3 4 7 8 9 10 13 14 15 16 17 19 20 21
((x + 1) + ((x2 mod (~1 + (2 * (x div 3)))) div 2))
A003964: 1 2 3 4 5 6 7 8 9 10 11 12 15 14 15 16
(1 + compr(\x.((x mod (1 + (8 * (x mod 2)))) mod 2),x))
A194377-A007957: 1 3 5 7 9 10 11 12 13 14 15 16 17 18 19 21
((x + 1) + ((x mod (~1 + (x mod ~7))) mod 2))
A114707: 1 2 3 4 5 7 7 8 9 11 11 13 13 15 15 16
((x + 1) + ((x - (((~x + 2) div 2) div 5)) div 2))
A247000: 1 2 4 6 7 9 10 12 13 15 16 18 19 21 23 24
((x + 1) + (2 * ((2 * (x + (x div 2))) div 5)))
A288552: 1 2 5 6 9 10 13 16 17 20 23 24 27 28 31 32
(1 + (x * ((x + 2) - ((x + 1) mod 10))))
A044911: 1 2 3 4 5 6 7 8 9 100 111 122 133 144 155 166
((x + 1) + ((x - ((x + 1) mod (1 + (x mod 4)))) div 2))
A187351: 1 2 4 5 7 8 9 11 13 14 15 17 19 20 22 23
((x + ~1) + (2 * (x - ((x + ~1) div (3 + (x div 2))))))
A045930: 1 2 5 8 11 14 17 18 21 24 27 30 33 36 39 42
(1 + (x * ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2)))
A304404-A290480: 1 1 1 1 1 6 1 1 1 10 1 12 1 14 15 1
(1 + compr(\x.(~2 + ((x + 1) mod (1 + (x div (2 + (x mod 2)))))),x))
A067319: 1 2 3 4 5 6 8 10 12
A141341: 1 2 3 4 5 6 8 10 12 18 24 30
((x + 1) + ((3 * (x div 7)) div 2))
A082463: 1 2 3 4 5 6 7 9 10
A032896-A032855: 1 2 3 4 5 6 7 9 10 11 12 13 14 15 18 19
((x + 1) + (2 * ((2 * (((x + 1) div 2) div 2)) div 3)))
A175857: 1 2 3 4 5 6 7 10 11 12 13 16 17 18 19 20
((x + 1) + ((3 * ((((x + 1) div 2) div 2) div 2)) div 2))
A082463: 1 2 3 4 5 6 7 9 10
A284837: 1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 19
(1 + compr(\x.((x - ((~x + (x div 3)) div 3)) mod 2),x))
A193600: 1 2 4 7 9 12 14 15 17 19 20 22 25 27 30 32
((x + 1) + ((x2 mod (1 + ((x + (x div 2)) div 2))) div 2))
A072618: 1 2 3 4 5 6 7 8 9 12 13 14 15 18 19 20
((x + ~1) + ((x + 2) div (2 - (((x div 2) div ~2) div 2))))
A039250: 0 1 2 3 5 6 7 9 10 11 12 13 14 15 17 18
((x + 1) + (2 * ((x - (x div 9)) div 2)))
A188258: 1 2 5 6 9 10 13 14 17 18 19 22 23 26 27 30
(x mod ((x + ~1) + (2 * ((~x + 2) mod 10))))
A004177: 0 1 0 3 4 5 6 7 8 9 10 11 1 13 14 15
(1 + compr(\x.((x mod (~2 + (((~x + 2) div 2) div 3))) mod 2),x))
A325131: 1 3 4 5 7 8 11 13 15 16 17 19 21 23 25 27
((x + 1) + ((((x2 + 2x) - (x div 3)) div 2) div 2))
A024177: 1 2 5 7 10 14 18 23 28 34 40 47 54 61 70 78
((x + 1) + ((((1 - (x div 4)) mod (x + 1)) div 2) div 2))
A173016: 1 2 3 4 5 6 7 8 11 12 13 14 15 17 18 19
((x + 1) + ((x - (x mod (~2 + ((x div 2) mod ~2)))) div 2))
A156246: 1 3 4 5 7 9 10 12 13 15 17 18 19 21 22 23
((x + 1) + (((x - ((x mod 5) div 2)) div 2) div 2))
A153381: 1 2 3 4 5 7 8 9 10 11 13 14 15 17 18 19
((x + 1) + (2 * (x - (2 div (x + ~16)))))
A036686: 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 50
((x + 1) + ((x + 2) div (4 + (x div 8))))
A188013: 1 2 4 5 6 7 9 10 11 12 13 14 15 17 18 19
(x div ((x + ~1) + (x mod (4 + ((x div 4) mod 2)))))
A091447-A091444-A076478: 0 1 0 0 0 1 1 0 1 1 0 0 0 0 0 1
((x + 1) + (((x - ((x div 3) mod 4)) div 2) div 2))
A303234: 1 2 3 4 5 7 8 9 10 11 12 14 16 17 18 19
((x + 1) + ((x - ((0 - ((x div 2) mod 4)) div 2)) div 2))
A187974: 1 2 4 6 7 9 11 12 13 14 16 18 19 21 23 24
((x + 1) + (2 * (x mod (x - ((x + ~1) mod 8)))))
A008817: 1 2 3 4 5 6 7 8 9 10 13 16 19 22 25 28
((x + 1) - ((x2 + ~2) div (x + 16)))
A177876: 2 3 3 4
A047785: 2 3 3 4 5 5 6 6 7 7 8 8 8 9 9 9
(1 - ((~x2 + 2x) div (x + 17)))
A025771: 1 1 1 2 2 2 3 3 3 4 4 5 6 6 7 8
((x2 div (x + 2)) div (~x + 17))
A326633: 0 0 0 0 0 0 0 0 0 0 1 1 2 2 4 6
((x + 1) + ((~2x mod (2 + (x div 4))) div 2))
A000015: 1 2 3 4 5 7 7 8 9 11 11 13 13 16 16 16
(1 + ((x2 + 2) div (x + (4 * (2 + (x mod 2))))))
A326670: 1 1 1 1 2 2 3 3 5 4 6 6 8 7 10 9
((x + 1) + (x2 mod (x - ((x + ~1) mod 8))))
A059765: 1 2 3 4 5 6 7 8 9 10 12 16
((x + 1) + (((2 - (x div 3)) * (x div 4)) div 2))
A263283: 1 2 3 4 5 6 7 8 9 9 10 11 10 11 12 11
((x + 1) + (((((2 - (x div 2)) div 2) mod (x + 2)) div 2) div 2))
A178596: 1 2 3 4 5 6 8 10 11 12 13 14 16 17 18 19
((x + 1) + (2 * ((((x div 4) mod 2) + (x div 2)) div 2)))
A285506: 1 2 3 4 7 8 11 12 13 14 15 16 19 20 23 24
((x + 1) + ((x div (1 + (x div 4))) + (x div 4)))
A183855: 1 3 5 7 8 9 11 12 13 15 16 17 19 20 21 22
((x + 1) + (2 * ((x + (2x div 5)) div 2)))
A276882: 1 2 5 8 9 12 15 16 19 22 25 26 29 32 33 36
((x + 1) + (2 * ((x + ((x mod (1 + (x div 2))) div 2)) div 2)))
A276886: 1 2 5 6 9 12 13 16 17 20 23 24 27 30 31 34
((x + 1) + (2 * (2x + (2x div 5))))
A276879: 1 6 11 18 23 30 35 40 47 52 59 64 69 76 81 88
((x + 1) + (2 * ((3 * (x mod 3)) + (x mod 2))))
A329772: 1 10 15 6
((x + 1) + (2 * (x + (x div 13))))
A308014: 1 4 7 10 13 16 19 22 25 28 31 34 37 42 45 48
((x + 1) + ((x + (((x + ~2) div 5) mod 2)) div 2))
A187689: 1 3 4 5 7 8 10 12 13 15 16 18 19 20 22 23
((x + 1) + ((x + ((x mod (2 + ((x div 2) mod 2))) mod 2)) div 2))
A189665: 1 3 4 5 7 9 10 12 13 15 16 17 19 21 22 23
((x + 1) + ((x + ((x2 + ~x) div 8)) div 2))
A259280: 1 2 4 5 7 9 11 14 16 19 21 24 27 30 33 36
((x + 1) + (2 * (x + (x div (~2 + ((~x + 2) div 4))))))
A045928: 1 2 5 8 9 12 15 18 21 22 25 28 31 34 37 40
((x + 1) + ((x + (((x + (x div 2)) div 4) mod 2)) div 2))
A285954: 1 2 4 6 7 9 10 11 13 15 16 17 19 20 22 24
(x mod (1 + (x2 mod (x + ((x + 2) * (2 + (x mod 2)))))))
A004179: 0 1 2 3 0 5 6 7 8 9 10 11 12 13 1 15
((x2 + 2x + 1) + (2x2 div 5))
A025720: 1 4 10 19 31 46 63 83 106 132 161 192 226 263 303 346
(4x4 + 16x3 + 21x2 + 10x + 1)
A079414: 1 52 297 976 2425 5076 9457 16192 26001 39700 58201 82512 113737 153076 201825 261376
(3x4 + 8x3 + 8x2 + 4x + 1)
A092181: 1 24 153 544 1425 3096 5929 10368 16929 26200 38841 55584 77233 104664 138825 180736
((x + 1) + ((x * (((x + 1) + (x div 2)) div 2)) div (x + 2)))
A288521: 1 2 4 5 7 8 10 11 13 15 17 18 20 22 24 25
((x + 1) + ((x * (4 + (x div 3))) div (x + 2)))
A288525: 1 3 5 7 8 9 11 12 13 15 16 17 19 20 22 23
((x + 1) * (1 + ((x + 3) div 7)))
A076079: 1 2 3 4 10 12 14 16 18 20 22 36 39 42 45 48
(61 div (x + 1))
A033381: 61 30 20 15 12 10 8 7 6 6 5 5 4 4 4 3
(59 div (x + 1))
A033379: 59 29 19 14 11 9 8 7 6 5 5 4 4 4 3 3
((x + 1) * (1 + (5 * ((x2 + x) div 2))))
A006564: 1 12 48 124 255 456 742 1128 1629 2260 3036 3972 5083 6384 7890 9616
(55 div (x + 1))
A033375: 55 27 18 13 11 9 7 6 6 5 5 4 4 3 3 3
(73 div (x + 1))
A033393: 73 36 24 18 14 12 10 9 8 7 6 6 5 5 4 4
(71 div (x + 1))
A033391: 71 35 23 17 14 11 10 8 7 7 6 5 5 5 4 4
((x + 1) * (1 + (3 * (1 + ((x2 + x) div 2)))))
A130423: 4 14 39 88 170 294 469 704 1008 1390 1859 2424 3094 3878 4785 5824
(6x3 + 15x2 + 11x + 2)
A213826: 2 34 132 332 670 1182 1904 2872 4122 5690 7612 9924 12662 15862 19560 23792
(6x3 + 24x2 + 31x + 13)
A094421: 13 74 219 484 905 1518 2359 3464 4869 6610 8723 11244 14209 17654 21615 26128
(95 div (x + 1))
A033415: 95 47 31 23 19 15 13 11 10 9 8 7 7 6 6 5
((x + 1) * (1 + ((2x3 + 4x) div 3)))
A100189: 1 6 27 92 245 546 1071 1912 3177 4990 7491 10836 15197 20762 27735 36336
((x + 1) * ((2x + 2) mod (1 + ((x div 2) div 3))))
A078547: 0 0 0 0 0 0 0 0 0 0 0 0 26 14 0 32
compr(\x.((x mod 6) mod (1 + (x div 3))),(x + 1))
A065385: 1 2 4 6 10 12 18 24 30 36 42 48 54 60 66 72
((1 + ((~1 + (x mod 4)) * (x mod 3))) div (x + 1))
A089811: 1 0 1 0 0 0 0 0 ~1 0 0 0 0 0 0 0
compr(\x.(~1 + ((x3 + 1) mod (1 + (x div 2)))),(x + 1))
A124134: 1 2 3 5 6 7 9 11 12 13 14 15 17 19 21 23
(8x3 + 32x2 + 41x + 17)
A253707: 17 98 291 644 1205 2022 3143 4616 6489 8810 11627 14988 18941 23534 28815 34832
((1 - (x mod (~1 + (2 * (~1 + (x div 3)))))) div (x + 1))
A016373: 1 1 0 0 0 0 0 0 0 0 0 ~1 ~1 ~1 ~1 0
(67 div (x + 1))
A033387: 67 33 22 16 13 11 9 8 7 6 6 5 5 4 4 4
compr(\x.(x mod ((x + 1) - (x mod 10))),(x + 1))
A076643: 1 2 3 4 5 6 7 8 9 11 21 31 41 51 61 71
((x + 1) * (2 - ((~x + 3) div 7)))
A068902: 2 4 6 8 15 18 21 24 27 30 33 48 52 56 60 64
(((~2x2 + 4x) div 7) mod (x + 1))
A194753: 0 0 0 3 2 1 0 6 4 2 10 7 4 1 12 8
(69 div (x + 1))
A033389: 69 34 23 17 13 11 9 8 7 6 6 5 5 4 4 4
((~1 + (2 * (x div (2 + ((x div 2) div 3))))) mod (x + 1))
A113215: 0 1 1 1 3 3 3 3 3 5 5 5 5 5 5 5
((x + 1) * (2 div (1 + ((x + 1) mod 16))))
A023927: 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32
(90 div (x + 1))
A033410: 90 45 30 22 18 15 12 11 10 9 8 7 6 6 6 5
((2x + 2) - ((1 + (x mod 8)) mod (x + 1)))
A241142: 2 4 6 8 10 12 14 16 17 18 19 20 21 22 23 24
(85 div (x + 1))
A033405: 85 42 28 21 17 14 12 10 9 8 7 7 6 6 5 5
(75 div (x + 1))
A033395: 75 37 25 18 15 12 10 9 8 7 6 6 5 5 5 4
compr(\x.((x mod 6) - (x mod 5)),(x + 1))
A032852: 1 2 3 4 6 7 8 9 12 13 14 18 19 24 30 31
((1 + ((x + 1) mod 4) - (x div 4)) div (x + 1))
A053622: 2 1 1 0 0 0 0 0 0 0 0 ~1 ~1 0 0 ~1
compr(\x.(((x2 + 2x) div 2) mod (1 + (x div 4))),(x + 1))
A094859: 1 2 3 4 6 10
A122907: 1 2 3 4 6 10 12 14 18 22 26 30 34 38 42 46
(99 div (x + 1))
A033419: 99 49 33 24 19 16 14 12 11 9 9 8 7 7 6 6
(93 div (x + 1))
A033413: 93 46 31 23 18 15 13 11 10 9 8 7 7 6 6 5
(x + (12x div (x + 1)) - (x div 2))
A283056: 0 7 9 11 11 13 13
((10x + 16) + (3 div (x + 1)))
A006626: 19 27 37 46 56
compr(\x.((x mod 10) * (x mod 3)),(x + 1))
A229307: 3 6 9 10 12 15 18 20 21 24 27 30 33 36 39 40
((~1 + ((x2 + ~2) div (x - ((~x + 2) div 2)))) mod (x + 1))
A091245: 0 0 0 0 1 2 3 3 4 5 6 6 7 7 8 9
(10x3 + 18x2 + 9x + 1)
A100167: 1 38 171 460 965 1746 2863 4376 6345 8830 11891 15588 19981 25130 31095 37936
(((~x + 1) + (((1 + (x div 2)) * (x div 2)) div 2)) div (x + 1))
A244465: 1 0 0 ~1 0 ~1 0 0 0 0 0 0 0 0 1 0
((1 + (x * (((x + 1) div 3) - (x mod 2)))) div (x + 1))
A282537-A058768: 1 0 1 0 1 1 1 1 2 1 2 2 3 2 4 3
((x2 + 2x + 1) * ((x mod (~3 + (x mod 2))) mod 2))
A106548: 0 4 9 16 0 36 0 64 81 100 0 144 0 196 225 256
((3x + 1) - ((2 + (x div 4)) mod (x + 1)))
A319515: 1 4 5 8 10 13 16 19 21 24 27 30 32 35 38 41
(x7 + x6 + x5 + x4 + x3 + x2 + x + 1)
A053717: 1 8 255 3280 21845 97656 335923 960800 2396745 5380840 11111111 21435888 39089245 67977560 113522235 183063616
compr(\x.(((x div 2) mod (1 + (x div 5))) mod 2),(x + 1))
A288666: 1 2 3 4 5 8 9 10 11 12 13 16 17 20 21 24
(98 div (x + 1))
A033418: 98 49 32 24 19 16 14 12 10 9 8 8 7 7 6 6
(94 div (x + 1))
A033414: 94 47 31 23 18 15 13 11 10 9 8 7 7 6 6 5
compr(\x.((x mod (1 + (6 mod (x + 1)))) mod 2),(x + 1))
A032957: 1 2 3 4 5 6 7 9 11 13 14 16 18 20 21 23
((x + 1) * (((x + ~2) mod (2 - (x div ~3))) mod 2))
A103688: 0 0 0 4 0 6 0 0 9 0 0 12 0 0 15 0
compr(\x.(~2 + ((x div 2) div (1 + (x mod 6)))),(x + 1))
A128649-A032894-A032853: 1 2 3 4 5 7 8 9 10 11 14 15 16 17 21 22
((x + 1) * ((x mod (3 - ((x div 4) mod 2))) div 2))
A308275: 0 0 3 0 0 0 0 0 9 0 0 12 0 0 0 0
(8x3 + 24x2 + 30x + 14)
A173962: 14 76 234 536 1030 1764 2786 4144 5886 8060 10714 13896 17654 22036 27090 32864
compr(\x.((x2 mod (4x + 9)) mod 2),(x + 1))
A279934: 2 4 7 9 10 12 15 17 18 20 22 23 25 28 30 31
((((x + ~1) div 2) - (x mod 10)) mod (x + 1))
A336430: 0 1 1 2 2 3 3 4 4 5 4 4 3 3 2 2
compr(\x.(x mod (2 + ((x * (x mod 2)) div 5))),(x + 1))
A285517: 2 4 6 8 9 10 12 14 15 16 18 20 22 24 26 28
compr(\x.((4x div (1 + (x div 4))) mod 2),(x + 1))
A178843: 1 2 3 4 5 6 7 8 9 11 12 14 16 18 21 22
((2x + 1) - (1 mod (~4x + 18)))
A079212: 0 2 4 6 8 12 18 24 30 36 42 48 54 60 66 72
((x + 1) * ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2))
A074591: 0 0 0 0 0 6 0 0 0 10 0 12 0 14 15 0
((((1 + (x * (x mod 2))) * (1 + (x div 2))) div 2) mod (x + 1))
A131728: 0 1 1 0 1 3 2 0 2 5 3 0 3 7 4 0
(x4 + 8x3 + 21x2 + 24x + 10)
A269538: 10 64 222 568 1210 2280 3934 6352 9738 14320 20350 28104 37882 50008 64830 82720
((x + 1) * ((5x2 + 13x + 8) div 2))
A142962: 4 26 81 184 350 594 931 1376 1944 2650 3509 4536 5746 7154 8775 10624
((x + 1) * ((x6 + x5) div 2))
A163275: 0 2 144 1944 12800 56250 190512 537824 1327104 2952450 6050000 11595672 21026304 36386714 60505200 97200000
((2x + 4) - (((x2 + ~3x + 2) div 2) div (x + 1)))
A186387: 3 6 8 10 12 13 15 17 18 20 21 23 24 26 27 29
compr(\x.((x mod (2 - (x mod ~8))) mod 2),(x + 1))
A226946: 2 4 5 6 8 9 10 11 12 14 15 16 17 18 20 22
((x + 1) * (((2x mod (2 + (x div 2))) div ~2) mod 2))
A322015: 0 0 3 0 0 6 7 0 0 0 11 12 0 14 15 0
((x + 1) * (1 - ((~x + 2) div (2 - (x div ~4)))))
A340301: 0 2 3 8 10 12 14 24 27 30 33 36 39 42 45 64
(92 div (x + 1))
A033412: 92 46 30 23 18 15 13 11 10 9 8 7 7 6 6 5
((1 - (2 * ((1 + ((x + (x div 2)) div 2)) div 2))) mod (x + 1))
A275868: 0 1 2 3 2 3 4 3 4 5 4 5 4 5 6 5
(4x3 + 24x2 + 24x + 4)
A192845: 4 56 180 400 740 1224 1876 2720 3780 5080 6644 8496 10660 13160 16020 19264
(4x3 + 16x2 + 36x + 24)
A167561: 24 80 192 384 680 1104 1680 2432 3384 4560 5984 7680 9672 11984 14640 17664
compr(\x.(~2 + (x mod (2 + (x mod (4 + (x mod 2)))))),(x + 1))
A176554: 1 2 4 5 6 8 10 11 12 14 15 16 17 18 19 20
((2x + 2) * (2 + (x mod (2 + (x mod (2 + (x mod 2)))))))
A195199: 4 12 12 24 20 36 28 48 36 60 44 120 52 84 60 96
((2 - (x mod (~2 + (((2 - (x div 2)) div 2) div 2)))) mod (x + 1))
A278354: 0 1 2 3 2 3 2 4 3 2 4 3 2 4 4 3
compr(\x.(~2 + ((x3 mod (2 + (x div 2))) div 2)),(x + 1))
A055201: 1 2 3 4 5 6 7 8 9 11 12 13 15 17 18 22
((1 - (2 * ((x - (x mod (2 + (x mod 2)))) div 2))) mod (x + 1))
A066727: 0 1 2 3 2 5 2 3 2 3 2 5 2 3 2 3
(8x5 + 24x4 + 16x3)
A192839: 0 48 768 4320 15360 42000 96768 197568 368640 641520 1056000 1661088 2515968 3690960 5268480 7344000
((8x + 8) + (x div (4 + (x div 2))))
A028438: 8 16 24 32 40 48 56 65 73 81 89 97 105 113 121 129
compr(\x.((x mod 6) - (x div 8)),(x + 1))
A297258-A296702: 6 12 13 18 19 20 24 25 26 27 30 31 32 33 34 36
compr(\x.((~4 + (x div 2)) * (x mod 8)),(x + 1))
A079239-A079041: 1 2 3 4 5 6 7 8 9 16 24 32 40 48 56 64
((x + 1) * (1 - (2 * ((x mod ((x + ~2) + (x div 2))) mod 2))))
A160356: 1 2 3 ~4 5 6 7 ~8 9 ~10 11 ~12 13 ~14 15 ~16
((((x + 4) * (x2 - (x div 2))) div 2) div (x + 1))
A222010: 0 1 3 7
A333996: 0 1 3 7 11 17 23 31 40 50 60 72 84 98 113 129
((4x + 4) + ((x + 1) div 7))
A187385: 4 8 12 16 20 24 29 33 37 41 45 49 53 58 62 66
((4x + 4) + (2 div (x + ~16)))
A103543: 3 7 11 15 19 23 27 31 35 39 43 47 51 55 59 62
((4x + 4) + ((x + 2) div ~7))
A329840: 3 7 11 15 19 23 26 30 34 38 42 46 50 53 57 61
((4x + 4) + ((x + ((x div 2) div 3)) div 2))
A127264: 4 8 13 17 22 26 31 36 40 45 49 54 59 63 68 72
(36x2 + 68x + 32)
A304380: 32 136 312 560 880 1272 1736 2272 2880 3560 4312 5136 6032 7000 8040 9152
(36x2 + 52x + 16)
A304505: 16 104 264 496 800 1176 1624 2144 2736 3400 4136 4944 5824 6776 7800 8896
((x2 div ((~x + ~3) - (x div 2))) mod (x + 1))
A074796: 0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 7
((x + 4) - ((2 - (x2 div 4)) div (x + 1)))
A186493: 2 4 6 7 9 10 11 13 14 15 17 18 19 20 22 23
(((2x2 + ~x) + (x2 div 4)) div (x + 1))
A113903: 0 0 2 4 6 8 10 12 15 17 19 21 24 26 28 30
((((~x + 1) * (x mod 10)) div 2) mod (x + 1))
A194747: 0 0 2 1 4 2 6 3 8 4 0 7 2 10 4 13
((x + 1) * ((3x3 + 3x2 + ~2x) div 2))
A162673: 0 4 48 204 580 1320 2604 4648 7704 12060 18040 26004 36348 49504 65940 86160
((x2 + 3x + 2) + ((x2 + x) div 5))
A194138: 2 6 13 22 34 48 64 83 104 128 154 182 213 246 282 320
((x * (5 + (((x + 1) div 2) div 2))) div (x + 1))
A329202-A318994: 0 2 3 4 4 5 5 6 6 6 6 7 7 7 7 8
(25x2 + 49x + 24)
A157514: 24 98 222 396 620 894 1218 1592 2016 2490 3014 3588 4212 4886 5610 6384
((2x2 + 14x + 6) div (x + 1))
A072540: 6 11 14 16 18 21
(((x2 + ~2x) div (x + 16)) mod (x + 1))
A238208: 0 1 0 0 0 0 1 1 2 2 3 3 4 4 5 6
((x + ~1) * (((x + ~1) * ((x3 + ~x2) div 2)) div 2))
A019584: 0 0 1 18 108 400 1125 2646 5488 10368 18225 30250 47916 73008 107653 154350
((x + ~1) * ((x3 + 3x2 + ~6x) div 2))
A060783: 0 0 4 36 132 340 720 1344 2296 3672 5580 8140 11484 15756 21112 27720
((x + ~1) * ((x3 + 5x2 + ~2x) div 2))
A289223: 0 0 12 66 204 480 960 1722 2856 4464 6660 9570 13332 18096 24024 31290
(2x3 + 21x2 + ~23x)
A248598: 0 0 54 174 372 660 1050 1554 2184 2952 3870 4950 6204 7644 9282 11130
(2 - ((~x2 + x + ~1) * ((x2 + ~1) div 3)))
A309115: 1 2 5 16
A019502: 1 2 5 16 67
(4x4 + 3x3 + 2x2 + 1)
A209262: 1 10 97 424 1249 2926 5905 10732 18049 28594 43201 62800 88417 121174 162289 213076
(1 + (x3 div (x2 + 16)))
A330513: 1 1 1 2 3 4 5 6 7 8 9 10 11 12 13 15
(((x3 + 2) div (2x + ~1)) mod (x2 + 1))
A081946: 0 1 3 5 9 14 19 26 34 43 52 63 75 87 101 116
(((x - ((x div 5) mod 2)) mod 3) mod ~2)
A059651: 0 ~1 0 0 ~1 ~1 0 0 ~1 0 ~1 0 0 ~1 0 0
(x - (((3 * ((x2 + ~x) div 2)) div 2) div ~2))
A096228: 0 1 3 5 9 13 17 23 29 36 44 52 62 72 82 94
(x + (x div ~8) - (2 * (x div 3)))
A229878: 0 0 1 0 1 2
A253092: 0 0 1 0 1 2 1 2 3 1 2 3 2 3 4 3
(((x + 1) mod 4) mod (2 - ((x div 4) div ~2)))
A026840: 1 0 1 0 1 2 0 0 1 2 0 0 1 2 3 0
(x - ((x div ~2) + ((3 * (x div 4)) div 2)))
A092391: 0 2 3 5 5 7 8 10 9 11 12 14 14 16 17 19
((1 + ((x div 2) mod (1 + (x mod 7)))) mod 2)
A294623: 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 0
((1 + ((x + ~2) mod (1 + ((x div 2) mod 5)))) mod 2)
A267687: 1 1 1 0 1 1 1 0 0 1 1 1 1 0 1 0
(((x + ~1) - (x mod (~1 - (x mod 5)))) mod 2)
A318963: 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 0
((1 + ((1 + (x div 2)) div (1 + (x mod 5)))) mod 2)
A342460: 0 1 1 1 1 0 1 0 0 0 1 0 1 0 0 1
((1 + ((~2 + (x div 2)) mod (1 + (x mod 5)))) mod 2)
A267533-A130304: 1 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1
((1 + ((1 + (x div 2)) div (1 + ((x + ~1) mod 3)))) mod 2)
A119498: 1 0 0 1 0 0 0 1 1 0 1 0 1 0 1 1
(2 * ((x + 1) - ((~x + 2) div 11)))
A309374: 2 4 6 10 12
A336066: 2 4 6 10 12 14 16 18 20 22 24 26 28 30 34 36
(2 * (1 + ((x div 2) mod (1 + ((2 * (x div 2)) mod 3)))))
A071928: 2 2 4 4 2 2 2 2 4 4 4 4 2 2 4 4
((1 + (2x mod (~1 + ((~x + (x mod 2)) div 3)))) mod 2)
A182741: 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1
(((x + 1) - ((~2x + 2) mod (1 + (x div 3)))) div 2)
A048620: 0 1 1 2 2 3 2 4 4 5 4 6 5 6 5 7
((1 + ((2 + (x * (x div 2))) mod (1 + (x div 3)))) mod 2)
A295316-A181183: 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0
((x - ((x + ~1) div (1 + (x mod (1 + (x div 3)))))) mod 2)
A267708: 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 0
((x div 2) - ((x mod (1 + (x div (1 + (x mod 3))))) div 2))
A328903: 0 0 1 0 2 2 0 2 3 0 3 4 0 3 5 0
(((x + 1) - (x mod (~1 + (x mod (~1 + ((~x + 1) div 2)))))) mod 2)
A176412: 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1
((1 + (x div (1 + (16 mod (x + 1))))) mod 2)
A089024: 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0
((x div (1 + ((x + ~1) mod (2 - (x mod ~3))))) mod 2)
A285274: 0 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1
(((x + ~1) - (x2 div (3 - (x div ~2)))) mod 2)
A123504: 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0
((x + 4) - (x div (~1 + (x div (~1 + (x div ~2))))))
A105447: 4 6 7 9 10 11 12 14 15 16 18 19 20 22 23 24
((x div (~1 + (x div (~1 + (2 * (~1 + (x div 3))))))) mod 2)
A164980: 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1
((1 + (2x div (3 + (x div 5)))) mod 2)
A176178: 1 1 0 1 1 1 0 0 1 1 1 1 1 0 0 0
((1 + (x mod (~1 + (2 * (x div (1 + (x div 4))))))) mod 2)
A128810: 1 1 1 0 0 1 0 1 1 1 1 0 1 0 1 1
((1 + (x2 mod (1 + (2 * (1 + (x mod 4)))))) mod 2)
A208614-A023960: 1 0 1 1 0 1 0 1 0 0 1 1 1 1 1 1
((1 + (x2 mod (1 + (2 * ((x + 1) mod 3))))) div 2)
A045833: 0 1 0 0 1 0 0 2 0 0 0 0 0 2 0 0
((1 + (x mod (~1 + (2 * (((~x + 2) div 2) div 3))))) mod 2)
A303913: 1 1 1 1 1 0 1 1 0 0 1 1 0 1 0 1
((1 + ((~x + (x div 4)) mod 7)) mod 2)
A087371: 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1
((x mod (~1 + ((~x2 + x) div 7))) mod 2)
A341609-A064911: 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 0
(((x + ~1) - (2x div (1 + (x mod 6)))) mod 2)
A286064: 1 1 0 1 0 1 1 1 0 0 1 1 1 1 0 1
((1 + ((x + 8) div (1 + ((x + 1) div 2)))) mod 2)
A039985: 1 1 0 0 1 0 0 0 0 1 0 1 1 1 1 1
((x mod (3 - (2x div ~5))) mod 2)
A141474: 0 1 0 1 0 0 0 1 1 0 1 1 0 0 1 0
(2 * ((x + 1) - ((x + (x div 2)) div ~5)))
A141105: 2 6 8 10 14 16 18 20 24 26 28 32 34 36 40 42
(1 - (2 * ((x + 1) mod (~1 + (x div ~5)))))
A249947: 1 1 3 1 3 1 5 3 1 5 3 1 7 5 3 1
((1 + (x mod (1 + (2 * (2 + ((x + ~1) mod 3)))))) mod 2)
A229940: 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1
(1 - ((x mod (1 + (x div (1 + (((x + 1) div 2) div 2))))) div 2))
A088534: 1 1 0 1 1 0 0 1 0 1 0 0 1 1 0 0
(2 * ((x + 1) - (x div (~3 + (x div ~4)))))
A005795: 2 6 8 10 12 14 18
A157502: 2 6 8 10 12 14 18 20 22 24 26 28 30 32 34 38
((1 + (x div (1 + (4 * ((x + 1) mod 4))))) mod 2)
A323152: 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 0
((1 + (2x div (2x + ~17))) mod 2)
A029404: 1 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1
((1 + (x div (3 + (x mod (2 + ((x div 2) mod 2)))))) mod 2)
A266978: 1 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0
((1 + ((x3 + ~2x) mod 9)) mod 2)
A266789: 1 1 1 0 1 0 1 0 0 1 1 1 0 1 0 1
(x - ((x - (2 div (1 + (x mod 9)))) div 2))
A056039: 1 1 1 2 2 3 3 4 4 6 6 6 6 7 7 8
(2 * (1 + ((2x + 1) div (3 + (x div 4)))))
A111650: 2 4 4 6 6 6 8 8 8 8 10 10 10 10 10 12
(((x + ~1) - (x mod (1 + (x div (2 * (2 + (x mod 2))))))) mod 2)
A317906: 1 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0
((1 + (x2 div (3 + (x div (2 + (x mod 2)))))) mod 2)
A143220-A118269-A118268: 1 1 0 1 0 1 1 0 0 0 1 1 1 1 0 1
((1 + ((x div 3) div (1 + ((x + 1) mod 4)))) mod 2)
A325321: 1 1 1 0 1 1 1 1 0 0 1 0 1 0 0 0
(((~x + 2) mod (1 + ((2x + 1) div 5))) div 2)
A011685: 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0
(((~x + 2) mod (1 + ((~x + ~1) mod 5))) div 2)
A025896: 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1
(((2x + ~2) div (1 + ((x + 1) div 5))) mod 2)
A092241: 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1
(((2x + 1) mod (1 + ((x + 1) mod 5))) div 2)
A044934: 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 0
((((x + ~1) div 2) div (1 + ((x + ~1) mod 5))) mod 2)
A029433: 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1
(((~2 + (x div 2)) mod (1 + ((x + ~1) mod 5))) mod 2)
A186714: 1 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0
(1 - (((x + 2) mod (1 + ((x + ~1) mod 5))) div 2))
A327177: 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0
((1 + (2x mod (5 + ((x + 1) div 2)))) mod 2)
A219967-A176505-A176048-A156072: 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1
((x - (x div (~1 + (((~x + 2) div 2) div 5)))) div 2)
A306726: 0 1 2 2 3 4 4 5 6 7 7 8 9 9 9 10
((1 + (((x + 2) * (x mod 3)) div 5)) mod 2)
A285952: 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1
(x div (2 + (2x div (1 + (2x mod 5)))))
A334996: 0 0 1 0 1 0 1 1 0 1 0 1 2 0 1 0
(2 + ((x + 2) div (1 + (3x div 5))))
A036444: 4 5 4 4 4 3 4 3 4 3 3 3 3 3 3 3
((1 + ((~x + ((~x + 1) mod 3)) mod 5)) mod 2)
A188076: 0 1 1 0 0 1 1 0 1 1 1 0 1 1 0 0
(((x + ~1) - (x div (1 - ((~x + 1) div 5)))) mod 2)
A070886: 1 1 0 1 1 0 0 0 1 1 0 1 0 1 0 1
(((x + ~1) div (1 + ((x * (x div 2)) mod 5))) mod 2)
A025899: 1 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0
((((x + 1) + (x div 2)) div (1 + (x div 5))) mod 2)
A285083: 1 0 0 1 1 0 1 1 0 1 1 1 0 0 1 1
(((x2 + ~2x + 2) div (1 + (x div 5))) mod 2)
A267188-A154104: 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1
((1 + ((x * (~x + (x div 3))) div 5)) mod 2)
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(10x4 + 20x2 + 2)
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((1 + (x div (1 + ((~x + ((~x + 2) div 2)) mod 4)))) mod 2)
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((1 + (x div (1 + ((2 * (x mod 2)) + (x div 4))))) mod 2)
A011751: 1 1 1 0 1 0 0 0 1 0 0 1 0 1 0 1
(((x + ~1) - ((2 * (x div 2)) div (1 + (x div 4)))) mod 2)
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((x div (~1 - (x2 mod (x + 5)))) mod 2)
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(32x2 + 24x + 2)
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((1 + ((x mod 11) mod 3)) mod 2)
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(((x + 1) div (1 + (3 * (x mod 5)))) mod 2)
A029420: 1 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0
((1 + (x mod 2) - (((x + 1) div 3) mod 3)) div 2)
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(((x + 1) mod (1 + (3 * ((~x + 2) mod 3)))) mod 2)
A120524: 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0
(2 * (1 + (((x mod 4) * (x div 3)) mod 3)))
A294078: 2 2 2 2 2 4 4 2 2 2 2 2 2 4 6 2
((1 + (((2 - ((x + ~1) div 2)) mod (x + 1)) mod 3)) div 2)
A109072: 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1
(((x div ~4) div (1 + ((x + ~1) mod 3))) mod 2)
A135947-A075897: 0 1 1 1 1 1 1 0 1 1 1 0 1 0 0 0
(2 * (1 + ((x - (2 * ((x div 2) div 3))) div 3)))
A106160: 2 2 2 4 4 4 4 4 6 6 6 8 6 8 8 8
((x div (~1 + (x div (x + ~18)))) mod 2)
A288670: 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1
(((2 + (x div 2)) div (1 + (((x + 1) div 2) mod 3))) mod 2)
A189081: 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 1
(x3 mod 46)
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((1 + ((((x2 - (x div 2)) div 2) div 2) mod 3)) div 2)
A137331-A135136: 0 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0
((1 + ((((x2 * (x div 2)) div 2) div 2) div 3)) mod 2)
A327866: 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0
((x - (x div (~11 + (x div 2)))) div 2)
A103355: 0 1 1 2 2 3 3 4 5 5 6 6 7 8 9 9
(x4 mod 26)
A070569: 0 1 16 3 22 1 22 9 14 9 16 3 14 13 14 3
(2 * (x - ((~x2 + 1) div 13)))
A191965: 0 2 6 8 12 14 18 22 26 32
(x4 mod 22)
A070541: 0 1 16 15 14 9 20 3 4 5 12 11 12 5 4 3
(((x + 1) mod 2) - ((x mod 11) mod 2))
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((1 + (x mod (3 + ((x * (x mod 2)) div 4)))) mod 2)
A082960: 1 0 1 1 0 0 1 0 1
A132138: 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 0
(((~x + 3) div (1 + ((2 + (x div 2)) div 3))) mod 2)
A120528: 1 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1
((((x + 1) div 2) div (1 + ((2 + (x div 2)) div 3))) mod 2)
A288864: 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0
((1 + (x mod (3 + ((~x * (x div 2)) div 2)))) mod 2)
A323045: 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0
(((2x + ~1) div (~1 + (3 * (~2 + (x mod 2))))) mod 2)
A082410: 0 1 1 0 1 1 0 0 1 1 1 0 0 1 0 0
((1 + (((x * (~1 + (x * (x div 2)))) div 2) div 3)) mod 2)
A029694: 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1
(((~x + 1) mod (1 + (((x2 + ~x) div 2) div 3))) div 2)
A258470: 0 0 0 0 0 0 0 1 1 2 3 4 6 7 9 11
(((2 + (x div 2)) mod (~1 + (((~x + 2) div 2) div 3))) mod 2)
A343606: 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1
((1 + (((x + 2) * (1 - (x div 4))) div 3)) mod 2)
A246500: 1 0 0 0 1 1 1 1 1 1 1 0 1 1 0 1
((1 + (((2x - (x mod 2)) * (x div 2)) div 3)) div 2)
A211541: 0 0 1 1 3 3 6 7 11 11 17 18 24 25 33 34
(2 + (x mod 2) - ((x div (1 + ((x div 2) div 3))) mod 2))
A194318: 2 2 2 2 2 2 1 2 2 3 1 2 2 3 2 2
(1 - (((~x2 + 2) div (1 + ((x div 2) div 3))) mod 2))
A335833: 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0
((1 + ((x + (x mod (1 + (x div 3)))) mod 3)) mod 2)
A071982: 1 0 1 0 0 1 1 1 0 0 1 1 1 0 1 1
((1 + ((x + (8 div (x + 1))) mod 3)) mod 2)
A188082-A085369: 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1
(1 - (((2x + 2) mod (~1 + ((~x + 2) div 3))) div 2))
A255350: 1 1 1 1 1 1 2 2 1 1 2 1 3 2 1 3
((1 + ((x mod (4 - (x * (x div 2)))) mod 3)) mod 2)
A121967: 1 0 1 1 1 1 0 1 0 0 1 1 0 1 0 0
((1 + ((x div (2 * (~2 + (x mod 2)))) + (x div 3))) mod 2)
A285617: 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 0
(((1 + (x mod ~4)) mod (1 + (x div 3))) mod 2)
A244063: 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0 0
(((~4x + 5) mod (1 + (x div 3))) div 2)
A079692: 0 0 0 0 0 0 1 0 0 0 0 0 1 1 2 2
(x mod (2 + ((~x2 + 3x + ~2) mod (1 + (x div 3)))))
A338498: 0 1 0 1 0 1 0 1 0 1 0 3 0 3 2 3
((1 - ((~x3 + x2) div (1 + (x div 3)))) mod 2)
A127872: 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 0
(((~x2 + ~2x + 8) mod (1 + (x div 3))) div 2)
A035447: 0 0 0 0 0 0 1 1 0 0 0 0 0 1 2 2
(((x div 2) div (1 + (((x div 2) mod 2) + (x mod 3)))) mod 2)
A152592-A059437: 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1
((x - (((x + 1) + (x div 2)) div (1 + (x mod 3)))) mod 2)
A115955-A106344-A077051: 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 0
((1 + ((x2 + (x div 5)) mod 3)) mod 2)
A283876-A024939: 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 1
((1 + (x mod (~1 + (2 * (~x + (2 * (2 + (x mod 2)))))))) mod 2)
A276799: 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 1
(2 * ((x + 1) - ((2 + (x2 div 2)) div (x + 3))))
A020887: 2 4 6 6 8 10 10 12 12 14 14 16 18 18 20 20
(((x + 1) div (1 + (3x mod (x + 3)))) mod 2)
A082960: 1 0 1 1 0 0 1 0 1
A118174-A075438: 1 0 1 1 0 0 1 0 1 0 0 0 1 1 1 1
(4x3 + 6x2 + 14x + 8)
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(((x + 1) mod (1 + (6 mod (1 + (x div 2))))) div 2)
A036857: 0 0 0 0 0 0 0 1 0 0 0 0 3 0 0 1
(((x + 1) - ((x mod 8) mod (1 + (x div 2)))) div 2)
A072376: 0 1 1 1 2 2 2 2 4 4 4 4 4 4 4 4
((x mod 2) - ((x mod (1 + (4 mod (1 + (x div 2))))) mod 2))
A334195: 0 1 0 1 0 0 0 1 ~1 1 0 0 0 0 0 1
((x mod (1 + ((~3x + 4) mod (1 + (x div 2))))) div 2)
A151755: 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 3
((1 + (x2 div (1 + ((x div 3) + (x mod 2))))) mod 2)
A255887: 1 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1
((1 + (x3 mod (1 + (x div (2 - (x mod 2)))))) div 2)
A160588: 0 1 0 2 1 3 0 4 1 5 2 6 3 7 0 8
(52x + 50)
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((1 + ((2 + (x mod (2 + ((x div 2) mod 2)))) mod (x + 1))) div 2)
A286574: 0 1 1 1 1 2 1 2 1 2 2 2 1 2 2 1
((1 + ((0 - (x mod (4 + (x div 2)))) mod (x + 1))) mod 2)
A029435: 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1
((1 + ((2 + (x * (x div (2 + (x mod 2))))) div (x + 1))) mod 2)
A095111: 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1
(((~x + ~1) mod (2 - ((x div 2) div ~3))) div 2)
A095808: 0 0 0 1 0 0 1 0 1 1 0 0 1 1 0 2
(2 - ((~x + 2) div (2 - (x div (~2 + (x mod ~3))))))
A340033: 1 2 2 3 3 3 3 4 4 3 4 4 4 4 4 4
((x2 div (1 + (2 * (1 + ((~x + 1) mod 3))))) mod 2)
A191322: 0 0 0 1 1 1 1 0 1 0 1 1 0 0 0 1
((1 + (((~x2 + 2) mod (1 + (x div 3))) div 2)) mod 2)
A082451: 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1
(((~2x + 4) div (1 + (2 * (1 + (x mod 3))))) mod 2)
A090172: 1 0 0 1 1 1 1 0 0 1 0 1 1 1 0 1
((x div (~1 + (x div (~2 + (x mod (~1 + (x div ~2))))))) mod 2)
A165191: 0 1 1 1 0 1 0 1 1 1 1 1 1 0 1 0
((1 + ((x mod (2 - (x div ~5))) div 2)) mod 2)
A205083: 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1
(2 + (1 div (~1 + (2 * ((x + 2) mod 9)))))
A194322: 2 2 2 2 2 2 2 1 3 2 2 2 2 2 2 2
((x mod (1 + (2 * (2 - (x mod 9))))) mod 2)
A288596: 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0
((1 + (x2 div (2 + ((x + 2) mod 5)))) mod 2)
A189289: 1 1 1 1 0 1 0 1 1 0 0 1 1 1 0 1
((x mod (1 + (2 * ((1 - (x div 2)) mod 5)))) mod 2)
A285949: 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 0
(((2x + ~2) div (3 + (x div 5))) mod 2)
A030315: 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0
(((x + 4) mod (3 + (x div 5))) mod 2)
A266672: 1 0 0 1 0 1 0 1 0 1 0 0 1 0 1 1
(((~x + 2) mod (1 + (2 * (1 + ((~x + 2) mod 4))))) mod 2)
A175253: 0 1 0 0 1 0 0 0 1 1 1 0 0 0 0 1
((1 + ((x - (x div (1 + ((~x + 2) mod 4)))) div 2)) mod 2)
A266848: 1 1 1 0 0 0 1 0 0 1 1 1 1 0 1 1
(((~x + 2) mod (3 + (x div (1 + (x mod 4))))) mod 2)
A026921: 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1
(((2x + 1) mod (1 + (2 * (1 + ((x div 2) mod 2))))) mod 2)
A029428: 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1
(((x + 2) div ((x + ~1) - (2 * (1 + ((x div 2) mod 2))))) mod 2)
A260552: 1 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1
(((x + 1) div (1 + ((1 + (x div (2 + (x mod 2)))) div 2))) mod 2)
A325336-A319368-A068934: 1 0 1 0 0 1 0 0 1 1 0 0 1 0 1 0
((x mod (1 + (2 * ((~1 + (x div 3)) mod 3)))) div 2)
A060175: 0 0 1 0 0 0 0 0 1 2 0 0 0 0 0 0
(x - (2 * (x div (3 + ((x div 3) mod 3)))))
A216209: 0 1 2 3 2 3 4 5 6 3 4 5 6 7 8 9
(((x + 1) - (x div (~2 + (x mod ~6)))) mod 2)
A295895: 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1
(1 - ((x mod (~1 + (2 * ((2 * (x div 2)) div 3)))) div 2))
A308035-A221131: 1 1 1 1 1 1 1 1 0 1 1 1 ~1 ~2 1 1
(((x + 2) mod (~1 + (2 * (((~x + 2) div 2) div 3)))) mod 2)
A288372: 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0
(2 - ((2x div (1 + (2 * (2x mod 3)))) mod 2))
A270647: 2 2 1 2 1 1 2 2 1 2 2 1 2 1 1 2
(1 - ((~x mod (3 + ((x div 2) mod 3))) div 2))
A117201: 1 0 0 1 1 1 1 0 1 0 1 ~1 1 0 0 1
((x + 1) mod (2 * (1 + ((1 + (x div 2)) mod 6))))
A322629: 1 2 3 4 5 6 7 8 9 10 1 0 1 2 3 4
((x - ((~x + 1) div (1 + ((x + ~1) mod 6)))) mod 2)
A284653: 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0
((1 + (((2x + 2) + (x div 2)) mod 6)) div 2)
A190491: 1 2 1 2 0 1 3 1 2 0 2 3 1 2 1 2
((x mod 2) - ((~1 + ((2 + (x div 2)) mod 6)) div 2))
A137412: 0 1 ~1 0 ~1 0 ~2 ~1 1 2 0 1 0 1 ~1 0
(2 * ((2x + 2) - ((x + 1) mod 7)))
A194390: 2 4 6 8 10 12 28 30 32 34 36 38 40 56 58 60
(((~2 + (x * (x mod 3))) mod 7) mod 2)
A295889: 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1
(2 + (7 * ((x2 + 3x) div 2)))
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(((x3 + 2x2 + ~x + ~2) div 7) mod 2)
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(x5 mod 14)
A070599: 0 1 4 5 2 3 6 7 8 11 12 9 10 13 0 1
(((x * (~3 + (x mod 2))) div 7) mod 2)
A074322-A054638: 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1
(2 + (7 * (x + ((x div 2) div 3))))
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((x2 + 2x) div (2 + ((~x + 1) mod 7)))
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(((x3 + ~2x2 + ~x) div 7) mod 2)
A200244: 0 1 1 0 0 0 1 0 1 1 0 0 0 1 0 1
(((x * (2 + (x mod 3))) mod 7) mod 2)
A332219-A122257: 0 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0
(((x * ((x + 2) + (x div 2))) div 7) mod 2)
A289112-A289025-A276794: 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1
(((x2 + (x div 3)) div 7) mod 2)
A093386: 0 0 0 1 0 1 1 1 1 0 0 1 1 0 0 0
(x div (1 - ((~x + 1) div (3 + (x mod 6)))))
A262689-A064876: 0 1 1 1 2 2 2 2 2 3 3 3 2 3 3 3
(2 * (1 + ((3 * (x + ((x div 2) div 3))) div 2)))
A132895: 2 4 8 10 14 16 22 26 28 32 34 38 44 46 50 52
(2x mod (2 + (x mod (1 + (2 * ((~x + 1) mod 3))))))
A035639: 0 0 0 0 0 0 0 0 1 0 0 1 0 0 4 0
(2 * (1 + (((x * ((1 + (x div 2)) div 2)) div 3) mod 2)))
A195051: 2 2 2 4 4 4 2 2 4 2 2 4 2 4 2 2
((x div (3 + ((x + ((x div 2) mod 2)) mod 3))) div 2)
A342846-A045888: 0 0 0 0 0 0 0 0 0 1 1 1 2 1 2 1
(((x + ~2) mod (3 + ((x + (x mod 2)) div 3))) mod 2)
A288375: 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 1
((1 + ((((x + 1) mod 3) + (x div 3)) div 2)) div 2)
A053260: 0 1 0 1 1 0 1 1 1 1 1 1 1 2 1 2
((~1 + ((4x + 4) div (2 + (x div 3)))) div 2)
A325120-A080773: 0 1 2 2 2 3 3 3 4 3 3 4 3 4 4 4
(2 * ((~x + 1) mod (1 + (x div 2) - ((x div 3) mod 2))))
A066285: 0 0 2 0 2 0 6 4 6 0 2 0 6 4 6 0
((1 + ((x - ((2 + (x div 2)) * (x mod 3))) div 2)) mod 2)
A155029-A134540-A089052-A059883: 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 0
((x + 1) div (2 + ((x + 1) mod (3 + (x mod 3)))))
A175001: 0 0 0 1 1 2 2 4 1 3
((1 + (((x * (x + (x div 2))) + (x mod 3)) div 2)) mod 2)
A181656: 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0
((1 + (((x + 2) mod (1 + ((x div 2) * (x div 2)))) div 2)) div 2)
A237720: 0 0 0 0 0 1 2 2 3 3 3 3 4 4 4 4
((1 + (((~2x + 3) mod (1 + (x div 2))) div 2)) mod 2)
A268240: 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1
((x - ((2x + ~1) div (1 + ((1 + (x div 2)) div 2)))) div 2)
A337634: 0 0 0 0 0 0 1 1 1 2 3 3 3 3 4 5
(((x2 + 2x + ~2) div (1 + ((1 + (x div 2)) div 2))) mod 2)
A093318: 0 1 1 0 1 0 1 0 0 0 1 1 1 0 0 0
((x2 div (1 + (((~x + 2) mod (1 + (x div 2))) div 2))) mod 2)
A061265: 0 1 0 1 0 1 0 0 1 0 1 0 0 0 1 0
((1 + ((x3 div ((x + 1) + (x div 2))) div 2)) mod 2)
A190233: 1 1 0 1 1 0 1 0 0 1 0 0 0 1 1 0
((1 + (((x + 1) * ((2 + (x div 2)) div 3)) div 2)) mod 2)
A307837: 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1
((1 + (((~2 + ((x div 2) div 3)) mod (x + 1)) div 2)) mod 2)
A316917: 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1
((1 + (x2 div (2 + (6 mod (x + 1))))) mod 2)
A319372-A319367-A176510-A176047-A106465-A051031: 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1
(2 div (2 + ((x3 + ~2x2) mod (2x + 3))))
A231367: 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0
(((~3x + 7) div (1 + ((x + 1) div 2))) mod 2)
A011747: 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 1
(((x3 + ~2x2 + x) div (1 + ((x + 1) div 2))) mod 2)
A065715: 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0
(((8x + ~2) div (1 + ((x + 1) div 2))) mod 2)
A263657: 0 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1
(((x div 8) - (x mod ~5)) mod 2)
A219071: 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1
(((~x + 1) mod (1 + (x mod 2) - (x div ~4))) div 2)
A236358-A236325-A234503: 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 2
(((x + 1) - (((x + ~1) mod (2 - (x div ~2))) div 2)) div 2)
A194241: 0 1 1 1 2 2 3 4 4 5 5 5 6 6 6 7
((1 + ((x - ((~x + 2) mod (2 - (x div ~2)))) div 2)) mod 2)
A286813: 1 1 0 1 0 0 1 0 1 1 1 1 0 0 1 1
(((x + 1) mod (1 + (2 * ((1 + (x div 4)) div 2)))) div 2)
A285716: 0 0 0 0 1 0 0 1 0 0 1 0 1 2 0 0
(2 * (4 mod (1 + (2 * ((1 + (x div 4)) div 2)))))
A330487: 0 0 0 0 2 2 2 2 2 2 2 2 8 8 8 8
((x2 div (1 + (2 * (2 + ((x div 2) mod 3))))) mod 2)
A093383: 0 0 0 1 1 0 1 1 1 1 1 1 0 1 0 0
((x mod (~5 + ((x2 div 2) mod 3))) mod 2)
A327222: 0 0 1 1 0 0 0 1 1 1 0 0 1 0 1 1
((x div (1 + (x div (2 + ((x + 2) mod 6))))) mod 2)
A174282: 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 1
(((1 + (x div 2)) div (1 + (2 * (x mod 6)))) mod 2)
A025911: 1 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1
((1 + (x3 div (4 + (x div 3)))) mod 2)
A104338: 1 1 1 0 1 0 1 0 0 1 1 1 1 1 0 0
(((2x + 1) div (~1 + (4 * (x div 3)))) mod 2)
A305080: 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1
((1 + ((x + 2) div (4 - ((x mod 3) mod 2)))) mod 2)
A267679: 1 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1
((1 + (((x2 mod (3x + ~1)) div 2) div 2)) mod 2)
A260397: 1 1 0 1 0 1 1 1 1 1 0 1 0 1 1 0
((x - ((x2 + 1) mod (1 + (((x + 1) div 2) div 2)))) div 2)
A338624: 0 0 1 1 1 2 2 2 3 4 4 4 5 5 6 7
(4x2 + 36x + 42)
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((1 + ((x - (((x + ~1) * (x div 3)) div 2)) div 2)) mod 2)
A194677-A194667: 1 1 0 0 0 0 1 1 1 1 1 1 0 1 1 1
((1 + (((~1 + (x mod 3)) * ((x + ~1) div 2)) div 2)) mod 2)
A082416: 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 1
(2 * ((x + 3) - (x div (~2 + (x div ~4)))))
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((1 + (x div (2 * (~2 + (((x + ~2) div 3) mod 2))))) mod 2)
A029437: 1 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1
((1 + (x div (2 + (x div (2 + (x mod 6)))))) mod 2)
A133081: 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0
(((x + ~1) div (1 + (2 * (2 + ((x mod 3) mod 2))))) mod 2)
A266608: 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0
(((x + ~1) mod (3 + (((1 + (x div 2)) div 2) div 2))) div 2)
A090723: 1 0 0 1 0 0 0 1 1 0 0 1 1 0 1 2
((x - (x div (~5 + (x mod ~4)))) mod 2)
A052344: 0 0 1 0 1 0 1 1 0 1 0 1 1 1 0 0
((1 + ((x div (2 * (~2 + ((x mod 3) div 2)))) div 2)) mod 2)
A029405: 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 1
((1 + (x div (2 * (~2 + (x mod ~7))))) mod 2)
A025917: 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0
(x - ((1 + (x div (2x + ~32))) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A191890: 0 1 2 3 4 5 6 7 8 9 10 12 13 14 16 19
((1 + (x div (2 * (2 + (x mod (2 + ((x div 2) mod 2))))))) mod 2)
A010056: 1 1 1 1 0 1 0 0 1 0 0 0 0 1 0 0
((1 + (((x + 1) mod (6 + (x mod 2))) div 2)) mod 2)
A288929: 1 0 0 1 1 0 1 1 0 0 1 1 1 1 0 0
((x2 mod (1 + (8 * (~2 + (x mod 2))))) mod 2)
A180433: 0 0 1 1 0 1 1 0 1 1 1 1 0 0 0 0
(x mod (2 * (1 + (2 * (1 - (x mod ~7))))))
A269165: 0 1 2 3 4 5 6 1 8 9 10 11 12 3 2 15
((((~x2 + 2) div 2) mod 17) mod 2)
A320655-A285313-A189298-A065043: 1 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1
(x4 mod 34)
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((x div (~1 + ((x2 + x) mod 16))) mod 2)
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(((x + 1) mod (1 + (2 * ((~x + 1) mod 8)))) mod 2)
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(((~x + 3) mod (2x + ~17)) mod 2)
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((1 + ((x + (x mod 2)) mod (4 + (x div 4)))) mod 2)
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((1 + ((x - ((~x + 1) div (2 + (x mod 4)))) div 2)) mod 2)
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((1 + ((x + 1) div (2 + (x div (2 + (x mod 4)))))) mod 2)
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((1 + (x mod (2 + ((x + 2) div (2 + ((x div 2) mod 2)))))) mod 2)
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((x mod (~5 + ((x + 2) mod (2 + (x mod 2))))) mod 2)
A143542: 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 0
(((x2 + ~2) div (1 + (4 * (2 + (x mod 2))))) mod 2)
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((1 + ((x + 1) div (2 + (x div (2 * (2 + (x mod 2))))))) div 2)
A318464: 0 1 1 1 1 2 1 1 1 2 1 2 1 2 2 2
(((x + 1) mod (1 + (2 * (((x + ~1) div 2) mod 4)))) div 2)
A227837: 0 0 0 0 1 0 1 0 1 0 0 0 0 2 0 1
((2x mod (~1 + (2 * (((~x + 2) div 2) mod 4)))) div 2)
A324351-A004198: 0 0 0 0 1 0 0 0 0 0 0 1 2 1 0 0
(2x - ((~1 + ((x - ((x div 2) mod 4)) div 2)) div 2))
A287724-A284590: 1 3 5 6 8 10 12 14 15 17 19 20 22 24 26 28
((1 - ((x + 1) mod (~1 + (x div ~7)))) mod 2)
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(~2 + (9 * ((x2 + 3x + 2) div 2)))
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((2x + 2) - ((2x div 9) mod 2))
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(2 + (x div ((x + ~1) + (2x mod 9))))
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((x mod (~9 + (x * (x mod 3)))) mod 2)
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(((x * (2 + (x * (x mod 2)))) div 9) mod 2)
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((2x + 1) mod (2 + (x mod (1 + (x div 8)))))
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(((x + 1) + ((x div 2) mod 2) - (x div 8)) div 2)
A157477: 0 1 2 2 2 3 4 4 4 4 5 6 6 6 7 8
((1 + ((2 + (x div 2)) div (2 + ((~x + 1) mod 4)))) div 2)
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((1 + ((3x + ~3) div (2 + (x div 4)))) mod 2)
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(((x + ~1) - ((2x + 1) mod (2 + (x div 4)))) mod 2)
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(((1 + (x div 3)) div (1 + (2 * (x mod 4)))) mod 2)
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((1 + ((2x3 mod (x + 4)) div 2)) mod 2)
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((1 + ((2x2 + 4) div (x + 6))) mod 2)
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((1 + (((~x2 + 3x) mod (x + 4)) div 2)) mod 2)
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((1 + (x mod (2 + ((2x + 1) mod (2 + (x div 2)))))) mod 2)
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((1 + ((2 + (x div 3)) div (2 + ((x div 2) mod 2)))) div 2)
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(((x + ~1) div (1 + (x mod (4 * (2 - (x mod 2)))))) mod 2)
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((x - ((2x + 4) div (1 + (2 * (2 + (x mod 2)))))) mod 2)
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(((x * (x div 2)) - (x div (1 + (2 * (2 + (x mod 2)))))) mod 2)
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(2 + ((x div 2) mod (1 + (x2 mod (2 * (2 + (x mod 2)))))))
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(1 - ((x mod (1 + ((~1 + (x div ~2)) mod 4))) div 2))
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(((x + ~1) mod (~1 + (4 * ((x + ~2) div 3)))) mod 2)
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(((x + ~1) + (2 div (1 + ((1 + (x div 2)) mod 4)))) div 2)
A194167: 0 0 0 1 1 2 3 4 4 4 4 5 5 6 7 8
(((x + 1) div (1 + (x mod (x - ((x + 1) mod 4))))) mod 2)
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(1 - ((x mod (1 + (((~x2 + x) div 2) mod 4))) div 2))
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(((x2 mod (2x + ~5)) mod 5) mod 2)
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(2 * ((12x + 12) div 5))
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((((2x + ~2) mod (x + 3)) mod 5) mod 2)
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(((~1 + (x * ((x + 1) + (x div 2)))) div 5) mod 2)
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(((~1 + (x * (x div (2 + (x mod 2))))) div 5) mod 2)
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((((x + 1) * ((~x + 2) mod 3)) mod 5) div 2)
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(2 * ((16x + 16) div 5))
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((x div 2) - ((x + ~1) div (2 + ((x + 1) div 5))))
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((x - ((1 + (x * (x + (x div 2)))) div 5)) mod 2)
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(2 * (x - (5 * ((x div 5) mod 2))))
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((((1 + ((~x + 1) * (x div 2))) div 2) div 5) mod 2)
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(((~2 + ((x + 2) * (x div 4))) div 5) mod 2)
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((((~x2 + 1) mod (x + 4)) mod 5) mod 2)
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(((~x2 * (2 + (x div 2))) div 5) mod 2)
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(((~2 + (x * (1 + (2 * (x mod 2))))) div 5) mod 2)
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((((x + ~2) - (x * (x div 3))) mod 5) mod 2)
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(((~2 + (x * (((x + 1) div 2) div 2))) div 5) mod 2)
A179830: 1 1 1 0 0 0 0 0 0 1 1 0 0 1 0 1
((x + 2) - (x div (~2 + (((~x + 2) div 2) div 5))))
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((~x + 1) mod (1 - (2 * (((~x + 2) div 2) div 5))))
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(x div (x - (2 * ((x - ((~x + 2) div 2)) div 5))))
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(((2x + 2) div (x - ((x + 2) mod 5))) mod 2)
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((((x + 1) div 3) - ((x + ~2) mod 5)) mod 2)
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(((x + 1) div ((x + ~2) + (2x mod 5))) mod 2)
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((2 + (x div 3)) div (2 + (2x mod 5)))
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((x + 1) mod (2 - (x div (2 + ((x div 2) mod 5)))))
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(0 - (x div (~10 + (x mod (1 + (x div 2))))))
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(x - ((x + 2) div (~10 + ((x + 1) div 2))))
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(((~x + ~2) - (x div 4)) mod 10)
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((x4 + ~4) mod 10)
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(10x + (x mod 10))
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(x - ((5 * (~x + ((x + ~1) div 3))) div 2))
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(x - ((5 * (~x + ((x + ~2) div 3))) div 2))
A047556: 3 6 7 11 14 15 19 22 23 27 30 31 35 38 39 43
(1 - (((x div 2) - ((x2 + x) div 5)) div 2))
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(((1 - (x * (((x + 1) div 2) div 2))) div 5) mod 2)
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(1 - ((x + 4) mod (~2 + ((~x + 2) div 5))))
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((((x2 + 2) div 3) - (x div 5)) div 2)
A211533: 0 0 1 1 3 4 5 8 10 13 16 19 23 27 32 36
((((x + (x mod 3)) div 2) + (x div 5)) div 2)
A229878: 0 0 1 0 1 2
A025128: 0 0 1 0 1 2 2 2 3 2 3 4 4 4 5 5
((2x + 2) - (((x mod 2) - (x div 5)) div 2))
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((2x + 10) + ((x div 5) mod 2))
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((2 + (x div 5)) div (2 + (x mod 5)))
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((1 + ((x + (6 mod (x + 1))) mod 4)) div 2)
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(2 * ((x + 1) - (((~x + 2) - (x div 4)) div 4)))
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A141104: 2 4 6 10 12 14 18 20 22 26 28 30 34 36 38 40
((1 + ((x + (2x mod (2 + (x div 2)))) div 4)) mod 2)
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(x - (((x mod 2) - (x div (~1 + ((~x + 2) div 4)))) div 2))
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(((~1 + (x div 3)) div (1 + ((~x + 2) mod 4))) mod 2)
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((x div 2) div (2 + ((~x + 1) mod (1 + ((~x + 2) mod 4)))))
A294232: 0 0 0 0 1 1 1 0 1 2 2 1 2 3 3 1
((x + 3) mod (2 + ((x + 1) mod (1 + (x div 4)))))
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(1 - ((((~x + 2) div 4) * (1 + (x div 4))) div 2))
A035450: 1 1 1 2 2 2 2 3 4 4 4 6 7 7 7 9
((x mod (2 - ((~x + 3) div (1 + (x mod 4))))) div 2)
A297173-A286470-A243055-A242411: 0 0 0 0 0 1 0 0 0 2 0 1 0 3 1 0
((x2 div ((2x + ~1) - (x2 div 4))) mod 2)
A244992: 0 1 0 1 1 0 0 1 0 1 1 0 0 0 1 1
((1 + (((x * (1 + (x mod ~3))) div 2) div 2)) mod 2)
A319843: 1 0 1 1 0 1 0 1 1 1 0 1 0 1 1 0
((1 + ((x4 + ~x3) div (x + 4))) mod 2)
A328102: 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 1
(2x2 + 28x + 78)
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((x2 mod (1 + ((x2 + ~x) mod (x + 4)))) mod 2)
A242018: 0 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1
((1 + (((x + 1) - (2 * (x mod 2))) mod (2 + (x div 2)))) div 2)
A029263: 1 0 0 1 1 0 1 1 2 1 2 2 3 2 3 3
((1 + ((x3 + x2 + x) div (2 + (x div 2)))) mod 2)
A156062: 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0
((x - ((x + ~1) div (2 - (x div (1 + ((x div 2) mod 2)))))) mod 2)
A328308: 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0
((x - ((~x + 1) div (2 - (x div (1 + ((x div 2) mod 2)))))) mod 2)
A092248-A069513: 0 1 1 1 1 0 1 1 1 0 1 0 1 0 0 1
(((x * (x + (x div 2))) div (1 + (2 * (2 - (x mod 2))))) mod 2)
A028999: 0 0 1 0 0 1 0 1 1 1 0 0 1 0 0 0
(((2 - (x div 3)) mod (1 + (x div (2 + (x mod 2))))) div 2)
A263280: 0 0 0 0 0 0 0 0 0 1 2 1 2 1 3 1
((x - ((x + 1) mod (2 - (x div (~3 + (x mod 2)))))) mod 2)
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((x + 2) div (2 + (3 * (x div (1 + (x div 3))))))
A025845: 1 0 0 1 0 0 1 1 1 1 1 1 1 1 2 2
((3 * ((x2 + x) div 7)) div 2)
A194226: 0 0 0 1 3 6 9 12 15 18 22 27 33 39 45 51
(2 - ((3 * (~1 + ((~x + 2) mod 6))) div 2))
A156283: 1 2 4 ~4 ~2 ~1 1 2 4 ~4 ~2 ~1 1 2 4 ~4
(((1 + (x div (1 - (2 * (x div 3))))) mod 3) mod 2)
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((3 * ((x div 2) div (1 + (2 * (1 + (x mod 2)))))) div 2)
A035648: 0 0 0 0 0 0 1 0 1 0 1 1 3 1 3 1
(((x3 mod (2x + 3)) div 3) mod 2)
A011664: 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1
(x - ((3 * (2x div ~5)) div 2))
A047515: 0 3 4 6 7 8 11 12 14 15 16 19 20 22 23 24
((((x + 2) div (~1 + (2 * (x mod 4)))) mod 3) mod 2)
A294878: 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0
((x div (1 - (3 * (1 + ((x + 1) mod 4))))) mod 2)
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(((x - ((x2 + 1) mod 5)) div 3) mod 2)
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(x - ((3 * ((~2x + 2) div 5)) div 2))
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(x - ((3 * ((~2x + 1) div 5)) div 2))
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(((x + ~1) div (3 * (1 + ((~x + 2) mod 4)))) mod 2)
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((((x2 + ~2) mod (2x + 5)) div 3) mod 2)
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(4 div ((x - (3 * (~3 + (x div 2)))) div 2))
A339219: 1 0 1 1 1 1 1 1 2 1 2 2 4 2 4 4
((3 * (x - ((~1 + (x div ~2)) div 3))) div 2)
A225647: 1 3 4 6 7
A330172: 1 3 4 6 7 10 12 13 15 16 18 21 22 24 25 27
(x - (2 * ((x - ((x div 3) mod 3)) div 3)))
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(1 - (((x div (3 * (~2 + (x mod 2)))) mod 3) div 2))
A209402-A184171: 1 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1
(((x + 1) div 2) - ((3 * ((x div 2) div 3)) div 2))
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((2 - ((((~x + 2) div 2) * (x div 3)) div 3)) div 2)
A337206: 1 1 1 1 1 1 2 2 2 3 3 3 4 5 5 7
((2 + (x div 3)) div (2 + (3 * (x mod 3))))
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((x - ((1 + ((x * (x div 3)) div 2)) mod 3)) mod 2)
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(((1 + ((1 - (x div 3)) * (x div 2))) mod 3) mod 2)
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(2 * (((1 + ((x div 2) mod 2)) * (1 + (x div 2))) div 3))
A237120: 0 0 2 2 2 2 4 4 2 2 8 8 4 4 10 10
(((x + ~1) mod (3 + ((x + ~2) mod (1 + (x div 2))))) div 2)
A035435-A029269: 1 0 0 1 1 0 1 1 1 1 2 2 2 2 3 3
((((x + ~1) * (2 - ((x div 4) mod 2))) div 3) mod 2)
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(((x div 7) + ((x + ~1) mod 3)) div 2)
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((x - ((2x div (2 - (x div ~2))) mod 3)) div 2)
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((2 - (x div (3 * (~3 + (x mod 3))))) div 2)
A263104: 1 1 1 1 1 2 1 2 2 1 2 3 2 2 3 2
(2 + (3 * ((x2 mod (2x + ~5)) mod 2)))
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((x + 2) - ((~x + 1) div (x - (((x + ~1) div 2) div 3))))
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(((x - (2 * ((2 - (x div 3)) div 2))) div 3) mod 2)
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((x - ((x div (2 + ((x div 3) mod 2))) mod 3)) div 2)
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((3 * ((x div 3) - (((x + ~1) div 2) div 2))) div 2)
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((3 * ((x + 2) div (4 * (2 + (x mod 2))))) div 2)
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(x - ((3 * ((x + 2) div ~7)) div 2))
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((2 - (x2 div ~21)) div 2)
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(2 + (((x + ~1) + ((~x + 1) mod 8)) div 3))
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(2 * (x - (((x + ~2) - (x2 div 4)) div 3)))
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((x - ((((~x2 + ~x + 2) div 2) div 2) div 3)) div 2)
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((((0 - ((x2 + (x div 2)) div 2)) div 2) div 3) mod 2)
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(x div ((3 * (2 + (((x div 2) - (x mod 2)) div 2))) div 2))
A273190: 0 1 0 1 1 1 1 1 1 2 1 1 1 2 2 2
(x div (4 - (x2 mod ~10)))
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((2x + 2) - ((x2 div 12) mod 2))
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(2 + ((4 * (x + (x div 5))) div 3))
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((3 * ((3x + 3) + (x div 4))) div 2)
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((3 * (x div (2 * (8 - (x div 2))))) div 2)
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(x - (3 mod (1 - (2 * ((2 * (x div 2)) div 3)))))
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A087087-A050742: 0 1 2 3 4 5 6 7 8 9 12 13 16 17 18 19
(2 * ((2 * (x + (6 div (x + 1)))) div 3))
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((x2 div (4x + ~11)) mod 2)
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(x - ((x - (((1 - (x div 2)) mod (x + 2)) mod 3)) div 2))
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((((1 - ((x div 2) * (x div 2))) mod (x + 2)) div 3) mod 2)
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(x - ((~6x3 + ~9x2 + 6x) div 2))
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(x - (2 * (x div (8 - ((x + ~2) div 3)))))
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(2 + (x div 2) - ((~x + 2) div (2 + (2x div 3))))
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(((5x + 5) + ((x div 2) div 3)) div 2)
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((x mod ((2 * (1 + (x mod 2))) + ((x div 2) div 3))) div 2)
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(x - (~14 * ((x div 2) div 3)))
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(2 + (x div 2) - ((~x + 2) div (2 + ((x div 2) div 3))))
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(x - ((x + 2) div (~6 + (((x + ~1) div 2) div 2))))
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((x mod (x - ((x + 1) mod 8))) mod 6)
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(7x2 + 16x + ~6)
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(1 - (((x + (x div 12)) mod 3) div 2))
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(2 * ((x * ((x + ~1) + ((x div 2) div 3))) div 3))
A157416: 0 0 0 4 8 12 24 32 42 54
(((~x + (((~x + 2) * (x div 2)) div 3)) div 3) mod 2)
A189476-A140591: 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 0
((x + 2) mod (2 + ((x + (x2 div 3)) mod 3)))
A339872: 0 0 0 1 0 1 0 1 2 1 0 1 0 1 1 1
(((x + ((x + 3) mod 8)) div 3) mod 2)
A004547: 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1
(x - ((x - ((x * (2 + (x div 4))) div 3)) div 2))
A084689: 0 1 2 3 4 5 6 7 9
A222030: 0 1 2 3 4 5 6 7 9 11 12 13 16 17 19 20
((21x2 + x) div 2)
A022279: 0 11 43 96 170 265 381 518 676 855 1055 1276 1518 1781 2065 2370
(x - (((x div 2) - ((x * (x div 4)) div 3)) div 2))
A084689: 0 1 2 3 4 5 6 7 9
A191852: 0 1 2 3 4 5 6 7 9 10 11 12 15 17 18 19
((x - (2 mod (2 - ((x2 + 4x) div 3)))) div 2)
A156023: 0 0 1 3 5 8 11 14 18 22 26 31 36 41 47 53
((x - ((~x4 + 4x2) div 3)) div 2)
A326278: 0 0 1 9 34 90 195 371 644 1044 1605 2365 3366 4654 6279 8295
(2 * (x - ((x2 + 2) div ((x + 3) + (x div 2)))))
A116568: 0 2 2 4 4 6 6 8 8 8 10 10 12 12 12 12
((((2x + ~1) - (x div 3)) * (x div 3)) div 2)
A211546: 0 0 0 2 3 4 9 11 13 21 24 27 38 42 46 60
(2 * (((x - (x mod 4)) div 3) + (x div 3)))
A211514: 0 0 0 2 4 4 6 6 8 10 10 10 16 16 16 18
((((~x + ((x div 2) mod 2)) mod 3) + (x div 3)) div 2)
A092695: 0 1 1 1 1 1 1 1 1 1 1 2 2 3 3 3
(((x + 1) mod (((x + 1) mod 4) + (x div 3))) div 2)
A051659: 0 0 0 0 0 0 1 0 0 0 2 0 1 1 0 0
((((2x + ~4) div (x + 4)) + (x div 3)) mod 2)
A176329: 1 1 0 1 1 1 0 0 1 0 0 0 1 1 1 0
(2 * ((4x + 2) + (x div 2) - (x div 3)))
A063246: 4 12 22 28 38 46 54 62 72 78 88 96 104 112 122 128
((((x + ~3) mod (2 + (x div 2))) + (x div 3)) mod 2)
A330268: 1 0 0 1 0 1 1 0 1 1 1 0 1 0 0 0
(((x + 1) - ((~x + 1) mod 3)) div (2 + (x div 3)))
A015718: 0 1 0 1 1 1 1 2 1 1 2 2 2 2 2 2
(((x + 1) * (3 - (x mod 2))) div (2 + (x div 3)))
A291303: 1 2 4 2 5 4 5
(x - ((x - (x2 div 4)) div (2 + (x div 3))))
A079057: 0 1 2 3 4 6 7 9 10 12 13 15 16 18 20 21
(((x div 2) mod (1 + ((x mod 4) + (x mod 3)))) div 2)
A323069: 0 0 0 0 0 1 0 1 0 0 0 2 0 0 1 1
(x - (2 * (((x div 3) mod 3) - (x mod 3))))
A181099: 0 3 6 1 4 7 2 5 8 9 12 15 10 13 16 11
(x div (2 + (x div ((2 * (1 + (x mod 2))) + (x mod 3)))))
A339929: 0 0 1 1 1 2 1 2 2 2 2 3 1 3 2 3
(((x + 2) div (2 + (((x div 2) mod 2) + (x mod 3)))) mod 2)
A267001: 1 1 0 1 0 1 0 0 0 1 1 0 1 1 1 1
(4 div (4 + (x mod 3) - (x div 4)))
A029268: 1 0 0 1 1 0 1 1 1 2 1 1 4 2 1 4
(((~2x + 1) mod (2 + ((x div 2) + (x mod 3)))) mod 2)
A116937: 1 0 0 1 1 1 0 1 1 1 1 0 1 0 0 1
(1 - ((((x + 1) div 2) mod 4) div (2 + (x mod 3))))
A248392: 1 1 1 0 1 1 0 1 1 1 1 1 0 0 1 1
((((x div 3) mod 3) div 2) + ((x mod 3) div 2))
A330168-A273513-A093955-A081603: 0 0 1 0 0 1 1 1 2 0 0 1 0 0 1 1
((2 * (x - ((~x + 1) div 3))) + ((x mod 3) div 2))
A047525: 0 2 7 8 10 15 16 18 23 24 26 31 32 34 39 40
((2 * ((x + 2) + (x div 3))) - ((x mod 3) div 2))
A047506: 4 6 7 12 14 15 20 22 23 28 30 31 36 38 39 44
((2 - ((x mod (2 + (x div 2))) mod 2)) * ((x mod 3) mod 2))
A337985: 0 1 0 0 2 0 0 2 0 0 1 0 0 1 0 0
((15x2 + ~11x) div 2)
A226489: 0 2 19 51 98 160 237 329 436 558 695 847 1014 1196 1393 1605
((3 * (x2 + (3 * (x2 div 2)))) div 2)
A195046: 0 1 15 31 60 91 135 181 240 301 375 451 540 631 735 841
((x div 2) div (2 + ((x2 + (x div 4)) mod 3)))
A240872: 0 0 0 0 0 0 1 0 2 1 2 2 3 2 2 3
(((x2 + ((x + ~2) * (x div 3))) div 3) mod 2)
A302480: 0 0 1 1 0 1 0 1 1 0 1 1 1 1 1 0
(x - ((((x + ~1) div 3) - (x2 div 3)) div 2))
A236343: 1 1 3 5 6 9 12 14 18 22 25 30 35 39 45 51
((1 + ((x * (x div (~1 - (x mod 3)))) div 2)) mod 2)
A166253: 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0
((1 + (x div (2 + (1 mod ((~x + 1) + (x mod 3)))))) mod 2)
A114915: 1 1 0 0 1 0 0 1 1 1 1 0 1 1 1 1
(x - ((~1 + ((~x + ((x div 2) mod 5)) div 2)) div 2))
A261466: 1 2 3 4 5 7 8 9 10 11 13 15 16 17 18 19
(x - ((~1 + (2x mod (x + 10))) div 2))
A079596: 1 1 1 1 1 1 1 1 1 1 11 11 12 12 13 13
(x div (2 * (1 + (x2 mod (2x + 16)))))
A276580: 0 0 0 0 0 0 0 0 4 0 0 0 0 3 0 0
(x - ((~1 + ((x + ((2 - (x div 2)) mod 4)) div 2)) div 2))
A330881: 0 1 2 3 4 5 5 5 6 7 8 9 10 11 11 11
((x + 1) div (2 + (x div (3 - ((x * (x div 2)) mod 2)))))
A112758: 0 1 1 1 1 2 1 1 2 2 2 1 2 2 2 1
(((x2 div (3 + (x div 2))) mod (x + 3)) mod 2)
A288306-A164056: 0 0 1 0 1 1 0 0 1 1 0 1 1 0 0 0
(2 * ((2x + 1) + (x2 div (3x + ~2))))
A285658: 2 8 12 16 20 24 30 34 38 44 48 52 58 62 66 72
(2x2 + 24x + 30)
A154599: 30 56 86 120 158 200 246 296 350 408 470 536 606 680 758 840
((2x3 + 11x2 + 11x + 3) div 2)
A162265: 1 13 42 94 175 291 448 652 909 1225 1606 2058 2587 3199 3900 4696
(x - (2 * ((~2x + ~1) + ((x - (x div 4)) div 2))))
A066097-A035336: 2 7 10 15 20 23 28 31 36 41 44 49 54 57 62 65
(~2 + ((2x + 1) * ((x2 + 5x) div 2)))
A162257: ~2 7 33 82 160 273 427 628 882 1195 1573 2022 2548 3157 3855 4648
((4x + 2) + ((x + (x div 2)) div 5))
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((4x + 2) + (((x + 1) + (x div 4)) div 2))
A287726: 2 7 11 16 21 25 30 34 39 44 48 53 58 62 67 71
((4x + 2) + ((~x + 2) div (4 + (x mod 2))))
A247785: 2 6 10 13 17 21 25 29 32 36 40 44 47 51 55 59
(((~x + (2 * (x mod 8))) mod (2x + 1)) div 2)
A035657: 0 0 1 1 2 2 3 3 4 6 7 9 10 12 13 15
((6x3 + ~7x2 + 3x) div 2)
A071230: 0 1 13 54 142 295 531 868 1324 1917 2665 3586 4698 6019 7567 9360
((1 + (((~1 + ((x + 1) mod 4)) div 2) * (x div 2))) div 2)
A130507: 0 0 1 0 0 0 2 ~1 0 0 3 ~2 0 0 4 ~3
(((x - (3 * (x div ~2))) * (1 + (x div 2))) div 2)
A195014: 0 2 5 9 15 21 30 38 50 60 75 87 105 119 140 156
(((x div 2) - (~4x div (1 + (x div 2)))) div 2)
A079243: 0 2 2 3
A060018: 0 2 2 3 4 4 4 5 5 6 6 6 6 7 7 7
(((2 * (x2 div (x + 4))) mod (1 + (x div 2))) div 2)
A238213: 0 0 0 0 0 0 1 0 0 1 1 2 2 2 2 3
(((2 - ((~x2 + x) div 4)) div (1 + (x div 2))) mod 2)
A318757-A318753: 0 0 1 0 1 0 0 1 1 0 0 1 1 1 0 0
(x - ((((~2x + ~4) + (x div 2)) * (1 + (x div 2))) div 2))
A241200: 2 4 9 12 19 23 32 37 48 54 67 74 89 97 114 123
(((2x + ((x div 2) mod 3)) * (1 + (x div 2))) div 2)
A321130: 0 1 5 7 15 18 24
((x2 - ((~2x + (x div 2)) * (1 + (x div 2)))) div 2)
A210978: 0 1 5 9 17 24 36 46 62 75 95 111 135 154 182 204
(((x div 2) - (2x3 div (1 + (x div 2)))) mod 2)
A308187: 0 0 1 0 0 1 1 0 0 1 0 0 1 1 1 0
(x + (2 * (1 + (x div 2))) - (((1 + (x div 2)) div 2) div 2))
A188084: 2 3 6 7 10 11 13 14 17 18 21 22 25 26 28 29
(x + (((1 - (x div 2)) mod 4) + (2 * (1 + (x div 2)))))
A288731: 3 4 6 7 13 14 16 17 19 20 22 23 29 30 32 33
(((x * (3 + (x mod 3))) div (1 + (x div 2))) mod 2)
A214845: 0 0 1 0 1 0 0 1 0 1 0 1 1 1 0 1
(((2 * (x div 2)) div 3) - ((x mod (1 + (x div 2))) div 2))
A103502: 0 0 0 0 1 0 1 1 1 0 1 1 2 1 1 1
(((x + 1) div (1 + ((x div 5) + (x mod 2)))) mod 2)
A098370: 1 1 1 0 1 0 1 0 0 1 1 1 0 1 1 1
((1 + (((x - ((x div 3) mod 2)) div 2) + (x mod 2))) div 2)
A147981: 0 1 1 1 1 2 2 2 2 3 2 3 3 4 4 4
(2 + ((x + ((x2 + 2x) div 4)) div (1 + (x mod 2))))
A201500: 2 2 6 5 12 8 20 13 30 18 42 25 56 32 72 41
(((3x + 1) * ((x3 + x2) div 2)) div 2)
A213827: 0 2 21 90 260 600 1197 2156 3600 5670 8525 12342 17316 23660 31605 41400
(2 * (1 + compr(\x.(((x2 + ~x) div 8) mod 2),x)))
A194406: 2 4 6 8 12 26 30 32 34 36 38 40 44 58 62 64
((8x3 + 17x2 + 10x + 1) div 2)
A262402: 0 18 76 200 412 738 1200 1824 2632 3650 4900 6408 8196 10290 12712 15488
((6x3 + 9x2 + 4x + 1) div 2)
A248575: 0 10 46 128 272 498 822 1264 1840 2570 3470 4560 5856 7378 9142 11168
((4x3 + 9x2 + 7x + 2) div 2)
A213772: 1 11 42 106 215 381 616 932 1341 1855 2486 3246 4147 5201 6420 7816
((x - ((1 - (x mod 7)) div (x + 1))) mod 2)
A190938: 1 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1
(((~1 + (((1 + (x * (x div 2))) div 2) div 2)) mod (x + 1)) mod 2)
A330037: 0 1 0 0 1 1 1 0 1 0 0 1 0 0 0 1
(((1 + ((x + 1) mod ~7)) div (x + 1)) mod 2)
A267800: 1 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1
(((1 - ((x * (x div 3)) div 3)) mod (x + 1)) mod 2)
A284789: 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 0
(((x2 div (3 + (x * (x mod 2)))) mod (x + 1)) mod 2)
A075603: 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0
(x - (x div (2 + ((4 - (x mod 3)) mod (x + 1)))))
A129229: 0 1 2 2 4 4 5 6 6 8 8 9 10 11 11 13
(2 + ((x + 1) * ((x + 2) - (2 div (~1 + (x2 div 2))))))
A162522: 6 12 8 22 32 44
(2 + ((x + 1) * ((8 mod (x + 2)) div (x + 1))))
A072865: 2 4 2 2 2 2 2 10 2 2 2 2 2 2 2 2
((x div 2) div (2 + (14 mod (x + 1))))
A097027: 0 0 0 0 0 0 1 0 0 0 1 1 2 3 0 0
((2x3 + 11x2 + 15x + 6) div 2)
A144640: 3 17 48 102 185 303 462 668 927 1245 1628 2082 2613 3227 3930 4728
(((x + 1) * ((x3 + x2 + 4x + 4) div 2)) div 2)
A125641: 1 5 18 52 125 261 490 848 1377 2125 3146 4500 6253 8477 11250 14656
(2 + (((4 + (x div 2)) * ((x + 1) div 2)) div (x + 1)))
A274047: 2 4 3 4 4 5 5 5 5 6 6 6 6 7 7 7
(2 div (2 + ((2 * ((~x + 2) mod 6)) mod (x + 1))))
A133080: 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 0
((x2 + ~1) mod (2 + (16 mod (x + 1))))
A069531: 1 0 0 0 0 0 3 0 0 0 1 0 3 0 0 0
((8x3 + x2 + ~7x) div 2)
A256646: 0 1 27 102 250 495 861 1372 2052 2925 4015 5346 6942 8827 11025 13560
((4x3 + 11x2 + 9x + 2) div 2)
A135712: 1 13 48 118 235 411 658 988 1413 1945 2596 3378 4303 5383 6630 8056
((2x3 + 11x2 + 21x + 12) div 2)
A162267: 6 23 57 114 200 321 483 692 954 1275 1661 2118 2652 3269 3975 4776
((4x3 + 13x2 + 13x + 4) div 2)
A125200: 2 17 57 134 260 447 707 1052 1494 2045 2717 3522 4472 5579 6855 8312
((3x3 + 17x2 + 22x + 8) div 2)
A180569: 4 25 72 154 280 459 700 1012 1404 1885 2464 3150 3952 4879 5940 7144
(((x3 + 3x2 + 4x + 2) * (2 + (x mod 2))) div 2)
A093917: 2 15 30 102 130 333 350 780 738 1515 1342 2610 2210 4137 3390 6168
((((x2 + x) div 5) + (2 mod (x + 1))) div 2)
A237118: 0 0 1 2 3 4 5 6 8 10 12 14 16 19 22 25
(2 * (x + (((x - ((x div 2) mod 2)) div 2) + (2 mod (x + 1)))))
A176100: 0 2 8 12 16 18 20 24 28 30 32 36 40 42 44 48
(((x + 1) * (2 + (x * (3 + (x mod 4))))) div 2)
A122061: 1 6 18 40 35 66 112 176 117 190 286 408 247 378 540 736
((2x3 + 11x2 + 7x + ~2) div 2)
A162258: ~1 9 36 86 165 279 434 636 891 1205 1584 2034 2561 3171 3870 4664
(((x + 1) * (x - ((~x4 + x3) div 2))) div 2)
A288962: 0 1 9 60 250 765 1911 4144 8100 14625 24805 39996 61854 92365 133875 189120
((((x + (x2 div (2 + (x div 2)))) div 2) mod (x + 1)) mod 2)
A155899: 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 0
(((x2 + 3x + 2) * (4 + ((x div 2) mod 2))) div 2)
A061726: 4 12 30 50 60 84 140 180 180 220 330 390 364 420 600 680
(((x2 + 3x + 2) + ((~1 + (x div 2)) * (x div 2))) div 2)
A111712: 1 3 6 10 16 22 31 39 51 61 76 88 106 120 141 157
(((x2 + 3x + 2) + (((x + ~1) div 2) * (x div 2))) div 2)
A194144-A025701: 1 3 6 10 16 23 31 40 51 63 76 90 106 123 141 160
(((((x div ~4) mod 2) - (x div 2)) mod (x + 1)) div 2)
A071806: 0 0 0 0 2 2 2 2 2 3 3 4 4 4 4 4
((0 - ((x + 1) mod 9)) mod (2x + 2))
A256299: 1 2 3 4 5 6 7 8 0 19 20 21 22 23 24 25
((2x + 2) + ((~x + ((~x + 2) div 2)) div 5))
A081477: 2 3 5 7 9 10 12 14 15 17 19 20 22 24 26 27
((2x + 2) + ((~x + 3) mod (2x2 + ~1)))
A094446: 2 4 7 8 40
((2x + 2) + ((x - (x div 9)) div 2))
A022840: 2 4 7 9 12 14 17 19 22 24 26 29 31 34 36 39
((0 - ((x + 1) mod 10)) mod (2x + 2))
A169930-A048379: 1 2 3 4 5 6 7 8 9 0 21 22 23 24 25 26
((2x + 2) + ((x - (x div 12)) div 2))
A329994-A064995: 2 4 7 9 12 14 17 19 22 24 27 29 31 34 36 39
((2x + 2) + (((x + 1) + (x div 8)) div 2))
A292653-A028250: 2 5 7 10 12 15 17 20 23 25 28 30 33 35 38 40
((2x + 2) + ((x - (x div ~8)) div 2))
A059536: 2 5 7 10 12 15 17 20 22 25 28 30 33 35 38 40
((2x + 2) + ((x - ((x div 4) div ~2)) div 2))
A186321: 2 4 7 9 12 15 17 20 22 25 27 30 33 35 38 40
((2x + 2) + ((~x + 2) div (2 - (x div ~4))))
A286809: 3 4 6 7 9 11 13 14 16 18 20 22 24 26 28 29
((2x + 2) + ((((x + 1) + (x div 4)) div 2) div 2))
A184978: 2 4 6 9 11
A187339: 2 4 6 9 11 13 16 18 20 23 25 27 30 32 34 36
((2x + 2) + (((x - (x div ~4)) div 2) div 2))
A184978: 2 4 6 9 11
A059545: 2 4 6 9 11 13 16 18 20 23 25 27 29 32 34 36
((2x + 2) + ((x + ((x div 2) mod 4)) div 4))
A184978: 2 4 6 9 11
A322532: 2 4 6 9 11 13 16 18 20 22 24 27 29 31 34 36
((2x + 2) + ((x div 4) mod 2) - (x mod 4))
A069908: 2 3 4 5 11 12 13 14 18 19 20 21 27 28 29 30
((2x + 2) + ((x - ((~x + (x mod 3)) div 2)) div 2))
A190279: 2 4 7 10 13 15 18 21 23 27 29 32 35 37 40 43
((2x + 2) + ((((x div 2) div 3) + (x mod 2)) div 2))
A187908-A187233: 2 4 6 8 10 12 14 17 18 21 22 25 27 29 31 33
((2x + 2) + ((x + ((x mod (1 + (x div 2))) div 2)) div 2))
A026356: 2 4 7 9 12 15 17 20 22 25 28 30 33 36 38 41
((3x + 2) + ((x - (x div 3)) div 3))
A184747: 2 5 8 11 15 18 21 24 28 31 34 37 40 44 47 50
((3x + 2) + ((~x + 2) div (4 + (x mod 2))))
A247780: 2 5 8 10 13 16 19 22 24 27 30 33 35 38 41 44
(((5x + 2) - (x div 2)) * ((x + 1) div 2))
A132355: 0 7 11 32 40 75 87 136 152 215 235 312 336 427 455 560
((2 * ((3 * (x div 4)) div 2)) - ((x + 1) div 2))
A290885: 0 ~1 ~1 ~2 0 ~1 ~1 ~2 2 1 1 0 2 1 1 0
((x div (~10 + (x div 2))) + ((x + 1) div 2))
A235613: 0 0 0 1 1 2 2 3 2 3 3 3 3 3 2 3
(2x + (((1 - (x div 2)) mod 3) + ((x + 1) div 2)))
A188095: 1 4 5 8 12 15 16 19 20 23 27 30 31 34 35 38
(2x + ((x div (4 + (x mod 2))) + ((x + 1) div 2)))
A022852: 0 3 5 8 11 14 16 19 22 24 27 30 33 35 38 41
((23x2 + 23x) div 2)
A195039: 0 23 69 138 230 345 483 644 828 1035 1265 1518 1794 2093 2415 2760
((11x2 + 23x + 12) div 2)
A026817: 6 23 51 90 140 201 273 356 450 555 671 798 936 1085 1245 1416
((7x3 + x2 + ~6x) div 2)
A256718: 0 1 24 90 220 435 756 1204 1800 2565 3520 4686 6084 7735 9660 11880
((9x3 + x2 + ~8x) div 2)
A256649: 0 1 30 114 280 555 966 1540 2304 3285 4510 6006 7800 9919 12390 15240
(x5 * ((x3 + x2) div 2))
A168635: 0 1 192 4374 40960 234375 979776 3294172 9437184 23914845 55000000 116923026 232906752 439239619 790601280 1366875000
(13x2 + ~16x + 5)
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(((x + ~1) * ((x3 + 3x2 + ~4x) div 2)) div 2)
A188667: 0 0 3 21 72 180 375 693 1176 1872 2835 4125 5808 7956 10647 13965
(((x2 + ~3x + 2) * ((x2 + 2x) + (x mod 2))) div 2)
A279905: 0 0 0 16 72 216 480 960 1680 2800 4320 6480 9240 12936 17472 23296
((x4 + 4x3 + ~4x2 + ~x) div 2)
A135916: 0 0 15 75 222 510 1005 1785 2940 4572 6795 9735 13530 18330 24297 31605
((x8 + x6) div 2)
A168527: 0 1 160 3645 34816 203125 863136 2941225 8519680 21789081 50500000 108065221 216483840 410278765 741659296 1287140625
(((x3 + 2x) div 3) - ((x2 + ~1) div 2))
A168582: 1 1 3 7 17 33 59 95 145 209 291 391 513 657 827 1023
((x8 + x5) div 2)
A168371: 0 1 144 3402 33280 196875 843696 2890804 8404992 21552885 50050000 107259966 215115264 408051007 738163440 1281825000
((x + 4) - ((~x + 2) div (2 - (x div ~4))))
A288134: 3 5 6 8 9 10 11 13 14 15 16 17 18 19 20 22
((2 + ((x div 2) div 3)) div (2 - (x mod ~4)))
A025871: 1 0 0 0 1 0 0 1 1 0 0 1 2 0 1 1
((2 + (x mod (1 + (x div 2)))) div (2 - (x mod ~4)))
A025830: 1 0 0 1 1 0 1 1 2 1 1 2 3 1 2 3
(((x + 1) div 5) - (x div (~2 + (x div ~2))))
A029865: 0 1 1 1 2 2 3 3 3 4 4
A072747: 0 1 1 1 2 2 3 3 3 4 4 4 4 4 5 5
(100x + 4)
A102439: 4 104 204 304 404 504 604 704 804 904 1004 1104 1204 1304 1404 1504
(((x - ((~x + 1) mod (1 + (x div 5)))) div 2) mod 2)
A285031: 0 0 1 1 0 0 0 1 1 0 1 0 1 0 0 0
(((2 - ((x + ~1) mod (1 + (x mod 5)))) div 2) mod 2)
A267683: 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1
(((x + 1) div (2 + (2 mod (1 + (x mod 5))))) mod 2)
A309754: 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 0
(((~1 + (x div (1 + (x2 mod (2 + (x div 2)))))) div 2) mod 2)
A176917-A077049: 1 1 0 1 1 0 1 0 0 0 1 1 1 0 0 1
(x3 mod 44)
A070506: 0 1 8 27 20 37 40 35 28 25 32 11 12 41 16 31
(((2 - ((x + ~1) mod (1 + ((x + 2) div 3)))) div 2) mod 2)
A189097: 1 1 0 1 1 0 0 0 1 1 1 1 0 1 0 0
(2 * (2 + ((x2 + ~x) mod (1 + ((x + 2) div 3)))))
A162281: 4 4 4 4 4 8 4 8 4 4 4 4 8 4 8 4
(2 + ((x mod (2 - (x div (1 + ((x div 2) mod 3))))) mod 2))
A081412: 2 2 2 2 2 2 2 3 2 3 2 2 2 3 3 2
(2 + ((x mod (1 + ((x div 4) + (x div 3)))) mod 2))
A098014: 2 2 2 3 3 2 2 3 3 3 2 3 2 3 2 2
(((1 + ((x - (x div ~2)) div (1 + (x mod 2)))) div 2) div 2)
A308453: 0 0 1 0 1 1 2 1 3 2 4 2 4 2 5 3
(16x2 + 36x + 24)
A325958: 24 76 160 276 424 604 816 1060 1336 1644 1984 2356 2760 3196 3664 4164
(2 + ((x mod (1 + ((2 * (2 + (x mod 2))) mod (x + 1)))) mod 2))
A108128: 2 2 2 2 2 2 3 2 3 2 2 2 2 2 2 3
(1 - (2 * ((x mod (~1 - (4 mod (x + 1)))) mod 2)))
A325931: 1 1 1 1 ~1 1 1 ~1 1 ~1 1 1 ~1 1 ~1 1
(2 + ((x + ~2) div (2 + (x div (2 - (x mod ~3))))))
A342739: 1 1 2 2 2 3 2 3 3 3 4 3 3 4 4 3
(2 * ((1 + (x div (4 - ((x div 2) div 3)))) div 2))
A063468: 0 0 0 0 2 2 2 2 2 4 4 4 6 6 8 8
(2 + ((7 * ((x + 1) mod 3)) div 2))
A214395: 5 9 2 5 9 2 5 9 2 5 9 2 5 9 2 5
(x div (x - (4 * ((x + ~1) div 7))))
A279061: 0 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2
(x4 mod 28)
A070571: 0 1 16 25 4 9 8 21 8 9 4 25 16 1 0 1
(1 - (((x - (x2 div 7)) div 2) div 2))
A016085: 1 1 1 1 1 1 1 1 2 2 2 3 3 4 5 6
(2 + (((x + 4) mod (1 + (2 * (x div 3)))) mod 2))
A091787: 2 2 2 3 2 2 2 3 2 2 2 3 3 2 2 2
((x - ((x mod ((x + 1) - (2 * (x div 3)))) div 2)) mod 2)
A285080: 0 1 1 1 0 1 0 0 1 1 0 1 1 1 0 0
(2 * ((1 + (x div (2 - ((x - (x mod 3)) div 2)))) mod 2))
A239395: 2 2 0 0 2 0 2 0 2 0 0 2 0 2 2 0
(2 - ((((x + 1) mod (~2x + 7)) div 2) mod 2))
A026535: 2 1 2 2 2 2 2 1 2 1 1 2 2 1 1 2
(2 * ((1 + (((x + 1) * (x - (2 * (x mod 2)))) div 2)) div 2))
A250108: 0 0 4 2 10 10 22 20 36 36 56 54 78 78 106 104
(((1 + (((x + ~1) * ((x + 2) div 3)) div 2)) div 2) div 2)
A165684: 0 0 0 0 1 1 1 2 2 3 4 5 5 7 8 9
(x - ((x - (x div ((~1 + (x div ~4)) div 2))) div 2))
A270433: 0 0 0 0 0 1 2 2 2 2 3 3 3 4 5 5
((x mod (~2 + ((x + ~1) div (~1 + (x mod ~4))))) mod 2)
A306710: 0 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1
(((~1 + ((((x + 1) * (2 + (x div 2))) div 2) div 2)) div 2) mod 2)
A303907: 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 1
(((x + 2) div (~3 + (x div ~7))) mod 2)
A266605: 1 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1
(((1 + ((x2 * (x mod 2)) div 8)) div 2) div 2)
A035647: 0 0 0 0 0 1 0 1 0 2 0 4 0 5 0 7
(((9x2 + 18x + 9) div 2) div 2)
A173102: 2 9 20 36 56 81 110 144 182 225 272 324 380 441 506 576
((x - (((x div 2) mod (1 + (x mod 8))) div 2)) mod 2)
A193496: 0 1 0 1 1 0 1 0 0 1 1 1 0 1 0 0
(4 * ((x + 1) - ((~x2 + 2x) div 8)))
A033691: 4 8 12 20 24 32 40 52 60 72 84 100 112 128 144 164
(((2 - ((~x + 1) mod (1 + (2 * (x mod 4))))) div 2) mod 2)
A214330: 1 1 1 0 1 0 1 0 1 0 0 1 1 1 0 1
(4 * ((5x + 3) + (x div 2)))
A166959: 12 32 56 76 100 120 144 164 188 208 232 252 276 296 320 340
(2 + ((x mod (1 + (2x mod (4 + (x div 2))))) mod 2))
A075370: 2 3 2 3 3 2 2 2 2 2 3 3 2 2 2 2
(x div (4 + (x mod (1 + ((2 - (x div 2)) mod 4)))))
A165924: 0 0 0 0 1 1 1 1 1 2 2 2 3 3 2 2
(4 + (((x2 + x) div 4) div 5))
A140744: 4 4 4 4 5 5 6 6 7 8 9 10 11 13 14 16
(2 - (((x - ((1 - (x div 2)) mod 5)) div 2) mod 2))
A122497-A006345: 1 2 1 1 2 2 1 2 1 1 2 1 2 2 1 1
((x + 4) - ((~x + 4) mod 10))
A169933: 0 2 4 6 8 0 2 4 6 8 10 12 14 16 18 10
((x + ~10) mod 20)
A180176: 10 11 12 13 14 15 16 17 18 19 0 1 2 3 4 5
(x - (2x div (~x + 22)))
A265359: 0 1 2 3 4 5 6 7 7 8 9 9 10 11 11 11
(x5 mod 20)
A070604: 0 1 12 3 4 5 16 7 8 9 0 11 12 13 4 15
(x div ((2x + 2) div (2 + (x mod 10))))
A103303: 0 1 2 3 4 5 6 7 8 9
A004430: 0 1 2 3 4 5 6 7 8 9 0 1 2 2 2 3
((x div (~2 - ((x2 + ~x) mod 5))) mod 2)
A211487: 0 1 1 1 1 1 1 0 1 1 1 0 1 1 0 0
((x div 2) div (2 + ((x div 2) div (2 + (x mod 5)))))
A254687: 0 0 0 0 1 0 1 1 2 2 1 1 2 2 2 1
((x + 1) div (4 + ((~x2 + 2) mod 5)))
A129985: 0 0 0 0 1 1 1 1 1 2 1 2 1 2 3 2
(20x3 + ~3x)
A160699: 0 17 154 531 1268 2485 4302 6839 10216 14553 19970 26587 34524 43901 54838 67455
(2 - ((x div (2 + ((x div 2) div (1 + (x mod 4))))) mod 2))
A085301: 2 2 1 1 1 1 2 1 1 2 1 1 1 2 1 1
(8x3 + 48x2 + 96x + 60)
A224335: 60 212 508 996 1724 2740 4092 5828 7996 10644 13820 17572 21948 26996 32764 39300
(((x - ((x2 + 2) mod (3 + (x div 2)))) div 2) mod 2)
A288220-A240315: 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0
(((x + 1) div (2 + (x2 mod (~1 + (2 * (x div 2)))))) mod 2)
A118247: 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0
(x - (2 * ((x - (x mod (1 + (x div (2 + (x mod 2)))))) div 2)))
A287477: 0 1 0 1 2 1 2 1 4 1 4 3 6 3 6 3
((x + 3) div (2 + (x mod (2 * (1 + (2 * (x mod 2)))))))
A289187: 1 1 2 1 3 1 4 3 5 2 6 2 7 5 8 3
(x - (2 * ((3 * (x div 7)) div 2)))
A245352: 0 1 2 3 4 5 6 5 6 7 8 9 10 11 8 9
(x div (2 + (x div (2 + ((x div 5) mod 3)))))
A258595: 0 0 0 1 1 1 1 1 2 1 2 2 2 2 2 1
((x + 2) mod (2 + ((3 * ((x div 2) mod 3)) div 2)))
A140083: 0 1 1 2 1 2 0 1 1 2 2 3 0 1 1 2
(((1 + (x div 2)) mod (~2 + (3 * (x mod 3)))) div 2)
A089495: ~1 0 1 0 0 1 0 0 0 ~1 0 1 ~1 0 0 0
(1 - (2 * ((((x + ~1) mod (1 + (x div 2))) mod 3) mod 2)))
A065357: 1 1 ~1 1 1 ~1 ~1 1 1 1 1 ~1 ~1 1 1 1
((((3x + 3) * (x2 div 4)) div 2) div 2)
A256313: 0 0 2 6 15 27 47 72 108 150 206 270 351 441 551 672
(1 - (x div (~2 + (x div (~2 - ((x + ~1) mod 3))))))
A330780: 1 2 2 2 2 3 3 3 3 3 3 3 4 3 3 4
(2 + (((x mod (4 + (x div 4))) mod 3) mod 2))
A182006: 2 3 2 2 3 2 3 2 2 2 3 2 2 2 2 3
(4 + ((x - ((x - (x div 4)) mod 2)) div 3))
A134994: 4 4 4 4 5 5 5 6 6 6 7 7 7 8 8 9
(x div (4 + ((x - ((2 - (x div 2)) div 2)) mod 3)))
A230502: 0 0 0 0 0 0 1 1 2 1 2 2 2 3 2 3
(((x + (x div 2)) mod (2 + ((2 * (x div 2)) div 3))) div 2)
A014082: 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 2
((x + 1) mod (2 + (((x - ((x div 2) mod 2)) div 3) mod 2)))
A239706: 1 0 1 0 2 0 1 0 1 1 2 0 1 0 1 0
(x - (((2 - (3 * ((x2 + x) div 2))) div 2) div 2))
A024224: 0 2 4 7 11 16 22 28 35 43 51 60 70 81 93 105
(((3 * ((x + 2) + (x2 div 4))) div 2) div 2)
A283968-A022782: 1 2 3 5 7 9 12 15 19 23 27 32 37 42 48 54
(4x2 + 32x + 36)
A153642: 36 72 116 168 228 296 372 456 548 648 756 872 996 1128 1268 1416
(x - (2 * (((x3 div (x + 2)) mod 3) div 2)))
A062302: 0 1 0 1 4 3 6 5 8 9 8 11 12 11 14 15
(((((~x + 1) mod 3) + ((x div 2) div 3)) div 2) mod 2)
A288936: 0 0 1 0 0 1 1 0 1 1 0 1 1 1 0 1
(1 - (x div (~2 + (x div (~6 + (x div 3))))))
A192688: 1 2 2 2 3 3 3 3 3 3 3 3 3 3 3 2
(((1 + (x div 2)) div (x - ((x + 1) mod 6))) mod 2)
A118553: 1 1 0 0 1 0 0 0 1 1 1 0 0 0 0 0
((2 + ((x div 2) div 3)) div (2 + (x mod 6)))
A025901: 1 0 0 0 0 0 1 1 0 0 0 0 2 1 1 0
(2 + (((x + (x mod (1 + (x div 3)))) div 3) mod 2))
A094321: 2 2 2 3 3 2 2 2 3 3 2 2 2 3 2 2
(x - (((3 * (~x + (x div 5))) div 2) div 2))
A047511: 0 2 4 6 7 8 10 12 14 15 16 18 20 22 23 24
(((((~1 + (x div 2)) div 2) * ((~x + 2) mod 3)) div 2) mod 2)
A194675: 1 1 0 0 0 0 1 0 0 1 1 0 0 1 0 1
(((x + (x div 2)) mod (2 + ((x + (x mod 2)) div 3))) div 2)
A078595: 0 0 0 0 0 1 0 1 0 1 0 2 0 0 1 0
(2 * (2 - ((2x mod (~2 - (x div 3))) mod 2)))
A046595: 4 4 4 4 2 4 4 4 4 4 4 2 4 4 4 2
(2 + (((((x + 1) + (x div 2)) div 2) * (x div 3)) mod 2))
A094915: 2 2 2 2 3 2 2 2 2 3 2 2 2 2 2 3
(x2 - (((((x + ~1) div 2) * (x div 3)) div 2) div 2))
A052118: 0 1 4 9 16 25 35 48 63 78 97 118 139 163 190 217
(((2x mod (8 + (x div 3))) div 2) mod 2)
A296657: 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 0
(2 * ((((x2 + x) div 4) + (x div 3)) div 2))
A233036: 0 0 0 4 6 8 12 16 20 24 30 36 42 48 56 64
(((x - ((2 - ((x div 2) mod 2)) * (x div 3))) div 2) div 2)
A187450: 0 0 0 0 0 0 1 1 1 0 1 2 1 1 2 2
(((x mod 3) - ((x + ~1) div (2 + (x mod 3)))) mod 2)
A189292: 1 1 0 1 0 1 0 1 1 0 0 0 1 1 1 1
(((x div (2 * (~2 + (x mod 2)))) mod (2 + (x mod 3))) div 2)
A286490-A217831: 0 1 1 0 1 0 0 1 1 0 0 1 0 1 0 0
((x div 2) div (2 + ((2 + (x div 2)) mod (2 + (x mod 3)))))
A236256: 0 0 0 0 0 1 1 0 1 2 1 1 3 1 2 2
((((x2 + ~2x) div (x + 2)) + ((x mod 3) mod 2)) div 2)
A210469: 0 0 0 0 1 1 1 2 2 2 3 3 4 5 5 5
((1 - ((x + 1) mod (2 - ((x - (x mod 3)) div 2)))) div 2)
A159046-A029937: 0 0 0 0 0 0 0 0 0 0 1 0 2 1 1 2
(x + (x mod 2) - ((x - ((x - (x mod 3)) div 2)) mod 2))
A227370: 0 1 2 4 3 6 5 8 7 9 10 11 12 13 14 16
(x - (((~1 + ((x * ((x div 2) div 3)) div 2)) div 2) div 2))
A071520: 1 2 3 4 5 6 6 7 8 9 9 10 10 10 11 12
((((2 - (x mod 5)) mod (x + 3)) div 2) mod 2)
A025887: 1 0 0 0 0 1 0 0 1 1 1 0 0 1 1 1
((x - ((((x + 1) div 3) * (1 + (x div 2))) div 2)) mod 2)
A286484: 0 1 1 0 1 0 0 1 1 0 1 1 0 1 0 1
(((2 - ((~3x + 3) mod (1 + (x div 2)))) div 2) mod 2)
A321756: 1 1 0 1 1 1 0 0 1 0 1 1 0 0 0 0
(((~x + 1) mod (2 + ((x2 + 2) mod (1 + (x div 2))))) mod 2)
A267053: 1 0 1 1 1 0 1 0 0 0 1 0 1 1 1 1
(2 - ((x - (x div (2 + (x mod (3 - (x mod 2)))))) mod 2))
A025143: 2 1 2 2 1 2 1 1 2 2 1 2 2 1 1 2
(1 - (2 * (((~x2 + 2) div (3x + ~1)) mod 2)))
A337004: 1 1 ~1 ~1 1 1 1 ~1 ~1 1 1 1 ~1 ~1 ~1 1
((((x + 1) * (1 + ((~1 + (x div 2)) mod 3))) div 2) mod 2)
A339653: 1 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0
(2 * (((2 * (x mod (~3 + (x mod 2)))) mod (x + 1)) div 2))
A276093: 0 0 0 2 0 4 0 6 6 8 6 10 0 12 12 14
(1 - (2 * ((((~2 + (x div 2)) * (x div 2)) mod (x + 1)) mod 2)))
A121238: 1 1 1 ~1 1 1 ~1 ~1 1 1 1 ~1 ~1 1 ~1 ~1
(2 * ((2x + 2) + (((x + 1) + (x div 4)) div 2)))
A283234: 4 10 14 20 26 30 36 40 46 52 56 62 68 72 78 82
(2 * ((2x + 2) + ((x - (x div 8)) div 2)))
A189676: 4 8 14 18 24 28 34 38 42 48 52 58 62 68 72 78
(x - (2 * ((~2x + ~2) + ((x - (x div 4)) div 2))))
A089910: 4 9 12 17 22 25 30 33 38 43 46 51 56 59 64 67
((((2x + 1) - (x div ~2)) * ((x + 1) div 2)) div 2)
A057569: 0 2 3 9 11 21 24 38 42 60 65 87 93 119 126 156
((((x + 1) + (3 * (x div 2))) * ((x + 1) div 2)) div 2)
A222010: 0 1 3 7
A063437: 0 1 3 7 11 18
A210977: 0 1 3 7 11 18 24 34 42 55 65 81 93 112 126 148
(((2 * ((~x + 2) div (1 + (x div 2)))) + ((x + 1) div 2)) div 2)
A335824: 2 1 0 0 0 0 0 0 0 0 0 1 1 1 1 2
(2 + ((2 + ((x2 + ~x) * (x div 2))) * ((x + 1) div 2)))
A294447: 2 4 6 18 54
(((((~x + 2) mod (2 + (x div 2))) div 2) + ((x + 1) div 2)) div 2)
A087180: 0 0 0 1 1 1 1 2 2 3 4 4 4 4 5 5
((1 + (((x div 2) - (x mod 2)) div 2)) * (((x + 1) div 2) div 2))
A296159: 0 0 0 1 2 1 2 4 6 4 6 9 12 9 12 16
(~2 + ((9x2 + 25x + 16) div 2))
A235332: 6 23 49 84 128 181 243 314 394 483 581 688 804 929 1063 1206
(x - ((((1 + (x div 2)) div 2) div 2) + (((x + ~1) div 2) div 2)))
A135414: 1 1 2 3 4 4 4 5 6 6 7 8 9 9 9 10
(4 * ((x2 + 1) + ((~x + 3) * (x div 2))))
A006640: 4 8 24 40 60 88
((2x + 2) div (2 + (x mod 2) - (x div ~4)))
A092333: 1 1 2 2 3 2 3 3 4 3 4 4 5 4 5 4
(2 * (2x + ((x div ~2) mod 2) - (x div 4)))
A028919: 0 6 10 12 14 20 24 26 28 34 38 40 42 48 52 54
((2 - (x div (~4 + (x div 7)))) div 2)
A279220: 1 1 1 1 1 2 2 2 2 2 3 3 3 3 4 5
(1 - (2 * ((x - ((x mod 7) div 2)) mod 2)))
A210245: 1 ~1 ~1 1 1 ~1 ~1 ~1 1 1 ~1 ~1 1 1 1 ~1
(2 + (((~1 + (((x + 1) * (x div 3)) div 2)) div 2) div 2))
A029057: 1 1 1 2 2 2 3 3 4 5 5 6 8 8 9 11
((~x + 2) + (2 * (4 + (x mod 9))))
A100830: 10 11 12 13 14 15 16 17 18 1 2 3 4 5 6 7
(x div (2 + (x div (2 + (((x + 2) mod 5) div 2)))))
A213911: 0 0 1 1 1 1 1 2 1 1 2 2 2 1 1 2
((x div (0 - (2 * (2 + (2x mod 5))))) mod 2)
A189727: 0 1 1 1 1 0 1 1 0 1 1 0 1 1 0 0
((x - ((x + ~2) div (4 + (x div 5)))) mod 2)
A338353: 1 0 0 1 0 1 0 0 1 0 1 0 1 0 0 0
(1 - ((x mod (2 + (x mod (2 * (1 + (2 * (x mod 2))))))) div 2))
A124385: 1 1 1 0 1 ~1 1 1 1 ~1 1 ~1 1 1 1 1
(x div (4 + ((x + 2) mod (2 + ((x + 1) mod 3)))))
A068307: 0 0 0 0 0 1 1 1 2 1 2 2 2 1 3 2
(1 - (x div (2 + (x div (2 + (((x + ~2) div 3) mod 2))))))
A014042: 1 1 1 0 0 0 0 0 0 0 0 ~1 ~1 ~1 0 0
((x + 1) div (2 + (x div (2 + (((x div 2) mod 3) mod 2)))))
A121561: 0 1 1 1 1 1 1 1 2 2 1 1 1 1 2 2
(x - ((((3 * ((~x2 + x) div 2)) div 2) div 2) div 2))
A226331: 0 1 3 5 7 9 12 15 19 23 27 32 37 43 49 55
(1 - (2 * ((x mod (~6 + (x div 3))) mod 2)))
A127252: 1 ~1 1 1 ~1 1 1 ~1 1 1 1 ~1 1 ~1 1 1
((x - ((x mod (6 + (x div 4))) div 2)) mod 2)
A219189: 0 1 1 0 0 1 1 1 0 1 1 0 1 1 0 0
(4 * (2x + (x div 2) - (x mod 6)))
A328849: 0 4 12 16 24 28 60 64 72 76 84 88 120 124 132 136
(x div (2 + (2x div (4 + ((~x + 1) mod 3)))))
A305830: 0 0 1 1 1 1 1 1 2 1 1 2 2 1 2 1
(2 - (((((~x + 3) * (x div 3)) div 2) div 2) mod 2))
A270648: 2 2 2 2 1 1 2 2 1 1 2 2 1 2 1 1
((2 - ((((1 - (x div 2)) * (x div 3)) div 2) div 2)) div 2)
A005134: 1 1 1 1 1 1 1 1 2 2 2 2 3 3 4 5
(2 + (((2x + 6) mod (2 + (x div 3))) div 2))
A341829: 2 2 2 2 3 2 3 2 3 4 2 3 2 3 4 2
(x div (2 + (x div (2 + (x mod 2) - ((x div 3) mod 2)))))
A191515: 0 0 0 1 0 1 1 1 1 1 0 1 1 2 1 1
(((2x + ~1) div (2 + (x div (2 + (x mod 3))))) mod 2)
A115198: 1 0 1 1 0 1 0 1 1 0 1 1 0 0 1 1
((x - ((x mod ((~x + 2) + ((x mod 3) div 2))) div 2)) mod 2)
A336111-A062172: 0 1 0 1 0 0 1 1 1 0 1 0 0 0 0 1
(((((2x + ~1) * (2 - (x div 3))) div 2) div 2) mod 2)
A167364: 1 0 1 1 1 0 0 0 0 1 1 0 0 1 0 0
(x - ((~x + 1) div (4 - (((1 + (x div 2)) div 2) mod 2))))
A191979: 0 1 3 4 5 7 8 9 10 11 13 15 16 17 18 19
((2x + 2) - (((x - ((~1 + (x div 2)) div 2)) div 2) div 2))
A184587: 2 4 6 8 9 11 13 15 17 18 20 22 24 26 28 29
(x div ((~x + 2) + (8 * (3 - (x mod 2)))))
A175958: 0 0 0 0 0 0 0 0 0 1 0 1 0 2 1 5
(((((x + ~1) + ((x * (x div 2)) div 3)) div 2) div 2) mod 2)
A029692: 1 0 0 0 1 1 0 1 0 1 0 1 0 1 1 0
((((2x3 + 3x2 + 2x + 1) div 2) div 2) div 2)
A019298: 0 1 4 11 23 42 69 106 154 215 290 381 489 616 763 932
(2 - (((((x + 1) * (((x + ~1) div 2) div 2)) div 2) div 2) mod 2))
A331034: 1 2 2 2 2 1 1 2 2 1 1 2 2 2 1 2
(((x2 mod (2 + (8 mod (x + 1)))) div 2) div 2)
A253638: 0 0 0 0 0 0 0 0 1 0 0 0 1 2 1 1
((x + ~2) - (4 * ((~4x + ~4) + (x div 2))))
A161454: 14 31 44 61 74 91 104 121 134 151 164 181 194 211 224 241
(((((x div 2) * (x div 2)) div 2) * (((x + 1) div 2) div 2)) div 2)
A008218: 0 0 0 0 1 1 2 4 8 8 12 18 27 27 36 48
(2 - (((((x + 1) div 2) div 2) mod 2) + ((x div 4) mod 2)))
A131079: 2 2 2 1 0 0 0 1 2 2 2 1 0 0 0 1
((1 - ((x - (((x + ~1) * ((x + ~1) div 2)) div 2)) div 2)) div 2)
A319400: 0 0 0 0 0 0 0 1 1 2 2 4 4 6 7 9
(x - ((0 - ((x - ((x div 2) mod ~4)) div 2)) div 2))
A039129: 0 1 3 5 6 7 8 9 10 11 13 15 16 17 18 19
(1 - (((x - ((x2 - (x div ~2)) div 2)) div 2) div 2))
A029032: 1 1 1 2 3 4 5 6 8 10 12 14 17 20 23 27
(128x + 112)
A297970-A296185: 112 240 368 496 624 752 880 1008 1136 1264 1392 1520 1648 1776 1904 2032
(120x + 16)
A139616: 16 136 256 376 496 616 736 856 976 1096 1216 1336 1456 1576 1696 1816
(((x + 2) div (2 + (((x mod (1 + (x div 2))) div 2) mod 2))) mod 2)
A267520: 1 1 0 0 1 0 0 1 1 1 0 0 1 1 1 1
(x - ((x - (x mod (1 - (2 * (((x + 1) div 2) div 2))))) div 2))
A134403: 0 1 1 2 2 3 3 3 4 5 4 4 5 6 7 5
(2 * (1 - (2x div (~4 + (x div ~4)))))
A113724: 2 4 4 6 6 6 6 8 8 8 8 10 10 10 10 10
((x + 2) - (2x div (~4 + (x div ~4))))
A183573: 2 4 5 7 8 9 10 12 13 14 15 17 18 19 20 21
(x div (2 + (x mod (2 * (4 + (x mod 6))))))
A308924: 0 0 0 0 0 0 0 0 0 0 0 0 2 2 3 5
(2 + ((x - (((x - ((x mod 3) div 2)) div 2) div 2)) mod 2))
A282162: 2 3 2 3 3 2 3 2 3 3 2 3 3 2 3 2
((~2x mod (4 + (((x + 1) div 2) div 2))) div 2)
A216191: 0 1 0 2 1 0 1 2 1 0 2 3 2 1 0 1
((((((x3 + ~3x2 + 2x) div 2) div 2) div 2) div 2) div 2)
A011914: 0 0 0 0 0 1 3 6 10 15 22 30 41 53 68 85
(((x2 + x) div 2) mod 64)
A105335: 0 1 3 6 10 15 21 28 36 45 55 2 14 27 41 56
(x4 div 64)
A060494: 0 0 0 1 4 9 20 37 64 102 156 228 324 446 600 791
((x - ((~x2 + x) div 32)) mod 2)
A099104-A066829: 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0
(1 div (4 + (x mod (~1 - (x mod 8)))))
A290531: 0 0 0 0 0 0 0 0 0 0 0 0 1 ~1 0 0
(1 - (2 * (((x mod (~2 + ((~x + 2) div 4))) div 2) mod 2)))
A343785: 1 ~1 1 1 ~1 ~1 1 ~1 1 1 ~1 1 1 ~1 ~1 1
(1 - (2 * ((2x div (4 + (x div 4))) mod 2)))
A122188: 1 1 ~1 ~1 ~1 1 1 1 1 ~1 ~1 ~1 ~1 ~1 1 1
(x - (4 * ((x div 2) - (2 * ((x div 4) mod 2)))))
A053985: 0 1 ~2 ~1 4 5 2 3 ~8 ~7 ~10 ~9 ~4 ~3 ~6 ~5
((x + 2) - (2 * (x div (2 + ((x mod (2 + (x mod 2))) div 2)))))
A112048: 2 3 2 3 2 5 2 3 2 3 2 7 2 3 2 3
((x - (x div (0 - (2 * (2 + ((x + 1) mod 4)))))) mod 2)
A317748: 0 0 1 0 1 0 1 1 0 1 1 0 0 1 0 1
(1 - (2 * (((x + 1) div (2 + ((x + 2) mod 4))) mod 2)))
A174351: 1 1 ~1 ~1 ~1 ~1 ~1 1 1 1 ~1 1 ~1 1 ~1 ~1
((2x + 2) - (x div (4 + ((x div 2) mod 4))))
A324847-A304711-A289509: 2 4 6 8 10 12 14 15 16 18 20 22 24 26 28 30
(x div (4 + ((3x + 3) mod 8)))
A236508-A236480: 0 0 0 0 0 0 0 1 1 0 2 1 1 2 1 3
(x - (4 * ((2x + 1) div ~7)))
A283775: 4 5 6 7 12 13 14 19 20 21 22 27 28 29 34 35
((x - (((x2 + 2) mod ~7) div 2)) div 2)
A083036: 1 1 1 2 3 3 4 5 5 5 6 6 6 7 8 8
((2 - ((x + 1) mod (~2 + (x div ~7)))) div 2)
A078703: 1 1 1 2 1 1 2 1 2 2 1 1 2 2 1 3
(2 + (((x + 1) mod (1 - (x mod ~7))) mod 2))
A024677: 2 2 3 2 3 2 3 2 2 2 3 2 3 2 2 2
(1 - ((~x + 2) div (4 + ((x + 1) mod 8))))
A124230: 1 1 1 2 2 2 2 3 3 3 3 3 3 3 3 5
((x + 2) - ((x + ~1) div (~10 + (x div 2))))
A193533: 2 3 5 6 7 8 9 10 12 13 14 15 17 18 21 22
(x - (((((~x + 2) * (x div 2)) div 8) div 2) div 2))
A138083: 0 1 2 4 5 6
A201997-A039246: 0 1 2 4 5 6 7 8 9 10 12 13 14 16 17 18
((2 - ((x div 4) mod ~15)) div 2)
A195141: 1 1 1 1 8 8 8 8 7 7 7 7 7 7 7 7
(x div (2 + (((x2 + x) div 2) mod 16)))
A120648: 0 0 0 0 0 0 0 0 1 0 1 2 0 1 1 1
(x mod (1 - (x mod (~32 + (x div 2)))))
A103303: 0 1 2 3 4 5 6 7 8 9
A043273: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 2 4
(x - ((0 - (x div (~x + 18))) div 2))
A191844: 0 1 2 3 4 5 6 7 8 10 11 12 13 14 16 18
(((x div 2) - ((x + 2) div (x + ~16))) mod 2)
A226912: 1 1 0 0 1 1 0 0 0 0 1 0 0 1 1 0
(((x + ~2) div (2 + (x div (2 + ((~x + 2) mod 4))))) mod 2)
A266892: 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 0
(((x - (x2 mod (~2 - (x div 4)))) div 2) mod 2)
A288861: 0 1 1 0 1 1 1 0 0 0 1 1 0 1 1 1
(((~x + 1) mod (2 + ((x + 1) mod (2 + (x div 4))))) div 2)
A086012: 0 0 1 0 0 0 0 1 1 0 0 0 2 0 0 0
(1 - (2 * (((2x + 2) mod (2 + (x div 4))) mod 2)))
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((x + 1) div (4 + ((x + 2) mod (2 + (x div 4)))))
A187449: 0 0 0 0 1 1 1 2 1 1 2 2 1 3 3 2
(2 + ((3x + ~2) div (4 + (x div 4))))
A300154: 1 2 3 3 4 4 5 5 5 6 6 7 6 7 7 8
((x + 2) - ((~2x + 1) div (4 + (x div 4))))
A184008-A014132: 2 4 5 7 8 9 11 12 13 14 16 17 18 19 20 22
((x - (((((x + ~2) * (2 - (x div 2))) div 2) div 2) div 2)) mod 2)
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(4 - ((((2x + ~1) mod (2 + (x div 2))) div 2) mod 2))
A073259: 4 4 4 3 3 4 4 3 3 4 4 4 3 4 4 3
((((~1 + (x2 div 2)) mod (4 + (x div 2))) div 2) mod 2)
A167501: 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0
((x + 2) - (2 * ((x + (x div 2)) div (4 + (x div 2)))))
A244904: 2 3 4 5 4 5 6 7 8 9 10 11 12 13 14 13
(2 * (2 + (((x div 2) - ((~x + 2) div (2 + (x div 2)))) div 2)))
A156686: 2 4 4 6 6 6 8 8 8 10 10 10 12 12 12 12
(2x - (x mod (4 * (4 - ((x div 2) mod 2)))))
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A023794: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 26 27
((2 - (((x - ((x2 + (x div 2)) div 2)) div 2) div 2)) div 2)
A003114: 1 1 1 1 2 2 3 3 4 5 6 7 9 10 12 14
(x div (2 * (2 + ((~1 + ((x * (x mod 2)) div 2)) mod 4))))
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(x - ((0 - ((x - ((1 + (x div 2)) mod 4)) div 2)) div 2))
A039147: 0 1 2 3 4 6 8 9 10 11 12 13 14 16 18 19
((x + 1) div (2 + (2x div (2 + ((x + 1) mod 4)))))
A205745: 0 1 1 0 1 1 1 0 1 1 1 0 1 1 2 0
(2 + (((2x + ~1) mod (x - ((x + 1) mod 4))) mod 2))
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((x mod 2) - ((x - (x div (2 + ((x div 2) mod 4)))) mod 2))
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(4 div (2 + ((3x + 3) mod 8)))
A191269: 0 0 1 0 0 1 0 2 0 0 1 0 0 1 0 2
((x + 2) - (2 mod ((2x + 1) div ~7)))
A242455: 2 3 4 5 6 7 8 10 11 12 13 15 16 17 19 20
(((x + 1) div 3) - (x div ~14))
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(x div ((x + 1) div (1 - (x div ~14))))
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((2x + 2) - (x mod (x - ((x + ~1) mod 8))))
A257219: 2 4 6 8 10 12 14 16 18 20 21 22 23 24 25 26
((x + 2) - (1 mod (8 + ((~x2 + x) div 2))))
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(18 - ((~x + 2) mod 6))
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(((x2 + ~x) - ((x2 + 2x) div 8)) div 2)
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(((x + 1) div 2) - ((x + ~1) div (2 + (x div 8))))
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(((x * (x div 2)) - (x div (~2 + ((~x + 2) div 4)))) mod 2)
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(x3 mod (2 + (x mod (2 + ((~x + 2) mod 4)))))
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(1 - (((2x + 4) mod (~2 - (x div 4))) div 2))
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(((x * (x div 2)) - ((x + 1) mod (2 + (x div 4)))) mod 2)
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(2 - ((~2x + 5) div (4 + (x div 4))))
A060646: 1 2 2 3 3 3 4 4 4 5 5 5 5 5 6 6
(2 - ((~4x + 4) div (4 + (x div 4))))
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(((x + 1) div (~2 + (x * (x mod 2)) - (x div 4))) mod 2)
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(6x mod (2 + (x div (2 + (x mod 4)))))
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((((x2 + x) - ((~x2 + x) div 4)) div 2) div 2)
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(((x + ~1) mod (1 - (x mod (~4 + ((~x + 1) div 2))))) div 2)
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(((((x + 2) * (x div ~5)) div 2) div 2) mod 2)
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(x div (4 + ((2x2 + ~2x) mod (x + 4))))
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(((((x2 + ~2) - (x div 2)) mod (x + 4)) div 2) mod 2)
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((2x + 2) - ((x2 + ~2) div (x + 6)))
A105206: 3 5 6 8 9 10 12 13 14 15 16 17 19 20 21 22
(16x + ((x2 + 3x) div 2))
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(14x + ((x2 + x) div 2))
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(((((x mod (3 + (x mod 2))) * (x div 2)) div 2) div 2) div 2)
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(1 - (2 * ((x mod (2 - (((x mod 2) - (x div 2)) div 2))) div 2)))
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((((2 + ((x * (x mod 2)) div 2)) * (2 + (x div 2))) div 2) div 2)
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A099735: 1 1 1 2 2 4 2 6 3 9 3 12 4 16 4 20
((x - (((~4x + 2) mod (2 + (x div 2))) div 2)) mod 2)
A111748: 0 1 0 0 1 0 1 1 0 0 0 1 1 0 0 1
(2 + ((x + ~2) div (2 + ((x div 2) div (2 - ((x div 2) mod 2))))))
A299230: 1 1 2 2 2 3 2 3 3 3 3 3 4 4 3 3
((x + 2) div (2 + (x mod (2 + ((x + 2) mod (2 + (x mod 2)))))))
A291323: 1 1 2 1 3 1 4 3 5 3 6 3 7 5 8 3
((2x + 4) mod ((2 - (x div (2 * (~2 + (x mod 2))))) div 2))
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(((x * ((x + 1) div 2)) - (x mod (2 * (~2 + (x mod 2))))) div 2)
A302406: 0 1 2 3 4 8 10 14 16 23 26 33 36 46 50 60
(2 div (2 - (((x div 4) - ((x + 1) mod 4)) div 2)))
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((2x + 1) div (2 + ((x - (x div ~2)) div 4)))
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(3x - ((x + 4) div ~7))
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(x - ((x + 2) div (~8 + (x mod 8))))
A247334: 1 2 3 4 6 8 10 16
(x - (8 * (~x + (x mod 10))))
A103303: 0 1 2 3 4 5 6 7 8 9
A024664: 0 1 2 3 4 5 6 7 8 9 90 91 92 93 94 95
(56x2 + ~32x)
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((x + ~8) * (x - (x mod 9)))
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((9x + 9) + (x div 8))
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((x div (2 + ((x div 2) div 3))) + (x div 8))
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(2 + (x div 8) - ((~x + 1) div (2 + (x div 2))))
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(x - ((~x + (x mod 8)) * (x mod 8)))
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((8x2 + ~8x) + ((x2 + x) div 2))
A051871: 0 1 19 54 106 175 261 364 484 621 775 946 1134 1339 1561 1800
((3x + 2) div ((~x2 + 2) mod 8))
A324036: 1 5 1 11 7 17 3 23 13 29 5 35 19 41 7 47
((x + 2) - ((~x + ((~1 + (x div 2)) mod 3)) div 4))
A152854: 2 3 5 6 7 8 9 11 12 14 15 16 17 18 20 21
(x - (((x * (2 + (x div 5))) div 4) mod 2))
A113638: 0 1 1 2 4 4 6 6 8 9 10 10 12 12 14 15
((x - ((x + (2x mod (2 + (x div 2)))) div 4)) mod 2)
A165221: 0 1 0 1 1 0 0 1 1 1 0 0 1 0 1 1
((x div 8) - (x div (~2 + ((~x + 2) div 4))))
A217038-A076411: 0 1 1 1 2 2 2 2 3 4 4 4 4 4 4 4
((((x + 2) div (1 + (x div 3))) + (x div 4)) div 2)
A085761: 1 1 2 1 2 2 1 2 2 2 2 2 2 3 3 2
(x - (((2 - (((x + 1) div 2) div 2)) * (x div 4)) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A200001-A174995: 0 1 2 3 4 5 6 7 8 9 10 12 14 15 16 18
(2 - ((~2 + ((x + ~1) div 3)) mod (2 + (x div 4))))
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(((x div 2) div 3) - ((x + ~2) div (2 + (x div 4))))
A185059: 1 1 0 0 0 ~1 0 0 0 0 ~1 ~1 0 0 0 0
(x + ((x div 4) mod 2) - ((~x + 2) div 5))
A039183: 0 1 2 4 6 7 8 9 10 11 12 13 15 17 18 19
(((1 + (x div 5)) mod 2) + ((x div 4) mod 2))
A191340: 1 1 1 1 2 1 1 1 0 0 1 1 2 2 2 1
(2 + (2 * ((2x + 4) - (x mod 4))) - (x mod 2))
A214864: 10 11 14 15 26 27 30 31 42 43 46 47 58 59 62 63
((2 * (1 + (x div 8))) div (2 + (x mod 4)))
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((2 - (((x * (~1 + ((~x + 2) div 3))) div 2) div 2)) div 2)
A029053: 1 1 1 2 2 2 3 4 4 5 6 6 8 9 10 12
(2 + (((x + ((~x2 + 1) mod 5)) div 2) div 2))
A279596: 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 6
(x - ((((x * ((1 - (x div 2)) div 3)) div 2) div 2) div 2))
A095274: 0 1 2 3 5 6 7 8 9 11 13 14 15 17 18 19
(1 - ((((2 - (x * ((x div 2) div 3))) div 2) div 2) div 2))
A046774: 1 1 1 1 1 1 2 2 2 2 2 3 4 4 5 5
(x - (((1 - ((~x + (x2 div 3)) div 2)) div 2) div 2))
A067570: 0 1 2 3 4 5 7
A025199: 0 1 2 3 4 5 7 8 10 11 13 15 17 18 20 23
(x mod (5 - ((~x + (x2 mod 3)) div 2)))
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A004429: 0 1 2 3 4 5 6 7 8 9 0 1 1 2 2 2
((x + 2) - ((((~x + 1) * (x div 8)) div 2) div 2))
A178338: 2 3 4 5 6 7 8 9 12 13 15 16 17 18 20 21
((2x + 2) - (((~x + ((x div 2) div ~2)) div 2) div 2))
A184749: 2 5 7 9 12 14 16 19 21 23 26 28 30 32 35 37
((((x - ((~x + 2) div 2)) * (x - ((~x + 2) div 2))) div 2) div 2)
A274221: 0 0 1 4 6 12 16 25 30 42 49 64 72 90 100 121
(4 + ((x5 + x2 + 2x) div 2))
A165164: 4 6 24 133
(2 + (2 * (x - (2 * ((~x + ~2) + (x mod 2))))) - (x div 2))
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(((2x3 + 7x2 + 8x + 4) div 2) div 2)
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((((1 - (x div (1 + (x mod 4)))) mod (x + 2)) div 2) mod 2)
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(((6x2 + 12) div (x + 4)) mod 2)
A079559: 1 1 0 1 1 0 0 1 1 0 1 1 0 0 0 1
(((1 + (x * (2 + (x mod 4)))) div (x + 4)) mod 2)
A143538: 0 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0
((x - ((x4 + ~2) div (x + 4))) mod 2)
A159638: 1 0 0 0 1 0 1 1 1 1 0 0 1 0 0 1
((3x2 + 9) div (x + 6))
A214051: 1 1 2 4 5 7 9 12 14 16 19 21 24 27 29 32
((3x2 + ~3x + 6) div (x + 6))
A062417: 1 0 1 2 4 6 8 10 12 14 17 19 22 24 27 30
((4x + 8) + ((x2 + x + 1) div 3))
A006619: 8 13 18 24 31 38 46 55
(1 - ((((~2 + ((x div 2) mod 3)) * (x div 2)) div 2) div 2))
A102481: 1 1 2 2 1 1 3 3 2 2 1 1 4 4 3 3
(((((x + ~2) mod (2 + (x div 3))) + (x div 2)) div 2) mod 2)
A269242: 0 0 0 1 0 1 1 0 1 1 0 0 1 1 1 0
(8x - ((x - ((2 - (x div 2)) div 2)) div 2))
A338857: 1 8 15 23 30 38 45 52 60 67 74 82 89 97 104 111
(((3x2 + 3x + ~2) div (2 + (x div 2))) mod 2)
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(x - (((x div 2) - (4x div (2 + (x div 2)))) div 2))
A048947: 0 2 3 5 5 7 7 8 9 10 10 12 12 13 14 15
(2 - (((x3 + 2x2 + ~x + ~2) div (2 + (x div 2))) mod 2))
A233136: 1 2 2 1 2 2 2 2 1 2 1 2 2 1 2 1
(((x2 + ~x) - ((x2 div 2) div (2 + (x div 2)))) div 2)
A083704: 0 0 1 2 5 8 13 19 25 33 41 51 61 73 86 99
(((x * (~1 + (2 * (x div 4)))) mod (2 + (x div 2))) div 2)
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(((x * (2 + (x div 5))) mod (2 + (x div 2))) div 2)
A329308: 0 0 0 0 0 1 1 0 0 1 2 1 0 2 1 1
(2 - ((x div (2 + (((x + ~1) mod 3) + (x mod 2)))) mod 2))
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(x div (2 * (8 - ((x + ~2) div (2 + (x mod 2))))))
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((3x + 3) - ((~x + 2) div (4 + (x mod 2))))
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(4 * ((x3 + ~3x2 + ~x) div 3))
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(1 - (((x - ((x div 2) mod 5)) div 2) mod 4))
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(((x3 div 3) mod 6) mod 4)
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(x - (((~x + 2) - (((~x + 2) div 2) mod 4)) div 4))
A039136: 0 1 2 4 6 7 8 9 10 11 12 14 16 17 18 19
((((x2 + ~x) mod 5) * (x div 2)) mod 4)
A211996: 0 0 2 1 0 0 0 2 0 0 0 0 0 2 2 0
((x + 4) + (x div (3 + ((x div 4) mod 2))))
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((x + ((~x + 2) mod (3 + (x div 4)))) div 4)
A089361: 0 0 0 1 1 1 1 2 3 3 3 3 3 3 3 5
((x + (((x + 1) + (x div 2)) mod 5)) div 4)
A229878: 0 0 1 0 1 2
A289120: 0 0 1 0 1 2 1 2 2 3 2 3 4 3 4 4
((x + 4) + ((x - (2 mod (x + 1))) div 5))
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((x + 4) + ((x - (x div ~3)) div 3))
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A248188: 4 5 7 8 10 11 12 14 15 17 18 20 21 23 24 25
((x + (9 mod (1 + (x div 2)))) div 4)
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((x * (((x * (x div 3)) mod 3) mod 2)) div 4)
A218234: 0 0 0 0 1 0 0 0 2 0 0 0 0 3 0 0
(4 * (x + (((x - (x mod ~3)) div 2) div 2)))
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((5 mod (~x + 16)) mod 4)
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((1 div (~x + (4 * (4 - (x mod 2))))) mod 4)
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((4x + 4) - ((x + (x div 4)) mod 4))
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(((8x + 4) div 3) - (x div 4))
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(4x + ((~x + 1) mod 4) - (x div 4))
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(x + (x mod 4) - (3 * ((x div 4) mod 2)))
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((((x div 2) mod 7) div 2) + (x mod 4))
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((x2 - (x2 div 4)) * (x2 div 4))
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((1 mod (8 - (x div 2))) + (x2 div 4))
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((2 - ((~x + (2x mod (1 + (x div 3)))) div 2)) div 2)
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((2x + 2) - ((~x + (x mod (1 + (x div 3)))) div 2))
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(4x2 + 28x + 68)
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(2 * ((x + 2) + ((x - (x div ~3)) div 3)))
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((x + 2) mod (2 * ((x + ((~1 + (x div 2)) mod 3)) div 2)))
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((15x2 + 13x + 2) div 2)
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((2x + 2) - (x2 div ((x + 2) + (x div 3))))
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((2 - ((x * (~1 + ((x div 2) mod 2) - (x mod 2))) div 2)) div 2)
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(2 - ((((~x + 1) * ((x + 2) mod 5)) div 2) mod 2))
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((2 + ((x2 + ~x) div 2)) * (2 + ((x2 + x) div 2)))
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((x + 2) - (1 mod (5 - ((x2 + ~x) div 2))))
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(32x2 + ~26x)
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(1 - (((x * (~2 + ((~x2 + 2x) div 4))) div 2) div 2))
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((2x - ((~x + ((1 + (x div 2)) mod 4)) div 2)) div 2)
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A039151: 0 1 2 3 4 5 7 9 10 11 12 13 14 15 17 19
(1 - (((x mod 5) - ((x2 + 2x) div 2)) div 2))
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((1 + (x mod ~3)) mod (2 + ((x * (x div 2)) mod 2)))
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(4x3 + 28x2 + 66x + 52)
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(((x + 2) * (1 + (x mod (~2 * (1 + (x mod 2)))))) div 2)
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(((x + 2) * (1 + ((x2 + 6x + 8) div 2))) div 2)
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(((3 * (2 - (2 * (x div 3)))) div (x + 2)) mod 2)
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(2 - (((~2 + ((x + ~2) div 5)) mod (x + 2)) mod 2))
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(((2 + ((x + 2) div (2 + (x mod 4)))) mod (x + 2)) mod 2)
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(2 + ((4x + (x2 div 4)) div (x + 2)))
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(x + (((~x2 + 4x + ~4) div (x + 2)) mod 2) - (x mod 2))
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(4 div (24 div (x + 4)))
A297824: 0 1 1 1 1 2 2 2 2 4 4 4 4 4 4 4
((x * (x mod (1 + ((~x + 2) mod 4)))) div (x + 4))
A097249: 0 0 0 1 0 0 0 1 1 0 0 2 0 0 0 2
((2x + 5) + ((x + ~2) mod (3 - (x mod 2))))
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((3x + 4) + ((x - ((~x + 2) div 4)) div 2))
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(x4 + 8x3 + 18x2 + 12x + 2)
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(4x + ((~x + 1) div (1 + (((x + 1) div 2) div 2))))
A247157: 1 4 7 11 14 18 21 26 29 33 37 41
(4x + ((x2 + 1) div (4x + 1)))
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(4x + ((1 + ((x * (x div 2)) div 2)) div (x + 1)))
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(4x + ((~x + ((x div 2) div ~3)) div 2))
A258834: 0 3 6 10 13 17 20 24 27 30 34 37 41 44 47 51
(4x + ((x + ((x mod (1 + (x div 2))) div 2)) div 2))
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(5x + (x div ~9))
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(5x + (((2 - (x div 2)) div (x + 2)) mod 2))
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(2 * (3x + ((x + (x div 2)) div 8)))
A246977: 0 6 12 18 24 30 38 44 50 56 62 70 76 82 88 94
((~1 + ((((1 + (x div 2)) div 2) mod 4) + (x div 2))) div 2)
A073578: ~1 ~1 0 0 1 1 2 2 2 2 3 3 4 4 3 3
(x - (~62 * (x div 2)))
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(((x + 2) * (1 + ((x mod 3) mod 2))) mod (2 + (x div 2)))
A291307: 0 0 1 2 0 3 3 3 4 5 3 6 6 6 7 8
((x + (x mod (1 + ((x + 2) div 3)))) div (2 + (x div 2)))
A333355: 0 1 0 1 1 1 1 2 1 1 1 1 1 1 1 2
(1 + ((x div 2) mod 2) - (((2 - (x div 2)) mod (x + 2)) mod 2))
A334540: 1 1 1 1 1 1 1 2 1 0 1 2 1 0 1 2
(((2 mod (1 + (x div 4))) + (x mod 2)) - ((x div 2) mod 2))
A318438: 0 1 ~1 0 0 1 ~1 0 2 3 1 2 2 3 1 2
((1 + (((((x + 1) div 2) div 2) mod 4) + (x mod 2))) div 2)
A109969: 0 1 0 1 1 1 1 2 1 2 1 2 2 2 2 1
(((3 * ((x + 1) - (x div 4))) + (x mod 2)) div 2)
A230300: 1 3 4 6 6 8 9 11 10 12 13 15 15 17 18 20
(~2 + (3 * (2 - ((~x + 2) div (x + 2)))) - (x mod 2))
A225647: 1 3 4 6 7
A129000: 1 3 4 6 7 6 7 6 7 6 7 6 7 6 7 6
((((x + ((x div 4) mod 2)) mod 3) - (x mod 2)) div 2)
A111113: 0 0 1 ~1 1 ~1 0 0 1 ~1 0 0 0 0 0 0
(((x div (~x + 17)) + (x mod 2)) div 2)
A206560: 0 0 0 0 0 0 0 0 0 1 0 1 1 2 2 4
(((5x2 + 7x + 2) - (x mod 2)) div 2)
A153126: 1 6 18 33 55 80 112 147 189 234 286 341 403 468 540 615
(((4x div (2 + (x div 3))) + (x mod 2)) div 2)
A345380: 0 1 2 2 2 3 3 4 4 4 4 4 4 4 4 4
(2 - ((((~x + 2) div (2 + (x div 4))) - (x mod 2)) div 2))
A266119: 2 3 2 3 3 3 3 4 3 4 3 4 3 4 4 4
((2 - (2 div (1 + (x div 5)))) mod (2 + (x mod 2)))
A277146: 0 0 0 0 0 1 1 1 1 1 0 2 0 2 0 2
((1 + ((x2 + ~x) mod (2 + (x div 2)))) mod (2 + (x mod 2)))
A275784: 1 1 1 1 1 1 1 0 1 1 1 0 1 2 1 1
((2 + (2 * ((x div 4) - (x mod 2)))) div (2 + (x mod 2)))
A025804: 1 0 1 0 2 0 2 0 3 1 3 1 4 2 4 2
((2 + (x div 3) - (x mod 4)) div (2 + (x mod 2)))
A029352: 1 0 0 0 1 0 1 0 2 1 1 0 3 1 2 1
((1 + ((x2 + 2x) div 4)) * (1 - (2 * (x mod 2))))
A152032: 1 ~1 3 ~4 7 ~9 13 ~16 21 ~25 31 ~36 43 ~49 57 ~64
((x + 4) + compr(\x.((x + 2) mod (1 + (x div 4))),x))
A167179: 4 6 8 10 12 15 20 25 30 35 40 45 50 55 60 65
(((x + (x2 div ((~x + 1) + (x mod 4)))) div 2) mod 2)
A144101: 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1
(1 - ((~x + (x div (1 + ((x + 1) div 5)))) div 2))
A064952: 1 1 1 1 2 3 3 3 3 4 5 5 5 6 7 7
((25x2 + x) div 2)
A022283: 0 13 51 114 202 315 453 616 804 1017 1255 1518 1806 2119 2457 2820
((25x2 + ~x) div 2)
A022282: 0 12 49 111 198 310 447 609 796 1008 1245 1507 1794 2106 2443 2805
((27x2 + x) div 2)
A022285: 0 14 55 123 218 340 489 665 868 1098 1355 1639 1950 2288 2653 3045
((27x2 + ~x) div 2)
A022284: 0 13 53 120 214 335 483 658 860 1089 1345 1628 1938 2275 2639 3030
((6x3 + 9x2 + 2x) div 2)
A100583: 0 8 44 124 268 492 816 1256 1832 2560 3460 4548 5844 7364 9128 11152
((6x3 + 15x2 + 5x) div 2)
A163833: 0 13 59 156 322 575 933 1414 2036 2817 3775 4928 6294 7891 9737 11850
((x + 2) + (2 div (5 - ((x + ~2) div 3))))
A317469: 2 3 4 5 6 7 8 9 10 11 12 14 15 16 18 19
((21x2 + ~x) div 2)
A022278: 0 10 41 93 166 260 375 511 668 846 1045 1265 1506 1768 2051 2355
(2 + compr(\x.((x + 1) mod (1 + (x2 mod (1 + (x div 2))))),x))
A174894-A088948-A078174: 2 3 4 5 7 8 9 11 13 15 16 17 19 21 23 25
((x + 2) + (((x2 + x) div 2) div 7))
A024926: 2 3 4 5 7 9 11 13 15 17 19 22 25 28 31 34
(1 - ((~x + (x div (1 + (2 * (2 + (x mod 4)))))) div 2))
A165907: 1 2 2 3 3 4 4 5 5 5 6 6 6 7 8 8
((~x + ((x * (x + (x div 2))) div 9)) div 2)
A292043: 0 ~1 ~1 ~1 ~1 ~1 0 0 1 2 3 4 6 7 9 10
(2 + compr(\x.((x + 1) mod (1 + (x mod (2 + (x div 4))))),x))
A326621: 2 3 4 5 7 8 9 10 11 13 16 17 19 20 21 22
(x mod ((x + 2) + (x div (1 + (2 * (4 - (x div 2)))))))
A103303: 0 1 2 3 4 5 6 7 8 9
A134778: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 1 1
(2 + compr(\x.((x + ~2) mod (1 + (2 * (x mod (2 + (x mod 2)))))),x))
A050505: 2 4 5 6 8 10 11 12 14 16 17 18 19 20 22 23
((x * (1 + (((x2 + 2) div 3) mod 4))) div 2)
A187601: 0 1 3 6 6 5 3 7 12 18 15 11 6 13 21 30
((x + 2) + (((2x + 1) + (x mod 2)) div 5))
A284931: 2 3 5 6 7 9 10 12 13 15 16 17 19 20 21 23
((11x2 + ~7x) div 2)
A180223: 0 2 15 39 74 120 177 245 324 414 515 627 750 884 1029 1185
(2 * compr(\x.(((x + 1) * (x mod 4)) mod 5),x))
A092456: 0 8 16 18 24 28 32 38 40 48 56 58 64 68 72 78
((11x2 + 9x) div 2)
A211013: 0 10 31 63 106 160 225 301 388 486 595 715 846 988 1141 1305
(x - (2 * (~x + ((2 * (~2 + (x div 2))) div 5))))
A187581: 2 5 8 11 12 15 18 21 24 27 28 31 34 37 38 41
((x + 2) + ((x - ((x div 2) mod 4)) div 5))
A121603: 2 3 4 5 6 7 8 9 11
A251726-A069899-A066311: 2 3 4 5 6 7 8 9 11 12 13 15 16 17 18 19
((19x2 + x) div 2)
A022277: 0 10 39 87 154 240 345 469 612 774 955 1155 1374 1612 1869 2145
((x + (2x div (2 - ((~x + 1) div 5)))) div 2)
A097873: 0 1 1 2 3 4 5 5 6 6 7 8 8 9 9 10
((x + 2) + (x2 div ((2x + 1) - (x div 4))))
A186541: 2 3 4 6 8 9 11 12 14 15 17 18 20 22 23 25
(x - ((~x + ((0 - (x div 5)) mod 3)) div 2))
A336487: 0 2 3 5 6 7 8 10 11 13 15 16 18 19 21 23
((13x2 + ~9x) div 2)
A226488: 0 2 17 45 86 140 207 287 380 486 605 737 882 1040 1211 1395
(compr(\x.((x + 1) mod (3 * (1 + (x mod 4)))),x) div 2)
A134191: 2 4 5 8 10 11 13 14 16 17 20 22 23 26 28 29
((19x2 + ~x) div 2)
A022276: 0 9 37 84 150 235 339 462 604 765 945 1144 1362 1599 1855 2130
((x + ((3x + 3) * (x + (2 * (x mod 2))))) div 2)
A322465: 0 9 10 31 32 65 66 111 112 169 170 239 240 321 322 415
((x + 2) + ((x - ((((x + ~1) div 2) div 2) mod 2)) div 3))
A225647: 1 3 4 6 7
A206587: 1 3 4 6 7 8 9 11 12 14 15 16 18 19 20 21
((x + 2) + ((x2 + x) div 24))
A184115: 2 3 4 5 6 8 9 11 13 14 16 18 20 22 24 27
(2 * (x + ((2 * (x2 - (x mod 4))) div 3)))
A161212: 0 2 6 14 28 42 56
((23x2 + x) div 2)
A022281: 0 12 47 105 186 290 417 567 740 936 1155 1397 1662 1950 2261 2595
((x + 2) + ((x - (x mod (~2 + ((x div 2) mod 2)))) div 3))
A285974: 2 3 4 6 7 9 10 11 12 14 15 16 18 19 20 22
((x + 2) + ((2 * (x - (x mod (2 + (x mod 2))))) div 3))
A187332: 2 3 5 7 8 9 12 13 15 17 18 19 22 23 25 27
((x + 2) + ((2 * (x + ((x + ~1) div 3))) div 3))
A187687: 1 3 5 7 9 11 12 15 16 18 20 22 24 26 28 29
((x + 2) + (((2x2 + 4) div (x + 2)) div 3))
A186326: 2 3 5 6 8 9 11 12 14 16 17 19 20 22 24 25
((x + 2) + ((x + (5 mod (x + 1))) div 3))
A317091-A247180: 2 3 5 6 7 10 11 13 14 15 17 18 19 21 22 23
(1 - ((x * ((~x + 1) - ((x mod 3) + (x mod 2)))) div 2))
A231408: 1 2 4 6 9
A192079: 1 2 4 6 9 19
((~x + ((4x - (x div 2)) * (1 + (x div 2)))) div 2)
A118277: 0 1 6 9 19 24 39 46 66 75 100 111 141 154 189 204
(2 * ((x + 1) - ((x + 1) mod (~1 + ((~x + 2) * (x div 2))))))
A345986: 2 4 6 8 10 14 26
((23x2 + ~x) div 2)
A022280: 0 11 45 102 182 285 411 560 732 927 1145 1386 1650 1937 2247 2580
((31x2 + x) div 2)
A022289: 0 16 63 141 250 390 561 763 996 1260 1555 1881 2238 2626 3045 3495
((31x2 + ~x) div 2)
A022288: 0 15 61 138 246 385 555 756 988 1251 1545 1870 2226 2613 3031 3480
((x + 2) + ((~1 + (2 * ((1 + (x div 2)) div 2))) mod (x + 1)))
A111688: 2 4 5 6 7 8 11 12 13 14 17 18 19 20 23 24
((x2 + 16x) div (x2 + x + 2))
A023977: 0 4 4 4 3 3 3 2 2 2 2 2 2 2 1 1
((2 * ((x2 + 2x) - (x div 2))) + ((x2 + x) div 2))
A195016: 0 7 17 34 54 81 111 148 188 235 285 342 402 469 539 616
((x + 2) + ((x mod (1 + (2 * (2 - (x mod 4))))) mod 2))
A071193: 2 4 4 5 6 7 8 9 11 11 12 13 14 16 16 17
((x + 2) + ((x - (x mod (1 + (x mod (2 + (x div 2)))))) div 2))
A055562: 2 3 4 6 8 9 11 12 13 15 16 18 19 21 22 24
((x + 1) - (1 mod ((~x + ((x + 2) mod 6)) div 2)))
A166527: 1 2 3 4 6 7 8 9 10 11 15 16 17 18 19 20
((x + 2) + (((x2 div 3) + (x div 3)) div 2))
A236337: 2 3 4 7 9 11 15 18 21 26 30 34 40 45 50 57
((x * ((2x3 + ~3x2 + 2x) div 2)) div 2)
A212681: 0 0 4 24 88 230 504 966 1696 2772 4300 6380 9144 12714 17248 22890
((8x3 + 9x2 + 3x) div 2)
A302302: 0 10 53 153 334 620 1035 1603 2348 3294 4465 5885 7578 9568 11879 14535
((x + (((x + 1) * ((2 - (x div 2)) mod (x + 2))) div 2)) mod 2)
A189702: 0 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1
(1 - ((~x + (2x div (1 - (x div ~4)))) div 2))
A074794: 1 1 1 1 1 2 2 3 3 4 4 4 4 5 6 6
(x - (2 * (~x + (4 * ((x div 3) mod 3)))))
A163327: 0 3 6 1 4 7 2 5 8 27 30 33 28 31 34 29
((x + 2) + ((((x + ~1) * (x div 8)) div 2) div 2))
A121603: 2 3 4 5 6 7 8 9 11
A031185: 2 3 4 5 6 7 8 9 11 13 14 15 16 18 19 20
((x + (((x2 - ((x div 2) div ~2)) div 2) div 2)) div 2)
A250000: 0 0 1 2 4 5 7 9 12 14 17 21 24 28 32
((x + 2) + ((x - ((x + (x div 2)) div ~4)) div 2))
A121347: 2 4 5 7 9 10 12 14 15 17 19 20 22 24 26 27
((x + 2) + (((x - ((x mod 5) div 2)) div 2) div 2))
A288712: 2 3 4 5 6 8 9 10 11 12 14 15 16 18 19 20
((x + 2) + (2 * ((x - (((x div 2) div ~2) div 2)) div 2)))
A190674: 2 3 6 9 10 13 14 17 18 21 24 25 28 29 32 33
((x + 2) + ((((((x + ~1) * (x div 2)) div 2) div 2) div 2) div 2))
A132018: 2 3 4 5 6 7 8 10 11 13 14 16 18 19 21 23
((x + 2) + ((2x + 4) div (4 + (x div 4))))
A182835: 3 4 6 7 8 9 11 12 13 14 16 17 18 19 20 21
((x + 2) + ((x - ((~x + 1) div (2 + (x div 4)))) div 2))
A003258: 2 3 5 7 8 10 12 13 15 16 18 20 21 23 24 26
(x - ((2x + 2) div (3x + ~16)))
A295266: 1 2 3 5 7 17
(1 - ((~x + ((((~x + 2) div 2) * (x div 4)) div 2)) div 2))
A175268: 1 2 2 3 4 4 5 6 7 8 8 9 11 12 13 14
(1 - ((~x + (((~2x + 4) mod (2 + (x div 2))) div 2)) div 2))
A080677: 1 2 2 3 3 3 4 5 5 5 5 6 6 7 8 9
((x + 2) + ((x - ((~x + ((x div 4) mod 2)) div 2)) div 2))
A284535: 2 4 5 7 9 10 12 14 16 18 19 21 23 24 26 28
((x * ((x3 + ~6x2 + 13x + ~8) div 2)) div 2)
A327319: 0 0 1 3 12 40 105 231 448 792 1305 2035 3036 4368 6097 8295
((x + 2) + (2 * (2x + (2x div 5))))
A188039: 2 7 12 19 24 31 36 41 48 53 60 65 70 77 82 89
(6 div ((~2x + 4) + (x2 div 3)))
A331058: 1 3 6 6 6 3 1
((x + 2) + (2 * (x + (5 * (x div 4)))))
A246442: 2 5 8 11 24 27 30 33 46 49 52 55 68 71 74 77
((x + 2) + ((x + ((2 - ((x div 2) mod 2)) mod (x + 1))) div 2))
A175089: 2 3 5 7 9 10 11 13 15 16 17 19 21 22 23 25
(((x2 + 2x) + (2x3 div 3)) div 2)
A236773: 0 1 6 16 33 59 96 145 210 292 393 515 660 829 1026 1252
((x + 2) + ((x + 2) div (12 - (x div 2))))
A162722: 2 3 4 5 6 7 8 10 11 12 13 14 16 17 19 20
(2 * ((~1 + (4 * (x + (x div 2)))) * (x + (x div 2))))
A117794: 0 6 66 120 276 378 630 780 1128 1326 1770 2016 2556 2850 3486 3828
((x - (x mod 9)) mod (2 + (x * (x mod 2))))
A329725: 0 0 0 0 0 0 0 0 0 9 1 9 1 9 1 9
((x * ((x5 + ~x4 + x2) div 2)) div 2)
A079241: 0 0 10 127
((~1 + ((2x2 + x) div 5)) mod (x + 2))
A092093: 1 2 1 3 0 3 6 2 6 0 5 10 3 9 0 7
(x4 + 8x3 + 21x2 + 23x + 10)
A268945: 10 63 220 565 1206 2275 3928 6345 9730 14311 20340 28093 37870 49995 64816 82705
compr(\x.(x mod (1 + (2 * ((x2 div 2) mod 3)))),(x + 2))
A191916: 3 5 6 7 9 10 11 12 13 15 17 18 19 20 21 23
(1 div ((~1 + (4 * (2x div 3))) mod (x + 2)))
A173860: 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0
((~1 + ((x - ((x2 * (x div 2)) div 2)) div 2)) mod (x + 2))
A111607: 1 2 3 3 5 3 7 2 9 10 11 9 13 7 15 4
((3 + ((x * ((x + ~1) + (x div 2))) div 2)) div (x + 2))
A265436: 1 1 1 1 2 2 3 3 4 5 6 6 7 8 8 9
((3 + (x * (2x div 5))) div (x + 2))
A145703: 1 1 0 1 1 1 1 1 2 2 3 3 3 4 4 5
((x + 2) * ((x + 2) - ((~2x + 2) div (x + 3))))
A297190: 4 9 20 30 42 56 80 99 120 143 168 195 224 255 288 323
compr(\x.((~x + ~1) + (x2 mod (x - ((~x + 2) div 2)))),(x + 2))
A332487: 2 3 4 5 6 8 9 10 11 12 15 16 17 18 21 22
((2 * (1 + ((1 + (x * (x div 2))) div 3))) div (x + 2))
A029204: 1 0 1 0 1 1 1 1 2 2 3 2 3 3 4 4
((2 * ((x + 1) mod 11)) mod (x + 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A080464: 0 1 2 3 4 5 6 7 8 9 0 2 4 6 8 10
compr(\x.(((2 + (x * (x div 2))) div 5) mod 2),(x + 2))
A190225: 2 4 5 6 7 8 10 12 13 14 16 18 19 20 21 22
(1 - ((2 - (2x mod (2 + (x div 3)))) div (x + 2)))
A293451-A115722-A115721: 0 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1
((2 + ((1 + (((x + ~1) div 2) mod 4)) div 2)) mod (x + 2))
A079243: 0 2 2 3
A115777: 0 2 2 3 3 3 3 4 4 2 2 3 3 3 3 4
compr(\x.((x mod 5) - (2 * (x mod 4))),(x + 2))
A028805: 2 3 5 6 7 10 11 14 15 17 18 19 20 21 22 23
((x2 + 4x + 4) + (x4 div 4))
A144686: 4 9 20 45 100
((2x + 2) - (2 div (1 + (~x mod 5))))
A001745: 0 4 6 8 9 10 14 16 18 19 20 24 26 28 29 30
(2x + ((1 - (x mod (1 + (x mod 3)))) mod 3))
A190247: 1 2 6 7 9 12 13 14 18 19 21 24 25 26 30 31
(2x + ((~x + ((2 * (x div 2)) div 3)) div 3))
A037086: 0 1 3 5 7 8 10 12 14 15 17 19 21 23 24 26
(2x + (3 * (x + ((x mod (1 + (x div 2))) div 2))))
A045775: 0 5 10 15 20 28 33 38 43 51 56 61 66 74 79 84
(2x * ((x + 1) + (2 * (2 + ((x mod 3) div 2)))))
A076515: 0 12 36 48 72 120
(2x + ((x - (x div ~12)) div 2))
A029919: 0 3 5 8 10 13 15 18 20 23 25 28 30 33 36 38
(2x + (((x2 + x) div ~8) mod 2))
A001969: 0 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30
((2x + 2) - ((x + ~1) mod (2 + ((x div 3) mod 2))))
A327223: 1 4 5 6 10 11 13 16 17 18 22 23 25 28 29 30
(2x + (((x3 mod (2x + ~1)) div 2) mod 2))
A268272: 0 2 5 7 8 10 13 14 17 19 20 22 25 27 28 31
(2x + ((((~1 + ((x2 + x) div 2)) div 2) div 2) mod 2))
A000069: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 31
(2x + ((~x + ((~1 + (x div 2)) mod 3)) div 4))
A190785: 0 2 3 5 7 9 11 12 14 15 17 19 21 23 24 26
((2x + 1) - (1 mod (~x2 + 4x + ~1)))
A231408: 1 2 4 6 9
A096398: 1 2 4 6 9 16 25 36 49 64 81 100 121 144 169 196
(2x + (((3 * (x div 4)) div 2) + (x div 2)))
A004134: 0 2 5 7 11 13 16 18 23 25 28 30 34 36 39 41
(3x + (x div 2) - (x div (4 + (x mod 2))))
A029918: 0 3 7 10 13 16 20 23 26 30 33 36 39 43 46 49
(2x + ((((x + ~1) div (2 + (x div 2))) mod 2) + (x mod 2)))
A026449: 1 3 4 7 8 12 13 16 17 20 21 24 25 28 29 32
94x2
A174337: 0 94 376 846 1504 2350 3384 4606 6016 7614 9400 11374 13536 15886 18424 21150
(1 + ((2 * ((2x + ~8) mod (x + 1))) + (x div 2)))
A301974: 1 1 6 6 3 7
((((x mod 4) * (x div 3)) mod 3) + (x div 2))
A081399: 0 0 1 1 2 3 4 3 4 4 5 5 6 7 9 7
((3 * ((4x + 1) + (x mod 2))) - (x div 2))
A169598: 3 18 26 41 49 64 72 87 95 110 118 133 141 156 164 179
((((2 * (~2 + (x div 2))) mod (x + 1)) div 3) + (x div 2))
A121260: 0 0 1 1 2 2 3 3 5 5 7 7 8 8 10 10
((2x + 4) - (x div (12 - (x div 2))))
A185604: 4 6 8 10 12 14 16 18 19 21 23 25 26 28 30 31
((x + 1) + ((2 div (~x + 16)) + (x div 2)))
A119905: 1 2 4 5 7 8 10 11 13 14 16 17 19 20 23 25
(((3 * (2x + (x div 4))) div 2) + (x div 2))
A120738: 0 3 7 10 15 18 22 25 31 34 38 41 46 49 53 56
((3 - ((~x + (x mod 4)) div 3)) * (x div 2))
A278832: 0 0 3 3 10 10 15 15 24 24
(((~x + 2) div (2 + ((((x + 1) div 2) div 2) div 2))) + (x div 2))
A029228: 1 0 1 0 1 0 1 1 2 1 2 2 2 2 3 3
((x2 + 2x + 1) div (16 + (x div 2)))
A241730: 0 0 0 0 1 2 2 3 4 5 5 6 7 8 9 11
(x - (3x div (16 - (x div 2))))
A189730: 0 1 2 3 4 4 5 6 6 7 8 8 9 10 10 10
(((7 * (x div 4)) div 2) + (x div 2))
A157276: 0 0 1 1 5 5 6 6 11 11 12 12 16 16 17 17
((4 * ((x div 8) + (x mod 2))) + (x div 2))
A080414: 0 4 1 5 2 6 3 7 8 12 9 13 10 14 11 15
(((x + ((x + 2) mod (2 + ((x div 2) mod 2)))) div 2) + (x div 2))
A067570: 0 1 2 3 4 5 7
A336285-A222249: 0 1 2 3 4 5 7 6 8 9 10 11 12 13 14 15
(((x + 2) div (12 - (x div 2))) + (x div 2))
A218445: 0 0 1 1 2 2 3 4 5 5 6 6 8 8 10 10
(x + ((2 * ((3 * (x div 4)) div 2)) + (x div 2)))
A068056: 0 1 3 4 8 9 11 12 18 19 21 22 26 27 29 30
(x2 + (((3 * (x div 4)) div 2) + (x div 2)))
A134467: 0 1 5 10 19 28 40 53 71 88 108 129 154 179 207 236
(((x + 1) div (1 + (x div (1 + (x div 3))))) - (x mod 2))
A025797: 1 0 1 1 1 1 2 1 3 2 3 3 4 3 5 4
((1 + (((x + ~1) * (x div 4)) mod 3)) * (x mod 2))
A322983: 0 1 0 1 0 2 0 1 0 2 0 3 0 1 0 1
((x div ((x + ~1) - (x mod ~8))) + (x mod 2))
A337101: 0 1 0 1 0 1 0 2 1 1 0 1 0 1 0 2
((1 + (x div (2 + (x div (1 + (x mod 4)))))) * (x mod 2))
A301979: 0 1 0 2 0 2 0 3 0 2 0 3 0 2 0 4
((1 + (x mod (2 + ((x div 4) mod 3)))) * (x mod 2))
A132747: 0 2 0 2 0 3 0 2 0 2 0 4 0 2 0 2
((7 * ((x + (x div 2)) div 2)) + (x mod 2))
A151971: 0 1 7 15 21 22 28 36 42 43 49 57 63 64 70 78
((5 * (x - ((x div ~2) mod 2))) + (x mod 2))
A151980: 0 1 5 16 20 21 25 36 40 41 45 56 60 61 65 76
((x + 1) - ((x mod 2) + ((~x2 + (x div 2)) div (x + 2))))
A188072: 1 2 4 5 8 9 12 13 15 16 19 20 23 24 27 28
(1 - ((x mod 2) + (2 mod (~4x2 + ~4x + 2))))
A273405: 1 4 21 44 77 116 165 220 285 356 437 524 621 724 837 956
(x + (x mod 2) - ((x mod (~1 + (x div ~3))) mod 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A338466-A209862-A209861-A187769: 0 1 2 3 4 5 6 7 8 9 10 12 11 13 14 15
(((x div (1 + (x mod 9))) mod 2) + (x mod 2))
A037888: 0 1 0 1 0 1 0 1 0 2 1 2 1 1 0 1
(((x mod (~1 + (2 * ((x + ~2) div 3)))) mod 2) + (x mod 2))
A096972: 0 1 0 1 0 1 0 1 0 1 1 2 0 2 0 2
(((1 + ((2 + (x div 2)) mod 6)) div 2) - (x mod 2))
A104145: 1 0 2 1 2 1 3 2 0 ~1 1 0 1 0 2 1
(((2x div (1 + (2 * (x mod 4)))) mod 2) + (x mod 2))
A324852: 0 1 0 1 0 2 0 1 0 1 0 2 0 1 1 1
((x div (2 + (x div (3 + ((x div 2) mod 2))))) + (x mod 2))
A334098: 0 1 1 2 1 2 2 3 2 2 2 3 2 3 2 4
(((1 + ((x div 4) * (x div 4))) div 2) * (x mod 2))
A035686: 0 0 0 0 0 1 0 1 0 2 0 2 0 5 0 5
(((1 + (((x div 2) mod 2) + (x div 3))) div 2) + (x mod 2))
A277314: 0 1 1 2 1 2 2 3 1 3 2 3 2 3 3 4
((((~x + 2) div (2 + ((x div 2) mod 3))) mod 2) - (x mod 2))
A214505: 1 ~1 0 0 1 0 0 0 0 0 0 0 1 ~1 0 0
(((x - (2x div (2 + (x div 3)))) mod 2) + (x mod 2))
A101659: 0 1 0 2 0 1 1 1 0 1 0 2 0 2 0 2
((x div (2 + (x div (2 + ((x mod 3) div 2))))) + (x mod 2))
A238949: 0 1 1 2 1 2 1 2 2 2 1 3 1 2 2 2
(((2x div (~2 - (x div 4))) mod 2) + (x mod 2))
A287263: 0 2 0 2 1 1 0 2 0 2 1 1 1 1 0 1
((((x2 + ~2) div (4 + (x div 2))) mod 2) + (x mod 2))
A026611: 1 2 0 2 0 2 0 1 1 2 0 2 0 1 1 1
((1 - (2 * ((~x + (x mod 3)) div 4))) * (x mod 2))
A272727: 0 1 0 3 0 3 0 5 0 7 0 7 0 7 0 9
((2 * ((x + 2) + (x div (4 + (x mod 2))))) + (x mod 2))
A137362: 4 7 8 11 14 17 18 21 24 25 28 31 34 35 38 41
((x div (2 + (x div (1 + (x mod 4))))) div (2 - (x mod 2)))
A124763: 0 0 0 1 0 1 0 2 0 1 1 2 0 1 1 3
((7x3 + ~5x2) div 2)
A262000: 0 1 18 72 184 375 666 1078 1632 2349 3250 4356 5688 7267 9114 11250
(2 + (x * (~x + (((x3 + ~x) div 2) div 3))))
A299198: 2 1 0 5 26 77 176 345 610 1001 1552 2301 3290 4565 6176 8177
(x2 - ((~x2 + ((x2 div 2) div 3)) div 2))
A293503: 0 2 6 13 23 36 51 70 91 115 142 172 204 240 278 319
((x2 + ((2 + (x mod (2 + (x mod 2)))) mod (x + 1))) div 2)
A118002: 0 1 3 5 9 14 19 26 33 41 51 62 73 86 99 113
(2x2 + ((x * ((x div 2) * (x div 2))) div 3))
A193389: 0 2 8 19 37 56
((x8 + x3) div 2)
A168180: 0 1 132 3294 32800 195375 839916 2882572 8388864 21523725 50000500 107180106 214991712 407866459 737895900 1281447000
((5x4 + 3x3) div 2)
A229146: 0 4 52 243 736 1750 3564 6517 11008 17496 26500 38599 54432 74698 100156 131625
compr(\x.(~1 + (x mod (3 + (x mod 3) - (x mod 2)))),x)
A139372: 0 1 3 4 5 6 7 9 12 13 15 16 17 18 19 20
(x * (1 + (~2 mod (1 + (x mod 10)))))
A230101: 0 1 4 9 16 25 36 49 64 81 10 11 24 39 56 75
compr(\x.(~1 + (x div (1 + (2 * (2 - (x mod 8)))))),x)
A261604: 0 1 3 4 5 6 7 8 11 12 13 14 15 19 20 21
compr(\x.(~1 + (x mod (1 + (2x mod (2 + (x div 4)))))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A092968: 0 1 2 3 4 5 6 7 8 9 10 13 15 16 18 19
compr(\x.(1 - (x mod (1 + (x mod (3 + (x mod 4)))))),x)
A186042: 1 2 3 5 7 8 9 11 13 14 15 17 18 19 20 21
compr(\x.(~1 + (((1 + (x * (x div 2))) div 3) mod 3)),x)
A084689: 0 1 2 3 4 5 6 7 9
A337133: 0 1 2 3 4 5 6 7 9 11 12 14 16 17 18 19
compr(\x.(~1 + (((((x + ~1) * (x div 2)) div 2) div 2) mod 3)),x)
A328592: 0 1 2 3 4 6 7 8 11 12 13 14 15 16 19 22
compr(\x.(~1 + (((x2 + ~x) div 8) mod 3)),x)
A191983: 0 1 2 3 4 6 8 9 11 12 13 14 16 17 19 21
compr(\x.(2 - ((x2 + x) mod 11)),x)
A188080: 1 2 4 5 6 8 9 12 13 15 16 17 19 20 23 24
compr(\x.(~1 + (((x * (x div ~4)) div 2) mod 3)),x)
A028974: 0 3 4 5 6 8 9 10 11 12 13 15 16 18 19 20
compr(\x.(2 - ((x div 4) div (1 + (2x mod 3)))),x)
A345498: 9 12 15 17 18 20 21 23 24 25 26 27 28 29 30 31
compr(\x.(~1 + ((((x + ~2) div 3) * (x div 2)) mod 3)),x)
A155905: 0 1 2 3 4 6 7 10 11 12 13 14 15 17 18 19
(x + (x div (~1 + (3 * (8 - (x div 2))))))
A103303: 0 1 2 3 4 5 6 7 8 9
A124097: 0 1 2 3 4 5 6 7 8 9 11 12 14 15 21 22
compr(\x.(2 - ((x div 4) div (1 + ((~x + 1) mod 3)))),x)
A345508: 10 13 16 18 19 21 22 24 25 26 27 28 29 30 31 32
compr(\x.(~1 + (2 * ((x + 1) mod 4)) - (x div 3)),x)
A061094: 3 4 7 8 9 11 12 13 15 16 17 18 19 20 21 22
(x + (x2 div ((x + 5) + (x div 3))))
A123663: 0 1 2 4 5 7 8 10 12 13 15 17 18 20 22 24
compr(\x.((x + 2) mod (2 - (x div (~1 - (x mod 3))))),x)
A267415: 0 1 3 6 8 9 12 15 18 21 24 27 30 33 36 39
(x + (x mod (1 + ((x2 + ~x + 2) div (x + 3)))))
A000394: 0 1 2 4 5 7 8 9 10 11 12 13 15 16 17 18
(16x3 + 24x2 + 9x)
A322675: 0 49 242 675 1444 2645 4374 6727 9800 13689 18490 24299 31212 39325 48734 59535
((x + 1) + (((~x2 + 2x) div (x + 4)) mod (x + 1)))
A046668: 1 2 3 7 9 10 11 12 14 15 16 17 18 19 20 21
compr(\x.(~1 + (x mod (2 + (x mod (~1 + (2 * (x div 4))))))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A133184: 0 1 2 3 4 5 6 7 8 9 10 12 15 16 18 20
compr(\x.(2 - ((x div 2) div (1 + (2 * (2x mod 3))))),x)
A344805: 6 9 12 14 15 17 18 20 21 22 23 24 25 26 27 28
(29x2 + ~28x)
A249911: 0 1 60 177 352 585 876 1225 1632 2097 2620 3201 3840 4537 5292 6105
(x + ((x * (((x + ~1) div 2) div 2)) div 7))
A326583: 0 1 2 3 4 5 6 8 9 11 12 14 15 18 20 21
compr(\x.((x mod 6) - (x mod 7)),x)
A032861-A023788: 0 1 2 3 4 5 6 12 13 18 19 20 24 25 26 27
((x + 1) + (((4 + (x div 4)) mod (x + 1)) div 2))
A032867: 1 2 3 4 5 8 9 10 12 13 14 15 16 17 18 19
(x + (x div (5 + ((x div 2) mod 5))))
A039273: 0 1 2 3 4 5 6 7 8 10 12 13 14 15 16 17
compr(\x.(x mod (1 + ((~x mod (2 + (x div 3))) div 2))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A048335-A048322-A048308-A029956: 0 1 2 3 4 5 6 7 8 9 10 12 24 36 48 60
compr(\x.(1 - (x mod (1 + (8 * ((x div 2) mod 2))))),x)
A230375: 2 3 6 7 10 11 14 15 19 22 23 26 30 31 34 35
(x + (x div (1 + (2 * (2 + ((x div 3) mod 4))))))
A103303: 0 1 2 3 4 5 6 7 8 9
A333762-A295235-A247805-A235028-A136490-A062014-A057890: 0 1 2 3 4 5 6 7 8 9 10 12 14 15 16 17
(x + (3x2 div 17))
A234363-A156024: 0 1 2 4 6 9 12 15 19 23 27 32 37 42 48 54
compr(\x.(1 - (x mod (1 + (x mod (2 * (2 + (x mod 4))))))),x)
A325113: 1 2 3 5 6 7 9 10 11 13 15 17 19 21 22 23
compr(\x.(x mod (~3 + (2x mod (4 + (x div 2))))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A278328: 0 1 2 3 4 5 6 7 8 9 10 11 12 15 21 22
(x + (x2 mod ((x + ~1) - (x div ~7))))
A084689: 0 1 2 3 4 5 6 7 9
A154799: 0 1 2 3 4 5 6 7 9 10 11 12 13 14 15 19
compr(\x.((x + 1) mod (1 + ((~x + ~2) mod 8))),x)
A328557: 3 5 6 7 11 13 14 15 17 19 20 21 22 23 27 29
compr(\x.((x mod 8) - (x mod 9)),x)
A032863-A023790: 0 1 2 3 4 5 6 7 8 16 17 24 25 26 32 33
compr(\x.(8 - (x div (1 + (x mod 8)))),x)
A297264-A297141-A296708: 8 16 17 24 25 26 32 33 34 35 40 41 42 43 44 48
((x + ~1) div ((x + ~1) + (2 * ((x div 2) - (x mod 4)))))
A218173: 1 0 ~1 ~1 0 0 0 1 0 0 0 0 0 0 0 0
compr(\x.(2 - ((x + 1) mod (3 + (x div (2 + (x mod 2)))))),x)
A080639: 1 2 5 7 8 9 10 12 14 16 17 18 19 20 21 22
(x + (5 * ((2 * (x div 2)) div 5)))
A214653: 0 1 2 3 4 5 11 12 13 14 20 21 22 23 24 25
(x + (10 * (1 + ((x div 2) div 3))))
A102490: 10 11 12 13 14 15 26 27 28 29 30 31 42 43 44 45
(x + ((x - (2 * (x mod 5))) div 5))
A187327: 0 0 1 2 3 6 6 7 8 9 12 12 13 14 15 18
(x + ((2x - (x mod 8)) div 5))
A192048: 0 1 2 3 4 6 7 8 11 12 13 14 16 17 18 19
compr(\x.(1 - ((x - ((~x + 1) mod 4)) mod 5)),x)
A039196: 0 1 2 3 4 6 8 9 10 11 12 13 14 15 17 19
(x + (4 div (4 - ((x + 2) div 5))))
A096157-A066522: 1 2 3 4 5 6 7 8 10 11 12 13 14 17 18 19
(x + ((x2 + x) mod (x - ((x + ~2) div 5))))
A330029-A286262-A063037: 0 1 2 3 4 5 6 9 10 11 12 13 18 19 20 21
compr(\x.((x div ~2) mod 2),(x + ((x div 2) div 5)))
A028970: 0 3 4 7 8 11 12 15 16 19 23 24 27 28 31 32
(5x + (((~x + 1) div 2) mod 5))
A227793: 0 5 14 19 23 28 32 37 41 46 50 55 64 69 73 78
(x + ((~x + ((x div 2) mod 5)) div 5))
A102670: 0 0 1 2 3 4 5 6 7 8 8 8 9 10 11 12
(10x3 + ~6x2 + x)
A104099: 0 5 58 219 548 1105 1950 3143 4744 6813 9410 12595 16428 20969 26278 32415
(x + ((x * ((1 + (x div 3)) div 2)) div 5))
A336231: 0 1 2 3 4 6 7 8 9 12 14 15 16 18 19 24
(x + ((x + ((2 - (x div 2)) mod 4)) div 5))
A039197: 0 1 2 3 4 6 7 9 10 11 12 13 14 15 17 18
compr(\x.(1 - ((x * (x mod (2 + (x mod 2)))) mod 5)),x)
A005776: 1 7 11 13 17 19 23 29
A007775: 1 7 11 13 17 19 23 29 31 37 41 43 47 49 53 59
(x * (1 + ((8x + ~2) div (x + 4))))
A130237: 0 2 6 12 16 25 30 35 48 54 60 66 72 91 98 105
(x + ((3x2 + 6) div (2x + 5)))
A241071: 1 2 4 6 8 10 12
A248563: 1 2 4 6 8 10 12 15 17 19 22 24 27 29 32 34
compr(\x.(2 - (2x mod (3 + (x div 2) - (x mod 2)))),x)
A146968: 4 5 7
A225387-A037259: 4 5 7 8 10 12 13 14 15 16 17 19 21 22 23 24
compr(\x.(((~x + 1) - (x div 7)) mod 3),x)
A140399: 1 4 9 12 14 17 20 22 25 30 33 35 38 41 43 46
(x + (3 * ((~2x + (x div 2)) div 5)))
A196279: 0 ~2 ~1 0 ~2 ~1 0 ~2 ~1 0 1 ~1 0 1 ~1 0
compr(\x.(x - (3 * (~1 + ((x + (x div 2)) div 4)))),x)
A345499: 24 27 30 32 33 35 36 38 39 40 41 42 43 44 45 46
(x + (((x div 5) * (x div 3)) div 3))
A335040: 0 1 2 3 4 5 6 7 8 10 12 13 14 15 16 20
(x + ((2 * (x - (((x + 1) div 2) mod 3))) div 3))
A321702: 0 1 2 3 5 8 10 11 12 13 15 18 20 21 22 23
(x + ((2 * ((x + (x div 3)) div 3)) div 3))
A039108: 0 1 2 3 4 6 7 9 10 11 12 13 15 16 18 19
(x + ((x - (x mod (4 + (x div 3)))) div 3))
A151988-A039255: 0 1 2 3 4 6 8 9 10 11 12 13 14 15 16 18
(x + ((4 * ((x mod (1 + (x div 2))) div 2)) div 3))
A043090: 0 1 2 3 4 6 7 8 9 11 12 13 14 17 18 19
(3 div (~x + (3 * (2 + (((x + 1) div 2) div 2)))))
A035690: 0 0 0 0 0 0 1 0 0 1 1 0 1 1 3 1
(x + ((2 * ((x - (x div 8)) div 2)) div 3))
A039104: 0 1 2 3 5 6 8 9 10 11 12 14 15 17 18 19
(49x2 + ~48x)
A261276: 0 1 100 297 592 985 1476 2065 2752 3537 4420 5401 6480 7657 8932 10305
(x + (3 * ((x - ((x + (x div 2)) div 4)) div 2)))
A131503: 0 1 5 6 7 11 12 13 14 18 19 20 24 25 26 30
compr(\x.((x + 2) - (3 * ((x - (x div 4)) div 2))),x)
A345478: 7 10 13 15 16 18 19 21 22 23 24 25 26 27 28 29
((x + 12) + ((x + ~2) div (1 + (x div 2))))
A124867: 10 12 14 15 16 18 19 20 21 22 23 24 25 26 27 28
((4x2 + 2x) div (x + 12))
A022819: 0 0 1 2 4 6 8 11 13 16 19 22 25 28 31 34
(x + (3 * ((x3 + x2 + ~x) div 4)))
A213488: 0 1 8 27 61 113 189 295 434 609 826 1091 1407 1777 2207 2703
(x + (6 * ((x + 2) + (3 * (x div 2)))))
A272100: 12 19 44 51 76 83 108 115 140 147 172 179 204 211 236 243
(x + ((((x2 - (x div 2)) mod (x + 2)) div 2) div 3))
A103303: 0 1 2 3 4 5 6 7 8 9
A267215-A247761: 0 1 2 3 4 5 6 7 8 9 11 13 14 15 16 17
(x + ((2 + (((x div 2) mod 4) + (x div 2))) div 3))
A039232: 0 1 3 4 6 7 8 9 10 11 12 13 15 16 18 19
(x + ((x + 1) div (8 - ((x + 2) div 3))))
A013939: 0 1 2 3 4 6 7 8 9 11 12 14 15 17 19 20
(x + ((1 + ((x div 3) mod 2)) * ((x div 2) div 3)))
A067570: 0 1 2 3 4 5 7
A050746: 0 1 2 3 4 5 7 8 9 11 12 13 14 15 16 19
(x div (~x + (3 * (7 - (x mod 2)))))
A034400: 0 0 0 0 0 0 0 0 0 1 0 1 1 2 2 5
(x + (6 div (6 - (x div 3))))
A318735-A115661: 1 2 3 4 5 6 7 8 9 11 12 13 15 16 17 21
compr(\x.(2 + (x div 3) - ((x + (x div 2)) div 4)),x)
A345490: 32 35 38 40 41 43 44 46 47 48 49 50 51 52 53 54
(x * (x2 div ((4x + ~4) + (x mod 3))))
A330373: 0 1 0 3 4 5 6 7 16 18 20 22 36 39 42 60
(2x4 + 7x3 + 13x2 + 5x)
A129028: 0 27 150 483 1188 2475 4602 7875 12648 19323 28350 40227 55500 74763 98658 127875
(x + ((~x + (x mod 10)) mod (2x + 1)))
A103303: 0 1 2 3 4 5 6 7 8 9
A122639: 0 1 2 3 4 5 6 7 8 9 21 24 27 30 33 36
compr(\x.(1 - ((x + 9) mod (1 + (x div 2)))),x)
A096997: 2 4 5 6 8 9 10 11 13 14 16 17 18 19 20 21
compr(\x.((8 * (x mod 4)) mod (1 + (x div 2))),x)
A214913: 0 1 2 3 4 6 7 8 11 12 14 15 16 20 23 24
(x4 + x3 + 6x2 + 6x + 5)
A304162: 5 19 65 185 445 935 1769 3085 5045 7835 11665 16769 23405 31855 42425 55445
(x + (2x2 div (x + 15)))
A125552: 0 1 2 4 5 7 9 11 13 15 18 20 22 25 27 30
compr(\x.((x + ~1) - ((x2 + ~1) mod (x + 8))),x)
A256007: 0 1 2 3 4 5 6 8 9 10 14 15 16 24 25 26
(x + ((2x * ((x div 2) * (1 + (x div 2)))) div (x + 1)))
A028444: 0 1 4 6 13
A266665: 0 1 4 6 13 15 26 28 43 45 64 66 89 91 118 120
(x + ((2 + ((x + ~1) mod 12)) mod (x + 1)))
A103303: 0 1 2 3 4 5 6 7 8 9
A342164: 0 1 2 3 4 5 6 7 8 9 10 11 12 15 17 19
(x + ((x + 3) div (2 - (x div ~8))))
A166937-A135130: 1 2 3 5 6 7 9 10 11 12 13 14 15 17 18 19
compr(\x.((1 + (x2 mod (4x + 9))) mod 2),x)
A279933: 1 3 5 6 8 11 13 14 16 19 21 24 26 27 29 32
compr(\x.((x2 mod ~13) mod 2),x)
A010376: 0 1 3 4 9 10 12
A010388: 0 1 3 4 9 10 12 13 14 16 17 22 23 25
compr(\x.((x div (1 + (x2 mod 12))) mod 2),x)
A063952: 0 1 2 3 4 5 6 9 10 12 13 14 17 18 20 21
compr(\x.(~2 + ((x + ~1) mod (~1 + (3 * (x mod 4))))),x)
A052047: 0 1 2 3 4 5 6 8 9 11 12 13 16 17 18 19
compr(\x.(1 - (x mod (2 + (4 mod (1 + (x div 3)))))),x)
A196990: 1 3 5 7 8 9 11 13 14 15 16 17 19 20 21 22
(x + ((x - ((x + 2) div (~1 + ((x div 2) div ~2)))) div 2))
A225647: 1 3 4 6 7
A141206: 1 3 4 6 7 9 10 12 14 15 16 18 20 21 23 24
(x + (14 * (2 mod (1 + (x div 2)))))
A217761: 0 1 2 3 32 33 34 35 36 37 38 39 40 41 42 43
compr(\x.(x - (2 * (~1 + (2 * (x mod 10))))),x)
A092597: 1 2 3 4 5 6 7 8 9 14 15 16 17 18 19 28
compr(\x.((x - ((~2x + 2) div 9)) mod 2),x)
A193599: 0 3 5 6 8 10 11 13 16 18 21 23 24 26 28 29
(x + (2 * (1 + (2 * (4x - ((x div 2) mod 2))))))
A161442: 2 19 32 49 70 87 100 117 138 155 168 185 206 223 236 253
compr(\x.(1 - (x mod (2 * (1 + ((~1 + (x div 2)) mod 4))))),x)
A196546: 1 3 5 7 9 11 13 14 15 17 19 21 22 23 25 27
compr(\x.(1 - (x mod (2 + ((~1 + (x div 2)) mod 5)))),x)
A338477: 1 3 4 5 6 7 8 9 10 11 13 14 17 18 19 20
compr(\x.(~2 + (((x * ((~x + 2) div 2)) div 2) mod 5)),x)
A192225: 0 1 2 5
A133508: 0 1 2 5 9 10 11 12 13 15
compr(\x.(1 - (x2 mod (2 + ((x + 2) mod 5)))),x)
A090563: 1 2 3 4 5 6 7 11 13 14 15 16 17 19 21 22
(x + ((((x + 2) div 3) + (x div 5)) div 2))
A045671: 0 1 2 3 5 6 7 9 10 11 13 14 15 16 17 19
((x + 2) + (((x2 + ~1) div 2) mod (1 + (x mod 4))))
A079228: 2 3 5 5 6 7 10 9 10 11 13 13 14 15 17 17
(x + ((3 * (1 + (2x div 5))) div 2))
A047561: 1 2 3 6 7 9 10 11 14 15 17 18 19 22 23 25
(x + ((3 * ((x + 1) div 7)) div 2))
A067570: 0 1 2 3 4 5 7
A230872: 0 1 2 3 4 5 7 8 9 10 11 12 13 16 17 18
(x + ((3 * ((2x + 2) div 5)) div 2))
A047545: 0 1 3 4 7 8 9 11 12 15 16 17 19 20 23 24
(x + ((3 * ((2x + 4) div 5)) div 2))
A047560: 0 2 3 6 7 8 10 11 14 15 16 18 19 22 23 24
compr(\x.((((1 - (x mod 4)) mod (x + 1)) mod 3) mod 2),x)
A261514: 0 1 2 3 5 6 7 9 13 14 15 17 18 19 21 25
(x + ((3 * ((x + 2) - ((x div 2) mod 3))) div 2))
A126590: 3 5 6 9 10 12 18 20 21 24 25 27 33 35 36 39
(~7x + 100)
A115020: 100 93 86 79 72 65 58 51 44 37 30 23 16 9 2
(~x + (2 * (12 + (x mod 8))))
A004465: 24 25 26 27 28 29 30 31 16 17 18 19 20 21 22 23
(x * (((x + 1) div 2) - ((3 * (x div 4)) div 2)))
A245788: 0 1 2 6 4 10 12 21 8 18 20 33 24 39 42 60
(x7 + 6x)
A054606: 0 7 140 2205 16408 78155 279972 823585 2097200 4783023 10000060 19487237 35831880 62748595 105413588 170859465
(12x3 + 9x2 + 2x)
A191745: 0 23 136 411 920 1735 2928 4571 6736 9495 12920 17083 22056 27911 34720 42555
compr(\x.((x2 mod (1 + (2 * (x + (x div 3))))) mod 2),x)
A026317: 0 2 3 5 6 9 12 15 18 19 21 22 24 25 27 28
(x + (2 * (x - ((~1 + (x * (x div 2))) div (x + 3)))))
A187583: 2 5 6 9 10 13 16 17 20 23 24 27 28 31 32 35
(~x + (2 * ((2 + (x mod 10)) mod (x + 1))))
A211011: 0 1 0 ~1 ~2 ~3 ~4 ~5 ~6 ~7 ~6 ~5 ~4 ~3 ~2 ~1
compr(\x.(1 - ((x + ~4) mod (2 - (x div ~4)))),x)
A317092-A102750: 2 3 5 6 7 10 11 12 13 14 15 17 19 20 21 22
compr(\x.(1 - ((2x + ~4) mod (2 - (x div ~4)))),x)
A276155-A273670: 1 3 4 5 7 9 10 11 13 15 16 17 18 19 20 21
compr(\x.(((x2 mod 13) div 2) mod 2),x)
A272669: 0 1 2 3 5 8 10 11 12 13 14 15 16 18
compr(\x.(2 - (x mod (4 + (x div (1 + (x mod 3)))))),x)
A246780: 2 3 4 6 8 9 11 12 13 14 15 16 17 18 19 21
((x + 4) + ((x + 1) div ((x + 1) - (2 mod (x + 1)))))
A087176: 5 6 9 9 9 10 11
(x + (4 * (1 + (2 * (2 - ((x div 4) mod 2))))))
A004461: 20 21 22 23 16 17 18 19 28 29 30 31 24 25 26 27
compr(\x.(2 + (x div 2) - (2 * (x mod 10))),x)
A069118: 1 2 3 4 5 6 7 8 9 15 16 17 18 19 28 29
(x + (((3 * (x - (x div 5))) div 2) div 2))
A047486: 0 1 3 5 7 8 9 11 13 15 16 17 19 21 23 24
(x + (2 * ((3 * ((x + ((x div 2) mod 2)) div 2)) div 2)))
A266297: 0 1 4 9 10 11 14 19 20 21 24 29 30 31 34 39
(x + (2 * (6 + (x div 9))))
A261921: 12 13 14 15 16 17 18 19 20 23 24 25 26 27 28 29
compr(\x.((((~x + 2) div 4) mod (2 + (x mod 3))) mod 2),x)
A010379: 0 1 2 4 8 9 13 15 16
compr(\x.((((x2 div 5) mod (x + 1)) div 2) mod 2),x)
A119024: 0 1 2 3 5 6 7 10 11 13 14 15 16 19 20 21
(x + ((x - (((x div 2) - (4 mod (x + 1))) div 2)) div 2))
A161579: 0 1 3 4 6 8 9 11 12 13 15 16 17 19 20 22
compr(\x.(((x + (x div 4)) * (x div ~4)) mod 2),x)
A047579: 0 2 5 6 7 8 10 13 14 15 16 18 21 22 23 24
(x + (2 * (4 + (x div 13))))
A046037: 8 9 10 11 12 13 14 15 16 17 18 19 20 23 24 25
61x2
A174333: 0 61 244 549 976 1525 2196 2989 3904 4941 6100 7381 8784 10309 11956 13725
(x + (x div (4 + (((x + 1) div 2) mod 8))))
A084689: 0 1 2 3 4 5 6 7 9
A031993-A023750-A003796: 0 1 2 3 4 5 6 7 9 10 11 12 13 14 15 18
compr(\x.(1 - (x mod (2 + (x mod (2 + ((x + ~1) mod 4)))))),x)
A065003: 1 2 3 4 5 7 8 10 11 13 14 16 17 19 22 23
compr(\x.(2 - (x mod (2 * (2 + (((x + ~1) div 2) mod 4))))),x)
A181709: 2 3 4 5 6 7 8 10 11 13 14 15 16 18 20 21
compr(\x.(1 - ((x div 2) mod (4 + ((x div 2) mod 4)))),x)
A037342: 2 3 4 5 6 7 18 19 20 21 22 23 26 27 28 29
compr(\x.(2 - ((1 + (x div 2)) mod (2 * (2 + (x mod 4))))),x)
A136416: 2 3 4 5 6 7 9 10 11 12 15 17 18 20 21 22
(x + (2 * ((x + 1) div (2 + ((x + ~1) div (2 + (x div 2)))))))
A305441-A121405: 2 3 4 7 8 9 10 11 14 15 16 19 20 21 24 25
compr(\x.(1 - (x mod (2 + (((x2 + ~x) div 2) mod 4)))),x)
A325366-A192189: 1 2 3 5 6 7 9 10 11 13 14 17 19 21 22 23
((4x2 + 9x + 2) div (x + 8))
A076829: 0 1 3 5 8 11 14 17 20 23 27 30 34 37 41 45
compr(\x.((x mod 7) - (x mod 8)),x)
A032862-A023789: 0 1 2 3 4 5 6 7 14 15 21 22 23 28 29 30
(x * (((x * (2 + (x div 5))) div 4) mod 2))
A331045-A331044: 0 0 2 3 0 5 0 7 0 0 0 11 0 13 0 0
((2x + 2) + ((x + (x div 2)) div 2) - (x mod 4))
A168484: 2 3 5 7 13 14 16 18 24 25 27 29 35 36 38 40
(x + ((2 - ((~x2 + 4x + ~4) div (x + 4))) div 2))
A245030-A245027: 1 2 3 4 5 6 8 9 10 12 13 15 16 18 19 20
((~x + 1) - (2 * (9 div (2 + (x div 2)))))
A291509: ~7 ~8 ~7 ~8 ~7 ~8 ~7 ~8 ~9 ~10 ~11 ~12 ~13 ~14 ~15 ~16
(x + ((x + (x div 2)) div 2) - (x * (~4 + (x div 2))))
A101116: 0 5 9 14 15 18
compr(\x.(1 - ((x mod (~1 + (x div ~4))) mod 4)),x)
A141114: 1 3 5 7 8 9 10 11 13 14 17 19 22 23 25 26
(x + (x3 div (2x - ((x + ~1) mod 4))))
A010393: 0 1 4 9 16 17 25
(x + ((x + ((2 + (x div 4)) mod 4)) div 4))
A039233: 0 1 3 4 5 7 8 9 10 11 12 13 15 16 17 19
(x + (2 * ((x + 2) + ((x - (x div ~4)) div 2))))
A190448: 4 9 12 17 20 25 30 33 38 43 46 51 54 59 64 67
(x + (2 * ((x + 2) + ((x - ((~x + 2) div 4)) div 2))))
A190460: 4 7 12 17 20 25 28 33 38 41 46 51 54 59 62 67
(~x + (2 * ((x + (x div (4 - ((x div 2) mod 2)))) div 2)))
A257806: 0 ~1 0 1 0 1 2 1 2 1 2 3 2 3 4 5
(x + (3x div (2 + (4x div (x + 2)))))
A246438: 0 2 3 5 7 8 9 11 12 14 16 17 19 20 22 24
(x + ((((x2 + 2x) mod 6) + (x div 2)) div 2))
A267453: 0 2 3 5 5 8 7 10 11 12 12 16 15 17 18 20
(x + ((x + ((1 - (x div 2)) mod 10)) div 2))
A023725: 0 2 3 4 10 12 13 14 15 17 18 19 20 22 23 24
(8x4 + 3x + 16)
A073396: 16 27 150
(1 - (x mod ((~x + 1) - (((x div 2) - (x * (x mod 2))) div 2))))
A304777: 1 1 1 1 1 2 1 2 2 2 2 4 3 4 3 6
(x5 + 6x4 + 8x3 + 3x + 4)
A280828: 4 22 202
((x2 + 2x) + (((2 + (x div 2)) * (1 + (x div 2))) div 2))
A213479: 1 4 11 18 30 41 58 73 95 114 141 164 196 223 260 291
(x + ((1 + (2 * ((2x + 2) - (x mod 2)))) * (x div 2)))
A274979: 0 1 15 18 46 51 93 100 156 165 235 246 330 343 441 456
(x + (((2x + 4) + (3 * (x div 2))) * (x div 2)))
A274978: 0 1 13 16 40 45 81 88 136 145 205 216 288 301 385 400
compr(\x.(1 - ((4 mod (1 + (x div 4))) + (x mod 2))),x)
A136443: 1 3 5 7 8 9 10 11 13 15 16 17 18 19 20 21
compr(\x.(1 - ((x mod 2) + ((1 - (x div 4)) mod 3))),x)
A039248: 0 1 2 3 5 7 8 9 10 11 12 13 14 15 17 19
compr(\x.(((~x + ((x + ~2) div 3)) mod 3) - (x mod 2)),x)
A285164: 1 3 7 8 11 12 15 16 17 19 21 25 26 29 30 33
compr(\x.((((~1 + (x div 3)) div 3) mod 2) - (x mod 2)),x)
A329779: 1 3 4 5 6 7 8 9 10 11 13 15 17 19 21 22
73x2
A174334: 0 73 292 657 1168 1825 2628 3577 4672 5913 7300 8833 10512 12337 14308 16425
compr(\x.(x + (x3 mod (~4x + ~1))),x)
A099356: 0 1 3 4 6 8 9 10 11 12 13 14 15 16 17 19
(~x + compr(\x.((x2 + ~1) mod (1 + (4 * (x mod 2)))),x))
A194225: 0 0 0 1 2 3 3 3 3 3 4 5 6 6 6 6
(13x3 + 15x2)
A085377: 0 28 164 486 1072 2000 3348 5194 7616 10692 14500 19118 24624 31096 38612 47250
(x + (3x2 div (x + 16)))
A129011: 0 1 2 4 6 8 10 13 16 18 21 24 27 30 33 36
(x2 + (7 * (x2 div 4)))
A195043: 0 1 11 23 44 67 99 133 176 221 275 331 396 463 539 617
(x2 + (9 * (x2 div 4)))
A195045: 0 1 13 27 52 79 117 157 208 261 325 391 468 547 637 729
(x2 + ((2x + 1) * (2 + (3 * (x div 2)))))
A274682: 2 7 29 44 88 113 179 214 302 347 457 512 644 709 863 938
((x2 + 1) + compr(\x.((x * ((x div 2) div 3)) mod 2),x))
A169627: 1 3 7 13 21 31
A063541: 1 3 7 13 21 31 43 58 75 94 114
(x2 + (2 * (2x2 div ~7)))
A227849: 0 ~1 0 3 6 9 14 21 26 33 42 51 60 71 84 95
(x4 + 64)
A272297: 64 65 80 145 320 689 1360 2465 4160 6625 10064 14705 20800 28625 38480 50689
loop(\(x,i).(2 + (if x <= 0 then 2 else loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x))),2,x)
A278290: 0 1 2 1 4 2 1 4 4 2 1 4 4 4 2 1
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0),2,x)),2,x)
A331857-A256999-A246593-A073138: 0 1 2 3 4 6 6 7 8 12 12 14 12 14 14 15
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).2x,i,2x),i,1)),(x + 1),0)
A178184: 4 36 548 16932 1065508 135283236 34495021604 17626681066020 18032025190548004 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else loop(\(x,i).(x + loop(\(x,i).(1 + (x * i)),i,1)),(x + ~1),0))
A001338: 1 0 2 7 23 88 414 2371 16071 125672 1112082 10976183 119481295 1421542640 18348340126 255323504931
(if x <= 0 then 1 else loop(\(x,i).x2,1,loop(\(x,i).(~2x + 3),x,0)))
A323210: 1 9 9 81 225 1089 3969 16641 65025 263169 1046529 4198401 16769025 67125249 268402689 1073807361
loop(\(x,i).(x + loop(\(x,i).x2,1,loop(\(x,i).(~2x + 1),i,0))),x,0)
A096977: 0 1 2 11 36 157 598 2447 9672 38913 155194 621683 2484908 9943269 39765790 159077719
loop(\(x,i).(~x + loop(\(x,i).(x + loop(\(x,i).x3,2,i)),i,0)),x,0)
A231308: 0 1 512 19684 262656 1972809 10340352 42326416 144558080 429746905 1144558080 2787694596 6304338432 13392193969 26965385216 51835553344
(if x <= 0 then 1 else loop(\(x,i).(x + loop(\(x,i).(x * (2 + i)),(1 + i),2)),x,0))
A054118: 1 24 144 864 5904 46224 409104 4037904 43954704 522956304 6749977104 93928268304 1401602636304 22324392524304 378011820620304 6780385526348304
(1 + loop(\(x,i).((if (~2 + i) <= 0 then 1 else x) * (1 + (if x <= 0 then 1 else x))),x,0))
A082732: 1 3 4 13 157 24493 599882557 359859081592975693 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(if x <= 0 then 1 else (2x - (if (x - i) <= 0 then 0 else 2))),x,0))
A060013: 1 2 3 5 9 15 27 51 99 195 387 771 1539 3075 6147 12291
loop(\(x,i).x2,1,(1 + loop(\(x,i).(x + (if (x + ~2) <= 0 then 1 else x)),x,0)))
A164840: 1 4 9 16 49 169
loop(\(x,i).2x,(~1 - loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x)),1)
A141020-A140997-A140996-A057728: 1 1 1 1 2 1 1 4 2 1 1 8 4 2 1 1
(~1 + loop(\(x,i).(x - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,i)),x,1))
A121924: 0 1 1 3 4 4 7 9 10 10 14 17 19 20 20 25
loop(\(x,i).~x,x,(if ((if x <= 0 then 1 else x) mod 5) <= 0 then 2 else 1))
A280569: 1 ~1 1 ~1 1 ~2 1 ~1 1 ~1 2 ~1 1 ~1 1 ~2
(if x <= 0 then 1 else (3 * (x - loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0))))
A241717: 1 3 3 9 3 9 15 21 3 9 15 21 27 33 39 45
loop(\(x,i).(x + (if (2 - i) <= 0 then x else 1)),x,loop(\(x,i).2x,x,3))
A158561: 3 7 26 100 392 1552 6176 24640 98432 393472 1573376 6292480 25167872 100667392 402661376 1610629120
(if x <= 0 then 2 else (1 + (2 * (x + loop(\(x,i).loop(\(x,i).x2,x,2),x,0)))))
A180269: 2 7 37 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,loop(\(x,i).2x,x,(~1 + loop(\(x,i).2x,x,2))))
A110206: 1 36 784 14400 246016 4064256 66064384 1065369600 17112825856 274341298176 4393752592384 70334388633600 1125625045712896 18012199553335296 288212784234102784 4611545282012774400
loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(if x <= 0 then 0 else (2x + 1)))
A085090: 0 3 5 7 0 11 13 0 17 19 0 23 0 0 29 31
(if x <= 0 then 2 else (loop(\(x,i).2x,x,1) - loop(\(x,i).2x,(x div 2),1)))
A032085: 2 1 2 6 12 28 56 120 240 496 992 2016 4032 8128 16256 32640
loop(\(x,i).2x,((1 - loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x)) div 2),1)
A105272: 1 1 2 1 2 2 1 4 2 2 1 4 4 2 2 1
loop(\(x,i).loop(\(x,i).(x * i),i,loop(\(x,i).(2x + (i mod 2)),x,0)),x,1)
A038081: 1 1 2 12 65520
(1 + compr(\x.loop(\(x,i).loop(\(x,i).(if x <= 0 then i else (x + ~1)),x,0),2,(x + ~1)),x))
A334169: 1 2 4 6 8 10 14 16 18 26 30 32 34 50 58 62
(1 - loop(\(x,i).2x,x,(if x <= 0 then 0 else loop(\(x,i).(2x + ~4),x,1))))
A270222: 1 5 33 161 705 2945 12033 48641 195585 784385 3141633 12574721 50315265 201293825 805240833 3221094401
(1 + loop(\(x,i).(x + (if (x mod 2) <= 0 then (if x <= 0 then 1 else ~2) else 2)),2,x))
A065165: 4 6 2 8 1 10 3 12 5 14 7 16 9 18 11 20
loop(\(x,i).(if x <= 0 then 1 else x),(x + ~2),loop(\(x,i).(2 * (~x + (i mod 2))),x,1))
A112691: 1 0 0 2 1 10 1 42 1 170 1 682 1 2730 1 10922
(loop(\(x,i).(x + i - (if x <= 0 then 1 else 0)),x,0) + loop(\(x,i).2x,x,1))
A116713: 1 2 5 12 24 45 83 154 290 555 1077 2112 4172 8281 16487 32886
(loop(\(x,i).(2x + (if x <= 0 then 1 else x)),x,0) + loop(\(x,i).2x,x,1))
A085279: 1 3 7 17 43 113 307 857 2443 7073 20707 61097 181243 539633 1610707 4815737
loop(\(x,i).(x2 + x + 1),(if x <= 0 then 0 else 1),loop(\(x,i).2x,x,1))
A135576: 1 7 21 73 273 1057 4161 16513 65793 262657 1049601 4196353 16781313 67117057 268451841 1073774593
loop(\(x,i).(x div 2),x,loop(\(x,i).(x2 div 2),x,loop(\(x,i).2x,x,1)))
A079597: 1 1 8 16384 35184372088832 4611686018427387903 4611686018427387903
loop(\(x,i).2x,loop(\(x,i).(x - (if ((~x + ~1) + i) <= 0 then i else 0)),x,x),1)
A141021-A140995-A140994: 1 1 1 1 2 1 1 2 4 1 1 2 4 8 1 1
loop(\(x,i).x2,1,(1 + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)))
A133819: 1 1 4 1 4 9 1 4 9 16 1 4 9 16 25 1
loop(\(x,i).x2,2,(1 + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)))
A133821: 1 1 16 1 16 81 1 16 81 256 1 16 81 256 625 1
loop(\(x,i).(x * (1 + i)),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1)
A166350: 1 1 2 1 2 6 1 2 6 24 1 2 6 24 120 1
loop(\(x,i).2x,(x - loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)),1)
A245235: 1 2 2 8 8 8 64 64 64 64 1024 1024 1024 1024 1024 32768
(1 - (if x <= 0 then 0 else loop(\(x,i).(~x + loop(\(x,i).((x + ~2) * i),i,0)),x,1)))
A231407: 1 4 6
A054094: 1 4 6 26 104 548 3366 24034 195168 1777652 17950550 199059674 2405063016 31448531956 442501797654 6666753146498
loop(\(x,i).(loop(\(x,i).2x,(~1 + i),x) + (if (~2 + i) <= 0 then 1 else x)),x,1)
A015486: 1 2 5 25 225 3825 126225 8204625 1058396625 272007932625 139540069436625 143028571172540625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(x + loop(\(x,i).(x * i),i,1)),(i div 2),1)),x,1)
A138016: 1 2 4 6 10 14 24 34 68 102 256 410 1284 2158 8072 13986
loop(\(x,i).(loop(\(x,i).(x * (~1 + (2 * i))),i,1) div (if x <= 0 then 1 else x)),x,1)
A235136: 1 1 3 5 21 45 231 585 3465 9945 65835 208845 1514205 5221125 40883535 151412625
loop(\(x,i).(~x + loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,i,1))),x,1)
A110614: 1 5 15 57 215 841 3319 13193 52599 210057 839543 3356809 13424503 53692553 214759287 859015305
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,i,1))),x,1)
A028365: 1 2 24 1344 322560 319979520 1290157424640 20972799094947840 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(0 - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)),1)
A130321: 1 2 1 4 2 1 8 4 2 1 16 8 4 2 1 32
loop(\(x,i).(x * i),(0 - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)),1)
A119502: 1 1 1 2 1 1 6 2 1 1 24 6 2 1 1 120
loop(\(x,i).x2,1,(~1 + loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)))
A055461: 1 4 1 9 4 1 16 9 4 1 25 16 9 4 1 36
loop(\(x,i).(x + loop(\(x,i).(x * (if (x mod 2) <= 0 then 1 else x)),2,(1 + i))),x,1)
A140158: 1 3 84 88 713 719 3120 3128 9689 9699 24340 24352 52913 52927 103552 103568
loop(\(x,i).loop(\(x,i).(x + loop(\(x,i).x3,2,i)),(1 + i),x),x,1)
A253637: 1 514 20710 303050 2538515 14851676 67518444 254402940 828707925 2403012910 6335265586 15427298614 35123831015 75481410200 154282348760 301802764056
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).(x + (i * i)),(1 + i),x),i,1)),x,1)
A005585: 1 7 27 77 182 378 714 1254 2079 3289 5005 7371 10556 14756 20196 27132
loop(\(x,i).(x + loop(\(x,i).((x + loop(\(x,i).(x * i),i,1)) * i),i,1)),x,1)
A121580: 1 3 11 53 317 2237 18077 164237 1656077 18348557 221561357 2895986957 40737113357 613623026957 9854521894157 168083120422157
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,i,2))),x,1)
A203307: 1 12 672 161280 159989760 645078712320 10486399547473920 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),(x + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 1)),x,x)),1)
A143084: 1 1 2 2 6 24 6 24 120 720 24 120 720 5040 40320 120
loop(\(x,i).(x + loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),(x + ~2),x)),x,1)
A080735: 1 2 4 5 10 11 22 23 46 47 94 95 96 97 194 195
loop(\(x,i).(~x + loop(\(x,i).loop(\(x,i).2x,x,(1 + (x div 2))),1,i)),x,1)
A140787: 1 1 7 9 39 57 199 313 967 1593 4551 7737 20935 36409 94663 167481
loop(\(x,i).loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),i,x),x,1)
A007685: 1 2 12 240 16800 4233600 3911846400 13425456844800 172785629592576000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x * i),loop(\(x,i).2x,x,1),1) div loop(\(x,i).(x * i),x,1))
A262032: 1 2 12 6720 871782912000 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x + (3x div (if i <= 0 then 1 else i))),i,x),x,1)
A087047: 1 4 40 800 28000 1568000 131712000 15805440000 2607897600000 573737472000000 164088916992000000 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 0 else (if ((x mod 5) mod (if x <= 0 then 1 else x)) <= 0 then 1 else 2))
A276134: 0 1 1 1 1 1 2 2 2 2 1 2 2 2 2 1
(2 * compr(\x.loop(\(x,i).loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0),2,x),(x + 1)))
A043765-A043756-A043748-A043741-A043735-A043730-A043569: 2 4 6 8 12 14 16 24 28 30 32 48 56 60 62 64
loop(\(x,i).(x * (~1 + (if (x * (~2 + i)) <= 0 then x else 0))),x,(if x <= 0 then 1 else 2))
A081478: 1 2 2 ~2 6 ~6 42 ~42 1806 ~1806 3263442 ~3263442 10650056950806 ~10650056950806 4611686018427387903 4611686018427387903
((1 - loop(\(x,i).((x + ~1) - (if x <= 0 then 0 else i)),x,x)) div (if x <= 0 then 1 else 2))
A131410: 1 1 1 2 2 2 3 3 3 3 5 5 5 5 5 8
(loop(\(x,i).2x,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1) div 2)
A229878: 0 0 1 0 1 2
A140531: 0 0 1 0 1 2 0 1 2 4 0 1 2 4 8 0
(loop(\(x,i).loop(\(x,i).(x + (loop(\(x,i).2x,i,i) * i)),i,x),x,1) div 2)
A337631: 0 1 10 55 228 801 2526 7387 20440 54229 139218 348111 851916 2047945 4849606 11337667
(if x <= 0 then 1 else (4 * (x - loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0))))
A256251: 1 4 4 12 4 12 20 28 4 12 20 28 36 44 52 60
loop(\(x,i).(x * i),x,(if x <= 0 then 1 else ((x + 2) + (if (x + ~2) <= 0 then x else 1))))
A052643: 1 4 12 36 168 960 6480 50400 443520 4354560 47174400 558835200 7185024000 99632332800 1482030950400 23538138624000
loop(\(x,i).loop(\(x,i).2x,x,(if x <= 0 then 1 else x)),1,((x2 + x) div 2))
A103904: 1 2 24 384 10240 491520 44040192 7516192768 2473901162496 1583296743997440 1981583836043018240 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then i else 0)),x,(2 * (if x <= 0 then 1 else x)))
A060264: 2 3 5 7 11 11 13 17 17 19 23 23 29 29 29 31
(if x <= 0 then 1 else loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 1 else 0)),x,(x + 2)))
A066169: 1 3 5 5 7 7 11 11 11 11 13 13 17 17 17 17
loop(\(x,i).(if (x mod (1 + (2 * i))) <= 0 then 0 else x),x,(if x <= 0 then 1 else 2x))
A099890: 1 2 4 0 8 0 0 0 16 0 0 0 0 0 0 0
loop(\(x,i).(if x <= 0 then 1 else (if (x mod 4) <= 0 then 2x else 0)),1,(x div 2))
A291692: 1 1 0 0 0 0 0 0 8 8 0 0 0 0 0 0
loop(\(x,i).2x,(0 - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)),2)
A090988: 2 4 2 8 4 2 16 8 4 2 32 16 8 4 2 64
loop(\(x,i).(x + loop(\(x,i).(~x + (if (~x + i) <= 0 then i else 0)),2x,x)),x,2)
A094763: 2 3 5 6 8 12 15 21 26 27 29 33 41 46 56 63
(~x + loop(\(x,i).(x + loop(\(x,i).(2 + (if (~x + i) <= 0 then 0 else x)),i,1)),x,0))
A192225: 0 1 2 5
A256249: 0 1 2 5 6 9 14 21 22 25 30 37 46 57 70 85
(x - loop(\(x,i).(x - loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0)),3,x))
A048967: 0 0 1 0 3 2 3 0 7 6 7 4 9 6 7 0
loop(\(x,i).x2,1,loop(\(x,i).(x + (if (~x + 2) <= 0 then x else 2)),x,(~x + 1)))
A272711: 1 4 9 16 36 64 144 256 576 1024 2304 4096 9216 16384 36864 65536
(x + loop(\(x,i).(x + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,i)),x,1))
A014370: 1 2 4 5 7 10 11 13 16 20 21 23 26 30 35 36
(x + loop(\(x,i).(x - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,i)),x,1))
A212013: 1 3 4 7 9 10 14 17 19 20 25 29 32 34 35 41
loop(\(x,i).((x + 1) + (if (~2 + (x div 2)) <= 0 then 1 else 2)),(if x <= 0 then 1 else 2),x)
A161539: 2 5 6 7 9 10 12 13 14 15 16 17 18 19 20 21
loop(\(x,i).(if x <= 0 then 1 else (if (x mod 2) <= 0 then (x div 2) else (x + ~2))),2x,x)
A011603: 0 1 ~1 ~1 1 1 1 ~1 ~1 1 ~1 ~1 ~1 1 1 ~1
loop(\(x,i).(0 - loop(\(x,i).(x - (if (~x + i) <= 0 then (1 + i) else 0)),x,x)),2,x)
A116433: 0 1 0 1 1 0 1 2 1 0 1 2 3 1 0 1
(1 - loop(\(x,i).(x - loop(\(x,i).2x,(~1 + (if x <= 0 then 0 else i)),1)),x,x))
A295514: 1 1 2 2 5 5 5 5 12 12 12 12 12 12 12 12
(1 - loop(\(x,i).(x - (if x <= 0 then 1 else (if (x mod (1 + i)) <= 0 then 2 else 1))),x,x))
A137293-A049711: 1 1 2 1 2 1 2 3 4 1 2 1 2 3 4 1
loop(\(x,i).(x2 + ~x),1,loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x))
A095832: 0 2 0 6 2 0 12 6 2 0 20 12 6 2 0 30
(0 - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + (if (x + ~1) <= 0 then x else i)))),x,x))
A343138: 0 1 0 1 1 0 1 2 1 0 1 3 2 1 0 1
compr(\x.loop(\(x,i).(loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x) mod (x + 2)),2,x),x)
A171886: 0 1 2 3 5 6 7 9 10 14 15 17 20 21 27 28
(loop(\(x,i).x2,x,loop(\(x,i).(x * i),x,1)) div (if x <= 0 then 1 else x2))
A260614: 1 1 4 186624 4611686018427387903
(x + (if x <= 0 then 1 else loop(\(x,i).(x - (if ((~x + 2) + i) <= 0 then i else 1)),x,x)))
A125568-A101504: 1 1 2 3 4 4 5 6 5 6 7 8 6 7 8 9
(x + loop(\(x,i).(x - (if x <= 0 then 1 else (2 * (if (~x + i) <= 0 then i else x)))),x,x))
A053188: 0 0 1 1 0 1 2 2 1 0 1 2 3 3 2 1
(if x <= 0 then 1 else (if (x mod 2) <= 0 then x2 else loop(\(x,i).x3,x,x)))
A004231: 1 1 4 7625597484987
(if (x mod 10) <= 0 then (if x <= 0 then 3 else ~1) else 0)
A030121: 3 0 0 0 0 0 0 0 0 0 ~1 0 0 0 0 0
(if (x mod (1 + (((x + 1) div 2) div 3))) <= 0 then (if x <= 0 then 0 else 1) else 0)
A302777: 0 1 1 1 1 0 1 0 1 0 1 0 1 0 0 1
(if (((x * (x div 3)) div 2) mod 3) <= 0 then (if x <= 0 then 0 else 1) else 0)
A305816-A280910: 0 1 1 0 0 0 1 0 0 0 1 0 1 0 0 0
(if (x mod 4) <= 0 then (((~x + 1) mod 3) - (if x <= 0 then 0 else 1)) else 0)
A014177-A014129: 1 0 0 0 ~1 0 0 0 1 0 0 0 0 0 0 0
(if (~1 + (x mod (3 + (if (~2 + (x div 2)) <= 0 then 0 else 2)))) <= 0 then 1 else 0)
A285898: 1 1 0 1 1 0 1 0 0 0 1 1 0 0 0 1
(if (2 - (x mod (3 + (if (~2 + (x div 2)) <= 0 then 0 else 2)))) <= 0 then 1 else 0)
A327396: 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0
(if (((x + (if (x mod 2) <= 0 then x else 2)) div 3) mod 3) <= 0 then 1 else 0)
A025912: 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0
(if x <= 0 then 2 else (if (((x + 2) mod 8) mod 3) <= 0 then 1 else 0))
A316825: 2 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0
((2 * (if x <= 0 then 2 else 0)) - (if (x mod 12) <= 0 then 1 else 0))
A010104: 3 0 0 0 0 0 0 0 0 0 0 0 ~1 0 0 0
(if (x mod 3) <= 0 then loop(\(x,i).4x,(x div 3),1) else 0)
A133851: 1 0 0 4 0 0 16 0 0 64 0 0 256 0 0 1024
(if (x mod 3) <= 0 then loop(\(x,i).~2x,(x div 3),1) else 0)
A077959: 1 0 0 ~2 0 0 4 0 0 ~8 0 0 16 0 0 ~32
(if x <= 0 then 1 else (if (16 mod (x + 1)) <= 0 then 3 else 0))
A127802: 1 3 0 3 0 0 0 3 0 0 0 0 0 0 0 3
(if (x mod 2) <= 0 then loop(\(x,i).(2 * (x - (2x * i))),(x div 2),1) else 0)
A067994: 1 0 ~2 0 12 0 ~120 0 1680 0 ~30240 0 665280 0 ~17297280 0
(if (x mod 2) <= 0 then loop(\(x,i).(10x + 1),x,1) else 0)
A279118: 1 0 111 0 11111 0 1111111 0 111111111 0 11111111111 0 1111111111111 0 111111111111111 0
loop(\(x,i).(3 * (x + loop(\(x,i).(2x + 4),i,0))),(x + 1),0)
A118979: 12 72 300 1080 3612 11592 36300 111960 342012 1038312 3139500 9467640 28501212 85700232 257493900 773268120
loop(\(x,i).x2,1,loop(\(x,i).(x + (2 * (i * (1 + i)))),(x + 1),0))
A208140: 16 256 1600 6400 19600 50176 112896 230400 435600 774400 1308736 2119936 3312400 5017600 7398400 10653696
loop(\(x,i).2x,x,loop(\(x,i).(5x + 8),(x + 1),0))
A060458: 8 96 992 9984 99968 999936 9999872 99999744 999999488 9999998976 99999997952 999999995904 9999999991808 99999999983616 999999999967232 9999999999934464
loop(\(x,i).(2x + ((x + loop(\(x,i).(x * i),i,1)) * i)),(x + 1),0)
A002538: 1 8 58 444 3708 33984 341136 3733920 44339040 568356480 7827719040 115336085760 1810992556800 30196376985600 532953524275200 9927928075161600
loop(\(x,i).(loop(\(x,i).(x * i),(~1 + i),1) + (x * (i * i))),(x + 1),0)
A061572: 1 5 47 758 18974 683184 33476736 2142516144 173543847984 17354385161280 2099880608143680 302382807612606720 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + loop(\(x,i).(x * i),(~1 + i),1)) * (1 + i)),(x + ~1),0)
A052881: 0 0 2 9 44 250 1644 12348 104544 986256 10265760 116915040 1446526080 19323757440 277238626560 4251984710400
(loop(\(x,i).3x,x,1) - loop(\(x,i).(2x + 2),(x + ~1),0))
A240506: 1 3 7 21 67 213 667 2061 6307 19173 58027 175101 527347 1586133 4766587 14316141
loop(\(x,i).(10x + 10),2x,(if x <= 0 then 1 else 0))
A267867: 1 110 11110 1111110 111111110 11111111110 1111111111110 111111111111110 11111111111111110 1111111111111111110 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(10x + 6),x,(if x <= 0 then 1 else 0))
A073548: 1 6 66 666 6666 66666 666666 6666666 66666666 666666666 6666666666 66666666666 666666666666 6666666666666 66666666666666 666666666666666
loop(\(x,i).(2 * ((2x + 2) - (x div (1 + i)))),x,(if x <= 0 then 1 else 0))
A171074: 1 4 18 68 250 922 3430 12868 48618 184754 705430 2704154 10400598 40116598 155117518 601080388
(if (x mod 8) <= 0 then loop(\(x,i).(x * (~1 + (2 * i))),x,1) else 0)
A271768: 1 0 0 0 0 0 0 0 2027025 0 0 0 0 0 0 0
(if (x + ~1) <= 0 then 1 else (if ((x + 1) mod 7) <= 0 then 2 else 0))
A087780: 1 1 0 0 0 0 2 0 0 0 0 0 0 2 0 0
(if x <= 0 then 1 else (if (x3 mod (2x + 3)) <= 0 then 2 else 0))
A256505: 1 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0
(if (~1 + (x div 2)) <= 0 then 1 else (if (~1 + (x mod (2 + (x mod 2)))) <= 0 then 2 else 0))
A044945: 1 1 1 1 2 0 2 2 2 2 2 0 2 2 2 2
(if (x mod 4) <= 0 then (if x <= 0 then 1 else (x2 mod 6)) else 0)
A028719-A028715-A028711-A028707-A028662-A028654-A028646-A028638-A028630: 1 0 0 0 4 0 0 0 4 0 0 0 0 0 0 0
(if x <= 0 then 1 else (if (x mod 9) <= 0 then (2x + 2) else 0))
A072840-A023921: 1 0 0 0 0 0 0 0 0 20 0 0 0 0 0 0
(loop(\(x,i).2x,x,2) - loop(\(x,i).(2x + 2),((x + 1) div 2),0))
A208900: 2 2 6 10 26 50 114 226 482 962 1986 3970 8066 16130 32514 65026
(if ((x mod (1 + ((1 + (x div 2)) div 2))) mod 2) <= 0 then (if x <= 0 then 1 else 2) else 0)
A080378: 1 2 2 0 2 0 2 0 2 2 2 0 2 0 2 2
(if (2x mod (4 + (x div 4))) <= 0 then (if x <= 0 then 1 else 2) else 0)
A136521: 1 0 2 0 0 2 0 0 0 2 0 0 0 0 2 0
(if x <= 0 then 1 else (if (x mod (2 + (x mod (2 * (2 + (x mod 2)))))) <= 0 then 2 else 0))
A338268: 1 0 0 0 2 0 0 0 2 0 0 0 2 0 0 2
(if x <= 0 then 1 else (if (x mod (4 + (x div 2))) <= 0 then 8 else 0))
A197623: 1 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0
(2 + (if x <= 0 then 1 else (if (x mod 4) <= 0 then 4 else 0)) - (x mod 2))
A010123: 3 1 2 1 6 1 2 1 6 1 2 1 6 1 2 1
(if x <= 0 then 1 else (if ((x + 2) mod 6) <= 0 then (x div 4) else 0))
A091398-A087781: 1 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0
loop(\(x,i).loop(\(x,i).10x,x,1),(x mod 4),0)
A279540: 0 1 10 10000000000
(if x <= 0 then 1 else (if ((x2 + 2x) mod 6) <= 0 then (x + ~2) else 0))
A123565: 1 0 0 0 2 0 4 0 0 0 8 0 10 0 0 0
loop(\(x,i).(x * i),x,(1 - loop(\(x,i).(2 * (x - (i mod 2))),(x + ~2),0)))
A052653: 1 1 2 18 120 1320 15120 216720 3427200 62052480 1237420800 27263174400 653837184000 17005993804800 476080648243200 14283727121664000
(loop(\(x,i).2x,x,1) - loop(\(x,i).(3x + ~2),2x,0))
A155593: 1 10 84 736 6576 59080 531504 4783096 43046976 387421000 3486785424 31381061656 282429540576 2541865836520 22876792471344 205891132127416
(if x <= 0 then 1 else (if (10 mod (x + 1)) <= 0 then (x div 2) else 0))
A028597: 1 0 0 0 2 0 0 0 0 4 0 0 0 0 0 0
(if (~x + 2) <= 0 then ((if ((x div 2) mod 3) <= 0 then 2 else 1) - (x mod 2)) else 0)
A328620-A305445-A040076: 0 0 1 0 1 0 2 1 1 0 1 0 2 1 1 0
((if (x mod (2 + (4 mod (x + 2)))) <= 0 then 1 else 0) + (if x <= 0 then 2 else 0))
A111025: 3 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0
loop(\(x,i).(10x + 12),x,(if x <= 0 then 2 else 0))
A073551: 2 12 132 1332 13332 133332 1333332 13333332 133333332 1333333332 13333333332 133333333332 1333333333332 13333333333332 133333333333332 1333333333333332
loop(\(x,i).x2,1,loop(\(x,i).(12x + 1),x,0))
A260862: 0 1 169 24649 3553225 511709641 73686731209 10610895808969 1527969074670025 220027547690625481 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (2 * (1 + (5 * (if x <= 0 then 1 else x))))),x,0)
A073556: 0 13 133 1333 13333 133333 1333333 13333333 133333333 1333333333 13333333333 133333333333 1333333333333 13333333333333 133333333333333 1333333333333333
(loop(\(x,i).3x,x,1) - loop(\(x,i).(2x + 3),x,0))
A001117: 1 0 0 6 36 150 540 1806 5796 18150 55980 171006 519156 1569750 4733820 14250606
loop(\(x,i).x2,1,loop(\(x,i).(16x + 1),x,0))
A260866: 0 1 289 74529 19088161 4886709025 1250999747361 320255971115809 81985529178309409 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,loop(\(x,i).(10x + 5),x,0))
A075414: 0 25 3025 308025 30858025 3086358025 308641358025 30864191358025 3086419691358025 308641974691358025 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else loop(\(x,i).(x + i - ((x + 1) div 5)),x,0))
A130248: 1 1 3 6 9 12 16 20 24 28 33 38 43 48 53 58
(if (x mod 2) <= 0 then 1 else loop(\(x,i).(10x + 10),x,0))
A280410: 1 10 1 1110 1 111110 1 11111110 1 1111111110 1 111111111110 1 11111111111110 1 1111111111111110
loop(\(x,i).2x,(x2 + ~x),loop(\(x,i).(4x + 1),x,0))
A127847: 0 1 20 1344 348160 357564416 1465657589760 24017731997138944 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).3x,x,1) - loop(\(x,i).(4x + ~1),x,0))
A085280: 1 4 14 48 166 584 2094 7648 28406 107064 408574 1575248 6123846 23963944 94261454 372262848
(1 - loop(\(x,i).(3 * (x - loop(\(x,i).(2x + 4),i,0))),x,0))
A006230: 1 13 73 301 1081 3613 11593 36301 111961 342013 1038313 3139501 9467641 28501213 85700233 257493901
loop(\(x,i).(if x <= 0 then 2 else (13x + ~12)),x,0)
A141012: 0 2 14 170 2198 28562 371294 4826810 62748518 815730722 10604499374 137858491850 1792160394038 23298085122482 302875106592254 3937376385699290
(1 - loop(\(x,i).3x,x,loop(\(x,i).(3x + ~6),x,0)))
A220978: 1 19 217 2107 19441 176419 1592137 14342347 129120481 1162202419 10460176057 94142647387 847287015121 7625592702019 68630363015977 617673353237227
(loop(\(x,i).(3x + 2),x,0) * loop(\(x,i).(2x + 1),x,0))
A059387: 0 2 24 182 1200 7502 45864 277622 1672800 10057502 60406104 362617862 2176246800 13059091502 78359364744 470170602902
loop(\(x,i).((x * (x div 2)) div 3),1,loop(\(x,i).(2x + 1),x,0))
A006095: 0 0 1 7 35 155 651 2667 10795 43435 174251 698027 2794155 11180715 44731051 178940587
loop(\(x,i).4x,(2x + ~1),loop(\(x,i).(2x + 1),x,0))
A163839: 0 4 192 7168 245760 8126464 264241152 8522825728 273804165120 8778913153024 281200098803712 9002801208229888 288160007407534080 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).3x,2x,1) - loop(\(x,i).(2x + 1),x,0))
A155600: 1 8 78 722 6546 59018 531378 4782842 43046466 387419978 3486783378 31381057562 282429532386 2541865820138 22876792438578 205891132061882
(loop(\(x,i).5x,x,1) + loop(\(x,i).(2x + 1),x,0))
A155588: 1 6 28 132 640 3156 15688 78252 390880 1953636 9766648 48830172 244144720 1220711316 6103532008 30517610892
(loop(\(x,i).5x,x,1) - loop(\(x,i).(2x + 1),x,0))
A155596: 1 4 22 118 610 3094 15562 77998 390370 1952614 9764602 48826078 244136530 1220694934 6103499242 30517545358
((~2 + loop(\(x,i).3x,x,1)) * loop(\(x,i).(2x + 1),x,0))
A090021: 0 1 21 175 1185 7471 45801 277495 1672545 10056991 60405081 362615815 2176242705 13059083311 78359348361 470170570135
(1 - loop(\(x,i).((2x + ~1) * (if (x mod 2) <= 0 then 1 else 4)),x,0))
A091052: 1 2 13 26 205 410 3277 6554 52429 104858 838861 1677722 13421773 26843546 214748365 429496730
loop(\(x,i).(1 + (x * (if (x mod 2) <= 0 then 10 else 1))),x,0)
A322925: 0 1 2 21 22 221 222 2221 2222 22221 22222 222221 222222 2222221 2222222 22222221
loop(\(x,i).((x + 1) + (x div (if (i mod 3) <= 0 then 4 else 1))),x,0)
A178784: 0 1 3 4 9 19 24 49 99
(loop(\(x,i).4x,x,1) - loop(\(x,i).(3x + 1),x,0))
A083314: 1 3 12 51 216 903 3732 15291 62256 252303 1019052 4105731 16511496 66311703 266043972 1066567371
(loop(\(x,i).(~2x + 1),x,0) - loop(\(x,i).(3x + ~1),x,0))
A344747: 0 2 3 16 35 132 343 1136 3195 10012 29183 89256 264355 799892 2386023 7185376
loop(\(x,i).((x + 1) + (2 * (x + loop(\(x,i).2x,(~2 + i),1)))),x,0)
A336337: 0 3 12 41 132 413 1272 3881 11772 35573 107232 322721 970212 2914733 8752392 26273561
loop(\(x,i).(6x - loop(\(x,i).(~2x + 1),i,1)),x,0)
A091055: 0 1 3 23 127 783 4655 28015 167919 1007855 6046447 36280047 217677551 1306070767 7836413679 47018503919
loop(\(x,i).(if x <= 0 then 2 else ((2x * (~1 + (2 * i))) div (1 + i))),x,0)
A262543: 0 2 4 10 28 84 264 858 2860 9724 33592 117572 416024 1485800 5348880 19389690
(1 - loop(\(x,i).(2x + 2),x,loop(\(x,i).(2x + ~6),x,0)))
A092841: 1 11 67 323 1411 5891 24067 97283 391171 1568771 6283267 25149443 100630531 402587651 1610481667 6442188803
(1 - loop(\(x,i).3x,x,loop(\(x,i).(2x + ~6),x,0)))
A212850: 1 19 163 1135 7291 45199 275563 1666495 10038331 60348079 362442763 2175719455 13057505371 78354598159 470156286763 2821023814015
loop(\(x,i).x2,1,loop(\(x,i).(10x + 2),x,0))
A075411: 0 4 484 49284 4937284 493817284 49382617284 4938270617284 493827150617284 49382715950617284 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).~4x,x,loop(\(x,i).(~2x + ~2),x,0))
A159277: 0 8 32 384 2560 22528 172032 1409024 11141120 89653248 715128832 5729419264 45801799680 366548615168 2931852050432 23456963887104
(loop(\(x,i).(3x + 6),x,1) - loop(\(x,i).(2x + 2),x,0))
A135914: 1 7 27 91 291 907 2787 8491 25731 77707 234147 704491 2117571 6360907 19099107 57330091
(loop(\(x,i).(4x + 2),x,2) - loop(\(x,i).(2x + 2),x,0))
A123290: 2 8 36 156 652 2668 10796 43436 174252 698028 2794156 11180716 44731052 178940588 715795116 2863245996
loop(\(x,i).x2,1,loop(\(x,i).(10x + ~8),x,0))
A075417: 0 64 7744 788544 78996544 7901076544 790121876544 79012329876544 7901234409876544 790123455209876544 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).2x,x,2) - loop(\(x,i).(4x + ~8),x,0))
A251743: 3 13 49 185 713 2793 11049 43945 175273 700073 2798249 11188905 44747433 178973353 715860649 2863377065
loop(\(x,i).x2,1,loop(\(x,i).(10x + 4),x,0))
A075413: 0 16 1936 197136 19749136 1975269136 197530469136 19753082469136 1975308602469136 197530863802469136 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(4x + 8),x,1) - loop(\(x,i).(2x + 4),x,0))
A272417: 1 8 44 204 876 3628 14764 59564 239276 959148 3840684 15370924 61500076 246033068 984197804 3936922284
(1 - loop(\(x,i).4x,x,(2 - loop(\(x,i).(2x + 4),x,0))))
A020523: ~1 9 161 1665 14849 124929 1024001 8290305 66715649 535298049 4288675841 34334572545 274777243649 2198620602369 17590575431681 140731045904385
loop(\(x,i).loop(\(x,i).(2x + 2),6,4x),x,0)
A295838: 0 126 32382 8289918 2122219134 543288098430 139081753198206 35604928818740862 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~3x + loop(\(x,i).2x,(~2 + i),1)),x,0)
A091004: 0 1 ~2 8 ~20 68 ~188 596 ~1724 5300 ~15644 47444 ~141308 425972 ~1273820 3829652
loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),x,0)
A226511: 0 3 24 147 816 4323 22344 113907 576096 2900163 14559864 72976467 365413776 1828663203 9148098984 45754843827
loop(\(x,i).x3,1,(1 - loop(\(x,i).(2 * (x - (i mod 2))),x,0)))
A253103: 1 27 125 1331 9261 79507 614125 5000211 39651821 318611987 2543302125 20368783891 162860787181 1303244200467 10424521926125 83401901988371
(loop(\(x,i).4x,x,1) - loop(\(x,i).(3x + 2),x,0))
A155609: 1 2 8 38 176 782 3368 14198 58976 242462 989528 4017158 16245776 65514542 263652488 1059392918
loop(\(x,i).(x * (x div 3)),1,loop(\(x,i).(3x + ~2),x,0))
A219205: 0 2 24 234 2160 19602 176904 1593594 14346720 129133602 1162241784 10460294154 94143001680 847288078002 7625595890664 68630372581914
(loop(\(x,i).4x,x,1) - loop(\(x,i).(3x + ~2),x,0))
A155602: 1 6 24 90 336 1266 4824 18570 72096 281826 1107624 4371450 17308656 68703186 273218424 1088090730
loop(\(x,i).(x - ((((x div 3) mod 2) - (if x <= 0 then 1 else x)) div 2)),x,0)
A172161: 0 1 2 3 4 6 9 13 20 30 45 67 101 151 227 340
loop(\(x,i).(2x + ~1),x,loop(\(x,i).(2x + 16),x,0))
A165130: 0 31 189 889 3825 15841 64449 259969 1044225 4185601 16759809 67074049 268365825 1073602561 4294688769 17179312129
loop(\(x,i).(2x + loop(\(x,i).(x + (2 * (x + (i mod 2)))),i,0)),x,0)
A174395: 0 2 10 40 140 462 1470 4580 14080 42922 130130 393120 1184820 3565382 10717990 32197660
loop(\(x,i).(~2x + loop(\(x,i).(3x + ~1),(~1 + i),1)),x,0)
A091001: 0 1 0 5 4 33 56 253 588 2105 5632 18261 52052 161617 473928 1443629
loop(\(x,i).(~2x + loop(\(x,i).5x,(~1 + i),1)),x,0)
A015528: 0 1 3 19 87 451 2223 11179 55767 279091 1394943 6975739 34876647 174387331 871928463 4359658699
loop(\(x,i).~3x,(x + ~1),loop(\(x,i).(~2x + 1),x,0))
A080424: 0 1 3 27 135 891 5103 31347 185895 1121931 6711903 40330467 241805655 1451365371 8706597903 52244370387
loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).(~2x + (i mod 2)),x,0))
A095129: 0 1 1 15 45 231 861 3655 14365 58311 232221 932295 3725085 14913991 59639581 238612935
loop(\(x,i).(if (x mod 2) <= 0 then (8 + (x div 2)) else (x div 2)),x,0)
A143845: 0 8 12 14 15 7 3 1 0 8 12 14 15 7 3 1
loop(\(x,i).(loop(\(x,i).(x * (~1 + (2 * i))),i,1) + (2x * i)),x,0)
A122649: 0 1 7 57 561 6555 89055 1381905 24137505 468934515 10033419375 234484536825 5943863027025 162446292283275 4761954230608575 149048910271886625
(1 - loop(\(x,i).2x,x,loop(\(x,i).((x + ~2) - ((1 + i) * i)),x,0)))
A027608: 1 9 49 209 769 2561 7937 23297 65537 178177 471041 1216513 3080193 7667713 18808833 45547521
(1 - loop(\(x,i).(2 * (2x - ((x + 1) div (if i <= 0 then 1 else i)))),x,0))
A244174: 1 3 7 21 71 253 925 3433 12871 48621 184757 705433 2704157 10400601 40116601 155117521
loop(\(x,i).(x2 div 2),1,(1 - loop(\(x,i).(2x - (i mod 2)),x,0)))
A241685: 0 2 4 18 60 242 924 3698 14620 58482 233244 932978 3729180 14916722 59655964 238623858
loop(\(x,i).(x + (9 * (if x <= 0 then 3 else x))),x,0)
A136926: 0 27 270 2700 27000 270000 2700000 27000000 270000000 2700000000 27000000000 270000000000 2700000000000 27000000000000 270000000000000
loop(\(x,i).(loop(\(x,i).(x * i),(~1 + i),1) + (x * (~1 + (2 * i)))),x,0)
A087547: 0 1 4 22 160 1464 16224 211632 3179520 54092160 1028113920 21594021120 496702402560 12418039065600 335293281792000 9723592350259200
loop(\(x,i).(loop(\(x,i).(2x * i),i,1) + (x * (~1 + (2 * i)))),x,0)
A192457: 0 2 14 118 1210 14730 208110 3350550 60580170 1215657450 26813382750 644830644150 16793095369050 470839138619850 14140985865756750 452938463797569750
loop(\(x,i).(if x <= 0 then 1 else (2x4 + x2 + x)),x,0)
A152463: 0 1 4 532
loop(\(x,i).(x * i),x,loop(\(x,i).(x + ((i * i * (1 + i)) div 2)),x,0))
A037960: 0 1 14 150 1560 16800 191520 2328480 30240000 419126400 6187104000 97037740800 1612798387200 28332944640000 524813313024000 10226013557760000
loop(\(x,i).(x * (x + (x div 2))),1,loop(\(x,i).(3x + 4),x,0))
A087292: 0 24 384 4056 38400 351384 3179904 28671576 258201600 2324286744 20919997824 188284231896 1694570841600 15251175838104 137260697334144 1235346620381016
(1 - loop(\(x,i).(x + loop(\(x,i).(x * i),(~1 + i),(1 - (2 * i)))),x,0))
A334155: 1 2 5 15 57 273 1593 10953 86553 771993 7666713 83871513 1001957913 12976997913 181106559513 2709277004313
loop(\(x,i).(x2 + loop(\(x,i).4x2,(~1 + i),1)),x,0)
A167424: 0 1 5 89 24305 1664474849 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(3x + 2),x,2) - loop(\(x,i).(2x + i),x,0))
A094618: 2 7 22 69 216 671 2066 6313 19180 58035 175110 527357 1586144 4766599 14316154 42981201
loop(\(x,i).2x,(x + ~1),loop(\(x,i).(x + ((3 + i) * i)),x,0))
A240434: 0 4 28 128 480 1600 4928 14336 39936 107520 281600 720896 1810432 4472832 10895360 26214400
loop(\(x,i).(x + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)),x,0)
A103976: 0 1 4 9 18 29 44 61 82 109 138 173 212 253 298 349
(loop(\(x,i).(3x + 1),x,1) + loop(\(x,i).(2x - i),x,0))
A036550: 1 3 9 29 95 307 973 3033 9339 28511 86537 261637 788983 2375115 7141701 21457841
loop(\(x,i).(x + loop(\(x,i).(10x + ~1),i,i)),x,0)
A338226: 0 9 198 3087 41976 530865 6419754 75308643 864197532 9753086421 108641975310 1197530864199 13086419753088 141975308641977 1530864197530866 16419753086419755
loop(\(x,i).(loop(\(x,i).(x * (i * i)),(~1 + i),1) + (x * (i * i))),x,0)
A001819: 0 1 5 49 820 21076 773136 38402064 2483133696 202759531776 20407635072000 2482492033152000 359072203696128000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + loop(\(x,i).(x * (1 + (2 * i))),(~2 + i),1)) * i),x,0)
A233481: 0 1 4 21 144 1245 13140 164745 2399040 39834585 742940100 15374360925 349484058000 8654336615925 231842662751700 6679510641428625
(~1 + loop(\(x,i).(x4 + 1),x,(if (x + ~1) <= 0 then 1 else 0)))
A308507: 0 1 1 16 83521 4611686018427387903 4611686018427387903
(3 * ((2 + (if x <= 0 then 0 else 2)) * (1 + (if (x mod 2) <= 0 then 2 else 0))))
A040308: 18 12 36 12 36 12 36 12 36 12 36 12 36 12 36 12
(5 * ((if x <= 0 then 1 else 2) * (1 + (if (x mod 2) <= 0 then 2 else 0))))
A040212: 15 10 30 10 30 10 30 10 30 10 30 10 30 10 30 10
(8 * ((if x <= 0 then 1 else 2) * (1 + (if (x mod 2) <= 0 then 2 else 0))))
A040554: 24 16 48 16 48 16 48 16 48 16 48 16 48 16 48 16
(1 + loop(\(x,i).(10 * (if x <= 0 then 1 else x)),2x,0))
A152756: 1 101 10001 1000001 100000001 10000000001 1000000000001 100000000000001 10000000000000001 1000000000000000001 4611686018427387903 4611686018427387903
(1 + (if (x mod 2) <= 0 then x else (if ((x div 2) mod 3) <= 0 then (x div 2) else 0)))
A160596: 1 1 3 1 5 1 7 4 9 1 11 1 13 7 15 1
loop(\(x,i).2x,loop(\(x,i).((x + 1) mod (2 + (i div 3))),x,0),1)
A138882: 1 2 1 2 4 1 2 4 8 16 1 2 4 8 16 32
(1 + loop(\(x,i).(x - ((if x <= 0 then 1 else x) div (~2 + (x mod ~2)))),x,0))
A007601: 1 2 3 4 5 7 10 13 19 28 37 55 82 109 163 244
(1 + loop(\(x,i).5x,2,loop(\(x,i).(2x + 4),x,0)))
A139701: 1 101 301 701 1501 3101 6301 12701 25501 51101 102301 204701 409501 819101 1638301 3276701
(1 + loop(\(x,i).(if x <= 0 then 3 else (2 * (2x - (x mod 2)))),x,0))
A307702: 1 4 11 41 161 641 2561 10241 40961 163841 655361 2621441 10485761 41943041 167772161 671088641
(1 + loop(\(x,i).(2x + loop(\(x,i).(3x + 4),i,0)),x,0))
A255459: 1 5 25 101 361 1205 3865 12101 37321 114005 346105 1046501 3155881 9500405 28566745 85831301
(x div (1 + loop(\(x,i).(if (x div 2) <= 0 then (1 + (2 * i)) else (x div 2)),x,0)))
A229878: 0 0 1 0 1 2
A115346: 0 0 1 0 1 2 0 1 2 4 0 1 2 4 7 0
(loop(\(x,i).2x,((1 + (x div 3)) div 2),1) + (if x <= 0 then 0 else 1))
A251547: 1 2 2 3 3 3 3 3 3 5 5 5 5 5 5 9
(loop(\(x,i).~10x,x,1) + (if x <= 0 then 0 else 1))
A103461: 1 ~9 101 ~999 10001 ~99999 1000001 ~9999999 100000001 ~999999999 10000000001 ~99999999999 1000000000001 ~9999999999999 100000000000001 ~999999999999999
(loop(\(x,i).((x + 2) + (x div (4 + i))),x,1) - (if x <= 0 then 0 else 1))
A134421: 1 2 4 6 8 11 14 17 20 23 26 29 32 35 39 43
(((x + 1) * loop(\(x,i).(~1 + (x * (1 + i))),x,1)) - (if x <= 0 then 0 else 1))
A082425: 1 1 5 27 169 1217 9939 90871 920069 10222989 123698167 1619321459 22805443881 343835923129 5525934478859 94309281772527
loop(\(x,i).(4x * (~1 + (2 * i))),(x + ~1),(if x <= 0 then 0 else 1))
A052714: 0 1 4 48 960 26880 967680 42577920 2214051840 132843110400 9033331507200 686533194547200 57668788341964800 4611686018427387903 4611686018427387903 4611686018427387903
(2 + (loop(\(x,i).2x,(x div 2),(2 + (x mod 2))) + (if x <= 0 then 0 else 1)))
A343177: 4 6 7 9 11 15 19 27 35 51 67 99 131 195 259 387
((loop(\(x,i).3x,x,1) + (if x <= 0 then 0 else 1)) - (2 * (x mod 2)))
A084182: 1 2 10 26 82 242 730 2186 6562 19682 59050 177146 531442 1594322 4782970 14348906
(x + (loop(\(x,i).10x,x,1) + (if x <= 0 then 0 else 1)))
A266959: 1 12 103 1004 10005 100006 1000007 10000008 100000009 1000000010 10000000011 100000000012 1000000000013 10000000000014 100000000000015 1000000000000016
(1 + loop(\(x,i).(2x + (if (i mod 3) <= 0 then 3 else 0)),x,0))
A122552: 1 1 1 4 7 13 28 55 109 220 439 877 1756 3511 7021 14044
loop(\(x,i).2x,(x - (if ((x div ~2) mod 3) <= 0 then 0 else 1)),1)
A128055: 1 1 2 4 8 32 64 64 128 256 512 2048 4096 4096 8192 16384
(~1 + (if x <= 0 then 2 else (if (10 mod (x + 2)) <= 0 then 0 else 1)))
A271102: 1 0 0 ~1 0 0 0 0 ~1 0 0 0 0 0 0 0
(~1 + loop(\(x,i).2x,(if (~x2 + 4x) <= 0 then (x + ~1) else 1),1))
A078485: 0 1 1 1 7 15 31 63 127 255 511 1023 2047 4095 8191 16383
loop(\(x,i).2x,loop(\(x,i).(x * (2 + i)),(x mod 5),1),1)
A133376: 2 8 4096 1152921504606846976 4611686018427387903
(~1 + loop(\(x,i).(x2 + x),1,(1 + loop(\(x,i).4x,x,1))))
A020531: 5 29 305 4289 66305 1051649 16789505 268484609 4295163905 68720263169 1099514773505 17592198627329 281475027042305 4503599828697089 72057594843234305 1152921507828072449
(~1 + loop(\(x,i).(x2 + x),1,(1 + loop(\(x,i).(x * (i * i)),x,1))))
A020551: 5 5 29 1405 333505 207403201 268740115201 645241358764801 2642908298242867201 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if (x mod 10) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1))
A252503-A085398: 3 2 2 2 2 2 2 2 2 2 5 2 2 2 2 2
(1 + (if (x + ~2) <= 0 then x else (if ((x + 2) mod 8) <= 0 then 2 else 1)))
A078832: 1 2 3 2 2 2 3 2 2 2 2 2 2 2 3 2
(if (x mod 2) <= 0 then (15 * (if x <= 0 then 1 else 2)) else 1)
A040239: 15 1 30 1 30 1 30 1 30 1 30 1 30 1 30 1
(if (x mod 2) <= 0 then (10 * (2 + (if x <= 0 then 0 else 2))) else 1)
A040419: 20 1 40 1 40 1 40 1 40 1 40 1 40 1 40 1
(if x <= 0 then 1 else (if (x mod 4) <= 0 then (2x mod 5) else 1))
A204129-A204114: 1 1 1 1 3 1 1 1 1 1 1 1 4 1 1 1
loop(\(x,i).(x + loop(\(x,i).2x,(~1 + i),x)),(4x + ~1),1)
A028363: 1 30 9845550 171634285407048750 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),(loop(\(x,i).2x,x,1) div (1 + (2 * (x div 2)))),1)
A212671: 1 2 1 2 6 720 362880 6402373705728000 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).2x,x,(3 + loop(\(x,i).3x,x,2))))
A279512: 6 19 85 457 2641 15649 93505 560257 3360001 20156929 120935425 725600257 4353576961 26121412609 156728377345 940370067457
(if (x mod 2) <= 0 then (9 * (2 + (if x <= 0 then 0 else 2))) else 1)
A040341: 18 1 36 1 36 1 36 1 36 1 36 1 36 1 36 1
(if x <= 0 then 2 else (if (~x + 4) <= 0 then 18 else 1))
A067095: 2 1 1 1 18 18 18 18 18 18 18 18 18 18 18 18
(if x <= 0 then 1 else (~1 + (3 * (~2 + loop(\(x,i).4x,x,1)))))
A271017: 1 5 41 185 761 3065 12281 49145 196601 786425 3145721 12582905 50331641 201326585 805306361 3221225465
(if (x mod 2) <= 0 then (24 * (if x <= 0 then 1 else 2)) else 1)
A040599: 24 1 48 1 48 1 48 1 48 1 48 1 48 1 48 1
(1 + ((x - loop(\(x,i).(x - (if x <= 0 then (2 - i) else 1)),x,2)) div 3))
A007305: 0 1 1 1 2 1 2 3 3 1 2 3 3 4 5 5
(loop(\(x,i).2x,x,1) - loop(\(x,i).2x,(2x div 3),1))
A215795: 0 1 2 4 12
A291779: 0 1 2 4 12 24 48 112 224 448 960 1920 3840 7936 15872 31744
(~1 + ((2 * loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)) mod 3))
A144473: ~1 ~1 1 ~1 1 0 ~1 1 0 ~1 ~1 1 0 ~1 1 ~1
(1 + (3 * loop(\(x,i).(x * (if (~1 + i) <= 0 then 2 else x2)),x,2)))
A181492: 7 13 193 786433
(~1 + (3 * loop(\(x,i).(x * (if (~1 + i) <= 0 then 2 else x2)),x,2)))
A181491: 5 11 191 786431
(1 + loop(\(x,i).(3 * (x + loop(\(x,i).2x,i,1))),x,3))
A126644: 4 16 58 196 634 1996 6178 18916 57514 174076 525298 1582036 4758394 14299756 42948418 128943556
(if (x + ~2) <= 0 then 1 else (1 + (if (~2 + (x mod 4)) <= 0 then x else 3)))
A334501: 1 1 1 4 5 6 7 4 9 10 11 4 13 14 15 4
(if ((if x <= 0 then 2 else ((x + 1) div 2)) mod 3) <= 0 then (x div 3) else 1)
A213919: 1 1 1 1 1 1 2 1 1 1 1 3 4 1 1 1
(loop(\(x,i).2x,x,2) - loop(\(x,i).~x,x,(~1 + (x mod 3))))
A130755: 3 4 7 15 32 65 129 256 511 1023 2048 4097 8193 16384 32767 65535
(1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then (1 + i) else 0)),x,x) div 3))
A118198: 1 0 1 1 0 1 1 1 0 1 1 1 2 0 1 1
(1 + (3 * (x + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 1)),x,x))))
A131432: 1 4 7 7 10 13 10 13 16 19 13 16 19 22 25 16
(1 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).x3,x,3)))
A129291: 7 703 387400807 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + loop(\(x,i).(x2 + x),2,2))),(2x + 1),1)
A155477: 43 79507 147008443 271818611107 502592611936843 929293739471222707 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).2x,(2x + ~1),1))
A233196: 1 3 36 528 8256 131328 2098176 33558528 536887296 8590000128 137439215616 2199024304128 35184376283136 562949970198528 9007199321849856 144115188344291328
(if (~x + 2) <= 0 then (1 + (if (x mod 8) <= 0 then 2 else (x mod 2))) else 1)
A082067-A082061: 1 1 1 2 1 2 1 2 3 2 1 2 1 2 1 2
(1 + loop(\(x,i).loop(\(x,i).(2 * (x + ((1 + i) mod 4))),x,1),x,1))
A128466: 2 7 311 4611686018427387903
(1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).8x,x,1)))
A020517: 3 73 4161 262657 16781313 1073774593 68719738881 4398048608257 281474993487873 18014398643699713 1152921505680588801 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).3x,x,1) + loop(\(x,i).4x,x,1)))
A074506: 3 8 26 92 338 1268 4826 18572 72098 281828 1107626 4371452 17308658 68703188 273218426 1088090732
(loop(\(x,i).x2,2x,2) div (1 + loop(\(x,i).4x,x,1)))
A116213: 1 3 3855 4611686018427387903
loop(\(x,i).x2,1,(1 + loop(\(x,i).10x,x,1)))
A033934: 4 121 10201 1002001 100020001 10000200001 1000002000001 100000020000001 10000000200000001 1000000002000000001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,2,(1 + loop(\(x,i).10x,x,1)))
A168576: 16 14641 104060401 1004006004001 10004000600040001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(~1 + loop(\(x,i).10x,x,1)))
A059988: 0 81 9801 998001 99980001 9999800001 999998000001 99999980000001 9999999800000001 999999998000000001 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,2,(~1 + loop(\(x,i).10x,x,1)))
A272067: 0 6561 96059601 996005996001 9996000599960001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).3x,x,3) + loop(\(x,i).2x,x,1)))
A066280: 5 12 32 90 260 762 2252 6690 19940 59562 178172 533490 1598420 4791162 14365292 43079490
(1 + (loop(\(x,i).3x,2x,1) + loop(\(x,i).2x,x,1)))
A074505: 3 12 86 738 6578 59082 531506 4783098 43046978 387421002 3486785426 31381061658 282429540578 2541865836522 22876792471346 205891132127418
(1 + loop(\(x,i).((x2 + x) + (x div 2)),1,loop(\(x,i).2x,x,1)))
A343176: 3 8 23 77 281 1073 4193 16577 65921 262913 1050113 4197377 16783361 67121153 268460033 1073790977
(1 + loop(\(x,i).(x2 + 6x),1,loop(\(x,i).2x,x,1)))
A188129: 8 17 41 113 353 1217 4481 17153 67073 265217 1054721 4206593 16801793 67158017 268533761 1073938433
(1 + (loop(\(x,i).5x,x,1) + loop(\(x,i).2x,x,1)))
A074501: 3 8 30 134 642 3158 15690 78254 390882 1953638 9766650 48830174 244144722 1220711318 6103532010 30517610894
((1 + loop(\(x,i).3x,x,1)) * (1 + loop(\(x,i).2x,x,1)))
A034488: 4 12 50 252 1394 8052 47450 282252 1686434 10097892 60526250 362976252 2177317874 13062296532 78368963450 470199366252
loop(\(x,i).(10x + 1),(if x <= 0 then 0 else (x + 1)),1)
A199979: 1 111 1111 11111 111111 1111111 11111111 111111111 1111111111 11111111111 111111111111 1111111111111 11111111111111 111111111111111 1111111111111111 11111111111111111
(1 + ((if (x mod 2) <= 0 then loop(\(x,i).(x * i),x,1) else 3) mod (x + 1)))
A135681: 1 2 3 4 5 4 7 4 1 4 11 4 13 4 1 4
(x mod loop(\(x,i).i,(loop(\(x,i).4x,(x div 2),1) mod (x + 1)),1))
A333791-A323135: 0 0 0 0 0 1 0 0 0 3 0 3 0 5 2 0
loop(\(x,i).(x div 2),2x,loop(\(x,i).5x,(x + 1),1))
A241203: 5 6 7 9 12 15 19 23 29 37 46 58 72 90 113 142
loop(\(x,i).(1 + (loop(\(x,i).(x * i),x,1) + (x div 3))),(x + ~1),1)
A075849: 1 1 2 3 8 40323
loop(\(x,i).((x + loop(\(x,i).(x * i),(~1 + i),1)) * (1 + i)),(x + ~1),1)
A125062: 1 1 4 15 68 370 2364 17388 144864 1349136 13894560 156831840 1925527680 25550778240 364416917760 5559659078400
loop(\(x,i).(2 * ((x + ~1) - (if (i mod 2) <= 0 then 2 else ~2))),(x + ~1),1)
A173197: 1 1 4 2 6 6 14 22 46 86 174 342 686 1366 2734 5462
loop(\(x,i).2x,(x + ~1),loop(\(x,i).(4x + ~2),(x + ~1),1))
A103334: 1 1 4 24 176 1376 10944 87424 699136 5592576 44739584 357914624 2863312896 22906494976 183251943424 1466015514624
((x + ~1) - loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,(x + ~1)))
A330241: 0 1 0 1 1 2 1 2 1 2 3 4 1 2 1 2
(1 + loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,(x + ~1)))
A237664: 0 1 7 41 211 1009 4621 20593 90091 388961 1662805 7054321 29745717 124807201 521515801 2171645281
(3 + (loop(\(x,i).2x,x,2) + loop(\(x,i).3x,x,1)))
A254028: 6 10 20 46 116 310 860 2446 7076 20710 61100 181246 539636 1610710 4815740 14414446
loop(\(x,i).(2x2 + ~x),1,(1 + loop(\(x,i).3x,x,1)))
A169723: 6 28 190 1540 13366 118828 1065070 9572500 86113126 774900028 6973745950 62762650660 564860667286 5083736439628 45753599258830 411782307236020
(~1 + loop(\(x,i).(x + (6x div (if i <= 0 then 1 else i))),x,1))
A124089: 0 6 27 83 209 461 923 1715 3002 5004 8007 12375 18563 27131 38759 54263
(~1 + loop(\(x,i).(x + (8x div (if i <= 0 then 1 else i))),x,1))
A165618: 0 8 44 164 494 1286 3002 6434 12869 24309 43757 75581 125969 203489 319769 490313
(1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).(x * (i * i * i)),x,1)))
A260076: 3 3 73 46873 191116801 2985985728001 139314069877248001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).loop(\(x,i).(x + (((2 * (i mod 2)) + i) * i)),i,x),x,1))
A286444: 0 3 10 32 70 143 252 424 660 995 1430 2008 2730 3647 4760 6128
(~1 + loop(\(x,i).(x + loop(\(x,i).3x,i,(i * i * i))),x,1))
A343808: 0 3 75 804 5988 36363 193827 943968 4303200 18652107 77701107 313483764 1231813812 4734541443 17859008379 66286569504
(if ((~x + 2) mod 3) <= 0 then (2 + (if (x mod 4) <= 0 then 2 else 0)) else 1)
A318666-A301391: 1 1 2 1 1 2 1 1 4 1 1 2 1 1 2 1
(~1 + (2 * (loop(\(x,i).4x,x,1) - (if (x + ~1) <= 0 then x else 0))))
A267938: 1 5 31 127 511 2047 8191 32767 131071 524287 2097151 8388607 33554431 134217727 536870911 2147483647
loop(\(x,i).~x,x,(1 + (loop(\(x,i).(((x + ~1) + i) * i),x,0) div 2)))
A009132: 1 ~1 2 ~7 31 ~161 976 ~6847 54797 ~493201 4932046 ~54252551 651030667 ~8463398737 118487582396 ~1777313736031
(1 + (2 * (if x <= 0 then 2 else loop(\(x,i).(2x2 + 4x),(x + ~1),1))))
A178497: 5 3 13 193 37633 1416317953 2005956546822746113 4611686018427387903 4611686018427387903
(if (~x + 2) <= 0 then (2 * (1 + (if (~2 + (x div 3)) <= 0 then 0 else 2))) else 1)
A214079: 1 1 2 2 2 2 2 2 2 6 6 6 6 6 6 6
(if x <= 0 then 0 else (if (x mod (3 + ((x div 2) div 3))) <= 0 then 2 else 1))
A296081: 0 1 1 2 1 1 1 1 2 1 1 1 1 1 1 2
(7 * (if (x mod 2) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1))
A040185: 14 7 28 7 28 7 28 7 28 7 28 7 28 7 28 7
(loop(\(x,i).2x,x,2) - loop(\(x,i).2x,(x mod 6),1))
A222011: 1 2 4 8
A138814: 1 2 4 8 16 32 127 254 508 1016 2032 4064
(if x <= 0 then 0 else (if (x mod (8 - (x div 3))) <= 0 then 2 else 1))
A276172: 0 1 1 1 1 1 2 1 1 1 2 1 2 1 1 2
loop(\(x,i).x2,1,(~1 + (loop(\(x,i).(x * (2 + i)),(x + 2),1) div 2)))
A181892: 25 841 32041 1585081 101586241 8229936961 823010025601 99584412681601 14340158060659201 2423486749613529601 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).x2,2,loop(\(x,i).2x2,(2x + ~1),2)))
A139297: 15 4095 1152921504606846975
(~1 + loop(\(x,i).loop(\(x,i).x2,2,x3),(1 + (x mod 2)),2))
A076154: 4095 4611686018427387903 4095 4611686018427387903 4095 4611686018427387903 4095
(1 + (loop(\(x,i).(1 + loop(\(x,i).(x * i),(x + ~2),3)),x,1) div 2))
A082213: 1 3 4 181 4611686018427387903
(1 + (2 * loop(\(x,i).(2x + 1),x,(1 + (2 div (if x <= 0 then 1 else x))))))
A336819: 7 15 23 31 63 127 255 511 1023 2047 4095 8191 16383 32767 65535 131071
loop(\(x,i).2x,(x + ~1),(1 + (loop(\(x,i).(2x + 4),x,1) div 2)))
A084213: 1 4 18 76 312 1264 5088 20416 81792 327424 1310208 5241856 20969472 83881984 335536128 1342160896
(if (x + ~1) <= 0 then x else (if (10 mod (x + 1)) <= 0 then 2 else 1))
A304886: 0 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1
loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),(x + 2),(2x + 3))
A145737: 1 5 7 1 11 13 1 17 19 1 23 1 1 29 31 1
(1 + loop(\(x,i).(x - (if (~2 + (x div 2)) <= 0 then 0 else 1)),2,((x + 1) div 2)))
A206915: 1 2 2 3 3 4 4 5 5 6 6 6 6 6 6 7
(loop(\(x,i).(x * i),x,1) div loop(\(x,i).(x * (1 + i)),((x + 1) div 2),1))
A262034: 1 0 1 1 4 5 30 42 336 504 5040 7920 95040 154440 2162160 3603600
loop(\(x,i).(x * i),x,(1 + loop(\(x,i).2x,(x div 2),((x + 1) mod 2))))
A052636: 2 1 6 6 120 120 6480 5040 685440 362880 119750400 39916800 31135104000 6227020800 11245999564800 1307674368000
(if (x mod 2) <= 0 then (13 * (if x <= 0 then 1 else 2)) else 1)
A040181: 13 1 26 1 26 1 26 1 26 1 26 1 26 1 26 1
(if (x mod 2) <= 0 then (11 * (if x <= 0 then 1 else 2)) else 1)
A040131: 11 1 22 1 22 1 22 1 22 1 22 1 22 1 22 1
(if (x mod 2) <= 0 then (17 * (if x <= 0 then 1 else 2)) else 1)
A040305: 17 1 34 1 34 1 34 1 34 1 34 1 34 1 34 1
(if (x mod 2) <= 0 then (14 * (if x <= 0 then 1 else 2)) else 1)
A040209: 14 1 28 1 28 1 28 1 28 1 28 1 28 1 28 1
(if (x mod 5) <= 0 then (8 * (if x <= 0 then 1 else 2)) else 1)
A010152: 8 1 1 1 1 16 1 1 1 1 16 1 1 1 1 16
(1 + (2 * loop(\(x,i).(x + loop(\(x,i).x2,1,(2 + (i div 2)))),x,1)))
A272000: 3 11 29 47 79 111 161 211 283 355 453 551 679 807 969 1131
(1 + (2 * (if x <= 0 then 0 else (2 * (if (~4 + (x div 2)) <= 0 then 2 else 0)))))
A269351: 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1
(1 + (((x - loop(\(x,i).(if x <= 0 then i else (x + ~3)),x,0)) div 2) div 2))
A194066: 1 1 2 1 2 1 2 3 1 2 3 4 1 2 3 4
loop(\(x,i).~3x,(x + ~1),(1 + (2 * (if x <= 0 then 0 else 2))))
A084244: 1 5 ~15 45 ~135 405 ~1215 3645 ~10935 32805 ~98415 295245 ~885735 2657205 ~7971615 23914845
(1 + ((loop(\(x,i).2x,x,(1 + (if (x + ~2) <= 0 then 2 else 0))) div 2) div 2))
A240277: 1 2 4 3 5 9 17 33 65 129 257 513 1025 2049 4097 8193
loop(\(x,i).(x + 2),(~x + 2),(if ((x + 2) mod 6) <= 0 then 2 else 1))
A174965: 5 3 1 1 2 1 1 1 1 1 2 1 1 1 1 1
(loop(\(x,i).2x,x,1) mod (~1 + loop(\(x,i).(x2 + 3x + 2),2,2)))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A036154: 1 2 4 8 16 32 64 128 75 150 119 57 114 47 94 7
(1 + (if x <= 0 then 1 else (2 * (if (x + ~1) <= 0 then (x + 2) else ((x + 1) mod 2)))))
A200439: 2 7 3 1 3 1 3 1 3 1 3 1 3 1 3 1
loop(\(x,i).(x * i),x,(if ((x + 1) mod (2 + (x mod 4))) <= 0 then 2 else 1))
A052699: 1 1 2 6 24 240 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000
(9 * (if (x mod 2) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1))
A040309: 18 9 36 9 36 9 36 9 36 9 36 9 36 9 36 9
(loop(\(x,i).2x,x,(if x <= 0 then 1 else ~2)) mod 9)
A154529: 1 5 1 2 4 8 7 5 1 2 4 8 7 5 1 2
loop(\(x,i).x2,1,(~1 + (2 * (2 + (if (x + ~2) <= 0 then x else (x + 2))))))
A112629: 9 25 49 169 225
(loop(\(x,i).2x,x,1) mod (1 + loop(\(x,i).((x + 2) * (x + i)),2,2)))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A036157: 1 2 4 8 16 32 64 128 59 118 39 78 156 115 33 66
(1 + (2 * (loop(\(x,i).2x,x,2) - loop(\(x,i).2x,(x div 2),2))))
A276918: 1 5 9 25 49 113 225 481 961 1985 3969 8065 16129 32513 65025 130561
loop(\(x,i).(x * i),(2 * (if x <= 0 then 1 else (2 * (2x - (x mod 2))))),1)
A045510: 2 24 20922789888000 2432902008176640000 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).3x,x,1) mod (~1 + loop(\(x,i).2x2,2,2)))
A036143: 1 3 9 27 81 116 94 28 84 125 121 109 73 92 22 66
(loop(\(x,i).2x,x,1) mod loop(\(x,i).(4x + 1),4,1))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A230579: 1 2 4 8 16 32 64 128 256 171 1 2 4 8 16 32
(loop(\(x,i).2x,x,1) mod (~1 + loop(\(x,i).(x2 + ~x),2,4)))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A036144: 1 2 4 8 16 32 64 128 125 119 107 83 35 70 9 18
(loop(\(x,i).(3x + 1),x,0) div (if (x mod 2) <= 0 then 4 else 1))
A152298: 0 1 1 13 10 121 91 1093 820 9841 7381 88573 66430 797161 597871 7174453
(3 * ((2 + (if x <= 0 then 0 else 2)) * (if (x mod 2) <= 0 then 4 else 1)))
A040555: 24 12 48 12 48 12 48 12 48 12 48 12 48 12 48 12
(5 * ((if x <= 0 then 1 else 2) * (if (x mod 2) <= 0 then 4 else 1)))
A040383: 20 10 40 10 40 10 40 10 40 10 40 10 40 10 40 10
loop(\(x,i).6x,(x div 2),(if (x mod 2) <= 0 then 4 else 1))
A166027: 4 1 24 6 144 36 864 216 5184 1296 31104 7776 186624 46656 1119744 279936
(5 * (if (x mod 2) <= 0 then (3 * (if x <= 0 then 1 else 2)) else 1))
A040215: 15 5 30 5 30 5 30 5 30 5 30 5 30 5 30 5
(5 * (if (x mod 2) <= 0 then (2 * (2 + (if x <= 0 then 0 else 2))) else 1))
A040387: 20 5 40 5 40 5 40 5 40 5 40 5 40 5 40 5
(5 * loop(\(x,i).x2,2,(~1 + loop(\(x,i).2x,x,2))))
A128866: 5 405 12005 253125 4617605 78764805 1300723205 21141253125 340920883205 5476114739205 87789257318405 1406000997253125 22507005033676805 360200017312153605 4611686018427387903
(loop(\(x,i).2x,x,1) mod loop(\(x,i).x3,1,5))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A201920: 1 2 4 8 16 32 64 3 6 12 24 48 96 67 9 18
(5 * loop(\(x,i).(x + (if (~x + 2) <= 0 then x else 2)),x,(~x + 1)))
A070004: 5 10 15 20 30 40 60 80 120 160 240 320 480 640 960 1280
(if x <= 0 then 1 else loop(\(x,i).(2 * (2x + (x div 2))),x,5))
A235702: 1 24 120 600 3000 15000 75000 375000 1875000 9375000 46875000 234375000 1171875000 5859375000 29296875000 146484375000
loop(\(x,i).loop(\(x,i).x2,3,x3),x,5)
A067483: 5 59604644775390625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,5)
A154286: 5 25 75 175 350 630 1050 1650 2475 3575 5005 6825 9100 11900 15300 19380
(~1 + loop(\(x,i).loop(\(x,i).x2,1,(x2 * (x div 2))),x,4))
A139301: 3 1023 288230376151711743
loop(\(x,i).2x,x,loop(\(x,i).i,(2x - (x2 div 4)),1))
A005104: 1 4 12 32 64 128 192 256 256
loop(\(x,i).x3,1,(~1 + loop(\(x,i).x2,x2,4)))
A195374: 27 3375 4611686018427387903
(loop(\(x,i).2x,x,1) mod (1 + loop(\(x,i).(2x2 + x),2,2)))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A036159: 1 2 4 8 16 32 64 128 45 90 180 149 87 174 137 63
(loop(\(x,i).3x,x,1) mod (1 + loop(\(x,i).(x2 + x),2,2)))
A036126: 1 3 9 27 38 28 41 37 25 32 10 30 4 12 36 22
(1 + (2 * loop(\(x,i).(2 * (x + loop(\(x,i).3x,i,1))),x,2)))
A126645: 5 21 77 261 845 2661 8237 25221 76685 232101 700397 2109381 6344525 19066341 57264557 171924741
(loop(\(x,i).3x,x,1) mod (~1 + loop(\(x,i).(x2 + 2x),2,2)))
A036134: 1 3 9 27 2 6 18 54 4 12 36 29 8 24 72 58
(~1 + (loop(\(x,i).loop(\(x,i).x3,1,2x2),x,2) div 2))
A139305: 0 255 72057594037927935 4611686018427387903
(1 + (loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),2,(x + 2)) div 2))
A330747: 1 2 1 3 1 4 1 5 2 6 1 7 1 8 3 9
loop(\(x,i).3x,2x,loop(\(x,i).(x2 + 4x + 4),2,1))
A120353: 121 1089 9801 88209 793881 7144929 64304361 578739249 5208653241 46877879169 421900912521 3797108212689 34173973914201 307565765227809 2768091887050281 24912826983452529
loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 2 else 0)),x,(2x + 5))
A107257: 5 7 11 11 13 17 17 19 23 23 29 29 29 31 37 37
(~1 + loop(\(x,i).8x2,(if x <= 0 then 1 else 2x),2))
A139295: 31 8191 2305843009213693951 4611686018427387903
(~1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).(2x + 2),2x,2)))
A020541: 5 209 3905 64769 1045505 16764929 268386305 4294770689 68718690305 1099508482049 17592173461505 281474926379009 4503599426043905 72057593232621569 1152921501385621505 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(4x + 1))
A016822: 1 9765625 3486784401 137858491849 2015993900449 16679880978201 95367431640625 420707233300201 1531578985264449 4808584372417849 13422659310152401 34050628916015625 79792266297612001 174887470365513049 362033331456891249 713342911662882601
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(4x + 1))
A016824: 1 244140625 282429536481 23298085122481 582622237229761 7355827511386641 59604644775390625 353814783205469041 1667889514952984961 4611686018427387903 4611686018427387903
(~1 + ((loop(\(x,i).x2,(x + ~1),2) + loop(\(x,i).x2,x,2)) div 2))
A110817: 1 2 9 135 32895 2147516415
(loop(\(x,i).2x,x,1) mod (~1 + loop(\(x,i).(x * (x2 + i)),2,2)))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A123464: 1 2 4 8 16 32 64 128 256 512
A101440: 1 2 4 8 16 32 64 128 256 512 5 10 20 40 80 160
(if x <= 0 then 1 else (3 * ((~x + 1) + loop(\(x,i).(2 * (x + i)),x,0))))
A321257: 1 6 21 60 147 330 705 1464 2991 6054 12189 24468 49035 98178 196473 393072
(3 * (if (x mod 2) <= 0 then (3 * (2 + (if x <= 0 then 0 else 2))) else 1))
A040317: 18 3 36 3 36 3 36 3 36 3 36 3 36 3 36 3
(if (x + ~2) <= 0 then 1 else (3 * (x - (if (x + ~3) <= 0 then 2 else 1))))
A089425: 1 1 1 3 9 12 15 18 21 24 27 30 33 36 39 42
(3 * (if (x mod 2) <= 0 then (5 * (if x <= 0 then 1 else 2)) else 1))
A040219: 15 3 30 3 30 3 30 3 30 3 30 3 30 3 30 3
(3 * (if (x mod 2) <= 0 then (8 * (if x <= 0 then 1 else 2)) else 1))
A040567: 24 3 48 3 48 3 48 3 48 3 48 3 48 3 48 3
(loop(\(x,i).2x,x,1) - (3 * loop(\(x,i).x2,2,3)))
A220089: ~242 ~241 ~239 ~235 ~227 ~211 ~179 ~115 13 269 781 1805 3853 7949 16141 32525
loop(\(x,i).loop(\(x,i).(3x + 1),x,0),(x mod 3),3)
A271393: 3 13 797161
loop(\(x,i).2x,(x div 2),((1 + loop(\(x,i).2x,x,2)) div 3))
A083333: 1 1 6 10 44 84 344 680 2736 5456 21856 43680 174784 349504 1398144 2796160
((1 + (2 * loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x))) div 3)
A141169: 0 0 1 0 1 1 0 1 1 2 0 1 1 2 3 0
(3 * loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).2x,x,1)))
A032125: 3 9 30 108 408 1584 6240 24768 98688 393984 1574400 6294528 25171968 100675584 402677760 1610661888
(3 * loop(\(x,i).(2x + ~1),(x + ~1),loop(\(x,i).2x,x,1)))
A032098: 3 6 21 87 363 1491 6051 24387 97923 392451 1571331 6288387 25159683 100651011 402628611 1610563587
loop(\(x,i).((x2 + 1) div 2),1,(loop(\(x,i).2x,x,1) div 3))
A241892: 0 0 1 2 13 50 221 882 3613 14450 58141 232562 931613 3726450 14911261 59645042
(6 * (if (x mod 2) <= 0 then (3 * (if x <= 0 then 1 else 2)) else 1))
A040311: 18 6 36 6 36 6 36 6 36 6 36 6 36 6 36 6
(6 * (if (x mod 2) <= 0 then (2 * (2 + (if x <= 0 then 0 else 2))) else 1))
A040559: 24 6 48 6 48 6 48 6 48 6 48 6 48 6 48 6
(3 * ((1 + (if (x mod 2) <= 0 then 4 else 0)) * (if x <= 0 then 1 else 2)))
A040214: 15 6 30 6 30 6 30 6 30 6 30 6 30 6 30 6
(6 * (if (5 mod (if x <= 0 then 1 else x)) <= 0 then 1 else 2))
A055665: 6 6 12 12 12 6 12 12 12 12 12 12 12 12 12 12
(loop(\(x,i).2x,x,1) mod loop(\(x,i).(x2 + 4),2,3))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A036152: 1 2 4 8 16 32 64 128 83 166 159 145 117 61 122 71
loop(\(x,i).8x,x,(3 * (if x <= 0 then 1 else 4)))
A094085: 3 96 768 6144 49152 393216 3145728 25165824 201326592 1610612736 12884901888 103079215104 824633720832 6597069766656 52776558133248 422212465065984
loop(\(x,i).(x * (x div 2)),1,(loop(\(x,i).2x,x,4) div 3))
A337348: 0 2 10 50 210 882 3570 14450 57970 232562 930930 3726450 14908530 59645042 238591090 954408050
(3 * (if (x + ~2) <= 0 then 2 else (if (x mod 2) <= 0 then x else (2x + ~4))))
A092937: 6 6 6 6 12 18 18 30
(if x <= 0 then 2 else (if x <= 0 then 1 else (3 * (~x mod (2 + (x div 2))))))
A190146: 2 3 3 0 0 9
(if x <= 0 then 1 else (((if (x mod 2) <= 0 then x else 0) + ((x div 2) mod 2)) div 3))
A035457: 1 0 1 0 1 0 2 0 2 0 3 0 4 0 5 0
(3 * (loop(\(x,i).(x * (if (~1 + i) <= 0 then 2 else x2)),x,2) div 2))
A092680: 3 6 96 393216
((loop(\(x,i).(x2 + x),1,loop(\(x,i).(~x + i),x,2)) div 2) div 3)
A008799: 1 0 2 0 3 0 5 1 7 2 9 3 12 5 15 7
((2 * (2x - loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0))) div 3)
A307485: 0 1 2 4 3 5 7 9 6 8 10 12 14 16 18 20
(loop(\(x,i).x2,1,loop(\(x,i).(3x + ~3),x,2)) div 3)
A238630: 1 3 12 75 588 5043 44652 399675 3590508 32294883 290594892 2615176875 23536060428 211822949523 1906401762732 17157601515675
(3 * (if x <= 0 then 0 else (1 - (2 * (if (x mod 2) <= 0 then x else (~x + 1))))))
A228935: 0 3 ~9 15 ~21 27 ~33 39 ~45 51 ~57 63 ~69 75 ~81 87
(loop(\(x,i).(x2 + x),1,loop(\(x,i).(2x + 2),x,2)) div 3)
A203241: 2 14 70 310 1302 5334 21590 86870 348502 1396054 5588310 22361430 89462102 357881174 1431590230 5726491990
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,6x)
A016918: 0 60466176 61917364224 3570467226624 63403380965376 590490000000000 3656158440062976 17080198121677824 64925062108545024 210832519264920576 604661760000000000 1568336880910795776 3743906242624487424
loop(\(x,i).loop(\(x,i).x2,2,x3),1,6x)
A016920: 0 2176782336 8916100448256 1156831381426176 36520347436056576 531441000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (3 * loop(\(x,i).(2x + 2),(x div 2),(x mod 2))))
A061776: 1 3 6 12 18 30 42 66 90 138 186 282 378 570 762 1146
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (3x + 1)),x,3)
A033478: 3 10 5 16 8 4 2 1 4 2 1 4 2 1 4 2
(loop(\(x,i).loop(\(x,i).((x2 + ~x) div 2),i,(x + 2)),2,x) div 3)
A337957: 1 15 126 715 3060 10626 31465 82251 194580 424270 864501 1663740 3049501 5359095 9078630 14891626
loop(\(x,i).(2 * (x + (4 * (x div (if i <= 0 then 1 else i))))),x,3)
A344564: 3 30 180 840 3360 12096 40320 126720 380160 1098240 3075072 8386560 22364160 58490880 150405120 381026304
(loop(\(x,i).3x,(x + 2),1) - loop(\(x,i).2x,x,3))
A169687: 6 21 69 219 681 2091 6369 19299 58281 175611 528369 1588179 4770681 14324331 42997569 129041859
loop(\(x,i).(6x + 4),2,loop(\(x,i).2x,x,3))
A304606: 136 244 460 892 1756 3484 6940 13852 27676 55324 110620 221212 442396 884764 1769500 3538972
(loop(\(x,i).3x,x,4) - loop(\(x,i).2x,x,3))
A166060: 1 6 24 84 276 876 2724 8364 25476 77196 233124 702444 2113476 6352716 19082724 57297324
loop(\(x,i).2x2,(x + ~2),loop(\(x,i).(x2 div 2),x,3))
A154714: 3 4 8 2048
((2 * (if x <= 0 then 1 else x)) - (if (x mod 3) <= 0 then 1 else (x div 3)))
A301728: 1 2 4 5 7 9 11 12 14 17 17 19 23 22 24 29
(if x <= 0 then 2 else (if ((x mod 3) div 2) <= 0 then 1 else (x - (x div 3))))
A003417: 2 1 2 1 1 4 1 1 6 1 1 8 1 1 10 1
((if (x mod 2) <= 0 then (if x <= 0 then 1 else 2) else ~2) * (1 - (x mod 3)))
A109265: 1 0 ~2 ~2 0 2 2 0 ~2 ~2 0 2 2 0 ~2 ~2
(2 + loop(\(x,i).3x,x,3) - loop(\(x,i).2x,x,1))
A304167: 4 9 25 75 229 699 2125 6435 19429 58539 176125 529395 1590229 4774779 14332525 43013955
loop(\(x,i).(2 * (x mod 2)),(x + ~2),loop(\(x,i).3x,x,3))
A114181: 3 9 27 2 0 0 0 0 0
loop(\(x,i).(x + (3 * (2x div (if i <= 0 then 1 else i)))),x,3)
A253943: 3 21 84 252 630 1386 2772 5148 9009 15015 24024 37128 55692 81396 116280 162792
loop(\(x,i).(x * (1 + loop(\(x,i).4x,(1 + i),x))),x,3)
A003009: 3 147 1383123 489735485064147 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + ~x),1,loop(\(x,i).x3,x,3))
A111404: 24 19656 7625597465304 4611686018427387903 4611686018427387903
(if (x + ~2) <= 0 then (x + (x div 2)) else loop(\(x,i).x3,x,3))
A266199: 0 1 3 7625597484987
loop(\(x,i).(x + (5x div (if i <= 0 then 1 else i))),x,3)
A253942: 3 18 63 168 378 756 1386 2376 3861 6006 9009 13104 18564 25704 34884 46512
(~1 + loop(\(x,i).(4x - loop(\(x,i).(~2x + 1),i,0)),x,2))
A253068: 1 6 28 112 456 1816 7288 29112 116536 465976 1864248 7456312 29826616 119303736 477220408 1908870712
(1 + loop(\(x,i).(x mod 2),(x mod 2),(if (~1 + (x mod 3)) <= 0 then x else 2)))
A267068: 1 2 3 2 5 1 7 2 3 2 11 1 13 2 3 2
(1 + ((x + (3 * loop(\(x,i).(if x <= 0 then i else (x + ~1)),x,0))) div 2))
A054429: 1 3 2 7 6 5 4 15 14 13 12 11 10 9 8 31
(1 + (2 * (if x <= 0 then 1 else (x * (1 + (2 * (if (x + ~2) <= 0 then 1 else x)))))))
A086208: 3 7 13 43 73
(~1 + loop(\(x,i).(1 + (2 * (2x - (x div (if i <= 0 then 1 else i))))),x,2))
A134762: 1 4 16 58 208 754 2770 10294 38608 145858 554266 2116294 8112466 31201798 120349798 465352558
loop(\(x,i).2x,x,(1 + loop(\(x,i).(5x + 1),x,2)))
A225107: 3 24 228 2256 22512 225024 2250048 22500096 225000192 2250000384 22500000768 225000001536 2250000003072 22500000006144 225000000012288 2250000000024576
(1 + loop(\(x,i).(~1 + (x * loop(\(x,i).(x2 + ~2),i,3))),x,2))
A088334: 3 14 611 1346270 6557470319843 4611686018427387903 4611686018427387903
((x + 1) - ((~x + loop(\(x,i).(if x <= 0 then (2 * i) else (x + ~1)),x,1)) div 2))
A114651: 1 3 2 4 6 8 10 5 7 9 11 13 15 17 19 21
loop(\(x,i).~x,(x div 2),(1 + (2 * (x + (if (x mod 2) <= 0 then x else 1)))))
A141124: 1 5 ~9 ~9 17 13 ~25 ~17 33 21 ~41 ~25 49 29 ~57 ~33
loop(\(x,i).(x * i),(x + 1),loop(\(x,i).(x * i),((x2 + x) div 2),1))
A127234: 1 2 36 17280 435456000 941525544960000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if x <= 0 then 1 else (2 * loop(\(x,i).(x + 1),(~4 + (x div 2)),x))))
A342008-A082664: 2 3 5 7 9 11 13 15 17 19 23 25 29 31 35 37
loop(\(x,i).3x,2x,(~1 + loop(\(x,i).4x,x,2)))
A094938: 1 63 2511 92583 3352671 120873303 4353033231 156723545223 5642176768191 203119525916343 7312313393341551 263243376303474663 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).(x * (2 + i)),(x div 2),1) div loop(\(x,i).2x,x,2)))
A165045: 1 1 1 1 1 1 1 1 1 1 2 1 3 2 6 3
(1 + loop(\(x,i).(4x + 2),x,2) - loop(\(x,i).2x,x,2))
A171477: 1 7 35 155 651 2667 10795 43435 174251 698027 2794155 11180715 44731051 178940587 715795115 2863245995
(loop(\(x,i).(3x + 6),x,0) * (~1 + loop(\(x,i).2x,x,2)))
A071539: 0 18 168 1170 7440 45738 277368 1672290 10056480 60404058 362613768 2176238610 13059075120 78359331978 470170537368 2821066664130
(loop(\(x,i).(3x + 1),x,1) * (~1 + loop(\(x,i).2x,x,2)))
A160869: 1 12 91 600 3751 22932 138811 836400 5028751 30203052 181308931 1088123400 6529545751 39179682372 235085301451 1410533397600
loop(\(x,i).x5,1,(~1 + loop(\(x,i).2x,x,2)))
A128833: 1 243 16807 759375 28629151 992436543 33038369407 1078203909375 34842114263551 1120413075641343 35940921946155007 1151514816750309375 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).7x,x,(~1 + loop(\(x,i).2x,x,2)))
A075921: 1 21 343 5145 74431 1058841 14941423 210003465 2945813311 41281739961 578226834703 8097153012585 113373983463391 1587332657497881 22223335428043183 311131443554114505
(1 + loop(\(x,i).(3x + (if (i mod 3) <= 0 then 2 else 0)),x,2))
A263334: 3 7 19 57 169 505 1515 4543 13627 40881 122641 367921 1103763 3311287 9933859 29801577
(1 + loop(\(x,i).loop(\(x,i).(2x + 1),(x div 2),(2 - (x mod 2))),x,2))
A253855: 3 6 8 16 256
loop(\(x,i).4x,x,loop(\(x,i).(4x + 1),(x + 2),1))
A166914: 21 340 5456 87360 1398016 22369280 357912576 5726617600 91625947136 1466015416320 23456247709696 375299967549440 6004799497568256 96076792028200960 1537228672719650816 4611686018427387903
(if x <= 0 then 1 else (if (((x + 2) div 3) mod 4) <= 0 then (x + 2) else 1))
A284372: 1 1 1 1 1 1 1 1 1 1 12 13 14 1 1 1
(if (x + ~1) <= 0 then 1 else (if ((x + 2) mod (2 + (x mod 2))) <= 0 then (x + 2) else 1))
A005451: 1 1 4 1 6 1 8 9 10 1 12 1 14 15 16 1
loop(\(x,i).(x * i),x,loop(\(x,i).(2x * (1 + (2 * i))),(x + 2),1))
A138898: 60 840 30240 1995840 207567360 31135104000 6351561216000 1689515283456000 567677135241216000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,((x + 3) * loop(\(x,i).(x * i),x,(x + 2))))
A162992: 36 144 1600 32400 1016064 45158400 2687385600 205752960000 19670999040000 2294425328025600 320461058211840000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,(x + 3))
A006411: 3 20 75 210 490 1008 1890 3300 5445 8580 13013 19110 27300 38080 52020 69768
(2 - loop(\(x,i).2x,(x + ~2),loop(\(x,i).((x + ~1) div 2),(x + ~2),1)))
A174316: 1 1 1 2 6 10 18 34 66 130 258 514 1026 2050 4098 8194
loop(\(x,i).(1 + loop(\(x,i).10x,2,x)),2x,1)
A144863: 1 10101 101010101 1010101010101 10101010101010101 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(if (x mod (1 + (2 * i))) <= 0 then 1 else x),(x + 1),2x))
A099893: 0 1 3 0 7 0 0 0 15 0 0 0 0 0 0 0
loop(\(x,i).(1 + loop(\(x,i).(x + (x div (~1 + (2 * i)))),x,i)),2x,1)
A099061: 1 7 19 39 63 91 133 181 223 289 349 399 481 567 649 763
loop(\(x,i).(~10x + (if x <= 0 then 1 else x)),2x,1)
A172174: 1 91 8191 737191 66347191 5971247191 537412247191 48367102247191 4353039202247191 391773528202247191 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x + (if (i mod 3) <= 0 then 1 else 0)),2x,1)
A037595: 1 9 84 757 6813 61320 551881 4966929 44702364 402321277 3620891493 32588023440 293292210961 2639629898649 23756669087844 213810021790597
(1 + loop(\(x,i).(x2 + ~x),x,loop(\(x,i).x3,2,2x)))
A066914: 1 261633 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(2x * i),x,(2x + 1)),1,(2x + 1))
A003031: 6 336 42240 9676800 3530096640 1880240947200 1377317368627200 1328346084409344000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(2x + 1))
A016763: 1 177147 48828125 1977326743 31381059609 285311670611 1792160394037 8649755859375 34271896307633 116490258898219 350277500542221 952809757913927 2384185791015625 5559060566555523 12200509765705829 25408476896404831
loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,(2x + 1))
A294486: 1 18 150 980 5670 30492 156156 772200 3719430 17551820 81477396 373173528 1690097500 7582037400 33738060600 149067936720
((3x + 1) + loop(\(x,i).(x - (if x <= 0 then 2 else (~2 + i))),x,x))
A006187: 1 6 10 13 15 16 16 18
loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,(2x + 1))
A051880: 1 15 75 245 630 1386 2730 4950 8415 13585 21021 31395 45500 64260 88740 120156
loop(\(x,i).(x + (5 * (if (~2 + i) <= 0 then 1 else x))),2x,1)
A067406: 1 11 396 14256 513216 18475776 665127936 23944605696 862005805056 31032208982016 1117159523352576 40217742840692736 1447838742264938496 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (6 * (if (~2 + i) <= 0 then 1 else x))),2x,1)
A067407: 1 13 637 31213 1529437 74942413 3672178237 179936733613 8816899947037 432028097404813 21169376772835837 1037299461868956013 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 5),x,loop(\(x,i).3x,2x,1))
A094986: 1 1 3 5 10 18 34 61 110 198 357 642 1156 2082 3748 6746
((x + 1) - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + (2 * i)))),x,2x))
A278818: 1 3 7 6 5 11 10 9 17 16 15 14 13 23 22 21
loop(\(x,i).(x * (~1 + (loop(\(x,i).2x,i,1) + (i mod 2)))),2x,1)
A003923: 1 6 720 1451520 47377612800 24815256521932800 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (8 * (if (~2 + i) <= 0 then 1 else x))),2x,1)
A067409: 1 17 1377 111537 9034497 731794257 59275334817 4801302120177 388905471734337 31501343210481297 2551608800048985057 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (6x div (if i <= 0 then 1 else i))),2x,1)
A053135: 1 28 210 924 3003 8008 18564 38760 74613 134596 230230 376740 593775 906192 1344904 1947792
loop(\(x,i).(x + (8x div (if i <= 0 then 1 else i))),2x,1)
A053137: 1 45 495 3003 12870 43758 125970 319770 735471 1562275 3108105 5852925 10518300 18156204 30260340 48903492
loop(\(x,i).(x + (5x div (if i <= 0 then 1 else i))),2x,1)
A002299: 1 21 126 462 1287 3003 6188 11628 20349 33649 53130 80730 118755 169911 237336 324632
loop(\(x,i).(1 + loop(\(x,i).10x,2,x)),(x div 2),1)
A279053: 1 1 101 101 10101 10101 1010101 1010101 101010101 101010101 10101010101 10101010101 1010101010101 1010101010101 101010101010101 101010101010101
(loop(\(x,i).(x * i),x,1) div loop(\(x,i).(x * (i * (1 + i))),(x div 2),1))
A057977: 1 1 1 3 2 10 5 35 14 126 42 462 132 1716 429 6435
(if (x mod 3) <= 0 then 1 else (~1 + loop(\(x,i).2x,x,2) - (x div 2)))
A094445: 1 3 6 1 29
loop(\(x,i).(if (x mod 2) <= 0 then x else 9),x,(1 + (x div 2)))
A228584: 1 9 2 2 9 9 4 4 9 9 6 6 9 9 8 8
(loop(\(x,i).3x,x,2) - loop(\(x,i).3x,(x div 2),1))
A120825: 1 5 15 51
A255442: 1 5 15 51 153 477 1431 4347 13041 39285 117855 354051 1062153 3187917 9563751 28695627
loop(\(x,i).(x + (6x div (if i <= 0 then 1 else i))),(x div 2),1)
A299338: 1 1 7 7 28 28 84 84 210 210 462 462 924 924 1716 1716
loop(\(x,i).(x + (5x div (if i <= 0 then 1 else i))),(x div 2),1)
A189980: 1 1 6 6 21 21 56 56 126 126 252 252 462 462 792 792
(loop(\(x,i).(2x * i),x,1) div loop(\(x,i).(x * (i * i)),(x div 2),1))
A253665: 1 2 8 48 96 960 1280 17920 17920 322560 258048 5677056 3784704 98402304 56229888 1686896640
(1 + loop(\(x,i).((x + 2) + (x div (if i <= 0 then 1 else i))),x,0) - (x mod 2))
A054248: 1 2 6 8 13 16 21 24 30 34 40 44 50 54 60 64
(if (2 - (x div 4)) <= 0 then (if (x mod 4) <= 0 then 2 else (x mod 2)) else 1)
A334947: 1 1 1 1 1 1 1 1 2 1 0 1 2 1 0 1
(~1 + loop(\(x,i).2x,(if (x mod 2) <= 0 then x else (~x + 2)),2) - (x mod 2))
A282414: 1 2 7 0 31 0 127 0 511 0 2047 0 8191 0 32767 0
(1 + loop(\(x,i).((x + 1) + (if (~x + 2) <= 0 then x else 2)),(x div 2),(x mod 2)))
A191535-A100598: 1 2 4 5 8 10
A094958: 1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320
(1 + loop(\(x,i).((x + 1) * (2 + (if x <= 0 then 1 else 2))),(x div 2),(x mod 2)))
A136326: 1 2 4 9 17 37 69 149 277 597 1109 2389 4437 9557 17749 38229
(1 + loop(\(x,i).(2 + (if x <= 0 then 1 else 4x)),(x div 2),(x mod 2)))
A136336: 1 2 4 7 15 27 59 107 235 427 939 1707 3755 6827 15019 27307
(~1 + loop(\(x,i).2x,x,1) - loop(\(x,i).2x,(x div 2),(x mod 2)))
A274638: 0 0 3 5 15 27 63 119 255 495 1023 2015 4095 8127 16383 32639
(1 + loop(\(x,i).(x + (2 * (1 + (if x <= 0 then 2 else x)))),(x div 2),(x mod 2)))
A072985: 1 2 7 6 21 18 63 54 189 162 567 486 1701 1458 5103 4374
((if x <= 0 then 1 else (2 + (if (x mod 3) <= 0 then 2 else 1))) div (1 + (x mod 2)))
A220128: 1 1 3 2 3 1 4 1 3 2 3 1 4 1 3 2
loop(\(x,i).(2x + (if (x + ~3) <= 0 then x else 0)),x,(1 + (x mod 2)))
A084431: 1 6 9 24 36 96 144 384 576 1536 2304 6144 9216 24576 36864 98304
(loop(\(x,i).2x,x,1) - loop(\(x,i).2x,(x div 2),(~1 + (x mod 2))))
A052957: 2 2 6 8 20 32 72 128 272 512 1056 2048 4160 8192 16512 32768
((x + 1) - (2 * loop(\(x,i).(x - (if (~x + i) <= 0 then (2 * i) else 0)),x,x)))
A020703: 1 4 3 2 9 8 7 6 5 16 15 14 13 12 11 10
(1 + (2 * loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x)))
A073310-A060266: 1 1 1 3 1 1 3 1 1 3 1 5 3 1 1 5
loop(\(x,i).(x * (x + (x div 2))),1,(1 + loop(\(x,i).3x,x,2)))
A169725: 12 70 532 4510 39772 355510 3192292 28708750 258313132 2324621350 20921001652 188287243390 1694579876092 15251202941590 137260778644612 1235346864312430
loop(\(x,i).(2 + (i div 2)),(loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2),1)
A020651: 1 1 2 1 3 2 3 1 4 3 4 2 5 3 5 1
(1 + (2 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,x),x)))
A191108: 1 5 13 17 37 41 49 53 109 113 121 125 145 149 157 161
(1 + (2 * compr(\x.loop(\(x,i).(if (x mod 4) <= 0 then x else (x div 2)),x,x),x)))
A247648: 1 3 5 7 11 13 15 21 23 27 29 31 43 45 47 53
(if (x + ~2) <= 0 then x else (1 + (if (x mod 12) <= 0 then 0 else x)))
A138083: 0 1 2 4 5 6
A004722: 0 1 2 4 5 6 7 8 9 10 11 12 1 14 15 16
loop(\(x,i).(x * i),(x + loop(\(x,i).(2x + 1),(x + ~3),0)),1)
A060001: 1 1 2 6 120 40320 6227020800 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(10x + (if (~x + 2) <= 0 then 1 else 0)),x,1)
A283508-A267623: 1 10 101 1011 10111 101111 1011111 10111111 101111111 1011111111 10111111111 101111111111 1011111111111 10111111111111 101111111111111 1011111111111111
(if x <= 0 then 0 else (1 + (if ((x + ~1) mod 10) <= 0 then 0 else x)))
A004721: 0 1 3 4 5 6 7 8 9 10 11 1 13 14 15 16
loop(\(x,i).(2x - (if (x mod 4) <= 0 then (x div 4) else 0)),x,1)
A018254: 1 2 4 7 14 28
A018330: 1 2 4 7 14 28 49 98 196
((x + 1) + loop(\(x,i).(x2 + x),1,loop(\(x,i).(2x + i),x,0)))
A302761: 1 4 23 136 707 3312 14527 61264 252515 1027192 4147343 16674984 66887875 267960544 1072726271 4292804896
loop(\(x,i).(4x - (x div (1 + (if (i mod 2) <= 0 then 2 else 0)))),x,1)
A018413: 1 3 11 33 121 363
loop(\(x,i).(13 - (if (~x + i) <= 0 then 0 else 1)),x,1)
A112126: 1 13 13 13 13 13 13 13 13 13 13 13 13 13 12 12
loop(\(x,i).~x,x,loop(\(x,i).((2x + 1) - (x mod 3)),x,1))
A078043: 1 ~2 3 ~7 14 ~27 55 ~110 219 ~439 878 ~1755 3511 ~7022 14043 ~28087
(1 + (x * loop(\(x,i).x2,1,(~1 + loop(\(x,i).(x * i),x,3)))))
A111340: 1 5 51 868
loop(\(x,i).(4x mod loop(\(x,i).3x,(1 + i),1)),x,1)
A073533: 1 4 16 64 13 52 208 832 3328 13312 53248 212992 851968 3407872 13631488 11479231
(x - loop(\(x,i).2x,loop(\(x,i).i,(x + ~9),x),1))
A328882: ~1 ~1 ~2 ~5 ~12 ~27 ~58 ~121 ~248 ~503 8 7 4 ~3 ~18 ~49
loop(\(x,i).(~1 + (2 * (4x + loop(\(x,i).2x,i,1)))),x,1)
A016203: 1 11 95 775 6231 49911 399415 3195575 25565111 204521911 1636177335 13089422775 104715390391 837723139511 6701785148855 53614281256375
loop(\(x,i).2x,x,loop(\(x,i).(1 + (4 * ((x * i) div 2))),x,1))
A296660: 1 2 20 232 3728 74528 1788736 50084480 1602703616 57697329664 2307893187584 101547300251648 4874270412083200 253462061428318208 4611686018427387903 4611686018427387903
loop(\(x,i).(5 * (x + loop(\(x,i).2x,(~1 + i),1))),x,1)
A083585: 1 10 60 320 1640 8280 41560 208120 1041240 5207480 26039960 130204920 651034840 3255194680 16276014360 81380153720
loop(\(x,i).3x2,1,loop(\(x,i).(4x + 1),x,1))
A060869: 3 75 1323 21675 348843 5589675 89467563 1431612075 22906317483 366503176875 5864059218603 93824981052075 1501199831050923 24019197833685675 384307167486454443 4611686018427387903
loop(\(x,i).(4x + ~1),x,loop(\(x,i).(4x + 1),x,1))
A345963: 1 19 331 5419 87211 1397419 22366891 357903019 5726579371 91625794219 1466014804651 23456245263019 375299957762731 6004799458421419 96076791871613611 1537228672093301419
loop(\(x,i).6x,x,loop(\(x,i).(4x + 1),x,1))
A089507: 1 30 756 18360 441936 10614240 254788416 6115201920 146766525696 3522406694400 84537821131776 2028908069959680 48693795855814656 1168651113600245760 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + 2),x,loop(\(x,i).(4x + 1),x,1))
A096047: 1 22 346 5482 87466 1398442 22370986 357919402 5726644906 91626056362 1466015853226 23456249457322 375299974539946 6004799525530282 96076792140049066 1537228673167043242
loop(\(x,i).4x,x2,loop(\(x,i).(4x + 1),x,1))
A088852: 1 20 5376 22282240 1464583847936 1536853372840181760 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((5x + ~1) + loop(\(x,i).2x,i,2)),x,1)
A016198: 1 8 47 250 1281 6468 32467 162590 813461 4068328 20343687 101722530 508620841 2543120588 12715635707 63578244070
loop(\(x,i).(x * i),x,loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),x,1))
A082491: 1 0 2 12 216 5280 190800 9344160 598066560 48443028480 4844306476800 586161043776000 84407190782745600 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3 * (2x - loop(\(x,i).(~2x + 2),i,0))),x,1)
A091054: 1 0 6 18 138 762 4698 27930 168090 1007514 6047130 36278682 217680282 1306065306 7836424602 47018482074
(~1 + (if x <= 0 then 1 else (x * loop(\(x,i).(x2 + ~2),3,3))))
A004931: 0 2206 4413 6620 8827 11034 13241 15448 17655 19862 22069 24276 26483 28690 30897 33104
loop(\(x,i).(6 * (2x + (x div (if i <= 0 then 1 else i)))),x,1)
A115903: 1 18 270 3780 51030 673596 8756748 112586760 1435481190 18182761740 229102797924 2874198737592 35927484219900 447711726432600 5564417171376600 68998772925069840
loop(\(x,i).(~6x + loop(\(x,i).4x,i,2)),x,1)
A083297: 1 2 20 8 464 ~736 12608 ~42880 388352 ~1805824 12932096 ~69203968 448778240 ~2558451712 15887581184 ~93178003456
loop(\(x,i).(7x + loop(\(x,i).2x,i,1)),x,1)
A016130: 1 9 67 477 3355 23517 164683 1152909 8070619 56494845 395464939 2768256621 19377800443 135644611293 949512295435 6646586100813
loop(\(x,i).(3 * (3x + (x div (if i <= 0 then 1 else i)))),x,1)
A004991: 1 12 126 1260 12285 117936 1120392 10563696 99034650 924323400 8596207620 79710288840 737320171770 6806032354800 62712726697800 576957085619760
loop(\(x,i).(6 * (2x - (x div (if i <= 0 then 1 else i)))),x,1)
A098658: 1 6 54 540 5670 61236 673596 7505784 84440070 956987460 10909657044 124965162504 1437099368796 16581915793800 191876454185400 2225766868550640
loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),3x,1)
A066802: 1 20 924 48620 2704156 155117520 9075135300 538257874440 32247603683100 1946939425648112 118264581564861424 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(3x + 1))
A016786: 1 1048576 282475249 10000000000 137858491849 1099511627776 6131066257801 26559922791424 95367431640625 296196766695424 819628286980801 2064377754059776 4808584372417849 10485760000000000
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(3x + 1))
A016788: 1 16777216 13841287201 1000000000000 23298085122481 281474976710656 2213314919066161 12855002631049216 59604644775390625 232218265089212416 787662783788549761 2386420683693101056 4611686018427387903
loop(\(x,i).(3 * (x + (4x div (if i <= 0 then 1 else i)))),x,1)
A036217: 1 15 135 945 5670 30618 153090 721710 3247695 14073345 59108049 241805655 967222620 3794488740 14635885140 55616363532
loop(\(x,i).(3 * (3x - (x div (if i <= 0 then 1 else i)))),x,1)
A004988: 1 6 45 360 2970 24948 212058 1817640 15677145 135868590 1182056733 10316131488 90266150520 791564704560 6954461332920 61199259729696
loop(\(x,i).x2,1,loop(\(x,i).(10x + 1),x,1))
A002477: 1 121 12321 1234321 123454321 12345654321 1234567654321 123456787654321 12345678987654321 1234567900987654321 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),x,loop(\(x,i).(10x + 1),x,1))
A323416: 1 11 222 6666 266664 13333320 799999920 55999999440 4479999995520 403199999959680 40319999999596800 4435199999995564800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (2 * (x + (x div (if (i mod 3) <= 0 then 1 else 2))))),x,1)
A018398: 1 3 9 37 111 333
(1 + compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)),x))
A053726: 5 8 11 13 14 17 18 20 23 25 26 28 29 32 33 35
(if x <= 0 then 1 else (1 + (((x2 + x) div 2) + (if (x mod 2) <= 0 then 1 else x))))
A266663: 1 3 5 10 12 21 23 36 38 55 57 78 80 105 107 136
loop(\(x,i).(1 + (if (x mod 2) <= 0 then (x div 2) else 5x)),x,1)
A082530: 1 6 4 3 16 9 46 24 13 66 34 18 10 6 4 3
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (5x + 1)),x,1)
A328011: 1 6 3 16 8 4 2 1 6 3 16 8 4 2 1 6
loop(\(x,i).3x,x2,loop(\(x,i).(3x + 1),x,1))
A088671: 1 12 1053 787320 5208653241 308413053837252 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),(x + 1),(1 + (x * loop(\(x,i).(1 + (x * i)),x,1))))
A262601: 1 6 66 1176 31320 1174320 59184720 3866728320 318176449920 32215365100800 3937433507884800 571715345296972800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (x * loop(\(x,i).x2,2,10))),x,1)
A330135: 1 10001 100010001 1000100010001 10001000100010001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + (x * (~2 + loop(\(x,i).(x3 + 2),2,2)))),x,1)
A261544: 1 1001 1001001 1001001001 1001001001001 1001001001001001 1001001001001001001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + loop(\(x,i).7x,(2 + i),x)),x,1)
A178191: 1 344 825945 13881657616 1633163136864785 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x * loop(\(x,i).(x2 + x),2,2)) + (2 div (x + 1))),x,1)
A170724-A170676-A170628-A170580-A170532-A170484-A170436-A170388-A170340-A170292-A170244-A170196-A170148-A170100-A170052-A170004-A169536-A169488-A169440-A169392-A169344-A169296-A169248-A169200-A169152-A169104-A169056-A169008-A168960-A168912-A168864-A168816-A168768-A168720-A167959-A167849-A167640-A167096-A166717: 1 43 1806 75852 3185784 133802928 5619722976 236028364992 9913191329664 416354035845888 17486869505527296 734448519232146432 4611686018427387903 4611686018427387903 4611686018427387903
A170762: 1 43 1806 75852 3185784 133802928 5619722976 236028364992 9913191329664 416354035845888 17486869505527296 734448519232146432 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 - loop(\(x,i).(x div 3),x,loop(\(x,i).((x + ~1) * (i * i)),x,1)))
A109132: 0 1 2 3 11 77
((x + 1) + loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,1))
A051743: 2 7 18 39 75 132 217 338 504 725 1012 1377 1833 2394 3075 3892
((~1 + loop(\(x,i).(2x * i),x,1)) div loop(\(x,i).(1 + (x * i)),x,1))
A293339: 0 0 1 2 5 11 23 47 94 188 376 753 1506 3013 6027 12054
loop(\(x,i).((5x * i) + loop(\(x,i).2x,i,1)),x,1)
A097821: 1 7 74 1118 22376 559432 16783024 587405968 23496238976 1057330754432 52866537722624 2907659574746368 174459574484786176 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((1 + (if (x mod (1 + i)) <= 0 then 0 else i)) * (1 + i))),x,1)
A192217: 1 4 36 144 3600 21600 1058400 8467200 76204800 762048000 92207808000 1106493696000 186997434624000 2617964084736000 39269461271040000 628311380336640000
loop(\(x,i).(1 + (loop(\(x,i).10x,2,x) + i)),x,1)
A030512: 1 102 10203 1020304 102030405 10203040506 1020304050607 102030405060708 10203040506070809 1020304050607080910 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).~4x,x,1))
A090407: 1 6 136 2016 32896 523776 8390656 134209536 2147516416 34359607296 549756338176 8796090925056 140737496743936 2251799780130816 36028797153181696 576460751766552576
loop(\(x,i).(2x2 + ~x),1,loop(\(x,i).~4x,x,1))
A090408: 1 36 496 8256 130816 2098176 33550336 536887296 8589869056 137439215616 2199022206976 35184376283136 562949936644096 9007199321849856 144115187807420416 2305843010287435776
(x div (if (x mod 2) <= 0 then (if (x mod 7) <= 0 then 2 else x) else 1))
A340086: 0 1 1 3 1 5 1 7 1 9 1 11 1 13 7 15
((x + 1) + (if x <= 0 then 0 else (2 + (if (x + ~2) <= 0 then x else 5))))
A275645: 1 5 7 11 12 13 14 15 16 17 18 19 20 21 22 23
loop(\(x,i).x3,1,((x + 1) + (if (~2 + (x div 2)) <= 0 then 1 else 2)))
A100571: 8 27 64 125 216 343 729 1000 1331 1728 2197 2744 3375 4096 4913 5832
loop(\(x,i).(2x + ~1),(x + ~1),loop(\(x,i).(2x + 6),x,1))
A171479: 1 8 43 197 841 3473 14113 56897 228481 915713 3666433 14672897 58705921 234852353 939466753 3757981697
loop(\(x,i).(5x + 2),2,loop(\(x,i).(2x + 2),x,1))
A304612: 37 112 262 562 1162 2362 4762 9562 19162 38362 76762 153562 307162 614362 1228762 2457562
(loop(\(x,i).(4x + 4),x,2) - loop(\(x,i).(2x + 2),x,1))
A171478: 1 8 42 190 806 3318 13462 54230 217686 872278 3492182 13974870 55911766 223671638 894735702 3579041110
(loop(\(x,i).(3x + 2),x,2) - loop(\(x,i).(2x + 2),x,1))
A168583: 1 4 16 58 196 634 1996 6178 18916 57514 174076 525298 1582036 4758394 14299756 42948418
(1 + loop(\(x,i).(x - ((loop(\(x,i).(x * i),x,x) mod (x + 1)) mod 2)),2,x))
A179278: 1 1 1 4 4 6 6 8 9 10 10 12 12 14 15 16
(if x <= 0 then 0 else (~1 + (x * (~2 + loop(\(x,i).(x2 + 4x + 4),2,2)))))
A004927: 0 321 643 965 1287 1609 1931 2253 2575 2897 3219 3541 3863 4185 4507 4829
(1 + loop(\(x,i).(if x <= 0 then 1 else (((x + 1) * (x div 2)) mod 4)),2,x))
A186187: 1 2 1 2 4 2 1 2 2 2 1 2 4 2 1 2
loop(\(x,i).(8 * (2x - (x div (if i <= 0 then 1 else i)))),x,1)
A098430: 1 8 96 1280 17920 258048 3784704 56229888 843448320 12745441280 193730707456 2958796259328 45368209309696 697972450918400 10768717814169600 166556168859156480
loop(\(x,i).(x - (2 * (~4x + loop(\(x,i).2x,i,1)))),x,1)
A176818: 1 5 37 317 2821 25325 227797 2049917 18448741 166037645 1494336757 13449026717 121041232261 1089371073965 9804339632917 88239056630717
loop(\(x,i).(8x + (if (i mod 3) <= 0 then 1 else 0)),x,1)
A033144: 1 8 64 513 4104 32832 262657 2101256 16810048 134480385 1075843080 8606744640 68853957121 550831656968 4406653255744 35253226045953
loop(\(x,i).(8x + loop(\(x,i).3x,i,1)),x,1)
A016140: 1 11 97 803 6505 52283 418993 3354131 26839609 214736555 1717951489 13743789059 109950843913 879608345627 7036871547985 56294986732787
loop(\(x,i).(8x + (if (i mod 3) <= 0 then 1 else 2)),x,1)
A037549: 1 10 82 657 5258 42066 336529 2692234 21537874 172302993 1378423946 11027391570 88219132561 705753060490 5646024483922 45168195871377
loop(\(x,i).(x div 5),x,loop(\(x,i).8x,x,1))
A094985: 1 1 2 4 6 10 16 26 42 68 109 175 281 450 720 1152
loop(\(x,i).(4 * (x + (2 * (2x div (if i <= 0 then 1 else i))))),x,1)
A040075: 1 20 240 2240 17920 129024 860160 5406720 32440320 187432960 1049624576 5725224960 30534533120 159719096320 821412495360 4161823309824
loop(\(x,i).(4 * (x + (3x div (if i <= 0 then 1 else i)))),x,1)
A038846: 1 16 160 1280 8960 57344 344064 1966080 10813440 57671680 299892736 1526726656 7633633280 37580963840 182536110080 876173328384
loop(\(x,i).(loop(\(x,i).3x,i,1) + (4x * i)),x,1)
A274823: 1 7 65
A097819: 1 7 65 807 12993 260103 6243201 174811815 5593984641 201383466759 8055338729409 354434904271143 17012875405546305 884669521090002183 4611686018427387903 4611686018427387903
loop(\(x,i).(4 * (4x - (x div (if i <= 0 then 1 else i)))),x,1)
A216702: 1 12 168 2464 36960 561792 8614144 132903936 2060011008 32044615680 499896004608 7816555708416 122459372765184 1921670157238272 30197673899458560 475110069351481344
loop(\(x,i).(4x + (if (x mod 2) <= 0 then (x div 4) else 0)),x,1)
A096881: 1 4 17 68 289 1156 4913 19652 83521 334084 1419857 5679428 24137569 96550276 410338673 1641354692
loop(\(x,i).(~4x + loop(\(x,i).3x,(~1 + i),1)),x,1)
A166035: 1 ~3 15 ~51 231 ~843 3615 ~13731 57111 ~221883 907215 ~3569811 14456391 ~57294123 230770815 ~918300291
loop(\(x,i).(4x + loop(\(x,i).(3x + 1),i,1)),x,1)
A016208: 1 8 45 220 1001 4368 18565 77540 320001 1309528 5326685 21572460 87087001 350739488 1410132405 5662052980
loop(\(x,i).(4x + loop(\(x,i).((2x + 1) + i),i,1)),x,1)
A227209: 1 8 43 198 849 3516 14311 57746 231997 930024 3724179 14904894 59635945 238576532 954371647 3817617642
loop(\(x,i).(4x + loop(\(x,i).(~3x + 1),i,1)),x,1)
A249997: 1 2 15 40 221 702 3355 11780 52041 193402 817895 3138720 12953461 50618102 206059635 813476860
loop(\(x,i).(~4x + loop(\(x,i).5x,i,1)),x,1)
A053428: 1 1 21 41 461 1281 10501 36121 246141 968561 5891381 25262601 143090221 648342241 3510146661 16476991481
(loop(\(x,i).3x,2x,1) + loop(\(x,i).4x,x,1))
A074614: 2 13 97 793 6817 60073 535537 4799353 43112257 387682633 3487832977 31385253913 282446313697 2541932937193 22877060890417 205892205836473
(loop(\(x,i).3x,2x,1) - loop(\(x,i).4x,x,1))
A118004: 0 5 65 665 6305 58025 527345 4766585 42981185 387158345 3485735825 31376865305 282412759265 2541798719465 22876524019505 205890058352825
(loop(\(x,i).3x,2x,1) mod loop(\(x,i).4x,x,1))
A139729: 0 1 1 25 161 681 3057 15225 55105 233801 269201 3471385 1882337 50495465 186023729 63600825
loop(\(x,i).(4x2 + ~x),1,loop(\(x,i).4x,x,1))
A115490: 3 60 1008 16320 261888 4193280 67104768 1073725440 17179803648 274877644800 4398045462528 70368739983360 1125899890065408 18014398442373120 288230375883276288 4611686017353646080
(loop(\(x,i).6x,x,1) + loop(\(x,i).4x,x,1))
A074612: 2 10 52 280 1552 8800 50752 296320 1745152 10339840 61514752 366991360 2193559552 13127802880 78632599552 471258726400
(loop(\(x,i).6x,x,1) - loop(\(x,i).4x,x,1))
A248337: 0 2 20 152 1040 6752 42560 263552 1614080 9815552 59417600 358602752 2160005120 12993585152 78095728640 469111242752
(loop(\(x,i).6x,x,1) mod loop(\(x,i).4x,x,1))
A138611: 0 2 4 24 16 608 1600 1408 41216 116224 697344 2086912 12521472 41574400 249446400 959807488
(loop(\(x,i).~3x,x,1) + loop(\(x,i).4x,x,1))
A087452: 2 1 25 37 337 781 4825 14197 72097 242461 1107625 4017157 17308657 65514541 273218425 1059392917
(loop(\(x,i).5x,x,1) + loop(\(x,i).4x,x,1))
A074611: 2 9 41 189 881 4149 19721 94509 456161 2215269 10814201 53022429 260917841 1287811989 6371951081 31591319949
(loop(\(x,i).5x,x,1) - loop(\(x,i).4x,x,1))
A005060: 0 1 9 61 369 2101 11529 61741 325089 1690981 8717049 44633821 227363409 1153594261 5835080169 29443836301
(loop(\(x,i).5x,x,1) mod loop(\(x,i).4x,x,1))
A138589: 0 1 9 61 113 53 3337 12589 62945 118117 328441 2690781 9259601 12743573 197935593 452807053
(loop(\(x,i).3x,x,4) + loop(\(x,i).4x,x,1))
A147536: 5 16 52 172 580 1996 7012 25132 91780 340876 1284772 4902892 18902980 73486156 287567332 1131137452
(loop(\(x,i).6x,x,2) - loop(\(x,i).4x,x,1))
A081626: 1 8 56 368 2336 14528 89216 543488 3293696 19893248 119883776 721399808 4336787456 26054279168 156459892736 939296227328
(loop(\(x,i).5x,x,2) - loop(\(x,i).4x,x,1))
A085351: 1 6 34 186 994 5226 27154 139866 715714 3644106 18482674 93461946 471504034 2374297386 11938595794 59961414426
loop(\(x,i).(5x + (if (i mod 3) <= 0 then 1 else 0)),x,1)
A033141: 1 5 25 126 630 3150 15751 78755 393775 1968876 9844380 49221900 246109501 1230547505 6152737525 30763687626
loop(\(x,i).(5x + (if (i mod 3) <= 0 then 1 else 2)),x,1)
A037546: 1 7 37 186 932 4662 23311 116557 582787 2913936 14569682 72848412 364242061 1821210307 9106051537 45530257686
loop(\(x,i).(5x + loop(\(x,i).~2x,i,2)),x,1)
A320469: 1 1 13 49 277 1321 6733 33409 167557 836761 4185853 20925169 104634037 523153801 2615801773 13078943329
loop(\(x,i).(4x + loop(\(x,i).4x,(~1 + i),i)),x,1)
A327999: 1 5 28 160 896 4864 25600 131072 655360 3211264 15466496 73400320 343932928 1593835520 7314866176 33285996544
loop(\(x,i).(2 * (2x + (3x div (if i <= 0 then 1 else i)))),x,1)
A002802: 1 10 70 420 2310 12012 60060 291720 1385670 6466460 29745716 135207800 608435100 2714556600 12021607800 52895074320
(1 + loop(\(x,i).(if (x mod 2) <= 0 then (3x + 3) else (x div 2)),2,x))
A075884: 2 4 5 1 8 10 11 2 14 16 17 3 20 22 23 4
(loop(\(x,i).2x,x,1) - loop(\(x,i).(x - (x div (~2 + (x mod 2)))),x,1))
A167762: 0 0 1 2 7 14 37 74 175 350 781 1562 3367 6734 14197 28394
((x + 1) - loop(\(x,i).(x + (if (x mod (1 + (2 * i))) <= 0 then i else 0)),2,x))
A005590: 0 1 1 0 1 ~1 0 1 1 ~2 ~1 1 0 1 1 0
((x + ~1) + (2 * (if (if (x mod 8) <= 0 then x else 0) <= 0 then 1 else x)))
A269357-A269355: 1 2 3 4 5 6 7 8 23 10 11 12 13 14 15 16
loop(\(x,i).(x2 + ~x),1,loop(\(x,i).10x,x,1))
A276352: 0 90 9900 999000 99990000 9999900000 999999000000 99999990000000 9999999900000000 999999999000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + 2x),1,loop(\(x,i).10x,x,1))
A134230: 3 120 10200 1002000 100020000 10000200000 1000002000000 100000020000000 10000000200000000 1000000002000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 3),x,loop(\(x,i).10x,x,1))
A094977: 1 3 11 37 123 411 1371 4572 15241 50805 169350 564502 1881676 6272254 20907515 69691719
(~1 + loop(\(x,i).loop(\(x,i).i,((x + 1) mod 10),x),2,x))
A138718: 1 2 3 4 5 6 7 8 8 8 1 2 3 4 5 6
loop(\(x,i).(2 * (x + (8 * (x div (if i <= 0 then 1 else i))))),x,1)
A140325: 1 18 180 1320 7920 41184 192192 823680 3294720 12446720 44808192 154791936 515973120 1666990080 5239111680 16066609152
((~x + ~1) + loop(\(x,i).(2 * (x + loop(\(x,i).3x,i,1))),x,2))
A094616: 1 8 35 126 417 1324 4111 12602 38333 116040 350187 1054678 3172249 9533156 28632263 85962354
(loop(\(x,i).4x,x,1) - loop(\(x,i).(2 * (x + (x div 2))),x,1))
A080643: 0 2 10 46 202 862 3610 14926 61162 249022 1009210 4076206 16422922 66045982 265246810 1064175886
((~x + ~1) + loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,2))
A134759: 1 2 9 36 135 498 1841 6856 25731 97230 369501 1410852 5408299 20801186
loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),1)
A135620: 1 2 8 32 512 2048 32768 131072 2097152 134217728 536870912 34359738368 549755813888 2199023255552 35184372088832 2251799813685248
(1 + (if x <= 0 then 2 else compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A039915: 3 2 4 6 10 12 16 18 22 28 30 36 40 42 46 52
loop(\(x,i).(2x + (if (x mod (2 + ((x * i) mod 2))) <= 0 then 1 else 0)),x,1)
A172411: 1 2 5 10
A266248: 1 2 5 10 21 43 86 173 346 693 1386 2773 5546 11093 22186 44373
loop(\(x,i).(2x + (if (x mod 4) <= 0 then ((x + 1) * i) else 0)),x,1)
A018279: 1 2 4 23 46 92
loop(\(x,i).(2x + loop(\(x,i).3x,((1 + i) div 2),1)),x,1)
A167710: 1 5 13 35 79 185 397 875 1831 3905 8053 16835 34399 70985 144157 294875
loop(\(x,i).(2x + loop(\(x,i).3x,(~2 + (2 * i)),1)),x,1)
A109498: 1 3 15 111 951 8463 75975 683391 6149751 55346223 498112935 4483010271 40347080151 363123696783 3268113221895 29413018898751
loop(\(x,i).(2x + (3 * (x + (if (x + ~1) <= 0 then 2 else 1)))),x,1)
A073720: 1 11 58 293 1468 7343 36718 183593 917968 4589843 22949218 114746093 573730468 2868652343 14343261718 71716308593
(loop(\(x,i).(~2x + ~4),x,1) * loop(\(x,i).(~2x + 1),x,1))
A255471: 1 6 24 100 396 1596 6364 25500 101916 407836 1631004 6524700 26097436 104392476 417564444 1670268700
loop(\(x,i).(2x + loop(\(x,i).((3x + 1) + i),i,1)),x,1)
A249999: 1 7 32 122 423 1389 4414 13744 42245 128771 390396 1179366 3554467 10696153 32153978 96592988
loop(\(x,i).(2x + loop(\(x,i).(2 * (x + (3 * i))),i,1)),x,1)
A271638: 1 10 48 170 512 1398 3580 8770 20808 48206 109652 245850 544864 1196134 2605164 5636210
loop(\(x,i).(~2x + loop(\(x,i).7x,i,1)),x,1)
A053573: 1 5 39 265 1871 13065 91519 640505 4483791 31386025 219703199 1537920345 10765446511 75358117385 527506838079 3692547833785
loop(\(x,i).(2x + ((x - (if (i mod 4) <= 0 then x else 1)) mod 2)),x,1)
A172411: 1 2 5 10
A266613: 1 2 5 10 20 41 82 165 330 661 1322 2645 5290 10581 21162 42325
loop(\(x,i).(x - (x mod 9)),1,loop(\(x,i).2x,x,1))
A153237: 0 0 0 0 9 27 63 126 252 504 1017 2043 4095 8190 16380 32760
loop(\(x,i).((x + ~1) * (x2 - (x div 2))),1,loop(\(x,i).2x,x,1))
A160873: 0 3 42 420 3720 31248 256032 2072640 16679040 133824768 1072169472 8583644160 68694312960 549655154688 4397643866112 35182761492480
(loop(\(x,i).(x2 + (x div 2)),2,3) - loop(\(x,i).2x,x,1))
A286812: 104 103 101 97 89 73 41 ~23 ~151 ~407 ~919 ~1943 ~3991 ~8087 ~16279 ~32663
(loop(\(x,i).(x3 + x),2,3) mod loop(\(x,i).2x,x,1))
A320916: 0 0 2 6 6 22 22 22 150 406 406 406 2454 2454 10646 27030
loop(\(x,i).((x2 + 5x) div 2),1,loop(\(x,i).2x,x,1))
A256873: 3 7 18 52 168 592 2208 8512 33408 132352 526848 2102272 8398848 33574912 134258688 536952832
loop(\(x,i).((x + (x2 div 3)) div 2),1,loop(\(x,i).2x,x,1))
A076024: 0 1 4 14 50 186 714 2794 11050 43946 175274 700074 2798250 11188906 44747434 178973354
(loop(\(x,i).2x,(x div 2),(~1 + (x mod 2))) + loop(\(x,i).2x,x,1))
A079242: 0 2 2 8
A014236: 0 2 2 8 12 32 56 128 240 512 992 2048 4032 8192 16256 32768
loop(\(x,i).((x * (x + (x mod 3))) div 2),1,loop(\(x,i).2x,x,1))
A032121: 1 4 10 40 136 544 2080 8320 32896 131584 524800 2099200 8390656 33562624 134225920 536903680
(loop(\(x,i).((3x + 1) - i),x,1) - loop(\(x,i).2x,x,1))
A263622: 0 1 4 14 47 153 486 1516 4669 14255 43268 130818 394491 1187557 3570850 10728920
(loop(\(x,i).7x,x,1) + loop(\(x,i).2x,x,1))
A074602: 2 9 53 351 2417 16839 117713 823671 5765057 40354119 282476273 1977328791 13841291297 96889018599 678223089233 4747561542711
(loop(\(x,i).7x,x,1) - loop(\(x,i).2x,x,1))
A190540: 0 5 45 335 2385 16775 117585 823415 5764545 40353095 282474225 1977324695 13841283105 96889002215 678223056465 4747561477175
(loop(\(x,i).7x,x,1) mod loop(\(x,i).2x,x,1))
A138616: 0 1 1 7 1 7 17 119 193 327 753 1175 2081 6375 3665 9271
loop(\(x,i).(1 + (x2 div 2) - (x mod 2)),2,loop(\(x,i).2x,x,1))
A092812: 1 4 40 544 8320 131584 2099200 33562624 536903680 8590065664 137439477760 2199025352704 35184380477440 562949986975744 9007199388958720 144115188612726784
(4 + (loop(\(x,i).3x,x,1) + loop(\(x,i).2x,x,1)))
A229354: 6 9 17 39 101 279 797 2319 6821 20199 60077 179199 535541 1602519 4799357 14381679
(loop(\(x,i).(6x + ~1),x,2) - loop(\(x,i).2x,x,1))
A016200: 1 9 61 381 2317 13965 83917 503757 3023053 18139341 108838093 653032653 3918204109 23509241037 141055478989 846332939469
((2 * loop(\(x,i).3x,(x + ~1),x)) + loop(\(x,i).2x,x,1))
A084859: 1 4 16 62 232 842 2980 10334 35248 118610 394684 1301126 4255624 13825658 44657428 143521838
((if x <= 0 then 0 else (6x + 8)) + loop(\(x,i).2x,x,1))
A100316: 1 16 24 34 48 70 108 178 312 574 1092 2122 4176 8278 16476 32866
loop(\(x,i).(x * (i * i)),(2x2 + ~x),loop(\(x,i).2x,x,1))
A272238: 1 2 2073600 4611686018427387903 4611686018427387903
(1 + compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),x))
A236246-A003278: 1 2 4 5 10 11 13 14 28 29 31 32 37 38 40 41
loop(\(x,i).~3x,x,loop(\(x,i).(~3x + 1),x,1))
A053535: 1 6 63 540 4941 44226 398763 3586680 32286681 290560446 2615103063 23535750420 211822285221 1906398972666 17157595536963 154418345483760
((x + 1) + loop(\(x,i).(x - (if x <= 0 then 1 else (2 * (1 + i)))),x,2x))
A127948: 1 0 2 ~1 1 3 ~2 0 2 4 ~3 ~1 1 3 5 ~4
(1 + compr(\x.loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,2x),x))
A104275: 1 5 8 11 13 14 17 18 20 23 25 26 28 29 32 33
(loop(\(x,i).(3x + 1),x,3) - (if (x mod 2) <= 0 then x else 1))
A195624: 3 9 29 93 279
loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).(x2 + (x mod 2)),x,1))
A188545: 1 3 10
A056006: 1 3 10 136 32896 2147516416
loop(\(x,i).(2 * (x + (6x div (if i <= 0 then 1 else i)))),x,1)
A002409: 1 14 112 672 3360 14784 59136 219648 768768 2562560 8200192 25346048 76038144 222265344 635043840 1778122752
loop(\(x,i).(2 * (x + (5x div (if i <= 0 then 1 else i)))),x,1)
A054849: 1 12 84 448 2016 8064 29568 101376 329472 1025024 3075072 8945664 25346048 70189056 190513152 508035072
loop(\(x,i).(2 * (loop(\(x,i).(x * (~1 + (2 * i))),i,1) + (x * i))),x,1)
A000779: 1 4 22 162 1506 16950 224190 3408930 58596930 1123663590 23782729950 550718680050 13849716607650 375904338960150 10952237584237950 340947694234397250
loop(\(x,i).(2 * (8x - (x div (if i <= 0 then 1 else i)))),x,1)
A097183: 1 14 210 3220 49910 778596 12198004 191682920 3019005990 47633205620 752604648796 11904837171864 188493255221180 2986893121197160 47363590921840680 751502309293205456
loop(\(x,i).(~x + 2),(1 + (x div 2)),((x + 1) * (if (x mod 2) <= 0 then 2 else 0)))
A267314: 0 2 6 0 ~8 2 14 0 ~16 2 22 0 ~24 2 30 0
((1 + loop(\(x,i).(if x <= 0 then (2 * i) else (x - (i mod 2))),x,0)) mod (x + 1))
A065052: 0 1 0 2 2 1 6 4 3 1 0 10 10 9 9 8
(loop(\(x,i).(x * i),(x + ~2),(2x - (if x <= 0 then 0 else 1))) div (x + 1))
A330346: 0 0 1 1 2 9 37
(loop(\(x,i).2x,(loop(\(x,i).2x,x,2) mod (x + 1)),1) mod (x + 1))
A180060: 0 1 1 1 4 4 4 1 4 6 4 4 4 2 1 1
(loop(\(x,i).(x + (if (x mod 2) <= 0 then (x div 2) else 1)),(x + ~1),1) div (x + 1))
A017844: 1 0 0 0 0 1 1 1 1 1 2 3 4 5 5 7
((~x + ~1) + loop(\(x,i).(x + loop(\(x,i).(2 * i),(~2 + i),x)),(x + ~1),1))
A305559: 0 ~1 ~1 0 1 4 9 16 25 36 49 64 81 100 121 144
(loop(\(x,i).loop(\(x,i).12x,x,1),2,1) div (x + 1))
A057074: 8916100448256 4458050224128 2972033482752 2229025112064 1783220089651 1486016741376 1273728635465 1114512556032 990677827584 891610044825 810554586205 743008370688 685853880635 636864317732 594406696550
(loop(\(x,i).loop(\(x,i).10x,x,1),2,1) div (x + 1))
A057072: 10000000000 5000000000 3333333333 2500000000 2000000000 1666666666 1428571428 1250000000 1111111111 1000000000 909090909 833333333 769230769 714285714 666666666 625000000
(1 - ((x + 1) * loop(\(x,i).(x - loop(\(x,i).(x * i),(~1 + i),1)),x,1)))
A014145: 0 1 4 13 46 199 1072 6985 53218 462331 4500244 48454957 571411270 7321388383 101249656696 1502852293009
(2 - ((x + 1) * loop(\(x,i).(x - loop(\(x,i).(x * i),(~1 + i),1)),x,1)))
A129867: 1 2 5 14 47 200 1073 6986 53219 462332 4500245 48454958 571411271 7321388384 101249656697 1502852293010
loop(\(x,i).2x,x,((x + 1) * loop(\(x,i).(x * i),3x,1)))
A065142: 1 24 8640 11612160 38320128000 251073478656000 2868263420166144000 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x - ((~x + (x div (if i <= 0 then 1 else i))) div 2)),x,1) div (x + 1))
A017898: 1 0 0 0 1 1 1 1 2 3 4 5 7 10 14 19
loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),(x + 1),(x + 1))
A000911: 6 60 420 2520 13860 72072 360360 1750320 8314020 38798760 178474296 811246800 3650610600 16287339600 72129646800 317370445920
((x + 1) * loop(\(x,i).(2x + (if (2 - i) <= 0 then x else 1)),x,(x + 1)))
A077616: 1 10 63 324 1485 6318 25515 99144 373977 1377810 4979799 17714700 62178597 215765046 741360195 2525407632
((x + 1) * loop(\(x,i).(x + loop(\(x,i).(2 * (x + i)),(1 + i),1)),x,1))
A287992: 1 26 129 444 1285 3366 8281 19544 44829 100770 223201 488916 1061749 2289854 4910505 10480176
(loop(\(x,i).(loop(\(x,i).(x * i),i,1) + (x * (1 + i))),x,1) div (x + 1))
A180589: 1 1 3 12 54 294 1866 13698 114064 1062864 10958530 123870240 1523289156 20247546240 289277533440 4420892649600
((x + 1) * loop(\(x,i).loop(\(x,i).2x,(x + ~2),(3 * i)),x,1))
A175719-A173604: 1 6 36 36864
((x + 1) + (loop(\(x,i).loop(\(x,i).(x + ((i * i) div 2)),i,x),x,1) div 2))
A222011: 1 2 4 8
A271480: 1 2 4 8 16 30 53 88 139 210 306 432 594 798 1051 1360
((3x + 5) + loop(\(x,i).(if x <= 0 then i else (x + ~1)),x,0))
A171763: 5 9 11 17 19 21 23 33 35 37 39 41 43 45 47 65
compr(\x.loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,2x),(x + 1))
A153238: 3 6 9 11 12 15 16 18 21 23 24 26 27 30 31 33
(loop(\(x,i).4x,x,4) mod loop(\(x,i).x2,2,(x + 1)))
A066608: 0 0 64 0 399 208 1978 0 6265 8576 6978 1792 19075 22864 36199 0
(1 - loop(\(x,i).(x - (if x <= 0 then 1 else (x div (1 + (x mod 2))))),x,(x + 1)))
A093048: 0 1 1 3 2 5 5 7 5 9 9 11 10 13 13 15
((if (x mod 2) <= 0 then loop(\(x,i).(3x + 4),x,1) else x) mod (x + 1))
A197943: 0 1 1 3 1 5 1 7 7 9 1 11 1 13 10 15
loop(\(x,i).(5x + (if (2 - i) <= 0 then x else 1)),x,(x + 1))
A081041: 1 11 96 756 5616 40176 279936 1912896 12877056 85660416 564350976 3688436736 23944605696 154551545856 992612745216 6347497291776
compr(\x.loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 0 else 2))),x,x),(x + 1))
A032924: 1 2 4 5 7 8 13 14 16 17 22 23 25 26 40 41
loop(\(x,i).(x + (5 * (if (2 - i) <= 0 then x else 1))),x,(x + 1))
A081106: 1 7 48 324 2160 14256 93312 606528 3919104 25194240 161243136 1027924992 6530347008 41358864384 261213880320 1645647446016
((x + 1) + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,x))
A089080: 1 2 3 2 4 2 3 2 5 2 3 2 4 2 3 2
((x + 1) * loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,x))
A119579: 0 4 36 240 1400 7560 38808 192192 926640 4375800 20323160 93117024 421848336 1892909200 8424486000 37228204800
compr(\x.loop(\(x,i).(if (x mod (1 + (2 * i))) <= 0 then x else ~x),x,x),(x + 1))
A053869: 1 6 9 10 12 14 20 22 24 25 26 28 30 34 38 40
compr(\x.(x + loop(\(x,i).(x - (if (x mod (2 + i)) <= 0 then 1 else 2)),x,x)),(x + 1))
A086304: 1 5 7 11 13 17 23 25 31 35 37 41 47 53 55 61
loop(\(x,i).(x + (6x div (if i <= 0 then 1 else i))),x,(x + 1))
A027818: 1 14 84 336 1050 2772 6468 13728 27027 50050 88088 148512 241332 379848 581400 868224
loop(\(x,i).(x + (8x div (if i <= 0 then 1 else i))),x,(x + 1))
A056003: 1 18 135 660 2475 7722 21021 51480 115830 243100 481338 906984 1637610 2848860 4796550 7845024
loop(\(x,i).(x + (5x div (if i <= 0 then 1 else i))),x,(x + 1))
A051922: 1 12 63 224 630 1512 3234 6336 11583 20020 33033 52416 80444
A027810: 1 12 63 224 630 1512 3234 6336 11583 20020 33033 52416 80444 119952 174420 248064
loop(\(x,i).2x,(x + ~1),loop(\(x,i).((x2 + ~x) div 2),2,(x + ~1)))
A052796: 0 0 0 0 24 240 1440 6720 26880 96768 322560 1013760 3041280 8785920 24600576 67092480
loop(\(x,i).(x div 5),2,loop(\(x,i).(x * (x - i)),2,(x + ~1)))
A011935: 0 0 0 0 0 4 14 33 67 120 201 316 475 686 960 1310
((x + ~1) + loop(\(x,i).((x + 2) + (if (x + ~2) <= 0 then x else 4)),2,x))
A185450: 5 10 13 17 19 21 23
loop(\(x,i).(~x + loop(\(x,i).(x + (((1 + i) div 2) * i)),(1 + i),0)),x,1)
A023855: 1 2 7 10 22 28 50 60 95 110 161 182 252 280 372 408
loop(\(x,i).(x * loop(\(x,i).(x + (((2 + i) * (1 + i)) div 2)),i,0)),x,1)
A118714: 1 3 27 513 17442 959310 79622730 9475104870 1553917198680 340307866510920 96987741955612200 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 2),x,loop(\(x,i).11x,x,1))
A094972: 1 5 30 166 915 5032 27680 152243 837339 4605366 25329516 139312339 766217865 4214198259 23178090428 127479497357
loop(\(x,i).(x + (if (x mod 6) <= 0 then (x + ~3) else 1)),x,1)
A168009: 1 2 3 4 5 6 9 10 11 12 21 22 23 24 45 46
loop(\(x,i).(x * (1 + (if (x mod 2) <= 0 then 6 else (1 + i)))),x,1)
A328778: 1 3 12 84 588 4116 28812 201684 1411788 9882516 69177612 484243284 3389702988 23727920916 166095446412 1162668124884
loop(\(x,i).(x + loop(\(x,i).(x * (i * i * i * i)),(1 + i),1)),x,1)
A289945: 1 17 1313 333089 207693089 268946253089 645510228813089 2643553803594573089 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 3),x,loop(\(x,i).7x,x,1))
A094975: 1 2 5 12 29 69 161 376 878 2050 4783 11162 26044 60771 141799 330865
loop(\(x,i).(x div 4),x,loop(\(x,i).7x,x,1))
A094980: 1 1 3 5 9 16 28 50 87 153 269 471 825 1443 2526 4421
loop(\(x,i).(~5x + loop(\(x,i).3x,i,2)),x,1)
A083229: 1 1 13 ~11 217 ~599 4453 ~17891 102577 ~473519 2485693 ~12074171 61433737 ~303980039 1529466133 ~7618632851
loop(\(x,i).(x * (x2 div 2)),1,loop(\(x,i).5x,x,1))
A130214: 0 60 7800 976500 122070000 15258787500 1907348625000 238418579062500 29802322387500000 3725290298460937500 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).4x,x2,loop(\(x,i).5x,x,1))
A135292: 1 20 6400 32768000 2684354560000 3518437208883200000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(4x2 + ~x),1,loop(\(x,i).3x,x,1))
A226508: 3 33 315 2889 26163 235953 2125035 19129689 172180323 1549662273 13947078555 125524061289 1129717614483 10167461718993 91507165036875 823564514029689
(loop(\(x,i).8x,x,1) + loop(\(x,i).3x,x,1))
A074609: 2 11 73 539 4177 33011 262873 2099339 16783777 134237411 1073800873 8590111739 68720008177 549757408211 4398051294073 35184386437739
(loop(\(x,i).8x,x,1) - loop(\(x,i).3x,x,1))
A190543: 0 5 55 485 4015 32525 261415 2094965 16770655 134198045 1073682775 8589757445 68718945295 549754219565 4398041728135 35184357739925
(loop(\(x,i).8x,x,1) mod loop(\(x,i).3x,x,1))
A138955: 0 2 1 26 46 206 433 2006 739 19034 53857 76562 435349 1357028 1290286 5539319
loop(\(x,i).(3x2 + 2x),1,loop(\(x,i).3x,x,1))
A061253: 5 33 261 2241 19845 177633 1595781 14353281 129153285 1162300833 10460471301 94143533121 847289672325 7625600673633 68630386930821 617673424981761
(loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1))
A074606: 2 8 34 152 706 3368 16354 80312 397186 1972808 9824674 49005272 244672066 1222297448 6108298594 30531927032
(loop(\(x,i).5x,x,1) - loop(\(x,i).3x,x,1))
A005058: 0 2 16 98 544 2882 14896 75938 384064 1933442 9706576 48650978 243609184 1219108802 6098732656 30503229218
(loop(\(x,i).5x,x,1) mod loop(\(x,i).3x,x,1))
A067602: 0 2 7 17 58 209 316 1580 3526 4508 22540 112700 209206 1046030 447181 11801843
((2 * (1 + loop(\(x,i).2x,x,2))) - loop(\(x,i).3x,x,1))
A135913: 5 7 9 7 ~15 ~113 ~471 ~1673 ~5535 ~17633 ~54951 ~168953 ~515055 ~1561553 ~4717431 ~14217833
(loop(\(x,i).3x,(x div 2),2) + loop(\(x,i).3x,x,1))
A262326: 3 5 15 33 99 261 783 2241 6723 19845 59535 177633 532899 1595781 4787343 14353281
(loop(\(x,i).5x,x,2) - loop(\(x,i).3x,x,1))
A081625: 1 7 41 223 1169 6007 30521 154063 774689 3886567 19472201 97479103 487749809 2439811927 12202248281 61020807343
((loop(\(x,i).4x,x,x) div 2) + loop(\(x,i).3x,x,1))
A086093: 1 5 25 123 593 2803 13017 59531 268705 1199331 5301929 23245819 101194737 437801939 1883831161 8067412587
(1 + loop(\(x,i).(x + (x div (if i <= 0 then 1 else (2 * i)))),3x,x))
A002491: 1 2 4 6 10 12 18 22 30 34 42 48 58 60 78 82
loop(\(x,i).loop(\(x,i).(x * (1 + (6 * i))),3,x),x,1)
A138130: 1 1729 2989441 5168743489 8936757492481 15451653704499649 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 + (i div 3)),loop(\(x,i).(x div (1 + (x mod 2))),x,x),1)
A228731-A003963: 1 1 2 1 3 2 4 1 4 3 5 2 6 4 6 1
loop(\(x,i).(loop(\(x,i).(2x * i),i,1) + (x * (1 + (2 * i)))),x,1)
A129890: 1 5 33 279 2895 35685 509985 8294895 151335135 3061162125 68000295825 1645756410375 43105900812975 1214871076343925 36659590336994625 1179297174137457375
loop(\(x,i).(x + (loop(\(x,i).(x * i),i,1) + (x * (1 + (2 * i))))),x,1)
A068102: 1 5 32 262 2644 31848 446592 7150512 128749536 2575353600 56661408000 1359913708800 35358235430400 990036819072000 29701191750451200 950439443688806400
loop(\(x,i).(loop(\(x,i).(2x * i),i,1) + (x * (~1 + (2 * i)))),x,1)
A192459: 1 3 17 133 1315 15675 218505 3485685 62607195 1250116875 27468111825 658579954725 17109329512275 478744992200475 14354443912433625 459128747151199125
loop(\(x,i).(x + loop(\(x,i).~x,(x + ((2 * i) div (x + 1))),1)),x,1)
A220098: 1 2 1 2 3 2 3 4 3 2 3 4 5 4 3 4
loop(\(x,i).(x * (1 + loop(\(x,i).6x,(x + ~2),x))),x,1)
A135408: 1 2 6 46662
A165710: 1 2 6 46662 4611686018427387903
loop(\(x,i).(x * ((~x2 + 1) + loop(\(x,i).(x * i),x,(x + 1)))),x,1)
A115658: 1 2 6 30030
loop(\(x,i).(x * loop(\(x,i).(9x + 1),i,1)),x,1)
A015008: 1 10 910 746200 5507702200 365876657146000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(~7x + 1),i,1)),x,1)
A015020: 1 ~6 ~258 77400 162617400 ~2391451484400 ~246183190158589200 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).10x2,i,1)),x,1)
A303786: 1 11 1011 10001011 1000000010001011 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),i,1)),x,1)
A173184: 1 1 2 4 13 57 322 2176 17009 150505 1485466 16170036 192384877 2483177809 34554278858 515620794592
loop(\(x,i).(x * loop(\(x,i).(~12x + 1),i,1)),x,1)
A015027: 1 ~11 ~1463 2333485 44665236385 ~10259202810507035 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(~9x + 1),i,1)),x,1)
A015023: 1 ~8 ~584 383104 2262229120 ~120223904353280 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(10x + 1),i,1)),x,1)
A015009: 1 11 1221 1356531 15072415941 1674711207620451 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(7x + 1),i,1)),x,1)
A015006: 1 8 456 182400 510902400 10017774259200 1375009641495014400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).((x + 1) + (x div (2 + (i mod 2)))),i,1)),x,1)
A053599: 1 3 7 13 23 37 59 89 135 197 291 417 607 861 1243 1753
loop(\(x,i).(x * loop(\(x,i).(~10x + 1),i,1)),x,1)
A015025: 1 ~9 ~819 744471 6767985861 ~615270826637649 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if 2x <= 0 then 2 else loop(\(x,i).(x * (7 - i)),x,1))
A036752: 2 6 30 120 360 720 720
loop(\(x,i).(x + loop(\(x,i).5x,(2 * i),(1 + i))),x,1)
A014943: 1 51 1926 64426 2017551 60611301 1769595676 50597720676 1423888736301 39570861392551 1088612609439426 29698842101626926 804559224181705051 4611686018427387903 4611686018427387903
(loop(\(x,i).x2,x,2) - loop(\(x,i).((2 * i) - (x * (1 + i))),x,1))
A291098: 1 4 12 266
loop(\(x,i).loop(\(x,i).(x + (((1 + (2 * i)) * i) div 2)),(1 + i),x),x,1)
A058195: 1 7 23 57 118 218 370 590 895 1305 1841 2527 3388 4452 5748 7308
loop(\(x,i).loop(\(x,i).(x + (i * i * i * i * i)),(1 + i),x),x,1)
A101092: 1 34 310 1610 6035 18236 47244 109020 229845 450670 832546 1463254 2465255 4005080 6304280 9652056
loop(\(x,i).(x + loop(\(x,i).12x,i,(1 + i))),x,1)
A014927: 1 25 457 7369 111049 1604041 22505929 309160393 4178995657 55776799177 736867805641 9652968253897 125562274081225 1623467149388233 20882244117621193 267394589311003081
loop(\(x,i).(x + loop(\(x,i).10x,i,(1 + i))),x,1)
A014925: 1 21 321 4321 54321 654321 7654321 87654321 987654321 10987654321 120987654321 1320987654321 14320987654321 154320987654321 1654320987654321 17654320987654321
loop(\(x,i).(x + loop(\(x,i).7x,i,(1 + i))),x,1)
A014920: 1 15 162 1534 13539 114381 937924 7526268 59409477 462945547 3570173286 27298094202 207234827815 1563680973513 11737027066248 87698011225336
(loop(\(x,i).(x * i),x,1) - loop(\(x,i).(x * (~1 + ((i mod 2) + i))),x,1))
A059838: 0 0 1 3 15 75 495 3465 29295 263655 2735775 30093525 370945575 4822292475 68916822975 1033752344625
loop(\(x,i).(loop(\(x,i).5x,i,1) + (x * (~1 + i))),x,1)
A195257: 1 5 30 185 1180 7845 54850 407225 3241200 27882725 260710150 2655929625 29459366500 354733101125 4617633830250 64677391201625
loop(\(x,i).(x + loop(\(x,i).(x + ((4 - (i mod 2)) * i)),i,1)),x,1)
A212968: 1 5 17 38 75 127 203 300 429 585 781 1010 1287 1603 1975 2392
loop(\(x,i).(x * (12 + (if (x + ~2) <= 0 then 1 else 2))),x,1)
A285399: 1 13 182 2548 35672 499408 6991712 97883968 1370375552 19185257728 268593608192 3760310514688 52644347205632 737020860878848 10318292052303872 144456088732254208
loop(\(x,i).(x * (16 - (if (x + ~2) <= 0 then 1 else 2))),x,1)
A170734-A170696-A170648-A170600-A170552-A170504-A170456-A170408-A170360-A170312-A170264-A170216-A170168-A170120-A170072-A170024-A169556-A169508-A169460-A169412-A169364-A169316-A169268-A169220-A169172-A169124-A169076-A169028-A168980-A168932-A168884-A168836-A168788-A168740-A168692-A167923: 1 15 210 2940 41160 576240 8067360 112943040 1581202560 22136835840 309915701760 4338819824640 60743477544960 850408685629440 11905721598812160 166680102383370240
(1 + compr(\x.loop(\(x,i).loop(\(x,i).(x div (1 + (x mod 2))),x,(x + 1)),2,x),x))
A164874: 2 5 6 11 13 14 23 27 29 30 47 55 59 61 62 95
(1 + compr(\x.loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),2,x),x))
A048645: 1 2 3 4 5 6 8 9 10 12 16 17 18 20 24 32
loop(\(x,i).x2,1,loop(\(x,i).(x + (((2 + i) * (1 + i)) div 2)),x,1))
A001249: 1 16 100 400 1225 3136 7056 14400 27225 48400 81796 132496 207025 313600 462400 665856
loop(\(x,i).(x * loop(\(x,i).(3x2 + x + 1),2,2)),x,1)
A288989: 1 691 477481 329939371 227988105361 157539780804451 108859988535875641 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x2 + ~x) div 2),1,loop(\(x,i).(x * (~2 + (i mod 2))),x,1))
A137173: 0 1 1 3 6 10 28 36 120 136 496 528 2016 2080 8128 8256
loop(\(x,i).(x + (2 * (if (i mod 3) <= 0 then (2x + 1) else x))),x,1)
A018445: 1 3 9 47 141 423
loop(\(x,i).(x div 3),x,loop(\(x,i).(x * (~2 + (3 * i))),x,1))
A020089: 1 0 0 1 3 14 79 505 3710 30920 288591 2982109 33797240 416832633 5557768440 79661347641
loop(\(x,i).(x + (2 * (8x div (if i <= 0 then 1 else i)))),x,1)
A010969: 1 17 153 969 4845 20349 74613 245157 735471 2042975 5311735 13037895 30421755 67863915 145422675 300540195
loop(\(x,i).(~x + loop(\(x,i).(2 * (2x - (x div (1 + i)))),i,2)),x,1)
A054108: 1 5 15 55 197 727 2705 10165 38455 146301 559131 2145025 8255575 31861025 123256495 477823895
loop(\(x,i).(loop(\(x,i).(x * (2 + i)),(~1 + i),1) + (x * (2 + i))),x,1)
A182541: 1 4 19 107 702 5274 44712 422568 4407120 50292720 623471040 8344624320 119938250880 1842662908800 30136443724800 522780938265600
(~1 + loop(\(x,i).(1 + (x * loop(\(x,i).(x2 + 2),2,2))),2,x2))
A158766: 38 1482 5814 13034 23142 36138 52022 70794 92454 117002 144438 174762 207974 244074 283062 324938
(loop(\(x,i).3x,x2,1) + loop(\(x,i).2x,x2,1))
A120800: 2 5 97 20195 43112257 847322163875 150094704016475857 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).3x,x2,1) - loop(\(x,i).2x,x2,1))
A120801: 0 1 65 19171 42981185 847255055011 150094566577522385 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,(x2 + 1))
A344399: 1 4 30 200 1190 6552 34188 171600 836550 3986840 18660356 86062704 392102620 1768102000 7902970200 35056559520
(if (x + ~1) <= 0 then 3x else loop(\(x,i).(x * i),x,(x2 + 1)))
A018932: 0 3 10 60 408 3120 26640 252000 2620800 29756160 366508800 4869849600 69455232000 1058593536000 17174123366400 295534407168000
loop(\(x,i).4x,x,loop(\(x,i).5x,x2,1))
A135420: 1 20 10000 125000000 39062500000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))
A274332-A139791-A005097: 1 2 3 5 6 8 9 11 14 15 18 20 21 23 26 29
loop(\(x,i).(3x - loop(\(x,i).~2x,(~1 + i),1)),x,1)
A133467: 1 2 8 20 68 188 596 1724 5300 15644 47444 141308 425972 1273820 3829652 11472572
(1 + compr(\x.loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 0 else 2))),x,x),x))
A153775: 1 2 3 5 6 8 9 14 15 17 18 23 24 26 27 41
loop(\(x,i).(x + (if (i mod 4) <= 0 then (4x + 1) else x)),x,1)
A222011: 1 2 4 8
A018395: 1 2 4 8 41 82 164 328
loop(\(x,i).(x + (if (x mod 4) <= 0 then (2x2 + 1) else x)),x,1)
A018304: 1 2 4 37 74 148
loop(\(x,i).(x + (if (i mod 3) <= 0 then (x2 + 2x + 1) else x)),x,1)
A018291: 1 2 4 29 58 116
loop(\(x,i).(x + (if (i mod 4) <= 0 then (x2 + 2x + 1) else x)),x,1)
A222011: 1 2 4 8
A018605: 1 2 4 8 89 178 356 712
loop(\(x,i).(x + loop(\(x,i).(x + (2 * (i * i)) - i),(1 + i),x)),x,1)
A213758: 1 9 40 130 355 871 1994 4360 9245 19205 39356 79934 161415 324755 651870 1306596
loop(\(x,i).(~x + loop(\(x,i).24x,i,x)),x,1)
A028693: 1 23 13225 182809175 60651514035625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + loop(\(x,i).11x,i,x)),x,1)
A027879: 1 10 1200 1596000 23365440000 3763004112000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((1 + (if (x mod 2) <= 0 then 3x else 0)) * i)),x,1)
A330229: 1 1 2 42 21336
loop(\(x,i).(x + compr(\x.(loop(\(x,i).(2x + 1),x,0) mod (x + 1)),i)),x,1)
A101301: 1 3 7 13 23 35 51 69 91 119 149 185 225 267 313 365
loop(\(x,i).(x * compr(\x.(loop(\(x,i).(~2x + 2),x,0) mod (x + 1)),i)),x,1)
A307826: 1 1 4 24 240 2880 46080 829440 18247680 510935040 15328051200 551809843200 22072393728000 927040536576000 42643864682496000 2217480963489792000
loop(\(x,i).loop(\(x,i).((2x * (1 + (2 * i))) div (1 + i)),i,x),x,1)
A203469: 1 3 30 1050 132300 61122600 104886381600 674943865596000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),i,x),x,1)
A003046: 1 1 2 10 140 5880 776160 332972640 476150875200 2315045555222400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (12x div (if i <= 0 then 1 else i))),x,1)
A010965: 1 13 91 455 1820 6188 18564 50388 125970 293930 646646 1352078 2704156 5200300 9657700 17383860
loop(\(x,i).(~x + (12x div (if i <= 0 then 1 else i))),x,1)
A010927: 1 11 55 165 330 462 462 330 165 55 11 1
loop(\(x,i).(x + (9x div (if i <= 0 then 1 else i))),x,1)
A000582: 1 10 55 220 715 2002 5005 11440 24310 48620 92378 167960 293930 497420 817190 1307504
loop(\(x,i).(~x + (16x div (if i <= 0 then 1 else i))),x,1)
A010931: 1 15 105 455 1365 3003 5005 6435 6435 5005 3003 1365 455 105 15 1
loop(\(x,i).(x + (10x div (if i <= 0 then 1 else i))),x,1)
A001287: 1 11 66 286 1001 3003 8008 19448 43758 92378 184756 352716 646646 1144066 1961256 3268760
loop(\(x,i).(~x + (10x div (if i <= 0 then 1 else i))),x,1)
A285198: 1 9 36 84 126 126 84 36 9 1
loop(\(x,i).(x + (7x div (if i <= 0 then 1 else i))),x,1)
A000580: 1 8 36 120 330 792 1716 3432 6435 11440 19448 31824 50388 77520 116280 170544
loop(\(x,i).(x * compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)),x,1)
A059861: 1 1 3 15 135 1485 22275 378675 7952175 214708725 6226553025 217929355875 8499244879125 348469040044125 15681106801985625 799736446901266875
loop(\(x,i).(loop(\(x,i).(1 + (2 * ((x * i) div 2))),i,1) + (x * i)),x,1)
A088128: 1 2 7 30 157 970 6931 56294 512569 5173074 57330271 692227822 9045871957 127205130650 1915394962027 30748771424310
(loop(\(x,i).2x,((x2 + ~x) div 2),1) - loop(\(x,i).(x * i),x,1))
A127429: 0 0 0 2 40 904 32048 2092112 268395136 68719113856 35184368460032 36028796979047168 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x2 * loop(\(x,i).(1 + (x * i)),x,1)) div loop(\(x,i).(x * i),x,1))
A330280: 0 2 10 24
A293412: 0 2 10 24 43 67 97 133 173 220 271 328 391 459 532 611
loop(\(x,i).(loop(\(x,i).(1 + (x * (i * i))),i,1) + (x * (i * i))),x,1)
A336809: 1 3 21 271 5649 174051 7447573 422836191 30767443521 2792343036259 309252314731701 41051709426337743 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((1 + (2x * (~1 + (2 * i)))) div (if i <= 0 then 1 else i)),x,1)
A029651: 1 3 9 30 105 378 1386 5148 19305 72930 277134 1058148 4056234 15600900 60174900 232676280
(2 + (if x <= 0 then 2 else (if ((x + 2) mod 7) <= 0 then 1 else 0)))
A338150: 4 2 2 2 2 3 2 2 2 2 2 2 3 2 2 2
(2 + (if (x mod 3) <= 0 then (if ((x + 2) mod 4) <= 0 then 2 else 1) else 0))
A245070: 3 2 2 3 2 2 4 2 2 3 2 2 3 2 2 3
loop(\(x,i).(2x + 2),x,(2 * loop(\(x,i).(2 * (x + i)),(x + ~1),0)))
A286778: 0 2 22 142 734 3390 14718 61694 253438 1029118 4151294 16683006 66904062 267993086 1072791550 4292935678
(loop(\(x,i).2x,x,2) - (if (~2 + (x div 5)) <= 0 then 0 else 2))
A025489: 2 4 8 16 32 64
A335891: 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65534
(if (~2 + (x div 2)) <= 0 then 1 else (2 + (if (x mod 5) <= 0 then 2 else 0)))
A216321: 1 1 1 1 1 1 2 2 2 2 4 2 2 2 2 4
(if x <= 0 then 1 else (if ((x + 1) mod (2 + (((x + ~1) div 2) mod 2))) <= 0 then 0 else 2))
A108352: 1 0 2 2 2 0 2 2 0 0 2 0 2 0 2 2
(if x <= 0 then 1 else (6x - (if (~2 + (x div 2)) <= 0 then 0 else 2)))
A315767: 1 6 12 18 24 30 34 40 46 52 58 64 70 76 82 88
(2 * loop(\(x,i).(3 * (x - (if (i mod 2) <= 0 then 2 else ~2))),x,0))
A226493: 0 12 24 84 240 732 2184 6564 19680 59052 177144 531444 1594320 4782972 14348904 43046724
(loop(\(x,i).(2x + ~2),x,loop(\(x,i).(3x + 1),x,0)) div 2)
A241275: 0 0 5 45 305 1905 11585 69825 419585 2518785 15115265 90696705 544190465 3265163265 19591020545 117546205185
(loop(\(x,i).(3x + loop(\(x,i).(~2x + 2),i,1)),x,0) div 2)
A091002: 0 0 1 2 9 22 77 210 673 1934 5973 17578 53417 158886 479389 1432706
(compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x) + (if x <= 0 then 0 else 2))
A249373-A004139: 3 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61
(loop(\(x,i).(x + ((x + loop(\(x,i).(x * i),i,i)) * (1 + i))),x,0) div 2)
A321853: 0 1 10 86 756 7092 71856 787824 9329760 118956960 1627067520 23786386560 370371536640 6122231942400 107109431654400 1977781262284800
((loop(\(x,i).(2x * i),x,1) + (if (x + ~2) <= 0 then x2 else 0)) div 2)
A052594: 0 1 6 24 192 1920 23040 322560 5160960 92897280 1857945600 40874803200 980995276800 25505877196800 714164561510400 21424936845312000
(loop(\(x,i).(x + loop(\(x,i).(1 + (x * i)),(~1 + i),1) - i),x,0) div 2)
A002807: 0 0 0 1 7 37 197 1172 8018 62814 556014 5488059 59740609 710771275 9174170011 127661752406
(if (x mod (1 + ((x + 2) div 5))) <= 0 then (if x <= 0 then 0 else 1) else 2)
A106149: 0 1 1 2 1 2 1 2 2 1 2 2 1 2 2 2
(if ((x + 1) mod (1 + (x div 5))) <= 0 then (if x <= 0 then 0 else 1) else 2)
A227944: 0 1 1 1 1 1 2 1 2 1 2 1 2 2 1 1
(if (x mod (1 + (((x + 1) div 2) div 3))) <= 0 then (if x <= 0 then 0 else 1) else 2)
A318306-A305832-A064547-A058061: 0 1 1 1 1 2 1 2 1 2 1 2 1 2 2 1
(if x <= 0 then 0 else (if (x mod (1 + (4 mod (1 + (x div 2))))) <= 0 then 1 else 2))
A196062: 0 1 1 1 1 2 1 1 2 2 1 2 2 2 2 1
loop(\(x,i).3x,x,((1 + loop(\(x,i).(x * i),(x + ~1),1)) div 2))
A032261: 1 3 9 27 243 2916 43740 787320 16533720 396809280 10713850560 321415516800 10606712054400 381841633958400 14891823724377600 625456596423859200
(2 * (if (x mod 2) <= 0 then (5 * (2 + (if x <= 0 then 0 else 2))) else 1))
A040399: 20 2 40 2 40 2 40 2 40 2 40 2 40 2 40 2
(loop(\(x,i).(x * i),(1 + (2 * (2x + (if x <= 0 then 2 else x)))),1) div 2)
A082670: 60 2520 3113510400 60822550204416000 4611686018427387903 4611686018427387903
(2 * (if (x mod 2) <= 0 then (9 * (if x <= 0 then 1 else 2)) else 1))
A040323: 18 2 36 2 36 2 36 2 36 2 36 2 36 2 36 2
(2 * (if (x mod 2) <= 0 then (6 * (2 + (if x <= 0 then 0 else 2))) else 1))
A040575: 24 2 48 2 48 2 48 2 48 2 48 2 48 2 48 2
(2 + loop(\(x,i).x2,x,(1 + loop(\(x,i).x2,2x,3))))
A219014: 6 6726 4611686018427387903
(2 * (1 + (3 * loop(\(x,i).loop(\(x,i).x2,x,2),x,(~x + 1)))))
A275006: 8 14 98 4611686018427387903
(loop(\(x,i).2x,x,(1 + loop(\(x,i).4x,2x,1))) div 2)
A214135: 1 17 514 16388 524296 16777232 536870944 17179869248 549755814016 17592186044672 562949953421824 18014398509483008 576460752303425536 4611686018427387903 4611686018427387903 4611686018427387903
((1 + loop(\(x,i).(x div 2),x,loop(\(x,i).(3x + 1),x,1))) div 2)
A136423: 1 1 2 3 4 6 9 13 19 29 43 65 97 146 219 328
((1 + loop(\(x,i).(2 * (~2x + (x div (if i <= 0 then 1 else i)))),x,1)) div 2)
A110556: 1 ~1 3 ~10 35 ~126 462 ~1716 6435 ~24310 92378 ~352716 1352078 ~5200300 20058300 ~77558760
loop(\(x,i).2x,x,((1 + loop(\(x,i).(2x + (i mod 2)),x,1)) div 2))
A179607: 1 4 12 56 208 864 3392 13696 54528 218624 873472 3495936 13979648 55926784 223690752 894795776
((loop(\(x,i).2x2,x,1) * (1 + loop(\(x,i).2x,x,1))) div 2)
A174972: 1 3 20 576 278528 35433480192 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).6x,x,(1 + loop(\(x,i).2x,x,1))) div 2)
A143079: 1 9 90 972 11016 128304 1516320 18055872 215830656 2584929024 30988915200 371685583872 4459138615296 53503133036544 641998414356480 7703745879785472
((1 + loop(\(x,i).(2x + loop(\(x,i).2x,(~1 + i),x)),x,1)) div 2)
A089709: 1 2 6 36 360 6480 220320 14541120 1890345600 487709164800 250682510707200 257200255985587200 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(~x + loop(\(x,i).4x,(2 * i),2)),(x + 1),1) div 2)
A154806: 15 240 3855 61680 986895 15790320 252645135 4042322160 64677154575 1034834473200 16557351571215 264917625139440 4238682002231055 67818912035696880 1085102592571150095 4611686018427387903
(2 * loop(\(x,i).((if (x mod 2) <= 0 then 2 else 0) * (~1 + (2 * i))),(x + ~1),1))
A181389: 2 2 0 12 20 28 36 44 52 60 68 76 84 92 100 108
(2 * (if x <= 0 then 2 else loop(\(x,i).(4 * (x + (x div 2))),(x + ~1),1)))
A084477: 4 2 8 48 288 1728 10368 62208 373248 2239488 13436928 80621568 483729408 2902376448 17414258688 104485552128
((1 + loop(\(x,i).(x + (if (~2 + (x div 4)) <= 0 then i else x)),x,1)) div 2)
A271520: 1 1 2 4 6 8 16 32
(if x <= 0 then 0 else ((x + 1) mod (2 * (1 + (if (x + ~4) <= 0 then 0 else 2)))))
A260187: 0 0 1 0 1 0 1 2 3 4 5 0 1 2 3 4
(if x <= 0 then 0 else (if ((x div 4) - (x mod 6)) <= 0 then 1 else 2))
A124765: 0 1 1 1 1 1 2 1 1 1 1 1 2 2 2 1
(2 * (if (x mod 2) <= 0 then (7 * (if x <= 0 then 1 else 2)) else 1))
A040195: 14 2 28 2 28 2 28 2 28 2 28 2 28 2 28 2
(2 * (if (x mod 3) <= 0 then (8 * (if x <= 0 then 1 else 2)) else 1))
A040252: 16 2 2 32 2 2 32 2 2 32 2 2 32 2 2 32
(if x <= 0 then 1 else (2 * loop(\(x,i).(2 + (x div 2)),(x + ~8),1)))
A104274: 1 2 2 2 2 2 2 2 2 4 6 6 6 6 6 6
(loop(\(x,i).(x * i),x,(if x <= 0 then 2 else (x + 7))) div 2)
A230056: 1 4 9 30 132 720 4680 35280 302400 2903040 30844800 359251200 4550515200 62270208000 915372057600 14384418048000
(if x <= 0 then 0 else (if (~2 + (3x mod (2 + (x div 2)))) <= 0 then 1 else 2))
A334028: 0 1 1 1 1 2 2 1 1 2 1 2 2 2 2 1
(if ((x - (if (~2 + (x div 4)) <= 0 then 1 else 0)) mod 4) <= 0 then 1 else 2)
A245225: 2 1 2 2 2 1 2 2 2 1 2 2 1 2 2 2
(if (x mod 2) <= 0 then (15 * (if x <= 0 then 1 else 2)) else 2)
A040224: 15 2 30 2 30 2 30 2 30 2 30 2 30 2 30 2
(2 + (5 * loop(\(x,i).(~2 + loop(\(x,i).x2,x,2)),x,1)))
A275005: 7 12 72 4611686018427387903
(loop(\(x,i).2x,x,1) mod loop(\(x,i).x2,2,10))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A123464: 1 2 4 8 16 32 64 128 256 512
A216095: 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 6384 2768
(if x <= 0 then 1 else (2 * (~1 + (2 * loop(\(x,i).(2 * (x - (i mod 2))),x,2)))))
A093380: 1 6 14 22 46 86 174 342 686 1366 2734 5462 10926 21846 43694 87382
(if (x + ~1) <= 0 then x else (if (x mod (2 + ((x * (x div 2)) mod 2))) <= 0 then 1 else 2))
A305831: 0 1 1 1 1 2 1 2 1 2 1 2 1 2 1 1
((3 * (if (8 mod (if x <= 0 then 1 else x)) <= 0 then x else 0)) div 2)
A099892: 0 1 3 0 6 0 0 0 12 0 0 0 0 0 0 0
(loop(\(x,i).2x,x,1) mod loop(\(x,i).(4x + 1),3,2))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A036147: 1 2 4 8 16 32 64 128 107 65 130 111 73 146 143 137
((3 * loop(\(x,i).x2,1,(~1 + loop(\(x,i).(x * i),x,2)))) div 2)
A020544: 1 1 13 181 3313 85681 3106081 152379361 9753972481 790089189121 79009114867201 9560105293939201 1376655193941350401 4611686018427387903 4611686018427387903 4611686018427387903
(2 + (3 * loop(\(x,i).loop(\(x,i).(3x + ~1),x,2),x,1)))
A172996: 5 17 1097 4611686018427387903
(loop(\(x,i).3x,x,1) mod (2 + loop(\(x,i).x2,2,3)))
A271350: 1 3 9 27 81 77 65 29 4 12 36 25 75 59 11 33
(if (x + ~1) <= 0 then 4x else (if (x + ~2) <= 0 then 1 else 6))
A021028: 0 4 1 6 6 6 6 6 6 6 6 6 6 6 6 6
((3 * loop(\(x,i).(x + (if x <= 0 then (1 + i) else 0)),x,(~x + 1))) div 2)
A104568: 1 3 1 4 3 1 6 4 3 1 7 6 4 3 1 9
(if x <= 0 then 1 else (2 + loop(\(x,i).(2 * (2x - (x mod 2))),x,3)))
A122973: 1 12 42 162 642 2562 10242 40962 163842 655362 2621442 10485762 41943042 167772162 671088642 2684354562
loop(\(x,i).2x,x,(loop(\(x,i).(x * (x - i)),2,(x + 3)) div 2))
A001816: 12 120 720 3360 13440 48384 161280 506880 1520640 4392960 12300288 33546240 89456640 233963520 601620480 1524105216
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(4x + 2))
A016834: 1024 60466176 10000000000 289254654976 3570467226624 26559922791424 141167095653376 590490000000000 2064377754059776 6278211847988224 17080198121677824 42420747482776576 97656250000000000 210832519264920576 430804206899405824 839299365868340224
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(4x + 2))
A016836: 4096 2176782336 1000000000000 56693912375296 1156831381426176 12855002631049216 95428956661682176 531441000000000000 2386420683693101056 4611686018427387903 4611686018427387903
loop(\(x,i).(2x2 + ~x),1,loop(\(x,i).2x,(2x + ~1),2))
A201186: 6 28 496 8128 130816 2096128 33550336 536854528
loop(\(x,i).2x,(if (x + ~2) <= 0 then x else ((2x + 1) - (x mod 2))),2)
A060815: 2 4 8 128 1024 2048
(loop(\(x,i).10x,(x + 1),(if x <= 0 then 2 else 1)) div 2)
A216156: 10 50 500 5000 50000 500000 5000000 50000000 500000000 5000000000 50000000000 500000000000 5000000000000 50000000000000 500000000000000 5000000000000000
((if x <= 0 then 0 else (1 + (x div (4 - (if (x mod 2) <= 0 then 1 else x))))) mod 2)
A206566: 0 1 1 0 0 0 1 0 1 1 0 1 1 1 1 1
loop(\(x,i).2x,(x + ~1),(loop(\(x,i).(3x + ~1),x,1) div 2))
A053524: 0 1 4 28 160 976 5824 35008 209920 1259776 7558144 45349888 272097280 1632587776 9795518464 58773127168
(loop(\(x,i).(2 * (x - loop(\(x,i).(x - (2 * (~x + i))),i,1))),x,1) div 2)
A187693: 0 0 1 11 57 229 815 2715 8701 27233 83979 256519 778745 2354637 7100743 21375923
((loop(\(x,i).3x,x,2) - loop(\(x,i).(2x + 4),x,1)) div 2)
A281773: 0 0 1 9 43 165 571 1869 5923 18405 56491 172029 521203 1573845 4742011 14266989
(loop(\(x,i).2x,(x + ~1),((x + 1) + loop(\(x,i).2x,x,2))) div 2)
A346317: 1 3 11 40 148 560 2160 8448 33344 132352 527104 2103296 8401920 33583104 134279168 537001984
((loop(\(x,i).(4x + ~2),x,1) + loop(\(x,i).2x,x,1)) div 2)
A007581: 1 2 5 15 51 187 715 2795 11051 43947 175275 700075 2798251 11188907 44747435 178973355
((loop(\(x,i).3x,(x + ~1),2) + loop(\(x,i).2x,x,1)) div 2)
A085281: 1 2 5 13 35 97 275 793 2315 6817 20195 60073 179195 535537 1602515 4799353
((loop(\(x,i).2x,((x + ~1) div 2),2) + loop(\(x,i).2x,x,1)) div 2)
A005418: 1 2 3 6 10 20 36 72 136 272 528 1056 2080 4160 8256 16512
(loop(\(x,i).5x,x,1) - (loop(\(x,i).2x,x,1) div 2))
A144465: 1 4 23 121 617 3109 15593 78061 390497 1952869 9765113 48827101 244138577 1220699029 6103507433 30517561741
(((if (x mod 2) <= 0 then 1 else (x2 + ~x)) + loop(\(x,i).2x,x,1)) div 2)
A236291: 1 1 2 7 8 26 32 85 128 292 512 1079 2048 4174 8192 16489
(((x + 1) * loop(\(x,i).(x + loop(\(x,i).(x * i),i,1)),(x + ~1),1)) div 2)
A051403: 0 1 3 8 25 102 539 3496 26613 231170 2250127 24227484 285705641 3660694198 50624828355 751426146512
(2 * loop(\(x,i).(2x + 2),x,((x + 1) * (if x <= 0 then 1 else 4))))
A196558: 2 36 108 284
loop(\(x,i).2x,(if x <= 0 then 3 else (4x2 + 4x)),2)
A099772: 16 512 33554432 562949953421312 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,x,(if x <= 0 then 1 else 2)) - ((x2 + 3x + 2) div 2))
A130104: 0 1 2 6 17 43 100 220 467 969 1982 4018 8101 16279 32648 65400
loop(\(x,i).loop(\(x,i).(((x + i) * i) div (x + 1)),x,2x),(x + 1),2)
A048577: 3 4 6 9 14 22 35 56 90 145 234 378 611 988 1598 2585
((2x + 2) + loop(\(x,i).x2,1,(~1 + loop(\(x,i).2x,x,2))))
A286191: 3 13 55 233 971 3981 16143 65041 261139 1046549 4190231 16769049 67092507 268402717 1073676319 4294836257
compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x + ~2),x),(2x + 2))
A099862: 6 9 12 15 18 21 24 26 28 32 34 36 39 42 45 48
compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x),(2x + 2))
A099861: 4 8 10 14 16 20 22 25 27 30 33 35 38 40 44 46
compr(\x.loop(\(x,i).(x div (if (x mod 2) <= 0 then ~2 else 1)),x,x),(2x + 2))
A248056: 6 10 18 24 30 34 40 46 54 58 66 72 78 86 90 96
loop(\(x,i).(if (x mod 4) <= 0 then 0 else 1),(~1 + (x div 2)),((x + 1) div 2))
A346100: 0 1 1 2 1 1 1 0 0 1 1 1 1 1 1 0
(loop(\(x,i).(~x + (if x <= 0 then 5 else 0)),x,1) * ((x + 1) div 2))
A266085: 0 ~1 6 ~12 22 ~33 48 ~64 84 ~105 130 ~156 186 ~217 252 ~288
(loop(\(x,i).(x + ((if (i mod 2) <= 0 then i else 1) * i)),x,1) + ((x + 1) div 2))
A093361: 1 3 7 11 27 33 69 77 141 151 251 263 407 421 617 633
(if x <= 0 then 0 else loop(\(x,i).(4x * (~1 + (2 * i))),(x + ~1),2))
A052713: 0 2 8 96 1920 53760 1935360 85155840 4428103680 265686220800 18066663014400 1373066389094400 115337576683929600 4611686018427387903 4611686018427387903 4611686018427387903
(if (x + ~1) <= 0 then x else loop(\(x,i).(2x * (~1 + (2 * i))),(x + ~1),2))
A052718: 0 1 4 24 240 3360 60480 1330560 34594560 1037836800 35286451200 1340885145600 56317176115200 2590590101299200 129529505064960000 4611686018427387903
(loop(\(x,i).3x,x,2) - loop(\(x,i).(~2x + 4),(x + ~1),2))
A120656: 0 4 18 50 166 474 1478 4330 13206 39194 118438 353610 1064246 3185914 9571398 28686890
(if (x + ~1) <= 0 then 1 else (((x + ~1) * loop(\(x,i).x3,x,x)) div 2))
A245490: 1 1 256 7625597484987 4611686018427387903
((1 + (if (x mod 2) <= 0 then 12 else 0)) * (if x <= 0 then 1 else 2))
A040168: 13 2 26 2 26 2 26 2 26 2 26 2 26 2 26 2
((1 + (if (x mod 2) <= 0 then 10 else 0)) * (if x <= 0 then 1 else 2))
A040120: 11 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2
((1 + (if (x mod 4) <= 0 then 6 else 0)) * (if x <= 0 then 1 else 2))
A010141: 7 2 2 2 14 2 2 2 14 2 2 2 14 2 2 2
((1 + (if (x mod 2) <= 0 then 16 else 0)) * (if x <= 0 then 1 else 2))
A040288: 17 2 34 2 34 2 34 2 34 2 34 2 34 2 34 2
((2 + (if (x mod 2) <= 0 then 12 else 0)) * (if x <= 0 then 1 else 2))
A040188: 14 4 28 4 28 4 28 4 28 4 28 4 28 4 28 4
(2 * ((1 + (if (x mod 2) <= 0 then 8 else 0)) * (if x <= 0 then 1 else 2)))
A040314: 18 4 36 4 36 4 36 4 36 4 36 4 36 4 36 4
(2 * ((if (x mod 2) <= 0 then 12 else 1) * (if x <= 0 then 1 else 2)))
A040563: 24 4 48 4 48 4 48 4 48 4 48 4 48 4 48 4
(2 * ((if (x mod 2) <= 0 then 10 else 1) * (if x <= 0 then 1 else 2)))
A040389: 20 4 40 4 40 4 40 4 40 4 40 4 40 4 40 4
(4 * ((1 + (if (x mod 2) <= 0 then 4 else 0)) * (if x <= 0 then 1 else 2)))
A040384: 20 8 40 8 40 8 40 8 40 8 40 8 40 8 40 8
(4 * ((if (x mod 2) <= 0 then 6 else 1) * (if x <= 0 then 1 else 2)))
A040557: 24 8 48 8 48 8 48 8 48 8 48 8 48 8 48 8
(compr(\x.(loop(\(x,i).(2x + 1),x,0) mod (x + 1)),x) + (if x <= 0 then 1 else 2))
A231407: 1 4 6
A055670: 1 4 6 8 12 14 18 20 24 30 32 38 42 44 48 54
(compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x) + (if x <= 0 then 1 else 2))
A299763: 1 3 4 6 8 12 14 18 20 24 30 32 38 42 44 48
loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,(if x <= 0 then 1 else 2))
A228403: 1 4 10 28 84 264 858 2860 9724 33592 117572 416024 1485800 5348880 19389690 70715340
(2 * loop(\(x,i).(x + loop(\(x,i).x2,1,(1 + ((1 + i) div 2)))),x,1))
A018227: 2 10 18 36 54 86 118 168 218 290 362 460 558 686 814 976
((loop(\(x,i).(2x + ~4),x,1) mod loop(\(x,i).3x,x,1)) div 2)
A094033: 0 0 0 3 18 75 270 903 2898 9075 27990 85503 259578 784875 2366910 7125303
(2 + loop(\(x,i).(x + ((2x + ~1) * (if (x mod 2) <= 0 then 1 else i))),x,1))
A046461: 3 4 7 34 97
((loop(\(x,i).(2x * i),(x div 2),1) + loop(\(x,i).(x * i),x,1)) div 2)
A113247: 1 1 2 4 16 64 384 2544 20352 181632 1816320 19960320 239523840 3113533440 43589468160 653837506560
(loop(\(x,i).loop(\(x,i).(x + (((2 + (i mod 2)) * i) + i)),i,x),x,1) div 2)
A342397: 0 2 7 18 35 62 98 148 210 290 385 502 637 798 980 1192
(loop(\(x,i).(x + (loop(\(x,i).2x,i,i) * i * i * i)),x,1) div 2)
A209359: 0 1 33 357 2405 12405 53877 207541 731829 2411445 7531445 22523829 64991157 181977013 496680885 1326120885
(2 + (if x <= 0 then 2 else (if ((x div 2) mod (3 + (x mod 2))) <= 0 then 1 else 2)))
A156743: 4 3 4 4 4 4 3 4 4 3 4 4 3 4 4 4
((loop(\(x,i).(x + loop(\(x,i).(x * (2 + i)),i,1)),(x + 1),1) div 2) div 2)
A117397: 1 4 19 109 739 5779 51139 504739 5494339 65369539 843747139 11741033539 175200329539 2790549065539 47251477577539 847548190793539
((2 + (x div (1 + (2 * loop(\(x,i).(if x <= 0 then i else (x div 2)),x,0))))) div 2)
A117502: 1 1 2 1 1 3 1 1 2 5 1 1 2 3 8 1
((if x <= 0 then 2 else (x mod (2 + (if (x mod 2) <= 0 then 1 else (x div 3))))) div 2)
A066032: 1 0 1 0 0 1 0 1 1 2 0 0 0 0 1 0
(loop(\(x,i).x2,2,loop(\(x,i).2x2,(2x + ~1),2)) div 2)
A139298: 8 2048 576460752303423488 4611686018427387903
(loop(\(x,i).2x,x,1) mod loop(\(x,i).(x2 + 3x + ~1),2,2))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A036140: 1 2 4 8 16 32 64 21 42 84 61 15 30 60 13 26
(2 * (if x <= 0 then 1 else (2 + (if (5 mod (x + 1)) <= 0 then x else 1))))
A117217: 2 6 6 6 12 6 6 6 6 6 6 6 6 6 6 6
(loop(\(x,i).4x,x,1) mod loop(\(x,i).(x2 + 2x + 1),2,2))
A001264: 1 4 16 64 56 24 96 84 36 44 76 4 16 64 56 24
(loop(\(x,i).3x,x,1) mod loop(\(x,i).(x2 + 2x + 1),2,2))
A001218: 1 3 9 27 81 43 29 87 61 83 49 47 41 23 69 7
loop(\(x,i).(2x2 + x),1,(2 + (loop(\(x,i).2x,x,1) div 2)))
A060852: 10 21 36 78 210
(2 * loop(\(x,i).(3x + ~3),x,(loop(\(x,i).2x,x,1) div 2)))
A059517: 0 0 12 138 1056 7050 44472 273378 1659936 10018650 60289032 362265618 2175188016 13055911050 78349815192 470141937858
(if x <= 0 then 1 else (2 * (2 + ((if (x + ~3) <= 0 then 2 else 1) mod (x + 1)))))
A329506: 1 4 8 8 6 6 6 6 6 6 6 6 6 6 6 6
(if (x + ~2) <= 0 then (if x <= 0 then 1 else 4x) else (((x + 1) div 2) div 2))
A154520: 1 4 8 1 1 1 1 2 2 2 2 3 3 3 3 4
(2 * (2 + (if x <= 0 then 1 else (if ((x + ~2) mod (2 + (x mod 2))) <= 0 then 0 else 2))))
A171784: 6 8 4 8 4 4 4 8 4 8 4 4 4 8 4 8
(2 + (if x <= 0 then 0 else loop(\(x,i).2x,((1 + (x div 3)) div 2),2)))
A251546: 2 4 4 6 6 6 6 6 6 10 10 10 10 10 10 18
(2 + ((((x + 1) - loop(\(x,i).(if x <= 0 then i else (x div 2)),x,2)) div 2) div 2))
A128219: 1 2 2 2 3 3 2 3 4 4 2 3 4 5 5 2
(2 * (loop(\(x,i).2x,x,2) - loop(\(x,i).2x,((x + 1) div 2),2)))
A297619: 0 0 8 16 48 96 224 448 960 1920 3968 7936 16128 32256 65024 130048
(if (x mod 4) <= 0 then 1 else (4 * (if (x mod 2) <= 0 then 1 else 4)))
A177499: 1 16 4 16 1 16 4 16 1 16 4 16 1 16 4 16
(4 * loop(\(x,i).3x,(x + 1),(if x <= 0 then 1 else 4)))
A183355: 12 144 432 1296 3888 11664 34992 104976 314928 944784 2834352 8503056 25509168 76527504 229582512 688747536
(loop(\(x,i).2x,x,loop(\(x,i).(2x + 1),x,8)) div 2)
A291009: 4 17 70 284 1144 4592 18400 73664 294784 1179392 4718080 18873344 75495424 301985792 1207951360 4831821824
((loop(\(x,i).2x,x,loop(\(x,i).((x + 1) + i),x,4)) div 2) div 2)
A072863: 1 3 9 26 72 192 496 1248 3072 7424 17664 41472 96256 221184 503808 1138688
((loop(\(x,i).2x,x,loop(\(x,i).(~1 + (x * i)),x,4)) div 2) div 2)
A317968: 1 1 5 28 220
(loop(\(x,i).2x,x,1) mod (~2 + loop(\(x,i).(x3 + 2),2,2)))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A123464: 1 2 4 8 16 32 64 128 256 512
A126605: 1 2 4 8 16 32 64 128 256 512 24 48 96 192 384 768
(loop(\(x,i).3x,x,1) mod loop(\(x,i).(1 + (x * i)),4,2))
A036136: 1 3 9 27 81 65 17 51 64 14 42 37 22 66 20 60
(2 + loop(\(x,i).(x + (if (x + ~2) <= 0 then 1 else 2)),(x div 2),(x div 4)))
A109763: 2 2 3 3 5 5 7 7 11 11 13 13 17 17 19 19
(loop(\(x,i).loop(\(x,i).(x * ((x + ~1) + i)),2,x2),x,4) div 2)
A001377: 2 32896 4611686018427387903 4611686018427387903
(if (x mod 6) <= 0 then 1 else (4 * (if (x + ~1) <= 0 then x else 2)))
A331067: 1 4 8 8 8 8 1
(4 * loop(\(x,i).(x2 + 3x),1,loop(\(x,i).2x,x,2)))
A235886: 40 112 352 1216 4480 17152 67072 265216 1054720 4206592 16801792 67158016 268533760 1073938432 4295360512 17180655616
loop(\(x,i).2x,x,(loop(\(x,i).2x3,(x + ~2),2) div 2))
A275203: 1 2 4 64
A219735: 1 2 4 64 65536 17592186044416 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,8x)
A017076: 0 68719476736 281474976710656 36520347436056576 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x2 + x) div 2),x,loop(\(x,i).x2,4x,2))
A051241: 2 2147516416 4611686018427387903
((loop(\(x,i).x2,1,((if (x mod 2) <= 0 then 2 else 0) + (x div 2))) div 2) div 2)
A008797: 1 0 2 0 4 1 6 2 9 4 12 6 16 9 20 12
(loop(\(x,i).5x,x,1) mod loop(\(x,i).(x2 + 2),2,2))
A070385: 1 5 25 11 17 9 7 35 23 1 5 25 11 17 9 7
(if x <= 0 then 0 else (if (x mod (1 + ((x + ~1) mod 4))) <= 0 then 1 else 4))
A193512: 0 1 1 1 1 1 1 4 1 1 1 4 1 1 1 1
(if (x mod 2) <= 0 then (if (x mod 4) <= 0 then (x div 4) else 1) else 4)
A174571: 0 4 1 4 1 4 1 4 2 4 1 4 3 4 1 4
loop(\(x,i).(2x + 6),(x div 2),(if (x mod 2) <= 0 then 1 else 4))
A063757: 1 4 8 14 22 34 50 74 106 154 218 314 442 634 890 1274
loop(\(x,i).5x,(x div 2),(if (x mod 2) <= 0 then 1 else 4))
A133632: 1 4 5 20 25 100 125 500 625 2500 3125 12500 15625 62500 78125 312500
(if x <= 0 then 1 else loop(\(x,i).(x * (~2 + (3 * i))),(x + ~1),4))
A091541: 1 4 4 16 112 1120 14560 232960 4426240 97377280 2434432000 68164096000 2113086976000 71844957184000 2658263415808000 106330536632320000
(if x <= 0 then 1 else loop(\(x,i).(1 + (x * i) - (2 * (i mod 2))),x,4))
A110149: 1 3 7 20 81 404 2425 16974 135793 1222136 12221361 134434970 1613219641 20971855332 293605974649 4404089619734
loop(\(x,i).loop(\(x,i).(x div 3),(x + ~1),(x + 2)),x,(x div 4))
A287561: 0 2 1 3 1 3 0 2 2 1 3 0 3 0 2 1
(loop(\(x,i).(x * (~1 + (2 * i))),x,1) div loop(\(x,i).(x * i),x,4))
A024505: 0 0 0 0 1 1 3 6 12 23 45 86 165 317 612 1183
(x div (2 + (if (x mod 2) <= 0 then 1 else (2 + (if (x mod 3) <= 0 then 1 else x)))))
A082023: 0 0 0 0 1 0 2 0 2 1 3 0 4 0 4 3
(2 * loop(\(x,i).loop(\(x,i).3x,(x2 div 4),1),x,2))
A274992: 4 6 18 6973568802
(loop(\(x,i).((4x + 2) + (if (x + ~2) <= 0 then 2 else 1)),x,2) div 2)
A267536: 1 6 25 103 415 1663 6655 26623 106495 425983 1703935 6815743 27262975 109051903 436207615 1744830463
(loop(\(x,i).4x,x,loop(\(x,i).(4x + 1),x,2)) div 2)
A166927: 1 18 296 4768 76416 1223168 19572736 313171968 5010784256 80172679168 1282763390976 20524216352768 328387470032896 5254199554080768 84067192999510016 1345075088529031168
(loop(\(x,i).2x,x,loop(\(x,i).(1 + (2 * (x - (i mod 2)))),x,2)) div 2)
A083424: 1 3 14 52 216 848 3424 13632 54656 218368 873984 3494912 13981696 55922688 223698944 894779392
loop(\(x,i).4x,x,(loop(\(x,i).(3x + ~1),x,2) div 2))
A053536: 1 8 112 1280 15616 186368 2240512 26869760 322502656 3869769728 46438285312 557255229440 6687079530496 80244887257088 962938915520512 11555265912504320
(loop(\(x,i).(1 + loop(\(x,i).(x + (x div (2 * (2 + i)))),2,x)),x,2) div 2)
A018124: 1 1 2 2 3 4 5 7 9 12 16 21 28 37 49 64
(loop(\(x,i).5x,x,1) mod loop(\(x,i).(x2 + x),2,2))
A070388: 1 5 25 41 37 17 1 5 25 41 37 17 1 5 25 41
(2 * (2 + loop(\(x,i).(1 + (if (x + ~4) <= 0 then x else (x + 2))),2,x)))
A337252: 8 10 12 14 20 26 28 30 32 34 36 38 40 42 44 46
(loop(\(x,i).(~x + 1),x,loop(\(x,i).(2x - ((x div 2) mod 2)),x,2)) div 2)
A077972: 1 ~1 2 ~5 9 ~18 37 ~73 146 ~293 585 ~1170 2341 ~4681 9362 ~18725
(loop(\(x,i).(x2 + ~x),1,loop(\(x,i).((x2 + x) div 2),x,2)) div 2)
A145272: 1 3 15 210 26565 358999410 64449908117864115
(loop(\(x,i).(2x * (1 + (if (x mod (1 + i)) <= 0 then 0 else i))),x,2) div 2)
A141900: 1 2 12 24 240 480 6720 13440 241920 483840 10644480 21288960 553512960 1107025920 2214051840 4428103680
(2 * loop(\(x,i).(2x + (if ((~1 + i) mod 4) <= 0 then 2 else 0)),x,2))
A102651: 4 12 24 48 96 196 392 784 1568 3140 6280 12560 25120 50244 100488 200976
loop(\(x,i).loop(\(x,i).(((x + i) * i) div (x + 1)),x,(x + 2)),(x + 2),2)
A020706: 4 6 9 14 22 35 56 90 145 234 378 611 988 1598 2585 4182
loop(\(x,i).2x,x,(2 + loop(\(x,i).2x,(x + 2),2) - (x mod 2)))
A001446: 10 34 136 520 2080 8224 32896 131200 524800 2097664 8390656 33556480 134225920 536879104 2147516416 8589967360
loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,(x + 4))
A027764: 4 25 90 245 560 1134 2100 3630 5940 9295 14014 20475 29120 40460 55080 73644
loop(\(x,i).2x,x,loop(\(x,i).(3x + 2),x,(2x + 4)))
A298198: 4 40 320 2368 16832 116608 793088 5318656 35271680 231786496 1511653376 9795518464 63126683648 404881506304 2586017398784 16456474427392
(loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,(x + 2)) div 2)
A085373: 1 9 60 350 1890 9702 48048 231660 1093950 5080790 23279256 105462084 473227300 2106121500 9307051200 40873466520
((loop(\(x,i).3x,x,2) - loop(\(x,i).2x,x,(x + 2))) div 2)
A066810: 0 0 1 7 33 131 473 1611 5281 16867 52905 163835 502769 1532883 4651897 14070379
(2 * loop(\(x,i).(x + (if (x + ~2) <= 0 then 3 else x)),x,(~2x + 1)))
A320674: 2 4 6 8 10 12 16 20 24 32 40 48 64 80 96 128
(2 + loop(\(x,i).(1 - (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),2,2x))
A214061: 2 4 6 2 10 12 2 16 3 2 22 24 2 3 30 2
loop(\(x,i).~x,x,loop(\(x,i).(2x * (1 + (2 * i))),2x,2))
A024343: 2 ~120 30240 ~17297280 17643225600 ~28158588057600 64764752532480000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 4) <= 0 then x else (if (x mod 2) <= 0 then (x div 2) else 4x))
A246943: 0 4 1 12 4 20 3 28 8 36 5 44 12 52 7 60
(2 * loop(\(x,i).(x - (if (2x mod (1 + i)) <= 0 then 2 else 1)),x,2x))
A308044: 0 0 2 4 2 8 10 8 14 16 14 20 18 16 26 28
((if x <= 0 then 1 else (2 + (if (x mod 2) <= 0 then (~x + 2) else x))) + ((x div 2) mod 2))
A327824: 1 3 3 6 0 7
(loop(\(x,i).3x,x,2) - loop(\(x,i).3x,(x div 2),2))
A262414: 0 4 12 48 144 468 1404 4320 12960 39204 117612 353808 1061424 3187188 9561564 28693440
(if (if (x mod (2 + ((x + ~1) mod 3))) <= 0 then x else 0) <= 0 then (x mod 2) else 2)
A339975: 0 1 0 1 2 1 0 1 0 1 2 1 2 1 0 1
((if ((if x <= 0 then 1 else x) mod 3) <= 0 then 2 else 1) * (1 - (2 * (x mod 2))))
A281727: 1 ~1 1 ~2 1 ~1 2 ~1 1 ~2 1 ~1 2 ~1 1 ~2
(2 * (loop(\(x,i).4x,x,2) - loop(\(x,i).3x,x,2)))
A145544: 0 4 28 148 700 3124 13468 56788 235900 969844 3958108 16068628 64983100 262058164 1054609948 4237571668
(loop(\(x,i).(x + ((x + (if (i mod 2) <= 0 then 2 else 0)) div 3)),x,2) div 2)
A240840: 1 1 1 2 3 4 5 7 9 12 17 22 30 40 53 71
(2 + (loop(\(x,i).(x2 + (x mod 2)),x,1) + loop(\(x,i).x2,x,2)))
A092733: 5 8 22 274 65794
(if x <= 0 then 1 else (4 + (x * (if (x + ~2) <= 0 then 1 else x3))))
A053611: 1 5 6 85
(loop(\(x,i).(x + (loop(\(x,i).(1 + (x * i)),(~1 + i),1) + i)),x,2) div 2)
A222011: 1 2 4 8
A116723: 1 2 4 8 18 53 219 1201 8055 62860 556070 5488126 59740688 710771367 9174170117 127661752527
(2 * loop(\(x,i).(loop(\(x,i).(1 + (x * i)),(1 + i),1) + (x * i)),x,2))
A259104: 4 14 60 310 1892 13374 107644 972710 9754500 107518702 1292197244 16818292374 235673103460 3537700674590 56637064388412 963304044932614
(if x <= 0 then 0 else loop(\(x,i).(10x + ~6),x,2))
A073554: 0 14 134 1334 13334 133334 1333334 13333334 133333334 1333333334 13333333334 133333333334 1333333333334 13333333333334 133333333333334 1333333333333334
((x * loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,(x + ~1),1))) div 2)
A082134: 0 1 6 30 144 680 3168 14560 66048 296064 1313280 5772800 25178112 109078528 469819392 2013388800
loop(\(x,i).((x * (1 + (2 * i))) - loop(\(x,i).(x * i),(~1 + i),1)),x,2)
A303108: 2 5 24 166 1488 16344 212352 3184560 54132480 1028476800 21597649920 496742319360 12418518067200 335299508812800 9723679528550400 301433978206771200
loop(\(x,i).(loop(\(x,i).((x2 + ~x) div 2),2,(x + 2)) div 3),x,2)
A100009: 2 5 70 1088430 4611686018427387903
loop(\(x,i).(6x + (if (i mod 3) <= 0 then 2 else 1)),x,2)
A037555: 2 13 79 476 2857 17143 102860 617161 3702967 22217804 133306825 799840951 4799045708 28794274249 172765645495 1036593872972
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(3x + 2))
A016798: 1024 9765625 1073741824 25937424601 289254654976 2015993900449 10240000000000 41426511213649 141167095653376 420707233300201 1125899906842624 2758547353515625 6278211847988224 13422659310152401 27197360938418176 52599132235830049
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(3x + 2))
A016800: 4096 244140625 68719476736 3138428376721 56693912375296 582622237229761 4096000000000000 21914624432020321 95428956661682176 353814783205469041 1152921504606846976 3379220508056640625
(if x <= 0 then 1 else (2 * (x + ((if (x + ~4) <= 0 then 1 else x) div 3))))
A301587: 1 2 4 6 8 12 16 18 20 24
((x + 2) + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))
A061228: 2 4 6 6 10 8 14 10 12 12 22 14 26 16 18 18
(2 * compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)),x))
A309355: 8 14 20 24 26 32 34 38 44 48 50 54 56 62 64 68
(loop(\(x,i).(~x + 1),(x + ~1),(x + loop(\(x,i).(1 + (x * i)),x,1))) div 2)
A009578: 0 1 ~3 9 ~34 165 ~981 6853 ~54804 493209 ~4932055 54252561 ~651030678 8463398749 ~118487582409 1777313736045
((x + ~2) + loop(\(x,i).(1 + loop(\(x,i).(x * ((x + 1) div 2)),i,x)),x,1))
A154737: ~1 1 3 164 4611686018427387903
(2 + (if x <= 0 then 2 else (x + loop(\(x,i).(6 + (x div 2)),x,1))))
A033662: 4 9 13 15 17 18 19 20 21 22 23 24 25 26 27 28
((if (x mod 4) <= 0 then (x div 2) else (x + (if (x mod 2) <= 0 then x else 1))) div 2)
A065173: 0 1 2 2 1 3 6 4 2 5 10 6 3 7 14 8
((x + 2) - loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 2 else 1)),(x + 1),x))
A146968: 4 5 7
A033557: 4 5 7 7 9 9 11 13 15 13 15 15 17 19 21 19
loop(\(x,i).loop(\(x,i).(x * (~2 + (i mod 2))),x,1),1,((x2 + x) div 2))
A183895: 1 ~1 ~2 8 32 ~128 ~1024 16384 262144 ~4194304 ~134217728 8589934592 549755813888 ~35184372088832 ~4503599627370496 1152921504606846976
((if ((x + 2) mod 8) <= 0 then 2 else 1) - ((if x <= 0 then 1 else x) mod 2))
A292242: 0 0 1 0 1 0 2 0 1 0 1 0 1 0 2 0
((if (x mod 3) <= 0 then 4 else 1) * (2 - ((if x <= 0 then 1 else x) mod 2)))
A010126: 4 1 2 4 2 1 8 1 2 4 2 1 8 1 2 4
((x + (if ((if x <= 0 then 2 else ((x + 1) div 2)) mod 4) <= 0 then 0 else 2)) div 2)
A110266: 1 1 2 2 3 3 4 3 4 5 6 6 7 7 8 7
(loop(\(x,i).(2 + (loop(\(x,i).2x,x,3) mod (x + 1))),2,x) div 2)
A231867: 1 1 1 1 1 1 1 1 1 2 1 1 1 2 7 1
loop(\(x,i).x2,2,loop(\(x,i).32x,x,2))
A013878: 16 16777216 17592186044416 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 2 else ((x + 2) + (2 * (if (x + ~4) <= 0 then 1 else 4))))
A220655: 2 5 6 7 8 15 16 17 18 19 20 21 22 23 24 25
loop(\(x,i).(8x + (if (i mod 3) <= 0 then 2 else 1)),x,2)
A037557: 2 17 137 1098 8785 70281 562250 4498001 35984009 287872074 2302976593 18423812745 147390501962 1179124015697 9432992125577 75463937004618
((loop(\(x,i).x3,2,x) + loop(\(x,i).x2,4,x)) div 2)
A170789: 0 1 33024 21533202 2147614720 76294921875 1410559992576 16616485461604 140737555464192 926510288136165 5000000500000000 22974866110759926 92442132027408384 332708309893839607 1088976679235208960
loop(\(x,i).(4x + (if (~1 + (i mod 3)) <= 0 then 2 else 1)),x,2)
A037561: 2 10 41 166 666 2665 10662 42650 170601 682406 2729626 10918505 43674022 174696090 698784361 2795137446
(loop(\(x,i).(~x + ~1),x,3) mod loop(\(x,i).4x,x,2))
A266255: 1 4 3 124 3 2044 3 32764 3 524284 3 8388604 3 134217724 3 2147483644
(loop(\(x,i).2x,(x + ~1),(x + loop(\(x,i).((x + 2) + i),x,2))) div 2)
A084266: 1 3 11 34 96 256 656 1632 3968 9472 22272 51712 118784 270336 610304 1368064
(2 + (if x <= 0 then 0 else compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)))
A173135: 2 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61
loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),2)
A061286: 2 4 16 64 1024 4096 65536 262144 4194304 268435456 1073741824 68719476736 1099511627776 4398046511104 70368744177664 4503599627370496
(2 * loop(\(x,i).(x * loop(\(x,i).(2x + 2),x,2)),1,(x2 + 2x)))
A244056: 0 180 16352 3932100 3221225376 9620726742900 108086391056891712 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).3x,(x + 1),loop(\(x,i).(2x + (i mod 2)),x,2))
A262415: 6 45 270 1701 10206 61965 371790 2237301 13423806 80601885 483611310 2902199301 17413195806 104483957805 626903746830 3761465527701
(loop(\(x,i).~x,x,(~1 + (x mod 3))) + loop(\(x,i).2x,x,2))
A130785: 1 4 9 17 32 63 127 256 513 1025 2048 4095 8191 16384 32769 65537
loop(\(x,i).(x4 + x3 + x2 + x),1,loop(\(x,i).2x,x,2))
A115500: 30 340 4680 69904 1082400 17043520 270549120 4311810304 68853957120 1100586419200 17600780175360 281543712968704 4504149450301440 72061992352890880 1152956690052710400 4611686018427387903
loop(\(x,i).(4x2 + ~3x + ~1),1,loop(\(x,i).2x,x,2))
A220236: 9 51 231 975 3999 16191 65151 261375 1047039 4191231 16771071 67096575 268410879 1073692671 4294868991 17179672575
(loop(\(x,i).(x * (4 + i)),x,3) - loop(\(x,i).2x,x,2))
A123367: 1 11 82 614 5008 45296 453472 4989344 59874688 778376576 10897284352 163459291904 2615348727808 44460928495616 800296713183232 15205637551038464
(loop(\(x,i).2x,(x div 2),(~1 + (x mod 2))) mod loop(\(x,i).2x,x,2))
A287470: 1 0 6 0 28 0 120 0 496 0 2016 0 8128 0 32640 0
(loop(\(x,i).(~3 + (x div ~2)),x,1) mod loop(\(x,i).2x,x,2))
A283709: 1 0 7 13 30 62 126 254 510 1022 2046 4094 8190 16382 32766 65534
(loop(\(x,i).(~1 + (x * (~2 + (i mod 2)))),x,1) mod loop(\(x,i).2x,x,2))
A282417: 1 2 3 12 7 56 15 240 31 992 63 4032 127 16256 255 65280
loop(\(x,i).(12x + ~12),2,loop(\(x,i).2x,x,2))
A278128: 132 420 996 2148 4452 9060 18276 36708 73572 147300 294756 589668 1179492 2359140 4718436 9437028
(((if (x + ~1) <= 0 then 3 else 0) - (x mod 2)) mod loop(\(x,i).2x,x,2))
A277928: 1 2 0 15 0 63 0 255 0 1023 0 4095 0 16383 0 65535
(loop(\(x,i).(2x + 2),(x div 2),(x mod 2)) + loop(\(x,i).2x,x,2))
A159230: 2 5 10 20 38 74 142 278 542 1070 2110 4190 8318 16574 33022 65918
(2 + compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),x))
A033159: 2 3 5 6 11 12 14 15 29 30 32 33 38 39 41 42
loop(\(x,i).(3x + (if (~1 + (i mod 3)) <= 0 then 2 else 1)),x,2)
A037560: 2 8 25 77 233 700 2102 6308 18925 56777 170333 511000 1533002 4599008 13797025 41391077
(2 + compr(\x.loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,2x),x))
A153043: 2 6 9 12 14 15 18 19 21 24 26 27 29 30 33 34
((x + (loop(\(x,i).(x + (if (x - i) <= 0 then x else 0)),x,1) * (x mod 2))) div 2)
A038572: 0 1 1 3 2 6 3 7 4 12 5 13 6 14 7 15
loop(\(x,i).x2,1,loop(\(x,i).(2x - (((x div 2) + i) mod 2)),x,2))
A262334: 4 16 64 225 841 3249 12996 51984 207936 829921 3316041 13256881 53027524 212110096 848440384 3393645025
((x + 2) + loop(\(x,i).(if x <= 0 then 1 else (x3 + ~3x2 + 2x)),2,x))
A242915: 2 4 5 125
compr(\x.loop(\(x,i).(loop(\(x,i).(x div (2 - (x mod 2))),x,x) div 2),2,x),(x + 2))
A173786: 2 3 4 5 6 8 9 10 12 16 17 18 20 24 32 33
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),(x + 2))
A090459-A090417-A020631: 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67
loop(\(x,i).(x - (2 * (if (x + ~1) <= 0 then x else 2))),(1 + (x div 2)),(x + ~2))
A230075: 2 1 0 1 ~2 ~1 0 ~1 2 1 0 1 ~2 ~1 0 ~1
(if x <= 0 then 1 else (2x + (if (x div 4) <= 0 then (x + ~3) else 1)))
A267881: 1 0 3 6 9 11 13 15 17 19 21 23 25 27 29 31
(~2x + loop(\(x,i).2x,(x + ~1),(1 + (if (x + ~2) <= 0 then x else 1))))
A130102: 1 0 2 2 8 22 52 114 240 494 1004 2026 4072 8166 16356 32738
compr(\x.loop(\(x,i).(x div (if (x mod 2) <= 0 then ~2 else 1)),x,(x + 1)),2x)
A225227: 1 7 13
A157971: 1 7 13 21 25 31 37 41 49 55 61 69 73 81 87 93
(2x + (if x <= 0 then 1 else (2 * loop(\(x,i).((x - i) * i),(x div 2),x))))
A231407: 1 4 6
A295523: 1 4 6 10 12 18 30
(x - loop(\(x,i).(x - (if (2x mod (1 + i)) <= 0 then 2 else 1)),x,2x))
A238737: 0 1 1 1 3 1 1 3 1 1 3 1 3 5 1 1
(2x * loop(\(x,i).(2x + (if (2 - i) <= 0 then x else 1)),(x + ~1),x))
A062189: 0 2 20 126 648 2970 12636 51030 198288 747954 2755620 9959598 35429400 124357194 431530092 1482720390
(~x - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * (1 + i)))),x,2x))
A114327: 0 1 ~1 2 0 ~2 3 1 ~1 ~3 4 2 0 ~2 ~4 5
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x + ~2),x)),2x)
A031368: 2 5 11 17 23 31 41 47 59 67 73 83 97 103 109 127
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),2x)
A031215: 3 7 13 19 29 37 43 53 61 71 79 89 101 107 113 131
compr(\x.(1 - loop(\(x,i).(x div (if (x mod 2) <= 0 then ~2 else 1)),x,x)),2x)
A091855: 1 4 7 11 13 16 19 21 25 28 31 35 37 41 44 47
((if (loop(\(x,i).(x2 + 2x),2,2) mod (x + 1)) <= 0 then 0 else 1) + (x mod 2))
A294883: 0 1 1 1 0 2 1 1 1 1 1 2 1 2 1 1
((if ((x div 3) mod 2) <= 0 then (if x <= 0 then 1 else 2) else ~1) + (x mod 2))
A131290: 1 3 2 0 ~1 0 2 3 2 0 ~1 0 2 3 2 0
(loop(\(x,i).4x,(x div (if (~x + 2) <= 0 then 2 else 1)),1) - (x mod 2))
A287199: 1 3 4 3 16 15 64 63 256 255 1024 1023 4096 4095 16384 16383
(loop(\(x,i).(x * ((if (i mod 2) <= 0 then 1 else (2 * i)) - i)),x,1) * (x mod 2))
A177698: 0 1 0 ~3 0 45 0 ~1575 0 99225 0 ~9823275 0 1404728325 0 ~273922023375
loop(\(x,i).2x,(x + ~1),loop(\(x,i).(2x + ~1),(x div 2),(x mod 2)))
A098656: 0 1 ~2 4 ~24 16 ~224 64 ~1920 256 ~15872 1024 ~129024 4096 ~1040384 16384
loop(\(x,i).2x,x,(2 - loop(\(x,i).(~x + ~1),(x div 2),(x mod 2))))
A237275: 2 2 12 32 32 32 192 512 512 512 3072 8192 8192 8192 49152 131072
loop(\(x,i).((2x + 2) * (2 + (if x <= 0 then 0 else 2))),(x div 2),(x mod 2))
A220788: 0 1 4 16
A206918: 0 1 4 16 40 136 328 1096 2632 8776 21064 70216 168520 561736 1348168 4493896
loop(\(x,i).((x + 1) * loop(\(x,i).(x2 + 2x),(~1 + i),1)),x,(x mod 2))
A122570: 0 2 6 150 27030 2523490710 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).4x,x,3) - loop(\(x,i).3x,x,2))
A255463: 1 6 30 138 606 2586 10830 44778 183486 747066 3027630 12228618 49268766 198137946 795740430 3192527658
((x + 2) + loop(\(x,i).((x * i) - (if (~2 + (x div 2)) <= 0 then 0 else 1)),2,x))
A055048: 2 5 8 11 14 17 18 20 23 26 29 32 35 38 41 44
(2 + compr(\x.loop(\(x,i).loop(\(x,i).(x div (1 + (x mod 2))),x,(x + 1)),2,x),x))
A095029: 3 6 7 12 14
A175332: 3 6 7 12 14 15 24 28 30 31 48 56 60 62 63 96
((x * loop(\(x,i).(x2 + x),1,loop(\(x,i).x3,2,x))) div 2)
A170801: 0 1 262656 581160258 137439477760 9536748046875 304679900238336 5699447733924196 72057594574798848 675425860579888245 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(2 * (2x - (x div (1 + i)))),i,2)),x,2)
A066796: 2 8 28 98 350 1274 4706 17576 66196 250952 956384 3660540 14061140 54177740 209295260 810375650
(loop(\(x,i).2x,(x + ~1),loop(\(x,i).(x + (i * i)),x,x2)) div 2)
A085385: 0 1 9 46 184 640 2032 6048 17152 46848 124160 321024 813056 2023424 4960256 12001280
(2 - loop(\(x,i).(2x + loop(\(x,i).(3x + ~3),i,0)),x,2))
A005173: 0 1 12 61 240 841 2772 8821 27480 84481 257532 780781 2358720 7108921 21392292 64307941
(2 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))
A006254: 2 3 4 6 7 9 10 12 15 16 19 21 22 24 27 30
(if x <= 0 then 2 else (2 - loop(\(x,i).((~x2 + ~1) + ((x + ~1) div 2)),x,2)))
A147782: 2 7 31 859
(x * loop(\(x,i).(x + loop(\(x,i).(x * (x - i)),2,(2 + i))),(x + 1),0))
A162669: 0 144 1008 4032 12096 30240 66528 133056 247104 432432 720720 1153152 1782144 2673216 3907008 5581440
(x * loop(\(x,i).(x * i),(x + ~2),loop(\(x,i).(2x + 1),(x + ~1),0)))
A052840: 0 0 2 9 56 450 4464 52920 731520 11566800 206035200 4083488640 89137843200 2124970848000 54929029478400 1530259226496000
(x * loop(\(x,i).(loop(\(x,i).(x * i),i,1) + (x * (1 + i))),(x + ~1),0))
A006675: 0 0 2 15 104 770 6264 56196 554112 5973264 69998400 886897440 12089295360 176484597120 2748022986240 45472329504000
(x * loop(\(x,i).(loop(\(x,i).(x * (i * i)),i,1) + (x * i)),(x + ~1),0))
A217239: 0 0 2 18 216 3960 110160 4399920 238412160 16777031040 1484589254400 161180565638400 21054377854540800 3256459838542310400 4611686018427387903 4611686018427387903
(x * loop(\(x,i).(loop(\(x,i).(x * i),(~1 + i),2) + (x * i)),(x + ~2),0))
A052745: 0 0 0 6 24 110 600 3836 28224 235224 2191680 22584672 255087360 3134139840 41620400640 594082771200
(x * loop(\(x,i).(if x <= 0 then 1 else (x * ((1 + i) * (1 + (2 * i))))),x,0))
A002456: 0 1 30 1260 75600 6237000 681080400 95351256000 16672848192000 3563821301040000 914714133933600000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~x + loop(\(x,i).(2x + loop(\(x,i).(2x + i),(~1 + i),i)),x,0))
A226315: 0 0 5 27 99 307 867 2307 5891 14595 35331 83971 196611 454659 1040387 2359299
(~x + loop(\(x,i).(x + (if (x div 2) <= 0 then 1 else (2 + (x div (2 + i))))),x,0))
A005357: 0 0 0 1 2 3 5 7 9 11 13 15 17 19 22 25
compr(\x.(1 - ((x + 1) mod (1 + loop(\(x,i).(if x <= 0 then i else (x + ~1)),x,0)))),x)
A158582: 4 8 9 10 12 16 17 18 19 20 21 22 24 25 26 28
(x + loop(\(x,i).(x * loop(\(x,i).(x2 div 2),2,(x + 2))),(x + ~1),1))
A155733: 1 2 10 10003 4611686018427387903
(x * loop(\(x,i).(loop(\(x,i).~2x,i,1) + (x * i)),(x + ~1),1))
A335111: 0 1 ~2 6 ~8 40 48 784 5248 49536 490240 5403904 64822272 842742784 11798284288 176974510080
(~x + loop(\(x,i).3x,(~x + 2),(3 + (if x <= 0 then 0 else 2))))
A173896: 27 14 3 2 1
(1 mod (if x <= 0 then 2 else (if ((x + 2) mod (2 + ((x div 2) mod 2))) <= 0 then 1 else x)))
A266786: 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1 1
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,5x)
A016858: 0 9765625 10000000000 576650390625 10240000000000 95367431640625 590490000000000 2758547353515625 10485760000000000 34050628916015625 97656250000000000 253295162119140625 604661760000000000 1346274334462890625 2824752490000000000
loop(\(x,i).loop(\(x,i).x2,2,x3),1,5x)
A016860: 0 244140625 1000000000000 129746337890625 4096000000000000 59604644775390625 531441000000000000 3379220508056640625 4611686018427387903 4611686018427387903 4611686018427387903
(x + (if (x mod 2) <= 0 then (2 + (if (~1 + (x mod 3)) <= 0 then x else 2)) else 1))
A140524: 2 2 6 4 10 6 14 8 12 10 22 12 26 14 18 16
compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 5)),x)
A153052: 2 5 8 10 11 14 15 17 20 22 23 25 26 29 30 32
(if x <= 0 then 1 else (x * (if (x mod 6) <= 0 then (~2 + (x div 2)) else 1)))
A219209: 1 1 2 3 4 5 6 7 8 9 10 11 48 13 14 15
loop(\(x,i).(if x <= 0 then 1 else ((x3 + ~x) div 2)),1,3x)
A157024: 1 12 105 360 858 1680 2907 4620 6900 9828 13485 17952 23310 29640 37023 45540
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,3x)
A016775: 0 177147 362797056 31381059609 743008370688 8649755859375 64268410079232 350277500542221 1521681143169024 5559060566555523 17714700000000000 50542106513726817 131621703842267136 317475837322472439 717368321110468608
loop(\(x,i).loop(\(x,i).3x,x,(x + 1)),1,(x + (x div 3)))
A164985: 1 6 27 405 1458 5103 59049 196830 649539 6908733 22320522 71744535 731794257 2324522934 7360989291 73222472421
compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,(x div 3)),x)
A196747: 0 1 2 6 7 8 18 19 20 24 25 26 54 55 56 60
compr(\x.(3 + loop(\(x,i).(x - (if (~x + i) <= 0 then (2 * i) else 0)),x,x)),x)
A217570: 9 16 17 25 26 27 36 37 38 39 49 50 51 52 53 64
(x + loop(\(x,i).(4x + loop(\(x,i).(x * i),x,1)),(x + ~2),1))
A131959: 1 2 3 8
A112237: 1 2 3 8 144 4611686018427387903
(x + loop(\(x,i).(x + (if (~4 + (x div 2)) <= 0 then 1 else 0)),(x + ~2),1))
A153809: 1 2 3 5 7 9 11 13 15 17 19 21 22 23 24 25
compr(\x.loop(\(x,i).(~2 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,(2x + 1)),x)
A153053: 1 4 7 9 10 13 14 16 19 21 22 24 25 28 29 31
(x + (if x <= 0 then 2 else loop(\(x,i).(2 * (2x - (i mod 2))),(x div 2),1)))
A302400: 2 2 4 5 12 13 36 37
compr(\x.loop(\(x,i).(x div (if (x mod 2) <= 0 then ~2 else 1)),x,(1 + (x div 2))),x)
A081706: 2 3 10 11 14 15 18 19 26 27 34 35 42 43 46 47
((x + ~1) + loop(\(x,i).loop(\(x,i).(((x + i) * i) div (x + 1)),x,i),x,2))
A097911: 1 3 5 8
A232896: 1 3 5 8 12 18 27 41 63 98 154 244 389 623 1001 1612
loop(\(x,i).(if x <= 0 then 1 else (2 * (x - (x div ~2)))),(x + ~1),(~x + 1))
A326339: 1 0 1 4 12 36 108 324
compr(\x.((x div 2) mod 2),loop(\(x,i).(x + (if x <= 0 then (1 + i) else 0)),x,(~x + 1)))
A104571: 1 4 1 5 4 1 8 5 4 1 9 8 5 4 1 12
loop(\(x,i).((1 + (2 * (2 + (x mod 2)))) * (if x <= 0 then 1 else x)),x,(~x + 1))
A083224: 1 5 49 245 2401 12005 117649 588245 5764801 28824005 282475249 1412376245 13841287201 69206436005 678223072849 3391115364245
compr(\x.(~1 + loop(\(x,i).(x div (if (x mod 2) <= 0 then 4 else 1)),3,x)),x)
A227992: 0 1 2 4 6 8 10 16 18 24 26 32 34 40 42 64
(if x <= 0 then 1 else (x * (1 + ((x mod 8) mod (if x <= 0 then 1 else x)))))
A114799: 1 1 2 3 4 5 6 7 8 18 30 44 60 78 98 120
compr(\x.(1 + loop(\(x,i).(x - (if (x mod 2) <= 0 then i else 1)),(x div 4),x)),x)
A327374: 52 53 54 55 60 61 62 63 64 65 66 67 68 69 70 71
(x * (if (x div 4) <= 0 then 1 else (if (x mod (2 + (x mod 2))) <= 0 then x else 1)))
A103390: 0 1 2 3 16 5 36 7 64 81 100 11 144 13 196 225
compr(\x.(1 + loop(\(x,i).(0 - (if (x mod (1 + i)) <= 0 then 0 else x)),(x div 2),x)),x)
A002145: 3 7 11 19 23 31 43 47 59 67 71 79 83 103 107 127
(x * loop(\(x,i).x2,1,loop(\(x,i).3x,(x + 1),(x + 1))))
A128992: 0 324 13122 314928 5904900 95659380 1406192886 19284931008 251048476872 3138105960900 37971082126890 447368385785904 5154903899851212 58290067175240628 648557066098144350
(x + (if x <= 0 then 2 else loop(\(x,i).(x - (x div 4)),4,(x + 1))))
A285980: 2 3 5 6 7 8 9 10 12 13 15 16 17 19 20 21
(x * loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then i else 0)),(x div 2),(x + 1)))
A013636: 0 2 6 15 20 35 42 77 88 99 110 143 156 221 238 255
(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1)))
A265331-A001511: 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5
compr(\x.((x + 1) + loop(\(x,i).((x + 1) - (if x <= 0 then 2 else (2 * i))),x,x)),x)
A189151: 5 10 11 17 18 19 26 27 28 29 37 38 39 40 41 50
(loop(\(x,i).3x,(x + ~1),x) - loop(\(x,i).2x,(x + ~1),x))
A344215: 0 0 2 15 76 325 1266 4655 16472 56745 191710 638275 2101188 6855485 22205834 71498775
(loop(\(x,i).(2x * (1 + (2 * i))),(x + ~1),1) div (if x <= 0 then 1 else x))
A006963: 1 1 3 20 210 3024 55440 1235520 32432400 980179200 33522128640 1279935820800 53970627110400 2490952020480000 124903451312640000 4611686018427387903
((1 + (2 * (if x <= 0 then 2 else x4))) div (if x <= 0 then 1 else x))
A184537: 5 3 16 54 128 250 432 686 1024 1458 2000 2662 3456 4394 5488 6750
(loop(\(x,i).6x2,3,x) div (if x <= 0 then 1 else x))
A016915: 0 279936 35831808 612220032 4586471424 21870000000 78364164096 230539333248 587068342272 1338925209984 2799360000000 5455160701056 10030613004288 17565568854912 29509034655744
(loop(\(x,i).8x2,3,x) div (if x <= 0 then 1 else x))
A017071: 0 2097152 268435456 4586471424 34359738368 163840000000 587068342272 1727094849536 4398046511104 10030613004288 20971520000000 40867559636992 75144747810816 131593177923584
(loop(\(x,i).5x2,3,x) div (if x <= 0 then 1 else x))
A016855: 0 78125 10000000 170859375 1280000000 6103515625 21870000000 64339296875 163840000000 373669453125 781250000000 1522435234375 2799360000000 4902227890625 8235430000000 13348388671875
(x + loop(\(x,i).(x + loop(\(x,i).(i - ((1 + i) mod (x + 1))),i,0)),x,1))
A342474: 1 3 5 9 13 17
A063915: 1 3 5 9 13 17 21 29 37 45 53 61 69 77 85 101
((x + 1) + compr(\x.(loop(\(x,i).(2x + ~2),x,1) mod (if x <= 0 then 1 else x)),x))
A173137: 1 3 5 7 10 13 18 21 26 29 34 41 44 51 56 59
(x + loop(\(x,i).(x + loop(\(x,i).(x + ((i div 2) + i)),(1 + i),2)),x,1))
A289877: 1 8 19 36 60 93 136 191 259 342 441 558 694 851 1030 1233
(x + loop(\(x,i).(x + (loop(\(x,i).(x div (1 + (x mod 2))),x,i) div 2)),x,1))
A191535-A100598: 1 2 4 5 8 10
A174989: 1 2 4 5 8 10 14 15 20 23 29 31 38 42 50 51
(x + loop(\(x,i).(x + loop(\(x,i).(x + (x div (~1 + (2 * i)))),x,i)),x,1))
A099074: 1 4 11 24 43 70 109 158 221 300 391 500 633 780 961 1168
(if x <= 0 then 1 else (x + (if (~2 + (x div 3)) <= 0 then 3 else ~2)))
A178052: 1 4 5 6 7 8 9 10 11 7 8 9 10 11 12 13
compr(\x.(loop(\(x,i).(x div 2),x,loop(\(x,i).(3x + 2),x,0)) mod 2),x)
A073634: 0 2 9 11 13 16 19 23 24 26 28 29 31 36 37 39
((x + 1) - loop(\(x,i).(~9 + (if x <= 0 then 1 else x)),2,x))
A168099: 9 10 11 12 13 14 15 16 17 18 19 19 19 19 19 19
(~x + ((3 * loop(\(x,i).(x + (if (x - i) <= 0 then x else 0)),x,1)) div 2))
A337909: 1 2 4 3 8 7 6 5 16 15 14 13 12 11 10 9
(if x <= 0 then 1 else loop(\(x,i).(x - (x div ~12)),2,x))
A194378: 1 3 4 5 6 7 8 9 10 11 12 13 15 17 18 19
loop(\(x,i).(x - ((if (x mod 3) <= 0 then x else (~x + 1)) div 3)),2,x)
A295484: 0 1 2 3 7
A168222: 0 1 2 3 7 9 5 6 15 4 17 10 11 23 25 13
(x * (loop(\(x,i).(x * i),x,(1 + loop(\(x,i).(x * i),x,(x + 2)))) div 2))
A294193: 0 2 18 279 6960 252300 12443760 800168040 65028257280 6518255405760 790091384544000 113924591159702400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.(loop(\(x,i).i,(loop(\(x,i).(x div (2 - (x mod 2))),x,x) div 2),1) mod 2),x)
A225836: 5 9 10 13 17 18 20 21 25 26 29 33 34 36 37 40
loop(\(x,i).(x div (2 - (x mod 2))),x,(x + (loop(\(x,i).2x,x,1) div 2)))
A271573: 0 1 1 7 3 21 19 71 17 265 261 1035 515 4109 4103 16399
loop(\(x,i).(2 - (loop(\(x,i).~2x2,2,2) mod (x + 1))),2,x)
A092505: 1 1 2 1 2 2 2 1 2 2 2 2 2 4 2 1
(x + (if (x + ~2) <= 0 then 1 else (2 + (if (~2 + (x div 4)) <= 0 then 0 else 2))))
A022306: 1 2 3 5 6 7 8 9 10 11 12 13 16 17 18 19
loop(\(x,i).((x3 div 8) + (if x <= 0 then 1 else 2)),2,x)
A218086: 2 3 5 17 127
loop(\(x,i).(if x <= 0 then 1 else ((x + 2) - ((((x + 1) div 2) div 2) div 2))),2,x)
A196008: 3 5 6 7 8 8 9 9 10 11 12 13 14 15 15 15
loop(\(x,i).((if x <= 0 then 1 else x) - (x div 7)),4,x)
A071640: 1 1 2 3 4 5 6 6 6 6 6 7 8 9 9 10
(x + loop(\(x,i).(1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2))),(x + ~2),2))
A341016: 2 3 4 6 8 10 12 16 20 24 28 32 36 40 44 48
compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),x,(~4x + 1)),x)
A005099: 1 2 3 5 6 8 11 12 15 17 18 20 21 26 27 32
compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,4x),x)
A083097-A083095: 0 2 5 6 14 15 18 20 41 42 45 47 54 56 59 60
compr(\x.loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,4x),x)
A045751: 0 2 5 6 8 11 12 14 16 17 19 20 21 23 26 29
(x + ((x - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * i))),x,2x)) div 2))
A128217: 0 1 4 5 8 9 10 15 16 17 18 23 24 25 26 27
compr(\x.((2 * (if x <= 0 then 1 else x)) mod loop(\(x,i).x2,2,(2 + (x mod 2)))),x)
A185359: 8 16 24 32 40 48 56 64 72 80 81 88 96 104 112 120
loop(\(x,i).(x * (1 + (if (x mod 9) <= 0 then 0 else 2))),2,x)
A109050: 0 9 18 9 36 45 18 63 72 9 90 99 36 117 126 45
loop(\(x,i).loop(\(x,i).(x + (x div (~1 + (4 * (1 + i))))),2,x),2,x)
A277025: 0 1 2 3 4 5 6 9 10 12 14 15 17 18 20 21
loop(\(x,i).(if x <= 0 then 1 else (x + ((((x + ~1) div 3) * i) div 2))),2,x)
A076144: 1 1 2 3 5 6 7 10 11 13 14 15 17 19 21 22
(~x + loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 2 else 1)),(x + ~2),(x + 2)))
A007918: 2 2 2 3 5 5 7 7 11 11 11 11 13 13 17 17
loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,(x2 + 2x))
A144454: 0 1 8 5 8 35 16 7 80 11 40 143 56 65 224 85
loop(\(x,i).(if x <= 0 then 1 else (3 * (x + (x mod 2)))),2,(x2 + 2x))
A208064: 6 36 72 144 216 324 432 576 720 900 1080 1296 1512 1764 2016 2304
(if (x + ~2) <= 0 then 0 else loop(\(x,i).(2x * (~1 + (2 * i))),(x + ~2),x))
A052711: 0 0 0 6 48 600 10080 211680 5322240 155675520 5189184000 194075481600 8045310873600 366061644748800 18134130709094400 971471287987200000
compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),(x div 2),(~2x + 1)),x)
A111333: 1 2 3 4 6 7 9 10 12 15 16 19 21 22 24 27
(~x + loop(\(x,i).(x + ((if (i mod 2) <= 0 then 1 else x) * (1 + (2 * i)))),x,2))
A135066: 2 7 11 101
compr(\x.loop(\(x,i).loop(\(x,i).~x,3x,((~x + ~1) + i)),x,2),x)
A231407: 1 4 6
A003662: 1 4 6 8 11 13 16 18 23 25 28 30 35 37 40 42
compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + 2))),x)
A088110: 0 1 3 9
A067201: 0 1 3 9 15 21 33 39 45 57 81 99 105 111 117 123
(loop(\(x,i).3x,2x,1) + loop(\(x,i).x3,2,x))
A185277: 1 10 593 20412 268705 2012174 10609137 45136576 177264449 774840978 4486784401 33739007300 287589316833 2552470327702 22897453501745 205929575454024
(loop(\(x,i).3x,2x,1) - loop(\(x,i).x3,2,x))
A024110: 1 8 ~431 ~18954 ~255583 ~1894076 ~9546255 ~35570638 ~91171007 0 2486784401 29023111918 277269756129 2531261328956 22856131408177 205852688735274
(loop(\(x,i).6x,x,1) - loop(\(x,i).x3,2,x))
A024071: 1 5 ~476 ~19467 ~260848 ~1945349 ~10031040 ~40073671 ~132538112 ~377342793 ~939533824 ~1995150635 ~2982998016 2456194643 57703117312 431741625201
(loop(\(x,i).8x,x,1) - loop(\(x,i).x3,2,x))
A024097: 1 7 ~448 ~19171 ~258048 ~1920357 ~9815552 ~38256455 ~117440512 ~253202761 73741824 6231986901 63559696384 539151314515 4377385464320 35145928729457
(loop(\(x,i).x3,2,(x + 1)) + loop(\(x,i).x3,2,x))
A036087: 1 513 20195 281827 2215269 12030821 50431303 174571335 521638217 1387420489 3357947691 7517728043 15764279725 31265546157 59104406159 107162836111
(loop(\(x,i).x3,2,(x + 1)) - loop(\(x,i).x3,2,x))
A022525: 1 511 19171 242461 1690981 8124571 30275911 93864121 253202761 612579511 1357947691 2801832661 5444719021 10056547411 17782312591 30276117361
(loop(\(x,i).5x,x,1) - loop(\(x,i).x3,2,x))
A024058: 1 4 ~487 ~19558 ~261519 ~1950000 ~10062071 ~40275482 ~133827103 ~385467364 ~990234375 ~2309119566 ~4915639727 ~9383796248 ~14557531159 ~7925781250
compr(\x.loop(\(x,i).(if x <= 0 then ((x + ~1) + (2 * i)) else 0),2x,~x),x)
A280682: 0 4 5 6 7 8 16 17 18 19 20 21 22 23 24 36
compr(\x.(x + loop(\(x,i).((x + 1) - (2 * (if x <= 0 then 0 else i))),(x + ~1),1)),x)
A244216: 4 10 11 12 13 28 29 30 31 32 33 34 35 36 37 38
loop(\(x,i).(if ((x mod 3) div 2) <= 0 then x else ((x + 1) div 3)),x,x)
A286577: 0 1 1 3 4 1 6 7 3 9 10 4 12 13 1 15
loop(\(x,i).x3,1,(x2 * loop(\(x,i).x2,2,3)))
A017166: 0 531441 34012224 387420489 2176782336 8303765625 24794911296 62523502209 139314069504 282429536481 531441000000 941480149401 1586874322944 2565164201769 4001504141376 6053445140625
(~x + compr(\x.loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),x,(2x + 1)),x))
A163301: 1 3 5 7 8 8 10 10 11 13 14 14 15 15 17 17
(x * loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x + ~1),x))
A037966: 0 1 8 54 320 1750 9072 45276 219648 1042470 4862000 22355476 101582208 457002364 2038517600 9026235000
loop(\(x,i).((2x * i) - loop(\(x,i).(x * (~1 + (2 * i))),i,1)),x,x)
A035101: 0 1 9 87 975 12645 187425 3133935 58437855 1203216525 27125492625 664761133575 17600023616175 500706514833525 15234653491682625 493699195087473375
compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(~2 + (x div 2)),x)),x)
A046022: 1 2 3 4 5 7 11 13 17 19 23 29 31 37 41 43
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(~2 + (x div 2)),x)),x)
A175787: 2 3 4 5 7 11 13 17 19 23 29 31 37 41 43 47
(~x + loop(\(x,i).(x + ((x - (if (~2 + (x div 2)) <= 0 then 0 else 1)) mod 2)),2,x))
A307198: 0 1 0 1 0 2 1 0 1 0 1 0 1 0 1 0
(x + (if x <= 0 then 1 else loop(\(x,i).(~x - (x div (4 + i))),2,x)))
A072154: 1 3 5 7 9 12 15 17 19 21 24 27 29 31 33 36
compr(\x.(1 - loop(\(x,i).(0 - (if (x mod (1 + i)) <= 0 then 0 else x)),(x div 2),x)),x)
A280084: 1 5 13 17 29 37 41 53 61 73 89 97 101 109 113 137
compr(\x.(2 - loop(\(x,i).(0 - (if (x mod (1 + i)) <= 0 then 0 else x)),(x div 2),x)),x)
A175768-A002144: 5 13 17 29 37 41 53 61 73 89 97 101 109 113 137 149
(loop(\(x,i).4x,x,1) - (x * loop(\(x,i).x3,2,x)))
A024046: 1 3 ~1008 ~58985 ~1048320 ~9764601 ~60462080 ~282458865 ~1073676288 ~3486522257 ~9998951424 ~25933230297 ~61900587008 ~137791382985 ~288986219520 ~575576648801
(loop(\(x,i).3x,x,1) - (x * loop(\(x,i).x3,2,x)))
A024033: 1 2 ~1015 ~59022 ~1048495 ~9765382 ~60465447 ~282473062 ~1073735263 ~3486764718 ~9999940951 ~25937247454 ~61916832783 ~137856897526 ~289249872007 ~576636041718
((~x2 + ~1) + loop(\(x,i).(x - i),x,loop(\(x,i).3x,x,1)))
A061983: 0 0 1 11 54 202 671 2109 6460 19556 58893 176959 531218 1594062 4782667 14348561
loop(\(x,i).loop(\(x,i).x3,i,(x div 3)),(x + ~1),x2)
A058125: 0 1 1 387420489 4611686018427387903
(~x2 + loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,1))
A027966: 1 4 11 26 54 101 174 281 431 634 901 1244 1676 2211 2864 3651
(~x2 + loop(\(x,i).(x + loop(\(x,i).(x + ((2 + i) * i)),i,1)),x,2))
A201371: 2 5 14 36 80 157 280 464 726 1085 1562 2180 2964 3941 5140 6592
(loop(\(x,i).3x,2x,1) - loop(\(x,i).x2,2,x2))
A024109: 1 8 ~175 ~5832 ~58975 ~331576 ~1148175 ~981832 26269505 344373768 3386784401 31166700728 281999554785 2541050097608 22875316665905 205888569204024
(loop(\(x,i).6x,x,1) - loop(\(x,i).x2,2,x2))
A024070: 1 5 ~220 ~6345 ~64240 ~382849 ~1632960 ~5484865 ~15097600 ~32969025 ~39533824 148438175 1746800640 12244963295 76888375040 467622093951
(loop(\(x,i).8x,x,1) + loop(\(x,i).x2,2,x2))
A198401: 1 9 320 7073 69632 423393 1941760 7861953 33554432 177264449 1173741824 8804293473 69149458432 550571544609 4399522300160 35186934979457
(loop(\(x,i).8x,x,1) - loop(\(x,i).x2,2,x2))
A024096: 1 7 ~192 ~6049 ~61440 ~357857 ~1417472 ~3667649 0 91171007 973741824 8375575711 68289495040 548940083167 4396570722048 35181809198207
(loop(\(x,i).x2,3,(x + 1)) + loop(\(x,i).x2,2,x2))
A036086: 1 257 6817 72097 456161 2070241 7444417 22542017 59823937 143046721 314358881 644340577 1245712417 2291519777 4038679681 6857857921
(loop(\(x,i).x2,3,(x + 1)) - loop(\(x,i).x2,2,x2))
A022524: 1 255 6305 58975 325089 1288991 4085185 11012415 26269505 56953279 114358881 215622815 385749025 660058335 1087101569 1732076671
(loop(\(x,i).5x,x,1) - loop(\(x,i).x2,2,x2))
A024057: 1 4 ~231 ~6436 ~64911 ~387500 ~1663991 ~5686676 ~16386591 ~41093596 ~90234375 ~165530756 ~185841071 404972404 4627726569 27954687500
(loop(\(x,i).2x,x,1) - (x2 * loop(\(x,i).x3,2,x)))
A024021: 1 1 ~2044 ~177139 ~4194288 ~48828093 ~362796992 ~1977326615 ~8589934336 ~31381059097 ~99999998976 ~285311668563 ~743008366592 ~1792160385845 ~4049565153280 ~8649755826607
(x2 * loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,x))
A005429: 0 2 48 540 4480 31500 199584 1177176 6589440 35443980 184756000 938929992 4672781568 22850118200 110079950400 523521630000
(~x + compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),(x div 2),~x),x))
A073170: 0 0 1 2 3 6 7 10 11 14 19 20 25 28 29 32
compr(\x.loop(\(x,i).(x - (if ((x + 2) mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x)
A105760: 0 2 3 5 6 8 11 12 15 17 18 20 23 26 27 30
(~x + loop(\(x,i).loop(\(x,i).(2x div (1 + i)),x,(1 + (2 * i))),x,x))
A296064: 0 2 1 ~3 5 ~5 7 ~7 9 ~9 11 ~11 13 ~13 15 ~15
compr(\x.loop(\(x,i).(if ((x + ~1) mod 4) <= 0 then x else (x div 4)),x,x),x)
A023709: 0 2 3 8 10 11 12 14 15 32 34 35 40 42 43 44
compr(\x.(x * (2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x + ~2),x))),x)
A182986: 0 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
compr(\x.loop(\(x,i).(if ((x + (x div 2)) mod 4) <= 0 then x else (x div 2)),x,x),x)
A086638: 0 1 2 4 5 9 10 18 20 21 36 37 41 42 73 74
(loop(\(x,i).4x,x,1) - loop(\(x,i).x2,2,x3))
A024048: 1 3 ~4080 ~531377 ~16776960 ~244139601 ~2176778240 ~13841270817 ~68719411200 ~282429274337 ~999998951424 ~3138424182417 ~8916083671040 ~23298018013617 ~56693643939840 ~129745264148801
(loop(\(x,i).3x,x,1) - loop(\(x,i).x2,2,x3))
A024035: 1 2 ~4087 ~531414 ~16777135 ~244140382 ~2176781607 ~13841285014 ~68719470175 ~282429516798 ~999999940951 ~3138428199574 ~8916099916815 ~23298083528158 ~56693907592327 ~129746323541718
compr(\x.(x - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,x2)),x)
A049422: 0 2 4 8 10 14 22 28 38 50 52 62 64 70 74 76
(x + loop(\(x,i).(~1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),x,x2))
A159918: 0 1 1 2 1 3 2 3 1 3 3 5 2 4 3 4
compr(\x.(1 - loop(\(x,i).(if (x mod (1 + (2 * i))) <= 0 then x else ~x),x,x)),x)
A053868: 2 3 4 5 7 8 11 13 15 16 17 18 19 21 23 27
(~x + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))
A008507: 0 0 0 1 1 2 2 3 5 5 7 8 8 9 11 13
loop(\(x,i).(x + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,x)
A007504: 0 2 5 10 17 28 41 58 77 100 129 160 197 238 281 328
((x div 2) - (if (2 - (x mod 13)) <= 0 then 1 else 0))
A007963: 0 0 0 0 1 1 2 2 3 3 4 4 5 6 7 6
(if (x mod (~1 + (2 * ((x2 div 2) mod 5)))) <= 0 then 1 else 0)
A263428: 1 1 0 0 0 0 0 1 0 1 1 1 1 0 0 1
(if (x mod (1 + (2 * ((x - (x div 3)) mod 3)))) <= 0 then 1 else 0)
A266444: 1 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1
(if ((x2 + 2x) mod (1 + (2 * ((~x + 1) mod 4)))) <= 0 then 1 else 0)
A341603: 1 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1
(if ((2x + 2) mod (2 - ((~x + 2) div 5))) <= 0 then 1 else 0)
A115512: 1 1 1 0 0 1 0 0 0 1 0 1 0 0 1 0
((2x + 4) - (if (2x mod (x + 5)) <= 0 then 1 else 0))
A258050: 3 6 8 10 12 13 16 18 20 22 24 26 28 30 32 34
(if (2x mod (1 + ((2x + ~2) mod (2 + (x div 2))))) <= 0 then 1 else 0)
A279733: 1 1 0 1 0 1 1 0 0 0 1 0 0 1 0 1
(if ((x - ((x2 div 2) div 5)) mod 3) <= 0 then 1 else 0)
A285427: 1 0 0 1 1 1 1 1 0 0 1 0 0 1 0 0
(if (((x2 + ~2x) mod (x + 5)) mod 3) <= 0 then 1 else 0)
A145377: 1 0 1 1 0 0 0 0 1 0 0 1 0 0 0 1
(if ((((x + 2) * (x2 div 2)) div 3) mod 3) <= 0 then 1 else 0)
A331238: 1 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0
(if (~x + 2) <= 0 then (1 + ((x - ((x div 2) mod 3)) div 3)) else 0)
A131808: 0 0 1 1 1 2 3 3 3 3 3 4 5 5 5 5
(if (x mod 7) <= 0 then (1 + ((x + 2) div 3)) else 0)
A340977: 1 0 0 0 0 0 0 4 0 0 0 0 0 0 6 0
((((x div 2) - (x div 3)) div 2) + (if (x mod 3) <= 0 then 1 else 0))
A029320: 1 0 0 1 0 0 1 0 1 1 1 1 2 1 1 2
(if (((x2 + 2) mod 6) mod (1 + (x div 2))) <= 0 then 1 else 0)
A189222: 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 0
(if (x mod (31 div (x + 1))) <= 0 then 1 else 0)
A025893: 1 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1
(if ((x mod 2) - ((~1 + ((x + 2) mod 5)) div 2)) <= 0 then 1 else 0)
A092079-A092078: 1 1 1 0 1 0 1 1 0 0 1 1 1 0 1 0
(if (((~x + (((x + ~1) div 2) mod 2)) mod 5) div 2) <= 0 then 1 else 0)
A025892: 1 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1
(if (~1 + ((x mod 3) + ((x mod 5) div 2))) <= 0 then 1 else 0)
A261430: 1 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1
(if (x mod 4) <= 0 then ((1 + (x div 2)) mod 7) else 0)
A118112: 1 0 0 0 3 0 0 0 5 0 0 0 0 0 0 0
(if (((4 * (2 + (x mod 2))) mod (1 + (x div 2))) div 2) <= 0 then 1 else 0)
A330986: 1 1 1 1 0 1 1 1 0 0 0 1 1 0 1 0
(if (~x + 2) <= 0 then ((2x + ~1) - ((x + ~2) mod 8)) else 0)
A137937: 0 0 3 4 5 6 7 8 9 10 19 20 21 22 23 24
(x + (if (~2 + (x div 4)) <= 0 then 1 else 0) - (x div 5))
A172103: 1 2 3 4 5 5 6 7 8 9 9 10 10 11 12 12
(if (~2 + (x div 3)) <= 0 then (1 + (x mod (2 * (~2 + (x mod 2))))) else 0)
A014389-A014349-A014269-A014229: 1 0 ~1 0 1 0 ~1 0 1 0 0 0 0 0 0 0
(if (x mod 7) <= 0 then ((x + 1) - (2 * (x mod 2))) else 0)
A340979: 1 0 0 0 0 0 0 6 0 0 0 0 0 0 15 0
((x mod 2) - (if (x mod 4) <= 0 then ((x div 3) mod 3) else 0))
A088705: 0 1 0 1 ~1 1 0 1 ~2 1 0 1 ~1 1 0 1
(if (10 mod (x + 1)) <= 0 then ((x + 2) div 3) else 0)
A037213: 0 1 0 0 2 0 0 0 0 3 0 0 0 0 0 0
((2x + 4) - (if (16 mod (x + 2)) <= 0 then 1 else 0))
A096604: 3 6 7 10 12 14 15 18 20 22 24 26 28 30 31 34
(if ((x * (x mod 3)) mod 5) <= 0 then (1 + (x div 2)) else 0)
A102389: 1 0 0 2 0 3 4 0 0 5 6 0 7 0 0 8
(if ((x + 2) mod 12) <= 0 then (x2 + 2x + 1) else 0)
A106547: 0 0 0 0 0 0 0 0 0 0 121 0 0 0 0 0
loop(\(x,i).(1 + (2 * (5x + (i mod 2)))),(x + 1),0)
A037589: 3 31 313 3131 31313 313131 3131313 31313131 313131313 3131313131 31313131313 313131313131 3131313131313 31313131313131 313131313131313 3131313131313131
loop(\(x,i).(11x + 9),(x + 1),0)
A268839: 9 108 1197 13176 144945 1594404 17538453 192922992 2122152921 23343682140 256780503549 2824585539048 31070440929537 341774850224916 3759523352474085 41354756877214944
(if ((((x2 + 2x) div 2) div 5) mod 2) <= 0 then (x + 1) else 0)
A175880: 1 2 3 0 5 0 7 8 9 0 11 12 13 0 15 0
loop(\(x,i).((x + 1) + (2 * (4x + (i mod 2)))),(x + 1),0)
A037588: 3 28 255 2296 20667 186004 1674039 15066352 135597171 1220374540 10983370863 98850337768 889653039915 8006877359236 72061896233127 648557066098144
loop(\(x,i).(10x + 27),(x + 1),0)
A083813: 27 297 2997 29997 299997 2999997 29999997 299999997 2999999997 29999999997 299999999997 2999999999997 29999999999997 299999999999997
loop(\(x,i).(x + ((i * i * (1 + i) * (1 + i)) div 2)),(x + 1),0)
A086755: 2 20 92 292 742 1624 3192 5784 9834 15884 24596 36764 53326 75376 104176 141168
loop(\(x,i).(x + (((((2 + i) * i) div 2) * (1 + i)) div 2)),(x + 1),0)
A233329: 1 7 21 51 102 186 310 490 735 1065 1491 2037 2716 3556 4572 5796
((30x + 6) + (if x <= 0 then 1 else 0))
A063168: 7 36 66 96 126 156 186 216 246 276 306 336 366 396 426 456
((4x3 + 12x2 + 12x + 4) + (if x <= 0 then 1 else 0))
A184536: 5 32 108 256 500 864 1372 2048 2916 4000 5324 6912 8788 10976 13500 16384
((32x + 10) + (if x <= 0 then 1 else 0))
A063152: 11 42 74 106 138 170 202 234 266 298 330 362 394 426 458 490
((2 * ((3x + 2) + (x div 3))) - (if x <= 0 then 1 else 0))
A063209: 3 10 16 24 30 36 44 50 56 64 70 76 84 90 96 104
(~1 + ((x mod 2) + (if (x mod (1 + (x mod 8))) <= 0 then 2 else 0)))
A166698: 1 0 ~1 0 ~1 0 ~1 0 1 0 ~1 0 ~1 0 1 0
(1 - (if ((x mod (2 + (x div 5))) mod 3) <= 0 then 2 else 0))
A098417: ~1 1 ~1 1 ~1 1 ~1 1 1 ~1 1 ~1 ~1 1 1 ~1
(1 - (if ((x + 1) mod 7) <= 0 then 6 else 0))
A291578: 1 1 1 1 1 1 ~5 1 1 1 1 1 1 ~5 1 1
loop(\(x,i).(10x + (i mod 2)),(2x + 2),0)
A163662: 10 1010 101010 10101010 1010101010 101010101010 10101010101010 1010101010101010 101010101010101010 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 - (if ((1 + (x div 4)) mod (2 + (x mod 4))) <= 0 then 2 else 0))
A209661: 1 1 1 1 ~1 1 1 1 1 ~1 1 1 ~1 1 ~1 1
(x div (2 + (if (x mod 5) <= 0 then 4 else 0) - (x mod 2)))
A106611: 0 1 1 3 2 1 3 7 4 9 1 11 6 13 7 3
(if (x mod 3) <= 0 then ((((~1 + (x div 2)) div 2) mod 2) - (x mod 2)) else 0)
A014207-A014135: 1 0 0 ~1 0 0 1 0 0 0 0 0 0 0 0 0
loop(\(x,i).(35x + 1),x,0)
A240129: 0 1 36
A218738: 0 1 36 1261 44136 1544761 54066636 1892332261 66231629136 2318107019761 81133745691636 2839681099207261 99388838472254136 3478609346528894761 4611686018427387903 4611686018427387903
loop(\(x,i).(45x + 1),x,0)
A218748: 0 1 46 2071 93196 4193821 188721946 8492487571 382161940696 17197287331321 773877929909446 34824506845925071 1567102808066628196 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(50x + 1),x,0)
A218752: 0 1 51 2551 127551 6377551 318877551 15943877551 797193877551 39859693877551 1992984693877551 99649234693877551 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(10x + 81),x,0)
A086580: 0 81 891 8991 89991 899991 8999991 89999991 899999991 8999999991 89999999991 899999999991 8999999999991 89999999999991 899999999999991 8999999999999991
loop(\(x,i).((4x + 1) mod 13),x,0)
A021067: 0 1 5 8 7 3 0 1 5 8 7 3 0 1 5 8
loop(\(x,i).(39x + 1),x,0)
A218742: 0 1 40 1561 60880 2374321 92598520 3611342281 140842348960 5492851609441 214221212768200 8354627297959801 325830464620432240 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(7x + 49),x,0)
A168572: 0 49 392 2793 19600 137249 960792 6725593 47079200 329554449 2306881192 16148168393 113037178800 791260251649 5538821761592 38771752331193
loop(\(x,i).(7 * ((x + 1) - (2 * (x mod 2)))),x,0)
A271427: 0 7 42 301 2100 14707 102942 720601 5044200 35309407 247165842 1730160901 12111126300 84777884107 593445188742 4154116321201
loop(\(x,i).(29x + 1),x,0)
A218732: 0 1 30 871 25260 732541 21243690 616067011 17865943320 518112356281 15025258332150 435732491632351 12636242257338180 366451025462807221 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) - (x div (~2 + (x div ~7)))),x,0)
A213706: 0 1 3 5 8 11 15 19 24 29 35 41 48 55 62 69
loop(\(x,i).(9x + 81),x,0)
A247842: 0 81 810 7371 66420 597861 5380830 48427551 435848040 3922632441 35303692050 317733228531 2859599056860 25736391511821 231627523606470 2084647712458311
loop(\(x,i).(10x + 90),x,0)
A124167: 0 90 990 9990 99990 999990 9999990 99999990 999999990 9999999990 99999999990 999999999990 9999999999990 99999999999990 999999999999990 9999999999999990
(8 - loop(\(x,i).(10x + ~10),x,0))
A173734: 8 18 118 1118 11118 111118 1111118 11111118 111111118 1111111118 11111111118 111111111118 1111111111118 11111111111118 111111111111118 1111111111111118
(1 - loop(\(x,i).(10x + ~60),x,0))
A173805: 1 61 661 6661 66661 666661 6666661 66666661 666666661 6666666661 66666666661 666666666661 6666666666661 66666666666661 666666666666661 6666666666666661
(1 - loop(\(x,i).(10x + ~80),x,0))
A173810: 1 81 881 8881 88881 888881 8888881 88888881 888888881 8888888881 88888888881 888888888881 8888888888881 88888888888881 888888888888881 8888888888888881
loop(\(x,i).(10x + 100),x,0)
A124166: 0 100 1100 11100 111100 1111100 11111100 111111100 1111111100 11111111100 111111111100 1111111111100 11111111111100 111111111111100 1111111111111100 11111111111111100
loop(\(x,i).(44x + 1),x,0)
A218747: 0 1 45 1981 87165 3835261 168751485 7425065341 326702875005 14374926500221 632496766009725 27829857704427901 1224513738994827645 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(47x + 1),x,0)
A218750: 0 1 48 2257 106080 4985761 234330768 11013546097 517636666560 24328923328321 1143459396431088 53742591632261137 2525901806716273440 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(46x + 1),x,0)
A218749: 0 1 47 2163 99499 4576955 210539931 9684836827 445502494043 20493114725979 942683277395035 43363430760171611 1994717814967894107 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + (x div (1 + (x mod 7)))),x,0)
A165804: 0 1 2 3 4 5 6 7 15 23 31 39 47 55 63 127
loop(\(x,i).(41x + 1),x,0)
A218744: 0 1 42 1723 70644 2896405 118752606 4868856847 199623130728 8184548359849 335566482753810 13758225792906211 564087257509154652 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(37x + 1),x,0)
A218740: 0 1 38 1407 52060 1926221 71270178 2636996587 97568873720 3610048327641 133571788122718 4942156160540567 182859777940000980 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(49x + 1),x,0)
A218753: 0 1 50 2451 120100 5884901 288360150 14129647351 692352720200 33925283289801 1662338881200250 81454605178812251 3991275653761800300 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + ((x2 div 3) div (x + 3))),x,0)
A067570: 0 1 2 3 4 5 7
A117598: 0 1 2 3 4 5 7 9 12 16 21 28 37 49 65 86
loop(\(x,i).((x + 1) + (x div (2 + (x div 7)))),x,0)
A088236: 0 1 2 4 7 10 14 18 23 28 33 39 45 51 57 63
loop(\(x,i).((x + 1) + (4 * (3x + (x div 2)))),x,0)
A239284: 0 1 14 211 3164 47461 711914 10678711 160180664 2402709961 36040649414 540609741211 8109146118164 121637191772461 1824557876586914 27368368148803711
(2x - loop(\(x,i).((x + 2) - ((x div 5) mod 2)),x,0))
A072229: 0 0 0 0 1 2 3 4 4 4 4 5 6 7 8 8
loop(\(x,i).((x + 2) - ((x mod (2 + (x mod 5))) mod 2)),x,0)
A247875: 0 2 4 6 8 9 10 12 14 16 17 18 19 20 22 24
(x - loop(\(x,i).(~x + ((i div 2) + ((x + (x div 2)) div 4))),x,0))
A129231: 0 1 1 3 2 5 3 6 5 7 7 8 8 10 9 12
(1 - loop(\(x,i).(3x + ~64),x,0))
A036547: 1 65 257 833 2561 7745 23297 69953 209921 629825 1889537 5668673 17006081 51018305 153054977 459164993
loop(\(x,i).(2x + ((1 - (2 * (i mod 2))) * i * i * i)),x,0)
A232604: 0 ~1 6 ~15 34 ~57 102 ~139 234 ~261 478 ~375 978 ~241 2262 1149
(((1 + (x div 3)) mod 2) - loop(\(x,i).(2x - (i mod 2)),x,0))
A024494: 1 2 3 5 10 21 43 86 171 341 682 1365 2731 5462 10923 21845
loop(\(x,i).(x + ((1 + (8 * (~1 + i))) * i * i)),x,0)
A172080: 0 1 37 190 590 1415 2891 5292 8940 14205 21505 31306 44122 60515 81095 106520
(if ((x + 2) mod (3 - ((((x + 1) div 2) div 2) mod 2))) <= 0 then 0 else 1)
A189295: 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 1
(1 + (if (x mod 2) <= 0 then (((x + 1) div 5) mod 3) else 0))
A175494: 1 1 1 1 2 1 2 1 2 1 3 1 3 1 1 1
(if ((x - (~x mod (1 + (x div 4)))) mod 3) <= 0 then 0 else 1)
A286400: 0 1 1 0 1 1 0 0 1 0 1 1 0 1 0 1
(if ((((x2 + ~2) div 3) div 3) mod 3) <= 0 then 0 else 1)
A267673: 1 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0
(~1 + loop(\(x,i).(10x + 12),(x + 1),0))
A185127: 11 131 1331 13331 133331 1333331 13333331 133333331 1333333331 13333333331 133333333331 1333333333331 13333333333331 133333333333331 1333333333333331 13333333333333331
(1 + (if (x mod (1 + ((x2 + 2) mod (x + 3)))) <= 0 then 2 else 0))
A095346: 3 1 3 1 1 1 3 1 3 1 1 1 3 1 1 1
(1 + (if ((1 + ((x + (x div 2)) div 2)) mod 5) <= 0 then 2 else 0))
A115069: 1 1 1 1 1 1 3 1 1 1 1 1 3 3 1 1
(1 + (if ((x - ((~1 + (x div 2)) div 2)) mod 5) <= 0 then 2 else 0))
A326057: 1 1 1 1 1 3 3 1 1 1 1 1 3 1 1 1
(1 + (if ((x + 1) mod 7) <= 0 then 6 else 0))
A268354: 1 1 1 1 1 1 7 1 1 1 1 1 1 7 1 1
(if ((x + 1) mod (4 - ((x mod 5) div 2))) <= 0 then 0 else 1)
A108788: 1 1 0 1 1 1 1 1 0 0 1 0 1 1 1 0
(1 + (if (x mod 2) <= 0 then (x div (2 + (x div (2 + (x mod 3))))) else 0))
A055399: 1 1 2 1 2 1 2 1 3 1 3 1 2 1 3 1
(1 + (if ((1 + (x div 4)) mod (2 + (x mod 4))) <= 0 then 2 else 0))
A256452: 1 1 1 1 3 1 1 1 1 3 1 1 3 1 3 1
(~1 + (if ((((x + ~1) div 2) * (x mod 3)) mod 4) <= 0 then 2 else 0))
A155040: 1 1 1 1 ~1 1 1 ~1 ~1 1 1 ~1 1 ~1 1 1
(1 + (if ((((x + 1) div 2) div 2) mod 2) <= 0 then (x div 8) else 0))
A316894: 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 2
(1 + (if ((x + 2) mod 6) <= 0 then ((x div 2) mod 4) else 0))
A030381: 1 1 1 1 3 1 1 1 1 1 2 1 1 1 1 1
((7x + 7) + (if (~2 + (x div 2)) <= 0 then 0 else 1))
A028437: 7 14 21 28 35 42 50 57 64 71 78 85 92 99 106 113
(11x + (if (~2 + (x div 2)) <= 0 then 0 else 1))
A004940: 0 11 22 33 44 55 67 78 89 100 111 122 133 144 155 166
(1 + (if ((~x + 1) mod 3) <= 0 then (2 * (x + (x div 3))) else 0))
A078688: 1 3 1 1 11 1 1 19 1 1 27 1 1 35 1 1
(1 + loop(\(x,i).(10x + (i mod 2)),2x,0))
A127961: 1 11 1011 101011 10101011 1010101011 101010101011 10101010101011 1010101010101011 101010101010101011 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x mod (1 + (if (x mod (3 + (x mod 4))) <= 0 then (x div 2) else 0)))
A055242-A055241: 0 0 0 0 0 0 0 0 0 0 4 0 5 0 0 0
(1 + loop(\(x,i).(x + i - (x mod 11)),x,0))
A032947: 1 2 3 4 5 6 7 8 9 10 11 12 24 36 48 60
(1 + (if ((x mod 6) mod (1 + (x div 3))) <= 0 then x else 0))
A089026-A080305: 1 2 3 1 5 1 7 1 1 1 11 1 13 1 1 1
(1 + (if (~1 + ((2x + 1) mod (2 + (x div 4)))) <= 0 then x else 0))
A100994: 1 2 3 4 5 1 7 8 9 1 11 1 13 1 1 16
(1 + (if (2 - ((x div 2) div (~1 + (2 * (x mod 4))))) <= 0 then x else 0))
A080304: 1 1 1 1 1 6 1 1 1 10 1 1 1 14 15 1
(1 + loop(\(x,i).((x + 3) - ((x div 3) mod 3)),x,0))
A231407: 1 4 6
A104211: 1 4 6 8 9 10 13 15 17 18 19 22 24 26 27 28
(1 + loop(\(x,i).(1 + (((x + 1) + (i div (2 + (x mod 2)))) div 2)),x,0))
A284359: 1 2 3 4 4 4 5 6 6 6 6 6 7 8 8 8
((2x + 1) div (1 + loop(\(x,i).(i - ((1 + i) mod (x + 1))),x,0)))
A194449: 1 1 2 1 2 2 3 1 2 2 2 2 3 3 3 1
(1 + loop(\(x,i).((2 * (1 + (x * (~1 + (2 * i))))) div (1 + i)),x,0))
A141351: 1 2 3 6 15 43 133 430 1431 4863 16797 58787 208013 742901 2674441 9694846
(1 + loop(\(x,i).(2 * ((~x + 2) mod 14)),x,0))
A070378: 1 5 25 13 9 17 1 5 25 13 9 17 1 5 25 13
(1 + loop(\(x,i).(2 * ((5x + 2) - (i mod 2))),x,0))
A099913: 1 3 25 243 2425 24243 242425 2424243 24242425 242424243 2424242425 24242424243 242424242425 2424242424243 24242424242425 242424242424243
(if (x - ((x3 + x) mod (x + 8))) <= 0 then 0 else 1)
A024937: 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1
(1 + loop(\(x,i).(x + i - ((2x div (2 + (x div 2))) mod 2)),x,0))
A220315: 1 2 3 5 9 14
A076027: 1 2 3 5 9 14 19 25 32 40 49 59 70 82 95 109
((28x + 7) - (if x <= 0 then 0 else 1))
A063166: 7 34 62 90 118 146 174 202 230 258 286 314 342 370 398 426
(((2 * ((x + 2) mod 5)) mod 3) - (if x <= 0 then 0 else 1))
A163818: 1 ~1 1 ~1 1 0 ~1 1 ~1 1 0 ~1 1 ~1 1 0
(((x2 + 8x) div (x + 3)) + (if x <= 0 then 0 else 1))
A057716: 0 3 5 6 7 9 10 11 12 13 14 15 17 18 19 20
(((x mod (1 - (x mod (~1 + (x div ~2))))) div 2) + (if x <= 0 then 0 else 1))
A336123: 0 1 1 1 1 1 1 2 2 1 1 2 1 1 2 2
(((2x mod (1 + ((1 + (x div 2)) div 2))) div 2) + (if x <= 0 then 0 else 1))
A054868: 0 1 1 1 1 1 1 2 1 1 1 2 1 2 2 1
(((1 + (x2 div 16)) div 2) + (if x <= 0 then 0 else 1))
A051066: 0 1 1 1 2 2 2 3 3 4 4 5 6 6 7 8
(((((x * (x div 2)) div 2) div 5) mod 2) + (if x <= 0 then 0 else 1))
A332992: 0 1 1 1 1 2 2 1 2 2 2 2 2 2 2 1
((((x div 2) mod (1 + (~x mod 4))) div 2) + (if x <= 0 then 0 else 1))
A327804: 0 1 1 1 1 2 1 1 1 1 2 1 1 2 1 1
(((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2) + (if x <= 0 then 0 else 1))
A328512-A322307-A302041-A302031-A294893-A293460-A237353-A001221: 0 1 1 1 1 2 1 1 1 2 1 2 1 2 2 1
(((((x + ~1) * (x div 4)) mod 3) div 2) + (if x <= 0 then 0 else 1))
A249615: 0 1 1 1 1 1 2 1 2 1 1 2 1 1 1 1
((2 * (1 - ((~x + 2) div 12))) + (if x <= 0 then 0 else 1))
A225577: 2 3 3 5 5 5 5 5 5 5 5 5 5 5 5 7
((12x2 + ~10x) + (if x <= 0 then 0 else 1))
A288918: 0 3 29 79 153 251 373 519 689 883 1101 1343 1609 1899 2213 2551
((2 * ((4x + 2) + (x div 3))) + (if x <= 0 then 0 else 1))
A063219: 4 13 21 31 39 47 57 65 73 83 91 99 109 117 125 135
((2x + 2) + ((((x + 1) div 2) div 3) + (if x <= 0 then 0 else 1)))
A169865: 2 5 7 9 11 14 16 18 20 22 24 27 29 31 33 35
(2 + (((x + ~1) * ((x3 + ~x2) div 2)) + (if x <= 0 then 0 else 1)))
A093522: 2 3 5 21 75
((2 * ((x div (1 + (x div 5))) mod 2)) - (if x <= 0 then 0 else 1))
A324672: 0 1 ~1 1 ~1 ~1 1 1 ~1 ~1 1 1 ~1 ~1 ~1 1
((((~x + 2) mod (2 + (x div 5))) div 2) + (if x <= 0 then 0 else 1))
A248623: 0 1 1 1 1 1 2 1 1 2 1 2 2 1 1 2
((((x - (x mod (~3 + (x mod 2)))) div 2) div 2) + (if x <= 0 then 0 else 1))
A034973: 0 1 1 2 2 2 2 3 3 3 4 4 4 4 4 5
(x - ((if x <= 0 then 0 else 1) + (2 * ((~x2 + 2x) div 8))))
A256535: 0 0 1 4 5 8 11 16 19 24 29 36 41 48 55 64
((((2x + 1) mod (2 + (x div 4))) div 2) + (if x <= 0 then 0 else 1))
A337531-A316556-A316555: 0 1 1 1 1 2 1 1 1 2 1 2 1 2 3 1
((2x + 2) div (2 + ((x div (2 + (x mod 2))) + (if x <= 0 then 0 else 1))))
A340805: 1 1 1 2 2 3 2 3 2 3 2 4 2 4 3 4
(((x div 2) + (if x <= 0 then 0 else 1)) - (x div (2 + ((x * (x div 2)) mod 2))))
A294892: 0 1 1 1 1 1 1 2 1 1 1 3 1 1 1 3
(((((x + ~2) * (x div 3)) mod (x + 2)) mod 2) + (if x <= 0 then 0 else 1))
A328390: 0 1 1 2 1 2 1 2 1 1 1 2 1 1 1 1
((2 * ((6x + 3) + (x div 2))) + (if x <= 0 then 0 else 1))
A063233: 6 19 33 45 59 71 85 97 111 123 137 149 163 175 189 201
((22x + 10) - (if x <= 0 then 0 else 1))
A063154: 10 31 53 75 97 119 141 163 185 207 229 251 273 295 317 339
(((x2 mod (x - ((~x + 2) div 2))) div (x + 2)) + (if x <= 0 then 0 else 1))
A324119-A279060: 0 1 1 1 1 1 1 2 1 1 1 1 1 2 2 1
(((x2 + ~x) div 5) + (x div 2) + (if x <= 0 then 0 else 1))
A248578: 0 1 2 3 5 7 10 12 16 19 24 28 33 38 44 50
(x + ((1 + ((x * (x div 2)) div 4)) div 2) - (if x <= 0 then 0 else 1))
A295556: 0 0 1 2 4 5 7 9 11 13 15 17 20 22 25 27
(1 + loop(\(x,i).(x + i - (x mod 13)),x,0))
A032949: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 28 42
(1 + loop(\(x,i).(x + (5 * (x + (2 * (i mod 2))))),x,0))
A092164: 1 11 61 371 2221 13331 79981 479891 2879341 17276051 103656301 621937811 3731626861 22389761171 134338567021 806031402131
(1 + ((~x + 1) mod (1 + (if ((x + ~2) mod 5) <= 0 then 2 else 0))))
A030557: 1 1 3 1 1 1 1 1 1 1 1 1 2 1 1 1
(1 + ((x2 + 3x + 2) div (1 + (if (x mod 3) <= 0 then 2 else 0))))
A225227: 1 7 13
A046163: 1 7 13 7 31 43 19 73 91 37 133 157 61 211 241 91
(1 + (2x div (1 + (if (x mod 10) <= 0 then 2 else 0))))
A237292: 1 3 5 7 9 11 13 15 17 19 7 23 25 27 29 31
(1 + (x div (1 + (if (x mod (4 + (x div 4))) <= 0 then 2 else 0))))
A333696: 1 2 3 4 5 2 7 8 9 10 11 12 13 14 5 16
(x mod (1 + (2x mod (1 + (if (x mod 2) <= 0 then (x + ~4) else 0)))))
A143073: 0 0 0 0 0 0 0 0 0 0 3 0 5 0 0 0
(~1 + (2 div (1 + (x mod (1 + (if (x mod 2) <= 0 then 6 else 1))))))
A087003: 1 0 ~1 0 ~1 0 ~1 0 0 0 ~1 0 ~1 0 1 0
loop(\(x,i).2x,(~1 + (2x2 mod (1 + (x div 3)))),1)
A271205: 1 1 1 1 1 1 1 2 2 2 1 2 4 4 2 1
loop(\(x,i).(x * i),x,(1 + (x div (1 + (2 mod (1 + (x mod 3)))))))
A194130: 1 2 2 24 120 240 5040 40320 120960 3628800 39916800 159667200 6227020800 87178291200 435891456000 20922789888000
(1 - (2 div (1 + (x mod (1 + (if (x mod 2) <= 0 then 6 else 1))))))
A099991: ~1 0 1 0 1 0 1 0 0 0 1 0 1 0 ~1 0
(if x <= 0 then 0 else (1 + (x mod (1 + (x div (3 + (x div 3)))))))
A245192: 0 1 1 1 1 2 1 2 1 2 1 2 1 2 3 2
(1 + ((x * (x div 2)) mod (1 + (if (x mod 8) <= 0 then 2 else 1))))
A249740-A249739-A205792-A071773: 1 1 1 2 1 1 1 2 3 1 1 2 1 1 1 2
loop(\(x,i).2x,(~1 + (2x div (3 + (x div 4)))),1)
A113402: 1 1 1 2 2 2 4 4 4 4 8 8 8 8 8 16
(x div (1 + ((x div 2) div (1 + (if (x mod (2 + (x mod 2))) <= 0 then 2 else 1)))))
A333609: 0 1 2 3 4 2 3 3 4 4 5 3 4 3 4 5
(1 + (x div (1 + (if (x mod 2) <= 0 then 1 else ((x + 2) div 5)))))
A078451: 1 2 2 2 3 3 4 4 5 4 6 4 7 4 8 4
loop(\(x,i).x2,1,(1 + (x mod (1 + ((x + 2) div 5)))))
A126114: 1 1 1 4 1 4 1 4 9 1 4 9 1 4 9 16
loop(\(x,i).(x * i),(~1 + (5 * (2x + (x mod 2)))),1)
A072295: 1 87178291200 121645100408832000 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 0 else (1 + (x2 mod (1 + (x div (1 + (x mod 4)))))))
A169818: 0 1 1 1 2 2 1 2 2 2 1 2 2 2 2 2
(1 + loop(\(x,i).6x,x,11))
A199415: 12 67 397 2377 14257 85537 513217 3079297 18475777 110854657 665127937 3990767617 23944605697 143667634177 862005805057 5172034830337
(1 + loop(\(x,i).8x,x,11))
A199558: 12 89 705 5633 45057 360449 2883585 23068673 184549377 1476395009 11811160065 94489280513 755914244097 6047313952769 48378511622145 387028092977153
(~1 + loop(\(x,i).8x,x,11))
A198858: 10 87 703 5631 45055 360447 2883583 23068671 184549375 1476395007 11811160063 94489280511 755914244095 6047313952767 48378511622143 387028092977151
(1 + loop(\(x,i).x2,1,(9x + ~5)))
A154295: 26 17 170 485 962 1601 2402 3365 4490 5777 7226 8837 10610 12545 14642 16901
(2x + loop(\(x,i).i,(~1 + ((x + ~2) div 3)),1) - (x div 2))
A225647: 1 3 4 6 7
A226901: 1 3 4 6 7 9 10 12 13 15 16 19 20 22 24 26
loop(\(x,i).(x * i),((x + 1) - (3 * (~2x + (x mod 2)))),1)
A045509: 1 120 1307674368000 121645100408832000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (~1 + (x mod 5)) <= 0 then (1 + ((x div 2) div 3)) else 1)
A114088-A114087: 1 1 1 1 1 1 2 1 1 1 2 2 1 1 1 3
(~1 + ((x + 2) div (1 + (if (~1 + (x mod 3)) <= 0 then x else 3))))
A263415: 1 0 0 0 0 0 0 0 1 0 0 2 0 0 3 0
loop(\(x,i).6x,(9x + 1),1)
A067484: 6 60466176 609359740010496 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (x div (1 + (if ((x * (x div 2)) mod 2) <= 0 then x else (x mod 3)))))
A327939-A234957: 1 1 1 4 1 1 1 4 1 1 1 4 1 1 1 16
(1 + (x div (1 + (x mod (1 + loop(\(x,i).(x div (2 + (x mod 2))),2,x))))))
A138221: 1 2 3 4 5 6 7 4 3 5 11 6 13 7 5 8
(~1 + loop(\(x,i).2x2,1,(8x + 9)))
A157337: 161 577 1249 2177 3361 4801 6497 8449 10657 13121 15841 18817 22049 25537 29281 33281
(~1 + loop(\(x,i).2x2,1,(8x + 7)))
A157331: 97 449 1057 1921 3041 4417 6049 7937 10081 12481 15137 18049 21217 24641 28321 32257
(1 + loop(\(x,i).(2 * (5x + (x div 2))),(x + 1),1))
A199764: 11 111 1211 13311 146411 1610511 17715611 194871711 2143588811 23579476911 259374246011 2853116706111 31384283767211 345227121439311 3797498335832411 41772481694156511
(~1 + loop(\(x,i).(2 * (5x + (x div 2))),(x + 1),1))
A199030: 9 109 1209 13309 146409 1610509 17715609 194871709 2143588809 23579476909 259374246009 2853116706109 31384283767209 345227121439309 3797498335832409 41772481694156509
loop(\(x,i).12x,(4x + 3),1)
A013797: 1728 35831808 743008370688 15407021574586368 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).10x,(4x + 3),1)
A013793: 1000 10000000 100000000000 1000000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).7x,(4x + 3),1)
A013787: 343 823543 1977326743 4747561509943 11398895185373143 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + 1),1))
A001453: 1 4 13 41 131 428 1429 4861 16795 58785 208011 742899 2674439 9694844 35357669 129644789
(1 + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x + ~1),1))
A260878: 2 2 4 11 36 127 463 1717 6436 24311 92379 352717 1352079 5200301 20058301 77558761
(1 + (x div (3 + (if (x + ~10) <= 0 then 2 else 0))))
A029105: 1 1 1 1 1 2 2 2 2 2 3 4 5 5 5 6
((x + 1) - (x div (3 + (if (~2 + (x div 4)) <= 0 then 2 else 0))))
A331266: 1 2 3 4 5 5 6 7 8 9 9 10 9 10 11 11
(x div (1 + (if (x mod 2) <= 0 then (2 * (1 + ((x mod 3) div 2))) else 1)))
A071281: 0 0 0 1 1 2 2 3 1 4 3 5 4 6 2 7
(1 + (if ((x + 1) mod (1 - (x div ~5))) <= 0 then 2 else 1))
A237347: 3 3 2 3 2 3 2 2 3 2 2 3 2 2 2 3
(1 + (if (x + ~2) <= 0 then x else (1 + (2 * (1 + (x div 8))))))
A174901: 1 2 3 4 4 4 4 4 6 6 6 6 6 6 6 6
(x div (1 + (x div (1 + (if (x mod (2 + (x div 4))) <= 0 then 1 else 2)))))
A058062: 0 1 1 1 2 2 1 2 1 2 2 2 2 2 2 1
(if (x mod 2) <= 0 then (1 + (2 * ((~x + 2) mod (1 + (x div 4))))) else 1)
A143069: 1 1 1 1 1 1 1 1 1 1 3 1 5 1 1 1
loop(\(x,i).i,(x mod (1 + (2 * (((1 + (x div 2)) div 2) mod 3)))),1)
A341216-A261363: 1 1 2 1 1 2 1 2 3 4 1 1 1 1 2 1
loop(\(x,i).2x,(x - (x div (3 + ((x div 2) div 3)))),1)
A089887: 1 2 4 4 8 16 32 64 64 128 256 512 1024 2048 4096 4096
(1 + ((if (x + ~2) <= 0 then x else (x + 4)) mod 7))
A210530: 1 2 3 1 2 3 4 5 6 7 1 2 3 4 5 6
(2 div (1 + ((1 - (if (x mod 2) <= 0 then x else 2)) mod 7)))
A194024: 1 0 0 0 0 0 0 0 2 0 0 0 0 0 1 0
loop(\(x,i).x2,1,((x + 1) - (2x div 7)))
A080819: 1 4 9 16 16 25 36 36 49 64 81 81 100 121 121 144
(1 + loop(\(x,i).10x,x,7))
A199687: 8 71 701 7001 70001 700001 7000001 70000001 700000001 7000000001 70000000001 700000000001 7000000000001 70000000000001 700000000000001 7000000000000001
(~1 + loop(\(x,i).10x,x,7))
A198699: 6 69 699 6999 69999 699999 6999999 69999999 699999999 6999999999 69999999999 699999999999 6999999999999 69999999999999 699999999999999 6999999999999999
(1 + loop(\(x,i).(x2 + ~5x),x,7))
A067686: 8 15 127 15247 232364287 53993160246468367 4611686018427387903 4611686018427387903
(if x <= 0 then 2 else (1 + (x div ((x + 1) - (x mod (2 + (x mod 3)))))))
A248371: 2 2 3 2 2 2 1 2 1 2 2 2 1 2 2 2
((~x + 1) mod (1 + (if (x mod 4) <= 0 then (2 * (x mod 3)) else 1)))
A271620: 0 0 1 0 0 0 1 0 3 0 1 0 0 0 1 0
(1 + ((2 * (x + (x div 3))) + (if (x mod 3) <= 0 then 2 else 1)))
A047413: 3 4 6 11 12 14 19 20 22 27 28 30 35 36 38 43
(1 + ((x + 1) div (if (16 mod (x + 1)) <= 0 then 2 else 1)))
A320672: 1 2 4 3 6 7 8 5 10 11 12 13 14 15 16 9
((~x + 1) mod (1 + (if ((x div 3) mod 2) <= 0 then ((x + 1) div 2) else 1)))
A072681: 0 0 1 0 1 0 3 4 3 0 1 0 3 4 3 0
(1 + (if (x mod 2) <= 0 then (x div (2 * (2 + ((x + ~1) mod 3)))) else 1))
A235708: 1 2 1 2 2 2 1 2 2 2 3 2 2 2 3 2
((1 - (x * (x div 2))) mod (1 + (if (x mod 8) <= 0 then 2 else 1)))
A328248: 1 1 1 0 1 1 1 0 2 1 1 0 1 1 1 0
(1 + (x div (if ((x + 1) mod 8) <= 0 then 8 else 1)))
A050985: 1 2 3 4 5 6 7 1 9 10 11 12 13 14 15 2
(2 div (1 + ((1 - (if (~x + 2) <= 0 then x else 0)) mod 9)))
A331918: 1 1 0 0 0 0 0 0 0 1 2 0 0 0 0 0
(if x <= 0 then 0 else (1 + ((4x + ~1) mod 9)))
A180594: 0 4 8 3 7 2 6 1 5 9 4 8 3 7 2 6
(if x <= 0 then 0 else (1 + ((~2x + ~1) mod 9)))
A180597: 0 7 5 3 1 8 6 4 2 9 7 5 3 1 8 6
(if x <= 0 then 0 else (1 + ((x2 + x + ~1) mod 9)))
A251755: 0 2 6 3 2 3 6 2 9 9 2 6 3 2 3 6
loop(\(x,i).(x2 + x),(2 - ((x + 2) mod 9)),1)
A284761: 1 1 1 1 1 1 1 6 2 1 1 1 1 1 1 1
(1 + loop(\(x,i).7x,x,9))
A199487: 10 64 442 3088 21610 151264 1058842 7411888 51883210 363182464 2542277242 17795940688 124571584810 872001093664 6104007655642 42728053589488
loop(\(x,i).2x,((2x + 1) div (3 + (x div 4))),1)
A137688: 1 2 2 4 4 4 8 8 8 8 16 16 16 16 16 32
(if x <= 0 then 0 else (1 + (2 mod (1 + (((x + ~2) mod (2 + (x div 2))) div 2)))))
A091407: 0 1 1 1 1 1 3 1 1 1 1 1 1 1 1 3
(1 + (if (x mod 2) <= 0 then (x div 2) else (x mod (1 + (2 * ((x div 2) mod 2))))))
A250028: 1 1 2 1 3 1 4 2 5 1 6 3 7 1 8 1
(1 + loop(\(x,i).(2x + 4),(x div 2),(1 + (4 * (x mod 2)))))
A078113: 2 6 7 15 17 33 37 69 77 141 157 285 317 573 637 1149
(if (x mod 5) <= 0 then (1 + ((x div ~2) mod 4)) else 1)
A107688: 1 1 1 1 1 2 1 1 1 1 4 1 1 1 1 1
(if x <= 0 then 0 else (1 + ((x + 2) mod (1 + ((2 - (x div 2)) mod 4)))))
A264990: 0 1 1 2 1 1 1 2 2 3 1 2 1 1 1 2
loop(\(x,i).x2,3,(10x + 6))
A017348: 1679616 4294967296 208827064576 2821109907456 20047612231936 96717311574016 360040606269696 1113034787454976 2992179271065856 7213895789838336 15938480745308416 32784148919812096 63527879748485376
loop(\(x,i).x3,1,(10x + 6))
A017343: 216 4096 17576 46656 97336 175616 287496 438976 636056 884736 1191016 1560896 2000376 2515456 3112136 3796416
loop(\(x,i).x3,2,(10x + 6))
A017349: 10077696 68719476736 5429503678976 101559956668416 922190162669056 5416169448144896 23762680013799936 84590643846578176 257327417311663616 692533995824480256 1689478959002692096 3802961274698203136
(~1 + (5 * loop(\(x,i).(x2 * (1 + i)),2,(x + 1))))
A248974: 59 959 4859 15359 37499 77759 144059 245759 393659 599999 878459 1244159 1713659 2304959 3037499 3932159
(loop(\(x,i).2x,x,1) mod 29)
A222011: 1 2 4 8
A036122: 1 2 4 8 16 3 6 12 24 19 9 18 7 14 28 27
(1 + (loop(\(x,i).(x * (2 + i)),(x + 3),2) div 5))
A139152: 25 145 1009 8065 72577 725761 7983361 95800321 1245404161 17435658241 261534873601 4184557977601 71137485619201 1280474741145601 24329020081766401 486580401635328001
(~1 + (loop(\(x,i).(x * (2 + i)),(x + 3),2) div 5))
A139175: 23 143 1007 8063 72575 725759 7983359 95800319 1245404159 17435658239 261534873599 4184557977599 71137485619199 1280474741145599 24329020081766399 486580401635327999
loop(\(x,i).x3,2,(10x + 11))
A038685: 2357947691 794280046581 26439622160671 327381934393961 2334165173090451 11694146092834141 45848500718449031 150094635296999121 427929800129788411 1093685272684360901
loop(\(x,i).x2,3,(10x + 9))
A017384: 43046721 16983563041 500246412961 5352009260481 33232930569601 146830437604321 513798374428641 1517108809906561 3936588805702081 9227446944279201 19925626416901921 40213853471634241 76686282021340161
loop(\(x,i).x3,1,(10x + 9))
A017379: 729 6859 24389 59319 117649 205379 328509 493039 704969 970299 1295029 1685159 2146689 2685619 3307949 4019679
loop(\(x,i).x3,2,(10x + 9))
A017385: 387420489 322687697779 14507145975869 208728361158759 1628413597910449 8662995818654939 35452087835576229 119851595982618319 350356403707485209 913517247483640899 2171893279442309389
(~1 + (10 * (2 + loop(\(x,i).x2,x,4))))
A160681: 59 179 2579 655379 42949672979 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,x,1) mod 41)
A222011: 1 2 4 8
A070348: 1 2 4 8 16 32 23 5 10 20 40 39 37 33 25 9
(loop(\(x,i).2x,x,1) mod 39)
A222011: 1 2 4 8
A070340: 1 2 4 8 16 32 25 11 22 5 10 20 1 2 4 8
loop(\(x,i).x2,1,((x + 1) - ((~2x + 2) div 5)))
A087055: 1 4 16 25 49 64 81 121 144 196 225 256 324 361 441 484
(1 + ((2 * loop(\(x,i).(x div (2 - (x mod 2))),2,x)) div 5))
A335421: 1 1 1 2 1 3 2 3 1 4 3 5 2 6 3 7
((if x <= 0 then 1 else x) div (1 + (((x + 2) + (x mod 2)) div 5)))
A137735: 1 1 2 1 2 2 3 2 2 3 3 3 4 3 3 3
(1 + (5 * loop(\(x,i).7x,x,2)))
A199488: 11 71 491 3431 24011 168071 1176491 8235431 57648011 403536071 2824752491 19773267431 138412872011 968890104071 6782230728491 47475615099431
(~1 + (5 * loop(\(x,i).7x,x,2)))
A198691: 9 69 489 3429 24009 168069 1176489 8235429 57648009 403536069 2824752489 19773267429 138412872009 968890104069 6782230728489 47475615099429
((x + 3) - ((~x + (if (x + ~2) <= 0 then x else 0)) div 5))
A183574: 3 4 5 7 8 9 11 12 13 14 15 17 18 19 20 21
loop(\(x,i).2x,((x * ((1 + (x div 2)) mod 2)) div 5),1)
A174842: 1 1 1 1 1 2 1 1 2 2 1 1 4 4 1 1
(~1 + loop(\(x,i).2x,x,1) - ((x + (x div 2)) div 5))
A222010: 0 1 3 7
A139817: 0 1 3 7 14 30 62 125 253 509 1020 2044 4092 8188 16379 32763
(3 + ((if (x + ~1) <= 0 then x else 2x) + (x div 5)))
A187477: 3 4 7 9 11 14 16 18 20 22 25 27 29 31 33 36
(if x <= 0 then 1 else ((x mod 5) mod (1 + (x div 5))))
A029427: 1 0 0 0 0 0 1 0 1 0 0 1 2 0 1 0
(if (x mod 3) <= 0 then 1 else ((~x + 1) mod (1 + (x div 5))))
A025852: 1 0 0 1 0 0 1 0 1 1 0 2 1 0 2 1
(1 + loop(\(x,i).11x,x,5))
A199755: 6 56 606 6656 73206 805256 8857806 97435856 1071794406 11789738456 129687123006 1426558353056 15692141883606 172613560719656 1898749167916206 20886240847078256
((if x <= 0 then 0 else 1) - (2 mod (1 + (x mod (1 + ((~x + 2) mod 4))))))
A070238: 0 1 1 ~1 1 1 1 ~1 ~1 1 1 ~1 1 1 1 ~1
(1 + (x mod (1 + (if (x mod (2 + (x mod 2))) <= 0 then 1 else (x div 4)))))
A051881: 1 1 1 2 1 2 1 2 1 2 1 3 1 2 1 2
(1 + ((2 * (1 + (if (x mod 2) <= 0 then x else 0))) mod (1 + (x div 4))))
A079790: 1 1 1 1 1 1 1 1 1 3 2 3 3 3 3 3
(1 - (if (x mod 3) <= 0 then (2 - (2 div (1 + (x div 4)))) else 1))
A016079-A015719-A015539-A015179-A014999-A014639-A011645: 1 0 0 1 0 0 0 0 0 ~1 0 0 ~1 0 0 ~1
loop(\(x,i).20x,(4x + 1),1)
A013812: 20 3200000 512000000000 81920000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).15x,(4x + 1),1)
A013802: 15 759375 38443359375 1946195068359375 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).18x,(4x + 1),1)
A013808: 18 1889568 198359290368 20822964865671168 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).24x,(4x + 1),1)
A013820: 24 7962624 2641807540224 876488338465357824 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).14x,(4x + 1),1)
A013800: 14 537824 20661046784 793714773254144 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).13x,(4x + 1),1)
A013798: 13 371293 10604499373 302875106592253 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).11x,(4x + 1),1)
A013794: 11 161051 2357947691 34522712143931 505447028499293771 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).17x,(4x + 1),1)
A013806: 17 1419857 118587876497 9904578032905937 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).4x,(4x div (3 + (x div 2))),1)
A307138: 1 4 16 64 64 256 256 256 256 1024 1024 1024 1024
(2 div (1 + (if (x + ~3) <= 0 then x else (1 + (x mod (2 + (x mod 2)))))))
A246398: 2 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1
(~1 + ((if (x mod 2) <= 0 then ((~x + 1) mod 5) else 1) mod 3))
A286133: 0 0 0 0 1 0 ~1 0 ~1 0 0 0 0 0 1 0
((x + 2) mod (1 + ((x - (if (~2 + (x div 2)) <= 0 then 2 else 1)) mod 3)))
A161116: 0 0 0 1 0 0 2 0 0 2 0 1 2 0 0 2
(1 + (((x2 - (if x <= 0 then 0 else 1)) div 5) mod 3))
A095955: 1 1 1 2 1 2 2 1 1 2 2 1 2 1 1 3
(loop(\(x,i).2x,x,1) mod 37)
A222011: 1 2 4 8
A036124: 1 2 4 8 16 32 27 17 34 31 25 13 26 15 30 23
(loop(\(x,i).2x,x,1) mod 35)
A222011: 1 2 4 8
A070339: 1 2 4 8 16 32 29 23 11 22 9 18 1 2 4 8
(1 + ((loop(\(x,i).(2x + ~1),x,0) mod (2x + 1)) div 3))
A300650: 1 1 1 1 2 1 1 3 1 1 3 1 2 6 1 1
loop(\(x,i).3x,(x div 2),(1 + (3 * (1 + (x mod 2)))))
A228879: 4 7 12 21 36 63 108 189 324 567 972 1701 2916 5103 8748 15309
(1 + ((loop(\(x,i).(x - (2x * i)),x,1) mod (x + 1)) div 3))
A159269: 1 1 1 1 1 2 1 1 1 2 1 4 1 3 1 1
(if x <= 0 then 1 else (1 + (((x + 1) * (4 + (x div 2))) div 3)))
A282167: 1 3 6 7 11 13 17 19 25 27
loop(\(x,i).x2,3,(12x + 11))
A017660: 214358881 78310985281 2251875390625 23811286661761 146830437604321 645753531245761 2252292232139041 6634204312890625 17181861798319201 40213853471634241 86730203469006241 174859124550883201
loop(\(x,i).x3,1,(12x + 11))
A017655: 1331 12167 42875 103823 205379 357911 571787 857375 1225043 1685159 2248091 2924207 3723875 4657463 5735339 6967871
loop(\(x,i).x3,2,(12x + 11))
A017661: 2357947691 1801152661463 78815638671875 1119130473102767 8662995818654939 45848500718449031 186940255267540403 630249409724609375 1838459212420154507 4611686018427387903
(6 div loop(\(x,i).~x,x,(1 + ((x + 1) mod 3))))
A131969: 3 ~2 6 ~3 2 ~6 3 ~2 6 ~3 2 ~6 3 ~2 6 ~3
(1 + ((loop(\(x,i).(x2 div 3),2,x) div (x + 1)) mod 3))
A333161-A180980-A176353-A156044-A111007-A103691-A103441-A081206: 1 1 1 1 2 1 1 2 2 1 1 3 3 3 1 1
(loop(\(x,i).4x,x,1) mod 19)
A187532: 1 4 16 7 9 17 11 6 5 1 4 16 7 9 17 11
(loop(\(x,i).3x,x,1) mod 19)
A070342: 1 3 9 8 5 15 7 2 6 18 16 10 11 14 4 12
(1 + (if (~2 + (x div 3)) <= 0 then x else 18))
A092596: 1 2 3 4 5 6 7 8 9 19
A087121: 1 2 3 4 5 6 7 8 9 19 19 19 19 19 19 19
((x + 1) - ((if x <= 0 then 1 else x) div (x + ~18)))
A261355-A084384: 2 3 4 5 6 7 8 9 10 11 13 14 15 17 19 21
(1 + (loop(\(x,i).(x * (3 + i)),(x + 3),2) div 3))
A139156: 81 561 4481 40321 403201 4435201 53222401 691891201 9686476801 145297152001 2324754432001 39520825344001 711374856192001 13516122267648001 270322445352960001 4611686018427387903
(~1 + (loop(\(x,i).(x * (3 + i)),(x + 3),2) div 3))
A139184: 79 559 4479 40319 403199 4435199 53222399 691891199 9686476799 145297151999 2324754431999 39520825343999 711374856191999 13516122267647999 270322445352959999 4611686018427387903
loop(\(x,i).x2,3,(12x + 7))
A017612: 5764801 16983563041 852891037441 11688200277601 83733937890625 406067677556641 1517108809906561 4702525276151521 12667700813876161 30590228625390625 67675234241018881 139353667211683681
loop(\(x,i).x3,1,(12x + 7))
A017607: 343 6859 29791 79507 166375 300763 493039 753571 1092727 1520875 2048383 2685619 3442951 4330747 5359375 6539203
loop(\(x,i).x3,2,(12x + 7))
A017613: 40353607 322687697779 26439622160671 502592611936843 4605366583984375 27206534396294947 119851595982618319 427929800129788411 1304773183829244583 3517876291919921875 4611686018427387903
loop(\(x,i).x2,1,(~11x + ~7))
A017474: 49 324 841 1600 2601 3844 5329 7056 9025 11236 13689 16384 19321 22500 25921 29584
loop(\(x,i).x2,2,(~11x + ~7))
A017476: 2401 104976 707281 2560000 6765201 14776336 28398241 49787136 81450625 126247696 187388721 268435456 373301041 506250000 671898241 875213056
loop(\(x,i).x2,3,(12x + 5))
A017588: 390625 6975757441 500246412961 7984925229121 62259690411361 318644812890625 1235736291547681 3936588805702081 10828567056280801 26584441929064321 59604644775390625 124097929967680321
loop(\(x,i).x3,1,(12x + 5))
A017583: 125 4913 24389 68921 148877 274625 456533 704969 1030301 1442897 1953125 2571353 3307949 4173281 5177717 6331625
loop(\(x,i).x3,2,(12x + 5))
A017589: 1953125 118587876497 14507145975869 327381934393961 3299763591802133 20711912837890625 95151694449171437 350356403707485209 1093685272684360901 3004041937984268273 4611686018427387903
(1 + ((2 * (loop(\(x,i).2x,x,(x mod 2)) mod (x + 1))) div 3))
A323409: 1 1 1 1 1 2 1 1 1 2 1 6 1 2 1 1
(if (((~1 + (2x mod (2 + (x div 2)))) div 2) mod 2) <= 0 then 3 else 1)
A099545: 1 1 3 1 1 3 3 1 1 1 3 3 1 3 3 1
loop(\(x,i).3x,((4 * (x div 3)) div 3),1)
A060828: 1 1 1 3 3 3 9 9 9 81 81 81 243 243 243 729
(1 + ((2 + (loop(\(x,i).8x,x,1) div 2)) div 3))
A039305: 1 3 12 87 684 5463 43692 349527 2796204 22369623 178956972 1431655767 11453246124 91625968983 733007751852 5864062014807
loop(\(x,i).x2,1,((x + 1) - (3 * (((x + 1) div 2) div 2))))
A007892: 1 4 9 1 4 9 16 4 9 16 25 9 16 25 36 16
(if x <= 0 then 1 else (~1 + ((2 * ((x + 2) mod 8)) mod 3)))
A014677: 1 ~1 1 0 ~1 1 ~1 1 0 ~1 1 0 ~1 1 ~1 1
(loop(\(x,i).2x,x,1) mod 47)
A222011: 1 2 4 8
A070351: 1 2 4 8 16 32 17 34 21 42 37 27 7 14 28 9
(1 + (3 * loop(\(x,i).(2x + 2),x,16)))
A250653: 49 103 211 427 859 1723 3451 6907 13819 27643 55291 110587 221179 442363 884731 1769467
((x + ~1) - (3 * ((if x <= 0 then 1 else x) div ~7)))
A174887: 2 3 4 5 6 7 8 9 13 14 15 16 17 18 19 23
(loop(\(x,i).3x,x,1) mod 25)
A070343: 1 3 9 2 6 18 4 12 11 8 24 22 16 23 19 7
(loop(\(x,i).3x,x,1) mod 23)
A070356: 1 3 9 4 12 13 16 2 6 18 8 1 3 9 4 12
(1 + ((loop(\(x,i).(~2x + 2),x,(x + 4)) div 2) div 3))
A084219: 1 ~1 4 ~8 20 ~44 100 ~220 484 ~1052 2276 ~4892 10468 ~22300 47332 ~100124
loop(\(x,i).2x2,1,(~1 + (x div ~11)))
A138300: 2 8 8 8 8 8 8 8 8 8 8 8 18 18 18 18
(loop(\(x,i).6x,x,1) mod 13)
A070393: 1 6 10 8 9 2 12 7 3 5 4 11 1 6 10 8
(loop(\(x,i).(x * (x - i)),2,(x + ~1)) div 13)
A011923: 0 0 0 0 1 9 27 64 129 232 387 609 913 1320 1848 2520
(loop(\(x,i).5x,x,1) mod 13)
A070368: 1 5 12 8 1 5 12 8 1 5 12 8 1 5 12 8
(13 * ((2 - (x mod 2)) * (if x <= 0 then 1 else 2)))
A040651: 26 26 52 26 52 26 52 26 52 26 52 26 52 26 52 26
loop(\(x,i).(x3 + 3x),x,13)
A145187: 13 2236 11179326964 4611686018427387903 4611686018427387903
(loop(\(x,i).~3x,x,1) mod 11)
A048271: 1 8 9 6 4 10 3 2 5 7 1 8 9 6 4 10
(loop(\(x,i).~4x,x,1) mod 11)
A070404: 1 7 5 2 3 10 4 6 9 8 1 7 5 2 3 10
(loop(\(x,i).(x * (x - i)),2,(x + ~1)) div 11)
A011921: 0 0 0 0 2 10 32 76 152 274 458 720 1080 1560 2184 2978
(11 * ((2 - (x mod 2)) * (if x <= 0 then 1 else 2)))
A040463: 22 22 44 22 44 22 44 22 44 22 44 22 44 22 44 22
loop(\(x,i).(x3 + 3x),x,11)
A145185: 11 1364 2537720636 4611686018427387903 4611686018427387903
(1 + ((x - (if (x mod 3) <= 0 then 1 else (2x + ~4))) div 3))
A135997: 0 2 1 1 1 0 2 0 ~1 3 ~1 ~2 4 ~2 ~3 5
loop(\(x,i).(6x + 1),12x,1)
A022230: 1 2612138803 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(8x + 1),12x,1)
A022252: 1 78536544841 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~8x + 1),12x,1)
A015431: 1 61083979321 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,3,(~11x + ~1))
A017408: 1 429981696 78310985281 1785793904896 16815125390625 96717311574016 406067677556641 1370114370683136 3936588805702081 10000000000000000 23045377697175681 49077072127303936 97906861202319841
(1 + ((2 * loop(\(x,i).(2x + (i mod 2)),x,2x)) div 3))
A102301: 1 4 13 36 93 228 541 1252 2845 6372 14109 30948 67357 145636 313117 669924
(1 + (loop(\(x,i).(2x + 2),((x div 2) - (x mod 2)),2) div 3))
A112447: 1 1 3 1 5 3 11 5 21 11 43 21 85 43 171 85
loop(\(x,i).3x,(x div 2),(1 + (6 * (x mod 2))))
A166481: 1 7 3 21 9 63 27 189 81 567 243 1701 729 5103 2187 15309
(1 + (6 * loop(\(x,i).(x * (5 + i)),x,2)))
A139157: 13 73 505 4033 36289 362881 3991681 47900161 622702081 8717829121 130767436801 2092278988801 35568742809601 640237370572801 12164510040883201 243290200817664001
(~1 + (6 * loop(\(x,i).(x * (5 + i)),x,2)))
A139185: 11 71 503 4031 36287 362879 3991679 47900159 622702079 8717829119 130767436799 2092278988799 35568742809599 640237370572799 12164510040883199 243290200817663999
(1 + (((x + 2) + (if (~4 + (x div 2)) <= 0 then 2 else 0)) div 3))
A132914: 2 2 3 3 3 4 4 4 5 5 5 5 5 6 6 6
loop(\(x,i).x2,3,(9x + 7))
A017252: 5764801 4294967296 152587890625 1785793904896 11688200277601 53459728531456 191707312997281 576480100000000 1517108809906561 3596345248055296 7837433594376961 15938480745308416 30590228625390625
loop(\(x,i).x3,1,(9x + 7))
A017247: 343 4096 15625 39304 79507 140608 226981 343000 493039 681472 912673 1191016 1520875 1906624 2352637 2863288
loop(\(x,i).x3,2,(9x + 7))
A017253: 40353607 68719476736 3814697265625 60716992766464 502592611936843 2779905883635712 11694146092834141 40353607000000000 119851595982618319 316478381828866048 760231058654565217 1689478959002692096
loop(\(x,i).x2,3,(9x + 5))
A017228: 390625 1475789056 78310985281 1099511627776 7984925229121 39062500000000 146830437604321 457163239653376 1235736291547681 2992179271065856 6634204312890625 13685690504052736 26584441929064321
loop(\(x,i).x3,1,(9x + 5))
A017223: 125 2744 12167 32768 68921 125000 205379 314432 456533 636056 857375 1124864 1442897 1815848 2248091 2744000
loop(\(x,i).x3,2,(9x + 5))
A017229: 1953125 20661046784 1801152661463 35184372088832 327381934393961 1953125000000000 8662995818654939 31087100296429568 95151694449171437 257327417311663616 630249409724609375 1423311812421484544
loop(\(x,i).3x,((4x2 + 2x) div 3),1)
A122251: 1 9 729 4782969 282429536481 150094635296999121 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((2 * (x + loop(\(x,i).(4 - (x div 2)),x,1))) div 3))
A049008: 1 4 3 5 5 6 7 7 8 9 9 10 11 11 12 13
(1 + (3 * loop(\(x,i).(10x + ~8),x,2)))
A173766: 7 37 337 3337 33337 333337 3333337 33333337 333333337 3333333337 33333333337 333333333337 3333333333337 33333333333337 333333333333337 3333333333333337
(3 - ((if ((2 + (x div 2)) mod 4) <= 0 then x else 2) mod 3))
A322482-A209156: 1 1 1 1 2 1 1 1 1 1 1 1 3 2 1 1
(1 + (loop(\(x,i).(3x + 6),(x + ~1),(x + 2)) div 3))
A038765: 1 2 7 24 81 270 891 2916 9477 30618 98415 314928 1003833 3188646 10097379 31886460
(if (10 mod (x + 1)) <= 0 then ((x + 2) div 3) else 1)
A056926: 0 1 1 1 2 1 1 1 1 3 1 1 1 1 1 1
(1 + (((x + 2) * (x + (if (~2 + (x div 2)) <= 0 then 1 else x))) div 3))
A116582: 1 3 5 7 11 15 33
(~1 + (loop(\(x,i).(2 + ((x2 + x) div 2)),2,(x + ~2)) div 3))
A006522: 1 0 0 1 4 11 25 50 91 154 246 375 550 781 1079 1456
loop(\(x,i).x2,1,((x + ~1) - (3 * (2x + (x mod 2)))))
A273372: 1 81 121 361 441 841 961 1521 1681 2401 2601 3481 3721 4761 5041 6241
loop(\(x,i).x5,1,(6x + 1))
A016925: 1 16807 371293 2476099 9765625 28629151 69343957 147008443 282475249 503284375 844596301 1350125107 2073071593 3077056399 4437053125 6240321451
(x div (1 + (((if (x mod 4) <= 0 then x else 1) - (x mod 2)) mod 3)))
A165342: 0 1 1 3 2 5 3 7 2 9 5 11 12 13 7 15
(1 + (3 * loop(\(x,i).11x,x,2)))
A199756: 7 67 727 7987 87847 966307 10629367 116923027 1286153287 14147686147 155624547607 1711870023667 18830570260327 207136272863587 2278499001499447 25063489016493907
(~1 + (3 * loop(\(x,i).11x,x,2)))
A199024: 5 65 725 7985 87845 966305 10629365 116923025 1286153285 14147686145 155624547605 1711870023665 18830570260325 207136272863585 2278499001499445 25063489016493905
(1 + ((2 * (x + (if ((x mod 3) div 2) <= 0 then 1 else x))) div 3))
A269098: 1 2 3 3 4 7 5 6 11 7 8 15 9 10 19 11
(1 + ((loop(\(x,i).(2 * ((x + 2) + (i mod 2))),x,x) div 2) div 3))
A172481: 1 2 5 11 25 55 121 263 569 1223 2617 5575 11833 25031 52793 111047
((x2 + 3x + 1) - loop(\(x,i).(x * (x + i)),2,3))
A212325: ~167 ~163 ~157 ~149 ~139 ~127 ~113 ~97 ~79 ~59 ~37 ~13 13 41 71 103
((x + 1) - ((~x + (if (~2 + (x div 3)) <= 0 then 2 else 0)) div 3))
A285375: 1 2 3 5 6 7 9 10 11 13 15 16 17 19 20 21
loop(\(x,i).6x,(5x + 3),1)
A013840: 216 1679616 13060694016 101559956668416 789730223053602816 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).8x,(5x + 3),1)
A013848: 512 16777216 549755813888 18014398509481984 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).5x,(5x + 3),1)
A013836: 125 390625 1220703125 3814697265625 11920928955078125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else ((x + ~1) - (3 * (~x + ((x + ~1) mod 3)))))
A240670: 1 3 4 5 15 16
(if x <= 0 then 1 else ((x + 3) - ((~x + (x div 3)) div 3)))
A288857: 1 5 6 7 8 10 11 12 13 14 16 17 18 19 21 22
loop(\(x,i).(x * i),x,(9x2 + 3x + 1))
A082036: 1 13 86 546 3768 28920 246960 2333520 24232320 274700160 3378412800 44826566400 638509132800 9720379468800 157531172198400 2708193616128000
(1 + (3 * compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x)))
A176003: 1 4 7 13 19 31 37 49 55 67 85 91 109 121 127 139
loop(\(x,i).(3x * (1 + i)),(3x2 + 3x),1)
A080657: 1 3674160 4611686018427387903 4611686018427387903
A080662-A080661-A080660-A080659-A080658-A080656-A075152-A074914: 1 3674160 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (x div 2)),1,(~3x2 + ~3x + ~1))
A079903: 1 28 190 703 1891 4186 8128 14365 23653 36856 54946 79003 110215 149878 199396 260281
(1 + ((x + loop(\(x,i).2x,(x div 2),((x + ~1) div 2))) div 3))
A004693: 0 1 1 2 3 5 8 11 19
loop(\(x,i).2x,(1 - ((~x + ((x div ~2) mod 2)) div 3)),1)
A046971: 2 2 4 4 8 8 8 16 16 16 16 32 32 32 64 64
(1 + ((~x + (x div ((if (x mod 2) <= 0 then 1 else x) mod 4))) mod 3))
A115362: 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 3
(1 + (3 * compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A132227: 1 4 10 16 28 34 46 52 64 82 88 106 118 124 136 154
(if (((x + 1) div (1 + (x mod 4))) mod 2) <= 0 then (x div 3) else 1)
A156839: 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 5
(if (x + ~1) <= 0 then 0 else (1 + ((x2 + 1) div 2) - (x div 3)))
A337503: 0 0 3 5 8 13 17 24 31 39
(1 + (((x + 2) * (1 + (if (x + ~1) <= 0 then x else 2))) + (x div 3)))
A061289: 3 7 13 17 20 23
(loop(\(x,i).3x,(2 - (x div 2)),1) * (1 + (x div 3)))
A226204: 9 9 3 6 2 2
((if (x mod 2) <= 0 then (x div 5) else 2) mod (1 + (x div 3)))
A254690: 0 0 0 0 0 0 1 2 1 2 2 2 2 2 2 2
((if x <= 0 then 1 else x) - ((x mod 6) mod (1 + (x div 3))))
A070320: 1 1 2 2 4 4 6 6 6 6 10 10 12 12 12 12
(x mod (1 + (loop(\(x,i).(x div (2 - (x mod 2))),2,x) * (x div 3))))
A193508: 0 0 0 3 0 5 6 7 3 9 10 11 12 13 14 15
(1 + loop(\(x,i).(3x + 3),(x div 3),(x mod 3)))
A329774: 1 2 3 4 7 10 13 22 31 40 67 94 121 202 283 364
((2x + 1) + (if (~2 + (x div 2)) <= 0 then 1 else 2) - (x mod 3))
A246444: 2 3 4 8 9 10 15 16 17 21 22 23 27 28 29 33
(if x <= 0 then 1 else (x div ((2 + (x div 4)) * (1 + (x mod 3)))))
A048141: 1 0 0 1 0 0 2 1 0 2 1 0 2 1 0 3
loop(\(x,i).6x,(3x + (x mod 3)),1)
A067492: 1 1296 1679616 10077696 13060694016 16926659444736 101559956668416 131621703842267136 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) - (3 * (x - loop(\(x,i).(x div (1 + (x mod 2))),x,x))))
A328154: 1 ~1 3 ~5 5 ~3 7 ~13 9 ~5 11 ~15 13 ~7 15 ~29
(1 + (loop(\(x,i).(x4 + ~x3 + 2),x,x) div 3))
A128935: 1 1 3001 4611686018427387903 4611686018427387903
(1 + ((x2 + 2x) mod (1 + (if (~2 + (x div 3)) <= 0 then x else 2))))
A066750: 1 2 3 4 5 6 7 8 9 1 1 3 1 1 3 1
(1 + ((0 - (4 * (x mod 2))) mod (~1 + loop(\(x,i).2x,x,2))))
A287197: 1 3 1 12 1 60 1 252 1 1020 1 4092 1 16380 1 65532
(if x <= 0 then 2 else (1 + ((2x2 + 8) div (x + 3))))
A050418: 2 3 4 5 6 8 9 11 13 15 17 18 20 22 24 26
(1 + ((x + 3) * loop(\(x,i).((x + 2) + ((2 + i) * i)),x,2)))
A229795: 7 29 86 205 421 777 1324 2121 3235 4741 6722 9269 12481 16465 21336 27217
loop(\(x,i).21x,(2x + 1),1)
A013726: 21 9261 4084101 1801088541 794280046581 350277500542221 154472377739119461 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(2x + 1),1)
A100033: 3 35 462 6435 92378 1352078 20058300 300540195 4537567650 68923264410 1052049481860 16123801841550 247959266474052 3824345300380220 59132290782430712 916312070471295267
loop(\(x,i).22x,(2x + 1),1)
A013727: 22 10648 5153632 2494357888 1207269217792 584318301411328 282810057883082752 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(0 - loop(\(x,i).(~10x + 2),(2x + 1),1))
A097818: 8 818 81818 8181818 818181818 81818181818 8181818181818 818181818181818 81818181818181818 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).19x,(2x + 1),1)
A013724: 19 6859 2476099 893871739 322687697779 116490258898219 42052983462257059 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).23x,(2x + 1),1)
A013728: 23 12167 6436343 3404825447 1801152661463 952809757913927 504036361936467383 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).31x,(2x + 1),1)
A262716: 31 29791 28629151 27512614111 26439622160671 25408476896404831 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(2x + ~1),1)
A259557: 1 3 35 462 6435 92378 1352078 20058300 300540195 4537567650 68923264410 1052049481860 16123801841550 247959266474052 3824345300380220 59132290782430712
((1 + (x mod 2)) div (1 + (if (~1 + (x mod 3)) <= 0 then (x div 2) else 1)))
A105348: 1 2 0 1 0 1 0 0 0 0 0 1 0 0 0 0
(2 div (1 + ((1 + (if (x mod 3) <= 0 then x else 0)) mod (1 + (x div 2)))))
A090406: 2 2 1 2 1 1 0 1 1 2 1 1 0 1 1 2
((x + 2) mod (1 + (loop(\(x,i).~2x,x,1) mod (1 + (x div 2)))))
A283979: 0 0 0 0 0 1 0 0 0 3 2 3 0 3 0 0
(if ((1 + ((x * (x div 2)) div 4)) mod 2) <= 0 then (~1 + (x div 2)) else 1)
A180184: 1 1 1 1 1 1 1 2 1 3 1 4 1 5 1 1
loop(\(x,i).(10x + 1),(x div (1 + (x mod 2))),1)
A290233: 1 1 111 11 11111 111 1111111 1111 111111111 11111 11111111111 111111 1111111111111 1111111 111111111111111 11111111
(1 + loop(\(x,i).(2 - (4x mod 7)),x,1))
A174737: 2 ~1 ~3 ~2 1 3 2 ~1 ~3 ~2 1 3 2 ~1 ~3 ~2
loop(\(x,i).12x,(5x + 1),1)
A013862: 12 2985984 743008370688 184884258895036416 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).10x,(5x + 1),1)
A013854: 10 1000000 100000000000 10000000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).7x,(5x + 1),1)
A013842: 7 117649 1977326743 33232930569601 558545864083284007 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).20x,(3x + 1),1)
A013766: 20 160000 1280000000 10240000000000 81920000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).15x,(3x + 1),1)
A013756: 15 50625 170859375 576650390625 1946195068359375 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).18x,(3x + 1),1)
A013762: 18 104976 612220032 3570467226624 20822964865671168 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).24x,(3x + 1),1)
A013774: 24 331776 4586471424 63403380965376 876488338465357824 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).14x,(3x + 1),1)
A013754: 14 38416 105413504 289254654976 793714773254144 2177953337809371136 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((3x + 1) * loop(\(x,i).((x2 + x) div 2),x,2)))
A062609: 3 13 43 211
loop(\(x,i).13x,(3x + 1),1)
A013752: 13 28561 62748517 137858491849 302875106592253 665416609183179841 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).11x,(3x + 1),1)
A013748: 11 14641 19487171 25937424601 34522712143931 45949729863572161 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).17x,(3x + 1),1)
A013760: 17 83521 410338673 2015993900449 9904578032905937 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((x2 + x + 1) * loop(\(x,i).(x2 + x),2,(x + 1))))
A053716: 7 127 1093 5461 19531 55987 137257 299593 597871 1111111 1948717 3257437 5229043 8108731 12204241 17895697
(~1 + ((x2 + 2x + 1) * loop(\(x,i).(2x2 + 4),2,1)))
A158765: 75 303 683 1215 1899 2735 3723 4863 6155 7599 9195 10943 12843 14895 17099 19455
(~1 + ((x2 + 2x + 1) * loop(\(x,i).x3,2,(x + 1))))
A258812: 0 2047 177146 4194303 48828124 362797055 1977326742 8589934591 31381059608 99999999999 285311670610 743008370687 1792160394036 4049565169663 8649755859374 17592186044415
(~1 + ((x2 + 2x + 1) * loop(\(x,i).(2x2 + ~2),2,2)))
A158736: 69 279 629 1119 1749 2519 3429 4479 5669 6999 8469 10079 11829 13719 15749 17919
(~1 + ((x2 + 2x + 1) * loop(\(x,i).(x2 + x + 2),2,2)))
A158744: 73 295 665 1183 1849 2663 3625 4735 5993 7399 8953 10655 12505 14503 16649 18943
(~1 + ((x2 + 2x + 1) * (~2 + loop(\(x,i).(x2 + 2x),2,2))))
A158771: 77 311 701 1247 1949 2807 3821 4991 6317 7799 9437 11231 13181 15287 17549 19967
(~1 + ((x2 + 2x + 1) * loop(\(x,i).((x2 + x) + i),2,2)))
A158668: 57 231 521 927 1449 2087 2841 3711 4697 5799 7017 8351 9801 11367 13049 14847
(~1 + ((x + 1) * loop(\(x,i).((x2 + 4x + 4) * (2 + i)),2,0)))
A158399: 783 1567 2351 3135 3919 4703 5487 6271 7055 7839 8623 9407 10191 10975 11759 12543
(1 + ((x + 1) * (1 + loop(\(x,i).(x * (x + i)),2,5))))
A158414: 962 1923 2884 3845 4806 5767 6728 7689 8650 9611 10572 11533 12494 13455 14416 15377
(~1 + (loop(\(x,i).(2 + i),(x mod 10),1) mod (x + 1)))
A331375: ~1 0 0 0 0 0 0 0 0 0 0 2 3 4 5 6
(1 + ((x + 1) * (1 + loop(\(x,i).(4x2 + ~1),2,2))))
A158407: 901 1801 2701 3601 4501 5401 6301 7201 8101 9001 9901 10801 11701 12601 13501 14401
(1 + ((x + 1) * (if ((x + ~2) mod (4 + (x mod 2))) <= 0 then 2 else 1)))
A201363: 2 3 7
A076986: 2 3 7 5 6 7 15 17 10 11 23 13 14 15 31 17
(1 + ((1 + (2 * (2 + (if (~2 + (x div 2)) <= 0 then x else 2)))) mod (x + 1)))
A308432: 1 2 1 4 4 4 3 2 1 10 10 10 10 10 10 10
(1 + ((1 + (if ((x + ~1) mod 4) <= 0 then 2 else (x mod 2))) mod (x + 1)))
A111336: 1 2 2 3 2 4 2 3 2 4 2 3 2 4 2 3
(1 + compr(\x.((1 + loop(\(x,i).2x,(x div 2),1)) mod (x + 1)),(x + 1)))
A042999: 2 3 5 11 13 19 29 37 43 53 59 61 67 83 101 107
loop(\(x,i).x3,1,(4x2 + 8x + 3))
A069076: 27 3375 42875 250047 970299 2924207 7414875 16581375 33698267 63521199 112678587 190109375 307546875 480048687 726572699 1070599167
loop(\(x,i).(x - (5x div (~1 - i))),(x + 1),1)
A036837: 4 11 25 50 92 158 257 400 600 873 1237 1713 2325 3100 4069 5266
(x mod (1 + (loop(\(x,i).~x2,2,6) mod (x + 1))))
A246004: 0 0 0 0 4 0 6 0 0 4 1 0 2 6 4 0
((~x + 1) mod (1 + (loop(\(x,i).2x,x,((x + 1) mod 2)) mod (x + 1))))
A318659-A318513: 0 0 1 0 1 0 1 0 3 0 1 0 1 0 2 0
loop(\(x,i).(2 * (x - (4 * (x - (2x * i))))),(x + 1),1)
A268730: 10 260 10920 633360 46868640 4218177600 447126825600 54549472723200 7527827235801600 1159285394313446400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + ~4x),1,(4x + 3))
A133766: 15 315 1287 3315 6783 12075 19575 29667 42735 59163 79335 103635 132447 166155 205143 249795
loop(\(x,i).x5,1,(4x + 3))
A016841: 243 16807 161051 759375 2476099 6436343 14348907 28629151 52521875 90224199 147008443 229345007 345025251 503284375 714924299 992436543
(loop(\(x,i).4x,x,4) div (4x + 3))
A191640: 1 2 5 17 53 178 606 2114 7489 26886 97541 356962 1315860 4880644 18199013 68174084
(2 div (1 + ((x + 1) * (if (x mod 3) <= 0 then 1 else (x + ~4)))))
A185778: 1 ~1 ~1 0 2 0 0 0 0 0 0 0 0 0 0 0
(1 + ((2x + 2) * (if (~x + 2) <= 0 then (2x + 5) else x)))
A307991: 1 5 55 89
(1 + (loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2) mod (x + 1)))
A059289: 1 1 3 3 3 1 3 7 3 7 3 5 3 7 1 7
(1 + (if (~4 + (x div 3)) <= 0 then x else (x2 + 3x + 2)))
A246337: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 273
((x div 2) div (1 + (loop(\(x,i).x3,2,2x) mod (x + 1))))
A336551-A292380: 0 0 0 1 0 0 0 3 2 0 0 1 0 0 0 7
(1 + ((loop(\(x,i).2x,x,(2 + (x mod 2))) - (x mod 2)) mod (x + 1)))
A079065: 1 2 3 4 3 6 3 8 9 6 3 12 3 6 9 16
((2x + 1) - (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))
A339597: 1 2 5 4 9 10 13 8 17 18 21 20 25 26 29 16
((2 - (x div 4)) mod (if ((x + 1) mod 4) <= 0 then (x + ~1) else 1))
A127708: 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 13
(1 + (if ((x mod (1 + ((x + ~1) mod 4))) mod 2) <= 0 then x2 else 1))
A172411: 1 2 5 10
A059591: 1 2 5 10 17 26 37 2 65 82 101 122 145 170 197 226
(1 + (if (x mod (1 + (2 * (x div (2 * (2 + (x mod 2))))))) <= 0 then 0 else 2))
A046540: 1 1 1 1 3 1 1 3 3 1 1 3 3 3 1 1
(1 + ((if (x mod 2) <= 0 then ((~x2 + x) mod 5) else 0) div 2))
A161223: 1 1 2 1 2 1 1 1 3 1 1 1 2 1 2 1
(1 + (if ((x mod 11) mod 3) <= 0 then 0 else 2))
A103585: 1 3 3 1 3 3 1 3 3 1 3 1 3 3 1 3
((x div 4) div (1 + (if (x mod 10) <= 0 then 0 else 2)))
A262257: 0 0 0 0 0 0 0 0 0 0 2 0 1 1 1 1
(1 + (if (x mod (2 + (3 * ((x mod 3) div 2)))) <= 0 then 0 else 2))
A064353: 1 3 3 3 1 1 1 3 3 3 1 3 1 3 3 3
(2x - (x div (1 + (if (~6 + (x div 2)) <= 0 then 0 else 2))))
A103303: 0 1 2 3 4 5 6 7 8 9
A023767: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 24 25
(1 + (if ((1 + (x div 4)) mod (2 + (x mod 4))) <= 0 then 0 else 2))
A081334: 3 3 3 3 1 3 3 3 3 1 3 3 1 3 1 3
(~1 + (x mod 2) - (if (x mod (2 + (4 mod (x + 2)))) <= 0 then 0 else 2))
A308567: ~1 ~2 ~1 ~2 ~3 ~2 ~1 ~2 ~3 ~2 ~3 ~2 ~1 ~2 ~3 ~2
(if (((~1 + (2x mod (2 + (x div 2)))) div 2) mod 2) <= 0 then ~2 else 1)
A317335: 1 1 ~2 1 1 ~2 ~2 1 1 1 ~2 ~2 1 ~2 ~2 1
(1 + (loop(\(x,i).(x + i - ((~1 + (x div 4)) div 2)),x,0) div 2))
A241907: 1 2 3 5 7 9 11 14 17 20 23 26 29 33 36 40
(1 + (2 * ((2 * (x div 7)) + (if x <= 0 then 0 else 1))))
A122916: 1 3 3 3 3
A343515: 1 3 3 3 3 3 3 7 7 7 7 7 7 7 11 11
(2x div (1 + (2 * (x div (1 + (if (x mod 4) <= 0 then 2 else 1))))))
A327491: 0 2 1 2 2 2 1 2 3 2 1 2 2 2 1 2
(1 + (if (x + ~1) <= 0 then x else (2 * (1 + (((x + 1) div 2) div 3)))))
A284397: 1 2 3 3 3 5 5 5 5 5 5 7 7 7 7 7
(if x <= 0 then 0 else (1 + ((~x mod (1 + (2x div 3))) div 2)))
A071335: 0 1 1 1 2 2 3 2 3 3 3 3 4 3 4 4
(~1 + (2 * (if ((x + 1) mod 5) <= 0 then (x div 3) else 1)))
A101025: 1 1 1 1 1 1 1 1 1 5 1 1 1 1 7 1
loop(\(x,i).5x,(8x + 6),1)
A191560: 15625 6103515625 2384185791015625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~3 + loop(\(x,i).(10x + 4),(x + 1),1))
A205084: 11 141 1441 14441 144441 1444441 14444441 144444441 1444444441 14444444441 144444444441 1444444444441 14444444444441 144444444444441 1444444444444441 14444444444444441
(2x div (1 + ((1 + loop(\(x,i).((x mod (1 + i)) + i),x,1)) div 2)))
A124830: 0 1 1 2 1 2 1 2 2 3 1 2 2 2 3 1
((x + 1) - ((~x + 2) div (2 + (if ((x div 2) mod 3) <= 0 then 2 else 1))))
A337050-A336590-A000452: 1 2 3 5 6 7 8 10 11 13 14 15 16 17 19 21
(if (x + ~1) <= 0 then 1 else ((x + ~1) - (2 * (x div 7))))
A284000: 1 1 1 2 3 4 5 4 5 6 7 8 9 10 9 10
(if x <= 0 then 2 else (1 + ((x - (x div (1 + ((1 + (x div 2)) div 2)))) mod 2)))
A105690: 2 1 2 1 1 2 1 2 1 1 1 2 2 1 1 1
(1 + loop(\(x,i).((x + 2) * (x + (x div 2))),(2x + 3),2))
A116265: 96013 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).((x + 2) * (x + (x div 2))),(2x + 3),2))
A116228: 96011 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * (1 + (if (x + ~2) <= 0 then x else (x - (x div ~4))))))
A319801: 3 5 7 11 13 17 19 21 23 27 29 31 33 37 39 41
(~1 + (2 * (~1 + (2 * loop(\(x,i).x3,(2x + ~1),2)))))
A172041: 5 29 536870909 4611686018427387903
(1 + ((x mod (1 + (4 * (if (x mod 3) <= 0 then 0 else 2)))) mod 2))
A205600: 1 2 1 1 1 2 1 2 1 1 2 1 1 1 2 1
(1 + (x div (if (~2 + (x mod (2 - (x mod ~4)))) <= 0 then 1 else 2)))
A074044: 1 2 3 4 5 6 7 8 9 5 11 12 13 7 15 16
(if (~x + 2) <= 0 then (2 + (x2 div 15)) else 1)
A029023: 1 1 2 2 3 3 4 5 6 7 8 10 11 13 15 17
(1 + (2 * (if (x + ~1) <= 0 then x else (1 + ((x mod (2 + (x mod 2))) mod 2)))))
A122916: 1 3 3 3 3
A333819: 1 3 3 3 3 3 3 5 3 3 3 3 3 5 3 3
(1 + (if ((x mod ~11) mod 4) <= 0 then 1 else 2))
A007538: 2 3 3 2 3 3 3 2 3 3 3 2 3 3 2 3
(1 + (2 * (loop(\(x,i).~2x,x,3) div 5)))
A078066: 1 ~3 5 ~9 19 ~39 77 ~153 307 ~615 1229 ~2457 4915 ~9831 19661 ~39321
(1 + (if (x + ~1) <= 0 then x else (2 + (2x2 div 5))))
A231408: 1 2 4 6 9
A006697: 1 2 4 6 9 13 17 22 28 35 43 51 60 70 81 93
(1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 10))
A099551: 1 1 3 1 5 3 7 1 9 5 1 3 3 7 5 1
(1 + loop(\(x,i).(x2 + ~8x),x,10))
A110383: 11 21 241 55681 3099816961 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if (x + ~2) <= 0 then x else ((x + 2) - ((~x + 2) div 5))))
A299497: 1 2 3 7 8 9 10 11 13 14 15 16 17 19 20 21
(1 div (~1 + (2 * ((if (x mod 2) <= 0 then (~x + 1) else x) mod 5))))
A016392-A016379-A016375-A016361-A016352-A016344-A014019: 1 1 0 0 0 ~1 ~1 0 0 0 1 1 0 0 0 ~1
(1 + (((1 + (x div 2)) div 3) * (if (x + ~4) <= 0 then 1 else 2)))
A284725: 1 1 1 1 2 3 3 3 3 3 5 5 5 5 5 5
((2x + 2) - ((~x + 1) div (1 + (if (x + ~4) <= 0 then 1 else 2))))
A304501: 2 4 7 9 12 14 16 18 21 23 25 28 30 32 35 37
(if x <= 0 then 2 else (1 + ((x - (4 mod (1 + (x div 4)))) div 2)))
A285578: 2 1 2 2 3 3 4 4 4 5 5 6 7 7 8 8
(1 + (2 * ((x + 1) + ((if (x + ~1) <= 0 then x else 2) + (x div 4)))))
A158942: 3 7 11 13 17 19 21 23 27 29 31 33 37 39 41 43
(1 + (((if x <= 0 then 1 else x) mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2))
A230799: 2 1 1 1 1 2 1 1 1 2 1 2 1 2 2 1
(1 + (if x <= 0 then 2 else ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2)))
A117544: 3 1 1 1 1 2 1 1 1 2 1 2 1 2 2 1
(2x div (1 + (2 * (1 + (if (x + ~2) <= 0 then 0 else (2 + (x mod 2)))))))
A070093: 0 0 1 0 1 1 1 1 2 2 2 2 3 2 4 3
(1 + (2 * ((loop(\(x,i).(~2x + 4),x,1) mod (x + 1)) div 3)))
A346095: 1 1 1 1 1 1 1 3 5 1 1 1 1 1 1 9
(~1 + (2 * (if (x + ~1) <= 0 then x else (((x2 + ~1) div 2) mod 3))))
A226915: ~1 1 1 1 1 ~1 3 ~1 1 1 1 ~1 3 ~1 1 1
loop(\(x,i).2x,((x div 2) - ((3 * (x div 4)) div 2)),1)
A151565-A060632: 1 1 2 2 2 2 4 4 2 2 4 4 4 4 8 8
(if x <= 0 then 1 else (~1 + ((x + 2) mod (2 + ((2 * (x div 2)) div 3)))))
A097454: 1 0 ~1 0 ~1 0 ~1 0 1 2 1 2 1 2 3 4
(~1 + (if x <= 0 then 2 else ((3 * ((x2 + 3x) div 2)) div 2)))
A175967: 1 2 6 12 20 29 39 51 65 80 96 114 134 155 177 201
(1 + (if x <= 0 then 1 else (2 * (x - (6 * (~x + (x mod 2)))))))
A028868: 2 3 29 31
(if (x div 2) <= 0 then 0 else (x2 mod (3 + ((x div 2) div 3))))
A343720: 0 0 1 0 1 1 0 1 0 1 0 1 4 4 1 0
(if x <= 0 then 1 else (~1 + ((x + ~2) mod (2 + ((x2 div 2) mod 3)))))
A317161: 1 0 ~1 0 1 0 ~1 0 1 0 ~1 0 ~1 0 ~1 0
(1 + ((x - (if (x + ~6) <= 0 then 1 else 0)) mod 6))
A106687: 6 1 2 3 4 5 6 2 3 4 5 6 1 2 3 4
(1 + (x mod ((x + 1) div (if (x + ~4) <= 0 then 1 else 6))))
A255826: 1 2 3 4 5 1 1 1 1 1 1 2 1 2 1 2
(if ((1 + ((x + 1) div 2)) mod 8) <= 0 then 6 else 1)
A046620-A046619: 1 1 1 1 1 1 1 1 1 1 1 1 1 6 6 1
(x - (x div (if ((x mod (2 + (x mod 2))) div 2) <= 0 then 6 else 1)))
A181578: 0 1 2 3 4 0 5 6 7 8 9 0 10 11 12 13
((x + 1) - ((if x <= 0 then 1 else x) div (~6 + (x div 4))))
A063538: 2 3 4 5 6 7 9 10 11 13 14 15 17 19 20 21
(21 * (2 - ((if x <= 0 then 1 else x) mod 2)))
A040421: 21 21 42 21 42 21 42 21 42 21 42 21 42 21 42 21
(7 * loop(\(x,i).8x,x,(x + 1)))
A212702: 7 112 1344 14336 143360 1376256 12845056 117440512 1056964608 9395240960 82678120448 721554505728 6253472382976 53876069761024 461794883665920 3940649673949184
(loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) mod 7)
A099548: 1 1 3 1 5 3 0 1 2 5 4 3 6 0 1 1
((loop(\(x,i).(x * (x - i)),2,(x + ~1)) div 2) div 7)
A011924: 0 0 0 0 1 8 25 60 120 216 360 565 848 1225 1716 2340
(14 * ((2 - (x mod 2)) * (if x <= 0 then 1 else 2)))
A040757: 28 28 56 28 56 28 56 28 56 28 56 28 56 28 56 28
(28 * loop(\(x,i).(2x + 4),x,1))
A305270: 28 168 448 1008 2128 4368 8848 17808 35728 71568 143248 286608 573328 1146768 2293648 4587408
(if x <= 0 then 1 else (7 * (x - (x div 8))))
A020646: 1 7 14 21 28 35 42 49 49 56 63 70 77 84 91 98
((4 * loop(\(x,i).(~2x + 4),x,2)) div 7)
A077903: 1 0 2 ~3 6 ~12 25 ~48 98 ~195 390 ~780 1561 ~3120 6242 ~12483
((if (~2 + (x div 5)) <= 0 then x else 2) mod 7)
A309958: 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 2
(x - loop(\(x,i).2x2,1,((x + 2) div 7)))
A227181: 0 1 2 3 4 3 4 5 6 7 8 9 4 5 6 7
(7 * loop(\(x,i).8x,x,(x + 2)))
A159738: 14 168 1792 17920 172032 1605632 14680064 132120576 1174405120 10334765056 90194313216 781684047872 6734508720128 57724360458240 492581209243648 4186940278571008
((if x <= 0 then 2 else (3x + 3)) + (x div 7))
A120701: 2 6 9 12 15 18 21 25 28 31 34 37 40 43 47 50
loop(\(x,i).(x + (x div 7)),x,7)
A182308-A023388: 7 8 9 10 11 12 13 14 16 18 20 22 25 28 32 36
loop(\(x,i).(x + (x mod 10)),x,7)
A102041: 7 14 18 26 32 34 38 46 52 54 58 66 72 74 78 86
(1 + (2 * ((x + (if (~2 + (x div 4)) <= 0 then 2 else 0)) div 3)))
A080605: 1 3 3 3 5 5 5 7 7 7 9 9 9 9 9 11
(1 + (if x <= 0 then 1 else (2 * ((x + 1) + ((x div 2) + (x div 3))))))
A063203: 2 5 9 13 17 19 25 27 31 35 39 41 47 49 53 57
(~1 + (if x <= 0 then 1 else (2 * (x - ((x div 3) + (x div ~2))))))
A063081: 0 3 5 7 9 13 13 17 19 21 23 27 27 31 33 35
(1 + (loop(\(x,i).(1 + (x div (2 - (x mod 2)))),x,(x div 3)) div 2))
A082863: 1 1 2 2 2 2 2 2 2 3 2 3 3 2 3 2
(1 + ((if (x mod 2) <= 0 then 1 else (x div 3)) * ((x mod 3) div 2)))
A233285-A233284: 1 1 2 1 1 2 1 1 2 1 1 4 1 1 2 1
(~1 + (if ((x div 2) mod 2) <= 0 then 2 else (x mod 2)) - ((x mod 3) div 2))
A115525: 1 1 ~2 0 1 0 ~1 0 0 1 ~1 ~1 1 1 ~2 0
(1 + (2 * (1 + loop(\(x,i).(10x + ~8),x,2))))
A173193: 7 27 227 2227 22227 222227 2222227 22222227 222222227 2222222227 22222222227 222222222227 2222222222227 22222222222227 222222222222227 2222222222222227
(if x <= 0 then 0 else (1 + (((x * (x2 div 2)) div (x + 3)) mod 2)))
A182907: 0 1 1 1 1 2 1 1 2 1 1 2 2 1 1 2
(1 + ((if ((x div 2) mod 3) <= 0 then 2 else 0) * ((1 + (x div 2)) div 2)))
A028277: 1 1 1 1 1 1 5 5 1 1 1 1 7 7 1 1
(1 + (loop(\(x,i).(2x + 4),(2x + ~1),(1 + (x mod 2))) div 2))
A263245: 1 5 19 95 319 1535 5119 24575 81919 393215 1310719 6291455 20971519 100663295 335544319 1610612735
loop(\(x,i).x2,3,(10x + 3))
A017312: 6561 815730721 78310985281 1406408618241 11688200277601 62259690411361 248155780267521 806460091894081 2252292232139041 5595818096650401 12667700813876161 26584441929064321 52389094428262881
loop(\(x,i).x3,1,(10x + 3))
A017307: 27 2197 12167 35937 79507 148877 250047 389017 571787 804357 1092727 1442897 1860867 2352637 2924207 3581577
loop(\(x,i).x3,2,(10x + 3))
A017313: 19683 10604499373 1801152661463 46411484401953 502592611936843 3299763591802133 15633814156853823 58871586708267913 186940255267540403 520411082988487293 1304773183829244583 3004041937984268273
(1 + (2 * loop(\(x,i).(3 + ((x * (1 + (x div 2))) div 2)),x,1)))
A253850: 3 7 13 31 127
(~1 + (2 * loop(\(x,i).((2x + ~1) + (x mod (2 + (x mod 2)))),x,1)))
A147758: 1 3 5 9 21 45 93 189 381 765 1533 3069 6141 12285 24573 49149
(1 + (loop(\(x,i).(1 + (x2 * ((x + ~1) + (i * i)))),x,1) div 2))
A290873: 1 2 11 6396
(~1 + (2 * loop(\(x,i).(2 * (x + (3 * (i * (1 + i))))),x,1)))
A026917: 1 27 127 399 1039 2439 5383 11439 23743 48567 98455 198495 398863 799911 1602343 3207567
(1 + (2 * ((x + 1) + loop(\(x,i).(x - (x div 4)),2,(x div 2)))))
A285519: 3 5 9 11 15 17 21 23 25 27 29 31 35 37 41 43
(1 + ((loop(\(x,i).~x,x,(x mod 5)) mod (x + 1)) div 2))
A275937: 1 1 2 1 3 1 1 4 2 4 1
(~1 + loop(\(x,i).(x4 + x3 + x2 + x + 2),(x + 1),2))
A051155: 31 1082401 4611686018427387903 4611686018427387903
(1 + (x div (2 + (loop(\(x,i).2x,x,(~2 + (x mod 2))) mod (x + 1)))))
A128708-A087653: 1 1 1 2 1 1 1 4 3 1 1 2 1 1 2 8
(1 + (2 * ((x + 1) + (2 * loop(\(x,i).x3,x2,2)))))
A057664: 11 37 4611686018427387903 4611686018427387903
(2 - (2 div (1 + ((loop(\(x,i).(2 * (x - i)),x,2) mod (x + 1)) div 2))))
A294891-A294879-A087624: 0 0 0 1 0 2 0 1 1 2 0 2 0 2 2 1
((x + 1) div (1 + ((loop(\(x,i).2x,x,(x mod 2)) mod (x + 1)) div 2)))
A319677-A294650: 1 2 3 4 5 3 7 8 9 5 11 2 13 7 15 16
loop(\(x,i).(2x3 + 4x2 + ~x + 1),(2x + 2),1)
A144956: 571 4611686018427387903 4611686018427387903 4611686018427387903
((2x + 3) * (4x - (if (~x + 2) <= 0 then 1 else 0)))
A303295: 0 20 49 99 165 247 345 459 589 735 897 1075 1269 1479 1705 1947
((2x + 3) * loop(\(x,i).2x,x,(x + 6)))
A059224: 18 70 224 648 1760 4576 11520 28288 68096 161280 376832 870400 1990656 4513792 10158080 22708224
((loop(\(x,i).(x * (x - i)),2,(x + 2)) div 2) div (2x + 3))
A278212: 0 2 8 20 38 64
A032767: 0 2 8 20 38 64 100 148 208 282 373 480 606 753 921 1112
((2x + 3) * loop(\(x,i).(4x * (1 + i)),x,2))
A167570: 6 80 1344 27648 675840 19169280 619315200 22460497920 903704739840 39953262182400 1925366729932800 100453916344320000 4611686018427387903 4611686018427387903 4611686018427387903
(if ((x + ~1) mod (2 + (x mod (2 + (x mod 2))))) <= 0 then ((x + 1) div 2) else 1)
A049077: 1 1 1 2 1 3 1 4 1 5 1 1 1 7 1 8
(loop(\(x,i).(x * (1 + i)),x,(1 + (x div 2))) div (1 + ((x + 1) div 2)))
A068941: 1 1 6 16
A152663: 1 1 6 16 120 540 5040 32256 362880 3024000 39916800 410572800 6227020800 76281004800 1307674368000 18598035456000
((2x + (if (~x + 2) <= 0 then x else (x + 1))) div (1 + ((x + 1) div 2)))
A049108: 1 2 3 3 4 3 4 4 4 4 5 4 5 4 5 5
(~1 + (loop(\(x,i).(x - (3 * (~2 + (x div 2)))),x,(x + 1)) div 2))
A020944: ~1 1 0 1 1 0 1 1 2 1 1 0 1 1 2 1
(1 + ((x - (x div loop(\(x,i).(x div (~2 + (x mod 2))),x,(x + 1)))) div 2))
A109168: 1 2 2 4 3 4 4 8 5 6 6 8 7 8 8 16
((x + 1) div (if ((x + 2) mod 5) <= 0 then ((x + ~1) div 2) else 1))
A160597: 1 2 3 4 5 6 7 8 3 10 11 12 13 2 15 16
loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),((x + ~1) div 2),1)
A208355: 1 1 1 2 2 5 5 14 14 42 42 132 132 429 429 1430
((x + 3) div (1 + ((2 + (x mod 3)) * (if x <= 0 then 1 else 2))))
A025831: 1 0 0 1 1 0 1 1 1 2 1 1 3 2 1 3
(3 + (if (((x + 2) mod 8) mod 3) <= 0 then 0 else 2))
A194584: 5 3 5 5 3 5 3 5 5 3 5 5 3 5 3 5
(1 + ((2 + (x div 2)) mod (2 + (if (~4 + (x div 2)) <= 0 then 0 else 2))))
A112050: 1 1 2 2 1 1 2 2 1 1 4 4 1 1 2 2
loop(\(x,i).(x * i),(2 - ((~x + 2) div (1 - (x div ~4)))),1)
A178801: 1 2 2 6 6 6 24 24 24 24 24 120 120 120 120 120
loop(\(x,i).3x2,1,(1 + (2 * (x - (x div ~2)))))
A229852: 3 75 147 363 507 867 1083 1587 1875 2523 2883 3675 4107 5043 5547 6627
(1 + ((loop(\(x,i).((x + 2) + (((2 + i) * i) div 2)),x,0) div 2) div 2))
A106607: 1 1 3 5 9 13 20 28 39 51 67 85 107 131 160 192
(if x <= 0 then 0 else (~1 + (2 * (((x + ~2) div (1 + (x div 3))) mod 2))))
A011612: 0 1 ~1 ~1 1 1 1 1 ~1 1 ~1 ~1 ~1 ~1 ~1 ~1
(1 + (2 * ((1 + loop(\(x,i).(2 * (x + i)),x,(1 + (x mod 2)))) div 2)))
A051842: 3 7 13 39 69
(1 + (if x <= 0 then 1 else ((x div (2 + (x div 7))) mod 2)))
A296299: 2 1 2 2 1 1 2 1 1 2 2 2 1 1 2 2
(1 + (2 * (if (~2 + (x mod (2 - (x mod ~4)))) <= 0 then 1 else 2)))
A176171: 3 3 3 3 3 3 3 3 3 5 3 3 3 5 3 3
(1 + (2 * (loop(\(x,i).(x + (i div 2)),(x + ~8),1) div 2)))
A323529: 1 1 1 1 1 1 1 1 1 1 3 3 5 7 11 13
(~1 + (2 * (((if x <= 0 then 1 else (x div 3)) mod 5) mod 2)))
A063747: 1 ~1 ~1 1 1 1 ~1 ~1 ~1 1 1 1 ~1 ~1 ~1 ~1
loop(\(x,i).x3,(x mod 2),21)
A135823: 21 9261 21 9261 21 9261
(((if x <= 0 then 1 else x) mod 2) div (~1 + (2 * ((x div 5) mod 2))))
A073097: ~1 ~1 0 ~1 0 1 0 1 0 1 0 ~1 0 ~1 0 1
(~1 + (2 * ((if x <= 0 then 2 else (2x mod (1 + (x mod 4)))) div 2)))
A332433: 1 ~1 ~1 1 ~1 ~1 ~1 1 ~1 ~1 1 1 ~1 ~1 ~1 1
(1 + ((x - ((x mod (1 + (2 * (if (x mod 2) <= 0 then x else 2)))) div 2)) div 2))
A232479: 1 1 1 2 2 3 2 4 3 4 3 6 4 7 4 8
(5 + loop(\(x,i).2x,(~x + 2),(x + 5)))
A215537: 25 17 12 13 14 15 16 17 18 19 20 21 22 23 24 25
(~1 + loop(\(x,i).8x,(8x + 2),2))
A135982: 127 2147483647 36028797018963967 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((loop(\(x,i).(2x + 4),x,(3 + (x mod 2))) div 2) div 2))
A133600: 1 4 7 16 28 64 112 256 448 1024 1792 4096 7168 16384 28672 65536
(if x <= 0 then 1 else (x div (5 + ((~1 + (x div 2)) mod 3))))
A017901-A017866-A017865-A017864: 1 0 0 0 0 0 0 1 1 1 1 1 1 1 2 3
loop(\(x,i).i,(x div (2 * (2 + ((x2 div 4) mod 3)))),1)
A123548: 1 1 1 1 1 1 1 1 1 1 1 2 3 3 2 1
(1 + (x mod (2 + (if ((x + 1) mod 4) <= 0 then 1 else 6))))
A072400: 1 2 3 1 5 6 7 2 1 2 3 3 5 6 7 1
loop(\(x,i).2x,(x div 3),(1 + (2 * (2 + (x mod 3)))))
A336122: 5 7 9 10 14 18 20 28 36 40 56 72 80 112 144 160
(~1 + (2 * (~2 + loop(\(x,i).(x + (x mod 8)),x,3))))
A175376: 1 7 19 27 27 27 27 27 27 27 27 27 27 27 27 27
loop(\(x,i).x2,3,(~7x + ~5))
A017048: 390625 429981696 16983563041 208827064576 1406408618241 6553600000000 23811286661761 72301961339136 191707312997281 457163239653376 1001129150390625 2044140858654976 3936588805702081
(1 + (2 * (2 + loop(\(x,i).(10x + ~4),x,1))))
A165246: 7 17 117 1117 11117 111117 1111117 11111117 111111117 1111111117 11111111117 111111111117 1111111111117 11111111111117 111111111111117 1111111111111117
(1 + ((x - ((loop(\(x,i).(2 * (x - i)),x,2) mod (x + 1)) div 2)) div 2))
A290731: 1 1 2 2 3 2 4 4 4 3 6 4 7 4 6 8
(1 + (loop(\(x,i).(3x + 3),(x + 2),((x + 1) mod 2)) div 2))
A198310: 11 20 101 182 911 1640 8201 14762 73811 132860 664301 1195742 5978711 10761680 53808401 96855122
loop(\(x,i).(10x + 1),(2 * ((x + ~1) div 2)),1)
A283351: 1 1 1 111 111 11111 11111 1111111 1111111 111111111 111111111 11111111111 11111111111 1111111111111 1111111111111 111111111111111
((2x + 1) - (((x2 - loop(\(x,i).(x * i),x,1)) div 2) div 2))
A254225: 2 3 5 7 11 35
loop(\(x,i).(2x + 1),(0 - (x div (~2 + (x div ~4)))),1)
A132197: 1 3 3 3 7 7 7 7 7 7 7 15 15 15 15 15
(if ((x + 1) mod 4) <= 0 then 0 else (1 + ((x div ~4) mod 2)))
A285193: 1 2 2 0 2 1 1 0 1 2 2 0 2 1 1 0
(1 + (2 * ((x mod (2 + (if (x mod 8) <= 0 then x else 1))) div 2)))
A139378: 1 1 3 1 1 3 1 1 9
A091840-A038500: 1 1 3 1 1 3 1 1 9 1 1 3 1 1 3 1
(1 + (x2 div (4 * (2 + (if (~2 + (x div 2)) <= 0 then 1 else 2)))))
A029064: 1 1 1 1 2 3 3 4 5 6 7 8 10 11 13 15
(1 + (8 * loop(\(x,i).(2x + 4),(x + 3),2)))
A304385: 353 737 1505 3041 6113 12257 24545 49121 98273 196577 393185 786401 1572833 3145697 6291425 12582881
(loop(\(x,i).3x,x,1) mod 31)
A036123: 1 3 9 27 19 26 16 17 20 29 25 13 8 24 10 30
(if (~x + 2) <= 0 then (((~x + 2) div (2 + (x div 8))) mod 2) else 1)
A189091: 1 1 0 1 1 0 0 1 0 1 1 1 0 0 0 1
loop(\(x,i).i,(((2x + 1) mod (4 + (x div 4))) div 2),1)
A122191-A097847: 1 1 1 1 2 1 1 1 2 1 1 2 2 3 1 1
loop(\(x,i).2x,((x - (((x - (x div 4)) div 2) mod 2)) div 2),1)
A140839: 1 1 1 2 2 4
A101651: 1 1 1 2 2 4 8 8 8 16 32 32 64 64 64 128
(1 + (2 * (((if x <= 0 then 2 else x2) div (2 + (x mod 4))) mod 2)))
A279340: 3 1 3 3 1 1 3 3 1 3 3 1 1 1 3 3
(~1 + (4 * loop(\(x,i).(x2 * (x div 2)),(x + 4),2)))
A183078: 8796093022207 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * ((loop(\(x,i).(x2 div 2),2,(~2 + (x div 2))) div 2) div 2)))
A146237: 1 1 1 1 1 1 1 1 1 1 5 5 17 17 37 37
(if (~x + 2) <= 0 then ((x div (2 + (x mod (2 + ((x div 2) mod 2))))) mod 2) else 1)
A189163-A189129: 1 1 0 1 0 1 1 0 0 1 1 0 0 0 1 1
((if x <= 0 then 1 else 2) div (1 + (x mod (2 * (2 + ((x + 2) mod 4))))))
A332015: 1 1 0 0 0 0 0 1 2 0 0 0 0 0 0 0
(loop(\(x,i).6x,x,1) mod 17)
A070394: 1 6 2 12 4 7 8 14 16 11 15 5 13 10 9 3
(loop(\(x,i).(x * (x - i)),2,(x + ~1)) div 17)
A011927: 0 0 0 0 1 7 21 49 98 177 296 465 698 1009 1413 1927
(loop(\(x,i).5x,x,1) mod 17)
A070371: 1 5 8 6 13 14 2 10 16 12 9 11 4 3 15 7
(loop(\(x,i).(x * (x - i)),2,(x + ~1)) div 15)
A011925: 0 0 0 0 1 8 24 56 112 201 336 528 792 1144 1601 2184
(15 * ((2 - (x mod 2)) * (if x <= 0 then 1 else 2)))
A040871: 30 30 60 30 60 30 60 30 60 30 60 30 60 30 60 30
(loop(\(x,i).2x,(x + ~1),1) - (x div 15))
A220469: 1 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16383
loop(\(x,i).(x3 + 3x),x,15)
A145189: 15 3420 40001698260 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,((x + 1) - (2 div (x + ~16))))
A144913: 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 324
(x + (if (~2 + (x div 4)) <= 0 then 2 else 1) - (x div 5))
A121604: 2 3 4 5 6 6 7 8 9
A340767: 2 3 4 5 6 6 7 8 9 10 10 11 11 12 13 13
(1 + (if (x + ~2) <= 0 then x else (4 - ((x - (x div 4)) mod 2))))
A110007: 1 2 3 4 4 5 4 5 5 4 5 4 4 5 4 5
(if ((1 + (x div 4)) mod (4 - (x mod 4))) <= 0 then 2 else 1)
A093914: 1 1 1 2 1 1 2 2 1 2 1 2 2 1 2 2
(1 + (4 * (~2 + loop(\(x,i).10x,x,2))))
A169830-A100412: 1 73 793 7993 79993 799993 7999993 79999993 799999993 7999999993 79999999993 799999999993 7999999999993 79999999999993 799999999999993 7999999999999993
loop(\(x,i).2x,x,(4x2 + 16x + 23))
A217529: 23 86 284 856 2416 6496 16832 42368 104192 251392 596992 1398784 3239936 7430144 16891904 38109184
((x + 1) - ((loop(\(x,i).(~x + 1),(x + ~2),(2 + (x div 2))) div 2) div 2))
A246698: 1 2 3 5 4 7 6 9 8 12 10 14 11 16 13 18
(1 + (2 * (4 + loop(\(x,i).4x,x,(2 - (x mod 2))))))
A108265: 13 17 73 137 1033
((x + 2) div (if (((2x + ~4) mod (x + 2)) mod 4) <= 0 then 2 else 1))
A111618: 1 3 2 5 3 7 4 9 10 11 6 13 14 15 8 17
(1 + (2 * (if ((x mod (2 + (x mod 2))) div 2) <= 0 then (x mod 2) else 4)))
A073575: 1 3 1 3 1 9 1 3 1 3 1 9 1 3 1 3
(9 + loop(\(x,i).10x,x,1))
A253213: 10 19 109 1009 10009 100009 1000009 10000009 100000009 1000000009 10000000009 100000000009 1000000000009 10000000000009 100000000000009 1000000000000009
((~x + ~1) + (loop(\(x,i).2x,x,1) + ((x + 1) mod 8)))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A343844: 1 2 4 8 16 32 64 120
((x + 1) - loop(\(x,i).i,(x mod (8 + (x div 4))),1))
A123895: 0 1 1 1 1 1 1 1 1 1 10 11 12 12 12 12
(9 + loop(\(x,i).4x,x,(2 - (x mod 2))))
A108264: 11 13 41 73 521
(loop(\(x,i).((2x + 4) - (x div 2)),x,0) mod 9)
A140262: 0 4 1 1 6 0 4 6 4 1 6 0 4 6 4 6
(27 * (2 - ((if x <= 0 then 1 else x) mod 2)))
A040703: 27 27 54 27 54 27 54 27 54 27 54 27 54 27 54 27
(loop(\(x,i).8x,(x + 2),1) div 9)
A152776: 7 56 455 3640 29127 233016 1864135 14913080 119304647 954437176 7635497415 61083979320 488671834567 3909374676536 31274997412295 250199979298360
(9 * loop(\(x,i).(3x + 7),x,1))
A277105: 9 90 333 1062 3249 9810 29493 88542 265689 797130 2391453 7174422 21523329 64570050 193710213 581130702
(1 + (loop(\(x,i).2x,x,1) div 9) - (x mod 2))
A328881: 1 0 1 0 2 3 8 14 29 56 114 227 456 910 1821 3640
(loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) mod 9)
A099550: 1 1 3 1 5 3 7 1 0 5 2 3 4 7 6 1
(18 * (~1 + loop(\(x,i).(2 * (x + i)),x,2)))
A059138: 18 90 270 666 1494 3186 6606 13482 27270 54882 110142 220698 441846 884178 1768878
(9 * (if (~1 + (x div 2)) <= 0 then 1 else ((x + 1) div 2)))
A242893: 9 9 9 9 18 27 27 36
((loop(\(x,i).(x * (x - i)),2,(x + ~1)) div 2) div 9)
A011928: 0 0 0 0 1 6 20 46 93 168 280 440 660 953 1334 1820
(if x <= 0 then 1 else (9 * ((x3 + x) div 2)))
A289721: 1 9 45 135 306 585 999 1575 2340 3321 4545 6039 7830 9945 12411 15255
(9 * (if (~4 + (x div 2)) <= 0 then x else (x + 2)))
A131418: 0 9 18 27 36 45 54 63 72 81 108 117 126 135 144 153
loop(\(x,i).10x,(x div 2),9)
A050683: 9 9 90 90 900 900 9000 9000 90000 90000 900000 900000 9000000 9000000 90000000 90000000
loop(\(x,i).(x - ((1 - (x div 2)) div 3)),x,9)
A120185: 9 10 12 14 16 19 22 26 30 35 41 48 56 65 76 89
(loop(\(x,i).~4x,(x + ~1),x) mod 9)
A156060: 0 1 1 3 5 2 3 7 4 0 8 8 6 4 7 6
(9 * (x + (if (~2 + (x div 3)) <= 0 then 1 else 2)))
A044052: 9 18 27 36 45 54 63 72 81 99 108 117 126 135 144 153
(9 * (x + (if (~4 + (x div 2)) <= 0 then 1 else 2)))
A052223: 9 18 27 36 45 54 63 72 81 90 108 117 126 135 144 153
loop(\(x,i).(x + (x div 9)),x,9)
A182362-A023392: 9 10 11 12 13 14 15 16 17 18 20 22 24 26 28 31
loop(\(x,i).(x + (x mod 10)),x,9)
A102042: 9 18 26 32 34 38 46 52 54 58 66 72 74 78 86 92
((x * (~x2 + (if (x + ~1) <= 0 then 1 else 0))) mod 9)
A021929: 0 0 1 0 8 1 0 8 1 0 8 1 0 8 1 0
(1 + ((if ((x div 4) mod 2) <= 0 then x else ~x) mod 8))
A181975: 1 2 3 4 5 4 3 2 1 2 3 4 5 4 3 2
((x div 2) div (1 + (x div ((if (x mod 2) <= 0 then 1 else x) mod 8))))
A035446: 0 0 0 0 0 1 0 1 0 0 0 1 0 2 0 2
(2 - (if ((x + 1) mod 8) <= 0 then (x + ~8) else 1))
A318667-A317941: 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 ~5
(1 + loop(\(x,i).11x,x,8))
A199759: 9 89 969 10649 117129 1288409 14172489 155897369 1714871049 18863581529 207499396809 2282493364889 25107427013769 276181697151449 3037998668665929 33417985355325209
(~1 + loop(\(x,i).11x,x,8))
A199027: 7 87 967 10647 117127 1288407 14172487 155897367 1714871047 18863581527 207499396807 2282493364887 25107427013767 276181697151447 3037998668665927 33417985355325207
(x - ((2 * (if x <= 0 then 1 else x)) div (~3 + ((~x + 2) div 4))))
A285601: 1 2 4 5 6 8 9 10 12 13 14 15 16 18 19 20
((~x + 1) mod (~1 + (2 * (if (x mod 3) <= 0 then 2 else (x div 4)))))
A263142: 1 0 0 1 0 0 1 0 2 1 0 2 1 3 2 1
(1 - (if (x mod 2) <= 0 then ((2x + 2) mod (2 + (x div 4))) else 1))
A016229-A015869-A015749-A015389-A015149-A015029-A014789-A014669-A011637: 1 0 1 0 0 0 ~1 0 ~1 0 ~1 0 0 0 1 0
loop(\(x,i).x2,3,(12x + 9))
A017636: 43046721 37822859361 1406408618241 16815125390625 111429157112001 513798374428641 1853020188851841 5595818096650401 14774554437890625 35114532758015841 76686282021340161 156225851787813921
loop(\(x,i).x3,1,(12x + 9))
A017631: 729 9261 35937 91125 185193 328509 531441 804357 1157625 1601613 2146689 2803221 3581577 4492125 5545233 6751269
loop(\(x,i).x3,2,(12x + 9))
A017637: 387420489 794280046581 46411484401953 756680642578125 6351461955384057 35452087835576229 150094635296999121 520411082988487293 1551328215978515625 4108400332687853397
loop(\(x,i).x2,1,(~11x + ~9))
A017498: 81 400 961 1764 2809 4096 5625 7396 9409 11664 14161 16900 19881 23104 26569 30276
loop(\(x,i).x2,2,(~11x + ~9))
A017500: 6561 160000 923521 3111696 7890481 16777216 31640625 54700816 88529281 136048896 200533921 285610000 395254161 533794816 705911761 916636176
(1 + (loop(\(x,i).(x * (1 + i)),x,(2 + ((x2 + x) div 2))) div 2))
A308606: 2 4 16 97 721 6121 57961 604801 6894721 85276801 1137628801 16286054401 249080832001 4053790540801 69960578688001 1276290183168001
(1 + ((loop(\(x,i).(2x + 4),x,((x2 + ~x) div 2)) div 2) div 2))
A081908: 1 2 5 14 40 112 304 800 2048 5120 12544 30208 71680 167936 389120 892928
(1 + (2 * (2 + loop(\(x,i).(10x + ~8),x,2))))
A173262: 9 29 229 2229 22229 222229 2222229 22222229 222222229 2222222229 22222222229 222222222229 2222222222229 22222222222229 222222222222229 2222222222222229
(~1 + (2 * (loop(\(x,i).((x + 2) div (2 - (x mod 2))),2,(x + 2)) div 2)))
A247617: 1 5 3 7 1 9 5 11 3 13 7 15 3 17 9 19
(if ((x + 1) mod 12) <= 0 then (x + 6) else 1)
A089170: 1 1 1 1 1 1 1 1 1 1 1 17 1 1 1 1
(1 + (4 * (if (x + ~10) <= 0 then x else (x + 2))))
A334526: 1 5 9 13 17 21 25 29 33 37 41 53 57 61 65 69
loop(\(x,i).x5,1,(8x + 1))
A017081: 1 59049 1419857 9765625 39135393 115856201 282475249 601692057 1160290625 2073071593 3486784401 5584059449 8587340257 12762815625 18424351793 25937424601
loop(\(x,i).((x2 + x) div 2),1,(~7x + 1))
A081591: 1 15 78 190 351 561 820 1128 1485 1891 2346 2850 3403 4005 4656 5356
(1 + (if x <= 0 then 1 else (2 * (x - (((x mod 3) * (x div 2)) mod 2)))))
A226047: 2 3 5 7 9 11 13 13 17 19 19 23 25 27 29 31
(if (x + ~1) <= 0 then x else (1 + (((x2 + ~2x) mod (2 + (x div 2))) mod 2)))
A069010: 0 1 1 1 1 2 1 1 1 2 2 2 1 2 1 1
(1 + (4 * loop(\(x,i).(~x + 6),(x div 2),(x mod 2))))
A070376: 1 5 25 21 1 5 25 21 1 5 25 21 1 5 25 21
(1 + (loop(\(x,i).(2x + (i mod 2)),x,1) div (4 + (x mod 2))))
A305750: 1 1 2 3 7 11 27 43 107 171 427 683 1707 2731 6827 10923
((if (x + ~2) <= 0 then 1 else (x div 3)) div (1 + (4 * (x mod 2))))
A008613: 1 0 1 0 1 0 2 0 2 0 3 0 4 0 4 1
loop(\(x,i).6x,(x div 2),(1 + (4 * (x mod 2))))
A166023: 1 5 6 30 36 180 216 1080 1296 6480 7776 38880 46656 233280 279936 1399680
(if x <= 0 then 1 else ((x + ~1) + (((x div 2) mod 2) + (4 * (x mod 2)))))
A126091: 1 4 2 7 3 8 6 11 7 12 10 15 11 16 14 19
(if ((1 + ((x + 1) div 3)) mod 5) <= 0 then 4 else 1)
A243756-A172985: 1 1 1 1 1 1 1 1 1 1 1 4 4 4 1 1
((1 - (if (x mod (2 + (x mod 4))) <= 0 then x else 0)) mod 5)
A284345: 1 1 1 1 2 1 1 1 3 2 1 1 4 1 1 1
loop(\(x,i).x2,1,(5x2 + 15x + 5))
A207597: 25 625 3025 9025 21025 42025 75625 126025 198025 297025 429025 600625 819025 1092025 1428025 1836025
(loop(\(x,i).2x,x,1) mod 45)
A222011: 1 2 4 8
A070350: 1 2 4 8 16 32 19 38 31 17 34 23 1 2 4 8
(if (x + ~2) <= 0 then 1 else (5 * (1 + (x div 8))))
A094636: 1 1 1 5 5 5 5 5 10 10 10 10 10 10 10 10
(25 * (2 - ((if x <= 0 then 1 else x) mod 2)))
A040601: 25 25 50 25 50 25 50 25 50 25 50 25 50 25 50 25
((3 * (1 + ((x + 2) * (if x <= 0 then 1 else x)))) div 5)
A184535: 1 2 5 9 15 21 29 38 48 60 72 86 101 117 135 153
(5 * loop(\(x,i).((3x + 1) - (i mod 2)),x,1))
A340395: 5 15 50 150 455 1365 4100 12300 36905 110715 332150 996450 2989355 8968065 26904200 80712600
(loop(\(x,i).(2x * (2 + (i mod 3))),x,1) mod 5)
A131015: 1 1 3 2 2 1 4 4 2 3 3 4 1 1 3 2
(((x + 1) * loop(\(x,i).((x2 + 2) + i),2,2)) div 5)
A190326: 10 21 31 42 53 63 74 84 95 106 116 127 137 148 159 169
((((x + 1) * loop(\(x,i).(x2 + 2x),2,x)) div 2) div 5)
A164938: 0 3 24 102 312 777 1680 3276 5904 9999 16104 24882 37128 53781 75936 104856
((2 * loop(\(x,i).((x2 + ~x) div 2),2,(x + ~1))) div 5)
A011930: 0 0 0 0 1 6 18 42 84 151 252 396 594 858 1201 1638
((2 * (2 + (x2 div (if (~x + 2) <= 0 then 2 else 1)))) div 5)
A231056: 0 1 1 2 4 5 8 10 13 16 20 24 29 34 40 45
(if x <= 0 then 1 else ((x - ((1 + (x div 2)) mod 4)) div 5))
A025151: 1 0 0 0 0 0 1 1 1 1 1 1 1 2 2 3
(if x <= 0 then 2 else (10x + 120))
A300292: 2 130 140
(if x <= 0 then 1 else (20x3 + 10x))
A101098: 1 30 180 570 1320 2550 4380 6930 10320 14670 20100 26730 34680 44070 55020 67650
loop(\(x,i).((x2 + x) div 2),1,((~2x + 2) div 5))
A327142: 0 0 0 0 1 1 1 3 3 6 6 6 10 10 15 15
((if x <= 0 then 1 else 4x) - ((~2x + 2) div 5))
A312928: 1 4 9 13 18 22 26 31 35 40 44 48 53 57 62 66
loop(\(x,i).x2,1,((x + 2) - ((~2x + 2) div 5)))
A087058: 4 9 25 36 64 81 100 144 169 225 256 289 361 400 484 529
(((x * loop(\(x,i).(x * (x - i)),2,(x + ~2))) div 2) div 5)
A300847: 0 0 0 0 0 12 72 252 672 1512 3024 5544 9504 15444 24024 36036
(if x <= 0 then 1 else (6x - ((x + 2) div 5)))
A315707: 1 6 12 17 23 29 35 41 46 52 58 64 70 75 81 87
(if x <= 0 then 1 else (5x - ((x + 2) div 5)))
A313568: 1 5 10 14 19 24 29 34 38 43 48 53 58 62 67 72
(((2 + (if (x + ~4) <= 0 then 0 else 2)) * (x div 2)) div 5)
A237819: 0 0 0 0 0 1 2 2 3 3 4 4 4 4 5 5
loop(\(x,i).~x,x,(2 - ((x3 + 2) mod 5)))
A253262: 0 1 2 2 1 0 ~1 ~2 ~2 ~1 0 1 2 2 1 0
((if ((x div 5) mod 2) <= 0 then x else ~x) mod 5)
A203571: 0 1 2 3 4 0 4 3 2 1 0 1 2 3 4 0
(x - ((0 - (if (~4 + (x div 2)) <= 0 then 1 else x)) div 5))
A164707-A161604-A129523-A125121-A108549-A045779: 1 2 3 4 5 6 7 8 9 10 12 14 15 16 17 18
loop(\(x,i).(11x + ~5),x,5)
A199762: 5 50 545 5990 65885 724730 7972025 87692270 964614965 10610764610 116718410705 1283902517750 14122927695245 155352204647690 1708874251124585 18797616762370430
loop(\(x,i).7x,3x,5)
A324265: 5 1715 588245 201768035 69206436005 23737807549715 8142067989552245 2792729320416420035 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,5)
A212344: 5 5 10 25 70 210 660 2145 7150 24310 83980 293930 1040060 3714500 13372200 48474225
loop(\(x,i).((2x * (x mod 2)) - (x div ~2)),x,5)
A185454: 5 13 33 83 208 104 52 26 13 33 83 208 104 52 26 13
((x + (2 * (2 + (if (x + ~4) <= 0 then 1 else x)))) div 5)
A063882: 1 1 1 1 2 3 4 5 5 6 6 7 8 8 9 9
(loop(\(x,i).i,((2x + ~2) mod (2 + (x div 2))),x) div 5)
A035468: 0 0 0 0 0 1 1 0 0 0 0 1 1 2 1 0
((x + 2) - (if (x div 4) <= 0 then 1 else ((~x + 2) div 5)))
A231003: 1 2 3 4 7 8 9 10 12 13 14 15 16 18 19 20
(if x <= 0 then 1 else (5x - ((~x + 2) div 5)))
A313873: 1 5 10 16 21 26 31 36 42 47 52 57 62 68 73 78
(5 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))
A298252: 6 8 10 14 16 20 22 26 32 34 40 44 46 50 56 62
(5 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A113935: 5 6 8 10 14 16 20 22 26 32 34 40 44 46 50 56
loop(\(x,i).x2,1,((x + 2) - ((~x + (x mod 2)) div 5)))
A030140: 4 9 25 36 49 64 100 121 144 169 196 225 289 324 361 400
((if (x + ~10) <= 0 then 0 else 2) + (x div 5))
A035645: 0 0 0 0 0 1 1 1 1 1 2 4 4 4 4 5
((loop(\(x,i).(2x + 2),x,2) div (x + 2)) + (x div 5))
A244742: 1 2 3 6 10 19 32 57
((if (~2 + (x div 3)) <= 0 then 1 else 2) div (1 + (~x mod 4)))
A025875: 1 0 0 0 1 0 0 0 1 0 0 1 2 0 0 1
(1 + ((if ((x div 3) mod 3) <= 0 then x else ~x) mod 4))
A343180: 1 2 3 2 1 4 3 2 1 2 3 4 1 4 3 2
(~1 + (if x <= 0 then 2 else (4 * (x + ((x div 2) div 5)))))
A334228: 1 3 7 11 15 19 23 27 31 35 43 47 51 55 59 63
(1 + ((x - (2 mod (if (x mod (2 + (x mod 2))) <= 0 then 1 else x))) mod 4))
A003324: 1 2 3 4 1 4 3 2 1 2 3 2 1 4 3 4
(1 + ((~1 + (x div 3)) mod ((if (x mod 2) <= 0 then 1 else x) mod 4)))
A331024-A326514-A316979-A115561-A077565: 1 1 1 1 1 1 1 2 1 1 1 3 1 1 1 2
loop(\(x,i).x2,1,(12x2 + 8x + 1))
A014793: 1 441 4225 17689 50625 116281 231361 416025 693889 1092025 1640961 2374681 3330625 4549689 6076225 7958041
(1 + (if x <= 0 then 1 else 4x) - ((x + (x div 2)) div 4))
A284624: 2 5 9 12 16 20 23 27 30 34 38 41 45 49 52 56
(if ((x + ~1) mod 4) <= 0 then 1 else (1 + ((x + (x div 2)) div 4)))
A321341: 1 1 1 2 2 1 3 3 4 1 4 5 5 1 6 6
(if (2 - ((x mod 7) div 2)) <= 0 then (x div 4) else 1)
A209007-A005135: 1 1 1 1 1 1 1 1 1 1 1 2 3 3 1 1
((if (x mod 5) <= 0 then (x + ~1) else 1) mod (1 + (x div 4)))
A117929: 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 2
(if x <= 0 then 1 else (((x div 2) mod 5) mod (1 + (x div 4))))
A029413: 1 0 0 0 0 0 1 1 1 1 0 0 1 1 2 2
((if (x mod 2) <= 0 then (x div 2) else 6) mod (1 + (x div 4)))
A070101: 0 0 0 0 0 0 1 0 1 0 2 0 2 2 3 2
(if (x mod 3) <= 0 then 1 else ((2x + ~4) mod (1 + (x div 4))))
A239928: 1 0 0 1 0 0 1 0 0 1 1 0 1 2 0 1
((4x2 + 1) * (if x <= 0 then 1 else 8x))
A117216: 1 40 272 888 2080 4040 6960 11032 16448 23400 32080 42680 55392 70408 87920 108120
(3 + ((x + (if (x mod (3 + (x div 2))) <= 0 then 2 else 1)) div 2))
A073260: 4 4 4 5 5 6 7 7 7 8 8 9 9
(~1 + (2 * loop(\(x,i).(10x + 17),x,2)))
A173807: 3 73 773 7773 77773 777773 7777773 77777773 777777773 7777777773 77777777773 777777777773 7777777777773 77777777777773 777777777777773 7777777777777773
(1 + (loop(\(x,i).((2x + 1) + ((2 + i) * (1 + i))),x,2) div 2))
A054136: 2 6 18 46 107 235 498 1032 2109 4273 8612 17302 34695 69495 139110 278356
(x5 mod (1 + loop(\(x,i).(x2 + x),2,2)))
A070626: 0 1 32 28 35 29 36 37 2 10 25 16 34 31 23 38
(~1 + (2 * loop(\(x,i).(10x + 22),x,2)))
A173811: 3 83 883 8883 88883 888883 8888883 88888883 888888883 8888888883 88888888883 888888888883 8888888888883 88888888888883 888888888888883 8888888888888883
(if x <= 0 then 1 else ((x + ~1) - (2 * ((~x + ((x div 4) mod 2)) div 2))))
A304028: 1 2 3 6 7 8 11 12 15 18 19 22 23 24 27 28
(1 + ((if x <= 0 then 1 else ((x + ((x mod (2 + (x div 2))) div 2)) div 2)) mod 2))
A087888: 2 1 2 2 1 1 2 1 1 2 2 1 2 2 1 2
(1 + (2 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A072055: 5 7 11 15 23 27 35 39 47 59 63 75 83 87 95 107
loop(\(x,i).2x,(((x + 1) div 2) - (2 * ((x * (x div 2)) mod 2))),1)
A137399: 1 2 2 1 4 8 8 4 16 32 32 16 64 128 128 64
(1 + (((x + 2) * (x + (if (x mod 2) <= 0 then (x2 + 2x) else 0))) div 2))
A298822: 1 2 21 8 85 18 217 32 441 50 781 72 1261 98 1905 128
(20 div (~1 + (2 * (if x <= 0 then 1 else 2x))))
A161997: 20 6 2 1 1
(loop(\(x,i).((x * (x + i)) div 2),2,(x + 1)) div (4x + 1))
A062433: 1 1 2 4 7 11 16 23 32 42 54 69 86 105 128 153
loop(\(x,i).x6,1,(4x + 1))
A016818: 1 15625 531441 4826809 24137569 85766121 244140625 594823321 1291467969 2565726409 4750104241 8303765625 13841287201 22164361129 34296447249 51520374361
((5x + 1) + loop(\(x,i).5x,x,1))
A176916: 2 11 36 141 646 3151 15656 78161 390666 1953171 9765676 48828181 244140686 1220703191 6103515696 30517578201
(loop(\(x,i).2x,(x + ~5),x) div (4x + ~1))
A101333: 0 0 0 0 0 0 0 1 2 4 8 16 32 65 130 260
(1 + (((if (x mod 4) <= 0 then 0 else (x div 4)) + (x div 2)) div 2))
A005707: 1 1 1 1 2 2 3 3 3 4 4 4 4 5 6 6
((1 + (x div 3)) div (1 + (if ((x div 2) mod 2) <= 0 then (x div 2) else 2)))
A239509: 1 1 0 0 0 0 1 1 0 0 1 1 0 0 1 2
(1 + loop(\(x,i).(x + ((2x + 1) * i)),x,0) - ((x div 2) mod 2))
A220092: 1 2 7 52 473 5198 67567 1013512 17229713 327364538 6874655287 158117071612 3952926790313 106729023338438 3095141676814687 95949391981255312
(1 + ((loop(\(x,i).(x * ((1 + i) div 2)),(x div 2),1) - (x mod 2)) div 2))
A319622: 1 1 1 1 1 1 2 1 3 2 7
(~1 + (2 * (((x + 1) * (2 + (if (x + ~1) <= 0 then x else 2))) + (x mod 2))))
A273312: 3 13 23 33 39 49 55 65 71 81 87 97 103 113 119 129
(1 + (loop(\(x,i).(2 + (x * (2 + (x mod 2)))),(x div 2),(x mod 2)) div 2))
A098293: 1 1 2 3 4 9 8 27 16 81 32 243 64 729 128 2187
(if ((~x + 2) mod 3) <= 0 then ((1 + (x div 2)) div (2 + (x mod 2))) else 1)
A343388: 1 1 1 1 1 1 1 1 2 1 1 2 1 1 4 1
(loop(\(x,i).8x,x,3) div (3 + (x mod 2)))
A083225: 1 6 64 384 4096 24576 262144 1572864 16777216 100663296 1073741824 6442450944 68719476736 412316860416 4398046511104 26388279066624
loop(\(x,i).(x2 + 2x),1,((x + 1) div (1 + (x div (2 + (x mod 2))))))
A125025: 3 8 3 8 3 15 3 8 3 8 3
(~1 + (loop(\(x,i).10x,x,1) + (2 * (x mod 2))))
A098611: 0 11 99 1001 9999 100001 999999 10000001 99999999 1000000001 9999999999 100000000001 999999999999 10000000000001 99999999999999 1000000000000001
(1 + loop(\(x,i).10x,x,1) - (2 * (x mod 2)))
A098610: 2 9 101 999 10001 99999 1000001 9999999 100000001 999999999 10000000001 99999999999 1000000000001 9999999999999 100000000000001 999999999999999
(~1 + (loop(\(x,i).2x,(x div 2),(2 - (x mod 2))) + (2 * (x mod 2))))
A140407: 1 2 3 3 7 5 15 9 31 17 63 33 127 65 255 129
((~1 + loop(\(x,i).4x,(x div 2),2)) div (1 + (2 * (x mod 2))))
A282799: 1 0 7 2 31 10 127 42 511 170 2047 682 8191 2730 32767 10922
(((if (x + ~2) <= 0 then 2 else ((x + 1) div 2)) div 2) div (1 + (2 * (x mod 2))))
A029240: 1 0 1 0 1 0 1 0 2 0 2 1 3 1 3 1
loop(\(x,i).5x,(2 * (x div 2)),(1 + (2 * (x mod 2))))
A083298: 1 3 25 75 625 1875 15625 46875 390625 1171875 9765625 29296875
A083222: 1 3 25 75 625 1875 15625 46875 390625 1171875 9765625 29296875 244140625 732421875 6103515625 18310546875
loop(\(x,i).10x,(x div 2),(1 + (2 * (x mod 2))))
A188545: 1 3 10
A004663: 1 3 10 30 100 300 1000 3000 10000 30000 100000 300000 1000000 3000000 10000000 30000000
loop(\(x,i).((x + (i mod 2)) * (1 + (2 * i))),x,(1 + (2 * (x mod 2))))
A007308: 1 12 30 427
(1 + (((x + loop(\(x,i).(3x + ~6),(x + ~1),x)) div 2) div 2))
A121365: 1 1 1 2 9 43 185 732 2737 9845 34449 118102 398585 1328607 4384393 14348912
(1 + (4 * loop(\(x,i).(x + ((1 + (4 * i)) * i)),x,x)))
A114254: 1 25 101 261 537 961 1565 2381 3441 4777 6421 8405 10761 13521 16717 20381
((x - (if ((~1 + (x div 3)) mod 4) <= 0 then 1 else 0)) mod 3)
A204423: 0 1 2 2 0 1 0 1 2 0 1 2 0 1 2 2
(3 * (if ((1 + ((x * (x div 2)) div 2)) mod 4) <= 0 then 2 else 0))
A280508: 0 0 0 0 0 0 0 0 0 0 0 6 0 6 0 0
(3 * loop(\(x,i).(10x + 21),x,0))
A086578: 0 63 693 6993 69993 699993 6999993 69999993 699999993 6999999993 69999999993 699999999993 6999999999993 69999999999993 699999999999993 6999999999999993
((2 - loop(\(x,i).(x - (2 * (~2x + (i mod 2)))),x,0)) div 3)
A178577: 0 1 4 18 87 434 2170 10851 54254 271268 1356337 6781684 33908420 169542101 847710504 4238552518
(3 - (loop(\(x,i).((x + ~2) + (x div 4)),x,0) div 3))
A299114: 3 4 5 6 8 10
A120162: 3 4 5 6 8 10 12 15 19 24 30 37 46 58 72 90
((1 + loop(\(x,i).(~x + (2 * (4x + i))),x,0)) div 3)
A156002: 0 1 6 44 311 2178 15250 106755 747288 5231022 36617161 256320132 1794240932 12559686533 87917805738 615424640176
(3 * (if x <= 0 then 0 else (1 + (((x + ~1) div 3) mod 3))))
A281258: 0 3 3 3 6 6 6 9 9 9 3 3 3 6 6 6
(2 - (((x + 2) mod (1 + (3 * (if x <= 0 then 0 else 2)))) mod 3))
A284387: 2 2 1 0 2 2 1 0 2 1 0 2 2 1 0 2
((1 + (loop(\(x,i).(2x * i),x,4) div 3)) div 3)
A220103: 0 1 3 21 171
(x - ((0 - (if (~x + 2) <= 0 then (x2 div 3) else 1)) div 3))
A096061: 1 2 3 4 6 8 10 13 15 18 21 25 28 32 36 40
((1 + loop(\(x,i).((x + ~1) * (2 + (i div 3))),x,1)) mod 3)
A287368: 2 1 2 1 1 1 0 2 1 2 1 2 1 1 1 0
((1 + loop(\(x,i).3x2,(x + ~1),(x + 1))) div 3)
A323517: 0 1 9 2304
((if ((2 + (x div 2)) mod 8) <= 0 then (x + ~1) else 1) mod 3)
A194341: 1 1 1 1 1 1 1 1 1 1 1 1 2 0 1 1
(3 * (1 + (2 * loop(\(x,i).(2 + (x div 2)),(~1 + (x div 2)),1))))
A251558: 9 9 9 9 15 15 21 21 21 21 21 21 21 21 21 21
((1 + ((x mod (1 + (2 * (if (x mod 2) <= 0 then x else 2)))) div 2)) div 3)
A318282: 0 0 0 0 1 0 1 0 1 1 2 0 2 0 2 0
((1 + (loop(\(x,i).(x * i),x,(4x + 1)) div 2)) div 3)
A186371: 0 1 3 13 68 420 3000 24360 221760 2237760 24796800 299376000 3911846400 55005350400 828193766400 13294689408000
(3 * loop(\(x,i).2x,(x div 3),7))
A158772: 21 21 21 42 42 42 84 84 84 168 168 168 336 336 336 672
(3 * (1 + (2 * loop(\(x,i).(2x + 8),x,3))))
A304514: 21 87 219 483 1011 2067 4179 8403 16851 33747 67539 135123 270291 540627 1081299 2162643
(3 * loop(\(x,i).2x,(x div 2),(1 + (2 * (1 + (x mod 2))))))
A070876: 9 15 18 30 36 60 72 120 144 240 288 480 576 960 1152 1920
((1 + (2 * (loop(\(x,i).2x,(x div 2),1) div (x + 1)))) div 3)
A245146: 1 0 0 0 0 0 1 1 1 1 1 1 3 3 5 5
((1 + loop(\(x,i).3x3,(x + ~1),2)) div 3)
A246959: 1 1 8 13824 71328803586048 4611686018427387903
((x - (if ((~1 + (x div 3)) mod 4) <= 0 then 2 else 1)) mod 3)
A204427: 2 0 1 1 2 0 2 0 1 2 0 1 2 0 1 1
((if x <= 0 then 1 else (~1 + (x mod (2 + ((x + 1) mod 4))))) mod 3)
A091397: 1 0 1 0 0 0 0 0 1 0 2 0 2 0 0 0
(3 * (1 + (if (2 - (x div 4)) <= 0 then x else 8)))
A291516: 27 27 27 27 27 27 27 27 27 30 33 36 39 42 45 48
loop(\(x,i).3x,(10x + 5),3)
A013852: 729 43046721 2541865828329 150094635296999121 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((1 + (4 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 3)
A260401-A003159: 1 3 4 5 7 9 11 12 13 15 16 17 19 20 21 23
((1 + (4 * (x + (if (~2 + (x div 2)) <= 0 then 1 else 2)))) div 3)
A325130: 1 3 4 5 7 8 11 12 13 15 16 17 19 20 21 23
loop(\(x,i).x2,3,(~11x + ~3))
A017432: 6561 1475789056 152587890625 2821109907456 23811286661761 128063081718016 513798374428641 1677721600000000 4702525276151521 11716593810022656 26584441929064321 55895067029733376
((1 + loop(\(x,i).2x,((x + 1) div 2),(2 + (x mod 2)))) div 3)
A112387: 1 2 1 4 3 8 5 16 11 32 21 64 43 128 85 256
((((x + ~1) * (if (x + ~2) <= 0 then 0 else x2)) div 3) mod 3)
A298177-A298146-A297814: 0 0 0 0 1 0 0 2 2 0 0 1 0 1 0 0
(3 * (if x <= 0 then 1 else (12x2 + 6x)))
A068380: 3 54 180 378 648 990 1404 1890 2448 3078 3780 4554 5400 6318 7308 8370
(loop(\(x,i).(x - (x div ~5)),x,3) div 3)
A134345-A112193: 1 1 1 2 2 3 4 5 6 7 9 11 13 16 19 23
((~1 + loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2)) mod 3)
A228817: 1 2 1 0 2
A137992: 1 2 1 0 2 2 2 2 1 0 2 0 1 2 2 2
(3 * (1 + loop(\(x,i).(10x + ~8),x,2)))
A173764: 9 39 339 3339 33339 333339 3333339 33333339 333333339 3333333339 33333333339 333333333339 3333333333339 33333333333339 333333333333339 3333333333333339
((1 + ((x + loop(\(x,i).(x2 + ~1),2,(x + 2))) div 2)) div 3)
A024202: 1 11 38 96 205 385 662 1068 1635 2401 3410 4706 6339 8365 10840 13826
((3x + 9) * loop(\(x,i).2x,(x + 2),(x + 2)))
A308136: 72 288 960 2880 8064 21504 55296 138240 337920 811008 1916928 4472832 10321920 23592960 53477376 120324096
(x3 - loop(\(x,i).x2,1,(3x + 9)))
A153259: ~81 ~143 ~217 ~297 ~377 ~451 ~513 ~557 ~577 ~567 ~521 ~433 ~297 ~107 143 459
((1 + ((x + 2) * (x + (if x <= 0 then 1 else (x div 4))))) mod 3)
A152723: 0 1 0 1 1 1 0 1 2 2 1 2 1 1 0 1
(3 + ((2x + 1) * loop(\(x,i).(x2 + x),2,4)))
A096024: 423 1263 2103 2943 3783 4623 5463 6303 7143 7983 8823 9663 10503 11343 12183 13023
((6x + 3) * (loop(\(x,i).(x2 + x),2,x) div 2))
A048396: 0 27 315 1638 5670 15345 35217 71820 134028 233415 384615 605682 918450 1348893 1927485 2689560
loop(\(x,i).x5,1,(6x + 3))
A016949: 243 59049 759375 4084101 14348907 39135393 90224199 184528125 345025251 601692057 992436543 1564031349 2373046875 3486784401 4984209207 6956883693
(3 + ((if (x mod 2) <= 0 then 3 else ~2) mod (1 + (x div 2))))
A003034: 3 3 4 3 3 4 6 5 6 6 6 7
((1 + ((~x2 + loop(\(x,i).(1 + (x * i)),x,0)) div 2)) div 3)
A268218: 0 0 0 0 4 30 200 1435 11536 103908 1039200 11431365 137176600 1783296086 24966145568 374492183975
(if x <= 0 then 1 else ((x + 2) - (((~x + ~1) + (x div 3)) div 3)))
A061578: 1 4 5 6 8 9 10 11 13 14 15 16 17 19 20 21
(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1) mod 3)
A039968: 1 0 1 2 0 0 0 0 1 2 0 2 1 0 0 0
(2 - (loop(\(x,i).((x + ~1) + (x div 5)),x,1) div 3))
A120171: 2 2 3 3 4 5 6 7 8 10 12 14 17 20 24 29
(3 * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x)))
A112773: 3 6 9 15 21 33 39 51 57 69 87 93 111 123 129 141
(loop(\(x,i).((2 * (x - (2x * i))) div (1 + i)),x,1) mod 3)
A039965: 1 2 2 1 2 0 0 0 2 1 2 2 1 2 0 0
(x - (((~x + ~1) + (if (~2 + (x div 4)) <= 0 then 0 else 2)) div 3))
A276341: 1 2 3 5 6 7 9 10 11 13 14 15 16 17 19 20
(3 * ((x + ~1) + (2 * (8 + (if x <= 0 then 0 else 1)))))
A295802: 45 54 57 60
(1 + (loop(\(x,i).8x,x,1) div 3) - (x mod 2))
A007613: 1 2 22 170 1366 10922 87382 699050 5592406 44739242 357913942 2863311530 22906492246 183251937962 1466015503702 11728124029610
((((1 + (x div 2)) mod 3) + loop(\(x,i).2x,x,1)) div 3)
A131708: 0 1 2 3 5 10 21 43 86 171 341 682 1365 2731 5462 10923
((((~1 + (x div 2)) mod 3) + loop(\(x,i).2x,x,1)) div 3)
A024493: 1 1 1 2 5 11 22 43 85 170 341 683 1366 2731 5461 10922
((((x2 div 2) mod 3) + loop(\(x,i).2x,x,1)) div 3)
A242563: 0 0 2 3 6 10 21 42 86 171 342 682 1365 2730 5462 10923
loop(\(x,i).x2,3,(~12x + ~10))
A017648: 100000000 54875873536 1785793904896 20047612231936 128063081718016 576480100000000 2044140858654976 6095689385410816 15938480745308416 37588592026706176 81573072100000000 165312903998914816
(((2x + 2) * ((x + 2) + (if (~x + 2) <= 0 then x else 2))) div 3)
A184637: 2 6 12 21 33 48 65 85 108 133 161 192 225 261 300 341
(3 * (if (x + ~2) <= 0 then x else (x3 + 3x2 + 4x + 2)))
A163423: 0 3 6 204
((loop(\(x,i).((x2 + x) div 2),2,2x) div (x + 1)) div 3)
A138357: 0 1 6 19 44 85 146 231 345 490 671 892 1157 1470 1836 2257
((3x + 3) * loop(\(x,i).7x,x,2))
A212701: 6 84 882 8232 72030 605052 4941258 39530064 311299254 2421216420 18643366434 142367525496 1079620401678 8138676874188 61040076556410 455765904954528
(loop(\(x,i).5x,(x + 1),1) mod (3x + 3))
A083529: 2 1 8 1 5 1 5 1 26 25 5 1 5 25 35 1
(4x + ((if (x + ~2) <= 0 then 1 else x) + ((x + 1) div 3)))
A313890: 1 5 10 16 21 27 32 37 43 48 53 59 64 69 75 80
(1 - ((loop(\(x,i).(x2 div 3),2,x) div (x + 1)) mod 3))
A176259: 1 1 1 1 0 1 1 0 0 1 1 ~1 ~1 ~1 1 1
((if ((~1 + (x div 3)) mod 4) <= 0 then x else (x + 1)) mod 3)
A204425: 1 2 0 0 1 2 1 2 0 1 2 0 1 2 0 0
(~3 + (2 * loop(\(x,i).(2x + 4),(x + 8),0)))
A098808: 2037 4085 8181 16373 32757 65525 131061 262133 524277 1048565 2097141 4194293 8388597 16777205 33554421 67108853
(3 * (~2 + loop(\(x,i).10x,(x + 1),1)))
A086941: 24 294 2994 29994 299994 2999994 29999994 299999994 2999999994 29999999994 299999999994 2999999999994 29999999999994 299999999999994 2999999999999994 29999999999999994
(6 * loop(\(x,i).(2x + 16),(x + 1),1))
A304377: 108 312 720 1536 3168 6432 12960 26016 52128 104352 208800 417696 835488 1671072 3342240 6684576
((if x <= 0 then 1 else x) - (6 * (x div 7)))
A033927: 1 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3
((2 * (1 + (2 * (if (x + ~4) <= 0 then x else (x + 1))))) div 3)
A121539: 0 2 3 4 6 8 10 11 12 14 15 16 18 19 20 22
(x div (3 * (if ((2x + ~4) mod (2 + (x div 2))) <= 0 then 1 else 2)))
A261627: 0 0 0 0 1 0 1 2 2 1 1 1 2 2 2 2
(x div (3 * (if (4x mod (2 + (x div 2))) <= 0 then 1 else 2)))
A290342: 0 0 0 1 1 1 1 1 1 3 1 1 4 2 2 2
((x + 2) - ((if x <= 0 then 1 else x) div (x + ~18)))
A154660: 3 4 5 6 7 8
A216442: 3 4 5 6 7 8 9 10 11 12 14 15 16 18 20 22
((loop(\(x,i).2x,x,1) - (x2 mod 6)) div 3)
A111927: 0 0 0 1 4 10 21 42 84 169 340 682 1365 2730 5460 10921
((2 + ((if (x mod 4) <= 0 then 2 else 0) + (x div 3))) div 3)
A339382: 1 0 0 1 1 1 1 1 2 1 1 1 2 2 2 2
((2 * ((x2 + 4x + 4) + (if (~x + 2) <= 0 then 2 else 1))) div 3)
A181026: 3 6 12 18 25 34 44
loop(\(x,i).x2,3,(~11x + ~6))
A017468: 1679616 6975757441 377801998336 5352009260481 39062500000000 191707312997281 722204136308736 2252292232139041 6095689385410816 14774554437890625 32784148919812096 67675234241018881
(((if x <= 0 then 2 else (4x mod (1 + (x div 2)))) div 2) mod 3)
A029406: 1 0 0 0 0 1 0 0 1 0 2 1 0 1 0 2
((loop(\(x,i).(2x * i),(x + ~2),(1 + (x mod 2))) div 2) div 3)
A215969: 0 0 0 0 1 16 64
(6 * (1 + loop(\(x,i).(x + (x div 2)),(2 * (x div 2)),x)))
A126857: 6 12 30 42 120
loop(\(x,i).x3,1,(7x + 5))
A017043: 125 1728 6859 17576 35937 64000 103823 157464 226981 314432 421875 551368 704969 884736 1092727 1331000
loop(\(x,i).x3,2,(7x + 5))
A017049: 1953125 5159780352 322687697779 5429503678976 46411484401953 262144000000000 1119130473102767 3904305912313344 11694146092834141 31087100296429568 75084686279296875 167619550409708032
(12 * (~1 + (2 * loop(\(x,i).(2x + 4),x,1))))
A305261: 12 132 372 852 1812 3732 7572 15252 30612 61332 122772 245652 491412 982932 1965972 3932052
(if x <= 0 then 1 else ((x mod (4 + ((x + ~1) mod 3))) div 3))
A322134: 1 0 0 1 0 0 0 1 1 1 0 0 0 0 1 1
((2 * (x mod (2 + (if (x mod 2) <= 0 then 1 else (x div 3))))) div 3)
A079548: 0 0 1 0 0 1 0 2 1 2 0 0 0 0 1 0
((4 * ((x + 1) + (if (x + ~4) <= 0 then 1 else 2))) div 3)
A026435: 2 4 5 6 8 10 12 13 14 16 17 18 20 21 22 24
(((loop(\(x,i).((x2 + ~x) div 2),2,(x + ~1)) div 2) div 2) div 3)
A011850: 0 0 0 0 0 1 3 8 17 31 52 82 123 178 250 341
((1 - ((x mod ((if x <= 0 then 1 else x) div ~4)) div 2)) mod 3)
A000377: 1 1 1 1 1 2 1 2 1 1 2 2 1 0 2 2
loop(\(x,i).~x,x,(1 - ((2 * (((x + 1) div 2) div 2)) div 3)))
A014163: 1 ~1 1 ~1 1 ~1 1 0 0 0 0 1 ~1 1 ~1 1
(((x - (if (~2 + (x div 2)) <= 0 then 1 else 2)) mod 8) mod 3)
A116948: 1 0 1 2 0 1 1 2 0 1 0 1 2 0 1 2
(6 * ((if x <= 0 then 1 else 2) - ((~x2 + x) div 4)))
A037230: 6 12 18 24 30 42 60
((4 * (if x <= 0 then 1 else (2x3 + 4x))) div 3)
A008412: 1 8 32 88 192 360 608 952 1408 1992 2720 3608 4672 5928 7392 9080
(loop(\(x,i).(2x + 1),x,(4 * (2 - (x mod 2)))) div 3)
A129670: 2 3 11 13 47 53 191
((4 * (if x <= 0 then 1 else (~2x3 + 2x))) div 3)
A136264: 1 0 ~16 ~64 ~160 ~320 ~560 ~896 ~1344 ~1920 ~2640 ~3520 ~4576 ~5824 ~7280 ~8960
((x + 12) - (if (~2 + (x div 3)) <= 0 then 1 else 0))
A236403-A038687: 11 12 13 14 15 16 17 18 19 21 22 23 24 25 26 27
(12 + loop(\(x,i).(2x + 2),(x div 2),(x mod 2)))
A209725: 12 13 14 16 18 22 26 34 42 58 74 106 138 202 266 394
loop(\(x,i).(7x + ~6),x,12)
A199492: 12 78 540 3774 26412 184878 1294140 9058974 63412812 443889678 3107227740 21750594174 152254159212 1065779114478 7460453801340 52223176609374
((4 * (x + (if (~2 + (x div 4)) <= 0 then 1 else 2))) div 3)
A079709: 1 2 4 5 6 8 9 10 12 13 14 16 18 20 21 22
((4 * (x + (if (~4 + (x div 2)) <= 0 then 1 else 2))) div 3)
A143028: 1 2 4 5 6 8 9 10 12 13 16 17 18 20 21 22
((if x <= 0 then 1 else (x + 2)) - ((1 - (x2 div 4)) div 3))
A225647: 1 3 4 6 7
A244239: 1 3 4 6 7 9 11 13 15 18 20 23 26 29 32 36
((2 * (2 + loop(\(x,i).(2x + ~1),(x mod 3),x))) div 3)
A225055: 1 2 4 3 6 12 5 10 20 7 14 28 9 18 36 11
(if x <= 0 then 1 else ((((x2 - (x div 2)) mod (x + 2)) div 2) div 3))
A244464: 1 0 0 0 0 0 0 0 0 0 1 2 2 2 2 2
loop(\(x,i).7x,x,(6x + 12))
A159736: 12 126 1176 10290 86436 705894 5647152 44471322 345888060 2663338062 20338217928 154231485954 1162668124884 8720010936630 65109414993504 484251274014186
loop(\(x,i).x5,1,12x)
A017525: 0 248832 7962624 60466176 254803968 777600000 1934917632 4182119424 8153726976 14693280768 24883200000 40074642432 61917364224 92389579776 133827821568 188956800000
loop(\(x,i).x3,1,(11x + 1))
A017403: 1 1728 12167 39304 91125 175616 300763 474552 704969 1000000 1367631 1815848 2352637 2985984 3723875 4574296
loop(\(x,i).x3,2,(11x + 1))
A017409: 1 5159780352 1801152661463 60716992766464 756680642578125 5416169448144896 27206534396294947 106868920913284608 350356403707485209 1000000000000000000 2558036924386500591
loop(\(x,i).x2,3,(11x + 2))
A017420: 256 815730721 110075314176 2251875390625 20047612231936 111429157112001 457163239653376 1517108809906561 4304672100000000 10828567056280801 24759631762948096 52389094428262881
loop(\(x,i).x3,1,(11x + 2))
A017415: 8 2197 13824 42875 97336 185193 314432 493039 729000 1030301 1404928 1860867 2406104 3048625 3796416 4657463
loop(\(x,i).x3,2,(11x + 2))
A017421: 512 10604499373 2641807540224 78815638671875 922190162669056 6351461955384057 31087100296429568 119851595982618319 387420489000000000 1093685272684360901 2773078757450186752
(3 * (loop(\(x,i).2x,x,(8 - (x mod 2))) div 2))
A137480: 12 21 48 84 192 336 768 1344 3072 5376 12288 21504 49152 86016 196608 344064
(loop(\(x,i).3x,(x div 2),(4 - (x mod 2))) div 3)
A074324: 1 1 4 3 12 9 36 27 108 81 324 243 972 729 2916 2187
((4x + ~1) + ((2 * loop(\(x,i).x2,x,2)) div 3))
A309178: 0 5 17 181
(((if ((x div 3) - (x mod 4)) <= 0 then 0 else x) div 2) div 3)
A237168: 0 0 0 0 0 0 0 0 1 1 1 0 2 2 2 2
(if x <= 0 then 2 else (6 * (x + (x div 9))))
A069087: 2 6 12 18 24 30 36 42 48 60 66 72 78 84 90 96
(3 + (2 * loop(\(x,i).(x + i),(((x + ~1) div 2) div 3),x)))
A333854: 3 5 7 9 11 13 15 19 21 23 25 27 29 35 37 39
(loop(\(x,i).((x + 1) + (x div (1 + (x mod 3)))),x,2) div 3)
A048329: 0 1 2 3 5 10 15 21 42 63 85 170 255 341 682 1023
((loop(\(x,i).(x3 + ~x),1,(x2 + ~x)) div 2) div 3)
A055658: 0 0 1 35 286 1330 4495 12341 29260 62196 121485 221815 383306 632710 1004731 1543465
(loop(\(x,i).(x3 + ~x2),1,((x2 + ~x) div 2)) div 3)
A292061: 0 0 0 6 60 300 1050 2940 7056 15120 29700 54450 94380 156156 248430 382200
(loop(\(x,i).(x3 + 2x),1,((x2 + ~x) div 2)) div 3)
A282816: 0 0 1 11 76 340 1135 3101 7336 15576 30405 55495 95876 158236 251251 385945
((x + ~1) + ((if ((x + 1) mod 8) <= 0 then x else 2) mod 3))
A254926-A155919: 1 2 3 4 5 6 7 7 9 10 11 12 13 14 15 14
(if x <= 0 then 1 else (x - ((1 - ((x2 + 4x) div 2)) div 3)))
A231408: 1 2 4 6 9
A061536: 1 2 4 6 9 12 16 20 24 28 33 38 44 50 56 62
((2 * (x + loop(\(x,i).(4x + ~2),(x div 2),2))) div 3)
A166753: 1 2 5 6 17 18 61 62 233 234 917 918 3649 3650 14573 14574
(3 * (2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)))
A127329: 15 21 33 39 51 57 69 87 93 111 123 129 141 159 177 183
(3 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A001748: 6 9 15 21 33 39 51 57 69 87 93 111 123 129 141 159
((loop(\(x,i).(x3 + ~x),1,(x2 + 2x)) div 2) div 3)
A178208: 0 4 84 560 2300 7140 18424 41664 85320 161700 287980 487344 790244 1235780 1873200 2763520
((((1 - (x div 2)) mod 3) + loop(\(x,i).2x,x,2)) div 3)
A130781: 1 1 2 5 11 22 43 85 170 341 683 1366 2731 5461 10922 21845
(((x + 2) + (if (x mod 8) <= 0 then 2 else (x mod 2))) div 3)
A171482: 1 1 1 2 2 2 2 3 4 4 4 4 4 5 5 6
(if x <= 0 then 1 else ((x + 3) - (((~x + 1) * (x div 2)) div (x + 2))))
A231407: 1 4 6
A225551: 1 4 6 7 8 10 11 12 14 15 17 18 20 21 23 24
(1 + ((if (4 mod (x + 1)) <= 0 then 0 else 1) + ((x + 2) div 3)))
A081315: 1 2 3 2 4 4 4 5 5 5 6 6 6 7 7 7
((if x <= 0 then 1 else 2x) - (((x2 + ~2x) div (x + 2)) div 3))
A187415: 1 3 4 6 8 10 11 13 15 17 18 20 22 23 25 27
((2x + loop(\(x,i).2x,(((x + 1) div 2) div 2),1)) div 3)
A262265: 0 1 1 2 3 4 4 6 6 7 8 10 10 11 12 15
loop(\(x,i).x6,1,6x)
A016914: 0 46656 2985984 34012224 191102976 729000000 2176782336 5489031744 12230590464 24794911296 46656000000 82653950016 139314069504 225199600704 351298031616 531441000000
(6x + (if x <= 0 then 1 else ((~x + ((x div 2) mod 2)) div 2)))
A301710: 1 5 11 17 22 27 33 39 44 49 55 61 66 71 77 83
((((loop(\(x,i).2x,x,x) mod (x + 1)) div 2) * (x div 2)) mod 3)
A257994: 0 0 1 0 1 1 0 0 2 1 1 1 0 0 2 0
(((x * (x + (if (x mod 4) <= 0 then 2 else 0))) - (x div 2)) div 3)
A114532: 0 0 1 2 7 7 11 15
(((if (~2 + (x mod 8)) <= 0 then 1 else 0) - (x mod 2)) mod 3)
A156596: 1 0 1 2 0 2 0 2 1 0 1 2 0 2 0 2
(3 - (if ((x + 2) mod 5) <= 0 then (x mod 2) else 3))
A092197: 0 0 0 2 0 0 0 0 3 0 0 0 0 2 0 0
((loop(\(x,i).(2x - (i mod 2)),(x + ~2),x) + (x mod 2)) div 3)
A275434: 0 0 0 2 4 12 28 68 156 356 796 1764 3868 8420 18204 39140
(((x * (x + (loop(\(x,i).(x * i),x,1) div (x + 2)))) div 2) div 3)
A075441: 0 0 0 2 5 18 96
(loop(\(x,i).2x,x,1) - (((~x3 + x) div 2) div 3))
A116725: 1 2 5 12 26 52 99 184 340 632 1189 2268 4382 8556 16839 33328
(compr(\x.(if (x mod 2) <= 0 then ((x div 3) mod 3) else 0),x) mod 3)
A036580: 0 1 2 0 2 1 0 1 2 1 0 2 0 1 2 0
((x + 2) - ((~x + (if (~2 + (x div 3)) <= 0 then 2 else 0)) div 3))
A284941: 2 3 4 6 7 8 10 11 12 14 16 17 18 20 21 22
(3 * ((x + 1) + (3 * loop(\(x,i).x2,2,(x + 1)))))
A141326: 12 150 738 2316 5640 11682 21630 36888 59076 90030 131802 186660 257088 345786 455670 589872
((if (((x + 2) div (2 + (x mod 3))) mod 2) <= 0 then 1 else x) mod 3)
A067461: 0 1 2 1 1 2 1 1 1 0 1 2 0 1 1 1
loop(\(x,i).(6x + ((~1 + i) mod 4)),x,3)
A037760: 3 18 109 656 3939 23634 141805 850832 5104995 30629970 183779821 1102678928 6616073571 39696441426 238178648557 1429071891344
loop(\(x,i).(6x + ((~x + 1) mod 4)),x,3)
A037795: 3 20 121 726 4359 26156 156937 941622 5649735 33898412 203390473 1220342838 7322057031 43932342188 263594053129 1581564318774
(if x <= 0 then 2 else (x2 mod ((x + 3) + ((x div 2) div 3))))
A253515: 2 1 4 3 2 1 6 5 4 3 2 1 8 7 6 5
(9x + loop(\(x,i).3x,2x,1))
A221911: 1 18 99 756 6597 59094 531495 4783032 43046793 387420570 3486784491 31381059708 282429536589 2541865828446 22876792455087 205891132094784
(~9x + loop(\(x,i).3x,2x,1))
A198399: 1 0 63 702 6525 59004 531387 4782906 43046649 387420408 3486784311 31381059510 282429536373 2541865828212 22876792454835 205891132094514
loop(\(x,i).x5,1,9x)
A017165: 0 59049 1889568 14348907 60466176 184528125 459165024 992436543 1934917632 3486784401 5904900000 9509900499 14693280768 21924480357 31757969376 44840334375
(((x + 1) + (loop(\(x,i).2x,x,(x + 1)) div (x + 2))) mod 3)
A057276: 1 0 0 1 0 0 0 1 2 1 1 0 0 0 0 1
loop(\(x,i).((x + ~1) + (4 * ((x + 1) + (x div 2)))),x,3)
A037586: 3 22 157 1100 7703 53922 377457 2642200 18495403 129467822 906274757 6343923300 44407463103 310852241722 2175965692057 15231759844400
(x2 div (x - (3 * ((~x + 2) - (if (x mod 2) <= 0 then x else 1)))))
A035458: 0 1 0 1 0 1 1 1 1 2 1 2 1 3 2 3
(if x <= 0 then 1 else ((x + 3) + (6x div (x + 1))))
A008536: 1 7 9 10 11 13 14 15 16 17 18 19 20 21 22 23
(loop(\(x,i).(2 * (x + ((x * i) div (1 + i)))),(x + 1),x) mod 3)
A084888-A063725: 0 0 1 0 0 2 0 0 1 0 2 0 0 2 0 0
(~3 + loop(\(x,i).(5x + 4),6,x))
A254029: 15621 31246 46871 62496 78121 93746 109371 124996 140621 156246 171871 187496 203121 218746 234371 249996
((x * loop(\(x,i).x2,1,((x2 + 3x + 2) div 2))) div 3)
A004282: 0 3 24 100 300 735 1568 3024 5400 9075 14520 22308 33124 47775 67200 92480
(loop(\(x,i).x2,1,(x + ((x2 + 3x + 2) div 2))) div 3)
A033275: 0 5 21 56 120 225 385 616 936 1365 1925 2640 3536 4641 5985 7600
(2x - (if (~2 + (x mod (2 + (x mod 3)))) <= 0 then x else 3))
A103303: 0 1 2 3 4 5 6 7 8 9
A321767: 0 1 2 3 4 5 6 7 8 9 10 19 12 13 14 15
((x + 3) + (((x - (if (~2 + (x div 2)) <= 0 then x else 1)) div 2) div 2))
A154660: 3 4 5 6 7 8
A073071: 3 4 5 6 7 8 10 11 12 14 15 16 17 19 20 21
loop(\(x,i).(8x + ((x + 1) mod 4)),x,3)
A037762: 3 24 193 1546 12371 98968 791745 6333962 50671699 405373592 3242988737 25943909898 207551279187 1660410233496 13283281867969 106266254943754
loop(\(x,i).(8x + ((x + ~1) mod 4)),x,3)
A037797: 3 26 209 1672 13379 107034 856273 6850184 54801475 438411802 3507294417 28058355336 224466842691 1795734741530 14365877932241 114927023457928
(2 - (if x <= 0 then 1 else ~21x2))
A010011: 1 23 86 191 338 527 758 1031 1346 1703 2102 2543 3026 3551 4118 4727
((x + ~3) + (2 * (if (~2 + (x div 3)) <= 0 then 2 else (x + ~2))))
A122619: 1 2 3 4 5 6 7 8 9 20 23 26 29 32 35 38
loop(\(x,i).(4x + ((x + (x div 2)) mod 4)),x,3)
A037653: 3 12 50 203 812 3250 13003 52012 208050 832203 3328812 13315250 53261003 213044012 852176050 3408704203
loop(\(x,i).(5x + ((~1 + i) mod 4)),x,3)
A037759: 3 15 76 382 1913 9565 47826 239132 1195663 5978315 29891576 149457882 747289413 3736447065 18682235326 93411176632
(x - (3 * (~x + (((x div 4) - (if x <= 0 then 1 else x)) div 2))))
A190711: 3 7 11 18 22 26 33 37 41 48 52 59 63 67 74 78
((if (~2 + (x div 3)) <= 0 then x else (x + 4)) + (x div 3))
A138083: 0 1 2 4 5 6
A023717: 0 1 2 4 5 6 8 9 10 16 17 18 20 21 22 24
((2x + 4) - ((if x <= 0 then 2 else ((~x + 2) div 2)) + (x div 3)))
A049637: 2 6 8 10 12 15 16 19 21 23 25 28 29 32 34 36
(2x + (if ((x div 2) mod 3) <= 0 then 2 else 1) - (x div 3))
A249025-A065502: 2 4 5 6 8 10 12 14 15 16 18 20 22 24 25 26
(x + ((if (~2 + (x div 3)) <= 0 then 1 else 4) + (x div 3)))
A284509: 1 2 3 5 6 7 9 10 11 16 17 18 20 21 22 24
(((if (x + ~2) <= 0 then 1 else (x div 3)) mod 3) * (x mod 3))
A309953: 0 1 2 0 1 2 0 2 4 0 0 0 0 1 2 0
loop(\(x,i).(2x mod 5),(x div 3),(x mod 3))
A131186: 0 1 2 0 2 4 0 4 3 0 3 1 0 1 2 0
(4 + (if x <= 0 then 1 else 2) - ((x mod 3) + (x mod 4)))
A309442: 5 4 2 3 5 3
(x + (x mod 3) - (2 * (if (~2 + (x div 3)) <= 0 then 0 else 2)))
A262478: 0 2 4 3 5 7 6 8 10 5 7 9 8 10 12 11
(2x + (if (~2 + (x div 3)) <= 0 then 1 else 2) - (x mod 3))
A026310: 1 2 3 7 8 9 13 14 15 20 21 22 26 27 28 32
(2x + (if (~2 + (x div 4)) <= 0 then 1 else 2) - (x mod 3))
A070752: 1 2 3 7 8 9 13 14 15 19 20 21 26 27 28 32
(3 * loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,x))
A062561: 0 3 12 45 168 630 2376 9009 34320 131274 503880 1939938 7488432 28973100 112326480 436268025
((x + 3) + loop(\(x,i).((x * i) - (x div 8)),2,x))
A212662: 3 6 9 12 15 18 21 24 25 27 30 33 36 39 42 45
((x + 3) + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))
A014690: 4 7 10 15 18 23 26 31 38 41 48 53 56 61 68 75
((x2 * loop(\(x,i).((x2 + ~x) div 2),2,(x + 2))) div 3)
A085284: 0 1 20 135 560 1750 4536 10290 21120 40095 71500 121121 196560 307580 466480 688500
((x + 3) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A014688: 3 5 8 11 16 19 24 27 32 39 42 49 54 57 62 69
((x + 3) + loop(\(x,i).(x - (x div (8 - i))),2,x))
A231773-A007617: 3 5 7 9 11 13 14 15 17 19 21 23 25 26 27 29
(3 * compr(\x.loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,x),x))
A277335: 0 3 6 12 15 24 27 30 48 51 54 60 63 96 99 102
((if x <= 0 then 1 else 4x) - ((~x3 + x) div 3))
A140226: 1 4 10 20 36 60 94 140 200 276 370 484 620 780 966 1180
(1 + ((x + loop(\(x,i).(3 * (x - (i div ~2))),x,0)) div 2))
A193418: 1 3 8 23 69 206 616 1846 5537 16609 49824 149469 448405 1345212 4035632 12106892
(~1 + (2 * (x + loop(\(x,i).2x,(~3 + (x div 3)),1))))
A161957: 1 3 5 7 9 11 13 15 17 19 21 23 27 29 31 37
(1 + ((x + loop(\(x,i).((x + ~1) mod (1 + (2 * i))),(x + ~1),1)) div 2))
A080374: 1 2 2 4 4 4 4 4 12 12 12 12 12 12 12 12
(1 + ((if (~2 + (x mod (2 - (x mod ~4)))) <= 0 then 1 else x) div 2))
A284254-A284252: 1 1 1 1 1 1 1 1 1 5 1 1 1 7 1 1
(1 + ((x + (x div (if ((x + 1) mod 8) <= 0 then 2 else 1))) div 2))
A117656: 1 2 3 4 5 6 7 6 9 10 11 12 13 14 15 12
loop(\(x,i).12x,(5x + 2),1)
A013863: 144 35831808 8916100448256 2218611106740436992 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).10x,(5x + 2),1)
A013855: 100 10000000 1000000000000 100000000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).7x,(5x + 2),1)
A013843: 49 823543 13841287201 232630513987207 3909821048582988049 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).10x,10x,1)
A244450: 1 10000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((~x + 1) mod (1 + (if (2 - (x mod (3 + (x div 2)))) <= 0 then x else 2)))
A049241: 1 0 2 2 2 2 1 0 2 2 2 2 2 2 2 2
(loop(\(x,i).2x,x,1) div (1 + ((x * (2x div 3)) div 2)))
A303846: 1 2 2 2 3 4 4 8 12
loop(\(x,i).20x,(3x + 2),1)
A013767: 400 3200000 25600000000 204800000000000 1638400000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).15x,(3x + 2),1)
A013757: 225 759375 2562890625 8649755859375 29192926025390625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).18x,(3x + 2),1)
A013763: 324 1889568 11019960576 64268410079232 374813367582081024 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).24x,(3x + 2),1)
A013775: 576 7962624 110075314176 1521681143169024 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).14x,(3x + 2),1)
A013755: 196 537824 1475789056 4049565169664 11112006825558016 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).13x,(3x + 2),1)
A013753: 169 371293 815730721 1792160394037 3937376385699289 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).11x,(3x + 2),1)
A013749: 121 161051 214358881 285311670611 379749833583241 505447028499293771 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).17x,(3x + 2),1)
A013761: 289 1419857 6975757441 34271896307633 168377826559400929 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((x + ((x * loop(\(x,i).((x + 1) * i),x,0)) div 3)) div 2))
A005143: 1 1 3 10 45 274
(1 + ((x * loop(\(x,i).(6x + 4),2x,1)) div 2))
A118641: 1 33 2333
(1 + ((~x + loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),x,1)) div 2))
A216778: 1 0 0 0 3 20 130 924 7413 66744 667476 7342280 88107415 1145396460 16035550518 240533257860
(1 + (2 * compr(\x.(loop(\(x,i).(x * (1 + (i div 2))),x,1) mod (x + 1)),x)))
A166257: 1 7 11 15 17 19 23 27 29 31 35 39 41 43 47 49
loop(\(x,i).x2,3,(10x + 7))
A017360: 5764801 6975757441 282429536481 3512479453921 23811286661761 111429157112001 406067677556641 1235736291547681 3282116715437121 7837433594376961 17181861798319201 35114532758015841 67675234241018881
loop(\(x,i).x3,1,(10x + 7))
A017355: 343 4913 19683 50653 103823 185193 300763 456533 658503 912673 1225043 1601613 2048383 2571353 3176523 3869893
loop(\(x,i).x3,2,(10x + 7))
A017361: 40353607 118587876497 7625597484987 129961739795077 1119130473102767 6351461955384057 27206534396294947 95151694449171437 285544154243029527 760231058654565217 1838459212420154507 4108400332687853397
(~1 + loop(\(x,i).((1 + (x mod 2)) * (x div 2)),1,((x2 + x) div 2)))
A176126: ~1 ~1 1 2 4 13 19 13 17 43 53 32 38 89 103 59
loop(\(x,i).11x,((x2 + ~x) div 2),1)
A110195: 1 1 11 1331 1771561 25937424601 4177248169415651 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (((2 + ((x div ~2) mod 3)) mod (if x <= 0 then 1 else x)) div 2))
A308890: 1 1 1 1 2 2 2 3 3 2 2 2 2 3 3 2
(1 + ((x * ((~1 + (if (x mod 6) <= 0 then x else 1)) div 2)) div 2))
A331927: 1 1 1 1 1 1 7 1 1 1 1 1 31 1 1 1
(1 + (2 * (x + (2 * (1 + (if (x + ~1) <= 0 then x else 8))))))
A154297: 5 11 41 43
(~1 + loop(\(x,i).(2x - ((((x + 1) div 2) div 3) mod 2)),x,2))
A266791: 1 3 7 14 29 58 117 234 468 937 1875 3751 7502 15005 30010 60021
(1 + (x mod (2 + (if ((x + 1) mod (2 + (x div 4))) <= 0 then 2 else x))))
A053626: 1 2 3 4 5 2 7 8 9 10 11 4 13 14 3 16
(1 + (x mod (2 + (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then 2 else x))))
A323130-A028233: 1 2 3 4 5 2 7 8 9 2 11 4 13 2 3 16
(1 + (if x <= 0 then 1 else (2 * (x + ((2 + (x div 2)) * (x div 4))))))
A215658-A192579: 2 3 5 7 17
A072885: 2 3 5 7 17 19 23
loop(\(x,i).(x * (1 + (2 * i))),(x2 div (x - ((~x + 2) div 2))),1)
A133227: 1 3 15 15 105 105
(1 + ((x * (2 + (if (~6 + (x div 2)) <= 0 then 0 else x))) div 2))
A161952: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 113 128
(if (1 + (x div 2) - (2 * (x mod 2))) <= 0 then (x2 + 2x + 2) else 1)
A066787: 1 5 1 17 1 1 1 1 1 1 1 1 1 1 1 1
(1 + ((x + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 2)))) div 2))
A323467: 1 1 3 2 3 3 7 4 5 5 7 6 7 7 15 8
(1 + (loop(\(x,i).(x * (1 + (6 * i))),(x + ~2),x) div 2))
A288556: 1 1 2 11 183
(~1 + ((3 * ((x mod 3) div 2)) + loop(\(x,i).2x,x,2)))
A188545: 1 3 10
A186575: 1 3 10 15 31 66 127 255 514 1023 2047 4098 8191 16383 32770 65535
(2 div (1 + (loop(\(x,i).2x,(2x div 3),1) mod (x + 2))))
A332006: 1 1 0 0 0 1 2 0 0 0 0 0 0 1 2 0
(~1 + ((x + 2) * (1 + loop(\(x,i).(x * (2 - (x div (2 + i)))),x,2))))
A277351: 5 14 19 44 53 62 71 152 169 186 203 220 237 254 271 560
loop(\(x,i).24x,(x2 + 4x + 4),1)
A013913: 331776 2641807540224 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x2 + 4x + 3) * loop(\(x,i).4x,x,(x + 2)))
A006044: 6 96 960 7680 53760 344064 2064384 11796480 64880640 346030080 1799356416 9160359936 45801799680 225485783040 1095216660480 5257039970304
(loop(\(x,i).(x2 div 3),2,(x + 3)) div (x + 3))
A222011: 1 2 4 8
A085891-A006501: 1 2 4 8 12 18 27 36 48 64 80 100 125 150 180 216
((loop(\(x,i).(x * (2 + i)),4,(x + 1)) div 2) div (x + 3))
A100659: 60 90 108 120 128 135 140 144 147 150 152 154 156 157 158 160
((if x <= 0 then 1 else (10x + ~4)) div (x + 3))
A130234: 0 1 3 4 5 5 6 6 6 7 7 7 7 7 8 8
(if x <= 0 then 0 else (2 - ((~8x + 1) div (x + 3))))
A102691: 0 4 5 6 7 7 8 8 8 8 9 9 9 9 9 9
(if x <= 0 then 1 else (2 - ((~8x + 1) div (x + 3))))
A067471: 1 4 5 6 7 7 8 8 8 8 9 9 9 9 9 9
loop(\(x,i).((x + 2) + (x div 7)),2,(x + 3))
A105860: 7 8 10 11 13 14 15 16 18 19 20 22 23 24 26 27
(loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2) div (x + 3))
A054577: 0 1 4 11 36 115 381 1287 4420 15396 54264 193154 693373 2507287 9124560 33393355
(loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2) mod (x + 3))
A131381: 2 2 0 4 0 4 3 0 0 4 0 0 5 8 0 0
((x + 3) * (loop(\(x,i).2x,x,(x + 8)) div 2))
A060621: 12 36 100 264 672 1664 4032 9600 22528 52224
((x2 + 5x + 6) * loop(\(x,i).((x2 + ~x) div 2),2,x))
A065949: 0 0 0 90 630 2520 7560 18900 41580 83160 154440 270270 450450 720720 1113840 1670760
loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,(x + 3))
A092443: 3 12 50 210 882 3696 15444 64350 267410 1108536 4585308 18929092 78004500 320932800 1318498920 5409723510
loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,(x + 3))
A038665: 3 8 25 84 294 1056 3861 14300 53482 201552 764218 2912168 11143500 42791040 164812365 636438060
(1 + ((~x + loop(\(x,i).((x + 2) + (x div 3)),x,1)) div (x + 2)))
A018121: 1 1 2 2 2 3 4 5 6 7 9 11 14 17 22 27
(~1 + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(x + 2)))
A000777: 1 2 7 24 83 293 1055 3860 14299 53481 201551 764217 2912167 11143499 42791039 164812364
(1 + ((x + 2) * (x + loop(\(x,i).x3,1,(x + 4)))))
A250814: 129 379 873 1731 3097 5139 8049 12043 17361 24267 33049 44019 57513 73891 93537 116859
((x2 + (x mod 2)) div (1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2))))
A081609: 0 1 1 2 3 4 4 5 5 6 7 8 9 10 11 12
(1 + (loop(\(x,i).(x - ((~x + 2) div 5)),x,x) div (x + 2)))
A136421: 1 1 1 2 2 2 3 3 4 5 6 7 8 10 12 14
loop(\(x,i).~29x,2x,1)
A121499: 1 841 707281 594823321 500246412961 420707233300201 353814783205469041 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((2x + ~1) + (if x <= 0 then 1 else (x2 div 12)))
A084555-A084505: 0 1 3 5 8 11 14 17 20 23 27 31 35 39 43 47
((2x + 1) + ((x + ((if (x + ~2) <= 0 then 1 else x) mod 2)) div 3))
A304500: 1 3 6 8 10 13 15 17 19 22 24 27 29 31 33 36
loop(\(x,i).((10x + 1) + (x mod 2)),2x,1)
A137466: 1 121 12121 1212121 121212121 12121212121 1212121212121 121212121212121 12121212121212121 1212121212121212121 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((10x + 1) + (i div 2)),2x,1)
A180027: 1 112 11223 1122334 112233445 11223344556 1122334455667 112233445566778 11223344556677889 1122334455667789000 4611686018427387903 4611686018427387903
loop(\(x,i).(10x + (2 div (x + 1))),2x,1)
A266299: 1 110 11000 1100000 110000000 11000000000 1100000000000 110000000000000 11000000000000000 1100000000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((2 * (1 + (x * (~1 + (2 * i))))) div (1 + i)),2x,1)
A260775: 1 4 28 264 2860 33592 416024 5348880 70715340 955277400 13128240840 182965127280 2579808294648 36734706144304 527495903500720 7629973004184608
((2x + 1) + ((x div (if (x mod 4) <= 0 then 4 else 1)) mod 2))
A026491: 1 4 5 8 10 12 13 16 17 20 21 24 26 28 29 32
(1 + loop(\(x,i).(((x div 4) * (x div 4)) div 2),2,2x))
A147472-A146914: 1 1 1 1 1 1 1 1 3 3 5 5 9 9 19 19
loop(\(x,i).((12 * (x mod 2)) + (x div 2)),2x,1)
A070396: 1 6 13 9 8 2 12 3 18 16 4 1 6 13 9 8
((2x + 1) * (if x <= 0 then 0 else ((2x + 3) - (x mod 2))))
A280364: 0 12 35 56 99 132 195 240 323 380 483 552 675 756 899 992
(loop(\(x,i).2x2,3,(2x + 1)) div (2x + 1))
A016831: 128 279936 10000000 105413504 612220032 2494357888 8031810176 21870000000 52523350144 114415582592 230539333248 435817657216 781250000000 1338925209984 2207984167552 3521614606208
((~1 + loop(\(x,i).2x,(x div 2),2) - (x mod 2)) div (2x + 1))
A258259: 1 0 0 0 0 0 1 0 1 1 3 2 5 4 8 8
((loop(\(x,i).2x,x,1) div (x2 + ~x + 1)) div (2x + 1))
A182722: 1 0 0 0 0 0 0 0 0 0 0 0 1 1 3 5
loop(\(x,i).(x5 + 4x),1,(2x + 1))
A069071: 5 255 3145 16835 59085 161095 371345 759435 1419925 2476175 4084185 6436435 9765725 14349015 20511265 28629275
((2x + 1) * loop(\(x,i).(x * (4 + i)),2x,(x + 1)))
A091033: 1 180 25200 4233600 898128000 239740300800 79332244992000 32011868528640000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((2x + 1) * (~1 - loop(\(x,i).2x,(2x + ~1),1)))
A228767: ~2 ~9 ~45 ~231 ~1161 ~5643 ~26637 ~122895 ~557073 ~2490387 ~11010069 ~48234519 ~209715225 ~905969691 ~3892314141 ~16642998303
loop(\(x,i).(x * ((x + 7) - i)),2,(2x + 1))
A069080: 84 864 3300 8736 18900 35904 62244 100800 154836 228000 324324 448224 604500 798336 1035300 1321344
loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,(2x + 1))
A257589: 1 9 50 245 1134 5082 22308 96525 413270 1755182 7407036 31097794 130007500 541574100 2249204040 9316746045
loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,(2x + 1))
A214955: 1 6 25 98 378 1452 5577 21450 82654 319124 1234506 4784276 18572500 72209880 281150505 1096087770
((3x + 1) + loop(\(x,i).(x + ((x div 2) div 3)),2,x))
A314680: 1 5 9 13 17 21 27 31 35 39 43 48 53 57 61 65
((loop(\(x,i).((x + 2) + (x div 3)),x,1) div 2) div (2x + ~1))
A286316: 0 1 1 1 1 1 1 1 1 2 2 3 4 5 6 8
((~2x + 1) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A131733: 1 0 0 0 2 2 4 4 6 10 10 14 16 16 18 22
loop(\(x,i).(5x3 + ~3x),2x,1)
A250488: 1 34 37889062373143906
loop(\(x,i).((5x + 5) * (2 - (x mod 2))),(x div 2),1)
A285612: 1 1 10 10 110 110 1110 1110 11110 11110 111110 111110 1111110 1111110 11111110 11111110
(~1 + loop(\(x,i).(2x * (~1 + (2 * i))),x,3) - (x div 2))
A307143: 2 5 34 358
loop(\(x,i).((10x + 1) - (x mod 2)),(x div 2),1)
A287742: 1 1 10 10 101 101 1010 1010 10101 10101 101010 101010 1010101 1010101 10101010 10101010
(1 + compr(\x.(loop(\(x,i).(x2 + 2x),2,3) mod (x + 1)),(x div 2)))
A087745: 1 1 3 3 5 5 15 15 17 17 51 51 85 85 255 255
loop(\(x,i).2x,(((3 * (x div 4)) div 2) + (x div 2)),1)
A060818: 1 1 2 2 8 8 16 16 128 128 256 256 1024 1024 2048 2048
(if ((x * (x mod 3)) mod 5) <= 0 then 0 else (1 + (x div 2)))
A102390: 0 1 2 0 3 0 0 4 5 0 0 6 0 7 8 0
((1 + (if (x mod 2) <= 0 then 10 else 0)) * (1 + (x div 2)))
A282868: 11 1 22 2 33 3 44 4 55 5 66 6 77 7 88 8
((if (~x + 2) <= 0 then ((x2 + ~x) div 3) else 1) div (1 + (x div 2)))
A116579: 1 1 0 1 1 2 2 3 3 4 5 6 6 7 7 8
((1 + (if (x mod 2) <= 0 then 2 else x)) * (1 + (x div 2)) * (1 + (x div 2)))
A114798: 3 2 12 16 27 54 48 128 75 250 108 432 147 686 192 1024
(loop(\(x,i).((x * (2 + i)) div (1 + (i div 2))),x,1) * (1 + (x div 2)))
A107231: 1 3 12 30 90 210 560 1260 3150 6930 16632 36036 84084 180180 411840 875160
((4 + (if (x mod 2) <= 0 then 1 else 8)) * (1 + (x div 2)))
A195031: 5 12 10 24 15 36 20 48 25 60 30 72 35 84 40 96
(if (x div (4 * (2 + (x mod 4)))) <= 0 then 1 else (~1 + (x div 2)))
A277604: 1 1 1 1 1 1 1 1 3 1 1 1 5 5 1 1
(1 + (((2 + loop(\(x,i).2x,x,1)) div 5) + (x mod 2)))
A118406: 1 2 2 4 4 8 14 28 52 104 206 412 820 1640 3278 6556
(1 + ((if (12 mod (x + 1)) <= 0 then 0 else 2) + (x mod 2)))
A246017: 1 2 1 2 3 2 3 4 3 4 3 2 3 4 3 4
(1 + (if (16 mod (x + 2)) <= 0 then 0 else 2) - (x mod 2))
A192099: 1 2 1 2 3 2 1 2 3 2 3 2 3 2 1 2
(1 + (2 * (2x - (if (~2 + (x div 2)) <= 0 then 0 else 1))) - (x mod 2))
A285419: 1 4 9 12 17 20 23 26 31 34 39 42 47 50 55 58
(1 + (((x mod (if (x + ~2) <= 0 then 1 else (x div 3))) div 2) + (x mod 2)))
A226898: 1 2 1 2 1 2 1 2 1 2 1 3 1 2 2 2
(1 + ((((x + 1) * (x + (if (x + ~1) <= 0 then x else 2))) div 2) + (x mod 2)))
A227589: 1 4 7 12 16 23 29 38 46 57 67 80 92 107 121 138
(1 + ((2 - ((x div 2) mod 2)) * (2 + (if x <= 0 then 1 else 2))) - (x mod 2))
A217516: 7 8 5 4 9 8 5 4 9 8 5 4 9 8 5 4
(1 + (loop(\(x,i).x2,1,((x + 2) + (x div 2))) div 2) - (x mod 2))
A302392: 3 4 13 18 33 40 61 72 99 112 145 162 201 220 265 288
(~1 + loop(\(x,i).((4x + ~1) + (x mod 2)),x,(2 - (x mod 2))))
A176963: 1 3 27 59 443 955 7099 15291 113595 244667 1817531 3914683 29080507 62634939 465288123 1002159035
loop(\(x,i).(10x + 1),(x div (2 - (x mod 2))),1)
A285540: 1 11 11 1111 111 111111 1111 11111111 11111 1111111111 111111 111111111111 1111111 11111111111111 11111111 1111111111111111
(1 + loop(\(x,i).((2x + 2) + (2 mod (x + 1))),(x div 2),(x mod 2)))
A060482: 1 2 3 5 9 13 21 29 45 61 93 125 189 253 381 509
(1 + loop(\(x,i).((2x + 2) - (x div 4)),(x div 2),(x mod 2)))
A193622: 1 2 3 5 7 10
A054405: 1 2 3 5 7 10 14 19 26 35 47 63 84 112 149 198
(~1 + (loop(\(x,i).4x,(x div 2),(2 - (x mod 2))) + (x mod 2)))
A282453: 1 1 7 4 31 16 127 64 511 256 2047 1024 8191 4096 32767 16384
((1 + (if (x mod 5) <= 0 then 4 else 0)) * (1 + (x mod 2)))
A089086: 5 2 1 2 1 10 1 2 1 2 5 2 1 2 1 10
((1 + (2 * (if (x mod 5) <= 0 then 0 else 2))) * (1 + (x mod 2)))
A296420: 1 10 5 10 5 2 5 10 5 10 1 10 5 10 5 2
loop(\(x,i).(8x + 2),(1 + (x div 2)),(1 + (x mod 2)))
A198309: 10 18 82 146 658 1170 5266 9362 42130 74898 337042 599186 2696338 4793490 21570706 38347922
loop(\(x,i).(6x + 2),(1 + (x div 2)),(1 + (x mod 2)))
A198307: 8 14 50 86 302 518 1814 3110 10886 18662 65318 111974 391910 671846 2351462 4031078
loop(\(x,i).(5x + 2),(1 + (x div 2)),(1 + (x mod 2)))
A198306: 7 12 37 62 187 312 937 1562 4687 7812 23437 39062 117187 195312 585937 976562
(loop(\(x,i).(9x + 1),x,1) div (1 + (x mod 2)))
A152299: 1 5 91 410 7381 33215 597871 2690420 48427561 217924025 3922632451 17651846030 317733228541 1429799528435 25736391511831 115813761803240
(loop(\(x,i).14x,x,1) div (1 + (x mod 2)))
A156359: 1 7 196 1372 38416 268912 7529536 52706752 1475789056 10330523392 289254654976 2024782584832 56693912375296 396857386627072 11112006825558016 77784047778906112
(((x + 1) * (1 + (if (x mod 3) <= 0 then 0 else 2))) div (1 + (x mod 2)))
A262343: 1 3 9 2 15 9 7 12 27 5 33 18 13 21 45 8
(((if (x + ~2) <= 0 then 2 else 1) - ((x mod 3) div 2)) div (1 + (x mod 2)))
A092510: 2 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0
((loop(\(x,i).(3x + 1),(x div 2),2) div 2) * (1 + (x mod 2)))
A018268: 1 2 3 6 11 22 33 66
((if (~2 + (x div 3)) <= 0 then 1 else (x div 4)) div (1 + (x mod 2)))
A029242: 1 0 1 0 1 0 1 0 1 1 2 1 3 1 3 1
((if (~4 + (x div 2)) <= 0 then 1 else (x div 4)) div (1 + (x mod 2)))
A029244: 1 0 1 0 1 0 1 0 1 0 2 1 3 1 3 1
loop(\(x,i).13x,(x div 2),(1 + (x mod 2)))
A018400: 1 2 13 26 169 338
loop(\(x,i).11x,(x div 2),(1 + (x mod 2)))
A018351: 1 2 11 22 121 242
loop(\(x,i).17x,(x div 2),(1 + (x mod 2)))
A018529: 1 2 17 34 289 578
(((if (x + ~2) <= 0 then 1 else (x div 3)) - (x mod 2)) div (1 + (x mod 2)))
A029221: 1 0 1 0 1 0 2 0 2 1 3 1 4 1 4 2
loop(\(x,i).((x + ~1) + (3 * (x + (x mod 2)))),x,(1 + (x mod 2)))
A267926: 1 7 23 119 375 1911 6007 30583 96119 489335 1537911 7829367 24606583 125269879 393705335 2004318071
(1 + ((if ((x - (x div 3)) mod 3) <= 0 then 1 else x) * (x mod 2)))
A340346-A329379-A328479-A327832-A193267: 1 2 1 4 1 6 1 8 1 2 1 12 1 2 1 16
(1 + (if (x + ~2) <= 0 then 0 else (x + (x2 div 4))) - (x mod 2))
A209350: 1 0 1 5 9 11 16 19 25 29 36 41 49 55 64 71
((36x + 9) + (if x <= 0 then 2 else 1))
A063158: 11 46 82 118 154 190 226 262 298 334 370 406 442 478 514 550
(1 + ((x - loop(\(x,i).(x - ((~2 + (x div 2)) div 3)),x,x)) div 2))
A096401: 1 0 0 0 1 1 1 1 1 1 1 2 2 3 3 4
(1 + (2 * (~x + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A239636: 1 1 3 5 11 13 19 21 27 37 39 49 55 57 63 73
((if x <= 0 then 1 else (2 * (1 + (2 * (x mod 2))))) * (1 + (x2 div 2)))
A066714: 1 6 6 30 18 78 38 150 66 246 102 366 146 510 198 678
(1 + (2 * compr(\x.loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,x),x)))
A118113: 1 3 5 9 11 17 19 21 33 35 37 41 43 65 67 69
(1 + (2 * loop(\(x,i).(x + (7 * (i * i))),x,x)))
A063494: 1 17 75 203 429 781 1287 1975 2873 4009 5411 7107 9125 11493 14239 17391
(~x mod (1 + (x * loop(\(x,i).(2x2 + 8x + 8),2,0))))
A004966: 0 200 399 598 797 996 1195 1394 1593 1792 1991 2190 2389 2588 2787 2986
(1 + compr(\x.(if (x mod 2) <= 0 then (2x mod (4 + (x div 2))) else 0),x))
A263800: 1 2 4 6 8 9 10
A110262: 1 2 4 6 8 9 10 12 14 16 18 20 22 24 25 26
(1 + compr(\x.(~1 + (x mod (~1 + (loop(\(x,i).2x,x,x) mod (x + 1))))),x))
A329366-A328957-A326848-A326534-A325371-A325247-A323306-A306013-A298538-A268082-A247199-A195943-A164336-A087441-A046686-A036116-A000961: 1 2 3 4 5 7 8 9 11 13 16 17 19 23 25 27
loop(\(x,i).((8x + 1) - (x mod ~3)),x,1)
A037615: 1 11 90 721 5771 46170 369361 2954891 23639130 189113041 1512904331 12103234650 96825877201 774607017611 6196856140890 49574849127121
(~1 + compr(\x.(2 - (x mod (1 + (x div (if (x mod 2) <= 0 then 4 else 1))))),x))
A153347: 2 4 6 7 8 10 12 13 14 16 17 18 19 20 21 22
loop(\(x,i).(60x + 1),x,1)
A269025: 1 61 3661 219661 13179661 790779661 47446779661 2846806779661 170808406779661 10248504406779661 614910264406779661 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(10x + 61),x,1)
A173806: 1 71 771 7771 77771 777771 7777771 77777771 777777771 7777777771 77777777771 777777777771 7777777777771 77777777777771 777777777777771 7777777777777771
loop(\(x,i).(10x + 81),x,1)
A170955: 1 91 991 9991 99991 999991 9999991 99999991 999999991 9999999991 99999999991 999999999991 9999999999991 99999999999991 999999999999991 9999999999999991
(1 + loop(\(x,i).(x + 5),(~1 + (x div 5)),x))
A081385: 1 2 3 4 5 6 7 8 9 10 16 17 18 19 20 26
loop(\(x,i).((6x + 1) + ((x + 1) mod 3)),x,1)
A037613: 1 9 56 337 2025 12152 72913 437481 2624888 15749329 94495977 566975864 3401855185 20411131113 122466786680 734800720081
loop(\(x,i).((21x + 1) + i),x,1)
A014905: 1 23 486 10210 214415 4502721 94557148 1985700116 41699702445 875693751355 18389568778466 386180944347798 8109799831303771 170305796457379205 3576421725604963320 4611686018427387903
((x + 1) + loop(\(x,i).(x * (x - i)),2,11))
A342351: 11881 11882 11883 11884 11885 11886 11887 11888 11889 11890 11891 11892 11893 11894 11895 11896
loop(\(x,i).((5x + 1) + (2x mod 3)),x,1)
A037612: 1 8 42 211 1058 5292 26461 132308 661542 3307711 16538558 82692792 413463961 2067319808 10336599042 51682995211
loop(\(x,i).((8x + 1) - ((x div 2) mod 3)),x,1)
A033135: 1 9 72 577 4617 36936 295489 2363913 18911304 151290433 1210323465 9682587720 77460701761 619685614089 4957484912712 39659879301697
loop(\(x,i).((9x + 1) + (x mod 3)),x,1)
A037609: 1 11 102 919 8273 74460 670141 6031271 54281442 488532979 4396796813 39571171320 356140541881 3205264876931 28847383892382 259626455031439
loop(\(x,i).((10x + 1) + (i mod 3)),x,1)
A037610: 1 12 123 1231 12312 123123 1231231 12312312 123123123 1231231231 12312312312 123123123123 1231231231231 12312312312312 123123123123123 1231231231231231
loop(\(x,i).((7x + 1) + (i mod 3)),x,1)
A037607: 1 9 66 463 3243 22704 158929 1112505 7787538 54512767 381589371 2671125600 18697879201 130885154409 916196080866 6413372566063
(1 + compr(\x.(~1 + (loop(\(x,i).(2x + 6),x,1) mod (x + 1))),x))
A106317: 1 2 3 5 7 11 13 17 19 21 23 29 31 37 41 43
(1 + compr(\x.(~1 + (loop(\(x,i).(2 * (x - (i mod 2))),x,1) mod (x + 1))),x))
A193622: 1 2 3 5 7 10
A087246: 1 2 3 5 7 10 11 13 14 15 17 19 21 22 23 26
(1 + compr(\x.(x mod (1 + (loop(\(x,i).2x,x,(x + ~1)) mod (x + 1)))),x))
A127072: 1 2 3 4 5 7 8 9 11 13 16 17 19 23 27 29
(1 + compr(\x.(2 - (x mod (~1 + (loop(\(x,i).2x,x,x) mod (x + 1))))),x))
A335080-A325411-A323304-A168638-A106543-A064040-A024619: 6 10 12 14 15 18 20 21 22 24 26 28 30 33 34 35
(1 + compr(\x.(x mod (if (x mod (1 + (2 * (x mod 3)))) <= 0 then 2 else 1)),x))
A329780: 1 2 3 5 7 8 9 11 12 13 14 15 17 18 19 20
loop(\(x,i).(3x * (1 + i)),7x,1)
A054434: 1 88179840 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((5x + 1) + ((x div ~2) mod 2)),x,1)
A037538: 1 7 36 181 907 4536 22681 113407 567036 2835181 14175907 70879536 354397681 1771988407 8859942036 44299710181
loop(\(x,i).(1 + (4 * ((~x + 2) mod 9))),x,1)
A070383: 1 5 25 17 13 29 1 5 25 17 13 29 1 5 25 17
loop(\(x,i).(18x * (1 + (2 * i))),x,1)
A254620: 1 54 4860 612360 99202320 19642059360 4596241890240 1240985310364800 379741504971628800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((9x + 1) + ((x div 2) mod 2)),x,1)
A037534: 1 10 92 829 7462 67160 604441 5439970 48959732 440637589 3965738302 35691644720 321224802481 2891023222330 26019209000972 234172881008749
((x + 1) + (loop(\(x,i).(2x + 4),(x + ~1),0) div 5))
A066000: 1 2 3 6 10 18 31 58
loop(\(x,i).(x + i - (((x + ~1) + (x mod 2)) div 5)),x,1)
A276208: 1 2 4 7 10 14 18 22 26 30 35 39 44 49 54 59
((x + 1) + loop(\(x,i).x2,1,(10x + 10)))
A055438-A031698: 101 402 903 1604 2505 3606 4907 6408 8109 10010 12111 14412 16913 19614 22515 25616
loop(\(x,i).((19x + 1) + i),x,1)
A014903: 1 21 402 7642 145203 2758863 52418404 995949684 18923044005 359537836105 6831218886006 129793158834126 2466070017848407 46855330339119747 890251276443275208 4611686018427387903
loop(\(x,i).x5,1,(5x + 1))
A016865: 1 7776 161051 1048576 4084101 11881376 28629151 60466176 115856201 205962976 345025251 550731776 844596301 1252332576 1804229351 2535525376
loop(\(x,i).(5 * (x + (4x div (1 + i)))),x,1)
A036083: 1 15 175 1750 15750 131250 1031250 7734375 55859375 391015625 2666015625 17773437500 116210937500 747070312500 4731445312500 29571533203125
(1 + compr(\x.(loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 5),x))
A222011: 1 2 4 8
A242313: 1 2 4 8 11 16 21 22 31 32 41 42 44 51 61 62
loop(\(x,i).(1 + (2 * (2x + (x mod 2))) - ((x div 2) mod 2)),x,1)
A037709: 1 7 30 120 481 1927 7710 30840 123361 493447 1973790 7895160 31580641 126322567 505290270 2021161080
loop(\(x,i).((10x + 1) + ((x div 2) mod 2)),x,1)
A037535: 1 11 112 1121 11211 112112 1121121 11211211 112112112 1121121121 11211211211 112112112112 1121121121121 11211211211211 112112112112112 1121121121121121
loop(\(x,i).((10x + 1) - ((x div 2) mod 2)),x,1)
A259661: 1 11 110 1100 11001 110011 1100110 11001100 110011001 1100110011 11001100110 110011001100 1100110011001 11001100110011 110011001100110 1100110011001100
loop(\(x,i).(2x * ((1 + (2 * i)) * (1 + (4 * i)))),x,1)
A091544: 1 30 2700 491400 150368400 69470200800 45155630520000 39285398552400000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) + (3 * (if x <= 0 then 0 else (3 * (1 + (x div 2))))))
A118853-A117841: 1 11 21 22 32 33 43 44 54 55 65 66 76 77 87 88
loop(\(x,i).(3 * ((2x div (1 + i)) * (1 + (2 * i)))),x,1)
A098399: 1 9 90 945 10206 112266 1250964 14073345 159497910 1818276174 20827527084 239516561466 2763652632300 31979409030900 370961144758440 4312423307816865
loop(\(x,i).(3 * ((2x div (1 + i)) * (~1 + (2 * i)))),x,1)
A151383-A005159: 1 3 18 135 1134 10206 96228 938223 9382230 95698746 991787004 10413763542 110546105292 1184422556700 12791763612360 139110429284415
((x + 1) + loop(\(x,i).x2,1,(12x + 12)))
A031702: 145 578 1299 2308 3605 5190 7063 9224 11673 14410 17435 20748 24349 28238 32415 36880
((~x + ~1) + loop(\(x,i).x2,1,(12x + 12)))
A156635: 143 574 1293 2300 3595 5178 7049 9208 11655 14390 17413 20724 24323 28210 32385 36848
((x + 1) + (loop(\(x,i).((x2 + ~x) div 2),2,(x + 1)) div 3))
A101338: 1 2 4 9 20 41 77 134 219 340 506 727 1014 1379 1835 2396
loop(\(x,i).(9x + ((x + 1) mod 3)),x,1)
A037510: 1 11 99 892 8030 72270 650431 5853881 52684929 474164362 4267479260 38407313340 345665820061 3110992380551 27998931424959 251990382824632
loop(\(x,i).(9x + ((x + ~1) mod 3)),x,1)
A037502: 1 9 83 748 6732 60590 545311 4907799 44170193 397531738 3577785642 32200070780 289800637021 2608205733189 23473851598703 211264664388328
loop(\(x,i).(10x + ((1 + i) mod 3)),x,1)
A037511: 1 12 120 1201 12012 120120 1201201 12012012 120120120 1201201201 12012012012 120120120120 1201201201201 12012012012012 120120120120120 1201201201201201
loop(\(x,i).(7x + ((1 + i) mod 3)),x,1)
A037508: 1 9 63 442 3096 21672 151705 1061937 7433559 52034914 364244400 2549710800 17847975601 124935829209 874550804463 6121855631242
loop(\(x,i).(3 * ((~x + (3x * i)) div (1 + i))),x,1)
A097188: 1 3 15 90 594 4158 30294 227205 1741905 13586859 107459703 859677624 6943550040 56540336040 463630755528 3824953733106
((x + 1) + ((4 * loop(\(x,i).i,(~2 + (x div 2)),1)) div 3))
A121603: 2 3 4 5 6 7 8 9 11
A256476: 2 3 4 5 6 7 8 9 11 12 15 16 18 19 21 22
(1 + loop(\(x,i).(2 * (2x - (x mod 8))),3,x))
A145849: 1 9 33 41 129 137 161 169 513 521 545 553 641 649 673 681
loop(\(x,i).((23x + 1) + i),x,1)
A014909: 1 25 578 13298 305859 7034763 161799556 3721389796 85591965317 1968615202301 45278149652934 1041397442017494 23952141166402375 550899246827254639 4611686018427387903 4611686018427387903
((x + 1) + (3 * loop(\(x,i).(x * (2 - (x div (2 + i)))),x,2)))
A004759: 7 14 15 28 29 30 31 56 57 58 59 60 61 62 63 112
loop(\(x,i).(3 * ((2x * (1 + (2 * i))) div (2 + i))),x,1)
A101600: 1 6 45 378 3402 32076 312741 3127410 31899582 330595668 3471254514 36848701764 394807518900 4263921204120 46370143094805 507343918566690
loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),3x,1)
A187364: 1 35 1716 92378 5200300 300540195 17672631900 1052049481860 63205303218876 3824345300380220 232714176627630544 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x6,1,(3x + 1))
A016782: 1 4096 117649 1000000 4826809 16777216 47045881 113379904 244140625 481890304 887503681 1544804416 2565726409 4096000000 6321363049 9474296896
((3x + ~1) * loop(\(x,i).(x * (3 + i)),(x + ~1),x))
A108033: 0 2 40 480 5280 58800 685440 8467200 111283200 1556755200 23151744000 365318553600 6102480384000 107665189632000 2001613565952000 39125617090560000
loop(\(x,i).(3x * (1 + (2 * (x mod 6)))),x,1)
A067422: 1 9 189 3969 83349 1750329 36756909 771895089 16209796869 340405734249 7148520419229 150118928803809 3152497504879989 66202447602479769 1390251399652075149 4611686018427387903
loop(\(x,i).(x + ((4x div (2 + i)) + (x div 3))),x,1)
A222011: 1 2 4 8
A007673: 1 2 4 8 15 28 51 90
(1 + compr(\x.(if ((x + 2) mod 8) <= 0 then 0 else (x mod 3)),x))
A055054: 1 4 7 10 13 15 16 19 22 23 25 28 31 34 37 39
loop(\(x,i).(20x + (x mod 3)),x,1)
A170740-A170702-A170654-A170606-A170558-A170510-A170462-A170414-A170366-A170318-A170270-A170222-A170174-A170126-A170078-A170030-A169562-A169514-A169466-A169418-A169370-A169322-A169274-A169226-A169178-A169130-A169082-A169034-A168986-A168938-A168890-A168842-A168794-A168746-A168698-A167933-A167681: 1 21 420 8400 168000 3360000 67200000 1344000000 26880000000 537600000000 10752000000000 215040000000000 4300800000000000 86016000000000000 1720320000000000000 4611686018427387903
loop(\(x,i).(32x + (x mod 3)),x,1)
A170752-A170714-A170666-A170618-A170570-A170522-A170474-A170426-A170378-A170330-A170282-A170234-A170186-A170138-A170090-A170042-A169574-A169526-A169478-A169430-A169382-A169334-A169286-A169238-A169190-A169142-A169094-A169046-A168998-A168950-A168902-A168854-A168806-A168758-A168710-A167949-A167765-A167391-A167086: 1 33 1056 33792 1081344 34603008 1107296256 35433480192 1133871366144 36283883716608 1161084278931456 37154696925806592 1188950301625810944 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(8x + ((x mod 2) + (x mod 3))),x,1)
A037541: 1 10 81 649 5194 41553 332425 2659402 21275217 170201737 1361613898 10892911185 87143289481 697146315850 5577170526801 44617364214409
((x + 1) + (if (x + ~1) <= 0 then x else (2 - ((~x2 + 2x) div 3))))
A112509: 1 3 5 7 10 13 17 22 27 33 40 47 55 64 73 83
loop(\(x,i).(10x + ((1 - i) mod 3)),x,1)
A037503: 1 10 102 1021 10210 102102 1021021 10210210 102102102 1021021021 10210210210 102102102102 1021021021021 10210210210210 102102102102102 1021021021021021
loop(\(x,i).(7x + ((1 - i) mod 3)),x,1)
A037500: 1 7 51 358 2506 17544 122809 859663 6017643 42123502 294864514 2064051600 14448361201 101138528407 707969698851 4955787891958
loop(\(x,i).(x + (i div 3) - (x div ~5)),x,1)
A193622: 1 2 3 5 7 10
A036469: 1 2 3 5 7 10 14 19 25 33 43 55 70 88 110 137
loop(\(x,i).((x + ~1) - ((x * (1 - (x * (1 + (2 * i))))) div 2)),x,1)
A144017: 1 1 2 14 888
loop(\(x,i).((8x div (1 + i)) * (1 + (2 * i))),x,1)
A098400: 1 12 160 2240 32256 473088 7028736 105431040 1593180160 24216338432 369849532416 5671026163712 87246556364800 1346089726771200 20819521107394560 322702577164615680
loop(\(x,i).(2x - ((~1 + (2 * (i mod 2))) * (~1 + (2 * i)))),x,1)
A095342: 1 1 5 5 17 25 61 109 233 449 917 1813 3649 7273 14573 29117
loop(\(x,i).(((4x + 2) div (1 + i)) * (~1 + (2 * i))),x,1)
A181282: 1 3 12 60 336 2016 12672 82368 549120 3734016 25798656 180590592 1278025728 9128755200 65727037440 476521021440
loop(\(x,i).((x + 1) + ((3x + 1) div (1 + (2 * i)))),x,1)
A342711: 1 3 6 9 13 17 22 27 32 38 44 50 57 64 71 78
((x + 1) + ((x2 + x + 1) * loop(\(x,i).(1 + (x * i)),x,1)))
A001340: 2 8 38 212 1370 10112 84158 780908 8000882 89763320 1094915222 14431179908 204423631178 3097603939952 50001759773870 856665220770332
((x + 1) + loop(\(x,i).(4x - ((x + 1) div (1 + i))),x,1))
A030126: 2 5 14 45 161
(2 - loop(\(x,i).((x + ~1) + ((2x2 + x) div (1 + i))),x,1))
A079947: 1 1 1 2 3 4 5 5 5 5 5 5 5 5 5 6
(1 + compr(\x.(loop(\(x,i).(4x2 + 8),2,0) mod (x + 1)),x))
A018362: 1 2 3 4 6 8 11 12 22 24 33 44 66 88 132 264
(1 + compr(\x.(loop(\(x,i).(4x + 8),4,0) mod (x + 1)),x))
A191535-A100598: 1 2 4 5 8 10
A018589: 1 2 4 5 8 10 17 20 34 40 68 85 136 170 340 680
(1 + compr(\x.(loop(\(x,i).(2x + 16),x,0) mod (x + 1)),x))
A176176: 1 2 3 4 5 7 8 11 13 16 17 19 23 28 29 31
(1 + compr(\x.(loop(\(x,i).(2 + (x * (x + i))),3,1) mod (x + 1)),x))
A018629: 1 2 3 4 6 7 9 12 14 18 21 27 28 36 42 54
(1 + compr(\x.(loop(\(x,i).(4x2 + 4x),2,1) mod (x + 1)),x))
A018376: 1 2 3 4 6 8 9 12 16 18 24 32 36 48 72 96
(1 + compr(\x.((~1 + loop(\(x,i).x2,2,8)) mod (x + 1)),x))
A003524: 1 3 5 7 9 13 15 21 35 39 45 63 65 91 105 117
(1 + compr(\x.(loop(\(x,i).((x + 2) * i),8,1) mod (x + 1)),x))
A191535-A100598: 1 2 4 5 8 10
A018391: 1 2 4 5 8 10 16 20 32 40 64 80 160 320
(1 + compr(\x.(loop(\(x,i).(4x2 + 8x),2,1) mod (x + 1)),x))
A018585: 1 2 3 4 6 7 8 12 14 16 21 24 28 32 42 48
(1 + compr(\x.(loop(\(x,i).(2x2 + 8x + 8),2,1) mod (x + 1)),x))
A191535-A100598: 1 2 4 5 8 10
A018653: 1 2 4 5 8 10 16 20 25 32 40 50 80 100 160 200
(1 + compr(\x.(loop(\(x,i).(4x + 8),4,1) mod (x + 1)),x))
A018731: 1 2 3 4 6 8 9 12 13 18 24 26 36 39 52 72
(1 + compr(\x.((~1 + loop(\(x,i).x3,2,4)) mod (x + 1)),x))
A003528: 1 3 7 9 19 21 27 57 63 73 133 171 189 219 399 511
(1 + compr(\x.(loop(\(x,i).(x2 + x),2,5) mod (x + 1)),x))
A018255: 1 2 3 5 6 10 15 30
A018727: 1 2 3 5 6 10 15 30 31 62 93 155 186 310 465 930
(1 + compr(\x.(loop(\(x,i).(x * (x + i)),2,5) mod (x + 1)),x))
A067319: 1 2 3 4 5 6 8 10 12
A324107-A018744-A018478: 1 2 3 4 5 6 8 10 12 15 16 20 24 30 32 40
(1 + compr(\x.(loop(\(x,i).(x * (1 + (2 * i))),4,1) mod (x + 1)),x))
A018736: 1 3 5 7 9 15 21 27 35 45 63 105 135 189 315 945
(1 + compr(\x.(1 - (loop(\(x,i).(x * (2 + i)),4,1) mod (x + 1))),x))
A110547: 7 11 13 14 16 17 19 21 22 23 25 26 27 28 29 31
(1 + compr(\x.(loop(\(x,i).(2x2 + 8x),2,1) mod (x + 1)),x))
A018371: 1 2 4 5 7 8 10 14 20 28 35 40 56 70 140 280
(1 + compr(\x.(loop(\(x,i).(2x3 + 4x),2,1) mod (x + 1)),x))
A323383: 1 2 3 4 6 8 12
A018465: 1 2 3 4 6 8 12 19 24 38 57 76 114 152 228 456
(1 + compr(\x.(loop(\(x,i).((x2 + 2x) * (2 + i)),2,1) mod (x + 1)),x))
A018431: 1 2 3 4 6 9 11 12 18 22 33 36 44 66 99 132
(1 + compr(\x.(loop(\(x,i).(x * (x + i)),3,3) mod (x + 1)),x))
A233576: 1 2 3 4 6 7 8 9 12 14 18 19 21 24 27 28
(1 + compr(\x.(loop(\(x,i).(x * (x - i)),3,3) mod (x + 1)),x))
A018490: 1 2 3 4 6 7 8 9 12 14 18 21 24 28 36 42
(1 + compr(\x.(loop(\(x,i).(x2 + 3x + 2),2,3) mod (x + 1)),x))
A018468: 1 2 3 6 7 11 14 21 22 33 42 66 77 154 231 462
(1 + compr(\x.(loop(\(x,i).4x2,2,3) mod (x + 1)),x))
A262609-A114334-A018690-A003586: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54
(1 + compr(\x.(loop(\(x,i).(x2 + 3x),2,3) mod (x + 1)),x))
A018423: 1 2 3 6 7 9 14 18 21 27 42 54 63 126 189 378
(1 + compr(\x.(loop(\(x,i).(x * ((x + 1) + i)),2,3) mod (x + 1)),x))
A018365: 1 2 3 5 6 9 10 15 18 27 30 45 54 90 135 270
(1 + compr(\x.(loop(\(x,i).(x * (1 + (x * i))),2,3) mod (x + 1)),x))
A018382: 1 2 3 4 5 6 10 12 15 20 25 30 50 60 75 100
(1 + compr(\x.(loop(\(x,i).(x * (2x + i)),2,3) mod (x + 1)),x))
A018723: 1 2 3 4 6 7 11 12 14 21 22 28 33 42 44 66
(1 + compr(\x.(2 - ((~1 + loop(\(x,i).4x,x,2)) mod (x + 1))),x))
A193166: 4 8 9 10 12 14 16 18 20 21 22 24 25 26 27 28
(1 + compr(\x.(loop(\(x,i).x2,2,10) mod (x + 1)),x))
A191535-A100598: 1 2 4 5 8 10
A133075-A133020: 1 2 4 5 8 10 16 20 25 40 50 80 100 125 200 250
(1 + compr(\x.(loop(\(x,i).(x3 + x2),3,2) mod (x + 1)),x))
A095037: 1 2 3 4 6 8 9 12 13 16 18
A308299: 1 2 3 4 6 8 9 12 13 16 18 24 26 27 32 36
(1 + compr(\x.(loop(\(x,i).(x3 + 2x2),3,2) mod (x + 1)),x))
A291719: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 27
(1 + compr(\x.(loop(\(x,i).x3,1,6) mod (x + 1)),x))
A018338: 1 2 3 4 6 8 9 12 18 24 27 36 54 72 108 216
(1 + compr(\x.(loop(\(x,i).(x2 + ~x),2,6) mod (x + 1)),x))
A018693: 1 2 3 5 6 10 15 29 30 58 87 145 174 290 435 870
(1 + compr(\x.(loop(\(x,i).(x2 + ~2x),2,6) mod (x + 1)),x))
A018502: 1 2 3 4 6 8 11 12 16 22 24 33 44 48 66 88
(1 + compr(\x.(loop(\(x,i).(x * (x - i)),2,6) mod (x + 1)),x))
A018676: 1 2 3 4 5 6 7 8 10 12 14 15 20 21 24 28
(1 + compr(\x.(loop(\(x,i).(x * ((x + 2) - i)),3,2) mod (x + 1)),x))
A082463: 1 2 3 4 5 6 7 9 10
A178877: 1 2 3 4 5 6 7 9 10 12 14 15 18 20 21 28
(1 + compr(\x.(loop(\(x,i).(x * (2x + i)),3,2) mod (x + 1)),x))
A018339: 1 2 4 5 10 11 20 22 44 55 110 220
(1 + compr(\x.(loop(\(x,i).((~x + 2) * i),6,2) mod (x + 1)),x))
A323383: 1 2 3 4 6 8 12
A018718: 1 2 3 4 6 8 12 16 19 24 38 48 57 76 114 152
(1 + compr(\x.(loop(\(x,i).(2x3 + 2x2),2,2) mod (x + 1)),x))
A257997-A250089-A070023-A051037-A035303: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25
(1 + compr(\x.(loop(\(x,i).(x3 + 2x2 + x),2,2) mod (x + 1)),x))
A018251: 1 2 3 6 9 18
A018402: 1 2 3 6 9 18 19 38 57 114 171 342
(1 + compr(\x.(loop(\(x,i).((x2 + x) * (1 + i)),2,2) mod (x + 1)),x))
A018471: 1 2 3 4 6 9 12 13 18 26 36 39 52 78 117 156
(1 + compr(\x.(loop(\(x,i).(~x3 + ~x2 + x + 1),2,2) mod (x + 1)),x))
A191535-A100598: 1 2 4 5 8 10
A018565: 1 2 4 5 8 10 16 20 32 40 64 80 128 160 320 640
(1 + compr(\x.(loop(\(x,i).(2x3 + ~2x2),2,2) mod (x + 1)),x))
A018708: 1 2 4 7 8 14 16 28 32 56 64 112 128 224 448 896
(1 + compr(\x.(loop(\(x,i).(x3 + x2 + ~2x),2,2) mod (x + 1)),x))
A018519: 1 2 4 5 7 8 10 14 16 20 28 35 40 56 70 80
(1 + compr(\x.(loop(\(x,i).(~x3 + ~1),2,2) mod (x + 1)),x))
A018614: 1 2 4 7 8 13 14 26 28 52 56 91 104 182 364 728
(1 + compr(\x.((~2 + loop(\(x,i).(x2 + 3x + 2),2,2)) mod (x + 1)),x))
A018321: 1 2 3 4 5 6 9 10 12 15 18 20 30 36 45 60
(1 + compr(\x.(loop(\(x,i).((2x + 2) * (x + i)),2,2) mod (x + 1)),x))
A191535-A100598: 1 2 4 5 8 10
A018631: 1 2 4 5 8 10 19 20 38 40 76 95 152 190 380 760
(1 + compr(\x.(loop(\(x,i).(2x2 + 8),2,2) mod (x + 1)),x))
A191535-A100598: 1 2 4 5 8 10
A018498: 1 2 4 5 8 10 13 20 26 40 52 65 104 130 260 520
(1 + compr(\x.(loop(\(x,i).((x + ~1) * i),8,2) mod (x + 1)),x))
A191535-A100598: 1 2 4 5 8 10
A018310: 1 2 4 5 8 10 16 20 32 40 80 160
(1 + compr(\x.(loop(\(x,i).(~4x2 + x),2,2) mod (x + 1)),x))
A018652: 1 2 3 6 7 14 19 21 38 42 57 114 133 266 399 798
(1 + compr(\x.(loop(\(x,i).(~4x2 + 2x),2,2) mod (x + 1)),x))
A067319: 1 2 3 4 5 6 8 10 12
A018541: 1 2 3 4 5 6 8 10 12 15 20 24 25 30 40 50
(1 + compr(\x.((~2 + loop(\(x,i).(x3 + 2),2,2)) mod (x + 1)),x))
A191535-A100598: 1 2 4 5 8 10
A018767: 1 2 4 5 8 10 20 25 40 50 100 125 200 250 500 1000
(1 + compr(\x.(loop(\(x,i).((x + 1) * (x + i)),4,2) mod (x + 1)),x))
A003591: 1 2 4 7 8 14 16 28 32 49 56 64 98 112 128 196
(1 + compr(\x.(loop(\(x,i).(x2 + x),2,8) mod (x + 1)),x))
A018271: 1 2 3 4 6 8 9 12 18 24 36 72
(1 + compr(\x.(loop(\(x,i).(x * (x - i)),2,8) mod (x + 1)),x))
A108319: 1 2 3 4 6 7 8 9 12 14 16 18 21 24 27 28
(1 + compr(\x.(loop(\(x,i).(x * (2 + (x * i))),4,2) mod (x + 1)),x))
A200381: 1 2 3 4 6 7 8 9 11 12 14 16 18 21 22 24
(1 + compr(\x.(loop(\(x,i).(x * (2x + i)),4,2) mod (x + 1)),x))
A191535-A100598: 1 2 4 5 8 10
A018699: 1 2 4 5 8 10 11 16 20 22 40 44 55 80 88 110
(1 + compr(\x.(loop(\(x,i).(x * (x + (i * i))),4,2) mod (x + 1)),x))
A051661: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 23 24
(1 + compr(\x.(loop(\(x,i).(2x2 + 6x),2,2) mod (x + 1)),x))
A191535-A100598: 1 2 4 5 8 10
A018722: 1 2 4 5 8 10 20 23 40 46 92 115 184 230 460 920
(1 + compr(\x.(loop(\(x,i).(4x2 + ~2x),2,2) mod (x + 1)),x))
A323383: 1 2 3 4 6 8 12
A018515: 1 2 3 4 6 8 12 23 24 46 69 92 138 184 276 552
(1 + compr(\x.(loop(\(x,i).((x + 2) * (x + (x div 2))),2,2) mod (x + 1)),x))
A018357: 1 2 3 4 6 7 9 12 14 18 21 28 36 42 63 84
(1 + compr(\x.((2 + loop(\(x,i).x2,2,4x)) mod (x + 1)),x))
A018359: 1 2 3 6 43 86 129 258
(1 + compr(\x.(loop(\(x,i).((x + 1) * (x + i)),2,4) mod (x + 1)),x))
A018599: 1 2 3 6 9 13 18 26 27 39 54 78 117 234 351 702
(1 + compr(\x.(loop(\(x,i).(2x * (x + i)),2,4) mod (x + 1)),x))
A178878: 1 2 3 4 5 6 7 8 10 12 14 15 16 20 21 24
loop(\(x,i).12x,(5x + 4),1)
A013865: 20736 5159780352 1283918464548864 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).10x,(5x + 4),1)
A013857: 10000 1000000000 100000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).7x,(5x + 4),1)
A013845: 2401 40353607 678223072849 11398895185373143 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.(loop(\(x,i).(4x2 + ~x),2,2) mod (x + 1)),x))
A018636: 1 2 5 7 10 11 14 22 35 55 70 77 110 154 385 770
(1 + compr(\x.(loop(\(x,i).(x * (~1 + (x * (2 + i)))),2,2) mod (x + 1)),x))
A018429: 1 2 3 5 6 10 13 15 26 30 39 65 78 130 195 390
(1 + compr(\x.((x mod 2) - (loop(\(x,i).(x2 + 2x),2,2) mod (x + 1))),x))
A285510: 1 3 5 6 7 9 11 12 13 14 15 17 18 19 21 22
(1 + compr(\x.(loop(\(x,i).(x * (3x + i)),2,2) mod (x + 1)),x))
A018552: 1 2 4 7 8 11 14 22 28 44 56 77 88 154 308 616
(1 + compr(\x.(loop(\(x,i).(x2 + ~1),2,4x) mod (x + 1)),x))
A018341: 1 2 4 7 8 14 16 28 32 56 112 224
(1 + compr(\x.(loop(\(x,i).(x2 + ~x),2,4x) mod (x + 1)),x))
A018424: 1 2 4 5 10 19 20 38 76 95 190 380
(1 + compr(\x.(loop(\(x,i).(x4 + x2),2,2) mod (x + 1)),x))
A191535-A100598: 1 2 4 5 8 10
A018433: 1 2 4 5 8 10 16 20 25 40 50 80 100 200 400
(1 + compr(\x.(loop(\(x,i).(~x4 + x),2,2) mod (x + 1)),x))
A018559: 1 2 3 5 6 7 9 10 14 15 18 21 30 35 42 45
loop(\(x,i).(18x + (2 div (x + 1))),x,1)
A170738-A170700-A170652-A170604-A170556-A170508-A170460-A170412-A170364-A170316-A170268-A170220-A170172-A170124-A170076-A170028-A169560-A169512-A169464-A169416-A169368-A169320-A169272-A169224-A169176-A169128-A169080-A169032-A168984-A168936-A168888-A168840-A168792-A168744-A168696-A167929-A167676: 1 19 342 6156 110808 1994544 35901792 646232256 11632180608 209379250944 3768826516992 67838877305856 1221099791505408 21979796247097344 395636332447752192 4611686018427387903
loop(\(x,i).(24x + (2 div (x + 1))),x,1)
A170744-A170706-A170658-A170610-A170562-A170514-A170466-A170418-A170370-A170322-A170274-A170226-A170178-A170130-A170082-A170034-A169566-A169518-A169470-A169422-A169374-A169326-A169278-A169230-A169182-A169134-A169086-A169038-A168990-A168942-A168894-A168846-A168798-A168750-A168702-A167940-A167696-A167212: 1 25 600 14400 345600 8294400 199065600 4777574400 114661785600 2751882854400 66045188505600 1585084524134400 38042028579225600 913008685901414400 4611686018427387903 4611686018427387903
(1 + compr(\x.(loop(\(x,i).(~x2 + x),3,(x + ~2)) mod (x + 1)),x))
A185092: 1 2 3 4 6 12
A018309: 1 2 3 4 6 12 13 26 39 52 78 156
(1 + compr(\x.(loop(\(x,i).(x3 + x2),2,2x) mod (x + 1)),x))
A323383: 1 2 3 4 6 8 12
A018261: 1 2 3 4 6 8 12 16 24 48
(1 + compr(\x.(loop(\(x,i).(x3 + ~2x),2,2x) mod (x + 1)),x))
A018265: 1 2 4 7 8 14 28 56
(1 + loop(\(x,i).((2x + ~4) div (1 + i)),(x + ~1),(x2 + x)))
A161435: 1 3 5 6 5 3 1 0 0 0 0 0 0 0 0 0
(if (x + ~2) <= 0 then x else (4x3 + 8x2 + 8x + 4))
A110899: 0 1 2 208
(1 + compr(\x.(loop(\(x,i).(x * (~1 + (x * i))),3,x) mod (x + 1)),x))
A018284: 1 2 3 6 17 34 51 102
(1 + compr(\x.(loop(\(x,i).(i - (x * i)),6,x) mod (x + 1)),x))
A323383: 1 2 3 4 6 8 12
A018253: 1 2 3 4 6 8 12 24
A018758: 1 2 3 4 6 8 12 24 41 82 123 164 246 328 492 984
(1 + compr(\x.(loop(\(x,i).(~x3 + 2x2 + ~x),2,x) mod (x + 1)),x))
A018256: 1 2 3 4 6 9 12 18 36
(1 + compr(\x.(loop(\(x,i).(x3 + x + ~2),2,x) mod (x + 1)),x))
A018270: 1 2 5 7 10 14 35 70
(1 + compr(\x.(loop(\(x,i).((x2 + ~2x) * (~x + i)),2,x) mod (x + 1)),x))
A323383: 1 2 3 4 6 8 12
A018280: 1 2 3 4 6 8 12 16 24 32 48 96
(1 + compr(\x.(loop(\(x,i).((x3 + ~2x2) * i),2,x) mod (x + 1)),x))
A018278: 1 2 3 5 6 9 10 15 18 30 45 90
(1 + compr(\x.(loop(\(x,i).(x * ((x2 + 2) + i)),2,x) mod (x + 1)),x))
A191535-A100598: 1 2 4 5 8 10
A018275: 1 2 4 5 8 10 16 20 40 80
(1 + compr(\x.(loop(\(x,i).(x3 + ~3x2),2,x) mod (x + 1)),x))
A018289: 1 2 4 7 8 14 16 28 56 112
(1 + compr(\x.(loop(\(x,i).(x * (2x2 + i)),2,x) mod (x + 1)),x))
A018266: 1 2 3 4 5 6 10 12 15 20 30 60
(1 + compr(\x.(loop(\(x,i).(x2 + ~x),2,(~x2 + 2x)) mod (x + 1)),x))
A018297: 1 2 3 4 6 11 12 22 33 44 66 132
(1 + compr(\x.(loop(\(x,i).(x2 + ~2x),2,(~x2 + 2x)) mod (x + 1)),x))
A018329: 1 3 5 13 15 39 65 195
(1 + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x + ~1),x))
A289719: 1 2 7 31 141 631 2773 12013 51481 218791 923781 3879877 16224937 67603901 280816201 1163381401
((x2 + ~x + 1) + (2 * (((x div 2) mod 2) + (if x <= 0 then 0 else 1))))
A169626: 1 3 7 11 15 23 35
((~x + ~1) + loop(\(x,i).(x + ((3x + 4) div (2 + i))),x,1))
A034198: 0 1 3 6 10 16 23 32 43 56 71 89 109 132 158 187
loop(\(x,i).((25x + 1) + i),x,1)
A014914: 1 27 678 16954 423855 10596381 264909532 6622738308 165568457709 4139211442735 103480286068386 2587007151709662 64675178792741563 1616879469818539089 4611686018427387903 4611686018427387903
loop(\(x,i).((26x + 1) + i),x,1)
A229463: 1 28 731 19010 494265 12850896 334123303 8687205886 225867353045 5872551179180 152686330658691 3969844597125978 103215959525275441 2683614947657161480 4611686018427387903 4611686018427387903
loop(\(x,i).(x - (~11x div (1 + i))),x,1)
A215054: 1 7 33 124 397 1125 2893 6871 15269 32065 64130 122916 226922 405218 702378 1185263
loop(\(x,i).((8x * (~1 + (2 * i))) div (1 + i)),x,1)
A151403: 1 4 32 320 3584 43008 540672 7028736 93716480 1274544128 17611882496 246566354944 3489862254592 49855175065600 717914520944640 10409760553697280
loop(\(x,i).((4x * (1 + (2 * (i div 2)))) div (1 + i)),x,1)
A060899: 1 2 8 24 96 320 1280 4480 17920 64512 258048 946176 3784704 14057472 56229888 210862080
loop(\(x,i).((22x + 1) + i),x,1)
A014907: 1 24 531 11686 257097 5656140 124435087 2737571922 60226582293 1324984810456 29149665830043 641292648260958 14108438261741089 310385641758303972 4611686018427387903 4611686018427387903
loop(\(x,i).(x - ((~10x + 1) div (1 + i))),x,1)
A032169: 1 6 26 91 273 728 1768 3978 8398 16796 32065 58786 104006 178296 297160 482885
loop(\(x,i).((x + 1) + ((4x div (1 + i)) + i + i)),x,1)
A005712: 1 6 19 45 90 161 266 414 615 880 1221 1651 2184 2835 3620 4556
(1 + loop(\(x,i).(x div (1 + (x mod (1 + (x mod 6))))),2,x))
A214685-A165725: 1 1 1 1 1 1 7 1 1 1 11 1 13 7 1 1
loop(\(x,i).(2 * (~1 + (5 * ((x + ~1) + (x mod 2))))),x,1)
A073555: 1 8 68 668 6668 66668 666668 6666668 66666668 666666668 6666666668 66666666668 666666666668 6666666666668 66666666666668 666666666666668
loop(\(x,i).(3x mod 22),x,1)
A070355: 1 3 9 5 15 1 3 9 5 15 1 3 9 5 15 1
(1 + loop(\(x,i).((x div 2) div (1 + (x mod (2 * (1 + (x mod 2)))))),2,x))
A110963: 1 1 1 1 2 1 1 1 3 2 2 1 4 1 1 1
loop(\(x,i).(3x mod 34),x,1)
A070359: 1 3 9 27 13 5 15 11 33 31 25 7 21 29 19 23
loop(\(x,i).(2 * (1 + (x mod 5) - (2 * (i mod 2)))),x,1)
A091085: 1 0 2 2 6 0 2 2 6 0 2 2 6 0 2 2
(1 + loop(\(x,i).(x + 6),(~2 + ((x + ~1) div 3)),x))
A032979: 1 2 3 4 5 6 7 8 9 10 17 18 19 26 27 28
(1 + loop(\(x,i).((2 * (x + ((x div 3) mod 2))) div 3),2,x))
A003160: 1 1 1 2 3 4 4 4 5 5 5 6 6 6 7 8
(1 + loop(\(x,i).(x - (x div 9)),6,x))
A285762: 1 2 3 4 5 6 7 8 9 9 9 9 9 9 9 10
loop(\(x,i).(9x + ((x div 3) mod 2)),x,1)
A033127: 1 9 82 739 6651 59860 538741 4848669 43638022 392742199 3534679791 31812118120 286309063081 2576781567729 23191034109562 208719306986059
loop(\(x,i).(2 * (9x div (1 + (x mod 2)))),x,1)
A067421: 1 8 144 2592 46656 839808 15116544 272097792 4897760256 88159684608 1586874322944 28563737812992 514147280633856 9254651051409408 166583718925369344 2998506940656648192
(19 * loop(\(x,i).(2x + 2),x,1))
A304513: 19 76 190 418 874 1786 3610 7258 14554 29146 58330 116698 233434 466906 933850 1867738
loop(\(x,i).(2 * ((2x * (i * (~1 + (2 * i)))) div (1 + i))),x,1)
A152029: 1 2 16 240 5376 161280 6082560 276756480 14760345600 903333150720 62412108595200 4805732361830400 408117579035443200 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (16x - (x div ~2))),x,1)
A170753-A170715-A170667-A170619-A170571-A170523-A170475-A170427-A170379-A170331-A170283-A170235-A170187-A170139-A170091-A170043-A169575-A169527-A169479-A169431-A169383-A169335-A169287-A169239-A169191-A169143-A169095-A169047-A168999-A168951-A168903-A168855-A168807-A168759-A168711-A167950-A167785-A167396-A167087: 1 34 1122 37026 1221858 40321314 1330603362 43909910946 1449027061218 47817893020194 1577990469666402 52073685498991266 1718431621466711778 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).((x + 2) - ((~x + 2) div (2 - (x div ~2)))),2,x))
A224778: 2 5 6 8 9 10 11 13 14 15 17 18 19 20 21 22
loop(\(x,i).(2 * (10x - (x div ~2))),x,1)
A170741-A170703-A170655-A170607-A170559-A170511-A170463-A170415-A170367-A170319-A170271-A170223-A170175-A170127-A170079-A170031-A169563-A169515-A169467-A169419-A169371-A169323-A169275-A169227-A169179-A169131-A169083-A169035-A168987-A168939-A168891-A168843-A168795-A168747-A168699-A167935-A167693: 1 22 462 9702 203742 4278582 89850222 1886854662 39623947902 832102905942 17474161024782 366957381520422 7706105011928862 161828205250506102 3398392310260628142 4611686018427387903
loop(\(x,i).(10x + ((x div ~2) mod 2)),x,1)
A033137: 1 11 110 1101 11011 110110 1101101 11011011 110110110 1101101101 11011011011 110110110110 1101101101101 11011011011011 110110110110110 1101101101101101
((x + 1) + (x div (2 + (if ((x div 3) mod 3) <= 0 then 1 else 2))))
A087919: 1 2 3 4 6 7 8 9 11 13 14 15 16 17 18 19
loop(\(x,i).(3x mod 28),x,1)
A070357: 1 3 9 27 25 19 1 3 9 27 25 19 1 3 9 27
loop(\(x,i).(x - (x div (1 - (2 * (2 + (x mod 5)))))),x,1)
A271317: 1 2 3 4 5 7 8 9 10 14 16 20
loop(\(x,i).(x - (((3 * (x div ~4)) div 2) div 2)),x,1)
A304632: 1 2 3 4 5 7 9 12 15 18 22 27 33 40 48 57
((x + 1) + (if (x + ~2) <= 0 then 1 else (4 + ((x div 2) div 3))))
A288860: 2 3 4 8 9 10 12 13 14 15 16 17 19 20 21 22
loop(\(x,i).(x - (((0 - ((x + 1) * (x + (x div 2)))) div 2) div 2)),x,1)
A309115: 1 2 5 16
A037075: 1 2 5 16 118
loop(\(x,i).(10x + (((x + ~1) div 2) mod 2)),x,1)
A033146: 1 10 100 1001 10010 100100 1001001 10010010 100100100 1001001001 10010010010 100100100100 1001001001001 10010010010010 100100100100100 1001001001001001
(1 + loop(\(x,i).((~2x + 2) mod (2 - (x div ~4))),2,x))
A105103-A103684: 1 1 1 2 1 1 2 1 2 1 2 1 3 1 1 2
loop(\(x,i).(2 * (2 + ((2x + 2) mod (2 - (x div ~2))))),x,1)
A272966: 1 6 12 8 4 8 4 8
((x + 1) + (2 * (((x - (if (~2 + (x div 2)) <= 0 then x else 1)) div 2) div 2)))
A032975: 1 2 3 4 5 6 9 10 11 14 15 16 17 20 21 22
loop(\(x,i).(2 * (x - ((x2 div (4 + (x div 2))) mod 2))),x,1)
A222011: 1 2 4 8
A164203: 1 2 4 8 16 30 58 114 226 452 904 1808 3616 7232 14464 28928
(1 + loop(\(x,i).i,(((2x + 1) mod (2 + (x div 4))) div 2),x))
A304181: 1 2 3 4 5 2 7 8 9 2 11 2 13 2 3 16
((x + 1) + (if (x + ~1) <= 0 then x else (2 + ((x - ((x div 2) mod 2)) div 2))))
A085621: 1 3 5 7 9 10 11 13 15 16 17 19
(9 mod (if ((x + 1) mod 8) <= 0 then x else 1))
A088806: 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 9
(if (x + ~12) <= 0 then x else (x + 9))
A103303: 0 1 2 3 4 5 6 7 8 9
A023766: 0 1 2 3 4 5 6 7 8 9 10 11 12 22 23 24
(1 + loop(\(x,i).(x + 9),(x + ~8),x))
A092596: 1 2 3 4 5 6 7 8 9 19
A190876-A088473: 1 2 3 4 5 6 7 8 9 19 29 39 49 59 69 79
(1 + loop(\(x,i).(x + 10),(x + ~8),x))
A290951: 1 2 3 4 5 6 7 8 9 20 31 42 53 64 75 86
((x + ~1) + (2 * (if (~4 + (x div 2)) <= 0 then 1 else (x div 4))))
A194403: 1 2 3 4 5 6 7 8 9 10 13 14 17 18 19 20
((x + ~1) + (if (~4 + (x div 2)) <= 0 then 1 else (2 * (x div 4))))
A103303: 0 1 2 3 4 5 6 7 8 9
A055568: 0 1 2 3 4 5 6 7 8 9 13 14 17
(5 mod (if ((x + ~1) mod (2 + (x mod 4))) <= 0 then x else 1))
A199092: 0 0 0 0 0 0 0 0 0 0 0 5 0 5 0 0
(1 + loop(\(x,i).(x + 1),(~4 + ((x + ((x div 2) mod 2)) div 2)),x))
A178863-A178862-A178861-A178860-A178858-A176526-A161466-A117296-A100952-A096503-A079333-A070331-A063938-A055238-A002473: 1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20
loop(\(x,i).((8x + 1) + ((i mod 3) div 2)),x,1)
A037533: 1 9 74 593 4745 37962 303697 2429577 19436618 155492945 1243943561 9951548490 79612387921 636899103369 5095192826954 40761542615633
loop(\(x,i).(8x + ((~1 + (i mod 3)) mod 2)),x,1)
A033126: 1 8 65 521 4168 33345 266761 2134088 17072705 136581641 1092653128 8741225025 69929800201 559438401608 4475507212865 35804057702921
loop(\(x,i).(8x + (((x + ~1) div 2) mod 4)),x,1)
A037594: 1 8 67 537 4296 34371 274969 2199752 17598019 140784153 1126273224 9010185795 72081486361 576651890888 4613215127107 36905721016857
((x + 1) + (2 * (((if (~2 + (x div 2)) <= 0 then 1 else 2) + (x div 2)) div 2)))
A137708: 1 2 5 6 7 8 11 12 15 16 17 18 21 22 23 24
loop(\(x,i).((10x + 2) - ((x div 2) mod 2)),x,1)
A037551: 1 12 122 1221 12212 122122 1221221 12212212 122122122 1221221221 12212212212 122122122122 1221221221221 12212212212212 122122122122122 1221221221221221
loop(\(x,i).(4 * ((2x * (1 + (2 * i))) div (2 + i))),x,1)
A269796: 1 8 80 896 10752 135168 1757184 23429120 318636032 4402970624 61641588736 872465563648 12463793766400 179478630236160 2602440138424320 37965009078190080
((x mod 10) mod (if ((x + 1) mod 4) <= 0 then x else 1))
A090750: 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 5
loop(\(x,i).(9x + ((1 + i) mod 4)),x,1)
A037700: 1 11 102 918 8263 74369 669324 6023916 54215245 487937207 4391434866 39522913794 355706224147 3201356017325 28812204155928 259309837403352
loop(\(x,i).(10x + ((1 + i) mod 4)),x,1)
A037701: 1 12 123 1230 12301 123012 1230123 12301230 123012301 1230123012 12301230123 123012301230 1230123012301 12301230123012 123012301230123 1230123012301230
loop(\(x,i).(7x + ((1 + i) mod 4)),x,1)
A037698: 1 9 66 462 3235 22647 158532 1109724 7768069 54376485 380635398 2664447786 18651134503 130557941523 913905590664 6397339134648
loop(\(x,i).(10x + ((~x + 1) mod 4)),x,1)
A037687: 1 10 103 1032 10321 103210 1032103 10321032 103210321 1032103210 10321032103 103210321032 1032103210321 10321032103210 103210321032103 1032103210321032
loop(\(x,i).((5 * (x mod 4)) + (x div 4)),x,1)
A070373: 1 5 6 11 17 9 7 16 4 1 5 6 11 17 9 7
loop(\(x,i).(7x + ((1 - i) mod 4)),x,1)
A037684: 1 7 52 366 2563 17941 125590 879132 6153925 43077475 301542328 2110796298 14775574087 103429018609 724003130266 5068021911864
loop(\(x,i).(2x + 100),x,1)
A140062: 1 102 304 708 1516 3132 6364 12828 25756 51612 103324 206748 413596 827292 1654684 3309468
((x + ~1) + (2 * (x - (((x div 4) - (if x <= 0 then 1 else x)) div 2))))
A085048: 1 4 7 12 15 18 23
A276880: 1 4 7 12 15 18 23 26 29 34 37 42 45 48 53 56
loop(\(x,i).(2 * (x - ((x div (~x + 16)) mod 2))),x,1)
A222011: 1 2 4 8
A164161: 1 2 4 8 14 26 50 100 200 400 800 1600 3200 6400 12800 25600
loop(\(x,i).(5x + ((x div 5) mod 2)),x,1)
A033123: 1 5 26 131 655 3276 16381 81905 409526 2047631 10238155 51190776 255953881 1279769405 6398847026 31994235131
loop(\(x,i).(5x + (((2 + i) * (1 + i)) div 2)),x,1)
A052244: 1 8 46 240 1215 6096 30508 152576 762925 3814680 19073466 95367408 476837131 2384185760 11920928920 59604644736
loop(\(x,i).(2 * (20x - (x div 2))),x,1)
A170721-A170673-A170625-A170577-A170529-A170481-A170433-A170385-A170337-A170289-A170241-A170193-A170145-A170097-A170049-A170001-A169533-A169485-A169437-A169389-A169341-A169293-A169245-A169197-A169149-A169101-A169053-A169005-A168957-A168909-A168861-A168813-A168765-A168717-A167956-A167829-A167538-A167093-A166693: 1 40 1560 60840 2372760 92537640 3608967960 140749750440 5489240267160 214080370419240 8349134446350360 325616243407664040 4611686018427387903 4611686018427387903 4611686018427387903
A170759-A063820: 1 40 1560 60840 2372760 92537640 3608967960 140749750440 5489240267160 214080370419240 8349134446350360 325616243407664040 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (15x - (x div 2))),x,1)
A170749-A170711-A170663-A170615-A170567-A170519-A170471-A170423-A170375-A170327-A170279-A170231-A170183-A170135-A170087-A170039-A169571-A169523-A169475-A169427-A169379-A169331-A169283-A169235-A169187-A169139-A169091-A169043-A168995-A168947-A168899-A168851-A168803-A168755-A168707-A167945-A167715-A167370-A167083: 1 30 870 25230 731670 21218430 615334470 17844699630 517496289270 15007392388830 435214379276070 12621216999006030 366015292971174870 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (18x - (x div 2))),x,1)
A170755-A170717-A170669-A170621-A170573-A170525-A170477-A170429-A170381-A170333-A170285-A170237-A170189-A170141-A170093-A170045-A169577-A169529-A169481-A169433-A169385-A169337-A169289-A169241-A169193-A169145-A169097-A169049-A169001-A168953-A168905-A168857-A168809-A168761-A168713-A167952-A167815-A167429-A167089-A063819: 1 36 1260 44100 1543500 54022500 1890787500 66177562500 2316214687500 81067514062500 2837362992187500 99307704726562500 3475769665429687500 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (24x - (x div 2))),x,1)
A170729-A170681-A170633-A170585-A170537-A170489-A170441-A170393-A170345-A170297-A170249-A170201-A170153-A170105-A170057-A170009-A169541-A169493-A169445-A169397-A169349-A169301-A169253-A169205-A169157-A169109-A169061-A169013-A168965-A168917-A168869-A168821-A168773-A168725-A167980-A167863-A167645-A167101-A166854: 1 48 2256 106032 4983504 234224688 11008560336 517402335792 24317909782224 1142941759764528 53718262708932816 2524758347319842352 4611686018427387903 4611686018427387903 4611686018427387903
A170767-A063822: 1 48 2256 106032 4983504 234224688 11008560336 517402335792 24317909782224 1142941759764528 53718262708932816 2524758347319842352 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * ((2 * ((x + 1) - (2 * (i mod 2)))) + (x div 2))),x,1)
A123010: 1 0 4 16 84 416 2084 10416 52084 260416 1302084 6510416 32552084 162760416 813802084 4069010416
loop(\(x,i).(2 * (14x - (x div 2))),x,1)
A170747-A170709-A170661-A170613-A170565-A170517-A170469-A170421-A170373-A170325-A170277-A170229-A170181-A170133-A170085-A170037-A169569-A169521-A169473-A169425-A169377-A169329-A169281-A169233-A169185-A169137-A169089-A169041-A168993-A168945-A168897-A168849-A168801-A168753-A168705-A167943-A167699-A167235-A063817: 1 28 756 20412 551124 14880348 401769396 10847773692 292889889684 7908027021468 213516729579636 5764951698650172 155653695863554644 4202649788315975388 4611686018427387903 4611686018427387903
loop(\(x,i).(49x + ~2),x,1)
A327770: 1 47 2301 112747 5524601 270705447 13264566901 649963778147 31848225129201 1560563031330847 76467588535211501 3746911838225363547 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x - ((~x + ((x div 2) div 7)) div 2)),x,1)
A077868: 1 2 3 5 8 12 18 27 40 59 87 128 188 276 405 594
(1 - (x mod ((~x + ~1) + ((if (~4 + (x div 2)) <= 0 then 1 else x) div 2))))
A300358: 1 2 2 2 2 2 2 2 2 2 3 4 3 4 3 4
(2 - loop(\(x,i).(x - ((2 - (x * ((x + ~1) mod 3))) div 2)),x,1))
A140298: 1 2 3 4 5 9 13 14 27 40 41 81 121 122 243 364
(1 + loop(\(x,i).(x + (2 div (6 - (x div 3)))),2,x))
A238368: 1 2 3 4 5 6 7 8 9 10 11 12 15 16 18 20
loop(\(x,i).(2 * (~x + ((x + 1) * (x + (x2 div (x + 2)))))),x,1)
A060599: 1 2 14 752
(1 + loop(\(x,i).(x + (8x div (x2 + 1))),2,x))
A003880: 1 7 7 7 7 8 9 9 9
(1 + loop(\(x,i).(x + ((x mod (1 + ((~x + 2) mod 4))) div 2)),2,x))
A067535: 1 2 3 5 5 6 7 10 10 10 11 13 13 14 15 17
loop(\(x,i).(2x * (2 + (3 * (x mod 6)))),x,1)
A067427: 1 10 280 7840 219520 6146560 172103680 4818903040 134929285120 3778019983360 105784559534080 2961967666954240 82935094674718720 2322182650892124160 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 2) + i - ((~x + 1) div (2 + (x div 3)))),x,1)
A004120: 1 4 9 16 25 35 46 58 71 85 100 116 133 151 170 190
((x + ~1) + (if (x + ~2) <= 0 then 2 else (x2 div (x - ((~x + 2) div 2)))))
A171511: 1 2 3 4 6 7 9 10 12 14 16 17 19 20 22 24
((~x + ~1) + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,2))
A132788: 1 2 7 24 79 258 851 2852 9715 33582 117561 416012 1485787 5348866 19389675 70715324
(1 + compr(\x.(x - (loop(\(x,i).(~2x + 1),x,3) mod (x + 2))),x))
A094859: 1 2 3 4 6 10
A068499: 1 2 3 4 6 10 12 16 18 22 28 30 36 40 42 46
(1 + compr(\x.((x + 1) mod (loop(\(x,i).(2x + 2),x,1) mod (x + 2))),x))
A241071: 1 2 4 6 8 10 12
A114871: 1 2 4 6 8 10 12 16 18 20 22 28 30 32 36 40
loop(\(x,i).((2x + 1) * (x - ((1 + i) * i))),(x2 + 2x),1)
A090162: 1 3003 4611686018427387903
((x2 + 2x + 1) * loop(\(x,i).(x * (3 + i)),x,(x + 1)))
A154306: 1 32 540 7680 105000 1451520 20744640 309657600 4849891200 79833600000 1381360780800 25107347865600 478826764416000 9568689242112000 200074178304000000 4370687116443648000
((x2 + 2x + 1) * loop(\(x,i).4x,(x + 1),(x + 2)))
A129004: 8 192 2304 20480 153600 1032192 6422528 37748736 212336640 1153433600 6090129408 31406948352 158779572224 789200240640 3865470566400 18691697672192
((x2 + 2x + 1) * loop(\(x,i).3x,(x + 1),(x + 2)))
A129003: 6 108 972 6480 36450 183708 857304 3779136 15943230 64953900 257217444 994857552 3772168218 14061928860 51656065200 187339329792
((x2 + 2x + 1) * loop(\(x,i).6x,(x + 1),x))
A128989: 0 144 3888 62208 777600 8398080 82301184 752467968 6530347008 54419558400 438984437760 3448023220224 26487087464448 199671890116608 1481082701414400 10833062044631040
((x2 + 2x + 1) * loop(\(x,i).8x,(x + 1),x))
A128991: 0 256 9216 196608 3276800 47185920 616562688 7516192768 86973087744 966367641600 10393820856320 108851651149824 1114904790564864 11206222510292992 110830772079820800 1080863910568919040
((x2 + 2x + 1) * loop(\(x,i).5x,(x + 1),x))
A128988: 0 100 2250 30000 312500 2812500 22968750 175000000 1265625000 8789062500 59082031250 386718750000 2475585937500 15551757812500 96130371093750 585937500000000
(1 + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + ~2),x))
A306666: 1 2 3 7 21
A323230: 1 2 3 7 21 71 253 925 3433 12871 48621 184757 705433 2704157 10400601 40116601
loop(\(x,i).(2x + (5x * (1 + (2 * i)))),x,1)
A035276: 1 17 459 16983 798201 45497457 3048329619 234721380663 20420760117681 1980813731415057 211947069261411099 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x + (((~x + 1) div (1 + (x mod 4))) mod 2)),x,1)
A172411: 1 2 5 10
A267515: 1 2 5 10 21 42 84 169 338 677 1354 2709 5418 10836 21673 43346
(1 + (if (~1 + (x mod (1 + ((~x + 2) mod 4)))) <= 0 then (x mod 2) else x))
A100762: 1 2 1 4 1 2 1 8 9 2 1 12 1 2 1 16
loop(\(x,i).(10x + (i mod (2 - (x mod 2)))),x,1)
A266071: 1 10 100 1001 10010 100101 1001010 10010101 100101010 1001010101 10010101010 100101010101 1001010101010 10010101010101 100101010101010 1001010101010101
loop(\(x,i).(30x2 + x),x,1)
A176349: 1 31 28861 24988748491 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 2) + (13 * (i * i))),x,1)
A063493: 1 16 70 189 399 726 1196 1835 2669 3724 5026 6601 8475 10674 13224 16151
loop(\(x,i).((x + 2) + (11 * (i * i))),x,1)
A063492: 1 14 60 161 339 616 1014 1555 2261 3154 4256 5589 7175 9036 11194 13671
loop(\(x,i).((6x * (~1 + (2 * i))) div (2 + i)),x,1)
A000168: 1 2 9 54 378 2916 24057 208494 1876446 17399772 165297834 1602117468 15792300756 157923007560 1598970451545 16365932856990
loop(\(x,i).((3 * (x + (3x * i))) div (2 + i)),x,1)
A185047: 1 4 21 126 819 5616 40014 293436 2200770 16805880 130245570 1021926780 8102419470 64819355760 522606055815 4242331511910
loop(\(x,i).(x + (4x div (2 + i)) - (x div (1 + i))),x,1)
A231408: 1 2 4 6 9
A001304: 1 2 4 6 9 13 18 24 31 39 49 60 73 87 103 121
((if (x mod 6) <= 0 then 12 else 0) div (x + 1))
A236238: 12 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
((x + 1) * loop(\(x,i).(x + ((i * i * (1 + i)) div 2)),(x + 1),0))
A108650: 1 14 75 260 700 1596 3234 6000 10395 17050 26741 40404 59150 84280 117300 159936
((x + 1) * loop(\(x,i).(1 + (x * (1 + i)) - (2 * (x mod 2))),x,0))
A086325: 0 2 6 36 220 1590 12978 118664 1201464 13349610 161530270 2114578092 29780308116 448995414686 7215997736010 123153028027920
(loop(\(x,i).(2 * ((2x + 2) - (x div (1 + i)))),x,0) mod (x + 1))
A246130: 0 0 0 0 0 4 0 4 0 4 0 2 0 4 13 4
((x + 1) + loop(\(x,i).(6x + ((i mod 2) * i)),x,0))
A154606: 1 3 9 43 239
((x + 1) * (1 + (if (16 mod (x + 1)) <= 0 then 2 else 0)))
A275535: 3 6 3 12 5 6 7 24 9 10 11 12 13 14 15 48
((1 + (if (x mod (2 + (x div 2))) <= 0 then 8 else 0)) div (x + 1))
A223082: 9 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0
((~1 + loop(\(x,i).10x,(x + 1),1)) div (x + 1))
A066558: 9 49 333 2499 19999 166666 1428571 12499999 111111111 999999999 9090909090 83333333333 769230769230 7142857142857 66666666666666 624999999999999
(1 - ((1 + loop(\(x,i).(x * (i * i)),((x + 1) div 2),1)) mod (x + 1)))
A267133: 1 1 ~1 0 1 0 ~1 0 0 0 ~1 0 1 0 0 0
((1 - (x mod (1 + (x div (if (x mod 2) <= 0 then 4 else 1))))) div (x + 1))
A114591: 1 0 0 ~1 0 ~1 0 ~1 ~1 ~1 0 ~1 0 ~1 ~1 ~1
((~1 + ((2 + (if (~x + 2) <= 0 then x else 0)) mod 5)) div (x + 1))
A185295: 1 0 1 ~1 0 0 0 0 ~1 0 0 0 0 ~1 0 0
(if (x - (5 * (((x + ~1) div 2) div 2))) <= 0 then 1 else (x + 1))
A241479: 1 2 3 4 5 1 7 8 9 1 1 12 13 1 1 1
(loop(\(x,i).(x * i),x,(~1 + ((~x + 2) div 5))) mod (x + 1))
A062590: 0 1 1 0 2 0 2 0 0 0 3 0 3 0 0 0
(loop(\(x,i).10x2,3,1) div (x + 1))
A033425: 10000000 5000000 3333333 2500000 2000000 1666666 1428571 1250000 1111111 1000000 909090 833333 769230 714285 666666 625000
(loop(\(x,i).(2 * i),((x + 1) mod 12),1) mod (x + 1))
A292994: 0 0 0 0 0 0 0 0 0 0 0 1 2 4 6 8
(loop(\(x,i).7x2,3,1) div (x + 1))
A057069: 823543 411771 274514 205885 164708 137257 117649 102942 91504 82354 74867 68628 63349 58824 54902 51471
((1 + ((2x + 1) * loop(\(x,i).((x + 1) * i),x,0))) div (x + 1))
A006373: 1 2 7 26 115 596
((x + 1) * (1 + (if (x + ~12) <= 0 then (x mod 2) else 1)))
A082895: 1 4 3 8 5 12 7 16 9 20 11 24 13 28 30 32
((x + 1) * (1 + ((if x <= 0 then 0 else 9) div (x + 1))))
A317180-A187285: 1 10 12 12 10 12 14 16 18 10 11 12 13 14 15 16
((x + 1) * (1 + ((x + 1) * loop(\(x,i).x2,2,5))))
A031728: 626 2502 5628 10004 15630 22506 30632 40008 50634 62510 75636 90012 105638 122514 140640 160016
((x + 1) * (1 + ((x + 1) * loop(\(x,i).(x2 + 4x + 4),2,1))))
A173267-A031700: 122 486 1092 1940 3030 4362 5936 7752 9810 12110 14652 17436 20462 23730 27240 30992
((x + 1) * (1 + ((x + 1) * loop(\(x,i).x2,2,6))))
A031750: 1297 5186 11667 20740 32405 46662 63511 82952 104985 129610 156827 186636 219037 254030 291615 331792
((x + 1) * (1 + ((x + 1) * loop(\(x,i).4x2,2,2))))
A031742: 1025 4098 9219 16388 25605 36870 50183 65544 82953 102410 123915 147468 173069 200718 230415 262160
((x + 1) * (1 + ((x + 1) * loop(\(x,i).(x2 + 4x + 4),2,2))))
A031714: 325 1298 2919 5188 8105 11670 15883 20744 26253 32410 39215 46668 54769 63518 72915 82960
((x + 1) * (1 + ((x + 1) * loop(\(x,i).((x + 2) * (x + i)),2,2))))
A031706: 197 786 1767 3140 4905 7062 9611 12552 15885 19610 23727 28236 33137 38430 44115 50192
((x + 1) * (~1 + ((x + 1) * loop(\(x,i).((x + 2) * (x + i)),2,2))))
A158003: 195 782 1761 3132 4895 7050 9597 12536 15867 19590 23705 28212 33111 38402 44085 50160
(loop(\(x,i).13x,(x + 1),1) mod (x + 1))
A116609: 0 1 1 1 3 1 6 1 1 9 2 1 0 1 7 1
(loop(\(x,i).11x,(x + 1),1) mod (x + 1))
A066441: 0 1 2 1 1 1 4 1 8 1 0 1 11 9 11 1
(loop(\(x,i).i,((x + ~2) mod (2 + (x div 5))),1) mod (x + 1))
A225485: 0 1 1 1 1 1 1 2 1 1 1 1 2 3 1 3
((x + 1) * (if (x mod (3 * (1 + (x div 4)))) <= 0 then 2 else 1))
A205374: 2 2 3 8 5 6 14 8 9 20 11 12 26 14 15 16
((if ((x + 1) mod 5) <= 0 then 6 else 1) mod (x + 1))
A293901: 0 1 1 1 1 1 1 1 1 6 1 1 1 1 6 1
((1 + loop(\(x,i).(x2 div (1 + i)),2,(2x + 2))) div (x + 1))
A184538: 2 11 36 85 166 288 457 682 972 1333 1774 2304 2929 3658 4500 5461
(loop(\(x,i).(x * (1 + i)),2x,(2x + 3)) div (x + 1))
A138896: 3 15 280 11340 798336 86486400 13343616000 2778808032000 750895681536000 255454710858547200 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) * (3 - ((loop(\(x,i).(x * i),x,x) mod (x + 1)) mod 2)))
A175029: 3 4 6 12 10 18 14 24 27 30 22 36 26 42 45 48
compr(\x.(x mod (1 + (4 * (if (x mod 4) <= 0 then 0 else 2)))),(x + 1))
A053443: 4 8 9 12 16 18 20 24 27 28 32 36 40 44 45 48
(1 - ((if ((x div (2 + (x mod 2))) mod 4) <= 0 then 2 else 1) mod (x + 1)))
A204220: 1 1 0 0 0 0 0 0 ~1 0 0 0 0 ~1 0 0
loop(\(x,i).~x,x,(1 - ((1 + (x mod 8)) mod (x + 1))))
A323633: 1 ~1 1 ~1 1 ~1 1 ~1 0 1 ~2 3 ~4 5 ~6 7
((x + 1) * (if (x mod (8 - ((x div 2) mod 2))) <= 0 then 2 else 1))
A141286: 2 2 3 4 5 6 7 16 18 10 11 12 13 14 30 16
(loop(\(x,i).x5,1,5) div (x + 1))
A057067: 3125 1562 1041 781 625 520 446 390 347 312 284 260 240 223 208 195
(loop(\(x,i).x5,1,5) mod (x + 1))
A245972: 0 1 2 1 0 5 3 5 2 5 1 5 5 3 5 5
(loop(\(x,i).(2x2 * (x div 2)),2,5) div (x + 1))
A033426: 1000000 500000 333333 250000 200000 166666 142857 125000 111111 100000 90909 83333 76923 71428 66666 62500
loop(\(x,i).(2x + 1),(x + 1),(x2 + 6x + 5))
A107464: 11 51 175 527 1471 3903 9983 24831 60415 144383 339967 790527 1818623 4145151 9371647 21037055
(loop(\(x,i).(x * i),x,(~1 + ((~x + 1) div (2 + (x div 2))))) mod (x + 1))
A029832: 0 1 2 0 2 0 2 0 0 0 3 0 3 0 0 0
(loop(\(x,i).x2,1,((x2 + ~x + ~1) div 3)) mod (x + 1))
A226787: 0 1 0 1 4 0 4 1 0 9 5 0 3 11 0 9
((x + 1) + loop(\(x,i).x2,2,(3 * (x div 8))))
A109752: 1 2 3 4 5 6 7 8 90
A028430: 1 2 3 4 5 6 7 8 90 91 92 93 94 95 96 97
((6 * loop(\(x,i).(2x + 4),x,4)) div (x + 1))
A003176: 24 36 56 90 148 252 435 765 1362 2455 4466 8190 15121 28085 52427 98302
((~1 + loop(\(x,i).(i - (2 * (~x + (x div 3)))),x,2)) div (x + 1))
A076970: 1 2 3 4 5 7 9 11 14 18 23 29 37 47 59 75
(loop(\(x,i).(2x * (1 + (2 * (i div 2)))),2x,1) div (x + 1))
A052510: 1 6 240 25200 5080320 1676505600 821966745600 560992303872000 508633022177280000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x + i - ((~x + 2) div 5)),x,1) div (x + 1))
A008674: 1 1 1 2 2 3 4 5 6 8 10 11 14 16 19 23
((x + 1) * (1 + (x * (1 + loop(\(x,i).x2,(~2x + 4),2)))))
A074155: 1 36 21 40 65 96 133 176 225 280 341 408 481 560 645 736
((~x + ~1) + loop(\(x,i).(x + i - (x div (1 + (4 * i)))),x,1))
A033440: 0 0 1 3 6 10 15 21 28 35 43 52 62 73 85 98
(loop(\(x,i).(x + (x div 3) - (i div ~2)),x,1) div (x + 1))
A129528: 1 1 1 1 2 2 3 4 5 7 9 11 15 19 24 30
(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1) mod (x + 1))
A099905: 0 1 1 3 1 0 1 3 1 8 1 2 1 10 0 3
(loop(\(x,i).((x + 1) + (2 * ((x div 2) div 3))),x,1) div (x + 1))
A146930: 1 1 1 1 1 1 1 1 1 2 2 3 3 4 6 7
((x + 1) * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x)))
A164931: 1 4 9 20 35 66 91 136 171 230 319 372 481 574 645 752
((x + 1) * ((x + ~1) + loop(\(x,i).(x * (2 + i)),4,(x + 1))))
A158307: 359 1440 3243 5768 9015 12984 17675 23088 29223 36080 43659 51960 60983 70728 81195 92384
((x + 1) * (~1 + loop(\(x,i).(3x + 2),6,x)))
A158394: 727 2912 6555 11656 18215 26232 35707 46640 59031 72880 88187 104952 123175 142856 163995 186592
((x + 1) + loop(\(x,i).(x - (x mod (1 + (2 * i)))),3,(x + 1)))
A032980: 1 2 3 4 5 6 7 8 9 10 11 19 20 21 29 30
loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x + 1),(x + 1))
A000917: 3 20 105 504 2310 10296 45045 194480 831402 3527160 14872858 62403600 260757900 1085822640 4508102925 18668849760
((x + 1) * (x - ((x + 1) * loop(\(x,i).(~x2 + 1),2,4))))
A156813: 224 898 2022 3596 5620 8094 11018 14392 18216 22490 27214 32388 38012 44086 50610 57584
((x + 1) * (x - ((x + 1) * loop(\(x,i).(x * (~x + i)),2,4))))
A157998: 168 674 1518 2700 4220 6078 8274 10808 13680 16890 20438 24324 28548 33110 38010 43248
loop(\(x,i).(x3 div 2),1,(4x2 + 8x + 4))
A291826: 32 2048 23328 131072 500000 1492992 3764768 8388608 17006112 32000000 56689952 95551488 154457888 240945152 364500000 536870912
loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x + ~1),(x + 1))
A097070: 1 2 9 40 175 756 3234 13728 57915 243100 1016158 4232592 17577014 72804200 300874500 1240940160
((x + 1) * ((2x + 1) - loop(\(x,i).(x div (1 + (x mod 2))),x,x)))
A091519: 1 6 9 28 25 54 49 120 81 150 121 252 169 294 225 496
(loop(\(x,i).(x + (12 mod (1 + i))),x,1) div (x + 1))
A017853: 1 0 0 0 0 0 1 1 1 1 1 1 2 3 3 4
((x + 1) * (if (x + ~2) <= 0 then 1 else (x5 + x3)))
A228127: 1 2 3 1080
((2x + 2) * (~1 + ((x + 1) * loop(\(x,i).x3,2,2))))
A158420: 1022 4092 9210 16376 25590 36852 50162 65520 82926 102380 123882 147432 173030 200676 230370 262112
((x + 1) * (if (~2 + (x mod (1 + (2 * (x mod 3))))) <= 0 then 1 else 2))
A066759: 1 2 3 4 5 6 7 8 18 10 11 12 13 14 30 16
(((x mod 2) - (2 * (if ((x div 2) mod 3) <= 0 then 2 else 1))) mod (x + 1))
A033558: 0 1 1 3 3 5 3 5 7 9 9 11 9 11 13 15
(loop(\(x,i).(x2 + x),4,10) mod (x + 1))
A173956: 0 0 0 2 0 0 0 2 6 0 0 6 0 0 0 10
((x + 1) * (if (x + ~1) <= 0 then x else (2 + ((2 * (x div 2)) div 3))))
A128913: 0 2 6 8 15 18 28 32 36 40 55 60 78 84 90 96
(loop(\(x,i).(x2 + (x div 2)),3,6) mod (x + 1))
A345940-A076998: 0 0 0 2 0 0 0 2 6 0 0 6 0 0 0 2
((x + 1) * ((if (x mod 2) <= 0 then 2 else (x2 + 2x)) mod 6))
A087560: 2 6 6 12 10 30 14 24 18 30 22 60 26 42 30 48
((x + 1) * (2 + ((x + 1) * loop(\(x,i).x2,2,5))))
A158382-A031703: 627 2504 5631 10008 15635 22512 30639 40016 50643 62520 75647 90024 105651 122528 140655 160032
((x + 1) * (~2 + ((x + 1) * loop(\(x,i).x2,2,5))))
A158373: 623 2496 5619 9992 15615 22488 30611 39984 50607 62480 75603 89976 105599 122472 140595 159968
((x + 1) * (2 + ((x + 1) * loop(\(x,i).(x2 + 4x + 4),2,1))))
A181679: 123 488 1095 1944 3035 4368 5943 7760 9819 12120 14663 17448 20475 23744 27255 31008
((x + 1) * (~2 + ((x + 1) * loop(\(x,i).(x2 + 4x + 4),2,1))))
A157040: 119 480 1083 1928 3015 4344 5915 7728 9783 12080 14619 17400 20423 23688 27195 30944
((x + 1) * (2 + ((x + 1) * loop(\(x,i).x2,3,3))))
A031759: 6563 26248 59055 104984 164035 236208 321503 419920 531459 656120 793903 944808 1108835 1285984 1476255 1679648
((x + 1) * (2 + loop(\(x,i).12x,2,(x + 1))))
A158132: 146 580 1302 2312 3610 5196 7070 9232 11682 14420 17446 20760 24362 28252 32430 36896
((x + 1) * (~2 + loop(\(x,i).12x,2,(x + 1))))
A158135: 142 572 1290 2296 3590 5172 7042 9200 11646 14380 17402 20712 24310 28196 32370 36832
((x + 1) * (2 + loop(\(x,i).3x,6,(x + 1))))
A158396-A031705: 731 2920 6567 11672 18235 26256 35735 46672 59067 72920 88231 105000 123227 142912 164055 186656
((2 * loop(\(x,i).x2,2,(2x2 + 4x + 2))) div (x + 1))
A291829: 32 4096 69984 524288 2500000 8957952 26353376 67108864 153055008 320000000 623589472 1146617856 2007952544 3373232128 5467500000 8589934592
(loop(\(x,i).(2 * (2x - (x div (1 + i)))),(x + 1),2) div (x + 1))
A024499: 6 10 23 63 184 572 1838 6077 20528 70543 245832 866716 3085892 11079822 40072026 145850388
((x + 1) * (2 + ((x + 1) * loop(\(x,i).(x2 + 2x + 1),2,2))))
A158127: 102 404 906 1608 2510 3612 4914 6416 8118 10020 12122 14424 16926 19628 22530 25632
((x + 1) * (~2 + ((x + 1) * loop(\(x,i).(x2 + 2x + 1),2,2))))
A158129: 98 396 894 1592 2490 3588 4886 6384 8082 9980 12078 14376 16874 19572 22470 25568
((x + 1) * (2 + ((x + 1) * loop(\(x,i).(x2 + 4x + 4),2,2))))
A158271: 326 1300 2922 5192 8110 11676 15890 20752 26262 32420 39226 46680 54782 63532 72930 82976
((x + 1) * (~2 + ((x + 1) * loop(\(x,i).(x2 + 4x + 4),2,2))))
A158305: 322 1292 2910 5176 8090 11652 15862 20720 26226 32380 39182 46632 54730 63476 72870 82912
((x + 1) * (2 + ((x + 1) * loop(\(x,i).((x + 2) * (x + i)),2,2))))
A158222: 198 788 1770 3144 4910 7068 9618 12560 15894 19620 23738 28248 33150 38444 44130 50208
((x + 1) * (~2 + ((x + 1) * loop(\(x,i).((x + 2) * (x + i)),2,2))))
A158224: 194 780 1758 3128 4890 7044 9590 12528 15858 19580 23694 28200 33098 38388 44070 50144
(x2 - (loop(\(x,i).(~x2 + x),2,(2x + 2)) div (x + 1)))
A093033: 6 79 314 807 1654 2951 4794 7279 10502 14559 19546 25559 32694 41047 50714 61791
(x + ((x + 1) * (if x <= 0 then 1 else 2)) - ((x + (x div 2)) div 4))
A022413: 1 5 8 10 13 16 18 21 23 26 29 31 34 37 39 42
(x + (((x + (x div 2)) div 4) + ((x + 1) * (if x <= 0 then 1 else 2))))
A108173: 1 5 8 12 15 18 22 25 29 32 35 39 42 45 49 52
((~x + ~1) + (2 * ((8x + 8) + (if x <= 0 then 1 else 2))))
A013577: 17 34 49 64 79
((x + 1) * ((loop(\(x,i).(x * (x - i)),2,(x + 4)) div 2) div 2))
A054559: 30 180 630 1680 3780 7560 13860 23760 38610 60060 90090 131040 185640 257040 348840 465120
(loop(\(x,i).(2x2 + 7x + 3),4,2) mod (x + 1))
A336563: 0 0 0 2 0 0 0 6 3 0 0 6 0 0 0 14
((x + 1) + loop(\(x,i).(~x + 1),x,(x div (~2 + ((~x + 2) div 4)))))
A097467: 1 4 2 6 3 9 5 11 7 14 8 16 10 18 12 20
((~2 + (2 * loop(\(x,i).((x + 2) * ((2 + i) * i)),x,2))) div (x + 1))
A309146: 2 11 74 854
((if ((x mod (2 + (x mod 3))) div 2) <= 0 then 1 else 4) mod (x + 1))
A333807: 0 1 1 1 1 1 1 1 1 1 1 4 1 1 4 1
loop(\(x,i).(x3 + 3x2 + ~x + ~3),1,(4x + 4))
A133767: 105 693 2145 4845 9177 15525 24273 35805 50505 68757 90945 117453 148665 184965 226737 274365
((4x + 4) + (if ((x + ~1) mod 3) <= 0 then 2x else 1))
A282740: 5 10 13 17 28
((4x + 4) + loop(\(x,i).3x,(x + ~4),2))
A243709: 6 10 14 18 22 30 46
loop(\(x,i).(x + ((((x + 1) div 2) div 2) div 2)),2,(4x + 4))
A190346: 4 10 14 20 24 30 35 40 45 50 55 60 65 71 75 81
((x + 1) + loop(\(x,i).(x3 + 3x),2,(x div 4)))
A173573: 1 2 3 4 81 82 83 84
((x + 1) * (loop(\(x,i).(x * (1 + i)),x,(3x + 2)) div 2))
A138782: 1 10 72 528 4200 36720 352800 3709440 42456960 526176000 7025356800 100590336000 1538074137600 25020169574400 431532541440000 7866968997888000
compr(\x.((loop(\(x,i).(x div (2 - (x mod 2))),x,(~x + 1)) div 2) mod 2),(x + 1))
A060833: 1 4 7 8 12 13 15 16 20 23 24 25 28 29 31 32
(loop(\(x,i).2x,x,1) div ((x + 1) * (2 + ((x2 + ~x) div 2))))
A326471: 0 0 0 0 0 0 0 0 0 1 1 2 4 7 11 19
((if x <= 0 then 2 else (3x2 + 16x + 16)) div (x + 1))
A075683: 2 17 20 22 25 28 31 34 37 40
loop(\(x,i).(2x + (((x + 1) + (x div 4)) div 2)),2,(x + 1))
A101642: 8 13 21 29 34 42 47 55 63 68 76 84 89 97 102 110
((if x <= 0 then 1 else ((8x + ~2) + (x div 2))) div (x + 1))
A029912: 1 3 5 5 6 6 7 7 7 7 7 7 7 7 7 7
(loop(\(x,i).((x + 3) - ((~x + 1) div 3)),x,2) div (x + 1))
A177876: 2 3 3 4
A182229: 2 3 3 4 5 6 7 9 11 14 17 21 26 33 41 52
((2x + 2) * (x + (if (x + ~1) <= 0 then 2 else (3x + ~3))))
A221855: 4 12 30 72 130 204 294 400 522 660 814 984 1170 1372 1590 1824
((2 + compr(\x.(loop(\(x,i).(2x + 1),x,0) mod (x + 1)),x)) mod (x + 1))
A096197: 0 0 0 0 2 2 4 4 6 0 10 2 3 2 3 6
((x + 1) * ((x + 2) + loop(\(x,i).(x * (2 + i)),4,(x + 1))))
A031716: 362 1446 3252 5780 9030 13002 17696 23112 29250 36110 43692 51996 61022 70770 81240 92432
((2 * (x + (loop(\(x,i).(2 * (x - i)),x,2) mod (x + 1)))) div (x + 1))
A294901: 0 1 1 2 1 3 1 2 2 3 1 3 1 3 3 2
(2 - ((x + 1) * (1 - (2 * loop(\(x,i).(x2 + x),(x + ~1),x)))))
A005026: 1 4 35 1246
((2 * (if (x mod 2) <= 0 then x else (3x2 + 2x))) div (x + 1))
A019429: 0 5 1 16 1 28 1 40 1 52 1 64 1 76 1 88
((x + 1) * (((x2 + 2x) * loop(\(x,i).x2,2,(x + 1))) div 2))
A292045: 0 48 972 7680 37500 136080 403368 1032192 2361960 4950000 9663060 17791488 31188612 52437840 85050000 133693440
((x + 1) * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A033286: 2 6 15 28 55 78 119 152 207 290 341 444 533 602 705 848
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod (x + 1))
A004648: 0 1 2 3 1 1 3 3 5 9 9 1 2 1 2 5
((2 + compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x)) mod (x + 1))
A004649: 0 1 1 3 3 5 5 7 2 1 4 5 4 5 8 11
((x + 1) * loop(\(x,i).4x,(x + 1),(x2 + 2x + 2)))
A127369: 8 160 1920 17408 133120 909312 5734400 34078720 193462272 1059061760 5628755968 29192355840 148310589440 740344987648 3639984783360 17660905521152
((x + 1) * loop(\(x,i).3x,(x + 1),(x2 + 2x + 2)))
A121607: 6 90 810 5508 31590 161838 765450 3411720 14526054 59639490 237731274 924707340 3523453830 13191428502 48642794730 177008116752
((x2 + 3x + 2) * loop(\(x,i).6x,(x + 1),x))
A128964: 0 216 5184 77760 933120 9797760 94058496 846526464 7255941120 59861514240 478892113920 3735358488576 28524555730944 213934167982080 1579821548175360 11510128422420480
((x2 + 3x + 2) * loop(\(x,i).8x,(x + 1),x))
A128967: 0 384 12288 245760 3932160 55050240 704643072 8455716864 96636764160 1063004405760 11338713661440 117922622078976 1200666697531392 12006666975313920 118219490218475520 1148417904979476480
((x2 + 3x + 2) * loop(\(x,i).5x,(x + 1),x))
A128963: 0 150 3000 37500 375000 3281250 26250000 196875000 1406250000 9667968750 64453125000 418945312500 2666015625000 16662597656250 102539062500000 622558593750000
((x2 + 3x + 2) * loop(\(x,i).3x,(2x + 2),x))
A128969: 0 486 17496 393660 7085880 111602610 1607077584 21695547384 278942752080 3451916556990 41422998683880 484649084601396 5551434969070536 62453643402043530 691794203838020640
compr(\x.(loop(\(x,i).((x * (x mod 2)) + (x div 2)),x,x) - (x mod 2)),(x + 1))
A039503: 1 3 11 15 29 39 43 53 57 59 65 69 71 77 79 85
((x + loop(\(x,i).7x,(x + 1),1)) div (x + 1))
A129791: 7 25 115 601 3362 19609 117649 720601 4483735 28247525 179756977 1153440601 7453000801 48444505204 316504100663 2077058160601
loop(\(x,i).(x * ((1 + (2 * (1 + i))) * (~1 + (2 * i)))),x,(x + 1))
A291561: 1 10 315 18900 1819125 255405150 49165491375 12417798393000 3981456609755625 1579311121869731250 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x - (compr(\x.(loop(\(x,i).(2x + 1),x,0) mod (x + 1)),x) mod (x + 1)))
A068901: 0 1 1 1 4 5 4 5 4 1 2 11 11 13 13 11
((x + 1) * (~x + ((x + 1) * loop(\(x,i).(x2 + 1),3,2))))
A031730: 677 2706 6087 10820 16905 24342 33131 43272 54765 67610 81807 97356 114257 132510 152115 173072
((x + 1) * (~x + ((x + 1) * loop(\(x,i).(x3 + 1),2,2))))
A031732: 730 2918 6564 11668 18230 26250 35728 46664 59058 72910 88220 104988 123214 142898 164040 186640
((x + 1) * (~x + ((x + 1) * loop(\(x,i).(x2 + 1),2,4))))
A031712: 290 1158 2604 4628 7230 10410 14168 18504 23418 28910 34980 41628 48854 56658 65040 74000
((x + 1) + loop(\(x,i).(x - (2x div 7)),2,x))
A299542: 1 3 5 7 8 9 11 12 14 15 17 18 20 22 23 24
((x + 1) + loop(\(x,i).(((x * (x div 2)) div 2) div 5),2,x))
A247397: 1 2 3 4 5 6 7 8 9 10 12 13
A093668-A026501-A000926: 1 2 3 4 5 6 7 8 9 10 12 13 15 16 18 21
((x + 1) + loop(\(x,i).(x - ((x - ((x * i) div 3)) div 2)),2,x))
A182829: 1 3 4 6 8 9 10 12 13 15 17 18 20 22 23 24
loop(\(x,i).(2 * ((2x * (1 + (2 * i))) div (2 + i))),x,(x + 1))
A245391: 1 8 60 448 3360 25344 192192 1464320 11202048 85995520 662165504 5112102912 39557939200 306726174720 2382605107200 18537602088960
((4x + 4) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))
A059159: 4 8 4 16 4 8 4 32 4 8 4 16 4 8 4 64
((x + 1) + (if (x mod 3) <= 0 then 8 else (~x + (x mod 2))))
A239908: 9 2 1 12 1 2
loop(\(x,i).((x + (4x div (1 + i))) * (2 + i)),x,(x + 1))
A062141: 1 18 252 3360 45360 635040 9313920 143700480 2335132800 39956716800 719220902400 13599813427200 269729632972800 5602076992512000 121645100408832000 2757288942600192000
loop(\(x,i).(~x + (12x div (1 + i))),x,(x + 1))
A010926: 1 10 45 120 210 252 210 120 45 10 1
loop(\(x,i).(x + (16x div (1 + i))),x,(x + 1))
A010970: 1 18 171 1140 5985 26334 100947 346104 1081575 3124550 8436285 21474180 51895935 119759850 265182525 565722720
((x + loop(\(x,i).(1 - ((x * (x mod 2)) + (x div 2))),2,x)) div (x + 1))
A340853: 0 1 1 2 1 1 1 2 1 1 1 2 1 1 1 3
((x + ~1) * (if ((x + 1) mod (2 + (x mod 5))) <= 0 then 2 else 0))
A189764: 0 0 0 0 0 8 0 12 0 0 0 20 0 0 0 28
((x + ~1) + loop(\(x,i).(x + i - (x div 5)),(x + ~1),1))
A130246: 0 1 3 6 10 14 18 23 28 33 38 44 50 56 62 68
loop(\(x,i).((x2 + ~x) div (1 + ((~1 + (2 * i)) * i))),2,(x + ~1))
A011938: 0 0 0 0 0 4 12 30 60 108 180 282 424 612 858 1170
((x + ~1) * (((x + loop(\(x,i).3x,(x + ~2),x)) div 2) div 2))
A082149: 0 0 1 6 30 140 615 2562 10220 39384 147645 541310 1948650 6908772 24180611 83702010
((x + ~1) * (loop(\(x,i).12x,(x + ~2),x) div 2))
A081142: 0 0 1 36 864 17280 311040 5225472 83607552 1289945088 19349176320 283787919360 4086546038784 57954652913664 811365140791296 11234286564802560
((x + ~1) * (loop(\(x,i).10x,(x + ~2),x) div 2))
A081140: 0 0 1 30 600 10000 150000 2100000 28000000 360000000 4500000000 55000000000 660000000000 7800000000000 91000000000000 1050000000000000
((x + ~1) + (if (~4 + (x div 2)) <= 0 then 10 else x))
A317591: 9 10 11 12 13 14 15 16 17 18 19 21 23 25 27 29
((x + 1) div (1 + loop(\(x,i).(1 + (((x + 1) div 2) mod 3)),x,x)))
A227911: 1 0 1 1 1 2 2 2 3 2 2 4 4 4 5 4
loop(\(x,i).(x * (1 + (3 * (4 + (2 mod (x + 1)))))),x,1)
A196665: 1 13 247 4693 89167 1694173 32189287 611596453 11620332607 220786319533 4194940071127 79703861351413 1514373365676847 28773093947860093 546688785009341767 4611686018427387903
loop(\(x,i).((x + 1) + (((x * (1 + i)) mod 5) mod 2)),x,1)
A288258: 1 2 4 6 7 8 10 11 12 13 15 16 18 19 20 21
loop(\(x,i).(x + (7 * ((1 + (i * i)) * i))),x,1)
A160747: 1 15 85 295 771 1681 3235 5685 9325 14491 21561 30955 43135 58605 77911 101641
loop(\(x,i).((5x + 1) - ((i mod 3) div 2)),x,1)
A033132: 1 6 30 151 756 3780 18901 94506 472530 2362651 11813256 59066280 295331401 1476657006 7383285030 36916425151
(1 + loop(\(x,i).(x div (1 + (x mod (2 + ((x mod 3) div 2))))),x,x))
A140215-A065330: 1 1 1 1 5 1 7 1 1 5 11 1 13 7 5 1
(1 + (x2 * (~1 + loop(\(x,i).(2x3 + ~4x),2,2))))
A237991: 1 992 3965 8920 15857 24776 35677 48560 63425 80272 99101 119912 142705 167480 194237 222976
loop(\(x,i).(x * (24 - (x mod 3))),x,1)
A170742-A170704-A170656-A170608-A170560-A170512-A170464-A170416-A170368-A170320-A170272-A170224-A170176-A170128-A170080-A170032-A169564-A169516-A169468-A169420-A169372-A169324-A169276-A169228-A169180-A169132-A169084-A169036-A168988-A168940-A168892-A168844-A168796-A168748-A168700-A167937-A167694-A167174: 1 23 506 11132 244904 5387888 118533536 2607737792 57370231424 1262145091328 27767192009216 610878224202752 13439320932460544 295665060514131968 4611686018427387903 4611686018427387903
loop(\(x,i).(x + ((((2 + i) * (1 + i)) div 2) * (1 + (2 * i)))),x,1)
A002419: 1 10 40 110 245 476 840 1380 2145 3190 4576 6370 8645 11480 14960 19176
((x + 1) + loop(\(x,i).(x - ((x + ~1) div (3 + (x div 2)))),2,x))
A066935: 2 3 5 7 9 11 13 14 15 17 19 21 23 25 27 29
loop(\(x,i).(x * (2 + (9 * (i * (1 + i))))),x,1)
A091535: 1 20 1120 123200 22422400 6098892800 2317579264000 1172695107584000 762251819929600000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 - (2 * (((1 - (2 * (i mod 2))) * i) div 2)))),x,1)
A046126: 1 3 ~3 ~15 45 315 ~1575 ~14175 99225 1091475 ~9823275 ~127702575 1404728325 21070924875 ~273922023375 ~4656674397375
loop(\(x,i).(3x - ((~1 + (2 * (i mod 2))) * (2 + i))),x,1)
A076148: 1 0 4 7 27 74 230 681 2053 6148 18456 55355 166079 498222 1494682 4484029
loop(\(x,i).(x + ((4x * (1 + (2 * i))) div (2 + i))),x,1)
A034164: 1 5 30 198 1386 10098 75735 580635 4528953 35819901 286559208 2314516680 18846778680 154543585176 1274984577702 10574872085646
(~1 + loop(\(x,i).(20x + 1),2,x2))
A158601: 20 420 1620 3620 6420 10020 14420 19620 25620 32420 40020 48420 57620 67620 78420 90020
(~1 + loop(\(x,i).(15x + 1),2,x2))
A158557: 15 240 915 2040 3615 5640 8115 11040 14415 18240 22515 27240 32415 38040 44115 50640
(~1 + loop(\(x,i).(18x + 1),2,x2))
A158590: 18 342 1314 2934 5202 8118 11682 15894 20754 26262 32418 39222 46674 54774 63522 72918
(~1 + loop(\(x,i).(24x + 1),2,x2))
A158637: 24 600 2328 5208 9240 14424 20760 28248 36888 46680 57624 69720 82968 97368 112920 129624
(1 + loop(\(x,i).(~11x + ~1),2,x2))
A158536: 11 132 495 1100 1947 3036 4367 5940 7755 9812 12111 14652 17435 20460 23727 27236
(~1 + loop(\(x,i).(32x + 1),2,x2))
A158685: 32 1056 4128 9248 16416 25632 36896 50208 65568 82976 102432 123936 147488 173088 200736 230432
(1 + loop(\(x,i).(~14x + ~1),2,x2))
A158555: 14 210 798 1778 3150 4914 7070 9618 12558 15890 19614 23730 28238 33138 38430 44114
(~1 + loop(\(x,i).(13x + 1),2,x2))
A158548: 13 182 689 1534 2717 4238 6097 8294 10829 13702 16913 20462 24349 28574 33137 38038
(~1 + loop(\(x,i).(17x + 1),2,x2))
A158585: 17 306 1173 2618 4641 7242 10421 14178 18513 23426 28917 34986 41633 48858 56661 65042
((x2 + ~1) * loop(\(x,i).(x * ((x + ~1) + i)),2,x3))
A033669: 0 0 12480 4257360 251719680 5859750000 76189014720 664387432800 4329343549440 22594405433760 99000099000000 376611617793840 1275002791096320 3914079111480720 11055314381442240 29063182239000000
((x + 1) + loop(\(x,i).(x - (2x div (1 + (4 * i)))),x,x))
A336410: 1 3 5 6 8 9 11 12 13 15 16 18 19 20 21 22
(x - (2 * ((x div 3) - (if (~4 + (x div 2)) <= 0 then 1 else 0))))
A216197: 2 3 4 3 4 5 4 5 6 5 4 5 4 5 6 5
(2 + loop(\(x,i).(x + (((2 + (i * i)) * (1 + i)) div 2)),(x + 1),0))
A211562: 5 14 36 81 162 295 499 796 1211 1772 2510 3459 4656 6141 7957 10150
(loop(\(x,i).(x + ((1 + ((~1 + (2 * i)) * i)) * i)),(x + 1),0) div 2)
A132117: 1 8 32 90 205 406 728 1212 1905 2860 4136 5798 7917 10570 13840 17816
(2 * loop(\(x,i).(x + ((3 + i) * i * (~1 + i))),(x + ~1),0))
A172200: 0 0 0 20 92 260 580 1120 1960 3192 4920 7260 10340 14300 19292 25480
(2 + (if ((x + 3) mod (2 + (x div 5))) <= 0 then 2 else 0))
A336409: 2 4 2 4 2 2 4 2 2 4 2 2 2 4 2 2
(loop(\(x,i).(x * (1 + i)),x,(1 + (x div 2))) * (2 - (x div ~2)))
A152668: 2 6 36 192 1440 10800 100800 967680 10886400 127008000 1676505600 22992076800 348713164800 5492232345600 94152554496000 1673823191040000
(2 * loop(\(x,i).(3 * ((x + 1) - (2 * (~x + (x mod 2))))),x,0))
A231104: 0 6 48 438 3936 35430 318864 2869782 25828032 232452294 2092070640 18828635766 169457721888 1525119496998 13726075472976 123534679256790
(2 + loop(\(x,i).(4x4 + ~2x2 + 1),x,0))
A303371: 2 3 5 309
((x - (if (x mod (1 + (2 * ((~x + 1) mod 4)))) <= 0 then 0 else 1)) mod 2)
A155897: 0 1 1 0 1 1 1 0 1 1 1 0 0 1 0 1
(2 * (1 + loop(\(x,i).((x + 1) mod (2 + (i div 3))),(x + ~1),0)))
A331118: 2 2 4 2 4 6 2 4 6 8 10 2 4 6 8 10
(2 * (1 + (if ((x + 2) mod (4 + (x div 3))) <= 0 then 2 else 0)))
A286540: 2 2 6 6 2 2 2 2 2 2 2 2 2 2 6 2
(x mod ((~1 + (if ((x2 + x) mod 5) <= 0 then x else 0)) div 2))
A287299: 0 0 0 0 0 1 0 0 0 1 2 0 0 0 2 1
((1 + loop(\(x,i).((2x + 1) mod (2 * (2 + (i div 2)))),x,0)) div 2)
A201908: 0 1 2 1 2 4 3 1 2 4 1 2 4 8 7 5
((if (x + ~1) <= 0 then 2 else (1 + ((x + ~1) mod (1 + (x div 3))))) div 2)
A112224: 1 1 0 0 1 0 1 0 1 0 1 1 1 1 2 1
((1 + (x div (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))) div 2)
A048105: 0 0 0 1 0 0 0 2 1 0 0 2 0 0 0 3
(if ((x + 1) mod (1 + (4x mod (1 + (x div 2))))) <= 0 then 1 else 2)
A095684: 1 1 1 1 2 1 1 1 1 1 2 1 2 2 1 2
(if ((x div 2) mod (1 + (2 * (x mod (1 + (x div 3)))))) <= 0 then 1 else 2)
A093921: 1 1 1 2 1 2 1 1 2 2 1 2 2 2 2 1
((1 + (loop(\(x,i).2x,x,2) div 17)) div 2)
A191497: 0 0 0 0 1 2 4 8 15 30 60 120 241 482 964 1928
((2 + (x mod 2)) div (if ((x + ~1) mod 9) <= 0 then 1 else 2))
A030576: 1 3 1 1 1 1 1 1 1 1 2 1 1 1 1 1
((1 + (if (x mod 2) <= 0 then (((x + 2) div 3) mod 4) else 1)) div 2)
A098055: 0 1 1 1 1 1 1 1 2 1 0 1 0 1 1 1
(if x <= 0 then 1 else (30x2 + 2))
A005903: 1 32 122 272 482 752 1082 1472 1922 2432 3002 3632 4322 5072 5882 6752
((1 + ((if (~2 + (x div 2)) <= 0 then x else (x + 1)) mod 5)) mod 2)
A156728: 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 0
((x - (if x <= 0 then 1 else (x div (1 + ((x + ~1) mod 5))))) mod 2)
A285136: 1 0 1 0 1 0 0 0 0 1 0 0 0 1 1 0
(2 * (~1 + (5 * ((x + 4) + (if x <= 0 then 1 else 2)))))
A100409: 48 68 78 88 98
(if x <= 0 then 1 else (40x2 + 2))
A010022: 1 42 162 362 642 1002 1442 1962 2562 3242 4002 4842 5762 6762 7842 9002
((if x <= 0 then 1 else (2x mod (1 + ((x div 2) mod 5)))) mod 2)
A027359: 1 0 0 0 0 1 0 0 1 1 0 0 0 0 1 0
((1 + ((if (x mod 2) <= 0 then (x div 2) else 2) + (x div 5))) div 2)
A256587: 0 1 1 1 1 2 2 2 3 2 4 2 4 2 5 3
((if x <= 0 then 2 else (1 + ((x + 3) mod (1 + (x div 4))))) div 2)
A025866: 1 0 0 0 1 0 1 0 1 0 1 1 2 0 1 1
(if (2x mod (3 + ((x + ((x div 2) mod 2)) div 2))) <= 0 then 1 else 2)
A081592: 1 2 1 2 2 1 1 1 2 2 2 2 2 2 2 2
(if x <= 0 then 1 else (2 * (~1 + ((1 + (x div (2 - (x mod 2)))) mod 3))))
A184334: 1 2 2 0 ~2 ~2 0 2 2 0 ~2 ~2 0 2 2 0
(if x <= 0 then 1 else (((x2 + 2x) mod (1 + ((x + 1) div 3))) div 2))
A341021: 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1
((loop(\(x,i).2x,x,2) mod 19) div 2)
A222011: 1 2 4 8
A254065: 1 2 4 8 6 3 7 4 9 8 7 5 1 3 6 2
loop(\(x,i).x3,1,(12x + 10))
A017643: 1000 10648 39304 97336 195112 343000 551368 830584 1191016 1643032 2197000 2863288 3652264 4574296 5639752 6859000
loop(\(x,i).x3,2,(12x + 10))
A017649: 1000000000 1207269217792 60716992766464 922190162669056 7427658739644928 40353607000000000 167619550409708032 572994802228616704 1689478959002692096 4435453859151328768
(2 * (1 + (6 * (2 + loop(\(x,i).2x,(x + 2),2)))))
A304605: 122 218 410 794 1562 3098 6170 12314 24602 49178 98330 196634 393242 786458 1572890 3145754
(loop(\(x,i).(x + (x div 2)),x,23) div 2)
A120139: 11 17 25 38 57 85 128 192 288 432 648 972 1458 2187 3280 4920
(if ((x mod (2 + ((2 - (x div 2)) mod (x + 2)))) mod 3) <= 0 then 1 else 2)
A074295: 1 2 2 1 1 2 1 2 2 1 2 2 1 1 2 2
((1 + (x2 div ((x + 3) + (if (x mod 2) <= 0 then x else 2)))) mod 2)
A331414: 1 1 1 0 0 1 1 1 0 0 1 0 0 0 1 0
((x + 2) div (2 + (if ((x mod 3) mod 2) <= 0 then (x div 3) else 1)))
A096446: 1 1 2 1 2 2 2 3 2 2 4 2
(2 * ((x + 3) + ((if (x + ~1) <= 0 then x else 2) + (x div 3))))
A115036: 6 10 14 18 20 22 26 28 30 34 36 38 42 44 46 50
(if x <= 0 then 1 else (x - (((2x + ~1) mod (1 + (x div 3))) div 2)))
A136623: 1 1 2 3 4 5 5 7 8 9 9 11 11 13 13 13
(((1 + (x * (if (x mod 2) <= 0 then 1 else x))) mod (1 + (x div 3))) div 2)
A219185: 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 2
(if x <= 0 then 1 else (((x2 * (x div 2)) div (1 + (x mod 3))) mod 2))
A280816: 1 0 1 1 0 0 0 1 1 0 0 1 0 1 1 1
(2 * (1 + (loop(\(x,i).(2x + 4),(x + ~2),0) div (2x + 1))))
A334125: 2 2 2 2 4 6 10 18 30 54 98 178 328 608 1130 2114
(x div (2 + ((x2 + ~x) div (1 + loop(\(x,i).2x,(x div 2),1)))))
A018243: 0 0 1 0 1 0 1 1 1 1 2 2 3 3 4 5
(if x <= 0 then 1 else (((x + 1) - ((2x + ~2) mod (1 + (x div 2)))) div 2))
A003036: 1 1 1 2 2 2 2 4 2 4 5 5 6
((x + 3) - ((if (x + ~2) <= 0 then 1 else x) mod (3 - (x mod 2))))
A063932: 2 3 4 5 6 7 9 9 9 11 12 13 15 15 15 17
((1 + loop(\(x,i).((x + 1) + ((2 + (i div 2)) * (i div 2))),x,1)) div 2)
A008610: 1 1 3 5 10 14 22 30 43 55 73 91 116 140 172 204
((1 + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1)) div 2)
A130380: 1 1 1 3 7 21 66 215 715 2431 8398 29393 104006 371450 1337220 4847423
((1 + loop(\(x,i).(2 * (6x + (x mod 2))),x,1)) div 2)
A067413: 1 7 84 1008 12096 145152 1741824 20901888 250822656 3009871872 36118462464 433421549568 5201058594816 62412703137792 748952437653504 8987429251842048
((1 + loop(\(x,i).(x - ((~x + ((i mod 3) mod 2)) div 2)),x,1)) div 2)
A173696: 1 1 1 2 2 3 5 7 10 15 23 34 51 77 115 173
(loop(\(x,i).((4x + 1) + ((x + i) mod 2)),(x + 1),1) div 2)
A037751: 2 11 45 180 722 2891 11565 46260 185042 740171 2960685 11842740 47370962 189483851 757935405 3031741620
(loop(\(x,i).(4x + ((x + 1) mod 4)),(x + 1),1) div 2)
A037779: 3 13 54 216 867 3469 13878 55512 222051 888205 3552822 14211288 56845155 227380621 909522486 3638089944
(loop(\(x,i).(2 * ((~x + 2) mod 7)),(x + ~1),1) div 2)
A021979: 0 0 1 0 2 5 6 4 1 0 2 5 6 4 1 0
((1 + loop(\(x,i).(((3 * (x div 4)) div 2) + i),x,1)) div 2)
A173633: 1 1 1 2 2 3 4 4 6 6 7 8 8 10 10 11
(x - ((x + 1) mod (1 - (2 * (1 + (if (x + ~4) <= 0 then 0 else 2))))))
A171572: 0 1 2 3 4 9 9 9 9 9 14 14 14 14 14 19
(2 * (if x <= 0 then 2 else (1 + (x div (2 - ((x div 4) div ~2))))))
A179411: 4 2 4 4 4 4 6 6 6 8 8 8 8 8 8 8
(loop(\(x,i).(x3 + x2),1,(x - (x div ~3))) div 2)
A015224: 0 6 18 40 126 196 288 550 726 936 1470 1800 2176 3078 3610 4200
((1 + (loop(\(x,i).2x,(x + ~7),1) div 2)) div 2)
A104144: 0 0 0 0 0 0 0 0 1 1 2 4 8 16 32 64
((1 + (loop(\(x,i).2x,(x + ~9),1) div 2)) div 2)
A168082: 0 0 0 0 0 0 0 0 0 0 1 1 2 4 8 16
(2 * (~3 + loop(\(x,i).10x,(x + 1),1)))
A086946: 14 194 1994 19994 199994 1999994 19999994 199999994 1999999994 19999999994 199999999994 1999999999994 19999999999994 199999999999994 1999999999999994 19999999999999994
((x mod (1 + (2 * (1 + (x mod (if (~2 + (x div 2)) <= 0 then 1 else 2)))))) div 2)
A159459: 0 0 1 0 0 1 0 1 1 2 0 0 0 1 1 0
(if x <= 0 then 1 else (2 * (1 + ((x mod (1 + ((1 + (x div 2)) div 2))) mod 2))))
A100374: 1 2 2 4 2 4 2 4 2 2 2 4 2 4 2 2
((x mod 2) - (if (~2 + (x mod (3 + (x div 4)))) <= 0 then 1 else 2))
A156709: ~1 0 ~1 0 ~1 0 ~1 ~1 ~2 ~1 ~1 0 ~1 0 ~1 ~1
(1 - ((x2 + ~x) mod (2 + (if ((x div 2) mod 3) <= 0 then 2 else 1))))
A186039: 1 1 ~1 1 1 ~1 ~1 ~1 ~1 1 1 ~1 1 1 ~1 1
(if x <= 0 then 1 else (28x2 + 2))
A010018: 1 30 114 254 450 702 1010 1374 1794 2270 2802 3390 4034 4734 5490 6302
(2 + (if ((x + (x div (2 + (x div 4)))) mod 3) <= 0 then 2 else 1))
A108171: 4 3 4 3 3 4 3 4 3 3 4 3 3 4 3 4
((x + 2) div (2 + (if (~2 + (x div 3)) <= 0 then 1 else 2) - (x mod 2)))
A155043: 0 1 1 2 2 3 2 4 3 3 3 4 3 5 4 5
((x div 2) - ((1 + (x div 2)) div (2 + (if (x mod 3) <= 0 then 2 else 1))))
A024695: 0 0 1 1 1 1 2 2 3 3 3 3 5 4 5 5
(2 * (~1 + (2 * (16 + loop(\(x,i).2x,x,1)))))
A250739: 66 70 78 94 126 190 318 574 1086 2110 4158 8254 16446 32830 65598 131134
(2 * (x mod (1 + (x div (2 + (loop(\(x,i).(x * i),x,1) mod (x + 1)))))))
A073759: 0 0 0 0 0 4 0 6 6 8 0 10 0 12 12 14
(if (~2 + ((2 * ((~x + 2) mod 5)) mod (x + 1))) <= 0 then 1 else 2)
A343856-A218541: 1 1 1 1 1 2 1 1 2 2 2 1 1 2 2 2
((~1 + loop(\(x,i).(4x - (i mod 4)),(x + 1),2)) div 2)
A037765: 3 12 50 201 807 3228 12914 51657 206631 826524 3306098 13224393 52897575 211590300 846361202 3385444809
(2 * (1 + (2 * (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))))
A100892: 2 6 2 14 2 6 2 30 2 6 2 14 2 6 2 62
(((~x + ~1) mod (3 + (if (~2 + (x div 2)) <= 0 then 0 else 2))) div 2)
A212551: 1 0 0 1 0 0 1 1 0 0 2 1 1 0 0 2
((2 - (if x <= 0 then 1 else (x mod (~1 + (x div (~2 + (x mod ~2))))))) div 2)
A133989: 0 1 1 1 2 1 2 1 2 2 2 3 2
(if x <= 0 then 1 else (2 * (1 + ((x2 mod (2 + (x div 3))) div 2))))
A057467: 1 2 2 2 2 2 2 2 2 2 2 2 2 2 6 2
((if x <= 0 then 1 else x) - ((1 + ((x - ((x div 3) mod 2)) div 2)) div 2))
A053756: 1 1 1 2 3 4 4 5 6 7 8 8 9 10 10 11
(2 * (if (x + ~1) <= 0 then 1 else (1 + (2 * (x - ((1 + (x div 2)) div 2))))))
A080456: 2 2 6 10 14 18 18 22 26 30 30 34 38 42 42 46
(if (~2 + (x mod (2 + (((x + 1) div 2) mod 8)))) <= 0 then 1 else 2)
A242217: 1 1 1 2 1 1 1 1 1 1 2 2 2 2 2 1
(if (x + ~2) <= 0 then 1 else (2 + (x2 div 17)))
A296371-A029043: 1 1 1 2 2 3 4 4 5 6 7 9 10 11 13 15
(4x - ((x - (if (~2 + (x div 4)) <= 0 then 2 else 1)) div 2))
A186276: 1 5 8 12 15 19 22 26 29 33 36 40 43 46 50 53
((1 + ((loop(\(x,i).~2x,x,(x + 4)) div 2) div 2)) div 2)
A081037: 1 ~1 3 ~7 16 ~36 80 ~176 384 ~832 1792 ~3840 8192 ~17408 36864 ~77824
(if x <= 0 then 1 else (27x2 + 2))
A010017: 1 29 110 245 434 677 974 1325 1730 2189 2702 3269 3890 4565 5294 6077
((x + 2) div (if (x + ~2) <= 0 then 1 else (2 * (1 + (x div 8)))))
A262304: 2 3 4 2 3 3 4 4 2 2 3 3 3 3 4 4
(((x div 3) - (if ((x * (x div 2)) mod 4) <= 0 then 2 else 1)) mod 2)
A127523: 0 0 1 0 1 0 1 1 0 1 0 0 0 1 1 0
loop(\(x,i).2x,((2x + 1) div (3 + (x div 4))),2)
A140513: 2 4 4 8 8 8 16 16 16 16 32 32 32 32 32 64
((x + 1) mod (2 * (if (~x + 2) <= 0 then ((x - (x div 4)) div 2) else 1)))
A156549: 1 0 1 0 1 2 3 2 3 4 3 4 5 4 5 4
((1 + ((loop(\(x,i).((x2 + ~1) div 2),2,(x + ~2)) div 2) div 2)) div 2)
A000241: 0 0 0 0 0 1 3 9 18 36 60 100 150
A028723: 0 0 0 0 0 1 3 9 18 36 60 100 150 225 315 441
(if x <= 0 then 1 else ((x div (3 + ((x + 1) mod (2 + (x mod 2))))) mod 2))
A004555: 1 0 0 0 1 1 1 1 0 0 0 1 1 0 1 1
loop(\(x,i).2x,(10x + 45),2)
A320863: 70368744177664 72057594037927936 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~2 + loop(\(x,i).(x2 + ~2),1,(10x + 5)))
A152161: 21 221 621 1221 2021 3021 4221 5621 7221 9021 11021 13221 15621 18221 21021 24021
(4 - (((if x <= 0 then 1 else (2 + (x div 2))) mod 5) mod 2))
A073322: 3 4 3 3 4 4 4 4 3 3 4 4 3 3 4 4
(if x <= 0 then 1 else (2 * (2x - ((~2x + 2) div 5))))
A310409: 1 4 10 14 20 24 28 34 38 44 48 52 58 62 68 72
(10 * (if x <= 0 then 1 else (2x2 + 8x)))
A208375: 10 100 240 420 640 900 1200 1540 1920 2340 2800 3300 3840 4420 5040 5700
(if x <= 0 then 1 else (2 * ((x div 4) - ((x + 2) div 5))))
A255365: 1 0 0 ~2 0 0 0 0 0 0 0 0 2 0 0 0
(if x <= 0 then 1 else (2 * (3x - ((x + 2) div 5))))
A315654: 1 6 12 16 22 28 34 40 44 50 56 62 68 72 78 84
(if x <= 0 then 1 else ((x div 2) - (((1 - (x div 2)) div 5) mod 2)))
A029156: 1 0 1 1 1 1 2 2 3 3 4 4 5 5 7 7
(if x <= 0 then 1 else (2 + (((x2 div 2) - (x mod 2)) div 5)))
A029013: 1 1 2 2 3 4 5 6 8 9 12 13 16 18 21 24
(x mod (if ((x div 2) mod 5) <= 0 then 1 else 10))
A004176: 0 0 2 3 4 5 6 7 8 9 0 0 2 3 4 5
((x + 10) + loop(\(x,i).i,(~1 + (x div 3)),1))
A293728: 11 12 13 14 15 16 17 18 19 21 22 23 25 26 27 29
loop(\(x,i).(10x + ~1),x,10)
A179555: 10 99 989 9889 98889 988889 9888889 98888889 988888889 9888888889 98888888889 988888888889 9888888888889 98888888888889 988888888888889 9888888888888889
((x * (if (~4 + (x div 2)) <= 0 then 1 else x)) mod 10)
A103303: 0 1 2 3 4 5 6 7 8 9
A095187: 0 1 2 3 4 5 6 7 8 9 0 1 4 9 6 5
loop(\(x,i).(7x + 6),x,10)
A198692: 10 76 538 3772 26410 184876 1294138 9058972 63412810 443889676 3107227738 21750594172 152254159210 1065779114476 7460453801338 52223176609372
(10 * loop(\(x,i).(x + ~2),(x + ~5),x))
A095973: 0 10 20 30 40 50 40 30 20 10 0
(((if (x + ~1) <= 0 then 1 else (x * (1 + (x mod 2)))) mod 5) mod 2)
A189920: 1 1 0 1 0 0 1 0 1 1 0 0 0 1 0 0
((if x <= 0 then 1 else ((x + ((x + 1) * (x mod 2))) div 5)) mod 2)
A104015: 1 0 0 1 0 0 1 1 1 1 0 0 0 1 0 0
(if x <= 0 then 0 else (2 + ((~x + (x2 div 4)) div 5)))
A090184: 0 1 1 1 2 2 2 3 3 4 5 5 6 7 9 10
(if x <= 0 then 1 else (25x2 + 2))
A010015: 1 27 102 227 402 627 902 1227 1602 2027 2502 3027 3602 4227 4902 5627
(((x + (if (~2 + (x div 2)) <= 0 then 3 else x)) mod 5) mod 2)
A322353: 1 0 0 1 0 1 0 0 1 1 0 0 0 1 1 0
((~1 + loop(\(x,i).(4x - (i mod 4)),x,4)) div 2)
A037702: 1 7 28 114 457 1831 7324 29298 117193 468775 1875100 7500402 30001609 120006439 480025756 1920103026
(if x <= 0 then 0 else (1 - (((x + 1) mod (~1 - (x div 4))) div 2)))
A065373: 0 1 1 1 2 1 2 1 1 2 2 1 3 2 2 1
((1 + (loop(\(x,i).(1 + (2 * ((x + 2) - (i mod 2)))),x,2) div 2)) div 2)
A172411: 1 2 5 10
A026633: 1 2 5 10 22 44 90 180 362 724 1450 2900 5802 11604 23210 46420
(~2 - (x div (~1 + ((~x + 2) div (2 + ((if x <= 0 then 2 else x) div 2))))))
A064662: ~2 ~1 0 0 0 1 1 2 2 1 2 2 2 3 3 3
(2 + (if x <= 0 then 2 else (x - ((x2 + 2) div (x + 5)))))
A056641: 4 3 4 4 4 5 5 5 5 6 6 6 6 6 6 6
(~2 + loop(\(x,i).~11x,(2x + 4),1))
A133858: 14639 1771559
loop(\(x,i).x5,1,(8x + 2))
A017093: 32 100000 1889568 11881376 45435424 130691232 312500000 656356768 1252332576 2219006624 3707398432 5904900000 9039207968 13382255776 19254145824 27027081632
((if x <= 0 then 2 else ((x + 1) mod (1 + (2x div (2 + (x div 2)))))) div 2)
A065712: 1 0 0 0 1 0 0 1 0 1 1 0 0 1 1 0
(x + (((x2 + 2x) div 4) + (if (~2 + (x div 2)) <= 0 then 1 else 2)))
A013660: 1 2 5 7 11
A001225: 1 2 5 7 11 14 20 24 30 35
((3 * (3x2 + (if (x + ~1) <= 0 then 1 else 0))) div 2)
A299256: 1 6 18 40 72 112 162 220 288 364 450 544 648 760 882 1012
(2 * (loop(\(x,i).(x + i),(x + ~7),0) div 3))
A309882: 0 0 0 0 0 0 0 0 0 2 4 6 10 14 18 24
(2 * (loop(\(x,i).((x + 2) + (x div 2)),(~2 + (x div 2)),1) div 3))
A309686: 0 0 0 0 0 0 2 2 4 4 6 6 12 12 18 18
((3 * (1 + (if (~4 + (x div 2)) <= 0 then x else (x + 2)))) div 2)
A225647: 1 3 4 6 7
A072561: 1 3 4 6 7 9 10 12 13 15 19 21 22 24 25 27
((3 * loop(\(x,i).2x,(x + ~1),(3x + 1))) div 2)
A113070: 1 6 21 60 156 384 912 2112 4800 10752 23808 52224 113664 245760 528384 1130496
(~2 + ((3x + 3) * (if (~x + 2) <= 0 then 3x else 1)))
A110908: 1 4 52 106
(2 + ((loop(\(x,i).2x2,2,4) mod (x + 1)) div 3))
A344888: 2 2 2 2 3 2 3 2 3 4 2 4 4 3 4 2
(6 - ((if x <= 0 then 2 else ((x + 1) * (x div 2))) mod 3))
A081261: 4 6 6 5 5 6 6 6 6 5 5 6 6 6 6 5
(loop(\(x,i).(3x + 1),x,1) + (((x + 1) div 3) mod 2))
A132357: 1 4 14 41 122 364 1093 3280 9842 29525 88574 265720 797161 2391484 7174454 21523361
(2 * ((loop(\(x,i).(x2 div 3),2,x) div (x + 1)) mod 3))
A181111: 0 0 0 0 2 0 0 2 2 0 0 4 4 4 0 0
(loop(\(x,i).(3x + 1),x,1) + (((x + ~1) div 3) mod 2))
A133453: 2 4 13 40 122 365 1094 3280 9841 29524 88574 265721 797162 2391484 7174453 21523360
((if x <= 0 then 2 else (x div (2 - (3 * (x mod ~4))))) div 2)
A029373: 1 0 0 0 1 0 0 0 2 0 0 1 3 0 0 1
(if x <= 0 then 1 else (2 + (16x2 div 3)))
A299255: 1 7 23 50 87 135 194 263 343 434 535 647 770 903 1047 1202
((x + ~2) - (3 * ((if x <= 0 then 1 else x) div ~7)))
A032972: 1 2 3 4 5 6 7 8 12 13 14 15 16 17 18 22
((loop(\(x,i).x3,1,(2 + (x div 4))) div 3) div 2)
A190718: 1 1 1 1 4 4 4 4 10 10 10 10 20 20 20 20
(((1 + (if x <= 0 then 1 else x)) div 2) - ((3 * (x div 4)) div 2))
A106487: 1 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4
(if x <= 0 then 1 else (2 + ((((x2 div 2) - (x mod 2)) div 2) div 3)))
A029018: 1 1 2 2 3 3 5 5 7 8 10 11 14 15 18 20
((x - ((if (x div 4) <= 0 then 1 else ((~x + 2) div 2)) mod 3)) mod 2)
A074381: 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1
(loop(\(x,i).(3x + 1),x,1) + (((x + ~2) div 3) mod 2))
A133448: 2 5 13 40 121 365 1094 3281 9841 29524 88573 265721 797162 2391485 7174453 21523360
loop(\(x,i).x5,1,(6x + 2))
A016937: 32 32768 537824 3200000 11881376 33554432 79235168 164916224 312500000 550731776 916132832 1453933568 2219006624 3276800000 4704270176 6590815232
((x + 2) - (if x <= 0 then 1 else (x div (~2 + ((1 - (x div 2)) div 3)))))
A164515: 1 4 5 7 8 9 10 12 13 14 15 16 17 19 20 21
(((if (x mod 4) <= 0 then 2 else (x mod 2)) + ((x div 2) div 3)) div 2)
A029365: 1 0 0 0 1 0 0 1 1 1 0 1 2 1 1 1
(if x <= 0 then 1 else (2 + (((2x2 + 4x) - (x mod 2)) div 3)))
A178464: 1 3 7 11 18 25 34 43 55 67 82 97
(loop(\(x,i).(2x + ~1),((x + 1) div 2),(3 * (x mod 2))) div 2)
A137206: 0 2 ~1 4 ~2 8 ~4 16 ~8 32 ~16 64 ~32 128 ~64 256
(loop(\(x,i).2x,x,((x + 2) - ((x2 div 2) div 3))) div 2)
A005103: 1 3 8 16 32 48 64 64
((if (((x div 2) div 3) mod 2) <= 0 then x else ~x) mod 6)
A203572: 0 1 2 3 4 5 0 5 4 3 2 1 0 1 2 3
(x - ((0 - (if (~2 + (x div 4)) <= 0 then 2 else x)) div 6))
A290492: 1 2 3 4 5 6 7 8 9 10 11 12 14
A337149-A330236-A302593-A129304: 1 2 3 4 5 6 7 8 9 10 11 12 14 16 17 18
(6 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A175221: 6 7 9 11 15 17 21 23 27 33 35 41 45 47 51 57
loop(\(x,i).31x,x,6)
A222335: 6 186 5766 178746 5541126 171774906 5325022086 165075684666 5117346224646 158637732964026 4917769721884806 152450861378428986 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(11x + 10),x,6)
A199026: 6 76 846 9316 102486 1127356 12400926 136410196 1500512166 16505633836 181561972206 1997181694276 21968998637046 241658985007516 2658248835082686 29240737185909556
((4x + 2) - ((~x + (if (x + ~2) <= 0 then 0 else 1)) div 3))
A184485: 2 7 11 15 19 24 28 32 37 41 45 50 54 58 63 67
(((if x <= 0 then 1 else x) mod 2) - (((x * (x div 3)) mod 3) mod 2))
A229343: 1 1 0 1 ~1 1 0 1 ~1 1 0 1 0 0 0 1
(~2 + loop(\(x,i).((2x div (1 + i)) * (~1 + (2 * i))),x,3))
A171556: 1 1 4 13 40 124 394 1285 4288 14584 50386 176356 624034 2228698 8023318 29084533
(6 * (x + (if (x + ~1) <= 0 then 1 else ((1 + (x div 2)) div 2))))
A242650: 6 12 18 24 30 36 48 54 60 66 78 84
(2 + (3 * (x + (loop(\(x,i).x2,(x2 + ~2),2) div 2))))
A275003: 5 8 32 4611686018427387903
(loop(\(x,i).(4x + ((x + 1) mod 4)),x,3) div 2)
A037688: 1 6 24 99 397 1590 6360 25443 101773 407094 1628376 6513507 26054029 104216118 416864472 1667457891
(2 * (3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A089241: 6 8 12 16 24 28 36 40 48 60 64 76 84 88 96 108
(((if ((x * (x div 2)) mod 4) <= 0 then 2 else 1) + (x div 3)) div 2)
A169989: 1 1 0 1 1 1 1 1 2 2 2 2 3 2 2 3
((loop(\(x,i).(x - (x div ~2)),(x div 2),1) + (x div 3)) div 2)
A240870: 0 0 1 1 2 2 3 3 5 5 7 7 11 11 15 16
(x div (2 + (((if (x mod 2) <= 0 then 2 else x) mod 4) * (x div 3))))
A130654: 0 0 1 0 1 1 1 0 1 1 1 1 1 2 1 0
((if ((x + 1) mod 5) <= 0 then 2 else 0) + ((x mod 3) div 2))
A268389: 0 0 1 0 2 1 0 0 1 2 0 1 0 0 3 0
((if (x mod 2) <= 0 then 1 else (2 + (x div 4))) * ((x mod 3) div 2))
A337923: 0 0 1 0 0 3 0 0 1 0 0 4 0 0 1 0
((if (x mod 2) <= 0 then 1 else (2 + ((x div 2) mod 2))) + ((x mod 3) div 2))
A083040: 1 2 2 3 1 3 1 3 2 2 1 4 1 2 2 3
(2 + ((x * (x + loop(\(x,i).(x * (1 + i)),(x div 2),1))) div 3))
A118988: 2 2 4 7 15 20 62
((if x <= 0 then 1 else 2x) - (((x div 2) - (x2 mod 3)) div 2))
A029900: 1 3 4 6 8 10 11 13 15 16 18 20 21 24 25 27
(2 + ((x div 2) div (1 + (if (2 - (x mod 5)) <= 0 then x else 2))))
A068049: 2 2 2 2 2 2 3 2 2 2 3 3 2 2 2 4
((~1 + loop(\(x,i).(3 * (x mod 7)),x,2)) div 2)
A021039: 0 2 8 5 7 1 4 2 8 5 7 1 4 2 8 5
((1 + ((x + (3 * ((if x <= 0 then 1 else x) mod 3))) div 2)) div 2)
A033923: 1 1 2 1 2 3 2 3 4 2 3 4 3 4 5 4
(if x <= 0 then 1 else (20x2 + ~4x + 2))
A022145: 1 18 74 170 306 482 698 954 1250 1586 1962 2378 2834 3330 3866 4442
loop(\(x,i).2x,((x + 1) - (2 * (~x + (x mod 6)))),2)
A147639: 4 8 16 32 64 128 1048576
((1 + (loop(\(x,i).2x,(x + ~1),(3x + 4)) div 2)) div 2)
A098156: 1 2 5 13 32 76 176 400 896 1984 4352 9472 20480 44032 94208 200704
((1 + ((x * ((if (x mod 4) <= 0 then 1 else 2) + (x mod 2))) div 2)) div 2)
A030065: 0 1 1 2 1 4 3 5 2 7 5 8 3 10 7 11
(~2 + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x + 2),1))
A222346: 8 33 124 460 1714 6433 24308 92376 352714 1352076
((2x + 6) * (x2 + loop(\(x,i).4x,x,2)))
A036398: 12 72 360 1644
(x div (2 + (loop(\(x,i).(~2x + 2),x,3) mod (2x + 1))))
A327622: 0 0 1 0 1 1 0 1 1 1 0 1 1 3 1 0
((x + 1) div (2 + (loop(\(x,i).4x,x,1) mod (2x + 1))))
A292594: 0 0 1 1 0 2 2 1 3 3 1 4 0 0 5 5
(~2 + ((2x + 1) * (x + ((if (x mod 2) <= 0 then 2 else 0) + (x div 2)))))
A316724: 0 1 23 26 70 75 141 148 236 245 355 366 498 511 665 680
loop(\(x,i).x6,1,(4x + 2))
A016830: 64 46656 1000000 7529536 34012224 113379904 308915776 729000000 1544804416 3010936384 5489031744 9474296896 15625000000 24794911296 38068692544 56800235584
(if x <= 0 then 1 else ((4x + 2) + ((x + (x div 4)) div 2)))
A247974: 1 6 11 15 20 25 29 34 39 43 48 52 57 62 66 71
loop(\(x,i).x2,1,((4x + 6) * (1 + (x div 2))))
A014738: 36 100 784 1296 4356 6084 14400 18496 36100 44100 76176 90000 142884 164836 246016 278784
(((~1 + (if x <= 0 then 1 else (x - ((~x + 2) div 2)))) * (1 + (x div 2))) div 2)
A258087: 0 0 1 3 6 9 14 18 25 30 39 45 56 63 76 84
((if x <= 0 then 2 else (((x + ~2) * (x div 3)) mod (1 + (x div 2)))) div 2)
A144225-A110855: 1 0 0 0 1 0 0 1 1 0 0 1 2 1 0 0
(loop(\(x,i).(x * ((1 + i) div 2)),x,1) + ((x mod (1 + (x div 2))) mod 2))
A243013: 1 1 1 3 5 12 36
(if x <= 0 then 1 else (2 * ((6x2 + 1) - (x mod 2))))
A110907: 1 12 50 108 194 300 434 588 770 972 1202 1452 1730 2028 2354 2700
((if (x mod 4) <= 0 then 2 else ((x div 2) div (3 - (x mod 2)))) div 2)
A046771: 1 0 0 0 1 0 0 0 1 1 0 1 1 1 1 1
(~2 + loop(\(x,i).(3x + 3),(1 + (x div 2)),(1 + (x mod 2))))
A164265: 4 7 19 28 64 91 199 280 604 847 1819 2548 5464 7651 16399 22960
(2 * (x - (if (x mod 3) <= 0 then (~x + ((x + ~1) div 3)) else 1)))
A335756: 2 0 2 12 6 8 22 12 14 32 18 20 42 24 26 52
(2 + loop(\(x,i).((x + 3) + compr(\x.((x div 4) mod 2),i)),x,1))
A171835: 3 7 12 18 29 41 54 68 87 107 128 150 177 205 234 264
(2 * ((x + 1) + ((if (x mod 3) <= 0 then 1 else x) * (1 + (x mod 2)))))
A238749: 4 8 10 12 18 32
(2 * loop(\(x,i).(1 + (x * ((x * (1 + (2 * (i mod 2)))) div 2))),x,1))
A106274: 2 4 6 26 158
(2 * (1 + compr(\x.(loop(\(x,i).(x * (1 + (i div 2))),x,1) mod (x + 1)),x)))
A139270: 2 8 12 16 18 20 24 28 30 32 36 40 42 44 48 50
(2 * (1 + loop(\(x,i).(x + 3),(~2 + ((x + ~1) div 3)),x)))
A134930: 2 4 6 8 10 12 14 16 18 20 28 30 32 40 42 44
(2 + loop(\(x,i).(26x + ~2),x,1))
A112612: 3 26 624
(0 - loop(\(x,i).(4x * (1 - (2 * (2 + i)))),x,1))
A259057: ~1 20 ~560 20160 ~887040 46126080 ~2767564800 188194406400 ~14302774886400 1201433090457600 ~110531844322099200 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).((10 * (x mod 2)) + (x div 2)),x,1) div 2)
A021023: 0 5 2 6 3 1 5 7 8 9 4 7 3 6 8 4
(2 + ((x + 1) * (((x3 + x2) div 2) + (if x <= 0 then 0 else 1))))
A217200: 2 6 23 78 207 458 891 1578 2603 4062 6063 8726 12183 16578 22067 28818
(((~1 + loop(\(x,i).4x,(2 * (x div 2)),2)) mod (x + 1)) div 2)
A055654: 0 0 0 1 0 0 0 3 2 0 0 3 0 0 0 7
(loop(\(x,i).(1 + (x div (2 + ((~x + 2) mod 4)))),2,(x + 1)) div 2)
A317992: 0 1 0 1 1 1 1 0 1 2 0 1 1 1 1 1
((loop(\(x,i).(x * i),x,(~2 + ((~x + 1) div 3))) mod (x + 1)) div 2)
A165619: 0 0 0 1 1 0 2 0 0 0 2 0 3 0 0 0
loop(\(x,i).(x2 + 2x),1,((x2 + 7x + 6) div 2))
A104473: 15 63 168 360 675 1155 1848 2808 4095 5775 7920 10608 13923 17955 22800 28560
((x + 1) div (2 + (loop(\(x,i).~2x2,2,2) mod (x + 1))))
A213330: 0 1 1 2 1 1 1 4 1 2 1 2 3 1 1 8
(((1 - loop(\(x,i).2x,((x * (x mod 2)) div 2),2)) mod (x + 1)) div 2)
A104594: 0 0 1 0 2 2 3 0 4 4 5 4 6 6 7 0
(2 + compr(\x.(~2 + (loop(\(x,i).(~2x + 1),x,1) mod (x + 2))),(x + 1)))
A246955-A239929: 3 5 7 10 11 13 14 17 19 22 23 26 29 31 34 37
(((x + 1) * (((x + 2) * loop(\(x,i).2x,(x + ~2),x)) div 2)) div 2)
A346174: 0 1 6 30 120 420 1344 4032 11520 31680 84480 219648 559104 1397760 3440640 8355840
(((x + 1) * (2 + (if (x mod 2) <= 0 then (2x + 4) else (x div 2)))) div 2)
A070260: 3 2 15 6 35 12 63 20 99 30 143 42 195 56 255 72
(((x + 1) * (2 + (x * (1 + loop(\(x,i).(x2 + x),2,2))))) div 2)
A098924: 1 45 132 262 435 651 910 1212 1557 1945 2376 2850 3367 3927 4530 5176
(((x2 + 3x + 2) * loop(\(x,i).(x + (i * i)),(x + 1),0)) div 2)
A108674: 1 15 84 300 825 1911 3920 7344 12825 21175 33396 50700 74529 106575 148800 203456
(2 * (loop(\(x,i).x3,(2x + 1),(x + 2)) div (x + 1)))
A059933: 16 7625597484986 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x2 + x),1,((x2 + 3x + 2) div 2))
A213824: 4 30 114 310 690 1344 2380 3924 6120 9130 13134 18330 24934 33180 43320 55624
loop(\(x,i).x5,1,((x2 + 3x + 2) div 2))
A059860: 1 243 7776 100000 759375 4084101 17210368 60466176 184528125 503284375 1252332576 2887174368 6240321451 12762815625 24883200000 46525874176
loop(\(x,i).7x,x,((x2 + 3x + 2) div 2))
A027474: 1 21 294 3430 36015 352947 3294172 29647548 259416045 2219448385 18643366434 154231485954 1259557135291 10173346092735 81386768741880 645668365352248
(((x + 1) * (if (~2 + (x div 5)) <= 0 then x else (x + 2))) div 2)
A077366: 0 1 3 6 10 15 21 28 36 45 55 66 78 91 105 136
(((x + 1) * loop(\(x,i).(x * (1 + (2 * (1 + i)))),x,(x + 2))) div 2)
A001880: 1 15 210 3150 51975 945945 18918900 413513100 9820936125 252070693875 6957151150950 205552193096250 6474894082531875 216659917377028125 4611686018427387903 4611686018427387903
(((x + 1) * loop(\(x,i).(x * (1 + (2 * (2 + i)))),x,(x + 2))) div 2)
A001881: 1 21 378 6930 135135 2837835 64324260 1571349780 41247931725 1159525191825 34785755754750 1109981842719750 37554385678684875 1343291487737574375 4611686018427387903 4611686018427387903
(((x + 1) * loop(\(x,i).(x * (6 + i)),x,(x + 2))) div 2)
A062260: 1 21 336 5040 75600 1164240 18627840 311351040 5448643200 99891792000 1917922406400 38532804710400 809188898918400 17739910476288000 405483668029440000 4611686018427387903
((x + 2) div (2 + (loop(\(x,i).x3,2,2x) mod (x + 1))))
A073752-A003557-A000190: 1 1 1 2 1 1 1 4 3 1 1 2 1 1 1 8
((2x + 2) + loop(\(x,i).(~x + i),((x + 1) + (x div 4)),1))
A214991: 2 6 7 11 14 15 19 20 23 27 28 32 35 36 40 41
(loop(\(x,i).7x,(x + 1),1) mod (2x + 2))
A083530: 1 1 1 1 7 1 7 1 1 9 7 1 7 21 13 1
loop(\(x,i).(x5 + 3x3 + 2x),1,(2x + 2))
A289156: 60 1224 8436 34320 103020 254040 546084 1060896 1907100 3224040 5185620 8004144 11934156 17276280 24381060 33652800
(if x <= 0 then 1 else ((2x + 2) + (2x div 9)))
A231407: 1 4 6
A186291: 1 4 6 8 10 13 15 17 19 22 24 26 28 30 33 35
(((x + 1) + loop(\(x,i).4x,x,4)) mod (2x + 2))
A015943: 1 2 1 4 9 10 11 8 1 6 15 4 17 2 19 16
((2x + 2) + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))
A341522: 2 5 6 11 10 13 14 23 18 21 22 27 26 29 30 47
((2x + 4) + ((x + (x div 2)) div (if (~x + 2) <= 0 then 2 else 1)))
A247985: 4 7 9 12 15 17 20 23 26 28 31 34 37 39 42 45
((2x + 2) + (((x + (x div 4)) div 2) + (if x <= 0 then 1 else 2)))
A305849: 3 6 9 11 14 17 19 22 25 27 30 32 35 38 40 43
((2x + 2) + (if x <= 0 then 1 else x) - ((x + (x div 2)) div 4))
A184733: 3 5 8 10 13 16 18 21 23 26 29 31 34 37 39 42
((2x + 2) + (((if (~2 + (x div 2)) <= 0 then 1 else 2) + (x div 2)) div 2))
A287723: 2 4 7 9 11 13 16 18 21 23 25 27 30 32 34 36
loop(\(x,i).(x + (2x div 7)),2,(2x + 2))
A190332: 2 6 9 12 15 19 23 25 29 32 36 38 42 46 48 52
((~2x + ~2) + loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2))
A144657: 0 2 14 62 242 912 3418 12854 48602 184736 705410 2704132 10400574 40116572 155117490 601080358
((2x + 2) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A129726: 2 5 9 13 19 23 29 33 39 47 51 59 65 69 75 83
((loop(\(x,i).(x * i),x,(1 + ((x + 1) div 2))) div 2) * ((x + 1) div 2))
A152887: 0 1 2 18 72 720 4320 50400 403200 5443200 54432000 838252800 10059033600 174356582400 2440992153600 47076277248000
(~2 + (loop(\(x,i).(x + (x div 2)),(~2 + (x div 2)),2) + ((x + 1) div 2)))
A242634: 0 1 1 2 2 3 4 5 6 7 9 10 13 14 18 19
(((4 * (if x <= 0 then 1 else x)) div (x + 4)) + ((x + 1) div 2))
A079411: 1 1 2 3 4 5 5 6 6 7 7 8 9 10 10 11
((1 + (x div (if (x mod 8) <= 0 then 2 else 1))) * ((x + 1) mod 2))
A318517: 1 0 3 0 5 0 7 0 5 0 11 0 13 0 15 0
(((x + loop(\(x,i).4x,(x mod 4),1)) mod (x + 1)) div 2)
A242869: 0 0 0 1 0 1 0 3 0 1 2 1 0 1 0 7
(2 * ((x + 1) + (x2 div (x + (if x <= 0 then 1 else (x div 3))))))
A189680: 2 6 10 12 16 20 22 26 30 32 36 40 44 46 50 54
(2 * loop(\(x,i).(4x * (1 + (2 * (1 + i)))),x,(x + 1)))
A123828: 2 80 3360 161280
(((x + 1) * (x + loop(\(x,i).10x,x,2))) div 2)
A081553: 1 21 303 4006 50010 600015 7000021 80000028 900000036 10000000045 110000000055 1200000000066 13000000000078 140000000000091 1500000000000105 16000000000000120
(((x2 + x) * loop(\(x,i).(x * (4 + i)),(x + ~1),x)) div 2)
A037961: 0 1 30 540 8400 126000 1905120 29635200 479001600 8083152000 142702560000 2637143308800 50999300352000 1031319184896000 21785854970880000 480178027929600000
(2 + loop(\(x,i).((x2 + ~2) div 7),2,(x + ~1)))
A004047: 1 1 1 1 1 2 3 4 6 10 19
(loop(\(x,i).(x + (((4 + i) * i) div 2)),(x + 2),(x + ~1)) div 2)
A035107: 3 9 17 29 44 64 88 118 153 195 243 299 362 434 514 604
((~2x + 2) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A173072: 2 1 1 1 3 3 5 5 7 11 11 15 17 17 19 23
(2 + ((x + ~1) * (x + (if x <= 0 then 1 else (3 * (x + (x div 2)))))))
A084828: 1 2 13 32 68
(((x + ~1) * loop(\(x,i).7x,(x + ~2),x)) div 2)
A081137: 0 0 1 21 294 3430 36015 352947 3294172 29647548 259416045 2219448385
((13x2 + 1) * (if x <= 0 then 1 else 2))
A010016: 1 28 106 236 418 652 938 1276 1666 2108 2602 3148 3746 4396 5098 5852
((11x2 + 1) * (if x <= 0 then 1 else 2))
A010012: 1 24 90 200 354 552 794 1080 1410 1784 2202 2664 3170 3720 4314 4952
(((x mod (1 - (x mod (~1 + (x div ~2))))) div 2) + (if x <= 0 then 1 else 2))
A336313: 1 2 2 2 2 2 2 3 3 2 2 3 2 2 3 3
((((x * (x div 3)) div 5) mod 2) + (if x <= 0 then 1 else 2))
A270966: 1 2 2 2 2 3 2 2 3 3 2 2 3 2 3 3
(((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2) + (if x <= 0 then 1 else 2))
A294903-A287841-A105561-A087133-A083399: 1 2 2 2 2 3 2 2 2 3 2 3 2 3 3 2
((((2x + 1) mod (2 + (x div 4))) div 2) + (if x <= 0 then 1 else 2))
A324292: 1 2 2 2 2 3 2 2 2 3 2 3 2 3 4 2
((2 * ((5x + 2) + (x div 2))) + (if x <= 0 then 1 else 2))
A063228: 5 16 28 38 50 60 72 82 94 104 116 126 138 148 160 170
(x + (((x + (x2 mod 3)) div 4) + (if x <= 0 then 1 else 2)))
A184425: 1 3 4 5 7 8 9 11 12 13 14 16 17 18 19 20
(19x2 + (if x <= 0 then 1 else 2))
A010009: 1 21 78 173 306 477 686 933 1218 1541 1902 2301 2738 3213 3726 4277
(23x2 + (if x <= 0 then 1 else 2))
A010013: 1 25 94 209 370 577 830 1129 1474 1865 2302 2785 3314 3889 4510 5177
(31x2 + (if x <= 0 then 1 else 2))
A010020: 1 33 126 281 498 777 1118 1521 1986 2513 3102 3753 4466 5241 6078 6977
(2 + loop(\(x,i).((x + 1) + ((x div (~2 + ((i div 2) mod 2))) mod 2)),x,1))
A091066: 3 5 7 9 10 11 13 15 17 18 19 21 22 23 25 27
(loop(\(x,i).(x + (x div 9)),2,(x2 + 1)) div 2)
A293408: 0 1 2 6 10 15 22 30 40 50 62 75 89 104 121 139
(2 * (2x - (((x div 2) - (if (~2 + (x div 2)) <= 0 then 1 else 0)) div 2)))
A285342: 2 6 8 12 16 20 22 26 28 32 36 40 42 46 50 54
(4 * loop(\(x,i).((x + ~1) + (4 * (i * i))),(x + 1),0))
A199531: 12 72 212 464 860 1432 2212 3232 4524 6120 8052 10352 13052 16184 19780 23872
((loop(\(x,i).(4 * (4x + i)),(x + 1),0) div 2) div 2)
A048447: 1 18 291 4660 74565 1193046 19088743 305419896 4886718345 78187493530 1250999896491 20015998343868 320255973501901 5124095576030430 81985529216486895 4611686018427387903
(2 + (loop(\(x,i).(x + ((~1 + ((2 + i) * i)) * i)),(x + 1),0) div 2))
A290061: 3 10 31 77 162 303 520 836 1277 1872 2653 3655 4916 6477 8382 10678
((x3 + ~x) div (2 + (if ((~x + 2) mod 4) <= 0 then 0 else 2)))
A276670: 0 0 3 6 15 30 105 84 126 180 495 330 429 546 1365 840
((1 + ((x mod 6) + (if (~2 + (x div 2)) <= 0 then 0 else 2))) div 2)
A328481-A089293: 0 1 1 2 2 3 1 2 2 3 3 4 1 2 2 3
(2 - (loop(\(x,i).(x + (x div 9)),x,~2) div 2))
A182280: 3 4 4 5 5 6 6 7 7 8 9 10 11 12 14 15
((2x + 4) div (2 + (if (x mod 7) <= 0 then 1 else 2)))
A078935: 1 1 2 2 3 3 4 6 5 5 6 6 7 7 10 8
(2 + ((x - ((if x <= 0 then 1 else x) div (1 + (x div 5)))) div 2))
A321162: 1 2 2 2 2 3 3 4 4 4 5 6 6 6 7 8
(2 + (if (x + ~1) <= 0 then x else (2 * (1 + (((x + 1) div 2) div 3)))))
A131798: 2 3 4 4 4 6 6 6 6 6 6 8 8 8 8 8
(loop(\(x,i).(x + (x div 2)),x,26) div 2)
A120140: 13 19 29 43 65 97 146 219 328 492 738 1107 1661 2491 3737 5605
(2 * ((1 + loop(\(x,i).(x * (x - (i mod 2))),2x,3)) div 2))
A297105: 4 36 1587600 4611686018427387903
(2 + (if ((x + (x div (2 + (x div 4)))) mod 3) <= 0 then 1 else 2))
A276867: 3 4 3 4 4 3 4 3 4 4 3 4 4 3 4 3
(if (x mod 2) <= 0 then 1 else (2 * ((2x div (1 + (x div 3))) mod 2)))
A107016: 1 0 1 2 1 2 1 0 1 0 1 2 1 2 1 2
(~4 + loop(\(x,i).(10x + 5),(x + 1),1))
A205085: 11 151 1551 15551 155551 1555551 15555551 155555551 1555555551 15555555551 155555555551 1555555555551 15555555555551 155555555555551 1555555555555551 15555555555555551
((loop(\(x,i).(x2 + 2x),1,(x - (x div ~3))) div 2) div 2)
A226023: 0 2 3 6 12 15 20 30 35 42 56 63 72 90 99 110
(4 + ((x + 1) mod (1 + ((1 + (x mod 2)) * (if x <= 0 then 0 else 2)))))
A055166: 4 6 4 8 6 5 5
(if (x + ~3) <= 0 then x else (4 + (x div 7)))
A325282: 0 1 2 3 4 4 4 5 5 5 5 5 5 5 6 6
(4 + loop(\(x,i).5x,(4x + ~2),1))
A228028: 5 29 15629 9765629
(((if x <= 0 then 2 else (x - (x div (1 + ((1 + (x div 2)) div 2))))) div 2) mod 2)
A004609: 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0
(4 + (if x <= 0 then 0 else (1 + ((8 mod (x + 1)) mod 2))))
A103671: 4 5 5 5 6 5 6 5 5 5 5 5 5 5 5 5
(2 * ((1 + ((if x <= 0 then 2 else (x - ((x div 3) mod 2))) div 2)) div 2))
A244478: 2 0 2 2 2 2 4 4 4 4 4 6 6 6 8 8
(x - (x div (~2 - (if ((x + 1) mod 8) <= 0 then 1 else 2))))
A245231: 0 2 3 4 5 7 8 10 10 12 13 14 15 17 18 20
((x div 2) div (2 + ((x + ~1) mod (2 + (if (x mod 4) <= 0 then 2 else 1)))))
A266715: 0 0 0 0 0 0 0 1 0 1 2 1 1 3 2 1
(2 + (if ((x mod ~11) mod 4) <= 0 then 1 else 2))
A276865: 3 4 4 3 4 4 4 3 4 4 4 3 4 4 3 4
(2 + (if (x + ~2) <= 0 then x else (2 + ((2x + 1) div 5))))
A104135: 2 3 4 5 5 6 6 7 7 7 8 8 9 9 9 10
((x + 4) - (if (x + ~2) <= 0 then 1 else (2x div 5)))
A198458: 3 4 5 6 7 7 8 9 9 10 10 11 12 12 13 13
(if (x mod 2) <= 0 then x else (x3 mod 20))
A222237: 0 1 2 7 4 5 6 3 8 9 10 11 12 17 14 15
((if x <= 0 then 2 else (x - (((x div 2) - (x mod 5)) div 2))) div 2)
A301426: 1 1 1 2 2 2 2 3 4 4 4 4 5 6 6 6
(if x <= 0 then 1 else (2 * (((x div 2) mod (1 + (~x mod 4))) div 2)))
A339430: 1 0 0 0 0 2 0 0 0 0 2 0 0 2 0 0
((x + 1) div (if x <= 0 then 1 else (4 * (1 + (~x mod 4)))))
A029362: 1 0 0 0 1 0 0 1 2 0 0 1 3 0 1 2
((((~1 + (if (~x + 2) <= 0 then x else 0)) * (1 + (x div 4))) div 2) mod 2)
A255851: 1 1 0 1 1 0 1 0 0 0 1 1 0 0 0 0
(if (x mod 2) <= 0 then 1 else (2 + (x div (2 + (x div (1 + (x mod 4)))))))
A306248: 1 2 1 3 1 3 1 4 1 3 1 4 1 3 1 5
((if x <= 0 then 2 else ((x - (3 * (x div 5))) div 2)) div 2)
A029363: 1 0 0 0 1 0 0 1 1 1 1 1 1 1 2 1
(2 + ((3 * ((if (x mod 2) <= 0 then x else (~x + 2)) mod 3)) div 2))
A262565: 2 3 5 5 3 2 2 3 5 5 3 2 2 3 5 5
((x + 4) - ((0 - (if (~x + 2) <= 0 then (x div 2) else 1)) div 3))
A155771: 5 6 7 8 9 10 11 12 14 15 16 17 18 19 21 22
((x - (if x <= 0 then 1 else (x mod (~2 + (3 * (x div 4)))))) mod 2)
A299197: 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0
(if x <= 0 then x else (~2 + ((x + 2) mod (2 + ((2 * (x div 2)) div 3)))))
A072731: 0 ~1 ~2 ~1 ~2 ~1 ~2 ~1 0 1 0 1 0 1 2 3
(~2 + (if x <= 0 then 2 else ((3 * ((x2 + 3x) div 2)) div 2)))
A051349: 0 1 5 11 19 28 38 50 64 79 95 113 133 154 176 200
loop(\(x,i).x2,3,(~11x + ~4))
A017444: 65536 2562890625 208827064576 3512479453921 28179280429056 146830437604321 576480100000000 1853020188851841 5132188731375616 12667700813876161 28525864220672256 59604644775390625 117033789351264256 218041257467152161 388379855336079616
(if (x + ~1) <= 0 then x else (((x + ~1) div (2 + ((x div 2) div 3))) mod 2))
A291291: 0 1 0 1 1 0 1 0 0 0 1 1 0 1 1 1
(2 * loop(\(x,i).(7x + 16),x,6))
A304827: 12 116 844 5940 41612 291316 2039244 14274740 99923212 699462516 4896237644 34273663540 239915644812 1679409513716 11755866596044 82291066172340
(2 * ((3 * (x + loop(\(x,i).i,((x + ~1) div 3),1))) div 2))
A213638: 2 6 8 12 14 18 20 26 30 32 38 42 44 50 54 56
(((3 * (x + (if (~2 + (x div 4)) <= 0 then 2 else 1))) div 2) div 2)
A120503: 1 2 3 3 4 5 6 6 7 8 9 9 9 10 11 12
loop(\(x,i).2x,((3 * (x + ((x div 2) div 3))) div 2),2)
A269758: 2 4 16 32 128 256 2048 8192 16384 65536 131072 524288 4194304 8388608 33554432 67108864
(2 + (if x <= 0 then 1 else (2 * (5x - (x div 3)))))
A063107: 3 12 22 30 40 50 58 68 78 86 96 106 114 124 134 142
((if x <= 0 then 1 else (((1 + ((x + 1) div 2)) * (x mod 3)) div 2)) mod 2)
A095901: 1 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0
(2 + ((if (x mod 2) <= 0 then 1 else (x div 3)) * ((x mod 3) div 2)))
A152727: 2 2 3 2 2 3 2 2 3 2 2 5 2 2 3 2
((~x + 1) mod (if x <= 0 then 1 else (x - ((x - ((x mod 3) div 2)) div 2))))
A229878: 0 0 1 0 1 2
A338630: 0 0 1 0 1 2 1 2 3 2 1 2 1 2 3 2
(if x <= 0 then 1 else (2 * (((x3 + x2) div (x + 3)) mod 2)))
A339441: 1 0 0 0 2 0 0 2 0 2 0 2 0 2 0 0
((((x2 + 3x) * loop(\(x,i).2x,(x + ~1),x)) div 2) div 2)
A058645: 0 1 10 54 224 800 2592 7840 22528 62208 166400 433664 1105920 2768896 6823936 16588800
(2 + (loop(\(x,i).((x + 1) + ((x div 2) div 3)),(x + ~2),1) div 2))
A120179: 2 2 2 3 3 4 4 5 6 7 8 9 11 13 15 17
loop(\(x,i).x5,1,(8x + 4))
A017117: 1024 248832 3200000 17210368 60466176 164916224 380204032 777600000 1453933568 2535525376 4182119424 6590815232 10000000000 14693280768 21003416576 29316250624
((8x + 4) + (if x <= 0 then 1 else (2 * (x + (x mod 2)))))
A063243-A063232: 5 16 24 36 44 56 64 76 84 96 104 116 124 136 144 156
loop(\(x,i).((x2 + x) div 2),1,(~7x + ~4))
A061792: 6 55 153 300 496 741 1035 1378 1770 2211 2701 3240 3828 4465 5151 5886
((if (x mod 2) <= 0 then 1 else (~x + ~1)) + (2 * ((1 + (x div 2)) div 2)))
A110516: 1 ~2 3 ~2 3 ~4 5 ~4 5 ~6 7 ~6 7 ~8 9 ~8
((((3x + 1) * loop(\(x,i).2x,(x + ~1),x)) div 2) div 2)
A276289: 0 1 7 30 104 320 912 2464 6400 16128 39680 95744 227328 532480 1232896 2826240
(4 * (1 + compr(\x.(loop(\(x,i).(2x + 1),x,0) mod (x + 1)),x)))
A062876: 4 12 20 28 44 52 68 76 92 116 124 148 164 172 188 212
(4 + loop(\(x,i).(2 + (3x2 div (1 + i))),x,1))
A116048: 5 7 15 96
((loop(\(x,i).(2 * (2x - (x div (2 + (i mod 2))))),x,1) div 2) div 2)
A136853: 0 1 3 10 30 100 300 1000 3000 10000 30000 100000 300000 1000000 3000000 10000000
(2 * (2 + (loop(\(x,i).x2,2,(4x + ~1)) div (x + 1))))
A306244: 6 84 1604
((if x <= 0 then 2 else ((((x2 div 2) div 3) mod (x + 1)) div 2)) div 2)
A029392: 1 0 0 0 0 1 1 0 0 0 1 2 2 0 0 1
((loop(\(x,i).(5x + ~1),(x + 1),(x + 1)) div 2) div 2)
A014917: 1 11 86 586 3711 22461 131836 756836 4272461 23803711 131225586 717163086 3890991211 20980834961 112533569336 600814819336
((((x + 1) * (if (x mod 2) <= 0 then ((x div 3) mod 2) else 2)) div 2) div 2)
A260437: 0 1 0 2 1 3 0 4 0 5 2 6 0 7 0 8
(if x <= 0 then 1 else (2 + (((2 + (x mod 2) - (x div 2)) mod (x + 1)) div 2)))
A275383: 1 2 2 3 2 2 5 2 5
(((x - (loop(\(x,i).(3x + 3),x,2) mod (x + 1))) div 2) div 2)
A070102: 0 0 0 0 0 0 1 0 1 0 2 0 2 1 3 2
(3 mod (2 + ((loop(\(x,i).(2 * (x - i)),x,2) mod (x + 1)) div 2)))
A306268: 1 1 1 0 1 3 1 0 0 3 1 3 1 3 3 0
((if (x + ~2) <= 0 then x else (x2 div 3)) + (((x + 1) div 2) div 2))
A319158: 0 1 2 4 6 9 13 18 23 29 35 43 51
((if x <= 0 then 1 else (2 + (2x div 3))) - (((x + 1) div 2) div 2))
A346373: 1 2 3 3 3 4 5 4 5 6 6 6 7 7 8 8
((((x + ~1) * (if (x mod 2) <= 0 then ((x mod 3) div 2) else 2)) div 2) div 2)
A279119-A249738: 0 0 0 1 0 2 0 3 1 4 0 5 0 6 3 7
(loop(\(x,i).(x + (2x div (2 + (x div 3)))),(x + ~1),2) div 2)
A062418: 1 1 2 3 4 6 8 10 12 15 17 20 22 25 27 30
(2 + ((2 + (x div 2)) mod (2 + (if (~4 + (x div 2)) <= 0 then 0 else 2))))
A112046: 2 2 3 3 2 2 3 3 2 2 5 5 2 2 3 3
(8 * (1 + loop(\(x,i).(2x + 8),(x + 1),1)))
A304519: 88 232 520 1096 2248 4552 9160 18376 36808 73672 147400 294856 589768 1179592 2359240 4718536
(4 + (if ((x - (x div 4)) mod 5) <= 0 then 1 else 2))
A018246: 5 6 6 6 6 6 5 6 6 6 6 6 6 5 6 6
(2 * (~4 + loop(\(x,i).10x,(x + 1),1)))
A086948: 12 192 1992 19992 199992 1999992 19999992 199999992 1999999992 19999999992 199999999992 1999999999992 19999999999992 199999999999992 1999999999999992 19999999999999992
(4 * (~2 + loop(\(x,i).10x,(x + 1),1)))
A086942: 32 392 3992 39992 399992 3999992 39999992 399999992 3999999992 39999999992 399999999992 3999999999992 39999999999992 399999999999992 3999999999999992 39999999999999992
(8 * (~1 + (2 * (loop(\(x,i).2x,x,2) + (x mod 2)))))
A090860: 24 72 120 264 504 1032 2040 4104 8184 16392 32760 65544 131064 262152 524280 1048584
(x - ((if x <= 0 then 1 else x) div (~4 + (((x + ~1) div 3) mod 2))))
A238369: 1 2 3 4 6 7 8 9 10 12 14 15 16 17 18 19
(if x <= 0 then 1 else (2 + ((((x + ~1) + ((x div 2) div 3)) div 2) mod 2)))
A110012: 1 2 2 3 3 2 3 3 2 2 3 3 2 3 3 2
(((x + 1) div (if x <= 0 then 1 else (x - (2 * (x mod 6))))) mod 2)
A029417: 1 0 0 0 0 0 1 1 0 1 1 0 1 1 1 1
(((x + 1) mod (2 + (if (x mod 2) <= 0 then 1 else (2 + (x mod 3))))) div 2)
A338326: 0 1 0 0 1 0 0 1 0 1 1 0 0 2 0 0
((if x <= 0 then 1 else (((1 + ((x * ((x + 1) div 2)) div 2)) div 2) div 2)) mod 2)
A112609: 1 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1
(8 * (1 + loop(\(x,i).(x + (i * i)),(2x + 1),x)))
A167471: 16 128 464 1152 2320 4096 6608 9984 14352 19840 26576 34688 44304 55552 68560 83456
(8 * loop(\(x,i).(4 * (2x + (x div 2))),x,1))
A047900: 8 64 640 6400 64000 640000 6400000 64000000 640000000 6400000000 64000000000 640000000000 6400000000000 64000000000000 640000000000000 6400000000000000
(8 * loop(\(x,i).(2 * (4x - (x div 2))),x,1))
A223564: 8 64 448 3136 21952 153664 1075648 7529536 52706752 368947264 2582630848 18078415936 126548911552 885842380864 6200896666048 43406276662336
(8 * loop(\(x,i).(x div (2 - (x mod 2))),3,(x + 1)))
A205382: 8 8 24 8 40 24 56 8 72 40 88 24 104 56 120 16
(((2 - ((x - (loop(\(x,i).2x,x,1) div (x + 1))) div 2)) div 2) div 2)
A058932: 0 0 0 0 0 0 1 1 3 5 11 20
loop(\(x,i).(x2 div 4),1,(x - (2 * (((x + 1) div 2) div 2))))
A229878: 0 0 1 0 1 2
A296141: 0 0 1 0 1 2 4 2 4 6 9 6 9 12 16 12
(2 + (4 * loop(\(x,i).(2 + ((x2 + ~x) div 2)),x2,1)))
A275004: 6 10 50 4611686018427387903
(8 * (2 + loop(\(x,i).(2x + 16),x,1)))
A305165: 24 160 432 976 2064 4240 8592 17296 34704 69520 139152 278416 556944 1114000 2228112 4456336
(2 * ((x + 2) - ((if x <= 0 then 1 else x) div (~2 + (x mod ~4)))))
A092121: 6 8 10 12 16 16 20 24 28
(16 * loop(\(x,i).3x,(2x + 1),2))
A203979: 96 864 7776 69984 629856 5668704 51018336 459165024 4132485216 37192366944 334731302496 3012581722464 27113235502176 244019119519584 2196172075676256 19765548681086304
loop(\(x,i).(2x + 6),x,64)
A250654: 64 134 274 554 1114 2234 4474 8954 17914 35834 71674 143354 286714 573434 1146874 2293754
(2 + (if (x + ~2) <= 0 then x else (2 + ((x - ((x div 4) mod 2)) div 2))))
A198454: 2 3 4 5 5 6 6 7 8 8 9 9 9 10 10 11
(2 + (x mod (if ((x + 1) mod 6) <= 0 then 8 else 2)))
A260233: 2 3 2 3 2 7 2 3 2 3 2 5 2 3 2 3
((if x <= 0 then 0 else 1) - (((x - (x2 div 8)) div 2) div 2))
A054911: 0 1 1 1 1 1 1 1 1 2 2 2 3 3 4 5
(2 + ((x - ((if x <= 0 then 1 else x) div (~2 + ((~x + 2) div 4)))) mod 2))
A082844: 3 2 3 2 2 3 2 3 2 2 3 2 3 2 3 2
((x + 2) div (2 + (x div (2 + (if (x mod 2) <= 0 then (x div 4) else 2)))))
A067595: 1 1 1 2 2 2 2 3 2 2 3 3 3 3 4 3
(((x + 2) + ((if (x + ~2) <= 0 then 1 else 2) + ((x div 4) mod 2))) div 2)
A099249: 1 2 2 3 4 5 5 6 6 6 7 7 8 9 9 10
((x + 2) - (if (x + ~1) <= 0 then 1 else (2 * ((x - (x div 4)) div 2))))
A165359: 1 2 2 3 4 3 4 3 4 5 4 5 6 5 6 5
(4 + (if x <= 0 then 1 else (4 * (4x - (x div 2)))))
A063133: 5 20 32 48 60 76 88 104 116 132 144 160 172 188 200 216
(if x <= 0 then 1 else ((x mod 2) - ((x mod (4 + ((x div 2) mod 2))) mod 2)))
A228591: 1 0 0 0 0 0 ~1 1 0 0 0 0 0 0 0 1
((((loop(\(x,i).(2x + 2),(x div 2),(x mod 2)) div 2) div 2) div 2) div 2)
A024792: 0 0 0 0 0 0 0 1 1 2 3 5 7 11 15 23
((if x <= 0 then 2 else (x mod (2 + ((2 - (x div 3)) mod 4)))) div 2)
A319000: 1 0 1 0 0 1 0 0 0 2 0 0 0 0 1 0
((x + ~2) + (2 * (if (~4 + (x div 2)) <= 0 then 1 else 8)))
A103303: 0 1 2 3 4 5 6 7 8 9
A133505-A133134: 0 1 2 3 4 5 6 7 8 9 24 25 26 27 28 29
(if (8 mod (x + 1)) <= 0 then (x + 1) else 16)
A232503: 1 2 16 4 16 16 16 8 16 16 16 16 16 16 16 16
(16 + loop(\(x,i).(2x + 2),(x div 2),(x mod 2)))
A209726: 16 17 18 20 22 26 30 38 46 62 78 110 142 206 270 398
((if (x + ~6) <= 0 then 1 else 2) mod (2 + (x mod 8)))
A044948: 1 1 1 1 1 1 1 2 0 2 2 2 2 2 2 2
((if x <= 0 then 2 else (((x mod 5) * (x div 4)) div 2)) div 2)
A263141: 1 0 0 0 1 0 0 0 1 2 0 0 1 2 3 0
(if x <= 0 then 2 else (1 div ((2x + ~1) mod (4 + (x div 4)))))
A073423: 2 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1
loop(\(x,i).x2,1,(x - (4 div (~4 + (x div 4)))))
A100498: 1 4 9 16 36 49 64 81 100 121 144 169 256 289 324 361
(if x <= 0 then 1 else (2 + ((((x + 2) * (((x + ~1) div 2) div 2)) div 2) mod 2)))
A127992: 1 2 2 2 2 3 2 2 3 3 2 3 2 2 2 3
(2 * (2 + loop(\(x,i).((x + 2) + (((1 + i) * i) div 2)),(x + 2),2)))
A026040: 24 40 64 98 144 204 280 374 488 624 784 970 1184 1428 1704 2014
(if x <= 0 then 1 else (4 * (4x + ((~x + 1) mod 3))))
A176869: 1 16 40 52 64 88 100 112 136 148 160 184 196 208 232 244
(2 + (if x <= 0 then 1 else (2 + ((((x + (x div 2)) div 2) * (x div 2)) mod 2))))
A332420: 3 4 5 4 4 4 4 5 4 4 5 4 4 4 4 5
(if x <= 0 then 1 else (x - (((x + (x div 2)) div (4 + (x div 2))) mod 2)))
A024698: 1 1 2 3 3 4 5 6 7 8 9 10 11 12 13 15
(2 * (if x <= 0 then 2 else ((2x + 4) - ((x - ((x div 2) mod 2)) div 2))))
A119622: 4 12 16 18 20 24 28 30 32 36 40
loop(\(x,i).4x,(x div 2),(1 - (8 * (x mod 2))))
A140721: 1 ~7 4 ~28 16 ~112 64 ~448 256 ~1792 1024 ~7168 4096 ~28672 16384 ~114688
(2x - (((x div 2) - (if (~2 + (x div 2)) <= 0 then 1 else 4)) div 2))
A247422: 1 3 4 6 8 10 13 15 16 18 20 22 23 25 27 29
(8 + (if ((x + 1) mod 10) <= 0 then 0 else 1))
A116667: 9 9 9 9 9 9 9 9 9 8 9 9 9 9 9 9
(8 * ((x + 2) mod loop(\(x,i).(x * i),(x div 4),1)))
A165110: 0 0 0 0 0 0 0 0 0 8 0 8 16 24 32 40
((loop(\(x,i).(x * i),x,3) div (x + 3)) mod 8)
A213611: 1 0 1 3 2 5 0 0
(8 + loop(\(x,i).(10x + 1),x,1))
A165247: 9 19 119 1119 11119 111119 1111119 11111119 111111119 1111111119 11111111119 111111111119 1111111111119 11111111111119 111111111111119 1111111111111119
loop(\(x,i).x2,1,((x - (2 * ((x div 2) mod 2))) mod 8))
A170985: 0 1 0 1 16 25 16 25 0 1 0 1 16 25 16 25
loop(\(x,i).(11x + ~10),x,8)
A199758: 8 78 848 9318 102488 1127358 12400928 136410198 1500512168 16505633838 181561972208 1997181694278 21968998637048 241658985007518 2658248835082688 29240737185909558
(8 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A139049: 8 9 11 13 17 19 23 25 29 35 37 43 47 49 53 59
((loop(\(x,i).(x * i),x,1) div 8) * (x div 8))
A029575: 0 0 0 0 0 0 0 0 5040 45360 453600 4989600 59875200 778377600 10897286400 163459296000
((if (x mod 4) <= 0 then 2 else (x mod 2)) div (2 - (x div 8)))
A029370: 1 0 0 0 1 0 0 0 2 1 0 1 2 1 0 1
loop(\(x,i).(11x + 10),x,8)
A199029: 8 98 1088 11978 131768 1449458 15944048 175384538 1929229928 21221529218 233436821408 2567805035498 28245855390488 310704409295378 3417748502249168 37595233524740858
loop(\(x,i).(x + ((2x2 + ~x) div (x + 2))),x,8)
A295933: 8 20 55 160 475 1420 4255 12760 38275 114820 344455 1033360 3100075 9300220 27900655 83701960
(2 * ((if (x mod 2) <= 0 then (~1 + ((~x + 2) div 4)) else x) mod 4))
A281961: 6 2 6 6 4 2 4
((x + 2) - ((0 - (if (~2 + (x div 4)) <= 0 then 2 else x)) div 4))
A154660: 3 4 5 6 7 8
A108473: 3 4 5 6 7 8 9 10 11 12 13 14 17 19 20 21
(loop(\(x,i).(4x + ((x + 1) mod 4)),x,4) div 2)
A037723: 2 8 35 141 566 2264 9059 36237 144950 579800 2319203 9276813 37107254 148429016 593716067 2374864269
(loop(\(x,i).(4x + ((x + ~1) mod 4)),x,4) div 2)
A037737: 2 9 39 156 626 2505 10023 40092 160370 641481 2565927 10263708 41054834 164219337 656877351 2627509404
(x - loop(\(x,i).(x2 + 2x),1,(x div (~2 + ((~x + 2) div 4)))))
A277425: 0 2 3 4 4 5 6 7 8 6 7 8 9 10 11 12
loop(\(x,i).x2,1,(x - ((x - ((x + (x div 2)) div 4)) div 2)))
A065737: 0 1 1 4 9 9 16 25 36 36 49 64 64 81 100 100
((x + 2) div (2 + (if ((~x + 2) mod 4) <= 0 then 1 else (x div 4))))
A308622: 1 1 1 2 2 2 2 3 2 2 4 3 2 3 5 3
((if ((x + 2) mod 4) <= 0 then (x + ~1) else 0) mod (2 + (x div 4)))
A285720: 0 0 1 0 0 0 2 0 0 0 1 0 0 0 3 0
((2 * (if (~2 + (x div 3)) <= 0 then 1 else 2)) div (2 + (x mod 4)))
A029375: 1 0 0 0 1 0 0 0 1 1 1 0 2 1 1 0
(if x <= 0 then 1 else ((((x * (~1 + ((~x + 2) div 3))) div 2) div 2) mod 2))
A266623: 1 1 1 0 0 1 1 0 0 1 0 1 1 1 0 1
(~2 + (4 * (x + loop(\(x,i).(2 * i),(((x + ~1) div 2) div 2),1))))
A194282: 2 6 10 14 18 26 30 34 38 50 54 58 62 74 78 82
(if x <= 0 then 1 else (2 * ((1 - ((~x + ((x div 2) mod 3)) div 2)) div 2)))
A260984: 1 2 2 2 2 2 4 4 4 4 4 6 6 8 8 8
loop(\(x,i).x2,3,(~11x + ~8))
A017492: 16777216 16983563041 656100000000 7984925229121 53459728531456 248155780267521 899194740203776 2724905250390625 7213895789838336 17181861798319201 37588592026706176 76686282021340161 147578905600000000 270281038127131201 474373168346071296
(2 + ((loop(\(x,i).(5x + ~1),(x + 1),x) div 2) div 2))
A277975: 1 6 56 431 2931 18556 112306 659181 3784181 21362306 119018556 656127931 3585815431 19454956056 104904174806 562667846681
((2 + ((x + loop(\(x,i).(x - (x div ~4)),x,2)) div 2)) div 2)
A052839: 1 2 2 3 3 4 5 6 7 9 11 13 16 19 23 28
(4 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A001749: 8 12 20 28 44 52 68 76 92 116 124 148 164 172 188 212
(2 * (2 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) div 2)))
A175216: 4 4 6 8 12 14 18 20 24 30 32 38 42 44 48 54
(if (x mod 4) <= 0 then 0 else (1 - (2 * (((x + (x div 2)) div 2) mod 2))))
A075553: 0 1 ~1 1 0 ~1 1 ~1 0 1 ~1 1 0 ~1 1 ~1
((4x + 8) * ((x + 1) + (2 * ((if x <= 0 then 1 else x) mod 2))))
A098427: 24 48 48 120 120
(2 * loop(\(x,i).((2x * (4 + i)) div (1 + i)),2x,2))
A054322: 4 80 896 7680 56320 372736 2293760 13369344 74711040 403701760 2122317824 10905190400 54962159616 272461987840 1331439861760 6425271074816
loop(\(x,i).x6,1,8x)
A017070: 0 262144 16777216 191102976 1073741824 4096000000 12230590464 30840979456 68719476736 139314069504 262144000000 464404086784 782757789696 1265319018496 1973822685184 2985984000000
((x - (if x <= 0 then 1 else (((x div 5) * (x div 2)) div 2))) mod 2)
A075532: 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1
(2 + (((if (~2 + (x mod 5)) <= 0 then 1 else 2) + (x div 2)) div 2))
A100197: 2 2 3 3 4 3 4 4 5 5 5 5 5 6 6 6
(if x <= 0 then 1 else (2 + (((x mod ~7) * (x div 2)) mod 2)))
A086410: 1 2 3 2 2 2 3 2 2 2 2 3 2 2 2 2
(2 * ((if ((x mod (2 + (x mod 2))) mod 2) <= 0 then 1 else x) mod (2 + (x div 2))))
A338507: 2 2 2 2 2 2 2 4 2 2 2 2 2 10 2 2
(1 - (((if (x mod 2) <= 0 then (x2 div 2) else 1) + ((x div 2) mod 2)) div 2))
A276168: 1 1 0 0 ~3 1 ~8 0 ~15 1
(4 + loop(\(x,i).(8x + 24),2,(x mod 2)))
A203777: 220 284 220 284 220 284 220 284 220 284 220 284 220 284 220 284
(loop(\(x,i).2x,x,(14 + (x mod 2))) div 2)
A229462: 7 15 28 60 112 240
(loop(\(x,i).(2 * (x - (x div ~2))),(x div 2),(2 + (x mod 2))) div 2)
A083658: 1 1 3 5 9 15 27 45 81 135 243 405 729 1215 2187 3645
(x6 mod loop(\(x,i).(x2 + 2),2,2))
A070661: 0 1 26 7 30 7 30 1 20 11 30 1 20 11 26 11
((1 - (if (x mod (2 + (x mod 6))) <= 0 then x else 0)) mod 4)
A101874: 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 2
((x2 div (if (x mod 3) <= 0 then 2 else (1 + (x div 2)))) mod 4)
A091728: 0 1 2 0 1 0 2 0 0 0 0 0 0 0 0 0
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) mod 4)
A159981: 1 1 2 1 2 2 0 1 2 2 0 2 0 0 0 1
loop(\(x,i).(2x + 4),(((x + 1) div 2) div 2),((x + 1) mod 4))
A200678: 1 2 3 4 6 8 10 12 16 20 24 28 36 44 52 60
((x + loop(\(x,i).i,((~x + 2) mod 7),1)) mod 4)
A084352: 2 2 3 1 1 1 1 1 1 2 0 0 0 0 0 0
((if (((2x mod (2 + (x div 2))) div 2) mod 2) <= 0 then 1 else x) mod 4)
A146289: 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 3
loop(\(x,i).(x - ((2x + 4) div ~7)),x,4)
A020747: 4 6 9 13 18 24 32 42 55 72 94 122 158 204 263 339
loop(\(x,i).x2,1,((x + 4) + (x div (4 + (x div 2)))))
A319388: 16 25 36 49 64 81 100 144 169 196 225 256 289 324 361 400
(if (((x * (~1 + (x mod 3))) div 2) mod 2) <= 0 then 1 else (x div 4))
A116679: 1 1 0 1 1 1 1 1 1 2 1 2 1 1 3 1
((if ((x + 1) mod 4) <= 0 then (x + 4) else 1) + (x div 4))
A138996: 1 1 1 7 2 2 2 12 3 3 3 17 4 4 4 22
((if (x mod 9) <= 0 then x else (x + 1)) + (x div 4))
A153287: 0 2 3 4 6 7 8 9 11 11 13 14 16 17 18 19
((2x + 4) div ((2 * (2 + (if x <= 0 then 0 else 2))) - (x div 4)))
A219610: 1 0 1 1 1 2 2 2 3 3 4 4 5 6 6 6
(x + ((if (x + ~12) <= 0 then 1 else 2) + (x div 4)))
A188042: 1 2 3 4 6 7 8 9 11 12 13 14 16 18 19 20
(x + ((if (~1 + (x div 4)) <= 0 then 1 else 4) + (x div 4)))
A036796: 1 2 3 4 6 7 8 9 14 15 16 17 19 20 21 22
(4 * loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,x))
A128650: 0 4 16 60 224 840 3168 12012 45760 175032 671840 2586584 9984576 38630800 149768640 581690700
loop(\(x,i).(x + ((5x + 10) div (1 + i))),x,4)
A166808: 4 19 54 124 250 460 790 1285 2000 3001 4366 6186 8566 11626 15502 20347
((x + 4) + loop(\(x,i).(x - (x div 12)),2,x))
A032583: 4 6 8 10 12 14 16 18 20 22 24 26 27 28 30 32
(2 + loop(\(x,i).(1 + (6 * ((x + 2) - (i mod 2)))),x,2))
A232956: 4 21 129 771 4629 27771 166629 999771 5998629 35991771 215950629 1295703771 7774222629 46645335771 279872014629 1679232087771
(if x <= 0 then 1 else (2 + ((x + ((x div 2) mod (1 + (x mod 3)))) div 2)))
A296020: 1 2 3 3 4 5 5 6 6 6 7 8 8 8 9 9
(if x <= 0 then 1 else (2 * (x - (2 * (~x + ((x + 2) div 5))))))
A315610: 1 6 12 14 20 26 32 38 40 46 52 58 64 66 72 78
(loop(\(x,i).(6x + ((x + ~1) mod 3)),x,2) div 2)
A037592: 1 6 39 235 1410 8463 50779 304674 1828047 10968283 65809698 394858191 2369149147 14214894882 85289369295 511736215771
(loop(\(x,i).(x + i - (x div ~12)),x,2) div 2)
A008762: 1 2 3 5 8 11 15 20 26 33 41 50 61 73 86 101
loop(\(x,i).x5,1,(6x + 4))
A016961: 1024 100000 1048576 5153632 17210368 45435424 102400000 205962976 380204032 656356768 1073741824 1680700000 2535525376 3707398432 5277319168 7339040224
(loop(\(x,i).(2x * (~1 + (2 * i))),x,(3x + 2)) div 2)
A023999: 1 5 48 660 11760 257040 6652800 198918720 6745939200 255826771200 10727081164800 492775291008000 24610605962342400 1327677426915840000 4611686018427387903 4611686018427387903
(loop(\(x,i).(x2 + ~x),1,((3x2 + x) div 2)) div 2)
A116689: 0 1 21 105 325 780 1596 2926 4950 7875 11935 17391 24531 33670 45150 59340
(x6 mod loop(\(x,i).(x2 + x),2,2))
A070665: 0 1 22 15 22 1 36 7 22 15 22 1 36 1 28 15
(x mod (2 + (if ((x - (x div (1 + (x mod 4)))) mod 2) <= 0 then x else 2)))
A342410: 0 1 2 3 4 1 6 7 8 1 2 3 12 1 14 15
(loop(\(x,i).(2 + (3 * (x mod 7))),x,2) div 2)
A020806: 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2 8
(loop(\(x,i).((5x + 2) - ((x div 2) mod 2)),x,2) div 2)
A037591: 1 5 28 141 705 3528 17641 88205 441028 2205141 11025705 55128528 275642641 1378213205 6891066028 34455330141
(loop(\(x,i).((4x + 2) - ((i mod 3) mod 2)),x,2) div 2)
A037590: 1 4 19 77 308 1235 4941 19764 79059 316237 1264948 5059795 20239181 80956724 323826899 1295307597
(if x <= 0 then 1 else (2 * (2x - ((~x + ((x div 4) mod 2)) div 2))))
A315306: 1 6 10 16 20 24 30 34 40 46 50 56 60 64 70 74
((loop(\(x,i).(x * (3 + i)),x,(3x + 4)) div 2) div 2)
A005460: 1 7 50 390 3360 31920 332640 3780000 46569600 618710400 8821612800 134399865600 2179457280000 37486665216000 681734237184000 13071512982528000
(if x <= 0 then 1 else (2 + ((x + (((x mod 3) * (x div 2)) mod 2)) div 2)))
A229790: 1 2 3 3 4 4 5 6 6 6 7 7 8 8 9 9
((loop(\(x,i).(x + ((2 - (x div 3)) mod 4)),2,x) div 2) div 2)
A029128: 1 1 1 1 1 1 1 1 2 3 3 4 4 4 4 4
((x + 4) + (loop(\(x,i).x2,(x + ~1),~2) div (x + 2)))
A002887: 3 4 7 10 50
(loop(\(x,i).(x + (((x * i) div 5) + (x div 2))),x,2) div 2)
A210517: 1 1 2 5 11 28 76
(2 * ((1 + ((if (~x + 2) <= 0 then x else 0) + (x * (x2 div 2)))) div 2))
A178465: 0 0 6 16 36 66 114 176 264 370 510 672 876 1106 1386 1696
(2 - ((x + 1) mod (~2 + ((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)))))
A243160: 3 2 2 2 0 2 0 0 0 2 0 2 0 0 0 2
(((x + 2) * loop(\(x,i).((x * (4 + (i mod 2))) div 2),x,1)) div 2)
A026955: 1 3 8 25 60 175 400 1125 2500 6875 15000 40625 87500 234375 500000 1328125
((((x + 1) * loop(\(x,i).(x * (2 + i)),(x + 1),x)) div (x + 2)) div 2)
A055602: 0 4 45 432 4200 43200 476280 5644800 71850240 979776000 14270256000 221298739200 3642807168000 63465795993600 1167099373440000 22596613079040000
((3 * (if x <= 0 then 1 else (4 * (x div 2)))) mod (x + 4))
A254280: 3 0 0 5 0 6
(loop(\(x,i).2x,x,2) div (x3 + 8x2 + 20x + 16))
A326596: 0 0 0 0 0 0 0 0 0 0 1 1 2 4 7 11
((if x <= 0 then 1 else 4x) - ((x2 + ~2) div (x + 4)))
A257984: 2 5 8 11 15 18 21 24 27 30 33 37 40 43 46 49
((x * (1 + (if (x mod (2 + (x mod 2))) <= 0 then 2 else 1))) div (x + 4))
A238529: 0 0 1 1 1 1 1 1 2 2 2 1 2 1 2 2
loop(\(x,i).((x + 1) div (2 - ((x mod 3) div 2))),x,(x + 4))
A255524: 4 6 2 3 3 3 2 3 3
loop(\(x,i).(x * ((1 + (2 * i)) * (1 + (2 * i)))),x,(2x + 4))
A003955: 4 54 1800 110250 10716300 1512784350 292183491600 73958946311250 23749039426612500 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((2x + 4) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A078916: 4 7 11 15 21 25 31 35 41 49 53 61 67 71 77 85
(4x div (2 + (if (~4 + (x div 2)) <= 0 then x else (x + 2))))
A321857: 0 1 2 2 2 2 3 3 3 3 2 2 3 3 3 3
(2 - ((if (x mod 5) <= 0 then 1 else (x2 div (x + 2))) mod 2))
A175077: 1 2 1 1 2 1 2 1 2 1 1 1 2 1 2 1
(loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,(x + ~2)) div 2)
A246434: ~1 ~1 0 7 42 198 858 3575 14586 58786 235144 936054 3714500 14709420 58169070 229824855
loop(\(x,i).(1 + ((x + 1) * (1 + (4 mod (x + 1))))),2x,2)
A176941: 2 41 1061
(2 + (if x <= 0 then 1 else (2x + (~2 mod (1 + (x div 4))))))
A135667: 3 4 6 8 10 12 14 16 19 21 23 25 28 30 32 34
(2 + loop(\(x,i).((x + 1) - (x div 7)),2,2x))
A115683-A046349: 4 6 8 9 10 12 14 15 16 18 20 21 22 24 25 27
(if x <= 0 then 1 else (2 * (2x + (((((x + 1) div 2) div 2) div 2) mod 2))))
A311178: 1 4 8 12 16 20 24 30 34 38 42 46 50 54 58 60
(if x <= 0 then 1 else (2 * (2x + (x div (4 + (x div 4))))))
A311344: 1 4 8 12 16 22 26 30 34 38 42 46 50 54 60 64
(if x <= 0 then 2 else (x - (2 * (~2x + ((x + (x div 2)) div 4)))))
A188434: 2 5 10 13 18 23 26 31 34 39 44 47 52 57 60 65
(if x <= 0 then 1 else (2 * (2x + ((x + ((x div 4) mod 2)) div 2))))
A310419: 1 4 10 14 20 26 30 36 40 44 50 54 60 66 70 76
(4x + (if x <= 0 then 1 else (2x div 7)))
A311441: 1 4 8 12 17 21 25 30 34 38 42 47 51 55 60 64
(4x + loop(\(x,i).(2 + (x div 2)),(x + ~8),1))
A314671: 1 5 9 13 17 21 25 29 33 38 43 47 51 55 59 63
(4x + (if x <= 0 then 1 else ((x + (x mod 2)) div 5)))
A311255: 1 4 8 12 16 21 25 29 33 38 42 46 50 54 58 63
((x div (4 - ((x div 2) mod 2))) + (if x <= 0 then 1 else 4x))
A058759: 1 4 8 13
A311847-A311846: 1 4 8 13 17 21 26 30 34 38 43 47 51 55 60 65
(((x + ((x mod 3) div 2)) div 2) + (if x <= 0 then 1 else 4x))
A312941: 1 4 9 13 18 23 27 31 36 40 45 50 54 58 63 67
(((x + ((x div 4) mod 2)) div 2) + (if x <= 0 then 1 else 4x))
A312943: 1 4 9 13 18 23 27 32 36 40 45 49 54 59 63 68
(x + (if x <= 0 then 1 else 4x) - ((~x + ((x div 2) mod 2)) div 2))
A301708: 1 6 11 16 22 28 33 38 44 50 55 60 66 72 77 82
(4x + (if (x + ~1) <= 0 then 1 else (6x + ~4)))
A227586: 1 5 16 26 36 46 56 66 76 86 96 106 116 126 136 146
(4x + (if x <= 0 then 1 else (~2 + (((x + ~1) div 2) * (x div 2)))))
A078476: 1 2 6 11 16 22 28 35 42 50 58 67 76 86 96 107
loop(\(x,i).2x,(((3 * (x div 4)) div 2) + (x div 2)),2)
A086117: 2 2 4 4 16 16 32 32 256 256 512 512 2048 2048 4096 4096
(2 + (x div 2) - (if x <= 0 then 1 else (2 div (8 - (x div 2)))))
A206916-A113609: 1 2 3 3 4 4 5 5 6 6 7 7 7 7 7 7
((if ((x + 2) mod 7) <= 0 then 2 else 1) - ((x div 2) mod 2))
A128582: 1 1 0 0 1 2 0 0 1 1 0 0 2 1 0 0
((if (x mod 2) <= 0 then (x + 20) else (x div 2)) div 2)
A196081: 10 0 11 0 12 1 13 1 14 2 15 2 16 3 17 3
((x + 1) div (2 + (loop(\(x,i).i,(x + ~8),1) + (x mod 2))))
A031284: 0 0 1 1 1 1 2 2 3 2 2 2 2 1 1 1
(loop(\(x,i).(6x + 3),(1 + (x div 2)),(x mod 2)) div 2)
A026534: 1 4 10 28 64 172 388 1036 2332 6220 13996 37324 83980 223948 503884 1343692
(3 - (if ((1 + (x div 3)) mod 4) <= 0 then (x mod 2) else 2))
A171457-A039735-A008406: 1 1 1 1 1 1 1 1 1 2 3 2 1 1 1 1
((if ((x div 2) mod (2 + ((x div 2) mod 2))) <= 0 then 2 else 1) mod (2 + (x mod 2)))
A091297: 0 2 1 1 0 2 0 2 0 2 1 1 0 2 1 1
loop(\(x,i).10x,(1 + (x div 2)),(2 + (x mod 2)))
A181639: 20 30 200 300 2000 3000 20000 30000 200000 300000 2000000 3000000 20000000 30000000
loop(\(x,i).(2x * (1 + (2 * i))),2x,(1 - (2 * (x mod 2))))
A009564: 1 ~60 15120 ~8648640 8821612800 ~14079294028800 32382376266240000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x + (loop(\(x,i).(2 * (x + (x mod 2))),(x + ~1),1) + (2 * (x mod 2))))
A231407: 1 4 6
A007977: 1 4 6 13 20 39 70
(if x <= 0 then 1 else (2 + (13x2 div 2)))
A299289: 1 8 28 60 106 164 236 320 418 528 652 788 938 1100 1276 1464
(~2 + loop(\(x,i).((x + ~1) + i - ((1 + (x div 4)) div 2)),x,2))
A194176: 0 0 1 3 5 8 12 16 21 26 31 37 43 49 56 63
(loop(\(x,i).(x + ((3x2 + 2x) div (2 + i))),x,2) div 2)
A119669: 1 3 23 695
(2 + compr(\x.(~1 + (x mod (~1 + (loop(\(x,i).2x,x,x) mod (x + 1))))),x))
A005236: 2 3 4 5 6 8 9 10 12 14 17 18 20 24 26 28
(2 + compr(\x.(~1 + (x mod (1 + (2 * (if (x mod 3) <= 0 then 0 else 2))))),x))
A028728: 2 3 5 7 8 11 12 13 14
A028743: 2 3 5 7 8 11 12 13 14 17 18 20 22 23 26 27
(2 * loop(\(x,i).(x + 5),(~1 + (x div 5)),x))
A030143: 0 2 4 6 8 10 12 14 16 18 30 32 34 36 38 50
loop(\(x,i).((6x + 1) + ((x + 1) mod 3)),x,2)
A037634: 2 13 81 488 2929 17577 105464 632785 3796713 22780280 136681681 820090089 4920540536 29523243217 177139459305 1062836755832
loop(\(x,i).((8x + 1) + ((1 + i) mod 3)),x,2)
A037643: 2 19 153 1226 9811 78489 627914 5023315 40186521 321492170 2571937363 20575498905 164603991242 1316831929939 10534655439513 84277243516106
loop(\(x,i).((5x + 1) + ((1 + i) mod 3)),x,2)
A037640: 2 13 66 332 1663 8316 41582 207913 1039566 5197832 25989163 129945816 649729082 3248645413 16243227066 81216135332
loop(\(x,i).((9x + 1) + (x mod 3)),x,2)
A037644: 2 21 190 1712 15411 138700 1248302 11234721 101112490 910012412 8190111711 73711005400 663399048602 5970591437421 53735322936790 483617906431112
loop(\(x,i).((8x + 1) + ((1 - i) mod 3)),x,2)
A037636: 2 17 139 1114 8913 71307 570458 4563665 36509323 292074586 2336596689 18692773515 149542188122 1196337504977 9570700039819 76565600318554
(2 + compr(\x.(~1 + (loop(\(x,i).4x,x,1) mod (2x + 1))),x))
A277992: 2 3 4 5 7 8 10 11 13 16 17 20 22 23 25 28
(compr(\x.(~1 + (loop(\(x,i).4x,x,1) mod (2x + 1))),x) div 2)
A075518: 0 0 1 1 2 3 4 4 5 7 7 9 10 10 11 13
(loop(\(x,i).(x2 + x),1,(x3 + 3x2 + x)) div 2)
A055659: 0 15 253 1653 6786 21115 54615 123753 253828 481671 858705 1454365 2359878 3692403 5599531 8264145
((x + loop(\(x,i).(x + i - (x div 8)),(x + ~1),1)) div 2)
A215260: 0 1 2 3 5 8 10 13 16 19 23 26 30 33 37 41
((x + 2) + loop(\(x,i).((2 * (((x + ~1) div 2) div 2)) + i),(x + ~1),1))
A308168: 3 4 5 7 9 11 13 17 19 23 25 29 31 35 37 41
(if x <= 0 then 1 else (x - ((~x + ((x + ~1) mod 7)) div 2)))
A210585: 1 2 3 4 5 6 7 8 12 13 14 15 16 17 18 23
(2 + (x * (if ((x + 2) mod (2 - (x mod ~4))) <= 0 then 2 else 1)))
A064919: 2 3 6 5 10 7 14 16 18 11 22 13 26 28 30 17
((x + 2) + (if (~x + 2) <= 0 then (2 - ((~x + 2) div 8)) else 1))
A325209: 3 4 6 8 9 10 11 12 13 14 15 17 18 19 20 21
loop(\(x,i).x5,1,(5x + 2))
A016877: 32 16807 248832 1419857 5153632 14348907 33554432 69343957 130691232 229345007 380204032 601692057 916132832 1350125107 1934917632 2706784157
loop(\(x,i).x5,1,10x)
A017273: 0 100000 3200000 24300000 102400000 312500000 777600000 1680700000 3276800000 5904900000 10000000000 16105100000 24883200000 37129300000 53782400000 75937500000
loop(\(x,i).(1 + (2 * (2x + (x mod 2))) - ((x div 2) mod 2)),x,2)
A037716: 2 8 33 135 542 2168 8673 34695 138782 555128 2220513 8882055 35528222 142112888 568451553 2273806215
((x + 2) + (3 * (x - ((if x <= 0 then 1 else x) div ~3))))
A187573: 5 9 13 17 24 28 32 39 43 47 54 58 62 69 73 77
loop(\(x,i).(9x + ((x + 1) mod 3)),x,2)
A037518: 2 18 163 1469 13221 118990 1070912 9638208 86743873 780694859 7026253731 63236283580 569126552222 5122138969998 46099250729983 414893256569849
loop(\(x,i).(9x + ((x + ~1) mod 3)),x,2)
A037526: 2 19 171 1541 13870 124830 1123472 10111249 91001241 819011171 7371100540 66339904860 597059143742 5373532293679 48361790643111 435256115788001
loop(\(x,i).(3 * ((x * (~2 + (3 * i))) div (1 + i))),x,2)
A155579: 2 3 12 63 378 2457 16848 120042 880308 6602310 50417640 390736710 3065780340 24307258410 194458067280 1567818167445
loop(\(x,i).(10x + ((~1 + i) mod 3)),x,2)
A037519: 2 20 201 2012 20120 201201 2012012 20120120 201201201 2012012012 20120120120 201201201201 2012012012012 20120120120120 201201201201201 2012012012012012
loop(\(x,i).(7x + ((~1 + i) mod 3)),x,2)
A037516: 2 14 99 695 4865 34056 238394 1668758 11681307 81769151 572384057 4006688400 28046818802 196327731614 1374294121299 9620058849095
loop(\(x,i).((x + ~1) + (6 * ((x + 1) + (x div 2)))),x,2)
A229975: 2 25 252 2525 25252 252525 2525252 25252525 252525252 2525252525 25252525252 252525252525 2525252525252 25252525252525 252525252525252 2525252525252525
((x + 2) + (3 * (2 + (if (x + ~2) <= 0 then 1 else 8))))
A306583: 11 12 13 35 36 37 38 39 40 41 42 43 44 45 46 47
(if x <= 0 then 1 else ((x + 2) + ((x - ((x div 4) mod 2)) div 3)))
A225647: 1 3 4 6 7
A188435: 1 3 4 6 7 8 9 11 12 14 15 16 17 19 20 21
((~1 + loop(\(x,i).4x,x,4)) div (3x + 2))
A191638: 1 3 7 23 73 240 819 2849 10082 36157 131071 479349 1766022 6547206 24403223 91382282
loop(\(x,i).x6,1,(3x + 2))
A016794: 64 15625 262144 1771561 7529536 24137569 64000000 148035889 308915776 594823321 1073741824 1838265625 3010936384 4750104241 7256313856 10779215329
loop(\(x,i).((10x + 2) - (i mod 3)),x,2)
A037527: 2 21 210 2102 21021 210210 2102102 21021021 210210210 2102102102 21021021021 210210210210 2102102102102 21021021021021 210210210210210 2102102102102102
loop(\(x,i).((7x + 2) - (i mod 3)),x,2)
A037524: 2 15 105 737 5160 36120 252842 1769895 12389265 86724857 607074000 4249518000 29746626002 208226382015 1457584674105 10203092718737
(2 * ((~2x2 + ~x) + loop(\(x,i).8x,x,1)))
A003222: 2 10 108 982 8120 65426 524132 4194094 33554160 268435114 2147483228 17179868678 137438952872 1099511627074 8796093021396 70368744176734
(if x <= 0 then 1 else ((x + 2) + (x2 div ((x + 1) + (x div 3)))))
A187685: 1 3 5 6 8 10 12 13 15 17 19 21 22 24 26 27
((x * loop(\(x,i).(((x + 1) - (2 * (x mod 2))) * (1 + i)),x,1)) div 2)
A065087: 0 0 3 12 90 660 5565 51912 533988 6007320 73422855 969181620 13744757598 208462156812 3367465610145 57727981888080
loop(\(x,i).((x + 1) + ((i div (1 + ((x div 2) mod 3))) mod 2)),x,2)
A134623: 2 3 5 7 8 9 11 12 13 15 17 19 20 21 23 25
((x * loop(\(x,i).(2 * (x + (2 * (2x + (x mod 2))))),x,1)) div 2)
A085708: 0 7 140 2100 28000 350000 4200000 49000000 560000000 6300000000 70000000000 770000000000 8400000000000 91000000000000 980000000000000 10500000000000000
(2 + compr(\x.(loop(\(x,i).4x2,2,3) mod (x + 1)),x))
A055600: 2 3 4 5 7 9 10 13 17 19 25 28 33 37 49 55
(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x + 1),x) div 2)
A002737: 0 5 35 189 924 4290 19305 85085 369512 1587222 6760390 28601650 120349800 504131940 2103781365 8751023325
(~2 + loop(\(x,i).(12x + 1),2,(x2 + x)))
A001538: 11 299 875 1739 2891 4331 6059 8075 10379 12971 15851 19019 22475 26219 30251 34571
(~2 + loop(\(x,i).(10x + 1),2,(x2 + x)))
A001535: 9 209 609 1209 2009 3009 4209 5609 7209 9009 11009 13209 15609 18209 21009 24009
(1 + (loop(\(x,i).(2 * (x - i)),x,2x) + ((x2 + x) div 2)))
A104747: 1 4 12 33 87 222 550 1327 3129 7236 16464 36957 82027 180346 393354 852123
((x + (loop(\(x,i).(x2 + 4x + 1),2,x) div (x + 1))) div 2)
A117561: 3 15 38 73 124 194 286 403 548 724 934 1181 1468 1798 2174 2599
(2 * (x + loop(\(x,i).(x - ((~1 + (x div 4)) div 2)),2,(x + ~1))))
A191256-A067368: 2 6 10 14 16 18 22 26 30 34 38 42 46 48 50 54
(4x - ((((x div 4) mod 2) - (if x <= 0 then 1 else x)) div 2))
A314829: 1 5 9 14 18 22 27 31 36 41 45 50 54 58 63 67
((15x + 5) + ((if x <= 0 then 1 else x) mod 2))
A063126: 6 21 35 51 65 81 95 111 125 141 155 171 185 201 215 231
((15x + 6) + ((if x <= 0 then 1 else x) mod 2))
A063157: 7 22 36 52 66 82 96 112 126 142 156 172 186 202 216 232
(19 * (2 - ((if x <= 0 then 1 else x) mod 2)))
A040343: 19 19 38 19 38 19 38 19 38 19 38 19 38 19 38 19
(23 * (2 - ((if x <= 0 then 1 else x) mod 2)))
A040507: 23 23 46 23 46 23 46 23 46 23 46 23 46 23 46 23
(31 * (2 - ((if x <= 0 then 1 else x) mod 2)))
A040931: 31 31 62 31 62 31 62 31 62 31 62 31 62 31 62 31
(loop(\(x,i).(1 + ((~1 + (x2 div 2)) div 5)),2,x) div 2)
A026812: 0 0 0 0 0 0 1 1 2 3 5 7 11 14 20 26
((x + 2) + (x div (2 + (if (~6 + (x div 2)) <= 0 then 2 else 1))))
A080919: 2 3 4 5 7 8 9 10 12 13 14 15 17 18 20 22
((x + 2) + (2 * (if (~2 + (x div 2)) <= 0 then 1 else 12)))
A288658: 4 5 6 7 8 9 32 33 34 35 36 37 38 39 40 41
(loop(\(x,i).(1 + (x * ((4x + 3) + i))),2,x) div 2)
A094081: 5 185 1313 4925 13325 29585 57545 101813 167765 261545 390065 561005 782813 1064705 1416665 1849445
((x + 2) + (2 * (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A100710: 2 5 4 11 6 9 8 23 10 13 12 19 14 17 16 47
(((x + 1) - (loop(\(x,i).(x + ((i * i) div ~2)),x,1) div 2)) div 2)
A175826: 0 1 2 4 6 10 15 22 30 41 54 70 88 110 135 164
((x + 2) + (((x2 - (if (~2 + (x div 2)) <= 0 then 1 else 2)) div 2) div 2))
A072441: 1 3 4 7 9 13 16 20 25 30 36 42 49 56 64 72
((x + (if (x + ~2) <= 0 then 1 else ((x + 2) div (2 + (x div 4))))) mod 2)
A129372: 1 0 1 1 0 1 0 0 0 1 1 0 0 0 1 0
((if (~x + 4) <= 0 then 2 else 1) - ((~x + ((x div 4) mod 2)) div 2))
A317137: 1 2 2 3 4 4 5 5 6 7 7 8 8 8 9 9
((x + 2) + ((loop(\(x,i).(x * (~1 + (2 * i))),x,(x + 2)) div 2) div 2))
A201363: 2 3 7
A281529: 2 3 7 23 163
loop(\(x,i).(8x + ((~x + 2) mod 5)),x,2)
A037720: 2 16 129 1035 8282 66256 530049 4240395 33923162 271385296 2171082369 17368658955 138949271642 1111594173136 8892753385089 71142027080715
loop(\(x,i).x2,1,(1 - ((~x + ((x mod (2 + (x div 2))) div 2)) div 2)))
A246934: 1 4 4 9 9 16 16 16 25 25 36 36 36 49 49 49
loop(\(x,i).((9x + 2) - ((x div 2) mod 2)),x,2)
A037558: 2 19 172 1550 13951 125560 1130042 10170379 91533412 823800710 7414206391 66727857520 600550717682 5404956459139 48644608132252 437801473190270
loop(\(x,i).((10x + 2) - ((x div 2) mod 2)),x,2)
A024763: 2 21 212 2122
A037575: 2 21 212 2122 21221 212212 2122122 21221221 212212212 2122122122 21221221221 212212212212 2122122122122 21221221221221 212212212212212 2122122122122122
loop(\(x,i).(10x + ((2 + i) mod 4)),x,2)
A037750: 2 23 230 2301 23012 230123 2301230 23012301 230123012 2301230123 23012301230 230123012301 2301230123012 23012301230123 230123012301230 2301230123012301
(2 * (x + (if x <= 0 then 2 else (4 + (x * (x - ((~x + 2) div 2)))))))
A099956: 4 12 20 38 56 88
(if x <= 0 then 1 else (2 * (x + (x div (8 - (x div 4))))))
A241071: 1 2 4 6 8 10 12
A340521-A049225-A002202-A002174: 1 2 4 6 8 10 12 16 18 20 22 24 28 30 32 36
((x + 2) + ((x + 1) mod (if (x mod 6) <= 0 then (x + ~2) else 2)))
A112276: 1 3 5 5 7 7 11 9 11 11 13 13 17 15 17 17
(~13 mod loop(\(x,i).4x,x,2))
A267802: 1 3 19 115 499 2035 8179 32755 131059 524275 2097139 8388595 33554419 134217715 536870899 2147483635
(loop(\(x,i).(2x + ~1),(x + ~1),(3x2 + 2x)) div 2)
A183264: 0 2 15 64 220 672 1904 5120 13248 33280 81664 196608 465920 1089536 2519040 5767168
(2 + compr(\x.(loop(\(x,i).(x * (2 + i)),((x + 1) div 2),1) mod (x + 2)),x))
A176423: 3 6 9 10 12 14 15 16 18 20 21 22 24 25 26 27
(2 + compr(\x.(x - (loop(\(x,i).~2x,x,4) mod (x + 2))),x))
A116974: 2 3 5 6 7 11 13 17 19 23 29 31 37 41 43 47
(loop(\(x,i).((x + 2) * (1 + (x * (x mod 2)))),1,(x2 + 2x)) div 2)
A094260: 1 10 5 136 13 666 25 2080 41 5050 61 10440 85 19306 113 32896
(2 + loop(\(x,i).(10x + 8),2,(x2 + 2x)))
A158490: 90 390 890 1590 2490 3590 4890 6390 8090 9990 12090 14390 16890 19590 22490 25590
loop(\(x,i).(12x + ~12),2,(x2 + 2x + 2))
A158543: 132 564 1284 2292 3588 5172 7044 9204 11652 14388 17412 20724 24324 28212 32388 36852
(2 + compr(\x.(1 - (loop(\(x,i).3x2,2,x) mod (x + 2))),x))
A059485: 5 7 10 11 13 14 15 17 19 20 21 22 23 25 26 28
(loop(\(x,i).2x,(x div 2),(2 + (x mod 2))) * (2 + (x * (x mod 2))))
A297439: 4 9 8 30 16 84 32 216 64 528 128 1248 256 2880 512 6528
((x + 2) * loop(\(x,i).((x2 + ~x) div (1 + i)),2,(x + 3)))
A027789: 4 30 120 350 840 1764 3360 5940 9900 15730 24024 35490 50960 71400 97920 131784
(if x <= 0 then 1 else ((2x2 + 9x + ~5) div (x + 2)))
A286808: 1 2 5 8 10 12 15 17 19 21 23 25 27 30 32 34
compr(\x.(2 - (loop(\(x,i).(2x + 2),x,2) mod (1 + (x div 2)))),(x + 2))
A037263: 7 8 10 12 13 14 15 16 18 20 21 22 23 24 25 27
(loop(\(x,i).(~1 + (x mod (1 + (4 * (x mod 2))))),x,1) mod (x + 2))
A264756: 1 0 3 3 2 6 3 2 9 3 2 12 3 2 15 3
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) mod (x + 2))
A067770: 1 1 2 0 2 0 4 6 0 0 8 0 0 10 8 0
(loop(\(x,i).(2x + 2),(x div (4 + (x mod 2))),2) div (x + 2))
A029377: 1 0 0 0 1 0 0 0 1 0 1 1 2 0 1 1
(x div ((x + 2) - (loop(\(x,i).(x2 + 1),2,4) mod (x + 2))))
A228488: 0 1 1 0 1 1 1 1 0 1 1 1 3 1 1 0
((x + 2) * (2 + loop(\(x,i).(x + ((3 + i) * i)),(x + 1),x)))
A200887: 12 51 144 325 636 1127 1856 2889 4300 6171 8592 11661 15484 20175 25856 32657
(loop(\(x,i).((x + 2) + (2x div 5)),x,2) div (x + 2))
A134816: 1 1 1 2 2 3 4 5 7 9 12 16 21 28 37 49
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod (x + 2))
A004650: 0 0 1 2 5 6 1 1 3 7 7 11 13 13 15 2
((if (x mod 4) <= 0 then (1 + (x div 2)) else x) + ((x + 2) * (x mod 2)))
A065171: 1 4 2 8 3 12 6 16 5 20 10 24 7 28 14 32
((x * (2 + (if (x mod 10) <= 0 then 2 else 1))) div (x + 2))
A024708: 0 1 1 1 2 2 2 2 2 2 3 2 2 2 2 2
((x + 2) + loop(\(x,i).(x + i - (x div 12)),2,x))
A099047-A084926: 5 7 9 11 13 15 17 19 21 23 25 26 27 29 31 33
((x + (2 * (loop(\(x,i).(2x + 2),x,2) mod (x + 2)))) div (x + 2))
A340594: 0 0 1 0 1 0 2 2 1 0 1 0 1 1 2 0
((x + ~1) + (((x * (x div 2)) mod 2) + (if (x + ~2) <= 0 then 1 else (x + ~2))))
A007818: 0 1 2 4 5 7 9 12 13 15 17 20 21 23 25 28
(2x + (if ((x div 4) - ((~x + 1) mod 3)) <= 0 then 1 else 0))
A190061: 1 3 5 7 8 11 13 14 17 18 20 23 24 26 28 30
(2x + loop(\(x,i).(1 + (2 * (x mod 2))),(x div 5),0))
A241176: 0 2 4 6 8 11 13 15 17 19 23 25 27 29 31 33
(~2x + loop(\(x,i).(2x + (5 * (i * i))),x,0))
A169832: 0 3 26 99 282 695 1578 3411 7154 14727 29970 60563 121866 244599 490202 981555
(2x + (if (~x + 2) <= 0 then ((x2 + 2x + ~1) div 3) else 1))
A240443: 1 3 6 10 15 21 27 34 42 50
(2x + (if ((x * (x mod 3)) mod 5) <= 0 then 2 else 1))
A133484: 2 3 5 8 9 12 14 15
A181155: 2 3 5 8 9 12 14 15 17 20 22 23 26 27 29 32
(2x + (if (((x + 2) mod (2x + ~1)) mod 3) <= 0 then 2 else 1))
A185392: 2 4 5 8 10 11 13 16 17 19 22 23 25 28 29 31
(2x + (if (((x + 2) mod 8) mod 3) <= 0 then 2 else 1))
A287658: 1 4 5 7 10 11 14 15 17 20 21 23 26 27 30 31
(2x + (if ((x2 + x) mod 12) <= 0 then 2 else 1))
A285253: 2 3 5 8 9 11 13 15 18 19 21 24 26 27 29 32
(2x + (if (~2 + (x2 mod 7)) <= 0 then 2 else 1))
A286687: 2 4 5 8 10 11 14 16 18 19 22 24 25 28 30 32
loop(\(x,i).(x4 + 2x3 + x + 1),3,2x)
A092675: 881 4611686018427387903 4611686018427387903
(((3x2 div (x + 2)) div 2) + (if x <= 0 then 1 else 2x))
A248184: 1 2 5 8 12 15 18 22 25 29 32 35 39 42 46 49
(((x + (2x div 5)) div 2) + (if x <= 0 then 1 else 2x))
A126281: 1 2 5 8 10 13 16 18 21 24 27 29 32 35 37 40
(2x + (if ((x * (x mod 3)) mod 5) <= 0 then 1 else 2))
A231407: 1 4 6
A133483: 1 4 6 7 10 11 13 16
A026147: 1 4 6 7 10 11 13 16 18 19 21 24 25 28 30 31
(2x + (if (((x + 2) mod (2x + ~1)) mod 3) <= 0 then 1 else 2))
A208327: 1 3 6 7 9 12 14 15 18 20 21 24 26 27 30 32
(2x + (if (((x + 2) mod 8) mod 3) <= 0 then 1 else 2))
A287659: 2 3 6 8 9 12 13 16 18 19 22 24 25 28 29 32
(2x + (if ((x2 + x) mod 12) <= 0 then 1 else 2))
A231407: 1 4 6
A285254: 1 4 6 7 10 12 14 16 17 20 22 23 25 28 30 31
(2x + (if (~2 + (x2 mod 7)) <= 0 then 1 else 2))
A286686: 1 3 6 7 9 12 13 15 17 20 21 23 26 27 29 31
(if x <= 0 then 1 else compr(\x.((1 + (x mod (4 - (x mod 2)))) div 2),2x))
A313232: 1 4 9 15 20 24 28 33 39 44 48 52 57 63 68 72
(if x <= 0 then 1 else (2x + ((x div (4 * (2 - (x mod 2)))) mod 2)))
A226722: 1 2 4 6 8 11 12 15 17 18 21 22 25 27 29 31
(~2x + (loop(\(x,i).(x3 + x2 + 1),2x,2) div 2))
A210847: 1 1181 4611686018427387903
loop(\(x,i).((3x2 + ~x) div 2),1,(2x + (x div 2)))
A117793: 0 5 35 70 145 210 330 425 590 715 925 1080 1335 1520 1820 2035
(2x + loop(\(x,i).(3x + (x div (3 + i))),x,2))
A072842: 2 8 23 66 196
(3x + (if (~1 + (2x mod (1 + (x div 2)))) <= 0 then 2 else 1))
A190057: 2 5 8 11 13 17 20 22 26 28 31 34 37 40 43 46
(3x + (if ((x + 2) mod (1 + (x mod 4))) <= 0 then 2 else 1))
A287522: 2 4 7 10 14 16 19 22 26 28 32 34 38 40 43 46
(3x + (if (~2 + (x div (1 + (x mod 4)))) <= 0 then 2 else 1))
A190305: 2 5 8 11 13 17 20 23 25 28 31 35 37 40 43 46
(3x + (if (~2 + (x mod (2 + (x mod 3)))) <= 0 then 2 else 1))
A189386: 2 5 8 11 14 17 20 23 26 29 32 34 38 41 44 47
(3x + (if ((x div ~4) mod 4) <= 0 then 1 else 2))
A308010: 1 5 8 11 14 17 20 23 26 29 32 35 38 40 43 46
(1 + (if (x mod 3) <= 0 then (2 * (2 + (x div 2))) else 1) - (x div 2))
A276524: 5 2 1 6 0
((if (x mod 2) <= 0 then 27 else 1) + (x div 2))
A059952: 27 1 28 2 29 3 30 4 31 5 32 6 33 7 34 8
(if x <= 0 then 1 else ((5 * ((x + 2) + (x mod 2))) + (x div 2)))
A118865-A118608: 1 20 21 31 32 42 43 53 54 64 65 75 76 86 87 97
((if (x mod 2) <= 0 then 1 else 27) + (x div 2))
A059953: 1 27 2 28 3 29 4 30 5 31 6 32 7 33 8 34
(1 + ((if (x mod (2 + ((x + ~1) mod 3))) <= 0 then 0 else x) + (x div 2)))
A026206-A026198-A026182: 1 2 4 5 3 8 10 11 13 14 6 17 7 20 22 23
((1 + (x * loop(\(x,i).(2x + 8),(x + ~2),1))) * (x div 2))
A121147: 0 0 3 31 226
((loop(\(x,i).(x + (((x div 2) + i) div 4)),x,2) div 2) + (x div 2))
A161254: 1 1 2 2 4 4 6 7 10 11 14 17 21 24 29 34
(x + ((if ((x + 1) mod (2 + (x div 3))) <= 0 then 2 else 1) + (x div 2)))
A285970: 1 3 4 5 7 9 10 12 13 15 16 17 19 20 22 23
(x + ((if ((1 + (x div 2)) mod 5) <= 0 then 1 else 2) + (x div 2)))
A187335: 2 3 5 6 8 9 11 12 13 14 17 18 20 21 23 24
(x + ((if ((x + 2) mod (1 + (x mod 4))) <= 0 then 1 else 2) + (x div 2)))
A189669: 1 3 5 6 7 9 11 12 13 15 16 18 19 21 23 24
((if (~4 + ((x + 1) mod 8)) <= 0 then 1 else 0) + (x mod 2))
A125925: 1 2 1 2 0 1 0 2 1 2 1 2 0 1 0 2
(loop(\(x,i).(10x + 10),(x div 2),0) + (x mod 2))
A094026: 0 1 10 11 110 111 1110 1111 11110 11111 111110 111111 1111110 1111111 11111110 11111111
(1 + ((x mod (1 + (loop(\(x,i).2x,x,x) mod (x + 1)))) + (x mod 2)))
A285336-A067695: 1 2 3 2 5 2 7 2 3 2 11 3 13 2 3 2
((if (~x + 2) <= 0 then ((x div 2) - ((x + ~1) div 3)) else 1) - (x mod 2))
A025814: 1 0 1 0 1 0 2 0 2 1 2 1 3 1 3 2
(if x <= 0 then 0 else (1 + (((x - ((x div 2) div ~2)) div 2) + (x mod 2))))
A262991: 0 2 2 4 3 5 5 6 6 7 7 9 8 10 10 11
((if (x mod 3) <= 0 then 1 else (2 mod (1 + (x div 4)))) * (x mod 2))
A283978: 0 0 0 1 0 0 0 0 0 1 0 2 0 2 0 1
((if (x mod 4) <= 0 then 1 else (((x + ~1) div 2) div 3)) + (x mod 2))
A053275: 1 1 0 1 1 1 0 2 1 2 1 2 1 3 2 3
((if x <= 0 then 2 else ((3x + 3) - (x div 3))) + (x mod 2))
A049638: 2 7 9 12 14 18 19 23 25 28 30 34 35 39 41 44
(loop(\(x,i).((x2 + ~3x + 2) div 2),2,(x + 3)) - (x mod 2))
A331429: 0 0 10 35 91 189 351 594 946 1430 2080 2925 4005 5355 7021 9044
(1 + loop(\(x,i).i,((x2 + 2x) mod 6),x) - (x mod 2))
A096015: 1 3 3 3 5 5 7 3 3 3 11 5 13 3 3 3
((if ((x + 1) mod (1 + (x div (2 + (x mod 2))))) <= 0 then 0 else 2) + (x mod 2))
A265745: 0 1 2 1 2 1 2 3 2 3 2 1 2 3 2 3
((if ((x mod 7) mod 3) <= 0 then 1 else 2) + (x mod 2))
A207384: 1 3 2 2 2 3 1 2 2 3 1 3 2 2 1 3
((if ((x * (x mod 8)) mod 3) <= 0 then 1 else 2) - (x mod 2))
A056562: 1 1 2 0 2 1 1 1 1 0 2 0 1 1 1 0
(((if x <= 0 then 1 else ((x + 2) mod (1 + (x div 3)))) mod 2) - (x mod 2))
A284585: 1 ~1 0 0 0 0 0 ~1 1 0 0 0 0 ~1 1 0
((if (((x2 + 1) mod (2 + (x div 2))) div 2) <= 0 then 1 else 2) + (x mod 2))
A327567: 1 2 2 2 1 3 2 2 2 3 2 3 1 3 2 2
(((if x <= 0 then 1 else ((x2 + 2) mod (1 + (x div 2)))) mod 2) - (x mod 2))
A279479-A255320-A089802: 1 ~1 0 0 0 ~1 0 0 1 0 0 0 0 0 0 0
((if ((x2 mod 5) - (x mod 2)) <= 0 then 1 else 2) + (x mod 2))
A123582: 1 2 2 3 2 2 2 3 2 2 1 2
(8 + ((x * (1 + (if (~x + 2) <= 0 then x else 2))) + (x mod 2)))
A114414: 8 12 14 21 28
((1 + (if (x mod 5) <= 0 then 4 else 0)) * (2 - (x mod 2)))
A109013: 10 1 2 1 2 5 2 1 2 1 10 1 2 1 2 5
loop(\(x,i).5x,(x div 2),((x + 2) div (2 - (x mod 2))))
A188545: 1 3 10
A026950: 1 3 10 25 75 175 500 1125 3125 6875 18750 40625 109375 234375 625000 1328125
loop(\(x,i).(10x + 11),(x div 2),(x mod 2))
A094623: 0 1 11 21 121 221 1221 2221 12221 22221 122221 222221 1222221 2222221 12222221 22222221
loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x div 2),(x mod 2))
A138364: 0 1 0 3 0 10 0 35 0 126 0 462 0 1716 0 6435
loop(\(x,i).(3x + ((x + ~1) mod 3)),(x div 2),(x mod 2))
A295484: 0 1 2 3 7
A037078: 0 1 2 3 7 11 21 34 65 102 196 308 588 925 1766 2775
(loop(\(x,i).(1 + (2 * ((x2 + 2x) div 4))),2,x) + (x mod 2))
A212742: 1 2 17 32 97 162 337 512 881 1250 1921 2592 3697 4802 6497 8192
loop(\(x,i).((x + 1) + ((x div (2 * (2 + (x mod 4)))) mod 2)),x,2)
A113508: 2 3 4 6 7 8 9 11 13 14 16 17 18 19 21 23
(if x <= 0 then 1 else ((x + 2) + ((x2 + x) div (x + 8))))
A225647: 1 3 4 6 7
A236444: 1 3 4 6 7 9 11 12 14 16 18 19 21 23 25 27
loop(\(x,i).(x + ((x + (((x div 2) mod 5) mod 2)) div 2)),x,2)
A333589: 2 3 5 7 11 16 24 36 54 81 121 181 271 406 609 913
((3x + 3) mod loop(\(x,i).(x * (2 - (x div (2 + i)))),x,2))
A328034: 1 2 1 4 7 2 5 8 11 14 1 4 7 10 13 16
(1 + ((2 * ((if (~x + 2) <= 0 then 2 else 1) + (x mod 2))) + (x2 div 2)))
A147513: 3 5 7 11 13 19 23 31 37 47
((if x <= 0 then 1 else (6x2 + 2)) - (x2 div 2))
A054275: 1 8 24 52 90 140 200 272 354 448 552 668 794 932 1080 1240
loop(\(x,i).x2,1,((x6 + x3) div 2))
A249586: 0 1 1296 142884 4326400 62015625 549246096 3480528016 17247043584 70801227225 250500250000 785786510916 2231605748736 5829824737009 14183810499600 32455809000000
(loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,x2) div 2)
A145885: 0 1 10 63 336 1650 7722 35035 155584 680238 2939300 12584726 53488800 225990180 950094810 3977737875
(loop(\(x,i).(x4 + x2),1,x4) div 2)
A170780: 0 1 32896 21526641 2147516416 76294140625 1410555793536 16616468167201 140737496743936 926510115949281 5000000050000000 22974865038965521 92442129662509056 332708304999455281 1088976669642580096
((x2 * (x2 + loop(\(x,i).x2,2,x3))) div 2)
A168346: 0 1 8200 2391525 134217856 3051758125 39182082696 339111537625 2199023257600 11438396230761 50000000005000 189874916798941 641959232284800 1968688192863925 5556003412798216 14596463012720625
((x2 * loop(\(x,i).(x3 + x),1,x3)) div 2)
A168412: 0 1 1040 88695 2097664 24415625 181402416 988671775 4294983680 15690559329 50000050000 142655915831 371504309760 896080382665 2024782853744 4324878309375
((x2 * loop(\(x,i).(x * ((x + ~1) + i)),2,x3)) div 2)
A170778: 0 1 8320 2394765 134250496 3051953125 39182921856 339114418825 2199031644160 11438417750841 50000050000000 189875023971061 641959447265280 1968688600715005 5556004150673536 14596464294140625
(loop(\(x,i).(x3 + x2),1,x5) div 2)
A170797: 0 1 16896 7203978 537395200 15263671875 235122725376 2373921992596 17592722915328 102947309439525 500005000000000 2088637053420126 7703541745975296 25593015436291303 77784192406233600
(loop(\(x,i).(x3 + x),1,x5) div 2)
A168507: 0 1 16400 7174575 536871424 15258790625 235092496176 2373780763375 17592186060800 102945566076849 500000000050000 2088624084788351 7703510787417600 25592946507231025 77784047779175024 218946945190809375
((x * loop(\(x,i).(x5 + x3),1,x2)) div 2)
A168661: 0 1 1088 89667 2105344 24453125 181538496 989075143 4296015872 15692921289 50005000000 142665578891 371522101248 896111571277 2024835291584 4324963359375
(loop(\(x,i).(x5 + x3),1,x3) div 2)
A170788: 0 1 16640 7184295 537001984 15259765625 235097531136 2373800931775 17592253153280 102945759757569 500000500000000 2088625263681671 7703513367183360 25592951809295065 77784058109429504
(loop(\(x,i).(x5 + x2),1,x3) div 2)
A168633: 0 1 16416 7174818 536872960 15258796875 235092515616 2373780813796 17592186175488 102945566313045 500000000500000 2088624085593606 7703510788786176 25592946509458783 77784047782670880
((x3 * (x2 + loop(\(x,i).x3,2,x))) div 2)
A168432: 0 1 2064 265842 8389120 122071875 1088395056 6920652004 34359754752 141214797765 500000050000 1569214268886 4458050348544 11649042746887 28346956456560 64873169325000
((x * loop(\(x,i).(x3 + x2),1,x4)) div 2)
A170786: 0 1 4352 807003 33685504 611328125 6535385856 48464682007 274945015808 1271126624409 5000500000000 17262535045811 53499182579712 151442855545813 396867717150464 973116755859375
((x * loop(\(x,i).(x3 + x),1,x4)) div 2)
A168462: 0 1 4112 797283 33554944 610353125 6530350896 48444513607 274877923328 1270932943689 5000000050000 17261356152491 53496602813952 151437553481773 396857386895984 973097534559375
((x * loop(\(x,i).(x2 + x),1,x5)) div 2)
A168627: 0 1 1056 88938 2099200 24421875 181421856 988722196 4295098368 15690795525 50000500000 142656721086 371505678336 896082610423 2024786349600 4324883625000
((x * loop(\(x,i).(x4 + x3),1,x3)) div 2)
A170795: 0 1 4608 826686 34078720 615234375 6560580096 48585742828 275414777856 1272676306365 5005000000000 17274324784266 53527561371648 151506482542051 397002013954560 973385859375000
((x * loop(\(x,i).(x4 + x),1,x3)) div 2)
A168345: 0 1 4104 797202 33554560 610351875 6530347656 48444506404 274877908992 1270932917445 5000000005000 17261356079286 53496602699904 151437553310407 396857386646280 973097534205000
(x + (if ((x + 1) mod 10) <= 0 then (x + 3) else 0))
A236836: 0 1 2 3 4 5 6 7 8 21 10 11 12 13 14 15
(x + (if ((1 + (x div 2)) mod 6) <= 0 then (1 + (x div 2)) else 0))
A103303: 0 1 2 3 4 5 6 7 8 9
A305458: 0 1 2 3 4 5 6 7 8 9 16 17 12 13 14 15
(4x div (x + (if (8 mod (x + 1)) <= 0 then 2 else 0)))
A135282: 0 1 4 2 4 4 4 3 4 4 4 4 4 4 4 4
(x + loop(\(x,i).((x + 1) - ((~x + 1) div (2 + (x div 4)))),x,0))
A328659: 0 2 4 7 10 14 18 23 28 33 38 43 49 55 61 67
(2x - (if (~2 + (x div 2)) <= 0 then (~1 + (x div 5)) else 1))
A277599: 1 3 5 7 9 10 11 13 15 17 19 21 23 25 27 29
(x + (if (~1 + (x div 2)) <= 0 then (1 + (3 * ((~x + 2) div 2))) else 1))
A178915: 4 2 3 1 5 6 7 8 9 10 11 12 13 14 15 16
(x * (1 + loop(\(x,i).(x * (x - i)),2,(4x + 3))))
A322745: 0 1681 23762 131043 465124 1275125 2948406 6041287 11309768 19740249 32580250 51369131 77968812 114594493 163845374 228735375
compr(\x.(~1 + (x mod (1 + (loop(\(x,i).(~2x + 4),x,2) mod (x + 1))))),x)
A172233: 0 1 2 3 4 5 6 8 9 10 11 12 13 16 18 20
(x + loop(\(x,i).(x + i),((2x + ~4) div 7),1))
A193299: 1 2 3 4 5 6 8 9 10 13 14 15 16 20 21 22
(x + loop(\(x,i).i,(5 * (~1 + (((x + 1) div 2) div 2))),1))
A032985: 1 2 3 4 5 6 7 12 13 14 15 21 22 23 24 30
(x + loop(\(x,i).x2,1,(~1 + ((~x + (x mod 2)) div 5))))
A162917: 1 2 6 7 8 9 15 16 17 18 19 20 28 29 30 31
(x + (if (x div 2) <= 0 then 1 else ((x + ~1) - ((x div 3) mod 3))))
A255770: 1 2 3 4 6 8 9 11 13 17 19 21
(x * (1 + (3 * (if (x mod 7) <= 0 then 0 else 2))))
A109048: 0 7 14 21 28 35 42 7 56 63 70 77 84 91 14 105
(x + loop(\(x,i).2x,(1 - ((x div 2) div ~6)),1))
A126388: 2 3 6 7 8 9 10 11 12 13 14 15 16 17 22 23
((~x + 1) + (loop(\(x,i).(2x - (x mod (1 + i))),x,2) div 3))
A326340: 1 1 1 1 4 9 19 42
(x + loop(\(x,i).i,(x div (3 * (8 - (x div 2)))),1))
A290492: 1 2 3 4 5 6 7 8 9 10 11 12 14
A334139-A178864-A058226-A028828: 1 2 3 4 5 6 7 8 9 10 11 12 14 15 18 20
compr(\x.((x2 + 1) mod (1 + loop(\(x,i).(x * (x + i)),2,3))),x)
A156718: 70 99 239 268 408 437 577 606 746 775 915 944 1084 1113 1253 1282
compr(\x.((x2 + ~2) mod (~1 + loop(\(x,i).(x * (x + i)),2,3))),x)
A204766: 13 154 180 321 347 488 514 655 681 822 848 989 1015 1156 1182 1323
loop(\(x,i).(1 + (x div 2)),(x mod (1 + (x mod (3 - (x mod 2))))),x)
A220096: 0 1 2 2 4 3 6 4 3 5 10 6 12 7 5 8
compr(\x.(~1 + (if (((x + ((x div 2) div 3)) div 2) mod 2) <= 0 then x else 1)),x)
A090892: 0 1 2 3 6 9 10 12 13 16 17 19 20 23 26 27
(x + loop(\(x,i).((x + 1) + (2 * ((x div 4) mod 2))),(x + ~1),1))
A301587: 1 2 4 6 8 12 16 18 20 24
A238443-A174973-A125225-A103288-A092903-A005153: 1 2 4 6 8 12 16 18 20 24 28 30 32 36 40 42
(x + ((~x + 1) mod loop(\(x,i).10x,(x + ~1),1)))
A056810: 0 1 11 101 1001 10001 100001 1000001 10000001 100000001 1000000001
((x + ~1) + (loop(\(x,i).(~x + (i * i * (1 + i))),(x + 1),0) div 2))
A256666: 0 5 14 29 51 82 123 176 242 323 420 535 669 824 1001 1202
(x + (if (~x + 4) <= 0 then 26 else 1))
A028426: 1 2 3 4 30 31 32 33 34 35 36 37 38 39 40 41
(x + ((x + 2) div (1 + (2 * (if (~4 + (x div 2)) <= 0 then 2 else 1)))))
A138083: 0 1 2 4 5 6
A260375: 0 1 2 4 5 6 7 8 10 11 14 15 16
((x + 1) + ((x2 + 2x) mod (if (x + ~2) <= 0 then 1 else 6)))
A241082: 1 2 3 7 5 11 7 11 11 13 11 17 13 17 17 19
loop(\(x,i).x5,1,7x)
A016985: 0 16807 537824 4084101 17210368 52521875 130691232 282475249 550731776 992436543 1680700000 2706784157 4182119424 6240321451 9039207968 12762815625
loop(\(x,i).(~6 + (x * i)),x,7x)
A229003: 0 1 10 66 426 2964 22818 195000 1842234 19120260 216604194 2662063728 35297775930 502460232684 7644691295970 123824090015544
loop(\(x,i).(9 * i),(x + ~7),x)
A084689: 0 1 2 3 4 5 6 7 9
A048319: 0 1 2 3 4 5 6 7 9 18 27 36 45 54 63 72
((x div ~3) mod (x + (if (~2 + (x div 4)) <= 0 then 2 else 1)))
A099801: 0 2 3 4 4 5 6 6 7 8 8 9 9 9 10 11
(x + (27 * (if (x + ~2) <= 0 then 0 else 2)))
A201217: 0 1 2 57 58 59 60 61 62 63 64 65 66 67 68 69
(x + loop(\(x,i).x2,1,(~1 + (x div (~2 + ((~x + 2) div 4))))))
A165776: 1 5 6 7 13 14 15 16 17 25 26 27 28 29 30 31
compr(\x.(~1 + ((x2 + 2) mod loop(\(x,i).((x2 + 2) + i),2,2))),x)
A155107: 23 30 76 83 129 136 182 189 235 242 288 295 341 348 394 401
compr(\x.((x2 + ~1) mod (1 + loop(\(x,i).(x2 + ~1),2,4))),x)
A056026: 1 26 199 224 226 251 424 449 451 476 649 674 676 701 874 899
compr(\x.(~1 + ((loop(\(x,i).(x div (2 - (x mod 2))),x,x) div 2) mod 4)),x)
A002479: 0 1 2 3 4 6 8 9 11 12 16 17 18 19 22 24
loop(\(x,i).((x + 1) - ((~x + 1) div (2 + (x div 2)))),5,x)
A345488: 8 11 14 16 17 19 20 22 23 24 25 26 27 28 29 30
loop(\(x,i).x2,3,(11x + 5))
A017456: 390625 4294967296 282429536481 4347792138496 33232930569601 167961600000000 645753531245761 2044140858654976 5595818096650401 13685690504052736 30590228625390625 63527879748485376 124097929967680321 230193853492166656 408485828788939521
loop(\(x,i).x3,1,(11x + 5))
A017451: 125 4096 19683 54872 117649 216000 357911 551368 804357 1124864 1520875 2000376 2571353 3241792 4019679 4913000
loop(\(x,i).x3,2,(11x + 5))
A017457: 1953125 68719476736 7625597484987 165216101262848 1628413597910449 10077696000000000 45848500718449031 167619550409708032 520411082988487293 1423311812421484544 3517876291919921875
loop(\(x,i).x2,3,(11x + 10))
A017516: 100000000 37822859361 1099511627776 11688200277601 72301961339136 318644812890625 1113034787454976 3282116715437121 8507630225817856 19925626416901921 42998169600000000 86730203469006241
loop(\(x,i).x3,1,(11x + 10))
A017511: 1000 9261 32768 79507 157464 274625 438976 658503 941192 1295029 1728000 2248091 2863288 3581577 4410944 5359375
loop(\(x,i).x3,2,(11x + 10))
A017517: 1000000000 794280046581 35184372088832 502592611936843 3904305912313344 20711912837890625 84590643846578176 285544154243029527 833747762130149888 2171893279442309389 4611686018427387903
(x + (10 * (if (~2 + (x div 4)) <= 0 then 0 else 2)))
A103303: 0 1 2 3 4 5 6 7 8 9
A004851: 0 1 2 3 4 5 6 7 8 9 10 11 32 33 34 35
loop(\(x,i).x6,1,5x)
A016854: 0 15625 1000000 11390625 64000000 244140625 729000000 1838265625 4096000000 8303765625 15625000000 27680640625 46656000000 75418890625 117649000000 177978515625
compr(\x.(1 - ((x + (if (x mod 4) <= 0 then 2 else 0)) mod 5)),x)
A191991: 0 1 2 3 4 6 7 9 11 12 13 14 16 17 18 19
compr(\x.(if (x mod 2) <= 0 then 1 else ((x * (x mod 3)) mod 5)),x)
A086748: 3 5 9 15 21 25 27 33 35 39 45 51 55 57 63 65
(x + loop(\(x,i).x2,1,(2 - ((~x + (x mod 2)) div 5))))
A317304: 4 5 11 12 13 14 22 23 24 25 26 27 37 38 39 40
((3x + 1) - ((if (x + ~4) <= 0 then 1 else x) div 4))
A186327: 1 4 7 10 13 15 18 21 23 26 29 32 34 37 40 43
(x + ((2x div 5) + (if (~x + 4) <= 0 then 2 else 1)))
A325600: 1 2 3 5 7 9 10 11 13 14 16 17 18 20 21 23
(x + ((1 + (if (x mod (4 + (x div 2))) <= 0 then x else 0)) mod 3))
A304481: 1 2 3 4 5 6 7 9 8 10 11 12 13 14 15 16
(x + (if x <= 0 then 1 else (3 * (1 + ((x3 + ~x2) div 2)))))
A179905: 1 4 11 33 79 158 279 451 683 984 1363 1829 2391 3058 3839 4743
(x + (if x <= 0 then 1 else 99))
A000865: 1 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114
loop(\(x,i).x3,1,(11x + 3))
A017427: 27 2744 15625 46656 103823 195112 328509 512000 753571 1061208 1442897 1906624 2460375 3112136 3869893 4741632
loop(\(x,i).x3,2,(11x + 3))
A017433: 19683 20661046784 3814697265625 101559956668416 1119130473102767 7427658739644928 35452087835576229 134217728000000000 427929800129788411 1195092568622310912 3004041937984268273
(x + (if x <= 0 then 1 else ((x - ((x * (x div 2)) div 3)) div 3)))
A114955: 1 1 2 3 4 5 6 7 7 8 8 8 8 8 8 8
(x + (loop(\(x,i).(2 + ((x2 + x) div 2)),2,(x + ~1)) div 3))
A222011: 1 2 4 8
A000127: 1 2 4 8 16 31 57 99 163 256 386 562 794 1093 1471 1941
loop(\(x,i).x3,1,(11x + 6))
A017463: 216 4913 21952 59319 125000 226981 373248 571787 830584 1157625 1560896 2048383 2628072 3307949 4096000 5000211
loop(\(x,i).x3,2,(11x + 6))
A017469: 10077696 118587876497 10578455953408 208728361158759 1953125000000000 11694146092834141 51998697814228992 186940255267540403 572994802228616704 1551328215978515625 3802961274698203136
(x + (if x <= 0 then 1 else (((x3 + 3x2 + 2x) div 2) div 3)))
A003600: 1 2 6 13 24 40 62 91 128 174 230 297 376 468 574 695
(x + ((2 * (x - (if ((x div 2) mod 3) <= 0 then 0 else 2))) div 3))
A202267: 0 1 2 3 5 7 10 11 12 13 15 17 20 21 22 23
(x + ((2 * (if (x + ~2) <= 0 then x else (2 - (x div ~2)))) div 3))
A095117: 0 1 3 5 6 8 9 11 12 13 14 16 17 19 20 21
(x + ((2 * ((x + (if (~2 + (x div 2)) <= 0 then 1 else 0)) div 2)) div 3))
A039099: 0 1 2 4 5 7 8 9 10 11 13 14 16 17 18 19
(~x + ((loop(\(x,i).((x + ~1) * (x + i)),2,(x + 2)) div 2) div 3))
A212755: 1 10 37 96 205 386 665 1072 1641 2410 3421 4720 6357 8386 10865 13856
(x + ((2 * (if (~2 + (x div 5)) <= 0 then 2 else x)) div 3))
A267016: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 25
(x + loop(\(x,i).(x2 + ~x),1,(~9x + 3)))
A156676: 6 43 242 603 1126 1811 2658 3667 4838 6171 7666 9323 11142 13123 15266 17571
compr(\x.((2 + (x * loop(\(x,i).(x div (2 - (x mod 2))),x,x))) mod 3),x)
A084087: 1 4 5 7 11 13 16 17 19 20 23 25 28 29 31 35
loop(\(x,i).(x + (2x div (1 + (2 * (i mod 2))))),x,3x)
A187275: 0 5 30 75 300 625 2250 4375 15000 28125 93750 171875 562500 1015625 3281250 5859375
(x + ((x + (if ((x div 3) mod 3) <= 0 then 2 else 0)) div 3))
A230709: 0 2 3 4 5 6 8 9 10 12 14 15 16 17 18 20
(x + (loop(\(x,i).(1 + (x * ((x + ~1) div 3))),2,x) div 3))
A023773: 0 1 2 3 6 7 11 27
(~x + loop(\(x,i).(x + ((4x + 8) div (1 + i))),x,3))
A005718: 3 12 31 65 120 203 322 486 705 990 1353 1807 2366 3045 3860 4828
((x + ~1) + loop(\(x,i).(x + ((x div 5) + (i div 2))),x,2))
A231408: 1 2 4 6 9
A026906: 1 2 4 6 9 13 18 24 32 42 54 69 87 109 136 168
(~x + ((4x + 2) * (8 - (if x <= 0 then 0 else 1))))
A188861: 16 41 68 95 122 149 176 203 230 257 284 311 338 365 392 419
(x + loop(\(x,i).i,(3x + ~30),1))
A263564: 1 2 3 4 5 6 7 8 9 10 11 14 18 22 26 30
compr(\x.((~x + 1) + loop(\(x,i).x2,1,(x mod 10))),x)
A308105: 10 11 12 13 20 21 22 23 24 30 31 32 33 34 35 40
((x + ~1) + loop(\(x,i).(3 + ((x2 + ~2x) div (x + 2))),2,x))
A286972: 2 3 4 5 7 9 11 12 13 15 17 19 21 23 25 27
(~x + loop(\(x,i).(2 * (x - (2 * ((((x + ~1) div 2) div 2) mod 2)))),x,1))
A055614: 1 1 2 5 8 19 38
(x + loop(\(x,i).i,((x2 + x) div (x + 16)),1))
A327261: 1 2 3 4 5 6 7 9 11 12 14 15 17 19 21 22
((x + 1) + loop(\(x,i).(x + ((x div 7) mod 2)),2,x))
A200982: 1 3 5 7 9 11 13 17 19 21 23 25 27 28 29 31
compr(\x.(loop(\(x,i).4x2,2,5) mod (x + 1)),x)
A158911: 0 1 3 4 7 9 15 19 24 31 39 49 63 79 99 124
(x + loop(\(x,i).(x - (x div 12)),3,(x + 1)))
A251238: 1 3 5 7 9 11 13 15 17 19 21 22 23 24 26 28
(x + (loop(\(x,i).((x + 1) + (((x div 2) * i) div 2)),x,1) div (x + 1)))
A118985: 1 2 3 5 7 11 19 40
(x + loop(\(x,i).(1 + (x2 div (x + 8))),2,(x + 1)))
A094222: 1 2 3 4 5 6 8 9 10 12 14 16 17 18 20 22
loop(\(x,i).x5,1,(5x + 4))
A016901: 1024 59049 537824 2476099 7962624 20511149 45435424 90224199 164916224 282475249 459165024 714924299 1073741824 1564031349 2219006624 3077056399
loop(\(x,i).(2 * (2x - (x div (1 + i)))),(x + ~1),(x2 + x))
A119578: 0 2 18 120 700 3780 19404 96096 463320 2187900 10161580 46558512 210924168 946454600 4212243000 18614102400
loop(\(x,i).(~11x + ~1),2,(x2 + x))
A001536: 10 252 736 1462 2430 3640 5092 6786 8722 10900 13320 15982 18886 22032 25420 29050
(x + ((x + loop(\(x,i).(x2 + 3x),(x + ~1),1)) div (x + 1)))
A327059: 1 2 4 10 178
(x + loop(\(x,i).(x + ((4 * (i * i)) div 3)),x,(x + 1)))
A051462: 1 4 11 25 48 83 133 200 287 397 532 695 889 1116 1379 1681
(x * loop(\(x,i).((1 + (x2 div 8)) div 2),2,(x + ~1)))
A326444: 0 0 0 0 0 0 0 0 8 9 20 22 48 65 112 135
((~x2 + x) + loop(\(x,i).(x + (2 * (i * i)) - i),(x + 2),0))
A223833: 7 22 48 89 149 232 342 483 659 874 1132 1437 1793 2204 2674 3207
((x2 + ~x) * loop(\(x,i).((x + ~1) * (x2 div 4)),2,x))
A327375: 0 0 0 72 4752
(x - ((0 - (2 * (x mod 7))) mod (if x <= 0 then 1 else x)))
A043267: 0 1 2 3 4 5 6 7 2 4 6 8 10 12 14 2
(((5x2 + 10x + 5) div 2) - (if x <= 0 then 1 else x))
A128153: 1 9 20 37 58 85 116 153 194 241 292 349 410
((2 * (2x - ((~x + 2) div 5))) + (if x <= 0 then 1 else x))
A313975: 1 5 10 17 22 27 32 37 44 49 54 59 64 71 76 81
((x2 div (~x + 32)) + (if x <= 0 then 1 else x))
A008758: 1 1 2 3 4 5 7 8 10 12 14 16 19 21 24 28
(x + loop(\(x,i).((x + ~1) + i - (((x + 1) div 2) div 3)),x,1))
A198759: 1 2 4 7 11 15 20 25 30 36 42 48 54 60 66 73
(x + loop(\(x,i).(x + (20 * (i * i))),x,1))
A095265: 1 22 103 284 605 1106 1827 2808 4089 5710 7711 10132 13013 16394 20315 24816
(x + loop(\(x,i).(x + ((1 + (2 * (1 + (4 * i)))) * i)),x,1))
A213837: 1 13 52 134 275 491 798 1212 1749 2425 3256 4258 5447 6839 8450 10296
(x + loop(\(x,i).(x + (2 * ((1 + (8 * i)) * i))),x,1))
A213839: 1 20 89 240 505 916 1505 2304 3345 4660 6281 8240 10569 13300 16465 20096
(x + (loop(\(x,i).(x + ((~1 + (i * i * i)) * (2 + i))),x,0) div 2))
A231303: 0 1 16 82 272 707 1568 3108 5664 9669 15664 24310 36400 52871 74816 103496
loop(\(x,i).((x + 1) - ((((~x + 2) div 2) * i) div 5)),2,x)
A028788: 2 3 5 7 8 10 11 12 13 14 15 17 18 20 22 23
(x + (if (x + ~2) <= 0 then 1 else (2 * (1 + (2 mod (1 + (x div 4)))))))
A244217: 1 2 3 5 6 7 8 9 14 15 16 17 18 19 20 21
loop(\(x,i).(1 + ((((x + ~1) * (x div 3)) div 2) div 3)),2,x)
A067284: 1 1 1 1 1 1 1 1 1 1 1 2 3 5 5 8
(x + (if x <= 0 then 1 else ((x mod (~1 + (x mod (~1 + ((~x + 1) div 2))))) mod 2)))
A014684: 1 1 2 4 4 6 6 8 9 10 10 12 12 14 15 16
(x + ((1 + loop(\(x,i).((2x + ~1) * ((2 + i) * i)),x,1)) div 2))
A153230: 1 3 22 596
loop(\(x,i).((2x + 1) - ((x div 7) mod 2)),2,x)
A190694: 3 7 11 14 18 22 26 29 33 37 41 44 48 52 59 63
loop(\(x,i).(x - (7 * ((~x2 + x) div 2))),2,x)
A264894: 0 1 261 1956 7291 19500 42846 82621 145146 237771 368875 547866 785181 1092286 1481676 1966875
loop(\(x,i).(1 + (x div (4 - (x mod (2 + (x mod 3)))))),2,x)
A073808: 1 1 2 2 2 2 2 2 2 2 2 4 2 2 3 2
loop(\(x,i).(1 + ((~16 mod (x + 1)) div 2)),2,x)
A326700: 1 1 2 1 1 2 1 1 2 1 3 2 3 1 2 1
(x + (2 * (1 + (4 * loop(\(x,i).i,(~4 + (x div 2)),1)))))
A062997: 10 11 12 13 14 15 16 17 18 19 20 21 30 31 40 41
loop(\(x,i).(1 + ((x - (x mod (2 + (x div 5)))) div 2)),2,x)
A120425: 1 1 2 2 2 2 3 3 3 2 2 2 4 4 4 4
(x + (2 * (if (2 - (x div 2)) <= 0 then (4 + (x div 4)) else 1)))
A037340: 2 3 4 5 14 15 16 17 20 21 22 23 26 27 28 29
(x + (if (x + ~3) <= 0 then 2 else (((x + 1) - ((x div 2) mod 2)) div 2)))
A225736-A225735-A225734-A225733-A225732-A080671: 2 3 4 5 6 8 9 10 12 14 15 16 18 20 21 22
loop(\(x,i).(((x + 1) div 2) - ((1 + (x div 3)) div 3)),2,x)
A303399: 0 1 1 1 1 2 1 2 2 2 2 3 3 2 2 2
loop(\(x,i).((~3x + ~3) + ((x - (x div 4)) div 2)),2,x)
A101864: 5 13 18 26 34 39 47 52 60 68 73 81 89 94 102 107
(x + (2 * (if (x + ~1) <= 0 then 1 else ((4x + ~4) div 3))))
A223578: 2 3 4 7 12 15 18 23 26 29 34 37 40 45 48 51
(x + (if (~2 + (x div 3)) <= 0 then 1 else (2 * ((x div 2) div 3))))
A342339-A317589-A243068-A242413-A081061-A072303: 1 2 3 4 5 6 7 8 9 11 12 13 16 17 18 19
compr(\x.((x div 2) - (if (x mod 6) <= 0 then x else 6)),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A213517: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 18 24
compr(\x.(((x + 1) mod (1 + (2 * (if (x mod 4) <= 0 then 2 else x)))) mod 2),x)
A139711: 1 3 4 5 7 8 9 11 13 15 16 17 19 21 23 24
(x - loop(\(x,i).(x - ((x mod 6) mod (1 + (x div 2)))),2,x))
A328480: 0 0 0 1 2 3 0 1 2 3 4 5 0 1 2 3
(~x + (loop(\(x,i).(x div (1 + (x mod 2))),x,(3x + 1)) div 2))
A246425: 0 1 ~2 2 ~1 3 ~4 4 ~2 5 ~10 6 ~3 7 ~9 8
((x + 2) + ((if (~2 + (x div 2)) <= 0 then 1 else (2x + ~4)) mod (x + 1)))
A026446: 2 4 5 6 7 8 9 11 13 15 17 19 21 23 25 27
(x + (((if (~2 + (x div 3)) <= 0 then 2 else (x div 2)) mod (x + 1)) div 2))
A039237: 0 1 3 4 5 6 7 8 9 11 12 13 15 16 17 18
loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),((x + ~1) div 2),x)
A218073: 0 1 2 9 12 50 60 245 280 1134 1260 5082 5544 22308 24024 96525
((x2 + x) - loop(\(x,i).((x * ((x + ~1) - i)) div (1 + i)),2,x))
A094696: 0 1 6 13 19 21
(x + (if (x + ~1) <= 0 then 1 else ((2x + ~4) - (x div ~4))))
A248187: 1 2 3 6 9 13 16 19 22 26 29 32 35 39 42 45
(1 - (1 mod (~x + (2 * ((if x <= 0 then 1 else x) mod 10)))))
A259567: 0 1 0 0 0 0 0 0 0 0 10 9 8 7 6 5
loop(\(x,i).(x - ((x + i) div (~2 + (((~x + 2) div 2) div 3)))),2,x)
A183867: 3 4 6 8 9 10 12 13 15 16 17 18 20 21 22 24
loop(\(x,i).x3,1,(11x + 4))
A017439: 64 3375 17576 50653 110592 205379 343000 531441 778688 1092727 1481544 1953125 2515456 3176523 3944312 4826809
loop(\(x,i).x3,2,(11x + 4))
A017445: 262144 38443359375 5429503678976 129961739795077 1352605460594688 8662995818654939 40353607000000000 150094635296999121 472161363286556672 1304773183829244583 3251948521156637184
(x + (if (x + ~1) <= 0 then 1 else (2 * (x div (2 + ((x div 2) div 3))))))
A117070: 1 2 4 5 8 9 10 11 12 15 16 17 18 19 20 21
(x + (if (x + ~2) <= 0 then 1 else x) - ((x - ((x mod 3) div 2)) div 2))
A320928: 1 2 3 5 6 8 9 11 13 14 15 17 18 20 22 23
(x + (2 * (if x <= 0 then 1 else ((x mod 2) - ((x - (x mod 3)) div 2)))))
A087242: 2 3 2 3 2 5 0 3 2 3 2 5 0 3 2 3
(~x + ((0 - (loop(\(x,i).(x * (~1 + (2 * i))),(x + ~2),1) div 2)) div 2))
A118998: 0 ~1 ~2 ~3 ~5 ~9 ~32
compr(\x.((x3 + ~x) mod loop(\(x,i).(x2 + 2x + 1),2,2)),x)
A008856: 0 1 24 25 49 51 75 76 99 100 101 124 125 149 151 175
((x2 + 1) div (x + (2 * (2 + (if (x mod 3) <= 0 then 0 else 2)))))
A131187: 0 0 0 1 1 2 3 3 4 6 5 6 9 8 8 11
(x - loop(\(x,i).(x - ((x - ((~1 + (x div 4)) div 2)) mod 2)),2,x))
A341279: 1 0 1 0 0 1 0 1 0 1 0 1 2 0 1 0
((if x <= 0 then 1 else x) - (x2 div (x + (4 * (2 + (x mod 2))))))
A226142: 1 1 2 3 3 4 4
A294991: 1 1 2 3 3 4 4 5 4 6 5 6 5 7 6 7
loop(\(x,i).(1 + ((2x + 4) div 3)),(x + ~8),x)
A328289: 0 1 2 3 4 5 6 7 8 8 8 7 7 7 7 7
loop(\(x,i).x3,1,(11x + 8))
A017487: 512 6859 27000 68921 140608 250047 405224 614125 884736 1225043 1643032 2146689 2744000 3442951 4251528 5177717
loop(\(x,i).x3,2,(11x + 8))
A017493: 134217728 322687697779 19683000000000 327381934393961 2779905883635712 15633814156853823 66540410775079424 231616946283203125 692533995824480256 1838459212420154507 4435453859151328768 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 - (2 * (x - (x2 div (x - ((~x + 2) div 2)))))),2,x)
A210746: 1 1 1 1 1 3 3 3 3 3 3 5 5 7 7 7
(x + ((loop(\(x,i).(((x + 1) * (1 + i)) + (x div 2)),x,2) div 2) div 2))
A121894: 0 2 8 34 177 1131
(x + (if x <= 0 then 1 else (x - ((4x div (x + 4)) mod 2))))
A098177: 1 2 3 5 8 10 12 14 16 18 20 22 23 25 27 29
loop(\(x,i).(x + (x div 7)),(~4 + (x div 2)),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A252996-A252495-A182175: 0 1 2 3 4 5 6 7 8 9 11 12 14 16 20 21
compr(\x.(if (x div 4) <= 0 then 0 else ((x - (x div 4)) mod 4)),x)
A048301: 0 1 2 3 5 10 15 16 21 26 31 32 37 42 47 48
loop(\(x,i).((x + 1) - (2 * (~1 + (x mod 4)))),(x div 4),x)
A295484: 0 1 2 3 7
A234612: 0 1 2 3 7 6 5 4 8 9 10 11 15 14 13 12
(if x <= 0 then 1 else (x + ((4x div (x + 2)) + (x div 4))))
A056127: 1 2 4 5 7 8 10 11 13 14 15 16 18 19 20 21
loop(\(x,i).((16 - (x mod (1 + i))) div (x + 2)),2,x)
A124229: 1 2 2 3 3 3 3 5 5 5 5 5 5 5 5 8
((1 + loop(\(x,i).3x,x,3)) div (3x + 4))
A191634: 1 1 2 6 15 38 99 262 703 1904 5210 14363 39858 111231 311932 878504
(x * (loop(\(x,i).(0 - (2x * (1 + (2 * i)))),x,(x + 2)) div 2))
A085799: 0 ~9 240 ~6300 181440 ~5821200 207567360 ~8172964800 352864512000 ~16593453676800 844757641728000 ~46306798060723200 2720119606364160000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x + i - ((x * (x - i)) div (x + 4))),2,x)
A047700: 5 8 11 13 14 16 17 19 20 21 22 23 24 25 26 27
(x * loop(\(x,i).8x3,2,4x))
A017074: 0 1073741824 1099511627776 63403380965376 1125899906842624 10485760000000000 64925062108545024 303305489096114176 1152921504606846976 3743906242624487424 4611686018427387903
loop(\(x,i).((x + 2) + ((x * (2 + i)) div (x + 8))),2,x)
A105432: 4 6 7 8 10 12 13 14 15 16 17 18 19 20 21 22
compr(\x.(~2 + (if ((x div (2 + ((x div 2) div 3))) mod 2) <= 0 then 1 else x)),x)
A138083: 0 1 2 4 5 6
A326749: 0 1 2 4 5 6 7 8 16 17 20 21 22 23 24 25
loop(\(x,i).(x + ((x + ((x + 2) * i)) div (1 + (2 * (2 + i))))),2,x)
A190719: 0 1 3 5 7 8 11 12 13 15 17 19 20 23 24 25
loop(\(x,i).(x + ((4 * (((x + 1) div 2) div 2)) div 3)),2,x)
A192225: 0 1 2 5
A153384: 0 1 2 5 6 7 9 11 12 15 16 20 21 22 23 26
(x + (if x <= 0 then 1 else ((x + 2) + ((x2 * (x mod 2)) div 3))))
A231407: 1 4 6
A132149: 1 4 6 11 10 20 14
(x * (((3x + 4) * loop(\(x,i).x2,2,(x + 1))) div 2))
A182866: 0 56 810 4992 20000 61560 158466 358400 734832 1395000 2488970 4219776 6854640 10737272 16301250 24084480
(x + ((2 + loop(\(x,i).5x,(x + ~1),x)) div (x + 2)))
A142153: 1 2 5 18 87 451
loop(\(x,i).(~16x + ~16),2,(x2 + 2x))
A158562: 240 1008 2288 4080 6384 9200 12528 16368 20720 25584 30960 36848 43248 50160 57584 65520
loop(\(x,i).(~11x + ~11),2,(x2 + 2x))
A158539: 110 473 1078 1925 3014 4345 5918 7733 9790 12089 14630 17413 20438 23705 27214 30965
loop(\(x,i).(~14x + ~14),2,(x2 + 2x))
A158553: 182 770 1750 3122 4886 7042 9590 12530 15862 19586 23702 28210 33110 38402 44086 50162
loop(\(x,i).(~15x + ~15),2,(x2 + 2x))
A158559: 210 885 2010 3585 5610 8085 11010 14385 18210 22485 27210 32385 38010 44085 50610 57585
(x * loop(\(x,i).((1 + (x2 div 8)) div 2),2,(x + ~2)))
A326523: 0 0 0 0 0 0 0 0 0 9 10 22 24 52 70 120
compr(\x.((~2x + 1) + loop(\(x,i).(x div (2 - (x mod 2))),x,x2)),x)
A082662: 1 2 4 6 8 12 16 20 24 28 32 40 48 56 64 72
((x + 1) + ((2 * loop(\(x,i).(2x + ~4),(x + ~2),x)) + (x div 2)))
A018196: 1 4 8 9 15 32
((3x + 2) + loop(\(x,i).((x + 1) + (x div 4)),2,x))
A321370: 4 8 12 17 22 26 31 35 40 45 49 53 59 63 67 71
(x - loop(\(x,i).((x + 1) - (x mod (1 + (2 * (2 + (x mod 2)))))),x,x))
A060511: 0 0 1 2 3 4 0 1 2 3 4 5 6 7 8 0
loop(\(x,i).(1 + ((x5 + ~2x4 + x3) div 2)),x,x)
A262596: 0 1 1001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2x + loop(\(x,i).(3x2 + 2x + ~1),2,(x + 1)))
A173377: 55 706
((3x + 1) + loop(\(x,i).((x2 + ~x) div (x + 2)),2,x))
A090852: 1 4 7 10 13 16 20 24 27 31 35 39 43 47 51 55
(x + loop(\(x,i).(1 + (x div 2) - ((x div 4) div ~2)),2,x))
A130048: 1 2 4 5 8 9 10 11 13 14 15 16 18 19 21 22
(x + loop(\(x,i).((x + 1) - (x div (6 - (x mod 2)))),2,x))
A296214: 2 4 6 8 9 10 12 14 16 18 20 21 22 24 26 27
(x + (if (~2 + (x div 5)) <= 0 then 10 else x))
A133506: 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 30
(x + loop(\(x,i).(1 + (x2 div (x + 10))),2,x))
A320057: 1 2 3 4 5 6 7 8 10 11 13 14 15 17 19 21
(x + loop(\(x,i).((x2 + ~x) div (8 * (1 + i))),2,x))
A103303: 0 1 2 3 4 5 6 7 8 9
A030141: 0 1 2 3 4 5 6 7 8 9 10 12 14 16 18 21
(x + loop(\(x,i).((1 + (x2 div (4 + (x div 2)))) div 2),2,x))
A067570: 0 1 2 3 4 5 7
A343857-A213715: 0 1 2 3 4 5 7 8 9 11 13 15 16 17 19 21
(~x + (x * loop(\(x,i).(2x2 + 14x + 12),2,2)))
A178027: 0 5291 10582 15873 21164 26455 31746 37037 42328 47619 52910 58201 63492 68783 74074 79365
(x + loop(\(x,i).(x + (((x2 + x) div 2) div (~1 + (2 * i)))),2,x))
A327032: 0 4 12 27 53 95 159 252 382 558 790 1089 1467 1937 2513 3210
(~x + loop(\(x,i).(x + (((~x2 + 1) mod (1 + (x div 2))) div 2)),2,x))
A046779: 0 0 0 0 0 0 0 0 1 0 1 0 4 0 5 0
((x2 + ~1) + (3 * loop(\(x,i).(x * (1 + i)),2x,2)))
A118018: 5 36 723
((x2 + ~1) + (2 * (if (x + ~1) <= 0 then 1 else ((~x + 1) * (x mod 2)))))
A134916: 1 2 3 4 15
A081350: 1 2 3 4 15 16 35 36 63 64 99 100 143 144 195 196
((~x2 + 1) + (x * loop(\(x,i).x2,(x + ~2),(x2 + 1))))
A260967: 1 2 7 292
(~x2 + ((x + 1) * loop(\(x,i).x2,(x2 + ~1),(x + 1))))
A112406: 1 3 19679 4611686018427387903
(x2 + loop(\(x,i).(x + ((1 + (2 * i)) * i)),(2x + 1),x))
A213848: 3 36 131 320 635 1108 1771 2656 3795 5220 6963 9056 11531 14420 17755 21568
(~x4 + loop(\(x,i).12x,x,1))
A024144: 1 11 128 1647 20480 248207 2984688 35829407 429977600 5159773791 61917354224 743008356047 8916100427520 106993205350511 1283918464510448 15407021574535743
(~x4 + loop(\(x,i).10x,x,1))
A024118: 1 9 84 919 9744 99375 998704 9997599 99995904 999993439 9999990000 99999985359 999999979264 9999999971439 99999999961584 999999999949375
(~x4 + loop(\(x,i).7x,x,1))
A024079: 1 6 33 262 2145 16182 116353 821142 5760705 40347046 282465249 1977312102 13841266465 96888981846 678223034433 4747561459318
(~x6 + loop(\(x,i).4x,x,1))
A024042: 1 3 ~48 ~665 ~3840 ~14601 ~42560 ~101265 ~196608 ~269297 48576 2422743 13791232 62282055 260905920 1062351199
(~x6 + loop(\(x,i).3x,x,1))
A024029: 1 2 ~55 ~702 ~4015 ~15382 ~45927 ~115462 ~255583 ~511758 ~940951 ~1594414 ~2454543 ~3232486 ~2746567 2958282
loop(\(x,i).6x,x,x6)
A198403: 0 6 2304 157464 5308416 121500000 2176782336 32934190464 440301256704 5355700839936 60466176000000 642717115324416 6499837226778624 63041475422674944 590045794670739456 4611686018427387903
(~x7 + loop(\(x,i).2x,x,1))
A024017: 1 1 ~124 ~2179 ~16368 ~78093 ~279872 ~823415 ~2096896 ~4782457 ~9998976 ~19485123 ~35827712 ~62740325 ~105397120 ~170826607
(~x7 + loop(\(x,i).(x * i),x,1))
A196414: 1 0 ~126 ~2181 ~16360 ~78005 ~279216 ~818503 ~2056832 ~4420089 ~6371200 20429629 443169792 6164272283 87072877696 1307503508625
(~x5 + loop(\(x,i).3x,2x,1))
A024106: 1 8 49 486 5537 55924 523665 4766162 43013953 387361440 3486684401 31380898558 282429287649 2541865457036 22876791917137 205891131335274
(~x5 + loop(\(x,i).6x,x,1))
A024067: 1 5 4 ~27 272 4651 38880 263129 1646848 10018647 60366176 362636005 2176533504 13060322723 78363626272 470184225201
(~x5 + loop(\(x,i).8x,x,1))
A024093: 1 7 32 269 3072 29643 254368 2080345 16744448 134158679 1073641824 8589773541 68719227904 549755442595 4398045973280 35184371329457
(x5 + loop(\(x,i).5x,x,1))
A001593: 1 6 57 368 1649 6250 23401 94932 423393 2012174 9865625 48989176 244389457 1221074418 6104053449 30518337500
(~x5 + loop(\(x,i).5x,x,1))
A024054: 1 4 ~7 ~118 ~399 0 7849 61318 357857 1894076 9665625 48667074 243891793 1220331832 6102977801 30516818750
(x3 * loop(\(x,i).x2,2,x5))
A010811: 0 1 8388608 94143178827 70368744177664 11920928955078125 789730223053602816 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.loop(\(x,i).(x div (2 - (((x + 1) * (x div 4)) mod 2))),x,x),x)
A263133: 0 1 2 3 5 7 10 11 15 21 23 31 42 43 47 63
((x + 1) - loop(\(x,i).(x - (x div (~x + 16))),x,x))
A273735: 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 16
compr(\x.loop(\(x,i).(x div (2 - ((x2 div 8) mod 2))),x,x),x)
A048715: 0 1 2 4 8 9 16 17 18 32 33 34 36 64 65 66
(~x3 + loop(\(x,i).11x,x,1))
A024130: 1 10 113 1304 14577 160926 1771345 19486828 214358369 2357946962 25937423601 285311669280 3138428374993 34522712141734 379749833580497 4177248169412276
(1 + (x mod (1 + ((1 + (x div 2)) mod (1 + (x div 5))))))
A327499: 1 1 1 1 1 2 1 1 1 2 1 1 1 2 3 1
(1 + ((~x + 4) mod (1 + (x mod (1 + (x div 5))))))
A345934-A060775: 1 1 1 1 1 2 1 2 1 2 1 3 1 2 3 2
(1 + (x div (1 + (x mod (1 + ((x div 2) div (3 + (x mod 2))))))))
A122425: 1 2 3 4 5 6 7 8 9 5 11 6 13 7 5 8
((x + ~1) mod (1 + (x mod (1 + (x mod (1 + ((x + 1) div 3)))))))
A131488: 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 2
(1 + (x div (2 - (x div (~1 + (x mod (~1 + ((~x + 1) div 3))))))))
A220413: 1 1 1 1 1 2 1 2 1 2 2 3 3 2 3 3
(1 + (x mod (1 + ((x + ~6) mod (1 + (x div 3))))))
A329888: 1 1 1 2 1 2 1 2 3 2 1 2 1 2 3 4
(1 + (x mod (1 + ((4 + (x div 2)) mod (1 + (x div 3))))))
A308993-A162401-A000188: 1 1 1 2 1 1 1 2 3 1 1 2 1 1 1 4
(1 + (x mod (1 + ((2 + (x2 div 2)) mod (1 + (x div 3))))))
A047100-A047010: 1 1 1 1 1 1 1 2 1 1 1 3 3 2 1 1
(1 + (x mod (1 + ((2 + (x * (x div 2))) mod (1 + (x div 3))))))
A327857: 1 1 1 2 1 1 1 2 1 1 1 2 3 1 1 4
(1 + (~2x mod (1 + (2x mod (1 + (x div 3))))))
A225630-A152157-A123320-A119269-A096669-A096591-A054123: 1 1 1 1 1 1 1 2 1 1 1 3 2 1 1 1
(1 + (2x2 mod (1 + (2x mod (1 + (x div 3))))))
A191523-A132890: 1 1 1 1 1 1 1 3 1 1 1 3 4 1 1 1
(1 + (x mod (1 + ((x2 + (x mod 2)) mod (1 + (x div 3))))))
A331461-A323718-A297299-A220708-A208891-A185812-A152798-A130580-A124279-A110541-A047120-A047030: 1 1 1 1 1 1 1 2 1 1 1 3 3 1 1 1
(1 + (((x2 + x) div 2) mod (1 + (x mod (1 + (x div 3))))))
A277325: 1 1 1 1 1 2 1 1 1 2 2 3 1 4 1 1
(3 mod (1 + ((x div 2) mod (1 + (x mod (1 + (x div 3)))))))
A346012-A317946: 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 3
(1 + ((2x + 2) mod (1 + ((x div 2) div (1 + (x mod 3))))))
A015137: 1 1 1 1 1 1 3 1 1 1 2 1 6 1 1 1
(~1 - (x mod (1 + (x mod (1 + (~x mod (1 + (x div 2))))))))
A339791: ~1 ~1 ~1 ~2 ~1 ~2 ~1 ~2 ~3 ~2 ~1 ~2 ~1 ~2 ~3 ~2
(1 + (x mod (1 + (x mod (1 + (x div (2 + (x div 5))))))))
A095165-A059981-A033676: 1 1 1 2 1 2 1 2 3 2 1 3 1 2 3 4
(1 + ((x + ~1) mod (1 + (x mod (~1 + (2 * ((x + ~1) div 3)))))))
A326323-A291709-A257493: 1 1 1 1 1 1 1 1 2 1 1 1 3 6 1 1
(1 + (2x mod (1 + (x mod (~1 + (2 * ((x + ~1) div 3)))))))
A275062-A247005: 1 1 1 1 1 1 1 1 2 1 1 1 1 6 1 1
(1 + (x div (1 + (5 mod (1 + (x mod 6))))))
A060789: 1 1 1 2 5 1 7 4 3 5 11 2 13 7 5 8
(1 + (x div (1 + (x mod (1 + ((x mod (2 + (x div 4))) div 2))))))
A324932: 1 2 3 4 5 3 7 8 9 10 11 6 13 7 5 16
(x div (1 + (x mod (1 + (x div (3 + ((x + 1) mod 4)))))))
A099311: 0 1 2 1 4 2 6 3 2 4 10 2 12 6 4 3
(1 + (x mod (1 + (2x mod (~1 + (2 * ((x + ~1) mod 4)))))))
A209972-A184957-A046854: 1 1 1 1 1 1 1 2 1 1 1 2 3 1 1 1
(1 + ((x + 2) mod (1 + (2x mod (~1 + (2 * (x div 4)))))))
A270061: 1 1 1 1 1 1 1 1 1 1 1 2 5 2 1 1
(1 + ((x + 1) mod (1 + (x mod (1 + (x div (2 + (x mod 4))))))))
A206824: 1 1 1 1 2 1 1 1 2 1 2 1 2 3 1 1
(1 + ((x + 1) mod (1 + (x mod (1 + (x div (2 + ((x div 2) mod 2))))))))
A123529: 1 1 1 1 2 1 1 1 2 1 3 1 2 1 1 1
(1 + (x div (1 + ((2x + 4) mod (1 + ((x + 1) mod 4))))))
A344758: 1 2 3 4 5 2 7 8 9 5 11 12 13 14 15 16
(1 + (2x mod (1 + ((x div 2) mod (1 + ((x + ~1) mod 4))))))
A030598: 1 1 1 1 3 1 1 1 1 1 1 2 1 1 1 1
(1 + (((x div 2) div 3) div (1 + ((x + 1) mod 5))))
A046213: 1 1 1 1 1 1 1 1 1 2 1 1 1 1 3 2
(1 + (((x + 1) * (1 + (x mod 2))) mod (1 + (x div 5))))
A318831: 1 1 1 1 1 1 2 1 2 1 3 1 2 2 1 1
(1 + ((x div (2 * (~2 + (x mod 2)))) mod (1 + (x div 5))))
A214247: 1 1 1 1 1 2 1 1 1 2 1 1 1 3 3 1
(1 + ((5 * (x div 2)) mod (1 + (x div 5))))
A290262: 1 1 1 1 1 1 2 2 1 1 2 2 1 1 3 4
(1 + (((x mod 3) + (x mod 2)) mod (1 + (x div 5))))
A070242: 1 1 1 1 1 2 1 1 1 2 2 1 1 3 3 2
((x + 1) - (x div (1 + ((x + 1) mod (1 + ((~x + 2) mod 4))))))
A204160: 1 1 1 1 4 1 1 1 1 1 1 1 7 1 1 1
(1 + ((x + ~1) mod (1 + ((2 * (x div 2)) div (1 + (x div 4))))))
A121884: 1 1 2 3 1 2 2 3 2 3 2 3 4 1 2 3
(1 + (2x mod (1 + ((x div 3) div (1 + (x mod 4))))))
A256384: 1 1 1 1 1 1 1 1 2 1 1 1 5 3 1 1
(1 + ((1 + (x div 2)) mod (1 + ((x div 2) div (1 + (x mod 4))))))
A326840: 1 1 1 1 1 2 1 1 1 3 1 1 1 4 3 1
(1 - ((~x + 1) div (1 + (x mod (1 + (x mod (3 + (x mod 2))))))))
A122811: 0 1 2 2 4 3 6 3 4 5 10 4 12 7 6 5
(1 + (x mod (1 + ((x2 + ~x) mod (1 + (x div (2 + (x mod 2))))))))
A303864: 1 1 1 1 1 1 1 1 1 1 1 3 6 2 1 1
(1 + ((~1 + (x div 2)) mod (1 + ((x div 2) div (1 + (2 * (x mod 2)))))))
A101279: 1 1 1 1 2 1 3 1 4 2 5 1 6 3 7 1
(1 + (x mod (1 + ((2 - ((x + 1) div 5)) mod 3))))
A328231: 1 2 3 1 1 2 1 2 1 1 1 1 1 1 3 1
(1 + ((x2 + x) mod (~1 + (3 * (x div 5)))))
A341850-A341847: 1 1 1 1 1 1 1 1 1 1 1 3 2 3 1 1
(1 + (((~x + 1) + (x mod 2)) mod (1 + ((1 + (x div 2)) div 3))))
A118668: 1 1 1 1 2 2 2 2 2 2 1 1 2 2 3 3
(1 + (((x2 + 2x) div 2) mod (1 + ((1 + (x div 2)) div 3))))
A342083-A323091-A320889-A318357-A316364-A296133-A045778: 1 1 1 1 1 2 1 2 1 2 1 3 1 2 2 2
(1 + (13 mod (1 + ((x + 1) div 3))))
A327343: 1 1 2 2 2 2 2 2 2 2 2 4 4 4 2 2
(1 + (24 mod (1 + ((x + 1) div 3))))
A172359: 1 1 1 1 1 1 1 1 1 1 1 5 5 5 1 1
(1 + (x mod (1 + (((x + ~1) * (2x div 3)) mod 3))))
A329376: 1 1 1 2 1 1 1 1 3 1 1 2 1 1 1 1
(x div (1 + (2x2 mod 19)))
A036856-A036855: 0 0 0 0 0 0 0 1 0 0 0 0 3 0 1 1
(1 + ((x * (~2 + (x div 2))) div 19))
A264591: 1 0 0 0 1 1 1 1 1 1 2 2 3 3 4 4
(1 + (x mod (1 + (((x - ((x div 2) div ~2)) div 2) mod 3))))
A290695: 1 1 1 1 2 1 1 2 3 1 1 2 1 2 1 1
((x + 1) - ((x + 1) mod (1 + (6 * (2 + (x mod 2))))))
A345191: 0 0 0 0 0 0 0 0 0 0 0 0 13 0 13 0
(1 + (x mod (1 + ((1 - ((2 + (x div 2)) mod 4)) mod 3))))
A069349: 1 2 1 2 1 2 1 1 3 1 1 2 1 2 1 1
(26x2 + 52x + 25)
A158551: 25 103 233 415 649 935 1273 1663 2105 2599 3145 3743 4393 5095 5849 6655
(1 + ((2x2 + 8x + 8) div 13))
A025695: 1 2 3 4 6 8 10 13 16 19 23 27 31 35 40 45
(22x2 + 44x + 21)
A158540: 21 87 197 351 549 791 1077 1407 1781 2199 2661 3167 3717 4311 4949 5631
(11x2 + 55x + 43)
A292578: 43 109 197 307 439 593 769 967 1187 1429 1693 1979 2287 2617 2969 3343
(1 + (11 * ((x2 + 3x) div 2)))
A166144: 1 23 56 100 155 221 298 386 485 595 716 848 991 1145 1310 1486
(1 + ((~x + (x2 div 3)) div 11))
A006141: 1 0 0 1 1 1 1 1 2 2 3 3 4 4 5 6
(1 + (x div 8) - (x div (~1 + ((~x + 1) div 3))))
A321318: 1 2 2 3 3 3 3 4 4 5 5 5 5 5 5 5
(1 + (x mod (1 + ((x * (x - ((x div 4) mod 2))) mod 3))))
A274382: 1 2 1 1 1 3 1 1 1 1 1 2 1 1 3 1
(2 div (1 + (x mod (2 - (2x div (~1 + ((~x + 2) div 3)))))))
A331812: 2 1 0 0 0 0 2 2 2 0 0 0 0 0 0 1
(1 + ((x + 1) mod (1 + (x mod (1 - ((~x + (x mod 2)) div 3))))))
A101875-A101871: 1 1 1 1 2 1 1 1 1 1 1 1 2 3 1 1
(1 + (x div (1 + ((1 + ((x mod 3) div 2)) * (x div 3)))))
A065067: 1 2 3 2 3 2 3 3 2 3 3 2 3 3 2 3
((x + 1) - (x2 div ((2x + 3) - (x div 3))))
A047740: 1 2 3 3 4 4 5 5 6 6 6 7 7 8 8 8
((x + 1) - ((x + 1) div (9 - (x div 3))))
A099848: 1 2 3 4 5 6 6 7 8 9 10 10 11 12 12 12
(1 + ((x2 + ~x) div ((2x + 5) - (x div 3))))
A125059: 1 1 1 1 2 2 3 3 3 4 5 5 6 6 7 8
(x mod (1 + ((3 * ((x + 1) div 2)) mod (1 + (x div 3)))))
A049502: 0 0 0 0 0 1 0 0 0 1 2 2 0 1 0 0
(1 + ((2 - (x div (3 + (x mod 2)))) mod (1 + (x mod 3))))
A088429: 1 1 3 1 2 2 1 2 1 1 2 1 1 2 2 1
(1 + ((~x + 1) mod (1 + ((4x + ~4) mod (1 + (x div 2))))))
A136605: 1 1 1 1 1 1 1 1 2 2 1 1 2 3 3 1
(1 + (x mod (1 + ((4x2 + ~8x) mod (1 + (x div 2))))))
A073408: 1 1 1 1 2 1 1 1 3 1 2 1 3 2 1 1
((1 + (2 * ((x + 2) div 3))) * (1 + (x mod ~3)))
A138188: 1 ~3 0 3 ~5 0 5 ~7 0 7 ~9 0 9 ~11 0 11
(1 + (2 div (1 + ((x + 3) mod 14))))
A227141: 1 1 1 1 1 1 1 1 1 1 1 3 2 1 1 1
(1 + (x mod (1 + (2 * ((x + 1) mod (1 + (((x + 1) div 2) div 2)))))))
A106177: 1 1 1 1 2 1 1 3 1 1 1 1 1 4 1 1
(1 + (x2 mod (1 + (x mod (2 * (1 + (((x + 1) div 2) div 2)))))))
A227903: 1 2 1 2 1 2 1 2 2 2 1 2 5 2 1 4
(1 + (x div (1 + ((x mod (~1 + (x mod ~7))) mod 2))))
A295126: 1 2 3 4 5 3 7 8 9 5 11 6 13 7 15 16
(1 + (2 div (1 + (((~2x + 2) mod 9) div 2))))
A308184: 2 3 1 1 2 3 1 1 1 2 3 1 1 2 3 1
(1 + (x mod (1 + ((x mod (1 + (2 * (~x mod 4)))) div 2))))
A082062: 1 1 1 1 1 3 1 1 1 2 1 2 1 2 3 1
(1 + (x div (1 + (2 * ((x + 1) div (3 + (x div 4)))))))
A274701: 1 2 1 2 2 2 3 2 3 2 3 3 3 3 3 4
(1 + (x div (1 + ((x mod (1 + (x mod (2 + (x div 4))))) div 2))))
A319626-A053627: 1 2 3 4 5 3 7 8 9 10 11 6 13 14 5 16
(1 + (x2 mod (1 + ((x2 + ~x) mod 10))))
A083279: 1 1 2 3 2 1 1 2 2 1 1 1 1 2 2 1
(x div (1 + ((2x + 2) mod (1 + ((x mod 5) div 2)))))
A097448: 0 1 2 3 2 5 6 7 8 3 10 11 12 13 14 15
(1 + ((2 + (x div 4)) mod (1 + ((x mod 5) div 2))))
A211354-A211352: 1 1 1 1 1 1 1 2 1 2 1 1 2 2 3 1
(x mod (1 + (x div (3 + ((1 + ((x + 1) div 2)) mod 3)))))
A327188: 0 0 0 1 0 1 0 1 0 1 2 2 0 1 2 3
(1 + ((~x + 1) mod (1 + ((x - ((x div 3) mod 3)) div 2))))
A043554: 1 1 2 1 2 3 2 1 2 3 4 3 2 3 2 1
((x + 1) - (1 div (~1 + (2 * ((x + 2) mod 12)))))
A306866-A239086: 1 2 3 4 5 6 7 8 9 10 12 11 13 14 15 16
((x + 1) - (5 mod (1 + ((x + 1) mod 6))))
A291306: 0 0 2 4 0 6 6 6 8 10 6 12 12 12 14 16
(1 + ((x + 2) mod (1 + ((x - (x div 4)) mod 6))))
A177868: 1 2 2 2 3 3 3 1 1 2 1
(1 + ((2x - (x div 5)) mod 7))
A131214: 1 3 5 7 2 3 5 7 2 4 5 7 2 4 6 7
(1 + (21 * ((x2 + x) div 2)))
A069178: 1 22 64 127 211 316 442 589 757 946 1156 1387 1639 1912 2206 2521
((3x + 1) - ((2x + 1) div 7))
A184589: 1 4 7 9 12 15 18 20 23 26 28 31 34 37 39 42
(1 + (((x + 1) + (2 * (x div 3))) mod 7))
A274767: 2 3 4 7 1 2 5
(1 + (((x + 1) * (1 + (x div 3))) div 7))
A086160-A029047: 1 1 1 2 2 2 4 4 4 6 7 7 10 11 11 14
(28x2 + 56x + 27)
A158554: 27 111 251 447 699 1007 1371 1791 2267 2799 3387 4031 4731 5487 6299 7167
((2x + 3) - ((2x + 2) div 7))
A185050: 3 5 7 8 10 12 13 15 17 19 20 22 24 25 27 29
((3x + 1) - ((2x + 4) div 7))
A231407: 1 4 6
A060644: 1 4 6 9 12 14 17 20 23 25 28 31 33 36 39 42
((3x + 1) - ((2x + ~4) div 7))
A057347: 2 5 7 10 13 16 18 21 24 26 29 32 35 37 40 43
(1 + (((~x + (x2 div 3)) div 2) div 7))
A179046: 1 0 0 1 1 1 1 1 1 2 2 3 3 4 4 5
(1 + (((x * (~2 + (x div 3))) div 2) div 7))
A017852: 1 0 0 0 0 0 1 1 1 1 1 1 2 2 3 4
((3x + 1) - ((~2x + 4) div 7))
A081834: 1 4 7 11 14 17 21 24 27 30 34 37 40 44 47 50
(x div ((x + 1) - (((x2 + ~2x) div 2) div 7)))
A027195: 0 0 0 0 0 1 1 1 1 1 1 2 2 3 4 5
(1 + ((x * (1 + (x div 5))) div 7))
A029093: 1 1 1 1 1 2 2 3 3 3 5 5 6 6 7 9
((2x + 1) - ((x + (x mod 3)) div 7))
A187413: 1 3 5 7 9 10 13 14 16 18 20 22 24 25 27 29
(1 + ((x + ~7) * ((((x + 1) div 2) div 2) div 2)))
A274840: 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 17
(1 + (((x + 2) div 5) + (x div 7)))
A120501: 1 1 1 2 2 2 2 3 4 4 4 4 4 5 6 6
(2x div ((2x + 1) - (x2 mod 7)))
A185058: 0 1 4 1 1 1 1 0 1 1 1 1 1 1 0 1
(1 + ((x div 5) div (1 + (x2 mod 6))))
A094102: 1 1 1 1 1 1 2 1 1 1 1 2 3 2 1 1
(1 + (((x2 + 2x) div 2) mod (1 + (x div (2 + (x div 3))))))
A333749: 1 1 1 2 1 2 1 2 2 2 1 3 1 2 2 2
(1 + ((x div 5) div (1 + (x mod (2 + (x mod 3))))))
A242397: 1 1 1 1 1 1 2 1 2 1 2 1 3 2 1 2
(1 + (x mod 2) - ((~x + 1) div (1 + (2 * (3 - (x mod 2))))))
A338720: 1 2 2 3 2 3 2 4 2 4 3 4 3 5 3 5
(1 + (2 mod (1 + (x mod (2 + (12 mod (x + 1)))))))
A060839: 1 1 1 1 1 1 3 1 3 1 1 1 3 3 1 1
(x div (1 + (x div (2 - (2x mod (~1 + (x div ~4)))))))
A329656: 0 1 1 1 1 2 1 2 2 3 1 3 1 4 3 1
(1 + (2x mod (1 + ((~x + 2) mod (2 - (x mod ~4))))))
A344972-A224765: 1 1 1 1 1 2 1 1 1 3 1 1 1 2 1 1
(1 + ((x div 2) div (1 + (2 * (x mod (2 * (1 + (2 * (x mod 2)))))))))
A130747: 1 1 2 1 3 1 4 2 5 1 6 1 7 3 8 2
(1 + ((~x + 2) div (1 + (2 * (2 + ((x2 div 2) mod 3))))))
A016408: 1 1 1 0 0 0 0 0 0 0 0 ~1 ~1 ~2 ~1 ~1
(1 + ((x div 2) div (1 + (2 * ((x2 + ~2) mod 6)))))
A297877: 1 1 1 1 1 1 1 1 1 2 2 1 1 1 2 3
(1 + ((x + ~1) mod (~1 + (2 * ((~x + 1) mod (2 + (x div 3)))))))
A111946-A094392: 1 1 1 1 1 2 1 1 1 3 1 1 1 1 5 1
(1 + (x mod (~1 + (4 * (x mod (2 * (1 + (2 * (x mod 2)))))))))
A256908: 1 2 1 4 1 6 1 2 1 10 1 12 1 2 1 5
((x + 1) - (x div (1 + (2 * (2 + (((x + ~1) div 3) mod 2))))))
A157466: 1 2 3 4 5 6 7 7 8 9 10 11 12 12 13 13
(x div (1 + (x mod (5 + ((x + 2) mod 6)))))
A343102: 0 0 0 0 0 0 0 0 0 0 10 1 2 2 2 2
(1 + ((x + 1) div (3 + (x div (2 + (x mod 6))))))
A331853: 1 1 2 2 2 3 2 2 2 3 3 4 2 3 3 3
(1 + (x div (1 + ((x + 2) div (4 + ((x div 3) mod 2))))))
A331245: 1 2 2 2 3 3 3 3 3 4 4 4 4 4 3 4
(1 + (x mod (1 + (x div (2 + (x div (2 + ((x mod 3) div 2))))))))
A217581: 1 1 1 2 1 2 1 2 3 2 1 3 1 2 3 2
(1 + (x mod (1 + (2 * (((x div 2) - ((x + ~1) mod 4)) div 2)))))
A086767: 1 1 1 1 1 3 1 1 1 5 1 3 1 7 1 1
(34x2 + 68x + 33)
A158588: 33 135 305 543 849 1223 1665 2175 2753 3399 4113 4895 5745 6663 7649 8703
(30x2 + 60x + 29)
A158560: 29 119 269 479 749 1079 1469 1919 2429 2999 3629 4319 5069 5879 6749 7679
((2x + 1) - (x div (5 + ((~x + 1) mod 4))))
A187347: 1 3 5 7 9 10 13 14 16 18 20 22 23 25 28 29
(1 + (x div (1 + (((2x + 1) mod (2 + (x div 4))) div 2))))
A322035-A217434: 1 2 3 4 5 3 7 8 9 5 11 6 13 7 5 16
((~x + ~1) mod (1 + (x mod (1 + (2 * (2 + (x div 4)))))))
A035584: 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 4
(1 + ((x + ~1) mod (1 + ((x + 2) div (2 * (2 + (x mod 4)))))))
A103689: 1 1 1 1 2 1 2 1 2 1 2 1 4 1 2 1
(1 - (x2 mod (1 + (x mod (1 + (2 * ((x + 1) mod 4)))))))
A267292: 1 0 0 1 1 1 0 1 0 0 1 1 1 0 1 1
(1 + (2x mod (~1 + (2 * (((1 + (x div 2)) div 2) mod 4)))))
A304972-A152176-A152175: 1 1 1 1 1 1 1 3 2 1 1 3 5 2 1 1
((x + 1) - ((x + 1) div (11 - (x div 2))))
A252649: 1 2 3 4 5 6 7 7 8 9 10 10 11 12 12 12
(1 + ((~3x2 + ~2x) mod 9))
A193090: 1 5 3 4 8 6 7 2 9 1 5 3 4 8 6 7
(1 + ((18x + 9) * (x + (x mod 2))))
A128880: 1 55 91 253 325 595 703 1081 1225 1711 1891 2485 2701 3403 3655 4465
(1 + (x div 3) - ((~x + 3) div 9))
A156077: 1 1 1 2 3 3 4 4 4 5 5 5 6 7 7 8
(1 + (9 * (2 + (x mod 9))))
A084364: 19 28 37 46 55 64 73 82 91 19 28 37 46 55 64 73
(1 + (18 * (x - ((~x + 2) div 4))))
A301617: 1 19 37 73 91 109 127 163 181 199 217 253 271 289 307 343
(1 + (9 * ((3x2 + x) div 2)))
A093485: 1 19 64 136 235 361 514 694 901 1135 1396 1684 1999 2341 2710 3106
((3x + 1) - ((~2x + 2) div 9))
A342279: 1 4 8 11 14 17 21 24 27 30 33 37 40 43 46 50
((x div 3) div (1 + ((~2x + 1) mod 9)))
A333979: 0 0 0 0 0 1 0 0 0 1 0 0 0 1 4 0
((x2 + ~x) mod (~1 + ((x2 + ~x) mod 9)))
A022882: 0 0 0 1 0 0 0 2 0 0 0 0 2 0 0 0
(1 + (8 mod (1 + ((x2 + x) mod 8))))
A110550: 1 3 2 4 4 2 3 1 1 3 2 4 4 2 3 1
(1 + ((~x2 + 1) mod (~1 + ((x2 + ~x) mod 8))))
A031244: 1 1 1 3 1 1 1 1 1 1 1 1 2 1 1 1
(1 + ((x2 + 2x) div (1 + ((x2 + 2x) mod 8))))
A152020: 1 1 9 2 25 9 49 8 81 25 121 18 169 49 225 32
(1 + (((((x + 1) div 2) div 2) div 2) * (1 + (x div 8))))
A035441: 1 1 1 1 1 1 1 2 3 3 3 3 3 3 3 5
(1 + ((x div 4) mod (1 + ((x + 1) mod (2 + (x div 4))))))
A264404: 1 1 1 1 2 1 2 2 1 3 3 1 4 4 1 2
(1 + ((2x + 1) mod (1 + (2x mod (2 + (x div 4))))))
A335521-A335450-A332288-A326516-A324837-A324191-A323087-A322373-A303707-A300831-A285572-A179926-A081707-A008480: 1 1 1 1 1 2 1 1 1 2 1 3 1 2 2 1
(1 + (((x2 + 2x) div 2) mod (1 + (x div (2 + (x div 4))))))
A337135-A113309: 1 1 1 2 1 2 1 2 2 2 1 3 1 2 2 4
(1 + (x div (1 + (((x - ((x div 2) mod 2)) div (2 + (x mod 2))) mod 2))))
A235602: 1 2 3 4 5 3 7 8 9 5 11 6 13 14 15 16
(1 + (x div (1 + (((x2 + 2x) div 2) mod (2 * (2 + (x mod 2)))))))
A111701-A076934: 1 1 3 2 5 1 7 4 9 5 11 2 13 7 15 8
(x mod (1 + ((x * (x div 2)) div (3 + (x div (2 + (x mod 2)))))))
A237531: 0 0 0 0 0 2 2 2 3 2 3 1 3 1 4 1
(1 + (x mod (1 + ((x div 2) div (4 - (x mod (2 + (x mod 2))))))))
A060938: 1 1 1 1 1 2 1 2 1 2 1 3 1 2 1 2
(1 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4))))
A331178-A324912-A322885-A292582-A290109-A290107-A212180-A091050-A072411-A008479-A005361: 1 1 1 2 1 1 1 3 2 1 1 2 1 1 1 4
(1 + (25 * ((x2 + x) div 2)))
A262221: 1 26 76 151 251 376 526 701 901 1126 1376 1651 1951 2276 2626 3001
(1 + ((x - ((1 - (x div 2)) div 5)) mod 5))
A053344: 1 2 3 4 1 2 3 4 5 1 2 3 4 5 2 3
(1 + ((18x + 12) div 5))
A322533: 3 7 10 14 17 21 25 28 32 35 39 43 46 50 53 57
(1 + ((3 * ((x2 + 3x) div 2)) div 5))
A231408: 1 2 4 6 9
A025705-A025697-A022792: 1 2 4 6 9 13 17 22 27 33 40 47 55 63 72 82
(40x2 + 80x + 39)
A158598: 39 159 359 639 999 1439 1959 2559 3239 3999 4839 5759 6759 7839 8999 10239
((6x + 5) + ((x + 1) div 5))
A184525: 5 11 17 23 30 36 42 48 54 61 67 73 79 85 92 98
((2x + 2) - (~2 mod (1 + ((x + 1) div 5))))
A248609: 2 4 6 8 10 12 14 16 18 19 21 23 25 27 28 30
((x + 1) + ((x div 5) + ((x + 1) div 5)))
A047302-A039034: 1 2 3 4 6 8 9 10 11 13 15 16 17 18 20 22
(x4 mod 29)
A070572: 0 1 16 23 24 16 20 23 7 7 24 25 1 25 20 20
(1 + (5 * ((3x2 + 7x + 4) div 2)))
A093500: 11 36 76 131 201 286 386 501 631 776 936 1111 1301 1506 1726 1961
(1 + ((6x2 + 6x + 4) div 5))
A265078: 1 4 9 16 25 37 52 69 88 109 133 160 189 220 253 289
(x4 mod 41)
A070584: 0 1 16 40 10 10 25 23 37 1 37 4 31 25 40 31
(x4 mod 39)
A070582: 0 1 16 3 22 1 9 22 1 9 16 16 27 13 1 3
((x + 1) - (5 * (x div (6 - (x mod 2)))))
A338491: 1 2 3 4 5 1 2 3 4 5 6 2 3 4 5 1
(1 + (((x2 + x) - (x2 div 4)) div 5))
A190269: 1 1 2 3 4 5 7 9 12 15 18 21 25 29 33 37
(1 + (5 * ((x + 2) + (((x + 1) div 2) div 3))))
A227080: 11 16 21 26 31 41 46 51 56 61 66 76 81 86 91 96
((4x + 3) - ((~2x + 2) div 5))
A286923: 3 7 12 16 21 25 29 34 38 43 47 51 56 60 65 69
(1 + (5 * ((5x2 + ~x) div 2)))
A081587: 1 11 46 106 191 301 436 596 781 991 1226 1486 1771 2081 2416 2776
(~1 + (((x5 + ~x) div 2) div 5))
A131176: ~1 ~1 2 23 101 311 776 1679 3275 5903 9998 16103 24881 37127 53780 75935
(1 + (((x * (2 - (x div ~4))) div 2) div 5))
A025772: 1 1 1 1 2 3 3 3 4 5 6 6 7 8 9 10
((~x + ~1) mod (1 + (x div 2) - (2x div 5)))
A322389: 0 0 1 0 1 0 1 0 1 0 1 0 2 0 0 0
((1 + (x div 8)) div (1 + (2x mod 5)))
A025888: 1 0 0 0 0 1 0 0 1 0 2 0 0 1 0 2
((x + 1) div (~1 + (5 * (8 - (x div 2)))))
A210631: 0 0 0 0 0 0 0 0 0 0 0 0 1 1 3 4
((4x + 1) - (((~x + 2) - (x div 2)) div 5))
A001958: 1 5 10 14 18 22 27 31 35 40 44 48 53 57 61 65
((1 + (x div 8)) div (1 + (~x mod 5)))
A025891: 1 0 0 0 0 1 0 0 0 1 2 0 0 0 1 2
(4 mod (1 + ((x * (1 + (x div 3))) mod 5)))
A308278-A308277: 0 0 1 0 0 0 0 0 4 0 0 4 0 0 0 0
((x + 1) - ((~x + ((x div 2) mod 5)) div 5))
A039211: 1 3 4 5 6 7 8 9 10 11 13 15 16 17 18 19
((4x + 1) - ((x + (x div 3)) div 5))
A080590: 1 5 9 13 16 20 24 28 31 35 39 43 46 50 54 57
((x + 1) - ((~x + ((x div 2) mod 6)) div 5))
A105048: 1 3 4 5 6 7 8 9 10 11 12 14 16 17 18 19
(((~x + 1) div 5) mod (1 + ((~x + 2) mod 5)))
A071692: 0 0 0 4 3 2 1 0 3 2 1 0 0 2 1 0
(1 + (2x div 3) - ((x + (x mod 2)) div 5))
A156262: 1 1 2 3 3 3 4 4 5 5 5 6 7 7 8 8
(1 + (((x2 + 1) div 5) + (x div 5)))
A117450: 1 1 2 3 4 7 9 12 15 18 23 27 32 37 42 49
((2x + 1) - ((x div 5) + ((~x + 2) div 4)))
A097911: 1 3 5 8
A189755: 1 3 5 8 10 11 13 16 18 20 21 24 26 28 30 32
((x div 2) div (2 - ((x + 1) mod (~1 - (x div 5)))))
A161310-A161296-A161244-A161080-A161029-A160975: 0 0 0 0 1 1 1 1 1 2 1 2 1 2 3 3
(((x + ~1) - ((x mod 3) mod 2)) mod (1 + (x div 5)))
A230196: 0 0 0 0 0 0 1 1 1 0 2 1 2 2 1 2
(((2x mod (2 + (x div 2))) mod 2) * (1 + (x div 5)))
A308223: 0 0 1 0 0 0 0 0 0 0 0 3 0 0 3 4
((x + 2) - ((x div 3) + (2 div (1 + (x div 5)))))
A140200: 0 1 2 2 3 5 5 6 7 7 9 10 10 11 12 12
(((x + ((x div 4) mod 2)) div 2) div (1 + (x div 5)))
A081355: 0 0 1 1 2 1 1 2 2 2 1 1 2 2 2 2
((~x + ((x * (x div 2)) div 4)) mod (1 + (x div 5)))
A036865: 0 0 0 0 0 1 0 0 0 0 2 2 0 0 1 3
((2x + 25) - (x mod 5))
A140058: 25 26 27 28 29 35 36 37 38 39 45 46 47 48 49 55
((~5x + ~5) mod (1 + (x mod 5)))
A037882-A037846: 0 0 0 0 0 0 1 2 3 0 0 0 1 2 0 0
(1 + ((x + (x div (~x + 16))) div 5))
A005854: 1 1 1 1 1 2 2 2 2 3 3 3 4 4 5 7
((1 + (x div 8)) div (1 + (x2 mod 5)))
A029409: 1 0 0 0 0 1 0 0 0 1 2 1 0 0 1 2
(x mod (1 + ((1 + (x div 4)) div (1 + (~x mod 4)))))
A051777: 0 0 0 0 1 0 0 1 0 0 0 1 2 1 0 0
(((x div 2) div 3) div (1 + (x mod (1 + ((~x + 2) mod 4)))))
A322795-A079071: 0 0 0 0 0 0 1 0 0 0 1 0 2 1 2 0
(((x + ~1) div 2) mod (1 + ((2x + ~1) mod (1 + (x div 4)))))
A236533: 0 0 0 0 1 0 0 1 0 1 0 0 1 0 2 1
(((1 + (x div 2)) div 3) div (1 + (x mod (1 + (x mod 4)))))
A214625: 0 0 0 0 1 0 1 0 1 0 1 0 2 1 0 0
(1 + (17x div (x + 5)))
A137203: 1 3 5 7 8 9 10 10 11 11 12 12 13 13 13 13
(1 + ((x * (x2 div (x + 3))) div (x + 5)))
A029086: 1 1 1 1 1 2 3 3 4 4 5 6 7 8 9 10
((x + 1) - ((~x + 2) div (1 + (2 * (8 - (x div 2))))))
A284763-A144146-A119605-A090240: 1 2 3 5 6 7 8 9 10 11 13 14 15 17 19 21
(x div (1 + (x div (3 + ((x mod 3) div 2) - (x mod 2)))))
A263569: 0 1 2 1 2 2 2 1 2 1 2 2 2 1 3 1
(1 + ((1 - (x div 3)) mod (1 + ((~x + 2) mod (2 + (x mod 2))))))
A030612: 1 2 1 1 1 1 1 2 1 2 1 1 1 2 1 3
(1 - ((x + 1) mod (~1 - (x mod (1 + (x div (2 + (x mod 2))))))))
A165818: 1 1 1 1 2 1 3 1 4 1 5 1 6 3 7 1
(1 + ((1 + (((x + ~2) * ((x + ~1) div 2)) div 3)) div 3))
A050365: 1 1 1 1 1 2 2 3 3 4 4 6 6 8 9 11
((x + 1) - (3 * (~1 + (3 * (~2x + (x div 2))))))
A169599: 4 23 33 52 62 81 91 110 120 139 149 168 178 197 207 226
(1 + (((x div 4) div (1 + ((~x + 1) mod 3))) mod 3))
A308972: 1 1 1 1 2 1 1 2 1 2 3 1 2 1 2 2
(1 + (((x2 + x + 1) mod 7) div 3))
A028293: 1 2 1 3 1 2 1 1 2 1 3 1 2 1 1 2
((x + 2) mod (1 + (((x + 1) mod 7) mod 3)))
A071325-A064727: 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 2
(1 + ((3x2 mod (1 + ((x + 1) div 2))) div 3))
A206487: 1 1 1 1 1 2 1 1 1 2 1 3 2 2 2 1
(1 + (((x + 2) div (2 - (x mod ~5))) div 3))
A319193: 1 1 1 1 1 2 1 1 1 2 3 1 1 2 2 3
(1 + (((x + 1) - ((1 + (x div 2)) mod 8)) div 3))
A092670: 1 1 1 1 1 2 2 2 2 2 2 3 3 3 6 6
((x + 1) - ((1 - (x2 div 9)) div 3))
A056177: 1 2 3 4 5 7 8 10 11 13 15 16 18 20 22 24
(1 + (((x div 2) - (x mod (3 + (x div 4)))) div 3))
A060244: 1 0 0 1 1 1 1 1 1 1 2 2 3 2 2 2
(~1 + ((1 - ((~x + 2) mod (~1 + (2 * (x mod 4))))) mod 3))
A072786: 0 0 0 ~1 0 0 1 0 0 0 ~1 ~1 0 0 0 1
(1 + (3 * (x div (5 * (1 + (x mod 4))))))
A131299: 1 1 1 1 1 1 1 1 4 1 1 1 7 4 1 1
(((x + ~1) div 2) mod (1 + (((x + 1) mod 5) mod 3)))
A278515: 1 0 0 1 0 0 2 0 1 0 0 2 0 0 0 1
(x2 div (~1 + (3 * (x - (2x div 5)))))
A194198: 0 0 0 1 2 3 3 3 4 4 5 6 6 7 7 8
((x + 1) - (3 * ((~3x + 2) div 5)))
A079259: 1 5 6 10 11 15 19 20 24 25 29 33 34 38 39 43
((3x + 1) - ((x - (x div 5)) div 3))
A180122-A062458: 1 4 7 9 12 15 18 20 23 26 29 31 34 37 39 42
(1 + (((x3 + ~x2) mod (2x + 5)) mod 3))
A306211: 1 1 2 2 1 2 2 1 2 2 1 2 1 2 2 1
(1 + (3 * (2x - (3 * ((x div 2) div 3)))))
A225227: 1 7 13
A080199: 1 7 13 19 25 31 28 34 40 46 52 58 55 61 67 73
(1 + ((x - (((~x + ~1) + (x div 3)) div 3)) mod 3))
A190496: 2 3 1 2 1 2 3 1 3 1 2 3 1 3 1 2
((x + 2) mod (1 + (((1 + (x * (x div 2))) div 3) mod 3)))
A333487: 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 2
((x + 1) - (3 * ((x - ((x div 4) mod 2)) div 3)))
A338482-A281367-A104246: 1 2 3 1 2 3 4 2 3 1 2 3 4 2 3 4
(x4 mod 37)
A070580: 0 1 16 7 34 33 1 33 26 12 10 26 16 34 10 9
(8x mod 35)
A344538: 0 8 16 24 32 5 13 21 29 2 10 18 26 34 7 15
(x4 mod 35)
A070578: 0 1 16 11 11 30 1 21 1 16 25 11 16 1 21 15
(1 + ((((4x + 1) mod (x + 2)) div 3) mod 3))
A238013: 1 1 1 2 2 1 1 1 2 2 2 3 3 3 1 1
(1 + (((2 - ((~x + 1) div 3)) * (x div 3)) div 3))
A029054: 1 1 1 2 2 2 3 3 4 6 6 7 9 9 10 12
((x + ~2) mod (1 + ((1 + ((x div 2) + (x div 3))) mod 3)))
A126205: 0 1 0 0 0 1 0 0 0 1 0 0 1 2 0 1
(2x2 div ((x + 1) - ((1 - (x div 3)) div 3)))
A176693: 0 1 2 4 6 8 9 10 12 14 16 18 20 22 24 25
(~1 + (((x2 + ~x + ~1) * (2 - (x div 3))) mod 3))
A318706: 0 0 1 1 1 0 ~1 ~1 ~1 0 0 1 1 1 0 ~1
(1 + (((2x + 1) * (~1 + ((x + 1) mod 3))) div 3))
A332056: 1 2 ~1 1 4 ~3 1 6 ~5 1 8 ~7 1 10 ~9 1
(1 + (((2x + 1) * (1 + ((x mod 3) mod 2))) div 3))
A332057: 1 3 2 3 7 4 5 11 6 7 15 8 9 19 10 11
((1 + (2x * (x div 2))) mod (1 + ((1 + (x div 2)) div 3)))
A061358: 0 0 0 0 1 1 1 1 1 1 2 0 1 1 2 1
((x2 * (~1 + (x div 2))) mod (1 + ((1 + (x div 2)) div 3)))
A284264-A089310: 0 0 0 0 0 1 0 0 0 1 1 1 0 2 0 0
((1 + (x mod 8)) mod (1 + ((1 + (x div 2)) mod 3)))
A320808: 1 0 0 1 0 0 1 0 1 2 0 0 1 0 1 2
(9x3 + 18x2 + 12x + 2)
A287335: 2 41 170 443 914 1637 2666 4055 5858 8129 10922 14291 18290 22973 28394 34607
(15x2 + 33x + 19)
A165806: 19 67 145 253 391 559 757 985 1243 1531 1849 2197 2575 2983 3421 3889
((x + 1) - (((x + 1) * (~x3 div 2)) div 3))
A332866: 1 3 7 23 59
(1 + (3 * ((2x2 + 2x) + ((x2 + ~x) div 2))))
A220083: 1 13 40 82 139 211 298 400 517 649 796 958 1135 1327 1534 1756
(2 * (((2x + 4) div 3) * (1 + ((x + 1) div 3))))
A324174: 2 4 8 12 16 24 30 36 48 56 64 80 90 100 120 132
(36x2 + 36x + 5)
A001513: 5 77 221 437 725 1085 1517 2021 2597 3245 3965 4757 5621 6557 7565 8645
(1 + ((2 * (1 + ((2 * (x + (x mod 2))) div 3))) div 3))
A082479: 1 2 2 3 3 4 4 5 5 5 5 7 7 7 7 8
(1 + ((2 * (x mod (~1 + (2 * ((x + ~1) div 3))))) div 3))
A287641-A265312: 1 1 1 1 1 1 1 1 2 1 1 1 2 5 1 1
(1 + ((2 * (1 + ((x - ((x div 2) div 3)) div 2))) div 3))
A171895: 1 1 2 2 3 3 3 3 3 4 4 5 5 5 5 5
((x + 1) - (6 * ((x + 1) div 7)))
A338495-A338480-A234533: 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4
(1 - (x div (~1 + (3 * (~2 + (x mod ~5))))))
A303378: 1 2 2 2 2 2 2 2 2 2 3 2 2 2 3 4
(1 + ((((x + ~3) mod 9) div 2) mod 3))
A268811-A100480: 1 1 2 1 1 2 2 3 3 1 1 2 1 1 2 2
(1 + ((2 + ((x2 + 2x) div 9)) div 3))
A000929: 1 1 1 2 2 2 3 4 4 5 6 6 7 8 9 11
(1 + (3 * (((1 + ((x + 1) div 2)) mod 5) mod 2)))
A053239: 4 1 1 4 4 1 1 1 1 4 4 1 1 4 4 1
(1 + ((~x + 1) div (3 * (2 + ((x + ~1) mod 5)))))
A016426-A016405-A016394-A014031: 1 1 0 0 0 0 0 0 0 0 0 ~1 ~1 0 0 0
(1 + (((x2 + ~x) div (2 + (x div 5))) mod 3))
A228349: 1 1 2 1 1 1 2 3 1 1 2 1 1 1 1 1
((x div 2) mod (1 + ((x - ((x div 5) mod 2)) div 3)))
A178930: 0 0 0 1 0 0 1 0 1 1 1 1 1 1 2 2
(1 + ((x mod (~2 + (x2 mod (x + 5)))) div 3))
A342323: 1 1 1 1 2 1 1 1 3 1 1 2 1 2 1 1
(6x2 + 30x + 55)
A027865: 55 91 139 199 271 355 451 559 679 811 955 1111 1279 1459 1651 1855
((x3 + ~3x2 + 2x) div 19)
A011901: 0 0 0 0 1 3 6 11 17 26 37 52 69 90 114 143
(x5 mod 19)
A070603: 0 1 13 15 17 9 5 11 12 16 3 7 8 14 10 2
(1 + ((2 * (1 + (2 * (x + (x div 5))))) div 3))
A047501: 1 3 4 5 7 9 11 12 13 15 17 19 20 21 23 25
(36x2 + 48x + 7)
A085026: 7 91 247 475 775 1147 1591 2107 2695 3355 4087 4891 5767 6715 7735 8827
(2x div (~1 + (3 * (2 + ((x div 2) div (1 + (x mod 2)))))))
A035439: 0 0 0 1 0 1 0 1 0 1 1 2 1 1 1 2
(1 + ((x mod (2 + ((2x + ~8) mod (x + 1)))) div 3))
A072906: 1 1 1 2 1 1 1 3 3 1 1 2 1 1 1 3
((6x + 7) + (x mod (2 * (~2 + (x mod 2)))))
A091573: 7 12 17 24 31 36 41 48 55 60 65 72 79 84 89 96
((6x + 5) - (((x + 1) div 2) div 3))
A190337: 5 11 17 23 29 34 40 46 52 58 64 69 75 81 87 93
((5x + 3) - (((x + 1) div 2) div 3))
A184921: 3 8 13 18 23 27 32 37 42 47 52 56 61 66 71 76
(1 + (((x3 + 9x2 + 8x) div 2) div 3))
A027378: 1 4 11 23 41 66 99 141 193 256 331 419 521 638 771 921
((2x + 1) - (((x3 + ~3x2 + 2x) div 2) div 3))
A081498: 1 3 5 6 5 1 ~7 ~20 ~39 ~65 ~99 ~142 ~195 ~259 ~335 ~424
(1 + ((x div 2) div (2 - (x2 mod ~12))))
A326851: 1 1 1 1 1 1 2 1 1 1 1 1 4 1 1 2
(1 + ((1 - (((x * (x div 3)) div ~2) div 2)) div 3))
A029102: 1 1 1 1 1 2 2 2 2 3 4 4 5 5 6 7
(~1 + (3 * ((x + 2) - ((x + (x div 4)) div ~2))))
A284396: 5 11 14 20 26 29 35 38 44 50 53 59 65 68 74 77
(1 + ((4 * (2x - (x mod ~3))) div 3))
A047591: 1 6 7 9 14 15 17 22 23 25 30 31 33 38 39 41
(1 + ((4 * (x - (x div ~5))) div 3))
A047584: 1 3 5 6 7 9 11 13 14 15 17 19 21 22 23 25
(1 + ((4 * (x - ((~x + 1) div 5))) div 3))
A047580: 1 2 5 6 7 9 10 13 14 15 17 18 21 22 23 25
(1 + (6 * (2 + (3 * (x + (x div 4))))))
A301622: 13 31 49 67 103 121 139 157 193 211 229 247 283 301 319 337
(1 + ((4 * ((2x + 2) - (x mod 3))) div 3))
A047443: 3 5 6 11 13 14 19 21 22 27 29 30 35 37 38 43
(5x mod 49)
A336483: 0 5 10 15 20 25 30 35 40 45 1 6 11 16 21 26
(x4 mod 47)
A070590: 0 1 16 34 21 14 27 4 7 28 36 24 9 32 17 6
((x + 3) div (~1 + (3 * (2 + (x div 8)))))
A338521: 0 0 1 1 1 1 1 2 1 1 1 1 1 2 2 2
(1 + (((2x + ~1) div (4 + (x div 4))) mod 3))
A204253: 3 1 1 2 2 2 3 3 3 3 1 1 1 1 1 2
(1 + ((1 - (2x mod (4 + (x div 4)))) div 3))
A124749: 1 0 1 0 0 1 0 0 0 1 0 0 0 ~1 1 0
(1 + (x mod 4) - (6 * ((x div 4) mod 2)))
A131974: 1 2 3 4 ~5 ~4 ~3 ~2 1 2 3 4 ~5 ~4 ~3 ~2
(120x + 49)
A216870: 49 169 289 409 529
(1 + ((2 * (2x - (((2 - (x div 2)) div 2) div 2))) div 3))
A007071: 1 2 3 5 6 7 9 11 12 13 15 16 17 19 21 22
((x3 + ~3x2 + 2x) div 25)
A011907: 0 0 0 0 0 2 4 8 13 20 28 39 52 68 87 109
(x - ((~2x2 + 4) div 25))
A275672: 0 1 3 4 6 7 9
A006855: 0 1 3 4 6 7 9 11 13 16 18 21 24 27 30 33
(1 - ((x2 + 2x) div (x + ~25)))
A018122: 1 2 2 2 3 3 4 5 6 8 9 12 14 18 22 27
(x5 mod 25)
A070609: 0 1 7 18 24 0 1 7 18 24 0 1 7 18 24 0
((x3 + ~3x2 + 2x) div 23)
A011905: 0 0 0 0 1 2 5 9 14 21 31 43 57 74 94 118
(((x3 + 2x) div 2) div 23)
A175777: 0 0 0 0 1 2 4 7 11 16 22 29 38 48 60 74
(x5 mod 23)
A070607: 0 1 9 13 12 20 2 17 16 8 19 5 18 4 15 7
(1 + ((x2 + x) div (~x + 25)))
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(1 + (3 * ((x2 + (x mod 4)) mod 8)))
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((x + 1) - ((x + 1) div (8 - ((x + 2) div 3))))
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((6x + 1) + (2x div 7))
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((6x + 1) + (x div (~2 + ((~x + 2) div 4))))
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((x2 + x) - (x2 mod (9x + 1)))
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((x mod 4) mod (1 + (2x mod (2 - ((~x + 1) div 3)))))
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((x + 1) + (x div 3) - ((~x + 1) div 9))
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((x + 2) - (x2 div ((2x + 3) - (x div 3))))
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((1 + (x div 8) - (x mod 2)) div (1 + (x mod 3)))
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((x + 2) mod (1 + (x div (~2x + 33))))
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((2x + 3) - ((x2 div 3) div (x + 3)))
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(1 + ((x * (6 + (x div 3))) div (x + 3)))
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(1 + ((4 * ((x + 1) - (2 * (x mod 2)))) mod (2x + 1)))
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((~x + 3) + ((2 + ((x + ~1) mod 3)) * (1 + (x div 2))))
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(1 + ((x + ((((x + ~1) div 2) * (x div 2)) div 2)) div (1 + (x mod 2))))
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(1 + ((x5 + x3 + x2) div (1 + (x mod 2))))
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(x4 + 6x3 + 11x2 + 10x + 6)
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(x4 + 6x3 + 17x2 + 20x + 9)
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(24x2 + 52x + 29)
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(1 + compr(\x.((x mod (~2 + (((~x + 2) div 2) div 3))) mod 2),(x + 1)))
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(~1 + ((2x + 2) * ((2x + 4) - ((1 + (x div 2)) mod 2))))
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(1 + ((2x + 2) * ((x mod (~2 - (x mod 4))) mod 2)))
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(1 + ((((x + 4) * (x2 - (x div 2))) div 2) div (x + 1)))
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(4x7 + 3x6)
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(1 + ((((~x + 1) * (x mod 10)) div 2) mod (x + 1)))
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(x2 + 3x + 43)
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(13x2 + 33x + 21)
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(x8 + x6 + x4 + x2 + 1)
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((x + 1) mod (1 + (4x mod (2 - ((x div 2) div ~2)))))
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((x + 3) - (x div (x + ~19)))
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(~1 + ((x - (x div (~11 + (x div 2)))) div 2))
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(1 + (2 * ((~1 + (x div 2)) mod (1 + ((2 + (x div 2)) div 3)))))
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(1 + ((1 + (((x + (x2 div 4)) div 2) div 3)) div 2))
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(1 + (x div (2 + (x mod (1 + ((x * (2 - (x mod 2))) div 3))))))
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((x + 1) - (2 * ((x mod 6) mod (1 + (x div 3)))))
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(1 + (((x + 1) - ((x3 + ~1) mod (1 + (x div 2)))) div 2))
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(1 + ((x mod (1 + ((6 mod (x + 2)) mod (x + 1)))) mod 2))
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(1 + ((1 + ((x mod (1 + ((x - (x mod 3)) div 2))) div 2)) div 2))
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(3 + ((x div 3) div (3 + ((x + ~1) mod 3))))
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(1 + ((x - ((x * (1 - (x div 2))) div 9)) div 2))
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(1 + (((x * (2 - (x * (x div 2)))) div 9) mod 2))
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((2x + 11) - ((x div 5) mod 2))
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((2x2 + 18x + 16) div 7)
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((3x + 2) - ((2x + 2) div 7))
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(2 - (4x4 mod 7))
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((3x + 2) - ((2x + ~4) div 7))
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((2x + 2) - ((2 * (x + (x mod 2))) div 7))
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(7 div (2 - ((x + ~2) div 7)))
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((3x + 2) - ((~2x + 1) div 7))
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(1 - (x mod (1 - ((~2x2 + 2x) mod 7))))
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((x3 + 3x2 + 4x + 2) + (x div 7))
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(1 + (2x mod (2 + ((x + (x2 div 3)) mod 3))))
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((x + 1) - (2 * ((x div 12) + (x div 3))))
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((x + 5) + (x2 div 4) - (x div 3))
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(1 + ((1 + (x2 div ((x + 2) + ((x div 3) mod 2)))) div 2))
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(1 + ((1 + ((3x * (x mod 3)) div (x + 2))) div 2))
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(1 + (2 * ((x * (4 + (x div 4))) div (x + 3))))
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((x + 1) - (2 * ((~2x + ~1) + ((x - (x div 4)) div 2))))
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((x + 1) - ((((~2x + ~4) + (x div 2)) * (1 + (x div 2))) div 2))
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(1 + (((x div 2) - (2x3 div (1 + (x div 2)))) mod 2))
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((x - (3 * (~x + (x mod 2)))) mod (1 + ((1 + (x div 2)) div 2)))
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(1 + (2 * ((x + 1) + (((x div 2) - ((x div 4) mod 2)) div 2))))
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(1 + (((1 + ((x + (x div 2)) mod 5)) mod (x + 1)) div 2))
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((x + 1) - (2 * ((~x + ~1) + ((x + 1) mod 7))))
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(1 + (((2 - (x div (1 + ((x mod 3) div 2)))) mod (x + 1)) div 2))
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(1 + (x div (2 + ((5 * (1 + (x div 2))) mod (x + 1)))))
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(1 + (((x + 1) * (2 + ((x * (1 + ((x + 1) div 2))) div 2))) div 2))
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(1 + (2 * (x + (((x - ((x div 2) mod 2)) div 2) + (2 mod (x + 1))))))
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((2x + 3) + ((x mod (~2 - (x div 3))) mod 2))
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((2x + 3) + ((x - ((~x + 1) div (2 + (x div 2)))) div 2))
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(10x3 + 45x2 + 65x + 30)
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(8x3 + 36x2 + 46x + 15)
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(64x2 + 128x + 48)
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((2x + 3) * ((3x2 + 7x + 4) div 2))
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(4x3 + 18x2 + 42x + 36)
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(2x2 + 26x + 33)
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((2x + 3) + ((x2 + ~x) div (3x + 4)))
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(~1 + (((5x + 2) - (x div 2)) * ((x + 1) div 2)))
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(3 + ((2x div (2 + (x div 3))) + ((x + 1) div 2)))
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(1 + ((19x2 + 19x) div 2))
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(1 + ((23x2 + 23x) div 2))
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(1 + ((11x2 + 19x + 8) div 2))
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((x + 3) - ((~x + 2) div (2 - (x div ~8))))
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((4x + 2) - ((x + (x div 2)) div ~5))
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((2x + 32) + (x div ~5))
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((4x + 1) - ((x + (x div 4)) mod ~4))
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((x + 5) - ((~x + 2) div (2 - (x div ~4))))
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(x div (1 + (x div 3) - (x mod (~3 + (x mod ~2)))))
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(1 + (2 * ((1 + (x div (3 + (((x + ~1) div 2) mod 2)))) div 2)))
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(1 + (2 * ((x + 2) mod (2 * (1 + (2x div 5))))))
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(x mod (~1 + (2 * (((x + 1) - ((1 + (x div 2)) mod 3)) div 2))))
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(1 + ((x mod (2 + ((x div 2) div (1 + (2x mod 3))))) div 2))
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(3 + ((x mod (2 - (x div (1 + ((x div 2) mod 3))))) mod 2))
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(1 + ((((2x + 2) mod (~1 + ((~x + 1) div 3))) div 2) mod 2))
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(1 + (x div (2 * (2 + ((2x + ~4) mod 9)))))
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(1 + (x div (2 * (2 + ((~2x + 1) mod 9)))))
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(1 + (4 * ((x + 1) - (x div (~2 + ((~x + 2) div 4))))))
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((x + 1) - (((5 * ((~x + 1) div 3)) div 2) div 2))
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((~x + 1) mod (1 + (2 * (((~1 + (x div 2)) mod 5) div 2))))
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(5 + ((2x2 + 4x + 2) div 5))
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(1 + (((x + 2) div (2 + (((~x + 2) div 2) mod 5))) mod 2))
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(1 + (x div 2) - (x div (4 + ((x div 2) mod 5))))
A256555-A117119: 1 1 2 2 3 3 4 3 4 4 4 4 5 5 6 6
(3x - (2x mod 21))
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A004850: 0 1 2 3 4 5 6 7 8 9 10 32 33 34 35 36
(x5 mod 21)
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(1 + (((5 * (x + (x div 8))) div 2) div 2))
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((x + 1) - (2 * ((x - ((x2 + 2x) div 5)) div 2)))
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(1 + (((~1 + (x mod 3)) mod (2 + (x div 5))) mod 2))
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(1 + ((x - ((2x + ~1) div (2 + (x div 5)))) div 2))
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(1 + ((((x div 2) - ((~x2 + x) div 5)) div 2) div 2))
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(1 + (((~1 + ((x * (x mod (2 + (x div 2)))) div 4)) div 2) div 2))
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((x + 1) - (((3 * ((~x2 + 2x) div 4)) div 2) div 2))
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((x + 1) - ((2x + 1) div (4 + ((x div 2) div 3))))
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((x + 2) mod (1 + (x div (2 + (x div (2 + ((x div 2) mod 3)))))))
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(1 + (x div (2 + ((x + 1) div (2 + ((x * (x div 2)) mod 3))))))
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(x2 + ~16x + 43)
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(1 + ((~x + 1) div (2 + ((((x + 1) div 2) * (x div 3)) div 2))))
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((4x + 1) - ((x - ((2 - (x div 3)) div 2)) div 2))
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(~1 + ((((2x + 1) + (x mod 2)) mod (2 + (x div 3))) div 2))
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((2x + 1) - (((x3 mod (2x + ~1)) div 2) mod 2))
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(1 + (((1 + (((x2 + x) div 4) + (x div 2))) div 2) div 2))
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(1 + (((1 + (((x * (x div 3)) div 2) + (x div 2))) div 2) div 2))
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(1 + ((x mod (~2 + ((x div 8) * (1 + (x div 2))))) div 2))
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((2 + (x div 2) - (x mod 2)) mod (1 + (((1 + (x div 2)) div 2) div 2)))
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((x + 1) - ((((~x + ((~x + 2) div 2)) * (1 + (x div 2))) div 2) div 2))
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(1 + ((((x + 1) + (x mod (~2 + ((~x + 2) div 4)))) div 2) div 2))
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A255977: 1 2 4 6 9 13 17 22 27 33 40 47 55 64 73 83
((x + 1) - (2 * ((~2x + ~2) + ((x - (x div 4)) div 2))))
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(1 + (((x2 div 9) + ((x + 1) div 2)) div 2))
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(((x + 1) - (x div 8)) div (1 + (((x + 1) div 2) div 2)))
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((~2 + (3 * (2 - (x div 2)))) mod (1 + (((x + 1) div 2) div 2)))
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((((x + ~1) mod (2 + (x div 2))) div 2) * (~1 + (((x + 1) div 2) div 2)))
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((x + 3) - (2 * ((x + ((x div 2) div 3)) div ~2)))
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((x + 1) - (((((x + ~1) div 3) * (x div ~2)) div 2) div 2))
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(64x2 + 64x + 7)
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(1 + (4 * ((x mod (~1 + (2 * ((x + ~1) div 3)))) div 2)))
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(1 + (2 * (((x + 2) div (1 - (2 * (x mod 5)))) mod 2)))
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(1 + (((x + ~1) div (2 * (2 + ((x div 3) mod 3)))) div 2))
A276825: 0 1 1 1 1 1 1 1 1 2 2 2 1 2 2 1
(1 + (x div (2 + ((x + 1) div (4 + ((x + 1) mod 3))))))
A097849: 1 1 2 2 3 2 3 3 3 3 4 3 4 4 3 4
((x + 1) - ((((((x + ~1) div 2) * (x div 3)) div 2) div 2) div 2))
A128635: 1 2 3 4 5 6 7 8 9 9 10 11 11 11 12 12
(1 + ((x - ((x mod ((~x + 2) + ((x mod 3) div 2))) div 2)) mod 2))
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(1 - (x mod (~1 + (x div 3) - (2 * (((x + 1) div 2) div 2)))))
A251717: 1 1 1 2 1 2 1 3 2 2 1 2 1 3 2 2
(1 + ((x - (3x div (~2 + (x div ~4)))) div 2))
A091863: 1 2 3 4 5 5 6 7 8 8 9 10 11 11 11 12
(1 + (((x - (x3 div (~2 + (x mod ~2)))) div 2) div 2))
A135445: 1 1 2 4 10
A301338: 1 1 2 4 10 12 29 31
((x + 2) div (1 + (2 * (2 + ((x mod (2 + (x div 3))) mod 2)))))
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A290832: 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 13
((x + 1) div (~1 + (4 * (4 - (((x + ~1) div 2) div 2)))))
A046780: 0 0 0 0 0 0 0 0 0 1 1 1 1 4 5 5
((x3 + ~x2) div 65)
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(1 + (x mod (2 * (2 + ((x2 + ~x) mod 16)))))
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(3 + (((x - ((~x2 + x) div 8)) div 2) div 2))
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(~1 + (2 * (((2 - ((x - ((~x + 2) div 4)) div 2)) div 2) mod 2)))
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A331472: 0 1 2 3 4 5 6 7 8 9 1 11 3 4 5 6
(1 + (4 * ((x - (2 * ((x div 2) mod 2))) mod 8)))
A145825: 1 5 1 5 17 21 17 21 1 5 1 5 17 21 17 21
(~1 + (4 * ((2x + 4) - ((x + 2) mod 8))))
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((x + 1) - (((((~x + 2) * (x div 2)) div 8) div 2) div 2))
A039213: 1 2 3 5 6 7 8 9 10 11 13 14 15 17 18 19
(x5 mod 33)
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((x3 + ~3x2 + 2x) div 31)
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((x3 + 4x) div 31)
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(x5 mod 31)
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((x + ~1) mod (1 + ((x mod (2 + ((~x + 1) mod 8))) div 2)))
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(x div (1 + ((x - ((x + 2) mod (2 + (x div 8)))) div 2)))
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(x div (1 + ((x - ((x div (2 + ((~x + 2) mod 4))) div 2)) div 2)))
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((x + 1) - (2 * ((((1 - (x div 2)) * (x div 4)) div 2) div 2)))
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(x div (1 + (x div (2 + (((x + 2) mod (2 + (x div 4))) mod 2)))))
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(3 + (2x div (2 + (2x div (2 + (x div 4))))))
A145288: 3 3 4 4 5 5 5 5 5 6 5 6 7 6 7 6
(1 + (4 mod (2 + (2x mod (4 + (x div 4))))))
A046607: 1 1 1 1 5 1 1 5 5 1 1 5 5 5 1 1
(2 div ((x2 + 2) mod (1 + (2 * (4 + (x div 4))))))
A230279: 1 0 0 1 0 0 0 0 2 0 0 0 0 0 0 1
((x + 1) - ((~x + 2) div (4 + (x mod (2 + (x div 4))))))
A181092: 1 2 3 5 6 7 8 9 11 12 13 14 15 16 17 20
(1 + (4 * (x div (4 * (8 - (x div 2))))))
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((x + 5) - ((~2x + 2) div (4 + (x div 2))))
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(x div (1 + (x div (2 + (((x + ~2) mod (4 + (x div 2))) mod 2)))))
A322869: 0 1 1 1 1 2 1 2 1 2 1 1 1 2 2 1
((~x + 1) mod (1 + (2 * ((((~x + 2) mod (2 + (x div 2))) div 2) mod 2))))
A284969: 0 0 0 1 0 0 0 0 0 0 0 0 1 0 2 0
(1 + ((x + 1) div (2 * (2 + (((x2 + ~1) div 2) mod 4)))))
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((x + 1) - (2x div (~2 + (2x div ~7))))
A137624: 1 3 5 6 7 9 10 12 13 14 15 16 17 19 20 21
(1 - ((2x + 1) mod (~1 + (2 * (x div ~7)))))
A194899-A194871-A054073: 1 1 2 3 1 2 3 1 4 2 5 3 1 4 2 5
(x6 mod 17)
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(105x + 15)
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(((x3 + ~3x2 + 2x) div 2) div 15)
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((5x + 5) - (x div 15))
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(x mod ((x + 1) - (((x * (x mod 4)) div 8) div 2)))
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((4x + 1) - ((x - ((2 - (x div 4)) div 2)) div 2))
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(1 + (((x mod 2) - (((2 - (x div 2)) * (x div 4)) div 2)) div 2))
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(1 + (x mod (2 * (2 + ((x3 div 2) mod (x + 4))))))
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A072438: 1 2 3 4 1 6 7 8 9 2 11 12 1 14 3 16
(x div (1 + ((x - (x div (2 + (x2 mod (x + 4))))) div 2)))
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(1 + ((x mod (2 + (((x div 5) * (x div 2)) div 2))) div 2))
A063746: 1 1 1 1 1 2 1 1 1 1 2 3 3 3 3 2
(1 + (2 * ((x mod (2 + (x div (8 - (x div 2))))) div 2)))
A147266-A147152: 1 1 1 1 1 1 1 1 1 1 1 1 5 5 15 15
(1 + ((((~1 + (x * (x mod 4))) mod (2 + (x div 2))) div 2) div 2))
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(1 + (((((x2 + (x div 2)) div 2) mod (2 + (x div 2))) div 2) div 2))
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(x div (1 + ((x + 1) div (2 + ((x2 mod (2 + (x div 2))) mod 2)))))
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((x div 3) mod (1 + (2 * (x mod (2 + (x mod (2 + (x mod 2))))))))
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(1 + ((((x + 1) div 2) - (((x + 2) div 3) mod 4)) div 2))
A195852-A029132: 1 1 1 1 1 1 1 1 1 2 3 4 4 4 4 4
(1 + ((((x + (x div 2)) div 4) + ((x + 1) mod 4)) div 2))
A137419: 1 2 2 1 2 2 3 2 3 3 4 3 3 4 5 3
((x + 9) - (x div ~9))
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(1 - ((~2x + 2) div (3 - (x div ~7))))
A060021: 1 1 2 2 3 3 4 4 4 5 5 5 6 6 7 6
((x2 + x + 1) - (x mod (x - ((x + ~1) mod 8))))
A169627: 1 3 7 13 21 31
A025728: 1 3 7 13 21 31 43 57 73 91 110 131 154 179 206 235
(9x3 + 27x2 + 36x + 9)
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(((x3 + ~3x2 + 2x) div 3) div 9)
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(x - (27 * ((~x2 + x) div 2)))
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(((2x + 1) * (1 - (2 * (x mod 2)))) mod 9)
A112282: 1 6 5 2 0 7 4 3 8 8 3 4 7 0 2 5
((3x + 2) - ((2x + 1) div 9))
A249118-A093609: 2 5 8 11 13 16 19 22 25 27 30 33 36 38 41 44
(((3x + 1) * (1 + (x mod 2))) mod 9)
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(9 * ((x + 1) + (4 * (x + (x mod 2)))))
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(x + ((~x + 3) div 9) - (x div 3))
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(2x - (9 * ((x div 5) mod 2)))
A169910: 0 2 4 6 8 1 3 5 7 9 20 22 24 26 28 21
(9 * (x - (2 div (x + ~16))))
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((4x + 2) - ((~2x + 2) div 9))
A299637-A035487: 2 6 11 15 19 23 28 32 36 40 44 49 53 57 61 66
(((3x + 2) * (2 - (x mod 2))) mod 9)
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A177883: 4 5 7 2 1 8 4 5 7 2 1 8 4 5 7 2
(9 * ((x4 + 2x3 + ~x2) div 2))
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(x - (9 * (~x + (x mod 10))))
A103303: 0 1 2 3 4 5 6 7 8 9
A171120-A092907-A051022-A001633: 0 1 2 3 4 5 6 7 8 9 100 101 102 103 104 105
((10x + 10) + (x div 9))
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(18x - (x div 9))
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((x mod 2) - ((x div 9) + ((x div 2) div ~2)))
A057526-A033265: 0 1 1 2 1 2 2 3 2 2 2 3 2 3 3 4
((10x + 10) + (x mod 9))
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A346261: 10 21 32 43 54 65 76 87 98 100 111 122 133 144 155 166
((2 + (x * (x div 2))) mod (~1 + ((x2 + ~x) mod 8)))
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(1 + (((x2 + ~x) div (x + 4)) + (x div 8)))
A100476: 1 1 1 1 2 3 4 4 6 7 8 9 10 11 12 13
((1 - (x div ~8)) * (1 + (x div 8)))
A280263: 1 2 2 2 2 2 2 2 4 6 6 6 6 6 6 6
(((x + 1) - (x mod 8)) * (1 + (x mod 8)))
A032944: 1 2 3 4 5 6 7 8 9 18 27 36 45 54 63 72
((x + 3) - ((~x + ((x + 1) mod 6)) div 4))
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(1 + (x div 8) - (x div (~2 + ((~x + 2) div 4))))
A104055: 1 2 2 2 3 3 3 3 4 5 5 5 5 5 5 5
(1 + ((1 + ((x div (2 + (x mod 3))) + (x div 4))) div 2))
A343378: 1 1 1 2 2 2 3 3 3 4 4 3 6 5 4 6
(1 + ((((x mod (1 + (x div 2))) mod 3) + (x div 4)) div 2))
A182134: 1 1 1 1 2 2 2 1 2 2 2 3 3 2 2 3
((x + 1) div (1 + (2 * (((x + ~1) mod 3) + (x div 4)))))
A222759: 0 2 1 0 1 1 1 2 1 1 2 1 1 2 1 1
(1 + ((((1 + ((x * (x div 2)) div 2)) div 2) - (x div 4)) div 2))
A267597: 1 1 1 1 1 2 3 3 4 4 6 7 8
((~2x + 5) mod (1 + (2x mod (2 + (x div 4)))))
A184159: 0 0 0 0 0 1 0 0 0 2 0 1 1 1 1 0
(x - ((2x + 1) mod (1 + (2x mod (2 + (x div 4))))))
A162906: 0 1 2 3 4 4 6 7 8 8 10 9 12 12 13 15
((x2 + ~x) mod ((x + 1) - ((~x + 1) div (2 + (x div 4)))))
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(5 - ((x + 2) mod (3 - ((x div 4) mod 2))))
A081361: 3 5 4 3 5 4 5 4 4 3 5 4 5 4 5 4
(x div (3 + (((1 + (x div 2)) mod 3) + (x mod 4))))
A260088: 0 0 0 0 1 1 1 1 1 1 2 1 3 2 2 1
(1 + ((((x + ((x + 1) * (x div 5))) div 2) div 2) div 2))
A029097: 1 1 1 1 1 2 2 2 3 3 5 5 5 6 6 8
((x + 1) - (2 * ((0 - (x2 mod (x - ((~x + 2) div 2)))) div 2)))
A263881: 1 2 3 6 7 10 11
A278965: 1 2 3 6 7 10 11 18 19
((2x + 1) - (((3x2 div (x + 2)) div 2) div 2))
A256543: 1 3 5 6 7 9 10 11 13 14 15 17 18 19 20 22
(x div (~1 + (2 * (2 + ((1 - (2 * (x mod 4))) mod (x + 2))))))
A281477: 0 0 0 1 0 0 0 0 1 0 0 0 2 0 0 0
(1 + ((x - (((2 + (x * (x + (x div 2)))) div (x + 2)) div 2)) mod 2))
A321696-A321020: 1 2 2 1 1 2 2 2 1 1 1 2 2 2 2 1
(1 + (2 * ((2x + 5) + (x div 2) - (x mod 4))))
A045798: 11 13 17 19 31 33 37 39 51 53 57 59 71 73 77 79
((4x + 9) + ((x - ((~x + 2) div 4)) div 2))
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(1 + (2 * (4x + (((((x + ~1) div 2) div 2) div 2) mod 2))))
A329422: 3 9 17 25 33 41 49 57 65 75
((x + 1) - ((0 - ((((1 + (x div 2)) div 2) * (x div 2)) div 2)) div 2))
A070124-A070118: 1 2 3 4 6 7 9 10 11 12 15 16 18 19 22 23
(x - ((x + 1) mod (1 + (x mod (2 + ((~x + 1) mod (2 + (x div 2))))))))
A262882: 0 1 2 3 3 5 6 7 7 7 7 11 11 13 14 15
(1 + (2 * (2x + ((~x + 2) div (2 + (x div 2))) - (x div 2))))
A077799: 3 5 7 9 11 15 17 21 23 25 27 31 33 37 39 43
((2x + 1) - (((x div 2) - ((~x + 2) div (2 + (x div 2)))) div 2))
A092979: 2 3 5 6 8 10 11 13 15 16 18 20 21 23 25 27
(1 + ((1 + (x div 4)) div (2 + (x2 mod (2 + (x div 2))))))
A329325: 1 1 1 1 2 1 1 1 1 1 1 1 3 2 1 3
(1 + (2 * (((3 * (x + (x div 4))) - (x mod 2)) div 2)))
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(1 + (x div (2 * (8 - ((x + ~2) div (2 + (x mod 2)))))))
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((5x + 1) - ((~x + 2) div (4 + (x mod 2))))
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((x + 1) div (1 - ((~2x + 1) div (1 + (2 * (2 + (x mod 2)))))))
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(5 mod (1 - ((~x + 2) div (1 + (2 * (2 + (x mod 2)))))))
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((1 + (x mod (1 + (x div 4)))) div (1 + ((x + 1) mod 4)))
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(1 - (5 mod (1 + ((2x + (x div 2)) mod 4))))
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(25x2 + 50x + 20)
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(5 * (1 + (5 * ((x2 + x) div 2))))
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((6x2 + 18x + 11) div 5)
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(5 * (1 + (2 * (x - (((~x + 2) div 2) div 3)))))
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((x mod (x - ((x + 1) mod 7))) mod 5)
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(x4 mod 45)
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(x - (25 * ((~x2 + x) div 2)))
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(5 * (x - (5 * ((~x2 + x) div 2))))
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(((x2 + 2x + 2) + (x div 5)) div 5)
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(5 + ((~1 + (x mod 3)) mod (3 + (x mod 2))))
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((12x2 + 12x + 6) div 5)
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((3 * ((2x + 2) + (x div 4))) div 5)
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(((3x + 6) + (x mod 6)) div 5)
A293428: 1 2 2 3 4 5 4 5 6 7 8 8 8 9 10 10
(((1 - (x mod (3 + (x mod 2)))) mod (x + 1)) div 5)
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((2x + 2) - ((2x2 + 4x + 2) mod 5))
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((9x + 8) - ((x + 1) div 5))
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(45x2 + 65x + 20)
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(x2 - ((5x + ~5) * ((~x2 + x) div 2)))
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(100x2 + 10)
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(2x - ((2 * ((x + ~1) - (x div 4))) div 5))
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(x - ((2 + (((x + 1) * (x div 2)) div 3)) div 5))
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((2 + (3 * (2 + ((x div 2) * (x div 2))))) div 5)
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(x - ((0 - (2 * (1 + (2 * (x + (x mod 2)))))) div 5))
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(x2 mod (x2 + ~2x + 20))
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(20 * (2x - (x mod 5)))
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(x5 mod 40)
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(1 + (((x2 + x) div 4) div 5) - (x mod 2))
A116928: 1 0 1 0 2 1 3 2 4 4 6 6 8 9 11 12
(10 * ((x + 2) + (2 mod (1 + (x div 4)))))
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(x2 + 29x + 20)
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(x - (((x + 4) * (1 - (2 * (x mod 2)))) div 5))
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(2x - ((2 * (x + (x mod 5))) div 5))
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(x - (10 * (~x + (x mod 10))))
A103303: 0 1 2 3 4 5 6 7 8 9
A181352-A056143: 0 1 2 3 4 5 6 7 8 9 110 111 112 113 114 115
(2x - (((x + ~2) + (~x mod 4)) div 5))
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(~5 + ((x + 2) * ((x + 3) - ((x div 2) mod 2))))
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((2x + 32) - ((x + 2) div 5))
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(x + (((x + 1) div 5) + ((x + 2) div 5)))
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(~5x2 + 85x + 2)
A120826: 2 82 152
((x div 2) - ((~x + ((x * (x div 2)) div 3)) div 5))
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((x + 1) - ((x mod 2) + ((x + (x div 3)) div 5)))
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(x + ((~x + 1) div 5) - (x div 9))
A005375: 0 1 1 2 3 4 5 5 6 6 7 8 8 9 10 11
((x + (2 * (2 + (x2 mod 5)))) div 5)
A058207: 0 1 2 3 2 1 2 3 4 3 2 3 4 5 4 3
((x + (2 * (x div (4 + (x mod 4))))) mod 5)
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(((1 + (x div 2)) div 2) - ((x + (2 * (x mod 2))) div 5))
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((3x + 2) - ((~x + ((~x + 2) div 2)) div 5))
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((2x + 2) - (x2 div ((x + 5) + (x div 2))))
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(((8x + 4) div 3) - (x div 5))
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A190081: 1 4 6 9 12 13 16 19 21 24 26 28 31 34 36 38
(x + (x div 5) - (2 * (x div ~5)))
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((((x2 + 1) + (2 mod (x + 1))) div 2) + (x div 5))
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((3x + 2) + (x div 4) - (x div 5))
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(((x + ((x div 2) mod 4)) div 4) - (x div 5))
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(x - ((x div 5) + ((~x + 4) * (x div 4))))
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A050763: 0 1 2 3 4 5 7 9 15 18
(x + ((2 * ((x + 1) div 5)) + (x div 5)))
A088414: 0 1 2 3 6 8
A047405: 0 1 2 3 6 8 9 10 11 14 16 17 18 19 22 24
(((x + 1) mod 3) mod (2 - ((~x2 + x) mod 5)))
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((2x + 1) - ((x + ((1 + (x div 2)) mod 3)) div 4))
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A286992: 1 3 4 6 8 10 12 13 15 17 19 21 22 24 25 27
(1 + ((x + (9 mod (1 + (x div 2)))) div 4))
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((2x + 1) - ((x + ((~x2 + x) div 4)) div 4))
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(1 + ((x + (((((x + 1) div 2) div 2) * (x div 2)) div 2)) div 4))
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((2x + 1) - ((x2 + ~2x) div ((x + 4) + (x div 2))))
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(1 + ((x2 + 2x) mod ((4x + 4) + (x div 4))))
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(2 + (x mod (1 + (x div 4))) - ((~x + 2) div (2 + (x div 2))))
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((18x + 17) - (x mod 4))
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((x + 1) + (x mod 4) - (3 * ((x div 4) mod 2)))
A271833: 1 3 5 7 2 4 6 8 9 11 13 15 10 12 14 16
(1 + ((x + 2) mod (2 * ((x + ((~1 + (x div 2)) mod 3)) div 2))))
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(1 + (2 * (x - ((~x2 + x) div ((x + 2) + (x div 3))))))
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(3 + ((x + (2x div (2 + ((x div 2) div 3)))) div 2))
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A050270: 3 4 5 6 7 8 8 8 9 10 11 12 12 12 13 14
((x + 1) - ((0 - (x2 div (x + 10))) div 2))
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((x + 1) + (x mod 2) - ((x2 div (x - ((~x + 2) div 2))) mod 2))
A105363: 1 2 3 5 4 6 7 9 8 11 10 12 13 15 14 17
(3 + ((4x + (x2 div 4)) div (x + 2)))
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((2x + 1) - (((2 + (x * (x + (x div 2)))) div (x + 2)) div 2))
A225647: 1 3 4 6 7
A184429: 1 3 4 6 7 9 10 11 13 14 15 17 18 19 20 22
(1 + (2 * (2x + ((x + ((x mod (1 + (x div 2))) div 2)) div 2))))
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A284621: 1 5 11 15 21 27 31 37 41 47 53 57 63 69 73 79
(1 + (2 * (2x + ((6x + 1) * (x div 2)))))
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(32x3 + 32x2 + 10x + 1)
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(24x3 + 26x2 + 9x + 1)
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((4x + 1) + ((((x div 2) - (x mod 4)) div 2) div 2))
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((5x + 1) + (x div (~2 + ((~x + 2) div 4))))
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(24x3 + ~26x2 + 9x + ~1)
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(1 + ((((x2 + x) div 7) + (x div 2)) div 2))
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(1 + ((x + 1) div (2 * (((~1 + (x div 2)) mod 3) + (x div 2)))))
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((x + 3) - ((x + 2) div (12 - (x div 2))))
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A247485: 3 4 5 6 7 8 9 9 10 11 12 13 13 14 14 15
((x + 1) - ((((x2 + 2x) mod 6) + (x div 2)) div 2))
A267451: 1 1 2 2 4 3 6 5 6 7 9 7 10 10 11 11
(1 + (2 * (2x + (x div 2) - (x mod (2 * (2 - (x mod 2)))))))
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(1 + (((x + 1) + (4 * (x + (x div 2)))) div (2 + (x div 2))))
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A005670: 1 4 6 7 8 9 9 10 10 11 11 11 11 12 12 12
(1 + (((x mod (1 + (x mod (1 + (x div 3))))) + (x mod 2)) div 2))
A062362: 1 1 1 2 1 2 1 2 2 2 1 3 1 2 3 3
(~1 + (2 * (2x + ((2 - (x div 4)) div 2) - (x mod 2))))
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(x div (1 + ((2 + ((x div 2) + (x div 3))) div (2 + (x mod 2)))))
A318471: 0 1 1 1 1 2 1 2 1 2 1 2 1 2 2 3
((x + 2) div (~1 + ((2 + (x div 8)) * (2 + (x mod 2)))))
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(~1 + (((3x2 + 12x + 12) + (x2 div 2)) div 2))
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((1 + ((x div 2) div (1 + (x mod 9)))) mod 3)
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((1 + (5 mod (1 + ((x + 1) div 3)))) mod 3)
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(3 * ((x + 1) - ((~x + 1) div 11)))
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((1 + ((2 + (x div 3)) div (1 + (x mod 3)))) div 3)
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((1 + (x mod (1 + ((x2 + ~2) mod 6)))) mod 3)
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((1 + ((2x + 2) mod (~1 + (x div ~4)))) mod 3)
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((1 + (((x + 1) div 2) div (1 + (x mod 8)))) mod 3)
A044949: 1 1 1 1 1 1 1 1 2 0 2 2 2 2 2 2
(3 * (1 + ((2x + 1) div (3 + (x div 4)))))
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((1 + ((2x + 1) div (3 + (x div 4)))) mod 3)
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((x mod (1 + (x mod (1 + (x div (2 + ((x div 2) mod 2))))))) mod 3)
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((1 + (x mod (1 + (2 * ((x + ~1) mod (2 + (x mod 2))))))) mod 3)
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(((x + 1) - ((2 - (x div 3)) mod 5)) mod 3)
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((1 + (((x * (x div 3)) div 2) mod 5)) mod 3)
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((x mod (~1 + (3 * (2 + (x mod 2) - (x div 2))))) mod 3)
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(((x3 + 2x2) div (1 + ((x div 2) div 3))) mod 3)
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(x - ((~1 + ((x * ((2 - (x div 2)) div 2)) div 3)) div 3))
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A167207-A037143: 1 2 3 4 5 6 7 9 10 11 13 14 15 17 19 21
(x - ((~5 * (1 + (x div 3))) div 3))
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(((~2 + (x div (~2 + (x mod 2)))) mod (1 + (x div 3))) mod 3)
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(x - (((1 - (x div 4)) * (1 + (x div 3))) div 3))
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A326643: 0 1 2 3 4 5 6 7 9 11 12 13 16 17 18 19
((x mod (1 + ((~2x2 + 2x) mod (1 + (x div 2))))) mod 3)
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((1 + ((x + 1) * ((x + 2) mod 7))) mod 3)
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(3 * (1 + (2 * (1 + ((x mod (2 + (x div 2))) div 3)))))
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(((x + 2) div (1 + (2 * ((x + ~1) mod 5)))) div 3)
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(1 - ((x mod (~1 + (2 * (((~x + 2) div 2) div 3)))) div 3))
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((((x2 + ~2x) * (x div 2)) mod 7) div 3)
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(((x * ((x mod 2) * (x div 2))) div 7) mod 3)
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(3 * (x - (7 * ((~x2 + x) div 2))))
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(3 * (1 + ((0 - (x mod 3)) mod (2 + (x div 3)))))
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((1 + (((x + 1) * (x mod (4 + (x mod 2)))) div 2)) mod 3)
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(5 - ((~x + 2) div (1 - (x div ~5))))
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((~x + 2) + (3 * (x - (x div (~1 + (x div ~4))))))
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((1 + ((~2x + 2) mod (4 + (x div 4)))) div 3)
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((1 + ((~2x + 1) div (4 + (x div 4)))) mod 3)
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((~1 + ((~2x + 1) div (4 + (x div 4)))) mod 3)
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((1 + (2x2 mod (4 + (x div 4)))) mod 3)
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(3 * (x - (9 * ((~x2 + x) div 2))))
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((x + ~9) mod 27)
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(x5 mod 27)
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((1 - (x mod (~1 + (2 * ((x mod 2) - (x div 4)))))) mod 3)
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(1 - (((1 - (x div 2)) mod (~1 + (2 * (x mod 4)))) mod 3))
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((x + 2) - ((1 + (x2 div (4 + (x div 2)))) div 3))
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(x - (3 * (((~2x + ~1) + (x div 2)) div 5)))
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((x + 3) - ((4 * (~x + (x mod 2))) div 5))
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(x - ((((~x + 1) div 3) * (x div 5)) div 3))
A296241-A070932: 0 1 2 3 4 6 7 8 9 10 12 14 15 16 18 20
(((8x + 8) + (x div 5)) div 3)
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((4x + 2) - ((x - (x div 5)) div 3))
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((1 + (((x2 + ~2x) * (x div 2)) div (x + 4))) div 3)
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((7 mod ((x + 1) - ((x div 2) mod 2))) mod 3)
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(((~x + 1) mod (3 + ((x + 2) div (2 - (x mod 2))))) mod 3)
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((x + 3) - (x mod (3 * (1 + ((x div 2) mod 3)))))
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(((~x + 1) - ((x - (x div 5)) div 3)) mod 3)
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(((((~x + 2) div 2) mod 3) + ((x + 1) div 3)) div 3)
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((x - ((2 * (2x div 5)) div 3)) mod 3)
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(x - (3 * ((4 * (x div 5)) div 3)))
A245341: 0 1 2 3 4 2 3 4 5 6 4 5 6 7 8 3
(1 - ((x2 + 2x) div (x + ~36)))
A018050: 1 2 2 2 2 3 3 4 4 5 6 7 8 10 12 14
(x5 mod 36)
A070619: 0 1 32 27 16 29 0 31 8 9 28 23 0 25 20 27
(x - ((x - ((~2 + (x * (x div 3))) div 3)) div 3))
A062462: 0 1 1 2 3 4 5 6 7 9 10 11 13 14 16 18
((((x2 + ~1) mod 5) + (x div 3)) div 3)
A219607: 1 0 1 1 0 1 0 1 1 1 2 1 2 2 1 3
(3x - ((~x + (x mod 2) - (x div 3)) div 3))
A198268: 0 3 7 10 14 17 21 24 28 31 35 38 42 45 48 52
((9x2 + ~9x) + ((x2 + x) div 2))
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((x2 mod (~1 + (2 * (x + (3 * (x div 2)))))) mod 3)
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(3x3 + 30x2 + 99x + 108)
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(x3 + ~3x2 + ~18x + ~27)
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((4x3 + 24x2 + 44x + 24) div 3)
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(3 * ((x + 3) + (2 * (2x - ((x div 2) mod 2)))))
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((6x + 3) + (2x div 7))
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((7x + 3) - ((1 + (x div 3)) div 2))
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((1 + ((3x4 + x3) div 2)) div 3)
A212089: 0 1 9 45 139 333 684 1258 2133 3402 5167 7542 10656 14647 19665 25875
((1 + ((3x4 + ~x3) div 2)) div 3)
A212088: 0 0 7 36 117 292 612 1143 1963 3159 4833 7099 10080 13914 18751 24750
(((x + 1) + (((x div 4) mod 2) * (x div 3))) div 3)
A087182: 0 0 1 1 2 2 3 3 3 3 3 4 5 6 6 7
((x5 + 5x4 + 9x3 + 7x2 + 2x) div 3)
A143945: 0 8 72 320 1000 2520 5488 10752 19440 33000 53240 82368 123032 178360 252000 348160
((2x3 + 12x2 + 19x + 9) div 3)
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(((x + 1) * (1 + (x mod (2 * (2 + (x div 3)))))) mod 3)
A087372: 1 1 0 1 1 0 1 1 0 1 2 0 1 1 0 2
((2x3 + 6x2 + 13x + 9) div 3)
A047667: 3 10 25 52 95 158 245 360 507 690 913 1180 1495 1862 2285 2768
((x4 mod (5x + 5)) mod 3)
A337930: 0 1 1 1 0 1 1 1 1 2 0 1 1 1 1 2
(((x + 1) * ((2 + ((x * (x div 2)) div 2)) div 3)) mod 3)
A055668: 0 0 0 1 1 0 0 2 0 0 0 0 0 2 0 0
(((2x + 2) * ((x div 2) div (3 - (x mod 2)))) mod 3)
A141702: 0 0 0 0 0 0 2 1 0 1 1 0 1 0 0 0
(((x + 1) + (2 * (((x div 3) mod 3) div 2))) div 3)
A189635: 0 0 1 1 1 2 3 3 3 3 3 4 4 4 5 6
((6x + 6) * (2 + ((x2 + 4x + 4) div 2)))
A192833: 24 72 180 336 600 936 1428 2016 2808 3720 4884 6192 7800 9576 11700 14016
((11x + 12) + (x div 8))
A104340: 12 23 34 45 56 67 78 89
A228157: 12 23 34 45 56 67 78 89 101 112 123 134 145 156 167 178
(x + ((2x3 + 6x2 + 4x) div 3) - (x div 2))
A111746: 0 5 17 42 82 143 227 340 484 665 885 1150 1462 1827 2247 2728
((10x3 + 18x2 + 8x) div 3)
A035005: 0 12 56 152 320 580 952 1456 2112 2940 3960 5192 6656 8372 10360 12640
((3x + 3) + ((2x + 1) div 9))
A330115: 3 6 9 12 16 19 22 25 28 32 35 38 41 45 48 51
((3x + 3) + (((x + ~1) + (x div 4)) div 3))
A184119: 2 6 9 12 16 19 23 26 30 33 36 40 43 47 50 53
((3x + 3) + (2 * ((2x + 2) div 5)))
A189380: 3 6 11 14 19 22 25 30 33 38 41 44 49 52 57 60
((3x + 3) + ((x - ((~2 + (x div 2)) div 3)) div 2))
A288999: 3 7 10 14 17 20 24 27 31 34 37 41 44 48 51 55
((3x + 3) + ((x - (x div ~8)) div 2))
A098005: 3 7 10 14 17 21 24 28 31 35 39 42 46 49 53 56
((3x + 3) + (((x - (x div ~4)) div 2) div 2))
A080081-A059550: 3 6 9 13 16 19 23 26 29 33 36 39 42 46 49 52
((3x + 3) + ((x - ((x + (x div 2)) div 4)) div 2))
A080667: 3 6 10 13 16 20 23 26 29 33 36 39 43 46 49 53
(x + ((x + 1) div 3) - ((x + 2) div ~7))
A189796: 1 2 4 5 6 8 10 11 13 14 15 17 18 20 22 23
(((((2 - (x div 2)) mod (x + 2)) div 2) div 2) + ((x + 1) div 3))
A081610: 0 0 1 1 1 2 3 4 5 5 5 6 6 6 7 8
(1 + ((x2 + 4x + 4) div 3) - ((x + 1) mod 3))
A130205: 1 2 6 8 11 17 21 26 34 40 47 57 65 74 86 96
((3x4 + 7x3 + 6x2 + 2x) div 3)
A292057: 0 6 44 164 440 970 1876 3304 5424 8430 12540 17996 25064 34034 45220 58960
((14x + 12) + ((x + ~1) div 3))
A193107: 11 26 40 54 69
(x - (((x + ((x div 4) mod 2)) div 2) + ((x + ~1) div 3)))
A099386: 1 1 1 2 1 1 2 1 2 3 2 3 3 2 3 3
((2 + (x div (1 + ((x2 + 2) mod 5)))) div 3)
A220492: 0 0 1 1 1 1 1 1 2 1 1 1 2 2 1 2
(36x2 + 72x + 30)
A158462: 30 138 318 570 894 1290 1758 2298 2910 3594 4350 5178 6078 7050 8094 9210
((2 * (x div (1 + (2 * (2 - ((x mod 3) mod 2)))))) div 3)
A049824: 0 0 0 0 0 0 0 1 0 0 2 1 1 2 1 2
(x - (6 * (2x div 15)))
A240832: 0 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3
((2 + ((1 + ((x * (x mod 2)) div 2)) mod 5)) div 3)
A194297: 1 1 1 1 1 1 1 2 1 0 1 1 1 1 1 1
(((2x + 1) mod (2 + (2x div 5))) div 3)
A260804: 0 0 0 0 0 1 0 1 0 1 1 1 0 2 0 2
((1 - (((x + 1) mod (~1 - (x div 4))) div 2)) mod 3)
A192013: 1 1 1 1 2 1 2 1 1 2 2 1 0 2 2 1
(1 - ((2 * (x - (4 mod (1 + (x div 4))))) mod 3))
A291137: 1 ~1 0 1 ~1 0 1 ~1 ~1 0 1 ~1 1 ~1 0 1
(((x3 + 9x2 + 20x) div 2) div 3)
A005586: 0 5 14 28 48 75 110 154 208 273 350 440 544 663 798 950
(x - (3 * ((3 * (x div 7)) div 2)))
A245349: 0 1 2 3 4 5 6 4 5 6 7 8 9 10 5 6
(78x + 66)
A278126: 66 144 222 300 378 456 534 612 690 768 846 924 1002 1080 1158 1236
(3 * (((x + 1) div 2) - ((3 * (x div 4)) div 2)))
A324467: 0 3 3 6 3 6 6 9 3 6 6 9 6 9 9 12
((2 * (2 - (((~x2 + 2x) div 4) div 3))) div 3)
A058360: 1 1 1 2 2 2 2 3 4 5 6 7 8 9 10 12
((x + ~3) mod ((2 * (2 - ((~x + 1) div 3))) div 3))
A324393: 0 0 1 0 1 0 1 0 2 0 1 0 1 2 3 0
((2 * (1 + (2 * (x + ((x + 1) div 5))))) div 3)
A047547-A014456: 0 2 3 4 7 8 10 11 12 15 16 18 19 20 23 24
((2 + ((~3x + 5) mod (1 + (x div 2)))) div 3)
A280737-A117118: 0 0 1 0 1 1 1 0 1 1 2 1 2 1 1 0
(((x * ((1 + ((x div 2) mod 2)) * (1 + (x div 2)))) div 2) mod 3)
A114448: 0 0 1 0 0 1 0 1 2 1 0 0 0 0 1 0
((2 * (1 + (x * (1 + ((x * (x div 2)) div 3))))) div 3)
A122026: 0 1 2 4 8 14 28
((2 * (2x div (~x + 17))) div 3)
A326528: 0 0 0 0 0 0 0 0 0 1 1 2 2 4 6 10
(27x2 + 33x + 12)
A304164: 12 72 186 354 576 852 1182 1566 2004 2496 3042 3642 4296 5004 5766 6582
((2 * ((4x + 4) + (x div 8))) div 3)
A284774: 2 5 8 10 13 16 18 21 24 27 30 32 35 38 40 43
(((~x3 + 3x2 + 16x + 12) div 2) div 3)
A167541: 2 5 8 10 10 7 0 ~12 ~30 ~55 ~88 ~130 ~182 ~245 ~320 ~408
(((x5 + 5x4 + 8x3 + 4x2) div 2) div 3)
A004256: 0 3 32 150 480 1225 2688 5292 9600 16335 26400 40898 61152 88725 125440 173400
((7x + 6) - (((x + 1) div 2) div 3))
A187393: 6 13 20 27 34 40 47 54 61 68 75 81 88 95 102 109
((5x + 6) + ((x mod (1 + (x div 2))) div 2))
A184487: 6 11 16 21 26 32 37 42 47 53 58 63 68 74 79 84
(1 + ((x div (2 * (2 + (x mod 2)))) + (((x + 1) div 2) div 3)))
A087504: 1 1 1 1 2 2 3 3 4 3 4 4 6 5 6 5
(2 + (((x + 1) div 2) div 3) - ((~x + 2) div (2 + (x div 2))))
A082447: 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 6
(((5x3 + 3x2 + ~2x) div 2) div 3)
A002413: 0 1 8 26 60 115 196 308 456 645 880 1166 1508 1911 2380 2920
(((5x3 + 9x2 + 4x) div 2) div 3)
A162147: 0 3 14 38 80 145 238 364 528 735 990 1298 1664 2093 2590 3160
(((2x4 + 2x3 + ~5x2 + x) div 2) div 3)
A330700: 0 0 5 29 94 230 475 875 1484 2364 3585 5225 7370 10114 13559 17815
(((2x4 + ~x3 + x2 + ~2x) div 2) div 3)
A071246: 0 0 4 23 76 190 400 749 1288 2076 3180 4675 6644 9178 12376 16345
(~1 mod (((x4 + ~x2 + ~1) div 2) div 3))
A257051: 0 0 0 10 38 98 208 390 670 1078 1648 2418 3430 4730 6368 8398
(((x6 + ~2x4 + x2) div 2) div 3)
A179058: 0 0 6 96 600 2400 7350 18816 42336 86400 163350 290400 490776 794976 1242150 1881600
(7x + (x div ~12))
A172330: 0 6 13 20 27 34 41 48 55 62 69 76 83 89 96 103
(3 * (4 + (4 div (1 + ((x + ~1) mod 3)))))
A274339: 15 24 18 15 24 18 15 24 18 15 24 18 15 24 18 15
(144x2 + 12)
A158546: 12 156 588 1308 2316 3612 5196 7068 9228 11676 14412 17436 20748 24348 28236 32412
((2 * (x - (x div (2 * (1 + ((x div 2) div 3)))))) div 3)
A340203: 0 0 0 1 1 2 3 4 4 4 5 6 6 7 8 8
((2 + (x mod ((x + ~2) - ((x + 1) mod 5)))) div 3)
A275332: 0 0 0 0 0 1 0 1 0 1 1 2 2 2 1 1
(((x + 2) div (4 + ((x + ~1) mod 5))) mod 3)
A086967: 0 0 0 0 0 0 2 1 1 1 1 0 2 2 2 2
((x + 2) div (3 * (2 + ((~x + 4) mod 6))))
A037880-A037844: 0 0 0 0 1 0 0 0 0 1 2 0 0 1 1 1
((((x + 2) * ((2 + (x div 2)) * ((x + 1) div 2))) div 2) div 3)
A192225: 0 1 2 5
A006918: 0 1 2 5 8 14 20 30 40 55 70 91 112 140 168 204
((2 + ((~x + 2) mod 28)) div 3)
A114054: 1 1 0 9 9 9 8 8 8 7 7 7 6 6 6 5
((2 + ((x + 1) mod (2 + ((x mod (1 + (x div 2))) div 2)))) div 3)
A227551: 1 0 1 0 1 0 1 1 0 1 1 0 1 2 0 1
((2 - ((((~x3 + 3x2 + ~2x) div 2) div 2) div 2)) div 3)
A053618: 0 0 0 1 1 3 5 9 14 21 30 42 55 72 91 114
((4 * ((x + 2) - (((x div 2) div ~2) div 2))) div 3)
A085492: 2 4 6 8 9 10 12 13 14 16 18 20 21 22 24 25
(12 * (2 + (((x mod 5) div 2) div 2)))
A217140: 24 24 24 24 36 24 24 24 24 36 24 24 24 24 36 24
((2 * ((x + 2) div (2 + ((((x + 1) div 2) div 2) div 2)))) div 3)
A131841: 0 0 1 1 2 2 2 2 2 2 2 2 2 3 3 2
((((~2x + 2) mod (4 + (x div 4))) div 2) mod 3)
A106262: 1 0 1 0 2 1 0 1 2 1 0 2 0 2 1 0
((x div (4 + (((x + 1) div 3) mod 4))) mod 3)
A175800: 0 0 0 0 0 0 1 1 1 1 1 2 0 0 2 0
(x - ((2 * ((2x + 1) div ~7)) div 3))
A137409-A037041: 1 2 3 4 6 7 8 9 10 11 12 14 15 16 18 19
(x5 mod 48)
A070631: 0 1 32 3 16 5 0 7 32 9 16 11 0 13 32 15
(1 - ((2 * ((x + 2) mod (~2 - (x div 4)))) div 3))
A214651: 1 2 1 2 1 3 2 1 3 2 1 3 2 1 4 3
(2x - (3 * ((x div 2) - (2 * ((x div 4) mod 2)))))
A057300: 0 2 1 3 8 10 9 11 4 6 5 7 12 14 13 15
(6 * (x div (4 * (2 - ((x * (x div 2)) mod 2)))))
A173067: 0 0 0 0 0 0 0 6 6 6 6 12 6
(3 + (8 * (((x div 2) - (x * (x mod 2))) div 2)))
A134429: 3 ~5 3 ~5 11 ~13 11 ~13 19 ~21 19 ~21 27 ~29 27 ~29
((x + 3) - (2 * (~8x + (x mod 4))))
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((1 - ((2x2 mod (4 + (x div 2))) div 2)) mod 3)
A017857: 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 2
((2 + ((x2 + 2x + 2) div (2 + ((x div 2) mod 2)))) mod 3)
A287516: 0 1 2 1 0 2 0 2 1 1 0 2 0 1 2 0
(x - ((x2 + 3x + 2) div ~23))
A187102: 1 2 3 4 6 7 9 11
A056176: 1 2 3 4 6 7 9 11 12 14 16 18 20 23 25 27
((x2 + 4x + 4) div (~x + 26))
A111133: 0 0 0 1 1 2 3 4 5 7 9 11 14 17 21 26
(~x + ((x div 2) + (6 * (x - ((~x + 2) div 4)))))
A184552: 0 5 11 22 28 33 39 50 56 61 67 78 84 89 95 106
(1 - ((2 * ((x div 8) + (x mod 4))) div 3))
A180494: 1 1 0 ~1 1 1 0 ~1 1 0 ~1 ~1 1 0 ~1 ~1
(3x - (((x + ~2) - (x2 div 4)) div 3))
A182112: 1 4 7 10 13 16 20 24 28 32 36 40 45 50 55 60
(61x + 23)
A304839: 23 84 145 206 267 328 389 450 511 572 633 694 755 816 877 938
(((((x + 1) div (2 - ((x * (x div 2)) mod 2))) div 2) div 2) mod 3)
A326695: 0 0 0 1 0 0 0 2 1 1 1 0 1 1 1 1
((2 * (16x div (x + 4))) div 3)
A007600: 0 2 3 4 5 5 6 6 6 7 7 7 8 8 8 8
((2x + 11) + ((~x + (x mod 2)) div 3))
A320427: 11 13 14 16 17 19 21 23 24 26 27 29 31 33 34 36
((~x + 1) + ((2x3 + 12x2 + 16x) div 3))
A192023: 1 10 31 68 125 206 315 456 633 850 1111 1420 1781 2198 2675 3216
(2x div (2 - ((2 * ((~x + 1) div (2 + (x mod 2)))) div 3)))
A112754-A064515: 0 1 1 2 2 2 3 3 3 4 3 4 4 5 4 5
(1 - ((x2 + 2x + 1) mod (6 * (~2 + (x mod 2)))))
A129197: 12 3 4 3 12 1 12 3 4 3 12 1 12 3 4 3
((x + 12) - (x div ~12))
A043701-A043651: 12 14 15 16 17 18 19 20 21 22 23 24 25 27 28 29
(((x2 + 2x + 1) * (1 + (x mod 2))) mod 12)
A205185: 1 8 9 8 1 0 1 8 9 8 1 0 1 8 9 8
(11x + (x div 12))
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((4 * (x + (x div 11))) div 3)
A138083: 0 1 2 4 5 6
A277018-A277008: 0 1 2 4 5 6 8 9 10 12 13 16 17 18 20 21
(((x * ((2x + 1) - (x mod 4))) div 4) mod 3)
A160382: 0 0 1 0 0 0 1 0 1 1 2 1 0 0 1 0
(2x - ((~2 + ((x mod 3) + (x div 4))) div 3))
A189750: 1 3 4 7 8 10 13 14 16 18 20 22 24 26 27 30
(x - ((0 - (((x * (((x + ~1) div 2) div 2)) div 2) div 2)) div 3))
A236860-A236842: 0 1 2 3 4 6 7 8 9 11 12 13 14 16 18 19
((2 * ((x + (((2 + (x mod 2)) * (x div 2)) div 2)) div 2)) div 3)
A251631: 0 0 0 1 2 2 2 3 4 4 4 6 6 7 6 8
((2 - ((~x + 1) div (2 * (2 - ((x * (x div 2)) mod 2))))) div 3)
A161091: 0 0 1 1 1 1 1 1 1 1 1 2 1 1 2 3
(((2x4 + x3) mod (x + 4)) mod 3)
A276204: 0 0 1 0 0 1 2 2 1 0 0 1 0 0 1 2
(((x3 + 9x2 + 14x) div 2) div 3)
A000297: 0 4 12 25 44 70 104 147 200 264 340 429 532 650 784 935
((2x + 2) - ((2 * ((x2 + ~x) div (x + 2))) div 3))
A184012-A080037: 2 4 6 8 9 11 12 14 15 16 18 19 20 22 23 24
((2 * (2x + (((x div 3) mod 3) mod 2))) div 3)
A153343: 0 1 2 4 6 7 8 9 10 12 13 14 16 18 19 20
(((x + 1) div 2) - (((x div 2) div (2 - ((x div 2) mod 2))) div 3))
A048621: 0 1 1 2 2 3 2 3 4 5 4 5 5 6 5 6
(((x * (1 + (x mod (5 + (x mod 2))))) div 2) mod 3)
A105964: 0 1 0 0 1 0 0 1 1 0 2 0 0 1 2 0
((32x3 + ~2x) div 3)
A267031: 0 10 84 286 680 1330 2300 3654 5456 7770 10660 14190 18424 23426 29260 35990
(((3x4 + 2x3 + x) div 2) div 3)
A212560: 0 1 11 50 150 355 721 1316 2220 3525 5335 7766 10946 15015 20125 26440
(((3x4 + ~2x3 + ~x) div 2) div 3)
A212523: 0 0 5 31 106 270 575 1085 1876 3036 4665 6875 9790 13546 18291 24185
((~x2 + 3x) + (((x3 + ~x) div 2) div 3))
A060163: 0 2 3 4 6 10 17 28 44 66 95 132 178 234 301 380
(((x7 + ~x) div 2) div 3)
A108495: 0 0 21 364 2730 13020 46655 137256 349524 797160 1666665 3247860 5971966 10458084 17568915 28476560
((2x * (((x + 1) * (2 + (x div 4))) div 2)) mod 3)
A117896: 0 1 0 0 2 0 0 0 0 0 2 0 0 1 1 0
(3 + ((x * (2 + ((x3 + ~2x2 + ~x + 2) div 2))) div 2))
A289121: 3 4 5 12 37 98 219 430 767 1272 1993 2984 4305 6022 8207 10938
((x mod 2) - ((((x2 + ~2x) * (x div 3)) div 2) mod 3))
A030201: 0 1 0 0 ~1 0 0 ~1 0 0 0 0 0 0 0 0
(((x + 2) * (6 + ((x2 + x) div 2))) div 3)
A188554: 4 7 12 20 32 49 72 102 140 187 244 312 392 485 592 714
((3x + 6) + (2 * ((x - ((~x + 2) div 4)) div 2)))
A095098: 6 9 14 19 22 27 30 35 40 43 48 53 56 61 64 69
(6x + ((1 - (x2 div 2)) div (2x + 1)))
A315541: 1 6 11 17 23 29 34 40 46 51 57 63 69 74 80 86
(6x + (4x div ~7))
A276853: 0 5 10 16 21 27 32 38 43 48 54 59 65 70 76 81
(6x + (x div 2) - (x div (4 + (x mod 2))))
A075727: 0 6 13 19 25 31 38 44 50 57 63 69 75 82 88 94
(6x + ((x + (x div 8)) div 4))
A038130: 0 6 12 18 25 31 37 43 50 56 62 69 75 81 87 94
(6x + ((~x + ((x div 2) div 5)) div 2))
A172327: 0 5 11 16 22 27 33 38 44 49 55 61 66 72 77 83
(6x + ((~x2 + 2) div (3x + 2)))
A315537: 1 6 11 17 23 28 34 39 45 51 56 62 68 73 79 85
(((~x + 2) div (2 + (x div 5))) + (2x div 3))
A025795: 1 0 1 1 1 2 2 2 3 3 4 4 5 5 6 7
(((1 + (x mod 8)) mod (x + 1)) + ((x div 2) div 3))
A034153: 0 0 0 0 0 0 1 1 2 3 4 5 7 8 9 10
(x + ((2x div (4 + (x div 2))) + ((x div 2) div 3)))
A138083: 0 1 2 4 5 6
A035500: 0 1 2 4 5 6 8 10 11 12 13 14 16 17 18 19
(1 - ((((x2 + 2x) div 5) + (x mod 2)) mod 3))
A089510: 1 0 0 0 0 ~1 1 0 0 ~1 1 ~1 1 0 ~1 0
((((2x2 + ~6x + 4) div 3) + (x mod 2)) div 3)
A140402: 0 0 0 0 1 3 4 7 9 12 16 20 24 29 34 40
(((5x4 + x2) div 2) div 3)
A008354: 0 1 14 69 216 525 1086 2009 3424 5481 8350 12221 17304 23829 32046 42225
((2x + 4) + (x mod 2) - (((~x2 + x) div 2) div 3))
A266936: 4 7 9 12 14 19 21 26 30 35 39 46 50 57 63 70
((2x2 + ~4x) - (((~x3 + x) div 2) div 3))
A026057: 0 ~2 1 10 26 50 83 126 180 246 325 418 526 650 791 950
((x + (x div (1 + ((~x + 2) mod 7)))) mod 3)
A061264: 0 1 1 0 1 0 1 0 0 0 2 0 2 1 0 1
(15x3 + ~15x2 + 4x)
A272134: 0 4 68 282 736 1520 2724 4438 6752 9756 13540 18194 23808 30472 38276 47310
(3 + compr(\x.(~1 + ((x2 + ~x) mod (1 + (x div 4)))),x))
A154660: 3 4 5 6 7 8
A026452: 3 4 5 6 7 8 9 10 12 13 15 16 19 21 24 25
((x * (1 + (x div (2 + (x div 12))))) mod 3)
A227839: 0 1 1 0 0 0 0 1 1 0 0 0 0 2 1 0
(2 - ((x + (((x + ~1) + (x mod 2)) mod 5)) mod 3))
A143667: 1 0 2 2 1 0 2 2 1 1 0 2 1 1 0 2
((x + (5 * (x mod 10))) div 3)
A263042: 0 2 4 6 8 10 12 14 16 18 3 5 7 9 11 13
((x + 3) + ((2x - (x mod 4)) div 5))
A298007: 3 4 5 6 8 9 11 12 14 15 16 17 19 21 22 23
((2x + 2) - ((~x + ((x div 3) mod 3)) div 3))
A286991: 2 5 7 9 11 14 16 18 20 23 26 28 30 32 35 37
(3 * (x + ((2 * (x2 - (x mod 4))) div 3)))
A161214: 0 3 9 21 42 63 84
((x + 3) + ((2 * ((x + ((x div 2) mod 2)) div 2)) div 3))
A179779: 3 4 5 7 8 9 11 12 13 14 16 18 19 20 21 23
((x + ((x * (~x + ((x2 + ~x) div 2))) div 3)) div 3)
A061866: 0 0 0 1 2 4 8 13 20 30 42 57 76 98 124 155
((x + 4) - ((~2x + 2) div (2 - ((~x + 1) div 3))))
A096849-A093373: 3 5 7 9 10 11 13 14 15 17 18 19 20 21 22 23
((7x3 + ~3x2 + ~x) div 3)
A214659: 0 1 14 53 132 265 466 749 1128 1617 2230 2981 3884 4953 6202 7645
((3x2 + 3x + 1) - ((x2 + x) div 4))
A301709: 1 7 18 34 56 84 117 155 199 249 304 364 430 502 579 661
((x + 3) + (2 * (x - (((~x2 + x) div 2) div 3))))
A200182: 3 6 11 14 19 26 31 38 47 54 63 74 83 94 107 118
((x + (((x2 div 4) div (x + 3)) mod 2)) mod 3)
A059835: 0 1 2 0 1 2 1 2 0 1 2 2 0 1 2 1
((x + 3) + ((x - (((x + ~2) * (x div 2)) div (x + 1))) div 2))
A183860: 3 4 6 7 9 10 11 13 14 15 16 18 19 20 21 23
((x + 3) + (2 * ((x div 2) - ((x div 4) div ~2))))
A284491: 3 4 7 8 13 14 17 18 21 22 25 26 31 32 35 36
(((x + 2) + (x mod (2 + ((x div 2) div 5)))) div 3)
A076695: 0 1 1 2 2 2 2 3 3 4 4 5 4 5 6 5
((x + ((x mod (~2 + ((~x + 1) div 5))) div 2)) mod 3)
A337086: 0 0 1 0 0 1 0 0 2 1 0 1 1 0 1 0
((x + 3) + (x div (4 + ((x div 5) mod 2))))
A025020: 3 4 5 6 8 9 10 11 12 13 15 16 18 19 20 21
(3 + compr(\x.((x mod (x - ((x + 1) mod 8))) mod 2),x))
A154660: 3 4 5 6 7 8
A114036: 3 4 5 6 7 8 9 10 12 14 16 17 18 20 22 24
((x + 3) - ((x2 + ~2x) div (x + 16)))
A331859: 3 5 5 6 7 8 8 9 9 10 10 11 11 12 12 12
((x + 4) - ((~x + ((x + 1) mod 8)) div 3))
A214420: 4 5 6 7 8 9 10 14 15 16 17 18 19 20 21 24
((x + 3) + ((2x div (1 + (x div 2))) + (x div 4)))
A288938: 3 6 7 9 10 12 13 14 16 17 18 19 21 22 23 24
((7x3 + ~6x2 + 2x) div 3)
A051673: 0 1 12 47 120 245 436 707 1072 1545 2140 2871 3752 4797 6020 7435
((3x + 3) - ((~x + ((x * (x div 2)) mod 2)) div 3))
A297466: 3 7 10 13 17 20 23 26 30 33 37 40 43 47 50 53
((x + (18x div (x + 2))) div 3)
A202306: 0 2 3 4 5 5 6 7 7 7 8 8 9 9 9 10
((x + 2) + (x div 3) - (x div (~1 + ((~x + 2) div 3))))
A186354: 2 4 6 8 9 11 12 14 15 17 18 19 21 22 23 25
(1 + (((x + ((x div 4) mod 2)) div 4) + (x div 3)))
A166493: 1 1 1 2 3 3 4 5 5 6 6 6 8 8 8 10
((x + 1) - ((x div 3) + ((~x2 + 1) div (x + 4))))
A189404: 1 2 4 5 6 8 9 11 13 14 16 17 18 20 22 23
(x - ((x div 3) + ((~1 + ((x + ~1) div 3)) div 3)))
A156250: 1 2 3 3 3 4 4 5 6 6 7 8 8 8 9 9
compr(\x.((x + 1) mod (1 + ((x2 div 2) mod (x + 2)))),(x div 3))
A035643: 0 0 0 1 1 1 2 2 2 5 5 5 8 8 8 14
(((2x2 mod (1 + ((x + 1) div 2))) mod 2) * (x div 3))
A230819: 0 0 0 0 0 0 0 2 2 0 0 0 4 0 0 0
(((x2 mod (2 + (2x div 3))) div 2) + (x div 3))
A035658: 0 0 0 1 1 1 2 2 2 3 5 5 6 8 8 9
(((3x2 + 4x) div 8) - (x div 3))
A266813: 0 0 2 3 7 10 14 19 26 31 39 47 56 65 76 86
(2x + (((1 + ((x2 + x) div 2)) div 2) + (x div 3)))
A253620: 0 3 6 10 14 19 25 30 36
((((x div 2) div 7) + (x div 2)) - (x div 3))
A325590: 0 0 1 0 1 1 1 1 2 1 2 2 2 2 4 3
((2 * (2x - (x mod 9))) - (x mod 3))
A039592-A037454: 0 1 2 6 7 8 12 13 14 36 37 38 42 43 44 48
((x + (x * (x3 div (4x + 2)))) mod 3)
A284557: 0 1 2 0 1 0 0 0 2 0 0 1 0 2 0 0
(1 + ((x * (1 + (3 * (1 + ((x2 + 2x) div 2))))) div 2))
A178947: 1 4 17 38 81 138 229 340 497 680 921 1194 1537 1918 2381 2888
(1 + (((x + 1) + ((x mod ~4) mod (2x + 1))) div 2))
A026218-A026200: 1 2 4 6 3 8 10 12 5 14 16 18 7 20 22 24
(1 + ((x * (1 + ((1 + (x * (x div 2))) * (1 + (x div 2))))) div 2))
A054981: 1 2 8 14 57
((x + 1) - (2 * (~x + ((2x + 2) div 7))))
A188376: 1 4 7 8 11 14 15 18 21 24 25 28 31 32 35 38
(1 + (2 * (x + ((x2 - (x div 2)) div 7))))
A342474: 1 3 5 9 13 17
A123509: 1 3 5 9 13 17 21 27 33 41 47 55
(8x3 + 28x2 + 26x + 1)
A083079: 1 63 229 547 1065 1831 2893 4299 6097 8335 11061 14323 18169 22647 27805 33691
(1 + (2 * (x + ((1 + (2 * (x + (x mod 2)))) div 5))))
A086398: 1 5 7 9 11 15 17 21 23 27 29 33 35 37 39 43
(1 + (2 * (x + (x div (2 - (x div (~1 + ((~x + 2) div 4))))))))
A247424: 1 3 5 7 11 13 15 17 19 21 23 27 29 31 33 37
(1 + ((13x2 + 9x) div 2))
A342914: 1 12 36 73 123 186 262 351 453 568 696 837 991 1158 1338 1531
(1 + (2 * (x + (x2 div (x + 17)))))
A306069: 1 3 5 7 9 13 15 19 21 25 27 31 33 37 41 45
((x3 + 6x2 + 12x + 7) - ((x2 + x) div 2))
A162264: 7 25 60 118 205 327 490 700 963 1285 1672 2130 2665 3283 3990 4792
(1 + ((x + ((1 + (4x mod (1 + (x div 2)))) div 2)) div 2))
A076897-A076502: 1 1 2 2 3 4 4 4 5 6 7 7 8 8 8 9
(1 + (2 * (x + (2 * ((x - (x div ~3)) div 3)))))
A190238: 1 3 9 11 17 19 21 27 29 35 37 43 45 51 53 55
(1 + (2 * (x + ((3 * ((((x + 1) div 2) div 2) div 2)) div 2))))
A327755-A322903: 1 3 5 7 9 11 13 17 19 21 23 25 27 29 31 37
(1 + (2 * (x + (2 * ((((x + ~1) div 2) * (x div 2)) div 3)))))
A289873: 1 3 5 7 9 15 21 27 33 39 45 55 65 75 85 95
((x + 1) - ((~x + ((x div (2 + ((x div 2) div 3))) mod 2)) div 2))
A184419: 1 3 4 5 7 9 10 12 13 14 16 17 19 20 22 23
(1 + ((x + ((x2 + 2x) div (2 + ((x mod 3) div 2)))) div 2))
A097108: 1 2 3 6 9 9 16 20 18 30 36 30 49 56 45 72
(1 + ((x * (2 + ((x3 + ~3x2 + 4) div 2))) div 2))
A094697: 1 2 3 7 25 73
(58x2 + 1)
A158666: 1 59 233 523 929 1451 2089 2843 3713 4699 5801 7019 8353 9803 11369 13051
(1 + ((x + ((x * (x + (x div 2))) div 16)) div 2))
A125573: 1 1 2 2 3 4 5 6 8 9 10 12 13 15 17 18
(1 + (2 * (x + (2 * (((x div 4) * (x div 4)) div 2)))))
A033034: 1 3 5 7 9 11 13 15 25 27 29 31 41 43 45 47
((2x + 1) - (((x2 + 1) div (x + 8)) div 2))
A208672: 1 3 5 7 9 10 12 14 15 17 19 20 22 23 25 27
(1 + (((x * (x mod 2)) - (x div 2)) mod (x + 10)))
A302389: 1 2 12 3 13 4 14 5 15 6 16 7 17 8 18 9
(1 + ((x * ((x * ((x mod (2 + (x mod 2))) div 2)) div 4)) div 2))
A326697: 1 1 1 1 1 3 1 1 1 1 1 12 1 1 1 1
((4x + 4) - (x mod (1 + ((x + (x div 4)) div 2))))
A305848: 4 8 12 15 19 23 26 30 34 37 41 44 48 52 55 59
((2x + 1) - ((x2 + 2x) div (2x - ((~x + 2) div 2))))
A026277: 1 2 3 5 7 9 10 12 13 15 16 18 20 21 23 25
(16x3 + 10x2 + 4x + 1)
A272130: 1 31 177 535 1201 2271 3841 6007 8865 12511 17041 22551 29137 36895 45921 56311
((1 + (2 * ((x2 + 2x) div 2))) * (1 + ((x2 + 2x) div 2)))
A204558: 1 6 45 120 325 630 1225 2016 3321 4950 7381 10296 14365 19110 25425 32640
(1 + (2 * (x + ((x div (6 - (x mod 2))) + (x div 2)))))
A284894: 1 3 7 9 13 17 21 23 27 29 33 37 41 43 47 51
((x + 1) mod ((2x2 + 1) div (1 + (2 * (x + (x div 2))))))
A065864: 0 0 0 0 1 0 1 0 4 4 5 5 6 6 6 6
(x5 + 5x4 + 5x3 + ~5x2 + ~5x + 1)
A230586: 1 2 123 724 2525 6726 15127 30248 55449 95050 154451 240252 360373 524174 742575 1028176
(1 + ((x + 2) * (1 + (2 * (x mod 15)))))
A281153: 3 10 21 36 55 78 105 136 171 210 253 300 351 406 465 18
(1 + compr(\x.(x mod (1 + (2 * ((x2 div 2) mod 3)))),(x + 2)))
A151757: 4 6 7 8 10 11 12 13 14 16 18 19 20 21 22 24
(~1 + compr(\x.(~2 + ((2x + 1) mod (1 + (x div 4)))),(x + 2)))
A178538: 1 2 3 4 5 6 7 8 9 10 11 13 16 17 20 23
((2x + 1) - ((2 * (~x + (x2 div 3))) div (x + 2)))
A231407: 1 4 6
A183870: 1 4 6 7 9 11 12 13 15 16 18 19 20 22 23 24
compr(\x.(x mod (1 + (4 * (x mod (2 + (x mod 2)))))),(x + 3))
A340268-A340058-A140347-A051035-A002808: 4 6 8 9 10 12 14 15 16 18 20 21 22 24 25 26
((x3 + 6x2 + 11x + 6) * (1 - (2 * (x mod 2))))
A331433: 6 ~24 60 ~120 210 ~336 504 ~720 990 ~1320 1716 ~2184 2730 ~3360 4080 ~4896
(3x div (2 - ((~4x + 2) div (x + 3))))
A120565: 0 1 1 2 3 3 3 4 4 5 6 6 6 6 7 7
((x + 3) * ((x2 + 6x + 10) + (x mod 2)))
A308137: 30 72 130 228 350 528 738 1020 1342 1752 2210 2772 3390 4128 4930 5868
(((x * (x + ((x div 3) mod 3))) div 2) div (x + 3))
A255070: 0 0 0 1 1 1 2 3 3 3 3 4 5 5 6 7
(1 + ((x + 2) * (x + ((x3 + 3x2 + 2x) div 3))))
A178073: 1 10 41 116 265 526 945 1576 2481 3730 5401 7580 10361 13846 18145 23376
((2x + 1) + ((x * (1 + (x div 2))) div 7))
A079511: 1 3 5 7 10 13 16 19 22 25 29 32 37
((2x + 1) + ((2 * ((x2 + ~x) div (x + 2))) div 3))
A057640: 1 3 5 7 10 12 15 17 20 23 25 28 31 33 36 39
((2x + 1) + ((x div (1 + (((~x + 2) div 2) mod 4))) mod 2))
A013951: 1 4 5 7 10 12 13 16 17 20 21 23 26 27 29 32
((2x + 1) + (((x - (x div ~2)) div 5) mod 2))
A097911: 1 3 5 8
A073608: 1 3 5 8 10 12
A206909: 1 3 5 8 10 12 14 15 17 19 22 24 26 27 29 31
((2x + 1) + (((x + ~4) mod (2 + (x div 3))) mod 2))
A285307: 1 4 5 7 9 12 13 16 17 19 22 23 25 28 29 31
((2x + 1) + ((x2 + 3x + 2) div 16))
A097911: 1 3 5 8
A186150: 1 3 5 8 10 13 16 19 22 25 29 32 36 40 44 48
((2x + 1) + ((((x mod 5) + (x div 2)) div 2) div 2))
A097911: 1 3 5 8
A189377: 1 3 5 8 10 11 14 16 18 21 22 24 27 29 31 32
((2x + 1) + (((x2 + ~x + ~1) mod (2 + (x div 2))) mod 2))
A286047: 2 4 6 7 10 12 13 16 18 20 22 23 26 28 30 31
((2x + 1) + (((x4 + ~4x3 + 4x2) div 2) div 2))
A306838: 1 3 5 9 25 67
((2x + 1) + ((x + ((x2 div 2) div 5)) div 2))
A265899: 1 3 6 8 11 14 17 20 24 27 31 34 38 41 45 49
((3x + 1) - ((~x + ((~2 + (x div 2)) div 3)) div 2))
A184579: 2 5 9 12 15 19 22 26 29 33 36 39 43 46 50 53
((2x + 1) + ((x + ((x mod (2 + ((x div 2) mod 2))) mod 2)) div 2))
A231407: 1 4 6
A075325: 1 4 6 8 11 14 16 19 21 24 26 28 31 34 36 38
((2x + 1) + (((4x + 1) - (x div 2)) * (x div 2)))
A318165: 1 3 13
A211438: 1 3 13 19 39 49 79 93 133 151 201 223 283 309 379 409
(20x3 + 30x2 + 12x + 1)
A160674: 1 63 305 847 1809 3311 5473 8415 12257 17119 23121 30383 39025 49167 60929 74431
((2x + 1) * (1 + (5 * ((x2 + x) div 2))))
A063495: 1 18 80 217 459 836 1378 2115 3077 4294 5796 7613 9775 12312 15254 18631
(24x3 + 36x2 + 14x + 1)
A193252: 1 75 365 1015 2169 3971 6565 10095 14705 20539 27741 36455 46825 58995 73109 89311
(32x3 + 48x2 + 18x + 1)
A322830: 1 99 485 1351 2889 5291 8749 13455 19601 27379 36981 48599 62425 78651 97469 119071
((2x + 1) + (((x + 2) * (2 + (x * (x mod 2)))) mod 3))
A201363: 2 3 7
A327224: 2 3 7 8 9 12 14 15 19 20 21 24 26 27 31 32
((2x4 + 4x3 + 3x2 + 2x + 1) div (2x + 1))
A227012: 1 4 16 43 91 166 275 422 614 857 1158 1521 1953 2460 3049 3724
(18x3 + 29x2 + 12x + 1)
A100148: 1 60 285 784 1665 3036 5005 7680 11169 15580 21021 27600 35425 44604 55245 67456
((3x + 1) + ((~x3 + x2) mod 5))
A190679: 1 4 8 12 15 16 19 23 27 30 31 34 38 42 45 46
((3x + 1) + (((x - ((x mod 3) div 2)) div 2) div 2))
A191402: 1 4 7 10 14 17 20 23 26 30 33 36 40 43 46 49
((3x + 1) + (((x - ((2 - (x div 2)) div 2)) div 2) div 2))
A080600: 0 4 7 10 14 17 20 24 27 30 34 37 40 43 47 50
(4x4 + 12x3 + 7x2 + ~7x)
A215687: 0 16 174 690 1876 4140 7986 14014 22920 35496 52630 75306 104604 141700 187866 244470
(1 + ((5 * (x + (3 * (x mod 2)))) + (x div 2)))
A166033: 1 21 12 32 23 43 34 54 45 65 56 76 67 87 78 98
(1 + (((2x3 + 6x2 + 4x) div 3) + (x div 2)))
A056640: 1 5 18 42 83 143 228 340 485 665 886 1150 1463 1827 2248 2728
((x + 1) - ((~2x + 1) div (12 - (x div 2))))
A256421: 1 3 4 5 6 7 9 10 11 13 14 15 17 19 21 22
(1 + (((x div (3 + ((x div 2) div 3))) mod 2) + (x div 2)))
A070546: 1 1 2 3 4 4 5 5 5 5 6 6 7 7 8 9
(1 + ((2 * (((x2 + 2x) + ((x div 2) mod 2)) div 2)) + (x div 2)))
A188545: 1 3 10
A171834: 1 3 10 18 27 37 52 68 85 103 126 150 175 201 232 264
(1 + (((x + ((x + 2) mod (2 + ((x div 2) mod 2)))) div 2) + (x div 2)))
A100708: 1 2 3 4 5 6 8 7 9 10 11 12 13 14 15 16
((1 + (2 mod (1 + (x mod (1 + (x mod 4)))))) mod (1 + (x div 2)))
A155828: 0 0 1 1 1 1 1 3 1 1 1 3 1 1 3 3
((x div (1 + ((x2 + 2x) mod 6))) mod (1 + (x div 2)))
A244329: 0 0 0 0 1 0 2 1 2 2 4 1 5 3 4 3
((1 + (4 * ((x2 + x) mod 3))) mod (1 + (x div 2)))
A285770: 0 0 1 1 0 1 1 1 1 1 3 1 1 2 1 1
(((x + ~3) + ((x div 2) mod 5)) mod (1 + (x div 2)))
A230431-A082853: 0 0 0 1 0 1 2 3 4 0 1 2 3 4 5 6
((((x div 2) mod 5) - (x div 3)) mod (1 + (x div 2)))
A187498: 0 0 1 0 1 1 1 1 2 1 3 3 4 4 6 5
((x + 1) * (((x + 1) div 2) * (1 + (x div 2)) * (1 + (x div 2))))
A212761: 0 2 12 32 90 162 336 512 900 1250 1980 2592 3822 4802 6720 8192
((21 - (x mod 2)) * (1 + (x div 2)))
A195033: 21 20 42 40 63 60 84 80 105 100 126 120 147 140 168 160
((1 + (7 * (2 - (x mod 2)))) * (1 + (x div 2)))
A195035: 15 8 30 16 45 24 60 32 75 40 90 48 105 56 120 64
((2 + ((3 * ((x div 2) div 3)) div 2)) mod (1 + (x div 2)))
A089881: 0 0 0 0 2 2 3 3 3 3 3 3 5 5 5 5
(1 - ((2 - ((x div (2 + (x mod 3))) mod 2)) mod (1 + (x div 2))))
A016362: 1 1 1 0 0 0 0 ~1 ~1 ~1 0 ~1 ~1 ~1 0 0
(24 div (8 div (1 + (x div 2))))
A280510: 3 3 6 6 12 12 12 12 24 24 24 24 24 24 24 24
(((x + 2) + ((x mod (1 + (x div 4))) div 2)) mod (1 + (x div 2)))
A333750-A276771-A088432-A072670: 0 0 0 1 0 1 0 1 1 1 0 2 0 1 1 2
((x + 1) + (((2x div (2 + (x div 3))) mod 2) + (x div 2)))
A187691: 1 3 4 5 7 9 11 12 13 15 16 17 19 20 22 23
(1 + (((x + 1) div (1 + (2 * (3 - (x mod 2))))) + (x mod 2)))
A338718: 1 2 1 2 1 3 2 3 2 4 2 4 2 4 3 5
(1 + ((3 * (x - (2 * (~x + (x div 4))))) + (x mod 2)))
A057538: 1 11 19 29 31 41 49 59 61 71 79 89 91 101 109 119
(1 + (3 * (((x mod 3) div 2) - (x mod 2))) - (x mod 2))
A078070: 1 ~3 4 ~3 1 0 1 ~3 4 ~3 1 0 1 ~3 4 ~3
(1 + ((1 + (8 mod (1 + (x div 2)))) div 2) - (x mod 2))
A023416: 1 0 1 0 2 1 1 0 3 2 2 1 2 1 1 0
(1 + ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2) - (x mod 2))
A325392: 1 0 1 0 1 1 1 0 1 1 1 1 1 1 2 0
((x + 1) + (x mod 2) - ((x - (((x + 1) div 2) div 3)) mod 2))
A120750: 1 2 3 4 5 7 6 9 8 11 10 12 13 14 15 16
(~1 + (2 * (((x + ~2) div (1 + (x mod 3))) mod 2)) - (x mod 2))
A175816: ~1 0 ~1 0 1 0 ~1 ~2 ~1 0 ~1 0 ~1 0 ~1 0
(1 + (((x div 4) - ((x mod 3) div 2)) div 2) - (x mod 2))
A029354: 1 0 0 0 1 0 1 0 1 1 2 0 2 1 2 1
(1 + ((x div (2 + (x div (2 + ((x mod 3) div 2))))) + (x mod 2)))
A306312: 1 2 2 3 2 3 2 3 3 3 2 4 2 3 3 3
(1 + (2 * (x div (2 + ((x mod (2 + (x mod 2))) div 2)))) - (x mod 2))
A133945: 1 0 3 2 5 2 7 6 9 8 11 6 13 12 15 14
(1 + (((x2 mod (3x + 2)) div 2) mod 2) - (x mod 2))
A286627: 1 0 1 0 2 0 1 1 1 1 1 0 2 0 1 0
(((x mod (1 + ((~x + 2) mod 4))) div 2) * (3 - (x mod 2)))
A063958: 0 0 0 2 0 0 0 2 3 0 0 2 0 0 0 2
(1 + ((2 * (x + ((3 * (x div 4)) div 2))) + (x mod 2)))
A285566: 1 4 5 8 11 14 15 18 23 26 27 30 33 36 37 40
((((x + ~1) div (1 + ((x div 2) div 3))) mod 2) * (1 + (x mod 2)))
A330460: 1 0 1 0 1 0 0 2 1 0 0 2 1 0 0 0
(x div ((2 + (x div (2 + ((x mod 3) div 2)))) * (1 + (x mod 2))))
A340832: 0 0 1 0 1 0 1 0 2 0 1 1 1 0 2 0
((x + 1) + (((x3 + 3x2 + 2x) div 3) + (x mod 2)))
A167238: 1 5 11 25 45 77 119 177 249 341 451 585 741 925 1135 1377
(1 + ((x2 + ((x4 div 2) div 3)) div 2))
A274250: 1 1 4 12 30 65 127 225 374 588 884 1281 1801 2465 3300 4332
(1 + ((x3 * (1 + (x3 * (x mod 2)))) div 2))
A035128: 1 2 5 379
(5 mod (2 - (16 mod (~x + ~1))))
A205109: 1 1 1 1 5 1 5 1 1 5 5 5 5 5 5 1
(1 + compr(\x.(~1 + (x mod (1 + (10 * (x mod 2))))),x))
A069149: 1 2 3 5 7 9 11 12 13 15 17 19 21 23 24 25
(1 + compr(\x.(~1 + ((x div 2) mod (1 + (6 * (x mod 2))))),x))
A339968: 1 2 3 4 5 7 9 11 13 15 16 17 18 19 21 23
(1 + compr(\x.(~1 + (2x mod (~1 + (2 * ((1 + (x div 2)) div 2))))),x))
A082463: 1 2 3 4 5 6 7 9 10
A331802: 1 2 3 4 5 6 7 9 10 11 14 15 19 23
(1 + compr(\x.((x + 1) mod (1 + (x div (3 + ((x div 2) mod 2))))),x))
A064438: 1 2 3 4 6 8 9 12 16 18 20 21 24 28 30 32
((x + 1) + ((2x + 2) mod 19))
A161351: 3 6 9 12 15 18 21 24 27 11 14 17 20 23 26 29
((x + 1) + ((x2 + 3x + 2) div 13))
A280724-A023543: 1 2 3 5 7 9 11 13 15 18 21 24 27 30 33 36
(1 + (x * ((x + 2) - ((x + 1) mod 13))))
A044914: 1 2 3 4 5 6 7 8 9 10 11 12 169 183 197 211
(1 + (x * ((x + 2) - ((x + 1) mod 11))))
A044912: 1 2 3 4 5 6 7 8 9 10 121 133 145 157 169 181
((x + 1) + (x mod (1 + ((x + (2 * ((x div 2) mod 2))) div 3))))
A113459: 1 2 3 5 5 7 7 11 11 11 11 13
(1 + compr(\x.(x mod (1 + ((6 * (x mod 2)) mod (x + 1)))),x))
A247945: 1 2 3 4 5 6 7 8 9 11 13 15 17 19 21 22
(1 + compr(\x.(x mod (1 + ((x mod ((x + ~1) - (x mod 4))) div 2))),x))
A275616-A115405: 1 2 3 4 5 7 8 9 11 13 15 16 17 19 21 23
((x + 1) + ((3x2 + 6x) div 7))
A184009: 1 3 6 10 15 21 27 35 43 52 62 73 85 97 111 125
(1 + compr(\x.((x div 2) mod (1 + ((x2 + 2x) mod 6))),x))
A259749: 1 2 5 7 10 11 13 17 19 23 25 26 29 31 34 35
(1 + compr(\x.(~1 + ((8x mod (1 + (x div 2))) div 2)),x))
A130676: 1 2 3 4 5 6 7 8 10 11 15 16 17 18 20 22
((x + 1) + (x div (5 + ((~1 + (x div 2)) mod 3))))
A082463: 1 2 3 4 5 6 7 9 10
A342524-A328161-A325456: 1 2 3 4 5 6 7 9 10 11 12 13 14 15 17 19
(1 + (x * (1 + ((x div 8) + (((x + 1) div 2) div 2)))))
A345745: 1 2 3 7 9 11 13 22 33 37 41 56 61 66 71 91
((x + 1) + (x div (1 + (2 * (2 + ((x div ~4) mod 2))))))
A071000: 1 2 3 4 5 7 8 9 10 11 12 13 14 16 17 19
((x + 1) + ((x2 + 4x + 4) div 15))
A185546: 1 2 4 5 7 9 11 13 15 18 20 23 26 29 32 35
(1 + compr(\x.(((x2 + 4x + 4) div 2) mod 9),x))
A072557: 5 11 16 17 18 23 29 34 35 36 41 47 52 53 54 59
((x + 1) + ((x * (((x + 1) div 2) div 2)) div 9))
A082463: 1 2 3 4 5 6 7 9 10
A191325: 1 2 3 4 5 6 7 9 10 12 13 15 17 18 19 22
(1 + compr(\x.((x * (2 + (x * (x mod 2)))) mod 9),x))
A236653: 1 8 10 19 26 28 37 44 46 55 62 64 73 80 82 91
((x + 1) + ((1 + ((x * (x div 2)) div 4)) div 5))
A196127: 1 2 3 4 5 6 8 9 10 12 13 14 16 18 20 21
((x + 1) + ((8 * (1 + (x div 2))) div 5))
A287775: 2 3 6 7 9 10 13 14 17 18 20 21 24 25 27 28
(25x2 + 35x + 6)
A085025: 6 66 176 336 546 806 1116 1476 1886 2346 2856 3416 4026 4686 5396 6156
(1 + compr(\x.(2 - ((x + ((x + ~1) div 3)) mod 5)),x))
A229081: 1 3 4 7 8 11 12 14 15 16 18 19 22 23 26 27
((x + 1) + ((x * (((x + 1) div 2) div 3)) div 5))
A305504: 1 2 3 4 5 7 8 9 10 11 13 16 17 19 20 22
((x + 1) + ((x + (((~x + 2) div 2) mod 4)) div 5))
A137407: 1 2 3 5 6 7 8 9 10 11 13 14 16 17 18 19
((x + 1) + (((x + ~2) div 5) * (x div 5)))
A082463: 1 2 3 4 5 6 7 9 10
A033948: 1 2 3 4 5 6 7 9 10 11 13 14 17 18 19 22
((3x + 5) - (x mod (~4x + 7)))
A189320: 5 7 11 16 22 28 34 40 46 52 58 64 70 76 82 88
((x + 1) + (((x3 + x2) div 2) div (4x + ~1)))
A024195: 1 2 3 5 7 9 12 15 18 21 25 28 32 37 41 46
((x + 1) + (3 * ((~2x + 1) div 7)))
A194515: 1 ~1 0 1 2 0 1 2 0 1 2 3 1 2 3 1
((x + 1) + (3 * ((~2x + (x div 2)) div 5)))
A194519: 1 ~1 0 1 ~1 0 1 ~1 0 1 2 0 1 2 0 1
(1 + compr(\x.(x - (3 * (~1 + ((x + (x div 2)) div 4)))),x))
A345509: 25 28 31 33 34 36 37 39 40 41 42 43 44 45 46 47
((x + 1) + ((x + 2) div (8 - ((x + 1) div 3))))
A285901: 1 2 3 4 5 7 8 9 11 12 13 15 16 17 20 21
((x + 1) + (3 * ((x * ((x + ~1) div 3)) div (x + 1))))
A032976: 1 2 3 4 5 6 7 11 12 13 17 18 19 23 24 25
((x + 1) + ((2 * ((x + (x div 3)) div 3)) div 3))
A039082: 1 2 3 4 5 7 8 10 11 12 13 14 16 17 19 20
((x + 1) + (2x div (2 - (x mod ~12))))
A180968: 1 2 3 4 5 7 8 10 11 13 16 19
((x + 1) + (3 * (4 + (x div 9))))
A297275-A296745: 13 14 15 16 17 18 19 20 21 25 26 27 28 29 30 31
((~x + ~1) + (3 * (((3 * (2 + (x div 2))) div 2) div 2)))
A320642: 2 1 3 2 4 3 2 1 3 2 4 3 5 4 3 2
((x + 1) + ((2 + ((x + (x div 2)) * ((x + 1) div 2))) div 3))
A146994: 1 3 4 7 9 13 16 22 25 32 36 44 49 59 64 75
((x + 1) + (x div (3 * (2 + ((x + 1) mod 8)))))
A327626: 1 2 3 4 5 6 7 9 9 10 11 12 13 14 15 18
(1 + compr(\x.((x3 + ~x2) mod 24),x))
A172411: 1 2 5 10
A103215: 1 2 5 10 13 17 25 26 29 34 37 41 49 50 53 58
(1 + (5x div (~x + 24)))
A035429: 1 1 1 1 2 2 2 3 3 4 4 5 6 6 8 9
(5x2 div (x + 13))
A067850: 0 0 1 2 4 6 9 12 15 18 21 25 28 32 36 40
((x + 1) + ((2 * ((x + 2) + (2x div 3))) div 3))
A187473: 2 4 6 8 10 12 15 16 19 21 23 25 27 29 31 34
(18x3 + 36x2 + 22x + 4)
A192790: 4 80 336 880 1820 3264 5320 8096 11700 16240 21824 28560 36556 45920 56760 69184
(54x2 + 66x + 16)
A304506: 16 136 364 700 1144 1696 2356 3124 4000 4984 6076 7276 8584 10000 11524 13156
((x + 1) + ((x + (((~x + 2) mod (2 + (x div 2))) div 2)) div 3))
A321372: 1 2 3 5 6 7 9 10 11 13 15 16 18 19 20 21
((x + 1) + ((1 + (2 * ((x + ~1) div 3))) * (x div 3)))
A251599: 1 2 3 5 8 9 13 18 19 25 32 33 41 50 51 61
(1 + compr(\x.(2 + (x div 3) - ((x + (x div 2)) div 4)),x))
A345500: 33 36 39 41 42 44 45 47 48 49 50 51 52 53 54 55
(1 + (2x div (~2x + 23)))
A319638: 1 1 1 1 1 1 2 2 3 4 7
(4x4 + 3x3 + 2x2 + x + 1)
A130886: 1 11 99 427 1253 2931 5911 10739 18057 28603 43211 62811 88429 121187 162303 213091
(4x4 + ~3x3 + 2x2 + ~x + 1)
A131465: 1 3 47 259 861 2171 4603 8667 14969 24211 37191 54803 78037 107979 145811 192811
((x + 1) + ((x2 + ~x) div (x + 15)))
A214981: 1 2 3 4 5 7 8 9 11 13 14 16 17 19 21 23
(1 + compr(\x.((1 - ((x + 2) mod 12)) mod (x + 1)),x))
A297274-A296744-A044960-A044822-A043714: 1 2 3 4 5 6 7 8 9 10 12 24 36 48 60 72
((x + 1) + ((2 + (x mod 11)) mod (x + 1)))
A026511: 1 3 4 5 6 7 8 9 10 11 12 14 16 18 20 22
(1 + compr(\x.((1 - ((x + 2) mod 10)) mod (x + 1)),x))
A297268-A297145-A296709-A044958-A044820-A043712-A037407: 1 2 3 4 5 6 7 8 10 20 30 40 50 60 70 80
(x4 + 9x3 + 28x2 + 35x + 17)
A061222: 17 90 287 698 1437 2642 4475 7122 10793 15722 22167 30410 40757 53538 69107 87842
(x6 + 3x5 + 5x4 + 6x3 + 5x2 + 3x + 1)
A069779: 1 24 315 2080 8925 29016 77959 182400 384345 746200 1356531 2336544 3847285 6097560 9352575 13943296
((x + 1) + (2 * (x mod ((x + ~1) - (x mod 12)))))
A246088: 1 2 3 4 5 6 7 8 9 10 11 12 15 18 21 24
(1 + compr(\x.(((2 - (x mod 4)) mod (1 + (x div 3))) mod 2),x))
A063743: 1 2 3 5 7 8 9 11 13 15 17 19 20 21 23 25
(1 + compr(\x.(1 - (x mod (2 + ((~x + 1) mod (1 + (x div 3)))))),x))
A324694: 2 4 5 6 8 10 12 14 15 16 17 18 20 22 23 24
((x + 1) + (2 * (x div (1 + (x div (2 + (x div 5)))))))
A255137: 1 4 5 6 7 10 11 12 13 14 17 18 19 20 21 22
((x + 1) + (2 * ((x2 + ~2x + 1) div 7)))
A008824: 1 2 3 4 7 10 13 18 23 28 33 40 47 54 63 72
(1 + (x * ((x + 2) - ((x + 1) mod 14))))
A044915: 1 2 3 4 5 6 7 8 9 10 11 12 13 196 211 226
(1 + compr(\x.((x - ((~2x + 2) div 9)) mod 2),x))
A231407: 1 4 6
A193627: 1 4 6 7 9 11 12 14 17 19 22 24 25 27 29 30
(1 + compr(\x.(1 - ((x + 1) mod (2 * (1 + (x div 8))))),x))
A080259: 1 3 5 7 9 10 11 13 14 15 17 19 20 21 22 23
((x + 1) + (2 * ((1 + (2 * (x + (x mod 2)))) div 5)))
A284371: 1 4 5 6 7 10 11 14 15 18 19 22 23 24 25 28
((x + 1) + (((x3 + ~x2) div (1 + (x div 4))) mod 2))
A082463: 1 2 3 4 5 6 7 9 10
A089657: 1 2 3 4 5 6 7 9 10 10 11 13 13 15 16 17
((x + 1) + ((3 * ((x div ~4) div ~2)) div 2))
A088451: 1 2 3 4 5 7 8 9 10 11 12 13 14 17 18 19
((x + 1) + ((3 * (x div (4 + (x div 4)))) div 2))
A022293: 1 2 3 4 5 7 8 9 10 11 12 13 14 15 18 19
(1 + compr(\x.(x3 mod (2 + (3 * (x mod 4)))),x))
A285627: 1 3 5 6 7 9 11 12 13 15 17 19 21 23 25 26
((~x + 1) + ((x2 - (((x2 + 2x) div 2) div 3)) div 2))
A059293: 1 0 0 1 3 6 9 13 18 24 31 39 47 56 66 77
((x + 1) + (x div (2 + (3 * (8 - (x div 2))))))
A119885-A007964: 1 2 3 4 5 6 7 8 9 10 11 13 14 15 17 19
((x + 3) + ((1 - (x mod (2 + (x mod 2)))) mod (2x + 1)))
A154661: 3 4 6 7 8 18
((x + 1) + (2 * ((2 + (x mod (4 + (x div 2)))) mod (x + 1))))
A285623: 1 4 5 6 7 8 9 12 13 16 17 20 21 24 25 28
((x + 1) + (4 * ((x + 1) - ((x + 1) div 5))))
A101889: 5 10 15 20 21 26 31 36 41 42 47 52 57 62 63 68
((x + 1) + (2x div (4 + ((x div 2) div 5))))
A026496: 1 2 4 5 7 8 10 11 13 14 15 16 17 19 20 22
((3x + 3) div (~x + 21))
A015741: 0 0 0 0 0 1 1 1 2 2 3 3 4 5 6 8
((x + 1) + (((3 * ((x + (x div 2)) div 4)) div 2) div 2))
A229302: 1 2 3 4 5 6 8 9 11 12 13 15 16 17 18 19
((x + 1) + ((x + (x div 2)) div (4 + ((x div 2) div 3))))
A121518: 1 2 3 5 6 7 8 10 11 12 14 15 16 17 18 19
((x + 1) + (((((x2 + 2x) div 2) + (x mod 3)) div 2) div 2))
A191535-A100598: 1 2 4 5 8 10
A144876: 1 2 4 5 8 10 13 16 19 22 26 30 34 38
((x + 1) + (((1 + ((x * ((x + ~1) div 3)) div 2)) div 2) div 2))
A088232: 1 2 3 4 5 6 8 10 11 12 15 16 17 20 22 23
((x + 1) + (((1 + ((x * ((x div 2) div 3)) div 2)) div 2) div 2))
A250482: 1 2 3 4 5 6 8 9 10 11 12 13 16 17 18 20
((x + 1) + (2 * ((1 + (((x div 4) mod 2) + (x div 2))) div 2)))
A285663: 1 2 5 6 9 10 11 12 13 14 17 18 21 22 23 24
(1 + compr(\x.((((x + ~1) * ((((x + ~1) div 2) div 2) div 2)) div 2) mod 2),x))
A230776: 1 2 3 4 5 6 7 8 9 10 11 14 15 18 20 22
((x + 1) + (2 * (4 + ((~x + ~1) mod 8))))
A004464: 23 22 21 20 19 18 17 16 31 30 29 28 27 26 25 24
((x + 1) + (((x - (x2 div ~7)) div 2) div 2))
A248560: 1 2 3 5 6 8 10 11 13 15 17 19 21 23 25 28
((x + 1) + (4 * (x mod (x - ((x + ~1) mod 8)))))
A231848: 1 2 3 4 5 6 7 8 9 10 15 20 25 30 35 40
((x + 1) + (x div (4 + (((x + 1) div 2) mod 8))))
A343107: 1 2 3 4 5 6 7 8 10 11 12 13 14 15 16 19
((x + 1) + ((4x + 1) div (4 + (x div 4))))
A221056: 1 3 5 7 8 10 12 13 14 16 17 19 20 21 23 24
((x + 1) + (((x2 - ((~x2 + 2x) div 4)) div 2) div 2))
A231408: 1 2 4 6 9
A022331: 1 2 4 6 9 13 17 22 28 34 41 48 56 65 74 84
((x + 1) + (((x div 2) - (((x + 1) div 3) mod 4)) div 2))
A206718: 1 2 3 4 5 6 7 8 9 10 12 14 16 17 18 19
((x + 1) + ((x2 + ~x) div (10 + (x div 2))))
A187102: 1 2 3 4 6 7 9 11
A225086: 1 2 3 4 6 7 9 11 13 15 17 19 21 23 25 28
((x + 1) + ((x - ((x2 div ((x + 2) + (x div 2))) mod 2)) div 2))
A187683: 1 2 4 5 7 8 9 11 13 14 15 17 18 20 22 23
((x + 1) + (2 * (((2 + (x * (x + (x div 2)))) div (x + 2)) div 2)))
A000277: 1 2 5 6 9 10 13 16 17 20 23 24 27 30 33 34
((x + 1) + (2 * (4x + ((x mod (1 + (x div 2))) div 2))))
A276871: 1 10 19 28 37 48 57 66 75 86 95 104 113 124 133 142
((x + 1) + (((x + (x div (2 + (x mod 5)))) div 2) div 2))
A026514: 1 2 3 4 6 7 9 10 11 12 14 15 16 17 19 21
((x + 1) + (2 * ((x + 2) + ((x - ((~x + 2) div 4)) div 2))))
A101345: 5 8 13 18 21 26 29 34 39 42 47 52 55 60 63 68
((x + 1) + (2 * (2x + (2x div 9))))
A276872: 1 6 11 16 21 28 33 38 43 50 55 60 65 70 77 82
((x + 1) + (((x div (4 - ((x div 2) mod 2))) + (x div 2)) div 2))
A230391: 1 2 3 5 6 7 9 10 12 13 15 16 17 18 20 22
((x + 1) + ((x + ((x * (x + (x div 2))) div 5)) div 2))
A231408: 1 2 4 6 9
A157795: 1 2 4 6 9 12 15 18 22 26 31 35 40
((x + 1) + (2 * (x + ((x + ((x div 2) div 3)) div 3))))
A085048: 1 4 7 12 15 18 23
A276875: 1 4 7 12 15 18 23 26 31 34 37 42 45 50 53 56
((x + 1) + (((x2 + x) + ((((x + 1) div 2) div 2) div 2)) div 2))
A025731: 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 137
((x + 1) + (2 * (x + (2 * (4x div 5)))))
A339215: 1 4 11 18 25 32 35 42 49 56 63 66 73 80 87 94
((x + ~1) + (2 * (x + ((~x + 2) div (2 - (x div ~4))))))
A050487: 1 2 5 6 9 12 15 16 19 22 25 28 31 34 37 38
((x + 1) + (2 * (x + ((x + ((x div 2) div 5)) div 2))))
A276873: 1 4 9 12 17 20 25 28 33 36 41 46 49 54 57 62
((x + 1) + (2 * (x + ((x + ((x mod (1 + (x div 2))) div 2)) div 2))))
A276885: 1 4 9 12 17 22 25 30 33 38 43 46 51 56 59 64
(65x2 + 130x + 65)
A165798: 65 260 585 1040 1625 2340 3185 4160 5265 6500 7865 9360 10985 12740 14625 16640
((x2 + 2x + 1) * ((x3 + 5x2 + 8x + 4) div 2))
A099903: 2 36 216 800 2250 5292 10976 20736 36450 60500 95832 146016 215306 308700 432000 591872
(x6 + 8x5 + 25x4 + 38x3 + 28x2 + 8x)
A101213: 0 108 1152 6000 21600 61740 150528 326592 648000 1197900 2090880 3480048 5564832 8599500 12902400 18865920
(1 + compr(\x.(((x + 1) mod (1 + ((x div 2) div 3))) - (x mod 2)),x))
A067319: 1 2 3 4 5 6 8 10 12
A064481: 1 2 3 4 5 6 8 10 12 15 16 18 20 24 25 26
((x + 1) + (2 * (x2 + (((x2 + 2x) div 2) div 3))))
A212901: 1 4 13 26 45 66 95 126 163 204 251 300 357 416 481 550
((x + 1) * (1 + ((2x + 2) mod (1 + ((x div 2) div 3)))))
A078546: 1 2 3 4 5 6 7 8 9 10 11 12 39 28 15 48
(8x3 + 36x2 + 51x + 23)
A253679: 23 118 333 716 1315 2178 3353 4888 6831 9230 12133 15588 19643 24346 29745 35888
(36x2 + 73x + 37)
A157324: 37 146 327 580 905 1302 1771 2312 2925 3610 4367 5196 6097 7070 8115 9232
(36x2 + 71x + 35)
A157286: 35 142 321 572 895 1290 1757 2296 2907 3590 4345 5172 6071 7042 8085 9200
((x + 1) * (1 + ((2x + 1) div (3 + (x div 4)))))
A231407: 1 4 6
A251630: 1 4 6 12 15 18 28 32 36 40 55 60 65 70 75 96
(25x2 + 51x + 26)
A173089: 26 102 228 404 630 906 1232 1608 2034 2510 3036 3612 4238 4914 5640 6416
((30x + 9) div (x + 1))
A228610: 9 19 23 24 25 26
compr(\x.(~1 + (x mod 6) - (x mod 5)),(x + 1))
A032893: 1 2 3 4 6 7 8 9 12 13 14 18 19 24 25 26
compr(\x.((x2 div 2) mod (1 + ((1 + (x div 2)) div 3))),(x + 1))
A141807: 1 2 3 4 5 6 7 8 9 11 12 13 16 17 19 20
compr(\x.(~1 + (((x * (2 + (x div 3))) div 2) mod 3)),(x + 1))
A288674: 1 3 4 5 6 8 9 10 11 12 13 14 15 18 19 21
((1 + (3 * ((2 + (x mod 4)) * (x mod 2)))) mod (x + 1))
A094924: 0 0 1 0 1 4 1 0 1 0 1 4 1 10 1 0
((x + 1) * (1 + ((x2 + 5x + 6) div (1 + (x mod 2)))))
A295388: 7 14 63 64 215 174 511 368 999 670 1727 1104 2743 1694 4095 2464
(16x3 + 48x2 + 47x + 15)
A069975: 15 126 429 1020 1995 3450 5481 8184 11655 15990 21285 27636 35139 43890 53985 65520
(64x2 + 129x + 65)
A031694: 65 258 579 1028 1605 2310 3143 4104 5193 6410 7755 9228 10829 12558 14415 16400
(64x2 + 127x + 63)
A157948: 63 254 573 1020 1595 2298 3129 4088 5175 6390 7733 9204 10803 12530 14385 16368
((1 + (2 * ((~x + 1) mod (1 + (2x div 3))))) div (x + 1))
A321692: 1 0 1 0 0 0 0 1 1 1 1 1 1 0 1 1
compr(\x.(1 - (x mod (1 + (2 * (1 + ((x div 2) mod 3)))))),(x + 1))
A260402: 2 3 4 5 7 8 9 10 11 13 14 16 17 19 21 22
compr(\x.(~1 + ((x2 mod (~1 + (2 * (x div 3)))) div 2)),(x + 1))
A095135: 1 2 3 4 5 6 7 8 9 10 11 13 14 15 17 22
((1 + ((x - (x mod (1 + (((x + 1) div 2) div 2)))) mod 2)) mod (x + 1))
A175078: 0 0 1 1 1 1 1 1 1 2 2 1 1 1 1 2
compr(\x.(x mod (1 + (2 * (x mod (1 + (x div 8)))))),(x + 1))
A178859-A165412: 1 2 3 4 5 6 7 8 9 10 12 14 15 18 20 21
compr(\x.(4x mod (1 + ((1 + (x div 4)) div 2))),(x + 1))
A271239-A263808-A180477: 1 2 3 4 5 6 7 8 9 10 11 12 15 18 20 21
compr(\x.(~1 + (x mod (2 + ((~x + 1) mod (1 + (x div 4)))))),(x + 1))
A247397: 1 2 3 4 5 6 7 8 9 10 12 13
A091402: 1 2 3 4 5 6 7 8 9 10 12 13 16 25
((x + 1) * (1 + ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2)))
A229347: 1 2 3 4 5 12 7 8 9 20 11 24 13 28 30 16
((1 + ((x + 1) mod (2 * (1 + (x mod (2 + (x mod 2))))))) mod (x + 1))
A175830: 0 1 2 1 2 1 2 1 2 1 2 1 2 3 2 1
((2 - ((x + ~1) mod (3 + ((x div 2) mod 3)))) div (x + 1))
A078580: 0 1 0 0 ~1 ~1 0 0 ~1 0 ~1 0 0 0 0 0
((x - ((~2x2 + 4x) div 7)) mod (x + 1))
A194751: 0 1 2 0 2 4 6 1 4 7 0 4 8 12 2 7
compr(\x.((x mod 6) - (x mod 7)),(x + 1))
A032885: 1 2 3 4 5 6 12 13 18 19 20 24 25 26 27 30
((1 + ((x + 1) mod (2 + ((x * (x div 2)) mod 3)))) mod (x + 1))
A194448: 0 1 1 1 2 1 2 1 2 1 4 1 2 1 4 1
((1 + (2 * (((x mod (2 + (x div 4))) div 2) mod 2))) mod (x + 1))
A073780: 0 1 1 1 1 3 1 1 1 1 3 3 3 3 1 1
compr(\x.((x mod 8) - (x mod 9)),(x + 1))
A032887: 1 2 3 4 5 6 7 8 16 17 24 25 26 32 33 34
((x + 6) - ((1 + (x mod 8)) mod (x + 1)))
A168096: 6 7 8 9 10 11 12 13 13 13 13 13 13 13 13 13
((x2 div 4) - ((1 + (x mod 8)) mod (x + 1)))
A294060: 0 0 1 2 4 6 9 12 15 18 22 26 31 36 42 48
(1 - ((1 - ((x div 2) div (~1 + (2 * (x mod 4))))) div (x + 1)))
A327500-A322818-A066922: 0 1 1 1 1 2 1 1 1 2 1 1 1 2 2 1
((1 + (((((x div 2) div ~2) * (x div 2)) div 2) mod 2)) mod (x + 1))
A192227: 0 1 2 2 2 2 2 2 1 1 1 1 2 2 1 1
((x + 1) * (1 + (((x2 + 2x) div 2) mod (2 * (2 + (x mod 2))))))
A114562: 1 4 3 8 5 36 7 16 9 20 11 72 13 28 15 32
((~1 + (((3x2 + ~x) div 2) div 4)) mod (x + 1))
A194733: 0 1 0 2 4 1 4 0 4 8 2 7 12 4 10 1
compr(\x.(2 - ((~1 + ((x + 1) * (x div 2))) mod 5)),(x + 1))
A285500: 1 2 3 4 7 9 10 11 12 13 14 17 19 20 21 22
compr(\x.(1 - ((x * (x mod (2 + (x mod 2)))) mod 5)),(x + 1))
A070884: 7 11 13 17 19 23 29 31 37 41 43 47 49 53 59 61
compr(\x.(x div ((2 + (x div 4)) * (1 + (x mod 4)))),(x + 1))
A078135: 1 2 3 5 6 7 10 11 14 15 19 23
compr(\x.(~1 + (2x2 mod (2 + ((x * (x mod 2)) div 2)))),(x + 1))
A256389: 1 2 3 4 6 8 9 10 12 14 15 16 18 20 22 24
(8x2 + 55x + 79)
A250658: 79 142 221 316 427 554 697 856 1031 1222 1429 1652 1891 2146 2417 2704
((1 + (2 * ((1 + ((x + ~1) mod 3)) * (x div 2)))) div (x + 1))
A127242: 1 0 1 1 1 1 2 0 1 2 1 1 2 0 1 2
((x + 1) * (1 - (x mod (~1 + (((x div 3) - (x div 2)) div 2)))))
A327262: 1 2 3 4 5 12 7 16 9 20 11 24 13 28 30 32
compr(\x.((x div 2) - (3 * (x mod 7))),(x + 1))
A032878-A032845: 1 2 3 4 5 6 9 10 11 12 13 17 18 19 20 25
((x + 1) * (((~x2 + 3x) mod (1 + (x div 2))) div 3))
A308122: 0 0 0 0 0 0 0 0 0 0 0 0 13 14 30 16
(25x2 + 48x + 23)
A154376: 23 96 219 392 615 888 1211 1584 2007 2480 3003 3576 4199 4872 5595 6368
compr(\x.(x - (3 * (2 + (x div (2 * (2 + (x mod 2))))))),(x + 1))
A271168-A103969: 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 24
(((x + 1) div 2) - ((3 * (~2x + (x mod 2))) div (x + 1)))
A036496: 0 3 5 6 7 8 9 9 10 11 11 12 12 13 13 14
((1 - ((~x * (x div (1 + (x mod 2)))) div 3)) div (x + 1))
A029227: 1 0 1 0 1 0 1 1 2 1 3 1 3 1 4 2
compr(\x.((x mod 11) * (x mod 3)),(x + 1))
A230193-A201462: 3 6 9 11 12 15 18 21 22 24 27 30 33 36 39 42
(((1 + (x mod 12)) * (1 + (x div 2))) mod (x + 1))
A213186: 0 0 0 0 0 0 0 0 0 0 0 0 7 0 9 0
(7x3 + 12x2 + 6x + 1)
A100162: 1 26 117 316 665 1206 1981 3032 4401 6130 8261 10836 13897 17486 21645 26416
(x5 + 5x4 + 10x3 + 7x2 + 2x + 1)
A269658: 1 26 225 988 3065 7686 16681 32600 58833 99730 160721 248436 370825 537278 758745 1047856
((x2 + 2x + 1) * (((x + 1) mod (1 + (x div 3))) mod 2))
A108321: 0 0 0 0 25 0 49 0 0 0 121 0 169 0 0 0
(x8 + x7 + x6 + x5 + x4 + x3 + x2 + x)
A228292: 0 8 510 9840 87380 488280 2015538 6725600 19173960 48427560 111111110 235794768 469070940 883708280 1589311290 2745954240
(36x2 + 74x + 38)
A158064: 38 148 330 584 910 1308 1778 2320 2934 3620 4378 5208 6110 7084 8130 9248
(36x2 + 70x + 34)
A158062: 34 140 318 568 890 1284 1750 2288 2898 3580 4334 5160 6058 7028 8070 9184
((x + 1) * ((2x div (1 + ((x div 2) div (1 + (x mod 2))))) mod 2))
A308147: 0 0 0 0 0 6 7 8 9 0 11 12 13 0 15 16
(64x2 + 126x + 62)
A158067: 62 252 570 1016 1590 2292 3122 4080 5166 6380 7722 9192 10790 12516 14370 16352
compr(\x.(~2 + (x mod ((x + 1) - (x mod 10)))),(x + 1))
A254785: 1 2 3 4 5 6 7 8 9 11 12 13 21 22 23 31
((1 - (2 * ((x div 2) - (x div 7)))) mod (x + 1))
A282691: 0 1 2 3 2 3 2 5 4 5 4 5 4 5 6 7
((1 - (x2 mod (3 + (x mod 6)))) div (x + 1))
A000480: 1 0 ~1 ~1 ~1 0 0 0 ~1 ~1 ~1 0 0 0 0 ~1
(((x + 1) mod (2 * (1 + (x mod (2 * (1 + (x mod 2))))))) mod (x + 1))
A229878: 0 0 1 0 1 2
A080940: 0 0 1 0 1 2 1 0 1 2 1 4 1 2 1 0
compr(\x.((x - (2x div 15)) mod 2),(x + 1))
A184978: 2 4 6 9 11
A327213: 2 4 6 9 11 13 16 18 20 22 23 25 27 29 30 32
((2 + (x mod (9 + (x div 4)))) mod (x + 1))
A316080: 0 1 1 1 1 1 1 1 1 1 1 2 2 3 4 5
((2 + ((x3 + x) mod 9)) mod (x + 1))
A049803: 0 0 0 1 2 0 1 2 0 2 4 3 5 7 6 8
(25x2 + 52x + 27)
A154377: 27 104 231 408 635 912 1239 1616 2043 2520 3047 3624 4251 4928 5655 6432
compr(\x.((x mod 2) - (((x - (x div 3)) div 3) mod 2)),(x + 1))
A190237: 2 4 5 6 7 8 10 12 13 14 15 16 18 20 22 23
((x + 1) * (((x + 1) div 2) - ((3 * (x div 4)) div 2)))
A249154: 0 2 3 8 5 12 14 24 9 20 22 36 26 42 45 64
((x + 1) + (2 * ((~x + (((x + 1) * (x div 2)) mod 2)) div 3)))
A127255: 1 0 1 2 1 2 3 2 3 4 5 4 5 4 5 6
compr(\x.(1 - (x mod (1 - ((~x + 1) div (2 + (x div 3)))))),(x + 1))
A112250: 5 7 8 10 11 13 14 17 18 19 21 22 23 25 26 27
((2x + 2) * ((x2 + 5x + 7) + (x mod 2)))
A192846: 14 56 126 256 430 696 1022 1472 1998 2680 3454 4416 5486 6776 8190 9856
compr(\x.((2x2 div (x + 9)) mod 2),(x + 1))
A189131: 1 2 4 6 7 10 11 15 16 17 18 24 25 26 27 28
compr(\x.(((1 + (x mod 7)) mod (x + 1)) mod 2),(x + 1))
A067319: 1 2 3 4 5 6 8 10 12
A033058: 1 2 3 4 5 6 8 10 12 15 17 19 22 24 26 29
((x + 1) * ((((~x2 + 2x + ~2) * (x div 2)) div (x + 1)) mod 2))
A308254: 0 0 3 0 0 0 0 0 9 0 0 12 13 14 0 16
compr(\x.(1 - ((x + ~4) mod (2 - (x div ~4)))),(x + 1))
A154663: 3 5 6 7 10 11
A028983: 3 5 6 7 10 11 12 13 14 15 17 19 20 21 22 23
((~x + ~1) + (2 * (((x + 1) * (x mod 2)) mod 10)))
A121758: ~1 2 ~3 4 ~5 6 ~7 8 ~9 ~10 ~11 ~8 ~13 ~6 ~15 ~4
compr(\x.((x + ~2) + (x div (~2 + ((x div 5) mod 2)))),(x + 1))
A073526: 1 2 3 4 5 6 7 8 9 15 16 17 18 19 25 26
(2 - ((1 - ((x + 2) mod (2 + (x mod 6)))) div (x + 1)))
A052298: 1 2 2 2 2 2 2 2 3 2 2 3 2 2 2 3
compr(\x.((x mod 2) - ((2x div (2 + (x div 3))) mod 2)),(x + 1))
A026509: 1 2 4 5 6 7 8 9 10 12 14 16 18 20 22 23
((2 + ((x - (x div (2 + ((~x + 1) mod 3)))) mod 2)) mod (x + 1))
A069903: 0 1 2 2 2 2 2 2 2 2 3 3 2 3 3 2
(4x3 + 16x2 + 52x + 40)
A192791: 40 112 240 448 760 1200 1792 2560 3528 4720 6160 7872 9880 12208 14880 17920
compr(\x.((x + ~1) mod (x - ((x + 1) mod 16))),(x + 1))
A297286-A296756-A044964-A044826-A043718: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 16 32
compr(\x.(1 - (((x + ~1) * (x div 4)) mod 8)),(x + 1))
A088721: 5 6 7 8 10 11 12 13 14 15 16 18 20 21 22 23
((8x + 8) + (x div 15))
A186544: 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120 129
((8x + 8) + ((2x + 1) div 5))
A182767: 8 16 25 33 41 50 58 67 75 83 92 100 109 117 125 134
((8x + 8) + ((x + 2) div ~7))
A292639: 7 15 23 31 39 47 54 62 70 78 86 94 102 109 117 125
compr(\x.((x mod 7) - (x mod 8)),(x + 1))
A032886: 1 2 3 4 5 6 7 14 15 21 22 23 28 29 30 31
(((1 - ((3x2 + ~x) div 4)) div 2) mod (x + 1))
A194734: 0 0 2 1 0 4 2 7 4 1 8 4 0 9 4 14
((2 * (4x + (x2 div 5))) div (x + 1))
A121855: 0 4 5 6 7 8 8 9 9 10 10 11 11 12 12 13
((4x + 4) + (4x div 7))
A004081: 4 8 13 17 22 26 31 36 40 45 49 54 58 63 68 72
((4x + 4) + ((~x + ((x + ~2) div 3)) div 3))
A292637-A279608: 3 7 11 15 18 22 26 30 34 37 41 45 49 52 56 60
((4x + 4) + (((x - (x div ~4)) div 2) div 2))
A001956: 4 8 12 17 21 25 30 34 38 43 47 51 55 60 64 68
((4x + 4) + ((2x + 2) div ~7))
A000572: 3 7 11 14 18 22 26 29 33 37 40 44 48 52 55 59
((4x + 4) + ((~x + (((~x + 2) div 2) div 3)) div 2))
A184623-A184581: 4 7 11 14 17 21 24 28 31 34 38 41 45 48 52 55
compr(\x.((x + ((x div 2) div 7)) mod 4),(x + 1))
A190697-A190687: 4 8 12 15 19 23 27 30 34 38 45 49 53 56 60 64
compr(\x.(((x + ((x div 2) div 7)) div 2) mod 2),(x + 1))
A190671: 1 4 5 8 9 12 13 15 16 19 20 23 24 27 30 31
compr(\x.(((x2 + ~2) mod (x + 10)) mod 2),(x + 1))
A115836: 1 2 4 5 6 8 10 11 12 13 14 16 18 20 22 23
((2 * (((x mod (1 + (x div 4))) div 2) + (x mod 2))) mod (x + 1))
A161840: 0 0 0 2 0 2 0 2 2 2 0 4 0 2 2 4
(~1 + (((1 + (x mod 8)) mod (x + 1)) + (2 div (x + 1))))
A097045: 1 0 ~1 ~1 ~1 ~1 ~1 ~1 0 1 2 3 4 5 6 7
(x - ((((~x + 1) * (x mod 10)) div 2) mod (x + 1)))
A194749: 0 1 0 2 0 3 0 4 0 5 10 4 10 3 10 2
((x2 + 3x + 2) + (2x div ~11))
A245207: 2 5 11 19 29 41 54 70 88 108 130 154 179 207 237 269
(49x2 + 97x + 48)
A157923: 48 194 438 780 1220 1758 2394 3128 3960 4890 5918 7044 8268 9590 11010 12528
(x6 + ~x5 + ~x4 + ~x3 + ~x2 + ~x)
A152030: 0 ~4 2 366 2732 11720 37326 98042 224696 465012 888890 1594406 2714532 4424576 6950342 10577010
((2x + 1) + ((((x + 1) + (x div 2)) * (x + (x div 2))) div 2))
A026381: 1 4 11 17 30 39 58 70 95 110 141 159 196 217 260 284
((x + ~1) * ((x5 + ~3x4 + 2x3 + x2 + ~x) div 2))
A101384: 0 0 1 60 594 3040 10875 30996 75460 163584 324405 599500 1046166 1740960 2783599 4301220
(5x5 + ~3x3 + ~2x2)
A134630: 0 0 128 1116 4896 15200 38160 82908 162176 292896 496800 801020 1238688 1849536 2680496 3786300
((x mod (2 - (x mod (~1 + (x mod (~1 + (x div ~3))))))) div 2)
A326844-A261079: 0 0 0 0 0 1 0 0 0 2 0 2 0 3 1 0
((1 + ((x + 2) mod (1 + (x div (2 - (x mod ~3)))))) div 2)
A339871: 0 0 0 1 0 1 0 1 1 1 0 1 0 2 1 1
((1 + ((2x + 2) div (1 + (x mod 9)))) div 2)
A094175: 1 1 1 1 1 1 1 1 1 10 6 4 3 3 3 2
((1 + ((1 + (x div 2)) div (1 + (x mod (1 + (x div 4)))))) div 2)
A173305: 1 1 1 1 2 1 2 1 1 3 2 1 4 2 1 1
((1 + ((x + (x div 3)) div (1 + ((x + 1) div 3)))) div 2)
A245760: 0 1 1 1 1 1 1 2 1 2 2 1 2 2 2 2
((1 + (x2 mod (1 + (3 * (2 - ((x div 2) mod 2)))))) div 2)
A048823: 0 1 0 1 1 2 0 1 1 2 0 1 2 1 0 1
((1 + (x2 div (1 + ((x div 4) + (x div 3))))) mod 2)
A341753: 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 0
((1 + ((8x + ~2) mod (1 + (x div 3)))) div 2)
A241272: 0 0 0 0 0 0 1 0 1 1 1 1 2 1 0 2
((1 + ((x + 1) mod (1 + (((x div 2) * (x div 2)) mod (x + 1))))) mod 2)
A190188: 1 1 0 1 1 0 0 1 0 0 0 1 1 0 1 1
(2 + ((2x + ~1) div (1 + (x mod 2) - (x div ~3))))
A060607: 1 2 3 3 4 4 5 4 5 5 5 5 6 5 6 6
(((x div 3) - (x div (~1 + (x mod (~1 + (x div ~2)))))) mod 2)
A116927: 0 1 0 0 1 1 0 0 1 0 1 0 0 0 1 1
((1 + ((x div 2) div (1 + (((x + 1) mod 5) mod 2)))) mod 2)
A088025: 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 0
((1 + (x mod (~1 + (2 * ((x div (2 - (x mod 2))) div 3))))) div 2)
A316401: 0 0 0 0 0 0 0 1 0 2 0 1 0 3 1 3
(2 * ((2x + 1) - ((2x + 1) div 7)))
A190003: 2 6 10 12 16 20 24 26 30 34 36 40 44 48 50 54
((1 + ((2 * (x - ((x div 2) mod 2))) mod 7)) div 2)
A179868: 0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 0
((1 + (((x * (x mod 2)) + (x div 2)) mod 7)) mod 2)
A071001: 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0
((1 + ((x * (2 + (x div 3))) div 7)) mod 2)
A258869: 1 1 1 0 0 1 0 1 1 1 0 0 1 0 1 0
((1 + ((x * (x div 2)) div (1 + (x2 mod 6)))) mod 2)
A333397: 1 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1
((1 + ((x + 1) div (1 + (x div (2 - (x mod ~4)))))) div 2)
A326038: 1 1 2 1 1 2 2 1 1 3 2 2 1 2 2 1
((1 + (x2 div (3 - (x div (~2 + (x mod ~2)))))) mod 2)
A342531: 1 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1
((1 + ((x + 1) div (1 + (2 * (2 - ((x mod 3) div 2)))))) div 2)
A056138: 0 0 1 0 1 1 1 1 2 1 1 2 1 1 3 2
((1 + (x mod (1 + (2 * (x div (2 * (2 + ((x div 2) mod 2)))))))) div 2)
A332548: 0 0 0 0 1 1 0 1 2 2 1 1 3 3 2 0
((1 + (x2 mod (1 + (8 * (~2 + (x mod 2)))))) mod 2)
A004601: 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 1
((1 + (x div (2 - (x mod (~1 + (4 * (~2 + (x mod 2)))))))) div 2)
A229969: 0 0 0 0 0 1 1 1 1 2 1 1 1 2 1 4
(((~x + 1) mod (1 + ((x2 + ~1) mod 9))) mod 2)
A288004-A128937: 1 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0
((1 + ((x * (x - ((~x + 2) div 2))) div 9)) mod 2)
A071003-A071002: 1 1 1 0 1 0 0 0 0 0 0 0 1 0 0 1
((1 + ((x + 2) mod (1 + ((x + 2) div (2 + (x div 4)))))) div 2)
A227698: 0 1 1 1 0 1 1 1 1 1 0 1 1 2 0 1
((1 + ((1 + (x * (x + ((x div 2) mod 2)))) div 5)) mod 2)
A266666: 1 1 0 1 0 0 1 0 0 1 1 1 0 1 1 1
(((x + 2) mod (1 + (((x + ~2) - (x mod 2)) mod 5))) div 2)
A332014: 1 1 0 0 0 0 1 2 0 0 0 0 0 0 0 1
(((1 + (x div 4)) mod (1 + ((~x + 1) mod 5))) div 2)
A341840-A048113: 0 0 0 0 1 0 0 1 1 0 0 0 2 0 0 0
(((x - (x mod 5)) * (1 + (x div 5))) div 2)
A246839: 0 0 0 0 0 5 5 5 5 5 15 15 15 15 15 30
(((1 + (x div 4)) div (1 + (x2 mod 5))) mod 2)
A267841: 1 0 0 0 1 0 1 0 0 1 1 1 0 0 0 0
((2 - ((x div 2) mod (1 + (x mod (1 + ((~x + 2) mod 4)))))) div 2)
A307425-A299406: 1 1 1 0 1 1 1 ~1 0 1 1 0 1 1 1 ~1
(x mod (2 * (1 + ((x mod (3 + (x mod 4))) mod 3))))
A307672: 0 1 2 1 0 1 2 3 2 1 0 5 0 1 2 1
(((x + 1) - ((x2 mod (2x + ~5)) mod 3)) div 2)
A227386: 0 0 1 2 2 3 3 3 4 5 5 5 5 6 7 8
(x div (2 + (x div (1 + ((1 + ((x + 2) * (x div 2))) mod 3)))))
A342656: 0 0 1 0 1 0 1 1 2 0 1 0 1 1 2 0
((1 + (((x3 + 2) div (1 + (x div 2))) mod 3)) div 2)
A282343: 1 0 1 1 1 0 0 1 0 1 1 0 1 1 1 1
((x - (((x + ~1) div 2) mod (1 + ((1 + (x div 2)) div 3)))) div 2)
A234016: 0 0 1 1 1 2 3 3 3 4 4 4 5 6 7 7
(2 * (((x2 + 2x) div 2) mod (1 + ((1 + (x div 2)) div 3))))
A200213: 0 0 0 0 0 2 0 2 0 2 0 4 0 2 2 2
(((1 + (x2 div 3)) mod (1 + ((x + 1) div 3))) div 2)
A317683: 0 0 0 0 0 0 0 1 1 0 1 0 2 1 0 2
(1 - (x div (~2 - ((x div 2) div (1 + ((x + ~1) mod 3))))))
A100678: 1 2 2 3 2 3 3 3 3 4 3 4 4 3 4 5
(((x + 1) div (~1 + (6 * (~1 + (x mod 4))))) mod 2)
A267056: 1 0 0 0 1 0 1 0 0 0 0 1 0 0 1 1
((1 + (3 * (((x + 2) + (x div 2)) * ((x + 1) div 2)))) div 2)
A302393: 0 5 8 18 24 41 50 72 84 113 128 162 180 221 242 288
(((x + 1) - (x mod (3 * (2 + (x mod 8))))) div 2)
A059107: 0 0 0 0 0 0 0 0 3 5 0 0 0 0 0 0
(x4 mod 46)
A070589: 0 1 16 35 26 27 8 9 2 29 18 13 36 41 6 25
((1 - (x mod (~1 + ((2 + (x div (~2 + (x mod 2)))) div 3)))) div 2)
A293896: 0 0 0 1 0 1 0 1 0 2 0 1 0 1 1 2
(x5 mod 22)
A070606: 0 1 10 1 12 1 10 21 10 1 10 11 12 21 12 1
(2 - (((~x2 + ~x + 1) div 11) mod 2))
A192393: 2 1 1 1 2 1 2 1 1 1 2 2 1 1 1 2
((1 + (((x * (x div 3)) - (x mod 4)) div 3)) mod 2)
A178580: 1 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1
((1 + ((((x div 2) - (x mod 2)) * (2 + (x div 2))) div 3)) div 2)
A026923: 0 0 1 0 1 1 3 2 4 3 6 5 8 7 11 9
((2x + 1) mod (2 + (x div (~1 + (3 * (2 + (x mod 2)))))))
A282716: 1 1 1 1 1 1 1 1 2 1 1 2 1 0 1 1
((2 + (x div 2)) div (2 + (x div (~1 + (3 * (2 + (x mod 2)))))))
A116543: 1 1 1 1 2 2 1 2 2 2 1 2 2 2 2 3
(((x mod 3) - ((x + 1) mod (1 + ((x div 2) div 3)))) mod 2)
A104894-A104893: 0 1 0 0 1 0 1 1 1 0 0 0 1 1 0 1
(x - (2 * ((x + (x div 2)) div (1 + (3 * (2 - (x mod 2)))))))
A276638: 0 1 2 1 4 3 4 3 6 3 6 3 8 5 8 5
(2 - ((~x + 2) div (2 + (x div (1 + (3 * (2 - (x mod 2))))))))
A026099: 1 2 2 3 3 3 4 4 4 4 5 5 6 5 5 5
((x mod 2) - ((~1 + (2x mod (2 - ((~x + 1) div 3)))) div 2))
A240592: 1 2 0 2 0 1 1 1 0 0 1 0 1 1 1 1
((((2x + 2) - (x div 3)) * (1 + (x div 3))) div 2)
A212985: 1 2 3 7 9 11 18 21 24 34 38 42 55 60 65 81
(2 - (((5x + 10) div (1 + (x div 3))) mod 2))
A156263: 2 1 2 2 1 1 1 1 2 1 1 2 2 1 2 2
(2 + ((2 + ((x div 3) mod 3)) mod (1 + (x mod 3))))
A102640: 2 2 4 2 3 2 2 2 3 2 2 4 2 3 2 2
(((x - ((~x + 1) div (2 + (x div 2)))) * (~1 + (x mod 3))) mod 2)
A156729: 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1
(4x3 + 30x2 + 70x + 50)
A165676: 50 154 342 638 1066 1650 2414 3382 4578 6026 7750 9774 12122 14818 17886 21350
((1 + ((x2 + 2x) div (7 + (x div 2)))) div 2)
A242976: 0 0 1 1 1 2 2 3 4 5 5 6 6 8 8 9
((x mod 2) - ((x div (1 + ((x mod 4) mod (1 + (x div 2))))) mod 2))
A158924: 0 0 0 0 0 1 0 0 0 1 ~1 1 0 1 0 0
((1 + (((~x + 2) + ((~x + 1) mod 3)) mod (1 + (x div 2)))) mod 2)
A156254: 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1
(2 + ((x + 2) mod (1 + ((x + (x div 4)) mod (1 + (x div 2))))))
A130192: 2 2 2 3 2 2 2 2 2 3 2 3 2 2 2 4
(2 * (1 + (2x2 div ((x + 1) + (x2 div 4)))))
A060659: 2 4 6 8 8 10 10 10 12 12 12 12 12 14 14 14
((1 + ((1 - (x3 mod 5)) mod (x + 1))) mod 2)
A181115: 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 0
(3 + (((x2 + ~2x) div (1 + (x div 4))) div (x + 1)))
A182021: 3 2 3 3 3 4 4 5 4 5 5 5 5 5 5 6
(((x + ~1) mod (1 + ((3 * ((x + ~1) div 2)) mod (x + 1)))) div 2)
A330657: 0 0 0 1 1 0 2 0 0 1 0 1 1 1 0 1
((1 + (x3 mod (2 - (x div ~8)))) div 2)
A235987: 0 1 1 0 1 1 0 1 1 1 0 2 0 1 0 2
(2 * ((x + 1) - ((((x div 4) mod 2) + (x div 2)) div ~2)))
A285626: 2 4 8 10 14 16 18 20 22 24 28 30 34 36 38 40
(2 * ((x div 5) - ((x div 3) div ~3)))
A156726: 0 0 0 2 2 4 4 4 4 4 6 6 8 8 8 10
((x mod (1 + (x mod (2 * (1 + ((x + 2) div 5)))))) div 2)
A173440: 0 0 0 1 0 0 0 1 1 0 0 2 0 0 0 3
(2 + (1 div (~1 + (2 * ((~x + 2) mod 11)))))
A194306: 2 3 1 2 2 2 2 2 2 2 2 2 3 1 2 2
((1 + (x div (2 + ((x + ~3) mod (1 + (x div 3)))))) mod 2)
A267152: 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 0
((1 + ((((x + 2) div 3) * (~1 + (x div ~2))) div 2)) mod 2)
A325899: 1 0 0 1 0 1 1 1 1 0 1 1 1 1 1 0
((x mod (1 + (2 * (x div (1 + (2 * (1 + ((x div 2) mod 2)))))))) div 2)
A136438: 0 0 0 0 0 1 0 0 1 1 0 0 1 2 2 0
((1 + (x mod (1 - (2 * ((~x + 1) div 7))))) div 2)
A236532: 0 0 1 0 1 1 0 1 1 2 0 1 1 2 2 0
((1 + ((x - (x div (3 + ((x + 2) mod 4)))) div 2)) mod 2)
A127015: 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1
(((x + ~1) - (((x div 2) mod (1 + (x mod 8))) div 2)) mod 2)
A030658: 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 1
(2 * (1 + (((~1 + (x div 2)) mod (~1 + (2 * (x mod 4)))) div 2)))
A307378: 2 2 2 2 2 2 4 4 2 2 2 6 2 2 2 2
((x mod (1 + (x div (2 + ((~x + 3) mod 5))))) div 2)
A035582: 0 0 0 0 0 0 0 0 1 0 0 1 1 3 1 1
((1 + ((x - ((2 * (x div 3)) mod 5)) div 2)) div 2)
A239500: 0 0 1 0 1 1 1 1 1 2 2 3 2 3 3 4
((2 - (x mod (1 + (2 * (2 - (2x mod 5)))))) div 2)
A318277: 1 1 1 1 1 1 1 2 0 1 1 1 1 0 1 1
(x div (2 + (2x div (1 + (x mod (2 * (1 + (x mod 4))))))))
A124762: 0 0 0 1 0 0 0 2 0 0 1 1 0 0 1 3
(((x + 1) mod (1 + (2 * (x div (1 + (2 * (2 - (x mod 2)))))))) div 2)
A250213: 0 0 0 0 0 0 0 1 0 1 0 2 1 2 0 2
((x mod (1 + (x div (2 + ((x mod 5) mod 3))))) div 2)
A036864: 0 0 0 0 0 1 0 0 1 0 2 1 0 3 2 3
((x - ((2 + (x div 2)) div (1 + (2 * ((x + ~1) mod 3))))) mod 2)
A309218: 0 1 1 1 0 0 1 0 0 0 1 1 1 1 1 0
(2 * ((x + 1) - (2 * ((x - ((x div 2) div ~2)) div 3))))
A267654: 2 4 2 4 6 4 6 4 6 8 6 8 6 8 6 8
(((x + 2) mod (1 + (2 * ((((x + ~1) div 2) div 2) mod 3)))) div 2)
A029431: 1 0 0 0 0 0 1 0 0 0 1 1 2 0 0 0
((x mod (1 + (2 * ((x3 div 4) mod 3)))) div 2)
A227189-A227186: 0 0 1 0 0 1 0 0 1 2 0 0 0 0 2 0
((1 - (x mod (~1 + (x div (~2 + (((~x + 2) div 2) div 3)))))) div 2)
A324966-A005090: 0 1 0 1 1 1 0 1 0 2 1 1 0 1 1 1
(((~1 + ((x3 + ~x2) div 2)) div 7) mod 2)
A190897: 1 1 0 1 1 1 0 0 1 0 0 0 1 0 1 0
((x div 2) - ((x + ~1) div (2 + ((x + 1) div 7))))
A029215: 1 0 1 0 1 0 2 1 2 2 2 2 3 3 4 4
(x6 mod 14)
A070637: 0 1 8 1 8 1 8 7 8 1 8 1 8 1 0 1
(1 - (((x mod 2) - ((x2 + 2x) div 7)) div 2))
A029020: 1 1 2 2 3 3 4 5 7 8 10 11 13 14 17 19
((1 + (x div (2 + ((x + ((x + ~1) div 3)) mod 3)))) mod 2)
A275601: 1 1 1 0 0 1 1 0 1 1 0 1 1 0 0 0
(2 + (x mod (1 + (x2 mod (2 + (3x * (x mod 2)))))))
A108077: 2 3 2 5 2 7 2 5 2 11 2 13 2 3 2 17
((1 + ((2x mod (8 + (x div 3))) div 2)) mod 2)
A176330: 1 0 1 0 1 1 0 1 0 0 1 1 1 0 1 1
(((x + ~1) mod (1 + ((x + ~4) mod (2 + (x div 3))))) div 2)
A067150: 0 0 0 1 0 0 1 1 0 0 0 0 1 0 1 2
(((4x + 1) mod ((x + 1) - (2 * (x div 3)))) div 2)
A186230: 0 0 0 0 1 0 0 0 1 0 0 1 2 2 0 0
((1 + (((~x + 1) mod (2 - ((~x2 + 2x) div 3))) div 2)) div 2)
A000933: 0 0 0 0 1 1 1 2 3 4 5 6 8 10 11 13
((1 + (((~4x + 12) mod (1 + (x div 2))) div 2)) div 2)
A340391: 0 0 0 0 1 0 0 0 0 0 1 1 2 1 1 0
((1 + (((x2 div (x + 4)) * (1 + (x div 2))) div 2)) mod 2)
A179763: 1 1 1 0 0 0 1 1 1 0 0 1 0 0 1 1
((x + 1) div (2 + ((x + 3) div (1 + (2 * (1 + (x mod 2)))))))
A245661: 0 1 1 1 1 2 1 2 1 2 1 3 1 2 2 3
((6x3 + 15x2 + 11x + 3) div 2)
A024215: 1 17 66 166 335 591 952 1436 2061 2845 3806 4962 6331 7931 9780 11896
(((1 - ((x div 2) div (1 + (x mod 2)))) mod (2x + 3)) mod 2)
A033772: 1 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1
(x div (x - ((2 - ((2x + ~1) mod (1 + ((x + 1) div 2)))) div 2)))
A286419: 0 1 1 1 1 1 0 0 1 0 1 1 1 1 0 1
((((x + 1) div 2) - (2x div (~1 + (x div ~4)))) div 2)
A269371: 0 1 1 2 3 3 3 4 5 5 5 6 6 6 6 7
((1 + ((x + 1) div (4 - ((x mod 5) mod 2)))) mod 2)
A267136: 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1
(x + ((x mod (1 + (2 * (x mod 6)))) mod 2) - (x mod 2))
A084689: 0 1 2 3 4 5 6 7 9
A180199-A180198: 0 1 2 3 4 5 6 7 9 8 11 10 12 13 14 15
((x mod (3 + ((2x + ~1) mod (2 + (x div 3))))) div 2)
A240857: 0 0 1 1 0 1 0 1 1 2 1 1 2 0 1 1
((1 + ((((2x + 1) * (x div ~3)) div 2) div 2)) mod 2)
A004539: 1 0 1 1 0 1 0 1 0 0 0 0 0 1 0 0
((1 + (((x4 mod (2x + ~1)) div 2) div 2)) mod 2)
A172099: 1 1 1 1 0 0 1 1 1 1 0 0 0 1 0 0
((1 + (((x + 2) mod (2 + ((x div 2) div (1 + (x mod 2))))) div 2)) div 2)
A260803: 0 0 0 0 1 0 1 0 1 1 1 0 2 0 2 1
(2 + (((x2 + ~x) div 4) * (1 + (((x + 1) div 2) div 2))))
A302613: 2 2 2 4 8 12 16 32
((1 + ((((x + ~1) * (1 - (2 * (x div 3)))) div 2) div 2)) mod 2)
A093692: 0 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1
((1 + (((x + ((x div 2) div 3)) * ((x + ~1) div 2)) div 2)) mod 2)
A189141: 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0
(1 - ((x2 mod (1 + (2 * ((x + ~1) mod ~4)))) div 2))
A342477: 1 1 2 1 1 1 3 2 1 1 1 2 1 1 3 1
((x mod (3 + ((2x mod (2 + (x div 3))) div 2))) div 2)
A179952: 0 0 1 0 0 1 0 1 1 0 0 1 0 0 2 1
(2 * (1 + (((~x + 2) div (2 + (x div (2 + (x mod 4))))) mod 2)))
A194688: 4 2 2 4 4 4 2 2 4 2 2 4 2 2 4 4
(((1 + ((x * (x div 2)) div 2)) mod 17) mod 2)
A143262: 1 1 0 0 1 0 0 1 0 0 1 1 1 0 0 0
(x5 mod 34)
A070617: 0 1 32 5 4 31 24 11 26 25 6 27 20 13 12 19
((1 + ((x + 1) div (2 + ((x div 2) mod (2 + (x mod 4)))))) div 2)
A104484: 0 1 1 1 1 1 1 1 2 2 2 3 3 4 2 2
((((x + 1) div 2) div (1 + (x div (4 + (x mod 4))))) mod 2)
A123506: 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 0
(((x + 1) - (((x2 + 2x) mod (4 + (x div 2))) div 2)) mod 2)
A186447: 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 1
((1 + (x div (4 - (~x mod (2 + ((x div 2) mod 2)))))) div 2)
A131810: 0 0 0 0 1 1 1 2 1 2 3 2 2 2 2 2
(((x + ~1) - (((((x2 + 2x) - (x div 2)) div 2) div 2) div 2)) mod 2)
A282339: 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 1
(2 * (1 + ((x - ((x - ((x + 2) mod (2 + (x mod 2)))) div 2)) div 2)))
A289256: 2 2 2 4 4 4 4 6 6 8 6 8 8 8 8 10
((1 + (x div (2 + (x2 mod (2 + (x div (2 + (x mod 2)))))))) div 2)
A338776: 0 0 0 1 1 1 1 1 1 2 1 2 3 2 1 3
(~2 + ((x4 + x3 + 2x2 + 2x) mod 9))
A158137: ~2 4 ~2 4 ~2 ~2 1 1 ~2 ~2 4 ~2 4 ~2 ~2 1
(2 + (9 * ((x mod (3 - (x mod 2))) div 2)))
A283454: 2 2 11 2 2 2 2 2 11 2 2 2 2 2 11 2
(2 - (((x + ((~x + 2) mod 4)) mod 9) div 2))
A037867: 1 1 1 ~1 ~1 ~1 ~1 2 2 2 2 0 0 0 0 2
(((3x + 12) - (x div 9)) div 2)
A248178: 6 7 9 10 12 13 15 16 18 19 20 22 23 25 26 28
((1 + (x mod 3) - (x div (~2 - (x mod 4)))) div 2)
A282518: 0 1 2 1 2 2 1 2 3 2 2 3 3 3 3 2
(2 - ((x mod (1 + (2 * (~2 + ((x mod 2) + (x mod 4)))))) div 2))
A194326: 2 2 2 1 3 2 2 1 3 2 2 2 2 2 2 2
((1 + (((x2 + 2x) - ((~x2 + 2x) div 4)) div 2)) div 2)
A183136: 0 1 2 4 7 10 14 18 23 29 35 42 50 58 67 76
((1 + (((2x3 + 9x2 + 10x) div 2) div 2)) div 2)
A007518: 0 3 9 21 39 66 102 150 210 285 375 483 609 756 924 1116
((1 + (((((x + ~2) * (x div 3)) - (x div 2)) div 2) div 2)) mod 2)
A247795: 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 1
((2 - ((x + 1) mod (~1 + (2 * ((~x + 1) div (2 + (x div 2))))))) div 2)
A115514: 1 1 1 2 1 1 2 2 1 1 3 2 2 1 1 3
(x div (2 * (1 + (x div (2 + ((x + 1) mod (4 - (x mod 2))))))))
A051764: 0 0 1 0 1 0 1 1 1 1 1 0 1 1 2 1
((x + ~1) div (2 * ((x + 1) - (2 * ((x + 1) div (2 + (x mod 2)))))))
A063277: ~1 0 0 0 1 1 2 0 3 1 4 1 5 1 6 1
((1 + ((2 + (x div 2) - (x mod 2)) mod (4 + (x mod 2)))) div 2)
A190427: 1 1 2 1 0 2 1 2 1 0 2 1 0 1 1 2
(2 * ((x2 + 2x) mod (1 + (x div (2 + (x div (2 + (x mod 2))))))))
A096158: 0 0 0 2 0 2 0 2 0 2 0 4 0 0 0 0
((x - ((~1 + (x div 4)) div (1 + ((x + ~1) mod 4)))) mod 2)
A129174: 1 0 1 0 0 1 0 1 0 0 0 1 0 1 1 1
((2x + 2) - ((x div (1 + (((~x + 2) div 2) mod 4))) mod 2))
A013952: 2 3 6 8 9 11 14 15 18 19 22 24 25 28 30 31
(((1 + (2x div (1 + (2 * (x mod 2))))) mod 5) mod 2)
A243753: 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1
(2 * ((17x + 17) div 5))
A286927: 6 12 20 26 34 40 46 54 60 68 74 80 88 94 102 108
(2 * (x - ((~2 * ((x + 1) + (x mod 2))) div 5)))
A284753: 2 6 8 10 12 16 18 22 24 28 30 34 36 38 40 44
((2x + 2) - (((x - (x div ~2)) div 5) mod 2))
A206910: 2 4 6 7 9 11 13 16 18 20 21 23 25 28 30 32
((x + 1) mod (2 + ((~2 + (x div ~4)) mod 5)))
A215151: 1 2 3 0 1 0 1 2 0 0 1 0 1 2 3 4
(x - (10 * (2 div (x + ~16))))
A174140: 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 35
(((x - (x2 mod (2x + 8))) mod 5) div 2)
A084440: 0 0 1 2 2 1 0 1 1 0 2 0 0 0 1 0
(((x mod 2) - (((~x2 + x) div 4) div 5)) div 2)
A240864: 0 0 0 1 0 1 1 2 1 2 2 3 3 4 5 6
((2x - ((x - ((x2 + ~x) div 2)) div 5)) div 2)
A067570: 0 1 2 3 4 5 7
A062469: 0 1 2 3 4 5 7 8 10 12 13 15 17 19 22 24
((2x + 2) - ((~2x + (2 mod (x + 1))) div 5))
A187416: 2 5 7 9 12 14 16 19 21 24 26 28 31 33 36 38
((1 + (3 * ((x2 + x) div 2))) mod 10)
A213472: 1 4 0 9 1 6 4 5 9 6 6 9 5 4 6 1
((x + 10) - (x div ~9))
A329448: 10 12 13 14 15 16 17 18 19 20 22 23 24 25 26 27
((x + 10) - ((x div ~2) div 5))
A288040-A280824-A139819-A139704-A043638-A031955-A029742: 10 12 13 14 15 16 17 18 19 20 21 23 24 25 26 27
(((3x2 + 5x + 2) div 2) mod 10)
A161462: 1 5 2 2 5 1 0 2 7 5 6 0 7 7 0 6
(((x + 6) * (2 + (x mod 2))) mod 10)
A172430: 2 1 6 7 0 3 4 9 8 5 2 1 6 7 0 3
((1 + (x div 2) - (2 * (x + (x mod 2)))) mod 10)
A194642: 1 7 8 4 5 1 2 8 9 5 6 2 3 9 0 6
((x + 10) + (x div 11))
A110429: 10 11 12 13 14 15 16 17 18 19 20 22 23 24 25 26
((10x + 10) + (x mod 10))
A104341: 10 21 32 43 54 65 76 87 98
A065438: 10 21 32 43 54 65 76 87 98 109 110 121 132 143 154 165
(((x + 1) mod 10) * (x mod 10))
A118373-A077252: 0 2 6 12 20 30 42 56 72 0 0 2 6 12 20 30
((2x + 20) - (x mod 10))
A007930: 20 21 22 23 24 25 26 27 28 29 40 41 42 43 44 45
(x - ((5 * (~x + (x mod 9))) div 2))
A004848: 0 1 2 3 4 5 6 7 8 32 33 34 35 36 37 38
(((x + (2x2 div (1 + (x div 2)))) mod 5) div 2)
A263635: 0 1 0 1 2 0 2 0 1 0 1 0 1 0 1 0
((x + 2) - ((~x - (4 mod (x + 1))) div 5))
A047839: 2 4 5 6 8 9 10 12 13 14 15 16 18 19 20 21
((((x2 + ~x) + ((x + ~1) div 3)) mod 5) mod 2)
A011659: 0 0 0 1 1 1 1 0 1 0 1 1 0 0 1 0
(2 * (x - (5 * (~x + ((x div 5) mod 2)))))
A059691: 0 12 24 36 48 50 62 74 86 98 120 132 144 156 168 170
(x - (2 * ((x div 9) + (x div 5))))
A308937: 0 1 2 3 4 3 4 5 6 5 4 5 6 7 8 7
((~x3 + ~2x2 + ~2x + ~3) mod (2 + (x div 5)))
A209318: 1 0 1 0 1 1 0 1 1 0 1 2 1 0 1 2
(x + (((x + 1) div 5) + (2 * (x div 5))))
A047607: 0 1 2 3 5 8 9 10 11 13 16 17 18 19 21 24
((2 * (1 + (x div 8))) div (2 + (x mod 5)))
A029412: 1 0 0 0 0 1 0 0 0 0 2 1 1 0 0 2
((x + 2) div (2 - (x div (~1 - (x2 mod 5)))))
A047070: 1 1 1 1 1 1 1 2 2 1 1 1 2 3 1 1
(((x + 2) div (1 + ((x + ((x + 1) mod 3)) mod 4))) mod 2)
A266669: 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 1
((x + 2) - ((x - (5 mod (1 + (x div 4)))) div 2))
A177876: 2 3 3 4
A123387: 2 3 3 4 5 5 6 6 7 8 8 9 9 9 10 10
(1 - (((2 + (x mod 6)) div (1 + (x div 4))) div 2))
A320857: 0 0 ~1 ~1 0 0 1 1 1 1 0 0 1 1 1 1
((((2x + 2) - (x div 4)) * (1 + (x div 4))) div 2)
A212989: 1 2 3 4 9 11 13 15 24 27 30 33 46 50 54 58
(2x - ((((x + 1) div 2) div 2) + ((~1 + (x div 4)) div 2)))
A320472: 1 3 5 6 7 9 11 12 14 16 18 19 20 22 24 25
((x + 2) - (1 mod ((2x + 3) - (x2 div 4))))
A124868: 1 2 3 4 5 6 7 8 9 11 13 17
(x - ((1 + (((x * ((2 - (x div 4)) div 2)) div 2) div 2)) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A247760-A247750: 0 1 2 3 4 5 6 7 8 9 10 11 13 15 16 17
((1 + (((x + 2) * (2 + ((x + ((x div 2) mod 2)) div 2))) div 2)) div 2)
A030050: 1 2 3 5 6 7 10 14 15
((((2x2 + x) * (x div 2)) div (x + 5)) mod 2)
A324967: 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0
(~2 + (((x + 2) + (3 * (x div 2))) * (1 + (2 * (x div 2)))))
A303299: 0 1 19 22 58 63 117 124 196 205 295 306 414 427 553 568
(((x3 + 3x2 + 3x + 2) - ((x div 2) mod 2)) div 2)
A212747: 1 4 13 32 63 108 171 256 365 500 665 864 1099 1372 1687 2048
((x + 2) div (2 + ((x2 div 4) mod (3 + (x mod 2)))))
A091335: 1 1 1 1 2 1 4 4 3 5 4
((3 * ((x + 1) - ((~2x + 2) div 5))) div 2)
A189387: 1 3 6 7 10 12 13 16 18 21 22 24 27 28 31 33
((x - ((1 + ((x * (x div 2)) div 5)) mod 3)) mod 2)
A266619: 1 0 1 0 0 1 1 1 1 1 0 1 0 0 0 0
(x - ((x - ((x div (1 + ((x + ~1) mod 3))) mod 3)) div 2))
A249037: 0 1 2 2 3 4 4 4 5 5 6 7 7 7 8 9
(((x + 1) div 2) div (2 + (x mod (3 * (1 + (x mod 3))))))
A239689: 0 0 0 1 0 0 1 1 0 2 0 1 3 2 1 4
((3 * (1 + (((x2 + ~2x) * ((x + ~1) div 2)) div 2))) div 2)
A110864: 1 1 1 3 7 24
((((x + ~1) - (2 * ((~x + 2) div 8))) div 3) mod 2)
A120527: 1 0 0 1 1 0 0 0 1 1 1 0 1 1 1 0
(x div (2 + ((~x + 2) mod (3 * (1 + (2 * (2 + (x mod 2))))))))
A034390: 0 0 1 0 0 0 0 0 0 0 1 0 1 1 2 1
((1 - ((x div (~3 + (x mod (2 + (x mod 2))))) div 3)) mod 2)
A025885: 1 0 0 0 0 1 0 1 0 0 1 1 1 0 1 1
((3 * ((3 * (x2 div 2)) div 5)) div 2)
A033442: 0 0 1 3 6 10 15 21 28 36 45 54 64 75 87 100
(1 - (((x mod 2) - ((x div (1 + ((x div 2) mod 2))) div 3)) div 2))
A295218: 1 1 1 1 2 1 2 1 2 2 2 1 3 3 2 2
((3 * ((3x + 3) + ((x div 2) div 3))) div 2)
A330179: 4 9 13 18 22 27 33 37 42 46 51 55 61 66 70 75
(2 * ((x - (((x mod (1 + (x div 2))) div 2) mod 3)) div 3))
A073504: 0 0 0 2 2 2 2 4 4 4 4 6 6 8 8 10
(2 * ((x - (((x * ((~x + 2) div 2)) div 2) div 3)) div 3))
A183002: 0 0 0 2 2 4 4 6 8 10 10 14 14 16 18 22
(x - (2 * ((x + (x div 3) - ((x div 2) mod 2)) div 3)))
A266161: 0 1 2 1 2 1 2 3 2 1 2 3 2 3 4 3
((3 * ((x + 1) - ((~x + ((~x + 2) div 4)) div 2))) div 2)
A231407: 1 4 6
A292660: 1 4 6 9 12 13 16 19 21 24 25 28 31 33 36 39
(2 * ((3x + 3) + ((x - ((x div 2) div 3)) div 2)))
A189793: 6 12 20 26 34 40 46 54 60 68 74 82 88 94 102 108
((((1 - (x div 4)) mod 3) + ((x + 1) mod 3)) div 2)
A318133: 1 1 0 1 1 0 0 1 1 1 2 1 1 1 0 1
((((x + 1) div (1 + (x div 4))) + ((x + ~1) div 3)) div 2)
A326370: 0 1 1 2 1 2 2 3 2 2 3 3 3 3 3 4
(((1 + (((x div 2) - (x mod 2)) div 2)) * ((x + ~1) mod 3)) div 2)
A029300: 1 0 0 1 0 0 2 0 1 2 0 1 4 0 2 4
(((x div (6 + (x mod 2))) + ((x + ~1) mod 3)) div 2)
A025853: 1 0 0 1 0 0 1 0 1 1 0 1 2 0 1 2
(2 + ((x - ((~1 + ((x + ~1) mod 5)) div 2)) div 3))
A091497: 1 2 2 3 3 3 4 4 4 4 5 6 6 6 6 6
(2 + (((~1 + (16 mod (x + 1))) div 2) div 3))
A225843: 1 1 2 1 2 2 2 1 3 2 2 2 2 2 2 1
(1 - ((x - ((2 + (x2 div 5)) div 3)) div 2))
A016409-A016402-A016382-A016369-A016363-A014023: 1 1 0 0 0 0 0 ~1 ~1 0 0 0 0 0 1 1
(2 * ((2 * (((~x + 2) mod (2 + (x mod 4))) div 2)) mod 3))
A005888-A005871: 0 0 0 2 0 0 0 0 0 4 0 0 0 0 0 4
((2 - (x2 div (x + ~26))) div 2)
A239905: 1 1 1 1 1 2 2 2 3 3 4 5 6 7 9 11
(x - ((x - ((((x + 2) div 3) mod 4) mod 3)) div 2))
A003002: 0 1 2 2 3 4 4 4 4 5 5 6 6 7 8 8
(x - (2 * ((x + 4) div (~12 + (x div 2)))))
A098908: 2 3 4 5 6 7 10 11 12 13 14 17 18 19 22 23
((x div 2) div (2 + ((2x2 + x) mod 12)))
A285118: 0 0 0 0 1 0 0 0 0 0 0 1 3 1 0 0
(x - (2 * ((4 * (~x + (x mod 8))) div 3)))
A024645: 0 1 2 3 4 5 6 7 30 31 32 33 34 35 36 37
(2 * (x - (((~2x + ~4) + (x mod 6)) div 3)))
A271346: 4 6 8 12 14 16 24 26 28 32 34 36 44 46 48 52
(((x + 1) mod 2) - (((((~x + 1) * (x div 2)) div 2) div 3) mod 2))
A284316: 1 0 0 ~1 0 0 0 ~1 0 0 1 ~1 0 0 1 ~1
(2 - ((0 - (((x + (x2 div 4)) div 2) div 3)) div 2))
A120203: 2 2 2 2 3 3 3 4 4 4 5 5 6 7 7 8
(2 + ((x2 + 16x + 28) div 3))
A006621: 11 17 23 30 38 46 55
(x - (2 * ((x + 1) div (8 - ((x + 2) div 3)))))
A123066: 0 1 2 3 4 3 4 5 6 5 6 5 6 5 4 5
((3 * ((10x + 10) + (x div 2))) div 2)
A330175: 15 30 46 61 78 93 109 124 141 156 172 187 204 219 235 250
((4x + 2) - ((x - ((1 - (x div 2)) div 3)) div 2))
A184621: 2 6 9 13 16 19 23 26 30 33 36 40 43 47 50 54
(2 + ((x + ~2) div (2 + (x div 2))) - (((x div 2) div 3) mod 2))
A229895: 1 1 2 2 2 2 1 2 2 2 2 2 3 3 3 3
(x2 - ((((~x4 + x2) div 2) div 3) div 2))
A006008: 0 1 5 15 36 75 141 245 400 621 925 1331 1860 2535 3381 4425
(x mod (6 + ((x3 + ~1) mod (1 + (x div 2)))))
A054634: 0 1 2 3 4 5 6 7 1 0 1 1 1 2 1 3
((x - (2 * ((1 - (x div 2)) div 5))) mod 6)
A014588: 0 1 2 3 0 1 2 3 4 5 0 1 2 3 0 1
(2x - ((x + 2) div (~6 + (((x + ~1) div 2) div 2))))
A082767: 1 3 5 7 9 12 14 16 18 21 23 26 28 31 34 36
((x + 6) - (2x div (~2 + (x div ~4))))
A138890: 6 8 10 11 13 14 15 17 18 19 20 22 23 24 25 26
(2x div (2 + ((x + ((x + 1) mod 8)) div 3)))
A340500: 0 0 1 1 1 2 2 3 3 3 3 3 3 3 3 4
(x div (2 + (x div (1 + (((~x + 1) mod 3) + (x div 3))))))
A147844: 0 0 1 1 1 1 2 1 2 3 2 3 3 3 3 3
(x - (((3 + (x div 8)) * (x div 3)) div 2))
A061295: 0 1 2 2 3 4 3 4 4 3 4 5 4 5 6 5
(x - (((2 - (x div ~8)) * (x div 3)) div 2))
A061282: 0 1 2 2 3 4 3 4 5 3 4 5 4 5 6 5
(2 * (((3 * ((x div 2) div 3)) div 2) + (x div 3)))
A211512: 0 0 0 2 2 2 6 6 6 8 8 8 14 14 14 16
((((3x2 + 8x + 4) div 2) - (x div 3)) div 2)
A322598: 1 3 8 13 20 29 39 50 64 78 94 112 131 151 174 197
(((((~2x + 2) - (x div 2)) div (x + 2)) + (x div 3)) mod 2)
A189921: 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 0
((2 + (((x2 + ~x) div 2) div 3)) div (2 + (x div 3)))
A029124: 1 1 1 1 1 1 1 2 2 2 3 4 4 4 5 5
((((x mod 2) + (x mod 3)) - (x div ~5)) div 2)
A304093: 0 1 1 1 1 2 1 2 2 1 1 3 1 2 2 2
((x + 2) - ((x mod (2 + (((x div 2) mod 2) + (x mod 3)))) div 2))
A334819: 2 3 3 5 6 7 8 8 10 11 11 13 14 15 14 17
((((x + ~1) mod 3) + (x div 3)) div (2 + (x mod 3)))
A029303: 1 0 0 1 0 0 2 0 0 2 1 1 3 1 1 3
((2 - (x mod (2 + ((x * (x div 2)) mod 2)))) mod (2 + (x mod 3)))
A101674: 0 1 2 0 2 1 0 1 2 1 2 0 0 1 2 0
((2 * (((x div 3) mod 3) div 2)) + ((x mod 3) div 2))
A289814: 0 0 1 0 0 1 2 2 3 0 0 1 0 0 1 2
(2 + ((4x4 + x3 + ~2x2) div 3))
A093504: 2 3 23 113
((3 * (x2 + (5 * (x2 div 2)))) div 2)
A195049: 0 1 21 43 84 127 189 253 336 421 525 631 756 883 1029 1177
(76x + 26)
A136293: 26 102 178 254 330 406 482 558 634 710 786 862 938 1014 1090 1166
(2 + (x2 div (1 + ((x + ((x2 div 2) div 3)) div 2))))
A060207: 2 3 4 5 6 7 7 8 8 8 9 9 9 10 10 10
((2x + 2) - ((~1 + ((~x + ((x div 4) mod 2)) div 2)) div 2))
A306683: 3 5 7 10 12 14 16 18 21 23 25 28 30 32 34 36
((2x3 + 19x2 + 39x) div 2)
A130862: 0 30 85 171 294 460 675 945 1276 1674 2145 2695 3330 4056 4879 5805
((6x3 + 21x2 + 19x + 5) div 2)
A269232: 2 25 87 206 400 687 1085 1612 2286 3125 4147 5370 6812 8491 10425 12632
((4x + 2) + ((~x + 2) div (2 - (x div ~4))))
A288205: 3 6 10 13 17 21 25 28 32 36 40 44 48 52 56 59
((4x + 2) + (((x - ((2 - (x div 2)) div 2)) div 2) div 2))
A284675: 1 6 10 14 19 23 27 32 36 40 45 49 53 57 62 66
(((1 + (2 * ((~x + 1) mod 8))) mod (1 + (x div 2))) div 2)
A241825: 0 0 0 0 1 0 1 0 1 0 1 0 2 1 3 2
(((x - (5 * (x div ~2))) * (1 + (x div 2))) div 2)
A195020: 0 3 7 13 21 30 42 54 70 85 105 123 147 168 196 220
(((3 * (x - ((x + ~1) mod 3))) mod (1 + (x div 2))) div 2)
A065683: 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 3
(((2 + (x mod (1 + (x mod 6)))) mod (1 + (x div 2))) div 2)
A340390: 0 0 0 0 0 0 1 1 2 1 1 0 1 1 2 2
(((4 - (((x + ~1) div 3) mod 2)) mod (1 + (x div 2))) div 2)
A331383: 0 0 0 0 0 0 1 0 2 2 1 1 1 2 2 2
(2 + (((x + 2) + (2 * (2 - ((x div 2) mod 2)))) * (1 + (x div 2))))
A059869: 8 9 14 16 32
(((2x + ((~2 + (x div 2)) * (x div 2))) * (1 + (x div 2))) div 2)
A057587: 0 1 3 5 12 15 30 34 60 65 105 111 168 175 252 260
((3x2 + 8x + 5) + ((1 + (x div 2)) div 2))
A227720: 5 16 34 57 86 121 163 210 263 322 388 459 536 619 709 804
(x mod ((x + 2) - ((5x + 8) mod (1 + (x div 2)))))
A030567: 0 1 2 3 4 5 0 1 1 1 2 1 3 1 4 1
((x mod (1 + (((x - ((x div 3) mod 2)) div 2) + (x mod 2)))) div 2)
A238220: 0 0 0 0 0 0 1 1 1 1 0 2 2 2 3 3
((((x + 1) - ((x div 4) div ~2)) div (1 + (x mod 2))) mod 2)
A303340: 1 1 1 0 0 1 0 0 0 1 0 0 1 0 1 1
((1 + ((x * (x + ((4x + 2) * (x mod 2)))) div 2)) div 2)
A245625: 0 2 1 13 4 34 9 65 16 106 25 157 36 218 49 289
(((x + 1) + ((x + ((x2 div 2) div 5)) div 2)) div 2)
A025209: 0 1 2 2 3 4 5 6 8 9 10 11 13 14 15 17
(2 * ((x + 1) + ((x + ((x mod (2 + ((x div 2) mod 2))) mod 2)) div 2)))
A284794: 2 6 8 10 14 18 20 24 26 30 32 34 38 42 44 46
(x - (2 * ((~x + ~1) + ((x + 1) mod 11))))
A103303: 0 1 2 3 4 5 6 7 8 9
A004849: 0 1 2 3 4 5 6 7 8 9 32 33 34 35 36 37
((2x3 + 11x2 + 3x + ~6) div 2)
A162262: ~3 5 30 78 155 267 420 620 873 1185 1562 2010 2535 3143 3840 4632
((8x3 + 17x2 + 11x + 2) div 2)
A213832: 1 19 78 202 415 741 1204 1828 2637 3655 4906 6414 8203 10297 12720 15496
((x + 2) div (2 + ((1 + (x mod ~8)) mod (x + 1))))
A327502: 1 1 1 2 1 1 1 4 3 1 1 1 1 1 1 8
(2 + ((1 + (2 * (2 - (2 div (1 + (x div 4)))))) mod (x + 1)))
A097224: 2 3 3 3 5 5 5 5 7 7 7 7 7 7 7 7
((x + 2) div (2 + ((1 + (2 * (1 + (2 * (x mod 2))))) mod (x + 1))))
A103957: 1 1 2 1 1 2 1 1 2 1 2 1 2 1 3 1
(x - ((~10x3 + ~9x2 + x) div 2))
A045950: 0 10 59 177 394 740 1245 1939 2852 4014 5455 7205 9294 11752 14609 17895
(((x + 1) * (2 - ((~x + 1) div (1 + ((~x + 2) mod 4))))) div 2)
A272589: 1 2 4 6 7 12 24
(2 * compr(\x.((x mod 10) * (x mod 3)),(x + 1)))
A228870: 6 12 18 20 24 30 36 40 42 48 54 60 66 72 78 80
(x - ((~8x3 + ~3x2 + 5x) div 2))
A211612: 0 4 35 117 274 530 909 1435 2132 3024 4135 5489 7110 9022 11249 13815
(((2 + ((2x + 1) mod (1 + (x div 3)))) mod (x + 1)) div 2)
A061498: 0 0 1 1 1 1 1 1 2 2 1 2 1 2 3 1
(((2 + (x mod (~1 + (2 * ((x + ~1) mod 4))))) mod (x + 1)) div 2)
A037826: 0 0 1 1 0 1 1 1 2 1 1 2 2 1 1 1
(2 + ((2 - (x mod (2 * (1 + (4 * (x mod 2)))))) div (x + 1)))
A205032: 4 2 2 1 2 1 2 1 2 1 2 2 2 1 2 1
(((2 - (x div (~2 + (((~x + 2) div 2) div 3)))) mod (x + 1)) div 2)
A230261: 0 0 0 1 2 2 2 2 2 2 2 2 2 3 3 2
((6x3 + 21x2 + 23x + 8) div 2)
A024394: 4 29 93 214 410 699 1099 1628 2304 3145 4169 5394 6838 8519 10455 12664
(((x + 1) * ((x2 + 8x + 13) div 2)) div 2)
A295622: 3 11 24 46 75 117 168 236 315 415 528 666 819 1001 1200 1432
(((2 + ((x + 5) mod (1 + (x div 2)))) mod (x + 1)) div 2)
A258594: 0 0 0 1 1 1 2 1 2 3 2 3 2 3 2 3
(2 + ((2 + (20 mod (x + 1))) div (x + 1)))
A120927: 4 3 3 2 2 2 3 2 2 2 3 2 2 2 2 2
((4x3 + 17x2 + 19x + 6) div 2)
A126335: 3 23 72 162 305 513 798 1172 1647 2235 2948 3798 4797 5957 7290 8808
(((x + 1) * (x - (2 * ((x + (x div 4)) div ~2)))) div 2)
A026271: 0 3 6 14 25 33 49 60 81 105 121 150 182 203 240 264
(2 + ((~2 + (x2 mod ((x + 2) + (x div 3)))) div (x + 1)))
A253589: 0 1 1 2 2 1 2 2 2 2 2 2 1 3 2 2
(((2x2 + 6x + 4) + (((x + ~1) div 2) * (x div 2))) div 2)
A194110: 2 6 12 20 31 44 59 76 96 118 142 168 197 228 261 296
((9x3 + 27x2 + 26x + 8) div 2)
A228887: 4 35 120 286 560 969 1540 2300 3276 4495 5984 7770 9880 12341 15180 18424
((2x3 + 11x2 + ~x + ~10) div 2)
A162259: ~5 1 24 70 145 255 406 604 855 1165 1540 1986 2509 3115 3810 4600
((3x3 + 23x2 + 48x + 28) div 2)
A059997: 14 51 120 230 390 609 896 1260 1710 2255 2904 3666 4550 5565 6720 8024
(((x2 + x) div 5) + ((x2 + 3x + 2) div 2))
A194102: 1 3 7 12 19 27 36 47 59 73 88 104 122 141 162 184
(((x2 + ~x) div 5) + ((x2 + 3x + 2) div 2))
A083462: 1 3 6 11
A025722-A022775: 1 3 6 11 17 25 34 44 56 69 84 100 117 136 156 178
((2x + 2) + ((x div 2) div (1 + (3 * (2 - (x mod 2))))))
A187350: 2 4 6 8 10 12 14 16 18 21 22 25 26 29 31 33
((2x + 2) + ((2x + 1) div (3 + (x div 4))))
A195437: 2 5 7 10 12 14 17 19 21 23 26 28 30 32 34 37
((2x + 2) + (x div (2 - (x div (~1 + ((~x + 2) div 4))))))
A287777: 2 4 6 8 11 13 15 17 19 21 23 26 28 30 32 35
((2x + 2) + ((~x + (((x + 1) * (x div 2)) mod 2)) div 3))
A285977: 2 3 5 7 8 10 12 13 15 17 19 20 22 23 25 27
((2x + 2) + ((~x + ((((x + 1) div 2) div 2) mod 2)) div 3))
A226249: 2 3 5 7 9 10 12 13 15 17 18 20 22 24 25 27
((2x + 2) + (((x * (x + (x div 2))) div 2) div (x + 3)))
A184978: 2 4 6 9 11
A276223: 2 4 6 9 11 14 17 19 22 24 27 30 33 35 38 41
((2x + 2) + ((1 + ((x - ((~x + 2) div 4)) div 2)) div 2))
A024812: 2 4 7 9 11 14 16 18 21 23 25 28 30 32 34 37
((2x + 2) + (((2x div (1 + (x div 2))) mod 3) div 2))
A299232: 2 5 7 8 11 12 14 16 18 20 22 24 26 28 30 32
((2x + 2) + (((x2 + x) div ~8) mod 2))
A140592: 2 5 7 8 11 12 14 17 19 20 22 25 26 29 31 32
((2x + 2) + (((x + ~4) mod (2 + (x div 3))) mod 2))
A284777: 2 5 6 8 10 13 14 17 18 20 23 24 26 29 30 32
compr(\x.(((((~x + 1) * (x div 3)) div 2) div 2) mod 2),(2x + 2))
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((2x + 2) + ((x - ((~x + ((x div 4) mod 2)) div 2)) div 2))
A285207: 2 5 7 10 13 15 18 21 24 27 29 32 35 37 40 43
((2x + 2) + ((x + ((x div 2) div ~6)) div 2))
A184978: 2 4 6 9 11
A224995: 2 4 6 9 11 14 16 19 21 24 26 29 31 34 36 38
((2x + 2) + ((x + ((x - ((x div 3) mod 2)) div 2)) div 2))
A089972-A008062: 2 4 7 10 12 15 18 21 24 26 29 32 35 37 40 43
((2x + 2) + ((2x + (x2 div 4)) div (x + 2)))
A287074: 2 4 7 9 12 14 16 18 21 23 25 28 30 32 34 37
((2x + 2) + (((3 * (x div 4)) div 2) + (x div 2)))
A288933: 2 4 7 9 13 15 18 20 25 27 30 32 36 38 41 43
((2x + 2) + ((2x + 2) div (8 - (x mod 2))))
A184978: 2 4 6 9 11
A187842: 2 4 6 9 11 13 15 18 20 22 24 27 29 32 33 36
((3x + 2) + ((x div 3) div (1 + (x div 4))))
A193767: 2 5 8 12 14 17 21 24 26 30 33 36 39 42 45 48
((3x + 2) + ((x - (x div 9)) div 2))
A190506: 2 5 9 12 16 19 23 26 30 33 36 40 43 47 50 54
((3x + 2) + ((x mod (1 + ((x + 2) mod 4))) div 2))
A190361: 2 5 8 11 14 17 20 23 27 29 32 35 38 41 44 47
((3x + 2) + (x2 div (x + 16)))
A172262: 2 5 8 11 14 18 21 25 28 32 35 39 43 46 50 54
(((2x + 1) - (3 * (x div ~2))) * ((x + 1) div 2))
A219191: 0 6 8 26 30 60 66 108 116 170 180 246 258 336 350 440
((6 * (x - (x div ~4))) - ((x + 1) div 2))
A184551: 0 11 17 22 28 39 45 50 56 67 73 78 84 95 101 106
(((x + 2) div (2 - ((1 - (x div 2)) div 3))) + ((x + 1) div 2))
A216411: 1 2 3 4 4 5 5 7 7 8 8 9 9 10 11 12
((1 + (2 * (x + (3 * (x + (x mod 2)))))) * ((x + 1) div 2))
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((x + 1) * (((x + 1) div 2) * (1 + (x div 2)) * ((x + 1) div 2)))
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(((x + 2) - (3 * (~2x + (x div 2)))) * ((x + 1) div 2))
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((2 * (((x mod (1 + (x div 2))) div 2) + (x mod 2))) + ((x + 1) div 2))
A115659: 0 3 1 4 2 7 5 8 6 11 9 12 10 15 13 16
(((x + 2) + (3 * (2x + (x mod 2)))) * ((x + 1) div 2))
A219390: 0 12 16 52 60 120 132 216 232 340 360 492 516 672 700 880
((2 div (8 - ((x * (x mod 2)) div 2))) * ((x + 1) div 2))
A007393: 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 16
((41x2 + 41x) div 2)
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((49x2 + 49x) div 2)
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(2x4 + 12x3 + 19x2 + 9x + 2)
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((2x3 + 11x2 + 25x + 16) div 2)
A151675: 8 27 63 122 210 333 497 708 972 1295 1683 2142 2678 3297 4005 4808
(((2x - (x3 div (x + 4))) mod (x + 1)) div 2)
A124757: 0 0 0 1 0 1 2 3 0 1 2 3 3 4 5 6
(((x3 + 2x) div 3) + ((x3 + x2) div 2))
A203551: 0 2 10 29 64 120 202 315 464 654 890 1177 1520 1924 2394 2935
(((3 * (2x div 5)) div 2) - ((x + ~1) div 2))
A029384: 1 0 0 0 0 1 1 0 1 0 2 1 1 1 1 2
((2 * ((4x + 1) - (x div 3))) - ((x + ~1) div 2))
A063245: 3 10 18 23 31 38 44 51 59 64 72 79 85 92 100 105
(2 * ((((x * (x div 3)) mod 3) mod 2) * ((x + ~1) div 2)))
A132792: 0 0 0 0 2 0 0 0 6 0 0 0 0 12 0 0
(((x3 + 2x) div 3) + ((x3 + ~x2) div 2))
A203552: 0 1 6 20 48 95 166 266 400 573 790 1056 1376 1755 2198 2710
((x9 + x7) div 2)
A168636: 0 1 320 10935 139264 1015625 5178816 20588575 68157440 196101729 505000000 1188717431 2597806080 5333623945 10383230144 19307109375
compr(\x.((x div 2) mod 2),(2 - ((~x + 2) div (2 - (x div ~4)))))
A140341: 1 4 4 5 5 5 5 8 8 8 8 8 8 8 8 9
(2 * (1 - (2 * ((x + 1) mod (~1 + (x div ~5))))))
A167268: 2 2 6 2 6 2 10 6 2 10 6 2 14 10 6 2
(((1 + (x div (2 - (x2 mod (1 + (x div 4)))))) div 2) div 2)
A233918: 0 0 0 0 0 1 1 2 2 1 2 3 1 3 2 4
(2 - (((~1 + (x div (1 + (x2 mod (2 + (x div 2)))))) div 2) mod 2))
A281527: 1 1 2 1 1 2 1 2 2 2 1 1 1 2 2 1
((x + 2) div (2 + (x div (3 + (x mod (3 + (x mod 2)))))))
A067752: 1 1 2 2 2 2 2 3 3 2 3 4 2 3 4 4
(((1 + (4x div (1 + (x div (2 + (x mod 2)))))) div 2) div 2)
A345345-A341596-A337176-A140774-A099042-A056924: 0 1 1 1 1 2 1 2 1 2 1 3 1 2 2 2
(((x + ~1) mod (3 + ((1 + (x div 3)) div 3))) div 2)
A137677: 1 0 0 1 0 0 0 1 1 0 0 1 1 0 0 2
(x4 mod 44)
A070587: 0 1 16 37 36 9 20 25 4 5 12 33 12 5 4 25
(12x2 + 72x + 124)
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(x - (((~1 + ((((~x + 1) * (x div 2)) div 2) div 3)) div 2) div 2))
A320058: 1 2 3 4 5 6 7 8 10 11 13 14 15 17 19 20
(1 - (2 * (((2 + (x * (x div 2))) mod (1 + (x div 3))) mod 2)))
A162511: 1 1 1 ~1 1 1 1 1 ~1 1 1 ~1 1 1 1 ~1
(4 * ((x + 1) - ((2 + (x2 div 2)) div (x + 3))))
A120427-A060830: 4 8 12 12 16 20 20 24 24 28 28 32 36 36 40 40
(2 * (3 + (x div 2) - (~2x div (1 + (x div 2)))))
A135711: 6 10 12 14 16 18 18 20 22 22 24 24 26 26 28 28
(2 - (((1 + (((x + 2) div (1 + (x mod 3))) div 2)) div 2) mod 2))
A212810: 1 2 2 1 1 1 2 1 1 1 2 1 2 2 1 2
(2 + ((1 + ((8 mod (1 + ((x + 1) div 2))) div 2)) mod 2))
A075074: 3 3 3 2 2 3 3 2 2 2 2 3 3 3 3 3
(1 - (2 * ((x mod (~1 + (2 * ((2 * (x div 2)) div 3)))) div 2)))
A307860: 1 1 1 1 1 1 1 1 ~1 1 1 1 ~3 ~5 1 1
(x5 mod 28)
A070612: 0 1 4 19 16 17 20 7 8 25 12 23 24 13 0 15
(2 - ((~2x + 1) div (4 + (x div 7))))
A177876: 2 3 3 4
A073047: 2 3 3 4 4 5 5 5 5 6 6 7 7 7 7 7
((((x + 1) - ((((~x + 2) div 2) * (x div 3)) div 2)) div 2) div 2)
A163464: 0 0 0 1 1 1 2 2 3 4 4 5 5 6 6 8
(((2 - (2x mod ((x + 1) - (2 * (x div 3))))) div 2) mod 2)
A033770: 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 1
((((x + 1) - (x mod (2 * (4 - (x mod 3))))) div 2) div 2)
A181834: 0 0 0 0 0 1 0 1 2 2 1 2 2 3 3 2
(((~1 + (((x + 1) * ((x2 + (x div 2)) div 2)) div 2)) div 2) mod 2)
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(2 + (((2x + 1) mod (~1 + (x div (~2 + (x mod ~2))))) mod 2))
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(((x - (x div (1 + (x mod (2 + ((x mod 3) div 2)))))) div 2) div 2)
A328708: 0 0 0 0 0 1 0 1 1 1 0 2 0 1 2 2
(4 * ((x + 3) - (x div (~2 + (x div ~4)))))
A136724: 12 20 24 28 36 40 44 48 52 56 60 68 72 76 80 84
(2 + ((x - (x div (11 - (x div 2)))) div 2))
A104103: 2 2 3 3 4 4 5 5 5 6 6 7 7 7 7 8
(2 div ((3 + (((~x + 2) - (x div 2)) mod 8)) div 2))
A339086: 1 1 0 0 0 0 1 2 0 0 0 1 2 0 0 0
(x mod (4 + (~4x mod 9)))
A031045: 0 1 2 3 4 5 6 7 0 1 1 1 2 1 3 1
(2 + (x div (2 + ((x + 1) div (1 + (x mod (2 + (x mod 4))))))))
A266225: 2 2 2 3 2 3 3 3 2 2 4 3 2 3 4 2
(4 * ((1 + ((x * (x div 2)) div 3)) div 5))
A278933: 0 0 0 0 0 0 4 4 8 8 12 12 20 20 24 28
((x + 2) - (((x - ((1 - (x div 2)) mod 5)) div 2) mod 2))
A137901: 1 3 3 4 6 7 7 9 9 10 12 12 14 15 15 16
((x + 1) - (2 * (((x + 1) * (x mod 2)) mod 10)))
A121759: 1 ~2 3 ~4 5 ~6 7 ~8 9 10 11 8 13 6 15 4
(~2 + ((2 - ((x div 5) + ((x div 2) mod 3))) div 2))
A160764: ~1 ~1 ~2 ~2 ~2 ~3 ~2 ~2 ~2 ~2 ~3 ~3 ~2 ~2 ~3 ~3
((x div 2) - ((2x + ~1) div (4 + (x div 5))))
A029213: 1 0 1 0 1 1 1 1 1 1 2 2 3 2 3 3
(1 - (2 * (((x2 + (x mod 3)) mod 5) mod 2)))
A232544: 1 1 ~1 1 1 1 ~1 1 ~1 ~1 ~1 ~1 1 1 ~1 1
((x - (x mod (~2 - (x div (1 + ((~x + 2) mod 4)))))) div 2)
A228942: 0 1 2 2 3 4 4 4 4 6 6 6 6 8 8 7
(32x2 + 112x + 68)
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(x - (4 * ((~x + ~5) + (x mod 5))))
A133895: 20 21 22 23 24 45 46 47 48 49 70 71 72 73 74 95
(((1 + (x div (2 - (((~x2 + 2x) div (x + 2)) mod 2)))) div 2) div 2)
A343332: 0 0 0 1 0 1 1 1 2 1 2 1 3 1 3 2
(((~1 + ((2x + ~2) mod (2 + (x div 2) - (x mod 2)))) div 2) mod 2)
A164057: 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1
(2 * ((3 * ((x + 1) - (x div ~6))) div 2))
A005796: 2 8 12 14 18 20 24 30
((((x2 + ~x) mod (3 * (1 + (x div 3)))) div 2) div 2)
A035629: 0 0 0 0 0 0 0 1 0 0 1 0 3 1 0 3
(2 * (2 - ((((x2 + 2x + 1) div 3) mod 3) div 2)))
A067395: 4 4 4 2 2 4 4 4 4 4 4 4 2 2 4 4
(x - (2 * (~2 + (3 * ((~x + 2) div 12)))))
A089119: 4 5 6 13 14 15 16 17 18 19 20 21 22 23 24 31
(1 - (2 * ((((x2 + 2x) - (x div 3)) div 3) mod 2)))
A216430: 1 ~1 1 1 ~1 ~1 ~1 1 1 1 ~1 1 1 ~1 ~1 ~1
(2 + ((x - (3x mod (x - ((x + 1) mod 3)))) mod 2))
A299229: 2 3 2 2 2 3 3 2 2 2 2 3 3 3 2 2
(((x - ((~x3 + 2x) div 12)) div 2) div 2)
A177205: 0 0 0 1 2 3 5 8 12 17 23 30 38 48 60 73
((x div 2) - (((3 * ((x + 1) div (2 + (x mod 2)))) div 2) div 2))
A241065: 0 0 1 1 1 1 1 2 1 2 2 2 2 3 2 4
(1 - (2 * (((x - ((x2 div 2) mod (x + 2))) div 3) mod 2)))
A020985: 1 1 1 ~1 1 1 ~1 1 1 1 1 ~1 ~1 ~1 1 ~1
(2 * (((5x + 5) + ((x div 2) div 3)) div 2))
A001581: 4 10 14 20 24 30 36 40 46 50 56 60 66 72 76 82
((2 - (2x div (~5 + (x mod 3)))) div 2)
A026903: 1 1 2 2 2 3 2 3 4 3 3 5 3 4 6 4
((2 + ((x + ((2x + ~2) mod 5)) div 3)) div 2)
A184956: 1 1 1 2 1 2 2 2 3 2 3 2 3 3 3 4
(4 * ((x2 + x + ~1) + (3 * (~x + (x mod 2)))))
A216871: ~4 4 ~4 20 28 68 92 148 188 260 316 404 476 580 668 788
(1 - (2 * (((((~1 + (x div 2)) div 2) div 2) + (x div 3)) mod 2)))
A306638: ~1 ~1 1 ~1 ~1 ~1 1 1 1 ~1 1 1 ~1 ~1 ~1 1
((x + 2) - (((((2 - (x div 2)) div 2) * (x div 3)) div 2) div 2))
A026470: 2 3 4 5 6 7 9 10 11 12 14 15 16 17 19 21
((2x + 2) - (((x + ~4) mod (2 + (x div 3))) mod 2))
A285306: 2 3 6 8 10 11 14 15 18 20 21 24 26 27 30 32
((((((x + 1) div 2) div 2) div 2) + (x mod (2 + (x mod 3)))) mod 2)
A327180: 0 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1
(2x div (2 - ((~x + 1) div (4 - ((x mod 3) div 2)))))
A280079: 0 1 1 2 2 2 3 3 3 4 4 3 4 5 4 5
((x - (((x div 2) - (x3 div (x + 3))) div 2)) div 2)
A194252: 0 0 1 2 4 6 8 11 14 18 23 28 33 39 45 52
(2 * (x - (2 * ((~2x + ~1) + ((x - (x div 4)) div 2)))))
A075319: 4 14 20 30 40 46 56 62 72 82 88 98 108 114 124 130
(2 + ((~31 mod (1 + (x div 2))) div 2))
A322168: 2 2 2 2 3 3 2 2 4 4 4 4 4 4 2 2
(2 + (((x + ~2) div (2 + (x div 2))) + (((1 + (x div 2)) div 2) div 2)))
A309196: 1 1 2 2 2 2 3 4 4 4 4 4 4 4 5 5
((x mod (2 + ((((x + 1) div 2) div 3) * (1 + (x mod 2))))) div 2)
A337976: 0 0 0 0 0 0 0 1 1 0 0 2 0 0 1 1
(((((2x + 4) - (x div 2)) * ((x + 1) + (x div 2))) div 2) div 2)
A294479: 1 3 7 11 17 24 32 41 52 63 76 89 104 120 137 155
((x + 2) mod (2 + ((x3 mod ((x + 1) + (x div 2))) mod 2)))
A037281: 0 0 0 1 0 1 0 1 1 2 0
A034876: 0 0 0 1 0 1 0 1 1 2 0 1 0 0 0 2
((x div (2 + ((1 + (x mod ~5)) mod (x + 1)))) div 2)
A037873-A037855: 0 0 0 0 1 0 0 0 0 2 1 0 0 0 3 2
((((3 * ((x + ~1) mod 8)) mod (x + 1)) div 2) div 2)
A102037: 0 0 0 0 1 0 0 0 0 0 0 1 2 3 0 0
((((2 * (x mod (~2 + (x div ~4)))) mod (x + 1)) div 2) div 2)
A282355: 0 0 0 0 0 0 0 1 0 2 0 1 1 1 1 2
((((x + 1) * (4 + ((2 + (x mod 2)) * (x div 2)))) div 2) div 2)
A276164: 1 2 4 7 10 15 17 26 27 40
(2 * (((x + 1) * (2 + ((x * (~1 + (x mod 3))) div 2))) div 2))
A087570: 2 4 8 0 10 24
(x - (2 * ((~2x + ~2) + ((~2x + 2) div 5))))
A140868: 4 9 16 21 28 33 38 45 50 57 62 67 74 79 86 91
(x - (2 * ((~2x + ~2) + (x2 div (x - ((~x + 2) div 2))))))
A026372: 4 7 10 15 18 23 26 31 34 37 40 45 48 53 56 59
(((x2 + ~x) div (12 - ((x + 1) div 2))) div 2)
A309830: 0 0 0 0 0 1 1 2 3 5 6 9 11 15 18 26
((((x + ~1) div 2) - (x div ~4)) * (((x + 1) div 2) div 2))
A272104: 0 0 0 2 2 4 4 10 10 14 14 24 24 30 30 44
(2 + ((17x2 + ~13x + ~4) div 2))
A180232: 0 2 21 57 110 180 267 371 492 630 785 957 1146 1352 1575 1815
(~2 + ((x4 + 6x3 + 5x2 + 6x + 4) div 2))
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(1 - ((x + 1) mod (1 - (2 * (1 - (x div (~2 + (x div ~2))))))))
A194877: 1 2 1 3 2 1 4 3 2 1 5 4 3 2 1 5
(1 - (((x + 1) div (2 + ((1 + ((x div 2) div 3)) mod 2))) div 2))
A016397: 1 1 1 1 1 0 0 ~1 ~1 ~1 ~1 ~2 ~1 ~1 ~1 ~1
(6 + (x div 2) - (x div (~1 + ((~x + 1) div 3))))
A114459: 6 7 8 9 10 10 11 12 12 13 14 14 15 15 16 16
(2 * (2 + ((x mod (1 + ((x div 4) + (x div 3)))) mod 2)))
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(64x2 + 128x + 56)
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(((x - (x div (~2 + ((x2 div 2) mod ~3)))) div 2) div 2)
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(x div (4 + (x3 mod 14)))
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(x div (4 + ((~x + 1) mod (2 * (1 + (2 * (x mod 3)))))))
A071287: 0 0 0 0 0 0 1 1 1 2 1 2 2 3 1 3
(2 * (2 + ((x mod (1 + (2 * (((~x + 2) div 2) mod 4)))) mod 2)))
A130331: 4 4 4 6 4 4 6 6 4 4 4 4 6 6 4 4
((x - (2 * ((x + ~2) div (2 + ((x div 2) div 5))))) div 2)
A120004: 1 1 1 1 1 1 1 1 1 1 3 2 3 3 3 3
((1 - (4x mod ~19)) div 2)
A093019: 0 8 6 4 2 9 7 5 3 1 9 7 5 3 1 8
(2 + ((((x mod 6) + (x mod 5)) div 2) mod 2))
A023397: 2 3 2 3 2 2 2 3 2 3 2 3 3 2 3 3
(x div (2 * (2 + ((x2 + 2x) mod (2 * (3 + (x mod 2)))))))
A342657: 0 0 0 0 1 0 1 0 1 0 2 0 3 1 1 0
((x + 4) - ((x - ((0 - (x div 4)) mod 3)) div 2))
A205842: 4 5 5 6 7 8 8 9 9 9 10 10 10 11 11 12
(x - ((0 - ((x - (((x + 1) div 2) mod 6)) div 2)) div 2))
A264387: 0 1 2 3 5 6 7 8 9 10 11 14 15 16 17 18
((x + 4) - ((x + ~2) div (~6 + (x div 4))))
A336379: 4 5 6 8 9 10 11 12 14 15 16 18 20 21 22 24
(4 * ((x + 6) + ((x div 2) div 5)))
A268540: 24 28 32 36 40 44 48 52 56 60 68 72 76 80 84 88
((x + 1) - (x mod (2 * (2 - (x div (~4 + (x mod 3)))))))
A105769: 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 13
(x + ((((~1 + ((x2 + x) div 2)) div 2) div 2) mod 2) - (x mod 2))
A143579: 1 0 2 3 4 5 7 6 8 9 11 10 13 12 14 15
(x - (8 * (~1 + (2 * (~x + (x div 8))))))
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((((2x3 + 9x2 + 14x + 5) div 2) div 2) div 2)
A248851: 0 3 10 22 41 68 105 153 214 289 380 488 615 762 931 1123
(2 + ((x - ((2 - (8 mod (1 + (x div 2)))) div 2)) div 2))
A343174-A102548: 1 2 2 3 4 4 4 5 6 7 7 7 8 8 8 9
(6 + (x div 2) - (~2x div (1 + (x div 2))))
A182619: 6 8 9 10 11 12 12 13 14 14 15 15 16 16 17 17
((x + 4) - (2 * ((2 + (x2 div 3)) div (x + 1))))
A067628: 0 3 4 5 6 7 6 7 8 9 8 9 10 9 10 11
((x + 1) mod ((2 + ((((x * (x div 2)) div 2) mod (x + 1)) div 2)) div 2))
A088950: 0 0 0 0 1 0 0 0 1 1 0 0 1 2 1 0
(2 + ((((x + 1) div 2) div 2) div 2) - ((~x + 2) div (2 + (x div 2))))
A074198: 1 2 2 3 3 3 3 4 4 5 5 5 5 5 5 6
((x - ((((x + ~1) * (1 + (x div 5))) div 2) div 2)) div 2)
A276034: 0 0 1 1 2 1 2 2 2 2 2 2 2 2 2 0
(2 + ((((x + ~1) * (1 + ((x * (x div 2)) div 4))) div 2) div 2))
A230381: 1 2 2 2 4 5 8 11
((((3x4 + 4x2 + 1) div 2) div 2) div 2)
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((((3x4 + ~2x3 + ~3x2 + 2x) div 2) div 2) div 2)
A228317: 0 0 3 21 75 195 420 798 1386 2250 3465 5115 7293 10101 13650 18060
((x2 + x + 1) div (2 + ((x - (x div ~4)) div 2)))
A099308: 0 1 2 3 5 6 7 9 10 11 13 14 17 18 19 21
(256x2 + 16)
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((x + 1) div (4 + (x div (4 * (1 + (2 * (x mod 2)))))))
A321014-A211271: 0 0 0 1 1 1 1 2 1 2 1 3 1 2 2 3
(x - (2 * ((x - (x div (2 + (x div (2 + (x mod 3)))))) div 2)))
A303536: 0 1 2 1 2 1 2 1 2 1 2 3 2 3 2 1
((x + 1) div (2 + (x div (2 + (x mod (2 + ((x mod 3) div 2)))))))
A211270: 0 1 1 1 1 2 1 2 2 2 1 3 1 2 3 2
(2 + (((((x + 1) * ((x div 2) - (2 div (x + 1)))) div 2) div 2) div 2))
A029024: 1 1 2 2 3 3 4 5 6 7 8 9 11 12 15 16
(3 mod ((2 - (x mod (1 - (2 * (((x + 1) div 2) div 2))))) div 2))
A035691: 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 3
((x + 1) - ((x - (x mod (1 - (2 * (((x + 1) div 2) div 2))))) div 2))
A134482: 1 2 2 3 3 4 4 4 5 6 5 5 6 7 8 6
((2 - (((((~x + 1) div 3) * ((x + ~1) div 2)) div 2) div 2)) div 2)
A116492-A103263: 1 1 1 1 1 1 1 2 2 2 2 3 3 4 5 5
(64x2 + 192x + 96)
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(((((x2 - ((1 + (x div 4)) mod 2)) div 2) div 2) div 2) div 2)
A220838: ~1 0 0 0 1 1 2 3 3 5 6 7 9 10 12 14
(4 + ((x - (((x - ((x mod 3) div 2)) div 2) div 2)) mod 2))
A276868: 4 5 4 5 5 4 5 4 5 5 4 5 5 4 5 4
(6 + (((((x div 2) - (x mod 4)) div 2) div 2) mod 2))
A023409: 6 7 7 7 6 6 6 6 7 6 6 6 7 7 7 7
(2 + (((x - (x div (0 - (2 * (2 + (x mod 4)))))) div 2) mod 2))
A251619: 2 3 3 2 2 3 3 2 3 3 2 2 3 2 2 2
(2 - ((x - ((~x2 + x) div 32)) mod 2))
A007421: 2 1 1 2 1 2 1 1 2 2 1 1 1 2 2 2
(x div (4 + ((x + ~1) mod (2 + ((~x + 2) mod 8)))))
A130633: 0 0 0 0 0 0 0 1 1 1 2 2 1 1 2 1
((x + 4) - ((~x + 3) div (2 + (x div 8))))
A186495: 3 4 6 7 9 10 12 13 14 15 17 18 19 21 22 23
((1 - ((x + 1) mod (1 - (2 * (2 + (x div 8)))))) div 2)
A195011: 1 1 0 1 1 0 1 1 1 0 2 2 1 1 0 2
(((x + 2) div (2 + (x mod (2 + (x div (2 * (2 + (x mod 2)))))))) div 2)
A214841: 0 0 1 0 1 1 2 1 2 2 1 1 1 2 1 1
(2 * (4 - (((x + ~1) mod (2 + (x div (2 + (x mod 2))))) mod 2)))
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((x + 2) div (2 + (2x div (4 + ((x + 1) mod 4)))))
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((x + 1) div (2 + (x div (2 + (x mod (2 + ((x + 1) mod 4)))))))
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((2 - (x2 div (~16 + ((x + 1) div 2)))) div 2)
A094983: 1 1 1 1 2 2 2 3 4 5 6 7 8 10 12 15
(x6 mod 32)
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((((x + ~1) * (x div 2)) div (~x + 18)) div 2)
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((x - (x div (2 - ((x3 div 8) mod 2)))) div 2)
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((x + 2) - ((~3x + 3) div (4 + (x div 4))))
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(((2x2 + ~4x + 2) mod (4 + (x div 4))) div 2)
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(((2x + 1) * (1 + (x * (x div 2)))) mod 16)
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(~1 + (((x2 + x) div 2) + ((x + 1) mod 16)))
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((x2 + 2x + 1) mod (x2 + x + 10))
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((16x2 + ~16x) + ((x2 + x) div 2))
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(x + (x div 2) - ((x mod 4) + (2 * ((x div 4) mod 2))))
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(2 + ((((~1 + (~x mod 5)) mod (x + 2)) div 2) mod 2))
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(((((x + 1) - (x div 8)) * (2 + (x div 2))) div 2) mod 2)
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((2x + 2) - (((x2 + ~x + ~1) mod (2 + (x div 2))) mod 2))
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(6x - ((2x + 4) div ~7))
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(8 + ((x2 + 2x + 1) * (4 - (x div 2))))
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((x + 8) - (x mod (x - ((x + ~1) mod 8))))
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(8 * (x + (2 * (x mod (1 + (x div 8))))))
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(((1 + (x div 3)) div 2) - (x div (~2 + ((~x + 2) div 4))))
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(x2 mod (2 + ((1 + ((~x + 2) mod 4)) * (x div 4))))
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(((5x + 5) * (x div 2)) mod (2 + (x div 4)))
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((x + 3) div (2 + ((x + (2 * (x mod 2))) * (x div 4))))
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(2 * ((2 * (2x - (x mod 8))) - (x mod 4)))
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((2x + 1) div (2 + (x div (4 - ((x * (x div 2)) mod 2)))))
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(4 + ((8x2 + 8x + 1) div (x + 2)))
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(4 + ((x + 2) * ((4x + 9) - (x mod 2))))
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((2x + 2) - (((2 + (x * (x + (x div 2)))) div (x + 2)) div 2))
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((2x + 8) + (x2 div ((x + 2) + (x div 3))))
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(2 * ((2x + 5) + ((x + ~2) mod (3 - (x mod 2)))))
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(8x + ((x + (x div 12)) div 2))
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(2x - (((((1 - (x div 2)) div 3) * (x div 2)) div 2) div 2))
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(x - (((x div 2) - ((((~x + 1) div 3) * (x div 2)) div 2)) div 2))
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((5x + 2) - ((2x + 2) div (2 + (x div 2))))
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(2 * ((3 * ((x + 2) + (x div 4))) - ((x div 2) mod 2)))
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(x div (2 * (2 + ((((2 - (x div 2)) div 2) mod 3) + (x mod 2)))))
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((2x + 2) + (x div (6 - (x mod 2))) - (x mod 2))
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(((x3 + 3x2 + 3x + 2) div 2) + (4 * (x mod 2)))
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((~x mod (5 * (1 + (x mod 4)))) mod 4)
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((((x + 1) mod (3 - (x mod 2))) * (1 + (x div 2))) mod 4)
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(1 - (((1 + (x2 div (2 * (2 - (x mod 2))))) div 2) mod 4))
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(x - (4 * (1 - (2 * ((2x + 2) - (x div 4))))))
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((4x + 4) - (((~x + 2) + (x div 4)) mod 4))
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(4 + compr(\x.((x + 1) mod (1 + (x2 mod (1 + (x div 2))))),x))
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((x + ((4x + 2) mod 9)) div 4)
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(4 * (x + ((2 * (x2 - (x mod 4))) div 3)))
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(x - ((x + (9 mod (1 + (x div 2)))) div 4))
A243285-A085972: 0 1 2 2 3 4 5 5 5 6 7 8 9 10 11 11
((x + 4) + ((x - ((x div (1 + (x mod 3))) mod 2)) div 2))
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A231507: 4 5 7 8 10 11 13 14 16 17 18 20 22 23 25 26
((x + 4) + ((x mod (x - ((x + ~1) mod 8))) div 2))
A299487: 4 5 6 7 8 9 10 11 12 13 14 16 17 19 20 22
(4 + compr(\x.(2 - ((x3 + 1) mod (x + 4))),x))
A340325: 5 6 10 11 12 13 14 15 17 18 19 20 22 23 24 25
(1 + (x div (3 - (x mod ~4))) - (x div 4))
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(((1 + ((2 * (x div 2)) div 3)) mod 3) * (x div 4))
A328842-A276009: 0 0 0 0 2 2 0 0 0 0 2 2 6 6 6 6
((x div (3 * (8 - (x div 2)))) + (x div 4))
A239513: 0 0 0 0 1 1 1 1 2 2 3 3 5 5 7 8
((2 * ((2x + 2) + (x div 8))) + (x div 4))
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((x + 1) div (2 + (((x div 3) mod 4) + (x div 4))))
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(((x + 2) * (6 + ((~x + 2) div 2))) - (x div 4))
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((x4 + 15x2) div 4)
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(((x3 + ~x) div 3) + ((~x2 + 2x) div 4))
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(4x4 + 17x2 + 4)
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((((x2 + ~3x + 2) div 2) div 3) * (x2 div 4))
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(x4 + 6x2 + 4x + 4)
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(2 + (((x + 1) + ((2 + ((x div 3) mod 2)) mod (x + 1))) div 2))
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(((x2 + 2x) - ((x + (x div 12)) div 2)) div 2)
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A118027: 0 1 3 7 11 16 22 30 38 47 57 69 81 94 108 123
((x + 4) + ((~x + ((~2 + (x div 2)) * (x div 2))) div (x + 1)))
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(2 + ((3x2 + ~6) div (x + 10)))
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(2 + ((x + ((((x + ~2) * (2 + (x2 div 2))) div 2) div 2)) div 2))
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(2 + ((x + ((x + (((1 + (x div 2)) div 2) mod 4)) div 2)) div 2))
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(2 + (((x2 + 2x) + (((x2 + ~1) div 2) div 3)) div 2))
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(1 - ((((~x2 + ~2x) + ((x2 div 2) div 3)) div 2) div 2))
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(((~1 + (24 * (x div 2))) div (x + 2)) mod 2)
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(2 * ((6x + (x2 div 4)) div (x + 2)))
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(2 * ((2 * ((x + 1) mod 11)) mod (x + 2)))
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((x + 2) - (((~2x + 1) - (x2 div 4)) div (x + 2)))
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((x + 2) - ((2 - (((x + (x div 2)) div 2) * (x div 2))) div (x + 2)))
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((2x + 4) + ((2 mod ((~x + ~1) + (x mod (2 + (x mod 2))))) mod 2))
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((2x + 4) + ((2x + ~1) div (4 + (x div 4))))
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((2x + 4) + ((x2 mod (2x - ((~x + 2) div 2))) mod 2))
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((3x + 4) + ((x - ((~x + 2) div 4)) div 3))
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A184118: 4 7 10 14 17 21 24 28 31 34 38 41 45 48 51 55
(25x2 + ~14x + 2)
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(2 * (2x + (((x2 + x) div ~8) mod 2)))
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(2 * (2x + ((((~1 + ((x2 + x) div 2)) div 2) div 2) mod 2)))
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(4x + ((~x + (1 mod (8 - (x div 2)))) div 2))
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(5x + (((2x + 2) div (2 + (x div 2))) mod 2))
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((3x + 2) + (((x mod (2 + (x div 3))) div 2) div 2))
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((x + 2) + (x div 2) - ((2 * (1 - (x div 2))) div 5))
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(2 + (((x div (1 + (x mod 9))) mod 2) + (x div 2)))
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((x + 2) + (x div 2) - (((2 + (x div 2)) mod 5) mod 2))
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((x + 2) - (x2 div ((2x + 10) - (x div 2))))
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(2 + (((3 * (2x + (x div 4))) div 2) + (x div 2)))
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(((x2 div (4 + (((x + 1) div 2) div 2))) + (x div 2)) div 2)
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(2 + ((2 * (x + ((2 * (x div 2)) div 5))) + (x div 2)))
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((x + 1) mod (12 - (2x div (2 + (x div 2)))))
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(2 * (((x mod (~1 + (2 * (x div 3)))) mod 2) * (~2 + (x div 2))))
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(((x + 2) mod (2 + ((2 * (x div 2)) mod 3))) + ((x div 2) mod 2))
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(x div (2 * ((3 * (1 + ((~x + 1) mod 3))) - (x mod 2))))
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(2 * (((x div (1 + (x mod 9))) mod 2) + (x mod 2)))
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((2 + (((~2x + 4) mod (2 + (x div 2))) div 2) - (x mod 2)) div 2)
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((1 + ((~x + 1) mod (1 - (x div ~4)))) mod (2 + (x mod 2)))
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((2 + ((x + 1) div (3 + (x mod 3)))) div (2 + (x mod 2)))
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((2 + ((x + (x2 div 3)) div 4)) div (2 + (x mod 2)))
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((2 - ((x2 + 2) mod 5)) * (1 - (2 * (x mod 2))))
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(((x + 1) * ((x + 1) + (x2 div 3))) + (2 * (x mod 2)))
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((1 + ((x3 + ~x2) div 3) - (x2 div 2)) div 2)
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(1 - ((~x + ((1 - (x div 2)) mod (1 + (x div 5)))) div 2))
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((21x2 + ~17x) div 2)
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((x + 2) + ((x2 + 3x + 2) div 11))
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(((x + 1) + (((x + ~2) mod ~4) mod (2x + 1))) div 2)
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(((x + 1) + ((x + ((x div 3) mod 2)) mod (1 + (x div 2)))) div 2)
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((8x3 + ~3x2 + 3x) div 2)
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((x + 2) + ((~x + 1) mod (1 + (x div 2) - ((x div 3) mod 2))))
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(2 * (x + (x div (1 + (2 * (2 + (x mod (2 + (x div 4)))))))))
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((29x2 + x) div 2)
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((29x2 + ~x) div 2)
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((x + 2) + ((x mod 10) mod 9))
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((x + 2) + ((x + 1) mod (1 + (x div (2 + (x mod (2 + (x mod 2))))))))
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((x + 2) + ((1 + ((x * (x div 2)) div 4)) div 5))
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((x + (((x * (x - (x div 3))) div 2) div 5)) div 2)
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((x + 2) + (((x * (((x + ~1) div 2) div 2)) div 2) div 5))
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((x + (5 * (2x + ((~x + 1) mod 4)))) div 2)
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(25x2 + 45x + 14)
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(10x + (x div (~3 + (x div ~2))))
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((25x2 + ~39x) div 2)
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((19x2 + ~15x) div 2)
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((x + ((1 + (x mod (2 * (1 + (x div 4))))) mod 3)) div 2)
A267110: 0 1 1 2 2 3 3 4 4 5 6 5 7 6 7 8
((x + 2) + ((x - (((x + 2) div 3) mod 3)) div 3))
A031177: 2 3 4 5 6 8 9 11 12 14 15 16 17 18 20 21
((x + (((x2 + 2x) - ((x + ~1) div 3)) div 3)) div 2)
A233524: 0 1 2 4 5 8
A095031: 0 1 2 4 5 8 10
A126026: 0 1 2 4 5 8 10 13 17 20 24 28 33 38 43 49
((x + ((1 - (8 mod (1 + (x div 2)))) mod 3)) div 2)
A244989: 0 1 1 2 3 3 3 4 4 5 6 6 6 6 7 8
(x div (((x + 2) - (((2 - (x div 2)) mod (x + 1)) mod 3)) div 2))
A080356: 0 1 2 1 1 1 1 1 2 2 2 1 1 1 2 2
((x + 2) + (3 * (6 + ((1 + (x div 2)) div 2))))
A295488: 20 21 25 26 27 28 32
((x + 2) + (3 * (4 + ((x div 2) div 5))))
A297278-A296748: 14 15 16 17 18 19 20 21 22 23 27 28 29 30 31 32
((x + 2) + (3 * (((x - (x div ~4)) div 2) div 2)))
A246293: 2 3 4 8 9 10 14 15 16 20 21 22 23 27 28 29
((x + 2) - (x2 div (x + (3 * (2 + (x div 4))))))
A089058: 2 3 4 4 5 6 6 6 7 8 8 8 9 9 10 10
((x + 2) + ((((x * (((x + ~1) div 2) div 2)) div 2) div 2) div 3))
A005524: 2 3 4 5 6 7 8 9 10 12 13 14 16 18 19 20
(3 div ((x + 2) + ((((~x + 2) * (x div 2)) div 2) div 3)))
A108658: 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 3
((x - (x * (x - (((x3 + ~x) div 2) div 3)))) div 2)
A117662: 0 0 0 3 14 40 90 175 308 504 780 1155 1650 2288 3094 4095
(((~x + (((~x + 2) div 2) div 3)) div 2) mod (3x + 2))
A233473: 0 4 7 9 11 14 16 19 21 23 26 28 31 33 36 38
(12x3 + 21x2 + 12x + 2)
A128822: 2 47 206 551 1154 2087 3422 5231 7586 10559 14222 18647 23906 30071 37214 45407
(1 - ((~x + (x mod 3) - ((x2 + 2x) div 3)) div 2))
A188623: 1 2 2 5 7 8 12 15 17 22 26 29 35 40 44 51
(2 + compr(\x.(2 + (x div 3) - ((x + (x div 2)) div 4)),x))
A345510: 34 37 40 42 43 45 46 48 49 50 51 52 53 54 55 56
((~x + ((x + (3 * (x + (x div 2)))) * (1 + (x div 2)))) div 2)
A195313: 0 1 10 13 31 36 63 70 106 115 160 171 225 238 301 316
(2 + compr(\x.(~1 + (4x mod (8 - (x mod 2)))),x))
A285129: 2 4 6 8 9 10 11 12 14 16 18 20 22 23 24 25
(x - ((~23x2 + 23x) div 2))
A255184: 0 1 25 72 142 235 351 490 652 837 1045 1276 1530 1807 2107 2430
(x - ((~31x2 + 31x) div 2))
A098938-A098923: 0 1 33 96 190 315 471 658 876 1125 1405 1716 2058 2431 2835 3270
(((~x + 1) + compr(\x.(~1 + (2x mod (1 + (x div 4)))),x)) div 2)
A034403: 0 0 0 0 0 0 0 0 0 0 1 1 1 3 4 5
((2x3 + 5x2 + 13x) div 2)
A163655: 0 10 31 69 130 220 345 511 724 990 1315 1705 2166 2704 3325 4035
((2x3 + 5x2 + 17x) div 2)
A163661: 0 12 35 75 138 230 357 525 740 1008 1335 1727 2190 2730 3353 4065
((2x3 + 5x2 + 15x) div 2)
A163673: 0 11 33 72 134 225 351 518 732 999 1325 1716 2178 2717 3339 4050
((x + ((2 * (1 + (x2 mod (x + 4)))) div (x + 1))) div 2)
A087816: 1 1 2 2 2 3 4 4 4 4 5 5 6 7 8 8
((8x2 + 32x + 32) + ((x2 + ~x) div 2))
A250756: 32 72 129 203 294 402 527 669 828 1004 1197 1407 1634 1878 2139 2417
((9x4 + 4x3 + ~x) div 2)
A047786: 0 6 87 417 1278 3060 6261 11487 19452 30978 46995 68541 96762 132912 178353 234555
((x + 2) + (((2x + 2) div (1 + (x mod 5))) mod 2))
A161659: 2 3 4 5 6 7 9 10 10 11 12 13 14 16 16 17
(2 + compr(\x.((1 + ((~x + 1) mod (1 + (x div (2 + (x mod 2)))))) mod 2),x))
A155878: 4 8 10 12 14 15 16 18 20 21 22 24 26 27 28 30
((x + 2) + (x div (2 + ((x2 + 2) mod 7))))
A344414: 2 3 4 5 6 7 9 10 11 12 13 14 15 17 19 20
((x + 2) + ((2 - (2 mod (~2x + 11))) div 2))
A172248: 2 3 4 5 6 8 9 10 12 14 16 18 20 22 24 26
(2 + compr(\x.(1 - ((x + 2) mod (2 + (x mod 9)))),x))
A065877: 11 13 14 15 16 17 19 22 23 25 26 28 29 31 32 33
((x + 2) + ((3 * ((((x + 1) + (x div 2)) div 2) div 2)) div 2))
A028781: 2 3 5 6 7 10 11 12 14 15 18 19 20 22 23 24
((x + ~2) + (2 * (12 + (x div 8))))
A236404: 22 23 24 25 26 27 28 29 32 33 34 35 36 37 38 39
((x + 2) + ((((x2 + 1) div 2) * (x - (x div 3))) div 2))
A240802: 2 3 6 10 18 33
((x + ((1 + (x2 div 2)) mod (2 + (x2 div 3)))) div 2)
A224985: 0 1 1 1 3 4 5 7 9 10 13 15 17 20 23 25
((x + ((x - (x div (9 - (x div 2)))) div 2)) div 2)
A278617: 0 0 1 2 3 3 4 5 5 6 7 7 8 8 8 9
((x + ((x + ((x2 div 3) + (2 mod (x + 1)))) div 2)) div 2)
A111208: 0 0 2 3 4 6 8 9 11 14 16 18 21 24 27 30
((~x + 2) + ((3x2 + 2x + 1) * ((x + 1) div 2)))
A154298: 2 7 17 67
((x + ((2x + 1) div (2 - (((x div 2) div ~2) div 2)))) div 2)
A005376: 0 1 1 2 3 4 5 6 6 7 7 8 9 9 10 11
((x + (((x + (3 * (x div 2))) * ((x + 1) div 2)) div 2)) div 2)
A055607: 0 0 2 4 7 10 14 19 24 30 36 44 51 60 68 79
((x + 2) - ((x2 + 3x + 2) div (x + 16)))
A094192: 2 3 4 4 5 5 6 6 7 7 7 8 8 8 8 9
((x + 2) + ((3x + 1) div (4 + (x div 4))))
A186352: 2 4 5 7 8 10 11 13 14 15 17 18 19 20 22 23
(~2 + compr(\x.(2 - (x2 mod ((x + 4) - (x div 4)))),x))
A192225: 0 1 2 5
A288659: 0 1 2 5 6 7 8 9 22 23 24 25 26 27 28 29
((x + ((((x + 2) * (2 - (x div ~4))) div 2) div 2)) div 2)
A267302: 0 1 2 3 4 6 7 8 9 11 12 13 14 17 19 20
((x + 2) + ((((2 + ((x * (x div 2)) mod 2)) * (x div 2)) div 2) div 2))
A185024: 2 3 4 5 7 8 9 11 12 13 14 16 17 18 19 22
(2 + compr(\x.((x - (x div ~14)) mod 4),x))
A190713: 2 5 9 13 20 24 28 31 35 39 43 46 50 54 58 61
(2 * compr(\x.(1 - ((~x + (x2 div 8)) mod 4)),x))
A098807: 2 4 6 8 10 12 14 18 20 24 28 30 34 36 38 40
((x + 2) + ((x + (x div 2) - ((2 - (x div 4)) div 2)) div 2))
A187833: 1 3 5 6 9 10 12 14 16 17 19 21 23 25 27 28
(x - ((~x + 4) * (x mod (x - ((x + ~1) mod 8)))))
A103303: 0 1 2 3 4 5 6 7 8 9
A133059: 0 1 2 3 4 5 6 7 8 9 16 25 36 49 64 81
((x + (2 * (x + (((x div 2) mod 5) div 3)))) div 2)
A093579: 0 1 3 4 6 7 10 11 13 14 15 16 18 19 21 22
(25x2 + 14x + 2)
A007533: 2 41 130 269 458 697 986 1325 1714 2153 2642 3181 3770 4409 5098 5837
((x + 2) + ((x + ((x2 mod 9) mod 2)) div 2))
A285354: 2 4 5 6 8 10 11 12 14 15 17 18 20 22 23 24
((x + 2) + ((x + ((x + (~x mod (2 + (x div 2)))) div 2)) div 2))
A287175: 2 4 5 7 9 11 13 15 17 18 20 22 24 25 27 29
((x + 2) + ((4x + (x2 div 4)) div (x + 2)))
A183569: 2 4 6 7 9 10 12 13 14 16 17 18 20 21 22 23
(((x2 + 2x) + ((x div (1 + (~x mod 4))) mod 2)) div 2)
A156324: 0 1 4 8 12 18 24 32 40 49 60 72 84 98 112 128
(1 + (x div 3) - ((~1 + ((x + 1) mod 3)) mod (x + 2)))
A122918: 1 0 ~2 2 1 ~4 3 2 ~6 4 3 ~8 5 4 ~10 6
((x2 mod (1 + (8x div 3))) div (x + 2))
A227740: 0 0 1 0 0 1 0 1 2 0 1 0 0 1 0 1
((6 * (2x + ((x + ~1) mod 3))) div (x + 2))
A303134: 6 4 7 9 8 9
((2x2 - (((x2 + 2x) div 2) div 3)) div (x + 2))
A280762: 0 0 1 3 4 6 8 9 11 13 15 16 18 20 22 24
((3 * ((x2 + 5x + 4) + (x div 2))) div (x + 2))
A248632: 6 10 14 17 21 24 27 30 33 36 39 42 45 48 51 54
(((x * (4 + (x div 4))) + (x mod 3)) div (x + 2))
A262518: 0 1 2 2 3 3 3 4 5 4 5 5 6 6 6 6
(((8x + 2) + (x2 div 3)) div (x + 2))
A225179: 1 3 4 5 6 7 7 8 8 9 9 10 10 10 11 11
compr(\x.(1 - (x mod (2 * (2 + (((x + 1) div 2) div 3))))),(x + 2))
A217129: 3 5 7 8 9 10 11 12 13 14 15 17 18 19 21 22
(2 - ((2 - (2x mod (4 + (x div 4)))) div (x + 2)))
A278597: 1 2 2 2 3 2 2 3 3 2 2 3 3 3 2 2
compr(\x.(((x2 + ~2) mod (x + 10)) mod 2),(x + 2))
A080653: 2 4 5 6 8 10 11 12 13 14 16 18 20 22 23 24
((x * ((x2 + (x div 2)) div 7)) mod (x + 2))
A194761: 0 0 0 3 2 1 6 4 2 9 6 3 0 10 6 2
((x * (2 + (((x + ~1) mod (2 + ((x div 2) mod 2))) mod 2))) div (x + 2))
A335225: 0 0 1 1 2 1 1 1 2 1 1 2 2 1 2 1
(((~x2 + ~2x + 1) div (x + 16)) mod (x + 2))
A265912: 0 2 3 4 4 5 5 6 6 7 7 7 8 8 8 8
((2x + 1) + ((x + ~2) div (~6 + (x div 4))))
A191777: 1 3 5 6 8 10 12 14 15 17 19 20 21 23 25 26
(2x + ((~x + (5 mod (x + 1))) div 5))
A019271: 0 2 4 5 7 10 11 13 15 17 19 20 22 24 26 28
(2x + ((~x + (x2 div 3) - (x div 2)) div 3))
A036604: 0 1 3 5 7 10 13 16 19 22 26 30 34 38 42
((2x + 2) + (x div (3 + (2x mod 5))))
A345981: 2 4 6 8 10 13 15 17 20 21 25
(2x + ((x mod ((x + ~1) - ((x + 2) mod 8))) mod 2))
A059009: 0 2 5 6 8 11 13 14 17 18 20 23 24 27 29 30
(2x + ((2 - ((x * (x div 8)) div 3)) div 2))
A134322: 1 3 5 7 9 11 13 15 16 17 19 21 23 25 27 28
(2x + (((3 * (x + (x div 8))) div 2) div 2))
A140101: 0 2 5 8 11 13 16 19 22 25 28 31 33 36 39 42
(2x + ((2 * (2x - (x mod 2))) div (4 + (x div 2))))
A236019: 0 2 5 8 10 13 15 17 20 22 24 26 28 31 33 35
(2x + (((1 + ((2 - (x div 2)) * (x mod 2))) mod (x + 2)) mod 2))
A285347: 1 2 5 6 9 11 13 14 17 18 21 23 25 26 29 31
(2x + (1 mod (~4x + 30)))
A206545: 1 3 5 7 9 11 13 15 15 13 11 9 7 5 3 1
(3x + ((2 - ((x - ((x div 2) mod 4)) div 2)) div 2))
A285210: 1 4 7 9 12 15 18 21 23 26 29 31 34 37 40 43
(1 + (3 * (x2 - (2 * ((x div 2) mod 2)))) - (x div 2))
A231407: 1 4 6
A151520: 1 4 6 21 47
(1 + ((2 * (x - (x div (~5 + (x mod 2))))) + (x div 2)))
A022160: 1 5 8 10 13 17 20 22 25 29 30 34 37 41 42 46
(1 + (((x2 + 2x) div 2) + ((x mod 3) div 2) + (x div 2)))
A106352: 1 2 7 9 15 21 28 35 46 54 66 78 91 104 121 135
(1 + ((2 * ((1 + (x2 div 8)) div 2)) + (x div 2)))
A258376: 1 1 2 4 5 7 8 10 13 15 18 22 25 29 32 36
((x mod (1 + ((~x2 mod (2 + (x div 2))) div 2))) + (x div 2))
A266341: 0 0 1 1 2 3 3 3 4 5 6 7 6 7 7 7
(1 + (((x + 1) div (2 + (((x div 2) - (x mod 2)) div 2))) + (x div 2)))
A108942: 1 3 3 4 4 6 6 6 7 8 8
((x + 1) + (((x - (x div (1 + (x div 4)))) div 2) + (x div 2)))
A096603: 1 2 4 5 8 9 11 13 16 17 19 21 23 25 27 29
(((x div (1 + (((x + 1) div 3) mod 4))) mod 2) + (x div 2))
A189709: 0 1 2 2 2 3 3 3 4 4 5 6 6 7 8 8
((2 * (x - ((~1 + (2 * (x div 2))) div 5))) + (x div 2))
A188468-A005653: 2 4 5 7 10 12 13 15 18 20 23 25 26 28 31 33
(((2 - (x div (9 - (x div 2)))) div 2) + (x div 2))
A114214: 1 1 2 2 3 3 3 3 4 4 5 5 5 5 4 4
((((x2 + ~x) div 2) div 3) * ((x + ~1) div 2) * (x div 2))
A212519: 0 0 0 1 4 12 30 63 108 192 300 450 660 936 1260 1715
(((~2x + 4) div (4 + ((x div 2) div 3))) + (x div 2))
A046773: 1 0 1 0 1 0 1 1 1 1 1 1 2 2 3 2
((x2 div ((x + 2) + ((x div 5) mod 2))) - (x div 2))
A268383: 0 0 0 0 0 1 1 1 1 2 3 4 4 5 5 5
((x + 1) - ((x div 2) + (((x2 + ~2x) mod (1 + (x div 2))) mod 2)))
A248801: 1 2 2 2 3 4 4 4 4 5 6 6 6 7 8 8
(2 + (x mod 2) - ((~x + 1) div (1 + (3 * (1 + (x mod 2))))))
A177876: 2 3 3 4
A179846: 2 3 3 4 3 4 4 4 4 5 5 5 5 5 6 5
(1 + (2 * ((x + 2) - (2 div (1 + (x div 4))))) - (x mod 2))
A284488: 1 2 5 6 11 12 15 16 21 22 25 26 29 30 33 34
(1 + (((~x2 + 2) div (4 + (x div 2))) mod 2) - (x mod 2))
A026613: 1 0 2 0 2 0 2 1 1 0 2 0 2 1 1 1
((54x + 27) - (x mod 2))
A129254: 27 80 135 188 243 296 351 404 459 512 567 620 675 728 783 836
(((2 * (2x + (x div 2))) mod 9) + (x mod 2))
A180595: 0 5 1 6 2 7 3 8 4 9 5 1 6 2 7 3
((2 - ((2x + 4) mod (1 + (2 * (x div 4))))) * (x mod 2))
A079208: 0 2 0 2 0 0 0 2 0 0 0 1 0 0 0
((1 + ((2 + (x div 8)) * ((x div 2) mod 2))) * (x mod 2))
A053385: 0 1 0 3 0 1 0 3 0 1 0 4 0 1 0 4
(3 * ((~1 + ((x - (x div 3)) mod 3)) * (x mod 2)))
A158678: 0 0 0 3 0 0 0 3 0 ~3 0 3 0 ~3 0 0
((6 * ((x div 7) mod 2)) + (x mod 2))
A093349: 0 1 0 1 0 1 0 7 6 7 6 7 6 7 0 1
(((2 + (x mod (2 + ((x div 2) mod 3)))) mod 3) + (x mod 2))
A323756: 2 1 1 3 2 1 2 1 1 3 1 3 2 1 1 3
((1 - (((x + ~1) mod (2 + (x div 4))) mod 3)) * (x mod 2))
A289741: 0 1 0 1 0 0 0 1 0 1 0 ~1 0 ~1 0 0
(1 - ((x mod 2) + ((x2 + 2x) div ~11)))
A029010: 1 1 2 2 4 4 6 6 9 9 12 13 17 18 22 24
(((x mod (1 + ((x + 1) mod 7))) mod 2) - (x mod 2))
A178779: 0 0 0 0 0 0 0 0 0 0 0 0 1 ~1 0 ~1
((((2x + ~6) div (1 + (x div 3))) mod 2) + (x mod 2))
A033264: 0 1 0 1 1 1 0 1 1 2 1 1 1 1 0 1
((((~2 + (x * (x div 2))) mod (1 + (x div 3))) mod 2) + (x mod 2))
A101660: 0 1 0 2 0 1 1 2 0 1 0 2 0 2 1 2
((((x + 3) div (1 + (4 mod (x + 1)))) mod 2) + (x mod 2))
A342595: 1 1 0 1 1 2 1 1 0 1 0 1 1 2 1 2
(((((x + ~1) * ((x + 1) div 2)) div 5) mod 2) - (x mod 2))
A295304: 0 ~1 0 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 0 ~1
(((3 * ((x mod (1 + (x div 2))) div 3)) div 2) + (x mod 2))
A247050: 0 1 0 1 0 1 0 2 1 2 1 2 1 4 3 4
(((((1 - (x mod 4)) mod (x + 1)) mod 3) mod 2) + (x mod 2))
A037870: 0 1 0 1 1 1 0 1 1 1 1 2 1 1 0 1
(1 - ((x mod 2) + (x div (~2 + (3 * (x div ~4))))))
A078313: 1 1 2 1 2 1 2 1 2 1 2 1 3 1 2 2
(((x - ((x div 2) div 3)) div (2 + (x div 3))) + (x mod 2))
A323880: 0 1 1 2 1 2 1 2 1 2 1 3 1 2 2 2
((((3 * ((x div 2) mod 2)) - (x mod 3)) div 2) * (x mod 2))
A228557: 0 ~1 0 1 0 ~1 0 1 0 0 0 0 0 ~1 0 1
((((~5x + 5) mod (1 + (x div 2))) mod 2) + (x mod 2))
A104234: 0 1 1 1 0 2 1 1 0 1 1 1 1 2 1 1
((((x2 + ~2) mod (x + 9)) mod 2) + (x mod 2))
A341345: 1 2 0 2 1 2 0 2 1 2 1 2 0 2 0 2
(((((~x2 + 2x + ~1) mod (1 + (x div 2))) div 2) mod 2) + (x mod 2))
A340379: 0 1 0 1 0 2 1 1 0 1 1 2 0 2 1 1
((x div (2 + (x div (2 + (((x div 2) mod 3) mod 2))))) + (x mod 2))
A036430: 0 1 1 2 1 2 1 2 2 2 1 2 1 2 2 3
((2 * (((x + 2) div (2 + ((~x + 1) mod 3))) mod 2)) - (x mod 2))
A165575: 0 1 2 1 2 1 0 ~1 0 1 0 1 0 1 0 1
(((x mod (2 + (x div 2) - ((x mod 3) div 2))) div 2) + (x mod 2))
A035434: 0 1 0 1 0 2 0 2 1 2 1 3 2 3 3 4
((4 * (3x - (~x mod 4))) + (x mod 2))
A151981: 0 1 16 33 48 49 64 81 96 97 112 129 144 145 160 177
((17 * (x2 div 4)) + (x mod 2))
A195047: 0 1 17 35 68 103 153 205 272 341 425 511 612 715 833 953
((1 + (x div (2 + (x div (2 + (x mod 4)))))) div (2 - (x mod 2)))
A290090: 0 1 1 2 1 2 1 3 1 2 1 3 1 3 1 4
((x div (2 + (x div (1 + ((~x + 2) mod 4))))) div (2 - (x mod 2)))
A083661: 0 0 0 1 0 1 0 2 1 1 0 2 1 1 0 3
((2 + (x mod (1 + (x div (2 * (2 - (x mod 2))))))) div (2 - (x mod 2)))
A330756: 1 2 1 3 1 4 1 5 2 6 1 7 1 8 2 9
(((6x + (x div 3)) div (x + 2)) - (x mod 2))
A007456: 0 1 3 2 4 3 4 3 5 4 5 4 5 4 5 4
((4x4 + 6x3 + 5x2 + x) div 2)
A247112: 0 8 67 267 746 1690 3333 5957 9892 15516 23255 33583 47022 64142 85561 111945
(1 + (((2x2 + 5x + 2) div 3) + (x2 div 2)))
A213495: 1 4 9 16 27 38 53 70 89 110 135 160 189 220 253 288
(((2x3 + 6x2 + 4x) div 3) - (x2 div 2))
A213045: 0 4 14 36 72 128 206 312 448 620 830 1084 1384 1736 2142 2608
(((4x3 + 2x) div 3) - (x2 div 2))
A059924: 0 2 10 34 80 158 274 438 656 938 1290 1722 2240 2854 3570 4398
((x9 + x4) div 2)
A168196: 0 1 264 9882 131200 976875 5039496 20178004 67110912 193713525 500005000 1178981166 2579900544 5302263967 10330542600 19221705000
(x + ((~x + 1) div (1 + (x mod (1 + (x mod (3 - (x mod 2))))))))
A341866: 1 1 1 2 1 3 1 4 5 5 1 6 1 7 9 8
compr(\x.(~1 + (x div (~1 + (2 * (x div (1 + (x mod 8))))))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A032344-A023764: 0 1 2 3 4 5 6 7 8 9 16 17 18 24 25 26
compr(\x.(1 + (x mod 4) - ((x + 1) mod 7)),x)
A004827: 0 1 2 3 4 5 8 9 10 11 12 16 17 18 19 24
compr(\x.(~1 + (x mod (1 + ((~x mod (2 + (x div 3))) div 2)))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A191889: 0 1 2 3 4 5 6 7 8 9 10 12 13 16 19 21
compr(\x.(1 + (x mod (~1 + (2 * (x mod (~2 + ((x div 2) mod ~2))))))),x)
A013660: 1 2 5 7 11
A243047: 1 2 5 7 11 13 14 17 19 22 23 25 26 29 31 34
compr(\x.(~1 + ((x div 2) mod (1 + (2 * ((((x + 1) div 2) div 2) div 2))))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A259624: 0 1 2 3 4 5 6 7 8 9 12 13 14 20 21 22
compr(\x.(1 + (x mod (1 + (2 * (x div (1 - (2 * (x mod 4)))))))),x)
A126949: 5 7 9 10 11 13 14 17 18 19 21 22 23 25 26 27
compr(\x.((x + 1) mod (~1 + ((x2 + 2x) mod 9))),x)
A010383: 0 1 4 7 9 15 16 18
compr(\x.((x + 1) mod (1 + (x mod (1 + ((~x + 1) mod 8))))),x)
A067570: 0 1 2 3 4 5 7
A051204: 0 1 2 3 4 5 7 8 9 12 14 15 16 17 20 21
compr(\x.(~1 + (x mod (1 + ((~x2 + (x div 2)) mod 8)))),x)
A153329: 0 1 3 4 5 7 9 10 11 13 15 16 17 18 19 21
compr(\x.((x * (2 - (x div 2))) mod (1 + ((x + ~1) mod 5))),x)
A023761: 0 1 2 3 4 5 6 10 11 12 15 16 17 18 20 21
compr(\x.(3 - (((x2 + x) div 4) mod 5)),x)
A174871: 3 7 8 11 12 16 23 27 28 31 32 36 43 47 48 51
compr(\x.((x + 1) mod (1 + ((~x + 1) mod (1 + (2 * (2 - (x mod 2))))))),x)
A181766: 1 3 5 6 7 9 11 13 14 15 16 17 19 21 23 25
compr(\x.(1 - (x mod (1 + (3 * (1 + ((x div ~2) mod 2)))))),x)
A001948: 1 2 3 5 6 7 9 10 11 13 15 17 18 19 22 23
compr(\x.(x mod (1 + ((2 + (x div 4)) * ((x + ~1) mod 3)))),x)
A010380: 0 1 4 7 9 10 13 16
A010389: 0 1 4 7 9 10 13 16 19 22 25
((x + 1) + (3 * (((x3 + 2x2 + 1) div 2) div 2)))
A213487: 1 5 15 37 77 138 223 338 489 679 911 1191 1525 1916 2367 2884
compr(\x.((x + ~1) - (3 * (~2 + ((x - (x div 4)) div 2)))),x)
A345480: 31 34 37 39 40 42 43 45 46 47 48 49 50 51 52 53
compr(\x.((x + 1) - (3 * (~2 + ((x + (x div 2)) div 4)))),x)
A345494: 56 59 62 64 65 67 68 70 71 72 73 74 75 76 77 78
(x + (13 * (x div 7)))
A024639: 0 1 2 3 4 5 6 20 21 22 23 24 25 26 40 41
compr(\x.((x + ~1) mod (x - ((x + 1) mod 13))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A048336-A048323-A048309-A029957: 0 1 2 3 4 5 6 7 8 9 10 11 13 26 39 52
compr(\x.((x + ~1) mod (x - ((x + 1) mod 11))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A344550-A343524-A335779-A306273-A295010-A266140-A257054-A244514-A240601-A175688-A141033-A109882-A048321-A048307-A030285-A010785-A002113: 0 1 2 3 4 5 6 7 8 9 11 22 33 44 55 66
((~x + ~1) + (3 * ((3 + (x2 div 2)) div (x + 2))))
A083056: 2 1 0 ~1 ~2 0 ~1 1 0 ~1 1 0 2 1 3 2
compr(\x.(1 - ((3x2 + 2x) mod (1 + (x div 3)))),x)
A025051: 3 5 7 8 9 11 12 13 14 15 16 17 19 20 21 23
compr(\x.(1 + ((x div 5) mod 3) - (x mod 3)),x)
A194415: 1 2 4 5 8 16 17 19 20 23 31 32 34 35 38 46
compr(\x.(~1 + ((3 * (x div 5)) mod (1 + (x div 2)))),x)
A032860: 0 1 2 3 4 5 10 11 15 16 17 20 21 22 23 26
compr(\x.((2x + 1) mod (1 + ((4 * (x mod 2)) mod (x + 1)))),x)
A257282: 0 1 2 3 4 6 7 8 10 12 14 16 17 18 20 22
compr(\x.(~1 + ((x + 2) mod (2 + (x mod 11)))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A061430: 0 1 2 3 4 5 6 7 8 9 10 11 14 19 20 22
compr(\x.(~1 + (((x + ~1) mod (1 + (2 * (2 + (x mod 3))))) div 2)),x)
A145733: 1 2 3 4 6 9 10 11 12 16 18
((x + 1) + (x div (2 + (((x div 2) * (x div 2)) div 5))))
A178344: 1 2 4 5 7 8 9 10 10 11 12 13 14 15 16 17
((x + 2) - ((~x + 1) div (1 + (2 * ((~x + 2) mod 5)))))
A323252: 2 3 5 6 7 8 10 15
compr(\x.(x mod (1 + ((x + ~1) mod (2 + (3 * (x mod 3)))))),x)
A062849: 0 1 2 3 4 5 6 8 9 10 12 15 16 17 18 20
(x + (x div (3 + ((2 + ((x div 2) div 3)) mod 3))))
A156657: 0 1 2 3 4 6 8 9 10 12 13 14 15 16 17 18
((x + 1) - ((x + ~2) mod (1 + ((3 * (x div 4)) div 2))))
A094802: 1 2 3 4 5 5 7 7 7 7 11 11 13 13 13 13
(1 mod (x + (7 * ((~x2 + 4x + ~4) div 2))))
A277125: ~13 ~5 1 ~3
(x + ((x div ~7) * (x mod 7)))
A194755: 0 0 0 0 0 0 0 7 6 5 4 3 2 1 14 12
compr(\x.(1 + (x mod 7) - (x mod 8)),x)
A297261-A297138-A296705: 7 14 15 21 22 23 28 29 30 31 35 36 37 38 39 42
(x7 + 7x)
A180357: 0 8 142 2208 16412 78160 279978 823592 2097208 4783032 10000070 19487248 35831892 62748608 105413602 170859480
compr(\x.((x + 1) mod (1 + ((~x + 1) mod (2 + (4 mod (x + 1)))))),x)
A325395: 1 2 3 5 7 9 11 13 17 19 23 25 29 31 35 37
((x + 1) + (x div (2 + ((x div 4) + ((x div ~2) mod 2)))))
A031975: 1 2 3 5 6 7 8 10 11 11 13 14 15 16 17 19
compr(\x.(1 + (x mod (2 * (1 - (2 * ((x div 2) mod 5)))))),x)
A154660: 3 4 5 6 7 8
A075493: 3 4 5 6 7 8 9 13 14 15 16 17 18 19 23 25
compr(\x.(1 - (x mod (3 + ((x2 div 2) mod 6)))),x)
A094387: 1 2 3 4 5 7 8 9 11 13 14 15 16 17 19 22
compr(\x.(1 - (x mod (1 + (x mod (4 - (x mod ~4)))))),x)
A325162: 1 2 3 5 7 11 13 14 17 19 22 23 26 29 31 33
compr(\x.((x + 1) mod (5 + ((x mod (2 + (x mod 2))) div 2))),x)
A162698: 4 5 9 11 14 17 19 23 24 29 34 35 39 41 44 47
(x + ((4x2 + ~2x) div 17))
A194172: 0 1 2 4 7 10 13 17 22 27 32 38 44 51 58 66
compr(\x.((x + ~1) mod (x - ((x + 1) mod 15))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A048338-A048325-A048311-A029959: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 15 30
((x + 1) + ((x - (((x div 3) + (x div 2)) mod 4)) div 2))
A331593-A210994: 1 2 3 4 5 7 9 11 12 13 16 17 18 19 20 23
compr(\x.(~1 + ((x - ((x div 2) div 5)) mod 8)),x)
A130881: 0 1 8 9 10 17 18 26 27 35 36 44 45 53 54 62
(x + (54 * (x + (x mod 2))))
A263194: 0 109 110 219 220 329 330 439 440 549 550 659 660 769 770 879
(x + (9 * (2 div (8 - (x div 2)))))
A103303: 0 1 2 3 4 5 6 7 8 9
A064222: 0 1 2 3 4 5 6 7 8 9 10 11 21 22 32 33
(x + ((x * (1 + (x div 5))) div 9))
A059325: 0 1 2 3 4 6 7 8 9 11 13 14 16 17 18 21
compr(\x.(1 - (x mod (1 + (2 * ((2 + (x div 2)) mod (2 + (x mod 2))))))),x)
A261034: 1 2 5 7 10 11 13 14 17 19 22 23 26 29 31 34
(x + (5 * (2 - (2 div (1 + (x div 5))))))
A174139: 0 1 2 3 4 10 11 12 13 14 20 21 22 23 24 25
(x + (5 * ((x + 1) - (((x + 1) div 2) div 3))))
A000966: 5 11 17 23 29 30 36 42 48 54 60 61 67 73 79 85
compr(\x.(2 - (((2x + 1) - ((x div 2) mod 2)) mod 5)),x)
A285416: 1 2 4 6 7 8 9 11 13 14 16 19 21 22 24 26
compr(\x.(((x + 1) * (1 + (x div 5))) mod 5),x)
A337572: 4 9 14 19 20 21 22 23 24 29 34 39 44 45 46 47
(x + (((x + 2) div 5) * ((x + ~1) div 5)))
A067570: 0 1 2 3 4 5 7
A037014: 0 1 2 3 4 5 7 8 10 11 12 15 16 19 20 21
(101x + 10)
A159551: 10 111 212 313 414 515 616 717 818 919 1020 1121 1222 1323 1424 1525
compr(\x.(2 - ((x2 - ((x div 4) mod 2)) mod 5)),x)
A112055: 2 3 5 7 8 12 13 15 17 18 20 22 23 27 28 30
(x + (x div (~1 + ((~x + ((x div 2) mod 5)) div 4))))
A080087: 0 0 1 1 2 2 3 3 4 6 7 8 9 9 10 12
compr(\x.(1 - (x mod (1 + (((x div 2) div 3) + (x mod 4))))),x)
A336224-A336222-A274034-A252895-A197680: 1 2 3 5 6 7 10 11 13 14 15 16 17 19 21 22
compr(\x.(1 - (x mod (1 + ((3x + ~1) mod (x + 4))))),x)
A116545: 1 2 3 5 6 7 8 11 13 14 15 17 18 19 20 21
(x * (((x + 1) div 3) - (2x div (3 + (x div 2)))))
A308809: 0 0 0 0 0 0 0 0 8 9 10 22 24 26 42 30
(x + (3 * (1 + (3 * (2 + (x div 2) - (x mod 2))))))
A118296: 21 13 32 24 43 35 54 46 65 57 76 68 87 79 98 90
(x + ((1 - ((x + 1) mod (1 + (x mod 6)))) mod 3))
A239088: 1 2 3 4 5 6 7 8 9 11 10 12 13 14 15 16
compr(\x.(1 - ((2x2 div (1 + ((x + 1) div 2))) mod 3)),x)
A182654: 1 2 4 7 8 11 12 14 15 16 18 19 21 22 24 25
compr(\x.(1 - ((x mod (~3 + (x mod ~4))) mod 3)),x)
A044951: 1 3 4 5 6 7 8 11 13 14 15 16 17 18 19 20
compr(\x.(1 - ((x2 mod (4x + 7)) mod 3)),x)
A345921: 1 2 4 5 6 7 8 9 11 12 14 16 17 18 19 20
compr(\x.(((x + ~1) + (2x2 mod 5)) mod 3),x)
A194418: 7 10 11 13 14 22 25 26 28 29 37 40 41 43 44 52
(x + ((1 - (x mod (((~x + 2) div 2) - (x mod 3)))) mod 3))
A065307-A065306: 1 2 3 4 5 6 7 9 8 10 11 12 13 15 14 16
compr(\x.(2 + ((x + 1) mod 3) - (x mod 10)),x)
A342226-A066310: 2 3 4 5 6 7 8 9 14 15 16 17 18 19 23 24
(x + (x2 div ((2x + 8) - ((x + ~1) div 3))))
A038161: 0 1 2 3 5 6 7 9 10 12 14 15 16 18 20 21
(x + (6 * (1 - ((~x + 2) div 12))))
A272344: 6 7 8 15 16 17 18 19 20 21 22 23 24 25 26 33
(x + (((1 + ((x * ((~1 + (x div 2)) div 2)) div 2)) div 2) div 3))
A103303: 0 1 2 3 4 5 6 7 8 9
A191841: 0 1 2 3 4 5 6 7 8 9 11 13 14 15 17 18
(x + (((1 + (x div 4)) div 2) + (((x + 1) div 2) div 3)))
A039103: 0 1 2 3 5 7 8 9 10 11 12 14 16 17 18 19
(x + ((2 * (2 + (x2 div (x + 5)))) div 3))
A282131: 1 2 3 5 6 7 9 11 12 13 15 17 18 20 22 23
(x + ((2 * (2 + ((x + ((x div 2) mod 2)) div 3))) div 3))
A039158: 1 2 4 5 6 7 8 9 10 12 13 15 16 17 18 19
((~x + 3) + (8 * (1 + ((x div 4) mod 2))))
A004452: 11 10 9 8 15 14 13 12 3 2 1 0 7 6 5 4
((x + 2) div (~x + (6 * (2 + (x div 8)))))
A033106: 0 0 0 0 0 1 1 1 1 1 1 1 2 3 4 5
compr(\x.(1 - (x mod (2 - (3 * (~2 + (x div 8)))))),x)
A330697: 1 2 3 4 5 6 7 8 9 11 12 13 14 17 19 21
compr(\x.((x + 2) - (3 * (~2 + ((x - (x div 4)) div 2)))),x)
A345483: 55 58 61 63 64 66 67 69 70 71 72 73 74 75 76 77
(x + ((x - (2x2 div ~7)) div 3))
A174059: 0 1 3 5 7 9 11 14 17 20 23 26 30 33 37 41
(x + ((2 + ((x * ((~1 + (x div 2)) div 3)) div 2)) div 3))
A084690: 0 1 2 3 4 5 6 7 10
A023777: 0 1 2 3 4 5 6 7 10 11 12 13 14 15 19 20
(x + ((2 * (12x div (x + 2))) div 3))
A157319: 0 3 6 7 9 10 12 13 14 15 16 17 18 19 20 21
(3x + ((~1 + ((x mod 5) div 2)) mod 3))
A190678: 2 5 6 9 13 17 20 21 24 28 32 35 36 39 43 47
(3x + ((~1 + ((x + (x div 2)) div 4)) mod 3))
A190768: 2 5 8 9 12 15 19 22 26 29 32 33 36 39 43 46
(x + (3 * (x + (((x - (x mod ~3)) div 2) div 2))))
A045750: 0 4 8 12 19 23 27 34 38 42 49 53 57 61 65 69
((x + 1) + ((4 mod (1 + (x div 3))) + (x div 3)))
A061854: 1 2 3 5 6 7 10 11 12 13 14 15 21 22 23 25
compr(\x.((2 * (~2x mod 5)) - (x div 3)),x)
A123122: 0 5 7 10 12 14 15 17 19 20 21 22 24 25 26 27
(x + ((((x + 1) div (1 + (x mod 4))) mod 2) + (x div 3)))
A079111: 1 2 3 5 6 7 8 9 11 13 14 15 17 18 19 20
compr(\x.(((x - ((x div 2) div 5)) mod 2) + (x mod 3)),x)
A274319: 0 6 15 24 33 39 42 48 51 57 60 66 75 84 93 99
(x + (3x div (~2x + 31)))
A295796: 0 1 2 3 4 5 6 8 9 11 12 14 17 20
(x + ((4 * (x - (x div ~4))) div (x + 3)))
A103202: 0 3 4 5 6 8 9 10 11 13 14 15 16 17 18 19
(x + ((1 + (x div (2 + ((x div 2) div 3)))) mod (1 + (x div 2))))
A328119: 0 1 2 3 4 5 9 10 11 13 14 15 16 17 18 19
(x + (2x2 div (13 + (x div 2))))
A053044: 0 1 2 4 6 8 10 13 15 18 21 24 27 30 33 37
(4x4 + 8x3 + 11x2 + x)
A166756: 0 24 174 642 1716 3780 7314 12894 21192 32976 49110 70554 98364 133692 177786 231990
((~x + 1) + compr(\x.(~1 + (x3 mod (2 + (x div 4)))),x))
A010671: 1 1 1 1 1 2 2 2 2 2 6 8
((x + 1) + (x * ((x2 + x + 1) div ((x + 2) + (x div 2)))))
A345890: 1 3 5 10 13 21 25 36 49 64 71 89 97 118 141 166
(x + ((x + 1) * (2 - (7 * (x div ~2)))))
A120276: 2 19 29 67
(x + compr(\x.(1 - (x mod (2 + (x2 mod 6)))),(x + 1)))
A190327: 2 4 6 8 11 13 15 17 19 22 24 27 29 32 34 36
compr(\x.(x mod (x - (64 div (x + 1)))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A004861: 0 1 2 3 4 5 6 7 8 9 10 64 65 66 67 68
(x4 + 3x3 + 8x2 + 9x + 2)
A270868: 2 23 92 263 614 1247 2288 3887 6218 9479 13892 19703 27182 36623 48344 62687
(5x5 + ~3x3 + 2x2)
A134631: 0 4 144 1152 4960 15300 38304 83104 162432 293220 497200 801504 1239264 1850212 2681280 3787200
(4x3 + 13x2 + 20x + 12)
A307921: 12 49 136 297 556 937 1464 2161 3052 4161 5512 7129 9036 11257 13816 16737
compr(\x.((1 + (x2 mod ~13)) mod 2),x)
A028726: 2 5 6 7 8 11
A028739: 2 5 6 7 8 11 15 18 19 20 21 24
compr(\x.((1 + (x2 mod (1 + (2 * (x div (2 + (x mod 2))))))) mod 2),x)
A337140: 2 4 5 6 8 10 12 13 14 15 16 17 18 20 22 24
compr(\x.(((x + 3) mod (1 + ((x + 2) div 5))) mod 2),x)
A228373: 0 1 2 3 5 7 8 9 11 12 13 15 17 19 21 22
compr(\x.(2 - (x mod (2 + (x div (1 + (x mod (1 + (x mod 4)))))))),x)
A228651: 4 6 8 9 10 11 12 13 14 16 17 18 20 21 22 23
((x + 2) + ((3x + ~3) div (3 - (x div ~2))))
A225647: 1 3 4 6 7
A061208: 1 3 4 6 7 9 10 11 13 14 15 16 17 18 19 20
compr(\x.(((x + ~1) div (1 + (2 * (~x mod 5)))) mod 2),x)
A074780: 1 2 3 5 6 7 9 13 14 15 17 19 21 23 25 26
compr(\x.((1 + (x mod (2 + (3 * ((x + ~1) mod 4))))) mod 2),x)
A154611: 1 3 5 6 7 9 11 12 13 15 16 17 18 19 20 21
(x + ((7 * (6 + (x div 2))) div 2))
A295747: 21 22 26 27 32
compr(\x.((x + ~1) mod (x - ((x + 1) mod 14))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A048337-A048324-A048310-A029958: 0 1 2 3 4 5 6 7 8 9 10 11 12 14 28 42
(x + ((1 + (((1 - ((x + ~1) div 3)) mod (x + 1)) div 2)) div 2))
A236562: 0 1 2 3 4 5 6 9 10 11 12 14 15 16 17 18
compr(\x.(~2 + (x mod (1 + (2 * (x mod (2 * (1 + (x mod 3)))))))),x)
A020756: 0 1 2 3 4 6 7 9 10 11 12 13 15 16 18 20
(x + (2 * (1 + (2 * (2 + ((~1 + ((~x + 1) div 2)) mod 4))))))
A004463: 22 23 20 21 18 19 16 17 30 31 28 29 26 27 24 25
compr(\x.((x mod 9) - (x mod 10)),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A032864-A023791: 0 1 2 3 4 5 6 7 8 9 18 19 27 28 29 36
compr(\x.(((x * ((x + 1) - ((x div 2) mod 2))) div 5) mod 2),x)
A233524: 0 1 2 4 5 8
A010440: 0 1 2 4 5 8 9 10 11 13 16 18 19 20 21 22
((x + 1) - (((x div 2) - (x2 div (3 + (x div 2)))) div 2))
A332076: 1 2 3 5 6 8 9 11 12 14 15 17 18 20 21 24
(x + ((3 * (x - (x mod 13))) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A004852: 0 1 2 3 4 5 6 7 8 9 10 11 12 32 33 34
(x + ((3 * (2 - ((~x + 2) div 7))) div 2))
A296095: 3 4 5 7 8 9 10 11 12 13 16 17 18 19 20 21
compr(\x.(1 - (x mod (2 + ((x div ~7) mod 3)))),x)
A336591-A268335-A162644-A072510-A036537: 1 2 3 5 6 7 8 10 11 13 14 15 17 19 21 22
(~x + ((x2 + 1) div 2) - ((3 * (x div 4)) div 2))
A127944: 0 0 0 2 3 7 11 17 21 29 37 47 56 68 80 94
(x + ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2))
A138083: 0 1 2 4 5 6
A007238: 0 1 2 4 5 6 7 10 11 12 13 15 16 17 18 22
(x + ((2 - ((~x + 1) div (2 + (x div 2)))) * ((x mod 3) div 2)))
A319053: 0 1 5 3 4 8 6 7 12 9 10 15 12 13 18 15
compr(\x.((1 + ((x + ((x div 2) div 7)) div 2)) mod 2),x)
A190670: 2 3 6 7 10 11 14 17 18 21 22 25 26 28 29 32
(x + ((x2 + ~x) div (~2x + 34)))
A067570: 0 1 2 3 4 5 7
A063487: 0 1 2 3 4 5 7 9 11 13 16 20 25
compr(\x.(((1 + (x mod ~9)) div (x + 1)) mod 2),x)
A131959: 1 2 3 8
A309017: 1 2 3 8 9 17 18 26 27
compr(\x.(((2 * (2 - (x mod ~5))) div (x + 1)) mod 2),x)
A325413: 0 1 3 5 8 9 10 12 13 14 15 16 17 18 19 20
(x + ((x - ((2 + ((x + ~2) mod 5)) mod (x + 1))) div 2))
A023776: 0 1 2 3 4 5 6 9 10 11 12 13 17 18 19 20
(x + (((1 + ((x div 4) mod 2) - (x div 2)) mod (x + 1)) div 2))
A158573: 0 1 2 3 4 5 9 10 11 12 13 15 16 18 19 20
(x + (2 * ((5x + 4) + (4 div (x + 1)))))
A006616: 16 23 32 43 52
(x + (((x2 + 3x + 2) + ((~1 + (x div 2)) * (x div 2))) div 2))
A058759: 1 4 8 13
A265382: 1 4 8 13 20 27 37 46 59 70 86 99 118 133 155 172
(x + ((((x + 1) - ((x div 2) mod ~5)) div 2) div 2))
A039175: 0 1 3 5 6 7 8 9 10 11 12 14 16 17 18 19
(x + ((x - ((2 - ((~x + 2) mod 7)) div 2)) div 2))
A192225: 0 1 2 5
A210449: 0 1 2 5 7 8 9 10 12 13 16 17 18 20 21 22
(x + (4 * (1 + (2 * (2x - ((x div 4) mod 2))))))
A161444: 4 21 38 55 64 81 98 115 140 157 174 191 200 217 234 251
compr(\x.(2 - (x mod (2 * (2 + (((x + ~1) * (x div 2)) mod 3))))),x)
A028765: 2 3 5 6 7 8 10 11 14 15 18 19 20 21 22 23
compr(\x.(1 - (x mod (2 + (((x * (x mod 2)) div 2) mod 6)))),x)
A005763: 1 5 7 9 11 13 17
A339910-A303578: 1 5 7 9 11 13 17 19 21 23 25 29 31 33 37 41
(x + ((((x2 + ~2x) div (x + 2)) + ((x mod 3) mod 2)) div 2))
A065896: 0 1 2 3 5 6 7 9 10 11 13 14 16 18 19 20
(x + (4 * (1 + ((x + ((x div 2) div 5)) div 2))))
A327311: 4 5 10 11 16 17 22 23 28 29 34 39 40 45 46 51
(x + ((((1 + (((x + 2) * ((x + 1) div 2)) div 2)) div 2) div 2) div 2))
A211264: 0 1 2 3 4 6 7 9 10 12 13 16 17 19 21 23
compr(\x.(2 - (x mod (4 + ((~x2 + 2x) mod 6)))),x)
A285514: 2 3 4 5 6 7 9 10 11 13 14 17 18 19 22 23
(x + (((2 + (x div 8)) * (((x + 1) div 2) div 2)) div 2))
A138083: 0 1 2 4 5 6
A099593: 0 1 2 4 5 6 7 9 11 12 13 15 16 17 18 21
(x + (8 * ((2x mod (1 + (x div 4))) mod 2)))
A264974: 0 1 2 3 4 5 6 7 16 9 10 19 12 13 14 15
compr(\x.(((~x2 + 2) div (2 + ((((x + 1) div 2) div 2) div 2))) mod 2),x)
A152212: 1 3 5 7 11 12 13 15 16 17 19 20 21 23 27 29
(x + ((((x + 2) div 3) - (x div ~7)) div 2))
A131511: 0 2 3 4 5 6 7 9 10 11 13 14 15 16 17 19
compr(\x.(2 + (x div 8) - ((x + 1) mod 8)),x)
A215726: 1 2 3 4 5 6 10 11 12 13 14 19 20 21 22 28
(x - ((~4x2 + 8) div (x + 16)))
A016040: 0 1 3 5 7 10 13 16 19 22 26 29 33 37 40 44
(2x - ((~1 + ((x div 2) + ((~x + 2) div 8))) div 2))
A187835: 1 3 4 7 8 10 12 14 15 17 19 21 23 25 26 28
compr(\x.(((6x + 6) mod (2 + (x div 4))) div 2),x)
A084689: 0 1 2 3 4 5 6 7 9
A131617: 0 1 2 3 4 5 6 7 9 11 14 15 16 17 18 19
(x + (2 * (x + ((x div 4) mod 2) - (x mod 8))))
A059590: 0 1 2 3 6 7 8 9 24 25 26 27 30 31 32 33
(x + (((((x + 2) * ((1 - (x div 2)) div 3)) div 2) div 2) div 2))
A189579: 0 1 2 3 3 4 5 5 6 7 7 7 8 9 10 10
(x + (((x - (((x mod 6) - (x div 2)) div 2)) div 2) div 2))
A039107: 0 1 2 3 4 6 8 9 10 11 12 13 15 17 18 19
(x + ((((x2 + 3x + 2) div 2) + ((x + 2) mod 4)) div 2))
A011980: 1 4 5 8 12 17 20
compr(\x.((16 mod (~x + ~1)) mod 8),x)
A222010: 0 1 3 7
A309274: 0 1 3 7 11 15 23 31 39 47 55 63 71 79 87 95
((~1 + (2 * (x - (x mod 8)))) mod (x + 8))
A168097: 7 8 9 10 11 12 13 14 15 15 15 15 15 15 15 15
((2x + 4) - ((x2 + 3x + 2) div (x + 8)))
A001690: 4 6 7 9 10 11 12 14 15 16 17 18 19 20 22 23
(x + (8 * (x + (x mod (1 + (x div 8))))))
A178896: 0 9 18 27 36 45 54 63 72 89 90 107 108 125 126 143
(x + ((((x2 + x) div 5) + (x div 4)) div 2))
A025224: 0 1 2 4 6 8 10 13 16 19 22 25 29 32 36 40
(x + ((((x * (1 + (((x + ~1) div 2) div 3))) div 2) div 2) div 2))
A102705: 0 1 2 3 4 5 6 8 10 11 12 13 15 17 19 20
(x2 div ((x + 2) + (((x * ((x + ~2) div 3)) div 2) mod 2)))
A218443: 0 0 1 1 2 3 4 4 6 6 8 9 10 10 12 13
(x + (4 * ((x + 2) + (((x + ~1) mod (1 + (x div 2))) div 2))))
A187227: 8 13 18 23 28 33 38 47 52 57 62 71 76 81 86 95
(x + (((x4 - ((x2 + ~2x) div 2)) div 2) div 2))
A332081: 0 1 6 23 67 159
((x + 2) + ((x + 1) div 2) - (x div (2 + ((x * (x div 2)) mod 2))))
A211390: 2 4 4 6 6 8 8 11 10 12 12 16 14 16 16 20
compr(\x.(1 - (x mod (2 + ((x3 + ~2) mod (x + 4))))),x)
A183213: 1 3 4 5 7 9 10 12 13 14 15 17 19 20 21 22
(x + ((((3 * (x2 div 3)) + (x div 2)) div 2) div 2))
A159325: 0 1 3 5 8 11 15 19 24 30 36 42 49 56 64 73
(x + ((x + ((~x + 2) mod (3 + (x div 4)))) div 4))
A138083: 0 1 2 4 5 6
A255165: 0 1 2 4 5 6 7 9 11 12 13 14 15 16 17 20
(x + ((x + ((x2 - (x div 2)) mod 5)) div 4))
A039176: 0 1 3 4 6 7 8 9 10 11 12 14 15 17 18 19
(x + (((x + 2) + ((~x + 1) mod (1 + (2 * (x div 3))))) div 2))
A184333: 1 2 4 6 7 9 10 13 14 17 18 19 22 23 24 27
(x + (((x + ((x * ((x + ~1) div 3)) div 3)) div 2) div 2))
A211265: 0 1 2 3 5 6 8 9 11 12 15 16 18 20 22 23
((2x + 2) - ((~x2 + 1) div ((x + 2) + (x div 3))))
A186325: 2 4 7 10 13 15 18 21 24 26 29 32 34 37 40 43
(x + ((x - (((~x + 1) * ((x3 + 2x2) div 2)) div 2)) div 2))
A211380: 0 1 5 15 42 94 189 340 572 903 1365 1981 2790 3820 5117 6714
(91x + 64)
A195233: 64 155 246 337 428 519 610 701 792 883 974 1065 1156 1247 1338 1429
compr(\x.(1 - (x mod (2 + ((2 - (x mod 8)) mod (x + 2))))),x)
A020486: 1 3 4 5 7 11 12 13 15 17 19 20 21 23 25 27
(x + ((((9x + 6) div 2) * (x div 2)) div 2))
A195160: 0 1 8 11 25 30 51 58 86 95 130 141 183 196 245 260
(x + ((x2 + ~x) div (~2x + 48)))
A177738: 0 1 2 3 4 5 6 8 9 11 13 15 17 20 23 26
(x + (((x2 + x) + (((x + 1) div 3) mod 4)) div 2))
A152888: 0 2 5 9 14 21 28 36 45 55 66 77 90 104 119 135
(x + (8x2 div (x + 10)))
A130236: 0 1 4 8 13 18 24 30 36 43 50 57 64 71 79 87
((2x + 2) + ((x + ((~x + 4) * (x div 2))) div (x + 2)))
A248637: 2 4 7 8 10 12 14 15 17 19 20 22 23 25 26 28
(1 + (x2 div (x + ((x + 2) * (2 + (x mod 2))))) - (x mod 2))
A025803: 1 0 1 0 2 0 2 1 3 1 3 2 4 2 5 3
(~x + (((x3 + 2x) div 3) + ((~x + 1) * (x div 2))))
A225972: 0 0 1 6 14 32 55 94 140 208 285 390 506 656 819 1022
compr(\x.((((~x + 1) div (1 + ((x div 2) mod 4))) mod 2) - (x mod 2)),x)
A103826: 1 3 5 6 7 9 11 12 13 14 15 17 19 21 22 23
(x + (((x2 + x) div ~8) mod 2) - (x mod 2))
A266154-A266089-A160017: 0 1 3 2 5 4 6 7 9 8 10 11 12 13 15 14
compr(\x.((((2x + ~1) div (2 + (x div 4))) mod 2) - (x mod 2)),x)
A079945: 1 3 4 5 7 9 10 11 12 13 15 17 19 21 22 23
compr(\x.(2 - ((x mod 2) + ((1 - (x div 5)) mod 4))),x)
A188545: 1 3 10
A104702: 1 3 10 11 12 13 14 15 16 17 18 19 21 23 30 31
compr(\x.(x - (x2 mod (x + 36))),x)
A191886: 0 1 2 3 4 5 6 8 9 11 13 14 15 16 17 19
compr(\x.((3x2 + 3x) mod (x + 16)),x)
A169926: 0 2 4 8 14 20 24 29 32 44 56 64 74 104 128 164
(x + ((2x2 + 8) div (x + 16)))
A076521: 0 1 2 4 6 7 9 11 13 15 18 20 22 24 27 29
(2x + (((((x + ~1) div 2) div 5) mod 2) + (x mod 2)))
A026444: 1 3 4 7 8 11 12 15 16 19 20 24 25 28 29 32
((x2 + 2) - ((x div ~2) div (~1 + (2 * (x mod 4)))))
A335892: 2 4 7 12 16 30
(x2 + (15 * (x2 div 4)))
A195048: 0 1 19 39 76 115 171 229 304 381 475 571 684 799 931 1065
(x3 + (((x3 + 3x2 + 2x) div 2) div 3))
A185788: 0 2 12 37 84 160 272 427 632 894 1220 1617 2092 2652 3304 4055
(x3 + ((6x + 4) * (1 + (x mod 2))))
A133784: 4 21 24 71
loop(\(x,i).loop(\(x,i).loop(\(x,i).loop(\(x,i).loop(\(x,i).(x * i),i,x),i,x),i,x),i,x),x,1)
A057528: 1 1 2 96 31850496 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + loop(\(x,i).loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0),2,x)),x,1)
A099627: 1 2 3 4 5 7 8 9 11 15 16 17 19 23 31 32
loop(\(x,i).(x + loop(\(x,i).(x - (if x <= 0 then 1 else i)),x,x)),1,loop(\(x,i).2x,x,1))
A057046: 1 1 1 2 1 4 9 8 3 16 34 32 1 64 94 128
loop(\(x,i).(1 - loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x)),1,loop(\(x,i).2x,x,1))
A057047: 1 2 3 3 6 5 3 9 21 17 12 33 91 65 88 129
loop(\(x,i).(if x <= 0 then 0 else loop(\(x,i).loop(\(x,i).(x * i),i,x),(x + ~2),1)),1,2x)
A296607: 0 1 2 288 24883200 5056584744960000 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.loop(\(x,i).(if x <= 0 then 2 else loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)),2,x),x)
A020904: 2 4 7 9 11 13 16 18 22 24 27 29 31 34 37 39
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).3x,(1 + i),x),i,1)),(x + 1),0)
A178186: 9 252 19935 4802904 3491587305 7629089072292 50039174188071999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(if x <= 0 then 1 else (x * loop(\(x,i).(x * (x - i)),2,(2 + i)))),(x + 1),0)
A010798: 1 120 43200 36288000 60963840000 184354652160000 929147446886400000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,x,2) - (if (x mod 2) <= 0 then loop(\(x,i).2x,(x div 2),2) else 0))
A156232: 0 4 4 16 24 64 112 256 480 1024 1984 4096 8064 16384 32512 65536
loop(\(x,i).(2x + 1),(x + ~1),(if (x + ~1) <= 0 then 1 else (if (x mod 2) <= 0 then 2 else 0)))
A290074: 1 1 5 3 23 15 95 63 383 255 1535 1023 6143 4095 24575 16383
loop(\(x,i).((loop(\(x,i).(x * i),(~1 + i),1) + (x * i)) - (if x <= 0 then 0 else 1)),x,0)
A186760: 0 1 2 7 33 188 1247 9448 80623 765926 8022139 91872328 1142384735 15330003154 220847064955 3399884265524
loop(\(x,i).~x,x,loop(\(x,i).((x * i) - loop(\(x,i).(x * i),(~1 + i),1)),x,0))
A081048: 0 1 ~3 11 ~50 274 ~1764 13068 ~109584 1026576 ~10628640 120543840 ~1486442880 19802759040 ~283465647360 4339163001600
loop(\(x,i).loop(\(x,i).2x,x,loop(\(x,i).(x * (1 + (2 * i))),(~2 + i),1)),x,0)
A048830: 0 1 2 12 61440
(loop(\(x,i).x2,1,(~1 + loop(\(x,i).2x,x,2))) - (if (x + ~1) <= 0 then x else 0))
A270007: 1 8 49 225 961 3969 16129 65025 261121 1046529 4190209 16769025 67092481 268402689 1073676289 4294836225
(if (x + ~1) <= 0 then 1 else loop(\(x,i).(2x + 1),x,loop(\(x,i).(2x + 2),x,0)))
A267812: 1 1 27 119 495 2015 8127 32639 130815 523775 2096127 8386559 33550335 134209535 536854527 2147450879
loop(\(x,i).(4 * ((if x <= 0 then 1 else 2x) - (x div (if i <= 0 then 1 else i)))),x,0)
A069722: 0 4 24 160 1120 8064 59136 439296 3294720 24893440 189190144 1444724736 11076222976 85201715200 657270374400 5082890895360
(loop(\(x,i).(2x + (if x <= 0 then 1 else x)),x,0) + loop(\(x,i).(~2x + 1),x,0))
A140431: 0 2 2 12 22 92 222 772 2102 6732 19342 59732 175782 534172 1588862 4793892
(loop(\(x,i).4x,x,1) - loop(\(x,i).(2x + (if x <= 0 then 1 else x)),x,0))
A318165: 1 3 13
A093834: 1 3 13 55 229 943 3853 15655 63349 255583 1028893 4135255 16600069 66577423 266841133 1068958855
loop(\(x,i).(x + loop(\(x,i).(loop(\(x,i).(x * i),(~1 + i),1) + (x * i)),i,0)),x,0)
A097422: 0 1 4 15 65 339 2103 15171 124755 1151331 11779971 132323811 1618766691 21421525731 304887173091 4644050174691
loop(\(x,i).(~x + loop(\(x,i).(loop(\(x,i).(x * i),(~1 + i),1) + (x * i)),i,0)),x,0)
A330016: 0 1 2 9 41 233 1531 11537 98047 928529 9700111 110843729 1375599151 18427159889 265038487471 4074124514129
loop(\(x,i).(x + loop(\(x,i).(loop(\(x,i).2x,i,1) + (x * i)),(~1 + i),1)),x,0)
A295518: 0 1 4 14 52 220 1092 6388 43588 341444 3022660 29835844 324782916 3864151876 49875956548 694041238340
loop(\(x,i).(x + compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x + ~2),x),i)),x,0)
A053767: 0 4 10 18 27 37 49 63 78 94 112 132 153 175 199 224
loop(\(x,i).2x,x,(1 + (if (x mod 2) <= 0 then loop(\(x,i).2x,(x div 2),2) else 0)))
A098655: 3 2 20 8 144 32 1088 128 8448 512 66560 2048 528384 8192 4210688 32768
(loop(\(x,i).2x,x,2) - loop(\(x,i).2x,(if (x mod 2) <= 0 then (x div 2) else 0),1))
A285543: 1 3 6 15 28 63 120 255 496 1023 2016 4095 8128 16383 32640 65535
(1 + loop(\(x,i).((x + 1) * (if ((if x <= 0 then 1 else x) mod 2) <= 0 then (x + ~1) else 1)),x,0))
A283526: 1 2 3 4 5 16 17 256 257 65536 65537 4294967296 4294967297 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 0 else (1 + loop(\(x,i).2x,(loop(\(x,i).2x,x,2) mod (x + 1)),1)))
A321577: 0 2 5 2 5 17 5 2 257 17 5 17 5 17 257 2
loop(\(x,i).(loop(\(x,i).(x * i),(~1 + i),1) + loop(\(x,i).(x * i),x,1)),(x + ~1),1)
A005604: 1 1 2 3 8 40326
(loop(\(x,i).x2,x,2) - loop(\(x,i).loop(\(x,i).2x,i,x2),(x + ~1),1))
A001320: 1 3 14 240 63488 4227858432 4611686018427387903 4611686018427387903 4611686018427387903
(if (~x + 2) <= 0 then (1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x)) else 1)
A305429-A136548: 1 1 2 3 3 5 5 7 7 7 7 11 11 13 13 13
(1 + loop(\(x,i).(~x + loop(\(x,i).(x + loop(\(x,i).(x * i),i,1)),(1 + i),1)),x,1))
A134316: 2 4 8 28 128 748 5168 41068 368048 3669868 40284848 482671468 6267305648 87660962668 1313941673648 21010450850668
loop(\(x,i).2x,(~1 - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)),1)
A155038: 1 1 1 2 1 1 4 2 1 1 8 4 2 1 1 16
(~1 + loop(\(x,i).loop(\(x,i).(x * i),(x * i),1),x,1) - loop(\(x,i).(x * i),x,1))
A256509: ~1 ~1 ~1 713 4611686018427387903
(if (x mod 2) <= 0 then (if x <= 0 then 1 else (2 + (if (x mod 5) <= 0 then 2 else 0))) else 1)
A280986: 1 1 2 1 2 1 2 1 2 1 4 1 2 1 2 1
(1 + (2 * loop(\(x,i).(if x <= 0 then 1 else (2 * (x - (if (~x + i) <= 0 then 1 else 0)))),x,0)))
A248604: 1 3 5 9 13 21 37 69 133 261 517 1029 2053 4101 8197 16389
(if (x mod 3) <= 0 then (2 * (if (x mod 2) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1)) else 1)
A010125: 4 1 1 2 1 1 8 1 1 2 1 1 8 1 1 2
(1 + (2 * compr(\x.loop(\(x,i).loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0),2,x),(x + 1))))
A261033: 3 5 7 9 13
A224195: 3 5 7 9 13 15 17 25 29 31 33 49 57 61 63 65
loop(\(x,i).(x * i),(loop(\(x,i).(x + loop(\(x,i).(x * i),(x + ~2),1)),x,1) div 2),1)
A167446: 1 1 1 2 6 1307674368000
(if x <= 0 then 1 else (~3 + loop(\(x,i).(x2 + ~2x),1,loop(\(x,i).2x,x,2))))
A269911: 1 5 45 221 957 3965 16125 65021 261117 1046525 4190205 16769021 67092477 268402685 1073676285 4294836221
(~1 + loop(\(x,i).(x * loop(\(x,i).(x - (if x <= 0 then 0 else (~x + i))),x,x)),2x,2))
A096618: 1 12367 4611686018427387903
(if x <= 0 then 1 else loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,3))
A144706: 1 6 18 60 210 756 2772 10296 38610 145860 554268 2116296 8112468 31201800 120349800 465352560
(if x <= 0 then 2 else loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 2 else 0)),x,(2x + 1)))
A224911-A060308-A020482: 2 3 5 7 7 11 13 13 17 19 19 23 23 23 29 31
(if x <= 0 then 1 else loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),(x div 2),(2x + ~1)))
A128059: 1 1 3 5 7 1 11 13 1 17 19 1 23 1 1 29
loop(\(x,i).4x,(if x <= 0 then 1 else (loop(\(x,i).2x,x,2) - (x mod 2))),1)
A138835: 4 64 65536 1073741824 4611686018427387903 4611686018427387903
(1 + (if x <= 0 then 1 else (loop(\(x,i).loop(\(x,i).((x + 2) mod (1 + i)),x,0),x,x) div 2)))
A243036: 2 1 2 1 2 2 4 1 2 2 4 2 4 4 8 1
(~1 + loop(\(x,i).2x,(0 - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)),2))
A130330: 1 3 1 7 3 1 15 7 3 1 31 15 7 3 1 63
loop(\(x,i).x2,1,(~1 + (2 * loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x))))
A237587: 1 9 1 25 9 1 49 25 9 1 81 49 25 9 1 121
(1 + ((if x <= 0 then 1 else (2 - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * i))),x,x))) div 2))
A100144: 1 2 2 4 4 4 4 6 6 6 6 6 6 10 10 10
(~1 + loop(\(x,i).4x,(if x <= 0 then 1 else 2),loop(\(x,i).x3,x,2)))
A253851: 7 127 8191 2147483647 4611686018427387903
(1 + (loop(\(x,i).(x2 + x),1,loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x)) div 2))
A209438: 1 1 1 1 2 1 1 4 2 1 1 7 4 2 1 1
(1 + loop(\(x,i).(x - loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0)),x,3x))
A134660: 1 4 4 4 4 16 4 8 4 16 16 4 4 16 8 16
(1 + loop(\(x,i).(x + (if (x mod 2) <= 0 then (if x <= 0 then 1 else ~2) else 2)),3,x))
A065166: 6 8 4 10 2 12 1 14 3 16 5 18 7 20 9 22
loop(\(x,i).(1 + loop(\(x,i).(x + (x div (if i <= 0 then 1 else (2 * i)))),x,(2 * i))),x,1)
A112557: 1 4 10 18 30 42 58 78 102 118 150 174 210 240 274 322
loop(\(x,i).x2,1,loop(\(x,i).2x,x,loop(\(x,i).(3x + 1),x,1)))
A144843: 1 64 2704 102400 3748096 135675904 4893282304 176265625600 6346852335616 228502162898944 8226263614357504 296147719133593600 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).3x,i,x),x,loop(\(x,i).(3x + 1),x,1))
A203148: 1 12 351 29160 7144929 5223002148 11433166050879 75035879252272080 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 1 else 0)),(x div 2),x)),x,1)
A010063: 1 2 4 6 8 12 14 18 20 24 28 30 32 36 38 42
(~1 + loop(\(x,i).x2,(x + ~2),(if x <= 0 then 1 else (x + (if (x mod 2) <= 0 then x else 1)))))
A076046: 0 1 3 15 4095
loop(\(x,i).(x * i),x,loop(\(x,i).4x,x,loop(\(x,i).(1 + (x * i)),x,1)))
A052140: 1 8 160 6144 399360 40058880 5771427840 1131282432000 289610945003520 93834041307955200 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(if x <= 0 then 0 else (1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2)))),2,x))
A107756: 1 4 5 6 7 10 13 14 15 16 17 18 19 20 21 22
loop(\(x,i).2x,x,loop(\(x,i).(2 * loop(\(x,i).x2,(~1 + i),2x)),x,1))
A067512-A067505: 1 8 512 68719476736 4611686018427387903
loop(\(x,i).(4x + loop(\(x,i).(x + (if (x + ~2) <= 0 then 1 else x)),i,1)),x,1)
A171475: 1 6 27 114 468 1896 7632 30624 122688 491136 1965312 7862784 31454208 125822976 503304192 2013241344
loop(\(x,i).x2,1,loop(\(x,i).(2 * (~2x + (x div (if i <= 0 then 1 else i)))),x,1))
A002894: 1 4 36 400 4900 63504 853776 11778624 165636900 2363904400 34134779536 497634306624 7312459672336 108172480360000 1609341595560000 24061445010950400
loop(\(x,i).x2,2,loop(\(x,i).(2 * (~2x + (x div (if i <= 0 then 1 else i)))),x,1))
A186420: 1 16 1296 160000 24010000 4032758016 728933458176 138735983333376 27435582641610000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,loop(\(x,i).(~2x + 1),x,loop(\(x,i).(~2x + 2),x,1)))
A110241: 1 2 28 152 1456 10592 88768 693632 5614336 44652032 358263808 2861914112 22912086016 183229571072 1466104987648 11727766126592
loop(\(x,i).((x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,i,1))) div 2),x,1)
A002884: 1 1 6 168 20160 9999360 20158709760 163849992929280 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1,(x2 + 2x)))
A057049: 1 1 3 1 4 8 4 9 3 9 1 8 16 6 15 3
(~1 + loop(\(x,i).2x,(if (~x + 2) <= 0 then x else 0),2) - (if (x + ~2) <= 0 then x else 1))
A283591: 1 0 5 14 30 62 126 254 510 1022 2046 4094 8190 16382 32766 65534
loop(\(x,i).(2x + (if loop(\(x,i).(x div (1 + (x mod 2))),x,i) <= 0 then 1 else 0)),x,1)
A267367: 1 3 6 13 26 52 104 209 418 836 1672 3344 6688 13376 26752 53505
loop(\(x,i).loop(\(x,i).(2x + 1),(if (i mod 4) <= 0 then 2 else 0),2x),x,1)
A222011: 1 2 4 8
A018507: 1 2 4 8 67 134 268 536
loop(\(x,i).((x div 2) * i),loop(\(x,i).(2x + 1),x,0),loop(\(x,i).2x,x,1))
A067667: 1 1 3 315 638512875 4611686018427387903 4611686018427387903
(loop(\(x,i).((2x + 1) + (if x <= 0 then 1 else x)),x,0) + loop(\(x,i).2x,x,1))
A090327: 1 4 11 30 83 234 671 1950 5723 16914 50231 149670 446963 1336794 4002191 11990190
(loop(\(x,i).(2x + (if (2 - i) <= 0 then x else 1)),x,2) - loop(\(x,i).2x,x,1))
A084171: 1 3 11 37 119 373 1151 3517 10679 32293 97391 293197 881639 2649013 7955231 23882077
loop(\(x,i).(~1 + loop(\(x,i).4x,i,2)),(x + ~2),loop(\(x,i).2x,x,1))
A233868: 1 2 4 7 31 127 511 2047 8191 32767 131071 524287 2097151 8388607 33554431 134217727
loop(\(x,i).(2x + ~1),(x + (if (x + ~1) <= 0 then x else 2)),loop(\(x,i).2x,x,1))
A273385: 1 5 49 225 961 3969 16129 65025 261121 1046529 4190209 16769025 67092481 268402689 1073676289 4294836225
loop(\(x,i).loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1,(x2 + 3x + 2))
A309714: 1 0 2 5 2 6 1 6 12 5 12 3 11 0 9 19
(if x <= 0 then 2 else loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then i else 0)),(x div 2),(x + 1)))
A151800: 2 2 3 5 5 7 7 11 11 11 11 13 13 17 17 17
((x + 1) * (if x <= 0 then 1 else (x * (~1 + loop(\(x,i).loop(\(x,i).(x * i),x,2),x,1)))))
A071352: 1 2 18 564 4611686018427387903
compr(\x.loop(\(x,i).loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0),2,3x),(x + 1))
A191535-A100598: 1 2 4 5 8 10
A181666: 1 2 4 5 8 10 16 20 21 32 40 42 64 80 84 85
(if (x + ~2) <= 0 then 1 else loop(\(x,i).x2,(x + ~2),loop(\(x,i).(x * i),x,(x + 1))))
A064031: 1 1 1 576 207360000 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 1 else 0)),x,(x + 2)),2,(x + ~1))
A242189: 3 5 5 7 7 11 11 13 13 13 13 17 17 19 19 19
(2x - loop(\(x,i).(x - loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0)),x,(x + ~1)))
A267582: 1 2 3 5 5 9 9 11 9 17 17 19 17 23 21 23
loop(\(x,i).x3,1,(1 + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)))
A133820: 1 1 8 1 8 27 1 8 27 64 1 8 27 64 125 1
loop(\(x,i).(((x + 1) div 2) + i),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1)
A092080: 1 1 2 1 2 3 1 2 3 5 1 2 3 5 7 1
loop(\(x,i).(~x + (if x <= 0 then 1 else ((if x <= 0 then 1 else ~2) * (1 + (2 * i))))),x,1)
A132899: 1 ~7 8 ~22 23 ~45 46 ~76 77 ~115 116 ~162 163 ~217 218 ~280
loop(\(x,i).(x * loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A263394: 1 5 95 6175 1302925 866445125 1784010512375 11248186280524375 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + loop(\(x,i).((2x div (if i <= 0 then 1 else i)) * (2 + i)),i,1)),x,1)
A102841: 1 5 19 61 179 493 1299 3309 8211 19949 47635 112109 260627 599533 1366547 3089901
loop(\(x,i).4x,(0 - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)),1)
A262616: 1 4 1 16 4 1 64 16 4 1 256 64 16 4 1 1024
loop(\(x,i).3x,(0 - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)),1)
A140303: 1 3 1 9 3 1 27 9 3 1 81 27 9 3 1 243
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).3x,i,1))),x,1)
A028665: 1 6 432 303264 1965150720 115562653240320 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(loop(\(x,i).(x * i),i,1) + (x * (1 + i))),i,1)),x,1)
A126675: 1 3 33 1650 452100 797504400 10421787499200 1142061161312332800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).(x + (i * i * i)),(1 + i),x),i,1)),x,1)
A101094: 1 11 57 203 574 1386 2982 5874 10791 18733 31031 49413 76076 113764 165852 236436
(if x <= 0 then 0 else (~1 - loop(\(x,i).(x - (if x <= 0 then 1 else (1 + (i * i)))),x,x)))
A228423: 0 0 0 4 4 4 4 4 13 13 13 13 13 13 13 13
loop(\(x,i).(x + loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),i,2)),x,1)
A054113: 1 5 17 57 197 701 2549 9413 35153 132393 501905 1912769 7321081 28122281 108355481 418590521
loop(\(x,i).(x + (if (x + ~2) <= 0 then 1 else (x + (if (x mod (1 + i)) <= 0 then 2 else 0)))),x,1)
A259098: 1 2 3 6 12 26 52 104 208 416 832 1664
loop(\(x,i).(x + loop(\(x,i).(2x + 1),(if (x mod (1 + i)) <= 0 then x else 0),x)),x,1)
A018397: 1 2 4 83 166 332
loop(\(x,i).(x + (x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).x2,i,2)))),x,1)
A260982: 1 13 3133 204525373 878416384666881853 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(x * loop(\(x,i).(2x + ~1),(x + ~2),x)),1,i)),x,1)
A116757: 1 2 6 21 73 238 724 2075 5667 14892 37942 94273 229453 548954 1294440 3014775
loop(\(x,i).x2,1,loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,1))
A288876: 1 25 225 1225 4900 15876 44100 108900 245025 511225 1002001 1863225 3312400 5664400 9363600 15023376
loop(\(x,i).(x - i),x,loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,1))
A086274: 1 4 12 29 60 111 189 302 459 670 946 1299 1742 2289 2955 3756
loop(\(x,i).(x + ((x * loop(\(x,i).x2,2,3)) div (if i <= 0 then 1 else i))),x,1)
A017745: 1 82 3403 95284 2024785 34826302 504981379 6348337336 70625252863 706252528630 6426898010533 53752237906276 416579843773639 3012192716517082 20439879147794485 130815226545884704
loop(\(x,i).(x + ((x * loop(\(x,i).(x2 + 2x),2,2)) div (if i <= 0 then 1 else i))),x,1)
A017744: 1 81 3321 91881 1929501 32801517 470155077 5843355957 64276915527 635627275767 5720645481903 47325339895743 362827605867363 2595612872743443 17427686431277403 110375347398090219
loop(\(x,i).loop(\(x,i).(4 * (2x - (x div (if i <= 0 then 1 else i)))),i,x),x,1)
A203517: 1 4 96 15360 17203200 138726604800 8203736501452800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).~x,x,loop(\(x,i).(loop(\(x,i).(x * i),(~1 + i),1) + (x * i)),x,1))
A081046: 1 ~2 5 ~17 74 ~394 2484 ~18108 149904 ~1389456 14257440 ~160460640 1965444480 ~26029779840 370643938560 ~5646837369600
loop(\(x,i).(loop(\(x,i).(loop(\(x,i).2x,i,1) + (x * i)),i,1) + (x * i)),x,1)
A081923: 1 4 18 92 536 3552 26608 223456 2085504 21450752 241320704 2949474816 38933066752 552141672448 8374148696064 135274709700608
loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),x,loop(\(x,i).(x * i),x,1))
A212307: 1 1 2 2 8 40 80 560 4480 4480 44800 492800 1971200 25625600 358758400 1793792000
loop(\(x,i).(~x + (if x <= 0 then 2 else (loop(\(x,i).(x div (1 + (x mod 2))),x,x) - i))),x,1)
A215898: 1 ~2 4 ~3 5 ~8 10 ~7 9 ~14 16 ~11 13 ~20 22 ~15
loop(\(x,i).x2,1,loop(\(x,i).loop(\(x,i).(x * ((~1 + (2 * i)) * i)),i,x),x,1))
A271386: 1 1 36 291600 1851776640000 4611686018427387903 4611686018427387903 4611686018427387903
((if x <= 0 then 2 else (1 - loop(\(x,i).((x + ~2) + (x div (if i <= 0 then 1 else i))),x,0))) div 2)
A062430: 1 1 3 5 7 10 13 16 19 22 26 29 33 36 40 44
loop(\(x,i).(x - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * i))),x,x)),1,(2x + 2))
A185870: 3 8 10 17 19 21 30 32 34 36 47 49 51 53 55 68
loop(\(x,i).x2,1,loop(\(x,i).(x + loop(\(x,i).3x,i,x)),(x + ~1),2))
A119600: 4 4 64 6400 5017600 33738342400 2008645953126400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).loop(\(x,i).2x,i,x),x,1) + loop(\(x,i).2x,x2,1)) div 2)
A200564: 1 2 12 288 33280 16793600 34360786944 281475110928384 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 + (loop(\(x,i).2x,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1) div 2))
A221999: 2 2 3 2 3 4 2 3 4 6 2 3 4 6 10 2
((loop(\(x,i).x2,1,loop(\(x,i).(~2x + (if x <= 0 then 1 else 2)),x,2)) div 2) div 2)
A068941: 1 1 6 16
A083885: 1 1 6 16 72 256 1056 4096 16512 65536 262656 1048576 4196352 16777216 67117056 268435456
(if x <= 0 then 1 else (~4 + loop(\(x,i).(x2 + ~2x),1,loop(\(x,i).2x,x,2))))
A269907: 1 4 44 220 956 3964 16124 65020 261116 1046524 4190204 16769020 67092476 268402684 1073676284 4294836220
loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,(if x <= 0 then 1 else 4))
A146534: 1 8 24 80 280 1008 3696 13728 51480 194480 739024 2821728 10816624 41602400 160466400 620470080
loop(\(x,i).loop(\(x,i).x2,2,x3),1,loop(\(x,i).(x * i),(x + 2),2))
A114967: 16777216 8916100448256 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).2x,x,1),(x + ~2),(if x <= 0 then 1 else (4 - (x mod 2))))
A001695: 1 3 4 8 65536
(2 * (~x + loop(\(x,i).(x + loop(\(x,i).(2 + (if (~x + i) <= 0 then 0 else x)),i,1)),x,0)))
A266538: 0 2 4 10 12 18 28 42 44 50 60 74 92 114 140 170
((~x + loop(\(x,i).(x + loop(\(x,i).(2 + (if (~x + i) <= 0 then 0 else x)),i,1)),x,0)) div 2)
A266540-A266530-A266510: 0 0 1 2 3 4 7 10 11 12 15 18 23 28 35 42
(2x * loop(\(x,i).loop(\(x,i).(x * i),x,(if (x + ~2) <= 0 then x else 1)),1,(x + ~1)))
A052645: 0 0 4 24 48 240 1440 10080 80640 725760 7257600 79833600 958003200 12454041600 174356582400 2615348736000
(2 * (x + loop(\(x,i).(x - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,i)),x,1)))
A212014: 2 6 8 14 18 20 28 34 38 40 50 58 64 68 70 82
(2 + loop(\(x,i).(if x <= 0 then 0 else (1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2)))),2,x))
A028726: 2 5 6 7 8 11
A170944-A074940: 2 5 6 7 8 11 14 15 16 17 18 19 20 21 22 23
(if x <= 0 then 3 else loop(\(x,i).(2 * (~2x + (x div (if i <= 0 then 1 else i)))),x,2))
A217477: 3 ~4 12 ~40 140 ~504 1848 ~6864 25740 ~97240 369512 ~1410864 5408312 ~20801200 80233200 ~310235040
(loop(\(x,i).(0 - ((x + 1) * (if x <= 0 then 1 else 2))),x,1) mod loop(\(x,i).2x,x,2))
A278755: 1 0 3 8 7 48 15 224 31 960 63 3968 127 16128 255 65024
loop(\(x,i).x2,1,loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 1 else 0)),x,(x + 2)))
A093867: 4 9 25 25 49 49 121 121 121 121 169 169 289 289 289 289
(if x <= 0 then 1 else compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x),2x))
A175228: 1 4 8 10 14 16 20 22 25 27 30 33 35 38 40 44
loop(\(x,i).(x + (if x <= 0 then 1 else (if (i mod 2) <= 0 then 1 else 2x))),(x + ~1),(x mod 2))
A120463: 0 1 1 4 6 13 21 40 66 121 201 364 606 1093 1821 3280
loop(\(x,i).2x,x,(1 - loop(\(x,i).(~2x + (if x <= 0 then 2 else 0)),x,(x mod 2))))
A266846: 1 6 20 104 336 1696 5440 27264 87296 436736 1397760 6989824 22368256 111845376 357908480 1789558784
loop(\(x,i).(x2 + ~x),1,loop(\(x,i).(x * (~1 + (if (x * i) <= 0 then x else 0))),x,2))
A298759: 2 6 30 42 1722 1806
loop(\(x,i).(x * (loop(\(x,i).3x,i,1) + loop(\(x,i).2x,i,1))),x,2)
A323715: 2 10 130 4550 441350 121371250 96247401250 222812733893750 1518914406953693750 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * loop(\(x,i).x2,i,x)),2,x2),1,(x2 + 2))
A139571: 1073741824 205891132094649 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (x - ((~x + loop(\(x,i).(x - (2 * (if x <= 0 then 0 else i))),x,x)) div 2)))
A255527: 1 2 3 6 7 8 9 13 14 15 16 17 18 23 24 25
(if x <= 0 then 1 else loop(\(x,i).(2x + (if (~2 + i) <= 0 then 1 else 3x)),x,2))
A141496: 1 5 11 55 275 1375 6875 34375 171875 859375 4296875 21484375 107421875 537109375 2685546875 13427734375
(~x + loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).(x + ((2 + i) * i)),i,x),i,1)),x,0))
A130857: 0 3 17 57 147 322 630 1134 1914 3069 4719 7007 10101 14196 19516 26316
(2x - loop(\(x,i).(x - loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0)),3,x))
A071042: 0 1 3 3 7 7 9 7 15 15 17 15 21 19 21 15
(0 - loop(\(x,i).loop(\(x,i).(x - (if x <= 0 then 1 else (2 * i))),x,x),1,3x))
A168039: 0 4 4 9 9 16 16 25 25 25 25 36 36 36 36 49
(x * (if (x + ~2) <= 0 then 0 else loop(\(x,i).loop(\(x,i).(x * i),(x + ~2),x),1,(x + ~1))))
A052747: 0 0 0 6 12 40 180 1008 6720 51840 453600 4435200 47900160 566092800 7264857600 100590336000
((if x <= 0 then 2 else (1 + (if (x mod 2) <= 0 then 6 else x))) div (if x <= 0 then 1 else x))
A084189: 2 2 3 1 1 1 1 1 0 1 0 1 0 1 0 1
(loop(\(x,i).x3,x,x) - loop(\(x,i).x3,2,(if x <= 0 then 1 else x)))
A058124: ~1 0 0 7625597465304
(~x + loop(\(x,i).loop(\(x,i).(x * i),(x * i),1),x,1) - loop(\(x,i).(x * i),x,1))
A256669: 0 ~1 ~2 711 4611686018427387903
loop(\(x,i).(1 + (if (x + ~2) <= 0 then 0 else loop(\(x,i).(x + (x div 2)),(x + ~1),2))),2,x)
A337434: 1 1 1 10 20 64
(~x + (2 * (x + loop(\(x,i).(x + loop(\(x,i).(~1 + (if x <= 0 then i else x)),i,0)),x,0))))
A261692: 0 1 4 5 12 17 20 21 36 49 60 69 76 81 84 85
(~x + loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then i else 0)),x,(2 * (if x <= 0 then 1 else x))))
A088633: 2 2 3 4 7 6 7 10 9 10 13 12 17 16 15 16
(if x <= 0 then 1 else loop(\(x,i).(x + (2 * (1 + (if (x + ~4) <= 0 then 0 else 2)))),2,x))
A228357: 1 5 6 11 12 17 18 19 20 21 22 23 24 25 26 27
loop(\(x,i).loop(\(x,i).(x + (if x <= 0 then (1 + i) else 0)),x,(~x + 1)),1,(x2 + 2x))
A057050: 1 3 2 6 4 1 7 3 11 6 16 10 3 15 7 21
loop(\(x,i).(0 - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)),1,(x2 + 2x))
A230038: 0 2 1 5 3 0 6 2 10 5 15 9 2 14 6 20
loop(\(x,i).(if x <= 0 then 1 else loop(\(x,i).x2,1,((x * i) div 3))),2x,x)
A275587: 0 1 1 4 46656
compr(\x.(1 - (loop(\(x,i).(1 - loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x)),x,x) div 2)),x)
A020907: 2 5 9 11 14 17 20 24 27 32 35 37 41 44 47 51
loop(\(x,i).(compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x + 2)),x) + i),2,x)
A050435: 9 12 15 16 18 21 24 25 26 28 32 33 34 36 38 39
(if x <= 0 then 2 else compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),(x div 2),~x),x))
A076074-A075643: 2 1 3 5 7 11 13 17 19 23 29 31 37 41 43 47
compr(\x.loop(\(x,i).(if x <= 0 then 2 else (~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x))),2,x),x)
A099628: 2 4 5 8 9 11 16 17 19 23 32 33 35 39 47 64
(x + loop(\(x,i).((x + 1) - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)),2,x))
A063657: 3 7 8 13 14 15 21 22 23 24 31 32 33 34 35 43
compr(\x.loop(\(x,i).((if x <= 0 then 2 else loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 2),2,x),x)
A030130: 0 2 5 6 11 13 14 23 27 29 30 47 55 59 61 62
(x + loop(\(x,i).(x - (if (if (x mod (1 + i)) <= 0 then x else 0) <= 0 then 1 else (~1 + i))),x,x))
A340836: 0 1 3 3 5 5 7 7 9 9 11 11 11 11 15 15
(if (x mod 5) <= 0 then (((x + 1) mod 3) - (if x <= 0 then 0 else 1)) else 0)
A014159: 1 0 0 0 0 ~1 0 0 0 0 1 0 0 0 0 0
(2 - (if x <= 0 then 1 else ((x mod 2) - (if (x mod 7) <= 0 then 1 else 0))))
A342824: 1 1 2 1 2 1 2 2 2 1 2 1 2 1 3 1
(if x <= 0 then 1 else (if (x mod 4) <= 0 then (x div (1 + ((x div 2) mod 3))) else 0))
A239261: 1 0 0 0 1 0 0 0 4 0 0 0 12 0 0 0
((if (((x + 2) div 3) mod 4) <= 0 then 2 else 1) - (if (x + ~1) <= 0 then 1 else 0))
A128522-A124278: 1 0 1 1 1 1 1 1 1 1 2 2 2 1 1 1
(if (x mod 2) <= 0 then loop(\(x,i).(10x + 1),(x div 2),1) else 0)
A287468: 1 0 11 0 111 0 1111 0 11111 0 111111 0 1111111 0 11111111 0
((2 * ((x div 8) + (if x <= 0 then 1 else 2))) + (if (~x + 2) <= 0 then 1 else 0))
A253415: 2 4 5 5 5 5 5 5 7 7 7 7 7 7 7 7
(if (~1 + (x mod 3)) <= 0 then loop(\(x,i).10x,x,1) else 0)
A092804: 1 10 0 1000 10000 0 1000000 10000000 0 1000000000 10000000000 0 1000000000000 10000000000000 0 1000000000000000
(if x <= 0 then 0 else (if (x mod (1 + (x mod (1 + (x div 3))))) <= 0 then (x + 1) else 0))
A145091: 0 2 3 0 5 0 7 0 0 0 0 0 13 0 0 0
loop(\(x,i).(loop(\(x,i).(x * i),(~1 + i),1) + (3x * i)),(x + 1),0)
A274823: 1 7 65
A069015: 1 7 65 786 11814 212772 4468932 107259408 2896044336 86881692960 2867099496480 103215621790080 4025409728814720 169067214837239040 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,loop(\(x,i).(8x + 24),(x + 1),0))
A059158: 24 432 7008 112320 1797504 28760832 460174848 7362800640 117804816384 1884877074432 30158033215488 482528531496960 7720456504049664 123527304064991232 1976436865040252928
loop(\(x,i).(3x + loop(\(x,i).8x,i,1)),(x + 1),0)
A271939: 8 88 776 6424 52040 418264 3351944 26833048 214716872 1717892440 13743611912 109950312472 879606751304 7036866765016 56294972383880 450359893862296
loop(\(x,i).loop(\(x,i).(x + ((i * i * (1 + i)) div 2)),i,~x),(x + 1),0)
A070893: 1 6 19 46 94 172 290 460 695 1010 1421 1946 2604 3416 4404 5592
loop(\(x,i).(x + loop(\(x,i).10x,(2 + i),1)),(x + 1),0)
A161770: 1000 11000 111000 1111000 11111000 111111000 1111111000 11111111000 111111111000 1111111111000
loop(\(x,i).(loop(\(x,i).(x * (2 + i)),(~1 + i),1) + (x * (2 + i))),(x + 1),0)
A001711: 1 7 47 342 2754 24552 241128 2592720 30334320 383970240 5231113920 76349105280 1188825724800 19675048780800 344937224217600 6386713749964800
(loop(\(x,i).(3x + 1),x,0) * loop(\(x,i).(2x + 1),(x + ~1),0))
A059945: 0 0 4 39 280 1815 11284 68859 416560 2509455 15086764 90610179 543928840 3264374295 19588645444 117539063499
(loop(\(x,i).(~2x + 1),x,0) - loop(\(x,i).(3x + ~1),(x + ~1),0))
A094556: 0 1 0 7 8 51 100 407 1008 3451 9500 30207 87208 268451 791700 2402407
((4 * (~1 + loop(\(x,i).(2x + 4),x,4))) + (if x <= 0 then 1 else 0))
A159742: 13 44 108 236 492 1004 2028 4076 8172 16364 32748 65516 131052 262124 524268 1048556
(loop(\(x,i).(10x + ~6),x,2) + (if x <= 0 then 1 else 0))
A073550: 3 14 134 1334 13334 133334 1333334 13333334 133333334 1333333334 13333333334 133333333334 1333333333334 13333333333334 133333333333334 1333333333333334
(if (x mod 9) <= 0 then loop(\(x,i).(x * (~1 + (2 * i))),x,1) else 0)
A271769: 1 0 0 0 0 0 0 0 0 34459425 0 0 0 0 0 0
(if (x mod 10) <= 0 then loop(\(x,i).(x * (~1 + (2 * i))),x,1) else 0)
A271770: 1 0 0 0 0 0 0 0 0 0 654729075 0 0 0 0 0
(if (~x + 2) <= 0 then (if ((x + 1) mod (1 + (x div 5))) <= 0 then 1 else 2) else 0)
A055734: 0 0 1 1 1 1 2 1 2 1 2 1 2 2 1 1
(1 - (if (if x <= 0 then 1 else (x mod (1 + (((x + 1) div 2) div 3)))) <= 0 then 2 else 0))
A064179: 1 ~1 ~1 ~1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 1 ~1
(if x <= 0 then 1 else (if (x mod (1 + ((1 + (x div 2)) div (1 + (x mod 2))))) <= 0 then 2 else 0))
A260671: 1 2 0 0 2 0 0 0 0 2 0 0 0 0 0 2
(if x <= 0 then 1 else (if ((x3 + 1) mod 7) <= 0 then 2 else 0))
A028928: 1 0 0 2 0 2 2 0 0 0 2 0 2 2 0 0
(1 - (if x <= 0 then 1 else (if ((x + ~2) mod (1 + ((~x + 2) mod 4))) <= 0 then 2 else 0)))
A011609: 0 1 ~1 1 1 1 ~1 1 ~1 1 ~1 1 1 1 ~1 1
(if x <= 0 then 1 else (if (x mod 9) <= 0 then (4x + 2) else 0))
A023930: 1 0 0 0 0 0 0 0 0 38 0 0 0 0 0 0
(if x <= 0 then 1 else (if (x mod 10) <= 0 then (4x + 2) else 0))
A023932: 1 0 0 0 0 0 0 0 0 0 42 0 0 0 0 0
(if (~x + 2) <= 0 then (if (x - (x2 mod (x + 8))) <= 0 then 1 else 2) else 0)
A113971: 0 0 1 1 1 1 1 2 2 1 1 2 2 2 1 1
(if x <= 0 then 1 else (if (x mod 13) <= 0 then (2x + 2) else 0))
A023925: 1 0 0 0 0 0 0 0 0 0 0 0 0 28 0 0
(if x <= 0 then 1 else (if (x mod 11) <= 0 then (2x + 2) else 0))
A023923: 1 0 0 0 0 0 0 0 0 0 0 24 0 0 0 0
(1 - (if x <= 0 then 1 else (if ((x * ((x + 1) div 2)) mod 6) <= 0 then 2 else 0)))
A011623: 0 1 1 ~1 1 1 ~1 1 1 1 1 ~1 ~1 1 1 ~1
(1 - (if x <= 0 then 1 else (if ((x + ~2) mod (2 + (((x + ~1) div 2) mod 2))) <= 0 then 2 else 0)))
A011631: 0 1 ~1 1 1 1 ~1 1 ~1 1 ~1 ~1 1 1 ~1 1
(1 - (if x <= 0 then 0 else (if (x mod (2 + ((~x + 2) mod 8))) <= 0 then 2 else 0)))
A269529: 1 1 ~1 1 1 1 ~1 1 ~1 ~1 ~1 1 1 1 1 ~1
loop(\(x,i).(x + i),(2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)),0)
A144519: 6 15 28 66 91 153 190 276 435 496 703 861 946 1128 1431 1770
loop(\(x,i).(x + i),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),0)
A034953: 3 6 15 28 66 91 153 190 276 435 496 703 861 946 1128 1431
(loop(\(x,i).4x,x,1) - loop(\(x,i).(3x + ~2),2x,0))
A155620: 1 12 96 792 6816 60072 535536 4799352 43112256 387682632 3487832976 31385253912 282446313696 2541932937192 22877060890416 205892205836472
loop(\(x,i).x2,1,loop(\(x,i).(10x + 6),x,0))
A075415: 0 36 4356 443556 44435556 4444355556 444443555556 44444435555556 4444444355555556 444444443555555556 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,loop(\(x,i).(15x + 1),x,0))
A260865: 0 1 256 58081 13075456 2942086081 661970995456 148943498386081 33512287502995456 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((4x + 1) - loop(\(x,i).(2 * (x - (i mod 2))),i,1)),x,0)
A109765: 0 1 5 23 97 399 1617 6511 26129 104687 419089 1677039 6709521 26840815 107368721 429485807
loop(\(x,i).x2,1,loop(\(x,i).(10x + 3),x,0))
A075412: 0 9 1089 110889 11108889 1111088889 111110888889 11111108888889 1111111088888889 111111110888888889 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,loop(\(x,i).(10x + ~7),x,0))
A075416: 0 49 5929 603729 60481729 6049261729 604937061729 60493815061729 6049382595061729 604938270395061729 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(3x + ~3),x,1) + loop(\(x,i).(4x + 1),x,0))
A162725: 1 1 2 9 46 221 1002 4369 18566 77541 320002 1309529 5326686 21572461 87087002 350739489
(loop(\(x,i).(3x + ~1),x,1) + loop(\(x,i).(4x + 1),x,0))
A188545: 1 3 10
A085282: 1 3 10 35 126 463 1730 6555 25126 97223 379050 1486675 5858126 23166783 91869970 365088395
(loop(\(x,i).5x,x,1) - loop(\(x,i).(4x + 1),x,0))
A155485: 1 4 20 104 540 2784 14260 72664 368780 1865744 9416100 47430024 238548220 1198333504 6014037140 30159664184
loop(\(x,i).x2,1,loop(\(x,i).(13x + ~1),x,0))
A260863: 0 1 196 33489 5664400 957345481 161792190756 27342890695849 4620948663553600 780940325907974961 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,loop(\(x,i).(11x + 1),x,0))
A260861: 0 1 144 17689 2143296 259371025 31384248336 3797497946089 459497294348544 55599173087763361 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,x,1) - loop(\(x,i).(7x + ~6),x,0))
A155590: 1 8 52 350 2416 16838 117712 823670 5765056 40354118 282476272 1977328790 13841291296 96889018598 678223089232 4747561542710
loop(\(x,i).x2,1,loop(\(x,i).(14x + 1),x,0))
A260864: 0 1 225 44521 8732025 1711559641 335466848025 65751518430361 12887297839395225 2525910379700086681 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + x),1,loop(\(x,i).(10x + 1),x,0))
A186194: 0 2 132 12432 1235432 123465432 12345765432 1234568765432 123456798765432 12345679098765432 1234567902098765432 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).4x,(x + ~1),loop(\(x,i).(~1 + (2 * (x + (i mod 2)))),x,0))
A091904: 0 1 4 48 320 2816 21504 176128 1392640 11206656 89391104 716177408 5725224960 45818576896 366481506304 2932120485888
(loop(\(x,i).3x,x,1) - loop(\(x,i).(~1 + (2 * (x + (i mod 2)))),x,0))
A093833: 1 2 8 24 76 232 708 2144 6476 19512 58708 176464 530076 1591592 4777508 14337984
(loop(\(x,i).(x + (2 * (x + (i mod 2)))),x,0) - loop(\(x,i).(2x + 1),x,0))
A140420: 0 1 3 13 45 151 483 1513 4665 14251 43263 130813 394485 1187551 3570843 10728913
(loop(\(x,i).7x,x,1) - loop(\(x,i).(2x + 1),x,0))
A155598: 1 6 46 336 2386 16776 117586 823416 5764546 40353096 282474226 1977324696 13841283106 96889002216 678223056466 4747561477176
(loop(\(x,i).(3x + 1),x,4) * loop(\(x,i).(2x + 1),x,0))
A253512: 0 13 120 847 5460 33883 206640 1249807 7528620 45260803 271831560 1631788567 9793126980 58765944523 352617206880 2115767844127
(loop(\(x,i).(4x + 2),x,0) - loop(\(x,i).(3x + 1),x,0))
A081674: 0 1 6 29 130 561 2366 9829 40410 164921 669526 2707629 10919090 43942081 176565486 708653429
loop(\(x,i).((x3 + x2) div 2),1,loop(\(x,i).(3x + 1),x,0))
A152257: 0 1 40 1183 32800 893101 24180520 653473003 17649155200 476575627801 12867977828200 347439324082423 9380897054183200 253284538196972101 4611686018427387903 4611686018427387903
loop(\(x,i).5x,(x + ~1),loop(\(x,i).(3x + 1),x,0))
A304723: 0 1 20 325 5000 75625 1137500 17078125 256250000 3844140625 57664062500 864970703125 12974609375000 194619384765625 2919291992187500 43789385986328125
loop(\(x,i).((x + 1) * (if (16 mod (x + 1)) <= 0 then 2 else 1)),x,0)
A053754: 0 2 3 8 9 10 11 12 13 14 15 32 33 34 35 36
loop(\(x,i).((~x + 1) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,0)
A008347: 0 2 1 4 3 8 5 12 7 16 13 18 19 22 21 26
(loop(\(x,i).3x,x,3) - loop(\(x,i).(2x + 6),x,0))
A245023: 3 3 9 39 153 543 1809 5799 18153 55983 171009 519159 1569753 4733823 14250609 42850119
loop(\(x,i).(3x2 + 3x + 1),1,loop(\(x,i).(2x + 2),x,0))
A169727: 1 19 127 631 2791 11719 48007 194311 781831 3136519 12564487 50294791 201252871 805158919 3220930567 12884312071
(loop(\(x,i).(2 * ((x + 1) + (x div 2))),x,1) - loop(\(x,i).(2x + 2),x,0))
A168605: 1 2 8 30 104 342 1088 3390 10424 31782 96368 291150 877544 2640822 7938848 23849310
(loop(\(x,i).4x,x,1) - loop(\(x,i).(5x + ~4),x,0))
A155616: 1 8 40 188 880 4148 19720 94508 456160 2215268 10814200 53022428 260917840 1287811988 6371951080 31591319948
(loop(\(x,i).3x,x,1) - loop(\(x,i).(5x + ~4),x,0))
A155603: 1 7 33 151 705 3367 16353 80311 397185 1972807 9824673 49005271 244672065 1222297447 6108298593 30531927031
(~1 + loop(\(x,i).3x,x,4) - loop(\(x,i).(2x + 4),x,0))
A169650: 3 7 23 79 263 847 2663 8239 25223 76687 232103 700399 2109383 6344527 19066343 57264559
loop(\(x,i).2x,x,(1 - loop(\(x,i).(x - (2 * (~2x + (i mod 2)))),x,0)))
A279085: 1 6 44 424 4176 41696 416704 4166784 41666816
loop(\(x,i).(~4x + loop(\(x,i).6x,(~1 + i),1)),x,0)
A051958: 0 1 2 28 104 880 4256 29632 161408 1033984 5941760 36699136 216000512 1312780288 7809572864 47125872640
loop(\(x,i).(4x + loop(\(x,i).3x,(~2 + (2 * i)),1)),x,0)
A016153: 0 1 13 133 1261 11605 105469 953317 8596237 77431669 697147165 6275373061 56482551853 508359743893 4575304803901 41178011670565
loop(\(x,i).(x * ((x + 1) + (x div 2))),1,loop(\(x,i).(3x + 2),x,0))
A109774: 0 8 104 1040 9680 88088 795704 7170080 64556960 581091368 5230058504 47071235120 423643241840 3812795553848 34315179116504 308836669444160
(loop(\(x,i).8x,x,1) + loop(\(x,i).(3x + 2),x,0))
A155606: 1 10 72 538 4176 33010 262872 2099338 16783776 134237410 1073800872 8590111738 68720008176 549757408210 4398051294072 35184386437738
(loop(\(x,i).8x,x,1) - loop(\(x,i).(3x + 2),x,0))
A155613: 1 6 56 486 4016 32526 261416 2094966 16770656 134198046 1073682776 8589757446 68718945296 549754219566 4398041728136 35184357739926
(loop(\(x,i).5x,x,1) - loop(\(x,i).(3x + 2),x,0))
A155610: 1 3 17 99 545 2883 14897 75939 384065 1933443 9706577 48650979 243609185 1219108803 6098732657 30503229219
loop(\(x,i).(2 * (x + (4 * (if (x + ~1) <= 0 then 8 else x)))),x,0)
A136957: 0 64 640 6400 64000 640000 6400000 64000000 640000000 6400000000 64000000000 640000000000 6400000000000 64000000000000 640000000000000
loop(\(x,i).(2x + 1),compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),0)
A135630: 0 1 7 31 511 2047 32767 131071 2097151 134217727 536870911 34359738367 549755813887 2199023255551 35184372088831 2251799813685247
(loop(\(x,i).(3x + ~1),(x + ~1),1) - loop(\(x,i).(~2x + 1),x,0))
A094554: 1 0 3 2 19 30 143 322 1179 3110 10183 28842 89939 262990 802623 2380562
loop(\(x,i).(1 + ((x2 + 2x) div 2)),1,loop(\(x,i).(2x + (i mod 2)),x,0))
A241894: 1 2 5 18 61 242 925 3698 14621 58482 233245 932978 3729181 14916722 59655965 238623858
(loop(\(x,i).(3x + 1),x,1) - loop(\(x,i).(2x + (i mod 2)),x,0))
A004054: 1 3 11 35 111 343 1051 3195 9671 29183 87891 264355 794431 2386023 7163531 21501515
loop(\(x,i).(3x + loop(\(x,i).(~1 + (2 * (x + (i mod 2)))),i,0)),x,0)
A094705: 0 1 4 15 50 161 504 1555 4750 14421 43604 131495 395850 1190281 3576304 10739835
loop(\(x,i).(~x + loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),(~1 + i),1)),x,0)
A002741: 0 1 ~1 2 0 9 35 230 1624 13209 120287 1214674 13469896 162744945 2128047987 29943053062
loop(\(x,i).(x + loop(\(x,i).(x + (((2 + (i mod 2)) * i) + i)),(~1 + i),1)),x,0)
A061349: 0 1 6 17 40 75 130 203 304 429 590 781 1016 1287 1610 1975
loop(\(x,i).(x + loop(\(x,i).x2,1,(1 + ((~1 + i) mod 8)))),x,0)
A231685: 0 1 5 14 30 55 91 140 204 205 209 218 234 259 295 344
loop(\(x,i).(loop(\(x,i).(x * (~1 + (2 * i))),i,1) + (x * (1 + (2 * i)))),x,0)
A334670: 0 1 8 71 744 9129 129072 2071215 37237680 741975345 16236211320 387182170935 9995788416600 277792140828825 8269430130712800 262542617405726175
loop(\(x,i).(loop(\(x,i).(x * (i * (1 + i))),(~1 + i),1) + (x * (i * i))),x,0)
A329930: 0 1 6 66 1200 32880 1270080 65862720 4418426880 372523898880 38569208832000 4811724352512000 712008517828608000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(1 + (if ((x div 2) mod 3) <= 0 then (x div 3) else 0)))
A014726: 1 1 1 1 1 1 9 9 1 1 1 1 25 25 1 1
(~1 + (if x <= 0 then 1 else (if (x mod (1 + ((x + 1) div 5))) <= 0 then 2 else 0)))
A165481-A011598: 0 1 1 1 1 ~1 1 ~1 1 1 ~1 ~1 1 ~1 ~1 ~1
(if x <= 0 then 0 else (1 + (if (x mod (1 + (3 * (x mod 4)))) <= 0 then 2 else 0)))
A306346: 0 1 1 1 3 1 1 1 3 1 1 1 3 1 3 1
(~1 + (if x <= 0 then 1 else (if (x - (x2 mod (x + 5))) <= 0 then 2 else 0)))
A011590: 0 1 1 ~1 1 1 ~1 ~1 1 1 1 ~1 ~1 ~1 ~1 ~1
(loop(\(x,i).(x div (2 - (x mod 2))),2,x) div (1 + (if (x mod 3) <= 0 then 2 else 0)))
A051724: 0 1 1 1 1 5 1 7 2 3 5 11 1 13 7 5
loop(\(x,i).(x div (2 - (x mod 2))),x,(x div (1 + (if (x mod 3) <= 0 then 2 else 0))))
A109375-A051712: 0 1 1 1 1 5 1 7 1 3 5 11 1 13 7 5
(if x <= 0 then 0 else (1 - (x mod (1 + (if ((x + ~2) mod 8) <= 0 then 2 else 0)))))
A013595: 0 1 ~1 1 1 1 1 1 1 1 0 1 1 1 1 1
(x * (loop(\(x,i).(x * (x - i)),2,(x + ~2)) * (if (~2 + (x div 2)) <= 0 then 0 else 1)))
A052800: 0 0 0 0 0 0 720 2520 6720 15120 30240 55440 95040 154440 240240 360360
(5 * ((2 + (if x <= 0 then 0 else 2)) * (1 + (if (x mod 2) <= 0 then 2 else 0))))
A040872: 30 20 60 20 60 20 60 20 60 20 60 20 60 20 60 20
(9 * ((if x <= 0 then 1 else 2) * (1 + (if (x mod 2) <= 0 then 2 else 0))))
A040704: 27 18 54 18 54 18 54 18 54 18 54 18 54 18 54 18
(7 * ((if x <= 0 then 1 else 2) * (1 + (if (x mod 2) <= 0 then 2 else 0))))
A040422: 21 14 42 14 42 14 42 14 42 14 42 14 42 14 42 14
(1 + (if (~x + 2) <= 0 then ((if ((x div 2) mod 3) <= 0 then 2 else 1) - (x mod 2)) else 0))
A057217: 1 1 2 1 2 1 3 2 2 1 2 1 3 2 2 1
(1 + loop(\(x,i).((x + 1) + ((if (x + ~4) <= 0 then 1 else x) div 4)),x,0))
A054961: 1 2 3 4 5 6 8 10 13 17
A086736: 1 2 3 4 5 6 8 10 13 17 22 28 35 44 55 69
(1 + (loop(\(x,i).(3x + ~1),x,2) * loop(\(x,i).(2x + 2),x,0)))
A001240: 1 11 85 575 3661 22631 137845 833375 5019421 30174551 181222405 1087861775 6528756781 39177307271 235078159765 1410511939775
(1 + loop(\(x,i).(2 * (2x + loop(\(x,i).3x,(2 * i),2))),x,0))
A166132: 1 37 469 4789 45397 417781 3796885 34319413 309464533 2787540085 25097297941 225913430197 2033371866709 18300950780149 164710972940437 1482408420140341
(1 + loop(\(x,i).(2x + (if (x mod (1 + (x mod 4))) <= 0 then 2 else 0)),x,0))
A077465: 1 3 5 11 21 43 87 173 347 693 1387 2775 5549 11099 22197 44395
(1 + loop(\(x,i).(2x + loop(\(x,i).(2x + 6),(~1 + i),1)),x,0))
A048500: 1 2 11 43 135 375 967 2375 5639 13063 29703 66567 147463 323591 704519 1523719
(1 + loop(\(x,i).(2x + loop(\(x,i).(2x + 8),(~1 + i),1)),x,0))
A048502: 1 2 13 53 169 473 1225 3017 7177 16649 37897 85001 188425 413705 901129 1949705
(1 + loop(\(x,i).(2x + loop(\(x,i).(5x + ~1),i,2)),x,0))
A093953: 1 10 63 344 1781 9030 45403 227524 1138641 5695250 28480343 142409904 712065901 3560362270 17801876883 89009515484
((x + 1) div (1 - (x div (~1 - loop(\(x,i).(if x <= 0 then i else (x div 2)),x,0)))))
A098805: 1 1 1 2 1 1 3 2 1 1 5 4 2 1 1 8
((2 mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1)) + (if x <= 0 then 0 else 1))
A337322-A309307: 0 1 1 1 1 3 1 1 1 3 1 3 1 3 3 1
(if (((~x2 + 4x + ~4) div 3) mod 3) <= 0 then 2 else (if x <= 0 then 0 else 1))
A190592: 0 1 2 1 1 2 2 2 2 1 1 2 1 1 2 2
((2 * loop(\(x,i).(2x + ~1),2x,8)) + (if x <= 0 then 0 else 1))
A292537: 16 59 227 899 3587 14339 57347 229379 917507 3670019 14680067 58720259 234881027 939524099 3758096387 15032385539
(1 + loop(\(x,i).8x,2,loop(\(x,i).(3x + 4),x,0)))
A036549: 1 257 1025 3329 10241 30977 93185 279809 839681 2519297 7558145 22674689 68024321 204073217 612219905 1836659969
(1 + loop(\(x,i).(~x + compr(\x.(loop(\(x,i).(2x + 1),x,0) mod (x + 1)),i)),x,0))
A086910: 1 3 3 5 7 7 11 9 15 15 17 21 21 23 25 29
(1 + (if x <= 0 then 2 else (if ((x + ~1) mod (1 + (4 mod (x + 1)))) <= 0 then 0 else 1)))
A319956: 3 1 2 1 2 2 1 2 2 2 2 1 2 2 2 2
(1 + (x div (1 + loop(\(x,i).(if (x div 2) <= 0 then (1 + (2 * i)) else (x div 2)),x,0))))
A193588: 1 1 2 1 2 3 1 2 3 5 1 2 3 5 8 1
loop(\(x,i).(x * i),(1 + ((x + ~1) mod (1 + (4 * (if x <= 0 then 0 else 2))))),1)
A269221: 1 1 2 6 24 120 720 5040 40320 362880 1 2 6 24 120 720
(1 + (x div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))))
A326139-A325641-A325563-A302042-A302032-A280498-A280497-A280496-A280495-A159353-A079880-A032742: 1 1 1 2 1 3 1 4 3 5 1 6 1 7 5 8
(1 + (loop(\(x,i).(3x + 2),x,0) * (1 + loop(\(x,i).2x,x,1))))
A057009: 1 7 41 235 1361 7987 47321 281995 1685921 10096867 60524201 362972155 2177309681 13062280147 78368930681 470199300715
(~1 + ((1 + loop(\(x,i).3x,x,1)) * (1 + loop(\(x,i).2x,x,1))))
A074528: 3 11 49 251 1393 8051 47449 282251 1686433 10097891 60526249 362976251 2177317873 13062296531 78368963449 470199366251
(1 + (x div (1 + (x mod (1 + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x))))))
A244734: 1 2 3 4 5 2 7 4 3 5 11 6 13 7 3 16
(if (x mod 2) <= 0 then (21 * (if x <= 0 then 1 else 2)) else 1)
A040461: 21 1 42 1 42 1 42 1 42 1 42 1 42 1 42 1
(if (x mod 2) <= 0 then (14 * (2 + (if x <= 0 then 0 else 2))) else 1)
A040811: 28 1 56 1 56 1 56 1 56 1 56 1 56 1 56 1
(if (x mod 2) <= 0 then (27 * (if x <= 0 then 1 else 2)) else 1)
A040755: 27 1 54 1 54 1 54 1 54 1 54 1 54 1 54 1
loop(\(x,i).(x * i),(1 + (if (~1 + (x div 4)) <= 0 then x else 8)),1)
A109834: 1 2 6 24 120 720 5040 40320 362880 362880 362880 362880 362880 362880 362880 362880
loop(\(x,i).(x * i),(~1 + (2 * ((if x <= 0 then 2 else (3x + ~2)) div 2))),1)
A137149: 1 1 6 120 362880 39916800 1307674368000 355687428096000 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if (x + ~2) <= 0 then x else (if (x mod 2) <= 0 then (((x + ~1) div 2) mod 4) else 1)))
A103266: 1 2 3 2 2 2 3 2 4 2 1 2 2 2 3 2
(if (x mod 2) <= 0 then (15 * (2 + (if x <= 0 then 0 else 2))) else 1)
A040929: 30 1 60 1 60 1 60 1 60 1 60 1 60 1 60 1
(1 + ((2 * (1 + loop(\(x,i).(if x <= 0 then i else (x div 2)),x,0))) div 5))
A027293: 1 1 1 2 1 1 3 2 1 1 5 3 2 1 1 7
(if (x mod 2) <= 0 then (25 * (if x <= 0 then 1 else 2)) else 1)
A040649: 25 1 50 1 50 1 50 1 50 1 50 1 50 1 50 1
(if (x mod 4) <= 0 then (10 * (2 + (if x <= 0 then 0 else 2))) else 1)
A040406: 20 1 1 1 40 1 1 1 40 1 1 1 40 1 1 1
loop(\(x,i).loop(\(x,i).2x,x,1),(x - (x2 div (x + 5))),1)
A230874: 1 2 4 4 16 16 16 16 65536 65536 65536 65536 65536 65536 65536 65536
(if x <= 0 then 2 else (1 + (2x mod (if (~x + 2) <= 0 then (x div (2 + (x mod 2))) else 1))))
A069347: 2 1 1 1 1 1 1 1 1 1 1 2 1 3 1 1
(if x <= 0 then 0 else loop(\(x,i).10x,(3x + ~3),1))
A029802: 0 1 1000 1000000 1000000000 1000000000000 1000000000000000 1000000000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (3 * loop(\(x,i).(x2 + x),1,loop(\(x,i).3x,x,1))))
A198410: 7 37 271 2269 19927 177877 1596511 14355469 129159847 1162320517 10460530351 94143710269 847290203767 7625602267957 68630391713791 617673439330669
(1 + ((2 * (1 + (loop(\(x,i).(if x <= 0 then i else (x div 2)),x,0) div 2))) div 3))
A287920: 1 1 1 2 1 1 3 2 1 1 5 3 2 1 1 6
loop(\(x,i).(x * i),((2 * ((x + 1) + (if (x mod 2) <= 0 then x else 2))) div 3),1)
A073475: 1 2 6 24 720 120
(13 * (if (x mod 2) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1))
A040653: 26 13 52 13 52 13 52 13 52 13 52 13 52 13 52 13
(11 * (if (x mod 2) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1))
A040465: 22 11 44 11 44 11 44 11 44 11 44 11 44 11 44 11
(loop(\(x,i).2x,x,2) - loop(\(x,i).2x,(x mod 12),1))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A123464: 1 2 4 8 16 32 64 128 256 512
A138815: 1 2 4 8 16 32 64 128 256 512 1024 2048 8191 16382 32764 65528
(1 + ((2 * (x + loop(\(x,i).(if x <= 0 then (2 * i) else (x + ~1)),x,0))) div 3))
A132171: 1 3 3 3 9 9 9 9 9 9 9 9 9 27 27 27
(1 + ((2 + loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)) div 3))
A263111: 1 2 1 2 1 3 1 4 1 1 1 5 1 6 1 1
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(6x + 1))
A016930: 1 282475249 137858491849 6131066257801 95367431640625 819628286980801 4808584372417849 21611482313284249 79792266297612001 253295162119140625 713342911662882601 1822837804551761449
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(6x + 1))
A016932: 1 13841287201 23298085122481 2213314919066161 59604644775390625 787662783788549761 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((2 * loop(\(x,i).(x - (if (~x + i) <= 0 then (1 + i) else 0)),x,x)) div 3))
A180177: 1 0 1 1 0 1 1 2 0 1 1 2 3 0 1 1
(~1 + (3 * loop(\(x,i).(8x - (if x <= 0 then 0 else 1)),2,x)))
A063354: ~1 164 356 548 740 932 1124 1316 1508 1700 1892 2084 2276 2468 2660 2852
(~1 + loop(\(x,i).2x,x,1) - ((x + (if (x mod 2) <= 0 then x else 2)) mod 3))
A192225: 0 1 2 5
A282153: 0 1 2 5 13 30 63 127 254 509 1021 2046 4095 8191 16382 32765
(1 + (3 * ((x2 + 2x) + loop(\(x,i).2x,x,(if x <= 0 then 1 else 2)))))
A290709: 4 22 49 94 169 298 529 958 1777 3370 6505 12718 25081 49738 98977 197374
(if (x mod 3) <= 0 then 1 else (if (x mod 5) <= 0 then (x + ~3) else 1))
A305567: 1 1 1 1 1 2 1 1 1 1 7 1 1 1 1 1
(if (x mod 3) <= 0 then 0 else loop(\(x,i).5x,(x div 3),1))
A133337: 0 1 1 0 5 5 0 25 25 0 125 125 0 625 625 0
(1 + loop(\(x,i).(x3 + ~2x2),1,loop(\(x,i).3x,x,3)))
A212925: 10 568 18226 518320 14230810 386357608 10450787266 282343443040 7624822644010 205884158525848 5558997804436306 150094070437926160 4052550069287319610 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).x3,x,2) div loop(\(x,i).3x,x,3)))
A234039: 1 1 19 1657009 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).2x,x,2) - ((x + (if (x mod 2) <= 0 then 2 else x)) mod 3))
A130750: 1 3 8 17 33 64 127 255 512 1025 2049 4096 8191 16383 32768 65537
(1 + (3 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,x),x)))
A055246: 1 7 19 25 55 61 73 79 163 169 181 187 217 223 235 241
(x - (x div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))))
A302043-A060681: 0 1 2 2 4 3 6 4 6 5 10 6 12 7 10 8
(if ((x * (x mod 2)) div 2) <= 0 then (1 + (if (~1 + (x mod 3)) <= 0 then x else 2)) else 1)
A326584: 1 2 3 1 5 1 7 1 3 1 11 1 13 1 3 1
(1 + (loop(\(x,i).(3x + 4),x,1) mod (~1 + loop(\(x,i).2x,x,2))))
A297446: 1 2 5 5 25 35 27 185 264 737 1104 3185 5268 15515 29727 55760
loop(\(x,i).4x,x,loop(\(x,i).(4x + 1),(x + 3),1))
A166917: 85 1364 21840 349504 5592320 89478144 1431654400 22906486784 366503854080 5864061927424 93824991887360 1501199874392064 24019198007050240 384307168179912704 4611686018427387903
loop(\(x,i).(1 + loop(\(x,i).10x,2,x)),(2x + 1),1)
A031982: 101 1010101 10101010101 101010101010101 1010101010101010101 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3x + (if (i mod 3) <= 0 then 1 else 0)),(2x + 1),1)
A037665: 3 28 252 2271 20440 183960 1655643 14900788 134107092 1206963831 10862674480 97764070320 879876632883 7918889695948 71270007263532 641430065371791
loop(\(x,i).(x * (~1 + (loop(\(x,i).2x,i,1) + (i mod 2)))),(2x + 1),1)
A090770: 2 48 23040 185794560 24257337753600 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (6x div (if i <= 0 then 1 else i))),(2x + 1),1)
A053128: 7 84 462 1716 5005 12376 27132 54264 100947 177100 296010 475020 736281 1107568 1623160 2324784
loop(\(x,i).(x + (8x div (if i <= 0 then 1 else i))),(2x + 1),1)
A053130: 9 165 1287 6435 24310 75582 203490 490314 1081575 2220075 4292145 7888725 13884156 23535820 38608020 61523748
(loop(\(x,i).2x,x,2) - loop(\(x,i).2x,(x - (x div (1 + (x mod 2)))),1))
A290234: 1 2 7 12 31 56 127 240 511 992 2047 4032 8191 16256 32767 65280
(1 + (if (x + ~2) <= 0 then x else (~1 + loop(\(x,i).(x + (x2 div 3)),x,2))))
A226961: 1 2 3 18 126 5418
(1 + loop(\(x,i).((x + 1) * (if (x mod 3) <= 0 then (2 * (x div 2)) else 1)),x,1))
A283874: 2 3 4 9 10 81 82 6561 6562 43046721 43046722 1853020188851841 1853020188851842 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * i),(1 + compr(\x.((loop(\(x,i).(x * i),x,x) mod (x + 1)) mod 2),x)),1)
A062313: 1 24 720 40320 362880 3628800 479001600 87178291200 1307674368000 20922789888000 6402373705728000 2432902008176640000 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).3x,2x,1) + loop(\(x,i).4x,x,1)))
A074515: 3 14 98 794 6818 60074 535538 4799354 43112258 387682634 3487832978 31385253914 282446313698 2541932937194 22877060890418 205892205836474
(1 + loop(\(x,i).3x,2x,1) - loop(\(x,i).4x,x,1))
A155630: 1 6 66 666 6306 58026 527346 4766586 42981186 387158346 3485735826 31376865306 282412759266 2541798719466 22876524019506 205890058352826
(1 + (loop(\(x,i).6x,x,1) + loop(\(x,i).4x,x,1)))
A074512: 3 11 53 281 1553 8801 50753 296321 1745153 10339841 61514753 366991361 2193559553 13127802881 78632599553 471258726401
(~1 + (loop(\(x,i).6x,x,1) + loop(\(x,i).4x,x,1)))
A155617: 1 9 51 279 1551 8799 50751 296319 1745151 10339839 61514751 366991359 2193559551 13127802879 78632599551 471258726399
(1 + loop(\(x,i).6x,x,1) - loop(\(x,i).4x,x,1))
A155627: 1 3 21 153 1041 6753 42561 263553 1614081 9815553 59417601 358602753 2160005121 12993585153 78095728641 469111242753
(1 + (loop(\(x,i).5x,x,1) + loop(\(x,i).4x,x,1)))
A074511: 3 10 42 190 882 4150 19722 94510 456162 2215270 10814202 53022430 260917842 1287811990 6371951082 31591319950
(1 + loop(\(x,i).5x,x,1) - loop(\(x,i).4x,x,1))
A155626: 1 2 10 62 370 2102 11530 61742 325090 1690982 8717050 44633822 227363410 1153594262 5835080170 29443836302
(1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).10x,x,1)))
A066138: 3 111 10101 1001001 100010001 10000100001 1000001000001 100000010000001 10000000100000001 1000000001000000001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).10x,x,1)))
A168624: 1 91 9901 999001 99990001 9999900001 999999000001 99999990000001 9999999900000001 999999999000000001 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x3,1,(1 + loop(\(x,i).10x,x,1)))
A168575: 8 1331 1030301 1003003001 1000300030001 1000030000300001 1000003000003000001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + 2),1,(~1 + loop(\(x,i).10x,x,1)))
A169601: 2 83 9803 998003 99980003 9999800003 999998000003 99999980000003 9999999800000003 999999998000000003 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x3,1,(~1 + loop(\(x,i).10x,x,1)))
A272066: 0 729 970299 997002999 999700029999 999970000299999 999997000002999999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x3,2,(~1 + loop(\(x,i).10x,x,1)))
A319358: 0 387420489 913517247483640899 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x4 + x3 + x2 + x),1,loop(\(x,i).2x,x,1)))
A020514: 5 31 341 4681 69905 1082401 17043521 270549121 4311810305 68853957121 1100586419201 17600780175361 281543712968705 4504149450301441 72061992352890881 1152956690052710401
(1 + loop(\(x,i).(x4 + ~x3 + x2 + ~x),1,loop(\(x,i).2x,x,1)))
A020518: 1 11 205 3641 61681 1016801 16519105 266354561 4278255361 68585520641 1098438933505 17583600302081 281406274007041 4503049938657281 72053196259835905 1152886321308467201
(1 + (loop(\(x,i).((4x + ~1) - i),x,1) + loop(\(x,i).2x,x,1)))
A243514: 3 5 10 25 76 263 978 3773 14824 58771 234046 934121 3732372 14921279 59668714 238642069
(1 + (loop(\(x,i).7x,x,1) + loop(\(x,i).2x,x,1)))
A074503: 3 10 54 352 2418 16840 117714 823672 5765058 40354120 282476274 1977328792 13841291298 96889018600 678223089234 4747561542712
(1 + (loop(\(x,i).2x,(x div 2),(2 + (x mod 2))) + loop(\(x,i).2x,x,1)))
A183978: 4 6 9 15 25 45 81 153 289 561 1089 2145 4225 8385 16641 33153
((1 + loop(\(x,i).5x,x,1)) * (1 + loop(\(x,i).2x,x,1)))
A034517: 4 18 130 1134 10642 103158 1015690 10078254 100390882 1001953638 10009766650 100048830174 1000244144722 10001220711318 100006103532010 1000030517610894
((~1 + loop(\(x,i).2x,(x + 2),4)) * (1 + loop(\(x,i).2x,x,1)))
A165133: 30 93 315 1143 4335 16863 66495 264063 1052415 4201983 16792575 67139583 268496895 1073864703 4295213055 17180360703
((x + 2) div (1 + loop(\(x,i).(if (x div 2) <= 0 then (1 + (2 * i)) else (x div 2)),x,1)))
A208343: 1 0 2 0 1 3 0 1 2 5 0 1 2 5 8 0
loop(\(x,i).i,(loop(\(x,i).2x,x,(~1 + (~x mod 4))) mod (x + 1)),1)
A166361: 1 1 1 1 4 4 1 1 5 4 1 1
loop(\(x,i).x2,1,loop(\(x,i).(12x + ~6),(x + 1),1))
A127860: 36 4356 617796 88849476 12792967236 1842170994756 265272427798596 38199227257643076 4611686018427387903 4611686018427387903
(if (x + ~1) <= 0 then 2x else (1 + (loop(\(x,i).(x * i),(x + ~2),1) div (x + 1))))
A061545: 0 2 1 1 1 2 4 16
(loop(\(x,i).(x * i),x,1) div ((x + 1) - (loop(\(x,i).(x * i),x,1) mod (x + 1))))
A092043: 1 1 2 3 24 20 720 630 4480 36288 3628800 3326400 479001600 444787200 5811886080 81729648000
loop(\(x,i).(i mod 3),(loop(\(x,i).(x * (2 + i)),4,2) mod (x + 1)),1)
A035160: 1 1 1 1 1 1 0 1 1 1 2 1 2 0 1 1
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(4x + 3))
A016846: 59049 282475249 25937424601 576650390625 6131066257801 41426511213649 205891132094649 819628286980801 2758547353515625 8140406085191601 21611482313284249 52599132235830049 119042423827613001
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(4x + 3))
A016848: 531441 13841287201 3138428376721 129746337890625 2213314919066161 21914624432020321 150094635296999121 787662783788549761 3379220508056640625 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + x),1,loop(\(x,i).10x,(x + 1),1))
A163664: 110 10100 1001000 100010000 10000100000 1000001000000 100000010000000 10000000100000000 1000000001000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 div 2),1,loop(\(x,i).(2x * (1 + (2 * i))),(x + 1),1))
A072477: 18 1800 352800 114307200 55324684800 37399486924800 33659538232320000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,(x + ~2),loop(\(x,i).3x,(x2 + 3x + 2),1))
A255510: 9 729 531441 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~1 + loop(\(x,i).4x,i,1) - (2 * i))),(x + 1),1)
A237187: 1 11 627 154869 156882297 640550418651 10485169802898219 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 2 else (1 + (loop(\(x,i).(4x + 1),(x + ~2),x) div (x + 1))))
A127966: 2 1 1 4 14 57
((x + 1) - loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1)))
A101921: 0 1 4 4 8 9 12 11 16 17 20 20 24 25 28 26
loop(\(x,i).2x,x,(1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A130188: 1 4 4 32 16 64 64 1024 256 1024 1024 8192 4096 16384 16384 524288
loop(\(x,i).2x,(x - (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))),1)
A059991: 1 1 4 1 16 16 64 1 256 256 1024 256 4096 4096 16384 1
(if x <= 0 then 0 else loop(\(x,i).(1 + (2x * (i * (~1 + (2 * i))))),(x + ~1),1))
A051396: 0 1 3 37 1111 62217 5599531 739138093 134523132927 32285551902481 9879378882159187 3754163975220491061 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((4 * (if (~x + 2) <= 0 then x else 2)) - (x mod 3)),(x + ~1),1)
A056120: 1 1 7 27 108 432 1728 6912 27648 110592 442368 1769472 7077888 28311552 113246208 452984832
(if x <= 0 then 0 else loop(\(x,i).(8x * (~1 + (2 * i))),(x + ~1),1))
A052734: 0 1 8 192 7680 430080 30965760 2724986880 283398635520 34007836262400 4625065731686400 703009991216332800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(3x + ~1),x,1) - loop(\(x,i).(2x + 2),(x + ~1),1))
A094734: 0 1 1 4 19 76 271 904 2899 9076 27991 85504 259579 784876 2366911 7125304
(if (x + ~1) <= 0 then (x + 2) else loop(\(x,i).10x,(x + ~1),1))
A155148: 2 3 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000 10000000000
(loop(\(x,i).(3x + ~1),(x + ~1),1) - loop(\(x,i).2x,(x + ~1),1))
A000392: 0 0 0 1 6 25 90 301 966 3025 9330 28501 86526 261625 788970 2375101
(loop(\(x,i).2x,((x2 + ~x) div 2),1) - loop(\(x,i).2x,(x + ~1),1))
A326289: 0 0 0 4 56 1008 32736 2097088 268435328 68719476480 35184372088320 36028797018962944 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + loop(\(x,i).(5x + 1),i,1))),(x + ~1),1)
A015506: 1 1 7 224 35168 27501376 107447876032 2098671914657024 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (x + ~1) <= 0 then 1 else (x4 + ~1))),(x + ~1),1)
A112969: 1 1 2 17 83537 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (x * loop(\(x,i).(6x + 1),i,1))),(x + ~1),1)
A015507: 1 1 8 352 91520 142405120 1328924579840 74403829376081920 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (x * loop(\(x,i).(8x + 1),i,1))),(x + ~1),1)
A015509: 1 1 10 740 433640 2030302480 76034827876000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).((2x * (1 + (2 * i))) div (1 + i)),i,x),(x + ~1),1)
A296590: 1 1 3 30 1050 132300 61122600 104886381600 674943865596000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x + loop(\(x,i).2x,(i - (2x div (1 + i))),1)),x,1))
A260794: 2 3 5 7 11 15 19 27 35 43
(1 + (loop(\(x,i).8x,x,1) + loop(\(x,i).3x,x,1)))
A074510: 3 12 74 540 4178 33012 262874 2099340 16783778 134237412 1073800874 8590111740 68720008178 549757408212 4398051294074 35184386437740
(1 + (loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1)))
A074507: 3 9 35 153 707 3369 16355 80313 397187 1972809 9824675 49005273 244672067 1222297449 6108298595 30531927033
loop(\(x,i).4x,loop(\(x,i).(x * (i - (x div (3 + i)))),x,1),1)
A101407: 4 4 16 4096 281474976710656 4611686018427387903
(1 + loop(\(x,i).(2x2 + ~2x),1,loop(\(x,i).(x * (~2 + (i mod 2))),x,1)))
A171663: 1 5 5 13 25 41 113 145 481 545 1985 2113 8065 8321 32513 33025
(~1 + loop(\(x,i).(x + (9x div (if i <= 0 then 1 else i))),x,1))
A035927: 0 9 54 219 714 2001 5004 11439 24309 48619 92377 167959 293929 497419 817189 1307503
(~1 + loop(\(x,i).(x + (7x div (if i <= 0 then 1 else i))),x,1))
A124090: 0 7 35 119 329 791 1715 3431 6434 11439 19447 31823 50387 77519 116279 170543
(1 + loop(\(x,i).(x4 + x3 + x2 + x),1,loop(\(x,i).(x * i),x,1)))
A259264: 5 5 31 1555 346201 209102521 269112327121 645369332030641 2642973843312270721 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x4 + ~x3 + x2 + ~x),1,loop(\(x,i).(x * i),x,1)))
A260077: 1 1 11 1111 318505 205646281 268365829681 645113283892561 2642842746670654081 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * loop(\(x,i).(if x <= 0 then 1 else (x + (3 * (x + (i mod 2))))),x,0)))
A330795: 1 3 9 39 153 615 2457 9831 39321 157287 629145 2516583 10066329 40265319 161061273 644245095
(if (~x + 2) <= 0 then (2 * (~1 + ((x + (if (x mod 2) <= 0 then 2 else x)) mod 3))) else 1)
A257076: 1 1 0 ~2 ~2 0 2 2 0 ~2 ~2 0 2 2 0 ~2
(1 + (2 * (1 + loop(\(x,i).(x * (if (~1 + i) <= 0 then 2 else (x2 div 2))),x,1))))
A071781: 5 7 11 67 32771
(if x <= 0 then 0 else (if ((x + 2) mod (1 + (4 * (x mod 4)))) <= 0 then 2 else 1))
A174541: 0 1 1 1 2 1 1 1 2 1 1 2 2 2 1 1
((if (x mod 3) <= 0 then 2 else 1) div (if ((x div 3) mod 3) <= 0 then 2 else 1))
A091950: 1 0 0 2 1 1 2 1 1 1 0 0 2 1 1 2
(1 + (2 * ((2 * loop(\(x,i).(x + (if (x - i) <= 0 then x else 0)),x,1)) div 3)))
A098971: 1 3 5 5 11 11 11 11 21 21 21 21 21 21 21 21
loop(\(x,i).2x,(if (x + ~1) <= 0 then x else (2 + ((2 * (x div 2)) div 3))),1)
A048656: 1 2 4 4 8 8 16 16 16 16 32 32 64 64 64 64
loop(\(x,i).(x * i),(if (x + ~1) <= 0 then x else (2 + ((2 * (x div 2)) div 3))),1)
A132369: 1 1 2 2 6 6 24 24 24 24 120 120 720 720 720 720
(5 * ((if x <= 0 then 1 else 2) * (if (x mod 2) <= 0 then 6 else 1)))
A040875: 30 10 60 10 60 10 60 10 60 10 60 10 60 10 60 10
(7 * (if (x mod 2) <= 0 then (3 * (if x <= 0 then 1 else 2)) else 1))
A040425: 21 7 42 7 42 7 42 7 42 7 42 7 42 7 42 7
(7 * (if (x mod 2) <= 0 then (2 * (2 + (if x <= 0 then 0 else 2))) else 1))
A040763: 28 7 56 7 56 7 56 7 56 7 56 7 56 7 56 7
(14 * (if (x mod 2) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1))
A040759: 28 14 56 14 56 14 56 14 56 14 56 14 56 14 56 14
loop(\(x,i).((x + 1) * ((if (x mod 2) <= 0 then 2 else x) div 2)),x,7)
A076602: 7 24 25 312 313 48984 48985 1199765112 1199765113 719718163185951384 719718163185951385 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 2) <= 0 then 2 else (if (~x + 2) <= 0 then ((x2 + 2x) mod 6) else 1))
A214720: 2 1 2 3 2 5 2 3 2 3 2 5 2 3 2 3
(~1 + (2 * (~1 + loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,2))))
A134770: 1 5 21 77 277 1005 3693 13725 51477 194477 739021 2821725 10816621 41602397 160466397 620470077
loop(\(x,i).x2,1,(1 + (2 * ((x + 1) + (if (x + ~4) <= 0 then 1 else 2)))))
A110484: 25 49 81 121 169 289 361 441 529 625 729 841 961 1089 1225 1369
(~1 + (2 * (loop(\(x,i).(x2 + x + ~2),x,2) - loop(\(x,i).2x,x,1))))
A099084: 1 3 27 663
((2 + loop(\(x,i).3x,x,1)) * (3 + loop(\(x,i).2x,x,1)))
A195116: 12 25 77 319 1577 8575 48977 286759 1699817 10137775 60645377 363332599 2178384857 13065493375 78378545777 470228096839
loop(\(x,i).((x2 + x) div 2),x,loop(\(x,i).2x2,(2x + 2),1))
A051269: 8 536887296 4611686018427387903 4611686018427387903
(1 + ((if (x + ~2) <= 0 then 1 else x) + loop(\(x,i).2x,x,1) + ((x + 1) div 2)))
A309832: 3 5 7 14 23 41 74
(1 + (2 * loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,(x + 1))))
A054906: 3 3 5 3 3 5 3 3 5 3 7 5 3 3 7 5
(1 + loop(\(x,i).2x,(x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))),2))
A002586: 3 5 3 17 3 5 3 257 3 5 3 17 3 5 3 65537
(1 + (loop(\(x,i).(x + (if (~2 + (x div 3)) <= 0 then 1 else 2)),x,(x + 1)) div 2))
A026285: 1 2 3 4 5 7 9 11 13 15 16 18 19 21 22 24
(~1 + loop(\(x,i).loop(\(x,i).(((x + i) * i) div (x + 1)),x,2x),(x + ~1),2))
A185357: 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987
loop(\(x,i).(2x + 1),x,loop(\(x,i).(4x + 1),((x + ~1) div 2),1))
A263806: 1 3 7 47 95 703 1407 11007 22015 175103 350207 2797567 5595135 44744703 89489407 715849727
(1 + ((loop(\(x,i).2x,(x + ~2),x) + ((x + ~1) * (if x <= 0 then 1 else x))) div 2))
A222010: 0 1 3 7
A129984: 0 1 3 7 15 31 64 134 285 613
(if (x mod 2) <= 0 then (19 * (if x <= 0 then 1 else 2)) else 1)
A040379: 19 1 38 1 38 1 38 1 38 1 38 1 38 1 38 1
(if (x mod 2) <= 0 then (23 * (if x <= 0 then 1 else 2)) else 1)
A040551: 23 1 46 1 46 1 46 1 46 1 46 1 46 1 46 1
(if (x mod 4) <= 0 then (11 * (if x <= 0 then 1 else 2)) else 1)
A010195: 11 1 1 1 22 1 1 1 22 1 1 1 22 1 1 1
(if (x mod 4) <= 0 then (17 * (if x <= 0 then 1 else 2)) else 1)
A040294: 17 1 1 1 34 1 1 1 34 1 1 1 34 1 1 1
(if (x mod 2) <= 0 then ((1 + (2 * ((x + ~1) mod 4))) * (if x <= 0 then 1 else 2)) else 1)
A010146: 7 1 6 1 14 1 6 1 14 1 6 1 14 1 6 1
(if (x mod 2) <= 0 then ((~1 + (2 * ((x + ~1) mod 4))) * (if x <= 0 then 1 else 2)) else 1)
A010131: 5 1 2 1 10 1 2 1 10 1 2 1 10 1 2 1
(if (x mod 2) <= 0 then (26 * (if x <= 0 then 1 else 2)) else 1)
A040701: 26 1 52 1 52 1 52 1 52 1 52 1 52 1 52 1
(if (x mod 2) <= 0 then (22 * (if x <= 0 then 1 else 2)) else 1)
A040505: 22 1 44 1 44 1 44 1 44 1 44 1 44 1 44 1
(if (x mod 4) <= 0 then (14 * (if x <= 0 then 1 else 2)) else 1)
A040200: 14 1 1 1 28 1 1 1 28 1 1 1 28 1 1 1
((4x + 4) - (if (x mod 8) <= 0 then (if x <= 0 then 1 else 2) else 1))
A189534: 3 7 11 15 19 23 27 31 34 39 43 47 51 55 59 63
loop(\(x,i).3x,(2 * (1 + (x * (x + (if (x mod 2) <= 0 then 2 else 0))))),1)
A115988: 9 81 387420489 3486784401 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).(x + loop(\(x,i).(x + ((i mod 2) * (1 + i))),i,1)),x,1) div 2))
A208971: 1 3 4 8 11 18 24 35 45 61 76 98 119 148 176 213
(if x <= 0 then 0 else loop(\(x,i).i,((2x + 1) mod (1 - (x div ~4))),1))
A333856: 0 1 1 1 1 2 1 1 2 3 1 3 1 2 4 1
(1 + (2 * (loop(\(x,i).(x + loop(\(x,i).(x * (2 + i)),i,1)),(x + ~1),1) div 2)))
A293458: 1 1 5 17 77 437 2957 23117 204557 2018957 21977357 261478157 3374988557 46964134157 700801318157 11162196262157
(if (x + ~1) <= 0 then 2x else (1 + (2 * (if (~2 + (x div 3)) <= 0 then 1 else 2))))
A295977: 0 2 3 3 3 3 3 3 3 5 5 5 5 5 5 5
(if x <= 0 then 0 else (if ((x + 1) mod (2 + (x2 mod 5))) <= 0 then 2 else 1))
A275811: 0 1 1 1 1 2 1 1 1 1 1 2 1 1 2 2
(~1 + (loop(\(x,i).x2,2,loop(\(x,i).2x2,(2x + ~1),2)) div 2))
A139299: 7 2047 576460752303423487
(1 + (2 * (2 + loop(\(x,i).(1 + loop(\(x,i).(2x + ~1),x,2x)),x,1))))
A084963: 7 13 233 4611686018427387903
(~1 + (2 * (if x <= 0 then 1 else (2 + (if (5 mod (x + 1)) <= 0 then x else 1)))))
A101597: 1 5 5 5 11 5 5 5 5 5 5 5 5 5 5 5
(loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (1 + (((x + 1) div 2) div 2)))
A079904: 0 0 1 0 2 4 0 3 6 9 0 4 8 12 16 0
(1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (((x + 1) div 2) div 2)))
A162609: 1 1 1 1 2 3 1 3 5 7 1 4 7 10 13 1
(1 + (2 * (2 + (if x <= 0 then 1 else (2 + loop(\(x,i).(2x - (i mod 2)),x,1))))))
A112090: 7 11 13 15 21 31
(if (x mod 3) <= 0 then (2 + ((if x <= 0 then 1 else (((x + 1) div 2) div 2)) mod 2)) else 1)
A111625: 3 1 1 3 1 1 3 1 1 2 1 1 3 1 1 2
(loop(\(x,i).2x,x,1) mod (1 + (2 * loop(\(x,i).(1 + (x * i)),4,2))))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A036153: 1 2 4 8 16 32 64 128 77 154 129 79 158 137 95 11
(15 * (if (x mod 2) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1))
A040873: 30 15 60 15 60 15 60 15 60 15 60 15 60 15 60 15
loop(\(x,i).2x,x,(1 + (4 * loop(\(x,i).(2x + 2),(x + 2),2))))
A176635: 57 242 996 4040 16272 65312 261696 1047680 4192512 16773632 67101696 268421120 1073713152 4294909952 17179754496 68719247360
(9 * (if (x mod 2) <= 0 then (3 * (if x <= 0 then 1 else 2)) else 1))
A040707: 27 9 54 9 54 9 54 9 54 9 54 9 54 9 54 9
loop(\(x,i).~2x,x,(~1 + loop(\(x,i).~2x,x,8)))
A120470: 7 34 124 520 2032 8224 32704 131200 524032 2097664 8387584 33556480 134213632 536879104 2147467264 8589967360
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(8x + 1))
A017086: 1 3486784401 2015993900449 95367431640625 1531578985264449 13422659310152401 79792266297612001 362033331456891249 1346274334462890625 4297625829703557649 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(8x + 1))
A017088: 1 282429536481 582622237229761 59604644775390625 1667889514952984961 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 2) <= 0 then 1 else (if (x mod 3) <= 0 then (4 - ((x div 2) mod 2)) else 1))
A135939: 1 1 1 3 1 1 1 1 1 4 1 1 1 1 1 3
(~1 + loop(\(x,i).2x,x,2) - ((loop(\(x,i).(x + (x div 2)),x,2) div 2) div 2))
A038359: 1 3 6 14 29 60 123 248
(1 + (if x <= 0 then 2 else loop(\(x,i).(x3 + ~3x),(x + ~1),4)))
A087602: 3 5 53 140453
(loop(\(x,i).3x,x,1) mod (~1 + loop(\(x,i).(x2 + ~x),2,4)))
A271351: 1 3 9 27 81 112 74 91 11 33 99 35 105 53 28 84
((x2 + 2) div loop(\(x,i).3x,2,(if (x mod 2) <= 0 then 4 else 1)))
A262397: 0 0 0 1 0 3 1 5 1 9 2 13 4 19 5 25
loop(\(x,i).x2,1,((x2 + 4x) div (if (x mod 2) <= 0 then 4 else 1)))
A171638: 0 25 9 441 64 2025 225 5929 576 13689 1225 27225 2304 48841 3969 81225
(5 * (if (x mod 2) <= 0 then (3 * (2 + (if x <= 0 then 0 else 2))) else 1))
A040881: 30 5 60 5 60 5 60 5 60 5 60 5 60 5 60 5
(5 * (if (x mod 2) <= 0 then (5 * (if x <= 0 then 1 else 2)) else 1))
A040609: 25 5 50 5 50 5 50 5 50 5 50 5 50 5 50 5
(loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,1) div 5)
A222010: 0 1 3 7
A051170: 0 1 3 7 14 25 42 66 99 143 200 273 364 476 612 775
loop(\(x,i).2x,x,(5 * loop(\(x,i).(3x + ~1),x,2)))
A154410: 10 50 280 1640 9760 58400 350080 2099840 12597760 75584000 453498880 2720983040 16325877760 97955225600 587731271680 3526387466240
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (3x + ~1)),x,5)
A003079: 5 14 7 20 10 5 14 7 20 10 5 14 7 20 10 5
loop(\(x,i).2x,x,loop(\(x,i).(5x + ~2),x,5))
A169963: 5 46 452 4504 45008 450016 4500032 45000064 450000128 4500000256 45000000512 450000001024 4500000002048 45000000004096 450000000008192 4500000000016384
(5 + compr(\x.loop(\(x,i).(x - (if (x mod (2 + i)) <= 0 then 0 else 1)),x,x),x))
A123123: 5 6 7 9 13 15 19 21 25 31 33 39 43 45 49 55
(1 + (x div (2 + (if (x mod 2) <= 0 then 1 else (2 + (if (x mod 3) <= 0 then 1 else x))))))
A331991: 1 1 1 1 2 1 3 1 3 2 4 1 5 1 5 4
(loop(\(x,i).3x,x,1) mod (1 + loop(\(x,i).(2x2 + x),2,2)))
A271352: 1 3 9 27 81 32 96 77 20 60 180 118 143 7 21 63
(loop(\(x,i).5x,x,1) mod (1 + loop(\(x,i).(x2 + x),2,2)))
A070389: 1 5 25 39 23 29 16 37 13 22 24 34 41 33 36 8
(3 + loop(\(x,i).(2x2 + x),1,loop(\(x,i).4x,x,2)))
A195464: 13 139 2083 32899 524803 8390659 134225923 2147516419 34359869443 549756338179 8796095119363 140737496743939 2251799847239683 36028797153181699 576460752840294403 4611686018427387903
loop(\(x,i).5x,(x + ~1),(if x <= 0 then 1 else (x + 5)))
A081105: 1 6 35 200 1125 6250 34375 187500 1015625 5468750 29296875 156250000 830078125 4394531250 23193359375 122070312500
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(4x + 1))
A016823: 1 48828125 31381059609 1792160394037 34271896307633 350277500542221 2384185791015625 12200509765705829 50542106513726817 177917621779460413 550329031716248441 1532278301220703125 3909821048582988049 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,loop(\(x,i).(x * ((~1 + (2 * i)) * i)),4x,1))
A210281: 1 5040 326918592000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(x div 2),(~1 + (2 * (loop(\(x,i).2x,x,1) + (x mod 2)))))
A083332: 1 5 14 34 124 260 1016 2056 8176 16400 65504 131104 524224 1048640 4194176 8388736
loop(\(x,i).4x,x,(~1 + (2 * (loop(\(x,i).2x,x,1) + (x mod 2)))))
A271494: 1 20 112 1088 7936 66560 520192 4210688 33488896 268697600 2146435072 17184063488 137422176256 1099578736640 8795824586752 70369817919488
(1 + (2 * loop(\(x,i).(2 + (if x <= 0 then 1 else 4x)),(x div 2),(x mod 2))))
A283323: 1 3 7 13 29 53 117 213 469 853 1877 3413 7509 13653 30037 54613
(1 + loop(\(x,i).2x,x,1) - loop(\(x,i).2x,(x div 2),(2 + (x mod 2))))
A274230: 0 0 1 3 9 21 49 105 225 465 961 1953 3969 8001 16129 32385
loop(\(x,i).2x2,1,(~1 + loop(\(x,i).2x,(x div 2),(2 + (x mod 2)))))
A267638: 2 8 18 50 98 242 450 1058 1922 4418 7938 18050 32258 72962 130050 293378
(1 + loop(\(x,i).(2x + 4),x,loop(\(x,i).2x,(x div 2),(2 + (x mod 2)))))
A159229: 3 11 29 77 189 509 1277 3581 9213 26621 69629 204797 540669 1605629 4259837 12713981
((if x <= 0 then 1 else (if ((x div 2) mod 2) <= 0 then (x mod 5) else 0)) mod 3)
A076948: 1 1 0 0 1 0 0 0 0 1 0 0 2 0 0 0
(if x <= 0 then 1 else (3 * (if ((x + 2) mod 9) <= 0 then x else 0)))
A209614: 1 0 0 0 0 0 0 21 0 0 0 0 0 0 0 0
(loop(\(x,i).(x * (x2 div 2)),1,loop(\(x,i).(2x + 1),x,0)) div 3)
A026740: 0 0 4 56 560 4960 41664 341376 2763520 22238720 178433024 1429559296 11444858880 91592417280 732873539584 5863525154816
((1 + loop(\(x,i).2x,x,(1 + (if (x mod 3) <= 0 then 2 else 0)))) div 3)
A087462: 1 1 1 8 5 11 64 43 85 512 341 683 4096 2731 5461 32768
(3 * (if (x mod 2) <= 0 then (5 * (2 + (if x <= 0 then 0 else 2))) else 1))
A040889: 30 3 60 3 60 3 60 3 60 3 60 3 60 3 60 3
(3 * (if (x mod 2) <= 0 then (9 * (if x <= 0 then 1 else 2)) else 1))
A040719: 27 3 54 3 54 3 54 3 54 3 54 3 54 3 54 3
(3 * (if (x mod 4) <= 0 then (3 * (2 + (if x <= 0 then 0 else 2))) else 1))
A040316: 18 3 3 3 36 3 3 3 36 3 3 3 36 3 3 3
((1 + (loop(\(x,i).2x,(x div 2),1) + loop(\(x,i).2x,x,1))) div 3)
A090596-A018240: 1 1 2 3 7 12 24 45 91 176 352 693 1387 2752 5504 10965
((1 + (loop(\(x,i).3x,x,1) + loop(\(x,i).2x,x,1))) div 3)
A087211: 1 2 4 12 32 92 264 772 2272 6732 20024 59732 178512 534172 1599784 4793892
(loop(\(x,i).(x * (x2 div 2)),1,(1 + loop(\(x,i).2x,x,1))) div 3)
A092055: 1 4 20 120 816 5984 45760 357760 2829056 22500864 179481600 1433753600 11461636096 91659526144 733141975040 5864598896640
(loop(\(x,i).(x2 div 2),1,(1 + loop(\(x,i).3x,x,1))) div 3)
A275636: 0 2 16 130 1120 9922 88816 797890 7176640 64576642 581150416 5230235650 47071766560 423644836162 3812800336816 34315193465410
(3 * (if (x mod 2) <= 0 then (7 * (if x <= 0 then 1 else 2)) else 1))
A040433: 21 3 42 3 42 3 42 3 42 3 42 3 42 3 42 3
(((~1 + loop(\(x,i).2x,x,(if x <= 0 then 1 else x))) div 5) mod 3)
A321005: 0 0 1 1 0 1 1 2 1 0 1 2 2 2 2 2
((1 + loop(\(x,i).2x,((if (x mod 2) <= 0 then 2 else 0) + (x div 2)),2)) div 3)
A112031: 3 1 5 1 11 3 21 5 43 11 85 21 171 43 341 85
(if x <= 0 then 1 else (3 * loop(\(x,i).(2 * (2x - (x mod 2))),x,3)))
A277451: 1 30 120 480 1920 7680 30720 122880 491520 1966080 7864320 31457280 125829120 503316480 2013265920 8053063680
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(6x + 3))
A016954: 59049 3486784401 576650390625 16679880978201 205891132094649 1531578985264449 8140406085191601 34050628916015625 119042423827613001 362033331456891249 984930291881790849 2446194060654759801 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(6x + 3))
A016956: 531441 282429536481 129746337890625 7355827511386641 150094635296999121 1667889514952984961 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (x mod (2 + i)) <= 0 then 2 else 0)),x,(6x + 3))
A175073: 3 11 17 23 29 37 41 47 53 59 67 71 79 83 89 97
(loop(\(x,i).(x * (x div 2)),1,(1 + loop(\(x,i).3x,x,2))) div 3)
A082413: 1 7 57 495 4401 39447 354537 3189375 28700001 258286887 2324542617 20920765455 188286534801 1694577750327 15251196564297 137260759512735
(loop(\(x,i).(3 * (~x + loop(\(x,i).2x,(~2 + i),1))),x,1) div 3)
A091005: 0 0 1 ~1 7 ~13 55 ~133 463 ~1261 4039 ~11605 35839 ~105469 320503 ~953317
((loop(\(x,i).(3x + ~3),x,2) + loop(\(x,i).2x,x,1)) div 3)
A087432: 1 1 3 7 19 51 143 407 1179 3451 10183 30207 89939 268451 802623 2402407
((loop(\(x,i).5x,x,2) + loop(\(x,i).2x,x,1)) div 3)
A082685: 1 4 18 86 422 2094 10438 52126 260502 1302254 6510758 32552766 162761782 813804814 4069015878 20345063006
((3x + 3) * (~1 + loop(\(x,i).loop(\(x,i).(x * i),i,2x),x,1)))
A079244: 0 6 63 1140
(((x + 1) * (loop(\(x,i).2x,x,2) + (if (x + ~2) <= 0 then 1 else 2))) div 3)
A245762: 1 3 9 24 56 132
((if x <= 0 then 1 else (loop(\(x,i).2x,(x div 2),(x mod 2)) mod (x + 1))) mod 3)
A113048: 1 1 0 2 0 1 0 0 0 0 0 2 0 2 0 0
(if x <= 0 then 1 else ((loop(\(x,i).(x2 div 3),2,x) div (x + 1)) mod 3))
A110857: 1 0 0 0 1 0 0 1 1 0 0 2 2 2 0 0
(3 * loop(\(x,i).(x + (3 * (if (~x + 2) <= 0 then x else 4))),x,1))
A292542: 3 39 156 624 2496 9984 39936 159744 638976 2555904 10223616 40894464 163577856 654311424 2617245696 10468982784
(3 * (2 + (loop(\(x,i).2x,x,2) + loop(\(x,i).3x,x,1))))
A087719: 15 27 57 135 345 927 2577 7335 21225 62127 183297 543735 1618905 4832127 14447217 43243335
(3 + (2 * (1 + loop(\(x,i).(if x <= 0 then 2 else ((2x + ~1) - i)),x,0))))
A254154: 5 9 7 1 9 1 9
(6 * (if (x mod 2) <= 0 then (5 * (if x <= 0 then 1 else 2)) else 1))
A040879: 30 6 60 6 60 6 60 6 60 6 60 6 60 6 60 6
(3 * (if (x mod 2) <= 0 then (9 * (if x <= 0 then 1 else 2)) else 2))
A040710: 27 6 54 6 54 6 54 6 54 6 54 6 54 6 54 6
((2 + ((if (x + ~3) <= 0 then x else 0) + loop(\(x,i).2x,x,1))) div 3)
A322051: 1 1 2 4 6 11 22 43 86 171 342 683 1366 2731 5462
((2 * (if x <= 0 then 2 else (x - (loop(\(x,i).(x * i),x,2) mod (x + 1))))) div 3)
A239968: 1 0 0 2 0 3 0 4 5 6 0 7 0 8 9 10
(3 * ((1 + (if (x mod 2) <= 0 then 6 else 0)) * (if x <= 0 then 1 else 2)))
A040426: 21 6 42 6 42 6 42 6 42 6 42 6 42 6 42 6
(6 * ((1 + (if (x mod 2) <= 0 then 4 else 0)) * (if x <= 0 then 1 else 2)))
A040874: 30 12 60 12 60 12 60 12 60 12 60 12 60 12 60 12
(3 + (2 * loop(\(x,i).(x + loop(\(x,i).x2,1,(2 + (i div 2)))),x,1)))
A271997: 5 13 31 49 81 113 163 213 285 357 455 553 681 809 971 1133
(loop(\(x,i).5x,x,1) mod loop(\(x,i).(x2 + 1),2,3))
A271379: 1 5 25 24 19 95 71 52 58 88 36 79 92 56 78 87
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,12x)
A017530: 0 61917364224 63403380965376 3656158440062976 64925062108545024 604661760000000000 3743906242624487424 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,12x)
A017532: 0 8916100448256 36520347436056576 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x * i),(x + ~1),loop(\(x,i).(3x + ~3),x,2)) div 3)
A321398: 0 1 2 10 84 984 14640 262800 5513760 132289920 3571464960 107140320000 3535590643200 127280784153600 4963944354969600 208485575730432000
(loop(\(x,i).(x2 + x),1,loop(\(x,i).(3x + ~1),x,2)) div 3)
A051405: 2 10 70 574 5002 44530 399310 3589414 32291602 290585050 2615147350 23535971854 211822683802 1906400965570 17157599124190 154418363419894
(loop(\(x,i).3x,(x + 2),1) + loop(\(x,i).2x,(x + 2),3))
A235877: 21 51 129 339 921 2571 7329 21219 62121 183291 543729 1618899 4832121 14447211 43243329 129533379
(if x <= 0 then 2 else ((if ((x div 2) mod 3) <= 0 then 1 else 2) + ((x + 2) div 3)))
A339082: 2 2 3 3 4 4 3 4 5 5 6 6 5 6 7 7
loop(\(x,i).2x,(x + ~1),(if x <= 0 then 1 else (7x + ~1)))
A229572: 1 6 26 80 216 544 1312 3072 7040 15872 35328 77824 169984 368640 794624 1703936
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,6x)
A016919: 0 362797056 743008370688 64268410079232 1521681143169024 17714700000000000 131621703842267136 717368321110468608 3116402981210161152 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,9x)
A017170: 0 3486784401 3570467226624 205891132094649 3656158440062976 34050628916015625 210832519264920576 984930291881790849 3743906242624487424 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,9x)
A017172: 0 282429536481 1156831381426176 150094635296999121 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(3 + compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)),x))
A153040: 7 10 13 15 16 19 20 22 25 27 28 30 31 34 35 37
(if x <= 0 then 1 else (3 + (if (x + ~4) <= 0 then x else (x + 8))))
A053738: 1 4 5 6 7 16 17 18 19 20 21 22 23 24 25 26
(loop(\(x,i).(x * i),(x + ~1),loop(\(x,i).((x2 + ~x) div 2),2,x)) div 3)
A216119: 0 0 0 2 30 360 4200 50400 635040 8467200 119750400 1796256000 28540512000 479480601600 8499883392000 158664489984000
loop(\(x,i).2x,(~x + 2),loop(\(x,i).10x,x,3))
A114307: 12 60 300 3000 30000 300000 3000000 30000000 300000000 3000000000 30000000000 300000000000 3000000000000 30000000000000 300000000000000 3000000000000000
(3 + compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),x))
A033162: 3 4 6 7 12 13 15 16 30 31 33 34 39 40 42 43
(3 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),x))
A081601: 0 3 9 12 27 30 36 39 81 84 90 93 108 111 117 120
(3 * compr(\x.loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,2x),x))
A179899: 0 12 21 30 36 39 48 51 57 66 72 75 81 84 93 96
(if (if ((x + 2) mod 5) <= 0 then (x mod 2) else 0) <= 0 then x else (x mod 3))
A004178: 0 1 2 0 4 5 6 7 8 9 10 11 12 1 14 15
(loop(\(x,i).4x,(x + 1),2) + loop(\(x,i).3x,x,3))
A213659: 11 41 155 593 2291 8921 34955 137633 543971 2156201 8565755 34085873 135812051 541653881 2161832555 8632981313
(1 - ((x + (if (x + ~2) <= 0 then 1 else (if (x mod 2) <= 0 then x else (~x + 1)))) mod 3))
A227625: 0 ~1 1 0 ~1 0 1 0 0 0 ~1 0 1 0 0 0
(loop(\(x,i).2x,x,4) - ((if (x mod 2) <= 0 then (~x + 2) else x) mod 3))
A130869: 2 7 16 32 63 126 254 511 1024 2048 4095 8190 16382 32767 65536 131072
(3 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))
A098090: 3 4 5 7 8 10 11 13 16 17 20 22 23 25 28 31
(3 * loop(\(x,i).(x + (6x div (if i <= 0 then 1 else i))),x,x))
A266733: 0 21 168 756 2520 6930 16632 36036 72072 135135 240240 408408 668304 1058148 1627920 2441880
loop(\(x,i).(x + (7x div (if i <= 0 then 1 else i))),x,3)
A253944: 3 24 108 360 990 2376 5148 10296 19305 34320 58344 95472 151164 232560 348840 511632
(1 + (2 * compr(\x.((x + 1) mod (1 + loop(\(x,i).(if x <= 0 then i else (x + ~1)),x,0))),x)))
A081118: 1 3 5 7 11 13 15 23 27 29 31 47 55 59 61 63
(1 + (compr(\x.((x + 1) mod (1 + loop(\(x,i).(if x <= 0 then i else (x + ~1)),x,0))),x) div 2))
A143038: 1 1 2 2 3 4 4 6 7 8 8 12 14 15 16 16
(~1 + loop(\(x,i).4x,((x + 1) + (3 * (if x <= 0 then 0 else 2))),2))
A247791: 7 131071 524287
loop(\(x,i).8x,x,(1 + loop(\(x,i).6x,x,2)))
A233251: 3 104 4672 221696 10620928 509640704 24461443072 1174138781696 56358577635328 2705211055407104 129850125290831872 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)),x)))
A326586-A071904: 9 15 21 25 27 33 35 39 45 49 51 55 57 63 65 69
(~1 + (2 * compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)),x)))
A092409-A007921: 7 13 19 23 25 31 33 37 43 47 49 53 55 61 63 67
loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),((x2 + x) div 2),1)
A135757: 1 2 20 924 184756 155117520 538257874440 7648690600760440 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x + ~1) <= 0 then 1 else loop(\(x,i).(x * i),(x + ~1),(1 + ((x2 + x) div 2))))
A187742: 1 1 4 14 66 384 2640 20880 186480 1854720 20321280 243129600 3153427200 44068147200 660064204800 10548573235200
(if x <= 0 then 0 else (1 + (2x * loop(\(x,i).(4x + 2),4,2))))
A004970: 0 1365 2729 4093 5457 6821 8185 9549 10913 12277 13641 15005 16369 17733 19097 20461
loop(\(x,i).x2,1,(1 + loop(\(x,i).(10x + ~8),x,2)))
A151997: 9 169 12769 1238769 123498769 12346098769 1234572098769 123456832098769 12345679432098769 1234567905432098769 4611686018427387903
(~1 + (2 * loop(\(x,i).x2,1,loop(\(x,i).(3x + 2),4,x))))
A157509: 12799 51841 117127 208657 326431 470449 640711 837217 1059967 1308961 1584199 1885681 2213407 2567377 2947591 3354049
(loop(\(x,i).(3x + 1),x,1) * (~1 + loop(\(x,i).4x,x,2)))
A269255: 1 28 403 5080 61831 745108 8952763 107475760 1289869711 15479049388 185750955523 2229020652040 26748283770391 320979546636868 3851755118036683 46221063628493920
(1 + loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),2))
A278741: 3 5 17 65 1025 4097 65537 262145 4194305 268435457 1073741825 68719476737 1099511627777 4398046511105 70368744177665 4503599627370497
(~1 + loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),2))
A098102: 1 3 15 63 1023 4095 65535 262143 4194303 268435455 1073741823 68719476735 1099511627775 4398046511103 70368744177663 4503599627370495
(loop(\(x,i).(5x + 1),x,0) * (~1 + loop(\(x,i).2x,x,2)))
A160874: 0 3 42 465 4836
(loop(\(x,i).(5x + 1),x,1) * (~1 + loop(\(x,i).2x,x,2)))
A046915: 1 18 217 2340 24211 246078 2480437 24902280 249511591 2497558338 24987792457 249938963820 2499694822171 24998474116998 249992370597277 2499961853010960
(1 + (2 * compr(\x.loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,2x),x)))
A155474-A067800-A046446-A014076: 1 9 15 21 25 27 33 35 39 45 49 51 55 57 63 65
loop(\(x,i).(x * i),((((x div 2) * (x div 2)) div 2) + (if x <= 0 then 1 else 2x)),1)
A177771: 1 2 24 720 3628800 479001600 20922789888000 6402373705728000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~4x + loop(\(x,i).3x,(2 * i),1)),2x,1)
A165259: 1 61 4621 369181 29821741 2414250301 195533302861 15837861987421 1282861452271981 103911691734684541 4611686018427387903 4611686018427387903 4611686018427387903
((2x + 1) * (if x <= 0 then 1 else (if (x mod 12) <= 0 then 2 else 0)))
A023936: 1 0 0 0 0 0 0 0 0 0 0 0 50 0 0 0
(loop(\(x,i).(x + ((x div (if i <= 0 then 1 else i)) * (1 + i))),x,1) div (2x + 1))
A092483: 1 1 1 2 3 5 9 17 32 60 114 218 418 803 1549 2995
(loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,2) mod (2x + 1))
A192225: 0 1 2 5
A336257: 0 1 2 5 5 9 2 9 2 17 17 21 12 22 2 29
loop(\(x,i).loop(\(x,i).2x,(x mod 5),1),(x mod 2),(2x + 1))
A235995: 1 8 5 4 9 2
compr(\x.(1 - loop(\(x,i).(x div (if (x mod 2) <= 0 then ~2 else 1)),x,x)),(2x + 1))
A091785: 3 5 9 12 15 17 20 23 27 29 33 36 39 43 45 48
(if x <= 0 then 0 else ((2x + ~1) * (1 + (if (x mod 2) <= 0 then 8 else 0))))
A204877: 0 1 27 5 63 9 99 13 135 17 171 21 207 25 243 29
(loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1) div (2x + ~1))
A284016: ~1 2 2 4 10 28 84 264 858 2860 9724 33592 117572 416024 1485800 5348880
loop(\(x,i).(x + loop(\(x,i).i,(x div (2 + (x div 5))),1)),2x,1)
A108923: 1 3 6 10 15 21 28 36 44 52 60 68 76 84 92 100
(loop(\(x,i).6x,x,1) + loop(\(x,i).3x,2x,1))
A074621: 2 15 117 945 7857 66825 578097 5062905 44726337 397498185 3547250577 31743856665 284606318817 2554926522345 22955156619057 206361317079225
(loop(\(x,i).8x,x,1) + loop(\(x,i).3x,2x,1))
A074624: 2 17 145 1241 10657 91817 793585 6880121 59823937 521638217 4560526225 39970994201 351149013217 3091621642217 27274838966065 241075504183481
(loop(\(x,i).5x,x,1) + loop(\(x,i).3x,2x,1))
A074618: 2 14 106 854 7186 62174 547066 4861094 43437346 389373614 3496550026 31429887734 282673677106 2543086531454 22882895970586 205921649672774
((2x + 1) - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + (2 * i)))),x,2x))
A100555: 1 4 9 9 9 16 16 16 25 25 25 25 25 36 36 36
loop(\(x,i).(~x - ((x + loop(\(x,i).(x * i),i,1)) * (1 + i))),2x,1)
A201546: 1 14 444 25584 2342880 312888960 57424792320 13869128448000 4264876094976000 1627055289796608000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (7 * (if (~2 + i) <= 0 then 1 else x))),2x,1)
A067408: 1 15 960 61440 3932160 251658240 16106127360 1030792151040 65970697666560 4222124650659840 270215977642229760 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (9x div (if i <= 0 then 1 else i))),2x,1)
A053138: 1 55 715 5005 24310 92378 293930 817190 2042975 4686825 10015005 20160075 38567100 70607460 124403620 211915132
loop(\(x,i).(x + (10x div (if i <= 0 then 1 else i))),2x,1)
A196789: 1 66 1001 8008 43758 184756 646646 1961256 5311735 13123110 30045015 64512240 131128140 254186856 472733756 847660528
loop(\(x,i).(x + (7x div (if i <= 0 then 1 else i))),2x,1)
A053136: 1 36 330 1716 6435 19448 50388 116280 245157 480700 888030 1560780 2629575 4272048 6724520 10295472
(loop(\(x,i).(x2 + 1),x,2) - loop(\(x,i).8x,(x div 2),1))
A295223: 1 4 18 669
(loop(\(x,i).x2,1,loop(\(x,i).(x * (1 + (i div 2))),x,1)) div (1 + (x div 2)))
A327904: 1 1 2 8 48 432 5184 82944 1658880 41472000 1244160000 44789760000 1881169920000 92177326080000 5161930260480000 330363536670720000
(((x * loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)) div 2) mod (1 + (x div 2)))
A259016: 0 0 1 0 2 2 0 3 3 3 0 5 5 5 4 0
(1 + (if (x + ~1) <= 0 then 1 else (if (x mod 8) <= 0 then 1 else 2)) - (x mod 2))
A110917: 2 1 3 2 3 2 3 2 2 2 3 2 3 2 3 2
(~1 + (loop(\(x,i).x2,1,(loop(\(x,i).2x,x,2) - (x mod 2))) + (x mod 2)))
A085435: 3 9 63 225 1023 3969 16383 65025 262143 1046529 4194303 16769025 67108863 268402689 1073741823 4294836225
(loop(\(x,i).(2x + (if (~2 + i) <= 0 then 1 else x)),(x div 2),1) * (1 + (x mod 2)))
A018258: 1 2 3 6 7 14 21 42
(loop(\(x,i).2x,x,1) - loop(\(x,i).(2x + 2),(x div 2),(1 + (x mod 2))))
A027556: 0 0 0 2 6 18 42 98 210 450 930 1922 3906 7938 16002 32258
loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x div 2),(1 + (x mod 2)))
A063886: 1 2 2 4 6 12 20 40 70 140 252 504 924 1848 3432 6864
(1 + compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,x),x) - (x mod 2))
A055247: 1 2 7 8 19 20 25 26 55 56 61 62 73 74 79 80
(~1 + loop(\(x,i).(x * (1 + loop(\(x,i).6x,(x + ~2),x))),x,2))
A165711: 1 5 46661 4611686018427387903
(1 mod (3 div (1 + (2 * loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)))))
A251635: 1 ~2 1 0 ~2 1 0 0 ~2 1 0 0 0 ~2 1 0
(0 - loop(\(x,i).2x,x,loop(\(x,i).(x + ((2 - i) * (1 + i))),x,2)))
A167592: ~2 ~8 ~16 0 160 896 3584 12288 38400 112640 315392 851968 2236416 5734400 14417920 35651584
(1 + (2 * compr(\x.loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),2,x),x)))
A209492: 1 3 5 7 9 11 15 17 19 23 31 33 35 39 47 63
loop(\(x,i).x2,1,loop(\(x,i).(10x + 6),x,1))
A309827: 1 256 27556 2775556 277755556 27777555556 2777775555556 277777755555556 27777777555555556 2777777775555555556 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,loop(\(x,i).(10x + ~6),x,1))
A102807: 1 16 1156 111556 11115556 1111155556 111111555556 11111115555556 1111111155555556 111111111555555556 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,loop(\(x,i).(10x + 21),x,1))
A098207: 1 961 109561 11095561 1110955561 111109555561 11111095555561 1111110955555561 111111109555555561 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,2,loop(\(x,i).(10x + 21),x,1))
A098208: 1 923521 12003612721 123111473904721 1234222258516824721 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((7x + ~1) + loop(\(x,i).2x,i,2)),x,1)
A016201: 1 10 77 554 3909 27426 192109 1345018 9415637 65910482 461375421 3229632042 22607432485 158252043778 1107764339213 7754350440026
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (9x + 1)),x,1)
A033962: 1 10 5 46 23 208 104 52 26 13 118 59 532 266 133 1198
loop(\(x,i).((4x + ~1) - loop(\(x,i).3x,(~2 + i),1)),x,1)
A087433: 1 2 6 20 70 252 926 3460 13110 50252 194446 758100 2973350 11716252 46333566 183739940
loop(\(x,i).(1 + (x mod (2 + (i div (1 + (if (x mod 3) <= 0 then 0 else 2)))))),x,1)
A194103: 1 2 1 2 3 4 1 2 3 4 5 1 2 3 4 5
loop(\(x,i).x2,1,loop(\(x,i).(10x + 3),x,1))
A309907: 1 169 17689 1776889 177768889 17777688889 1777776888889 177777768888889 17777777688888889 1777777776888888889 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~1 + (2 * (6x + loop(\(x,i).2x,i,1)))),x,1)
A016207: 1 15 187 2259 27139 325731 3908899 46907043 562885027 6754621347 81055458211 972665502627 11671986039715 140063832492963 1680765989948323 20169191879445411
loop(\(x,i).(~1 + (2 * (5x + loop(\(x,i).2x,i,1)))),x,1)
A016205: 1 13 137 1385 13881 138873 1388857 13888825 138888761 1388888633 13888888377 138888887865 1388888886841 13888888884793 138888888880697 1388888888872505
(if x <= 0 then 0 else (1 + (x * (1 + loop(\(x,i).(2x2 + 8),2,2)))))
A004968: 0 522 1043 1564 2085 2606 3127 3648 4169 4690 5211 5732 6253 6774 7295 7816
loop(\(x,i).(x - (if (x div 3) <= 0 then ~8x else 1)),x,1)
A132673: 1 9 8 7 6 5 4 3 2 18 17 16 15 14 13 12
loop(\(x,i).((9x + ~1) + loop(\(x,i).2x,i,2)),x,1)
A016204: 1 12 115 1050 9481 85392 768655 6918150 62263861 560375772 5043383995 45390460050 408514148641 3676627354152 33089646220135 297806816046750
loop(\(x,i).(3x - (x div (if (x mod 4) <= 0 then 4 else 1))),x,1)
A018259: 1 2 4 11 22 44
A018480: 1 2 4 11 22 44 121 242 484
(if x <= 0 then 2 else ((x + ~1) + (5 * (if (x + ~4) <= 0 then 1 else 2))))
A134026: 2 5 6 7 8 14 15 16 17 18 19 20 21 22 23 24
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(5x + 1))
A016870: 1 60466176 25937424601 1099511627776 16679880978201 141167095653376 819628286980801 3656158440062976 13422659310152401 42420747482776576 119042423827613001 303305489096114176 713342911662882601 1568336880910795776 3255243551009881201
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(5x + 1))
A016872: 1 2176782336 3138428376721 281474976710656 7355827511386641 95428956661682176 787662783788549761 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(5 * (x + (4x div (if i <= 0 then 1 else i)))),x,1)
A036071: 1 25 375 4375 43750 393750 3281250 25781250 193359375 1396484375 9775390625 66650390625 444335937500 2905273437500 18676757812500 118286132812500
loop(\(x,i).(x div 2),(x mod 5),loop(\(x,i).(4x + 1),x,1))
A172411: 1 2 5 10
A263307: 1 2 5 10 21 1365 2730
loop(\(x,i).(x * ((x + 1) + (x div 2))),1,loop(\(x,i).(4x + ~1),x,1))
A208402: 2 15 187 2795 43947 700075 11188907 178973355 2863377067 45813246635 733008800427 11728128223915 187650001250987 3002399818689195 48038396293720747 768614337478306475
((x + 1) + ((2 * loop(\(x,i).(if (~x + i) <= 0 then x else 2x),x,1)) div 3))
A189128: 1 2 4 6 7 11 12 13 14 20 21 22 23 24 25 26
loop(\(x,i).(12 * (2x - (x div (if i <= 0 then 1 else i)))),x,1)
A119309: 1 12 216 4320 90720 1959552 43110144 960740352 21616657920 489977579520 11171488813056 255928652808192 5886359014588416 135839054182809600 3143703825373593600 4611686018427387903
loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),x,1)
A016135: 1 13 147 1625 17891 196833 2165227 23817625 261994131 2881935953 31701296507 348714263625 3835856903971 42194425951873 464138685486987 5105525540389625
loop(\(x,i).(6 * (x + (4 * (x div (if i <= 0 then 1 else i))))),x,1)
A139626: 1 30 540 7560 90720 979776 9797760 92378880 831409920 7205552640 60526642176 495217981440 3961743851520 31084451758080 239794342133760 1822437000216576
loop(\(x,i).(7x - loop(\(x,i).2x,(~1 + i),1)),x,1)
A083426: 1 6 40 276 1924 13452 94132 658860 4611892 32282988 225980404 1581861804 11073030580 77511209964 542578461556 3798049214508
loop(\(x,i).(6x + loop(\(x,i).(4x + 1),i,1)),x,1)
A016222: 1 11 87 607 3983 25263 157039 964079 5871855 35580655 214882031 1294884591 7791677167 46839541487 281395162863 1689802632943
loop(\(x,i).(6x + loop(\(x,i).8x,i,1)),x,1)
A016170: 1 14 148 1400 12496 107744 908608 7548800 62070016 506637824 4113568768 33271347200 268347559936 2159841173504 17357093552128 139326933401600
(loop(\(x,i).3x,2x,1) mod loop(\(x,i).6x,x,1))
A139731: 0 3 9 81 81 4617 18225 24057 1056321 4468041 40212369 180512793 1624615137 8091189225 72820703025 420293834937
(loop(\(x,i).8x,x,1) + loop(\(x,i).6x,x,1))
A074620: 2 14 100 728 5392 40544 308800 2377088 18456832 144295424 1134208000 8952731648 70896259072 562816507904 4476410675200 35654557073408
(loop(\(x,i).8x,x,1) mod loop(\(x,i).6x,x,1))
A138964: 0 2 28 80 208 1664 28864 137600 1660672 3207680 45816832 245602304 1239224320 1206665216 9653321728 390683230208
(loop(\(x,i).5x,x,1) + loop(\(x,i).6x,x,1))
A074615: 2 11 61 341 1921 10901 62281 358061 2070241 12030821 70231801 411625181 2420922961 14281397141 84467679721 500702562701
loop(\(x,i).(7x + (if (i mod 3) <= 0 then 1 else 0)),x,1)
A033143: 1 7 49 344 2408 16856 117993 825951 5781657 40471600 283301200 1983108400 13881758801 97172311607 680206181249 4761443268744
loop(\(x,i).(7x + loop(\(x,i).4x,i,1)),x,1)
A016150: 1 11 93 715 5261 37851 269053 1899755 13363821 93808891 657710813 4608169995 32273967181 225984879131 1582162589373 11076211867435
loop(\(x,i).(7x + loop(\(x,i).3x,i,1)),x,1)
A016138: 1 10 79 580 4141 29230 205339 1439560 10083481 70604050 494287399 3460188940 24221854021 169554572470 1186886790259 8308221880720
loop(\(x,i).(7x + (if (i mod 3) <= 0 then 1 else 2)),x,1)
A037548: 1 9 65 456 3194 22360 156521 1095649 7669545 53686816 375807714 2630654000 18414578001 128902046009 902314322065 6316200254456
(1 + loop(\(x,i).(if (x mod 2) <= 0 then (3x + 3) else (x div 2)),3,x))
A076536: 1 2 16 4 4 5 34 1 7 8 52 10 10 11 70 2
loop(\(x,i).x2,1,loop(\(x,i).(2x * (~1 + (2 * i))),3x,1))
A166371: 1 14400 442597478400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(3x + 1))
A016787: 1 4194304 1977326743 100000000000 1792160394037 17592186044416 116490258898219 584318301411328 2384185791015625 8293509467471872 25408476896404831 70188843638032384 177917621779460413
loop(\(x,i).(3 * (x + loop(\(x,i).3x,((~1 + i) div 2),1))),x,1)
A107660: 1 6 21 72 225 702 2133 6480 19521 58806 176661 530712 1592865 4780782 14344533 43040160
loop(\(x,i).(3 * (x + (3 * (2x div (if i <= 0 then 1 else i))))),x,1)
A036220: 1 21 252 2268 17010 112266 673596 3752892 19702683 98513415 472864392 2192371272 9865670724 43257171636 185387878440 778629089448
loop(\(x,i).(3 * (x + ((2x div (if i <= 0 then 1 else i)) * (1 + i)))),x,1)
A004992: 1 15 180 1980 20790 212058 2120580 20902860 203802885 1970094555 18912907728 180532301040 1715056859880 16227076443480 152998149324240 1438182603647856
(1 + compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,(x div 3)),x))
A105266: 1 2 3 7 8 9 19 20 21 25 26 27 55 56 57 61
loop(\(x,i).(3 * (x + (8x div (if i <= 0 then 1 else i)))),x,1)
A036222: 1 27 405 4455 40095 312741 2189187 14073345 84440070 478493730 2583866142 13389124554 66945622770 324428787270 1529449997130 7035469986798
loop(\(x,i).(3 * (x + (5x div (if i <= 0 then 1 else i)))),x,1)
A036219: 1 18 189 1512 10206 61236 336798 1732104 8444007 39405366 177324147 773778096 3288556908 13660159464 55616363532 222465454128
loop(\(x,i).(2 * ((2x - (x div (if i <= 0 then 1 else i))) * (~1 + (2 * i)))),x,1)
A092563: 1 2 18 300 7350 238140 9604980 463783320 26087811750 1675417243500 120965124980700 9699203657543400 855146455806743100 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,x,1) - loop(\(x,i).((x * (1 + i)) div (1 + (i div 2))),x,1))
A093387: 0 0 1 2 6 12 29 58 130 260 562 1124 2380 4760 9949 19898
(1 + compr(\x.(loop(\(x,i).loop(\(x,i).(x * (x + i)),2,(x + 2)),2,0) mod (x + 1)),x))
A291686: 1 2 3 4 5 6 8 10 11 12 15 16 17 20 22 24
(1 + (if (x + ~2) <= 0 then 0 else compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x)))
A171525: 1 1 1 5 7 11 13 17 19 23 29 31 37 41 43 47
loop(\(x,i).x2,1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x)))
A280076: 1 4 9 25 49 121 169 289 361 529 841 961 1369 1681 1849 2209
loop(\(x,i).((x + 1) + (if (x mod (2 - (x mod ~4))) <= 0 then 1 else 2)),x,1)
A231407: 1 4 6
A330215: 1 4 6 9 12 14 17 20 22 25 27 29 32 34 37 40
loop(\(x,i).(x * i),x,loop(\(x,i).(2x * (~1 + (2 * i))),(x2 + x),1))
A283627: 1 12 1330560
(~1 + (if x <= 0 then 2 else (x + (loop(\(x,i).(x2 + ~2x),3,x) div (x + 1)))))
A118710: 1 1 1 2 444
loop(\(x,i).((x + 1) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,1)
A083462: 1 3 6 11
A014284: 1 3 6 11 18 29 42 59 78 101 130 161 198 239 282 329
loop(\(x,i).((~x + 1) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,1)
A036467: 1 1 2 3 4 7 6 11 8 15 14 17 20 21 22 25
(1 + (((x + ~6) - loop(\(x,i).2x,x,1)) mod (if x <= 0 then 1 else x)))
A275379: 1 1 1 2 3 3 3 7 3 5
loop(\(x,i).((2x + ~1) + (if (i mod 3) <= 0 then x3 else 1)),x,1)
A018373: 1 2 4 71 142 284
((~x + ~1) + loop(\(x,i).(x + (6x div (if i <= 0 then 1 else i))),x,1))
A062989: 0 5 25 80 205 456 917 1708 2994 4995 7997 12364 18551 27118 38745 54248
((x + 1) + loop(\(x,i).(x + (5x div (if i <= 0 then 1 else i))),x,1))
A051745: 2 8 24 60 131 258 469 800 1296 2012 3014 4380 6201 8582 11643 15520
loop(\(x,i).((x + 1) + (if x <= 0 then 0 else ((((x + 1) div 2) div (1 + i)) + i))),x,1)
A025729-A025714: 1 3 6 10 16 23 31 41 52 64 77 92 108 125 144 164
loop(\(x,i).(10x + loop(\(x,i).4x,i,1)),x,1)
A016157: 1 14 156 1624 16496 165984 1663936 16655744 166622976 1666491904 16665967616 166663870464 1666655481856 16666621927424 166666487709696 1666665950838784
loop(\(x,i).x2,1,loop(\(x,i).((2 * (x - (2x * i))) div (1 + i)),x,1))
A151342: 1 1 4 25 196 1764 17424 184041 2044900 23639044
A001246: 1 1 4 25 196 1764 17424 184041 2044900 23639044 282105616 3455793796 43268992144 551900410000 7152629313600 93990019574025
loop(\(x,i).2x,(x - (2 * (x mod 2))),loop(\(x,i).(2x * (1 + i)),x,1))
A188895: 1 4 96 384 30720
loop(\(x,i).(10x + loop(\(x,i).3x,i,1)),x,1)
A016145: 1 13 139 1417 14251 142753 1428259 14284777 142854331 1428562993 14285688979 142857066937 1428571200811 14285713602433 142857140807299 1428571422421897
(~1 + loop(\(x,i).((x + 1) - ((if (x + ~4) <= 0 then 1 else x) div 3)),2,x))
A131754: 1 2 3 4 4 4 4 4 5 5 6 6 6 7 8 8
loop(\(x,i).2x,(x + ~1),loop(\(x,i).(2 * ((x + 1) - (2 * (i mod 2)))),x,1))
A054881: 1 0 4 8 48 160 704 2688 11008 43520 175104 698368 2797568 11182080 44744704 178946048
loop(\(x,i).(x + ((if (i mod 3) <= 0 then 1 else 0) + ((1 + (x div 2)) div 2))),x,1)
A134157: 1 1 1 2 3 4 6 8 10 14 18 23 30 38 48 61
loop(\(x,i).((3x2 + ~x) div 2),1,loop(\(x,i).(2x + 2),x,1))
A169722: 1 22 145 715 3151 13207 54055 218695 879751 3528967 14135815 56583175 226412551 905809927 3623559175 14494875655
((x + 1) - loop(\(x,i).(x - (if (~2 + (x div 2)) <= 0 then 0 else 1)),((x + 1) div 2),x))
A134679: 1 1 1 1 1 1 2 3 4 5 6 7 7 8 8 9
((x + 1) + loop(\(x,i).(x + (loop(\(x,i).(x * i),x,2) div (x + 1))),(x + ~1),2))
A092839: 3 4 6 10 216
(loop(\(x,i).2x,x,1) div (1 + (x * loop(\(x,i).(2x2 + 2x),2,2))))
A245675: 1 0 0 0 0 0 0 0 0 0 0 0 1 2 3 7
loop(\(x,i).x2,1,loop(\(x,i).(x - (x div (~4 + (x div 4)))),x,1))
A018228: 1 4 9 16 36 64 144 576
((if (~2 + (x div 2)) <= 0 then 1 else 2) div (if ((x + 1) mod 8) <= 0 then x else 1))
A044947: 1 1 1 1 1 1 2 0 2 2 2 2 2 2 2 0
loop(\(x,i).(8 * (x + (2 * (2x div (if i <= 0 then 1 else i))))),x,1)
A172510: 1 40 960 17920 286720 4128768 55050240 692060160 8304721920 95965675520 1074815565824 11725260718080 125069447659520 1308418837053440 13458022323978240 136374626216312832
loop(\(x,i).(8 * (x + (3x div (if i <= 0 then 1 else i)))),x,1)
A140802: 1 32 640 10240 143360 1835008 22020096 251658240 2768240640 29527900160 307090161664 3126736191488 31267361914880 307863255777280 2990671627550720 28710447624486912
loop(\(x,i).(8x + loop(\(x,i).(3x + 1),i,1)),x,1)
A016214: 1 12 109 912 7417 59700 478693 3832824 30672433 245408988 1963360477 15707149536 125657993449 1005266339076 8042137887061 64337124619848
loop(\(x,i).(8x + loop(\(x,i).5x,i,1)),x,1)
A016162: 1 13 129 1157 9881 82173 673009 5462197 44088201 354658733 2847035489 22825112037 182845036921 1463980998493 11717951503569 93774129606677
(loop(\(x,i).3x,2x,1) - loop(\(x,i).8x,x,1))
A016185: 0 1 17 217 2465 26281 269297 2685817 26269505 253202761 2413042577 22791125017 213710059745 1992110014441 18478745943857 170706760005817
(loop(\(x,i).3x,2x,1) mod loop(\(x,i).8x,x,1))
A139733: 0 1 17 217 2465 26281 7153 588665 9492289 118985033 265558929 5611255833 7551629537 342842572777 886559899441 29969271650489
(loop(\(x,i).5x,x,1) + loop(\(x,i).8x,x,1))
A074617: 2 13 89 637 4721 35893 277769 2175277 17167841 136170853 1083507449 8638762717 68963617361 550976517013 4404150026729 35214889666957
loop(\(x,i).3x,2x2,loop(\(x,i).8x,x,1))
A135427: 1 72 419904 198359290368 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(9x + (if (i mod 3) <= 0 then 1 else 0)),x,1)
A033145: 1 9 81 730 6570 59130 532171 4789539 43105851 387952660 3491573940 31424165460 282817489141 2545357402269 22908216620421 206173949583790
loop(\(x,i).(~7x + loop(\(x,i).3x,i,1)),x,1)
A201865: 1 ~4 37 ~232 1705 ~11692 82573 ~575824 4037329 ~28241620 197750389 ~1384075576 9689060473 ~67821828988 474757585885 ~3323288752288
loop(\(x,i).(9x + (if (i mod 3) <= 0 then 1 else 2)),x,1)
A037550: 1 11 101 910 8192 73730 663571 5972141 53749271 483743440 4353690962 39183218660 352648967941 3173840711471 28564566403241 257081097629170
loop(\(x,i).(2 * (4x + (3x div (if i <= 0 then 1 else i)))),x,1)
A004986: 1 14 154 1540 14630 134596 1211364 10729224 93880710 813632820 6997242252 59794615608 508254232668 4300612737960 36248021648520 304483381847568
loop(\(x,i).(4 * (x + (6x div (if i <= 0 then 1 else i)))),x,1)
A054337: 1 28 448 5376 53760 473088 3784704 28114944 196804608 1312030720 8396996608 51908706304 311452237824 1820797698048 10404558274560 58265526337536
loop(\(x,i).(4 * (x + (8x div (if i <= 0 then 1 else i)))),x,1)
A054339: 1 36 720 10560 126720 1317888 12300288 105431040 843448320 6372720640 45883588608 317013884928 2113425899520 13655982735360 85837605765120 526470648692736
loop(\(x,i).(4 * (x + (5x div (if i <= 0 then 1 else i)))),x,1)
A045543: 1 24 336 3584 32256 258048 1892352 12976128 84344832 524812288 3148873728 18320719872 103817412608 574988746752 3121367482368 16647293239296
loop(\(x,i).(loop(\(x,i).(x * (~1 + (2 * i))),i,1) + (4x * i)),x,1)
A090470: 1 5 43 531 8601 172965 4161555 116658675 3735104625 134498225925 5380583766075 236759435017875 11364769115001225 590975899833644325 4611686018427387903 4611686018427387903
((x mod 2) - loop(\(x,i).(2 * (x - (2 * (x + (if (i mod 2) <= 0 then 2 else 0))))),x,1))
A145593: ~1 3 4 ~7 24 ~47 104 ~207 424 ~847 1704 ~3407 6824 ~13647 27304 ~54607
loop(\(x,i).(2 * (2x + loop(\(x,i).(~1 + (2 * (x + (i mod 2)))),i,0))),x,1)
A255467: 1 6 26 110 450 1822 7330 29406 117794 471518 1886754 7548382 30196258 120790494 483172898 1932713438
loop(\(x,i).(2 * (2x + loop(\(x,i).3x,(~2 + (2 * i)),1))),x,1)
A165314: 1 6 42 330 2778 24234 215034 1923018 17258010 155125482 1395342906 12554940426 112981880922 1016786596650 9150878043258 82357097082954
(1 + compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),x,(~4x + 1)),x))
A156287: 2 3 4 6 7 9 12 13 16 18 19 21 22 27 28 33
loop(\(x,i).(4x + loop(\(x,i).(5x + 1),i,1)),x,1)
A016218: 1 10 71 440 2541 14070 75811 400900 2091881 10808930 55442751 282806160 1436400421 7271480590 36715316891 185008240220
loop(\(x,i).(4x + loop(\(x,i).(0 - (2 * (x + (x div 2)))),i,1)),x,1)
A290124: 1 2 14 38 206 662 3134 11078 48686 181622 765854 2945318 12135566 47479382 193106174 762858758
loop(\(x,i).(4x + loop(\(x,i).(1 - (2 * (x + (i mod 2)))),i,1)),x,1)
A249993: 1 1 11 29 147 525 2227 8653 35123 139469 559923 2235597 8950579 35785933 143176499 572640461
(loop(\(x,i).10x,x,1) - loop(\(x,i).4x,x,1))
A248338: 0 6 84 936 9744 98976 995904 9983616 99934464 999737856 9998951424 99995805696 999983222784 9999932891136 99999731564544 999998926258176
(loop(\(x,i).10x,x,1) mod loop(\(x,i).4x,x,1))
A139735: 0 2 4 40 16 672 576 5760 57600 182784 779264 3598336 10817536 41066496 8011776 616988672
(loop(\(x,i).7x,x,1) + loop(\(x,i).4x,x,1))
A074613: 2 11 65 407 2657 17831 121745 839927 5830337 40615751 283523825 1981521047 13858064417 96956119271 678491508305 4748635251767
(loop(\(x,i).7x,x,1) - loop(\(x,i).4x,x,1))
A190542: 0 3 33 279 2145 15783 113553 807159 5699265 40091463 281426673 1973132439 13824509985 96821901543 677954637393 4746487768119
(loop(\(x,i).7x,x,1) mod loop(\(x,i).4x,x,1))
A138654: 0 3 1 23 97 423 2961 4343 63169 245575 408305 1809559 84001 50919655 155110993 548906039
(loop(\(x,i).5x,x,4) + loop(\(x,i).4x,x,1))
A235115: 5 24 116 564 2756 13524 66596 328884 1628036 8074644 40111076 199506804 993339716 4949921364 24682497956 123144054324
loop(\(x,i).(~5x + loop(\(x,i).4x,(~1 + i),1)),x,1)
A166036: 1 ~4 24 ~104 584 ~2664 14344 ~67624 354504 ~1706984 8797064 ~42936744 218878024 ~1077612904 5455173384 ~27007431464
loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),x,1)
A016163: 1 14 151 1484 13981 128954 1176211 10664024 96366841 869254694 7833057871 70546348964 635161281301 5717672234834 51465153629131 463216900240304
loop(\(x,i).(~5x + loop(\(x,i).3x,(2 * i),1)),x,1)
A118005: 1 4 61 424 4441 36844 347221 3046864 27812401 248358484 2244991981 20156099704 181649037961 1633620638524 14708689262341 132347685782944
loop(\(x,i).(5x + loop(\(x,i).(3x + ~3),i,1)),x,1)
A087439: 1 5 22 98 451 2135 10312 50468 249061 1235465 6147802 30650438 152986471 764135195 3818284492 19084248008
loop(\(x,i).(5x + loop(\(x,i).(3x + 1),i,1)),x,1)
A016209: 1 9 58 330 1771 9219 47188 239220 1205941 6059229 30384718 152189310 761743711 3811110039 19062724648 95335146600
loop(\(x,i).2x,(2x2 + ~x),loop(\(x,i).(2 * (2 - (i mod 2))),x,1))
A122249: 1 4 256 65536 1073741824 70368744177664 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(4 * (4x - (x div (if i <= 0 then 1 else (i * i))))),x,1)
A000515: 1 12 180 2800 44100 698544 11099088 176679360 2815827300 44914183600 716830370256 11445589052352 182811491808400 2920656969720000 46670906271240000 745904795339462400
loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).10x,x,1))
A037156: 1 55 5050 500500 50005000 5000050000 500000500000 50000005000000 5000000050000000 500000000500000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x2 + ~x) div 2),1,loop(\(x,i).10x,x,1))
A037182: 0 45 4950 499500 49995000 4999950000 499999500000 49999995000000 4999999950000000 499999999500000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).4x,x,2) - loop(\(x,i).(2x * (1 + (i mod 2))),x,1))
A091143: 1 4 24 96 448 1792 7680 30720 126976 507904 2064384 8257536 33292288 133169152 534773760 2139095040
(loop(\(x,i).~5x,x,1) * loop(\(x,i).(~2x + 2),x,1))
A091883: 1 0 50 250 3750 31250 343750 3281250 33593750 332031250 3339843750 33300781250 333496093750 3332519531250 33337402343750 333312988281250
loop(\(x,i).((x + 1) + i),compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x),1)
A006308: 3 10 21 55 78 136 171 253 406 465 666 820 903 1081 1378 1711
loop(\(x,i).(x + (2 * i)),compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x),1)
A160772: 13 31 91 133 241 307 463 757 871 1261 1561 1723 2071 2653 3307 3541
loop(\(x,i).((x + 1) + i),compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),1)
A188545: 1 3 10
A008837: 1 3 10 21 55 78 136 171 253 406 465 666 820 903 1081 1378
loop(\(x,i).4x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),1)
A139292: 1 4 64 1024 262144 4194304 1073741824 17179869184 4398046511104 18014398509481984 288230376151711744 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A005722: 1 4 16 36 100 144 256 324 484 784 900 1296 1600 1764 2116 2704
((x2 + 2x + 1) * loop(\(x,i).2x,x,(2 + loop(\(x,i).2x,x,2))))
A192831: 4 48 360 2304 13600 76032 407680 2113536 10658304 52531200 254003200 1208549376 5672083456 26309885952 120803328000 549772591104
(loop(\(x,i).(x * i),(x + ~1),(x + 1)) * (if x <= 0 then 2 else (x2 + 2x + 1)))
A276940: 2 8 27 128 750 5184 41160 368640 3674160 40320000 482993280 6270566400 87697209600 1314380390400 21016195200000 357082280755200
loop(\(x,i).((x + 2) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,1)
A110895: 1 4 8 14 22 34 48 66 86 110 140 172 210 252 296 344
(1 - loop(\(x,i).loop(\(x,i).10x,(i mod 2),(x + ~2)),x,1))
A094621: 0 11 13 141 143 1441 1443 14441 14443 144441 144443 1444441 1444443 14444441 14444443 144444441
loop(\(x,i).(2x + loop(\(x,i).((3x + 1) - (i mod 2)),i,1)),x,1)
A243869: 1 5 20 70 231 735 2290 7040 21461 65065 196560 592410 1782691 5358995 16098830 48340180
loop(\(x,i).loop(\(x,i).(x2 + x + 1),(1 - (x mod 4)),2x),x,1)
A018378: 1 2 4 73 146 292
((if (x mod 2) <= 0 then 3 else ~2) + loop(\(x,i).(2x + (i mod 2)),x,1))
A344109: 4 1 9 11 29 51 109 211 429 851 1709 3411 6829 13651 27309 54611
((1 + loop(\(x,i).(~6x + 12),x,1)) mod loop(\(x,i).2x,x,1))
A325893: 0 1 1 5 5 21 21 21 149 149 149 1173 1173 1173 9365 9365
loop(\(x,i).(4x + ((x2 + ~x) div 2)),1,loop(\(x,i).2x,x,1))
A257272: 4 9 22 60 184 624 2272 8640 33664 132864 527872 2104320 8402944 33583104 134275072 536985600
(loop(\(x,i).3x,(2x + 2),3) + loop(\(x,i).2x,x,1))
A188526: 28 245 2191 19691 177163 1594355 14348971 129140291 1162261723 10460353715 94143179851 847288611491 7625597489083 68630377373075 617673396300331 5559060566588291
(loop(\(x,i).(x - (2 * (~x + (i mod 2)))),x,3) - loop(\(x,i).2x,x,1))
A133510: 2 5 17 53 167 515 1577 4793 14507 43775 131837 396533 1191647 3579035 10745297 32252273
(loop(\(x,i).3x,((x * (x mod 2)) div 2),1) + loop(\(x,i).2x,x,1))
A014556: 2 3 5 11 17 41
A085613: 2 3 5 11 17 41 65 155 257 593 1025 2291 4097 8921 16385 34955
(loop(\(x,i).(2 * (x + ((x - i) div 3))),x,1) div loop(\(x,i).2x,x,1))
A336351: 1 1 1 1 1 1 1 2 3 4 5 7 9 12 16 22
(loop(\(x,i).11x,x,1) - loop(\(x,i).2x,x,1))
A139740: 0 9 117 1323 14625 161019 1771497 19487043 214358625 2357947179 25937423577 285311668563 3138428372625 34522712135739 379749833566857 4177248169382883
((x + 4) + loop(\(x,i).3x,x,1) - loop(\(x,i).2x,x,1))
A290651: 4 6 11 26 73 220 675 2070 6317 19184 58039 175114 527361 1586148 4766603 14316158
(loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2) - loop(\(x,i).2x,x,1))
A085781: 1 4 16 62 236 892 3368 12742 48364 184244 704408 2702108 10396504 40108408 155101136 601047622
loop(\(x,i).(3x + loop(\(x,i).(1 - (2 * (x + (i mod 2)))),i,1)),x,1)
A249992: 1 0 7 6 49 84 379 882 3157 8448 27391 78078 242425 710892 2165443 6430794
loop(\(x,i).(2 * (x + (9x div (if i <= 0 then 1 else i)))),x,1)
A140354: 1 20 220 1760 11440 64064 320320 1464320 6223360 24893440 94595072 343982080 1203937280 4074864640 13388840960 42844291072
loop(\(x,i).(2 * (x + (10x div (if i <= 0 then 1 else i)))),x,1)
A172242: 1 22 264 2288 16016 96096 512512 2489344 11202048 47297536 189190144 722362368 2648662016 9372188672 32133218304 107110727680
loop(\(x,i).(2 * (x + (7x div (if i <= 0 then 1 else i)))),x,1)
A054851: 1 16 144 960 5280 25344 109824 439296 1647360 5857280 19914752 65175552 206389248 635043840 1905131520 5588385792
loop(\(x,i).((x + 2) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)),x,1)
A237589-A138981: 1 4 9 16 27 40 57 76 99 128 159 196 237 280 327 380
loop(\(x,i).(loop(\(x,i).(2x * (~1 + (2 * i))),i,1) + (2x * i)),x,1)
A076729: 1 4 28 288 3984 70080 1506240 38384640 1133072640 38038533120 1431213235200 59645279232000 2726781752217600 135661078090137600 4611686018427387903 4611686018427387903
((0 - loop(\(x,i).(x2 + ~x),2,loop(\(x,i).(2x + 1),x,0))) mod (x + 1))
A066503: 0 0 0 2 0 0 0 6 6 0 0 6 0 0 0 14
((x + 1) * loop(\(x,i).(loop(\(x,i).(x * i),(~1 + i),1) + (2x * i)),x,0))
A242091: 0 2 15 128 1310 15864 222936 3572736 64354608 1287495360 28328889600 679936896000 17678878214400 495015296025600 14850552286080000 475219068007219200
((x + 1) + loop(\(x,i).(x + i - (if (x + ~1) <= 0 then 0 else (2 * (1 + i)))),x,0))
A046901: 1 3 6 2 7 1 8 16 7 17 6 18 5 19 4 20
(loop(\(x,i).2x,x,(1 - loop(\(x,i).((x + 4) * i),x,0))) mod (x + 1))
A115869-A115859: 0 0 0 0 0 0 3 0 0 0 7 0 5 6 0 0
((1 + (loop(\(x,i).((x + 1) * (x + i)),2,x) + (if x <= 0 then 1 else 0))) div (x + 1))
A197602: 8 15 37 76 140 234 364 536 756 1030 1364 1764 2236 2786 3420 4144
((x + 1) * (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))
A285109: 1 4 9 8 25 12 49 16 27 20 121 24 169 28 45 32
((1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)) mod (x + 1))
A271419: 0 0 0 2 0 2 0 2 3 2 0 2 0 2 3 2
(loop(\(x,i).(x * i),(x - (loop(\(x,i).(x * i),x,1) mod (x + 1))),1) div (x + 1))
A055637: 1 0 0 0 0 20 0 630 4480 36288 0 3326400 0 444787200 5811886080 81729648000
((x + 1) * loop(\(x,i).(x + loop(\(x,i).(x + (i * i)),(~1 + i),i)),(x + ~1),1))
A302612: 1 2 6 20 65 186 462 1016 2025 3730 6446 10572 16601 25130 36870 52656
(loop(\(x,i).loop(\(x,i).11x,x,1),2,1) div (x + 1))
A057073: 285311670611 142655835305 95103890203 71327917652 57062334122 47551945101 40758810087 35663958826 31701296734 28531167061 25937424601 23775972550 21947051585 20379405043 19020778040
compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(4x + ~1)),(x + 1))
A045752: 4 7 9 10 13 14 16 19 22 23 24 25 28 29 30 31
((0 - (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)) mod (x + 1))
A318827: 0 1 1 3 1 5 1 7 7 9 1 11 1 13 13 15
compr(\x.loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),x,(3x + 1)),(x + 1))
A334919: 5 8 9 13 16 17 18 21 23 25 28 29 30 33 37 38
((x + 1) * loop(\(x,i).(1 + loop(\(x,i).10x,2,x)),x,1))
A064100: 1 202 30303 4040404 505050505 60606060606 7070707070707 808080808080808 90909090909090909 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((if x <= 0 then 1 else (0 - loop(\(x,i).(2 * (x - (2x * i))),x,1))) div (x + 1))
A292220: 1 1 ~4 30 ~336 5040 ~95040 2162160 ~57657600 1764322560 ~60949324800 2346549004800 ~99638080819200 4626053752320000 ~233153109116928000 4611686018427387903
loop(\(x,i).2x,(2 - (loop(\(x,i).(2x + i),x,0) mod (x + 1))),(x + 1))
A066560: 4 4 6 4 10 6 14 8 9 10 22 12 26 14 15 16
(loop(\(x,i).2x,x,loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))) div (x + 1))
A084623: 1 1 4 2 16 16 64 16 256 256 1024 512 4096 4096 16384 2048
(loop(\(x,i).(2x + ~4),loop(\(x,i).(x div (1 + (x mod 2))),x,x),1) mod (x + 1))
A318305: 0 1 1 1 1 4 1 1 1 6 1 4 1 8 7 1
(loop(\(x,i).(loop(\(x,i).~x,i,3) + (x * (2 + i))),x,1) div (x + 1))
A316666: 1 0 1 3 15 87 597 4701 41787 413691 4512993 53779833 695000919 9680369943 144560191149 2303928046437
(loop(\(x,i).(x + (loop(\(x,i).(1 + (2x * i)),i,1) + i)),x,1) mod (x + 1))
A235138: 0 1 2 2 4 1 6 4 6 3 10 2 12 5 7 8
compr(\x.((1 + loop(\(x,i).(x div 2),x,loop(\(x,i).3x,x,1))) mod 2),(x + 1))
A073632: 1 3 4 5 6 7 8 10 12 14 15 17 18 20 21 22
((x + 1) * (if (x + ~1) <= 0 then x else (if ((x + ~2) mod (2 + (x mod 2))) <= 0 then 1 else 2)))
A242480: 0 2 3 8 5 6 7 16 9 20 11 12 13 28 15 32
loop(\(x,i).(6x * loop(\(x,i).x2,2,2x)),2,(x + 1))
A066543: 782757789696 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 - (if (x mod 8) <= 0 then 0 else (x div 3))),2,(x + 1))
A334144: 1 1 1 1 1 2 2 1 2 2 2 2 2 2 3 1
((~x + ~1) + (2 * loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 1 else 0)),x,(x + 2))))
A087030: 3 4 7 6 9 8 15 14 13 12 15 14 21 20 19 18
compr(\x.loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,4x),(x + 1))
A095277: 3 6 8 9 12 13 15 18 21 22 23 24 27 28 29 30
((x + 1) * (loop(\(x,i).(~x + 1),x,(x + loop(\(x,i).(1 - (x * i)),x,1))) div 2))
A145222: 0 0 3 0 30 120 945 7392 66780 667440 7342335 88107360 1145396538 16035550440 240533257965 3848532125760
((loop(\(x,i).3x,x,3) - loop(\(x,i).2x,x,2)) div (x + 1))
A191694: 1 2 6 16 42 110 294 788 2130 5802 15918 43945 122010 340470 954409 2686324
compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 4 else 0))),x,2x),(x + 1))
A037453: 1 2 5 6 7 10 11 12 25 26 27 30 31 32 35 36
compr(\x.(loop(\(x,i).(x div (if (x mod (2 + (x mod 2))) <= 0 then 2 else 1)),x,x) div 2),(x + 1))
A115422: 1 2 3 4 6 8 9 12 16 18 24 32 33 36 48 64
compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x2),(x + 1))
A176189: 1 2 3 6 9 11 16 18 19 27 29 33 48 54 55 57
loop(\(x,i).(7x + (if (2 - i) <= 0 then x else 1)),x,(x + 1))
A081043: 1 15 176 1856 18432 176128 1638400 14942208 134217728 1191182336 10468982784 91268055040 790273982464 6803228196864 58274116272128 496979255754752
((x + 1) * loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),(x + ~1),x))
A119582: 0 2 36 360 2800 18900 116424 672672 3706560 19691100 101615800 512143632 2531090016 12303909800 58971402000 279211536000
(loop(\(x,i).2x,x,1) div ((x + 1) * (if (x + ~1) <= 0 then 2 else (x2 + ~x))))
A326595: 0 0 0 0 0 0 0 0 0 0 1 1 2 3 6 9
((x + loop(\(x,i).(2x - (x mod (0 - (if i <= 0 then 1 else i)))),x,1)) div (x + 1))
A128021: 1 1 2 3 5 8 14 25 44 79 144 264 487 905 1689 3167
loop(\(x,i).(9x + (if (2 - i) <= 0 then x else 1)),x,(x + 1))
A081045: 1 19 280 3700 46000 550000 6400000 73000000 820000000 9100000000 100000000000 1090000000000 11800000000000 127000000000000 1360000000000000 14500000000000000
(loop(\(x,i).((~x + 1) - (if (x mod (1 + (2 * i))) <= 0 then x else 0)),2,x) div (x + 1))
A291437: 0 0 0 2 0 0 1 0 0 1 0 1 1 0 0 1
(loop(\(x,i).x2,x,(x + 1)) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))
A307031: 1 4 27 65536 30517578125 4611686018427387903 4611686018427387903
loop(\(x,i).(x + ((x * loop(\(x,i).(x2 + x),2,2)) div (1 + i))),x,(x + 1))
A010996: 1 44 990 15180 178365 1712304 13983816 99884400 636763050 3679075400 19499099620 95722852680 438729741450 1889912732400 7694644696200 29752626158640
loop(\(x,i).(~x + ((x * loop(\(x,i).(x2 + x),2,2)) div (1 + i))),x,(x + 1))
A010956: 1 40 780 9880 91390 658008 3838380 18643560 76904685 273438880 847660528 2311801440 5586853480 12033222880 23206929840 40225345056
loop(\(x,i).(~x + ((x * loop(\(x,i).(x2 + 2x),2,2)) div (1 + i))),x,(x + 1))
A017794: 1 78 3003 76076 1426425 21111090 256851595 2641902120 23446881315 182364632450 1258315963905 7778680504140 43430966148115 220495674290430 1023729916348425 4367914309753280
((x + 1) * loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,x2))
A119580: 0 4 72 720 5600 37800 232848 1345344 7413120 39382200 203231600 1024287264 5062180032 24607819600 117942804000 558423072000
((x + 1) + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))
A097911: 1 3 5 8
A175540: 1 3 5 8 10 13 15 18 22 24 28 31 33 36 40 44
((x + 1) * (loop(\(x,i).(2x * (1 + i)),x,1) - loop(\(x,i).(x * i),x,x)))
A086984: 1 6 60 696 9120 134640 2227680 41005440 833172480 18546796800 449223667200 11766674304000 331501679308800 9997170543360000 321355745238528000 4611686018427387903
loop(\(x,i).(x + (9x div (if i <= 0 then 1 else i))),x,(x + 1))
A056114: 1 20 165 880 3575 12012 35035 91520 218790 486200 1016158 2015520 3821090 6963880 12257850 20920064
loop(\(x,i).(x + (7x div (if i <= 0 then 1 else i))),x,(x + 1))
A056001: 1 16 108 480 1650 4752 12012 27456 57915 114400 213928 381888 655044 1085280 1744200 2728704
(loop(\(x,i).(2x * (1 + (2 * i))),x,1) + loop(\(x,i).(x * i),x,(x + 1)))
A226730: 2 8 66 864 15240 333360 8653680 259499520 8821975680 335224915200 14079333945600 647648004326400 32382382493260800 1748648405555251200 4611686018427387903 4611686018427387903
loop(\(x,i).((~x2 + x) + loop(\(x,i).(x2 + ~x),3,x)),1,(x + ~1))
A064321: 0 0 0 0 864 17280 144000 756000 2963520 9483264 26127360 64152000 143748000 298995840 584648064 1085142240
((x + ~1) * ((x * loop(\(x,i).(x + loop(\(x,i).(x * i),i,1)),(x + ~1),1)) div 2))
A061834: 0 0 2 12 60 340 2310 18354 165592 1664424 18410130 222085270 2901011124 40790592492 614247917374 9862468172970
loop(\(x,i).(x + (if (~4 + (x div 2)) <= 0 then 1 else (x div 4))),2,(x + ~1))
A036965: 1 2 3 4 5 6 7 8 9 10 12 15 16 18 20 21
loop(\(x,i).(x + (if (((2x * i) div (1 + i)) div (1 + i)) <= 0 then i else 0)),x,1)
A088650: 1 2 4 4 4 4 10 10 10 10 10 10 10 10 10 10
((x2 + x + 1) mod (1 + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)))
A174624-A174433: 0 0 1 0 1 1 0 1 1 3 0 1 1 3 1 0
loop(\(x,i).(x * (1 + loop(\(x,i).(2x2 + 2x),i,5))),x,1)
A068533: 1 61 446581 47864301941221 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(10x + 1),3,1)),x,1)
A291945: 1 1111 1234321 1371330631 1523548331041 1692662195786551 1880547699518858161 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + loop(\(x,i).(2x2 + 2x),(1 + i),3))),x,1)
A068534: 1 1201 3461763601 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 3),x,loop(\(x,i).11x,x,1))
A318165: 1 3 13
A094978: 1 3 13 49 180 662 2430 8910 32671 119796 439252 1610592 5905506 21653524 79396256 291119607
loop(\(x,i).(x div 4),x,loop(\(x,i).11x,x,1))
A094982: 1 2 7 20 57 157 432 1189 3270 8994 24735 68023 187064 514428 1414678 3890365
loop(\(x,i).(~x + loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),(~1 + i),1)),x,1)
A000757: 1 0 0 1 1 8 36 229 1625 13208 120288 1214673 13469897 162744944 2128047988 29943053061
loop(\(x,i).(x * (x2 div 2)),1,loop(\(x,i).7x,x,1))
A130215: 0 168 58800 20176632 6920642400 2373780746568 814206798896400 279272932041230232 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 5),x,loop(\(x,i).7x,x,1))
A094984: 1 1 1 2 3 5 7 10 14 20 28 40 56 79 111 155
loop(\(x,i).(x * loop(\(x,i).(10x + 1),4,1)),x,1)
A291946: 1 11111 123454321 1371700960631 15240969373571041 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~5x + loop(\(x,i).6x,i,1)),x,1)
A053430: 1 1 31 61 991 2821 32551 117181 1093711 4609141 37420471 175694701 1298308831 6569149861 45518414791 242592910621
(loop(\(x,i).3x,2x,1) - loop(\(x,i).5x,x,1))
A191466: 0 4 56 604 5936 55924 515816 4704844 42656096 385467364 3477018776 31332231484 282185395856 2540645125204 22870688939336 205860614516524
(loop(\(x,i).3x,2x,1) mod loop(\(x,i).5x,x,1))
A139730: 0 4 6 104 311 2799 191 17344 77971 701739 456276 33403359 202973981 361922079 815892461 19550063399
(loop(\(x,i).6x,x,1) - loop(\(x,i).5x,x,1))
A016160: 0 1 11 91 671 4651 31031 201811 1288991 8124571 50700551
A005062: 0 1 11 91 671 4651 31031 201811 1288991 8124571 50700551 313968931 1932641711 11839990891 72260648471 439667406451
(loop(\(x,i).6x,x,1) mod loop(\(x,i).5x,x,1))
A138649: 0 1 11 91 46 1526 15406 45561 117116 312071 1872426 21000181 223657336 853662766 5121976596 12421312701
(loop(\(x,i).8x,x,1) - loop(\(x,i).5x,x,1))
A191468: 0 3 39 387 3471 29643 246519 2019027 16386591 132264603 1063976199 8541106467 68475336111 548535110763 4391942995479 35153854510707
(loop(\(x,i).8x,x,1) mod loop(\(x,i).5x,x,1))
A138959: 0 3 14 12 346 1518 12144 65902 370966 1405228 9288699 45012717 115961111 439407638 3515261104 28122088832
loop(\(x,i).2x,(x - (2 * (x mod 2))),loop(\(x,i).5x,x,1))
A156276: 1 5 100 250 10000 25000 1000000 2500000 100000000 250000000 10000000000 25000000000 1000000000000 2500000000000 100000000000000 250000000000000
(loop(\(x,i).6x,x,2) - loop(\(x,i).5x,x,1))
A085352: 1 7 47 307 1967 12427 77687 481747 2968607 18202267 111166727 676765987 4109424047 24900684907 150624812567 909852391027
((3 * (2 + loop(\(x,i).2x,x,1))) + loop(\(x,i).3x,x,1))
A254362: 10 15 27 57 135 345 927 2577 7335 21225 62127 183297 543735 1618905 4832127 14447217
(loop(\(x,i).~3x,(x div 2),1) + loop(\(x,i).3x,x,1))
A318609: 2 4 6 24 90 252 702 2160 6642 19764 58806 176904 532170 1595052 4780782 14346720
(loop(\(x,i).(x - (x div (~2 + (x mod 2)))),x,1) + loop(\(x,i).3x,x,1))
A032124: 2 5 12 33 90 261 756 2241 6642 19845 59292 177633 532170 1595781 4785156 14353281
(loop(\(x,i).10x,x,1) + loop(\(x,i).3x,x,1))
A245806: 2 13 109 1027 10081 100243 1000729 10002187 100006561 1000019683 10000059049 100000177147 1000000531441 10000001594323 100000004782969 1000000014348907
(loop(\(x,i).10x,x,1) - loop(\(x,i).3x,x,1))
A248226: 0 7 91 973 9919 99757 999271 9997813 99993439 999980317 9999940951 99999822853 999999468559 9999998405677 99999995217031 999999985651093
(loop(\(x,i).10x,x,1) mod loop(\(x,i).3x,x,1))
A139734: 0 1 1 1 37 127 541 1036 3799 5185 51850 164206 224884 1185958 3887965 5398867
(loop(\(x,i).7x,x,1) + loop(\(x,i).3x,x,1))
A074608: 2 10 58 370 2482 17050 118378 825730 5771362 40373290 282534298 1977503890 13841818642 96890604730 678227855818 4747575858850
(loop(\(x,i).7x,x,1) - loop(\(x,i).3x,x,1))
A190541: 0 4 40 316 2320 16564 116920 821356 5758240 40333924 282416200 1977149596 13840755760 96887416084 678218289880 4747547161036
(loop(\(x,i).7x,x,1) mod loop(\(x,i).3x,x,1))
A138617: 0 1 4 19 52 40 280 1231 4243 3457 43882 11929 437797 407374 2851618 10395388
(loop(\(x,i).5x,x2,1) + loop(\(x,i).3x,x,1))
A120802: 2 8 634 1953152 152587890706 298023223876953368 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).5x,x2,1) - loop(\(x,i).3x,x,1))
A120830: 0 2 616 1953098 152587890544 298023223876952882 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).7x,x,2) - loop(\(x,i).3x,x,1))
A081657: 1 11 89 659 4721 33371 234569 1644899 11523041 80687531 564891449 3954476339 27682042961 193776426491 1356441362729 9495108670979
loop(\(x,i).(x + ((x + loop(\(x,i).4x,i,1)) div (2x + 1))),x,1)
A292528: 1 2 5 11 22
A084188: 1 2 5 11 22 45 90 181 362 724 1448 2896 5792 11585 23170 46340
loop(\(x,i).(x + loop(\(x,i).x5,1,(1 + (2 * i)))),x,1)
A002594: 1 244 3369 20176 79225 240276 611569 1370944 2790801 5266900 9351001 15787344 25552969 39901876 60413025 89042176
loop(\(x,i).(loop(\(x,i).(x * (~1 + (2 * i))),i,1) + (x * (1 + (2 * i)))),x,1)
A004041: 1 4 23 176 1689 19524 264207 4098240 71697105 1396704420 29985521895 703416314160 17901641997225 491250187505700 14459713484342175 454441401368236800
loop(\(x,i).(x + (loop(\(x,i).(2x * i),i,1) + (x * (1 + (2 * i))))),x,1)
A203159: 1 6 44 400 4384 56448 836352 14026752 262803456 5441863680 123436892160 3044235018240 81112101027840 2322150583173120 71092846618214400 2317820965473484800
loop(\(x,i).(x * (~1 + (2 * i))),2x,loop(\(x,i).(x * (~1 + (2 * i))),x,1))
A139541: 1 3 315 155925 212837625 618718975875 3287253918823875 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(~11x + 1),i,1)),x,1)
A015026: 1 ~10 ~1110 1354200 18174718200 ~2683133647866000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).10x3,i,1)),x,1)
A050647: 1 11 10011 10000000010011 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(1 + (x * (2 + i)) - (2 * (x mod 2))),i,1)),x,1)
A001277: 1 3 12 56 321 2175 17008 150504 1485465 16170035 192384876 2483177808 34554278857 515620794591 8212685046336
loop(\(x,i).(x * loop(\(x,i).(1 + (x * (2 + i)) - (2 * (x mod 2))),i,1)),x,1)
A131631: 1 2 18 792 209880 389117520 5771780174160 770509566129663360 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(~13x + 1),i,1)),x,1)
A015028: 1 ~12 ~1884 3843360 101929750560 ~35142523960072320 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(11x + 1),i,1)),x,1)
A015011: 1 12 1596 2336544 37630041120 6666387564654720 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),i,1)),x,1)
A079309: 1 4 14 49 175 637 2353 8788 33098 125476 478192 1830270 7030570 27088870 104647630 405187825
loop(\(x,i).(~x + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),i,1)),x,1)
A054109: 1 2 8 27 99 363 1353 5082 19228 73150 279566 1072512 4127788 15930512 61628248 238911947
loop(\(x,i).(x + loop(\(x,i).((x + 1) + ((2 + (i div 2)) * (i div 2))),i,1)),x,1)
A005994: 1 3 9 19 38 66 110 170 255 365 511 693 924 1204 1548 1956
loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),x,1)
A002110: 1 2 6 30 210 2310 30030 510510 9699690 223092870 6469693230 200560490130 7420738134810 304250263527210 13082761331670030 614889782588491410
loop(\(x,i).(x + loop(\(x,i).(((x + 1) - (2 * (x mod 2))) * (1 + i)),i,1)),x,1)
A177265: 1 1 4 12 57 321 2176 17008 150505 1485465 16170036 192384876 2483177809 34554278857 515620794592 8212685046336
loop(\(x,i).(~x + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),i,1)),x,1)
A033297: 1 1 4 10 32 100 329 1101 3761 13035 45751 162261 580639 2093801 7601044 27756626
(1 - ((2x + 1) mod (~1 + loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x))))
A138530: 1 2 1 3 2 1 4 1 2 1 5 2 3 2 1 6
loop(\(x,i).loop(\(x,i).(x + (i * i * i * i * i * i)),(1 + i),x),x,1)
A101093: 1 66 860 5750 26265 93436 278256 725220 1703625 3682030 7431996 14167946 25730705 44823000 75305920 122566056
loop(\(x,i).(x + loop(\(x,i).20x,i,(1 + i))),x,1)
A014937: 1 41 1241 33241 833241 20033241 468033241 10708033241 241108033241 5361108033241 118001108033241 2575601108033241 55823601108033241 1202703601108033241 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).15x,i,(1 + i))),x,1)
A014930: 1 31 706 14206 267331 4823581 84557956 1451432956 24517448581 408951042331 6752105339206 110549175651706 1797251568229831 29043982525261081 466937872906120456 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).18x,i,(1 + i))),x,1)
A014935: 1 37 1009 24337 549217 11886625 249972193 5147732449 104327377633 2087920281313 41363059774177 812583980724961 15851391939265249 307372900058661601 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).24x,i,(1 + i))),x,1)
A014942: 1 49 1777 57073 1715953 49491697 1387212529 38078983921 1028756811505 27446832213745 724884022832881 18985057740861169 493749574409596657 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).14x,i,(1 + i))),x,1)
A014929: 1 29 617 11593 203673 3430617 56137369 899445401 14181546905 220792014745 3402593219481 51997375255449 789018236134297 11901025061692313 178581127445062553 2667670656370058137
loop(\(x,i).(x + loop(\(x,i).13x,i,(1 + i))),x,1)
A014928: 1 27 534 9322 152127 2379885 36167548 538155684 7879732173 113924725903 1630368136242 23136292864686 326011399456939 4566262891748481 63626908677237816 882601196902689928
loop(\(x,i).(x + loop(\(x,i).11x,i,(1 + i))),x,1)
A014926: 1 23 386 5710 78915 1045221 13446148 169343516 2098573445 25678050355 310989720966 3734729768298 44534298665671 527852268680705 6224099772429320 73060070483079736
loop(\(x,i).(x + loop(\(x,i).17x,i,(1 + i))),x,1)
A014934: 1 35 902 20554 438159 8957301 177920284 3460629668 66242446637 1252121211607 23428054116546 434690809808142 8008779893795035 146672872354478153 2672340270745492088 4611686018427387903
loop(\(x,i).(x + (if (x - (x2 mod (x + 6))) <= 0 then 1 else 2)),x,1)
A244016: 1 2 3 5 7 8 9 11 13 14 15 16 18 20 22 24
(1 + loop(\(x,i).(x div (2 - ((loop(\(x,i).(x * i),x,x) mod (x + 1)) mod 2))),x,x))
A039635: 1 2 3 2 5 3 7 2 5 5 11 3 13 7 2 2
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,(2 * (1 + (3 * i))))),x,1)
A091546: 1 56 10192 3872960 2517424000 2497284608000 3511182158848000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).x3,1,(((2 + i) * (1 + i)) div 2))),x,1)
A085438: 1 28 244 1244 4619 13880 35832 82488 173613 339988 627484 1102036 1855607 3013232 4741232 7256688
loop(\(x,i).x3,1,loop(\(x,i).(x + (((2 + i) * (1 + i)) div 2)),x,1))
A270272: 1 64 1000 8000 42875 175616 592704 1728000 4492125 10648000 23393656 48228544 94196375 175616000 314432000 543338496
loop(\(x,i).(x + loop(\(x,i).(2 * (2x - (x div (1 + i)))),(~1 + i),2)),x,1)
A006134: 1 3 9 29 99 351 1275 4707 17577 66197 250953 956385 3660541 14061141 54177741 209295261
loop(\(x,i).(x + (if x <= 0 then 3 else (2x - (~x mod 4)))),x,1)
A118264: 1 0 3 8 24 72 216 648 1944 5832 17496 52488 157464 472392 1417176 4251528
(1 + compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(~2 + (x div 2)),x)),x))
A087743: 3 4 5 6 8 12 14 18 20 24 30 32 38 42 44 48
(x - ((x + 2) div (1 + (if x <= 0 then 2 else loop(\(x,i).(x div (2 - (x mod 2))),x,x)))))
A273724: 0 0 0 2 1 4 4 6 3 8 8 10 9 12 12 14
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,(2 + (5 * i)))),x,1)
A091545: 1 42 5544 1507968 696681216 489070213632 485157651922944 646229992361361408 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),x,1)
A054640: 1 3 12 72 576 6912 96768 1741824 34836480 836075520 25082265600 802632499200 30500034969600 1281001468723200 56364064623820800 2705475101943398400
loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),x,1)
A070826: 1 3 15 105 1155 15015 255255 4849845 111546435 3234846615 100280245065 3710369067405 152125131763605 6541380665835015 307444891294245705 4611686018427387903
loop(\(x,i).5x,x,loop(\(x,i).6x,x2,1))
A135421: 1 30 32400 1259712000 1763193692160000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i))),x2,1)
A081623: 1 1 6 126 12870 5200300 9075135300 63205303218876 1832624140942590534 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).3x,2x,loop(\(x,i).8x,x2,1))
A135320: 1 72 331776 97844723712 1846757322198614016 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).6x,x,loop(\(x,i).5x,x2,1))
A135349: 1 30 22500 421875000 197753906250000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (x mod 4) <= 0 then (6x + 3) else x)),x,1)
A018294: 1 2 4 31 62 124
loop(\(x,i).(x + (if (x mod 4) <= 0 then (x3 + x2 + x + 1) else x)),x,1)
A018410: 1 2 4 89 178 356
loop(\(x,i).(x + loop(\(x,i).(x - ((x + 1) div 7)),2,x)),x,1)
A222011: 1 2 4 8
A164391: 1 2 4 8 14 25 44 77 134 233 405 703 1220 2117 3673 6372
loop(\(x,i).(3x + loop(\(x,i).~4x,(~1 + i),1)),x,1)
A165458: 1 4 8 40 56 424 248 4840 ~1864 59944 ~82312 801640 ~1789384 11409064 ~32881672 169790440
loop(\(x,i).(x + loop(\(x,i).10x,((1 + i) * i),x)),x,1)
A292686: 1 101 101000101 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + loop(\(x,i).23x,i,x)),x,1)
A028692: 1 22 11616 141320256 39547060439040 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(((2x * i) div (1 + i)) * (1 + (2 * i))),i,x),x,1)
A093883: 1 3 60 12600 38102400 2112397056000 2609908810629120000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * compr(\x.(loop(\(x,i).(x * (1 + (i div 2))),x,1) mod (x + 1)),i)),x,1)
A067546: 1 3 15 105 840 7560 83160 1081080 15135120 227026800 3859455600 73329656400 1466593128000 30798455688000 708364480824000 17000747539776000
loop(\(x,i).(x + (20x div (if i <= 0 then 1 else i))),x,1)
A010973: 1 21 231 1771 10626 53130 230230 888030 3108105 10015005 30045015 84672315 225792840 573166440 1391975640 3247943160
loop(\(x,i).(~x + (20x div (if i <= 0 then 1 else i))),x,1)
A282288-A010935: 1 19 171 969 3876 11628 27132 50388 75582 92378 92378 75582 50388 27132 11628 3876
loop(\(x,i).(x + (15x div (if i <= 0 then 1 else i))),x,1)
A010968: 1 16 136 816 3876 15504 54264 170544 490314 1307504 3268760 7726160 17383860 37442160 77558760 155117520
loop(\(x,i).(~x + (15x div (if i <= 0 then 1 else i))),x,1)
A010930: 1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14 1
loop(\(x,i).(x + (18x div (if i <= 0 then 1 else i))),x,1)
A010971: 1 19 190 1330 7315 33649 134596 480700 1562275 4686825 13123110 34597290 86493225 206253075 471435600 1037158320
loop(\(x,i).(~x + (18x div (if i <= 0 then 1 else i))),x,1)
A010933: 1 17 136 680 2380 6188 12376 19448 24310 24310 19448 12376 6188 2380 680 136
loop(\(x,i).(x + (24x div (if i <= 0 then 1 else i))),x,1)
A010977: 1 25 325 2925 20475 118755 593775 2629575 10518300 38567100 131128140 417225900 1251677700 3562467300 9669554100 25140840660
loop(\(x,i).(~x + (24x div (if i <= 0 then 1 else i))),x,1)
A010939: 1 23 253 1771 8855 33649 100947 245157 490314 817190 1144066 1352078 1352078 1144066 817190 490314
loop(\(x,i).(x + (32x div (if i <= 0 then 1 else i))),x,1)
A010985: 1 33 561 6545 58905 435897 2760681 15380937 76904685 350343565 1471442973 5752004349 21090682613 73006209045 239877544005 751616304549
loop(\(x,i).(~x + (32x div (if i <= 0 then 1 else i))),x,1)
A010947: 1 31 465 4495 31465 169911 736281 2629575 7888725 20160075 44352165 84672315 141120525 206253075 265182525 300540195
loop(\(x,i).(x + (14x div (if i <= 0 then 1 else i))),x,1)
A010967: 1 15 120 680 3060 11628 38760 116280 319770 817190 1961256 4457400 9657700 20058300 40116600 77558760
loop(\(x,i).(~x + (14x div (if i <= 0 then 1 else i))),x,1)
A010929: 1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1
loop(\(x,i).(x + (13x div (if i <= 0 then 1 else i))),x,1)
A010966: 1 14 105 560 2380 8568 27132 77520 203490 497420 1144066 2496144 5200300 10400600 20058300 37442160
loop(\(x,i).(x + (11x div (if i <= 0 then 1 else i))),x,1)
A001288: 1 12 78 364 1365 4368 12376 31824 75582 167960 352716 705432 1352078 2496144 4457400 7726160
loop(\(x,i).(~x + (17x div (if i <= 0 then 1 else i))),x,1)
A010932: 1 16 120 560 1820 4368 8008 11440 12870 11440 8008 4368 1820 560 120 16
loop(\(x,i).((2x + ~1) * ((x2 + ~x) div 2)),1,loop(\(x,i).(x * i),x,1))
A020545: 0 0 3 165 12972 1706460 372470760 127985964120 65545882234560 47784528317211840 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(((x + 1) * loop(\(x,i).(x * i),(x + ~1),(x + 1))) + loop(\(x,i).(x * i),x,1))
A001344: 2 5 11 38 174 984 6600 51120 448560 4394880 47537280 562464000 7224940800 100111334400 1488257971200 23625316915200
loop(\(x,i).loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),i,(x * i)),x,1)
A338550: 1 1 4 60 3360 705600 558835200 1678182105600 19198403288064000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + compr(\x.(loop(\(x,i).(2x + 1),x,0) mod (x + 1)),i) - i),x,1)
A112997: 1 2 4 7 13 20 30 41 55 74 94 119 147 176 208 245
(if (x + ~1) <= 0 then 1 else (if (x mod (1 + ((x + 2) div 5))) <= 0 then 0 else 2))
A116127: 1 1 0 2 0 2 0 2 2 0 2 2 0 2 2 2
(2 + (if x <= 0 then 3 else (if (2x mod (x + 5)) <= 0 then 2 else 0)))
A303579: 5 2 2 2 2 4 2 2 2 2 2 2 2 2 2 2
((if x <= 0 then loop(\(x,i).(4x2 + ~x + 3),2,2) else 0) div 2)
A246229: 571 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(loop(\(x,i).(x + ((x + loop(\(x,i).(x * i),i,1)) * (1 + i))),(x + 2),0) div 2)
A024187: 7 47 342 2754 24552 241128 2592720 30334320 383970240 5231113920 76349105280 1188825724800 19675048780800
loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),x,(x - (x div ~2)))
A185727: 0 2 1 5 2 8 1 11 4 14 5 17 2 20 7 23
(2 + loop(\(x,i).(1 + (2 * (2 + (loop(\(x,i).2x,x,2) div (x + 1))))),x,0))
A104337: 2 11 211 4611686018427387903
(loop(\(x,i).(6x + loop(\(x,i).(~2x + 2),i,1)),x,0) div 2)
A091056: 0 0 1 5 33 193 1169 6993 42001 251921 1511697 9069841 54419729 326517009 1959104785 11754623249
(~2 + loop(\(x,i).x5,1,loop(\(x,i).(2x + 1),x,0)))
A098879: ~2 ~1 241 16805 759373 28629149 992436541 33038369405 1078203909373 34842114263549 1120413075641341 35940921946155005 1151514816750309373 4611686018427387903 4611686018427387903 4611686018427387903
(2 * loop(\(x,i).((x + 1) + (if (i mod (1 + (x mod 4))) <= 0 then 0 else 1)),x,0))
A114270: 0 2 4 6 8 10 12 16 18 22 26 30 32 34 36 38
((loop(\(x,i).3x,(x + ~1),1) + loop(\(x,i).(~2x + 1),x,0)) div 2)
A094555: 0 1 1 6 11 46 111 386 1051 3366 9671 29866 87891 267086 794431 2396946
(loop(\(x,i).loop(\(x,i).((2x * (~1 + (2 * i))) + i),3,x),x,0) div 2)
A101830: 0 41 5021
(loop(\(x,i).(loop(\(x,i).(2x * i),i,1) + (x * (~1 + (2 * i)))),x,0) div 2)
A192458: 0 1 7 59 605 7365 104055 1675275 30290085 607828725 13406691375 322415322075 8396547684525 235419569309925 7070492932878375 226469231898784875
(2 * (1 + (loop(\(x,i).(x * (2 + i)),x,1) + (if (x + ~1) <= 0 then 1 else ~1))))
A109095: 6 10 24 120 720 5040 40320
(2 + (x div (1 + loop(\(x,i).(if (x div 2) <= 0 then (1 + (2 * i)) else (x div 2)),x,0))))
A222127-A222027: 2 2 3 2 3 4 2 3 4 6 2 3 4 6 9 2
(if (x mod (1 + ((~2x + 2) mod (1 + (x div 2))))) <= 0 then (if x <= 0 then 0 else 1) else 2)
A196942: 0 1 1 1 1 2 1 1 1 2 1 2 2 2 1 1
(if x <= 0 then 0 else (if (x mod (1 + ((2x + ~2) mod (1 + (x div 2))))) <= 0 then 1 else 2))
A325225-A325169-A322862-A322306-A240086-A206719: 0 1 1 1 1 2 1 1 2 2 1 2 1 2 2 1
(2 * (if (x mod 2) <= 0 then (15 * (if x <= 0 then 1 else 2)) else 1))
A040899: 30 2 60 2 60 2 60 2 60 2 60 2 60 2 60 2
((if (x mod 3) <= 0 then 2 else loop(\(x,i).3x,(x div 3),1)) div 2)
A140313: 1 0 0 1 1 1 1 4 4 1 13 13 1 40 40 1
((1 + (if ((if x <= 0 then 2 else ((x + 1) div 2)) mod 3) <= 0 then (x div 2) else 1)) div 2)
A327482: 1 1 1 1 1 1 2 1 1 1 1 3 3 1 1 1
((1 + (loop(\(x,i).(x * i),x,1) div loop(\(x,i).(x * (i * i)),(x div 2),1))) div 2)
A275324: 1 1 1 3 3 15 10 70 35 315 126 1386 462 6006 1716 25740
(1 - ((1 + loop(\(x,i).(x - ((if x <= 0 then (x + ~1) else i) div 3)),x,1)) div 2))
A060826: 0 0 0 1 0 1 0 1 1 0 2 1 1 0 2 1
(2 - ((1 + loop(\(x,i).loop(\(x,i).(x + ~1),(x * (i div 2)),(x + 1)),x,1)) div 2))
A152545: 1 1 1 1 2 1 2 2 1 3 2 2 1 4 3 3
((1 + loop(\(x,i).(2 * (3x + (if (~2 + i) <= 0 then 1 else 0))),x,1)) div 2)
A055846: 1 4 25 150 900 5400 32400 194400 1166400 6998400 41990400 251942400 1511654400 9069926400 54419558400 326517350400
((1 + loop(\(x,i).((2x div (if i <= 0 then 1 else i)) * (4 + i)),x,1)) div 2)
A080951: 1 5 30 140 560 2016 6720 21120 63360 183040 512512 1397760 3727360 9748480 25067520 63504384
((1 + loop(\(x,i).(2 * (x + (3x div (if i <= 0 then 1 else i)))),x,1)) div 2)
A082138: 1 4 20 80 280 896 2688 7680 21120 56320 146432 372736 931840 2293760 5570560 13369344
(loop(\(x,i).(2 * (4x + (x div (if i <= 0 then 1 else i)))),(x + 1),1) div 2)
A088505: 5 45 390 3315 27846 232050 1922700 15862275 130423150 1069469830 8750207700 71460029550 582674087100 4744631852100 38589672397080 313541088226275
(loop(\(x,i).(4x + (if (i mod 3) <= 0 then 1 else 2)),(x + 1),1) div 2)
A037660: 3 13 52 211 845 3380 13523 54093 216372 865491 3461965 13847860 55391443 221565773 886263092 3545052371
(~2 + loop(\(x,i).(x + (8x div (if i <= 0 then 1 else i))),(x + 1),1))
A166813: 7 43 163 493 1285 3001 6433 12868 24308 43756 75580 125968 203488 319768 490312 735469
((1 + loop(\(x,i).(x div 2),(x + ~1),loop(\(x,i).(x * (~1 + (2 * i))),x,1))) div 2)
A020045: 1 1 1 2 7 30 162 1056 7918 67304 639384 6713531 77205601 965070017 13028445232 188912455860
(loop(\(x,i).(x * i),(x + ~1),(1 + loop(\(x,i).(x * (~1 + (2 * i))),x,1))) div 2)
A137729: 1 1 2 16 318 11352 623760 48648960 5108105520 694702028160 118794043549440 24946749109094400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((1 + loop(\(x,i).2x,x,(1 - (x div loop(\(x,i).(x * (0 - i)),x,1))))) div 2)
A288700: 1 2 0 8 8 32 32 128 128 512 512 2048 2048 8192 8192 32768
((x + 1) div (if (x + ~2) <= 0 then 1 else (2 * (1 + (if (x + ~4) <= 0 then 0 else 2)))))
A076224: 1 2 3 2 2 1 1 1 1 1 1 2 2 2 2 2
((1 + (loop(\(x,i).(x + i),((if (x mod 2) <= 0 then 2 else 0) + (x div 2)),0) div 2)) div 2)
A008720: 1 0 2 0 3 1 4 2 5 3 7 4 9 5 11 7
(2 + ((x + 2) div (1 + (2 * (1 + loop(\(x,i).(if x <= 0 then i else (x div 2)),x,0))))))
A222111: 2 2 3 2 3 4 2 3 4 5 2 3 4 5 7 2
(if (x mod 2) <= 0 then (21 * (if x <= 0 then 1 else 2)) else 2)
A040440: 21 2 42 2 42 2 42 2 42 2 42 2 42 2 42 2
(if (x mod 2) <= 0 then (14 * (2 + (if x <= 0 then 0 else 2))) else 2)
A040783: 28 2 56 2 56 2 56 2 56 2 56 2 56 2 56 2
(if x <= 0 then 0 else (if (x mod 2) <= 0 then 2 else ((x mod (1 + ((1 + (x div 2)) div 2))) mod 2)))
A107279: 0 0 2 1 2 1 2 1 2 0 2 1 2 1 2 0
((loop(\(x,i).2x,x,3) - loop(\(x,i).2x,((x + 1) div 2),1)) div 2)
A172411: 1 2 5 10
A136488-A135098: 1 2 5 10 22 44 92 184 376 752 1520 3040 6112 12224 24512 49024
(loop(\(x,i).2x,x,(1 + loop(\(x,i).2x,(x div 2),((x + 1) mod 2)))) div 2)
A098657: 1 1 6 4 40 16 288 64 2176 256 16896 1024 133120 4096 1056768 16384
(2 * (if (x mod 2) <= 0 then (13 * (if x <= 0 then 1 else 2)) else 1))
A040675: 26 2 52 2 52 2 52 2 52 2 52 2 52 2 52 2
(2 * (if (x mod 2) <= 0 then (11 * (if x <= 0 then 1 else 2)) else 1))
A040483: 22 2 44 2 44 2 44 2 44 2 44 2 44 2 44 2
((1 + ((loop(\(x,i).(x + (if (~2 + (x div 2)) <= 0 then 1 else i)),x,1) div 2) div 2)) div 2)
A172992: 0 0 0 1 1 1 2 2 3 5 6 7 9 10 12 14
(if (x mod 2) <= 0 then (27 * (if x <= 0 then 1 else 2)) else 2)
A040728: 27 2 54 2 54 2 54 2 54 2 54 2 54 2 54 2
loop(\(x,i).(x * i),(~1 + (2 * ((if x <= 0 then 2 else (3x + ~2)) div 2))),2)
A130718: 2 2 12 240 725760 79833600 2615348736000 711374856192000 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 2) <= 0 then (25 * (if x <= 0 then 1 else 2)) else 2)
A040624: 25 2 50 2 50 2 50 2 50 2 50 2 50 2 50 2
(loop(\(x,i).3x,x,1) mod loop(\(x,i).x2,2,10))
A216097: 1 3 9 27 81 243 729 2187 6561 9683 9049 7147 1441 4323 2969 8907
(if x <= 0 then 2 else loop(\(x,i).x3,(x2 + ~x),10))
A252707: 2 10 1000000000
(if x <= 0 then 0 else ((x + 2) + ((if (x + ~2) <= 0 then 1 else 2) + (x div 5))))
A168044: 0 4 5 7 8 10 11 12 13 14 16 17 18 19 20 22
(if x <= 0 then 1 else (2 * (1 + (if (x + ~1) <= 0 then x else ((x2 + 2x) div 4)))))
A231407: 1 4 6
A256137: 1 4 6 8 14 18 26 32 42 50 62 72 86 98 114 128
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(8x + 2))
A017098: 1024 10000000000 3570467226624 141167095653376 2064377754059776 17080198121677824 97656250000000000 430804206899405824 1568336880910795776 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(8x + 2))
A017100: 4096 1000000000000 1156831381426176 95428956661682176 2386420683693101056 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((if ((x + 2) mod 6) <= 0 then 2 else 1) * (if (~2 + (x div 2)) <= 0 then 1 else 2))
A077197: 1 1 1 1 2 1 2 2 2 2 4 2 2 2 2 2
(if x <= 0 then 1 else (2 * (if (x + ~1) <= 0 then x else ((x div 2) mod (1 + (2 * (x mod 2)))))))
A096500: 1 2 0 2 0 4 0 0 0 2 0 4 0 0 0 2
((1 + (loop(\(x,i).(~3x + loop(\(x,i).2x,i,1)),x,2) div 2)) div 2)
A091003: 1 ~1 4 ~10 34 ~94 298 ~862 2650 ~7822 23722 ~70654 212986 ~636910 1914826 ~5736286
(2 + (3 * (1 + loop(\(x,i).((x + 2) + loop(\(x,i).(x * i),x,2)),x,0))))
A097490: 5 17 167 4611686018427387903 4611686018427387903
(~2 + loop(\(x,i).3x,(x + ~2),(3 * (2 + (if x <= 0 then 1 else 2)))))
A079004: 7 10 10 34 106 322 970 2914 8746 26242 78730 236194 708586 2125762 6377290 19131874
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(6x + 2))
A016942: 1024 1073741824 289254654976 10240000000000 141167095653376 1125899906842624 6278211847988224 27197360938418176 97656250000000000 303305489096114176 839299365868340224 2113922820157210624
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(6x + 2))
A016944: 4096 68719476736 56693912375296 4096000000000000 95428956661682176 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,((if (x mod 2) <= 0 then 2 else (x2 + 2x)) mod 6))
A204919-A089090: 4 9 4 9 4 25 4 9 4 9 4 25 4 9 4 9
loop(\(x,i).(x + (3 * (2x div (if i <= 0 then 1 else i)))),x,6)
A253946: 6 42 168 504 1260 2772 5544 10296 18018 30030 48048 74256 111384 162792 232560 325584
loop(\(x,i).(x + (5x div (if i <= 0 then 1 else i))),x,6)
A253945: 6 36 126 336 756 1512 2772 4752 7722 12012 18018 26208 37128 51408 69768 93024
(loop(\(x,i).(x2 + x),1,loop(\(x,i).(x * i),x,1)) div (2 + (x div 3)))
A288555: 1 1 3 14 200
(2 + (3 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,x),x)))
A190640: 2 8 20 26 56 62 74 80 164 170 182 188 218 224 236 242
(2 * (3 + compr(\x.loop(\(x,i).(x - (if (x mod (2 + i)) <= 0 then 0 else 1)),x,x),x)))
A073582: 6 8 10 14 22 26 34 38 46 58 62 74 82 86 94 106
((x + 1) mod (2 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))
A080063: 1 2 3 1 5 0 7 2 1 1 11 0 13 2 3 1
((1 + (loop(\(x,i).(2 + loop(\(x,i).x2,1,(~2 + (x div 2)))),2,x) div 2)) div 2)
A146261-A146193-A146176: 1 1 1 1 1 1 1 1 1 1 3 3 13 13 31 31
(2 + (loop(\(x,i).(3x + 4),x,1) mod (~1 + loop(\(x,i).2x,x,2))))
A060692: 2 3 6 6 26 36 28 186 265 738 1105 3186 5269 15516 29728 55761
(x - (x div ((if ((x div 2) mod 3) <= 0 then 2 else 1) + (if (x + ~2) <= 0 then 1 else 2))))
A069754: 0 1 1 2 3 4 5 6 6 6 7 8 9 10 10 10
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(4x + 2))
A016835: 2048 362797056 100000000000 4049565169664 64268410079232 584318301411328 3670344486987776 17714700000000000 70188843638032384 238572050223552512 717368321110468608 1951354384207722496
loop(\(x,i).(x * (~1 + (loop(\(x,i).2x,i,1) + (i mod 2)))),(2x + 1),2)
A027638: 4 96 46080 371589120 48514675507200 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * loop(\(x,i).loop(\(x,i).2x2,1,(x3 + x)),2x,1))
A324439: 2 1081600 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(2x + 1),((x + 1) div 2),loop(\(x,i).2x,(x div 2),1)) div 2)
A192225: 0 1 2 5
A056326: 0 1 2 5 9 19 35 71 135 271 527 1055 2079 4159 8255 16511
(loop(\(x,i).(x * i),x,(1 + loop(\(x,i).(x * i),x,(x + 1)) - (x mod 2))) div 2)
A137730: 1 1 7 72 1452 43200 1814760 101606400 7315680960 658409472000 72425043734400 9560105533440000 1491376463456140800 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,x,(1 + (2 * (2 + (if x <= 0 then 0 else 2))) - (x mod 2))) div 2)
A190787: 2 8 18 32 72 128 288 512 1152 2048 4608 8192 18432 32768 73728 131072
((if x <= 0 then 2 else (~1 + loop(\(x,i).(x + ((x - (x div 4)) div 2)),x,2))) div 2)
A094995: 1 1 1 2 3 4 6 9 12 17 24 33 45 62 86 118
(2 * (1 + compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)),x)))
A238204: 10 16 22 26 28 34 36 40 46 50 52 56 58 64 66 70
(loop(\(x,i).(((x2 + 2x) div 3) + loop(\(x,i).2x,x,1)),x,1) div 2)
A317485: 0 1 6 4128
(if x <= 0 then 1 else (2 + (2 mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1))))
A034444: 1 2 2 2 2 4 2 2 2 4 2 4 2 4 4 2
((loop(\(x,i).2x,x,1) - loop(\(x,i).(2 * (x div (~2 + (i mod 2)))),x,1)) div 2)
A113979: 0 2 1 6 6 20 28 72 120 272 496 1056 2016 4160 8128 16512
(2 * (loop(\(x,i).2x,x,2) - loop(\(x,i).(2 * (x div (~2 + (i mod 2)))),x,1)))
A251421: 2 12 12 40 56 144 240 544 992 2112 4032 8320 16256 33024 65280 131584
((loop(\(x,i).6x,x,1) + loop(\(x,i).4x,x,1)) div 2)
A081187: 1 5 26 140 776 4400 25376 148160 872576 5169920 30757376 183495680 1096779776 6563901440 39316299776 235629363200
((loop(\(x,i).6x,x,1) - loop(\(x,i).4x,x,1)) div 2)
A081199: 0 1 10 76 520 3376 21280 131776 807040 4907776 29708800 179301376 1080002560 6496792576 39047864320 234555621376
((1 + loop(\(x,i).(x + (if (~2 + (x div 3)) <= 0 then 1 else 2)),(x + 2),x)) div 2)
A158023: 1 2 3 4 6 8 10 12 14 16 17 19 20 22 23 25
((loop(\(x,i).(2 * (x + (x div 2))),x,3) - loop(\(x,i).2x,x,1)) div 2)
A188545: 1 3 10
A053581: 1 3 10 32 100 308 940 2852 8620 25988 78220 235172 706540 2121668 6369100 19115492
((loop(\(x,i).2x,(x div 2),(~1 + (x mod 2))) + loop(\(x,i).2x,x,1)) div 2)
A007179: 0 1 1 4 6 16 28 64 120 256 496 1024 2016 4096 8128 16384
((loop(\(x,i).(2 * (x div (~2 + (i mod 2)))),x,1) + loop(\(x,i).2x,x,1)) div 2)
A113980: 1 0 3 2 10 12 36 56 136 240 528 992 2080 4032 8256 16256
((loop(\(x,i).(4x + ~4),(x + ~1),2) + loop(\(x,i).2x,x,1)) div 2)
A274232: 1 2 4 10 30 102 374 1430 5590 22102 87894 350550 1400150 5596502 22377814 89494870
(2 * compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)),(x + 1)))
A186193: 14 20 24 26 32 34 38 44 48 50 54 56 62 64 68 74
((2 - (loop(\(x,i).2x,(if (x mod 3) <= 0 then x else 0),2) mod (x + 1))) div 2)
A238429: 1 1 0 1 0 0 0 0 0 ~1 0 0 0 0 0 1
(loop(\(x,i).(x * loop(\(x,i).(x * (2 + i)),4,3)),2,(x + 1)) div 2)
A050518: 583200 1166400 1749600 2332800 2916000 3499200 4082400 4665600 5248800 5832000 6415200 6998400 7581600 8164800 8748000 9331200
(((x + 1) * loop(\(x,i).((x + loop(\(x,i).(x * i),i,1)) * (2 + i)),x,2)) div 2)
A098107: 1 9 66 500 4110 37044 365904 3945024 46195920 584575200 7955893440 115942544640 1802051072640 29763892972800 520699560192000 9619862405529600
(2 * compr(\x.loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,2x),(x + 1)))
A146538: 6 12 18 22 24 30 32 36 42 46 48 52 54 60 62 66
loop(\(x,i).(loop(\(x,i).(x * (~1 + (2 * i))),i,1) + (2x * i)),(x + 1),2)
A306185: 5 23 153 1329 14235 181215 2672145 44781345 840523635 17465201775 397983749625 9867844134225 264469801070475 7618612476650175 234748657653134625 4611686018427387903
loop(\(x,i).((1 + loop(\(x,i).2x,x,1)) div (2x + 1)),1,(2x + 2))
A191641: 1 1 5 15 48 163 565 1985 7085 25575 93206 342392 1266205 4709393 17602325 66076419
(loop(\(x,i).(~x + (if x <= 0 then 7 else 0)),x,1) * ((x + 1) div 2))
A266086: 0 ~1 8 ~16 30 ~45 66 ~88 116 ~145 180 ~216 258 ~301 350 ~400
loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x div 2),((x + 1) mod 2))
A126869: 1 0 2 0 6 0 20 0 70 0 252 0 924 0 3432 0
(2 + (loop(\(x,i).(1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2))),2,x) mod (x + 1)))
A253591: 2 3 3 3 3 5 7 7 7 7 7 7 7 7 7 7
(2 * loop(\(x,i).(2 * (4x - (if (2 - i) <= 0 then x else 1))),x,(x + 1)))
A229581: 2 28 264 2160 16416 119232 839808 5785344 39191040 262020096 1733363712 11367641088 74010599424 478892113920 3082323787776 19747769352192
(if (x mod 2) <= 0 then 2 else (x div (2 * loop(\(x,i).(x div (~2 + (x mod 2))),x,(x + 1)))))
A118821: 2 ~1 2 ~2 2 ~1 2 ~4 2 ~1 2 ~2 2 ~1 2 ~8
(if (x + ~1) <= 0 then 1 else (((x + ~1) * loop(\(x,i).(x * i),(x + ~1),(x + 2))) div 2))
A202365: 1 1 2 10 54 336 2400 19440 176400 1774080 19595520 235872000 3073593600 43110144000 647610163200 10374216652800
(((x + ~1) * loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,x)) div 2)
A240440: 0 0 15 105 420 1260 3150 6930 13860 25740 45045 75075 120120 185640 278460 406980
((if ((x + ~1) mod 6) <= 0 then (x div 3) else 0) + (if x <= 0 then 1 else 2))
A083261: 1 2 2 2 2 2 2 4 2 2 2 2 2 6 2 2
((1 + (if (x mod 2) <= 0 then 18 else 0)) * (if x <= 0 then 1 else 2))
A040360: 19 2 38 2 38 2 38 2 38 2 38 2 38 2 38 2
((1 + (if (x mod 3) <= 0 then 10 else 0)) * (if x <= 0 then 1 else 2))
A040118: 11 2 2 22 2 2 22 2 2 22 2 2 22 2 2 22
((if (x mod 2) <= 0 then 23 else 1) * (if x <= 0 then 1 else 2))
A040528: 23 2 46 2 46 2 46 2 46 2 46 2 46 2 46 2
((if (x mod 4) <= 0 then 13 else 1) * (if x <= 0 then 1 else 2))
A040166: 13 2 2 2 26 2 2 2 26 2 2 2 26 2 2 2
((if (x mod 2) <= 0 then 31 else 1) * (if x <= 0 then 1 else 2))
A040960: 31 2 62 2 62 2 62 2 62 2 62 2 62 2 62 2
(2 * ((1 + (if (x mod 2) <= 0 then 12 else 0)) * (if x <= 0 then 1 else 2)))
A040662: 26 4 52 4 52 4 52 4 52 4 52 4 52 4 52 4
(2 * ((1 + (if (x mod 2) <= 0 then 10 else 0)) * (if x <= 0 then 1 else 2)))
A040472: 22 4 44 4 44 4 44 4 44 4 44 4 44 4 44 4
((if (x mod (1 + ((1 + (x div 2)) div 3))) <= 0 then 1 else 2) * (if x <= 0 then 1 else 2))
A286575: 1 2 2 2 2 4 2 4 2 4 4 4 2 4 4 2
((if (x mod (1 + (((x + 1) div 2) div 3))) <= 0 then 1 else 2) * (if x <= 0 then 1 else 2))
A335385-A318307-A037445: 1 2 2 2 2 4 2 4 2 4 2 4 2 4 4 2
(2 * ((if (x mod 2) <= 0 then 15 else 1) * (if x <= 0 then 1 else 2)))
A040884: 30 4 60 4 60 4 60 4 60 4 60 4 60 4 60 4
(2 * ((if (x mod 2) <= 0 then 14 else 1) * (if x <= 0 then 1 else 2)))
A040769: 28 4 56 4 56 4 56 4 56 4 56 4 56 4 56 4
((if (x - (x2 mod (x + 6))) <= 0 then 1 else 2) * (if x <= 0 then 1 else 2))
A214212: 1 2 2 4 2 4 4 2 2 4 4 4 4 2 2 2
(2 * ((2 + (if (x mod 2) <= 0 then 12 else 0)) * (if x <= 0 then 1 else 2)))
A040762: 28 8 56 8 56 8 56 8 56 8 56 8 56 8 56 8
loop(\(x,i).x2,1,((x div (4 + (x div 4))) + (if x <= 0 then 1 else 2)))
A213083: 1 4 4 4 4 9 9 9 9 9 9 9 9 9 16 16
loop(\(x,i).(x - (5 * ((~x2 + x) div 2))),x,(if x <= 0 then 1 else 2))
A099153: 1 7 112 31192 2432305372 4611686018427387903 4611686018427387903 4611686018427387903
(x + (compr(\x.(loop(\(x,i).(2x + 1),x,0) mod (x + 1)),x) + (if x <= 0 then 1 else 2)))
A176628: 1 5 8 11 16 19 24 27 32 39 42 49 54 57 62 69
((loop(\(x,i).3x,(x div 2),1) + loop(\(x,i).3x,x,1)) div 2)
A001444: 1 2 6 15 45 126 378 1107 3321 9882 29646 88695 266085 797526 2392578 7175547
((loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1)) div 2)
A081186: 1 4 17 76 353 1684 8177 40156 198593 986404 4912337 24502636 122336033 611148724 3054149297 15265963516
((loop(\(x,i).5x,x,1) - loop(\(x,i).3x,x,1)) div 2)
A005059: 0 1 8 49 272 1441 7448 37969 192032 966721 4853288 24325489 121804592 609554401 3049366328 15251614609
(loop(\(x,i).(3x - loop(\(x,i).~2x,(~1 + i),1)),x,1) div 2)
A140725: 0 1 4 10 34 94 298 862 2650 7822 23722 70654 212986 636910 1914826 5736286
(2 + ((~1 + loop(\(x,i).(x + loop(\(x,i).(1 + (x * i)),(i div 2),x)),x,0)) div 2))
A155745: 1 1 2 3 7 21 143
((loop(\(x,i).x2,1,(1 + loop(\(x,i).~4x,x,1))) div 2) div 2)
A070775: 1 2 72 992 16512 261632 4196352 67100672 1073774592 17179738112 274878431232 4398044413952 70368752566272 1125899873288192 18014398643699712 288230375614840832
(x div (x - (if x <= 0 then 1 else (2 * (x div (2 + (if (x mod 3) <= 0 then 2 else 1)))))))
A283682: 0 1 1 1 2 1 1 2 2 1 2 2 2 2 2 1
(if x <= 0 then 1 else (2 + ((x mod (3 + (if (x + ~4) <= 0 then 0 else 2))) mod 2)))
A270226: 1 3 2 2 3 2 3 2 3 2 2 3 2 3 2 2
(loop(\(x,i).3x,x,1) mod loop(\(x,i).(8x + 1),2,2))
A036145: 1 3 9 27 81 106 44 132 122 92 2 6 18 54 25 75
(2 + ((1 + ((loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x) mod (x + 2)) div 2)) div 2))
A181948: 2 2 3 2 3 4 2 4 4 5 2 4 5 5 6 2
(loop(\(x,i).2x,x,(~2 + (3 * (x + (if (x + ~1) <= 0 then 2 else 1))))) div 2)
A176662: 2 7 14 40 104 256 608 1408 3200 7168 15872 34816 75776 163840 352256 753664
(2 * loop(\(x,i).5x,x,loop(\(x,i).2x,(x + ~3),2)))
A216099: 4 20 100 500 5000 50000 500000 5000000 50000000 500000000 5000000000 50000000000 500000000000 5000000000000 50000000000000 500000000000000
(2 + (if x <= 0 then 1 else (2 * (1 + (if (x mod 3) <= 0 then 3x else 2)))))
A161432: 3 8 8 22 8
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(8x + 4))
A017122: 1048576 61917364224 10240000000000 296196766695424 3656158440062976 27197360938418176 144555105949057024 604661760000000000 2113922820157210624 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(8x + 4))
A017124: 16777216 8916100448256 4096000000000000 232218265089212416 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).5x,x,1) mod loop(\(x,i).(2x2 + 1),2,2))
A271380: 1 5 25 125 136 28 140 48 77 59 132 8 40 37 22 110
(loop(\(x,i).5x,x,1) mod loop(\(x,i).(2x2 + ~1),2,2))
A036137: 1 5 25 28 43 21 8 40 6 30 53 71 64 29 48 46
((loop(\(x,i).2x,x,((x + 1) + loop(\(x,i).2x,x,3))) div 2) div 2)
A087438: 1 4 15 56 212 816 3184 12544 49728 197888 789248 3151872 12596224 50360320 201388032 805437440
loop(\(x,i).((x2 + x) div 2),1,((loop(\(x,i).(2x + 4),x,1) div 2) div 2))
A141499: 0 1 10 45 190 780 3160 12720 51040 204480 818560 3275520 13104640 52423680 209704960 838840320
(loop(\(x,i).3x,2x,1) mod loop(\(x,i).(x2 + 2x + 1),2,2))
A014393: 1 9 81 29 61 49 41 69 21 89 1 9 81 29 61 49
(loop(\(x,i).6x,x,1) mod loop(\(x,i).(x2 + 2x + 1),2,2))
A001311: 1 6 36 16 96 76 56 36 16 96 76 56 36 16 96 76
(4 * (loop(\(x,i).2x,(x div 2),(x mod 2)) + loop(\(x,i).2x,x,1)))
A253122: 4 12 16 40 64 144 256 544 1024 2112 4096 8320 16384 33024 65536 131584
(2 + (((x + 1) * loop(\(x,i).(x + loop(\(x,i).(x * i),i,1)),(x + ~1),1)) div 2))
A088938: 2 3 5 10 27 104 541 3498 26615 231172 2250129 24227486 285705643 3660694200 50624828357 751426146514
(2 + loop(\(x,i).loop(\(x,i).(((x + i) * i) div (x + 1)),x,2x),(x + 1),2))
A169622: 5 6 8 11 16 24 37 58 92 147 236 380 613 990 1600 2587
loop(\(x,i).4x,x,(2 + loop(\(x,i).5x,(x + 1),2)))
A307691: 12 208 4032
(x - (loop(\(x,i).2x,x,((x + 1) - loop(\(x,i).2x,(x + ~1),2))) div 2))
A288687: 1 1 4 19 92 421 1830 7687 31624 128521 518666 2084875 8361996 33497101 134094862 536608783
(2 * loop(\(x,i).(x * (1 + (2 * i))),x,(1 mod loop(\(x,i).x2,(x + ~1),2))))
A068215: 2 6 30 210 1890 20790 270270 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 + (loop(\(x,i).(x * (1 + (5 * i))),x,1) div 2)))
A011556: 1 5 35 530
(loop(\(x,i).3x,x,1) mod loop(\(x,i).(1 + ((x2 + 2x) * i)),2,2))
A036158: 1 3 9 27 81 44 132 197 193 181 145 37 111 134 4 12
loop(\(x,i).x2,1,(if x <= 0 then 1 else (x - (x div (~2 + (x div ~4))))))
A068952: 1 4 9 16 36 49 64 81 100 121 144 196
(((loop(\(x,i).x2,1,(1 + loop(\(x,i).((~x + ~1) + i),x,2))) div 2) div 2) div 2)
A008801: 1 0 2 0 3 0 4 0 6 1 8 2 10 3 12 4
(2 - (if x <= 0 then 0 else (if (x mod 3) <= 0 then 1 else (2 * ((x div 4) mod 2)))))
A078336-A076441: 2 2 2 1 0 0 1 0 2 1 2 2 1 0 0 1
(loop(\(x,i).3x,x,1) mod (~2 + loop(\(x,i).(x3 + 2),2,2)))
A216096: 1 3 9 27 81 243 729 187 561 683 49 147 441 323 969 907
(8 + loop(\(x,i).(x2 + x),1,loop(\(x,i).(2x + 2),x,2)))
A281699: 14 50 218 938 3914 16010 64778 260618 1045514 4188170 16764938 67084298 268386314 1073643530 4294770698 17179475978
loop(\(x,i).(if (x + ~1) <= 0 then 1 else (x2 div 4)),1,(x + ~8))
A224812: 1 1 1 1 1 1 1 1 1 1 1 2 4 6 9 12
((~x + (if (x mod 2) <= 0 then (if x <= 0 then 1 else 4) else x)) mod (2 + (x div 4)))
A202385: 1 0 0 0 0 0 1 0 0 0 2 0 2 0 0 0
(2 + (loop(\(x,i).3x,(x + 2),1) + loop(\(x,i).2x,(x + 2),2)))
A183624: 19 45 115 309 859 2445 7075 20709 61099 181245 539635 1610709 4815739 14414445 43177795 129402309
((loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (x + (i * i))),2,(x + 2)) div 2) div 2)
A027357: 1 0 0 0 1 1 0 1 2 1 0 1 2 2 1 2
(loop(\(x,i).(4x + loop(\(x,i).2x,(~1 + i),1)),2x,2) div 2)
A166965: 1 19 316 5104 81856 1310464 20970496 335540224 5368692736 85899280384 1374389272576 21990231506944 351843716694016 5629499517435904 90071992480301056 1441151880490123264
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,8x)
A017075: 0 8589934592 17592186044416 1521681143169024 36028797018963968 419430400000000000 3116402981210161152 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,~7x)
A016990: 0 282475249 289254654976 16679880978201 296196766695424 2758547353515625 17080198121677824 79792266297612001 303305489096114176 984930291881790849 2824752490000000000 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,~7x)
A016992: 0 13841287201 56693912375296 7355827511386641 232218265089212416 3379220508056640625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 + (2 * loop(\(x,i).loop(\(x,i).((2x + 2) + i),x,0),(x mod 2),(x div 2))))
A121173: 2 2 4 8 6 22 8 52 10 114 12 240 14 494 16 1004
(loop(\(x,i).2x,x,(2 + (loop(\(x,i).2x,(x + 2),2) + (x mod 2)))) div 2)
A240525: 5 19 68 268 1040 4144 16448 65728 262400 1049344 4195328 16780288 67112960 268447744 1073758208 4295016448
((loop(\(x,i).2x,x,(loop(\(x,i).(2x + 1),x,2) + (x mod 2))) div 2) div 2)
A181278: 0 3 11 48 188 768 3056 12288 49088 196608 786176 3145728 12581888 50331648 201322496 805306368
loop(\(x,i).(10x + 1),x,loop(\(x,i).(x2 + 2),2,2))
A187078: 38 381 3811 38111 381111 3811111 38111111 381111111 3811111111 38111111111 381111111111 3811111111111 38111111111111 381111111111111 3811111111111111 38111111111111111
(4 + (2 * loop(\(x,i).(x + loop(\(x,i).x2,1,(2 + (i div 2)))),x,1)))
A271996: 6 14 32 50 82 114 164 214 286 358 456 554 682 810 972 1134
(loop(\(x,i).x2,1,loop(\(x,i).(x + 1),(x + ~8),2)) div 4)
A224811: 1 1 1 1 1 1 1 1 1 2 4 6 9 12 16 20
(4 + compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)),x))
A153039: 8 11 14 16 17 20 21 23 26 28 29 31 32 35 36 38
loop(\(x,i).x2,(~1 + (x mod 3)),((if (x mod 2) <= 0 then 1 else x) mod 4))
A060901: 1 1 1 3 1 1 1 3 1 1 1 9 1 1 1 3
loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),4)
A034785: 4 8 32 128 2048 8192 131072 524288 8388608 536870912 2147483648 137438953472 2199023255552 8796093022208 140737488355328 9007199254740992
(4 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 2 else 1)),x,(x + 2)),x))
A005381: 9 10 15 16 21 22 25 26 27 28 33 34 35 36 39 40
(4 + compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),x))
A146968: 4 5 7
A033164: 4 5 7 8 13 14 16 17 31 32 34 35 40 41 43 44
loop(\(x,i).loop(\(x,i).(10x + 1),x,0),2,(x mod 4))
A290390: 0 1 11111111111 4611686018427387903
(4 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))
A089253: 4 5 6 8 9 11 12 14 17 18 21 23 24 26 29 32
(loop(\(x,i).(5 * (~x + loop(\(x,i).4x,i,1))),x,2) div 2)
A165470: 1 5 15 85 215 1485 2815 26885 29415 508285 80015 10085685 ~8485385 210199085 ~379906785 4583888485
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(6x + 4))
A016966: 1048576 10000000000 1099511627776 26559922791424 296196766695424 2064377754059776 10485760000000000 42420747482776576 144555105949057024 430804206899405824 1152921504606846976 2824752490000000000
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(6x + 4))
A016968: 16777216 1000000000000 281474976710656 12855002631049216 232218265089212416 2386420683693101056 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,x,loop(\(x,i).(10x + 1),x,2)) div 2)
A067895: 1 21 422 8444 168888 3377776 67555552 1351111104 27022222208 540444444416 10808888888832 216177777777664 4323555555555328 86471111111110656 1729422222222221312 4611686018427387903
loop(\(x,i).5x,x,(loop(\(x,i).(3x + ~1),x,2) div 2))
A053537: 1 10 175 2500 38125 568750 8546875 128125000 1922265625 28832031250 432490234375 6487304687500 97309814453125 1459645996093750 21894696044921875 328420410156250000
(2 + ((x * loop(\(x,i).((x + 1) * (x + loop(\(x,i).(x * i),i,1))),x,1)) div 2))
A336832: 2 4 32 1676
(((x + 2) + loop(\(x,i).(x + (2 * (if (2 - i) <= 0 then x else 1))),x,(x + 1))) div 2)
A082306: 1 3 9 29 97 327 1097 3649 12033 39371 127945 413349 1328609 4251535 13551753 43046729
(loop(\(x,i).2x,x,1) div (2 * (2 + loop(\(x,i).(x + (i * i)),(x + ~1),x))))
A326470: 0 0 0 0 0 0 0 0 0 1 1 2 3 6 9 15
(~2 + loop(\(x,i).(2x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i))),x,2))
A218008: 0 0 2 4 10 18 38 68 138 250 502 922 1846 3430 6862 12868
(loop(\(x,i).(10x + (if (~2 + i) <= 0 then 0 else 2)),x,2) div 2)
A267524: 1 10 100 1001 10011 100111 1001111 10011111 100111111 1001111111 10011111111 100111111111 1001111111111 10011111111111 100111111111111 1001111111111111
(2 * loop(\(x,i).(x3 + x2),1,loop(\(x,i).~4x,x,2)))
A107391: 24 ~896 67584 ~4161536 268959744 ~17171480576 1099645845504 ~70366596694016 4503633987108864 ~288229826395897856 4611686018427387903 4611686018427387903 4611686018427387903
((if x <= 0 then 2 else (x div (2 + (if (x mod 2) <= 0 then ((x mod 3) div 2) else x)))) div 2)
A027640: 1 0 0 0 1 0 1 0 1 0 2 0 3 0 2 0
(loop(\(x,i).(4x + loop(\(x,i).(2x + 8),i,1)),x,2) div 2)
A171480: 1 9 50 232 996 4124 16780 67692 271916 1089964 4364460 17467052 69886636 279583404 1118407340 4473776812
loop(\(x,i).(x * i),(2 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x)),2)
A131491: 4 12 240 10080 79833600 12454041600 711374856192000 243290200817664000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * (2 + (if x <= 0 then 0 else compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x))))
A197638: 4 14 22 26 34 38 46 58 62 74 82 86 94 106 118 122
(if x <= 0 then 1 else (2 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A207574: 1 6 10 14 22 26 34 38 46 58 62 74 82 86 94 106
(2 * (2 + (if x <= 0 then 2 else compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x))))
A196226: 8 10 14 22 26 34 38 46 58 62 74 82 86 94 106 118
(~2 + (loop(\(x,i).2x,(x + ~8),1) + loop(\(x,i).2x,x,2)))
A123121: 1 3 7 15 31 63 127 255 511 1024 2050 4102 8206 16414 32830 65662
(2 * (loop(\(x,i).(3x + ~1),(x + 2),2) - loop(\(x,i).2x,x,2)))
A185940: 24 74 228 698 2124 6434 19428 58538 176124 529394 1590228 4774778 14332524 43013954 129074628 387289418
(2 * (loop(\(x,i).2x,(x div 2),(2 + (x mod 2))) + loop(\(x,i).2x,x,2)))
A211525: 8 14 24 44 80 152 288 560 1088 2144 4224 8384 16640 33152 66048 131840
(((~1 + loop(\(x,i).(x - (if (~x + i) <= 0 then (1 + i) else 0)),x,x)) mod (x + 2)) div 2)
A072741: 0 0 1 0 2 3 0 0 4 5 0 0 1 6 7 0
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),(x + 4))
A334321-A296520-A241059-A235154-A045921-A034845: 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73
(loop(\(x,i).(x2 + x),1,(if (~4 + (x div 2)) <= 0 then x else (x + 2))) div 2)
A050760: 0 1 3 6 10 15 21 28 36 45 78 91 105 120 136 153
(loop(\(x,i).(x + (5x div (if i <= 0 then 1 else i))),x,(x + 2)) div 2)
A051923: 1 9 42 140 378 882 1848 3564 6435 11011 18018 28392 43316 64260 93024 131784
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x + ~2),x)),4x)
A031385: 2 11 23 41 59 73 97 109 137 157 179 197 227 241 269 283
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),4x)
A031378: 3 13 29 43 61 79 101 113 139 163 181 199 229 251 271 293
((x + 2) - loop(\(x,i).(x - (if (2x mod (1 + i)) <= 0 then 2 else 1)),x,2x))
A020481: 2 3 3 3 5 3 3 5 3 3 5 3 5 7 3 3
(2 * compr(\x.(1 - loop(\(x,i).(x div (if (x mod 2) <= 0 then ~2 else 1)),x,x)),2x))
A248057: 2 8 14 22 26 32 38 42 50 56 62 70 74 82 88 94
(x - (2 * loop(\(x,i).(if (x * (x - i)) <= 0 then (x + ~1) else 1),(x div 2),(x div 2))))
A181694: 0 1 2 3 4 5 8 9 6 7 10 11 14 15 12 13
(2 + ((if (~1 + (x div 2)) <= 0 then (1 + (2 * (if x <= 0 then 0 else 2))) else 0) + (x mod 2)))
A202478: 3 8 7 8 2
(2 + loop(\(x,i).((2x + 1) * (2 + (if x <= 0 then 1 else x))),(x + ~1),(x mod 2)))
A062597: 2 3 5 211
(loop(\(x,i).2x,(x + ~1),(loop(\(x,i).(2x + 1),x,2) - (x mod 2))) div 2)
A181270: 1 2 11 44 188 752 3056 12224 49088 196352 786176 3144704 12581888 50327552 201322496 805289984
(loop(\(x,i).2x,x,1) - (2 * loop(\(x,i).3x,(x div 2),(x mod 2))))
A167784: 1 0 4 2 16 14 64 74 256 350 1024 1562 4096 6734 16384 28394
(if (x mod 4) <= 0 then (5 * (if x <= 0 then 1 else 2)) else (2 + (x mod 2)))
A040022: 5 3 2 3 10 3 2 3 10 3 2 3 10 3 2 3
(loop(\(x,i).2x,(x + 2),2) - loop(\(x,i).2x,(x div 2),(2 + (x mod 2))))
A086652: 6 13 28 58 120 244 496 1000 2016 4048 8128 16288 32640 65344 130816 261760
(2 * loop(\(x,i).(x + ((x + 1) * loop(\(x,i).(x * (x - i)),2,2x))),x,2))
A219012: 4 724 198924689265124 4611686018427387903
(4 * (2x + (if (x + ~1) <= 0 then 1 else (2 * (if (x + ~2) <= 0 then x else 1)))))
A273387: 4 12 32 32 40 48 56 64 72 80 88 96 104 112 120 128
(2 * (2 + compr(\x.loop(\(x,i).loop(\(x,i).(x div (1 + (x mod 2))),x,(x + 1)),2,x),x)))
A118586: 6 12 14 24 28 30 48 56 60 62 96 112 120 124 126 192
(2 * loop(\(x,i).(x4 + 2x3 + x2),1,loop(\(x,i).x2,x,2)))
A330829: 72 800 147968 8657174528 4611686018427387903
loop(\(x,i).(1 + (3 * (2 + loop(\(x,i).2x2,x,3)))),x,2)
A238119: 2 1951 4611686018427387903
(if x <= 0 then 1 else ((x + 2) + (x div (if ((x + 1) mod 8) <= 0 then 2 else 1))))
A231407: 1 4 6
A276040: 1 4 6 8 10 12 14 12 18 20 22 24 26 28 30 24
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(5x + 2))
A016882: 1024 282475249 61917364224 2015993900449 26559922791424 205891132094649 1125899906842624 4808584372417849 17080198121677824 52599132235830049 144555105949057024 362033331456891249 839299365868340224 1822837804551761449 3743906242624487424
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(5x + 2))
A016884: 4096 13841287201 8916100448256 582622237229761 12855002631049216 150094635296999121 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,10x)
A017278: 0 10000000000 10240000000000 590490000000000 10485760000000000 97656250000000000 604661760000000000 2824752490000000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,10x)
A017280: 0 1000000000000 4096000000000000 531441000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~2 + compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(4x + 1)),x))
A153464: 0 3 4 6 9 10 12 14 15 17 18 19 21 24 27 28
((x + 2) + (if x <= 0 then 1 else (3 * (1 + (if (x + ~4) <= 0 then 0 else 2)))))
A220656: 3 6 7 8 9 16 17 18 19 20 21 22 23 24 25 26
loop(\(x,i).(6x + (if (~1 + (i mod 3)) <= 0 then 2 else 1)),x,2)
A037563: 2 14 85 512 3074 18445 110672 664034 3984205 23905232 143431394 860588365 5163530192 30981181154 185887086925 1115322521552
loop(\(x,i).(7x + (if (i mod 3) <= 0 then 2 else 1)),x,2)
A037556: 2 15 106 744 5209 36464 255250 1786751 12507258 87550808 612855657 4289989600 30029927202 210209490415 1471466432906 10300265030344
(loop(\(x,i).4x,x,1) div loop(\(x,i).(3 * (x - (i mod 2))),x,2))
A023434: 0 1 1 2 3 4 6 8 11 15 20 27 36 48 64 85
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(3x + 2))
A016799: 2048 48828125 8589934592 285311670611 4049565169664 34271896307633 204800000000000 952809757913927 3670344486987776 12200509765705829 36028797018963968 96549157373046875 238572050223552512 550329031716248441 1196683881290399744
((x + loop(\(x,i).(x + (loop(\(x,i).2x,x,1) div (x + 1))),(x + ~2),1)) div 2)
A045504: 0 1 1 2 3 5 8 55
(((x mod 2) + loop(\(x,i).(3x + ~1),x,2)) - loop(\(x,i).2x,x,2))
A092438: 0 2 6 26 90 302 966 3026 9330 28502 86526 261626 788970 2375102 7141686 21457826
(~2 + compr(\x.(1 + loop(\(x,i).(0 - (if (x mod (1 + i)) <= 0 then 0 else x)),(x div 2),x)),x))
A097538: 1 5 9 17 21 29 41 45 57 65 69 77 81 101 105 125
(loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,(x2 + x)) div 2)
A145911: 0 1 1 2 10 5 7 28 4 5 55 22 26 91 35 40
loop(\(x,i).loop(\(x,i).2x,(x div 2),(x mod ~2)),1,((x2 + x) div 2))
A183896: 0 ~1 ~2 0 0 ~128 ~1024 0 0 ~4194304 ~134217728 0 0 ~35184372088832 ~4503599627370496 0
((x + 2) + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1)))
A244055: 3 4 3 5 3
A090739: 3 4 3 5 3 4 3 6 3 4 3 5 3 4 3 7
loop(\(x,i).((x + 1) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,2)
A036439: 2 4 7 12 19 30 43 60 79 102 131 162 199 240 283 330
((x * loop(\(x,i).(x * loop(\(x,i).(2x + i),(x + ~2),0)),1,(x + ~1))) div 2)
A342404: 0 0 0 0 6 40 165 546 1596 4320 11115 27610 66858 158808 371553 858690
loop(\(x,i).((~x + 1) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,2)
A083236: 2 0 3 2 5 6 7 10 9 14 15 16 21 20 23 24
(3 - ((if x <= 0 then 1 else x) + loop(\(x,i).(1 + (2 * (2x - i))),x,0)))
A340495: 2 3 8 33 138 563 2268 9093 36398 145623 582528 2330153 9320658 37282683 149130788 596523213
(loop(\(x,i).(10x + 1),x,1) * ((if x <= 0 then 1 else x) mod 2))
A277560: 1 11 0 1111 0 111111 0 11111111 0 1111111111 0 111111111111 0 11111111111111 0 1111111111111111
(compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + 1))),x) div 2)
A001912: 1 2 3 5 7 8 10 12 13 18 20 27 28 33 37 42
((x + 1) mod (2 + (if (x mod 2) <= 0 then 1 else (if ((~x + 1) mod 3) <= 0 then 2 else x))))
A083218: 1 2 0 4 2 6 1 0 0 10 2 12 1 2 0 16
(2 * (x + (if (x + ~2) <= 0 then 1 else (2 + (if (~2 + (x div 4)) <= 0 then 0 else 2)))))
A309374: 2 4 6 10 12
A022305: 2 4 6 10 12 14 16 18 20 22 24 26 32 34 36 38
((if x <= 0 then 1 else 8) mod (if ((x + 1) mod 8) <= 0 then x else 2))
A288323: 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 8
loop(\(x,i).(8x + (if (~1 + (i mod 3)) <= 0 then 2 else 1)),x,2)
A037565: 2 18 145 1162 9298 74385 595082 4760658 38085265 304682122 2437456978 19499655825 155997246602 1247977972818 9983823782545 79870590260362
loop(\(x,i).(8x + (if ((~1 + i) mod 3) <= 0 then 1 else 2)),x,2)
A037573: 2 17 138 1106 8849 70794 566354 4530833 36246666 289973330 2319786641 18558293130 148466345042 1187730760337 9501846082698 76014768661586
(~2 + compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),x,(~4x + 1)),x))
A089986: ~1 0 1 3 4 6 9 10 13 15 16 18 19 24 25 30
(loop(\(x,i).3x,2x,3) + loop(\(x,i).4x,x,2))
A138233: 5 35 275 2315 20195 179195 1602515 14381675 129271235 1162785755 10462450355 94151567435 847322163875 7625731702715 68630914235795 617675543767595
(loop(\(x,i).6x,x,3) - loop(\(x,i).4x,x,2))
A016149: 1 10 76 520 3376 21280 131776 807040 4907776 29708800 179301376 1080002560 6496792576 39047864320 234555621376 1408407470080
(loop(\(x,i).5x,x,3) - loop(\(x,i).4x,x,2))
A193656: 1 7 43 247 1363 7327 38683 201607 1040803 5335087 27199723 138095767 698867443 3527891647 17773675963 89405250727
(2 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,4x),x))
A074939: 0 4 10 12 28 30 36 40 82 84 90 94 108 112 118 120
loop(\(x,i).(5x + (if (~1 + (i mod 3)) <= 0 then 2 else 1)),x,2)
A037562: 2 12 61 307 1537 7686 38432 192162 960811 4804057 24020287 120101436 600507182 3002535912 15012679561 75063397807
loop(\(x,i).(x * (2 + i)),compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x),2)
A039716: 2 6 120 5040 39916800 6227020800 355687428096000 121645100408832000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + i),compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),2)
A072205: 2 4 11 22 56 79 137 172 254 407 466 667 821 904 1082 1379
loop(\(x,i).4x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),2)
A139290: 2 8 128 2048 524288 8388608 2147483648 34359738368 8796093022208 36028797018963968 576460752303423488 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A001248: 4 9 25 49 121 169 289 361 529 841 961 1369 1681 1849 2209 2809
loop(\(x,i).x2,2,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A030514: 16 81 625 2401 14641 28561 83521 130321 279841 707281 923521 1874161 2825761 3418801 4879681 7890481
loop(\(x,i).2x,x,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A110295: 2 6 20 56 176 416 1088 2432 5888 14848 31744 75776 167936 352256 770048 1736704
loop(\(x,i).(2x + i),compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),2)
A100105: 2 5 27 121 2037 8179 131055 524269 8388585 536870883 2147483617 137438953435 2199023255511 8796093022165 140737488355281 9007199254740939
(2 + (if (x + ~1) <= 0 then x else compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x)))
A201363: 2 3 7
A045319: 2 3 7 11 13 17 19 23 29 31 37 41 43 47 53 59
compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x),(x2 + 2x + 2))
A073171: 4 9 16 26 38 52 69 88 111 133 159 187 217 250 287 323
(2 + compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),(x div 2),(~2x + 1)),x))
A124678: 3 4 5 6 8 9 11 12 14 17 18 21 23 24 26 29
loop(\(x,i).((x + 2) + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),i)),x,2)
A343859: 2 7 14 25 38 55 74 97 126 157 194 235 278 325 378 437
loop(\(x,i).((x + 2) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)),x,2)
A301273: 2 5 10 17 28 41 58 77 100 129 160 197 238 281 328 381
loop(\(x,i).((x + ~2) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)),x,2)
A282329: 2 ~1 ~6 ~13 ~24 ~37 ~54 ~73 ~96 ~125 ~156 ~193 ~234 ~277 ~324 ~377
((x + 2) * loop(\(x,i).((x + loop(\(x,i).(x * i),(~1 + i),1)) * (1 + i)),x,0))
A180218: 0 6 36 220 1500 11508 98784 940896 9862560 112923360 1402980480 18804839040 270532604160 4158579398400 68031755366400 1180252336435200
(loop(\(x,i).(2x + 1),(if (x mod 2) <= 0 then (1 + (x div 2)) else 0),1) mod (x + 2))
A135521: 1 1 3 1 3 1 7 1 3 1 7 1 3 1 15 1
(if (1 - ((x - (if (~2 + (x div 2)) <= 0 then 0 else 1)) mod 3)) <= 0 then 1 else (x + 2))
A088347: 2 1 1 5 1 1 1 9 1 1 12 1 1 15 1 1
((1 + loop(\(x,i).(x - ((~x + (x div (if i <= 0 then 1 else i))) div 2)),x,1)) div (x + 2))
A017834: 1 0 0 0 1 1 1 1 2 3 4 5 7 9 13 18
compr(\x.(1 + loop(\(x,i).(1 - (if (x mod (2 + i)) <= 0 then 0 else x)),(x div 2),x)),(x + 2))
A161897: 11 23 47 59 83 107 167 179 227 263 347 359 383 467 479 503
((x + 2) * loop(\(x,i).x2,1,loop(\(x,i).3x,(x + 1),(x + 1))))
A129009: 18 972 26244 524880 8857350 133923132 1874923848 24794911296 313810596090 3835462841100 45565298552268 528708092292432 6014054549826414 67257769817585340 741208075540736400
(loop(\(x,i).(loop(\(x,i).(2x * i),i,1) + (x * (1 + i))),x,1) mod (x + 2))
A091528: 1 1 0 3 4 2 0 6 6 5 0 3 8 0 0 13
(((x + 2) + (3 * loop(\(x,i).(if x <= 0 then i else (x div 2)),x,0))) div (x + 2))
A129264: 1 2 1 2 1 1 3 2 1 1 3 2 1 1 1 3
(if (x + ~3) <= 0 then (x + 1) else ((x + 2) * loop(\(x,i).(2x + 2),x,2)))
A172998: 1 2 3 4 372
(loop(\(x,i).2x,x,loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 2))) div (x + 2))
A036296: 1 2 1 8 8 32 8 128 128 512 256 2048 2048 8192 1024 32768
(3 - loop(\(x,i).(if (x mod 4) <= 0 then 1 else (x div 3)),x,(x + 2)))
A086411: 1 2 3 2 3 2 3 3 2 3 3 3 2 3 3 3
((x + 2) + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))
A184978: 2 4 6 9 11
A163057: 2 4 6 9 11 14 16 19 23 25 29 32 34 37 41 45
loop(\(x,i).(1 + (4 * loop(\(x,i).(x + (i * i)),(x + ~1),x))),1,2x)
A081586: 1 13 73 245 593 1181 2073 3333 5025 7213 9961 13333 17393 22205 27833 34341
(loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1) div (~2x + 1))
A002420: 1 ~2 ~2 ~4 ~10 ~28 ~84 ~264 ~858 ~2860 ~9724 ~33592 ~117572 ~416024 ~1485800 ~5348880
compr(\x.loop(\(x,i).(x div (if (x mod 2) <= 0 then ~2 else 1)),(x + ~1),(x + 1)),2x)
A157970: 5 9 17 23 29 33 39 45 53 57 65 71 77 85 89 95
loop(\(x,i).(x + (if x <= 0 then 1 else (x - ((1 + (x * i)) div 3)))),2,2x)
A312908: 1 4 9 13 17 23 27 31 36 40 44 49 53 57 63 67
(~2x + loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 2 else 1)),(x + ~2),(x + 2)))
A007920: 2 1 0 0 1 0 1 0 3 2 1 0 1 0 3 2
loop(\(x,i).(1 + (2 * (x + ((if x <= 0 then 1 else x2) mod 3)))),1,(x div 2))
A088524: 3 3 5 5 7 7 7 7 11 11 13 13 13 13 17 17
((if (x + ~1) <= 0 then 0 else (1 + (if ((x div 2) mod 2) <= 0 then 4 else 0))) + (x mod 2))
A138279: 0 1 1 2 5 6 1 2 5 6 1 2 5 6 1 2
((if x <= 0 then 1 else (if (x mod (3 * (2 + (x mod 2)))) <= 0 then 2 else 1)) - (x mod 2))
A280750: 1 0 1 0 1 0 2 0 1 1 1 0 2 0 1 0
((if x <= 0 then 0 else (if ((x2 div 2) mod (x + 3)) <= 0 then 2 else 1)) - (x mod 2))
A292262: 0 1 1 0 1 0 2 0 1 0 1 0 1 0 1 0
(loop(\(x,i).4x,x,(if (~x + 2) <= 0 then (2 * (x mod 2)) else 1)) - (x mod 2))
A266380: 1 3 0 127 0 2047 0 32767 0 524287 0 8388607 0 134217727 0 2147483647
(loop(\(x,i).2x,x,(~1 + loop(\(x,i).2x,(x * (x mod 2)),2))) - (x mod 2))
A266668: 1 5 4 119 16 2015 64 32639 256 523775 1024 8386559 4096 134209535 16384 2147450879
loop(\(x,i).x3,1,(loop(\(x,i).(3x + 1),x,1) + (x mod 2)))
A119633: 1 125 2197 68921 1771561 48627125 1305751357 35319837041 953054410321 25737699078125 694870802988517 18761935323400361 506568440928284281 4611686018427387903 4611686018427387903 4611686018427387903
((if ((x + ~1) mod (2 + (if (x mod 3) <= 0 then 0 else 2))) <= 0 then x else 1) + (x mod 2))
A247339: 1 2 1 4 1 6 1 2 1 10 1 2 1 14 1 16
(2 * (loop(\(x,i).(2 + i),loop(\(x,i).(x div (1 + (x mod 2))),x,x),1) * (x mod 2)))
A319697: 0 2 0 2 0 8 0 2 0 12 0 8 0 16 0 2
(if (x + ~1) <= 0 then 1 else ((if ((x div 2) mod 3) <= 0 then 2 else 1) * (2 - (x mod 2))))
A034693: 1 1 2 1 2 1 4 2 2 1 2 1 4 2 2 1
(loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,x) div (2 - (x mod 2)))
A106619: 0 1 1 1 2 5 1 7 4 1 5 11 2 13 7 5
loop(\(x,i).(if x <= 0 then 1 else (10x + ~8)),(x div 2),(x mod 2))
A305753: 0 1 1 2 2 12 12 112 112 1112 1112 11112 11112 111112 111112 1111112
(compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),x) + (x mod 2))
A186776: 0 2 3 5 9 11 12 14 27 29 30 32 36 38 39 41
loop(\(x,i).(3x2 + ~x),1,loop(\(x,i).5x,x,2))
A291658: 10 290 7450 187250 4686250 117181250 2929656250 73242031250 1831053906250 45776363281250 1144409160156250 28610229394531250 715255736816406250 4611686018427387903 4611686018427387903 4611686018427387903
(2 + compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),3,x),x))
A186041: 2 3 4 5 8 11 13 14 17 18 20 23 25 26 28 29
(loop(\(x,i).5x,x,3) - loop(\(x,i).3x,x,2))
A080961: 1 9 57 321 1713 8889 45417 230001 1158753 5820009 29178777 146130081 731358993 3658920729 18300980937 91524036561
(loop(\(x,i).(4x + 1),(x + ~2),x) div loop(\(x,i).3x,x,2))
A241549: 0 0 0 0 0 0 1 1 2 3 5 8 12 17 25 35
(2 * compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(~2 + (x div 2)),x)),x))
A161344: 4 6 8 10 14 22 26 34 38 46 58 62 74 82 86 94
(2 * compr(\x.(1 - loop(\(x,i).(loop(\(x,i).(x div (2 - (x mod 2))),x,x) div 2),2,x)),x))
A266214: 14 22 26 28 30 38 42 44 46 50 52 54 56 58 60 62
(if x <= 0 then 1 else (2 * (x + loop(\(x,i).(~x - (x div (4 + i))),2,x))))
A315187: 1 6 10 14 18 24 30 34 38 42 48 54 58 62 66 72
((x + 2) + loop(\(x,i).(~1 + (if (x mod (1 + i)) <= 0 then 0 else x)),x,(x2 + 2x)))
A089120: 2 5 2 17 2 37 2 5 2 101 2 5 2 197 2 257
(2 * compr(\x.(2 - loop(\(x,i).(0 - (if (x mod (1 + i)) <= 0 then 0 else x)),(x div 2),x)),x))
A262998: 10 26 34 58 74 82 106 122 146 178 194 202 218 226 274 298
(2 + compr(\x.(2 - loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x)),x))
A104278: 13 17 25 28 32 38 43 46 47 58 59 60 61 62 67 71
(1 + (loop(\(x,i).((x2 + x) * (2 - i)),x,2) + loop(\(x,i).x2,x,2)))
A265851: 5 11 17 257 65537
loop(\(x,i).(if (x mod 11) <= 0 then 1 else 0),(x div 2),~x)
A343453: 0 ~1 0 0 1 1 0 0 1 1 0 1 1 1 0 0
(x * (loop(\(x,i).3x,x,1) - loop(\(x,i).(2x + 3),x,0)))
A178759: 0 0 0 18 144 750 3240 12642 46368 163350 559800 1881066 6229872 20406750 66273480 213759090
(x + loop(\(x,i).2x,(~1 + loop(\(x,i).(x * i),(x div 5),1)),1))
A247397: 1 2 3 4 5 6 7 8 9 10 12 13
A094270: 1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 47
(x * (~2 + loop(\(x,i).loop(\(x,i).(((x + i) * i) div (x + 1)),x,i),x,2)))
A179023: 0 1 4 12 28 60 120 231 432 792 1430 2552 4512 7917 13804 23940
(x * (1 + loop(\(x,i).(x * loop(\(x,i).(x * (x - i)),2,(x + ~2))),1,(x + ~1))))
A001096: 0 1 2 3 4 5 726 5047 20168 60489 151210 332651 665292 1235533 2162174 3603615
compr(\x.(1 + loop(\(x,i).(x div (if (x mod 2) <= 0 then ~2 else 1)),x,((x + 1) div 2))),x)
A344346: 3 4 11 12 15 16 19 20 27 28 35 36 43 44 47 48
loop(\(x,i).(x * loop(\(x,i).(x * (x - i)),2,(x + ~2))),1,5x)
A054778: 0 120 30240 360360 1860480 6375600 17100720 38955840 78960960 146611080 254251200 417451320 655381440 991186560 1452361680 2071126800
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,5x)
A016859: 0 48828125 100000000000 8649755859375 204800000000000 2384185791015625 17714700000000000 96549157373046875 419430400000000000 1532278301220703125 4611686018427387903 4611686018427387903
((x + 1) + (loop(\(x,i).(2x - (if x <= 0 then 0 else 1)),(x + ~1),(x + ~2)) div 2))
A089243: 0 1 3 4 9 22 55
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(4x + 1))),x)
A005098: 1 3 4 7 9 10 13 15 18 22 24 25 27 28 34 37
compr(\x.((1 + loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x + ~2),x)) mod 3),x)
A003627: 2 5 11 17 23 29 41 47 53 59 71 83 89 101 107 113
(x + (if (x + ~2) <= 0 then 1 else (3 * (if (~2 + (x div 3)) <= 0 then 1 else 2))))
A272799: 1 2 3 6 7 8 9 10 11 15 16 17 18 19 20 21
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x + ~2),x)),3x)
A031377: 2 7 17 29 41 53 67 79 97 107 127 139 157 173 191 199
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),3x)
A252802: 3 11 19
A031369: 3 11 19 31 43 59 71 83 101 109 131 149 163 179 193 211
(x + ((x + (if (x + ~2) <= 0 then 1 else (if (x mod 2) <= 0 then x else (~x + 1)))) mod 3))
A014685: 1 3 2 4 6 6 6 8 9 10 12 12 12 14 15 16
(~x + (if x <= 0 then 2 else (~1 + ((x + 2) * (x + (if (x + ~4) <= 0 then 1 else x))))))
A253849: 2 4 9 16 25 64
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x + 1)),x)
A153085: 1 4 5 7 10 11 13 15 16 18 19 20 22 25 28 29
loop(\(x,i).2x,x,(if (x div 5) <= 0 then 1 else (2x2 + ~x)))
A222011: 1 2 4 8
A164312: 1 2 4 8 16 1440
compr(\x.(1 + loop(\(x,i).(0 - (if ((x + 1) mod (1 + i)) <= 0 then 0 else x)),x,2x)),x)
A292911: 1 3 7 9 15 19 21 27 31 37 45 49 51 55 57 69
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(3x + 1))),x)
A309374: 2 4 6 10 12
A024892: 2 4 6 10 12 14 20 22 24 26 32 34 36 42 46 50
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + x + 1))),x)
A002384: 1 2 3 5 6 8 12 14 15 17 20 21 24 27 33 38
compr(\x.(2 - loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),x,(x2 + x + 1))),x)
A096176: 2 3 5 6 8 12 14 15 17 20 21 24 27 33 38 41
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + x + ~1))),x)
A045546: 2 3 4 5 6 8 9 10 11 13 15 16 19 20 21 24
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + ~x + 1))),x)
A066271: 3 4 6 7 9 13 15 16 18 21 22 25 28 34 39 42
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + ~x + ~1))),x)
A002328: 3 4 5 6 7 9 10 11 12 14 16 17 20 21 22 25
((x + ~1) + loop(\(x,i).(if x <= 0 then 1 else (10x + 10)),2,x))
A032613: 19 210 311 412 513 614 715 816 917 1018 1119 1220 1321 1422 1523 1624
(x * (1 + loop(\(x,i).(x2 - loop(\(x,i).(4x + 1),i,1)),2,x)))
A121672: 0 ~4 ~38 ~12 404 1900 5646 13412 27688 51804 90050 147796 231612 349388 510454 725700
(x + (loop(\(x,i).(x + loop(\(x,i).((x + 2) mod (1 + i)),i,1)),x,1) div (x + 1)))
A244017: 1 2 2 4 5 6 7 8 10 11 13 14 15 16 17 18
compr(\x.loop(\(x,i).(if (x mod 4) <= 0 then 0 else (1 + (x div 4))),2,(x + 1)),x)
A337250: 3 7 11 12 13 14 15 19 23 27 28 29 30 31 35 39
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(5x + 4))
A016906: 1048576 3486784401 289254654976 6131066257801 63403380965376 420707233300201 2064377754059776 8140406085191601 27197360938418176 79792266297612001 210832519264920576 511116753300641401
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(5x + 4))
A016908: 16777216 282429536481 56693912375296 2213314919066161 36520347436056576 353814783205469041 2386420683693101056 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,(4x + 4)),x)
A153086: 2 5 7 8 11 12 14 17 20 21 22 23 26 27 28 29
(x + (loop(\(x,i).x2,1,((~x + ~2) + loop(\(x,i).(x * i),x,1))) div (x + 1)))
A091323: 1 3 3 3 68
loop(\(x,i).x2,1,(x + ((x + 1) * loop(\(x,i).(x * (x - i)),2,2x))))
A239610: 0 1 131044 11309769 228735376 2258625625 14430255876 68689595569 264286471744 865363202001 2496558002500 6503780163001 15577324963344 34772403556969 73108895539876 145988618630625
(x + compr(\x.loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,2x),(x + 1)))
A336407: 3 7 11 14 16 20 22 25 29 32 34 37 39 43 45 48
(~x + compr(\x.loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,2x),(x + 1)))
A008508: 3 5 7 8 8 10 10 11 13 14 14 15 15 17 17 18
((~x2 + ~x) + loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,1))
A289715: 1 4 24 128 610 2742 11970 51424 218718 923690 3879766 16224804 67603744 280816018 1163381190 4808642880
loop(\(x,i).(2x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,(x2 + x))
A145909: 0 8 8 16 80 40 56 224 32 40 440 176 208 728 280 320
(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - ((x div 2) mod 2))))),x,(x + 1)))
A136480: 1 1 1 2 2 1 1 3 3 1 1 2 2 1 1 4
loop(\(x,i).(2 * (if (~1 + i) <= 0 then 1 else (2x * (~1 + (2 * i))))),(x + ~1),x)
A052712: 0 1 2 24 480 13440 483840 21288960 1107025920 66421555200 4516665753600 343266597273600 28834394170982400 2652764263730380800 4611686018427387903 4611686018427387903
(loop(\(x,i).10x2,3,x) div (if x <= 0 then 1 else x))
A017275: 0 10000000 1280000000 21870000000 163840000000 781250000000 2799360000000 8235430000000 20971520000000 47829690000000 100000000000000 194871710000000 358318080000000 627485170000000
(loop(\(x,i).9x2,3,x) div (if x <= 0 then 1 else x))
A017167: 0 4782969 612220032 10460353203 78364164096 373669453125 1338925209984 3938980639167 10030613004288 22876792454961 47829690000000 93206534790699 171382426877952 300124211606973
(loop(\(x,i).12x2,3,x) div (if x <= 0 then 1 else x))
A017527: 0 35831808 4586471424 78364164096 587068342272 2799360000000 10030613004288 29509034655744 75144747810816 171382426877952 358318080000000 698260569735168 1283918464548864 2248392813428736
compr(\x.(1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then x else 5)),x,x)),x)
A172407: 1 3 7 9 13 19 21 27 31 33 37 43 49 51 57 61
compr(\x.(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then x else 3)),x,x)),x)
A155722: 1 2 4 5 7 10 11 14 16 17 19 22 25 26 29 31
compr(\x.(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then x else (1 + i))),x,x)),x)
A153762: 1 4 8 10 11 13 16 23 28 29 31 34 38 41 43 49
((x + 1) + loop(\(x,i).(if (x mod 10) <= 0 then ~x else i),x,x))
A338742: 1 3 5 7 9 11 13 15 17 19 21 2 23 4 25 6
loop(\(x,i).(x + (x div 4)),2,(x + (if (~4 + (x div 2)) <= 0 then 1 else 2)))
A076436: 1 2 3 6 7 8 10 12 13 15 18 20 21 22 25 26
(x + ((3 * (1 + loop(\(x,i).(x + (if (x - i) <= 0 then x else 0)),x,1))) div 2))
A304588: 3 5 9 10 17 18 19 20 33 34 35 36 37 38 39 40
(x + (if (x + ~1) <= 0 then 1 else (2 + (x div (2 + (if (x mod 4) <= 0 then 2 else 1))))))
A075313: 1 2 4 6 7 8 10 11 12 14 15 16 17 19 20 22
(x + loop(\(x,i).x3,1,loop(\(x,i).(x3 + ~x + 1),2,2)))
A342350: 38272753 38272754 38272755 38272756 38272757 38272758 38272759 38272760 38272761 38272762 38272763 38272764 38272765 38272766 38272767 38272768
(x + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (((x + 1) div 2) div 2)))
A126890: 0 1 2 3 5 7 6 9 12 15 10 14 18 22 26 15
loop(\(x,i).((if x <= 0 then 1 else 4x) mod (4 + (x div 4))),2,x)
A263655: 0 1 1 1 0 1 1 0 0 1 1 0 4 0 1 1
(x mod loop(\(x,i).(if x <= 0 then 1 else (x - ((x div (2 * (2 - (x mod 2)))) mod 2))),2,x))
A174806: 0 0 0 1 0 0 1 2 0 0 0 1 2 0 1 2
compr(\x.loop(\(x,i).(if ((x + 1) mod (2 + i)) <= 0 then 0 else x),x,8x),x)
A127260: 0 1 3 4 6 7 8 10 13 15 16 18 19 20 21 22
(if x <= 0 then 5 else (x * (if (x + ~2) <= 0 then 1 else (4 * (x mod 2)))))
A289690: 5 1 2 12 0
compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 4 else 0))),x,4x),x)
A108337: 0 1 3 5 6 13 15 16 18 25 26 28 30 31 63 65
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,4x)),x)
A095278: 0 1 2 4 5 7 10 11 14 16 17 19 20 25 26 31
compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(3x + 2))),x)
A024893: 0 1 3 5 7 9 13 15 17 19 23 27 29 33 35 37
(x + loop(\(x,i).x2,1,(if (x + ~2) <= 0 then 1 else (4x2 + 2x))))
A323518: 1 2 3 1767
compr(\x.(~2 + loop(\(x,i).(2 + (loop(\(x,i).(x div (2 - (x mod 2))),x,x) div 2)),2,x)),x)
A233524: 0 1 2 4 5 8
A095031: 0 1 2 4 5 8 10
A191985: 0 1 2 4 5 8 10 13 16 20 26 29 32 40 52 58
(x * ((loop(\(x,i).x3,2,x) + loop(\(x,i).x2,4,x)) div 2))
A170799: 0 1 66048 64599606 8590458880 381474609375 8463359955456 116315398231228 1125900443713536 8338592593225485 50000005000000000 252723527218359186 1109305584328900608 4325208028619914891 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (x + (if (x + ~2) <= 0 then 2 else (x2 div (x - ((~x + 2) div 2))))))
A171512: 1 3 4 5 7 8 10 11 13 15 17 18 20 21 23 25
compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + 2x + 2))),x)
A089593: 0 1 3 5 9 13 15 19 23 25 35 39 53 55 65 73
loop(\(x,i).(0 - ((x + 1) * loop(\(x,i).(x2 + 2),2,2))),2,(x2 + 2x))
A158764: 1406 5738 12958 23066 36062 51946 70718 92378 116926 144362 174686 207898 243998 282986 324862 369626
loop(\(x,i).(x + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),(x + 2),x)
A071148: 3 8 15 26 39 56 75 98 127 158 195 236 279 326 379 438
(~x + (if (x mod 2) <= 0 then (if (x mod 4) <= 0 then (x div 4) else 0) else 2x))
A255563: 0 1 ~2 3 ~3 5 ~6 7 ~6 9 ~10 11 ~9 13 ~14 15
(1 - loop(\(x,i).(~1 + (2 * loop(\(x,i).(x div (1 + (x mod 2))),x,x))),2x,x))
A120777: 1 4 8 64 128 512 1024 16384 32768 131072 262144 2097152 4194304 16777216 33554432 1073741824
loop(\(x,i).((x + 2) - loop(\(x,i).(x + 2),(x + ~1),~3)),2x,x)
A271859: 0 1 2 3 4 5 6 5 4 3 2 1 2 3 4 5
(~x + (if (x mod 2) <= 0 then (if (x mod 8) <= 0 then x else 2x) else (x div 2)))
A334952: 0 ~1 2 ~2 4 ~3 6 ~4 0 ~5 10 ~6 12 ~7 14 ~8
compr(\x.loop(\(x,i).(~1 + loop(\(x,i).(x div (~2 + (x mod 2))),x,x)),(x mod 2),(x div 2)),x)
A173601: 0 1 3 5 7 9 11 15 17 19 23 27 31 33 35 39
compr(\x.(1 - loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x2)),x)
A146968: 4 5 7
A219115: 4 5 7 8 10 12 13 14 15 17 20 21 22 23 24 25
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,2x2)),x)
A192225: 0 1 2 5
A216968: 0 1 2 5 7 8 22 23 28 37 40 43 47 50 55 62
(loop(\(x,i).12x,x,1) - loop(\(x,i).x3,2,x))
A024149: 1 11 ~368 ~17955 ~241408 ~1704293 ~7091712 ~4521799 295763968 4772359863 60917364224 740650422997 8910940667904 106982600879699 1283897803502080 15406983131226993
(loop(\(x,i).10x,x,1) - loop(\(x,i).x3,2,x))
A024123: 1 9 ~412 ~18683 ~252144 ~1853125 ~9077696 ~30353607 ~34217728 612579511 9000000000 97642052309 994840219648 9989395500627 99979338953216 999961556640625
(loop(\(x,i).7x,x,1) - loop(\(x,i).x3,2,x))
A024084: 1 6 ~463 ~19340 ~259743 ~1936318 ~9960047 ~39530064 ~128452927 ~347066882 ~717524751 ~380620948 8681506849 86284511034 657562026065 4709118150568
(x * (x + loop(\(x,i).(x + (if x <= 0 then 2 else ((x + 1) + ((2 + i) * i)))),x,0)))
A020874: 0 3 30 135 452 1295 3378 8295 19560 44847 100790 223223 488940 1061775 2289882 4910535
compr(\x.(1 - ((x div 2) mod 3)),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x))
A222438: 2 2 3 2 3 4 2 3 4 5 2 3 4 5 8 2
compr(\x.((((x + ~1) div 2) div 2) mod 2),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x))
A253573: 1 1 2 1 2 3 1 2 3 4 1 2 3 4 9 1
(1 - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + (3 * (i * (1 + i)))))),x,x))
A333884: 1 7 6 5 4 3 2 1 19 18 17 16 15 14 13 12
loop(\(x,i).x3,1,(x2 * loop(\(x,i).(x2 + 4x + 4),2,1)))
A017394: 0 1771561 113379904 1291467969 7256313856 27680640625 82653950016 208422380089 464404086784 941480149401 1771561000000 3138428376721 5289852801024 8550986578849 13339032325696
(x + loop(\(x,i).(x - (if (x mod 2) <= 0 then ((x div 4) mod 2) else 1)),3,x))
A010381: 0 1 4 5 6 7 9 11 16 17
((2x + 1) + loop(\(x,i).(if x <= 0 then 0 else (~1 + (2 * (x2 div 2)))),2,x))
A282901: 1 3 12 54 232
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,(x2 + x))),x)
A027752: 0 1 4 7 10 19 22 25 34 37 55 70 79 94 100 112
compr(\x.(~x + loop(\(x,i).x2,1,loop(\(x,i).(x div (~2 + (x mod 2))),x,(x + 1)))),x)
A112714: 1 3 7 11 15 23 31 39 47 55 63 79 95 111 127 143
loop(\(x,i).((x * i) - loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),i,1)),x,x)
A180191: 0 1 3 13 67 411 2921 23633 214551 2160343 23897269 288102189 3760013027 52816397219 794536751217 12744659120521
(x - loop(\(x,i).(x - (if x <= 0 then 0 else (i - ((~1 + i) mod 6)))),x,x))
A171597: 0 1 2 3 4 5 6 13 13 13 13 13 13 13 20 20
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (1 - (2 * ((x div 4) mod 2)))),x,x)
A011602: 0 1 1 1 1 ~1 1 ~1 1 1 ~1 1 1 ~1 ~1 ~1
((x + 1) - loop(\(x,i).(x - (if (~2 + (x div 2)) <= 0 then 0 else 1)),8,x))
A185137: 1 1 1 1 1 1 2 3 4 5 6 7 8 9 9 9
compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),x)
A181747: 1 3 5 11 17 29 41 59 71 101 107 137 149 179 191 197
(~x + compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),(x div 2),(~2x + 1)),x))
A129768: 1 1 1 1 2 2 3 3 4 6 6 8 9 9 10 12
(2x + loop(\(x,i).(if x <= 0 then 1 else (x - ((~x + 1) div 3))),2,2x))
A315535: 1 6 11 17 23 27 33 39 44 50 56 61 67 73 77 83
(2x + (if x <= 0 then 0 else ((x + 1) + (loop(\(x,i).(x * i),x,2) + (x mod 2)))))
A076855: 0 7 11 23 61
(loop(\(x,i).3x,2x,1) - (x * loop(\(x,i).x3,2,x)))
A024111: 1 8 ~943 ~58320 ~1042015 ~9706576 ~59934735 ~277692280 ~1030695103 ~3099363912 ~6513215599 5443635008 220512172257 2404007336480 22587537799985 205314481704024
(loop(\(x,i).6x,x,1) - (x * loop(\(x,i).x3,2,x)))
A024072: 1 5 ~988 ~58833 ~1047280 ~9757849 ~60419520 ~282195313 ~1072062208 ~3476706705 ~9939533824 ~25574627545 ~59740581888 ~124797797833 ~210890490880 ~106465406049
(loop(\(x,i).8x,x,1) - (x * loop(\(x,i).x3,2,x)))
A024098: 1 7 ~960 ~58537 ~1044480 ~9732857 ~60204032 ~280378097 ~1056964608 ~3352566673 ~8926258176 ~17347490009 6802112512 411897322039 4108791856128 34607721698207
(loop(\(x,i).5x,x,1) - (x * loop(\(x,i).x3,2,x)))
A024059: 1 4 ~999 ~58924 ~1047951 ~9762500 ~60450551 ~282397124 ~1073351199 ~3484831276 ~9990234375 ~25888596476 ~61673223599 ~136637788724 ~283151139351 ~546132812500
loop(\(x,i).10x,x,(x * loop(\(x,i).x3,2,x)))
A198479: 0 10 102400 59049000 10485760000 976562500000 60466176000000 2824752490000000 107374182400000000 3486784401000000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).2x2,2,(x3 + x2 + 1)),1,x2)
A235368: 8 648 344373768
(~x2 + (if x <= 0 then 0 else (1 + loop(\(x,i).((x2 + ~x) div 2),2,(x + 2)))))
A211958: 0 3 12 37 90 186 343 582 927 1405 2046 2883 3952 5292 6945 8956
(loop(\(x,i).12x,x,1) - loop(\(x,i).x2,2,x2))
A024148: 1 11 ~112 ~4833 ~44800 ~141793 1306368 30067007 413204480 5116733631 61817364224 742794011807 8915670466560 106992389648351 1283916988759808 15407019011695743
(loop(\(x,i).10x,x,1) - loop(\(x,i).x2,2,x2))
A024122: 1 9 ~156 ~5561 ~55536 ~290625 ~679616 4235199 83222784 956953279 9900000000 99785641119 999570018304 9999184269279 99998524210944 999997437109375
(loop(\(x,i).7x,x,1) - loop(\(x,i).x2,2,x2))
A024083: 1 6 ~207 ~6218 ~63135 ~373818 ~1561967 ~4941258 ~11012415 ~2693114 182475249 1762967862 13411305505 96073279686 676747283793 4744998619318
(loop(\(x,i).4x,x,1) - (x2 * loop(\(x,i).x3,2,x)))
A024047: 1 3 ~2032 ~177083 ~4194048 ~48827101 ~362792960 ~1977310359 ~8589869056 ~31380797465 ~99998951424 ~285307476307 ~742991593472 ~1792093285173 ~4049296734208 ~8648682117551
(loop(\(x,i).3x,x,1) - (x2 * loop(\(x,i).x3,2,x)))
A024034: 1 2 ~2039 ~177120 ~4194223 ~48827882 ~362796327 ~1977324556 ~8589928031 ~31381039926 ~99999940951 ~285311493464 ~743007839247 ~1792158799714 ~4049560386695 ~8649741510468
(x2 * loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,x2))
A069121: 0 2 96 1620 17920 157500 1197504 8240232 52715520 318995820 1847560000 10328229912 56073378816 297051536600 1541119305600 7852824450000
compr(\x.loop(\(x,i).(x - (if ((x + 4) mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x)
A101448: 0 1 3 4 6 9 10 13 15 16 18 21 24 25 28 30
compr(\x.(0 - loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then x else 3)),x,x)),x)
A155723: 0 3 6 8 9 12 13 15 18 20 21 23 24 27 28 30
compr(\x.(1 - loop(\(x,i).(if ((x + 1) mod 8) <= 0 then x else (x div 2)),x,x)),x)
A004781: 7 14 15 23 28 29 30 31 39 46 47 55 56 57 58 59
compr(\x.(1 - loop(\(x,i).(if ((x + 2) mod 8) <= 0 then x else (x div 2)),x,x)),x)
A004749: 6 12 13 14 22 24 25 26 27 28 29 30 38 44 45 46
compr(\x.(1 - loop(\(x,i).(if (((x + 1) div 2) mod 4) <= 0 then x else (x div 2)),x,x)),x)
A286261-A136037: 7 8 14 15 16 17 23 24 28 29 30 31 32 33 34 35
compr(\x.((x + ~1) + loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),2x,x2)),x)
A242137: 0 1 2 4 6 9 11 14 16 21 23 26 28 33 35 38
(loop(\(x,i).3x,2x,1) - loop(\(x,i).x2,2,x3))
A024113: 1 8 ~4015 ~530712 ~16770655 ~244081576 ~2176250895 ~13836504232 ~68676430015 ~282042115992 ~996513215599 ~3107047317112 ~8633670911775 ~20756219294152 ~33817119920335 76144794204024
(loop(\(x,i).6x,x,1) - loop(\(x,i).x2,2,x3))
A024074: 1 5 ~4060 ~531225 ~16775920 ~244132849 ~2176735680 ~13841007265 ~68717797120 ~282419458785 ~999939533824 ~3138065579665 ~8913923665920 ~23285024428465 ~56615548211200 ~129276152906049
(loop(\(x,i).8x,x,1) - loop(\(x,i).x2,2,x3))
A024100: 1 7 ~4032 ~530929 ~16773120 ~244107857 ~2176520192 ~13839190049 ~68702699520 ~282295318753 ~998926258176 ~3129838442129 ~8847380971520 ~22748329308593 ~52295865864192 ~94561965801793
(loop(\(x,i).5x,x,1) - loop(\(x,i).x2,2,x3))
A024061: 1 4 ~4071 ~531316 ~16776591 ~244137500 ~2176766711 ~13841209076 ~68719086111 ~282427583356 ~999990234375 ~3138379548596 ~8915856307631 ~23296864419356 ~56687808859671 ~129715820312500
(x3 + loop(\(x,i).(((x2 + ~x) div 2) + (if x <= 0 then 0 else 1)),2,x))
A211905: 0 2 10 34 86 181 337 575 919 1396 2036 2872 3940 5279 6931 8941
(if (~x + 2) <= 0 then (1 + ((x + ~1) mod (1 + ((x + 1) div 5)))) else 0)
A237260: 0 0 1 1 2 1 2 1 2 3 1 2 3 1 2 3
(if (x mod 5) <= 0 then (1 + ((x div 2) div (1 + (x mod 3)))) else 0)
A046775: 1 0 0 0 0 1 0 0 0 0 3 0 0 0 0 8
(if (x mod 2) <= 0 then (1 + (x div (1 + (2 * (2 + ((~x + 2) mod 4)))))) else 0)
A104477: 1 0 1 0 1 0 2 0 1 0 3 0 2 0 3 0
(if (x mod 2) <= 0 then (1 + ((1 + ((x * (x div 2)) div 4)) div 3)) else 0)
A035385: 1 0 1 0 2 0 2 0 4 0 5 0 7 0 9 0
(if (x mod 2) <= 0 then ((1 + (x div 3)) mod (1 + (2 * (x mod 3)))) else 0)
A333767: 0 0 1 0 2 0 0 0 3 0 1 0 0 0 0 0
(if (x mod 2) <= 0 then (1 + ((x mod (2 + (((~x + 2) div 2) mod 4))) div 2)) else 0)
A172293: 1 0 1 0 3 0 2 0 2 0 1 0 2 0 2 0
(x + (if ((x mod 3) - ((x + 1) mod 4)) <= 0 then 1 else 0) - (x div 2))
A048686: 1 2 2 3 3 4 4 4 4 6 6 6 7 8 8 9
(if (2x mod (4 + (x div 4))) <= 0 then (1 + (x div 4)) else 0)
A134402: 1 0 1 0 0 2 0 0 0 3 0 0 0 0 4 0
(if (x mod 2) <= 0 then ((1 + ((x2 + (x div 2)) div 3)) mod 3) else 0)
A091394: 1 0 2 0 1 0 2 0 2 0 0 0 0 0 2 0
(if (x mod 3) <= 0 then ((~2 + ((x div 2) mod 5)) mod 3) else 0)
A023670: 1 0 0 2 0 0 1 0 0 2 0 0 2 0 0 0
loop(\(x,i).(8x + (((x + ~1) div 2) mod 4)),(x + 1),0)
A037664: 3 25 200 1603 12825 102600 820803 6566425 52531400 420251203 3362009625 26896077000 215168616003 1721348928025 13770791424200 110166331393603
loop(\(x,i).(9x + ((1 + i) mod 4)),(x + 1),0)
A037749: 2 21 189 1702 15320 137883 1240947 11168524 100516718 904650465 8141854185 73276687666 659490188996 5935411700967 53418705308703 480768347778328
loop(\(x,i).(7x + ((1 + i) mod 4)),(x + 1),0)
A037747: 2 17 119 834 5840 40883 286181 2003268 14022878 98160149 687121043 4809847302 33668931116 235682517815 1649777624705 11548443372936
((28x + 10) + (if x <= 0 then 1 else 0))
A063146: 11 38 66 94 122 150 178 206 234 262 290 318 346 374 402 430
((2 * ((6x + 2) - (x div 3))) + (if x <= 0 then 1 else 0))
A063135: 5 16 28 38 50 62 72 84 96 106 118 130 140 152 164 174
((2 * ((5x + 2) - (x div 3))) + (if x <= 0 then 1 else 0))
A063238: 5 14 24 32 42 52 60 70 80 88 98 108 116 126 136 144
((((x - ((2 + (x div 2)) * (x mod 3))) div 2) mod 2) - (if x <= 0 then 1 else 0))
A176890: ~1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 1
(if (~x + 2) <= 0 then (1 - (2 * ((x mod (1 + (((x + 1) div 2) div 2))) mod 2))) else 0)
A173950: 0 0 1 ~1 1 ~1 1 ~1 1 1 ~1 ~1 1 ~1 1 1
(1 - (if ((2x + 2) mod (4 + (((x + 1) div 2) div 2))) <= 0 then 2 else 0))
A110515: 1 ~1 1 1 ~1 1 1 1 ~1 1 1 1 1 ~1 1 ~1
loop(\(x,i).(x + 1),(~2 + ((2x + 1) mod (4 + (x div 4)))),0)
A048154: 0 1 0 1 2 0 1 0 3 0 1 3 2 4 0 1
(if (x mod 3) <= 0 then ((2 - (x mod (2 + (x div (2 + (x mod 2)))))) div 2) else 0)
A016354-A016329-A016151-A015647-A015395-A014027: 1 0 0 1 0 0 0 0 0 ~1 0 0 ~1 0 0 0
(x - (if ((x + 1) mod 7) <= 0 then ~7 else 0))
A325693: 0 1 2 3 4 5 13 7 8 9 10 11 12 20 14 15
loop(\(x,i).(1 + (((x div 2) - (2 * (x mod 2))) mod 9)),x,0)
A021058: 0 1 8 5 1 8 5 1 8 5 1 8 5 1 8 5
loop(\(x,i).((x + 1) + (2x div 3) - ((1 + (x div 2)) div 2)),x,0)
A200310: 0 1 2 3 5 8 12 18 26 37 53 76 108 154 218 309
(((1 + (x div (~2 + (x mod 2)))) mod 3) + loop(\(x,i).(2x + 1),x,0))
A281166: 1 1 3 8 17 33 64 127 255 512 1025 2049 4096 8191 16383 32768
(((1 + (x div (2 - (x mod 2)))) mod 3) + loop(\(x,i).(2x + 1),x,0))
A097911: 1 3 5 8
A141775: 1 3 5 8 15 31 64 129 257 512 1023 2047 4096 8193 16385 32768
loop(\(x,i).((x + 2) - (((x + 2) div (2 - (x mod ~4))) mod 2)),x,0)
A292868: 0 1 3 4 5 6 8 9 11 13 14 16 17 18 19 20
((6x + 6) - (if ((x + 1) mod 5) <= 0 then 0 else 1))
A189938: 5 11 17 23 30 35 41 47 53 60 65 71 77 83 90 95
(if ((x mod (6 + ((~x + 1) mod 4))) mod 3) <= 0 then 0 else 1)
A094217: 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1
(1 + (if (x mod 11) <= 0 then 10 else 0))
A109014: 11 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1
(1 + (if ((x + 1) mod 5) <= 0 then (x mod 10) else 0))
A094635: 1 1 1 1 5 1 1 1 1 10 1 1 1 1 5 1
((7x + 6) div (1 + (if (x mod 3) <= 0 then 2 else 0)))
A105452: 2 13 20 9 34 41 16 55 62 23 76 83 30 97 104 37
((2x + 1) div (1 + (if ((x + ~2) mod 5) <= 0 then 4 else 0)))
A096431: 1 3 1 7 9 11 13 3 17 19 21 23 5 27 29 31
(1 + loop(\(x,i).((x + 1) + (2x div (1 + (2 * (x mod 3))))),x,0))
A297180: 1 2 3 4 11 18 25 74 123 172 515 858 1201 3602 6003 8404
(((x + ~1) mod (1 + (x mod (2 + (x div 5))))) + (if x <= 0 then 0 else 1))
A343407: 0 1 1 1 1 2 1 1 2 1 1 3 1 1 2 1
((x mod (1 + ((~x2 mod (2 + (x div 2))) div 2))) + (if x <= 0 then 0 else 1))
A277315: 0 1 1 1 1 2 1 1 1 2 2 3 1 2 1 1
(1 + ((((x - ((x div 2) mod 2)) div (2 + (x mod 2))) mod 2) + (if x <= 0 then 0 else 1)))
A278293: 1 2 2 2 2 3 2 2 2 3 2 3 2 2 2 2
(((2 + ((x2 div 2) div 5)) div 3) + (if x <= 0 then 0 else 1))
A164066-A053251: 0 1 1 1 2 2 2 3 3 4 5 5 6 7 8 9
((((x + 1) mod (1 + ((x + 1) div 5))) mod 2) + (if x <= 0 then 0 else 1))
A023518: 0 1 1 1 2 1 2 1 2 2 1 1 2 1 2 1
(((2x div (1 + ((x + 1) div 5))) mod 2) + (if x <= 0 then 0 else 1))
A060500: 0 1 1 1 1 2 1 2 1 1 1 2 1 1 2 2
(((x mod (2 - (x div (1 + ((x div 2) mod 3))))) mod 2) + (if x <= 0 then 0 else 1))
A302790: 0 1 1 1 1 1 1 2 1 2 1 1 1 2 2 1
(((x mod (~1 + (((~x + 2) * (x div 2)) div 3))) mod 2) + (if x <= 0 then 0 else 1))
A054740: 0 1 1 2 1 2 1 2 2 1 2 2 2 1 2 2
((2 * ((2 * ((x2 + ~x) div (x + 2))) div 3)) + (if x <= 0 then 0 else 1))
A157966: 0 1 1 1 3 3 5 5 7 9 9 11 13 13 15 17
((x div (2 + ((1 + ((~x + 2) mod 4)) mod (x + 1)))) + (if x <= 0 then 0 else 1))
A231205: 0 1 1 2 1 2 3 2 2 3 4 2
((((1 + (3x mod (2 + (x div 2)))) div 2) div 2) + (if x <= 0 then 0 else 1))
A319443-A124767: 0 1 1 1 1 2 2 1 1 2 1 2 2 3 2 1
((((1 + (((~x + 2) * (x div 3)) div 2)) div 2) mod 2) + (if x <= 0 then 0 else 1))
A091221: 0 1 1 1 1 2 1 1 2 2 1 2 1 2 1 1
((((2x + 1) mod (1 - (x div ~4))) div 2) + (if x <= 0 then 0 else 1))
A091954: 0 1 1 1 1 2 1 1 2 2 1 2 1 2 3 1
((2 * ((10x + 4) - (x div 2))) - (if x <= 0 then 0 else 1))
A063142: 8 27 45 65 83 103 121 141 159 179 197 217 235 255 273 293
(((x2 div (~x + 32)) mod 2) + (if x <= 0 then 0 else 1))
A251138: 0 1 1 1 1 1 2 2 1 2 1 2 2 1 1 2
(1 + (x mod (1 + (if ((x + 1) mod 5) <= 0 then (x div 3) else 0))))
A181937: 1 1 1 1 1 1 1 1 1 2 1 1 1 1 5 1
(1 + ((x div 2) mod (1 + (if (x mod 2) <= 0 then ((x + 2) div 5) else 1))))
A286569: 1 1 1 2 1 1 2 2 2 1 3 2 1 1 4 2
(1 + ((if (x mod 2) <= 0 then 1 else x) mod (1 + (x mod (1 + (x div 5))))))
A191373: 1 1 1 1 1 2 1 2 1 2 2 3 1 2 2 4
(1 + (2x div (1 + loop(\(x,i).i,(x mod (1 + ((~x + 2) mod 4))),1))))
A254503: 1 2 3 2 5 6 7 4 6 10 11 6 13 14 15 8
(if (2 - (x div 2)) <= 0 then (1 + (x mod (1 + (x mod (3 + (x mod 2)))))) else 1)
A345942: 1 1 1 1 1 2 1 4 3 2 1 4 1 2 3 4
(1 + (x mod (1 + (x div (1 + (loop(\(x,i).2x,x,2) mod (2x + 1)))))))
A295666: 1 1 1 2 1 1 1 4 3 1 1 4 1 1 1 4
(1 + (x div (1 + (x mod (1 + (loop(\(x,i).2x,x,2) mod (2x + 1)))))))
A085731: 1 1 1 4 1 1 1 4 3 1 1 4 1 1 1 16
(1 + (x div (1 + (x mod (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))))
A343249-A327656: 1 1 3 1 5 3 7 1 9 5 11 3 13 7 5 1
(1 + (x div (1 + (x mod (1 + (loop(\(x,i).(2x + i),x,0) mod (x + 1)))))))
A336650: 1 1 3 1 5 3 7 1 9 5 11 3 13 7 3 1
(1 + (x mod (1 + (x mod (1 + (loop(\(x,i).((x + 1) * i),x,0) mod (x + 1)))))))
A248666: 1 2 1 4 5 2 1 4 1 10 1 4 13 2 5 4
(~1 + ((x + 2) mod (1 + (if (~1 + (x mod 7)) <= 0 then 2 else 1))))
A316441: 1 ~1 ~1 0 ~1 0 ~1 ~1 0 0 ~1 0 ~1 0 0 1
(1 + (x div (2 - (x div (~1 + (x mod 2) - (if (x mod 3) <= 0 then 2 else 1))))))
A068108: 1 1 1 1 2 1 2 1 2 2 2 1 3 1 2 2
((x + 1) - ((x * (x div 2)) mod (1 + (if (x mod 8) <= 0 then 2 else 1))))
A070321: 1 2 3 3 5 6 7 7 7 10 11 11 13 14 15 15
loop(\(x,i).i,((x2 + x) mod ((x + 1) - (x mod 9))),1)
A298782: 1 1 1 1 1 1 1 1 1 1 1 2 6 2 1 1
((x div 2) mod (1 + (if (x mod 2) <= 0 then ((x + ~1) mod (1 + (x div 4))) else 1)))
A064874: 0 0 0 1 0 0 1 1 0 0 0 1 2 0 1 1
(2x div (1 + ((x + 1) div loop(\(x,i).i,(x mod (1 + (x div 4))),1))))
A046929: 0 0 1 1 1 1 1 1 3 1 1 3 1 1 3 5
loop(\(x,i).2x,x,(1 + (x div (1 + (2 mod (1 + (x mod (2 + (x mod 2)))))))))
A090634: 1 4 12 32 80 64 448 1024 2304 5120 11264 8192 53248 114688 245760 524288
(1 + (x mod (1 + (3 * (if ((x + 1) mod 8) <= 0 then 2 else 1)))))
A078978: 1 2 3 4 1 2 3 1 1 2 3 4 1 2 3 2
(1 + ((x + 2) mod (1 + ((x - (if (~2 + (x div 2)) <= 0 then 2 else 1)) mod 3))))
A095374: 1 1 1 2 1 1 3 1 1 3 1 2 3 1 1 3
loop(\(x,i).i,((8x + 4) mod (1 + ((x + 1) div 3))),1)
A274468: 1 1 1 1 1 2 1 1 1 1 1 2 1 3 2 4
loop(\(x,i).2x,((x + 1) - ((2 * ((x2 + ~1) div 2)) mod 3)),1)
A007361: 1 4 2 4 8 64 64 256
(1 + loop(\(x,i).10x,x,11))
A199691: 12 111 1101 11001 110001 1100001 11000001 110000001 1100000001 11000000001 110000000001 1100000000001 11000000000001 110000000000001 1100000000000001 11000000000000001
(~1 + loop(\(x,i).10x,x,11))
A198700: 10 109 1099 10999 109999 1099999 10999999 109999999 1099999999 10999999999 109999999999 1099999999999 10999999999999 109999999999999 1099999999999999 10999999999999999
(1 + loop(\(x,i).(x div (1 + (x mod 2))),2,(1 + ((x + (x mod 2)) div 3))))
A127197: 1 1 1 3 3 1 1 1 1 5 5 3 3 3 3 7
(1 + (loop(\(x,i).x2,2,(x + 6)) mod (1 + (x div 3))))
A317994: 1 1 1 2 1 2 1 2 2 2 1 2 2 2 1 4
(1 + (x mod (1 + (loop(\(x,i).2x,x,(1 + (x mod 2))) mod (2x + 1)))))
A007913: 1 2 3 1 5 6 7 2 1 10 11 3 13 14 15 1
(1 + loop(\(x,i).(x * i),(1 + ((x3 div 3) + (x mod 2))),1))
A201363: 2 3 7
A088332: 2 3 7 39916801 4611686018427387903 4611686018427387903 4611686018427387903
(x div (1 + ((x + ~1) mod (1 + (if (x mod (1 + (x mod 4))) <= 0 then x else 1)))))
A093411: 0 1 1 3 1 5 1 7 1 9 5 11 1 13 7 15
(1 + ((x + ~1) mod (1 + (loop(\(x,i).(3x + 3),x,0) mod (x + 1)))))
A335341: 1 1 1 3 1 1 1 7 4 1 1 3 1 1 1 15
(1 + (x mod (1 + ((~1 + loop(\(x,i).(2x2 + x),2,2)) mod (x + 1)))))
A165743: 1 2 3 2 5 6 7 2 3 10 1 6 1 14 15 2
loop(\(x,i).20x,(4x + 3),1)
A013813: 8000 1280000000 204800000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).15x,(4x + 3),1)
A013803: 3375 170859375 8649755859375 437893890380859375 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).18x,(4x + 3),1)
A013809: 5832 612220032 64268410079232 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).24x,(4x + 3),1)
A013821: 13824 4586471424 1521681143169024 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).14x,(4x + 3),1)
A013801: 2744 105413504 4049565169664 155568095557812224 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).13x,(4x + 3),1)
A013799: 2197 62748517 1792160394037 51185893014090757 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).11x,(4x + 3),1)
A013795: 1331 19487171 285311670611 4177248169415651 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).17x,(4x + 3),1)
A013807: 4913 410338673 34271896307633 2862423051509815793 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((x2 + 2x) mod (1 + ((1 - loop(\(x,i).2x,x,2)) mod (x + 1)))))
A182816: 1 2 3 2 5 4 7 2 3 4 11 4 13 4 9 2
(x mod (if (x mod 3) <= 0 then ((x + 2) mod ~9) else 1))
A088194: 0 0 0 ~1 0 0 0 0 0 ~5 0 0 0 0 0 0
loop(\(x,i).(2x + 3),(~1 + ((3 * (x div 4)) div 2)),1)
A290854: 1 1 1 1 1 1 1 1 13 13 13 13 29 29 29 29
(1 + (loop(\(x,i).(3x + 8),x,0) div 7))
A139782: 1 2 5 15 46 139 417 1250 3749 11247 33742 101227 303681 911042 2733125 8199375
(2 div (1 + ((if (x + ~1) <= 0 then 1 else (~x + ~1)) mod 7)))
A332007: 1 1 0 0 0 1 2 0 0 0 0 0 1 2 0 0
loop(\(x,i).2x,(7 * ((((x + 1) div 2) div 2) div 2)),1)
A248773: 1 1 1 1 1 1 1 128 128 128 128 128 128 128 128 16384
(5 mod (1 + ((x + 1) mod (if (~x + 2) <= 0 then 6 else 1))))
A316568: 0 0 1 0 5 0 1 2 1 0 5 0 1 2 1 0
(1 + ((x + 3) mod (1 + (2 * ((if (x mod 2) <= 0 then 1 else x) mod 3)))))
A100833: 1 2 3 1 2 4 1 2 3 1 2 5 1 2 3 1
(1 + ((x div 5) div (1 + (if (x mod 2) <= 0 then (x mod 3) else 2))))
A185147: 1 1 1 1 1 1 2 1 1 1 2 1 3 1 1 2
(1 + (x mod (1 + (x mod (2 + (loop(\(x,i).(2 * (x + i)),x,1) mod (x + 1)))))))
A132741: 1 2 1 4 5 2 1 8 1 10 1 4 1 2 5 16
loop(\(x,i).i,((x + 2) mod (1 + (2 * ((1 + (((x + 1) div 2) div 2)) div 2)))),1)
A050412: 1 1 1 2 1 1 2 1 1 2 1 3 4 1 1 2
(1 + (if (x mod 2) <= 0 then (x div (2 * (2 + ((x div 2) mod 5)))) else 1))
A330721: 1 2 1 2 1 2 1 2 1 2 3 2 3 2 2 2
(1 + ((x + 1) div (1 + (x mod (2 + (x div (if (~2 + (x div 2)) <= 0 then 1 else 2)))))))
A247869: 2 2 2 2 2 2 4 3 4 3 3 3 3 3 3 3
(((x + ~1) div 2) mod (1 + (if ((1 + (x div 2)) mod 6) <= 0 then 2 else 1)))
A151692: 1 0 0 1 1 0 0 1 1 0 1 2 1 0 0 1
(if (~x + 2) <= 0 then (x div (3 + ((x2 + 2x) mod 6))) else 1)
A090379: 1 1 0 0 1 0 2 1 1 1 3 1 4 2 2 2
((x + ~1) mod (if x <= 0 then 2 else (1 + (x div (1 + (2 * (2 + (x mod 3))))))))
A005813: 1 0 0 0 0 0 1 0 0 0 1 0 2 0 1 2
(x div (1 + ((x + 2) div (1 + (if (x mod 2) <= 0 then ((x mod 3) div 2) else 2)))))
A037281: 0 0 0 1 0 1 0 1 1 2 0
A247977: 0 0 0 1 0 1 0 1 1 2 0 2 0 2 1 2
(2 div (1 + ((x + 1) mod (5 + (if (x mod 3) <= 0 then 1 else 2)))))
A017847: 1 0 0 0 0 0 1 1 0 0 0 0 1 2 1 0
loop(\(x,i).(x * i),(~1 + ((2x + ~2) mod (4 + (x div 4)))),1)
A273730: 1 1 1 1 1 2 1 1 1 6 1 1 1 2 24 1
(1 + (loop(\(x,i).(x + ((2 + i) * i)),(x + 1),0) div 9))
A056178: 1 2 3 6 10 15 22 31 42 56 71 90 112 137 165 197
(~1 + (9 * (1 + loop(\(x,i).(2x + 4),(x + 2),2))))
A099945: 188 404 836 1700 3428 6884 13796 27620 55268 110564 221156 442340 884708 1769444 3538916 7077860
(if x <= 0 then 0 else (1 + ((~1 + ((x2 + x) div 2)) mod 9)))
A145389: 0 1 3 6 1 6 3 1 9 9 1 3 6 1 6 3
(~1 + (9 * loop(\(x,i).(x * ((x + 1) - i)),2,(x + 2))))
A069759: 107 647 2159 5399 11339 21167 36287 58319 89099 130679 185327 255527 343979 453599 587519 749087
(2 div (1 + ((if (x mod 8) <= 0 then 1 else x) mod 9)))
A219481: 1 1 0 0 0 0 0 0 1 2 1 0 0 0 0 0
(1 + loop(\(x,i).11x,x,9))
A199763: 10 100 1090 11980 131770 1449460 15944050 175384540 1929229930 21221529220 233436821410 2567805035500 28245855390490 310704409295380 3417748502249170 37595233524740860
(1 + loop(\(x,i).(x2 + ~7x),x,9))
A110368: 10 19 199 37819 1429936399 2044718092315659619 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(x mod (1 + ((~2x + 4) mod (2 + (x div 4))))),1)
A140218: 1 1 1 1 2 1 1 2 1 1 1 4 1 2 1 1
loop(\(x,i).x2,1,(1 + ((2x + 1) div (3 + (x div 4)))))
A093995: 1 4 4 9 9 9 16 16 16 16 25 25 25 25 25 36
loop(\(x,i).3x,((2x + 1) div (3 + (x div 4))),1)
A098355: 1 3 3 9 9 9 27 27 27 27 81 81 81 81 81 243
loop(\(x,i).(x * (1 + i)),((2x + 1) div (3 + (x div 4))),1)
A130493: 1 2 2 6 6 6 24 24 24 24 120 120 120 120 120 720
(x - (if x <= 0 then 0 else (1 + (x mod (1 + ((x + ~1) mod (4 + (x div 2))))))))
A261914: 0 0 1 2 3 4 5 6 7 8 9 9 11 11 11 11
(~1 + (if x <= 0 then 2 else (x div (1 + (x div (2 + ((x div 2) mod (2 + (x mod 2)))))))))
A190164: 1 0 1 0 0 1 1 0 0 1 1 2 0 0 1 1
(~1 + (5 * (if ((x + ~2) mod 12) <= 0 then 2 else 1)))
A202388: 4 4 9 4 4 4 4 4 4 4 4 4 4 4 9 4
(loop(\(x,i).2x,x,1) mod 61)
A222011: 1 2 4 8
A036130: 1 2 4 8 16 32 3 6 12 24 48 35 9 18 36 11
(if (x mod 3) <= 0 then 1 else 59)
A273183: 1 59 59 1
(loop(\(x,i).2x,x,1) mod 59)
A222011: 1 2 4 8
A036129: 1 2 4 8 16 32 5 10 20 40 21 42 25 50 41 23
(1 + (loop(\(x,i).x2,1,(~1 + ((x2 + ~2x) div 2))) div 5))
A309088: 1 1 1 1 2 8 25
(1 + ((1 + (if (~2 + (x div 3)) <= 0 then x else (x + 2))) mod 5))
A106652: 2 3 4 5 1 2 3 4 5 3 4 5 1 2 3 4
((if x <= 0 then 1 else 2x) - ((x + ~1) mod (1 + ((x + 1) div 5))))
A274431: 1 2 4 6 7 10 11 14 15 16 20 21 22 26 27 28
(1 + (5 * (if (x mod 11) <= 0 then 0 else 2)))
A084066: 1 11 11 11 11 11 11 11 11 11 11 1 11 11 11 11
loop(\(x,i).x2,1,((2x + 1) - (5 * (x div ~2))))
A061099: 1 64 100 289 361 676 784 1225 1369 1936 2116 2809 3025 3844 4096 5041
(loop(\(x,i).3x,x,1) mod 29)
A070344: 1 3 9 27 23 11 4 12 7 21 5 15 16 19 28 26
(1 + (if (~2 + (x div 3)) <= 0 then x else (10x + 10)))
A056525: 1 2 3 4 5 6 7 8 9 101 111 121 131 141 151 161
(1 + ((2 * loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))) div 5))
A336161-A336160: 1 1 2 1 3 2 3 1 4 3 5 2 6 3 7 1
(loop(\(x,i).3x,x,1) mod 41)
A070361: 1 3 9 27 40 38 32 14 1 3 9 27 40 38 32 14
(if (x mod 2) <= 0 then (x div 2) else (1 + (8x div 5)))
A082010: 0 2 1 5 2 9 3 12 4 15 5 18 6 21 7 25
(1 + ((if ((x * (x div 2)) mod 6) <= 0 then x else 2) div 5))
A259342: 1 1 1 1 1 1 2 1 1 2 1 1 3 3 1 1
(1 + (5 * loop(\(x,i).(10x + 16),x,2)))
A205088: 11 181 1881 18881 188881 1888881 18888881 188888881 1888888881 18888888881 188888888881 1888888888881 18888888888881 188888888888881 1888888888888881 18888888888888881
((if (~2 + (x div 3)) <= 0 then 1 else 2) div (1 + (2x mod 5)))
A321445: 1 0 0 0 0 1 0 0 0 0 2 0 0 1 0 2
((if x <= 0 then 1 else 2) div (1 + (((x * (x mod 2)) - (x div 2)) mod 5)))
A219496: 1 1 0 0 0 0 0 0 1 2 2 1 0 0 0 0
((x + ~1) mod (1 + (if x <= 0 then 1 else ((x + (x div 3)) div 5))))
A289871: 1 0 0 0 1 0 1 0 1 2 0 1 3 0 1 4
loop(\(x,i).3x,(x - ((~x3 + x2) div 5)),1)
A051576: 1 3 27 2187 4782969 847288609443 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((~2 + (x mod 2)) mod (1 + ((x + (if (x mod 2) <= 0 then x else 1)) div 5)))
A308450: 0 0 0 0 0 1 1 1 2 2 3 2 3 2 4 3
(1 + (loop(\(x,i).(6x + 4),(x + 1),x) div 5))
A014918: 1 13 121 985 7465 54121 380713 2620201 17736745 118513705 783641641 5137206313 33435376681 216285092905 1391747554345 8914707307561
loop(\(x,i).2x3,1,(5x2 + 5x + 1))
A109119: 2 2662 59582 453962 2060602 6885902 18787862 44376082 94091762 183467702 334568302 577609562 952759082 1512116062 2321871302 3464647202
(~1 + loop(\(x,i).(2 * (1 + (2 * (2x + (x mod 2))))),x,5))
A117644: 4 45 369 2961 23697 189585 1516689 12133521 97068177 776545425 6212363409 49698907281 397591258257 3180730066065 25445840528529 203566724228241
(1 + (((x2 + 2x) + (if (~2 + (x div 2)) <= 0 then 1 else 0)) div 5))
A085577: 1 1 2 4 6 8 10 13 17 20 25 29 34 40 45 52
(if (x mod 3) <= 0 then 1 else ((x + 3) mod (1 + (x div 5))))
A029319: 1 0 0 1 0 0 1 0 1 1 1 2 1 1 2 1
(if ((x + 1) mod (2 - (x div ~4))) <= 0 then (x mod 5) else 1)
A059342: 1 1 2 1 1 1 1 2 1 4 1 1 1 1 1 1
(~1 + (loop(\(x,i).x3,(x + 1),2) * (1 + (~x mod 4))))
A056235: 7 2047 402653183 4611686018427387903 4611686018427387903
((x + 1) div (1 + (if (x mod 3) <= 0 then 2 else (x div (1 + (x div 4))))))
A077774: 0 1 1 1 1 2 2 2 3 3 2 3 4 3 3 5
(1 + ((if (x mod 2) <= 0 then ((x div 2) mod 2) else 3) * (1 + (x mod 4))))
A070406: 1 7 4 13 1 7 4 13 1 7 4 13 1 7 4 13
(if x <= 0 then 0 else (1 + (x mod (~1 + (2 * ((x + (x mod (2 + (x mod 2)))) div 2))))))
A107286: 0 1 1 1 2 1 2 1 2 3 2 1 2 1 2 3
(1 + ((x2 + 2x) mod (7 * (if (x + ~2) <= 0 then 2 else 1))))
A254159: 1 4 9 2 4 1
loop(\(x,i).21x,(4x + 1),1)
A013814: 21 4084101 794280046581 154472377739119461 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).22x,(4x + 1),1)
A013816: 22 5153632 1207269217792 282810057883082752 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).19x,(4x + 1),1)
A013810: 19 2476099 322687697779 42052983462257059 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).23x,(4x + 1),1)
A013818: 23 6436343 1801152661463 504036361936467383 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x div 2) div (1 + (x mod (1 + (if (~1 + (x mod 3)) <= 0 then (x div 2) else 2)))))
A243223: 0 0 0 0 1 0 1 0 1 0 1 1 1 0 2 0
((~1 + loop(\(x,i).2x,x,2)) div (1 + (2 mod (1 + (x mod (2 + (x mod 2)))))))
A090633: 1 3 7 15 31 21 127 255 511 1023 2047 1365 8191 16383 32767 65535
(1 + loop(\(x,i).8x,(1 + (x div 2)),(1 + (2 * (x mod 2)))))
A209530: 9 25 65 193 513 1537 4097 12289 32769 98305 262145 786433 2097153 6291457 16777217 50331649
(1 + ((x - (if ((~1 + (x div 3)) mod 4) <= 0 then 1 else 0)) mod 3))
A204259: 1 2 3 3 1 2 1 2 3 1 2 3 1 2 3 3
(1 + ((1 + (if (x mod (4 + (x mod 4))) <= 0 then x else 0)) mod 3))
A194286: 2 2 2 2 3 1 2 3 1 2 2 2 2 2 2 2
(1 + (((x + 2) div (1 + ((1 + (if x <= 0 then 1 else x)) mod 3))) mod 3))
A188817: 1 2 2 3 3 2 2 1 2 3 2 2 2 3 2 3
(~1 + (loop(\(x,i).((x + 1) + (x div 8)),(x + 1),1) mod 3))
A014240: 1 ~1 0 1 ~1 0 1 0 ~1 1 0 0 0 0 1 ~1
(1 + (loop(\(x,i).(x * (2 + i)),x,(4x + 3)) div 3))
A308599: 2 8 45 301 2281 19321 181441 1874881 21168001 259459201 3432844801 48778329601 741015475201 11987015040001 205740767232001 3734717995008001
(~1 + ((if (16 mod (x + 1)) <= 0 then (x + ~1) else 1) mod 3))
A154269: 1 ~1 0 1 0 0 0 ~1 0 0 0 0 0 0 0 1
(if x <= 0 then 2 else (1 + ((x mod (1 + (2 * (1 + (2 * (x mod 2)))))) div 3)))
A207668: 2 1 1 2 1 2 1 1 1 1 1 2 1 3 1 1
(1 + loop(\(x,i).2x,x,2) - ((1 + (x div (~2 + (x mod 2)))) mod 3))
A130752: 2 5 9 16 31 63 128 257 513 1024 2047 4095 8192 16385 32769 65536
(1 + ((((x + ~1) * (if (x + ~2) <= 0 then 0 else x2)) div 3) mod 3))
A093557: 1 1 1 1 2 1 1 3 3 1 1 2 1 2 1 1
(loop(\(x,i).3x,x,1) mod 37)
A070346: 1 3 9 27 7 21 26 4 12 36 34 28 10 30 16 11
(loop(\(x,i).3x,x,1) mod 35)
A070345: 1 3 9 27 11 33 29 17 16 13 4 12 1 3 9 27
loop(\(x,i).2x,x,(~1 + ((2x3 + 3x2 + ~2x) div 3)))
A167581: ~1 0 28 192 880 3328 11200 34816 102144 286720 777216 2048000 5271552 13303808 33013760 80740352
(1 + (((x + 1) * loop(\(x,i).(2 + i - ((x div 2) mod 2)),x,0)) mod 3))
A002636: 1 1 1 2 1 1 2 2 1 2 2 1 3 2 1 2
(1 + ((loop(\(x,i).(2 + (x * (x + i))),2,3) mod (x + 1)) div 3))
A126347: 1 1 1 1 1 2 1 1 1 3 3 4 2 1 1 1
(1 + ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3))
A320266: 1 1 1 2 1 2 1 3 2 2 1 4 1 2 2 6
(~1 + (3 * (~2 + loop(\(x,i).10x,(x + 1),1))))
A086943: 23 293 2993 29993 299993 2999993 29999993 299999993 2999999993 29999999993 299999999993 2999999999993 29999999999993 299999999999993 2999999999999993 29999999999999993
(1 + ((2 * (if (x + ~2) <= 0 then x else (2 - (x div ~3)))) div 3))
A130822: 1 1 2 3 3 3 3 4 4 4 5 5 5 5 5 5
((x div 2) - (if x <= 0 then 0 else (~1 + ((2 * ((x + 1) div 3)) div 3))))
A076223: 0 1 2 2 3 2 3 3 3 3 4 4 5 5 5 5
(1 + (6 * loop(\(x,i).(2x + ~1),x,12)))
A196655: 73 139 271 535 1063 2119 4231 8455 16903 33799 67591 135175 270343 540679 1081351 2162695
(loop(\(x,i).6x,x,1) mod 19)
A070395: 1 6 17 7 4 5 11 9 16 1 6 17 7 4 5 11
(1 + ((2 * (if (x + ~2) <= 0 then 0 else (2 - ((~x + 1) div 3)))) div 3))
A147752: 1 1 1 3 3 3 3 3 4 4 4 5 5 5 5 5
loop(\(x,i).x2,3,(~11x + ~7))
A017480: 5764801 11019960576 500246412961 6553600000000 45767944570401 218340105584896 806460091894081 2478758911082496 6634204312890625 15938480745308416 35114532758015841 72057594037927936 139353667211683681 256289062500000000 451447246258894081
(1 + (3 * loop(\(x,i).(10x + 5),(x + 1),2)))
A137146: 76 766 7666 76666 766666 7666666 76666666 766666666 7666666666 76666666666 766666666666 7666666666666 76666666666666 766666666666666
loop(\(x,i).x5,1,(6x + 5))
A016973: 3125 161051 1419857 6436343 20511149 52521875 115856201 229345007 418195493 714924299 1160290625 1804229351 2706784157 3939040643 5584059449 7737809375
loop(\(x,i).2x,(x - (((~x3 + 3x2 + ~2x) div 2) div 3)),1)
A218148: 1 2 4 16 256 32768 67108864 4398046511104 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).3x,(x - ((4 * (x div 3)) div 3)),1)
A125824: 1 3 9 9 27 81 81 243 729 243 729 2187 2187 6561 19683 19683
(1 + (3 * ((x mod (2 + (if (x mod 8) <= 0 then x else 1))) div 2)))
A080278: 1 1 4 1 1 4 1 1 13 1 1 4 1 1 4 1
(1 + ((2 * ((loop(\(x,i).(2 * (x - i)),x,2) mod (x + 1)) div 2)) div 3))
A324537: 1 1 1 1 1 2 1 1 1 3 1 4 1 5 3 1
(~1 + (3 * (2 + loop(\(x,i).(2x2 + 2x),(x2 + 1),2))))
A091314: 41 941 4611686018427387903
(loop(\(x,i).3x,x,1) mod 47)
A070364: 1 3 9 27 34 8 24 25 28 37 17 4 12 36 14 42
(loop(\(x,i).5x,x,1) mod 23)
A036121: 1 5 2 10 4 20 8 17 16 11 9 22 18 21 13 19
(1 + ((2 * (4x + (if (~2 + (x div 2)) <= 0 then 1 else 2))) div 3))
A080902: 1 4 7 9 12 15 18 21 23 26 29 31 34 37 39 42
((loop(\(x,i).(x * (x - i)),2,(x + ~1)) div 2) div 13)
A011936: 0 0 0 0 0 4 13 32 64 116 193 304 456 660 924 1260
((x2 * loop(\(x,i).x3,2,x)) mod 13)
A167628: 0 1 7 9 10 8 11 2 5 3 4 6 12 0 1 7
((loop(\(x,i).(x * (x - i)),2,(x + ~1)) div 2) div 11)
A011932: 0 0 0 0 1 5 16 38 76 137 229 360 540 780 1092 1489
((if (x mod 2) <= 0 then (x2 + 4x + 4) else 2) div 11)
A049689: 0 0 1 0 3 0 5 0 9 0 13 0 17 0 23 0
(11 * loop(\(x,i).2x,(x div 2),(2 - (x mod 2))))
A108732: 22 11 44 22 88 44 176 88 352 176 704 352 1408 704 2816 1408
(11 * (x + loop(\(x,i).i,(~2 + (x div 3)),1)))
A080195: 11 22 33 44 55 66 77 88 99 110 121 132 154 165 176 198
(11 * (x + (if (~2 + (x div 3)) <= 0 then 1 else 2)))
A068900: 11 22 33 44 55 66 77 88 99 121 132 143 154 165 176 187
(1 + ((loop(\(x,i).(2 * ((x + 2) + (i mod 2))),x,(x + 2)) div 2) div 3))
A175656: 1 3 6 14 30 66 142 306 654 1394 2958 6258 13198 27762 58254 121970
loop(\(x,i).(~7x + 1),12x,1)
A015430: 1 12111126301 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~12x + 1),12x,1)
A015436: 1 8230246567621 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~9x + 1),12x,1)
A015432: 1 254186582833 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~10x + 1),12x,1)
A015433: 1 909090909091 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x5,1,(12x + 1))
A017537: 1 371293 9765625 69343957 282475249 844596301 2073071593 4437053125 8587340257 15386239549 25937424601 41615795893 64097340625 95388992557 137858491849 194264244901
(1 + ((loop(\(x,i).(x2 + 2x),1,((x div 2) - (x mod 2))) div 2) div 3))
A029138: 1 0 1 1 2 1 3 2 5 3 6 5 9 6 11 9
(~1 + (6 * (x + loop(\(x,i).(2x2 + 2),(x + ~2),1))))
A171713: 5 11 17 41 227
(1 + ((2 * loop(\(x,i).((x + ~2) + ((x div 4) mod 2)),2,x)) mod 3))
A129979: 1 3 3 2 3 1 3 2 2 1
(~1 + (if x <= 0 then 1 else (x - ((1 - ((x2 + 4x) div 2)) div 3))))
A046992: 0 1 3 5 8 11 15 19 23 27 32 37 43 49 55 61
(1 + ((2 * compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 3))
A276988: 1 3 1 2 1 2 1 2 1 1 2 2 1 2 1 1
(x mod (if (((x + 1) mod 5) mod 2) <= 0 then ((x + 2) div 3) else 1))
A245492: 0 0 0 0 0 0 0 0 2 0 0 3 0 3 4 0
((x + 2) div (1 + ((loop(\(x,i).2x,x,(~x + 2)) mod (x + 2)) div 3)))
A071829: 2 3 4 5 3 7 8 3 5 11 6 13 7 5 16 17
loop(\(x,i).(x3 + 6x2 + 8x),1,(6x + 1))
A001520: 15 693 3315 9177 19575 35805 59163 90945 132447 184965 249795 328233 421575 531117 658155 803985
loop(\(x,i).x6,1,(6x + 1))
A016926: 1 117649 4826809 47045881 244140625 887503681 2565726409 6321363049 13841287201 27680640625 51520374361 90458382169 151334226289 243087455521 377149515625 567869252041
(1 + (3 * loop(\(x,i).(6x + 4),(x div 2),(x mod 2))))
A026567: 1 4 13 31 85 193 517 1165 3109 6997 18661 41989 111973 251941 671845 1511653
(if (x + ~2) <= 0 then 1 else ((x + 1) - (((~x3 + x) div 2) div 3)))
A318111: 1 1 1 8 15 26 42 64 93 130 176 232 299 378 470 576
(1 + ((~x + (if ((~1 + (x div 3)) mod 4) <= 0 then 1 else 0)) mod 3))
A204257: 1 3 2 2 1 3 1 3 2 1 3 2 1 3 2 2
(1 + (compr(\x.(if (x mod 2) <= 0 then ((x div 3) mod 3) else 0),x) mod 3))
A007413: 1 2 3 1 3 2 1 2 3 2 1 3 1 2 3 1
(1 + ((x + loop(\(x,i).(2 * (2x + (i mod 2))),(x + ~1),1)) div 3))
A008984: 1 1 3 10 35 133
(1 + ((~x + loop(\(x,i).((x * (2 + i)) - (x div 2)),(x + ~1),1)) div 3))
A099952: 1 1 1 3 16 91 595
loop(\(x,i).12x,(5x + 3),1)
A013864: 1728 429981696 106993205379072 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).10x,(5x + 3),1)
A013856: 1000 100000000 10000000000000 1000000000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).7x,(5x + 3),1)
A013844: 343 5764801 96889010407 1628413597910449 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~12x + 1),9x,1)
A015384: 1 ~4762874171 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x5,1,(9x + 1))
A017177: 1 100000 2476099 17210368 69343957 205962976 503284375 1073741824 2073071593 3707398432 6240321451 10000000000 15386239549 22877577568 33038369407 46525874176
(1 + (loop(\(x,i).(2 + ((x div 2) div (1 + (x mod 3)))),2,x) div 3))
A345699: 1 1 1 2 2 1 1 2 2 2 2 2 2 1 2 3
(if (x mod 2) <= 0 then (x div 2) else (9x2 + 6x + ~1))
A071713: 0 14 1 98
(1 + (3 * loop(\(x,i).(7x2 + 3x),2,x)))
A134158: 1 2191 24583 109513 324013 759811 1533331 2785693 4682713 7414903 11197471 16270321 22898053 31369963 42000043 55126981
((1 + (if (((x + (x div 2)) div 2) mod 2) <= 0 then x else 1)) mod (1 + (x div 3)))
A279103: 0 0 0 0 0 0 1 2 0 2 2 0 2 2 0 2
((x + 1) * ((if (~2 + (x div 3)) <= 0 then 1 else 2) * (1 + (x div 3))))
A131959: 1 2 3 8
A132327: 1 2 3 8 10 12 21 24 27 80 88 96 130 140 150 192
((x mod 2) - (if ((x2 div 2) mod 3) <= 0 then (0 - (x mod 3)) else 1))
A131185: 0 2 ~1 0 ~1 3 0 2 ~1 0 ~1 3 0 2 ~1 0
(1 + (if (x mod 2) <= 0 then (x2 mod 7) else (x mod 3)))
A233384: 1 2 5 1 3 3 2 2 2
(1 + loop(\(x,i).(5x + 4),(x div 3),(x mod 3)))
A133335: 1 2 3 5 10 15 25 50 75 125 250 375 625 1250 1875 3125
((x + 3) div ((3 + (if x <= 0 then 0 else 2)) * (1 + (x mod 3))))
A029312: 1 0 0 1 0 0 1 1 0 2 1 0 3 1 1 3
(x mod (1 + ((x + (if ((x div 3) mod 3) <= 0 then 1 else x)) div 3)))
A262403: 0 0 0 0 1 1 1 2 2 1 2 1 3 4 4 4
((2x + 1) div (1 + (3 * loop(\(x,i).(x div (1 + (x mod 2))),x,x))))
A135534: 1 3 0 7 0 1 0 15 0 1 0 3 0 1 0 31
(1 + (3 * compr(\x.loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,x),x)))
A048297: 1 4 7 13 16 25 28 31 49 52 55 61 64 97 100 103
(1 + (x mod (1 + (2 * (if (x mod (2 + ((x + ~1) mod 3))) <= 0 then 2 else x)))))
A262401: 1 2 3 4 5 6 7 8 9 10 1 12 3 14 15 16
(1 + (x div ((x + ~2) + ((x + 1) mod (1 + (2 * (if (x mod 2) <= 0 then 2 else x)))))))
A094293: 1 2 1 1 3 1 2 1 1 1 2 1 1 1 2 1
loop(\(x,i).(1 + (2 * (5x + (i mod 2)))),(2x + 1),1)
A156641: 13 1313 131313 13131313 1313131313 131313131313 13131313131313 1313131313131313 131313131313131313 4611686018427387903 4611686018427387903 4611686018427387903
(x - (x mod (1 + (loop(\(x,i).2x,x,(1 + (x mod 2))) mod (2x + 1)))))
A326128: 0 0 0 3 0 0 0 6 8 0 0 9 0 0 0 15
loop(\(x,i).29x,(2x + 1),1)
A262715: 29 24389 20511149 17249876309 14507145975869 12200509765705829 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).41x,(2x + 1),1)
A262787: 41 68921 115856201 194754273881 327381934393961 550329031716248441 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).37x,(2x + 1),1)
A262786: 37 50653 69343957 94931877133 129961739795077 177917621779460413 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((2x + 2) div (1 + (if (x mod 6) <= 0 then 2 else (x mod 2)))))
A328185: 1 3 7 5 11 7 5 9 19 11 23 13 9 15 31 17
(1 + (x mod (1 + ((2 * (if (x mod 3) <= 0 then 2 else (x mod 2))) + (x mod 2)))))
A070194: 1 2 1 4 1 2 2 4 1 4 1 4 3 2 1 4
(2 div (1 + (3 div (1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2)))))
A329697: 0 0 1 0 1 1 2 0 2 1 2 1 2 2 2 0
(1 + ((x + ~1) mod (1 + (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then 1 else x))))
A345937: 1 1 2 3 4 1 6 7 8 1 10 1 12 1 2 15
loop(\(x,i).20x,(5x + 1),1)
A013894: 20 64000000 204800000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).15x,(5x + 1),1)
A013874: 15 11390625 8649755859375 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).18x,(5x + 1),1)
A013886: 18 34012224 64268410079232 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).24x,(5x + 1),1)
A013910: 24 191102976 1521681143169024 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).14x,(5x + 1),1)
A013870: 14 7529536 4049565169664 2177953337809371136 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).13x,(5x + 1),1)
A013866: 13 4826809 1792160394037 665416609183179841 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).11x,(5x + 1),1)
A013858: 11 1771561 285311670611 45949729863572161 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).17x,(5x + 1),1)
A013882: 17 24137569 34271896307633 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(6x + 120),x,1))
A062588: 2 127 877
loop(\(x,i).21x,(3x + 1),1)
A013768: 21 194481 1801088541 16679880978201 154472377739119461 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).22x,(3x + 1),1)
A013770: 22 234256 2494357888 26559922791424 282810057883082752 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).19x,(3x + 1),1)
A013764: 19 130321 893871739 6131066257801 42052983462257059 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).23x,(3x + 1),1)
A013772: 23 279841 3404825447 41426511213649 504036361936467383 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x div (1 + (x2 mod ((x + 1) + (if (~4 + (x div 2)) <= 0 then x else 1)))))
A330955: 0 0 0 1 0 1 0 1 0 1 2 2 2 2 2 3
(~1 + (if (((x - (((x + 1) mod 5) mod 2)) div 2) mod 2) <= 0 then x else 1))
A322016: 0 0 1 0 3 4 0 0 7 8 9 0 0 12 0 0
(1 + ((x mod 4) mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1)))
A051119: 1 1 1 1 1 2 1 1 1 2 1 4 1 2 3 1
(1 + loop(\(x,i).((x5 + x2 + 2x) + (x div 2)),x,1))
A306785: 2 5 1051
(1 + (((x mod 2) - (if (x mod (4 + (x div 2))) <= 0 then 1 else 0)) mod (x + 1)))
A062754: 1 2 1 2 1 2 1 1 9 2 1 2 1 2 1 2
(1 + compr(\x.(~1 + (x mod (~1 + (loop(\(x,i).2x,x,x) mod (x + 1))))),(x + 1)))
A337935-A327473-A326847-A326837-A326645-A246655-A144711-A137944-A128603-A096165-A089352-A086486-A071139-A059046-A030230: 2 3 4 5 7 8 9 11 13 16 17 19 23 25 27 29
(1 + ((1 + (2 * loop(\(x,i).(3 * (2 + (x div 2))),x,0))) div (x + 1)))
A308550: 2 7 11 14 19 25 33
((x + 1) - ((1 + (if (x mod 2) <= 0 then ((x div 3) mod 2) else 2)) mod (x + 1)))
A214920: 1 1 2 1 3 3 6 5 8 7 9 9 12 11 14 13
((x + 1) - ((1 + (2 * (2 + (if (~2 + (x div 2)) <= 0 then x else 2)))) mod (x + 1)))
A334473: 1 1 3 1 2 3 5 7 9 1 2 3 4 5 6 7
(x mod (1 + ((~1 + loop(\(x,i).2x,(x div (2 + (x mod 2))),2)) mod (x + 1))))
A115378: 0 1 0 3 1 1 0 7 3 3 1 3 1 1 0 15
loop(\(x,i).(5 * (2x - ((x div 2) mod 3))),(x + 1),1)
A063945: 10 90 900 9000 90000 900000 9000000 90000000 900000000 9000000000 90000000000 900000000000 9000000000000 90000000000000 900000000000000 9000000000000000
(1 + (loop(\(x,i).(1 + (2 * (x - (x div (2 + (i mod 2)))))),x,1) div (x + 1)))
A085886: 2 2 2 3 3 3 3 4 4 5 4 5 5 6 6 8
(1 + compr(\x.(~2 + (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 0)),(x + 1)))
A316525: 2 3 4 5 7 8 9 11 13 16 17 19 20 21 23 25
(~1 + (loop(\(x,i).(2 * (2x - (x div (1 + i)))),(x + ~1),2) div (x + 1)))
A141364: 1 0 1 4 13 41 131 428 1429 4861 16795 58785 208011 742899 2674439 9694844
loop(\(x,i).x5,1,(8x + 7))
A017153: 16807 759375 6436343 28629151 90224199 229345007 503284375 992436543 1804229351 3077056399 4984209207 7737809375 11592740743 16850581551 23863536599 33038369407
loop(\(x,i).x6,1,(4x + 3))
A016842: 729 117649 1771561 11390625 47045881 148035889 387420489 887503681 1838265625 3518743761 6321363049 10779215329 17596287801 27680640625 42180533641 62523502209
loop(\(x,i).(7x + 1),(2x2 + 6x + 4),1)
A102170: 2801 16148168401 4611686018427387903
(1 + ((x + 1) * (2 + ((if ((x + ~1) mod 3) <= 0 then 1 else x) * (x mod 2)))))
A157102: 3 7 7 21 11 43 15 25 19 111 23 157 27 43 31 273
(1 + ((x + 1) * (2 + (if (x + ~1) <= 0 then 5 else 3x))))
A169875: 8 15 25 45
(x - ((x div 2) div (1 + (loop(\(x,i).x3,2,2x) mod (x + 1)))))
A010848: 0 1 2 2 4 5 6 4 6 9 10 10 12 13 14 8
(~1 + ((4x + 4) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))
A088837: 3 7 3 15 3 7 3 31 3 7 3 15 3 7 3 63
(~1 + ((x2 + 3x + 2) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))
A092525: 1 5 3 19 5 13 7 71 9 21 11 51 13 29 15 271
(1 + ((x + loop(\(x,i).((x + (x2 div 3)) div 2),2,x)) div (x + 1)))
A261772: 1 1 1 2 2 3 4 5 6 8 9 11 14 16 20 24
loop(\(x,i).((x + 1) + (((x div 2) div 3) + (x div 4))),(x + ~1),1)
A003143: 1 1 2 3 4 6 9 13 19 27 38 54 77 109 155 219
loop(\(x,i).(2 * ((2x * (~1 + (4 * i))) div (1 + i))),(x + ~1),1)
A025749: 1 1 6 56 616 7392 93632 1230592 16612992 228890112 3204461568 45445091328 651379642368 9419951751168 137262154088448 2013178259963904
loop(\(x,i).(2 * (((2x * (1 + (2 * i))) div (2 + i)) * i)),(x + ~1),1)
A005431: 1 1 4 40 672 16128 506880 19768320 922521600 50185175040 3120605429760 218442380083200 17004899126476800 1457562782269440000 4611686018427387903 4611686018427387903
loop(\(x,i).(x + ((4x div (1 + i)) * (~1 + (2 * i)))),(x + ~1),1)
A025748: 1 1 3 15 90 594 4158 30294 227205 1741905 13586859 107459703 859677624 6943550040 56540336040 463630755528
(1 + ((x + ~1) * loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,x)))
A237622: 1 1 5 31 169 841 3961 18019 80081 350065 1511641 6466461 27457585 115892401 486748081 2035917451
(1 + loop(\(x,i).(x + ((2 + (i div 3)) * (1 + (i div 3)))),x,1))
A225566: 2 4 6 12 18 24 36 48 60 80 100 120 150 180 210 252
(1 + ((x2 * loop(\(x,i).x2,2,x3)) div (x2 + 1)))
A270204: 1 1 3277 478297 15790321 234750601 2117950381 13564461457 67662254017 278985273841 990099009901 3112703553961 8854610100337 23161037562937 56406126018061 129172239050401
((1 - (2 * ((x div 3) mod 2))) * (1 + (if (x mod 3) <= 0 then 0 else 2)))
A154595: 1 3 3 ~1 ~3 ~3 1 3 3 ~1 ~3 ~3 1 3 3 ~1
(1 + (loop(\(x,i).((x + 2) + (x div 7)),(x + ~1),0) div 2))
A218906: 1 1 2 3 4 5 6 8 10 12 14 17 20 23 27 32
(1 + ((x div 2) mod (2 + (if (((x + ~1) div 2) mod 6) <= 0 then 2 else 0))))
A218344: 1 1 2 2 1 1 2 2 1 1 2 2 1 3 4 2
((x div (2 - (x mod 2))) mod (1 + (if (x mod (4 + (x div 2))) <= 0 then 0 else 2)))
A163536: 0 1 1 0 2 2 0 0 0 0 2 2 0 1 1 0
(1 + (x div 2) - (2 * (if ((x + 2) mod 5) <= 0 then (x mod 2) else 0)))
A291304: 1 1 2 0 3 3 4 4 5 5 6 6 7 5 8 8
(1 + (loop(\(x,i).((x + 1) - ((~x + 2) div (4 + (x mod 2)))),x,0) div 2))
A304883: 1 1 2 2 3 4 5 7 9 11 14 17 21 26 32 39
(1 + ((x - (if ((x3 + 2x) mod (1 + (x div 2))) <= 0 then 0 else 1)) mod 2))
A305393-A293630: 1 2 1 1 1 2 1 1 2 1 1 1 2 1 2 1
((x + 1) - ((1 + (x div (1 + (if ((x mod 3) mod 2) <= 0 then 2 else 0)))) div 2))
A117900: 1 1 3 3 3 5 6 4 8 8 6 10 11 7 13 13
(1 + ((1 + (x div (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))) div 2))
A181591: 1 1 1 2 1 1 1 3 2 1 1 3 1 1 1 4
(1 + ((1 + (x div (1 + ((1 - loop(\(x,i).2x,x,2)) mod (x + 1))))) div 2))
A326975: 1 1 1 2 1 2 1 3 2 2 1 2 1 2 2 5
(if x <= 0 then 0 else (1 + (x div (1 - (x div (~3 + (x mod ~3)))))))
A019569: 0 1 2 2 3 2 3 3 3 3 4 3 3 4 3 3
(1 + (if ((x + 1) mod (1 + (x div (2 * (2 + ((x div 2) mod 2)))))) <= 0 then 1 else 2))
A217403: 2 2 2 2 3 2 3 2 2 3 3 2 3 3 2 3
(x div (1 + (2 * (1 + (if (x mod 3) <= 0 then (2 * (x div 4)) else 1)))))
A218491: 0 0 0 1 0 1 0 1 1 0 2 2 0 2 2 1
(1 + (if (x + ~1) <= 0 then 1 else (2 * (1 + ((2 * (x div 2)) div 5)))))
A055377: 2 2 3 3 3 3 5 5 5 5 7 7 7 7 7 7
(1 + (loop(\(x,i).5x,(~5 + (x div 2)),1) div 2))
A147136-A147032-A146844: 1 1 1 1 1 1 1 1 1 1 1 1 3 3 13 13
(~1 + ((if x <= 0 then 2 else (2x - (x mod (1 + (x div 5))))) div 2))
A239906: 0 0 1 2 3 3 5 5 7 7 8 9 11 11 12 12
(1 + ((1 + (x div (~1 + (2 * loop(\(x,i).(2 + (x mod (1 + i))),x,2))))) div 2))
A316782-A294336: 1 1 1 2 1 1 1 2 2 1 1 1 1 1 1 4
(~1 + (2 * (if x <= 0 then 1 else (~1 + (3 * (x - ((~x + 2) div 4)))))))
A251535: 1 3 9 21 27 33 39 51 57 63 69 81 87 93 99 111
(if (x + ~1) <= 0 then x else (1 + (2 * (1 + (3 * ((x2 + 2x) div 2))))))
A113481: 0 1 27 45 75
(1 + (2 * ((x + 3) + ((if (x + ~1) <= 0 then x else 2) + (x div 3)))))
A130569: 7 11 15 19 21 23 27 29 31 35 37 39 43 45 47 51
(if x <= 0 then 0 else (1 + (((~x + 5) mod (1 + (x div 3))) div 2)))
A104360: 0 1 1 1 1 1 2 1 1 1 2 2 2 2 1 2
(if x <= 0 then 0 else (1 + (((~x + 8) mod (1 + (x div 3))) div 2)))
A126207: 0 1 1 1 1 1 2 1 1 2 2 1 1 1 3 3
(1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))))
A332741-A052126: 1 1 1 2 1 2 1 4 3 2 1 4 1 2 3 8
(1 + (loop(\(x,i).x3,1,(4x2 + 4x + 1)) div 2))
A175113: 1 365 7813 58825 265721 885781 2413405 5695313 12068785 23522941 42883061 74017945 122070313 193710245 297411661 443751841
(1 + ((x mod (1 + (2 * (1 + (x mod (if (~2 + (x div 2)) <= 0 then 1 else 2)))))) div 2))
A281530-A050205: 1 1 2 1 1 2 1 2 2 3 1 1 1 2 2 1
loop(\(x,i).(2x + 1),((x mod (~1 + (2 * ((x + ~1) div 3)))) div 2),1)
A195644: 1 1 1 1 1 1 1 1 3 1 1 1 3 15 1 1
(1 + ((1 + ((if ((x * (x div 2)) mod 2) <= 0 then x else (x mod 3)) div 2)) div 2))
A295283: 1 1 2 1 2 2 3 1 3 3 4 2 4 4 5 1
(x div (1 + loop(\(x,i).2x,(x div (1 + (2 * (3 - (x mod 2))))),2)))
A089048: 0 0 0 1 1 1 2 1 1 1 2 1 2 1 1 0
(~1 + (2 * loop(\(x,i).(3x3 + 6x),(2x + 2),1)))
A139068: 4481 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,x,1) mod 67)
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A036131: 1 2 4 8 16 32 64 61 55 43 19 38 9 18 36 5
(if (~x + 2) <= 0 then (2 * (1 + (x div (4 * (2 + (x mod 4)))))) else 1)
A003642: 1 1 2 2 2 2 2 2 4 2 2 2 4 4 2 2
(1 + (if x <= 0 then 2 else (((1 + ((x + 1) div 3)) mod 5) mod 2)))
A079948: 3 2 1 1 1 2 2 2 1 1 1 1 1 1 2 2
(1 + (2 * (((2x + 1) + (if (x mod 2) <= 0 then 2 else x)) mod 5)))
A140899: 7 9 5 1 3 3 1 5 9 7 7 9 5 1 3 3
(1 + (2 * (loop(\(x,i).2x,x,(2 * (2 + (x mod 2)))) div 5)))
A255490: 1 5 7 19 25 77 103 307 409 1229 1639 4915 6553 19661 26215 78643
(1 + (2 * (loop(\(x,i).(2x + 2),(x div 2),(x mod 2)) mod 5)))
A138055: 1 3 5 9 3 1 9 5 1 3 5 9 3 1 9 5
(1 + ((((x mod 2) - (if (x mod 3) <= 0 then 0 else x)) mod 5) div 2))
A118914: 1 1 2 1 1 1 1 3 2 1 1 1 1 2 1 1
(3 + (if x <= 0 then 1 else (3x - ((~x + 1) div 5))))
A186514: 4 6 10 13 16 19 22 26 29 32 35 38 42 45 48 51
((x + 1) mod loop(\(x,i).2x,((x div 2) - (2 * (x div 5))),1))
A089631: 0 0 1 0 1 0 1 0 1 2 1 0 1 2 7 0
(1 + (((~x + loop(\(x,i).(x div (1 + (x mod 2))),x,x)) mod 5) div 2))
A319658: 1 3 1 2 1 2 1 2 1 1 1 1 1 2 1 1
loop(\(x,i).x5,1,(8x + 3))
A017105: 243 161051 2476099 14348907 52521875 147008443 345025251 714924299 1350125107 2373046875 3939040643 6240321451 9509900499 14025517307 20113571875 28153056843
(1 + ((x mod (1 + (2 * ((if (x mod 3) <= 0 then 2 else 1) + (x mod 2))))) mod 2))
A336532: 1 2 1 2 2 1 2 1 1 1 2 2 1 2 1 2
(1 + ((1 + (x div (2 * ((if (x mod 3) <= 0 then 2 else 1) + (x mod 2))))) div 2))
A185278: 1 1 2 1 2 2 2 2 3 2 4 2 3 3 5 2
(1 + ((3 * (loop(\(x,i).(2x + (i mod 2)),x,0) div (x + 1))) div 2))
A333188: 1 1 1 2 4 5 10 16 28 52 94 170 316 586 1093 2048
loop(\(x,i).(x * i),(x - (2 * ((4 * (x div 3)) div 3))),1)
A269223: 1 1 2 1 2 6 2 6 24 1 2 6 2 6 24 6
(~1 + ((3 * (x - ((if x <= 0 then 1 else x) div ~7))) div 2))
A097702: 0 2 3 5 6 8 9 11 14 15 17 18 20 21 23 26
(12 - (if ((x + 2) mod 12) <= 0 then 2 else 1))
A231472: 11 11 11 11 11 11 11 11 11 11 10 11 11 11 11 11
(~1 + (2 * ((4 * (x + (if (~2 + (x div 2)) <= 0 then 1 else 2))) div 3)))
A171947: 1 3 7 9 11 15 19 23 25 27 31 33 35 39 41 43
loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)
A285741-A001316: 1 2 2 4 2 4 4 8 2 4 4 8 4 8 8 16
loop(\(x,i).(x * i),(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)
A093659: 1 1 1 2 1 2 2 6 1 2 2 6 2 6 6 24
(1 + ((loop(\(x,i).(3x + 1),x,1) - ((x div 2) mod 3)) div 2))
A132868: 1 3 7 20 60 182 547 1641 4921 14762 44286 132860 398581 1195743 3587227 10761680
(if ((1 + ((x + 1) div 3)) mod 5) <= 0 then 6 else 1)
A172360: 1 1 1 1 1 1 1 1 1 1 1 6 6 6 1 1
(2 div (1 + ((1 + (if (x mod 5) <= 0 then 0 else x)) mod 6)))
A025880-A017837: 1 0 0 0 0 1 1 0 0 0 1 2 1 0 0 1
(loop(\(x,i).10x,(x + 1),1) div 7)
A241217: 1 14 142 1428 14285 142857 1428571 14285714 142857142 1428571428 14285714285 142857142857 1428571428571 14285714285714 142857142857142 1428571428571428
(((~1 + loop(\(x,i).(x * (2 + i)),x,2)) div 3) mod 7)
A021100: 0 1 0 4 1 6 6 6 6 6 6 6 6 6 6 6
((loop(\(x,i).(x * (x - i)),2,(x + ~1)) div 3) div 7)
A011931: 0 0 0 0 1 5 17 40 80 144 240 377 565 817 1144 1560
(7 * (if x <= 0 then 1 else (2 + ((~x + 1) mod (1 + (x div 2))))))
A242888: 7 14 21 14 14 28
((loop(\(x,i).(x - (2 * (~x + (i mod 2)))),x,1) div 2) div 7)
A133409: 0 0 0 0 1 4 13 39 117 351 1054 3163 9490 28470 85410 256230
((2 + (loop(\(x,i).(3x + ~1),x,1) div 2)) div 7)
A133405: 0 0 0 1 3 9 26 78 234 703 2109 6327 18980 56940 170820 512461
(if x <= 0 then 1 else (((x2 + ~5x + 6) div 2) div 7))
A263362: 1 0 0 0 0 0 0 1 2 3 4 5 6 7 9 11
loop(\(x,i).((2x * (x mod 2)) - (x div ~2)),x,7)
A185455: 7 18 9 23 58 29 73 183 458 229 573 1433 3583 8958 4479 11198
(7 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A175222: 7 8 10 12 16 18 22 24 28 34 36 42 46 48 52 58
((if (~x + 2) <= 0 then (2 + (x div 4)) else 1) - (x div 7))
A238268: 1 1 2 2 3 3 3 2 3 3 3 3 4 4 3 3
((if (x + ~12) <= 0 then 1 else 2) + (x div 7))
A109701-A103374: 1 1 1 1 1 1 1 2 2 2 2 2 2 3 4 4
((if (x mod 2) <= 0 then 1 else (x div 8)) + (x div 7))
A029226: 1 0 1 0 1 0 1 1 2 2 2 2 2 2 3 3
(~1 + loop(\(x,i).(x + (5x div (1 + i))),x,6))
A062988: 5 20 55 125 251 461 791 1286 2001 3002 4367 6187 8567 11627 15503 20348
(1 + (2 * (3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A129069: 7 9 13 17 25 29 37 41 49 61 65 77 85 89 97 109
(1 + (if x <= 0 then 1 else (2 * (4x - ((x div 3) + (x div 2))))))
A063105: 2 9 15 21 27 35 39 47 53 59 65 73 77 85 91 97
(1 + ((if ((x + 1) mod 5) <= 0 then 2 else 0) + ((x mod 3) div 2)))
A277818: 1 1 2 1 3 2 1 1 2 3 1 2 1 1 4 1
(((2x div (1 + (x div 4))) mod 2) * (if (x mod 3) <= 0 then 2 else 1))
A051517: 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 2
(1 + ((3 * compr(\x.loop(\(x,i).(x div (1 + (2 * (x mod 2)))),x,x),x)) div 2))
A191109: 1 2 5 8 14 17 23 26 41 44 50 53 68 71 77 80
(1 + (2 * (1 + (2 * (x + (loop(\(x,i).x3,x,2) div (x + 1)))))))
A193855: 11 23 691
(if x <= 0 then 0 else (1 + (((x + 1) div (3 - ((x * (x div 2)) mod 2))) div 2)))
A071068: 0 1 1 2 1 2 2 3 2 2 2 4 3 3 3 5
(1 + ((1 + (loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 2)) mod (x + 2))) div 2))
A194550: 1 1 2 1 3 1 2 1 4 1 3 1 5 1 2 1
loop(\(x,i).3x2,1,(1 + (2 * ((2x + 1) + (x div 2)))))
A192328: 27 147 507 867 1587 2187 3267 4107 5547 6627 8427 9747 11907 13467 15987 17787
(1 + ((((x + (if (x mod 2) <= 0 then x else 1)) div 3) mod (1 + (x div 2))) div 2))
A278109: 1 1 1 1 2 2 1 2 1 2 1 3 1 3 1 3
(1 + ((x mod (1 + (loop(\(x,i).2x,(x div 3),1) * (x mod 2)))) div 2))
A081652: 1 1 1 1 1 2 1 2 1 1 1 2 1 7 1 8
(~1 + (2 * loop(\(x,i).(8x + ~2),(x div 2),(1 + (x mod 2)))))
A113836: 1 3 11 27 91 219 731 1755 5851 14043 46811 112347 374491 898779 2995931 7190235
(1 + (2x div (2 + (if ((x2 + 2x) mod 6) <= 0 then x else 1))))
A322587: 1 1 2 3 2 4 2 5 6 7 2 8 2 9 10 11
(1 + ((1 + loop(\(x,i).(x - ((2 - (x mod 2)) * (x div 3))),2,x)) div 2))
A320011: 1 2 2 2 2 2 2 3 2 2 2 3 2 4 2 3
(1 + (x div (2 + (loop(\(x,i).((x + 4) + (x div 2)),x,0) mod (x + 1)))))
A271325: 1 1 1 1 2 1 1 1 2 2 2 4 1 2 2 2
(1 + (((~1 + loop(\(x,i).2x,x,(x - ((x div 2) mod 2)))) mod (x + 1)) div 2))
A055034: 1 1 1 2 2 2 3 4 3 4 5 4 6 6 4 8
((1 + loop(\(x,i).(2x + 4),((x + 1) div 2),2)) div (2x + 3))
A288005: 1 1 1 2 1 3 3 5 4 9 8 15 14 26 24 46
((2x + 3) + (loop(\(x,i).6x,(x + ~1),1) div 2))
A003187: 3 5 10 27 119
((2x + 3) * loop(\(x,i).6x,x,8))
A268966: 24 240 2016 15552 114048 808704 5598720 38071296 255301632 1693052928 11125776384 72559411200 470184984576 3030081011712 19434312695808 124128835928064
(loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2) mod (2x + 3))
A256277: 2 1 6 7 10 1 12 1 18 19 22 6 11 1 30 9
((2x + 3) * loop(\(x,i).x3,1,(x2 + 4x + 4)))
A209594: 192 3645 28672 140625 513216 1529437 3932160 9034497 19000000 37202781 68677632 120670225 203297472 330328125 520093696 796539777
(1 + (((x2 + x) * (3 + (if (x + ~1) <= 0 then x else 2x))) div 2))
A273677: 1 5 22 55 111 196 316 477 685 946 1266 1651 2107 2640 3256 3961
loop(\(x,i).(1 + ((2x * (~1 + (2 * i))) div (1 + i))),((x + ~1) div 2),1)
A322111: 1 1 1 2 2 5 5 13 13 37 37
(1 + ((loop(\(x,i).(2x - (i mod 2)),x,1) div 3) * ((x + ~1) div 2)))
A161746: 1 1 1 2 3 7 15 43
loop(\(x,i).3x,((x3 + 8x2 + x + 8) div 2),1)
A100533: 81 19683 847288609443 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (2 * (~2 + loop(\(x,i).(10x + 8),(x + 1),0))))
A205087: 11 171 1771 17771 177771 1777771 17777771 177777771 1777777771 17777777771 177777777771 1777777777771 17777777777771 177777777777771 1777777777777771 17777777777777771
((x2 + 2x + 1) - (2 * (if (~2 + (x div 5)) <= 0 then 0 else 2)))
A331221: 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 252
((x + 1) - ((0 - (x div (2 + (if (~2 + (x div 3)) <= 0 then 2 else 0)))) div 2))
A296858: 1 2 3 4 6 7 8 9 10 12 14 15 16 17 19 20
(1 + (loop(\(x,i).(2x + 1),(x div 2),((x mod 2) - (x div ~2))) div 2))
A262258: 1 2 2 4 6 10 16 24 40 56 96 128 224 288 512 640
(1 + (2 * (loop(\(x,i).((x + 2) + ((x + (x div 2)) div (1 + i))),x,0) div 2)))
A342474: 1 3 5 9 13 17
A340520: 1 3 5 9 13 17 23 29 35 41 49 57 65 73 81 91
loop(\(x,i).(x2 + x),(x - (4 * (1 + (x div 5)))),1)
A165680: 1 1 1 1 1 1 1 1 1 2 1 1 1 2 6 1
(if x <= 0 then 1 else ((2x + 1) div (1 + (4 * (1 + (x mod 3))))))
A029253: 1 0 0 1 1 0 2 1 1 3 2 1 5 3 2 6
(1 + (((1 + loop(\(x,i).(x + ((i div 3) + (x div 2))),x,1)) div 2) div 2))
A143951: 1 1 1 1 2 3 4 6 9 14 21 31 47 71 107 161
(1 + (2 * ((1 + (loop(\(x,i).(x * (2 + i)),4,2) mod (x + 1))) div 2)))
A271498: 1 1 1 1 1 1 7 1 1 1 7 1 7 7 1 1
(~1 + (2 * ((((x + 1) * (if x <= 0 then 1 else 2)) mod 7) mod 2)))
A114523: 1 ~1 ~1 1 1 1 ~1 ~1 ~1 ~1 1 1 1 ~1 ~1 ~1
((x + ~1) - (2 * ((x + ~1) div (2 + (if (~2 + (x div 3)) <= 0 then 2 else 1)))))
A071933: 1 0 1 2 3 2 3 4 5 4 3 4 5 4 5 6
(1 + (2 * (4 - (loop(\(x,i).2x,x,1) mod 9))))
A154870: 7 5 1 ~7 ~5 ~1 7 5 1 ~7 ~5 ~1 7 5 1 ~7
(if x <= 0 then 0 else (1 + ((x mod (2 + (x div (3 + (x mod 4))))) div 2)))
A275806: 0 1 1 1 1 2 1 1 1 1 2 2 1 2 2 2
(if x <= 0 then 0 else (~1 + (2 * ((x2 mod (1 + (2 * (2 + (x div 2))))) mod 2))))
A011585: 0 1 ~1 ~1 1 1 1 1 ~1 1 ~1 1 ~1 ~1 ~1 ~1
(2 div (1 + (x div (2 + ((x + 2) mod (2 * (if (x mod 2) <= 0 then 4 else 1)))))))
A096831: 2 2 2 1 2 1 0 0 0 0 1 0 1 0 0 0
(3 + (if (x + ~2) <= 0 then x else (2 + ((2x + 1) div 5))))
A104136: 3 4 5 6 6 7 7 8 8 8 9 9 10 10 10 11
(1 + (2 * loop(\(x,i).(x2 + 2x),(2x + 1),10)))
A120377: 241 428717761
(loop(\(x,i).5x,x,1) mod 21)
A070374: 1 5 4 20 16 17 1 5 4 20 16 17 1 5 4 20
(~1 + (2 * (((if x <= 0 then 1 else x) mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2)))
A076479: 1 ~1 ~1 ~1 ~1 1 ~1 ~1 ~1 1 ~1 1 ~1 1 1 ~1
(1 + (((3 * (x div (if ((x + ~1) mod 4) <= 0 then 2 else 1))) div 2) div 2))
A295887: 1 1 2 3 4 2 5 6 7 4 8 9 10 5 11 12
(1 + (4 * loop(\(x,i).(2x + 32),x,3)))
A305262: 13 153 433 993 2113 4353 8833 17793 35713 71553 143233 286593 573313 1146753 2293633 4587393
(2x div (5 + ((if (x mod 2) <= 0 then (~x + 2) else x) mod 3)))
A080344: 0 0 0 1 1 1 1 2 3 3 3 3 3 4 5 6
loop(\(x,i).x5,1,(8x + 5))
A017129: 3125 371293 4084101 20511149 69343957 184528125 418195493 844596301 1564031349 2706784157 4437053125 6956883693 10510100501 15386239549 21924480357 30517578125
(5 + ((if (x + ~1) <= 0 then 2 else ((x + 1) div 2)) * (1 + (x div 2))))
A246506: 7 7 7 9 11 14 17 21 25 30
(1 + ((loop(\(x,i).((x + 1) - ((~x + 2) div 5)),x,1) div 2) div 2))
A097793: 1 1 1 2 2 3 4 4 5 7 8 10 12 14 17 21
(1 + ((loop(\(x,i).((x + 1) + ((x + i) div 5)),x,1) div 2) div 2))
A280663-A266748: 1 1 1 2 2 3 4 5 7 9 11 14 17 21 26 32
(1 + ((x - ((x2 - loop(\(x,i).(3x + 1),x,1)) div 2)) div 2))
A262592: 1 2 4 10 29 88 268 812 2449 7366 22124 66406 199261 597836 1793572 5380792
(1 + (((loop(\(x,i).(2x + 4),5,2) mod (x + 1)) div 2) div 2))
A239957: 1 1 1 1 1 1 2 2 3 3 1 3 2 2 3 4
(1 + ((((x + 1) * (if (x mod 2) <= 0 then ((x div 3) mod 2) else 2)) div 2) div 2))
A260429: 1 2 1 3 2 4 1 5 1 6 3 7 1 8 1 9
(loop(\(x,i).i,(x mod 7),x) mod (1 + (((x + 1) div 2) div 2)))
A037281: 0 0 0 1 0 1 0 1 1 2 0
A089615-A069160: 0 0 0 1 0 1 0 1 1 2 0 0 1 2 2 1
(1 + (((loop(\(x,i).((2x + 1) - (x div 3)),x,0) div 2) div 2) div 2))
A186085: 1 1 1 1 2 3 5 8 13 22 36 60 100 166 277 461
(if x <= 0 then 0 else (1 + (((x - (x mod (2 * (1 + (x mod 3))))) div 2) div 2)))
A053276: 0 1 1 1 2 1 2 2 2 3 3 2 4 4 4 4
(~1 + (2 * (~4 + loop(\(x,i).10x,(x + 1),1))))
A185123: 11 191 1991 19991 199991 1999991 19999991 199999991 1999999991 19999999991 199999999991 1999999999991 19999999999991 199999999999991 1999999999999991 19999999999999991
(1 + (2 * (4 + (if ((x + 1) mod 12) <= 0 then 2 else 1))))
A317244: 11 11 11 11 11 11 11 11 11 11 11 13 11 11 11 11
(1 + (((x + ~2) mod (2 + (x div (2 + (if (x mod 3) <= 0 then 2 else 1))))) div 2))
A299825: 1 1 1 1 2 1 1 1 2 2 2 3 1 3 1 2
(if x <= 0 then 1 else (1 + (2 * (((~1 + (2x mod (2 + (x div 2)))) div 2) mod 2))))
A089607: 1 3 1 3 3 1 1 3 3 3 1 1 3 1 1 3
(1 + (((loop(\(x,i).(2x + 2),x,(3x + 6)) div 2) div 2) div 2))
A106472: 1 3 7 17 40 92 208 464 1024 2240 4864 10496 22528 48128 102400 217088
(if x <= 0 then 1 else (x div (1 + (2 * (2 + ((x2 div 2) mod 6))))))
A152067: 1 0 0 0 0 1 1 1 0 0 1 2 2 2 1 1
(if x <= 0 then 0 else (1 + (((((2x + ~1) * ((~x + 2) div 2)) div 2) div 2) mod 2)))
A086288: 0 1 1 1 1 2 1 1 1 2 2 2 2 1 2 2
(1 + (2 * (((~1 + (if (x mod (4 + (x div 2))) <= 0 then 1 else x)) div 2) div 2)))
A056611: 1 1 1 1 1 3 3 1 1 5 5 5 5 7 7 7
(5 + (loop(\(x,i).((x + 2) + ((x div 2) div 3)),x,1) div 2))
A120182: 5 6 7 8 10 11 13 15 18 21 24 28 33 38 45 52
(if x <= 0 then 0 else (2 - ((1 - (x div 2)) div (1 + ((((x + 1) div 2) div 2) div 2)))))
A196048: 0 1 2 2 3 3 4 3 4 4 4 4 5 5 5 4
(1 + (x mod (6 + (if ((x + 1) mod 8) <= 0 then 1 else 2))))
A277546: 1 2 3 4 5 6 7 1 1 2 3 4 5 6 7 2
(if x <= 0 then 2 else (1 + (2 * ((x - (((3 * (x div 2)) div 2) div 2)) mod 2))))
A039702: 2 3 1 3 3 1 1 3 3 1 3 1 1 3 3 1
(if x <= 0 then 0 else ((x + 5) - (x div ~14)))
A345435: 0 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22
(3 + (if (x + ~2) <= 0 then x else (2 + ((x - ((x div 4) mod 2)) div 2))))
A198466: 3 4 5 6 6 7 7 8 9 9 10 10 10 11 11 12
(loop(\(x,i).5x,x,1) mod 33)
A070381: 1 5 25 26 31 23 16 14 4 20 1 5 25 26 31 23
(loop(\(x,i).6x,x,1) mod 31)
A070399: 1 6 5 30 25 26 1 6 5 30 25 26 1 6 5 30
(5 + (loop(\(x,i).2x,x,(5x + ~8)) div 2))
A139628: 1 2 9 33
A048498: 1 2 9 33 101 277 709 1733 4101 9477 21509 48133 106501 233477 507909 1097733
loop(\(x,i).(x div ~2),(~2 + (2x mod (4 + (x div 4)))),1)
A185917: 1 1 1 1 ~1 1 1 0 0 1 1 0 ~1 0 1 1
(1 + (((2 + (((if (x + ~4) <= 0 then 1 else x) * (x div 2)) div 2)) div 2) div 2))
A049810: 1 1 1 1 1 2 3 4 5 6 7 8 10 11 13 14
(if x <= 0 then 0 else (1 + (((x + 2) mod (2 + (x mod (2 * (2 + (x mod 2)))))) div 2)))
A039927: 0 1 1 1 1 1 1 1 1 1 1 4 1 1 1 2
(loop(\(x,i).7x,x,1) mod 17)
A070407: 1 7 15 3 4 11 9 12 16 10 2 14 13 6 8 5
(1 div (2 - (loop(\(x,i).x2,2,x2) mod 17)))
A165581-A165471-A011584: 0 1 1 ~1 1 ~1 ~1 ~1 1 1 ~1 ~1 ~1 1 ~1 1
(loop(\(x,i).((x2 + ~x) div 2),2,(x + ~1)) div 15)
A011795: 0 0 0 0 0 1 3 7 14 25 42 66 99 143 200 273
((loop(\(x,i).(x * (x - i)),2,(x + ~1)) div 2) div 15)
A011940: 0 0 0 0 0 4 12 28 56 100 168 264 396 572 800 1092
(1 + (x div (2 * (2 + ((if ((x mod 3) mod 2) <= 0 then 2 else x) mod 4)))))
A085031: 1 1 1 1 2 1 1 1 2 2 2 2 2 3 2 2
(2 div (1 + ((1 - (if (~x + 2) <= 0 then x else 0)) mod (4 + (x div 4)))))
A331984: 1 1 0 0 0 1 2 0 0 0 0 0 0 0 1 2
(2 div (1 + ((1 + (2 * (if x <= 0 then 1 else x))) mod (4 + (x div 4)))))
A231642: 0 0 1 0 0 1 0 2 0 1 0 0 0 0 1 0
(1 - ((if x <= 0 then 0 else 1) div (~1 + (2x mod (4 + (x div 4))))))
A166124: 1 0 2 0 1 2 0 1 1 2 0 1 1 1 2 0
(1 + (((loop(\(x,i).((x + 2) + (x div 5)),x,2) div 2) div 2) div 2))
A036821: 1 1 1 2 2 3 3 4 5 6 7 9 10 12 15 18
(if (x mod 3) <= 0 then 1 else (x div (1 + (2 * (4 - ((x div 2) mod 2))))))
A025848: 1 0 0 1 0 0 1 1 0 1 1 1 1 1 2 1
loop(\(x,i).2x,(((2x + 1) mod (x - ((x + 1) mod 4))) div 2),1)
A245163-A232089: 1 1 1 1 1 2 1 1 2 4 1 1 2 4 8 1
(9 * (1 + ((x + (if (x mod 2) <= 0 then x else 2)) mod 3)))
A242892: 9 9 18 27 27 18
((loop(\(x,i).(x * (x - i)),2,(x + ~1)) div 3) div 9)
A011937: 0 0 0 0 0 4 13 31 62 112 186 293 440 635 889 1213
(9 * (1 + (if (~2 + (x div 3)) <= 0 then x else (x + 2))))
A249605: 9 18 27 36 45 54 63 72 81 108 117 126 135 144 153 162
(loop(\(x,i).4x,(x + ~2),(1 + (x mod 2))) div 9)
A215970: 0 0 0 0 1 14 28
(loop(\(x,i).(10x + 1),x,1) div 9)
A057932: 0 1 12 123 1234 12345 123456 1234567 12345679 123456790 1234567901 12345679012 123456790123 1234567901234 12345679012345 123456790123456
(loop(\(x,i).2x,x,(x3 + 2x + 1)) mod 9)
A144750: 1 8 7 2 7 5 4 5 1 8 1 2 7 2 4 5
(9 * loop(\(x,i).10x,x,(x + 1)))
A212704: 9 180 2700 36000 450000 5400000 63000000 720000000 8100000000 90000000000 990000000000 10800000000000 117000000000000 1260000000000000 13500000000000000 144000000000000000
(loop(\(x,i).(x + (((2 + i) * (1 + i)) div 2)),x,1) mod 9)
A133883: 1 4 1 2 8 2 3 3 3 4 7 4 5 2 5 6
(9 * (x div (2 + (if (~4 + (x div 2)) <= 0 then 2 else 1))))
A068395: 0 0 0 0 9 9 9 9 18 18 27 27 36 36 36 45
(9 * (2 - loop(\(x,i).i,(x + ~9),2)))
A056965: 0 0 0 0 0 0 0 0 0 0 9 0 ~9 ~18 ~27 ~36
(9 * loop(\(x,i).(2x + 5),x,6))
A304172: 54 153 351 747 1539 3123 6291 12627 25299 50643 101331 202707 405459 810963 1621971 3243987
(if x <= 0 then 1 else (36x2 + ~8x))
A318778: 1 28 128 300 544 860 1248 1708 2240 2844
(18 * loop(\(x,i).(3x + 2),4,x))
A157508: 1440 2898 4356 5814 7272 8730 10188 11646 13104 14562 16020 17478 18936 20394 21852 23310
((if x <= 0 then 1 else 4x) - ((~2x + 4) div 9))
A058759: 1 4 8 13
A311816: 1 4 8 13 17 21 25 30 34 38 42 46 51 55 59 63
(9 * loop(\(x,i).10x,x,(x + 2)))
A159740: 18 270 3600 45000 540000 6300000 72000000 810000000 9000000000 99000000000 1080000000000 11700000000000 126000000000000 1350000000000000 14400000000000000 153000000000000000
(9 * (loop(\(x,i).10x,x,x) div 2))
A034967: 0 45 900 13500 180000 2250000 27000000 315000000 3600000000 40500000000 450000000000 4950000000000 54000000000000 585000000000000 6300000000000000 67500000000000000
((if ((x div 5) mod 2) <= 0 then x else ~x) mod 9)
A093150: 0 1 2 3 4 4 3 2 1 0 1 2 3 4 5 3
(9 * (x + (if (x + ~10) <= 0 then 1 else 2)))
A016096: 9 18 27 36 45 54 63 72 81 90 99 117 126 135 144 153
(9 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A175223: 9 10 12 14 18 20 24 26 30 36 38 44 48 50 54 60
((if (~2 + (x div 3)) <= 0 then 1 else 2x) + (x mod 9))
A108690: 1 2 3 4 5 6 7 8 9 18 21 24 27 30 33 36
(loop(\(x,i).(10x + 8),x,x) div 9)
A294328: 0 2 32 432 5432 65432 765432 8765432 98765432 1098765432 12098765432 132098765432 1432098765432 15432098765432 165432098765432 1765432098765432
(1 + loop(\(x,i).(x - ((~x + 2) div 7)),x,8))
A120193: 9 10 11 13 15 17 19 22 25 29 33 38 43 49 56 64
loop(\(x,i).(x + 1),((x + ~8) + ((x div 2) div 5)),1)
A094798: 1 1 1 1 1 1 1 1 1 2 4 5 6 7 8 9
loop(\(x,i).11x,2,(1 + (x mod 8)))
A131973: 121 242 363 484 605 726 847 968 121 242 363 484 605 726 847 968
((if (~2 + (x div 3)) <= 0 then 1 else 2) div (1 + (x2 mod 8)))
A029376: 1 0 0 0 1 0 0 0 1 1 0 1 2 1 0 1
(1 + (if (x + ~1) <= 0 then x else (2 + ((x + ((x div 4) mod 2)) div 4))))
A221671: 1 2 3 3 4 4 4 5 5 5 5 5 6 6 6 7
(1 + (x mod (if (x mod 2) <= 0 then 1 else (1 - (x div (~2 + ((~x + 2) div 4)))))))
A178544: 1 2 1 2 1 3 1 2 1 2 1 4 1 2 1 4
(~1 + (2 * (if x <= 0 then 1 else 2x)) - (x div (~2 + ((~x + 2) div 4))))
A311426: 1 4 8 12 17 21 25 29 33 38 42 46 50 54 58 62
(1 + (2 * (2x + (if x <= 0 then 1 else x) - ((x + (x div 2)) div 4))))
A288709: 3 7 13 17 23 29 33 39 43 49 55 59 65 71 75 81
(if x <= 0 then 1 else (((x2 + 2x) div 2) mod (1 + (x div (2 + (x div 4))))))
A339846: 1 0 0 1 0 1 0 1 1 1 0 2 0 1 1 3
(~1 + (2 * loop(\(x,i).x2,1,(4x3 + ~3x))))
A243132: ~1 1 1351 19601 119071 470449 1431431 3650401 8193151 16692641 31521799 55989361 94558751 153090001 239104711 362074049
loop(\(x,i).x2,3,(~11x + ~9))
A017504: 43046721 25600000000 852891037441 9682651996416 62259690411361 281474976710656 1001129150390625 2992179271065856 7837433594376961 18509302102818816 40213853471634241 81573072100000000
((~1 + loop(\(x,i).2x,x,2)) div (1 + (4 * ((x * (x div 2)) mod 2))))
A213244: 1 3 7 3 31 63 127 51 511 1023 2047 819 8191 16383 32767 13107
(1 + ((loop(\(x,i).(x + ((x div 8) + (i div 2))),x,2) div 2) div 2))
A287997-A034144: 1 1 1 2 2 3 4 5 6 8 10 12 15 18 22 26
loop(\(x,i).x6,1,(8x + 1))
A017082: 1 531441 24137569 244140625 1291467969 4750104241 13841287201 34296447249 75418890625 151334226289 282429536481 496981290961 832972004929 1340095640625 2081951752609 3138428376721
(1 - (if x <= 0 then 0 else (1 + (((x3 + ~2x2) mod (2 + (x div 2))) mod 2))))
A290975: 1 ~1 0 0 0 ~1 0 0 0 ~1 0 0 0 ~1 ~1 0
(x - (if (x + ~1) <= 0 then x else (1 + (((x2 + ~2x) mod (2 + (x div 2))) mod 2))))
A239904: 0 0 1 2 3 3 5 6 7 7 8 9 11 11 13 14
((1 + (x div 4)) mod loop(\(x,i).2x,((x mod (2 + (x div 2))) div 2),1))
A278478: 0 0 1 0 0 0 0 0 1 1 1 3 0 0 0 4
(1 + (2 * ((x + 1) div (2 + (if ((x + ~1) mod 4) <= 0 then 2 else (x mod 2))))))
A335115: 1 1 3 3 5 3 7 5 9 5 11 9 13 7 15 11
loop(\(x,i).(5x + 5),(x div 2),(1 + (4 * (x mod 2))))
A133629: 1 5 10 30 55 155 280 780 1405 3905 7030 19530 35155 97655 175780 488280
loop(\(x,i).7x,(x div 2),(1 + (4 * (x mod 2))))
A018353: 1 5 7 35 49 245
(1 + (2 * loop(\(x,i).((2x + 1) * (1 + (x mod 2))),x,(2 * (x mod 2)))))
A334930: 1 11 13 91 109 731 877 5851 7021 46811 56173 374491 449389 2995931 3595117 23967451
((if (x + ~2) <= 0 then 1 else (2 + (x div 2))) mod (1 + (((x + 1) div 2) mod 4)))
A039997-A039995-A035232: 0 1 1 0 1 0 1 0 0 0 1 1 2 0 1 0
(5 * loop(\(x,i).(x + ((1 + (i * i)) * i * i)),(x + 1),0))
A249845: 10 110 560 1920 5170 11830 24080 44880 78090 128590 202400 306800 450450 643510 897760 1226720
(loop(\(x,i).2x,(x - (2 * (x div 5))),1) mod 5)
A275117: 1 2 4 3 1 3 1 2 4 3 4 3 1 2 4 2
loop(\(x,i).x5,1,(10x + 5))
A017333: 3125 759375 9765625 52521875 184528125 503284375 1160290625 2373046875 4437053125 7737809375 12762815625 20113571875 30517578125 44840334375 64097340625 89466096875
(loop(\(x,i).(4x + 1),(x + 1),(1 + (x mod 2))) div 5)
A118108: 1 7 17 119 273 1911 4369 30583 69905 489335 1118481 7829367 17895697 125269879 286331153 2004318071
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) mod 5)
A159984: 1 1 2 0 4 2 2 4 0 2 1 1 2 0 0 0
loop(\(x,i).x3,1,(10x2 + 20x + 10))
A234787: 1000 64000 729000 4096000 15625000 46656000 117649000 262144000 531441000 1000000000 1771561000 2985984000 4826809000 7529536000 11390625000 16777216000
(5 * (~2 + loop(\(x,i).10x,(x + 1),1)))
A177096: 40 490 4990 49990 499990 4999990 49999990 499999990 4999999990 49999999990 499999999990 4999999999990 49999999999990 499999999999990 4999999999999990 49999999999999990
(10 * (~1 + loop(\(x,i).10x,x,2)))
A173813: 10 190 1990 19990 199990 1999990 19999990 199999990 1999999990 19999999990 199999999990 1999999999990 19999999999990 199999999999990 1999999999999990 19999999999999990
loop(\(x,i).x3,1,(11x + 9))
A017499: 729 8000 29791 74088 148877 262144 421875 636056 912673 1259712 1685159 2197000 2803221 3511808 4330747 5268024
loop(\(x,i).x3,2,(11x + 9))
A017505: 387420489 512000000000 26439622160671 406671383849472 3299763591802133 18014398509481984 75084686279296875 257327417311663616 760231058654565217 1999004627104432128 4611686018427387903
((if x <= 0 then 1 else 6x) - ((2x + 2) div 5))
A315525: 1 6 11 17 22 28 34 39 45 50 56 62 67 73 78 84
((if x <= 0 then 1 else 5x) - ((2x + 2) div 5))
A314840: 1 5 9 14 18 23 28 32 37 41 46 51 55 60 64 69
((((x + 1) * loop(\(x,i).(x2 + 2x),3,x)) div 2) div 5)
A288604: 0 51 1968 26214 195312 1007769 4035360 13421772 38742048 99999999 235794768 515978034 1060449936 2066104677 3844335936 6871947672
((if x <= 0 then 1 else 5x) - ((~2x + 2) div 5))
A314145: 1 5 11 16 22 27 32 38 43 49 54 59 65 70 76 81
(5 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A001750: 10 15 25 35 55 65 85 95 115 145 155 185 205 215 235 265
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 5)
A039703: 2 3 0 2 1 3 2 4 3 4 1 2 1 3 2 3
(if x <= 0 then 1 else (2x - ((1 - ((x2 + ~2x) div 2)) div 5)))
A231408: 1 2 4 6 9
A014011: 1 2 4 6 9 12 15 18 21 24 28 32 36 40 45 50
((x + 1) mod (if x <= 0 then 2 else (2 - ((~x2 + 4x + ~4) mod 5))))
A015941-A015605-A015437-A015101-A014933-A011643: 1 0 1 0 0 0 ~1 0 ~1 0 0 0 1 0 0 0
(loop(\(x,i).x2,1,((2x + ~1) + (x div 3))) mod 5)
A082999: 1 1 4 1 4 0 4 0 4 0 4 1 4 1 1 1
((if (x mod 2) <= 0 then 1 else (x div 8)) + ((x div 2) div 5))
A029241: 1 0 1 0 1 0 1 0 1 1 2 2 2 2 2 2
((if ((x mod (1 - (2 * (x mod 4)))) mod 2) <= 0 then 1 else x) mod 5)
A295632: 1 1 2 1 1 1 1 2 1 1 1 1 1 1 4 1
loop(\(x,i).(21x + ~10),x,5)
A233077: 5 95 1985 41675 875165 18378455 385947545 8104898435 170202867125 3574260209615 75059464401905 1576248752439995 33101223801239885 695125699826037575 4611686018427387903 4611686018427387903
loop(\(x,i).(((x3 + ~3x2 + 2x) div 2) div 3),x,5)
A251702: 5 10 120 280840 3691654113991480 4611686018427387903
((x + 5) + (x div (2 + (if (~2 + (x div 4)) <= 0 then 2 else 0))))
A005049: 5 6 7 8 10 11 12 13 15 16 17 18 23 24 26 27
((x + 5) + (x div (2 + (if (~2 + (x div 4)) <= 0 then 1 else 2))))
A178096: 5 6 7 9 10 11 13 14 15 17 18 19 20 21 22 23
(~5 + loop(\(x,i).(2 + ((x3 + 2x) div 3)),2,x))
A234281: 1 8 73 738
(5 * (x + (4 * (if (~2 + (x div 4)) <= 0 then 0 else 2))))
A061821: 0 5 10 15 20 25 30 35 40 45 50 55 100 105 110 115
(x - (((~x + 1) - (4 * (if (x + ~2) <= 0 then 0 else 2))) div 5))
A167707: 0 1 3 5 7 8 9 10 11 13 14 15 16 17 19 20
((if x <= 0 then 1 else (2 - (((x mod 2) - (x div 2)) div 2))) - (x div 5))
A342866: 1 2 3 2 3 2 3 2 3 3 3 2 3 3 4 2
(2x + ((if (~2 + (x div 4)) <= 0 then 1 else 0) + (x div 5)))
A190328: 1 3 5 7 9 12 14 16 18 20 23 25 26 28 30 33
((if x <= 0 then 1 else (2 div (8 - (x div 2)))) + (x div 5))
A185325: 1 0 0 0 0 1 1 1 1 1 2 2 3 3 4 5
(if ((x div 4) - (x mod 5)) <= 0 then 1 else (x mod 5))
A250205: 1 1 1 1 1 0 1 1 1 1 0 1 2 1 1 0
(x - ((~x - (if (~4 + (x div 2)) <= 0 then 1 else x)) div 5))
A324845: 1 2 3 4 5 7 8 9 10 11 14 16 17 19 20 21
loop(\(x,i).(x + ((6x + 12) div (1 + i))),x,5)
A166810: 5 26 82 208 460 922 1714 3001 5003 8006 12374 18562 27130 38758 54262 74611
(if x <= 0 then 1 else (11 div (1 + (~x mod 4))))
A130165: 1 2 3 5 11 2 3 5 11 2 3 5 11 2 3 5
(2 div (1 + ((x + (if (x2 mod (1 + (x div 2))) <= 0 then 1 else 2)) mod 4)))
A339060: 1 0 0 1 0 0 0 1 0 0 2 1 0 0 2 1
(((2 + loop(\(x,i).2x,x,1)) div 5) div (1 + (x div 4)))
A260666: 0 0 1 2 1 3 6 13
((if ((x + (x div 3)) mod 3) <= 0 then 1 else x) div (1 + (x div 4)))
A332921: 1 1 2 3 2 0 3 0 2 0
(1 + (4 * compr(\x.loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,x),x)))
A022341: 1 5 9 17 21 33 37 41 65 69 73 81 85 129 133 137
(x mod (3 + ((x + (if (x mod 2) <= 0 then (x mod 8) else 1)) div 2)))
A031007: 0 1 2 3 4 5 6 0 1 1 1 2 1 3 1 4
(1 + (((x + (if (x mod 6) <= 0 then (2 + (x div 2)) else 1)) div 2) div 2))
A097561: 1 1 1 2 2 2 3 3 3 3 3 4 6 4 4 5
(x6 mod (1 + loop(\(x,i).(x2 + x),2,2)))
A070666: 0 1 21 41 11 16 1 1 16 4 35 4 21 16 21 11
(1 + (loop(\(x,i).(2 + (3 * (x mod 7))),x,2) div 2))
A182480: 2 5 3 9 6 8 2 5 3 9 6 8 2 5 3 9
((3x + 4) div (~1 + (2 * loop(\(x,i).(2 + (x mod (1 + i))),x,2))))
A187816: 1 2 1 4 2 1 1 8 4 2 2 1 1 1 1 16
(~1 + (4 * (x + (if (~2 + (x div 3)) <= 0 then 1 else (x div 4)))))
A118894: 3 7 11 15 19 23 27 31 35 43 47 51 59 63 67 71
(2 div (1 + (loop(\(x,i).((x * (x mod 2)) + (x div 2)),(x + ~1),(x + 2)) div 2)))
A326915: 1 1 1 0 1 0 2 0 0 2 2 0 0 2 2 0
(1 + ((if ((x + 2) mod 4) <= 0 then (x div 2) else 2x) mod (x + 4)))
A255820: 1 3 2 7 1 2 4 4
(1 + (if x <= 0 then 2 else (x - (2 * (~2x + ((x + (x div 2)) div 4))))))
A047924: 3 6 11 14 19 24 27 32 35 40 45 48 53 58 61 66
((4x + 1) + ((x + (if (x mod 3) <= 0 then 2 else 1)) div 4))
A299405: 1 5 9 14 18 22 27 31 35 39 43 48 52 56 60 65
(1 + loop(\(x,i).(x + ((x div 2) div 7)),2,4x))
A314754: 1 5 9 13 19 23 27 33 37 41 46 51 55 59 65 69
(1 + loop(\(x,i).(x + (x div 15)),2,4x))
A314752: 1 5 9 13 19 23 27 31 37 41 45 50 55 59 63 69
((4x + 1) * loop(\(x,i).x2,1,(x + 7)))
A245033: 49 320 729 1300 2057 3024 4225 5684 7425 9472 11849 14580 17689 21200 25137 29524
loop(\(x,i).x7,1,(4x + 1))
A016819: 1 78125 4782969 62748517 410338673 1801088541 6103515625 17249876309 42618442977 94931877133 194754273881 373669453125 678223072849 1174711139837 1954897493193 3142742836021
loop(\(x,i).(x + (x div 15)),2,(4x + 1))
A314753: 1 5 9 13 19 23 27 32 37 41 45 51 55 59 64 69
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(4x + 1))
A051944: 1 5 18 65 238 882 3300 12441 47190 179894 688636 2645370 10192588 39373700 152443080 591385545
((x + 1) - ((x + 2) mod (2 + (if (x mod 2) <= 0 then (x mod 3) else (x div 2)))))
A318516: 1 1 3 2 5 3 7 4 7 5 11 6 13 7 15 8
(~1 + (if ((x mod 6) mod (1 + (x div 3))) <= 0 then (x mod 2) else 2))
A324113: ~1 0 ~1 1 ~1 1 ~1 1 1 1 ~1 1 ~1 1 1 1
(1 + (2 * (loop(\(x,i).2x,(x div 2),(3 + (x mod 2))) + (x mod 2))))
A245179: 7 11 13 19 25 35 49 67 97 131 193 259 385 515 769 1027
loop(\(x,i).2x,(((3 * (x + (x div 4))) + (x mod 2)) div 2),1)
A327493: 1 4 8 32 128 512 1024 4096 32768 131072 262144 1048576 4194304 16777216 33554432 134217728
loop(\(x,i).2x,(((3 * (x + (x div 4))) - (x mod 2)) div 2),1)
A046161: 1 2 8 16 128 256 1024 2048 32768 65536 262144 524288 4194304 8388608 33554432 67108864
(1 + (2 * loop(\(x,i).(2x2 + 2x + 5),(x div 2),(x mod 2))))
A192591: 1 3 11 19 131
(~1 + (loop(\(x,i).4x,(x div 2),(2 - (x mod 2))) + (2 * (x mod 2))))
A094360: 1 2 7 5 31 17 127 65 511 257 2047 1025 8191 4097 32767 16385
loop(\(x,i).(5x + 3),(x div 2),(1 + (2 * (x mod 2))))
A026384: 1 3 8 18 43 93 218 468 1093 2343 5468 11718 27343 58593 136718 292968
loop(\(x,i).(10x + 4),(x div 2),(1 + (2 * (x mod 2))))
A094627: 1 3 14 34 144 344 1444 3444 14444 34444 144444 344444 1444444 3444444 14444444 34444444
loop(\(x,i).13x,(x div 2),(1 + (2 * (x mod 2))))
A318165: 1 3 13
A018492: 1 3 13 39 169 507
loop(\(x,i).17x,(x div 2),(1 + (2 * (x mod 2))))
A018691: 1 3 17 51 289 867
(1 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + (2 * (x mod 2))))
A172022: 1 4 4 8 10 14 16 20 22 30 30 38 40 44 46 54
(1 + (compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x) + (2 * (x mod 2))))
A176569: 1 6 6 12 12 18 18 24 28 32 36 42 42 48 52 60
((if (~1 + (2x mod (4 + (x div 2)))) <= 0 then (x + 1) else 0) div 3)
A083925: 0 0 0 1 0 0 0 2 3 0 0 0 0 0 0 0
((1 + (if (x mod (2 * (2 - ((x div 4) mod 2)))) <= 0 then x else 0)) div 3)
A114511: 0 0 0 0 1 0 2 0 3 0 0 0 4 0 5 0
((x + ~1) + (loop(\(x,i).i,(x mod (1 + (4 mod (x + 1)))),1) mod 3))
A127388-A127382-A127381-A127380-A127379-A122350-A122349-A122282-A085170-A085169-A073289-A073288: 0 1 2 3 4 5 6 8 7 9 10 11 13 12 14 15
((1 + (x mod (1 + (2 * (if (x mod 2) <= 0 then 1 else (x div 4)))))) div 3)
A284938: 0 0 1 0 0 1 0 0 1 1 0 0 0 2 1 0
(3 * (~1 + (3 * loop(\(x,i).(2x + 4),(x + 1),3))))
A304509: 87 213 465 969 1977 3993 8025 16089 32217 64473 128985 258009 516057 1032153 2064345 4128729
(if x <= 0 then 1 else (3 * (~1 + ((1 + (x div (2 - (x mod 2)))) mod 3))))
A084103: 1 3 3 0 ~3 ~3 0 3 3 0 ~3 ~3 0 3 3 0
((1 + loop(\(x,i).(4x + 4),x,((~x + 2) mod 3))) div 3)
A113841: 1 3 7 71 199 455 4551 12743 29127 291271 815559 1864135 18641351 52195783 119304647 1193046471
((1 + (((if (x mod 2) <= 0 then 2 else 0) + (x div 2)) * (1 + (x div 2)))) div 3)
A008796: 1 0 2 1 4 2 7 4 10 7 14 10 19 14 24 19
((1 + ((x + 1) * (if (x mod 7) <= 0 then 2 else 0))) div 3)
A340978: 1 0 0 0 0 0 0 5 0 0 0 0 0 0 10 0
(3 * (~3 + loop(\(x,i).10x,(x + 1),1)))
A086947: 21 291 2991 29991 299991 2999991 29999991 299999991 2999999991 29999999991 299999999991 2999999999991 29999999999991 299999999999991 2999999999999991 29999999999999991
(((2x + 3) * loop(\(x,i).(x * (i * (2 + i))),x,1)) div 3)
A060080: 1 5 56 1080 31680 1310400 72576000 5181926400 463325184000 50697529344000 6663103856640000 1035678099456000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(3 * (if (x mod (2 + (5 mod (1 + (x div 2))))) <= 0 then 2 else 1))
A023407: 6 3 3 6 6 3 6 3 6 3 3 3 3 3 6 3
((1 + ((loop(\(x,i).(x * i),x,(3x + ~1)) div 2) div 2)) div 3)
A227404: 0 0 1 4 22 140 1020 8400 77280 786240 8769600 106444800 1397088000 19718899200 297859161600 4794806016000
(loop(\(x,i).5x,x,1) mod 27)
A070377: 1 5 25 17 4 20 19 14 16 26 22 2 10 23 7 8
((1 + (4 * ((x + (if (~2 + (x div 2)) <= 0 then 1 else 0)) div 2))) div 3)
A319198: 0 1 1 3 3 4 4 4 5 5 7 7 8 8 9 9
(if x <= 0 then 1 else (3 * ((8x + 2) div 5)))
A316026: 1 6 9 15 18 24 30 33 39 42 48 54 57 63 66 72
(3 + (if ((x + 1) mod 5) <= 0 then 1 else (x div 5)))
A179847: 3 3 3 3 4 4 4 4 4 4 5 5 5 5 4 6
(((x + 5) * loop(\(x,i).(x * (2 + i)),(x + ~1),1)) div 3)
A097900: 1 2 7 32 180 1200 9240 80640 786240 8467200 99792000 1277337600 17643225600 261534873600 4140968832000 69742632960000
(((16x + 8) + (if (x + ~2) <= 0 then 2 else 1)) div 3)
A028252: 3 8 14 19 24 29 35 40 45 51
loop(\(x,i).x5,1,(12x + 3))
A017561: 243 759375 14348907 90224199 345025251 992436543 2373046875 4984209207 9509900499 16850581551 28153056843 44840334375 68641485507 101621504799 146211169851 205236901143
(if x <= 0 then 1 else ((2x + 4) - ((1 + (x div (~2 + (x mod 2)))) mod 3)))
A161186: 1 6 8 9 10 12 15 18
(~3 + loop(\(x,i).(6x2 + 24),2,3))
A011770: 36525 36525 36525 36525 36525 36525 36525 36525 36525 36525 36525 36525 36525 36525 36525 36525
(x - ((x - ((if (x + ~1) <= 0 then 2 else ((x + 1) div 2)) mod 3)) div 3))
A131807: 1 2 2 3 4 4 4 5 6 7 8 8 8 9 10 11
(3 * ((x + 25) - (if x <= 0 then 2 else 0)))
A295806: 69 78 81
((loop(\(x,i).(x + ~2),(x + ~8),x) + (x div 3)) div 3)
A210480: 0 0 0 1 1 2 2 3 3 3 3 2 2 2 2 2
((if x <= 0 then 1 else 2x) - ((x - (x3 div 3)) div 3))
A222011: 1 2 4 8
A053798: 1 2 4 8 14 22 34 50 70 96 128 166 212 266 328 400
((1 + loop(\(x,i).(2 * (x - (2 * (~1 + (x mod 3))))),x,2)) div 3)
A078010: 1 0 1 3 4 9 19 36 73 147 292 585 1171 2340 4681 9363
(if (~1 + (x mod 3)) <= 0 then 1 else (3 * (1 + ((x * (x div 2)) mod 2))))
A230405: 1 1 3 1 1 3 1 1 3 1 1 6 1 1 3 1
(3 * loop(\(x,i).(2 * (6x - (x div 2))),(x + 2),1))
A203927: 396 4356 47916 527076 5797836 63776196 701538156 7716919716 84886116876 933747285636 10271220141996 112983421561956 1242817637181516 13670994008996676 150380934098963436 1654190275088597796
(((x + 3) * loop(\(x,i).((x2 + x) div 2),2,(x + 1))) div 3)
A244882: 1 8 35 110 280 616 1218 2220 3795 6160 9581 14378 20930 29680 41140 55896
(((x + 3) * loop(\(x,i).(x * (1 + (2 * i))),x,(x + 1))) div 3)
A261065: 1 8 75 840 11025 166320 2837835 54054000 1137161025 26189163000 655383804075 17709112020600 513880482740625 15938200818540000 526174085058496875 4611686018427387903
(((2x + 1) * loop(\(x,i).(2 * (x + (x div 2))),x,3)) div 3)
A113071: 1 8 40 168 648 2376 8424 29160 99144 332424 1102248 3621672 11809800 38263752 123294312 395392104
(((2x + 1) * loop(\(x,i).3x,(x + ~1),4)) div 3)
A167682: 1 4 20 84 324 1188 4212 14580 49572 166212 551124 1810836 5904900 19131876 61647156 197696052
loop(\(x,i).x6,1,(6x + 3))
A016950: 729 531441 11390625 85766121 387420489 1291467969 3518743761 8303765625 17596287801 34296447249 62523502209 107918163081 177978515625 282429536481 433626201009 646990183449
(((2x + 1) * loop(\(x,i).(1 + (x2 div 3)),2,x)) mod 3)
A133698: 1 0 1 0 0 2 0 0 0 1 0 0 0 0 2 0
(((if (x + ~2) <= 0 then 1 else (2x * (x div 2))) div (1 + (x div 2))) mod 3)
A339445: 1 1 0 0 2 0 0 1 0 2 1 0 2 1 0 2
(1 - (((if ((x + ~1) mod 3) <= 0 then 1 else x) * (~1 + (x mod 2))) div 3))
A260438: 1 1 2 1 2 1 3 1 4 1 2 1 5 1 6 1
((1 + compr(\x.(if (x mod 2) <= 0 then ((x div 3) mod 3) else 0),x)) mod 3)
A036579: 1 2 0 1 0 2 1 2 0 2 1 0 1 2 0 1
((~1 + compr(\x.(if (x mod 2) <= 0 then ((x div 3) mod 3) else 0),x)) mod 3)
A036586: 2 0 1 2 1 0 2 0 1 0 2 1 2 0 1 2
((6x + 3) - ((1 + (if (x + ~2) <= 0 then 0 else x)) div 3))
A261190: 3 9 15 20 26 31 37 43 48 54 60 65 71 77 82 88
loop(\(x,i).x5,1,(9x + 3))
A017201: 243 248832 4084101 24300000 90224199 254803968 601692057 1252332576 2373046875 4182119424 6956883693 11040808032 16850581551 24883200000 35723051649 50049003168
(3 * ((x + 1) + loop(\(x,i).x3,1,(4x + 4))))
A295130: 195 1542 5193 12300 24015 41490 65877 98328 139995 192030 255585 331812 421863 526890 648045 786480
(((1 - loop(\(x,i).(2x + ~4),(x div 3),0)) mod (x + 1)) mod 3)
A049239: 0 1 1 1 0 2 0 2 1 0 1 2 0 2 1 1
(((1 - (if ((x div 2) mod 3) <= 0 then (x div 2) else 0)) mod (x + 1)) mod 3)
A306440: 0 1 1 1 1 1 2 0 1 1 1 1 2 0 1 1
(1 - (((if (x mod 2) <= 0 then ((~x + 1) div 3) else 1) mod (x + 1)) mod 3))
A185276: 1 0 ~1 0 0 0 ~1 0 1 0 ~1 0 1 0 0 0
(((x + 1) * ((x + 1) - (loop(\(x,i).2x,x,2) mod (x + 1)))) mod 3)
A113448: 1 1 0 1 0 0 2 1 0 0 0 0 2 2 0 1
(((x + 1) * loop(\(x,i).(x3 + 2x2),1,(2x + 1))) div 3)
A100430: 1 30 175 588 1485 3146 5915 10200 16473 25270 37191 52900 73125 98658 130355 169136
(loop(\(x,i).((5x2 + ~x) div 2),2,(x + 1)) div 3)
A238471: 3 66 364 1197 2990 6293 11781 20254 32637 49980 73458 104371 144144 194327 256595 332748
(loop(\(x,i).7x,(x + 1),1) mod (3x + 3))
A191562: 1 1 1 1 7 1 7 1 1 19 7 1 7 7 28 1
loop(\(x,i).((2x * (~1 + (2 * i))) div (2 + i)),x,(3x + 3))
A038629: 3 4 9 24 70 216 693 2288 7722 26520 92378 325584 1158924 4160240 15043725 54747360
(if x <= 0 then 2 else ((10x + ~10) + ((x + 1) div 3)))
A274177: 2 0 11 21 31
(if (x mod 7) <= 0 then 1 else (x mod (x - ((x + 1) mod 3))))
A025847: 1 0 0 1 0 0 1 1 0 1 2 0 1 2 1 1
(3 * compr(\x.loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,x),(x + 1)))
A290258: 3 6 12 15 24 27 30 48 51 54 60 63 96 99 102 108
((x + ~1) + (loop(\(x,i).(2 + ((x2 + x) div 2)),2,(x + ~1)) div 3))
A222010: 0 1 3 7
A055795: 0 1 3 7 15 30 56 98 162 255 385 561 793 1092 1470 1940
(((x2 + ~3x + 2) * loop(\(x,i).3x,(x + ~2),x)) div 3)
A052791: 0 0 0 6 72 540 3240 17010 81648 367416 1574640 6495390 25981560 101328084 386889048 1450833930
(3 * ((x + ~1) + loop(\(x,i).(x - ((~2 + (x div 2)) div 3)),2,x)))
A277569: 3 9 15 18 21 27 33 39 45 51 54 57 63 69 75 81
(2x - ((~2 * (x + (if (x + ~4) <= 0 then 1 else 2))) div 3))
A231407: 1 4 6
A079255: 1 4 6 9 12 15 18 20 23 26 28 31 34 36 39 42
((2 * ((2 * (if x <= 0 then 1 else x)) - (x2 div ~3))) div 3)
A231408: 1 2 4 6 9
A075354: 1 2 4 6 9 12 16 20 25 30 36 42 48 55 62 70
(6 * (3 + loop(\(x,i).(2x + 16),x,1)))
A305159: 24 126 330 738 1554 3186 6450 12978 26034 52146 104370 208818 417714 835506 1671090 3342258
(6 * (~1 + ((2x + 4) * loop(\(x,i).x2,2,(x + 2)))))
A224337: 378 2910 12282 37494 93306 201678 393210 708582 1199994 1932606 2985978 4455510 6453882 9112494 12582906 17038278
(if x <= 0 then 1 else (x div (3 * (2 + ((x + 1) mod (3 + (x mod 2)))))))
A014678: 1 0 0 0 0 0 0 1 1 0 0 1 1 1 2 2
loop(\(x,i).2x,((x div 2) - ((3 * (x div 4)) div 2)),3)
A160745: 3 3 6 6 6 6 12 12 6 6 12 12 12 12 24 24
(loop(\(x,i).(1 - (2 * (2 + (x mod (1 + i))))),x,6) mod 3)
A205593: 0 0 0 1 0 0 2 0 0 1 2 2 1 0 0 2
(loop(\(x,i).2x,x,1) - (3 * ((x mod 2) - ((x div 3) mod 2))))
A274817: 1 ~1 4 8 19 32 64 125 256 512 1027 2048 4096 8189 16384 32768
((2 * ((x * (x + (if (~2 + (x div 2)) <= 0 then 2 else 1))) div 3)) div 3)
A194240: 0 0 1 3 5 7 9 12 16 20 24 29 34 40 46 53
((6x + 18) * loop(\(x,i).2x,(x + 2),(x + 2)))
A137885: 144 576 1920 5760 16128 43008 110592 276480 675840 1622016 3833856 8945664 20643840 47185920 106954752 240648192
loop(\(x,i).x5,1,(12x + 6))
A017597: 7776 1889568 24300000 130691232 459165024 1252332576 2887174368 5904900000 11040808032 19254145824 31757969376 50049003168 75937500000 111577100832 159494694624 222620278176
loop(\(x,i).x3,1,(11x + 7))
A017475: 343 5832 24389 64000 132651 238328 389017 592704 857375 1191016 1601613 2097152 2685619 3375000 4173281 5088448
loop(\(x,i).x3,2,(11x + 7))
A017481: 40353607 198359290368 14507145975869 262144000000000 2334165173090451 13537086546263552 58871586708267913 208215748530929664 630249409724609375 1689478959002692096 4108400332687853397 4611686018427387903 4611686018427387903 4611686018427387903
(6 * loop(\(x,i).(10x + 21),x,1))
A175237: 6 186 1986 19986 199986 1999986 19999986 199999986 1999999986 19999999986 199999999986 1999999999986 19999999999986 199999999999986 1999999999999986 19999999999999986
((loop(\(x,i).(x - (((~x + 1) - i) div 5)),x,1) div 2) div 3)
A241093: 0 0 0 0 1 1 1 2 3 4 5 7 8 11 13 17
((loop(\(x,i).(x3 + ~2x2),1,(x2 + 3x + 2)) div 2) div 3)
A253285: 0 24 240 1200 4200 11760 28224 60480 118800 217800 377520 624624 993720 1528800 2284800 3329280
(3 * (((x + 1) * loop(\(x,i).(x * (~1 + (2 * i))),x,(x + 2))) div 2))
A001194: 3 9 54 450 4725 59535 873180 14594580 273648375 5685805125 129636356850 3217338674550 86331921100425 2490343877896875 76844896803675000 2525635608280785000
loop(\(x,i).(9x2 + 2),(2x + 2),3)
A128879: 62003 4611686018427387903 4611686018427387903 4611686018427387903
((((x + 1) * loop(\(x,i).((x + 1) * (1 + (x * i))),2,x)) div 2) div 3)
A052459: 1 15 95 374 1105 2701 5775 11180 20049 33835 54351 83810 124865 180649 254815 351576
(if x <= 0 then 1 else ((((x + ~1) * ((x2 + ~2x) div 4)) div 2) div 3))
A274523: 1 0 0 0 1 2 5 8 14 20 30 40 55 70 91 112
(loop(\(x,i).(x * i),x,1) - (((x3 + ~3x2 + 2x) div 2) div 3))
A129949: 1 1 2 5 20 110 700 5005 40264 362796 3628680 39916635 479001380 6227020514 87178290836 1307674367545
((loop(\(x,i).(x3 + ~x),1,(x3 + 1)) div 2) div 3)
A282612: 0 1 120 3654 45760 333375 1703016 6784540 22500864 64836045 167167000 393877506 861456960 1769830699 3447273480 6412923000
(6 * (~2 + loop(\(x,i).(2x + 16),(x + 1),1)))
A304830: 96 300 708 1524 3156 6420 12948 26004 52116 104340 208788 417684 835476 1671060 3342228 6684564
(~3 + (4 * (~1 + loop(\(x,i).2x,(~4 + (x div 2)),2))))
A147340: 1 1 1 1 1 1 1 1 1 1 9 9 25 25 57 57
((4 - (x mod (~2 - (if (~2 + (x div 2)) <= 0 then 2 else 1)))) mod 3)
A287364: 1 1 0 2 1 1 1 0 2 1 0 2 1 0 2 1
(if x <= 0 then 1 else (x div (3 * (2 + (x mod (2 + (x mod 5)))))))
A321378: 1 0 0 0 0 0 1 0 0 0 1 0 2 0 1 1
((2 * (loop(\(x,i).(x + (x div 4)),x,5) div 2)) div 3)
A130084: 1 2 2 2 3 4 4 6 7 8 10 13 16 20 26 32
(4x - ((2 * (x - (if (x + ~4) <= 0 then 1 else 2))) div 3))
A284930: 1 4 8 11 14 18 22 25 28 32 35 38 42 45 48 52
((loop(\(x,i).(x div (2 - (x mod 2))),x,(2x + 6)) div 2) div 3)
A029357: 1 0 0 0 1 0 1 0 1 0 2 1 2 0 2 1
((4 * (1 + (if (~2 + (x div 3)) <= 0 then x else (x + 2)))) div 3)
A095775: 1 2 4 5 6 8 9 10 12 16 17 18 20 21 22 24
(loop(\(x,i).x2,1,((2 * (x div 2)) - (((x + 1) div 2) div 2))) div 3)
A272212: 0 0 1 0 3 3 8 5 12 12 21 16 27 27 40 33
((((loop(\(x,i).(x2 + 1),2,(x + 3)) div 2) div 2) div 2) div 3)
A203286: 4 12 28 57 104 176 280 425 620 876 1204 1617 2128 2752 3504 4401
((2 + ((if x <= 0 then 1 else (((x + 1) div 2) div 2)) mod 2) - (x div 2)) mod 3)
A287160: 0 2 1 2 1 1 0 2 1 1 0 1 0 0 2 1
((if x <= 0 then 1 else (x2 mod (4 + (((x + 1) div 2) div 2)))) mod 3)
A338859-A301343-A265892-A153764: 1 1 0 1 1 0 1 1 1 0 1 2 1 1 0 1
(if (x + ~8) <= 0 then x else (x + 21))
A024651: 0 1 2 3 4 5 6 7 8 30 31 32 33 34 35 36
(3 + ((loop(\(x,i).((x + 4) + (x div 3)),x,2) div 2) div 2))
A120150: 3 4 6 8 10 14 18 24 32 43 57 76 102 136 181 241
((4 * (if x <= 0 then 1 else (4x3 + 2x))) div 3)
A035471: 1 8 48 152 352 680 1168 1848 2752 3912 5360 7128 9248 11752 14672 18040
((2 + (loop(\(x,i).((x2 div 2) div 3),2,(x + ~2)) div 2)) div 3)
A308927: 0 0 0 0 0 0 0 1 1 2 3 5 7 11 16 22
((loop(\(x,i).(x2 + x),1,(2 + (x div 2) - (x mod 2))) div 2) div 3)
A008731: 1 0 2 1 3 2 5 3 7 5 9 7 12 9 15 12
((2 + (((x + 4) * (if x <= 0 then 1 else 2)) div (2 + (x mod 2)))) div 3)
A304117: 1 1 2 2 3 2 4 3 4 3 5 4 6 4 6 4
(if x <= 0 then 1 else (12 + (x div ~11)))
A112122: 1 11 11 11 11 11 11 11 11 11 11 11 10 10 10 10
((if (((x div 2) div 3) mod 2) <= 0 then x else ~x) mod 12)
A271832: 0 1 2 3 4 5 6 5 4 3 2 1 0 1 2 3
(((x2 + 2x) * loop(\(x,i).x2,2,(x + 1))) div 12)
A208954: 0 4 54 320 1250 3780 9604 21504 43740 82500 146410 247104 399854 624260 945000 1392640
(12 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A175225: 12 13 15 17 21 23 27 29 33 39 41 47 51 53 57 63
(6 * (2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)))
A091455: 30 42 66 78 102 114 138 174 186 222 246 258 282 318 354 366
(6 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A138636: 12 18 30 42 66 78 102 114 138 174 186 222 246 258 282 318
loop(\(x,i).x6,1,12x)
A017526: 0 2985984 191102976 2176782336 12230590464 46656000000 139314069504 351298031616 782757789696 1586874322944 2985984000000 5289852801024 8916100448256 14412774445056 22483074023424
((if (x mod 3) <= 0 then 1 else (((x mod 4) * (x div 2)) div 2)) mod 3)
A209354: 1 0 1 1 0 1 1 1 0 1 2 1 1 0 1 1
(x - ((1 - (2 * (x + (if (~4 + (x div 2)) <= 0 then 2 else 0)))) div 3))
A188046: 1 3 5 6 8 10 11 13 15 16 17 18 20 22 23 25
((x + 5) + (if (x + ~2) <= 0 then x else (2 - (x div ~3))))
A175382: 5 7 9 11 13 14 15 17 18 19 21 22 23 25 26 27
loop(\(x,i).x5,1,(9x + 6))
A017237: 7776 759375 7962624 39135393 130691232 345025251 777600000 1564031349 2887174368 4984209207 8153726976 12762815625 19254145824 28153056843 40074642432 55730836701
(loop(\(x,i).(2x3 + 4x),1,((x2 + ~x) div 2)) div 3)
A282819: 0 0 2 22 152 680 2270 6202 14672 31152 60810 110990 191752 316472 502502 771890
((2 * (x + (if ((x + ~1) mod 7) <= 0 then 1 else 2))) div 3)
A249569: 1 1 2 3 4 4 5 6 6 7 8 8 9 10 10 10
(if x <= 0 then 1 else (6 * (x + (x3 div 8))))
A225384: 1 6 18 36 72 120
((2 * (x + (loop(\(x,i).(~2x + 2),x,3) mod (x + 2)))) mod 3)
A069848: 2 0 2 1 0 1 0 0 2 1 0 1 2 0 1 1
(3 + ((2x * (x + (if (~2 + (x div 2)) <= 0 then 1 else 2))) div (x + 2)))
A201471: 3 4 6 7 9 11 15 17 19 21 23 25 27 29 31 33
compr(\x.(((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)) div 2),((x + 2) div 3))
A220845: 0 1 1 1 3 3 3 4 4 4 5 5 5 8 8 8
((if (~2 + (x div 5)) <= 0 then x else (x + 2)) + ((x + 2) div 3))
A029597: 0 2 3 4 6 7 8 10 11 12 14 15 16 18 19 22
(((~x + ((x div 4) mod 2)) div 2) + (if x <= 0 then 1 else 6x))
A314161: 1 5 11 16 22 28 33 39 44 49 55 60 66 72 77 83
(7x + loop(\(x,i).7x,x,1))
A221909: 1 14 63 364 2429 16842 117691 823592 5764857 40353670 282475319 1977326820 13841287285 96889010498 678223072947 4747561510048
(~7x + loop(\(x,i).7x,x,1))
A198397: 1 0 35 322 2373 16772 117607 823494 5764745 40353544 282475179 1977326666 13841287117 96889010316 678223072751 4747561509838
(~3 + (2 * (~x2 + loop(\(x,i).(x * (2 + i)),(x + 1),4))))
A143843: 21 91 469
(4x - ((~x2 + 2x + ~1) div loop(\(x,i).x2,2,3)))
A312890: 1 4 9 13 17 21 25 29 33 37 41 46 50 54 59 63
((1 - compr(\x.(if (x mod 2) <= 0 then ((x div 3) mod 3) else 0),x)) mod 3)
A036578: 1 0 2 1 2 0 1 0 2 0 1 2 1 0 2 1
((2 - compr(\x.(if (x mod 2) <= 0 then ((x div 3) mod 3) else 0),x)) mod 3)
A036577: 2 1 0 2 0 1 2 1 0 1 2 0 2 1 0 2
(1 - (compr(\x.(if (x mod 2) <= 0 then ((x div 3) mod 3) else 0),x) mod 3))
A029883: 1 0 ~1 1 ~1 0 1 0 ~1 0 1 ~1 1 0 ~1 1
loop(\(x,i).x5,1,(5x + 3))
A016889: 243 32768 371293 1889568 6436343 17210368 39135393 79235168 147008443 254803968 418195493 656356768 992436543 1453933568 2073071593 2887174368
(if x <= 0 then 1 else (x - (((~x + 1) - (x2 div 5)) div 3)))
A231405: 1 1 3 4 6 8 10 12 15 17 20 23 25 28 32 35
loop(\(x,i).(3 * ((2x div (1 + i)) * (~1 + (2 * i)))),x,3)
A025226: 3 9 54 405 3402 30618 288684 2814669 28146690 287096238 2975361012 31241290626 331638315876 3553267670100 38375290837080 417331287853245
((if x <= 0 then 1 else 4x) - ((~x + ((x div 2) mod 3)) div 3))
A314677: 1 5 9 13 17 21 26 31 35 39 43 47 52 57 61 65
((x * loop(\(x,i).(((x + 1) - (2 * (x mod 2))) * (1 + i)),x,1)) div 3)
A305730: 0 0 2 8 60 440 3710 34608 355992 4004880 48948570 646121080 9163171732 138974771208 2244977073430 38485321258720
(2x - (3 * (((x + (x div 2)) div 4) - (if x <= 0 then 1 else x))))
A285679: 3 5 10 12 17 22 24 29 31 36 41 43 48 53 55 60
((x + (2 * (x div (3 * (if (x mod 3) <= 0 then 2 else 1))))) div 3)
A054860: 0 0 0 1 2 2 2 3 4 3 5 5 5 7 7 6
((x + 3) + (if (x + ~1) <= 0 then x else (2 + ((x - ((x div 2) mod 2)) div 2))))
A340855: 3 5 7 9 11 12 13 15 17 18 19 21 23 24 25 27
(if x <= 0 then 1 else (x - ((~x + (((x + (x div 2)) div 2) mod 4)) div 3)))
A194467: 1 2 3 4 5 6 8 9 10 12 13 15 16 17 18 19
((~x + 3) + (2 * compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A134591: 3 4 7 10 17 20 27 30 37 48 51 62 69 72 79 90
loop(\(x,i).(2x + (10x div (1 + i))),x,3)
A080952: 3 21 112 504 2016 7392 25344 82368 256256 768768 2236416 6336512 17547264 47628288 127008768 333398016
((if (x mod 2) <= 0 then 10 else 1) mod (3 + (x * (x div 2))))
A288697: 1 1 0 1 10 1 10 1 10 1 10 1 10 1 10 1
(1 + ((x div (1 + (if ((x mod 3) mod 2) <= 0 then 2 else 0))) + (x div 3)))
A226122: 1 2 1 3 6 3 5 10 5 7 14 7 9 18 9 11
(if (x mod (1 + (2 * (x div (2 * (2 + (x mod 2))))))) <= 0 then 1 else (x div 3))
A034928: 1 1 1 1 1 1 1 2 2 1 1 3 4 4 1 1
(6 + (loop(\(x,i).2x,x,1) + (x div 3)) - (x div 2))
A076599: 7 8 9 14 21 37
(2 + ((loop(\(x,i).(x2 + ~2x),3,x) div (x + 1)) + (x div 3)))
A087038: 2 3 2 3 444
(x + ((if ((2 - (x div 3)) mod 4) <= 0 then 2 else 1) + (x div 3)))
A119316: 1 2 3 5 6 7 10 11 12 13 14 15 17 18 19 21
(loop(\(x,i).~8x,(x div 3),1) * (x mod 3))
A088138: 0 1 2 0 ~8 ~16 0 64 128 0 ~512 ~1024 0 4096 8192 0
(~2 + (3 * ((2 * (if x <= 0 then 2 else x)) mod 3)) - (x mod 3))
A167373: 1 3 ~1 ~2 3 ~1 ~2 3 ~1 ~2 3 ~1 ~2 3 ~1 ~2
((x + loop(\(x,i).(1 + ((2x + 4) div 3)),3,x)) mod 3)
A129688: 1 0 1 2 0 1 0 2 0 1 2 0 2 0 1 0
(1 + (2 * loop(\(x,i).(x + 5),(~1 + (x div 5)),x)))
A066640-A014261: 1 3 5 7 9 11 13 15 17 19 31 33 35 37 39 51
(1 + ((x * (1 + (if (x mod 6) <= 0 then (~2 + (x div 2)) else 1))) div 2))
A071786: 1 2 3 4 5 6 7 8 9 10 11 12 31 14 15 16
(1 + (2 * compr(\x.(~1 + (loop(\(x,i).x2,2,x2) mod (2x + 1))),x)))
A018358: 1 3 5 15 17 51 85 255
(~1 + loop(\(x,i).(5x - (2x mod 5)),x,2))
A037675: 1 5 27 138 691 3455 17277 86388 431941 2159705 10798527 53992638 269963191 1349815955 6749079777 33745398888
loop(\(x,i).20x,(5x + 2),1)
A013895: 400 1280000000 4096000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).15x,(5x + 2),1)
A013875: 225 170859375 129746337890625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).18x,(5x + 2),1)
A013887: 324 612220032 1156831381426176 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).24x,(5x + 2),1)
A013911: 576 4586471424 36520347436056576 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).14x,(5x + 2),1)
A013871: 196 105413504 56693912375296 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).13x,(5x + 2),1)
A013867: 169 62748517 23298085122481 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).11x,(5x + 2),1)
A013859: 121 19487171 3138428376721 505447028499293771 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).17x,(5x + 2),1)
A013883: 289 410338673 582622237229761 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(9x + 1),10x,1)
A022261: 1 3922632451 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~12x + 1),10x,1)
A015401: 1 57154490053 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~9x + 1),10x,1)
A015397: 1 3138105961 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~10x + 1),10x,1)
A015398: 1 9090909091 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x5,1,(10x + 1))
A017285: 1 161051 4084101 28629151 115856201 345025251 844596301 1804229351 3486784401 6240321451 10510100501 16850581551 25937424601 38579489651 55730836701 78502725751
(1 + (2 * loop(\(x,i).(2 * (2x - (x mod 8))),3,x)))
A145850: 1 17 65 81 257 273 321 337 1025 1041 1089 1105 1281 1297 1345 1361
(1 + (loop(\(x,i).(2 * (2x - (x mod 8))),3,x) div 2))
A145818: 1 5 17 21 65 69 81 85 257 261 273 277 321 325 337 341
loop(\(x,i).21x,(3x + 2),1)
A013769: 441 4084101 37822859361 350277500542221 3243919932521508681 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).22x,(3x + 2),1)
A013771: 484 5153632 54875873536 584318301411328 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).19x,(3x + 2),1)
A013765: 361 2476099 16983563041 116490258898219 799006685782884121 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).23x,(3x + 2),1)
A013773: 529 6436343 78310985281 952809757913927 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (2 * (x + (if (~6 + (x div 2)) <= 0 then 2 else (x div 3)))))
A077797: 3 5 7 9 11 13 15 17 19 21 23 25 27 29 35 39
(1 + (compr(\x.((x + 1) mod (1 + (loop(\(x,i).2x,x,x) mod (x + 2)))),x) div 2))
A241912: 1 2 3 4 5 7 8 11 13 15 16 17 18 19 23 29
(1 + ((x + ((x2 + x + 1) * loop(\(x,i).(1 + (x * i)),x,1))) div 2))
A082030: 1 4 19 106 685 5056 42079 390454 4000441 44881660 547457611 7215589954 102211815589 1548801969976 25000879886935 428332610385166
(1 + ((x + loop(\(x,i).(x + i - (2x div (2 + (x div 2)))),x,1)) div 2))
A302833: 1 2 3 4 6 8 10 12 15 19 23 27 32 38 44 50
(1 + (2 * compr(\x.(loop(\(x,i).4x2,2,3) mod (x + 1)),x)))
A190812: 1 3 5 7 11 15 17 23 31 35 47 53 63 71 95 107
(~1 + (2 * (x + (if (x + ~2) <= 0 then 2 else (8x2 + 8x)))))
A174271: 3 5 7 197
((x + 1) - loop(\(x,i).(~x2 + x),1,(10x + 8)))
A157651: 57 308 759 1410 2261 3312 4563 6014 7665 9516 11567 13818 16269 18920 21771 24822
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),((x2 + x) div 2),1)
A135758: 1 1 5 132 16796 9694845 24466267020 263747951750360 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * (x + ((x + 2) div (2 + (if (~4 + (x div 2)) <= 0 then 2 else 1))))))
A105585: 1 3 7 9 11 13 17 19 21 23 29 31 33 37 39 41
(1 + (2 * compr(\x.((x2 + x) mod loop(\(x,i).(x2 + 2x + 1),2,2)),x)))
A265423: 1 49 151 199 201 249 351 399 401 449 551 599 601 649 751 799
((x + 1) mod (if (x mod 3) <= 0 then (2 - ((~x + ((x div 2) mod 2)) div 2)) else 1))
A035377: 1 0 0 1 0 0 2 0 0 3 0 0 5 0 0 7
(1 + (loop(\(x,i).(10x + 12),(x + ~2),x) div 2))
A307852: 1 1 2 22 267
(1 + compr(\x.(loop(\(x,i).(x * (x + i)),2,5) mod (x + 1)),(x + 2)))
A299114: 3 4 5 6 8 10
A051916: 3 4 5 6 8 10 12 15 16 20 24 30 32 40 48 60
loop(\(x,i).22x,(x2 + 4x + 4),1)
A013905: 234256 1207269217792 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).23x,(x2 + 4x + 4),1)
A013909: 279841 1801152661463 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 3) * loop(\(x,i).((x2 + ~x) div (1 + i)),2,(x + 3)))
A027777: 6 40 150 420 980 2016 3780 6600 10890 17160 26026 38220 54600 76160 104040 139536
loop(\(x,i).(13x2 + 8x),1,(x + 3))
A228598: 141 240 365 516 693 896 1125 1380 1661 1968 2301 2660 3045 3456 3893 4356
loop(\(x,i).(2x4 + 10x3 + 14x2 + 6x),(x + 2),1)
A144588: 2439360 4611686018427387903
loop(\(x,i).(4x5 + 12x4 + 8x3),(x + 2),1)
A064586: 35942400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) - ((~2x + 4) div 9)),(x + ~2),1)
A318155: 1 1 1 2 3 5 7 10 13 17 22 28 35 44 55 68
loop(\(x,i).3x,(2x + (x div 11)),1)
A074118: 1 9 81 729 6561 59049 531441 4782969 43046721 387420489 3486784401 94143178827 847288609443 7625597484987 68630377364883 617673396283947
((2x + 1) + ((x + (if ((2 + (x div 2)) mod 4) <= 0 then 2 else 1)) div 2))
A231407: 1 4 6
A298468: 1 4 6 9 12 14 16 19 21 24 26 29 32 34 36 39
((2x + 1) * (1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A219931: 1 6 5 28 9 22 13 120 17 38 21 92 25 54 29 496
((2x + 1) * (1 + (2 * (3 + (if x <= 0 then 4 else (x + 1))))))
A277385: 15 33 65 105 153 209 273 345 425 513 609 713 825 945 1073 1209
((~1 + loop(\(x,i).3x,x,(2 + (x div 4)))) div (2x + 1))
A296852: 1 1 3 7 26 66
(loop(\(x,i).3x2,3,(2x + 1)) div (2x + 1))
A016951: 2187 4782969 170859375 1801088541 10460353203 42618442977 137231006679 373669453125 897410677851 1954897493193 3938980639167 7446353252589 13348388671875 22876792454961 37725479487783
(loop(\(x,i).4x2,3,(2x + 1)) div (2x + 1))
A017119: 16384 35831808 1280000000 13492928512 78364164096 319277809664 1028071702528 2799360000000 6722988818432 14645194571776 29509034655744 55784660123648 100000000000000 171382426877952 282621973446656 450766669594624
(loop(\(x,i).((x + 2) + ((x - ((x div 2) mod 2)) div 2)),x,1) div (2x + 1))
A206739: 1 1 1 1 1 2 3 4 5 7 10 14 19 26 37 52
(if x <= 0 then 1 else (4x - ((1 - (x2 div 2)) div (2x + 1))))
A312895: 1 4 9 13 17 21 26 30 34 39 43 47 51 56 60 64
((~3x + ~1) + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x))
A168580: 2 1 2 1 2 1 2 5 4 7 8 7 8 11 14 13
(~1 + loop(\(x,i).(2 + (((x2 div 2) + (x div 3)) div 2)),1,(x div 2)))
A226748: 1 1 1 1 2 2 3 3 5 5 7 7 11 11 14 14
(1 + (((3x + 3) * ((if x <= 0 then 1 else x) + (x mod 2))) + (x div 2)))
A228138: 4 13 20 50 63 111 130 196 221 305 336 438 475 595 638 776
loop(\(x,i).4x,(((3 * (x div 4)) div 2) + (x div 2)),1)
A124399: 1 1 4 4 64 64 256 256 16384 16384 65536 65536 1048576 1048576 4194304 4194304
(((if (~2 + (x div 2)) <= 0 then 1 else 2) * (1 + (x mod 3))) div (1 + (x div 2)))
A175832: 1 2 1 0 0 1 0 1 1 0 0 1 0 0 0 0
loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x div 2),(1 + (x div 2)))
A117187: 1 1 4 4 15 15 56 56 210 210 792 792 3003 3003 11440 11440
(if (~x + 2) <= 0 then (1 + (((x mod (1 + (x div 4))) div 2) + (x mod 2))) else 1)
A336737-A327400-A327399-A323303-A320732-A305149-A038548: 1 1 1 2 1 2 1 2 2 2 1 3 1 2 2 3
(if x <= 0 then 1 else (~1 + (3 * (((x + ~2) div 3) mod 2)) - (x mod 2)))
A100051: 1 1 ~1 ~2 ~1 1 2 1 ~1 ~2 ~1 1 2 1 ~1 ~2
(~1 + (loop(\(x,i).(10x + 2),(x div 2),1) + (x mod 2)))
A094624: 0 1 11 12 121 122 1221 1222 12221 12222 122221 122222 1222221 1222222 12222221 12222222
(1 + ((2 mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1)) + (x mod 2)))
A333570: 1 2 1 2 1 4 1 2 1 4 1 4 1 4 3 2
(1 + ((if (x - (x2 mod (x + 5))) <= 0 then 0 else 2) + (x mod 2)))
A105498: 1 2 1 4 1 2 3 4 1 2 1 4 3 4 3 4
((1 + ((x mod (if (x + ~2) <= 0 then 1 else (x div 3))) div 2)) * (1 + (x mod 2)))
A074944: 1 2 1 2 1 2 1 2 1 2 1 4 1 2 2 2
loop(\(x,i).(7x + 2),(1 + (x div 2)),(1 + (x mod 2)))
A198308: 9 16 65 114 457 800 3201 5602 22409 39216 156865 274514 1098057 1921600 7686401 13451202
(loop(\(x,i).(x * (2 + (x mod 2))),(x div 2),(1 + (x mod 2))) div (1 + (x mod 2)))
A258439: 1 1 3 2 9 4 27 8 81 16 243 32 729 64 2187 128
(loop(\(x,i).30x,x,1) div (1 + (x mod 2)))
A157462: 1 15 900 13500 810000 12150000 729000000 10935000000 656100000000 9841500000000 590490000000000 8857350000000000 531441000000000000 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).22x,x,1) div (1 + (x mod 2)))
A156863: 1 11 484 5324 234256 2576816 113379904 1247178944 54875873536 603634608896 26559922791424 292159150705664 12855002631049216 141405028941541376 4611686018427387903 4611686018427387903
(loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,1) div (1 + (x mod 2)))
A234040: 1 1 5 7 42 66 429 715 4862 8398 58786 104006 742900 1337220 9694845 17678835
loop(\(x,i).(4x + ((~x + 1) mod 4)),(x div 2),(1 + (x mod 2)))
A283216: 1 2 4 11 17 46 68 187 273 750 1092 3003 4369 12014 17476 48059
loop(\(x,i).19x,(x div 2),(1 + (x mod 2)))
A018610: 1 2 19 38 361 722
(x * ((1 + (2 * (if (x mod 5) <= 0 then 0 else 2))) * (1 + (x mod 2))))
A109051: 0 10 10 30 20 10 30 70 40 90 10 110 60 130 70 30
(1 + (2 * (x + (if (x + ~1) <= 0 then 2 else (x + ((x + ((x div 2) mod 2)) div 2))))))
A282739: 5 7 11 17 21 25 31 37
(1 + (x * loop(\(x,i).(10x + 10),5,0)))
A135403: 1 111111 222221 333331 444441 555551 666661 777771 888881 999991 1111101 1222211 1333321 1444431 1555541 1666651
(1 + (4x div (x + (if (8 mod (x + 1)) <= 0 then 2 else 0))))
A226123: 1 2 5 3 5 5 5 4 5 5 5 5 5 5 5 5
(1 + compr(\x.(~1 + (x mod (1 + (2 * (if (x mod 2) <= 0 then (x div 4) else 1))))),x))
A190850: 1 2 3 4 5 7 8 10 11 14 15 16 19 20 22 23
loop(\(x,i).((9x + 1) + ((x + 1) mod 3)),x,1)
A037616: 1 12 110 991 8922 80300 722701 6504312 58538810 526849291 4741643622 42674792600 384073133401 3456658200612 31109923805510 279989314249591
loop(\(x,i).((x + ~1) + ((x + 1) div (1 + ((x div 2) div 3)))),x,1)
A222011: 1 2 4 8
A336627: 1 2 4 8 11 16 20 24 28 32 36 40 44 48 52 56
loop(\(x,i).((10x + 1) + ((2 * i) mod 3)),x,1)
A037617: 1 13 132 1321 13213 132132 1321321 13213213 132132132 1321321321 13213213213 132132132132 1321321321321 13213213213213 132132132132132 1321321321321321
((x + 1) + (if (x + ~2) <= 0 then x else (1 + ((x + (x div 4)) div 3))))
A288513: 1 3 5 6 7 9 10 11 13 14 16 17 19 20 21 23
(1 + compr(\x.(loop(\(x,i).(2x + 8),x,0) mod (1 + (x div 3))),x))
A082463: 1 2 3 4 5 6 7 9 10
A121166: 1 2 3 4 5 6 7 9 10 11 12 13 17 19 22 23
(1 + compr(\x.(~1 + (loop(\(x,i).(4x + 2),(x div 2),1) mod (x + 1))),x))
A261271-A257691-A257689-A257688-A186891: 1 2 3 5 7 11 13 17 19 23 25 29 31 37 41 43
(1 + compr(\x.(2 - (x mod ((x + 1) - (loop(\(x,i).2x,x,1) mod (x + 1))))),x))
A327907-A177713: 4 8 9 12 15 16 20 21 24 25 27 28 32 33 35 36
(1 + compr(\x.(~1 + (loop(\(x,i).(x + (i * i * i * i)),x,1) mod (x + 1))),x))
A326715-A201879: 1 2 3 5 7 11 13 17 19 23 29 30 31 37 41 43
(1 + compr(\x.(~1 + ((loop(\(x,i).(3x + 3),x,1) div 2) mod (x + 1))),x))
A166684: 1 2 3 4 5 7 9 11 13 17 19 23 25 29 31 37
(1 + compr(\x.(~1 + (loop(\(x,i).(2x2 + ~1),2,4) mod (x + 1))),x))
A067319: 1 2 3 4 5 6 8 10 12
A281624-A003401: 1 2 3 4 5 6 8 10 12 15 16 17 20 24 30 32
(if (x + ~1) <= 0 then x else (1 + compr(\x.(1 - (x mod (2 - (x mod ~3)))),x)))
A045762: 0 1 4 6 8 9 10 11 12 14 15 16 18 20 21 22
loop(\(x,i).(x - (((4x div (1 + i)) + i) div ~3)),x,1)
A196126: 1 2 4 7 10 14 19 25 32 39 47 56 66 77 89 102
(1 + (x * (1 + (if (x + ~1) <= 0 then x else (2 + ((2 * (x div 2)) div 3))))))
A345888: 1 3 7 10 17 21 31 36 41 46 61 67 85 92 99 106
(2 div (1 + (if ((x + 1) mod (4 - ((x div 2) mod 3))) <= 0 then 1 else x)))
A100204: 2 1 1 0 0 1 0 1 1 0 0 1 0 0 1 0
loop(\(x,i).x5,1,(7x + 1))
A016997: 1 32768 759375 5153632 20511149 60466176 147008443 312500000 601692057 1073741824 1804229351 2887174368 4437053125 6590815232 9509900499 13382255776
loop(\(x,i).((9x + 1) - ((x div 3) mod 2)),x,1)
A033136: 1 10 90 811 7300 65700 591301 5321710 47895390 431058511 3879526600 34915739400 314241654601 2828174891410 25453574022690 229082166204211
loop(\(x,i).((9x + 1) + ((x div ~2) mod 2)),x,1)
A037542: 1 11 100 901 8111 73000 657001 5913011 53217100 478953901 4310585111 38795266000 349157394001 3142416546011 28281748914100 254535740226901
((x + 1) + (9 * loop(\(x,i).i,(x + ~8),1)))
A161561-A070839: 10 11 12 13 14 15 16 17 18 19 29 39 49 59 69 79
((x + 1) + loop(\(x,i).x2,1,(15x + 15)))
A156814-A031708: 226 902 2028 3604 5630 8106 11032 14408 18234 22510 27236 32412 38038 44114 50640 57616
((x + 1) + loop(\(x,i).x2,1,(20x + 20)))
A031718: 401 1602 3603 6404 10005 14406 19607 25608 32409 40010 48411 57612 67613 78414 90015 102416
loop(\(x,i).(5 * ((2x * (~1 + (2 * i))) div (1 + i))),x,1)
A156058: 1 5 50 625 8750 131250 2062500 33515625 558593750 9496093750 164023437500 2870410156250 50784179687500 906860351562500 16323486328125000 295863189697265625
((x + 1) + loop(\(x,i).x2,1,(x + ~40)))
A060566: 1601 1523 1447 1373 1301 1231 1163 1097 1033 971 911 853 797 743 691 641
((x + 1) + (if (x + ~1) <= 0 then 1 else (2 - (((~x + 2) div 2) div 5))))
A337139: 2 3 5 7 8 9 10 11 12 13 14 15 16 18 19 20
loop(\(x,i).(x3 + 6x2 + 8x),1,(5x + 1))
A079610: 15 480 2145 5760 12075 21840 35805 54720 79335 110400 148665 194880 249795 314160 388725 474240
loop(\(x,i).x6,1,(5x + 1))
A016866: 1 46656 1771561 16777216 85766121 308915776 887503681 2176782336 4750104241 9474296896 17596287801 30840979456 51520374361 82653950016 128100283921 192699928576
loop(\(x,i).(5 * (x + ((4x * i) div (1 + i)))),x,1)
A034687: 1 15 275 5500 115500 2502500 55412500 1246781250 28398906250 653174843750 15141780468750 353308210937500 8289154179687500 195387205664062500 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(x + ((~x2 + 2x + 1) div (x + 5))),1)
A207872: 1 2 4 4 8 8 8 16 16 16 16 16 32 32 32 32
((x + 1) + (18 * (if (x + ~4) <= 0 then 0 else 2)))
A028427: 1 2 3 4 5 42 43 44 45 46 47 48 49 50 51 52
loop(\(x,i).(3 * (9x - (x div 3))),x,1)
A170746-A170708-A170660-A170612-A170564-A170516-A170468-A170420-A170372-A170324-A170276-A170228-A170180-A170132-A170084-A170036-A169568-A169520-A169472-A169424-A169376-A169328-A169280-A169232-A169184-A169136-A169088-A169040-A168992-A168944-A168896-A168848-A168800-A168752-A168704-A167942-A167698-A167226: 1 27 702 18252 474552 12338352 320797152 8340725952 216858874752 5638330743552 146596599332352 3811511582641152 99099301148669952 2576581829865418752 4611686018427387903 4611686018427387903
loop(\(x,i).(3 * ((4x div (1 + i)) * (~1 + (2 * i)))),x,1)
A156128: 1 6 72 1080 18144 326592 6158592 120092544 2401850880 48997757952 1015589892096 21327387734016 452796847276032 9702789584486400 209580255024906240 4558370546791710720
((x + 1) + (((x + 1) * (if (x + ~2) <= 0 then 1 else 2x2)) div 3))
A110881: 1 2 4 28 58
((x + 1) + (loop(\(x,i).((4x div (1 + i)) + i),x,1) div 3))
A299495: 1 3 5 7 8 10 11 12 13 14 16 17 18 19 21 22
loop(\(x,i).((7x + 3) - ((~1 + i) mod 3)),x,1)
A037614: 1 10 72 505 3538 24768 173377 1213642 8495496 59468473 416279314 2913955200 20397686401 142783804810 999486633672 6996406435705
((x + 1) - loop(\(x,i).(~x2 + x),1,(7x + 6)))
A157373: 31 158 383 706 1127 1646 2263 2978 3791 4702 5711 6818 8023 9326 10727 12226
((x + 1) + ((2 * (if (x + ~2) <= 0 then x else (2 - (x div ~2)))) div 3))
A064427: 1 2 4 6 7 9 10 12 13 14 15 17 18 20 21 22
((x + 1) + ((4 * ((x + 2) div (1 + (if x <= 0 then 1 else 2)))) div 3))
A288927: 2 3 4 5 7 8 9 12 13 14 16 17 18 20 21 22
loop(\(x,i).3x,(x + ((4 * (x div 3)) div 3)),1)
A067623: 1 3 9 81 243 729 6561 19683 59049 1594323 4782969 14348907 129140163 387420489 1162261467 10460353203
((x + 1) + (3 * (4 + (if (~2 + (x div 4)) <= 0 then 1 else 2))))
A297284-A296754: 16 17 18 19 20 21 22 23 24 25 26 27 31 32 33 34
(if x <= 0 then 1 else ((x + ~1) + ((x - (x mod ~7)) div 3)))
A032880-A032847: 1 2 3 4 5 6 7 8 11 12 13 14 15 16 17 21
(if x <= 0 then 0 else (1 + ((x2 + ~x) div (~x + 24))))
A061287: 0 1 1 1 1 2 2 3 4 5 7 9 12 15 19 24
((x + 1) + ((2 * ((if (~2 + (x div 3)) <= 0 then 0 else x) div 2)) div 3))
A226900: 1 2 3 4 5 6 7 8 9 12 14 15 17 18 19 20
(x6 + loop(\(x,i).6x,x,1))
A001594: 1 7 100 945 5392 23401 93312 397585 1941760 10609137 61466176 364568617 2179768320 13065520825 78371693632 470196375201
loop(\(x,i).((7x + 1) + ((i mod 3) div 2)),x,1)
A037532: 1 8 58 407 2850 19952 139665 977656 6843594 47905159 335336114 2347352800 16431469601 115020287208 805142010458 5635994073207
loop(\(x,i).x7,1,(3x + 1))
A016783: 1 16384 823543 10000000 62748517 268435456 893871739 2494357888 6103515625 13492928512 27512614111 52523350144 94931877133 163840000000 271818611107 435817657216
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(3x + 1))
A051924: 1 4 14 50 182 672 2508 9438 35750 136136 520676 1998724 7696444 29716000 115000920 445962870
loop(\(x,i).((2x * (~1 + (2 * i))) div (2 + i)),x,(3x + 1))
A181490: 1 2 6 18
A071721: 1 2 6 18 56 180 594 2002 6864 23868 83980 298452 1069776 3863080 14040810 51325650
(2x div loop(\(x,i).~x,x,(~1 + (x div ((~x + 1) - (x mod 3))))))
A255368: 0 1 ~2 2 ~4 5 ~4 7 ~8 6 ~10 11 ~8 13 ~14 10
loop(\(x,i).(4x * ((~1 + (2 * i)) * i * (1 + (2 * i)))),x,1)
A161149: 1 12 1440 604800 609638400 1207084032000 4142712397824000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(((2x * (~1 + (2 * i))) div (1 + i)) * (1 + (i mod 2))),x,1)
A137697: 1 2 4 20 56 336 1056 6864 22880 155584 537472 3762304 13312768 95091200 342328320 2481880320
loop(\(x,i).((x + 1) + (x div (3 * (2 + (x mod 5))))),x,1)
A180042: 1 2 3 4 5 6 7 8 9 10 12 14 15 18 20 24
loop(\(x,i).((x + 1) + ((1 + (2 * (x + (x div 2)))) div (1 + (2 * i)))),x,1)
A097911: 1 3 5 8
A001463: 1 3 5 8 11 15 19 23 28 33 38 44 50 56 62 69
loop(\(x,i).((x + 1) + ((x div (3 + ((x div 2) div 3))) mod 2)),x,1)
A080587: 1 2 3 5 7 9 10 11 12 13 14 15 17 19 21 23
loop(\(x,i).((x + 1) + (x div (2 + (5 mod (1 + (x div 2)))))),x,1)
A193622: 1 2 3 5 7 10
A119565: 1 2 3 5 7 10 12 14 17 20 23 27 31 36 42 49
loop(\(x,i).((x + 1) + (((((x + 1) * (2 - (x div 2))) div 2) div 2) mod 2)),x,1)
A076054: 1 3 5 6 7 8 10 12 14 16 17 19 21 22 23 24
loop(\(x,i).((x + 1) + ((((x2 + ~2x) div 8) div 2) mod 2)),x,1)
A092253: 1 3 4 5 6 8 10 12
A284746: 1 3 4 5 6 8 10 12 14 15 16 17 19 20 21 22
loop(\(x,i).((x + 1) + (((2x + ~4) div (2 + (x div 4))) mod 2)),x,1)
A079905: 1 3 5 6 7 9 11 12 13 14 15 17 19 21 23 24
((~x + ~1) + loop(\(x,i).((x + 2) + ((x + (x div 3)) div (1 + i))),x,1))
A109512: 0 1 3 6 9 13 17 22 27 32 38 44 50 57 64 71
(1 + compr(\x.(loop(\(x,i).(~x2 + x + 6),3,0) mod (x + 1)),x))
A018537: 1 2 3 6 9 11 18 22 27 33 54 66 99 198 297 594
(1 + compr(\x.(loop(\(x,i).(3x2 + 12x + 12),2,0) mod (x + 1)),x))
A018534: 1 2 3 4 6 7 12 14 21 28 42 49 84 98 147 196
(1 + compr(\x.(loop(\(x,i).(~4x2 + 16),2,0) mod (x + 1)),x))
A018772: 1 2 3 4 6 7 8 9 12 14 16 18 21 24 28 36
(1 + compr(\x.((x div 4) - (loop(\(x,i).(2x + 2),x,0) mod (x + 1))),x))
A196149: 1 2 3 4 6 8 9 10 12 15 16 18 20 21 24 27
(1 + compr(\x.(loop(\(x,i).(2x2 + 4x),5,1) mod (x + 1)),x))
A054784: 1 2 3 4 6 7 8 12 14 16 21 24 28 31 32 42
((x + 1) + loop(\(x,i).x2,1,(13x + 13)))
A173275-A031704: 170 678 1524 2708 4230 6090 8288 10824 13698 16910 20460 24348 28574 33138 38040 43280
(1 + compr(\x.((~1 + loop(\(x,i).2x3,3,2)) mod (x + 1)),x))
A003546: 1 3 5 11 15 17 25 31 33 41 51 55 75 85 93 123
(1 + compr(\x.(loop(\(x,i).(3x2 + 9x),2,1) mod (x + 1)),x))
A134950-A018509: 1 2 3 4 5 6 9 10 12 15 18 20 27 30 36 45
(1 + compr(\x.(loop(\(x,i).(x3 + 4x2 + 3x),2,1) mod (x + 1)),x))
A018649: 1 2 3 4 6 8 9 11 12 18 22 24 33 36 44 66
(1 + compr(\x.(loop(\(x,i).(2x3 + 3x2 + x),2,1) mod (x + 1)),x))
A018511: 1 2 3 6 7 13 14 21 26 39 42 78 91 182 273 546
(1 + compr(\x.(loop(\(x,i).((x2 + 2x + 1) * (x + i)),2,1) mod (x + 1)),x))
A018659: 1 2 3 5 6 9 10 15 18 27 30 45 54 81 90 135
(1 + compr(\x.(loop(\(x,i).(3x2 + 7x + 4),2,1) mod (x + 1)),x))
A018594: 1 2 3 5 6 10 15 23 30 46 69 115 138 230 345 690
(1 + compr(\x.((1 + loop(\(x,i).(4x2 + ~1),2,2)) mod (x + 1)),x))
A018710: 1 2 3 4 5 6 9 10 12 15 18 20 25 30 36 45
(1 + compr(\x.((~1 + loop(\(x,i).x2,3,8)) mod (x + 1)),x))
A003553-A003532: 1 3 5 7 9 13 15 17 21 35 39 45 51 63 65 85
(1 + compr(\x.(1 - (loop(\(x,i).(x * (2 + i)),8,1) mod (x + 1))),x))
A191599-A068191: 11 13 17 19 22 23 26 29 31 33 34 37 38 39 41 43
loop(\(x,i).(i - ((1 + (x div (2 + (x mod (2 + (x mod 2)))))) mod (x + 1))),x,1)
A151662: 1 0 2 1 3 3 4 4 5 7 7 8 7 10 8 10
(1 + compr(\x.((1 + loop(\(x,i).(x3 + ~1),2,4)) mod (x + 1)),x))
A003594: 1 3 7 9 21 27 49 63 81 147 189 243 343 441 567 729
(1 + compr(\x.((1 + loop(\(x,i).(~1 + (x2 * i)),2,4)) mod (x + 1)),x))
A018462: 1 2 3 5 6 9 10 15 18 25 30 45 50 75 90 150
(1 + compr(\x.(loop(\(x,i).4x2,2,5) mod (x + 1)),x))
A191535-A100598: 1 2 4 5 8 10
A192716-A159765-A003592: 1 2 4 5 8 10 16 20 25 32 40 50 64 80 100 125
(1 + compr(\x.(loop(\(x,i).((x + 2) * (x - i)),2,5) mod (x + 1)),x))
A018642: 1 2 3 4 5 6 10 12 13 15 20 26 30 39 52 60
(1 + compr(\x.(loop(\(x,i).(x2 * (x - i)),2,5) mod (x + 1)),x))
A108513: 1 2 4 5 7 8 10 14 16 20 25 28 32 35 40 49
(1 + compr(\x.(loop(\(x,i).(2x2 + 10x),2,1) mod (x + 1)),x))
A323383: 1 2 3 4 6 8 12
A018438: 1 2 3 4 6 8 12 17 24 34 51 68 102 136 204 408
(1 + compr(\x.(loop(\(x,i).x3,2,(3 + (x mod 2))) mod (x + 1)),x))
A006899: 1 2 3 4 8 9 16 27 32 64 81 128 243 256 512 729
(1 + compr(\x.(loop(\(x,i).(3x2 + ~3x),2,3) mod (x + 1)),x))
A018721: 1 2 3 6 9 17 18 27 34 51 54 102 153 306 459 918
(1 + compr(\x.(loop(\(x,i).((x + 1) * ((x + 2) + i)),2,3) mod (x + 1)),x))
A018598: 1 2 4 5 7 10 14 20 25 28 35 50 70 100 140 175
(1 + compr(\x.(loop(\(x,i).((x2 + x) * (1 + i)),2,3) mod (x + 1)),x))
A329469: 1 2 3 4 5 6 8 9 10 12 15 18 20 24 25 30
(1 + compr(\x.(loop(\(x,i).((x + 1) * ((x + i) * i)),2,3) mod (x + 1)),x))
A018550: 1 2 3 4 6 9 12 17 18 34 36 51 68 102 153 204
(1 + compr(\x.(loop(\(x,i).(2x3 + 4),2,3) mod (x + 1)),x))
A185092: 1 2 3 4 6 12
A018419: 1 2 3 4 6 12 31 62 93 124 186 372
(1 + compr(\x.(loop(\(x,i).(2x * ((x + ~1) + i)),2,3) mod (x + 1)),x))
A018591: 1 2 3 4 6 9 12 18 19 36 38 57 76 114 171 228
(1 + compr(\x.(loop(\(x,i).((x + 2) * (x + (x div 2))),2,3) mod (x + 1)),x))
A018578: 1 2 3 4 5 6 10 11 12 15 20 22 30 33 44 55
(1 + compr(\x.(loop(\(x,i).(2x2 - (x div 2)),2,3) mod (x + 1)),x))
A018524: 1 2 3 5 6 10 15 19 30 38 57 95 114 190 285 570
(1 + compr(\x.(loop(\(x,i).((~x3 + x) div 2),2,3) mod (x + 1)),x))
A018687: 1 2 3 6 11 13 22 26 33 39 66 78 143 286 429 858
(1 + compr(\x.(loop(\(x,i).(x2 + 5x),2,3) mod (x + 1)),x))
A323383: 1 2 3 4 6 8 12
A018253: 1 2 3 4 6 8 12 24
A018597: 1 2 3 4 6 8 12 24 29 58 87 116 174 232 348 696
(1 + compr(\x.(loop(\(x,i).(x * (2x + (i mod 2))),2,3) mod (x + 1)),x))
A018700: 1 2 3 6 7 9 14 18 21 42 49 63 98 126 147 294
(1 + compr(\x.(loop(\(x,i).(x2 + 2x),2,(~3x + 6)) mod (x + 1)),x))
A057245-A018282: 1 3 9 11 33 99
A027894: 1 3 9 11 33 99 101 303 909 1111 3333 9999
(1 + compr(\x.(loop(\(x,i).((x3 + ~x2) div 2),2,(x + ~1)) mod (x + 1)),x))
A018295: 1 2 3 6 7 9 14 18 21 42 63 126
(1 + compr(\x.(loop(\(x,i).((x3 + x) div 2),2,(x + ~1)) mod (x + 1)),x))
A172411: 1 2 5 10
A018296: 1 2 5 10 13 26 65 130
(1 + compr(\x.(loop(\(x,i).(x3 + x2 + ~2x),3,2) mod (x + 1)),x))
A027902: 1 2 4 5 7 8 10 13 14 16 20 26 28 32 35 40
(1 + compr(\x.(loop(\(x,i).(2x2 + 3x + ~2),3,2) mod (x + 1)),x))
A018393: 1 2 3 4 6 9 12 18 27 36 54 81 108 162 324
(1 + compr(\x.(loop(\(x,i).(x * ((x + 1) + (2 * i))),3,2) mod (x + 1)),x))
A018305: 1 2 3 5 6 10 15 25 30 50 75 150
(1 + compr(\x.(loop(\(x,i).((3x + 6) * (x + i)),2,2) mod (x + 1)),x))
A185092: 1 2 3 4 6 12
A018343: 1 2 3 4 6 12 19 38 57 76 114 228
(1 + compr(\x.(loop(\(x,i).(2x3 + ~3x2 + x),2,2) mod (x + 1)),x))
A018396: 1 2 3 5 6 10 11 15 22 30 33 55 66 110 165 330
(1 + compr(\x.(loop(\(x,i).(2x2 + 5x + 3),2,2) mod (x + 1)),x))
A018762: 1 2 3 5 6 9 10 11 15 18 22 30 33 45 55 66
(1 + compr(\x.(loop(\(x,i).((x + 1) * (1 + (x * (x + i)))),2,2) mod (x + 1)),x))
A222011: 1 2 4 8
A018277: 1 2 4 8 11 22 44 88
A018749: 1 2 4 8 11 22 44 88 121 242 484 968
(1 + compr(\x.(loop(\(x,i).(x2 + 7x + 6),2,2) mod (x + 1)),x))
A018626: 1 2 3 5 6 10 15 25 30 50 75 125 150 250 375 750
(1 + compr(\x.(loop(\(x,i).((x2 + 4x + 4) * (1 + i)),2,2) mod (x + 1)),x))
A185092: 1 2 3 4 6 12
A018333: 1 2 3 4 6 12 17 34 51 68 102 204
(1 + compr(\x.(loop(\(x,i).(~4x2 + ~4x + 8),2,2) mod (x + 1)),x))
A018740: 1 2 4 7 8 14 17 28 34 56 68 119 136 238 476 952
(1 + compr(\x.(loop(\(x,i).x2,2,(4 * (2 + (x mod 2)))) mod (x + 1)),x))
A333978-A064527-A007694: 1 2 4 6 8 12 16 18 24 32 36 48 54 64 72 96
(1 + compr(\x.(loop(\(x,i).(x * (x - i)),3,8) mod (x + 1)),x))
A318400: 1 2 3 4 6 7 8 9 12 14 16 18 19 21 24 27
(1 + compr(\x.(loop(\(x,i).(2x2 + 5x),4,2) mod (x + 1)),x))
A018251: 1 2 3 6 9 18
A018619: 1 2 3 6 9 18 41 82 123 246 369 738
(1 + compr(\x.(loop(\(x,i).(3x2 + 4x + ~4),2,2) mod (x + 1)),x))
A018669: 1 2 3 4 6 9 12 18 23 36 46 69 92 138 207 276
(1 + compr(\x.(loop(\(x,i).(2x + 2),x,(4 * (x mod 2))) mod (x + 1)),x))
A193622: 1 2 3 5 7 10
A194948: 1 2 3 5 7 10 11 13 17 19 23 29 31 37 41 43
(1 + compr(\x.(2 - (loop(\(x,i).(2x2 + ~1),2,4) mod (x + 1))),x))
A004169: 7 9 11 13 14 18 19 21 22 23 25 26 27 28 29 31
(1 + compr(\x.(loop(\(x,i).(~x3 + ~1),2,4) mod (x + 1)),x))
A018461: 1 2 4 7 8 14 16 28 32 56 64 112 224 448
loop(\(x,i).20x,(5x + 4),1)
A013897: 160000 512000000000 1638400000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).15x,(5x + 4),1)
A013877: 50625 38443359375 29192926025390625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).18x,(5x + 4),1)
A013889: 104976 198359290368 374813367582081024 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).14x,(5x + 4),1)
A013873: 38416 20661046784 11112006825558016 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).13x,(5x + 4),1)
A013869: 28561 10604499373 3937376385699289 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).11x,(5x + 4),1)
A013861: 14641 2357947691 379749833583241 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).17x,(5x + 4),1)
A013885: 83521 118587876497 168377826559400929 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.(loop(\(x,i).(x * (2 + ((x2 + x) * i))),2,2) mod (x + 1)),x))
A191282: 1 2 3 4 6 7 8 12 13 14 16 21 24 26 28 32
(1 + compr(\x.(loop(\(x,i).(x2 + 10x),2,2) mod (x + 1)),x))
A323383: 1 2 3 4 6 8 12
A018662: 1 2 3 4 6 8 12 16 17 24 34 48 51 68 102 136
(1 + compr(\x.(loop(\(x,i).(x2 + ~3x + 2),2,4x) mod (x + 1)),x))
A018254: 1 2 4 7 14 28
A018660: 1 2 4 7 14 28 29 58 116 203 406 812
(1 + compr(\x.(loop(\(x,i).(~x2 + 3x + ~2),2,4x) mod (x + 1)),x))
A222011: 1 2 4 8
A018763: 1 2 4 8 16 31 32 62 124 248 496 992
(1 + compr(\x.(loop(\(x,i).(x2 + ~2x + ~2),2,4x) mod (x + 1)),x))
A018456: 1 2 3 6 73 146 219 438
(1 + compr(\x.(loop(\(x,i).(x2 - (x div 2)),2,4x) mod (x + 1)),x))
A018388: 1 3 5 7 9 15 21 35 45 63 105 315
(1 + compr(\x.(loop(\(x,i).(x4 + 3x2),2,2) mod (x + 1)),x))
A018645: 1 2 4 7 8 14 16 28 49 56 98 112 196 392 784
(1 + compr(\x.(loop(\(x,i).(~x4 + x3 + ~x2),2,2) mod (x + 1)),x))
A018302: 1 2 3 4 6 8 9 12 16 18 24 36 48 72 144
loop(\(x,i).(30x + (2 div (x + 1))),x,1)
A170750-A170712-A170664-A170616-A170568-A170520-A170472-A170424-A170376-A170328-A170280-A170232-A170184-A170136-A170088-A170040-A169572-A169524-A169476-A169428-A169380-A169332-A169284-A169236-A169188-A169140-A169092-A169044-A168996-A168948-A168900-A168852-A168804-A168756-A168708-A167946-A167756-A167378-A167084: 1 31 930 27900 837000 25110000 753300000 22599000000 677970000000 20339100000000 610173000000000 18305190000000000 549155700000000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(40x + (2 div (x + 1))),x,1)
A170722-A170674-A170626-A170578-A170530-A170482-A170434-A170386-A170338-A170290-A170242-A170194-A170146-A170098-A170050-A170002-A169534-A169486-A169438-A169390-A169342-A169294-A169246-A169198-A169150-A169102-A169054-A169006-A168958-A168910-A168862-A168814-A168766-A168718-A167957-A167830-A167598-A167094-A166714: 1 41 1640 65600 2624000 104960000 4198400000 167936000000 6717440000000 268697600000000 10747904000000000 429916160000000000 4611686018427387903 4611686018427387903 4611686018427387903
A170760: 1 41 1640 65600 2624000 104960000 4198400000 167936000000 6717440000000 268697600000000 10747904000000000 429916160000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(36x + (2 div (x + 1))),x,1)
A170718-A170670-A170622-A170574-A170526-A170478-A170430-A170382-A170334-A170286-A170238-A170190-A170142-A170094-A170046-A169578-A169530-A169482-A169434-A169386-A169338-A169290-A169242-A169194-A169146-A169098-A169050-A169002-A168954-A168906-A168858-A168810-A168762-A168714-A167953-A167818-A167468-A167090-A166689: 1 37 1332 47952 1726272 62145792 2237248512 80540946432 2899474071552 104381066575872 3757718396731392 135277862282330112 4611686018427387903 4611686018427387903 4611686018427387903
A170756: 1 37 1332 47952 1726272 62145792 2237248512 80540946432 2899474071552 104381066575872 3757718396731392 135277862282330112 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(48x + (2 div (x + 1))),x,1)
A170730-A170682-A170634-A170586-A170538-A170490-A170442-A170394-A170346-A170298-A170250-A170202-A170154-A170106-A170058-A170010-A169542-A169494-A169446-A169398-A169350-A169302-A169254-A169206-A169158-A169110-A169062-A169014-A168966-A168918-A168870-A168822-A168774-A168726-A167988-A167879-A167646-A167102-A166855: 1 49 2352 112896 5419008 260112384 12485394432 599298932736 28766348771328 1380784741023744 66277667569139712 3181328043318706176 4611686018427387903 4611686018427387903 4611686018427387903
A170768: 1 49 2352 112896 5419008 260112384 12485394432 599298932736 28766348771328 1380784741023744 66277667569139712 3181328043318706176 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(34x + (2 div (x + 1))),x,1)
A170754-A170716-A170668-A170620-A170572-A170524-A170476-A170428-A170380-A170332-A170284-A170236-A170188-A170140-A170092-A170044-A169576-A169528-A169480-A169432-A169384-A169336-A169288-A169240-A169192-A169144-A169096-A169048-A169000-A168952-A168904-A168856-A168808-A168760-A168712-A167951-A167789-A167405-A167088: 1 35 1190 40460 1375640 46771760 1590239840 54068154560 1838317255040 62502786671360 2125094746826240 72253221392092160 2456609527331133440 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.((2 + loop(\(x,i).x2,2,5x)) mod (x + 1)),x))
A018557: 1 3 11 19 33 57 209 627
(1 + compr(\x.((2 + (x * loop(\(x,i).2x2,2,(x + ~2)))) mod (x + 1)),x))
A018569: 1 2 17 19 34 38 323 646
(1 + compr(\x.(loop(\(x,i).(x3 + 3x),2,(x + ~2)) mod (x + 1)),x))
A018287: 1 2 3 4 6 9 12 18 27 36 54 108
(1 + compr(\x.(loop(\(x,i).(2x2 + ~x),2,(~2x + 1)) mod (x + 1)),x))
A018454: 1 3 5 15 29 87 145 435
(1 + compr(\x.(loop(\(x,i).(3x2 + 1),2,2x) mod (x + 1)),x))
A018493: 1 2 4 127 254 508
(1 + compr(\x.(loop(\(x,i).(3x2 + 3),2,2x) mod (x + 1)),x))
A018588: 1 2 3 6 113 226 339 678
(1 + compr(\x.(loop(\(x,i).(3x2 + 6),2,2x) mod (x + 1)),x))
A018755: 1 2 3 6 163 326 489 978
(1 + compr(\x.(loop(\(x,i).(~3x2 + x),2,2x) mod (x + 1)),x))
A018542: 1 2 7 14 43 86 301 602
(1 + compr(\x.(loop(\(x,i).(2x2 + ~6x + 4),2,2x) mod (x + 1)),x))
A018774: 1 2 4 11 22 23 44 46 92 253 506 1012
(1 + compr(\x.(loop(\(x,i).((2x + ~2) * (x - i)),2,2x) mod (x + 1)),x))
A222011: 1 2 4 8
A018510: 1 2 4 8 16 17 32 34 68 136 272 544
(1 + compr(\x.(loop(\(x,i).(3x2 + 2),2,2x) mod (x + 1)),x))
A172411: 1 2 5 10
A018535: 1 2 5 10 59 118 295 590
(1 + compr(\x.(loop(\(x,i).(4x2 + ~2),2,2x) mod (x + 1)),x))
A018643: 1 2 17 23 34 46 391 782
(1 + compr(\x.(loop(\(x,i).(4x2 + ~4),2,2x) mod (x + 1)),x))
A018525: 1 2 4 11 13 22 26 44 52 143 286 572
(1 + compr(\x.(loop(\(x,i).(2 * (2 + (x2 * i))),2,2x) mod (x + 1)),x))
A005018: 1 2 4 5 10 20
A018530: 1 2 4 5 10 20 29 58 116 145 290 580
(1 + compr(\x.(loop(\(x,i).(2x3 + 2x),2,2x) mod (x + 1)),x))
A191535-A100598: 1 2 4 5 8 10
A018257: 1 2 4 5 8 10 20 40
(1 + compr(\x.(loop(\(x,i).(2x2 + ~3x),2,2x) mod (x + 1)),x))
A018406: 1 2 5 7 10 14 25 35 50 70 175 350
(1 + compr(\x.(loop(\(x,i).(3x2 + x),2,2x) mod (x + 1)),x))
A172411: 1 2 5 10
A018386: 1 2 5 10 31 62 155 310
(1 + compr(\x.(loop(\(x,i).(x * (1 + (x * (2 + i)))),2,2x) mod (x + 1)),x))
A172411: 1 2 5 10
A018439: 1 2 5 10 41 82 205 410
(1 + compr(\x.(loop(\(x,i).(~2x2 + 3x + 2),2,2x) mod (x + 1)),x))
A018392: 1 2 7 14 23 46 161 322
(1 + compr(\x.(loop(\(x,i).(~2x2 + 5x + ~2),2,2x) mod (x + 1)),x))
A018711: 1 2 11 22 41 82 451 902
(1 + compr(\x.(loop(\(x,i).(3x2 + ~2x),2,2x) mod (x + 1)),x))
A222011: 1 2 4 8
A018618: 1 2 4 8 16 23 32 46 92 184 368 736
(1 + loop(\(x,i).(3x3 + 6x2 + 3x),1,(x2 + x)))
A008402: 1 55 883 6085 26461 86491 232975 545833 1151065 2235871 4065931 7004845 11535733 18284995 28048231 41818321
((1 + (loop(\(x,i).(4x + 2),x,1) div 2)) div (x2 + x + 1))
A135445: 1 1 2 4 10
A245900: 1 1 2 4 10 27 79 239
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(x2 + x + 1))
A034275: 1 3 14 65 294 1302 5676 24453 104390 442442 1864356 7818538 32657884 135950700 564306840 2336457645
(1 + compr(\x.(loop(\(x,i).(2x2 + ~4),2,3x) mod (x + 1)),x))
A018428: 1 2 4 97 194 388
(1 + compr(\x.(loop(\(x,i).(~2x2 + x),2,3x) mod (x + 1)),x))
A018712: 1 3 7 21 43 129 301 903
(1 + compr(\x.(loop(\(x,i).(2x2 + x),2,3x) mod (x + 1)),x))
A018470: 1 3 5 15 31 93 155 465
(1 + compr(\x.(loop(\(x,i).(2x2 + ~x),2,3x) mod (x + 1)),x))
A018689: 1 3 7 21 41 123 287 861
(1 + compr(\x.(loop(\(x,i).(~x2 + 4x),2,3x) mod (x + 1)),x))
A018501: 1 3 5 7 15 21 25 35 75 105 175 525
(1 + compr(\x.(loop(\(x,i).(5x2 + ~10x),2,x) mod (x + 1)),x))
A018753: 1 3 5 13 15 25 39 65 75 195 325 975
(1 + compr(\x.(loop(\(x,i).(~5x2 + 5x),2,x) mod (x + 1)),x))
A172411: 1 2 5 10
A018514: 1 2 5 10 11 22 25 50 55 110 275 550
(1 + compr(\x.(loop(\(x,i).(6 * (x2 + i)),2,x) mod (x + 1)),x))
A185092: 1 2 3 4 6 12
A018698: 1 2 3 4 6 12 73 146 219 292 438 876
(1 + compr(\x.(loop(\(x,i).(~x3 + 4x2 + ~5x + 2),2,x) mod (x + 1)),x))
A172411: 1 2 5 10
A018288: 1 2 5 10 11 22 55 110
(1 + compr(\x.(loop(\(x,i).(6x2 + 4),2,x) mod (x + 1)),x))
A018544: 1 2 4 151 302 604
(1 + compr(\x.(loop(\(x,i).(4 * (1 + (x2 * i))),2,x) mod (x + 1)),x))
A185092: 1 2 3 4 6 12
A018496: 1 2 3 4 6 12 43 86 129 172 258 516
(1 + compr(\x.(loop(\(x,i).(~8x2 + 2x),2,x) mod (x + 1)),x))
A005018: 1 2 4 5 10 20
A018664: 1 2 4 5 10 20 41 82 164 205 410 820
(1 + compr(\x.(loop(\(x,i).(x3 + 2x2 + 3x + 6),2,x) mod (x + 1)),x))
A018290: 1 2 3 6 19 38 57 114
(1 + compr(\x.(loop(\(x,i).(2 * (4x2 + i)),2,x) mod (x + 1)),x))
A185092: 1 2 3 4 6 12
A018655: 1 2 3 4 6 12 67 134 201 268 402 804
(1 + compr(\x.(loop(\(x,i).(x * (1 + (x2 * (1 + i)))),2,x) mod (x + 1)),x))
A018276: 1 2 3 4 6 7 12 14 21 28 42 84
(1 + compr(\x.(loop(\(x,i).(8x2 + ~x),2,x) mod (x + 1)),x))
A018564: 1 3 9 71 213 639
(1 + compr(\x.(loop(\(x,i).(5x2 + ~x),2,x) mod (x + 1)),x))
A018318: 1 2 3 6 29 58 87 174
(1 + compr(\x.(loop(\(x,i).(~8x2 + x),2,x) mod (x + 1)),x))
A018576: 1 3 9 73 219 657
(1 + compr(\x.(loop(\(x,i).(5x2 + ~8x),2,x) mod (x + 1)),x))
A318165: 1 3 13
A018621: 1 3 13 19 39 57 247 741
(1 + compr(\x.(loop(\(x,i).(x2 * ((2 * (2 + i)) + i)),2,x) mod (x + 1)),x))
A018483: 1 2 5 7 10 14 35 49 70 98 245 490
(1 + compr(\x.(loop(\(x,i).(x * (8x + i)),2,x) mod (x + 1)),x))
A018437: 1 2 7 14 29 58 203 406
((1 + ((2x mod (2 + (x div 3))) mod 2)) * (1 + (if x <= 0 then 1 else x)))
A205006: 2 2 3 4 5 12 7 8 9 20 11 12 13 14 15 16
(x3 div loop(\(x,i).((3 * (x + (i * i))) div (1 + i)),x,1))
A229093: 0 0 1 2 4 6 9 12 17 22 27 34 41 48 57 66
loop(\(x,i).(((x * (i * (1 + i))) div 2) * (~1 + (2 * i)) * (1 + i)),x,1)
A306266: 1 2 54 6480 2268000 1837080000 2970558360000 8650265944320000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(((4x + 2) + (x2 div 4)) div (1 + i)),x,1)
A161696: 1 3 5 7 8 8 7 5 3 1 0 0 0 0 0 0
(~1 + loop(\(x,i).(27x + 19),2,x))
A156772: 531 1260 1989 2718 3447 4176 4905 5634 6363 7092 7821 8550 9279 10008 10737 11466
loop(\(x,i).(5x mod 22),x,1)
A070375: 1 5 3 15 9 1 5 3 15 9 1 5 3 15 9 1
(~1 + loop(\(x,i).((x + ~1) + (x mod (1 + (6 * (x mod 2))))),2,x))
A140577: 3 0 0 8 4 9
((x + 1) + ((1 + (loop(\(x,i).((2x + 1) * i),(x + ~1),0) div 2)) div 2))
A007364: 1 2 3 6 15 85
(~1 + loop(\(x,i).((x + 1) - (((x - ((x mod 3) div 2)) div 2) div 2)),2,x))
A275890: 1 2 3 3 3 4 5 6 7 7 7 8 8 9 9 10
loop(\(x,i).(5x mod 34),x,1)
A070382: 1 5 25 23 13 31 19 27 33 29 9 11 21 3 15 7
loop(\(x,i).(2 * (21x - (x div 2))),x,1)
A170723-A170675-A170627-A170579-A170531-A170483-A170435-A170387-A170339-A170291-A170243-A170195-A170147-A170099-A170051-A170003-A169535-A169487-A169439-A169391-A169343-A169295-A169247-A169199-A169151-A169103-A169055-A169007-A168959-A168911-A168863-A168815-A168767-A168719-A167958-A167848-A167599-A167095-A166716: 1 42 1722 70602 2894682 118681962 4865960442 199504378122 8179679503002 335366859623082 13750041244546362 563751691026400842 4611686018427387903 4611686018427387903 4611686018427387903
A170761: 1 42 1722 70602 2894682 118681962 4865960442 199504378122 8179679503002 335366859623082 13750041244546362 563751691026400842 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x + (x div 9)),10,x))
A103951: 1 2 3 4 5 6 7 8 9 21 23 25 27 29 32 35
loop(\(x,i).((x + 2) + ((x div 8) + (x div 5))),x,1)
A097911: 1 3 5 8
A167385: 1 3 5 8 12 17 24 33 45 61 82 110 147 196 261 347
loop(\(x,i).(2 * (19x - (x div 2))),x,1)
A170719-A170671-A170623-A170575-A170527-A170479-A170431-A170383-A170335-A170287-A170239-A170191-A170143-A170095-A170047-A169579-A169531-A169483-A169435-A169387-A169339-A169291-A169243-A169195-A169147-A169099-A169051-A169003-A168955-A168907-A168859-A168811-A168763-A168715-A167954-A167827-A167492-A167091-A166690: 1 38 1406 52022 1924814 71218118 2635070366 97497603542 3607411331054 133474219248998 4938546112212926 182726206151878262 4611686018427387903 4611686018427387903 4611686018427387903
A170757: 1 38 1406 52022 1924814 71218118 2635070366 97497603542 3607411331054 133474219248998 4938546112212926 182726206151878262 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (25x - (x div 2))),x,1)
A170731-A170683-A170635-A170587-A170539-A170491-A170443-A170395-A170347-A170299-A170251-A170203-A170155-A170107-A170059-A170011-A169543-A169495-A169447-A169399-A169351-A169303-A169255-A169207-A169159-A169111-A169063-A169015-A168967-A168919-A168871-A168823-A168775-A168727-A167989-A167880-A167647-A167103-A166856: 1 50 2450 120050 5882450 288240050 14123762450 692064360050 33911153642450 1661646528480050 81420679895522450 3989613314880600050 4611686018427387903 4611686018427387903 4611686018427387903
A170769: 1 50 2450 120050 5882450 288240050 14123762450 692064360050 33911153642450 1661646528480050 81420679895522450 3989613314880600050 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.(x mod (2 + (if (x mod 2) <= 0 then 1 else (x div 12)))),x))
A225227: 1 7 13
A279831: 1 7 13 16 19 22 25 31 37 43 46 49 55 61 64 67
((x + 1) + (x3 div loop(\(x,i).x3,1,6)))
A226189: 1 2 3 4 5 6 8 9 11 13 15 18 21 24 27 31
((x + ~1) + (2 * ((if ((x div 2) mod 3) <= 0 then 1 else 2) + (x div 3))))
A072955: 1 2 5 8 9 10 11 12 15 18 19 20 21 22 25 28
((x + 1) + (((if (~2 + (x div 2)) <= 0 then 1 else 4) + (x div 3)) div 2))
A345172-A339741-A335433-A212167-A179983-A175082: 1 2 3 5 6 7 10 11 12 13 14 15 17 18 19 20
(1 + loop(\(x,i).(x + (x div 7)),((~1 + (x div 2)) div 2),x))
A082463: 1 2 3 4 5 6 7 9 10
A292050: 1 2 3 4 5 6 7 9 10 11 13 14 15 17 21 22
(1 + compr(\x.(~2 + (loop(\(x,i).(5x + 2),x,0) mod (x + 1))),x))
A097296: 1 2 3 4 5 6 7 10 11 12 13 14 17 19 20 22
(1 + compr(\x.(~2 + (loop(\(x,i).(2x + 4),x,(2 * (x mod 2))) mod (x + 1))),x))
A193461: 1 2 3 4 5 6 7 11 13 17 19 23 29 31 37 41
loop(\(x,i).(2 * ((8x * (~1 + (2 * i))) div (1 + i))),x,1)
A156270: 1 8 128 2560 57344 1376256 34603008 899678208 23991418880 652566593536 18034567675904 504967894925312 14294475794808832 408413594137395200 4611686018427387903 4611686018427387903
loop(\(x,i).(4 * (2x mod 25)),x,1)
A014392: 1 8 64 12 96 68 44 52 16 28 24 92 36 88 4 32
loop(\(x,i).(3x mod 44),x,1)
A070362: 1 3 9 27 37 23 25 31 5 15 1 3 9 27 37 23
((x + 1) + (if (x + ~2) <= 0 then 1 else x) - ((x - ((x mod 3) div 2)) div 2))
A189725: 2 3 4 6 7 9 10 12 14 15 16 18 19 21 23 24
(1 + loop(\(x,i).((3x + 2) + (x div 7)),2,x))
A107223: 9 18 28 37 47 56 65 78 87 97 106 116 125 135 147 157
((x + 1) + (2 * (x div (2 + (if ((x div 3) mod 3) <= 0 then 1 else 2)))))
A261412: 1 2 3 4 7 8 9 10 13 16 17 18 19 20 21 22
loop(\(x,i).((x + 2) - ((x div (8 * (~2 + (x mod 2)))) mod 2)),x,1)
A032959: 1 2 3 4 5 6 7 8 9 11 13 15 17 18 20 22
loop(\(x,i).(28x + (2 div (1 + i))),x,1)
A170748-A170710-A170662-A170614-A170566-A170518-A170470-A170422-A170374-A170326-A170278-A170230-A170182-A170134-A170086-A170038-A169570-A169522-A169474-A169426-A169378-A169330-A169282-A169234-A169186-A169138-A169090-A169042-A168994-A168946-A168898-A168850-A168802-A168754-A168706-A167944-A167714-A167285-A167082: 1 29 812 22736 636608 17825024 499100672 13974818816 391294926848 10956257951744 306775222648832 8589706234167296 240511774556684288 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) - loop(\(x,i).(x - ((x2 div (x - ((~x + 2) div 2))) mod 2)),2,x))
A088198: 1 2 1 1 2 3 1 1 2 1 2 3 1 1 2 1
loop(\(x,i).(10x + ((i * i) mod 3)),x,1)
A267209: 1 11 111 1110 11101 111011 1110110 11101101 111011011 1110110110 11101101101 111011011011 1110110110110 11101101101101 111011011011011 1110110110110110
(1 + (x2 mod ((x + 1) - (x div ((if (x mod 2) <= 0 then 1 else x) mod 4)))))
A014651: 1 1 1 1 1 1 1 2 1 1 1 5 1 1 1 6
(1 + loop(\(x,i).((x + 1) - (2 * (~1 + (x mod 4)))),(x div 4),x))
A263694: 1 2 3 4 8 7 6 5 9 10 11 12 16 15 14 13
loop(\(x,i).(2 * (22x - (x div 2))),x,1)
A170725-A170677-A170629-A170581-A170533-A170485-A170437-A170389-A170341-A170293-A170245-A170197-A170149-A170101-A170053-A170005-A169537-A169489-A169441-A169393-A169345-A169297-A169249-A169201-A169153-A169105-A169057-A169009-A168961-A168913-A168865-A168817-A168769-A168721-A167960-A167854-A167641-A167097-A166723: 1 44 1892 81356 3498308 150427244 6468371492 278139974156 11960018888708 514280812214444 22114074925221092 950905221784506956 4611686018427387903 4611686018427387903 4611686018427387903
A170763-A063821: 1 44 1892 81356 3498308 150427244 6468371492 278139974156 11960018888708 514280812214444 22114074925221092 950905221784506956 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((3 * (2x + (x mod 3))) + ((x div 2) mod 2)),x,1)
A037599: 1 9 54 325 1953 11718 70309 421857 2531142 15186853 91121121 546726726 3280360357 19682162145 118092972870 708557837221
loop(\(x,i).(2 * (23x - (x div 2))),x,1)
A170727-A170679-A170631-A170583-A170535-A170487-A170439-A170391-A170343-A170295-A170247-A170199-A170151-A170103-A170055-A170007-A169539-A169491-A169443-A169395-A169347-A169299-A169251-A169203-A169155-A169107-A169059-A169011-A168963-A168915-A168867-A168819-A168771-A168723-A167962-A167861-A167643-A167099-A166739: 1 46 2070 93150 4191750 188628750 8488293750 381973218750 17188794843750 773495767968750 34807309558593750 1566328930136718750 4611686018427387903 4611686018427387903 4611686018427387903
A170765: 1 46 2070 93150 4191750 188628750 8488293750 381973218750 17188794843750 773495767968750 34807309558593750 1566328930136718750 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * ((6 * (2x - (x mod 2))) - (x mod 2))),x,1)
A067423: 1 10 240 5760 138240 3317760 79626240 1911029760 45864714240 1100753141760 26418075402240 634033809653760 15216811431690240 365203474360565760 4611686018427387903 4611686018427387903
((x + 1) + ((~x + 1) mod ((x + (if ((x div 2) mod 3) <= 0 then 2 else 0)) div 2)))
A064778: 1 2 3 4 6 6 10 10 10 10 12 12 16 16 16 16
((x + 1) + (2 * ((x2 + ~x) div (x + (if x <= 0 then 1 else (x div 3))))))
A033292: 1 2 5 6 9 12 13 16 19 22 23 26 29 32 35 36
loop(\(x,i).((x + 2) + (x div (4 + (x div (4 - (x mod 2)))))),x,1)
A097911: 1 3 5 8
A248611: 1 3 5 8 11 14 18 22 26 30 34 38 42 47 51 55
((x2 + 2x + ~1) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A073497: ~1 1 4 9 14 23 32 45 58 71 90 107 128 153 178 203
((x2 + 2x + 1) * loop(\(x,i).x2,2,(5x + 5)))
A106321: 625 40000 455625
(loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2) div (x2 + 2x + 1))
A024500: 2 1 2 4 10 25 70 201 600 1847 5830 18778 61542 204676 689411 2347970
((x2 + 2x + 1) * loop(\(x,i).6x,(x + 1),(x + 2)))
A129006: 12 432 7776 103680 1166400 11757312 109734912 967458816 8162933760 66512793600 526781325312 4074936532992 30901602041856 230390642442240 1692665944473600 12277470317248512
((x2 + 2x + 1) * loop(\(x,i).8x,(x + 1),(x + 2)))
A129008: 16 768 18432 327680 4915200 66060288 822083584 9663676416 108716359680 1181116006400 12472585027584 128642860449792 1300722255659008 12930256742645760 126663739519795200 1224979098644774912
((x2 + 2x + 1) * loop(\(x,i).7x,(x + 1),x))
A128990: 0 196 6174 115248 1680700 21176820 242121642 2582630848 26149137336 254227724100 2392565359030 21924598926384 196490913105396 1728112389619252 14954818756320450 127614453387267840
((x + 1) + ((x * (3 + (if (x + ~4) <= 0 then 0 else 2))) div (x + 2)))
A275319: 1 3 4 5 7 9 10 11 13 14 15 16 17 18 19 20
loop(\(x,i).(2x + (((x + 1) div (2 + (x div 8))) mod 2)),x,1)
A125049: 1 3 6 13 26 53 106 213 427 855 1711 3423 6847 13695 27391 54783
loop(\(x,i).(2x + (((x - ((2 - (x div 4)) div 2)) div 2) mod 2)),x,1)
A222011: 1 2 4 8
A195904: 1 2 4 8 16 32 65 130 260 520 1040 2080 4161 8322 16644 33288
(((x mod 2) + loop(\(x,i).2x,x,1)) - (3 * ((x div 3) mod 2)))
A143100: 1 3 4 6 13 30 64 129 256 510 1021 2046 4096 8193 16384 32766
loop(\(x,i).(6x + (((x + 1) mod 3) + (x mod 2))),x,1)
A037711: 1 9 56 336 2017 12105 72632 435792 2614753 15688521 94131128 564786768 3388720609 20332323657 121993941944 731963651664
((x + 1) * (if (((x + 1) mod (1 + (x div 3))) mod 2) <= 0 then (x + 1) else 0))
A106546: 1 4 9 16 0 36 0 64 81 100 0 144 0 196 225 256
((x + 1) * (1 + (if (~2 + (x div 3)) <= 0 then 10 else 0)))
A073729: 11 22 33 44 55 66 77 88 99 10 11 12 13 14 15 16
compr(\x.(x - loop(\(x,i).2x,(~1 + (x mod 9)),1)),(x + 1))
A032991: 1 2 3 4 5 6 7 8 14 15 16 17 24 25 26 34
compr(\x.(x - loop(\(x,i).2x,(~1 + (x mod 10)),1)),(x + 1))
A032992: 1 2 3 4 5 6 7 8 9 15 16 17 18 19 26 27
(loop(\(x,i).2x,(~1 + (x div (2 + ((~x + 2) mod 4)))),1) div (x + 1))
A046770: 1 0 0 0 0 0 0 0 0 0 1 0 0 0 4 0
((x + 1) * loop(\(x,i).(10x + 1),5,1))
A154549: 111111 222222 333333 444444 555555 666666 777777 888888 999999 1111110 1222221 1333332 1444443 1555554 1666665 1777776
(((x + 1) - (loop(\(x,i).x2,2,(x + 1)) div 5)) mod (x + 1))
A226783: 0 1 2 1 0 5 3 5 2 0 9 5 8 3 0 13
compr(\x.(x mod (1 + (6 * (if (x mod 3) <= 0 then 0 else 2)))),(x + 1))
A230215: 3 6 9 12 13 15 18 21 24 26 27 30 33 36 39 42
(loop(\(x,i).(x * i),x,(~2 + (x mod 2) - (x div 3))) mod (x + 1))
A049084: 0 1 2 0 3 0 4 0 0 0 5 0 6 0 0 0
((x + 1) * (1 + (2 mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1))))
A333046: 1 2 3 4 5 18 7 8 9 30 11 36 13 42 45 16
((x + 1) * (1 + ((x + 1) * loop(\(x,i).x2,2,7))))
A031776: 2402 9606 21612 38420 60030 86442 117656 153672 194490 240110 290532 345756 405782 470610 540240 614672
((x + 1) * (1 + ((x + 1) * (1 + loop(\(x,i).(x * (x + i)),2,4)))))
A031720: 442 1766 3972 7060 11030 15882 21616 28232 35730 44110 53372 63516 74542 86450 99240 112912
((x + 1) * (1 + ((x + 1) * loop(\(x,i).(x3 + 4x2 + 4x),2,1))))
A031744: 1090 4358 9804 17428 27230 39210 53368 69704 88218 108910 131780 156828 184054 213458 245040 278800
((x + 1) * (1 + ((x + 1) * loop(\(x,i).((x + 2) * (x + i)),2,3))))
A031722: 485 1938 4359 7748 12105 17430 23723 30984 39213 48410 58575 69708 81809 94878 108915 123920
compr(\x.(x mod (1 + (loop(\(x,i).(2x + 8),x,1) mod (x + 1)))),(x + 1))
A064915: 1 2 3 4 5 6 7 8 9 10 12 14 16 18 22 24
((x + 1) * (1 + ((x + 1) * (loop(\(x,i).(x2 + x),2,(x + 1)) div 2))))
A163279: 4 86 705 3364 11630 32514 78211 168200 331704 610510 1062149 1763436 2814370 4342394 6507015 9504784
((x + 1) * (1 + ((x + 1) * loop(\(x,i).(x2 + 4x + 4),2,4))))
A031754: 1445 5778 12999 23108 36105 51990 70763 92424 116973 144410 174735 207948 244049 283038 324915 369680
((x + 1) * ((x + ~1) - ((x + 1) * loop(\(x,i).(~x2 + 1),2,4))))
A158226: 223 896 2019 3592 5615 8088 11011 14384 18207 22480 27203 32376 37999 44072 50595 57568
((x + 1) * ((x + ~1) - ((x + 1) * loop(\(x,i).(x * (~x + i)),2,4))))
A158218: 167 672 1515 2696 4215 6072 8267 10800 13671 16880 20427 24312 28535 33096 37995 43232
((x + 1) * (1 + ((x + 1) * loop(\(x,i).(x * ((x2 + 1) + i)),2,2))))
A031762: 1765 7058 15879 28228 44105 63510 86443 112904 142893 176410 213455 254028 298129 345758 396915 451600
((x + 1) * (1 + ((x + 1) * loop(\(x,i).(~2x3 + x2),2,2))))
A157861: 3601 14402 32403 57604 90005 129606 176407 230408 291609 360010 435611 518412 608413 705614 810015 921616
((x + 1) * (~1 + ((x + 1) * loop(\(x,i).(~2x3 + x2),2,2))))
A157857: 3599 14398 32397 57596 89995 129594 176393 230392 291591 359990 435589 518388 608387 705586 809985 921584
(loop(\(x,i).((x + 1) + ((x + (x div 2)) div 4)),(x + ~1),1) div (x + 1))
A225501: 1 0 0 0 1 1 1 1 2 2 3 4 5 7 9 12
(loop(\(x,i).(2 * (x - ((x + (x div 2)) div 4))),(x + ~1),1) div (x + 1))
A033295: 1 0 0 1 1 1 1 1 2 2 2 3 3 4 5 6
((1 + (2 * (loop(\(x,i).x2,2,(x + 1)) div 5))) div (x + 1))
A184634: 1 3 11 25 50 86 137 204 291 400 532 691 878 1097 1350 1638
((x + 1) * (1 + (((x + 1) * loop(\(x,i).(x3 + 2x2),2,2)) div 2)))
A031774: 2305 9218 20739 36868 57605 82950 112903 147464 186633 230410 278795 331788 389389 451598 518415 589840
((x + 1) * (if ((x + 2) mod 9) <= 0 then (2x + 2) else 1))
A270436: 1 2 3 4 5 6 7 128 9 10 11 12 13 14 15 16
((1 + (4 * (1 + loop(\(x,i).x3,2,4)))) mod (x + 1))
A318989: 0 1 0 1 1 3 2 5 0 1 6 9 1 9 6 5
((x + 1) * loop(\(x,i).(10x + 1),8,1))
A172525: 111111111 222222222 333333333 444444444 555555555 666666666 777777777 888888888 999999999 1111111110 1222222221 1333333332 1444444443 1555555554 1666666665 1777777776
(if (x mod 2) <= 0 then (1 + (x div 2)) else ((1 + (x mod 8)) mod (x + 1)))
A008821-A008809: 1 0 2 0 3 0 4 0 5 2 6 4 7 6 8 8
((x + 1) * loop(\(x,i).(2x2 + ~x),2,(1 + (2 * (x div 4)))))
A120024: 1 2 3 4 2175
((1 + ((if (x div 8) <= 0 then x else 3) mod 4)) mod (x + 1))
A065680: 0 0 0 0 1 2 3 4 4 4 4 4 4 4 4 4
((x + 1) * (if (x + ~2) <= 0 then 1 else (10x2 + 5)))
A097654: 1 2 3 380
((x + 1) * loop(\(x,i).(2 + (x * ((x + 4) + i))),2,5))
A086746: 3018 6036 9054 12072 15090 18108 21126 24144 27162 30180 33198 36216 39234 42252 45270 48288
((1 + (((x + loop(\(x,i).(x + (x div 2)),x,3)) div 2) div 2)) div (x + 1))
A334626: 1 1 1 1 1 1 1 1 2 2 3 4 6 8 12 16
((1 + (2 * (2x + loop(\(x,i).3x,(x + ~1),x)))) div (x + 1))
A005312: 1 3 7 16 46 138
compr(\x.((if ((x * (x div 2)) mod 2) <= 0 then (x div 3) else 1) mod 3),(x + 1))
A320919: 1 2 9 10 18 20 28 29 36 37 38 45 46 54 56 64
((3 * loop(\(x,i).(x2 div (2 + (x mod 2))),2,(x + 1))) mod (x + 1))
A226784: 0 0 0 0 1 0 6 0 0 0 2 0 11 0 0 0
((x + 1) * ((x + 3) + loop(\(x,i).(x * (2 + i)),4,(x + 1))))
A158309-A031697: 363 1448 3255 5784 9035 13008 17703 23120 29259 36120 43703 52008 61035 70784 81255 92448
((x + 1) + loop(\(x,i).((2x + 8) - (x div 2)),2,(x mod 3)))
A217150: 21 25 28 24
loop(\(x,i).((2x * (4 + i)) div (1 + i)),(2x + 1),(x + 1))
A054323: 5 140 2016 21120 183040 1397760 9748480 63504384 392232960 2321285120 13264486400 73610035200 398475657216 2111580405760 10984378859520 56221121904640
((x + 1) * (1 + (if (x mod (1 + (((x + 1) div 2) div 3))) <= 0 then 0 else x)))
A274029: 1 2 3 4 5 36 7 64 9 100 11 144 13 196 225 16
((x + 1) * (1 + compr(\x.(loop(\(x,i).(x * (1 + (i div 2))),x,1) mod (x + 1)),x)))
A171523: 1 8 18 32 45 60 84 112 135 160 198 240 273 308 360 400
((x + 1) * ((~x + 1) + ((x + 1) * loop(\(x,i).(x2 + 1),2,4))))
A158254-A031695: 291 1160 2607 4632 7235 10416 14175 18512 23427 28920 34991 41640 48867 56672 65055 74016
((x + 1) * ((x + ~1) + ((x + 1) * loop(\(x,i).(x * (x + i)),2,4))))
A157737: 439 1760 3963 7048 11015 15864 21595 28208 35703 44080 53339 63480 74503 86408 99195 112864
((x + 1) * ((x + ~1) + loop(\(x,i).(x * (3 + i)),4,(x + 1))))
A158401: 839 3360 7563 13448 21015 30264 41195 53808 68103 84080 101739 121080 142103 164808 189195 215264
((x + 1) + loop(\(x,i).(((1 + (x div 2)) * i) + ((1 + (x div 2)) div 2)),x,1))
A118332: 2 3 5 11 23
A175234: 2 3 5 11 23 61
((x + 1) * (~1 + loop(\(x,i).(17x + 16),2,x)))
A158252: 287 1152 2595 4616 7215 10392 14147 18480 23391 28880 34947 41592 48815 56616 64995 73952
(loop(\(x,i).((x + 2) + (2 * (2x div (3 + i)))),x,1) div (x + 1))
A029004-A008753: 1 1 2 3 4 5 7 8 10 12 15 17 21 24 28 32
((x + 1) * loop(\(x,i).(10x + 1),(x2 + 2x),1))
A118116: 1 2222 333333333 4444444444444444 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) * (1 + loop(\(x,i).(x3 + 4x2 + 4x),1,(x2 + 2x))))
A239065: 1 152 2403 17344 81125 287496 840007 2129408 4841289 10099000 19646891 36078912 63117613 105948584 171615375 269479936
((loop(\(x,i).3x,x,3) div (x2 + 2x + 1)) div (x + 1))
A062278: 3 1 1 1 1 3 6 12 27 59 133 307 725 1743 4251 10509
(loop(\(x,i).3x,x,3) mod (x3 + 3x2 + 3x + 1))
A066607: 0 1 0 17 118 81 129 417 0 49 124 945 1498 177 1782 1857
compr(\x.(loop(\(x,i).(2x + 17),x,0) mod (x + 1)),(x + 1))
A309374: 2 4 6 10 12
A128984: 2 4 6 10 12 16 18 22 28 30 36 40 42 46 50 52
compr(\x.(2 - (loop(\(x,i).((2x + 1) + (x mod 2)),x,0) mod (x + 1))),(x + 1))
A254671: 8 11 14 15 17 19 20 23 24 26 27 29 31 32 34 35
((x + 1) * ((x + loop(\(x,i).10x,x,1)) div (x + 1)))
A053041: 1 10 102 1000 10000 100002 1000006 10000000 100000008 1000000000 10000000010 100000000008 1000000000012 10000000000004 100000000000005 1000000000000000
loop(\(x,i).(2 * ((2x * (1 + (2 * i))) div (2 + i))),(x + ~1),(x + 1))
A082142: 1 2 12 80 560 4032 29568 219648 1647360 12446720 94595072 722362368
A069723: 1 2 12 80 560 4032 29568 219648 1647360 12446720 94595072 722362368 5538111488 42600857600 328635187200 2541445447680
((2x + 2) * (1 + (if (~x + 4) <= 0 then 16 else 1)))
A061085: 4 8 12 16 170 204 238 272 306 340 374 408 442 476 510 544
((2 * (if (x mod 2) <= 0 then (2x mod 9) else 1)) div (x + 1))
A255308: 0 1 2 0 3 0 0 0 1 0 0 0 0 0 0 0
((x + 1) * (if x <= 0 then 1 else ((x mod (~1 + (x mod (~1 + ((~x + 1) div 2))))) mod 2)))
A191558: 1 0 0 4 0 6 0 8 9 10 0 12 0 14 15 16
((~2 + (x mod 2)) mod ((2x + 2) * (if (x mod 2) <= 0 then 8 else 1)))
A060782: 14 3 46 7 78
((x + 1) * (if ((x + 1) mod 5) <= 0 then 1 else 10))
A237416: 10 20 30 40 5 60 70 80 90 10 110 120 130 140 15 160
(loop(\(x,i).x5,1,10) div (x + 1))
A033427: 100000 50000 33333 25000 20000 16666 14285 12500 11111 10000 9090 8333 7692 7142 6666 6250
compr(\x.(~2 + (if (x mod (1 + (8 * (x mod 2)))) <= 0 then x else 1)),(x + 1))
A320055: 1 2 3 5 7 11 13 15 17 19 21 23 25 29 31 33
((x + 1) * (2 + ((x + 1) * (1 + loop(\(x,i).(x * (x + i)),2,3)))))
A158220: 171 680 1527 2712 4235 6096 8295 10832 13707 16920 20471 24360 28587 33152 38055 43296
((x + 1) * (2 + ((x + 1) * loop(\(x,i).x2,2,7))))
A031727: 2403 9608 21615 38424 60035 86448 117663 153680 194499 240120 290543 345768 405795 470624 540255 614688
((x + 1) * (2 + ((x + 1) * (1 + loop(\(x,i).(x2 + ~1),4,2)))))
A031741: 3971 15880 35727 63512 99235 142896 194495 254032 321507 396920 480271 571560 670787 777952 893055 1016096
((x + 1) * (2 + ((x + 1) * (1 + loop(\(x,i).(x2 + ~1),2,4)))))
A158228: 227 904 2031 3608 5635 8112 11039 14416 18243 22520 27247 32424 38051 44128 50655 57632
((x + 1) * (2 + ((x + 1) * (1 + loop(\(x,i).(x * (x + i)),2,4)))))
A158321-A031699: 443 1768 3975 7064 11035 15888 21623 28240 35739 44120 53383 63528 74555 86464 99255 112928
((x + 1) * (2 + ((x + 1) * loop(\(x,i).(x3 + 4x2 + 4x),2,1))))
A031711: 1091 4360 9807 17432 27235 39216 53375 69712 88227 108920 131791 156840 184067 213472 245055 278816
((x + 1) * (2 + ((x + 1) * loop(\(x,i).((x + 2) * (x + i)),2,3))))
A158325: 486 1940 4362 7752 12110 17436 23730 30992 39222 48420 58586 69720 81822 94892 108930 123936
((x + 1) * (~2 + ((x + 1) * loop(\(x,i).((x + 2) * (x + i)),2,3))))
A158329: 482 1932 4350 7736 12090 17412 23702 30960 39186 48380 58542 69672 81770 94836 108870 123872
((x + 1) * (2 + loop(\(x,i).20x,2,(x + 1))))
A158312: 402 1604 3606 6408 10010 14412 19614 25616 32418 40020 48422 57624 67626 78428 90030 102432
((x + 1) * (~2 + loop(\(x,i).20x,2,(x + 1))))
A158316: 398 1596 3594 6392 9990 14388 19586 25584 32382 39980 48378 57576 67574 78372 89970 102368
((x + 1) * (2 + ((x + 1) * loop(\(x,i).(x2 + 2x + 1),2,4))))
A158385: 678 2708 6090 10824 16910 24348 33138 43280 54774 67620 81818 97368 114270 132524 152130 173088
((x + 1) * (~2 + ((x + 1) * loop(\(x,i).(x2 + 2x + 1),2,4))))
A158392: 674 2700 6078 10808 16890 24324 33110 43248 54738 67580 81774 97320 114218 132468 152070 173024
((2x + 2) * ((x + (x div 2)) div (if (x mod 2) <= 0 then 4 else (x + 1))))
A303223: 0 0 0 8 10 12 28 16 54 20 66 24 104 28 150 32
compr(\x.(~2 + (loop(\(x,i).2x,(x div 2),(x mod 4)) mod (x + 1))),(x + 1))
A336444: 1 2 3 4 6 7 8 11 12 14 15 16 20 22 23 24
((x + 1) * loop(\(x,i).x2,1,((x3 + 3x2 + 4x + 2) div 2)))
A052460: 1 50 675 4624 21125 73926 214375 540800 1225449 2550250 4952651 9082800 15873325 26622974 43095375 67634176
(((x + ((x mod (2 + (x div 2))) div 2)) div 2) + ((x + 1) * (if x <= 0 then 1 else 2)))
A007073-A007064: 1 4 7 9 12 14 17 20 22 25 27 30 33 35 38 41
compr(\x.(1 - (x mod (2 + (if ((x div 3) mod 3) <= 0 then 1 else 2)))),(x + 1))
A122144-A064052-A048839: 2 3 5 6 7 10 11 13 14 15 17 19 20 21 22 23
compr(\x.(1 - (x mod (2 + (if (x mod (2 + (x div 4))) <= 0 then 1 else 2)))),(x + 1))
A279814: 2 3 5 7 8 9 10 11 13 14 17 19 22 23 25 26
(x - (loop(\(x,i).(x4 + 2x3 + 2x2 + 2x + 1),2,2) mod (x + 1)))
A245974: 0 1 1 3 3 1 0 7 7 3 2 7 6 7 13 7
((x + 1) * (2 + (4 * (if (x + ~3) <= 0 then 1 else 6))))
A020333: 6 12 18 24 130 156 182 208 234 260 286 312 338 364 390 416
(15 mod (if (~2 + (x mod 4)) <= 0 then 2 else (x + 1)))
A140670: 1 1 1 3 1 1 1 7 1 1 1 3 1 1 1 15
((x + 2) mod ((x + 2) - (loop(\(x,i).2x2,2,4) mod (x + 1))))
A284272: 0 0 0 0 0 2 0 0 0 2 2 3 0 4 0 0
loop(\(x,i).(8x div 5),2,(4x + 4))
A330171: 9 19 30 40 51 60 70 81 91 102 112 121 132 142 153 163
((~x + ~1) + loop(\(x,i).(3x - (x mod (1 + (2 * i)))),x,4))
A220950: 3 9 29 88 269
((x + 1) * ((x + 4) + ((loop(\(x,i).(x * (0 - i)),x,1) div 2) div 2)))
A070213: 4 8 18 20 70
((x + 1) * (x div (2x - (if x <= 0 then 1 else (((x div 2) * (x div 2)) div 2)))))
A308102: 0 0 0 0 0 0 0 0 9 0 11 12 26 14 45 32
((x + 1) + (if x <= 0 then 1 else 4x) - ((x + 1) mod (2 + (x mod 2))))
A310461: 1 4 10 15 20 26 30 34 40 45 50 56 60 64 70 75
((x + 1) * (if ((x + 1) mod 6) <= 0 then (x div 2) else (2 + (x mod 2))))
A208570: 2 6 6 12 10 12 14 24 18 30 22 60 26 42 30 48
compr(\x.(2 * (3 mod (if (x mod (1 + (x mod 4))) <= 0 then 1 else x))),(x + 1))
A279083: 1 3 4 6 8 12 16 18 20 24 28 30 32 36 40
((2 * (if (x mod 2) <= 0 then x else (4x2 + 3x))) div (x + 1))
A019431: 0 7 1 22 1 38 1 54 1 70 1 86 1 102 1 118
(x - loop(\(x,i).(~x + (4x mod 9)),2,(x + 1)))
A133293: 0 1 2 3 ~5 5 ~3 ~2 ~1 0 1 2 3 ~5 5 ~3
((x + 1) * ((x + 2) + loop(\(x,i).(x * (3 + i)),4,(x + 1))))
A031736: 842 3366 7572 13460 21030 30282 41216 53832 68130 84110 101772 121116 142142 164850 189240 215312
((x + 1) * ((x + 2) + loop(\(x,i).(x * (4 + i)),4,(x + 1))))
A031760: 1682 6726 15132 26900 42030 60522 82376 107592 136170 168110 203412 242076 284102 329490 378240 430352
((x + 1) * loop(\(x,i).6x,(x + 1),(x2 + 2x + 2)))
A128043: 12 360 6480 88128 1010880 10357632 97977600 873400320 7437339648 61070837760 486873649152 3787601264640 28864133775360 216128364576768 1593927097712640 11600403939459072
((x + 1) * loop(\(x,i).8x,(x + 1),(x2 + 2x + 2)))
A128048: 16 640 15360 278528 4259840 58195968 734003200 8724152320 99052683264 1084479242240 11527692222464 119571889520640 1214960348692480 12129812277624832 119275021381140480 1157425104234217472
((x + 1) * loop(\(x,i).5x,(x + 1),(x2 + 2x + 2)))
A128013: 10 250 3750 42500 406250 3468750 27343750 203125000 1441406250 9863281250 65527343750 424804687500 2697753906250 16833496093750 103454589843750 627441406250000
((x2 + 3x + 2) * loop(\(x,i).(x * (3 + i)),x,(x + 3)))
A001805: 6 96 1200 14400 176400 2257920 30481920 435456000 6586272000 105380352000 1780927948800 31732897996800 594991837440000 11716762337280000 241867451105280000 4611686018427387903
((x2 + 3x + 2) * loop(\(x,i).7x,(x + 1),x))
A128965: 0 294 8232 144060 2016840 24706290 276710448 2905459704 29054597040 279650496510 2610071300760 23751648836916 211605598728888 1851548988877770 15951806673408480 135590356723972080
(((if ((x + ~1) mod 7) <= 0 then 2 else 1) + (x mod 2)) mod (x + 1))
A072410: 0 1 1 2 1 2 1 2 2 2 1 2 1 2 1 3
((2x + 2) * (x + loop(\(x,i).(x + ((3 + i) * i)),(x + 1),x)))
A086114: 8 64 216 528 1080 1968 3304 5216 7848 11360 15928 21744 29016 37968 48840 61888
loop(\(x,i).(9 * (x + (2x div (1 + i)))),x,(x + 1))
A173187: 1 36 810 14580 229635 3306744 44641044 573956280 7102708965 85232507580 997220338686 11422705697676 128505439098855 1423444863864240 15556218869373480 168007163789233584
loop(\(x,i).(5 * (x + (4x div (1 + i)))),x,(x + 1))
A050982: 1 30 525 7000 78750 787500 7218750 61875000 502734375 3910156250 29326171875 213281250000 1510742187500 10458984375000 70971679687500 473144531250000
((x + (if (~1 + (x div 4)) <= 0 then 2 else (x div 5))) mod (x + 1))
A143535: 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 2
((x + (6 * loop(\(x,i).(2x + 4),x,4))) div (x + 1))
A003177: 24 36 56 90 149 252 436 765 1363 2456 4467 8190 15122 28086 52428 98303
((2x + 1) + ((2 * (x + (if (x + ~4) <= 0 then 1 else 0))) div 3))
A007072: 1 4 7 9 12 14 17 19 22 25 27 30 33 35 38 41
loop(\(x,i).(3 * (x + (8x div (1 + i)))),x,(x + 1))
A036223: 1 30 495 5940 57915 486486 3648645 25019280 159497910 956987460 5454828522 29753610120 156206453130 793048146660 3908594437110 18761253298128
((x + (loop(\(x,i).((x2 + x) div 4),2,x) div 3)) div (x + 1))
A241089: 0 0 0 1 1 1 2 3 4 5 6 8 10 13 16 20
((x + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1)) div (x + 1))
A188669: 1 2 4 9 26 77 246 805 2702 9238 32066 112674 400024 1432736 5170584 18783763
((x + 1) * (~x + ((x + 1) * loop(\(x,i).(x2 + 1),2,6))))
A031752: 1370 5478 12324 21908 34230 49290 67088 87624 110898 136910 165660 197148 231374 268338 308040 350480
((x + 1) * (~x + ((x + 1) * loop(\(x,i).(4x2 + 1),2,2))))
A031746: 1157 4626 10407 18500 28905 41622 56651 73992 93645 115610 139887 166476 195377 226590 260115 295952
((x + 1) * (~x + ((x + 1) * loop(\(x,i).(2 + (x * (x + i))),2,4))))
A031724: 530 2118 4764 8468 13230 19050 25928 33864 42858 52910 64020 76188 89414 103698 119040 135440
loop(\(x,i).(((2x * (1 + (2 * i))) div (2 + i)) * (1 + i)),x,(x + 1))
A092956: 1 8 90 1344 25200 570240 15135120 461260800 15878903040 609493248000 25812039052800 1195656969830400 60138698780160000 3264143527636992000 4611686018427387903 4611686018427387903
((x + 1) + loop(\(x,i).(x - (9 * (x div ~2))),2,x))
A056082: 1 57 68 124 126 182 193 249 251 307 318 374 376 432 443 499
((x + (loop(\(x,i).(x + (2 * (x + (i mod 2)))),x,0) div (x + 2))) div (x + 1))
A297074: 0 0 1 1 2 5 10 23 55
((x + (if (x + ~2) <= 0 then 1 else (7x + ~14))) div (x + 1))
A030601: 1 1 1 2 3 4 4 5 5 5 6 6 6 6 6 6
((1 + (x * (2 + (x div 2)))) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))
A220466: 1 3 2 10 3 7 4 36 5 11 6 26 7 15 8 136
((8x + 8) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))
A037239: 8 16 8 32 8 16 8 64 8 16 8 32 8 16 8 128
loop(\(x,i).((6x * (~1 + (2 * i))) div (2 + i)),x,(x + 1))
A275607: 1 4 27 216 1890 17496 168399 1667952 16888014 173997720 1818276174 19225409616 205299909828 2210922105840 23984556773175 261854925711840
loop(\(x,i).((x + (6x div (1 + i))) * (2 + i)),x,(x + 1))
A062149: 1 24 432 7200 118800 1995840 34594560 622702080 11675664000 228324096000 4657811558400 99084354969600 2196369868492800 50685458503680000 1216451004088320000 4611686018427387903
((x + 1) + loop(\(x,i).((x + 1) - (x mod (2 + (x div 8)))),x,x))
A189204: 1 3 6 7 10 11 14 15 16 20 21 22 26 27 28 33
((x * loop(\(x,i).(x + (2 * (2x + (x mod 2)))),(x + 1),x)) mod (x + 1))
A220235: 0 1 2 1 0 1 5 1 8 3 5 1 5 13 5 1
loop(\(x,i).(~x + (20x div (1 + i))),x,(x + 1))
A010934: 1 18 153 816 3060 8568 18564 31824 43758 48620 43758 31824 18564 8568 3060 816
loop(\(x,i).(x + (18x div (1 + i))),x,(x + 1))
A010972: 1 20 210 1540 8855 42504 177100 657800 2220075 6906900 20030010 54627300 141120525 347373600 818809200 1855967520
loop(\(x,i).(~x + (24x div (1 + i))),x,(x + 1))
A010938: 1 22 231 1540 7315 26334 74613 170544 319770 497420 646646 705432 646646 497420 319770 170544
loop(\(x,i).(~x + (32x div (1 + i))),x,(x + 1))
A010946: 1 30 435 4060 27405 142506 593775 2035800 5852925 14307150 30045015 54627300 86493225 119759850 145422675 155117520
loop(\(x,i).(~x + (14x div (1 + i))),x,(x + 1))
A080559-A010928: 1 12 66 220 495 792 924 792 495 220 66 12 1
((3x + 1) + loop(\(x,i).((x + 2) + (x div (4 + i))),2,x))
A247128: 5 9 13 17 22 27 31 35 39 44 49 53 57 61 66 71
((x + ~1) + loop(\(x,i).2x,(((1 - (x div 2)) mod (x + 1)) div 3),1))
A004762: 0 1 2 3 5 6 7 10 11 12 13 14 15 20 21 22
((x + ~1) * ((x * loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),x,0)) div 2))
A065088: 0 0 1 6 54 440 3975 38934 415324 4805856 60073245 807651350 11630179506 178681848696 2918470195459 50511984152070
((~x + 1) + (2 * (if (2 - (x div 4)) <= 0 then 12 else x)))
A115309: 1 2 3 4 5 6 7 8 17 16 15 14 13 12 11 10
((~2x2 + 2x) + loop(\(x,i).((2x * (1 + (2 * i))) - i),x,1))
A214396: 1 5 44 657
((x2 + ~x) * ((1 + (loop(\(x,i).(2x * i),(x + ~2),1) div 2)) div 2))
A052671: 0 0 0 6 24 240 2880 40320 645120 11612160 232243200 5109350400 122624409600 3188234649600 89270570188800 2678117105664000
loop(\(x,i).((x + 1) + (2 * ((x div 2) div (1 + ((x mod 3) div 2))))),x,1)
A018274: 1 2 3 6 13 26 39 78
loop(\(x,i).((x + 1) + ((((x + 1) * (1 + i)) div 5) mod 2)),x,1)
A003233: 1 2 4 5 6 7 9 10 12 13 14 15 17 18 20 22
loop(\(x,i).((7x + 1) - ((i mod 3) mod 2)),x,1)
A033125: 1 7 50 351 2457 17200 120401 842807 5899650 41297551 289082857 2023580000 14165060001 99155420007 694087940050 4858615580351
loop(\(x,i).((x + 1) + (((x + i) div (4 + (x div 4))) mod 2)),x,1)
A101616: 1 2 4 6 7 8 9 10 12 14 16 18 20 22 23 24
loop(\(x,i).((x + 1) + (((x + 2) mod (2 + ((x + ~1) mod 4))) div 2)),x,1)
A325663-A277620-A156541: 1 2 3 4 5 6 8 9 10 11 12 15 16 18 20 22
loop(\(x,i).(5x + ((2x + 1) mod 5)),x,1)
A037710: 1 8 42 210 1051 5258 26292 131460 657301 3286508 16432542 82162710 410813551 2054067758 10270338792 51351693960
((x + ~1) + loop(\(x,i).(2 * (1 + ((x + (x div 2)) div 4))),3,x))
A008321: 1 2 3 6 7 8 11 12 15 16 17 18 19 20 21 22
loop(\(x,i).(x * (48 - (x mod 3))),x,1)
A170728-A170680-A170632-A170584-A170536-A170488-A170440-A170392-A170344-A170296-A170248-A170200-A170152-A170104-A170056-A170008-A169540-A169492-A169444-A169396-A169348-A169300-A169252-A169204-A169156-A169108-A169060-A169012-A168964-A168916-A168868-A168820-A168772-A168724-A167978-A167862-A167644-A167100-A166740: 1 47 2162 99452 4574792 210440432 9680259872 445291954112 20483429889152 942237774900992 43342937645445632 1993775131690499072 4611686018427387903 4611686018427387903 4611686018427387903
A170766: 1 47 2162 99452 4574792 210440432 9680259872 445291954112 20483429889152 942237774900992 43342937645445632 1993775131690499072 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) + loop(\(x,i).((x + 1) - (~2 mod (1 + (x div 4)))),2,x))
A321499: 3 5 7 9 11 13 15 16 17 19 21 23 24 25 27 29
loop(\(x,i).(x * (i - ((((x + (x mod 2)) mod 5) div 2) div 2))),x,1)
A215716: 1 1 2 6 24 96 576 4032 32256 290304 2612736 28740096 344881152 4483454976 62768369664 878757175296
loop(\(x,i).(9x + ((~x + 1) mod 5)),x,1)
A037679: 1 9 83 750 6751 60759 546833 4921500 44293501 398641509 3587773583 32289962250 290609660251 2615486942259 23539382480333 211854442323000
(loop(\(x,i).3x,x,1) div (3x3 + 2x2 + 1))
A319764: 1 0 0 0 0 0 1 1 3 8 18
(~1 + loop(\(x,i).(30x + 1),2,x2))
A158672: 30 930 3630 8130 14430 22530 32430 44130 57630 72930 90030 108930 129630 152130 176430 202530
(1 + loop(\(x,i).(~19x + ~1),2,x2))
A158592: 19 380 1463 3268 5795 9044 13015 17708 23123 29260 36119 43700 52003 61028 70775 81244
(~1 + loop(\(x,i).(36x + 1),2,x2))
A158739: 36 1332 5220 11700 20772 32436 46692 63540 82980 105012 129636 156852 186660 219060 254052 291636
(~1 + loop(\(x,i).(27x + 1),2,x2))
A158645: 27 756 2943 6588 11691 18252 26271 35748 46683 59076 72927 88236 105003 123228 142911 164052
(1 + loop(\(x,i).(~23x + ~1),2,x2))
A158631: 23 552 2139 4784 8487 13248 19067 25944 33879 42872 52923 64032 76199 89424 103707 119048
(1 + loop(\(x,i).(~21x + ~1),2,x2))
A158603: 21 462 1785 3990 7077 11046 15897 21630 28245 35742 44121 53382 63525 74550 86457 99246
(1 + loop(\(x,i).(~22x + ~1),2,x2))
A158629: 22 506 1958 4378 7766 12122 17446 23738 30998 39226 48422 58586 69718 81818 94886 108922
(1 + loop(\(x,i).(~31x + ~1),2,x2))
A158675: 31 992 3875 8680 15407 24056 34627 47120 61535 77872 96131 116312 138415 162440 188387 216256
(1 + loop(\(x,i).(~28x + ~1),2,x2))
A158659: 28 812 3164 7084 12572 19628 28252 38444 50204 63532 78428 94892 112924 132524 153692 176428
(~1 + loop(\(x,i).(26x + 1),2,x2))
A158643: 26 702 2730 6110 10842 16926 24362 33150 43290 54782 67626 81822 97370 114270 132522 152126
(~1 + loop(\(x,i).(34x + 1),2,x2))
A158731: 34 1190 4658 10438 18530 28934 41650 56678 74018 93670 115634 139910 166498 195398 226610 260134
(~1 + loop(\(x,i).(33x + 1),2,x2))
A158688: 33 1122 4389 9834 17457 27258 39237 53394 69729 88242 108933 131802 156849 184074 213477 245058
((1 + (8 * (4 + (if x <= 0 then 2 else 0)))) div (x2 + 1))
A145583: 49 16 6 3
(1 + compr(\x.loop(\(x,i).(x div (2 - (((x + 1) * (x div 4)) mod 2))),x,x),x))
A263132: 1 2 3 4 6 8 11 12 16 22 24 32 43 44 48 64
(loop(\(x,i).(3 * ((x + 3) mod 7)),x,0) div 2)
A021025: 0 4 7 6 1 9 0 4 7 6 1 9 0 4 7 6
(loop(\(x,i).(1 + ((10 * (x mod 2)) + (x div 2))),x,0) div 2)
A021175: 0 0 5 8 4 7 9 5 3 2 1 6 3 7 4 2
(2 + (if ((x + 1) mod (1 + ((3 * (x div 4)) div 2))) <= 0 then 0 else 1))
A260235: 2 2 2 2 3 2 3 2 3 3 3 2 3 3 2 3
((x mod (1 + (x div (1 + (if (((x + ~1) div 2) mod 4) <= 0 then 2 else 1))))) div 2)
A239496: 0 0 0 0 0 1 1 1 1 0 1 2 2 3 3 3
((1 + (x mod 3)) div (if (x mod 11) <= 0 then 1 else 2))
A119624: 1 1 1 0 1 1 0 1 1 0 1 3 0 1 1 0
((1 + (x div (1 + ((~1 + loop(\(x,i).2x,(x + ~2),2)) mod (x + 1))))) div 2)
A325403: 0 0 1 0 1 1 1 0 2 1 1 1 1 1 4 0
(2 * loop(\(x,i).x2,1,((x + 1) - (x div ~9))))
A166259: 2 18 32 50 72 98 128 162 200 242 338 392 450 512 578 648
(if (x mod (1 + (2 * ((~x + 2) mod (1 + (2 * (1 + (x mod 2)))))))) <= 0 then 1 else 2)
A174314: 1 2 1 2 2 1 2 1 1 2 2 2 2 2 1 1
((if x <= 0 then 0 else (1 + (7 * ((~x + 1) mod 3)))) div 2)
A021139: 0 0 7 4 0 7 4 0 7 4 0 7 4 0 7 4
((1 + loop(\(x,i).10x,x,9)) div 2)
A137233: 5 45 450 4500 45000 450000 4500000 45000000 450000000 4500000000 45000000000 450000000000 4500000000000 45000000000000 450000000000000 4500000000000000
(2 * (1 + (loop(\(x,i).(3x + 7),x,1) div 5)))
A230929: 2 6 16 48 146 438 1312 3936 11810 35430 106288 318864 956594 2869782 8609344 25828032
(loop(\(x,i).(x + (x div 2)),x,29) div 2)
A120141: 14 21 32 48 72 108 162 243 364 546 819 1229 1843 2765 4147 6221
(loop(\(x,i).(x + (x div 2)),x,41) div 2)
A120145: 20 30 45 68 102 153 229 344 516 774 1161 1741 2612 3918 5877 8815
(if (x mod 4) <= 0 then (1 + (((~x2 + x) div 2) mod 5)) else 2)
A121358: 1 2 2 2 5 2 2 2 3 2 2 2 5 2 2 2
(2 * ((4 - (if (x + ~2) <= 0 then 1 else 2)) div (1 + (x mod 5))))
A141473: 6 2 2 0 0 4 2 0 0
((2 + (x mod 3)) div (if ((1 + (x div 3)) mod 3) <= 0 then 1 else 2))
A119985: 1 1 2 1 1 2 2 3 4 1 1 2 1 1 2 2
(if x <= 0 then 1 else (2 * (1 + (((x2 + ~1) div 5) mod 3))))
A082991: 1 2 2 4 2 4 4 2 2 4 4 2 4 2 2 6
(2 * (~1 + (3 * loop(\(x,i).(2x + 4),(x + 3),3))))
A304384: 310 646 1318 2662 5350 10726 21478 42982 85990 172006 344038 688102 1376230 2752486 5504998 11010022
(loop(\(x,i).(x + (x div 2)),x,35) div 2)
A120143: 17 26 39 58 87 131 196 294 441 662 993 1489 2234 3351 5026 7539
(if x <= 0 then 1 else (2 * (1 + ((8 mod (2x + ~1)) div 3))))
A076249: 1 2 2 4 2 6 6 6 6 6 6 6 6 6 6 6
(2 * loop(\(x,i).3x,(x div 2),(1 + (3 * (1 + (x mod 2))))))
A090993: 8 14 24 42 72 126 216 378 648 1134 1944 3402 5832 10206 17496 30618
(((if x <= 0 then 2 else ((~x + 1) mod 3)) * (1 + ((x + 1) div 3))) div 2)
A110355: 1 0 2 1 0 3 1 0 4 2 0 5 2 0 6 3
(((x + 1) div (1 + ((loop(\(x,i).2x,x,x) mod (x + 1)) div 3))) div 2)
A297404: 0 1 1 2 1 1 1 4 2 1 1 3 1 1 1 8
(2 * (1 + (6 * (5 + loop(\(x,i).2x,x,1)))))
A305265: 74 86 110 158 254 446 830 1598 3134 6206 12350 24638 49214 98366 196670 393278
(loop(\(x,i).(x + (x div 2)),x,47) div 2)
A120147: 23 35 52 78 117 176 264 396 594 891 1336 2004 3006 4509 6764 10146
(loop(\(x,i).2x,(x - (3 * (2 + (x div 8)))),1) div 2)
A251760: 0 0 0 0 0 0 0 1 0 0 1 2 4 8 16 32
(loop(\(x,i).3x,x,1) mod 46)
A070363: 1 3 9 27 35 13 39 25 29 41 31 1 3 9 27 35
((loop(\(x,i).4x,(x + ~1),1) mod 13) div 2)
A021466: 0 0 2 1 6 4 5 0 2 1 6 4 5 0 2 1
(~2 + (loop(\(x,i).4x,(x + ~1),2) mod 13))
A021158: 0 0 6 4 9 3 5 0 6 4 9 3 5 0 6 4
(if x <= 0 then 1 else (2 + ((~1 + (x div 2)) mod (1 + ((2 + (x div 2)) div 3)))))
A328577: 1 2 2 2 3 3 2 2 2 2 3 3 4 4 4 4
loop(\(x,i).x5,1,(12x + 2))
A017549: 32 537824 11881376 79235168 312500000 916132832 2219006624 4704270176 9039207968 16105100000 27027081632 43204003424 66338290976 98465804768 141985700000 199690286432
(loop(\(x,i).2x,((x + 1) div 2),1) div (2 * (1 + (3 * (x div 2)))))
A240867: 0 1 0 0 0 0 0 0 0 1 1 2 1 3 2 5
((1 + (3 * (x + loop(\(x,i).i,(x + ~9),1)))) div 2)
A194383: 2 3 5 6 8 9 11 12 14 15 17 20 23 26 29 32
((if (x mod 2) <= 0 then (2 + ((x div 2) mod 2)) else 1) - ((1 + (x mod 3)) mod 2))
A117199: 1 1 2 0 2 0 2 1 1 0 3 0 1 1 2 0
(if x <= 0 then 1 else (((1 + (x div 2)) div 2) - ((x div (1 + (x mod 3))) mod 2)))
A029217: 1 0 1 0 1 0 2 1 2 1 2 2 3 3 4 3
((1 + (loop(\(x,i).(x * (2 + i)),4,(x + 1)) div (x + 3))) div 2)
A069976: 60 90 108 120 129 135 140 144 147 150 152 154 156 158 159 160
(if x <= 0 then 1 else (2 * ((x + 1) - ((~4x + 2) div (x + 3)))))
A176587-A176552: 1 6 10 12 14 18 20 22 24 26 28 30 34 36 38 40
(loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(2x + 1),1) div 2)
A274822: 1 7 66
A065097: 1 7 66 715 8398 104006 1337220 17678835 238819350 3282060210 45741281820 644952073662 9183676536076 131873975875180 1907493251046152 27767032438524099
((if (x mod 4) <= 0 then 0 else (1 + (8 mod (1 + (x div 2))))) div 2)
A089311-A086784: 0 0 0 0 0 1 0 0 0 2 1 1 0 1 0 0
((if x <= 0 then 2 else (1 + ((2 * ((x div 2) - (x mod 2))) mod (1 + (x div 2))))) div 2)
A029327: 1 0 0 0 1 1 1 0 2 1 2 1 3 2 3 2
((1 + loop(\(x,i).2x,x,(13 - (x mod 2)))) div 2)
A223417: 7 12 26 48 104 192 416 768 1664 3072 6656 12288 26624 49152 106496 196608
((1 + loop(\(x,i).(6 * (4x - (x mod 2))),x,1)) div 2)
A067426: 1 9 216 5184 124416 2985984 71663616 1719926784 41278242816 990677827584 23776267862016 570630428688384 13695130288521216 328683126924509184 4611686018427387903 4611686018427387903
((1 + loop(\(x,i).((4x div (1 + i)) * (1 + (2 * i))),x,1)) div 2)
A082143: 1 3 20 140 1008 7392 54912 411840 3111680 23648768 180590592 1384527872 10650214400 82158796800 635361361920 4924050554880
((1 + loop(\(x,i).(2 * (x + (2 * (x - (x div ~4))))),x,1)) div 2)
A055270: 1 5 36 252 1764 12348 86436 605052 4235364 29647548 207532836 1452729852 10169108964 71183762748 498286339236 3488004374652
((1 + loop(\(x,i).(x5 + 5x4 + 6x3),x,1)) div 2)
A262187: 1 6 181440 4611686018427387903
(x - (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))))
A171462: 0 1 2 2 4 4 6 4 6 8 10 8 12 12 12 8
(loop(\(x,i).(1 + (3 * (2x - ((x div 2) mod 2)))),(x + 1),1) div 2)
A037669: 3 20 120 723 4340 26040 156243 937460 5624760 33748563 202491380 1214948280 7289689683 43738138100 262428828600 1574572971603
(loop(\(x,i).((5x + 1) + ((x div 2) mod 2)),(x + 1),1) div 2)
A037661: 3 16 80 403 2016 10080 50403 252016 1260080 6300403 31502016 157510080 787550403 3937752016 19688760080 98443800403
(loop(\(x,i).(6x + ((x + ~1) mod 3)),(x + 1),1) div 2)
A037662: 3 19 114 687 4123 24738 148431 890587 5343522 32061135 192366811 1154200866 6925205199 41551231195 249307387170 1495844323023
(loop(\(x,i).(5x + ((i * i) mod 3)),(x + 1),1) div 2)
A037654: 3 15 77 388 1940 9702 48513 242565 1212827 6064138 30320690 151603452 758017263 3790086315 18950431577 94752157888
(2 * (~1 + ((x + 1) * (2 + (if (~2 + (x div 5)) <= 0 then 0 else 2)))))
A132417-A103747: 2 6 10 14 18 22 26 30 34 38 42 46 50 54 58 126
((8x + 6) * loop(\(x,i).6x,x,2))
A268899: 12 168 1584 12960 98496 715392 5038848 34712064 235146240 1572120576 10400182272 68205846528 444063596544 2873352683520 18493942726656 118486616113152
loop(\(x,i).x5,1,(8x + 6))
A017141: 7776 537824 5153632 24300000 79235168 205962976 459165024 916132832 1680700000 2887174368 4704270176 7339040224 11040808032 16105100000 22877577568 31757969376
((1 + ((loop(\(x,i).(3x + ~1),x,1) + (x mod 2)) mod (x + 1))) div 2)
A276976: 0 1 1 2 1 2 1 4 3 2 1 2 1 2 3 4
(loop(\(x,i).(((2x * (1 + (2 * i))) div (2 + i)) * i),(x + 1),1) div 2)
A102693: 1 5 42 504 7920 154440 3603600 98017920 3047466240 106661318400 4151586700800 177925144320000 8326896754176000 422590010274432000 4611686018427387903 4611686018427387903
((1 + loop(\(x,i).(x + ((x + 1) div 2) - (x div (~1 + (2 * i)))),x,1)) div 2)
A000930: 1 1 1 2 3 4 6 9 13 19 28 41 60 88 129 189
(2 * (1 + (if ((x + 1) mod (1 - (x div ~5))) <= 0 then 1 else 2)))
A275161: 4 4 6 4 6 4 6 6 4 6 6 4 6 6 6 4
((1 + ((x mod (1 + (loop(\(x,i).(x2 + 2x),2,2) mod (x + 1)))) div 2)) div 2)
A065339: 0 0 1 0 0 1 1 0 2 0 1 1 0 1 1 0
((1 + ((1 + ((((x + 2) * (if x <= 0 then 2 else (x div 2))) div 2) div 2)) div 2)) div 2)
A058747-A034322: 1 0 1 1 1 1 2 2 3 3 4 4 6 6 7 8
(if x <= 0 then 1 else (2 * (1 + ((x div (1 + (2 * (4 - (x div 2))))) mod 2))))
A318465: 1 2 2 2 2 4 2 2 2 4 2 4 2 4 4 4
((8x + 8) - (if (x + ~10) <= 0 then 1 else 2))
A059562: 7 15 23 31 39 47 55 63 71 79 87 94 102 110 118 126
(if x <= 0 then 1 else (2 * (2x - ((~x + 3) div 7))))
A311586: 1 4 8 12 18 22 26 30 34 38 42 48 52 56 60 64
(2 + (if x <= 0 then 2 else (1 + (((x + (x2 div 3)) mod 3) mod 2))))
A023402: 4 4 3 3 3 4 3 3 3 3 4 3 3 3 4 3
(2 + ((x mod (~1 + (2 * (x div 3)))) mod 2) - ((if x <= 0 then 1 else x) mod 2))
A128428: 1 1 2 1 2 1 2 2 2 1 2 2 3 1 2 1
((1 + ((1 + (loop(\(x,i).(x + (x div 2)),(x + ~2),2) div (x + 2))) div 2)) div 2)
A017900-A017856-A017855: 1 0 0 0 0 0 1 1 1 1 1 1 2 3 4 5
loop(\(x,i).2x,(1 + (2 * ((4x + 1) div (x + 3)))),2)
A339570: 4 16 16 64 64 64 64 64 256 256 256 256 256 256 256 256
((x + ~1) mod (2 * (1 + (((1 - loop(\(x,i).2x,x,2)) mod (x + 1)) div 2))))
A058026: 1 0 1 0 3 0 5 0 3 0 9 0 11 0 3 0
(((if (~x + 2) <= 0 then (2 - (x div ~2)) else 1) * (1 + ((x + 1) div 2))) div 2)
A333616: 0 1 3 6 6 10 10 15 15 21 21 28 28 36 36 45
((1 + ((loop(\(x,i).2x,(x + (2 * (x mod 2))),x) mod (x + 1)) div 2)) div 2)
A140129: 0 0 1 0 1 1 2 0 1 1 3 1 3 2 3 0
(2 * (1 + ((if x <= 0 then 2 else (x mod (2 + (x mod (1 + (x div 3)))))) div 2)))
A303577: 4 2 2 2 2 4 2 2 2 2 4 2 2 4 4 2
(x div (2 + (x div (1 + (if (x mod 2) <= 0 then ((1 + (x div 4)) mod 2) else 2)))))
A329981: 0 0 0 1 0 1 0 1 1 1 1 2 0 2 0 2
(if x <= 0 then 1 else (2 * (1 + (((x2 mod (x + 5)) div 2) mod 2))))
A072048: 1 2 2 2 4 2 4 2 2 4 4 2 2 4 4 2
(if x <= 0 then 1 else (2 * (1 + (x2 div (2 + (x mod (2 + (x mod 3))))))))
A222011: 1 2 4 8
A192078: 1 2 4 8 12 18 38
((if x <= 0 then 2 else (1 + ((((x2 div 2) mod (x + 3)) div 2) div 2))) div 2)
A280152-A178691: 1 0 0 1 0 1 0 1 1 1 1 1 2 1 2 1
((x + 4) div (2 + (if (~x + 2) <= 0 then (4 * (1 + (x mod 2))) else 1)))
A316384: 1 1 1 0 1 0 1 1 2 1 2 1 2 1 3 1
(((x + 3) mod (1 + (2 * (2 + (if (x mod 3) <= 0 then 0 else 2))))) mod 2)
A118251: 1 0 1 1 1 0 0 1 0 0 0 1 0 1 0 1
((if x <= 0 then 2 else (1 + ((x div 2) div (4 - (((x + ~1) div 2) div 2))))) div 2)
A017854: 1 0 0 0 0 0 1 1 1 1 1 1 2 3 4 4
(if x <= 0 then 1 else (2 + (2x div (5 + ((x div 4) mod 2)))))
A028827: 1 2 2 3 3 3 4 4 5 5 6 6 6 6 6 7
((if (x + ~1) <= 0 then 0 else (1 + (x mod (2 + (x mod (2 + ((x div 2) mod 2))))))) div 2)
A090418: 0 0 1 1 0 1 0 1 0 0 1 2 0 1 1 1
(2 * (1 + (2 * (4 + loop(\(x,i).(x3 + x2),x2,2)))))
A116300: 26 66 4611686018427387903 4611686018427387903 4611686018427387903
((if x <= 0 then 2 else (2x mod (~1 + (2 * (((~x + 2) div 2) mod 4))))) div 2)
A107652: 1 0 0 0 1 0 0 0 0 0 0 1 2 1 0 0
(~2 + (if x <= 0 then 1 else (72x + ~9)))
A063337: ~1 61 133 205 277 349 421 493 565 637 709 781 853 925 997 1069
(if x <= 0 then 1 else (2 * (2x - ((~2x + 4) div 9))))
A312484: 1 4 8 14 18 22 26 32 36 40 44 48 54 58 62 66
(~2 + loop(\(x,i).(x4 + ~x3 + ~x2),x,9))
A062644: 7 5749
loop(\(x,i).x2,1,(2 + ((2x + 1) div (3 + (x div 4)))))
A140978: 4 9 9 16 16 16 25 25 25 25 36 36 36 36 36 49
(2 - (if x <= 0 then 2 else ((x - ((~1 + (x2 div 2)) div 5)) div 2)))
A316079: 0 1 1 1 1 1 1 1 1 1 2 2 3 4 5 6
(loop(\(x,i).(x + (x div 2)),x,50) div 2)
A120148: 25 37 56 84 126 189 283 425 637 956 1434 2151 3226 4839 7259 10888
(if x <= 0 then 1 else (2 * (3x - ((2x + 2) div 5))))
A315311: 1 6 10 16 20 26 32 36 42 46 52 58 62 68 72 78
(2 + ((x - (2 * (if (x mod 4) <= 0 then 2 else (x mod 2)))) div 5))
A335898: 1 1 2 2 2 2 3 3 2 3 4 3 3 4 4 4
(if x <= 0 then 1 else (2 + (((3x2 + x) div 2) div 5)))
A193622: 1 2 3 5 7 10
A136413: 1 2 3 5 7 10 13 17 22 27 33 39 46 54 62 71
((loop(\(x,i).(2 * (x - (i mod 2))),x,2) div 3) mod 10)
A167280: 0 0 1 2 4 7 4 8 7 4 8 5 0 0 1 2
((~1 + loop(\(x,i).(2x - ((i div 2) mod 2)),x,2)) mod 10)
A160590: 1 3 6 2 5 1 2 4 9 9 8 6 3 7 4 8
(((x + 1) + (if (x + ~3) <= 0 then x else 4)) mod 10)
A127050: 1 3 5 7 9 0 1 2 3 4 5 6 7 8 9 0
(loop(\(x,i).(x + (((2 + i) * (1 + i)) div 2)),x,1) mod 10)
A193108: 1 4 0 0 5 6 4 0 5 0 6 4 5 0 0 6
(10 * loop(\(x,i).(x div 3),(x div 2),(2 + (x mod 2))))
A171908: 20 30 0 10 0 0
((if ((x div 5) mod 2) <= 0 then x else ~x) mod 10)
A271751: 0 1 2 3 4 5 4 3 2 1 0 1 2 3 4 5
(10 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A175224: 10 11 13 15 19 21 25 27 31 37 39 45 49 51 55 61
(2 * (x - ((0 - (if (~4 + (x div 2)) <= 0 then 1 else x)) div 5)))
A272670: 2 4 6 8 10 12 14 16 18 20 24 28 30 32 34 36
((((if (x mod 2) <= 0 then (~x + 2) else x) mod 3) + (x div 5)) div 2)
A029381: 1 0 0 0 0 1 1 1 0 0 1 2 2 1 1 1
(loop(\(x,i).(3x + 1),x,3) mod (2 + (x div 5)))
A029211: 1 0 1 0 1 1 1 1 1 1 3 2 3 2 3 4
((if ((x + ~1) mod 5) <= 0 then 0 else 1) + (2 * (x div 5)))
A117451: 1 0 1 1 1 3 2 3 3 3 5 4 5 5 5 7
((1 + (loop(\(x,i).((x + 1) + (((x div 2) + i) div 4)),x,2) div 2)) div 2)
A298603: 1 1 1 2 2 3 4 5 6 7 9 11 13 16 19 22
(2 + (((x + 1) div 7) + (if (~x + 4) <= 0 then 2 else 1)))
A006671: 3 3 3 3 4 4 5 5 5 5 5 5 5 6 6 6
(if x <= 0 then 1 else (2 * ((2x + 1) - ((~x2 + 1) div (x + 4)))))
A315734: 1 6 12 18 22 28 34 40 46 52 58 62 68 74 80 86
loop(\(x,i).x6,1,(8x + 2))
A017094: 64 1000000 34012224 308915776 1544804416 5489031744 15625000000 38068692544 82653950016 164206490176 304006671424 531441000000 885842380864 1418519112256 2194972623936 3297303959104
(if x <= 0 then 1 else (2 * (1 - (x mod (~1 + (((x div 3) - (x div 2)) div 2))))))
A331109-A286324: 1 2 2 2 2 4 2 4 2 4 2 4 2 4 4 4
(2 * ((1 + loop(\(x,i).2x,(x + ~1),(x2 mod 3))) div 3))
A087464: 0 0 2 0 6 10 0 42 86 0 342 682 0 2730 5462 0
(2 * ((1 + (4 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 3))
A036554: 2 6 8 10 14 18 22 24 26 30 32 34 38 40 42 46
((3 * (loop(\(x,i).4x,x,1) div (1 + (2 * (x mod 2))))) div 2)
A266984: 1 1 24 31 384 511 6144 8191 98304 131071 1572864 2097151 25165824 33554431 402653184 536870911
(~2 + (3 * (~1 + (2 * (x + loop(\(x,i).i,(((x + ~1) div 2) div 2),1))))))
A225227: 1 7 13
A260682: 1 7 13 19 25 31 37 43 49 61 67 73 79 91 97 103
(((3x + 3) * (1 + (3 * (2 + (if x <= 0 then 2 else 0))))) div 2)
A167998: 19 21 31 42 52 63 73 84 94 105 115 126 136 147 157 168
(2 * (loop(\(x,i).(x3 + ~x2),1,(2x2 + 2x)) div 3))
A265021: 0 32 1056 8832 41600 141600 390432 928256 1976832 3866400 7066400 12220032 20182656 32064032 49274400 73574400
(2 - (if x <= 0 then 1 else ((x mod 2) - ((x mod (x - ((x + 1) mod 3))) div 2))))
A076755: 1 1 2 1 2 1 2 2 2 1 3 1 2 2 2 1
(2 * ((2 * (1 + (2 * (if (x + ~4) <= 0 then x else (x + 1))))) div 3))
A162648: 0 4 6 8 12 16 20 22 24 28 30 32 36 38 40 44
((3 * ((3 * ((x + 1) + (if (x + ~2) <= 0 then 1 else 2))) div 2)) div 2)
A085802: 4 6 9 13 15 18 19 22 24 27 28 31 33 36 37 40
(2 + (loop(\(x,i).((x + 2) + (x div 3)),(x + 3),2) div 3))
A005427: 5 7 9 12 16 22 29 39 52 69 92 123 164 218 291 388
(2 + (loop(\(x,i).(x3 + 2x),1,(4x + 2)) div 3))
A167498: 6 78 342 926 1958 3566 5878 9022 13126 18318 24726 32478 41702 52526 65078 79486
((loop(\(x,i).(3x + 1),x,1) + (((x + ~1) div 2) mod 3)) div 2)
A132353: 1 2 6 20 61 183 547 1640 4920 14762 44287 132861 398581 1195742 3587226 10761680
((x + 2) mod (2 + (if (x + ~1) <= 0 then 0 else (3 * (x mod ~4)))))
A221702: 0 1 0 0 0 0 0 0 0 ~3 0 0 0 ~6 0 0
(~2 + (3 * (~2 + loop(\(x,i).10x,(x + 1),2))))
A100413: 52 592 5992 59992 599992 5999992 59999992 599999992 5999999992 59999999992 599999999992 5999999999992 59999999999992 599999999999992 5999999999999992 59999999999999992
((3 * (x - ((if x <= 0 then 1 else x) div (~2 + ((~x + 2) div 4))))) div 2)
A286692: 1 3 4 6 9 10 12 13 15 18 19 21 22 24 25 27
(2 * ((4 * (if (~4 + (x div 2)) <= 0 then x else (x + 2))) div 3))
A036990: 0 2 4 8 10 12 16 18 20 24 32 34 36 40 42 44
(2 + (2x div 3) - (if x <= 0 then 1 else (x div 12)))
A099802: 1 2 3 4 4 5 6 6 7 8 8 9 9 9 10 11
loop(\(x,i).2x,x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)))
A135569: 0 2 4 16 16 64 128 384 256 1024 2048 6144 8192 24576 49152 131072
(1 - (if (x + ~1) <= 0 then x else ((((x2 + (x div 2)) div 2) div 3) mod 2)))
A266588: 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 1
((3 + ((x * (1 + ((if (x mod 2) <= 0 then 2 else x) mod 4))) div 2)) div 2)
A108355: 1 2 3 4 4 4 6 8 7 6 9 12 10 8 12 16
((3 * (2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) div 2)
A168565: 4 7 10 16 19 25 28 34 43 46 55 61 64 70 79 88
(2 + ((2 * compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x)) div 3))
A296058: 2 4 5 8 9 12 13 16 20 21 25 28 29 32 36 40
loop(\(x,i).x6,1,(6x + 2))
A016938: 64 262144 7529536 64000000 308915776 1073741824 3010936384 7256313856 15625000000 30840979456 56800235584 98867482624 164206490176 262144000000 404567235136 606355001344
((3 * (3x + (if (~2 + (x div 3)) <= 0 then 2 else 1))) div 2)
A330185: 3 7 12 16 21 25 30 34 39 42 46 51 55 60 64 69
((if x <= 0 then 2 else (1 - ((((~x + 2) div 4) * (x div 2)) div 3))) div 2)
A029249: 1 0 0 1 1 1 1 1 2 2 2 3 3 3 4 5
((((if (x mod 2) <= 0 then (~x + 2) else x) mod 3) + ((x div 2) div 3)) div 2)
A025876: 1 0 0 0 0 1 1 1 0 0 1 1 2 1 1 1
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) mod 6)
A259667: 1 1 2 5 2 0 0 3 2 2 2 4 4 4 0 3
((loop(\(x,i).6x,(x + 1),1) div (x + 1)) mod 6)
A308347: 0 0 0 0 1 0 0 0 0 3 0 0 0 2 2 0
((x + 6) - (if x <= 0 then 1 else (~2 + (((2 - (x div 2)) div 2) div 2))))
A093711: 5 9 10 11 12 13 15 16 17 18 19 20 21 22 24 25
loop(\(x,i).(x + (5x div (1 + i))),2x,6)
A053127: 6 56 252 792 2002 4368 8568 15504 26334 42504 65780 98280 142506 201376 278256 376992
((if (x mod 8) <= 0 then 0 else (x + (x mod 4))) div 6)
A330956: 0 0 0 1 0 1 1 1 0 1 2 2 2 2 2 3
(2 + ((x + (if ((x2 + ~x) mod (1 + (x div 2))) <= 0 then 0 else 1)) mod 3))
A107795: 2 3 4 2 3 2 3 4 2 3 3 2 3 4 2 3
(2 + ((if (((2x mod (2 + (x div 2))) div 2) mod 2) <= 0 then 1 else x) mod 3))
A332875: 3 3 3 3 3 4 2 3 3 3 3 3 3 3 3 2
(if x <= 0 then 1 else (2 * (x - (((~x + ~1) + ((x div 4) mod 2)) div 3))))
A231407: 1 4 6
A199536: 1 4 6 10 12 14 16 20 22 26 28 30 32 36 38 40
(if x <= 0 then 1 else (2 * (2x - ((~x + ((x div 2) mod 3)) div 3))))
A315178: 1 6 10 14 18 22 28 34 38 42 46 50 56 62 66 70
loop(\(x,i).x5,1,(9x + 2))
A017189: 32 161051 3200000 20511149 79235168 229345007 550731776 1160290625 2219006624 3939040643 6590815232 10510100501 16105100000 23863536599 34359738368 48261724457
((if x <= 0 then 1 else 2x) - (((x + (2 * (x div 3))) div 3) mod 2))
A191535-A100598: 1 2 4 5 8 10
A131396: 1 2 4 5 8 10 11 13 16 17 19 21 24 25 27 30
((3 * (x + ((x + (if (~2 + (x div 3)) <= 0 then 2 else 1)) div 2))) div 2)
A184903: 1 3 6 7 10 12 15 16 19 21 22 25 27 30 31 34
(x - (((if (x mod 9) <= 0 then 0 else 2) + (x div 3)) div 2))
A065328: 0 0 1 2 3 4 4 5 6 8 8 9 9 10 11 12
(if (x + ~1) <= 0 then (x + 1) else (((~x + 2) div ((x + 2) - (x div 3))) mod 2))
A194301: 1 2 0 1 1 1 1 1 1 1 1 1 1 1 1 0
((if ((x2 + 2x) mod 6) <= 0 then x else 2) div (2 + (x div 3)))
A069851: 0 1 1 0 1 0 1 0 0 0 2 0 2 0 0 0
(2 + (if (x mod 2) <= 0 then (x2 mod 7) else (x mod 3)))
A224910: 2 3 6 2 4 4 3 3 3
(((if ((x + 1) mod (1 + (x div 4))) <= 0 then 0 else 2) + (x mod 3)) div 2)
A327406-A284203-A005087: 0 0 1 0 1 1 1 0 1 1 1 1 1 1 2 0
((2 + (3 * (x + (if (x + ~2) <= 0 then 1 else 2))) - (x mod 3)) div 2)
A184810: 2 3 4 8 9 10 13 14 15 17 18 19 22 23 24 26
(1 - (((if (x mod 2) <= 0 then x else (~x + 2)) mod 3) + ((x mod 3) div 2)))
A101676: 1 0 ~2 ~1 0 0 1 0 ~2 ~1 0 0 1 0 ~2 ~1
((if ((x + 1) mod (1 + (x div 4))) <= 0 then 1 else 2) + ((x mod 3) div 2))
A099812-A080942: 1 1 2 1 2 2 2 1 2 2 2 2 2 2 3 1
(2 * (1 + (((x2 + x) + loop(\(x,i).(3x + ~1),x,2)) div 2)))
A057583: 4 8 22 54 144
((1 + ((9x + 3) * (2 + (if x <= 0 then 1 else x)))) div 2)
A000338: 5 18 42 75 117 168 228 297 375 462 558 663 777 900 1032 1173
((1 + (loop(\(x,i).(1 + ((x2 + ~x) div 8)),2,x) div 2)) div 2)
A069907: 0 0 0 0 0 0 1 1 2 3 4 6 9 12 16 22
(loop(\(x,i).(x2 + x),1,((x + 1) - ((~x + ((x div 2) mod 2)) div 2))) div 2)
A272398: 1 6 10 15 28 45 55 66 91 120 136 153 190 231 253 276
(if x <= 0 then 1 else (2 + ((5x2 + 5x) div (x + 3))))
A311208: 1 4 8 12 16 20 25 30 34 39 44 49 54 58 63 68
((2x2 + 8x + 6) * loop(\(x,i).x2,2,(2x + ~1)))
A323516: 6 16 2430
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(x + 3)) div 2)
A189176: 1 2 5 15 49 168 594 2145 7865 29172 109174 411502 1560090 5943200 22732740 87253605
loop(\(x,i).((10x + 1) + (x mod 2)),(2x + 1),2)
A153848: 21 2121 212121 21212121 2121212121 212121212121 21212121212121 2121212121212121 212121212121212121 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * loop(\(x,i).((6x + 3) * (2 + i)),2,(2x + 1)))
A157266: 1320 3048 4776 6504 8232 9960 11688 13416 15144 16872 18600 20328 22056 23784 25512 27240
(if x <= 0 then 1 else (2 * (2x - ((1 - (x2 div 2)) div (2x + 1)))))
A310372: 1 4 10 14 18 22 28 32 36 42 46 50 54 60 64 68
((4x + 2) + (if x <= 0 then 1 else (x2 div (3x + 4))))
A259646: 3 6 10 14 19 23 27 31 36 40 44 49 53 57 62 66
(if x <= 0 then 1 else (2 + ((3 * (1 - (2 * (x mod 2)))) mod (2x + ~1))))
A267046: 1 2 2 4 5 8 5 12 5 16 5 20 5 24 5 28
(if (x + ~2) <= 0 then 1 else ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2))
A073253: 1 1 1 0 1 0 0 1 1 0 0 1 2 1 0 0
((1 + (x div ((if (x mod 3) <= 0 then 2 else 1) + (x mod 2))) - (x mod 2)) div 2)
A055684: 0 0 1 0 2 1 2 1 4 1 5 2 3 3 7 2
(2 * (1 + compr(\x.(~1 + (x mod (~1 + (loop(\(x,i).2x,x,x) mod (x + 1))))),x)))
A138929: 2 4 6 8 10 14 16 18 22 26 32 34 38 46 50 54
(((x + 1) + (if (x mod 4) <= 0 then (x mod 9) else 1)) div 2)
A140472: 0 1 2 2 4 3 4 4 8 5 6 6 8 7 8 8
loop(\(x,i).x5,1,(10x + 2))
A017297: 32 248832 5153632 33554432 130691232 380204032 916132832 1934917632 3707398432 6590815232 11040808032 17623416832 27027081632 40074642432 57735339232 81136812032
(1 - (loop(\(x,i).(4x - (8 div (x + 1))),x,1) div 2))
A343164: 1 1 5 16 61 239
(1 - ((~x + 1) div (2 + (if ((x2 + 2x) mod 6) <= 0 then x else 1))))
A068324: 1 1 2 2 2 3 2 3 4 4 2 5 2 5 6 6
(2 * ((x + ~1) + (2 * (if (~4 + (x div 2)) <= 0 then 1 else (x div 4)))))
A194402: 2 4 6 8 10 12 14 16 18 20 26 28 34 36 38 40
(2 * (1 + loop(\(x,i).(x + 1),(~4 + ((x + ((x div 2) mod 2)) div 2)),x)))
A234521-A085125: 2 4 6 8 10 12 14 16 18 20 24 28 30 32 36 40
((x + 3) - loop(\(x,i).(x + ((x div (~3 + (x mod 2))) mod 2)),2,x))
A106601: 3 1 2 3 3 2 3 3 1 2 3 3 3 1 2 3
(2 - loop(\(x,i).(x - ((~1 + i) mod 13)),(x + 1),2))
A268291: 0 1 3 6 10 15 21 28 36 45 55 66 78 78 79 81
((x + 2) div (2 + (loop(\(x,i).4x,(x + 3),1) mod (x + 1))))
A318622: 1 1 1 2 1 1 2 4 1 1 1 2 1 2 2 8
(((x + 1) * loop(\(x,i).((x + 1) + (4 * (i * i))),(x + 1),1)) div 2)
A213846: 3 23 90 250 565 1113 1988 3300 5175 7755 11198 15678 21385 28525 37320 48008
(((x + 1) * (1 + (if ((x + 1) mod (2 + (x mod 3))) <= 0 then 0 else 2))) div 2)
A026217-A026197-A026178: 1 3 4 2 7 9 10 12 13 5 16 6 19 21 22 8
(((x + 1) * (if (~x + 2) <= 0 then (2 + ((2 * (x div 2)) div 3)) else 1)) div 2)
A140208: 0 1 3 4 7 9 14 16 18 20 27 30 39 42 45 48
((if x <= 0 then 2 else ((1 + ((x * (x mod 2)) mod 8)) mod (x + 1))) div 2)
A263396: 1 0 0 0 0 0 0 0 0 1 0 2 0 3 0 4
(((3 * (if (x2 mod (x + 4)) <= 0 then 2 else 1)) mod (x + 1)) div 2)
A049639: 0 0 0 1 0 1 1 1 1 1 1 1 3 1 1 1
(x div (2 + (loop(\(x,i).2x,((x + 2) mod 4),3) mod (x + 1))))
A229878: 0 0 1 0 1 2
A037897: 0 0 1 0 1 2 1 0 1 1 2 1 0 1 2 1
(((x + 1) * (1 + (x * (2x + (if (x mod 2) <= 0 then 1 else 4))))) div 2)
A342873: 0 7 16 62 92 213 276 508 616 995 1160 1722 1956 2737 3052 4088
(loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + 1),(x + 1)) div 2)
A002054: 1 5 21 84 330 1287 5005 19448 75582 293930 1144066 4457400 17383860 67863915 265182525 1037158320
(((x + 1) * (loop(\(x,i).(x3 + x2),1,(x + 4)) div 2)) div 2)
A005565: 20 75 189 392 720 1215 1925 2904 4212 5915 8085 10800 14144 18207 23085 28880
(((x2 + 3x + 2) * (1 + loop(\(x,i).(x2 + ~1),2,4))) div 2)
A027470: 225 675 1350 2250 3375 4725 6300 8100 10125 12375 14850 17550 20475 23625 27000 30600
(loop(\(x,i).(2x3 + 4x2 + ~x),1,(x2 + 3x + 2)) div 2)
A249961: 15 285 2010 8790 28785 77595 181860 383580 745155 1355145 2334750 3845010 6094725 9349095 13939080 20271480
loop(\(x,i).x6,1,((x2 + 3x + 2) div 2))
A059978: 1 729 46656 1000000 11390625 85766121 481890304 2176782336 8303765625 27680640625 82653950016 225199600704 567869252041 1340095640625 2985984000000 6327518887936
(x div ((x + 2) div (2 + (loop(\(x,i).x3,2,2x) mod (x + 1)))))
A075423: 0 1 2 1 4 5 6 1 2 9 10 5 12 13 14 1
((2x + 3) + (((x + ~1) * (if x <= 0 then 2 else (x * (x div 2)))) div 2))
A053614: 2 5 8 12 23 33
((2x + 2) + (if x <= 0 then 1 else (2 + ((x mod (~3 + (x mod 2))) mod 2))))
A097270: 3 7 9 11 12 15 16 19 21 23 24 27 28 31 33 35
((2x + 2) + (if x <= 0 then 1 else (x - (x2 div (2x + 8)))))
A137910: 3 5 8 11 13 16 19 21 24 26 29 31 34 37 39 42
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod (2x + 2))
A192327: 0 3 5 7 1 1 3 3 5 9 9 13 15 15 17 21
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(x div 2),((x + 1) mod 2))
A126120: 1 0 1 0 2 0 5 0 14 0 42 0 132 0 429 0
(~2 + loop(\(x,i).((x + 2) - (x div ~5)),4,(x + ~1)))
A169870: 9 10 14 15 17 20 21
(((x + ~1) * loop(\(x,i).11x,(x + ~2),x)) div 2)
A081141: 0 0 1 33 726 13310 219615 3382071 49603708 701538156 9646149645 129687123005 1711870023666 22254310307658 285596982281611 3624884775112755
((23x2 + 1) * (if x <= 0 then 1 else 2))
A005911: 1 48 186 416 738 1152 1658 2256 2946 3728 4602 5568 6626 7776 9018 10352
(((x mod (~1 + (((~x + 2) * (x div 2)) div 3))) mod 2) + (if x <= 0 then 1 else 2))
A049237: 1 2 2 3 2 3 2 3 3 2 3 3 3 2 3 3
(((((2x + ~2) mod (4 + (x div 2))) div 2) div 2) + (if x <= 0 then 1 else 2))
A278744: 1 2 2 3 2 2 2 3 3 2 2 2 2 3 3 3
(x + (((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2) + (if x <= 0 then 1 else 2)))
A229109: 1 3 4 5 6 8 8 9 10 12 12 14 14 16 17 17
(29x2 + (if x <= 0 then 1 else 2))
A010019: 1 31 118 263 466 727 1046 1423 1858 2351 2902 3511 4178 4903 5686 6527
(loop(\(x,i).(x + (((1 + (5 * i)) * (1 + i)) div 2)),x,1) div 2)
A212982: 0 3 11 27 53 92 146 218 310 425 565 733 931 1162 1428 1732
((2x2 + 2) * loop(\(x,i).(x * ((~1 + (4 * i)) * i)),x,1))
A060942: 2 12 420 27720
(~4 + loop(\(x,i).(10x + 15),(x + 1),0))
A205086: 11 161 1661 16661 166661 1666661 16666661 166666661 1666666661 16666666661 166666666661 1666666666661 16666666666661 166666666666661 1666666666666661 16666666666666661
((x + 1) div (2 + ((x + 1) div (2 + (if (x mod (2 + (x mod 2))) <= 0 then 2 else 0)))))
A167866: 0 0 1 1 1 1 2 1 2 2 2 1 2 1 3 2
(1 - (2 * (loop(\(x,i).((3x + ~1) + (x mod 3)),x,0) div 2)))
A046631: 1 3 3 7 21 57 169 507 1515 4543 13629 40881 122641 367923 1103763 3311287
(1 - (2 * (loop(\(x,i).(2x - ((1 + (x div 2)) mod 4)),x,0) div 2)))
A133190: 1 3 3 5 13 27 51 101 205 411 819 1637 3277 6555 13107 26213
(if x <= 0 then 1 else (x div (4 + (x div (1 + ((x + ~1) mod 5))))))
A029393: 1 0 0 0 0 1 0 1 1 1 1 0 1 1 2 2
((if x <= 0 then 1 else x) - ((((x + 1) - ((x div 2) mod 5)) div 2) div 2))
A006162: 1 1 2 3 4 4 5 6 7 8 8 8 9 10 11 12
(2 + ((x - loop(\(x,i).2x,((x - (x div 3)) div 3),1)) div 2))
A194339: 1 2 2 3 3 3 4 4 4 4 5 5 6 4 5 5
(if x <= 0 then 1 else (2 + (((x + 1) div (1 + (3 * (x mod 3)))) mod 2)))
A252229: 1 2 2 2 3 2 3 2 3 2 2 3 3 3 2 2
(2 + (((x + ~1) div (if ((x div 2) mod 3) <= 0 then 1 else 2)) mod 2) - (x mod 2))
A161916: 3 1 2 2 3 1 3 1 3 1 2 2 3 1 2 2
(if x <= 0 then 1 else (2 * (x - (((2x + ~1) mod (1 + (x div 3))) div 2))))
A238898: 1 2 4 6 8 10 10 14 16 18 18 22 22 26 26 26
((~x + 1) mod (if x <= 0 then 1 else (2 + ((x mod (1 + (4 mod (x + 1)))) div 2))))
A159200: 0 0 1 0 1 0 1 0 2 0 1 0 1 0 3 0
(4 * (~3 + loop(\(x,i).10x,(x + 1),1)))
A177108: 28 388 3988 39988 399988 3999988 39999988 399999988 3999999988 39999999988 399999999988 3999999999988 39999999999988 399999999999988 3999999999999988 39999999999999988
(if x <= 0 then 1 else (2 + (((x + ~2) mod (1 + (2 * ((~x + 1) mod 3)))) div 2)))
A067131: 1 2 2 2 2 3 2 2 2 2 2 4 2 2 3 2
((if x <= 0 then 0 else 1) - (2 * ((2x mod (1 + ((1 + (x div 2)) div 2))) div 2)))
A011630-A011597: 0 1 1 1 1 1 1 ~1 1 1 1 ~1 1 ~1 ~1 1
((2 + (x div (1 + (if (x mod 2) <= 0 then 6 else ~4)))) div 2)
A124751: 1 0 1 0 1 0 1 ~1 1 ~1 1 ~1 1 ~2 2 ~2
(1 - ((if x <= 0 then 2 else (x - ((1 + (x2 div 8)) div 2))) div 2))
A343633: 0 1 0 0 0 0 ~1 ~1 ~1 ~1 ~1 0 0 0 0 1
(2 * loop(\(x,i).2x,((2x + 1) div (3 + (x div 4))),2))
A098354: 4 8 8 16 16 16 32 32 32 32 64 64 64 64 64 128
(if x <= 0 then 1 else (2 + ((1 + ((3x mod (2 + (x div 2))) div 2)) div 2)))
A081743: 1 2 2 2 2 3 3 2 2 3 3 3 3 4 4 2
(2 + ((x - ((if (~2 + (x div 2)) <= 0 then 2 else (x + ~2)) mod 5)) div 2))
A130312: 1 1 2 2 3 3 3 5 5 5 5 5 8 8 8 8
(if x <= 0 then 1 else (2 * (x - (2 * ((~3x + 2) div 5)))))
A315889: 1 6 8 14 16 22 28 30 36 38 44 50 52 58 60 66
(4 + (((if (x mod 4) <= 0 then 2 else 0) - (x div 2)) mod 5))
A199815: 6 4 8 8 4 7
(if (x mod 5) <= 0 then 0 else (1 - (2 * ((x div 5) mod 2))))
A330025: 0 1 1 1 1 0 ~1 ~1 ~1 ~1 0 1 1 1 1 0
((if x <= 0 then 2 else (1 + (x div 4) - ((x mod 5) mod 2))) div 2)
A025859: 1 0 0 0 1 1 0 1 1 1 1 1 2 1 2 2
(2 + ((x - (if ((x2 div 2) mod 3) <= 0 then (x div 4) else 1)) div 2))
A074990: 2 2 2 3 3 4 4 5 5 6 6 6 6 7 8 9
(2 * loop(\(x,i).(x2 + x),1,(4x2 + 16x + 14)))
A160372: 420 2380 7812 19404 40612 75660 129540 208012 317604 465612 660100 909900 1224612 1614604 2091012 2665740
(2 + ((3 * (((x * (x div 2)) + (if x <= 0 then 0 else 1)) mod 3)) div 2))
A204895: 2 3 2 3 2 5 3 3 2 3 2 5 3 3 2 3
(if x <= 0 then 1 else (x - (2 * ((3 * ((1 + (x div 2)) div 3)) div 2))))
A162751: 1 1 2 3 2 3 4 5 6 7 4 5 6 7 8 9
(2 + (if (x + ~1) <= 0 then x else (2 + ((x - ((x div 2) mod 3)) div 3))))
A167991: 2 3 4 4 4 5 6 6 6 6 6 7 8 8 8 8
(2 * (loop(\(x,i).(3x + 1),x,1) + (((x + 1) div 3) mod 2)))
A135263: 2 8 28 82 244 728 2186 6560 19684 59050 177148 531440 1594322 4782968 14348908 43046722
(4 * (loop(\(x,i).(x + (x div 3)),(x + ~2),4) div 3))
A245356: 4 4 4 4 8 8 12 16 20 28 36 48 64 88 116 156
loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),2)
A117973: 2 4 4 8 4 8 8 16 4 8 8 16 8 16 16 32
((if x <= 0 then 1 else x) - (((x - (((x2 + ~x) div 2) div 3)) div 2) div 2))
A048856: 1 1 2 3 4 5 6 7 9 10 12 13 15 17 18 20
loop(\(x,i).x5,1,(12x + 4))
A017573: 1024 1048576 17210368 102400000 380204032 1073741824 2535525376 5277319168 10000000000 17623416832 29316250624 46525874176 71008211968 104857600000 150536645632 210906087424
(2 + (2 * loop(\(x,i).x2,1,((2x + 4) - (2x div 3)))))
A277449: 34 74 100 130 202 244 290 394 452 514 650 724 802 970 1060 1154
(2 + loop(\(x,i).(2x + 5),(x div 2),(2 + (3 * (x mod 2)))))
A133257: 4 7 11 17 25 37 53 77 109 157 221 317 445 637 893 1277
((2 + (loop(\(x,i).(x + ((x div 5) + i)),x,2) div 3)) div 2)
A261154: 1 1 1 2 3 4 6 8 11 14 18 24 30 38 48 60
(if x <= 0 then 1 else (2 * ((3 * (x + (x div 12))) div 2)))
A229488: 1 2 6 8 12 14 18 20 24 26 30 32 38 42 44 48
((loop(\(x,i).((x + 1) + (x div (1 + (x mod 4)))),x,3) div 2) div 2)
A048330: 0 1 2 3 4 6 12 18 24 31 62 93 124 156 312 468
(((3 * loop(\(x,i).(2 + ((x2 + ~x) div (x + 2))),2,x)) div 2) div 2)
A120505: 1 1 1 2 3 3 3 3 4 5 6 6 7 8 9 9
(4 * (3 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)))
A273801: 16 24 32 48 56 72 80 96 120 128 152 168 176 192 216 240
(~2 + ((3 * (x + (if (x + ~2) <= 0 then 2 else (x2 * (x div 2))))) div 2))
A255730: 1 2 4 16 52 80
(2 + (if x <= 0 then 1 else (2 * (4x + (x mod 2) - (x div 3)))))
A063229: 3 12 18 26 32 42 46 56 62 70 76 86 90 100 106 114
(((x + (if (x mod 2) <= 0 then x else 2)) mod 3) + (2 * ((x div 3) mod 2)))
A021697: 0 0 1 4 4 3 0 0 1 4 4 3 0 0 1 4
loop(\(x,i).x6,1,(8x + 4))
A017118: 4096 2985984 64000000 481890304 2176782336 7256313856 19770609664 46656000000 98867482624 192699928576 351298031616 606355001344 1000000000000 1586874322944 2436396322816
(if x <= 0 then 1 else (x div (4 + (16 mod (1 + (x div 2))))))
A264592: 1 0 0 0 0 1 1 1 1 1 1 1 2 2 3 3
((if (x + ~12) <= 0 then 1 else 2) - (((1 + (x div 2)) div 2) mod 2))
A281459: 1 1 0 0 0 0 1 1 1 1 0 0 0 1 2 2
(4 * loop(\(x,i).(5x + 2),(x div 2),(1 + (x mod 2))))
A117864: 4 8 28 48 148 248 748 1248 3748 6248 18748 31248 93748 156248 468748 781248
(2 + (if x <= 0 then 1 else (2 * ((x + 1) + (2 * (x div 3)) - (x mod 2)))))
A063227: 3 4 8 12 16 16 24 24 28 32 36 36 44 44 48 52
(x mod (((~1 + (x * (1 + (2 * (if (~2 + (x div 2)) <= 0 then 2 else 0))))) div 2) div 2))
A325817: 0 0 0 0 0 5 0 0 0 1 0 1 0 1 2 0
(4 * ((x + 1) + (x div (2 + (if (~2 + (x div 4)) <= 0 then 1 else 2)))))
A217319: 4 8 12 20 24 28 36 40 44 52 56 60 64 68 72 76
(2 * (loop(\(x,i).(2 * (x + (4 * (x + (2 * (x mod 2)))))),x,1) div 2))
A136921: 0 26 260 2600 26000 260000 2600000 26000000 260000000 2600000000 26000000000 260000000000 2600000000000 26000000000000 260000000000000
((((x + 1) * ((3x + 3) + (if (x + ~2) <= 0 then 1 else 0))) div 2) div 2)
A184534: 1 3 7 12 18 27 36 48 60 75 90 108 126 147 168 192
((((x + 1) * (1 + (if (x mod 2) <= 0 then x else ((1 + (x div 2)) mod 2)))) div 2) div 2)
A086111: 0 1 2 1 6 3 12 2 20 5 30 3 42 7 56 4
(2 * (2 + compr(\x.(~2 + (loop(\(x,i).(~2x + 1),x,1) mod (x + 2))),(x + 1))))
A085681: 6 10 14 20 22 26 28 34 38 44 46 52 58 62 68 74
((((x2 + 3x + 2) * loop(\(x,i).(x + (i * i)),(x + 1),1)) div 2) div 2)
A095166: 1 9 45 155 420 966 1974 3690 6435 10615 16731 25389 37310 53340 74460 101796
((if x <= 0 then 0 else 1) - (2 * ((((~2 + (x div 2)) * (x div 2)) mod (x + 1)) mod 2)))
A112347: 0 1 1 ~1 1 1 ~1 ~1 1 1 1 ~1 ~1 1 ~1 ~1
(x + (((x + 1) div 2) div 2) - ((if x <= 0 then 1 else x) div ~7))
A145353-A013936: 1 2 3 5 6 7 8 10 12 13 14 16 17 18 19 22
loop(\(x,i).(2 * (1 + (x div 2))),(x div 8),(((x + 1) div 2) div 2))
A082871: 0 0 0 1 1 1 1 2 4
A334897: 0 0 0 1 1 1 1 2 4 4 4 4 4 4 4 6
((loop(\(x,i).3x,x,1) - ((x3 + ~x2 + ~x + 1) div 2)) div 2)
A231255: 0 1 4 9 29 97
(2 + ((((x div 2) mod (1 + (~x mod 4))) div 2) + (if x <= 0 then 1 else 2)))
A332325: 3 4 4 4 4 5 4 4 4 4 5 4 4 5 4 4
(((x2 + 11x + 28) + (if x <= 0 then 1 else 2)) div 2)
A006625: 14 21 28 36 45
((x + 2) + (((x - (x div ~4)) div 3) + (if x <= 0 then 1 else 2)))
A346232: 3 5 7 8 9 11 12 14 15 17 18 19 21 22 24 25
(((loop(\(x,i).(x + ((i * i * i * i) div 2)),(x + 1),0) div 2) div 2) div 2)
A011888: 0 1 6 22 61 142 292 548 958 1583 2498 3794 5579 7980 11144 15240
(loop(\(x,i).(x + (x div 2)),x,44) div 2)
A120146: 22 33 49 74 111 166 249 374 561 841 1262 1893 2839 4259 6388 9582
(4 + (if (((x + 2) - ((x div 4) mod 2)) mod 3) <= 0 then 1 else 2))
A023408: 6 5 6 6 6 5 6 6 6 6 5 6 6 6 5 6
(((((2x + 1) * loop(\(x,i).(1 + (2x * i)),x,1)) div 2) div 2) div 2)
A327606: 0 1 8 69 712 8705 123456 1994293 36163184 727518177 16081980760 387499155461 10108673620728 283851555270049 8536572699232592 273759055527114165
(((loop(\(x,i).(x * ((1 + (2 * i)) * (1 + (2 * i)))),x,1) div 2) div 2) div 2)
A249348: 0 1 28 1378 111628 13507003 2282683528 513603793828 148431496416328 53583770206294453 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * (2 + (((x + 1) * ((x + 3) + (if (~x + 2) <= 0 then 2 else 1))) div 2)))
A248427: 8 14 24 36 48 64 80 100 120 144 168 196 224 256 288 324
(if x <= 0 then 1 else (((((x + 1) * (((~1 + (x div 2)) div 2) mod 2)) div 2) div 2) div 2))
A017858: 1 0 0 0 0 0 0 1 1 1 0 0 0 0 1 2
(2 + ((2 + (loop(\(x,i).(2x * (x + i)),x,4) div (x + 1))) div 2))
A007540: 5 13 563
(((2x + ~2) mod (2 + (((x div 2) div 3) + (if x <= 0 then 1 else 2)))) div 2)
A194942: 0 0 1 0 1 0 0 1 2 0 1 0 2 0 1 2
(1 - (x div (~2 + ((~x + 2) div (2 + (2 * (if (x mod 3) <= 0 then 0 else 2)))))))
A340542: 1 2 2 2 3 3 3 4 4 3 4 4 3 5 5 3
((((loop(\(x,i).((x + 1) + (x div (2 + (i mod 2)))),x,0) div 2) div 2) div 2) div 2)
A319473-A308990-A026814-A024793: 0 0 0 0 0 0 0 0 1 1 2 3 5 7 11 15
(loop(\(x,i).(2x + ~1),x,56) div 2)
A079731: 28 55 110 220 440 880 1760 3520
(16 * (9 + (if x <= 0 then 0 else (x + 2))))
A323614: 144 192 208 224 240 256 272 288 304 320 336 352 368 384 400 416
((if x <= 0 then 0 else 1) - (2 * ((x - (((3 * (x div 2)) div 2) div 2)) mod 2)))
A070750: 0 ~1 1 ~1 ~1 1 1 ~1 ~1 1 ~1 1 1 ~1 ~1 1
(4 + (if x <= 0 then 1 else (4 * (3x - (x div 3)))))
A063236: 5 16 28 36 48 60 68 80 92 100 112 124 132 144 156 164
((x + 1) div (if x <= 0 then 1 else (2 * (2 + ((x mod (2 + (x mod 3))) div 2)))))
A193677: 1 0 0 1 1 1 1 2 2 2 2 2 3 3 2 4
((x + 1) div (2 + (x div (2 + (if (x mod 2) <= 0 then ((x mod 3) div 2) else 2)))))
A345222-A317751-A122375-A106490: 0 1 1 2 1 2 1 2 2 2 1 3 1 2 2 3
(if x <= 0 then 1 else (2 + (((((x + 1) * ((x div 2) div 3)) div 2) div 2) mod 2)))
A183027: 1 2 2 2 2 2 3 2 2 2 2 3 2 3 3 2
(if x <= 0 then 0 else (1 - (2 * (((((x + ~1) * (1 + (x div 2))) div 2) div 2) mod 2))))
A011625: 0 1 1 ~1 1 ~1 ~1 1 1 1 ~1 ~1 ~1 ~1 1 1
(1 - (2 * ((2x div (2 + (x div (2 + (if (x + ~2) <= 0 then 0 else 2))))) mod 2)))
A181432: 1 ~1 ~1 ~1 1 ~1 1 1 1 1 ~1 ~1 1 ~1 ~1 1
(2 + (8 * loop(\(x,i).(x3 + ~x),(x2 + 1),2)))
A164986: 50 1682 4611686018427387903 4611686018427387903
((loop(\(x,i).x2,1,(x2 div 32)) div 2) div 2)
A035564: 0 0 0 0 0 0 0 0 1 1 2 2 4 6 9 12
((x + 2) - ((if x <= 0 then 2 else (x div (~10 + (x div 2)))) div 2))
A026462: 1 4 5 6 7 8 9 10 11 12 13 15 16 17 19 20
(2 * (if x <= 0 then 1 else (2 + (((x + ~1) mod (2 + (x div (2 + (x mod 2))))) mod 2))))
A138125: 2 4 6 4 6 6 4 4 6 6 4 4 6 4 4 4
(if x <= 0 then 1 else ((2x + 2) - (x div (4 + ((x div 2) mod 4)))))
A231407: 1 4 6
A322368: 1 4 6 8 10 12 14 15 16 18 20 22 24 26 28 30
(if (x + ~2) <= 0 then 1 else (2 * (1 - ((x3 div 8) mod 2))))
A099766: 1 1 1 0 2 0 0 2 2 0 0 2 2 2 0 0
(if x <= 0 then 1 else (2 * (3x - (x div (4 + (x div 4))))))
A315757: 1 6 12 18 24 28 34 40 46 52 58 64 70 76 80 86
(2 + ((x - (((x div 2) - (if (~2 + (x div 2)) <= 0 then (x + ~2) else 2)) div 2)) div 2))
A196155: 1 2 3 3 4 5 5 5 5 6 6 7 7 7 8 8
(if x <= 0 then 1 else (2 + (((2x + 1) mod (x - ((x + 1) mod 4))) div 2)))
A134868: 1 2 2 2 2 3 2 2 3 4 2 2 3 4 5 2
((2 + (if x <= 0 then 0 else 2)) div (2 - (2x mod ~15)))
A320318: 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 2
((2 + (x div 3)) div (if (x + ~1) <= 0 then 1 else (2 + (x mod 8))))
A240067-A240066: 2 2 0 0 0 0 0 0 2 1 1 1 1 0 0 0
((if x <= 0 then 0 else (2 - (((x mod 2) - ((x2 + ~x) div 4)) div 2))) div 2)
A114372-A112021: 0 1 1 1 2 2 3 3 4 5 6 7 9 10 12 14
((x mod (2 + ((~x + (if (~2 + (x div 4)) <= 0 then 0 else 2)) mod 4))) div 2)
A127326: 0 0 1 0 0 0 1 0 0 2 1 1 0 0 0 0
((if x <= 0 then 1 else 5x) - (x div (4 + (x div 4))))
A313721: 1 5 10 15 20 24 29 34 39 44 49 54 59 64 68 73
((2 + (if x <= 0 then 0 else (2 + ((x + ((~x + 1) mod (2 + (x div 2)))) div 2)))) div 2)
A196183: 1 2 3 3 3 3 3 4 5 5 5 5 6 6 6 6
((if x <= 0 then 0 else 1) - (2 * (((x3 + x2) div (x + 4)) mod 2)))
A011613-A011601: 0 1 1 ~1 1 1 ~1 ~1 1 1 1 1 ~1 ~1 ~1 ~1
(if x <= 0 then 1 else ((x + 2) - ((((2 + (x div 4)) * (x div 2)) div 2) div 2)))
A119476: 1 3 4 5 5 6 6 7 6 7 7 8 7 8 8 9
(if x <= 0 then 1 else (2 * (x + ((x2 div 4) + (2 * (2 + (x div 2)))))))
A245578: 1 10 18 22 32 38 50 58 72 82 98 110 128 142 162 178
((x + 2) - (((if (x mod 2) <= 0 then 2 else x3) mod (2 + (x div 2))) div 2))
A091937: 2 3 3 5 5 7 7 8 9 10 11 13 13 13 15 17
(6x - ((2 * (if x <= 0 then 1 else x)) div ~7))
A225227: 1 7 13
A004082: 1 7 13 19 26 32 38 44 51 57 63 70 76 82 88 95
((x div 7) - ((if x <= 0 then 1 else x) div ~7))
A025784: 1 1 1 1 1 1 1 2 3 3 3 3 3 3 4 5
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) mod 8)
A159987: 1 1 2 5 6 2 4 5 6 6 4 2 4 4 0 5
(~8 + (loop(\(x,i).10x,(x + 2),1) div 2))
A086944: 42 492 4992 49992 499992 4999992 49999992 499999992 4999999992 49999999992 499999999992 4999999999992 49999999999992 499999999999992 4999999999999992 49999999999999992
(8 + loop(\(x,i).(x + i - (x div (4 * (1 + i)))),x,2))
A290745: 10 11 13 16 20 25 31 38 46 55 64 74 85 97 110 124
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 8)
A039706: 2 3 5 7 3 5 1 3 7 5 7 5 1 3 7 5
loop(\(x,i).(x - ((~2x + 4) div 7)),x,8)
A275627-A010916: 8 10 13 17 22 28 36 46 59 76 98 126 162 208 267 343
(loop(\(x,i).8x,x,(x + 8)) div 8)
A081108: 1 9 80 704 6144 53248 458752 3932160 33554432 285212672 2415919104 20401094656 171798691840 1443109011456 12094627905536 101155069755392
(8 + loop(\(x,i).((x + 2) + (x div (4 * (1 + i)))),2,x))
A125290-A101594: 12 13 14 15 16 17 18 19 21 23 24 25 26 27 28 29
(loop(\(x,i).(5x + 8),(~2 + (x div 2)),x) div 8)
A124482: 0 0 0 0 0 0 4 5 31
(if x <= 0 then 1 else (2 * (2x - ((~x + ((x div 2) mod 4)) div 4))))
A315173: 1 6 10 14 18 22 26 30 36 42 46 50 54 58 62 66
(x - loop(\(x,i).(~x2 + x),1,(2 - (x div (~2 + ((~x + 2) div 4))))))
A317303: 2 7 8 9 16 17 18 19 20 29 30 31 32 33 34 35
(1 - (((if ((x + ~1) mod 8) <= 0 then x else 1) - (x div 4)) div 2))
A044931: 1 1 1 1 1 1 1 1 2 ~2 2 2 2 2 2 2
(if (x + ~2) <= 0 then x else (2 + (((((x + 1) div 2) div 2) div 2) + (x div 4))))
A269381: 0 1 2 2 3 3 3 4 5 5 5 5 6 6 6 7
((loop(\(x,i).(2x - ((x - (2 * (x mod 2))) div 3)),x,2) div 2) div 2)
A292432: 0 1 1 3 5 9 16 27 46 76
loop(\(x,i).x5,1,(12x + 8))
A017621: 32768 3200000 33554432 164916224 550731776 1453933568 3276800000 6590815232 12166529024 21003416576 34359738368 53782400000 81136812032 118636749824 168874213376 234849287168
(((loop(\(x,i).2x,x,(x2 + 7x + 8)) div 2) div 2) div 2)
A084851: 1 4 13 38 104 272 688 1696 4096 9728 22784 52736 120832 274432 618496 1384448
(x div (4 + ((1 - loop(\(x,i).3x,x,3)) mod (x + 2))))
A238660: 0 0 0 0 0 1 0 1 0 2 0 2 0 1 1 3
(10x + loop(\(x,i).i,(~4 + (x div 2)),x))
A178359: 0 11 22 33 44 55 66 77 88 99 101 111 122 132 143 153
loop(\(x,i).x6,1,~7x)
A016986: 0 117649 7529536 85766121 481890304 1838265625 5489031744 13841287201 30840979456 62523502209 117649000000 208422380089 351298031616 567869252041 885842380864 1340095640625
loop(\(x,i).x5,1,(7x + 2))
A017009: 32 59049 1048576 6436343 24300000 69343957 164916224 345025251 656356768 1160290625 1934917632 3077056399 4704270176 6956883693 10000000000 14025517307
((2 + (((x + 1) * loop(\(x,i).(x3 + 1),2,2)) + (x div 2))) div 2)
A033174: 366 731 1096 1461 1827 2192 2557 2922 3288 3653 4018 4383 4749 5114 5479 5844
((if x <= 0 then 1 else 4x) - (((x + 1) div (2 - ((x div 2) mod 2))) div 2))
A310704: 1 4 7 10 15 19 21 24 30 34 35 38 45 49 49 52
loop(\(x,i).2x,(((3 * (x + (x div 4))) - (x mod 2)) div 2),2)
A101926: 2 4 16 32 256 512 2048 4096 65536 131072 524288 1048576 8388608 16777216 67108864 134217728
(2x div (4 + (x div ((if (x mod 3) <= 0 then 1 else 2) + (x mod 2)))))
A326034: 0 0 0 1 1 2 1 2 2 2 2 3 1 3 2 2
(((x + 2) div (if x <= 0 then 1 else (2 + (((x div 3) mod 2) + (x mod 2))))) div 2)
A025813: 1 0 1 0 1 0 2 1 2 1 2 1 3 2 4 2
(4 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + (x mod 2)))
A107622: 4 6 7 10 13 16 19 22 25 32 33 40 43 46 49 56
(x7 mod loop(\(x,i).(x2 + 2),2,2))
A070719: 0 1 14 21 6 35 28 7 8 23 34 11 12 29 22 13
(1 - ((x mod (1 + (if (x mod 2) <= 0 then 12 else 1))) mod 4))
A011632: 1 0 ~1 0 1 0 ~1 0 1 0 ~1 0 1
A016221-A016053-A015997-A015885-A015717-A015661-A015493-A015325-A015213-A015157-A015045-A014877-A014821-A014653-A014541-A014485-A014373-A014317: 1 0 ~1 0 1 0 ~1 0 1 0 ~1 0 1 0 0 0
(((x * loop(\(x,i).x3,1,(1 + (x div 2)))) div 3) mod 4)
A174428: 0 0 1 0 0 1 0 1 1 3 0 0 0 2 1 0
((1 + (x div 2)) div ((1 + ((x div 3) mod 2)) * (if x <= 0 then 1 else 4)))
A025897: 1 0 0 0 0 0 1 1 1 0 0 0 1 1 2 1
loop(\(x,i).32x,(4x + 2),4)
A013880: 4096 4294967296 4503599627370496 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x mod (4 + ((x + (if (x mod 2) <= 0 then (x mod 5) else 1)) div 2)))
A031087: 0 1 2 3 4 5 6 7 8 0 1 1 1 2 1 3
((x + (if x <= 0 then 2 else (~1 + ((~x2 + x) mod 5)))) div 4)
A337926: 0 0 1 1 1 1 1 2 2 2 2 2 3 4 4 3
((x + 4) + ((if (~2 + (x div 3)) <= 0 then 0 else x) div 5))
A191842: 4 5 6 7 8 9 10 11 12 14 16 17 18 19 20 22
(4 * (x + loop(\(x,i).(x - ((~1 + (x div 4)) div 2)),2,(x + ~1))))
A213258: 4 12 20 28 32 36 44 52 60 68 76 84 92 96 100 108
(4x - ((((x div 2) mod 4) - (if x <= 0 then 1 else x)) div 4))
A314672: 1 5 9 13 17 21 25 29 34 39 43 47 51 55 59 63
(loop(\(x,i).2x,(x + ~1),(x + ((x2 + 3x + 2) div 2))) div 4)
A049611: 0 1 4 13 38 104 272 688 1696 4096 9728 22784 52736 120832 274432 618496
(2 div ((if (((x + 1) div (2 + (x mod 4))) mod 2) <= 0 then 2 else x) mod 4))
A000164: 1 1 1 1 1 1 1 0 1 2 1 1 1 1 1 0
(compr(\x.(((~1 + loop(\(x,i).2x,x,2)) mod (2 + (x div 2))) div 2),x) div 4)
A302929: 0 0 0 0 1 2 2 4 4 5 6 6 7 8 10 10
((x + 4) + ((x + (if (x mod 7) <= 0 then 1 else 2)) div 2))
A180638: 4 6 8 9 11 12 14 15 17 18 20 21 23 24 25 27
(1 + (((x + loop(\(x,i).2x,x,1)) div 5) + (x div 4)))
A068604: 1 1 2 3 6 9 16 29 55
((if ((x + 1) mod 4) <= 0 then (2 + (x div 4)) else 1) + (x mod 4))
A007880: 1 2 3 5 1 2 3 6 1 2 3 7 1 2 3 8
((x + 4) + loop(\(x,i).(x - (2x div (1 + (4 * i)))),x,x))
A137242-A049579: 4 6 8 9 11 12 14 15 16 18 19 21 22 23 24 25
(((x * loop(\(x,i).2x,(x + ~1),(3x + 5))) div 2) div 2)
A089658: 0 2 11 42 136 400 1104 2912 7424 18432 44800 107008 251904 585728 1347584 3072000
(2 + loop(\(x,i).(1 + ((x mod (2 * (2 + (x mod 2)))) + (x div 3))),x,2))
A146968: 4 5 7
A094328: 4 5 7 9 6 4 5 7 9 6 4 5 7 9 6 4
(2 - (2 * (2 + (if (x + ~8) <= 0 then 9 else x))))
A291522: ~20 ~20 ~20 ~20 ~20 ~20 ~20 ~20 ~20 ~20 ~22 ~24 ~26 ~28 ~30 ~32
loop(\(x,i).x5,1,(10x + 4))
A017321: 1024 537824 7962624 45435424 164916224 459165024 1073741824 2219006624 4182119424 7339040224 12166529024 19254145824 29316250624 43204003424 61917364224 86617093024
(x - (2 * ((x + (if ((x div 3) mod 2) <= 0 then (x div 4) else 1)) div 2)))
A002819: 0 1 0 ~1 0 ~1 0 ~1 ~2 ~1 0 ~1 ~2 ~3 ~2 ~1
((x + 4) + (3 * loop(\(x,i).(i - ((1 + i) mod (x + 1))),x,0)))
A004756: 4 8 9 16 17 18 19 32 33 34 35 36 37 38 39 64
loop(\(x,i).x6,1,(6x + 4))
A016962: 4096 1000000 16777216 113379904 481890304 1544804416 4096000000 9474296896 19770609664 38068692544 68719476736 117649000000 192699928576 304006671424 464404086784 689869781056
(if x <= 0 then 1 else (2 * (2x - ((~x2 + 2) div (3x + 2)))))
A310378: 1 4 10 14 18 24 28 34 38 42 48 52 56 62 66 70
((x + 4) + loop(\(x,i).((x2 + ~x) div (1 + i)),2,(x + 3)))
A177206: 6 15 36 77 148 261 430 671 1002 1443 2016 2745 3656 4777 6138 7771
(((x * loop(\(x,i).2x,(x + ~1),(5x + ~1))) div 2) div 2)
A084899: 0 1 9 42 152 480 1392 3808 9984 25344 62720 152064 362496 851968 1978368 4546560
((loop(\(x,i).((2x + 1) + (x2 div 3)),(x + 1),x) div 2) div 2)
A339305: 0 2 64 97920
(x7 div loop(\(x,i).(x2 + x),2,2))
A030180: 0 0 3 52 390 1860 6665 19608 49932 113880 238095 463980 853138 1494012 2509845 4068080
(if x <= 0 then 0 else (2 + ((x + (((x - (x div 3)) mod 3) div 2)) div 2)))
A073425: 0 2 3 4 4 4 5 6 6 6 7 8 8 8 9 9
((x + 6) + ((1 + (if (x + ~4) <= 0 then 1 else 2)) mod (x + 1)))
A085267: 6 7 10 11 12 14 15 16 17 18 19 20 21 22 23 24
(2 + loop(\(x,i).((x + 2) - ((x div (2 + ((x div 2) div 3))) mod 2)),x,2))
A226746: 4 5 6 8 10 12 13 14 15 16 17 18 20 21 22 24
(if x <= 0 then 1 else (2 + ((x + ((x mod (~2 + (x div ~4))) mod 2)) div 2)))
A100922: 1 2 3 3 4 5 5 6 6 7 7 7 8 9 9 10
(~2 + (loop(\(x,i).(1 - (2 * (2x - (x mod 8)))),2,x) div 2))
A158938: ~3 7 9 11 13 23 25 27 61 71 73 75 77 87 89 91
(2 + (if x <= 0 then 1 else (2 * (x + (x div (8 - (x div 4)))))))
A242932: 3 4 6 8 10 12 14 18 20 22 24 26 30 32 34 38
((x + 4) + (if (x + ~2) <= 0 then x else (2 - ((~x + ((x div 2) mod 2)) div 2))))
A090334: 4 6 8 10 12 14 15 16 18 20 21 22 24 26 27 28
(~2 + ((x + 2) * (if (~2 + (x div 5)) <= 0 then 1 else 6)))
A103303: 0 1 2 3 4 5 6 7 8 9
A055646: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 100
((if x <= 0 then 0 else 1) - (2 * ((x2 mod (x - ((~x + 2) div 2))) div (x + 2))))
A011629: 0 1 1 1 1 1 1 ~1 1 1 1 1 1 ~1 ~1 1
((1 + loop(\(x,i).(x - (x div (~1 + (i mod ~2)))),x,1)) mod (x + 4))
A254271: 2 3 5 0 5 1 7
((2x + 4) + ((x - (if (~2 + (x div 4)) <= 0 then 2 else 1)) div 3))
A184655: 3 5 8 10 12 15 17 19 22 24 26 29 31 34 36 38
((2x + 4) + (loop(\(x,i).((x2 + ~x) div 2),2,(x + 2)) div 3))
A229439: 4 7 13 25 47 84 142 228 350 517 739 1027 1393 1850 2412 3094
((3x + 4) + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))
A302338: 4 8 10 16 16 20 22 32 28 32 34 40 40 44 46 64
loop(\(x,i).(2x - (18 div (x + 1))),2x,2)
A208428: 2 14 54 216 864 3456 13824 55296 221184 884736 3538944 14155776 56623104 226492416 905969664 3623878656
(x + (((2x + ~1) div 5) + (2 * (if x <= 0 then 1 else 2x))))
A313877: 1 5 10 16 21 26 32 37 43 48 53 59 64 70 75 80
(if x <= 0 then 1 else (2 * (2x + ((x - (x div 7)) div 2))))
A310411: 1 4 10 14 20 24 30 34 38 44 48 54 58 64 68 72
(if x <= 0 then 1 else (2 * (2x + ((x - (x div 9)) div 2))))
A310412: 1 4 10 14 20 24 30 34 40 44 48 54 58 64 68 74
(if x <= 0 then 1 else (2 * (2x + ((x - (x div 12)) div 2))))
A310413: 1 4 10 14 20 24 30 34 40 44 50 54 58 64 68 74
loop(\(x,i).(((5x + 5) * (x2 div 2)) div 2),2x,2)
A067668: 2 4480 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 * (2x + ((x - (x div ~8)) div 2))))
A315308: 1 6 10 16 20 26 30 36 40 46 52 56 62 66 72 76
(if x <= 0 then 1 else (2 * (2x + ((((x + 1) - (x div 4)) div 2) div 2))))
A312472: 1 4 8 14 18 22 26 30 34 40 44 48 52 56 62 66
(if x <= 0 then 1 else (2 * (2x + ((x - (x div ~7)) div 2))))
A315309: 1 6 10 16 20 26 30 36 42 46 52 56 62 66 72 78
(if x <= 0 then 1 else (2 * (2x + ((x + ((x div 2) mod 4)) div 4))))
A312506: 1 4 8 14 18 22 28 32 36 40 44 50 54 58 64 68
(if x <= 0 then 1 else ((4x + 2) - (2 div (1 + (x div 5)))))
A311253: 1 4 8 12 16 21 25 29 33 37 42 46 50 54 58 62
(if x <= 0 then 1 else (4x + (2x div (5 - (x mod 2)))))
A058759: 1 4 8 13
A311933: 1 4 8 13 17 22 26 31 35 40 44 49 52 58 61 67
(4x + (if x <= 0 then 1 else ((2 * ((x + 1) div 3)) div 3)))
A311258: 1 4 8 12 16 21 25 29 34 38 42 46 50 54 59 63
(4x + (if x <= 0 then 1 else (x - ((x * (1 + (x div 2))) mod 3))))
A313249: 1 4 9 15 20 25 30 34 39 45 50 55 60 64 69 75
(if x <= 0 then 1 else (4x + (2 div (16 div (x + 1)))))
A311257: 1 4 8 12 16 21 25 29 34 38 42 46 50 54 58 62
(((x - (x div 9)) div 2) + (if x <= 0 then 1 else 4x))
A312932: 1 4 9 13 18 22 27 31 36 40 44 49 53 58 62 67
(((((x + 1) - (x div 4)) div 2) div 2) + (if x <= 0 then 1 else 4x))
A058759: 1 4 8 13
A311804: 1 4 8 13 17 21 25 29 33 38 42 46 50 54 59 63
(((((2 - (x div 2)) mod (x + 1)) div 2) div 2) + (if x <= 0 then 1 else 4x))
A311188: 1 4 8 12 16 20 25 29 33 38 42 46 50 54 58 62
((x div (2 * (2 + ((x div 4) mod 2)))) + (if x <= 0 then 1 else 4x))
A311191: 1 4 8 12 16 20 25 29 34 38 42 46 50 54 58 62
((x div (4 + ((x div 2) mod 4))) + (if x <= 0 then 1 else 4x))
A311160-A311159: 1 4 8 12 16 20 24 29 34 38 42 46 50 54 58 62
(((x - (x div ~7)) div 2) + (if x <= 0 then 1 else 4x))
A314838: 1 5 9 14 18 23 27 32 37 41 46 50 55 59 64 69
(((((2 - (x div 2)) mod (x + 2)) div 2) div 2) + (if x <= 0 then 1 else 4x))
A311197: 1 4 8 12 16 20 25 30 34 38 42 46 50 54 58 63
(((x + ((x div 2) mod 4)) div 4) + (if x <= 0 then 1 else 4x))
A058759: 1 4 8 13
A311843: 1 4 8 13 17 21 26 30 34 38 42 47 51 55 60 64
(((x + (((x div 2) div 3) mod 2)) div 2) + (if x <= 0 then 1 else 4x))
A312933: 1 4 9 13 18 22 27 32 36 41 45 50 54 58 63 67
(x + (if x <= 0 then 1 else 4x) - ((~x + ((x div 4) mod 2)) div 2))
A315520: 1 6 11 17 22 27 33 38 44 50 55 61 66 71 77 82
(x + ((x div (4 + (x div 4))) + (if x <= 0 then 1 else 4x)))
A313746: 1 5 10 15 20 26 31 36 41 46 51 56 61 66 72 77
(4x + (if (x + ~10) <= 0 then 1 else (x div 4)))
A314669: 1 5 9 13 17 21 25 29 33 37 41 46 51 55 59 63
((x + ~1) + (if x <= 0 then 2 else (4x + ((x + 1) mod (2 + (x mod 2))))))
A315257: 1 6 10 15 20 24 30 36 40 45 50 54 60 66 70 75
(~2 + (((2x + 2) * (2 + (if (x mod 2) <= 0 then 4 else 0))) + (x div 2)))
A234974: 10 6 35 15
(loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x div 2),(x div 2)) div 2)
A116400: 0 0 1 1 5 5 21 21 84 84 330 330 1287 1287 5005 5005
(1 + (2 * (1 + (if (x mod 4) <= 0 then 2 else (x mod 2)))) - ((x div 2) mod 2))
A135537: 7 5 2 4 7 5 2 4 7 5 2 4 7 5 2 4
(2 + ((1 + (if (x mod 3) <= 0 then (2 - ((x div 2) mod 2)) else 0)) * (x mod 2)))
A066482: 2 3 2 4 2 3 2 3 2 5 2 3 2 3 2 4
((x + 1) div (2 + ((if (~1 + (x mod 5)) <= 0 then 1 else 2) + (x mod 2))))
A333708: 0 0 0 0 1 1 2 1 2 2 3 3 3 2 3 4
((((if (x mod 5) <= 0 then 2 else 1) + (x div 4)) - (x mod 2)) div 2)
A008682: 1 0 0 0 1 1 1 0 1 1 2 1 2 1 2 2
((1 + (x div 5)) div (if (x mod 3) <= 0 then (2 - (x mod 2)) else 2))
A173636: 0 0 0 1 0 1 1 1 1 2 1 1 1 1 1 4
(if ((x mod (1 + ((~x + 2) mod 4))) div 2) <= 0 then 1 else (4 - (x mod 2)))
A295295: 1 1 1 3 1 1 1 3 4 1 1 3 1 1 1 3
(loop(\(x,i).((4x + 4) + (x div 4)),x,0) mod (2 + (x mod 2)))
A236470: 0 1 1 0 1 1 0 1 0 0 1 1 0 2 1 2
(if (2 - ((x + 1) mod (1 + (2 * (x mod 3))))) <= 0 then 1 else (2 + (x mod 2)))
A214717: 2 1 1 3 1 3 2 1 1 3 1 1 2 1 2 3
(2 - ((if (8 mod (1 + (x div 2))) <= 0 then 1 else 2) mod (2 + (x mod 2))))
A114708: 1 1 1 1 2 0 1 1 2 0 2 0 2 0 1 1
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (2 + (x mod 2)))
A107621: 4 9 10 21 22 39 34 57 46 87 62 111 82 129 94 159
((if ((x2 + 1) mod (x + 4)) <= 0 then 2 else 1) + (x div (2 + (x mod 2))))
A211316: 1 1 2 2 3 2 4 3 5 4 6 4 7 6 8 6
((if (x mod 3) <= 0 then 1 else (0 - (x mod 3))) * (1 - (2 * (x mod 2))))
A132419: 1 1 ~2 ~1 ~1 2 1 1 ~2 ~1 ~1 2 1 1 ~2 ~1
(loop(\(x,i).((x + 2) + (x div 4) - (x div (1 + (2 * i)))),x,2) div 2)
A123015: 1 2 3 4 6 8 10 13 17 21 26 33 41 50 62 77
loop(\(x,i).((9x + 1) + ((x + 1) mod 3)),x,2)
A037637: 2 19 174 1568 14113 127020 1143182 10288639 92597754 833379788 7500418093 67503762840 607533865562 5467804790059 49210243110534 442892187994808
loop(\(x,i).((10x + 1) + ((1 + i) mod 3)),x,2)
A037645: 2 23 231 2312 23123 231231 2312312 23123123 231231231 2312312312 23123123123 231231231231 2312312312312 23123123123123 231231231231231 2312312312312312
loop(\(x,i).((7x + 1) + ((1 + i) mod 3)),x,2)
A037642: 2 17 120 842 5897 41280 288962 2022737 14159160 99114122 693798857 4856592000 33996144002 237973008017 1665811056120 11660677392842
loop(\(x,i).((10x + 1) + ((1 - i) mod 3)),x,2)
A037638: 2 21 213 2132 21321 213213 2132132 21321321 213213213 2132132132 21321321321 213213213213 2132132132132 21321321321321 213213213213213 2132132132132132
((~x + ~2) + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x + 1),1))
A048775: 1 7 31 121 456 1709 6427 24301 92368 352705 1352066 5200287 20058286 77558745 300540179 1166803093
(2 * (x + loop(\(x,i).((x + 1) + (2 * ((x div 4) mod 2))),(x + ~1),1)))
A047836: 2 4 8 12 16 24 32 36 40 48 56 60 64 72 80 84
(2 * ((x + 1) + (loop(\(x,i).(x + ((x + (i div 2)) * i)),(x + ~1),1) div 2)))
A081473: 2 4 8 16 44 194
(((x + 1) + ((loop(\(x,i).(x - ((i * i) div ~2)),x,1) div 2) div 2)) div 2)
A175848: 0 1 2 3 4 6 9 13 17 23 30 38 47 58 71 86
((x + 2) + (if (~x + 2) <= 0 then (2 + (x div 2) - ((x div 4) mod 2)) else 1))
A086986: 3 4 7 8 9 10 12 13 16 17 19 20 21 22 24 25
((5x + 2) + ((x + 2) div (2 + (if (~x + 2) <= 0 then 2 else 1))))
A184519: 2 8 13 18 23 28 34 39 44 49 55 60 65 70 76 81
loop(\(x,i).x6,1,(5x + 2))
A016878: 64 117649 2985984 24137569 113379904 387420489 1073741824 2565726409 5489031744 10779215329 19770609664 34296447249 56800235584 90458382169 139314069504 208422380089
(10x + loop(\(x,i).10x,x,1))
A213223: 1 20 120 1030 10040 100050 1000060 10000070 100000080 1000000090 10000000100 100000000110 1000000000120 10000000000130 100000000000140 1000000000000150
(~10x + loop(\(x,i).10x,x,1))
A198400: 1 0 80 970 9960 99950 999940 9999930 99999920 999999910 9999999900 99999999890 999999999880 9999999999870 99999999999860 999999999999850
loop(\(x,i).x6,1,10x)
A017274: 0 1000000 64000000 729000000 4096000000 15625000000 46656000000 117649000000 262144000000 531441000000 1000000000000 1771561000000 2985984000000 4826809000000 7529536000000 11390625000000
(10x + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2))
A108685: 0 10 21 30 42 51 63 70 84 92 105 111 126 133 147 150
((x + 2) + (((x + 1) * (if (x + ~2) <= 0 then 1 else 2x2)) div 3))
A331399: 2 3 5 29 59
((x + 2) + ((2 * ((x - (if (~2 + (x div 2)) <= 0 then 1 else 2)) div 2)) div 3))
A298606: 1 3 4 5 6 8 9 10 12 13 14 15 17 18 20 21
((~x + ~2) + (loop(\(x,i).(2 + ((x2 + x) div 2)),2,(x + 2)) div 3))
A223718: 3 9 22 46 86 148 239 367 541 771 1068 1444 1912 2486 3181 4013
loop(\(x,i).x7,1,(3x + 2))
A016795: 128 78125 2097152 19487171 105413504 410338673 1280000000 3404825447 8031810176 17249876309 34359738368 64339296875 114415582592 194754273881 319277809664 506623120463
loop(\(x,i).(24x + 24),2,(3x + 2))
A157325: 1752 3480 5208 6936 8664 10392 12120 13848 15576 17304 19032 20760 22488 24216 25944 27672
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(3x + 2))
A051960: 2 5 16 55 196 714 2640 9867 37180 140998 537472 2057510 7904456 30458900 117675360 455657715
(if x <= 0 then 1 else (4x - ((~x2 + 2) div (3x + 2))))
A312902: 1 4 9 13 17 22 26 31 35 39 44 48 52 57 61 65
(loop(\(x,i).((2x * (~1 + (2 * i))) div (2 + i)),x,3x) div 2)
A088110: 0 1 3 9
A000245: 0 1 3 9 28 90 297 1001 3432 11934 41990 149226 534888 1931540 7020405 25662825
((x + (3 * (if (x mod (1 + (2 * (2 + (x mod 2))))) <= 0 then 1 else x))) div 2)
A241071: 1 2 4 6 8 10 12
A345444: 1 2 4 6 8 10 12 5 16 18 6 22 24 26 28 30
((x + loop(\(x,i).(5 + ((2x + 4) div 3)),x,1)) div 2)
A225668: 0 4 6 8 9 10 11 12 12 13 13 14 14 15 15 16
loop(\(x,i).((x + 1) + (((2x + ~4) div (2 + (x div 4))) mod 2)),x,2)
A080637: 2 3 5 6 7 9 11 12 13 14 15 17 19 21 23 24
loop(\(x,i).x5,1,(10x + 8))
A017369: 32768 1889568 17210368 79235168 254803968 656356768 1453933568 2887174368 5277319168 9039207968 14693280768 22877577568 34359738368 50049003168 71008211968 98465804768
((x2 + x + 2) + (3 * loop(\(x,i).(2x + 4),(x + 1),2)))
A250605: 26 64 140 290 586 1172 2336 4654 9278 18512 36964 73850 147602 295084 590024 1179878
(loop(\(x,i).((x * (1 + i)) div (1 + (i div 2))),x,1) - ((x2 + x) div 2))
A129937: 1 1 0 0 0 5 14 42 90 207 407 858 1638 3341 6330 12750
(x + (loop(\(x,i).i,(x + ~10),1) + ((x2 + x) div 2)))
A025724: 1 3 6 10 15 21 28 36 45 55 66 78 92 107 123 140
(4x - (((((x div 2) div 3) mod 2) - (if x <= 0 then 1 else x)) div 2))
A314836: 1 5 9 14 18 23 27 31 36 40 45 49 54 59 63 68
(29 * (2 - ((if x <= 0 then 1 else x) mod 2)))
A040813: 29 29 58 29 58 29 58 29 58 29 58 29 58 29 58 29
((21x + 8) + ((if x <= 0 then 1 else x) mod 2))
A063150: 9 30 50 72 92 114 134 156 176 198 218 240 260 282 302 324
(((x + 1) + loop(\(x,i).(2 + ((x - ((~x + 1) mod 3)) div 2)),x,x)) div 2)
A079243: 0 2 2 3
A139327: 0 2 2 3 4 4 5 5 6 7 7 8 8 8 9 10
(2 + loop(\(x,i).(27x + 7),2,x))
A156771: 198 927 1656 2385 3114 3843 4572 5301 6030 6759 7488 8217 8946 9675 10404 11133
(2 * (x + (if (x + ~3) <= 0 then 2 else (((x + 1) - ((x div 2) mod 2)) div 2))))
A051756: 4 6 8 10 12 16 18 20
A068354: 4 6 8 10 12 16 18 20 24 28 30 32 36 40 42 44
(if x <= 0 then 1 else (2 * (x + (((x - ((x div 2) mod 6)) div 2) div 2))))
A241071: 1 2 4 6 8 10 12
A076450: 1 2 4 6 8 10 12 16 18 20 22 24 30 32 34 36
loop(\(x,i).((x + 2) - (((x - ((x - i) mod 6)) div 2) mod 2)),x,2)
A285143: 2 4 5 6 8 10 11 12 14 16 18 20 21 22 24 26
((x + 2) + ((x - ((if (x + ~2) <= 0 then 2 else (((x + 1) div 2) div 2)) div 2)) div 2))
A276214: 1 3 4 6 8 9 11 12 13 15 16 18 19 21 22 23
(loop(\(x,i).(2 + ((x + 2) div (2 + (x mod (2 + (x div 4)))))),2,x) div 2)
A078380: 1 1 2 1 2 1 3 1 2 1 1 2 1 1 2 2
(if x <= 0 then 1 else (2 * (x + (2 * ((x - (x div ~7)) div 2)))))
A315886: 1 6 8 14 16 22 24 30 36 38 44 46 52 54 60 66
loop(\(x,i).(x + (x mod 8) - ((x + 1) div 5)),x,2)
A163522: 2 4 7 13 16 13 16 13 16 13 16 13 16 13 16 13
(2 - (if x <= 0 then 2 else (x - ((x + (((x + (x div 2)) div 4) mod 2)) div 2))))
A332251: 0 1 1 1 0 0 ~1 ~2 ~2 ~2 ~3 ~4 ~4 ~5 ~5 ~5
((x + 2) + ((((if (~2 + (x div 2)) <= 0 then 1 else (x + ~2)) + (x div 2)) div 2) div 2))
A234853: 2 3 4 5 6 7 9 11 12 13 15 16 18 19 20 22
((x + ((x + (loop(\(x,i).(x - (2 * (~x + i))),x,x) div 3)) div 2)) div 2)
A293492: 0 0 2 6 20 75 278
((x + 2) + ((x + (if (x + ~2) <= 0 then 1 else (2 - ((~1 + (x div 2)) div 2)))) div 2))
A185550: 2 4 5 7 9 10 11 13 14 16 17 18 20 21 22 24
((x + 2) + (if x <= 0 then 1 else (x - ((~x + ((x mod (2 + (x div 2))) div 2)) div 2))))
A184741: 3 5 7 10 12 15 17 19 22 24 27 29 31 34 36 38
(2 + compr(\x.((x + 1) mod (loop(\(x,i).(~2x + 2),x,3) mod (x + 2))),x))
A328232-A318589-A316857-A189710-A132630: 2 3 5 7 9 11 13 17 19 23 29 31 37 41 43 47
(2 + compr(\x.(1 - (loop(\(x,i).(x * (1 + (i div 3))),x,1) mod (x + 2))),x))
A001751: 2 3 4 5 6 7 10 11 13 14 17 19 22 23 26 29
(compr(\x.((loop(\(x,i).(~2x + 4),(x div 2),2) - (x mod 2)) mod (x + 2)),x) div 2)
A235623: 0 1 4 7 8 9 13 19 20 21
(2 + loop(\(x,i).(18x + 16),2,(x2 + 2x)))
A158589: 306 1278 2898 5166 8082 11646 15858 20718 26226 32382 39186 46638 54738 63486 72882 82926
loop(\(x,i).(20x + ~20),2,(x2 + 2x + 2))
A158597: 380 1580 3580 6380 9980 14380 19580 25580 32380 39980 48380 57580 67580 78380 89980 102380
(~2 - (if (x + ~4) <= 0 then 9 else 2x))
A291498: ~11 ~11 ~11 ~11 ~11 ~12 ~14 ~16 ~18 ~20 ~22 ~24 ~26 ~28 ~30 ~32
((x + loop(\(x,i).(2 + ((x * (((x + ~1) div 2) div 2)) div 2)),2,2x)) div 2)
A341824: 1 1 2 3 4 9 14 33
(2 + loop(\(x,i).(3 * (1 + ((2 * (x div 2)) div 3))),(x div 2),x))
A092749: 2 3 5 5 11 11 11 11 11 11 17 17 17 17 17 17
loop(\(x,i).(6x + (((x + 1) mod 3) + (x mod 2))),x,2)
A037718: 2 12 73 441 2648 15888 95329 571977 3431864 20591184 123547105 741282633 4447695800 26686174800 160117048801 960702292809
loop(\(x,i).((5x + 2) + (x mod 2) - (x mod 3)),x,2)
A037717: 2 10 51 258 1292 6460 32301 161508 807542 4037710 20188551 100942758 504713792 2523568960 12617844801 63089224008
((x + ((x2 + loop(\(x,i).(x + i),x4,1)) div 2)) div 2)
A240129: 0 1 36
A054622: 0 1 36 834 8230 48915 210126 720916 2097684 5381685 12501280 26796726 53750346 101969959 184478490 320367720
(((x5 + 1) * loop(\(x,i).x3,2,x)) div 2)
A170787: 0 1 8448 2401326 134348800 3052734375 39187120896 339131713228 2199090364416 11438589937725 50000500000000 189876095765466 641961812164608 1968693495099331 5556013743302400 14596482234375000
((~1 + (5 * (if (x + ~6) <= 0 then 1 else 2))) mod (x + 2))
A279406: 0 1 0 4 4 4 4 0 9 9 9 9 9 9 9 9
loop(\(x,i).(x + (x div 8)),(~1 + (x div 5)),(x + 2))
A059389: 2 3 4 5 6 7 8 9 10 11 13 14 15 16 18 21
((~1 + (if ((x2 + 2x) mod 6) <= 0 then 2x else 1)) mod (x + 2))
A241663: 1 0 0 0 1 0 3 0 0 0 7 0 9 0 0 0
(if ((x - ((2x + 4) div 7)) mod 2) <= 0 then 1 else (x + 2))
A089029: 1 3 4 1 6 7 1 9 1 1 12 1 1 15 1 17
((1 + (2 * loop(\(x,i).((x + 1) - ((~x + 1) div 3)),x,1))) div (x + 2))
A017980: 1 1 2 2 3 3 4 5 6 8 10 13 16 20 25 32
((x + 2) * (2 + ((x2 + 2x + 1) * (2 + (if x <= 0 then 1 else (x + 2))))))
A269679: 10 66 224 570 1212 2282 3936 6354 9740 14322 20352 28106 37884 50010 64832 82722
((2 + ((x - (if (x + ~6) <= 0 then 0 else 2)) * (x div 2))) div (x + 2))
A029168: 1 0 1 1 1 1 2 1 2 2 3 3 4 4 5 5
(loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2) mod (x2 + 4x + 4))
A065350: 2 6 4 20 0 42 40 72 20 110 120 156 56 0 208 272
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(x2 + 4x + 4))
A119574: 4 9 32 125 504 2058 8448 34749 143000 588302 2418624 9934834 40770352 167152500 684656640 2801810205
((x + 2) + compr(\x.(~1 + (loop(\(x,i).(2x + 6),x,1) mod (x + 1))),x))
A048171: 2 4 6 9 12 17 20 25 28 31 34
((x + 2) * loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x + ~1),x))
A119581: 0 3 24 150 840 4410 22176 108108 514800 2406690 11085360 50438388 227149104 1014058500 4493059200 19777483800
((x + 2) + loop(\(x,i).(2 + ((x + ((x div 5) mod 2)) div 2)),2,x))
A037361: 5 6 7 8 10 12 13 14 15 17 18 19 20 21 23 24
((x * loop(\(x,i).((x2 + ~x) div (1 + i)),2,(x + 4))) div (x + 2))
A052472: 0 10 35 84 168 300 495 770 1144 1638 2275 3080 4080 5304 6783 8550
(2x + (if (~x + 2) <= 0 then ((2x + 2) div 7) else 1))
A111499: 1 3 4 7 9 11 14 16 18 20 23 25 27 30 32 34
(2x + (if x <= 0 then 1 else (x2 div 19)))
A081527: 1 2 4 6 8 11 13 16 19 22 25 28 31 34 38 41
(if x <= 0 then 1 else (2x + (2x2 div 13)))
A126022: 1 2 4 7 10 13 17 21 25 30 35 40 46 52 58 64
(if x <= 0 then 1 else (2x + ((x2 + 2) div 11)))
A134886: 1 2 4 7 9 12 15 18 22 25 29 33 37 41 46 50
(2x + (if ((x + 1) mod (3 + ((x div 2) div 3))) <= 0 then 2 else 1))
A284879: 1 3 6 7 9 12 13 16 17 19 21 24 25 27 30 31
(2x + loop(\(x,i).2x,(~2 + (3 * ((x div 2) div 3))),1))
A033038: 1 3 5 7 9 11 14 16 18 20 22 24 40 42 44 46
((~2x + ~1) + (loop(\(x,i).(2x + 4),x,(3x + 6)) div 2))
A066374: 2 8 25 67 165 387 881 1967 4333 9451 20457 44007 94181 200675 425953 901087
(2x + loop(\(x,i).(~1 + (4 * (~1 + (2 * i)))),((x + ~1) div 2),1))
A231716: 1 3 5 9 11 21 23 33 35 45 47 57 59 69 71 81
(2x + (if (x mod (2 + ((~x + 1) mod (2 + (x div 4))))) <= 0 then 2 else 1))
A285257: 2 3 5 7 10 11 14 15 17 19 22 23 26 27 29 32
(2x + (if x <= 0 then 1 else ((x2 + 3x + 1) div 5)))
A129403: 1 3 6 9 13 18 23 28 33 39 46 53
(2x + (5 * (2 + loop(\(x,i).2x,x,5))))
A250764: 35 62 114 216 418 820 1622 3224 6426 12828 25630 51232 102434 204836 409638 819240
(2x + (if (x div 2) <= 0 then 1 else (~5 + ((x2 + ~x) div 2))))
A074171: 1 3 0 4 9 15 22 30 39 49 60 72 85 99 114 130
(2x + (if ((2x mod 7) - (x mod 2)) <= 0 then 2 else 1))
A287374: 2 3 5 7 9 11 13 16 17 19 21 24 25 27 30 31
(2x + (if x <= 0 then 1 else (((x2 + ~1) div 5) mod 3)))
A333975: 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28 32
(2x + (loop(\(x,i).(2 + ((x2 + x) div 2)),2,(x + ~1)) div 3))
A083462: 1 3 6 11
A055417: 1 3 6 11 20 36 63 106 171 265 396 573 806 1106 1485 1956
((x + 1) - loop(\(x,i).(2 + (x div (2 + (x mod 3)))),3,2x))
A063278: ~1 0 0 1 2 3 4 5 6 7 8 7 10 11 12 11
((((x + 1) div (1 + ((~x + 2) mod 4))) mod 2) + (if x <= 0 then 1 else 2x))
A189401: 1 3 5 7 9 11 13 14 17 19 21 23 24 27 29 30
(2x + (if ((x + 1) mod (3 + ((x div 2) div 3))) <= 0 then 1 else 2))
A284880: 2 4 5 8 10 11 14 15 18 20 22 23 26 28 29 32
(2x + (if (x mod (2 + ((~x + 1) mod (2 + (x div 4))))) <= 0 then 1 else 2))
A231407: 1 4 6
A285256: 1 4 6 8 9 12 13 16 18 20 21 24 25 28 30 31
(if x <= 0 then 1 else (2x + (((x2 + x) div ~8) mod 2)))
A075311: 1 3 5 6 9 10 12 15 17 18 20 23 24 27 29 30
(2x + (loop(\(x,i).(x + ((x + (x div 2)) div 2)),2,(2 + (x div 2))) div 2))
A283967: 2 4 8 10 14 16 19 21 24 26 30 32 36 38 41 43
(2x + (if x <= 0 then 1 else (x - (((x2 + ~2x) div 2) div (x + 4)))))
A231407: 1 4 6
A007074: 1 4 6 9 12 15 17 20 22 25 28 30 33 35 38 40
(2x + loop(\(x,i).((x + 1) - ((x + 1) div 5)),2,2x))
A189400: 2 6 8 12 16 18 22 25 28 32 35 38 41 45 48 51
loop(\(x,i).(~1 + ((x div 2) + ((x div 2) mod (1 + (x mod 4))))),x,2x)
A165586-A011611: 0 1 ~1 ~1 1 1 1 1 ~1 1 ~1 1 ~1 1 ~1 ~1
(2x + (if x <= 0 then 2 else (x + ((x mod (2 + (x mod 5))) mod 2))))
A309374: 2 4 6 10 12
A082417: 2 4 6 10 12 16 18 22 25 28 30 33 36 40 42 46
((if (x mod 2) <= 0 then 51 else 1) + (x div 2))
A087408: 51 1 52 2 53 3 54 4 55 5 56 6 57 7 58 8
(1 + ((2 * ((x * (if (x mod 2) <= 0 then 2 else x)) div 8)) + (x div 2)))
A276163: 1 1 2 4 5 9 6 16 9 25
(1 + (x div 2) - (x div (1 + (2 * (if ((x + 1) mod 3) <= 0 then x else 2)))))
A167227: 1 1 2 2 3 3 3 3 5 4 4 6 5 5 8 5
((loop(\(x,i).((x2 + ~x) div 2),2,((x + ~1) div 2)) div 3) * (x div 2))
A333320: 0 0 0 0 0 0 0 3 4 20 25 75 90 210 245 490
((if (x mod (1 + ((~2x + 2) mod (1 + (x div 2))))) <= 0 then 1 else 2) + (x div 2))
A239105-A046699: 1 1 2 2 3 4 4 4 5 6 6 7 8 8 8 8
(2x + ((((if (~2 + (x div 2)) <= 0 then 1 else 2) + (x div 2)) mod 2) + (x div 2)))
A003255: 1 3 5 7 11 13 16 18 20 22 26 28 30 32 36 38
((x + 1) + (((x + ((if (x + ~2) <= 0 then 1 else x) mod 2)) div 3) + (x div 2)))
A187476: 1 2 5 6 8 10 12 13 15 17 19 21 23 24 26 28
((if ((x * (x mod 3)) mod 7) <= 0 then 1 else 0) - (x mod 2))
A112211: 1 ~1 0 0 0 ~1 1 0 0 0 0 ~1 1 ~1 1 0
((if (x mod (2 + ((x2 + ~2x) mod (x + 4)))) <= 0 then 1 else 0) + (x mod 2))
A338822: 1 1 1 1 1 1 1 1 1 1 0 2 0 1 0 1
((if ((x mod 3) - ((((x + 1) div 2) div 2) mod 2)) <= 0 then 0 else 1) - (x mod 2))
A074290: 0 0 1 ~1 0 0 0 0 1 ~1 1 0 0 ~1 1 ~1
((1 + ((x + ~1) div (3 + (if (x mod 3) <= 0 then 0 else 2)))) * (x mod 2))
A035442: 0 1 0 1 0 1 0 2 0 3 0 3 0 3 0 5
((if ((1 + ((x + (x div 2)) div 2)) mod 5) <= 0 then 2 else 1) - (x mod 2))
A275851: 1 0 1 0 1 0 2 0 1 0 1 0 2 1 1 0
(((~x + (x div ((if (x mod 2) <= 0 then 1 else x) mod 4))) mod 3) + (x mod 2))
A147648: 0 1 0 2 0 1 0 2 0 1 0 2 0 1 0 3
((if (((x + 1) mod 3) - (x mod 2)) <= 0 then 1 else (x div 3)) + (x mod 2))
A086421: 0 1 1 2 1 2 2 3 1 2 3 2
(1 + (loop(\(x,i).(2 * (2x - (x mod 4))),2,(x div 2)) + (x mod 2)))
A098871: 1 2 5 6 17 18 21 22 65 66 69 70 81 82 85 86
(x div (2 + (if (x mod 7) <= 0 then (x div 2) else 0) - (x mod 2)))
A106615: 0 1 1 3 2 5 3 1 4 9 5 11 6 13 1 15
((if ((x + 2) mod (1 + (2x div 5))) <= 0 then 1 else 2) - (x mod 2))
A107455: 1 0 1 1 1 1 2 0 2 1 2 1 2 1 2 1
(2 - ((x mod 2) + (((x + ~2) mod (1 + (if x <= 0 then 2 else (x div 3)))) mod 2)))
A287341: 1 1 2 0 2 0 1 1 2 0 2 0 2 0 2 0
((if (x mod (2 + ((x - (x div 3)) div 3))) <= 0 then 1 else 2) + (x mod 2))
A106824: 1 3 1 3 2 3 1 3 1 3 2 3 1 3 2 2
((if x <= 0 then 1 else (2 + ((x2 + 2) div 9))) - (x mod 2))
A029009: 1 1 2 2 4 4 6 6 9 10 13 14 18 20 24 26
((x div (2 + (x div (1 + ((if (x mod 2) <= 0 then 2 else x) mod 4))))) + (x mod 2))
A076649: 0 1 1 2 1 2 1 3 2 2 2 3 2 2 2 4
(2 + (3 * (loop(\(x,i).2x,x,2) div 5)) - (x mod 2))
A226309: 2 1 5 10 20 37 77 154 308 613 1229 2458 4916 9829 19661 39322
(x + (x mod 2) - (if x <= 0 then 0 else (1 - (2 * (x - (2 * (x div 3)))))))
A063202: 0 3 5 5 7 11 9 13 15 15 17 21 19 23 25 25
((((~x + 1) div (2 + (if (~1 + (x mod 3)) <= 0 then x else 2))) mod 2) - (x mod 2))
A129950: 0 ~1 1 0 1 0 1 0 0 0 1 0 1 0 0 0
(loop(\(x,i).(13x + 1),x,0) div (2 - (x mod 2)))
A152436: 0 1 7 183 1190 30941 201117 5229043 33988780 883708281 5744103827 149346699503 970753546770 25239592216021 164057349404137 4265491084507563
(loop(\(x,i).(17x + 1),x,0) div (2 - (x mod 2)))
A152437: 0 1 9 307 2610 88741 754299 25646167 217992420 7411742281 62999809389 2141993519227 18206944913430 619036127056621 5261807079981279 178901440719363487
((if ((x + 3) mod 9) <= 0 then 2 else 1) * (2 - (x mod 2)))
A214716: 2 1 2 1 2 1 4 1 2 1 2 1 2 1 2 2
(x * ((1 + (2 * (if (x mod 5) <= 0 then 0 else 2))) * (2 - (x mod 2))))
A227109: 0 5 20 15 40 5 60 35 80 45 20 55 120 65 140 15
loop(\(x,i).(~x + (6 * ((x + 1) + (x div 2)))),(x div 2),(x mod 2))
A341943: 0 1 6 11 54 91 438 731 3510 5851 28086 46811 224694 374491 1797558 2995931
(if x <= 0 then 1 else (41x2 + 2))
A206399: 1 43 166 371 658 1027 1478 2011 2626 3323 4102 4963 5906 6931 8038 9227
loop(\(x,i).((x + 1) + (((x + 2) mod (2 + ((x + ~1) mod 4))) div 2)),x,2)
A130176: 2 3 4 5 6 8 9 10 11 12 15 16 18 20 22 23
(if x <= 0 then 1 else (2 * (x + compr(\x.(x mod (1 + (8 * (x mod 2)))),x))))
A315755: 1 6 12 18 24 28 32 38 44 50 56 62 68 74 80 84
((x + 2) + loop(\(x,i).(((~1 + (x div 2)) div 2) - ((~x + 1) div 3)),2,x))
A180734: 1 2 3 4 5 8 9 10 11 12 14 16 17 18 20 21
((x + loop(\(x,i).(2 * ((x + 1) + (4 * (x + (x mod 2))))),2,x)) div 2)
A305395: 11 101 112 202 213 303 314 404 415 505
(x - ((x * loop(\(x,i).(1 - (4x * ((x + ~1) div 2))),2,x)) div 2))
A191942: 0 1 1 398
((x + 2) + loop(\(x,i).(x + (x div 2) - ((x + 1) div 5)),2,x))
A308357: 2 4 8 10 12 15 19 20 24 25
(loop(\(x,i).(x7 + x5),1,x2) div 2)
A170796: 0 1 8704 2421009 134742016 3056640625 39212315136 339252774049 2199560126464 11440139619681 50005000000000 189887885503921 641990190956544 1968757122095569 5556148040106496 14596751337890625
(loop(\(x,i).(x7 + x3),1,x2) div 2)
A168632: 0 1 8224 2391849 134219776 3051765625 39182105376 339111595249 2199023386624 11438396493201 50000000500000 189874917677401 641959233767424 1968688195263049 5556003416543776 14596463018390625
(((x5 + 1) * loop(\(x,i).x2,2,x2)) div 2)
A170777: 0 1 4224 800442 33587200 610546875 6531186816 48447387604 274886295552 1270954437525 5000050000000 17261463251406 53496817680384 151437961161487 396858124521600 973098815625000
((if x <= 0 then 1 else (10x2 + 2)) + (x2 div 2))
A007899: 1 12 44 96 170 264 380 516 674 852 1052 1272 1514 1776 2060 2364
((x4 * (x2 + loop(\(x,i).x3,2,x))) div 2)
A168631: 0 1 4128 797526 33556480 610359375 6530370336 48444564028 274878038016 1270933179885 5000000500000 17261356957746 53496604182528 151437555709531 396857390391840 973097539875000
((x2 * loop(\(x,i).(x2 + x),1,x5)) div 2)
A168662: 0 1 2112 266814 8396800 122109375 1088531136 6921055372 34360786944 141217159725 500005000000 1569223931946 4458068140032 11649073935499 28347008894400 64873254375000
(loop(\(x,i).(x2 + x),1,x7) div 2)
A168664: 0 1 8256 2392578 134225920 3051796875 39182222016 339111948196 2199024304128 11438398618965 50000005000000 189874926535206 641959250190336 1968688224223903 5556003465485760 14596463098125000
((x2 * loop(\(x,i).(x4 + x),1,x3)) div 2)
A168471: 0 1 8208 2391606 134218240 3051759375 39182085936 339111544828 2199023271936 11438396257005 50000000050000 189874916872146 641959232398848 1968688193035291 5556003413047920 14596463013075000
(loop(\(x,i).(x4 + x2),1,x5) div 2)
A170802: 0 1 524800 1743421725 549756338176 47683720703125 1828079250264576 39896133290043625 576460752840294400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x * loop(\(x,i).(x3 + x),1,x5)) div 2)
A168634: 0 1 32800 21523725 2147485696 76293953125 1410554977056 16616465343625 140737488486400 926510094691641 5000000000500000 22974864932671861 92442129449011200 332708304594003325 1088976668908450336
((3x + 2) + loop(\(x,i).((~x + 2) + (x div 5)),2,x))
A184929: 2 6 10 13 17 20 24 28 32 35 38 42 46 50 54 57
((x * loop(\(x,i).(x5 + x3),1,x3)) div 2)
A170798: 0 1 33280 21552885 2148007936 76298828125 1410585186816 16616606522425 140738025226240 926511837818121 5000005000000000 22974877900498381 92442160406200320 332708373520835845 1088976813532013056
((x * loop(\(x,i).(x5 + x2),1,x3)) div 2)
A168666: 0 1 32832 21524454 2147491840 76293984375 1410555093696 16616465696572 140737489403904 926510096817405 5000000005000000 22974864941529666 92442129465434112 332708304622964179 1088976668957392320
(x + (if ((x + 2) mod 6) <= 0 then (1 + (2 * (x div 3))) else 0))
A295484: 0 1 2 3 7
A235801: 0 1 2 3 7 5 6 7 8 9 17 11 12 13 14 15
(x + (if ((1 + (x div 2)) mod 6) <= 0 then 12 else 0))
A103303: 0 1 2 3 4 5 6 7 8 9
A305463: 0 1 2 3 4 5 6 7 8 9 22 23 12 13 14 15
(x + loop(\(x,i).((x + 1) - (x div (~2 + (x div ~7)))),x,0))
A213707: 0 2 5 8 12 16 21 26 32 38 45 52 60 68 76 84
(~x + loop(\(x,i).((x + 2) + ((x - ((~x + 1) div 3)) div (1 + i))),x,0))
A145197: 0 1 3 5 8 11 15 19 23 28 33 38 44 50 56 62
((6x2 + 11x + 15) + (if x <= 0 then 0 else 1))
A228321: 15 33 62 103 156 221 298 387 488 601 726 863 1012 1173 1346 1531
(x + (if (~x + 2) <= 0 then (2 - ((~x + 2) div 11)) else 1))
A138888: 1 2 4 6 7 8 9 10 11 12 13 14 15 16 18 19
compr(\x.((x + 1) mod (1 + (if ((x + ~1) mod 7) <= 0 then 2 else 1))),x)
A120212: 3 5 7 8 9 11 13 17 19 21 23 25 27 29 31 33
compr(\x.(1 - (x mod (1 + (if (x mod (1 - (x div ~4))) <= 0 then 2 else 1)))),x)
A343983-A074583-A001092: 1 2 3 4 5 7 9 11 13 17 19 23 25 27 29 31
compr(\x.(1 - (x mod (~1 + (5 * (if (x mod 3) <= 0 then 2 else 1))))),x)
A225354: 1 2 3 5 6 7 10 11 12 13 14 15 17 19 21 22
(~x + ((2x + (if (x + ~2) <= 0 then 1 else 2)) * (1 + (x div 5))))
A227230: 1 2 3 5 6 19 22
compr(\x.(x mod (~1 + (6 * (if (~2 + (x div 3)) <= 0 then 0 else 2)))),x)
A118600: 0 1 2 3 4 5 6 7 8 11 22 33 44 55 66 77
loop(\(x,i).x5,1,11x)
A017393: 0 161051 5153632 39135393 164916224 503284375 1252332576 2706784157 5277319168 9509900499 16105100000 25937424601 40074642432 59797108943 86617093024 122298103125
(x + (if (~x + 2) <= 0 then ((x + ~2) + (((x2 + 2x) div 2) mod 3)) else 1))
A014593: 1 2 3 5 6 10 10 13 15
(x * (1 + ((x + ~1) * loop(\(x,i).(2x2 + 4x + 1),2,4))))
A167149: 0 1 10000 29997 59992 99985 149976 209965 279952 359937 449920 549901 659880 779857 909832 1049805
(x + loop(\(x,i).(x + (2x div (1 + (x div 5)))),(x + ~1),1))
A116727: 1 2 5 12 22 32 42 52 62 72 82 92 102 112 122 132
((x + 1) div (if (x mod 4) <= 0 then (1 + (x mod 10)) else x))
A113607: 1 2 1 1 1 1 1 1 1 1 1 1 4 1 1 1
((x + 1) + (loop(\(x,i).(2 * ((x2 + x) - (x div 3))),x,1) div 2))
A065401: 1 4 22 1474
((~x + 1) + (loop(\(x,i).(2 * ((x * (1 + i)) - (x div 3))),x,1) div 2))
A245903: 1 2 10 79 753
((~x + 1) + (2 * ((x + 1) + loop(\(x,i).(x - (x div 4)),2,(x div 2)))))
A285503: 3 4 7 8 11 12 15 16 17 18 19 20 23 24 27 28
(x + (if (~x + 2) <= 0 then (2 + ((x - (((x div 2) div 3) mod 2)) div 2)) else 1))
A299417: 1 2 5 6 8 9 10 12 13 15 16 18 20 21 23 24
(x + loop(\(x,i).(3x + 1),(x div (4 + (x div 4))),1))
A098464-A068586-A068585: 1 2 3 4 5 9 10 11 12 13 14 15 16 17 27 28
(if (x mod 2) <= 0 then (x3 mod 30) else x)
A222232: 0 1 8 3 4 5 6 7 2 9 10 11 18 13 14 15
(if (x mod 5) <= 0 then (x div 5) else 5x)
A283442: 0 5 10 15 20 1 30 35 40 45 2 55 60 65 70 3
compr(\x.(~1 + ((x * (loop(\(x,i).(~2x + 2),x,2) mod (x + 2))) div 4)),x)
A238526: 0 1 2 3 5 7 9 11 15 17 21 27 29 35 39 41
compr(\x.((if (x mod 4) <= 0 then 2 else (x mod 2)) - (x mod (1 + (x div 4)))),x)
A092206: 2 5 6 7 8 10 11 13 14 15 17 18 19 20 21 22
(2x mod ((x + 1) + (2 * ((if (~2 + (x div 2)) <= 0 then 2 else 1) + (x mod 2)))))
A103694: 0 2 4 6 8 10 3 2 5 4 7 6 9 8 11 10
(x + ((((x2 div 2) div 5) - (if x <= 0 then 0 else 1)) div 3))
A316681: 0 0 1 2 4 5 6 8 9 11 13 14 16 18 20 22
(x + (3 * ((x + 1) - ((1 - (if (~x + 2) <= 0 then x else 2)) div 3))))
A187682: 6 10 14 18 22 29 33 37 44 48 52 59 63 67 74 78
(x + (9 * (~1 + (if (~4 + (x div 2)) <= 0 then 1 else x))))
A103303: 0 1 2 3 4 5 6 7 8 9
A071271: 0 1 2 3 4 5 6 7 8 9 91 101 111 121 131 141
loop(\(x,i).x5,1,(7x + 3))
A017021: 243 100000 1419857 7962624 28629151 79235168 184528125 380204032 714924299 1252332576 2073071593 3276800000 4984209207 7339040224 10510100501 14693280768
(~x + ((((1 + (x div 2)) mod 3) + loop(\(x,i).2x,x,1)) div 3))
A111926: 0 0 0 0 1 5 15 36 78 162 331 671 1353 2718 5448 10908
(x + (if x <= 0 then 1 else ((4x3 + 12x2 + 8x) div 3)))
A273744: 1 9 34 83 164 285 454 679 968 1329 1770 2299 2924 3653 4494 5455
(if x <= 0 then 1 else (x + (((((x + ~1) div 2) * (x div 3)) div 2) div 3)))
A066022: 1 1 2 3 4 5 6 8 9 11 12 13 15 17 18 20
loop(\(x,i).x5,1,(7x + 6))
A017057: 7776 371293 3200000 14348907 45435424 115856201 254803968 503284375 916132832 1564031349 2535525376 3939040643 5904900000 8587340257 12166529024 16850581551
(x + ((4 * ((x + 1) + (if (x + ~4) <= 0 then 1 else 2))) div 3))
A260480: 2 5 7 9 12 15 18 20 22 25 27 29 32 34 36 39
(x + (3 * (4 + (if (x + ~10) <= 0 then 1 else 2))))
A297281-A296751: 15 16 17 18 19 20 21 22 23 24 25 29 30 31 32 33
(x + loop(\(x,i).(x * (x + i)),3,(x div ~11)))
A103303: 0 1 2 3 4 5 6 7 8 9
A049872: 0 1 2 3 4 5 6 7 8 9 10 11 100 101 102 103
(x + ((~2 + (if x <= 0 then 2 else (x + (x mod (2 * (1 + (x mod 2))))))) div 3))
A038669: 0 1 2 4 4 6 7 9 10 11 12 15 15 17 18 20
(3x + (if (x mod 2) <= 0 then 2 else 0) - (x div 12))
A327312: 2 3 8 9 14 15 20 21 26 27 32 33 37 38 43 44
(10 mod (x + (3 * (if (x mod 4) <= 0 then 1 else x))))
A083457: 1 2 2 10 3 10 10 10 10 10 10 10 10 10 10 10
(x + (loop(\(x,i).(x + 4),(~2 + ((x + ~1) div 3)),x) div 3))
A138083: 0 1 2 4 5 6
A267137: 0 1 2 4 5 6 8 9 10 12 14 16 17 20 21 22
((x + 1) - loop(\(x,i).(x - (x div 7)),(x div 3),x))
A307467: 1 1 1 1 1 1 1 2 3 4 4 4 5 5 6 7
((x + 1) + (2 * (x + loop(\(x,i).(1 + (x * (3 + i))),(x + ~1),1))))
A003323: 3 6 17 62 327
loop(\(x,i).(8x + 1),(10x + 1),x)
A022251: 1 9817068105 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~8x + 1),(10x + 1),x)
A015413: 1 ~7635497415 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) + (loop(\(x,i).(3 * ((x + ~1) + (2 * i))),(x + ~1),x) div 2))
A087448: 1 2 7 26 93 322 1091 3642 12025 39362 127935 413338 1328597 4251522 13551739 43046714
(~x + ((2x + 1) * loop(\(x,i).(6x + 4),2,2x)))
A156711: 28 299 858 1705 2840 4263 5974 7973 10260 12835 15698 18849 22288 26015 30030 34333
loop(\(x,i).(x - (((~x2 + x) div 2) div 3)),1,(2x2 + ~x))
A341735: 0 1 11 50 154 375 781 1456 2500 4029 6175 9086 12926 17875 24129 31900
((2x2 + ~x) * loop(\(x,i).(x * (2 + ((x + ~1) mod 3))),x,1))
A229679: 0 2 36 360 2688 17280 101376 559104 2949120 15040512 74711040 363331584 1736441856 8178892800 38050725888 175154135040
compr(\x.(1 - (x mod (1 + ((if (~4 + (x div 2)) <= 0 then 2 else 1) + (x mod 2))))),x)
A322546: 1 2 3 4 5 7 8 9 11 13 17 19 23
A280619: 1 2 3 4 5 7 8 9 11 13 17 19 23 25 29 31
(if x <= 0 then 1 else (~x + ((16x + ~8) * (1 + (x mod 2)))))
A236107: 1 15 22 77
loop(\(x,i).(2x7 + ~x6),x,(~x + 1))
A330730: 1 0 ~5103 4611686018427387903 4611686018427387903
((x + ~1) + loop(\(x,i).(2 * (~1 + (~7 * (x div 2)))),2,x))
A095764: 11 12 111 112 211 212 311 312 411 412 511 512 611 612 711 712
(~x + loop(\(x,i).((x + 1) - ((~x + 1) div (2 - (x div ~4)))),x,1))
A072831: 1 1 2 3 5 7 10 13 16 19 22 26 29 33 37 41
(~x + loop(\(x,i).((x + 1) - ((~x + 1) div (6 + (x mod 2)))),x,1))
A075535: 1 1 2 3 4 6 8 11 14 18 22 28 34 42 50 61
(~x + loop(\(x,i).((x + 2) + ((2 * (x mod (2 + (x div 2)))) div 3)),x,1))
A094054: 1 2 3 4 6 9 13 19 27 38 53 74 102 139 189 256
loop(\(x,i).((x + 1) + (x div (1 + (x mod 10)))),(x + 1),x)
A241175: 1 3 5 7 9 21 43 65 87
compr(\x.(2 - (loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,1) mod (x + 1))),x)
A064528: 2 3 6 7 8 10 12 14 15 17 18 19 20 21 22 23
(~x + ((x2 + 2x + 1) * (2 + loop(\(x,i).x2,(x + ~2),3))))
A154302: 5 19 43 173
loop(\(x,i).x5,1,(9x + 8))
A017261: 32768 1419857 11881376 52521875 164916224 418195493 916132832 1804229351 3276800000 5584059449 9039207968 14025517307 21003416576 30517578125 43204003424 59797108943
loop(\(x,i).x6,1,(5x + 4))
A016902: 4096 531441 7529536 47045881 191102976 594823321 1544804416 3518743761 7256313856 13841287201 24794911296 42180533641 68719476736 107918163081 164206490176 243087455521
(x + ((x + 1) * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A083723: 2 7 17 31 59 83 125 159 215 299 351 455 545 615 719 863
(~x + ((x + 1) * loop(\(x,i).(x + ((3x + 6) div (1 + i))),x,2)))
A007972: 2 15 52 129 266 487 820 1297 1954 2831 3972 5425 7242 9479 12196 15457
loop(\(x,i).(2x3 + 9x2 + 6x + 1),1,(x2 + x))
A008516: 1 65 793 4825 19721 62281 164305 379793 793585 1531441 2771561 4757545 7812793 12356345 18920161 28167841
((x2 + x) + (loop(\(x,i).((x2 + ~x) div 2),2,(x + 1)) div 3))
A318054: 0 2 7 17 35 65 112 182 282 420 605 847 1157 1547 2030 2620
((x2 + x) + (loop(\(x,i).x2,1,(3 * (x + (x mod 2)))) div 2))
A219392: 0 20 24 84 92 192 204 344 360 540 560 780 804 1064 1092 1392
compr(\x.(1 - (loop(\(x,i).((x2 + ~x) div 2),2,3x) mod (x + 1))),x)
A296484: 1 3 6 7 8 9 10 12 13 15 16 17 18 19 20 21
((24x2 + ~12x + 1) div (if x <= 0 then 1 else x))
A101103: 1 13 36 60 84 108 132 156 180 204 228 252 276 300 324 348
(((x - ((~1 + (x2 div 2)) div 5)) div 2) + (if x <= 0 then 1 else x))
A136687-A086706: 1 2 3 4 5 6 7 8 9 10 10 11 11 11 11 11
(x * (~1 + loop(\(x,i).(x3 + 7x2 + 14x + 8),1,x2)))
A261540: 0 29 478 4287 24476 101785 337434 946043 2333752 5206581 10714070 20633239 37597908 65378417 109216786 176222355
(2x - (((x div 2) - (if ((x + 2) mod 5) <= 0 then 0 else 1)) div 2))
A187343: 1 3 4 6 8 10 11 13 14 17 18 20 22 23 25 27
(x + (loop(\(x,i).(x + 5),(~1 + (x div 5)),1) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A247811: 0 1 2 3 4 5 6 7 8 9 13 14 15 16 17 20
compr(\x.(1 - (x mod (2 + (x mod (1 + (if (~4 + (x div 2)) <= 0 then 2 else 1)))))),x)
A327782: 1 2 3 4 5 7 9 11 13 17 19 23 25 29 31 35
(if x <= 0 then 1 else compr(\x.((x mod (1 + (x mod (1 + (2 * (2 + (x mod 2))))))) mod 2),x))
A136499: 1 2 4 6 7 8 9 10 12 13 14 16 18 20 21 23
loop(\(x,i).(1 + ((1 + ((x * ((x + 1) div 2)) div 2)) div 5)),2,x)
A005863: 1 1 1 1 1 1 1 2 2 2 3 4 4 6 7 10
loop(\(x,i).(1 - (x mod (1 + ((x * (x mod 3)) mod 5)))),2,x)
A260942: 0 1 ~2 0 1 0 0 1 0 0 0 ~2 0 1 ~2 0
(x + (2 * (~1 + (loop(\(x,i).i,(~3 + ((x + ~1) div 2)),1) mod 3))))
A103303: 0 1 2 3 4 5 6 7 8 9
A302028-A302027: 0 1 2 3 4 5 6 7 8 9 10 13 14 11 12 15
loop(\(x,i).(x - (x mod (1 + ((x2 + ~x + 2) div (x + 3))))),2,x)
A249040: 0 1 2 2 2 2 3 3 4 5 6 7 7 8 9 9
(x + (if x <= 0 then 0 else (2 - ((x div (1 + (2 * ((x + ~1) mod 3)))) mod 2))))
A058317: 0 2 4 5 6 6 7 8 10 10 12 12 14 14 16 16
((x + 2) - ((~x + 1) div (2 + (if ((x div ~2) mod 3) <= 0 then 2 else 1))))
A304364: 2 3 5 6 7 8 10 11 13 14 15 16 17 19 21 22
(2 div loop(\(x,i).(1 + ((2x + 1) mod (4 + (x div 4)))),2,x))
A286561: 1 0 1 0 1 1 0 0 0 1 0 0 1 2 1 0
(0 - loop(\(x,i).(~1 + ((~2x + 2) mod (4 + (x div 4)))),2,x))
A265602: 1 0 1 0 1 1 0 ~1 1 1 0 1 ~1 1 1 0
((x + 2) + (if x <= 0 then 1 else ((1 + (2 * (x + (x mod 2)))) div 5)))
A298006: 3 4 5 6 7 9 10 12 13 15 16 18 19 20 21 23
(x + (if (x + ~1) <= 0 then 1 else ((x div 2) - (((x + ~1) div 5) mod 2))))
A268377-A209921-A201010-A004144: 1 2 3 4 6 7 8 9 11 12 14 16 18 19 21 22
(x + (if (x mod 2) <= 0 then 1 else ((x + 2) - ((x + 1) mod 10))))
A217556: 1 2 3 4 5 6 7 8 9 20 11 22 13 24 15 26
(x + ((1 + ((if (x mod (4 + (x div 2))) <= 0 then 1 else x) mod 4)) div 2))
A138311: 1 2 3 5 4 6 7 8 9 10 11 13 12 14 15 17
(x + (if x <= 0 then 1 else (2x - ((x mod (1 + ((~x + 2) mod 4))) mod 2))))
A298474: 1 2 6 8 11 14 18 20 24 26 30 32 36 38 42 44
(2 div (if ((x - (2 * (((x + 1) div 2) div 3))) mod 3) <= 0 then 2 else x))
A104162: 1 2 1 1 0 1 0 0 1 0 0 0 0 1 0 0
compr(\x.(((x + 2) mod (3 * ((if (x mod 2) <= 0 then 1 else x) mod 4))) div 2),x)
A190853: 1 2 4 5 7 8 10 13 14 16 17 20 22 25 26 28
(~x + (2 * ((4 * (x + (if (~2 + (x div 2)) <= 0 then 1 else 2))) div 3)))
A098740: 2 3 6 7 8 11 14 17 18 19 22 23 24 27 28 29
loop(\(x,i).2x,(((x + ~1) div 2) - ((3 * (x div 4)) div 2)),x)
A335063: 0 1 2 6 4 10 12 28 8 18 20 44 24 52 56 120
(x + (if (x div 4) <= 0 then 1 else (x - ((x - ((x div 2) div 3)) div 2))))
A335999: 1 2 3 4 6 8 10 11 13 14 16 17 19 21 22 24
(x + (((3 * ((x div 2) div 3)) div 2) + (if (x + ~2) <= 0 then 1 else 2)))
A329133: 1 2 3 5 6 7 9 10 11 12 13 14 17 18 19 20
(x * (((x + 1) * loop(\(x,i).(x + (i * i * (1 + i))),(x + 2),0)) div 2))
A293608: 0 50 390 1680 5320 13860 31500 64680 122760 218790 370370 600600 939120 1423240 2099160 3023280
(4x div ((x + 2) + (loop(\(x,i).(2x + 2),x,0) mod (x + 1))))
A333870-A072086: 0 1 2 1 2 2 3 1 2 2 3 2 3 3 2 1
(x * loop(\(x,i).((2x * (1 + (2 * i))) div (3 + i)),(x + 1),2))
A028379: 0 6 28 108 396 1430 5148 18564 67184 244188 891480 3268760 12034980 44482230 165002460 614106900
((x + 4) + (if (~x + 2) <= 0 then (2 - ((x div 2) div ~3)) else 1))
A227006: 5 6 9 10 11 12 13 14 16 17 18 19 20 21 23 24
((x + 2) + ((x - ((x div 2) mod (1 + (if (~2 + (x div 2)) <= 0 then 2 else 1)))) div 2))
A062974: 2 3 4 6 7 8 10 12 14 15 16 18 20 21 22 24
compr(\x.(1 - (x mod (2 + (if (((x + 1) div 2) mod 5) <= 0 then 1 else 2)))),x)
A321453: 1 2 3 5 6 7 10 11 13 14 15 17 18 19 20 21
(x + (2 * (if x <= 0 then 1 else ((x mod (~1 + (x mod (~1 + ((~x + 1) div 2))))) mod 2))))
A167482: 2 1 2 5 4 7 6 9 10 11 10 13 12 15 16 17
((~x + ~2) + (loop(\(x,i).x2,1,((x + 3) - (x div ~2))) div 2))
A324275: 2 9 14 27 34 53 64 89 102 133 150 187 206 249 272 321
loop(\(x,i).(2 * (x - (5 * ((x div 5) mod 2)))),2,x)
A059627: 0 4 8 2 6 0 4 8 2 6 40 44 48 42 46 40
(x + (2 * (((if x <= 0 then 1 else x) mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2)))
A076480: 2 1 2 3 4 7 6 7 8 11 10 13 12 15 16 15
loop(\(x,i).((((x + 1) * i) div 2) - ((3 * (x div 4)) div 2)),2,x)
A105264: 1 2 2 3 2 3 3 4 2 3 3 4 3 4 4 4
(0 - (x3 div loop(\(x,i).(~3x2 + x),2,2)))
A237757: 0 1 1 1 1 1 1 2 2 3 4 5 6 8 9 11
loop(\(x,i).x5,1,(9x + 4))
A017213: 1024 371293 5153632 28629151 102400000 282475249 656356768 1350125107 2535525376 4437053125 7339040224 11592740743 17623416832 25937424601 37129300000 51888844699
loop(\(x,i).(x3 + 2x2 + ~x + ~2),1,(7x + 4))
A001561: 90 1560 6460 16848 34782 62320 101520 154440 223138 309672 416100 544480 696870 875328 1081912 1318680
loop(\(x,i).x5,1,(7x + 4))
A017033: 1024 161051 1889568 9765625 33554432 90224199 205962976 418195493 777600000 1350125107 2219006624 3486784401 5277319168 7737809375 11040808032 15386239549
(x + (4 * (if (2 - (x div 4)) <= 0 then 8 else (x + 1))))
A120433: 4 9 14 19 24 29 34 39 40 41 42 43 44 45 46 47
(x + (2 * (4 + (((x div 2) div 5) + (if x <= 0 then 1 else 2)))))
A241144: 10 13 14 15 16 17 18 19 20 21 24 25 26 27 28 29
(x + (4 * (4x - ((if x <= 0 then 1 else x) div ~4))))
A188219: 4 21 38 55 72 93 110 127 144 165 182 199 216 237 254 271
compr(\x.(((x + 1) div (2 + (2 * (if (~2 + (x div 3)) <= 0 then 1 else 2)))) mod 2),x)
A206331: 0 1 2 7 8 11 12 13 14 15 16 23 24 25 26 27
(x mod loop(\(x,i).(x - (((x - ((x + 2) div (2 + (x mod 2)))) div 2) div 2)),2,x))
A102605: 0 0 0 0 0 0 0 1 0 1 2 2 2 3 3 4
compr(\x.(if (x mod 4) <= 0 then 1 else ((((x2 + (x div 2)) div 2) div 2) mod 2)),x)
A285138: 1 3 5 10 14 15 17 19 21 26 30 31 33 35 37 42
compr(\x.((x4 + ~x) mod (~2 + loop(\(x,i).2x2,2,2))),x)
A010424: 0 1 4 7 9 16 18 22 25 28 36 37 43 46 49 58
loop(\(x,i).(5 * i),(x mod (x - ((x + ~1) mod 8))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A257296: 0 1 2 3 4 5 6 7 8 9 5 10 15 20 25 30
loop(\(x,i).(4x2 + 17x + 18),1,(x + 8))
A157431: 410 495 588 689 798 915 1040 1173 1314 1463 1620 1785 1958 2139 2328 2525
(~x + (2 * ((if x <= 0 then 1 else 4x) - ((x + (x div 2)) div 4))))
A285682: 2 7 14 19 26 33 38 45 50 57 64 69 76 83 88 95
(x + (4 * (x - ((x mod 10) mod (if x <= 0 then 1 else x)))))
A092454: 0 5 10 15 20 25 30 35 40 45 50 51 52 53 54 55
(~x + loop(\(x,i).(x + ((5x + 10) div (1 + i))),x,4))
A027659: 4 18 52 121 246 455 784 1278 1992 2992 4356 6175 8554 11613 15488 20332
compr(\x.(1 - (x mod (2 + ((x + loop(\(x,i).i,(x div 5),1)) mod 2)))),x)
A328674-A325394-A321698-A320324-A316476-A056867: 1 2 3 4 5 7 8 9 11 13 15 16 17 19 23 25
(x * (loop(\(x,i).(1 + ((~1 + (x2 div 2)) div 5)),2,x) div 2))
A308867: 0 0 0 0 0 0 6 7 16 27 50 77 132 182 280 390
(~x + (2 * loop(\(x,i).(x - ((((2 - (x div 2)) mod (x + 2)) div 2) div 2)),2,x)))
A271800: 0 1 2 3 4 5 4 3 2 1 2 3 4 5 6 5
(x + (loop(\(x,i).(2x + (8 div (1 + i))),(x div 2),x) div 2))
A162951: 0 1 6 8 17 20 41
loop(\(x,i).(25x + 25),2,(x2 + 2x))
A157915: 650 2525 5650 10025 15650 22525 30650 40025 50650 62525 75650 90025 105650 122525 140650 160025
loop(\(x,i).(40x + 40),2,(x2 + 2x))
A158775: 1640 6440 14440 25640 40040 57640 78440 102440 129640 160040 193640 230440 270440 313640 360040 409640
loop(\(x,i).(~24x + ~24),2,(x2 + 2x))
A158636: 552 2280 5160 9192 14376 20712 28200 36840 46632 57576 69672 82920 97320 112872 129576 147432
loop(\(x,i).(~21x + ~21),2,(x2 + 2x))
A145678: 420 1743 3948 7035 11004 15855 21588 28203 35700 44079 53340 63483 74508 86415 99204 112875
loop(\(x,i).(~13x + ~13),2,(x2 + 2x))
A158550: 156 663 1508 2691 4212 6071 8268 10803 13676 16887 20436 24323 28548 33111 38012 43251
loop(\(x,i).(~17x + ~17),2,(x2 + 2x))
A158587: 272 1139 2584 4607 7208 10387 14144 18479 23392 28883 34952 41599 48824 56627 65008 73967
loop(\(x,i).(~23x + ~23),2,(x2 + 2x))
A158633: 506 2093 4738 8441 13202 19021 25898 33833 42826 52877 63986 76153 89378 103661 119002 135401
loop(\(x,i).(~22x + ~22),2,(x2 + 2x))
A158627: 462 1914 4334 7722 12078 17402 23694 30954 39182 48378 58542 69674 81774 94842 108878 123882
loop(\(x,i).(~19x + ~19),2,(x2 + 2x))
A158595: 342 1425 3230 5757 9006 12977 17670 23085 29222 36081 43662 51965 60990 70737 81206 92397
loop(\(x,i).(~32x + ~32),2,(x2 + 2x))
A158683: 992 4064 9184 16352 25568 36832 50144 65504 82912 102368 123872 147424 173024 200672 230368 262112
loop(\(x,i).(~28x + ~28),2,(x2 + 2x))
A158657: 756 3108 7028 12516 19572 28196 38388 50148 63476 78372 94836 112868 132468 153636 176372 200676
loop(\(x,i).(~30x + ~30),2,(x2 + 2x))
A158669: 870 3570 8070 14370 22470 32370 44070 57570 72870 89970 108870 129570 152070 176370 202470 230370
loop(\(x,i).(~31x + ~31),2,(x2 + 2x))
A158679: 930 3813 8618 15345 23994 34565 47058 61473 77810 96069 116250 138353 162378 188325 216194 245985
(x + ((~x + loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2)) div (x + 2)))
A290953: 1 2 6 16 45 136 434 1436 4869 16804 58795 208022 742911 2674452 9694858 35357684
compr(\x.((if (((x + ~1) - (x div 4)) mod 4) <= 0 then 0 else 1) - (x mod 2)),x)
A284852: 1 3 5 6 7 9 11 12 13 15 17 19 21 22 23 25
(~x + ((if x <= 0 then 1 else (2 * (x - (2 * (~x + (x div 3)))))) + (x mod 2)))
A063214: 1 6 10 12 16 22 22 28 32 34 38 44 44 50 54 56
(x * (loop(\(x,i).(x4 + x2),1,x4) div 2))
A170790: 0 1 65792 64579923 8590065664 381470703125 8463334761216 116315277170407 1125899973951488 8338591043543529 50000000500000000 252723515428620731 1109305555950108672 4325207964992918653
(2x + ((x2 + x) div 2) - loop(\(x,i).(2x + ~6),x,0))
A239745: 0 9 25 54 108 211 411 804 1582 3129 6213 12370 24672 49263 98431 196752
(x2 * loop(\(x,i).(8x3 + ~4x2),(x + ~1),1))
A060616: 0 1 16 4032
loop(\(x,i).(x - ((x + 1) mod (1 + (x div (2 + (3 * (x mod 2))))))),x,x)
A325401: 0 1 1 3 1 5 3 7 1 9 5 11 3 11 7 15
loop(\(x,i).(x div (2 - ((x mod (2 + (x mod (2 + (x mod 2))))) mod 3))),x,x)
A244568: 0 1 1 3 1 5 3 7 1 9 5 5 3 13 7 15
(~x + loop(\(x,i).((x + 1) - ((x div (1 + (x div 5))) mod 2)),2,x))
A168313-A072575: 1 0 1 0 2 1 0 0 2 1 0 0 2 2 1 0
(~x + loop(\(x,i).(x + ((((~2 + (x div 2)) * (x div 2)) mod (x + 1)) mod 2)),2,x))
A070176: 0 0 0 1 0 0 2 1 0 0 0 2 1 0 2 1
(2x + loop(\(x,i).((x + 1) - (x div 7)),2,2x))
A190055: 2 6 10 13 16 20 24 27 30 34 38 41 44 48 51 55
loop(\(x,i).(2x - ((x + (x div 3)) div 5)),1,x2)
A293410: 0 2 7 16 28 44 63 85 111 141 174 210 250 293 340 390
loop(\(x,i).(x7 + ~x6 + ~x4 + x3),1,x2)
A037248: 0 0 12096 4245696 251596800 5859000000 76185748800 664376138496 4329310519296 22594320403200 98999901000000 376611192619200 1275001937104896 3914077489672896 11055311444923200 29063177136000000
(~x2 + loop(\(x,i).(x + (5 * ((1 + (2 * i)) * i))),x,1))
A220084: 1 15 62 162 335 601 980 1492 2157 2995 4026 5270 6747 8477 10480 12776
(~x2 + loop(\(x,i).(x + ((1 + (5 * i)) * (1 + i))),x,2))
A102296: 2 13 43 102 200 347 553 828 1182 1625 2167 2818 3588 4487 5525 6712
(~x4 + loop(\(x,i).11x,x,1))
A024131: 1 10 105 1250 14385 160426 1770265 19484770 214354785 2357941130 25937414601 285311655970 3138428355985 34522712115370 379749833544825 4177248169365026
(~x6 + loop(\(x,i).3x,2x,1))
A024107: 1 8 17 0 2465 43424 484785 4665320 42784577 386889048 3485784401 31379288048 282426550497 2541861001520 22876784925425 205891120704024
(~x6 + loop(\(x,i).6x,x,1))
A024068: 1 5 ~28 ~513 ~2800 ~7849 0 162287 1417472 9546255 59466176 361025495 2173796352 13055867207 78356634560 470173593951
(~x6 + loop(\(x,i).8x,x,1))
A024094: 1 7 0 ~217 0 17143 215488 1979503 16515072 133686287 1072741824 8588163031 68716490752 549750987079 4398038981568 35184360698207
(~x6 + loop(\(x,i).5x,x,1))
A024055: 1 4 ~39 ~604 ~3471 ~12500 ~31031 ~39524 128481 1421684 8765625 47056564 241154641 1215876316 6095986089 30506187500
(~x7 + loop(\(x,i).4x,x,1))
A024043: 1 3 ~112 ~2123 ~16128 ~77101 ~275840 ~807159 ~2031616 ~4520825 ~8951424 ~15292867 ~19054592 4360347 163021952 902882449
(~x7 + loop(\(x,i).3x,x,1))
A024030: 1 2 ~119 ~2160 ~16303 ~77882 ~279207 ~821356 ~2090591 ~4763286 ~9940951 ~19310024 ~35300367 ~61154194 ~100630535 ~156510468
(~x5 + loop(\(x,i).12x,x,1))
A024145: 1 11 112 1485 19712 245707 2978208 35815001 429948928 5159721303 61917264224 743008209637 8916100199424 106993205007779 1283918464011040 15407021573826993
(~x5 + loop(\(x,i).10x,x,1))
A024119: 1 9 68 757 8976 96875 992224 9983193 99967232 999940951 9999900000 99999838949 999999751168 9999999628707 99999999462176 999999999240625
(~x5 + loop(\(x,i).7x,x,1))
A024080: 1 6 17 100 1377 13682 109873 806736 5732033 40294558 282375249 1977165692 13841038369 96888639114 678222535025 4747560750568
loop(\(x,i).(1 + ((x + ((x2 div 2) div 3)) div 2)),1,x3)
A274251: 1 1 10 75 374 1365 3997 9976 22102 44652 83834 148296 249697 403333 628834 950907
((~x3 + 1) + (2 * loop(\(x,i).(x + ((1 + i) * i)),2x,x)))
A100187: 1 18 77 204 425 766 1253 1912 2769 3850 5181 6788 8697 10934 13525 16496
(3x + (if x <= 0 then 1 else compr(\x.((x * ((x div 2) div 3)) mod 2),x)))
A311167: 1 4 8 12 16 20 24 29 34 39 43 47 51 55 59 63
(x div (1 + ((x + 1) div (2 + (x mod (1 + (2x mod 3)))))))
A337772: 0 1 1 1 2 1 1 2 1 1 2 2 1 2 1 1
(1 + (3 mod (1 + ((x div 2) mod (1 + (x mod (1 + (x div 3))))))))
A344417-A255231-A050377: 1 1 1 2 1 1 1 2 2 1 1 2 1 1 1 4
(1 + (x div (1 + (x mod (1 + (x mod (1 + (~x mod (1 + (x div 2))))))))))
A117818: 1 2 3 2 5 3 7 4 3 5 11 6 13 7 5 8
(1 + (x mod (1 + (x mod (1 + ((x div 2) mod (3 + (x mod 3))))))))
A087267: 1 1 1 2 1 3 1 4 1 2 1 1 1 2 3 2
(1 + (x div (1 + (x mod (1 + (x mod (1 + (x div (4 + (x mod 2))))))))))
A322445: 1 2 3 4 5 3 7 4 3 5 11 4 13 7 5 4
(1 + ((2x + 1) mod (1 + (2x mod (1 + ((x + 1) div 3))))))
A345992: 1 1 1 1 1 2 1 1 1 2 1 3 1 2 5 1
(1 + (x div (1 + (x mod (1 + ((4 * (x div 3)) div 3))))))
A341679: 1 2 3 2 5 3 7 4 3 2 11 6 13 7 5 8
(1 + (x mod (1 + ((1 + ((x + 1) mod 3)) mod (1 + (x div 3))))))
A337375: 1 1 1 1 1 2 1 1 1 1 3 2 1 2 1 1
(1 + (x mod (1 + ((4x + 9) mod (1 + (x div 3))))))
A327979: 1 1 1 2 1 2 1 2 3 2 1 2 1 2 1 4
(1 + ((x + 2) mod (1 + ((4 + (x div 2)) mod (1 + (x div 3))))))
A294874: 1 1 1 2 1 1 1 2 2 1 1 2 1 1 1 6
(1 + ((1 + ((x + 1) div 2)) mod (1 + (2x mod (1 + (x div 3))))))
A288627: 1 1 1 1 1 1 1 3 2 1 1 2 3 1 1 1
(3 - ((~x + 1) div (1 + (x mod (1 + (x mod (3 - (x mod 2))))))))
A111234: 2 3 4 4 6 5 8 6 6 7 12 8 14 9 8 10
(1 + ((x + ~1) mod (1 + ((x div 2) mod (~1 + (2 * (x mod 5)))))))
A060176: 1 1 2 1 1 1 1 1 3 4 1 1 1 1 1 1
(1 + (x div (1 + (x mod (1 + ((x mod ((x + ~1) - (x mod 4))) div 2))))))
A327393: 1 2 3 4 5 3 7 8 9 5 11 4 13 7 15 16
(1 + ((x + ~1) mod (1 + (x mod (~1 + (2 * ((2 * (x div 2)) div 3)))))))
A187783: 1 1 1 1 1 1 1 1 2 1 1 1 6 6 1 1
(1 + ((x2 + 2x) mod (1 + (x div (3 + ((x div 2) div 3))))))
A067815: 1 1 1 2 1 2 1 2 3 1 1 3 1 1 3 4
(1 + ((~x + 1) mod (1 + ((x + 1) mod (1 + (2 * ((x div 2) div 3)))))))
A232088: 1 1 1 1 1 1 2 1 1 1 1 1 2 4 1 1
(1 + ((x + ~1) mod (1 + (x mod (1 + (2 * (x div (3 - (x mod 2)))))))))
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(1 + ((((x2 + x) div 2) div 5) + (x div 5)))
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(((x + 1) div 2) - ((1 - (x div 3)) mod (1 + (x div 5))))
A048475: 0 1 1 2 2 3 2 3 3 5 4 5 6 7 7 8
((2x + 1) + (x div 5) - ((~x + 1) div (2 + (x div 2))))
A190325-A189937: 1 3 6 8 10 13 15 18 20 22 25 27 29 31 33 36
((x + 1) + ((2 * ((x + 1) div 5)) + (x div 5)))
A047548: 1 2 3 4 7 9 10 11 12 15 17 18 19 20 23 25
((x + 1) + ((2 div (8 - (x div 2))) + (x div 5)))
A174905-A129511-A060683: 1 2 3 4 5 7 8 9 10 11 13 14 16 17 19 21
((1 + (x div 8)) div (1 + (~x2 mod 5)))
A029407: 1 0 0 0 0 1 0 0 1 0 2 0 1 1 0 2
(1 + ((x3 + 3x2 + x + 2) mod (1 + (x div 4))))
A231568: 1 1 1 1 1 2 1 2 1 3 2 1 3 4 1 4
(1 + ((x - ((x + 2) div 7)) mod (1 + (x div 4))))
A243732: 1 1 1 1 1 1 2 1 2 3 1 2 3 4 1 2
(1 + ((1 + (2 * (x mod 4)) - (x mod 2)) mod (1 + (x div 4))))
A249718-A249717: 1 1 1 1 2 1 2 1 2 3 3 1 2 3 2 3
(1 + (((2x + ~2) div (2 + (x div 3))) mod (1 + (x div 4))))
A145515: 1 1 1 1 1 1 1 2 1 1 1 2 4 1 1 1
(1 - ((x div 2) mod (1 + ((1 + (x mod 3)) mod (1 + (x mod 4))))))
A339885: 1 1 1 0 1 1 0 1 1 1 ~1 0 1 1 1 0
(1 + (x div ((2 + ((~x + 1) mod 6)) * (1 + (x mod 4)))))
A227578-A181783: 1 1 1 1 1 1 1 1 2 1 1 1 5 4 1 1
((2x + 3) - ((x2 div 3) div (x + 5)))
A248564: 3 5 7 9 11 13 14 16 18 20 21 23 25 26 28 30
((2x + 1) - (((x * (x + (x div 2))) div 2) div (x + 5)))
A171508: 1 3 5 7 8 10 11 13 14 15 16 18 19 21 22 23
(~1 + ((1 + ((x + 1) mod (~1 + (2 * ((x + ~1) mod 4))))) mod 3))
A307423: 1 0 0 1 0 0 0 ~1 1 0 0 0 0 0 0 1
(1 + ((1 + ((~2x + 1) mod (3 + (x div 4)))) div 3))
A344772: 1 2 1 1 1 2 1 2 1 2 1 2 1 3 2 1
((x + 1) - (((2 * (x div 2)) div (1 + ((x + ~1) mod 3))) mod 3))
A157887: 1 2 2 4 4 4 5 8 8 8
((x + 1) - ((1 + (x mod (((~x + 2) div 2) - (x mod 3)))) mod 3))
A273862: 0 1 2 3 4 5 6 8 7 9 10 11 12 14 13 15
(1 + (((x + 1) - ((((x + 1) div 3) mod 3) div 2)) mod 3))
A131989: 2 3 1 2 3 3 1 2 1 2 3 1 2 3 3 1
(1 + (((x + 1) - (((((x + ~1) div 2) div 2) mod 3) mod 2)) mod 3))
A305390: 2 3 1 2 3 3 1 2 3 2 3 1 2 3 1 2
(x - ((x + 2) mod (1 + (((x + 1) mod 7) mod 3))))
A338228: 0 1 2 2 4 5 6 6 7 9 10 10 12 13 14 13
(1 + (((x * (x - (x mod 3))) mod 7) div 3))
A070879: 1 1 1 1 2 1 1 1 3 2 3 1 2 1 1 1
(~1 + ((1 + (2 * ((2x2 + 4) div (x + 3)))) div 3))
A260816: 0 0 0 1 2 3 4 6 7 8 9 10 12 13 14 16
(1 + ((1 + ((x + ~4) mod (2 - (x div ~4)))) div 3))
A278161: 1 1 1 2 1 1 2 2 1 1 1 2 2 2 2 3
(1 + ((x - (1 div (~1 + (2 * (x mod 10))))) mod 3))
A105497: 2 1 3 1 2 3 1 2 3 1 3 2 1 2 3 1
(1 + (((x2 + 2x) mod (1 + (2 * (2 + (x div 3))))) mod 3))
A237983: 1 1 1 2 1 1 1 1 3 1 2 1 1 1 1 1
(1 + ((x mod (1 + (2 * (((~x + 2) mod (2 + (x div 2))) div 2)))) mod 3))
A327659-A327519: 1 1 1 1 2 1 1 1 1 2 1 2 3 1 1 1
(~1 + (((x + 1) - ((2 - (x div 5)) mod 4)) mod 3))
A085241: 1 ~1 0 1 ~1 1 ~1 0 1 ~1 1 ~1 0 1 ~1 0
(1 + (((0 - ((x * (x mod 2)) div 3)) mod 5) mod 3))
A175023: 1 1 1 2 1 2 1 1 1 3 1 3 1 2 1 1
((x + 1) - (3 * (((~2x + ~2) + (x div 2)) div 5)))
A070751: 4 5 6 10 11 12 16 17 18 22 23 24 25 29 30 31
((x + 1) mod (1 + ((((x div 2) mod 2) - (x div 5)) mod 3)))
A138954: 0 0 1 0 0 0 0 0 0 1 2 0 1 0 0 0
(((x + 1) div 2) mod (1 + (((~x + 2) + (x div 5)) mod 3)))
A323591: 0 1 0 2 0 1 0 1 0 0 0 0 0 0 1 2
((4x + 3) - ((x - (x div 5)) div 3))
A059568-A003512: 3 7 11 14 18 22 26 29 33 37 41 44 48 52 55 59
((x * (x2 div 2)) div 73)
A331444: 0 0 0 0 0 0 1 2 3 4 6 9 11 14 18 23
(x5 mod 37)
A070620: 0 1 32 21 25 17 6 9 23 34 26 27 7 35 29 24
(x5 mod 35)
A070618: 0 1 32 33 9 10 6 7 8 4 5 16 17 13 14 15
((x + 1) - (3 * ((~2x + ~1) + ((x - (x div 4)) div 2))))
A190509: 4 11 15 22 29 33 40 44 51 58 62 69 76 80 87 91
(1 + ((10x3 + ~9x2 + 2x) div 3))
A034721: 1 2 17 66 169 346 617 1002 1521 2194 3041 4082 5337 6826 8569 10586
(1 + ((1 + (x2 div (~x + 24))) div 3))
A274159: 1 1 1 1 1 1 2 2 2 3 3 4 5 6 7 9
((x + 2) div ((x + 1) - (((~x + ~1) + (x2 div 4)) div 3)))
A274165: 1 1 1 1 1 1 1 1 1 1 1 2 2 3 4 5
(1 + ((1 - ((2x mod 9) mod (x + 1))) div 3))
A237621: 1 1 1 0 0 1 0 ~1 ~1 1 0 0 ~1 ~2 1 0
(1 + (((x + 1) * ((x mod 2) - ((x2 + 2x) div ~2))) div 3))
A168388: 1 3 5 13 21 39 57 89 121 171 221 293 365 463 561 689
(1 + ((4x3 + 12x2 + 14x + 6) div 3))
A166911: 3 13 39 89 171 293 463 689 979 1341 1783 2313 2939 3669 4511 5473
(((2x + 1) - (x mod 6)) mod (1 + ((x + 1) div 3)))
A343713: 0 0 1 0 1 0 1 2 3 0 1 3 0 1 3 4
((1 + (2 * ((x - (x mod 3)) div 2))) div (1 + ((x + 1) div 3)))
A025126: 1 1 0 1 1 1 2 2 1 2 2 1 2 2 2 2
((2x + 1) + ((((x mod 2) - (x div 2)) div 2) + ((x + 1) div 3)))
A097911: 1 3 5 8
A211703: 1 3 5 8 9 12 13 16 18 20 21 25 26 28 30 33
((2x2 + ~x + 1) - ((x3 + ~3x2 + 2x) div 3))
A161702: 1 2 7 14 21 26 27 22 9 ~14 ~49 ~98 ~163 ~246 ~349 ~474
(1 + (((2x3 + 2x2 + 2x + 2) * (x + (x mod 2))) div 3))
A060843: 1 6 21 107
((2x + 5) - (3 * ((x + (x div 4)) div ~2)))
A285683: 5 10 12 17 22 24 29 31 36 41 43 48 53 55 60 62
(1 + ((2 * (x - (~2 mod (1 + (x div 5))))) div 3))
A284724: 1 1 2 3 3 4 5 5 6 7 7 7 8 9 9 9
(~1 + (6 * (1 + (3 * ((x + 1) + (x div 4))))))
A301623: 23 41 59 77 113 131 149 167 203 221 239 257 293 311 329 347
(1 + (6 * (1 + (3 * (x - (x div ~4))))))
A301628: 7 43 61 79 97 133 151 169 187 223 241 259 277 313 331 349
(1 + (((x2 + x) mod 22) mod 3))
A080426: 1 3 1 1 3 3 3 1 1 3 1 1 3 1 1 3
(1 + ((2 + ((2 - (x mod 4)) mod (1 + (x div 3)))) div 3))
A316112: 1 1 1 2 1 2 1 2 2 2 1 2 2 2 1 3
(1 + ((2 * (1 - (x div (~1 + (x div ~8))))) div 3))
A316847: 1 2 2 3 3 3 3 4 4 3 4 4 4 5 5 5
(1 + ((2 * (1 + (2 * ((x - ((x div 2) mod 4)) div 2)))) div 3))
A295084: 1 1 1 3 3 3 3 4 7 7 7 8 8 8 8 9
(1 + (6 * ((x + 1) - ((x + 2) div ~7))))
A227092: 13 19 25 31 37 43 55 61 67 73 79 85 91 103 109 115
(1 + ((2 * ((x + 1) div (1 + (x div (2 + (x div 4)))))) div 3))
A328806: 1 2 1 2 2 3 2 2 3 3 3 3 3 3 4 3
(1 + (6 * (1 + (x div 2) - (((2 - (x div 2)) div 2) div 2))))
A335895: 7 7 13 13 19 19 31 31 37 37 43 43 49 49 61 61
(1 + (((2x + 1) mod (2 + (2x div 5))) div 3))
A338648: 1 1 1 1 1 2 1 2 1 2 2 2 1 3 1 3
(1 + (x div (3 * (2 + (((x + ~1) * (x div 4)) mod 3)))))
A055184: 1 1 1 1 1 1 1 2 1 2 2 1 3 3 3 3
(171x + 19)
A139619: 19 190 361 532 703 874 1045 1216 1387 1558 1729 1900 2071 2242 2413 2584
(x6 mod 19)
A070642: 0 1 7 7 11 7 11 1 1 11 11 1 1 11 7 11
(1 + (3 * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)))
A204028: 1 1 1 1 4 1 1 4 4 1 1 4 7 4 1 1
(1 + ((((x + 1) * ((x3 + 3x2 + 2x) div 2)) div 2) div 3))
A079034: 1 2 7 21 51 106 197 337 541 826 1211 1717 2367 3186 4201 5441
((x + ~1) - (3 * ((~2x + ~2) + ((x - (x div 4)) div 2))))
A342089: 5 12 16 23 30 34 41 45 52 59 63 70 77 81 88 92
((6x + 7) + ((x + (x div 2)) div 8))
A184521: 7 13 19 25 31 37 44 50 56 62 68 75 81 87 93 99
((x + 1) + ((4x div (x + 2)) + (((x + 1) div 2) div 3)))
A333228-A291166: 1 3 5 6 7 9 11 12 13 14 15 17 18 19 20 21
(1 + ((2 * ((2x + 4) - (x div ~8))) div 3))
A134407: 3 5 7 8 9 11 12 13 15 17 18 19 21 22 23 25
(60x2 + 60x + 13)
A332243: 13 133 373 733 1213 1813 2533 3373 4333 5413 6613 7933 9373 10933 12613 14413
(1 + ((2 + (x div (2 + ((~2x + 2) mod 5)))) div 3))
A194824: 1 1 1 2 1 2 2 2 2 2 2 3 2 3 2 2
(1 + (12 * (1 + (2 * ((2x + 4) + (x div 2))))))
A283792: 109 157 229
(~1 + (6 * (2 + (3 * (x - ((~x + 2) div 4))))))
A301621: 11 29 47 83 101 119 137 173 191 209 227 263 281 299 317 353
((x + 1) - (x2 div (3 + (2 * (((x + 1) + (x div 2)) div 2)))))
A060020: 1 2 3 3 4 4 5 5 5 6 6 6 7 7 8 7
(~1 + (3 * (2 + ((5x2 + 7x + 2) div 2))))
A129111: 8 26 59 107 170 248 341 449 572 710 863 1031 1214 1412 1625 1853
(1 + (((x + 1) mod (2 + (((x2 div 2) mod (x + 1)) div 2))) mod 3))
A160267: 2 1 1 1 3 1 1 1 2 1 2 1 1 1 1 1
(1 + ((2 * ((x - ((x mod 9) div 2)) div 2)) div 3))
A029121: 1 1 1 1 1 1 1 2 2 3 4 4 4 4 5 5
(1 + ((2 + ((((x + 1) * (2x div 3)) div 2) div 2)) div 3))
A029044: 1 1 1 2 2 3 4 4 5 6 7 8 10 11 12 15
(1 + ((2 * ((((x + ~1) * ((x div 2) div 3)) div 2) div 2)) div 3))
A032578: 1 1 1 1 1 1 1 1 1 2 2 2 4 5 5 5
(~x mod (1 + (12 * ((((x + 1) div 2) div 2) div 2))))
A249347: 0 0 0 0 0 0 0 6 5 4 3 2 1 0 12 10
(1 + ((x + 1) div (3 * (2 + ((x + 3) mod 8)))))
A341149: 1 1 1 1 1 2 1 1 1 1 1 1 1 3 2 2
(x5 mod 49)
A167527: 0 1 32 47 44 38 34 0 36 4 40 37 10 20 0 22
(x5 mod 47)
A070630: 0 1 32 8 37 23 21 28 9 17 31 29 14 40 3 43
(1 + (((x mod 2) - (2x mod (4 + (x div 4)))) div 3))
A124744: 1 0 1 0 0 1 0 0 ~1 1 0 0 0 ~1 1 0
(1 + ((x - (2 * (4x div (4 + (x div 2))))) div 3))
A029243: 1 0 1 0 1 0 1 0 1 1 1 2 2 2 2 2
(1 + ((2 + (x mod (1 - (2 * ((~x + 1) div (2 + (x div 2))))))) div 3))
A140223: 1 1 2 1 2 2 1 2 2 3 1 2 2 2 3 1
(1 + (((2x - (x mod 5)) mod 8) div 3))
A316841: 1 1 1 2 2 1 2 2 2 3 2 2 3 3 1 3
(x6 mod 25)
A070648: 0 1 14 4 21 0 6 24 19 16 0 11 9 9 11 0
(x6 mod 23)
A070646: 0 1 18 16 2 8 12 4 13 3 6 9 9 6 3 13
(1 + ((x2 + 4x + 4) div (~x + 25)))
A266751: 1 1 1 2 2 3 4 5 6 8 10 13 16 19 24 29
(1 + ((x2 + 4x + 4) div (~x + 26)))
A288001-A288000-A287998-A280664-A092833-A034320-A034150-A034149-A034148-A034147-A034146-A034145-A000009: 1 1 1 2 2 3 4 5 6 8 10 12 15 18 22 27
((8x + 1) - (3 * ((x - (x div 4)) div 2)))
A151915: 1 9 14 22 30 35 43 48 56 64 69 77 85 90 98 103
(1 + ((4 * (x - ((1 mod (~2x + 1)) div (x + 2)))) div 3))
A014528: 1 2 5 6 7 10 11 13 14 15 17 18 19 21 22 23
((x3 + 2x + 1) div (3x + 19))
A346311: 0 0 0 1 2 4 6 8 12 16 20 26
(1 + ((2 + ((x2 * (x div 3)) div (x + 4))) div 3))
A272397: 1 1 1 2 2 2 4 4 5 7 8 9 13 14 16 21
((x + 11) - (x div ~11))
A043700-A043645: 11 13 14 15 16 17 18 19 20 21 22 23 25 26 27 28
((x + 8) - ((2x + 2) mod 13))
A226293: 6 5 4 3 2 1 13 12 11 10 9 8 20 19 18 17
((((x + 1) div 2) * (1 + (x div 2))) - (x div 13))
A194254-A194164: 0 1 2 4 6 9 12 16 20 25 30 36 42 48 55 63
(x7 mod 13)
A070695: 0 1 11 3 4 8 7 6 5 9 10 2 12 0 1 11
(((x2 + x) div 2) - ((x2 + 2) div 11))
A129230: 0 1 3 5 9 13 18 24 30 38 46 55 65 76 87 100
(x7 mod 11)
A070693: 0 1 7 9 5 3 8 6 2 4 10 0 1 7 9 5
(1 div (2 - (x5 mod 11)))
A011582: 0 1 ~1 1 1 1 ~1 ~1 ~1 1 ~1 0 1 ~1 1 1
(((x2 + ~x) div 2) - (x mod ((x + ~1) - (x mod 12))))
A033443: 0 0 1 3 6 10 15 21 28 36 45 55 65 76 88 101
(1 + ((4 * (x + (x div 13))) div 3))
A083347: 1 2 3 5 6 7 9 10 11 13 14 15 17 19 21 22
(1 + ((4 * (x + ((x + (x div 2)) div 8))) div 3))
A103841: 1 2 3 5 6 7 10 11 13 14 15 18 19 21 22 23
(1 + ((2 * ((x + ((x2 + x) div 5)) div 2)) div 3))
A062491: 1 1 1 2 3 4 5 7 8 9 11 13 15 17 19 21
((2x + 1) - ((2 * ((~x + ((~x + 2) div 4)) div 2)) div 3))
A231407: 1 4 6
A189532: 1 4 6 9 11 13 16 19 21 23 25 28 31 33 35 38
(1 + ((4x3 + 24x2 + 8x) div 3))
A274974: 1 13 49 117 225 381 593 869 1217 1645 2161 2773 3489 4317 5265 6341
((x div 4) div (1 + ((2 + ((x + 2) * (x div 4))) mod 3)))
A056175: 0 0 0 0 0 1 0 0 1 2 0 1 1 1 1 1
(1 + (((2x4 + x3) mod (x + 4)) mod 3))
A343026: 1 1 2 1 1 2 3 3 2 1 1 2 1 1 2 3
(1 + (((4x3 + 15x2 + 14x) div 2) div 3))
A213388: 1 6 21 48 93 158 249 368 521 710 941 1216 1541 1918 2353 2848
((2x + 1) - ((2 * (~x + (x div 7))) div 3))
A189367: 1 4 7 9 12 15 17 19 22 25 27 30 33 35 37 40
(1 + (3 * (x - ((~x2 + x) div ((x + 2) + (x div 3))))))
A143804: 1 4 10 13 19 25 28 34 40 46 49 55 61 67 73 76
((x3 + 2x2 + 1) - (((x3 + ~x) div 2) div 3))
A114211: 1 4 16 42 87 156 254 386 557 772 1036 1354 1731 2172 2682 3266
((1 + ((x + 1) div 2)) mod (1 + (((x * (2 - (x div 2))) div 2) mod 3)))
A081221: 0 0 0 1 0 0 0 2 1 0 0 1 0 0 0 1
((3x + 5) * ((3x2 + 7x + 4) div 2))
A228888: 10 56 165 364 680 1140 1771 2600 3654 4960 6545 8436 10660 13244 16215 19600
((1 + (x div 8) - (x mod 2)) div (1 + (2x mod 3)))
A029425: 1 0 0 0 0 0 1 0 1 1 0 0 2 0 1 1
((2x + 1) - ((((x div ~4) mod 2) + (x div 2)) div 3))
A187224: 1 3 5 7 8 11 12 14 16 18 19 21 23 25 27 29
((2x + 1) - ((~x + ((x2 + ~2x) div 5)) div 3))
A231407: 1 4 6
A078941: 1 4 6 8 10 12 14 15 17 18 19 21
((x + 1) - (((~x + 1) - ((x div 5) mod 3)) div 3))
A039032: 1 2 4 5 6 8 9 11 12 13 15 16 18 19 20 21
(81x2 + 81x + 8)
A001534: 8 170 494 980 1628 2438 3410 4544 5840 7298 8918 10700 12644 14750 17018 19448
((x + 1) + (((x + ~1) mod (2 + (x div 2))) div 2) - ((~x + 1) div 3))
A260399: 1 2 4 6 7 8 9 10 12 14 15 17 18 20 22 23
((2 - ((x2 + 2) mod 5)) * (~1 + ((~x + 1) mod 3)))
A316569: 0 1 1 0 1 0 0 ~1 1 0 0 ~1 0 ~1 ~1 0
(1 + ((x + (((x2 div 4) div (x + 3)) mod 2)) mod 3))
A059832: 1 2 3 1 2 3 2 3 1 2 3 3 1 2 3 2
(1 + ((x + (((2x + (x div 2)) * (1 + (x div 2))) div 2)) div 3))
A008368: 1 1 3 4 7 8 13 14 20 22 29 31 40
A023054: 1 1 3 4 7 8 13 14 20 22 29 31 40 42 52 55
(1 + ((x - (x2 mod (~x + ~15))) mod 3))
A088426: 1 2 1 1 2 3 1 1 2 1 2 3 1 2 1 1
(1 + ((x * (1 - ((x3 div 8) mod 2))) div 3))
A046688: 1 1 1 1 2 1 1 3 3 1 1 4 5 5 1 1
(1 - ((~x + 2) mod (1 + ((x + (((x div 2) * (x div 2)) div 2)) mod 3))))
A330262: 1 0 1 1 1 0 1 0 1 ~1 1 1 1 0 1 1
(~1 + ((x + 1) div (1 + (((x div 2) mod 5) + (x div 3)))))
A268643: 0 1 0 0 0 0 0 0 0 0 1 2 1 1 1 1
(1 + (((x mod (~1 + (2 * ((x + ~1) div 3)))) div 2) * (x div 3)))
A341033-A293012: 1 1 1 1 1 1 1 1 3 1 1 1 5 13 1 1
((2x + 4) - (x2 div ((x + 5) + (x div 3))))
A121150: 4 6 8 9 11 12 14 15 16 18 19 20 22 23 24 25
((1 + (3x2 div 5)) mod (1 + (x div 3)))
A034395: 0 0 0 0 0 0 1 0 0 1 1 1 2 2 3 4
(1 - ((2x mod (4 + (x div 4))) div (1 + (x div 3))))
A256983: 1 ~1 1 0 0 1 1 0 0 1 1 0 1 0 1 1
(~1 + ((x + 2) * (1 - ((x2 + x) mod 3))) - (x div 3))
A138187: 1 ~4 3 3 ~8 5 5 ~12 7 7 ~16 9 9 ~20 11 11
((x + 1) + ((3 * (x + (x div 8))) + (x div 3)))
A287243: 1 5 9 14 18 22 27 31 38 43 47 51 56 60 64 69
(0 - (x div (~1 + (x div ~7) - (x mod 3))))
A232615: 0 1 1 2 2 2 3 3 2 3 3 3 4 4 3 4
(1 - ((x + 1) mod (1 + ((x + ~1) mod (6 - (x mod 3))))))
A109017: 0 1 0 0 0 1 0 1 0 0 0 1 0 ~1 0 0
(x div ((1 + (x mod 2) - (x div ~3)) * (1 + (x mod 3))))
A325334: 0 0 0 1 0 0 2 0 0 1 1 0 2 0 0 2
((1 + ((3 * ((x div 2) div 3)) div 2)) div (1 + (x mod 3)))
A029296: 1 0 0 1 0 0 2 1 0 2 1 0 4 2 1 4
((x + 1) div (1 + ((3x * (2 + (x mod 2))) div (x + 3))))
A053279: 1 0 1 0 1 1 1 1 1 1 2 1 2 1 3 2
((2x + 1) - ((2 * (~x + (x2 div 3))) div (x + 3)))
A231407: 1 4 6
A186497: 1 4 6 7 9 11 12 14 15 16 18 19 21 22 23 25
(1 + (((x * (x + ((x div 3) mod 3))) div 2) div (x + 3)))
A006949: 1 1 1 2 2 2 3 4 4 4 4 5 6 6 7 8
(8x2 + 88x + 43)
A086760: 43 139 251 379 523 683 859 1051 1259 1483 1723 1979 2251 2539 2843 3163
(1 + (x mod (~1 + (((x mod (~1 + (2 * (x div 3)))) mod 2) * (x div 2)))))
A220632-A125653-A104445: 1 1 1 1 1 1 1 2 1 1 1 4 3 1 1 1
(1 + ((1 + (2 mod (1 + (x mod (1 + (x mod 4)))))) mod (1 + (x div 2))))
A060594: 1 1 2 2 2 2 2 4 2 2 2 4 2 2 4 4
(1 + ((x div (1 + ((x2 + 2x) mod 6))) mod (1 + (x div 2))))
A244327: 1 1 1 1 2 1 3 2 3 3 5 2 6 4 5 4
(1 + ((x mod (1 + ((x2 + 2x) mod 8))) mod (1 + (x div 2))))
A135517: 1 1 1 2 1 2 1 4 1 2 1 4 1 2 1 8
(1 + (((x + ~3) + ((x div 2) mod 5)) mod (1 + (x div 2))))
A086742-A082854: 1 1 1 2 1 2 3 4 5 1 2 3 4 5 6 7
((x + 1) - (x mod (1 + ((2 * ((x div 5) mod 2)) + (x mod 2)))))
A226482: 1 1 3 3 5 5 7 5 7 9 11 11 13 13 15 13
(5x4 + 10x3 + 20x2 + 15x + 11)
A115565: 11 61 281 911 2311 4961 9461 16531 27011 41861 62161 89111 124031 168361 223661 291611
(1 + (x2 div ((x + 1) + ((3 * ((x div 2) div 3)) div 2))))
A006163: 1 1 2 3 4 5 5 6 7 8 9 10 10 10 11 12
(18x3 + 37x2 + 20x + 2)
A338588: 2 77 334 881 1826 3277 5342 8129 11746 16301 21902 28657 36674 46061 56926 69377
(46x2 + 92x + 45)
A158634: 45 183 413 735 1149 1655 2253 2943 3725 4599 5565 6623 7773 9015 10349 11775
(66x2 + 132x + 65)
A158693: 65 263 593 1055 1649 2375 3233 4223 5345 6599 7985 9503 11153 12935 14849 16895
(62x2 + 124x + 61)
A158680: 61 247 557 991 1549 2231 3037 3967 5021 6199 7501 8927 10477 12151 13949 15871
(1 + compr(\x.(1 - (x mod (1 + (x mod (5 + (x mod 2)))))),(x + 1)))
A299114: 3 4 5 6 8 10
A121540: 3 4 5 6 8 10 12 14 15 16 18 19 20 22 23 24
((x + 1) - ((1 + (x mod (6 + (x div 3)))) mod (x + 1)))
A328307: 1 2 3 4 5 6 7 8 8 9 9 9 10 10 10 11
(1 + ((1 + (((x + 2) div (1 + ((x + 1) mod 3))) mod 2)) mod (x + 1)))
A071215: 1 1 2 2 2 3 2 3 2 3 2 3 3 3 2 2
(1 + ((x - ((~2x2 + 4x) div 7)) mod (x + 1)))
A194752: 1 2 3 1 3 5 7 2 5 8 1 5 9 13 3 8
(1 + ((1 + (2 * ((x - ((x div 3) mod 3)) mod 2))) mod (x + 1)))
A329586: 1 2 2 2 4 2 2 4 2 4 2 4 4 2 4 4
(1 + ((1 + (2 * (((x2 + ~2x) mod (2 + (x div 2))) mod 2))) mod (x + 1)))
A277561: 1 2 2 2 2 4 2 2 2 4 4 4 2 4 2 2
(1 + ((~1 + (((3x2 + ~x) div 2) div 4)) mod (x + 1)))
A019588: 1 2 1 3 5 2 5 1 5 9 3 8 13 5 11 2
(x8 + x7 + x6 + x5 + x4 + x3 + x2 + x + 1)
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(1 + (2 * ((x + 1) div (2 + (8 div (1 + (x mod 3)))))))
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(1 + (x div (2 * (2 + ((~x * (x div 2)) mod 7)))))
A290084: 1 1 1 1 1 1 1 2 1 1 1 2 1 1 4 4
((x + 1) - (2 * ((x - ((x2 + 2x) div 7)) div 2)))
A008814: 1 2 3 4 5 6 7 10 13 16 19 22 25 28 33 38
(1 + (x div (4 + (x div (1 + ((x2 + 2x) mod 6))))))
A069016: 1 1 1 1 1 2 1 2 2 2 1 3 1 2 2 3
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(1 + (2 * (2 + (1 mod (~1 + (2x mod (4 + (x div 4))))))))
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(1 + (x div (2 * (2 + ((~2x2 + 2x) mod 9)))))
A152141: 1 1 1 1 1 1 1 1 1 3 3 1 1 2 2 2
(1 + (2 * ((1 + (((x + 2) mod (2 + (x mod 4))) mod 4)) div 2)))
A291448: 1 1 1 1 1 3 1 1 1 3 1 5 1 1 1 3
((2x + 4) - (x div (5 + ((x div 2) mod 5))))
A330948: 4 6 8 10 12 14 16 18 20 21 22 24 26 28 30 32
(x6 mod 21)
A070644: 0 1 1 15 1 1 15 7 1 15 1 1 15 1 7 15
(1 + (((x + ~1) mod (2 + ((x + (2 * (x mod 2))) div 5))) div 2))
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(1 + (((1 + (((x * (x - (x div ~3))) div 2) div 2)) div 2) div 2))
A034140: 1 1 1 2 2 3 4 5 6 8 10 11 13 15 17 20
(1 + (((1 + (((3x + 5) * (x div 2)) div 2)) div 2) div 2))
A341123: 1 1 2 3 5 6 9 11 15 17 23 25 32 34 42 45
(~1 + (2 * ((3 * ((x + 1) - (x div ~6))) div 2)))
A005776: 1 7 11 13 17 19 23 29
((x + 1) div (1 + (2 * (2 + (((x + ~1) * (x div 4)) mod 3)))))
A226916: 0 0 0 0 1 0 0 1 1 1 2 1 2 2 3 3
((2x + 3) - (((3 * (x div ~4)) div 2) div 2))
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(1 + (((x + ~1) mod (2 + (3 * ((((x + 1) div 2) div 2) div 2)))) div 2))
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(1 + (((3 * (x mod (x - ((x + ~1) mod 8)))) div 2) div 2))
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(1 + (((3 * (2 + ((x div ~4) mod (x + 2)))) div 2) div 2))
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((2x + 1) - (((3 * ((x2 + ~2x) div (x + 2))) div 2) div 2))
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(~1 + (2 * (x - ((x + 2) div (~6 + (((x + ~1) div 2) div 2))))))
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((x + 1) div (1 + (2 * ((x mod 2) - (x div (~2 + ((~x + 1) div 3)))))))
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A005862: 1 1 1 1 1 1 1 2 2 2 2 3 4 4 5 6
(1 + (2 * (((x + 1) mod (((x + 1) mod 4) + (x div 3))) div 2)))
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(1 + (((5 * ((~x + 2) div 2)) mod (2 + (x div 3))) div 2))
A219244: 1 1 1 1 1 2 2 1 1 1 1 1 3 1 1 1
(1 + (2 * (x - ((x - (x2 div 4)) div (2 + (x div 3))))))
A327573: 1 3 5 7 9 13 15 19 21 25 27 31 33 37 41 43
(1 + ((x2 mod 7) div (2 + ((x div 3) mod 2))))
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((x + 1) - (((1 + ((x * (((2 - (x div 2)) div 2) div 2)) div 2)) div 2) div 2))
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(1 + ((x mod (2 + ((~1 + (((x + ~1) div 2) mod 4)) mod (x + 1)))) div 2))
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(1 + ((((3 * (x2 mod 6)) mod (x + 1)) div 2) div 2))
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A144372: 1 1 1 1 1 1 1 1 1 2 2 3 2 4 2 4
(1 + (x div (4 + ((2 * (1 + (x mod 6))) mod (x + 1)))))
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(1 + ((((x + 1) * (2 + (x div (2 + ((x div 2) div 3))))) div 2) div 2))
A030319: 1 2 3 4 6 7 8 9 10 13 14 16 17 18 19 21
(1 + ((((x + 1) * ((((x + ~2) mod (2 + (x div 2))) div 2) mod 2)) div 2) div 2))
A323017: 1 1 1 1 2 2 1 1 1 1 1 4 4 4 4 1
(1 + ((((1 - (3x mod (2 + (x div 2)))) mod (x + 1)) div 2) div 2))
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((x + 1) mod (1 + ((x + 2) mod (2 + (((x2 div 2) mod (x + 1)) div 2)))))
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((x + 1) - (2 * ((~2x + ~2) + ((~2x + 2) div 5))))
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((20x + 19) - (((x + 1) div 2) div 2))
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((2x + 31) mod (1 + (((x + 1) div 2) div 2)))
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A225644: 1 1 1 2 2 3 3 3 3 4 4 5 5 6 5 5
(x - ((2x + ~1) div (1 + (2 * (2 + ((x div ~3) mod 2))))))
A226142: 1 1 2 3 3 4 4
A103297: 1 1 2 3 3 4 4 6 6 7 7 7 8 10 11 11
((x + 1) - (x mod (4 * (2 + ((x div 2) div 7)))))
A290238-A286833: 1 1 1 1 1 1 1 1 9 9 9 9 9 9 13 13
(x div (1 + (4 * (2 - ((x mod (~1 + (2 * (x div 3)))) mod 2)))))
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(1 + ((((5 * (~1 + (x2 div 4))) div 2) div 2) div 2))
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(1 + ((x - (x div (2 + (x div (2 + (x2 mod 5)))))) div 2))
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(1 + (2 * (2x mod (2 + ((x mod (1 + ((~x + 2) mod 4))) div 2)))))
A094853: 1 1 1 1 1 1 1 5 3 1 1 3 1 1 1 1
(1 + (8 * ((x + (x mod 4)) * (1 + (x div 4)))))
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((x + 1) div (~1 + (2 * (((~1 + (2x mod (2 + (x div 2)))) div 2) mod 2))))
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A132680: 1 1 1 3 1 3 3 3 1 3 3 3 3 3 3 5
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(1 + (x div (1 + (2 * (2 + (((x div 2) div 3) mod 2))))) - (x mod 2))
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(1 + (2 * (2 + (((x2 div (2 + (x mod 2))) mod (x + 3)) mod 2))))
A204911: 5 5 5 7 7 5 5 5 5 7 7 5 5 5 7 7
(1 + (2 * (x div (4 + (16 mod (1 + (x div 2)))))))
A210745: 1 1 1 1 1 3 3 3 3 3 3 3 5 5 7 7
(1 + (8 * ((x mod (~1 + (2 * ((x + ~1) div 3)))) div 2)))
A293724: 1 1 1 1 1 1 1 1 9 1 1 1 9 25 1 1
(1 + ((x mod (2 + (x div (2 + (((x div 2) mod 5) div 2))))) div 2))
A262611: 1 1 2 1 1 2 2 2 1 1 2 3 3 3 2 1
(1 + ((x + 1) div (2 + (x div (4 + ((x mod 5) mod 2))))))
A217865: 1 2 2 3 2 3 3 3 4 3 3 4 3 4 4 4
(1 + (4 * (((3 * (x + (x div 8))) div 2) div 2)))
A122798: 1 1 5 9 13 13 17 21 25 29 33 37 37 41 45 49
((2x + 1) - ((x div (4 + ((x mod ~4) div 2))) mod 2))
A212439: 1 3 5 6 8 11 13 15 17 19 20 22 24 27 29 30
(x2 div (~8x + 145))
A326527: 0 0 0 0 0 0 0 0 0 1 1 2 2 4 5 9
((x * (x div 2)) div (~4x + 73))
A326594: 0 0 0 0 0 0 0 0 0 0 1 1 2 3 5 8
(1 + ((2 - (((~2x + 2) mod (4 + (x div 4))) div 2)) div 2))
A128185: 1 2 1 2 1 1 2 1 1 1 2 1 0 1 1 2
(1 + ((((((x + 4) * ((x + 1) + (x div 2))) div 2) div 2) div 2) div 2))
A049807: 1 1 2 3 4 5 7 8 10 12 15 16 20 22 25 28
(1 + (8 * (x div (4 * (8 - (x div 2))))))
A146868-A146591: 1 1 1 1 1 1 1 1 1 1 1 1 9 9 25 25
(~1 + (2 * (1 - (((x mod 2) - (x div (4 + ((x div 2) mod 2)))) div 2))))
A110919: 1 1 1 1 3 1 3 1 3 3 3 3 5 3 3 3
(1 + (((x + 2) mod (2 + ((x - (x mod (2 * (2 + (x mod 2))))) div 2))) div 2))
A132422: 1 1 1 1 2 1 1 3 3 1 1 2 4 4 1 1
(~1 + ((x + 2) div (2 + (2x div (4 + ((x + 1) mod 4))))))
A105553: 0 0 1 0 1 1 1 0 1 1 2 0 1 1 1 0
(((x + ~1) * (x2 div 3)) div 33)
A194211: 0 0 0 0 0 0 1 2 4 6 9 12 16 20 25 31
(x6 mod 33)
A070656: 0 1 31 3 4 16 27 4 25 9 1 22 12 31 25 15
(x6 mod 31)
A070654: 0 1 2 16 4 1 1 4 8 8 2 4 2 16 8 16
(((x * (x div 2)) div 2) div (~2x + 37))
A326593-A326592-A326591-A326590-A326589-A319475-A026816: 0 0 0 0 0 0 0 0 0 0 1 1 2 3 5 7
(1 + ((x - (x div (2 - ((x3 div 8) mod 2)))) div 2))
A329330-A324592-A318274-A178059-A176427-A116188-A096589: 1 1 1 1 2 1 1 3 3 1 1 4 4 4 1 1
(1 + (((2x + 1) mod (2 + (x div (2 + ((~x + 2) mod 4))))) div 2))
A323023: 1 1 2 1 1 2 2 1 1 3 1 2 1 2 2 1
((3x + 1) - (((x - ((2 - (x div 4)) div 2)) div 2) div 2))
A186224: 2 4 7 10 12 15 18 21 23 26 29 32 34 37 40 42
(1 + (2 * (2 - ((~2x + 5) div (4 + (x div 4))))))
A126611: 3 5 5 7 7 7 9 9 9 11 11 11 11 11 13 13
(2 - (2 div (1 + (((2x + 1) mod (4 + (x div 4))) div 2))))
A049771: 0 1 0 1 2 0 1 0 2 0 1 2 2 2 0 1
((x + 1) div (1 + (2 * (2 - ((x mod (~2 - (x mod 4))) div 2)))))
A302479: 0 0 0 0 1 0 1 0 1 2 1 1 2 2 2 3
((x + 1) - (((x - ((((2 - (x div 2)) * (x div 2)) div 2) div 2)) div 2) div 2))
A196266: 1 2 3 4 4 5 6 6 7 8 8 9 9 10 10 10
(1 + (x div (2 + (x div (2 + (((x2 div 2) mod (2 + (x div 2))) div 2))))))
A137921: 1 1 2 2 2 2 2 3 3 3 2 3 2 3 4 4
(x div (1 + (x div 3) - (x div (4 * (2 + ((x div 2) mod 2))))))
A029550: 0 1 2 1 2 2 2 2 4
A231577: 0 1 2 1 2 2 2 2 4 3 2 2 3 3 3 3
((x + 1) - (x div (0 - (2 * (2 + ((((x + 1) div 2) div 2) mod 4))))))
A026500: 1 3 4 5 6 7 8 9 10 12 13 14 15 16 17 20
(x7 mod 17)
A070699: 0 1 9 11 13 10 14 12 15 2 5 3 7 4 6 8
((x3 + 6x2 + 14x + 12) div 15)
A026036: 0 2 4 9 15 23 35 49 68 90 116 148 184 227 275 329
(x div (1 + ((x - (((x mod 5) * (x div 4)) div 2)) div 2)))
A331958: 0 1 1 1 2 1 1 1 2 3 1 1 2 2 2 1
(1 + ((((x2 + 2x) div 2) div 3) div (4 + (x div 4))))
A025777: 1 1 1 1 1 2 2 3 3 3 4 4 5 5 6 7
(1 + (~1 mod (2 - ((2x + 1) mod (4 + (x div 4))))))
A306437-A286563-A167271-A156348-A147861: 1 1 1 1 0 1 1 2 0 1 1 0 0 0 1 1
(1 - ((x + 1) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))))
A177121: 1 1 1 1 ~1 1 1 1 1 1 1 1 ~2 ~1 1 1
((~2 + (x mod 2)) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))
A259572: 0 0 0 0 1 0 0 1 1 0 0 2 3 2 0 0
((~x2 + 2) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))
A247505: 0 0 0 0 1 0 0 1 1 0 0 1 3 1 0 0
(1 - ((~1 + (x div 2)) mod (~1 + (2x mod (4 + (x div 4))))))
A114700: 1 1 1 1 0 1 1 ~1 1 1 1 0 0 0 1 1
((2 + (x div 3)) mod (~1 + (2x mod (4 + (x div 4)))))
A303636-A298100: 0 0 0 0 1 0 0 1 1 0 0 2 0 2 0 0
(1 + (x div (8 + (2 * ((x div 4) mod 2)) - (x div 2))))
A029118: 1 1 1 1 1 1 1 2 3 3 4 4 4 4 5 6
(1 + (2 * (x - ((((x * ((1 - (x div 2)) div 3)) div 2) div 2) div 2))))
A336374-A272872-A187929: 1 3 5 7 11 13 15 17 19 23 27 29 31 35 37 39
(1 + (((((x + 2) * (2 + (x * (x - (x div 3))))) div 2) div 2) div 2))
A113913: 1 2 4 6 11 20 27
(1 + ((x + 1) div (2 + ((1 + (x2 div 2)) mod (2x + 8)))))
A155586: 1 1 1 1 1 1 1 2 1 1 1 5 2 1 1 1
((x + 1) - (x2 div (4 * (2 - (((x mod 2) - (x div 2)) div 2)))))
A292127: 1 2 3 3 4 4 5 4 5 5 6 5 6 6 7 5
((x + 1) mod (1 + (2 * ((4x2 mod (2 + (x div 2))) div 2))))
A305212: 0 0 0 0 0 0 2 0 4 0 0 0 0 4 0 0
((6x + 1) - ((2x + 2) div ~7))
A246299: 2 8 14 21 27 33 39 46 52 58 65 71 77 83 90 96
(9 * (x mod ((x + ~1) - (x mod 12))))
A108782: 0 0 0 0 0 0 0 0 0 0 0 0 9 18 27 36
(117x + 45)
A305069: 45 162 279 396 513 630 747 864 981 1098 1215 1332 1449 1566 1683 1800
((((x3 + 3x2 + 2x) div 2) div 3) mod 9)
A279816: 0 1 4 1 2 8 2 3 3 3 4 7 4 5 2 5
(45x2 + 72x + 27)
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((18x + 9) * ((x2 + 3x + 2) div 2))
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(((2x + ~1) * ((x2 + ~x) div 3)) div 9)
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(4 - (((x + (x div 2)) * (1 + (x mod 2))) mod 9))
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(9 * ((1 + ((x - ((x mod 3) div 2)) div 2)) div 2))
A206011: 0 0 0 9 9 9 18 18 18 18 27 27 27 27 27 36
(x - (9 * ((2x div 9) mod 2)))
A316823: 0 1 2 3 4 ~4 ~3 ~2 ~1 9 10 11 12 13 5 6
(36 * (1 + (2 * (x - (x div ~2)))))
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(81x2 + 162x + 72)
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((5x + 2) - ((~2x + 2) div 9))
A001966: 2 7 13 18 23 28 34 39 44 49 54 60 65 70 75 81
(x - (18 * (~x + (x mod 10))))
A103303: 0 1 2 3 4 5 6 7 8 9
A039723: 0 1 2 3 4 5 6 7 8 9 190 191 192 193 194 195
((x + ((~2x + 4) mod 9)) div 9)
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(2x - (9 * (~x + ((x div 2) div 5))))
A108773: 0 11 22 33 44 55 66 77 88 99 101 112 123 134 145 156
(9 * (~x + (6 * ((x + 2) + (x div 2)))))
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(2x - (((x + ~2) div 5) + (x div 9)))
A027440: 1 3 4 6 8 10 12
A029902: 1 3 4 6 8 10 12 13 15 16 18 20 21 23 25 27
(((x + 1) mod 11) - (x mod 9))
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((x + 1) + ((~x + 1) mod 8) - (x mod 10))
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(x mod (1 + ((x - ((x * (((~x + 2) div 2) div 3)) div 4)) div 2)))
A089049: 0 0 0 0 1 1 1 2 2 1 2 2 2 2 3 1
(1 + (((2 + (((x + ~2) mod (1 + (x div 2))) div 2)) * (x div 4)) div 2))
A304633: 1 1 1 1 2 2 2 2 3 4 4 4 5 7 7 7
(1 + (((x div (4 - ((x * (x div 2)) mod 2))) - (x mod 4)) div 2))
A029339: 1 0 0 0 1 1 0 0 2 1 1 1 2 2 1 2
(x - ((x2 + 2) div (1 + (2 * (2 + ((x + (x div 4)) div 2))))))
A235963: 0 1 2 2 2 3 3 4 4 4 4 4 5 5 5 6
(1 + (2 * (x - ((((~x2 + 4x + ~4) * (x div 3)) div 2) div 2))))
A123069: 1 3 5 9 11 17 29 41
(1 + ((2x + 1) div (2 + (x div (4 - ((x * (x div 2)) mod 2))))))
A265690-A073933: 1 2 3 3 4 4 5 4 5 5 6 5 6 6 6 5
(1 + (2 * (2 + ((4x + (x2 div 4)) div (x + 2)))))
A143730: 5 7 9 9 11 11 13 13 13 15 15 15 17 17 17 17
((2x + 3) - (((2 + (x * (x + (x div 2)))) div (x + 2)) div 2))
A184675: 3 5 6 8 9 11 12 13 15 16 17 19 20 21 22 24
(3x3 + 36x2 + 117x + 84)
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((32x + 16) div (2x + 9))
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A234948: 1 4 6 7 8 9 9 10 10 11 11 11 12 12 12 12
((x + 1) - ((((((~x + 2) div 2) div 5) * (x div 2)) div 2) div 2))
A256450: 1 2 3 5 6 7 8 9 10 11 13 14 15 17 19 20
(1 + ((x - (x mod (x + ((x div 2) mod 2) - ((x + ~1) div 3)))) div 2))
A287635: 1 1 1 1 2 3 4 4 4 4 5 5 5 5 6 7
(1 + ((x - ((x mod ~11) div 3)) mod 4))
A176360: 1 2 2 3 4 4 1 2 2 3 4 4 1 1 2 3
((1 + (x2 mod (1 + (x div 3)))) mod (1 + ((x + 1) mod 4)))
A335489-A323439: 1 1 1 0 1 2 1 0 0 2 1 0 1 2 2 0
(1 + ((2 + ((2x + 1) div (3 + (x div 4)))) mod 4))
A204255: 3 4 4 1 1 1 2 2 2 2 3 3 3 3 3 4
(1 + (((x + 2) mod (2 + (3 * ((x mod 3) div 2)))) mod 4))
A161506: 1 2 1 2 1 3 1 2 1 2 1 4 1 2 2 2
(1 + ((((3 * (x div 4)) div 2) - ((x + 1) div 2)) mod 4))
A106147: 1 4 4 3 4 3 3 2 4 3 3 2 3 2 2 1
(1 + ((x - (((2 + (x * (x + (x div 2)))) div (x + 2)) div 2)) mod 4))
A079730: 1 2 2 3 3 4 4 4 1 1 1 2 2 2 2 3
(1 + (((4x + (x2 div 4)) div (x + 2)) mod 4))
A063826: 1 2 3 3 4 4 1 1 1 2 2 2 3 3 3 3
(15x2 + 75x + 125)
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((1 + ((x + ((x + 1) mod 3)) * (1 + (x mod 2)))) div 5)
A117172: 0 1 0 1 1 2 1 3 1 4 2 4 2 6 3 6
(x - ((~1 + (x2 div 14)) div 5))
A308936: 1 2 3 4 4 5 6 7 8 9 9 10 11 11 12 12
(2 - ((1 + (2 * ((x - (x div 3)) div 3))) mod 5))
A037868: 1 1 1 1 ~1 ~1 ~1 ~1 2 2 2 2 2 0 0 0
(x5 mod 45)
A070628: 0 1 32 18 34 20 36 22 8 9 10 41 27 43 29 0
(5 * ((4x3 + 6x2 + 2x) div 3))
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(x + ((12x + 12) div 5) - (x div 2))
A190336: 2 5 8 11 14 17 19 23 25 29 31 34 37 40 43 46
((3 * (x - (2 * (x div 7)))) div 5)
A194227: 0 0 1 1 2 3 3 3 3 4 4 5 6 6 6 6
((x + 1) mod (2 - (((x div 3) * (x div 3)) mod 5)))
A014429: 1 0 1 0 0 0 ~1 0 ~1 0 ~1 0 0 0 0 0
(x - ((~1 + (2 * (~x + ((x div 2) mod 5)))) div 5))
A175020: 1 2 3 4 5 7 8 9 10 12 15 16 17 18 19 21
((x4 + 8x3 + 19x2 + 12x) div 5)
A032768: 0 8 36 100 224 432 756 1232 1900 2808 4004 5544 7488 9900 12852 16416
(x5 mod 50)
A167528: 0 1 32 43 24 25 26 7 18 49 0 1 32 43 24 25
(((3 * (x2 - (x div ~4))) div 2) div 5)
A228848: 0 0 1 3 5 8 11 15 19 25 30 37 44 51 60 68
(~11x mod 30)
A064264: 0 19 8 27 16 5 24 13 2 21 10 29 18 7 26 15
(11x mod 30)
A064263: 0 11 22 3 14 25 6 17 28 9 20 1 12 23 4 15
((10x + 10) + ((x + 1) mod 10))
A302575-A160861-A067042: 11 22 33 44 55 66 77 88 99 100 111 122 133 144 155 166
(5 * ((x2 + x) div (2 * (2 - ((x div ~2) mod 2)))))
A330082: 0 5 15 15 25 75 105 70 90 225 275 165 195 455 525 300
(x6 mod 40)
A070663: 0 1 24 9 16 25 16 9 24 1 0 1 24 9 16 25
((2 * (12x - (x div 4))) div 5)
A172329: 0 4 9 14 18 23 28 33 37 42 47 52 56 61 66 70
(2x - ((2 * (x + ((x + 1) mod 5))) div 5))
A047542: 0 1 2 4 7 8 9 10 12 15 16 17 18 20 23 24
(250x + 240)
A154378: 240 490 740 990 1240 1490 1740 1990 2240 2490 2740 2990 3240 3490 3740 3990
((x + 1) mod (2 - (((~x + (x2 div 3)) div 2) mod 5)))
A014093: 1 0 ~1 0 1 0 0 0 0 0 0 0 0 0 1 0
(2 - ((2 + ((~x + 1) * (4 + (x div 4)))) div 5))
A270189: 1 2 3 4 5 6 7 8 10 12 13 14 17 19 20 22
(5x3 + 30x2 + 90x + 100)
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((x + ((x3 + 2x) div 9)) div 5)
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((x + 5) - ((x2 + 2x) div (x + 12)))
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((x2 + 6x + 10) - ((~x + 1) div 5))
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(((x2 + x) + ((x3 div 2) div 3)) div 5)
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((x + ((x3 + ~2x) div 16)) div 5)
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((x + 5) + (((x div 2) - ((~x + 2) div (2 + (x div 2)))) div 2))
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((6x + 2) - ((~x + ((x div 2) mod 2)) div 5))
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((x + 1) + (x div 5) - (2 * (x div ~5)))
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(((3 * (x div 2)) div 2) + (x div 3) + (x div 5))
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((22x + 22) + (x div 5))
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((5 mod (1 + (x div 5))) + (x mod 5))
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(((4x2 + 4x + 1) div 3) + (x mod 5))
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(x + (x mod 5) - (4 * ((x div 5) mod 2)))
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((2x + 1) - ((x + (x3 mod 5)) div 4))
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(1 + (((((((x + 1) div 2) div 2) * (x div 2)) div 2) div 2) + (x div 4)))
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(1 + (((x + (3 * ((x div 8) + (x div 2)))) div 2) div 2))
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(1 + (((x + ((3 + ((x div 3) mod 2)) mod (x + 1))) div 2) mod 2))
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(1 + (2 * ((x + 2) + (2 * ((x - (((x div 2) div ~2) div 2)) div 2)))))
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((2x + 3) - (((x2 + 1) div (x + 8)) div 2))
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(1 + (2 * ((x + 2) + ((x + 2) div (12 - (x div 2))))))
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((x + 1) div (1 + (2 * ((2 * (x div (~2 + (x mod ~2)))) mod (x + 2)))))
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(((5x2 + 9) div 2) div (x + 5))
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(1 + (2 * (2x + (((x2 + x) div ~8) mod 2))))
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(1 + (2 * (2x + ((((~1 + ((x2 + x) div 2)) div 2) div 2) mod 2))))
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(1 + (2 * (2x + ((x + 1) div (2 + ((x + ~1) div (2 + (x div 2))))))))
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(100x2 + 49x + 6)
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((5x + 1) + (x2 div ((x + 2) + (x div 4))))
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(1 + (2 * ((3 * (1 + (2 * (2x + (x mod 2))))) + (x div 2))))
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(1 + (2 * ((4 * (1 + (2 * (x - (x div ~2))))) + (x div 2))))
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(1 + (2 * ((3 * ((x + 2) + (3 * (x div 2)))) - (x mod 2))))
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(((x2 + 3x + 2) div 2) * (1 + (x div 2)) * (~1 + (2 * (x mod 2))))
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(((1 + ((x + ~1) mod 3)) * (1 + (x div 5))) div 3)
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((1 + ((5x + 4) mod 12)) div 3)
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((1 + ((~x + (x3 div 5)) div 3)) mod 3)
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(((2x + 1) - ((x mod (~2 - (x div 3))) mod 2)) mod 3)
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((1 + (4 * (x - ((~1 + (x div ~4)) div 2)))) div 3)
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(((~2x + 1) mod (1 + (2 * (2 + (x div 8))))) div 3)
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(x6 mod 27)
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(1 + (((x + ~1) mod (3 + (x div 4))) div 3) - (x mod 2))
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((x + 3) div ((~x + 2) + (3 * (5 + (x mod 2)))))
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((1 + ((2x mod (~1 + ((~x + 1) div 3))) mod 4)) mod 3)
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((1 - ((x mod 5) mod (1 + ((x + ~1) mod 4)))) mod 3)
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((1 + ((2x mod (4 + (x div 4))) mod 4)) mod 3)
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(((((~x + 2) + (x mod (2 + (x mod 2)))) div 2) mod 5) mod 3)
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((5x + 4) - ((x - (x div 5)) div 3))
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((1 + (((2x4 + 4x3 + x2 + 2x) div 2) div 2)) div 3)
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((x + 2) div (3 * (1 + (2 * (x mod (8 - (x mod 2)))))))
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((1 - (x div (3 * (1 + ((x + 1) mod 6))))) mod 3)
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(x - ((x - (((2x + ~1) div 5) mod 3)) div 3))
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((~x + 1) + (3 * (2x - (3 * (x div 5)))))
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(((64 mod (x + 1)) div 3) mod 3)
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(((16x + 16) + ((x + 1) div 3)) div 3)
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(((2 + ((~1 + ((x div 2) mod 3)) mod (x + 1))) div 3) mod 3)
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((x + ~2) + (3 * ((2x + 2) - (((x + 1) div 2) div 3))))
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(((4x + 2) div (x - (((x + ~1) div 2) div 3))) mod 3)
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((2x4 + ~x2) mod 36)
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((x - ((x2 mod (8 + (x div 2))) div 3)) mod 3)
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((3x + 3) - ((~x + (x mod 2) - (x div 3)) div 3))
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((2 + (((x2 div 3) mod (x + 1)) + (x mod 3))) div 3)
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(27x2 + 105x + 105)
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(((x2 + 4x + 3) * ((x2 + 3x + 2) div 2)) div 3)
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(12x3 + 72x2 + 87x + 27)
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(3 + ((2x + 1) * ((x3 + 4x2 + ~x + ~4) div 2)))
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((6x + 3) + ((2x + 1) div 7))
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((2x3 + 6x2 + 8x + 4) div (6x + 3))
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((6x + 3) + ((1 + ((x - (x div 4)) div 2)) div 2))
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(((2x + 1) * (x - (x div (~x + 16)))) mod 3)
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(((1 - ((x mod 3) + (2 * (x mod 2)))) mod (2x + ~1)) div 3)
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(((1 + (x mod (~1 + ((~x + 2) div 3)))) mod (1 + (x div 2))) mod 3)
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(((20x + 1) mod (1 + (x div 2))) mod 3)
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((x + 1) div (3 * ((1 + (x div 8)) * (1 + (x mod 2)))))
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(36x3 + 96x2 + 84x + 24)
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((3x + 3) * (1 + ((3x2 + 6x) div 4)))
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(compr(\x.(2 - (x mod (4 + (x mod 5)))),(x + 1)) mod 3)
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(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)
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((3x + 3) + (((x + ~4) mod (2 + (x div 3))) mod 2))
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((3x + 3) + ((x div 8) + (((x + 1) div 2) div 2)))
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((x + 2) + ((x + 1) div 3) - ((x div 3) div ~3))
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(x - ((2 * ((1 + (x div 3)) div 3)) + ((x + 1) div 3)))
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(2 + ((x + 1) div 3) - ((~x + 2) div (2 - (x div ~4))))
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(x + (((((2 - (x div 2)) mod (x + 2)) div 2) div 2) + ((x + 1) div 3)))
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(x + ((((x + 1) + (x2 div 4)) div 2) + ((x + 1) mod 3)))
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(((x + 1) * (x + (5 * ((x2 + x) div 2)))) div 3)
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((3x4 + 8x3 + 9x2 + 4x) div 3)
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(3 * ((1 + (x2 mod (1 + (2 * ((x + 1) mod 3))))) div 2))
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((2 + (3x div (1 + ((x + 2) div 5)))) div 3)
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(6 * ((x + ~1) mod (1 + ((x * (x mod 2)) div 5))))
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((2 * ((x + 1) - ((~1 + (x div 2)) mod (1 + (x div 4))))) div 3)
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(3 * ((1 + ((~1 + (2 * (x div 4))) * (x div 3))) div 2))
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((2x + 5) div (3 * (2 + (x div 7))))
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(1 + ((2 + (x2 div 7)) div 3) - (x mod 2))
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((2 * (1 + (((x + 1) div 2) div (2 - ((x mod 3) mod 2))))) div 3)
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((2 * (1 + (2 * ((1 + ((x2 + x) div 4)) div 2)))) div 3)
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((((x + 1) - (2x mod (4 + (x div 4)))) div 2) mod 3)
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((x - (((1 - (2x div 3)) mod 5) div 2)) mod 3)
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((2 * ((2x + 4) - ((1 - (x div 2)) div 5))) div 3)
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(6 * ((x + 1) - (((~x + 2) - (x div 4)) div 4)))
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((2 * (2 - ((~x + 4) mod (~1 + ((~x + 2) div 4))))) div 3)
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(((((x3 + 2x2) div 2) mod (x + 5)) div 2) div 3)
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((x2 + ~x) mod (3 * (2 + ((1 - (x div 3)) mod 3))))
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((x + ~1) + (6 * (1 - ((~x + 2) div 12))))
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(2 - ((2 + ((((~x + 2) div 2) mod 4) + (x mod 3))) div 3))
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((2 * ((2x + 1) + ((2 div (1 + (x div 4))) mod 2))) div 3)
A317544: 0 2 3 4 6 8 9 10 11 12 14 15 16 18 19 20
((((x + 1) * ((x4 + 3x3 + 2x2) div 2)) div 2) div 3)
A004302: 0 1 12 60 200 525 1176 2352 4320 7425 12100 18876 28392 41405 58800 81600
((2 + ((2 * ((x + ((x + ~1) mod 3)) div 2)) mod (x + 1))) div 3)
A295989: 0 0 1 0 2 0 1 2 3 0 4 0 1 4 5 0
(((3x2 + ~2x) * ((x2 + 3x + 2) div 2)) div 3)
A220212: 0 1 16 70 200 455 896 1596 2640 4125 6160 8866 12376 16835 22400 29240
(((x3 + 15x2 + 38x + 24) div 2) div 3)
A060488: 4 13 28 50 80 119 168 228 300 385 484 598 728 875 1040 1224
((6x + 6) + ((2x + ~2) div 7))
A246300: 5 12 18 24 30 37 43 49 56 62 68 74 81 87 93 100
((6x + 6) + ((x - (x div 12)) div 2))
A135358: 6 12 19 25 32 38 45 51 58 64 71 77 83 90 96 103
((6x + 6) + ((((x + 1) + (x div 4)) div 2) div 2))
A108587: 6 12 18 25 31 37 44 50 56 63 69 75 82 88 94 100
(1 + (((1 - (x div 2)) div 5) + (((x + 1) div 2) div 3)))
A213126-A087698: 1 1 1 1 0 1 1 1 1 1 1 2 2 2 1 1
(x + ((2 - (x div 2)) div (x + 2)) - (((x + 1) div 2) div 3))
A120508: 1 1 2 3 4 4 4 5 6 7 8 8 9 10 11 12
(((1 + (x div (~2 + (x mod 2)))) mod 3) - (((x + 1) div 2) mod 3))
A135694: 1 ~1 ~1 ~1 0 2 1 ~1 ~1 ~1 0 2 1 ~1 ~1 ~1
(((16x3 + 15x2 + ~x) div 2) div 3)
A304659: 0 5 31 94 210 395 665 1036 1524 2145 2915 3850 4966 6279 7805 9560
(((x4 + 5x3 + 11x2 + 7x) div 2) div 3)
A332697: 0 4 19 56 130 260 469 784 1236 1860 2695 3784 5174 6916 9065 11680
(((7x3 + 9x2 + 2x) div 2) div 3)
A255211: 0 3 16 46 100 185 308 476 696 975 1320 1738 2236 2821 3500 4280
(((7x3 + 3x2 + ~4x) div 2) div 3)
A007584: 0 1 10 34 80 155 266 420 624 885 1210 1606 2080 2639 3290 4040
(((2x5 + x4 + ~x3 + 2x2 + 2x) div 2) div 3)
A101383: 0 1 14 94 380 1135 2786 5964 11544 20685 34870 55946 86164 128219 185290 261080
(((7x3 + 15x2 + 8x) div 2) div 3)
A245301: 0 5 22 58 120 215 350 532 768 1065 1430 1870 2392 3003 3710 4520
((2 * (2 + (x div (1 + (2 * (1 + ((x + ~1) mod 3))))))) div 3)
A000003: 1 1 1 1 2 2 1 2 2 2 3 2 2 4 2 2
((4 * ((2x + 1) - ((((x + 1) div 2) div 2) div 2))) div 3)
A231407: 1 4 6
A189366: 1 4 6 9 12 14 17 18 21 24 26 29 32 34 37 38
(~3 + (4 * (1 + ((2x2 + ~x) mod 8))))
A070380: 1 5 25 29 17 21 9 13 1 5 25 29 17 21 9 13
((x2 - ((x mod (~2 + (((~x + 2) div 2) div 3))) mod 2)) mod 3)
A288424: 0 0 1 0 1 0 0 1 0 2 1 0 0 0 1 0
((4 * ((4x + 4) + ((x div 2) div 3))) div 3)
A189678: 5 10 16 21 26 32 38 44 49 54 60 65 72 77 82 88
(1 - (((1 - ((x + 1) mod (1 - (2 * (x div 3))))) div 2) mod 3))
A187037: 1 1 1 1 1 1 0 0 1 1 ~1 ~1 0 1 1 0
(54x2 + ~78x + 36)
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((1 - (((~x + 4) mod (2 - (x div ~4))) div 2)) mod 3)
A035202: 1 1 0 1 1 0 0 1 1 1 2 0 0 0 0 1
((2 * (2 + ((1 + (((x + 1) * (x div 3)) div 2)) div 2))) div 3)
A029048: 1 1 1 2 2 2 4 4 4 6 6 7 10 10 11 14
(x - ((1 - (2 * (2 + ((x - ((x div 2) div 3)) div 2)))) div 3))
A074232-A007417: 1 2 4 5 7 8 9 10 11 13 14 16 17 18 19 20
((4 * ((2x + 2) + ((x div 2) div 5))) div 3)
A330214: 2 5 8 10 13 16 18 21 24 26 30 33 36 38 41 44
((4 * ((2x + 2) + (x div 12))) div 3)
A189535: 2 5 8 10 13 16 18 21 24 26 29 32 36 38 41 44
((x2 + ~x) div (~6x + 108))
A326467-A326466-A326465-A319474-A026815-A024794: 0 0 0 0 0 0 0 0 0 1 1 2 3 5 7 11
((2 * ((x + 2) - ((~x2 + x) div (4 + (x div 2))))) div 3)
A287549: 1 2 3 4 5 7 8 10 11 13 14 17 18 20 22 24
((2 * ((2x + 2) - (x div (4 - ((x div 2) mod 2))))) div 3)
A014246: 1 2 4 4 6 7 8 9 10 12 12 14 15 16 17 18
(((2 - (x mod (2 + ((2 - (x div 3)) mod 4)))) div 2) mod 3)
A134023: 1 0 0 1 0 0 1 0 1 2 1 0 1 0 0 1
(x - (~42 * (x div 8)))
A024647: 0 1 2 3 4 5 6 7 50 51 52 53 54 55 56 57
(x6 mod 48)
A070688: 0 1 16 9 16 25 0 1 16 33 16 25 0 25 16 33
(((x + 2) - ((3x + ~3) div (2 + (x div 4)))) mod 3)
A028961: 1 0 0 2 0 0 0 0 2 2 0 0 2 2 0 0
((8x + 8) - (3 * ((x - (x div 4)) div 2)))
A188438: 8 16 21 29 37 42 50 55 63 71 76 84 92 97 105 110
((8x + 2) - (3 * ((x - (x div 4)) div 2)))
A134861: 2 10 15 23 31 36 44 49 57 65 70 78 86 91 99 104
((8x + 4) - (3 * ((x - (x div 4)) div 2)))
A134860-A095099: 4 12 17 25 33 38 46 51 59 67 72 80 88 93 101 106
(1 - ((2 * ((x - ((~x + ((x div 4) mod 2)) div 2)) div 2)) mod 3))
A112299: 1 ~1 ~1 0 1 1 ~1 0 1 ~1 ~1 0 1 1 ~1 0
((2 + (((x * ((3x + 3) + (x div 2))) div 2) div 2)) div 3)
A213172: 0 1 2 3 6 9 12 16 21 26 32 38 45 52 61 69
(1 + ((2 + (((x div 3) * (x div 2)) div 2)) div 3) - (x mod 2))
A029176: 1 0 1 0 2 1 2 1 3 2 4 3 5 4 6 6
(11x - (x div ~11))
A004960: 0 12 23 34 45 56 67 78 89 100 111 122 134 145 156 167
((x + 14) - (x div ~14))
A043703-A043663: 14 16 17 18 19 20 21 22 23 24 25 26 27 28 29 31
((x div 2) - (((1 - (x div ~4)) * (x div 4)) div 3))
A129363: 0 0 1 1 2 1 2 2 2 2 3 3 2 1 2 2
((x2 + 3x + 2) - (((~x3 + x) div 4) div 3))
A026052: 2 6 13 22 35 52 74 100 132 170 215 266 325 392 468 552
((2 * (2 + compr(\x.(x mod (1 + (2 * (1 + (x mod 3))))),x))) div 3)
A020491: 1 3 5 7 8 9 10 11 13 15 17 18 19 21 23 24
(~x + ((x div 2) + (6 * ((x + 2) + (3 * (x div 2))))))
A155096: 12 17 41 46 70 75 99 104 128 133 157 162 186 191 215 220
(((3x4 + ~11x3 + 12x2 + ~4x) div 2) div 3)
A096200: 0 0 0 7 40 130 320 665 1232 2100 3360 5115 7480 10582 14560 19565
((x - (4 * (~x + ((x + 1) div ~7)))) div 3)
A188015: 1 3 4 6 8 9 11 14 16 17 19 21 22 24 27 29
(1 - (((2x + ~4) * ((x div 3) * ((~x + 2) div 2))) div 3))
A089891: 1 1 1 2 3 5 12 21
((x + 2) - (3 * ((~3x2 + ~8x + ~4) div 2)))
A250230: 8 27 52 89 132 187 248 321 400 491 588 697 812 939 1072 1217
((x + ~1) + ((2x3 + 12x2 + 28x + 24) div 3))
A224141: 7 22 49 92 155 242 357 504 687 910 1177 1492 1859 2282 2765 3312
(3 + ((~1 + (2 * ((x div ~3) mod 2))) * (2 + (x mod 2))))
A185273: 1 6 5 6 1 0 1 6 5 6 1 0 1 6 5 6
((x + 3) - (2 * (~x + ((2x + 2) div 7))))
A188299: 3 6 9 10 13 16 17 20 23 26 27 30 33 34 37 40
((x + 3) - (2 * (~x + (((x + 1) + (x mod 2)) div 5))))
A187577: 3 6 9 10 13 16 19 22 25 26 29 32 35 36 39 42
(67x + 57)
A304841: 57 124 191 258 325 392 459 526 593 660 727 794 861 928 995 1062
((8x3 + 36x2 + 46x + 16) div 3)
A162540: 5 35 105 231 429 715 1105 1615 2261 3059 4025 5175 6525 8091 9889 11935
((2x3 + 2x2) - (((x3 + ~x) div 2) div 3))
A132112: 0 4 23 68 150 280 469 728 1068 1500 2035 2684 3458 4368 5425 6640
((2x3 + ~x) - (((x3 + ~x) div 2) div 3))
A004467: 0 1 13 47 114 225 391 623 932 1329 1825 2431 3158 4017 5019 6175
((2x3 + x2) - (((x3 + ~x) div 2) div 3))
A215646: 0 3 19 59 134 255 433 679 1004 1419 1935 2563 3314 4199 5229 6415
(((2x + 4) - (3 mod (1 + (x div 3)))) div 3)
A269362: 1 2 2 3 3 4 5 6 6 6 7 7 8 9 9 10
((x + 5) - (2x div (~2 + (x div ~3))))
A116451: 5 7 9 10 11 13 14 15 17 18 19 20 21 22 23 25
(((x + ((x2 + 2x + 1) mod 10)) div 2) div 3)
A293429: 0 0 1 1 1 1 2 1 1 1 1 2 3 3 3 3
(((x6 + x3 + 2x2 + 2x) div 2) div 3)
A006565: 0 1 14 130 700 2635 7826 19684 43800 88725 166870 295526 498004 804895 1255450 1899080
((2 * (x + ((3 * (2x + (x div 2))) div (x + 2)))) div 3)
A060019: 0 2 3 4 6 6 7 8 9 10 10 11 12 12 13 14
(((x + 2) * (1 + ((x2 + 4x + 4) div 2) - (x mod 2))) div 3)
A168380: 2 4 12 20 38 56 88 120 170 220 292 364 462 560 688 816
(((x + 2) * (2 + ((x2 div 2) div 9))) mod 3)
A113063: 1 0 2 1 0 0 2 0 2 0 0 2 2 0 0 1
((3x + 6) + ((x3 + 3x2 + 2x + 6) div 3))
A229446: 8 13 22 37 60 93 138 197 272 365 478 613 772 957 1170 1413
((6x + 2) - ((x + ((x div 2) div 5)) div 2))
A247783: 2 8 13 19 24 30 35 41 46 52 57 62 68 73 79 84
((~x + 1) + (3 * ((16x + 8) + (x div 2))))
A182323: 25 72 122 169 219 266 316 363 413 460 510 557 607 654 704 751
(2x + ((1 - (x div 2)) div 3) - (((x + 1) div 2) mod 3))
A010375: 0 1 3 4 5 9
A010384: 0 1 3 4 5 9 11 12 14 15 16 20
(x - (((~7x2 + ~7x) + (x div 2)) div 3))
A115007: 0 6 16 31 50 75 103 137 175 218 265 318 374 436 502 573
(x2 div ((~x + 1) + (3 * (16 - (x div 2)))))
A026930: 0 0 0 0 0 0 1 1 2 2 4 5 7 9 14 17
((x div 2) - (((x div (6 + (x mod 2))) * (x div 2)) div 3))
A308403: 0 0 1 1 2 2 2 2 3 3 4 4 2 4 3 3
((16x3 + 6x2 + 8x) div 3)
A137931: 0 10 56 170 384 730 1240 1946 2880 4074 5560 7370 9536 12090 15064 18490
((2 * (2x + (((x * (1 + (x div 3))) div 2) div 2))) div 3)
A321501: 0 1 2 4 6 8 10 12 14 18 20 22 26 28 30 34
((2x2 + 3x + 1) - (((~x3 + x) div 2) div 3))
A134465: 1 6 16 32 55 86 126 176 237 310 396 496 611 742 890 1056
((x3 + 2x2 + x) - (((~x3 + x) div 2) div 3))
A304993: 0 4 19 52 110 200 329 504 732 1020 1375 1804 2314 2912 3605 4400
((x3 + 3x2 + 2x) - (((~x3 + x) div 2) div 3))
A255687: 0 6 25 64 130 230 371 560 804 1110 1485 1936 2470 3094 3815 4640
((2x2 + 6x) - (((~x3 + x) div 2) div 3))
A275874: 0 8 21 40 66 100 143 196 260 336 425 528 646 780 931 1100
((2x3 + ~x) - (((~x3 + x) div 2) div 3))
A062025: 0 1 15 55 134 265 461 735 1100 1569 2155 2871 3730 4745 5929 7295
((x3 + x2 + x) - (((~x3 + x) div 2) div 3))
A101165: 0 3 15 43 94 175 293 455 668 939 1275 1683 2170 2743 3409 4175
((x + 3) + ((x2 + 3x + 2) div 11))
A229173: 3 4 6 7 9 11 14 16 19 22 25 28 31 35 38 42
(x - (((~x + ~1) + (((x * ((~x + 2) div 2)) div 2) div 3)) div 3))
A094820: 1 2 3 5 6 8 9 11 13 15 16 19 20 22 24 27
(x - (((~x + ~1) + ((x + ((x div 2) div 3)) mod 3)) div 3))
A285964: 1 2 3 5 6 7 8 9 11 12 13 15 16 18 19 20
(3 + compr(\x.(2 - ((x + 1) mod (1 + (2x mod (1 + (x div 2)))))),x))
A190482: 7 10 12 13 14 16 18 19 20 21 22 23 24 25 26 27
((x * (1 + ((~2x + 2) mod (4 + (x div 4))))) mod 3)
A023565: 0 1 0 0 2 0 0 1 1 0 1 1 0 2 0 0
((x + 2) - (((~x + ~1) + ((x + 2) mod ~7)) div 3))
A214419: 4 5 6 7 8 9 13 14 15 16 17 18 19 22 23 24
((x + 3) + ((x + 1) mod (1 + (x div (2 + (x mod (2 + (x mod 2))))))))
A338281: 3 4 6 6 9 8 12 12 15 12 18 14 21 20 24 18
(2x - (3 * (~x + ((x - ((~x + 2) div 2)) div 5))))
A190545: 3 5 10 15 17 22 27 29 34 39 44 46 51 56 58 63
(3 + compr(\x.((x3 + ~x2) mod 24),x))
A280991: 3 4 7 12 15 19 27 28 31 36 39 43 51 52 55 60
((x + (x3 div (x + 17))) div 3)
A062441: 0 0 0 1 2 3 5 7 9 12 15 19 23 28 34 40
((x + 3) + ((1 + ((x - (x div (~2 + (x mod ~2)))) div 2)) div 2))
A047984: 3 5 6 7 9 10 11 13 14 15 17 18 20 21 22 23
((x + 3) + (2 * (x - (5 * ((~x + 2) div 4)))))
A327140: 3 6 9 22 25 28 31 44 47 50 53 66 69 72 75 88
((x * (((3 * (x div 4)) div 2) - ((x + 1) div 2))) mod 3)
A284575: 0 2 1 0 2 2 0 0 1 0 1 0 0 0 0 0
(x + (x div 2) - ((x + ((x2 + ~x) div 8)) div 3))
A067782: 0 1 3 3 5 5 6 6 7 7 8 8 9 9 9 9
((x + ((x * ((2x + 1) - (x mod 4))) div 4)) mod 3)
A160381: 0 1 0 0 1 2 1 1 0 1 0 0 0 1 0 0
((2x + 2) - ((x2 + 2) div ((x + 3) + (x div 4))))
A183862: 2 4 5 7 8 9 11 12 13 15 16 17 18 19 21 22
((x + 3) + (2 * ((x + 2) + (5 * (x div 4)))))
A327137-A026319: 7 10 13 16 29 32 35 38 51 54 57 60 73 76 79 82
((x + 3) + (2 * (x + (5 * (1 + (x div 4))))))
A246451: 13 16 19 22 35 38 41 44 57 60 63 66 79 82 85 88
((x + 3) + ((4x + (x2 div 4)) div (x + 2)))
A049068: 3 5 7 8 10 11 13 14 15 17 18 19 21 22 23 24
((x + 3) - ((x div 3) + (((x + ~1) mod (1 + (x div 2))) div 2)))
A106501: 3 4 5 5 6 7 7 7 8 8 9 9 9 10 11 10
(x div ((~x + 13) + (x div 3) - (x mod 2)))
A034396: 0 0 0 0 0 0 0 1 1 1 1 2 2 4 4 7
(1 + (x div 2) - ((x div 3) + ((~x + ((x div 2) div 3)) div 2)))
A287292: 1 2 3 3 4 5 5 5 7 6 8 8 8 9 10 10
((x + 4) + (x div 3) - ((~x + 1) div (1 + (x div 3))))
A186346: 3 5 7 9 11 12 14 15 17 18 20 21 23 24 25 27
((((x + 1) div (2 + ((x div 2) mod 5))) mod 2) + (x div 3))
A283303: 0 1 1 2 2 2 3 3 3 4 4 3 4 4 5 5
((2x + 4) - (x2 div ((2x + 8) - (x div 3))))
A184016: 4 6 8 10 11 13 14 16 18 19 20 22 23 25 26 28
((((x - (x div (1 + (x mod 3)))) mod 2) + (x div 3)) - (x mod 2))
A102722: 0 0 0 0 1 0 2 1 2 2 4 2 4 4 4 4
((((x - (x div 7)) div 2) + (x mod 2)) - (x div 3))
A085342: 0 1 1 1 1 2 1 2 1 2 1 3 1 3 2 2
(((2x div (~1 - (x mod 3))) mod 3) - (x mod 3))
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(2 + (2 * (x - (((~x + 1) - (x mod 2)) div 3))) - (x mod 3))
A273324: 2 5 6 10 11 14 18 21 22 26 27 30 34 37 38 42
(1 + ((x + (((~x + 2) + (x div 4)) mod (1 + (x div 3)))) div 2))
A076896: 1 1 2 3 3 3 4 5 6 7 7 7 8 8 8 9
(1 + (2 * (x + ((x * (((x + ~1) div 2) div 2)) div 7))))
A326581-A080429-A062090: 1 3 5 7 9 11 13 17 19 23 25 29 31 37 41 43
(1 + (2 * compr(\x.(1 - ((x * (x mod (2 + (x mod 2)))) mod 5)),x)))
A106403: 3 15 23 27 35 39 47 59
(1 + (2 * (x + ((x - (((x + 1) div 5) mod 2)) div 3))))
A319009: 1 3 5 9 11 13 15 19 21 25 27 29 33 35 37 39
(1 + ((x + (3 * (((x + 1) + (x div 2)) * ((x + 1) div 2)))) div 2))
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(1 + (2 * (x + ((4 * ((x + 1) div 5)) div 3))))
A325570: 1 3 5 7 11 13 15 17 19 23 25 27 29 31 37 39
(1 + (2 * (x + ((4 * ((2 * (x div 2)) div 3)) div 3))))
A255602: 1 3 5 7 11 13 17 19 21 23 29 31 35 37 39 41
(x3 div (2x + 95))
A177339: 0 0 0 0 0 1 2 3 4 6 8 11 14 18 22 27
(~1 + (2 * compr(\x.(1 - (2x mod (2 + ((x div 2) + (x mod 3))))),x)))
A134454: 1 3 7 9 11 13 19 21 25 27 29 31 33 35 37 39
(1 + (2 * (x + ((1 + ((x * (1 + (x div 4))) div 4)) div 2))))
A109860: 1 3 5 7 11 13 17 19 23 25 29 31 37 41 43 47
(1 + ((x + ((((x2 - ((x div 4) mod 2)) div 2) div 2) div 2)) div 2))
A236294: 1 1 2 3 3 5 6 7 9 10 12 14 15 18 20 22
(1 + ((x2 + 3x + 2) div (~2x + 64)))
A076269: 1 1 1 1 1 1 2 2 2 3 4 4 5 6 7 9
(1 + ((x + ((((x + 2) * (2 - (x div ~4))) div 2) div 2)) div 2))
A267303: 1 2 3 4 5 7 8 9 10 12 13 14 15 18 20 21
(1 + ((x + (((x + ((x2 div 2) * ((x + 1) div 2))) div 2) div 2)) div 2))
A060677: 1 1 2 3 5 8 11 17 22 31 38 52
(1 + ((x + ((x + (2x div (1 + (x div 5)))) div 2)) div 2))
A297351: 1 2 3 4 6 6 7 8 9 10 10 11 12 12 13 14
(16x2 + 111x + 159)
A250659: 159 286 445 636 859 1114 1401 1720 2071 2454 2869 3316 3795 4306 4849 5424
compr(\x.(1 - (x mod (1 + (x mod (2 * (1 + (x mod 4))))))),(x + 3))
A325797-A279244: 5 7 9 11 13 14 15 17 19 21 22 23 25 26 27 29
((x + 3) * (2 + (9 * ((x2 + x) div 2))))
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((2x + 1) + ((~x + ((x * (x div 2)) div 3)) div 5))
A332687: 1 2 4 6 8 10 13 15 17 19 22 24 27 29 32 35
((2x + 1) + ((x mod (2 - (x mod (~1 - (x div 4))))) mod 2))
A284906: 1 4 5 8 9 11 13 16 17 20 21 23 25 28 29 31
((2x + 1) + ((((x2 + ~x) div 8) + (x div 2)) div 2))
A276498: 1 3 5 7 10 13 16 19 22 25 29 32 36 39 43 47
((2x + 1) + ((x + ((x + 2) div (2 + (x div 8)))) div 2))
A189526: 1 4 7 9 12 15 18 20 22 25 28 30 33 36 38 41
(30x3 + 45x2 + 17x + 1)
A193248: 1 93 455 1267 2709 4961 8203 12615 18377 25669 34671 45563 58525 73737 91379 111631
(40x3 + 60x2 + 22x + 1)
A193251: 1 123 605 1687 3609 6611 10933 16815 24497 34219 46221 60743 78025 98307 121829 148831
(48x3 + 36x2 + 8x + 1)
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((2x + 1) + ((((x div 3) mod 3) - (x div 2)) div 3))
A189521: 1 3 4 7 8 10 12 14 16 17 19 21 23 25 27 29
((x - (3 * (~x + (x mod 10)))) mod (2x + 1))
A103303: 0 1 2 3 4 5 6 7 8 9
A261729-A261725-A174025-A118758-A118757-A106649-A003100: 0 1 2 3 4 5 6 7 8 9 19 18 17 16 15 14
((3x + 1) - (((x2 + ~2x) div 3) div (x + 3)))
A186542: 1 5 7 10 13 16 19 21 24 27 29 32 35 38 40 43
(18x3 + 49x2 + 42x + 11)
A274119: 11 120 435 1064 2115 3696 5915 8880 12699 17480 23331 30360 38675 48384 59595 72416
((3x + 1) + (((~x + 1) div (1 + ((1 + (x div 2)) div 2))) mod 2))
A022442: 2 4 8 11 13 16 19 22 26 29 32 35 38 41 44 47
((3x + 1) + ((x - ((x + (x div 3)) div 3)) div 2))
A248228: 1 4 8 11 14 17 21 24 27 30 34 37 40 44 47 50
(24x4 + 4x3 + ~16x2 + 4x)
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(1 + ((3 * ((x + 1) + (2 * (2x + (x mod 2))))) + (x div 2)))
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(1 - (x mod (~1 + (((x mod (~1 + (2 * (x div 3)))) mod 2) * (x div 2)))))
A146314: 1 1 1 1 1 1 1 0 1 1 1 ~2 ~1 1 1 1
(~1 + ((2 * (x - ((2 * (~2 + (x div 2))) div 5))) + (x div 2)))
A187952: 1 3 6 8 9 11 14 16 19 21 22 24 27 29 30 32
(~1 + ((2 * (x - (((~x + ~2) + (x mod 2)) div 5))) + (x div 2)))
A190493: 1 3 6 8 13 15 18 20 23 25 30 32 35 37 42 44
((1 + (x mod (1 + (x mod (2 * (1 + (x mod 4))))))) mod (1 + (x div 2)))
A229878: 0 0 1 0 1 2
A080941: 0 0 1 0 1 2 1 0 1 2 1 4 1 2 3 0
((3 + (2 * (x - (2 * ((~x + ~2) + (x mod 2)))))) * (1 + (x div 2)))
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(1 + ((3 * (1 + ((x div 2) div 3) - (x mod 2))) + (x div 2)))
A067061: 4 1 5 2 6 3 10 7 11 8 12 9 16 13 17 14
((2 + ((x3 + 3x2 + 2x + 6) div 3)) mod (1 + (x div 2)))
A268584: 0 0 0 0 2 2 0 0 4 4 0 0 4 4 4 4
((((x div 2) mod 5) div 2) * (8 mod (1 + (x div 2))))
A175917: 0 0 0 0 2 2 0 0 6 6 0 0 0 0 0 0
((3x + 8) - ((x div 2) + ((~x + 1) div (1 + (x div 2)))))
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((x + 1) + ((2 * ((x - ((x div 2) mod 3)) div 3)) + (x div 2)))
A190235: 1 2 4 5 7 10 14 15 17 18 20 23 27 28 30 31
(1 + ((x div (3 * (2 + ((x + 1) mod 8)))) + (x mod 2)))
A235726: 1 2 1 2 1 2 1 3 1 2 1 2 1 2 1 4
(1 + ((((x + ~1) mod (1 + ((x + 1) div 5))) mod 2) + (x mod 2)))
A083165: 1 2 1 2 2 2 2 2 2 2 1 3 1 2 2 2
(1 + (((x div (1 + (x2 mod 12))) mod 2) + (x mod 2)))
A336041: 1 2 1 2 1 2 1 3 2 2 1 3 1 2 1 3
(1 + (((2 + (x * (x div 2))) mod (1 + (x div 3))) mod 2) - (x mod 2))
A328372: 1 0 1 1 1 0 1 0 2 0 1 1 1 0 1 1
(1 + ((x mod (~1 + (4 * (x mod 5)))) mod 2) - (x mod 2))
A263099: 1 1 1 1 1 0 1 0 1 1 1 0 2 0 1 0
(1 + ((x div (1 + ((x2 + ~x) mod 8))) mod 2) - (x mod 2))
A341969: 1 1 1 0 1 1 1 0 1 1 2 1 1 0 1 1
(x mod ((x + ~1) + (x mod 2) - ((x mod (~1 + (2 * (x div 4)))) mod 2)))
A211159: 0 0 0 0 1 0 1 0 1 0 2 0 1 1 1 0
(1 + (((3 * ((~x + 2) div 2)) div 5) mod 2) - (x mod 2))
A091830: 1 0 1 1 2 0 1 0 1 1 2 1 2 0 1 1
(1 + (2 * ((2 * (1 + (x mod 6))) div 3)) - (x mod 2))
A153990: 1 2 5 4 7 8 1 2 5 4 7 8 1 2 5 4
(1 + ((x - (2x div (2 + (x div 5)))) div 2) - (x mod 2))
A029197: 1 0 1 0 1 1 2 1 2 1 3 3 4 3 4 4
(1 + ((((x2 mod ((x + ~3) - (x mod 2))) div 2) mod 2) + (x mod 2)))
A271418: 1 3 1 2 1 2 1 2 1 2 2 3 1 3 1 2
(x div (1 + (2 * (2 + ((x + 1) mod (2 + ((x div 2) mod 2))))) - (x mod 2)))
A157235: 0 0 0 0 0 1 0 0 1 2 1 2 1 3 2 2
(1 + (2 * (x + (((x div 4) * (x div 4)) div 2))) - (x mod 2))
A285502: 1 2 5 6 9 10 13 14 21 22 25 26 33 34 37 38
((1 + (x div (8 - ((x + ~2) div 3)))) div (1 + (x mod 2)))
A029229: 1 0 1 0 1 0 1 1 2 1 2 1 3 1 4 2
((1 + ((1 + (x2 div 16)) div 2)) div (1 + (x mod 2)))
A029177: 1 0 1 0 2 1 2 1 3 2 4 2 6 3 7 4
((1 + ((x + 1) div 2)) mod ((1 + ((x mod 3) div 2)) * (1 + (x mod 2))))
A335487: 0 0 0 1 0 0 0 1 1 0 0 3 0 0 0 1
((1 + (x div (2 * (2 + ((x div 3) mod 3))))) div (1 + (x mod 2)))
A029236: 1 0 1 0 1 0 1 0 2 1 3 1 3 1 3 1
((1 + (x div (2 * (2 + ((2 - (x div 2)) mod 4))))) * (1 + (x mod 2)))
A130831: 1 2 1 2 2 4 1 2 2 4 2 4 4 8 2 4
((1 + ((x + (x2 div 3)) div 8)) div (1 + (x mod 2)))
A029171: 1 0 1 0 2 1 3 1 4 2 6 3 8 4 10 6
((1 + (((x + ~2) * (x div 2)) div (x + 6))) div (1 + (x mod 2)))
A029216: 1 0 1 0 1 0 2 1 2 1 3 1 4 2 5 2
((x + 1) div ((2 + ((x + ~2) div (2 + (x div 4)))) * (1 + (x mod 2))))
A066075: 1 1 1 1 2 1 2 1 3 1 2 1 3 1 3 2
(1 + (((x3 + 3x2 + 2x) div 3) + (x div (1 + (x mod 2)))))
A178946: 1 3 11 22 45 73 119 172 249 335 451 578 741 917 1135 1368
(1 + compr(\x.(x mod (1 + ((~x + 1) mod (1 + (x mod 9))))),x))
A278997: 1 2 4 7 10 11 13 16 17 19 20 22 25 26 28 29
(~1 + compr(\x.(1 - (x mod (1 + (~x mod (1 + (x div 5)))))),x))
A327776-A060679: 4 6 8 9 10 12 14 16 18 20 21 22 24 25 26 27
(1 + compr(\x.(x mod (1 + ((x + 5) mod (1 + (x div 3))))),x))
A247397: 1 2 3 4 5 6 7 8 9 10 12 13
A249575: 1 2 3 4 5 6 7 8 9 10 12 13 16 17 19 21
(1 + compr(\x.(~1 + ((x div 4) div (1 + (x mod (2 * (1 + (x mod 2))))))),x))
A029750: 1 2 3 4 5 6 7 8 10 12 14 16 20 24 28 32
(1 + compr(\x.(~1 + (x mod (1 + ((~x mod (2 + (x div 3))) div 2)))),x))
A334294: 1 2 3 4 5 6 7 8 9 10 11 13 14 17 20 22
(1 + compr(\x.((x + 1) mod (1 + (x div (1 + (~x mod 8))))),x))
A305759-A143513: 1 2 3 4 5 6 8 9 10 12 15 16 17 18 20 24
(1 + compr(\x.(x mod (1 + ((x + 2) mod (1 + (x div (2 + (x div 4))))))),x))
A162535: 1 2 3 5 7 8 9 10 11 13 14 15 17 19 21 23
(1 + compr(\x.(~1 + ((2 * (~x + (x2 div 3))) mod 5)),x))
A231407: 1 4 6
A112082: 1 4 6 9 10 11 14 16 19 21 24 25 26 29 31 34
(1 + compr(\x.(~1 + ((x mod 7) mod (1 + (x div 4)))),x))
A037173: 1 2 3 4 5 6 7 8 9 11 12 13 15 16 20 21
(~1 + compr(\x.(1 - (x mod (1 + ((~2x + 1) mod (1 + (x div 4)))))),x))
A013920: 4 6 8 9 12 14 15 16 18 20 21 22 25 26 28 30
(1 + compr(\x.((x + 1) mod (1 + ((x div 2) div (1 + (2 * (2 - (x mod 2))))))),x))
A337741-A308560-A285829-A285815-A235697-A235507-A234474-A225782-A225780-A085135-A085133-A005349: 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27
(1 + compr(\x.((x + 1) mod (1 + (x mod (3 * (1 + (x mod 4)))))),x))
A225837-A035246: 1 2 3 4 6 7 8 9 12 13 14 16 18 19 21 24
((x + 1) + (5x2 div 13))
A025719: 1 2 4 7 11 15 20 26 33 41 49 58 68 79 90 102
((x + 1) + ((4x2 + ~x) div 11))
A025710: 1 2 4 7 10 14 19 25 31 38 46 55 64 74 85 96
(1 + compr(\x.(1 - (((x + ~1) * (1 + (x div 2))) mod (1 + (x div 3)))),x))
A279289: 5 7 9 11 13 14 15 16 17 19 20 21 22 23 25 26
(1 + compr(\x.((x + 1) mod (1 + ((1 + (2x mod 3)) mod (x + 1)))),x))
A240911: 1 2 3 4 6 8 9 10 12 15 16 18 20 21 22 24
(~1 + compr(\x.(2 - (x mod (1 + ((x2 div ~4) mod (x + 1))))),x))
A231407: 1 4 6
A324704: 1 4 6 7 8 10 12 13 14 16 17 18 19 20 21 22
(1 + compr(\x.(~1 + (x mod (2 + ((x + 4) mod (1 + (x div 4)))))),x))
A032974: 1 2 3 4 5 7 8 9 10 12 13 14 16 17 21 22
((x + 1) + (((x3 + x) div (x + 2)) div 7))
A280706: 1 2 3 4 6 8 10 13 16 19 23 26 30 35 39 44
((x + 1) + ((x div ~7) * (x mod 7)))
A194756: 1 1 1 1 1 1 1 8 7 6 5 4 3 2 15 13
((x + 1) + (x div (5 + ((((x + ~1) div 2) div 2) mod 3))))
A172251: 1 2 3 4 5 6 8 9 10 11 12 13 14 16 17 19
((x + 1) + ((3x2 + 2x) div 17))
A225087: 1 2 3 5 8 11 14 17 21 25 29 34 39 45 51 57
((x2 + 2x + 1) - (x * ((x + 1) mod 15)))
A044916: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 225 241
((x + 1) + ((x * (((x + 1) div 2) div 2)) div 15))
A190856: 1 2 3 4 5 6 7 8 10 11 12 14 15 16 17 20
((x + 1) + ((x * (1 + (x div 5))) div 9))
A024898: 1 2 3 4 5 7 8 9 10 12 14 15 17 18 19 22
((x + 1) + ((((x + 1) div 2) div 3) * (1 + (x div 8))))
A344609-A344586-A329139-A325370-A319161-A268375-A265640-A246716-A212165-A130091-A119848: 1 2 3 4 5 7 8 9 11 12 13 16 17 18 19 20
((x + 1) + ((2x + 1) mod (1 + (2x mod (2 + (x div 4))))))
A306369-A291784: 1 2 3 4 5 7 7 8 9 11 11 14 13 15 16 16
((x + 1) + (x div (5 * (1 + (x mod (3 + (x mod 2)))))))
A130916: 1 2 3 4 5 6 8 8 9 10 12 12 15 15 15 16
((x + 1) + ((3 * ((2x + 1) + (x mod 2))) div 5))
A231407: 1 4 6
A190330: 1 4 6 8 10 13 14 17 19 22 23 26 28 30 32 35
((x + 1) + ((12 * (1 + (x div 2))) div 5))
A286904: 3 4 7 8 12 13 16 17 21 22 25 26 29 30 34 35
((x + 1) + ((1 + ((x * ((1 + (x div 2)) div 2)) div 2)) div 5))
A193988: 1 2 3 4 5 6 8 9 10 12 14 15 16 18 20 22
((x + 1) + (((((x + 2) * (~2 + (x div 2))) div 2) div 2) div 5))
A191894: 0 1 2 3 5 6 7 8 10 11 12 13 15 17 19 20
((x + 1) + ((x + 4) mod (~1 + ((2x + ~4) mod (2 + (x div 2))))))
A290492: 1 2 3 4 5 6 7 8 9 10 11 12 14
A246081: 1 2 3 4 5 6 7 8 9 10 11 12 14 16 18 21
((x + 1) + (3 * ((x + 1) - (((~x + 2) - (x div 2)) div 4))))
A190703-A188088: 4 8 15 19 23 30 34 38 45 49 56 60 64 71 75 79
((x + 1) + (3 * ((x + 1) - ((~x + (x mod 3)) div 4))))
A187571: 4 8 12 19 23 27 34 38 42 49 53 57 61 65 69 76
(1 + compr(\x.((((x + ~1) + (x mod 8)) div 3) mod 3),x))
A189465: 2 6 7 10 11 15 19 23 24 27 28 32 36 40 44 45
((x + 1) + ((x - (((x + 1) mod 7) div 2)) div 3))
A160532: 1 2 3 4 5 6 9 10 11 12 13 15 16 18 19 20
((x + 1) + ((2 * (x2 div (3 * (2 + (x div 2))))) div 3))
A228803: 1 2 3 4 5 7 8 10 11 12 13 15 17 18 19 21
((x + 1) + ((2 * ((x - ((x div 2) mod 5)) div 2)) div 3))
A082463: 1 2 3 4 5 6 7 9 10
A123101: 1 2 3 4 5 6 7 9 10 11 14 15 16 18 19 20
((x + 1) + ((2 * (x - ((x - (4 mod (x + 1))) div 2))) div 3))
A289240: 1 2 4 5 7 9 10 12 13 14 15 17 18 20 21 22
(~1 + compr(\x.((x + 2) - (3 * (~2 + ((x - (x div 4)) div 2)))),x))
A344809: 54 57 60 62 63 65 66 68 69 70 71 72 73 74 75 76
((x + 1) + (3 * ((x + 2) - (((~x + 2) - (x div 2)) div 4))))
A188074: 7 11 18 22 26 33 37 41 48 52 59 63 67 74 78 82
(((x2 + 4x + 4) div 2) div (~x + 23))
A309879: 0 0 0 0 0 1 1 2 3 4 5 7 8 11 14 18
((x + 1) + (((x * (1 + (x * (x2 div 3)))) div 2) div 3))
A011955: 1 2 4 9 19 40 80
((x + 1) + ((x div (4 + (x div 4))) + ((x + 2) div 3)))
A136495: 1 3 4 5 7 9 10 12 13 14 16 17 18 20 22 23
(48x3 + 112x2 + 80x + 16)
A207450: 16 256 1008 2560 5200 9216 14896 22528 32400 44800 60016 78336 100048 125440 154800 188416
((x + 1) + ((x + ((x div 2) mod (1 + (~x mod 4)))) div 3))
A187480: 1 2 4 5 6 8 9 10 11 13 15 16 17 19 20 21
(1 + compr(\x.((1 - ((x + 2) mod 13)) mod (x + 1)),x))
A297277-A296747-A044961-A044823-A043715: 1 2 3 4 5 6 7 8 9 10 11 13 26 39 52 65
(1 + compr(\x.((1 - ((x + 2) mod 11)) mod (x + 1)),x))
A346217-A342826-A324988-A297271-A297148-A296712-A283870-A276354-A276115-A248954-A227858-A227001-A214019-A193413-A193408-A190217-A160818-A147882-A110785-A110784-A110751-A109872-A087992-A084982-A082937-A082810-A071267-A062687-A044959-A044821-A043713-A032573: 1 2 3 4 5 6 7 8 9 11 22 33 44 55 66 77
(1 + compr(\x.((1 - ((x + 2) mod 15)) mod (x + 1)),x))
A297283-A296753-A044963-A044825-A043717: 1 2 3 4 5 6 7 8 9 10 11 12 13 15 30 45
(1 + compr(\x.((2 - ((x + 3) mod 12)) mod (x + 1)),x))
A228017: 1 2 3 4 5 6 7 8 9 12 24 36 48
(1 + compr(\x.((1 - ((x + 2) mod 14)) mod (x + 1)),x))
A290492: 1 2 3 4 5 6 7 8 9 10 11 12 14
A297280-A296750-A044962-A044824-A043716: 1 2 3 4 5 6 7 8 9 10 11 12 14 28 42 56
((x2 + x + 1) + ((x - (((x - (x div 4)) div 2) mod 2)) div 2))
A173209: 1 3 7 14 22 33 46 60 76 95 116 138 163 189 217 248
((x2 + x + 1) + ((x4 + 3x2) div 4))
A066375: 1 4 14 40 97 206 394 694 1145 1792 2686 3884 5449 7450 9962 13066
((x2 + x + 1) * (1 + (5 * ((x2 + x) div 2))))
A160765: 1 18 112 403 1071 2356 4558 8037 13213 20566 30636 44023 61387 83448 110986 144841
((x + 1) + ((x - ((x + ~1) mod (1 + ((x + 1) div 5)))) div 2))
A247161: 1 2 4 5 6 8 9 11 12 13 16 17 18 20 21 22
((x + 1) + ((7 * (1 + ((x div 2) div 3))) div 2))
A123977: 4 5 6 7 8 9 14 15 16 17 18 19 23 24 25 26
((x + 1) + (2 * (x2 div 65)))
A296861: 1 2 3 4 5 6 7 8 9 12 13 14 17 18 21 22
((x + 1) + (2 * ((8 * (1 + (x div 2))) div 5)))
A137709: 3 4 9 10 13 14 19 20 25 26 29 30 35 36 39 40
((x + 1) + (2 * ((2x - (x2 div 4)) div 5)))
A341191: 1 2 3 4 5 6 7 8 9 8 9 8 7 6 5 4
((x + 1) + ((x + (x div 5) - ((x div 2) div 3)) div 2))
A189629: 1 2 4 5 7 9 10 11 13 14 16 18 19 20 22 24
(x2 mod ((x + 1) + ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2)))
A340227-A273711: 0 1 1 1 1 4 1 1 1 4 1 4 1 4 4 1
((x + 1) + ((3 * (((x + 1) - (x div 3)) div 3)) div 2))
A049095: 1 2 4 5 6 7 8 11 12 13 14 16 17 18 19 20
((x + 1) + ((3 * ((x + ((x div ~2) mod 2)) div 3)) div 2))
A005528: 1 2 4 5 6 9 10 11 12 14 15 16 19 20 22 23
((x + 1) + ((3 * ((x2 div 4) div (x + 3))) div 2))
A302540-A230780: 1 2 3 4 5 6 8 9 10 11 12 15 16 17 18 20
((x + 1) + ((3 * ((1 + ((x + (x div 2)) div 4)) div 2)) div 2))
A182942: 1 2 3 5 6 7 8 9 12 13 14 15 16 17 19 20
((x + 1) + ((x - ((x - ((((x + 1) div 2) div 2) div 2)) mod 3)) div 2))
A107746: 1 2 3 5 6 7 10 11 12 13 16 17 18 20 21 23
((x + ~1) + (2 * (12 + ((((x + 1) div 2) div 2) div 2))))
A062999: 23 24 25 26 27 28 29 32 33 34 35 36 37 38 39 42
((x + 1) + (((((x + 1) div 2) div 3) * ((x + 2) div 3)) div 2))
A324759-A324758: 1 2 3 4 5 7 8 9 10 11 13 16 17 19 20 21
((~x + 1) + (2 * ((x + 1) div (8 - ((x + 2) div 3)))))
A174863: 1 0 ~1 ~2 ~3 ~2 ~3 ~4 ~5 ~4 ~5 ~4 ~5 ~4 ~3 ~4
((2x + 4) - (x2 div ((x + 1) + (2 * ((x div 2) div 3)))))
A216845: 4 6 7 8 9 10 12 14 15 16 17 18 20 21 22 23
(14x3 + 12x2 + 6x + 1)
A155883: 1 33 173 505 1113 2081 3493 5433 7985 11233 15261 20153 25993 32865 40853 50041
((~x + 1) + (2 * (x2 div ((x + 1) + (2 * (x div 5))))))
A071995: 1 0 1 2 3 2 3 2 3 4 3 4 5 6 7 6
((x + 1) + (63 * ((x + 1) div 2)))
A174928: 1 65 66 130 131 195 196 260 261 325 326 390 391 455 456 520
((x + 1) + (4 * (1 + (2 * (2 + ((x div 2) div 5))))))
A199934: 21 22 23 24 25 26 27 28 29 30 39 40 41 42 43 44
((x + 1) + ((x - ((1 + ((x mod (2 + (x div 2))) mod 4)) div 2)) div 2))
A053661: 1 2 3 5 7 8 9 11 12 13 15 17 19 20 21 23
((x + 1) + (((17 * (1 + (x div 2))) div 2) div 2))
A277095: 5 6 11 12 17 18 24 25 30 31 36 37 42 43 49 50
((x + 1) + ((((x + 1) * ((x2 + 4x + 3) div 2)) div 2) div 2))
A180861: 1 4 8 16 26 42 61 88 119 160 206 264 328 406 491 592
((x + 1) + (2 * ((2x + 2) + ((x - (x div 8)) div 2))))
A098022: 5 10 17 22 29 34 41 46 51 58 63 70 75 82 87 94
((x + 1) + ((((((x + 2) div 3) * (1 + (x div 2))) div 2) div 2) div 2))
A328413: 1 2 3 4 5 6 8 9 10 11 14 15 16 18 20 21
((~x + 1) + (2 * (4 + (x mod (x - ((x + ~1) mod 8))))))
A199264: 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6
(1 + compr(\x.(1 - (x mod (2 + (x mod (2 + ((x - (x div 4)) div 2)))))),x))
A130225: 2 3 4 5 6 7 8 9 10 11 12 14 16 18 20 23
((3x2 + 6x + 3) div (x + 17))
A135676: 0 0 1 2 3 4 6 8 9 11 13 15 17 19 21 24
(1 + compr(\x.((16 mod (~x + ~1)) mod 8),x))
A222011: 1 2 4 8
A070173: 1 2 4 8 12 16 24 32 40 48 56 64 72 80 88 96
((6x2 + 12x + 6) div (x + 9))
A326299: 0 2 4 8 11 15 19 24 28 33 38 43 48 53 58 64
((x + 1) + (14x div (x + 6)))
A231407: 1 4 6
A078941: 1 4 6 8 10 12 14 15 17 18 19 21
A078942: 1 4 6 8 10 12 14 15 17 18 19 21 22 23 24 26
((x + 1) + ((x - ((((x + 2) mod 6) - (x div 2)) div 2)) div 2))
A141489: 0 2 3 4 7 9 10 11 13 14 17 18 20 21 23 24
((x + 1) + (((x + (((~x + 1) mod (4 + (x div 2))) div 2)) div 2) div 2))
A289002: 1 2 4 5 6 7 8 9 11 12 13 15 17 18 19 20
((~x + 1) + (2 * ((x + (((~2x + 4) mod (2 + (x div 2))) div 2)) div 2)))
A004074: 1 0 1 0 1 2 1 0 1 2 3 2 3 2 1 0
((x + 1) + ((x + ((x + (x mod 8)) div 5)) div 2))
A320474: 1 2 4 6 7 9 11 12 13 15 17 18 20 22 24 25
((x + 1) + ((x + ((2x mod ~5) div 3)) div 2))
A207432: 1 2 3 4 6 8 9 11 12 14 16 17 18 19 21 23
((x + 1) + (2 * (x + ((((~1 + ((x2 + x) div 2)) div 2) div 2) mod 2))))
A286728: 3 4 7 12 13 18 21 22 25 30 33 34 39 40 43 48
((x + 1) + ((x + (2x2 div (8 + (x div 2)))) div 2))
A186152: 1 2 4 6 8 11 13 15 18 21 23 26 29 32 35 38
(x5 + 8x4 + 23x3 + 31x2 + 20x + 5)
A221465: 5 88 513 1856 5125 11880 24353 45568 79461 131000 206305 312768 459173 655816 914625 1249280
((3x + 1) + ((x - (x2 div (x + 5))) mod 2))
A022441: 1 5 7 10 14 17 20 23 25 28 31 34 37 40 43 46
(1 + (x div ((~x + 12) + (x div 2) - (x mod 3))))
A261796: 1 1 1 1 1 1 1 2 2 2 2 3 3 4 5 4
((x + 1) + ((x2 + 2x + 1) div (16 + (x div 2))))
A214977: 1 2 3 4 6 8 9 11 13 15 16 18 20 22 24 27
((x + 1) + ((x - (((3 * (x div 2)) div 2) div 2)) mod 2) - (x mod 2))
A332807-A332805: 1 2 3 4 6 5 7 8 10 9 12 11 13 14 16 15
compr(\x.(1 - (x mod (1 + (x mod (1 + ((x + 1) div 5)))))),(x + 1))
A091901: 7 11 13 14 15 17 19 21 22 23 25 26 27 28 29 31
compr(\x.(x mod (1 + (x mod ((x + 1) - (x mod 10))))),(x + 1))
A178158-A034709: 1 2 3 4 5 6 7 8 9 11 12 15 21 22 24 25
((x + 1) * (1 + ((x + 1) div (1 + (x div (2 + (x mod (2 + (x mod 2)))))))))
A129902: 2 6 6 12 10 24 14 24 18 30 22 60 26 42 30 48
((1 + (3 * (((x div ~3) mod 2) - (x mod 2)))) mod (x + 1))
A343408: 0 1 1 1 1 4 1 1 4 1 1 10 1 1 4 1
(49x2 + 99x + 50)
A173141-A031692: 50 198 444 788 1230 1770 2408 3144 3978 4910 5940 7068 8294 9618 11040 12560
compr(\x.(x mod (1 + ((0 - ((x + 1) mod 8)) mod (x + 1)))),(x + 1))
A033072: 1 2 3 4 5 6 7 9 15 17 23 25 31 33 39 41
((((x3 + x) div (x + 2)) div 7) mod (x + 1))
A284173: 0 0 0 0 1 2 3 5 7 9 1 2 4 7 9 12
((x + 1) * (16 - ((x div 2) div 7)))
A044856: 16 32 48 64 80 96 112 128 144 160 176 192 208 224 225 240
compr(\x.((x + (x mod 10)) mod 7),(x + 1))
A190495: 7 12 19 24 36 41 48 53 65 70 77 82 89 94 106 111
(2 - ((1 - ((x div 2) mod (1 + (x2 mod 6)))) div (x + 1)))
A064656: 1 2 2 2 3 2 2 2 3 2 2 2 2 2 3 3
((1 + (x mod ((2 - (x mod ((~x + ~1) + (x mod 4)))) div 2))) mod (x + 1))
A300239-A174726: 0 1 1 1 1 1 1 2 1 1 1 4 1 1 1 4
((1 + (2x div (~x + 22))) mod (x + 1))
A265410: 0 1 1 1 1 1 1 1 2 2 2 3 3 3 4 5
((3 - (((x + 2) div (2 - (x mod ~4))) mod 2)) mod (x + 1))
A268317: 0 1 2 2 2 2 3 2 2 3 2 3 2 2 3 2
((x + 1) * (1 + (x div (2 + ((1 + (x div 5)) mod 4)))))
A131959: 1 2 3 8
A190650: 1 2 3 8 10 12 14 16 27 30 33 36 39 42 45 128
((1 + (((x + 1) mod 4) + (x mod 9))) mod (x + 1))
A072516: 0 0 0 0 1 2 3 0 1 3 5 3 5 7 9 7
((9x + 1) - ((x div ~2) div 5))
A302563: 1 11 20 29 38 47 56 65 74 83 92 102 111 120 129 138
compr(\x.((x mod 9) - ((x div 2) mod 5)),(x + 1))
A297267-A297144-A296711: 9 18 19 27 28 29 36 37 38 39 45 46 47 48 49 54
((x + 1) * ((x + 1) - (((2 + (x * (x + (x div 2)))) div (x + 2)) div 2)))
A231407: 1 4 6
A104236: 1 4 6 12 15 24 28 32 45 50 55 72 78 84 90 112
compr(\x.((x - (2x mod 13)) mod 3),(x + 1))
A191103: 3 6 7 10 14 17 21 24 28 31 35 38 39 42 45 46
((x + 1) + ((x2 + ~x) div ((x + 3) - ((x div 2) div 3))))
A120836: 1 2 3 5 6 8 10 12 14 16 18 20 23 25 27 29
(49x2 + 96x + 47)
A157362: 47 192 435 776 1215 1752 2387 3120 3951 4880 5907 7032 8255 9576 10995 12512
((x + 1) * ((x + 3) + (2 * ((x - ((~x + 2) div 4)) div 2))))
A101332: 3 8 21 40 55 84 105 144 189 220 275 336 377 448 495 576
((x + 1) * (1 + ((7x2 + 5x) div 2)))
A100171: 1 14 60 160 335 606 994 1520 2205 3070 4136 5424 6955 8750 10830 13216
((x + 1) * (1 + (x * ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2))))
A062509-A061537: 1 2 3 4 5 36 7 8 9 100 11 144 13 196 225 16
((x + 1) + (10x div (x + 9)))
A322741: 1 3 4 6 8 9 11 12 13 15 16 17 18 19 21 22
((~x + ~1) + compr(\x.(1 - (x mod (2 + (3 * (x mod 3))))),(x + 1)))
A087846: 1 1 1 1 2 3 4 5 5 5 5 5 6 6 6 6
compr(\x.((8x mod 13) mod 2),(x + 1))
A283767: 1 4 7 8 10 11 13 14 17 20 21 23 24 26 27 30
((2 + ((2x2 + ~x) mod 13)) div (x + 1))
A091704: 2 1 2 1 0 1 0 0 0 1 0 1 0 0 0 0
((~x + ~1) + (2 * (~1 + (2 * ((4x + 4) + ((x div 2) mod 2))))))
A161453: 13 28 47 62 73 88 107 122 133 148 167 182 193 208 227 242
(((1 + (((x + 2) div (1 + (2 * (x mod 2)))) mod 4)) div 2) mod (x + 1))
A301652: 0 1 0 1 1 1 0 2 1 2 0 0 1 1 0 1
compr(\x.((x mod 9) - (x mod 10)),(x + 1))
A032888: 1 2 3 4 5 6 7 8 9 18 19 27 28 29 36 37
((x + 1) * ((x div (1 - (3 * (1 + ((x + 1) mod 4))))) mod 2))
A145105: 0 2 3 0 5 6 7 0 0 0 11 0 13 0 0 0
compr(\x.(1 - (x mod (2 + ((1 - (2x div 3)) mod 3)))),(x + 1))
A340787: 3 5 7 10 11 13 14 15 17 19 21 22 23 25 26 28
compr(\x.(1 - (x mod (2 + ((x div ~7) mod 3)))),(x + 1))
A084116-A002035: 2 3 5 6 7 8 10 11 13 14 15 17 19 21 22 23
((4 + ((x mod (~1 + (x div ~2))) + (x div 3))) mod (x + 1))
A119707: 0 1 1 1 3 2 4 3 4 4 5 4 6 5 6 6
((1 - (x mod (2 + ((x2 + 4) mod (x + 3))))) div (x + 1))
A128430: 1 0 ~1 0 ~1 ~1 0 ~1 0 0 0 ~1 ~1 ~1 ~1 0
compr(\x.(1 - (x mod (2 + ((~x2 + 2x + ~1) mod (1 + (x div 2)))))),(x + 1))
A122686: 2 3 5 6 7 8 11 12 13 14 15 17 19 21 22 23
(49x2 + 100x + 51)
A157365: 51 200 447 792 1235 1776 2415 3152 3987 4920 5951 7080 8307 9632 11055 12576
((x + 1) * ((5x3 + 15x2 + 12x + 2) div 2))
A269237: 1 34 189 616 1525 3186 5929 10144 16281 24850 36421 51624 71149 95746 126225 163456
compr(\x.(1 - (x mod (2 + ((x mod (1 + (2 * (x mod 4)))) mod 2)))),(x + 1))
A230203: 5 7 9 11 13 17 19 21 23 25 26 27 29 31 33 35
compr(\x.(1 - (x mod (2 + (((x2 + ~x) div 2) mod 6)))),(x + 1))
A007989: 2 3 5 6 7 8 9 11 13 14 17 18 19 20 21 22
((4x + 4) * ((x2 + 2x + 1) + (x2 div 3)))
A239056: 4 32 120 304 600 1056 1708 2560 3672 5080 6776 8832 11284 14112 17400 21184
compr(\x.((((x mod (1 + (x div 4))) * (1 + (x div 2))) div 2) mod 2),(x + 1))
A187102: 1 2 3 4 6 7 9 11
A026468: 1 2 3 4 6 7 9 11 12 14 15 16 19 21 22 23
((~x + ~1) + (8 * (1 + (2 * (x + (x div 8))))))
A161447: 7 22 37 52 67 82 97 112 143 158 173 188 203 218 233 248
compr(\x.(x2 mod (x + 60)),(x + 1))
A162820: 12 15 20 30 40 60 84 90 120 140 165 180 240 300 340 390
((x + 1) + (2 * (((((x3 + ~4x2 + 4x) div 2) div 2) div 2) div 2)))
A094863: 1 2 3 4 7 10 19 28
((x + 1) * (4 - ((((2x + 1) mod (2 + (x div 2))) div 2) mod 2)))
A162215: 4 8 9 16 20 18 21 32 36 40 44 36 52 42 45 64
((1 + (x mod 8) - (~x mod 5)) div (x + 1))
A185125: 1 ~1 0 0 0 1 0 0 ~1 0 0 0 0 0 0 0
((4x + 4) + (((2x + 1) - (x mod 4)) div 3))
A189370: 4 8 13 17 23 27 31 36 41 46 50 54 60 64 69 73
compr(\x.((3 * (x mod 10)) - (x div 4)),(x + 1))
A297270-A297147-A296714-A267759-A210589-A071590: 10 20 21 30 31 32 40 41 42 43 50 51 52 53 54 60
((x + 1) * ((15x2 + 31x + 2) div 2))
A130566: 1 48 186 460 915 1596 2548 3816 5445 7480 9966 12948 16471 20580 25320 30736
(((x + ~1) div (2 + ((x div 7) + (x mod 2)))) mod (x + 1))
A232548: 0 0 0 0 1 1 2 1 2 2 3 2 3 3 3 2
((x + 1) + (2 mod (x + 1)) - (((~x3 + x) div 2) div 3))
A180739: 1 2 6 10 17 28 44 66 95 132 178 234
(x5 + 10x4 + 37x3 + 63x2 + 49x + 14)
A269469: 14 174 852 2780 7170 15834 31304 56952 97110 157190 243804 364884 529802 749490 1036560 1405424
(x6 + 7x5 + 17x4 + 16x3 + 3x2 + ~2x)
A214945: 0 42 696 4260 16680 50190 126672 281736 569520 1068210 1886280 3169452 5108376 7947030 11991840 17621520
(x5 + 10x4 + 40x3 + 77x2 + 70x + 24)
A269777: 24 222 984 3060 7680 16674 32592 58824 99720 160710 248424 370812 537264 758730 1047840 1419024
((x + 1) + (((7 * (x div 4)) div 2) + (x div 2)))
A156799: 1 2 4 5 10 11 13 14 20 21 23 24 29 30 32 33
compr(\x.(x + (9 * (1 - (x div 8)))),(x + 1))
A296878: 80 81 88 89 90 96 97 98 99 104 105 106 107 108 112 113
((~x + 1) + compr(\x.(~1 + ((x div 2) mod (1 + (6 * (x mod 2))))),x))
A006160: 1 1 1 1 1 2 3 4 5 6 6 6 6 6 7 8
(x3 + 71x + 1)
A124363: 1 73 151 241 349 481 643 841 1081 1369 1711 2113 2581 3121 3739 4441
(16x3 + 15x2 + 6x + 1)
A005910: 1 38 201 586 1289 2406 4033 6266 9201 12934 17561 23178 29881 37766 46929 57466
(((1 + ((x mod 3) div 2)) * (1 + (x mod 3))) mod (x2 + 1))
A021892: 0 0 1 1 2 6 1 2 6 1 2 6 1 2 6 1
((1 + (x mod (1 + (((x * (x mod 2)) div 2) + (x div 5))))) div 2)
A229951: 0 0 0 1 0 1 0 1 0 2 1 2 0 2 1 2
((~1 + ((1 + ((x + ~1) mod 3)) * (1 + (x div 5)))) div 2)
A029277: 1 0 0 1 0 1 2 0 1 2 1 2 4 1 2 5
((1 + ((1 + (x * ((1 + (x div 2)) mod 2))) mod (1 + (x div 3)))) div 2)
A122923: 0 0 0 1 1 0 1 1 0 1 1 1 2 2 1 1
((1 + (x mod (1 + ((x mod (3 + (x mod 2))) mod (1 + (x div 2)))))) div 2)
A308427-A276806: 0 0 0 1 0 1 0 2 1 1 0 2 0 1 1 2
((1 + (x mod (1 + ((x2 mod 6) mod (1 + (x div 2)))))) div 2)
A334107: 0 0 0 1 0 1 0 1 2 1 0 1 0 1 2 2
((x mod (1 + (x mod (1 + (2 * ((x + 2) mod (1 + (x div 4)))))))) div 2)
A331594: 0 0 0 0 0 1 0 0 1 2 0 1 0 3 0 0
((1 + ((x2 + 2x + 1) mod (1 + (2 * ((x + ~1) mod 3))))) div 2)
A126825: 1 0 0 1 0 0 2 0 0 0 0 0 2 0 0 1
(2 * (1 + (x div (3 + ((x2 mod (x + 5)) div 2)))))
A105681: 2 2 2 4 2 4 4 6 2 4 4 4 4 6 6 8
((1 + ((x3 div 2) div 31)) div 2)
A059291: 0 0 0 0 1 1 2 3 4 6 8 11 14 18 22 27
(x mod (2 + ((x div 2) div (1 + ((~2x + 1) mod 9)))))
A325960: 0 1 0 1 0 1 0 1 2 1 0 1 0 1 5 1
(2 + ((2x + 1) mod (1 + (2x mod (3 + (x div 4))))))
A133829: 2 2 3 2 2 4 2 2 3 5 2 4 2 2 6 2
(((x + 1) - ((1 + ((x2 + 2x) div 4)) mod 5)) div 2)
A194214: 0 0 0 0 1 1 2 3 4 5 5 5 5 5 6 6
(x + (((x + 1) div 5) + (2 * (1 + (x div 5)))))
A047502: 2 3 4 5 7 10 11 12 13 15 18 19 20 21 23 26
((1 + (((x * ((~x + 2) div 4)) div 2) mod (1 + (x div 4)))) div 2)
A070088: 0 0 0 0 0 1 1 1 1 0 1 1 1 0 2 1
((1 + ((x + 1) mod (1 + (2x div (2 + (x div 2) - (x mod 2)))))) div 2)
A102550: 0 1 1 0 1 1 1 0 0 1 1 0 1 1 2 0
(x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2)))))))
A253559-A252736-A140748: 0 0 0 1 0 1 0 2 1 1 0 2 0 1 1 3
(x - (2 * ((x div 2) div (1 + (3 * ((x div 2) mod 5))))))
A103303: 0 1 2 3 4 5 6 7 8 9
A309589: 0 1 2 3 4 5 6 7 8 9 0 1 10 11 12 13
(2 * (1 + ((2 * (1 + (2 * (x + (x div 5))))) div 3)))
A260400: 2 6 8 10 14 18 22 24 26 30 34 38 40 42 46 50
((1 + ((x + 1) div (2 + (((x + 1) div 2) div 3) - (x mod 2)))) div 2)
A193929: 0 1 1 2 1 2 1 2 2 3 2 2 2 2 2 3
(((2 + (x mod 5)) div (1 + (((x + 1) div 2) mod 3))) div 2)
A264620: 1 0 1 0 1 1 1 1 1 1 0 1 2 1 1 0
(x5 mod 46)
A070629: 0 1 32 13 12 43 2 17 16 31 42 5 18 27 38 7
(x6 mod 26)
A070649: 0 1 12 1 14 25 12 25 12 1 14 25 14 13 14 25
(x - ((13 * (~x + (x mod 8))) div 2))
A024648: 0 1 2 3 4 5 6 7 60 61 62 63 64 65 66 67
(x6 mod 22)
A070645: 0 1 20 3 4 5 16 15 14 9 12 11 12 9 14 15
(((x + 1) - (((x * ((~x2 + 2x) div 4)) div 2) div 3)) div 2)
A292444: 0 1 1 2 3 5 6 9 12 17 22
(1 - (3x div (~2 + (x div (~1 + ((1 - (x div 2)) div 3))))))
A196241: 1 2 3 3 4 4 5 5 5 5 6 7 7 7 7 8
(2 * ((x + 1) - (((~x + 1) - ((x div 3) mod 3)) div 3)))
A232745: 2 4 8 10 14 16 20 22 24 26 28 32 34 38 40 44
(2 * ((x mod 4) mod (1 + (2x mod (2 - ((~x + 1) div 3))))))
A318879: 0 0 0 0 0 2 0 0 0 2 0 6 0 2 0 0
(114x + 94)
A304609: 94 208 322 436 550 664 778 892 1006 1120 1234 1348 1462 1576 1690 1804
(((x + 1) mod (1 + (((x + ~1) div 5) * (x div 3)))) div 2)
A239428: 0 0 0 0 0 0 0 1 0 1 1 2 2 2 3 2
(((x + 1) mod (1 + (x div (2 + (((x div 2) mod 2) + (x mod 3)))))) div 2)
A340860: 0 0 0 0 0 0 0 0 0 0 1 0 3 2 0 2
(2 + (x mod (1 + (((x + 1) * (x2 div 3)) mod (1 + (x div 2))))))
A307590: 2 2 2 2 2 2 2 2 5 2 4 2 2 2 8 2
(2 * ((x + ~1) mod (1 + (((x + ~2) * (x div 3)) mod (1 + (x div 2))))))
A231037: 0 0 0 0 0 0 0 0 2 0 0 4 10 0 0 0
((1 + (x div (2 + (((x div ~4) mod 2) + (x mod 2))))) div 2)
A308452: 0 0 0 0 1 1 2 1 2 1 2 1 2 2 4 3
(2 * (~1 + compr(\x.((x2 mod (4x + 9)) mod 2),(x + 1))))
A191331: 2 6 12 16 18 22 28 32 34 38 42 44 48 54 58 60
((x mod (1 + (((~4x + 8) * (x div 3)) mod (x + 1)))) div 2)
A035666: 0 0 0 0 0 0 1 0 0 1 1 0 1 3 1 1
((1 + ((x * (5 + ((x2 + x) div 2))) div (x + 1))) div 2)
A134953: 0 2 3 4 6 8 11 14 18 23 27
((x + ~1) mod (2 + (x mod (1 + (x mod (2 - ((x div 4) div ~2)))))))
A229297: 1 0 1 2 1 0 1 0 3 0 1 2 1 0 1 4
((1 + ((1 + (x div (1 + ((x + ~2) mod (2 + ((x div 2) mod 2)))))) div 2)) div 2)
A340274: 0 0 1 1 1 1 1 1 2 1 1 3 3 2 4 2
(2 * (1 + ((x mod (~1 + (((~1 + (x div 2)) div 2) * (x div 3)))) div 2)))
A098708: 2 2 2 2 2 2 2 2 2 2 2 2 6 8 4 2
(x - ((~1 + ((x mod (1 + ((2 - (x mod 4)) mod (x + 1)))) div 2)) div 2))
A063659: 1 2 3 3 5 6 7 6 8 10 11 9 13 14 15 12
((x + 3) - ((x - (x div (1 + ((1 + (x div 3)) div 2)))) div 2))
A009070: 3 4 5 5 6 7 8 8 9 9 10 10 11 12 12 12
(1 - ((x mod (1 + (2 * (x div (~1 + (4 * (~2 + (x mod 2)))))))) div 2))
A290267: 1 1 1 1 1 1 1 2 1 1 2 3 1 2 2 1
(2 * (1 + ((x - (x div (11 - (x div 2)))) div 2)))
A096494: 2 2 4 4 6 6 8 8 8 10 10 12 12 12 12 14
((1 + ((5 * (2x - (x mod ~4))) div 2)) div 2)
A001746: 0 6 8 9 10 16 18 19 20 26 28 29 30 36 38 39
(2 * (1 + (((x + 1) mod ((x + ~2) + (2x mod 5))) mod 2)))
A064127: 4 2 4 2 2 2 4 2 2 2 4 4 4 2 2 4
((x mod (1 + (2 * (1 - ((x div 2) mod (1 + ((~x + 2) mod 4))))))) div 2)
A143518: 0 0 1 0 0 1 0 ~1 0 0 0 0 0 0 1 0
((1 + ((1 + (((x * ((x2 + ~2x) div (x + 2))) div 2) div 2)) div 2)) div 2)
A340751: 0 0 0 0 1 1 1 2 2 3 4 5 6 8 9 11
((1 + (x2 div ((x + 2) - ((x div 5) mod 3)))) div 2)
A071823: 0 0 1 1 1 2 3 3 4 4 5 6 6 7 7 7
((1 + (x div (2 + (((x + 1) * (2 - ((x div 2) mod 2))) mod 3)))) div 2)
A161104-A161065: 0 0 1 1 1 1 1 1 2 1 1 3 2 2 4 3
((1 + ((((x + 1) mod 5) + ((x + 1) mod 3)) div 2)) div 2)
A262124-A215401: 1 1 1 1 1 0 1 1 1 0 1 1 1 2 0 1
((1 + (x div (2 + ((x + ~1) mod (3 + ((x div 3) mod 2)))))) div 2)
A230241: 0 0 0 0 0 1 1 2 1 2 2 1 2 3 2 2
((1 + (x div (2 + ((x2 + 2x + 2) mod 12)))) div 2)
A243840: 0 0 0 0 1 1 1 1 0 1 1 2 2 1 1 1
(2 * ((2x + 2) - ((2 * (x + (x mod 2))) div 7)))
A285374: 4 8 12 14 18 22 26 28 32 36 40 42 46 48 52 56
(2 - (((x div (~2 + (x mod ~2))) + (x div 7)) mod 2))
A270645: 2 1 1 1 2 2 1 2 1 2 2 1 1 2 1 1
(x div (2 * (1 + ((1 + (x div 4)) div (2 - ((x mod 3) mod 2))))))
A024327: 0 0 1 1 0 1 1 1 2 2 1 2 2 1 2 2
(x - ((1 + ((1 + ((x * (((x + 1) div 2) div 3)) div 2)) div 2)) div 2))
A277814: 0 1 2 3 4 4 5 6 7 8 8 8 9 9 10 11
(((x + 5) mod (1 + (2 * ((x div 2) div (1 + (x mod 2)))))) div 2)
A249441: 0 0 0 0 2 0 2 0 2 2 2 0 2 2 2 3
((1 + (((x + 1) * ((x + 1) - (x2 div (x + 4)))) div 2)) div 2)
A035058: 0 1 2 3 4 6 7 8 9 10 11 12 13 18 19 20
(2 * ((x + 1) - ((0 - ((2 + (x mod 8)) mod (x + 1))) div 2)))
A173634: 2 6 8 10 12 14 16 18 20 24 26 30 32 36 38 42
((1 + (x mod (2 + ((x + ~1) mod (2 - ((x div 4) div ~2)))))) div 2)
A105241: 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 2
(((x2 + x + 1) - ((x - ((x + 1) mod 6)) div 2)) div 2)
A262136: 1 2 4 7 11 14 20 27 35 44 54 64 76 89 103 118
(2 * ((2 + (x div 2)) div (3 + ((x2 + 2x) mod 6))))
A160812: 0 0 0 0 2 0 2 0 2 2 4 0 4 2 2 2
((1 + ((x + 1) div (2 + (((x2 + 1) mod (1 + (x div 2))) div 2)))) div 2)
A102382: 0 1 1 1 1 1 2 1 2 2 1 2 2 2 2 3
(2 * ((x + 1) - (2 * ((~2x + ~2) + ((x - (x div 4)) div 2)))))
A101869: 10 20 26 36 46 52 62 68 78 88 94 104 114 120 130 136
((1 + (x div 3)) div (2 + ((~x + 1) mod (1 + (((x + 1) div 2) div 2)))))
A276167: 0 0 0 1 0 1 1 1 0 1 2 1 1 2 1 2
(x - (2 * (x div (3 + ((((x + ~2) mod (1 + (x div 2))) div 2) mod 2)))))
A165477: 0 1 2 1 2 3 2 3 4 5 6 7 6 5 6 5
((1 + (((((x + 1) * (x - (x2 mod 3))) div 2) div 2) div 2)) div 2)
A145806: 0 0 0 1 1 2 3 3 4 6 6 8 10 11 12 15
(1 - (x div (~2 - ((x div 2) div (1 + ((((x + 1) div 2) div 2) div 2))))))
A106161: 1 2 2 2 2 3 3 4 3 4 4 4 4 4 4 5
(x - ((1 + (((((~x + 1) div 3) * ((x + ~1) div 2)) div 2) div 2)) div 2))
A293168: 0 1 2 3 4 5 6 8 9 10 11 13 14 16 18 19
(x6 mod 34)
A070657: 0 1 30 15 16 19 8 9 4 21 26 25 2 33 32 13
((2 - ((2x + 1) mod (~1 + (2 * ((~x + 2) div 8))))) div 2)
A103956: 1 1 1 2 1 1 2 1 1 2 1 2 1 2 1 3
((1 + ((x + 1) mod ((x + 2) - ((x * (x mod 2)) mod 8)))) div 2)
A008723: 1 0 2 0 3 0 4 0 5 0 6 1 7 2 8 3
((1 + ((x3 + ~2x2 + x) mod (4 + (x div 4)))) div 2)
A242249: 0 0 1 0 1 0 0 1 1 0 0 1 2 2 0 0
((1 + (((((x * (2 + (x2 div 4))) div 2) div 2) div 2) div 2)) div 2)
A238006: 0 0 0 0 1 1 2 3 5 6 8 11 14 18 22 27
((1 + ((x + 1) div (2 + (((x2 + 1) div (2 + (x div 2))) mod 2)))) div 2)
A340134: 0 0 1 1 1 2 1 2 2 2 3 2 3 2 3 3
(x - ((9 * ((2 * (x div 2)) div 5)) div 2))
A119281: 0 1 2 3 4 5 2 3 4 5 1 2 3 4 5 6
(x - ((9 * (~x + (x mod 9))) div 2))
A024653: 0 1 2 3 4 5 6 7 8 50 51 52 53 54 55 56
(1 - ((1 + ((x * ((x * ((~x + 2) div 2)) div 2)) div 8)) div 2))
A332557: 1 1 1 1 1 3 3 6 7 11 13 20
(3 + (((x + ~4) * (((x + 1) - ((x div 2) mod 2)) div 2)) div 2))
A211939: 3 1 2 2 3 4 6 7 11 15
(2 * ((1 + (x div 4)) div (1 + (x div (2 + (x div (2 + (x mod 2))))))))
A036476: 2 2 2 0 2 2 2 2 2 2 2 2 4 2 4 2
(((1 + (2 * (x mod 11))) mod 5) div 2)
A277731: 0 1 0 1 2 0 1 0 1 2 0 0 1 0 1 2
(x - (2 * (((2x + 1) - ((x + 1) mod 4)) div 5)))
A277214: 0 1 2 1 2 3 2 1 2 3 4 3 4 3 4 3
(2 - ((((x + 1) + ((x + (x div 2)) div 4)) mod 5) div 2))
A190672: 2 1 1 2 2 1 0 2 1 1 0 2 1 1 2 2
((((x + 1) * (2 - (x mod (2 + ((x div 2) mod 2))))) mod 5) div 2)
A035185: 1 1 0 1 0 0 2 1 1 0 0 0 0 2 0 1
((x + 2) - (((x - ((x2 + ~x) div 3)) div 2) div 5))
A133194: 2 3 4 5 6 8 9 10 11 13 14 16 18 19 21 23
(x - (2 * ((2 * (x + ((((x + ~1) div 2) div 2) mod 2))) div 5)))
A214526: 0 1 2 1 2 1 2 1 2 3 2 3 4 3 2 3
((((~x + 1) - ((x2 + 1) div (x + 3))) mod 5) div 2)
A095734: 0 0 1 1 0 1 0 2 1 0 2 1 0 1 0 2
((((x + 2) + (x div (2 + ((~x + 2) mod 4)))) mod 5) div 2)
A286320-A284171-A104276: 1 1 0 0 1 1 0 0 1 2 1 0 1 2 1 0
(x - (2 * ((x + ((2 + (x mod 2)) * (x div 4))) div 5)))
A240834: 0 1 2 3 2 3 4 3 4 3 6 5 6 5 6 7
((x + 3) + (x div 5) - (x div (~1 + (x div ~2))))
A161373: 3 5 6 7 9 11 12 13 14 15 17 18 19 20 21 23
(1 - (((x div 5) mod 2) + ((~x + 2) div (4 + (x mod 2)))))
A143488: 1 1 1 2 2 1 1 1 2 2 3 3 4 4 4 3
(((2 + (x div 5)) div (1 + ((x + (x div 2)) mod 4))) div 2)
A219486: 1 0 0 1 0 0 0 0 1 0 0 2 0 0 1 0
((2x + 2) - ((x mod (2 - (x mod (~1 - (x div 4))))) mod 2))
A284907: 2 3 6 7 10 12 14 15 18 19 22 24 26 27 30 32
((2x + 2) + (2 * (1 + (x div 4))) - ((x * (x div 2)) mod 2))
A262389-A118951: 4 6 8 9 14 16 18 19 24 26 28 29 34 36 38 39
(2 * ((x + 1) - (((x + ~2) * ((x div 3) * ((~x + 2) div 2))) div 2)))
A309374: 2 4 6 10 12
A064374: 2 4 6 10 12 18 30
(2 * (((4x + 4) * (2 + (x mod 2))) mod (x + 5)))
A064373: 6 0 6 0 8 4 2
(1 - ((x - ((4x2 + 4x) div (x + 5))) div 2))
A338375: 1 1 2 3 3 5 6 7 8 9 11 12 13 15 16 18
((1 + ((x2 + 2x + 1) div 5) - ((x div 2) mod 2)) div 2)
A282847: 0 0 0 1 3 4 4 6 8 10 12 14 17 20
(x div (2 * (1 + ((1 + ((x div (1 + (x mod 4))) + (x mod 2))) div 2))))
A027348: 0 0 1 0 0 0 1 1 0 1 1 1 0 1 2 2
((3 * (1 + (x mod (1 + (x div (3 + (x div 3))))))) div 2)
A334464: 1 1 1 1 1 3 1 3 1 3 1 3 1 3 4 3
(2 * ((1 + ((2 * ((x2 + x) div 4)) div 3)) div 3))
A345256: 0 0 0 2 2 2 4 6 8 10 12 14 18 20 22 26
(x - ((x - ((1 + (8 mod (1 + (x div 2)))) mod 3)) div 2))
A244988: 1 1 2 2 2 3 4 4 5 5 5 6 7 8 8 8
((x + 1) div ((x + 2) - (3 * (2x div 7))))
A241675: 0 0 0 0 1 1 1 2 2 2 1 3 2 2 3 3
(2x - ((x - ((1 + ((x mod (1 + (x div 2))) div 2)) mod 3)) div 2))
A188019: 1 2 4 5 7 9 10 12 13 14 15 17 18 20 22 23
(1 + ((3 * (3x div 5)) div 2) - (x div 2))
A068962: 1 1 1 1 2 3 2 4 3 4 5 5 5 5 6 7
((3 * ((1 + ((x + 1) div 3)) mod (1 + (x div 4)))) div 2)
A227898: 0 0 0 0 0 1 1 1 1 1 1 3 1 1 3 3
(4x3 + 34x2 + 92x + 86)
A097693: 86 216 438 776 1254 1896 2726 3768 5046 6584 8406 10536 12998 15816 19014 22616
((3 * (1 + ((x + 3) mod (2 + (x2 div (x + 2)))))) div 2)
A210622: 3 1 4 1 6 6 6 6 6 6 6 6 6 6 6 6
((3 * (x - ((~1 + (2 * ((~x + 2) div 4))) div 3))) div 2)
A225647: 1 3 4 6 7
A094178: 1 3 4 6 7 9 10 13 15 16 18 21 22 24 25 27
((3 * ((3x + 3) + ((x div 2) div 5))) div 2)
A330183: 4 9 13 18 22 27 31 36 40 45 51 55 60 64 69 73
((3 * ((3x + 2) - (((x + 1) div 2) div 3))) div 2)
A189797: 3 7 12 16 21 24 28 33 37 42 46 49 54 58 63 67
(x - (x2 div ((x + 2) - (3 * (((~x + 2) div 2) div 3)))))
A055768: 0 1 1 2 3 3 3 3 4 5 5 5 5 5 6 7
((9 * ((2 mod (1 + (x mod 3))) + (x mod 2))) div 2)
A178143: 0 4 9 4 0 13 0 4 9 4 0 13 0 4 9 4
(x - (2 * (((x + 1) div 3) - ((1 - (x div 3)) div 3))))
A119995-A062756: 0 1 0 1 2 1 0 1 0 1 2 1 2 3 2 1
((3 * (((x div 4) + (x div 3)) - ((x + ~1) div 2))) div 2)
A090176-A029356: 1 0 0 0 1 0 1 0 1 1 1 0 3 1 1 1
((((1 - ((x + 1) mod 8)) mod (2x + 1)) div 3) div 2)
A073139: 0 0 0 0 0 1 1 0 0 3 3 3 3 3 3 0
((3 * (1 + compr(\x.(x mod (1 + (2 * (x mod (2 + (x mod 2)))))),x))) div 2)
A231407: 1 4 6
A189715: 1 4 6 7 9 10 13 15 16 19 22 24 25 28 31 33
((((x + (x div 3)) div 5) + ((x + ~1) mod 3)) div 2)
A025837: 1 0 0 1 0 1 1 0 1 2 1 1 2 1 2 3
(((x div (2 + (x div (1 + (x mod 4))))) + ((x + ~1) mod 3)) div 2)
A117274: 1 0 1 1 0 1 1 1 0 1 1 1 1 0 1 2
((((3 * (x div 5)) div 2) + ((x + ~1) mod 3)) div 2)
A029291: 1 0 0 1 0 1 1 0 1 1 1 2 2 1 2 3
(x - (2 * ((x - ((~1 + (x mod 12)) div 2)) div 3)))
A275727: 0 1 2 3 2 3 4 5 6 7 6 7 4 5 6 7
((3 * ((2x + 2) - ((2 + (x div 2)) mod 6))) div 2)
A185256: 0 3 4 7 9 12 13 16 27 30 31 34 36 39 40 43
(2 + ((2 + ((~3x + 5) mod (1 + (x div 2)))) div 3))
A216195: 2 2 3 2 3 3 3 2 3 3 4 3 4 3 3 2
(2 * (x - ((2 * ((2x + 1) div ~7)) div 3)))
A058817: 2 4 6 8 12 14 16 18 20 22 24 28 30 32 36 38
(((x * (2 - (x mod 2))) + ((3 * (x div 4)) div 2)) - (x div 2))
A273926: 0 1 3 2 7 4 10 5 15 8 18 9 22 11 25 12
(x mod (2 + ((2 * ((x + 2) + ((x div 5) mod 2))) div 3)))
A103303: 0 1 2 3 4 5 6 7 8 9
A031298: 0 1 2 3 4 5 6 7 8 9 0 1 1 1 2 1
((x div 2) - ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2))
A048881: 0 0 1 0 1 1 2 0 1 1 2 1 2 2 3 0
(2 + (3 * (x - (((x * (1 - (x3 div 2))) div 2) div 2))))
A006574: 2 5 14 38 107
((3 * ((x + (((x div 4) * (x div 4)) div 2)) div 2)) div 2)
A325123: 0 0 1 1 3 3 4 4 7 7 9 9 12 12 13 13
((((x + 2) + ((x2 + 2x + 1) mod 5)) div 3) div 2)
A345128: 0 1 1 1 1 1 2 2 1 1 2 2 3 2 2 3
(2 + (3 * (2x + ((x + ((x mod (1 + (x div 2))) div 2)) div 2))))
A284395: 2 8 17 23 32 41 47 56 62 71 80 86 95 104 110 119
(((~x + 1) + (3 * ((5x + 10) + (x div 2)))) div 2)
A006615: 15 22 31 38 46
((1 + ((x + 1) * ((x mod (1 + (x div 4))) div 2))) mod 6)
A046592-A046564: 1 1 1 1 1 1 1 1 4 1 1 1 1 1 4 5
(6 + (((~x + ((x div 2) mod 2)) div 2) mod (2x + 3)))
A343311: 6 10 12 14 15 16 18 20 21 22 24 26 27 28 30 32
(~7 + (2 * (x + (x div 3))) - ((x div 2) mod 2))
A179177: ~7 ~5 ~4 0 3 5
(6 + ((x5 mod (2x + ~1)) mod 2))
A276861: 6 6 6 7 6 6 6 7 6 6 7 6 6 6 7 6
((x + 2) - ((3 * (~x + ((~2x + 2) div 5))) div 2))
A190329: 2 5 9 11 15 18 20 24 27 31 33 36 40 42 46 49
(((((x + 1) * (~1 + (x mod 4))) mod 3) + (x div 3)) div 2)
A029270: 1 0 0 1 1 0 1 1 1 1 2 1 3 2 2 3
(((~x + 1) mod (2 + ((((x + ~1) div 2) mod 4) + (x div 3)))) div 2)
A034391: 0 0 0 1 0 0 0 0 0 1 0 1 1 2 1 3
((((4 * (x div 5)) div 3) + (x mod 3)) div 2)
A036863: 0 0 1 0 0 1 0 1 1 0 1 2 1 1 2 2
((((x mod (2 + ((~x + 2) mod 5))) div 2) + (x mod 3)) div 2)
A279952: 0 0 1 0 1 1 0 0 1 1 1 1 0 0 2 0
((2 + (((x2 div 3) mod (x + 1)) div 2) - (x mod 3)) div 2)
A025844: 1 0 0 1 0 0 2 0 0 2 0 1 3 0 1 3
((2 + (x div 3) - ((x div 2) mod 3)) div (2 + (x mod 3)))
A025841: 1 0 0 1 0 0 2 1 0 2 1 0 3 2 1 3
((1 + ((x * ((~x + 1) + (4 * (x + ((x div 2) mod 2))))) div 2)) div 2)
A154293: 0 1 6 11 13 20 35 46 50 63 88 105 111 130 165 188
(2 * (1 + (2 * (x + ((((x + 1) - ((x div 2) mod 3)) div 2) div 2)))))
A000952: 2 6 10 14 18 26 30 38 42 46 50 54 62
(2 * compr(\x.(x mod (1 + (4 * (x mod (2 + (x mod 2)))))),(x + 3)))
A282671-A192991-A091375: 8 12 16 18 20 24 28 30 32 36 40 42 44 48 50 52
((4x + 12) * (2 + ((x2 + 6x + 8) div 2)))
A137883: 72 144 280 456 728 1056 1512 2040 2728 3504 4472 5544 6840 8256 9928 11736
(2 * (((x * (x + ((x div 3) mod 3))) div 2) div (x + 3)))
A236840: 0 0 0 2 2 2 4 6 6 6 6 8 10 10 12 14
(((1 + (2 * ((~x + 1) mod 10))) mod (1 + (x div 2))) div 2)
A034393: 0 0 0 0 0 0 1 0 1 0 1 0 2 1 3 2
((((x + 1) + (3 * (0 - (x mod 3)))) mod (1 + (x div 2))) div 2)
A242165: 0 0 0 0 1 0 1 0 1 0 1 0 3 2 0 0
((x + 1) div (2 + ((2 * (1 + ((x + ~1) mod 3))) mod (1 + (x div 2)))))
A176725: 0 1 1 2 1 2 1 2 1 3 2 2 1 3 2 2
(x + ((5 * (x div 8)) + ((1 + (x div 2)) div 2)))
A023729: 0 1 3 4 5 6 8 9 15 16 18 19 20 21 23 24
(2x6 + 2x5 + 6x4 + 6x3 + 6x2 + 4x + 6)
A276351: 6 32 374 2664 12278 42176 118182 285704 617894 1225248 2266646 3961832 6605334 10581824 16382918 24625416
(2 * ((x + 1) + ((4 * ((x + 1) div 5)) div 3)))
A254748: 2 4 6 8 12 14 16 18 20 24 26 28 30 32 38 40
(((x + 1) + (3 * ((4x + 4) + (x div 4)))) div 2)
A189378: 6 13 19 26 34 40 47 53 61 68 74 81 89 95 102 108
(((x + 1) + ((((x2 + 2x) div 2) div (2 + (x mod 2))) div 3)) div 2)
A159050: 0 1 1 2 3 3 5 5 7 7 10 9 13 12 16 15
(2 * ((x + 1) + (2x div (4 + ((x div 2) div 5)))))
A342050: 2 4 8 10 14 16 20 22 26 28 30 32 34 38 40 44
(((x + 1) + (x div (2 + (x div (2 + (x2 mod 5)))))) div 2)
A066683-A055038: 0 1 2 2 3 3 4 5 5 5 6 7 8 8 8 8
(((x + 1) + (((2x + ~1) mod (4 + (x div 4))) div 2)) div 2)
A132919: 1 1 2 2 3 4 3 4 5 6 5 6 7 8 9 8
(((1 + (x mod (1 + (x mod (2 * (2 + ((x div 2) mod 2))))))) mod (x + 1)) div 2)
A334739-A069023: 0 0 0 0 0 1 0 1 0 1 0 3 0 1 1 2
(((1 + (x mod (3 * (2 + ((x div 4) mod 2))))) mod (x + 1)) div 2)
A237769: 0 0 0 0 0 0 0 0 1 2 2 3 2 2 3 3
(((~1 + (((4 + (x div 2)) * ((x + ~1) div 2)) div 2)) mod (x + 1)) div 2)
A229878: 0 0 1 0 1 2
A278164: 0 0 1 0 1 2 3 0 1 2 3 4 5 0 1 2
(((1 + (2 * ((x div 2) mod (2 - (x div ~4))))) mod (x + 1)) div 2)
A234580: 0 0 0 1 0 2 0 3 0 4 0 0 1 0 1 1
(x div (2 + ((1 - ((x2 + 2x + 1) div 5)) mod (x + 1))))
A229878: 0 0 1 0 1 2
A067586: 0 0 1 0 1 2 0 1 1 3 0 1 1 2 4 0
((25x2 + 47x + 22) div 2)
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(2 + ((1 - (x mod (2 - ((x + ~2) mod ((~x + ~1) + (x mod 2)))))) div (x + 1)))
A065310: 3 2 2 1 1 2 2 1 1 2 2 1 1 2 1 1
(2 + ((2 - (x mod (2 + (2x mod (1 + (x div 3)))))) div (x + 1)))
A137239: 4 2 2 2 2 2 2 1 2 2 2 1 2 2 1 2
(x div (2 + ((2 * (1 + (2 * ((x + (x mod 2)) div 3)))) mod (x + 1))))
A282870: 0 0 0 0 1 0 1 1 2 1 2 1 1 2 2 1
((45x2 + 47x + 2) div 2)
A095311: 1 47 138 274 455 681 952 1268 1629 2035 2486 2982 3523 4109 4740 5416
(2 + compr(\x.(1 - (x mod (2 * (1 + ((~1 + (x div 2)) mod 4))))),(x + 1)))
A343064-A106505: 5 7 9 11 13 15 16 17 19 21 23 24 25 27 29 31
(((x + 1) * ((5 * (1 + ((x2 + 2x) div 2))) div 2)) div 2)
A236364: 1 5 18 40 80 135 217 320 459 625 836 1080 1378 1715 2115 2560
(((x + 1) * ((1 + ((x2 + 10x + 16) div 2)) div 2)) div 2)
A003452: 2 7 15 28 45 69 98 136 180 235 297 372 455 553 660 784
(2 * compr(\x.(1 - (x mod (2 + (3 * ((x div 2) mod 3))))),(x + 1)))
A069148: 4 6 8 10 14 16 18 20 22 26 28 34 38 42 44 46
(((2 + ((x div (~2 + ((x div 4) mod 2))) mod 3)) mod (x + 1)) div 2)
A306615: 0 0 0 1 2 1 1 2 2 1 1 1 1 2 1 1
((3x3 + 21x2 + 26x + 8) div 2)
A192025: 4 29 84 178 320 519 784 1124 1548 2065 2684 3414 4264 5243 6360 7624
((12x3 + 21x2 + 11x + 2) div 2)
A214092: 1 23 102 274 575 1041 1708 2612 3789 5275 7106 9318 11947 15029 18600 22696
(~2 + compr(\x.(1 - (x mod (2 + ((~2x + 4) mod (1 + (x div 2)))))),(x + 1)))
A101358: 1 3 5 6 8 9 11 13 14 15 16 17 19 20 21 22
(((x + 1) * ((3x3 + 11x2 + 12x + 4) div 2)) div 2)
A126274: 1 15 72 220 525 1071 1960 3312 5265 7975 11616 16380 22477 30135 39600 51136
(((x + 1) * ((x4 + 5x3 + 10x2 + 10x + 4) div 2)) div 2)
A328994: 1 15 90 340 975 2331 4900 9360 16605 27775 44286 67860 100555 144795 203400 279616
(((x + 1) * ((~x3 + 3x2 + 8x + 4) div 2)) div 2)
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(2 * compr(\x.(1 - ((x + ~4) mod (2 - (x div ~4)))),(x + 1)))
A295076-A088829: 6 10 12 14 20 22 24 26 28 30 34 38 40 42 44 46
(((x + 1) * (4 + ((~1 + ((x3 + 2x) div 2)) div 2))) div 2)
A076859: 1 4 9 22 52
(18 div (2 + (16 div (x + 1))))
A226142: 1 1 2 3 3 4 4
A086333: 1 1 2 3 3 4 4 4 6 6 6 6 6 6 6 6
(x div (2 + ((2 - (x mod (~3 - (x div 4)))) mod (x + 1))))
A070099: 0 0 1 0 1 0 1 1 1 1 2 1 3 1 1 2
((2x3 + 11x2 + 27x + 18) div 2)
A162263: 9 29 66 126 215 339 504 716 981 1305 1694 2154 2691 3311 4020 4824
(2 + compr(\x.(((x2 + ~2) mod (x + 10)) mod 2),(x + 1)))
A007378: 3 4 6 7 8 10 12 13 14 15 16 18 20 22 24 25
(((x + 1) * ((3x3 + 9x2 + 8x + 4) div 2)) div 2)
A213818: 1 12 60 190 465 966 1792 3060 4905 7480 10956 15522 21385 28770 37920 49096
((2x + 2) * (((2 + (x * (x mod 6))) div (x + 2)) mod 2))
A121206: 2 4 6 0 10 12 0 16 18 0 22 0 0 28 30 0
(2 + ((2 * (((x mod (1 + (x div 4))) div 2) + (x mod 2))) mod (x + 1)))
A161841: 2 2 2 4 2 4 2 4 4 4 2 6 2 4 4 6
(((x + 1) * ((x + 2) + ((2x3 + 4x) div 3))) div 2)
A081492: 1 5 18 54 135 291 560 988 1629 2545 3806 5490 7683 10479 13980 18296
((49x2 + 147x + 98) div 2)
A027469: 49 147 294 490 735 1029 1372 1764 2205 2695 3234 3822 4459 5145 5880 6664
((4x4 + 22x3 + 43x2 + 35x + 10) div 2)
A076455: 5 57 246 710 1635 3255 5852 9756 15345 23045 33330 46722 63791 85155 111480 143480
((2x4 + 16x3 + 43x2 + 47x + 18) div 2)
A269410: 9 63 222 570 1215 2289 3948 6372 9765 14355 20394 28158 37947 50085 64920 82824
((2x5 + 14x4 + 36x3 + 41x2 + 19x + 2) div 2)
A076459: 1 57 390 1510 4335 10311 21532 40860 72045 119845 190146 290082 428155 614355 860280 1179256
(((1 + (x mod 8)) mod (x + 1)) + ((x2 + 3x + 2) div 2))
A194153-A025737: 1 3 6 10 15 21 28 36 46 57 69 82 96 111 127 144
((x mod (x - ((x + ~1) mod 8))) + ((x2 + 3x + 2) div 2))
A025746: 1 3 6 10 15 21 28 36 45 55 67 80 94 109 125 142
(((x + 1) * ((2 * (2 + (x div (1 + (x mod 4))))) + (x mod 2))) div 2)
A073825: 2 5 6 10 30
((2x + 2) + ((x3 + x + 2) div 7))
A193840: 2 4 7 12 20 30 46
((2x + 2) + ((x2 + (x div 2)) div 15))
A027919: 2 4 6 8 11 13 16 19 22 25 29 32 36 39 43 47
((2x + 1) + ((1 - ((x + (x div 2)) div 4)) mod 4))
A307830: 2 4 6 7 9 11 16 18 19
((2x + 2) + ((x - (2 * ((1 + (x div 2)) div 3))) div 3))
A187225: 2 4 6 9 10 13 15 17 20 22 24 26 28 31 33 35
((2x + 2) + ((3 * (x - (x div 9))) div 2))
A189461: 2 5 9 12 16 19 23 26 30 32 35 39 42 46 49 53
((2x + 2) + ((x + ((x2 div 4) + (x div 3))) div 2))
A211372: 2 4 7 11 14 18 22 26 31 36
((2x + 2) + ((2x + 1) div (4 + ((x div 2) div 3))))
A330085: 2 4 7 9 12 14 16 19 21 23 26 28 30 32 34 37
((2x + 2) + (((x2 div 4) - (((x + 1) div 2) div 2)) div 2))
A060655: 2 4 6 8 11 14 18 21 25 29 33 37
((2x + 2) + ((x + (((2x + ~1) div (2 + (x div 2))) mod 2)) div 2))
A285968: 2 4 7 10 12 14 17 19 22 24 27 30 32 35 37 40
((2x + 2) + ((x + (x2 div (8 + (x div 2)))) div 2))
A276209: 2 4 7 10 12 15 18 21 24 27 30 34 37 40 43 47
((3x + 2) + ((2 * ((x + 2) mod 5)) div 3))
A190677-A188091: 3 7 10 11 14 18 22 25 26 29 33 37 40 41 44 48
((3x + 2) + ((x - (((~x + 2) div 2) div 5)) div 2))
A247986: 2 5 9 13 16 20 23 27 30 34 37 41 44 48 52 55
((3x + 2) + (((x + ~4) mod (2 + (x div 3))) mod 2))
A189666: 2 6 8 11 14 18 20 24 26 29 33 35 38 42 44 47
((3x + 2) + ((((~1 + ((x2 + x) div 2)) div 2) div 2) mod 2))
A285953: 3 5 8 12 14 18 21 23 26 30 33 35 39 41 44 48
(1 + ((4 mod (1 + ((x + 2) div 5))) + ((x + 1) div 2)))
A079685: 1 2 2 3 3 4 4 5 6
A137222-A077641: 1 2 2 3 3 4 4 5 6 7 7 8 8 8 8 9
(((~x + 2) + (5 * (2x + (x mod 2)))) * ((x + 1) div 2))
A219395: 0 16 20 68 76 156 168 280 296 440 460 636 660 868 896 1136
(1 + ((x + 1) div 2) - ((x mod (1 + (x mod (1 + (x div 3))))) div 2))
A341721: 1 2 2 3 3 4 4 5 4 6 6 6 7 8 6 8
((2 * ((x + 1) - (x div (6 - (x mod 2))))) + ((x + 1) div 2))
A188016: 2 5 7 10 12 13 15 18 20 23 25 26 28 31 33 34
((2 * (x - (((x + ~1) + (x mod 2)) div 5))) + ((x + 1) div 2))
A295085: 2 3 5 8 10 11 13 16 18 21 23 24 26 29 31 32
(x + ((x + 1) div 2) - ((((3 * ((~x + 2) div 2)) div 2) div 2) mod 2))
A155941: 0 2 3 4 5 8 9 10 11 13 14 17 18 19 20 23
((x + 2) + ((x + 1) div 2) - ((2x2 mod (2 + (x div 2))) mod 2))
A078934: 2 4 5 7 8 10 11 12 14 16 17 19 20 22 22 25
((2 + ((3 * (2x + (x mod 2))) + (x div 2))) * ((x + 1) div 2))
A219389: 0 11 15 48 56 111 123 200 216 315 335 456 480 623 651 816
(2 + ((x + 1) div 2) - ((2 - (2x mod (2 + (x div 2)))) div (x + 2)))
A196179: 1 3 3 4 4 5 5 7 7 7 8 8 8 9 9 11
((12x3 + 33x2 + 29x + 8) div 2)
A213823: 4 41 147 358 710 1239 1981 2972 4248 5845 7799 10146 12922 16163 19905 24184
(25x2 + ~36x + 13)
A154355: 13 2 41 130 269 458 697 986 1325 1714 2153 2642 3181 3770 4409 5098
((2x + ~2) + (x2 div 65))
A058210: ~2 0 2 4 6 8 10 12 14 17 19 21 24 26 29 31
((6 * (1 + (2 * (x - (x div ~2))))) + ((x + ~1) div 2))
A169610: 5 30 42 67 79 104 116 141 153 178 190 215 227 252 264 289
((4x + 4) - (((2x mod (2 + (x div 2))) div ~2) mod 2))
A317331: 4 8 11 16 20 23 27 32 36 40 43 47 52 55 59 64
(2 + (x div 8) - ((~x + 2) div (2 - (x div ~4))))
A071860: 1 2 2 3 3 3 3 4 5 5 5 5 5 5 5 6
(1 + (((((x + ~1) mod (2 + (x div 2))) div 2) mod 2) + ((x div ~2) mod 2)))
A273915-A273429-A270969: 1 2 2 2 2 2 2 1 1 3 3 2 2 2 2 1
(2 * (2 + ((x2 + 1) mod (1 + (2x mod (1 + (x div 3)))))))
A049109: 4 4 4 4 4 4 4 8 6 6 4 8 4 4 6 4
((((x + 1) - (5 * (x div ~7))) div 2) div 2)
A200245: 0 1 2 2 2 2 3 3 4 5 5 5 5 6 6 7
(4 * (1 - ((x + 1) mod (~10x + 9))))
A167632: 0 4 36 72 108 144 180 216 252 288 324 360 396 432 468 504
(x - (4 * ((x div 5) div (1 + (x mod 5)))))
A319653: 0 1 2 3 4 1 6 7 8 9 2 7 12 13 14 3
(4x2 + 60x + 196)
A224667: 196 260 332 412 500 596 700 812 932 1060 1196 1340 1492 1652 1820 1996
(x div (2 + (2 * (1 + ((x + ~2) mod (1 + (2x div (2 + (x div 2)))))))))
A219923: 0 0 0 0 0 1 1 0 2 0 1 1 1 1 3 2
(x5 mod 44)
A070627: 0 1 32 23 12 1 32 43 32 1 32 11 12 21 12 23
(x - ((0 - (x mod ((x + ~2) - (x mod 11)))) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A030477: 0 1 2 3 4 5 6 7 8 9 10 12 14 15 17 18
(4 * (1 + ((4 * (x + ((x div 2) div 3))) div 3)))
A133466: 4 8 12 20 24 28 40 44 52 56 60 68 76 84 88 92
(x mod (2 + (x div 4) - ((2x div (1 + (x div 3))) mod 2)))
A242062: 0 1 0 0 1 1 0 1 2 1 1 2 2 1 2 3
(2 * (((x + 1) mod (1 + ((2 * (1 + (x mod 3))) mod (x + 1)))) div 2))
A179011: 0 0 0 0 0 0 0 2 2 0 0 4 0 4 0 0
(4 * (1 + (((x div 2) div (1 + (x mod (4 + (x div 2))))) mod 2)))
A105682: 4 4 4 4 4 4 4 8 4 4 4 8 4 8 8 8
(2 + ((x mod (1 + (((x div 2) - (2 * (x mod 2))) mod 6))) div 2))
A160493: 2 2 2 3 2 2 3 2 3 2 4 3 2 3 2 3
((~x + 3) + (4 * ((2x + ~2) div 7)))
A194514: ~1 2 1 0 ~1 2 1 0 3 2 1 0 3 2 1 4
(x6 mod 28)
A070651: 0 1 8 1 8 1 8 21 8 1 8 1 8 1 0 1
((2 + ((x * ((x + (x div 2)) div 4)) div 7)) div 2)
A084827: 1 1 1 1 1 1 1 2 2 2 3 4 4 4 6 6
(x mod ((2 - ((x + 1) mod (1 - (2 * (x mod 7))))) div 2))
A089313: 0 0 0 0 0 1 0 0 0 1 1 1 0 3 0 0
(2 + (((~1 + (((x + 1) * (x div 3)) div 2)) div 2) div 2) - (x mod 2))
A029139: 1 0 1 1 2 1 3 2 4 4 5 5 8 7 9 10
(x - (2 * ((1 + ((((1 + (x div 2)) div 2) * ((x + ~1) div 2)) div 2)) div 2)))
A165482: 0 1 2 3 4 3 4 3 4 5 4 3 4 3 2 1
(2 + (((2x + 1) mod (1 + (2 * (2 + (x div 8))))) div 2))
A076050: 2 3 2 3 4 2 3 2 3 4 2 3 4 5 2 3
(((1 + (x mod (2 * (2 + ((x + 2) mod (2 * (2 + (x mod 2)))))))) div 2) div 2)
A277142: 0 0 0 1 1 1 0 2 0 2 0 1 1 1 0 0
((x div (2 + (x div (1 + (x mod (2 * (2 + ((~x + 1) mod 4)))))))) div 2)
A303206: 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 2
(1 - (((x - ((2x2 + 4x) div 9)) div 2) div 2))
A036016: 1 1 1 1 2 2 2 3 4 5 5 6 8 9 10 12
((2 + ((x mod 5) div (1 + (((x + ~1) div 2) mod 4)))) div 2)
A165022: 1 1 2 1 2 1 1 1 1 3 1 1 1 1 1 1
(2 * (2 + (5 * (x - (x div ~9)))))
A166727: 4 24 34 44 54 64 74 84 94 104 124 134 144 154 164 174
(x - (((~x + 2) + ((x - ((1 - (x div 2)) mod 5)) div 2)) div 2))
A039190: 0 1 2 3 5 7 8 9 10 11 12 13 14 16 18 19
(2 + (x mod 2) - ((x - (5 * (x + (x div 4)))) div 2))
A104857: 2 5 6 9 13 16 17 20 23 26 27 30 34 37 38 41
((x + 1) div (2 + (x div (2 + ((x + ~4) mod (1 + (x div 4)))))))
A319695: 0 1 1 1 1 2 1 2 2 2 1 2 1 2 3 3
((8x + 4) - ((((x + 1) - (x div 4)) div 2) div 2))
A285526: 4 12 20 27 35 43 51 59 67 74 82 90 98 106 113 121
((x - ((x + 1) mod ((x + ~2) + ((x mod (1 + (x mod 4))) div 2)))) div 2)
A161228: 0 0 1 1 1 2 1 2 2 3 3 4 4 5 6 6
(((3 * (x - ((x2 + ~2x) div (2x + 3)))) div 2) div 2)
A194819: 0 1 1 2 3 3 3 3 4 4 5 6 6 6 6 7
((((x2 div 4) mod (3 * (1 + (x div 4)))) div 2) div 2)
A112762: 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 2
(2 - ((x + 2) div (2 + ((3 * (x div (3 + (x mod 2)))) div 2))))
A112208: 1 1 0 0 0 0 1 ~1 0 0 0 0 1 0 0 0
(x - (2 * ((x - ((((~x + 2) div 2) + (x mod 3)) div 3)) div 2)))
A277889: 0 1 0 ~1 0 1 0 ~1 0 ~1 0 ~1 ~2 ~1 ~2 ~3
(((3 * (2 + (x2 div 24))) div 2) div 2)
A262950-A029094: 1 1 1 1 1 2 2 3 3 3 4 5 6 6 7 8
(4 * ((16x3 + ~16x) div 3))
A123293: 0 0 128 512 1280 2560 4480 7168 10752 15360 21120 28160
(2 div (2 + (((x - (x2 mod 16)) div 3) div 2)))
A333058: 1 1 2 2 1 2 1 0 0 0 0 1 0 1 0 0
(2x - (((3 * (x - ((x2 + ~x) div 4))) div 2) div 2))
A226330: 0 2 3 5 8 10 13 17 21 25 29 34 40 46 52 58
(x - (2 * ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2)))
A075425: 0 1 2 1 2 3 4 1 2 3 4 3 4 5 6 1
(((x2 div 2) div (2 + (3 * (8 - (x div 2))))) div 2)
A326447: 0 0 0 0 0 0 0 0 1 1 2 2 4 5 9 11
(2 * (x - (((x2 + ~2x) - ((x3 div 2) div 3)) div 2)))
A289424: 0 4 6 8 10 16 24 36
(x + ((x mod (6 + ((1 + (x div 2)) div 2))) mod 2) - (x mod 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A335133: 0 1 2 3 4 5 6 7 8 9 11 10 13 12 14 15
(((2x + ~1) mod (2 + (2x div (2 - ((~x + 1) div 3))))) div 2)
A035445: 0 0 0 0 1 0 0 1 0 1 0 0 2 0 1 2
(2 + ((((x div 2) div (~1 - (x mod 4))) + (x div 3)) div 2))
A156051: 2 2 1 2 1 2 2 2 1 2 2 2 1 2 2 3
(8x2 + 56x + 140)
A276026: 140 204 284 380 492 620 764 924 1100 1292 1500 1724 1964 2220 2492 2780
(((1 + ((x + (x3 div 16)) div 2)) div 2) div 2)
A059290: 0 0 0 0 1 1 2 3 5 7 9 12 15 19 23 28
(20x2 + 108x + 132)
A253503: 132 260 428 636 884 1172 1500 1868 2276 2724 3212 3740 4308 4916 5564 6252
((x + 4) - ((2 * (~x + (x2 div 3))) div (x + 3)))
A000703: 4 6 7 7 8 9 9 10 10 10 11 11 12 12 12 13
(((((1 + (x div (~2 + (x mod 2)))) mod 3) * (1 + (x div 2))) div 2) div 2)
A130632: 0 0 0 0 1 1 1 0 0 1 3 3 1 0 0 2
((2 - (x mod (~2 - ((3x + ~6) mod (1 + (x div 2)))))) div 2)
A319989: 1 1 1 1 1 1 1 2 2 1 1 3 1 1 3 2
((2 + ((2 * (4 - (x mod ~3))) mod (1 + (x div 2)))) div 2)
A345063: 1 1 1 1 1 1 1 1 1 2 1 3 1 3 2 1
(2 + (((2 * ((x + ~1) div (2 + (x div 4)))) mod (1 + (x div 2))) div 2))
A092363: 2 2 2 2 3 3 3 2 3 4 4 4 4 4 4 4
(1 - (2 * ((((~x + 4) + (x div 4)) mod (1 + (x div 2))) mod 2)))
A121241: 1 1 1 ~1 ~1 1 ~1 1 ~1 1 1 ~1 1 ~1 ~1 1
(2 + (((x + 1) + ((x + (((x + 1) div 3) * (x div 2))) div 2)) div 2))
A121603: 2 3 4 5 6 7 8 9 11
A091897: 2 3 4 5 6 7 8 9 11 12 13 15 17 18 21 22
(x mod (2 * (2 + ((~1 + ((x mod 6) mod 4)) mod (x + 1)))))
A330342: 0 1 2 3 4 1 6 3 2 1 10 3 12 1 2 7
((((2 - (x mod (6 + (x mod 3)))) mod (x + 1)) div 2) div 2)
A223175: 0 0 0 0 0 0 0 0 0 2 2 2 0 2 2 3
((x mod (2 + (((1 + (x mod 4)) * (1 + (x mod 2))) mod (x + 1)))) div 2)
A054015: 0 0 0 0 0 2 0 0 1 1 0 0 0 0 2 2
((((2 - (((~1 + (x div 2)) * (x div 3)) div 2)) mod (x + 1)) div 2) div 2)
A324496: 0 0 0 0 0 0 0 0 2 2 1 2 1 1 1 0
((((4 * (x - (x mod (3 + (x mod 2))))) mod (x + 1)) div 2) div 2)
A281497: 0 0 0 0 0 1 0 0 1 0 0 2 2 1 0 0
((2 + ((~2 + ((x mod 5) + (x mod 4))) mod (x + 1))) div 2)
A171712: 1 1 2 1 2 3 1 2 1 2 1 2 1 2 3 1
((x - (((4 * ((~x + 2) - (x div 3))) mod (x + 1)) div 2)) div 2)
A330918: 0 0 1 1 1 2 2 2 3 4 5 5 4 4 4 5
(2 + (((x + 1) * ((x + 2) + ((~2x + 1) mod 5))) div 2))
A059868: 3 9 11 12 24
((((x + 1) * ((x + 2) + (2 * (x - (2 * ((x div 2) mod 2)))))) div 2) div 2)
A268539: 0 2 3 7 17 25 28 38 58 72 77 93 123 143 150 172
((((2x + 1) - (3 * (x div ~2))) * ((x + 1) div 2)) div 2)
A057570: 0 3 4 13 15 30 33 54 58 85 90 123 129 168 175 220
((((x + 1) + (x div (4 * (2 + (x mod 2))))) * ((x + 1) div 2)) div 2)
A308578: 0 1 1 4 5 9 10 16 20 25 30 36
((34x + 34) + (((x + 1) div 2) div 2))
A277113: 34 68 102 137 171 205 239 274 308 342 376 411 445 479 513 548
((2 * (2x div 15)) + (((x + 1) div 2) div 2))
A082871: 0 0 0 1 1 1 1 2 4
A132345: 0 0 0 1 1 1 1 2 4 4 4 5 5 5 5 8
(4x + (((x + 1) div 2) div 2) - ((((x + ~1) div 2) div 2) div 2))
A058759: 1 4 8 13
A311815: 1 4 8 13 17 21 25 30 34 37 41 46 50 54 58 63
(8 * (1 + (x div (11 - (x div 2)))))
A245401: 8 8 8 8 8 8 8 8 16 16 16 16 24 24 32 32
((x + 4) - ((1 + ((x2 div 4) div 5)) div 2))
A248355: 4 5 6 7 8 8 9 10 10 11 11 12 12 13 13 13
((x2 + 2x) - ((((~1 + (3 * (x2 div 2))) div 2) div 2) div 2))
A194149: 1 4 8 14 22 31 42 55 69 85 102 121 142 164 188 214
(2 + (((((x + ~2) - (x div 3)) * (1 + (x div 3))) div 2) div 2))
A035397: 1 1 2 2 2 3 3 4 5 6 7 8 9 10 12 14
(x - (2 * ((x - ((1 + (8 mod (1 + (x div 2)))) div 2)) div 2)))
A037834: 0 1 0 1 2 1 0 1 2 3 2 1 2 1 0 1
((~x + 1) + (2 * ((x - (x div ((~1 + (x div ~4)) div 2))) div 2)))
A270434: 1 2 3 4 5 4 3 4 5 6 5 6 7 6 5 6
(8 * (1 + (8 * (x + (x div 8)))))
A044576: 8 72 136 200 264 328 392 456 584 648 712 776 840 904 968 1032
(~4 + ((2 + ((x + 1) * (2 - (x mod 2)))) mod 10))
A141035: 0 0 4 2 ~2 4 2 ~4 ~4 ~2 0 0 4 2 ~2 4
(4 * ((x + 2) - ((x - ((x - (x div 4)) mod 2)) div 3)))
A081925: 8 12 16 20 20 24 28 28 32 36 36 40 44 44 48 48
(2 + (((3 * (x - ((x + ((x + ~1) mod 3)) div 2))) div 2) div 2))
A285582: 1 2 2 2 3 3 3 5 5 5 5 5 5 7 7 7
((x div 3) - ((x div (2 + (x mod (2 + ((~x + 1) mod 3))))) mod 2))
A249871: 0 0 0 0 1 0 1 2 2 3 2 3 4 4 3 4
((3x + 3) - ((((~1 + ((x2 + x) div 2)) div 2) div 2) mod 2))
A285951: 2 6 9 11 15 17 20 24 27 29 32 36 38 42 45 47
(1 - ((((24 mod (~x + ~1)) div 2) div 2) div 2))
A308964: 1 1 1 1 2 1 2 1 2 2 3 1 2 2 2 2
((1 - (((32 mod (~x + ~1)) div 2) div 2)) div 2)
A206442: 0 0 1 0 1 1 1 0 1 1 1 1 1 2 2 0
(4 * ((((x + ~1) mod (1 + (2 * ((~x + 1) mod 3)))) div 2) mod 2))
A036480: 4 0 0 4 0 0 4 0 4 4 0 0 4 0 4 4
(x - (2 * ((x - ((x mod (2 + ((~x + 2) mod 5))) div 2)) div 2)))
A228110: 0 1 0 1 2 1 0 1 2 3 2 1 0 1 2 1
(x - (x2 div (x - (2 * (~2 + (x div (~4 + (x mod ~2))))))))
A331535: 0 1 2 2 3 3 4 4 4 5 5 6 6 6 7 6
(4 + ((((2x4 + ~x3 + 2x + ~1) div 2) div 2) div 2))
A124082: 3 4 7 21 60
(1 - (2 * ((x - ((~x2 + x) div 32)) mod 2)))
A008836: 1 ~1 ~1 1 ~1 1 ~1 ~1 1 1 ~1 ~1 ~1 1 1 1
((x + 2) - ((0 - ((x - ((1 + (x div 2)) mod 8)) div 2)) div 2))
A179439: 2 3 4 5 6 8 9 10 11 12 13 14 15 17 20 21
(((((x + 2) * (x div 2)) div (~x + 18)) div 2) div 2)
A051061: 0 0 0 0 0 0 0 0 1 1 1 2 3 4 7 9
(x - (2 * ((x - ((0 - (x mod (~2 + ((~x + 2) div 4)))) div 2)) div 2)))
A272728: 0 1 0 1 2 1 0 1 0 1 2 3 2 1 0 1
(4 mod (2 + (((~2x + 2) mod (4 + (x div 4))) div 2)))
A272774-A147312-A136630: 1 0 1 0 0 1 0 1 0 1 0 0 4 0 1 0
(2 * (1 - ((~x + 1) div (4 - (((x - (x div 4)) div 2) mod 2)))))
A105678: 2 2 4 4 4 4 6 6 8 8 8 8 8 10 12
(2 + ((x + 1) div (2 + (x div (2 + (x2 mod (2 * (2 + (x mod 2)))))))))
A177876: 2 3 3 4
A285203: 2 3 3 4 3 4 3 4 3 5 3 4 3 4 3 5
(x7 mod 32)
A271572: 0 1 0 11 0 13 0 23 0 25 0 3 0 5 0 15
(1 - ((x - (x div (2 - ((x3 div 8) mod 2)))) div 2))
A098593: 1 1 1 1 0 1 1 ~1 ~1 1 1 ~2 ~2 ~2 1 1
((1 + (x div 3)) div (2 + ((x mod (~2 + ((~x + 2) div 4))) mod 2)))
A024317: 0 0 0 1 1 0 1 1 1 1 2 2 1 2 1 2
(2 + (2 * (((2x + ~2) mod (2 + (x div 4))) mod 2)) - (x mod 2))
A116933: 2 1 2 1 2 1 4 1 2 1 2 1 2 1 4 3
(2x div ((x + 2) - ((~x2 + 2x) mod (4 + (x div 4)))))
A244231: 0 1 1 1 2 1 1 1 1 2 2 2 3 2 1 1
((x + 1) div (2 + (x div (2 + (((~2x + 4) mod (2 + (x div 2))) div 2)))))
A095407: 0 1 1 1 1 2 1 1 1 2 2 2 2 2 2 1
(2x div (2 + ((x + 2) div (8 + (x div ~4)))))
A059572: 0 1 2 3 4 3 4 4 5 4 5 5 6 5 4 5
(2 * (6 + compr(\x.(1 - (x mod (1 + (x mod 6)))),x)))
A241178: 14 16 18 20 22 26 28 30 34 38 40 42 44 46 50 52
(1 - (((x mod 3) - (((((x + ~1) div 2) * (x div 2)) div 2) div 2)) div 2))
A328796: 1 1 0 1 1 1 2 2 2 3 3 3 5 5 5 7
((1 - ((x2 mod 7) mod 3)) mod 8)
A002394: 1 0 0 7 7 0 0 1
((6x + 3) - ((2x + 2) div ~7))
A246297: 4 10 16 23 29 35 41 48 54 60 67 73 79 85 92 98
(2x + (x div ~7) - (x div 7))
A191275: 0 1 3 5 7 9 11 12 13 15 17 19 21 23 24 25
((x + 8) + ((~2x + 2) div (3 + (x div 3))))
A320304: 8 9 9 10 10 11 12 12 13 14 15 15 16 17 18 19
(x - ((x mod (1 + ((x + 1) div 5))) + (x div 8)))
A061984: 0 1 2 3 4 4 6 6 7 8 8 8 11 11 11 11
(((3 * (x + (x div 4))) + (x div 2)) - (x mod 8))
A062879: 0 2 5 7 13 15 18 20 34 36 39 41 47 49 52 54
(compr(\x.(x mod ((x + 1) - (x mod 8))),x) + (x mod 8))
A319808-A055956: 0 2 4 6 8 10 12 14 9 18 27 36 45 54 63 72
((5x4 + ~4x2) div 8)
A212673: 0 0 8 46 152 378 792 1476 2528 4060 6200 9090 12888 17766 23912 31528
((x3 * (7 + (x mod 2))) div 8)
A309335: 0 1 7 27 56 125 189 343 448 729 875 1331 1512 2197 2401 3375
((x + 1) - (2 * (((x + 1) div (~x + 16)) div 4)))
A291579: 1 2 3 4 5 6 7 8 9 10 11 12 13 12 13 8
((1 + ((x mod (2 * (2 - ((x div 4) mod 2)))) + (x div 4))) div 2)
A326753: 0 1 1 2 1 1 1 1 1 2 2 3 2 2 2 2
((2 + (x div 4) - (((1 + (x div 2)) div (2 + (x mod 2))) mod 2)) div 2)
A298604: 1 1 0 1 1 1 1 1 2 1 1 2 2 2 2 2
(2 + (((x + ((2x div (1 + (x div 4))) mod 3)) div 2) mod 2))
A080748: 2 3 3 3 2 3 3 2 3 2 3 2 2 2 3 2
(((x + 2) - ((x + ((x - (x div 3)) mod 8)) div 2)) div 2)
A179932: 1 1 1 1 1 1 1 1 1 2 2 4 4 4 4 4
((2 + ((x + ((x3 + ~x2) div (x + 6))) div 2)) div 2)
A071764: 1 1 1 2 3 4 6 8 11 14 17 21 26 30 36 42
(2 * (2 + ((6x + (x2 div 4)) div (x + 2))))
A235382: 4 8 10 12 12 14 14 16 16 16 18 18 18 20 20 20
(8x + ((2x + 3) * ((x2 + x) div 2)))
A163675: 0 13 37 78 142 235 363 532 748 1017 1345 1738 2202 2743 3367 4080
(((((5 * ((x2 + x) div 2)) div 2) + (x div 2)) div 2) div 2)
A247179: 0 0 2 4 6 9 13 18 23 29 35 42 50 58 67 76
(2 * ((x + 2) - (x2 div ((2x + 10) - (x div 2)))))
A167146: 4 6 8 10 10 12 14 14 16 16 16 18 18 20 20 22
(2 * ((x + 2) - (3x div (16 - (x div 2)))))
A061408: 4 6 8 10 12 12 14 16 16 18 20 20 22 24 24 24
((((((x + 1) + (2 * (x div 3))) mod 4) + (x div 2)) div 2) div 2)
A114775: 0 0 1 0 1 0 1 0 1 1 1 1 1 2 2 2
(x - (2 * ((((x + ((~x + 1) mod 3)) mod 4) + (x div 2)) div 2)))
A342872: 0 1 2 3 2 1 0 1 2 3 4 5 6 7 8 9
((1 + (2x mod (1 + (x div 4)))) mod (2 * (2 - ((x div 2) mod 2))))
A144409: 1 1 1 1 1 1 1 1 2 1 1 0 1 3 1 1
(x div (4 + (((x + 2) div (1 + (x mod 3))) mod 2) - (x mod 2)))
A306433: 0 0 0 0 0 1 1 2 1 2 2 3 3 3 2 3
(((((5x2 + 11x + 2) div 2) + (x mod 2)) div 2) div 2)
A013927: 0 2 5 10 15 23 31 40
((1 + ((x * (x mod (2 * (1 + (x mod 2))))) div 5)) mod 4)
A101211: 1 1 1 2 1 2 1 1 1 2 1 3 1 3 1 2
((1 - ((1 - ((x + 1) mod 7)) mod (x + 1))) mod 4)
A017861: 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 2
((x2 mod (9 + (x mod 2))) + ((x + 1) mod 4))
A331066: 1 3 7 9 8 7 3
(((x mod 2) - ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2)) mod 4)
A193525: 0 1 0 1 0 0 0 1 0 0 0 0 0 0 3 1
(((2 - (x div (2 + (10 mod (x + 1))))) div 2) mod 4)
A074063: 1 1 1 1 0 1 0 0 0 3 1 1 0 0 0 0
(((x + 2) + (x2 div (4 * (3 - (x mod 2))))) div 4)
A340285: 0 0 1 1 1 2 2 3 3 5 5 7 6 9 8 11
(3x2 + 50x + 12)
A304833: 12 65 124 189 260 337 420 509 604 705 812 925 1044 1169 1300 1437
(4 + compr(\x.(2 - ((~2x + 4) mod (4 + (x div 4)))),x))
A037084: 5 7 9 10 13 14 17 18 19 20 21 23 25 26 27 28
((x + 4) + ((8x + (x div 3)) div (x + 2)))
A127958: 4 7 10 12 13 14 16 17 18 19 20 22 23 24 25 26
((x + 1) + (x div 4) - ((~x + 2) div (3 + (x div 4))))
A202728: 1 2 3 5 7 8 9 11 13 14 15 16 18 19 20 22
(x - (((1 + ((2 * (x div 2)) div 3)) mod 3) * (x div 4)))
A328841-A276008: 0 1 2 3 2 3 6 7 8 9 8 9 6 7 8 9
((3x + 3) + (((x div 2) div 5) + (x div 4)))
A184906: 3 6 9 12 16 19 22 25 29 32 36 39 43 46 49 52
((x + (x div ((x + 1) - (2 * (2x mod 3))))) div 4)
A331904: 0 0 1 0 2 1 1 2 2 2 2 3 3 3 3 3
(2 + (((x + 1) + (x div (1 + ((x + 2) div 7)))) div 2))
A195879: 2 3 4 5 6 6 7 7 8 9 10 10 10 11 11 12
(4 + compr(\x.(x mod (1 + (x mod ((x + 1) - (x mod 8))))),x))
A194283: 4 5 6 7 8 9 10 11 13 14 16 21
(2 + (((x + 1) + (((x + 4) * ((x + ~1) div 3)) div 2)) div 2))
A240115: 1 3 3 4 6 7 8 11 12 13 18 19 20 26 27 29
(4 + compr(\x.((x + 1) mod (1 + (2 * ((~x + 2) mod (2 + (x mod 2)))))),x))
A137353: 4 6 8 9 10 12 13 14
A336371: 4 6 8 9 10 12 13 14 15 16 18 20 21 22 24 26
(x - (((x + ((1 + (x * ((x + ~1) div 3))) div 3)) div 2) div 2))
A048182: 0 1 2 3 3 4 4 4 5 6 5 6 6 6 6 7
(((x2 + 4x) - ((x + (x div 12)) div 2)) div 2)
A024390: 0 2 5 10 15 21 28 37 46 56 67 80 93 107 122 138
(2 * ((x + 2) + ((x + 2) div (8 - ((x + ~2) div 3)))))
A051756: 4 6 8 10 12 16 18 20
A322839-A074827: 4 6 8 10 12 16 18 20 22 24 28 30 32 36 40 42
((x + 4) + ((x + (((x + 1) div (2 + (x mod 2))) div 2)) div 3))
A089585: 4 5 6 8 9 11 12 13 15 16 18 19 21 22 23 24
(1 - (2 * (x2 - (2 * (x + ((x3 + 2x) div 3))))))
A322597: 1 7 17 39 81 151 257 407 609 871 1201 1607 2097 2679 3361 4151
(x2 + 52x + 30)
A155461: 30 83 138 195 254 315 378 443 510 579 650 723 798 875 954 1035
((x + 2) - ((~x - ((x + (x2 div 4)) div 4)) div 2))
A027921: 2 4 5 7 9 11 13 15 17 19 21 24 26 28 31 33
(~2 + ((9x3 + 33x2 + 40x + 16) div 2))
A232495: 6 47 148 336 638 1081 1692 2498 3526 4803 6356 8212 10398 12941 15868 19206
(2 + ((x + ((x + (((x - (x2 div 4)) div 2) div 2)) div 2)) div 2))
A057062: 2 2 3 4 5 5 6 6 7 8 8 9 9 9 10 10
(2 + ((x + ((((~x + (2 mod (x + 1))) div 2) mod 2) + (x2 div 2))) div 2))
A217123: 2 3 4 6 8 10 14 18 22 26 32 38 44 50 58 66
(((x + 2) * (1 + ((x - ((~x3 + x2) div 2)) div 3))) div 2)
A004036: 1 1 4 12 30 66 132
(2 * ((x - (4 * (~6 + (x div 3)))) div (x + 2)))
A033826: 24 16 12 8 8 6 4 4 4 2
(2 * (2 - ((2 - (2x mod (4 + (x div 4)))) div (x + 2))))
A278481: 2 4 4 4 6 4 4 6 6 4 4 6 6 6 4 4
((2x + 4) + ((x - ((x2 + ~2x) div 7)) div 2))
A174724: 4 7 9 11 13 15 17 19 21 22 23 24 25 26 27 28
((2x + 4) + ((4x + (x2 div 4)) div (x + 2)))
A078633: 4 7 10 12 15 17 20 22 24 27 29 31 34 36 38 40
((3x + 4) + ((x - ((~x + 1) div (2 + (x div 4)))) div 2))
A247432: 4 7 11 15 18 22 26 29 33 36 40 44 47 51 54 58
((x - ((x + (3 * (x mod 10))) div (x + 2))) div 2)
A123575: 0 0 0 0 1 1 1 2 2 3 5 5 5 6 6 7
(2 * (2x + ((((x + 2) div 3) + (x div 5)) div 2)))
A045672: 0 4 8 12 18 22 26 32 36 40 46 50 54 58 62 68
((4x + 1) + ((2 * ((x2 + 2) div (x + 2))) div 3))
A314886: 1 5 9 14 19 23 27 32 37 41 46 51 55 60 65 69
(4x + (((3 * (x + (x div 4))) - (x mod 2)) div 2))
A272666: 0 5 11 16 23 28 34 39 47 52 58 63 70 75 81 86
((3x + 2) + (((~2x + 4) mod (1 + (x div 3))) mod 2))
A184910: 2 5 8 11 14 17 21 23 26 29 32 35 38 42 45 47
(2 + (((4 * ((2 * (x div 2)) div 3)) div 3) + (x div 2)))
A085885: 2 2 3 3 5 5 7 7 8 8 11 11 13 13 14 14
(((2x + 1) + (((x2 + 2) mod 6) + (x div 2))) div 2)
A071047: 1 3 3 6 5 8 9 10 10 14 13 15 16 18 18 21
(2 * ((2 * (x - ((~1 + (2 * (x div 2))) div 5))) + (x div 2)))
A191330: 4 8 10 14 20 24 26 30 36 40 46 50 52 56 62 66
(1 + (((x mod (1 + (4 mod (1 + (x div 2))))) mod 2) + ((x div 2) mod 2)))
A304094: 1 1 2 2 1 2 2 2 2 1 2 3 1 2 2 2
((1 + ((((1 + ((x + 1) div 2)) mod 5) div 2) + (x mod 2))) div 2)
A194821: 0 1 1 1 1 2 1 1 0 1 0 1 1 1 1 2
(((x + 3) div (1 + ((((1 + (x div 2)) div 2) div 2) + (x mod 2)))) div 2)
A300712-A282463: 1 1 2 1 3 2 2 1 2 2 3 2 3 2 2 2
(x - ((1 + (x mod 2) - ((x - (x div 8)) mod 3)) div 2))
A035044: 0 1 3 2 4 5 6 7 8 9 10 11 13 12 14 15
(3 + ((~x + 2) div (2 + ((2x div 3) + (x mod 2)))))
A073871: 4 3 3 2 2 2 2 2 2 2 2 2 2 2 1 2
((1 + (((x + 2) mod (3 + (x mod 4))) div 2)) mod (2 + (x mod 2)))
A036581: 0 2 1 0 1 2 0 2 1 2 0 1 0 2 1 0
(((x + ~1) + (3 * (x mod 7))) mod (2 + (x mod 2)))
A030351: 1 0 1 2 1 1 1 0 0 2 0 1 0 0 1 2
(1 + (((((~2 + (x div 2)) * (x div 2)) mod (x + 1)) mod 2) + (2 * (x mod 2))))
A301848: 1 3 1 4 1 3 2 4 1 3 1 4 2 3 2 4
(1 + ((((x div 2) - ((x div 4) div ~2)) mod 2) + (2 * (x mod 2))))
A089214: 1 3 2 4 2 4 1 3 2 4 1 3 1 3 2 4
(2 + compr(\x.(x mod (1 + ((~x + 1) mod (1 + (x mod 9))))),x))
A189716: 2 3 5 8 11 12 14 17 18 20 21 23 26 27 29 30
(2 + compr(\x.(1 - (x mod (1 + (3 * (x mod (1 + (x mod 4))))))),x))
A256455: 3 4 5 7 9 11 12 13 15 17 19 21 23 24 25 27
(2 * compr(\x.((x + ~1) mod (x - ((x + 1) mod 11))),x))
A152966: 0 2 4 6 8 10 12 14 16 18 22 44 66 88 110 132
(2 + compr(\x.(x mod (1 + ((x + 1) mod (2 * (1 + (x div 8)))))),x))
A229991: 2 3 4 5 6 7 8 9 10 11 13 14 17 19 20 22
(2 + compr(\x.(~1 + (x mod (2 + ((5 * (x mod 2)) mod (x + 1))))),x))
A172121: 2 3 4 5 6 8 9 10 12 14 16 17 18 20 22 23
((x + 3) + ((x - (((x + 1) mod (4 + (x div 2))) div 2)) div 2))
A299114: 3 4 5 6 8 10
A055563: 3 4 5 6 8 10 12 13 15 16 17 19 20 21 23 24
((x + 2) + ((x * (1 + (x div 5))) div 9))
A153134: 2 3 4 5 6 8 9 10 11 13 15 16 18 19 20 23
(~2 + compr(\x.(2 - ((x * ((x + (x div 2)) div 2)) mod 9)),x))
A093110: 0 1 2 3 4 5 6 8 9 12 13 14 15 17 18 21
(2 + compr(\x.(1 - ((x + 1) mod (1 + (x div (2 + (x mod (2 + (x mod 2)))))))),x))
A192607: 4 6 8 9 10 12 14 15 16 18 19 20 21 22 24 26
((x + ((6x2 + 24x + 24) div 5)) div 2)
A086849: 2 5 10 16 23 31 41 52 64 77 91 106 123 141 160 180
((x + 2) + (((x + 2) * ((2x + 4) - (x div 2))) div 5))
A000791: 3 6 9 14 18 23 28 36
((x + ~2) + (5 * ((4x + 16) - (x div 2))))
A295699: 78 99 115
((x + 2) + (2x div 3) - ((x + (x mod 2)) div 5))
A156271: 2 3 5 7 8 9 11 12 14 15 16 18 20 21 23 24
((x + 2) + ((1 - (x mod (((~x + 2) div 2) - (x mod 3)))) mod 3))
A154660: 3 4 5 6 7 8
A260580: 3 4 5 6 7 8 9 11 10 12 13 14 15 17 16 18
((x + 2) + ((2 * (2x - ((~1 + (x div 2)) div 3))) div 3))
A187836: 2 5 6 9 11 13 16 18 20 22 24 27 29 31 33 35
(8x - ((~x + (x div ~12)) div 2))
A121282: 0 9 18 26 35 43 52 60 69 77 86 94 103 112 120 129
(2 + compr(\x.((x + 2) - (3 * (~2 + ((x - (x div 4)) div 2)))),x))
A345505: 57 60 63 65 66 68 69 71 72 73 74 75 76 77 78 79
(2 * (x + ((x - (x mod (~x + ((x + ~1) mod 8)))) div 3)))
A195066: 0 2 4 8 10 12 16 18 20 24 32 34 36 38 40 42
((x + 2) + ((x + (2 * (((x div 4) * (x div 2)) div 2))) div 3))
A331819: 2 3 4 6 8 9 10 12 15 16 18 20 24 25 27 28
(x - ((~16x3 + 21x2 + ~5x) div 2))
A260260: 0 1 29 132 358 755 1371 2254 3452 5013 6985 9416 12354 15847 19943 24690
((x * ((~x + ~1) + (2 * (x mod (x - ((x + ~1) mod 8)))))) div 2)
A187845: 0 ~1 ~3 ~6 ~10 ~15 ~21 ~28 ~36 ~45 ~45 ~44 ~42 ~39 ~35 ~30
(2 + compr(\x.(2 - ((x + 1) mod (1 + (2x mod (x + 8))))),x))
A154660: 3 4 5 6 7 8
A096829: 3 4 5 6 7 8 9 12 14 15 18 19 20 21 22 23
(x - (2 * ((~5x + ~4) + (x mod 9))))
A052222: 8 17 26 35 44 53 62 71 80 107 116 125 134 143 152 161
(2 + compr(\x.((x + 2) mod (2 + (x mod (1 + ((x + 1) div 5))))),x))
A227197: 2 4 6 8 9 10 12 14 15 16 18 20 22 24 25 26
((x + ~2) + ((7 * (1 + (((x + 1) div 2) div 2))) div 2))
A131959: 1 2 3 8
A283776: 1 2 3 8 9 10 11 15 16 17 18 23 24 25 26 30
((x + 2) + ((x - (x div (11 - (x div 2)))) div 2))
A161188: 2 3 5 6 8 9 11 12 13 15 16 18 19 20 21 23
(~2 + compr(\x.(2 - ((2x + 1) mod (2 + ((x + 1) div 5)))),x))
A186348: 3 6 7 9 11 12 14 16 17 18 20 21 23 24 25 27
(x - ((x + ((5 * ((x mod (1 + (x div 2))) div 2)) div 2)) div 2))
A103183: 0 1 1 2 2 2 2 3 3 2 3 3 4 3 4 4
((x + 2) + ((3 * (2 - ((x div 3) div ~3))) div 2))
A191850: 5 6 7 9 10 11 12 13 14 15 16 17 20 21 22 23
((x + 2) + ((3 * (2x div (4 + (x div 3)))) div 2))
A341646-A317090-A109421-A094784-A089105-A085971-A065872-A052485-A028769-A007916: 2 3 5 6 7 10 11 12 13 14 15 17 18 19 20 21
(x - ((~x + (x mod (~2 + (3 * (8 - (x div 2)))))) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A125506: 0 1 2 3 4 5 6 7 8 9 14 15 18 19 21 23
((x + ((3 * (x + (((x + ~2) * (x div 2)) div (x + 1)))) div 2)) div 2)
A158791: 0 1 2 3 5 7 8 9 11 12 14 16 18 19 21 22
((x + 2) + (((0 - (((x + 1) div 2) div 3)) * (x div 3)) div 2))
A121604: 2 3 4 5 6 6 7 8 9
A195918: 2 3 4 5 6 6 7 8 9 9 10 10 10 11 12 12
(2x * (2 + ((x + ~1) * (4x + ((x2 + ~x) div 2)))))
A265081: 0 4 44 192 544 1220
((x + 2) + ((x - ((1 + ((x mod (2 + (x div 2))) mod 4)) div 2)) div 2))
A026433: 2 3 4 6 8 9 10 12 13 14 16 18 20 21 22 24
((x + 2) + (((3 * ((x + ((x div 2) mod 2)) div 3)) div 2) div 2))
A152757: 2 3 4 5 6 7 9 10 11 13 14 16 17 18 19 20
((x + (2 * ((1 + ((x * ((2x + ~1) div 3)) div 2)) div 2))) div 2)
A145809: 0 0 2 2 4 6 8 10 14 15 20 24
(((x + 2) - ((((x + 1) * (~4x + (x mod 2))) div 2) div 2)) div 2)
A290268: 1 2 5 8 13 18 25 31 41 49 61 71 85 97 113 126
(2 * (x + (8 * ((2x mod (1 + (x div 4))) mod 2))))
A264986: 0 2 4 6 8 10 12 14 32 18 20 38 24 26 28 30
(2 + compr(\x.((x - (x div (~4 - ((x div 4) mod 2)))) mod 2),x))
A077164: 2 3 5 7 8 10 11 13 15 17 18 19 21 22 23 25
(x - ((x + (((x + ((~x + 3) * (x div 3))) div 2) div 2)) div 2))
A237119: 0 1 1 2 2 3 3 4 5 6 7 8 9 10 11 14
((x + 2) + (2 * (x + ((1 + (2 * (x + (x mod 2)))) div 5))))
A026364: 2 7 10 13 16 21 24 29 32 37 40 45 48 51 54 59
((x + ((x + ((x * (2x div 5)) div 3)) div 2)) div 2)
A220506: 0 0 1 2 3 4 5 6 8 9 10 11 13 15 16 18
((x + 2) + ((x + (x div (2 + (((x + ~2) mod (2 + (x div 2))) div 2)))) div 2))
A062132: 2 3 5 7 8 10 11 14 16 17 19 20 22 23 25 26
(((2x + 1) * (~5 + (x mod 2))) mod (x2 + 2x + 2))
A145736: 1 3 5 6 7 30
((x + ((x * (4x + (x2 div 4))) div (x + 2))) div 2)
A002821: 0 1 3 5 8 11 15 19 23 27 32 36 42 47 52 58
((3x + 2) + ((x div 2) div (3 + (x mod 8))))
A184905: 2 5 8 11 14 17 20 23 27 30 33 35 38 41 44 47
((x + ((x2 + x) div (20 - (x div 2)))) div 2)
A176615: 0 0 1 1 2 3 4 5 6 7 8 9 11 13 15 16
(2 + compr(\x.((((x + 1) div (1 + (x mod 5))) mod 2) - (x mod 2)),x))
A326980: 3 5 7 9 10 11 13 14 15 17 18 19 20 21 23 25
((1 + ((x + 1) div (1 + (x div (2 + (x mod (2 + (x mod 2)))))))) mod (x + 2))
A199968: 0 0 2 3 2 4 2 3 2 3 2 5 2 3 2 3
((x + 2) * (1 + ((x + 1) mod (1 + (x div (2 + (x mod (2 + (x mod 2)))))))))
A070935: 2 3 8 5 18 7 32 27 50 11 72 13 98 75 128 17
((~1 + (2 * ((x2 + (x div 2)) div 7))) mod (x + 2))
A194760: 1 2 3 1 3 5 1 4 7 1 5 9 13 4 9 14
((1 + (2 * (2 + ((x mod 15) div 2)))) mod (x + 2))
A139713: 1 2 3 2 3 2 3 2 3 2 3 2 3 2 3 5
(((8x + 1) + ((x2 + 2) div 3)) div (x + 2))
A121857: 0 3 4 5 6 7 7 8 8 9 9 10 10 10 11 11
compr(\x.((4 * (x mod 10)) - (x div 3)),(x + 2))
A014368: 20 21 30 31 32 40 41 42 43 50 51 52 53 54 60 61
compr(\x.((~1 + (x mod (2 + ((x2 + 2x) mod 6)))) div 2),(x + 2))
A014661: 2 4 6 7 8 10 12 14 15 16 18 20 21 22 23 24
compr(\x.((x mod 2) - (((1 + (x div 2)) div (2 + (x mod 3))) mod 2)),(x + 2))
A062975: 3 4 6 7 8 10 11 12 14 16 18 19 20 21 22 23
compr(\x.(~2 + ((x mod 2) + (x mod (4 + (x mod (2 + (x mod 2))))))),(x + 2))
A336375: 2 4 6 8 9 10 12 14 16 18 20 21 22 24 25 26
((3x + 2) - ((x + ((~x2 + x) div 4)) div 4))
A135677: 2 5 8 11 14 17 21 24 28 32 36 40 44 48 52 57
((3x + 2) + ((x + (((x2 + 1) * (x div 2)) div 2)) div 2))
A064513: 2 5 10 15 24 32 50
(((x + 2) - ((x + 4) mod 13)) mod (x + 2))
A265524: 0 1 2 3 4 5 6 7 8 0 11 11 11 11 11 11
((2x + 1) + ((x + ~1) mod (1 + (x2 mod (2 + (x div 4))))))
A306639: 1 3 5 7 10 11 13 15 17 19 21 23 26 29 30 31
((2x + 1) + ((x - ((x mod 5) mod 3)) div 3))
A097911: 1 3 5 8
A073608: 1 3 5 8 10 12
A193714: 1 3 5 8 10 12 14 16 19 21 24 26 28 31 33 36
((2x + 1) + (((1 + (x * ((1 + (x div 2)) mod 3))) div 2) mod 2))
A285260: 1 4 5 8 9 11 14 15 17 20 21 23 25 28 29 32
(2x + ((2 * (((x2 + 4x) div 2) div 3)) div 3))
A163516: 0 2 5 8 11 14 18 22 26 30 35 40 45 50 56 61
(2x + ((((x2 + ~x) div 8) + (x div 3)) div 2))
A050502: 0 2 4 6 9 11 14 17 20 24 27 30 34 37 41 45
(2x + ((((~x + (x2 div 4)) div 2) - (x div 3)) div 2))
A278451: 0 1 3 5 7 9 11 14 17 19 22 25 28 31 34 37
((2x + 2) - (((1 + (x * ((1 + (x div 2)) mod 3))) div 2) mod 2))
A285259: 2 3 6 7 10 12 13 16 18 19 22 24 26 27 30 31
(2x + ((x + ((3 * (2 - ((x div 2) div 3))) div 2)) div 2))
A231407: 1 4 6
A234373: 1 4 6 9 11 14 15 18 20 23
A189756: 1 4 6 9 11 14 15 18 20 23 25 28 30 32 35 37
(3x + ((1 - ((x + 1) mod ~7)) div 3))
A140398: 2 5 7 10 13 15 18 23 26 28 31 34 36 39 44 47
(1 + ((2x3 + 6x2 + 6x + 4) div 3) - (x div 2))
A076857: 2 7 18 43 83
(((((x + 1) * (x + (x div 3))) div 2) div 5) + (x div 2))
A227800: 0 0 1 2 4 5 8 10 13 16 19 21 26 29 34 39
((4x + 1) + ((x2 div (2x + 5)) + (x div 2)))
A313616: 1 5 10 14 20 24 30 34 40 44 50 54 59 64 69 74
((3 * (x - (2 * (~1 + (2 * (~2x + (x div 2))))))) - (x div 2))
A171141: 6 33 47 74 88 115 129 156 170 197 211 238 252 279 293 320
(2x - ((x div 2) + ((~2 + (((~x + 2) * (x div 2)) div 2)) div 3)))
A027440: 1 3 4 6 8 10 12
A092137: 1 3 4 6 8 10 12 15 17 20 23 26 29 32 36 39
((x + 1) + ((((x div 2) - ((x div 4) div ~2)) mod 2) + (x div 2)))
A286727: 1 2 5 6 8 9 10 11 14 15 16 17 19 20 23 24
(((2x mod (~1 + (2 * (x mod 7)))) div 2) * (x div 2))
A194659: 0 0 0 0 0 0 0 0 0 0 0 0 18 12 0 0
(((~x + 1) div (2 + (x div (1 + (x mod (2 * (1 + (x mod 2)))))))) + (x div 2))
A308308: 0 0 0 0 1 1 2 1 3 2 4 2 5 4 6 4
((2x + 2) + (x div 2) - ((x mod (~2 - (x div 3))) mod 2))
A201363: 2 3 7
A328982: 2 3 7 9 12 13 17 18 22 23 27 29 32 33 37 39
(1 + (x div (x - (3 * ((x + ~1) div 5)))) - (x mod 2))
A066451: 1 1 2 1 2 1 3 1 2 1 2 2 3 1 2 1
(1 + ((((2x + 8) mod (1 + (x div 2))) mod 3) + (x mod 2)))
A193335: 1 2 1 2 2 2 1 4 2 3 2 2 2 2 2 2
((x + 1) + (x mod 2) - (x div (x - (3 * (((x + ~1) div 2) div 2)))))
A288774: 1 2 2 4 4 5 5 8 8 8 9 11 11
((1 + ((1 + ((x2 + 2x) mod (1 + (x div 3)))) div 2)) * (x mod 2))
A339012: 0 1 0 2 0 2 0 1 0 3 0 3 0 1 0 3
(1 + (((x2 + 2) mod (1 + ((x + 1) div 3))) mod 2) - (x mod 2))
A036475: 1 0 1 1 1 0 1 0 1 1 1 1 2 1 1 1
(1 + ((2 * ((x + 1) - ((~x + (x mod 4)) div 3))) + (x mod 2)))
A285569: 3 6 7 10 15 18 19 22 25 28 29 32 35 38 39 42
((1 + (x div (2 + ((x div 2) div (1 + (2 * ((x div 2) mod 2))))))) * (x mod 2))
A183063: 0 1 0 2 0 2 0 3 0 2 0 4 0 2 0 4
((1 + ((1 + ((((x + ~1) div 3) * (x div 2)) div 2)) div 2)) * (x mod 2))
A035376: 0 1 0 1 0 2 0 3 0 3 0 5 0 7 0 8
((1 - ((0 - (x2 div 4)) div 7)) * (x mod 2))
A035455: 0 1 0 2 0 2 0 3 0 4 0 6 0 7 0 9
(1 + (((x * (((x + 1) div 2) mod 4)) div 3) mod 2) - (x mod 2))
A087116: 1 0 1 0 1 1 1 0 1 1 2 1 1 1 1 0
(1 + ((x mod (1 - (x div (~2 - (x mod 3))))) mod 2) - (x mod 2))
A203949: 1 1 1 0 2 0 1 1 1 1 1 1 2 1 1 0
(1 + ((2 * (((2 * (~2 + (x div 2))) mod (1 + (x div 2))) div 2)) + (x mod 2)))
A080916: 1 2 1 2 1 2 3 4 5 6 1 2 1 2 3 4
(2x div ((5 * (8 - (x div 2))) - (x mod 2)))
A326634: 0 0 0 0 0 0 0 0 0 0 1 1 2 2 5 7
(((1 + (x2 div (x + 16))) mod 3) * (x mod 2))
A208575: 0 1 0 1 0 2 0 0 0 1 0 2 0 0 0 2
(((x mod (1 + ((x + 1) mod (1 + (x div (2 + (x mod 2))))))) div 2) + (x mod 2))
A290399: 0 1 0 1 0 1 1 1 1 1 2 1 2 2 3 1
((((~x + 1) div (1 + ((1 - (x div 3)) mod 3))) mod 2) + (x mod 2))
A105242: 0 1 1 1 1 1 0 1 1 1 1 2 1 1 1 2
((x div (2 + ((x div 2) div (1 + (((x div 2) mod 3) mod 2))))) + (x mod 2))
A324117: 0 1 1 2 1 2 1 2 2 3 1 2 1 2 2 4
(((x mod (~1 + (2 * (x div (x + ~16))))) mod 2) + (x mod 2))
A084927: 0 1 1 1 0 2 0 1 1 2 0 2 0 2 1 1
((((x3 mod (2x + 3)) div 3) mod 2) + (x mod 2))
A001822: 0 1 0 1 1 1 0 2 0 2 1 1 0 2 1 2
((2 * ((((x2 + ~x) div 4) mod 4) div 3)) + (x mod 2))
A221167: 0 1 0 1 2 1 2 1 0 1 0 3 0 3 0 1
((((x2 div (3 + (x div 2))) mod (x + 3)) mod 2) + (x mod 2))
A037135: 0 1 1 1 1 2 0 1 1 2 0 2 1 1 0 1
((2 * (((2x + 1) mod (1 + (2 * (x mod 4)))) mod 2)) + (x mod 2))
A319148: 0 1 0 1 0 1 2 3 0 3 2 1 0 1 0 3
((2 * (((1 + (x * (x + (x div 2)))) div 5) mod 2)) + (x mod 2))
A246960: 0 1 2 1 2 3 2 1 2 3 0 3 2 3 2 1
((x div (2 + (x div (2 + (((x + 1) div 2) mod 5))))) + (x mod 2))
A109129: 0 1 1 2 1 2 2 3 2 2 1 3 2 3 2 4
((x div (2 + (x div (2 + (2x mod (1 + (x mod 4))))))) + (x mod 2))
A124768: 0 1 1 2 1 2 1 3 1 2 2 3 1 2 2 4
((x div (2 + (x div (2 + ((~x + 1) mod (1 + (x mod 4))))))) + (x mod 2))
A319841-A305079: 0 1 1 2 1 2 1 3 1 2 1 3 1 2 2 4
((((1 + (((x + 2) * (2x div 3)) div 2)) div 2) mod 2) + (x mod 2))
A101665: 0 1 1 2 1 2 0 2 1 2 0 2 0 1 0 2
((2 * ((((1 - (x mod 4)) mod (x + 1)) mod 3) mod 2)) + (x mod 2))
A080468: 0 1 0 1 2 1 0 1 2 1 2 3 2 1 0 1
((x div (4 + ((x2 + 2x) mod 12))) + (x mod 2))
A059451: 0 1 0 1 1 1 1 2 0 2 2 1 3 2 1 3
((x div (2 + (x div (2 + ((x2 + 2x) mod 6))))) + (x mod 2))
A071575: 0 1 1 2 1 3 1 3 2 4 1 4 1 4 2 4
((x div (2 + ((x + 1) div (2 + (x mod (2 + ((x div 2) mod 2))))))) + (x mod 2))
A026904: 0 1 1 1 1 2 1 2 1 2 2 3 1 3 2 2
((23 * (x2 div 4)) + (x mod 2))
A195058: 0 1 23 47 92 139 207 277 368 461 575 691 828 967 1127 1289
(49x2 + 20x + 2)
A157368: 2 71 238 503 866 1327 1886 2543 3298 4151 5102 6151 7298 8543 9886 11327
(((3x3 + 7x2 + 4x) div 3) - (x2 div 2))
A213492: 0 4 18 48 98 178 290 442 640 890 1196 1568 2008 2524 3122 3808
((3x + 2) + (((3 - (x div 2)) mod (2x + 1)) mod 2))
A284882: 2 5 8 11 15 18 20 23 26 29 33 36 38 41 45 48
compr(\x.(~1 + ((x + 1) mod (1 + ((x div 2) div (1 + ((x div 2) mod 3)))))),x)
A067570: 0 1 2 3 4 5 7
A014122: 0 1 2 3 4 5 7 8 9 10 11 13 15 17 19 23
((2x + 1) - ((x + 2) mod (1 + (x div (3 + (x div 4))))))
A167384: 1 3 5 6 9 10 13 14 17 18 21 22 23 27 28 29
(x + (x mod (1 + ((3 * ((x + 1) div 2)) mod (1 + (x div 3))))))
A246594: 0 1 2 3 4 6 6 7 8 10 12 13 12 14 14 15
compr(\x.((~x + 1) mod (1 + (x mod (1 + ((2x + ~1) mod (1 + (x div 2))))))),x)
A067570: 0 1 2 3 4 5 7
A071163: 0 1 2 3 4 5 7 8 9 10 12 13 17 18 21 22
compr(\x.(x mod (1 + (x mod (1 + ((2x2 + 2) mod (1 + (x div 2))))))),x)
A221178: 0 1 2 3 4 6 7 8 10 12 15 16 18 20 22 24
compr(\x.(~1 + (x div (~1 + (2 * (x div (1 + (x mod 9))))))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A032345-A023765: 0 1 2 3 4 5 6 7 8 9 10 18 19 20 27 28
compr(\x.(1 - (x mod (1 + ((x + (x div 4)) mod (1 + ((x + 1) div 2)))))),x)
A095033: 1 4 5 6 7 9 11 16 17
compr(\x.(1 - (x2 mod (1 + (2x mod 17)))),x)
A331125: 1 2 3 4 5 6 7 8 9 11 13 14 15 19 20 23
compr(\x.(1 - (x mod (1 + ((2 * (x div ~2)) mod 9)))),x)
A050687: 1 2 3 4 5 6 7 10 11 12 13 14 16 19 20 21
compr(\x.(x mod (1 + ((x3 + 4x2) mod 9))),x)
A278996: 0 3 5 6 8 9 12 14 15 18 21 23 24 27 30 32
(64x3 + 24x2 + 3x)
A165220: 0 91 614 1953 4492 8615 14706 23149 34328 48627 66430 88121 114084 144703 180362 221445
compr(\x.(1 - (x mod (1 + (((x + 2) + (x div 3)) mod 5)))),x)
A322546: 1 2 3 4 5 7 8 9 11 13 17 19 23
(x2 div ((x + 1) + (((x2 + 2x) div 2) mod (3 + (x mod 2)))))
A075795: 0 0 1 1 3 3 5 4 6 7 9 8 11 11 12 11
compr(\x.(1 + (x2 mod (1 - (3 * (x mod 9))))),x)
A167211: 1 2 3 4 5 6 7 8 11 13 15 16 17 19 21 23
compr(\x.((x2 + ~2) mod 73),x)
A159007: 32 41 105 114 178 187 251 260 324 333 397 406 470 479 543 552
((x + 1) + ((2 * ((x + ~1) + (2 div (1 + (x div 4))))) div 3))
A284015: 1 3 5 6 7 9 11 12 13 15 17 18 20 22 23 25
compr(\x.((x5 + 1) mod 11),x)
A028735: 2 6 7 8 10 13 17 18 19 21
A267541: 2 6 7 8 10 13 17 18 19 21 24 28 29 30 32 35
compr(\x.((x mod 10) - (x mod 11)),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A032865-A009995: 0 1 2 3 4 5 6 7 8 9 10 20 21 30 31 32
compr(\x.((~x5 + 1) mod 11),x)
A095028: 1 3 4 5 9
A267755: 1 3 4 5 9 12 14 15 16 20 23 25 26 27 31 34
compr(\x.(12 - (x div (1 + (x mod 12)))),x)
A297276-A296749: 12 24 25 36 37 38 48 49 50 51 60 61 62 63 64 72
compr(\x.(1 - (x mod (1 + (((~x2 + 2x) - (x div 2)) mod (1 + (x div 2)))))),x)
A146968: 4 5 7
A196004: 4 5 7 9 10 11 13 15 16 17 18 19 21 22 23 24
((x + 1) + ((6 * ((2 * (x div 2)) div 3)) mod (x + 1)))
A064764: 1 2 3 4 6 6 12 12 12 12 18 18 24 24 24 24
compr(\x.(1 - (x mod (2 - (x mod (~1 - (2 * ((x + ~1) mod 3))))))),x)
A286758: 1 2 3 5 7 8 11 12 13 14 15 17 18 19 20 21
(x + (7 * ((x + 1) - ((((x + 1) div 2) div 2) div 2))))
A136768: 7 15 23 31 39 47 55 56 64 72 80 88 96 104 112 113
(x + (23 * (x div 7)))
A024640: 0 1 2 3 4 5 6 30 31 32 33 34 35 36 60 61
compr(\x.((x4 + ~x) mod 21),x)
A010383: 0 1 4 7 9 15 16 18
A010403: 0 1 4 7 9 15 16 18 21 22 25 28 30 36 37 39
compr(\x.((x + 1) mod (1 + (2 * ((1 + (x2 div (x + 4))) mod 2)))),x)
A028776: 2 3 5 6 8 10 11 12 13 14 15 17 19 20 21 23
compr(\x.(1 - (x mod (1 + ((x div 2) mod (4 + ((x div 2) mod 3)))))),x)
A154660: 3 4 5 6 7 8
A026421: 3 4 5 6 7 8 9 10 11 13 14 16 17 19 22 23
((x + 1) + (8 * (2 div (6 - (x div 3)))))
A252490-A032981: 1 2 3 4 5 6 7 8 9 10 11 12 21 22 23 32
compr(\x.(2 - ((x + 1) mod (1 + (4 * (2 - ((x div 3) mod 2)))))),x)
A253239: 1 2 3 6 7 11 12 13 14 16 17 19 20 21 22 23
(x + ((x3 + ~x2) div 65))
A175869: 0 1 2 3 4 6 8 11 14 18 23 29 36 44 53 63
compr(\x.(2 - ((2x + 1) mod (1 + (8 * ((x div 2) mod 2))))),x)
A062837: 2 3 6 7 10 11 14 15 19 23 26 30 34 35 38 39
((x + 1) + (2 * (2 - ((x - (2 * ((x div 2) mod 2))) mod 8))))
A004446: 5 4 7 6 1 0 3 2 13 12 15 14 9 8 11 10
compr(\x.(1 + (x mod 15) - (x mod 8)),x)
A297285-A296758: 15 30 31 45 46 47 60 61 62 63 75 76 77 78 79 90
(~x + (9 * ((x + 1) - (x mod 10))))
A061601: 9 8 7 6 5 4 3 2 1 0 89 88 87 86 85 84
(x + ((x * (2 + ((2 * (x div 2)) div 3))) div 9))
A179180: 0 1 2 3 5 6 8 10 11 13 15 17 20 21 23 25
(x + (31 * (x div 9)))
A024652: 0 1 2 3 4 5 6 7 8 40 41 42 43 44 45 46
(x + (((1 + (x div 5)) div 2) * (1 + (x div 8))))
A345914: 0 1 2 3 4 6 7 8 10 11 12 13 14 15 16 19
compr(\x.(1 - (x mod (1 + ((3x + 1) mod (2 + (x div 4)))))),x)
A028736: 5 7 10 11 14 15 17 19 20 21 22
compr(\x.(2 - (x mod ((x + ~2) + (2x mod (3 + (x div 4)))))),x)
A104523: 6 9 10 12 14 15 16 17 19 20 22 23 24 25 26 27
(x + (5 * (1 + ((3 * (x div 5)) div 2))))
A174138: 5 6 7 8 9 15 16 17 18 19 30 31 32 33 34 40
(x + (5 * (((x3 + 3x2 + 2x) div 2) div 3)))
A092185: 0 6 22 53 104 180 286 427 608 834 1110 1441 1832 2288 2814 3415
(x + ((13 * (1 + (x div 2))) div 5))
A201363: 2 3 7
A287675: 2 3 7 8 11 12 16 17 21 22 25 26 30 31 34 35
(x + ((2 + ((x div 2) div 7)) * (1 + (x div 4))))
A169606: 2 3 4 5 8 9 10 11 14 15 16 17 20 21 26 27
compr(\x.((x - ((2x + 2) mod 13)) mod 3),x)
A098019: 1 4 8 11 12 15 18 19 22 26 29 33 36 40 43 47
compr(\x.(2 - ((x - (2x mod 13)) mod 3)),x)
A191105: 1 4 8 11 15 18 22 25 26 29 32 33 36 40 43 47
(x + (((x2 + 1) - ((~x + ((x div 2) mod 2)) div 3)) div 3))
A024204: 0 2 4 6 10 14 19 24 30 37 44 53 61 71 81 92
(x + (((x + 1) - (2 * ((((~x + 2) div 2) div 3) mod 2))) mod 3))
A191672: 1 3 2 5 4 6 8 7 9 10 12 11 13 15 14 17
(x + (3 * (2x - (2x mod 17))))
A024654: 0 1 2 3 4 5 6 7 8 60 61 62 63 64 65 66
compr(\x.(1 - ((x - ((x div 4) mod (1 + (x mod 4)))) mod 3)),x)
A175416: 1 2 4 5 6 8 10 14 16 17 18 19 20 21 22 23
(x + (3 * ((x + 1) div (8 - ((x + 2) div 3)))))
A069811: 0 1 2 3 4 8 9 10 11 15 16 20 21 25 29 30
(x + (((x2 + ~x) div (6 - (x div 3))) div 3))
A074715: 0 1 2 3 4 6 8 10 12 17 20
(x + ((((x + 1) mod (2 * (2 + (x mod 2)))) + (x div 3)) div 3))
A322407: 0 1 3 4 4 5 7 8 9 11 12 12 13 15 16 18
(x + (((1 + (((x + 1) div 2) div 2)) div 2) + ((1 + (x div 2)) div 3)))
A039098: 0 1 2 4 6 7 8 9 10 11 13 15 16 17 18 19
(x + (((2x + 1) + ((~x + 2) mod (2 + (x div 4)))) div 3))
A083028: 0 2 3 5 7 8 11 12 14 15 17 19 20 23 24 26
(x + ((2 * (1 + ((x + ((x div 4) mod 2)) div 3))) div 3))
A039184: 0 1 2 4 5 7 8 9 10 11 12 13 15 16 18 19
(x + (6 * ((x + 1) - ((x + 1) mod ~7))))
A133897: 42 43 44 45 46 47 48 91 92 93 94 95 96 97 140 141
compr(\x.((2 + (x mod (1 + ((~x2 + 2) mod 8)))) mod 3),x)
A161153: 1 3 4 5 7 9 11 13 15 16 17 18 19 21 22 23
compr(\x.(((x + ~1) * ((x2 + ~x) div 2)) mod 18),x)
A230240: 0 1 4 7 9 13 16 19 25 27 28 31 36 37 40 43
(x + ((((x - ((x + ~1) mod 3)) * (x div 3)) div 2) div 3))
A067570: 0 1 2 3 4 5 7
A228234: 0 1 2 3 4 5 7 9 10 12 15 16 18 21 22 25
((x + 1) - ((x + 1) mod ((2 * (2 - ((x div 2) div ~2))) div 3)))
A161764: 1 2 2 4 4 6 6 8 8 10 9 12 12 12 12 16
(x + ((2 * (2 + (x2 div (3 * (2 + (x div 2)))))) div 3))
A239161: 1 2 3 5 6 7 8 10 11 13 14 15 17 19 20 21
compr(\x.(((x - (((~x + 2) + ((x div 2) div 3)) div 2)) div 2) mod 3),x)
A189464: 1 5 9 13 14 17 18 22 26 30 31 34 35 39 43 47
(x + (6 * (2 + (2 * (2 - (2 div (1 + (x div 4))))))))
A272270: 12 13 14 15 28 29 30 31 44 45 46 47 48 49 50 51
(x + ((4 * (2 + ((x - ((x div 2) div 3)) div 2))) div 3))
A188078: 2 3 6 7 9 10 11 13 14 17 18 20 21 22 24 25
(x + ((2 * (2x div (4 + (x div 8)))) div 3))
A039191: 0 1 2 3 5 6 8 9 10 11 12 13 14 16 17 19
(x + ((2 * ((x + 2) - (((x + ~1) mod (2 + (x div 2))) div 2))) div 3))
A284752: 1 3 4 5 7 9 11 13 14 15 17 19 20 21 23 25
compr(\x.((x - (x2 mod (x + 14))) mod 3),x)
A080722: 0 1 3 4 7 8 9 10 13 16 19 20 21 22 23 24
(x + (3 * (((((1 - (x div 2)) div 3) * (x div 2)) div 2) div 2)))
A025481: 0 1 2 3 1 2 3 4 5 6 1 2 3 4 2 3
compr(\x.((x div (1 + (x mod 12))) mod 12),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A023793: 0 1 2 3 4 5 6 7 8 9 10 11 12 24 25 36
(x + ((2 * ((x + 2) + ((x * (x div 2)) div 5))) div 3))
A057057: 1 3 4 6 8 11 13 15 18 21 24 27 30 33 37 40
(x + ((2 * ((x + 2) + (x div (2 + (x div (2 + (x mod 2))))))) div 3))
A284658: 1 3 4 7 8 10 12 13 15 17 18 21 22 24 25 27
(x + (((x + 1) div 7) + ((2 * (x div 2)) div 3)))
A230044: 0 1 2 3 5 6 9 10 11 12 14 15 17 19 20 21
(x + (3 * (((x div (1 + ((~x + 1) mod 3))) mod 2) - (x mod 2))))
A222251: 0 1 2 3 4 5 9 7 8 6 10 11 12 13 14 15
(x + (((~x + ~2) - (x div 3)) mod 3) - (x mod 3))
A288119: 1 0 2 3 5 4 8 7 6 10 9 11 12 14 13 17
((x + 1) + (((x2 + x + 1) + ((x * (x div 2)) div 4)) div 2))
A294481: 1 3 6 10 16 22 30 39 49 60 72 85 100 115 132 149
(~x + ((1 + (3 * (x + (x div 2))) - (x mod 2)) * (1 + (x div 2))))
A266956: 1 2 18 21 53 58 106 113 177 186 266 277 373 386 498 513
((~x + 1) + compr(\x.((x + ~1) mod (1 + ((x mod (2 + (x div 3))) div 2))),x))
A035430: 1 1 1 1 1 1 2 2 3 3 3 3 4 5 6 7
(x + ((1 + (x mod (2 * (1 + (x mod 12))))) mod (x + 1)))
A103303: 0 1 2 3 4 5 6 7 8 9
A344452: 0 1 2 3 4 5 6 7 8 9 10 11 13 15 17 23
(~x + ((x + 1) * (1 + (((~x2 + 2) mod (3 + (x div 2))) mod 2))))
A089028: 1 3 1 5 6 1 1 9 10 11 1 13 1 1 1 17
((x2 + x) + ((x + ((x3 + 2x) div 3)) div (x + 2)))
A088207: 0 2 7 14 24 37 52 70 90 113 139 167 198 232 268 307
compr(\x.(((x + 1) mod (1 + ((x2 + ~x) mod 9))) mod 2),x)
A169655: 0 1 2 3 5 8 9 10 11 12 13 14 15 17 18 19
(x + ((1 + (((x3 + x2) div 2) div (x + 5))) div 2))
A194201: 0 1 2 4 6 9 12 15 19 23 28 34 40 46 53 60
compr(\x.(((x div 2) div (1 + (((x * (x div 2)) div 3) mod 3))) mod 2),x)
A274231: 0 1 3 4 5 8 9 10 12 13 14 15 16 17 20 24
compr(\x.(((x3 + ~1) mod 19) mod 2),x)
A010381: 0 1 4 5 6 7 9 11 16 17
A010399: 0 1 4 5 6 7 9 11 16 17 19 20 23 24 25 26
compr(\x.((x - ((4x + 1) mod 11)) mod 2),x)
A026316: 1 4 7 8 10 11 13 14 16 17 20 23 26 29 30 32
(x + (2 * (1 + ((x * (1 + (x div 2))) div (x - ((~1 + (x div 2)) div 2))))))
A284370: 2 3 8 9 12 13 16 17 20 21 26 27 30 31 36 37
(x + (((((x + 1) - ((x div 2) mod 2)) div 2) * (1 + ((x + 1) div 2))) div 2))
A102282: 0 2 3 4 7 11 12 14
((x + 2) + (x div (3 + (((x + (x div 4)) div 3) mod 2))))
A340608: 2 3 4 5 7 8 10 11 12 13 15 16 17 18 19 22
(x + ((((x mod (2 + (x div 2))) div 2) * (1 + (((x + 1) div 2) div 2))) div 2))
A174788: 0 1 2 3 4 5 6 8 9 10 11 15 16 17 18 22
compr(\x.(1 - (x mod (2 + (x div (1 + (8 * (x mod 4))))))),x)
A173001: 1 3 4 5 7 8 11 12 13 15 16 17 19 20 21 22
compr(\x.(1 - (x mod (2 + (x mod (7 - (x div 4)))))),x)
A322030: 1 2 3 4 5 7 8 9 11 13 14 16 17 19 23 25
compr(\x.((1 + (x div (2 + (x mod (2 + (x div (2 * (2 - (x mod 2))))))))) mod 2),x)
A060863: 2 3 4 5 6 7 9 11 12 13 15 17 18 19 21 22
(x + ((5 * (4 + ((x2 + 2) div 3))) div 2))
A335016: 10 13 17 20 29
(x + ((1 + (((x + 2) * ((x + 1) - ((x div 2) div ~2))) div 2)) div 2))
A004131: 1 3 6 9 13 17 24 30 36 42
compr(\x.(1 - (x mod (2 + (x mod (3 * (1 + ((~x + 1) mod 3))))))),x)
A316465: 1 2 3 4 5 7 8 9 10 11 13 16 17 19 21 22
(x + ((3 * (x div (~x + 19))) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A246422: 0 1 2 3 4 5 6 7 8 9 11 12 13 16 17 19
(x + ((3 * (2 - ((~2x + 2) div 9))) div 2))
A179872: 3 4 6 7 8 9 12 13 14 15 16 18 19 20 21 24
compr(\x.(1 - (x mod (2 + ((x - ((x + ~1) div 5)) mod 3)))),x)
A242417: 1 2 3 4 5 6 7 8 9 11 13 16 17 19 21 23
(x + ((x - ((~1 + (((2x + ~4) mod (x + 2)) div 2)) div 3)) div 2))
A257047: 0 2 3 4 6 7 9 11 12 13 15 16 18 19 20 22
compr(\x.(1 - (x mod (2 + ((1 + ((x div 3) * (x div 2))) mod 3)))),x)
A193622: 1 2 3 5 7 10
A122428: 1 2 3 5 7 10 11 13 14 15 17 19 20 21 23 25
((3x + 4) - ((((x + ~2) mod (1 + (x div 2))) mod 3) mod 2))
A104280: 4 7 10 12 16 19 22 24 27 31 34 37 40 42 45 49
(x + ((((x2 + x) div 8) + ((x + 1) div 3)) div 2))
A156625: 0 1 2 4 5 7 9 11 14 16 18 21 23 26 29 32
(x + (2 * ((x - (2 * ((x div 5) mod 3))) div 3)))
A192225: 0 1 2 5
A039044: 0 1 2 5 6 7 8 9 12 13 14 15 16 19 20 25
(x + ((((x * (1 - ((~x2 + 2x) div 3))) div 2) div 3) div 2))
A175842: 0 1 2 3 5 7 10 14 19 25 33 42 53 66 80 97
compr(\x.(1 - ((x2 + 2x + 8) mod (2 + (x div 3)))),x)
A081606: 1 3 4 5 7 9 10 11 12 13 14 15 16 17 19 21
(x + (((x + 1) * (x - (2 * ((x + (x div 4)) div ~2)))) div 2))
A026353: 0 4 8 17 29 38 55 67 89 114 131 161 194 216 254 279
(x + (2 * ((1 + ((x * (x div 4)) div 7)) div 2)))
A175585: 0 1 2 3 4 5 6 9 10 11 12 15 18 19 20 21
(~x + (4 * (2x - ((x - ((~x + 2) div 2)) div 5))))
A188319: 4 7 14 21 24 31 38 41 48 55 62 65 72 79 82 89
(x + ((2 - (((2 - ((x + ~1) div 2)) * (x div 5)) div 2)) div 2))
A247397: 1 2 3 4 5 6 7 8 9 10 12 13
A306424: 1 2 3 4 5 6 7 8 9 10 12 13 14 16 17 20
(x + (2 * ((x + ~2) - ((~2x3 + 6x2 + ~4x) div 3))))
A030441: ~4 ~1 2 13 40 91 174 297 468 695 986 1349 1792 2323 2950 3681
(x + (((3 * (2 - ((~x + ((x div 2) div 3)) div 2))) div 2) div 2))
A225647: 1 3 4 6 7
A122409: 1 3 4 6 7 8 9 10 12 13 15 16 17 19 20 21
compr(\x.(1 - (2x mod (4 + ((x + (x div 3)) div 3)))),x)
A286053: 1 3 4 5 8 9 10 11 12 13 14 16 17 19 20 21
(x + (((((x + 1) * (x2 div (x + 2))) + (x div 3)) div 2) div 2))
A194178: 0 1 2 4 6 9 13 17 22 27 32 38 45 52 60 68
(x + ((((((x + ~1) mod (2 + (x div 2))) div 2) * (1 + (x div 2))) div 2) div 2))
A007298: 0 1 2 3 4 5 6 7 8 10 11 12 13 16 18 19
(~x + ((((2 * (1 + (x div 2))) - (x div 3)) * ((x + 1) div 2)) div 2))
A126167: 0 0 0 0 1 2 3 5 8 8 12
((x + 1) - (x mod (2 * (4 + ((x div 2) div 7)))))
A290624: 1 1 1 1 1 1 1 1 9 9 9 9 9 9 11 11
compr(\x.(((2 + (x div (1 + ((x + ~1) mod (2 + (x div 4)))))) div 2) mod 2),x)
A159559: 3 5 6 7 8 11 12 14 15 17 18 19 20 21 22 23
(x + ((x - ((x - (x div (2 + ((x div 2) mod 5)))) div 2)) div 2))
A138083: 0 1 2 4 5 6
A081694: 0 1 2 4 5 6 8 9 10 11 14 15 16 17 18 19
(x + (((x - ((x div 2) mod 2)) div 3) + ((((x + 1) div 2) div 2) div 2)))
A203076: 0 1 2 3 5 6 7 10 11 13 14 15 17 18 19 21
(x + (2 * ((((1 + (((x + 2) * ((x + 1) div 2)) div 2)) div 2) div 2) div 2)))
A026808: 0 1 2 3 4 7 8 11 12 15 16 21 22 25 28 31
(x + (2 * (((2 - (((x div 2) div 3) * ((x + ~1) div 2))) div 2) div 2)))
A308973-A269757: 0 1 2 3 4 5 6 5 6 7 8 9 8 7 8 9
(x + (8 * ((x mod (x - ((x + ~1) mod 8))) div 2)))
A103303: 0 1 2 3 4 5 6 7 8 9
A280657-A119246: 0 1 2 3 4 5 6 7 8 9 10 19 20 29 30 39
((8x2 + 8x) div (x + 32))
A006463: 0 0 1 2 4 6 8 11 14 17 20 24 28 32 36 40
compr(\x.(1 - (x mod (2 + ((((x2 div 2) mod (x + 4)) div 2) mod 2)))),x)
A277334-A091377: 1 2 3 5 7 9 11 13 15 17 19 21 23 25 29 31
(x + (62 * (x div 8)))
A024649: 0 1 2 3 4 5 6 7 70 71 72 73 74 75 76 77
(~x + (2 * ((2x + 4) - ((~x + ((x div 2) div ~2)) div 2))))
A095097: 8 13 18 21 26 29 34 39 42 47 52 55 60 63 68 73
compr(\x.(2 - (x mod (2 + (x mod (4 * (1 + (x mod (2 + (x mod 2))))))))),x)
A235991: 2 3 5 6 7 10 11 13 14 17 18 19 22 23 26 27
(x + (41 * (x div 8)))
A237344: 0 1 2 3 4 5 6 7 49 50 51 52 53 54 55 56
compr(\x.(2 + ((x + ~1) mod 9) - (x mod 8)),x)
A297266-A297140-A296707: 10 11 12 13 14 15 19 20 21 22 23 28 29 30 31 37
(x + (((5x2 + 4x) div 2) div (x + 6)))
A325946: 0 1 3 6 8 11 14 17 20 23 26 30 33 36 39 43
(x + (2 * ((((1 - (x div 5)) mod 3) + (x div 2)) div 2)))
A161674: 0 1 4 5 6 7 8 9 12 13 16 17 20 21 22 23
((2x + ~1) + ((1 - ((x - ((x div 2) div 3)) div 2)) mod 4))
A039022: 0 2 3 5 10 12 14 15 17 18 20 21 23 25 30 32
compr(\x.(2 + (((x + ~1) div 2) mod 4) - (x mod 10)),x)
A174876: 2 3 4 5 6 7 8 9 14 15 16 17 18 19 25 26
compr(\x.(((x - (3x div ~7)) div 2) mod 4),x)
A231000: 0 5 6 11 17 22 23 28 33 34 39 45 50 51 56 61
(x + (x2 div (24 - ((x + 2) mod 4))))
A205805: 0 1 2 3 4 6 7 9 10 12 14 16 18 21 22 24
compr(\x.((((~x + 2) - ((x + (x div 3)) div 5)) div 2) mod 2),x)
A191338: 1 2 4 5 8 11 14 17 18 20 21 23 24 27 30 33
(x + (2 * ((x + 2) + ((1 + ((x - ((~x + 2) div 4)) div 2)) div 2))))
A024813: 4 7 12 15 18 23 26 29 34 37 40 45 48 51 54 59
(x8 + x4 + 2x2 + 4x)
A054607: 0 8 288 6672 65840 391320 1681008 5767328 16781472 43053480 100010240 214373808 430002768 815759672 1475827920 2562941760
(x + ((((x + ~1) - (3 * (~x + (x mod 4)))) * (x div 2)) div 2))
A273553: 0 1 2 4 19 21
((x + 2) + (((x div (1 + (2 * (1 + (x mod 3))))) mod 2) + (x div 2)))
A137698: 2 3 5 7 8 9 11 13 15 16 17 19 20 21 23 25
compr(\x.(((x + 1) + ((x + (x div 12)) div 3)) mod 2),x)
A327422: 1 4 7 10 13 14 16 17 19 20 22 23 26 29 32 35
((2x + 2) + ((x + (((~x2 + 2x) mod (1 + (x div 2))) div 2)) div 2))
A189677: 2 4 7 9 12 14 17 19 22 25 28 30 33 35 37 40
(x6 + 6x5 + 9x4 + x3 + ~x2 + 2x)
A215229: 0 18 408 2940 12600 40110 105168 240408 496080 945450 1690920 2870868 4667208 7313670 11104800 16405680
(x + ((1 + (2 * (x + (5 * (1 + (x div 2)))))) * (x div 2)))
A316729: 0 1 27 30 82 87 165 172 276 285 415 426 582 595 777 792
(x + (((2x + 1) + (5 * (1 + (x div 2)))) * (x div 2)))
A218864: 0 1 17 20 52 57 105 112 176 185 265 276 372 385 497 512
(x + (((1 + ((x mod (1 + (4 mod (x + 1)))) div 2)) mod 2) + (x div 2)))
A092289: 1 2 4 5 7 8 10 10 12 14 16 17 18 19 22 23
((x + 20) - (1 mod (8 - (x div 2))))
A018824: 19 20 21 22 23 24 25 26 27 28 29 30 31 32 34 35
compr(\x.(((1 + (x mod (1 + (2 * (x mod 6))))) mod 2) - (x mod 2)),x)
A247459: 1 3 5 7 8 9 10 11 13 15 16 17 19 21 23 25
(x + (((x - ((~x + 2) div (2 - (x div ~4)))) mod 2) + (x mod 2)))
A333470: 1 3 2 4 5 6 7 9 8 11 10 13 12 15 14 16
(2x - ((~12x + 2) * (2x - (x mod 2))))
A298397: 0 12 92 176 376 532 852 1080 1520 1820 2380 2752 3432 3876 4676 5192
((2x + 1) + ((x2 div (8 - (x div 3))) mod 2))
A097911: 1 3 5 8
A189213: 1 3 5 8 9 12 13 15 17 19 21 23 25 27 30 32
((2x + 1) + (((x2 + ~x) div (4 + (x * (x mod 2)))) mod 2))
A206812: 1 3 5 7 10 11 14 16 17 20 21 24 26 28 30 32
(~x + compr(\x.(1 - ((x + ((2x + ~1) div 5)) mod 3)),x))
A102676: 0 0 0 0 0 1 2 3 4 5 5 5 5 5 5 6
(9x7 + 2x2)
A237695: 0 11 1160
(5x5 + 3x3 + ~2x2)
A134632: 0 6 176 1278 5280 15950 39456 84966 165248 297270 502800 809006 1249056 1862718 2696960 3806550
((3x + 2) - ((x mod (2 + ((x div 4) mod 3))) div 2))
A189369: 2 5 8 11 14 16 20 23 26 29 31 34 38 41 44 47
((x2 + 1) + (2 * ((2x + 1) - ((x mod (2 + (x mod 2))) div 2))))
A335753: 3 8 15 24 35 46 63 80
((x2 + 1) + (2 * (x - ((1 + (x2 div 5)) div 2))))
A004630: 1 4 9 14 21 30 41 54 69 84
(x3 div (x2 + 54))
A005358: 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 12
(x3 + (3 * ((3 * ((x2 + x) div 2)) div 2)))
A213485: 0 4 20 54 109 191 309 469 674 930 1246 1628 2079 2605 3215 3915
(x3 + (((x + 2) + (3 * (x div 2))) * ((x + 1) div 2)))
A213498: 0 4 15 43 88 164 267 415 600 844 1135 1499 1920 2428 3003 3679
loop(\(x,i).((x + 2) + loop(\(x,i).loop(\(x,i).(if x <= 0 then i else (x + ~1)),x,0),2,(x + 1))),x,1)
A131437: 1 3 5 7 9 13 15 17 21 29 31 33 37 45 61 63
loop(\(x,i).((if x <= 0 then 0 else 1) - loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)),2,(x + 1))
A114219: 1 0 1 0 1 1 0 1 2 1 0 1 2 3 1 0
(if x <= 0 then 0 else (x - loop(\(x,i).(x - loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0)),x,(x + ~1))))
A261366: 0 1 1 2 1 4 3 4 1 8 7 8 5 10 7 8
loop(\(x,i).(x + loop(\(x,i).2x,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,i),1)),x,1)
A288349: 1 2 4 5 7 11 12 14 18 26 27 29 33 41 57 58
loop(\(x,i).loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,i,1))),i,x),x,1)
A203305: 1 2 48 64512 20808990720 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 + loop(\(x,i).(if x <= 0 then (x + ~1) else loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)),2,x))
A057945: 0 1 2 1 2 3 1 2 3 2 1 2 3 2 3 1
loop(\(x,i).(x * i),x,loop(\(x,i).loop(\(x,i).(~1 + (x * i)),x,1),(x + ~1),(if x <= 0 then 1 else x)))
A122685: 1 1 ~2 6 0 120 0 5040 0 362880 0 39916800 0 6227020800 0 1307674368000
(if x <= 0 then 1 else (0 - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + (if (x + ~1) <= 0 then x else i)))),x,x)))
A321391-A256140-A244003-A118344: 1 1 0 1 1 0 1 2 1 0 1 3 2 1 0 1
(if (x mod 7) <= 0 then loop(\(x,i).(2x + 2),x,(if x <= 0 then 1 else 0)) else 0)
A144855: 1 0 0 0 0 0 0 254 0 0 0 0 0
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).5x,(1 + i),x),i,1)),(x + 1),0)
A178188: 25 3150 1956275 6105471900 95373537112525 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x + ~1) <= 0 then x else (if (x mod 2) <= 0 then 1 else (if ((x + 1) mod 8) <= 0 then 2 else 0)))
A073068: 0 1 1 0 1 0 1 2 1 0 1 0 1 0 1 2
loop(\(x,i).~x,x,(loop(\(x,i).2x,x,1) - loop(\(x,i).(3x + 2),x,0)))
A083321: 1 0 ~4 18 ~64 210 ~664 2058 ~6304 19170 ~58024 175098 ~527344 1586130 ~4766584 14316138
loop(\(x,i).(x + loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),(~1 + i),1)),x,0)
A277178: 0 1 7 37 177 807 3579 15591 67071 285861 1209641 5089517 21314453 88918353 369734553 1533115953
loop(\(x,i).(x + loop(\(x,i).(loop(\(x,i).3x,i,1) + (x * i)),(~1 + i),1)),x,0)
A295519: 0 1 5 22 100 493 2701 16678 116704 923473 8204077 81069166 882762292 10503611245 135576241957 1886597854894
loop(\(x,i).(x + i),compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x),0)
A030005: 0 1 3 10 15 28 36 55 91 105 153 190 210 253 325 406
loop(\(x,i).(loop(\(x,i).(loop(\(x,i).(x * i),(~1 + i),1) + (x * i)),i,0) - (x * i)),x,0)
A092692: 0 1 1 8 18 184 660 8448 42000 648576 4142880 74972160 586776960 12174658560 113020427520 2643856588800
loop(\(x,i).x2,1,(1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))
A088377: 1 4 9 4 25 4 49 4 9 4 121 4 169 4 9 4
loop(\(x,i).x2,2,(1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))
A088379: 1 16 81 16 625 16 2401 16 81 16 14641 16 28561 16 81 16
loop(\(x,i).2x,x,(1 + (loop(\(x,i).3x,x,1) + loop(\(x,i).2x,x,1))))
A074533: 3 12 56 288 1568 8832 50816 296448 1745408 10340352 61515776 366993408 2193563648 13127811072 78632615936 471258759168
(1 + (loop(\(x,i).(x2 + x),1,loop(\(x,i).(if x <= 0 then i else (x div 2)),x,0)) mod (x + 1)))
A131247: 1 1 1 1 3 1 1 5 3 1 1 7 7 3 1 1
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).4x,i,1))),(x + ~1),1)
A028666: 1 1 12 2880 11612160 758041804800 794088208701849600 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 div (1 + loop(\(x,i).x2,1,(1 + loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)))))
A167194: 1 2 1 1 2 1 0 1 2 1 0 0 1 2 1 0
((x + 1) div (1 + (2 * (if x <= 0 then 0 else (1 + loop(\(x,i).(if x <= 0 then i else (x div 2)),x,0))))))
A202451: 1 0 1 0 1 2 0 0 1 3 0 0 1 2 5 0
(1 + (loop(\(x,i).2x,x,(if x <= 0 then 1 else (3 + loop(\(x,i).2x,x,2)))) div 2))
A036562: 1 8 23 77 281 1073 4193 16577 65921 262913 1050113 4197377 16783361 67121153 268460033 1073790977
(if (x mod 2) <= 0 then ((1 + (if (x mod 4) <= 0 then 4 else 1)) * (if x <= 0 then 1 else 2)) else 1)
A010132: 5 1 4 1 10 1 4 1 10 1 4 1 10 1 4 1
(if (x mod 2) <= 0 then (2 * ((if (x mod 4) <= 0 then 4 else 1) * (if x <= 0 then 1 else 2))) else 1)
A010156: 8 1 4 1 16 1 4 1 16 1 4 1 16 1 4 1
(~1 + (2 * loop(\(x,i).(x * (2 + i)),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1)))
A105060: 1 1 5 1 5 23 1 5 23 119 1 5 23 119 719 1
(loop(\(x,i).x2,1,(1 + loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x))) mod 5)
A290457: 1 1 0 1 1 0 1 4 1 0 1 4 4 1 0 1
loop(\(x,i).loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 2 else 0)),x,(x + 2)),(x + 4),1)
A273906-A268031-A226108-A167847-A120533-A108871: 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71
(~1 + loop(\(x,i).4x,(if x <= 0 then 1 else (loop(\(x,i).2x,x,2) - (x mod 2))),2))
A134722: 7 127 131071 2147483647 4611686018427387903
((1 + (if (2 - loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)) <= 0 then x else 2)) div 3)
A099573: 1 1 1 1 1 2 1 1 3 3 1 1 4 4 5 1
(loop(\(x,i).loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 2 else 0)),i,(x + 2)),x,1) div 3)
A144769-A073518: 0 1 1 2 3 4 5 6 7 9 10 12 13 14 15 17
((2 + (if x <= 0 then 0 else loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x + 2)))) div 3)
A085199: 0 1 0 2 0 3 0 0 0 4 0 5 0 0 0 6
((if x <= 0 then 1 else (2x - loop(\(x,i).(~1 + (if x <= 0 then (2 * i) else x)),x,2))) div 3)
A229878: 0 0 1 0 1 2
A220660: 0 0 1 0 1 2 3 4 5 0 1 2 3 4 5 6
(3 + loop(\(x,i).(if x <= 0 then 0 else (1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2)))),2,x))
A189822: 3 6 7 8 9 12 15 16 17 18 19 20 21 22 23 24
(~1 + loop(\(x,i).(2x + ~4),(if x <= 0 then 0 else 3),loop(\(x,i).(2x + 2),x,2)))
A036564: 1 19 83 211 467 979 2003 4051 8147 16339 32723 65491 131027 262099 524243 1048531
loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,(~1 + loop(\(x,i).2x,x,2)))
A213246-A059990: 1 1 7 5 31 7 127 85 511 341 2047 455 8191 5461 32767 21845
loop(\(x,i).(1 + loop(\(x,i).2x,x,loop(\(x,i).x2,x,3))),1,(2x + 1))
A182374: 19 52489 59296646043258913 4611686018427387903 4611686018427387903
((if (x + ~2) <= 0 then 1 else 2) div (if x <= 0 then 2 else (loop(\(x,i).2x,x,2) mod (2x + 1))))
A336352: 0 1 0 1 0 0 0 2 1 0 0 1 0 0 0 1
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).4x,i,1))),2x,1)
A144547: 1 2880 758041804800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (if (x + ~2) <= 0 then x else loop(\(x,i).(x * (i - (2 * (i * i)))),2x,1)))
A273729: 1 1 2 7484400
(if (x mod 2) <= 0 then 1 else loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),(x div 2),1))
A046212: 1 1 1 6 1 30 1 140 1 630 1 2772 1 12012 1 51480
loop(\(x,i).2x,x,loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x div 2),1))
A249308: 1 2 8 16 96 192 1280 2560 17920 35840 258048 516096 3784704 7569408 56229888 112459776
(if x <= 0 then (x mod 2) else ((x + ~1) + (if (8 mod (if x <= 0 then 1 else x)) <= 0 then x else 0)))
A153151: 0 1 3 2 7 4 5 6 15 8 9 10 11 12 13 14
(~1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).(x + (if x <= 0 then (1 + i) else 0)),x,(~x + 1))))
A131782: 1 5 1 11 5 1 19 11 5 1 29 19 11 5 1 41
loop(\(x,i).(1 + (x * loop(\(x,i).(1 + (x * (if (x + ~1) <= 0 then 1 else (x + ~1)))),i,1))),x,1)
A188545: 1 3 10
A334211: 1 3 10 71 3054 5518579 18009568007498 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) * loop(\(x,i).((x2 + 1) - loop(\(x,i).2x,x,2)),2,x)),x,1)
A323725: 1 6 57960 4611686018427387903
loop(\(x,i).(x div 2),x,((x + 1) + (if x <= 0 then 0 else loop(\(x,i).(2x + (x div 2)),x,2))))
A003860: 1 3 3 4 5
A104803: 1 3 3 4 5 6 7 9 11 14 17 22 27 34 43 54
loop(\(x,i).x2,1,loop(\(x,i).(~2x + ((2 * (if x <= 0 then 1 else x)) div (1 + i))),x,1))
A018224: 1 1 4 9 36 100 400 1225 4900 15876 63504 213444 853776 2944656 11778624 41409225
loop(\(x,i).2x,x,(loop(\(x,i).(3x + ~1),x,1) - loop(\(x,i).2x,x,1)))
A228701: 0 0 4 48 400 2880 19264 123648 774400 4776960 29185024 177205248 1071616000 6463242240 38913654784 234018766848
loop(\(x,i).4x,(x + ~1),loop(\(x,i).(x2 + 2x),1,loop(\(x,i).2x,x,1)))
A233163: 3 8 96 1280 18432 278528 4325376 68157440 1082130432 17246978048 275414777856 4402341478400 70403103916032 1126174784749568 18016597532737536 288247968337756160
(loop(\(x,i).(x2 + x),1,loop(\(x,i).3x,x,1)) + loop(\(x,i).2x,x,1))
A074531: 3 14 94 764 6658 59324 532234 4785284 43053538 387440684 3486844474 31381238804 282430072018 2541867430844 22876797254314 205891146476324
(loop(\(x,i).3x,x,1) - loop(\(x,i).(~x2 + x),1,loop(\(x,i).2x,x,1)))
A083319: 1 5 21 83 321 1235 4761 18443 71841 281315 1106601 4369403 17304561 68694995 273202041 1088057963
loop(\(x,i).x3,1,loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1))
A002897: 1 8 216 8000 343000 16003008 788889024 40424237568 2131746903000 114933031928000 6306605327953216 351047164190381568 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 3),x,loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1))
A024503: 1 0 0 0 0 1 1 1 1 2 3 3 5 6 8 10
loop(\(x,i).2x,x2,loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1))
A111637: 1 4 96 10240 4587520 8455716864 63496796504064 1932044240141942784 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(~x + loop(\(x,i).(x + (x div (~1 + (2 * i)))),x,i)),x,1),1,(x + 1))
A073359: 1 3 6 9 13 19 24 31 39 45 54 66 73 90 103 111
loop(\(x,i).(1 - loop(\(x,i).(x - (if x <= 0 then 0 else (i - (i div 3)))),x,x)),1,(x + 1))
A128118: 1 2 1 2 1 3 2 1 4 3 2 1 4 3 2 1
(loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,i,1))),x,1) div (x + 1))
A258745: 1 1 8 336 64512 53329920 184308203520 2621599886868480 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) * (if x <= 0 then 1 else (2 * (2 + loop(\(x,i).loop(\(x,i).(x2 + 2),x,2),x,0)))))
A175720-A173605: 1 16 240 4611686018427387903
loop(\(x,i).(if x <= 0 then 1 else (8x + (if (2 - i) <= 0 then x else 1))),x,(x + 1))
A081044: 1 17 225 2673 29889 321489 3365793 34543665 349156737 3486784401 34480423521 338218086897 3295011258945 31914537622353 307565765227809 2951106226689969
compr(\x.loop(\(x,i).((if x <= 0 then 2 else loop(\(x,i).(x div (2 - (x mod 2))),x,x)) div 2),2,x),(x + 1))
A018900: 3 5 6 9 10 12 17 18 20 24 33 34 36 40 48 65
(if x <= 0 then 1 else loop(\(x,i).loop(\(x,i).(x * (1 + (2 * (1 + i)))),(x + ~2),x),1,(x + ~1)))
A288950: 1 0 1 2 15 140 1575 20790 315315 5405400 103378275 2182430250 50414138775 1264936572900 34258698849375 996137551158750
((x + ~1) + loop(\(x,i).((x + 1) - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)),2,x))
A217575: 2 6 7 12 13 14 20 21 22 23 30 31 32 33 34 42
loop(\(x,i).(x + loop(\(x,i).x2,1,loop(\(x,i).(x + (i * i * i)),(1 + i),0))),x,1)
A085439: 1 82 1378 11378 62003 256484 871140 2550756 6651381 15802006 34776742 71791798 140366759 261917384 469277384 811379400
loop(\(x,i).(x * (1 + loop(\(x,i).(if x <= 0 then 1 else x3),(~1 + i),4))),x,1)
A292687: 1 5 325 85197125 4611686018427387903 4611686018427387903
(loop(\(x,i).~x,x,(1 + loop(\(x,i).2x,x,1))) + loop(\(x,i).3x,x,1))
A135399: 3 0 14 18 98 210 794 2058 6818 19170 60074 175098 535538 1586130 4799354 14316138
(loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).3x,x,1))
A074526: 3 9 29 99 353 1299 4889 18699 72353 282339 1108649 4373499 17312753 68711379 273234809 1088123499
(loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1)) - loop(\(x,i).3x,x,1))
A083324: 1 3 11 45 191 813 3431 14325 59231 242973 990551 4019205 16249871 65522733 263668871 1059425685
(loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,x,1)) - loop(\(x,i).3x,x,1))
A137786: ~1 ~1 3 29 159 749 3303 14069 58719 241949 988503 4015109 16241679 65506349 263636103 1059360149
(if x <= 0 then 0 else loop(\(x,i).(2 + (i div 3)),loop(\(x,i).(x div (1 + (x mod 2))),x,x),1))
A163507: 0 1 2 1 3 2 4 1 4 3 5 2 6 4 6 1
loop(\(x,i).(loop(\(x,i).10x,i,1) + (if (~2 + i) <= 0 then 1 else x)),x,1)
A290111: 1 11 101 1101 11101 111101 1111101 11111101 111111101 1111111101 11111111101 111111111101 1111111111101 11111111111101 111111111111101 1111111111111101
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).4x,(2 * i),1))),x,1)
A028678: 1 240 15667200 262787825664000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).x2,1,loop(\(x,i).x3,1,(1 + (2 * i))))),x,1)
A259322: 1 730 16355 134004 665445 2437006 7263815 18654440 42792009 89837890 175604011 323639900 567780525 955201014 1550024335 2437528016
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).3x,(2 * i),1))),x,1)
A028671: 1 72 466560 247608990720 4611686018427387903 4611686018427387903 4611686018427387903
(2 - loop(\(x,i).((~x2 + ~x) + loop(\(x,i).(~x + (if x <= 0 then 2 else 1)),x,3)),x,1))
A001543: 1 6 11 71 4691 21982031 483209576974811 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(x + loop(\(x,i).3x,i,(1 + i))),i,(x + 1))),x,1)
A163941: 1 9 52 246 1039 4083 15274 55152 193957 668397 2266816 7589418 25143355 82571751 269173078 871958244
loop(\(x,i).(x + loop(\(x,i).(x + (if (x2 div (1 + i)) <= 0 then 2x else 0)),x,1)),x,1)
A338130: 1 4 7 10 19 28 37 46 55 64 73 82 109 136 163 190
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).6x,i,1))),x,1)
A028668: 1 30 37800 1755432000 2946176634240000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).8x,i,1))),x,1)
A028670: 1 56 225792 59074412544 990862210530017280 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(4x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A269576: 1 7 259 45325 35398825 119187843775 1692109818073675 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(2 * (x + (2 * (2x div (if i <= 0 then 1 else i))))),i,1)),x,1)
A211386: 1 11 71 351 1471 5503 18943 61183 187903 553983 1579007 4374527 11829247 31326207 81461247 208470015
loop(\(x,i).(x * loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A126679: 1 6 150 13500 4063500 3925341000 11874156525000 110785880378250000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x2 + x),1,(~1 + loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)))
A103217: 1 6 1 15 6 1 28 15 6 1 45 28 15 6 1 66
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).5x,i,1))),x,1)
A028667: 1 20 12000 186000000 72540000000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).(x + (i * i * i * i)),(1 + i),x),i,1)),x,1)
A101090: 1 19 135 605 2054 5778 14178 31350 63855 121693 219505 378027 625820 1001300 1555092 2352732
loop(\(x,i).(x + loop(\(x,i).(x + loop(\(x,i).(x + (((1 + i) * i) div 2)),i,1)),i,1)),x,1)
A027658: 1 4 12 31 71 147 280 498 837 1342 2068 3081 4459 6293 8688 11764
loop(\(x,i).(~x + loop(\(x,i).(x + (6x div (if i <= 0 then 1 else i))),i,1)),x,1)
A001769: 1 6 22 62 148 314 610 1106 1897 3108 4900 7476 11088 16044 22716 31548
(1 + compr(\x.loop(\(x,i).((if x <= 0 then 2 else loop(\(x,i).(x div (2 - (x mod 2))),x,x)) div 2),2,x),x))
A231407: 1 4 6
A340161: 1 4 6 7 10 11 13 18 19 21 25 34 35 37 41 49
loop(\(x,i).(x + (if x <= 0 then 1 else (2x - (if (x mod (3 + i)) <= 0 then 1 else x)))),x,1)
A222011: 1 2 4 8
A018627: 1 2 4 8 16 47 94 188 376 752
loop(\(x,i).(i * i),(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,x)),1)
A123726: 1 1 4 1 9 1 4 1 16 1 4 1 9 1 4 1
loop(\(x,i).(x + loop(\(x,i).(if (x mod 2) <= 0 then 1 else (4x2 + 4x)),1,i)),x,1)
A271062: 1 9 10 58 59 179 180 404 405 765 766 1294 1295 2023 2024 2984
(if x <= 0 then 0 else loop(\(x,i).(~x + (10x div (if i <= 0 then 1 else i))),x,1))
A175673: 0 9 36 84 126 126 84 36 9 1
loop(\(x,i).(x + ((x * loop(\(x,i).(2x2 + ~2),2,2)) div (if i <= 0 then 1 else i))),x,1)
A017734: 1 71 2556 62196 1150626 17259390 218618940 2404808340 23446881315 205811513765 1646492110120 12124169174520 82848489359220 528955739755020 3173734438530120 17984495151670680
(loop(\(x,i).(4x + 1),(x div 2),1) * loop(\(x,i).loop(\(x,i).2x,i,x),x,1))
A181175: 1 2 40 320 21504 688128 178257920 22817013760 23433341566976 11997870882291712 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) - loop(\(x,i).(x + loop(\(x,i).(x * (i - (x div (if i <= 0 then 1 else i)))),2,i)),x,1))
A060446: 0 1 8 39 136 377 888 1855 3536 6273 10504 16775 25752 38233 55160 77631
loop(\(x,i).(x * i),x,loop(\(x,i).(loop(\(x,i).(x * (~1 + (2 * i))),i,1) + (x * i)),x,1))
A034405: 1 2 14 216 5976 262800 16945200 1511395200 178458940800 26959810348800 5071861902240000 1162523770531200000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(loop(\(x,i).(loop(\(x,i).~2x,i,1) + (x * i)),i,1) + (x * i)),x,1)
A087981: 1 0 2 4 24 128 880 6816 60032 589312 6384384 75630080 972387328 13483769856 200571078656 3185540657152
loop(\(x,i).(loop(\(x,i).(loop(\(x,i).3x,i,1) + (x * i)),i,1) + (x * i)),x,1)
A081924: 1 5 27 159 1029 7353 58095 506691 4860297 51023277 583097859 7215769575 96210083853 1375803720801 21012273704151 341449444105227
(loop(\(x,i).(loop(\(x,i).(x * i),i,1) + (x * (1 + i))),x,0) + loop(\(x,i).(x * i),x,1))
A121555: 1 2 7 32 178 1164 8748 74304 704016 7362720 84255840 1047358080 14054739840 202514376960 3118666924800 51119166873600
loop(\(x,i).loop(\(x,i).loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),i,x),i,x),x,1)
A055746: 1 1 2 20 2800 16464000 12778698240000 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 2 else (if (x mod 3) <= 0 then 1 else (if ((x + 1) mod 5) <= 0 then 0 else 2)))
A076451: 2 2 2 1 0 2 1 2 2 1 2 2 1 2 0 1
(2 * loop(\(x,i).loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 2 else 0)),x,(x + 2)),(x + ~1),1))
A077017: 2 2 6 10 14 22 26 34 38 46 58 62 74 82 86 94
((loop(\(x,i).2x,x,loop(\(x,i).(2x + 2),x,1)) + (if (x + ~1) <= 0 then 2 else 1)) div 2)
A269716: 1 5 20 88 368 1504 6080 24448 98048 392704 1571840 6289408 25161728 100655104 402636800 1610579968
(if (x mod 2) <= 0 then (if (x mod 3) <= 0 then (8 * (if x <= 0 then 1 else 2)) else 1) else 2)
A010149: 8 2 1 2 1 2 16 2 1 2 1 2 16 2 1 2
loop(\(x,i).i,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),((x div 5) mod 2))
A229878: 0 0 1 0 1 2
A329221: 0 0 1 0 1 2 1 1 2 3 0 1 2 3 4 1
(loop(\(x,i).2x,(0 - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)),3) div 2)
A131031-A130452: 1 3 1 6 3 1 12 6 3 1 24 12 6 3 1 48
(if x <= 0 then 1 else loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),(2x + ~1),2))
A166337: 1 12 280 5544 102960 1847560 32449872 561632400 9617286240 163352435400 2756930576400 46290177201840 773942488394400 12893881856650704 214163336821292320 3547937446945842720
(if (x mod 2) <= 0 then loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x div 2),1) else 2)
A081668: 1 2 2 2 6 2 20 2 70 2 252 2 924 2 3432 2
(1 - ((1 + loop(\(x,i).(1 + loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)),2,x)) div 2))
A264391-A116598: 1 0 1 1 0 1 1 1 0 1 2 1 1 0 1 2
((loop(\(x,i).(x2 + x),1,loop(\(x,i).(if x <= 0 then i else (x div 2)),x,0)) mod (x + 1)) div 2)
A319082: 0 0 0 0 1 0 0 2 1 0 0 3 3 1 0 0
loop(\(x,i).(1 - loop(\(x,i).(x - (if x <= 0 then 0 else (i - (x mod 2)))),x,x)),1,(2x + 2))
A122196-A023117: 1 2 3 1 4 2 5 3 1 6 4 2 7 5 3 1
(0 - loop(\(x,i).loop(\(x,i).(x - (if x <= 0 then 0 else (i - (x mod 2)))),x,x),1,(2x + 2)))
A082375-A025644-A022332: 0 1 2 0 3 1 4 2 0 5 3 1 6 4 2 0
loop(\(x,i).loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),x,(2x + 1)),1,((x + 1) div 2))
A110560: 1 3 3 5 5 7 7 1 1 11 11 13 13 1 1 17
(x + ((if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1) + (if x <= 0 then 1 else 2)))
A231407: 1 4 6
A159475: 1 4 6 6 10 8 14 10 12 12 22 14 26 16 18 18
(loop(\(x,i).2x,(1 - loop(\(x,i).(x - (if (~x + 2) <= 0 then (2 + i) else 0)),x,x)),1) div 2)
A140649: 1 0 2 1 0 4 2 1 0 8 4 2 1 0 16 8
(if x <= 0 then 1 else (2 * ((loop(\(x,i).(2x * i),x,1) + (if (x + ~2) <= 0 then x else 1)) div 2)))
A052576: 1 2 10 48 384 3840 46080 645120 10321920 185794560 3715891200 81749606400 1961990553600 51011754393600 1428329123020800 42849873690624000
(loop(\(x,i).2x,(x div 2),(2 + (if (x mod 2) <= 0 then ((if x <= 0 then 2 else x) div 2) else 2))) div 2)
A211227: 1 2 3 4 8 8 20 16 48 32 112 64 256 128 576 256
loop(\(x,i).x2,2,(loop(\(x,i).4x,x,loop(\(x,i).x2,(x div 2),2)) div 2))
A278142: 1 256 1048576 268435456 17592186044416 4503599627370496 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 3),x,(if x <= 0 then 1 else loop(\(x,i).x3,(x + ~1),4)))
A152007: 1 1 7 9709 222399981598543 4611686018427387903
((2x + (if x <= 0 then 1 else (x - loop(\(x,i).(x - (if x <= 0 then 2 else (~2 + i))),x,x)))) div 2)
A260466: 0 0 1 3 5 7 10 12 14 16 20 22 24 26 28 32
((loop(\(x,i).x2,1,(2 - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x))) div 2) div 2)
A128177: 1 2 1 4 2 1 6 4 2 1 9 6 4 2 1 12
(if x2 <= 0 then 2 else loop(\(x,i).x2,x,(1 - (2 * loop(\(x,i).(x * i),x2,2)))))
A120314: 2 9 81450625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 + (if x <= 0 then 0 else (x + (if (x mod 2) <= 0 then (1 + (if (x mod 3) <= 0 then 2 else 0)) else 0))))
A126762-A082048: 2 3 5 5 7 7 11 9 11 11 13 13 17 15 17 17
(loop(\(x,i).(x + loop(\(x,i).(x + (if (i mod 2) <= 0 then i else 2)),i,1)),(x + 1),~x) div 2)
A083462: 1 3 6 11
A003453: 1 3 6 11 17 26 36 50 65 85 106 133 161 196 232 276
(if x <= 0 then 1 else (2 * compr(\x.((x + 1) mod (1 + loop(\(x,i).(if x <= 0 then i else (x + ~1)),x,0))),x)))
A087136: 1 2 4 6 10 12 14 22 26 28 30 46 54 58 60 62
(loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,1) mod (2 * (if x <= 0 then 1 else x)))
A053214: 1 0 2 2 6 2 0 2 6 2 16 2 4 2 20 0
loop(\(x,i).((((x div 2) - loop(\(x,i).~x,x,2)) div 2) + loop(\(x,i).2x,i,1)),x,2)
A226308: 2 1 5 10 17 37 74 145 293 586 1169 2341 4682 9361 18725 37450
loop(\(x,i).(x div 2),x,loop(\(x,i).(4x + (if (i mod 3) <= 0 then 2 else 1)),x,2))
A206927: 2 4 9 18 37 75 150 300 601 1202 2405 4811 9622 19244 38489 76978
((if (x mod 2) <= 0 then loop(\(x,i).(2x + (x div 2)),x,2) else 0) div loop(\(x,i).2x,x,2))
A079977: 1 0 1 0 2 0 3 0 5 0 8 0 13 0 21 0
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),(if x <= 0 then 0 else (x + 2)))
A179522: 3 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67
(loop(\(x,i).(2x + 4),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1) div (x + 2))
A229878: 0 0 1 0 1 2
A166373: 0 0 1 0 1 2 0 0 1 3 0 0 1 2 4 0
((~x + ~2) + loop(\(x,i).((x + 1) - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)),2,x))
A128076: 1 3 2 5 4 3 7 6 5 4 9 8 7 6 5 11
loop(\(x,i).(x + loop(\(x,i).(x - (if x <= 0 then 1 else (2 * (1 + (i div 2))))),x,x)),1,2x)
A025643-A025642: 0 1 0 2 1 3 0 2 4 1 3 5 0 2 4 6
(loop(\(x,i).2x,x,(if (x mod 2) <= 0 then 1 else loop(\(x,i).(2x + 2),x,0))) - (x mod 2))
A266516: 1 3 4 111 16 1983 64 32511 256 523263 1024 8384511 4096 134201343 16384 2147418111
(loop(\(x,i).(x2 + 2x),1,loop(\(x,i).2x,x,1)) - loop(\(x,i).3x,x,2))
A092880: 1 2 6 26 126 602 2766 12266 52926 223802 932526 3844106 15722526 63936602 258902286 1045109546
loop(\(x,i).(~x + loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 2 else 0)),x,(2x + 1))),x,2)
A062042: 2 3 4 7 10 13 16 21 22 25 28 31 36 37 42 47
(x - (loop(\(x,i).(x2 + x),1,loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)) div 2))
A133082: 0 1 2 2 4 5 3 6 8 9 4 8 11 13 14 5
(2 * loop(\(x,i).x2,1,loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,x)))
A254408: 0 8 288 7200 156800 3175200 61471872 1154305152 21201523200 382952512800 6826955907200 120427502203008 2105988385632768 36562298361680000 630861905459520000 4611686018427387903
(if x <= 0 then 1 else loop(\(x,i).(x + loop(\(x,i).(2 * (2x - (x div (1 + i)))),i,2)),x,2))
A054114: 1 8 28 98 350 1274 4706 17576 66196 250952 956384 3660540 14061140 54177740 209295260 810375650
loop(\(x,i).2x,compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x),2)
A061285: 2 4 8 32 64 256 512 2048 16384 32768 262144 1048576 2097152 8388608 67108864 536870912
(2 + loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (if ((x + ~1) mod 3) <= 0 then 1 else x)),x,x))
A177980: 2 3 3 5 3 7 5 3 3 11 7 13 5 3 3 17
(x - ((0 - (if (x + ~1) <= 0 then 1 else loop(\(x,i).(x - (if x <= 0 then 1 else i)),x,x))) div 2))
A076918: 1 2 2 3 3 4 5 4 5 6 7 6 7 8 9 10
((x + 1) div loop(\(x,i).(x - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),i,x)),x,2))
A164058: 0 2 1 1 0 0 1 0 0 1 0 0 0 0 1 1
loop(\(x,i).2x,x,(x + (if (x + ~1) <= 0 then 1 else loop(\(x,i).((2x + 2) + i),x,0))))
A273335: 1 4 48 224 960 3968 16128 65024 261120 1046528 4190208 16769024 67092480 268402688 1073676288 4294836224
compr(\x.(~1 + (loop(\(x,i).2x,x,1) mod (1 + loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,2)))),x)
A233524: 0 1 2 4 5 8
A095031: 0 1 2 4 5 8 10
A191986: 0 1 2 4 5 8 10 11 16 20 22 23 32 40 44 46
loop(\(x,i).2x,x,(if x <= 0 then 1 else (if (x mod 6) <= 0 then (x div 3) else x)))
A131135: 1 2 8 24 64 160 128 896 2048 4608 10240 22528 16384 106496 229376 491520
(if x <= 0 then 1 else loop(\(x,i).((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),(x div 3),x))
A103775: 1 1 2 0 1 0 3 0 0 0 0 0 0 0 0 0
((x + 1) + (2 * loop(\(x,i).(x - (if x <= 0 then 1 else (if (x mod (1 + i)) <= 0 then 2 else 1))),x,x)))
A345668: 1 2 1 4 3 6 5 4 3 10 9 12 11 10 9 16
(x + (if x <= 0 then 2 else loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then i else 0)),(x div 2),(x + 1))))
A013634: 2 3 5 8 9 12 13 18 19 20 21 24 25 30 31 32
(~x + (if x <= 0 then 2 else loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then i else 0)),(x div 2),(x + 1))))
A013632: 2 1 1 2 1 2 1 4 3 2 1 2 1 4 3 2
compr(\x.(if x <= 0 then 1 else loop(\(x,i).(loop(\(x,i).(2x + 1),x,0) mod (x + 1)),x,(x + ~1))),x)
A176847: 1 3 5 7 11 13 17 19 23 27 29 31 37 41 43 45
(0 - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + (if (x + ~1) <= 0 then x else i)))),x,(x + ~1)))
A332670-A119270: 1 0 1 0 1 1 0 1 2 1 0 1 3 2 1 0
(compr(\x.loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,2x),x) + (if x <= 0 then 1 else x))
A073432: 1 4 8 12 15 17 21 23 26 30 33 35 38 40 44 46
((x + 1) + loop(\(x,i).(x - (if (x - ((if (x mod 2) <= 0 then 1 else i) + i)) <= 0 then 1 else 0)),x,x))
A302245: 1 2 3 5 7 8 11 11 15 15 19 19 23 23 27 27
compr(\x.(1 + loop(\(x,i).(x div (if (x mod 2) <= 0 then ~2 else (if (~x + 2) <= 0 then 2 else 1))),x,x)),x)
A320730: 2 5 6 8 10 11 13 14 17 18 20 21 22 23 24 26
(if (x mod 2) <= 0 then ((if (x mod (1 + (if (x mod 4) <= 0 then 0 else 2))) <= 0 then 2 else x) div 2) else x)
A336898: 1 1 1 3 1 5 1 7 1 9 5 11 1 13 7 15
(1 - loop(\(x,i).(x - (if x <= 0 then 2 else (1 + loop(\(x,i).3x,(2 * i),1)))),x,x))
A262390-A131835: 1 10 11 12 13 14 15 16 17 18 19 100 101 102 103 104
compr(\x.(1 - loop(\(x,i).loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,2x),2,x)),x)
A123998: 1 3 9 15 18 39 48 69 78 99 105 114 135 153 165 168
compr(\x.loop(\(x,i).(if (x + ~1) <= 0 then 1 else (loop(\(x,i).(x div (2 - (x mod 2))),x,x) div 2)),2,x),x)
A136318: 5 9 10 17 18 20 33 34 36 40 65 66 68 72 80 129
(if x <= 0 then 2 else compr(\x.(1 - loop(\(x,i).(0 - (if (x mod (1 + i)) <= 0 then 0 else x)),(x div 2),x)),x))
A086807: 2 5 13 17 29 37 41 53 61
A002313: 2 5 13 17 29 37 41 53 61 73 89 97 101 109 113 137
compr(\x.(if ((x + 2) mod 4) <= 0 then 1 else loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)),x)
A129966: 0 1 3 15 21 28 36 45 55 91 105 120 136 153 171 231
(if (x mod 2) <= 0 then (1 - loop(\(x,i).(10 * (x - (i mod 2))),x,0)) else 0)
A279028: 1 0 101 0 10101 0 1010101 0 101010101 0 10101010101 0 1010101010101 0 101010101010101 0
((x + 1) - (if (x div 2) <= 0 then 2x else (if (x mod 12) <= 0 then 1 else 0)))
A333838: 1 0 3 4 5 6 7 8 9 10 11 12 12 14 15 16
(compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + (if (x + ~3) <= 0 then 1 else 0))
A231408: 1 2 4 6 9
A168434: 1 2 4 6 9 11 15 17 21 27 29 35 39 41 45 51
((if ((1 + (x div 3)) mod 4) <= 0 then 1 else 0) + (if (x mod 3) <= 0 then 1 else 0))
A330166-A081602-A077267: 1 0 0 1 0 0 1 0 0 2 1 1 1 0 0 1
(if (x + ~1) <= 0 then 1 else (if (16 mod (x + 1)) <= 0 then (x div 3) else 0))
A122698: 1 1 0 1 0 0 0 2 0 0 0 0 0 0 0 5
loop(\(x,i).(x + i),(1 + compr(\x.(loop(\(x,i).(x * (1 + (i div 2))),x,1) mod (x + 1)),x)),0)
A324600: 1 10 21 36 45 55 78 105 120 136 171 210 231 253 300 325
loop(\(x,i).4x,x,loop(\(x,i).(10x + 20),(x + 1),0))
A192370: 20 880 35520 1422080 56888320 2275553280 91022213120 3640888852480 145635555409920 5825422221639680 233016888886558720 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(1 - loop(\(x,i).(12x + ~6),(x + 1),0)))
A127861: 49 6241 889249 127938721 18421818529 2652725580961 381992288212129 55006887157191841 4611686018427387903 4611686018427387903
loop(\(x,i).(5x + (if (~1 + (i mod 3)) <= 0 then 2 else 1)),(x + 1),0)
A037570: 2 11 57 287 1436 7182 35912 179561 897807 4489037 22445186 112225932 561129662 2805648311 14028241557 70141207787
loop(\(x,i).(x + loop(\(x,i).(x * (i * i * i * i * i * i)),i,1)),(x + 1),0)
A289946: 1 65 46721 191149697 2986175149697 139317055679149697 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((if (x mod 2) <= 0 then 45 else 1) + (if x <= 0 then 1 else 0))
A267319: 46 1 45 1 45 1 45 1 45 1 45 1 45 1 45 1
(loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + 1),1) + (if x <= 0 then 1 else 0))
A230585: 3 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790
(1 - (if x <= 0 then 1 else (if ((x + 1) mod (1 + (2 * (x mod 5)))) <= 0 then 2 else 0)))
A011621-A011592: 0 1 1 1 1 ~1 1 1 1 1 ~1 ~1 1 ~1 1 ~1
((if x <= 0 then 0 else 1) - (if ((x3 + 1) mod 7) <= 0 then 2 else 0))
A011610: 0 1 1 ~1 1 ~1 ~1 1 1 1 ~1 1 ~1 ~1 1 1
(2 - (if x <= 0 then 1 else (if ((x + 1) mod (1 + (2 * ((~x + 2) mod 3)))) <= 0 then 2 else 0)))
A329491: 1 2 0 2 2 0 2 2 0 0 2 0 2 2 0 2
(if x <= 0 then 0 else (1 - (if (x mod (1 + (4 * (x mod 5)))) <= 0 then 2 else 0)))
A011616: 0 1 1 1 1 ~1 1 1 1 1 ~1 1 1 ~1 1 ~1
(if x <= 0 then 1 else (if (x mod 11) <= 0 then (4x + 2) else 0))
A023934: 1 0 0 0 0 0 0 0 0 0 0 46 0 0 0 0
(if x <= 0 then 1 else (if ((x + 1) mod (2 + ((((~x + 2) div 2) mod (x + 1)) mod 2))) <= 0 then 2 else 0))
A036274: 1 2 0 0 0 2 0 0 0 2 0 2 0 2 2 0
(1 - (if x <= 0 then 1 else (if ((x + 1) mod (2 + (x mod (4 + (x div 2))))) <= 0 then 2 else 0)))
A165596-A011620: 0 1 1 1 1 1 1 ~1 1 1 1 ~1 1 1 ~1 1
(1 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + (if (x mod 2) <= 0 then 2 else 0)))
A014686: 3 2 6 6 12 12 18 18 24 28 32 36 42 42 48 52
loop(\(x,i).(x + (i * i)),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),0)
A262247: 5 14 55 140 506 819 1785 2470 4324 8555 10416 17575 23821 27434 35720 51039
loop(\(x,i).3x,2x,loop(\(x,i).(6x + 2),2x,0))
A165028: 0 126 41958
loop(\(x,i).(x2 + 2x),1,loop(\(x,i).(10x + 6),x,0))
A098209: 0 48 4488 444888 44448888 4444488888 444444888888 44444448888888 4444444488888888 444444444888888888 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + x),1,loop(\(x,i).(10x + 3),x,0))
A181718: 0 12 1122 111222 11112222 1111122222 111111222222 11111112222222 1111111122222222 111111111222222222 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 + 2x),1,loop(\(x,i).(10x + 3),x,0))
A098210: 0 15 1155 111555 11115555 1111155555 111111555555 11111115555555 1111111155555555 111111111555555555 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,x,1) - loop(\(x,i).(11x + ~10),x,0))
A155595: 1 12 124 1338 14656 161082 1771624 19487298 214359136 2357948202 25937425624 285311672658 3138428380816 34522712152122 379749833599624 4177248169448418
loop(\(x,i).(x2 + x + 1),1,loop(\(x,i).(7x + ~6),x,0))
A212156: 1 31 2257 116623 5757601 282424831 13840934257 678220602223 33232913275201 1628413476849631 79792265450186257 3909821042651007823 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).4x,x,1) - loop(\(x,i).(7x + ~6),x,0))
A155618: 1 10 64 406 2656 17830 121744 839926 5830336 40615750 283523824 1981521046 13858064416 96956119270 678491508304 4748635251766
(loop(\(x,i).3x,x,1) - loop(\(x,i).(7x + ~6),x,0))
A155605: 1 9 57 369 2481 17049 118377 825729 5771361 40373289 282534297 1977503889 13841818641 96890604729 678227855817 4747575858849
loop(\(x,i).(~6x + loop(\(x,i).8x,(~1 + i),1)),x,0)
A080921-A053455: 0 1 2 52 200 2896 15392 169792 1078400 10306816 72376832 639480832 4753049600 40201179136 308548739072 2546754076672
loop(\(x,i).6x,(x + ~1),loop(\(x,i).(~1 + (2 * (x + (i mod 2)))),x,0))
A099138: 0 1 6 108 1080 14256 163296 2006208 23794560 287214336 3436494336 41298398208 495217981440 5944792559616 71324450021376 855971764420608
loop(\(x,i).5x,(x + ~1),loop(\(x,i).(~1 + (2 * (x + (i mod 2)))),x,0))
A091903: 0 1 5 75 625 6875 65625 671875 6640625 66796875 666015625 6669921875 66650390625 666748046875 6666259765625 66668701171875
(loop(\(x,i).11x,x,1) - loop(\(x,i).(2x + 1),x,0))
A155622: 1 10 118 1324 14626 161020 1771498 19487044 214358626 2357947180 25937423578 285311668564 3138428372626 34522712135740 379749833566858 4177248169382884
loop(\(x,i).((x + 1) + loop(\(x,i).(x mod 2),(x mod 2),(x div 7))),x,0)
A084689: 0 1 2 3 4 5 6 7 9
A246885: 0 1 2 3 4 5 6 7 9 11 13 15 16 19 20 23
(loop(\(x,i).(3x + ~1),x,0) - loop(\(x,i).(5x + ~1),x,0))
A007798: 0 0 2 18 116 660 3542 18438 94376 478440 2411882 12118458 60769436 304378620 1523487422 7622220078
loop(\(x,i).((x + ~1) + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),i,1)),x,0)
A284968: 0 1 5 18 59 190 618 2047 6908 23703 82488 290499 1033398 3707837 13402681 48760350
((2 * loop(\(x,i).2x,(x div 2),(2 + (x mod 2)))) + loop(\(x,i).(2x + 2),x,0))
A183977: 4 8 14 26 46 86 158 302 574 1118 2174 4286 8446 16766 33278 66302
loop(\(x,i).(if x <= 0 then 1 else (x - ((~2x + 1) div (4 + (x div 4))))),x,0)
A194242: 0 1 2 3 5 7 10 14 18 23 28 33 39 45 51 58
loop(\(x,i).(16x + loop(\(x,i).3x,(~1 + i),1)),x,0)
A180845: 0 1 19 313 5035 80641 1290499 20648713 330381595 5286112081 84577812979 1353245066713 21651921244555 346430740444321 5542891848703459 88686269584038313
(loop(\(x,i).3x,2x,1) - loop(\(x,i).(5x + ~4),x,0))
A155636: 1 13 105 853 7185 62173 547065 4861093 43437345 389373613 3496550025 31429887733 282673677105 2543086531453 22882895970585 205921649672773
(loop(\(x,i).6x,x,1) - loop(\(x,i).(5x + ~4),x,0))
A155633: 1 10 60 340 1920 10900 62280 358060 2070240 12030820 70231800 411625180 2420922960 14281397140 84467679720 500702562700
(loop(\(x,i).8x,x,1) - loop(\(x,i).(5x + ~4),x,0))
A155635: 1 12 88 636 4720 35892 277768 2175276 17167840 136170852 1083507448 8638762716 68963617360 550976517012 4404150026728 35214889666956
loop(\(x,i).(~3x + loop(\(x,i).5x,(~1 + i),1)),x,0)
A079773: 0 1 2 19 68 421 1862 10039 48008 246601 1213322 6125659 30451148 152787181 762341582 3816490879
(loop(\(x,i).10x,x,1) + loop(\(x,i).(3x + 2),x,0))
A155608: 1 12 108 1026 10080 100242 1000728 10002186 100006560 1000019682 10000059048 100000177146 1000000531440 10000001594322 100000004782968 1000000014348906
(loop(\(x,i).10x,x,1) - loop(\(x,i).(3x + 2),x,0))
A155615: 1 8 92 974 9920 99758 999272 9997814 99993440 999980318 9999940952 99999822854 999999468560 9999998405678 99999995217032 999999985651094
(loop(\(x,i).7x,x,1) - loop(\(x,i).(3x + 2),x,0))
A155612: 1 5 41 317 2321 16565 116921 821357 5758241 40333925 282416201 1977149597 13840755761 96887416085 678218289881 4747547161037
(1 - loop(\(x,i).(2x + ~4),compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),0))
A241676: 1 5 29 125 2045 8189 131069 524285 8388605 536870909 2147483645 137438953469 2199023255549 8796093022205 140737488355325 9007199254740989
loop(\(x,i).(2x + (if (x mod (2 + ((((x + 1) div 2) div 2) mod 2))) <= 0 then 1 else 2)),x,0)
A329361: 0 1 4 10 21 43 88 177 356 714 1429 2860 5722 11445 22891 45784
(if (x + ~2) <= 0 then ((x + 1) - (2 * (x mod 2))) else loop(\(x,i).(2x + (i mod 2)),x,0))
A284237: 1 0 3 5 10 21 42 85 170 341 682 1365 2730 5461 10922 21845
loop(\(x,i).(3x + loop(\(x,i).(2x + ((~1 + (2 * i)) * i)),i,0)),x,0)
A285361: 0 1 11 64 282 1071 3729 12310 39296 122773 378279 1154988 3505542 10598107 31957661 96200098
(loop(\(x,i).3x,2x,1) - loop(\(x,i).(5x + 4),x,0))
A155642: 1 5 57 605 5937 55925 515817 4704845 42656097 385467365 3477018777 31332231485 282185395857 2540645125205 22870688939337 205860614516525
(loop(\(x,i).6x,x,1) - loop(\(x,i).(5x + 4),x,0))
A155639: 1 2 12 92 672 4652 31032 201812 1288992 8124572 50700552 313968932 1932641712 11839990892 72260648472 439667406452
(loop(\(x,i).8x,x,1) - loop(\(x,i).(5x + 4),x,0))
A155641: 1 4 40 388 3472 29644 246520 2019028 16386592 132264604 1063976200 8541106468 68475336112 548535110764 4391942995480 35153854510708
loop(\(x,i).2x,(x + ~1),loop(\(x,i).(x + ((((1 + i) * i) div 2) * (1 + i))),x,0))
A084399: 0 2 22 140 680 2800 10304 34944 111360 337920 985600 2782208 7641088
A067057: 0 2 22 140 680 2800 10304 34944 111360 337920 985600 2782208 7641088 20500480 53903360 139264000
loop(\(x,i).(x + loop(\(x,i).(13x2 + ~12x),1,i)),x,0)
A256648: 0 1 29 110 270 535 931 1484 2220 3165 4345 5786 7514 9555 11935 14680
loop(\(x,i).(x + loop(\(x,i).(6x3 + ~5x2),1,i)),x,0)
A172075: 0 1 29 146 450 1075 2191 4004 6756 10725 16225 23606 33254 45591 61075 80200
(~1 + (if x <= 0 then 1 else (if ((x + ~1) mod (1 + (x mod 7))) <= 0 then 2 else 0)))
A103131: 0 1 ~1 ~1 ~1 ~1 ~1 1 ~1 ~1 ~1 1 ~1 ~1 1 1
(~1 + (if x <= 0 then 1 else (if ((x + 1) mod (1 + (2 * ((~x + 1) mod 3)))) <= 0 then 2 else 0)))
A330035: 0 1 ~1 ~1 1 ~1 ~1 1 ~1 ~1 1 ~1 ~1 1 1 ~1
(if x <= 0 then 0 else (1 + (if (x mod 3) <= 0 then (((x * (x mod 2)) div 2) mod 4) else 0)))
A092931: 0 1 1 2 1 1 1 1 1 1 1 1 1 1 1 4
(1 + loop(\(x,i).((2x + 1) * (if ((x div 3) mod 2) <= 0 then 1 else 2x)),x,0))
A018317: 1 2 4 43 86 172
loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),loop(\(x,i).(2x + 1),x,0),1)
A069954: 1 3 35 6435 300540195 916312070471295267 4611686018427387903 4611686018427387903
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),loop(\(x,i).(2x + 1),x,0),1)
A038003: 1 1 5 429 9694845 14544636039226909 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(1 + (x * (1 + (if (x mod (~1 + (2 * i))) <= 0 then 2x else 1)))),x,0))
A222011: 1 2 4 8
A018686: 1 2 4 8 107 214 428 856
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),loop(\(x,i).(2x + 2),x,0),1)
A135759: 1 2 132 2674440 3814986502092304 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(if x <= 0 then 2 else ((4x + ~4) - (x div 4))),x,0))
A307142: 1 3 5 12 39 140
(1 + (loop(\(x,i).2x,(x div 2),(2 + (x mod 2))) + loop(\(x,i).(2x + 4),x,0)))
A159217: 3 8 17 35 69 137 269 533 1053 2093 4157 8285 16509 32957 65789 131453
(1 + ((1 + loop(\(x,i).4x,x,2)) * loop(\(x,i).(3x + 2),x,0)))
A017161: 1 19 265 3355 41041 495859 5964505 71633035 859838881 10319056099 123832690345 1486008529915 17832167873521 213986278134739 2567836397009785 30814041016037995
(~1 + loop(\(x,i).(2x + 4),compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),0))
A241678: ~1 3 27 123 2043 8187 131067 524283 8388603 536870907 2147483643 137438953467 2199023255547 8796093022203 140737488355323 9007199254740987
((if ((x + 1) mod (2 + (x2 mod 5))) <= 0 then 2 else 1) + (if x <= 0 then 0 else 1))
A183024: 1 2 2 2 2 3 2 2 2 2 2 3 2 2 3 3
(loop(\(x,i).10x,x,9) - (if x <= 0 then 0 else 1))
A109002: 9 89 899 8999 89999 899999 8999999 89999999 899999999 8999999999 89999999999 899999999999 8999999999999 89999999999999 899999999999999
loop(\(x,i).((4x * (~1 + (2 * i))) div (1 + i)),(x + ~1),(if x <= 0 then 0 else 1))
A052701: 0 1 2 8 40 224 1344 8448 54912 366080 2489344 17199104 120393728 852017152 6085836800 43818024960
((if (x mod (1 + ((~2x + 2) mod (1 + (x div 2))))) <= 0 then 1 else 2) + (if x <= 0 then 0 else 1))
A196941: 1 2 2 2 2 3 2 2 2 3 2 3 3 3 2 2
((if (x mod (1 + (2 * (((x + ~1) div 2) mod 4)))) <= 0 then 1 else 2) + (if x <= 0 then 0 else 1))
A091322: 1 2 2 2 3 2 3 2 3 2 2 3 2 3 3 3
(((if (x mod (1 + (((x + 1) div 2) div 3))) <= 0 then 2 else x) div 2) + (if x <= 0 then 0 else 1))
A334868-A305979: 1 2 2 2 2 3 2 4 2 5 2 6 2 7 8 2
(1 + loop(\(x,i).(2x div (1 + i)),x,loop(\(x,i).(5x + 4),x,0)))
A088645: 1 5 17 42 84 139 199 249 276 276 251 209 161 115 77 48
(1 + ((x div 2) div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 0))))
A325352-A305438-A260739: 1 1 1 2 1 3 1 4 2 5 1 6 1 7 3 8
(if (~x + 2) <= 0 then (1 + (3 * (if (x mod 10) <= 0 then 0 else 2))) else 1)
A106705: 1 1 7 7 7 7 7 7 7 7 1 7 7 7 7 7
(~1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).(2x2 + 1),(2x + 1),1)))
A219013: 11 523451 4611686018427387903
(~1 + loop(\(x,i).(x2 + x),1,(1 + loop(\(x,i).10x,x,1))))
A171375: 5 131 10301 1003001 100030001 10000300001 1000003000001 100000030000001 10000000300000001 1000000003000000001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).2x,(~1 + compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x)),1))
A283107: 2 5 17 257 1025 16385 65537 1048577 67108865 268435457 17179869185 274877906945 1099511627777 17592186044417 1125899906842625 72057594037927937
loop(\(x,i).2x,(~1 + (loop(\(x,i).(1 + (2 * (x + (i mod 2)))),x,0) div (x + 1))),1)
A255133: 1 1 2 8 64 2048 1048576 68719476736 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).2x2,1,(1 + ((x + 1) * loop(\(x,i).x2,2,3)))))
A157506: 13447 53137 119071 211249 329671 474337 645247 842401 1065799 1315441 1591327 1893457 2221831 2576449 2957311 3364417
(~1 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).10x,(x + 1),1)))
A086695: 89 9899 998999 99989999 9999899999 999998999999 99999989999999 9999999899999999 999999998999999999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((if (x mod 3) <= 0 then 1 else 2) div loop(\(x,i).i,((x + 1) mod 7),1))
A219479: 1 1 0 0 0 0 1 2 1 0 0 0 0 2 2 0
(1 + (x div (3 + ((~1 + loop(\(x,i).(if x <= 0 then i else (x div 2)),x,2)) mod (x + 1)))))
A152977-A048887: 1 1 1 1 2 1 1 2 3 1 1 2 4 5 1 1
((x + 1) div (1 + (if (x + ~1) <= 0 then x else (3 + (if (x mod 3) <= 0 then 0 else 2)))))
A112218: 1 1 0 1 0 1 1 1 1 2 1 2 3 2 2 4
(1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (1 + (((x + 1) div 2) div 2))))
A076110: 1 1 2 1 3 5 1 4 7 10 1 5 9 13 17 1
(~1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (1 + (((x + 1) div 2) div 2))))
A144204: ~1 ~1 0 ~1 1 3 ~1 2 5 8 ~1 3 7 11 15 ~1
(1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (~1 + (((x + 1) div 2) div 2))))
A159798: 1 1 0 1 1 1 1 2 3 4 1 3 5 7 9 1
(1 + (if x <= 0 then 0 else loop(\(x,i).10x,x,9)))
A085952: 1 91 901 9001 90001 900001 9000001 90000001 900000001 9000000001 90000000001 900000000001 9000000000001 90000000000001 900000000000001 9000000000000001
(loop(\(x,i).2x,x,3) - loop(\(x,i).2x,((x + 1) mod 5),1))
A222011: 1 2 4 8
A018422: 1 2 4 8 47 94 188 376
(1 + (loop(\(x,i).(x + (if (~2 + (x div 4)) <= 0 then i else 1)),x,1) div 5))
A087848-A087844: 1 1 1 2 3 4 4 4 4 5 5 5 5 5 6 6
(1 + (loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,x) div 5))
A323228: 1 2 7 22 57 127 253 463 793 1288 2003 3004 4369 6189 8569 11629
(if (x mod 5) <= 0 then (9 * (2 + (if x <= 0 then 0 else 2))) else 1)
A040327: 18 1 1 1 1 36 1 1 1 1 36 1 1 1 1 36
(~1 + ((1 + loop(\(x,i).(4x - (if x <= 0 then 0 else 1)),3,x)) div 3))
A063300: ~1 13 35 56 77 99 120 141 163 184 205 227 248 269 291 312
loop(\(x,i).2x,((loop(\(x,i).(x2 div 3),2,x) div (x + 1)) mod 3),1)
A156074-A051287: 1 1 1 1 2 1 1 2 2 1 1 4 4 4 1 1
(~1 + (6 * (3 + loop(\(x,i).loop(\(x,i).(x2 + x),x,2),x,0))))
A274023: 17 29 269 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(6x + 5))
A016978: 9765625 25937424601 2015993900449 41426511213649 420707233300201 2758547353515625 13422659310152401 52599132235830049 174887470365513049 511116753300641401 1346274334462890625 3255243551009881201
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(6x + 5))
A016980: 244140625 3138428376721 582622237229761 21914624432020321 353814783205469041 3379220508056640625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(12x + 1))
A017542: 1 137858491849 95367431640625 4808584372417849 79792266297612001 713342911662882601 4297625829703557649 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(12x + 1))
A017544: 1 23298085122481 59604644775390625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 2 else (1 + (6 * (x + loop(\(x,i).(x * (2 + i)),(x + ~2),1)))))
A020601: 2 13 19 37 97
(loop(\(x,i).5x,x,1) mod (1 + loop(\(x,i).(x2 + x),2,3)))
A036149: 1 5 25 125 154 142 82 96 9 45 68 26 130 22 110 79
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(6x + 1))
A016931: 1 1977326743 1792160394037 116490258898219 2384185791015625 25408476896404831 177917621779460413 929293739471222707 3909821048582988049 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),3,x) mod 3))
A104232: 1 1 2 1 2 2 3 1 2 2 3 2 3 3 2 1
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(9x + 1))
A017182: 1 10000000000 6131066257801 296196766695424 4808584372417849 42420747482776576 253295162119140625 1152921504606846976 4297625829703557649 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(9x + 1))
A017184: 1 1000000000000 2213314919066161 232218265089212416 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).4x,((x + (loop(\(x,i).2x,x,2) div (x + 1))) div 3),1)
A010099: 1 4 4 16 64 1024 65536 67108864 4398046511104 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(1 + (if (~2 + (x mod (2 + (x mod 3)))) <= 0 then x else 3)))
A093837: 1 4 9 16 25 36 49 64 81 100 121 16 169 196 225 256
(1 + (3 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),x)))
A191107: 1 4 10 13 28 31 37 40 82 85 91 94 109 112 118 121
(1 + (3 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 0 else 2))),x,x),x)))
A259566: 1 4 7 13 16 22 25 40 43 49 52 67 70 76 79 121
(1 + (x div (1 + loop(\(x,i).(x mod 2),(x mod 2),(if (~1 + (x mod 3)) <= 0 then x else 2)))))
A189733: 1 1 1 2 1 6 1 4 3 5 1 12 1 7 5 8
(1 - (x div (~1 - (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))))
A325564-A323888: 1 2 2 3 2 4 2 5 4 6 2 7 2 8 6 9
((2x + 1) div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))
A244149: 1 1 1 3 1 5 1 7 5 9 1 11 1 13 9 15
(1 + loop(\(x,i).(x * i),((((x div 2) * (x div 2)) div 2) + (if x <= 0 then 1 else 2x)),1))
A060371: 2 3 25 721 3628801 479001601 20922789888001 6402373705728001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (10x div (if i <= 0 then 1 else i))),(2x + 1),1)
A196790: 11 286 3003 19448 92378 352716 1144066 3268760 8436285 20030010 44352165 92561040 183579396 348330136 635745396 1121099408
(~1 + loop(\(x,i).2x,x,(~1 + loop(\(x,i).2x,x,2))) - (1 div (2x + ~1)))
A267685: 1 4 27 119 495 2015 8127 32639 130815 523775 2096127 8386559 33550335 134209535 536854527 2147450879
(1 + (loop(\(x,i).6x,x,1) + loop(\(x,i).3x,2x,1)))
A074522: 3 16 118 946 7858 66826 578098 5062906 44726338 397498186 3547250578 31743856666 284606318818 2554926522346 22955156619058 206361317079226
(~1 + (loop(\(x,i).6x,x,1) + loop(\(x,i).3x,2x,1)))
A155647: 1 14 116 944 7856 66824 578096 5062904 44726336 397498184 3547250576 31743856664 284606318816 2554926522344 22955156619056 206361317079224
(1 + (loop(\(x,i).8x,x,1) + loop(\(x,i).3x,2x,1)))
A074525: 3 18 146 1242 10658 91818 793586 6880122 59823938 521638218 4560526226 39970994202 351149013218 3091621642218 27274838966066 241075504183482
(~1 + (loop(\(x,i).8x,x,1) + loop(\(x,i).3x,2x,1)))
A155663: 1 16 144 1240 10656 91816 793584 6880120 59823936 521638216 4560526224 39970994200 351149013216 3091621642216 27274838966064 241075504183480
(1 + (loop(\(x,i).5x,x,1) + loop(\(x,i).3x,2x,1)))
A074519: 3 15 107 855 7187 62175 547067 4861095 43437347 389373615 3496550027 31429887735 282673677107 2543086531455 22882895970587 205921649672775
(~1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).(2x + 2),(x div 2),(1 + (x mod 2)))))
A033622: 1 5 19 41 109 209 505 929 2161 3905 8929 16001 36289 64769 146305 260609
(1 + loop(\(x,i).3x,2x,1) - loop(\(x,i).6x,x,1))
A155652: 1 4 46 514 5266 51274 484786 4503034 41367106 377342794 3426318226 31018262554 280252754146 2528805134314 22798428290866 205420947110074
(1 + (loop(\(x,i).8x,x,1) + loop(\(x,i).6x,x,1)))
A074521: 3 15 101 729 5393 40545 308801 2377089 18456833 144295425 1134208001 8952731649 70896259073 562816507905 4476410675201 35654557073409
(~1 + (loop(\(x,i).8x,x,1) + loop(\(x,i).6x,x,1)))
A155646: 1 13 99 727 5391 40543 308799 2377087 18456831 144295423 1134207999 8952731647 70896259071 562816507903 4476410675199 35654557073407
(1 + loop(\(x,i).8x,x,1) - loop(\(x,i).6x,x,1))
A155651: 1 3 29 297 2801 24993 215489 1817217 15097601 124140033 1013275649 8227137537 66542694401 536695119873 4319682347009 34714187104257
(1 + (loop(\(x,i).5x,x,1) + loop(\(x,i).6x,x,1)))
A074516: 3 12 62 342 1922 10902 62282 358062 2070242 12030822 70231802 411625182 2420922962 14281397142 84467679722 500702562702
(1 + loop(\(x,i).(2 * (x - ((1 - loop(\(x,i).(x2 + ~1),x,2)) div (x + 1)))),x,1))
A101341: 2 5 1597 4611686018427387903
(1 + loop(\(x,i).3x,2x,1) - loop(\(x,i).8x,x,1))
A155666: 1 2 18 218 2466 26282 269298 2685818 26269506 253202762 2413042578 22791125018 213710059746 1992110014442 18478745943858 170706760005818
(1 + (loop(\(x,i).5x,x,1) + loop(\(x,i).8x,x,1)))
A074518: 3 14 90 638 4722 35894 277770 2175278 17167842 136170854 1083507450 8638762718 68963617362 550976517014 4404150026730 35214889666958
(1 + loop(\(x,i).(x3 + 5x2 + 6x),1,loop(\(x,i).4x,x,1)))
A020533: 13 169 5473 283009 17106433 1078990849 68803387393 4399388786689 281496451940353 18014742108438529 1152927002171277313 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).3x,3x,1) + loop(\(x,i).4x,x,1)))
A283716: 3 32 746 19748 531698 14349932 387424586 10460369588 282429602018 7625597747132 205891133143226 5559060570749828 150094635313776338 4052555153086085132 4611686018427387903 4611686018427387903
(~1 + (loop(\(x,i).10x,x,1) + loop(\(x,i).4x,x,1)))
A155621: 1 13 115 1063 10255 101023 1004095 10016383 100065535 1000262143 10001048575 100004194303 1000016777215 10000067108863 100000268435455 1000001073741823
(1 + loop(\(x,i).10x,x,1) - loop(\(x,i).4x,x,1))
A155631: 1 7 85 937 9745 98977 995905 9983617 99934465 999737857 9998951425 99995805697 999983222785 9999932891137 99999731564545 999998926258177
(1 + (loop(\(x,i).7x,x,1) + loop(\(x,i).4x,x,1)))
A074513: 3 12 66 408 2658 17832 121746 839928 5830338 40615752 283523826 1981521048 13858064418 96956119272 678491508306 4748635251768
(1 + loop(\(x,i).7x,x,1) - loop(\(x,i).4x,x,1))
A155628: 1 4 34 280 2146 15784 113554 807160 5699266 40091464 281426674 1973132440 13824509986 96821901544 677954637394 4746487768120
(1 + loop(\(x,i).(x2 + 4x),1,loop(\(x,i).10x,x,1)))
A225810: 6 141 10401 1004001 100040001 10000400001 1000004000001 100000040000001 10000000400000001 1000000004000000001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x div 3),(x + 1),loop(\(x,i).10x,x,1)))
A050624: 1 2 4 13 42 138 458 1525 5081 16936 56451 188168 627226 2090752 6969172 23230574
loop(\(x,i).(x * (i * i)),(1 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x)),1)
A177926: 1 4 576 518400 13168189440000 229442532802560000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * (2 + i)),compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x),1))
A139160: 2 4 61 2521 19958401 3113510401 177843714048001 60822550204416001 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(x * (2 + i)),compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x),1))
A139190: 0 2 59 2519 19958399 3113510399 177843714047999 60822550204415999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).4x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),1))
A139293: 0 3 63 1023 262143 4194303 1073741823 17179869183 4398046511103 18014398509481983 288230376151711743 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (2 * i)),(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1)
A119959: 3 7 21 43 111 157 273 343 507 813 931 1333 1641 1807 2163 2757
(3 + (loop(\(x,i).2x,(x div 2),(2 + (x mod 2))) + loop(\(x,i).2x,x,1)))
A100602: 6 8 11 17
A183979: 6 8 11 17 27 47 83 155 291 563 1091 2147 4227 8387 16643 33155
loop(\(x,i).(x * i),((x + 1) * ((x + 1) - (loop(\(x,i).(x * i),x,1) mod (x + 1)))),1)
A184391: 1 2 6 40320 120 4611686018427387903 5040 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,loop(\(x,i).(10x + ~3),(x + 1),1))
A109344: 49 4489 444889 44448889 4444488889 444444888889 44444448888889 4444444488888889 444444444888888889 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((x + 1) * (1 + loop(\(x,i).(x + (if (x mod (2 + i)) <= 0 then x else 0)),x,4))))
A087737: 6 11 28 37 46 55 120 137 154 171 188 205 222 239 496 529
((x + 1) div loop(\(x,i).2x,((2 + loop(\(x,i).x2,2,3)) mod (x + 1)),1))
A219480: 1 1 0 0 0 0 0 1 2 1 0 0 0 0 0 2
(x div (1 + ((~2 + loop(\(x,i).2x,x,loop(\(x,i).(1 + (x * i)),x,1))) mod (x + 1))))
A300396-A300360-A300356: 0 1 2 1 1 1 2 1 2 1 2 3 1 1 3 1
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(8x + 7))
A017158: 282475249 576650390625 41426511213649 819628286980801 8140406085191601 52599132235830049 253295162119140625 984930291881790849 3255243551009881201 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(8x + 7))
A017160: 13841287201 129746337890625 21914624432020321 787662783788549761 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(4x + 3))
A016847: 177147 1977326743 285311670611 8649755859375 116490258898219 952809757913927 5559060566555523 25408476896404831 96549157373046875 317475837322472439 929293739471222707 2472159215084012303 4611686018427387903 4611686018427387903
(5x mod loop(\(x,i).i,(loop(\(x,i).(x2 + 2x),2,2) mod (x + 1)),1))
A277815: 0 0 0 0 0 1 0 0 0 0 2 7 0 5 0 0
((if x <= 0 then 1 else x) div (1 + (loop(\(x,i).(2x + 2),x,(2 * (x mod 2))) mod (x + 1))))
A326060: 1 1 2 1 4 5 6 1 1 1 10 1 12 1 2 1
(1 + (loop(\(x,i).(2x + 1),x,(if ((x + 1) mod 3) <= 0 then x else 2)) mod (x + 1)))
A097272: 1 2 3 4 3 6 3 8 9 6 3 12 3 6 15 16
(loop(\(x,i).2x,x,2) div (1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A075101: 2 2 8 4 32 32 128 32 512 512 2048 1024 8192 8192 32768 4096
loop(\(x,i).3x,x,(1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A156180: 1 6 9 108 81 486 729 17496 6561 39366 59049 708588 531441 3188646 4782969 229582512
loop(\(x,i).x2,1,loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x + ~1),1))
A060150: 1 1 9 100 1225 15876 213444 2944656 41409225 590976100 8533694884 124408576656 1828114918084 27043120090000 402335398890000 6015361252737600
(loop(\(x,i).2x,x,1) - loop(\(x,i).((x * (1 + i)) div (1 + (i div 2))),(x + ~1),1))
A192225: 0 1 2 5
A045621: 0 1 2 5 10 22 44 93 186 386 772 1586 3172 6476 12952 26333
loop(\(x,i).(x * (1 + loop(\(x,i).(9x + 1),i,1))),(x + ~1),1)
A015511: 1 1 11 1012 830852 6133349464 407444538242984 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + loop(\(x,i).(10x + 1),i,1))),(x + ~1),1)
A015512: 1 1 12 1344 1494528 16607195136 1845258665951232 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (1 + loop(\(x,i).(7x + 1),i,1))),(x + ~1),1)
A015508: 1 1 9 522 209322 586520244 11501075464596 1578614616119517768 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (~2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),i))),(x + ~1),1)
A059863: 1 1 1 3 21 189 2457 36855 700245 17506125 472665375 15597957375 577124422875 22507852492125 967837657161375 47424045200907375
loop(\(x,i).(x + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),i,i)),(x + ~1),1)
A279561: 1 1 2 6 21 77 287 1079 4082 15522 59280 227240 873886 3370030 13027730 50469890
(1 + (loop(\(x,i).7x,x,1) + loop(\(x,i).3x,x,1)))
A074509: 3 11 59 371 2483 17051 118379 825731 5771363 40373291 282534299 1977503891 13841818643 96890604731 678227855819 4747575858851
(1 + loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),x,1))
A201363: 2 3 7
A006862: 2 3 7 31 211 2311 30031 510511 9699691 223092871 6469693231 200560490131 7420738134811 304250263527211 13082761331670031 614889782588491411
((if (x mod 2) <= 0 then x else ~x) mod (1 + (if (x mod (4 + (x div 2))) <= 0 then 0 else 2)))
A163537: 0 2 2 0 1 1 0 0 0 0 1 1 0 2 2 0
(1 + (loop(\(x,i).loop(\(x,i).((2x * (~1 + (2 * i))) + i),3,x),x,0) div 2))
A102967: 1 42 5022
(1 + (2 * loop(\(x,i).(~x + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,0)))
A086530: 1 3 3 7 7 15 11 23 15 31 27 35 39 43 43 51
(~1 + (2 * (if x <= 0 then 2 else (if (x mod 4) <= 0 then (2x mod 5) else 1))))
A204120: 3 1 1 1 5 1 1 1 1 1 1 1 7 1 1 1
(1 + (2 * (1 + (loop(\(x,i).(2x + 1),x,loop(\(x,i).2x,x,2)) div 3))))
A192465: 3 9 25 93 353 1389 5505 21933 87553 349869 1398785 5593773 22372353 89483949 357924865 1431677613
(1 + ((1 + (if x <= 0 then 0 else (loop(\(x,i).(x * i),(x div 2),1) div (1 + (x mod 2))))) div 2))
A204596: 1 1 2 1 2 2 4 3 13
((x + 1) - (if x <= 0 then 0 else ((x + 1) mod (2 * (1 + (if (x + ~4) <= 0 then 0 else 2))))))
A057144: 1 2 2 4 4 6 6 6 6 6 6 12 12 12 12 12
(1 + (2 * ((x + 2) div (1 + (2 * (1 + loop(\(x,i).(if x <= 0 then i else (x div 2)),x,0)))))))
A113759: 1 1 3 1 3 5 1 3 5 7 1 3 5 7 11 1
(if x <= 0 then 0 else (if ((x mod 5) mod (3 + ((x div 2) mod 2))) <= 0 then 2 else 1))
A115623-A103921: 0 1 1 1 1 2 1 1 2 1 2 1 1 2 2 2
(1 + loop(\(x,i).3x,x,loop(\(x,i).x3,x,10)))
A216347: 11 3001 9000000001 4611686018427387903
(1 + (2 * loop(\(x,i).(2x + ~2),x,(~1 + loop(\(x,i).4x,x,4)))))
A291537: 7 57 493 4053 32677 261957 2096773 16776453 134216197 1073738757 8589928453 68719464453 549755789317 4398046461957 35184371990533 281474976514053
loop(\(x,i).(x mod 2),(x div 2),(if x <= 0 then 0 else (3 + (x div (1 + (x mod 4))))))
A176851: 0 3 1 1 1 1 1 0 1 1 0 1 1 1 1 0
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(8x + 3))
A017110: 59049 25937424601 6131066257801 205891132094649 2758547353515625 21611482313284249 119042423827613001 511116753300641401 1822837804551761449 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(8x + 3))
A017112: 531441 3138428376721 2213314919066161 150094635296999121 3379220508056640625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).4x,x,(3 + loop(\(x,i).3x,2x,3)))
A029697: 6 120 3936 140160 5039616 181401600 6530359296 235092541440 8463329918976 304679870791680 10968475323334656 394865111539384320 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if ((x div 2) mod 2) <= 0 then 1 else (1 + (if ((x div 2) mod 3) <= 0 then 2 else 1) - (x mod 2)))
A072909: 1 1 2 1 1 1 3 2 1 1 2 1 1 1 2 1
(7 + loop(\(x,i).(x2 + x),1,loop(\(x,i).(2x + 2),x,2)))
A289999: 13 49 217 937 3913 16009 64777 260617 1045513 4188169 16764937 67084297 268386313 1073643529 4294770697 17179475977
loop(\(x,i).loop(\(x,i).x2,2,x5),x,7)
A067485: 7 79792266297612001 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (2 * loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,(2x + 1))))
A264527: 1 1 5 7 7 9 13 13 17 19 19 21 25 23 29 27
(1 + (loop(\(x,i).((3x + ~1) + (if (x mod (1 + i)) <= 0 then 0 else x)),x,1) div 2))
A334811: 1 2 5 12 46 182 726
loop(\(x,i).x2,(x + ~2),loop(\(x,i).2x,(((x + 1) + ((x div 2) mod 2)) div 2),1))
A114641: 1 2 4 16 256 16777216 4611686018427387903
(1 + (2 * (loop(\(x,i).4x,x,1) - loop(\(x,i).(2 * (2 - (i mod 2))),x,1))))
A267780: 1 5 25 125 505 2045 8185 32765 131065 524285 2097145 8388605 33554425 134217725 536870905 2147483645
(1 + ((loop(\(x,i).2x,(x div 2),(2 + (x mod 2))) + loop(\(x,i).2x,x,1)) div 2))
A257418: 2 3 5 8 13 23 41 77 145 281 545 1073 2113 4193 8321 16577
(loop(\(x,i).x2,1,loop(\(x,i).(~3x + 3),x,1)) div (2x + 3))
A215701: 0 0 1 4 40 276
(loop(\(x,i).2x,x,2) - loop(\(x,i).((2x + ~1) + (i mod 2)),((x + 1) div 2),1))
A289764: 1 2 6 13 29 58 122 245 501 1002 2026 4053 8149 16298 32682 65365
(1 + (((1 - loop(\(x,i).(x - (if (~x + i) <= 0 then (1 + i) else 0)),x,x)) mod (x + 1)) div 2))
A319421-A092479: 1 1 1 1 2 1 1 4 2 1 1 6 6 2 1 1
loop(\(x,i).(x + loop(\(x,i).10x,(2 + i),1)),(2x + ~2),1)
A267777: 1 1 11001 1111001 111111001 11111111001 1111111111001 111111111111001 11111111111111001 1111111111111111001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 2) <= 0 then (29 * (if x <= 0 then 1 else 2)) else 1)
A040869: 29 1 58 1 58 1 58 1 58 1 58 1 58 1 58 1
(if (x mod 4) <= 0 then (23 * (if x <= 0 then 1 else 2)) else 1)
A040536: 23 1 1 1 46 1 1 1 46 1 1 1 46 1 1 1
(if (x mod 5) <= 0 then (13 * (if x <= 0 then 1 else 2)) else 1)
A010227: 13 1 1 1 1 26 1 1 1 1 26 1 1 1 1 26
(if (x mod 8) <= 0 then (11 * (if x <= 0 then 1 else 2)) else 1)
A010194: 11 1 1 1 1 1 1 1 22 1 1 1 1 1 1 1
(if (x mod 2) <= 0 then ((1 + (3 * ((~x + 2) mod 4))) * (if x <= 0 then 1 else 2)) else 1)
A040052: 7 1 2 1 14 1 2 1 14 1 2 1 14 1 2 1
(if (x mod 7) <= 0 then (7 * (if x <= 0 then 1 else 2)) else 1)
A010143: 7 1 1 1 1 1 1 14 1 1 1 1 1 1 14 1
(if (x mod 2) <= 0 then ((1 + (4 * ((~x + 2) mod 4))) * (if x <= 0 then 1 else 2)) else 1)
A010166: 9 1 2 1 18 1 2 1 18 1 2 1 18 1 2 1
(if (x mod 2) <= 0 then ((~1 + (4 * ((x + ~1) mod 4))) * (if x <= 0 then 1 else 2)) else 1)
A010200: 11 1 6 1 22 1 6 1 22 1 6 1 22 1 6 1
(if (x mod 4) <= 0 then (26 * (if x <= 0 then 1 else 2)) else 1)
A040684: 26 1 1 1 52 1 1 1 52 1 1 1 52 1 1 1
(if (x mod 2) <= 0 then ((2 + (3 * ((x + ~1) mod 4))) * (if x <= 0 then 1 else 2)) else 1)
A010201: 11 1 10 1 22 1 10 1 22 1 10 1 22 1 10 1
((8x + 8) - (if (x mod 8) <= 0 then (if x <= 0 then 1 else 2) else 1))
A189754: 7 15 23 31 39 47 55 63 70 79 87 95 103 111 119 127
(1 + (2 * (1 + compr(\x.loop(\(x,i).loop(\(x,i).(x div (1 + (x mod 2))),x,(x + 1)),2,x),x))))
A190620: 5 11 13 23 27 29 47 55 59 61 95 111 119 123 125 191
(~1 + (2 * loop(\(x,i).(2x + ((if (x mod 2) <= 0 then (x div 2) else 1) div 3)),x,1)))
A269560: 1 3 7 15 33 67 145
(1 + (loop(\(x,i).(2x + (if (i mod 3) <= 0 then x3 else 1)),x,1) div 2))
A018608: 1 2 4 179 358 716
(~1 + (2 * loop(\(x,i).((2x + 2) + loop(\(x,i).(x - (2 * (~x + i))),x,2)),x,1)))
A113795: 1 15 6615 4611686018427387903
(1 + (((1 + ((x + 1) div (1 + loop(\(x,i).(if x <= 0 then i else (x + ~1)),x,0)))) div 2) div 2))
A309736: 1 1 2 1 1 2 3 1 1 1 1 2 2 3 5 1
(~1 + (2 * ((1 + loop(\(x,i).2x,x,2) - loop(\(x,i).2x,(x div 2),1)) div 2)))
A288827: 1 3 5 13 27 59 119 247 495 1007 2015 4063 8127 16319 32639 65407
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(8x + 5))
A017134: 9765625 137858491849 16679880978201 420707233300201 4808584372417849 34050628916015625 174887470365513049 713342911662882601 2446194060654759801 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(8x + 5))
A017136: 244140625 23298085122481 7355827511386641 353814783205469041 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if x <= 0 then 0 else ((if (x mod 6) <= 0 then 2 else 1) + (((x + 1) div 2) div 2))))
A194295: 1 2 2 3 3 3 4 4 4 4 4 5 6 5 5 6
(1 + (2 * loop(\(x,i).((x2 + x) div 2),x,loop(\(x,i).x3,(x + 1),2))))
A051157: 17 262657 4611686018427387903 4611686018427387903
(loop(\(x,i).6x,x,1) mod (~1 + loop(\(x,i).((x + 1) * (x + i)),2,2)))
A036141: 1 6 36 107 97 37 4 24 35 101 61 39 16 96 31 77
(~1 + (16 * loop(\(x,i).(x + (if (~x + 2) <= 0 then x else 2)),x,(~x + 1))))
A249452: 15 31 47 63 95 127 191 255 383 511 767 1023 1535 2047 3071 4095
(loop(\(x,i).2x,x,1) mod (1 + loop(\(x,i).(4x + 2),2,8)))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A036146: 1 2 4 8 16 32 64 128 117 95 51 102 65 130 121 103
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (3x + 1)),x,9)
A033479: 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(8x + 1))
A017087: 1 31381059609 34271896307633 2384185791015625 50542106513726817 550329031716248441 3909821048582988049 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(~7x + ~1))
A017002: 1 1073741824 576650390625 26559922791424 420707233300201 3656158440062976 21611482313284249 97656250000000000 362033331456891249 1152921504606846976 3255243551009881201 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(~7x + ~1))
A017004: 1 68719476736 129746337890625 12855002631049216 353814783205469041 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (15 * (if (~2 + (x div 4)) <= 0 then 0 else 2)))
A296522: 1 0 0 0 0 0 0 0 0 0 0 0 30
((loop(\(x,i).3x,x,2) + loop(\(x,i).2x,x,3)) div 5)
A178936: 1 2 6 15 42 116 330 951 2778 8180 24234 72087 215034 642644 1923018 5759223
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(10x + 5))
A017338: 9765625 576650390625 95367431640625 2758547353515625 34050628916015625 253295162119140625 1346274334462890625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(10x + 5))
A017340: 244140625 129746337890625 59604644775390625 3379220508056640625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(5 + (2 * loop(\(x,i).(x + loop(\(x,i).x2,1,(2 + (i div 2)))),x,1)))
A271995: 7 15 33 51 83 115 165 215 287 359 457 555 683 811 973 1135
(2 - (if x <= 0 then 1 else ((if ((x + (x div 2)) mod 4) <= 0 then x else 2) mod 5)))
A304362: 1 0 0 ~1 0 0 0 0 ~1 0 0 1 0 0 0 0
(if x <= 0 then 1 else (5 * (x + (if (x mod 2) <= 0 then (3x + ~6) else 1))))
A324494: 1 10 10 20 50 30
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (5x + 1)),x,5)
A259207: 5 26 13 66 33 166 83 416 208 104 52 26 13 66 33 166
(5 + compr(\x.loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,2x),x))
A153044: 5 9 12 15 17 18 21 22 24 27 29 30 32 33 36 37
(5 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))
A089192: 5 6 7 9 10 12 13 15 18 19 22 24 25 27 30 33
(1 + loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),4))
A098640: 5 9 33 129 2049 8193 131073 524289 8388609 536870913 2147483649 137438953473 2199023255553 8796093022209 140737488355329 9007199254740993
(~1 + loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),4))
A103901: 3 7 31 127
A001348: 3 7 31 127 2047 8191 131071 524287 8388607 536870911 2147483647 137438953471 2199023255551 8796093022207 140737488355327 9007199254740991
(loop(\(x,i).7x,x,1) mod (1 + loop(\(x,i).(x2 + x),2,2)))
A070425: 1 7 6 42 36 37 1 7 6 42 36 37 1 7 6 42
(3 + loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),2))
A229065: 5 7 19 67 1027 4099 65539 262147 4194307 268435459 1073741827 68719476739 1099511627779 4398046511107 70368744177667 4503599627370499
(1 + loop(\(x,i).2x,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),2))
A101304: 9 17 65 257 4097 16385 262145 1048577 16777217 1073741825 4294967297 274877906945 4398046511105 17592186044417 281474976710657 18014398509481985
(~1 + loop(\(x,i).2x,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),2))
A279882: 7 15 63 255 4095 16383 262143 1048575 16777215 1073741823 4294967295 274877906943 4398046511103 17592186044415 281474976710655 18014398509481983
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),(4x + 1))
A031370: 5 17 31 47 67 83 103 127 149 167 191 211 233 257 277 307
loop(\(x,i).(x + loop(\(x,i).((x + 1) + (5 * i)),i,1)),4x,1)
A218324: 1 115 645 1911 4233 7931 13325 20735 30481 42883 58261 76935 99225 125451 155933 190991
(~1 + (loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1) + (2 * (x mod 2))))
A286033: 0 3 5 21 69 253 923 3433 12869 48621 184755 705433 2704155 10400601 40116599 155117521
(loop(\(x,i).((x2 + x) div 2),1,(1 + loop(\(x,i).2x,(x + ~1),1))) div 3)
A124303: 1 1 2 5 15 51 187 715 2795 11051 43947 175275 700075 2798251 11188907 44747435
loop(\(x,i).2x,x,(3 * (1 + loop(\(x,i).2x,x,(3x + 3)))))
A227707: 12 78 444 2328 11568 55392 258240 1180032 5309184 23594496 103812096 452990976 1962946560 8455741440 36238835712 154618920960
(if x <= 0 then 1 else (3 * (1 + loop(\(x,i).x3,1,(2x2 + 2x)))))
A226105: 1 195 5187
((loop(\(x,i).(3x + ~1),x,1) + loop(\(x,i).2x,(x + ~1),1)) div 3)
A094039: 0 1 2 6 16 46 132 386 1136 3366 10012 29866 89256 267086 799892 2396946
(if x <= 0 then 1 else (if (x mod 3) <= 0 then ((x2 + 2) mod 5) else 3))
A083953: 1 3 3 1 3 3 3 3 3 3 3 3 1 3 3 2
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(12x + 3))
A017566: 59049 576650390625 205891132094649 8140406085191601 119042423827613001 984930291881790849 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(12x + 3))
A017568: 531441 129746337890625 150094635296999121 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(6x + 3))
A016955: 177147 31381059609 8649755859375 350277500542221 5559060566555523 50542106513726817 317475837322472439 1532278301220703125 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(~5x + ~3))
A016894: 59049 1073741824 137858491849 3570467226624 41426511213649 296196766695424 1531578985264449 6278211847988224 21611482313284249 64925062108545024 174887470365513049 430804206899405824 984930291881790849 2113922820157210624 4297625829703557649
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(~5x + ~3))
A016896: 531441 68719476736 23298085122481 1156831381426176 21914624432020321 232218265089212416 1667889514952984961 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).2x,x,1) - loop(\(x,i).(3x + 1),(x div 2),1)) div 3)
A000773: 0 0 0 1 1 6 8 29 45 130 220 561 1001 2366 4368 9829
(3 * (loop(\(x,i).3x,x,1) - loop(\(x,i).3x,(x div 2),1)))
A242278: 0 6 18 72 216 702 2106 6480 19440 58806 176418 530712 1592136 4780782 14342346 43040160
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(9x + 3))
A017206: 59049 61917364224 16679880978201 590490000000000 8140406085191601 64925062108545024 362033331456891249 1568336880910795776 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(9x + 3))
A017208: 531441 8916100448256 7355827511386641 531441000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(((if (x + ~2) <= 0 then 1 else (x2 div 2)) + loop(\(x,i).4x,x,1)) div 3)
A262293: 0 1 5 22 88 345
(3 * loop(\(x,i).(2x3 + ~3x2 + x),1,loop(\(x,i).2x,x,1)))
A020528: 0 18 252 2520 22320 187488 1536192 12435840 100074240 802948608 6433016832 51501864960 412165877760 3297930928128 26385863196672 211096568954880
((loop(\(x,i).(x - (2 * (~x + (i mod 2)))),x,1) + loop(\(x,i).2x,x,1)) div 3)
A192225: 0 1 2 5
A093379: 0 1 2 5 12 31 82 225 632 1811 5262 15445 45652 135591 404042 1206665
(if x <= 0 then 0 else (2 + ((loop(\(x,i).(x * i),x,1) mod (x + 1)) div 3) - (x mod 2)))
A260738-A055396: 0 1 2 1 3 1 4 1 2 1 5 1 6 1 2 1
(if x <= 0 then 1 else ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3))
A322435: 1 0 0 1 0 1 0 2 1 1 0 3 0 1 1 5
loop(\(x,i).x2,(x + ~2),loop(\(x,i).3x,(x2 + 3x + 2),3))
A075081: 27 2187 1594323 4611686018427387903 4611686018427387903
(3 * (1 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x)))
A179893: 3 6 9 15 18 24 27 33 42 45 54 60 63 69 78 87
(1 + (loop(\(x,i).2x,x,(if (x mod 3) <= 0 then 1 else 2)) div 3) - (x mod 2))
A087629: 1 1 3 2 11 21 22 85 171 170 683 1365 1366 5461 10923 10922
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(12x + 6))
A017602: 60466176 3570467226624 590490000000000 17080198121677824 210832519264920576 1568336880910795776 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(12x + 6))
A017604: 2176782336 1156831381426176 531441000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x),(6x + 6))
A175229: 10 20 27 35 44 51 58 66 75 82 90 96 105 114 120 126
loop(\(x,i).3x,x,(3 + loop(\(x,i).5x,(x + 1),2)))
A205163: 13 159 2277 33831 506493 7594479 113908437 1708600311 25628925933 384433652799 5766504083397 86497559125191 1297463380500573 19461950688376719 291929260268255157 4378938903851640471
((loop(\(x,i).(x2 + x),1,loop(\(x,i).(3x + ~1),x,2)) div 2) div 3)
A051406: 1 5 35 287 2501 22265 199655 1794707 16145801 145292525 1307573675 11767985927 105911341901 953200482785 8578799562095 77209181709947
(1 - ((((x + 2) * loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)) div 2) div 3))
A129262: 1 2 1 3 2 1 5 4 3 1 9 8 6 4 1 16
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,12x)
A017531: 0 743008370688 1521681143169024 131621703842267136 3116402981210161152 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,~11x)
A017398: 0 25937424601 26559922791424 1531578985264449 27197360938418176 253295162119140625 1568336880910795776 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,~11x)
A017400: 0 3138428376721 12855002631049216 1667889514952984961 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(9x + 6))
A017242: 60466176 576650390625 63403380965376 1531578985264449 17080198121677824 119042423827613001 604661760000000000 2446194060654759801 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(9x + 6))
A017244: 2176782336 129746337890625 36520347436056576 1667889514952984961 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,(3 * loop(\(x,i).(16x + 2),x,2)))
A115491: 6 204 6552 209712 6710880 214748352 6871947648 219902325504 7036874417664 225179981368320 7205759403792384 230584300921368576 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(3 * loop(\(x,i).(10x + 2),x,2)))
A102794: 36 4356 443556 44435556 4444355556 444443555556 44444435555556 4444444355555556 444444443555555556 4611686018427387903 4611686018427387903
((loop(\(x,i).(2x + 2),(x + ~1),2) * loop(\(x,i).(2x + 2),x,2)) div 3)
A270218: 1 4 28 140 620 2604 10668 43180 173740 697004 2792108 11176620 44722860 178924204 715762348 2863180460
(((x + 2) * (1 + (if (x mod 2) <= 0 then (1 - (if x <= 0 then 2 else 0)) else (x div 2)))) div 3)
A167151: 0 1 2 3 4 7 5 12 6 18 8 26 9 35 10 45
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),6x)
A031393: 3 19 43 71 101 131 163 193 229 263 293 337 373 409 443 479
loop(\(x,i).(4x2 + ~x),1,loop(\(x,i).3x,2x,3))
A136541: 33 2889 235953 19129689
(3 * ((x + 2) + loop(\(x,i).((x * i) - (if (~2 + (x div 2)) <= 0 then 0 else 1)),2,x)))
A055040: 6 15 24 33 42 51 54 60 69 78 87 96 105 114 123 132
(3 + (2 * compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),2,x),x)))
A056761: 3 5 7 9 15 21 25 27 33 35 39 45 51 55 57 63
(3 * (2 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x)))
A245685: 6 9 12 18 21 27 30 36 45 48 57 63 66 72 81 90
((if x <= 0 then 1 else 4x) - ((1 - (if (x mod 3) <= 0 then 0 else x)) div 3))
A301688: 1 4 9 12 17 22 24 30 35 36 43 48 48 56 61 60
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (9x + 1)),x,3)
A037102: 3 28 14 7 64 32 16 8 4 2 1 10 5 46 23 208
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (7x + ~1)),x,3)
A063871: 3 20 10 5 34 17 118 59 412 206 103 720 360 180 90 45
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,9x)
A017171: 0 31381059609 64268410079232 5559060566555523 131621703842267136 1532278301220703125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (7x + 1)),x,3)
A037101: 3 22 11 78 39 274 137 960 480 240 120 60 30 15 106 53
((if x <= 0 then 1 else 4x) - ((x + (if (x mod 3) <= 0 then x else 1)) div 3))
A298789: 1 4 7 10 15 18 20 26 29 30 37 40 40 48 51 50
loop(\(x,i).((x + 1) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,3)
A227547: 3 5 8 13 20 31 44 61 80 103 132 163 200 241 284 331
(loop(\(x,i).2x,x,1) - (loop(\(x,i).(2x - (i mod 2)),(x + ~1),x) div 3))
A139790: 1 2 3 5 7 9 7 ~7 ~57 ~199 ~569 ~1479 ~3641 ~8647 ~20025 ~45511
loop(\(x,i).x2,1,((x + 3) + (if (~4 + (x div 2)) <= 0 then 1 else 4)))
A245371: 16 25 36 49 64 81 100 121 144 169 289 324 361 400 441 484
(loop(\(x,i).5x,x,4) - loop(\(x,i).4x,x,3))
A257285: 1 8 52 308 1732 9428 50212 263348 1365892 7026068 35916772 182729588 926230852 4681485908 23608756132 118849087028
((x + 3) + loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,4x))
A125255: 3 7 11 3 19 23 3 31 5 3 43 47 3 5 59 3
loop(\(x,i).x2,1,(3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A110833: 9 16 36 64 144 196 324 400 576 900 1024 1444 1764 1936 2304 2916
loop(\(x,i).3x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),3)
A121858: 3 9 81 729 59049 531441 43046721 387420489 31381059609 22876792454961 205891132094649 150094635296999121 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 3) + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),(x div 2),(x + 2)))
A013635: 5 7 8 11 12 15 16 17 18 23 24 27 28 29 30 35
((~x + 3) + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))
A177018: 3 3 3 4 4 5 5 6 8 8 10 11 11 12 14 16
loop(\(x,i).(1 + (3 * (x + (if (x mod 3) <= 0 then 1 else 2)))),2,(x mod 3))
A332756: 19 37 46 19 37 46 19 37 46 19 37 46 19 37 46 19
(if x <= 0 then 0 else ((x + 3) + loop(\(x,i).(x - (x div 12)),2,x)))
A174392: 0 5 7 9 11 13 15 17 19 21 23 25 26 27 29 31
(3 * compr(\x.(2 - loop(\(x,i).(0 - (if (x mod (1 + i)) <= 0 then 0 else x)),(x div 2),x)),x))
A055131: 15 39 51 87 111 123 159 183 219 267 291 303 327 339 411 447
loop(\(x,i).(x * loop(\(x,i).x5,1,2x2)),x,3)
A324425: 3 5668704 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(10x + 1))
A017290: 1 25937424601 16679880978201 819628286980801 13422659310152401 119042423827613001 713342911662882601 3255243551009881201 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(10x + 1))
A017292: 1 3138428376721 7355827511386641 787662783788549761 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(1 + (x * (1 + (if (x mod 10) <= 0 then x else 0)))),x,2))
A028431: 1 2 3 4 5 6 7 8 9 110 111 112 113 114 115 116
(~1 + (2 * loop(\(x,i).x2,1,(x + loop(\(x,i).(x * (1 + i)),4,(x + 1))))))
A157610: 28799 116161 262087 466577 729631 1051249 1431431 1870177 2367487 2923361 3537799 4210801 4942367 5732497 6581191 7488449
(loop(\(x,i).2x,x,1) - loop(\(x,i).3x,((x + (x div 4)) div 2),1))
A063005: 0 1 1 5 7 5 37 47 13 269 295 1319 1909 1631 9823 13085
(1 + (2 * compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),x,(~4x + 1)),x)))
A090670: 3 5 7 11 13 17 23 25 31 35 37 41 43 53 55 65
(~1 + (2 * compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),x,(~4x + 1)),x)))
A104635: 1 3 5 9 11 15 21 23 29 33 35 39 41 51 53 63
(loop(\(x,i).(3x + 1),2x,1) * (~1 + loop(\(x,i).4x,x,2)))
A096054: 1 91 3751 138811 5028751 181308931 6529545751 235085301451 8463265086751 304679288612371 10968470088963751 394865064451017691 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * (i * i)),(2 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x)),1)
A061024: 4 36 14400 25401600 1593350922240000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * (2 + i)),compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x),2))
A139159: 3 7 121 5041 39916801 6227020801 355687428096001 121645100408832001 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(x * (2 + i)),compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x),2))
A139189: 1 5 119 5039 39916799 6227020799 355687428095999 121645100408831999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).4x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),2))
A139291: 1 7 127 2047 524287 8388607 2147483647 34359738367 8796093022207 36028797018963967 576460752303423487 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A066872: 5 10 26 50 122 170 290 362 530 842 962 1370 1682 1850 2210 2810
(~1 + loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A084920: 3 8 24 48 120 168 288 360 528 840 960 1368 1680 1848 2208 2808
loop(\(x,i).((x + 1) + i),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1)
A271511: 6 10 21 36 78 105 171 210 300 465 528 741 903 990 1176 1485
loop(\(x,i).3x,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1)
A057901: 9 27 243 2187 177147 1594323 129140163 1162261467 94143178827 68630377364883 617673396283947 450283905890997363 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (2 * i)),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1)
A060800: 7 13 31 57 133 183 307 381 553 871 993 1407 1723 1893 2257 2863
(1 + (loop(\(x,i).x2,1,compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x)) div 2))
A103729: 1 5 13 41 61 113 145 221 365 421 613 761 841 1013 1301 1625
(loop(\(x,i).(7x + 1),x,0) * (~1 + loop(\(x,i).2x,x,2)))
A160876: 0 3 56 855 12400
((1 + loop(\(x,i).8x,x,4)) * (~1 + loop(\(x,i).2x,x,2)))
A147539: 5 99 1799 30735 507935 8257599 133169279 2139095295 34292630015 549218943999 8791798056959 140703128621055 2251524935786495 36026597995724799 576443160117411839 4611686018427387903
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(~1 + loop(\(x,i).2x,x,2)))
A063016: 1 3 14 75 434 2646 16764 109395 730730 4973826 34381412 240728670 1703826292 12170930700 87633375480 635351667075
loop(\(x,i).x2,1,(1 + (2 * loop(\(x,i).(x + (2 * (i * (1 + i)))),2x,x))))
A014795: 1 1225 27225 207025 938961 3136441 8555625 20205025 42837025 83521321 152300281 262926225 433680625 688275225 1056835081 1576963521
(1 + loop(\(x,i).((x + 2) + compr(\x.(loop(\(x,i).(2x + 1),x,0) mod (x + 1)),i)),x,2))
A060939: 3 7 13 21 33 47 65 85 109 139 171 209 251 295 343 397
loop(\(x,i).x5,1,loop(\(x,i).(x2 + 4x + 4),(x + 2),1))
A120322: 25937424601 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((if x <= 0 then 2 else 0) - loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + ~2),1))
A115140: 1 ~1 ~1 ~2 ~5 ~14 ~42 ~132 ~429 ~1430 ~4862 ~16796 ~58786 ~208012 ~742900 ~2674440
loop(\(x,i).((10x + 1) - (if (x + ~1) <= 0 then x else 0)),2x,1)
A267622: 1 101 10111 1011111 101111111 10111111111 1011111111111 101111111111111 10111111111111111 1011111111111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 4 else 0))),x,2x),(2x + 1))
A218394: 1 5 7 11 25 27 31 35 37 51 55 57 61 125 127 131
loop(\(x,i).(x + (if ((2x * (1 + (2 * i))) mod (2 + i)) <= 0 then x else 0)),2x,1)
A242349: 1 4 8 16 16 32 32 64 64 64 64 128 128 128 128 256
(loop(\(x,i).10x,x,1) + loop(\(x,i).3x,2x,1))
A221904: 2 19 181 1729 16561 159049 1531441 14782969 143046721 1387420489 13486784401 131381059609 1282429536481 12541865828329 122876792454961 1205891132094649
(loop(\(x,i).10x,x,1) - loop(\(x,i).3x,2x,1))
A016189: 0 1 19 271 3439 40951 468559 5217031 56953279 612579511 6513215599 68618940391 717570463519 7458134171671 77123207545039 794108867905351
(loop(\(x,i).10x,x,1) mod loop(\(x,i).3x,2x,1))
A139739: 0 1 19 271 3439 40951 468559 434062 13906558 225159022 3026431198 5856821173 152711390557 2374402515013 8492830180156 176435471621404
(loop(\(x,i).7x,x,1) + loop(\(x,i).3x,2x,1))
A074623: 2 16 130 1072 8962 75856 649090 5606512 48811522 427774096 3769259650 33358386352 296270823682 2638754838736 23555015527810 210638693604592
loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),2x,1)
A099788: 1 6 210 30030 9699690 6469693230 7420738134810 13082761331670030 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 0 else loop(\(x,i).(0 - ((2x * (~1 + (2 * i))) div (1 + i))),(x div 2),1))
A106181: 0 1 ~1 ~1 2 2 ~5 ~5 14 14 ~42 ~42 132 132 ~429 ~429
loop(\(x,i).2x,((x + 1) mod ((if (x mod 4) <= 0 then ~1 else 2) + (x div 2))),1)
A060723: 1 1 1 2 1 4 4 8 1 16 16 32 8 64 64 128
(loop(\(x,i).(x * (~1 + (2 * i))),x,1) div loop(\(x,i).(x * (~1 + (2 * i))),(x div 2),1))
A161738: 1 1 3 15 35 315 693 9009 19305 328185 692835 14549535 30421755 760543875 1579591125 45808142625
(1 + (loop(\(x,i).x2,1,loop(\(x,i).(3x2 * i),x,1)) + (x mod 2)))
A072665: 2 11 2917
(if x <= 0 then 0 else (1 + (if ((1 + (x div 2)) mod 5) <= 0 then 0 else 2) - (x mod 2)))
A307200: 0 2 3 2 3 2 3 2 1 0 3 2 3 2 3 2
(loop(\(x,i).(1 + (x * (1 + (if (i mod 2) <= 0 then 4 else 1)))),x,1) * (1 + (x mod 2)))
A118640: 1 6 16 66 166 666 1666 6666 16666 66666 166666 666666
(1 + (compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),x) + (x mod 2)))
A004793: 1 3 4 6 10 12 13 15 28 30 31 33 37 39 40 42
loop(\(x,i).(x2 + x),1,(1 + ((if ((x + ~1) mod 3) <= 0 then 1 else x) * (x mod 2))))
A174857: 2 6 2 20 2 42 2 6 2 110 2 156 2 6 2 272
((2 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) + (if x <= 0 then 2 else 1))
A166496: 6 7 11 15 23 27 35 39 47 59 63 75 83 87 95 107
(~1 + loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),x,2))
A282704: 1 3 11 59 419 4619 60059 1021019 19399379 446185739 12939386459 401120980259 14841476269619 608500527054419 26165522663340059 1229779565176982819
(~1 + loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),x,2))
A057588: 1 5 29 209 2309 30029 510509 9699689 223092869 6469693229 200560490129 7420738134809 304250263527209 13082761331670029 614889782588491409 4611686018427387903
(2 div (1 + (loop(\(x,i).(~x + (if x <= 0 then 5 else 8)),x,x) div 2)))
A287174: 2 0 1 0 0 1 0 2 0 1 0 1 0 2 0 1
((x + 1) + loop(\(x,i).(~x + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,0))
A338467: 1 3 4 7 8 13 12 19 16 25 24 29 32 35 36 41
loop(\(x,i).(x * i),4,loop(\(x,i).(10x + 21),x,1))
A175604: 24 744 7944 79944 799944 7999944 79999944 799999944 7999999944 79999999944 799999999944 7999999999944 79999999999944 799999999999944 7999999999999944 79999999999999944
(1 + compr(\x.(~1 + (loop(\(x,i).(2x + 2),(if (x mod 2) <= 0 then x else 1),1) mod (x + 1))),x))
A067126: 1 2 3 4 5 7 9 11 13 17 19 23 29 31 37 41
(1 + compr(\x.(~1 + (loop(\(x,i).2x,x,loop(\(x,i).(x + (i * i)),x,1)) mod (x + 1))),x))
A326155: 1 2 3 4 5 7 8 9 11 12 13 16 17 19 23 29
loop(\(x,i).(9x - loop(\(x,i).4x,(~1 + i),1)),x,1)
A282563: 1 8 68 596 5300 47444 425972 3829652 34450484 309988820 2789637236 25105686548 225946984628 2033506084436 18301487651060 164713120424084
loop(\(x,i).(7 * (x + (3x div (if i <= 0 then 1 else i)))),x,1)
A140107: 1 28 490 6860 84035 941192 9882516 98825160 951192165 8877793540 80787921214 719746934452 6297785676455 54257845827920 461191689537320 3874010192113488
loop(\(x,i).(x - ((1 - loop(\(x,i).(2 + (x mod (1 + i))),x,2)) div 5)),x,1)
A143071: 1 2 3 4 5 6 8 9 10 12 15 16 17 18 20 23
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(5x + 1))
A016871: 1 362797056 285311670611 17592186044416 350277500542221 3670344486987776 25408476896404831 131621703842267136 550329031716248441 1951354384207722496 4611686018427387903
loop(\(x,i).(5 * (x + loop(\(x,i).6x,(~1 + i),1))),x,1)
A257286: 1 10 80 580 3980 26380 170780 1087180 6835580 42575980 263268380 1618672780 9907349180 60420657580 367406757980 2228854610380
loop(\(x,i).(5 * (x + (6x div (if i <= 0 then 1 else i)))),x,1)
A140405: 1 35 700 10500 131250 1443750 14437500 134062500 1173046875 9775390625 78203125000 604296875000 4532226562500 33120117187500 236572265625000 1656005859375000
loop(\(x,i).(5 * (x + (8x div (if i <= 0 then 1 else i)))),x,1)
A140346: 1 45 1125 20625 309375 4021875 46921875 502734375 5027343750 47480468750 427324218750 3690527343750 30754394531250 248400878906250 1951721191406250 14963195800781250
loop(\(x,i).((2x + 1) - (loop(\(x,i).(2x + 2),x,2) mod (x + 4))),x,1)
A188534: 1 2 3 5 11 23 29
(loop(\(x,i).(8x + 2),x,2) - loop(\(x,i).(4x + 1),x,1))
A016224: 1 13 125 1085 9021 73533 593725 4771645 38260541 306433853 2452868925 19628543805 157050720061 1256495238973 10052319825725 80419990261565
(loop(\(x,i).(5x + 2),x,2) - loop(\(x,i).(4x + 1),x,1))
A097165: 1 7 41 227 1221 6447 33601 173467 889181 4533287 23015961 116477907 587981941 2962279327 14900875121 74862289547
(~1 + loop(\(x,i).(2 + (x div (1 + (if (x mod 2) <= 0 then 6 else 1)))),3,x))
A325615: 1 1 1 2 1 1 1 1 2 1 2 3 2 2 1 1
loop(\(x,i).(12x + loop(\(x,i).3x,(2 * i),1)),x,1)
A016191: 1 21 333 4725 63261 818181 10349613 128978325 1590786621 19476859941 237209103693 2877890303925 34817113183581 420347224031301 5067043480830573 61010412902061525
loop(\(x,i).(12x + loop(\(x,i).(4x + 1),i,1)),x,1)
A016227: 1 17 225 2785 33761 406497 4883425 58622945 703562721 8443102177 101318624225 1215829083105 14589971366881 175079745881057 2100957308486625 25211489133495265
loop(\(x,i).(12x + loop(\(x,i).(3x + 1),i,1)),x,1)
A016217: 1 16 205 2500 30121 361816 4342885 52117900 625424641 7505125216 90061591165 1080739359700 12968873113561 155626479754216 1867517764225045 22410213192223900
loop(\(x,i).(12x + loop(\(x,i).5x,i,1)),x,1)
A016166: 1 17 229 2873 35101 424337 5107669 61370153 736832461 8843942657 106137077509 1273693758233 15284569239421 183416051576177 2200998722429749 26412015186735113
loop(\(x,i).(11x + loop(\(x,i).4x,i,1)),x,1)
A016158: 1 15 181 2055 22861 252495 2781541 30613335 336812221 3705196575 40758210901 448344514215 4931806433581 54249937878255 596749585096261 6564246509800695
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (11x + 1)),x,1)
A033963: 1 12 6 3 34 17 188 94 47 518 259 2850 1425 15676 7838 3919
loop(\(x,i).(11x + loop(\(x,i).(2x + 1),i,1)),x,1)
A016206: 1 14 161 1786 19677 216510 2381737 26199362 288193493 3170129446 34871425953 383585689578 4219442593549 46413868545422 510552554032409 5616078094422034
loop(\(x,i).(11x + loop(\(x,i).3x,i,1)),x,1)
A016146: 1 14 163 1820 20101 221354 2435623 26794040 294741001 3242170694 35663936683 392303480660 4315338818701 47468728600034 522156019383343 5743716227565680
loop(\(x,i).(6 * (x + (3 * (2x div (if i <= 0 then 1 else i))))),x,1)
A050988: 1 42 1008 18144 272160 3592512 43110144 480370176 5043886848 50438868480 484213137408 4489976365056 40409787285504 354362750042112 3037395000360960 25514118003032064
loop(\(x,i).(~6x + loop(\(x,i).5x,(~1 + i),1)),x,1)
A166149: 1 ~5 35 ~185 1235 ~6785 43835 ~247385 1562435 ~8983985 55857035 ~325376585 2001087635 ~11762385185 71795014235 ~424666569785
loop(\(x,i).(6x + loop(\(x,i).(8x + 1),i,1)),x,1)
A016243: 1 15 163 1563 14059 121803 1030411 8579211 70649227 577287051 4690855819 37962203019 306309762955 2466150936459 19823244488587 159150177890187
loop(\(x,i).(6x + loop(\(x,i).(5x + 1),i,1)),x,1)
A016228: 1 12 103 774 5425 36456 238267 1527258 9651829 60352380 374321311 2306963022 14146953913 86407602384 526075008835 3194597025666
loop(\(x,i).(6x + loop(\(x,i).(2 * (~2x + (x mod 2))),i,1)),x,1)
A083299: 1 4 32 160 1088 6016 38144 220672 1356800 8009728 48582656 289398784 1744781312 10435133440 62745018368 375933239296
loop(\(x,i).(6x + loop(\(x,i).10x,i,1)),x,1)
A016173: 1 16 196 2176 23056 238336 2430016 24580096 247480576 2484883456 24909300736 249455804416 2496734826496 24980408958976 249882453753856 2499294722523136
loop(\(x,i).(~6x + loop(\(x,i).7x,i,1)),x,1)
A065874: 1 1 43 85 1891 5461 84883 314245 3879331 17077621 180009523 897269605 8457669571 46142992981 401365114963 2339370820165
(loop(\(x,i).(x * i),6x,1) div loop(\(x,i).6x,x,1))
A210279: 1 120 13305600 29640619008000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).10x,x,1) mod loop(\(x,i).6x,x,1))
A139736: 0 4 28 136 928 6688 20224 202240 902656 2308096 23080960 230809600 856907776 8569077760 7326613504 386722791424
(loop(\(x,i).7x,x,1) + loop(\(x,i).6x,x,1))
A074619: 2 13 85 559 3697 24583 164305 1103479 7444417 50431303 342941425 2340123799 16018069537 109949704423 756587236945 5217746494519
(loop(\(x,i).7x,x,1) - loop(\(x,i).6x,x,1))
A016169: 0 1 13 127 1105 9031 70993 543607 4085185 30275911 222009073 1614529687 11664504865 83828316391 599858908753 4277376525367
(loop(\(x,i).7x,x,1) mod loop(\(x,i).6x,x,1))
A139786: 0 1 13 127 1105 1255 24337 263671 725953 42823 40610545 163341463 780593185 5464152295 51309760081 45711664183
(loop(\(x,i).7x,x,2) - loop(\(x,i).6x,x,1))
A085353: 1 8 62 470 3506 25838 188642 1367150 9849986 70629518 504484322 3591856430 25505792066 180717326798 1278081981602 9024938035310
loop(\(x,i).(7x + loop(\(x,i).3x,(2 * i),1)),x,1)
A016178: 1 16 193 2080 21121 206896 1979713 18640960 173533441 1602154576 14701866433 134294124640 1222488408961 11099284691056 100571785292353 909893629141120
loop(\(x,i).(7x + loop(\(x,i).(4x + 1),i,1)),x,1)
A016223: 1 12 105 820 6081 43932 312985 2212740 15576561 109385452 767096265 5375266260 37649233441 263634112572 1845796701945 12922008569380
loop(\(x,i).(7x + loop(\(x,i).(3x + ~3),i,1)),x,1)
A258340: 1 7 46 310 2131 14797 103216 721420 5046661 35316787 247187986 1730227330 12111325591 84778481977 593446982356 4154121702040
loop(\(x,i).(7x + loop(\(x,i).(3x + 1),i,1)),x,1)
A016212: 1 11 90 670 4811 34041 239380 1678940 11762421 82366471 576653870 4036842810 28258696831 197813269301 1384700059560 9692921940280
loop(\(x,i).(7x + loop(\(x,i).5x,i,1)),x,1)
A016161: 1 12 109 888 6841 51012 372709 2687088 19200241 136354812 964249309 6798573288 47834153641 336059778612 2358521965909 16540171339488
loop(\(x,i).(6 * (x + (8x div (if i <= 0 then 1 else i)))),x,1)
A172501: 1 54 1620 35640 641520 10007712 140107968 1801388160 21616657920 244988789760 2645878929408 27420927086592 274209270865920 2657720625315840 25058508752977920 230538280527396864
loop(\(x,i).(6 * (x + (5x div (if i <= 0 then 1 else i)))),x,1)
A036084: 1 36 756 12096 163296 1959552 21555072 221709312 2161665792 20175547392 181579926528 1584697540608 13469929095168 111904026329088 911218500108288 7289748000866304
loop(\(x,i).(2x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i))),3x,1)
A187442: 1 3 20 126 924 6435 48620 352716 2704156 20058300 155117520 1166803110 9075135300 68923264410 538257874440 4116715363800
(loop(\(x,i).x3,x,3) div loop(\(x,i).3x,3x,1))
A165624: 3 1 27 387420489 4611686018427387903 4611686018427387903
loop(\(x,i).(9x + loop(\(x,i).(4x + 1),i,1)),x,1)
A002451: 1 14 147 1408 13013 118482 1071799 9668036 87099705 784246870 7059619931 63542171784 571901915677 5147206719578 46325218390143 416928397167052
loop(\(x,i).(3 * (3x + loop(\(x,i).4x,(~1 + i),1))),x,1)
A277491: 1 12 120 1128 10344 93864 847848 7642920 68835432 619715496 5578225896 50207178792 451877192040 4066945060008 36602706866664 329425167106344
loop(\(x,i).(3 * (x + (10x div (if i <= 0 then 1 else i)))),x,1)
A172362: 1 33 594 7722 81081 729729 5837832 42532776 287096238 1818276174 10909657044 62482581252 343654196886 1824010737318 9380626649064 46903133245320
loop(\(x,i).(3 * (x + (7x div (if i <= 0 then 1 else i)))),x,1)
A036221: 1 24 324 3240 26730 192456 1250964 7505784 42220035 225173520 1148384952 5637526128 26778249108 123591918960 556163635320 2447119995408
loop(\(x,i).(x * (x div 2)),1,(0 - loop(\(x,i).(10x + 1),x,1)))
A099639: 1 66 6216 617716 61732716 6172882716 617284382716 61728399382716
A003555: 1 66 6216 617716 61732716 6172882716 617284382716 61728399382716 6172839549382716 617283951049382716 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~7x + loop(\(x,i).3x,(2 * i),1)),x,1)
A160958: 1 2 67 260 4741 25862 350407 2330120 26735881 200269322 2084899147 16786765580 164922177421 1387410586382 13164918350287 113736703642640
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (13x + 1)),x,1)
A033964: 1 14 7 92 46 23 300 150 75 976 488 244 122 61 794 397
loop(\(x,i).(1 + loop(\(x,i).10x,(1 + (x div 3)),x)),x,1)
A145571: 1 11 110001 4611686018427387903 4611686018427387903
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (17x + 1)),x,1)
A033965: 1 18 9 154 77 1310 655 11136 5568 2784 1392 696 348 174 87 1480
loop(\(x,i).5x,x2,loop(\(x,i).(5x + 1),x,1))
A088853: 1 30 19375 304687500 119171142578125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(5x + 1),x,1) div loop(\(x,i).(3x + 1),x,1))
A238777: 1 1 2 3 6 10 17 29 49 82 137 229 382 638 1063 1772
(loop(\(x,i).(6x + 2),x,2) - loop(\(x,i).(3x + 1),x,1))
A016211: 1 10 73 478 2989 18298 110881 668566 4021237 24156946 145030249 870447214 5223480445 31343274154 188066819377 1128422439622
(1 + compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(3x + 1))),x))
A153183: 3 5 7 11 13 15 21 23 25 27 33 35 37 43 47 51
(~1 + compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(3x + 1))),x))
A034936: 1 3 5 9 11 13 19 21 23 25 31 33 35 41 45 49
(1 + compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + x + 1))),x))
A089388-A055494: 2 3 4 6 7 9 13 15 16 18 21 22 25 28 34 39
(~1 + compr(\x.(2 - loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),x,(x2 + x + 1))),x))
A128815: 1 2 4 5 7 11 13 14 16 19 20 23 26 32 37 40
loop(\(x,i).(1 + (x * loop(\(x,i).(x3 + x2),1,10))),x,1)
A178348: 1 1101 1211101 1332211101 1465432211101 1611975432211101 1773172975432211101 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + (2 * ((x + (if (x mod 2) <= 0 then x else 1)) div 5))),x,1)
A094863: 1 2 3 4 7 10 19 28
A094862: 1 2 3 4 7 10 19 28 51
(1 + (if x <= 0 then 2 else compr(\x.(loop(\(x,i).(1 + (2 * (x + (i mod 2)))),x,0) mod (x + 1)),x)))
A275938: 3 5 7 11 13 17 19 23 29 31 37 41 43 47 49 53
(x div loop(\(x,i).(~1 + (2 * i) - (loop(\(x,i).(2x + 2),x,0) mod (x + 1))),x,1))
A060951: 0 1 0 1 0 0 1 0 0 0 2 0 1 0 1 0
(1 + compr(\x.((~1 + loop(\(x,i).x2,2,loop(\(x,i).2x2,2,2))) mod (x + 1)),x))
A003536: 1 3 5 15 29 43 87 113 127 129 145 215 339 381 435 565
(1 + compr(\x.(loop(\(x,i).((x + 2) * loop(\(x,i).x2,2,(x + 2))),2,1) mod (x + 1)),x))
A057253-A003595: 1 5 7 25 35 49 125 175 245 343 625 875 1225 1715 2401 3125
(1 + compr(\x.((loop(\(x,i).x3,2,2) - loop(\(x,i).2x,x,1)) mod (x + 1)),x))
A015932: 1 2 4 6 7 8 10 12 16 24 28 30 32 34 48 50
loop(\(x,i).x2,1,(1 + compr(\x.(loop(\(x,i).(x * (1 + (i div 2))),x,1) mod (x + 1)),x)))
A062312: 1 16 36 64 81 100 144 196 225 256 324 400 441 484 576 625
loop(\(x,i).x2,1,(1 + compr(\x.(1 - (loop(\(x,i).(x2 + 2x),2,2) mod (x + 1))),x)))
A169580: 9 36 49 81 121 144 169 196 225 289 324 361 441 484 529 576
loop(\(x,i).((x + 1) + loop(\(x,i).(x + (((2 + i) * (1 + i)) div 2)),i,2x)),x,1)
A097786: 1 7 31 113 374 1178 3618 10974 33087 99481 298729 896551 2690108 8070884 24213332 72640812
((x2 + x + 1) * loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,x))
A119576: 0 6 84 780 5880 39060 238392 1369368 7516080 39819780 205079160 1032047016 5094629904 24743027400 118504436400 560749834800
(1 + compr(\x.(loop(\(x,i).loop(\(x,i).x2,1,(~3x + 3)),2,x) mod (x + 1)),x))
A135553: 1 3 5 7 9 15 21 25 35 45 49 63 75 105 147 175
(loop(\(x,i).2x,x,1) mod (loop(\(x,i).2x,(x + ~1),2) div (x2 + ~x + 1)))
A181170: 1 0 0 0 0 0 0 0 0 1 1 14
(1 + loop(\(x,i).(x + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),(x + ~1),x))
A175965: 1 2 4 7 12 19 30 43 60 79 102 131 162 199 240 283
(1 + compr(\x.(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then x else (1 + i))),x,x)),x))
A005123: 2 5 9 11 12 14 17 24 29 30 32 35 39 42 44 50
loop(\(x,i).((x2 + 1) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,1)
A028301: 1 3 12 149 22208 493195275 243241579282325638 4611686018427387903 4611686018427387903
loop(\(x,i).x3,1,loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1))
A033536: 1 1 8 125 2744 74088 2299968 78953589 2924207000 114933031928 4738245926336 203152294091656 9000469593857728 410006814589000000 4611686018427387903 4611686018427387903
(if (~2 + (((x + 1) div 2) div 2)) <= 0 then (x + (if (~4 + (x div 2)) <= 0 then 1 else 2)) else 1)
A132575: 1 2 3 4 5 6 7 8 9 10 12 1 1 1 1 1
(if x <= 0 then 1 else ((x + 1) + (if (x + ~2) <= 0 then 1 else (2 + ((x + 1) div 5)))))
A121543: 1 3 4 6 8 9 10 11 12 14 15 16 17 18 20 21
(loop(\(x,i).3x,x,2) - loop(\(x,i).(2 * ((x + 1) - (2 * (i mod 2)))),x,1))
A175659: 1 6 16 52 156 476 1436 4332 13036 39196 117756 353612 1061516 3185916 9560476 28686892
loop(\(x,i).23x,(x + (if (x + ~2) <= 0 then 1 else 2)),1)
A147642: 23 529 12167 6436343
((x + 1) + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (((x + 1) div 2) div 2)))
A176798: 1 2 3 4 6 8 7 10 13 16 11 15 19 23 27 16
loop(\(x,i).(8x + loop(\(x,i).(5x + 1),i,1)),x,1)
A016233: 1 14 143 1300 11181 93354 766363 6228560 50316761 404975494 3252010983 26077123020 208922159941 1672903158434 13390854662003 107164984268680
loop(\(x,i).(8x + loop(\(x,i).10x,i,1)),x,1)
A016186: 1 18 244 2952 33616 368928 3951424 41611392 432891136 4463129088 45705032704 465640261632 4725122093056 47800976744448 482407813955584 4859262511644672
(loop(\(x,i).10x,x,1) - loop(\(x,i).8x,x,1))
A248343: 0 2 36 488 5904 67232 737856 7902848 83222784 865782272 8926258176 91410065408 931280523264 9450244186112 95601953488896 964815627911168
(loop(\(x,i).10x,x,1) mod loop(\(x,i).8x,x,1))
A139738: 0 2 36 488 1808 1696 213568 1611392 16113920 60475904 336323584 5510719488 37927325696 104395350016 3242976755712 14837581512704
(loop(\(x,i).7x,x,1) + loop(\(x,i).8x,x,1))
A074622: 2 15 113 855 6497 49575 379793 2920695 22542017 174571335 1356217073 10567261335 82560763937 646644824295 5076269583953 39931933598775
loop(\(x,i).7x,x2,loop(\(x,i).8x,x,1))
A135315: 1 56 153664 20661046784 136122083613085696 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(8x + (if (x + ~1) <= 0 then ~1 else (x + (x mod 2)))),x,1)
A055995: 1 7 64 576 5184 46656 419904 3779136 34012224 306110016 2754990144 24794911296 223154201664 2008387814976 18075490334784 162679413013056
loop(\(x,i).(4 * (x + (10x div (if i <= 0 then 1 else i)))),x,1)
A172978: 1 44 1056 18304 256256 3075072 32800768 318636032 2867724288 24216338432 193730707456 1479398129664 10848919617536 76776969601024 526470648692736 3509804324618240
loop(\(x,i).(4 * (x + (7x div (if i <= 0 then 1 else i)))),x,1)
A054338: 1 32 576 7680 84480 811008 7028736 56229888 421724160 2998927360 20392706048 133479530496 845370359808 5202279137280 31213674823680 183120225632256
loop(\(x,i).(~4x + loop(\(x,i).(16x + 1),i,1)),x,1)
A015253: 1 13 221 3485 55965 894621 14317213 229062301 3665049245 58640578205 938250090141 15011998086813 240191982810781 3843071671285405 61489146955314845 983826350426044061
loop(\(x,i).(4x + loop(\(x,i).(10x + 1),i,1)),x,1)
A016225: 1 15 171 1795 18291 184275 1848211 18503955 185126931 1851618835 18517586451 185181456915 1851836938771 18518458866195 185184946575891 1851850897414675
loop(\(x,i).(4x + loop(\(x,i).(x + (((2 + i) * (1 + i)) div 2)),i,1)),x,1)
A097788: 1 8 42 188 787 3204 12900 51720 207045 828400 3313886 13255908 53024087 212096908 848388312 3393554064
(loop(\(x,i).~7x,2x,1) + loop(\(x,i).4x,x,1))
A176946: 2 53 2417
(loop(\(x,i).11x,x,1) - loop(\(x,i).4x,x,1))
A139742: 0 7 105 1267 14385 160027 1767465 19470787 214293345 2357685547 25936376025 285307476307 3138411599505 34522645035067 379749565147785 4177247095673827
((x * loop(\(x,i).(x * (2 + (x mod 4))),x,1)) + loop(\(x,i).4x,x,1))
A086092: 1 7 46 289 1756 10399 60346 344509 1940536 10809019 59642326 326459929 1774589716 9588593239 51537966706 275731944949
loop(\(x,i).(4x + (10x div (if i <= 0 then 1 else i))),x,1)
A020918: 1 14 126 924 6006 36036 204204 1108536 5819814 29745716 148728580 730122120 3528923580 16830250920 79342611480 370265520240
(2 + loop(\(x,i).3x,x,1) - loop(\(x,i).(x - (x div (~2 + (x mod 2)))),x,1))
A032096: 2 3 8 23 74 227 704 2135 6482 19523 58808 176663 530714 1592867 4780784 14344535
loop(\(x,i).(x - loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(~2 + i),2)),x,1)
A106191: 1 ~1 ~3 ~7 ~17 ~45 ~129 ~393 ~1251 ~4111 ~13835 ~47427 ~164999 ~581023 ~2066823 ~7415703
loop(\(x,i).(10x + loop(\(x,i).(3x + 1),i,1)),x,1)
A016215: 1 14 153 1570 15821 158574 1586833 15871610 158725941 1587288934 15872977913 158730044850 1587301245661 15873014848094 158730155655393 1587301578077290
loop(\(x,i).3x,2x2,loop(\(x,i).10x,x,1))
A135321: 1 90 656100 387420489000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 7),x,loop(\(x,i).10x,x,1))
A094992: 1 1 2 2 4 5 8 12 17 24 35 50 72 103 147 210
(~1 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(3x + 2))),x))
A088879: ~1 0 2 4 6 8 12 14 16 18 22 26 28 32 34 36
(loop(\(x,i).3x,x,1) div loop(\(x,i).(x - (2 * (~x + (x div 3)))),x,1))
A308806: 1 1 1 1 1 2 3 4 5 6 8 11 14 18 23 30
(1 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + 2x + 2))),x))
A005574: 1 2 4 6 10 14 16 20 24 26 36 40 54 56 66 74
(1 + compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + 2x + ~2))),x))
A028873: 4 8 10 14 20 26 32 34 40 44 46 58 64 68 80 86
(~1 + compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + 2x + ~2))),x))
A162860: 2 6 8 12 18 24 30 32 38 42 44 56 62 66 78 84
loop(\(x,i).(~1 + (x mod (1 + i))),compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),1)
A145382: 1 0 2 0 4 2 14 12 8 2 0 26 22 20 16 10
loop(\(x,i).((x + 2) + (2 * i)),compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),1)
A306190: 1 5 19 41 109 155 271 341 505 811 929 1331 1639 1805 2161 2755
loop(\(x,i).(x2 + x),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A036689: 2 6 20 42 110 156 272 342 506 812 930 1332 1640 1806 2162 2756
loop(\(x,i).(2x + (if ((x + ~2) mod 13) <= 0 then 0 else 1)),x,1)
A291754: 1 3 7 15 30 61 123 247 495 991 1983 3967 7934 15869 31739 63479
loop(\(x,i).(2x + loop(\(x,i).(2 * (2x - (x div (1 + i)))),(~1 + i),2)),x,1)
A082590: 1 4 14 48 166 584 2092 7616 28102 104824 394404 1494240 5692636 21785872 83688344 322494208
loop(\(x,i).(~2x + loop(\(x,i).(2 * (2x - (x div (1 + i)))),(~1 + i),2)),x,1)
A167481: 1 0 6 8 54 144 636 2160 8550 31520 121716 462000 1780156 6840288 26436024 102245472
loop(\(x,i).(6x + ((x2 + ~x) div 2)),1,loop(\(x,i).2x,x,1))
A256871: 6 13 30 76 216 688 2400 8896 34176 133888 529920 2108416 8411136 33599488 134307840 537051136
loop(\(x,i).(16x2 + 17x + 1),1,loop(\(x,i).2x,x,1))
A165222: 34 99 325 1161 4369 16929 66625 264321 1052929 4203009 16794625 67143681 268505089 1073881089 4295245825 17180426241
loop(\(x,i).(x5 + x4 + x3 + x2 + x + 1),1,loop(\(x,i).2x,x,1))
A034665: 6 63 1365 37449 1118481 34636833 1090785345 34630287489 1103823438081 35253226045953 1127000493261825 36046397799139329 1153203048319815681 4611686018427387903 4611686018427387903
loop(\(x,i).((x3 + x) * ((x2 + 2) + i)),1,loop(\(x,i).2x,x,1))
A020532: 8 70 1292 34840 1065008 33685600 1074790592 34368127360 1099578737408 35184908961280 1125904201812992 36028831378708480 1152921779484766208 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1) - loop(\(x,i).2x,x,1))
A108958: 0 1 6 27 110 430 1652 6307 24054 91866 351692 1350030 5196204 20050108 77542376 300507427
(5x + (loop(\(x,i).3x,x,1) + loop(\(x,i).2x,x,1)))
A120845: 2 10 23 50 117 300 823 2350 6857 20240 60123 179250 535597 1602580 4799423 14381750
(5x + loop(\(x,i).3x,x,1) - loop(\(x,i).2x,x,1))
A120849: 0 6 15 34 85 236 695 2094 6345 19216 58075 175154 527405 1586196 4766655 14316214
(loop(\(x,i).(5x + 2),x,0) + loop(\(x,i).(~3x + 2),x,1))
A120612: 1 1 17 49 353 1441 8177 37969 198593 966721 4912337 24325489 122336033 609554401 3054149297 15251614609
loop(\(x,i).(2x + (if (i mod 3) <= 0 then (5x + 4) else x)),x,1)
A018543: 1 3 9 67 201 603
loop(\(x,i).(1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i) - (x div 2)),x,1)
A337823: 1 2 2 4 5 9 9 13 13 17 21 21 27 28 29 33
((~x + ~1) + loop(\(x,i).2x,x,2) - loop(\(x,i).(2x + ~1),(x div 2),(x mod 2)))
A114960: 1 1 6 11 30 57 128 247 518 1013 2068 4083 8242 16369 32880 65519
loop(\(x,i).(loop(\(x,i).(4x * (~1 + (2 * i))),i,1) + (2x * i)),x,1)
A089252: 1 6 72 1392 38016 1347840 58752000 3036579840 181428387840 12299042488320 932514044313600 78184097316864000 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).loop(\(x,i).x2,2,(7x + ~6)),2,0) mod (x + 1))
A245973-A214128: 0 0 0 0 1 0 1 0 0 6 5 0 1 8 6 0
(loop(\(x,i).(x + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)),x,0) mod (x + 1))
A090396: 0 1 1 1 3 5 2 5 1 9 6 5 4 1 13 13
(if x <= 0 then 1 else (loop(\(x,i).x2,2,23) mod (x + 1)))
A070674-A070668: 1 1 1 1 1 1 2 1 4 1 1 1 3 9 1 1
(loop(\(x,i).(~x + 2),x,(1 + (if ((x div 3) mod 2) <= 0 then 2x else 1))) div (x + 1))
A117907: 1 ~1 1 0 0 0 1 ~2 1 0 0 0 1 ~2 1 0
loop(\(x,i).loop(\(x,i).x3,1,((x + 1) + (x2 div 4))),1,(x + 1))
A267783: 8 64 216 729 1728 4096 8000 15625 27000 46656 74088 117649 175616 262144 373248 531441
((x + 1) * (if ((if ((x + ~1) mod 3) <= 0 then 1 else x) div 2) <= 0 then (x2 + ~1) else 1))
A132414: ~1 0 3 4 75
((1 + loop(\(x,i).2x,x,1) - ((if (x mod 2) <= 0 then 2 else x) mod 4)) mod (x + 1))
A339423: 0 0 0 2 0 2 0 6 3 2 0 6 0 2 3 14
((1 + (2 * ((x * loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)) div 2))) div (x + 1))
A167948: 1 0 1 0 1 1 0 0 1 2 0 0 1 2 3 0
((3 * loop(\(x,i).2x,x,loop(\(x,i).(1 + (x * i)),4,2))) mod (x + 1))
A249732: 0 0 0 0 2 0 1 0 6 4 3 0 7 2 3 0
loop(\(x,i).10x,x,((x + 1) * loop(\(x,i).x2,2,3)))
A096302: 81 1620 24300 324000 4050000 48600000 567000000 6480000000 72900000000 810000000000 8910000000000 97200000000000 1053000000000000 11340000000000000 121500000000000000 1296000000000000000
((x + 1) * loop(\(x,i).(x * i),x,loop(\(x,i).(2 * (x - (2x * i))),2x,1)))
A065236: 1 24 10080 15966720 62270208000 482718652416000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(4 * (4x + (x div (if i <= 0 then 1 else i)))),x,1) div (x + 1))
A034255: 1 10 120 1560 21216 297024 4243200 61526400 902387200 13355330560 199115837440 2986737561600 45030812467200 681895160217600 10364806435307520 158063298138439680
compr(\x.(~1 + loop(\(x,i).loop(\(x,i).(2 + (x mod 2)),(x mod 2),(x div 2)),4,x)),(x + 1))
A277549: 1 4 5 9 13 16 17 20 21 25 29 33 36 37 41 45
((x + 1) * loop(\(x,i).(2 * (2x + (3x div (if i <= 0 then 1 else i)))),x,1))
A007744: 1 20 210 1680 11550 72072 420420 2333760 12471030 64664600 327202876 1622493600 7909656300 38003792400 180324117000 846321189120
((~x + ~1) + loop(\(x,i).(2x + loop(\(x,i).(3x + 7),i,1)),x,1))
A060157: 0 10 58 236 836 2766 8814 27472 84472 257522 780770 2358708 7108908 21392278 64307926 193185944
(loop(\(x,i).(2 * (8x - (x div (if i <= 0 then 1 else i)))),x,1) div (x + 1))
A097184: 1 7 70 805 9982 129766 1742572 23960365 335445110 4763320562 68418604436 992069764322 14499481170860 213349508656940 3157572728122712 46968894330825341
((x + 1) + (loop(\(x,i).(x2 + ~x),2,loop(\(x,i).(2x + 1),x,0)) mod (x + 1)))
A323309-A322857: 1 2 3 6 5 6 7 10 12 10 11 18 13 14 15 18
((x + 1) * loop(\(x,i).(loop(\(x,i).(x * (2 + i)),(~1 + i),1) + (x * (2 + i))),x,1))
A307642: 1 8 57 428 3510 31644 312984 3380544 39664080 502927200 6858181440 100135491840 1559197261440 25797280723200 452046655872000 8364495012249600
((x + 1) * loop(\(x,i).(loop(\(x,i).10x,i,1) - (x * i)),x,1))
A110395: 1 18 246 3016 34920 390480 4266640 45866880 487198080 5128019200 53591788800 556898534400 5760319052800 59355533260800 609667001088000 6245327982592000
((if x <= 0 then 1 else (2 * (1 + (loop(\(x,i).x2,2,(x + 1)) div 3)))) div (x + 1))
A184630: 1 6 18 43 83 144 228 341 486 666 887 1152 1464 1829 2250 2730
((x + 1) + (2 * (1 + loop(\(x,i).2x,x,(~1 + loop(\(x,i).2x,x,2x))))))
A213748: 1 16 125 758 4071 20424 98185 458506 2096651 9436172 41941005 184545294 805298191 3489644560 15032352785 64424443922
(if (x div 2) <= 0 then 1 else ((2 * (1 + (if (x mod 3) <= 0 then (x mod 2) else 2))) mod (x + 1)))
A340984: 1 1 0 0 1 0 2 6
((x + 3) + (if (x + ~2) <= 0 then 1 else ((x + (if (x mod 2) <= 0 then x else 2)) mod 3)))
A033597: 4 5 6 8 9 9 9 10 12 14 15 15 15 16 18 20
((2 + (if (x mod 2) <= 0 then (if (x mod 7) <= 0 then 2 else x) else 1)) mod (x + 1))
A266875: 0 1 1 3 1 3 1 3 1 3 1 3 1 3 4 3
((x + 1) * (2 + loop(\(x,i).(x * (~1 + loop(\(x,i).(x2 + 2x),2,2))),2,(x + 1))))
A031757: 6243 24968 56175 99864 156035 224688 305823 399440 505539 624120 755183 898728 1054755 1223264 1404255 1597728
((x + 1) * (2 + loop(\(x,i).(x * loop(\(x,i).(1 + (x * i)),4,2)),2,(x + 1))))
A031767: 7923 31688 71295 126744 198035 285168 388143 506960 641619 792120 958463 1140648 1338675 1552544 1782255 2027808
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(~8x + ~6))
A017146: 60466176 289254654976 26559922791424 590490000000000 6278211847988224 42420747482776576 210832519264920576 839299365868340224 2824752490000000000 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(~8x + ~6))
A017148: 2176782336 56693912375296 12855002631049216 531441000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,8x),(x + 1))
A153236: 3 4 6 9 11 12 14 15 18 19 21 23 24 25 27 29
((2 + loop(\(x,i).x2,x,loop(\(x,i).2x,x,3))) div (4x + 4))
A255268: 1 4 1728 6879707136 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,(x2 + 5x + 4))
A070261: 4 10 2 28 40 6 70 88 12 130 154 20 208 238 30 304
compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 6 else 0))),x,2x),(x + 1))
A037461: 1 2 3 7 8 9 10 14 15 16 17 21 22 23 24 49
(compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),2x) mod (x + 1))
A105283: 0 1 1 3 4 1 1 5 7 1 2 5 10 9 8 3
((x + 1) + ((if ((if x <= 0 then 2 else ((x + 1) div 2)) mod 3) <= 0 then 0 else 2) + (x mod 2)))
A190136: 3 5 5 7 7 7 7 11 11 13 13 13 13 17 17 19
(loop(\(x,i).3x,(2x + 2),1) mod loop(\(x,i).x3,2,(x + 1)))
A066431: 0 81 729 6561 59049 531441 4782969 43046721 0 486784401 727739626 3801397473 7390478182 5013665073 26942641524 68218142337
((~x + ~1) + loop(\(x,i).(2x - (if (x mod 10) <= 0 then 1 else i)),x,2))
A127193: 1 1 1 1 1 1 1 1 1 9 17 33 65 129 257 513
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (3x + 1)),3x,(x + 1))
A006460: 1 2 2 4 4 4 2 1 2 1 4 1 1 4 4 2
((x + 1) + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,3x))
A104279: 1 5 8 11 14 18 20 23 26 29 33 35 39 41 44 48
((x + 1) * (x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1))))
A091512: 1 4 3 12 5 12 7 32 9 20 11 36 13 28 15 80
(loop(\(x,i).(1 + (x2 div loop(\(x,i).3x,(2 * i),1))),2,x) mod (x + 1))
A316078: 0 1 1 1 1 1 1 1 1 2 2 3 4 5 6 9
loop(\(x,i).x2,1,((2x + 2) div loop(\(x,i).(x div (~2 + (x mod 2))),x,(x + 1))))
A059152: 4 16 4 64 4 16 4 256 4 16 4 64 4 16 4 1024
compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1))
A096292-A093326-A054799-A001359: 3 5 11 17 29 41 59 71 101 107 137 149 179 191 197 227
compr(\x.(1 - loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1))
A111166: 2 5 11 17 29 41 59 71 101 107 137 149 179 191 197 227
((if ((x div 2) mod 3) <= 0 then 2 else 1) mod loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))
A340691: 0 0 1 0 1 1 2 0 1 1 1 1 2 2 1 0
(loop(\(x,i).(x * i),(x div 4),1) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))
A087255: 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 6
(loop(\(x,i).(x * (1 + (2 * i))),x,1) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))
A130187: 1 3 5 105 189 3465 19305 2027025 3828825 130945815 1249937325 105411381075 608142583125 30494006668125 412685556908625 191898783962510625
loop(\(x,i).(8 div (x + 1)),2,loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))
A082908: 1 1 2 1 4 2 4 1 8 4 8 2 8 4 8 1
(if (x mod 2) <= 0 then (3x + 4) else loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))
A306546: 4 1 10 1 16 3 22 1 28 5 34 3 40 7 46 1
loop(\(x,i).x2,1,loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,(x + 1)))
A337900: 1 16 225 3136 44100 627264 9018009 130873600 1914762564 28210561600 418151049316 6230734868736 93271169290000 1401915345465600 21147754404155625 320042195924198400
loop(\(x,i).x2,1,loop(\(x,i).(~x + (8x div (1 + i))),x,(x + 1)))
A113164: 1 36 225 400 225 36 1
loop(\(x,i).(x + ((x * loop(\(x,i).(2x2 + ~2),2,2)) div (1 + i))),x,(x + 1))
A017735: 1 72 2628 64824 1215450 18474840 237093780 2641902120 26088783435 231900297200 1878392407320 14002561581840 96851050941060 625806790696080 3799541229226200 21784036380896880
loop(\(x,i).(~x + ((x * loop(\(x,i).(x2 + x + 2),2,2)) div (1 + i))),x,(x + 1))
A017788: 1 72 2556 59640 1028790 13991544 156238908 1473109704 11969016345 85113005120 536211932256 3022285436352 15363284301456 70907466006720 298824321028320 1155454041309504
loop(\(x,i).(x + ((x * (~2 + loop(\(x,i).(x2 + 2x),2,2))) div (1 + i))),x,(x + 1))
A017743: 1 80 3240 88560 1837620 30872016 437353560 5373200880 58433559570 571350360240 5085018206136 41604694413840 315502265971620 2232785266876080 14832073558533960 92947660966812816
((x + ~1) + loop(\(x,i).(x * i),(1 + (2 * (if (~2 + (x div 3)) <= 0 then 0 else 2))),1))
A004870: 0 1 2 3 4 5 6 7 8 128 129 130 131 132 133 134
(if x <= 0 then 1 else ((x + ~1) + (if (~4 + (x div 2)) <= 0 then 10 else x)))
A248499-A069715: 1 10 11 12 13 14 15 16 17 18 19 21 23 25 27 29
((x2 + ~x) * loop(\(x,i).(x * loop(\(x,i).(x * (x - i)),2,(x + ~2))),1,(x + ~2)))
A159083: 0 0 0 0 0 0 0 5040 40320 181440 604800 1663200 3991680 8648640 17297280 32432400
(x div ((x + 2) div (1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x))))
A345698: 0 0 0 1 0 0 1 0 0 1 0 2 1 0 0 3
loop(\(x,i).((x + 1) + (if ((x + 1) mod 5) <= 0 then (x div 4) else 0)),x,1)
A031990: 1 2 3 4 6 7 8 9 12 13 14 18 19 24 31 32
loop(\(x,i).(x * (1 + (7 * (1 + (if (~x + 2) <= 0 then 2 else 1))))),x,1)
A196666: 1 15 330 7260 159720 3513840 77304480 1700698560 37415368320 823138103040 18109038266880 398398841871360 8764774521169920 192825039465738240 4242150868246241280 4611686018427387903
loop(\(x,i).(x * (1 + (i div (1 + (2 * (if (x mod 5) <= 0 then 0 else 2)))))),x,1)
A264656: 1 1 1 1 1 2 4 8 16 32 96 288 864 2592 7776 31104
loop(\(x,i).(x * loop(\(x,i).(10x + 1),5,1)),x,1)
A109716: 1 111111 12345654321 1371737997260631 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 5),x,loop(\(x,i).11x,x,1))
A094987: 1 2 4 10 23 51 113 249 548 1207 2655 5843 12855 28281 62218 136880
loop(\(x,i).(x + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(~1 + i),1)),x,1)
A024718: 1 2 5 15 50 176 638 2354 8789 33099 125477 478193 1830271 7030571 27088871 104647631
(loop(\(x,i).3x,2x,1) - loop(\(x,i).7x,x,1))
A191467: 0 2 32 386 4160 42242 413792 3959426 37281920 347066882 3204309152 29403732866 268588249280 2444976817922 22198569382112 201143570584706
(loop(\(x,i).3x,2x,1) div loop(\(x,i).7x,x,1))
A255575-A094991: 1 1 1 2 2 3 4 5 7 9 12 15 20 26 33 43
(loop(\(x,i).3x,2x,1) mod loop(\(x,i).7x,x,1))
A139732: 0 2 32 43 1759 8628 60845 665254 2693114 24238026 97081413 1721158464 5603792461 22751557747 495431050944 1745987167100
(loop(\(x,i).8x,x,1) - loop(\(x,i).7x,x,1))
A016177: 0 1 15 169 1695 15961 144495 1273609 11012415 93864121 791266575 6612607849 54878189535 452866803481 3719823438255 30436810578889
(loop(\(x,i).8x,x,1) mod loop(\(x,i).7x,x,1))
A138973: 0 1 15 169 1695 15961 26846 450066 5247614 13156907 226316077 680627620 13354327932 65310761853 328708074010 1951441519231
loop(\(x,i).2x,(x - (2 * (x mod 2))),loop(\(x,i).7x,x,1))
A182268: 1 7 196 686 38416 134456 7529536 26353376 1475789056 5165261696 289254654976 1012391292416 56693912375296 198428693313536 11112006825558016 38892023889453056
(loop(\(x,i).(x * i),5x,1) div loop(\(x,i).5x,x,1))
A210278: 1 24 145152 10461394944 3892643213082624 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).7x,x,1) + loop(\(x,i).5x,x,1))
A074616: 2 12 74 468 3026 19932 133274 901668 6155426 42306732 292240874 2026154868 14085427826 98109713532 684326588474 4778079088068
(loop(\(x,i).7x,x,1) - loop(\(x,i).5x,x,1))
A121213: 0 2 24 218 1776 13682 102024 745418 5374176 38400482 272709624 1928498618 13597146576 95668307282 672119557224 4717043931818
(loop(\(x,i).7x,x,1) mod loop(\(x,i).5x,x,1))
A138648: 0 2 24 93 526 1182 8274 42293 296051 1291107 9037749 24201743 169412201 453463532 732838474 17336900568
(2x + loop(\(x,i).5x,x,1) - loop(\(x,i).3x,x,1))
A120978: 0 4 20 104 552 2892 14908 75952 384080 1933460 9706596 48651000 243609208 1219108828 6098732684 30503229248
(2x + (loop(\(x,i).3x,x,1) + loop(\(x,i).5x,x,1)))
A120949: 2 10 38 158 714 3378 16366 80326 397202 1972826 9824694 49005294 244672090 1222297474 6108298622 30531927062
(~2x + (loop(\(x,i).3x,x,1) + loop(\(x,i).5x,x,1)))
A120950: 2 6 30 146 698 3358 16342 80298 397170 1972790 9824654 49005250 244672042 1222297422 6108298566 30531927002
(loop(\(x,i).7x,x,2) - loop(\(x,i).5x,x,1))
A081627: 1 9 73 561 4177 30489 219673 1568961 11138977 78754089 555184873 3905825361 27438433777 192557317689 1350342630073 9464605441761
((3 * loop(\(x,i).4x,(x + ~1),x)) + loop(\(x,i).3x,x,1))
A086091: 1 6 33 171 849 4083 19161 88203 399777 1789155 7923369 34780155 151526385 655905747 2823355257 12093944427
(loop(\(x,i).(7x + ~4),x,1) - loop(\(x,i).3x,x,1))
A109021: 0 0 8 88 720 5360 38488 272328 1915040 13431520 94099368 658931768 4613230960 32294742480 226069574648 1582506154408
(loop(\(x,i).11x,x,1) - loop(\(x,i).3x,x,1))
A139741: 0 8 112 1304 14560 160808 1770832 19484984 214352320 2357928008 25937365552 285311493464 3138427845280 34522710549608 379749828800272 4177248155066744
((loop(\(x,i).(2x + 2),x,(x + 4)) div 2) + loop(\(x,i).3x,x,1))
A267465: 3 9 24 62 160 418 1112 3018 8352 23522 67240 194554 568304 1672146 4946808 14692970
(~2x + loop(\(x,i).5x,x,1) - loop(\(x,i).3x,x,1))
A120990: 0 0 12 92 536 2872 14884 75924 384048 1933424 9706556 48650956 243609160 1219108776 6098732628 30503229188
(loop(\(x,i).17x,x,2) + loop(\(x,i).3x,x,1))
A333385: 3 37 587 9853 167123 2839957 48275867 820679533 13951521443 237175772677 4031987859947 68543792792413 1165244474990963 19809156067406197 336755653123584827 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(~2 + i),1)),x,1)
A155587: 1 2 3 5 10 24 66 198 627 2057 6919 23715 82501 290513 1033413 3707853
loop(\(x,i).(loop(\(x,i).(x * (1 + (2 * i))),(~2 + i),1) + (x * (~1 + (2 * i)))),x,1)
A114160: 1 2 7 38 281 2634 29919 399342 6125265 106156530 2051433495 43734832470 1019650457385 25807495577850 704708234182575 20649996837971550
loop(\(x,i).(x + loop(\(x,i).((11x + 1) + i),i,1)),x,1)
A229611: 1 14 160 1770 19485 214356 2357944 25937420 285311665 3138428370 34522712136 379749833574 4177248169405 45949729863560 505447028499280 5559917313492216
loop(\(x,i).(x + loop(\(x,i).((4x div (1 + i)) * (1 + (2 * i))),i,1)),x,1)
A098405: 1 7 47 327 2343 17127 126951 950631 7173991 54471527 415652711 3184708455 24485137255 188802730855 1459525454695 11307626564455
loop(\(x,i).(x + loop(\(x,i).((4x * (~1 + (2 * i))) div (1 + i)),i,1)),x,1)
A112696: 1 3 11 51 275 1619 10067 64979 431059 2920403 20119507 140513235 992530387 7078367187 50896392147 368577073107
loop(\(x,i).(~x + loop(\(x,i).((4x * (~1 + (2 * i))) div (1 + i)),i,1)),x,1)
A064306: 1 1 7 33 191 1153 7295 47617 318463 2170881 15028223 105365505 746651647 5339185153 38478839807 279201841153
(1 - ((4x + 1) mod (~1 + loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x))))
A275724: 1 2 1 3 2 1 4 2 2 1 5 4 3 2 1 6
loop(\(x,i).(x + loop(\(x,i).(x + i),i,(11 * (1 + i)))),x,1)
A101860: 1 24 60 110 175 256 354 470 605 760 936 1134 1355 1600 1870 2166
loop(\(x,i).loop(\(x,i).(x + (i * i * i * i * i * i * i)),(1 + i),x),x,1)
A250212: 1 130 2446 21146 117971 494732 1695036 4992492 13072917 31153342 68720938 142120342 278268263 519829688 932250488 1613106744
loop(\(x,i).(x + loop(\(x,i).21x,i,(1 + i))),x,1)
A014938: 1 43 1366 38410 1010815 25515421 625878268 15034586596 355440320845 8298240786655 191776931546866 4395106938053518 100020864586079851 2262634152933752305 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).22x,i,(1 + i))),x,1)
A014940: 1 45 1497 44089 1215369 32137161 825796489 20780659593 514663521417 12587355699337 304746506405001 7316566123340937 174431600326980745 4133772410690139273 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),i,(1 + i))),x,1)
A057552: 1 5 20 76 286 1078 4081 15521 59279 227239 873885 3370029 13027729 50469889 195892564 761615284
loop(\(x,i).(~x + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),i,(1 + i))),x,1)
A331473: 1 3 12 44 166 626 2377 9063 34695 133265 513381 1982763 7674937 29767223 115655452 450067268
loop(\(x,i).(x + loop(\(x,i).19x,i,(1 + i))),x,1)
A014936: 1 39 1122 28558 680163 15536757 344857924 7495831836 160347899205 3387224876995 70828953712806 1468712060491434 30241806008351527 618983574479950353 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).23x,i,(1 + i))),x,1)
A014941: 1 47 1634 50302 1449507 40067565 1076318788 28314922364 733113789893 18744640404523 474436263754662 11908153358721786 296798270974985959 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) - loop(\(x,i).(x - (if (16 mod (x + 1)) <= 0 then 0 else 2)),x,x))
A053641: 1 1 3 1 5 3 7 1 9 3 11 5 13 7 15 1
(1 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),x))
A192224: 2 4 6 12 18 30
A167777: 2 4 6 12 18 30 42 60 72 102 108 138 150 180 192 198
(1 + compr(\x.loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),(x div 2),(x + (x mod 2))),x))
A011990: 1 6 7 12
A171153: 1 6 7 12 13 18 19 22 23 24 25 30 31 32 33 36
loop(\(x,i).(3x + (loop(\(x,i).4x,(~1 + i),1) + (x mod 2))),x,1)
A269708: 1 5 20 76 292 1132 4420 17356 68452 270892 1074820 4273036 17013412 67817452 270561220 1080119116
loop(\(x,i).(~x + loop(\(x,i).((4x * (~1 + (2 * i))) div (1 + i)),i,2)),x,1)
A318165: 1 3 13
A062992: 1 3 13 67 381 2307 14589 95235 636925 4341763 30056445 210731011 1493303293 10678370307 76957679613 558403682307
(~1 + loop(\(x,i).loop(\(x,i).x2,1,(6x2 + 12)),1,x2))
A153874: 143 323 11663
loop(\(x,i).7x,x,loop(\(x,i).6x,x2,1))
A135314: 1 42 63504 3456649728 6773484887801856 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).7x,x,loop(\(x,i).8x,x2,1))
A135426: 1 56 200704 46036680704 675821419082285056 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).3x,2x,loop(\(x,i).10x,x2,1))
A135428: 1 90 810000 729000000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).6x,x,loop(\(x,i).7x,x2,1))
A135425: 1 42 86436 8716379112 43069878018202896 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).5x,x2,1) + loop(\(x,i).3x,x2,1))
A120838: 2 8 706 1972808 152630937346 298024071165562568 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).5x,x2,1) - loop(\(x,i).3x,x2,1))
A120840: 0 2 544 1933442 152544843904 298022376588343682 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then (9x + 1) else x)),x,1)
A018312: 1 2 4 41 82 164
loop(\(x,i).(x + (if (i mod 4) <= 0 then 21 else x)),x,1)
A222011: 1 2 4 8
A018346: 1 2 4 8 29 58 116 232
loop(\(x,i).(x + (if (x mod 4) <= 0 then (3x2 + 6x + 3) else x)),x,1)
A018389: 1 2 4 79 158 316
loop(\(x,i).(x + (if (x mod 2) <= 0 then 3 else (x + ((x + (x mod 2)) div 3)))),x,1)
A066267: 1 2 5 12 15 35
loop(\(x,i).(x2 * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),x,1)
A191555: 1 2 12 720 3628800 144850083840000 4611686018427387903 4611686018427387903
loop(\(x,i).(x + compr(\x.(~1 + (loop(\(x,i).4x,x,1) mod (2x + 1))),i)),x,1)
A005521: 1 2 4 7 12 18 26 35 46 60 75 93 113 134 157 183
loop(\(x,i).(x + loop(\(x,i).((x2 + 2x + 1) + (x2 div 4)),1,i)),x,1)
A212983: 1 5 15 33 62 104 162 238 335 455 601 775 980 1218 1492 1804
loop(\(x,i).(x + (30x div (if i <= 0 then 1 else i))),x,1)
A010983: 1 31 496 5456 46376 324632 1947792 10295472 48903492 211915132 847660528 3159461968 11058116888 36576848168 114955808528 344867425584
loop(\(x,i).(~x + (30x div (if i <= 0 then 1 else i))),x,1)
A010945: 1 29 406 3654 23751 118755 475020 1560780 4292145 10015005 20030010 34597290 51895935 67863915 77558760 77558760
loop(\(x,i).(x + (40x div (if i <= 0 then 1 else i))),x,1)
A010993: 1 41 861 12341 135751 1221759 9366819 62891499 377348994 2054455634 10272278170 47626016970 206379406870 841392966470 3245372870670 11899700525790
loop(\(x,i).(x + (25x div (if i <= 0 then 1 else i))),x,1)
A010978: 1 26 351 3276 23751 142506 736281 3365856 13884156 52451256 183579396 600805296 1852482996 5414950296 15084504396 40225345056
loop(\(x,i).(~x + (25x div (if i <= 0 then 1 else i))),x,1)
A010940: 1 24 276 2024 10626 42504 134596 346104 735471 1307504 1961256 2496144 2704156 2496144 1961256 1307504
loop(\(x,i).(x + (36x div (if i <= 0 then 1 else i))),x,1)
A010989: 1 37 703 9139 91390 749398 5245786 32224114 177232627 886163135 4076350421 17417133617 69668534468 262596783764 937845656300 3188675231420
loop(\(x,i).(~x + (36x div (if i <= 0 then 1 else i))),x,1)
A010951: 1 35 595 6545 52360 324632 1623160 6724520 23535820 70607460 183579396 417225900 834451800 1476337800 2319959400 3247943160
loop(\(x,i).(x + (27x div (if i <= 0 then 1 else i))),x,1)
A010980: 1 28 406 4060 31465 201376 1107568 5379616 23535820 94143280 348330136 1203322288 3910797436 12033222880 35240152720 98672427616
loop(\(x,i).(~x + (27x div (if i <= 0 then 1 else i))),x,1)
A010942: 1 26 325 2600 14950 65780 230230 657800 1562275 3124550 5311735 7726160 9657700 10400600 9657700 7726160
loop(\(x,i).(x + (48x div (if i <= 0 then 1 else i))),x,1)
A011001: 1 49 1225 20825 270725 2869685 25827165 202927725 1420494075 8996462475 52179482355 279871768995 1399358844975 6566222272575 29078984349975 122131734269895
loop(\(x,i).(~x + (48x div (if i <= 0 then 1 else i))),x,1)
A010963: 1 47 1081 16215 178365 1533939 10737573 62891499 314457495 1362649145 5178066751 17417133617 52251400851 140676848445 341643774795 751616304549
loop(\(x,i).(x + (21x div (if i <= 0 then 1 else i))),x,1)
A010974: 1 22 253 2024 12650 65780 296010 1184040 4292145 14307150 44352165 129024480 354817320 927983760 2319959400 5567902560
loop(\(x,i).(~x + (21x div (if i <= 0 then 1 else i))),x,1)
A010936: 1 20 190 1140 4845 15504 38760 77520 125970 167960 184756 167960 125970 77520 38760 15504
loop(\(x,i).(x + (64x div (if i <= 0 then 1 else i))),x,1)
A017728: 1 65 2145 47905 814385 11238513 131115985 1329890705 11969016345 97082021465 718406958841 4898229264825 31022118677225 183746395242025 1023729916348425 5391644226101705
loop(\(x,i).(x + (26x div (if i <= 0 then 1 else i))),x,1)
A010979: 1 27 378 3654 27405 169911 906192 4272048 18156204 70607460 254186856 854992152 2707475148 8122425444 23206929840 63432274896
loop(\(x,i).(x + (22x div (if i <= 0 then 1 else i))),x,1)
A010975: 1 23 276 2300 14950 80730 376740 1560780 5852925 20160075 64512240 193536720 548354040 1476337800 3796297200 9364199760
loop(\(x,i).(~x + (22x div (if i <= 0 then 1 else i))),x,1)
A010937: 1 21 210 1330 5985 20349 54264 116280 203490 293930 352716 352716 293930 203490 116280 54264
loop(\(x,i).(x + (34x div (if i <= 0 then 1 else i))),x,1)
A010987: 1 35 630 7770 73815 575757 3838380 22481940 118030185 563921995 2481256778 10150595910 38910617655 140676848445 482320623240 1575580702584
loop(\(x,i).(~x + (34x div (if i <= 0 then 1 else i))),x,1)
A010949: 1 33 528 5456 40920 237336 1107568 4272048 13884156 38567100 92561040 193536720 354817320 573166440 818809200 1037158320
loop(\(x,i).(x + (23x div (if i <= 0 then 1 else i))),x,1)
A010976: 1 24 300 2600 17550 98280 475020 2035800 7888725 28048800 92561040 286097760 834451800 2310789600 6107086800 15471286560
loop(\(x,i).(x + (33x div (if i <= 0 then 1 else i))),x,1)
A010986: 1 34 595 7140 66045 501942 3262623 18643560 95548245 445891810 1917334783 7669339132 28760021745 101766230790 341643774795 1093260079344
loop(\(x,i).(~x + (33x div (if i <= 0 then 1 else i))),x,1)
A010948: 1 32 496 4960 35960 201376 906192 3365856 10518300 28048800 64512240 129024480 225792840 347373600 471435600 565722720
loop(\(x,i).(x + (31x div (if i <= 0 then 1 else i))),x,1)
A010984: 1 32 528 5984 52360 376992 2324784 12620256 61523748 273438880 1121099408 4280561376 15338678264 51915526432 166871334960 511738760544
(if (x + ~4) <= 0 then 1 else (if ((x - (x div 4)) mod 5) <= 0 then 0 else 2))
A044946: 1 1 1 1 1 2 0 2 2 2 2 2 2 0 2 2
(loop(\(x,i).2x,x,((x + ~1) + (if (x mod 5) <= 0 then 4 else 0))) div 2)
A087982: 1 0 2 8 24 128
(loop(\(x,i).(x * (x2 div 3)),1,loop(\(x,i).(3x + 2),x,0)) div 2)
A026809: 0 1 84 2925 85320 2362041 64304604 1741001445 47050068240 1270739210481 34313445309924 926494403955165 25015631334908760 675424587904113321 4611686018427387903 4611686018427387903
(loop(\(x,i).(~2x + 1),compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x),0) div 2)
A121290: 0 1 5 85 341 5461 21845 349525 22369621 89478485 5726623061 91625968981 366503875925 5864062014805 375299968947541 24019198012642645
(2 + loop(\(x,i).(~x + (2 * compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),x,0))
A086529: 2 4 6 8 14 12 22 16 30 28 34 40 42 44 50 56
((1 + loop(\(x,i).(if x <= 0 then 1 else (x + ((2 * (x mod 2)) + (x div 3)))),x,0)) div 2)
A067570: 0 1 2 3 4 5 7
A272072: 0 1 2 3 4 5 7 10
A195944: 0 1 2 3 4 5 7 10 14
A099559: 0 1 2 3 4 5 7 10 14 19 25 33 44 59 79 105
((if (x mod 4) <= 0 then 0 else (1 + (if (x mod 3) <= 0 then (x div 3) else 1))) div 2)
A325144: 0 1 1 1 0 1 1 1 0 2 1 1 0 1 1 3
((1 + (if x <= 0 then 0 else (1 + ((x + ~1) mod (1 + (2 * (if (x mod 2) <= 0 then 2 else x))))))) div 2)
A278537: 0 1 1 2 2 3 1 4 2 5 3 6 1 7 2 8
((if x <= 0 then 2 else (1 + (x mod (1 + (x div (2 + (if (x mod 4) <= 0 then 1 else 2))))))) div 2)
A029395: 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 2
(if x <= 0 then 0 else (if (x mod (1 + (2 * (((~x + 2) mod (2 + (x div 2))) div 2)))) <= 0 then 1 else 2))
A328523: 0 1 1 1 2 1 1 1 1 2 2 2 2 2 1 1
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(12x + 2))
A017554: 1024 289254654976 141167095653376 6278211847988224 97656250000000000 839299365868340224 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(12x + 2))
A017556: 4096 56693912375296 95428956661682176 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * (1 + (3 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,x),x))))
A062548: 2 14 38 50 110 122 146 158 326 338 362 374 434 446 470 482
(2 * (~1 + (loop(\(x,i).(3x + ~1),x,2) * (1 + loop(\(x,i).2x,x,2)))))
A330170: 10 48 250 1392 8050 47448 282250 1686432 10097890 60526248 362976250 2177317872 13062296530 78368963448 470199366250 2821153019712
(2 * loop(\(x,i).(x * (2 + i)),loop(\(x,i).(1 + (5 * (1 + i))),x,1),1))
A045518: 6 6227020800 6402373705728000 4611686018427387903 4611686018427387903 4611686018427387903
((1 + loop(\(x,i).(6 * (2x - (x div (if i <= 0 then 1 else i)))),x,1)) div 2)
A098401: 1 3 27 270 2835 30618 336798 3752892 42220035 478493730 5454828522 62482581252 718549684398 8290957896900 95938227092700 1112883434275320
((1 + loop(\(x,i).((x + 1) * loop(\(x,i).(x2 + x),(x div 4),1)),x,1)) div 2)
A218270: 1 1 2 2 5 33 4611686018427387903
((1 + loop(\(x,i).(8 * (2x - (x div (if i <= 0 then 1 else i)))),x,1)) div 2)
A098402: 1 4 48 640 8960 129024 1892352 28114944 421724160 6372720640 96865353728 1479398129664 22684104654848 348986225459200 5384358907084800 83278084429578240
((1 + loop(\(x,i).(2 * (x + (6x div (if i <= 0 then 1 else i)))),x,1)) div 2)
A082140: 1 7 56 336 1680 7392 29568 109824 384384 1281280 4100096 12673024 38019072 111132672 317521920 889061376
((1 + loop(\(x,i).(2 * (x + (5x div (if i <= 0 then 1 else i)))),x,1)) div 2)
A082139: 1 6 42 224 1008 4032 14784 50688 164736 512512 1537536 4472832 12673024 35094528 95256576 254017536
(loop(\(x,i).(3 * (2x + (if (x mod 4) <= 0 then 1 else 0))),(x + 1),1) div 2)
A037648: 3 18 109 657 3942 23653 141921 851526 5109157 30654945 183929670 1103578021 6621468129 39728808774 238372852645 1430237115873
(loop(\(x,i).((x + 1) div 2),2x,loop(\(x,i).6x,(x + 1),1)) div 2)
A147789: 3 4 7 10 15 23 34 51 77 115 173 259 389 584 876 1314
(loop(\(x,i).(4x + (if ((x div 2) mod 3) <= 0 then 2 else 1)),(x + 1),1) div 2)
A037772: 3 13 52 210 843 3373 13492 53970 215883 863533 3454132 13816530 55266123 221064493 884257972 3537031890
(loop(\(x,i).(2x + loop(\(x,i).3x,(~1 + (2 * i)),2)),(x + 1),1) div 2)
A188527: 4 35 313 2813 25309 227765 2049853 18448613 166037389 1494336245 13449025693 121041230213 1089371069869 9804339624725 88239056614333 794151509512613
(2 * (if x <= 0 then 0 else loop(\(x,i).(8x * (~1 + (2 * i))),(x + ~1),1)))
A052737: 0 2 16 384 15360 860160 61931520 5449973760 566797271040 68015672524800 9250131463372800 1406019982432665600 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(3 + ((~2x + 2) mod (1 + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x))))
A227727: 3 3 3 3 3 4 3 3 4 3 3 3 5 3 7 3
(((x + 1) - (x mod loop(\(x,i).2x,loop(\(x,i).(x div (1 + (x mod 2))),x,x),1))) div 2)
A231563: 0 1 0 2 0 2 0 4 0 0 0 4 0 0 0 8
((1 + loop(\(x,i).(x + (if ((x + ~1) - i) <= 0 then (2x + 2) else ~2)),x,1)) div 2)
A132667: 1 3 2 6 5 4 12 11 10 9 8 7 21 20 19 18
((x + 3) mod (if x <= 0 then 1 else (2 * (1 + (if (~2 + (x div 3)) <= 0 then 0 else 2)))))
A303534: 0 0 1 0 1 0 1 0 1 0 1 2 3 4 5 0
((1 + ((x + 1) div (2 + (x mod (1 + loop(\(x,i).(if x <= 0 then i else (x div 2)),x,0)))))) div 2)
A229878: 0 0 1 0 1 2
A289251: 0 0 1 0 1 2 0 1 2 3 0 1 3 2 4 0
(if (x mod 3) <= 0 then (21 * (if x <= 0 then 1 else 2)) else 2)
A040436: 21 2 2 42 2 2 42 2 2 42 2 2 42 2 2 42
((1 + ((if x <= 0 then 2 else loop(\(x,i).3x,(x div 2),(x div 3))) div 2)) div 2)
A345370: 1 0 0 1 2 2 14
(3 + (2 * (if x <= 0 then 0 else (1 + (x * (2 + loop(\(x,i).x2,(x + ~1),2)))))))
A154300: 3 13 29 113
(2 * (if (x mod 3) <= 0 then (13 * (if x <= 0 then 1 else 2)) else 1))
A040670: 26 2 2 52 2 2 52 2 2 52 2 2 52 2 2 52
((1 + ((loop(\(x,i).(2x * i),(x div 2),1) + loop(\(x,i).(x * i),x,1)) div 2)) div 2)
A262480: 1 1 1 2 8 32 192 1272 10176 90816 908160 9980160 119761920 1556766720 21794734080 326918753280
((if x <= 0 then 2 else (1 + ((loop(\(x,i).(x * i),(x2 + 2x + 1),1) div 2) div 2))) div 2)
A086829: 1 3 45360 2615348736000 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 * (1 + (x div (2 + (if (x mod 10) <= 0 then 1 else 2))))))
A287155: 1 2 2 2 4 4 4 4 6 6 8 6 8 8 8 8
((1 + ((loop(\(x,i).(x + i),((if (x mod 2) <= 0 then 2 else 0) + (x div 2)),1) div 2) div 2)) div 2)
A029194: 1 0 1 0 1 1 2 1 3 1 4 2 5 3 6 4
(2 + (if (x + ~1) <= 0 then 1 else loop(\(x,i).(x2 + 2x),(x + ~2),9)))
A078225: 3 3 11 101 10001 100000001 10000000000000001 4611686018427387903 4611686018427387903
(if (x mod 4) <= 0 then (25 * (if x <= 0 then 1 else 2)) else 2)
A040620: 25 2 2 2 50 2 2 2 50 2 2 2 50 2 2 2
(loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1) mod 10)
A208279: 1 2 6 0 0 2 4 2 0 0 6 2 6 0 0 0
(if x <= 0 then 1 else ((x + 2) + ((if (x + ~4) <= 0 then 1 else 2) + (x div 5))))
A332486: 1 4 5 6 7 10 11 12 13 14 16 17 18 19 20 22
(if x <= 0 then 1 else (2 * (x mod (1 + (if (x mod (2 + (x mod 2))) <= 0 then 1 else (x div 4))))))
A264782: 1 0 0 2 0 2 0 2 0 2 0 4 0 2 0 2
((1 + loop(\(x,i).2x,(x + ~1),(loop(\(x,i).(3x + ~1),x,2) div 2))) div 2)
A154968: 1 1 7 40 244 1456 8752 52480 314944 1889536 11337472 68024320 408146944 2448879616 14693281792 88159682560
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(8x + 2))
A017099: 2048 100000000000 64268410079232 3670344486987776 70188843638032384 717368321110468608 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(~7x + ~2))
A017014: 1024 3486784401 1099511627776 41426511213649 590490000000000 4808584372417849 27197360938418176 119042423827613001 430804206899405824 1346274334462890625 3743906242624487424
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(~7x + ~2))
A017016: 4096 282429536481 281474976710656 21914624432020321 531441000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).2x,x,1) - (3 * loop(\(x,i).(2 * (2 - (i mod 2))),x,1))) div 2)
A254076: ~1 ~2 ~4 1 2 13 26 61 122 253 506 1021 2042 4093 8186 16381
(if x <= 0 then 1 else (((x + 1) div (3 * ((if (x mod 2) <= 0 then 2 else x) mod 4))) div 2))
A261139: 1 0 0 0 0 1 0 0 0 1 0 0 1 2 1 0
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(6x + 2))
A016943: 2048 8589934592 4049565169664 204800000000000 3670344486987776 36028797018963968 238572050223552512 1196683881290399744 4611686018427387903 4611686018427387903 4611686018427387903
(3 mod (2 + ((2 + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)) div 3)))
A144209: 1 1 0 1 0 0 1 0 0 0 1 0 0 0 3 1
(6 + compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)),x))
A153045: 10 13 16 18 19 22 23 25 28 30 31 33 34 37 38 40
(6 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))
A097069: 6 7 8 10 11 13 14 16 19 20 23 25 26 28 31 34
loop(\(x,i).(x + (7x div (if i <= 0 then 1 else i))),x,6)
A253947: 6 48 216 720 1980 4752 10296 20592 38610 68640 116688 190944 302328 465120 697680 1023264
(loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).(3x + 3),x,3)) div 2)
A203243: 3 39 390 3630 33033 298389 2688780 24208860 217909263 1961271939 17651713170 158866215690 1429798332693 12868192168689 115813751041560 1042323823944120
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(9x + 2))
A017194: 1024 25937424601 10240000000000 420707233300201 6278211847988224 52599132235830049 303305489096114176 1346274334462890625 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(9x + 2))
A017196: 4096 3138428376721 4096000000000000 353814783205469041 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 + (3 * compr(\x.loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,2x),x)))
A172048: 2 14 23 32 38 41 50 53 59 68 74 77 83 86 95 98
(2 + loop(\(x,i).7x,x,(~1 + loop(\(x,i).2x2,x,2))))
A091502: 3 51 6225
((1 + loop(\(x,i).(2x - ((2x - (x div (if i <= 0 then 1 else i))) mod 2)),x,2)) div 2)
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A123464: 1 2 4 8 16 32 64 128 256 512
A133025: 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8191 16382 32764
(2 * loop(\(x,i).(4x + loop(\(x,i).(3x + 1),i,1)),(x + 2),1))
A250870: 90 440 2002 8736 37130 155080 640002 2619056 10653370 43144920 174174002 701478976 2820264810 11324105960 45425564002 182089676496
(~2 + (loop(\(x,i).4x,x,4) + loop(\(x,i).3x,(x + 2),1)))
A288795: 11 41 143 497 1751 6281 22943 85217 321191 1225721 4725743 18371537 71891831 282784361 1116788543 4424107457
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),(4x + 2))
A031337: 7 19 37 53 71 89 107 131 151 173 193 223 239 263 281 311
((loop(\(x,i).5x,x,1) + loop(\(x,i).3x,2x,1)) div 2)
A081338: 1 7 53 427 3593 31087 273533 2430547 21718673 194686807 1748275013 15714943867 141336838553 1271543265727 11441447985293 102960824836387
(if x <= 0 then 1 else (loop(\(x,i).(3x + 1),(1 + (x div 2)),(1 + (x mod 2))) div 2))
A083462: 1 3 6 11
A297443: 1 3 6 11 20 33 60 101 182 303 546 911 1640 2733 4920 8201
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(10x + 2))
A017302: 1024 61917364224 26559922791424 1125899906842624 17080198121677824 144555105949057024 839299365868340224 3743906242624487424 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(10x + 2))
A017304: 4096 8916100448256 12855002631049216 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~2 + (if x <= 0 then 2 else (1 + (x * loop(\(x,i).(x2 + 4x + 6),2,3)))))
A004929: 0 842 1685 2528 3371 4214 5057 5900 6743 7586 8429 9272 10115 10958 11801 12644
((loop(\(x,i).~4x,x,1) + loop(\(x,i).6x,x,1)) div 2)
A083578: 1 1 26 76 776 3376 25376 131776 872576 4907776 30757376 179301376 1096779776 6496792576 39316299776 234555621376
((loop(\(x,i).8x,x,1) + loop(\(x,i).6x,x,1)) div 2)
A081189: 1 7 50 364 2696 20272 154400 1188544 9228416 72147712 567104000 4476365824 35448129536 281408253952 2238205337600 17827278536704
((loop(\(x,i).8x,x,1) - loop(\(x,i).6x,x,1)) div 2)
A081201: 0 1 14 148 1400 12496 107744 908608 7548800 62070016 506637824 4113568768 33271347200 268347559936 2159841173504 17357093552128
loop(\(x,i).6x,(x + ~1),(loop(\(x,i).(3x + ~1),x,1) div 2))
A099139: 0 1 12 252 4320 79056 1415232 25520832 459095040 8265390336 148766948352 2677865536512 48201216860160 867624080265216 15617220384079872 281110045277601792
(if (x + ~2) <= 0 then 1 else (~2 + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1)))
A289652: 1 1 1 3 12 40 130 427 1428 4860 16794 58784 208010 742898 2674438 9694843
(2 * loop(\(x,i).x2,1,loop(\(x,i).(x - (x div (~4 + (x div 4)))),x,1)))
A018229: 2 8 18 32 72 128 288 1152
(2 * (1 + compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),x,(~4x + 1)),x)))
A089257: 4 6 8 12 14 18 24 26 32 36 38 42 44 54 56 66
(2 + loop(\(x,i).((x2 + ~2x) div (1 + (x div 2))),1,loop(\(x,i).4x,x,1)))
A267847: 1 4 26 122 506 2042 8186 32762 131066 524282 2097146 8388602 33554426 134217722 536870906 2147483642
((loop(\(x,i).10x,x,1) + loop(\(x,i).4x,x,1)) div 2)
A081343: 1 7 58 532 5128 50512 502048 5008192 50032768 500131072 5000524288 50002097152 500008388608 5000033554432 50000134217728 500000536870912
loop(\(x,i).(2x + 1),(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),2)
A097743: 5 11 47 191 3071 12287 196607 786431 12582911 805306367 3221225471 206158430207 3298534883327 13194139533311 211106232532991 13510798882111487
loop(\(x,i).4x,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),2)
A139286: 8 32 512 8192 2097152 33554432 8589934592 137438953472 35184372088832 144115188075855872 2305843009213693952 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + loop(\(x,i).2x,x,1)) div 2)
A092176: 0 1 3 6 12 21 39 72 138 269 526 1041 2067 4116 8214 16409
loop(\(x,i).x2,1,(((x + 1) * (if (x mod 2) <= 0 then (2 + (x mod 4)) else 1)) div 2))
A227168: 1 1 36 4 25 9 196 16 81 25 484 36 169 49 900 64
(2 + compr(\x.loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,4x),(x + 1)))
A156288: 5 8 10 11 14 15 17 20 23 24 25 26 29 30 31 32
loop(\(x,i).((1 + ((loop(\(x,i).2x,x,2) mod (x + 1)) div 2)) div 2),1,(2x + 2))
A254434: 1 1 1 2 1 1 2 1 1 2 1 2 7 1 1 2
((3x + 2) - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * (1 + i)))),x,2x))
A185869: 2 7 9 16 18 20 29 31 33 35 46 48 50 52 54 67
(2 + (if x <= 0 then 2 else (loop(\(x,i).(2 * (~1 + (4 * (x div 2)))),2,x) mod (x + 1))))
A034927: 4 2 3 4 6 2 4 8
(if x <= 0 then 1 else loop(\(x,i).((4x * (~1 + (2 * i))) div (1 + i)),(x + ~1),2))
A115125: 1 2 4 16 80 448 2688 16896 109824 732160 4978688 34398208 240787456 1704034304 12171673600 87636049920
(loop(\(x,i).(10x + ~1),x,1) mod loop(\(x,i).2x,(x + ~1),2))
A234038: 1 1 1 1 9 25 57 57 57 57 569 1593 3641 3641 3641 3641
((1 + (if (x mod 2) <= 0 then 28 else 0)) * (if x <= 0 then 1 else 2))
A040840: 29 2 58 2 58 2 58 2 58 2 58 2 58 2 58 2
((1 + (if (x mod 3) <= 0 then 18 else 1)) * (if x <= 0 then 1 else 2))
A040350: 19 4 4 38 4 4 38 4 4 38 4 4 38 4 4 38
((if (x mod 4) <= 0 then 19 else 1) * (if x <= 0 then 1 else 2))
A040357: 19 2 2 2 38 2 2 2 38 2 2 2 38 2 2 2
((if (x mod 3) <= 0 then 31 else 1) * (if x <= 0 then 1 else 2))
A040954: 31 2 2 62 2 2 62 2 2 62 2 2 62 2 2 62
((if (x mod 4) <= 0 then 31 else 1) * (if x <= 0 then 1 else 2))
A040955: 31 2 2 2 62 2 2 2 62 2 2 2 62 2 2 2
((1 + (2 mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1))) * (if x <= 0 then 1 else 2))
A292586: 1 2 2 2 2 6 2 2 2 6 2 6 2 6 6 2
((if (x mod (1 + ((x + 1) mod (2 + (x div 4))))) <= 0 then 1 else 2) * (if x <= 0 then 1 else 2))
A160691: 1 2 2 2 4 2 2 4 2 2 4 2 2 4 2 4
((if (x mod 2) <= 0 then 1 else (x mod (x - ((x + ~1) mod 8)))) div (if x <= 0 then 1 else 2))
A263397: 1 0 0 0 0 0 0 0 0 0 0 1 0 2 0 3
((loop(\(x,i).3x,((x + 1) div 2),1) + loop(\(x,i).3x,x,1)) div 2)
A032120: 1 3 6 18 45 135 378 1134 3321 9963 29646 88938 266085 798255 2392578 7177734
((loop(\(x,i).7x,x,1) + loop(\(x,i).3x,x,1)) div 2)
A081336: 1 5 29 185 1241 8525 59189 412865 2885681 20186645 141267149 988751945 6920909321 48445302365 339113927909 2373787929425
(2 + ((2 * (4 + loop(\(x,i).2x,x,2))) + loop(\(x,i).3x,x,1)))
A254365: 15 21 35 69 155 381 995 2709 7595 21741 63155 185349 547835 1627101 4848515 14479989
((2 - ((2x + 1) mod (~1 + loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)))) div 2)
A177994: 1 1 1 2 1 1 2 1 1 1 3 1 2 1 1 3
(loop(\(x,i).2x,x,((~x + ~1) + loop(\(x,i).((x2 + 3x + 2) div 2),2,x))) div 2)
A033463: 1 8 50 248 1048 3952 13696 44480 137216 406016 1160704 3223552 8734720 23171072 60342272 154615808
loop(\(x,i).x2,2x,loop(\(x,i).10x,x,~4))
A204041: ~4 2560000 4611686018427387903 4611686018427387903 4611686018427387903
(2 * (loop(\(x,i).(2x + ~1),(x2 + ~x),loop(\(x,i).(2x + 1),x,0)) div 2))
A153836: 0 0 8 384 57344 31457280 66571993088 554153860399104 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 * ((1 + (loop(\(x,i).~2x,x,1) div 5)) div 2)))
A118405: 1 0 0 ~2 4 ~6 12 ~26 52 ~102 204 ~410 820 ~1638 3276 ~6554
(2 + (if x <= 0 then 3 else (2 * (if (~x + 2) <= 0 then 1 else 13))))
A052470: 5 28 4 4 4 4 4 4 4 4 4 4 4 4 4 4
(((1 + loop(\(x,i).(x + ((if ((x + ~1) mod 3) <= 0 then 1 else x) + i)),x,1)) div 2) div 2)
A192225: 0 1 2 5
A058668: 0 1 2 5 6 13 28
(2 + ((1 + (loop(\(x,i).(x + loop(\(x,i).2x,(x mod (1 + i)),2)),x,0) div 2)) div 2))
A078139: 2 3 5 7 11 19 23
(2 * (if x <= 0 then 0 else ((x + 2) + ((if (x + ~2) <= 0 then 1 else 2) + (x div 5)))))
A167692: 0 8 10 14 16 20 22 24 26 28 32 34 36 38 40 44
((loop(\(x,i).2x,x,(3 + (loop(\(x,i).2x,x,1) + (x mod 2)))) div 2) div 2)
A225826: 1 3 7 24 76 288 1072 4224 16576 66048 262912 1050624 4197376 16785408 67121152 268468224
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(12x + 4))
A017578: 1048576 1099511627776 296196766695424 10485760000000000 144555105949057024 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(12x + 4))
A017580: 16777216 281474976710656 232218265089212416 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(8x + 4))
A017123: 4194304 743008370688 204800000000000 8293509467471872 131621703842267136 1196683881290399744 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(~7x + ~4))
A017038: 1048576 25937424601 3570467226624 95367431640625 1125899906842624 8140406085191601 42420747482776576 174887470365513049 604661760000000000 1822837804551761449 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(~7x + ~4))
A017040: 16777216 3138428376721 1156831381426176 59604644775390625 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * loop(\(x,i).(x * (~1 + (loop(\(x,i).2x,i,1) + (i mod 2)))),(2x + 1),2))
A003956: 8 192 92160 743178240 97029351014400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).10x,x,1) mod loop(\(x,i).(2x2 + ~1),2,2))
A243239: 1 10 3 30 9 90 27 76 81 34 49 5 50 15 53 45
(loop(\(x,i).7x,x,1) mod loop(\(x,i).(x2 + 2x + 1),2,2))
A014390: 1 7 49 43 1 7 49 43 1 7 49 43 1 7 49 43
(4 + (if x <= 0 then 2 else (1 + (x2 * (2 + loop(\(x,i).x2,x,3))))))
A118949: 6 16 337
(if x <= 0 then 0 else (x - ((x + 1) mod (2 * (~1 - (if (x + ~4) <= 0 then 0 else 2))))))
A343045-A343041: 0 1 3 3 5 5 11 11 11 11 11 11 17 17 17 17
(if x <= 0 then 1 else (2 + ((x + 1) div (2 + (if ((x + ~1) mod 5) <= 0 then 1 else 2)))))
A194287: 1 2 2 3 3 3 4 4 4 4 4 6 5 5 5 6
((if x <= 0 then 2 else ((if (x mod 2) <= 0 then x else (~x + 1)) mod 20)) div 2)
A137301: 1 0 1 9 2 8 3 7 4 6 5 5 6 4 7 3
(((loop(\(x,i).x2,1,(1 + ((if (x mod 2) <= 0 then 2 else 0) + (x div 2)))) div 2) div 2) div 2)
A008734: 1 0 2 0 3 1 4 2 6 3 8 4 10 6 12 8
(2 + (if x <= 0 then 0 else (2 + (x div (2 + (if ((x div 3) mod 3) <= 0 then 1 else 2))))))
A104058: 2 4 4 4 5 5 5 5 6 7 7 7 7 7 7 7
(if (x mod 2) <= 0 then 1 else (2 * (if ((x + 1) mod 8) <= 0 then 8 else 2)))
A240226: 1 4 1 4 1 4 1 16 1 4 1 4 1 4 1 16
(4 + (if x <= 0 then 1 else ((x + 4) + (if (~2 + (x div 2)) <= 0 then 1 else 4))))
A262665: 5 10 11 12 13 14 18 19 20 21 22 23 24 25 26 27
(2 * loop(\(x,i).2x,(x + 2),(2 + loop(\(x,i).2x,(x div 2),(2 + (x mod 2))))))
A234133: 32 80 192 512 1280 3584 9216 26624 69632 204800 540672 1605632 4259840 12713984 33816576 101187584
(loop(\(x,i).6x,x,1) mod (~2 + loop(\(x,i).(x3 + 2),2,2)))
A216127: 1 6 36 216 296 776 656 936 616 696 176 56 336 16 96 576
(loop(\(x,i).5x,x,1) mod (~2 + loop(\(x,i).(x3 + 2),2,2)))
A216125: 1 5 25 125 625 125 625 125 625 125 625 125 625 125 625 125
(loop(\(x,i).(x + (8x div (if i <= 0 then 1 else i))),x,1) mod 8)
A133888: 1 1 5 5 7 7 3 3 6 6 6 6 2 2 2 2
(8 + compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)),x))
A153047: 12 15 18 20 21 24 25 27 30 32 33 35 36 39 40 42
(8 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))
A097363: 8 9 10 12 13 15 16 18 21 22 25 27 28 30 33 36
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(12x + 8))
A017626: 1073741824 10240000000000 1125899906842624 27197360938418176 303305489096114176 2113922820157210624 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(12x + 8))
A017628: 68719476736 4096000000000000 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).x2,1,loop(\(x,i).(10x + 2),x,2)) div 2) div 2)
A080162: 1 121 12321 1234321 123454321 12345654321 1234567654321 123456787654321 12345678987654321 4611686018427387903
A068117: 1 121 12321 1234321 123454321 12345654321 1234567654321 123456787654321 12345678987654321 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A261570-A173426: 1 121 12321 1234321 123454321 12345654321 1234567654321 123456787654321 12345678987654321 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),(x + 6))
A224534: 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83
(loop(\(x,i).(10x + (if (~2 + i) <= 0 then 0 else 2)),2x,2) div 2)
A267523: 1 100 10011 1001111 100111111 10011111111 1001111111111 100111111111111 10011111111111111 1001111111111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(8x + (if x <= 0 then 5 else (x + (if (x + ~2) <= 0 then 1 else x))))
A191595: 5 10 19 30 40 50
((x - (3 * (~1 + loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)))) div 4)
A332502: 0 1 1 3 2 2 4 4 3 3 6 5 5 4 4 8
(1 - ((if (x mod 2) <= 0 then (if (x mod 3) <= 0 then 1 else x) else (x mod 3)) mod 4))
A071859: 0 0 ~1 1 1 ~1 0 0 1 1 ~1 ~1 0 0 ~1 1
(4 * loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),(2x + ~1),x))
A268149: 0 24 1120 33264 823680 18475600 389398464 7862853600 153876579840 2940343837200 55138611528000 1018383898440480 18574619721465600 335240928272918304 4611686018427387903 4611686018427387903
((x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1))) mod 4)
A092412: 1 2 1 3 1 2 1 0 1 2 1 3 1 2 1 1
loop(\(x,i).((x + 1) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,4)
A073679: 4 6 9 14 21 32 45 62 81 104 133 164 201 242 285 332
((x * loop(\(x,i).(x + loop(\(x,i).3x,(x + ~2),x)),1,(x + ~1))) div 4)
A229665: 0 0 1 3 12 50 210 861 3416 13140 49230 180455 649572 2302950 8060234 27900705
(if x2 <= 0 then 1 else loop(\(x,i).x3,1,(12x + 16)))
A066693: 1 21952 64000
(4 * compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),x,(~4x + 1)),x))
A090658: 4 8 12 20 24 32 44 48 60 68 72 80 84 104 108 128
(4 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,4x),x))
A083094: 0 8 20 24 56 60 72 80 164 168 180 188 216 224 236 240
(~4 + loop(\(x,i).x2,1,compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)))
A245034: 5 21 77 117 221 285 437 725 837 1221 1517 1677 2021 2597 3245 3477
loop(\(x,i).4x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),4)
A139288: 4 16 256 4096 1048576 16777216 4294967296 68719476736 17592186044416 72057594037927936 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(2 * (~1 + (2 * (x + (i mod 2))))),x,1) + loop(\(x,i).~x,x,4))
A007572: 5 2 26 86 362 1430 5738 22934 91754 366998 1468010 5872022 23488106 93952406 375809642 1503238550
(~4 + compr(\x.(2 - loop(\(x,i).(0 - (if (x mod (1 + i)) <= 0 then 0 else x)),(x div 2),x)),x))
A097539: 1 9 13 25 33 37 49 57 69 85 93 97 105 109 133 145
loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),x,4)
A088860: 4 12 60 420 4620 60060 1021020 19399380 446185740 12939386460 401120980260 14841476269620 608500527054420 26165522663340060 1229779565176982820 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(10x + 4))
A017326: 1048576 289254654976 63403380965376 2064377754059776 27197360938418176 210832519264920576 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(10x + 4))
A017328: 16777216 56693912375296 36520347436056576 2386420683693101056 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(6x + 4))
A016967: 4194304 100000000000 17592186044416 584318301411328 8293509467471872 70188843638032384 419430400000000000 1951354384207722496 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(3 * (~x + (2 * (2x - (x div (if i <= 0 then 1 else i)))))),x,2) div 2)
A004987: 1 3 18 126 945 7371 58968 480168 3961386 33011550 277297020 2344420260 19927572210 170150808870 1458435504600 12542545339560
(2 + (if x <= 0 then 0 else (loop(\(x,i).(2 + (x div (2 + (3 * (x mod 2))))),2,x) div 2)))
A049837: 2 3 3 3 4 3 3 3 4 3 3 4 5 4 3 3
(2 * (loop(\(x,i).(5x + 2),x,2) - loop(\(x,i).4x,x,2)))
A054401: 0 8 60 368 2100 11528 61740 325088 1690980 8717048 44633820 227363408 1153594260 5835080168 29443836300 148292923328
(2 * loop(\(x,i).x2,1,(2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))))
A143928: 18 50 98 242 338 578 722 1058 1682 1922 2738 3362 3698 4418 5618 6962
(loop(\(x,i).x2,1,(2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) div 2)
A216244: 4 12 24 60 84 144 180 264 420 480 684 840 924 1104 1404 1740
(2 + loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A061725: 6 11 27 51 123 171 291 363 531 843 963 1371 1683 1851 2211 2811
(~2 + loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A049001: 2 7 23 47 119 167 287 359 527 839 959 1367 1679 1847 2207 2807
(2 * loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A079704: 8 18 50 98 242 338 578 722 1058 1682 1922 2738 3362 3698 4418 5618
loop(\(x,i).4x,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),2)
A100626: 32 128 2048 32768 8388608 134217728 34359738368 549755813888 140737488355328 576460752303423488 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * loop(\(x,i).x2,2,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A172191: 32 162 1250 4802 29282 57122 167042 260642 559682 1414562 1847042 3748322 5651522 6837602 9759362 15780962
loop(\(x,i).x2,1,(2 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A069262: 16 36 100 196 484 676 1156 1444 2116 3364 3844 5476 6724 7396 8836 11236
loop(\(x,i).2x,x,(2 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A265127: 4 12 40 112 352 832 2176 4864 11776 29696 63488 151552 335872 704512 1540096 3473408
(loop(\(x,i).2x,x,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A188545: 1 3 10
A239885: 1 3 10 28 88 208 544 1216 2944 7424 15872 37888 83968 176128 385024 868352
(2 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + loop(\(x,i).2x,x,2)))
A265160: 4 7 13 23 43 77 145 275 535 1053 2079 4133 8233 16427 32815 65589
loop(\(x,i).(((x3 + ~x) div 2) div 3),1,(2 * (if x <= 0 then 1 else (x + 2))))
A156126: 1 35 84 165 286 455 680 969 1330 1771 2300 2925 3654 4495 5456 6545
(compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + (2 * (if x <= 0 then 1 else (x + 2))))
A174008: 2 7 11 15 21 25 31 35 41 49 53 61 67 71 77 85
(loop(\(x,i).(x + (7x div (if i <= 0 then 1 else i))),x,(x + 2)) div 2)
A052181: 1 12 72 300 990 2772 6864 15444 32175 62920 116688 206856 352716 581400 930240 1449624
(if x <= 0 then 1 else (2 * (2x + loop(\(x,i).(2 + (x div 2)),(x + ~8),1))))
A315172: 1 6 10 14 18 22 26 30 34 40 46 50 54 58 62 66
(if x <= 0 then 1 else (2 * (2x + ((x + (if (~2 + (x div 4)) <= 0 then 1 else 2)) div 2))))
A315307: 1 6 10 16 20 26 30 36 40 46 50 56 62 66 72 76
(4x + (if x <= 0 then 1 else (x div (3 + (if (x + ~4) <= 0 then 0 else 2)))))
A058759: 1 4 8 13
A311801: 1 4 8 13 17 21 25 29 33 37 42 46 50 54 58 63
(((x + (if (~2 + (x div 4)) <= 0 then 1 else 2)) div 2) + (if x <= 0 then 1 else 4x))
A314837: 1 5 9 14 18 23 27 32 36 41 45 50 55 59 64 68
loop(\(x,i).(x + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),i,1)),2x,2)
A099975: 2 9 65 626 6918 82500 1033412 13402697 178405157 2423307047 33453694487 467995871777 6619846420553 94520750408709 1360510918810437 19720133460129650
(2x - ((x - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * (1 + i)))),x,2x)) div 2))
A116941: 0 1 3 2 4 6 5 7 9 11 8 10 12 14 16 13
loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),2x,2)
A099800: 2 30 2310 510510 223092870 200560490130 304250263527210 614889782588491410 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(((if x <= 0 then 2 else ((1 + loop(\(x,i).2x,x,1)) div 5)) + (x div 2)) div 2)
A321402: 1 0 1 1 2 4 8 14 27 53 105
(x + (loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,x) + (2 * (x div 2))))
A093051: 0 1 4 3 7 5 8 7 12 9 12 11 15 13 16 15
(2 * ((2 * (if (x mod 4) <= 0 then (3 * (if x <= 0 then 1 else 2)) else 1)) - (x mod 2)))
A040142: 12 2 4 2 24 2 4 2 24 2 4 2 24 2 4 2
(if x <= 0 then 1 else (2 * loop(\(x,i).(10x + 4),(x div 2),(x mod 2))))
A279193: 1 2 8 28 88 288 888 2888 8888 28888 88888 288888 888888 2888888 8888888 28888888
(2 + (compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),x) + (x mod 2)))
A033160: 2 4 5 7 11 13 14 16 29 31 32 34 38 40 41 43
(4 + compr(\x.loop(\(x,i).(if (x mod 4) <= 0 then 0 else (1 + (x div 4))),2,x),x))
A196032: 4 8 12 16 17 18 19 20 24 28 32 33 34 35 36 40
(loop(\(x,i).2x,x,loop(\(x,i).(x + (((4 + i) * (1 + i)) div 2)),x,2)) div 2)
A001794: 1 7 32 120 400 1232 3584 9984 26880 70400 180224 452608 1118208 2723840 6553600 15597568
(2 * (2 + compr(\x.(2 - loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x)),x)))
A061673: 26 34 50 56 64 76 86 92 94 116 118 120 122 124 134 142
(2 * compr(\x.(if (x mod 2) <= 0 then (if x <= 0 then 1 else (x2 mod (x + 6))) else 0),x))
A095300: 2 6 10 12 14 18 22 24 26 30 34 38 42 46 50 54
(if x <= 0 then 1 else (2 + compr(\x.(~1 + (x mod (~1 + (loop(\(x,i).2x,x,x) mod (x + 1))))),x)))
A063977: 1 3 4 5 6 8 9 10 12 14 17 18 20 24 26 28
(2 * (x + (if (~x + 2) <= 0 then (1 + (2 * ((x + 1) + (if (x + ~2) <= 0 then 1 else 2)))) else 1)))
A298471: 2 4 22 32 38 44 50 56 62 68 74 80 86 92 98 104
loop(\(x,i).x2,1,(if x <= 0 then 1 else (2 * (x + (x div 11)))))
A221285: 1 4 16 36 64 100 144 196 256 324 400 576 676 784 900 1024
(2 + (if (~x + 2) <= 0 then (1 + (4 * (2 + loop(\(x,i).2x,x,3)))) else x))
A299172: 2 3 59 107
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(5x + 2))
A016883: 2048 1977326743 743008370688 34271896307633 584318301411328 5559060566555523 36028797018963968 177917621779460413 717368321110468608 2472159215084012303 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,10x)
A017279: 0 100000000000 204800000000000 17714700000000000 419430400000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(4x + 1))),x))
A104636: 2 6 8 14 18 20 26 30 36 44 48 50 54 56 68 74
(2 * compr(\x.((1 + loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x + ~2),x)) mod 3),x))
A250398-A112774: 4 10 22 34 46 58 82 94 106 118 142 166 178 202 214 226
(2 * (x + (if (x + ~2) <= 0 then 1 else (3 * (if (~2 + (x div 3)) <= 0 then 1 else 2)))))
A067874: 2 4 6 12 14 16 18 20 22 30 32 34 36 38 40 42
(loop(\(x,i).3x,2x,3) - loop(\(x,i).6x,x,2))
A016172: 1 15 171 1755 17091 161595 1501011 13789035 125780931 1142106075 10339420851 93417584715 842935044771 7599476096955 68473649036691 616733026314795
loop(\(x,i).(7x + (if (~1 + (i mod 3)) <= 0 then 2 else 1)),x,2)
A037564: 2 16 113 793 5553 38872 272106 1904744 13333209 93332465 653327257 4573290800 32013035602 224091249216 1568638744513 10980471211593
compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),(3x + 2))
A031336: 5 13 23 37 47 61 73 89 103 113 137 151 167 181 197 223
(loop(\(x,i).2x,(x + ~1),(x + (3 * loop(\(x,i).2x,(x + ~1),x)))) div 2)
A133224: 0 2 14 78 400 1960 9312 43232 197120 885888 3934720 17307136 75509760 327182336 1409343488 6039920640
loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),x,((x2 + 3x) div 2))
A178978: 0 2 5 1 14 20 1 35 44 2 65 77 10 104 119 5
(2 + compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(3x + 1))),x))
A107303: 4 6 8 12 14 16 22 24 26 28 34 36 38 44 48 52
(~2 + compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(3x + 1))),x))
A089953: 0 2 4 8 10 12 18 20 22 24 30 32 34 40 44 48
(loop(\(x,i).(5x + 1),x,1) + loop(\(x,i).(3x + ~1),x,2))
A146086: 3 11 45 197 903 4271 20625 100937 498123 2470931 12295605 61300877 305972943 1528270391 7636568985 38168496017
(2 + compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + x + 1))),x))
A089358: 3 4 5 7 8 10 14 16 17 19 22 23 26 29 35 40
(2 + compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + x + ~1))),x))
A076597: 4 5 6 7 8 10 11 12 13 15 17 18 21 22 23 26
(2 + compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + ~x + ~1))),x))
A089362: 5 6 7 8 9 11 12 13 14 16 18 19 22 23 24 27
(if x <= 0 then 1 else (2 * ((x + 1) + loop(\(x,i).(x + (x div ((2 + i) * (1 + i)))),2,x))))
A315177: 1 6 10 14 18 22 28 32 36 40 44 50 56 60 64 68
(compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + 2x + ~1))),x) div 2)
A088572: 1 2 3 4 6 7 9 10 13 14 16 17 18 21 23 24
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(10x + 8))
A017374: 1073741824 3570467226624 296196766695424 6278211847988224 64925062108545024 430804206899405824 2113922820157210624 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(10x + 8))
A017376: 68719476736 1156831381426176 232218265089212416 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * (loop(\(x,i).(2x + 2),(x div 2),(x mod 2)) + loop(\(x,i).2x,(x + ~1),x)))
A208903: 0 4 12 32 76 180 412 940 2108 4700 10364 22716 49404 106876 229884 492284
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(x div 2),((if x <= 0 then 1 else x) mod 2))
A097331: 1 1 0 1 0 2 0 5 0 14 0 42 0 132 0 429
(2 * compr(\x.(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then x else 3)),x,x)),x))
A088967: 2 4 8 10 14 20 22 28 32 34 38 44 50 52 58 62
loop(\(x,i).(9x + (if (~1 + (i mod 3)) <= 0 then 2 else 1)),x,2)
A037566: 2 20 181 1631 14681 132130 1189172 10702550 96322951 866906561 7802159051 70219431460 631974883142 5687773948280 51189965534521 460709689810691
(((x + ~1) mod loop(\(x,i).(2 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2)),2,x)) div 2)
A035217: 1 0 0 1 1 0 1 0 1 0 0 0 2 0 0 1
(x div (if x <= 0 then 1 else (x mod (2 + (if ((x + 1) mod 5) <= 0 then 4 else x)))))
A058663: 0 1 1 1 1 1 1 1 1 3 1 1 1 1 7 1
(2 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 4 else 0))),x,4x),x))
A108783: 0 2 6 10 12 26 30 32 36 50 52 56 60 62 126 130
(2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,4x)),x))
A087915: 0 2 4 8 10 14 20 22 28 32 34 38 40 50 52 62
loop(\(x,i).((2x + 2) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)),x,2)
A110299: 2 7 19 45 101 215 447 913 1849 3727 7485 15007 30055 60153 120353 240759
loop(\(x,i).(10x + (if (~1 + (i mod 3)) <= 0 then 2 else 1)),x,2)
A037567: 2 22 221 2212 22122 221221 2212212 22122122 221221221 2212212212 22122122122 221221221221 2212212212212 22122122122122 221221221221221 2212212212212212
(2 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(3x + 2))),x))
A228121: 2 3 5 7 9 11 15 17 19 21 25 29 31 35 37 39
(2 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + 2x + 2))),x))
A090693: 2 3 5 7 11 15 17 21 25 27 37 41 55 57 67 75
loop(\(x,i).x2,4,(2 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x)))
A030635: 65536 43046721 152587890625 33232930569601 45949729863572161 665416609183179841 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 - loop(\(x,i).(~2x + 2),compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x),2))
A126614: 3 11 43 683 2731 43691 174763 2796203 178956971 715827883 45812984491 733007751851 2932031007403 46912496118443 3002399751580331 192153584101141163
(if x <= 0 then 1 else (2 + compr(\x.(1 - (loop(\(x,i).(x * (i * i)),(x div 2),1) mod (x + 2))),x)))
A026482-A026423: 1 3 4 5 6 7 8 10 11 13 14 17 19 22 23 26
(2 + compr(\x.(loop(\(x,i).(x * (1 + (if (x mod (1 + i)) <= 0 then 0 else i))),x,1) mod (x + 2)),x))
A268388-A089229: 6 8 10 12 14 15 18 20 21 22 24 26 27 28 30 32
(~2 + loop(\(x,i).2x,x,1) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A277801: ~1 ~1 ~1 1 5 19 47 109 233 483 993 2011 4055 8149 16337 32715
(~2 + loop(\(x,i).2x,x,2) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A088110: 0 1 3 9
A111209: 0 1 3 9 21 51 111 237 489 995 2017 4059 8151 16341 32721 65483
(2 + (if (x mod 2) <= 0 then 2x else compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A062720: 2 3 6 7 10 13 14 19 18 29 22 37 26 43 30 53
loop(\(x,i).x2,3,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A179645: 256 6561 390625 5764801 214358881 815730721 6975757441 16983563041 78310985281 500246412961 852891037441 3512479453921 7984925229121 11688200277601 23811286661761 62259690411361
loop(\(x,i).(x2 + x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A036690: 6 12 30 56 132 182 306 380 552 870 992 1406 1722 1892 2256 2862
(loop(\(x,i).2x,x,1) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A175036: 1 2 4 1 5 6 13 14 3 19 1 13 37 22 28 14
loop(\(x,i).x3,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A030078: 8 27 125 343 1331 2197 4913 6859 12167 24389 29791 50653 68921 79507 103823 148877
(loop(\(x,i).2x,x,2) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A064367: 0 1 3 2 10 12 9 9 6 9 2 26 33 1 9 28
loop(\(x,i).x3,2,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A179665: 512 19683 1953125 40353607 2357947691 10604499373 118587876497 322687697779 1801152661463 14507145975869 26439622160671 129961739795077 327381934393961 502592611936843 1119130473102767
(2 + compr(\x.(loop(\(x,i).x2,1,(loop(\(x,i).2x,x,2) - (x mod 2))) mod (x + 2)),x))
A115919-A038701: 2 3 4 5 7 8 9 11 13 16 17 19 23 25 29 31
loop(\(x,i).(2x + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),i,1)),x,2)
A088854: 2 7 24 83 292 1046 3808 14051 52412 197202 747120 2846318 10892936 41844172 161247104 623034403
(loop(\(x,i).(x + ((i mod 2) + (x div 3))),x,3) + loop(\(x,i).2x,x,2))
A169872: 5 9 14 25 44 81 150
loop(\(x,i).(x5 + x4 + x3 + x2 + x),1,loop(\(x,i).2x,x,2))
A115504: 62 1364 37448 1118480 34636832 1090785344 34630287488 1103823438080 35253226045952 1127000493261824 36046397799139328 1153203048319815680 4611686018427387903 4611686018427387903
(loop(\(x,i).(4x + ((x + 1) mod 4)),x,1) div loop(\(x,i).2x,x,2))
A212444: 0 1 3 6 13 27 54 108 216 433 867 1734 3469 6939 13878 27756
(((1 + (x * loop(\(x,i).x3,2,x))) * loop(\(x,i).x3,2,x)) div 2)
A170792: 0 1 262400 581140575 137439084544 9536744140625 304679875044096 5699447612863375 72057594105036800 675425859030206289 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) + (if x <= 0 then 0 else (~1 + loop(\(x,i).(2 * ((x * i) + (i div 2))),x,0))))
A032115: 1 1 4 17 120 1169 13980 195649 3130288 56345057 1126900980 24791821361 595003712424 15470096522737 433162702636300 12994881079088609
((1 + loop(\(x,i).(4 * (2x + (x div (if i <= 0 then 1 else i)))),x,1)) div (x + 2))
A082144: 1 4 30 224 1680 12672 96096 732160 5601024 42997760 331082752 2556051456 19778969600 153363087360 1191302553600 9268801044480
((x + 2) * loop(\(x,i).(x + (3 * (2x div (if i <= 0 then 1 else i)))),x,3))
A027811: 6 63 336 1260 3780 9702 22176 46332 90090 165165 288288 482664 779688 1220940 1860480 2767464
loop(\(x,i).((x * loop(\(x,i).(x3 + ~x),1,2x2)) div 2),1,(x + 2))
A253724: 504 8721 65472 312375 1119528 3293829 8388096 19131147 39999000 77947353 143325504 250991871 421651272 683434125 1073737728 1641349779
((((x + 1) * loop(\(x,i).((x + 2) + (x div (if i <= 0 then 1 else i))),x,2)) div 2) div (x + 2))
A278450: 0 2 4 6 9 12 14 17 21 24 27 31 34 38 41 45
((x2 + 2x + 1) mod loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 1 else 0)),x,(x + 2)))
A257231: 1 1 4 1 4 1 5 9 4 1 4 1 16 9 4 1
(2x + (if ((x - (if (~2 + (x div 4)) <= 0 then 1 else 2)) mod 4) <= 0 then 2 else 1))
A286050: 1 4 5 7 9 12 13 15 17 20 21 23 25 27 30 31
loop(\(x,i).(if x <= 0 then 1 else (2 * (x + ((x3 + 2x) div 3)))),1,2x)
A001386: 1 12 56 164 368 700 1192 1876 2784 3948 5400 7172 9296 11804 14728 18100
(loop(\(x,i).(4 * (2x - (x div (if i <= 0 then 1 else i)))),x,1) div (~2x + 1))
A098579: 1 ~4 ~8 ~32 ~160 ~896 ~5376 ~33792 ~219648 ~1464320 ~9957376 ~68796416 ~481574912 ~3408068608 ~24343347200 ~175272099840
(3x + (loop(\(x,i).3x,x,2) + loop(\(x,i).4x,x,1)))
A290720: 3 13 40 127 430 1525 5572 20779 78682 301537 1166704 4548631 17840134 70297549 278001436 1102439683
(2x + loop(\(x,i).(x - (if (x + ~1) <= 0 then 2 else (x div (2 - (x mod 2))))),x,(x + 1)))
A127750: 1 3 2 5 2 4 2 7 2 4 2 6 2 4 2 9
(2x + (if ((x - (if (~2 + (x div 4)) <= 0 then 1 else 2)) mod 4) <= 0 then 1 else 2))
A286051: 2 3 6 8 10 11 14 16 18 19 22 24 26 28 29 32
(2x + (if x <= 0 then 1 else (if (x div 5) <= 0 then 0 else ~7)))
A220102: 1 2 4 6 8 3 5 7 9 11 13 15 17 19 21 23
((if x <= 0 then 1 else (x + (2 * loop(\(x,i).(x + (i * i)),x,x)))) - (x div 2))
A174655: 1 5 15 36 70 123 197 298 428 593 795 1040 1330 1671 2065 2518
(loop(\(x,i).(10x + 1),(if (x mod 2) <= 0 then x else 1),1) - (x mod 2))
A282452: 1 10 111 10 11111 10 1111111 10 111111111 10 11111111111 10 1111111111111 10 111111111111111 10
((if x <= 0 then 1 else (1 + (2 * (if (x mod 2) <= 0 then 2 else (2x2 + 2x))))) - (x mod 2))
A272007: 1 8 5 48 5 120 5 224 5 360 5 528 5 728 5 960
((if ((2x div (2 + (x mod 2))) mod 3) <= 0 then (if x <= 0 then 1 else 2) else 1) - (x mod 2))
A280748: 1 1 1 0 1 1 2 0 1 1 1 0 2 0 1 0
(if (x + ~1) <= 0 then 1 else (loop(\(x,i).(10x + 1),x,1) * (x mod 2)))
A277927: 1 1 0 1111 0 111111 0 11111111 0 1111111111 0 111111111111 0 11111111111111 0 1111111111111111
((if x <= 0 then 0 else (if (x mod (1 + (4 mod (1 + (x div 2))))) <= 0 then 1 else 2)) - (x mod 2))
A305054: 0 0 1 0 1 1 1 0 2 1 1 1 2 1 2 0
((2 * ((if (x mod 4) <= 0 then 8 else 1) * (if x <= 0 then 1 else 2))) - (x mod 2))
A040249: 16 3 4 3 32 3 4 3 32 3 4 3 32 3 4 3
((if (x mod 3) <= 0 then (5 * (if x <= 0 then 1 else 2)) else 1) * (2 - (x mod 2)))
A010179: 10 1 2 10 2 1 20 1 2 10 2 1 20 1 2 10
((if (x mod 3) <= 0 then (8 * (if x <= 0 then 1 else 2)) else 1) * (2 - (x mod 2)))
A040261: 16 1 2 16 2 1 32 1 2 16 2 1 32 1 2 16
loop(\(x,i).(2x + 2),(if ((x + 2) mod 4) <= 0 then 0 else 1),(x div (2 - (x mod 2))))
A065260: 2 4 1 8 6 12 3 16 10 20 5 24 14 28 7 32
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),(2x - (x mod 2)))
A060192: 3 5 13 17 29 31 43 47 61 67 79 83 101 103 113 127
loop(\(x,i).((x + 1) * (if (8 mod (x + 1)) <= 0 then 2 else 1)),(x div 2),(x mod 2))
A307613: 0 1 2 4 3 5 8 6 9 7 10 16 11 17 12 18
(2 * loop(\(x,i).(3 * loop(\(x,i).(x + 4),(x mod 3),2x)),x,x))
A181685: 0 36 432 1296 15552 139968 559872 5038848 40310784 181398528 1451188224 10883911680 52242776064 391820820480 2821109907456 14105549537280
(2 + compr(\x.(~x + loop(\(x,i).x2,1,loop(\(x,i).(x div (~2 + (x mod 2))),x,(x + 1)))),x))
A080075: 3 5 9 13 17 25 33 41 49 57 65 81 97 113 129 145
(if x <= 0 then 1 else (2 * (2x + loop(\(x,i).(x - (x div 8)),2,(x + ~1)))))
A310531: 1 4 10 16 22 28 34 40 46 50 54 60 66 72 78 84
loop(\(x,i).(10x + (if (i mod 3) <= 0 then 2 else 1)),x,2)
A037559: 2 21 211 2112 21121 211211 2112112 21121121 211211211 2112112112 21121121121 211211211211 2112112112112 21121121121121 211211211211211 2112112112112112
(2 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),x))
A206023-A067829: 3 5 7 13 19 31 43 61 73 103 109 139 151 181 193 199
(loop(\(x,i).(x + (if ((x + 1) mod 10) <= 0 then (x + 2) else 1)),x,x) div 2)
A058185: 0 1 2 3 4 10 11 12 13 14 20 21 22 23 24 50
((x * loop(\(x,i).(x + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,x)) div 2)
A156778: 0 1 5 15 34 70 123 203 308 450 645 880 1182 1547 1967 2460
(x + loop(\(x,i).(if x <= 0 then 1 else ((2x * (~1 + (2 * i))) div (1 + i))),(x + ~1),0))
A192480: 0 1 3 5 9 19 48 139 437 1439 4872 16807 58798 208025 742914 2674455
(x + loop(\(x,i).((x2 + x) div 2),1,(1 - loop(\(x,i).(2x + ~4),(x + ~2),0))))
A288492: 1 2 3 18 95 440 1897 7882 32139 129804 521741 2092046 8378383 33533968 134176785 536789010
(2 - (if x <= 0 then 1 else (x + loop(\(x,i).(x + (x div 12) - i),x,0))))
A084267: 1 2 4 7 11 17 24 33 44 57 72 89 109 131 156 184
(x * loop(\(x,i).(4x + loop(\(x,i).6x,(~2 + i),1)),x,0))
A082136: 0 1 10 78 560 3880 26400 177632 1185280 7853184 51699200 338331136 2201948160 14258137088 91894620160 589744496640
(x * loop(\(x,i).(3x + loop(\(x,i).5x,(~2 + i),1)),x,0))
A082135: 0 1 8 51 304 1765 10104 57239 321248 1787337 9864040 54035707 294031632 1590368429 8556082136 45812239455
((x + 1) + loop(\(x,i).((x + 2) + (if (x mod (2 + (x div 4))) <= 0 then 1 else 2)),x,0))
A313717: 1 5 10 15 20 24 28 32 36 41 46 51 56 61 66 71
compr(\x.(loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (~1 + (x mod 5))),x)
A187127-A187126: 0 1 3 5 6 10 11 15 16 20 21 25 26 28 30 31
compr(\x.(~1 + (((x + 2) * loop(\(x,i).(2 + (if (~x + i) <= 0 then 0 else x)),x,1)) mod 3)),x)
A080723: 1 4 5 6 7 10 13 16 17 18 19 20 21 22 23 24
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,7x)
A016991: 0 1977326743 4049565169664 350277500542221 8293509467471872 96549157373046875 717368321110468608 3909821048582988049 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (x * loop(\(x,i).(10x + 1),8,1)))
A202174: 1 111111111 222222222 333333333 444444444 555555555 666666666 777777777 888888888 999999999
loop(\(x,i).loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 3)),1,5x)
A270968: 3 1 13 9 23 7 33 19 43 3 53 29 63 17 73 39
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),5x)
A031386: 3 17 37 59 79 103 131 157 181 211 239 269 293 331 359 389
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(4x + 1)),x)
A153129: 2 5 8 9 10 11 14 15 16 17 20 23 25 26 27 29
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(7x + 3))
A017026: 59049 10000000000 2015993900449 63403380965376 819628286980801 6278211847988224 34050628916015625 144555105949057024 511116753300641401 1568336880910795776 4297625829703557649
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(7x + 3))
A017028: 531441 1000000000000 582622237229761 36520347436056576 787662783788549761 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(7x + 6))
A017062: 60466176 137858491849 10240000000000 205891132094649 2064377754059776 13422659310152401 64925062108545024 253295162119140625 839299365868340224 2446194060654759801 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(7x + 6))
A017064: 2176782336 23298085122481 4096000000000000 150094635296999121 2386420683693101056 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.(1 + loop(\(x,i).(x - (if (x mod (3 + i)) <= 0 then x else 3)),x,(x + 2))),x)
A209837: 3 5 9 15 17 23 27 29 33 39 45 47 53 57 59 65
compr(\x.(x div loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,(2x + 1))),x)
A111215: 0 2 3 6 8 9 12 14 17 21 23 24 26 27 33 36
((x + 1) + compr(\x.(1 - loop(\(x,i).(x div (if (x mod 2) <= 0 then ~2 else 1)),x,x)),2x))
A285959: 2 6 10 15 18 22 26 29 34 38 42 47 50 55 59 63
((~4x + ~1) mod loop(\(x,i).(x + (if x <= 0 then (1 + i) else 0)),x,(~x + 1)))
A335435-A167192: 0 1 0 2 1 0 3 1 1 0 4 3 2 1 0 5
(~x + loop(\(x,i).((x + 1) - ((~x + (if (i mod 2) <= 0 then 2 else 0)) div 5)),x,1))
A272948: 1 2 3 4 5 7 9 12 16 21 27 35 44 56 70 87
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(3x + 1)),x)
A059324: 5 10 12 15 19 20 23 25 26 30 33 34 35 36 40 45
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),(x div 2),(3x + ~1))),x)
A087370: 1 2 4 6 8 10 14 16 18 20 24 28 30 34 36 38
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(3x + ~1)),x)
A046954: 0 4 8 9 14 15 19 20 22 24 28 29 31 34 36 39
(x * loop(\(x,i).((x + 1) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,1))
A083725: 0 3 12 33 72 145 252 413 624 909 1300 1771 2376 3107 3948 4935
(x * loop(\(x,i).x2,1,loop(\(x,i).((2 * (x - (2x * i))) div (1 + i)),x,1)))
A268085: 0 1 8 75 784 8820 104544 1288287 16359200 212751396 2821056160 38013731756 519227905728 7174705330000 100136810390400 1409850293610375
(3x + ((if x <= 0 then 1 else (x div 3)) + loop(\(x,i).(2x + 2),x,1)))
A332232: 2 7 16 32 59 110
(x * loop(\(x,i).x2,1,loop(\(x,i).(2 * (x - ((x * (2 - i)) div (1 + i)))),x,1)))
A267982: 0 4 32 300 3136 35280 418176 5153148 65436800 851005584 11284224640 152054927024 2076911622912 28698821320000 400547241561600 5639401174441500
compr(\x.(1 + loop(\(x,i).(~x + (if (x mod (1 + (2 * i))) <= 0 then x else 0)),(2 + (x mod 2)),x)),x)
A140461-A135779-A125845-A096489-A095862-A008364: 1 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67
(~x + ((x + 1) * (if x <= 0 then 1 else loop(\(x,i).(10x + 10),x,0))))
A121324: 1 19 328 4437 55546 666655 7777764 88888873 999999982 11111111091 122222222200 1333333333309 14444444444418 155555555555527 1666666666666636 17777777777777745
compr(\x.(loop(\(x,i).2x,x,(~1 + (loop(\(x,i).2x,x,2) mod (x + 2)))) mod (x + 1)),x)
A260124: 0 1 3 5 7 9 11 15 17 21 23 27 29 31 35 39
compr(\x.(1 - (loop(\(x,i).(x * i),((if (x mod 2) <= 0 then 2 else 0) + (x div 2)),1) mod (x + 1))),x)
A026438: 1 3 4 5 6 7 9 10 12 13 16 18 21 22 25 28
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(9x + 8))
A017266: 1073741824 2015993900449 141167095653376 2758547353515625 27197360938418176 174887470365513049 839299365868340224 3255243551009881201 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(9x + 8))
A017268: 68719476736 582622237229761 95428956661682176 3379220508056640625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(5x + 4))
A016907: 4194304 31381059609 4049565169664 116490258898219 1521681143169024 12200509765705829 70188843638032384 317475837322472439 1196683881290399744 3909821048582988049 4611686018427387903
(loop(\(x,i).(x - ((2 * (2x div 3)) div 3)),2,x) + (if x <= 0 then 1 else x))
A024616: 1 2 4 5 6 7 9 10 11 12 14 16 17 18 19 20
compr(\x.(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then x else 5)),x,x)),x)
A165741-A089559: 1 2 4 7 8 11 13 14 16 19 22 23 26 28 29 32
loop(\(x,i).(loop(\(x,i).6x,x,x2) mod 7),2,x)
A204453: 0 1 2 3 4 5 6 0 6 5 4 3 2 1 0 1
loop(\(x,i).(1 - (x mod (~1 + (2 * ((x mod 2) - (if (x mod 4) <= 0 then x else 1)))))),2,x)
A333769: 1 1 2 1 1 1 1 1 3 1 1 1 2 1 2 1
(x + (if (x + ~2) <= 0 then 1 else (2 + (3 * (if (~2 + (x div 3)) <= 0 then 0 else 2)))))
A247360: 1 2 3 5 6 7 8 9 10 17 18 19 20 21 22 23
(x + (if (x div 4) <= 0 then 1 else ((1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2))) div 2)))
A026281: 1 2 3 4 6 8 10 12 13 15 16 18 19 21 22 24
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(4x + 2)),x)
A231407: 1 4 6
A153235: 1 4 6 7 10 11 13 14 16 17 19 21 22 25 26 28
(2 div loop(\(x,i).(1 + loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,2x)),2,x))
A218622: 1 1 1 2 1 1 2 2 1 1 1 0 2 2 2 2
(if x <= 0 then 1 else (x * loop(\(x,i).x2,(x + ~2),((x3 + x2 + 2x + 2) div 2))))
A065402: 1 3 18 1452
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(9x + 4))
A017218: 1048576 137858491849 26559922791424 819628286980801 10485760000000000 79792266297612001 430804206899405824 1822837804551761449 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(9x + 4))
A017220: 16777216 23298085122481 12855002631049216 787662783788549761 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~x + (2 * (4 + loop(\(x,i).(2 * (x3 + (if x <= 0 then 1 else 2))),x,1))))
A255529: 10 19 878
compr(\x.loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,(2x + 12)),x)
A165740: 3 5 6 9 10 12 15 17 18 20 21 24 25 27 30 31
loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),x,(x2 + 6x))
A061039: 0 7 16 1 40 55 8 91 112 5 160 187 8 247 280 35
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,8x)),x)
A192225: 0 1 2 5
A005124: 0 1 2 5 7 8 10 13 16 17 20 22 26 28 31 35
compr(\x.loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,(6x + 4)),x)
A153219: 3 7 8 13 14 18 19 21 23 27 28 30 33 35 38 40
(~x + (2 * (loop(\(x,i).4x,x,2) - loop(\(x,i).(3x + ~1),x,2))))
A284850: 0 5 34 171 776 3361 14190 58967 242452 989517 4017146 16245763 65514528 263652473 1059392902 4251920559
loop(\(x,i).(x3 mod loop(\(x,i).(x2 + 2x + 1),2,2)),4x,x)
A100990: 0 1 52 3 4 25 56 7 8 9 0 11 12 13 64 75
loop(\(x,i).(x * (~3 + loop(\(x,i).(2x2 + x),2,2))),4x,x)
A052094: 0 1836036801 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.((if (x mod 3) <= 0 then 1 else (loop(\(x,i).(x div (2 - (x mod 2))),x,x) div 2)) mod 2),x)
A191535-A100598: 1 2 4 5 8 10
A072437: 1 2 4 5 8 10 13 16 17 20 25 26 29 32 34 37
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,(x2 + x + 2))),x)
A027754: 0 1 2 3 6 7 11 16 17 18 21 23 27 31 32 38
compr(\x.(((x + 1) + loop(\(x,i).loop(\(x,i).(2 - (x mod 2)),(x mod 2),(x div 2)),x,x)) mod 2),x)
A338692: 1 4 5 6 9 13 14 16 17 20 21 22 24 25 29 30
loop(\(x,i).(x2 + 4x),1,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A166010: 0 5 21 45 117 165 285 357 525 837 957 1365 1677 1845 2205 2805
loop(\(x,i).loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 5)),1,(x2 + 2x))
A243883: 5 1 13 5 29 5 53 17 85 13 125 37 173 25 229 65
loop(\(x,i).(x - (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))),1,(x2 + 2x))
A292531: 0 0 8 0 24 32 48 0 80 96 120 128 168 192 224 0
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(x2 + ~2))),x)
A066049: 2 3 4 6 7 8 10 11 13 15 17 18 21 22 24 25
compr(\x.(1 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,2x2)),x)
A097697: 1 2 4 5 7 11 14 19 25 26 31 32 35 37 38 46
(loop(\(x,i).11x,x,1) - loop(\(x,i).x3,2,x))
A024136: 1 10 ~391 ~18352 ~247503 ~1792074 ~8306135 ~20866436 80141153 1970527202 24937424601 282953722920 3133268596369 34512107644558 379729172536457 4177209726056276
(x * loop(\(x,i).(x + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),(x + ~1),x))
A083719: 0 1 6 18 44 90 174 294 472 702 1010 1430 1932 2574 3346 4230
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(x + 8)),x)
A153144: 1 3 4 7 8 10 13 15 16 18 19 22 23 25 28 29
compr(\x.(1 - loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),(x div 2),(x2 + 4x))),x)
A225227: 1 7 13
A145897: 1 7 13 19 37 43 67 79 97 103 109 127 163 193 223 229
compr(\x.loop(\(x,i).(x - ((if x <= 0 then (x + ~1) else (x * i)) div 5)),(x + ~2),x),x)
A167377: 0 7 9 11 13 14 16 17 19 20 21 23 24 25 26 28
(loop(\(x,i).12x,x,1) - (x * loop(\(x,i).x3,2,x)))
A024150: 1 11 ~880 ~57321 ~1027840 ~9516793 ~57480192 ~246643441 ~643760128 1672995951 51917364224 717070946087 8854183084032 106855346887223 1283629209893888 15406444924195743
(loop(\(x,i).10x,x,1) + (x * loop(\(x,i).x3,2,x)))
A177068: 1 11 1124 60049 1058576 9865625 61466176 292475249 1173741824 4486784401 20000000000 125937424601 1061917364224 10137858491849 100289254654976 1000576650390625
(loop(\(x,i).10x,x,1) - (x * loop(\(x,i).x3,2,x)))
A024124: 1 9 ~924 ~58049 ~1038576 ~9665625 ~59466176 ~272475249 ~973741824 ~2486784401 0 74062575399 938082635776 9862141508151 99710745345024 999423349609375
(loop(\(x,i).7x,x,1) - (x * loop(\(x,i).x3,2,x)))
A024085: 1 6 ~975 ~58706 ~1046175 ~9748818 ~60348527 ~281651706 ~1067977023 ~3446430794 ~9717524751 ~23960097858 ~48076077023 ~40969481442 388968417873 4170911119318
loop(\(x,i).(loop(\(x,i).((x2 + ~x) div 2),2,(x2 + 2)) div 3),1,x2)
A283026: 0 1 3876 1929501 183181376 6419043125 118091211876 1388168405001 11745311589376 77279801651001 416916712502500 1915356782994501 7705740009485376 27731516944463501 90762229896563876 273716119247180625
loop(\(x,i).((x + 1) * (~1 + loop(\(x,i).x2,1,(2 * (2x + i))))),1,x2)
A082942: 3 70 1615 14430 74035 270478 788655 1960150 4326595 8714550 16321903 28815790 48442035 78146110 121705615 183874278
loop(\(x,i).(((x + 1) * loop(\(x,i).((x3 + x2) div 2),2,x)) div 2),1,x2)
A146025: 0 1 82000
loop(\(x,i).(2x + (((x + (x div 4)) div 2) + (if x <= 0 then 1 else 2))),1,x2)
A008264: 1 4 12 25 44 67 96 130 170 214 264 319 380 445 516 592
(x2 + (loop(\(x,i).((if (i mod 3) <= 0 then 1 else i) + (x * i)),x,1) div (x + 1)))
A003039: 1 2 6 13 32 92
(~x2 + loop(\(x,i).(x + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)),x,1))
A108754: 1 1 1 1 3 5 9 13 19 29 39 53 69 85 103 125
(loop(\(x,i).11x,x,1) - loop(\(x,i).x2,2,x2))
A024135: 1 10 ~135 ~5230 ~50895 ~229574 91945 13722370 197581665 2314900970 25837424601 285097311730 3137998395025 34521896413210 379748357794185 4177245606525026
(loop(\(x,i).3x,2x,1) - (x2 * loop(\(x,i).x3,2,x)))
A024112: 1 8 ~1967 ~176418 ~4187743 ~48769076 ~362265615 ~1972543774 ~8546887871 ~30993639120 ~96513215599 ~253930611002 ~460578834207 749705434292 18827227285297 197241376235274
(loop(\(x,i).6x,x,1) - (x2 * loop(\(x,i).x3,2,x)))
A024073: 1 5 ~2012 ~176931 ~4193008 ~48820349 ~362750400 ~1977046807 ~8588254976 ~31370981913 ~99939533824 ~284948873555 ~740831588352 ~1779099700021 ~3971201005568 ~8179570874799
(loop(\(x,i).8x,x,1) - (x2 * loop(\(x,i).x3,2,x)))
A024099: 1 7 ~1984 ~176635 ~4190208 ~48795357 ~362534912 ~1975229591 ~8573157376 ~31246841881 ~98926258176 ~276721736019 ~674288893952 ~1242404580149 348481341440 26534616229457
(loop(\(x,i).5x,x,1) - (x2 * loop(\(x,i).x3,2,x)))
A024060: 1 4 ~2023 ~177022 ~4193679 ~48825000 ~362781431 ~1977248618 ~8589543967 ~31379106484 ~99990234375 ~285262842486 ~742764230063 ~1790939690912 ~4043461654039 ~8619238281250
compr(\x.loop(\(x,i).(x - (if ((x + 5) mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x)
A153081: 0 2 3 5 8 9 12 14 15 17 20 23 24 27 29 30
(x + loop(\(x,i).(~1 + (if x <= 0 then x else (1 + (((x + 1) div 2) div (1 + (x mod 2)))))),x,x))
A277329: 0 1 2 2 3 2 3 3 4 3 3 3 4 3 4 4
compr(\x.(1 - loop(\(x,i).(if ((x + 3) mod 8) <= 0 then x else (x div 2)),x,x)),x)
A004748: 5 10 11 13 20 21 22 23 26 27 29 37 40 41 42 43
(loop(\(x,i).12x,x,1) - loop(\(x,i).x2,2,x3))
A024152: 1 11 ~3952 ~529713 ~16756480 ~243891793 ~2173796352 ~13805455393 ~68289495040 ~277269756129 ~938082635776 ~2395420006033 0 83695120256591 1227224552173568 15277275236695743
(loop(\(x,i).10x,x,1) - loop(\(x,i).x2,2,x3))
A024126: 1 9 ~3996 ~530441 ~16767216 ~244040625 ~2175782336 ~13831287201 ~68619476736 ~281429536481 ~990000000000 ~3038428376721 ~7916100448256 ~13298085122481 43306087624704 870253662109375
(loop(\(x,i).7x,x,1) - loop(\(x,i).x2,2,x3))
A024087: 1 6 ~4047 ~531098 ~16774815 ~244123818 ~2176664687 ~13840463658 ~68713711935 ~282389182874 ~999717524751 ~3136451049978 ~8902259161055 ~23201196112074 ~56015689302447 ~124998776380682
(if (x mod 2) <= 0 then (1 + ((1 + ((x + 1) mod 4)) mod (1 + (x mod 3)))) else 0)
A284413: 1 0 2 0 1 0 1 0 3 0 1 0 1 0 2 0
(if (2x mod (4 + (x div 4))) <= 0 then (1 + (x div 5)) else 0)
A227344: 1 0 1 0 0 2 0 0 0 2 0 0 0 0 3 0
(if (x mod 3) <= 0 then (~1 + ((~1 + ((x - (x div 4)) div 2)) mod 3)) else 0)
A016124-A015944-A015854-A015674-A015404-A015314-A015044-A014864-A014774-A014594-A014504-A014324-A011636: 1 0 0 ~1 0 0 0 0 0 1 0 0 ~1 0 0 1
(3x + (if (~2 + (x div 3)) <= 0 then 1 else 0) - (x div 5))
A190362-A184904: 1 4 7 10 13 15 18 21 24 26 28 31 34 37 40 42
(if (x mod 2) <= 0 then (1 - ((x + ((x - (x mod 4)) div 3)) mod 3)) else 0)
A274719: 1 0 ~1 0 ~1 0 0 0 0 0 1 0 0 0 1 0
(if (((x + ~1) div 2) - ((3 * (x div 4)) div 2)) <= 0 then (2x + 1) else 0)
A099895: 1 3 5 0 9 0 0 0 17 0 0 0 0 0 0 0
loop(\(x,i).(2 + ((4 * (x + (x div 2))) + ((x div 2) mod 3))),(x + 1),0)
A037753: 2 15 91 546 3278 19671 118027 708162 4248974 25493847 152963083 917778498 5506670990 33040025943 198240155659 1189440933954
loop(\(x,i).(1 + (8 * (x mod 2)) - (x div 5)),(x + ~1),0)
A021509: 0 0 1 9 8 0 1 9 8 0 1 9 8 0 1 9
loop(\(x,i).(2x + 1),(((x + ~1) div 2) - ((3 * (x div 4)) div 2)),0)
A088512: 0 0 0 1 0 1 1 3 0 1 1 3 1 3 3 7
(x - loop(\(x,i).(2x + 1),((x div 2) - ((3 * (x div 4)) div 2)),0))
A309255: 0 1 1 2 3 4 3 4 7 8 7 8 9 10 7 8
((x + 1) div (1 - (if ((1 + (x div 4)) mod (2 + (x mod 4))) <= 0 then 2 else 0)))
A209662: 1 2 3 4 ~5 6 7 8 9 ~10 11 12 ~13 14 ~15 16
loop(\(x,i).(1 + ((~3x2 + ~2x) mod 9)),x,0)
A267017: 0 1 5 6 7 2 3 4 8 9 1 5 6 7 2 3
(1 + (if (x mod (1 + ((x2 + ~x) mod 8))) <= 0 then (x mod 3) else 0))
A280489: 1 2 1 1 1 3 1 1 3 1 1 1 1 1 3 1
(((x2 + 5x) div 2) div (1 + (if (~1 + (x mod 3)) <= 0 then 2 else 0)))
A027625: 0 1 7 4 6 25 11 14 52 21 25 88 34 39 133 50
(2 - ((~x + 1) div (1 + (if (x mod (3 + ((x div 2) div 3))) <= 0 then 2 else 0))))
A097450: 2 2 3 3 5 6 7 8 5 10 11 12 13 14 15 7
((x + 1) - (if (x mod 3) <= 0 then (4 * ((x div 5) mod 2)) else 0))
A096894: 1 2 3 4 5 6 3 8 9 6 11 12 13 14 15 12
(1 + (if (x mod 3) <= 0 then ((1 + (x div (2 * (2 - (x mod 2))))) mod 4) else 0))
A030360: 2 1 1 3 1 1 3 1 1 2 1 1 1 1 1 1
(1 + loop(\(x,i).((x + 1) + (x div (1 + (x mod (2 * (1 + (2 * (x mod 2)))))))),x,0))
A018258: 1 2 3 6 7 14 21 42
A018379: 1 2 3 6 7 14 21 42 49 98 147 294
A245479: 1 2 3 6 7 14 21 42 49 98 147 294 343 686 1029 2058
(1 + loop(\(x,i).((x + 1) + (((2x + ~4) div (2 + (x div 4))) mod 2)),x,0))
A080645: 1 2 4 6 7 8 10 12 13 14 15 16 18 20 22 24
((x mod (1 + (((x + 1) mod (~1 + (2 * (x div 3)))) div 2))) + (if x <= 0 then 0 else 1))
A300719: 0 1 1 1 1 1 1 2 1 1 1 2 1 1 1 4
(((~x + 1) mod (1 + ((x - ((x div 3) mod 3)) div 2))) + (if x <= 0 then 0 else 1))
A005811: 0 1 2 1 2 3 2 1 2 3 4 3 2 3 2 1
(((2x + 1) mod (1 + (2x mod (2 + (x div 4))))) + (if x <= 0 then 0 else 1))
A330757-A303838-A238946-A168324-A140747: 0 1 1 1 1 2 1 1 1 2 1 3 1 2 2 1
((x mod (1 + ((x + 1) mod (2 + (x div (2 * (2 - (x mod 2)))))))) + (if x <= 0 then 0 else 1))
A260439: 0 1 1 2 2 3 1 4 1 5 3 6 1 7 1 8
(((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4))) + (if x <= 0 then 0 else 1))
A302045-A302035-A157754-A088388-A087179-A067029-A051903: 0 1 1 2 1 1 1 3 2 1 1 2 1 1 1 4
((((x + 1) mod (1 + (2 * ((1 + (x div 4)) div 2)))) div 2) + (if x <= 0 then 0 else 1))
A091304: 0 1 1 1 2 1 1 2 1 1 2 1 2 3 1 1
((((x3 mod (2x + 3)) div 3) mod 2) + (if x <= 0 then 0 else 1))
A086412: 0 1 1 1 2 1 1 2 1 2 2 1 1 2 2 2
((x div (4 + ((~x + 1) mod (1 + (((x + 1) div 2) div 2))))) + (if x <= 0 then 0 else 1))
A336543: 0 1 1 1 1 2 2 2 2 2 3 2 3 4 3 4
((((2 + ((2 * (2 - (x mod 4))) mod (x + 1))) div 2) div 2) + (if x <= 0 then 0 else 1))
A295277: 0 1 1 2 2 2 1 3 2 2 1 4 2 2 1 5
((((1 + (8 mod (1 + (x div 2)))) div 2) + (if x <= 0 then 0 else 1)) - (x mod 2))
A080791: 0 0 1 0 2 1 1 0 3 2 2 1 2 1 1 0
((((2 - (x mod (~1 + ((~x + 2) div 4)))) div 2) + (if x <= 0 then 0 else 1)) - (x mod 2))
A342679: 1 1 2 1 2 1 2 2 2 1 3 1 2 2 3 1
(1 + ((x + ~1) mod (1 + (if (((x + 1) mod 8) mod 3) <= 0 then 2 else 0))))
A183014: 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 3
(1 + (3x mod (1 + (x mod (1 + (if (x mod 2) <= 0 then 6 else 0))))))
A340074: 1 1 1 1 3 1 5 1 1 1 3 1 1 1 1 1
(~1 + (x mod (1 + (x mod (2 + (if (x mod 2) <= 0 then (x div 2) else (x mod 3)))))))
A294448: ~1 0 1 0 ~1 0 ~1 0 1 0 1 2 1 0 1 0
(1 + (2x div (1 + ((x + 1) div loop(\(x,i).i,(x mod (1 + (x div 4))),1)))))
A051702: 1 1 2 2 2 2 2 2 4 2 2 4 2 2 4 6
(1 + (x mod (1 + (x mod (1 + (x mod ((if (x mod 2) <= 0 then 1 else x) + (x div 3))))))))
A326478: 1 1 1 4 1 6 1 8 3 10 1 12 1 14 5 16
(1 - (x mod (1 + (x mod (2 + (if (x mod 2) <= 0 then (x div 2) else (x mod 3)))))))
A317854-A317754-A088568: 1 0 ~1 0 1 0 1 0 ~1 0 ~1 ~2 ~1 0 ~1 0
(1 + ((x div 2) div (1 + (x mod (1 + (loop(\(x,i).2x,x,2) mod (2x + 1)))))))
A318324-A317934: 1 1 1 2 1 1 1 2 2 1 1 2 1 1 1 8
(1 + (x mod (1 + (x mod (1 + ((1 - loop(\(x,i).4x,x,2)) mod (x + 1)))))))
A053590: 1 2 3 2 5 6 7 2 3 2 11 6 13 2 15 2
(~1 + (2 div (1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 7))))
A209635: 1 1 ~1 1 ~1 ~1 ~1 1 0 ~1 ~1 ~1 ~1 ~1 1 1
(1 + (5 mod (1 + ((x + 1) mod (if (~x + 2) <= 0 then 6 else 1)))))
A193807-A085099: 1 1 2 1 6 1 2 3 2 1 6 1 2 3 2 1
(1 + (x mod (1 + (x div (1 + (2 * (loop(\(x,i).(2x + 2),x,0) mod (x + 1))))))))
A326691: 1 2 3 1 5 2 7 1 1 2 11 3 13 2 1 1
((x + 1) - (x mod (1 + (loop(\(x,i).(2 * (x + i)),x,0) mod (2x + 3)))))
A005765: 1 1 3 1 1 1 7 7 1 1 11 1 1 1 15 1
(1 + ((x div 2) div (1 + (x mod (1 + (if (~1 + (x mod 3)) <= 0 then (x div 2) else 2))))))
A117277: 1 1 1 1 2 1 2 1 2 1 2 2 2 1 3 1
((if x <= 0 then 1 else x) div (1 + (x mod (1 + (x mod (1 + (x div (2 * (2 - (x mod 2))))))))))
A063994: 1 1 2 1 4 1 6 1 2 1 10 1 12 1 4 1
(~1 + loop(\(x,i).2x2,1,(18x + 19)))
A154515: 721 2737 6049 10657 16561 23761 32257 42049 53137 65521 79201 94177 110449 128017 146881 167041
(~1 + loop(\(x,i).2x2,1,(18x + 17)))
A154514: 577 2449 5617 10081 15841 22897 31249 40897 51841 64081 77617 92449 108577 126001 144721 164737
(~1 + (if x <= 0 then 2 else (((x2 + 2x) div 2) mod (1 + ((1 + (x div 2)) div 3)))))
A114592: 1 ~1 ~1 ~1 ~1 0 ~1 0 ~1 0 ~1 1 ~1 0 0 0
(~1 + loop(\(x,i).10x,2x,11))
A133383: 10 1099 109999 10999999 1099999999 109999999999 10999999999999 1099999999999999 109999999999999999 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (x div (1 + ((x2 + 2x) mod (1 + (if (~2 + (x div 3)) <= 0 then x else 2))))))
A065517: 1 1 1 1 1 1 1 1 1 10 11 4 13 14 5 16
(x div (1 + (x mod (1 + (loop(\(x,i).2x,x,(1 + (x mod 2))) mod (2x + 1))))))
A336642: 0 0 0 3 0 0 0 3 8 0 0 3 0 0 0 15
(1 + ((x + ~1) mod (1 + (if (x mod (1 + (((x + 1) div 2) div 3))) <= 0 then x else 1))))
A340087: 1 1 2 3 4 1 6 1 8 1 10 1 12 1 2 15
(x mod (1 + ((1 + (x div 2)) mod (1 + (loop(\(x,i).~2x,x,1) mod (x + 1))))))
A178921-A100574-A100573-A049087-A046665: 0 0 0 0 0 1 0 0 0 3 0 1 0 5 2 0
(~1 + loop(\(x,i).2x2,1,(32x + 33)))
A157476: 2177 8449 18817 33281 51841 74497 101249 132097 167041 206081 249217 296449 347777 403201 462721 526337
(~1 + loop(\(x,i).2x2,1,(32x + 31)))
A157448: 1921 7937 18049 32257 50561 72961 99457 130049 164737 203521 246401 293377 344449 399617 458881 522241
loop(\(x,i).21x,(4x + 3),1)
A013815: 9261 1801088541 350277500542221 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).22x,(4x + 3),1)
A013817: 10648 2494357888 584318301411328 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).19x,(4x + 3),1)
A013811: 6859 893871739 116490258898219 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).23x,(4x + 3),1)
A013819: 12167 3404825447 952809757913927 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) - ((x + 1) div (1 + (2 * (if ((x + ~1) mod 5) <= 0 then 2 else 1)))))
A211317: 1 2 2 3 4 4 6 6 6 7 8 10 9 10
(x div (1 + ((x + 1) div (1 + (2 * (if ((x div 2) mod 5) <= 0 then 2 else 1))))))
A308342: 0 1 1 1 2 1 2 2 2 2 3 3 2 2 2 2
(~1 + (if x <= 0 then 0 else (1 + ((x mod (1 + (2 * (2 - ((x div 2) div 3))))) mod 2))))
A181101: ~1 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0
(2 div (1 + ((2x + 1) mod (1 + (2 * loop(\(x,i).2x,(x div 4),1))))))
A039975: 1 2 0 1 0 1 0 2 0 1 0 0 0 0 0 0
(1 + ((x + ~1) mod (1 + (if (x mod 2) <= 0 then ((x + 1) mod (1 + (x mod 4))) else 2))))
A087282: 1 1 1 3 1 2 2 1 1 3 1 2 1 1 1 3
(if (x mod 2) <= 0 then (1 + (2 * ((8 mod (~x + ~1)) mod 3))) else 1)
A254378: 1 1 5 1 3 1 1 1 5 1 1 1 3 1 5 1
(2 div (if x <= 0 then 2 else (1 + (x mod (1 + ((2 + (x div 3)) mod 6))))))
A175134: 1 1 0 0 2 1 1 0 0 0 0 0 2
(~1 + (21 * loop(\(x,i).(2x + 1),(x + 2),2)))
A304389: 230 482 986 1994 4010 8042 16106 32234 64490 129002 258026 516074 1032170 2064362 4128746 8257514
(1 + ((2 * (2 + loop(\(x,i).(x div (2 - (x mod 2))),x,x))) div 7))
A294442: 1 1 1 2 1 3 2 3 1 4 3 4 2 5 3 5
(~1 + (if x <= 0 then 2 else (((x2 + 2x) div 2) mod (1 + (x div (2 + (x div 3)))))))
A334743: 1 ~1 ~1 0 ~1 0 ~1 0 0 0 ~1 1 ~1 0 0 0
(1 + ((x div 2) div (1 + (x div (2 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))))
A285707: 1 1 1 2 1 2 1 4 3 2 1 3 1 2 3 8
(if (x + ~1) <= 0 then 0 else (1 + (x div (3 + ((x2 + 2x) mod 6)))))
A325224: 0 0 1 1 2 1 3 2 2 2 4 2 5 3 3 3
(1 + (x div (1 + ((x - ((loop(\(x,i).~2x,x,1) mod (x + 1)) div 2)) div 2))))
A322861: 1 2 2 2 2 3 2 2 3 4 2 3 2 4 3 2
(1 + (17 * (1 + loop(\(x,i).(2x + 4),x,4))))
A304518: 86 222 494 1038 2126 4302 8654 17358 34766 69582 139214 278478 557006 1114062 2228174 4456398
(1 + ((2x + 2) mod loop(\(x,i).i,(2x mod (4 + (x div 4))),1)))
A108886: 1 1 1 1 2 1 1 1 3 1 1 1 3 4 1 1
(if x <= 0 then 0 else (1 + (x div (3 + ((~2x + 1) mod (4 + (x div 2)))))))
A276605: 0 1 1 2 1 1 2 2 3 1 1 2 2 2 2 3
(x div (1 + ((1 + (x div 2)) div (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then 2 else 1))))
A280274: 0 1 1 1 1 2 1 1 1 3 1 2 1 3 2 1
((1 + (x mod 3)) mod (1 + (if ((2 - (x div 4)) mod 4) <= 0 then 2 else 1)))
A239366: 1 0 1 1 0 1 1 0 0 1 2 0 1 0 1 1
(~1 + (9 * (12x - (if x <= 0 then 0 else 1))))
A063369: ~1 98 206 314 422 530 638 746 854 962 1070 1178 1286 1394 1502 1610
(1 + ((if (~2 + (x div 3)) <= 0 then x else (x + 3)) mod 9))
A114288: 1 2 3 4 5 6 7 8 9 4 5 6 7 8 9 1
(1 + ((if (~2 + (x div 3)) <= 0 then x else (2x + 1)) mod 9))
A125959: 1 2 3 4 5 6 7 8 9 2 4 6 8 1 3 5
(1 + (9 * (2 + (if (~2 + (x div 3)) <= 0 then x else (x + 2)))))
A179955: 19 28 37 46 55 64 73 82 91 118 127 136 145 154 163 172
loop(\(x,i).(x * i),2x,(1 + (x mod (1 + ((x2 + 2x) mod 8)))))
A279110: 1 4 24 2880 40320 7257600 479001600 697426329600 20922789888000 12804747411456000 2432902008176640000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (x mod (~1 + (4 * (x mod (1 + (if (x mod 2) <= 0 then 6 else 0)))))))
A155457: 1 1 3 1 5 1 7 1 3 1 11 1 13 1 1 1
loop(\(x,i).(2 * i),((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4))),1)
A104404: 1 1 1 2 1 1 1 4 2 1 1 2 1 1 1 6
(1 + (loop(\(x,i).((x + 1) + (x div (1 + (x mod 4)))),x,0) div 5))
A273732: 1 1 1 1 1 2 3 4 5 10 15 20 25 50 75 100
loop(\(x,i).x5,1,(10x + 6))
A017345: 7776 1048576 11881376 60466176 205962976 550731776 1252332576 2535525376 4704270176 8153726976 13382255776 21003416576 31757969376 46525874176 66338290976 92389579776
((x3 + 2x2) div (~1 + (5 * (if (x mod 4) <= 0 then 0 else 2))))
A152839: 0 0 1 5 ~96
(1 + (5 * (~2 + loop(\(x,i).10x,(x + 1),1))))
A086949: 41 491 4991 49991 499991 4999991 49999991 499999991 4999999991 49999999991 499999999991 4999999999991 49999999999991 499999999999991 4999999999999991 49999999999999991
(loop(\(x,i).6x,x,1) mod 29)
A070398: 1 6 7 13 20 4 24 28 23 22 16 9 25 5 1 6
(loop(\(x,i).5x,x,1) mod 29)
A070379: 1 5 25 9 16 22 23 28 24 4 20 13 7 6 1 5
loop(\(x,i).x5,1,(10x + 9))
A017381: 59049 2476099 20511149 90224199 282475249 714924299 1564031349 3077056399 5584059449 9509900499 15386239549 23863536599 35723051649 51888844699 73439775749 101621504799
(loop(\(x,i).6x,x,1) mod 41)
A036125: 1 6 36 11 25 27 39 29 10 19 32 28 4 24 21 3
(loop(\(x,i).5x,x,1) mod 41)
A070387: 1 5 25 2 10 9 4 20 18 8 40 36 16 39 31 32
(loop(\(x,i).5x,x,1) mod 39)
A070386: 1 5 25 8 1 5 25 8 1 5 25 8 1 5 25 8
(1 + (5 * loop(\(x,i).(~x + 7),(x div 2),(x mod 2))))
A070400: 1 6 36 31 1 6 36 31 1 6 36 31 1 6 36 31
(2 div (1 + ((x + (if ((x + (x div 2)) mod 4) <= 0 then 1 else 2)) mod 5)))
A339087: 1 0 0 0 1 0 0 0 0 1 0 0 0 2 1 0
((if x <= 0 then 1 else 2x) - ((1 + (x div 3)) mod (1 + (x div 5))))
A334614: 1 2 4 6 8 10 11 13 15 18 19 21 22 24 26 28
((1 + (x div 2)) mod (1 + ((x - (if (~1 + (x div 4)) <= 0 then 2 else 0)) mod 3)))
A339088: 1 1 0 0 0 0 0 1 2 0 0 0 0 1 2 0
(1 + ((1 + (if (x mod (2 + ((~x + 2) mod 5))) <= 0 then x else 0)) div 3))
A325789: 1 1 2 1 1 1 3 1 1 1 1 1 5 1 1 1
(1 + ((1 + (x mod (1 + (loop(\(x,i).(x2 + 2x),2,2) mod (x + 1))))) div 3))
A286363: 1 1 2 1 1 2 2 1 4 1 2 2 1 2 2 1
(1 + ((x div (1 + (loop(\(x,i).(2x + 2),x,2) mod (x + 3)))) mod 3))
A254629: 1 1 1 1 1 1 3 2 1 2 1 3 2 1 1 2
(1 + ((1 + loop(\(x,i).(2 * (x - (2 * (~1 + (x mod 3))))),x,1)) div 3))
A166578: 1 2 1 2 4 5 10 20 37 74 148 293 586 1172 2341 4682
(1 + ((x - (if (x mod 3) <= 0 then ((((x + 1) div 2) div 2) mod 2) else 1)) mod 3))
A179542: 1 1 2 3 1 2 3 1 2 1 1 2 3 1 2 1
(if x <= 0 then 1 else ((x + 2) mod (1 + (((1 + (x * (x div 2))) div 3) mod 3))))
A339553-A325045-A303553-A294068-A259362-A188585: 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 2
(loop(\(x,i).5x,x,1) mod 37)
A070384: 1 5 25 14 33 17 11 18 16 6 30 2 10 13 28 29
(1 + (3 * (3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A129075: 10 13 19 25 37 43 55 61 73 91 97 115 127 133 145 163
loop(\(x,i).3x,(x + ~1),(~1 + ((1 + (x div (2 - (x mod 2)))) mod 3)))
A190963: 0 1 3 0 ~27 ~81 0 729 2187 0 ~19683 ~59049 0 531441 1594323 0
(1 + ((1 + compr(\x.(if (x mod 2) <= 0 then ((x div 3) mod 3) else 0),x)) mod 3))
A036582: 2 3 1 2 1 3 2 3 1 3 2 1 2 3 1 2
(1 + ((~1 + compr(\x.(if (x mod 2) <= 0 then ((x div 3) mod 3) else 0),x)) mod 3))
A036584: 3 1 2 3 2 1 3 1 2 1 3 2 3 1 2 3
loop(\(x,i).x5,1,(12x + 11))
A017657: 161051 6436343 52521875 229345007 714924299 1804229351 3939040643 7737809375 14025517307 23863536599 38579489651 59797108943 89466096875 129891985607 183765996899 254194901951
(1 + (loop(\(x,i).((x + 1) * ((x + 1) div 2)),(1 + (x div 2)),(x + ~1)) div 3))
A142960: 1 1 2 3 223
(1 + ((2 * (1 + (loop(\(x,i).(x div (2 - (x mod 2))),2,x) div 3))) div 3))
A120562: 1 1 1 2 1 2 2 3 1 3 2 3 2 4 3 5
(1 + ((2 * (1 + (2 * ((x + 2) + (if (x + ~4) <= 0 then 1 else 2))))) div 3))
A122904: 5 7 8 9 11 13 15 16 17 19 20 21 23 24 25 27
(1 + (3 * (if (x + ~1) <= 0 then 0 else ((1 + (x div (2 * (2 - (x mod 2))))) mod 2))))
A214333: 1 1 4 1 1 4 1 1 4 4 4 1 1 4 1 1
(1 + ((x - ((if (x + ~1) <= 0 then 1 else (((x + 1) div 2) div 3)) mod 2)) mod 3))
A078929: 3 1 3 1 2 2 3 1 2 3 1 3 1 2 3 1
(1 + ((2 * (1 + (if x <= 0 then 1 else (2 * (x + (x div 8)))))) div 3))
A175418-A078175: 2 3 4 5 7 8 9 11 13 15 16 17 19 20 21 23
loop(\(x,i).x5,1,(12x + 7))
A017609: 16807 2476099 28629151 147008443 503284375 1350125107 3077056399 6240321451 11592740743 20113571875 33038369407 51888844699 78502725751 115063617043 164130859375 228669389707
loop(\(x,i).x5,1,(12x + 5))
A017585: 3125 1419857 20511149 115856201 418195493 1160290625 2706784157 5584059449 10510100501 18424351793 30517578125 48261724457 73439775749 108175616801 154963892093 216699865625
(1 + ((x mod (2 + ((3 * loop(\(x,i).2x,x,2)) mod (x + 1)))) div 3))
A109390: 1 1 1 1 1 1 3 1 1 1 1 1 2 5 2 1
loop(\(x,i).x6,1,(6x + 5))
A016974: 15625 1771561 24137569 148035889 594823321 1838265625 4750104241 10779215329 22164361129 42180533641 75418890625 128100283921 208422380089 326940373369 496981290961 735091890625
(1 + (((loop(\(x,i).2x,((x + 1) mod 4),x) mod (x + 1)) div 2) mod 3))
A227739: 1 1 1 2 2 2 1 1 1 1 2 3 3 3 1 2
loop(\(x,i).3x,(x - (((~x3 + 3x2 + ~2x) div 2) div 3)),1)
A218149: 1 3 9 81 6561 14348907 2541865828329 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 0 else (1 + ((1 - (((x * (x div 3)) div ~2) div 2)) div 3)))
A241086: 0 1 1 1 1 2 2 2 2 3 4 4 5 5 6 7
(1 + ((4 * (1 + (if (~2 + (x div 3)) <= 0 then x else (x + 2)))) div 3))
A328393: 2 3 5 6 7 9 10 11 13 17 18 19 21 22 23 25
(if x <= 0 then 0 else (1 + ((2 * ((x mod (4 + (x div 4))) div 2)) div 3)))
A236859: 0 1 1 1 2 1 1 1 1 1 2 2 2 3 1 1
(loop(\(x,i).6x,x,1) mod 47)
A070401: 1 6 36 28 27 21 32 4 24 3 18 14 37 34 16 2
(loop(\(x,i).5x,x,1) mod 47)
A036127: 1 5 25 31 14 23 21 11 8 40 12 13 18 43 27 41
(loop(\(x,i).7x,x,1) mod 25)
A070410: 1 7 24 18 1 7 24 18 1 7 24 18 1 7 24 18
(loop(\(x,i).7x,x,1) mod 23)
A070409: 1 7 3 21 9 17 4 5 12 15 13 22 16 20 2 14
(1 + (if x <= 0 then 1 else (x - ((0 - ((x2 + ~2x) div 8)) div 3))))
A075465: 2 2 3 4 6 7 8 10 11 13 15 16 18 20 22 24
(1 + (((loop(\(x,i).(x2 + 2x),1,((x div 2) - (x mod 2))) div 2) div 2) div 3))
A029164: 1 0 1 1 1 1 2 1 3 2 3 3 5 3 6 5
(3 - (loop(\(x,i).(~3x + 3),x,1) mod 13))
A007945: 2 3 0 ~4 ~5 ~2 2 3 0 ~4 ~5 ~2 2 3 0 ~4
(loop(\(x,i).(8x + 2),(x + 1),2) div 13)
A037713: 1 11 90 720 5761 46091 368730 2949840 23598721 188789771 1510318170 12082545360 96660362881 773282903051 6186263224410 49490105795280
(if x <= 0 then 1 else (11 * (x - (x div 12))))
A048841: 1 11 22 33 44 55 66 77 88 99 110 121 121 132 143 154
(11 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A140353: 11 12 14 16 20 22 26 28 32 38 40 46 50 52 56 62
(if (x mod 6) <= 0 then 1 else (x mod ((x + ~1) - (x mod 12))))
A320317: 1 0 0 0 0 0 1 0 0 0 0 0 1 2 3 4
loop(\(x,i).x2,1,(1 + ((4 * (x + ((x div 2) div 3))) div 3)))
A062503: 1 4 9 25 36 49 100 121 169 196 225 289 361 441 484 529
(1 + (x2 div (5 + ((x + (if (x mod 3) <= 0 then 2 else 1)) div 2))))
A067314: 1 1 1 2 3 4 5 6 8 9 11 12 13 15 17 18
(~1 + (6 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A330410: 11 17 29 41 65 77 101 113 137 173 185 221 245 257 281 317
loop(\(x,i).(~11x + 1),12x,1)
A015434: 1 2876892678661 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~13x + 1),12x,1)
A015438: 1 21633936185161 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x6,1,(12x + 1))
A017538: 1 4826809 244140625 2565726409 13841287201 51520374361 151334226289 377149515625 832972004929 1677100110841 3138428376721 5534900853769 9294114390625 14976071831449 23298085122481
loop(\(x,i).x5,1,(9x + 7))
A017249: 16807 1048576 9765625 45435424 147008443 380204032 844596301 1680700000 3077056399 5277319168 8587340257 13382255776 20113571875 29316250624 41615795893 57735339232
loop(\(x,i).x5,1,(9x + 5))
A017225: 3125 537824 6436343 33554432 115856201 312500000 714924299 1453933568 2706784157 4704270176 7737809375 12166529024 18424351793 27027081632 38579489651 53782400000
(~1 + (3 * (2 + loop(\(x,i).(x2 + x + 2),(4x + 4),x))))
A260312: 16661 4611686018427387903 4611686018427387903
((~x + ~1) + loop(\(x,i).2x,x,1) - (((x3 + ~x) div 2) div 3))
A002663: 0 0 0 0 1 6 22 64 163 382 848 1816 3797 7814 15914 32192
(~1 + (if x <= 0 then 2 else (6x + ((~x2 + 1) div (x + 4)))))
A313780: 1 5 10 15 21 26 31 36 41 46 51 57 62 67 72 77
loop(\(x,i).x7,1,(6x + 1))
A016927: 1 823543 62748517 893871739 6103515625 27512614111 94931877133 271818611107 678223072849 1522435234375 3142742836021 6060711605323 11047398519097 19203908986159 32057708828125
((7x + 1) + loop(\(x,i).7x,x,1))
A176972: 2 15 64 365 2430 16843 117692 823593 5764858 40353671 282475320 1977326821 13841287286 96889010499 678223072948 4747561510049
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(6x + 1))
A050476: 1 7 26 95 350 1302 4884 18447 70070 267410 1024556 3938662 15184876 58689100 227327400 882230895
((2x + 1) + (if x <= 0 then 1 else x) - (((~x3 + x) div 2) div 3))
A201347: 2 4 8 14 23 36 54 78 109 148 196 254 323 404 498 606
(1 + ((1 - compr(\x.(if (x mod 2) <= 0 then ((x div 3) mod 3) else 0),x)) mod 3))
A005679: 2 1 3 2 3 1 2 1 3 1 2 3 2 1 3 2
(1 + ((2 - compr(\x.(if (x mod 2) <= 0 then ((x div 3) mod 3) else 0),x)) mod 3))
A036585: 3 2 1 3 1 2 3 2 1 2 3 1 3 2 1 3
loop(\(x,i).20x,(5x + 3),1)
A013896: 8000 25600000000 81920000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).15x,(5x + 3),1)
A013876: 3375 2562890625 1946195068359375 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).18x,(5x + 3),1)
A013888: 5832 11019960576 20822964865671168 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).24x,(5x + 3),1)
A013912: 13824 110075314176 876488338465357824 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).14x,(5x + 3),1)
A013872: 2744 1475789056 793714773254144 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).13x,(5x + 3),1)
A013868: 2197 815730721 302875106592253 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).11x,(5x + 3),1)
A013860: 1331 214358881 34522712143931 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).17x,(5x + 3),1)
A013884: 4913 6975757441 9904578032905937 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~11x + 1),9x,1)
A015383: 1 ~2161452050 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x6,1,(9x + 1))
A017178: 1 1000000 47045881 481890304 2565726409 9474296896 27680640625 68719476736 151334226289 304006671424 567869252041 1000000000000 1677100110841 2699554153024 4195872914689 6327518887936
(if x <= 0 then 1 else ((x + 1) - ((~x + ((~1 + (x mod 8)) div 2)) div 3)))
A083121: 1 3 4 5 6 7 9 10 12 13 15 16 17 18 19 20
(1 + (loop(\(x,i).((4x + 2) + ((x2 + x) div 2)),2,x) div 3))
A005287: 5 20 49 98 174 285 440 649 923 1274 1715 2260 2924 3723 4674 5795
(1 + ((3 * ((if (x mod 2) <= 0 then x else (~x + 2)) mod 3)) + (x div 3)))
A115021: 1 4 7 8 5 2 3 6 9
(((x div 2) - (if (x mod 7) <= 0 then 0 else 1)) mod (1 + (x div 3)))
A091731: 0 0 0 0 1 1 2 0 0 3 0 0 0 0 2 0
((1 + ((1 + (if (x mod 3) <= 0 then 0 else x)) div 3)) * (1 + (x div 3)))
A051495: 1 1 2 2 4 6 3 9 12 4 16 20 5 25 30 6
(2 * ((if (x mod 3) <= 0 then 1 else (2 + (x div 3))) * (1 + (x div 3))))
A221564: 2 4 4 4 12 12 6 24 24 8 40 40 10 60 60 12
(~1 + loop(\(x,i).3x,x,2) - (2 * ((x mod 3) * (x mod 3))))
A018477: 1 3 9 53 159 477
(((x mod 2) - (if ((x div 3) mod 2) <= 0 then ~1 else 2)) * (1 + (x mod 3)))
A130806: 1 4 3 ~1 ~4 ~3 1 4 3 ~1 ~4 ~3 1 4 3 ~1
(1 + ((x + loop(\(x,i).(1 + ((x * (x + i)) div 8)),2,x)) div 3))
A123946: 1 1 2 2 3 4 5 7 9 11 14 18 23 29 38 48
(1 + (x mod (1 + (x mod (2 + (if ((x + ~2) mod (1 + (x div 3))) <= 0 then 1 else x))))))
A001438: 1 2 3 4 1 6 7 8
A049073: 1 2 3 4 1 6 7 8 3 10 1 12 1 14 15 16
loop(\(x,i).i,((x + ~4) + ((x + 8) div (~1 + ((~x + 1) div 2)))),1)
A079789: 1 1 1 1 1 1 1 1 1 1 3 3 5 6 7 8
(~1 + loop(\(x,i).(10x + 90),(x + 2),1))
A039684: 1089 10989 109989 1099989 10999989 109999989
(1 + ((~1 + loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2)) div (x + 3)))
A054542: 1 2 4 12 36 116 382 1287 4420 15397 54264 193154 693374 2507288 9124560 33393355
loop(\(x,i).((10x + 1) - ((x div 2) mod 2)),(2x + 1),1)
A153435: 11 1100 110011 11001100 1100110011 110011001100 11001100110011 1100110011001100 110011001100110011 4611686018427387903 4611686018427387903 4611686018427387903
(x div (1 + (loop(\(x,i).2x,x,(1 + (x mod (2 + (x mod 2))))) mod (2x + 1))))
A319341: 0 0 0 1 0 0 0 3 4 0 0 2 0 0 0 7
(x div (1 + (x div (1 + ((if ((x div ~2) mod 4) <= 0 then 0 else 1) + (x mod 2))))))
A143792: 0 1 1 1 1 2 1 1 0 2 1 2 1 2 1 1
(1 + (x div (1 + ((((x + ~1) div 2) div 2) + (if (x + ~2) <= 0 then 2 else 1) + (x mod 2)))))
A023524: 1 1 1 2 3 2 3 2 3 2 3 3 4 3 3 3
(1 + (x div (1 + ((if ((x - (x div 3)) mod 3) <= 0 then 1 else x) * (x mod 2)))))
A328478-A300330: 1 1 3 1 5 1 7 1 9 5 11 1 13 7 15 1
(2 - ((~x + 1) div (1 + (if (x mod (1 + (((x + 1) div 2) div 3))) <= 0 then x else 1))))
A322822: 1 2 3 3 3 4 3 5 3 6 3 7 3 8 9 3
(x div (1 + ((x + ~1) mod (1 + (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then 1 else x)))))
A345939: 0 1 1 1 1 5 1 1 1 9 1 11 1 13 7 1
loop(\(x,i).21x,(5x + 1),1)
A013898: 21 85766121 350277500542221 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).22x,(5x + 1),1)
A013902: 22 113379904 584318301411328 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).19x,(5x + 1),1)
A013890: 19 47045881 116490258898219 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).23x,(5x + 1),1)
A013906: 23 148035889 952809757913927 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(1 + ((3 * (2x + (x mod 3))) + (x mod 2))),x,1))
A037620: 2 12 75 452 2712 16275 97652 585912 3515475 21092852 126557112 759342675 4556056052 27336336312 164018017875 984108107252
((x + ~1) + loop(\(x,i).((x + ~1) + ((2x2 + x) div (1 + i))),x,1))
A079954: 0 1 2 2 2 2 2 3 4 5 6 7 8 9 10 10
(1 + loop(\(x,i).((x + 1) + (x div (4 + (x2 mod (x + 4))))),x,1))
A079446: 2 3 4 5 7 8 9 11 13 17 18 19 20 21 23 25
((x + 1) - ((x mod 4) mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1)))
A345965: 1 2 3 4 5 5 7 8 9 9 11 9 13 13 13 16
((9x + 73) + (if (x + ~2) <= 0 then x else 1))
A217237: 73 83 93 101
(1 + (x div (1 + (if (~1 + (x mod (1 + ((~x + 2) mod 4)))) <= 0 then (x mod 2) else x))))
A082725: 1 1 3 1 5 3 7 1 1 5 11 1 13 7 15 1
(1 + compr(\x.(if (x mod 2) <= 0 then (~1 + (2x mod (4 + (x div 2)))) else 0),(x + 1)))
A337945: 2 4 6 8 9 10 12 14 16 18 20 22 24 25 26 27
(1 + compr(\x.(~1 + (x mod ((x + 1) - (loop(\(x,i).2x,x,1) mod (x + 1))))),(x + 1)))
A327906: 2 3 5 6 7 10 11 13 14 17 18 19 22 23 26 29
(1 + ((~1 + loop(\(x,i).2x,x,(3 * ((x div 3) mod 2)))) mod (x + 1)))
A330194-A330105-A330061: 1 2 3 4 3 6 7 8 9 6 3 12 13 14 15 16
(1 + compr(\x.(~1 + (loop(\(x,i).(4x + 2),(x div 2),1) mod (x + 1))),(x + 1)))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A335284-A325559-A308966-A206074: 2 3 5 7 11 13 17 19 23 25 29 31 37 41 43 47
((x + 2) mod (1 + ((1 + (2 * (2 + (if (~2 + (x div 2)) <= 0 then x else 2)))) mod (x + 1))))
A081134: 0 1 0 1 2 3 2 1 0 1 2 3 4 5 6 7
(x mod ((x + 1) - (loop(\(x,i).2x,(x + 16),1) mod (x + 1))))
A126308: 0 1 0 3 0 1 1 7 0 1 0 3 2 3 3 15
(1 + compr(\x.(2 - (loop(\(x,i).((2x + 1) + (x mod 2)),x,0) mod (x + 1))),(x + 1)))
A009188: 9 12 15 16 18 20 21 24 25 27 28 30 32 33 35 36
(1 + ((2 * (if (x mod 2) <= 0 then (2x mod 9) else 1)) div (x + 1)))
A293668: 1 2 3 1 4 1 1 1 2 1 1 1 1 1 1 1
loop(\(x,i).x6,1,(8x + 7))
A017154: 117649 11390625 148035889 887503681 3518743761 10779215329 27680640625 62523502209 128100283921 243087455521 433626201009 735091890625 1194052296529 1870414552161 2839760855281
(if x <= 0 then 1 else (x mod (1 + ((1 - ((x2 + 2x) mod 8)) mod (x + 1)))))
A153011: 1 0 0 0 0 0 0 1 0 0 0 4 0 0 0 4
loop(\(x,i).x7,1,(4x + 3))
A016843: 2187 823543 19487171 170859375 893871739 3404825447 10460353203 27512614111 64339296875 137231006679 271818611107 506623120463 897410677851 1522435234375 2488651484819 3938980639167
((4x2 + 4x + 1) * loop(\(x,i).x2,2,(4x + 1)))
A014799: 1 5625 164025 1399489 6765201 23532201 66015625 159138225 342731169 676572121 1246160601 2169230625 3603000625 5752160649 8877596841 13305853201
((x + 1) div (1 + (loop(\(x,i).(2x + 1),x,(4 - (x mod 2))) mod (x + 1))))
A284373: 1 1 1 1 1 3 1 1 4 1 2 1 2 1 3 1
(~1 + (loop(\(x,i).((x + 2) + (2x div 7)),x,2) div (x + 1)))
A094997: 1 1 1 1 2 2 3 4 4 6 7 9 11 13 16 20
(~1 + (loop(\(x,i).((x + 2) + ((x - (x div 3)) div 3)),x,2) div (x + 1)))
A240572: 1 1 1 1 1 2 2 3 3 4 4 5 6 7 9 10
(~1 + (loop(\(x,i).((x + 2) + ((x + (2 * (x mod 2))) div 3)),x,2) div (x + 1)))
A140881-A017979: 1 1 1 2 2 3 4 5 6 8 10 12 16 20 25 32
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(x2 + 3x + 1))
A141222: 1 5 22 95 406 1722 7260 30459 127270 529958 2200276 9111830 37650172 155266100 639191160 2627302995
(1 + (2 div (16 div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A226859: 1 1 1 1 1 1 2 1 3 1 3 1 3 2 3 1
(1 + ((2x2 + 5x + 2) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))
A182241: 3 10 7 36 11 26 15 136 19 42 23 100 27 58 31 528
(1 + (loop(\(x,i).(x - (((~x + ~1) + (x div 3)) div 3)),(x + ~1),0) div 2))
A258875: 1 1 1 2 2 3 4 5 6 8 10 12 15 19 23 29
(2 div (2 - ((x div 3) div (1 + (if (x mod 10) <= 0 then 0 else 2)))))
A044932: 1 1 1 1 1 1 1 1 1 2 ~2 2 2 2 2 2
loop(\(x,i).2x,(x - ((x div ~2) + ((3 * (x div 4)) div 2))),1)
A129195: 1 4 8 32 32 128 256 1024 512 2048 4096 16384 16384 65536 131072 524288
(1 + (2 * ((~1 + (x div 2)) mod (1 + (if (x mod 3) <= 0 then (x div 3) else 0)))))
A214228: 1 1 1 1 1 1 5 1 1 7 1 1 1 1 1 1
(1 + ((if x <= 0 then 0 else (1 + (7 * ((~x + 1) mod 3)))) div 2))
A261882: 1 1 8 5 1 8 5 1 8 5 1 8 5 1 8 5
((x + 2) mod (1 + ((x + 1) mod (2 + (x div (1 + (if (x mod 3) <= 0 then 2 else 1)))))))
A100820: 0 0 0 1 0 1 0 1 2 0 2 1 0 1 2 2
(1 + (2 * (x mod (1 + ((x + ~1) mod (1 + (2 * (if (x mod 4) <= 0 then 0 else 2))))))))
A274613: 1 1 1 1 1 1 1 3 1 3 1 1 1 3 5 1
(if x <= 0 then 1 else (1 + (2 * ((x + 1) - (((~x + ~1) + (x mod 2)) div 5)))))
A193071: 1 7 9 11 13 15 19 21 23 25 29 31 33 35 37 39
(1 + (2 * (1 + ((15x + 10) * (if x <= 0 then 1 else 2)))))
A241746: 23 103 163 223 283 343 403 463 523 583 643 703 763 823 883 943
(1 + ((1 + ((x + (if (~2 + (x div 4)) <= 0 then 2 else 1)) mod 5)) div 2))
A108132: 2 3 3 1 2 2 3 3 1 2 2 3 3 3 1 2
(if x <= 0 then 1 else (~1 + (2 * ((x * (1 + (x div 2))) mod (1 + (x div 5))))))
A010555: 1 ~1 ~1 ~1 ~1 1 ~1 ~1 ~1 1 ~1 ~1 ~1 1 1 ~1
(1 + ((1 + (3 mod (1 + (if (x mod 9) <= 0 then 0 else x)))) div 2))
A307558: 1 2 1 3 3 3 3 3 3 1 3 3 3 3 3 3
(1 + ((x + ~1) div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))))
A234541: 0 1 1 2 1 2 1 4 2 2 1 4 1 2 3 8
(2 div (1 + (if x <= 0 then 1 else ((x mod (1 + ((2 - (x mod 4)) mod (x + 1)))) div 2))))
A230594: 1 2 2 1 2 2 2 0 1 2 2 0 2 2 2 0
(1 + (2 * (1 + loop(\(x,i).(x + (5 * (x + (x mod 3)))),x,1))))
A092166: 5 25 155 925 5555 33325 199955 1199725 7198355 43190125 259140755 1554844525 9329067155 55974402925 335846417555 2015078505325
(1 + (2 * (if x <= 0 then 0 else (1 + (((x + ~4) mod (1 + (x div 4))) div 2)))))
A122916: 1 3 3 3 3
A339055: 1 3 3 3 3 3 3 3 3 5 3 3 3 3 5 5
loop(\(x,i).x2,1,(1 + (2 * (x - ((2x + 2) div 7)))))
A304035: 1 9 25 25 49 81 81 121 169 225 225 289 361 361 441 529
(1 + ((1 + (loop(\(x,i).((x + 1) + ((x + (x div 2)) div 4)),x,1) div 2)) div 2))
A022866: 1 2 2 2 3 4 5 6 8 11 15 20 27 37 51 70
(1 + ((1 + ((loop(\(x,i).(4x + (i div 2)),x,1) mod (x + 1)) div 2)) div 2))
A182594: 1 1 2 1 2 2 1 3 3 2 2 1 4 2 3 2
(1 + (2 * (1 + ((loop(\(x,i).2x,x,(((x + ~1) div 2) mod 2)) mod (x + 1)) div 2))))
A162844: 3 3 3 3 3 3 3 3 7 3 3 11 3 3 3 3
(1 + ((x div 2) div (2 * (1 + (x mod (2 * (2 + (if (x mod 4) <= 0 then 2 else 0))))))))
A210650: 1 1 1 1 1 1 1 1 3 2 1 1 1 2 2 1
loop(\(x,i).(2x + 1),(2 * (1 + (2 * (2 + (3 * (x + (x div 2))))))),1)
A236373: 2047 8388607 140737488355327 576460752303423487
(1 + ((x + 1) div (2 + (if (x mod (6 - ((x div 2) mod 2))) <= 0 then 2 else 1))))
A116513: 1 1 2 2 2 3 3 3 4 4 3 5 4 5 6 5
(1 + (2 * (1 + (2 * (4 + loop(\(x,i).(x3 + x2),x2,2))))))
A116353: 27 67 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 0 else (1 + (((x + ~1) mod (1 + (2 * (((x + 1) div 2) mod 4)))) mod 2)))
A189024: 0 1 2 1 2 1 2 1 1 1 1 1 2 2 1 1
(1 + (2 * (1 + (2 * loop(\(x,i).(10x + 4),(x + 2),2)))))
A108904: 979 9779 97779 977779 9777779 97777779 977777779 9777777779 97777777779 977777777779 9777777777779 97777777777779 977777777777779 9777777777777779 97777777777777779 977777777777777779
(1 + ((((if (x mod 3) <= 0 then 1 else x) + (x div 3)) mod 5) div 2))
A098281: 1 1 2 2 1 1 2 3 1 3 2 3 1 2 2 1
(1 + ((((if (x mod 3) <= 0 then 0 else x) - (x mod 3)) mod 5) div 2))
A076899: 1 1 1 1 2 2 1 1 1 1 3 3 1 2 2 1
(1 + ((if ((x div 5) mod 2) <= 0 then x else ~x) mod 10))
A232240: 1 2 3 4 5 6 5 4 3 2 1 2 3 4 5 6
(1 + ((1 + ((loop(\(x,i).(x + ((1 + i) * i)),(1 + (x div 2)),x) div 2) div 2)) div 2))
A099383: 1 1 2 2 4 4 7 7 11 11 16 16 24 24 33 33
(1 + ((1 + (((x + loop(\(x,i).((x + 2) + (x div 3)),x,1)) div 2) div 2)) div 2))
A018053: 1 2 2 3 3 4 6 7 9 12 16 21 27 36 47 62
(1 + (2 * (1 + (if x <= 0 then 0 else (2 + ((x + (((x div 2) div 3) mod 2)) div 2))))))
A096910: 3 7 9 9 11 11 13 15 15 17 17 19 19 19 21 21
(2 div (1 + ((1 + ((if (x div 3) <= 0 then 2 else ((x * (x mod 2)) div 2)) div 2)) div 2)))
A319981: 1 1 1 2 2 1 2 1 2 1 2 1 2 0 2 0
loop(\(x,i).x6,1,(8x + 3))
A017106: 729 1771561 47045881 387420489 1838265625 6321363049 17596287801 42180533641 90458382169 177978515625 326940373369 567869252041 941480149401 1500730351849 2313060765625 3462825991689
(1 + (loop(\(x,i).((x + 1) * (2 + (x mod 2))),(x div 2),(1 + (2 * (x mod 2)))) div 2))
A029746: 1 2 4 7 8 14 16 28 32 56 64 112 128 224 256 448
(1 + ((x div 2) div (2 + (3 * (if (x mod 12) <= 0 then 0 else 1)))))
A215847: 1 1 1 1 1 1 1 1 1 1 2 2 4 2 2 2
(if x <= 0 then 0 else (1 + ((x div (3 * (1 + ((1 + (x mod 4)) div 2)))) mod 2)))
A307322-A306737: 0 1 1 1 2 1 2 1 1 2 2 2 1 1 1 2
(1 + (2 * ((1 + (4 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 3)))
A072939: 3 7 9 11 15 19 23 25 27 31 33 35 39 41 43 47
(~1 + (2 * ((1 + (4 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 3)))
A079523: 1 5 7 9 13 17 21 23 25 29 31 33 37 39 41 45
((x + 2) mod (1 + (if (x + ~1) <= 0 then 1 else (2 * ((x - (x div 3)) div 3)))))
A340958: 0 1 0 0 0 1 2 0 0 1 2 3 4 1 2 3
(1 + ((3 * loop(\(x,i).((x + 1) + (x div (1 + (i mod 3)))),x,1)) div 2))
A192581: 2 4 5 11 17 23 47
(1 + (2 * ((((1 + (x div 2)) mod 3) + loop(\(x,i).2x,x,1)) div 3)))
A130759: 1 3 5 7 11 21 43 87 173 343 683 1365 2731 5463 10925 21847
(if x <= 0 then 2 else (~1 + (2 * ((2 * (1 + (2 * ((x + 2) div 3)))) div 3))))
A141784: 2 3 3 3 5 5 5 7 7 7 11 11 11 13 13 13
(~1 + ((loop(\(x,i).(3x + 1),x,1) + (((x + ~1) div 2) mod 3)) div 2))
A135266: 0 1 5 19 60 182 546 1639 4919 14761 44286 132860 398580 1195741 3587225 10761679
((x + 1) - (2 * ((2 * (if (x + ~2) <= 0 then x else (2 - (x div ~2)))) div 3)))
A118777: 1 2 1 0 1 0 1 0 1 2 3 2 3 2 3 4
loop(\(x,i).(2x + 1),(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)
A159913: 1 3 3 7 3 7 7 15 3 7 7 15 7 15 15 31
loop(\(x,i).(2x + 2),(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)
A160723: 1 4 4 10 4 10 10 22 4 10 10 22 10 22 22 46
loop(\(x,i).4x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)
A102376: 1 4 4 16 4 16 16 64 4 16 16 64 16 64 64 256
loop(\(x,i).3x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)
A048883: 1 3 3 9 3 9 9 27 3 9 9 27 9 27 27 81
(1 + (((2 + loop(\(x,i).x2,1,((x + ((x div 2) mod 2)) div 2))) div 3) div 2))
A035398: 1 1 1 2 2 2 2 4 4 4 5 7 7 7 9 12
(1 + (((2 + (x div 2) - ((if (x mod 2) <= 0 then 1 else x) mod 4)) div 3) mod 2))
A097026: 1 1 1 1 2 2 2 1 2 2 1 2 1 1 1 1
((loop(\(x,i).5x,(x + ~1),1) div 3) mod 7)
A021862: 0 0 1 1 6 5 5 0 1 1 6 5 5 0 1 1
(7 * loop(\(x,i).((10x + 1) + i),x,1))
A099674: 7 84 861 8638 86415 864192 8641969 86419746 864197523 8641975300 86419753077 864197530854 8641975308631 86419753086408 864197530864185 8641975308641962
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) mod 7)
A159986: 1 1 2 5 0 0 6 2 2 4 3 0 0 4 6 6
(14 * loop(\(x,i).(2x + 12),(x + 2),0))
A226265: 504 1176 2520 5208 10584 21336 42840 85848 171864 343896 687960 1376088 2752344 5504856 11009880 22019928
(7 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A272470: 14 21 35 49 77 91 119 133 161 203 217 259 287 301 329 371
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 7)
A039705: 2 3 5 0 4 6 3 5 2 1 3 2 6 1 5 4
((if x <= 0 then 1 else ((x mod ~7) mod 2)) + (x div 7))
A025817: 1 0 1 0 1 0 1 1 1 2 1 2 1 2 2 2
((x + 1) - (2 * ((x + (2 * (1 + (if (x + ~4) <= 0 then 0 else 2)))) div 3)))
A071993: 1 0 1 2 1 0 ~1 0 1 0 1 2 1 2 3 2
((if ((1 + (x div 3)) mod 3) <= 0 then 2 else 1) * (1 + ((x mod 3) div 2)))
A290092-A117592: 1 1 2 1 1 2 2 2 4 1 1 2 1 1 2 2
((if ((x + 1) mod (1 + (x div 4))) <= 0 then 1 else 2) * (1 + ((x mod 3) div 2)))
A246600-A068068: 1 1 2 1 2 2 2 1 2 2 2 2 2 2 4 1
(1 + ((1 + (loop(\(x,i).(1 + ((2x + 2) * (x mod 2))),(x div 2),x) div 2)) div 2))
A211164: 1 1 1 3 2 8 4 20 8 48 16 112 32 256 64 576
loop(\(x,i).(2 * (1 + i)),((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2),1)
A174093: 1 1 1 1 4 1 1 4 4 1 1 4 6 4 1 1
loop(\(x,i).4x,((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2),1)
A152716: 1 1 1 1 4 1 1 4 4 1 1 4 16 4 1 1
loop(\(x,i).x2,1,(1 + ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)))
A106314: 1 1 1 1 4 1 1 4 4 1 1 4 9 4 1 1
loop(\(x,i).(x2 + x),((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2),1)
A107044: 1 1 1 1 2 1 1 2 2 1 1 2 6 2 1 1
(1 + (if (x + ~1) <= 0 then x else ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)))
A323231: 1 2 1 1 2 1 1 2 2 1 1 2 3 2 1 1
(1 + (((x * (~1 - (if (x mod 3) <= 0 then 2 else 0))) mod (1 + (x div 2))) div 2))
A223135: 1 1 1 1 2 1 2 1 2 2 2 1 4 1 2 2
(if (x mod 3) <= 0 then 1 else ((x * (x div 2)) mod (1 + ((x mod (1 + (x div 2))) div 2))))
A029313: 1 0 0 1 0 0 1 1 0 1 2 1 1 2 2 1
(1 + ((1 + loop(\(x,i).((x + 2) + (x div (1 + (x mod 2)))),(x div 2),(x mod 2))) div 2))
A262699: 1 2 2 3 4 4 8 8 16 16 32 32 64 64 128 128
loop(\(x,i).x5,1,(10x + 3))
A017309: 243 371293 6436343 39135393 147008443 418195493 992436543 2073071593 3939040643 6956883693 11592740743 18424351793 28153056843 41615795893 59797108943 83841135993
(1 + (loop(\(x,i).(x - ((~x + ((~x + 1) div 3)) div 5)),x,1) div 2))
A127207: 1 2 2 3 3 4 5 7 9 11 14 18 23 29 37 47
(~1 + (2 * loop(\(x,i).(x + (i div 3) - (x div ~5)),x,1)))
A248956: 1 3 5 9 13 19 27 37 49 65 85 109 139 175 219 273
(1 + (loop(\(x,i).(x - ((~1 + (x div (~3 + (x mod ~2)))) div 2)),x,1) div 2))
A304631: 1 2 2 3 4 5 6 7 9 11 13 15 18 21 24 28
(x div ((x + 1) - (2 * (2 mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1)))))
A336388: 0 0 0 0 0 2 0 0 0 1 0 1 0 1 1 0
((x + 1) - (((~1 + loop(\(x,i).4x,(2 * (x div 2)),2)) mod (x + 1)) div 2))
A155918-A085314-A085310-A055653: 1 2 3 3 5 6 7 5 7 10 11 9 13 14 15 9
loop(\(x,i).(x * i),(2 * compr(\x.(1 - (x mod (1 + (4 * (x mod 2))))),(x + 1))),1)
A072238: 720 87178291200 6402373705728000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(((x2 + x) div 2) mod (1 + (2 * (loop(\(x,i).2x,(x + ~2),1) div (x + 1)))))
A241715: 0 0 0 0 0 0 1 1 6 20
(x6 mod loop(\(x,i).(2x2 + 3x + 1),2,1))
A085339: 0 1 64 1 1 64 64 77 64 1 1 64 1 78 14 64
(1 + ((loop(\(x,i).2x,x,(2 * (~1 + (2x mod 3)))) mod (x + 1)) div 2))
A116599: 1 1 1 1 2 1 3 1 1 4 2 1 6 3 1 1
(1 + (x div ((x + 2) div (2 + (loop(\(x,i).x3,2,2x) mod (x + 1))))))
A166140-A088835-A053166-A015053-A015052-A007947: 1 2 3 2 5 6 7 2 3 10 11 6 13 14 15 2
((4x + 2) - loop(\(x,i).((2x + 2) div (1 + i)),((x + 1) div 2),1))
A311262: 1 4 8 12 16 21 25 30 34 38 42 46 50 54 58 62
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (1 + ((x + 1) div 2)))
A083176: 2 6 10 21 33 52 68 95 115 174 186 259 287 344 376 477
(1 + (((x + 1) * loop(\(x,i).(x * (1 + (6 * i))),3,x)) div 2))
A130876: 1 1730 5188 10375 17291 25936 36310 48413 62245 77806 95096 114115 134863 157340 181546 207481
(1 + (((x + 1) * (x + (if (x mod 2) <= 0 then 2 else ((x2 + 3x + 2) div 2)))) div 2))
A343596: 2 5 7 27 16
(1 + (((((2x + ~2) mod (4 + (x div 2))) div 2) div 2) + (if x <= 0 then 1 else 2)))
A177876: 2 3 3 4
A071866: 2 3 3 4 3 3 3 4 4 3 3 3 3 4 4 4
((x + 2) div ((1 + (3 * (2x mod 3))) * (1 + (if x <= 0 then 1 else 2))))
A029302: 1 0 0 1 0 0 2 0 0 3 0 1 4 0 1 5
(1 + (x mod 2) - (2 * ((x - (if ((x + ~2) mod 5) <= 0 then 1 else 0)) mod 2)))
A083037: 1 0 ~1 0 1 0 1 2 1 0 1 0 ~1 0 1 0
loop(\(x,i).5x,(2 - ((~x + 2) div (2 - (x div ~4)))),1)
A039936: 5 25 25 125 125 125 125 625 625 625 625 625 625 625 625 3125
(1 + (((if ((~2x + 2) mod (4 + (x div 4))) <= 0 then x else 0) div 2) div 2))
A124944: 1 1 1 1 1 1 2 1 1 1 3 1 1 1 1 4
((x + 1) - (2 * (loop(\(x,i).(1 + ((i div (2 + (x mod 2))) + (x div 2))),x,0) div 2)))
A275892: 1 2 3 2 1 2 3 4 5 4 3 4 3 4 3 4
(~1 + (2 * ((1 + (if x <= 0 then 1 else (x - ((x + 1) mod (3 - (x mod 2)))))) div 2)))
A124741: 1 1 1 3 1 5 5 7 7 9 7 11 11 13 13 15
((x + 1) div (3 + (((x + 1) - (loop(\(x,i).2x,x,2) mod (x + 1))) div 2)))
A318663: 0 0 1 0 1 1 1 1 3 1 1 1 1 1 2 1
(1 + (2 * (if (x + ~1) <= 0 then 1 else (2 * (1 + (2 * ((1 + (x div 4)) div 2)))))))
A171710: 3 3 5 5 13 13 13 13 13 13 13 13 21 21 21 21
(if (x + ~1) <= 0 then (x + 1) else (1 + (2 * ((x mod (1 + (((x + 1) div 2) div 2))) mod 2))))
A079728: 1 2 1 3 1 3 1 3 1 1 3 3 1 3 1 1
(if x <= 0 then 0 else (1 + (x div (2 * (2 + ((2x + ~4) mod 9))))))
A127832: 0 1 1 1 1 1 1 2 1 1 1 3 2 2 1 1
(if x <= 0 then 0 else (1 + (3x div (4 + ((x div 2) div 5)))))
A268382: 0 1 2 3 4 4 5 6 7 7 7 7 8 8 9 10
loop(\(x,i).2x,(x div (2 + (x div (2 + ((~x + 1) mod (1 + (x mod 4))))))),1)
A327813: 1 1 2 2 2 2 2 4 2 2 2 4 2 2 4 8
(x3 div (1 + loop(\(x,i).x2,2,(4 * (1 + (2 * (x mod 2)))))))
A007386: 0 0 0 0 0 0 0 0 1 0 3 0 6 0 10 0
(1 + (((1 + (((x * (x + (if (x mod 3) <= 0 then 2 else 1))) div 2) div 2)) div 2) div 2))
A029041: 1 1 1 2 2 3 4 4 5 7 8 9 11 12 14 17
(~1 + (2 * ((3 * (~1 + (if x <= 0 then 1 else 9x))) div 2)))
A063321: ~1 23 49 77 103 131 157 185 211 239 265 293 319 347 373 401
(~1 + (2 * ((x - (((x + (if (x mod 2) <= 0 then x else 2)) div 3) mod 3)) mod 2)))
A014077: ~1 ~1 1 ~1 ~1 1 1 1 ~1 1 ~1 ~1 ~1 1 ~1 1
(1 + (if (x + ~1) <= 0 then x else (2 + ((3 * ((1 + (x div 4)) div 2)) div 2))))
A213253: 1 2 3 3 4 4 4 4 4 4 4 4 6 6 6 6
(~1 + (2 * ((3 * (x - ((if x <= 0 then 1 else x) div ~7))) div 2)))
A322271: 1 5 7 11 13 17 19 23
A276378: 1 5 7 11 13 17 19 23 29 31 35 37 41 43 47 53
(1 - (x div (~1 + (2 * (if (x mod 9) <= 0 then 0 else 6)))))
A068159: 1 1 1 1 1 1 1 1 1 10 1 0 0 0 0 0
(~1 + (2 * ((3 * (x + (if (x + ~10) <= 0 then 1 else 2))) div 2)))
A322271: 1 5 7 11 13 17 19 23
A231810: 1 5 7 11 13 17 19 23 25 29 31 37 41 43 47 49
(1 + (4 * (3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A129070: 13 17 25 33 49 57 73 81 97 121 129 153 169 177 193 217
(1 + loop(\(x,i).(~1 + (2 * (x + (i mod 2)))),x,0) - (2 * ((x div 3) mod 2)))
A130707: 1 2 2 2 4 10 22 44 86 170 340 682 1366 2732 5462 10922
loop(\(x,i).x6,1,(8x + 5))
A017130: 15625 4826809 85766121 594823321 2565726409 8303765625 22164361129 51520374361 107918163081 208422380089 377149515625 646990183449 1061520150601 1677100110841 2565164201769
(3 mod (1 + ((((if (x mod 3) <= 0 then 2 else 1) * (1 + (x div 2))) div 2) div 2)))
A336090: 0 0 0 1 0 0 0 1 1 0 1 1 3 1 0 3
(1 + (4 * ((x2 + x + 1) + loop(\(x,i).(x2 * i),2,3))))
A145202: 653 661 677 701 733 773 821 877 941 1013 1093 1181 1277 1381 1493 1613
(1 + ((loop(\(x,i).((x + 2) + ((2 * (x div 3)) div 3)),x,1) div 2) div 2))
A112192: 1 1 2 2 3 4 5 7 8 10 13 16 20 24 30 36
(1 + (((loop(\(x,i).(~2x + 4),(x mod 5),0) mod (x + 1)) div 2) div 2))
A027926: 1 1 1 1 1 1 2 2 1 1 1 2 3 4 3 1
(if x <= 0 then 2 else (1 + ((((3 * ((x + ~1) mod 4)) mod (x + 1)) div 2) div 2)))
A259154: 2 1 1 1 2 1 1 2 1 1 1 2 3 1 1 2
(1 + ((((x + 1) * ((x + 2) + (if (x mod 4) <= 0 then x else (x div 2)))) div 2) div 2))
A177101: 1 2 4 7 13 14 20
(~1 + (loop(\(x,i).(2 + (3 * (x mod 7))),(x + ~1),2) div 2))
A021319: 0 0 3 1 7 4 6 0 3 1 7 4 6 0 3 1
(1 + (2 * (loop(\(x,i).3x,x,1) div 28)))
A135344: 1 1 1 1 5 17 53 157 469 1405 4217 12653 37961 113881 341641 1024921
(1 + (((x div 2) - ((x + 1) mod (2 + (if (~2 + (x div 3)) <= 0 then 1 else 2)))) div 2))
A286528: 0 0 1 1 1 2 2 1 3 2 2 3 3 3 3 4
(if x <= 0 then 0 else (1 + ((x mod (2 + (x div (2 + ((x + 1) mod 5))))) div 2)))
A293433: 0 1 1 1 1 2 1 1 2 2 1 2 1 1 3 1
(if x <= 0 then 2 else (1 + ((x mod (2 + (x div (2 + ((x + ~1) mod 5))))) div 2)))
A075774: 2 1 1 1 1 1 1 2 1 1 1 3 1 2 2 2
(if x <= 0 then 0 else (1 + (x div (2 + ((x + 1) div (4 + ((x + 1) mod 3)))))))
A330808: 0 1 2 2 3 2 3 3 3 3 4 3 4 4 3 4
(1 + (2 * ((loop(\(x,i).x5,1,(2x + 1)) div 2) div 2)))
A175111: 1 121 1563 8403 29525 80525 185647 379687 709929 1238049 2042051 3218171 4882813 7174453 10255575 14314575
((if (~6 + (x div 2)) <= 0 then 1 else 2) * (1 + ((((x + 1) div 2) div 2) div 2)))
A248783: 1 1 1 1 1 1 1 2 2 2 2 2 2 2 4 6
(1 + (((((x + 1) * (x + (if (x + ~6) <= 0 then 1 else 0))) div 2) div 2) div 2))
A029005-A008754: 1 1 2 3 4 5 7 8 10 12 14 17 20 23 27 31
(~1 + (16 * (~1 + (4 * loop(\(x,i).(2x + 4),x,2)))))
A304516: 111 495 1263 2799 5871 12015 24303 48879 98031 196335 392943 786159 1572591 3145455 6291183 12582639
(3 + (if x <= 0 then 1 else (2 + ((x - ((x mod (2 + (x mod 3))) div 2)) div 2))))
A114458: 4 5 5 6 7 7 8 8 9 9 10 10 11 11 11 12
(1 + ((x mod (2 + ((x + 2) div (2 + (if (x mod 2) <= 0 then 1 else 8))))) div 2))
A136755: 1 1 2 1 1 1 2 1 2 1 3 2 1 1 1 1
(loop(\(x,i).7x,x,1) mod 33)
A070417: 1 7 16 13 25 10 4 28 31 19 1 7 16 13 25 10
(loop(\(x,i).7x,x,1) mod 31)
A070415: 1 7 18 2 14 5 4 28 10 8 25 20 16 19 9 1
(if x <= 0 then 0 else (1 + (((x div 2) - (x div (4 + ((~x + 1) mod 4)))) div 2)))
A235645: 0 1 1 1 2 1 2 2 2 2 3 3 3 2 3 3
(x div (if (x mod 2) <= 0 then (2 + (4x mod (4 + (x div 4)))) else 1))
A340083: 0 1 1 3 1 5 1 7 2 9 1 11 1 13 7 15
(2 - (if x <= 0 then 0 else (~1 + (2 * (((x + ~1) mod (2 + (x div (2 + (x mod 2))))) mod 2)))))
A126044: 2 3 1 3 1 1 3 3 1 1 3 3 1 3 3 3
(15 * (~1 + loop(\(x,i).10x,x,2)))
A177074: 15 285 2985 29985 299985 2999985 29999985 299999985 2999999985 29999999985 299999999985 2999999999985 29999999999985 299999999999985 2999999999999985 29999999999999985
((((x + 2) * loop(\(x,i).x2,2,(x + 2))) div 2) div 15)
A033455: 1 8 34 104 259 560 1092 1968 3333 5368 8294 12376 17927 25312 34952 47328
((x * loop(\(x,i).((x2 + ~x) div 2),2,(x + ~2))) div 15)
A000389: 0 0 0 0 0 1 6 21 56 126 252 462 792 1287 2002 3003
loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),16x,1)
A147715: 1 129644790 4611686018427387903 4611686018427387903 4611686018427387903
(2 div (if x <= 0 then 2 else (1 + (x mod (2 + ((~x2 mod (2 + (x div 2))) div 2))))))
A091400: 1 1 0 1 2 0 0 1 0 2 0 0 2 0 0 1
(loop(\(x,i).10x,x,1) div (1 + (8 * (x mod 2))))
A280411: 1 1 100 111 10000 11111 1000000 1111111 100000000 111111111 10000000000 11111111111 1000000000000 1111111111111 100000000000000 111111111111111
(loop(\(x,i).(10x + 8),(x + 2),0) div 9)
A057933: 9 98 987 9876 98765 987654 9876543 98765432 987654320 9876543209 98765432098 987654320987 9876543209876 98765432098765 987654320987654 9876543209876543
(2 - ((if x <= 0 then 1 else (3 * (x2 div 4))) mod 9))
A181982: 1 2 ~1 ~4 ~1 2 2 2 ~1 ~4 ~1 2 2 2 ~1 ~4
(9 * loop(\(x,i).(10x + 21),x,1))
A177107: 9 279 2979 29979 299979 2999979 29999979 299999979 2999999979 29999999979 299999999979 2999999999979 29999999999979 299999999999979 2999999999999979 29999999999999979
((1 + (x * (if (x mod 2) <= 0 then x else 7))) mod 9)
A254270: 1 8 5 4 8 0 1
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) mod 9)
A130851: 1 1 2 5 5 6 6 6 8 2 2 7 4 4 0 0
((1 + loop(\(x,i).3x,x,(x + 8))) div 9)
A188545: 1 3 10
A126184: 1 3 10 33 108 351 1134 3645 11664 37179 118098 373977 1180980 3720087 11691702 36669429
(18 * (1 + ((x + 1) * loop(\(x,i).x2,2,3))))
A157505: 1476 2934 4392 5850 7308 8766 10224 11682 13140 14598 16056 17514 18972 20430 21888 23346
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 9)
A038194: 2 3 5 7 2 4 8 1 5 2 4 1 5 7 2 8
(if x <= 0 then 0 else ((x + 9) + (x div 11)))
A063662: 0 10 11 12 13 14 15 16 17 18 19 21 22 23 24 25
(9 * (x + (x mod (if (~2 + (x div 4)) <= 0 then 1 else 4))))
A259729: 0 9 18 27 36 45 54 63 72 81 90 99 108 126 144 162
((if (~x + (8 mod (x + 2))) <= 0 then 1 else 0) * (1 + (x mod 8)))
A049267: 1 0 3 4 5 6 7 0 1 2 3 4 5 6 7 8
(~4 mod (1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 8)))
A336937: 0 0 2 0 1 2 3 0 0 1 2 2 1 3 3 0
(if x <= 0 then 1 else ((5x + ~1) - (x div (~2 + ((~x + 2) div 4)))))
A313781: 1 5 10 15 21 26 31 36 41 47 52 57 62 67 72 77
loop(\(x,i).x5,1,(12x + 9))
A017633: 59049 4084101 39135393 184528125 601692057 1564031349 3486784401 6956883693 12762815625 21924480357 35723051649 55730836701 83841135993 122298103125 173726604657 241162079949
(1 + (x mod (2 * (2 + ((if ((x + 1) mod (2 + (x div 4))) <= 0 then 2 else x) div 2)))))
A334684: 1 2 3 4 5 6 7 8 9 10 11 6 13 14 3 16
(if (x div 2) <= 0 then ((x + 1) mod 2) else (x - (x2 div (x + 7))))
A130247: 1 0 2 3 3 3 4 4 4 4 5 5 5 5 5 5
(~1 + (loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,(x + 4)) div 2))
A007851: 1 4 14 48 167 593 2144 7864 29171 109173 411501 1560089 5943199 22732739 87253604 335897864
((4x + 7) * loop(\(x,i).(10x + 1),x,1))
A095752: 7 121 1665 21109 255553 2999997 34444441 388888885 4333333329 47777777773 522222222217 5666666666661 61111111111105 655555555555549 6999999999999993 74444444444444437
loop(\(x,i).x7,1,(8x + 1))
A017083: 1 4782969 410338673 6103515625 42618442977 194754273881 678223072849 1954897493193 4902227890625 11047398519097 22876792454961 44231334895529 80798284478113 140710042265625
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(8x + 1))
A050478: 1 9 34 125 462 1722 6468 24453 92950 354926 1360476 5231954 20177164 78004500 302211720 1173076245
loop(\(x,i).x6,1,(~7x + ~1))
A016998: 1 262144 11390625 113379904 594823321 2176782336 6321363049 15625000000 34296447249 68719476736 128100283921 225199600704 377149515625 606355001344 941480149401 1418519112256
(1 + ((if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1) div (2 + ((x div 2) mod 2))))
A052125: 1 1 1 1 1 3 1 1 1 5 1 4 1 7 5 1
(3 - loop(\(x,i).2x,(((x + (x div 2)) div 2) mod (2 + ((x div 2) mod 2))),1))
A195679: 2 2 1 ~1 1 1 1 ~1 2 2 1 ~1 1 1 1 ~1
(1 + (((x + ((loop(\(x,i).(2x + 2),x,2) div (x + 2)) + (x div 2))) div 2) div 2))
A245879: 1 1 2 3 5 7 11 17 29 50
((x + 1) - (2 * ((x - (x div ((if (x mod 3) <= 0 then 2 else 1) + (x mod 2)))) div 2)))
A216475: 1 2 3 2 5 4 5 4 9 4 11 6 7 8 15 6
(1 + (4 * loop(\(x,i).(10x + 2),(x div 2),(x mod 2))))
A328333: 1 5 9 49 89 489 889 4889 8889 48889 88889 488889 888889 4888889 8888889 48888889
loop(\(x,i).13x,(x div 2),(1 + (4 * (x mod 2))))
A018678: 1 5 13 65 169 845
loop(\(x,i).11x,(x div 2),(1 + (4 * (x mod 2))))
A018545: 1 5 11 55 121 605
(5 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) - (x mod 2))
A107623: 5 5 8 9 14 15 20 21 26 31 34 39 44 45 50 55
(1 + ((~1 + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1)) mod 4))
A321319: 1 1 2 1 2 2 4 1 2 2 4 2 4 4 4 1
((x + 1) div (if ((1 + (x div 3)) mod 3) <= 0 then ((x + ~1) mod 4) else 1))
A038388: 1 2 3 4 5 6 7 4 3 10 11 12 13 14 15 8
(x - (5 * (if (x mod 5) <= 0 then (~1 + (2 * (x mod 2))) else 0)))
A222214: 5 1 2 3 4 0 6 7 8 9 15 11 12 13 14 10
(4 div ((1 - loop(\(x,i).(3 * ((x + ~1) div 2)),x,0)) mod 5))
A247004: 4 1 2 1 2 1 2 1 4 1 2 1 1 1 2 1
(2 div ((1 - (if ((x + 2) mod (2 + ((x div 2) mod 2))) <= 0 then x else 0)) mod 5))
A090044: 2 2 2 2 1 2 2 0 0 2 2 2 0 2 2 2
(5 * (1 + (5 * (if (x + ~4) <= 0 then x else (x + 1)))))
A044463: 5 30 55 80 105 155 180 205 230 255 280 305 330 355 380 405
(loop(\(x,i).2x,(x - (3 * (((x + 1) div 2) div 2))),1) div 5)
A035623: 0 0 0 0 0 0 1 0 0 1 3 0 1 3 6 1
(x div (5 * (1 + ((x div 2) mod (2 + (if (x mod 2) <= 0 then 4 else 0))))))
A081389: 0 0 0 0 0 1 0 0 0 1 0 1 2 2 1 1
(5 * (~3 + loop(\(x,i).10x,(x + 1),1)))
A177079: 35 485 4985 49985 499985 4999985 49999985 499999985 4999999985 49999999985 499999999985 4999999999985 49999999999985 499999999999985 4999999999999985 49999999999999985
((1 + ((1 + ((loop(\(x,i).(x + (x div 2)),x,2) div 2) div 2)) div 2)) div 5)
A130732: 0 0 0 0 0 0 0 1 1 1 2 3 5 8 12 18
(2x div (5 * loop(\(x,i).i,((x2 + 2x) mod 6),1)))
A144740: 0 0 0 0 1 0 2 0 1 1 4 0 4 1 2 2
(if x <= 0 then 1 else (5 * (((x3 + 3x2 + 2x) div 2) div 3)))
A134481: 1 5 20 50 100 175 280 420 600 825 1100 1430 1820 2275 2800 3400
((6 * (if x <= 0 then 1 else (4x2 + 2))) div 5)
A299254: 1 7 21 45 79 122 175 237 309 391 482 583 693 813 943 1082
((loop(\(x,i).((x2 + ~x) div 2),2,(2x + 4)) div 3) div 5)
A000970: 1 7 25 66 143 273 476 775 1197 1771 2530 3510 4750 6293 8184 10472
(if x <= 0 then 1 else (5 * (x - (((~x3 + x) div 2) div 3))))
A008487: 1 5 15 35 70 125 205 315 460 645 875 1155 1490 1885 2345 2875
loop(\(x,i).x6,1,(10x + 5))
A017334: 15625 11390625 244140625 1838265625 8303765625 27680640625 75418890625 177978515625 377149515625 735091890625 1340095640625 2313060765625 3814697265625 6053445140625 9294114390625
(5 * loop(\(x,i).(6x + 2),(x div 2),(1 + (x mod 2))))
A117865: 5 10 40 70 250 430 1510 2590 9070 15550 54430 93310 326590 559870 1959550 3359230
(loop(\(x,i).2x,(x + ((x + ((x div 4) mod 2)) div 2)),1) mod 5)
A138967: 1 2 3 1 4 1 2 3 1 2 3 1 4 1 2 3
((loop(\(x,i).(7x + 3),(x + 1),1) div 2) div 5)
A037677: 1 7 51 360 2521 17647 123531 864720 6053041 42371287 296599011 2076193080 14533351561 101733460927 712134226491 4984939585440
((2 + (loop(\(x,i).(7x + 7),x,0) div 2)) div 5)
A178397: 0 1 6 40 280 1961 13726 96080 672560 4707921 32955446 230688120 1614816840 11303717881 79126025166 553882176160
((if x <= 0 then 1 else (x + 2)) - ((4 * ((~x + 1) div 3)) div 5))
A116883: 1 3 5 6 7 9 10 11 13 14 15 17 18 19 20 21
(20 * (~1 + loop(\(x,i).10x,x,2)))
A177109: 20 380 3980 39980 399980 3999980 39999980 399999980 3999999980 39999999980 399999999980 3999999999980 39999999999980 399999999999980 3999999999999980 39999999999999980
(10 * (2 + ((x + 1) * loop(\(x,i).(x2 + 2x + 1),2,2))))
A157510: 1020 2020 3020 4020 5020 6020 7020 8020 9020 10020 11020 12020 13020 14020 15020 16020
(10 * (~2 + ((x + 1) * loop(\(x,i).(x2 + 2x + 1),2,2))))
A157515: 980 1980 2980 3980 4980 5980 6980 7980 8980 9980 10980 11980 12980 13980 14980 15980
(10 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A142342: 20 30 50 70 110 130 170 190 230 290 310 370 410 430 470 530
((x + 2) - ((1 - (if (~2 + (x div 2)) <= 0 then x else (x + 4))) div 5))
A326070: 2 3 5 6 7 8 10 11 13 14 15 16 17 19 20 21
((2 * ((1 + (if (x mod 8) <= 0 then 2 else 1)) * (x div 2))) div 5)
A217754: 0 0 0 0 1 1 2 2 4 3 4 4 4 4 5
(4x - ((0 - (if (~4 + (x div 2)) <= 0 then 1 else x)) div 5))
A314670: 1 5 9 13 17 21 25 29 33 37 42 47 51 55 59 63
((if x <= 0 then 1 else 4x) - ((~x + ((x + 1) mod 3)) div 5))
A312893: 1 4 9 13 17 21 25 29 34 38 42 47 51 55 59 63
((x * loop(\(x,i).((x2 + ~x) div (1 + i)),2,(x + 3))) div 5)
A277935: 0 2 12 42 112 252 504 924 1584 2574 4004 6006 8736 12376 17136 23256
((~x + loop(\(x,i).((x + 1) + (2 * ((x div 2) div 3))),x,1)) div 5)
A319472-A026813: 0 0 0 0 0 0 0 1 1 2 3 5 7 11 15 21
loop(\(x,i).(49x + ~2),x,5)
A327582: 5 243 11905 583343 28583805 1400606443 68629715705 3362856069543 164779947407605 8074217422972643 395636653725659505 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((if (2 - (x mod (1 + (2 * (2 + (x mod 3)))))) <= 0 then 1 else x) mod 4))
A143594: 1 2 2 2 2 2 3 4 2 2 2 2 2 2 2 4
((x div 2) - ((if (x mod 5) <= 0 then (x + ~1) else 1) mod (1 + (x div 4))))
A295630: 0 0 1 1 1 2 2 2 3 3 5 4 5 5 6 5
(1 + (loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,x2) mod 4))
A336099: 1 2 1 2 1 3 1 2 1 3 1 3 1 1 1 2
(1 + (2 * ((x + 2) + (if (x + ~1) <= 0 then 0 else (1 + ((x + 1) div 5))))))
A256387: 5 7 11 13 17 19 21 23 25 29 31 33 35 37 41 43
(1 + (2 * ((x + 2) + (x div (3 + (if (~4 + (x div 2)) <= 0 then 2 else 1))))))
A282057: 5 7 9 11 13 17 19 21 23 25 29 31 35 37 39 41
(1 + (((x + ((loop(\(x,i).((x + 2) * (x + i)),2,x) div 2) div 3)) div 2) div 2))
A084569: 1 3 9 21 44 82 142 230 355 525 751 1043 1414 1876 2444 3132
(x7 mod (1 + loop(\(x,i).(x2 + x),2,2)))
A070723: 0 1 42 37 1 37 6 7 42 36 6 1 37 36 36 36
(3 + (if x <= 0 then 1 else ((x + 2) - (x2 div (x + 16)))))
A123860: 4 6 7 8 9 9 10 10 11 11 12 12 12 13 13 13
(x - ((x + 1) mod (1 + (x mod (2 + (loop(\(x,i).(x + (i * i)),x,0) mod (x + 2)))))))
A073137: 0 1 2 3 4 5 5 7 8 9 9 11 9 11 11 15
(1 + (x mod (1 - (x div (~1 - ((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)))))))
A173614: 1 2 1 4 2 6 1 2 4 10 2 12 6 4 1 16
(1 + (loop(\(x,i).((x + 2) + ((x - (x div 4)) div 2)),x,2) div (x + 4)))
A130083: 1 2 2 3 3 4 5 6 8 10 13 17 22 28 36 47
((x + 5) * (if (x mod 12) <= 0 then (x div 3) else 0))
A282338-A281888: 0 0 0 0 0 0 0 0 0 0 0 0 68 0 0 0
(((2x + 2) * (2 + (if (~2 + (x div 2)) <= 0 then 1 else 2))) div (x + 5))
A165077: 1 2 2 3 3 3 5 5 5 5 5 6 6 6 6 6
(1 + loop(\(x,i).9x5,2x,2))
A216148: 3 17832200896513 4611686018427387903
((4x + 1) + (x2 div (1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2)))))
A313729: 1 5 10 15 20 25 29 33 38 43 48 53 58 63 68 73
loop(\(x,i).(2x + 4),((((x2 + 2x) mod 6) + (x div 2)) div 2),1)
A341202: 1 6 6 16 6 36 6
loop(\(x,i).4x,(((3 * (x + (x div 4))) + (x mod 2)) div 2),1)
A327496: 1 16 64 1024 16384 262144 1048576 16777216 1073741824 17179869184 68719476736 1099511627776 17592186044416 281474976710656 1125899906842624 18014398509481984
loop(\(x,i).4x,(((3 * (x + (x div 4))) - (x mod 2)) div 2),1)
A110258-A056982: 1 4 64 256 16384 65536 1048576 4194304 1073741824 4294967296 68719476736 274877906944 17592186044416 70368744177664 1125899906842624 4503599627370496
(1 + (x div (2 + (x div ((if (x mod (1 + (x mod 3))) <= 0 then 1 else 2) + (x mod 2))))))
A330437: 1 1 1 2 1 2 1 2 2 2 1 3 1 3 2 2
(loop(\(x,i).(x * (1 + (2 * (2 + (x mod 4))))),x,1) * (1 + (2 * (x mod 2))))
A182754: 1 21 77 1617 5929 124509 456533 9587193 35153041 738213861 2706784157 56842467297 208422380089 4376869981869 16048523266853 337018988603913
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(x div 2),(1 + (2 * (x mod 2))))
A126324: 1 3 1 3 2 6 5 15 14 42 42 126 132 396 429 1287
loop(\(x,i).(4x + ((~x + 1) mod 4)),(x div 2),(1 + (2 * (x mod 2))))
A281216: 1 3 4 14 17 59 68 238 273 955 1092 3822 4369 15291 17476 61166
loop(\(x,i).(x * (1 + (2 * (~x mod 4)))),(x div 2),(1 + (2 * (x mod 2))))
A018267: 1 3 7 9 21 63
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (~1 + (2 * (x mod 2))))
A273960: ~2 3 ~5 7 ~11 13 ~17 19 ~23 29 ~31 37 ~41 43 ~47 53
(~1 + ((x * loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),x,1)) + (2 * (x mod 2))))
A105926: ~1 1 1 7 35 221 1589 12979 118663 1201465 13349609 161530271 2114578091 29780308117 448995414685 7215997736011
(1 + (2 * ((x + (x * (loop(\(x,i).(2 * (x + (i mod 2))),x,1) div (x + 1)))) div 2)))
A079444: 1 3 7 15 33 65 133 267
(((x2 + 2x) - (if (16 mod (x + 1)) <= 0 then 0 else 1)) div 3)
A192225: 0 1 2 5
A239072: 0 1 2 5 7 11 15 21 26 32 39 47 55 64 74 85
((1 + loop(\(x,i).(2x - ((1 - (2 * (i mod 2))) * i)),(x + ~1),0)) div 3)
A139797: 0 0 0 0 1 1 3 4 10 18 39 75 153 302 608 1212
((((x + (if (x mod 2) <= 0 then 2 else x)) div 2) * (1 + (x div 5))) mod 3)
A039971: 1 1 2 0 0 1 2 2 1 0 0 0 0 0 0 0
((1 + ((((x + 1) * loop(\(x,i).((x + 1) * i),x,x)) div 2) div 3)) mod 3)
A065833: 1 1 2 2 2 2 0 2 1 1 1 0 2 0 2 0
(((x + 1) * ((if (x + ~4) <= 0 then 1 else 2) * (1 + (x div 3)))) mod 3)
A006996: 1 2 0 2 1 0 0 0 0 2 1 0 1 2 0 0
(loop(\(x,i).2x,x,1) div (3 * (1 + ((2x + 1) * (x + (x mod 2))))))
A051058: 0 0 0 0 0 0 0 0 0 0 1 2 4 7 13 21
(if (x + ~1) <= 0 then 1 else (3 * (1 + ((x3 + ~x2) * (~1 + (x div 2))))))
A071536: 1 1 3 3 147
(loop(\(x,i).((5x + 1) - (x mod 3)),(x + 1),1) div 3)
A037598: 1 8 40 201 1008 5040 25201 126008 630040 3150201 15751008 78755040 393775201 1968876008 9844380040 49221900201
(loop(\(x,i).((5x + 2) - (x mod 3)),(x + 1),1) div 3)
A037619: 2 10 53 267 1335 6678 33392 166960 834803 4174017 20870085 104350428 521752142 2608760710 13043803553 65219017767
(loop(\(x,i).((4x div (2 + i)) * (1 + (2 * i))),(x + 1),1) div 3)
A069731: 1 5 28 168 1056 6864 45760 311168 2149888 15049216 106502144 760729600 5477253120 39710085120 289650032640 2124100239360
((1 + ((1 + (loop(\(x,i).(2x + 2),x,~x) div (x + 1))) div 2)) mod 3)
A345164-A339742-A335452-A318370-A050326: 1 1 1 0 1 2 1 0 0 2 1 1 1 2 2 0
((1 + ((loop(\(x,i).x2,1,(x2 + ~x)) mod (x + 3)) div 2)) mod 3)
A240159-A191312: 1 1 0 1 0 1 1 0 1 1 1 0 2 1 2 1
(((2x + 3) * loop(\(x,i).((x2 + x) div 2),2,(x + 1))) div 3)
A244864: 1 10 49 165 440 1001 2030 3774 6555 10780 16951 25675 37674 53795 75020 102476
((1 + (x mod (2 + (if (x mod 3) <= 0 then 1 else (2 + (x div 3)))))) mod 3)
A260648: 1 2 0 1 2 1 1 2 0 1 1 2 1 0 1 1
(3 * (1 + (2 * ((x mod (2 + (if (x mod 8) <= 0 then x else 1))) div 2))))
A074724: 3 3 9 3 3 9 3 3 27 3 3 9 3 3 9 3
(((1 + (x * ((if x <= 0 then 1 else (x div 3)) mod 2))) mod 5) mod 3)
A321761: 1 1 1 1 0 1 1 1 1 0 1 2 1 1 1 1
(loop(\(x,i).(x + ((x - ((x div 2) div 3)) div 2)),x,5) div 3)
A001521: 1 2 3 4 6 9 13 19 27 38 54 77 109 154 218 309
loop(\(x,i).x6,1,(12x + 3))
A017562: 729 11390625 387420489 3518743761 17596287801 62523502209 177978515625 433626201009 941480149401 1870414552161 3462825991689 6053445140625 10090298369529 16157819263041 25002110044521
((loop(\(x,i).((x2 + ~3x + 2) div 2),2,(x + 3)) div 3) div 3)
A216172: 0 0 1 4 10 21 39 66 105 159 231 325 445 595 780 1005
((2x + 2) - (((x + (if (x mod 3) <= 0 then x else 1)) div 3) mod 3))
A285163: 2 4 5 6 9 10 13 14 18 20 22 23 24 27 28 31
((loop(\(x,i).4x,(x div 2),(2 - (x mod 2))) + (x mod 3)) div 3)
A135574: 0 0 3 1 11 6 42 21 171 85 683 342 2730 1365 10923 5461
(3 * (1 + loop(\(x,i).(x2 + ~x),1,(2 * (x + (3 * (x div 2)))))))
A128450: 3 9 273 399
(((2x + 1) * (1 + loop(\(x,i).(x - (x div 8)),2,x))) mod 3)
A029317: 1 0 0 1 0 0 1 0 1 2 0 2 2 0 2 2
loop(\(x,i).x6,1,(~5x + ~3))
A016890: 729 262144 4826809 34012224 148035889 481890304 1291467969 3010936384 6321363049 12230590464 22164361129 38068692544 62523502209 98867482624 151334226289 225199600704
(3 * (1 + ((if (~2 + (x div 5)) <= 0 then x else (x + 2)) + (x div 2))))
A114614: 3 6 12 15 21 24 30 33 39 42 48 51 57 60 66 75
loop(\(x,i).x6,1,(9x + 3))
A017202: 729 2985984 85766121 729000000 3518743761 12230590464 34296447249 82653950016 177978515625 351298031616 646990183449 1126162419264 1870414552161 2985984000000 4608273662721
((1 + (x * ((if (~2 + (x div 4)) <= 0 then 1 else 2) + (x div 3)))) mod 3)
A089650: 1 2 0 1 0 2 1 1 1 1 2 0 1 1 1 1
(3 * (1 + compr(\x.(loop(\(x,i).4x2,2,3) mod (x + 1)),x)))
A065119-A063996: 3 6 9 12 18 24 27 36 48 54 72 81 96 108 144 162
(3 * (1 + compr(\x.(loop(\(x,i).(x2 + 2x),2,6) mod (x + 1)),x)))
A070021: 3 6 9 12 15 18 24 30 36 45 48 60 72 75 90 96
(((x + 1) + (2 * (if (~4 + (x div 2)) <= 0 then 1 else (x div 3)))) div 3)
A081607: 1 1 1 2 2 2 3 3 3 4 5 6 7 7 7 8
(3 * (1 + loop(\(x,i).(x + 1),(~4 + ((x + ((x div 2) mod 2)) div 2)),x)))
A085126: 3 6 9 12 15 18 21 24 27 30 36 42 45 48 54 60
(((x + 1) * loop(\(x,i).(x3 + 2x),1,(2x + 3))) div 3)
A199394: 11 90 357 996 2255 4446 7945 13192 20691 31010 44781 62700 85527 114086 149265 192016
(((x + 1) * (~1 + loop(\(x,i).x2,1,(5x + 2)))) div 3)
A100164: 1 32 143 384 805 1456 2387 3648 5289 7360 9911 12992 16653 20944 25915 31616
(((x + 1) * loop(\(x,i).((x2 + 2x) div 4),1,(x + 3))) div 3)
A003451: 1 4 8 16 25 40 56 80 105 140 176 224 273 336 400 480
(((x + 1) * loop(\(x,i).(x * (1 + (2 * (1 + i)))),5,2)) div 3)
A147573: 30030 60060 90090 120120 150150 180180 210210 240240 270270 300300 330330 360360 390390 420420 450450 480480
((loop(\(x,i).(~6x2 + ~3),2,x) mod (x + 1)) mod 3)
A094713: 0 1 0 0 1 0 1 1 0 1 0 0 2 1 0 1
(3 * ((4x + 4) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))
A059161: 12 24 12 48 12 24 12 96 12 24 12 48 12 24 12 192
(3 * loop(\(x,i).(20x + (x * (1 + i))),x,1))
A157984: 3 66 1518 36432 910800 23680800 639381600 17902684800 519177859200 15575335776000 482835409056000 15450733089792000 509874191963136000 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).(x + ((2 + i) * i * i * (1 + i))),(x + 1),0) div 2) div 3)
A034263: 1 9 39 119 294 630 1218 2178 3663 5863 9009 13377 19292 27132 37332 50388
(6 * (1 + (6 * (if (~2 + (x div 2)) <= 0 then x else (x + 1)))))
A044489: 6 42 78 114 150 186 258 294 330 366 402 438 474 510 546 582
((2 * (1 + ((1 + ((1 + loop(\(x,i).2x,x,1)) div (x + 2))) div 2))) mod 3)
A117454: 1 1 1 1 1 0 1 1 1 0 1 1 0 2 0 1
((2 + (2 div (1 + ((loop(\(x,i).(2 * (x - i)),x,2) mod (x + 1)) div 2)))) mod 3)
A323090: 1 1 1 0 1 2 1 0 0 2 1 2 1 2 2 0
((loop(\(x,i).4x3,(x + 1),5) div 2) div 3)
A093676: 83 83333333 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),3)
A160713: 3 6 6 12 6 12 12 24 6 12 12 24 12 24 24 48
((2 * (loop(\(x,i).((x + 2) - ((x div 2) div ~2)),x,2) div 3)) div 3)
A239467: 0 0 1 2 3 4 6 8 11 14 19 24 31 39 50 62
((loop(\(x,i).(x3 + ~x),1,(3x2 + 3x)) div 2) div 3)
A240826: 0 35 969 7770 35990 121485 333375 790244 1679580 3280455 5989445 10349790 17083794 27128465 41674395 62207880
(if (x + ~1) <= 0 then 1 else ((x + ~1) + (((x - (x2 div 3)) div 2) div 3)))
A034136: 1 1 1 2 2 3 4 4 4 5 5 5 5 4 4 4
((2 * (1 + (if x <= 0 then 1 else (2 * (x + (x div 12)))))) div 3)
A027564: 1 2 3 4 6 7 8 10 11 12 14 15 18 19 20 22
loop(\(x,i).x6,1,(12x + 6))
A017598: 46656 34012224 729000000 5489031744 24794911296 82653950016 225199600704 531441000000 1126162419264 2194972623936 4001504141376 6906762437184 11390625000000 18075490334784
((((1 + (2 * (1 + (if (~x + 2) <= 0 then x else 0)))) * (1 + (x div 2))) div 2) mod 3)
A180981: 1 1 1 0 1 1 0 1 2 1 0 0 1 2 1 0
(((1 + compr(\x.(loop(\(x,i).(x2 + 2x),3,2) mod (x + 1)),x)) div 2) mod 3)
A192064: 0 1 2 2 1 2 2 1 1 2 2 1 2 2 1 0
(loop(\(x,i).((5x + 1) - (x mod 3)),(x + 1),2) div 3)
A037647: 3 15 76 383 1915 9576 47883 239415 1197076 5985383 29926915 149634576 748172883 3740864415 18704322076 93521610383
(loop(\(x,i).((5x + 2) - (x mod 3)),(x + 1),2) div 3)
A037668: 3 17 85 428 2142 10710 53553 267767 1338835 6694178 33470892 167354460 836772303 4183861517 20919307585 104596537928
(((loop(\(x,i).(~x + ~1),(x div 2),~4) mod (x + 1)) div 2) mod 3)
A153246: 0 0 0 1 0 1 1 1 2 0 1 1 1 2 1 1
((loop(\(x,i).3x,x,(x2 + 7x + 6)) div 2) div 3)
A080420: 1 7 36 162 675 2673 10206 37908 137781 492075 1732104 6022998 20726199 70681653 239148450 803538792
(3 * loop(\(x,i).(x2 + ~x),1,((3x2 + 5x + 2) div 2)))
A135037: 0 60 396 1386 3570 7650 14490 25116 40716 62640 92400 131670 182286 246246 325710 423000
((((x2 + 3x + 2) * (1 + (if (x mod 3) <= 0 then 2 else 0))) div 2) div 3)
A234041: 1 1 2 10 5 7 28 12 15 55 22 26 91 35 40 136
loop(\(x,i).x5,1,(7x + 5))
A017045: 3125 248832 2476099 11881376 39135393 102400000 229345007 459165024 844596301 1453933568 2373046875 3707398432 5584059449 8153726976 11592740743 16105100000
((6x + 6) + (x2 div (x + (if x <= 0 then 1 else (x div 3)))))
A309434: 6 13 20 26 33 40 46 53 60 66 73 80 87 93 100 107
(3 * loop(\(x,i).(x2 + ~x),1,((3x2 + 7x + 4) div 2)))
A268685: 6 126 630 1950 4680 9576 17556 29700 47250 71610 104346 147186 202020 270900 356040 459816
((((x2 + x) * loop(\(x,i).((x2 + ~x) div 2),2,(x + 2))) div 2) div 3)
A001297: 0 1 15 90 350 1050 2646 5880 11880 22275 39325 66066 106470 165620 249900 367200
loop(\(x,i).((x2 + ~x) div 2),1,(((x3 + 3x2 + 2x) div 2) div 3))
A054563: 0 0 6 45 190 595 1540 3486 7140 13530 24090 40755 66066 103285 156520 230860
(~x + loop(\(x,i).2x,x,1) - (((x3 + ~3x2 + 2x) div 2) div 3))
A084635: 1 1 2 4 8 17 38 86 192 419 894 1872 3864 7893 16006 32298
(1 - ((x + 1) mod (1 - (6 * (if (~2 + (x div 3)) <= 0 then 0 else 2)))))
A052037: 1 1 1 1 1 1 1 1 1 2 1 11 10 9 8 7
((if x <= 0 then 1 else ((x div 5) - (x div (~2 + (x mod ~2))))) mod 3)
A340453: 1 1 1 1 2 0 1 1 2 1 1 0 2 1 0 2
((2 + (if x <= 0 then 1 else ((1 + (x2 div 7)) div 2))) div 3)
A029245: 1 0 0 1 1 1 1 2 2 2 3 3 4 4 5 6
((2 * ((x + 2) - (if (~4 + (x div 2)) <= 0 then 1 else (x div 3)))) div 3)
A081608: 0 1 2 2 3 4 4 5 6 6 6 6 6 7 8 8
((if x <= 0 then 1 else 2x) - ((x - (x mod (4 + (x div 3)))) div 3))
A263800: 1 2 4 6 8 9 10
A100417: 1 2 4 6 8 9 10 12 14 16 18 20 22 24 26 27
((2 + ((((if (x mod 2) <= 0 then 2 else 0) + (x div 2)) * (1 + (x div 2))) div 2)) div 3)
A008742: 1 0 1 1 2 1 4 2 5 4 7 5 10 7 12 10
(12 * loop(\(x,i).(10x + 21),x,1))
A177112: 12 372 3972 39972 399972 3999972 39999972 399999972 3999999972 39999999972 399999999972 3999999999972 39999999999972 399999999999972 3999999999999972 39999999999999972
(3 + (4 * ((x + 1) + (3 * (3 + (if x <= 0 then 1 else 2))))))
A217236: 55 71 75 79
((2 + (((x + 1) * loop(\(x,i).(x * (i * i)),(2x + ~1),1)) div 2)) div 3)
A060617: 0 1 18 9600
(3 * ((loop(\(x,i).4x,x,(3x + 8)) div 2) div 2))
A291004: 6 33 168 816 3840 17664 79872 356352 1572864 6881280 29884416 128974848 553648128 2365587456 10066329600 42681237504
(12 * (~2 + loop(\(x,i).12x,2,(x + 1))))
A157287: 1704 3432 5160 6888 8616 10344 12072 13800 15528 17256 18984 20712 22440 24168 25896 27624
(((((loop(\(x,i).(x2 + ~2x),2,(x + 4)) div 2) div 2) div 2) div 2) div 3)
A001752: 1 4 11 24 46 80 130 200 295 420 581 784 1036 1344 1716 2160
(5 - (if x <= 0 then 1 else ((x - ((x2 + ~x) div 8)) mod 2)))
A023403: 4 4 5 4 4 4 4 5 4 5 4 5 5 5 5 4
((2 + ((loop(\(x,i).(x3 + ~2x2),1,(x2 + 2x)) div 2) div 2)) div 3)
A231304: 0 1 32 244 1056 3369 8832 20176 41600 79225 141600 240276 390432 611569 928256 1370944
((((loop(\(x,i).(x3 + ~x),1,(x2 + 2x)) div 2) div 2) div 2) div 3)
A337899: 0 1 21 140 575 1785 4606 10416 21330 40425 71995 121836 197561 308945 468300 690880
(((loop(\(x,i).(x3 + ~x),1,(x2 + 4x + 4)) div 2) div 2) div 3)
A126275: 5 60 340 1300 3885 9800 21840 44280 83325 147620 248820 402220 627445 949200 1398080 2011440
(((x + (if (~4 + (x div 2)) <= 0 then 1 else 2)) * ((x + 1) mod 4)) mod 3)
A000089: 1 1 0 0 2 0 0 0 0 2 0 0 2 0 0 0
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) mod 12)
A159989: 1 1 2 5 2 6 0 9 2 2 8 10 4 4 0 9
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 12)
A039710: 2 3 5 7 11 1 5 7 11 5 7 1 5 7 11 5
(3 + (2 * ((x + 2) + (loop(\(x,i).(x2 div 2),(x + 1),x) div 3))))
A302134: 7 9 11 353
(6 * (((x + 2) + ((2 * (if (x mod 2) <= 0 then x else 1)) mod (x + 1))) div 2))
A309118: 6 6 12 18 24 24 36 30 48 36 60 42 72 48 84 54
((2 * ((~1 + loop(\(x,i).(x2 + ~1),2,(x2 + 1))) div (x + 2))) mod 3)
A332040: 1 1 1 0 1 2 1 0 0 2 1 1 1 1 1 0
loop(\(x,i).x5,1,(11x + 1))
A017405: 1 248832 6436343 45435424 184528125 550731776 1350125107 2887174368 5584059449 10000000000 16850581551 27027081632 41615795893 61917364224 89466096875 126049300576
loop(\(x,i).x5,1,(11x + 2))
A017417: 32 371293 7962624 52521875 205962976 601692057 1453933568 3077056399 5904900000 10510100501 17623416832 28153056843 43204003424 64097340625 92389579776 129891985607
(((x + 2) + (((if x <= 0 then 1 else x) + (x div 2)) mod (1 + (x div 3)))) div 3)
A239913: 0 1 1 1 2 2 2 3 3 4 5 4 5 6 5 7
((2 + (if (x mod (1 - (2 * ((~x + 1) div (2 + (x div 2)))))) <= 0 then 1 else x)) div 3)
A117915-A117501: 1 1 1 1 2 2 1 3 3 3 1 4 4 5 5 1
loop(\(x,i).x6,1,(9x + 6))
A017238: 46656 11390625 191102976 1291467969 5489031744 17596287801 46656000000 107918163081 225199600704 433626201009 782757789696 1340095640625 2194972623936 3462825991689 5289852801024
((loop(\(x,i).(x3 + ~x),1,(5x + 4)) div 2) div 3)
A300522: 10 120 455 1140 2300 4060 6545 9880 14190 19600 26235 34220 43680 54740 67525 82160
(loop(\(x,i).(5x2 + ~2x),1,((x2 + x) div 2)) div 3)
A264853: 0 1 13 56 160 365 721 1288 2136 3345 5005 7216 10088 13741 18305 23920
((if x <= 0 then 1 else 4x) - ((2 * (~x + ((x div 3) mod 2))) div 3))
A313510: 1 5 10 14 18 23 28 33 38 42 46 51 56 61 66 70
(((x + 2) + (loop(\(x,i).(x + i - ((~x + 2) div 4)),x,2) div 2)) div 3)
A208856: 1 1 2 3 4 6 8 11 15 20 26 34 44 56 72 91
((~x2 + ~x + 1) + (loop(\(x,i).((x2 + ~x) div 2),2,(x + 2)) div 3))
A323847: 1 0 0 4 16 41 85 155 259 406 606 870 1210 1639 2171 2821
loop(\(x,i).(2x + (10x div (1 + i))),2x,3)
A054330: 3 112 2016 25344 256256 2236416 17547264 127008768 862912512 5571084288 34487664640 206108098560 1195426971648 6757057298432 37346888122368 202396038856704
(if x <= 0 then 1 else (6x + ((2 * (~x + ((x div 2) mod 2))) div 3)))
A314122: 1 5 11 16 21 26 32 38 42 48 54 59 64 69 75 80
(6x + (if x <= 0 then 1 else ((~x + ((x div 2) mod 3)) div 3)))
A314247: 1 5 11 17 23 29 34 39 45 51 57 63 68 73 79 85
(((~x + ((x div 2) mod 4)) div 4) + (if x <= 0 then 1 else 6x))
A314250: 1 5 11 17 23 29 35 41 46 51 57 63 69 75 81 87
(((~x + (((x div 2) div 3) mod 2)) div 2) + (if x <= 0 then 1 else 6x))
A314151: 1 5 11 16 22 27 33 39 44 50 55 61 66 71 77 82
(2 - ((if ((x + 1) mod (1 + (x div 5))) <= 0 then 1 else (x div 2)) mod 3))
A035212: 1 1 1 1 1 1 2 1 1 1 0 1 2 2 1 1
loop(\(x,i).2x,x,((1 - (2 * ((x div 2) mod 2))) * (1 - ((x div 2) mod 3))))
A120582: 1 2 0 0 ~16 ~32 ~64 ~128 0 0 1024 2048 4096 8192 0 0
((2 * (x + loop(\(x,i).(x - ((x - ((x mod 3) div 2)) div 2)),2,x))) mod 3)
A287072: 0 1 2 1 0 2 1 0 1 0 2 1 0 1 2 1
(5x - ((~x2 + 2x + ~1) div loop(\(x,i).x2,2,3)))
A314110: 1 5 11 16 21 26 31 36 41 46 51 57 62 67 73 78
((x div 2) - (loop(\(x,i).(x + 4),(~1 + (x div 5)),x) div 3))
A329885: 0 0 1 0 1 1 1 1 2 1 1 0 1 1 1 0
loop(\(x,i).((10x + 3) - (x mod 4)),x,3)
A037764: 3 30 301 3012 30123 301230 3012301 30123012 301230123 3012301230 30123012301 301230123012 3012301230123 30123012301230 301230123012301 3012301230123012
(3 * ((x + 1) + (2 * (loop(\(x,i).(2x + 2),(x div 2),(x mod 2)) div 2))))
A006639: 3 6 15 24 33 48 63 90
((x + 3) + (3 * (if ((x div 3) mod 3) <= 0 then 4 else 1)))
A004504: 15 16 17 9 10 11 12 13 14 24 25 26 18 19 20 21
((if x <= 0 then 1 else 4x) - ((~x + ((1 + (x div 2)) mod 3)) div 3))
A058759: 1 4 8 13
A312065: 1 4 8 13 18 22 26 30 34 39 44 48 52 56 60 65
(loop(\(x,i).(2 + (x2 div 13)),3,x) div 3)
A308995: 0 0 0 0 0 0 0 0 1 1 2 3 6 9 15 22
(3 * (x + ((2 * ((x + (if (~2 + (x div 2)) <= 0 then 1 else 0)) div 2)) div 3)))
A145204: 0 3 6 12 15 21 24 27 30 33 39 42 48 51 54 57
((~x + ~3) + (loop(\(x,i).(2 + ((x2 + x) div 2)),2,(x + 2)) div 3))
A051744: 2 8 21 45 85 147 238 366 540 770 1067 1443 1911 2485 3180 4012
((if x <= 0 then 1 else 5x) - ((~x + ((x div 2) mod 3)) div 3))
A315471: 1 6 11 16 21 26 32 38 43 48 53 58 64 70 75 80
(((2 - (2x mod (4 + (x div 4)))) mod (if x <= 0 then 1 else x)) div 3)
A074734: 0 0 0 0 1 0 0 1 2 0 0 3 3 3 0 0
((x + (2 * (1 + ((x div 2) mod (2 + (if (x mod 4) <= 0 then 2 else 0)))))) div 3)
A076235: 0 1 2 2 3 2 3 3 3 3 4 5 6 5 6 6
(3 + loop(\(x,i).((2x + 1) - ((x div 7) mod 2)),2,x))
A190712: 6 10 14 17 21 25 29 32 36 40 44 47 51 55 62 66
((x + ((5 * loop(\(x,i).(x + ((2 + i) * i)),x,1)) div 2)) div 3)
A227347: 0 3 10 23 43 73 113 166 233 316 416 536 676 839 1026 1239
loop(\(x,i).((x + 2) + ((x div 8) + (x div 5))),x,3)
A255981: 3 5 8 12 17
A018917: 3 5 8 12 17 24 33 45 61 82 110 147 196 261 347 461
((x + (x mod (if (x + ~10) <= 0 then 1 else 6))) div 3)
A077563: 0 0 0 1 1 1 2 2 2 3 3 5 4 4 5 6
((x + 3) + loop(\(x,i).2x,((3 * ((x div 2) div 3)) div 2),2))
A138469: 5 6 7 8 9 10 13 14 15 16 17 18 31 32 33 34
(~3 + loop(\(x,i).((x + 2) + ((~x + ((x * (x div 2)) mod 2)) div 3)),2,x))
A189660: 0 0 1 1 1 2 3 4 4 4 4 5 5 5 6 7
((x + (2 * loop(\(x,i).((x2 + 2x) div 16),2,x))) div 3)
A035632: 0 0 0 1 1 1 2 2 4 5 5 7 8 11 14 15
((x2 + 2x + 3) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A004232: 3 7 14 23 36 49 66 83 104 129 152 181 210 239 272 309
(1 + (x div 3) - (if x <= 0 then 0 else (1 + (x div (4 + ((x div 2) mod 2))))))
A035462: 1 0 0 1 0 0 1 1 0 1 1 1 1 1 2 2
((2x + (if (x + ~1) <= 0 then 1 else (~1 + ((x2 + 2x) div 4)))) div 3)
A234369: 0 1 1 2 4 5 7 9 11 13 16 18 21 24 27 30
((x + ~3) + loop(\(x,i).((x + 1) - ((2x + ~2) div (2 + (x div 2)))),2,x))
A245395: 0 1 2 3 5 6 7 9 11 13 15 17 19 20 22 23
((x + 3) + loop(\(x,i).(x - ((1 + ((x * (x div 2)) div 4)) div 2)),2,x))
A047747: 3 5 7 9 10 11 12 13 14 15 16 17 18 19 19 20
((x + loop(\(x,i).(x + ((2x2 + ~x) div (x + 4))),2,x)) div 3)
A293956: 0 0 2 4 6 9 11 14 18 20
(1 + (2 * compr(\x.(~1 + (x mod (1 + (2 * (if (x mod 2) <= 0 then (x div 4) else 1))))),x)))
A190857: 1 3 5 7 9 13 15 19 21 27 29 31 37 39 43 45
(1 + (2 * ((x + 1) + (loop(\(x,i).(2x + i),(x + 2),2) div 5))))
A006188: 7 15 29 57 109 213
(1 + loop(\(x,i).(1 + (3 * (x - (2 * ((~2x + 1) div 3))))),x,2))
A233083: 3 14 95 662 4631 32414 226895 1588262 11117831 77824814 544773695 3813415862 26693911031 186857377214 1308001640495 9156011483462
(~1 + (if x <= 0 then 1 else (2 * (x + (x mod ((x + ~1) - (x mod 12)))))))
A093031: 0 1 3 5 7 9 11 13 15 17 19 21 25 29 33 37
(1 + (2 * (x + loop(\(x,i).i,(x div (3 * (8 - (x div 2)))),1))))
A322660: 3 5 7 9 11 13 15 17 19 21 23 25 29 31 37 41
(~1 + (2 * (x + loop(\(x,i).((x + 1) + (2 * ((x div 4) mod 2))),(x + ~1),1))))
A279106: 1 3 7 11 15 23 31 35 39 47 55 59 63 71 79 83
(~1 + (2 * ((x + 1) + (2 * loop(\(x,i).((x + 2) + ((4 + i) * i)),x,1)))))
A090294: 5 35 93 187 325 515 765 1083 1477 1955 2525 3195 3973 4867 5885 7035
loop(\(x,i).21x,(5x + 2),1)
A013899: 441 1801088541 7355827511386641 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).22x,(5x + 2),1)
A013903: 484 2494357888 12855002631049216 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).19x,(5x + 2),1)
A013891: 361 893871739 2213314919066161 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).23x,(5x + 2),1)
A013907: 529 3404825447 21914624432020321 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~11x + 1),10x,1)
A015399: 1 23775972551 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~13x + 1),10x,1)
A015402: 1 128011456717 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x6,1,(10x + 1))
A017286: 1 1771561 85766121 887503681 4750104241 17596287801 51520374361 128100283921 282429536481 567869252041 1061520150601 1870414552161 3138428376721 5053913144281 7858047974841 11853911588401
(~1 + (2 * loop(\(x,i).x2,1,(25x + 24))))
A154374: 1151 4801 10951 19601 30751 44401 60551 79201 100351 124001 150151 178801 209951 243601 279751 318401
(1 + (if x <= 0 then 1 else (2 * (x + (x div (3 * (8 - (x div 2))))))))
A095737: 2 3 5 7 9 11 13 15 17 19 23 25 29 31 37 41
loop(\(x,i).x5,1,(10x + 7))
A017357: 16807 1419857 14348907 69343957 229345007 601692057 1350125107 2706784157 4984209207 8587340257 14025517307 21924480357 33038369407 48261724457 68641485507 95388992557
(1 + (if x <= 0 then 1 else (2 * (x + ((3 * ((((x + 1) div 2) div 2) div 2)) div 2)))))
A305103-A305078: 2 3 5 7 9 11 13 17 19 21 23 25 27 29 31 37
(~1 + (2 * ((x + 4) + (if x <= 0 then x else (2 - ((~x + 2) div 5))))))
A224773: 7 13 15 19 21 23 25 27 31 33 35 37 39 43 45 47
(1 + ((x2 + 2x) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A069547: 1 1 4 2 3 10 15 7 12 13 28 33 5 24 37 44
((x3 + 4x2 + 3x) * loop(\(x,i).(x * (x - i)),2,(x + 3)))
A057666: 0 960 10800 60480 235200 725760 1905120 4435200 9408960 18532800 34354320 60540480 102211200 166333440 262180800 401863680
(loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,2x) div (x + 3))
A099376: 0 1 4 14 48 165 572 2002 7072 25194 90440 326876 1188640 4345965 15967980 58929450
((2x + 1) + (x mod 2) - ((x div (1 + (if (x mod 4) <= 0 then 0 else 2))) mod 2))
A339690: 1 4 5 7 9 11 13 16 17 19 20 23 25 28 29 31
(1 + (if x <= 0 then 1 else (2x + ((x mod (2 + (((x + 1) div 2) div 3))) div 2))))
A284914: 2 3 5 7 9 12 13 15 18 19 21 24 25 27 30 32
loop(\(x,i).(2x + (14x div (1 + i))),2x,1)
A054331: 1 60 1584 27456 366080 4073472 39690240 349274112 2835283968 21554790400 155194490880 1067345510400 7058711642112 45127489814528 280101660917760 1693862087098368
loop(\(x,i).2x,(2x + (((3 * (x div 4)) div 2) + (x div 2))),1)
A123854-A088802: 1 4 32 128 2048 8192 65536 262144 8388608 33554432 268435456 1073741824 17179869184 68719476736 549755813888 2199023255552
(loop(\(x,i).(x * (1 + (4 * (i div 2)))),x,1) * ((2x + 1) + (x mod 2)))
A254796: 1 4 25 200 2025 24300 342225 5475600 98903025 1978060500 43616234025 1046789616600 27260146265625 763284095437500 22925783009390625 733625056300500000
((2x + 1) * loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),2x,1))
A186231: 1 15 210 3003 43758 646646 9657700 145422675 2203961430 33578000610 513791607420 7890371113950 121548660036300 1877405874732108 29065024282889672 450883717216034179
(if x <= 0 then 3 else (4x4 + 20x3 + 33x2 + 20x + 4))
A074386: 3 81 400
(loop(\(x,i).(4x + (x div (1 + (2 * (2 + i))))),x,1) div (2x + 1))
A339843: 1 1 3 9 29 97 336
(((x + 1) + ((if ((x + ~1) mod 3) <= 0 then 1 else x) * (x mod 2))) mod (2x + 1))
A239233: 0 0 3 0 5 0 7 9 9 0 11 0 13 15 15 0
((3x + 1) + (if (((x + 2) mod 8) mod 3) <= 0 then 2 else 0))
A287803: 1 6 7 10 15 16 21 22 25 30 31 34 39 40 45 46
((3x + 1) + (if ((x mod (4 + (x mod 2))) mod 3) <= 0 then 1 else 2))
A187690: 2 6 9 11 14 17 21 24 26 30 33 36 38 41 45 47
((3x + 1) + (if ((x2 mod (x + 4)) mod 3) <= 0 then 1 else 2))
A287445: 2 6 9 12 14 18 20 24 27 29 33 36 38 42 45 48
((2x + 1) + (if x <= 0 then 2 else (x + ((x mod (2 + (x mod 5))) mod 2))))
A100392: 3 5 7 11 13 17 19 23 26 29 31 34 37 41 43 47
((2x + 1) + loop(\(x,i).(x - (((x - ((~1 + (x div 2)) div 2)) div 2) div 2)),2,x))
A214641: 1 4 7 10 12 14 17 20 23 25 28 30 33 36 39 41
loop(\(x,i).2x,(((3 * (2x + (x div 4))) div 2) + (x div 2)),1)
A061549: 1 8 128 1024 32768 262144 4194304 33554432 2147483648 17179869184 274877906944 2199023255552 70368744177664 562949953421312 9007199254740992 72057594037927936
((4x + 1) + ((if (~2 + (x div 5)) <= 0 then 2 else 1) + (x div 2)))
A330181: 3 7 12 16 21 25 30 34 39 43 48 52 57 61 66 69
loop(\(x,i).(1 + (x mod 2) - (2 * ((x div 5) mod 2))),1,(~1 + (x div 2)))
A332384: 0 0 1 1 2 2 1 1 2 2 1 1 0 0 ~1 ~1
(if x <= 0 then 0 else (1 + ((x div (1 + (2 * ((x div 2) div 3)))) mod 2) - (x mod 2)))
A120936: 0 1 1 1 1 1 1 0 1 1 2 1 1 0 1 1
(1 + (((x * (if (~2 + (x div 2)) <= 0 then 1 else 2)) div 5) mod 2) - (x mod 2))
A341675: 1 0 1 0 1 1 1 0 2 1 1 0 1 1 2 0
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (3 - (x mod 2)))
A107620: 6 6 15 14 33 26 51 38 69 58 93 74 123 86 141 106
(1 + loop(\(x,i).(((2x + 2) * (2 - (x mod 2))) - (x mod 2)),(x div 2),(x mod 2)))
A107732: 1 2 5 4 21 8 85 16 341 32 1365 64 5461 128 21845 256
(1 + loop(\(x,i).(0 - ((2x * (1 + (2 * i))) div (2 + i))),(x div 2),(x mod 2)))
A129110: 1 2 1 ~1 1 6 1 ~13 1 43 1 ~131 1 430 1 ~1429
((1 + (if (x mod 7) <= 0 then 6 else 0)) * (1 + (x mod 2)))
A089129: 7 2 1 2 1 2 1 14 1 2 1 2 1 2 7 2
(if (x + ~1) <= 0 then x else ((1 + ((x mod (1 + (x div 4))) div 2)) * (1 + (x mod 2))))
A345936: 0 1 1 2 1 2 1 2 2 2 1 4 1 2 2 4
loop(\(x,i).((2x + 1) - ((x * (x div 2)) mod 2)),(1 + (x div 2)),(1 + (x mod 2)))
A173593: 3 5 6 11 13 22 27 45 54 91 109 182 219 365 438 731
((if ((x mod 3) - ((((x + 1) div 2) div 2) mod 2)) <= 0 then 1 else 2) * (1 + (x mod 2)))
A088570: 1 4 2 2 1 4 1 4 2 2 2 4 1 2 2 2
(((x + 1) div (if x <= 0 then 1 else (2 * (2 + (x div 8))))) div (1 + (x mod 2)))
A008622: 1 0 0 0 1 0 1 1 1 0 1 1 2 1 2 1
(~1 + (2 * (3x + (loop(\(x,i).(x2 + 1),2,(x + ~1)) div 3))))
A055426: 1 5 13 33 89 221 485 953 1713 2869 4541 6865 9993 14093 19349 25961
(1 + compr(\x.(~1 + (x mod (1 + ((loop(\(x,i).2x,x,1) - (x mod 2)) mod (x + 1))))),x))
A326533-A325396-A325362: 1 2 3 5 6 7 10 11 13 14 17 19 21 22 23 26
loop(\(x,i).(1 + (3 * ((~2x + 4) mod 13))),x,1)
A070422: 1 7 10 31 22 37 25 19 16 34 4 28 1 7 10 31
(1 + compr(\x.(x mod (~1 + (6 * (if (~2 + (x div 3)) <= 0 then 0 else 2)))),x))
A259236-A138141-A059043: 1 2 3 4 5 6 7 8 9 12 23 34 45 56 67 78
loop(\(x,i).(~9x + 1),11x,1)
A015414: 1 ~28242953648 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((6x + 1) + ((~x + 1) mod 3) - (x mod 2)),x,1)
A037676: 1 6 38 231 1387 8322 49934 299607 1797643 10785858 64715150 388290903 2329745419 13978472514 83870835086 503225010519
(1 + compr(\x.(~1 + (loop(\(x,i).(2x + 1),x,((x div 4) mod 2)) mod (x + 1))),x))
A193622: 1 2 3 5 7 10
A235050: 1 2 3 5 7 10 11 13 17 19 23 26 29 31 34 37
(1 + compr(\x.(~1 + ((2x + ~4) mod loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))),x))
A029748: 1 2 3 4 6 7 8 12 14 16 24 28 32 48 56 64
(1 + compr(\x.(2 - (x mod (1 + (2 * (if ((x + 1) mod 8) <= 0 then 2 else 1))))),x))
A182338: 3 6 8 9 12 15 18 21 24 27 30 33 36 39 40 42
loop(\(x,i).((10x + 1) - (((x + 1) div 3) mod 2)),x,1)
A265380: 1 11 111 1110 11101 111011 1110111 11101110 111011101 1110111011 11101110111 111011101110 1110111011101 11101110111011 111011101110111 1110111011101110
((x + 1) + loop(\(x,i).x2,1,(28x + 28)))
A031734: 785 3138 7059 12548 19605 28230 38423 50184 63513 78410 94875 112908 132509 153678 176415 200720
loop(\(x,i).(7 * ((2x * (~1 + (2 * i))) div (1 + i))),x,1)
A156266: 1 7 98 1715 33614 705894 15529668 353299947 8243665430 196199237234 4744454282204 116239129913998 2879153833254412 71978845831360300 1813866914950279560 4611686018427387903
loop(\(x,i).(7 * (x + (6x div (1 + i)))),x,1)
A053110: 1 28 588 10290 158466 2218524 28840812 353299947 4121832715 46164526408 499416240232 5243870522436 53648829191076 536488291910760 5257585260725448 50604258134482437
loop(\(x,i).(1 + (((3 * ((x + ~1) + (2 * (x mod 4)))) div 2) div 2)),x,1)
A090568: 1 2 4 3 7 10 10 10 10 10 10 10 10 10 10 10
(1 + compr(\x.((x + 1) mod (1 + (x div (2 + (if (x mod 2) <= 0 then 1 else 8))))),x))
A246352: 1 2 3 4 6 8 9 10 12 14 15 16 18 20 21 24
loop(\(x,i).(9 * ((2x div (1 + i)) * (~1 + (2 * i)))),x,1)
A156273: 1 9 162 3645 91854 2480058 70150212 2051893701 61556811030 1883638417518 58564030799196 1844766970174674 58748732742485772 1888352123865614100 4611686018427387903 4611686018427387903
((x + 1) + (9 * (if (x + ~12) <= 0 then 0 else 2)))
A323204-A323175: 1 2 3 4 5 6 7 8 9 10 11 12 13 32 33 34
((x + 1) + (9 * (10 + (if x <= 0 then 1 else 2))))
A134496: 100 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124
((x + 1) + (if (x + ~1) <= 0 then x else (2 - ((~2x + 2) div 9))))
A299493: 1 3 6 7 8 9 11 12 13 14 15 17 18 19 20 22
loop(\(x,i).(9 * ((2x * (1 + (2 * i))) div (2 + i))),x,1)
A260655: 1 18 405 10206 275562 7794468 227988189 6839645670 209293157502 6507114533244 204974107797186 6527636971387308 209816902651734900 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(9 * (x + (8x div (1 + i)))),x,1)
A053112: 1 45 1485 40095 938223 19702683 379980315 6839645670 116273976390 1883638417518 29282015399598 439230230993970 6385731819835410 90312492880529370 1246312401751305306 4611686018427387903
((x + 1) + loop(\(x,i).x2,1,(30x + 30)))
A031738: 901 3602 8103 14404 22505 32406 44107 57608 72909 90010 108911 129612 152113 176414 202515 230416
((x + 1) + loop(\(x,i).x2,1,(40x + 40)))
A031758: 1601 6402 14403 25604 40005 57606 78407 102408 129609 160010 193611 230412 270413 313614 360015 409616
loop(\(x,i).(5 * ((4x * (~1 + (2 * i))) div (1 + i))),x,1)
A156275: 1 10 200 5000 140000 4200000 132000000 4290000000 143000000000 4862000000000 167960000000000 5878600000000000 208012000000000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x7,1,(5x + 1))
A016867: 1 279936 19487171 268435456 1801088541 8031810176 27512614111 78364164096 194754273881 435817657216 897410677851 1727094849536 3142742836021 5455160701056 9095120158391 14645194571776
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(5x + 1))
A051945: 1 6 22 80 294 1092 4092 15444 58630 223652 856596 3292016 12688732 49031400 189885240 736808220
(if x <= 0 then 0 else (1 + compr(\x.(1 - (x mod (1 - (x div (~1 + ((~x + 2) div 4)))))),x)))
A079253: 0 3 5 6 7 8 10 12 14 15 16 17 18 19 20 22
loop(\(x,i).(3 * (15x - (x div 3))),x,1)
A170726-A170678-A170630-A170582-A170534-A170486-A170438-A170390-A170342-A170294-A170246-A170198-A170150-A170102-A170054-A170006-A169538-A169490-A169442-A169394-A169346-A169298-A169250-A169202-A169154-A169106-A169058-A169010-A168962-A168914-A168866-A168818-A168770-A168722-A167961-A167855-A167642-A167098-A166738: 1 45 1980 87120 3833280 168664320 7421230080 326534123520 14367501434880 632170063134720 27815482777927680 1223881242228817920 4611686018427387903 4611686018427387903 4611686018427387903
A170764: 1 45 1980 87120 3833280 168664320 7421230080 326534123520 14367501434880 632170063134720 27815482777927680 1223881242228817920 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(3 * (13x - (x div 3))),x,1)
A170720-A170672-A170624-A170576-A170528-A170480-A170432-A170384-A170336-A170288-A170240-A170192-A170144-A170096-A170048-A170000-A169532-A169484-A169436-A169388-A169340-A169292-A169244-A169196-A169148-A169100-A169052-A169004-A168956-A168908-A168860-A168812-A168764-A168716-A167955-A167828-A167537-A167092-A166691: 1 39 1482 56316 2140008 81320304 3090171552 117426518976 4462207721088 169563893401344 6443427949251072 244850262071540736 4611686018427387903 4611686018427387903 4611686018427387903
A170758: 1 39 1482 56316 2140008 81320304 3090171552 117426518976 4462207721088 169563893401344 6443427949251072 244850262071540736 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(54 mod (x + 1)),3,x))
A343431-A170825-A140214: 1 1 1 1 5 1 1 1 1 5 11 1 1 1 5 1
loop(\(x,i).(3 * ((x * (~1 + (9 * i))) div (1 + i))),x,1)
A097193: 1 12 204 3978 83538 1837836 41745132 970574319 22970258883 551286213192 13381219902024 327839887599588 8095123378420596 201221638263597672 4611686018427387903 4611686018427387903
((x + 1) + ((2 * (if (x + ~2) <= 0 then x else (2 - ((~x + 1) div 3)))) div 3))
A153351: 1 2 4 6 7 8 9 10 12 13 14 16 17 18 19 20
loop(\(x,i).(3 * (2x + (10x div (1 + i)))),x,1)
A036224: 1 21 336 4536 54432 598752 6158592 60046272 560431872 5043886848 44019376128 374164697088 3108445175808 25311625003008 202493000024064 1594632375189504
((3x + 1) + (((x + (if (~2 + (x div 4)) <= 0 then 1 else 2)) div 2) mod 2))
A022158: 1 5 8 10 13 17 20 22 25 29 32 34 38 41 43 46
loop(\(x,i).(3 * (x + ((4x div (1 + i)) * (~1 + (2 * i))))),x,1)
A254282: 1 9 135 2430 48114 1010394 22084326 496897335 11428638705 267430145697 6345388002447 152289312058728 3690087176807640 90143558176300920 2217531531137002632 4611686018427387903
loop(\(x,i).((x + 3) + (2 * ((x - ((x + 1) mod 5)) div 2))),x,1)
A139763: 1 2 3 4 11 22 43 84 171 342 683 1364 2731 5462 10923 21844
((x + 1) + (if (x + ~2) <= 0 then 0 else ((x + 1) - (((~x + ~1) + (x mod 2)) * (x div 2)))))
A291633: 1 2 3 11 20 22
loop(\(x,i).((4x div (1 + i)) * (~1 + (2 * i)) * (1 + (2 * i))),x,1)
A248045: 1 6 120 4200 211680 13970880 1141620480 111307996800 12614906304000 1629845894476800 236475822507724800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(((2x * i) div (1 + i)) * (~1 + (2 * i)) * (1 + (2 * i))),x,1)
A036770: 1 3 60 3150 317520 52390800 12843230400 4382752374000 1986847742880000 1155153277710432000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(((4x * (~1 + (2 * i))) div (1 + i)) * (~1 + (2 * i))),x,1)
A089835: 1 2 24 600 23520 1270080 87816960 7420533120 742053312000 85781362867200 11260753452748800 1655330757554073600 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + ((x + 1) mod (1 + ((x + (x div 3)) div 3)))),x,1)
A283808: 1 2 3 4 6 8 10 12 14 16 18 20 24 28 32 36
loop(\(x,i).((x + 1) + ((1 + ((x + ((x * i) div (1 + i))) div 3)) div 2)),x,1)
A231408: 1 2 4 6 9
A171861-A164315: 1 2 4 6 9 13 18 25 34 46 62 83 111 148 197 262
loop(\(x,i).((x + 1) + ((x + ((x div (2 + ((x div 2) div 3))) mod 2)) div 2)),x,1)
A054352: 1 2 4 7 11 18 28 43 65 99 150 226 340 511 768 1153
(1 + compr(\x.(loop(\(x,i).(2x + 32),(x + 1),0) mod (x + 1)),x))
A301587: 1 2 4 6 8 12 16 18 20 24
A305726-A177807-A124240-A068563: 1 2 4 6 8 12 16 18 20 24 32 36 40 42 48 54
(1 + compr(\x.(loop(\(x,i).(2x + 4),((x + 1) mod 8),0) mod (x + 1)),x))
A015929: 1 2 4 6 8 12 14 16 20 24 32 40 48 56 60 64
(1 + compr(\x.((1 + loop(\(x,i).(3x2 + ~1),2,3)) mod (x + 1)),x))
A185092: 1 2 3 4 6 12
A018309: 1 2 3 4 6 12 13 26 39 52 78 156
A245481: 1 2 3 4 6 12 13 26 39 52 78 156 169 338 507 676
(1 + compr(\x.((1 + loop(\(x,i).(x2 + x),2,6x)) mod (x + 1)),x))
A018728: 1 7 19 49 133 931
(1 + compr(\x.(loop(\(x,i).(~10x2 + 20),2,1) mod (x + 1)),x))
A018756: 1 2 4 5 7 10 14 20 28 35 49 70 98 140 196 245
(1 + compr(\x.((~1 + loop(\(x,i).x2,3,10)) mod (x + 1)),x))
A027890: 1 3 9 11 33 73 99 101 137 219 303 411 657 803 909 1111
(1 + compr(\x.(loop(\(x,i).(x3 + ~2x2),2,7) mod (x + 1)),x))
A108347: 1 3 5 7 9 15 21 25 27 35 45 49 63 75 81 105
(1 + compr(\x.(loop(\(x,i).(~2x3 + ~2x2 + ~2x + ~2),2,1) mod (x + 1)),x))
A018717: 1 2 5 7 10 13 14 26 35 65 70 91 130 182 455 910
(1 + compr(\x.(loop(\(x,i).(4x2 + 16x + 12),2,1) mod (x + 1)),x))
A245809: 1 2 3 4 5 6 7 10 11 12 14 15 20 21 22 28
(1 + compr(\x.(loop(\(x,i).(4x3 + 3x2 + ~x),2,1) mod (x + 1)),x))
A018748: 1 2 3 6 7 14 21 23 42 46 69 138 161 322 483 966
(1 + compr(\x.(loop(\(x,i).(x * (1 + i)),(2 - (x div ~4)),1) mod (x + 1)),x))
A081000: 1 2 3 4 6 8 10 12 14 15 16 18 20 21 24 27
(1 + compr(\x.(1 - (loop(\(x,i).(x * i),(4 + (x div 3)),1) mod (x + 1))),x))
A286609: 7 11 13 17 19 23 26 29 31 34 37 38 41 43 46 47
(1 + compr(\x.((~1 + loop(\(x,i).x2,2,32)) mod (x + 1)),x))
A003529: 1 3 5 11 15 25 31 33 41 55 75 93 123 155 165 205
((x + 1) + loop(\(x,i).x2,1,(31x + 31)))
A031740: 962 3846 8652 15380 24030 34602 47096 61512 77850 96110 116292 138396 162422 188370 216240 246032
(1 + compr(\x.((~1 + loop(\(x,i).x3,2,16)) mod (x + 1)),x))
A003543: 1 3 5 7 9 13 15 19 21 27 35 37 39 45 57 63
(1 + compr(\x.(loop(\(x,i).(x2 + x),2,17) mod (x + 1)),x))
A018384: 1 2 3 6 9 17 18 34 51 102 153 306
(1 + compr(\x.(loop(\(x,i).x3,2,15) mod (x + 1)),x))
A056754-A003593: 1 3 5 9 15 25 27 45 75 81 125 135 225 243 375 405
(1 + compr(\x.(1 - (loop(\(x,i).(x * i),(6 + (x mod 2)),1) mod (x + 1))),x))
A112588: 7 11 13 17 19 21 22 23 25 26 27 29 31 32 33 34
(1 + compr(\x.((~1 + loop(\(x,i).(2x2 + 1),2,8)) mod (x + 1)),x))
A018251: 1 2 3 6 9 18
A018638: 1 2 3 6 9 18 43 86 129 258 387 774
(1 + compr(\x.((1 + loop(\(x,i).(x4 + ~1),2,4)) mod (x + 1)),x))
A339345-A174688-A143512: 1 3 5 9 15 17 25 27 45 51 75 81 85 125 135 153
(1 + compr(\x.(loop(\(x,i).2x2,(1 + (x mod 2)),5) mod (x + 1)),x))
A191535-A100598: 1 2 4 5 8 10
A018332: 1 2 4 5 8 10 20 25 40 50 100 200
(1 + compr(\x.(loop(\(x,i).(2x3 + 4x2),2,5) mod (x + 1)),x))
A277121: 1 2 4 5 7 8 10 11 14 16 20 22 25 28 32 35
(1 + compr(\x.(loop(\(x,i).((x + 1) * (x + i)),4,5) mod (x + 1)),x))
A222011: 1 2 4 8
A003596: 1 2 4 8 11 16 22 32 44 64 88 121 128 176 242 256
(1 + compr(\x.(loop(\(x,i).(3x2 + ~4x),2,5) mod (x + 1)),x))
A151715: 1 5 7 11 23 35 55 77 115 161 253 385 805 1265 1771 8855
(1 + compr(\x.(loop(\(x,i).(x2 + 5x + 6),3,3) mod (x + 1)),x))
A018300: 1 2 3 6 23 46 69 138
(1 + compr(\x.(loop(\(x,i).(12x + 24),2,3) mod (x + 1)),x))
A323383: 1 2 3 4 6 8 12
A018253: 1 2 3 4 6 8 12 24
A018623: 1 2 3 4 6 8 12 24 31 62 93 124 186 248 372 744
(1 + compr(\x.(loop(\(x,i).(1 + ((x + 2) * (x + (x div 2)))),2,3) mod (x + 1)),x))
A018606: 1 2 3 6 7 14 17 21 34 42 51 102 119 238 357 714
(1 + compr(\x.(loop(\(x,i).(4x3 + 2x2),2,3) mod (x + 1)),x))
A336654: 1 2 3 4 6 7 8 9 11 12 14 18 21 22 23 24
(1 + compr(\x.(loop(\(x,i).(~2x3 + ~2x2 + 4x),2,3) mod (x + 1)),x))
A067319: 1 2 3 4 5 6 8 10 12
A067784: 1 2 3 4 5 6 8 10 12 15 16 20 24 29 30 40
(1 + compr(\x.(loop(\(x,i).(x5 + 2x3),2,3) mod (x + 1)),x))
A003597: 1 3 9 11 27 33 81 99 121 243 297 363 729 891 1089 1331
(1 + compr(\x.(x - (loop(\(x,i).(x3 + 2x2 + 2x),2,3) mod (x + 1))),x))
A018414: 1 2 4 7 13 14 26 28 52 91 182 364
(1 + compr(\x.((1 + loop(\(x,i).5x2,2,2x)) mod (x + 1)),x))
A133023: 1 3 23 29 69 87 667 2001
(1 + compr(\x.(loop(\(x,i).(4x2 + 8),2,(2x + 1)) mod (x + 1)),x))
A222011: 1 2 4 8
A018532: 1 2 4 8 73 146 292 584
(1 + compr(\x.(loop(\(x,i).(x3 + 9x2),2,1) mod (x + 1)),x))
A133040: 1 2 4 5 10 19 20 25 38 50 76 95 100 190 380 475
(1 + compr(\x.((1 + loop(\(x,i).(x2 + 2x + ~4),3,x)) mod (x + 1)),x))
A018301: 1 2 4 5 7 10 14 20 28 35 70 140
(1 + compr(\x.((1 + loop(\(x,i).(5x2 + ~10x),2,x)) mod (x + 1)),x))
A222011: 1 2 4 8
A018754: 1 2 4 8 16 61 122 244 488 976
(1 + compr(\x.((1 + loop(\(x,i).12x2,2,x)) mod (x + 1)),x))
A225227: 1 7 13
A133029: 1 7 13 19 91 133 247 1729
(1 + compr(\x.((1 + (x * loop(\(x,i).(~x2 + 1),2,4x))) mod (x + 1)),x))
A018342: 1 3 5 9 15 25 45 75 225
(1 + compr(\x.((1 + (x * loop(\(x,i).(x * (~x + i)),2,4x))) mod (x + 1)),x))
A018458: 1 3 7 9 21 49 63 147 441
(1 + compr(\x.(loop(\(x,i).(3 * (x2 div 2)),2,(~x + 3)) mod (x + 1)),x))
A258023: 1 2 3 4 5 6 8 9 12 15 16 18 24 25 27 32
(1 + compr(\x.((1 + loop(\(x,i).(5x2 + ~8x),2,x)) mod (x + 1)),x))
A018622: 1 2 7 14 53 106 371 742
(1 + compr(\x.((1 + (x * loop(\(x,i).(~2x2 + x),2,(x + ~2)))) mod (x + 1)),x))
A222011: 1 2 4 8
A018713: 1 2 4 8 113 226 452 904
(1 + compr(\x.((1 + (x * loop(\(x,i).4x2,2,2x))) mod (x + 1)),x))
A018781-A003523: 1 3 11 31 33 93 341 1023
(1 + compr(\x.((1 + (x * loop(\(x,i).(~x2 + 4x + ~4),2,2x))) mod (x + 1)),x))
A018394: 1 5 13 25 65 325
(1 + compr(\x.((1 + (x * loop(\(x,i).(x2 * (2 + i)),2,2x))) mod (x + 1)),x))
A018527: 1 5 23 25 115 575
(1 + compr(\x.((1 + (x * loop(\(x,i).(2x2 + ~x),2,2x))) mod (x + 1)),x))
A018326: 1 3 7 9 21 27 63 189
(1 + compr(\x.((32 - loop(\(x,i).2x,x,1)) mod (x + 1)),x))
A241071: 1 2 4 6 8 10 12
A015926: 1 2 4 6 8 10 12 16 18 24 30 31 32 36 42 48
(1 + compr(\x.(loop(\(x,i).(x3 + x),1,(~x2 + 3x + ~2)) mod (x + 1)),x))
A018340: 1 2 3 6 37 74 111 222
(1 + compr(\x.(1 - (loop(\(x,i).(x * (2 + ((~1 + i) mod 4))),x,1) mod (x + 1))),x))
A279622: 7 11 13 14 17 19 21 22 23 26 28 29 31 33 34 35
(1 + compr(\x.((1 + (x * loop(\(x,i).(2x2 + ~x),2,(~x + 2)))) mod (x + 1)),x))
A018453: 1 2 7 14 31 62 217 434
(1 + compr(\x.(loop(\(x,i).(x2 + x),4,10) mod (x + 1)),x))
A087006: 1 2 3 5 6 7 10 11 13 14 15 21 22 26 30 33
(1 + compr(\x.((2 + loop(\(x,i).(x2 + x),2,6x)) mod (x + 1)),x))
A018729: 1 2 4 233 466 932
(1 + compr(\x.(loop(\(x,i).(2x3 + 2x),2,6) mod (x + 1)),x))
A323383: 1 2 3 4 6 8 12
A018253: 1 2 3 4 6 8 12 24
A018703: 1 2 3 4 6 8 12 24 37 74 111 148 222 296 444 888
(1 + compr(\x.(loop(\(x,i).(~x4 + 3x2),3,2) mod (x + 1)),x))
A222011: 1 2 4 8
A107326: 1 2 4 8 13 16 26 32 52 64 104 128 169 208 256 338
(1 + compr(\x.(loop(\(x,i).(5x2 + 10x + 5),2,2) mod (x + 1)),x))
A005018: 1 2 4 5 10 20
A018467: 1 2 4 5 10 20 23 46 92 115 230 460
(1 + compr(\x.(loop(\(x,i).((5x + 10) * (x + i)),2,2) mod (x + 1)),x))
A005018: 1 2 4 5 10 20
A018554: 1 2 4 5 10 20 31 62 124 155 310 620
(1 + compr(\x.(loop(\(x,i).x2,2,(2 * (2 + (x2 mod 3)))) mod (x + 1)),x))
A284698: 1 2 3 4 6 8 9 12 16 18 24 27 36 48 54 64
(1 + compr(\x.(loop(\(x,i).(~4x3 + 4x2 + ~x),2,2) mod (x + 1)),x))
A018251: 1 2 3 6 9 18
A018582: 1 2 3 6 9 18 37 74 111 222 333 666
(1 + compr(\x.(loop(\(x,i).(2x3 + 2x2 + 8x + 8),2,2) mod (x + 1)),x))
A018430: 1 2 4 7 8 14 28 49 56 98 196 392
(1 + compr(\x.(loop(\(x,i).(6x3 + 6),2,2) mod (x + 1)),x))
A119988-A087005: 1 2 3 5 6 7 10 11 14 15 21 22 30 33 35 42
(1 + compr(\x.(loop(\(x,i).(~x2 + 3x),2,16) mod (x + 1)),x))
A222011: 1 2 4 8
A018335: 1 2 4 8 13 16 26 52 104 208
(1 + compr(\x.(loop(\(x,i).(x * (x2 div 2)),2,(x + ~8)) mod (x + 1)),x))
A333506-A303492: 1 2 3 4 6 8 9 10 12 16 18 20 24 27 30 32
(1 + compr(\x.(loop(\(x,i).(3x2 + ~2x),(2 + (x mod 2)),2) mod (x + 1)),x))
A222011: 1 2 4 8
A018408: 1 2 4 8 11 16 22 32 44 88 176 352
(1 + compr(\x.(loop(\(x,i).(6x2 + ~2x),2,4) mod (x + 1)),x))
A222011: 1 2 4 8
A018320: 1 2 4 8 11 16 22 44 88 176
(1 + compr(\x.(loop(\(x,i).(4x3 + x),2,4) mod (x + 1)),x))
A018360: 1 2 4 5 10 13 20 26 52 65 130 260
loop(\(x,i).21x,(5x + 4),1)
A013901: 194481 794280046581 3243919932521508681 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).19x,(5x + 4),1)
A013893: 130321 322687697779 799006685782884121 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.(loop(\(x,i).(2x2 + 3x + 1),2,4x) mod (x + 1)),x))
A018737: 1 2 11 22 43 86 473 946
(1 + compr(\x.(loop(\(x,i).(2x2 + 4x + 4),2,4x) mod (x + 1)),x))
A018701: 1 2 4 13 17 26 34 52 68 221 442 884
(1 + compr(\x.((2 + loop(\(x,i).(x2 + ~x),2,5x)) mod (x + 1)),x))
A222011: 1 2 4 8
A018694: 1 2 4 8 109 218 436 872
(1 + compr(\x.((2 + loop(\(x,i).10x2,2,x)) mod (x + 1)),x))
A018769: 1 2 3 6 167 334 501 1002
(1 + compr(\x.((2 + (x * loop(\(x,i).(x2 + x),2,4x))) mod (x + 1)),x))
A018308: 1 2 7 11 14 22 77 154
(1 + compr(\x.(x - ((2 + (x * loop(\(x,i).2x2,2,(x + ~2)))) mod (x + 1))),x))
A018568: 1 3 5 15 43 129 215 645
(1 + compr(\x.((2 + (x * loop(\(x,i).3x2,2,2x))) mod (x + 1)),x))
A172411: 1 2 5 10
A018451: 1 2 5 10 43 86 215 430
(1 + compr(\x.((2 + (x * loop(\(x,i).(x2 * (1 + i)),2,2x))) mod (x + 1)),x))
A172411: 1 2 5 10
A018327: 1 2 5 10 19 38 95 190
(1 + compr(\x.((2 + (x * loop(\(x,i).4x2,2,2x))) mod (x + 1)),x))
A018780: 1 2 7 14 73 146 511 1022
(1 + compr(\x.((2 + (x * loop(\(x,i).(x2 * (2 + i)),2,2x))) mod (x + 1)),x))
A018526: 1 2 7 14 41 82 287 574
(1 + compr(\x.(loop(\(x,i).(3x2 + ~4x),2,(~2x + 1)) mod (x + 1)),x))
A018551: 1 3 5 15 41 123 205 615
(1 + compr(\x.(loop(\(x,i).(3x2 + ~x + 2),2,2x) mod (x + 1)),x))
A018628: 1 2 13 26 29 58 377 754
(1 + compr(\x.(loop(\(x,i).(4x2 + x + 1),2,2x) mod (x + 1)),x))
A018720: 1 2 4 229 458 916
(1 + compr(\x.(loop(\(x,i).(4x2 + x + ~1),2,2x) mod (x + 1)),x))
A222011: 1 2 4 8
A018593: 1 2 4 8 16 43 86 172 344 688
(1 + compr(\x.(loop(\(x,i).(3x2 + ~2x + 1),2,2x) mod (x + 1)),x))
A018673: 1 2 3 6 139 278 417 834
(1 + compr(\x.(loop(\(x,i).(3x2 + ~2x + ~1),2,2x) mod (x + 1)),x))
A018567: 1 2 4 7 14 23 28 46 92 161 322 644
(1 + compr(\x.(loop(\(x,i).(~4x2 + ~3x + 1),2,2x) mod (x + 1)),x))
A222011: 1 2 4 8
A018380: 1 2 4 8 37 74 148 296
(1 + compr(\x.(loop(\(x,i).(4x2 + 4x + 2),2,2x) mod (x + 1)),x))
A018459: 1 2 13 17 26 34 221 442
(1 + compr(\x.(loop(\(x,i).(4x2 + 2x + 2),2,2x) mod (x + 1)),x))
A018661: 1 2 11 22 37 74 407 814
(1 + compr(\x.(loop(\(x,i).(3x2 + ~2x + 2),2,2x) mod (x + 1)),x))
A018732: 1 2 7 14 67 134 469 938
(1 + compr(\x.(loop(\(x,i).(x * (1 - (x * (1 + (2 * i))))),2,2x) mod (x + 1)),x))
A018764: 1 2 7 14 71 142 497 994
((x2 + x + 1) + (loop(\(x,i).((x2 + ~x) div 2),2,(x + 1)) div 3))
A227161: 1 3 8 18 36 66 113 183 283 421 606 848 1158 1548 2031 2621
((x2 + x + 1) + loop(\(x,i).(6x + 4),2,(x2 + 2x)))
A145980: 29 139 323 581 913 1319 1799 2353 2981 3683 4459 5309 6233 7231 8303 9449
(1 + compr(\x.(loop(\(x,i).(2x2 + 3),2,3x) mod (x + 1)),x))
A018702: 1 3 5 15 59 177 295 885
(1 + compr(\x.(x - (loop(\(x,i).(2x2 + 1),2,3x) mod (x + 1))),x))
A018611: 1 2 4 181 362 724
(1 + compr(\x.(loop(\(x,i).(~2x2 + 2x + 4),2,3x) mod (x + 1)),x))
A018674: 1 2 4 11 19 22 38 44 76 209 418 836
(1 + compr(\x.(loop(\(x,i).(5 * (2 + (x * (x + i)))),2,x) mod (x + 1)),x))
A172411: 1 2 5 10
A018549: 1 2 5 10 61 122 305 610
(1 + compr(\x.(loop(\(x,i).(5 * (2 + (x * (x - i)))),2,x) mod (x + 1)),x))
A172411: 1 2 5 10
A133035: 1 2 5 10 181 362 905 1810
(1 + compr(\x.(loop(\(x,i).(5x * (~1 + (x * i))),2,x) mod (x + 1)),x))
A172411: 1 2 5 10
A018739: 1 2 5 10 19 25 38 50 95 190 475 950
(1 + compr(\x.(loop(\(x,i).(5x2 + 20x),2,x) mod (x + 1)),x))
A018667: 1 3 5 11 15 25 33 55 75 165 275 825
(1 + compr(\x.(loop(\(x,i).(12x2 + ~3),2,x) mod (x + 1)),x))
A018750: 1 3 17 19 51 57 323 969
(1 + compr(\x.(loop(\(x,i).(9x2 + ~18),2,x) mod (x + 1)),x))
A018604: 1 3 9 79 237 711
(1 + compr(\x.(loop(\(x,i).(6x2 + ~18),2,x) mod (x + 1)),x))
A018251: 1 2 3 6 9 18
A018679: 1 2 3 6 9 18 47 94 141 282 423 846
(1 + compr(\x.(loop(\(x,i).(12x2 + ~6),2,x) mod (x + 1)),x))
A018448: 1 2 3 6 71 142 213 426
(1 + compr(\x.(loop(\(x,i).(6x2 + 6x + 12),2,x) mod (x + 1)),x))
A185092: 1 2 3 4 6 12
A018738: 1 2 3 4 6 12 79 158 237 316 474 948
(1 + compr(\x.(loop(\(x,i).(8x2 + ~4x + ~4),2,x) mod (x + 1)),x))
A018476: 1 2 4 7 14 17 28 34 68 119 238 476
(1 + compr(\x.(loop(\(x,i).(6x2 + ~5x + 1),2,x) mod (x + 1)),x))
A018656: 1 5 7 23 35 115 161 805
(1 + compr(\x.(loop(\(x,i).(~6x2 + 5x + ~1),2,x) mod (x + 1)),x))
A018724: 1 5 25 37 185 925
(1 + compr(\x.(loop(\(x,i).((2x2 + ~x) * (1 + (2 * i))),2,x) mod (x + 1)),x))
A018634: 1 3 5 9 15 17 45 51 85 153 255 765
(1 + compr(\x.(loop(\(x,i).(6x2 + ~2x + 4),2,x) mod (x + 1)),x))
A018677: 1 2 4 211 422 844
(1 + compr(\x.(loop(\(x,i).(8x2 + 2x + 2),2,x) mod (x + 1)),x))
A172411: 1 2 5 10
A018503: 1 2 5 10 53 106 265 530
(1 + compr(\x.(loop(\(x,i).(2 * ((3x2 + 1) + i)),2,x) mod (x + 1)),x))
A018546: 1 2 3 6 101 202 303 606
(1 + compr(\x.(loop(\(x,i).(12x2 + ~4),2,x) mod (x + 1)),x))
A018633: 1 2 4 191 382 764
(1 + compr(\x.(loop(\(x,i).(8x2 + 16x + ~4),2,x) mod (x + 1)),x))
A018742: 1 2 4 239 478 956
(1 + compr(\x.(loop(\(x,i).(16x2 + ~8),2,x) mod (x + 1)),x))
A222011: 1 2 4 8
A018777: 1 2 4 8 127 254 508 1016
(1 + compr(\x.(loop(\(x,i).(8x2 + ~3x),2,x) mod (x + 1)),x))
A018730: 1 5 11 17 55 85 187 935
(1 + compr(\x.(loop(\(x,i).(((x + ~2) * ((x2 + 2x) div 2)) div 2),2,x) mod (x + 1)),x))
A018313: 1 3 5 11 15 33 55 165
(1 + compr(\x.(loop(\(x,i).(10x2 + 2x),2,x) mod (x + 1)),x))
A222011: 1 2 4 8
A018575: 1 2 4 8 16 41 82 164 328 656
(1 + compr(\x.(loop(\(x,i).(~6x2 + ~9x + 6),2,x) mod (x + 1)),x))
A018520: 1 3 11 17 33 51 187 561
(1 + compr(\x.(loop(\(x,i).(9x2 + ~x),2,x) mod (x + 1)),x))
A172411: 1 2 5 10
A018704: 1 2 5 10 89 178 445 890
(1 + compr(\x.(loop(\(x,i).(x * (1 + (3x * (2 + i)))),2,x) mod (x + 1)),x))
A222011: 1 2 4 8
A018640: 1 2 4 8 97 194 388 776
(1 + compr(\x.(loop(\(x,i).(x * (1 + (4x * (1 + i)))),2,x) mod (x + 1)),x))
A018538: 1 5 7 17 35 85 119 595
(1 + compr(\x.(loop(\(x,i).(x * (~1 + (4x * (1 + i)))),2,x) mod (x + 1)),x))
A018746: 1 3 9 107 321 963
(1 + compr(\x.(loop(\(x,i).(8x2 + 17x),2,x) mod (x + 1)),x))
A018486: 1 3 5 9 11 15 33 45 55 99 165 495
(1 + compr(\x.(loop(\(x,i).(10x2 + x),2,x) mod (x + 1)),x))
A018663: 1 3 7 9 13 21 39 63 91 117 273 819
(1 + compr(\x.(loop(\(x,i).(x * ((6x + ~6) + i)),2,x) mod (x + 1)),x))
A018590: 1 2 11 22 31 62 341 682
(1 + compr(\x.(loop(\(x,i).(x * (~1 + (2x * (1 + (2 * i))))),2,x) mod (x + 1)),x))
A018479: 1 3 7 21 23 69 161 483
(1 + compr(\x.(loop(\(x,i).(x * (~1 + (x * (2 + (3 * i))))),2,x) mod (x + 1)),x))
A018372: 1 2 3 6 47 94 141 282
(1 + compr(\x.(loop(\(x,i).(x * (~1 + (5x * i))),2,x) mod (x + 1)),x))
A018409: 1 2 3 6 59 118 177 354
(1 + compr(\x.(loop(\(x,i).(x * (1 - (4x * (1 + i)))),2,x) mod (x + 1)),x))
A018757: 1 3 9 109 327 981
(1 + compr(\x.(loop(\(x,i).(~7x2 + 2x),2,x) mod (x + 1)),x))
A018533: 1 3 5 9 13 15 39 45 65 117 195 585
(1 + compr(\x.(loop(\(x,i).(9x2 + 2x),2,x) mod (x + 1)),x))
A018464: 1 5 7 13 35 65 91 455
(1 + compr(\x.(loop(\(x,i).(4x * (2x + (x div 2))),2,x) mod (x + 1)),x))
A068383: 1 2 4 5 6 8 10 12 16 18 20 24 25 30 32 36
(1 + compr(\x.(loop(\(x,i).(~5x2 + 9x + 2),2,x) mod (x + 1)),x))
A018668: 1 2 7 14 59 118 413 826
(1 + compr(\x.(loop(\(x,i).(~x3 + ~6x2 + ~8x),2,x) mod (x + 1)),x))
A018286: 1 3 5 7 15 21 35 105
(1 + compr(\x.(loop(\(x,i).(x2 * (~1 + (3 * (2 + i)))),2,x) mod (x + 1)),x))
A222011: 1 2 4 8
A018600: 1 2 4 8 11 16 22 32 44 64 88 176 352 704
(1 + compr(\x.(loop(\(x,i).(x2 * (~1 + (4 * (1 + i)))),2,x) mod (x + 1)),x))
A018508: 1 7 11 49 77 539
(1 + compr(\x.(loop(\(x,i).(x2 * (1 + (2 * (3 + i)))),2,x) mod (x + 1)),x))
A018705: 1 3 9 11 27 33 81 99 297 891
(1 + compr(\x.(loop(\(x,i).(x * (2 - (x * (1 + (2 * (1 + i)))))),2,x) mod (x + 1)),x))
A018411: 1 3 7 17 21 51 119 357
(1 + compr(\x.(loop(\(x,i).(x * (4 - (x * (4 + i)))),2,x) mod (x + 1)),x))
A018251: 1 2 3 6 9 18
A018499: 1 2 3 6 9 18 29 58 87 174 261 522
(1 + compr(\x.((x + (x * loop(\(x,i).8x2,2,x))) mod (x + 1)),x))
A018495: 1 3 9 19 27 57 171 513
(0 + (x div 2) - (x div ((3x + 12) div (if x <= 0 then 1 else x))))
A332656-A240708-A002375: 0 0 1 1 2 1 2 2 2 2 3 3 3 2 3 2
((x + 1) + (if (x + ~1) <= 0 then 1 else (2 * (1 + ((2 * (x div 2)) div 5)))))
A080220: 2 3 5 6 7 8 11 12 13 14 17 18 19 20 21 22
loop(\(x,i).(5x mod 46),x,1)
A070391: 1 5 25 33 27 43 31 17 39 11 9 45 41 21 13 19
loop(\(x,i).(7x mod 26),x,1)
A070411: 1 7 23 5 9 11 25 19 3 21 17 15 1 7 23 5
loop(\(x,i).(7x mod 22),x,1)
A070408: 1 7 5 13 3 21 15 17 9 19 1 7 5 13 3 21
((x + 1) + (if x <= 0 then 1 else (x - ((2x2 div (x + 5)) mod 2))))
A171781: 2 3 4 7 8 10 13 15 16 18 20 22 25 27 29 31
((x + 1) + ((3 * ((x div 7) + (if x <= 0 then 0 else 1))) div 2))
A332416: 1 3 4 5 6 7 8 11 12 13 14 15 16 17 19 20
((x + 1) + (2 * ((1 + (if (~2 + (x div 2)) <= 0 then x else (x + 4))) div 3)))
A284393: 1 2 5 6 7 10 13 16 17 18 21 22 23 26 27 28
((x + 1) + (2 * ((x + (2 * (1 + (if (x + ~4) <= 0 then 0 else 2)))) div 3)))
A003156: 1 4 5 6 9 12 15 16 17 20 21 22 25 26 27 30
((x + 1) + ((1 + ((x + loop(\(x,i).(x + ((2 + (i mod 2)) * i)),x,1)) div 2)) div 2))
A213685: 1 3 6 9 12 17 22 28 33 41 48 57 64
(1 + (4x div ((x + 2) + (loop(\(x,i).(2x + 2),x,0) mod (x + 1)))))
A137467: 1 2 3 2 3 3 4
A078627: 1 2 3 2 3 3 4 2 3 3 4 3 4 4 3 2
((x + 1) + (if (x + ~1) <= 0 then 1 else (24 + ((x + 1) div 2))))
A104313: 2 3 28 30 31
loop(\(x,i).(5x mod 44),x,1)
A070390: 1 5 25 37 9 1 5 25 37 9 1 5 25 37 9 1
((x + 1) + ((((x + 1) + ((x * (if (x + ~2) <= 0 then 1 else x)) div 3)) div 2) div 2))
A127721: 1 2 3 5 7 9 11 14 16 19 22 25 28 31 35 38
((~x + ~1) + ((loop(\(x,i).x2,1,(x + 17)) div 2) div 2))
A159025: 71 79 87 96 105 115 125 136 147 159 171 184 197 211 225 240
((x + 1) + (8 * (2 + (if (~2 + (x div 2)) <= 0 then x else 6))))
A171169: 17 26 35 44 53 62 71 72 73 74 75 76 77 78 79 80
((x + 9) * loop(\(x,i).(10x + 1),x,0))
A091692: 0 10 121 1332 14443 155554 1666665 17777776 188888887 1999999998 21111111109 222222222220 2333333333331 24444444444442 255555555555553 2666666666666664
((x + 1) + (2 * ((if (~2 + (x div 3)) <= 0 then x else (x + 2)) + (x div 4))))
A064368: 1 4 7 10 15 18 21 24 29 36 39 42 47 50 53 56
(1 + compr(\x.(~2 + loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) - (x mod 4)),x))
A323383: 1 2 3 4 6 8 12
A036451: 1 2 3 4 6 8 12 16 20 24 32 40 48 64 80 96
((9x + 1) + (if ((x + (x div 2)) mod 4) <= 0 then 1 else 2))
A304813: 2 12 21 29 39 48 57 66 74 84 93 101 111 120 129 138
((x + 1) + ((x + ((if (~2 + (x div 3)) <= 0 then 1 else 2) + ((x div 2) mod 2))) div 2))
A286908: 1 3 5 6 7 9 11 12 13 15 17 19 20 21 23 25
loop(\(x,i).(10x + ((2x + 1) mod 5)),x,1)
A037715: 1 13 132 1320 13201 132013 1320132 13201320 132013201 1320132013 13201320132 132013201320 1320132013201 13201320132013 132013201320132 1320132013201320
loop(\(x,i).(10x + ((1 - (2 * (i mod 2))) * (1 + i))),x,1)
A179980: 1 8 83 826 8265 82644 826447 8264462 82644629 826446280 8264462811 82644628098 826446280993 8264462809916 82644628099175 826446280991734
(~9x mod loop(\(x,i).10x,x,1))
A160154: 0 1 82 973 9964 99955 999946 9999937 99999928 999999919 9999999910 99999999901 999999999892 9999999999883 99999999999874 999999999999865
loop(\(x,i).((x + 2) + (((x + ((x div 2) div 3)) * (1 + i)) div (x + 1))),x,1)
A131937: 1 4 8 14 21 29 38 49 61 74 88 103 120 138 157 177
(if x <= 0 then 2 else ((x + 1) + ((x + (((x + ~1) mod (1 + (x div 4))) div 2)) div 2)))
A120326: 2 2 4 5 7 8 10 11 13 15 16 17 19 20 22 24
loop(\(x,i).((x + 2) + ((x + 2) div (2 + (x div (4 - ((x div 2) mod 2)))))),x,1)
A311288: 1 4 8 12 16 21 26 30 34 38 42 46 50 54 58 62
(loop(\(x,i).(2 * ((2x + 2) - (x div (1 + i)))),x,0) mod (x2 + 2x + 1))
A246132: 0 0 0 4 0 22 0 4 18 54 0 122 0 102 43 68
(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1) mod (x2 + 2x + 1))
A099906: 0 3 1 3 1 30 1 35 10 78 1 62 1 52 135 35
((x3 + 3x2 + 3x + 1) * loop(\(x,i).(x * (4 + i)),x,(x + 1)))
A154307: 1 80 2430 53760 1050000 19595520 363031200 6812467200 130947062400 2594592000000 53182390060800 1129830653952000 24898991749632000 569337009905664000 4611686018427387903 4611686018427387903
((x2 + 2x + 1) * loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,2))
A253487: 2 16 90 448 2100 9504 42042 183040 787644 3359200 14226212 59907456 251100200 1048380480 4362680250 18103127040
((x2 + 2x + 1) * loop(\(x,i).7x,(x + 1),(x + 2)))
A129007: 14 588 12348 192080 2521050 29647548 322828856 3320525376 32686421670 310722773900 2871078430836 25910889640272 229239398622962 1993975834176060 17091221435794800 144629713838903552
loop(\(x,i).(1 + (6 * (x - ((~x + 2) div 4))) - (x div 2)),x,1)
A037593: 1 7 52 365 2555 17888 125217 876519 6135636 42949453 300646171 2104523200 14731662401 103121636807 721851457652 5052960203565
loop(\(x,i).(7x + (((1 + i) mod 3) + (x mod 2))),x,1)
A037600: 1 10 70 491 3440 24080 168561 1179930 8259510 57816571 404716000 2833012000 19831084001 138817588010 971723116070 6802061812491
((x + 1) * (1 + (if (~1 + ((2x + 1) mod (2 + (x div 4)))) <= 0 then x else 0)))
A304233: 1 4 9 16 25 6 49 64 81 10 121 12 169 14 15 256
((x + 1) * (((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2) + (if x <= 0 then 0 else 1)))
A328260: 0 2 3 4 5 12 7 8 9 20 11 24 13 28 30 16
(loop(\(x,i).(x * i),(1 + (x div (3 + ((x div 2) div 3)))),1) mod (x + 1))
A157279: 0 1 1 2 2 2 2 2 6 6 6 6 6 6 6 8
((1 + ((~2 + (x div 2)) mod (1 + (if (x mod 2) <= 0 then (x div 4) else 1)))) mod (x + 1))
A320838: 0 1 1 2 1 1 2 2 3 1 1 2 1 1 2 2
((x + 1) * (if (x mod 2) <= 0 then (1 + (2 * ((~x + 2) mod (1 + (x div 4))))) else 1))
A141709: 1 2 3 4 5 6 7 8 9 10 33 12 65 14 15 16
((1 + loop(\(x,i).10x,x,9)) div (x + 1))
A061772: 10 45 300 2250 18000 150000 1285714 11250000 100000000 900000000 8181818181 75000000000 692307692307 6428571428571 60000000000000 562500000000000
compr(\x.(~1 + loop(\(x,i).x2,1,((x mod 3) - (x mod 5)))),(x + 1))
A287791: 1 2 6 7 8 10 11 15 16 17 21 22 23 25 26 30
((1 + (3 * ((1 + (loop(\(x,i).2x,x,1) div 2)) div (x + 2)))) div (x + 1))
A221840: 1 0 0 1 0 1 1 2 4 7
((1 + ((if ((x * (x div 2)) mod 4) <= 0 then 1 else 0) * (1 + (x mod 2)))) mod (x + 1))
A285718: 0 1 1 1 2 1 1 1 2 3 1 1 2 1 1 1
((x + 1) * (1 + ((x + 1) * (1 + loop(\(x,i).(x2 + ~1),2,6)))))
A031748: 1226 4902 11028 19604 30630 44106 60032 78408 99234 122510 148236 176412 207038 240114 275640 313616
((x + 1) * (1 + ((x + 1) * (1 + loop(\(x,i).(x * (x + i)),2,6)))))
A031764: 1850 7398 16644 29588 46230 66570 90608 118344 149778 184910 223740 266268 312494 362418 416040 473360
((x + 1) * (1 + ((x + 1) * (1 + loop(\(x,i).(x2 + ~2x),2,8)))))
A031772: 2210 8838 19884 35348 55230 79530 108248 141384 178938 220910 267300 318108 373334 432978 497040 565520
((x + 1) * (1 + ((x + 1) * loop(\(x,i).((x + 2) * (x + i)),2,5))))
A031766: 1937 7746 17427 30980 48405 69702 94871 123912 156825 193610 234267 278796 327197 379470 435615 495632
((x + 1) * (1 + ((x + 1) * loop(\(x,i).(x2 + 2x + 1),2,6))))
A031778: 2501 10002 22503 40004 62505 90006 122507 160008 202509 250010 302511 360012 422513 490014 562515 640016
((x + 1) * ((x + ~1) - ((x + 1) * loop(\(x,i).(x * (~x + i)),2,6))))
A158410: 959 3840 8643 15368 24015 34584 47075 61488 77823 96080 116259 138360 162383 188328 216195 245984
((x + 1) * ((x + ~1) - ((x + 1) * loop(\(x,i).(~4x2 + 1),2,2))))
A158408: 898 3596 8094 14392 22490 32388 44086 57584 72882 89980 108878 129576 152074 176372 202470 230368
((x + 1) * ((x + ~1) - ((x + 1) * loop(\(x,i).(~x2 + ~2x),2,4))))
A158364: 527 2112 4755 8456 13215 19032 25907 33840 42831 52880 63987 76152 89375 103656 118995 135392
compr(\x.(~1 + (loop(\(x,i).(2x + 2),x,(1 - (2 * (x mod 2)))) mod (x + 1))),(x + 1))
A091529: 1 2 4 5 6 8 9 10 12 13 16 18 21 22 25 28
((x + 1) * loop(\(x,i).((4x * (~1 + (2 * i))) div (2 + i)),(x + 1),1))
A085687: 1 6 36 224 1440 9504 64064 439296 3055104 21498880 152807424 1095450624 7911587840 57511157760 420459724800 3089600348160
(loop(\(x,i).(1 + (2 * (x - ((x + (x div 2)) div 4)))),(x + ~1),1) div (x + 1))
A173244: 1 0 1 1 1 2 2 3 3 4 5 5 7 8 9 11
compr(\x.(x mod (1 + ((x mod (1 + (2 * (if (x mod 3) <= 0 then 0 else 2)))) div 2))),(x + 1))
A184861: 1 2 3 5 6 8 9 10 11 12 15 16 18 20 21 22
compr(\x.(x mod (1 + (2 * (x div (3 * (if (x mod 2) <= 0 then 4 else 1)))))),(x + 1))
A275581: 1 2 3 4 6 8 10 12 18 30
((1 + (2 * ((1 + loop(\(x,i).2x,((x + ~1) div 2),x)) div 3))) div (x + 1))
A322112: 1 0 1 1 1 2 2 4 4 9 9
compr(\x.(x mod (1 + (if (x mod 9) <= 0 then 0 else 6))),(x + 1))
A305214: 7 9 14 18 21 27 28 35 36 42 45 49 54 56 63 70
((x + 1) * loop(\(x,i).2x,(0 - ((~x + 2) div (2 - (x div ~4)))),1))
A131959: 1 2 3 8
A097053: 1 2 3 8 10 12 14 32 36 40 44 48 52 56 60 128
(1 - ((if ((2x + ~2) mod (4 + (x div 4))) <= 0 then 2 else 1) mod (x + 1)))
A143434: 1 1 0 ~1 0 0 ~1 0 0 0 ~1 0 0 0 0 ~1
((~1 + (2 * (if x <= 0 then 1 else (4x + (x2 div 4))))) div (x + 1))
A079058: 1 3 5 6 7 8 9 9 10 11 11 12 12 13 13 14
((if (x mod 3) <= 0 then 1 else 30x) div (x + 1))
A171808: 1 15 20 0 24
((5 * loop(\(x,i).(2x2 + 4x),2,(2x + 1))) div (x + 1))
A331768: 480 4800 16800 40320 79200
((x + 1) * ((x + 3) + loop(\(x,i).(x * (4 + i)),4,(x + 1))))
A031719: 1683 6728 15135 26904 42035 60528 82383 107600 136179 168120 203423 242088 284115 329504 378255 430368
((x + 1) * loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + (i div 2))),2x,1))
A000897: 1 12 420 18480 900900 46558512 2498640144 137680171200 7735904619300 441233078286000 25467973278667920 1484298740174927040 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) + (((x + (if (x mod 2) <= 0 then x else 1)) div 5) * (1 + (x mod 2))))
A298866: 1 2 3 4 6 8 9 10 12 14 15 16 17 18 20 22
((~x + ~1) + loop(\(x,i).(x + (i div 3) - (x div ~5)),x,1))
A317910: 0 0 0 1 2 4 7 11 16 23 32 43 57 74 95 121
((x + 1) * ((~x + 1) + ((x + 1) * loop(\(x,i).(2 + (x * (x + i))),2,4))))
A158367-A031701: 531 2120 4767 8472 13235 19056 25935 33872 42867 52920 64031 76200 89427 103712 119055 135456
((x + 1) * ((~1 + loop(\(x,i).10x,(x + 1),1)) div (x + 1)))
A066557: 9 98 999 9996 99995 999996 9999997 99999992 999999999 9999999990 99999999990 999999999996 9999999999990 99999999999998 999999999999990 9999999999999984
((x + 1) + (loop(\(x,i).(2x2 + 7x + 3),4,2) mod (x + 1)))
A057723: 1 2 3 6 5 6 7 14 12 10 11 18 13 14 15 30
loop(\(x,i).(3 * ((2x * (1 + (2 * i))) div (2 + i))),(x + ~1),(x + 1))
A099044: 1 2 18 180 1890 20412 224532 2501928 28146690 318995820 3636552348 41655054168 479033122932 5527305264600 63958818061800 741922289516880
loop(\(x,i).(4 * ((2x * (1 + (2 * i))) div (2 + i))),(x + ~1),(x + 1))
A099045: 1 2 24 320 4480 64512 946176 14057472 210862080 3186360320 48432676864 739699064832 11342052327424 174493112729600 2692179453542400 41639042214789120
((1 + (x * loop(\(x,i).(x + (2 * (2x + (x mod 2)))),(x + 1),x))) mod (x + 1))
A341409: 0 0 0 2 1 2 6 2 0 4 6 2 6 0 6 2
((2x + 2) * (~1 + (3 * (2 + (if x <= 0 then 1 else 16)))))
A009440: 16 212 318 424 530 636 742 848 954 1060 1166 1272 1378 1484 1590 1696
((2x + 2) * (~1 + ((x + 1) * loop(\(x,i).((x + 2) * ((x + i) * i)),2,2))))
A158398: 782 3132 7050 12536 19590 28212 38402 50160 63486 78380 94842 112872 132470 153636 176370 200672
((3 + ((loop(\(x,i).(2x + 2),(x div 2),(x mod 2)) div 2) div 2)) div (x + 1))
A285000: 3 1 1 1 0 0 0 1 1 1 1 2 2 3 4 6
(loop(\(x,i).(x + (5x div (1 + i))),x,6) mod (x + 1))
A133625: 0 1 2 2 2 0 1 7 4 3 1 8 1 8 9 13
((x + 1) * (2 + ((x + 1) * (1 + loop(\(x,i).(x * (x + i)),2,5)))))
A158413-A031709: 963 3848 8655 15384 24035 34608 47103 61520 77859 96120 116303 138408 162435 188384 216255 246048
((x + 1) * (2 + ((x + 1) * (1 + loop(\(x,i).(x * (2 + i)),5,2)))))
A031749: 5043 20168 45375 80664 126035 181488 247023 322640 408339 504120 609983 725928 851955 988064 1134255 1290528
((x + 1) * (2 + ((x + 1) * (1 + loop(\(x,i).(x2 + ~1),2,6)))))
A031713: 1227 4904 11031 19608 30635 44112 60039 78416 99243 122520 148247 176424 207051 240128 275655 313632
((x + 1) * (2 + ((x + 1) * (1 + loop(\(x,i).(x * (x + i)),2,6)))))
A031721: 1851 7400 16647 29592 46235 66576 90615 118352 149787 184920 223751 266280 312507 362432 416055 473376
((x + 1) * (2 + ((x + 1) * (1 + loop(\(x,i).(x * (x - i)),2,6)))))
A158403-A031707: 843 3368 7575 13464 21035 30288 41223 53840 68139 84120 101783 121128 142155 164864 189255 215328
((x + 1) * (2 + ((x + 1) * (1 + loop(\(x,i).(4x2 + ~1),2,2)))))
A158406: 902 3604 8106 14408 22510 32412 44114 57616 72918 90020 108922 129624 152126 176428 202530 230432
((x + 1) * (2 + ((x + 1) * (1 + loop(\(x,i).(x2 + ~2x),2,8)))))
A031725: 2211 8840 19887 35352 55235 79536 108255 141392 178947 220920 267311 318120 373347 432992 497055 565536
((x + 1) * (2 + ((x + 1) * (1 + loop(\(x,i).(x * (x + i)),2,8)))))
A031751: 5331 21320 47967 85272 133235 191856 261135 341072 431667 532920 644831 767400 900627 1044512 1199055 1364256
((x + 1) * (2 + ((x + 1) * (1 + loop(\(x,i).(x * (x - i)),2,8)))))
A031733: 3027 12104 27231 48408 75635 108912 148239 193616 245043 302520 366047 435624 511251 592928 680655 774432
((x + 1) * (2 + ((x + 1) * loop(\(x,i).(x2 + 2x + 1),2,5))))
A031715: 1371 5480 12327 21912 34235 49296 67095 87632 110907 136920 165671 197160 231387 268352 308055 350496
((x + 1) * (2 + ((x + 1) * loop(\(x,i).(x2 + 4x + 4),2,5))))
A031729: 2603 10408 23415 41624 65035 93648 127463 166480 210699 260120 314743 374568 439595 509824 585255 665888
((x + 1) * (2 + ((x + 1) * loop(\(x,i).(x4 + 4x3 + 4x2),2,1))))
A031777: 9803 39208 88215 156824 245035 352848 480263 627280 793899 980120 1185943 1411368 1656395 1921024 2205255 2509088
((2x2 + 4x + 2) * loop(\(x,i).x2,2,(5x + 5)))
A106322: 1250 80000 911250
((x + 1) * (2 + ((x + 1) * loop(\(x,i).((x + 1) * (x + (i mod 2))),3,2))))
A031769: 8283 33128 74535 132504 207035 298128 405783 530000 670779 828120 1002023 1192488 1399515 1623104 1863255 2119968
((2x + 2) * ((~x + ~1) + loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2)))
A032260: 2 16 102 528 2470 11016 47950 205792 874998 3694920 15519262 64899456 270415262 1123264408 4653525150 19234571968
((x + 1) * ((x + 2) div (2 + (loop(\(x,i).x3,2,2x) mod (x + 1)))))
A131959: 1 2 3 8
A102631: 1 2 3 8 5 6 7 32 27 10 11 24 13 14 15 128
((2 * ((1 + (loop(\(x,i).(2 * (x - (x div 3))),x,1) div 2)) div 2)) div (x + 1))
A117357: 0 1 0 1 0 1 1 1 1 2 2 3 3 4 5 7
((if (x + ~1) <= 0 then 1 else (2 * (x - ((3 * (x div 4)) div 2)))) mod (x + 1))
A330960-A327189: 0 1 1 2 1 2 3 4 1 2 3 4 3 4 5 6
(((loop(\(x,i).x2,1,(2 + ((x3 + x2) div 2))) div 2) div 2) mod (x + 1))
A239871: 0 0 1 0 1 0 1 1 1 2 1 4 1 6 1 9
loop(\(x,i).x6,1,(~8x + ~6))
A017142: 46656 7529536 113379904 729000000 3010936384 9474296896 24794911296 56800235584 117649000000 225199600704 404567235136 689869781056 1126162419264 1771561000000 2699554153024
((loop(\(x,i).2x,(x - (x div (1 + (x mod 2)))),1) mod (2x + 4)) div (x + 1))
A158971: 1 1 0 1 0 1 0 2 0 1 0 1 0 0 0 1
((x + 1) * ((if (16 mod (x + 1)) <= 0 then 1 else 2) + (2 * (x mod 2))))
A340512: 1 6 6 12 10 24 14 24 18 40 22 48 26 56 30 48
(((x * (1 + (x mod (1 + (4 * (if (x mod 2) <= 0 then 2 else x)))))) div 2) mod (x + 1))
A096234: 0 1 0 2 0 3 0 4 0 5 10 6 11 7 12 8
((~x2 + ~3x + ~2) + loop(\(x,i).5x,(x2 + 3x + 2),1))
A273940: 23 15619 244140613
((1 + (if (((1 + (x div 2)) div 2) mod 3) <= 0 then 2 else 0) - (x mod 2)) mod (x + 1))
A344220: 0 0 1 0 1 0 1 0 1 0 3 2 3 2 1 0
((loop(\(x,i).2x,x,(1 + (x mod (2 * (1 + (x mod 2)))))) - (x mod 2)) mod (x + 1))
A322382: 0 1 1 3 1 3 1 7 4 3 1 7 1 3 4 15
compr(\x.((x mod (1 + (x div 3))) - (if (x mod (2 + (x mod 2))) <= 0 then 1 else x)),(x + 1))
A307360: 1 2 3 4 5 6 7 9 11 13 17 19 23 25 29 31
loop(\(x,i).(6 * (x + (8x div (1 + i)))),x,(x + 1))
A173123: 1 60 1980 47520 926640 15567552 233513280 3202467840 40831464960 489977579520 5585744406528 60935393525760 639821632020480 6496650417438720 64038411257610240 614768748073058304
((x + 1) + loop(\(x,i).(x + ((x div 2) div 7)),2,3x))
A314692: 1 5 9 13 17 23 27 31 35 40 45 49 53 57 63 67
((x + 1) * (~x + ((x + 1) * loop(\(x,i).(2 + (x * (x + i))),2,6))))
A156856-A031768: 2026 8102 18228 32404 50630 72906 99232 129608 164034 202510 245036 291612 342238 396914 455640 518416
((x + 1) * (~x + ((x + 1) * loop(\(x,i).(x2 + 4x + 5),2,4))))
A031756: 1522 6086 13692 24340 38030 54762 74536 97352 123210 152110 184052 219036 257062 298130 342240 389392
((x + 1) * (x + ((x + 1) * loop(\(x,i).((x + 2) * ((x + 2) + i)),2,4))))
A156855: 2024 8098 18222 32396 50620 72894 99218 129592 164016 202490 245014 291588 342212 396886 455610 518384
compr(\x.loop(\(x,i).((x + 1) * (x mod (1 + (((x + 1) div 2) div 3)))),2,x),(x + 1))
A096868: 1 2 3 4 5 6 7 8 9 10 12 14 15 20 25 30
((2x + 1) + loop(\(x,i).x2,1,(~2x + 40)))
A279241: 1601 1447 1301 1163 1033 911 797 691 593 503 421 347 281 223 173 131
((16x + 16) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))
A059164: 16 32 16 64 16 32 16 128 16 32 16 64 16 32 16 256
((x + 1) + (x * ((x2 * loop(\(x,i).x2,2,((x2 + ~x) div 2))) div 2)))
A056165: 1 2 7 1096
loop(\(x,i).(~x + (30x div (1 + i))),x,(x + 1))
A010944: 1 28 378 3276 20475 98280 376740 1184040 3108105 6906900 13123110 21474180 30421755 37442160 40116600 37442160
loop(\(x,i).(x + (40x div (1 + i))),x,(x + 1))
A010994: 1 42 903 13244 148995 1370754 10737573 73629072 450978066 2505433700 12777711870 60403728840 266783135710 1108176102180 4353548972850 16253249498640
loop(\(x,i).(x + (36x div (1 + i))),x,(x + 1))
A010990: 1 38 741 9880 101270 850668 6096454 38320568 215553195 1101716330 5178066751 22595200368 92263734836 354860518600 1292706174900 4481381406320
loop(\(x,i).(~x + (48x div (1 + i))),x,(x + 1))
A010962: 1 46 1035 15180 163185 1370754 9366819 53524680 260932815 1101716330 4076350421 13340783196 38910617655 101766230790 239877544005 511738760544
loop(\(x,i).(x + (28x div (1 + i))),x,(x + 1))
A010982: 1 30 465 4960 40920 278256 1623160 8347680 38608020 163011640 635745396 2311801440 7898654920 25518731280 78378960360 229911617056
((x + 1) * loop(\(x,i).(x5 + x4 + x3 + x2 + x + 1),1,x2))
A105067: 1 12 4095 265720 5592405 61035156 435356467 2306881200 9817068105 35303692060 111111111111 313842837672 810554586205 1941507093540 4361070182715 9267595563616
(loop(\(x,i).(x5 + ~x4 + ~x3 + x2),1,x3) div (x + 1))
A064587: 0 0 9408 3449628 211341312 5045250000 66856881600 591709998348 3901724295168 20560831566912 90818091000000 347842282071900 1184469255180288 3654470309235408 10367425399461312 27360256600687500
((x + ~1) * (loop(\(x,i).((4x * (~1 + (2 * i))) div (1 + i)),x,1) div 2))
A069721: 0 0 4 40 336 2688 21120 164736 1281280 9957376 77395968 601968640 4686094336 36515020800 284817162240 2223764766720
loop(\(x,i).(x - (2 * (x div (4 + ((x div 2) mod 5))))),2,(x + ~1))
A073635-A071532: 1 0 1 2 3 4 5 6 5 6 5 6 5 6 7 6
((2x + 2) mod ((~x + 1) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A212790: 0 0 0 2 4 5 4 5 4 1 2 24 26 28 30 32
loop(\(x,i).3x,(x2 * (1 + (x mod (1 + ((~x + 2) mod 4))))),1)
A067506: 1 9 81 150094635296999121
(~1 + loop(\(x,i).(35x + 1),2,x2))
A158733: 35 1260 4935 11060 19635 30660 44135 60060 78435 99260 122535 148260 176435 207060 240135 275660
(1 + loop(\(x,i).(~29x + ~1),2,x2))
A158665: 29 870 3393 7598 13485 21054 30305 41238 53853 68150 84129 101790 121133 142158 164865 189254
(1 + loop(\(x,i).(~39x + ~1),2,x2))
A158768: 39 1560 6123 13728 24375 38064 54795 74568 97383 123240 152139 184080 219063 257088 298155 342264
(~1 + loop(\(x,i).(37x + 1),2,x2))
A158741: 37 1406 5513 12358 21941 34262 49321 67118 87653 110926 136937 165686 197173 231398 268361 308062
((x2 + 1) * (if x <= 0 then 1 else (18x2 + 2)))
A008355: 1 40 370 1640 4930 11752 24050 44200 75010 119720 182002 265960 376130 517480 695410 915752
(1 + loop(\(x,i).(x4 + x3 + x2 + x),1,x5))
A269527: 1 5 1082401 3501192601 1100586419201 95397958987501 3656628685521505 79797014141614001 1152956690052710401 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x + (2 * (4x + ((2 + i) mod 4)))),(x + 1),0) div 2)
A037763: 3 27 244 2198 19785 178065 1602586 14423276 129809487 1168285383 10514568448 94631116034 851680044309 7665120398781 68986083589030 620874752301272
(1 - ((if (2x mod (4 + (x div 4))) <= 0 then (x div ~2) else 0) div 2))
A165430-A051340: 1 1 2 1 1 3 1 1 1 4 1 1 1 1 5 1
((if x <= 0 then 1 else 4x) - (((x - ((x div 4) mod 2)) div 2) div ~2))
A312894: 1 4 9 13 17 21 25 30 34 38 43 47 51 55 59 64
(((2x + 1) mod (1 + (2x mod (2 + (x div 4))))) + (if x <= 0 then 0 else 2))
A136164: 0 2 2 2 2 3 2 2 2 3 2 4 2 3 3 2
((((1 + (8 mod (1 + (x div 2)))) div 2) + (if x <= 0 then 0 else 2)) - (x mod 2))
A290251: 0 1 2 1 3 2 2 1 4 3 3 2 3 2 2 1
(if x <= 0 then 0 else ((x + 1) mod (2 * (1 + (x mod (1 + ((x + ~1) mod 5)))))))
A219175: 0 0 1 0 1 0 1 0 3 2 1 0 1 2 3 0
(if x <= 0 then 0 else ((x + 1) mod (2 * (1 + ((x + ~2) mod (1 + (x div 5)))))))
A229878: 0 0 1 0 1 2
A103528: 0 0 1 0 1 2 1 0 1 2 5 0 1 2 1 0
((1 + loop(\(x,i).10x,x,11)) div 2)
A110431: 6 55 550 5500 55000 550000 5500000 55000000 550000000 5500000000 55000000000 550000000000 5500000000000 55000000000000 550000000000000 5500000000000000
((~1 + loop(\(x,i).10x,x,11)) div 2)
A110430: 5 54 549 5499 54999 549999 5499999 54999999 549999999 5499999999 54999999999 549999999999 5499999999999 54999999999999 549999999999999 5499999999999999
((1 + ((x + (loop(\(x,i).2x,x,2) div (x + 1))) mod (1 + (x div 3)))) div 2)
A089616: 0 0 0 1 0 1 0 0 1 2 0 0 1 2 2 1
(((x + 1) - (x div (1 + (loop(\(x,i).2x,(2x + ~1),1) mod (x + 1))))) div 2)
A095201: 0 0 1 0 2 2 3 0 4 3 5 5 6 5 7 0
((1 + (x div (1 + ((~1 + loop(\(x,i).2x,x,(2 + (x mod 2)))) mod (x + 1))))) div 2)
A340502: 0 0 1 0 1 0 2 0 1 1 3 0 3 1 1 0
((1 + (9 * loop(\(x,i).(2 * (2x + (x div 2))),x,1))) div 2)
A113023: 5 18 90 450 2250 11250 56250 281250 1406250 7031250
((1 + ((x + (if (x mod 2) <= 0 then 6 else 1)) mod 9)) div 2)
A190457: 3 1 4 2 1 3 2 4 3 1 4 2 0 3 1 4
(if x <= 0 then 1 else ((x mod 2) - (((~x + 2) div (1 + (x mod 9))) mod 2)))
A343493: 1 1 0 0 ~1 0 ~1 0 ~1 0 0 0 ~1 0 0 1
loop(\(x,i).4x,(1 + (5 * (x + (x div 5)))),2)
A320864: 8 8192 8388608 8589934592 8796093022208 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((if x <= 0 then 2 else ((1 + (x div 4)) mod (1 + ((~x + 1) mod 5)))) div 2)
A125250: 1 0 0 0 1 0 0 1 1 0 0 0 2 0 0 0
(2 * (if x <= 0 then 1 else ((~1 - (x div 4)) mod (1 + (x div 5)))))
A104261: 2 0 0 0 0 0 0 0 2 2 0 0 4 4 4 0
((1 + loop(\(x,i).(2 * ((x + 2) + (x div 2))),(x div 2),(1 + (2 * (x mod 2))))) div 2)
A047081: 1 2 3 6 11 20 35 62 107 188 323 566 971 1700 2915 5102
loop(\(x,i).x5,1,(12x + 10))
A017645: 100000 5153632 45435424 205962976 656356768 1680700000 3707398432 7339040224 13382255776 22877577568 37129300000 57735339232 86617093024 126049300576 178689902368 247609900000
((if x <= 0 then 2 else (1 + ((x - ((x * (x div 2)) mod 8)) div 3))) div 2)
A255065: 1 0 0 0 1 1 1 0 1 1 1 1 2 1 2 2
((1 + ((2 + (loop(\(x,i).(x + ((x + i) div 3)),x,2) div 2)) div 3)) div 2)
A290137: 1 1 1 1 1 1 2 3 4 5 7 9 12 16 22 30
(22 * loop(\(x,i).2x,(x div 2),(2 - (x mod 2))))
A108213: 44 22 88 44 176 88 352 176 704 352 1408 704 2816 1408 5632 2816
((1 + ((2 + (if x <= 0 then 2 else ((x + (x2 div 4)) div 2))) div 3)) div 2)
A029159: 1 0 1 1 1 1 2 2 2 3 3 4 4 5 6 6
loop(\(x,i).x6,1,(12x + 2))
A017550: 64 7529536 308915776 3010936384 15625000000 56800235584 164206490176 404567235136 885842380864 1771561000000 3297303959104 5789336458816 9685390482496 15557597153344 24137569000000
((1 + (((x * (x + (if ((x div 2) mod 3) <= 0 then 1 else 2))) div 2) div 3)) div 2)
A238098: 0 0 1 1 2 3 4 5 7 8 10 12 13 15 19 21
((1 + loop(\(x,i).4x,(x + ~1),(10x + 1))) div 2)
A229473: 1 6 42 248 1312 6528 31232 145408 663552 2981888 13238272 58195968 253755392 1098907648 4731174912 20266876928
((1 + loop(\(x,i).(2 * (x + (5 * (2x + (x div 2))))),x,1)) div 2)
A067424: 1 11 297 8019 216513 5845851 157837977 4261625379 115063885233 3106724901291 83881572334857 2264802453041139 61149666232110753 1651040988266990331 4611686018427387903 4611686018427387903
(2 * (1 + ((if ((x + 1) mod 5) <= 0 then 5 else 0) mod (x + 1))))
A164898: 2 2 2 2 2 2 2 2 2 12 2 2 2 2 12 2
((1 + (loop(\(x,i).((x + 2) + (2x div 5)),x,0) div (x + 1))) div 2)
A173692: 0 1 1 1 1 1 2 2 3 4 5 6 8 11 14 19
(loop(\(x,i).(1 + (2 * ((2x + 2) - (x mod 5)))),(x + 1),1) div 2)
A037786: 3 14 56 225 903 3614 14456 57825 231303 925214 3700856 14803425 59213703 236854814 947419256 3789677025
((1 + ((loop(\(x,i).2x,((x2 + ~x) div 2),3) div 2) div (x + 1))) div 2)
A305028: 1 0 1 2 10 128
(loop(\(x,i).(5x + ((x div 5) mod 2)),(x + 1),1) div 2)
A037626: 2 13 65 327 1638 8190 40952 204763 1023815 5119077 25595388 127976940 639884702 3199423513 15997117565 79985587827
(((x + 1) mod (1 + ((4 * (if (x mod 2) <= 0 then (~x + 1) else x)) mod (x + 1)))) div 2)
A241273: 0 0 0 0 0 0 0 1 0 1 1 1 2 1 3 1
(loop(\(x,i).(3 * ((x + 3) mod 9)),(x + ~1),1) div 2)
A021148: 0 0 6 9 4 4 4 4 4 4 4 4 4 4 4 4
((1 + loop(\(x,i).(x + ((2 + (i div 3)) * (1 + (i div 3)))),x,1)) div 2)
A144677: 1 2 3 6 9 12 18 24 30 40 50 60 75 90 105 126
(1 - ((x mod (1 + (2 * (if ((x + 2) mod (2 + ((x div 2) mod 2))) <= 0 then 2 else 0)))) div 2))
A117947: 1 1 1 1 ~1 1 1 0 0 1 1 1 0 1 1 1
(2 * loop(\(x,i).2x,((1 + ((x * (x div 5)) div 3)) div 2),1))
A321213: 2 2 2 2 2 4 4 4 4 8 16 32
(if x <= 0 then 1 else (2 * (1 + (((~x + 5) mod (1 + (x div 3))) div 2))))
A104361: 1 2 2 2 2 2 4 2 2 2 4 4 4 4 2 4
(if x <= 0 then 1 else (2 * (1 + (((x2 + 4x) mod (1 + (x div 3))) div 2))))
A003648: 1 2 2 2 2 2 2 4 2 2 2 2 4 2 4 4
((1 + ((1 + (loop(\(x,i).(x * ((1 + i) div 2)),x,1) div (x + 3))) div 2)) div 2)
A241470: 0 0 0 0 0 1 1 4 13 60
((1 + ((1 + (loop(\(x,i).((x + 2) + (x div 2)),x,0) div (2x + ~1))) div 2)) div 2)
A316077: 0 1 1 1 1 1 1 1 2 2 3 4 5 7 10 14
((1 + ((if x <= 0 then 2 else (1 + ((~x2 + 2x + ~1) mod (1 + (x div 2))))) div 2)) div 2)
A112223: 1 0 1 0 0 1 1 0 1 1 1 1 2 1 2 1
(if x <= 0 then 1 else (2 * (1 + ((x mod (1 + ((2 - (x mod 4)) mod (x + 1)))) div 2))))
A328400: 1 2 2 4 2 2 2 8 4 2 2 12 2 2 2 16
((1 + ((1 + ((x + loop(\(x,i).((x + 2) + (x div 2)),x,0)) div (x + 1))) div 2)) div 2)
A173674: 0 1 1 1 1 1 2 2 3 4 5 7 10 13 18 25
(2 * (~1 + (2 * (~3 + loop(\(x,i).(2x + 16),(x + 1),1)))))
A305156: 58 194 466 1010 2098 4274 8626 17330 34738 69554 139186 278450 556978 1114034 2228146 4456370
(2x div (2 + (x div (1 + (if (x mod (2 + ((x + ~1) mod 3))) <= 0 then 1 else 2)))))
A196052: 0 1 2 2 2 3 3 3 4 3 2 4 3 4 4 4
((if x <= 0 then 2 else (1 - (x mod (~1 + (2 * ((~x + 1) div 7)))))) div 2)
A321400-A300705-A282750-A105821-A061198: 1 0 1 0 1 1 0 1 1 1 0 2 2 1 1 0
((1 + ((if x <= 0 then 2 else ((x + 1) mod (1 + (x div (2 + (x mod 3)))))) div 2)) div 2)
A029421: 1 0 0 0 0 0 1 1 0 0 1 0 2 1 1 0
((1 + ((1 + ((if ((x * (x div 2)) mod 2) <= 0 then x else (x mod 3)) div 2)) div 2)) div 2)
A337474: 0 0 1 0 1 1 1 0 1 1 2 1 2 2 2 0
(2 * (1 + ((1 + (loop(\(x,i).(2x - ((1 + i) mod (x + 1))),x,1) div 2)) div 2)))
A033827: 2 4 4 4 6 8 8 12 16 24
(3 + (((if (x mod 2) <= 0 then (x div 2) else (2x + 1)) mod 5) div 2))
A100867: 3 4 3 4 4 3 4 3 5 5 3 4 3 4 4 3
(if x <= 0 then 1 else (2 + ((~x + 1) mod (1 + ((x - ((x div 3) mod 3)) div 2)))))
A088748: 1 2 3 2 3 4 3 2 3 4 5 4 3 4 3 2
(((x + 2) mod (1 + (2 * (if (x + ~1) <= 0 then 1 else (((x + 1) div 2) div 3))))) div 2)
A029430: 1 0 0 0 0 0 1 0 0 1 0 1 2 0 0 1
(1 - (((if (x mod 8) <= 0 then x else 0) - (x div 7)) div 2))
A044930: 1 1 1 1 1 1 1 2 ~2 2 2 2 2 2 2 2
(2x + (if ((x div 4) - (x mod 6)) <= 0 then 1 else 2) - (x div 2))
A225647: 1 3 4 6 7
A103566: 1 3 4 6 7 9 11 12 13 15 16 18 20 22 23 24
(3 + ((1 + ((if (x + ~3) <= 0 then x else 4) + (x div 3))) div 2))
A079107: 3 4 4 5 6 6 6 6 6 7 7 7 7 7 7 8
((1 + ((if x <= 0 then 2 else (1 + ((x + (x2 div 5)) div 2))) div 2)) div 2)
A067842-A029148: 1 0 1 1 1 2 2 2 3 3 4 5 5 6 7 8
(if (x mod 2) <= 0 then (1 + (2 * (((~x2 + 1) - (x mod 2)) mod (x + 3)))) else 2)
A319044: 3 2 5 2 13 2 3 2
((1 + (((x + 1) * (if (x mod 2) <= 0 then (1 + ((1 + (x div 2)) div 2)) else 0)) div 2)) div 2)
A049641: 0 0 2 0 3 0 5 0 7 0 11 0 13 0 19 0
((1 + ((loop(\(x,i).2x,x,((~x2 + x) div 4)) mod (x + 1)) div 2)) div 2)
A306696: 0 0 1 0 1 1 2 0 2 1 3 1 2 2 3 0
(loop(\(x,i).3x,(1 - ((~x + 2) div (2 - (x div ~4)))),1) div 2)
A107680: 0 1 1 4 4 4 4 13 13 13 13 13 13 13 13 40
(1 - ((1 + (((1 + loop(\(x,i).(x - ((i - (x div 2)) div 2)),x,1)) div 2) div 2)) div 2))
A225500: 1 1 1 1 1 2 2 3 4 5 7 9 12 15 19 25
((1 + (((7 * loop(\(x,i).x2,2,(x + 1))) div 2) div 2)) div 2)
A186707: 1 14 71 224 547 1134 2101 3584 5741 8750 12811 18144 24991 33614 44297 57344
((1 + ((loop(\(x,i).x2,1,((x + 1) - (2 * (x div 3)))) div 2) div 2)) div 2)
A161103: 0 1 1 1 1 2 1 2 3 2 3 5 3 5 6 5
((if x <= 0 then 2 else (1 + (x div (2 * (2 + (~x2 mod 5)))))) div 2)
A025882: 1 0 0 0 0 1 0 1 1 0 1 0 1 1 1 2
((1 + ((x + 1) div (2 + ((loop(\(x,i).(2x + 1),x,0) mod (x + 1)) div 2)))) div 2)
A165915: 0 1 1 1 1 2 2 1 2 3 3 1 3 4 3 1
(2 + (if (x + ~1) <= 0 then 0 else (1 + (2 * (2 + (((x div 2) - (x div 3)) div 2))))))
A054085: 2 2 7 7 7 7 7 7 9 7 9 9 9 9 9 9
((1 + (((loop(\(x,i).((x * ((x + 1) div 2)) div 2),2,(x + ~1)) div 2) div 2) div 2)) div 2)
A308910: 0 0 0 0 0 0 1 1 3 4 8 10 18 20 32 38
(if x <= 0 then 1 else (2 * (1 + (2 * (((2x + 1) mod (2 + (x div 4))) div 2)))))
A324291: 1 2 2 2 2 6 2 2 2 6 2 6 2 6 10 2
(if x <= 0 then 1 else (2 * (3x - ((2x + 4) div 9))))
A315653: 1 6 12 16 22 28 34 38 44 50 56 62 66 72 78 84
((if x <= 0 then 1 else 6x) - ((x - (x div 9)) div 2))
A315523: 1 6 11 17 22 28 33 39 44 50 56 61 67 72 78 83
((~1 + loop(\(x,i).(3 * (x mod 7)),x,8)) div 2)
A068028: 3 1 4 2 8 5 7 1 4 2 8 5 7 1 4 2
(x + (if ((x div 2) - (x mod 8)) <= 0 then 1 else 2) - (((x + 1) div 2) div 2))
A309081: 1 2 3 3 4 5 6 6 8 9 10 10 11 12 13 12
(if x <= 0 then 1 else (2 + ((2x + 1) mod (1 + (2x mod (2 + (x div 4)))))))
A328830-A182860: 1 2 2 2 2 3 2 2 2 3 2 4 2 3 3 2
((1 + (loop(\(x,i).(2x + 4),(x div 2),(x mod 2)) mod (2 + (x div 4)))) div 2)
A030425: 0 1 0 0 0 1 1 0 0 0 0 0 1 1 2 1
(2 + loop(\(x,i).(5x + 10),(x div 2),(1 + (4 * (x mod 2)))))
A026396: 3 7 17 37 87 187 437 937 2187 4687 10937 23437 54687 117187 273437 585937
(1 - ((1 + (((x div (1 + (if (x mod 3) <= 0 then 2 else 0))) div 2) mod 4)) div 2))
A207710: 1 1 0 1 0 0 0 ~1 1 0 0 0 0 0 ~1 0
(if x <= 0 then 1 else (2 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4)))))
A067132: 1 2 2 3 2 2 2 4 3 2 2 3 2 2 2 5
(2 - (((2 - (if (x mod (4 - (x mod 2))) <= 0 then x else 0)) mod 5) div 2))
A306734: 1 1 1 0 1 1 1 1 0 1 1 1 2 1 1 1
loop(\(x,i).2x,(5 * (1 + (2 * (2x - (x mod 4))))),2)
A320862: 64 65536 67108864 68719476736 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(((if (((x + ~1) mod (2 + (x mod 2))) mod 2) <= 0 then (x + ~1) else 2) mod 5) div 2)
A015716: 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 2
(2x - ((if x <= 0 then 1 else (2 - (((x2 + ~x) div 2) div 5))) div 2))
A094227: 0 1 3 5 8 10 13 15 18 21 24 27 30 33 36 40
(if x <= 0 then 1 else (2 + (((x + 2) + (x mod 10)) div 5)))
A058889: 1 2 3 3 4 4 4 5 5 6 4 4 5 5 6 6
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) mod 10)
A152669: 1 1 2 5 4 2 2 9 0 2 6 6 2 0 0 5
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 10)
A007652: 2 3 5 7 1 3 7 9 3 9 1 7 1 3 7 3
((x + 10) + loop(\(x,i).(x - (x div 12)),2,x))
A088381: 10 12 14 16 18 20 22 24 26 28 30 32 33 34 36 38
(if x <= 0 then 1 else (2 * (2x - ((~x + ((x + 1) mod 3)) div 5))))
A310369: 1 4 10 14 18 22 26 30 36 40 44 50 54 58 62 66
(if x <= 0 then 1 else (2 + (11x2 div 5)))
A008260: 1 4 10 21 37 57 81 109 142 180 222 268 318 373 433 497
(if x <= 0 then 1 else (2 * ((2x + ~1) - ((~x + ((x div 2) mod 4)) div 4))))
A311155: 1 4 8 12 16 20 24 28 34 40 44 48 52 56 60 64
((1 + ((((x2 + x) + loop(\(x,i).(2 * (x + (i mod 2))),x,1)) div 2) div 2)) div 2)
A276661: 0 1 2 4 7 13 24 44 84 161
((1 + ((loop(\(x,i).2x,x,(7x + 16)) div 2) div 2)) div 2)
A335903: 2 6 15 37 88 204 464 1040 2304 5056 11008 23808 51200 109568 233472 495616
loop(\(x,i).x7,1,(8x + 2))
A017095: 128 10000000 612220032 8031810176 52523350144 230539333248 781250000000 2207984167552 5455160701056 12151280273024 24928547056768 47829690000000 86812553324672 150363025899136
loop(\(x,i).x6,1,(~7x + ~2))
A017010: 64 531441 16777216 148035889 729000000 2565726409 7256313856 17596287801 38068692544 75418890625 139314069504 243087455521 404567235136 646990183449 1000000000000 1500730351849
(1 - (if (x + ~1) <= 0 then 2x else ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2)))
A076699: 1 ~1 1 1 1 0 1 1 1 0 1 0 1 0 0 1
((1 + ((x + 3) mod (2 + ((if (~2 + (x div 2)) <= 0 then 1 else 2) + (x mod 2))))) div 2)
A174886: 0 0 1 1 1 0 1 0 2 1 1 2 2 1 1 2
(~2 + (3 * loop(\(x,i).(10x + 21),(x + 1),0)))
A086945: 61 691 6991 69991 699991 6999991 69999991 699999991 6999999991 69999999991 699999999991 6999999999991 69999999999991 699999999999991 6999999999999991 69999999999999991
(((x + 1) mod (3 * (1 + (x div (2 * (if (x mod 2) <= 0 then 4 else 1)))))) div 2)
A278529: 0 1 0 2 1 3 0 4 1 5 2 6 0 7 1 8
((if (x mod 3) <= 0 then 1 else 0) - (((x mod 7) mod 3) mod 2))
A015878-A015752-A015668-A015542-A015500-A015416-A015290-A015248-A015122-A014996-A014912-A014870-A014786-A014660-A014618-A014492-A014408-A014366: 1 ~1 0 1 ~1 0 1 0 ~1 1 0 ~1 1 0 0 0
(~2 + (3 * loop(\(x,i).x6,2x,3)))
A180225: 7 450283905890997361 4611686018427387903
(((if x <= 0 then 1 else x) - ((~1 + ((x * (~1 + (x mod 3))) div 2)) div 3)) div 2)
A130872: 1 1 1 2 2 2 4 4 3 5 5 5 7 7 6 9
((3 * ((1 + (loop(\(x,i).2x,(x + ~1),(x + 3)) div 2)) div 2)) div 2)
A084861: 1 1 4 9 21 48 108 240 528 1152 2496 5376 11520 24576 52224 110592
(if x <= 0 then 0 else (2 + (3 * ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2))))
A337228: 0 2 2 2 2 5 2 2 2 5 2 5 2 5 5 2
(if x <= 0 then 0 else (2 - (((x mod (2 + (3 * (x mod 3)))) mod 3) mod 2)))
A062501: 0 1 2 1 1 2 2 2 2 1 2 2 2 2 2 1
(if x <= 0 then 1 else (2 * ((2 * (4x - ((x div 2) div 3))) div 3)))
A310501: 1 4 10 16 20 26 30 36 40 46 52 56 60 66 72 76
(x - (2 * ((1 - (4 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 3)))
A003158: 2 7 10 13 18 23 28 31 34 39 42 45 50 53 56 61
(2 - (if x <= 0 then 1 else (x - (2 * ((2 + (x3 div (x + 2))) div 3)))))
A094055: 1 1 2 3 6 9 14 21
A094056: 1 1 2 3 6 9 14 21 28 37 48
((((x + 2) + loop(\(x,i).(x + (x div 4)),x,5)) div 3) div 2)
A125890: 1 1 1 2 2 3 3 4 5 6 7 9 10 13 15 19
((x2 + 2) + (((x3 + ~x) div 2) div 3) - (if x <= 0 then 1 else x))
A116721: 1 2 5 12 24 42 67 100 142 194 257 332 420 522 639 772
(if x <= 0 then 1 else (2 * (2x - ((2 * (~x + ((x div 3) mod 2))) div 3))))
A315639: 1 6 12 16 20 26 32 38 44 48 52 58 64 70 76 80
(2 * (((x - (x * loop(\(x,i).((x2 + ~x) div 2),2,(x + ~2)))) div 2) div 3))
A092712: 0 0 0 0 0 ~4 ~28 ~104
loop(\(x,i).x7,1,(6x + 2))
A016939: 128 2097152 105413504 1280000000 8031810176 34359738368 114415582592 319277809664 781250000000 1727094849536 3521614606208 6722988818432 12151280273024 20971520000000 34792782221696
((loop(\(x,i).(x + (x div 2)),(x + ~1),2) div 9) mod 6)
A343321: 0 0 0 0 0 1 1 2 3 4 1 4 3 5 5 4
(6 + (loop(\(x,i).((x + 2) + ((x div 2) div 5)),x,2) div 2))
A120208: 7 8 9 10 11 12 14 15 17 19 21 23 26 29 32 35
((x + 6) + (if (x + ~1) <= 0 then x else (2 + ((x - ((x div 2) mod 2)) div 2))))
A331201-A080257: 6 8 10 12 14 15 16 18 20 21 22 24 26 27 28 30
((3 * compr(\x.(1 - (x mod (1 + (if (x mod 8) <= 0 then 2 else 1)))),x)) div 2)
A097703: 1 4 7 10 12 13 16 19 22 24 25 28 31 34 37 40
(if x <= 0 then 1 else (2 * (2x - ((~x + ((x div 3) mod 3)) div 3))))
A315185: 1 6 10 14 18 24 28 32 36 42 48 52 56 60 66 70
(if x <= 0 then 1 else (2 * (2x - ((~x + ((1 + (x div 2)) mod 3)) div 3))))
A312655: 1 4 8 14 20 24 28 32 36 42 48 52 56 60 64 70
loop(\(x,i).x6,1,(9x + 2))
A017190: 64 1771561 64000000 594823321 3010936384 10779215329 30840979456 75418890625 164206490176 326940373369 606355001344 1061520150601 1771561000000 2839760855281 4398046511104 6611856250609
(((x + 3) + (loop(\(x,i).(x2 + x + 1),2,2) mod (1 + (x div 2)))) div 2)
A051134: 1 2 3 3 3 4 5 5 6 7 8 8 8 8 9 9
(2 + (((x + ~1) + loop(\(x,i).(x2 + 2x + 2),(x div 2),(x mod 2))) div 3))
A330990: 1 2 3 4 6 15 44
((3 * (x + (if (~1 + (x div 2)) <= 0 then 1 else (1 - (x div ~4))))) div 2)
A022297: 1 3 4 6 9 12 13 15 16 19 21 22 24 27 28 30
((3 * (x + ((x + (if (x + ~12) <= 0 then 2 else 1)) div 2))) div 2)
A330180: 1 3 6 7 10 12 15 16 19 21 24 25 28 30 31 34
(2 + (if x <= 0 then 1 else ((x + 2) - (((~x + 1) - ((x * (x div 2)) mod 2)) div 3))))
A183868: 3 5 7 8 9 11 12 14 15 16 17 19 20 21 23 24
((1 + ((if (~1 + (x div 4)) <= 0 then x else 8) + (x div 3))) div 2)
A094606: 0 1 1 2 3 3 4 5 5 6 6 6 6 6 6 7
(x div (if ((x mod (1 + ((1 + (x div 2)) div 2))) mod 2) <= 0 then 1 else (2 + (x div 3))))
A130758: 0 1 2 1 4 1 6 1 8 9 10 2 12 2 14 15
((if ((x + 1) mod (1 + (x div 5))) <= 0 then 1 else 2) - ((x mod 3) div 2))
A035180: 1 1 0 1 1 0 2 1 1 1 2 0 2 2 0 1
(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(3x + 2),1) div 2)
A187366: 5 231 12155 676039 38779380 2268783825 134564468610 8061900920775 486734856412028 29566145391215356 1804857108504066435 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 + loop(\(x,i).(x3 + 4x2 + 4x + 3),(x2 + x + 2),1))
A081208: 2357 4611686018427387903
((1 + ((x + (loop(\(x,i).(x + (x div 3)),x,5) div 2)) div 2)) div 2)
A173513: 1 1 2 2 3 3 4 5 7 9 11 14 18 23 30 38
(((x2 + 5x + 6) * loop(\(x,i).(x * (4 + i)),x,(x + 2))) div 2)
A037959: 6 90 1200 15750 211680 2963520 43545600 673596000 10977120000 188367379200 3399953356800 64457449056000 1281520880640000 26676557107200000 580481882652672000 4611686018427387903
(((x + loop(\(x,i).((x2 + x) div 2),2,(1 + (x div 2)))) mod (x + 3)) div 2)
A337178: 0 1 1 1 2 1 3 1 3 4 3
((1 + loop(\(x,i).(28 div (x + 1)),2,2x)) div 2)
A265535: 0 1 2 3 4 5 5 7 7 7 7 7 7 7 14 14
(if x <= 0 then 1 else ((5x + 2) - ((x - (x div 3)) div 3)))
A072354: 1 7 12 17 21 26 31 36 40 45 50 55 60 64 69 74
(2 + ((1 + (if (((x + 2) div 3) mod 4) <= 0 then 2 else 0)) mod (1 + (x div 2))))
A257244: 2 2 3 3 3 3 3 3 3 3 5 5 5 3 3 3
((if (~2 + (2x mod (4 + (x div 4)))) <= 0 then 2 else (1 + (x div 2))) div 2)
A047080-A036064: 1 1 1 1 1 1 1 2 2 1 1 3 3 3 1 1
((2 - (((x + (if (~2 + (x div 2)) <= 0 then 1 else 2)) mod 4) mod (1 + (x div 2)))) div 2)
A257234: 1 1 0 1 0 0 1 0 0 ~1 1 0 0 ~1 1 0
(if (x + ~2) <= 0 then (x div 2) else ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2))
A255517-A145153: 0 0 1 0 1 0 0 1 1 0 0 1 2 1 0 0
loop(\(x,i).x6,1,(10x + 2))
A017298: 64 2985984 113379904 1073741824 5489031744 19770609664 56800235584 139314069504 304006671424 606355001344 1126162419264 1973822685184 3297303959104 5289852801024 8198418170944
(loop(\(x,i).(~x + 1),x,((x + 1) + (9 * (x2 div 2)))) div 2)
A266087: 0 ~1 10 ~20 38 ~57 84 ~112 148 ~185 230 ~276 330 ~385 448 ~512
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(3x + ~1)) div 2)
A129869: ~1 1 5 20 77 294 1122 4290 16445 63206 243542 940576 3640210 14115100 54826020 213286590
(loop(\(x,i).((x + 1) + (((x div (4 + (x mod 2))) + (x div 2)) div 2)),x,1) div 2)
A064323: 0 1 1 2 3 4 6 8 11 15 21 29 40 55 75 103
(2 * (1 + compr(\x.((x div 4) - (loop(\(x,i).(2x + 2),x,0) mod (x + 1))),x)))
A231565: 2 4 6 8 12 16 18 20 24 30 32 36 40 42 48 54
(((x2 + x + 1) * loop(\(x,i).4x3,(x + ~1),1)) div 2)
A060614: 0 1 14 1664
((x + 3) + (if (x + ~1) <= 0 then x else (2 + (((x + ~1) div 5) mod 2))))
A047746: 3 5 7 8 9 10 12 13 14 15 16 16 17 18 19 20
(if x <= 0 then 1 else (2 * (1 + (2x * (x + ((x3 + 2x) div 3))))))
A008413: 1 10 50 170 450 1002 1970 3530 5890 9290 14002 20330 28610 39210 52530 69002
(((~1 + (2x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))) mod (x + 1)) div 2)
A083280: 0 0 0 0 0 1 0 2 0 1 0 3 0 1 0 6
((loop(\(x,i).3x,(2 - ((~x + 2) div (2 + (x div 2)))),1) div (x + 1)) div 2)
A277855: 1 2 1 3 2 2 1 1 1 4 3 3 3 2 2 2
(~x + ((x div 3) + (2 * (if x <= 0 then 1 else ((x2 div 3) mod (x + 1))))))
A131667: 2 ~1 0 4 ~3 0 6 ~5 0 8 ~7 0 10 ~9 0 12
(((x + 1) * (if ((x + 2) mod (2 - (x mod ~4))) <= 0 then (x + 2) else 1)) div 2)
A069268: 1 1 6 2 15 3 28 36 45 5 66 6 91 105 120 8
(x div (2 + (loop(\(x,i).(2 + (x * (1 + (4 * (i mod 2))))),x,1) mod (x + 1))))
A213727: 0 0 1 0 0 1 1 0 0 1 3 0 1 1 1 0
(2 + ((~2 + loop(\(x,i).x2,2,23)) mod (x + 1)))
A091733: 2 3 4 5 6 7 2 9 4 11 12 13 3 9 16 17
((loop(\(x,i).2x,x,(2 + ((x - ((~x + 1) mod 3)) div 2))) mod (x + 1)) div 2)
A279048: 0 0 1 0 2 0 2 0 1 1 3 0 3 1 1 0
(~2 + loop(\(x,i).(2 + ((x2 + 2x) div 20)),2,(x + 1)))
A318029: 0 0 0 0 0 1 1 2 2 4 4 6 7 9 11 14
(((x2 + 3x + 2) * loop(\(x,i).(10x + 1),x,1)) div 2)
A094760: 1 33 666 11110 166665 2333331 31111108 399999996 4999999995
(loop(\(x,i).15x,x,1) * ((x2 + 3x + 2) div 2))
A027476: 1 45 1350 33750 759375 15946875 318937500 6150937500 115330078125 2114384765625 38058925781250 674680957031250 11806916748046875 204350482177734375 3503151123046875000 4611686018427387903
loop(\(x,i).x7,1,((x2 + 3x + 2) div 2))
A059979: 1 2187 279936 10000000 170859375 1801088541 13492928512 78364164096 373669453125 1522435234375 5455160701056 17565568854912 51676101935731 140710042265625 358318080000000 860542568759296
(2 + (((if ((x + 2) mod (1 + (x div 4))) <= 0 then 1 else 2) + (x div 2)) mod (x + 1)))
A305397: 2 3 4 4 5 6 6 7 8 8 8 9 10 10 10 11
(2 + ((1 + (x div (2 + ((if (x + ~2) <= 0 then 1 else x) mod 2))) - (x mod 2)) mod (x + 1)))
A204908: 2 2 3 3 5 3 6 4 7 5 8 5 9 6 10 7
((2x + 2) + (if x <= 0 then 1 else (2 + ((2 * (1 + (x div 2))) div 5))))
A169863: 3 6 8 10 13 15 17 19 22 24 26 28 30 32 35 37
((3x + 2) + ((if (~2 + (x div 3)) <= 0 then x else (x + 2)) div 3))
A080753: 2 5 8 12 15 18 22 25 28 32 36 39 42 46 49 52
((3x + 2) + (loop(\(x,i).(2 + ((x2 + x) div 2)),2,x) div 3))
A227121: 3 7 13 23 40 68 112 178 273 405 583 817 1118 1498 1970 2548
(loop(\(x,i).((x + 1) - (~x2 div 8)),2,x) div (2x + 2))
A226503: 1 1 1 1 1 2 2 2 3 3 4 5 5 7 8 9
((x + loop(\(x,i).((x + 2) + ((x - (x div 4)) div 2)),x,2)) div (2x + 2))
A174619: 1 1 1 2 2 3 3 4 5 6 8 10 13 17 21 28
(1 + (loop(\(x,i).(x + (i div 2)),(x + ~8),1) div 2) - ((x + 1) div 2))
A292042: 1 0 0 ~1 ~1 ~2 ~2 ~3 ~3 ~4 ~3 ~4 ~3 ~3 ~1 ~1
((loop(\(x,i).((x2 + ~x) div 2),2,(~1 + (x div 2))) div 3) * ((x + 1) div 2))
A333321: 0 0 0 0 0 0 0 0 4 5 25 30 90 105 245 280
((1 + (if (~x + 2) <= 0 then 10 else 1) - (x mod 2)) * ((x + 1) div 2))
A053715: 0 1 11 20 22 30 33 40 44 50 55 60 66 70 77 80
(x + ((if x <= 0 then 1 else (x - ((x div (1 + (x mod 3))) mod 2))) + ((x + 1) div 2)))
A020959: 1 3 5 7 10 12 15 17 20 22 24 27 30 33 35 37
((1 - (((x div (3 * (~2 + (x mod 2)))) mod 3) div 2)) * (if x <= 0 then 1 else 2))
A339432: 1 0 0 0 0 2 0 2 2 2 2 0 2 2 2 2
((((5x2 + x) div 2) div (x + 4)) + (if x <= 0 then 1 else 2))
A185603: 1 2 3 5 7 9 11 13 15 17 20 22 24 27 29 32
((x + 2) - (x2 div ((x + 1) + (if (x mod 2) <= 0 then 7 else x))))
A176504: 2 3 4 4 5 5 6 6 6 7 7 8 7 9 8 10
(if x <= 0 then 1 else (2 * (2x - ((x + ((x + (x div 4)) div 2)) div ~2))))
A315655: 1 6 12 16 22 28 34 40 46 50 56 62 68 74 78 84
((loop(\(x,i).(5x2 + ~8x),(2x + 3),1) div 2) div 2)
A104284: 5813 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).2x,((x + ~1) - (2 * (2 + (x div 8)))),1) div 2) div 2)
A251746: 0 0 0 0 0 0 0 1 0 1 2 4 8 16 32 64
((loop(\(x,i).2x,x,(1 + (3 * (1 + ((x2 + ~x) div 2))))) div 2) div 2)
A300451: 1 2 7 26 88 272 784 2144 5632 14336 35584 86528 206848 487424 1134592 2613248
(2 * ((1 + (3 * loop(\(x,i).(x * (7 - i)),x,1))) div 2))
A036749: 4 18 90 360 1080 2160 2160
((loop(\(x,i).2x,x,(1 + (3 * ((x2 + 3x + 2) div 2)))) div 2) div 2)
A295288: 1 5 19 62 184 512 1360 3488 8704 21248 50944 120320 280576 647168 1478656 3350528
(x div (2 * (2 + (loop(\(x,i).2x,x,1) mod (1 + (x mod 12))))))
A337682: 0 0 0 0 0 0 1 1 0 1 1 0 3 3 2 3
(2 * ((1 + (3 * (x + loop(\(x,i).i,(x + ~9),1)))) div 2))
A194382: 4 6 10 12 16 18 22 24 28 30 34 40 46 52 58 64
((x + 1) div (if x <= 0 then 1 else (2 * (2 + ((x div 4) mod (1 + (x mod 3)))))))
A008678: 1 0 0 1 0 1 1 1 1 2 2 1 3 2 3 4
(4 * (1 + ((x + 2) div (1 + (if (x mod 6) <= 0 then 2 else (x mod 2))))))
A328184: 4 8 20 12 28 16 12 20 44 24 52 28 20 32 68 36
(2 + ((1 + loop(\(x,i).(24 div (x + 1)),2,(x + 1))) div 2))
A181742: 3 3 4 4 4 5 5 6 6 6 6 8 8 8 8 8
(((7 * (x + loop(\(x,i).i,(~2 + (x div 3)),1))) div 2) div 2)
A327212: 1 3 5 7 8 10 12 14 15 17 19 21 24 26 28 31
(loop(\(x,i).(2x + 2),x,(((x + ~1) mod (1 + (x mod 6))) mod 2)) div 2)
A329625: 0 1 5 7 23 31 63 127 383 511 1023 2047 4095 8191
loop(\(x,i).((2x + 3) * (1 + (2 * ((4x + 1) + i)))),2,2)
A122036: 351351
(2 * ((1 + ((loop(\(x,i).2x,x,(~2 + ((x2 + ~x) div 2))) div 2) div 2)) div 2))
A076616: 0 0 0 2 16 64 208 608 1664 4352 11008 27136 65536 155648 364544 843776
((2 + ((x2 + ~x) div (1 + (2 * (2 + (if (~2 + (x div 2)) <= 0 then x else 2)))))) div 2)
A049811: 1 1 1 1 1 1 2 3 4 5 6 7 8 9 11 12
(((5 * (if ((x + 1) mod 4) <= 0 then (x div 3) else 1)) div 2) div 2)
A318812-A317176: 1 1 1 1 1 1 1 2 1 1 1 3 1 1 1 6
(loop(\(x,i).7x,(x + 2),1) div 20)
A037754: 2 17 120 840 5882 41177 288240 2017680 14123762 98866337 692064360 4844450520 33911153642 237378075497 1661646528480 11631525699360
loop(\(x,i).(2 + ((x + ~1) mod 9)),x,20)
A118295: 20 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8
(if ((x + 1) mod 5) <= 0 then 0 else (1 - (2 * ((x div 5) mod 2))))
A099443: 1 1 1 1 0 ~1 ~1 ~1 ~1 0 1 1 1 1 0 ~1
(if (x mod 3) <= 0 then 1 else ((x mod (2 + ((~x + 1) mod (1 + (x div 4))))) div 2))
A060398: 1 0 0 1 0 0 1 0 0 1 0 1 1 0 2 1
((if x <= 0 then 1 else 6x) - ((((x + 1) - (x div 4)) div 2) div 2))
A315709: 1 6 12 17 23 29 35 41 47 52 58 64 70 76 81 87
(4 * ((1 + (4 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 3))
A108269: 4 12 16 20 28 36 44 48 52 60 64 68 76 80 84 92
(4 * (((2x + 1) * loop(\(x,i).6x,x,2)) div 3))
A229505: 0 48 480 4032 31104 228096 1617408 11197440 76142592 510603264 3386105856 22251552768 145118822400 940369969152 6060162023424 38868625391616
(4 + (loop(\(x,i).((x + 1) - (((x div 2) div ~2) div 2)),x,1) div 3))
A120197: 4 4 5 6 6 7 8 9 10 11 13 14 16 18 20 23
(((x + (3 * (if (x mod 8) <= 0 then 1 else 2)) - (x div 2)) div 2) div 2)
A326702: 0 1 1 2 2 2 2 2 1 2 2 3 3 3 3 3
(if x <= 0 then 1 else ((2x + 2) - ((x mod (2 + (((x + 1) div 2) div 3))) div 2)))
A231407: 1 4 6
A284913: 1 4 6 8 10 11 14 16 17 20 22 23 26 28 29 31
(~2 + (if x <= 0 then 1 else (2 * ((32x + 4) div 3))))
A063327: ~1 22 42 64 86 106 128 150 170 192 214 234 256 278 298 320
(4 * ((4 * (if (~4 + (x div 2)) <= 0 then x else (x + 2))) div 3))
A342642-A036993: 0 4 8 16 20 24 32 36 40 48 64 68 72 80 84 88
(4 + ((2 + loop(\(x,i).((x + 2) + (x div 8)),x,2)) div 3))
A120198: 5 6 6 7 8 9 10 11 13 14 16 18 20 23 26 29
((if x <= 0 then 0 else 1) - (2 * (((x - ((x2 div 2) mod (x + 2))) div 3) mod 2)))
A011588: 0 1 1 ~1 1 1 ~1 1 1 1 1 ~1 ~1 ~1 1 ~1
loop(\(x,i).x6,1,(12x + 4))
A017574: 4096 16777216 481890304 4096000000 19770609664 68719476736 192699928576 464404086784 1000000000000 1973822685184 3635215077376 6327518887936 10509215371264 16777216000000
(loop(\(x,i).(x + (5x div (1 + i))),2x,6) div 2)
A053132: 3 28 126 396 1001 2184 4284 7752 13167 21252 32890 49140 71253 100688 139128 188496
((1 + (x div 2)) div (2 + (if (x mod 2) <= 0 then ((x * (x div 3)) mod 3) else 2)))
A070091: 0 0 1 0 1 0 2 1 1 1 3 1 3 1 2 2
(2 * (if x <= 0 then 1 else (2 * ((2x + 1) - ((x div 3) + (x div ~2))))))
A295822: 2 16 24 32 40 52 56 68 76 84 92 104 108 120 128 136
((if x <= 0 then 1 else (2 + ((1 + ((1 + (x div 3)) div 2)) * (x div 3)))) div 2)
A108711: 0 1 1 2 2 2 3 3 3 5 5 5 7 7 7 11
(2 + (loop(\(x,i).(1 + (x div 2) - (2 * (x mod 2))),3,(x + 3)) div 2))
A280055: 1 2 1 2 3 1 2 3 2 3 1 2 3 2 3 4
(4 + loop(\(x,i).(24x2 + 1),2x,1))
A219011: 5 15005 4611686018427387903
((loop(\(x,i).x3,1,((2x + 1) * (1 - (2 * (x mod 2))))) div 2) div 2)
A305290: 0 ~7 31 ~86 182 ~333 549 ~844 1228 ~1715 2315 ~3042 3906 ~4921 6097 ~7448
loop(\(x,i).x6,1,(~7x + ~4))
A017034: 4096 1771561 34012224 244140625 1073741824 3518743761 9474296896 22164361129 46656000000 90458382169 164206490176 282429536481 464404086784 735091890625 1126162419264 1677100110841
(2 + (((if (((x + ~1) div 2) mod 3) <= 0 then 1 else (x + ~1)) mod (1 + (x div 2))) mod 2))
A334796: 2 2 3 2 2 3 3 3 3 3 3 2 2 3 3 2
((x div 2) - ((x - ((if x <= 0 then 2 else (6 mod (1 + (x div 2)))) div 2)) div 2))
A245037: 1 0 0 0 0 0 1 0 0 0 0 0 2 1 2 1
((if (~x + 2) <= 0 then (2 + ((x * (x div 2)) mod 2)) else 1) + (((1 + (x div 2)) div 2) div 2))
A137266: 1 1 2 3 2 2 3 4 3 3 3 4 3 3 4 5
(2 + (loop(\(x,i).(2x + 1),((x2 + 4x + 4) div 2),(1 + (x mod 2))) div 2))
A209529: 5 25 257 6145 262145 25165825 4294967297 1649267441665 1125899906842625 1729382256910270465 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(4 * loop(\(x,i).(10x + 81),x,1))
A177114: 4 364 3964 39964 399964 3999964 39999964 399999964 3999999964 39999999964 399999999964 3999999999964 39999999999964 399999999999964 3999999999999964 39999999999999964
(4 * (1 + loop(\(x,i).(x + 1),(~4 + ((x + ((x div 2) mod 2)) div 2)),x)))
A085127: 4 8 12 16 20 24 28 32 36 40 48 56 60 64 72 80
((((x + 1) * (~1 + (2 * loop(\(x,i).(x2 + 2),2,5)))) div 2) div 2)
A033171: 365 730 1095 1461 1826 2191 2556 2922 3287 3652 4017 4383 4748 5113 5478 5844
((((x + 1) * ((3x + 3) + (if (~2 + (x div 2)) <= 0 then 1 else 0))) div 2) div 2)
A341299: 1 3 7 13 20 28 36 48
(((loop(\(x,i).((~2x + 1) - (x div 4)),x,3) mod (x + 1)) div 2) div 2)
A116900: 0 0 0 0 1 0 0 0 1 1 1 0 2 0 2 1
(2 + loop(\(x,i).(28x + 6),(x + 1),2))
A005609: 64 1744 48784 1365904 38245264 1070867344 29984285584 839559996304 23507679896464 658215037100944 18430021038826384 516040589087138704 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x2 + x),1,((3x2 + 11x + 8) div 2)) div 2)
A024391: 10 66 231 595 1275 2415 4186 6786 10440 15400 21945 30381 41041 54285 70500 90100
(2 + (x div ((x + 2) div (2 + (loop(\(x,i).x3,2,2x) mod (x + 1))))))
A076618: 2 3 4 3 6 7 8 3 4 11 12 7 14 15 16 3
(if x <= 0 then 1 else ((2x + 4) + (7 * (1 + (x div 2)))))
A132131: 1 13 22 24 33 35 44 46 55 57 66 68 77 79 88 90
(if x <= 0 then 1 else (2 * (2x + ((x div (4 + (x mod 2))) + ((x + 1) div 2)))))
A315339: 1 6 10 16 22 28 32 38 44 48 54 60 66 70 76 82
(8 * (~3 + loop(\(x,i).(8x + 8),(x + 1),1)))
A132434: 104 1064 8744 70184 561704 4493864 35951144 287609384 2300875304 18407002664 147256021544 1178048172584 9424385380904 75395083047464 603160664379944 4825285315039784
(8 * (~3 + loop(\(x,i).10x,(x + 1),1)))
A175602: 56 776 7976 79976 799976 7999976 79999976 799999976 7999999976 79999999976 799999999976 7999999999976 79999999999976 799999999999976 7999999999999976 79999999999999976
(((((x + 5) * loop(\(x,i).2x,(x + ~1),(x + 2))) div 2) div 2) div 2)
A128183: 1 2 7 20 54 140 352 864 2080 4928
(4 + (if x <= 0 then 2 else (1 - ((((x2 + ~x) div 3) mod 3) div 2))))
A050815: 6 5 5 4 5 5 5 4 5 5 5 5 4 5 5 5
(if x <= 0 then 1 else (2 + ((x mod (~2 + ((1 - (2 * (x div 3))) div 3))) div 2)))
A072550: 1 1 2 2 1 1 2 1 1 0 1 1 0 1 1 2
(((loop(\(x,i).4x,x,(5x + 3)) div 2) div 2) div 2)
A229278: 0 4 26 144 736 3584 16896 77824 352256 1572864 6946816 30408704 132120576 570425344 2449473536 10468982784
(8 * (3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A240068: 24 32 48 64 96 112 144 160 192 240 256 304 336 352 384 432
(4 + (if x <= 0 then 1 else (2 * (7x - (x div 3)))))
A063125: 5 18 32 44 58 72 84 98 112 124 138 152 164 178 192 204
(loop(\(x,i).(x * (1 + (x div 3))),1,((x + 2) - ((x mod 3) div 2))) div 2)
A287195: 1 3 3 5 9 9 12 18 18 22 30 30 35 45 45 51
(8 * (1 + compr(\x.(loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 4),x)))
A106841: 8 16 32 40 64 72 80 104 128 136 144 160 168 200 208 232
(if (x mod 2) <= 0 then 1 else (2 + ((x mod (2 + ((x2 div 4) mod (x + 1)))) div 2)))
A089242: 1 2 1 3 1 2 1 2 1 2 1 3 1 2 1 4
compr(\x.(~1 + (x mod 9)),((if x <= 0 then 2 else (((x + 1) div 2) div 2)) div 2))
A288683: 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 9
(1 + (if ((x + 1) mod 4) <= 0 then x else 2x) - (2 * (((x + 1) div 2) div 2)))
A026208-A026184: 1 3 5 2 7 9 11 4 13 15 17 6 19 21 23 8
((((loop(\(x,i).((x + 1) + (x div (2 + (x mod 3)))),x,0) div 2) div 2) div 2) div 2)
A342684: 0 0 0 0 0 0 0 0 1 1 2 3 4 6 7 11
((x + 1) div (if x <= 0 then 1 else (2 * (2 + (((x - (x2 div 3)) div 2) mod 2)))))
A212295: 1 0 0 1 0 1 1 1 1 1 2 2 3 3 3 4
((1 + (x mod 2)) mod (if x <= 0 then 1 else (2 + (((x - ((~1 + (x div 2)) div 2)) div 2) mod 2))))
A272356: 0 2 1 2 1 0 1 2 1 0 1 0 1 2 1 0
(4 + ((loop(\(x,i).((x + 2) + (x div 9)),x,1) div 2) div 2))
A120205: 4 4 5 5 6 7 7 8 9 10 11 12 14 15 17 19
(if x <= 0 then 2x else (1 - (2 * (((((x + ~1) * (x div ~2)) div 2) div 2) mod 2))))
A011622: 0 1 ~1 ~1 1 ~1 1 1 ~1 1 1 ~1 ~1 ~1 ~1 1
(6 + (if x <= 0 then 1 else (4 * (4x - (x div ~2)))))
A063153: 7 26 42 62 78 98 114 134 150 170 186 206 222 242 258 278
(2 + (if x <= 0 then 1 else ((x + 2) - ((~x + 1) div (4 + ((x div 4) mod 2))))))
A131903: 3 5 7 8 9 10 11 13 14 15 17 18 19 20 21 22
((loop(\(x,i).2x,(x + ~1),(2 + ((x2 + 5x + 6) div 2))) div 2) div 2)
A139629: 1 2 6 17
A190050: 1 2 6 17 46 120 304 752 1824 4352 10240 23808 54784 124928 282624 634880
(6 + (loop(\(x,i).(~x + 17),x,(x + 2)) div 2))
A122874: 7 13 8 12 9 11 10 10 11 9 12 8 13 7 14 6
(2 div (2 + (if x <= 0 then 0 else (2 - ((x + 1) mod (2 + (x div (4 + (x mod 2)))))))))
A343914: 1 0 0 0 1 0 0 1 0 0 2 0 2 1 0 0
((if x <= 0 then 1 else 6x) - ((x - (x div ~7)) div 2))
A314148: 1 5 11 16 22 27 33 38 43 49 54 60 65 71 76 81
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) mod 16)
A289682: 1 1 2 5 14 10 4 13 6 14 12 2 12 4 8 13
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 16)
A193063-A165132: 2 3 5 7 11 13
A039714: 2 3 5 7 11 13 1 3 7 13 15 5 9 11 15 5
(~2 + loop(\(x,i).(x + (7x div (1 + i))),x,8))
A166812: 6 34 118 328 790 1714 3430 6433 11438 19446 31822 50386 77518 116278 170542 245155
(2 + (if x <= 0 then 1 else ((3x + 5) - ((x + (x div 2)) div 4))))
A022415: 3 10 13 15 18 21 23 26 28 31 34 36 39 42 44 47
((x + 1) mod (4 + ((if (x mod 2) <= 0 then (x div 2) else 2x) mod (x + 4))))
A030548: 1 2 3 4 5 1 0 1 1 1 2 1 3 1 4 1
(2 + ((loop(\(x,i).(x2 + x),1,((x3 + x2) + (x mod 2))) div 2) div 2))
A175172: 2 5 41 353
(~2 + ((1 + ((if ((x + ~2) mod 5) <= 0 then 2 else 0) + (x mod 2))) mod 4))
A123737: ~1 0 1 0 ~1 0 ~1 ~2 ~1 0 ~1 0 1 0 ~1 0
(8 + (if ((x + 2) mod (4 + ((x div 4) mod 2))) <= 0 then 2 else 1))
A118662: 9 9 10 9 9 9 9 9 9 9 10 9 9 10 9 9
loop(\(x,i).(x + (7x div (1 + i))),2x,8)
A053129: 8 120 792 3432 11440 31824 77520 170544 346104 657800 1184040 2035800 3365856 5379616 8347680 12620256
(if x <= 0 then 1 else (2 * (3x - ((x + ((x div 2) mod 4)) div 4))))
A315651: 1 6 12 16 22 28 32 38 44 50 56 60 66 72 76 82
(loop(\(x,i).2x,((x div 2) - ((x + ~1) div 3)),1) div (2 + (x mod 4)))
A147787: 1 0 0 0 1 0 1 0 2 1 1 0 4 1 2 1
(loop(\(x,i).((x3 + ~3x2 + 2x) div 3),1,(x2 div 4)) div 2)
A217482: 0 0 0 0 4 20 84 220 560 1140 2300 4060 7140 11480 18424 27720
(2 * ((x + 4) + (if (x + ~1) <= 0 then 0 else (1 + ((x + 1) div 5)))))
A100319: 8 10 14 16 20 22 24 26 28 32 34 36 38 40 44 46
(4 * (~2 + loop(\(x,i).(12x + 8),2,3x)))
A157263: 408 2136 3864 5592 7320 9048 10776 12504 14232 15960 17688 19416 21144 22872 24600 26328
loop(\(x,i).x6,1,(12x + 8))
A017622: 262144 64000000 1073741824 7256313856 30840979456 98867482624 262144000000 606355001344 1265319018496 2436396322816 4398046511104 7529536000000 12332795428864 19456426971136 29721861554176 44151665987584
(2 + (x mod (1 - (x div (~1 - ((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)))))))
A197862: 2 3 2 5 3 7 2 3 5 11 3 13 7 5 2 17
((4x + 2) + (if ((x div 4) - (x mod 5)) <= 0 then 1 else 2))
A292657: 3 7 11 15 19 24 27 31 35 39 44 48 52 55 59 64
(((x + 2) div (2 + ((if ((x + ~2) mod 5) <= 0 then 0 else 1) + (x mod 2)))) div 2)
A070094: 0 0 1 0 1 0 1 1 1 1 2 1 3 1 2 2
loop(\(x,i).4x,(((3 * (x + (x div 4))) - (x mod 2)) div 2),2)
A038533: 2 8 128 512 32768 131072 2097152 8388608 2147483648 8589934592 137438953472 549755813888 35184372088832 140737488355328 2251799813685248 9007199254740992
(loop(\(x,i).(1 + (2 * (x - (4 * (~x + (x mod 2)))))),x,(2 + (x mod 2))) div 2)
A290661: 1 11 101 1111 10111 111111 1011111 11111111 101111111 1111111111 10111111111 111111111111 1011111111111 11111111111111 101111111111111 1111111111111111
((1 + ((2 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 5)) mod 4)
A217743: 1 1 1 1 2 1 2 1 3 2 3 1 3 2 0 1
(((x + ~1) + ((if x <= 0 then 1 else x) mod 11)) mod 4)
A307193: 0 1 3 1 3 1 3 1 3 1 3 2 0 2 0 2
(loop(\(x,i).(x + (x div 3)),x,36) div 4)
A120154: 9 12 16 21 28 37 50 66 88 118 157 209 279 372 496 661
(((4x + ~4) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))) mod 4)
A119387: 0 0 1 0 2 1 2 0 3 2 3 1 3 2 3 0
(4 * ((x + 2) + (if (x div 2) <= 0 then (1 + (8 * (x mod 2))) else 1)))
A124351: 12 48 20 24 28 32 36 40 44 48 52 56 60 64 68 72
(((x2 + x) + loop(\(x,i).(2 * (x - (x div ~4))),x,1)) mod 4)
A024713: 1 2 0 2 2 0 2 0 0 2 0 2 2 2 0 0
((if x <= 0 then 1 else 6x) - ((x + ((x div 2) mod 4)) div 4))
A315704: 1 6 12 17 23 29 34 40 46 52 58 63 69 75 80 86
((if x <= 0 then 1 else 5x) - ((x + ((x div 2) mod 4)) div 4))
A313561: 1 5 10 14 19 24 28 33 38 43 48 52 57 62 66 71
((if x <= 0 then 1 else 5x) - ((~x + ((x div 2) mod 4)) div 4))
A315469: 1 6 11 16 21 26 31 36 42 48 53 58 63 68 73 78
((x + 4) + ((if ((1 + (x div 2)) mod 6) <= 0 then 0 else 1) + (x div 2)))
A158698: 5 6 8 9 11 12 14 15 17 18 19 20 23 24 26 27
(x - ((1 + (if (x mod ((x + ~2) - (x mod 3))) <= 0 then 0 else 1)) * (x div 4)))
A280026: 0 1 2 3 3 4 4 5 6 5 6 7 6 7 8 9
((if x <= 0 then 1 else (x div (3 * (8 - (x div 2))))) + (x div 4))
A008484: 1 0 0 0 1 1 1 1 2 2 3 3 5 5 7 8
loop(\(x,i).x6,1,(10x + 4))
A017322: 4096 7529536 191102976 1544804416 7256313856 24794911296 68719476736 164206490176 351298031616 689869781056 1265319018496 2194972623936 3635215077376 5789336458816 8916100448256
(2 + ((x + (3 * (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))) div 2))
A329486: 2 4 3 8 4 6 5 16 6 8 7 12 8 10 9 32
loop(\(x,i).x7,1,(6x + 4))
A016963: 16384 10000000 268435456 2494357888 13492928512 52523350144 163840000000 435817657216 1028071702528 2207984167552 4398046511104 8235430000000 14645194571776 24928547056768
(2 + (((x + 1) + loop(\(x,i).(2x + ((x + 1) div 5)),2,x)) div 2))
A189457: 2 5 8 10 14 17 19 22 25 29 31 34 37 39 43 46
(2 + (if x <= 0 then 1 else ((x + 2) + ((3 * ((1 + (x div 2)) div 3)) div 2))))
A080943-A052294: 3 5 6 7 9 10 11 12 13 14 17 18 19 20 21 22
((x + 4) + (if (x + ~1) <= 0 then x else (2 + (((x + ~1) div 5) mod 2))))
A047748: 4 6 8 9 10 11 13 14 15 16 17 17 18 19 20 21
((if x <= 0 then 1 else x) mod (2 + (((x + 2) + ((x - ((x div 4) mod 2)) div 2)) div 2)))
A075011: 1 1 2 3 4 5 6 7 8 0 0 0 1 1 1 1
(2 + (if x <= 0 then 1 else ((x + 2) + ((x - (2 div (8 - (x div 2)))) div 2))))
A185602: 3 5 7 8 10 11 13 14 16 17 19 20 21 23 24 25
(x - ((x - ((x + (loop(\(x,i).(2x2 + ~1),(x div 2),x) div 2)) div 2)) div 2))
A145996: 0 1 2 4 243
loop(\(x,i).x2,1,(2 + ((4x + (x2 div 4)) div (x + 2))))
A248928: 4 9 16 16 25 25 36 36 36 49 49 49 64 64 64 64
((2x + 4) + (if ((1 + ((x + (x div 2)) div 2)) mod 5) <= 0 then 2 else 1))
A241835: 5 7 9 11 13 15 18 19 21 23 25 27 30 32 33 35
((2x + 4) + ((1 - (loop(\(x,i).(2x + 2),x,2) mod (x + 2))) div (x + 1)))
A138966: 5 6 7 10 11 14 15 17 19 22 23 26 27 29 31 34
((2x + 4) + (if x <= 0 then 1 else ((3 * ((x + 2) + (x mod 2))) - (x div 2))))
A178365: 5 18 19 27 28 36 37 45 46 54 55 63 64 72 73 81
(2 * (2x + (if ((2x mod 7) - (x mod 2)) <= 0 then 2 else 1)))
A287375: 4 6 10 14 18 22 26 32 34 38 42 48 50 54 60 62
(if x <= 0 then 1 else (2 * (2x + ((2 * (x + ((x div 3) mod 2))) div 3))))
A310525: 1 4 10 16 22 28 32 36 42 48 54 60 64 68 74 80
(if x <= 0 then 1 else (2 * (2x + ((x + ((x div 3) mod 3)) div 3))))
A312555: 1 4 8 14 18 24 28 34 38 42 46 50 56 60 66 70
(if x <= 0 then 1 else (2 * (2x + ((1 + ((x - ((x div 4) mod 2)) div 2)) div 2))))
A310370: 1 4 10 14 18 22 26 32 36 40 46 50 54 58 62 68
(if x <= 0 then 1 else (2 * (2x + ((x - ((x + (x div 3)) div 3)) div 2))))
A310371: 1 4 10 14 18 22 28 32 36 40 46 50 54 60 64 68
(if x <= 0 then 1 else (2 * (2x + (x div (4 + ((x div 2) div 5))))))
A311593: 1 4 8 12 18 22 26 30 36 40 44 48 52 56 60 66
(if x <= 0 then 1 else (2 * (2x + ((x - (2x div ~7)) div 2))))
A315329: 1 6 10 16 22 26 32 36 42 48 52 58 64 68 74 80
(if x <= 0 then 1 else (2 * (2x + ((x + ((1 - (x div 2)) mod 4)) div 4))))
A311625: 1 4 8 12 18 24 28 32 36 40 44 48 54 60 64 68
(if x <= 0 then 1 else (2 * (2x + (2x div (2 + (4x div (x + 2)))))))
A310408: 1 4 10 14 20 24 28 32 38 42 48 52 56 62 66 72
(if x <= 0 then 1 else (2 * (2x + ((x + ((x + ((x div 2) mod 4)) div 2)) div 2))))
A310530: 1 4 10 16 22 28 34 40 44 48 54 60 66 72 78 84
(4x + (if (~2 + (x div 4)) <= 0 then 1 else ((x + 2) div 5)))
A314668: 1 5 9 13 17 21 25 29 33 37 41 45 50 55 59 63
(4x + (if x <= 0 then 1 else (x div (2 - (x div (~1 + ((~x + 2) div 4)))))))
A311422: 1 4 8 12 17 21 25 29 33 37 41 46 50 54 58 63
(4x + (if x <= 0 then 1 else ((2 * (x - ((x div 2) div 3))) div 3)))
A313045: 1 4 9 14 18 23 27 32 36 41 46 50 54 59 64 68
(4x + (if x <= 0 then 1 else ((2 * ((x - (x div 4)) div 2)) div 3)))
A311263: 1 4 8 12 16 21 25 30 34 38 42 46 50 55 59 64
(4x + (if x <= 0 then 1 else ((2 * (x + ((x div 3) mod 2))) div 3)))
A313110: 1 4 9 14 19 24 28 32 37 42 47 52 56 60 65 70
(4x + (if x <= 0 then 1 else ((x + ((x div 4) mod 3)) div 3)))
A058759: 1 4 8 13
A311924: 1 4 8 13 17 22 26 30 35 39 44 48 52 56 60 65
((x div (4 + ((x div 2) div 5))) + (if x <= 0 then 1 else 4x))
A311434: 1 4 8 12 17 21 25 29 34 38 42 46 50 54 58 63
(((x + ((1 - (x div 2)) mod 4)) div 4) + (if x <= 0 then 1 else 4x))
A311501: 1 4 8 12 17 22 26 30 34 38 42 46 51 56 60 64
((2x div (2 + (4x div (x + 2)))) + (if x <= 0 then 1 else 4x))
A312927: 1 4 9 13 18 22 26 30 35 39 44 48 52 57 61 66
(x + (if x <= 0 then 1 else 4x) - ((~x + (((x div 2) div 3) mod 2)) div 2))
A315522: 1 6 11 17 22 28 33 38 44 49 55 60 66 72 77 83
(((x + ((x + ((x div 2) mod 4)) div 2)) div 2) + (if x <= 0 then 1 else 4x))
A313115: 1 4 9 14 19 24 29 34 38 42 47 52 57 62 67 72
(x + (((x - (x div 12)) div 2) + (if x <= 0 then 1 else 4x)))
A314149: 1 5 11 16 22 27 33 38 44 49 55 60 65 71 76 82
(x + (((x + ((x div 2) mod 4)) div 4) + (if x <= 0 then 1 else 4x)))
A313875: 1 5 10 16 21 26 32 37 42 47 52 58 63 68 74 79
(1 + ((if (x mod 3) <= 0 then (2 * ((x div 4) mod 2)) else 1) + ((x div 2) mod 2)))
A304689: 1 2 3 2 2 2 4 3 2 1 3 3 3 2 3 4
(if x <= 0 then 1 else (2 * ((1 + ((x + (2 * (x mod 2))) div 5)) * (x mod 2))))
A082519: 1 2 0 4 0 4 0 4 0 6 0 6 0 8 0 8
(((3 * (if (~4 + (x div 2)) <= 0 then 1 else (x div 4))) - (x mod 2)) div 2)
A061901: 1 1 1 1 1 1 1 1 1 1 3 2 4 4 4 4
((1 + (x div (2 + (x mod 2)))) mod loop(\(x,i).3x,((x div 2) - (x mod 2)),2))
A291273: 1 1 2 0 3 2 4 3 5 4 6 4 7 5 8 6
((if (~x + 2) <= 0 then (((~x * (x div 2)) div 2) mod 3) else 1) mod (2 + (x mod 2)))
A085491: 1 1 0 1 0 1 0 1 0 0 0 2 0 0 0 1
((if (x mod 4) <= 0 then ((1 - (x div 3)) mod 3) else 1) - (2 * (x mod 2)))
A323191: 1 ~1 1 ~1 0 ~1 1 ~1 2 ~1 1 ~1 0 ~1 1 ~1
loop(\(x,i).((x + 1) - (x div (~1 + ((1 - (2 * (x div 3))) div 3)))),x,2)
A088907: 2 5 9 13 18 23 28 33 39 44 50 56 62 68 74 80
((x + 2) + loop(\(x,i).x2,1,(x + ~39)))
A073104: 1523 1447 1373 1301 1231 1163 1097 1033 971 911 853 797 743 691 641
((x + (if (x + ~1) <= 0 then 1 else ((2x + 1) - ((x + ~2) mod 5)))) div 2)
A326754: 0 1 3 4 5 6 7 11 12 13 14 15 18 19 20 21
(2 div (2 + (x * (if (x mod 2) <= 0 then (2 - ((x2 + x) mod 8)) else 1))))
A091069: 1 0 ~1 0 ~1 0 1 0 0 0 ~1 0 ~1 0 1 0
((x + 2) + ((2 * (1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2)))) div 5))
A284934: 2 3 5 6 8 9 11 13 14 15 17 18 20 21 22 24
((x + 2) + ((((((x + ~1) div 2) div 2) * (if x <= 0 then 1 else x)) div 2) div 5))
A234321: 1 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21
loop(\(x,i).x7,1,(5x + 2))
A016879: 128 823543 35831808 410338673 2494357888 10460353203 34359738368 94931877133 230539333248 506623120463 1028071702528 1954897493193 3521614606208 6060711605323 10030613004288 16048523266853
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(5x + 2))
A053368: 2 7 24 85 308 1134 4224 15873 60060 228514 873392 3350802 12896744 49774300 192559680 746503065
(if x <= 0 then 1 else (2 + compr(\x.(1 - (x mod (1 - (x div (~1 + ((~x + 2) div 4)))))),x)))
A231407: 1 4 6
A079000: 1 4 6 7 8 9 11 13 15 16 17 18 19 20 21 23
(((x + 1) + (((x * loop(\(x,i).((x + 1) + (x div 2)),(x + ~2),0)) div 2) div 2)) div 2)
A077373: 0 1 1 2 3 5 8 13 21 34 55 89
((x + 2) + (3 * (4 + (if (x + ~12) <= 0 then 1 else 2))))
A297287-A296757: 17 18 19 20 21 22 23 24 25 26 27 28 29 33 34 35
loop(\(x,i).(6x + ((x + ((x div 2) mod 3)) mod 4)),x,2)
A037627: 2 15 90 542 3255 19530 117182 703095 4218570 25311422 151868535 911211210 5467267262 32803603575 196821621450 1180929728702
((loop(\(x,i).(x * (2 + i)),(3x + 2),1) div 2) div (3x + 2))
A028918: 3 252 113400 141523200 373621248000 1788898535424000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 - (loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(x + ~2),(~x + 1)) div 2))
A052473: 2 2 3 3 5 12 37 128 464 1718 6437 24312 92380 352718 1352080 5200302
(((x + 1) + compr(\x.((x div (1 + (if (x mod 2) <= 0 then 6 else 1))) mod 2),x)) div 2)
A138083: 0 1 2 4 5 6
A330330: 0 1 2 4 5 6 8 10 11 13 14 15 16 17 20 22
((x + 2) + ((1 + ((x + (if (x mod 4) <= 0 then 1 else 2)) div 3)) mod (x + 1)))
A028757: 2 3 6 7 8 10 11 13 14 15 17 18 19 21 22 23
loop(\(x,i).x6,1,(10x + 8))
A017370: 262144 34012224 481890304 3010936384 12230590464 38068692544 98867482624 225199600704 464404086784 885842380864 1586874322944 2699554153024 4398046511104 6906762437184 10509215371264
loop(\(x,i).((8x + 1) * (1 + (x mod 2))),1,((x2 + x) div 2))
A222740: 1 18 50 49 81 242 338 225 289 722 882 529 625 1458 1682 961
(((~x2 + x) + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,2)) div 2)
A289451: 1 1 1 2 8 32 117 408 1402 4826 16751
((x + loop(\(x,i).(x + ((1 + (8 * (x mod 2))) * (1 + i))),x,1)) div 2)
A175403: 0 10 24 26 29
(loop(\(x,i).((x + ~1) - (9 * ((~x + ~2) + (x mod 2)))),2,x) div 2)
A044040-A043260-A039437: 89 98 189 198 289 298 389 398 489 498 589 598 689 698 789 798
(((2x + ~1) mod loop(\(x,i).(1 + ((2 * (x + (i mod 2))) div 3)),2,x)) div 2)
A332998: 0 0 0 1 0 0 1 1 0 1 0 0 1 2 1 2
((x + 2) + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))))
A335876: 2 3 4 6 6 8 8 12 12 12 12 16 14 16 18 24
((x + ((3 * (((x + 1) * (2 + (if (~x + 2) <= 0 then x else 2))) div 2)) div 2)) div 2)
A024403: 1 3 5 9 13 18 24 30 37 45 54 64 74 85 97 109
((x + 2) + ((3 * (((if (~2 + (x div 2)) <= 0 then 1 else 2) + (x div 2)) div 2)) div 2))
A284885: 2 3 5 6 7 8 11 12 14 15 16 17 20 21 22 23
(loop(\(x,i).((x + ~1) + (20 * (1 + (x div 2)))),2,x) div 2)
A039492: 109 119 230 240 351 361 472 482 593 603 714 724 835 845 956 966
((x + 2) + (if x <= 0 then 1 else (2 * ((x + 1) + (4 * ((x + 1) + (x div 2)))))))
A319976: 3 23 42 53
(((x + 2) + ((if ((x div 2) mod 3) <= 0 then 1 else 2) + ((x div ~2) mod 2))) div 2)
A241151: 1 2 3 3 4 5 5 5 6 7 7 7 7 8 9 9
((x + 2) + (4 * (2 + (if (~1 + (x div 4)) <= 0 then x else 8))))
A210652: 10 15 20 25 30 35 40 45 50 51 52 53 54 55 56 57
(if x <= 0 then 1 else ((x + 2) + (x div (2 * (2 + (((1 + (x div 2)) div 2) mod 4))))))
A026469: 1 3 4 5 6 7 8 9 11 12 13 14 15 16 19 20
(2 * ((~x + 2) + ((2 + (x * loop(\(x,i).x3,1,(x + 3)))) div 2)))
A152390: 6 68 252 648 1370 2556 4368 6992 10638 15540 21956 30168 40482 53228 68760 87456
(x - ((2 - (if x <= 0 then 2 else (x + ((x + (x2 div 3)) div 4)))) div 2))
A278453: 0 1 2 4 6 8 10 12 15 17 19 22 25 27 30 33
(~2 + loop(\(x,i).x7,x,(3x + 4)))
A162927: 2 823541 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 + (x * ((x + 2) + (5 * (if (x mod 2) <= 0 then (x div 2) else 2x)))))
A143660: 2 15 20 107
loop(\(x,i).(10x + ((2x + 1) mod 5)),x,2)
A037722: 2 20 201 2013 20132 201320 2013201 20132013 201320132 2013201320 20132013201 201320132013 2013201320132 20132013201320 201320132013201 2013201320132013
((x + 2) + ((x + ((2 * (x + (if (x mod 3) <= 0 then 0 else 2))) div (x + 1))) div 2))
A050103: 2 5 6 7 9 10 11 13 15 16 18 19 20 22 24 25
(if x <= 0 then 1 else ((x + 2) + ((x + (((x - (x div 3)) mod 3) div 2)) div 2)))
A060462: 1 3 5 7 8 9 11 13 14 15 17 19 20 21 23 24
(2 + loop(\(x,i).x3,2x,(11x + 16)))
A271975: 18 7625597484989 4611686018427387903
((x + 2) + ((x + (if (x + ~4) <= 0 then 1 else ((~x + 1) div (2 + (x div 2))))) div 2))
A215069: 2 4 5 7 8 9 10 11 13 14 16 17 19 20 22 23
(2 + loop(\(x,i).(26x + 24),2,(x2 + 2x)))
A158639: 650 2678 6058 10790 16874 24310 33098 43238 54730 67574 81770 97318 114218 132470 152074 173030
(2 + loop(\(x,i).(34x + 32),2,(x2 + 2x)))
A158729: 1122 4590 10370 18462 28866 41582 56610 73950 93602 115566 139842 166430 195330 226542 260066 295902
((x2 + 2x + 2) * loop(\(x,i).7x,(x + 1),(x + 1)))
A128051: 14 490 10290 163268 2184910 26118078 288240050 2997696520 29780961966 285300001490 2653572489106 24083839729740 214124712999470 1870539234917542 16094233518706770 136653810502199312
loop(\(x,i).(36x + ~36),2,(x2 + 2x + 2))
A158737: 1260 5148 11628 20700 32364 46620 63468 82908 104940 129564 156780 186588 218988 253980 291564 331740
(2 * loop(\(x,i).((x2 + 2x + 1) + (2 * (x mod 2))),(x + ~1),(x + (x mod 2))))
A342467: 0 4 18 1356
((1 + (3 * (if (x mod (2 + (4 mod (x + 2)))) <= 0 then 2 else 0))) mod (x + 2))
A157964: 1 1 3 1 1 1 7 1 1 1 1 1 7 1 1 1
((1 + ((x + 1) mod (3 * (1 + (if (x + ~4) <= 0 then 0 else 2))))) mod (x + 2))
A024865: 0 0 1 2 3 0 0 0 1 2 3 4 5 6 7 8
((loop(\(x,i).((x2 + ~x) div 2),2,(1 + ((x + 1) div 2))) div 3) div (x + 2))
A325695: 0 0 0 0 0 0 0 1 1 3 2 5 5 8 7 12
((~x + ~2) + loop(\(x,i).((x + 1) + ((4x div (1 + i)) + i + i)),x,1))
A014309: ~1 3 15 40 84 154 258 405 605 869 1209 1638 2170 2820 3604 4539
(((x + 1) * ((x + 8) + (if (~2 + (x div 2)) <= 0 then 1 else 2))) div (x + 2))
A133576: 4 6 8 9 10 12 14 15 16 17 18 19 20 21 22 23
(if x <= 0 then 1 else (2 + ((x2 mod (x - ((~x + 2) div 2))) div (x + 2)) - (x mod 2)))
A082477: 1 1 2 1 2 1 2 2 2 1 2 1 2 2 3 1
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(x2 + 2)) div (x + 2))
A344191: 1 1 3 11 42 162 627 2431 9438 36686 142766 556206 2169268 8469060 33096195 129454695
(2x + (if x <= 0 then 1 else (x - (~3x2 div 5))))
A022948-A022945-A022443: 1 4 9 15 22 30 40 51 63 76 90 106 123 141 160 180
(2x + (3 * ((if x <= 0 then 1 else 2x) - ((x + (x div 2)) div 4))))
A188012: 3 8 16 21 29 37 42 50 55 63 71 76 84 92 97 105
(2x + loop(\(x,i).(x + i - ((2x + 1) div 7)),x,1))
A002004: 1 4 8 12 17 22 27 32 37 42 47 53 58 64 69 75
(2x + (((x + ~1) div (1 + (x div (2 + (if (x mod 3) <= 0 then 2 else 0))))) mod 2))
A231408: 1 2 4 6 9
A227132: 1 2 4 6 9 11 12 15 17 18 21 23 24 27 29 31
loop(\(x,i).((x + 1) + ((x - ((x + (x div 3)) div 3)) div 2)),2,2x)
A189752: 2 6 9 12 15 19 21 25 28 32 35 38 42 44 48 51
((3x + 1) + (x * loop(\(x,i).(7 * i),(x + ~1),x)))
A339623: 1 5 21 52 97 156 229 316 417 532 661 804 961 1132 1317 1516
loop(\(x,i).(1 - (2 * (((~x + 2) div (2 + (x div 5))) mod 2))),x,2x)
A011619: 0 1 ~1 1 1 1 ~1 ~1 ~1 1 ~1 1 1 1 1 1
(3x + (if x <= 0 then 1 else compr(\x.((x * (x mod 3)) mod 5),x)))
A315423: 1 6 11 15 21 25 30 36 42 47 51 57 61 66 72 78
((4x + 1) + loop(\(x,i).(x + (x div ((2 + i) * (1 + i)))),2,x))
A315470: 1 6 11 16 21 26 32 37 42 47 52 58 64 69 74 79
((if x <= 0 then 1 else (6x + (x div ~7))) - (x div 2))
A313892: 1 5 10 16 21 27 32 38 42 48 53 59 64 70 75 80
(((x - (if (x mod (2 + (2x mod (2 + (x div 2))))) <= 0 then 1 else 0)) mod 2) + (x div 2))
A305845: 1 1 1 2 3 3 3 4 4 5 5 6 7 7 7 7
(((if x <= 0 then 2 else (x - ((~1 + (x2 div 2)) div 5))) div 2) + (x div 2))
A260254: 1 1 2 2 3 3 4 4 5 5 5 5 5 4 4 3
(x + (((x - (x div (1 + (x mod 4)))) mod 2) + (if x <= 0 then 1 else 2) + (x div 2)))
A174047: 1 4 5 7 8 10 11 12 14 16 18 19 20 22 23 24
(1 + ((loop(\(x,i).((x + 1) + (x div 5)),x,1) div 2) div 2) - (x mod 2))
A239948: 1 0 1 1 2 1 3 2 4 4 6 6 9 9 12 14
(((x - (if ((4x + 2) mod (2 + (x div 2))) <= 0 then 1 else 0)) mod 2) - (x mod 2))
A244525: 1 ~1 0 0 0 0 0 ~1 0 0 1 0 0 0 0 0
((2 * (1 + (if (~4 + ((x + 1) mod 8)) <= 0 then 1 else 0))) - (x mod 2))
A106049: 4 3 4 3 2 1 2 3 4 3 4 3 2 1 2 3
((if ((x + 1) mod (1 + (x mod (1 + (2 * (2 + (x mod 2))))))) <= 0 then 1 else 2) + (x mod 2))
A271721: 1 2 1 2 1 2 2 2 2 3 1 3 2 2 1 2
((2 * (~1 + (loop(\(x,i).~2x,x,1) mod 7))) - (x mod 2))
A021017: 0 7 6 9 2 3 0 7 6 9 2 3 0 7 6 9
(2 * (loop(\(x,i).((x2 + ~x) div 2),(x + ~1),(1 + (x mod 3))) * (x mod 2)))
A297968: 0 4 0 0 0 6 0 0 0 0 0 6 0 0 0 0
(x div (2 + (((~1 + loop(\(x,i).4x,(x div 2),2)) mod (x + 1)) + (x mod 2))))
A285725: 0 0 0 0 1 1 2 0 0 2 3 1 4 3 1 0
(((loop(\(x,i).2x,(x + ~1),(2x mod 3)) mod (x + 1)) div 2) + (x mod 2))
A119612: 0 1 1 1 0 3 0 1 1 1 0 3 0 2 1 1
((2 * ((x - (if ((x div 3) mod 5) <= 0 then 0 else 1)) mod 2)) + (x mod 2))
A307195: 0 3 0 1 2 1 2 1 2 1 2 1 2 1 2 3
((2 * ((if (((x + ~1) div 2) mod 3) <= 0 then 1 else x) mod 6)) - (x mod 2))
A192225: 0 1 2 5
A131716: 0 1 2 5 8 9 0 1 2 5 8 9 0 1 2 5
(2 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),((x + 1) div 2)) + (x mod 2)))
A308598: 2 4 3 6 5 8 7 12 11 14 13 18 17 20 19 24
((x div (2 + (x div (2 + (if (x mod 2) <= 0 then ((x mod 3) div 2) else 2))))) + (x mod 2))
A280363: 0 1 1 2 1 2 1 3 2 3 1 3 1 3 2 4
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(x div 2),x) div (2 - (x mod 2)))
A037952: 0 1 1 3 4 10 15 35 56 126 210 462 792 1716 3003 6435
((x + 2) + ((if x <= 0 then 1 else (4 * (2x - (x div 3)))) + (x mod 2)))
A063244: 3 12 20 26 34 44 48 58 66 72 80 90 94 104 112 118
(x + ((if x <= 0 then 1 else (x - (((x - (x2 div 4)) div 2) div 2))) + (x mod 2)))
A282166: 1 3 4 7 8 12 13 17 18 22 24 28 30 35 37 42
((x * ((x + 1) + (2 * loop(\(x,i).(x + (2 * ((2 + i) * (~1 + i)))),x,0)))) div 2)
A302710: 0 1 19 90 266 615 1221 2184 3620 5661 8455 12166 16974 23075 30681 40020
((x * loop(\(x,i).((2x * (~1 + (2 * i))) div (2 + i)),x,3x)) div 2)
A220101: 0 1 6 27 112 450 1782 7007 27456 107406 419900 1641486 6418656 25110020 98285670 384942375
(2 * (x + loop(\(x,i).(1 + (((x2 + x) div 4) div 5)),2,x)))
A118081: 2 4 6 8 10 12 14 16 20 22 26 28 32 38
((x + ~2) + (if (x + ~1) <= 0 then 2 else (x + (2 * ((x + 1) div 7)))))
A328593: 0 1 2 4 6 8 12 14 16 18 20 22 24 28 30 32
((x + loop(\(x,i).((x + 3) + (8x div (x + 2))),2,x)) div 2)
A230457: 5 8 10 11 12 13 15 16 17 18 19 20 21 22 24 25
((x + ~2) + loop(\(x,i).(2 + ((x - (x div (~4 + ((x div 2) mod 2)))) div 2)),2,x))
A092253: 1 3 4 5 6 8 10 12
A288597: 1 3 4 5 6 8 10 12 13 14 16 17 18 20 21 22
((x + 2) + (if x <= 0 then 1 else ((x + 1) - ((x + 1) mod (2 + ((x + 1) mod 4))))))
A128036: 3 3 4 9 9 11 13 17 19
(1 - ((x * (1 - loop(\(x,i).i,(2 - (((x mod 4) + (x div 2)) div 2)),x))) div 2))
A305333: 1 2 1 4 1 1 16
((x2 + 2) * (if (x + ~1) <= 0 then 1 else (2x - ((x + 1) div 5))))
A057665: 2 3 24 66 126
(2 + (x2 div 2) - ((1 + (x mod 8)) mod (1 + (if x <= 0 then 1 else x))))
A115065: 1 2 4 6 10 14 20 26 33 40 49 58 69 80 93 106
(loop(\(x,i).(x5 + x3),1,x5) div 2)
A283029: 0 1 16793600 423651479175 562950490292224 149011627197265625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).((x + 1) - (((~x2 + x) mod (3 + (x div 2))) mod 2)),x,x) div 2)
A305117: 0 1 2 2 2 4 4 4 4 4 6 6 6 8 8 8
((2x + (if x <= 0 then 2 else (x + ((x div (2 + ((x div 2) div 3))) mod 2)))) div 2)
A099467: 1 1 3 5 6 7 9 10 12 14 15 17 18 20 21 23
((x * loop(\(x,i).(x7 + x3),1,x2)) div 2)
A168665: 0 1 16448 7175547 536879104 15258828125 235092632256 2373781166743 17592187092992 102945568438809 500000005000000 2088624094451411 7703510805209088 25592946538419637 77784047831612864
((x * loop(\(x,i).(x2 + x),1,x7)) div 2)
A170779: 0 1 16512 7177734 536903680 15258984375 235093332096 2373783637372 17592194433024 102945587570685 500000050000000 2088624191887266 7703511002284032 25592946914910739 77784048516800640
((x + 1) + (x mod (if ((x + (x div 2)) mod 5) <= 0 then 6 else 1)))
A300903: 1 2 3 4 5 6 7 9 9 10 15 12 13 14 15 16
(x * (1 + (5 * (if (~2 + (x mod (2 + (x mod 3)))) <= 0 then 2 else 0))))
A109052: 0 11 22 33 44 55 66 77 88 99 110 11 132 143 154 165
(x + (if (x + ~1) <= 0 then 2 else (1 + (((x2 + 4x + 4) div 2) div 5))))
A214780: 2 3 4 6 8 10 13 16 19 22 25 28 32 36 40 44
(x + loop(\(x,i).2x,((x - (x div (1 + ((x div 2) div 3)))) div 3),1))
A031143: 1 2 3 4 5 6 8 9 10 11 12 15 16 21 22 23
(~x + (if x <= 0 then 1 else (x - ((~x2 + x) div 19))))
A140953-A046676-A000607: 1 0 1 1 1 2 2 3 3 4 5 6 7 9 10 12
loop(\(x,i).(10x + 1),(8x + 9),x)
A068538: 111111111 111111111111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.((~x + 1) mod (1 + ((x div 2) mod (2 + (if (x mod 5) <= 0 then 2 else 0))))),x)
A100991-A075821: 0 1 3 4 7 8 9 11 12 13 16 17 19 21 23 24
compr(\x.(1 - (x mod (1 + (2 * (2x mod (1 + (if (x mod 4) <= 0 then 0 else 2))))))),x)
A013660: 1 2 5 7 11
A113543: 1 2 5 7 11 13 14 17 19 22 23 26 29 31 34 35
(~x + (if x <= 0 then 1 else (x - ((0 - (x2 div 3)) div 7))))
A140952: 1 0 1 1 1 2 2 3 3 4 5 6 7 8 10 11
loop(\(x,i).(4x + 3),2,(x + ((x div 2) div 7)))
A044457: 15 31 47 63 79 95 111 127 143 159 175 191 207 223 255 271
loop(\(x,i).(x3 + 7x2 + 14x + 8),1,7x)
A001547: 8 792 4320 12650 27840 51948 87032 135150 198360 278720 378288 499122 643280 812820 1009800 1236278
loop(\(x,i).x7,1,7x)
A016987: 0 823543 105413504 1801088541 13492928512 64339296875 230539333248 678223072849 1727094849536 3938980639167 8235430000000 16048523266853 29509034655744 51676101935731
((~x + 1) + (2 * (2 + ((if (~2 + (x div 3)) <= 0 then 1 else 2) + (x mod 3)))))
A114514: 7 8 9 4 5 6 1 2 3 0
(x + ((if (~2 + (x div 5)) <= 0 then 1 else 2) * (1 + (((x + 1) div 2) div 2))))
A037459: 1 2 3 5 6 7 8 10 11 12 13 15 16 17 18 25
(x + (27 * (if (~4 + (x div 2)) <= 0 then 0 else 2)))
A103303: 0 1 2 3 4 5 6 7 8 9
A004860: 0 1 2 3 4 5 6 7 8 9 64 65 66 67 68 69
loop(\(x,i).x5,1,(11x + 5))
A017453: 3125 1048576 14348907 79235168 282475249 777600000 1804229351 3707398432 6956883693 12166529024 20113571875 31757969376 48261724457 71008211968 101621504799 141985700000
loop(\(x,i).x5,1,(11x + 10))
A017513: 100000 4084101 33554432 147008443 459165024 1160290625 2535525376 4984209207 9039207968 15386239549 24883200000 38579489651 57735339232 83841135993 118636749824 164130859375
(5x + (if (x mod 2) <= 0 then 1 else (2x mod (1 + (x div 4)))))
A137002: 1 5 11 15
A314038: 1 5 11 15 21 25 31 35 41 45 51 56 61 67 71 77
((x + 1) - (((~x + 1) - (4 * (if (x + ~2) <= 0 then 0 else 2))) div 5))
A263800: 1 2 4 6 8 9 10
A168496: 1 2 4 6 8 9 10 11 12 14 15 16 17 18 20 21
(x + ((if (x + ~2) <= 0 then 1 else (2 + ((x div 2) div 3))) + (x div 5)))
A187319: 1 2 3 5 6 8 10 11 12 13 15 16 18 19 20 22
(~x + (if (~x + 2) <= 0 then (2 + ((x + ((x2 + 2x) div 8)) div 2)) else 1))
A217569: 1 0 1 1 1 1 2 2 3 3 4 5 6 7 9 10
compr(\x.((x + 1) mod (1 + (x mod (2 + (loop(\(x,i).(x + (i * i)),x,0) mod (x + 2)))))),x)
A067570: 0 1 2 3 4 5 7
A328668: 0 1 2 3 4 5 7 8 9 11 15 16 17 19 21 23
((2x + 1) - (x2 div (2 + (if (~4 + (x div 2)) <= 0 then x else (x + 2)))))
A225647: 1 3 4 6 7
A114316: 1 3 4 6 7 8 9 10 11 12 14 15 16 18 19 20
compr(\x.(1 - (x mod (1 + (2 * ((if (~2 + (x div 3)) <= 0 then 2 else 1) - (x mod 2)))))),x)
A276706: 1 2 4 5 6 7 8 10 14 16 20 22 26 28 32 34
(x + ((if ((x div (1 + (x div (2 + (x mod 2))))) mod 2) <= 0 then (x + ~1) else 1) mod 3))
A114010: 2 2 3 4 5 6 7 7 9 11 11 12 13 13 15 17
compr(\x.((1 + ((x * (if (x mod 5) <= 0 then 1 else 2)) mod 4)) mod 3),x)
A241662: 1 3 7 9 10 11 13 17 19 21 23 27 29 30 31 33
loop(\(x,i).x5,1,(11x + 3))
A017429: 243 537824 9765625 60466176 229345007 656356768 1564031349 3276800000 6240321451 11040808032 18424351793 29316250624 44840334375 66338290976 95388992557 133827821568
loop(\(x,i).x6,1,(7x + 3))
A017022: 729 1000000 24137569 191102976 887503681 3010936384 8303765625 19770609664 42180533641 82653950016 151334226289 262144000000 433626201009 689869781056 1061520150601 1586874322944
(~x + (3 * ((x + 1) + (x2 div (x + (if x <= 0 then 1 else (x div 3)))))))
A190551: 3 8 13 15 20 25 27 32 37 39 44 49 54 56 61 66
compr(\x.((2 + (x mod (1 + (2 * (if (x mod 6) <= 0 then 2 else 1))))) mod 3),x)
A231407: 1 4 6
A277572: 1 4 6 7 10 13 16 19 22 24 25 28 31 34 36 37
loop(\(x,i).(2 * (x - (5 * ((x div 5) mod 2)))),3,x)
A059631: 0 8 6 4 2 0 8 6 4 2 80 88 86 84 82 80
(x + (if x <= 0 then 1 else (3 * ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2))))
A329717: 1 1 2 3 4 8 6 7 8 12 10 14 12 16 17 15
loop(\(x,i).x5,1,(11x + 6))
A017465: 7776 1419857 17210368 90224199 312500000 844596301 1934917632 3939040643 7339040224 12762815625 21003416576 33038369407 50049003168 73439775749 104857600000 146211169851
loop(\(x,i).x6,1,(7x + 6))
A017058: 46656 4826809 64000000 387420489 1544804416 4750104241 12230590464 27680640625 56800235584 107918163081 192699928576 326940373369 531441000000 832972004929 1265319018496 1870414552161
(x + (if x <= 0 then 1 else ((((x + ~1) * ((x2 + ~2x) div 4)) div 2) div 3)))
A330640: 1 1 2 3 5 7 11 15 22 29 40 51 67 83 105 127
(x + ((4 * (1 + ((x + (if (~2 + (x div 2)) <= 0 then 1 else 0)) div 2))) div 3))
A324470: 1 3 4 7 8 10 11 12 14 15 18 19 21 22 24 25
compr(\x.(loop(\(x,i).((x + 1) + (2 * (x div 4))),(x div 4),2) mod 3),x)
A161627: 4 5 6 7 20 21 22 23 28 29 30 31 36 37 38 39
((3x + 1) + ((~x + 2) mod (2 + (if (x mod 5) <= 0 then 2 else 0))))
A332075: 3 5 7 11 13 17 19 23 25 29 31 35 37 41 43 49
loop(\(x,i).(~12x + 1),(10x + 1),x)
A015421: 1 ~685853880635 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~10x + 1),(10x + 1),x)
A015417: 1 ~90909090909 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) + (((x + 1) + ((x + (if (x mod 2) <= 0 then (x div 2) else 2)) div 4)) div 2))
A187474: 1 3 4 6 8 9 11 13 15 16 18 19 21 22 25 26
compr(\x.((x + 1) - (loop(\(x,i).5x,x,2) mod (3x + 2))),x)
A154663: 3 5 6 7 10 11
A232682: 3 5 6 7 10 11 12 13 14 15 17 19 20 22 23 24
(x + ((x * loop(\(x,i).((x2 + ~x) div 2),3,(x + ~2))) div (x + 3)))
A084811: 0 1 2 3 4 6 76
(x + (if x <= 0 then 1 else ((4x + ~1) + ((x + ~2) mod (3 - (x mod 2))))))
A095948: 1 5 9 15 21
A315075: 1 5 9 15 21 25 30 35 39 45 51 55 60 65 69 75
(~x + loop(\(x,i).(i - (~24x div (x + 1))),x,1))
A101104: 1 12 23 24 24 24 24 24 24 24 24 24 24 24 24 24
(x + ((x + 1) * loop(\(x,i).3x,(~1 + (2 * (2x div 3))),1)))
A136985: 1 3 11 111 139
compr(\x.(loop(\(x,i).x2,2,((4 * (x mod 2)) - (x mod 3))) mod (x + 1)),x)
A256882: 0 3 6 12 15 18 24 30 36 42 48 54 60 63 66 72
(x + (if x <= 0 then 1 else 4x) - (2 div (16 div (x + 1))))
A313720: 1 5 10 15 20 24 29 34 38 43 48 53 58 63 68 73
loop(\(x,i).x6,1,(9x + 8))
A017262: 262144 24137569 308915776 1838265625 7256313856 22164361129 56800235584 128100283921 262144000000 496981290961 885842380864 1500730351849 2436396322816 3814697265625 5789336458816
loop(\(x,i).x7,1,(5x + 4))
A016903: 16384 4782969 105413504 893871739 4586471424 17249876309 52523350144 137231006679 319277809664 678223072849 1338925209984 2488651484819 4398046511104 7446353252589 12151280273024
((x2 + 2x + 1) - ((x mod 10) mod (if x <= 0 then 1 else x)))
A194148: 1 4 9 16 25 36 49 64 81 100 121 143 167 193 221 251
(~x + loop(\(x,i).(x - (((x2 + ~x) div 2) div (x + 3))),3,(x + ~1)))
A194260: ~1 ~1 ~1 ~1 ~1 ~1 ~2 ~3 ~4 ~5 ~6 ~7 ~7 ~8 ~9 ~10
((9 * (x mod 11)) mod (if x <= 0 then 1 else x))
A061467: 0 0 0 0 0 0 0 0 0 0 0 0 9 5 13 6
(x + (2 * (1 - (if ((1 + (x div 3)) mod 4) <= 0 then (x mod 3) else 1))))
A330091-A329303: 0 1 2 3 4 5 6 7 8 11 10 9 12 13 14 15
(~x + ((x - (loop(\(x,i).(3x + ~6),x,0) div 7)) div 2))
A178704: 0 0 1 4 15 49 153 465 1402 4213 12648 37954 113874 341634 1024915 3074758
compr(\x.((if (x mod 9) <= 0 then 0 else (x + 1)) mod 10),x)
A092457: 0 9 18 19 27 29 36 39 45 49 54 59 63 69 72 79
(x + (if x <= 0 then 1 else (x - ((x - (((1 - (x div 2)) div 3) mod 3)) div 2))))
A168543: 1 2 3 5 7 9 10 12 13 15 16 17 19 20 22 23
loop(\(x,i).(((5x3 + 3x2 + ~2x) div 2) div 3),2,x)
A329756: 0 1 456 14976 181780 1273970 6293756 24395756 79119496 223821235 568280240 1321714636 2858876956 5817509516 11237224740 20751835560
(2x - (((1 + (if (x mod (2 + ((x + ~1) mod 3))) <= 0 then x else 0)) div 2) div 2))
A198033: 0 2 4 6 7 10 12 14 16 18 18 22 21 26 28 30
loop(\(x,i).(2 + ((x + 1) div 2) - ((~x + 3) div 9)),2,x)
A205837: 3 4 4 5 6 6 6 7 7 7 7 8 8 9 9 9
((x + 2) + ((x - ((if (~2 + (x div 2)) <= 0 then 2 else (x + ~2)) mod 5)) div 2))
A183544: 1 2 4 5 7 8 9 12 13 14 15 16 20 21 22 23
loop(\(x,i).((3 * (x - ((2x + 2) div ~5))) div 2),2,x)
A151875: 3 7 13 16 19 27
(x + (2 * ((x + (3 * (if (~2 + (x div 2)) <= 0 then 1 else 2)) - (x div 2)) div 2)))
A028726: 2 5 6 7 8 11
A283974: 2 5 6 7 8 11 14 17 18 19 20 23 24 25 26 29
loop(\(x,i).x5,1,(11x + 4))
A017441: 1024 759375 11881376 69343957 254803968 714924299 1680700000 3486784401 6590815232 11592740743 19254145824 30517578125 46525874176 68641485507 98465804768 137858491849
loop(\(x,i).x6,1,(9x + 4))
A017214: 4096 4826809 113379904 887503681 4096000000 13841287201 38068692544 90458382169 192699928576 377149515625 689869781056 1194052296529 1973822685184 3138428376721 4826809000000
((x + 4) + (if x <= 0 then 0 else ((x + 1) + (((~x + 2) div 8) mod 2))))
A248561: 4 7 9 12 14 16 18 20 22 24 26 27 29 31 33 35
(x + ((if (~2 + (x div 4)) <= 0 then 0 else 5) + (((x + 1) div 2) div 2)))
A138083: 0 1 2 4 5 6
A023733: 0 1 2 4 5 6 7 9 10 11 12 14 20 21 22 24
compr(\x.(2 - (2x mod (2 + (if (x + ~2) <= 0 then 1 else 2) - (x div ~4)))),x)
A298874-A298871: 1 4 5 7 8 9 10 12 13 14 15 17 19 20 21 22
((x + 4) + (((x + 1) - ((x - (if (x + ~2) <= 0 then 0 else 1)) mod 3)) div 2))
A037354: 4 5 6 8 10 11 12 15 16 17 19 20 21 24 25 26
(x + (if x <= 0 then 1 else (2 * (2x - ((((x + 1) - (x div 4)) div 2) div 2)))))
A177152: 1 5 10 13 18 23 28 33 38 41 46 51 56 61 64 69
(x + (8 * (if (2 - (x div 4)) <= 0 then 8 else (x + 1))))
A338090-A043485: 8 17 26 35 44 53 62 71 72 73 74 75 76 77 78 79
compr(\x.((((1 + loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,x)) div 2) div 2) mod 2),x)
A173025: 0 1 2 4 5 7 8 9 10 14 15 16 17 18 20 21
(x * ((((loop(\(x,i).((x + 1) + (x div (2 + (i mod 2)))),x,0) div 2) div 2) div 2) div 2))
A308989: 0 0 0 0 0 0 0 0 8 9 20 33 60 91 154 225
(x + (if x <= 0 then 1 else (2 + ((x - ((0 - (((~x + 2) div 2) mod 4)) div 2)) div 2))))
A344291-A231564: 1 3 5 7 9 10 11 13 14 15 17 19 21 22 23 25
compr(\x.(2 * ((1 + (x div (if (x mod 4) <= 0 then 4 else 1))) mod 8)),x)
A004215: 7 15 23 28 31 39 47 55 60 63 71 79 87 92 95 103
loop(\(x,i).x5,1,(11x + 8))
A017489: 32768 2476099 24300000 115856201 380204032 992436543 2219006624 4437053125 8153726976 14025517307 22877577568 35723051649 53782400000 78502725751 111577100832 154963892093
compr(\x.(1 - (((loop(\(x,i).2x,(x div 2),~2) mod (x + 1)) div 2) mod 4)),x)
A026441: 2 4 5 6 8 10 12 13 14 16 17 18 20 21 22 26
(x + (4 * (x + loop(\(x,i).(x - ((~1 + (x div 4)) div 2)),2,(x + ~1)))))
A067396: 4 13 22 31 36 41 50 59 68 77 86 95 104 109 114 123
(x + (loop(\(x,i).((x + 1) - (x div (~2 + (((~x + 2) div 2) div 3)))),x,2) div 2))
A097911: 1 3 5 8
A052488: 1 3 5 8 11 14 18 21 25 29 33 37 41 45 49 54
(x + (if x <= 0 then 1 else ((4x + 1) - ((x + ~2) mod (3 - (x mod 2))))))
A137002: 1 5 11 15
A314015: 1 5 11 15 19 25 30 35 41 45 49 55 60 65 71 75
(x + (if x <= 0 then 1 else (4x + (2 div (16 div (x + 1))))))
A313747: 1 5 10 15 20 26 31 36 42 47 52 57 62 67 72 77
(x + ((x - (x mod ((7 * (if x <= 0 then 1 else 2)) - (x div 2)))) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A334918: 0 1 2 3 4 5 6 7 8 9 14 15 16 17 21 22
(x - loop(\(x,i).(x + ((~x + ((x div 2) mod 5)) div 5)),2,x))
A189819: 0 1 2 2 2 2 2 2 2 2 3 4 4 5 6 6
((~x2 + ~2x) + (loop(\(x,i).((x2 + ~x) div 2),2,(x + 4)) div 3))
A229422: 5 12 27 55 102 175 282 432 635 902 1245 1677 2212 2865 3652 4590
loop(\(x,i).(~27x + ~27),2,(x2 + 2x))
A158655: 702 2889 6534 11637 18198 26217 35694 46629 59022 72873 88182 104949 123174 142857 163998 186597
loop(\(x,i).(~25x + ~25),2,(x2 + 2x))
A157918: 600 2475 5600 9975 15600 22475 30600 39975 50600 62475 75600 89975 105600 122475 140600 159975
loop(\(x,i).(~40x + ~40),2,(x2 + 2x))
A158773: 1560 6360 14360 25560 39960 57560 78360 102360 129560 159960 193560 230360 270360 313560 359960 409560
loop(\(x,i).(~35x + ~35),2,(x2 + 2x))
A158735: 1190 4865 10990 19565 30590 44065 59990 78365 99190 122465 148190 176365 206990 240065 275590 313565
loop(\(x,i).(~33x + ~33),2,(x2 + 2x))
A158692: 1056 4323 9768 17391 27192 39171 53328 69663 88176 108867 131736 156783 184008 213411 244992 278751
loop(\(x,i).(~29x + ~29),2,(x2 + 2x))
A158667: 812 3335 7540 13427 20996 30247 41180 53795 68092 84071 101732 121075 142100 164807 189196 215267
loop(\(x,i).(~39x + ~39),2,(x2 + 2x))
A158770: 1482 6045 13650 24297 37986 54717 74490 97305 123162 152061 184002 218985 257010 298077 342186 389337
(~x + (if x <= 0 then 1 else (((2x3 + 6x2 + 4x) div 3) + (x mod 2))))
A006071: 1 4 14 38 76 136 218 330 472 652 870 1134 1444 1808 2226 2706
(~x + (((x2 + x + 2) + (loop(\(x,i).2x,x,1) div 8)) div 2))
A076202: 1 1 2 4 8 13
A130840: 1 1 2 4 8 13 20 30 45 69 110 184 323 591 1116 2154
(x * ((x * loop(\(x,i).(x4 + x2),1,x4)) div 2))
A170800: 0 1 131584 193739769 34360262656 1907353515625 50780008567296 814206940192849 9007199791611904 75047319391891761 500000005000000000 2779958669714828041 4611686018427387903 4611686018427387903
(x * ((x * loop(\(x,i).(x3 + x),1,x5)) div 2))
A168667: 0 1 65600 64571175 8589942784 381469765625 8463329862336 116315257405375 1125899907891200 8338590852224769 50000000005000000 252723514259390471 1109305553388134400 4325207959722043225
(x * ((x * loop(\(x,i).(x5 + x2),1,x3)) div 2))
A170781: 0 1 65664 64573362 8589967360 381469921875 8463330562176 116315259876004 1125899915231232 8338590871356645 50000000050000000 252723514356826326 1109305553585209344 4325207960098534327
(5x2 * (if (x mod 12) <= 0 then (x + 2) else 0))
A145836: 0 0 0 0 0 0 0 0 0 0 0 0 10080 0 0 0
(2x + (if (x + ~1) <= 0 then 1 else (0 - (3 * (x div 7)))))
A027440: 1 3 4 6 8 10 12
A169866: 1 3 4 6 8 10 12 11 13 15 17 19 21 23 22 24
(x + loop(\(x,i).((x + 1) - ((x - (x div (1 + ((x div 2) div 3)))) div 2)),2,x))
A154809: 2 4 6 8 10 11 12 13 14 16 18 19 20 22 23 24
(2x + (if x <= 0 then 1 else (2 * ((x - (((x + 2) div 3) mod 3)) div 2))))
A222011: 1 2 4 8
A166245: 1 2 4 8 10 12 16 20 24 26 28 32 34 36 40 42
(~x + loop(\(x,i).(x - (((x - ((x2 + ~x) div 8)) div 2) div 2)),2,x))
A308858: 0 0 0 0 0 0 0 0 0 0 2 2 3 5 6 8
(x + loop(\(x,i).(2 + ((x + (2x div (2 - ((~x + 1) div 3)))) div 2)),2,x))
A307206: 3 5 6 8 9 10 12 14 15 16 18 19 21 22 23 24
(2x + (if x <= 0 then 1 else (2 * compr(\x.((12 mod (x + 2)) mod 2),x))))
A311385: 1 4 8 12 16 22 28 34 38 42 46 50 54 58 62 66
(~x6 + loop(\(x,i).12x,x,1))
A024146: 1 11 80 999 16640 233207 2939328 35714159 429719552 5159248911 61916364224 743006599127 8916097462272 106993200552263 1283918457019328 15407021563195743
(~x6 + loop(\(x,i).10x,x,1))
A024120: 1 9 36 271 5904 84375 953344 9882351 99737856 999468559 9999000000 99998228439 999997014016 9999995173191 99999992470464 999999988609375
(~x6 + loop(\(x,i).7x,x,1))
A024081: 1 6 ~15 ~386 ~1695 1182 70993 705894 5502657 39822166 281475249 1975555182 13838301217 96884183598 678215543313 4747550119318
(~x7 + loop(\(x,i).3x,2x,1))
A024108: 1 8 ~47 ~1458 ~9823 ~19076 251505 3959426 40949569 382637520 3476784401 31361572438 282393704673 2541803079812 22876687041457 205890961235274
(~x7 + loop(\(x,i).6x,x,1))
A024069: 1 5 ~92 ~1971 ~15088 ~70349 ~233280 ~543607 ~417536 5294727 50466176 343309885 2140950528 12997945499 78258750592 470014125201
(~x7 + loop(\(x,i).8x,x,1))
A024095: 1 7 ~64 ~1675 ~12288 ~45357 ~17792 1273609 14680064 129434759 1063741824 8570447421 68683644928 549693065371 4397941097600 35184201229457
(~x7 + loop(\(x,i).5x,x,1))
A024056: 1 4 ~103 ~2062 ~15759 ~75000 ~264311 ~745418 ~1706527 ~2829844 ~234375 29340954 208308817 1157954608 5998102121 30346718750
loop(\(x,i).7x,x,x7)
A098803: 0 7 6272 750141 39337984 1313046875 32934190464 678223072849 12089663946752 193010051319183 2824752490000000 38532504363714053 495958345459089408 4611686018427387903 4611686018427387903
(~x5 + loop(\(x,i).11x,x,1))
A024132: 1 10 89 1088 13617 157926 1763785 19470364 214326113 2357888642 25937324601 285311509560 3138428127889 34522711772638 379749833045417 4177248168656276
(1 + (x div (1 + (x mod (1 + ((1 + (x div 2)) mod (1 + (x div 5))))))))
A327498: 1 2 3 4 5 3 7 8 9 5 11 12 13 7 5 16
(1 + (x div (1 + ((~x + 4) mod (1 + (x mod (1 + (x div 5))))))))
A140271: 1 2 3 4 5 3 7 4 9 5 11 4 13 7 5 8
(1 + (x div (1 + (x mod (1 + ((4 + (x div 2)) mod (1 + (x div 3))))))))
A066069-A019554: 1 2 3 2 5 6 7 4 3 10 11 6 13 14 15 4
(1 + (x div (1 + (x mod (1 + (x mod (1 + (x div (2 + (x div 5))))))))))
A095163-A033677: 1 2 3 2 5 3 7 4 3 5 11 4 13 7 5 4
(1 + (x mod (1 + (x mod (1 + (x mod (1 + (x div (2 + (x div 8))))))))))
A088445: 1 1 1 2 1 3 1 4 3 2 1 4 1 2 5 4
(~1 + (2 div (1 + ((x * (x div 2)) mod (1 + (x mod (1 + ((~x + 2) mod 4))))))))
A189021: 1 1 1 ~1 1 1 1 0 ~1 1 1 ~1 1 1 1 0
(1 + ((2x + 1) mod (1 + (~8 mod (1 + (x div 3))))))
A048858: 1 1 1 1 1 1 2 2 2 1 1 1 2 1 3 2
(1 + ((x + ~4) mod (1 + ((x mod 6) mod (1 + (x div 3))))))
A163109: 1 1 1 2 1 2 1 2 2 2 1 2 1 2 2 4
(1 + (x mod (1 + (((x + 2) * (2 - ((x div 2) mod 2))) mod (1 + (x div 3))))))
A071974-A056622: 1 1 1 2 1 1 1 1 3 1 1 2 1 1 1 4
(1 + ((x div 2) mod (1 + (x mod (1 + (7 mod (1 + (x div 2))))))))
A292589-A162510: 1 1 1 2 1 1 1 4 2 1 1 2 1 1 1 8
(1 + (x div (1 + (x mod (1 + ((x mod (3 + (x mod 2))) mod (1 + (x div 2))))))))
A102095: 1 2 3 2 5 3 7 2 3 5 11 3 13 7 5 4
(1 + ((1 + (x div 3)) mod (1 + (x mod (1 + ((x div 2) div (1 + (x mod 2))))))))
A303977: 1 1 1 1 1 1 1 2 4 1 5 2
(1 + (x div (1 + (x mod (1 + ((3 * ((x div 2) - (x mod 2))) mod (x + 1)))))))
A126352: 1 1 3 4 5 3 7 8 9 1 11 12 13 7 15 16
(1 + ((x + 1) div ((x + 1) + ((x div 2) mod 7) - (x mod 2))))
A064529: 2 3 1 2 1 1 1 1 1 1 1 1 1 1 2 2
(2 div (1 + ((1 + (x mod 5)) div (1 + (x div 7)))))
A029400: 1 0 0 0 0 1 0 1 0 0 2 1 1 0 1 2
(1 + (x div (1 + (x mod (1 + (x div (2 + (x div (2 + ((x mod 3) div 2))))))))))
A116548: 1 2 3 2 5 3 7 4 3 5 11 4 13 7 5 8
(1 + (2 div (1 + ((2 + ((x2 + ~2x) div 8)) mod 5))))
A129265: 1 2 1 1 1 1 3 2 1 1 1 1 1 1 1 2
(1 + ((1 + (x mod (1 - (x div ~4)))) mod (1 + (x div 5))))
A164002: 1 1 1 1 1 2 2 1 2 1 1 2 2 2 3 2
(1 + (((2x + 1) div (1 + (2 * (x mod 2)))) mod (1 + (x div 5))))
A057155: 1 1 1 1 1 2 2 2 2 1 1 2 2 1 3 3
(1 + (x mod (1 + ((x div 2) mod (1 + ((x + (x2 mod 3)) mod 4))))))
A125168: 1 1 1 2 1 3 1 1 1 1 1 1 1 1 3 4
(1 + (x mod (1 + (x mod ((1 + ((x div 3) mod 2)) * (1 + (x div 4)))))))
A072499: 1 1 1 2 1 2 1 2 3 2 1 6 1 2 3 8
(((x + 1) div 5) div (1 + (x mod (1 + (x mod (3 + (x mod 2)))))))
A102442: 0 0 0 0 1 0 1 0 0 1 2 0 2 1 1 0
(1 + ((~x + 1) mod (1 + ((1 + ((x div 2) mod 7)) mod 3))))
A145327: 2 1 3 2 1 1 2 1 3 2 1 1 2 1 2 1
(1 + ((x + 1) mod (1 + (((2x + 1) div 9) mod 3))))
A325509: 1 1 1 1 2 1 2 1 2 2 3 1 2 1 1 1
(x div (1 + (((x2 + 2x) div 2) mod 37)))
A306798: 0 0 0 0 0 0 0 0 2 0 0 0 1 0 7 0
(1 + (x div 2) - ((1 + (x div 3)) mod (1 + ((1 + (x div 2)) div 3))))
A284523: 1 1 2 2 3 3 3 3 4 5 5 5 5 5 6 8
(1 + (x mod (1 + ((x mod (2 + ((x2 div 4) mod (x + 1)))) div 3))))
A336643-A334039-A076933: 1 1 1 2 1 1 1 1 3 1 1 2 1 1 1 2
(1 + (x div (~1 + (3 * (2 - (2x mod (~2 - (x div 4))))))))
A055181: 1 1 1 1 1 1 2 1 2 1 3 2 2 1 2 4
((x + 1) mod (1 + ((~x + 1) mod (x - ((x + 1) mod 13)))))
A220164-A002962: 0 0 0 0 0 0 0 0 0 0 0 0 1 0 3 5
(1 + (((x + ~1) div 2) mod (1 + ((x - ((~x + 1) div (2 + (x div 2)))) mod 3))))
A275656: 1 1 1 2 2 1 1 1 2 2 1 2 3 1 1 2
((2x + 1) - ((x + 1) mod (1 + (x mod (1 - ((~x + (x mod 2)) div 3))))))
A296233: 1 3 5 7 8 11 13 15 17 19 21 23 24 25 29 31
(x mod (1 + ((x - ((~x + 1) mod 7)) mod (1 + (x div 3)))))
A255325: 0 0 0 0 0 0 0 0 2 1 0 3 2 1 2 3
(1 + (((1 - (x div 2)) mod (~1 + (2 * (x mod 4)))) mod (1 + (x div 3))))
A129713: 1 1 1 1 1 1 2 1 1 1 3 2 1 1 1 5
(1 + (5 mod (1 + (((x + 1) mod 5) mod (1 + (x div 2))))))
A285202: 1 1 2 1 1 2 3 2 1 1 2 3 2 1 1 2
((2x + 1) - (x mod (1 + ((x mod (3 + (x mod 2))) mod (1 + (x div 2))))))
A140584: 1 3 5 6 9 10 13 12 15 18 21 20 25 26
(1 + ((x + 2) mod (1 + ((5 * (x + (x div 4))) div (x + 1)))))
A236858: 1 1 1 2 1 2 3 4 5 6 1 2 3 4 5 6
(1 + ((x + ~1) mod (1 + ((x mod (1 + (2x mod 9))) div 2))))
A216784: 1 1 2 1 1 1 2 1 1 1 1 1 3 1 1 1
(1 + ((2x + ~1) mod (~1 + (2 * (1 + ((x2 + x) mod 5))))))
A053797: 1 2 1 1 1 1 2 2 1 1 1 2 3 1 1 1
(1 + (x div (1 + (2 * (x mod (1 + (x mod (1 + (x div (2 * (2 - (x mod 2))))))))))))
A284694: 1 2 3 2 5 2 7 2 2 2 11 2 13 2 3 2
(1 + (x mod (1 + (2 * ((2x + ~1) mod (1 + ((x * (x mod 2)) div 3)))))))
A328569: 1 1 1 1 1 3 1 2 1 1 1 3 1 1 1 5
(1 + (x mod (1 + (2 * ((x + ~1) mod (1 + (x div (2 + ((x div 2) mod 3)))))))))
A174447-A174374: 1 1 1 1 2 1 1 3 3 1 1 3 4 3 1 1
(1 + ((x + 1) mod (1 + (2 * ((x + 2) div (1 + (2 * (3 - (x mod 2)))))))))
A030111: 1 1 1 2 1 1 2 3 1 1 3 3 4 1 1 3
(1 + ((x + ~1) div (1 + (x div (2 + (x div (1 + (x mod (2 * (1 + (x mod 2)))))))))))
A089265: 0 1 2 2 4 3 6 3 8 5 10 4 12 7 14 4
(1 + (x div (1 + (2 * (1 + (((x + ~1) div (2 - (x div ~4))) mod 2))))))
A031281: 1 1 1 2 1 2 2 2 2 2 3 4 5 5 5 6
(1 + (x div (1 + (2 * (1 + (((x2 + ~x + 2) mod (x + 4)) div 2))))))
A284580-A284569-A227349: 1 1 1 2 1 1 2 3 1 1 1 2 2 2 3 4
(7 mod (1 + (x div (1 + (2 * (1 + ((~x + 2) mod 4)))))))
A253238: 0 0 0 0 0 1 1 0 1 1 3 1 1 1 2 1
(1 + ((1 + (x mod 9)) mod (1 + ((1 + (x div 4)) div 2))))
A177740: 1 1 1 1 2 1 2 1 2 2 1 2 2 3 1 2
(1 + (x mod (1 + (2 * ((x + (x div 3)) div (1 + (x mod (2 + (x mod 2)))))))))
A345708-A144786: 1 1 3 4 5 1 7 8 9 10 11 3 13 14 15 16
(1 + ((x2 + 2x + 1) mod (1 + ((x - ((x div 3) mod 3)) div 2))))
A183025: 1 1 2 1 2 1 2 2 2 1 2 1 2 1 2 5
((1 + (x div 3)) div (1 + (x div (1 + (x div (2 + ((x + 1) mod 3)))))))
A278912-A025839: 1 0 0 1 0 1 1 0 1 1 1 2 1 1 2 2
((4x + 1) - (((x2 + 3x + 2) div 2) mod 7))
A106672: 0 2 3 10 16 21 25
((6x + 5) - ((~2x + 2) div 7))
A004083: 5 11 18 24 30 37 43 49 55 62 68 74 81 87 93 99
((6x + 5) - ((~2x + 4) div 7))
A246296: 5 11 17 24 30 36 43 49 55 61 68 74 80 87 93 99
(1 + ((2x + 2) mod (1 + ((4x + 4) mod (2 + (x div 3))))))
A326568: 1 1 1 1 2 1 1 1 1 1 3 1 2 2 1 1
(1 + (2x2 mod (1 + ((4x + 4) mod (2 + (x div 3))))))
A134866: 1 1 1 1 3 1 1 1 1 1 1 3 4 3 1 1
(1 + (x mod (1 + (x mod (2 + ((x mod 7) mod (1 + (x div 2))))))))
A331310: 1 2 1 1 1 2 1 2 3 2 1 6 1 2 1 1
(1 + ((x + 1) div (1 + (2 * (1 + (((((x + 1) div 2) div 2) div 2) + (x mod 2)))))))
A263922: 1 1 2 1 2 2 3 2 2 2 3 2 3 3 4 2
(2 + (x mod (1 + (x mod (2 + (x div (3 - (x mod 2))))))) - (x mod 2))
A064130: 2 2 2 1 2 2 2 2 2 2 2 2 2 2 4 2
(1 + (x mod (1 + ((32x + 1) mod (2x + 2)))))
A327501-A304776-A243074-A052410: 1 2 3 2 5 6 7 2 3 10 11 12 13 14 15 2
(1 + (x div (1 + (2 * ((x mod (1 + ((2 - (x mod 4)) mod (x + 1)))) div 2)))))
A261969: 1 2 3 2 5 6 7 2 3 10 11 2 13 14 15 2
(1 + ((x + 2) mod (1 + (2 * (x div (2 + (5 * (x mod 4))))))))
A301314: 1 1 1 1 2 1 1 1 2 3 1 1 2 1 2 1
(1 + ((x + 2) mod (1 + (((x + 1) div (2 * (1 + (x mod (2 + (x mod 2)))))) div 2))))
A050431: 1 1 1 2 1 1 1 2 2 3 1 2 3 2 1 3
(1 + (2x mod (1 + (2 * ((5x mod (1 + (x div 2))) div 2)))))
A281680: 1 1 1 1 3 1 1 3 1 1 3 1 5 3 1 1
(x div (1 + (x div (1 + (2 * ((x + ~1) div (~x + 18)))))))
A308855: 0 0 0 0 0 0 0 0 0 0 2 2 2 4 4 7
(1 + ((x div 2) mod (1 + (2 * (((x + 2) div (~2 - (x div 4))) mod 2)))))
A237266: 1 1 1 2 1 3 1 1 2 2 3 1 1 1 1 1
(1 + (x mod (~1 + (2 * ((x * ((x + 1) mod 5)) div 8)))))
A155865-A010358-A010048: 1 1 1 1 1 1 1 2 2 1 1 3 6 3 1 1
(1 + (2x div (1 + (2x div (2 + (2x div (2 + (x div 4))))))))
A161357: 1 3 3 4 3 4 5 5 6 5 7 6 5 7 6 8
(2 div (1 + (4 mod (1 + ((~2x + 2) mod (4 + (x div 4)))))))
A114002: 1 2 1 2 0 1 2 2 0 1 2 0 0 0 1 2
(1 + ((~2 + (x mod 2)) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))))
A241926-A174446-A090806-A048570: 1 1 1 1 2 1 1 2 2 1 1 3 4 3 1 1
(1 + ((~x2 + 2) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))))
A327742-A238392-A144464-A138015-A103444-A099172: 1 1 1 1 2 1 1 2 2 1 1 2 4 2 1 1
(1 + ((1 - (x div 3)) mod (~1 + (2x mod (4 + (x div 4))))))
A161642: 1 1 1 1 1 1 1 3 3 1 1 2 2 2 1 1
(1 + (x div (1 + (x mod (2 * (2 + ((x3 div 2) mod (x + 4))))))))
A170818-A170817: 1 1 1 1 5 1 1 1 1 5 1 1 13 1 5 1
(1 + (((2x + 1) * (1 + (~x mod 4))) mod 9))
A302991: 2 4 7 6 1 9
(1 + (((x + 1) * (((x + 1) - ((x div 2) mod 2)) div 2)) div 9))
A029065: 1 1 1 1 2 3 3 3 5 6 7 7 9 11 12 13
((x div 3) div (1 + ((2 * ((x + 2) + (x div 2))) mod 9)))
A128113: 0 0 0 0 0 1 0 0 1 0 0 3 0 0 2 1
((5x + 3) - ((~2x + 2) div 9))
A184517: 3 8 14 19 24 29 35 40 45 50 55 61 66 71 76 82
(1 + ((x div (~2x + 32)) + (x div 9)))
A059185: 1 1 1 1 1 1 1 1 1 2 2 3 3 4 5 9
(1 + ((2x2 + 5x + 2) mod (1 + (2x mod (2 + (x div 4))))))
A211095: 1 1 1 1 1 2 1 1 1 3 1 3 1 2 1 1
((x + 1) - ((x2 + 2) div (1 + (2 * (2 + ((x + (x div 4)) div 2))))))
A193832: 1 2 3 3 3 4 4 5 5 5 5 5 6 6 6 7
(1 + ((x mod (1 + ((x mod 6) mod (1 + (x div 2))))) mod 5))
A132589: 1 1 1 2 1 3 1 2 3 2 1 1 1 2 3 4
(1 + (5 * (1 + (2 * (x - (x div ~9))))))
A166728: 6 26 36 46 56 66 76 86 96 106 126 136 146 156 166 176
(100x2 + 200x + 51)
A152579: 51 351 851 1551 2451 3551 4851 6351 8051 9951 12051 14351 16851 19551 22451 25551
(20x3 + 60x2 + 90x + 51)
A201813: 51 221 631 1401 2651 4501 7071 10481 14851 20301 26951 34921 44331 55301 67951 82401
(4 mod (1 + (((x + 1) * ((x + 2) + (x div 4))) mod 5)))
A331438: 1 0 1 0 0 0 0 0 0 0 4 0 0 1 0 0
(1 + (5 * (((2 + (x div 4)) mod (1 + (x mod 3))) mod 2)))
A138072: 1 1 1 1 6 1 1 6 6 1 1 6 1 6 1 1
(x6 mod 29)
A070652: 0 1 6 4 7 23 24 25 13 16 22 9 28 20 5 5
(x6 mod 41)
A070664: 0 1 23 32 37 4 39 20 31 40 10 33 36 2 9 5
(x6 mod 39)
A070662: 0 1 25 27 1 25 12 25 25 27 1 25 27 13 1 12
(1 + (x div 3) - ((x + 1) div (2 - ((~x + 1) div 5))))
A029266: 1 0 0 1 1 0 1 1 1 2 2 1 3 3 2 3
(1 + ((x * ((x mod (~1 + (2 * ((x + ~1) div 3)))) div 2)) div 5))
A251660: 1 1 1 1 1 1 1 1 2 1 1 1 3 8 1 1
(1 + ((x + (2 * (x mod (x - ((x + ~1) mod 8))))) div 5))
A109368: 1 1 1 1 1 2 2 2 2 2 3 4 4 5 5 6
(1 + ((9 * (x mod 5)) + (x div 5)))
A089756: 1 10 19 28 37 2 11 20 29 38 3 12 21 30 39 4
(1 + (((x mod (~1 + (2 * ((x + ~1) div 3)))) div 2) * (x div 5)))
A259844: 1 1 1 1 1 1 1 1 2 1 1 1 3 7 1 1
((x + 1) + (x div 5) - (5 * (~x + (x mod 4))))
A043309: 1 2 3 4 25 27 28 29 50 51 53 54 75 76 77 79
(((x + 2) + (((3 * (x div 2)) div 2) div 2)) * (1 + (x div 5)))
A048659: 2 3 4 5 7 16 20 22 26
((2x + 5) - ((~6x + 3) div (x + 5)))
A248634: 5 8 11 13 16 18 20 23 25 27 29 31 34 36 38 40
(1 + ((x * (1 + (x mod (1 + ((~x + 2) mod 4))))) div (x + 5)))
A073811: 1 1 1 2 1 2 1 3 2 2 1 3 1 2 1 4
(~1 + ((1 + ((x3 + x2 + ~x + ~1) mod 7)) mod 3))
A238468: 0 0 ~1 1 ~1 1 0 0 0 ~1 1 ~1 1 0 0 0
(1 + (((x + 1) mod (1 + ((x2 + ~x) mod 9))) mod 3))
A255481: 1 1 1 2 2 1 1 2 1 1 1 1 1 3 1 1
(1 + (((1 + (x div 5)) div (1 + ((x + ~1) mod 3))) mod 3))
A336431: 1 2 1 1 2 2 1 3 2 1 1 2 2 1 2 2
((~2x + 2) mod (1 + ((1 + (((x + 1) div 2) * (1 + (x div 2)))) div 3)))
A309711: 0 0 0 0 0 0 0 0 2 2 4 6 8 10 14 16
(1 + ((x mod (1 + (31 mod (x + 1)))) div 3))
A038538: 1 1 1 2 1 1 1 3 2 1 1 2 1 1 1 6
(1 + (x div (3 * (1 + (x mod (2 * (1 + ((x + 1) mod 6))))))))
A054722: 1 1 1 1 1 1 1 2 3 1 1 2 5 3 1 1
(1 + (((x + ~1) - (((1 - (x div 3)) mod 5) mod 2)) mod 3))
A220906: 2 3 1 3 1 2 3 1 2 2 3 1 3 1 2 2
((x + 1) - ((1 - (x mod (x - ((x + ~1) mod 7)))) mod 3))
A073295-A073294: 0 1 2 3 4 5 6 7 8 10 9 11 13 12 14 15
(((1 + (x div 3)) div 2) div (1 + ((x mod 7) mod 3)))
A035393: 0 0 0 1 0 0 1 1 0 0 2 1 0 2 2 1
(1 + ((1 + ((1 + ((x * ((x + (x mod 2)) div 3)) div 2)) div 2)) div 3))
A046052: 1 1 1 1 1 2 2 2 2 3 4 5
A029101: 1 1 1 1 1 2 2 2 2 3 4 5 5 5 6 7
(~1 + ((4x3 + 30x2 + 68x + 48) div 3))
A199899: 15 49 111 209 351 545 799 1121 1519 2001 2575 3249 4031 4929 5951 7105
(1 + (((~x + 1) mod (1 + (4 * ((x mod (1 + (x div 2))) div 2)))) mod 3))
A126433: 1 1 1 1 1 2 1 2 1 2 1 3 2 2 1 1
(~1 + ((2 div (~1 + ((~2x + 2) mod (4 + (x div 4))))) mod 3))
A155031: 1 0 1 0 ~1 1 0 0 ~1 1 0 ~1 ~1 ~1 1 0
((2x + 3) - ((1 + (x2 div (4 + (x div 2)))) div 3))
A186379: 3 5 7 9 10 12 13 15 16 18 19 21 22 24 25 26
(1 + (((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4))) mod 3))
A115568: 1 1 1 2 1 1 1 3 2 1 1 2 1 1 1 1
((x + ~1) mod (1 + (((8x + 8) div 5) mod 3)))
A091393: 1 0 1 0 0 0 2 0 1 0 0 0 2 0 0 0
((6x + 5) - ((x - (x div 5)) div 3))
A190334: 5 11 17 22 28 34 40 45 51 57 63 68 74 80 85 91
(x6 mod 37)
A070660: 0 1 27 26 26 11 36 26 36 10 1 1 10 11 36 27
(x6 mod 35)
A070658: 0 1 29 29 1 15 1 14 29 1 15 1 29 29 21 15
(1 + (3 * ((4 * (x + ((x div 2) div 5))) div 3)))
A084089: 1 4 7 13 16 19 25 28 31 37 43 49 52 55 61 64
((x + ~1) - (3 * (x - (3 * ((x + 2) + (3 * (x div 2)))))))
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((x + 1) - (((~x2 + x) - (((x2 + ~x) div 2) div 3)) div 3))
A023536: 1 2 4 7 10 14 19 25 31 38 46 55 65 75 86 98
(1 + (((2x + 2) + (x2 div 4) - (x div 3)) div 3))
A134030: 1 2 3 4 5 6 8 9 11 13 15 18 20 23 26 28
(1 + (((1 - ((x mod 3) + (2 * (x mod 2)))) mod (2x + ~1)) div 3))
A295885-A293892: 1 1 1 2 1 3 1 4 5 6 1 7 1 8 9 10
((x + 1) + ((x div (2 + ((x div 2) div 3))) + ((1 + (x div 2)) div 3)))
A248387: 1 2 4 5 8 9 10 11 12 14 16 17 18 19 20 21
(1 + ((x + 1) div (3 * ((1 + (x div 8)) * (1 + (x mod 2))))))
A060501: 1 1 2 1 2 2 3 2 2 1 2 2 3 2 3 2
(1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))
A329329-A306697-A297845-A296313-A259874-A256141-A196416-A183456-A183342-A174448-A114225-A077028-A072704-A038792: 1 1 1 1 2 1 1 3 3 1 1 4 5 4 1 1
(1 + (((x + 1) * (8x + ((x2 + x) div 2))) div 3))
A143058: 1 7 20 41 71 111 162 225 301 391 496 617 755 911
((x + 1) - (((((2 - (x div 2)) mod (x + 2)) div 2) div 2) + ((x + 1) div 3)))
A081611: 1 2 2 3 4 4 4 4 4 5 6 6 7 8 8 8
(1 + ((2 * (1 - (x div (~1 + ((~x + 1) div 9))))) div 3))
A093875: 1 2 2 3 3 3 3 4 4 5 5 4 4 5 5 5
(1 + ((2 + (3x div (1 + ((x + 2) div 5)))) div 3))
A178042: 1 2 3 3 3 4 4 5 4 4 5 5 5 4 5 5
(1 + ((2 * ((2x + 1) - ((1 - (x div 2)) div 5))) div 3))
A285343: 1 3 4 5 7 9 10 11 13 14 15 17 18 19 21 23
(x div (1 + ((2 * (1 + (x div (2 + (x mod (1 + (x div 4))))))) div 3)))
A078640: 0 1 1 1 1 2 2 2 2 2 3 3 2 3 4 5
(1 + ((2 * (1 + ((x * (((x + 1) div 2) div 2)) div 8))) div 3))
A029119: 1 1 1 1 1 1 1 2 3 3 3 4 4 4 5 6
(1 + ((2 * ((2x + 1) - ((~x + 1) div (2 + (x div 4))))) div 3))
A164028: 1 3 5 6 7 9 11 12 13 15 17 18 19 21 22 23
(1 + ((2 * (1 + ((((((x + 1) div 2) div 2) * (x div 2)) div 2) div 2))) div 3))
A029120: 1 1 1 1 1 1 1 2 3 3 3 3 4 4 5 6
(1 + (((1 + (2x mod (2 + ((~x + 1) mod (2 + (x div 2)))))) div 2) mod 3))
A134542-A106254: 1 1 1 1 2 1 1 2 2 1 1 3 3 2 1 1
(1 + ((x - (((1 - (2x div 3)) mod 5) div 2)) mod 3))
A274921: 1 2 3 2 3 2 3 1 3 1 2 1 3 1 2 1
(3x mod (1 + ((2 + ((x2 div 2) div 5)) div 3)))
A240923: 0 0 0 0 0 1 0 0 0 3 0 3 0 4 2 0
(2 - ((~x + 1) div (1 + ((2 * (1 + (x div (2 * (2 - (x mod 2)))))) div 3))))
A218007: 1 2 3 3 4 4 5 4 5 4 5 4 6 5 7 5
((~x + ~1) mod (1 + ((x - ((3 * (x div 4)) div 2)) mod 3)))
A079127: 0 0 0 0 0 0 2 0 0 0 1 0 2 0 1 2
(x - (19 * (~x + (x mod 9))))
A073790: 0 1 2 3 4 5 6 7 8 180 181 182 183 184 185 186
(x7 mod 19)
A070701: 0 1 14 2 6 16 9 7 8 4 15 11 12 10 3 13
(1 + ((2 * (1 + (2 * (x + (x div (2 + ((x div 2) div 3))))))) div 3))
A230078: 1 3 5 7 9 11 12 13 15 17 19 20 21 23 24 25
(1 + ((2 * (1 + ((x + (8x div (x + 2))) div 2))) div 3))
A241920: 1 2 3 3 4 5 5 5 6 6 7 7 7 7 8 9
(1 + ((x mod (2 + (11 mod (2x + 1)))) mod 3))
A105083: 1 2 3 1 1 2 1 2 3 1 2 3 1 1 2 3
(~1 + (6 * (1 + ((2 * (x + (3 * (x div 2)))) + (x div 2)))))
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(1 + ((((x + 1) * (2 + (((x + 1) + (x div 4)) div 2))) div 2) div 3))
A135279: 1 2 2 3 5 6 8 9 11 14 15
(1 + ((2 + ((2 * ((x + ((x + ~1) mod 3)) div 2)) mod (x + 1))) div 3))
A293248: 1 1 2 1 3 1 2 3 4 1 5 1 2 5 6 1
(1 + (((x + 1) mod (2 + ((x mod (1 + (4 mod (x + 1)))) div 2))) mod 3))
A272863: 2 1 2 1 2 1 2 3 1 3 2 1 2 3 1 1
(1 + (6 * ((x - (x div (~3 + (x div ~4)))) mod 2)))
A132728: 1 1 7 1 7 1 1 7 1 7 1 7 1 7 1 1
(1 + ((4 * (x - ((2 * (x div ~2)) div 5))) div 3))
A336353-A281995: 1 3 5 6 7 10 11 13 14 15 17 19 21 22 23 26
(1 + ((2 * ((1 + (((x * (1 + ((x + 1) div 2))) div 2) div 2)) div 2)) div 3))
A029068: 1 1 1 1 2 3 3 3 4 5 6 7 8 9 10 12
(1 + ((2 * (x - ((3 * (((1 + (x div 2)) div 2) div 2)) div 2))) div 3))
A226142: 1 1 2 3 3 4 4
A268060: 1 1 2 3 3 4 4 5 5 6 7 7 8 9 8 9
(1 + ((2 + (((x - ((~x + 1) * (x div 2))) * (1 + (x div 2))) div 2)) div 3))
A294496: 1 1 2 3 6 8 15 18 31 35 56 62
(x div (2 - ((~x + 1) div (1 + ((x - (((1 + (x div 2)) div 2) div 2)) mod 3)))))
A334158: 0 0 0 0 1 1 1 0 1 1 0 1 2 0 0 1
(1 + ((4 * ((x + 1) + (x div (6 - (x mod 2))))) div 3))
A284892-A167171-A144338: 2 3 5 6 7 10 11 13 14 15 17 19 21 22 23 26
(1 + (((x div (2 + (2 * (x mod (1 + ((x div 2) mod 3)))))) div 2) mod 3))
A138774: 1 1 1 1 1 1 2 2 3 2 2 1 1 1 1 2
(1 + (((x2 - (x div (2 + (x div (2 + (x mod 3)))))) div 2) mod 3))
A270488: 1 1 2 2 2 1 3 1 2 2 2 3 3 3 2 2
(1 + (24 * ((x mod (~1 + (2 * (x div 4)))) mod 2)))
A306454: 1 1 1 1 1 1 1 1 1 1 25 1 1 25 1 1
((x2 + ~x) div (~6x + 107))
A326468: 0 0 0 0 0 0 0 0 0 1 1 2 3 5 7 12
(x6 mod 47)
A070687: 0 1 17 24 7 21 32 8 25 12 28 37 27 3 42 34
((x + 2) mod (1 + ((x mod (~2 + (x mod (~2 + ((~x + 2) div 4))))) mod 3)))
A286998: 0 1 0 2 0 1 0 1 0 2 0 1 0 0 1 0
((x + ~1) - ((2 * (x - ((~x + 4) div (2 + (x div 4))))) div 3))
A029235: 1 0 1 0 1 0 1 1 1 1 1 2 2 2 3 2
((~x + 2) mod (1 + ((((((x + ~2) * (x2 div 2)) div 2) div 2) div 2) div 3)))
A058642: 0 0 0 0 0 1 0 1 3 5 9
(1 + ((4 * (4x + ((x mod (1 + (x div 2))) div 2))) div 3))
A315530: 1 6 11 17 22 29 34 39 45 51 57 62 67 74 79 85
((1 + (x div 8)) div (1 + (((x + 1) mod 8) mod 3)))
A035443: 0 0 1 0 0 1 0 1 1 0 2 1 0 2 1 2
(x7 mod 25)
A070706: 0 1 3 12 9 0 11 18 2 19 0 21 8 17 4 0
(x7 mod 23)
A070704: 0 1 13 2 8 17 3 5 12 4 14 7 16 9 19 11
(1 + (((x2 + 4x + 4) div 2) div (~x + 26)))
A335746: 1 1 1 1 1 2 2 3 3 4 5 6 8 9 11 14
(1 + ((2x2 + 3x) div (~x + 26)))
A122129: 1 1 1 2 3 4 5 7 9 12 15 19 24 30 37 46
(1 + ((4 * ((x + 2) + (x div (2 + ((x div 2) div 3))))) div 3))
A214547-A097218: 3 5 7 9 11 13 14 15 17 19 21 22 23 25 26 27
((x + 1) mod (1 + ((x - (((x + 2) div (2 + (x mod 2))) mod 4)) mod 3)))
A035187: 1 0 0 1 1 0 0 0 1 0 2 0 0 0 0 1
((8x2 + 22x + 14) div 13)
A083462: 1 3 6 11
A065504: 1 3 6 11 17 24 33 43 54 66 79 94 110 127 145 164
(((8x + 4) div 3) - (x div 13))
A231407: 1 4 6
A189533: 1 4 6 9 12 14 17 20 22 25 28 30 33 35 37 40
((13x + 13) + (x mod 13))
A136773: 13 27 41 55 69 83 97 111 125 139 153 167 181 182 196 210
(1 div (2 - (x6 mod 13)))
A011583: 0 1 ~1 1 1 ~1 ~1 ~1 ~1 1 1 ~1 1 0 1 ~1
((2x + 1) + (x div 11) - ((x + 1) mod 3))
A026309: 0 1 5 6 7 11 12 13 17 18 19 24 25 26 30 31
((11x + 11) + (x mod 11))
A136771: 11 23 35 47 59 71 83 95 107 119 131 132 144 156 168 180
((x + 10) - (x mod ((x + ~1) - (x mod 12))))
A168100: 10 11 12 13 14 15 16 17 18 19 20 21 21 21 21 21
((x2 + x + 1) - ((x4 + ~x2) div 12))
A080260: 1 3 6 7 1 ~19 ~62 ~139 ~263 ~449 ~714 ~1077 ~1559 ~2183 ~2974 ~3959
((2x2 + 2x + 1) - ((1 - ((x2 + x) div 4)) div 3))
A301673: 1 5 13 26 43 63 88 118 151 188 230 276 326 380 438 501
(1 + ((x - (((1 - (x div 3)) div 3) * (2 + (x mod 2)))) div 3))
A342249: 1 1 1 2 2 2 3 4 4 5 5 5 5 6 6 8
(x mod (1 + ((2 * (x + ((x + 1) div (1 + (x div 5))))) div 3)))
A103303: 0 1 2 3 4 5 6 7 8 9
A007376: 0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2
(~1 + ((x4 + 4x3 + 14x2 + 20x + 16) div 3))
A047668: 4 17 52 129 276 529 932 1537 2404 3601 5204 7297 9972 13329 17476 22529
(~1 + (((x + 2) * (1 + ((x2 + 4x + 4) div 2) - (x mod 2))) div 3))
A099955: 1 3 11 19 37 55 87
A219527: 1 3 11 19 37 55 87 119 169 219 291 363 461 559 687 815
((2x2 + 6x + 1) - (((~x3 + x) div 2) div 3))
A323221: 1 9 22 41 67 101 144 197 261 337 426 529 647 781 932 1101
((2x2 + 5x + ~1) - (((~x3 + x) div 2) div 3))
A034857: ~1 6 18 36 61 94 136 188 251 326 414 516 633 766 916 1084
((x + 1) - ((x + (x2 div 25)) div 3))
A194806: 1 2 3 3 4 4 5 6 6 6 7 7 8 8 8 8
(6x5 + 15x4 + 20x3 + 15x2 + 6x + 1)
A022522: 1 63 665 3367 11529 31031 70993 144495 269297 468559 771561 1214423 1840825 2702727 3861089 5386591
(1 + ((x + (2 * (4 - ((~x + 1) div (2 + (x div 4)))))) div 3))
A073169: 3 4 5 5 5 6 7 7 7 8 9 9 9 10 10 10
(~1 + (2 * (1 + ((1 + (x div (2 + ((x div 2) mod 2)))) div 2))) - (x div 3))
A206827: 1 1 1 2 2 2 1 1 3 2 2 2 3 3 1 2
((2x + 1) + ((x - (x div 7)) div 2) - (x div 3))
A184873: 1 3 6 7 10 12 14 16 18 20 22 25 26 29 31 32
((6x - (x div 7)) mod (1 + (x div 3)))
A236468: 0 0 0 0 0 0 0 2 2 1 3 1 1 2 2 4
((~1 + (3 * ((x div 3) mod 2)) - (x mod 2)) * (1 + (x div 3)))
A099470: ~1 ~2 ~1 2 4 2 ~3 ~6 ~3 4 8 4 ~5 ~10 ~5 6
((((x + 1) mod (1 - (x mod ~7))) mod 2) * (1 + (x div 3)))
A338504: 0 0 1 0 2 0 3 0 0 0 4 0 5 0 0 0
((1 mod (1 - (2x mod (4 + (x div 4))))) mod (1 + (x div 3)))
A320364-A318222-A317896: 0 0 0 0 1 0 0 1 1 0 0 2 4 2 0 0
(((~x + ~2) - ((x div 2) div 7)) mod (1 + (x div 3)))
A342301: 0 0 0 1 0 1 1 0 2 1 0 3 1 0 3 0
((1 + (~7 mod (1 + (x div 3)))) * (1 + (x mod 3)))
A006047: 1 2 3 2 4 6 3 6 9 2 4 6 4 8 12 6
((4x + 5) - ((x2 div 3) div (x + 3)))
A141135: 5 9 13 17 21 24 28 32 36 39 43 47 50 54 58 61
((x + 1) - (((x * (x + ((x div 3) mod 3))) div 2) div (x + 3)))
A088023-A073092: 1 2 3 3 4 5 5 5 6 7 8 8 8 9 9 9
(1 + ((4x + 2) * (1 + (2 * ((4x + 1) + (x mod 2))))))
A135051: 7 79 191 407 631 991 1327 1831 2279 2927 3487 4279 4951 5887 6671 7751
((2x + 1) mod (1 + ((2x - ((x div 2) mod 3)) mod (1 + (x div 2)))))
A037188: 0 0 1 1 0 2 0 0 0 1 0 2 1 3 1 1
(1 + ((x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4)))))) mod (1 + (x div 2))))
A325567-A072994-A009195: 1 1 1 2 1 2 1 4 3 2 1 4 1 2 1 8
((2x + 5) - ((x2 + 2x) div (x + 17)))
A080353: 5 7 9 11 12 14 15 17 18 20 21 22 24 25 26 28
(x mod (1 + ((1 + (x mod (1 + ((~x + 2) mod (2 + (x div 3)))))) mod (x + 1))))
A099584: 0 0 0 1 0 1 0 2 0 0 1 2 0 1 0 0
(1 + compr(\x.(1 - (x mod (1 + (3 * (x mod (3 + (x mod 2))))))),(x + 1)))
A080702: 3 4 6 8 9 10 11 12 14 16 18 20 21 22 23 24
((x + 1) - ((x - ((~2x2 + 4x) div 7)) mod (x + 1)))
A194750: 1 1 1 4 3 2 1 7 5 3 11 8 5 2 13 9
((x + 1) div (1 + ((~1 + (2x mod (4 + (x div 4)))) mod (x + 1))))
A131333: 1 1 1 2 1 1 3 2 2 1 5 3 4 2 1 8
(1 + ((1 + (((x mod (2 + ((x div 4) mod 2))) + (x div 2)) div 2)) mod (x + 1)))
A105096: 1 2 2 3 3 4 3 4 4
A176075: 1 2 2 3 3 4 3 4 4 4 4 5 5 5 6 5
((2x + 1) - ((3 * (x mod 13)) div (x + 1)))
A336119: 1 2 3 5 7 9 11 13 15 17 19 21 23 27 29 31
((x + 1) div (1 + ((2 - (3 * ((2 * (x div 2)) div 3))) mod (x + 1))))
A261794: 1 2 1 1 1 1 1 1 1 1 2 2 3 2 2 2
(~1 + compr(\x.(1 - (x mod (2 + ((x + 2) mod (5 + (x mod 2)))))),(x + 1)))
A328216: 1 2 3 4 5 6 8 9 10 12 13 14 15 16 18 21
(1 + compr(\x.(1 - (x mod (2 + ((2x mod (1 + (x div 4))) mod 2)))),(x + 1)))
A227180: 4 6 8 9 10 12 14 16 18 20 22 24 26 27 30 32
(4x7 + 6x6 + 2x5 + 2x + 3)
A225728: 3 17 967
((4x + 3) + (((x3 + 3x2 + 2x) div 2) div 3))
A238806: 3 8 15 25 39 58 83 115 155 204 263 333 415 510 619 743
(1 + compr(\x.((3 * (x mod 10)) - (x div 4)),(x + 1)))
A279769-A084854: 11 21 22 31 32 33 41 42 43 44 51 52 53 54 55 61
(30x3 + 105x2 + 75x + 15)
A207596: 15 225 825 1995 3915 6765 10725 15975 22695 31065 41265 53475 67875 84645 103965 126015
(x8 + ~x7 + x5 + ~x4 + x3 + ~x + 1)
A060889: 1 1 151 4561 49981 315121 1406371 4956001 14709241 38316961 90090991 195019441 394379701 753327121 1370877691 2392743361
((x3 + ~2x2 + x + 1) * (((x3 + ~x) div 2) div 3))
A202654: 0 0 3 52 370 1620 5285 14168 33012 69240 133815 242220 415558 681772 1076985 1646960
(1 + ((1 + (x mod (1 + (x mod (1 + (x div (2 + ((x + 1) mod 3)))))))) div 2))
A344773: 1 1 1 2 1 2 1 2 1 2 1 4 1 2 1 3
(1 + (2 * ((x div 2) div (1 + (x mod (1 + (x mod (1 + ((~x + 2) mod 4)))))))))
A318653: 1 1 3 1 5 3 7 1 3 5 11 3 13 7 15 3
(1 + (2 * ((x + 1) - (x mod (~1 + (3 * (((x + ~1) div 2) mod 3)))))))
A060265: 3 5 7 7 11 13 13 17 19 19 23 23 23 29 31 31
(1 + ((1 + (x mod (1 + (3 * ((2x mod (2 + (x div 2))) div 2))))) div 2))
A338428: 1 1 1 1 1 2 2 1 2 1 1 1 1 2 1 3
(1 + (2 * ((x div 3) div (1 + (x mod (~1 + (3 * (2 + (x mod 2)))))))))
A107294: 1 1 1 1 1 1 3 1 1 3 7 1 3 1 1 1
(1 + ((1 + ((~1 + ((x + ~1) mod 5)) mod (1 + (x div 3)))) div 2))
A014643: 1 1 1 2 1 2 2 1 2 2 3 3 1 2 2 3
(1 + ((1 + ((2 - ((x + ~1) mod 5)) mod (1 + (x div 3)))) div 2))
A256660: 1 1 1 1 2 1 2 2 1 3 2 2 2 1 3 3
(1 + ((1 + (((x + 1) + (x div 5)) mod (1 + (x div 3)))) div 2))
A182597: 1 1 1 1 2 2 2 1 2 3 2 2 1 2 2 2
(1 + ((1 + ((x2 + 2x + 8) mod (1 + (x div 3)))) div 2))
A332207: 1 1 1 2 1 2 2 2 2 3 1 3 2 3 2 4
(1 + (((1 + (x div 3)) div (1 + ((~x + 2) mod (1 + (x div 3))))) div 2))
A051574: 1 1 1 1 2 1 1 1 2 2 3 1 3 1 1 1
(1 + (x mod (2 * (1 + (x mod (1 + (7 mod (1 + (x div 2)))))))))
A325566-A324873: 1 2 1 4 1 2 1 8 3 2 1 4 1 2 1 16
(1 + ((1 + (x mod (1 + ((2 + ((x mod 3) div 2)) mod (1 + (x div 2)))))) div 2))
A335221: 1 1 1 1 2 1 1 2 1 1 2 3 1 2 2 1
(1 + ((1 + (x div (1 + (23 mod (x + 1))))) div 2))
A181776: 1 1 1 1 2 1 2 1 2 2 4 1 2 2 2 2
(1 + ((1 + (x div (1 + (x mod (2 * (1 + (x mod 9))))))) div 2))
A162235: 1 1 1 1 1 1 1 1 1 3 3 2 2 3 3 5
(1 + (2 * ((x + 1) mod (1 + (x mod (1 + (2 * (1 + (2x mod 3)))))))))
A346182: 1 1 1 1 1 1 1 1 3 1 7 1 1 1 1 1
(1 + ((1 + (x div (1 + (2 * (1 + (((x + 1) * (x div 4)) mod 2)))))) div 2))
A230443: 1 1 1 2 1 2 2 2 2 3 3 3 2 3 2 4
((x + 1) - ((x mod (1 + (x mod ((x + 1) - (x mod 10))))) div 2))
A275987: 1 2 3 4 5 6 7 8 9 10 6 12 13 14 14 16
(1 + (x div (2 + (x div (1 + ((x div 2) mod (1 + (x mod (2 * (1 + (x mod 2)))))))))))
A204988: 1 1 1 2 1 1 1 3 1 1 1 2 1 1 1 4
(1 + ((1 + (((x + 2) * (~2 + (x div 2))) mod (1 + (((x + 1) div 2) div 2)))) div 2))
A296773-A228369-A108244: 1 1 1 2 1 1 1 1 2 2 1 3 1 1 1 1
(1 + ((1 + ((x * (2 + (2x div 5))) div 5)) div 2))
A342517: 1 1 1 2 2 3 3 4 5 6 7 8 8 10 11 13
(1 + (x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))))
A329617-A329378-A320888-A319269-A296132-A179953-A086436: 1 1 1 2 1 2 1 3 2 2 1 3 1 2 2 4
(1 + (x div (2 + (x div (1 + (((x + 1) * (~1 + ((~x + 1) div 2))) mod 3))))))
A177025: 1 1 1 2 1 1 2 2 1 2 1 1 3 2 1 2
(1 + ((1 + (((x + 1) mod (1 + ((x + ~1) mod 3))) * (x div 3))) div 2))
A228202: 1 1 1 2 1 1 2 1 2 3 1 1 3 1 3 4
((x + 2) div (1 + (((1 + (x mod ~4)) mod (1 + (x div 3))) mod 2)))
A325943: 2 3 4 5 3 7 8 9 5 11 6 13 7 7 16 17
(~1 + ((1 + ((x + 1) div (1 + ((x div 5) + (x mod 3))))) div 2))
A241035: 0 0 0 1 0 0 1 0 0 2 0 0 1 1 1 1
(~1 + ((1 + (((x + 3) * (1 + (x mod 4))) div (1 + (x mod 2)))) div 2))
A176974: 1 1 7 5 3 3 13 9 5 5 19 13 7 7 25 17
(5 mod (1 + ((x mod (1 + ((2 - (x mod 4)) mod (x + 1)))) div 2)))
A318952: 0 0 0 1 0 0 0 1 1 0 0 5 0 0 0 5
(1 + (2 * ((2x + 1) - (((x + ((x div 4) mod 2)) div 2) div ~2))))
A285669: 3 7 13 17 21 27 31 35 39 43 49 53 57 63 67 71
(~1 + (2 * (1 + ((1 + (x mod (1 + (4 mod (1 + (x div 3)))))) div 2))))
A027023: 1 1 1 1 1 1 1 3 1 1 1 1 3 5 5 1
(1 + ((1 + ((1 + ((x + 2) mod (1 - ((~x + (x mod 2)) div 3)))) div 2)) div 2))
A264998: 1 1 1 2 1 2 2 1 2 2 2 2 2 1 2 3
(1 + ((x mod (1 + (2 * (1 + (((~1 + (x div (2 + (x mod 2)))) div 2) mod 2))))) div 2))
A162320: 1 1 2 1 1 2 1 1 2 3 1 1 1 2 3 1
(~1 + (2 * (1 + ((x mod (1 + (2 * (2 - (((x + ~1) div 2) mod 4))))) div 2))))
A093421: 1 1 3 1 1 1 1 1 1 5 1 3 1 1 1 1
(1 + (2 * (1 + ((x - (x div (11 - (x div 2)))) div 2))))
A117767: 3 3 5 5 7 7 9 9 9 11 11 13 13 13 13 15
(1 + (2 * (1 + ((5 * (x - (2 * ((~x + 2) div 4)))) div 2))))
A298360: 3 7 13 27 33 37 43 57 63 67 73 87 93 97 103 117
((x + 1) div (1 + (2 * (1 + (x div (2 + ((~2x + 2) mod 5)))))))
A280522: 0 0 1 0 1 1 0 1 1 2 1 0 1 1 2 1
(1 + ((1 + ((5 * (x + (x div 7))) div 2)) div 2))
A029903: 1 2 4 5 6 7 9 11 12 14 15 16 17 19 21 22
(1 + ((x2 + 2x) mod (2 + (x mod (1 + (x div (2 + (x div 5))))))))
A337908: 1 2 1 1 1 3 1 1 1 1 1 4 1 1 1 1
(3 + ((3 * (2 + ((x2 + x) div 2))) div 7))
A299114: 3 4 5 6 8 10
A130216: 3 4 5 6 8 10 12 15 19 23 27 32 37 42 48 55
(1 + (2 * (x - (((x - (x2 div 3)) div 2) div 7))))
A210719: 1 3 5 7 11 13 15 17 19 23 25 29 31 35 37 41
(2x div ((x + 1) + (2 * ((~x + 2) mod 7)) - (x mod 2)))
A212211: 0 0 1 0 0 0 0 1 1 2 0 1 1 1 1 1
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((7x + 6) - ((2x + 2) div 7))
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(((x7 + ~x) div 2) div 7)
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((2 - ((x + 1) mod (1 + (2 * (~2 + (x mod 2)))))) * (x div 7))
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(1 + ((x + 2) div (4 - (((x + 3) mod 7) mod 2))))
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((1 + (x div 5)) div (1 + (2 * (x mod (2 + (x mod 5))))))
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A029072: 1 1 1 1 2 2 3 3 4 4 5 6 8 8 9 10
(1 + (((1 + (((x * ((x div (2 + (x mod 2))) + (x div 2))) div 2) div 2)) div 2) div 2))
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(1 + ((((3 * ((x2 + 2x) + (x mod 2))) - (x mod 3)) div 2) div 2))
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(1 + ((x + 1) div (4 + ((~3x + 5) mod (1 + (x div 2))))))
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A220163-A207379: 1 1 1 1 1 1 2 2 1 1 2 2 2 1 1 4
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(1 + ((((2 - (2x mod (6 + (x mod 2)))) mod (x + 1)) div 2) div 2))
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A140751: 1 1 1 1 1 1 2 2 1 1 1 3 3 3 3 1
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(1 + ((((x div 2) div (1 + (~x mod 4))) mod 2) + (((x + 1) div 2) div 2)))
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(1 + ((1 + ((2x mod (1 + (x div 4))) + (((x + ~1) div 2) mod 2))) div 2))
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(64x2 + 120x + 71)
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(64x2 + 88x + 39)
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(x7 mod 33)
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(x7 mod 31)
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(1 + (2 * (x div (2 * (2 + ((3 + (x2 div 2)) mod (x + 4)))))))
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((15x + 15) + (x mod 15))
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((~1 + (x2 div 2)) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))
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((~x + 1) + (9 * ((x + 1) - (x mod 10))))
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(((4x + 6) * (x + (x div 4))) mod 9)
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(2x - (9 * ((2x div 9) mod 2)))
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(((((x + 1) * ((x div 2) mod 2)) div 2) div 3) + (x div 9))
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((2 - ((x div 2) div ~2)) mod (1 + ((2x + ~4) mod (2 + (x div 4)))))
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((x + 1) div (5 * (1 + (x mod (1 + (x mod (1 + (x mod 4))))))))
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(5 * (1 + (2 * (1 + (2 * (x - (2 * (x div ~3))))))))
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(x6 mod 45)
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(60x2 + 300x + 390)
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(((2x + 2) - (((x + 1) mod 8) mod 3)) mod 5)
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(250x + 260)
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(~x + ((x div 2) + (10 * ((2x + 1) - (x div ~2)))))
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((18x + 9) + (5 * ((x + 1) div 2)))
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(2 - ((~5x2 + ~26x + ~24) div 5))
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((4x + 2) + ((~2x + 2) div 5) - (x div 3))
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(46x - (2x div 5))
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((5x2 + 5x) + (((x3 + ~x) div 2) div 3))
A051943: 0 10 31 64 110 170 245 336 444 570 715 880 1066 1274 1505 1760
(1 + (3 * ((x2 + x) div 2)) - ((x2 + ~x) div 5))
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((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 5)
A277659: 0 0 0 0 0 0 0 1 1 0 0 2 4 2 0 0
(1 + (((2 + (x2 div 8)) div 3) + (x div 5)))
A027582: 1 1 1 2 2 3 4 4 5 6 7 8 9 10 11 14
((5 * (2x - (x mod 5))) + (x div 5))
A137935: 0 5 10 15 20 51 56 61 66 71 102 107 112 117 122 153
(((x div 5) div (1 + (x mod 5))) + (x mod 5))
A190594: 0 1 2 3 4 1 1 2 3 4 2 2 2 3 4 3
(3 + ((9x3 + 18x2 + 19x) div 2))
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(1 + (2 * (2 + compr(\x.((1 + (x mod (1 + (x mod 6)))) mod 3),x))))
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(1 + (2 * ((x + 2) + (((x + 1) + ((x div 3) mod 3)) div 3))))
A106571: 5 7 11 13 17 19 23 25 27 29 31 35 37 41 43 47
((x + 1) - (((x - (x3 div (x + 12))) div 2) div 2))
A161306: 1 2 3 4 5 7 9 11 14 17 20 24 28 33 38 44
(1 + (2 * ((x + 2) + (2x div (4 + ((x div 2) div 5))))))
A286265: 5 7 11 13 17 19 23 25 29 31 33 35 37 41 43 47
(1 + (4 * (x + (2 * ((3 * (x div 7)) div 2)))))
A334525: 1 5 9 13 17 21 25 37 41 45 49 53 57 61 81 85
(x div ((~x + 1) + (((x div 2) mod 2) + (2 * (x2 div (x - ((~x + 2) div 2)))))))
A294108: 0 0 0 1 1 2 1 2 2 2 1 2 2 3 2 2
(1 + (((x + 2) * ((x + 1) + (2 * ((x - ((~x + 2) div 4)) div 2)))) div 2))
A026275: 2 4 11 21 28 43 53 73 96 111 139 170 190 226 249 290
(1 + ((~1 + (x * (1 + (x mod (1 + ((~x + 2) mod 4)))))) div (x + 4)))
A326195-A325568: 0 1 1 2 1 2 1 3 2 2 1 3 1 2 1 4
((4x + 1) + (((x * ((x2 + ~2x) div 4)) div 2) div 3))
A093410: 1 4 9 13 18 23 31 38
(24x4 + 50x3 + 35x2 + 10x + 1)
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(1 + (2 * (1 + ((x * (~1 + ((2x + 1) * (x + (x div 2))))) + (x div 2)))))
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(1 + ((1 + (((2x + 1) mod (1 + ((x + 1) div 3))) + (x mod 2))) div 2))
A236103: 1 2 2 2 2 3 2 2 2 3 2 3 1 3 4 2
(1 + ((1 + (((x + 2) mod (3 + (x mod 4))) div 2)) mod (2 + (x mod 2))))
A036583: 1 3 2 1 2 3 1 3 2 3 1 2 1 3 2 1
((1 + ((3 * (((x + 1) div 2) div 3)) div 2)) div (1 + (2 * (x mod 2))))
A029225: 1 0 1 0 1 0 2 0 2 0 2 1 4 1 4 1
((1 + (x div (4 + ((x div 2) mod 5)))) div (1 + (2 * (x mod 2))))
A029239: 1 0 1 0 1 0 1 0 2 0 3 1 3 1 3 1
((1 + (2x mod (1 - (x mod ~7)))) * (1 + (2 * (x mod 2))))
A255896: 1 9 5 6 1
((1 + ((8x + 8) mod 13)) div 3)
A190445: 3 1 4 2 0 3 1 4 2 1 3 2 0 3 1 4
((1 + (x div (1 + (x div (3 * (2 - ((x * (x div 2)) mod 2))))))) div 3)
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A106752: 0 0 1 0 1 2 1 1 1 1 2 1 1 1 1 1
((1 + (x div (1 + (((1 + (x div 2)) div (2 - (x mod 2))) div 3)))) div 3)
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(2 - ((1 + ((2 * (x mod ~3)) mod (1 + (x div 3)))) mod 3))
A117468: 1 1 1 1 1 1 1 2 0 1 1 2 1 0 1 1
((x div (1 + ((x div 2) div (1 + ((x mod (1 + (x div 3))) div 2))))) mod 3)
A098082: 0 1 1 1 1 1 1 1 2 1 0 0 0 0 1 0
(3 * (1 + (x div 3) - ((2x + 4) div 7)))
A036477: 3 3 0 3 3 0 3 3 3 3 3 3 3 3 3 6
((1 + (x mod (1 + (2 * ((4 * (x mod 2)) + (x mod 3)))))) div 3)
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((1 + ((x + 1) div (~1 + (2 * ((x2 + ~1) mod 6))))) mod 3)
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((x + 1) mod (3 * (1 + (x mod (1 + ((x2 + 2x) mod 8))))))
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((1 + ((2 * (1 + ((x + 2) * (x + (x div 2))))) div 5)) mod 3)
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((1 + (5 * (2 + ((x + ~2) div (2 + (x div 4)))))) div 3)
A063905: 2 2 3 3 3 5 5 5 5 5 7 7 7 7 7 7
((1 + ((x * ((x + 2) mod (1 + (x div 4)))) mod 5)) mod 3)
A274886: 1 1 1 1 1 1 1 0 1 1 1 2 2 2 1 1
(((x + 1) - ((~x + (((x + ~1) div 2) * (x div 2))) div 5)) mod 3)
A077614: 1 0 1 2 0 1 1 2 0 0 0 1 1 1 1 1
((1 + (x div (3 * (~1 + (2 * (x mod 7)))))) mod 3)
A252911: 1 1 1 1 1 1 1 1 0 2 1 1 1 1 2 0
((1 + ((2 * (1 + (2x * (x2 div 3)))) div 3)) div 3)
A190798: 0 0 1 4 9 18 32 50 75 108 147 196 256 324 405 500
(3 * (~1 + (3 * ((3x2 + 11x + 6) div 2))))
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(3 * (1 + ((4 * (x - (x div ~5))) div 3)))
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(((x + 1) * ((1 - (x div ~4)) * (1 + (x div 3)))) mod 3)
A092037: 1 1 0 1 2 0 0 0 0 1 2 0 2 2 0 0
((x + 2) + ((1 + (x div 3)) div 3) - ((~x + 1) div (2 + (x div 2))))
A329898: 2 3 5 6 7 8 10 12 13 14 15 16 17 18 19 21
((1 + ((1 - ((2x + ~2) mod 7)) mod (x + 1))) mod 3)
A249603: 1 2 0 2 1 1 0 2 2 1 0 2 1 1 0 2
((16x3 + 60x2 + 68x + 24) div 3)
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((x5 + 5x4 + 11x3 + 13x2 + 9x + 3) div 3)
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((1 + (((x + 3) mod (1 + (2 * (x mod 6)))) div 2)) mod 3)
A072617: 1 1 1 1 1 2 1 1 1 0 0 2 1 1 2 0
((x - (x mod (~1 + (2 * ((~2x + 2) div 9))))) div 3)
A224458: 0 0 1 1 2 2 3 3 3 3 3 4 4 4 4 6
(1 - ((x - (x mod (1 + (2 * ((x - (x div 3)) mod 3))))) mod 3))
A143200: 1 1 1 1 0 1 1 ~1 ~1 1 1 0 0 0 1 1
(3 * ((x + 1) - (x div (~2 + ((1 - (2 * (x div 3))) div 3)))))
A194412: 3 9 12 15 21 24 27 33 36 39 42 45 48 51 54 57
((~x + 1) + (3 * (2x - ((2x + ~1) div 7))))
A190564: 4 6 11 16 18 23 28 33 35 40 45 47 52 57 62 64
(1 - ((((x2 + 2x + 1) + (x div 2)) mod 7) mod 3))
A086823: 0 0 1 1 1 1 1 0 0 1 1 ~1 1 1 0 0
((~x + 2) + (3 * (2x - ((2x + 2) div 7))))
A190548-A187971: 2 7 12 14 19 24 26 31 36 41 43 48 53 55 60 65
((~x + 2) + (3 * (2x - ((2x + 4) div 7))))
A190565: 2 7 9 14 19 21 26 31 36 38 43 48 50 55 60 65
((~x + 1) + (3 * (2x - ((2x + ~4) div 7))))
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(84x2 + ~104x)
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(3 * ((x + 3) - (x2 div ((2x + 4) - (x div 3)))))
A336756: 9 12 15 15 18 21 21 21 24 24 27 27 27 30 30 33
((1 - (((x2 + 2x) div 2) mod (1 + (x div (2 + (x div 3)))))) mod 3)
A340655: 1 1 1 0 1 0 1 0 0 0 1 2 1 0 0 0
((2x div (1 + (2 * ((x - ((x div 2) mod 5)) mod 2)))) mod 3)
A219026: 0 0 1 0 2 0 1 2 1 0 2 1 2 2 1 1
((1 + ((((~1 + (2 * (x mod 6))) mod (x + 1)) div 2) div 2)) mod 3)
A225803: 1 1 1 1 1 1 2 1 1 2 2 0 1 1 1 2
(x - ((1 + (2 * (x - ((~x + 2) div (2 - (x mod ~4)))))) div 3))
A319815: 1 0 1 0 1 1 1 1 1 2 2 2 1 2 3 2
(x div (3 * (1 + (x mod (4 + ((x mod 9) div 2))))))
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(1 - ((5x + 1) mod 51))
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((1 + ((~1 + (2 mod (~2x + 1))) mod (4 + (x div 4)))) div 3)
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(1 - ((~1 + ((2x2 + ~1) mod (4 + (x div 4)))) div 3))
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(x7 mod 27)
A070708: 0 1 20 0 22 14 0 16 8 0 10 2 0 4 23 0
((1 - ((2x + 1) mod (1 + (2x mod (2 + (x div 4)))))) mod 3)
A336569: 1 1 1 1 1 0 1 1 1 0 1 2 1 0 0 1
(x - ((5 * ((x - (x div ~7)) div 2)) div 3))
A280269: 0 0 1 0 1 0 1 1 0 1 0 1 1 2 1 0
((x2 + 12x + 35) - (x div 5))
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(3 * (3 + ((4x + (x2 div 4)) div (x + 2))))
A336754: 9 12 15 15 18 18 21 21 21 24 24 24 27 27 27 27
(3 + ((4x4 + 4x3 + ~x2 + 1) div 3))
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(x7 mod 36)
A070717: 0 1 20 27 4 5 0 7 8 9 28 11 0 13 32 27
(3 + ((4 * (x - (x2 div (3x + 4)))) div 3))
A196122: 3 4 5 7 7 8 9 11 11 12 13 13 15 16 16 17
(2 - (9 * ((~x + 1) - (2 * (2 + (x div 8))))))
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(((2x2 + 7x + 3) * ((x2 + 3x + 2) div 2)) div 3)
A051797: 1 12 50 140 315 616 1092 1800 2805 4180 6006 8372 11375 15120 19720 25296
((10x3 + 21x2 + 14x + 3) div 3)
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((12x4 + 14x3 + 6x2 + x) div 3)
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(((2x + ~1) * (3x2 + ((x2 + ~x) div 2))) div 3)
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(((2x + ~1) * (2 + (14 mod (x + 1)))) mod 3)
A091395: 1 2 0 2 0 0 1 2 0 0 2 0 0 2 0 2
((((x + 3) * ((x2 + 3x + 2) div 2)) div (1 + (x mod 2))) div 3)
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((10x3 + 18x2 + 11x + 3) div 3)
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(((0 - (x mod (1 + (2 * (x div (2 * (2 + (x mod 2)))))))) mod (x + 1)) div 3)
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((16x3 + 33x2 + 20x + 3) div 3)
A213842: 1 24 101 264 545 976 1589 2416 3489 4840 6501 8504 10881 13664 16885 20576
(3 + ((2 + ((2 - (2x mod 5)) mod (x + 1))) div (x + 1)))
A137240: 5 4 4 3 4 3 3 4 3 4 3 3 4 3 4 3
(((x + 1) * (((x + 1) * ((3 * (x div 4)) div 2)) div 2)) mod 3)
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(24x3 + 72x2 + 156x + 108)
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(2 - (compr(\x.(2 - (x mod (4 + (x mod 5)))),(x + 1)) mod 3))
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(288x2 + 480x + 192)
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(1 - (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))
A176270: 1 1 1 1 0 1 1 ~1 ~1 1 1 ~2 ~3 ~2 1 1
(((x + 1) * ((x2 + 17x + 30) div 2)) div 3)
A096941: 5 16 34 60 95 140 196 264 345 440 550 676 819 980 1160 1360
(((x + 1) * ((2x3 + 7x2 + 9x + 6) div 2)) div 3)
A066804: 1 8 34 100 235 476 868 1464 2325 3520 5126 7228 9919 13300 17480 22576
((3x2 + 9x + 6) + (((x3 + ~x) div 2) div 3))
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((3x + 3) + (((x + 1) div 7) + (x div 3)))
A184909: 3 6 9 13 16 19 24 27 30 34 37 40 44 48 51 55
((3x + 3) + (2 * (x - ((x - (x div 5)) div 3))))
A189405: 3 8 13 16 21 26 31 34 39 44 49 52 57 62 65 70
((x + 1) - ((2 * (2x div 9)) + ((x + 1) div 3)))
A117632: 1 2 2 3 4 2 3 4 4 3 4 4 5 6 4 5
(x - ((2 * ((((2 - (x div 2)) mod (x + 2)) div 2) div 2)) + ((x + 1) div 3)))
A287732: 0 1 1 2 3 3 2 1 1 2 3 3 4 5 5 4
(((x + (24 * (1 + (x div 2)))) div (x + 1)) mod 3)
A172444: 0 0 1 0 0 0 2 0 2 0 2 0 1 0 1 0
((69 mod (x2 + 1)) mod 3)
A326787: 0 1 1 0 1 2 2 1 1 0 0 0 0 0 0 0
(6 * (x mod (1 + (((x2 + ~1) div 2) mod (1 + (x div 3))))))
A194186: 0 0 0 0 0 0 0 0 0 0 0 0 0 18 12 0
((2 * ((2x + 5) - ((x div 3) div ~3))) div 3)
A134745: 3 4 6 8 9 10 12 13 14 16 17 18 20 22 23 24
(6 * ((x + 2) mod (1 + ((x + (x div 4)) mod (1 + (x div 2))))))
A005872: 0 0 0 6 0 0 0 0 0 6 0 6 0 0 0 12
(108x2 + 204x + 90)
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((2 * (1 + ((1 + (x div (2 + (((x + ~1) div 2) mod 3)))) div 2))) div 3)
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((2 * (2 - ((~x + 1) div (1 + (x div (2 + (3 * (x mod 2)))))))) div 3)
A067743: 0 1 2 2 2 2 2 3 2 4 2 4 2 4 2 4
((1 - ((2x mod (1 + (2 * ((1 + (x div 4)) div 2)))) div 2)) mod 3)
A337939: 1 1 1 1 0 1 1 0 1 1 0 1 2 1 0 1
((1 - ((2x mod (~1 + (2 * (((~x + 2) div 2) mod 4)))) div 2)) mod 3)
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(((x3 + 15x2 + 56x) div 2) div 3)
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(((1 + (((x + 2) * ((4 * (x mod 2)) + (x div 2))) div 2)) div 2) div 3)
A114209: 0 1 0 2 1 3 2 5 3 7 5 9 7 12 9 15
(((x3 + 15x2 + 50x) div 2) div 3)
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(~3 + ((6x2 + 99x + 48) div 2))
A283802: 21 73 132
(x - (6 * (x div (3 * (2 + (x mod 7))))))
A319655: 0 1 2 3 4 5 6 1 8 9 10 11 12 13 2 9
((2 + (x2 mod (6 * (1 + (x div 8))))) div 3)
A165579: 0 1 2 1 2 1 0 1 2 3 2 1 0 1 2 3
(3 + (x div (2 + ((4 * ((x + 1) div 5)) div 3))))
A090972: 3 3 4 4 4 4 5 5 5 5 5 5 6 6 5 5
((2 * ((x - (x mod (~3 - (x div 4)))) div 3)) div 3)
A157231: 0 0 0 0 0 1 1 1 2 2 2 3 2 4 4 4
(6 * (1 - (((x - ((x2 + ~x) div 4)) div 2) div 3)))
A245399: 6 6 6 6 6 6 12 12 12 18 18 24 30 36 42 48
((1 - ((1 + (x mod (2 + (x mod 4)))) div (2 + (x mod 3)))) mod 3)
A113045: 1 1 1 2 1 1 0 0 1 1 0 1 1 1 1 1
((((2x + 1) * (1 + ((x + ~1) mod 9))) div 2) mod 3)
A039964: 1 1 2 1 0 0 0 1 2 1 1 2 1 0 0 0
(3 * ((27x2 + 33x + 8) div 2))
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((((x2 + 2x + ~1) * ((x3 + 3x2 + 2x) div 2)) div 2) div 3)
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((((2 - ((x + ~2) mod (~1 + (2 * (x mod 4))))) mod (x + 1)) div 2) mod 3)
A342788: 0 0 1 0 1 1 0 1 1 1 0 2 1 1 1 1
(((x2 + 4x + 4) div 2) - (((x3 + x2 + ~x + ~1) div 2) div 3))
A081826: 3 4 7 7 6 0
((((x + 1) * ((1 - ((x - (x2 div 4)) div 2)) div 2)) div 2) div 3)
A319470: 0 0 0 0 0 1 1 2 3 5 7 10 13 18 22 29
(3 * ((4x3 + 21x2 + 23x + 6) div 2))
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(((5x3 + 21x2 + 28x + 12) div 2) div 3)
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(((x3 + 21x2 + 56x + 36) div 2) div 3)
A096957: 6 19 40 70 110 161 224 300 390 495 616 754 910 1085 1280 1496
(((11x3 + 21x2 + 10x) div 2) div 3)
A254407: 0 7 32 86 180 325 532 812 1176 1635 2200 2882 3692 4641 5740 7000
((((x + ~1) * ((x3 + 5x2 + ~2x) div 2)) div 2) div 3)
A328152: 0 0 2 11 34 80 160 287 476 744 1110 1595 2222 3016 4004 5215
(2 - (1 mod (3 - (((x3 + 3x2 + ~4x) div 2) div 3))))
A212346: 1 1 2 5 14 28 48 75 110 154 208 273 350 440 544 663
((2x3 + ~x) - (((x3 + ~3x2 + 2x) div 2) div 3))
A050441: 0 1 14 50 120 235 406 644 960 1365 1870 2486 3224 4095 5110 6280
((x * (x2 - (x div 2))) - (((x3 + ~3x2 + 2x) div 2) div 3))
A212570: 0 1 6 23 52 105 178 287 424 609 830 1111 1436 1833 2282 2815
(6 * ((1 + (x2 mod (1 + (2 * ((x + 1) mod 3))))) div 2))
A217219: 0 6 0 0 6 0 0 12 0 0 0 0 0 12 0 0
((x + ~1) + ((2 * ((2x + 4) - ((~1 + (x div 3)) div 2))) div 3))
A187834: 2 4 7 8 11 13 15 18 20 22 24 26 29 31 33 35
(6 * ((1 + (5x3 div (x + 1))) div 2))
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(~x + ((x div 2) + (12 * (1 + (2 * (x - (x div ~2)))))))
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(1 - ((2 * (2 + ((x + 1) mod (1 + (2 * ((x + 2) mod 4)))))) mod 3))
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((2 + ((1 + (x div 3)) mod (2 + ((x + 2) mod 5)))) div 3)
A206474: 1 1 1 0 1 1 1 1 1 1 0 2 2 1 1 1
((2 * (2 + ((2 + (x div (1 + ((x + 1) mod 3)))) div 3))) div 3)
A174273: 1 1 2 2 2 2 2 2 3 2 2 4 2 2 4 3
((4 * ((5x + 5) + ((x div 2) div 3))) div 3)
A189523: 6 13 20 26 33 40 48 54 61 68 74 81 89 96 102 109
((2 * ((((x + ~2) - ((~x + 2) div 4)) * (1 + (x div 2))) div 2)) mod 3)
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((2 * (2 + ((x * (4 + (x div 4))) mod (1 + (x div 2))))) div 3)
A064822: 1 1 1 1 2 2 2 3 3 4 1 1 1 1 2 2
((8 * (x div (~x + 19))) div 3)
A308857: 0 0 0 0 0 0 0 0 0 0 2 2 2 5 5 8
(3 * (2 + ((((x mod 6) + (x mod 5)) div 2) mod 2)))
A023410: 6 9 6 9 6 6 6 9 6 9 6 9 9 6 9 9
((x2 + ~2x + 1) div (~6x + 108))
A035565: 0 0 0 0 0 0 0 0 0 1 1 2 3 4 7 10
((2 - ((2x + 2) mod (1 - (2 * (2 + (x div 8)))))) div 3)
A320955-A318557-A309896-A294220-A288942-A276837-A276719-A262553-A247506-A240608-A238093-A214015-A192517-A182172-A143841-A080934: 1 1 0 1 1 0 1 1 1 0 1 1 2 1 0 1
(2 - ((2 + (x mod (2 + ((~x + 1) mod (2 + (x div (2 + (x mod 2)))))))) div 3))
A321787: 2 1 1 2 1 1 2 1 1 1 1 1 0 1 2 1
(3x mod (1 - ((x mod (~2 + (x mod ~7))) div 3)))
A140807: 0 3 0 1 0 1 0 1 0 0 0 0 0 1 0 1
(x7 mod 48)
A070728: 0 1 32 27 16 29 0 7 32 9 16 35 0 37 32 15
(((1 + (x mod (1 + (x div 5)))) * ((x + ~1) mod 4)) div 3)
A025870: 1 0 0 0 1 0 0 1 1 0 0 2 1 0 1 2
((4 * compr(\x.(~1 + (x mod 4) - (x mod 5)),x)) div 3)
A138083: 0 1 2 4 5 6
A035063: 0 1 2 4 5 6 8 9 10 12 16 17 18 21 22 24
((2 * (2 + ((x2 + ~x) div (~x + 24)))) div 3)
A005855: 1 1 1 1 1 2 2 2 3 4 5 6 8 10 13 16
((2 * ((x + 2) + ((x - (((~x + 2) div 2) mod 4)) div 3))) mod 3)
A194702: 2 0 2 1 0 1 0 1 0 1 0 0 1 0 1 0
((((x * (2 + ((2 + (x mod 8)) mod (x + 1)))) div 2) div 2) div 3)
A309793: 0 0 0 0 1 1 1 1 2 3 5 6 8 9 11 13
((16x3 + 48x2 + 38x + 12) div 3)
A152110: 4 38 136 330 652 1134 1808 2706 3860 5302 7064 9178 11676 14590 17952 21794
(x - (((x + 2) + ((x2 + ~2) div 11)) div 3))
A317359: 0 1 1 2 2 2 3 3 3 3 4 4 4 3 3 3
(((x * (x - (((~x3 + x) div 4) div 3))) div 2) mod 3)
A334108: 0 0 0 1 0 1 0 2 2 1 0 2 0 1 2 1
((5x + 4) - ((2 * (~x + ((x div 3) mod 2))) div 3))
A081260: 4 10 16 21 26 32 38 44 50 55 60 66 72 78 84 89
(6x + ((~2x + 4) div (4 + ((x div 2) div 3))))
A315700: 1 6 12 17 23 28 34 40 45 51 56 62 68 74 80 85
(((2 * ((4x + 4) + ((x + 1) div 3))) + (x div 2)) div 3)
A206904: 2 5 9 11 14 18 21 23 27 30 33 36 39 42 45 48
(((x * (1 - ((x3 div 8) mod 2))) + (x mod 2)) div 3)
A335683: 0 0 0 0 1 0 0 2 2 0 0 4 4 4 0 0
(x5 + 2x3 + 9x2 + 5)
A089923: 5 17 89 383
(((x * (x + (5 * ((x3 + x) div 2)))) div 2) div 3)
A139594: 0 1 9 39 116 275 561 1029 1744 2781 4225 6171 8724 11999 16121 21225
((x3 + 3x2 + 3x + 1) - (((~x3 + x) div 2) div 3))
A100182: 1 8 28 68 135 236 378 568 813 1120 1496 1948 2483 3108 3830 4656
(((x2 + 2x + 1) * (x div 2)) - (((~x3 + x) div 2) div 3))
A294473: 0 0 10 20 60 92 182 248 408 520 770 940 1300 1540 2030 2352
((x + 3) + ((x + 1) mod (1 + (x mod (1 + (x div (2 + (x mod 4))))))))
A096127: 3 4 5 6 8 8 9 10 12 12 14 14 16 18 17 18
((x + 3) + ((2 * ((2x - (x div 4)) div 3)) div 3))
A298108: 3 4 5 7 8 10 11 12 13 15 17 18 19 20 22 24
((x + ((x + (2 * (((x div 4) * (x div 2)) div 2))) div 3)) mod 3)
A276790: 0 1 2 1 0 1 2 1 1 2 1 0 1 2 1 2
((x + 3) + (2 * (2x - ((x + (x div 4)) div ~3))))
A328987: 3 10 15 20 27 32 39 44 51 56 61 68 73 80 85 90
((x + 3) + (2 * ((2x3 + 9x2 + 12x + 4) div 3)))
A208946: 5 22 57 122 223 366 563 820 1143 1544 2029 2604 3281 4066 4965 5990
((x + 3) + (2 * (x - (((x + 2) mod (1 + (~x mod 4))) div 2))))
A287450: 3 4 9 12 15 16 19 24 27 28 33 36 39 40 45 48
(((x + 2) + (x div (2 + (16 mod (1 + (x div 2)))))) div 3)
A060973: 0 1 1 2 2 2 3 4 4 4 4 4 5 6 7 8
((x + ~3) + (2 * ((2x + 2) - ((x2 div (x + 2)) mod 4))))
A292151: 1 6 9 14 17 20 31 34
((x + 3) + (2 * (2x - (((~x + 2) - (x div 4)) div 4))))
A303592: 3 8 13 20 25 30 37 42 47 54 59 64 71 76 81 86
((x + 3) + (2 * (x + (2 * ((((x + ~1) div 2) * (x div 2)) div 3)))))
A289761: 3 6 9 12 15 22 29 36 43 50 57 68 79 90 101 112
((x + 3) + ((x + (11x div (x + 2))) div 2))
A185547: 3 6 8 10 12 14 16 17 19 21 22 24 25 27 28 30
(compr(\x.((((~2x + 1) div 9) mod 2) - (x mod 2)),x) mod 3)
A085794: 0 1 0 2 0 1 2 0 2 1 0 1 2 0 1 0
(1 + (((x mod (1 + (((~x2 + x) div 2) mod 4))) div 2) + (x div 3)))
A272612: 1 1 2 2 2 3 3 4 3 4 5 4 5 5 5 7
((3x + 2) + (x div 3) - ((x + 1) div 7))
A190000: 2 5 8 12 15 18 21 24 27 31 34 37 41 43 46 50
(1 + ((x div 3) + (x div (~3 + (((2 - (x div 2)) div 2) div 2)))))
A029309: 1 0 0 1 0 0 1 1 1 1 1 1 2 1 2 3
(((1 + (((x mod (2 + (x mod 2))) mod 2) + (x mod 2))) mod (x + 1)) + (x div 3))
A234300: 0 1 1 3 2 3 3 5 3 5 4 5 5 7 5 7
((4x + 4) + (((x + 1) div 7) + (x div 3)))
A189527: 4 8 12 17 21 25 31 35 39 44 48 52 57 62 66 71
((((1 + ((x2 + ~x) div 8)) mod 2) + (x div 3)) - (x mod 2))
A029169: 1 0 1 1 1 1 2 1 2 2 3 2 5 3 5 5
(64x3 + 24x2 + 4x + 1)
A160250: 1 93 617 1957 4497 8621 14713 23157 34337 48637 66441 88133 114097 144717 180377 221461
(1 + ((x + (((x + 1) * (x + ((x2 + 2x) div 4))) div 3)) div 2))
A008369: 1 1 4 6 11 16 25 33 47 60 79 98 124
(1 + ((x + (3 * (4x + ((x mod (1 + (x div 2))) div 2)))) div 2))
A339950: 1 7 14 20 27 35 41 48 54 62 69 75 82 90 96 103
(1 + ((3x + 2) * (1 + ((3x2 + 7x + 4) div 2))))
A230018: 7 41 129 298 575 987 1561 2324 3303 4525 6017 7806 9919 12383 15225 18472
(1 + (2 * (x + ((x + (x div 5) - ((x div 2) div 3)) div 2))))
A284884: 1 3 7 9 13 17 19 21 25 27 31 35 37 39 43 47
(1 + ((~x + ((3 * (1 + ((x2 + ~2) div (x + 4)))) div 2)) div 2))
A029307: 1 0 0 1 0 0 1 1 1 1 2 1 1 2 2 2
(32x2 + 223x + 319)
A250660: 319 574 893 1276 1723 2234 2809 3448 4151 4918 5749 6644 7603 8626 9713 10864
(~1 + ((~1 + (2 * ((x2 + (x div 2)) div 7))) mod (x + 2)))
A194759: 0 1 2 0 2 4 0 3 6 0 4 8 12 3 8 13
((2x + 1) + ((2x2 + x) div 19))
A097911: 1 3 5 8
A027922: 1 3 5 8 10 13 17 20 24 28 32 36 40 45 50 55
((2x + 1) + ((x div (4 + (x div 4))) + ((x + 2) div 3)))
A231407: 1 4 6
A226250: 1 4 6 8 11 14 16 19 21 23 26 28 30 33 36 38
((2x + 1) + ((x - ((x - ((x div 2) mod 5)) div 3)) div 2))
A189679: 1 3 6 8 11 13 15 18 20 23 24 27 29 31 34 36
((2x + 1) + ((x + ((~x + 2) mod (3 + (x div 4)))) div 4))
A097911: 1 3 5 8
A073608: 1 3 5 8 10 12
A342871: 1 3 5 8 10 12 14 17 20 22 24 26 28 30 32 36
(50x3 + 75x2 + 27x + 1)
A193249: 1 153 755 2107 4509 8261 13663 21015 30617 42769 57771 75923 97525 122877 152279 186031
(60x3 + 90x2 + 32x + 1)
A193253: 1 183 905 2527 5409 9911 16393 25215 36737 51319 69321 91103 117025 147447 182729 223231
(120x3 + 60x2 + 2x + 1)
A272126: 1 183 1205 3787 8649 16511 28093 44115 65297 92359 126021 167003 216025 273807 341069 418531
((2x + 2) + (((3x * ((x + ~1) mod 3)) div 2) div 2))
A193841: 2 4 7 12 10 15 23
((((x + 1) * ((3x2 + 7x + 4) div 2)) div 2) div (2x + 1))
A025709-A025703: 1 2 4 7 11 15 20 26 33 40 48 57 67 78 89 101
(1 + (((((x + 1) * (x + (x div 3))) div 2) div 5) + (x div 2)))
A225527: 1 1 2 3 5 6 9 11 14 17 20 22 27 30 35 40
((2 - ((~x + 2) div (1 + (2 * (2 mod (1 + (x div 4))))))) mod (1 + (x div 2)))
A276646: 0 0 0 1 1 2 2 3 4 4 4 4 4 5 5 5
((5 + ((3x2 + 7x + 4) div 2)) * (1 + (x div 2)))
A218554: 7 12 40 62
(((x mod (~1 + (2 * (x div 3)))) mod 2) * (5 mod (1 + (x div 2))))
A189232: 0 0 0 0 0 0 0 1 0 0 0 5 5 0 0 0
(177 mod (1 + (x div 2)))
A340328: 0 0 1 1 0 0 1 1 2 2 3 3 2 2 1 1
((x - (3 * (3 - (2 * ((x + (x div 2)) div 2))))) mod (1 + (x div 2)))
A229878: 0 0 1 0 1 2
A324904: 0 0 1 0 1 2 1 0 0 1 1 2 1 2 1 0
(((1 + (x mod (2 + ((x mod 3) div 2)))) div (1 + (x div 2))) * (1 + (x div 2)))
A243310: 1 2 2 2 0 3 0 0 0 0 0 0 0 0 0 0
(((x + 1) + (x div (2 + ((x2 + 2x) mod 6)))) mod (1 + (x div 2)))
A308210: 0 0 1 0 1 0 2 1 1 1 4 1 5 2 2 3
(x - ((((x div 2) mod 5) div 2) * (8 mod (1 + (x div 2)))))
A064895: 0 1 2 3 2 3 6 7 2 3 10 11 12 13 14 15
((x + 2) + (((3x mod (~1 + (x div ~2))) mod 2) + (x div 2)))
A274436: 2 4 5 6 8 10 11 12 15 16 17 18 20 22 23 24
((x + 1) + (((2 * (x - ((((x + 1) div 2) div 2) div 2))) div 3) + (x div 2)))
A206815: 1 2 5 7 9 11 14 15 17 19 22 23 26 28 30 31
(((x2 + x) + (6 * (1 + (2 * (x div 2))))) div (1 + (x div 2)))
A328537: 6 8 12 15 16 20 21
(2 + (((~1 + (((x + ~1) * (x div 2)) div 2)) div 2) div 3) - (x mod 2))
A029141: 1 0 1 1 2 1 3 2 4 3 5 5 7 6 9 9
(1 + ((1 + ((1 + ((x2 + 2x) mod (1 + (x div 3)))) div 2)) * (x mod 2)))
A328570: 1 2 1 3 1 3 1 2 1 4 1 4 1 2 1 4
(1 + (((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4))) + (x mod 2)))
A325565-A065704: 1 2 1 3 1 2 1 4 2 2 1 3 1 2 1 5
((x + ~1) mod (1 + ((((x + 3) mod 7) mod 2) + (x mod 2))))
A307505: 1 0 1 0 0 1 0 0 0 2 0 0 1 0 1 0
(1 + ((1 + (((((x + ~1) * (1 + (x div 2))) div 2) div 2) div 2)) div 2) - (x mod 2))
A029172: 1 0 1 0 2 1 2 2 3 3 4 4 6 5 8 7
((x + 1) + (x mod 2) - ((1 + (x div 2) - ((~x + 2) div (2 + (x div 2)))) mod 2))
A307747: 1 2 3 4 5 7 6 8 9 10 11 13 12 14 15 17
(1 + ((((1 + (x div 3)) div (1 + (x mod (2 + (x mod 2))))) mod 2) + (x mod 2)))
A055020: 2 2 2 2 1 2 2 3 2 2 1 3 2 2 2 2
(1 + (((x2 + x + 1) div ((x + 1) + (x div 3))) mod 2) - (x mod 2))
A257857: 2 1 1 0 2 0 1 1 1 1 2 0 2 0 2 1
(1 + ((2 * (((1 + (x * (x + (x div 2)))) div 5) mod 2)) + (x mod 2)))
A105500: 1 2 3 2 3 4 3 2 3 4 1 4 3 4 3 2
(1 + ((2 * ((((1 - (x mod 4)) mod (x + 1)) mod 3) mod 2)) + (x mod 2)))
A100661: 1 2 1 2 3 2 1 2 3 2 3 4 3 2 1 2
(1 + ((2 * (((x - ((x2 div 2) mod (x + 2))) div 3) mod 2)) + (x mod 2)))
A105584: 1 2 1 4 1 2 3 2 1 2 1 4 3 4 1 4
(1 + ((((x div (~2 + (x mod ~2))) mod (2 + (x div 3))) div 2) + (x mod 2)))
A214180: 1 2 1 3 1 2 1 2 1 3 1 2 1 2 3 3
(1 + ((x div (2 + (x div (2 + ((x2 + 2x) mod 6))))) + (x mod 2)))
A326198-A076640: 1 2 2 3 2 4 2 4 3 5 2 5 2 5 3 5
(x + (x mod 2) - ((x2 mod (2 + (((x + 1) div 2) div 2))) mod 2))
A222234: 0 1 2 4 3 5 6 7 8 9 10 11 12 14 13 15
((2x + 5) + (((x mod (2 + (x div (2 + (x mod 2))))) mod 2) + (x mod 2)))
A127500: 5 9 9 12 13 16 18
((1 + ((1 + ((((x div 2) div 3) * (x div 2)) div 2)) div 2)) div (1 + (x mod 2)))
A029218: 1 0 1 0 1 0 2 1 2 1 2 1 4 2 5 2
(1 + compr(\x.(x mod (1 + (x mod (1 + ((2x2 + 2) mod (1 + (x div 2))))))),x))
A344979-A328867-A326536-A324769-A322902-A302040-A302036-A273130-A014567: 1 2 3 4 5 7 8 9 11 13 16 17 19 21 23 25
(1 + compr(\x.(~1 + ((x + 2) mod (1 + ((x - ((x div 3) mod 3)) div 2)))),x))
A182625: 1 2 3 4 5 6 8 10 11 12 14 19 20 21 22 24
(1 + compr(\x.((x + 1) mod (1 + (x div (1 + (2 * (2 - ((x mod 3) div 2))))))),x))
A187041-A097752-A014866: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 21 24
(1 + compr(\x.((x + 1) mod (1 + (x mod (1 + (x div (2 + (x div 8))))))),x))
A259227-A064150: 1 2 3 4 6 8 9 10 12 15 16 18 20 21 24 25
(1 + compr(\x.((x + 1) mod (1 + (x div (5 * (1 + (x mod 3)))))),x))
A248888-A124455-A112587-A072378: 1 2 3 4 5 6 8 9 10 12 14 15 16 18 20 24
(1 + compr(\x.((x + 1) mod (1 + ((x mod 5) mod (1 + (x div 4))))),x))
A067942: 1 2 3 4 5 6 8 9 10 11 12 15 16 18 20 21
(1 + (x2 div ((x + 1) + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))
A069345: 1 1 2 2 4 4 6 5 7 8 10 9 12 12 13 12
(1 + compr(\x.(~1 + (((x + ~1) + (x div (1 + (x div 5)))) mod 3)),x))
A028734: 2 3 5 6 8 10 11 12 13 14 17 19 20
(1 + compr(\x.(~1 + (((x + 1) * (1 + (((x + ~1) div 2) mod 4))) mod 3)),x))
A330998: 1 3 5 6 7 9 10 12 14 15 16 18 19 20 21 22
(~1 + compr(\x.(2 - ((x + 1) mod (1 + (6 * (2x mod 3))))),x))
A275672: 0 1 3 4 6 7 9
A126332: 0 1 3 4 6 7 9 10 15 16 18 21 22 25 27 28
(~1 + compr(\x.(1 - (x mod (1 + (3 * ((~x2 + x) mod 8))))),x))
A119356: 1 2 3 4 5 6 9 10 11 14 17 18 19 20 21 22
(1 + compr(\x.((x + 1) mod (1 + ((x - ((x + 1) mod 3)) mod (1 + (x div 2))))),x))
A323383: 1 2 3 4 6 8 12
A048597: 1 2 3 4 6 8 12 18 24 30
(1 + compr(\x.((x + 1) mod (1 + ((2 + ((x mod 3) div 2)) mod (1 + (x div 2))))),x))
A141551: 1 2 4 6 12 24 36 48 60 72 84 96 108 120 132 144
(1 + compr(\x.(1 - (x mod (1 + ((x + 2) mod (2 + ((~x + 1) mod (1 + (x div 2)))))))),x))
A324561: 2 4 6 7 8 10 11 12 13 14 16 18 20 21 22 23
(1 + compr(\x.((x + 1) mod (1 + (x mod (2 + (x div (2 + (x mod 5))))))),x))
A068090: 1 2 3 4 5 6 8 9 10 12 14 15 18 20 24 25
((x + 1) + ((x3 + 2x2) div 65))
A114829: 1 2 3 4 6 8 11 14 18 23 29 36 44 53 63 74
((x + 1) + (9 * (1 + (x mod 11))))
A194233: 10 20 30 40 50 60 70 80 90 100 110 21 31 41 51 61
((x + 1) + ((13 * (1 + (x div 2))) div 5))
A286750: 3 4 8 9 12 13 17 18 22 23 26 27 31 32 35 36
(1 + compr(\x.(1 - (((x + 1) * (1 + (x mod 8))) mod 5)),x))
A343109: 1 2 3 4 6 7 8 9 11 12 14 16 17 18 19 22
(1 + compr(\x.(1 - ((x + ((x + 2) div (2 + (x div 4)))) mod 5)),x))
A071591: 1 2 3 5 6 7 10 11 12 13 14 15 16 17 19 20
(1 + compr(\x.((x - ((2x + 2) mod 13)) mod 3),x))
A191104: 2 5 9 12 13 16 19 20 23 27 30 34 37 41 44 48
((~x + ~1) + (3 * (2x - ((2x + ~2) div 7))))
A190553: 2 4 9 14 19 21 26 31 33 38 43 48 50 55 60 62
((x + 1) + (3 * ((12x + 12) div 5)))
A188383: 7 14 24 31 41 48 55 65 72 82 89 96 106 113 123 130
(~1 + compr(\x.(1 - (((x2 + 2x) - ((~x + 2) div 5)) mod 3)),x))
A261406: 1 2 3 5 6 7 8 9 10 11 13 16 17 18 20 21
((x + 1) mod (2 - ((x + 1) mod ((~x + ~1) + ((x - (x div 3)) mod 3)))))
A330462: 1 0 1 0 1 0 0 2 1 0 0 2 2 0 0 0
((x + 1) + ((4 * ((2x + 1) div 9)) div 3))
A048264: 1 2 3 4 6 7 8 9 10 12 13 14 15 18 19 20
((x + 1) + ((x - (x mod (4 + ((x div 2) mod 5)))) div 3))
A279455: 1 2 3 4 5 6 7 10 11 12 13 14 16 17 19 20
((x + 1) + ((~x + (x3 div (x + 16))) div 3))
A008669: 1 1 2 3 4 6 8 10 13 16 20 24 29 34 40 47
((x + 1) + ((1 + compr(\x.(1 - (x mod (2 + (x mod 3)))),(x + 1))) mod (x + 1)))
A176590: 1 2 5 6 8 10 11 12 14 15 16 17 18 20 22 23
((x2 + x + 1) + ((x - ((x2 + (x2 div 4)) div 2)) div 2))
A194117: 1 3 7 12 18 26 35 45 57 70 85 101 118 137 157 178
(x9 + x8 + x7 + x6 + x5 + x4 + x3 + x2 + x)
A228293: 0 9 1022 29523 349524 2441405 12093234 47079207 153391688 435848049 1111111110 2593742459 5628851292 11488207653 22250358074 41189313615
(1 + compr(\x.((x mod (1 + (2 * ((x - ((~x + 1) div 3)) mod 3)))) mod 2),x))
A092253: 1 3 4 5 6 8 10 12
A136497: 1 3 4 5 6 8 10 12 13 15 16 17 18 19 21 22
((x + 1) + (2 * ((4x2 + 12x + 8) div 7)))
A159465: 3 8 15 26 39 54 71 90 111 134 161 190 221 254 289 326
((~x + ~1) + (2 * ((6x + 6) + (x div 9))))
A302438: 11 22 33 44 55 66 77 88 99 112 123 134 145 156 167 178
((x + 1) + ((3 * (1 + ((x2 div 4) div (x + 3)))) div 2))
A074946: 2 3 4 5 6 7 10 11 12 13 14 16 17 18 19 22
((x + 1) + ((3 * ((3 * (x2 div 2)) div 5)) div 2))
A025733: 1 2 4 7 11 16 22 29 37 46 56 66 77 89 102 116
((x + 1) + ((x - ((~1 + (((2x + ~4) mod (x + 2)) div 2)) div 3)) div 2))
A187482-A026347: 1 3 4 5 7 8 10 12 13 14 16 17 19 20 21 23
((x + 1) + (2 * ((x div (4 + (x div 4))) + ((x + 2) div 3))))
A288695: 1 4 5 6 9 12 13 16 17 18 21 22 23 26 29 30
((~x + ~1) + ((3 * ((10x + 10) + (x div 2))) div 2))
A321371: 14 28 43 57 73 87 102 116 132 146 161 175 191 205 220 234
((x + 1) + (((x - (5 * (x div ~2))) * (1 + (x div 2))) div 2))
A193053: 1 5 10 17 26 36 49 62 79 95 116 135 160 182 211 236
((3x + 1) - ((((x + 1) - ((x div 2) mod 5)) div 2) div 2))
A189514: 1 4 7 10 13 15 18 21 24 27 29 31 34 37 40 43
((x + 1) + (4 * ((x + 1) - (x mod (x - ((x + ~1) mod 8))))))
A257222: 5 10 15 20 25 30 35 40 45 50 51 52 53 54 55 56
((x + 1) + (2 * (x - (2 * ((2x + 1) div (3 + (x div 4)))))))
A342138: 1 0 3 2 5 8 7 10 13 16 15 18 21 24 27 26
((x + 1) + ((((3x2 + 3) - (x div 5)) div 2) div 2))
A083462: 1 3 6 11
A022338: 1 3 6 11 17 25 34 45 57 71 86 103 121 141 162 184
((x + 1) + (((3 * ((x div 5) + (x div 3))) div 2) div 2))
A228894: 1 2 3 4 5 7 9 10 11 13 14 15 17 18 19 22
((x + 1) + (4 * ((2x + 2) - ((x + 2) mod 12))))
A242594: 1 6 11 16 21 26 31 36 41 46 99 104 109 114 119 124
((x + 1) + (((x2 - (3 * ((x2 + ~x) div 4))) div 2) div 2))
A262439: 1 2 4 5 6 8 10 12 14 16 19 22 24 27 30 33
((x + 1) + (((((x + 1) * (1 + (((1 + (x div 2)) div 2) div 2))) div 2) div 2) div 2))
A302505: 1 2 3 4 5 6 8 10 11 12 13 15 16 17 20 22
((~x + ~1) + (4 * ((2x + 2) + (((x + 1) + (x div 4)) div 2))))
A101865: 7 18 25 36 47 54 65 72 83 94 101 112 123 130 141 148
((x + 1) + (4 * (((3 * (x + (x div 8))) div 2) div 2)))
A045929: 1 2 7 12 17 18 23 28 33 38 43 48 49 54 59 64
((x + 1) + (((x mod ((x + ~1) - (x mod 12))) * (x div 2)) div 2))
A193457: 1 2 3 4 5 6 7 8 9 10 11 12 16 20 25 30
((x + 1) + ((x + (((2 + (x div 3)) * (1 + (x div 4))) div 2)) div 2))
A027440: 1 3 4 6 8 10 12
A024511: 1 3 4 6 8 10 12 13 16 18 19 21 25 26 28 30
((x + 1) + ((x + (((x2 mod (x + 9)) div 2) div 2)) div 2))
A342778: 1 2 4 6 7 9 10 11 14 15 16 17 21 22 23 24
((x + 1) + ((x + ((x + (((x2 + 2x) - (x div 2)) div 3)) div 2)) div 2))
A025218: 1 3 5 7 9 12 15 18 21 24 28 31 35 39 43 47
((x2 + 2x + 1) + ((x2 - (((x2 + 2x) div 2) div 3)) div 2))
A022793: 1 4 10 19 31 46 63 83 106 132 161 193 227 264 304 347
(1 + compr(\x.(1 - (((x mod (~1 + (2 * ((x + ~2) div 3)))) mod 2) + (x mod 2))),x))
A153170: 2 4 6 8 10 11 12 14 16 18 20 21 22 24 25 26
((x + 1) * (1 + (x div (1 + (5 mod (1 + (x mod 6)))))))
A131959: 1 2 3 8
A129202: 1 2 3 8 25 6 49 32 27 50 121 24 169 98 75 128
((1 + ((x div 2) mod (1 + ((~x + 1) mod (1 + ((~x + 2) mod 4)))))) mod (x + 1))
A284154-A084115: 0 1 1 2 1 1 1 1 2 1 1 3 1 1 1 2
((x + 1) * (1 + (((x2 + 2x) div 2) mod (1 + ((1 + (x div 2)) div 3)))))
A344370: 1 2 3 4 5 12 7 16 9 20 11 36 13 28 30 32
((1 + ((~3x2 + ~4x) mod (1 + (x div 3)))) mod (x + 1))
A328195-A328026-A304687-A304465-A235875-A076558: 0 1 1 2 1 2 1 3 2 2 1 2 1 2 2 4
compr(\x.(~1 + (x div (~1 + (2 * (x div (1 + (x mod 9))))))),(x + 1))
A032906-A032872: 1 2 3 4 5 6 7 8 9 10 18 19 20 27 28 29
compr(\x.(~1 + (x mod 10) - (x div 9)),(x + 1))
A098395: 1 10 11 12 20 21 22 23 30 31 32 33 34 40 41 42
((x + 1) * (1 + ((2x + 1) mod (1 + (2x mod (2 + (x div 4)))))))
A135323: 1 2 3 4 5 12 7 8 9 20 11 36 13 28 30 16
((1 + (x mod (1 + ((~7 mod (2 + (x div 2))) div 2)))) mod (x + 1))
A245562: 0 1 1 2 1 1 1 2 3 1 1 1 1 1 1 2
compr(\x.((x + 1) mod (1 + (x div (5 * (1 + (x mod 3)))))),(x + 1))
A078448: 1 2 3 4 5 7 8 9 11 13 14 15 17 19 23 24
compr(\x.(x mod (1 + ((x - (x2 div (x + 5))) mod 3))),(x + 1))
A154660: 3 4 5 6 7 8
A066378: 3 4 5 6 7 8 10 12 14 16 18 20 21 24 27 30
((x + 1) * (1 + (9 * ((x + 1) - (x mod 8)))))
A020337: 10 20 30 40 50 60 70 80 738 820 902 984 1066 1148 1230 1312
((11 * (1 + (x mod 9))) mod (x + 1))
A103168: 0 0 0 0 0 0 0 0 0 1 0 9 5 13 6 13
compr(\x.((x mod 10) - (x mod 11)),(x + 1))
A308393-A032889: 1 2 3 4 5 6 7 8 9 10 20 21 30 31 32 40
((x + 1) * (1 + (3 * ((7x2 + 3x) div 2))))
A318159: 1 32 156 436 935 1716 2842 4376 6381 8920 12056 15852 20371 25676 31830 38896
((1 + (x mod (1 + (2 * (2 - (x * (((x div 2) div 3) mod 2))))))) div (x + 1))
A014044: 1 1 1 1 1 0 0 ~1 ~1 ~1 ~1 ~1 0 0 0 0
(x9 + x8 + x7 + x6 + x5 + x4 + x3 + x2 + x + 1)
A103623: 1 10 1023 29524 349525 2441406 12093235 47079208 153391689 435848050 1111111111 2593742460 5628851293 11488207654 22250358075 41189313616
compr(\x.(~1 + (x mod (2 + (x mod ((x + 1) - (x mod 10)))))),(x + 1))
A285523: 1 2 3 4 5 6 7 8 9 11 12 13 17 18 21 22
compr(\x.(x mod (1 + ((x mod ((x + 1) - (x mod 10))) div 2))),(x + 1))
A180478: 1 2 3 4 5 6 7 8 9 11 12 14 15 21 22 24
((x + 1) * (17 - (x div 15)))
A044857: 17 34 51 68 85 102 119 136 153 170 187 204 221 238 255 256
((9 * (1 + (x mod 11))) mod (x + 1))
A337171: 0 0 0 0 0 0 0 0 0 0 0 9 5 13 6 13
compr(\x.(x - ((x mod 10) * (1 + (x div 8)))),(x + 1))
A032998: 1 2 3 4 5 6 7 8 9 16 17 18 19 27 28 29
((3 - (((x * (2 + (x div 5))) div 4) mod 2)) mod (x + 1))
A073855: 0 1 2 2 3 2 3 2 3 3 3 2 3 2 3 3
(10x2 + 86x + 161)
A060641: 161 257 373 509 665 841 1037 1253 1489 1745 2021 2317 2633 2969 3325 3701
((x + 1) + (x mod 3) - ((x mod 13) mod 3))
A102452: 1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 14
(x mod (x - ((11 * ((x + ~1) div 3)) div (x + 1))))
A173883: 0 0 0 0 0 1 1 2 2 2 3 2 2 3 2 2
((((x5 + ~x4 + x2 + ~2x + 1) div 2) div 3) div (x + 1))
A245679: 0 0 0 6 25 69 154 300 531 875 1364 2034 2925 4081 5550 7384
(6x2 + 71x + 203)
A228320: 203 280 369 470 583 708 845 994 1155 1328 1513 1710 1919 2140 2373 2618
(24x4 + 24x3 + 10x2 + 11x + 1)
A169712: 1 70 639 2716 7885 18306 36715 66424 111321 175870 265111 384660 540709 740026 989955 1298416
((x + 1) * compr(\x.(x mod (1 + (4 * (x mod (2 + (x mod 2)))))),(x + 3)))
A071228: 4 12 24 36 50 72 98 120 144 180 220 252 286 336 375 416
((2x2 + 3x + 1) + (((x3 + 3x2 + 2x) div 2) div 3))
A051937: 1 7 19 38 65 101 147 204 273 355 451 562 689 833 995 1176
((1 + (((x mod (~5 + ((x div 2) mod 2))) mod 2) + (x mod 2))) mod (x + 1))
A171900: 0 0 1 3 2 2 1 3 1 3 1 3 2 2 1 3
((x + 1) * (1 + ((x2 * (1 + ((x3 + 2x) div 3))) div 2)))
A131509: 1 4 33 220 1005 3456 9709 23528 50985 101260 187561 328164 547573 877800 1359765 2044816
((~1 + compr(\x.(1 - (x mod (1 + (x mod (1 + ((x + 2) div 3)))))),x)) mod (x + 1))
A094699: 0 0 1 2 3 4 5 5 5 5 5 5 5 6 6 6
((x + 2) + compr(\x.(1 - (x mod (1 + ((x div ~2) mod 8)))),x))
A211218: 3 5 7 9 11 14 16 18 20 22 25 30 32 34 36 38
(19x3 + 30x2 + 12x + 1)
A100159: 1 62 297 820 1745 3186 5257 8072 11745 16390 22121 29052 37297 46970 58185 71056
compr(\x.(((x + 1) mod (1 + (2 * (2x mod (2 + (x div 3)))))) mod 2),(x + 1))
A243494: 1 2 3 4 5 6 8 10 11 12 13 14 16 20 22 23
compr(\x.((5x mod 33) mod 2),(x + 1))
A191176: 2 4 6 7 9 11 13 14 16 18 21 23 25 28 30 32
compr(\x.((7x mod 17) mod 2),(x + 1))
A188323: 2 3 6 9 10 12 13 16 17 19 20 23 26 27 29 30
((~x + ~1) + (10 * ((x + 1) - (x mod 9))))
A089186: 9 8 7 6 5 4 3 2 1 90 89 88 87 86 85 84
((x - (2 * ((x div (2 * (~2 + ((x * (x div 2)) mod 2)))) div 3))) mod (x + 1))
A102396: 0 1 1 1 1 1 1 3 1 1 1 3 1 3 3 5
((~x + ~1) + (4 * (1 + (2 * ((2x + 1) + ((x div 4) mod 2))))))
A161451: 11 26 41 56 79 94 109 124 131 146 161 176 199 214 229 244
((2 * ((1 + (((x + 2) * (x + (x mod (2 + (x mod 2))))) div 2)) div 2)) mod (x + 1))
A330492: 0 0 1 0 2 0 3 4 4 0 5 0 6 8 7 0
((x - (2 * ((x - ((~1 + (x div 2)) div (1 + (2 * (x mod 2))))) div 2))) mod (x + 1))
A287597: 0 1 0 1 2 1 2 1 4 1 4 1 6 1 6 3
((2 * ((4x + 2) + ((x2 + 2x) div 5))) div (x + 1))
A261491: 4 6 7 8 8 9 10 10 11 11 12 12 12 13 13 14
((2 * (2 + ((((((x + ~1) div 2) * (x div 2)) div 2) mod (x + 1)) div 2))) div (x + 1))
A266145: 4 2 1 1 0 1 0 1 1 1 1 0 0 0 0 0
((5x + 6) - ((2x + 4) div 9))
A072353: 6 11 16 20 25 30 35 39 44 49 54 59 63 68 73 78
((5x + 1) + (x2 div ((2x + 4) + (x mod 4))))
A315491: 1 6 11 16 22 27 33 38 44 49 54 60 66 71 76 82
((3x + 1) + ((x div (~1 - ((1 + (x div 2)) mod 3))) mod 2))
A189724: 1 5 8 11 13 17 20 22 26 29 31 35 37 41 44 47
compr(\x.((((x - (2 * ((x div 2) mod 2))) div 3) mod 3) - (x mod 2)),(x + 1))
A033055: 1 2 3 5 7 9 11 13 15 20 21 22 23 28 29 30
((x + 1) + (x3 div ((5x + 5) + (x2 div 2))))
A275341: 1 2 3 5 6 8 11 13 15 18 20 23 25 28 30 33
((2x + 1) + ((((~1 + (2 * (x mod 5))) mod (x + 1)) div 2) mod 2))
A189516: 1 3 5 7 10 11 13 16 17 20 22 23 26 27 30 32
((7x3 + 7x + 6) div (x2 + 1))
A168102: 6 10 15 21 28 35 42 49 56 63 70 77 84 91 98 105
(x10 + ~x5 + ~x2 + x)
A218133: 0 0 990 58800 1047540 9762480 60458370 282458400 1073709000 3486725280 9999899910 25937263440 61917115260 137858120400 289254116970 576649631040
((~1 + ((x + 1) div (1 + (2x div (1 + (2 * (2 + (x div 3)))))))) div 2)
A024880: 0 0 1 1 0 1 1 1 1 2 2 1 2 1 2 2
((1 + ((x + 1) div (1 + (x mod (1 + (2 * (2 + ((x div 3) mod 2)))))))) div 2)
A104368: 1 1 1 1 1 1 2 1 1 2 1 1 2 2 2 4
(2 * (1 + ((2x + 1) mod (1 + (2x mod (3 + (x div 4)))))))
A133946: 2 2 4 2 2 6 2 2 4 8 2 6 2 2 10 2
(x - (2 * (x mod (1 + ((3 * ((x + 1) div 2)) mod (1 + (x div 3)))))))
A283165: 0 1 2 3 4 3 6 7 8 7 6 7 12 11 14 15
((1 + ((x + 1) mod ((1 + ((x div 2) div 3)) * (1 + (x mod 3))))) div 2)
A245718: 0 0 0 0 1 0 1 0 2 0 2 0 1 1 3 1
((x + 1) div (2 + ((x div 2) div (1 + (x mod (1 + (x mod (3 - (x mod 2)))))))))
A124044: 0 1 1 2 1 2 1 2 3 2 1 3 1 2 3 3
((1 + ((x + 1) mod (1 + ((1 + (x mod (1 + (x mod 4)))) mod (x + 1))))) div 2)
A060209: 0 0 0 0 1 0 1 2 1 1 1 1 1 1 2 1
((1 + (x mod (1 + ((2 * (2x2 mod (2 + (x div 2)))) mod (x + 1))))) div 2)
A036414: 0 0 0 0 0 0 1 0 2 0 1 1 0 2 2 0
((1 + ((x + 1) mod (1 + ((2 - (x2 mod (x + 4))) mod (x + 1))))) div 2)
A286106: 0 0 1 0 1 0 2 1 1 0 0 0 1 0 1 1
((1 + ((x2 + 2x + 1) mod (1 + (2 * (1 + (x div 8)))))) div 2)
A339160-A301365-A290453-A185700-A180424-A123149-A055892-A055290: 1 1 0 1 1 0 1 1 1 0 1 2 2 1 0 1
((1 + (x div (1 + (x div (3 + ((x mod 6) mod 4)))))) div 2)
A256122: 0 1 1 2 1 1 1 2 2 2 1 2 1 2 2 3
(2 + ((x + 2) div (1 + ((x + 2) mod (1 + (x div (2 + ((x + 1) mod 3))))))))
A090370: 4 5 6 4 8 5 4 6 12 4 14 8 4 5 18 4
((1 + (((~3x + ~3) + (x div 3)) mod 7)) div 2)
A190431: 2 1 3 2 0 2 1 3 2 1 3 1 0 2 1 3
(((x + 1) - ((1 - (2 * (x div 4))) mod (1 + (((x + 1) div 2) div 2)))) div 2)
A338365: 0 1 1 1 2 2 3 3 4 5 5 5 5 5 6 8
(2 + ((1 + (x div 3)) mod (1 + (x div 2) - ((x + 1) div 5))))
A117183: 2 2 3 2 2 2 2 2 5 3 2 2 2 2 2 3
(((1 + (7 div (x + 1))) * (1 + (x div 5))) div 2)
A303599: 4 2 1 1 1 2 2 1 1 1 1 1 1 1 1 2
(2 + (2 * ((1 - (x div 3)) mod (1 + (x div 5)))) - (x mod 2))
A020738: 2 1 2 1 2 1 4 3 4 1 4 3 2 1 2 1
(x - (((~x + (x mod 10)) * (1 + (x div 5))) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A343403: 0 1 2 3 4 5 6 7 8 9 25 26 27 28 29 35
((1 + (3 * ((~1 + (x div 2)) mod (1 + ((2 + (x div 2)) div 3))))) div 2)
A328828: 0 0 0 0 2 2 0 0 0 0 2 2 3 3 3 3
(((x + 1) - ((x - ((2 - (x * (x div 2))) div 5)) mod 3)) div 2)
A269862: 0 0 0 1 2 2 3 3 3 4 4 5 5 6 7 8
((1 + ((2 + ((8 * (1 + (x mod 2))) mod (x + 1))) div 3)) div 2)
A335885-A335875: 0 0 1 0 1 1 1 0 2 1 2 1 2 1 2 0
(2 * ((x + 3) - ((2 * (2x div ~7)) div 3)))
A174164: 6 10 12 14 18 20 22 24 26 28 30 34 36 38 40 44
(((x2 + ~x) div (~3x + 53)) div 2)
A326469: 0 0 0 0 0 0 0 0 0 1 1 2 3 5 8 13
(x6 mod 46)
A070686: 0 1 18 39 2 31 12 27 36 3 6 9 32 29 26 13
(x7 mod 26)
A070707: 0 1 24 3 4 21 20 19 18 9 10 15 12 13 14 11
(x7 mod 22)
A070703: 0 1 18 9 16 3 8 17 2 15 10 11 12 7 20 5
(3 + (((x * (1 - (x div (~2 + ((~x + 2) div 4))))) div 2) div 3))
A002036: 3 3 3 4 5 5 6 6 7 9 9 10 11 11 12 13
(((3x + 7) * ((x3 + 5x2 + 8x + 4) div 2)) div 2)
A206808: 7 45 156 400 855 1617 2800 4536 6975 10285 14652 20280 27391 36225 47040 60112
(((((x + (x2 div 3)) div 2) mod 3) * (1 + (x div 3))) div 2)
A298139-A298087-A297876: 0 0 0 0 1 0 0 3 3 0 0 2 0 2 0 0
((x + 3) + ((1 + (x div 3)) div 2) - ((~x + 1) div (2 + (x div 2))))
A118300-A090864: 3 4 6 8 9 10 11 13 14 16 17 18 19 20 21 23
((1 + ((x + 1) div (1 + (((1 + (x div 2)) div 3) + (x mod 3))))) div 2)
A210763: 1 1 1 2 1 1 2 1 1 3 1 1 2 2 2 3
(x div (2 * (1 + ((x + 1) div (1 + ((4 * (x mod 2)) + (x mod 3)))))))
A294881: 0 0 0 1 0 2 0 1 1 1 0 2 0 2 1 1
(3 + ((x2 + 1) div (1 + ((x + (x2 div 5)) div 2))))
A205677: 4 5 5 6 7 7 8 8 8 9 9 9 9 10 10 10
((1 + ((1 + (x mod (2 * (1 + (x mod 6))))) mod (1 + (x div 2)))) div 2)
A060763: 0 0 1 0 1 0 1 0 2 1 1 0 1 1 2 0
((1 + ((2x2 mod (4 + (x div 4))) mod (1 + (x div 2)))) div 2)
A127499: 0 0 0 0 1 0 1 2 1 0 1 1 1 1 0 1
(2 - ((x mod ((x + 1) - (x3 div (5x + 1)))) mod 2))
A275308: 2 1 2 2 2 1 2 2 1 1 2 2 1 2 1 1
((1 + ((2 + (x3 div 11)) div (x + 1))) div 2)
A300788: 1 1 0 1 1 1 2 2 3 3 4 5 6 7 8 10
(x div (2 + (x div (1 + (x mod (2 * (1 + (x mod (1 + ((x + 1) mod 3))))))))))
A091064: 0 0 0 1 0 1 0 2 0 1 2 1 0 1 0 3
(x div (2 + (x div (1 + ((x mod (1 + ((~x + 1) mod 9))) div 2)))))
A257109: 0 0 0 1 1 1 0 1 1 0 0 1 2 2 1 0
((1 + ((x + 1) div (2 * (1 + ((x + 3) mod (1 + (x div 4))))))) div 2)
A324286: 0 1 1 1 1 2 1 2 1 3 1 1 1 4 2 1
((x mod 2) - (((x + 1) div (1 + (2 * (x div (1 + ((x div 2) mod 3)))))) mod 2))
A156707: ~1 1 ~1 0 ~1 1 0 1 ~1 0 ~1 0 0 1 ~1 0
(2 * (1 + ((x mod (1 + ((2x mod 9) mod (x + 1)))) mod 2)))
A066691: 2 2 2 2 2 4 2 4 2 2 4 4 4 2 2 4
((1 + (x div (2 * (1 + (x div (2 * (1 + ((x + 2) mod 6)))))))) div 2)
A056557: 0 0 1 1 0 1 1 2 2 2 0 1 1 2 2 2
((1 + ((1 + (x div 2)) div (2 * (1 + (x mod (1 - (x div ~4))))))) div 2)
A344981: 0 0 1 0 1 0 1 1 0 1 1 0 2 0 0 2
(2 * (1 + ((1 + (((x3 mod (x - ((~x + 2) div 2))) div 2) div 2)) div 2)))
A051464: 2 2 2 2 4 4 2 2 4 2 4 2 4 6 4 4
((1 + ((5 * (x - (x div ~14))) div 2)) div 2)
A266728: 0 3 4 5 6 8 9 10 11 13 14 15 16 18 19 21
(0 - (x div (~1 - (x div (2 + ((x + 2) mod (1 + (x div 4))))))))
A304333: 0 1 1 2 2 3 2 3 3 3 2 3 3 5 2 3
((1 + (((3x + 3) * ((x + 1) + (x2 div 4))) div 2)) div 2)
A256524: 1 3 9 18 34 54 84 120 169 225 297 378 478 588 720 864
(((x + ~1) mod (1 - ((x + 1) mod (~1 + (2 * (((~x + 2) div 2) div 3)))))) div 2)
A198066: 0 0 0 1 0 0 1 0 0 0 2 1 1 0 0 1
(1 - ((((x2 + 2x + 1) * (1 + (x mod 2))) mod 7) div 2))
A011635: 1 1 0 ~1 ~1 0 1 0 ~1 ~1 0 1 1
(2 div (2 + ((1 + (~x mod 4)) div 2) - (x div 7)))
A029360: 1 0 0 0 1 0 0 1 2 0 1 1 2 0 2 2
((1 + (((x div 2) - (((~x + 2) div 2) mod 3)) mod (2 + (x div 3)))) div 2)
A166291-A105422: 1 0 1 1 0 1 1 2 0 1 2 2 3 0 1 3
((1 + (x div (2 + (x div (1 + (((1 + (x div 2)) mod 3) + (x mod 2))))))) div 2)
A078508: 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 2
(3 + (((x + 1) * (1 + (2 * (x2 div (1 + (x mod 4)))))) div 2))
A254310: 3 4 7 13 85
((1 + (x div (2 + ((2 * ((x2 - (x div 2)) div 3)) mod (x + 1))))) div 2)
A133009: 0 0 0 1 0 1 1 0 1 2 1 1 2 1 1 4
((1 + (x div (2 + (((x2 mod 5) - (x div 2)) mod (x + 1))))) div 2)
A335621: 0 0 1 0 0 0 0 1 2 1 1 1 0 0 1 1
((1 + (((x + ~1) * (1 + (2 * ((2x + ~1) - (x div 3))))) div 2)) div 2)
A003192: 0 0 2 5 10 17 24 35 47
((1 + (((1 + ((1 + ((x + 1) * (x div (2 + (x mod 2))))) div 2)) div 2) div 2)) div 2)
A308302: 0 0 0 0 1 1 2 1 2 2 4 2 5 4 7 5
((1 + ((x + 1) div (2 + (((1 + (x2 div 2)) div 5) mod 2)))) div 2)
A174807: 0 1 1 1 1 2 1 1 2 3 3 3 3 2 3 4
((1 + (((x2 + x) - ((~1 + ((x2 + (x div 2)) div 2)) div 2)) div 2)) div 2)
A238381: 0 1 2 3 4 6 8 11 14 18 21 25 30 35 40
(2 + ((x2 + x) mod (1 + (2 * (x mod (2 + (((x + 1) div 2) div 3)))))))
A064132: 2 4 2 2 2 2 2 4 4 2 4 8 2 4 2 4
(2 - (x2 div (~3 - ((2x div (2 + (x div 3))) mod 2))))
A083132: 2 3 4 5 8 9 11 15 24
((1 + (((1 + ((x * ((2 * (x mod 2)) + (x div 3))) div 2)) div 2) div 2)) div 2)
A005044: 0 0 0 1 0 1 1 2 1 3 2 4 3 5 4 7
((1 + (((((x + 1) * (1 + ((x * (x div 2)) div 4))) div 2) div 2) div 2)) div 2)
A026810: 0 0 0 0 1 1 2 3 5 6 9 11 15 18 23 27
((x mod (1 + (x div (2 + (((((x + 1) * (x div 3)) div 2) div 2) mod 2))))) div 2)
A234504: 0 0 0 0 0 0 0 1 1 0 2 1 1 3 2 3
(x7 mod 34)
A070715: 0 1 26 11 30 27 14 29 32 19 22 3 24 21 6 25
(x - ((x - ((x3 + 2x2 + 2x) div 17)) div 2))
A175829: 0 1 2 3 5 8 12 17 23 31 41 52 66 82 100 121
((1 + ((2x + 2) mod (2 + ((~2x + 1) mod (2 + (x div 4)))))) div 2)
A286562: 1 1 0 1 1 0 1 0 0 0 1 2 1 0 0 1
(2 + ((~2 + (x mod 2)) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))))
A266547: 2 2 2 2 3 2 2 3 3 2 2 4 5 4 2 2
(2 + ((~x2 + 2) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))))
A138139: 2 2 2 2 3 2 2 3 3 2 2 3 5 3 2 2
(1 - ((1 + (x mod (2 + ((~1 - (x2 div 3)) mod 4)))) div 2))
A105966: 1 0 0 0 1 1 0 0 1 0 0 0 0 ~1 0 0
(~2 + (9 * (1 + ((1 + (x div (~2 + (x mod 2)))) mod 3))))
A131030: 16 7 7 16 25 25 16 7 7 16 25 25 16 7 7 16
(2 + ((x3 + 4x2 + ~3x + 10) mod 9))
A251754: 3 5 3 3 2 6 3 8 9 3 5 3 3 2 6 3
((x mod (1 + (2 * ((8x2 + 1) mod (2 + (x div 2)))))) div 2)
A052998: 0 0 0 0 0 1 3 0 0 0 1 2 0 0 0 0
((1 - (x mod (0 - ((2x + ~1) mod (4 * (2 - (x mod 2))))))) div 2)
A076849: 0 0 1 0 2 0 0 0 3 0 1 0 1 0 1 0
((1 + ((x mod (1 + (2 * (16 mod (x + 1))))) mod 4)) div 2)
A081396: 0 0 1 0 1 1 1 0 0 1 1 1 1 2 1 0
((5 * (1 + ((x + ~1) mod (1 + ((x + 1) div 5))))) div 2)
A107604: 2 2 2 2 5 2 5 2 5 7 2 5 7 2 5 7
(250x + ~180)
A154360: ~180 70 320 570 820 1070 1320 1570 1820 2070 2320 2570 2820 3070 3320 3570
(~2 + (10 * ((x + 1) - (x div ~9))))
A166729: 8 28 38 48 58 68 78 88 98 108 128 138 148 158 168 178
(250x + ~70)
A154361: ~70 180 430 680 930 1180 1430 1680 1930 2180 2430 2680 2930 3180 3430 3680
(((((x + 1) * (6 - (x mod 3))) div 2) mod 5) div 2)
A096587: 1 0 0 1 1 1 0 0 1 0 1 2 2 0 0 1
(x div ((x + ~1) + (x mod (1 - (x div (~2 + (((~x + 2) div 2) div 5)))))))
A277967: 0 1 2 1 1 0 1 0 1 1 1 1 0 0 0 1
(((3x + 3) + (x div 7)) mod 10)
A094561: 3 6 9 2 5 8 1 5 8 1 4 7 0 3 7 0
(((7x2 + 9x + 2) div 2) mod 10)
A194826: 1 9 4 6 5 1 4 4 1 5 6 4 9 1 0 6
(((x + (3 * (x + (x mod 2)))) * (2 + (x mod 2))) mod 10)
A140684: 0 1 6 5 2 9 8 3 4 7 0 1 6 5 2 9
(2 + ((x * (1 - ((x3 div 8) mod 2))) div 5))
A054125: 2 2 2 2 2 2 2 3 3 2 2 4 4 4 2 2
(((1 + (8 mod (1 + (x div 2)))) div 2) * ((1 + (x mod 4)) div 2))
A277899: 0 0 0 0 0 1 0 0 0 2 1 2 0 1 0 0
((1 + (x mod (2 + (((1 + (x mod 5)) mod 4) + (x mod 2))))) div 2)
A306345: 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 2
((3 * ((2x + 1) - ((~x + ((x + ~2) div 3)) div 3))) div 2)
A189513: 3 6 9 12 16 19 22 25 28 33 36 39 42 46 49 52
((3 * (1 + ((x mod (1 + (3x mod (2 + (x div 2))))) div 2))) div 2)
A231147: 1 1 1 1 1 1 3 1 1 1 1 4 3 4 1 1
(((2x + 1) mod (3 * (1 + (2 * ((x div 5) mod 2))))) div 2)
A330267: 0 0 1 0 0 1 2 3 4 0 0 1 0 0 1 2
((3 * ((17x + 17) div 5)) div 2)
A330173: 4 9 15 19 25 30 34 40 45 51 55 60 66 70 76 81
(2 + ((5 * (x + ((x div 2) div 7))) div 3))
A028738: 2 3 5 7 8 10 12 13 15 17 18 20 22 23
A028763: 2 3 5 7 8 10 12 13 15 17 18 20 22 23 27 28
((3 * (1 + ((x * (x mod (1 + ((x + ~1) mod 4)))) mod 4))) div 2)
A331735: 1 1 1 1 1 1 1 6 1 1 1 4 1 1 1 1
((3 * ((x2 mod (4 + (((x + 1) div 2) div 2))) mod 3)) div 2)
A072024: 0 1 0 1 1 0 1 1 1 0 1 3 1 1 0 1
((3 * ((4 * (x + ((((x + 1) div 2) div 2) div 2))) div 3)) div 2)
A061641: 0 1 3 6 7 9 12 15 18 19 21 24 25 27 30 33
(~2 + (3 * (1 + compr(\x.(((~x + (x * (x mod 2))) div 3) mod 3),x))))
A291745: 1 4 10 16 22 25 28 34 40 46 49 52 55 58 64 70
(((x div (3 * (8 - (x div 2)))) * ((x + ~1) div 3)) div 2)
A326636: 0 0 0 0 0 0 0 0 0 0 1 1 3 4 8 10
((((4 * (x div 5)) div 3) + ((x + ~1) mod 3)) div 2)
A025840: 1 0 0 1 0 1 1 0 1 1 1 1 2 1 1 3
(2 * ((2 + (5 * (x - (2 * (x div ~4))))) div 3))
A244033: 0 10 14 18 20 30 34 38 40 50 54 58 60 70 74 78
((3 * (((5x + 5) + ((x div 2) div 3)) div 2)) div 2)
A292662: 3 7 10 15 18 22 27 30 34 37 42 45 49 54 57 61
(((((x + 1) * (((x + ~1) mod 3) + (x div 3))) div 2) div 3) div 2)
A307018: 0 0 0 1 0 1 2 1 2 4 2 4 6 4 6 9
(x div (2 + ((4 * (x div (1 + (2 * (3 - (x mod 2)))))) div 3)))
A066272: 0 0 1 1 2 1 3 2 2 3 3 2 4 3 3 2
(2 + ((x + 1) div 2) - ((4 * ((2 * (x div 2)) div 3)) div 3))
A177876: 2 3 3 4
A085887: 2 3 3 4 3 4 3 4 4 5 3 4 3 4 4 5
((x + 2) - (3 * ((((2 - (x div 3)) * (x div 3)) div 2) div 2)))
A134932: 2 3 4 5 6 7 8 9 10 14 15 16 20 21 22 29
((3 * (x - ((((x * ((1 - (x div 2)) div 3)) div 2) div 2) div 2))) div 2)
A026140: 0 1 3 4 7 9 10 12 13 16 19 21 22 25 27 28
((3 * ((2 * (2x - (x mod 8))) - (x mod 4))) div 2)
A332206: 0 1 3 4 12 13 15 16 48 49 51 52 60 61 63 64
(2 + ((2 * ((x + 2) + (((~1 + (x2 div 4)) div 2) div 2))) div 3))
A243356: 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 22
((x + ~2) - (3 * ((~2x + ~4) + ((~2x + 2) div 5))))
A188302: 10 17 27 34 44 51 58 68 75 85 92 99 109 116 126 133
(2 + (((x * (~1 + ((2x + ~2) * (~x mod 4)))) div 2) div 3))
A088074: 2 1 3 3 1 21
((3 * (((x + 2) + (x mod (2 + (x div (2 * (2 - (x mod 2))))))) div 2)) div 2)
A011978: 1 3 3 3 4 6 6 7 7 10 10 12 12
((x + 6) - ((1 + (x2 div (4 + (x div 2)))) div 3))
A248418: 6 7 8 9 9 10 10 11 11 12 12 13 13 14 14 14
(2 * (x - (((~x + ~1) + (((x * ((~x + 2) div 2)) div 2) div 3)) div 3)))
A309374: 2 4 6 10 12
A161842: 2 4 6 10 12 16 18 22 26 30 32 38 40 44 48 54
(2 + (3 * compr(\x.((1 + (x mod (1 + (x mod 6)))) mod 3),x)))
A305496: 8 17 26 35 44 53 62 68 71 80 89 98 107 116 125 134
(9x2 + 39x + 83)
A210527: 83 131 197 281 383 503 641 797 971 1163 1373 1601 1847 2111 2393 2693
((3 * (x + ((x + 2) div (8 - ((x + ~2) div 3))))) div 2)
A138670: 0 1 3 4 6 9 10 12 13 15 18 19 21 24 27 28
(81x2 + 81x + 14)
A177072: 14 176 500 986 1634 2444 3416 4550 5846 7304 8924 10706 12650 14756 17024 19454
(~1 + (((x + 2) div (2 + (x div (2 * (2 + (x mod 2)))))) + (x div 3)))
A182921: 0 0 1 2 2 3 3 4 3 5 5 6 5 6 6 8
(x - (2 * (((x2 mod (x - ((~x + 2) div 2))) div (x + 1)) + (x div 3))))
A278603: 0 1 2 1 2 3 2 1 2 3 4 5 4 3 4 5
(((12x + 74) + (x div 3)) div 2)
A282111: 37 43 49 55 61 67 74 80 86 92 98 104 111 117 123 129
(1 + (x div (2 + (x div (3 + ((x div 2) mod 2))))) - ((x mod 3) div 2))
A182535: 1 1 1 2 2 1 3 3 2 2 3 2 3 3 2 4
((1 + (((x + 1) + ((x div 2) mod (1 + ((x + ~1) mod 5)))) div 2)) div 2)
A171481: 0 1 1 1 2 2 2 2 3 3 3 3 3 4 5 5
(((x2 + 3) + ((x + ((x + 1) mod 6)) div 2)) div 2)
A261878: 1 2 4 7 11 15 21 28 36 45 55 64 76 89 103 118
((1 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 2)) div 2)
A343046-A343042-A271917-A265080-A228275-A228250-A185651: 0 0 0 0 1 0 0 2 2 0 0 3 6 3 0 0
(2 * ((24x2 + 6x + 1) div (2x + 1)))
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(2 + ((2x + 1) * (2 + ((2x + 3) * (1 - (2 * (x mod 2)))))))
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((6x + 2) + (((x - ((~1 + (x div 2)) div 2)) div 2) mod 2))
A304803: 2 9 15 21 26 32 38 45 51 56 62 68 75 81 87 92
((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)
A341317-A229079-A101164: 0 0 0 0 1 0 0 2 2 0 0 3 7 3 0 0
(((8x + (x mod 2) - (x div ~2)) * (1 + (x div 2))) div 2)
A195032: 0 5 17 27 51 66 102 122 170 195 255 285 357 392 476 516
((2 + (x div (2 + ((2x mod 3) + (x mod 2)))) - (x mod 2)) div 2)
A167865: 1 0 1 1 1 1 2 1 2 2 2 1 4 1 3 3
((2 - ((x mod 2) + ((((~x + 2) div 2) * (x div 3)) div 3))) div 2)
A214130: 1 0 1 1 1 1 2 1 2 2 3 3 4 4 5 6
((2 - ((x mod 2) + ((((~x + 1) div 3) * (x div 3)) div 2))) div 2)
A097242: 1 0 1 1 1 1 2 1 2 3 3 3 5 4 6 7
(((7x + 7) - ((x + 2) div (1 + (x2 div 2)))) div 2)
A099261: 2 5 10 13 17 21 24 28 31 35 38 42 45 49 52 56
((x - ((30x + 24) div (~x + ~1))) div 2)
A275113: 12 14 15 16 16 17 18 18 19 19
(3 + compr(\x.(2 - ((x2 + 2x) mod (1 + (3 * (x mod 4))))),x))
A102554: 4 6 8 9 10 12 14 16 18 20 21 22 24 25 26 28
(((x + 1) + ((x - ((~x3 + x) div 7)) div 2)) div 2)
A175827: 0 1 2 3 5 8 12 17 24 33 43 56 71 88 108 131
(2 * ((x + 1) + (2 * (x div (5 + ((x div 2) mod 5))))))
A066122: 2 4 6 8 10 12 14 16 18 24 30 32 34 36 38 40
(2 * ((x + 1) + ((3 * ((1 + ((x + 2) div 5)) div 2)) div 2)))
A309374: 2 4 6 10 12
A120351: 2 4 6 10 12 14 16 18 20 22 24 26 28 34 36 38
((x + 3) + ((((x + 2) - (((1 + (x div 2)) div 2) mod 4)) div 2) div 2))
A231711: 3 4 5 7 8 9 10 11 13 14 15 16 17 19 21 22
(2 + ((15x + 15) div (x + 9)))
A070083: 3 5 6 7 7 8 9 9 9 10 10 11 11 11 11 12
(3x4 + 12x3 + 30x2 + 36x + 17)
A160827: 17 98 353 962 2177 4322 7793 13058 20657 31202 45377 63938 87713 117602 154577 199682
((5x4 + 4x3 + ~4x2 + ~3x) div 2)
A172118: 0 1 45 234 730 1755 3591 6580 11124 17685 26785 39006 54990 75439 101115 132840
(((x + 2) + (x mod (2 * (3 + ((x + 1) mod 8))))) div 2)
A038389: 1 2 3 4 5 6 7 5 5 10 11 12 13 14 15 10
((x + 1) div (2 + ((1 + (((x - ((~1 + (x div 2)) div 2)) div 2) mod 2)) mod (x + 1))))
A333701: 0 1 0 1 1 2 2 2 2 3 3 4 3 3 3 5
((x - ((0 - (3 * ((x + 1) mod 12))) div (x + 1))) div 2)
A096029: 1 2 2 3 3 4 4 5 5 6 6 5 6 7 7 8
(2 * compr(\x.((x mod 2) - (((x + ~1) mod (1 + ((1 + (x div 2)) div 2))) div 2)),(x + 1)))
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(((x + 1) * (6 + (((x2 + x) div 2) mod 5))) div 2)
A290642: 3 7 13 14 15 18
(((x + 1) * ((3x3 + 11x2 + 14x + 8) div 2)) div 2)
A213830: 2 18 78 230 540 1092 1988 3348 5310 8030 11682 16458 22568 30240 39720 51272
(((2 + compr(\x.(2 - (x mod (1 + (2 * (1 + (x mod 3)))))),x)) mod (x + 1)) div 2)
A210452: 0 0 0 0 1 1 2 2 2 2 1 2 2 3 3 3
((6x4 + 34x3 + 69x2 + 59x + 18) div 2)
A076456: 9 93 390 1110 2535 5019 8988 14940 23445 35145 50754 71058 96915 129255 169080 217464
(((x + 1) - (3 * (~x + (x mod 9)))) mod (2x + 2))
A179977-A108971: 1 2 3 4 5 6 7 8 9 17 16 15 14 13 12 11
((3x + 2) - ((x mod (2 - (x mod (~1 - (x div 4))))) mod 2))
A189670: 2 4 8 10 14 17 20 22 26 28 32 35 38 40 44 47
((2x + 2) + ((3 * ((x - (x div 9)) div 2)) div 2))
A277733: 2 4 7 9 13 15 18 20 24 26 28 31 33 37 39 42
((2x + 6) - (((((x + ~1) div 2) div 2) * (x div 4)) div 2))
A060652: 6 8 10 12 14 16 18 20 21 22 24 26 27 28 30 32
((x + 1) + ((2x2 div (x + 16)) + ((x + 1) div 2)))
A186154: 1 3 4 6 8 11 13 16 18 21 23 26 29 32 35 38
(((x + 2) + (3 * (x - (3 * (x div ~2))))) * ((x + 1) div 2))
A219394: 0 15 19 64 72 147 159 264 280 415 435 600 624 819 847 1072
(((x + 2) + (3 * (x + (3 * (x + (x mod 2)))))) * ((x + 1) div 2))
A217441: 0 24 28 100 108 228 240 408 424 640 660 924 948 1260 1288 1648
((x + 2) + (((((3 * ((~x + 2) div 2)) div 2) div 2) mod 2) + ((x + 1) div 2)))
A072008: 2 4 5 8 9 10 11 14 15 17 18 19 20 23 24 25
(((x2 + x) * (1 + (7 * ((x2 + x) div 2)))) div 2)
A008893: 0 8 66 258 710 1590 3108 5516 9108 14220 21230 30558 42666 58058 77280 100920
(((x + 1) * (x + ((4x3 + 12x2 + 8x) div 3))) div 2)
A330805: 0 9 51 166 410 855 1589 2716 4356 6645 9735 13794 19006 25571 33705 43640
((2x3 + 11x2 + 37x + 28) div 2)
A162266: 14 39 81 146 240 369 539 756 1026 1355 1749 2214 2756 3381 4095 4904
(((x - (((x * ((~x + 2) div 2)) div 2) div 5)) div 2) - ((x + ~1) div 2))
A112210: 1 0 1 1 1 1 2 2 2 2 3 3 4 4 5 6
(x - (x mod (3 * ((1 - (2 * (x mod 2))) * (2 - ((x div ~2) mod 2))))))
A161829: 0 3 0 6 0 6 6 12 6
(x6 mod 44)
A070684: 0 1 20 25 4 5 16 37 36 9 12 33 12 9 36 37
(4 * ((x + 1) - (((~x + 1) - ((x div 3) mod 3)) div 3)))
A306199: 4 8 16 20 28 32 40 44 48 52 56 64 68 76 80 88
(1 - (((1 + ((x2 + ~x) mod ((x + 3) + (x div 4)))) div 2) div 2))
A164925: 1 1 1 1 0 1 1 ~1 0 1 1 ~2 0 0 1 1
((x + 1) div (4 + ((2x + 1) mod (1 + (2 * (x div 5))))))
A227899: 0 0 0 1 1 1 1 2 1 2 2 1 3 2 1 2
(2 * (2 + (((x + 1) div 2) mod (1 + ((x div 2) mod (2 + ((x + ~1) mod 3)))))))
A059656: 4 4 6 4 4 4 10 4 4 4 6 4 4 4 6 4
(x - (((x - (((x3 + ~2x) div 2) div 7)) div 2) div 2))
A175868: 0 1 2 3 4 6 8 11 15 20 25 32 40 49 59 71
(x7 mod 28)
A070709: 0 1 16 3 4 5 20 7 8 9 24 11 12 13 0 15
(x - (2 * ((x div 2) - (((x + 1) div (3 + (2 mod (1 + (x div 2))))) mod 2))))
A275720: 0 1 2 3 2 3 2 3 2 1 0 1 0 1 2 3
(x div (2 + ((x + 1) div (2 * (1 + (x mod (4 + ((x div 2) div 3))))))))
A141298: 0 0 1 1 1 1 2 2 2 3 1 2 1 2 3 3
(x - (((1 + ((x - ((x3 + ~x2) div 8)) div 2)) div 2) div 2))
A175870: 0 1 2 3 4 6 8 11 14 18 23 29 35 43 52 62
(3 mod (2 + ((2x mod (~1 + (2 * (((~x + 2) div 2) mod 4)))) div 2)))
A239264: 1 1 1 1 0 1 1 1 1 1 1 0 3 0 1 1
((((x + 7) * ((x3 + 3x2 + 2x) div 2)) div 2) div 2)
A239568: 0 6 27 75 165 315 546 882 1350 1980 2805 3861 5187 6825 8820 11220
((x - ((5 * ((2 * (2x div 3)) div 3)) div 2)) div 2)
A346218: 0 0 1 0 1 0 0 1 0 ~1 0 0 0 0 ~1 0
(((5 * ((x + 1) - ((~x + ((~x + 2) div 4)) div 2))) div 2) div 2)
A190345: 1 3 5 7 10 11 13 16 17 20 21 23 26 27 30 32
(x - ((0 - ((5 * (x + (x div 7))) div 2)) div 2))
A029905: 0 2 5 7 9 11 14 17 19 22 24 26 28 31 34 36
(1 - ((x - ((5 * (x + (x div ~7))) div 2)) div 2))
A200247: 1 1 1 2 3 4 4 5 5 5 6 7 8 8 9 9
(x - (2 * ((1 + ((((x + 1) div 7) * (x div 2)) div 2)) div 2)))
A308590: 0 1 2 3 4 5 4 5 6 7 8 9 8 7 6 7
((((x2 + 7x + 1) * (1 + ((x div 2) mod 2))) div 2) div 2)
A217367: 0 2 9 15 11 15 39 49 30 36 85 99 57 65 147 165
(1 - (((3 * (((x - (x2 div 3)) div 2) div 3)) div 2) div 2))
A294621: 1 1 1 1 2 2 2 3 4 4 4 5 6 7 8 9
(2 + ((3 * (1 - (((x mod 4) - (x div 4)) div 3))) div 2))
A333537: 3 3 3 2 5 3 3 3 5 5 3 3 5 5 5 3
(2 * (4 - ((x - (24 div (x + 1))) div 3)))
A033824: 24 16 12 10 8 8 6 6 4 4 4 2
(((3 * ((4x + 4) + (((x + 1) + (x div 2)) div 2))) div 2) div 2)
A189524: 3 6 10 13 17 21 24 27 31 35 39 42 45 49 53 56
(((3 * (2 + ((x * (~1 + (x div 2))) div 9))) div 2) div 2)
A003106: 1 0 1 1 1 1 2 2 3 3 4 4 6 6 8 9
(2 + ((3 * ((2x + 2) - ((2 + (x div 2)) mod 6))) div 2))
A033161: 2 5 6 9 11 14 15 18 29 32 33 36 38 41 42 45
((2 + ((x mod (~4 + ((x + 1) mod ~7))) div 3)) div 2)
A226728: 1 ~1 0 0 0 1 0 0 0 ~1 0 0 0 0 0 0
(~2 + ((3 * compr(\x.(2 - (x mod (3 + (x mod 8)))),x)) div 2))
A072013: 1 2 4 5 7 8 10 14 16 17 19 20 25 28 29 31
(2 * ((1 + ((x * ((~x + 1) + (4 * (x + ((x div 2) mod 2))))) div 2)) div 2))
A193828: 0 2 12 22 26 40 70 92 100 126 176 210 222 260 330 376
((4x + 5) - (x div (~3 + ((~x + 2) div 4))))
A212448: 5 10 14 18 22 27 31 35 39 43 47 51 55 60 64 68
((2 + ((x * (1 + (2 * (2 + ((x + ~1) mod 3))))) div (1 + (x div 2)))) div 2)
A161775: 1 3 4 7 4 6 7 5 6
((x mod (2 + ((1 + (2 * ((x div 2) mod (3 - (x mod 2))))) mod (x + 1)))) div 2)
A309367: 0 0 0 1 0 1 0 1 1 0 1 0 0 0 2 0
(2 * (((0 - (2 * (x div (1 + (x mod 12))))) mod (x + 1)) div 2))
A051765: 0 0 0 0 0 0 0 0 0 0 0 0 2 2 6 10
(x div (4 + ((2 * (1 + (4 * (x mod 6)))) mod (x + 1))))
A046926: 0 0 0 0 0 1 1 1 2 0 2 1 2 0 2 1
(54x2 + 82x + 32)
A304381: 32 168 412 764 1224 1792 2468 3252 4144 5144 6252 7468 8792 10224 11764 13412
((x + 2) div (2 * (2 + (((x + 4) - ((~1 + (x div 2)) div 2)) mod (x + 1)))))
A237756: 0 0 1 0 0 0 1 1 1 1 2 2 2 2 4 4
((3x + 2) + (((x + 1) div 2) div 2) - ((x + 1) div 5))
A189531: 2 5 8 12 14 17 20 24 27 29 32 36 39 42 44 48
(x + (((2 * (2 - ((~x + 1) div 3))) div 3) + (((x + 1) div 2) div 2)))
A050481: 1 2 4 6 7 8 9 11 13 14 15 18 19 20 21 23
((((x2 + x) * (3 + (((x2 + 2x) div 2) + (x div 2)))) div 2) div 2)
A242709: 0 2 12 33 85 165 315 518 846 1260 1870 2607 3627 4823 6405 8220
(~2 + (((x + 1) * (x + (2 * (2 + (((x + 1) + (x div 4)) div 2))))) div 2))
A026357: 0 5 10 20 33 43 61 74 97 123 141 172 206 229 268 294
((x + 2) - (((1 + (x mod (7 - (x div 3)))) div 2) div 2))
A049877: 2 3 4 4 5 6 8 9 9 11 12 12 14 15 16 17
((x + 2) - (((1 + ((1 + ((x div 2) div 3)) * ((x + 1) div 2))) div 2) div 2))
A196362: 2 3 4 5 6 6 7 7 8 9 10 10 10 10 11 11
((4x + 6) - (x div (~3 + ((~x + 2) div 4))))
A212453: 6 11 15 19 23 28 32 36 40 44 48 52 56 61 65 69
((2 + ((5 * ((x + 1) - ((x div 4) div ~2))) div 2)) div 2)
A321131: 2 3 4 6 8 9 11 12 13 14 16 17 19 21 22 23
((3x + 2) - ((x + 1) div (2 * (2 + (x div (1 + (x mod 4)))))))
A189928: 2 5 8 10 14 17 20 22 26 29 31 34 38 41 43 46
(1 - (((x - ((x - (3 * ((~x * (x div 2)) div 2))) div 2)) div 2) div 2))
A088567: 1 1 1 2 2 3 4 5 6 7 9 10 13 14 18 19
((((3 * ((x + 2) + ((x + 1) mod (2 + ((x div 2) mod 2))))) div 2) div 2) div 2)
A342248: 1 1 1 2 2 2 3 4 4 4 5 4 5 5 6 6
(1 + (x div (4 + ((x * (x + (x div 2))) mod 6))) - (x mod 2))
A042961: 1 0 1 0 2 0 2 0 3 1 3 1 4 2 4 3
(8 * ((x + 1) + ((x + ((1 + (x div 2)) mod 3)) div 4)))
A219547: 8 16 32 40 48 56 64 80 88 96 104 112 128 136 152 160
(2 * ((2 * (2x div 15)) + (((x + 1) div 2) div 2)))
A132189: 0 0 0 2 2 2 2 4 8 8 8 10 10 10 10 16
(((x + 1) div 2) - ((((((x + 1) div 2) div 2) div 2) * (((x + 1) div 2) div 2)) div 2))
A060960: 0 1 1 2 2 3 3 3 3 4 4 5 5 6 6 4
(((x + ~1) - (2 * ((((x + 1) div 2) div 2) div 2))) * ((((x + 1) div 2) div 2) div 2))
A294237: 0 0 0 0 0 0 0 4 5 6 7 8 9 10 11 20
((2x + 2) + (((x * (x div 2)) div (x + 4)) + (((x + 1) div 2) div 2)))
A025057: 2 4 6 9 12 14 16 19 22 24 27 30 33 35 38 41
(((((x + ~1) * (x div (3 * (8 - (x div 2))))) div 2) div 2) div 2)
A326635: 0 0 0 0 0 0 0 0 0 0 1 1 2 3 6 8
((x + 2) - ((~2x + 2) div (6 + ((x div 2) mod 5))))
A028804: 2 3 5 6 7 8 10 11 12 13 15 17 18 19 20 21
(x - (2 * ((x - (x div (2 + (x div (2 + (x2 mod 5)))))) div 2)))
A072203: 0 1 2 1 2 1 2 3 2 1 2 3 4 3 2 1
((((((x + 3) * ((x + 1) mod 7)) div 2) div 2) div 2) div 2)
A069585: 0 0 0 1 2 3 0 0 1 2 3 4 5 0 1 2
((((((x + 1) * (2 - (x mod (~1 + ((~x + 2) div 4))))) div 2) div 2) div 2) div 2)
A220188: 0 0 0 0 0 1 0 2 1 1 2 2 1 4 3 2
(6 + (((x + 1) * (1 + ((x + (x2 div 4)) div 2))) div 2))
A169761: 6 7 9 12 18 24 34
(~3 mod (2 + ((4x mod (4 + (x div 4))) div 2)))
A204246: 1 1 1 1 1 1 1 0 0 1 1 0 2 0 1 1
(5 mod (2 + ((4x mod (4 + (x div 4))) div 2)))
A090737: 1 1 1 1 1 1 1 2 2 1 1 2 0 2 1 1
(3 div (4 - (((~2x + 2) mod (4 + (x div 4))) div 2)))
A244657: 1 0 1 0 1 1 0 1 1 1 0 1 3 1 1 0
((x + 2) - ((2 - ((((x + 2) * (x + (x div 8))) div 2) div 2)) div 2))
A269746: 1 2 4 6 8 10 13 16 20 24 28 32 36 40
(x - (2 * ((x - ((x div 2) div (2 - (((~x + 2) div (2 + (x div 2))) mod 2)))) div 2)))
A182101: 0 1 0 1 2 3 4 3 4 3 2 3 4 3 4 3
((1 + (((x + 1) div 2) div 2)) mod ((2x + ~1) mod (4 + (x div 4))))
A325165: 1 0 1 0 0 2 0 0 0 3 0 1 0 0 4 0
((x + 2) - ((2 - (((x * (~1 + (x div ~5))) div 2) div 2)) div 2))
A242453: 1 2 3 3 4 5 5 5 6 7 7 7 7 8 8 9
(6 + ((x * (4 + (16 div (x + 1)))) div 2))
A175952: 6 12 15 18 20 21 24
(x div (2 + ((1 + (x div 2)) div 2) - ((((1 - (x div 2)) mod (x + 2)) div 2) div 2)))
A233566: 0 0 0 1 2 2 2 2 2 4 3 3 4 4 3 3
(((2 + ((11 mod (2x + 1)) + (x div 2))) div 2) div 2)
A333534: 0 1 1 1 1 1 4 4 4 4 4 4 4 4 5 5
((((x mod ((x + ~1) - (x mod 12))) * (2 + (x div 2))) div 2) div 2)
A242521: 0 0 0 0 0 0 0 0 0 0 0 0 2 4 6 9
(((x mod 14) + (x mod 8)) div 8)
A237291: 0 0 0 0 1 1 1 1 1 1 1 1 2 2 0 1
(((x + 1) div (1 - (x div (~2 + ((~x + 2) div 4))))) + (x div 8))
A159805: 1 1 1 2 1 2 2 2 4 3 3 4 4 4 4 5
((x * (1 - ((x3 div 8) mod 2))) div (2 + (x div 4)))
A344837-A344834: 0 0 0 0 1 0 0 2 2 0 0 2 2 2 0 0
(4 + ((x * (~1 + ((x2 + 10x + 16) div 3))) div 2))
A302508: 4 8 16 29 50 76
((((x + (((((x * (x div 2)) div 2) * (2 + (x div 2))) div 2) div 2)) div 2) div 2) div 2)
A241313: 0 0 0 0 1 1 2 2 4 4 6 7 10 11 15 16
((2 + (((2 * (1 + ((x * (x div 3)) div 2))) div 3) + (x div 2))) div 2)
A029038: 1 1 1 2 3 3 4 5 6 7 8 9 12 13 14 17
((((x + 1) + (3 * ((x + 1) div 5))) mod (2 + (x div 2))) div 2)
A161271: 0 0 0 0 0 0 0 0 0 2 1 2 1 2 3 3
((((3x + 3) + ((x * (x div 2)) mod 2)) * (2 + (x div 2))) div 2)
A263621: 3 6 13 19 30 36
(((~1 + ((~2x + 2) mod (4 + (x div 4)))) * ((x div 2) mod 2)) div 2)
A072783: 0 0 0 ~1 0 0 ~1 1 0 0 ~1 1 0 0 0 ~1
((1 + (((2x + 2) mod (2 + (x div 4))) div 2)) mod (2 + ((x div 2) mod 2)))
A123517: 1 1 1 1 1 1 2 1 0 1 2 1 1 0 1 2
((2 + (((x2 + 1) + (2 * (2 + (((x div 2) div 3) mod 2)))) div 2)) div 2)
A217314: 2 2 3 4 6 8 11 15 18 23 27 33 38 44 51 58
(((x + 1) + (2 * (2 - (2x div (2 + ((x + ~1) mod 3)))))) mod 4)
A179765: 1 0 1 2 1 0 1 2 3 2 3 2 1 0 1 2
((14x3 + 9x2 + 2x) div 4)
A045949: 0 6 38 116 262 496 840 1314 1940 2738 3730 4936 6378 8076 10052 12326
((x + (3 * (x mod (1 + ((x + ~1) mod 9))))) div 4)
A008997: 0 0 0 0 1 1 1 1 2 2 2 3 3 4 6 6
(108x2 + 112x + 24)
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(((x2 + x) + (((x div 2) - ((x div 4) div ~2)) mod 2)) mod 4)
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((x + 4) + ((1 + ((((x + 2) * (1 + (x div 3))) div 2) div 2)) div 2))
A146968: 4 5 7
A191984: 4 5 7 8 10 11 13 14 16 19 20 22 25 26 28 32
((x + 4) + (4 * (x - ((x + 1) mod 13))))
A103303: 0 1 2 3 4 5 6 7 8 9
A004862: 0 1 2 3 4 5 6 7 8 9 10 11 64 65 66 67
((x + (2 * ((x + ((x3 + 2x) div 3)) div (x + 2)))) mod 4)
A221166: 0 1 0 3 0 3 2 3 0 3 0 1 0 1 2 1
(1 + ((x2 div (~x + 25)) + (x div 4)))
A036021: 1 1 1 1 2 3 3 4 6 8 9 11 15 18 21 26
((2x + 1) + ((x - (x div 7)) div 2) - (x div 4))
A190058: 1 3 6 8 10 12 15 17 18 21 23 26 27 30 32 34
(2 - (((2x + 1) + ((x mod (~2 - (x div 3))) mod 2)) mod 4))
A105931: 1 2 1 ~1 1 2 1 2 1 2 1 ~1 1 2 1 ~1
((x9 + x5 + 2x3) div 4)
A282613: 0 1 140 4995 65824 489125 2521476 10092775 33562880 96870249 250025500 589527851 1290008160 2651218765 5165397524 9611031375
(4 + compr(\x.(~1 + (((x + 1) + (x div 8)) mod 5)),x))
A078136: 4 8 9 12 13 17 18 21 22 26 27 30 31 35 39
(((x + 2) + (((x + 2) * ((x + 1) + (x div 3))) div 5)) div 2)
A291693: 1 2 3 5 6 8 11 13 16 19 22 26 30 34 38 44
((x + 4) + ((x - (((x2 + x) div 5) mod 3)) div 2))
A099049: 4 5 6 7 9 11 12 13 15 17 18 19 21 23 25 26
(2 * ((x + 2) + ((3x - ((x2 + ~x) div 4)) div 4)))
A110507: 4 6 10 14 16 18 20 22 24 26 28 28
((((x + 2) + (((x + 1) + ((~x + 1) mod 9)) div 2)) div 2) div 2)
A189575: 0 1 2 2 2 3 3 3 3 4 4 5 6 6 6 6
((2 + (3 * ((2x + 1) + ((x div 3) mod 2)))) div (x + 4))
A175214: 1 2 2 3 4 4 4 4 4 4 4 4 4 4 4 5
((3x + 2) + ((x div 2) div 3) - (x div 7))
A190006: 2 5 8 11 14 17 21 23 26 29 32 35 39 42 44 47
((2x + 2) + ((2x + 1) div (5 + (x div 8))))
A287235: 2 4 7 9 11 14 16 19 20 23 25 27 30 32 34 37
((4x + 1) + ((x2 + 2) div ((x + 3) + (x div 4))))
A313560: 1 5 10 14 19 24 28 33 38 42 47 52 57 62 66 71
((4x + 1) + ((x - (x div (1 + ((1 + (x div 2)) div 3)))) div 2))
A314708: 1 5 9 13 18 22 26 31 35 39 44 49 53 57 62 66
(5x + ((~2x + 4) div (4 + ((x div 2) div 3))))
A313540: 1 5 10 14 19 23 28 33 37 42 46 51 56 61 66 70
((1 + ((2 * (1 + (2 * (x + (2 * (x + ((x div 2) mod 2))))))) + (x div 2))) div 2)
A056021: 1 7 18 24 26 32 43 49 51 57 68 74 76 82 93 99
(((3 * (1 + (2 * (((x + 1) + (x div 4)) div 2)))) - (x div 2)) div 2)
A214990: 1 4 4 7 9 9 12 12 14 17 17 20 22 22 25 25
(~2 + ((6 * ((x + 2) + ((x div 2) + (x div 4)))) + (x div 2)))
A026320: 10 16 29 35 54 60 73 79 98 104 117 123 142 148 161 167
(((2 * (1 + (6 * (x - (x div 8))))) + (x div 2)) div 2)
A225227: 1 7 13
A277093: 1 7 13 19 26 32 38 44 45 51 57 63 70 76 82 88
((1 + ((1 + (6 mod (1 + (x div 2)))) div 3)) * ((x div 2) mod 2))
A227838-A050605: 0 0 1 1 0 0 2 2 0 0 1 1 0 0 3 3
(1 + (((3x + 3) mod (1 + (x div 3))) div 2) - ((x div 2) mod 2))
A142886: 1 1 0 0 1 1 0 0 1 2 0 0 3 2 0 0
(2 + ((1 + ((1 + ((x2 + 2x) mod (1 + (x div 3)))) div 2)) * (x mod 2)))
A339013: 2 3 2 4 2 4 2 3 2 5 2 5 2 3 2 5
(~1 + (2 * ((x + 4) - (2 div (1 + (x div 4))))) - (x mod 2))
A284506: 3 4 7 8 13 14 17 18 23 24 27 28 31 32 35 36
(2 + ((x div (2 + (x div (2 + ((x2 + 2x) mod 6))))) + (x mod 2)))
A177876: 2 3 3 4
A053475: 2 3 3 4 3 5 3 5 4 6 3 6 3 6 4 6
((3x + 4) - ((x2 + 2x) div (2x - ((~x + 2) div 2))))
A026278: 4 6 8 11 14 17 19 22 24 27 29 32 35 37 40 43
(2 + compr(\x.((x + 1) mod (1 + (x mod (1 + (2 * ((1 + (x div 4)) div 2)))))),x))
A316413: 2 3 4 5 7 8 9 10 11 13 16 17 19 21 22 23
((x + 2) + (x div (1 + (x mod (1 + ((3x mod (2 + (x div 2))) div 2))))))
A081472: 2 4 6 8 10 9 14 16 18 15 22 16 26 21 20 32
((x + 2) + ((x2 + ~1) mod ((x + 1) - ((~x + (x mod 2)) div 5))))
A201363: 2 3 7
A007607: 2 3 7 8 9 10 16 17 18 19 20 21 29 30 31 32
((x + 3) + ((x - (x div (1 + (2 * (1 + ((x div 4) mod 2)))))) div 2))
A298109: 3 4 6 7 9 10 11 13 14 15 16 18 20 21 23 24
((x * ((x + 1) - ((((~x4 + x2) div 2) div 3) div 2))) div 2)
A301973: 0 1 4 15 50 140 336 714 1380 2475 4180 6721 10374 15470 22400 31620
((x + 2) + ((2x + ~2) div (~2x + 35)))
A026481-A026417: 1 3 4 5 6 7 8 9 10 11 13 14 16 17 19 22
(2 * (x + (5 * (x + ((x3 + 3x2 + 2x) div 3)))))
A063498: 0 32 104 236 448 760 1192 1764 2496 3408 4520 5852 7424 9256 11368 13780
((x + 2) + (((x * (x + ((x div 2) mod 3))) div 2) div (x + 5)))
A288221: 2 3 4 5 7 8 9 11 12 14 16 17 18 19 21 23
((x - (x3 div (~x + ~35))) div 2)
A062435: 0 1 1 2 3 4 6 8 10 13 16 20 24 29 35 41
((x + 2) + (((1 - (2x mod (1 + (x div 4)))) mod (x + 1)) div 3))
A069751: 2 3 4 5 6 7 8 9 10 11 15 13 14 19 16 22
(((3x + 2) + ((x + 1) div 3) - (x mod 6)) div 2)
A001729: 1 2 3 4 5 7 11 12 13 14 15 17 21 22 23 24
((x + 2) + ((2 * (1 + (x div 2) - ((~x + 1) div (1 + (x div 2))))) div 3))
A193528: 2 3 6 7 8 10 12 13 14 15 17 18 20 21 22 23
(~2 + compr(\x.((2 + (((x * (((x + ~1) div 2) div 2)) div 2) div 3)) mod 3),x))
A186808: 4 5 6 10 12 13 18 21 23 26
(((x + 2) - (((x + (2 * (x mod 2))) * ((1 + (x div 2)) div 2)) mod 3)) div 2)
A087876: 1 1 1 1 2 3 4 4 4 5 6 6 7 7 7 7
((x + 2) + ((2 * (x + (x mod (1 + (((x + 1) div 2) div 3))))) div 3))
A284655: 2 3 5 7 8 11 12 14 15 17 18 21 22 24 26 27
((x + 2) + (((x + 2) + ((~x + 1) mod (2 - ((~x + 1) div 3)))) div 3))
A192450: 3 4 6 7 8 9 11 12 14 15 16 18 19 20 21 22
(x - ((~73x2 + 73x) div 2))
A098230: 0 1 75 222 442 735 1101 1540 2052 2637 3295 4026 4830 5707 6657 7680
((x + ((3 * (x + (3 * (x + (x div 4))))) div (x + 1))) div 2)
A202308: 0 3 5 6 7 8 8 9 10 10 11 11 12 13 13 13
((x + ((x + 1) * (1 + ((x * (~1 + ((x3 + 2x) div 2))) div 2)))) div 2)
A319491: 0 1 10 47 179
((x + 2) + ((1 + ((x + (1 mod (8 - (x div 2)))) div 2)) mod (x + 1)))
A093510: 2 3 6 8 9 11 12 14 15 17 18 20 21 23 24 25
((9 * ((1 + (x div 2)) * (x div 2))) + ((x2 + x) div 2))
A303814: 0 1 21 24 64 69 129 136 216 225 325 336 456 469 609 624
((2x3 + ~2x) + (((x3 + 3x2 + 2x) div 2) div 3))
A177890: 0 1 16 58 140 275 476 756 1128 1605 2200 2926 3796 4823 6020 7400
((x + 4) + ((1 + (x div 3)) div 2) - ((~x + 2) div (2 + (x div 2))))
A267312: 3 5 6 9 10 11 12 13 14 17 18 19 20 21 22 24
((x + (2 * (((x + 3) * (x div 3)) div 7))) div 2)
A212597: 0 0 1 1 3 3 5 5 7 9 10 11 14 15 16 19
((x + 2) + ((7 * (((x + 1) - ((x div 2) mod 2)) div 2)) div 2))
A088225: 2 6 7 8 13 17 18 19 24 28 29 30 35 39 40 41
((x + 2) + ((1 + ((((x + 1) div 5) * (x div 3)) div 2)) div 2))
A340682: 2 3 4 5 6 7 9 10 11 13 14 15 16 17 19 21
((x + 2) + ((1 + (((x - ((x div 3) mod 2)) div 2) + (x div 4))) div 2))
A324562: 2 3 5 6 7 9 10 11 13 14 15 17 19 20 21 22
((x + 2) + ((1 + ((((x + (x div 2)) div 5) * (x div 2)) div 2)) div 2))
A231876: 2 3 4 5 7 8 9 11 12 13 16 17 19 20 23 24
(2 * ((3x + 4) - ((((x + ~2) mod (1 + (x div 2))) mod 3) mod 2)))
A136798: 8 14 20 24 32 38 44 48 54 62 68 74 80 84 90 98
((x + ((3 * (x - (((x - (x2 div 3)) div 2) div 2))) div 2)) div 2)
A213511: 0 1 2 3 5 7 9 11 13 15 17 19 21 24 27 30
((x + ((3 * (2 + ((3x2 div (x + 2)) div 2))) div 2)) div 2)
A187102: 1 2 3 4 6 7 9 11
A192416: 1 2 3 4 6 7 9 11 12 14 15 16 18 20 22 23
(x mod ((x + ((3 * (((~1 + (x div 2)) mod 3) + (x div 2))) div 2)) div 2))
A059571: 0 1 0 1 0 1 0 0 1 2 1 1 0 1 2 3
((x + ~2) + (2 * ((2x + 1) mod (2 + (x mod (1 + (x div 8)))))))
A103303: 0 1 2 3 4 5 6 7 8 9
A337304-A333693-A333692-A322464-A235027-A057889: 0 1 2 3 4 5 6 7 8 9 10 13 12 11 14 15
(2 + compr(\x.(((3 * (x + ((2x mod (2 + (x div 2))) mod 2))) div 2) mod 2),x))
A120629: 2 4 5 6 9 10 13 14 16 17 18 20 21 22 24 25
(((31x + 32) + (((x + 1) div 2) div 2)) div 2)
A220000: 16 31 47 63 78 94 109 125 141 156 172 188 203 219 234 250
((x + 2) + (((2x div 7) * (((x + ~1) div 2) div 2)) div 2))
A058363: 2 3 4 5 6 7 8 10 11 13 14 16 17 19 22 23
((x + 4) - (x mod (4 + ((x mod (2 + ((x + 1) mod 4))) div 2))))
A120327: 4 4 4 4 8 8 8 8 9 12 12 12 16 16 16 16
(2 * compr(\x.(1 - ((2x + ~4) mod (2 + (2x div (2 + (x div 4)))))),x))
A305634: 2 6 10 12 14 18 20 22 24 26 28 30 34 38 40 42
(2 + compr(\x.(1 - ((x * ((x - (x div 3)) div 3)) mod 8)),x))
A309265: 6 7 8 9 11 12 13 15 16 17 19 21 23 24 25 27
((x + (2 * ((x + ((2x2 + 4) div (x + 5))) div 2))) div 2)
A201734: 0 1 2 3 6 7 9 10 13 14 16 18 20 22 24 25
((x2 + 2x + 2) + ((4x2 + ~1) div 7))
A022795: 1 5 12 22 35 51 70 92 118 147 179 214 252 293 337 385
(2 + compr(\x.(1 - (((x mod (~1 + (2 * ((x + ~2) div 3)))) mod 2) + (x mod 2))),x))
A275669: 3 5 7 9 11 12 13 15 17 19 21 22 23 25 26 27
((2 - ((((x + 1) div 2) * (1 + (x div 2))) mod 7)) div (x + 2))
A028863: 1 0 0 ~1 ~1 0 ~1 0 ~1 ~1 0 0 0 0 0 0
((x + 2) * (1 + ((x3 + 10x2 + 21x + 12) div 2)))
A249708: 14 69 208 485 966 1729 2864 4473 6670 9581 13344 18109 24038 31305 40096 50609
((~x + ~1) - (5 * ((~2x + 2) div 9)))
A194522: ~1 ~2 2 1 0 ~1 3 2 1 0 ~1 3 2 1 0 4
((2 * (1 + (x mod (8 + (2x div (2 + (x div 2))))))) mod (x + 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A227876: 0 1 2 3 4 5 6 7 8 9 2 2 4 6 8 10
((2 * ((x mod 2) - ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2))) mod (x + 2))
A193526: 0 2 0 2 0 0 0 2 0 0 0 0 0 0 14 2
((2x + 1) + (((x + 2) mod (1 + (2 * ((2 + (x div 2)) div 3)))) mod 2))
A082847: 1 3 6 7 9 12 13 15 17 20 21 24 25 27 29 32
((2x + 1) + ((~8 + (x div 2)) mod (2 + (x div 5))))
A188028: 1 3 6 8 9 11 14 16 19 21 22 24 27 29 32 35
((3x + 2) - ((2 - ((2 + ((x div 2) mod 2)) mod (1 + (x div 2)))) div 2))
A113553: 1 4 8 11 14 17 21 24 26 29 33 36 38 41 45 48
compr(\x.(1 - (((2x div ~7) mod (x + 1)) mod 4)),2x)
A209885: 1 3 6 8 12 14 17 19 23 25 28 30 32 35 37 41
(3x + ((x - ((2 - (x div 3)) mod 5)) mod 3))
A092296: 1 5 6 11 12 16 18 22 26 29 30 34 36 40 44 46
(3x + ((x + ((4 * (x div 3)) div 3)) mod 3))
A092292: 0 4 8 10 14 15 20 21 25 28 32 33 38 39 43 45
((3x + 1) - ((10 mod (1 + ((x + 1) div 2))) mod 2))
A284796: 1 4 7 9 12 16 19 22 25 28 31 33 36 40 43 45
(1 + ((2 * ((x + 1) - ((2 * (1 - (x div 2))) div 5))) + (x div 2)))
A190488-A187973: 3 5 8 10 15 17 20 22 27 29 32 34 37 39 44 46
(1 + (2 * (x - (7 * (x div ~4)))) - (x div 2))
A098159: 1 17 18 20 21 37 38 40 41 57 58 60 61 77 78 80
((4x + 4) + (((x - (x div ~7)) div 2) + (x div 2)))
A189517: 4 9 14 19 24 29 34 39 45 49 55 59 65 69 75 80
((((x div 2) - (x mod ((x + ~1) - (x mod 12)))) div 2) + (x div 2))
A025561: 0 0 1 1 3 3 4 4 6 6 7 7 8 8 9 8
(x mod ((x + ~1) + (x mod 2) - (x div (1 + (2 * (2 + ((x mod 3) div 2)))))))
A324938-A079413: 0 0 0 0 1 0 2 1 2 1 3 1 3 2 3 3
((1 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4)))) * (x mod 2))
A272216-A265330-A007814: 0 1 0 2 0 1 0 3 0 1 0 2 0 1 0 4
(1 + ((((x + ~1) mod (1 + (2 * ((x2 div 2) mod (x + 2))))) div 2) + (x mod 2)))
A278539: 1 2 1 3 2 4 1 5 2 6 3 7 1 8 2 9
(1 + ((2 * (((2x + ~4) mod (2 - ((~x + 1) div 3))) mod 2)) + (x mod 2)))
A229830: 1 2 1 2 3 2 1 2 1 2 3 2 1 2 3 4
(1 + (((x + 1) div (2 + (((x - (x div 4)) div 2) mod 2))) div 2) - (x mod 2))
A340756: 1 0 1 0 1 1 2 1 2 1 3 3 4 2 3 4
((x + ~1) + (x mod 2) - ((x - ((~x + ((x + ~1) mod 5)) div 2)) div 2))
A132203: 0 0 0 1 1 2 1 2 2 3 3 3 2 4 3 5
((2x div (2 + (x div (1 + (((x2 + 2x) div 2) mod 3))))) - (x mod 2))
A211261: 0 0 1 1 1 2 1 1 2 2 1 3 1 2 3 2
((x div (2 + ((x div 2) div (1 + (x mod (2 + ((x mod 3) div 2))))))) + (x mod 2))
A304793-A294926-A079167: 0 1 1 2 1 3 1 3 2 3 1 4 1 3 3 4
(x + (x mod 2) - (((x2 + 18x + 32) div (x + 1)) mod 2))
A222245: 0 1 2 3 4 6 5 7 8 9 10 11 12 13 14 16
((2 + (x div (2 + (x div (1 + (2 * ((((x + ~1) div 2) div 2) mod 2))))))) * (x mod 2))
A053399: 0 2 0 2 0 3 0 3 0 2 0 2 0 4 0 4
(0 - ((x div (2 + (x div (2 + ((~x + 1) mod (1 + (x mod 4))))))) + (x mod 2)))
A305052: 0 ~1 ~1 ~2 ~1 ~2 ~1 ~3 ~1 ~2 ~1 ~3 ~1 ~2 ~2 ~4
((x div (2 + (x div (2 + (((x - (x div 4)) div 2) mod 3))))) + (x mod 2))
A007302: 0 1 1 2 1 2 2 2 1 2 2 3 2 3 2 2
((2 * ((2 * (2x - (x mod 8))) - (x mod 4))) - (x mod 2))
A000695: 0 1 4 5 16 17 20 21 64 65 68 69 80 81 84 85
((61x2 + ~59x) div 2)
A098140: 0 1 63 186 370 615 921 1288 1716 2205 2755 3366 4038 4771 5565 6420
((x * (x + (((x5 + 3x3 + 2x) div 2) div 3))) div 2)
A046023: 0 1 12 87 416 1475 4236 10437 22912 45981 85900 151371 254112 409487 637196 962025
(2x2 * ((~x + 1) + (5 * ((x3 + x) div 2))))
A134633: 0 10 192 1314 5344 16050 39600 85162 165504 297594 503200 809490 1249632 1863394 2697744 3807450
((7x6 + 5x5) div 2)
A229148: 0 6 304 3159 16896 62500 182736 453789 999424 2007666 3750000 6603091 11073024 17822064 27697936 41765625
compr(\x.(~1 + ((x + 1) mod (1 + ((x + ~1) mod (1 + (2 * (3 + (x mod 2)))))))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A082324: 0 1 2 3 4 5 6 7 8 9 11 14 16 19 21 22
compr(\x.(~1 + (x div 2) - (x mod (1 + (6 * (x mod 5))))),x)
A023799: 0 1 2 3 4 6 7 8 9 11 12 13 14 18 19 24
compr(\x.(1 - (x mod (1 + (x div (1 + (2 * (1 + ((x + ~1) mod 5)))))))),x)
A059808: 7 9 11 13 15 16 17 19 21 22 23 25 26 27 28 29
compr(\x.((x2 + ~2) mod 113),x)
A206525: 51 62 164 175 277 288 390 401 503 514 616 627 729 740 842 853
compr(\x.(1 - (2x mod (~1 + (9 * (x mod 5))))),x)
A081754: 1 2 3 4 6 7 8 9 11 12 14 18 19 21 22 23
compr(\x.(~1 + (x div (1 + (2 * (((~x + 2) mod 5) - (x mod 4)))))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A068892: 0 1 2 3 4 5 6 7 8 9 11 13 15 17 22 26
compr(\x.(1 - ((x2 + 2x + 1) mod (1 + ((2x + 2) div 5)))),x)
A225793-A176995: 2 4 6 8 10 11 12 13 14 15 16 17 18 19 21 22
((x + 1) + (((x * (1 + (((x + 1) div 2) div 3))) div 2) div 5))
A325118: 1 2 3 4 5 7 8 9 10 11 13 15 16 17 19 20
compr(\x.(~1 + ((1 + (2x2 mod 17)) mod 3)),x)
A010379: 0 1 2 4 8 9 13 15 16
A136805-A010395: 0 1 2 4 8 9 13 15 16 17 18 19 21 25 26 30
compr(\x.(~1 + ((x div (5 - (((1 + (x div 2)) div 2) div 2))) mod 3)),x)
A023762: 0 1 2 3 4 5 6 7 12 13 14 18 19 20 21 24
(x * (1 + ((x2 + 4x + 4) div (~x + 26))))
A066189: 0 1 2 6 8 15 24 35 48 72 100 132 180 234 308 405
compr(\x.(~1 + (((1 + (x div 2)) div (2 + ((x + 1) mod (2 + (x mod 2))))) mod 3)),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A106801: 0 1 2 3 4 5 6 7 8 9 11 13 16 17 18 20
compr(\x.(2 - ((x + 1) mod (1 + (3 * (2 - ((x mod (2 + (x mod 2))) div 2)))))),x)
A318932: 1 2 3 4 5 8 9 10 12 15 16 17 18 19 22 24
(157x + 117)
A304610: 117 274 431 588 745 902 1059 1216 1373 1530 1687 1844 2001 2158 2315 2472
(155x + 117)
A304611: 117 272 427 582 737 892 1047 1202 1357 1512 1667 1822 1977 2132 2287 2442
compr(\x.(1 + (x mod 13) - (x mod 7)),x)
A297279-A296752: 13 26 27 39 40 41 52 53 54 55 65 66 67 68 69 78
((x + 1) + ((x + ((x div 2) div (2 - (x div (1 + ((x div 2) mod 2)))))) div 3))
A289017: 1 2 4 5 6 7 8 9 11 12 13 15 16 18 19 20
compr(\x.(1 + (4 * (x mod 11)) - (x div 3)),x)
A297273-A296746: 11 22 23 33 34 35 44 45 46 47 55 56 57 58 59 66
compr(\x.(1 - ((x + 1) mod ((1 + ((x div 2) mod 4)) * (1 + (x mod 3))))),x)
A334736: 2 4 5 6 10 12 13 14 16 18 20 21 22 26 28 29
compr(\x.((x + 1) mod (1 + (2 * (x mod (1 + ((x + ~1) mod 7)))))),x)
A023763: 0 1 2 3 4 5 6 7 8 14 15 16 21 22 23 24
compr(\x.(1 - (x mod (1 + (2 * (x div (3 + (x div (1 + (x mod 4))))))))),x)
A063547: 5 7 10 11 13 14 17 18 19 22 23 25 26 27 29 31
compr(\x.(1 - ((x + 1) mod (1 + (x div (2 + ((x div 2) mod 7)))))),x)
A054023: 4 6 8 10 12 14 16 18 20 21 22 24 25 26 28 30
compr(\x.(2 - (x mod (1 + (2 * (1 + (((x - ((~1 + (x div 2)) div 2)) div 2) mod 2)))))),x)
A028728: 2 3 5 7 8 11 12 13 14
A106735: 2 3 5 7 8 11 12 13 14 17 18 19 20 23 24 26
((~x + ~1) + (2 * (~1 + (4 * (2 + (4x2 div (x + 1)))))))
A281476: 13 28 51 82 105
compr(\x.(2 - (x mod (1 + (2 * (1 + ((x + 2) div (2 + (((x + 1) div 2) div 2)))))))),x)
A286421: 2 3 4 5 6 9 11 12 13 14 16 17 20 21 22 23
(x * (1 + ((x - (x mod 10)) * (x mod 10))))
A103303: 0 1 2 3 4 5 6 7 8 9
A061378: 0 1 2 3 4 5 6 7 8 9 10 121 252 403 574 765
(x + ((((x * (x2 - (x div 2))) div 2) div 3) div 7))
A175846: 0 1 2 3 5 7 10 14 19 25 32 41 51 63 77 92
compr(\x.(1 + ((x + 3) mod 7) - (x mod 8)),x)
A022561: 4 5 6 7 11 12 13 14 15 18 19 20 21 22 23 25
compr(\x.(((x + 1) * (1 + (x div 7))) mod 7),x)
A337141: 6 13 20 27 34 41 42 43 44 45 46 47 48 55 62 69
compr(\x.(2 - ((0 - ((x + 1) * (1 + (x mod 4)))) mod 7)),x)
A067570: 0 1 2 3 4 5 7
A075745: 0 1 2 3 4 5 7 8 10 14 15 16 17 18 19 21
compr(\x.(1 - (x mod (1 + (x mod (2 + ((3x + ~3) mod (1 + (x div 2)))))))),x)
A062062: 1 2 3 5 7 8 9 11 13 14 15 17 19 22 23 25
compr(\x.(x mod (1 + (((3 * (x + (x div 4))) mod (1 + (x div 2))) div 2))),x)
A115845: 0 1 2 3 4 5 6 7 8 10 12 14 16 17 20 21
compr(\x.(1 - ((x4 + ~x) mod 21)),x)
A028734: 2 3 5 6 8 10 11 12 13 14 17 19 20
A028755: 2 3 5 6 8 10 11 12 13 14 17 19 20 23 24 26
(x * (((x * (x div 2)) div 2) div (~2x + 37)))
A326588: 0 0 0 0 0 0 0 0 0 0 10 11 24 39 70 105
compr(\x.(1 - ((x + 1) mod (1 + (x mod (2 + (x div (2 + (x mod (2 + (x mod 2)))))))))),x)
A091886: 6 9 10 12 14 15 16 18 20 21 22 24 25 26 27 28
(x + (9 * (x mod ((x + ~1) - (x mod 12)))))
A103303: 0 1 2 3 4 5 6 7 8 9
A336956-A333659-A321474-A225805-A004186: 0 1 2 3 4 5 6 7 8 9 10 11 21 31 41 51
(x + ((5 * ((x2 + x) div 4)) div 9))
A117490: 0 1 2 4 6 8 11 14 18 21 25 29 33 38 42 48
(x + (((x + 1) * (1 + (x div 7))) div 9))
A094942: 0 1 2 3 4 5 6 8 10 11 12 13 14 16 19 20
compr(\x.(2 - ((~2 + ((x + 1) * (2 + (x div 4)))) mod 9)),x)
A289342: 1 2 3 4 5 7 8 9 10 13 15 17 18 21 22 23
compr(\x.(2 - ((x + (2x mod (4 + (x div 2)))) mod 9)),x)
A048263: 1 2 3 4 6 7 8 9 10 11 12 14 15 16 19 20
compr(\x.(2 + ((x + ~1) mod 9) - (x div 9)),x)
A304367-A298638-A291884-A173639: 19 28 29 37 38 39 46 47 48 49 55 56 57 58 59 64
((x + 1) + ((x div (~x + 18)) + (x div 8)))
A270427: 1 2 3 4 5 6 7 8 10 12 13 14 16 17 19 22
(x + ((2 * (2x - (x mod 15))) div 5))
A039046: 0 1 2 4 5 7 8 9 11 12 14 15 16 18 19 27
(x + (3 * (1 + (((x + 1) + ((x div 3) mod 3)) div 3))))
A219658: 3 4 8 9 13 14 18 19 20 21 22 26 27 31 32 36
(x + (x2 div (3 * ((x + 1) - (2 * ((x + 2) div 5))))))
A219640: 0 1 2 4 5 7 8 9 12 13 14 16 17 20 21 22
compr(\x.((1 + (2 * ((x2 mod 17) div 2))) mod 3),x)
A154663: 3 5 6 7 10 11
A028730: 3 5 6 7 10 11 12 14
A136806-A028747: 3 5 6 7 10 11 12 14 20 22 23 24 27 28 29 31
(x + (x div (3 * (2 + ((x2 + 3x + 2) mod 7)))))
A067570: 0 1 2 3 4 5 7
A343271: 0 1 2 3 4 5 7 7 8 9 10 11 14 15 15 15
(x * ((x2 + ~x) div (~6x + 108)))
A326464: 0 0 0 0 0 0 0 0 0 9 10 22 36 65 98 165
(x + ((2 * ((7x + 7) + (x div 4))) div 3))
A328986: 4 10 16 21 28 33 39 45 51 57 62 68 74 80 86 91
((3x + 1) - (((x - (((x + 1) div 5) mod 2)) div 2) mod 2))
A231407: 1 4 6
A317538: 1 4 6 9 12 16 19 21 24 28 30 33 37 40 43 45
((x + 1) + ((x + (x div 12)) mod 3) - (x mod 3))
A290492: 1 2 3 4 5 6 7 8 9 10 11 12 14
A191430: 1 2 3 4 5 6 7 8 9 10 11 12 14 15 13 17
(36x3 + ~81x2 + 46x)
A287702: 0 1 56 381 1192 2705 5136 8701 13616 20097 28360 38621 51096 66001 83552 103965
(x + (((x + 2) - ((x - (x div 5)) mod 8)) div 3))
A004742: 0 1 2 3 4 6 7 8 9 12 14 15 16 17 18 19
compr(\x.(((1 + (x div 4)) div (1 + (x mod 5))) - (x mod 3)),x)
A210576: 1 2 3 4 5 7 8 9 11 13 14 17 19 23 29
((x + 1) + (((x + 1) + (x mod (1 + (x2 div (x + 5))))) div 2))
A225647: 1 3 4 6 7
A183233: 1 3 4 6 7 10 11 13 15 16 18 19 21 22 24 25
(18x3 + 31x2 + 10x + 1)
A338109: 1 60 289 796 1689 3076 5065 7764 11281 15724 21201 27820 35689 44916 55609 67876
((x + 1) + ((3 * ((1 + (x * (x div 2))) div 3)) div 2) - (x mod 2))
A075709: 1 1 4 4 9 9 16 17 25 27 36
((~x + 1) + compr(\x.(~1 + ((~x + (x mod (1 + ((x div 2) div 3)))) mod 3)),x))
A272605: 1 2 2 3 3 3 3 3 5 5 5 5 5 5 7 7
((x + 1) + compr(\x.(~1 + (x mod (2 + (x mod (x - ((x + ~1) mod 8)))))),x))
A230104: 1 3 5 7 9 11 13 15 17 19 21 25 27 31 33 36
(6x5 + 5x4 + 4x3 + 3x2 + 2x + 1)
A113531: 1 21 321 2005 7737 22461 54121 114381 219345 390277 654321 1045221 1604041 2379885 3430617 4823581
((~x + 1) + compr(\x.((((x + ~1) mod (1 + (x div 5))) mod 2) - (x mod 2)),x))
A025782: 1 1 1 1 1 1 2 3 3 3 3 3 4 5 6 6
((~x + 1) + compr(\x.((((x - ((x - (x mod 3)) div 2)) div 2) mod 2) - (x mod 2)),x))
A123273: 1 1 2 3 4 4 4 5 6 6 6 6 6 6 6 7
(x + ((1 - ((x + 1) mod (1 + (2 * ((x + ~1) div 5))))) div (x + 1)))
A128559: 1 1 2 3 4 5 6 6 8 9 9 10 11 12 14 15
(~x + ((x * (4x - ((x + (x div 4)) div 3))) div (x + 1)))
A079527: 0 1 3 5 8 10 12 15 17 20 22 25 27 30 33 35
compr(\x.(((x + 1) - ((x + ~1) mod (1 + (x div (2 + ((x div 2) mod 3)))))) mod 2),x)
A097389: 1 3 4 5 6 7 8 9 14 15 18 19 20 21 22 23
compr(\x.(1 - (x mod (2 + ((x + 1) mod (1 + (2x mod 7)))))),x)
A122090: 1 2 3 4 5 7 9 10 11 13 17 19 21 22 23 25
((x + 2) + (x div (1 + ((x2 + 2x) mod (1 + ((2 - (x div 2)) mod 4))))))
A254733: 2 4 6 6 10 12 14 10 12 20 22 18 26 28 30 20
(x + ((((2 * (x div 3)) div 3) * (1 + (x div 5))) div 2))
A067570: 0 1 2 3 4 5 7
A050744: 0 1 2 3 4 5 7 8 9 11 13 14 15 16 17 21
compr(\x.((x - ((1 - (2x div 3)) div (1 + (x div 5)))) mod 2),x)
A225745: 1 2 3 5 6 8 9 10 13 15 17 19 21 23 25 27
compr(\x.(1 - (((x3 + ~1) mod 19) mod 2)),x)
A028732: 2 3 8 10 12 13 14 15 18
A028751: 2 3 8 10 12 13 14 15 18 21 22 27 29 31 32 33
((x + 2) + ((1 + (x div 3)) div 2) - ((~x + 1) div (2 + (x div 4))))
A197128: 2 3 5 7 8 10 11 12 13 15 17 18 19 20 21 23
compr(\x.(1 - (x mod (2 + (x mod (1 + (x div (2 + ((x div 2) mod 5)))))))),x)
A019470: 1 5 7 10 11 13 14 17 18 19 20 21 22 23 24 25
(x + ((((x + 1) div 7) * (1 + (((x + 1) div 2) div 2))) div 2))
A067570: 0 1 2 3 4 5 7
A191849: 0 1 2 3 4 5 7 8 9 10 11 13 14 17 18 20
compr(\x.((1 + ((((2 - ((x div 4) mod 2)) * ((x + 1) div 2)) div 2) div 2)) mod 2),x)
A043345-A023718: 3 7 11 12 13 14 19 23 27 28 29 30 35 39 43 44
compr(\x.(1 - (((x + 1) mod (1 + ((3 * (x mod 2)) + (x div 4)))) div 2)),x)
A118621: 1 7 9 10 14 15 16 17 18 19 20 21 22 23 24 25
compr(\x.(1 - (x mod (2 + ((1 + (x div (2 - (x mod 2)))) mod (1 + (x div 4)))))),x)
A046840: 1 3 4 5 7 11 12 13 15 16 17 19 20 21 23 25
compr(\x.(1 - (x mod (2 + ((1 + (x div (1 + ((x + ~1) mod 4)))) mod 3)))),x)
A275721: 1 2 3 5 7 11 13 14 15 17 19 23 25 26 29 31
(x + ((3 * (0 - (2x div (~3 + ((~x + 1) div 3))))) div 2))
A038100: 0 2 3 6 7 8 10 11 12 13 16 17 18 19 20 21
compr(\x.(1 - (x mod (2 + ((x - (x div (~1 - (x div 4)))) mod 3)))),x)
A167857: 1 2 3 5 7 9 10 11 13 17 19 22 23 25 29 31
compr(\x.(1 - (x mod (2 + ((x - (((x div 2) * (x div 2)) div 3)) mod 3)))),x)
A193622: 1 2 3 5 7 10
A046758: 1 2 3 5 7 10 11 13 14 15 16 17 19 21 23 25
compr(\x.((x div (1 + (((x - (x div (4 + (x mod 2)))) mod 2) + (x mod 2)))) mod 2),x)
A233524: 0 1 2 4 5 8
A327609: 0 1 2 4 5 8 9 10 12 13 16 17 18 20 24 25
(x * ((x3 + 7x2 + 26x + 20) div 2))
A129026: 0 27 108 282 600 1125 1932 3108 4752 6975 9900 13662 18408 24297 31500 40200
((x + 2) + ((0 - ((x - (((x div 2) - (x mod 4)) div 2)) div 2)) mod (x + 1)))
A050095: 2 4 6 7 10 11 12 14 16 17 19 20 23 24 25 27
((x + 2) + ((2 + (x2 div (x + 18))) mod (x + 1)))
A299407: 2 3 6 7 8 10 11 12 14 16 17 19 20 22 24 25
compr(\x.(2 - ((x + 3) mod (4 + ((x div 4) + ((x + 1) mod 2))))),x)
A174805: 0 3 5 6 8 10 11 12 13 15 17 18 19 20 21 22
(x + (((((x * (((x + ~1) div 2) div 2)) div 2) + (x div 5)) div 2) div 2))
A067570: 0 1 2 3 4 5 7
A212289: 0 1 2 3 4 5 7 8 9 11 13 14 15 18 19 21
(~x + (4 * ((x + 1) + (4 * ((x - (x div 3)) div 3)))))
A341282: 4 7 10 13 32 35 38 41 60 63 66 69 72 91 94 97
(1 div (~x + (2 * (2 + (37 mod (x + 1))))))
A286132: 0 0 0 0 0 1 0 0 ~1 0 0 ~1 0 0 0 ~1
(x + ((2 + ((5 * (((2 - (x div 2)) mod (x + 1)) div 2)) div 2)) div 2))
A032902-A032868-A032341: 1 2 3 4 5 6 10 11 12 15 16 17 18 20 21 22
(x + (2 * (((3 * (2 - ((~2x + 1) div 5))) div 2) div 2)))
A177987: 2 5 6 7 10 11 12 13 14 17 18 21 22 23 26 27
(x + (4 * (x - (2 * ((~2x + ~1) + ((x - (x div 4)) div 2))))))
A035339: 8 29 42 63 84 97 118 131 152 173 186 207 228 241 262 275
((x + 2) + ((x - ((2 - (x div (2 + (x div (1 + (x mod 4)))))) div 2)) div 2))
A232744: 1 3 5 6 7 9 11 12 13 15 17 18 19 21 23 25
(x + (2 * (6 + ((1 + (x div 2) - ((x div 4) mod 2)) div 2))))
A084622: 12 13 16 17 18 19 20 21 24 25 28 29 30 31 32 33
(x + (2 * ((x - (((x mod 10) + (x div 4)) div 2)) div 2)))
A192225: 0 1 2 5
A228090: 0 1 2 5 6 7 8 9 10 13 18 21 22 23 24 25
compr(\x.(((x div 2) - ((x - ((2x + 1) mod (2 + (x div 4)))) div 2)) mod 2),x)
A018195: 1 3 4 7 12 14 15 16
(0 - (((((~x + (x div (2 + (x mod 2)))) * (x div 4)) div 2) div 2) div 2))
A330216: 0 0 0 0 1 1 1 1 1 2 2 2 3 4 3 4
compr(\x.(2 - ((x + 1) mod (4 + (((((x + 1) div 2) div 2) * (x div 2)) mod 2)))),x)
A045989: 1 2 3 5 6 9 10 11 13 17 18 21 22 25 26 27
(x + (((x3 div 17) - (x div 4)) div 2))
A175831: 0 1 2 3 5 8 11 16 22 29 38 49 61 76 93 112
(x + ((((1 + ((x - ((x div 3) mod 3)) div 2)) * (x div 2)) div 2) div 2))
A239091: 0 1 2 3 5 6 8 9 12 14 17 18 21 23 26 27
((x + 4) + (((2x div (1 + (x mod 8))) mod 2) + (x div 2)))
A098015: 4 6 8 9 11 12 14 15 16 18 19 21 22 23 25 27
(x + ((x + ((x - ((((~x + 1) * (x div 2)) div 2) div 3)) mod 3)) div 2))
A171944: 0 2 3 5 7 8 9 11 12 13 15 17 19 20 21 23
(x + ((3x2 + 6) div (x + 26)))
A066026: 0 1 2 4 5 7 9 11 13 16 18 20 23 26 28 31
(~x + (2 * compr(\x.((((x + ~1) div (2 + (x div 5))) mod 2) - (x mod 2)),x)))
A080724: 2 3 4 7 10 11 12 13 14 15 16 19 22 25 28 31
(x + ((6 * ((x + 1) + (2 * (x div 5)))) div (x + 2)))
A296365: 3 5 6 7 9 11 12 13 14 15 17 18 19 20 21 22
((x2 + 2x + 1) + ((x + ((x3 + 2x) div 3)) div (x + 2)))
A283969: 1 4 10 18 29 43 59 78 99 123 150 179 211 246 283 323
(x + (((2x + 1) + (9 * (1 + (x div 2)))) * (x div 2)))
A303812: 0 1 25 28 76 81 153 160 256 265 385 396 540 553 721 736
((2x + 1) - compr(\x.((((x + 1) div ~7) mod 2) - (x mod 2)),x))
A102674: 0 0 0 0 1 2 3 4 5 6 6 6 6 6 7 8
compr(\x.(~x + (x5 mod 31)),x)
A344602: 0 1 2 4 7 8 11 13 14 16 19 21 22 25 26 28
(x * (~x + (9 * ((x + 1) - (x mod 10)))))
A084021: 0 8 14 18 20 20 18 14 8 0 890 968 1044 1118 1190 1260
((2x + 1) + (((2x + ~2) div (2 - ((~x + 2) div (2 + (x div 2))))) mod 2))
A285250: 1 3 6 8 9 11 14 15 17 19 21 24 26 27 29 32
((2x + 1) + ((1 + (x div 4)) div 2) - (x mod (1 + (x div 4))))
A189171: 1 3 5 7 10 11 14 15 16 20 21 22 27 28 29 30
(2x + (3 * (((x + 2) - ((~2x + 2) div 5)) div 2)))
A190557: 3 5 10 15 20 22 27 32 34 39 44 46 51 56 61 63
(2x + ((x - (3x mod 19)) div 2))
A004835: 0 1 2 3 4 5 6 16 17 18 19 20 21 32 33 34
((3x + 2) + (((x + 1) * (x2 div 4)) div (x + 4)))
A184430: 2 5 8 12 16 21 26 31 38 44 51 59 67 75 84 94
((~x2 + 1) + ((12x + 9) * ((x + 1) div 2)))
A228142: 1 21 30 82 99 183 208 324 357 505 546 726 775 987 1044 1288
((4x + 2) + (((~1 + (x * (x div 4))) div 3) mod 2))
A184422: 3 7 11 15 19 23 27 30 35 39 42 47 51 54 59 62
loop(\(x,i).loop(\(x,i).loop(\(x,i).loop(\(x,i).loop(\(x,i).loop(\(x,i).(x * i),i,x),i,x),i,x),i,x),i,x),x,1)
A260404: 1 1 2 192 6115295232 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).(2 * i),(if (i mod 2) <= 0 then 2 else 2x),x),(~1 + i),1)),x,0)
A177240: 0 1 5 9 25 29 45
((if (x mod 4) <= 0 then 1 else loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)) + (if x <= 0 then 0 else 1))
A334230: 1 1 2 1 2 3 1 2 2 4 1 2 2 4 5 1
(loop(\(x,i).x2,x,loop(\(x,i).2x,x,1)) - loop(\(x,i).(x * i),loop(\(x,i).2x,x,1),1))
A057157: 0 2 232 16736896 4611686018427387903 4611686018427387903
(if x <= 0 then 0 else loop(\(x,i).(loop(\(x,i).(x * i),(~1 + i),1) + loop(\(x,i).(x * i),x,1)),(x + ~1),1))
A114020: 0 1 2 3 8 40326
(1 - loop(\(x,i).loop(\(x,i).(x - (if x <= 0 then 0 else (1 + (2 * i)))),x,x),1,loop(\(x,i).2x,x,1)))
A056008: 3 2 5 1 9 4 17 16 33 17 65 68 129 89 257 356
loop(\(x,i).(if x <= 0 then 1 else (x + (if (8 mod (if x <= 0 then 1 else x)) <= 0 then x else 0))),1,(x + ~1))
A048167: 1 1 2 4 3 8 5 6 7 16 9 10 11 12 13 14
loop(\(x,i).(x + loop(\(x,i).x2,1,(1 + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,i)))),x,1)
A051678: 1 2 6 7 11 20 21 25 34 50 51 55 64 80 105 106
loop(\(x,i).(x + loop(\(x,i).(x + loop(\(x,i).x2,1,loop(\(x,i).x2,2,(1 + i)))),i,1)),x,1)
A253636: 1 258 7076 79430 542409 2685004 10592400 35277012 103008345 270739678 652829892 1464901802 3092704433 6196296120 11862778432 21824228040
loop(\(x,i).(x + loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).(x + (i * i)),(1 + i),x),i,1)),i,1)),x,1)
A040977: 1 8 35 112 294 672 1386 2640 4719 8008 13013 20384 30940 45696 65892 93024
loop(\(x,i).loop(\(x,i).((x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,i,1))) div 2),i,x),x,1)
A203303: 1 1 6 1008 20321280 203199794380800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(loop(\(x,i).(loop(\(x,i).2x,i,1) - (x div (if i <= 0 then 1 else i))),i,1) + (x * i)),x,1)
A003175: 1 2 8 31 139 724
(2 + loop(\(x,i).i,compr(\x.loop(\(x,i).loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x + 2)),2,x),x),1))
A133387-A105399: 3 7 13 19 23 31 37 43 47 53 61 67 73 79 83 89
(loop(\(x,i).loop(\(x,i).2x,x,x),1,loop(\(x,i).(x + (if x <= 0 then (1 + i) else 0)),x,(~x + 1))) div 2)
A130322: 1 4 1 12 4 1 32 12 4 1 80 32 12 4 1 192
(2x + (if x <= 0 then 2 else loop(\(x,i).(x + loop(\(x,i).(if x <= 0 then i else (x + ~1)),x,1)),1,(x + ~1))))
A079251: 2 3 5 10 12 14 22 24 26 28 30 32 46 48 50 52
(2 + compr(\x.loop(\(x,i).loop(\(x,i).loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x + 2)),2,x),2,x),x))
A201363: 2 3 7
A105792: 2 3 7 13 19 23 31 37 43 47 53 61 67 73 79 83
loop(\(x,i).2x,x,(if x <= 0 then 1 else loop(\(x,i).2x,(x div 2),loop(\(x,i).x3,x,2))))
A193134: 1 16 4096 2147483648 4611686018427387903 4611686018427387903
compr(\x.(if loop(\(x,i).((if x <= 0 then 2 else loop(\(x,i).(x div (2 - (x mod 2))),x,x)) div 2),2,x) <= 0 then x else 0),x)
A161989: 0 1 2 4 7 8 11 13 14 15 16 19 21 22 23 25
(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x - loop(\(x,i).(x - (if x <= 0 then 0 else i)),i,x)))),x,(x + 1)))
A173964: 1 2 1 2 3 2 3 1 2 3 4 3 4 2 3 4
(loop(\(x,i).2x,(if (8 mod (if x <= 0 then 1 else x)) <= 0 then x else 0),1) div (if x <= 0 then 1 else x))
A167001: 1 2 2 0 4 0 0 0 32 0 0 0 0 0 0 0
loop(\(x,i).(if x <= 0 then 2 else loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then i else 0)),(x div 2),(x + 1))),2,x)
A101300: 3 3 5 7 7 11 11 13 13 13 13 17 17 19 19 19
(if (x + ~2) <= 0 then x2 else loop(\(x,i).x2,1,loop(\(x,i).(x + (i * i)),(2x + 1),0)))
A003556: 0 1 4 19600
(if (x + ~1) <= 0 then 1 else (if (x mod 2) <= 0 then loop(\(x,i).(10x + 1),x,1) else 0))
A282411: 1 1 111 0 11111 0 1111111 0 111111111 0 11111111111 0 1111111111111 0 111111111111111 0
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).7x,(1 + i),x),i,1)),(x + 1),0)
A178190: 49 16856 40370463 678263443312 79792944561055313 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(if x <= 0 then 2 else (x * compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),(x + ~1),0)
A121406: 0 0 2 6 30 270 2970 44550 757350 15904350 429417450 12453106050 435858711750 16998489758250 696938080088250 31362213603971250
loop(\(x,i).2x,x,(if (x + ~1) <= 0 then 1 else (if (x mod 5) <= 0 then (2x + 2) else 0)))
A086260: 1 2 0 0 0 384 0 0
loop(\(x,i).(x + i),(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1))),0)
A115364: 1 3 1 6 1 3 1 10 1 3 1 6 1 3 1 15
loop(\(x,i).2x,x,(1 - loop(\(x,i).3x,x,loop(\(x,i).(2x + ~6),x,0))))
A089271: 1 38 652 9080 116656 1446368 17636032 213311360 2569812736 30898216448 371141389312 4455873443840 53483541999616 641880868118528 7703040602324992 92439308337643520
(loop(\(x,i).(x div 2),x,loop(\(x,i).(3x + 1),x,1)) + loop(\(x,i).(2x + 2),x,0))
A002804: 1 4 9 19 37 73 143 279 548 1079 2132 4223 8384 16673 33203 66190
loop(\(x,i).(loop(\(x,i).(loop(\(x,i).(x * i),(~1 + i),1) + (x * i)),i,1) + (x * (1 + i))),x,0)
A308729: 0 2 11 61 379 2668 21160 187388 1836396 19753416 231545016 2939000832 40172455296 588444153984 9197306248320 152803737342720
loop(\(x,i).(~x + loop(\(x,i).(x + (if x <= 0 then 1 else (x * (1 + i - (2 * (i mod 2)))))),i,1)),x,0)
A088110: 0 1 3 9
A121696: 0 1 3 9 63 297 2583 17577 184023 1630377 20142423 219358377 3133652823 40455492777 656970836823 9804424107177
loop(\(x,i).(x + (loop(\(x,i).2x,x,(if (~2 + i) <= 0 then 1 else x)) mod 10)),x,0)
A222010: 0 1 3 7
A118667: 0 1 3 7 13 19 21 23 27 33 39 41 43 47 53 59
loop(\(x,i).(x + loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i),2)),x,0)
A076793: 0 4 12 44 172 2220 10412 141484 665772 9054380 545925292 2693408940 140132362412 2339155617964 11135248640172 151872736995500
(1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).(10 * (if x <= 0 then 1 else x)),x,0)))
A135577: 1 111 10101 1001001 100010001 10000100001 1000001000001 100000010000001 10000000100000001 1000000001000000001 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).x2,(x + ~2),loop(\(x,i).2x,x2,loop(\(x,i).(2x + 1),x,0))))
A145572: 1 3 49 12845057 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 2),x2,(1 + loop(\(x,i).(if x <= 0 then 4 else x4),x,0)))
A093987: 1 2 16 8388608 4611686018427387903
(1 + loop(\(x,i).(x + (if (1 - (loop(\(x,i).(2x + 2),x,0) mod (x + 1))) <= 0 then 1 else i)),x,0))
A120797: 1 2 4 5 9 10 11 18 19 28 29 40 41 54 55 56
(1 + loop(\(x,i).2x,x,(~1 + loop(\(x,i).(2x + (if (x + ~2) <= 0 then 1 else 4)),x,1))))
A269815: 1 5 37 185 817 3425 14017 56705 228097 914945 3664897 14669825 58699777 234840065 939442177 3757932545
(1 + loop(\(x,i).x3,1,(~1 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,x,1)))))
A020526: 0 2 1332 166376 13651920 973242272 65499561792 4294977781376 278176525712640 17908846064302592 1149543810255025152 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 2) <= 0 then (3 * (if (x mod 4) <= 0 then (3 * (if x <= 0 then 1 else 2)) else 1)) else 1)
A010167: 9 1 3 1 18 1 3 1 18 1 3 1 18 1 3 1
(1 + ((2 + loop(\(x,i).(2 * i),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1)) mod 3))
A218828: 1 1 2 1 2 1 1 2 1 3 1 2 1 3 2 1
(1 + ((if x <= 0 then 1 else (2x - loop(\(x,i).(~1 + (if x <= 0 then (2 * i) else x)),x,2))) div 3))
A220661: 1 1 2 1 2 3 4 5 6 1 2 3 4 5 6 7
loop(\(x,i).2x,x,(~1 + loop(\(x,i).(2x + 2),x,2) - (if (x + ~2) <= 0 then x else 3)))
A271005: 1 8 44 208 928 3904 16000 64768 260608 1045504 4188160 16764928 67084288 268386304 1073643520 4294770688
loop(\(x,i).x3,1,(1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))
A088378: 1 8 27 8 125 8 343 8 27 8 1331 8 2197 8 27 8
(if x <= 0 then 2 else (x - (x div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))))
A242560: 2 1 2 2 4 3 6 4 6 5 10 6 12 7 10 8
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).4x,i,1))),(2x + ~1),1)
A144546: 1 12 11612160 794088208701849600 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 2) <= 0 then loop(\(x,i).(1 + (2 * (2x - (x div (if i <= 0 then 1 else i))))),(x div 2),1) else 1)
A134761: 1 1 3 1 11 1 39 1 139 1 503 1 1847 1
(~1 + loop(\(x,i).(x * i),x,loop(\(x,i).((x + 1) * ((if (x mod 2) <= 0 then 1 else x) mod 4)),x,1)))
A171554: 0 1 5 71 311
loop(\(x,i).2x,x,(1 + (loop(\(x,i).3x,x,1) + loop(\(x,i).4x,x,1))))
A074542: 3 16 104 736 5408 40576 308864 2377216 18457088 144295936 1134209024 8952733696 70896263168 562816516096 4476410691584 35654557106176
loop(\(x,i).loop(\(x,i).2x,i,x),(1 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x)),1)
A061591: 2 8 1024 2097152 36028797018963968 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).3x,x,(1 + (loop(\(x,i).3x,x,1) + loop(\(x,i).2x,x,1))))
A074557: 3 18 126 972 7938 67068 578826 5065092 44732898 397517868 3547309626 31744033812 284606850258 2554928116668 22955161402026 206361331428132
loop(\(x,i).(2x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i))),loop(\(x,i).2x,x,1),1)
A037293: 1 2 6 70 12870 601080390 1832624140942590534 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (loop(\(x,i).2x,((x2 + ~x) div 2),1) * (1 + loop(\(x,i).2x,x,1))))
A188545: 1 3 10
A337949: 1 3 10 72 1088 33792 2129920 270532608 68987912192 35253091565568 36063981391052800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(2x + loop(\(x,i).4x,(~1 + i),1)),i,1)),(x + 1),1)
A203478: 3 30 1080 146880 77552640 161309491200 1331771159347200 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (loop(\(x,i).(x * i),x,1) mod (x + 1)) <= 0 then loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) else 1)
A171435: 1 1 1 1 1 3 1 1 9 5 1 3 1 7 15 1
loop(\(x,i).(~x + loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 2 else 0)),x,(2x + 1))),(x + ~1),1)
A073627: 1 1 2 3 4 7 10 13 16 21 22 25 28 31 36 37
(x mod (1 + (x div loop(\(x,i).(x2 + 2x),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1))))
A332442: 0 1 0 3 0 0 6 1 0 0 10 3 0 0 0 15
(1 + (loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).3x,x,1)))
A001551: 4 10 30 100 354 1300 4890 18700 72354 282340 1108650 4373500 17312754 68711380 273234810 1088123500
(~1 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,x,1)) - loop(\(x,i).3x,x,1))
A147975: ~2 ~2 2 28 158 748 3302 14068 58718 241948 988502 4015108 16241678 65506348 263636102 1059360148
(1 + loop(\(x,i).(x * (2 + (if x <= 0 then 2 else (x - (if x <= 0 then 1 else (x div (2 - (i mod 2)))))))),x,1))
A201363: 2 3 7
A006695: 2 3 7 13 97 193 18817 37633 708158977 1416317953 1002978273411373057 2005956546822746113 4611686018427387903 4611686018427387903
(3 + loop(\(x,i).(1 + loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 1 else 0)),(x div 2),x)),x,0))
A033556: 3 4 5 7 9 11 15 17 21 23 27 31 33 35 39 41
(if (x mod 3) <= 0 then (2 * (if (x mod 2) <= 0 then (5 * (if x <= 0 then 1 else 2)) else 1)) else 1)
A010177: 10 1 1 2 1 1 20 1 1 2 1 1 20 1 1 2
(if (x mod 2) <= 0 then (2 * (if (x mod 3) <= 0 then (8 * (if x <= 0 then 1 else 2)) else 1)) else 1)
A040263: 16 1 2 1 2 1 32 1 2 1 2 1 32 1 2 1
(if (x mod 3) <= 0 then (2 * (if (x mod 2) <= 0 then (8 * (if x <= 0 then 1 else 2)) else 1)) else 1)
A040258: 16 1 1 2 1 1 32 1 1 2 1 1 32 1 1 2
(~1 + (2 * loop(\(x,i).2x,x,loop(\(x,i).(x div 2),x,loop(\(x,i).(3x + 1),x,1)))))
A018886: 1 7 23 79 223 703 2175 6399 19455 58367 176127 528383 1589247 4767743 14319615 42991615
loop(\(x,i).((x2 + x) div 2),1,(1 + (2 * loop(\(x,i).loop(\(x,i).(x2 + ~1),x,2),x,1))))
A276493: 6 28 8128 4611686018427387903
(1 + ((loop(\(x,i).(x2 + x),1,loop(\(x,i).(if x <= 0 then i else (x div 2)),x,0)) mod (x + 1)) div 2))
A228125-A227588-A172119-A092905-A052509: 1 1 1 1 2 1 1 3 2 1 1 4 4 2 1 1
loop(\(x,i).i,((loop(\(x,i).2x,x,(2 * (if (x mod 3) <= 0 then 0 else 2))) mod (x + 1)) div 2),1)
A105540: 1 1 1 1 2 1 1 1 3 1 2 4 1 4 1 1
((if x <= 0 then 2 else (x + ((loop(\(x,i).(x * i),x,x) mod (x + 1)) mod 2))) + (if (x + ~1) <= 0 then 2 else 1))
A113646: 4 4 4 4 6 6 8 8 9 10 12 12 14 14 15 16
(if (x mod 3) <= 0 then ((1 + (if (x mod 2) <= 0 then 6 else 1)) * (if x <= 0 then 1 else 2)) else 1)
A010142: 7 1 1 4 1 1 14 1 1 4 1 1 14 1 1 4
(1 + ((1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x)) * (if x <= 0 then 1 else 2)))
A020483: 2 3 3 5 3 3 5 3 3 5 3 7 5 3 3 7
(if (x mod 3) <= 0 then ((2 + (if (x mod 2) <= 0 then 8 else 1)) * (if x <= 0 then 1 else 2)) else 1)
A010176: 10 1 1 6 1 1 20 1 1 6 1 1 20 1 1 6
(1 + (2 * loop(\(x,i).x2,1,loop(\(x,i).loop(\(x,i).(2x + i),x,(i * i * i)),x,1))))
A191623: 3 19 11251 4611686018427387903
(if x <= 0 then 2 else (1 + (2 * (4 + loop(\(x,i).loop(\(x,i).(2x + 1),x,2),(x + ~1),1)))))
A067670: 2 11 19 199 4611686018427387903
(if loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) <= 0 then 1 else (x mod (1 + ((x + ~1) mod 4))))
A301342: 1 1 0 1 0 0 1 1 0 0 1 2 0 0 0 1
((if (x mod 3) <= 0 then (3 * (if x <= 0 then 1 else 2)) else 1) * (if (x mod 2) <= 0 then 4 else 1))
A040151: 12 1 4 6 4 1 24 1 4 6 4 1 24 1 4 6
loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x)),2,(2x + 5))
A231935: 5 7 7 11 13 13 17 19 19 23 23 23 29 31 31 31
loop(\(x,i).2x,x,(~1 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).(2x + 2),2x,2))))
A020539: 1 362 15124 514088 16695376 536215712 17174626624 549713871488 17591850501376 562947269069312 18014377034650624 576460580504741888 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((4x + 2) + loop(\(x,i).loop(\(x,i).(x + loop(\(x,i).2x,i,x)),x,1),x,0))
A092836: 2 7 13 149 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 2 else loop(\(x,i).(x + (if (x mod (1 + (2 * i))) <= 0 then 2 else 0)),x,(4x + 1)))
A118753: 2 5 11 13 17 23 29 29 37 37 41 47 53 53 59 61
loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x)),2,(3x + 3))
A118749: 3 5 7 11 13 17 19 23 23 29 31 31 37 41 43 47
loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x)),2,6x)
A067775: 2 5 11 17 23 29 31 41 47 53 59 61 71 73 83 89
(loop(\(x,i).(1 + (2 * (1 + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)))),2,x) div 3)
A225743: 1 1 2 1 2 1 1 2 1 3 1 2 1 3 1 1
(((if (x mod 2) <= 0 then x else 1) + (if x <= 0 then 0 else 1)) div (1 + (if (~1 + (x mod 3)) <= 0 then x else 2)))
A046094: 0 1 1 0 1 0 1 0 3 0 1 0 1 0 5 0
(1 + (loop(\(x,i).(2x + 4),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1) div (x + 2)))
A162319: 1 1 2 1 2 3 1 1 2 4 1 1 2 3 5 1
(if x <= 0 then 1 else ((2x + ~1) * loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,x)))
A273325: 1 2 36 300 1960 11340 60984 312312 1544400 7438860 35103640 162954792 746347056 3380195000 15164074800 67476121200
(loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).3x,2x,1))
A074536: 3 15 101 801 6833 60105 535601 4799481 43112513 387683145 3487834001 31385255961 282446317793 2541932945385 22877060906801 205892205869241
(loop(\(x,i).2x,x,2) - loop(\(x,i).2x,(loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2),1))
A185378: 1 3 6 15 28 62 120 255 496 1020 2016 4094 8128 16376
((x + 1) - (loop(\(x,i).(x2 + x),1,loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)) div 2))
A301853-A141419: 1 2 3 3 5 6 4 7 9 10 5 9 12 14 15 6
(1 + (2 * compr(\x.loop(\(x,i).loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)),2,x),x)))
A079699-A053176: 7 13 17 19 31 37 43 47 59 61 67 71 73 79 97 101
(1 + loop(\(x,i).loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1,(x + (x div 5))))
A274080: 1 1 2 1 2 1 2 3 4 1 3 4 5 1 2 4
loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,loop(\(x,i).(4x + 1),x,1))
A329006: 1 5 7 85 341 455 5461 21845 9709 349525 1398101 1864135 22369621 89478485 119304647 1431655765
loop(\(x,i).2x,x,loop(\(x,i).((5x + ~1) + loop(\(x,i).2x,i,2)),x,1))
A016292: 1 16 188 2000 20496 206976 2077888 20811520 208246016 2082983936 20831935488 208327741440 2083310964736 20833243856896 208332975423488 2083331901685760
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (1 + (x * (1 + loop(\(x,i).(x2 + x),2,2))))),x,1)
A033977: 1 44 22 11 474 237 10192 5096 2548 1274 637 27392 13696 6848 3424 1712
(loop(\(x,i).2x,x,(~1 + loop(\(x,i).2x,x,2))) - loop(\(x,i).(3x + 1),x,1))
A036239: 0 2 15 80 375 1652 7035 29360 120975 494252 2007555 8120840 32753175 131818052 529680075 2125927520
(if x <= 0 then (x div 3) else loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + x + 1)))
A108154: 0 3 7 13 0 31 43 0 73 0 0 0 157 0 211 241
((1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)) mod (1 + (if x <= 0 then 1 else x)))
A063918: 1 0 0 2 0 2 0 2 3 2 0 2 0 2 3 2
loop(\(x,i).(4x - loop(\(x,i).(2 * (~2x + (x div (if i <= 0 then 1 else i)))),i,1)),x,1)
A104970: 1 6 18 92 298 1444 4852 22840 78490 362580 1265564 5767688 20366596 91866984 327351336 1464522864
loop(\(x,i).loop(\(x,i).2x,loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),i,i),1),x,1)
A258169: 1 2 16 32768 72057594037927936 4611686018427387903
(1 + loop(\(x,i).((if x <= 0 then 1 else x) div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))),2,x))
A342257: 1 2 3 2 5 3 7 2 3 5 11 1 13 7 1 2
loop(\(x,i).((1 + ((x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,i,2))) div 2)) div 2),x,1)
A083402: 1 3 42 2520 624960 629959680 2560156139520 41781748196966400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,loop(\(x,i).(4x + loop(\(x,i).(3x + 1),i,1)),x,1))
A016305: 1 16 180 1760 16016 139776 1188160 9925120 81920256 670478336 5454525440 44180398080 356708356096 2873257885696 23103609323520 185534152048640
loop(\(x,i).~x,x,loop(\(x,i).(~4x + loop(\(x,i).(3x + 1),i,1)),x,1))
A249998: 1 0 13 12 169 312 2341 6084 34177 107184 517309 1803516 8011225 29653416 125788117 481629108
loop(\(x,i).(4x + loop(\(x,i).(2 * (~2x + (x div (if i <= 0 then 1 else i)))),i,1)),x,1)
A091520: 1 2 14 36 214 604 3340 9928 52582 161708 831588 2620920 13187836 42350744 209519576 682960784
loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A016269: 1 9 55 285 1351 6069 26335 111645 465751 1921029 7859215 31964205 129442951 522538389 2104469695 8460859965
loop(\(x,i).(4x + loop(\(x,i).(~2x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A249995: 1 5 27 121 539 2289 9619 39737 162987 663553 2690051 10865673 43783195 176086097 707220723 2837479129
(loop(\(x,i).3x,x,(1 + loop(\(x,i).2x,x,1))) + loop(\(x,i).4x,x,1))
A074548: 3 13 61 307 1633 9043 51481 298507 1751713 10359523 61573801 367168507 2194090993 13129397203 78637382521 471273075307
(loop(\(x,i).x2,x,loop(\(x,i).(4x + ~1),x,1)) + loop(\(x,i).4x,x,1))
A176947: 2 13 14657
(loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,1) - loop(\(x,i).4x,x,1))
A172060: 0 2 14 76 374 1748 7916 35096 153254 661636 2831300 12030632 50826684 213707336 894945944 3734901296
(loop(\(x,i).(x2 + x),1,loop(\(x,i).3x,x,1)) + loop(\(x,i).4x,x,1))
A074551: 3 16 106 820 6898 60316 536266 4801540 43118818 387702316 3487892026 31385431060 282446845138 2541934531516 22877065673386 205892220185380
(loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,x) - loop(\(x,i).4x,x,1))
A068554: ~1 ~2 ~4 ~4 24 236 1448 7640 37424 175436 798984 3565448 15672656 68098936 293196944 1253020976
loop(\(x,i).(x div (2 - (x mod 2))),x,loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,1))
A001803: 1 3 15 35 315 693 3003 6435 109395 230945 969969 2028117 16900975 35102025 145422675 300540195
loop(\(x,i).((x * loop(\(x,i).x2,1,loop(\(x,i).(2x * (~1 + (2 * i))),i,1))) div 2),x,1)
A103207: 1 2 144 1036800 1463132160000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).4x,x,loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),x,1))
A019677: 1 24 400 5760 77056 989184 12390400 152862720 1867841536 22682271744 274333696000 3309180026880 39847582498816 479270434504704 5760041038643200 69190860134154240
loop(\(x,i).3x,x,loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),x,1))
A017933: 1 18 225 2430 24381 234738 2205225 20404710 186995061 1703091258 15448694625 139763668590 1262226050541 11386154248578 102632111782425 924629361662070
(loop(\(x,i).(2 * (2x + loop(\(x,i).3x,i,1))),x,0) + loop(\(x,i).2x,x,1))
A027650: 1 8 46 230 1066 4718 20266 85310 354106 1455278 5938186 24104990 97478746 393095438 1581931306 6356390270
(loop(\(x,i).3x,x,1) - loop(\(x,i).((~x + 1) * (x div 2)),1,loop(\(x,i).2x,x,1)))
A094375: 1 4 15 55 201 739 2745 10315 39201 150499 582825 2273275 8918001 35144659 138992505 551203435
(loop(\(x,i).2x,(loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2),1) + loop(\(x,i).2x,x,1))
A185376: 2 3 6 9 20 34 72 129 272 516 1056 2050 4160 8200 16512 32769
loop(\(x,i).2x,(x + ~2),(loop(\(x,i).(3x + ~1),x,1) - loop(\(x,i).2x,x,1)))
A016283: 0 0 1 12 100 720 4816 30912 193600 1194240 7296256 44301312 267904000 1615810560 9728413696 58504691712
loop(\(x,i).3x,x,(loop(\(x,i).(3x + ~1),x,1) - loop(\(x,i).2x,x,1)))
A084874: 0 0 9 162 2025 21870 219429 2112642 19847025 183642390 1682955549 15327821322 139038251625 1257873017310 11360034454869 102475388237202
(loop(\(x,i).(x div 2),x,loop(\(x,i).7x,x,1)) mod loop(\(x,i).2x,x,1))
A211995: 0 1 0 2 6 13 46 33 246 479 398 883 20 6215 9467 16751
loop(\(x,i).2x,x,(loop(\(x,i).(6x + ~1),x,2) - loop(\(x,i).2x,x,1)))
A016294: 1 18 244 3048 37072 446880 5370688 64480896 773901568 9287342592 111450207232 1337410873344 16048964030464 192587702575104 2311052967755776 27732637760520192
loop(\(x,i).3x,x,(loop(\(x,i).(3x + ~3),x,2) - loop(\(x,i).2x,x,1)))
A084879: 1 3 18 189 2106 22113 220158 2114829 19853586 183662073 1683014598 15327998469 139038783066 1257874611633 11360039237838 102475402586109
loop(\(x,i).loop(\(x,i).(1 + (((x + 1) + (if (~x + 2) <= 0 then (x div 2) else 1)) div 2)),i,2x),x,1)
A329510: 1 3 6 8 8 7 6 6 6 6 6 6 6 6 6 6
loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1))
A037967: 1 3 21 210 2485 31878 427350 5891028 82824885 1181976510 17067482146 248817506028 3656231188246 54086245380300 804670817838300 12030722583033960
(loop(\(x,i).4x,x,1) - loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1))
A068551: 0 2 10 44 186 772 3172 12952 52666 213524 863820 3488872 14073060 56708264 228318856 918624304
loop(\(x,i).(x div (2 - (x mod 2))),x,loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1))
A001790: 1 1 3 5 35 63 231 429 6435 12155 46189 88179 676039 1300075 5014575 9694845
(loop(\(x,i).x2,1,loop(\(x,i).(2 * (~2x + (x div (if i <= 0 then 1 else i)))),x,1)) div (x + 1))
A151392-A000888: 1 2 12 100 980 10584 121968 1472328 18404100 236390440 3103161776 41469525552 562496897872 7726605740000 107289439704000 1503840313184400
((x + 1) * (if x <= 0 then 2 else loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then i else 0)),(x div 2),(x + 1))))
A053024: 2 4 9 20 25 42 49 88 99 110 121 156 169 238 255 272
compr(\x.(if x <= 0 then 1 else loop(\(x,i).(loop(\(x,i).(2x + 1),x,0) mod (x + 1)),x,(x + ~1))),(x + 1))
A067019: 3 5 7 11 13 17 19 23 27 29 31 37 41 43 45 47
loop(\(x,i).(if (x mod 4) <= 0 then 2 else (x div (1 + (if (x mod 3) <= 0 then 2 else 0)))),2,(x + 1))
A216913: 1 2 1 2 5 2 7 2 1 10 11 2 13 14 5 2
(loop(\(x,i).loop(\(x,i).x2,2,x3),1,loop(\(x,i).(x * i),(x + 2),2)) div (x + 1))
A118063: 16777216 4458050224128 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).x2,1,loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,2)) div (x + 1))
A267987: 4 8 48 400 3920 42336 487872 5889312 73616400 945561760 12412647104 165878102208 2249987591488 30906422960000 429157758816000 6015361252737600
(loop(\(x,i).(x + compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x + 2)),i)),x,2) mod (x + 1))
A194741: 0 0 0 3 2 1 0 6 4 2 0 9 6 3 14 10
loop(\(x,i).(4x + (if x <= 0 then 1 else (2x + (if (2 - i) <= 0 then x else 1)))),x,(x + 1))
A081042: 1 13 133 1225 10633 88837 722701 5764801 45294865 351652861 2703691669 20620693177 156208812697 1176509412085 8816899947037 65787638066353
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),(if (x + ~2) <= 0 then x else (x + 1)))
A106119: 3 5 7 13 17 19 23 29 31 37 41 43 47 53 59 61
(loop(\(x,i).(compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x + 2)),x) + i),2,x) mod (x + 1))
A076237: 0 0 0 0 3 3 3 1 8 8 10 9 8 8 8 7
((x + 1) + loop(\(x,i).(x - (if (if ((x + (x div 2)) mod 4) <= 0 then x else 0) <= 0 then 1 else 0)),x,x))
A118374: 1 2 3 7 8 9 10 11 17 18 19 23 24 25 26 27
(loop(\(x,i).4x,x,1) - loop(\(x,i).(x + (2 * (if (2 - i) <= 0 then x else 1))),x,(x + 1)))
A086443: 0 0 1 10 67 376 1909 9094 41479 183412 792697 3367618 14120011 58605808 241331965 987648382
((x + ~1) * (if x <= 0 then 0 else (loop(\(x,i).2x,(x + ~2),loop(\(x,i).x2,(x + ~1),2)) div 2)))
A087084: 0 0 2 32 1536 1048576 171798691840 4611686018427387903 4611686018427387903
((if x <= 0 then 1 else 2) mod ((x + 2) div (1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 2 else 0)),x,x))))
A089798: 1 0 ~2 0 0 0 0 0 2 0 0 0 0 0 0 0
loop(\(x,i).(8x div 3),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1)
A144224: 1 1 2 1 2 5 1 2 5 13 1 2 5 13 34 1
(loop(\(x,i).3x,x,1) - loop(\(x,i).(x * (~1 + (if (i mod 2) <= 0 then 4 else 0))),x,1))
A318610: 0 4 12 24 72 252 756 2160 6480 19764 59292 176904 530712 1595052 4785156 14346720
(loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).5x,x,1))
A074532: 3 11 45 197 897 4181 19785 94637 456417 2215781 10815225 53024477 260921937 1287820181 6371967465 31591352717
(loop(\(x,i).(x3 + x2),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).3x,x,1))
A074550: 3 15 89 603 4433 34035 266969 2115723 16849313 134499555 1074849449 8594306043 68736785393 549824517075 4398319729529 35185460179563
(loop(\(x,i).(x3 + x),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).3x,x,1))
A074530: 3 13 77 547 4193 33043 262937 2099467 16784033 134237923 1073801897 8590113787 68720012273 549757416403 4398051310457 35184386470507
loop(\(x,i).2x,(2x - loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),x,x)),1)
A120781: 1 8 32 512 2048 16384 65536 2097152 8388608 67108864 268435456 4294967296 17179869184 137438953472 549755813888 35184372088832
loop(\(x,i).2x,((x mod 2) - loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),x,x)),1)
A240988: 1 4 2 16 8 32 16 256 128 512 256 2048 1024 4096 2048 65536
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).12x,i,1))),x,1)
A028674: 1 132 2718144 8111637540864 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i),1)),x,1)
A080355: 1 3 7 23 87 1111 5207 70743 332887 4527191 272962647 1346704471 70066181207 1169577808983 5567624320087 75936368497751
loop(\(x,i).loop(\(x,i).(x * i),(1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x),x,1)
A111180: 1 2 12 1440 7257600 289700167680000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(2x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i))),i,1)),x,1)
A036256: 1 2 4 7 13 23 43 78 148 274 526 988 1912 3628 7060 13495
loop(\(x,i).(x * loop(\(x,i).(4x + loop(\(x,i).5x,i,1)),i,1)),x,1)
A269661: 1 9 549 202581 425622681 4907003889249 302963327126122509 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).10x,i,1))),x,1)
A028672: 1 90 891000 890109000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).7x,i,1))),x,1)
A028669: 1 42 98784 11587955904 66774437101209600 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).(x + (i * i * i * i * i)),(1 + i),x),i,1)),x,1)
A101099: 1 35 345 1955 7990 26226 73470 182490 412335 863005 1695551 3158805 5624060 9629140 15933420 25585476
loop(\(x,i).(x + loop(\(x,i).(x + loop(\(x,i).10x,i,(1 + i))),i,1)),x,1)
A272525: 1 22 343 4664 58985 713306 8367627 96021948 1083676269 12071330590 133058984911 1454046639232 15775034293553 170096021947874 1824417009602195 19478737997256516
loop(\(x,i).(x + loop(\(x,i).x2,1,loop(\(x,i).(x + (((2 + i) * (1 + i)) div 2)),i,1))),x,1)
A086020: 1 17 117 517 1742 4878 11934 26334 53559 101959 183755 316251 523276 836876 1299276 1965132
loop(\(x,i).(x + loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i),2)),x,1)
A320877: 1 5 13 45 173 2221 10413 141485 665773 9054381 545925293 2693408941 140132362413 2339155617965 11135248640173 151872736995501
loop(\(x,i).((x + 1) + i),compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x),1)
A061066: 1 3 6 15 21 36 45 66 105 120 171 210 231 276 351 435
loop(\(x,i).(x * (1 + i)),compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x),1)
A212158: 1 2 6 120 720 40320 362880 39916800 87178291200 1307674368000 6402373705728000 2432902008176640000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(loop(\(x,i).(2 + ((x2 + x) div 2)),2,x) div 3),1,i)),x,1)
A027928: 1 3 8 20 46 97 189 344 591 967 1518 2300 3380 4837 6763 9264
loop(\(x,i).3x,2x,loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,1))
A173000: 1 45 1215 25515 459270 7440174 111602610 1578379770 21308126895 277005649635 3490271185401 42835146366285 514021756395420 6049640671423020 70002984912180660 798034027998859524
loop(\(x,i).(x * (4 + i)),x,loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,1))
A001811: 1 25 450 7350 117600 1905120 31752000 548856000 9879408000 185513328000 3636061228800 74373979680000 1586644899840000 35272336619520000 816302647480320000 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),i,x),x,1)
A079264: 1 2 12 360 75600 174636000 5244319080000 2677277333530800000 4611686018427387903
A006939: 1 2 12 360 75600 174636000 5244319080000 2677277333530800000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 + (if (x mod 2) <= 0 then (loop(\(x,i).(2x2 + 3x + 1),2,1) * (if x <= 0 then 1 else 2)) else 0))
A283897: 93 2 184 2 184 2 184 2 184 2 184 2 184 2 184 2
(~2 + loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,loop(\(x,i).(2x + 1),x,0)))
A098939: ~2 ~1 177145 1977326741 8649755859373 25408476896404829 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 * loop(\(x,i).(~x + loop(\(x,i).(1 + (x * i)),(~1 + i),1)),x,0)))
A054093: 1 2 2 8 24 106 546 3368 24032 195170 1777650 17950552 199059672 2405063018 31448531954 442501797656
(2 + loop(\(x,i).(x + (if x <= 0 then 1 else (x - ((if (x mod 2) <= 0 then (~x + 1) else x) div (1 + i))))),x,0))
A341823: 2 3 4 7 11 19 34 70
(loop(\(x,i).(2x + loop(\(x,i).(loop(\(x,i).2x,i,1) + (x * (~1 + i))),i,1)),x,0) div 2)
A346394: 0 1 5 20 78 324 1520 8336 53872 405600 3492416 33798016 362543104 4264455168 54540715008 753246711808
(loop(\(x,i).2x,x2,(1 + loop(\(x,i).x2,1,(~1 + loop(\(x,i).2x,x,2))))) div 2)
A162677: 1 10 400 57856 31522816 66605547520 554222579875840 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(2x + 1),x,(if (x mod 2) <= 0 then (2 + ((if (x + ~2) <= 0 then 1 else x) mod 2)) else 1)) div 2)
A289099-A286826: 1 1 7 7 23 31 95 127 383 511 1535 2047 6143 8191 24575 32767
loop(\(x,i).2x,x,(2 * (~1 + loop(\(x,i).x2,1,loop(\(x,i).(2x + 2),2x,2)))))
A020542: 6 780 30744 1032240 33423456 1072693440 34351350144 1099444519680 35183835219456 1125895611878400 36028762659231744 1152921229728952320 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 * ((~1 + loop(\(x,i).2x,x,loop(\(x,i).(2x + 1),x,2))) div 3)))
A267689: 1 6 28 122 500 2026 8148 32682 130900 523946 2096468 8387242 33551700 134212266 536859988 2147461802
(if x <= 0 then 2 else ((loop(\(x,i).2x,x,loop(\(x,i).(~3x + 3),x,1)) mod (x + 1)) div 2))
A323913: 2 0 0 0 0 0 0 0 1 0 0 0 0 0 6 0
loop(\(x,i).(2x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i))),(x + ~2),(if x <= 0 then 1 else 2))
A182027: 1 2 2 2 4 6 12 20 40 70 140 252 504 924 1848 3432
loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),x,(if x <= 0 then 1 else 2))
A097250: 1 4 12 60 420 4620 60060 1021020 19399380 446185740 12939386460 401120980260 14841476269620 608500527054420 26165522663340060 1229779565176982820
loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),x,(if x <= 0 then 1 else 2))
A231209: 1 6 30 210 2310 30030 510510 9699690 223092870 6469693230 200560490130 7420738134810 304250263527210 13082761331670030 614889782588491410 4611686018427387903
((loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1)) - loop(\(x,i).3x,x,1)) div 2)
A053154: 0 1 5 22 95 406 1715 7162 29615 121486 495275 2009602 8124935 32761366 131834435 529712842
(2 * loop(\(x,i).(x + loop(\(x,i).x2,1,loop(\(x,i).x3,1,(1 + (2 * i))))),x,1))
A259323: 2 1460 32710 268008 1330890 4874012 14527630 37308880 85584018 179675780 351208022 647279800 1135561050 1910402028 3100048670 4875056032
(if x <= 0 then 1 else (4 + (loop(\(x,i).x2,1,loop(\(x,i).(2x + ~4),x,1)) div 3)))
A272706: 1 5 25 137 649 2825 11785 48137 194569 782345 3137545 12566537 50298889 201261065 805175305 3220963337
((if x <= 0 then 2 else ((loop(\(x,i).2x,x,(if (x mod 2) <= 0 then 3 else x)) mod (x + 1)) div 2)) div 2)
A086780: 1 0 0 0 0 1 0 0 0 2 0 1 0 3 3 0
((x + 4) - loop(\(x,i).(x - (if (x mod 2) <= 0 then ((if x <= 0 then 2 else x) div 2) else 1)),x,(x + 1)))
A287127: 3 4 5 7 8 10 11 14 15 17 18 21 22 24 25 29
(4 * loop(\(x,i).x2,1,((x + 1) - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x))))
A174426: 4 36 36 144 144 144 400 400 400 400 900 900 900 900 900 1764
(2 + ((loop(\(x,i).(x2 + ~2x),1,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)) div 2) div 2))
A127439: 2 2 1 2 1 2 2 1 2 2 2 1 2 2 4 2
((2 - (loop(\(x,i).x2,1,(2 + loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x))) div 2)) div 2)
A220962: 0 1 0 1 1 0 1 1 1 0 0 1 1 1 0 ~1
(loop(\(x,i).2x,x,(~1 + loop(\(x,i).2x,x,2))) + loop(\(x,i).3x,x,4))
A147535: 5 18 64 228 820 2988 11044 41388 157060 602508 2332324 9095148 35676100 140586828 555986404 2204846508
(loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1) div loop(\(x,i).2x,(x + 2),2))
A024506: 0 0 0 0 0 0 1 3 6 11 22 43 82 158 306 591
loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x)),2,(3x + 2))
A020581: 2 5 7 11 13 17
A081259: 2 5 7 11 13 17 19 23 23 29 31 31 37 41 43 47
(if x <= 0 then 1 else (2 * ((x + ~1) + loop(\(x,i).(x + (if (~2 + (x div 4)) <= 0 then 1 else 2)),2,x))))
A315170: 1 6 10 14 18 22 26 30 34 38 42 48 54 58 62 66
(loop(\(x,i).(x * loop(\(x,i).(x + (if (x + ~2) <= 0 then 1 else x)),i,1)),x,1) * ((x2 + x) div 2))
A279045: 0 2 18 216 4320 155520 10450944 1337720832 330225942528 158508452413440 148786600665415680 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (2x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1))),x,2)
A038721: 2 18 110 570 2702 12138 52670 223290 931502 3842058 15718430 63928410 258885902 1045076778 4208939390 16921719930
loop(\(x,i).loop(\(x,i).(x * i),x,x),1,(2 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x)))
A114574: 4 18 600 35280 439084800 80951270400 6046686277632000 2311256907767808000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).2x,x,x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A100042: 8 24 160 896 22528 106496 2228224 9961472 192937984 15569256448 66571993088 5085241278464 90159953477632 378231999954944 6614661952700416 477381560501272576
(loop(\(x,i).2x,x,2) div (loop(\(x,i).3x,x,3) mod loop(\(x,i).2x,x,2)))
A071353: 2 4 2 16 1 2 11 1 2 1 2 1 1 1 1 1
loop(\(x,i).((x + 1) * (1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x))),1,(x + 2))
A013637: 6 12 15 30 35 56 63 70 77 132 143 182 195 208 221 306
((1 + loop(\(x,i).(2x + 2),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1)) div (x + 2))
A079126: 1 0 1 0 0 1 0 0 1 2 0 0 0 1 2 0
((x + 2) + (if x <= 0 then 0 else (x + loop(\(x,i).(x + (if (x mod (2 + i)) <= 0 then x else 0)),x,3))))
A079252: 2 10 12 14 22 24 26 28 30 32 46 48 50 52 54 56
compr(\x.(if x <= 0 then 1 else loop(\(x,i).(if ((x + 1) mod 8) <= 0 then x else (x div 2)),x,x)),2x)
A097911: 1 3 5 8
A073608: 1 3 5 8 10 12
A305378: 1 3 5 8 10 12 16 18 20 22 25 27 33 35 37 40
((if (x mod 3) <= 0 then (2 * (if (x mod 2) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1)) else 1) + (x mod 2))
A010124: 4 2 1 3 1 2 8 2 1 3 1 2 8 2 1 3
(x - (loop(\(x,i).(x2 + 3x),1,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)) div 2))
A049780: 0 1 0 3 2 0 6 5 3 0 10 9 7 4 0 15
((x + loop(\(x,i).(1 - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * (1 + i)))),x,2x)),2,x)) div 2)
A066182: 1 3 2 6 4 5 10 7 8 9 15 11 12 13 14 21
(if x <= 0 then 1 else (2 * (x + (if x <= 0 then 0 else (if (x + ~1) <= 0 then 1 else (x * (4 - (x mod 2))))))))
A298040: 1 4 20 24 40 40 60 56 80 72 100 88 120 104 140 120
loop(\(x,i).(x + loop(\(x,i).(x + loop(\(x,i).(2 * (2x - (x div (1 + i)))),i,2)),i,2)),x,2)
A120278: 2 10 38 136 486 1760 6466 24042 90238 341190 1297574 4958114 19019254 73196994 282492254 1092867904
(x + (if x <= 0 then 1 else ((loop(\(x,i).2x,(x + ~1),1) - (if (x mod 2) <= 0 then 1 else x)) div 3)))
A057574: 1 1 2 3 6 8 16 26 50
(~x + loop(\(x,i).(1 + (x * loop(\(x,i).((x + 1) * ((x + 1) div 2)),i,(if x <= 0 then 1 else 2)))),x,1))
A319253: 1 3 31 1186
loop(\(x,i).x2,1,compr(\x.(1 + loop(\(x,i).(0 - (if (x mod (1 + i)) <= 0 then 0 else x)),(x div 2),x)),x))
A087691: 9 49 121 361 529 961 1849 2209 3481 4489 5041 6241 6889 10609 11449 16129
compr(\x.(x - loop(\(x,i).loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),x,(2x + 1)),2,(x + 1))),x)
A152843: 0 1 4 10 13 19 25 40 43 55 64 85 88 94 115 118
compr(\x.(1 - loop(\(x,i).loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,2x),2,(x + 1))),x)
A105610: 0 2 8 14 17 38 47 68 77 98 104 113 134 152 164 167
loop(\(x,i).(x + loop(\(x,i).(~1 + loop(\(x,i).(x div (~2 + (x mod 2))),x,x)),x,x)),1,(x2 + x))
A050493: 0 1 2 2 2 4 3 3 2 4 5 2 4 5 4 4
(x + (if x <= 0 then 1 else (2 * (1 + loop(\(x,i).(if x <= 0 then 1 else (x + (2 * (i * (1 + i))))),x,0)))))
A273480: 1 5 30 79 160 281 450 675 964 1325 1766 2295 2920 3649 4490 5451
((x + 2) + (if x <= 0 then 1 else (4 + loop(\(x,i).(if x <= 0 then 3 else (x2 + ~1)),x,1))))
A020590: 3 7 11 17 73
loop(\(x,i).(1 + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)),1,(x + (x div 8)))
A126260: 1 1 2 1 2 3 1 2 4 1 2 3 4 5 1 2
loop(\(x,i).loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)),1,(x + loop(\(x,i).x2,2,4)))
A276233: 257 129 259 65 261 131 263 33 265 133 267 67 269 135 271 17
loop(\(x,i).(0 - loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),x,x)),1,(x2 + 2x))
A091711: 0 3 7 15 22 34 46 63 78 97 116 142 165 193 221 255
(if x <= 0 then 1 else (x2 * (1 + ((loop(\(x,i).loop(\(x,i).x2,x,2),(x + ~2),1) div 2) div 2))))
A069874: 1 1 4 18 262160
compr(\x.loop(\(x,i).loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)),1,(x2 + x)),x)
A012132: 3 6 8 10 11 13 15 16 18 20 21 23 26 27 28 31
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))),x,x)
A089312: 0 1 1 3 1 1 3 7 1 1 1 3 3 1 7 15
loop(\(x,i).(4x - loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),i,1)),x,x)
A153338: 0 2 18 116 650 3372 16660 79592 371034 1697660 7654460 34106712 150499908 658707896 2863150440 12371226064
(if x <= 0 then 2 else (x * (x + (2 * loop(\(x,i).2x,(x + ~2),loop(\(x,i).(2x * i),x,2))))))
A272663: 2 9 68 1161
loop(\(x,i).x2,1,compr(\x.(2 - loop(\(x,i).(0 - (if (x mod (1 + i)) <= 0 then 0 else x)),(x div 2),x)),x))
A080109: 25 169 289 841 1369 1681 2809 3721 5329 7921 9409 10201 11881 12769 18769 22201
loop(\(x,i).x2,2,compr(\x.(2 - loop(\(x,i).(0 - (if (x mod (1 + i)) <= 0 then 0 else x)),(x div 2),x)),x))
A080175: 625 28561 83521 707281 1874161 2825761 7890481 13845841 28398241 62742241 88529281 104060401 141158161 163047361 352275361 492884401
(if (x + ~2) <= 0 then ((x + 1) mod 2) else (if (x mod 6) <= 0 then (1 + (x div 4)) else 0))
A325787: 1 0 1 0 0 0 2 0 0 0 0 0 4 0 0 0
(if x <= 0 then 1 else (if (2x mod (4 + (x div 4))) <= 0 then ((x + 2) div 3) else 0))
A174712-A127647: 1 0 1 0 0 2 0 0 0 3 0 0 0 0 5 0
loop(\(x,i).(9x + (if (~1 + (i mod 3)) <= 0 then 2 else 1)),(x + 1),0)
A037574: 2 19 173 1559 14032 126290 1136612 10229509 92065583 828590249 7457312242 67115810180 604042291622 5436380624599 48927425621393 440346830592539
(if x <= 0 then 1 else (if (2x mod (4 + (x div 4))) <= 0 then (2 - (x div ~2)) else 0))
A127775: 1 0 3 0 0 5 0 0 0 7 0 0 0 0 9 0
(1 - (if x <= 0 then 1 else (if ((x + 1) mod (1 + (~2x mod 5))) <= 0 then 2 else 0)))
A011586: 0 1 1 1 1 ~1 1 ~1 1 1 ~1 ~1 1 1 ~1 ~1
(1 - (if x <= 0 then 1 else (if (x mod (1 + (2 * (3 - ((x div 3) mod 2))))) <= 0 then 2 else 0)))
A165574: 0 1 1 1 1 ~1 1 ~1 1 1 ~1 1 1 1 ~1 ~1
(loop(\(x,i).(10x + 1),x,0) + (if (x + ~1) <= 0 then (2x + 2) else 0))
A069506: 2 5 11 111 1111 11111 111111 1111111 11111111 111111111 1111111111 11111111111 111111111111 1111111111111 11111111111111 111111111111111
(if (2x mod (4 + (x div 4))) <= 0 then ((x div 4) + (if x <= 0 then 1 else 2)) else 0)
A127648: 1 0 2 0 0 3 0 0 0 4 0 0 0 0 5 0
(if x <= 0 then 1 else ((((2x + 1) mod (2 + (x div 4))) div 2) + (if (x mod 2) <= 0 then 2 else 0)))
A068067: 1 0 2 0 2 1 2 0 2 1 2 1 2 1 4 0
(loop(\(x,i).10x,x,1) + loop(\(x,i).(3x + 2),2x,0))
A155669: 1 18 180 1728 16560 159048 1531440 14782968 143046720 1387420488 13486784400 131381059608 1282429536480 12541865828328 122876792454960 1205891132094648
(loop(\(x,i).10x,x,1) - loop(\(x,i).(3x + 2),2x,0))
A155671: 1 2 20 272 3440 40952 468560 5217032 56953280 612579512 6513215600 68618940392 717570463520 7458134171672 77123207545040 794108867905352
(loop(\(x,i).7x,x,1) + loop(\(x,i).(3x + 2),2x,0))
A155656: 1 15 129 1071 8961 75855 649089 5606511 48811521 427774095 3769259649 33358386351 296270823681 2638754838735 23555015527809 210638693604591
loop(\(x,i).x2,1,loop(\(x,i).(60x + 1),x,0))
A260860: 0 1 3721 13402921 48250954921 173703464074921 625332472251274921 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).10x,x,loop(\(x,i).(10x + 10),x,0))
A163663: 0 100 11000 1110000 111100000 11111000000 1111110000000 111111100000000 11111111000000000 1111111110000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).4x,x,1) - loop(\(x,i).(11x + ~10),x,0))
A155625: 1 14 136 1394 14896 162074 1775656 19503554 214424416 2358209834 25938473176 285315864914 3138445153936 34522779252794 379750102018696 4177249243157474
(loop(\(x,i).3x,x,1) - loop(\(x,i).(11x + ~10),x,0))
A155623: 1 13 129 1357 14721 161293 1772289 19489357 214365441 2357967373 25937483649 285311847757 3138428908161 34522713738253 379749838366209 4177248183764557
loop(\(x,i).3x,(x + ~1),loop(\(x,i).((x + 1) - (2 * (~2x + (x mod 2)))),x,0))
A239294: 0 1 12 189 2808 42201 632772 9492309 142382448 2135743281 32036129532 480542002029 7208129853288 108121948330761 1621829223367092 24327438355289349
(loop(\(x,i).6x,x,1) - loop(\(x,i).(7x + ~6),x,0))
A155645: 1 12 84 558 3696 24582 164304 1103478 7444416 50431302 342941424 2340123798 16018069536 109949704422 756587236944 5217746494518
(loop(\(x,i).8x,x,1) - loop(\(x,i).(7x + ~6),x,0))
A155655: 1 14 112 854 6496 49574 379792 2920694 22542016 174571334 1356217072 10567261334 82560763936 646644824294 5076269583952 39931933598774
(loop(\(x,i).5x,x,1) - loop(\(x,i).(7x + ~6),x,0))
A155634: 1 11 73 467 3025 19931 133273 901667 6155425 42306731 292240873 2026154867 14085427825 98109713531 684326588473 4778079088067
loop(\(x,i).6x2,1,loop(\(x,i).(10x + 1),x,0))
A271528: 0 6 726 73926 7405926 740725926 74073925926 7407405925926 740740725925926 74074073925925926 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + ((x2 + x) div 2)),1,loop(\(x,i).(10x + 1),x,0))
A202606: 1 2 67 6217 617717 61732717 6172882717 617284382717 61728399382717 6172839549382717 617283951049382717 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).((x * (1 + i)) div (1 + (i div 2))),(x + ~1),1) + loop(\(x,i).(2x + 1),x,0))
A172411: 1 2 5 10
A261681: 1 2 5 10 21 41 83 162 325 637 1275 2509 5019 9907 19815 39202
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) + loop(\(x,i).(2x + 1),x,0))
A132807: 1 2 5 12 29 73 195 556 1685 5373
(loop(\(x,i).(7x + 1),x,0) - loop(\(x,i).(3x + 1),x,0))
A341590: 0 0 4 44 360 2680 19244 136164 957520 6715760 47049684 329465884 2306615480 16147371240 113034787324 791253077204
(loop(\(x,i).(7x + 2),x,0) - loop(\(x,i).(3x + 1),x,0))
A109020: 0 1 12 101 760 5481 38852 273421 1918320 13441361 94128892 659020341 4613496680 32295539641 226071966132 1582513328861
(loop(\(x,i).(7x + 3),x,1) - loop(\(x,i).(3x + 1),x,0))
A165147: 1 9 69 501 3561 25089 176109 1234221 8643921 60520569 423683349 2965901541 20761665081 145332718449 1017332217789 7121335090461
(loop(\(x,i).7x,x,1) + loop(\(x,i).(5x + ~4),x,0))
A155640: 1 3 25 219 1777 13683 102025 745419 5374177 38400483 272709625 1928498619 13597146577 95668307283 672119557225 4717043931819
(loop(\(x,i).(3x + 1),2x,1) - loop(\(x,i).(5x + 2),x,0))
A165149: 1 11 109 1031 9529 87011 789349 7135391 64374769 580154171 5225293789 47047175351 423522234409 3812188390931 34312136924629 308821439352911
(loop(\(x,i).11x,x,1) - loop(\(x,i).(3x + 2),x,0))
A155624: 1 9 113 1305 14561 160809 1770833 19484985 214352321 2357928009 25937365553 285311493465 3138427845281 34522710549609 379749828800273 4177248155066745
loop(\(x,i).(2x + loop(\(x,i).27x,(~1 + i),1)),x,0)
A180844: 0 1 29 787 21257 573955 15496817 418414123 11297181449 305023899379 8235645283745 222362422662139 6003785411879801 162102206120758723 4376759565260493713 4611686018427387903
(loop(\(x,i).3x,2x,1) - loop(\(x,i).(7x + 6),x,0))
A155660: 1 3 33 387 4161 42243 413793 3959427 37281921 347066883 3204309153 29403732867 268588249281 2444976817923 22198569382113 201143570584707
(loop(\(x,i).8x,x,1) - loop(\(x,i).(7x + 6),x,0))
A155659: 1 2 16 170 1696 15962 144496 1273610 11012416 93864122 791266576 6612607850 54878189536 452866803482 3719823438256 30436810578890
loop(\(x,i).(x + loop(\(x,i).(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1,i)),x,0)
A000788: 0 1 2 4 5 7 9 12 13 15 17 20 22 25 28 32
loop(\(x,i).(x + loop(\(x,i).(((3 * (x + (x div 4))) - (x mod 2)) div 2),1,i)),x,0)
A122247: 0 1 4 8 15 23 33 44 59 75 93 112 134 157 182 208
(~1 + (if x <= 0 then 1 else (if ((x + 1) mod (1 + (2 * ((~x + 1) mod 5)))) <= 0 then 2 else 0)))
A011624: 0 1 ~1 ~1 1 1 1 ~1 ~1 1 ~1 1 ~1 1 1 ~1
(~1 + (if x <= 0 then 1 else 2) - (if (2 - (x mod (1 + (x2 mod (x + 4))))) <= 0 then 2 else 0))
A011626-A011600-A011589: 0 1 ~1 1 1 ~1 ~1 1 ~1 1 1 1 1 ~1 ~1 ~1
(1 + (if x <= 0 then 1 else (if (x mod (2 + (13 mod (x + 1)))) <= 0 then 2 else 0)))
A080209: 2 1 1 3 1 1 1 3 1 1 1 1 3 1 1 3
(3 mod (~1 + (if ((x + (if (~2 + (x div 4)) <= 0 then 1 else 2)) mod 4) <= 0 then x else 0)))
A285014: 0 0 0 1 0 0 0 3 0 0 0 3 0 0 3 0
(1 + loop(\(x,i).(if x <= 0 then (~1 + (i div 2)) else ((2x * (1 + (2 * i))) div (2 + i))),x,0))
A001647: 1 0 1 1 2 4 10 31
(((1 + (x div (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))) div 2) + (if x <= 0 then 0 else 1))
A267116-A136565: 0 1 1 2 1 1 1 3 2 1 1 3 1 1 1 4
((if ((x * (x mod 3)) mod 5) <= 0 then 0 else 2) - ((if x <= 0 then 0 else 1) + (x mod 2)))
A102565: 0 0 1 ~2 1 ~2 ~1 0 1 ~2 ~1 0 ~1 0 1 ~2
(if (x mod 2) <= 0 then (1 + (if (x mod 5) <= 0 then 0 else (1 + (x div 5)))) else 1)
A137163: 1 1 2 1 2 1 3 1 3 1 1 1 4 1 4 1
(~1 + (if (x mod 4) <= 0 then (loop(\(x,i).2x,x,2) mod 17) else 1))
A002337: 1 0 0 0 14 0 0 0 1
(1 + (x mod (1 + ((~1 + loop(\(x,i).2x,x,loop(\(x,i).(2 + (x * i)),x,2))) mod (x + 1)))))
A072436: 1 2 1 4 5 2 1 8 1 10 1 4 13 2 5 16
loop(\(x,i).(x2 div 3),1,(~1 + loop(\(x,i).10x,(x + 1),1)))
A178631: 27 3267 332667 33326667 3333266667 333332666667 33333326666667 3333333266666667 333333332666666667 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * (2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),i))),(x + 1),1))
A071555: 6 36 386 5006 85086 1616616 37182146 1078282206 33426748356 1236789689136 50708377254536 2180460221945006 102481630431415236 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),i))),(x + 1),1))
A071556: 8 78 1002 17018 323324 7436430 215656442 6685349672 247357937828 10141675450908 436092044389002 20496326086283048 1086305282573001492 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if x <= 0 then 0 else (if ((x mod 5) mod (3 + ((x div 2) mod 2))) <= 0 then 2 else 1)))
A234092: 1 2 2 2 2 3 2 2 3 2 3 2 2 3 3 3
(if (x mod 5) <= 0 then (14 * (2 + (if x <= 0 then 0 else 2))) else 1)
A040789: 28 1 1 1 1 56 1 1 1 1 56 1 1 1 1 56
(loop(\(x,i).(5x + 2),x,2) mod (1 + (if (~x + 2) <= 0 then 6 else 1)))
A021160: 0 0 6 4 1 0 2 5 6 4 1 0 2 5 6 4
(1 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).10x,(2x + 2),1)))
A187868: 9901 99990001 999999000001 9999999900000001
A145381: 9901 99990001 999999000001 9999999900000001 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).2x,(0 - (x div (2 * loop(\(x,i).(x div (~2 + (x mod 2))),x,(x + 1))))),1))
A260218: 2 3 2 5 2 3 2 17 2 3 2 5 2 3 2 257
(1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (3 + (((x + 1) div 2) div 2))))
A209297: 1 1 4 1 5 9 1 6 11 16 1 7 13 19 25 1
(if x <= 0 then 2 else (1 + loop(\(x,i).(x + (x div 9)),x,9)))
A108199: 2 11 12 13 14 15 16 17 18 19 21 23 25 27 29 32
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(10x + 6))
A017350: 60466176 1099511627776 141167095653376 3656158440062976 42420747482776576 303305489096114176 1568336880910795776 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(10x + 6))
A017352: 2176782336 281474976710656 95428956661682176 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).(if (x mod (3 + (i mod 2))) <= 0 then 1 else x),x,(x + 1)) div 5))
A075119: 1 1 1 1 2 1 2 1 1 3 3 1 3 3 1 1
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(10x + 9))
A017386: 3486784401 6131066257801 420707233300201 8140406085191601 79792266297612001 511116753300641401 2446194060654759801 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(10x + 9))
A017388: 282429536481 2213314919066161 353814783205469041 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 7) <= 0 then (10 * (2 + (if x <= 0 then 0 else 2))) else 1)
A040404: 20 1 1 1 1 1 1 40 1 1 1 1 1 1 40 1
(if x <= 0 then 1 else (1 + (5 * loop(\(x,i).(10x + ~16),x,2))))
A179956: 1 21 121 1121 11121 111121 1111121 11111121 111111121 1111111121 11111111121 111111111121 1111111111121 11111111111121 111111111111121 1111111111111121
(1 + ((x - (if x <= 0 then 2 else (if (6 mod (1 + (x div 2))) <= 0 then 1 else 0))) mod 3))
A091412: 2 1 2 3 1 2 1 2 3 1 1 2 1 2 3 1
(1 + (loop(\(x,i).2x,x,(2 - loop(\(x,i).(5x + ~2),x,0))) div 3))
A256493: 1 3 19 171 1675 16683 166699 1666731 16666795 166666923 1666667179 16666667691 166666668715 1666666670763 16666666674859 166666666683051
(x mod (1 + (x div (3 * (if (x mod 2) <= 0 then 2 else (1 + (if (x mod 3) <= 0 then 2 else 0)))))))
A229964: 0 0 0 0 0 1 0 1 0 1 0 3 0 3 2 1
(if x <= 0 then 0 else (1 + ((1 + loop(\(x,i).(x div (2 - (x mod 2))),x,((x + 1) div 2))) div 3)))
A295515: 0 1 1 1 1 2 2 1 1 3 3 2 2 3 3 1
(1 + (3 * loop(\(x,i).(x2 + x),1,loop(\(x,i).10x,x,1))))
A177019: 7 331 30301 3003001 300030001 30000300001 3000003000001 300000030000001 30000000300000001 3000000003000000001 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).(x2 + x),1,loop(\(x,i).10x,x,1)) div 3))
A074992: 1 37 3367 333667 33336667 3333366667 333333666667 33333336666667 3333333366666667 333333333666666667 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x * i),x,1) mod (x + 1)) div 3) - (x mod 2))))
A305437: 1 2 3 2 4 2 5 2 3 2 6 2 7 2 3 2
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(12x + 11))
A017662: 25937424601 41426511213649 2758547353515625 52599132235830049 511116753300641401 3255243551009881201 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(12x + 11))
A017664: 3138428376721 21914624432020321 3379220508056640625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (3 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),(x + 1))))
A089118: 2 8 11 26 29 35 38 80 83 89 92 107 110 116 119 242
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(12x + 7))
A017614: 282475249 6131066257801 819628286980801 21611482313284249 253295162119140625 1822837804551761449 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(12x + 7))
A017616: 13841287201 2213314919066161 787662783788549761 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(12x + 5))
A017590: 9765625 2015993900449 420707233300201 13422659310152401 174887470365513049 1346274334462890625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(12x + 5))
A017592: 244140625 582622237229761 353814783205469041 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + ((loop(\(x,i).(3x + ~3),x,2) * (2 + loop(\(x,i).2x,x,1))) div 3))
A246985: 1 3 11 49 251 1393 8051 47449 282251 1686433 10097891 60526249 362976251 2177317873 13062296531 78368963449
(1 + ((2 * (loop(\(x,i).2x,x,(if (x mod 4) <= 0 then 0 else 1)) mod (x + 1))) div 3))
A330742: 1 1 1 1 1 2 1 1 1 2 1 6 1 2 3 1
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(6x + 5))
A016979: 48828125 285311670611 34271896307633 952809757913927 12200509765705829 96549157373046875 550329031716248441 2472159215084012303 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 2) <= 0 then (3 * ((1 + (2 * ((~x + 2) mod 4))) * (if x <= 0 then 1 else 2))) else 1)
A040236: 15 1 6 1 30 1 6 1 30 1 6 1 30 1 6 1
(loop(\(x,i).3x,x,1) mod (1 + (3 * loop(\(x,i).(x2 + x + 2),2,2))))
A036160: 1 3 9 27 81 20 60 180 94 59 177 85 32 96 65 195
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(12x + 1))
A017543: 1 1792160394037 2384185791015625 177917621779460413 3909821048582988049 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(~11x + ~1))
A017410: 1 61917364224 41426511213649 2064377754059776 34050628916015625 303305489096114176 1822837804551761449 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(~11x + ~1))
A017412: 1 8916100448256 21914624432020321 2386420683693101056 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (3 * loop(\(x,i).(x2 + x),1,loop(\(x,i).12x,x,2))))
A220990: 19 1801 249697 35842177 5159904769 743009863681 106993223294977 15407021789577217 2218611109320327169 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (3 * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).12x,x,2))))
A220989: 7 1657 247969 35821441 5159655937 743006877697 106993187463169 15407021359595521 2218611104160546817 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(9x + 7))
A017254: 282475249 1099511627776 95367431640625 2064377754059776 21611482313284249 144555105949057024 713342911662882601 2824752490000000000 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(9x + 7))
A017256: 13841287201 281474976710656 59604644775390625 2386420683693101056 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(9x + 5))
A017230: 9765625 289254654976 41426511213649 1125899906842624 13422659310152401 97656250000000000 511116753300641401 2113922820157210624 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(9x + 5))
A017232: 244140625 56693912375296 21914624432020321 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(~1 + (3 * loop(\(x,i).(10x + ~8),x,2))))
A181719: 25 1225 112225 11122225 1111222225 111112222225 11111122222225 1111111222222225 111111112222222225 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),(6x + 1))
A031387: 5 23 47 73 103 137 167 197 233 269 307 347 379 419 449 487
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(9x + 1))
A017183: 1 100000000000 116490258898219 8293509467471872 177917621779460413 1951354384207722496 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (3 * (x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1)))))
A059139: 4 7 4 10 4 7 4 13 4 7 4 10 4 7 4 16
(~1 + (3 * compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),x,(~4x + 1)),x)))
A190105: 2 5 8 14 17 23 32 35 44 50 53 59 62 77 80 95
(~1 + (loop(\(x,i).(x + (if (x + ~2) <= 0 then 3 else x)),(x div 3),1) + (x mod 3)))
A067570: 0 1 2 3 4 5 7
A107684: 0 1 2 3 4 5 7 8 9 15 16 17 31 32 33 63
(1 + loop(\(x,i).(x * (2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),i))),x,3))
A071554: 4 16 106 1156 15016 255256 4849846 111546436 3234846616 100280245066 3710369067406 152125131763606 6541380665835016 307444891294245706 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(~1 + ((x + loop(\(x,i).((4x + 1) div (1 + i)),x,1)) div 2)),1)
A302254: 1 1 2 4 4 4 4 4 8 8 16 16 32 32 64 64
(~1 + loop(\(x,i).4x,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1))
A152099: 15 63 1023 16383 4194303 67108863 17179869183 274877906943 70368744177663 288230376151711743 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (x div (1 + loop(\(x,i).((x + 2) div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,2x))))
A056648: 1 1 1 1 1 2 1 1 2 4 1 2 2 1 2 2
(1 + (loop(\(x,i).7x,x,1) + loop(\(x,i).3x,2x,1)))
A074524: 3 17 131 1073 8963 75857 649091 5606513 48811523 427774097 3769259651 33358386353 296270823683 2638754838737 23555015527811 210638693604593
(~1 + (loop(\(x,i).10x,x,1) + loop(\(x,i).6x,x,1)))
A155648: 1 15 135 1215 11295 107775 1046655 10279935 101679615 1010077695 10060466175 100362797055 1002176782335 10013060694015 100078364164095 1000470184984575
(1 + loop(\(x,i).10x,x,1) - loop(\(x,i).6x,x,1))
A155653: 1 5 65 785 8705 92225 953345 9720065 98320385 989922305 9939533825 99637202945 997823217665 9986939305985 99921635835905 999529815015425
(1 + (loop(\(x,i).7x,x,1) + loop(\(x,i).6x,x,1)))
A074520: 3 14 86 560 3698 24584 164306 1103480 7444418 50431304 342941426 2340123800 16018069538 109949704424 756587236946 5217746494520
(1 + loop(\(x,i).7x,x,1) - loop(\(x,i).6x,x,1))
A155650: 1 2 14 128 1106 9032 70994 543608 4085186 30275912 222009074 1614529688 11664504866 83828316392 599858908754 4277376525368
loop(\(x,i).(2x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i))),(3x + 1),1)
A187443: 1 6 35 252 1716 12870 92378 705432 5200300 40116600 300540195 2333606220 17672631900 137846528820 1052049481860 8233430727600
(1 + (if (x + ~1) <= 0 then x else (1 + compr(\x.(loop(\(x,i).(x * (x - i)),2,(x div 2)) mod (x + 1)),x))))
A026479: 1 2 4 5 6 7 9 11 13 15 16 17 19 21 23 25
(~1 + (loop(\(x,i).10x,x,1) + loop(\(x,i).8x,x,1)))
A155664: 1 17 163 1511 14095 132767 1262143 12097151 116777215 1134217727 11073741823 108589934591 1068719476735 10549755813887 104398046511103 1035184372088831
(1 + loop(\(x,i).10x,x,1) - loop(\(x,i).8x,x,1))
A155667: 1 3 37 489 5905 67233 737857 7902849 83222785 865782273 8926258177 91410065409 931280523265 9450244186113 95601953488897 964815627911169
(1 + (loop(\(x,i).7x,x,1) + loop(\(x,i).8x,x,1)))
A074523: 3 16 114 856 6498 49576 379794 2920696 22542018 174571336 1356217074 10567261336 82560763938 646644824296 5076269583954 39931933598776
(1 + loop(\(x,i).11x,x,1) - loop(\(x,i).4x,x,1))
A155632: 1 8 106 1268 14386 160028 1767466 19470788 214293346 2357685548 25936376026 285307476308 3138411599506 34522645035068 379749565147786 4177247095673828
(1 + loop(\(x,i).(x2 + 5x),1,loop(\(x,i).10x,x,1)))
A171410: 7 151 10501 1005001 100050001 10000500001 1000005000001 100000050000001 10000000500000001 1000000005000000001 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x2 + 6x),1,loop(\(x,i).10x,x,1)))
A171461: 8 161 10601 1006001 100060001 10000600001 1000006000001 100000060000001 10000000600000001 1000000006000000001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x2 + 8x),1,loop(\(x,i).10x,x,1)))
A171513: 10 181 10801 1008001 100080001 10000800001 1000008000001 100000080000001 10000000800000001 1000000008000000001 4611686018427387903 4611686018427387903
loop(\(x,i).x5,1,(~1 + loop(\(x,i).10x,x,1)))
A272068: 0 59049 9509900499 995009990004999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + 1),(1 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)),1)
A210454: 341 5461 1398101 22369621 5726623061 91625968981 23456248059221 96076792050570581 1537228672809129301 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + 1),(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1)
A301797: 5 21 341 5461 1398101 22369621 5726623061 91625968981 23456248059221 96076792050570581 1537228672809129301 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).6x,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1)
A061234: 6 36 1296 46656 60466176 2176782336 2821109907456 101559956668416 131621703842267136 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((1 + loop(\(x,i).13x,x,1)) * (1 + loop(\(x,i).2x,x,1)))
A241030: 4 42 850 19782 485554 12252702 313742650 8094558822 209642795554 5440108178862 141304954146250 3672136647383862 95452254746808754 2481455748310337022 4611686018427387903 4611686018427387903
((1 + loop(\(x,i).11x,x,1)) * (1 + loop(\(x,i).2x,x,1)))
A241029: 4 36 610 11988 248914 5314716 115151530 2513845188 55090232674 1209627165996 26585860217050 584603613083988 12858141059430034 282844580595234876 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (1 + compr(\x.(~1 + (x mod (~1 + (loop(\(x,i).2x,x,x) mod (x + 1))))),(x + 1))))
A341416-A081376: 1 3 4 5 7 8 9 11 13 16 17 19 23 25 27 29
(1 + (compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x) + ((x + 1) * (if x <= 0 then 0 else 2))))
A171575: 1 6 9 13 17 23 27 33 37 43 51 55 63 69 73 79
loop(\(x,i).((x2 + 2x) div 2),1,(1 + loop(\(x,i).12x,2,(x + 1))))
A157326: 10657 42049 94177 167041 260641 374977 510049 665857 842401 1039681 1257697 1496449 1755937 2036161 2337121 2658817
(1 + ((2x + 2) * (1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x))))
A070846: 3 5 7 17 11 13 29 17 19 41 23 73 53 29 31 97
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(8x + 7))
A017159: 1977326743 8649755859375 952809757913927 25408476896404831 317475837322472439 2472159215084012303 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x2 + 3x + 3) + loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,1))
A223764: 4 12 28 56 101 169 267 403 586 826 1134 1522 2003 2591 3301 4149
(1 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1)))
A217259-A014574: 4 6 12 18 30 42 60 72 102 108 138 150 180 192 198 228
(~1 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1)))
A144834: 2 4 10 16 28 40 58 70 100 106 136 148 178 190 196 226
loop(\(x,i).3x,2x,(1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A156218: 1 18 81 2916 6561 118098 531441 38263752 43046721 774840978 3486784401 125524238436 282429536481 5083731656658 22876792454961 3294258113514384
loop(\(x,i).5x,x,(1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A156183: 1 10 25 500 625 6250 15625 625000 390625 3906250 9765625 195312500 244140625 2441406250 6103515625 488281250000
(if x <= 0 then 0 else loop(\(x,i).((8x * (~1 + (2 * i))) div (1 + i)),(x + ~1),1))
A052704: 0 1 4 32 320 3584 43008 540672 7028736 93716480 1274544128 17611882496 246566354944 3489862254592 49855175065600 717914520944640
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) - loop(\(x,i).2x,(x + ~1),1))
A125107: 0 0 0 1 6 26 100 365 1302 4606 16284 57762 205964 738804 2666248 9678461
(1 + (x div ((x + 2) div (1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x)))))
A078680-A067760: 1 1 1 2 1 1 2 1 1 2 1 3 2 1 1 4
(1 + (loop(\(x,i).7x,x,1) + loop(\(x,i).5x,x,1)))
A074517: 3 13 75 469 3027 19933 133275 901669 6155427 42306733 292240875 2026154869 14085427827 98109713533 684326588475 4778079088069
((1 + loop(\(x,i).7x,x,1)) * (1 + loop(\(x,i).3x,x,1)))
A034663: 4 32 500 9632 196964 4101152 85884500 1801914272 37828630724 794320419872 16680163512500 350279478046112 7355841353205284 154472474629724192 3243920610749364500 4611686018427387903
loop(\(x,i).x2,1,loop(\(x,i).(3x4 + 3x3),(x2 + 1),1))
A135240: 36 20575296
(1 + loop(\(x,i).(x + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(x div 2),x)),x,1))
A193064: 2 3 5 13
A115347: 2 3 5 13 1597
(1 + loop(\(x,i).(x + loop(\(x,i).((x + 2) - ((~x + 1) div (2 + (x div 4)))),1,i)),x,1))
A131938: 2 5 10 16 23 32 42 53 65 78 93 109 126 144 163 183
(~3 + loop(\(x,i).(2x + 4),compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),0))
A098815: ~3 1 25 121 2041 8185 131065 524281 8388601 536870905 2147483641 137438953465 2199023255545 8796093022201 140737488355321 9007199254740985
(if x <= 0 then 0 else (1 + (((x + 1) - (x mod (1 + (if (x mod 5) <= 0 then 0 else 2)))) div 2)))
A318241: 0 1 1 3 3 4 4 4 4 6 6 6 7 7 7 9
(1 + (2 * (loop(\(x,i).2x,x,1) - loop(\(x,i).2x,(x - (x div (1 + (x mod 2)))),1))))
A085903: 1 1 7 9 31 49 127 225 511 961 2047 3969 8191 16129 32767 65025
(~1 + (2 * loop(\(x,i).x2,1,(1 + ((x + 1) * loop(\(x,i).(x2 + 4x + 4),2,1))))))
A157614: 29767 118097 264991 470449 734471 1057057 1438207 1877921 2376199 2933041 3548447 4222417 4954951 5746049 6595711 7503937
(~1 + ((1 + compr(\x.loop(\(x,i).(x div (if (x mod 2) <= 0 then 4 else 1)),x,2x),(x + 1))) div 2))
A270804: 0 1 2 7 8 9 10 31 32 33 34 39 40 41 42 127
(1 + ((1 + ((1 + ((loop(\(x,i).2x,x,2) - (if x <= 0 then 0 else 1)) mod (x + 2))) div 2)) div 2))
A127669: 1 1 2 1 2 1 3 2 2 1 3 1 2 2 5 1
loop(\(x,i).2x,((1 + (loop(\(x,i).(2x - ((x div 2) div 3)),x,1) div 2)) div 2),1)
A063401: 1 2 2 4 16 128 8192 16777216 17592186044416 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).i,((1 + (loop(\(x,i).((x + 1) + ((x + (x div 2)) div 4)),x,1) div 2)) div 2),1)
A087221: 1 1 1 1 2 3 4 5 7 10 14 19 26 36 50 69
(1 + ((1 + (((loop(\(x,i).2x,x,2) + (if (x + ~2) <= 0 then 0 else 1)) mod (x + 1)) div 2)) div 2))
A336648: 1 1 2 1 2 2 2 1 1 2 2 2 2 2 3 1
(1 + (2 * (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (1 + (((x + 1) div 2) div 2)))))
A129801: 1 1 3 1 5 9 1 7 13 19 1 9 17 25 33 1
(1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) mod (2 + (x mod 9))))
A285730: 1 1 2 1 2 3 1 2 3 2 1 2 3 4 5 1
(~1 + (loop(\(x,i).(2x2 + x),1,(~1 + loop(\(x,i).4x,x,4))) div 2))
A152101: 9 231 3999 65151 1047039 16771071 268410879 4294868991 68719083519 1099510054911 17592179752959 281474951544831 4503599526707199 72057593635274751 1152921502996234239 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(8x + 3))
A017111: 177147 285311670611 116490258898219 5559060566555523 96549157373046875 929293739471222707 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (5x + 1)),x,7)
A028389: 7 36 18 9 46 23 116 58 29 146 73 366 183 916 458 229
(7 + compr(\x.loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,2x),x))
A153049: 7 11 14 17 19 20 23 24 26 29 31 32 34 35 38 39
(7 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))
A097338: 7 8 9 11 12 14 15 17 20 21 24 26 27 29 32 35
((2x + 2) div (3 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))
A116512: 0 1 1 2 1 3 1 4 3 5 1 6 1 7 6 8
(1 + (2 * (1 + loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),2))))
A241573: 7 11 35 131 2051 8195 131075 524291 8388611 536870915 2147483651 137438953475 2199023255555 8796093022211 140737488355331 9007199254740995
((if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1) div (1 + ((1 + (x div 2)) div 2)))
A029833: 0 1 1 0 2 0 2 0 0 0 2 0 3 0 0 0
(1 + (2 * ((if ((x + (if (x mod 2) <= 0 then 2 else x)) mod 3) <= 0 then 1 else x) mod (1 + (x div 2)))))
A172170: 1 1 1 3 3 5 5 7 7 3 3 11 11 13 13 3
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(10x + 3))
A017314: 59049 137858491849 41426511213649 1531578985264449 21611482313284249 174887470365513049 984930291881790849 4297625829703557649 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(10x + 3))
A017316: 531441 23298085122481 21914624432020321 1667889514952984961 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + ((1 + loop(\(x,i).(if x <= 0 then 1 else (2 * (~1 + ((x + 2) mod 5)))),2,x)) div 2))
A117452: 1 ~1 1 0 0 2 ~1 1 0 0 2 ~1 1 0 0 2
(1 + (2 * (1 + compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),x,(~4x + 1)),x))))
A089193: 5 7 9 13 15 19 25 27 33 37 39 43 45 55 57 67
(1 + (loop(\(x,i).(x * (2 + i)),compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x),1) div 2))
A139162: 31 1261 9979201 1556755201 88921857024001 30411275102208001 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (loop(\(x,i).(x * (2 + i)),compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x),1) div 2))
A139192: 29 1259 9979199 1556755199 88921857023999 30411275102207999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).4x,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),2))
A139287: 7 31 511 8191 2097151 33554431 8589934591 137438953471 35184372088831 144115188075855871 2305843009213693951 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + ((loop(\(x,i).((x * (1 + (i mod 2))) + (x mod 2)),x,1) + loop(\(x,i).2x,x,1)) div 2))
A222010: 0 1 3 7
A116362: 0 1 3 7 11 23 39 79 143 287 543 1087 2111 4223 8319 16639
((x + 1) div (1 + ((loop(\(x,i).2x,x,(if (x mod 4) <= 0 then 0 else 1)) mod (x + 1)) div 2)))
A330741: 1 2 3 4 5 3 7 8 9 5 11 2 13 7 5 16
(2 div (if x <= 0 then 2 else (~1 + (2 * (x - (loop(\(x,i).3x,x,3) mod (x + 1)))))))
A227395-A002448: 1 ~2 0 0 2 0 0 0 0 ~2 0 0 0 0 0 0
(~1 + (2 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,4x),(x + 1))))
A107757: 3 9 11 27 29 35 39 81 83 89 93 107 111 117 119 243
((2x + 3) * loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,(x + 1)))
A002738: 3 60 630 5040 34650 216216 1261260 7001280 37413090 193993800 981608628 4867480800 23728968900 114011377200 540972351000 2538963567360
(loop(\(x,i).3x,x,1) div loop(\(x,i).10x,((x + ~1) div 2),1))
A060956: 1 3 9 2 8 2 7 2 6 1 5 1 5 1 4 1
(if (x mod 4) <= 0 then (29 * (if x <= 0 then 1 else 2)) else 1)
A040850: 29 1 1 1 58 1 1 1 58 1 1 1 58 1 1 1
(if (x mod 2) <= 0 then ((~1 + (5 * ((x + ~1) mod 4))) * (if x <= 0 then 1 else 2)) else 1)
A040207: 14 1 8 1 28 1 8 1 28 1 8 1 28 1 8 1
(if (x mod 2) <= 0 then ((1 + (5 * ((~x + 2) mod 4))) * (if x <= 0 then 1 else 2)) else 1)
A010197: 11 1 2 1 22 1 2 1 22 1 2 1 22 1 2 1
(if (x mod 2) <= 0 then ((~1 + (5 * (2 - ((x div 2) mod 2)))) * (if x <= 0 then 1 else 2)) else 1)
A010169: 9 1 8 1 18 1 8 1 18 1 8 1 18 1 8 1
(if (x mod 5) <= 0 then (23 * (if x <= 0 then 1 else 2)) else 1)
A040533: 23 1 1 1 1 46 1 1 1 1 46 1 1 1 1 46
(if (x mod 2) <= 0 then ((1 + (6 * ((~x + 2) mod 4))) * (if x <= 0 then 1 else 2)) else 1)
A010231: 13 1 2 1 26 1 2 1 26 1 2 1 26 1 2 1
(if (x mod 2) <= 0 then ((~1 + (4 * (2 + ((~x + 2) mod 4)))) * (if x <= 0 then 1 else 2)) else 1)
A040238: 15 1 14 1 30 1 14 1 30 1 14 1 30 1 14 1
(if (x mod 2) <= 0 then ((~1 + (8 * ((x + ~1) mod 4))) * (if x <= 0 then 1 else 2)) else 1)
A040549: 23 1 14 1 46 1 14 1 46 1 14 1 46 1 14 1
(1 + (loop(\(x,i).(x * (~1 + (loop(\(x,i).(x2 + ~x),2,2x) * (1 + i)))),x,1) div 2))
A285086: 1 2 3914
((if x <= 0 then 1 else 6x) - (x div (3 + (if (x + ~4) <= 0 then 0 else 2))))
A315710: 1 6 12 17 23 29 35 41 47 53 58 64 70 76 82 87
((if x <= 0 then 1 else 5x) - (x div (3 + (if (x + ~4) <= 0 then 0 else 2))))
A313569: 1 5 10 14 19 24 29 34 39 44 48 53 58 63 68 72
(2x mod (1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) + ((x div ~2) mod 2))))
A258651: 0 0 1 0 0 2 0 0 1 3 0 0 0 1 4 0
(1 + (2 * ((1 + loop(\(x,i).loop(\(x,i).(x2 + x),(x + ~1),(2x + 1)),x,1)) div 2)))
A138154: 3 5 3193
(~1 + (2 * ((1 + (loop(\(x,i).(2x + 1),x,(if (x + ~3) <= 0 then 2 else 1)) div 2)) div 2)))
A290199: 1 1 5 11 15 31 63 127 255 511 1023 2047 4095 8191 16383 32767
(1 + ((loop(\(x,i).(2x + 4),x,(1 + (loop(\(x,i).(2x + 4),x,1) div 2))) div 2) div 2))
A087440: 1 4 13 46 172 664 2608 10336 41152 164224 656128 2622976 10488832 41949184 167784448 671113216
(~1 + ((loop(\(x,i).loop(\(x,i).x2,1,(~x + 5)),(2x + 2),1) div 2) div 2))
A219015: 29 45232349 4611686018427387903
(4x div (if (x mod 2) <= 0 then (4 * (if (x mod 4) <= 0 then 4 else 1)) else 1))
A188134: 0 4 2 12 1 20 6 28 2 36 10 44 3 52 14 60
(1 + (((3 * loop(\(x,i).(if (x mod 4) <= 0 then (x div 2) else x),x,(x + 1))) div 2) div 2))
A336474-A336149-A336148-A336146: 1 2 3 2 4 5 6 2 7 8 9 5 10 11 12 2
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(8x + 5))
A017135: 48828125 1792160394037 350277500542221 12200509765705829 177917621779460413 1532278301220703125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(~7x + ~5))
A017050: 9765625 61917364224 6131066257801 141167095653376 1531578985264449 10485760000000000 52599132235830049 210832519264920576 713342911662882601 2113922820157210624 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(~7x + ~5))
A017052: 244140625 8916100448256 2213314919066161 95428956661682176 1667889514952984961 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (loop(\(x,i).x2,1,(~2 + loop(\(x,i).12x,2,(x + 1)))) div 2))
A157288: 10081 40897 92449 164737 257761 371521 506017 661249 837217 1033921 1251361 1489537 1748449 2028097 2328481 2649601
(if (x mod 2) <= 0 then (2 * ((1 + (3 * (2 - (x mod 4)))) * (if x <= 0 then 1 else 2))) else 1)
A040205: 14 1 4 1 28 1 4 1 28 1 4 1 28 1 4 1
(loop(\(x,i).loop(\(x,i).(x * (x - i)),2,(~1 + i)),x,1) div 31)
A011941: 0 0 0 0 0 3 11 27 54 97 162 255 383 553 774 1056
(31 + loop(\(x,i).x2,2,loop(\(x,i).x3,x,2)))
A104069: 47 4127 68719476767 4611686018427387903
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (3x + 1)),x,15)
A033480: 15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4
(if x <= 0 then (x mod 2) else (~1 + (2 * ((x2 mod (2 + (if (x mod 2) <= 0 then 1 else (x + 2)))) mod 2))))
A165476: 0 1 1 ~1 1 1 ~1 1 1 1 1 1 ~1 ~1 1 ~1
(9 + (if x <= 0 then 1 else (2 + (if (~4 + (x div 2)) <= 0 then x else (x + 2)))))
A261907-A102850-A102357: 10 12 13 14 15 16 17 18 19 20 23 24 25 26 27 28
(9 + compr(\x.loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,2x),x))
A153051: 9 13 16 19 21 22 25 26 28 31 33 34 36 37 40 41
(9 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))
A097480: 9 10 11 13 14 16 17 19 22 23 26 28 29 31 34 37
(if x <= 0 then 0 else (if (2x mod (4 + (x div 4))) <= 0 then (2 + (x div 4)) else 1))
A216764: 0 1 2 1 1 3 1 1 1 4 1 1 1 1 5 1
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(12x + 9))
A017638: 3486784401 16679880978201 1531578985264449 34050628916015625 362033331456891249 2446194060654759801 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(12x + 9))
A017640: 282429536481 7355827511386641 1667889514952984961 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * (2 + loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),2))))
A241677: 9 13 37 133 2053 8197 131077 524293 8388613 536870917 2147483653 137438953477 2199023255557 8796093022213 140737488355333 9007199254740997
(1 + (4 * (loop(\(x,i).(2x + 2),(x div 2),(x mod 2)) + loop(\(x,i).2x,x,2))))
A184040: 9 21 41 81 153 297 569 1113 2169 4281 8441 16761 33273 66297
((8x + 1) * loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1))
A285043: 1 18 102 500 2310 10332 45276 195624 836550 3549260 14965236 62783448 262303132 1092063000 4533175800 18769219920
(1 + ((loop(\(x,i).2x,3,(~1 + (if x <= 0 then 2 else (x mod 2)))) mod (x + 1)) mod 4))
A206923: 1 1 2 1 3 1 3 1 2 1 4 1 2 1 4 1
(2 - (loop(\(x,i).(2x + ~2),x,(if (x mod (2 + (x mod 2))) <= 0 then 1 else 0)) mod 5))
A242073: 1 ~1 ~1 ~2 1 ~1 ~1 1 1 2 ~1 1 1 ~1 ~1 ~2
(6 + (2 * loop(\(x,i).(x + loop(\(x,i).x2,1,(2 + (i div 2)))),x,1)))
A271994: 8 16 34 52 84 116 166 216 288 360 458 556 684 812 974 1136
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(10x + 5))
A017339: 48828125 8649755859375 2384185791015625 96549157373046875 1532278301220703125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x + ~1),5))
A029609: 1 5 15 50 175 630 2310 8580 32175 121550 461890 1763580 6760390 26001500 100291500 387793800
(5 * (if ((if x <= 0 then 1 else x) mod 12) <= 0 then 1 else 6))
A056997: 30 30 30 30 30 30 30 30 30 30 30 30 5 30 30 30
(if (x mod 3) <= 0 then (if (x mod 2) <= 0 then 1 else ((x2 + 3x + 2) div 2)) else 5)
A331064: 1 5 5 10 5 5 1
(loop(\(x,i).(x2 + x),1,loop(\(x,i).(4x + 4),x,4)) div 5)
A203244: 4 84 1428 23188 372372 5963412 95436436 1527070356 24433475220 390937001620 6254997618324 100079984262804 1601279837683348 25620477760847508 409927645605215892 4611686018427387903
((loop(\(x,i).4x,x,3) + loop(\(x,i).3x,x,2)) div 5)
A318165: 1 3 13
A178934: 1 3 13 49 186 711 2749 10705 41946 165159 652765 2587441 10278906 40903047 162974461 649984657
((loop(\(x,i).4x,x,3) - loop(\(x,i).3x,x,2)) div 5)
A178935: 0 1 6 27 121 517 2166 8955 36697 149413 605526 2445723 9853753 39627589 159148086 638505531
(1 + (4 * compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),x,(~4x + 1)),x)))
A089217: 5 9 13 21 25 33 45 49 61 69 73 81 85 105 109 129
(~1 + loop(\(x,i).4x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),4))
A139289: 3 15 255 4095 1048575 16777215 4294967295 68719476735 17592186044415 72057594037927935 1152921504606846975 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) mod (1 + ((x + 2) div (2 + (if (x mod 2) <= 0 then (if (x mod 3) <= 0 then 1 else x) else 2)))))
A182662: 0 0 1 0 1 0 1 2 1 1 1 0 3 2 1 1
(1 + (loop(\(x,i).x2,1,(2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) div 2))
A066885: 5 13 25 61 85 145 181 265 421 481 685 841 925 1105 1405 1741
(~1 + (loop(\(x,i).x2,1,(2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) div 2))
A243887: 3 11 23 59 83 143 179 263 419 479 683 839 923 1103 1403 1739
(~3 + loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A182200: 1 6 22 46 118 166 286 358 526 838 958 1366 1678 1846 2206 2806
(~1 + (2 * loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))))
A179262: 7 17 49 97 241 337 577 721 1057 1681 1921 2737 3361 3697 4417 5617
(1 + (loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2))
A110494: 3 5 13 25 61 85 145 181 265 421 481 685 841 925 1105 1405
(1 + loop(\(x,i).x2,1,(2 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))))
A060429: 17 37 101 197 485 677 1157 1445 2117 3365 3845 5477 6725 7397 8837 11237
(1 + (2 * (2 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,(x + 2)),x))))
A269345: 25 33 49 55 63 75 85 91 93 115 117 119 121 123 133 141
(loop(\(x,i).(2 * (4x + (x div (if i <= 0 then 1 else i)))),x,1) div (4x + 1))
A004981: 1 2 10 60 390 2652 18564 132600 961350 7049900 52169260 388898120 2916735900 21987701400 166478310600 1265235160560
((2x + 1) - ((x - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * (1 + i)))),x,2x)) div 2))
A074147: 1 2 4 3 5 7 6 8 10 12 9 11 13 15 17 14
(3 + (compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),x) + (x mod 2)))
A033163: 3 5 6 8 12 14 15 17 30 32 33 35 39 41 42 44
(1 + (if (x mod 4) <= 0 then (~1 + (2 * (2 + (if x <= 0 then 0 else 2)))) else 2) - (2 * (x mod 2)))
A010127: 4 1 3 1 8 1 3 1 8 1 3 1 8 1 3 1
(1 + (2 * (x div loop(\(x,i).(x + 1),loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,x),2))))
A104489: 1 1 3 1 5 5 3 1 9 9 11 1 5 5 3 1
(1 + (2 * (2 + compr(\x.(2 - loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x)),x))))
A025583: 27 35 51 57 65 77 87 93 95 117 119 121 123 125 135 143
(loop(\(x,i).((~x + 1) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,0) mod 3)
A339448: 0 2 1 1 0 2 2 0 1 1 1 0 1 1 0 2
(if x <= 0 then 1 else ((1 + (x mod (1 + (2 * (if (x mod 2) <= 0 then 1 else (x div 4)))))) div 3))
A227819-A186084-A177517-A047998: 1 0 1 0 0 1 0 0 1 1 0 0 0 2 1 0
(if x <= 0 then 1 else (3 * (1 + (2 mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1)))))
A122916: 1 3 3 3 3
A074816: 1 3 3 3 3 9 3 3 3 9 3 9 3 9 9 3
((1 + (2 * (loop(\(x,i).2x,x,2) - loop(\(x,i).2x,((x + 1) div 2),1)))) div 3)
A129362: 1 1 4 8 19 37 80 160 331 661 1344 2688 5419 10837 21760 43520
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(12x + 3))
A017567: 177147 8649755859375 5559060566555523 317475837322472439 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(~11x + ~3))
A017434: 59049 289254654976 95367431640625 3656158440062976 52599132235830049 430804206899405824 2446194060654759801 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(~11x + ~3))
A017436: 531441 56693912375296 59604644775390625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (3 * (2x - ((1 + (if (x mod 3) <= 0 then 0 else x)) div 3))))
A301720: 1 6 9 18 21 24 36 36 39 54 51 54 72 66 69 90
(4 + (if x <= 0 then 0 else loop(\(x,i).((x + 2) + ((x + (x div 2)) div 4)),x,2)))
A054736: 4 8 11 15 21 29 40 55 76
((loop(\(x,i).(8x + 1),x,1) * (1 + loop(\(x,i).2x,x,2))) div 3)
A238538: 1 15 219 3315 51491 811395 12882499 205321155 3278747331 52408827075 838132189379 13406842675395 214483303960771 3431523432591555 54902699475185859 878429788032676035
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),(6x + 3))
A031372: 11 31 59 83 109 149 179 211 241 277 313 353 389 431 461 499
((if x <= 0 then 1 else 6x) - ((1 + (if (x mod 3) <= 0 then 0 else x)) div 3))
A315563: 1 6 11 18 23 28 36 40 45 54 57 62 72 74 79 90
(x - ((~1 + (if (if (x mod (1 + (x mod 6))) <= 0 then 1 else 0) <= 0 then 1 else x)) div 3))
A269524: 1 1 2 3 4 5 5 7 8 9 7 11 9 13 14 15
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(9x + 3))
A017207: 177147 743008370688 350277500542221 17714700000000000 317475837322472439 3116402981210161152 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x2,1,(3 * loop(\(x,i).(10x + 1),x,1)))
A178630: 18 2178 221778 22217778 2222177778 222221777778 22222217777778 2222222177777778 222222221777777778 4611686018427387903 4611686018427387903 4611686018427387903
(3 * loop(\(x,i).2x2,1,loop(\(x,i).(7x + 1),x,1)))
A060871: 6 384 19494 960000 47073606 2306841984 113036904294 5538819840000 271402252867206 13298710955443584 651636840771389094 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).10x,x,2) + loop(\(x,i).4x,x,1)) div 3)
A082414: 1 8 72 688 6752 67008 668032 6672128 66688512 666754048 6667016192 66668064768 666672259072 6666689036288 66666756145152 666667024580608
(3 * loop(\(x,i).((x + 1) + i),compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),1))
A179545: 3 9 30 63 165 234 408 513 759 1218 1395 1998 2460 2709 3243 4134
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(~12x + ~10))
A017650: 10000000000 26559922791424 2064377754059776 42420747482776576 430804206899405824 2824752490000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).(1 + (x * loop(\(x,i).(2x2 + ~2),2,2))),2,x) mod (x + 1)) div 3)
A225927: 0 0 0 1 0 0 0 1 1 0 0 2 2 0 0 1
(3 * loop(\(x,i).x3,1,loop(\(x,i).(x + (((2 + i) * (1 + i)) div 2)),x,1)))
A202109: 3 192 3000 24000 128625 526848 1778112 5184000 13476375 31944000 70180968 144685632 282589125 526848000 943296000 1630015488
(((x + 1) div (if (x + ~2) <= 0 then 1 else (2 + (if (x mod 8) <= 0 then 2 else 0)))) div 3)
A241087: 0 0 1 0 0 1 1 1 0 1 1 2 2 2 2 2
((2 * (1 + (loop(\(x,i).2x,x,1) div loop(\(x,i).(1 + (i div (x + 2))),x,1)))) mod 3)
A074080: 1 0 1 1 0 1 0 1 1 1 0 1 2 2 1 0
(if x <= 0 then 1 else (6 * (1 + loop(\(x,i).x3,1,(2x2 + 2x)))))
A207575: 1 390 10374
((loop(\(x,i).loop(\(x,i).x2,2,x3),x,7) div 2) div 3)
A022240: 1 2306881200 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (6 * (x - ((1 + (if (x mod 3) <= 0 then 0 else x)) div 3))))
A301682: 1 6 6 18 18 18 36 30 30 54 42 42 72 54 54 90
((loop(\(x,i).(x2 + ~x),1,loop(\(x,i).(~3x + 3),x,3)) div 2) div 3)
A015251: 1 7 70 610 5551 49777 448540 4035220 36321901 326882347 2941985410 26477735830 238300021051 2144698993717 19302294530680 173720640014440
((2 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,(2x + 1))) div 3)
A253887: 1 1 2 3 1 4 5 2 6 7 3 8 9 1 10 11
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(12x + 6))
A017603: 362797056 64268410079232 17714700000000000 717368321110468608 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(~11x + ~6))
A017470: 60466176 2015993900449 296196766695424 8140406085191601 97656250000000000 713342911662882601 3743906242624487424 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(~11x + ~6))
A017472: 2176782336 582622237229761 232218265089212416 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(((loop(\(x,i).4x,x,1) - loop(\(x,i).~3x,x,1)) div 2) div 3)
A192356: 0 1 1 15 29 211 561 3095 9829 46971 164921 728575 2707629 11450531 43942081 181348455
((loop(\(x,i).2x,(x + ~2),loop(\(x,i).((x2 + ~x) div 2),2,(x + ~1))) div 2) div 3)
A213432: 0 0 0 0 2 20 120 560 2240 8064 26880 84480 253440 732160 2050048 5591040
(if (x mod 2) <= 0 then 2 else (6 * ((if (x mod 3) <= 0 then 1 else x) mod 6)))
A276152: 2 6 2 6 2 30 2 6 2 6 2 30 2 6 2 6
((loop(\(x,i).(x2 + x),1,(loop(\(x,i).~2x,x,3) div 2)) div 2) div 3)
A117110: 0 1 7 22 100 376 1552 6112 24640 98176 393472 1572352 6292480 25163776 100667392 402644992
(3 * (2 + (if x <= 0 then 1 else (2 * (1 + (if (x mod 3) <= 0 then 3x else 2))))))
A161431: 9 24 24 66 24
(6 * loop(\(x,i).2x,(x + ~2),loop(\(x,i).5x,(x + 1),2)))
A096363: 60 300 1500 15000 150000 1500000 15000000 150000000 1500000000 15000000000 150000000000 1500000000000 15000000000000 150000000000000 1500000000000000 15000000000000000
((((loop(\(x,i).(x * (x div 2)),1,loop(\(x,i).(2x + i),x,0)) div 2) div 2) div 2) mod 3)
A112761: 0 0 1 0 0 1 0 2 0 1 1 0 2 0 1 0
((2 * (if x <= 0 then 1 else (2 + (if (x mod 4) <= 0 then 1 else (((x + 1) div 2) div 2))))) div 3)
A209253: 0 1 1 2 2 2 2 2 2 2 2 3 2 3 3 4
(((loop(\(x,i).(x3 + x2),1,loop(\(x,i).(2x + 2),x,2)) div 2) div 2) div 3)
A177730: 1 21 245 2325 20181 168021 1370965 11075925 89042261 714081621 5719635285 45785027925 366392038741 2931583636821 23454458533205 187642826282325
((2 + (loop(\(x,i).(x * (3 - (i mod 2))),x,1) + loop(\(x,i).2x,x,2))) div 3)
A172411: 1 2 5 10
A018344: 1 2 5 10 23 46 115 230
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(11x + 2))
A017422: 1024 137858491849 63403380965376 2758547353515625 42420747482776576 362033331456891249 2113922820157210624 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(11x + 2))
A017424: 4096 23298085122481 36520347436056576 3379220508056640625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else ((loop(\(x,i).(2x + ~1),x,0) div 2) - (3 * (1 - (2 * (x mod 2))))))
A156067: 1 2 ~5 ~1 ~11 ~13 ~35 ~61 ~131 ~253 ~515 ~1021 ~2051 ~4093 ~8195 ~16381
((x + ~1) + (loop(\(x,i).(x2 + x),1,loop(\(x,i).(2x + 5),x,2)) div 3))
A265037: 1 30 185 886 3855 16064 65569 264930 1065059 4270948 17105253 68463974 273941863 1095939432 4384101737 17537095018
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(9x + 6))
A017243: 362797056 8649755859375 1521681143169024 50542106513726817 717368321110468608 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((2 + loop(\(x,i).2x,(x + ~1),(x + (loop(\(x,i).(x * i),x,2) div (x + 1))))) div 3)
A122674: 1 1 2 8 35 240
loop(\(x,i).2x2,1,(3 * loop(\(x,i).(10x + 2),x,2)))
A178635: 72 8712 887112 88871112 8888711112 888887111112 88888871111112 8888888711111112 888888887111111112 4611686018427387903 4611686018427387903 4611686018427387903
(6 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,4x),x))
A083096: 0 12 30 36 84 90 108 120 246 252 270 282 324 336 354 360
((loop(\(x,i).7x,x,1) + loop(\(x,i).~2x,x,2)) div 3)
A191566: 1 1 19 109 811 5581 39259 274429 1921771 13450861 94159099 659107549 4613765131 32296331341 226074368539 1582520481469
(loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x))) div 3)
A024700: 8 16 40 56 96 120 176 280 320 456 560 616 736 936 1160 1240
(loop(\(x,i).x2,1,(compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x) div 2)) div 3)
A030006: 0 1 5 8 16 21 33 56 65 96 120 133 161 208 261 280
(3 * loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A079705: 12 27 75 147 363 507 867 1083 1587 2523 2883 4107 5043 5547 6627 8427
(loop(\(x,i).x2,1,(compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) div 2)) div 3)
A242090: 0 0 0 1 5 8 16 21 33 56 65 96 120 133 161 208
(loop(\(x,i).((2x + ~1) * ((x2 + ~x) div 2)),1,loop(\(x,i).2x,x,2)) div 3)
A016290: 1 14 140 1240 10416 85344 690880 5559680 44608256 357389824 2861214720 22898104320 183218384896 1465881288704 11727587164160 93822844764160
((if x <= 0 then 1 else 4x) - ((1 - (if (~2 + (x div 2)) <= 0 then x else (x + 2))) div 3))
A312903: 1 4 9 13 17 22 27 31 35 40 44 48 53 57 61 66
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (15x + 1)),x,3)
A037105: 3 46 23 346 173 2596 1298 649 9736 4868 2434 1217 18256 9128 4564 2282
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(5x + 3))
A016895: 177147 8589934592 1792160394037 64268410079232 952809757913927 8293509467471872 50542106513726817 238572050223552512 929293739471222707 3116402981210161152 4611686018427387903
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (11x + 1)),x,3)
A037103: 3 34 17 188 94 47 518 259 2850 1425 15676 7838 3919 43110 21555 237106
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (13x + 1)),x,3)
A037104: 3 40 20 10 5 66 33 430 215 2796 1398 699 9088 4544 2272 1136
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (17x + 1)),x,3)
A037106: 3 52 26 13 222 111 1888 944 472 236 118 59 1004 502 251 4268
(2x div (loop(\(x,i).2x,loop(\(x,i).(x div (1 + (x mod 2))),x,x),2) + (x div 3)))
A065334: 0 1 0 2 0 1 0 3 0 0 0 2 0 0 0 4
(x + ((if (x + ~1) <= 0 then 1 else (2 * (if (~2 + (x div 3)) <= 0 then 0 else 2))) + (x div 3)))
A089676: 1 2 2 4 5 6 8 9 10 16 17
loop(\(x,i).((x + 10) + (if x <= 0 then 0 else 1)),(x div 3),(x mod 3))
A101222: 0 1 2 10 12 13 21 23 24 32 34 35 43 45 46 54
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(10x + 1))
A017291: 1 285311670611 350277500542221 25408476896404831 550329031716248441 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(4x + 1))),x)))
A119681: 3 7 9 15 19 21 27 31 37 45 49 51 55 57 69 75
(~1 + (2 * (x + (if (x + ~2) <= 0 then 1 else (3 * (if (~2 + (x div 3)) <= 0 then 1 else 2))))))
A069977: 1 3 5 11 13 15 17 19 21 29 31 33 35 37 39 41
(1 + (loop(\(x,i).x2,1,(x + (3 * loop(\(x,i).x3,x2,2)))) div 2))
A138943: 19 313 4611686018427387903
(1 + (2 * compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + x + 1))),x)))
A088503: 3 5 7 11 13 17 25 29 31 35 41 43 49 55 67 77
(1 + (2 * compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + x + ~1))),x)))
A088502: 5 7 9 11 13 17 19 21 23 27 31 33 39 41 43 49
((x + 1) - ((~x + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,(x + 1))) div 2))
A327625: 1 2 4 4 5 8 7 8 13 10 11 16 13 14 20 16
(~1 + (2 * loop(\(x,i).x2,1,(x + ((x + 1) * loop(\(x,i).(x * (x + i)),2,4))))))
A157739: 387199 1552321 3495367 6216337 9715231 13992049 19046791 24879457 31490047 38878561 47044999 55989361 65711647 76211857 87489991 99546049
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(10x + 7))
A017362: 282475249 2015993900449 205891132094649 4808584372417849 52599132235830049 362033331456891249 1822837804551761449 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(10x + 7))
A017364: 13841287201 582622237229761 150094635296999121 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (2 * loop(\(x,i).x2,1,(x + ((x + 1) * loop(\(x,i).(x * (x - i)),2,2x))))))
A243136: ~1 1 262087 22619537 457470751 4517251249 28860511751 137379191137 528572943487 1730726404001 4993116004999 13007560326001 31154649926687 69544807113937 146217791079751 291977237261249
(~1 + (2 * (~x + compr(\x.loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,2x),(x + 1)))))
A160522: 5 9 13 15 15 19 19 21 25 27 27 29 29 33 33 35
(1 + ((x + ((1 + loop(\(x,i).2x,x,1) - loop(\(x,i).2x,(x div 2),2)) div 2)) div 2))
A154223: 1 1 2 3 5 9 16 32 61 125 246 502 999 2023 4040 8136
(1 + ((x * ((loop(\(x,i).3x2,x,1) + loop(\(x,i).2x,x,1)) div 2)) div 2))
A060597: 1 2 16 1646
((1 + loop(\(x,i).8x,x,4)) * (~1 + loop(\(x,i).4x,x,2)))
A147540: 5 231 7967 260223 8372735 268306431 8588894207 274869551103 8796026044415 281474440364031 9007194961870847 288230341800361983 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 4 else 0))),x,4x),x)))
A111363: 1 3 7 11 13 27 31 33 37 51 53 57 61 63 127 131
(~1 + (2 * compr(\x.(1 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,4x)),x)))
A141544: 1 3 7 9 13 19 21 27 31 33 37 39 49 51 61 63
(1 + (2 * compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(3x + 2))),x)))
A034934: 1 3 7 11 15 19 27 31 35 39 47 55 59 67 71 75
(1 + (compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + 2x + ~2))),x) div 2))
A083022: 2 4 5 7 10 13 16 17 20 22 23 29 32 34 40 43
(~1 + loop(\(x,i).(2 + (x mod (2 + i))),compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),2))
A088147: 1 3 3 7 7 11 3 7 15 27 31 11 19 23 31 43
(~1 + loop(\(x,i).(x2 + x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A319597: 5 11 29 55 131 181 305 379 551 869 991 1405 1721 1891 2255 2861
(if (2 div (x2 + ~2)) <= 0 then (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) else 1)
A161847: 2 3 1 7 11 13 17 19 23 29 31 37 41 43 47 53
loop(\(x,i).5x,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1)
A057902: 25 125 3125 78125 48828125 1220703125 762939453125 19073486328125 11920928955078125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(11x + 1),x,0) * (~1 + loop(\(x,i).2x,x,2)))
A160880: 0 3 84 1995 45384
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(x + 2),(~1 + loop(\(x,i).2x,x,2)))
A258390: 2 15 98 630 4092 27027 181610 1239810 8582756 60138078 425800564 3042175500 21906338040 158830645635 1158564772890 8496271312650
(1 + loop(\(x,i).compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x),1,((x * (x mod 2)) div 2)))
A130008: 1 1 1 2 1 3 1 5 1 7 1 11 1 13 1 17
((3 * loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,2)) div (x + 3))
A007946: 2 9 36 140 540 2079 8008 30888 119340 461890 1790712 6953544 27041560 105306075 410605200 1602881040
loop(\(x,i).(8x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i))),2x,1)
A216704: 1 56 3360 206080 12776960 797282304 49963024384 3140532961280 197853576560640 12486759054049280 789163172215914496 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x + (8x div (if i <= 0 then 1 else i))),2x,1) div (2x + 1))
A000973: 1 15 99 429 1430 3978 9690 21318 43263 82225 148005 254475 420732 672452 1043460 1577532
loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),1,((2x + 1) * (1 + (x mod 2))))
A329494: 1 2 5 14 3 22 13 10 17 38 7 46 25 18 29 62
(loop(\(x,i).11x,x,1) - loop(\(x,i).3x,2x,1))
A139747: 0 2 40 602 8080 102002 1240120 14704202 171312160 1970527202 22450640200 253930611002 2855998840240 31980846315602 356873041128280 3971357037321002
(1 + loop(\(x,i).(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),(x mod 2),(x div 2)))
A082500: 1 2 2 3 3 5 4 7 5 11 6 13 7 17 8 19
(1 + (loop(\(x,i).i,(x div (1 + ((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)))),1) + (x mod 2)))
A197861-A090662: 2 3 2 5 3 7 2 3 5 11 2 13 7 5 2 17
((x + 2) div (1 + loop(\(x,i).i,((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),1) - (x mod 2)))
A217663: 1 3 1 5 3 7 1 3 5 11 1 13 7 5 1 17
(1 + (loop(\(x,i).(x * ((~1 + (2 * i)) * i)),x,1) + (x mod 2)) - loop(\(x,i).2x,x,1))
A261008: 1 1 3 84 2505
(~1 + compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),(x + 1)) - (x mod 2))
A222010: 0 1 3 7
A082575: 0 1 3 7 9 10 12 25 27 28 30 34 36 37 39 79
(((1 + (if (x mod 3) <= 0 then 6 else 0)) * (if x <= 0 then 1 else 2)) div (1 + (x mod 2)))
A010144: 7 1 2 7 2 1 14 1 2 7 2 1 14 1 2 7
(1 + (compr(\x.(1 - loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),x) div 2))
A168497: 1 2 3 6 9 15 21 30 36 51 54 69 75 90 96 99
loop(\(x,i).(24x + 1),loop(\(x,i).x2,x3,2),1)
A292069: 601 346201 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(1 + compr(\x.(~1 + (x mod (~1 + (loop(\(x,i).2x,x,x) mod (x + 1))))),x)))
A056798: 1 4 9 16 25 49 64 81 121 169 256 289 361 529 625 729
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (25x + 1)),x,1)
A033969: 1 26 13 326 163 4076 2038 1019 25476 12738 6369 159226 79613 1990326 995163 24879076
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (27x + 1)),x,1)
A033970: 1 28 14 7 190 95 2566 1283 34642 17321 467668 233834 116917 3156760 1578380 789190
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (21x + 1)),x,1)
A033967: 1 22 11 232 116 58 29 610 305 6406 3203 67264 33632 16816 8408 4204
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(7x + 1))
A017003: 1 8589934592 8649755859375 584318301411328 12200509765705829 131621703842267136 929293739471222707 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(7 * (x + (8x div (if i <= 0 then 1 else i)))),x,1)
A170932: 1 63 2205 56595 1188495 21630609 353299947 5299499205 74192988870 980996186170 12360551945742 149450309889426 1743586948709970 19715944727720430 216875392004924730 2327795874186192102
loop(\(x,i).(7 * (x + (5x div (if i <= 0 then 1 else i)))),x,1)
A140404: 1 42 1029 19208 302526 4235364 54353838 652246056 7419298887 80787921214 848273172747 8636963213424 85649885199788 830145041167176 7886377891088172 73606193650156272
loop(\(x,i).(9 * (x + (3 * (2x div (if i <= 0 then 1 else i))))),x,1)
A173191: 1 63 2268 61236 1377810 27280638 491051484 8207574804 129269303163 1939039547445 27922169483208 388371993720984 5243021915233284 68965903654222428 886704475554288360 4611686018427387903
loop(\(x,i).(9 * (x + (8x div (if i <= 0 then 1 else i)))),x,1)
A053108: 1 81 3645 120285 3247695 75996063 1595917323 30778405515 554011299270 9418192087590 152574711818958 2371843247367438 35577648710511570 517244277406668210 4611686018427387903
loop(\(x,i).(9 * (x + (5x div (if i <= 0 then 1 else i)))),x,1)
A173188: 1 54 1701 40824 826686 14880348 245525742 3788111448 55401129927 775615818978 10470813556203 137072468372112 1747673971744428 21778706417122872 266011342666286508 3192136111995438096
(if x <= 0 then 1 else ((x + 1) + loop(\(x,i).(2x + 2),(2x div (4 + (x div 2))),1)))
A342791: 1 3 4 8 9 10 11 18 19 20 21 22 23 24 25 26
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (19x + 1)),x,1)
A033966: 1 20 10 5 96 48 24 12 6 3 58 29 552 276 138 69
(loop(\(x,i).4x,2x,1) - loop(\(x,i).15x,x,1))
A061252: 0 1 31 721 14911 289201 5386591 97576081 1732076671 30276117361 522861237151 8942430185041 151728638820031 2557404559011121 42864668012537311 715027614225987601
((x + 1) + (loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,x) div 5))
A145127: 1 3 9 25 61 132 259 470 801 1297 2013 3015 4381 6202 8583 11644
loop(\(x,i).(5 * (x + (9x div (if i <= 0 then 1 else i)))),x,1)
A140520: 1 50 1375 27500 446875 6256250 78203125 893750000 9496093750 94960937500 902128906250 8201171875000 71760253906250 607202148437500 4987731933593750 39901855468750000
loop(\(x,i).(5 * (x + (10x div (if i <= 0 then 1 else i)))),x,1)
A173113: 1 55 1650 35750 625625 9384375 125125000 1519375000 17092968750 180425781250 1804257812500 17222460937500 157872558593750 1396564941406250 11970556640625000 99754638671875000
loop(\(x,i).(5 * (x + (7x div (if i <= 0 then 1 else i)))),x,1)
A140220: 1 40 900 15000 206250 2475000 26812500 268125000 2513671875 22343750000 189921875000 1553906250000 12301757812500 94628906250000 709716796875000 5204589843750000
(1 + compr(\x.((~1 + loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1))) mod 3),x))
A177965: 1 4 7 10 16 19 22 31 34 37 40 49 52 55 64 70
((x + 1) + (loop(\(x,i).x2,1,(1 + loop(\(x,i).(2x + 4),x,4))) div 3))
A304370: 9 58 283 1244 5213 21342 86367 347488 1394017 5584226 22353251 89445732 357848421 1431524710 5726360935 22905967976
(1 + compr(\x.((1 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,x)) mod 3),x))
A026232: 3 6 7 9 12 15 16 18 19 21 24 25 27 30 33 34
loop(\(x,i).(6 * (6x + (x div (if i <= 0 then 1 else (0 - i))))),x,1)
A004994: 1 30 990 33660 1161270 40412196 1414426860 49707001080 1752171788070 61910069845140 2191616472517956 77702765843818440 2758448187455554620 4611686018427387903 4611686018427387903
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (23x + 1)),x,1)
A033968: 1 24 12 6 3 70 35 806 403 9270 4635 106606 53303 1225970 612985 14098656
loop(\(x,i).(12x + loop(\(x,i).(6x + 1),i,1)),x,1)
A016248: 1 19 271 3511 43687 533575 6458887 77842567 936126343 11245609351 135019871623 1620673815943 19450697930119 233424047994247 2801182612927879 33614755577116039
loop(\(x,i).(12x + loop(\(x,i).(8x + 1),i,1)),x,1)
A016260: 1 21 325 4485 58501 739461 9173125 112474245 1368864901 16579770501 200184379525 2412029622405 29022892013701 348902996523141 4191862297147525 50342558276728965
loop(\(x,i).(12x + loop(\(x,i).(5x + 1),i,1)),x,1)
A016239: 1 18 247 3120 38221 462558 5570227 66940380 803772841 9647715498 115784793007 1389478551240 16674047790661 200090099366838 2401088821796587 28813104008531700
loop(\(x,i).(12x + loop(\(x,i).10x,i,1)),x,1)
A016196: 1 22 364 5368 74416 992992 12915904 164990848 2079890176 25958682112 321504185344 3958050224128 48496602689536 591959232274432 7203510787293184 87442129447518208
loop(\(x,i).(12x + loop(\(x,i).7x,i,1)),x,1)
A016184: 1 19 277 3667 46405 573667 7001653 84843379 1023885349 12326977795 148206208789 1780451832211 21379263273733 256648048295203 3080454802615285 36970205192893363
loop(\(x,i).(11x + loop(\(x,i).(4x + 1),i,1)),x,1)
A016226: 1 16 197 2252 25113 277608 3059149 33672484 370484705 4075681280 44833892181 493178406396 5424984839977 59674922718232 656424507814493 7220671017615188
loop(\(x,i).(11x + loop(\(x,i).6x,i,1)),x,1)
A016174: 1 17 223 2669 30655 344981 3841447 42535853 469573999 5175391685 56989774711 627250318877 6901930289983 75934293883829 835355596886215 9189381750732941
loop(\(x,i).(11x + loop(\(x,i).8x,i,1)),x,1)
A016187: 1 19 273 3515 42761 503139 5796673 65860555 741243321 8287894259 92240578673 1023236299995 11324318776681 125117262357379 1380687932442273 15222751628953835
loop(\(x,i).(11x + loop(\(x,i).5x,i,1)),x,1)
A016165: 1 16 201 2336 26321 292656 3234841 35661376 392665761 4321276496 47543807081 523030706016 5753581906801 63290621677936 696202941972921 7658262879280256
loop(\(x,i).(6x + loop(\(x,i).(9x + 1),i,1)),x,1)
A016244: 1 16 187 1942 19033 180628 1681639 15470674 141251605 1283357680 11622778531 105040363246 947975408017 8547451504972 77021100541663 693754126856458
loop(\(x,i).(6x + loop(\(x,i).(10x + 1),i,1)),x,1)
A016246: 1 17 213 2389 25445 263781 2693797 27273893 274754469 2759637925 27668938661 277124743077 2773859569573 27754268528549 277636722282405 2776931444805541
loop(\(x,i).(6x + loop(\(x,i).(7x + 1),i,1)),x,1)
A016241: 1 14 141 1246 10277 81270 624877 4710062 34985973 256995046 1871524733 13536029598 97364345989 697223254742 4974599780109 35386420442254
loop(\(x,i).(6x + loop(\(x,i).(x + (((2 + i) * (1 + i)) div 2)),i,1)),x,1)
A229702: 1 10 70 440 2675 16106 96720 580440 3482805 20897050 125382586 752295880 4513775735 27082654970 162495930500 974975583816
(loop(\(x,i).11x,x,1) - loop(\(x,i).6x,x,1))
A139744: 0 5 85 1115 13345 153275 1724905 19207235 212679265 2347869995 25876958425 284948873555 3136251594385 34509651449915 379671469419145 4176777984431075
(loop(\(x,i).11x,x,1) div loop(\(x,i).6x,x,1))
A094989: 1 1 3 6 11 20 37 69 127 233 428 786 1441 2643 4845 8884
loop(\(x,i).(7x + loop(\(x,i).(8x + 1),i,1)),x,1)
A016249: 1 16 185 1880 17841 162336 1435945 12448360 106312481 897579056 7510186905 62388376440 515255179921 4235078618176 34671889197065 282913935338120
loop(\(x,i).(7x + loop(\(x,i).(5x + 1),i,1)),x,1)
A016230: 1 13 122 1010 7851 58863 431572 3118660 22318901 158673713 1122923022 7921496310 55755649951 391815428563 2750337394472 19290508733960
loop(\(x,i).(7x + loop(\(x,i).10x,i,1)),x,1)
A016181: 1 17 219 2533 27731 294117 3058819 31411733 319882131 3239174917 32674224419 328719570933 3301036996531 33107258975717 331750812830019 3322255689810133
loop(\(x,i).(6 * (x + (10x div (if i <= 0 then 1 else i)))),x,1)
A173124: 1 66 2376 61776 1297296 23351328 373621248 5444195328 73496636928 930957401088 11171488813056 127964326404096 1407607590445056 14942295960109056 153692187018264576 1536921870182645760
loop(\(x,i).(6 * (x + (7x div (if i <= 0 then 1 else i)))),x,1)
A141407: 1 48 1296 25920 427680 6158592 80061696 960740352 10808328960 115288842240 1175946190848 11545653510144 109683708346368 1012465000120320 9112185001082880 80187228009529344
loop(\(x,i).(~9x + loop(\(x,i).8x,(~1 + i),1)),x,1)
A166157: 1 ~8 80 ~656 6416 ~53648 515600 ~4378256 41501456 ~356735888 3344840720 ~29029824656 269858356496 ~2360005731728 21789807399440 ~191710220083856
loop(\(x,i).5x,(x + 2),loop(\(x,i).(10x + 1),x,1))
A192107: 25 1375 69375 3471875 173609375 8680546875 434027734375 21701388671875 1085069443359375 54253472216796875 2712673611083984375 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).10x,x,loop(\(x,i).(10x + 1),x,1))
A109241: 1 110 11100 1111000 111110000 11111100000 1111111000000 111111110000000 11111111100000000 1111111111000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + compr(\x.(2 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x + 1))),x))
A111199: 1 2 5 7 8 11 13 16 20 22 23 25 26 32 35 37
loop(\(x,i).(2x - loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(~2 + i),1)),x,1)
A158499: 1 1 1 0 ~5 ~24 ~90 ~312 ~1053 ~3536 ~11934 ~40664 ~140114 ~488240 ~1719380 ~6113200
(loop(\(x,i).4x,x,1) - loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1))
A008549: 0 1 6 29 130 562 2380 9949 41226 169766 695860 2842226 11576916 47050564 190876696 773201629
(loop(\(x,i).4x,x,2) - loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1))
A000346: 1 5 22 93 386 1586 6476 26333 106762 431910 1744436 7036530 28354132 114159428 459312152 1846943453
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (33x + 1)),x,1)
A033972: 1 34 17 562 281 9274 4637 153022 76511 2524864 1262432 631216 315608 157804 78902 39451
loop(\(x,i).24x,x,loop(\(x,i).(5x + 1),x,1))
A091037: 1 144 17856 2156544 259117056 31102009344 3732432224256 447896453382144 53747684481171456 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).7x,x,3) - loop(\(x,i).(3x + 1),x,1))
A261120: 2 17 134 989 7082 50057 351854 2467349 17284562 121031297 847337174 5931714509 41523064442 290664639737 2034662044094 14242663006469
(loop(\(x,i).3x,((x2 + ~x) div 2),1) * loop(\(x,i).(3x + 1),x,1))
A203197: 1 4 39 1080 88209 21493836 15683355351 34309958505840 225130514549271201 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(3x + 1)),x))
A046953: 6 11 13 16 20 21 24 26 27 31 34 35 36 37 41 46
(1 + compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,(3x + 1))),x))
A335031: 1 2 3 4 6 7 10 11 12 14 15 19 20 22 24 26
(1 + compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(3x + ~1)),x))
A272902: 1 5 9 10 15 16 20 21 23 25 29 30 32 35 37 40
(1 + compr(\x.(loop(\(x,i).x2,2,(~1 + (loop(\(x,i).2x,x,1) mod (x + 1)))) mod (x + 1)),x))
A061345: 1 3 5 7 9 11 13 17 19 23 25 27 29 31 37 41
(1 + compr(\x.(2 - ((~1 + loop(\(x,i).2x,x,(if (x mod 3) <= 0 then 1 else 2))) mod (x + 1))),x))
A179891: 4 6 8 9 12 14 15 16 18 20 21 24 25 26 27 28
(1 + compr(\x.((~1 + loop(\(x,i).x2,1,loop(\(x,i).2x2,3,2))) mod (x + 1)),x))
A003538: 1 3 7 9 11 21 31 33 63 77 93 99 151 217 231 279
(1 + compr(\x.(loop(\(x,i).loop(\(x,i).(10x + 1),x,1),2,1) mod (x + 1)),x))
A197318: 1 3 7 11 13 21 33 37 39 77 91 101 111 143 231 259
loop(\(x,i).x2,1,(1 + compr(\x.(loop(\(x,i).4x2,2,3) mod (x + 1)),x)))
A025620: 1 4 9 16 36 64 81 144 256 324 576 729 1024 1296 2304 2916
(1 + compr(\x.(loop(\(x,i).(x * (1 + (if (x mod (1 + i)) <= 0 then 0 else i))),(x div 2),1) mod (x + 1)),x))
A139118: 1 6 8 10 12 14 15 18 20 21 22 24 26 27 28 30
(1 + compr(\x.((loop(\(x,i).x2,2,8) - loop(\(x,i).2x,x,2)) mod (x + 1)),x))
A015937: 1 2 4 6 8 12 16 18 20 22 23 24 32 36 40 42
(~1 + compr(\x.(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then x else 5)),x,x)),x))
A173059: 0 1 3 6 7 10 12 13 15 18 21 22 25 27 28 31
loop(\(x,i).(11x + loop(\(x,i).(3x + 1),i,1)),x,1)
A016216: 1 15 178 1998 22099 243453 2679076 29473116 324214117 3566384811 39230321494 431533802154 4746872620855 52215601220889 574371620604232 6318087848169912
loop(\(x,i).((x2 + ~x) div 2),1,loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1))
A051789: 0 0 1 10 91 861 8646 91806 1021735 11817091 141044410 1727867505 21634392066 275949833550 3576313319580 46995004939590
loop(\(x,i).(x div (2 - (x mod 2))),x,loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1))
A098597: 1 1 1 5 7 21 33 429 715 2431 4199 29393 52003 185725 334305 9694845
loop(\(x,i).(2 * (x - loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(~2 + i),1))),x,1)
A126966: 1 0 ~2 ~8 ~26 ~80 ~244 ~752 ~2362 ~7584 ~24892 ~83376 ~284324 ~984672 ~3455144 ~12259168
(1 + compr(\x.((1 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x)) mod 2),x))
A138970: 2 5 6 9 11 12 15 17 20 23 24 25 28 29 32 34
loop(\(x,i).(8 * (x + (10x div (if i <= 0 then 1 else i)))),x,1)
A197321: 1 88 4224 146432 4100096 98402304 2099249152 40785412096 734137417728 12398765277184 198380244434944 3029807369551872 44437174753427456 628956934971588608 4611686018427387903 4611686018427387903
loop(\(x,i).(8x + (if ((x div 2) mod 2) <= 0 then (1 + (2 * (x mod 2))) else 0)),x,1)
A037601: 1 11 88 705 5643 45144 361153 2889227 23113816 184910529 1479284235 11834273880 94674191041 757393528331 6059148226648 48473185813185
loop(\(x,i).(~8x + loop(\(x,i).7x,(~1 + i),1)),x,1)
A166153: 1 ~7 63 ~455 3983 ~29463 252511 ~1902439 16043055 ~122579639 1020990719 ~7885450503 65060930767 ~506646158935 4150058281887 ~32522243182247
loop(\(x,i).(8x + loop(\(x,i).(9x + 1),i,1)),x,1)
A016256: 1 18 235 2700 28981 298278 2984095 29253600 282456361 2695498938 25486623955 239196683700 2231306698141 20710052641998 191416812647815 1762962024789000
loop(\(x,i).(8x + loop(\(x,i).(10x + 1),i,1)),x,1)
A016257: 1 19 263 3215 36831 405759 4357183 45968575 478859711 4941988799 50647021503 516287283135 5241409376191 53042386120639 535450200076223 5394712711720895
loop(\(x,i).(8x + loop(\(x,i).(2 * (3x + (x div 2))),i,1)),x,1)
A257288: 1 14 154 1526 14266 128534 1129114 9738806 82851706 697402454 5821341274 48265581686 397988613946 3266956634774 26716987140634 217805235562166
(loop(\(x,i).11x,x,1) - loop(\(x,i).8x,x,1))
A139746: 0 3 57 819 10545 128283 1509417 17390019 197581665 2223729963 24863682777 276721736019 3069708899985 33972956330043 375351787072137 4142063797326819
loop(\(x,i).(~7x + loop(\(x,i).6x,(~1 + i),1)),x,1)
A166152: 1 ~6 48 ~300 2316 ~14916 112188 ~738660 5450556 ~36474276 265397628 ~1797317220 12944017596 ~88431340836 632080079868 ~4346196394980
loop(\(x,i).(9x + loop(\(x,i).(5x + 1),i,1)),x,1)
A016234: 1 15 166 1650 15631 144585 1320796 11984820 108351661 977606355 8810664226 79357013190 714518294491 6432190529325 57897344158456 521114244398760
loop(\(x,i).(2 * ((x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))) div 2)),x,1)
A109664: 1 2 8 48 384 4608 64512 1161216 23224320 557383680 16721510400 535088332800 20333356646400 854000979148800 37576043082547200 1803650067962265600
loop(\(x,i).(~2 + ((x + 2) * (2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),i)))),x,1)
A240804: 1 13 103 1153 15013 255253 4849843 111546433 3234846613 100280245063 3710369067403 152125131763603 6541380665835013 307444891294245703 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + loop(\(x,i).(6x + (2 div (1 + i))),i,1)),x,1)
A080962: 1 11 86 596 3896 24656 153056 938816 5714816 34616576 209010176 1259303936 7576795136 45544656896 273603485696 1642963091456
(loop(\(x,i).18x,x,3) + loop(\(x,i).4x,x,1))
A334991: 4 58 988 17560 315184 5669728 102040768 1836676480 33059947264 595078133248 10711402728448 192805234432000 3470494161055744 62468894664122368 1124440103014678528 4611686018427387903
((((x + ~1) * loop(\(x,i).4x,(x + ~2),x)) div 2) + loop(\(x,i).4x,x,1))
A081910: 1 4 17 76 352 1664 7936 37888 180224 851968 3997696 18612224 85983232 394264576 1795162112 8120172544
loop(\(x,i).(5x + loop(\(x,i).(x + (((2 + i) * (1 + i)) div 2)),i,1)),x,1)
A097790: 1 9 55 295 1510 7606 38114 190690 953615 4768295 23841761 119209169 596046300 2980232060 14901160980 74505805716
loop(\(x,i).(5x + loop(\(x,i).(1 + (2 * (x - (x div ~2)))),i,2)),x,1)
A102105: 1 12 83 486 2645 13872 71303 362346 1829225 9198612 46150523 231225006 1157542205 5791962552 28972567343 144901100466
loop(\(x,i).(4x + (14x div (if i <= 0 then 1 else i))),x,1)
A020920: 1 18 198 1716 12870 87516 554268 3325608 19122246 106234700 573667380 3024791640 15628090140 79342611480 396713057400 1957117749840
(if x <= 0 then 2x else loop(\(x,i).(49x + ~2),x,1))
A052463: 0 47 2301 112747 5524601 270705447 13264566901 649963778147 31848225129201 1560563031330847 76467588535211501 3746911838225363547 4611686018427387903 4611686018427387903
loop(\(x,i).(3x2 + x + 3),1,loop(\(x,i).10x,x,1))
A171148: 7 313 30103 3001003 300010003 30000100003 3000001000003 300000010000003 30000000100000003 3000000001000000003 4611686018427387903 4611686018427387903
(loop(\(x,i).7x,x,1) + loop(\(x,i).10x,x,1))
A245807: 2 17 149 1343 12401 116807 1117649 10823543 105764801 1040353607 10282475249 101977326743 1013841287201 10096889010407 100678223072849 1004747561509943
loop(\(x,i).(11x + loop(\(x,i).3x,(2 * i),1)),x,1)
A016190: 1 20 301 4040 51001 620060 7352101 85656080 985263601 11225320100 126965305501 1427999420120 15990423157801 178436520564140 1985678518660501 22048354837360160
(2 - loop(\(x,i).((x + 2) + (2 * (x - loop(\(x,i).7x,i,2)))),x,1))
A058482: 1 25 265 2161 16081 115465 816985 5745121 40294561 282298105 1976795305 13839692881 96884227441 678208723945 4747518463225 33232801429441
((~x + ~1) + loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A182174: 3 7 22 45 116 163 282 353 520 831 950 1357 1668 1835 2194 2793
(1 + loop(\(x,i).(x * ((x div 2) mod 2)),2,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A163366: 1 1 4 1 1 12 16 1 1 28 1 36 40 1 1 52
loop(\(x,i).(x3 + x2),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A270775: 2 12 80 252 1100 1872 4352 6156 11132 22736 27900 47952 65600 75852 99452 143312
loop(\(x,i).(x div (~2 + (x mod 2))),2,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A236965: 1 1 1 3 5 3 4 9 11 7 15 9 10 21 23 13
loop(\(x,i).(x div (2 - (x mod 2))),x,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A057023: 1 1 1 3 5 3 1 9 11 7 15 9 5 21 23 13
(1 + (if (~1 + (x div 4)) <= 0 then x else compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A240963: 1 2 3 4 5 6 7 8 22
A053408: 1 2 3 4 5 6 7 8 22 28
(loop(\(x,i).2x,x,loop(\(x,i).(x * (1 + (2 * i))),(x div 2),1)) mod (x2 + 2x + 1))
A265694: 0 2 3 8 15 12 7 0 54 40 110 0 104 84 0 0
(loop(\(x,i).3x,((x + ~1) + (x2 div 4)),1) - (if (x + ~2) <= 0 then x else 1))
A326223: 1 0 7 80 2186
(loop(\(x,i).((2 * (x - (2x * i))) div (1 + i)),x,1) * loop(\(x,i).(~2x + 1),x,1))
A200375: 1 1 6 25 154 882 5676 36465 244530 1657942 11471668 80242890 568080772 4056976900 29212908120 211783889025
loop(\(x,i).((2x2 + ~3x + 1) * (x2 div 4)),1,loop(\(x,i).2x,x,1))
A160877: 0 3 84 1680 29760
(6 + (loop(\(x,i).2x,(x div 2),(2 + (x mod 2))) + loop(\(x,i).2x,x,1)))
A183980: 9 11 14 20 30 50 86 158 294 566 1094 2150 4230 8390 16646 33158
(((loop(\(x,i).(2x2 + 2x),(x + 1),3) div 2) div 2) div loop(\(x,i).2x,x,1))
A261066: 6 150 180150 519264540150 4611686018427387903 4611686018427387903
loop(\(x,i).(3x + loop(\(x,i).((x + 1) - (2 * (~2x + (x mod 2)))),i,1)),x,1)
A200864: 1 7 42 230 1211 6237 31732 160300 806421 4046867 20278622 101525970 508028431 2541337897 12710276712 63562145240
loop(\(x,i).(3x + loop(\(x,i).(2 * (2x - (x div (1 + i)))),(~1 + i),2)),x,1)
A132310: 1 5 21 83 319 1209 4551 17085 64125 240995 907741 3428655 12990121 49370963 188229489 719805987
loop(\(x,i).(2 * (2x + (11x div (if i <= 0 then 1 else i)))),x,1)
A020924: 1 26 390 4420 41990 352716 2704156 19315400 130378950 840219900 5209363380 31256180280 182327718300 1037865473400 5782393351800 31610416989840
loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,1))
A246860: 1 3 15 105 903 8778 92235 1023165 11821953 141061206 1727926291 21634600078 275950576450 3576315994020 46995014634435 625082431593285
(loop(\(x,i).4x,x,1) - loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,1))
A342906: 0 2 11 50 214 892 3667 14954 60674 245348 989790 3986292 16034316 64434424 258740611 1038384154
(loop(\(x,i).(x * i),x,(x + 1)) - loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,1))
A056986: 0 0 1 10 78 588 4611 38890 358018 3612004 39858014 478793588 6226277900 87175616760 1307664673155 20922754530330
((x + 1) * (1 + loop(\(x,i).8x,(if (x + ~6) <= 0 then 1 else 2),1)))
A020336: 9 18 27 36 45 54 63 520 585 650 715 780 845 910 975 1040
loop(\(x,i).(1 + (loop(\(x,i).2x,x,1) div 3) - ((x div 3) mod 2)),1,(x + 1))
A081374: 1 2 2 5 10 22 43 86 170 341 682 1366 2731 5462 10922 21845
compr(\x.(~1 + ((1 + loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),(x div 2),x)) mod 3)),(x + 1))
A045410: 3 5 11 17 23 29 41 47 53 59 71 83 89 101 107 113
((x + 1) * loop(\(x,i).(2x + 2),(2 - (loop(\(x,i).(2x + 2),x,0) mod (x + 1))),1))
A095208: 10 20 30 4 50 6 70 8 9 10 110 12 130 14 15 16
(loop(\(x,i).(x + (10x div (if i <= 0 then 1 else i))),(x + 1),1) mod (x + 1))
A133620: 0 0 1 1 3 4 2 6 2 6 1 2 1 10 5 7
loop(\(x,i).loop(\(x,i).(x * ((~1 + (2 * i)) * i)),x,1),1,(7x + 7))
A172709-A172604: 681080400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(1 - ((x mod (2 + (loop(\(x,i).2x,x,3) mod (x + 1)))) div 2)),1,(x + 1))
A123230: 1 1 1 ~1 1 1 1 0 1 1 1 0 ~1 1 1 1
compr(\x.((1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)) mod 5),(x + 1))
A327346-A030430: 11 31 41 61 71 101 131 151 181 191 211 241 251 271 281 311
((x + 1) + (loop(\(x,i).(x + loop(\(x,i).((x2 + ~x) div 2),2,(1 + i))),x,1) div 3))
A100605: 1 2 4 10 26
A154322: 1 2 4 10 26 62 133 260 471 802 1298 2014 3016 4382 6203 8584
(((x + 3) * (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)) div (x + 1))
A250480: 0 2 3 1 5 1 7 1 2 1 11 1 13 1 2 1
((1 + (x mod (1 - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * (1 + i)))),x,2x)))) mod (x + 1))
A258850: 0 0 1 0 0 2 0 0 1 3 0 0 0 2 4 0
(loop(\(x,i).2x,(x + (loop(\(x,i).(3x + ~1),x,2) mod (x + 1))),1) mod (x + 1))
A073816: 0 0 1 0 4 4 4 0 2 4 4 4 4 8 1 0
((x + 1) * loop(\(x,i).x2,2,loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1)))
A186416: 1 2 48 2500 192080 18670176 2125170432 270968717448 37634544090000 5588044012339360 875419364366134016 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).((2x * (~1 + (2 * i))) div (if i <= 0 then 2 else ((1 + i) div 2))),x,1) div (x + 1))
A151379: 1 1 4 15 84 420 2640 15015 100100 612612 4232592 27159132 192203088 1274816400 9178678080 62386327575
((x + 1) + (loop(\(x,i).2x,(x mod (2 * (2 - (x mod 2)))),2) + loop(\(x,i).2x,x,1)))
A104101: 4 8 15 16 23 42
((x + 1) * loop(\(x,i).x2,1,loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,1)))
A145600: 1 8 75 784 8820 104544 1288287 16359200 212751396 2821056160 38013731756 519227905728 7174705330000 100136810390400 1409850293610375 20002637245262400
((x + 1) * loop(\(x,i).(~x + loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),(~1 + i),1)),x,1))
A135799: 1 0 0 4 5 48 252 1832 14625 132080 1323168 14576076 175108661 2278429216 31920719820 479088848976
((x + 1) * loop(\(x,i).(loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),i,1) - (x * i)),x,1))
A002747: 1 ~2 9 ~28 185 ~846 7777 ~47384 559953 ~4264570 61594841 ~562923252 9608795209 ~102452031878 2017846993905 ~24588487650736
(x - loop(\(x,i).(x - loop(\(x,i).2x,(1 + ((x + ~2) div (2 + (x div 2)))),1)),2,(x + 1)))
A076272: 1 2 2 3 3 3 5 5 5 5 7 7 7 7 7 7
((2 * (1 + loop(\(x,i).(x * i),2x,loop(\(x,i).(x * (1 + i)),x,(x + 1))))) div (x + 1))
A109103: 4 9 288 34560
((6 * loop(\(x,i).(x2 + 1),1,loop(\(x,i).(2x + 2),x,0))) mod (x + 1))
A281662: 0 0 0 2 1 0 6 6 6 0 6 6 6 2 12 14
((x + 1) * (2 + ((x + 1) * loop(\(x,i).loop(\(x,i).x2,1,(3x + 2)),2,1))))
A031755: 5931 23720 53367 94872 148235 213456 290535 379472 480267 592920 717431 853800 1002027 1162112 1334055 1517856
((2x + 2) * (if x <= 0 then 1 else (2 + loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2))))
A112850: 2 32 132 576 2540 11112 48076 205952 875196 3695160 15519548 64899792 270415652 1123264856 4653525660 19234572544
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,8x),(x + 1))
A153348: 2 3 6 7 9 12 15 16 17 18 20 21 22 23 24 25
(if x <= 0 then 1 else (loop(\(x,i).(10x + 1),2x,1) - (2 div (x + 1))))
A267889: 1 110 11111 1111111 111111111 11111111111 1111111111111 111111111111111 11111111111111111 1111111111111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,10x),(x + 1))
A153403: 3 6 9 12 13 14 15 18 20 21 24 25 27 30 32 33
((2x + 2) * (x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1))))
A069895: 2 8 6 24 10 24 14 64 18 40 22 72 26 56 30 160
(loop(\(x,i).(x * (2 + i)),compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x),2) div (x + 1))
A157132: 2 3 40 1260 7983360 1037836800 50812489728000 15205637551104000 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) mod (x + 1))
A178211: 0 1 1 1 1 1 2 1 7 1 4 1 4 1 4 9
((x + 1) * loop(\(x,i).((x + 2) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)),x,2))
A167214: 2 10 30 68 140 246 406 616 900 1290 1760 2364 3094 3934 4920 6096
((loop(\(x,i).3x,x,1) - loop(\(x,i).3x,(x div 2),(x mod 2))) div (x + 1))
A046211: 1 1 3 6 16 39 104 270 729 1960 5368 14742 40880 113828 318864 896670
((x + 1) * (loop(\(x,i).4x,(x div 2),3) + loop(\(x,i).3x,x,2)))
A097574: 5 18 90 264
(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1) mod loop(\(x,i).x2,2,(x + 1)))
A099908: 0 3 10 35 126 462 1716 2339 4627 2378 1332 4238 2198 5148 1260 57635
(2 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + loop(\(x,i).x2,2,(x + 1))))
A089621: 3 19 86 263 636 1309 2418 4115 6584 10029 14672 20773 28602 38459 50672 65589
loop(\(x,i).(1 - (((x + 1) * (if (~2 + (x div 4)) <= 0 then 1 else 2)) mod 3)),x,(x + 1))
A016055-A015923-A015527-A015263-A015131-A011640: 1 1 0 ~1 ~1 0 1 1 0 ~1 ~1 ~1 0 1 1 0
((x + 1) + loop(\(x,i).(if x <= 0 then 2 else ((x * ((x2 + 2x) + (x mod 3))) div 2)),2,x))
A056684: 11 12 608
compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 4x))),(x + 1))
A023200-A015913: 3 7 13 19 37 43 67 79 97 103 109 127 163 193 223 229
compr(\x.(1 - loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),(x div 2),(x2 + 4x))),(x + 1))
A029710: 7 13 19 37 43 67 79 97 103 109 127 163 193 223 229 277
compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 3),(x2 + 2x))),(x + 1))
A124588-A063091: 2 3 5 11 17 29 41 59 71 101 107 137 149 179 191 197
(if (x mod (3 + (x mod 4))) <= 0 then 1 else loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))
A161825: 1 1 3 1 5 3 7 1 9 5 1 3 1 7 15 1
loop(\(x,i).((4x + ~4) div (x + 2)),1,loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))
A335884-A325033: 0 0 1 0 2 1 2 0 2 2 3 1 3 2 3 0
((x + 1) * loop(\(x,i).((x * i) - loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),i,1)),x,x))
A193465: 0 2 9 52 335 2466 20447 189064 1930959 21603430 262869959 3457226268 48880169351 739429561066 11918051268255 203914545928336
((x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - ((x * (x div 2)) mod 2))))),x,x)) mod (x + 1))
A285099: 0 0 0 1 0 2 2 1 0 3 3 1 3 2 2 1
(2 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + loop(\(x,i).(x * i),x,(x + 1))))
A121926: 3 5 11 31 131 733 5057 40339 362903 3628829 39916831 479001637 6227020841 87178291243 1307674368047 20922789888053
loop(\(x,i).loop(\(x,i).(x + (((~1 + (2 * (i mod 2))) * i) + (x * (1 + i)))),x,0),1,(x + ~1))
A161130: 0 0 1 2 13 74 523 4178 37609 376082 4136911 49642922 645357997 9035011946 135525179203 2168402867234
loop(\(x,i).(x div (2 - (x mod 2))),4,((2x + ~2) * (x + (if (x mod 2) <= 0 then x else 1))))
A185138: 0 0 1 1 3 3 15 6 14 10 45 15 33 21 91 28
((2x + ~1) + (if x <= 0 then 2 else loop(\(x,i).((x + 1) + ((2 + (i div 2)) * (i div 2))),x,1)))
A316261: 1 3 9 15 26 37 55 73 100 127 165 203 254 305 371 437
loop(\(x,i).2x,(x - (2 * (x mod 2))),loop(\(x,i).13x,x,1))
A157027: 1 13 676 4394 456976 2970344 308915776 2007952544 208827064576 1357375919744 141167095653376 917586121746944 95428956661682176 620288218300934144 4611686018427387903 4611686018427387903
loop(\(x,i).(x div 7),x,loop(\(x,i).11x,x,1))
A094993: 1 1 2 3 6 9 15 23 37 58 91 144 226 356 559 879
(loop(\(x,i).10x,x,1) - loop(\(x,i).7x,x,1))
A248341: 0 3 51 657 7599 83193 882351 9176457 94235199 959646393 9717524751 98022673257 986158712799 9903110989593 99321776927151 995252438490057
(loop(\(x,i).10x,x,1) mod loop(\(x,i).7x,x,1))
A139737: 0 3 2 314 396 15965 58808 117484 1998383 31513432 113366285 1133662850 3427321528 20431928079 301208291197 3012082911970
(loop(\(x,i).11x,x,1) - loop(\(x,i).5x,x,1))
A139743: 0 6 96 1206 14016 157926 1755936 19409046 213968256 2355994566 25927658976 285262842486 3138184236096 34521491440806 379743730067616 4177217651837526
((5 * (3 + loop(\(x,i).2x,x,1))) + loop(\(x,i).3x,x,1))
A254368: 21 28 44 82 176 418 1064 2842 7856 22258 64184 187402 551936 1635298 4864904 14512762
(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1) + loop(\(x,i).3x,x,1))
A191993: 2 6 19 62 207 705 2445 8622 30871 112061 411765 1529225 5731741 21652623 82341729 314889102
(loop(\(x,i).6x,x,1) div loop(\(x,i).(x * (4 - (i mod 3))),x,1))
A076738: 1 2 6 9 18 54 81 162 486 729 1458 4374 6561 13122 39366 59049
loop(\(x,i).(x + loop(\(x,i).(3 * ((2x div (1 + i)) * (~1 + (2 * i)))),i,1)),x,1)
A112697: 1 4 22 157 1291 11497 107725 1045948 10428178 106126924 1097913928 11511677470 122057782762 1306480339462 14098243951822 153208673236237
loop(\(x,i).(x + loop(\(x,i).((8x * (~1 + (2 * i))) div (1 + i)),i,1)),x,1)
A112698: 1 5 37 357 3941 46949 587621 7616357 101332837 1375876965 18987759461 265554114405 3755416368997 53610591434597 771525112379237 11181285666076517
loop(\(x,i).(~x + loop(\(x,i).((4x * (~1 + (2 * i))) div (1 + i)),(~1 + i),2)),x,1)
A064062: 1 1 3 13 67 381 2307 14589 95235 636925 4341763 30056445 210731011 1493303293 10678370307 76957679613
loop(\(x,i).((x + 2) + (((1 + loop(\(x,i).2x,x,1)) mod (3x + 1)) mod 2)),x,1)
A231407: 1 4 6
A134779: 1 4 6 8 11 14 16 18 21 24 27 30 33 36 38 40
(1 + compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(x + 8)),x))
A241572: 2 4 5 8 9 11 14 16 17 19 20 23 24 26 29 30
loop(\(x,i).(x + (if (x mod 4) <= 0 then (9x2 + 9) else x)),x,1)
A018558: 1 2 4 157 314 628
loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then ((2x2 + 4x + 1) + (x mod 2)) else x)),x,1)
A018337: 1 2 4 53 106 212
loop(\(x,i).(x + (56x div (if i <= 0 then 1 else i))),x,1)
A017720: 1 57 1653 32509 487635 5949147 61474519 553270671 4426165368 31966749880 210980549208 1285063345176 7282025622664 38650751381832 193253756909160 914734449370024
loop(\(x,i).(x + (35x div (if i <= 0 then 1 else i))),x,1)
A010988: 1 36 666 8436 82251 658008 4496388 26978328 145008513 708930508 3190187286 13340783196 52251400851 192928249296 675248872536 2250829575120
loop(\(x,i).(x + (54x div (if i <= 0 then 1 else i))),x,1)
A017718: 1 55 1540 29260 424270 5006386 50063860 436270780 3381098545 23667689815 151473214816 895068996640 4922879481520 25371763481680 123234279768160 566877686933536
loop(\(x,i).(x + (72x div (if i <= 0 then 1 else i))),x,1)
A017736: 1 73 2701 67525 1282975 19757815 256851595 2898753715 28987537150 260887834350 2139280241670 16141841823510 112992892764570 738799683460650 4538340912686850 26322377293583730
loop(\(x,i).(x + (45x div (if i <= 0 then 1 else i))),x,1)
A010998: 1 46 1081 17296 211876 2118760 18009460 133784560 886322710 5317936260 29248649430 148902215280 707285522580 3155581562280 13298522298180 53194089192720
loop(\(x,i).(x + (60x div (if i <= 0 then 1 else i))),x,1)
A017724: 1 61 1891 39711 635376 8259888 90858768 869648208 7392009768 56672074888 396704524216 2560547383576 15363284301456 86270750308176 456002537343216 2280012686716080
loop(\(x,i).(x + (50x div (if i <= 0 then 1 else i))),x,1)
A017714: 1 51 1326 23426 316251 3478761 32468436 264385836 1916797311 12565671261 75394027566 418094152866 2160153123141 10468434365991 47855699958816 207374699821536
loop(\(x,i).(x + (39x div (if i <= 0 then 1 else i))),x,1)
A010992: 1 40 820 11480 123410 1086008 8145060 53524680 314457495 1677106640 8217822536 37353738800 158753389900 635013559600 2403979904200 8654327655120
loop(\(x,i).(x + (51x div (if i <= 0 then 1 else i))),x,1)
A017715: 1 52 1378 24804 341055 3819816 36288252 300674088 2217471399 14783142660 90177170226 508271323092 2668424446233 13136858812224 60992558771040 268367258592576
loop(\(x,i).(x + (68x div (if i <= 0 then 1 else i))),x,1)
A017732: 1 69 2415 57155 1028790 15020334 185250786 1984829850 18855883575 161322559475 1258315963905 9036996468045 60246643120300 375382930211100 2198671448379300 12165982014365460
loop(\(x,i).(x + (46x div (if i <= 0 then 1 else i))),x,1)
A010999: 1 47 1128 18424 230300 2349060 20358520 154143080 1040465790 6358402050 35607051480 184509266760 891794789340 4047376351620 17345898649800 70539987842520
loop(\(x,i).(x + (66x div (if i <= 0 then 1 else i))),x,1)
A017730: 1 67 2278 52394 916895 13019909 156238908 1629348612 15071474661 125595622175 954526728530 6681687099710 43430966148115 263926640438545 1508152231077400 8144022047817960
loop(\(x,i).(x + (62x div (if i <= 0 then 1 else i))),x,1)
A017726: 1 63 2016 43680 720720 9657648 109453344 1078897248 9440350920 74473879480 536211932256 3558497368608 21944067106416 126600387152400 687259244541600 3527930788646880
loop(\(x,i).(~x + (37x div (if i <= 0 then 1 else i))),x,1)
A010952: 1 36 630 7140 58905 376992 1947792 8347680 30260340 94143280 254186856 600805296 1251677700 2310789600 3796297200 5567902560
loop(\(x,i).(x + (49x div (if i <= 0 then 1 else i))),x,1)
A017713: 1 50 1275 22100 292825 3162510 28989675 231917400 1652411475 10648873950 62828356305 342700125300 1742058970275 8308281242850 37387265592825 159518999862720
loop(\(x,i).(x + (47x div (if i <= 0 then 1 else i))),x,1)
A011000: 1 48 1176 19600 249900 2598960 22957480 177100560 1217566350 7575968400 43183019880 227692286640 1119487075980 5166863427600 22512762077400 93052749919920
loop(\(x,i).(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(~1 + i),1) + (x * i)),x,1)
A221957: 1 2 7 31 159 921 5988 43632 355491 3223729 32329668 355979064 4273100846 55555511298 777797216472 11667035805840
loop(\(x,i).(x * ((1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)) * i * i)),x,1)
A330087: 1 2 24 1080 120960 33264000 15567552000 12967770816000 15768809312256000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 4) <= 0 then 0 else ((x + 1) mod (2 + (if ((x + 1) mod 5) <= 0 then 2 else 0))))
A064287: 0 0 1 0 0 0 1 0 0 2 1 0 0 0 3 0
(~2 + loop(\(x,i).x7,1,loop(\(x,i).(2x + 1),x,0)))
A098940: ~2 ~1 2185 823541 170859373 27512614109 3938980639165 532875860165501 70110209207109373 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((if x <= 0 then 2 else (1 + (loop(\(x,i).2x,(2x + ~1),1) mod (1 + (x div 3))))) div 2)
A029416: 1 0 0 0 0 0 1 1 1 0 0 0 2 1 2 1
(loop(\(x,i).2x,x,(~1 + loop(\(x,i).(2 * (x + (x div 2))),x,7))) div 2)
A321002: 3 19 118 716 4312 25904 155488 933056 5598592 33592064 201553408 1209322496 7255939072 43535642624 261213872128 1567283265536
(2 * (if (x mod 5) <= 0 then (15 * (if x <= 0 then 1 else 2)) else 1))
A040894: 30 2 2 2 2 60 2 2 2 2 60 2 2 2 2 60
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(12x + 10))
A017652: 1000000000000 12855002631049216 2386420683693101056 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(12x + 2))
A017555: 2048 4049565169664 3670344486987776 238572050223552512 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((1 + (3 * (x + loop(\(x,i).(x + (if (~2 + (x div 4)) <= 0 then 1 else 0)),2,x)))) div 2)
A328168: 3 6 9 12 15 18 21 24 27 30 33 35 36 39 42 45
(2 - (if x <= 0 then 1 else ((0 - (x div (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))) div 2)))
A336500: 1 2 2 3 2 2 2 4 3 2 2 4 2 2 2 5
(if (x + ~1) <= 0 then 2x else (if ((4 * (1 + (x mod 2))) mod (1 + (x div 2))) <= 0 then 1 else 2))
A206498: 0 2 1 1 2 2 1 1 2 2 2 2 2 2 2 1
((1 + (if (x + ~1) <= 0 then 1 else loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1))) div 2)
A301749: 1 1 5 18 63 231 858
((1 + loop(\(x,i).((2x + 1) + (x div (1 + (if (x mod 2) <= 0 then 4 else 1)))),x,1)) div 2)
A090245: 1 2 4 9 20 45 112
((1 + loop(\(x,i).(2 * (x + (7x div (if i <= 0 then 1 else i)))),x,1)) div 2)
A082141: 1 8 72 480 2640 12672 54912 219648 823680 2928640 9957376 32587776 103194624 317521920 952565760 2794192896
(loop(\(x,i).(x2 + 2x),1,(1 + ((x + 1) * loop(\(x,i).(x2 + 2x + 1),2,2)))) div 2)
A157511: 5201 20401 45601 80801 126001 181201 246401 321601 406801 502001 607201 722401 847601 982801 1128001 1283201
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(8x + 6))
A017147: 362797056 4049565169664 584318301411328 17714700000000000 238572050223552512 1951354384207722496 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).((~x + ~1) + loop(\(x,i).32x,i,2)),(x + 1),1) div 2)
A154808: 31 992 31775 1016800 32537631 1041204192 33318534175 1066193093600 34118178995231 1091781727847392 34937015291116575 1117984489315730400 4611686018427387903 4611686018427387903 4611686018427387903
(1 - ((loop(\(x,i).2x,x,1) - loop(\(x,i).(3x * (i * i)),(x + ~1),1)) div 2))
A129892: 1 1 1 15 479
(loop(\(x,i).2x,x,(1 + loop(\(x,i).23x,x,1))) div 2)
A272690: 1 24 1060 48672 2238736 102981504 4737148480 217908828672 10023806116096 461095081334784 21210373741388800 975677192103862272 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x - ((x + 3) mod (if x <= 0 then 1 else (2 * (1 + (if (~2 + (x div 3)) <= 0 then 0 else 2))))))
A206913: 0 1 1 3 3 5 5 7 7 9 9 9 9 9 9 15
((1 + ((if x <= 0 then 2 else ((x + 1) mod (1 + (if (x mod 2) <= 0 then 6 else 1)))) div 2)) div 2)
A280749: 1 0 1 0 1 0 0 0 1 0 1 0 2 0 0 0
((1 + (loop(\(x,i).(x2 + x),1,(1 + (loop(\(x,i).(x * i),x,1) div 3))) div 2)) div 2)
A133338: 1 1 1 3 23 431
((1 + ((if x <= 0 then 2 else (1 + (loop(\(x,i).(2x + ~1),x,0) mod (1 + (x div 2))))) div 2)) div 2)
A116664: 1 0 1 1 0 1 1 1 0 1 1 2 0 2 1 1
((1 + (((if ((if x <= 0 then 1 else x) mod 3) <= 0 then 2 else 1) + (x mod 5)) div 2)) div 2)
A059282: 0 1 1 1 1 0 1 1 1 2 0 1 1 1 1 1
((loop(\(x,i).3x,(x + ~1),1) - loop(\(x,i).3x,((x + ~1) div 2),1)) div 2)
A167993: 0 0 1 3 12 36 117 351 1080 3240 9801 29403 88452 265356 796797 2390391
(if x <= 0 then 1 else (2 * (1 + (x div (2 + (if (((x + 1) div 2) mod 5) <= 0 then 1 else 2))))))
A287654: 1 2 2 2 4 4 4 4 6 8 8 6 8 8 8 8
((1 + loop(\(x,i).x2,1,(if x <= 0 then 1 else (2 * (1 - (((x div 2) div ~2) div 2)))))) div 2)
A137575: 1 2 8 8 8 8 8 8 8 8 18 18 18 18 18 18
((1 + (((loop(\(x,i).x2,1,(1 + loop(\(x,i).((~x + ~1) + i),x,2))) div 2) div 2) div 2)) div 2)
A029188: 1 0 1 0 2 0 2 0 3 1 4 1 5 2 6 2
(if (x mod 5) <= 0 then (1 + (x div (2 + (if (x mod 2) <= 0 then 1 else 8)))) else 2)
A063982: 1 2 2 2 2 1 2 2 2 2 4 2 2 2 2 2
(loop(\(x,i).7x,x,1) div (2 * (if (x mod 2) <= 0 then 8 else 1)))
A152418: 0 3 3 171 150 8403 7353 411771 360300 20176803 17654703 988663371 865080450 48444505203 42388942053 2373780754971
(2 * loop(\(x,i).4x,2x,(1 + (2 * loop(\(x,i).3x,2x,2)))))
A233252: 10 1184 166400 23896064 3439984640 495341010944 71328837140480 10271348253261824 1479074079750225920 4611686018427387903 4611686018427387903 4611686018427387903
(1 - ((1 + ((if x <= 0 then 2 else (x - (loop(\(x,i).(x * i),x,1) mod (x + 1)))) mod 4)) div 2))
A334090: 0 1 1 0 1 0 1 ~1 1 0 1 ~1 1 0 0 ~1
((5 * ((x + 2) + loop(\(x,i).(x - (if (~2 + (x div 2)) <= 0 then 0 else 1)),2,x))) div 2)
A182340: 5 10 15 20 25 30 32 35 40 45 50 55 60 65 70 75
((loop(\(x,i).(3x + ~1),x,1) - loop(\(x,i).2x,x,1)) mod 10)
A021610: 0 0 1 6 5 0 1 6 5 0 1 6 5 0 1 6
(loop(\(x,i).6x,(x + 1),1) mod loop(\(x,i).x2,2,10))
A216128: 6 36 216 1296 7776 6656 9936 9616 7696 6176 7056 2336 4016 4096 4576 7456
(10 + compr(\x.loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,2x),x))
A153041: 10 14 17 20 22 23 26 27 29 32 34 35 37 38 41 42
(10 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))
A098605: 10 11 12 14 15 17 18 20 23 24 27 29 30 32 35 38
((x + 2) div (2 + (3 * (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))))
A316432: 1 0 0 1 0 1 0 1 1 2 0 2 0 3 2 3
(~2 + (3 * (~1 + loop(\(x,i).(x + loop(\(x,i).(8 div (x + 1)),2,i)),x,2))))
A073121: 1 4 10 16 28 40 52 64 88 112 136 160 184 208 232 256
(if x <= 0 then 1 else (2 * (3x - ((1 + (if (x mod 3) <= 0 then 0 else x)) div 3))))
A315361: 1 6 10 18 22 26 36 38 42 54 54 58 72 70 74 90
(loop(\(x,i).x2,(x + ~2),loop(\(x,i).3x,(x2 + 3x + 2),3)) div 2)
A076481: 13 1093 797161 4611686018427387903 4611686018427387903
((3 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),(x + 1))) div 2)
A231407: 1 4 6
A137821: 1 4 6 13 15 18 19 40 42 45 46 54 55 58 60 121
(((loop(\(x,i).(x2 + x),1,(2 - (if (x mod 3) <= 0 then x else 0))) div 2) div 3) div 2)
A046777: 0 0 0 0 0 0 1 0 0 3 0 0 7 0 0 13
(if x <= 0 then 1 else (2 + ((2 * ((loop(\(x,i).(2 * (x - i)),x,2) mod (x + 1)) div 2)) div 3)))
A324538: 1 2 2 2 2 3 2 2 2 4 2 5 2 6 4 2
((3 * (loop(\(x,i).(2 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2)),2,x) div 2)) div 2)
A214635: 1 1 1 1 3 1 1 1 3 3 1 1 4 1 3 1
(if x <= 0 then 1 else (2 * (2x - ((1 - (if (~2 + (x div 2)) <= 0 then x else (x + 2))) div 3))))
A310379: 1 4 10 14 18 24 30 34 38 44 48 52 58 62 66 72
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),(6x + 2))
A031380: 7 29 53 79 107 139 173 199 239 271 311 349 383 421 457 491
((if x <= 0 then 1 else (loop(\(x,i).~2x,x,6) mod (x + 1))) mod 6)
A263145: 1 0 0 0 1 0 0 0 0 2 0 0 0 2 3 0
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(9x + 2))
A017195: 2048 285311670611 204800000000000 12200509765705829 238572050223552512 2472159215084012303 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((3 * (x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1)))) div 2)
A094603: 1 3 1 4 1 3 1 6 1 3 1 4 1 3 1 7
(2 + loop(\(x,i).(x * (2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),i))),x,3))
A240803: 5 17 107 1157 15017 255257 4849847 111546437 3234846617 100280245067 3710369067407 152125131763607 6541380665835017 307444891294245707 4611686018427387903 4611686018427387903
(~2 + loop(\(x,i).(x + (i div 2)),(2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)),1))
A074367: 1 5 11 29 41 71 89 131 209 239 341 419 461 551 701 869
(if x <= 0 then (x + ~1) else loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(2x + ~1),2))
A024491: ~1 2 10 84 858 9724 117572 1485800 19389690 259289580 3534526380 48932534040 686119227300 9723892802904 139067101832008 2004484433302736
((loop(\(x,i).5x,2x,1) + loop(\(x,i).3x,2x,1)) div 2)
A081421: 1 17 353 8177 198593 4912337 122336033 3054149297 76315468673 1907542343057 47685459212513 1192108586037617 29802463602463553 745059330625296977 4611686018427387903 4611686018427387903
((loop(\(x,i).7x,x,1) + loop(\(x,i).3x,2x,1)) div 2)
A081190: 1 8 65 536 4481 37928 324545 2803256 24405761 213887048 1884629825 16679193176 148135411841 1319377419368 11777507763905 105319346802296
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(10x + 2))
A017303: 2048 743008370688 584318301411328 36028797018963968 717368321110468608 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 + loop(\(x,i).3x,loop(\(x,i).(3x + 2),((x + ~1) div 3),x),1))
A108259: 3 5 11 29 4782971
((loop(\(x,i).10x,x,1) + loop(\(x,i).6x,x,1)) div 2)
A152105: 1 8 68 608 5648 53888 523328 5139968 50839808 505038848 5030233088 50181398528 501088391168 5006530347008 50039182082048 500235092492288
(2 * (1 + compr(\x.(loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 2 else 1)),(x + 1),x) mod 3),x)))
A342192: 6 10 14 22 26 34 38 46 58 62 74 82 86 94 100 106
((loop(\(x,i).(x - (x div (~2 + (x mod 2)))),x,1) + loop(\(x,i).(3x + ~1),x,1)) div 2)
A001998: 1 2 4 10 25 70 196 574 1681 5002 14884 44530 133225 399310 1196836 3589414
(2 * (~1 + (loop(\(x,i).2x,(x div 2),(2 + (x mod 2))) + loop(\(x,i).2x,(x + ~1),x))))
A208902: 2 6 14 34 78 182 414 942 2110 4702 10366 22718 49406 106878 229886 492286
((if (x mod 7) <= 0 then ((3 - (x mod 2)) * (if x <= 0 then 1 else x)) else 1) div 2)
A340980: 1 0 0 0 0 0 0 7 0 0 0 0 0 0 21 0
(loop(\(x,i).(2x - (loop(\(x,i).(x - (x div 8)),2,(x + ~1)) div 2)),x,1) div 2)
A173714: 0 1 2 3 5 9 14 23 38 61 99 161 260 421 682 1103
((loop(\(x,i).12x,x,1) + loop(\(x,i).8x,x,1)) div 2)
A163165: 1 10 104 1120 12416 140800 1624064 18964480 223379456 2646999040 31495553024 375799152640 4492409962496 53771480596480 644158255529984 7721102973337600
((loop(\(x,i).10x,x,1) + loop(\(x,i).8x,x,1)) div 2)
A081191: 1 9 82 756 7048 66384 631072 6048576 58388608 567108864 5536870912
A060531: 1 9 82 756 7048 66384 631072 6048576 58388608 567108864 5536870912 54294967296 534359738368 5274877906944 52199023255552 517592186044416
((loop(\(x,i).10x,x,1) - loop(\(x,i).8x,x,1)) div 2)
A081203: 0 1 18 244 2952 33616 368928 3951424 41611392 432891136 4463129088 45705032704 465640261632 4725122093056 47800976744448 482407813955584
(compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) mod (2 * (if (~x + 4) <= 0 then x else 1)))
A179437: 0 1 1 1 1 1 3 3 5 9 9 13 15 15 17 21
(2 * (1 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + 2x + 2))),x)))
A059793: 2 4 8 12 20 28 32 40 48 52 72 80 108 112 132 148
((loop(\(x,i).(2 * (2x - (x div (1 + i)))),(x + ~1),2) + loop(\(x,i).2x,x,1)) div 2)
A005317: 1 2 5 14 43 142 494 1780 6563 24566 92890 353740 1354126 5204396 20066492 77575144
(2 + (loop(\(x,i).(~x + 1),x,(if ((x + 2) mod (1 + (x mod 4))) <= 0 then 1 else 2)) mod (x + 1)))
A088491: 2 3 4 5 3 7 4 9 3 11 3 13 3 15 4 17
(2 + compr(\x.(x - loop(\(x,i).x2,2,(loop(\(x,i).(2x + 2),x,2) mod (x + 2)))),(x + 1)))
A343597-A199009: 4 6 8 9 10 12 14 15 16 18 20 21 24 25 27 28
(((x + 1) * loop(\(x,i).(x + (5x div (if i <= 0 then 1 else i))),x,(x + 2))) div 2)
A107417: 1 18 126 560 1890 5292 12936 28512 57915 110110 198198 340704 563108 899640 1395360 2108544
(((x + 1) * loop(\(x,i).(x + ((x * loop(\(x,i).x2,2,3)) div (1 + i))),x,2)) div 2)
A017746: 1 83 3486 98770 2123555 36949857 541931236 6890268572 77515521435 783768050065 7210666060598 60962903966874 477542747740513 3489735464257595 23929614612052080 154744841157936784
(loop(\(x,i).((x + 1) * (if ((x + 1) mod 8) <= 0 then 2 else 1)),x,1) mod (2x + 2))
A256298: 1 2 3 4 5 6 7 0 17 18 19 20 21 22 23 16
((~2x + ~2) + compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),2x))
A141101: 1 3 7 11 19 25 29 37 43 51 57 65 75 79 83 99
((3x + 2) + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1)))
A292608: 3 6 7 11 11 14 15 20 19 22 23 27 27 30 31 37
loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),x,(2x + 2))
A250130: 2 12 90 840 11550 180180 3573570 77597520 2007835830 64696932300 2206165391430 89048857617720 3955253425853730 183158658643380420 4611686018427387903 4611686018427387903
(2 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1)))
A006512: 5 7 13 19 31 43 61 73 103 109 139 151 181 193 199 229
(~2 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1)))
A256388: 1 3 9 15 27 39 57 69 99 105 135 147 177 189 195 225
(2 * compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1)))
A108605: 6 10 22 34 58 82 118 142 202 214 274 298 358 382 394 454
(2 * loop(\(x,i).(8 div (x + 1)),2,loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))
A307313: 2 2 4 2 8 4 8 2 16 8 16 4 16 8 16 2
(((x2 + x) * loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x + ~1),x)) div 2)
A037972: 0 1 12 108 800 5250 31752 181104 988416 5212350 26741000 134132856 660284352 3199016548 15288882000 72209880000
(if x <= 0 then 0 else loop(\(x,i).((8x * (~1 + (2 * i))) div (1 + i)),(x + ~1),2))
A052707: 0 2 8 64 640 7168 86016 1081344 14057472 187432960 2549088256 35223764992 493132709888 6979724509184 99710350131200 1435829041889280
((1 + (if (x mod 2) <= 0 then (5 * (2 - (x mod 4))) else 1)) * (if x <= 0 then 1 else 2))
A010187: 11 4 2 4 22 4 2 4 22 4 2 4 22 4 2 4
loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),(if x <= 0 then 1 else 2))
A167275: 1 4 4 8 4 8 8 16 4 8 8 16 8 16 16 32
((loop(\(x,i).3x,2x,1) - loop(\(x,i).7x,x,1)) div 2)
A081202: 0 1 16 193 2080 21121 206896 1979713 18640960 173533441 1602154576 14701866433 134294124640 1222488408961 11099284691056 100571785292353
((loop(\(x,i).5x,(x div 2),1) + loop(\(x,i).5x,x,1)) div 2)
A001447: 1 3 15 65 325 1575 7875 39125 195625 976875 4884375 24415625 122078125 610359375 3051796875 15258828125
((loop(\(x,i).7x,x,1) + loop(\(x,i).5x,x,1)) div 2)
A081188: 1 6 37 234 1513 9966 66637 450834 3077713 21153366 146120437 1013077434 7042713913 49054856766 342163294237 2389039544034
((loop(\(x,i).7x,x,1) - loop(\(x,i).5x,x,1)) div 2)
A081200: 0 1 12 109 888 6841 51012 372709 2687088 19200241 136354812 964249309 6798573288 47834153641 336059778612 2358521965909
(loop(\(x,i).(x + loop(\(x,i).((x + ~1) - (2 * ((((x + ~1) div 2) div 2) div 2))),1,i)),x,1) div 2)
A194221: 0 0 1 2 3 5 8 11 14 17 21 25 29 34 40 46
(if (x + ~1) <= 0 then 1 else (2 * ((1 + (loop(\(x,i).2x,(x + ~1),(x + 2)) div 3)) div 2)))
A093041: 1 1 2 6 16 38 86 192 426 938 2048 4438 9558 20480 43690 92842
(if x <= 0 then 1 else (2 + (if (x mod 3) <= 0 then 1 else ((2x mod (1 + (x div 3))) mod 2))))
A262945: 1 2 2 3 2 2 3 2 3 3 2 2 3 3 3 3
(if x <= 0 then 1 else (2 + ((x + 1) div (2 + (if (6 mod (1 + (x div 2))) <= 0 then 2 else 1)))))
A274533-A273263: 1 2 2 3 3 3 4 4 5 5 4 5 6 6 7 7
(if x <= 0 then 1 else (if (x mod 5) <= 0 then 0 else (1 - (2 * ((x div 5) mod 2)))))
A163812: 1 1 1 1 1 0 ~1 ~1 ~1 ~1 0 1 1 1 1 0
(2 + (loop(\(x,i).(x2 * loop(\(x,i).(2x2 + ~x),2,x)),x,5) div 2))
A074318: 4 50064 4611686018427387903
(loop(\(x,i).2x,x,(2 + (3 * (2 + loop(\(x,i).(2x + (i mod 2)),x,2))))) div 2)
A240526: 7 23 76 284 1072 4208 16576 65984 262912 1050368 4197376 16784384 67121152 268464128 1073790976 4295081984
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(12x + 4))
A017579: 4194304 17592186044416 8293509467471872 419430400000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(~11x + ~4))
A017446: 1048576 576650390625 141167095653376 4808584372417849 64925062108545024 511116753300641401 2824752490000000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(~11x + ~4))
A017448: 16777216 129746337890625 95428956661682176 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * ((if x <= 0 then 1 else (3 * (x + ((if (x mod 4) <= 0 then 1 else 2) + (x div 2))))) div 2))
A072835: 0 8 14 18 20 26 32 36 38 44 50 54 56 62 68 72
((loop(\(x,i).((x + (x div 2)) * (x div 2)),1,loop(\(x,i).3x,x,3)) div 2) div 2)
A006100: 1 13 130 1210 11011 99463 896260 8069620 72636421 653757313 5883904390 52955405230 476599444231 4289397389563 38604583680520 347441274648040
(2 * ((3 * (x + loop(\(x,i).(x + (if (~4 + (x div 2)) <= 0 then 1 else 0)),2,x))) div 2))
A126798: 6 12 18 24 30 36 42 48 54 56 60 66 72 78 84 90
(2 * loop(\(x,i).2x,x,loop(\(x,i).(2 * (2x - (x div (1 + i)))),(2x + 1),2)))
A183767: 12 280 7392 205920 5912192 173065984 5134924800 153876579840 4646469273600 141154845511680 4309194677698560 132086184685977600 4062564621910867968 4611686018427387903 4611686018427387903
(loop(\(x,i).x3,1,loop(\(x,i).(2x + 2),(x div 2),(2 * (1 + (x mod 2))))) div 2)
A267668: 4 32 108 500 1372 5324 13500 48668 119164 415292 1000188 3429500 8193532 27871484 66325500 224727548
(loop(\(x,i).(x2 + x),1,(loop(\(x,i).(1 + ((x3 + x2) div 2)),x,1) div 2)) div 2)
A226499: 0 1 6 4851
(if x <= 0 then 1 else (2 + (2x div (2 + (if ((x2 + 2x) mod 6) <= 0 then x else 1)))))
A329608-A325384-A323405-A323400-A323371-A323370-A323369-A323367-A322973-A322824-A322314-A322022-A319349-A319346-A318500-A305890-A305801: 1 2 3 4 3 5 3 6 7 8 3 9 3 10 11 12
((((x + 1) * loop(\(x,i).(~x + loop(\(x,i).(2x2 + ~2x + ~2),i,x)),x,1)) div 2) div 2)
A127623: 0 ~2 693 4611686018427387903
(4 + (loop(\(x,i).(~1 + loop(\(x,i).(2x2 + 4x + ~4),2,x)),(x + 1),1) div 2))
A058456: 9 80089 4611686018427387903
(8 * (1 + loop(\(x,i).2x,x,(~2 + loop(\(x,i).(2x + 4),(x + 1),1)))))
A235885: 40 232 1096 4744 19720 80392 324616 1304584 5230600 20946952 83836936 335446024
(((loop(\(x,i).loop(\(x,i).x2,2,x3),x,9) div 2) div 2) div 2)
A022262: 1 35303692060 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 - (4 * ((loop(\(x,i).2x,x,2) - loop(\(x,i).(4x + 2),x,1)) div 2)))
A273251: 1 5 37 181 789 3285 13397 54101 217429 871765 3491157 13972821 55907669 223663445 894719317 3579008341
((if x <= 0 then 2 else (((x + 2) - (loop(\(x,i).2x,x,(1 + (x mod 2))) mod (x + 1))) div 2)) div 2)
A029261: 1 0 0 1 1 0 1 2 1 1 2 2 3 2 3 4
(2 - (if x <= 0 then 1 else (2 * (if (x mod 3) <= 0 then 1 else ((x mod (4 + (x mod 2))) mod 2)))))
A123063: 1 0 2 0 2 2 0 2 2 0 2 0 0 0 2 0
((loop(\(x,i).5x,(1 + (x div 2)),(if (x mod 2) <= 0 then 1 else 4)) div 2) div 2)
A249222: 1 5 6 25 31 125 156 625 781 3125 3906 15625 19531 78125 97656 390625
(2 + (((loop(\(x,i).(x * i),x,(if (x + ~1) <= 0 then ~1 else (x2 + 2x))) div 2) div 2) div 2))
A171756: 1 1 4 13 74 527
(loop(\(x,i).7x,x,1) mod (~2 + loop(\(x,i).(x3 + 2),2,2)))
A216129: 1 7 49 343 401 807 649 543 801 607 249 743 201 407 849 943
(~2 + (((3 * (2 + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x))) div 2) mod 4))
A127442: 1 1 ~2 1 ~2 0 1 ~2 0 1 1 ~2 0 1 ~1 1
loop(\(x,i).loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1),2,(x mod 8))
A273399: 1 1 2 42 2674440 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x2,2,(10x + 4))),x,8)
A182010: 8 398297088 4611686018427387903 4611686018427387903
((2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)) * loop(\(x,i).x2,4,2))
A175744: 196608 327680 458752 720896 851968 1114112 1245184 1507328 1900544 2031616 2424832 2686976 2818048 3080192 3473408 3866624
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(12x + 8))
A017627: 8589934592 204800000000000 36028797018963968 1196683881290399744 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(~11x + ~8))
A017494: 1073741824 6131066257801 590490000000000 13422659310152401 144555105949057024 984930291881790849 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(~11x + ~8))
A017496: 68719476736 2213314919066161 531441000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(4 + loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A287922: 8 13 29 53 125 173 293 365 533 845 965 1373 1685 1853 2213 2813
(2 * (~2 + loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))))
A153480: 4 14 46 94 238 334 574 718 1054 1678 1918 2734 3358 3694 4414 5614
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(7x + 2))
A017015: 2048 31381059609 17592186044416 952809757913927 17714700000000000 177917621779460413 1196683881290399744 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 + (((if (~2 + (x mod 7)) <= 0 then 0 else 1) + (x div 2)) div 2)))
A134674: 1 2 2 3 3 3 4 3 4 4 5 5 5 5 5 5
(if x <= 0 then 1 else (4 * loop(\(x,i).(10x + 2),(x div 2),(x mod 2))))
A249572: 1 4 8 48 88 488 888 4888 8888 48888 88888 488888 888888 4888888 8888888 48888888
(if x <= 0 then 1 else (2 * (loop(\(x,i).~6x,(x + ~1),1) * (2 + (x mod 2)))))
A091097: 1 6 ~24 216 ~864 7776 ~31104 279936 ~1119744 10077696 ~40310784 362797056 ~1451188224 13060694016 ~52242776064 470184984576
(2 * (2 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x) - (x mod 2)))
A014687: 4 4 8 10 14 16 20 22 30 30 38 40 44 46 54 58
(2 * (4 + compr(\x.(2 - loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x)),x)))
A298366: 30 38 54 60 68 80 90 96 98 120 122 124 126 128 138 146
(loop(\(x,i).(if x <= 0 then 1 else ((2x * (~1 + (2 * i))) div (1 + i))),(x + ~1),0) mod 4)
A073267: 0 0 1 2 1 2 2 0 1 2 2 0 2 0 0 0
((x + ((~1 + loop(\(x,i).loop(\(x,i).(x * i),i,x),x,1)) div (2x + 3))) div 4)
A171737: 0 0 0 1 7 665
(4 * compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(4x + 1))),x))
A152680: 4 12 16 28 36 40 52 60 72 88 96 100 108 112 136 148
(if x <= 0 then 2 else (if ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2) <= 0 then 1 else (x mod 4)))
A248145: 2 1 1 1 1 1 1 1 1 1 1 3 1 1 2 1
(loop(\(x,i).4x,x,9) - loop(\(x,i).3x,x,4))
A291010: 5 24 108 468 1980 8244 33948 138708 563580 2280564 9200988 37040148 148869180 597602484 2396787228 9606280788
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(10x + 4))
A017327: 4194304 4049565169664 1521681143169024 70188843638032384 1196683881290399744 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,loop(\(x,i).x3,1,(2 * ((x + 2) + (3 * (x div 2))))))
A272914: 4096 46656 7529536 16777216 191102976 308915776 1544804416 2176782336 7256313856 9474296896 24794911296 30840979456 68719476736 82653950016 164206490176 192699928576
loop(\(x,i).8x,(2 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x)),2)
A100628: 128 1024 65536 4194304 17179869184 1099511627776 4503599627370496 288230376151711744 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~2 + loop(\(x,i).x3,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A153481: 6 25 123 341 1329 2195 4911 6857 12165 24387 29789 50651 68919 79505 103821 148875
(2 * loop(\(x,i).x3,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A172190: 16 54 250 686 2662 4394 9826 13718 24334 48778 59582 101306 137842 159014 207646 297754
(loop(\(x,i).((1 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),i)) * (x div 2)),x,2) div 2)
A246541: 1 2 6 30 180 1440 12960 142560 1995840
(2 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 2)))
A173176-A172057: 7 13 19 31 43 61 73 103 109 139 151 181 193 199 229 241
(if x <= 0 then 1 else (2 * (2x + ((x - (if (~2 + (x div 4)) <= 0 then 0 else 2)) div 3))))
A312507: 1 4 8 14 18 22 28 32 36 42 46 50 54 58 64 68
(loop(\(x,i).(2 * (4x - (x div (if i <= 0 then 1 else i)))),x,1) div (~4x + 1))
A004984: 1 ~2 ~6 ~28 ~154 ~924 ~5852 ~38456 ~259578 ~1788204 ~12517428 ~88759944 ~636112932 ~4599585816 ~33511268088 ~245749299312
(x + ((x div (3 + (if (x + ~4) <= 0 then 0 else 2))) + (if x <= 0 then 1 else 4x)))
A313872: 1 5 10 16 21 26 31 36 41 46 52 57 62 67 72 78
(x + (loop(\(x,i).(x - (x div 8)),2,(x + ~1)) + (if x <= 0 then 1 else 4x)))
A314251: 1 5 11 17 23 29 35 41 47 52 57 63 69 75 81 87
(loop(\(x,i).10x,x,3) - loop(\(x,i).3x,2x,2))
A097167: 1 12 138 1542 16878 181902 1937118 20434062 213906558 2225159022 23026431198 237237880782 2435140927038 24916268343342 254246415090078 2588217735810702
(if (2x + ~4) <= 0 then x else (~1 + ((x mod 2) + loop(\(x,i).(2x - (i mod 2)),(x div 2),2))))
A138587: 0 1 2 3 5 6 10 11 21 22 42 43 85 86 170 171
(x + (loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),(x + ~1),x) + (2 * (x div 2))))
A093052: 0 2 5 4 8 6 9 8 13 10 13 12 16 14 17 16
(2 * ((if (x mod 3) <= 0 then (5 * (if x <= 0 then 1 else 2)) else 1) * (2 - (x mod 2))))
A040397: 20 2 4 20 4 2 40 2 4 20 4 2 40 2 4 20
(if (x mod 4) <= 0 then (17 * (if x <= 0 then 1 else 2)) else (2 + (x mod 2)))
A040281: 17 3 2 3 34 3 2 3 34 3 2 3 34 3 2 3
(2 + (loop(\(x,i).(x + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,x) + (x mod 2)))
A262392: 2 5 7 13 19 31 43 61 79 103 131 163 199 241 283 331
(if ((x + ~1) mod 3) <= 0 then ((if (x mod 2) <= 0 then 1 else x) mod 4) else (1 - (2 * (x mod 2))))
A202150: 1 1 1 ~1 1 ~1 1 3 1 ~1 1 ~1 1 1 1 ~1
((2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)) * loop(\(x,i).x3,2,2))
A179692: 1536 2560 3584 5632 6656 8704 9728 11776 14848 15872 18944 20992 22016 24064 27136 30208
(2 + compr(\x.(~1 + ((1 + loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),x,(x + 2))) mod 3)),x))
A045309: 2 3 5 11 17 23 29 41 47 53 59 71 83 89 101 107
loop(\(x,i).(~1 + (6 * loop(\(x,i).(x2 + 2x + 1),x,8))),x,2)
A303738: 2 40343 4611686018427387903
loop(\(x,i).loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)),1,((x2 + 5x) div 2))
A236999: 1 1 1 13 19 13 17 43 53 1 19 89 103 59 67 151
(loop(\(x,i).(2 * ((2 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 3)),3,x) div 2)
A335881: 0 0 1 0 2 1 2 0 2 2 2 1 2 2 3 0
((if x <= 0 then 2 else loop(\(x,i).((2x * (~1 + (2 * i))) div (2 + i)),x,3x)) div 2)
A071724: 1 1 3 9 28 90 297 1001 3432 11934 41990 149226 534888 1931540 7020405 25662825
loop(\(x,i).((10x + 1) + loop(\(x,i).3x,(2 * i),1)),x,2)
A083446: 2 30 382 4550 52062 579670 6328142 68064390 723690622 7624326710 79730051502 828681574630 8569245282782 88234318656150 905219979016462 9258090922259270
(((~x + ~1) + loop(\(x,i).(x + loop(\(x,i).(x - (x div (3 + i))),x,(x + 1))),x,2)) div 2)
A131674: 0 1 3 5 8 12 17 23 29 36 44 53 63 74 86 99
(2 + compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(3x + 1)),x))
A153245: 7 12 14 17 21 22 25 27 28 32 35 36 37 38 42 47
(2 * compr(\x.(loop(\(x,i).2x,x,(~1 + (loop(\(x,i).2x,x,2) mod (x + 2)))) mod (x + 1)),x))
A260084: 0 2 6 10 14 18 22 30 34 42 46 54 58 62 70 78
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(10x + 8))
A017375: 8589934592 64268410079232 8293509467471872 238572050223552512 3116402981210161152 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2x * loop(\(x,i).(loop(\(x,i).(2x * (~1 + (2 * i))),(x + ~2),x) div 2),1,(x + ~1)))
A052733: 0 0 0 6 24 240 3600 70560 1693440 47900160 1556755200 57081024000 2328905779200 104589041356800 5124863026483200 272011960636416000
(2 * compr(\x.(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then x else 5)),x,x)),x))
A209838-A086303: 2 4 8 14 16 22 26 28 32 38 44 46 52 56 58 64
(loop(\(x,i).(1 + ((x + (if (x mod 2) <= 0 then 4 else (x mod ~2))) div 3)),2,x) div 2)
A029386: 1 0 0 0 0 1 1 0 1 0 1 1 2 1 1 1
(2 + compr(\x.loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,(2 * ((x + 1) + (x div 2)))),x))
A199593: 9 12 17 19 22 26 29 31 32 39 40 41 42 45 48 49
(loop(\(x,i).(8x + 5),(x + 1),0) mod loop(\(x,i).(2x + 2),x,2))
A213245: 1 3 1 15 31 9 127 255 73 1023 2047 585 8191 16383 4681 65535
(2 + compr(\x.((1 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x)) mod 2),x))
A080147: 3 6 7 10 12 13 16 18 21 24 25 26 29 30 33 35
(loop(\(x,i).12x,x,3) - loop(\(x,i).8x,x,2))
A016188: 1 20 304 4160 54016 680960 8433664 103301120 1256390656 15210905600 183604609024 2211845242880 26610862391296 319880104509440 3842959300624384 46150695979581440
(2 + compr(\x.(loop(\(x,i).x2,2,(1 + loop(\(x,i).(2x * i),4,1))) mod (x + 2)),x))
A036490: 5 7 11 25 35 49 55 77 121 125 175 245 275 343 385 539
(2 + compr(\x.(1 - (loop(\(x,i).(x * (1 + (if (x mod (1 + i)) <= 0 then 0 else i))),x,1) mod (x + 2))),x))
A050376-A009087: 2 3 4 5 7 9 11 13 16 17 19 23 25 29 31 37
(~2 + loop(\(x,i).(x * i),x,(x + 1)) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A261809: ~1 ~1 1 17 109 707 5023 40301 362857 3628771 39916769 479001563 6227020759 87178291157 1307674367953 20922789887947
loop(\(x,i).((x + 1) * (x div 2)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A084921: 3 4 12 24 60 84 144 180 264 420 480 684 840 924 1104 1404
loop(\(x,i).(x3 + x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A135178: 12 36 150 392 1452 2366 5202 7220 12696 25230 30752 52022 70602 81356 106032 151686
loop(\(x,i).(x3 + ~x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A135177: 4 18 100 294 1210 2028 4624 6498 11638 23548 28830 49284 67240 77658 101614 146068
((~1 + loop(\(x,i).2x,x,2)) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A192324: 1 0 2 1 9 11 8 8 5 8 1 25 32 0 8 27
loop(\(x,i).(2x2 + ~x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A117961: 6 15 45 91 231 325 561 703 1035 1653 1891 2701 3321 3655 4371 5565
loop(\(x,i).(x3 + ~x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A127917: 6 24 120 336 1320 2184 4896 6840 12144 24360 29760 50616 68880 79464 103776 148824
(loop(\(x,i).(x * i),x,(x + 1)) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A091858: 1 2 1 3 10 5 8 2 9 1 22 7 4 40 29 16
loop(\(x,i).(x * ((x + 1) - i)),2,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A138402: 12 72 600 2352 14520 28392 83232 129960 279312 706440 922560 1872792 2824080 3416952 4877472 7887672
(loop(\(x,i).(x * (2 + i)),x,2) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A153426: 0 0 4 1 5 9 13 18 21 11 16 17 15 41 41 7
((1 - loop(\(x,i).(1 + (2 * (2x - (x mod 4)))),x,0)) mod loop(\(x,i).2x,x,2))
A284238: 1 0 6 10 10 42 42 170 170 682 682 2730 2730 10922 10922 43690
(loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + 2),1) - loop(\(x,i).2x,x,2))
A289612: 3 10 34 116 397 1366 4734
(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (2 + loop(\(x,i).(x div (2 - (x mod 2))),x,x))),x))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A095405: 2 3 5 7 11 13 17 19 22 23 29 31 37 41 43 47
(2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(x2 + ~2))),x))
A090697: 4 6 8 12 14 16 20 22 26 30 34 36 42 44 48 50
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x2 + ~1)),(x + 2))
A094550: 4 6 9 11 14 15 16 17 19 21 22 23 24 25 26 29
((x + 3) + loop(\(x,i).(x - ((1 + (loop(\(x,i).2x,x,2) mod (x + 2))) mod 2)),2,x))
A284936: 1 5 6 9 10 13 14 15 17 21 22 25 26 27 29 33
((x + 2) * (((x + 1) * loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,x)) div 2))
A293476: 0 15 180 1050 4200 13230 35280 83160 178200 353925 660660 1171170 1987440 3248700 5140800 7907040
((loop(\(x,i).(x div (~2 + (x mod 2))),x,(x + 1)) + (if x <= 0 then 1 else 4x)) div (x + 2))
A129843: 1 1 2 2 3 2 3 3 4 2 4 3 4 3 4 3
((x + 2) * loop(\(x,i).((x + 2) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)),x,2))
A162867: 4 15 40 85 168 287 464 693 1000 1419 1920 2561 3332 4215 5248 6477
loop(\(x,i).(1 + ((loop(\(x,i).(x - (x div ~8)),x,1) div 2) div 2)),1,2x)
A057042: 1 1 2 2 3 4 5 6 8 10 13 17 22 27 35 44
(~2x + (3 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),x)))
A240400: 0 1 5 6 19 20 24 25 65 66 70 71 84 85 89 90
((~2x + 1) + (2 * compr(\x.loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,2x),x)))
A165971: 1 5 9 13 15 15 19 19 21 25 27 27 29 29 33 33
(2x + (if ((x + (if ((x div 3) mod 3) <= 0 then 1 else x)) mod 3) <= 0 then 1 else 2))
A285251: 2 4 5 7 10 12 13 16 18 20 22 23 25 28 30 31
(~2x + (if x <= 0 then 1 else (2 * loop(\(x,i).((x + 1) - ((~x + (i mod 2)) div 4)),x,1))))
A103257: 1 2 4 6 10 14 20 28 40 54 72 96 126 164 212 272
loop(\(x,i).((if x <= 0 then 2 else ((1 + ((x * (1 + (x mod 3))) div 2)) div 2)) div 2),2,2x)
A240871: 0 0 0 0 0 1 0 2 1 1 2 2 0 2 2 1
(~x - loop(\(x,i).(x - (if (x + ~7) <= 0 then (2 + i) else 1)),x,x))
A124158: 0 1 3 6 10 15 21 28 34 40 46 52 58 64 70 76
(3 - (if x <= 0 then 1 else (if (~1 + ((x div 3) mod 3)) <= 0 then 3 else (x div 2))))
A010103: 2 0 0 0 0 0 0 0 ~1 0 0 0 0 0 0 ~4
loop(\(x,i).(if x <= 0 then 1 else 4x),1,(x + (x div 2) - (x div (4 + (x mod 2)))))
A310564: 1 4 12 16 20 24 32 36 40 48 52 56 60 68 72 76
(loop(\(x,i).4x,(x div 2),(1 - loop(\(x,i).(2 * (x - (i mod 2))),x,0))) - (x mod 2))
A266842: 1 2 20 43 336 687 5440 10943 87296 174847 1397760 2796543 22368256 44740607 357908480 715833343
(loop(\(x,i).10x,((x + 1) div 2),1) - ((x mod 2) + (if x <= 0 then 0 else 1)))
A256162: 1 8 9 98 99 998 999 9998 9999 99998 99999 999998 999999 9999998 9999999 99999998
((if (x mod 2) <= 0 then 1 else (if (x mod 3) <= 0 then 2 else (1 + ((x + (x div 2)) div 2)))) + (x mod 2))
A119479: 1 2 1 3 1 5 1 7 1 3 1
((if x <= 0 then 0 else (if (x mod (1 + (16 mod (x + 1)))) <= 0 then 1 else 2)) - (x mod 2))
A330720: 0 0 1 0 1 0 1 0 1 1 2 1 1 1 1 0
((2 * (1 + (if x <= 0 then 0 else (if (x mod (2 + ((~x + 2) mod 4))) <= 0 then 1 else 2)))) - (x mod 2))
A102066: 2 5 4 5 4 5 4 5 4 3 4 5 4 5 4 3
((if (x mod 4) <= 0 then (15 * (if x <= 0 then 1 else 2)) else 2) - (x mod 2))
A040232: 15 1 2 1 30 1 2 1 30 1 2 1 30 1 2 1
(x div (1 + ((if (~1 + (x mod 3)) <= 0 then 2 else 0) + (if (x + ~2) <= 0 then 1 else 2) + (x mod 2))))
A117173: 0 0 1 0 0 1 1 1 2 1 2 2 2 2 4 2
(((if (x mod 4) <= 0 then 17 else 1) * (if x <= 0 then 1 else 2)) - (x mod 2))
A040297: 17 1 2 1 34 1 2 1 34 1 2 1 34 1 2 1
(((if (x mod 4) <= 0 then 13 else 2) * (if x <= 0 then 1 else 2)) + (x mod 2))
A010218: 13 5 4 5 26 5 4 5 26 5 4 5 26 5 4 5
((if (x mod 5) <= 0 then (3 * (2 + (if x <= 0 then 0 else 2))) else 1) * (2 - (x mod 2)))
A010211: 12 1 2 1 2 12 2 1 2 1 24 1 2 1 2 12
((if x <= 0 then 1 else 0) - loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(x div 2),(x mod 2)))
A210628: 1 ~1 0 ~1 0 ~2 0 ~5 0 ~14 0 ~42 0 ~132 0 ~429
((2x + 3) + loop(\(x,i).((loop(\(x,i).(x * i),x,2) div (x + 1)) + (x * i)),x,1))
A255340: 4 7 12 64 4611686018427387903
(loop(\(x,i).8x,(~x + 3),1) * loop(\(x,i).5x,x,2))
A084912: 1024 640 400 250
(loop(\(x,i).3x,(x + ~1),5x) - loop(\(x,i).3x,x,2))
A053566: ~2 ~1 12 81 378 1539 5832 21141 74358 255879 866052 2893401 9565938 31355019 102036672 330024861
loop(\(x,i).(x + ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)) * (1 + i))),x,2)
A014285: 2 8 23 51 106 184 303 455 662 952 1293 1737 2270 2872 3577 4425
(2 * (2x + (if x <= 0 then 2 else (x + (if (~2 + (x div 5)) <= 0 then 1 else 4)))))
A274968: 4 8 14 20 26 32 38 44 50 56 62 68 74 80 86 98
(x + (if (x + ~1) <= 0 then 1 else loop(\(x,i).((x + 1) + (x div (2 - (i div ~4)))),x,0)))
A231408: 1 2 4 6 9
A130025: 1 2 4 6 9 12 15 19 24 29 35 42 50 58 67 77
(x + (if x <= 0 then 1 else (x - (if (20 mod (x + 3)) <= 0 then 0 else 1))))
A258049: 1 2 4 5 7 9 11 14 15 17 19 21 23 25 27 29
((~x + 1) + (9 * (if x <= 0 then 2 else (if (~4 + (x div 2)) <= 0 then 1 else 2))))
A175674: 19 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4
compr(\x.(if x <= 0 then 1 else (x mod (1 + ((1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)) div 3)))),x)
A333964-A279537-A025487: 1 2 4 6 8 12 16 24 30 32 36 48 60 64 72 96
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,11x)
A017399: 0 285311670611 584318301411328 50542106513726817 1196683881290399744 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(6x + 1)),x)
A166563: 5 6 10 13 15 17 18 20 25 27 28 30 31 34 35 36
compr(\x.(2 - loop(\(x,i).(if (x mod (3 + i)) <= 0 then 0 else x),x,(6x + 1))),x)
A024899: 1 2 3 5 6 7 10 11 12 13 16 17 18 21 23 25
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(6x + ~1)),x)
A153383: 0 2 4 7 10 11 12 14 17 18 21 22 24 25 27 30
((x + 1) + compr(\x.(1 - loop(\(x,i).(x div (if (x mod 2) <= 0 then ~2 else 1)),x,x)),(2x + 1)))
A285961: 4 7 12 16 20 23 27 31 36 39 44 48 52 57 60 64
(x * (if (x + ~2) <= 0 then 1 else (~1 + loop(\(x,i).(6x * (~1 + (2 * i))),x,1))))
A340546: 0 1 2 9717
(x + (if x <= 0 then 1 else (1 + (2 * (1 + loop(\(x,i).(x + (2 * ((2 + i) * (~1 + i)))),x,1))))))
A273314: 1 6 23 64 137 250 411 628 909 1262 1695 2216 2833 3554 4387 5340
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(8x + 1)),x)
A153327: 1 4 5 7 8 10 13 15 16 19 20 21 22 25 27 28
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(11x + 5))
A017458: 9765625 1099511627776 205891132094649 6278211847988224 79792266297612001 604661760000000000 3255243551009881201 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(11x + 5))
A017460: 244140625 281474976710656 150094635296999121 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x + (if x <= 0 then 1 else ((11x + 5) - (if (x + ~2) <= 0 then 1 else x))))
A337663: 1 16 28 38 49 60
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(11x + 10))
A017518: 10000000000 16679880978201 1125899906842624 21611482313284249 210832519264920576 1346274334462890625 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(11x + 10))
A017520: 1000000000000 7355827511386641 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(10x + 1),x,1),((x div 2) div 5),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A249517: 0 1 2 3 4 5 6 7 8 9 11111111111
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(4x + 1))),x)
A105133: 0 1 3 4 6 7 12 13 18 19 21 22 24 28 33 34
(x + (if (x + ~2) <= 0 then 1 else (3 * (1 + (2 * (if (~2 + (x div 3)) <= 0 then 0 else 2))))))
A265334: 1 2 3 6 7 8 9 10 11 24 25 26 27 28 29 30
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(7x + 3))
A017027: 177147 100000000000 34271896307633 1521681143169024 25408476896404831 238572050223552512 1532278301220703125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.(loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x) + ((x + 1) mod 3)),x)
A173177: 2 5 8 14 17 20 29 32 35 38 47 50 53 62 68 74
compr(\x.((1 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x)) mod 3),x)
A138972: 2 4 6 9 10 12 16 17 19 20 23 25 27 29 32 34
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(7x + 6))
A017063: 362797056 1792160394037 204800000000000 5559060566555523 70188843638032384 550329031716248441 3116402981210161152 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(if x <= 0 then 1 else compr(\x.(x mod (1 + (6 * (x mod 2)))),x)),1,3x)
A315320: 1 6 10 16 21 26 32 36 42 48 52 58 63 68 74 78
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(5x + ~1)),x)
A153275: 0 2 5 8 9 11 12 14 16 17 20 22 23 26 29 30
(~x + (if (x + ~1) <= 0 then 1 else (1 + compr(\x.(loop(\(x,i).(x * (x - i)),2,(x div 2)) mod (x + 1)),x))))
A007599: 1 0 1 1 1 1 2 3 4 5 5 5 6 7 8 9
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(x2 + x + ~1))),x)
A027861: 1 2 4 5 7 9 12 14 17 19 22 24 25 29 30 32
compr(\x.(loop(\(x,i).x2,2,(3 * (if (x mod (2 + (x mod 2))) <= 0 then 2 else 0))) mod (x + 1)),x)
A014121: 0 1 2 3 5 7 8 11 13 15 17 19 23 25 26 29
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(9x + 8))
A017267: 8589934592 34271896307633 3670344486987776 96549157373046875 1196683881290399744 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((~x2 + ~x) + loop(\(x,i).(x + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)),x,0))
A135267: 0 ~1 ~2 ~3 ~2 ~1 2 5 10 19 28 41 56 71 88 109
((x2 + 2x + 1) - (if (5 mod (if (x mod 2) <= 0 then 2 else x)) <= 0 then 2 else 0))
A083783: 1 2 9 16
A085960: 1 2 9 16 25 34 49 64 81 100 121 144 169 196 225 256
loop(\(x,i).(~1 + loop(\(x,i).(2x * (1 + (2 * i))),(2x + 1),2)),1,(x2 + x))
A112854: 11 665279 3497296636753919999 4611686018427387903
(x + loop(\(x,i).(3 * (if x <= 0 then 0 else (7x + ~3))),1,(x + ~1)))
A024814: 0 1 14 36 58 80 102 124 146 168 190 212 234 256 278 300
loop(\(x,i).(1 - (((x + 1) * (if (~2 + (x div 4)) <= 0 then 1 else 2)) mod 3)),(x + ~1),x)
A000494: 0 1 1 0 ~1 ~1 0 1 1 0 ~1 ~1 ~1 0 1 1
(x + (if x <= 0 then 0 else loop(\(x,i).(x + ((3 * ((x div 2) div 3)) div 2)),2,(x + ~1))))
A340718: 0 1 3 5 7 9 11 15 17 19 21 23 27 31 33 35
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (3 div (if x <= 0 then 1 else x)))
A301869: 6 9 5 7 0 0 0 0 0
((~x + 1) + loop(\(x,i).(if x <= 0 then 1 else (x + (2 * (x div (~1 + (4 * (1 + i))))))),x,x))
A237716: 1 1 1 1 1 1 1 3 3 5 5 7 7 9 13 15
(x * loop(\(x,i).(~x + (loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),i,1) + (x * i))),x,1))
A105927: 0 0 2 12 84 640 5430 50988 526568 5940576 72755370 961839340 13656650172 207316760352 3351430059614 57487448630220
(x + loop(\(x,i).(x + loop(\(x,i).(2x - (x div (~2 + ((~x + 2) div 4)))),1,i)),x,1))
A326665: 1 5 11 19 30 43 58 75 94 116 140 166 194 224 256 290
(2 div (if (~1 + ((1 + (if ((x + ~2) mod 5) <= 0 then 1 else x)) mod 3)) <= 0 then 2 else x))
A101808: 1 2 1 1 0 1 1 0 1 1 0 1 0 0 1 1
(if ((x + 1) mod 12) <= 0 then 1 else (x + (if (~4 + (x div 2)) <= 0 then 1 else 2)))
A239235: 1 2 3 4 5 6 7 8 9 10 12 1 14 15 16 17
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(6x + 2)),x)
A166569: 4 7 9 14 15 19 20 21 24 26 28 29 32 33 34 35
(2 div loop(\(x,i).(1 + ((~1 + (2 * (if (x + ~1) <= 0 then 2 else (2x + ~1)))) mod (x + 2))),2,x))
A045706-A045634: 1 2 1 0 1 1 0 0 1 2 1 0 1 0 0 0
(~x + (if ((x mod 3) div 2) <= 0 then (1 + (if (x mod 3) <= 0 then 0 else x)) else (2x + ~2)))
A239286: 1 1 0 ~2 1 3 ~5 1 6 ~8 1 9 ~11 1 12 ~14
(x + (((3 * (1 + loop(\(x,i).(x - (if (~x + i) <= 0 then (2 * i) else 0)),x,x))) div 2) div 2))
A203554: 0 1 2 4 3 5 6 8 10 7 9 11 12 14 16 18
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(9x + 4))
A017219: 4194304 1792160394037 584318301411328 25408476896404831 419430400000000000 3909821048582988049 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(7x + 4))
A017039: 4194304 285311670611 64268410079232 2384185791015625 36028797018963968 317475837322472439 1951354384207722496 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((if x <= 0 then 1 else x) - ((((x2 div 5) mod (x + 1)) div 2) mod 2)),2,x)
A285719: 1 1 2 3 3 5 6 7 7 7 10 11 11 13 14 15
compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x + ~2),x)),(x + (x div 8)))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A049543: 2 3 5 7 11 13 17 19 29 31 37 41 43 47 53 59
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,8x)),x)
A092022: 0 1 4 5 8 10 11 13 14 19 26 29 31 34 35 40
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(6x + 4)),x)
A166570: 2 7 9 11 12 16 17 22 23 24 26 27 30 32 33 37
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,(6x + 4))),x)
A138083: 0 1 2 4 5 6
A153218: 0 1 2 4 5 6 9 10 11 12 15 16 17 20 22 24
compr(\x.(1 - loop(\(x,i).(if x <= 0 then 1 else (x + ~11)),x,4x)),x)
A327423: 2 3 5 6 8 9 11 12 15 18 21 24 25 27 28 30
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(5x + 2)),x)
A153308: 2 5 7 8 11 14 17 18 20 21 23 24 26 28 29 32
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,10x)),x)
A102338: 0 1 2 4 5 7 8 10 11 16 17 19 22 23 26 28
(~x + (if x <= 0 then 1 else (2 + compr(\x.(loop(\(x,i).((x + ~2) * (x2 div 2)),2,x) mod (x + 1)),x))))
A127240: 1 2 2 2 3 3 3 3 3 4 5 6 7 8 8 8
((~x2 + ~2x) + loop(\(x,i).(x + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),i)),x,0))
A134181: 0 0 0 2 4 8 12 18 28 38 52 68 84 102 124 150
((~x2 + ~2x + ~1) + (2 * loop(\(x,i).2x,x,(~1 + loop(\(x,i).(2 * (x + i)),x,2)))))
A213754: 1 16 111 576 2631 11292 46927 191680 775599 3122076 12531591 50220912 201088855 804798268 3220143903 12882607872
(x + (if x <= 0 then 1 else (2x + ((x + (if (x mod 3) <= 0 then 2x else 1)) div 3))))
A298788: 1 3 7 12 13 17 24 23 27 36 33 37 48 43 47 60
(~x + loop(\(x,i).(x + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(1 + i),1)),x,2))
A120279: 2 11 45 170 631 2346 8780 33089 125466 478181 1830258 7030557 27088856 104647615 405187809 1571990918
(~x + (if x <= 0 then 1 else ((x + loop(\(x,i).(6x2 + 8x + 4),2,x)) div 2)))
A334012: 1 1045 5985
(2x + ((1 + (x * loop(\(x,i).((x + 1) - (if x <= 0 then 2 else (2 * i))),x,x))) div (x + 1)))
A275119: 1 2 3 4 6 5 7 8 10 12 9 11 13 14 16 18
loop(\(x,i).(4x - loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),i,1)),x,x)
A038806: 0 1 10 69 406 2186 11124 54445 259006 1205790 5519020 24918306 111250140 492051124 2159081192 9409526397
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(x + 8))),x)
A153143: 0 2 5 6 9 11 12 14 17 20 21 24 26 27 30 32
(~x + loop(\(x,i).((2x + 12) + (if x <= 0 then ~4 else 1)),4,x))
A122475: 155 210 225 240 255
(~x + loop(\(x,i).(x + (if x <= 0 then 1 else ((x mod (~3 - (x div 4))) mod 2))),2,x))
A161123: 1 0 1 0 0 1 0 1 0 1 0 0 0 1 0 2
compr(\x.(20 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),x)
A231073: 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89
(((x + 1) * loop(\(x,i).x3,2,(x + 1))) + (x * loop(\(x,i).x3,2,x)))
A036088: 1 1025 60073 1107625 10814201 70231801 342941425 1356217073 4560526225 13486784401 35937424601 87854788825 199775856073 427113146825 865905045601 1676162018401
(((x + 1) * loop(\(x,i).x3,2,(x + 1))) - (x * loop(\(x,i).x3,2,x)))
A022526: 1 1023 58025 989527 8717049 50700551 222009073 791266575 2413042577 6513215599 15937424601 35979939623 75941127625 151396163127 287395735649 522861237151
(loop(\(x,i).11x,x,1) - (x * loop(\(x,i).x3,2,x)))
A024137: 1 10 ~903 ~57718 ~1033935 ~9604574 ~58694615 ~262988078 ~859382943 ~1128836710 15937424601 259374246010 3076511012497 34384853652082 379460578928265 4176671519025026
(loop(\(x,i).4x,x,1) - loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,x))
A319028: 1 2 6 22 88 364 1522 6374 26640 110980 460716 1906172 7862416 32341144 132707626 543376774
(loop(\(x,i).x3,2,(x2 + 2x + 1)) + loop(\(x,i).x3,2,x2))
A036096: 1 262145 387682633 69106897225 3883416742361 105374653934041 1729973554578865 19642812107392433 168109033806481105 1150094635296999121 4611686018427387903 4611686018427387903
(loop(\(x,i).12x,x,1) - (x2 * loop(\(x,i).x3,2,x)))
A024151: 1 11 ~1904 ~175419 ~4173568 ~48579293 ~359811072 ~1941494935 ~8159952896 ~26221279257 ~38082635776 457696700077 8173092077568 105201044985035 1279868899379200 15398371818726993
(loop(\(x,i).10x,x,1) - (x2 * loop(\(x,i).x3,2,x)))
A024125: 1 9 ~1948 ~176147 ~4184304 ~48728125 ~361797056 ~1967326743 ~8489934592 ~30381059609 ~90000000000 ~185311670611 256991629312 8207839605963 95950434830336 991350244140625
(loop(\(x,i).7x,x,1) - (x2 * loop(\(x,i).x3,2,x)))
A024086: 1 6 ~1999 ~176804 ~4191903 ~48811318 ~362679407 ~1976503200 ~8584169791 ~31340706002 ~99717524751 ~283334343868 ~729167083487 ~1695271383630 ~3371342096815 ~3902194349432
loop(\(x,i).11x,x,(x2 * loop(\(x,i).x3,2,x)))
A098880: 0 11 247808 235782657 61408804864 7863818359375 642717115324416 38532504363714053 1841328767004311552 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).11x,x,1) - loop(\(x,i).x2,2,x3))
A024139: 1 10 ~3975 ~530110 ~16762575 ~243979574 ~2175010775 ~13821800030 ~68505117855 ~280071588790 ~974062575399 ~2853116706110 ~5777672071535 11224627021450 323055921207945 4047501831525026
(if (x mod 3) <= 0 then (~1 + ((1 + ((x div (2 - (x mod 2))) div 3)) mod 3)) else 0)
A163533: 0 0 0 1 0 0 1 0 0 0 0 0 ~1 0 0 ~1
loop(\(x,i).((x + 1) + (((2x + 1) div 7) + (x div 3))),x,0)
A324015: 0 1 2 3 6 10 17 28 46 75 122 198 321 520 842 1363
(((x + 2) mod (1 + (((x + 1) mod 7) mod 3))) + (if x <= 0 then 0 else 1))
A299090-A185102: 0 1 1 2 1 1 1 2 2 1 1 2 1 1 1 3
(((x + 2) mod (1 + (((1 + (x * (x div 2))) div 3) mod 3))) + (if x <= 0 then 0 else 1))
A341593-A305253-A288636: 0 1 1 2 1 1 1 2 2 1 1 1 1 1 1 3
(((1 + (x mod (1 + ((x mod 6) mod (1 + (x div 2)))))) div 2) + (if x <= 0 then 0 else 1))
A084113: 0 1 1 2 1 2 1 2 2 2 1 4 1 2 2 3
((x div (2 + (2x div (1 + (x mod (2 * (1 + (x mod 4)))))))) + (if x <= 0 then 0 else 1))
A333381: 0 1 1 2 1 1 1 3 1 1 2 2 1 1 2 4
(2 + (((~x + 1) mod (1 + ((x - ((x div 3) mod 3)) div 2))) + (if x <= 0 then 0 else 1)))
A214613: 2 3 4 3 4 5 4 3 4 5 6 5 4 5 4 3
((((2x + 1) mod (1 + (x div (2 + ((x div 2) mod 3))))) div 2) + (if x <= 0 then 0 else 1))
A179647: 0 1 1 1 1 1 1 2 2 2 1 2 3 4 3 1
((((x + 1) mod (1 + (2 * ((1 + (((x + 1) div 2) div 2)) div 2)))) div 2) + (if x <= 0 then 0 else 1))
A134024: 0 1 1 1 2 1 1 2 1 1 2 2 2 3 1 1
(((x - (x div (2 - ((x3 div 8) mod 2)))) div 2) + (if x <= 0 then 0 else 1))
A049695: 0 1 1 1 2 1 1 3 3 1 1 4 4 4 1 1
((((x + ((((2x + ~2) mod (2 + (x div 2))) div 2) div 2)) div 2) mod 2) + (if x <= 0 then 0 else 1))
A283156: 0 1 2 2 1 1 2 2 1 2 2 1 1 1 1 2
((((x mod (1 + (10 mod (x + 1)))) mod 2) + (if x <= 0 then 0 else 1)) - (x mod 2))
A001877: 0 0 1 0 1 0 1 1 1 0 1 0 2 0 2 0
(1 + ((x + 1) div 2) - (if (x mod (1 + (2 * (x mod 7)))) <= 0 then 0 else 1))
A342515: 1 1 1 2 2 3 3 5 4 5 5 6 6 8 8 9
(1 + ((2 * ((7x + 3) + (x div 3))) + (if x <= 0 then 0 else 1)))
A063240: 7 22 36 52 66 80 96 110 124 140 154 168 184 198 212 228
(if x <= 0 then 0 else (1 + (3 mod (1 + ((x div 2) mod (1 + (x mod (1 + (x div 3)))))))))
A335428: 0 1 1 2 1 1 1 2 2 1 1 2 1 1 1 4
(if (x mod (1 + (x mod 3))) <= 0 then (1 + (x mod (1 + (x mod (1 + (x div 3)))))) else 1)
A327168: 1 1 1 2 1 1 1 1 1 2 2 1 1 1 1 4
((x + 3) - loop(\(x,i).2x,(1 + (x div (3 + ((x div 2) div 3)))),1))
A336860: 1 2 3 2 3 4 5 6 3 4 5 6 7 8 9 2
(~1 + (if x <= 0 then 2 else (x div (1 + (x mod (1 + (x mod (1 + (x div (2 * (2 - (x mod 2))))))))))))
A166586: 1 0 1 0 3 0 5 0 1 0 9 0 11 0 3 0
((x + 1) div (if (2 - (x div 2)) <= 0 then (1 + (x mod (1 + (x mod (3 + (x mod 2)))))) else 1))
A345941: 1 2 3 4 5 3 7 2 3 5 11 3 13 7 5 4
loop(\(x,i).x2,1,(1 + (x mod (1 + ((4 + (x div 2)) mod (1 + (x div 3)))))))
A162400-A008833: 1 1 1 4 1 1 1 4 9 1 1 4 1 1 1 16
(1 + (x mod ((x + 1) - ((if (x mod 4) <= 0 then 2 else (x mod 2)) mod (1 + (x div 3))))))
A194446: 1 2 3 1 5 1 7 1 2 1 11 1 2 1 15 1
(1 + (x mod (1 + ((1 + (x div 2)) mod (1 + (loop(\(x,i).~2x,x,1) mod (x + 1)))))))
A143201: 1 1 1 1 1 2 1 1 1 4 1 2 1 6 3 1
(1 + (x div (1 + (x mod (1 + (x mod (2 + (loop(\(x,i).(2 * (x + i)),x,1) mod (x + 1)))))))))
A132740: 1 1 3 1 1 3 7 1 9 1 11 3 13 7 3 1
((x + 1) div (1 + (x div (1 + (x mod (1 + (x div (2 + (if (x mod 3) <= 0 then 1 else 2)))))))))
A046805: 1 1 1 2 1 2 1 2 3 2 1 3 2 2 3 4
(1 + ((x + ~1) mod (1 + (9 * (if (x mod (2 + (x mod 2))) <= 0 then x else 1)))))
A118541: 1 1 2 3 4 5 6 7 8 9 10 1 12 3 14 15
loop(\(x,i).(x * i),(1 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4)))),1)
A112624: 1 1 1 2 1 1 1 6 2 1 1 2 1 1 1 24
(~1 + loop(\(x,i).2x2,1,(25x + 26)))
A154375: 1351 5201 11551 20401 31751 45601 61951 80801 102151 126001 152351 181201 212551 246401 282751 321601
(1 + (if x <= 0 then 0 else (1 + ((x div 2) mod (1 - ((x + 2) mod (~1 + ((~x + 2) div 4))))))))
A071188: 1 2 2 3 2 2 2 2 3 2 2 3 2 2 2 5
(1 + ((x + (9 * (if x <= 0 then 1 else 2))) mod (1 + ((x + 1) div 3))))
A038566: 1 1 1 2 1 3 1 2 3 4 1 5 1 2 3 4
(1 + loop(\(x,i).10x,(11x + 2),1))
A230304: 101 10000000000001 4611686018427387903
(1 + (loop(\(x,i).4x,x,2) div (1 + (((x mod 4) - (x div 2)) mod 3))))
A131342: 3 5 17 43 257 683
(if x <= 0 then 0 else (1 + ((x div (2 * (2 - ((x * (x div 2)) mod 2)))) mod (1 + (x div 3)))))
A064741: 0 1 1 2 2 2 2 1 3 3 3 2 4 4 4 2
(1 + loop(\(x,i).(1 + (5 * ((2x + 2) - (x mod 2)))),(2x + 1),1))
A156675: 17 1717 171717 17171717 1717171717 171717171717 17171717171717 1717171717171717 171717171717171717 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(10x + 90),(2x + 1),1))
A274743: 99 10989 1099989 109999989 10999999989 1099999999989 109999999999989 10999999999999989 1099999999999999989 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x - (x div (1 + (x mod (1 + (loop(\(x,i).2x,x,(1 + (x mod 2))) mod (2x + 1)))))))
A326055: 0 1 2 0 4 5 6 4 0 9 10 8 12 13 14 0
((1 + (x div 4)) div (1 + (x mod (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))))
A322076: 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 4
(x div (1 + ((x + ~1) mod (1 + (if (x mod (1 + (((x + 1) div 2) div 3))) <= 0 then x else 1)))))
A340089: 0 1 1 1 1 5 1 7 1 9 1 11 1 13 7 1
(1 + (x div (1 + ((x mod 4) mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1)))))
A323129-A305007-A053585: 1 2 3 4 5 3 7 8 9 5 11 3 13 7 5 16
(1 + (x div (1 + ((~1 + (loop(\(x,i).(2x + 1),x,0) * (1 + (x mod 2)))) mod (x + 1)))))
A089384: 1 1 1 2 1 3 1 2 3 5 1 6 1 7 5 2
((2x + 1) mod (1 + (x div (1 + ((~1 + loop(\(x,i).2x,(x + ~2),2)) mod (x + 1))))))
A053734: 0 0 1 0 1 1 1 0 2 1 1 2 1 1 5 0
(1 + (x div (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))))))
A327398-A324371-A323616-A276440-A162325-A006530: 1 2 3 2 5 3 7 2 3 5 11 3 13 7 5 2
((x + 2) mod (1 + (x mod (1 + (x div (2 + (if ((x + 1) mod 5) <= 0 then 2 else 1)))))))
A308638: 0 0 0 1 0 1 0 1 1 0 0 1 2 3 1 1
(1 + (x mod (1 + (2 * ((x + ~1) mod (1 + (x div (2 + (if (x mod 3) <= 0 then 1 else 2)))))))))
A202853: 1 1 1 1 2 1 2 1 3 1 1 3 1 1 3 1
(1 + (x mod (1 + (2 * (~1 + ((if (~2 + (x div 3)) <= 0 then 2 else ((x + 1) div 2)) div 2))))))
A065648: 1 1 1 1 1 1 1 1 1 1 2 2 3 4 5 2
(if (~1 + (x mod 5)) <= 0 then (1 + ((3 * ((x div 2) div 3)) div 2)) else 1)
A194799: 1 1 1 1 1 1 2 1 1 1 2 2 1 1 1 4
(1 + loop(\(x,i).3x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1))
A151712: 2 4 4 10 4 10 10 28 4 10 10 28 10 28 28 82
(loop(\(x,i).3x,x,1) mod 113)
A036142: 1 3 9 27 81 17 51 40 7 21 63 76 2 6 18 54
(~1 + (if x <= 0 then 1 else 6x) - ((~2x + 4) div 7))
A145005: 0 5 11 18 24 30 37 43 49 55 62 68 74 81 87 93
((x + 2) - loop(\(x,i).2x,(~1 + ((x - ((x2 div 2) div (x + 3))) div 2)),1))
A064067: 1 2 3 4 5 5 6 7 6 7 8 9 6 7 8 9
(1 + (if x <= 0 then 0 else (1 + ((x - ((x mod (2 - (x mod ~5))) div 2)) div 2))))
A023190: 1 2 2 3 4 4 5 5 6 6 7 6 7 8 8 9
(1 + (x mod (1 + (x div (2 + ((loop(\(x,i).(2x + 2),(x + ~2),2) mod (x + 1)) div 2))))))
A085392: 1 1 1 2 1 3 1 2 3 5 1 3 1 7 5 2
(1 - ((x * (x div 2)) mod (1 + (if ((x + 1) mod 8) <= 0 then 8 else 1))))
A087810: 1 1 1 0 1 1 1 ~2 1 1 1 0 1 1 1 ~5
(1 + ((~1 + loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2)) mod 9))
A086359: 2 6 2 7 9 6 3 9 2 4 3 7 2 9 9 9
(1 + ((if (~4 + (x div 2)) <= 0 then x else (x + 3)) + (x div 9)))
A050761: 1 2 3 4 5 6 7 8 9 11 15 16 17 18 19 20
(1 + (~4 mod (1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 8))))
A286357: 1 1 3 1 2 3 4 1 1 2 3 3 2 4 4 1
(12x mod (~1 + loop(\(x,i).(10x + 4),2,1)))
A121578: 0 12 24 36 48 60 72 84 96 108 120 132 1 13 25 37
(2 div (1 + ((1 + (if ((x + 2) mod (2 + ((x div 2) mod 2))) <= 0 then x else 0)) mod 5)))
A083093: 1 1 1 1 2 1 1 0 0 1 1 1 0 1 1 1
(1 + ((1 + (loop(\(x,i).(1 + (2x * (~1 + (2 * i)))),x,1) div 2)) div 5))
A320945: 1 1 3 20 268
loop(\(x,i).x6,1,(10x + 6))
A017346: 46656 16777216 308915776 2176782336 9474296896 30840979456 82653950016 192699928576 404567235136 782757789696 1418519112256 2436396322816 4001504141376 6327518887936 9685390482496
(loop(\(x,i).7x,x,1) mod 29)
A070413: 1 7 20 24 23 16 25 1 7 20 24 23 16 25 1 7
(~1 + (5 * (2 + loop(\(x,i).(10x + 8),(x + 2),1))))
A108896: 949 9449 94449 944449 9444449 94444449 944444449 9444444449 94444444449 944444444449 9444444444449 94444444444449 944444444444449 9444444444444449 94444444444444449 944444444444444449
(~1 + loop(\(x,i).x2,1,(~49x + ~10)))
A157370: 99 3480 11663 24648 42435 65024 92415 124608 161603 203400 249999 301400 357603 418608 484415 555024
((10x + 11) + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2))
A264646: 11 21 32 41 53 62 74 81 95 103 116 122 137 144 158 161
loop(\(x,i).x6,1,(10x + 9))
A017382: 531441 47045881 594823321 3518743761 13841287201 42180533641 107918163081 243087455521 496981290961 941480149401 1677100110841 2839760855281 4608273662721 7212549413161 10942526586601
(~1 + (10 * (2 + (if (~1 + (x div 4)) <= 0 then x else 8))))
A151360: 19 29 39 49 59 69 79 89 99 99 99 99 99 99 99 99
(loop(\(x,i).7x,x,1) mod 41)
A070424: 1 7 8 15 23 38 20 17 37 13 9 22 31 12 2 14
loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(5x2 + 10x),1)
A147714: 1 35357670 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((if (x mod 2) <= 0 then (~1 + ((16 mod (x + 1)) div 2)) else 0) mod 3))
A102368: 3 1 3 1 3 1 1 1 3 1 2 1 1 1 3 1
(if x <= 0 then 0 else (1 + ((x mod (1 + (x mod (1 + (x div (2 + ((x div 2) mod 2))))))) div 3)))
A165112: 0 1 1 1 1 1 1 1 1 2 1 2 1 3 2 2
(1 + (3 * loop(\(x,i).(6 * (3x + (x div 2))),(x + 1),1)))
A203872: 55 1135 23815 500095 10501975 220541455 4631370535 97258781215 2042434405495 42891122515375 900713572822855 18914985029279935 397214685614878615 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(((x * (x - (x mod 3))) mod 7) div 3),1)
A140130: 1 1 1 1 2 1 1 1 4 2 4 1 2 1 1 1
(~1 + (3 * loop(\(x,i).(7x + ~3),2x,5)))
A233078: 14 662 32414 1588262 77824814 3813415862 186857377214 9156011483462 448644562689614 21983583571791062 1077195595017762014 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((1 + ((x + 1) div (2 + (if (x mod 4) <= 0 then 3 else (x mod 2))))) div 3))
A006371: 1 1 1 1 1 2 2 2 1 2 3 2 2 2 3 3
(1 + (if x <= 0 then 1 else 5x) - ((1 + (x div (~2 + (x mod 2)))) mod 3))
A315405: 1 6 11 15 19 24 30 36 41 45 49 54 60 66 71 75
(loop(\(x,i).5x,x,1) mod 73)
A036133: 1 5 25 52 41 59 3 15 2 10 50 31 9 45 6 30
(loop(\(x,i).7x,x,1) mod 37)
A070420: 1 7 12 10 33 9 26 34 16 1 7 12 10 33 9 26
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),18x,1)
A147717: 1 477638700 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),18x,1)
A147769: 1 1767263190 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (if x <= 0 then 1 else 5x) - ((1 + (x div (2 - (x mod 2)))) mod 3))
A313280: 1 4 9 15 21 26 30 34 39 45 51 56 60 64 69 75
loop(\(x,i).x6,1,(12x + 11))
A017658: 1771561 148035889 1838265625 10779215329 42180533641 128100283921 326940373369 735091890625 1500730351849 2839760855281 5053913144281 8550986578849 13867245015625 21691961596369
(1 + (((x + 1) * (if (x + ~1) <= 0 then 3 else ((x + 2) div (2 + (x mod 2))))) mod 3))
A034002: 1 1 1 2 1 1 2 1 1 1 1 1 2 2 1 3
((x + 1) mod (1 + (6 * (if (16 mod (x + 1)) <= 0 then 2 else 0))))
A087263: 1 2 0 4 0 0 0 8 0 0 0 0 0 0 0 3
(~1 + ((1 - ((1 + ((if (x mod 2) <= 0 then x else ~x) mod 5)) div 2)) mod 3))
A330033: 0 1 ~1 ~1 1 0 ~1 1 1 ~1 0 1 ~1 ~1 1 0
(1 + ((2 * (1 + ((1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2)) div 2))) div 3))
A333860: 1 1 2 1 2 2 3 1 3 2 3 2 3 3 4 1
(if x <= 0 then 1 else ((2x + 2) div (~1 + (6 * (1 + (4 * (x mod 2)))))))
A005868: 1 0 1 0 2 0 2 0 3 0 4 0 5 0 6 1
(1 + (6 * (3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A129071: 19 25 37 49 73 85 109 121 145 181 193 229 253 265 289 325
loop(\(x,i).x6,1,(12x + 7))
A017610: 117649 47045881 887503681 6321363049 27680640625 90458382169 243087455521 567869252041 1194052296529 2313060765625 4195872914689 7212549413161 11853911588401 18755369578009
loop(\(x,i).x6,1,(12x + 5))
A017586: 15625 24137569 594823321 4750104241 22164361129 75418890625 208422380089 496981290961 1061520150601 2081951752609 3814697265625 6611856250609 10942526586601 17416274304961
(1 + ((2 + (((x + (if (x mod 2) <= 0 then x else 1)) div 3) mod (1 + (x div 2)))) div 3))
A175357: 1 1 2 2 2 2 1 2 1 2 1 3 2 3 2 3
loop(\(x,i).x7,1,(6x + 5))
A016975: 78125 19487171 410338673 3404825447 17249876309 64339296875 194754273881 506623120463 1174711139837 2488651484819 4902227890625 9095120158391 16048523266853 27136050989627
(if x <= 0 then 0 else (1 + ((2 * ((1 + (3x mod (2 + (x div 2)))) div 2)) div 3)))
A333632: 0 1 1 1 1 2 2 1 1 2 1 3 2 3 3 1
(x div (1 + ((4 * (((if (x mod 2) <= 0 then 2 else x) + (x div 2)) div 3)) div 3)))
A241664: 0 1 1 1 2 1 3 1 2 1 3 1 4 1 2 1
(1 + (((((x + 1) * (if x <= 0 then 1 else (x - ((~x + 2) div 4)))) div 2) div 2) mod 3))
A030410: 1 1 2 2 1 1 1 1 2 1 1 1 1 3 1 2
(if x <= 0 then 0 else (1 + ((2 * (((2x + 1) mod (2 + (x div 4))) div 2)) mod 3)))
A132468: 0 1 1 1 1 3 1 1 1 3 1 3 1 3 2 1
(loop(\(x,i).7x,x,1) mod 47)
A070429: 1 7 2 14 4 28 8 9 16 18 32 36 17 25 34 3
(~1 + ((2 * (2 + ((x + (if (~4 + (x div 2)) <= 0 then 1 else 4)) div 2))) div 3))
A295629: 0 1 1 1 1 2 2 3 3 3 5 5 5 5 6 6
(if (x mod 4) <= 0 then 1 else (1 + ((2 + (((x div 3) * (x div 2)) div 2)) div 3)))
A103626: 1 1 1 1 1 2 2 2 1 3 4 4 1 5 6 7
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 13)
A039711: 2 3 5 7 11 0 4 6 10 3 5 11 2 4 8 1
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) mod 11)
A159988: 1 1 2 5 3 9 0 0 0 0 10 2 2 4 10 6
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 11)
A039709: 2 3 5 7 0 2 6 8 1 7 9 4 8 10 3 9
loop(\(x,i).x7,1,(12x + 1))
A017539: 1 62748517 6103515625 94931877133 678223072849 3142742836021 11047398519097 32057708828125 80798284478113 182803912081669 379749833583241 736141813551277 1347646586640625 2351243277537493
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(12x + 1))
A050491: 1 13 50 185 686 2562 9636 36465 138710 529958 2032316 7818538 30161740 116635300 451980360 1754766945
loop(\(x,i).x6,1,(~11x + ~1))
A017406: 1 2985984 148035889 1544804416 8303765625 30840979456 90458382169 225199600704 496981290961 1000000000000 1870414552161 3297303959104 5534900853769 8916100448256 13867245015625
loop(\(x,i).11x,(x div 2),(1 + (6 * (x mod 2))))
A018680: 1 7 11 77 121 847
loop(\(x,i).x6,1,(9x + 7))
A017250: 117649 16777216 244140625 1544804416 6321363049 19770609664 51520374361 117649000000 243087455521 464404086784 832972004929 1418519112256 2313060765625 3635215077376 5534900853769
loop(\(x,i).x6,1,(9x + 5))
A017226: 15625 7529536 148035889 1073741824 4750104241 15625000000 42180533641 98867482624 208422380089 404567235136 735091890625 1265319018496 2081951752609 3297303959104 5053913144281
((if ((x + ((x div 2) div 3)) mod 3) <= 0 then 1 else 0) * (1 + (2x mod 3)))
A263146: 1 0 0 1 0 0 0 0 2 0 0 2 0 3 0 0
loop(\(x,i).21x,(5x + 3),1)
A013900: 9261 37822859361 154472377739119461 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).22x,(5x + 3),1)
A013904: 10648 54875873536 282810057883082752 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).19x,(5x + 3),1)
A013892: 6859 16983563041 42052983462257059 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).23x,(5x + 3),1)
A013908: 12167 78310985281 504036361936467383 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((x + loop(\(x,i).2x,(x + ~1),((x div 2) - ((x + ~1) div 3)))) div 3))
A191425: 1 1 2 3 5 8 24 24
loop(\(x,i).x7,1,(9x + 1))
A017179: 1 10000000 893871739 13492928512 94931877133 435817657216 1522435234375 4398046511104 11047398519097 24928547056768 51676101935731 100000000000000 182803912081669 318547390056832
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(9x + 1))
A050479: 1 10 38 140 518 1932 7260 27456 104390 398684 1528436 5878600 22673308 87662200 339653880 1318498920
(if x <= 0 then 0 else ((x + 1) - ((x * ((x mod (1 + ((~x + 2) mod 4))) div 2)) div 3)))
A337868: 0 2 3 3 5 6 7 6 7 10 11 9 13 14 15 11
(2 - (if (x mod 5) <= 0 then 1 else ((1 + (x mod 4)) mod (1 + (x mod 3)))))
A143477: 1 2 2 2 1 1 2 2 1 2 1 1 2 2 2 1
(1 + ((x div 2) div (1 + (x mod (2 + (if (16 mod (x + 1)) <= 0 then 1 else x))))))
A299152: 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 8
loop(\(x,i).2x,compr(\x.(x mod (1 + (4 * (x mod (2 + (x mod 2)))))),(x + 3)),1)
A073718: 16 64 256 512 1024 4096 16384 32768 65536 262144 1048576 2097152 4194304 16777216 33554432 67108864
(1 + ((x * (if (x mod 2) <= 0 then 4 else ((x + 1) mod (2 + (x mod 2))))) div (x + 3)))
A199570: 1 1 2 1 3 1 3 2 3 1 4 1 4 2 4 1
loop(\(x,i).2x,(~1 + (((3 * (2x + (x div 4))) div 2) + (x div 2))),1)
A224446: 1 4 64 512 16384 131072 2097152 16777216 1073741824 8589934592 137438953472 1099511627776 35184372088832 281474976710656 4503599627370496 36028797018963968
(1 + (x div (1 + ((if ((x + 2) mod (2 + (x mod 2))) <= 0 then 1 else 6) + (x mod 2)))))
A036445: 1 1 2 1 3 1 4 3 5 2 6 2 7 5 8 2
(1 + (x mod (1 + ((if ((x + 2) mod 8) <= 0 then 0 else 1) * (x div (2 - (x mod 2)))))))
A175542: 1 2 1 4 2 6 1 8 4 10 5 12 6 14 1 16
loop(\(x,i).(10x + 1),(17x + 1),1)
A004022: 11 1111111111111111111 4611686018427387903
(1 + (loop(\(x,i).i,((2x + 1) mod 19),1) mod (x + 1)))
A068505: 1 2 3 4 5 6 7 8 9 2 3 5 7 9 11 13
(1 + compr(\x.(~1 + ((x + 1) mod ((x + 1) - (loop(\(x,i).2x,x,1) mod (x + 1))))),(x + 1)))
A166159: 2 3 4 5 7 8 11 12 13 16 17 19 23 29 31 32
(1 + compr(\x.(~1 + (x mod (1 + ((loop(\(x,i).2x,x,1) - (x mod 2)) mod (x + 1))))),(x + 1)))
A339563: 2 3 5 6 7 10 11 13 14 17 19 21 22 23 26 29
(~1 + ((~1 + loop(\(x,i).2x,x,(8 - ((x + 2) div 3)))) div (x + 1)))
A272696: 6 5 8 12 18 30
(1 + compr(\x.(~1 + (loop(\(x,i).(2x + 1),(x div (1 + (x mod 2))),1) mod (x + 1))),(x + 1)))
A085118-A068422: 2 3 5 6 7 10 11 13 14 17 19 22 23 26 29 31
loop(\(x,i).(i div 3),((2 - (2x mod (4 + (x div 4)))) mod (x + 1)),1)
A321884-A086460: 1 1 0 1 1 0 1 2 2 0 1 3 4 3 0 1
loop(\(x,i).x7,1,(8x + 7))
A017155: 823543 170859375 3404825447 27512614111 137231006679 506623120463 1522435234375 3938980639167 9095120158391 19203908986159 37725479487783 69833729609375 122987386542487 207616015289871
((4x + 3) + (loop(\(x,i).((x2 + ~x) div 2),2,(x + 2)) div 3))
A227265: 3 8 16 30 54 93 153 241 365 534 758 1048 1416 1875 2439 3123
loop(\(x,i).(5 * (x + ((2x * (~1 + (2 * i))) div (1 + i)))),(x + ~1),1)
A025750: 1 1 10 150 2625 49875 997500 20662500 439078125 9513359375 209293906250 4661546093750 104884787109375 2380077861328125 54401779687500000 1251240932812500000
((x + 1) - ((if (2x mod (4 + (x div 4))) <= 0 then (x div ~2) else 0) div 2))
A132128: 1 2 4 4 5 8 7 8 9 13 11 12 13 14 19 16
(2 - (if (2 - (2x mod (4 + (x div 4)))) <= 0 then ((x div 2) div ~2) else 1))
A183110: 1 2 1 3 3 1 4 4 4 1 5 5 5 5 1 6
(1 + (loop(\(x,i).((x + 2) + (x div (1 + ((x div 2) mod (2 + (x mod 2)))))),x,0) div 2))
A043868-A043859-A043851-A043844-A043838: 1 2 3 5 10 15 21 42 63 85 170 255 341 682 1023 1365
(~1 + (2 * loop(\(x,i).i,((x div 2) div (1 + (x mod (1 + (x mod (3 + (x mod 2))))))),1)))
A307410-A305444: 1 1 1 1 3 1 5 1 1 3 9 1 11 5 3 1
(1 + ((1 + (x div (1 + (loop(\(x,i).(3 * (x + i)),x,0) mod (2x + 1))))) div 2))
A218775: 1 2 2 1 2 1 2 2 1 3 1 1 1 2 1 3
(x div (1 + ((1 + (x div (if (x mod (1 + ((x + 2) div 5))) <= 0 then 2 else 1))) div 2)))
A249809: 0 1 1 1 2 1 2 1 1 3 1 1 3 1 1 1
(1 + (2 * (1 + (7 * (5 + loop(\(x,i).2x,x,1))))))
A305266: 87 101 129 185 297 521 969 1865 3657 7241 14409 28745 57417 114761 229449 458825
(1 + ((1 + (x mod (1 + (x div (2 + (loop(\(x,i).2x,x,3) mod (x + 1))))))) div 2))
A333940: 1 1 1 2 1 2 1 3 1 2 2 4 1 2 1 5
(1 + ((1 + (loop(\(x,i).((x + 2) - ((~x + 1) div 3)),x,1) div 5)) div 2))
A147663: 1 1 2 2 3 3 4 5 7 9 12 16 21 28 37 50
(1 + (2 * ((2x + 1) div (1 + (3 * loop(\(x,i).(x div (1 + (x mod 2))),x,x))))))
A135561: 3 7 1 15 1 3 1 31 1 3 1 7 1 3 1 63
(1 + ((1 + ((1 + (x div 3)) div (1 + (loop(\(x,i).2x,x,1) mod (x + 2))))) div 2))
A319864: 1 1 2 1 1 1 3 2 1 1 1 1 1 2 4 1
(1 + (2 * (x mod (1 + ((~1 + loop(\(x,i).2x,(x div (2 + (x mod 2))),2)) mod (x + 1))))))
A135540: 1 3 1 7 3 3 1 15 7 7 3 7 3 3 1 31
(~1 + (x mod 2) - ((1 + ((x + 1) div loop(\(x,i).(x div (~2 + (x mod 2))),x,(x + 1)))) div 2))
A118824: ~2 1 ~2 2 ~2 1 ~2 4 ~2 1 ~2 2 ~2 1 ~2 8
(1 + (loop(\(x,i).(2 * (x - ((x + (x div 3)) div 5))),(x + ~1),1) div 2))
A068921: 1 1 2 3 4 6 9 13 19 28 41 60 88 129 189 277
(2 - (x div (~1 - ((x + 1) mod (2 * (1 + (if (x mod (2 + (x mod 2))) <= 0 then 0 else 2)))))))
A064916: 2 3 3 5 4 7 5 5 6 11 7 13 8 7 9 17
(~1 + (2 * (~1 + (2 * loop(\(x,i).(10x + 16),(2x + ~1),1)))))
A267920: 1 101 11101 1111101 111111101 11111111101 1111111111101 111111111111101 11111111111111101 1111111111111111101 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else ((2x + 3) - ((x div (1 + (2 * ((x + ~1) mod 3)))) mod 2)))
A007656: 1 4 7 9 11 12 14 16 19 20 23 24 27 28 31 32
(if x <= 0 then 0 else (1 + ((1 + (x div 3)) div (2 * (1 + ((x + 2) mod 6))))))
A253642: 0 1 1 1 2 1 1 1 1 1 3 2 1 1 1 1
(1 + ((1 + ((x + 2) mod (2 + ((~1 + loop(\(x,i).2x,x,4)) mod (x + 1))))) div 2))
A097028: 1 1 1 1 2 2 3 1 2 2 2 3 3 4 1 1
(1 + ((1 + (((x + 1) * (loop(\(x,i).2x,x,1) div (x2 + 2x + 2))) div 2)) div 2))
A304887: 1 1 1 1 1 1 3 3 8 14
(1 + ((x mod (1 + (2 * (if ((x + 2) mod (2 + (x div 5))) <= 0 then 0 else 2)))) div 2))
A240595-A083671: 1 1 1 2 1 1 1 1 2 3 1 1 2 2 1 1
loop(\(x,i).x2,1,(1 + ((x - (x div (11 - (x div 2)))) div 2)))
A065730: 1 1 4 4 9 9 16 16 16 25 25 36 36 36 36 49
(~1 + (2 * loop(\(x,i).x2,1,(8x + 81))))
A157433: 13121 15841 18817 22049 25537 29281 33281 37537 42049 46817 51841 57121 62657 68449 74497 80801
(1 + (2 * (1 + (4 * compr(\x.loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,x),x)))))
A252802: 3 11 19
A213540: 3 11 19 35 43 67 75 83 131 139 147 163 171 259 267 275
(1 + ((1 + (((x + (loop(\(x,i).((x2 + ~2x) div 2),2,x) div (x + 1))) div 2) div 2)) div 2))
A089333: 1 1 1 1 2 2 3 4 6 8 11 14 19 24 31 39
loop(\(x,i).x7,1,(8x + 3))
A017107: 2187 19487171 893871739 10460353203 64339296875 271818611107 897410677851 2488651484819 6060711605323 13348388671875 27136050989627 51676101935731 93206534790699 160578147647843
(1 + ((x mod (3 * (1 + (if (x mod 2) <= 0 then (x div 7) else 0)))) div 2))
A204901: 1 1 2 1 1 2 1 1 2 1 3 2 1 1 3 1
(1 + (2 * ((1 + (loop(\(x,i).(4x + 2),(x + ~2),1) div 3)) div 3)))
A120540: 1 1 1 3 7 25 95
(1 + ((3 * ((~1 + loop(\(x,i).(2x - ((x div 2) mod 2)),x,2)) div 3)) div 2))
A263366: 1 1 2 5 10 19 37 73 146 293 586 1171 2341 4681 9362 18725
((x + 1) mod (1 + (2 * ((loop(\(x,i).(x2 div 3),2,x) div (x + 1)) mod 3))))
A108498: 0 0 0 0 2 0 0 2 0 0 0 2 3 4 0 0
(1 + (2 * loop(\(x,i).x2,1,(25x + ~18))))
A154358: 649 99 2049 6499 13449 22899 34849 49299 66249 85699 107649 132099 159049 188499 220449 254899
(1 + (2 * ((2 + ((loop(\(x,i).(2x + 8),x,1) mod (x + 1)) div 2)) div 3)))
A328575: 1 1 1 1 1 3 1 1 1 1 1 3 1 5 5 5
(1 + (x div (2 + ((if (x mod 2) <= 0 then 7 else x) mod 12))))
A329198: 1 1 1 1 1 1 1 1 1 1 2 1 2 5 2 4
((x + 1) - (2 * ((1 - (4 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 3)))
A003157: 3 8 11 14 19 24 29 32 35 40 43 46 51 54 57 62
loop(\(x,i).6x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)
A256136: 1 6 6 36 6 36 36 216 6 36 36 216 36 216 216 1296
(x - loop(\(x,i).(2x + 1),(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1))
A064405: ~1 ~2 ~1 ~4 1 ~2 ~1 ~8 5 2 3 ~4 5 ~2 ~1 ~16
loop(\(x,i).(3x + ~1),(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)
A162784: 1 2 2 5 2 5 5 14 2 5 5 14 5 14 14 41
loop(\(x,i).((x * (2 + i)) div 2),(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)
A050315: 1 1 1 2 1 2 2 5 1 2 2 5 2 5 5 15
loop(\(x,i).5x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)
A256135: 1 5 5 25 5 25 25 125 5 25 25 125 25 125 125 625
loop(\(x,i).(3x + ~1),(((x + ~1) div 2) - ((3 * (x div 4)) div 2)),1)
A079318: 1 1 1 2 1 2 2 5 1 2 2 5 2 5 5 14
(7 * (~3 + loop(\(x,i).10x,(x + 1),1)))
A175775: 49 679 6979 69979 699979 6999979 69999979 699999979 6999999979 69999999979 699999999979 6999999999979 69999999999979 699999999999979 6999999999999979 69999999999999979
(7 * (1 - (if (2 - (x div 4)) <= 0 then (x mod 8) else 1)))
A055957: 0 0 0 0 0 0 0 0 7 0 ~7 ~14 ~21 ~28 ~35 ~42
((3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 7)
A122601: 3 4 6 1 5 0 4 6 3 2 4 3 0 2 6 5
(7 * loop(\(x,i).(8x + 2),(x div 2),(1 + (x mod 2))))
A117867: 7 14 70 126 574 1022 4606 8190 36862 65534 294910 524286 2359294 4194302 18874366 33554430
(~1 + ((3 * (x + loop(\(x,i).((x + 1) - (((x + 1) div 2) div 3)),2,x))) div 2))
A277574: 2 5 8 11 12 14 17 20 23 26 29 30 32 35 38 41
(if x <= 0 then 1 else (1 + ((x + 1) mod (2 * (1 + (x div (~2x + 32)))))))
A058656: 1 1 2 1 2 1 2 1 2 1 2 1 2 3 8 1
(1 + (((if (x mod 3) <= 0 then 1 else (~8 + (x div 2))) mod (1 + (x div 2))) div 2))
A102541: 1 1 1 1 1 1 1 2 1 1 2 2 1 3 4 1
loop(\(x,i).2x2,1,(1 + ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)))
A168281: 2 2 2 2 8 2 2 8 8 2 2 8 18 8 2 2
loop(\(x,i).5x,((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2),1)
A152717: 1 1 1 1 5 1 1 5 5 1 1 5 25 5 1 1
loop(\(x,i).x6,1,(10x + 3))
A017310: 729 4826809 148035889 1291467969 6321363049 22164361129 62523502209 151334226289 326940373369 646990183449 1194052296529 2081951752609 3462825991689 5534900853769 8550986578849
(1 + (2 * loop(\(x,i).((x + 1) + (x div (1 + ((x * i) mod 7)))),x,1)))
A020575: 3 5 7 11 13 19 23 47
(1 + (loop(\(x,i).((x + 1) + ((x + (x mod (x - ((x + 1) mod 3)))) div 2)),x,1) div 2))
A033320: 1 2 3 4 7 10 16 24 36 54 81 122 183 275 412 619
((x + 1) div (1 + (((~1 + loop(\(x,i).2x,x,(2 - ((x div 2) mod 2)))) mod (x + 1)) div 2)))
A078833-A039634: 1 2 3 2 5 3 7 2 2 5 11 3 13 7 7 2
(2x div ((x + 1) - ((loop(\(x,i).(2x - (i mod 2)),x,(x + 1)) mod (x + 1)) div 2)))
A325759: 0 1 1 2 1 2 1 2 1 3 1 2 1 3 3 2
((loop(\(x,i).((x2 + ~x) div 2),2,(~1 + (x div 2))) div 3) * (1 + ((x + 1) div 2)))
A047179: 0 0 0 0 0 0 0 0 5 6 30 35 105 120 280 315
(((1 + (if (~1 + (x mod 3)) <= 0 then 2 else 0)) div (2 - (x mod 2))) * (1 + ((x + 1) div 2)))
A323606: 1 6 0 9 3 4 4
(1 + (((x + 1) * (x + (if (x mod 2) <= 0 then 1 else (3 * (2x - (x mod 2)))))) div 2))
A269876: 1 5 5 37 13 97 25 185 41 301 61 445 85 617 113 817
((x + 1) div (1 + (2 * (((~x + 1) + (if (~1 + (x mod 3)) <= 0 then x else 2)) mod (x + 1)))))
A118816: 1 0 1 1 1 0 2 2 1 3 3 1 4 4 1 5
(1 + ((1 + loop(\(x,i).((x + 1) - (((2x + 2) mod (2 + (x div 2))) div 2)),x,x)) div 2))
A071112: 1 2 3 3 3 4 4 6 6 6 7 7 7 7 8 8
(1 + (2 * ((1 + (x div (1 + ((~1 + loop(\(x,i).2x,(x + ~2),2)) mod (x + 1))))) div 2)))
A275367-A023136: 1 1 3 1 3 3 3 1 5 3 3 3 3 3 9 1
(~1 + (4 * (1 + loop(\(x,i).(3x + 3),(x div 3),(x mod 3)))))
A145052: 3 7 11 15 27 39 51 87 123 159 267 375 483 807 1131 1455
(1 + (2 * ((1 + loop(\(x,i).((x2 + x) - (x div (2 div (~2 + (x mod 2))))),x,1)) div 2)))
A175138: 3 5 15 225 50625 2562890625 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) div (1 + (2 * ((1 + (x div (2 + (loop(\(x,i).(x * i),x,2) mod (x + 1))))) div 2))))
A340078-A323071-A055023: 1 2 3 1 5 2 7 1 1 2 11 1 13 2 1 1
((if (x mod 3) <= 0 then 2 else 1) mod (1 + (2 * (((x + 2) mod 9) mod 2))))
A191250: 0 1 0 2 0 1 0 0 1 0 1 0 2 0 1 0
(1 + (x div (4 + ((x * loop(\(x,i).(2x + 2),x,2)) mod 9))))
A090680: 1 1 1 1 1 2 1 1 2 3 1 3 2 2 2 4
loop(\(x,i).i,(4 * ((2x + 1) mod (1 + (2x mod (2 + (x div 4)))))),1)
A173675: 1 1 1 1 1 4 1 1 1 4 1 8 1 4 4 1
((x + ~1) mod (1 + (if x <= 0 then 1 else (2 * ((x mod (1 + (x mod (2 + (x div 4))))) div 2)))))
A092669: 1 0 0 0 0 1 0 0 0 0 0 1 0 0 3 0
(1 + (2 * loop(\(x,i).x2,1,(25x + ~7))))
A154359: 99 649 3699 9249 17299 27849 40899 56449 74499 95049 118099 143649 171699 202249 235299 270849
(1 + (4 * ((1 + (4 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 3)))
A249034: 5 13 17 21 29 37 45 49 53 61 65 69 77 81 85 93
(~1 + (4 * ((1 + (4 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 3)))
A131323: 3 11 15 19 27 35 43 47 51 59 63 67 75 79 83 91
(5 + (loop(\(x,i).((x + 2) + (x div 9)),x,1) div 3))
A120206: 5 6 6 7 8 9 10 11 12 13 15 16 18 20 22 25
(1 + (((3 * (x + (if (x mod 2) <= 0 then (1 - (2 * (x mod 4))) else x))) div 2) div 2))
A249693: 1 2 0 5 4 8 3 11 7 14 6 17 10 20 9 23
loop(\(x,i).x7,1,(8x + 5))
A017131: 78125 62748517 1801088541 17249876309 94931877133 373669453125 1174711139837 3142742836021 7446353252589 16048523266853 32057708828125 60170087060757 107213535210701 182803912081669
loop(\(x,i).x6,1,(~7x + ~5))
A017046: 15625 2985984 47045881 308915776 1291467969 4096000000 10779215329 24794911296 51520374361 98867482624 177978515625 304006671424 496981290961 782757789696 1194052296529 1771561000000
(((x + 2) div 3) mod (1 + (((1 + ((if (x mod 2) <= 0 then 1 else x) * (x div 2))) div 2) div 2)))
A082650: 0 0 0 1 0 2 0 3 1 3 0 4 0 5 2 5
(1 + (((1 + (loop(\(x,i).(x + ((2 + (i div 3)) * (1 + i))),x,x) div 2)) div 2) div 2))
A008764: 1 1 2 4 6 8 12 16 21 27 34 42 52 62 74 88
(1 + ((loop(\(x,i).((x + 1) + ((1 + ((x + (x div 4)) div 2)) div 2)),x,1) div 2) div 2))
A018052: 1 1 2 2 3 4 5 7 9 12 16 21 27 36 47 62
((x + 1) - loop(\(x,i).(2 * (1 + (x div 2))),(x div 8),(((x + 1) div 2) div 2)))
A335152-A064047: 1 2 3 3 4 5 6 6 5 6 7 8 9 10 11 10
(1 + ((x - (x div (2 + (if (((x + 2) mod 8) mod 3) <= 0 then 0 else 2)))) div 2))
A300066: 1 1 2 2 2 3 2 4 4 3 5 5 4 6 4 7
(1 + (8 * (3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A129074: 25 33 49 65 97 113 145 161 193 241 257 305 337 353 385 433
(5 + (if x <= 0 then 1 else (2 * (7x - (x div 3)))))
A063147: 6 19 33 45 59 73 85 99 113 125 139 153 165 179 193 205
((x + 1) - (2 * ((if (~2 + (x div 5)) <= 0 then 0 else 2) + (((x + 1) div 2) div 2))))
A065362: 1 2 3 2 3 4 5 4 5 6 7 6 7 8 9 4
((3 * ((2 - (x mod 2)) * (if x <= 0 then 1 else 2))) mod (~1 + (2 * (((x + 1) div 2) div 2))))
A286651: 0 0 0 0 0 0 0 0 0 0 0 1 2 1 2 6
(loop(\(x,i).3x,((x * (x mod 2)) div 2),1) mod (~1 + (2 * (((x + 1) div 2) div 2))))
A116992: 0 0 0 0 0 0 0 0 1 0 1 3 1 4 1 3
(1 + (2 * (4 + (loop(\(x,i).x2,2x,(5x + 5)) div 2))))
A173840: 13 10009 4611686018427387903 4611686018427387903
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 17)
A193063-A165132: 2 3 5 7 11 13
A039715: 2 3 5 7 11 13 0 2 6 12 14 3 7 9 13 2
(((x + 2) * loop(\(x,i).(2x + 2),3,(x + 1))) div 17)
A122221: 2 5 8 13 19 25 32 41 50 60 72 84 97 111 126 142
loop(\(x,i).39x,x,17)
A063941: 17 663 25857 1008423 39328497 1533811383 59818643937 2332927113543 90984157428177 3548382139698903 138386903448257217 4611686018427387903 4611686018427387903 4611686018427387903
(15 * loop(\(x,i).(10x + 21),x,1))
A177080: 15 465 4965 49965 499965 4999965 49999965 499999965 4999999965 49999999965 499999999965 4999999999965 49999999999965 499999999999965 4999999999999965 49999999999999965
(((x + 1) * loop(\(x,i).(x2 + 2x),2,(2x + 1))) div 15)
A081219: 1 34 259 1092 3333 8294 17927 34952 62985 106666 171787 265420 396045 573678 809999 1118480
(((x + 1) * (loop(\(x,i).(x * (x - i)),2,(x + ~1)) div 2)) div 15)
A210569: 0 0 0 0 4 24 84 224 504 1008 1848 3168 5148 8008 12012 17472
(30 * (~1 + loop(\(x,i).10x,x,2)))
A177097: 30 570 5970 59970 599970 5999970 59999970 599999970 5999999970 59999999970 599999999970 5999999999970 59999999999970 599999999999970 5999999999999970 59999999999999970
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 15)
A193063-A165132: 2 3 5 7 11 13
A039713: 2 3 5 7 11 13 2 4 8 14 1 7 11 13 2 8
(if x <= 0 then 1 else ((~x2 + 2) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))))
A122083: 1 0 0 0 1 0 0 1 1 0 0 1 3 1 0 0
(1 - ((2x + 3) mod loop(\(x,i).i,(2x mod (4 + (x div 4))),1)))
A109466: 1 0 1 0 ~1 1 0 0 ~2 1 0 0 1 ~3 1 0
(loop(\(x,i).10x,2x,1) div (1 + (8 * (x mod 2))))
A267035: 1 11 10000 111111 100000000 1111111111 1000000000000 11111111111111 10000000000000000 111111111111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((9x + 9) * loop(\(x,i).(3 * (2 + (x * (2 + i)))),2,x))
A305071: 702 3348 7938 14472 22950 33372 45738 60048 76302 94500 114642 136728 160758 186732 214650 244512
(18 * loop(\(x,i).(10x + 21),x,1))
A177098: 18 558 5958 59958 599958 5999958 59999958 599999958 5999999958 59999999958 599999999958 5999999999958 59999999999958 599999999999958 5999999999999958 59999999999999958
((x + 11) + (x mod (if (~2 + (x div 4)) <= 0 then 1 else 4)))
A162903: 11 12 13 14 15 16 17 18 19 20 21 22 23 25 27 29
loop(\(x,i).x6,1,(12x + 9))
A017634: 531441 85766121 1291467969 8303765625 34296447249 107918163081 282429536481 646990183449 1340095640625 2565164201769 4608273662721 7858047974841 12827693806929 20179187015625
((x + 7) * loop(\(x,i).(x + (((4 + i) * (1 + i)) div 2)),x,2))
A212347: 14 56 144 300 550 924 1456 2184 3150 4400 5984 7956 10374 13300 16800 20944
(1 + (4 * ((2x + 2) + loop(\(x,i).(10x + 20),x,0))))
A232229: 9 97 905 8913 88921 888929 8888937 88888945 888888953 8888888961 88888888969 888888888977 8888888888985 88888888888993 888888888889001 8888888888889009
(1 + (((4x + ~4) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))) mod 4))
A070940: 1 1 2 1 3 2 3 1 4 3 4 2 4 3 4 1
(loop(\(x,i).7x,x,1) mod 45)
A070427: 1 7 4 28 16 22 19 43 31 37 34 13 1 7 4 28
((30x + 30) * loop(\(x,i).(x2 + x),2,(x + 1)))
A099106: 180 2520 14040
loop(\(x,i).x7,1,(10x + 5))
A017335: 78125 170859375 6103515625 64339296875 373669453125 1522435234375 4902227890625 13348388671875 32057708828125 69833729609375 140710042265625 266001988046875 476837158203125 817215093984375
(5 * (1 + compr(\x.(loop(\(x,i).(2x3 + 2x2),2,2) mod (x + 1)),x)))
A080193: 5 10 15 20 25 30 40 45 50 60 75 80 90 100 120 125
(5 * (1 + loop(\(x,i).(x + 1),(~4 + ((x + ((x div 2) mod 2)) div 2)),x)))
A085128: 5 10 15 20 25 30 35 40 45 50 60 70 75 80 90 100
(x5 div loop(\(x,i).x5,1,5))
A185721: 0 0 0 0 0 1 2 5 10 18 32 51 79 118 172 243
((2 + (loop(\(x,i).4x,x,1) div 13)) div 5)
A135450: 0 0 0 1 4 16 63 252 1008 4033 16132 64528 258111 1032444 4129776 16519105
((10x + 10) + loop(\(x,i).12x,(x + 1),1))
A173393: 22 164 1758 20776 248882 2986044 35831878 429981776 5159780442 61917364324 743008370798 8916100448376 106993205379202 1283918464549004 15407021574586518 184884258895036576
loop(\(x,i).x5,1,(11x + 9))
A017501: 59049 3200000 28629151 130691232 418195493 1073741824 2373046875 4704270176 8587340257 14693280768 23863536599 37129300000 55730836701 81136812032 115063617043 159494694624
((loop(\(x,i).(2 + ((x + (x2 div 3)) div 2)),2,(x + ~1)) div 2) div 5)
A026811: 0 0 0 0 0 1 1 2 3 5 7 10 13 18 23 30
((2 * (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))) div 5)
A253556-A252735: 0 0 1 0 2 1 3 0 1 2 4 1 5 3 2 0
(40 * (~1 + loop(\(x,i).10x,x,2)))
A175603: 40 760 7960 79960 799960 7999960 79999960 799999960 7999999960 79999999960 799999999960 7999999999960 79999999999960 799999999999960 7999999999999960 79999999999999960
(2 div ((2 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 8)) mod 5))
A002654: 1 1 0 1 2 0 0 1 1 2 0 0 2 0 0 1
((2 * (2 + loop(\(x,i).((x + 2) + (((1 + i) * i) div 2)),(x + 2),2))) div 5)
A026042: 4 8 12 19 28 40 56 74 97 124 156 194 236 285 340 402
(loop(\(x,i).(10x + 1),x,1) - (10 * (x mod 2)))
A284351: 1 1 111 1101 11111 111101 1111111 11111101 111111111 1111111101 11111111111 111111111101 1111111111111 11111111111101 111111111111111 1111111111111101
loop(\(x,i).(x2 + 2x),1,(~49x + ~40))
A157375: 1520 7743 18768 34595 55224 80655 110888 145923 185760 230399 279840 334083 393128 456975 525624 599075
(5 * (2x - (if (~2 + (x div 2)) <= 0 then (~1 + (x div 5)) else 1)))
A277592-A121025: 5 15 25 35 45 50 55 65 75 85 95 105 115 125 135 145
((if x <= 0 then 1 else (x mod ((x + ~1) - (x mod 12)))) + (x div 5))
A017841: 1 0 0 0 0 1 1 1 1 1 2 2 3 4 5 7
(x + (x div 5) - ((((x div 2) mod 4) - (if x <= 0 then 1 else x)) div 4))
A293205-A046687: 1 2 3 4 5 7 8 9 11 13 15 16 17 18 19 21
(20 div (if (x mod 5) <= 0 then 1 else (x mod 5)))
A217517: 20 20 10 6 5 20 20 10 6 5 20 20 10 6 5 20
(1 + (((x + (loop(\(x,i).((x + 2) + ((x - (x div 4)) div 2)),x,2) div 2)) div 2) div 2))
A323360: 1 1 2 3 4 6 8 10 14 19 25 34 46 62 84 115
((if (~2 + (x div 5)) <= 0 then x else (x + 2)) + (x2 div (x + 5)))
A325101: 0 1 2 4 5 7 9 11 12 14 16 18 20 22 24 28
(1 + ((2x + loop(\(x,i).2x,((x + (x div 3)) div 5),1)) div 2))
A031942: 1 2 3 4 6 7 8 9 11 12 13 14 17 18 19 24
loop(\(x,i).8x,(((3 * (x + (x div 4))) - (x mod 2)) div 2),1)
A241756: 1 8 512 4096 2097152 16777216 1073741824 8589934592 35184372088832 281474976710656 18014398509481984 144115188075855872 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * (1 + (loop(\(x,i).(2 * (2x - (x mod 4))),2,(x div 2)) + (x mod 2)))))
A147568: 3 5 11 13 35 37 43 45 131 133 139 141 163 165 171 173
(3 * (1 + loop(\(x,i).(2x + 16),x,13)))
A304613: 42 129 303 651 1347 2739 5523 11091 22227 44499 89043 178131 356307 712659 1425363 2850771
(3 * (~1 + loop(\(x,i).(2x + 32),x,9)))
A305160: 24 147 393 885 1869 3837 7773 15645 31389 62877 125853 251805 503709 1007517 2015133 4030365
(3 * (~1 + (3 * (~1 + loop(\(x,i).(2x + 12),(x + 1),1)))))
A305066: 114 348 816 1752 3624 7368 14856 29832 59784 119688 239496 479112 958344 1916808 3833736 7667592
(((~2 + loop(\(x,i).3x,x,1)) mod 19) div 3)
A087778: 6 0 2 2 1 4 1
(2x div loop(\(x,i).2x,(x3 mod 11),3))
A221388: 0 0 0 0 0 0 0 1 0 0 0 7 4 0 0 0
((1 + ((1 + (loop(\(x,i).(~2x + 2),x,(2 * (x mod 2))) div (x + 1))) div 2)) mod 3)
A255317: 1 1 1 0 0 1 1 2 1 0 0 1 1 1 0 1
((1 + (2 * (if x <= 0 then 1 else (8x + ((x + 1) div 3))))) div 3)
A314218: 1 5 11 17 22 28 33 39 45 50 55 61 67 72 78 83
((1 + (2 * (if x <= 0 then 1 else (8x - ((x + 1) div 3))))) div 3)
A313773: 1 5 10 15 21 25 31 36 41 46 51 56 61 67 71 77
((1 + (loop(\(x,i).(2x + ((1 + i) * i * (1 + i))),(x + ~2),1) div 2)) div 3)
A056782: 0 0 0 1 5 18 53 135
((1 + (((x + 1) * (~1 + (loop(\(x,i).(x * i),(x + ~1),1) + (x mod 2)))) div 2)) div 3)
A204199: 0 0 0 1 4 24 139
((1 + (2 * (if x <= 0 then 1 else (2 * (4x - ((x + 1) div 3)))))) div 3)
A315050: 1 5 9 15 20 24 29 35 39 44 49 53 59 64 68 73
((1 + (4 * ((x + 4) + (if (~4 + (x div 2)) <= 0 then 1 else 2)))) div 3)
A210147: 7 8 9 11 12 13 15 16 17 19 21 23 24 25 27 28
(if x <= 0 then 0 else ((1 + ((2x mod (4 + (x div 4))) mod 4)) mod 3))
A083856: 0 0 1 0 1 1 0 1 1 1 0 1 1 2 1 0
((((2 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 3) mod 5) mod 3)
A101650: 0 0 1 0 2 1 2 0 0 2 1 1 1 2 0 0
((5 * ((1 + ((1 + (x div 2)) div 3)) * (if x <= 0 then 1 else 2))) div 3)
A108581: 1 3 3 3 6 6 6 6 6 6 10 10 10 10 10 10
(((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 5) mod 3)
A244738: 2 0 0 2 1 0 2 1 0 1 1 2 1 0 2 0
loop(\(x,i).x7,1,(12x + 3))
A017563: 2187 170859375 10460353203 137231006679 897410677851 3938980639167 13348388671875 37725479487783 93206534790699 207616015289871 425927596977747 817215093984375 1483273860320763 2569093262823519
loop(\(x,i).x6,1,(~11x + ~3))
A017430: 729 7529536 244140625 2176782336 10779215329 38068692544 107918163081 262144000000 567869252041 1126162419264 2081951752609 3635215077376 6053445140625 9685390482496 14976071831449
((loop(\(x,i).(x * (1 + (2 * (4 + (i mod 2))))),(x + 1),1) div 3) div 3)
A080445: 1 11 121 1089 11979 107811 1185921 10673289 117406179 1056655611 11623211721 104608905489 1150697960379 10356281643411 113919098077521 1025271882697689
(((loop(\(x,i).(x * i),x,((x3 + ~3x2 + 2x) div 2)) div 2) div 3) div 3)
A001810: 0 0 0 1 16 200 2400 29400 376320 5080320 72576000 1097712000 17563392000 296821324800 5288816332800 99165306240000
(loop(\(x,i).(4x4 + 12x3 + 8x2),1,(x + 3)) div 3)
A202196: 240 640 1400 2688 4704 7680 11880 17600 25168 34944 47320 62720 81600 104448 131784 164160
(((2x2 + 7x + 3) * loop(\(x,i).4x,x,(x + 1))) div 3)
A068548: 1 32 400 3584 26880 180224 1118208 6553600 36765696 199229440 1049624576 5402263552 27262976000 135291469824 661693399040 3195455668224
(((2x + 1) * (1 - (x mod (2 + (if (x mod 2) <= 0 then 1 else 8))))) mod 3)
A106594: 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 2
((1 + loop(\(x,i).((x * (1 + ((x div 2) div (1 + (x mod 2))))) div 2),3,x)) mod 3)
A079409: 1 1 0 1 1 0 1 2 0 0 1 1 1 0 0 1
loop(\(x,i).x7,1,(9x + 3))
A017203: 2187 35831808 1801088541 21870000000 137231006679 587068342272 1954897493193 5455160701056 13348388671875 29509034655744 60170087060757 114868566764928 207616015289871 358318080000000
(loop(\(x,i).(1 - ((~1 + (x mod 3)) mod (1 + (x mod 4)))),1,(x + 1)) mod 3)
A259287: 1 0 1 1 0 2 1 1 0 1 0 1 1 0 1 1
((x - compr(\x.(1 - (x mod (2 + (if (x mod 5) <= 0 then 2 else 0)))),(x + 1))) mod 3)
A092606: 0 2 1 0 0 0 2 1 0 2 1 0 2 1 0 0
((6x + 6) * (1 + (if (~x + 4) <= 0 then 16 else 1)))
A019550: 12 24 36 48 510 612 714 816 918 1020 1122 1224 1326 1428 1530 1632
(loop(\(x,i).(~2 + ((~2x + 2) mod (4 + (x div 4)))),2,(x + 1)) mod 3)
A253189-A111373: 1 0 1 0 0 1 1 0 0 1 0 2 0 0 1 0
((if x <= 0 then 1 else (2 * (2x + ((x + ((x div 2) mod 2)) div 2)))) - ((x + 1) div 3))
A313193: 1 4 9 15 19 22 28 34 37 41 47 52 56 60 65 71
(((x + ((x div 2) mod 2)) div 2) + (if x <= 0 then 1 else 4x) + ((x + 1) div 3))
A310440: 1 4 10 15 19 24 29 34 39 43 48 54 58 62 68 73
((((x + ((x div 2) mod 2)) div 2) + (if x <= 0 then 1 else 4x)) - ((x + 1) div 3))
A058759: 1 4 8 13
A301672: 1 4 8 13 17 20 25 30 33 37 42 46 50 54 58 63
(4x + ((x + 1) div 3) - ((((x div 2) mod 2) - (if x <= 0 then 1 else x)) div 2))
A313575: 1 5 10 14 19 25 29 33 39 44 48 53 58 63 68 72
(3 * (1 + compr(\x.loop(\(x,i).(x div (2 - (((x + 1) * (x div 4)) mod 2))),x,x),x)))
A173195: 3 6 9 12 18 24 33 36 48 66 72 96 129 132 144 192
((2 * (if x <= 0 then 2 else (1 + (x mod (1 + (2 * (x div (3 - (x mod 2))))))))) div 3)
A096577: 1 0 0 0 1 0 1 0 2 0 2 0 2 0 4
((2 * (1 + (loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) mod 5))) div 3)
A035204: 1 1 2 1 0 2 2 1 3 0 1 2 2 2 0 1
((loop(\(x,i).(x3 + ~x),1,(5x + 6)) div 2) div 3)
A300523: 35 220 680 1540 2925 4960 7770 11480 16215 22100 29260 37820 47905 59640 73150 88560
((2 * (1 + (loop(\(x,i).(7x + 1),x,1) div (x + 1)))) mod 3)
A035178: 1 1 1 1 0 1 2 1 1 0 0 1 2 2 0 1
(((~1 + loop(\(x,i).(x * i),(1 + (2 * (x - (x div ~2)))),1)) div 2) div 3)
A139194: 0 19 839 6652799 1037836799 59281238015999 20274183401471999 4611686018427387903 4611686018427387903 4611686018427387903
((2 * (1 + ((1 + (loop(\(x,i).(2x + ~4),x,(x + 2)) div (x + 1))) div 2))) mod 3)
A340653: 1 1 1 0 1 0 1 1 0 0 1 2 1 0 0 1
((2 * ((if (x mod 4) <= 0 then 2 else (x mod 2)) + (x div 7))) div 3)
A029359: 1 0 0 0 1 0 0 1 2 1 0 1 2 1 1 2
(3 + ((1 + (loop(\(x,i).(2 * (x - (2 * (x div 5)))),x,1) div 2)) div 2))
A182230: 3 4 4 5 6 7 8 9 11 13 15 18 21 25 30 36
((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3)
A307409-A147588-A070824: 0 0 0 1 0 2 0 2 1 2 0 4 0 2 2 3
(60 * (loop(\(x,i).(3x + ~1),x,2) div 2))
A309315: 60 120 420 1200 3660 10920 32820 98400 295260 885720 2657220 7971600 23914860 71744520 215233620 645700800
(~3 + (2 * (if x <= 0 then 2 else (x - (((x2 + ~2x) div (x + 2)) div 5)))))
A050828: 1 1 1 3 5 7 9 11 13 13 15 17 19 21 21 23
((if x <= 0 then 1 else 4x) - ((1 - (2 * ((2x + 1) div 3))) div 3))
A314710: 1 5 9 13 18 22 27 31 35 40 45 49 53 58 62 67
loop(\(x,i).3x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),3)
A162349: 3 9 9 27 9 27 27 81 9 27 27 81 27 81 81 243
((2 + (((x + 4) * (if (~4 + (x div 2)) <= 0 then 1 else 2)) div 3)) div 3)
A029130: 1 1 1 1 1 1 1 1 2 2 3 4 4 4 4 4
((2 * ((2 + ((if ((x + ~1) mod 3) <= 0 then 1 else x) + (x mod 2))) div 3)) div 3)
A225399: 0 0 0 1 0 1 1 0 2 2 0 2 2 0 3 4
((2 + loop(\(x,i).~x,x,(x div (3 * (8 - (x div 2)))))) div 3)
A246583: 0 0 0 0 0 0 0 0 0 0 1 0 1 0 2 ~1
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 18)
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A242119: 2 3 5 7 11 13 17 1 5 11 13 1 5 7 11 17
((if x <= 0 then 1 else 4x) - ((1 - (2 * (x - ((~x + 1) div 3)))) div 3))
A313703: 1 5 10 15 19 25 29 34 39 44 49 54 59 63 69 73
((if x <= 0 then 1 else 4x) - ((1 - (2 * ((x + (x mod 2)) div 3))) div 3))
A058759: 1 4 8 13
A311805: 1 4 8 13 17 21 25 29 33 38 42 47 51 55 59 63
loop(\(x,i).x7,1,(12x + 6))
A017599: 279936 612220032 21870000000 230539333248 1338925209984 5455160701056 17565568854912 47829690000000 114868566764928 250226879128704 504189521813376 953133216331392 1708593750000000
loop(\(x,i).x5,1,(11x + 7))
A017477: 16807 1889568 20511149 102400000 345025251 916132832 2073071593 4182119424 7737809375 13382255776 21924480357 34359738368 51888844699 75937500000 108175616801 150536645632
loop(\(x,i).x6,1,(~11x + ~6))
A017466: 46656 24137569 481890304 3518743761 15625000000 51520374361 139314069504 326940373369 689869781056 1340095640625 2436396322816 4195872914689 6906762437184 10942526586601 16777216000000 25002110044521
(6 * (1 + loop(\(x,i).(7x + 8),(x div 2),(x mod 2))))
A117866: 6 12 54 96 390 684 2742 4800 19206 33612 134454 235296 941190 1647084 6588342 11529600
((((5x + 1) * loop(\(x,i).3x,(x + ~1),x)) div 2) div 3)
A084900: 0 1 11 72 378 1755 7533 30618 119556 452709 1673055 6062364 21611934 75996063 264126177 908764110
((2 + loop(\(x,i).(32x + (x mod 3)),x,1)) div 3)
A067428: 1 11 352 11264 360448 11534336 369098752 11811160064 377957122048 12094627905536 387028092977152 12384898975268864 396316767208603648 4611686018427387903 4611686018427387903 4611686018427387903
(6 * (1 + compr(\x.(loop(\(x,i).4x2,2,3) mod (x + 1)),x)))
A033845: 6 12 18 24 36 48 54 72 96 108 144 162 192 216 288 324
(6 * (1 + loop(\(x,i).(x + 1),(~4 + ((x + ((x div 2) mod 2)) div 2)),x)))
A085129: 6 12 18 24 30 36 42 48 54 60 72 84 90 96 108 120
(6 * (1 + loop(\(x,i).(x + (2 div (6 - (x div 3)))),2,x)))
A078596: 6 12 18 24 30 36 42 48 54 60 66 72 90 96 108 120
((2 * (1 + loop(\(x,i).(x + (x2 div (x + 16))),2,x))) mod 3)
A190762: 2 1 0 2 1 1 2 2 1 0 2 1 1 2 1 1
((2 * ((~2 + loop(\(x,i).7x,(x + 1),1)) div (x + 1))) mod 3)
A035188: 1 1 1 1 2 1 0 1 1 2 0 1 0 0 2 1
((((x + ~1) * (0 - loop(\(x,i).(((x + 1) - (2 * (i mod 2))) * i),x,0))) div 2) div 3)
A000313: 0 0 0 1 4 30 220 1855 17304 177996 2002440 24474285 323060540 4581585866 69487385604 1122488536715
(if (x + ~1) <= 0 then x else (((x6 + ~2x4 + x2) div 2) div 3))
A303212: 0 1 6 96 600 2400 7350 18816 42336 86400 163350 290400 490776 794976 1242150 1881600
((1 - (((x + 2) mod (2 + (((x div 2) div 3) + (if x <= 0 then 0 else 1)))) div 2)) mod 3)
A335294: 1 1 1 0 1 1 1 1 0 0 1 1 2 1 1 0
((2 * (2 + (x div (1 + ((~1 + loop(\(x,i).2x,(x + ~2),2)) mod (x + 1)))))) div 3)
A336158-A335283: 1 1 2 1 2 2 2 1 4 2 2 2 2 2 6 1
(3 * loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),2))
A256257: 6 12 12 24 12 24 24 48 12 24 24 48 24 48 48 96
((2 * ((loop(\(x,i).5x,5,x) mod (x + 1)) div 2)) div 3)
A237130: 0 0 0 0 0 0 1 0 2 1 3 2 2 3 3 3
((2 * (2 + ((loop(\(x,i).~x2,4,3) mod (x + 1)) div 2))) mod 3)
A332602: 1 1 1 0 2 0 0 1 1 0 0 0 2 0 0 0
((loop(\(x,i).10x,x,1) mod 32) div 3)
A021036: 0 3 1 2 5 0 0 0 0 0 0 0 0 0 0 0
((if x <= 0 then 1 else (2 + ((~2x + 3) mod (4 + (x div 4))))) div 3)
A204016: 0 1 1 1 0 1 1 2 2 1 1 2 0 2 1 1
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 24)
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A229787: 2 3 5 7 11 13 17 19 23 5 7 13 17 19 23 5
(x + ((4 * (x + (if (~2 + (x div 2)) <= 0 then 1 else 2))) div 3) - (x div ~2))
A284933: 1 4 7 10 12 16 19 23 25 28 31 34 36 40 42 45
((2 * ((x + 2) + ((((x + 2) * (x + (if (x + ~2) <= 0 then 1 else x))) div 2) div 2))) div 3)
A222011: 1 2 4 8
A260090: 1 2 4 8 12 16 21 26 33 40 48 56 65 74 85
((if x <= 0 then 1 else 4x) - ((1 - (2 * ((x + ((x div 2) mod 2)) div 2))) div 3))
A312896: 1 4 9 13 17 21 26 31 35 39 43 48 52 56 61 65
(6 * (2 + compr(\x.(1 - (loop(\(x,i).3x2,2,x) mod (x + 2))),x)))
A091454: 30 42 60 66 78 84 90 102 114 120 126 132 138 150 156 168
loop(\(x,i).x6,1,(11x + 2))
A017418: 64 4826809 191102976 1838265625 9474296896 34296447249 98867482624 243087455521 531441000000 1061520150601 1973822685184 3462825991689 5789336458816 9294114390625 14412774445056
(3 + (2 * ((x + 2) + loop(\(x,i).(x - (2x div (1 + (4 * i)))),x,x))))
A176852: 7 11 15 17 21 23 27 29 31 35 37 41 43 45 47 49
loop(\(x,i).x7,1,(9x + 6))
A017239: 279936 170859375 4586471424 42618442977 230539333248 897410677851 2799360000000 7446353252589 17565568854912 37725479487783 75144747810816 140710042265625 250226879128704 425927596977747
(4x - ((2 * ((((x div 2) div 3) mod 2) - (if x <= 0 then 1 else x))) div 3))
A313556: 1 5 10 14 19 24 28 32 37 42 46 51 56 61 66 70
((if x <= 0 then 1 else 5x) - ((2 * (~x + ((x div 3) mod 2))) div 3))
A315693: 1 6 12 17 22 28 34 40 46 51 56 62 68 74 80 85
(3 + (2 * (x + (((if (~2 + (x div 3)) <= 0 then 2 else (x div 2)) mod (x + 1)) div 2))))
A296243: 3 5 9 11 13 15 17 19 21 25 27 29 33 35 37 39
(1 - (3 * ((x * (x - loop(\(x,i).x3,1,(3x + 2)))) div 2)))
A134163: 1 187 1531 5977 16441 36811 71947 127681 210817 329131 491371 707257 987481 1343707 1788571 2335681
(3 * (2 + compr(\x.(loop(\(x,i).x2,2,(3 * (1 + (x div 2)))) mod (x + 2)),x)))
A014766: 9 12 24 27 36 48 60 72 81 84 96 108 120
(1 + (loop(\(x,i).((x2 + ~x) div 2),2,(x + 2)) div 3) - ((x2 + ~x) div 2))
A116699: 1 2 5 13 30 61 112 190 303 460 671 947 1300 1743 2290 2956
(if x <= 0 then 1 else (6x + ((~x + ((x + 1) mod 3)) div 5)))
A315546: 1 6 11 17 23 29 35 41 46 52 58 63 69 75 81 87
(6x + (if x <= 0 then 1 else ((2 * (~x + ((x div 3) mod 2))) div 3)))
A301697: 1 5 10 16 22 27 32 37 42 48 54 59 64 69 74 80
((((x - ((x div 4) mod 2)) div 2) div ~2) + (if x <= 0 then 1 else 6x))
A315543: 1 6 11 17 23 29 35 40 46 52 57 63 69 75 81 86
(if x <= 0 then 1 else ((2x2 + 6x) - (((~x3 + x) div 2) div 3)))
A137742: 1 8 21 40 66 100 143 196 260 336 425 528 646 780 931 1100
loop(\(x,i).x7,1,(5x + 3))
A016891: 2187 2097152 62748517 612220032 3404825447 13492928512 42618442977 114415582592 271818611107 587068342272 1174711139837 2207984167552 3938980639167 6722988818432 11047398519097
((if x <= 0 then 1 else 5x) - ((x + ((x div 3) mod 3)) div 3))
A313538: 1 5 10 14 19 23 28 32 37 42 47 52 56 61 65 70
((if x <= 0 then 1 else 5x) - ((~x + ((x div 3) mod 3)) div 3))
A315475: 1 6 11 16 21 27 32 37 42 48 54 59 64 69 75 80
((x + ((1 + ((x + ~1) * (~1 + loop(\(x,i).4x,x,2)))) div (x + 1))) mod 3)
A345374: 0 1 0 0 1 1 0 0 0 2 1 0 0 1 1 0
((x + 3) + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))))
A269304: 3 4 5 7 7 9 9 13 13 13 13 17 15 17 19 25
((x + 3) + (2 * ((x + (2 * (1 + (if (x + ~4) <= 0 then 0 else 2)))) div 3)))
A284390: 3 6 7 8 11 14 17 18 19 22 23 24 27 28 29 32
loop(\(x,i).(10x + ((2x + 1) mod 5)),x,3)
A037792: 3 32 320 3201 32013 320132 3201320 32013201 320132013 3201320132 32013201320 320132013201 3201320132013 32013201320132 320132013201320 3201320132013201
compr(\x.((x div 2) mod 3),(3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A247159: 7 12 18 24 36 42 54 60 72 90 96 114 126 132 144 162
((x2 + 2x + 3) + (loop(\(x,i).((x2 + ~x) div 2),2,(x + 2)) div 3))
A219846: 3 7 16 33 62 108 177 276 413 597 838 1147 1536 2018 2607 3318
(2 + ((if x <= 0 then 0 else (1 - ((~x + 1) div (2 + ((x div 2) div 3))))) + (x div 3)))
A080680: 2 3 4 5 6 6 7 7 8 9 9 10 10 10 11 12
(1 + (2 * compr(\x.((x + 1) mod (1 + (x div (2 + (if (x mod 2) <= 0 then 1 else 8))))),x)))
A085493: 1 3 5 7 11 15 17 19 23 27 29 31 35 39 41 47
(~1 + (2 * (2x - ((2 * (if x <= 0 then 1 else x)) div (~3 + ((~x + 2) div 4))))))
A137002: 1 5 11 15
A285597: 1 5 11 15 19 25 29 33 39 43 47 51 55 61 65 69
(1 + (2 * compr(\x.((x2 + x) mod loop(\(x,i).(10x + 4),2,1)),x)))
A156702: 1 127 161 287 289 415 449 575 577 703 737 863 865 991 1025 1151
(1 + (2 * (x + (((x + 1) * (if (~4 + (x div 2)) <= 0 then 1 else 2)) div 5))))
A294674: 1 3 5 7 11 13 15 17 19 23 29 31 35 37 41 43
loop(\(x,i).x7,1,(10x + 1))
A017287: 1 19487171 1801088541 27512614111 194754273881 897410677851 3142742836021 9095120158391 22876792454961 51676101935731 107213535210701 207616015289871 379749833583241 662062621900811 1107984764452581 1789940649848551
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(10x + 1))
A050489: 1 11 42 155 574 2142 8052 30459 115830 442442 1696396 6525246 25169452 97319900 377096040 1463921595
(1 + (2 * (x + (((if (~4 + (x div 2)) <= 0 then 1 else 2) * (1 + (x div 2))) div 3))))
A334141: 1 3 5 7 11 13 15 17 19 21 29 31 33 35 39 41
(~1 + (2 * loop(\(x,i).x2,1,(49x + 48))))
A157364: 4607 18817 42631 76049 119071 171697 233927 305761 387199 478241 578887 689137 808991 938449 1077511 1226177
(1 + ((x + loop(\(x,i).((x + 1) + (2 * i) - ((x + ~1) div 5)),x,1)) div 2))
A083505: 1 3 6 10 14
A145913: 1 3 6 10 14 18 22 27 32 37 42 47 52 57 63 68
(1 + (((x + 1) + loop(\(x,i).(1 + ((2x2 + ~x) div (x + 3))),2,x)) div 2))
A077114: 2 2 3 4 6 8 10 12 14 16 19 21 23 26 28 31
(2x div (1 + ((x + ((~1 + loop(\(x,i).8x,x,2)) mod (x + 1))) div 2)))
A256757: 0 1 2 1 2 2 3 1 3 2 3 2 3 3 2 1
loop(\(x,i).x6,1,(10x + 7))
A017358: 117649 24137569 387420489 2565726409 10779215329 34296447249 90458382169 208422380089 433626201009 832972004929 1500730351849 2565164201769 4195872914689 6611856250609 10090298369529
(1 + ((x + ((x + loop(\(x,i).((x2 + ~x) div 4),2,(x + ~2))) div (x + 1))) div 2))
A143752: 1 1 2 2 3 3 4 5 6 7 8 10 11 14 17 20
(1 + ((x + (((2 * (if (~2 + (x div 3)) <= 0 then 0 else 2)) + (x mod 3)) div 2)) div 2))
A336095: 1 1 2 2 3 4 4 4 5 6 7 8 8 8 9 9
(1 + ((x + ((x + (loop(\(x,i).(5x + 1),x,1) div (x + 1))) div 2)) div 2))
A338660: 1 2 5 13 43 167
(1 + compr(\x.(~1 + (loop(\(x,i).(2x + 2),x,1) mod (1 + (x div (1 + (x mod 2)))))),(x + 2)))
A161346: 3 4 5 6 7 9 11 13 17 19 23 29 31 37 41 43
(x div (1 + ((~1 + loop(\(x,i).2x,(x + ((x + (x div 2)) div 4)),2)) mod (x + 2))))
A166396: 0 1 0 1 1 2 0 1 1 1 2 3 3 3 0 1
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(x2 + 6x + 9))
A119575: 9 16 50 180 686 2688 10692 42900 173030 700128 2838524 11522056 46802700 190182400 772913160 3141129780
(loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,(~x + 3)) div (x + 3))
A120009: 1 1 1 0 ~6 ~33 ~143 ~572 ~2210 ~8398 ~31654 ~118864 ~445740 ~1671525 ~6273135 ~23571780
(compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + (8 div (x + 3)))
A098392: 2 3 4 6 10 12 15 17 21 27 29 35 39 41 45 51
((x3 + 6x2 + 11x + 6) * loop(\(x,i).(x * (4 + i)),x,4))
A200979: 24 480 7200 100800 1411200 20321280 304819200 4790016000 79035264000 1369944576000 24932991283200 475993469952000 9519869399040000 199184959733760000 4353614119895040000 4611686018427387903
((x * (4 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div (x + 3))
A165994: 0 1 2 4 7 9 12 14 18 23 25 30 34 36 40 45
loop(\(x,i).4x,(2x + (((3 * (x div 4)) div 2) + (x div 2))),1)
A130036: 1 16 1024 16384 4194304 67108864 4294967296 68719476736 70368744177664 1125899906842624 72057594037927936 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x5 div 32),1,(2x + 1))
A219088: 0 7 97 525 1845 5032 11602 23730 44370 77378 127628 201135 305175 448403 640973 894660
((2x + 1) + loop(\(x,i).x2,1,((2x + 1) div (3 + (x div 4)))))
A231407: 1 4 6
A185868: 1 4 6 11 13 15 22 24 26 28 37 39 41 43 45 56
((2x + 1) * loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),3x,1))
A187365: 1 42 2145 117572 6686100 388934370 22974421470 1372238454600 82653088824684 5011211083256840 305437356823765089 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((3x + 1) + (if ((x + 1) mod (3 + ((x div 2) div 3))) <= 0 then 1 else 2))
A189630: 3 6 8 12 15 17 21 23 27 30 33 35 39 42 44 48
loop(\(x,i).4x,(((3 * (2x + (x div 4))) div 2) + (x div 2)),1)
A220853: 1 64 16384 1048576 1073741824 68719476736 17592186044416 1125899906842624 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((x div (1 + (loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)))) + (x mod 2)))
A086765-A079868: 1 2 3 2 5 2 7 2 3 3 11 2 13 4 4 2
(if x <= 0 then 1 else (2 + ((x mod (((~x + ~1) + (x mod 2)) div 3)) mod 2) - (x mod 2)))
A138553: 1 1 2 1 2 2 2 1 3 1 2 2 3 1 3 1
(if x <= 0 then 0 else (1 + (((2x + ~2) mod (2 + (x div 2))) div 5) - (x mod 2)))
A230106: 0 0 1 0 1 0 1 0 1 0 1 1 2 0 2 0
((x + ~1) mod (1 + (if (x div 4) <= 0 then 1 else ((2 * (x div 2)) div 3)) - (x mod 2)))
A238877: 1 0 1 0 1 0 2 0 1 0 1 1 1 0 3 2
(1 + ((x + 1) mod ((if ((x3 div (x + 2)) mod 3) <= 0 then 1 else 2) + (x mod 2))))
A245514: 1 1 2 2 2 1 1 3 1 1 2 1 1 3 1 1
loop(\(x,i).(x2 + x),(((1 + (8 mod (1 + (x div 2)))) div 2) - (x mod 2)),1)
A139329: 1 1 1 1 2 1 1 1 6 2 2 1 2 1 1 1
(1 + (((1 + ((if (x mod 2) <= 0 then x else ~x) mod 10)) div 2) + (x mod 2)))
A175408: 1 7 2 6 3 5 4 4 5 3 1 7 2 6 3 5
((x + 2) div (1 + ((if x <= 0 then 1 else (2 * (1 + (4 * (x mod 3))))) + (x mod 2))))
A029304: 1 0 0 1 0 0 2 0 0 2 1 0 4 1 0 4
(1 + ((x div (2 + (x div (2 + (if (x mod 2) <= 0 then ((x mod 3) div 2) else 2))))) + (x mod 2)))
A166469: 1 2 2 3 2 3 2 4 3 4 2 4 2 4 3 5
((1 + (x div 2)) div (1 + (2 * (if ((x div 2) mod 6) <= 0 then x else 2)) - (x mod 2)))
A017860: 1 0 0 0 0 0 0 1 1 1 1 1 0 0 1 2
(if x <= 0 then 0 else (1 + ((x div (2 + (x div (1 + ((~x + 2) mod 4))))) div (2 - (x mod 2)))))
A194548: 0 1 1 2 1 2 1 3 2 2 1 3 2 2 1 4
(6 - ((1 + (if ((x + 1) mod 5) <= 0 then 2 else 0)) * (1 + (x mod 2))))
A131369: 5 4 5 4 3 4 5 4 5 0 5 4 5 4 3 4
(loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),((x + ~1) div 2),1) div (1 + (x mod 2)))
A028303: 1 0 1 1 2 2 5 7 14 21 42 66 132 214 429 715
((if x <= 0 then 1 else ((9x2 + ~1) + (x mod 2))) div (1 + (x mod 2)))
A282284: 1 4 35 40 143 112 323 220 575 364 899 544 1295 760 1763 1012
(loop(\(x,i).((4x * (1 + (2 * (i div 2)))) div (1 + i)),x,1) div (1 + (x mod 2)))
A098664: 1 1 8 12 96 160 1280 2240 17920 32256 258048 473088 3784704 7028736 56229888 105431040
(1 + ((2 * loop(\(x,i).(1 + (3 * (1 + (x div 2)))),(x div 2),(x mod 2))) + (x mod 2)))
A098144: 1 4 9 10 21 22 39 40 63 64 99 100 153 154 237 238
(~1 + (2 * (x + loop(\(x,i).((x + 1) - ((((2 - (x div 2)) mod (x + 1)) div 2) div 2)),2,x))))
A124981: 3 7 11 15 19 21 23 27 31 33 35 39 43 47 51 55
(1 + compr(\x.(~1 + ((x + 1) mod (1 + (x div (2 + (if (x mod 5) <= 0 then 2 else 0)))))),x))
A084925-A055721-A045718: 1 2 3 4 6 8 10 12 14 16 18 20 22 24 28 30
(1 + compr(\x.((~x + 1) mod (~1 + (6 * (if (~2 + (x div 3)) <= 0 then 0 else 2)))),x))
A290950: 1 2 3 4 5 6 7 8 9 13 24 35 46 57 68 79
loop(\(x,i).(~13x + 1),11x,1)
A015422: 1 ~1664148937320 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).8x,(x + (7 * ((x + 2) div 3))),1)
A067494: 1 16777216 134217728 1073741824 18014398509481984 144115188075855872 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x7,1,(7x + 1))
A016999: 1 2097152 170859375 2494357888 17249876309 78364164096 271818611107 781250000000 1954897493193 4398046511104 9095120158391 17565568854912 32057708828125 55784660123648
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(7x + 1))
A050477: 1 8 30 110 406 1512 5676 21450 81510 311168 1192516 4585308 17681020 68346800 264769560 1027653570
(1 + compr(\x.((x + 1) mod (1 + (x div (2 + (loop(\(x,i).(2x + 2),x,1) mod (x + 1)))))),x))
A344296: 1 2 3 4 6 8 9 10 12 16 18 20 24 27 28 30
loop(\(x,i).(((4x * (~1 + (2 * i))) div (1 + i)) * (1 + (2 * (1 + i)))),x,1)
A157713: 1 10 280 12600 776160 60540480 5708102400 630745315200 79894406592000 11408921261337600 1812981305892556800 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((2x + 1) - (((32 mod (x + 1)) div 2) div 2)),x,1)
A147596: 1 3 7 15 31 63 119 231 455 903 1799 3591 7175 14343 28679 57351
((x + 1) + (9 * (1 + (if (x mod 9) <= 0 then x else 0))))
A228915: 10 11 12 13 14 15 16 17 18 100 20 21 22 23 24 25
loop(\(x,i).(5 * ((4x * (~1 + (2 * i))) div (3 + i))),x,1)
A156125: 1 5 60 1000 20000 450000 11000000 286000000 7800000000 221000000000 6460000000000 193800000000000 5943200000000000 185725000000000000 4611686018427387903 4611686018427387903
loop(\(x,i).(1 + ((19x + 1) div (x + 4))),x,1)
A137002: 1 5 11 15
A171418: 1 5 11 15 16 16 16 16 16 16 16 16 16 16 16 16
(~1 + compr(\x.(2 - ((x + 1) mod (3 + (if ((x + ~1) mod 8) <= 0 then 2 else 1)))),x))
A230239: 0 1 4 5 9 12 13 16 17 20 21 25 28 29 32 33
loop(\(x,i).(7x + (((x + 1) div ~7) mod 2)),x,1)
A033134: 1 8 56 393 2752 19264 134849 943944 6607608 46253257 323772800 2266409600 15864867201 111054070408 777378492856 5441649449993
((3x + 1) * loop(\(x,i).((2 * (x - (2x * i))) div (1 + i)),2x,1))
A228329: 1 8 98 1320 18590 268736 3952228 58837680 883941750 13373883600 203487733020 3110407163760 47726453450988 734694122886080 11341161925265480 175489379096245984
(loop(\(x,i).((x + 2) - ((~2x + 2) div 5)),x,1) div (3x + 1))
A017818: 1 0 0 1 1 1 1 2 3 3 4 6 8 10 13 18
(37 * loop(\(x,i).3x,3x,1))
A306472: 37 999 26973 728271 19663317 530909559 14334558093 387033068511 10449892849797 282147106944519 7617971887502013 205685240962554351 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((~x + ~1) + loop(\(x,i).((x + 1) + ((x div (3 + ((x div 2) div 3))) mod 2)),x,1))
A080585: 0 0 0 1 2 3 3 3 3 3 3 3 4 5 6 7
(2x mod loop(\(x,i).((x + 1) + (((1 - (((x mod 2) - (x div 2)) div 2)) div 2) mod 2)),x,1))
A034151: 0 0 0 0 0 0 1 1 2 3 4 5 6 6 6 6
(1 + compr(\x.(loop(\(x,i).(~2x + ~32),(x + 1),0) mod (x + 1)),x))
A279542-A067947: 1 2 3 4 6 8 9 12 16 18 20 24 27 32 36 40
(1 + compr(\x.(loop(\(x,i).(5x2 + 20x + 30),2,0) mod (x + 1)),x))
A133030: 1 2 3 5 6 9 10 15 18 19 27 30 38 45 54 57
(1 + compr(\x.((14 - loop(\(x,i).(2x + 2),x,0)) mod (x + 1)),x))
A015924: 1 2 4 6 7 8 12 16 20 24 28 40 44 48 52 60
((6x + 5) - compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))
A158635: 5 10 15 19 23 25 29 31 35 37 37 41 41 43 47 49
(1 + compr(\x.(loop(\(x,i).(10x + 1),5,1) mod (x + 1)),x))
A109492: 1 3 7 11 13 21 33 37 39 77 91 111 143 231 259 273
((x + 1) + (loop(\(x,i).2x,(3x div (1 + (x mod 4))),1) mod (x + 1)))
A239826: 1 2 4 4 6 8 8 8 10 12 12 16 14 16 19 16
(1 + compr(\x.(x - (loop(\(x,i).(3x2 + ~1),2,5) mod (x + 1))),x))
A185092: 1 2 3 4 6 12
A018460: 1 2 3 4 6 12 37 74 111 148 222 444
(1 + compr(\x.(loop(\(x,i).(3x3 + 6x2),2,5) mod (x + 1)),x))
A342572: 1 3 5 7 9 15 17 21 25 27 31 35 45 49 51 63
(1 + compr(\x.(loop(\(x,i).x2,2,(3 * (x div (~2 + (x mod ~2))))) mod (x + 1)),x))
A231960: 1 3 6 9 12 18 24 27 30 36 42 48 54 60 66 72
(1 + compr(\x.(loop(\(x,i).(8x2 + 18),2,3) mod (x + 1)),x))
A018347: 1 2 3 6 9 13 18 26 39 78 117 234
(1 + compr(\x.(loop(\(x,i).(2x2 + 5x),2,12) mod (x + 1)),x))
A185092: 1 2 3 4 6 12
A018405: 1 2 3 4 6 12 29 58 87 116 174 348
(1 + compr(\x.((1 + loop(\(x,i).(6x2 + 12x + ~6),2,x)) mod (x + 1)),x))
A018607: 1 5 11 13 55 65 143 715
(1 + compr(\x.((1 + loop(\(x,i).10x,6,x)) mod (x + 1)),x))
A027892: 1 3 7 9 11 13 21 27 33 37 39 63 77 91 99 111
(1 + compr(\x.((1 + loop(\(x,i).(8x2 + 18x),2,x)) mod (x + 1)),x))
A018555: 1 3 9 23 27 69 207 621
(1 + compr(\x.((1 + loop(\(x,i).(x * (1 + (4x * (1 + i)))),2,x)) mod (x + 1)),x))
A018539: 1 2 4 149 298 596
(1 + compr(\x.((1 + (x * loop(\(x,i).(2x2 + ~x + 1),2,2x))) mod (x + 1)),x))
A018345: 1 3 7 11 21 33 77 231
(1 + compr(\x.((1 + (x * loop(\(x,i).(2x2 + ~3x + 1),2,2x))) mod (x + 1)),x))
A018436: 1 3 5 9 15 27 45 81 135 405
(1 + compr(\x.((1 + (x * loop(\(x,i).(3x2 + ~2x),2,2x))) mod (x + 1)),x))
A018617: 1 3 5 7 15 21 35 49 105 147 245 735
(1 + compr(\x.(loop(\(x,i).(10x2 + 10),2,(x + 1)) mod (x + 1)),x))
A172411: 1 2 5 10
A018773: 1 2 5 10 101 202 505 1010
(1 + compr(\x.((1 + (x * loop(\(x,i).(2x2 + 2),2,3x))) mod (x + 1)),x))
A018654: 1 3 9 89 267 801
(1 + compr(\x.((1 + (x * loop(\(x,i).(2x2 + x),2,3x))) mod (x + 1)),x))
A222011: 1 2 4 8
A018469: 1 2 4 8 16 29 58 116 232 464
(1 + compr(\x.((1 + (x * loop(\(x,i).(2x2 + ~x),2,3x))) mod (x + 1)),x))
A005018: 1 2 4 5 10 20
A018688: 1 2 4 5 10 20 43 86 172 215 430 860
(1 + compr(\x.((1 + (x * loop(\(x,i).(x * (~1 + (x * i))),2,3x))) mod (x + 1)),x))
A018368: 1 5 11 25 55 275
(1 + compr(\x.((1 + (x * loop(\(x,i).10x2,2,x))) mod (x + 1)),x))
A018766: 1 3 9 27 37 111 333 999
(1 + compr(\x.((1 + (x * loop(\(x,i).(6x2 + 3),2,x))) mod (x + 1)),x))
A222011: 1 2 4 8
A018482: 1 2 4 8 61 122 244 488
(1 + compr(\x.((1 + (x * loop(\(x,i).(6x2 + 2),2,x))) mod (x + 1)),x))
A018426: 1 5 7 11 35 55 77 385
(1 + compr(\x.((1 + (x * loop(\(x,i).(8x2 + ~2),2,x))) mod (x + 1)),x))
A018374: 1 3 5 15 19 57 95 285
(1 + compr(\x.((1 + (x * loop(\(x,i).(4x2 + ~4x + 4),2,x))) mod (x + 1)),x))
A018504: 1 3 9 59 177 531
(1 + compr(\x.((1 + (x * loop(\(x,i).((2x2 + 1) * (2 + i)),2,x))) mod (x + 1)),x))
A018572: 1 3 7 21 31 93 217 651
(1 + compr(\x.((1 + (x * loop(\(x,i).(4x2 + ~9x),2,x))) mod (x + 1)),x))
A018251: 1 2 3 6 9 18
A018518: 1 2 3 6 9 18 31 62 93 186 279 558
(1 + compr(\x.((1 + (x * loop(\(x,i).(8x2 + ~x),2,x))) mod (x + 1)),x))
A018563: 1 2 11 22 29 58 319 638
(1 + compr(\x.((1 + (x * loop(\(x,i).(3x2 + ~12x),2,x))) mod (x + 1)),x))
A018485: 1 2 13 19 26 38 247 494
(1 + compr(\x.((1 + (x * loop(\(x,i).~7x2,2,x))) mod (x + 1)),x))
A222011: 1 2 4 8
A018403: 1 2 4 8 43 86 172 344
(1 + compr(\x.((1 + (x * loop(\(x,i).(5x2 + ~4x),2,x))) mod (x + 1)),x))
A222011: 1 2 4 8
A018416: 1 2 4 8 16 23 46 92 184 368
(1 + compr(\x.((1 + (x * loop(\(x,i).(5x2 + ~8x),2,x))) mod (x + 1)),x))
A005018: 1 2 4 5 10 20
A018620: 1 2 4 5 10 20 37 74 148 185 370 740
((x + 1) + loop(\(x,i).x2,1,(46x + 46)))
A031770: 2117 8466 19047 33860 52905 76182 103691 135432 171405 211610 256047 304716 357617 414750 476115 541712
(1 + compr(\x.(loop(\(x,i).(5x2 + 6x + 1),3,2) mod (x + 1)),x))
A018404: 1 3 5 15 23 69 115 345
(1 + compr(\x.(loop(\(x,i).(4x2 + x + 1),2,6) mod (x + 1)),x))
A185092: 1 2 3 4 6 12
A018369: 1 2 3 4 6 12 23 46 69 92 138 276
(1 + compr(\x.(loop(\(x,i).(4x3 + ~x),2,6) mod (x + 1)),x))
A087007: 1 2 3 5 6 7 10 11 13 14 15 17 21 22 26 30
(1 + compr(\x.((~2 + loop(\(x,i).(6x2 + 12),2,(x + 1))) mod (x + 1)),x))
A018696: 1 2 19 23 38 46 437 874
(1 + compr(\x.(x - (loop(\(x,i).x5,2,~4) mod (x + 1))),x))
A003554: 1 3 11 31 33 93 251 341 601 753 1023 1801 1803 2761 4051 5403
(1 + compr(\x.(loop(\(x,i).(x3 + x),2,20) mod (x + 1)),x))
A018401: 1 2 4 5 10 17 20 34 68 85 170 340
(1 + compr(\x.(loop(\(x,i).((3x + 3) * ((x + 2) + (x div 2))),2,2) mod (x + 1)),x))
A018251: 1 2 3 6 9 18
A018441: 1 2 3 6 9 18 23 46 69 138 207 414
(1 + compr(\x.(loop(\(x,i).(4x3 + 6x2 + 3x + 1),2,2) mod (x + 1)),x))
A222011: 1 2 4 8
A018671: 1 2 4 8 13 16 26 32 52 64 104 208 416 832
(1 + compr(\x.(loop(\(x,i).(x2 + 2x + 1),2,16x) mod (x + 1)),x))
A018463: 1 2 4 113 226 452
(1 + compr(\x.(loop(\(x,i).(10x2 + x),2,4) mod (x + 1)),x))
A185092: 1 2 3 4 6 12
A018484: 1 2 3 4 6 12 41 82 123 164 246 492
(1 + compr(\x.((2 + (x * loop(\(x,i).(3x2 + 3),2,2x))) mod (x + 1)),x))
A018263: 1 2 4 13 26 52
A018587: 1 2 4 13 26 52 169 338 676
(1 + compr(\x.((2 + (x * loop(\(x,i).(3x2 + ~3),2,2x))) mod (x + 1)),x))
A018349: 1 2 7 14 17 34 119 238
(1 + compr(\x.(x - ((2 + (x * loop(\(x,i).3x2,2,2x))) mod (x + 1))),x))
A018450: 1 3 11 13 33 39 143 429
(1 + compr(\x.((2 + (x * loop(\(x,i).(4x2 + 4x),2,2x))) mod (x + 1)),x))
A018375: 1 2 11 13 22 26 143 286
(1 + compr(\x.((2 + (x * loop(\(x,i).(2x2 + ~3x + 1),2,2x))) mod (x + 1)),x))
A018435: 1 2 4 101 202 404
(1 + compr(\x.((2 + (x * loop(\(x,i).(2x2 + 8),2,2x))) mod (x + 1)),x))
A018497: 1 2 7 14 37 74 259 518
(1 + compr(\x.((2 + (x * loop(\(x,i).(4x2 + 2x),2,2x))) mod (x + 1)),x))
A018540: 1 2 13 23 26 46 299 598
(1 + compr(\x.((2 + (x * loop(\(x,i).(4x2 + x),2,2x))) mod (x + 1)),x))
A018651: 1 2 4 199 398 796
(1 + compr(\x.((2 + (x * loop(\(x,i).(3x2 + x),2,2x))) mod (x + 1)),x))
A018385: 1 2 4 7 11 14 22 28 44 77 154 308
(1 + compr(\x.(loop(\(x,i).(6x2 + 6x + ~2),2,2x) mod (x + 1)),x))
A018577: 1 2 7 14 47 94 329 658
(1 + compr(\x.((2 + (x * loop(\(x,i).(x2 + x),2,5x))) mod (x + 1)),x))
A018443: 1 2 11 19 22 38 209 418
(1 + compr(\x.((2 + (x * loop(\(x,i).~2x2,2,3x))) mod (x + 1)),x))
A172411: 1 2 5 10
A018571: 1 2 5 10 13 25 26 50 65 130 325 650
(1 + compr(\x.((2 + (x * loop(\(x,i).(6x2 + 6),2,x))) mod (x + 1)),x))
A018254: 1 2 4 7 14 28
A018692: 1 2 4 7 14 28 31 62 124 217 434 868
(1 + compr(\x.((2 + (x * loop(\(x,i).(~8x2 + 2x),2,x))) mod (x + 1)),x))
A018665: 1 2 3 6 137 274 411 822
(1 + compr(\x.((2 + (x * loop(\(x,i).(6x2 + ~2x),2,x))) mod (x + 1)),x))
A018415: 1 2 3 6 61 122 183 366
(1 + compr(\x.((2 + (x * loop(\(x,i).(8x2 + ~x),2,x))) mod (x + 1)),x))
A225227: 1 7 13
A018562: 1 7 13 49 91 637
((x2 + x + 1) * loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x + ~1),x))
A119577: 0 3 42 390 2940 19530 119196 684684 3758040 19909890 102539580 516023508 2547314952 12371513700 59252218200 280374917400
(1 + compr(\x.(loop(\(x,i).(x4 + ~2x3),1,5x) mod (x + 1)),x))
A018697: 1 5 7 25 35 125 175 875
(1 + compr(\x.(loop(\(x,i).(2x * (2 + ((x + ~1) mod 3))),3,x) mod (x + 1)),x))
A323383: 1 2 3 4 6 8 12
A018328: 1 2 3 4 6 8 12 16 24 32 48 64 96 192
(1 + compr(\x.(loop(\(x,i).(x5 + x),1,3x) mod (x + 1)),x))
A018354: 1 2 3 6 41 82 123 246
(1 + compr(\x.(loop(\(x,i).(20 * (x + (x div 2))),2,x) mod (x + 1)),x))
A029461: 1 2 3 4 5 6 8 9 10 12 15 16 20 24 25 30
(1 + compr(\x.(loop(\(x,i).(12x2 + 24x + 3),2,x) mod (x + 1)),x))
A018630: 1 3 11 23 33 69 253 759
(1 + compr(\x.(x - (loop(\(x,i).(9x2 + 18x),2,x) mod (x + 1))),x))
A222011: 1 2 4 8
A018523: 1 2 4 8 71 142 284 568
(1 + compr(\x.(loop(\(x,i).(12x2 + ~24x + 12),2,x) mod (x + 1)),x))
A185092: 1 2 3 4 6 12
A018521: 1 2 3 4 6 12 47 94 141 188 282 564
(1 + compr(\x.(loop(\(x,i).(18x2 + ~12),2,x) mod (x + 1)),x))
A185092: 1 2 3 4 6 12
A018561: 1 2 3 4 6 12 53 106 159 212 318 636
(1 + compr(\x.(loop(\(x,i).(12 * (x + (x div 4))),2,x) mod (x + 1)),x))
A101170: 1 2 3 4 5 6 7 8 9 10 12 15 18 20 24 25
(1 + compr(\x.(loop(\(x,i).(16x2 + 10x + 1),2,x) mod (x + 1)),x))
A018685: 1 3 5 9 15 19 45 57 95 171 285 855
(1 + compr(\x.(x - (loop(\(x,i).(6x2 + ~5x + 1),2,x) mod (x + 1))),x))
A018657: 1 2 13 26 31 62 403 806
(1 + compr(\x.(x - (loop(\(x,i).(5x2 + ~5x + 2),2,x) mod (x + 1))),x))
A318165: 1 3 13
A018579: 1 3 13 17 39 51 221 663
(1 + compr(\x.(loop(\(x,i).(~6x2 + 2x + ~4),2,x) mod (x + 1)),x))
A018706: 1 2 4 223 446 892
(1 + compr(\x.(loop(\(x,i).(2 + ((2x2 + x) * (4 + i))),2,x) mod (x + 1)),x))
A222011: 1 2 4 8
A018560: 1 2 4 8 79 158 316 632
(1 + compr(\x.(loop(\(x,i).(12x2 + ~20),2,x) mod (x + 1)),x))
A018625: 1 2 4 11 17 22 34 44 68 187 374 748
(1 + compr(\x.(loop(\(x,i).(4 * (1 + ((x2 + 2x) * (2 + i)))),2,x) mod (x + 1)),x))
A018637: 1 2 4 193 386 772
(1 + compr(\x.(loop(\(x,i).(12x2 + 12x + ~8),2,x) mod (x + 1)),x))
A222011: 1 2 4 8
A018580: 1 2 4 8 83 166 332 664
(1 + compr(\x.(loop(\(x,i).(8 * (1 + ((x + 2) * (x + i)))),2,x) mod (x + 1)),x))
A222011: 1 2 4 8
A018658: 1 2 4 8 101 202 404 808
(1 + compr(\x.(x - (loop(\(x,i).(16x2 + ~8),2,x) mod (x + 1))),x))
A018778: 1 3 9 113 339 1017
(1 + compr(\x.(loop(\(x,i).(~8x2 + ~28x + ~32),2,x) mod (x + 1)),x))
A222011: 1 2 4 8
A018681: 1 2 4 8 16 53 106 212 424 848
(1 + compr(\x.(loop(\(x,i).(4x2 + 20x + ~8),2,x) mod (x + 1)),x))
A222011: 1 2 4 8
A133036: 1 2 4 8 227 454 908 1816
(1 + compr(\x.(loop(\(x,i).(10x2 + 36x + 32),2,x) mod (x + 1)),x))
A222011: 1 2 4 8
A018547: 1 2 4 8 16 19 32 38 76 152 304 608
(1 + compr(\x.(loop(\(x,i).(14x2 + 6x),2,x) mod (x + 1)),x))
A222011: 1 2 4 8
A018735: 1 2 4 8 16 59 118 236 472 944
(1 + compr(\x.(loop(\(x,i).(x6 + 2x2),1,(~x + 2)) mod (x + 1)),x))
A018624: 1 3 9 83 249 747
(1 + compr(\x.(x - (loop(\(x,i).(x * (1 + (3x * (2 + i)))),2,x) mod (x + 1))),x))
A018641: 1 3 7 21 37 111 259 777
(1 + compr(\x.(x - (loop(\(x,i).(5x2 + x + 10),2,x) mod (x + 1))),x))
A018771: 1 3 5 15 67 201 335 1005
(1 + compr(\x.(loop(\(x,i).(11x2 + 2x),2,x) mod (x + 1)),x))
A018716: 1 3 9 101 303 909
(1 + compr(\x.(loop(\(x,i).(~11x2 + ~2x),2,x) mod (x + 1)),x))
A018695: 1 3 9 97 291 873
(1 + compr(\x.(loop(\(x,i).(x * (~2 + (x * (2 + (5 * i))))),2,x) mod (x + 1)),x))
A018251: 1 2 3 6 9 18
A018741: 1 2 3 6 9 18 53 106 159 318 477 954
(1 + compr(\x.(x - (loop(\(x,i).(x2 * (~1 + (3 * (2 + i)))),2,x) mod (x + 1))),x))
A018601: 1 3 5 15 47 141 235 705
loop(\(x,i).(((2x * (1 + (2 * i))) div (2 + i)) * (~1 + (2 * i)) * (1 + i)),x,1)
A274056: 1 4 90 5040 529200 89812800 22475653200 7791559776000 3576325937184000 2100278686746240000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).((4x + 2) - ((x - (x div 5)) div 3)),2,x))
A188089: 11 26 41 52 67 82 97 108 123 138 153 164 179 194 205 220
loop(\(x,i).(7x mod 44),x,1)
A070426: 1 7 5 35 25 43 37 39 9 19 1 7 5 35 25 43
((x + ~1) + (2 * ((x + (3 * (if (~2 + (x div 2)) <= 0 then 1 else 2)) - (x div 2)) div 2)))
A288737: 1 4 5 6 7 10 13 16 17 18 19 22 23 24 25 28
((~x + ~1) + ((loop(\(x,i).x2,1,(x + 21)) div 2) div 2))
A159027: 109 119 129 140 151 163 175 188 201 215 229 244 259 275 291 308
((~x + 1) + (2 * ((1 + (loop(\(x,i).(2x + 2),x,0) + (x2 div (x + 2)))) div 2)))
A289098-A286825: 1 2 7 14 29 62 125 254 509 1022 2045 4094 8189 16382 32765 65534
loop(\(x,i).(2 * (x - (2 * ((x mod (2 + (6 mod (1 + (x div 2))))) div 2)))),x,1)
A222011: 1 2 4 8
A273109: 1 2 4 8 12 16 32 64 128 256 512 1024 2048 4096 8192 16384
(1 + compr(\x.((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) mod 8),x))
A210494: 1 3 5 7 11 13 17 19 23 29 31 35 37 41 43 47
loop(\(x,i).(4 * (2x + (14x div (1 + i)))),x,1)
A053111: 1 36 960 21120 405504 7028736 112459776 1686896640 23991418880 326283296768 4271344975872 54103703027712 665891729571840 7990700754862080 93757555523715072 1078211888522723328
((2 + (x div 12)) mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1))
A097106: 0 0 0 0 0 2 0 0 0 2 0 2 0 3 3 0
loop(\(x,i).2x,(x + (2 * (((3 * (x + (x div 4))) - (x mod 2)) div 2))),1)
A130034: 1 8 256 2048 262144 2097152 67108864 536870912 274877906944 2199023255552 70368744177664 562949953421312 72057594037927936 576460752303423488 4611686018427387903 4611686018427387903
((~x + ~1) + ((loop(\(x,i).x2,1,(x + 27)) div 2) div 2))
A159263: 181 194 207 221 235 250 265 281 297 314 331 349 367 386 405 425
loop(\(x,i).((10x + 1) - ((i mod 3) mod 2)),x,1)
A033128: 1 10 101 1011 10110 101101 1011011 10110110 101101101 1011011011 10110110110 101101101101 1011011011011 10110110110110 101101101101101 1011011011011011
((x + 1) + (loop(\(x,i).((x + 1) - ((~4x + 2) div (x + 3))),2,x) div 2))
A186155: 2 5 7 9 10 12 14 15 17 19 20 22 24 25 27 28
((~1 + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1)) mod (x2 + 2x + 1))
A056615: 0 2 0 2 0 29 0 34 9 77 0 61 0 51 134 34
((x + 1) * loop(\(x,i).(10x + 81),(x + 1),0))
A328683: 81 1782 26973 359964 4499955 53999946 629999937 7199999928 80999999919 899999999910 9899999999901 107999999999892 1169999999999883 12599999999999874 134999999999999865 1439999999999999856
((x + 1) * (~1 + ((x + 2) mod (1 + (if (~1 + (x mod 7)) <= 0 then 2 else 1)))))
A344369: 1 ~2 ~3 0 ~5 0 ~7 ~8 0 0 ~11 0 ~13 0 0 16
((x + 1) * (1 + loop(\(x,i).3x,(1 + (3x div (x + 4))),1)))
A020331: 4 8 30 40 50 60 70 80 252 280 308 336 364 392 420 448
((x + 1) * (1 + (x mod (1 + (loop(\(x,i).2x,x,(1 + (x mod 2))) mod (2x + 1))))))
A053143: 1 4 9 4 25 36 49 16 9 100 121 36 169 196 225 16
((1 + (x mod (1 + (2 * (2 + (if ((x + 1) mod 8) <= 0 then 1 else 2)))))) mod (x + 1))
A037902-A037894-A037840: 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 2
(x + ((1 + (if (~2 + ((2x + ~4) mod (x + 2))) <= 0 then x else 0)) mod 3))
A333324: 1 3 2 4 5 6 7 9 8 10 11 12 13 14 15 16
((1 + ((1 + (x mod (2 + (if (x mod 5) <= 0 then 1 else 2)))) mod 3)) mod (x + 1))
A055091: 0 1 1 2 2 1 1 2 2 3 3 2 2 3 1 2
((x + 1) * loop(\(x,i).(5 * (2x - ((x div 2) mod 3))),(x + 1),1))
A113119: 10 180 2700 36000 450000 5400000 63000000 720000000 8100000000 90000000000 990000000000 10800000000000 117000000000000 1260000000000000 13500000000000000 144000000000000000
((x + 1) * (1 + ((1 + ((if ((x + ~1) mod 3) <= 0 then 1 else x) * (x mod 2))) mod (x + 1))))
A238642: 1 2 6 4 10 6 14 24 18 10 22 12 26 42 30 16
(loop(\(x,i).((x + 1) + ((4 * (x div 3)) div 3)),(x + ~1),1) div (x + 1))
A017835: 1 0 0 0 1 1 1 1 2 3 4 5 7 10 13 18
((x + 1) * (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))))
A131959: 1 2 3 8
A342768: 1 2 3 8 5 12 7 32 27 20 11 48 13 28 45 128
((x + 1) * loop(\(x,i).(2x4 + 2x3 + ~x2 + ~x),1,(2x + 3)))
A253680: 204 2940 16296 57960 159060 368004 754320 1412496 2465820 4070220 6418104 9742200 14319396 20474580 28584480 39081504
((1 + (2 * ((1 + loop(\(x,i).(0 - (2x * (1 + (2 * i)))),x,1)) div 2))) div (x + 1))
A292221: 3 ~3 20 ~210 3024 ~55440 1235520 ~32432400 980179200 ~33522128640 1279935820800 ~53970627110400 2490952020480000 ~124903451312640000 4611686018427387903 4611686018427387903
((6 * (x div (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))) mod (x + 1))
A340317: 0 0 0 2 0 0 0 2 3 0 0 6 0 0 0 14
((x + 1) * (1 + ((x + ((x2 + x + 1) * loop(\(x,i).(1 + (x * i)),x,1))) div 2)))
A281912: 1 8 57 424 3425 30336 294553 3123632 36003969 448816600 6022033721 86587079448 1328753602657 21683227579664 375013198304025 6853321766162656
((~1 + loop(\(x,i).((x + 2) + ((x - ((x + (x div 2)) div 4)) div 2)),x,2)) div (x + 1))
A091493: 1 2 2 3 3 4 5 6 7 9 11 14 17 21 26 32
((x + 1) * (if (~x + 2) <= 0 then (1 + (((x mod (1 + (x div 4))) div 2) + (x mod 2))) else 1))
A131959: 1 2 3 8
A060872: 1 2 3 8 5 12 7 16 18 20 11 36 13 28 30 48
((x + 1) * loop(\(x,i).(5 * (x + ((4x * i) div (1 + i)))),x,1))
A049394: 1 30 825 22000 577500 15015000 387887500 9974250000 255590156250 6531748437500 166559585156250 4239698531250000 107759004335937500 2735420879296875000 4611686018427387903 4611686018427387903
(loop(\(x,i).(1 + ((2x * (1 + (2 * i))) div (2 + i)) - (x mod 2)),x,1) div (x + 1))
A135445: 1 1 2 4 10
A245898: 1 1 2 4 10 26 74 217
((~x + ~1) + loop(\(x,i).((x + 1) + ((x3 div (x - ((~x + 2) div 2))) mod 2)),x,1))
A202276: 0 1 1 1 2 2 2 2 3 4 5 5 5 5 5 6
((x + 1) * ((~x + 1) + ((x + 1) * loop(\(x,i).(2 + (x * (x + i))),2,6))))
A031723: 2027 8104 18231 32408 50635 72912 99239 129616 164043 202520 245047 291624 342251 396928 455655 518432
((x + 1) * ((~x + 1) + ((x + 1) * loop(\(x,i).(x2 + 4x + 5),2,4))))
A031717: 1523 6088 13695 24344 38035 54768 74543 97360 123219 152120 184063 219048 257075 298144 342255 389408
((~x + ~1) + loop(\(x,i).(8x div 5),2,(4x + 4)))
A189381: 8 17 27 36 46 54 63 73 82 92 101 109 119 128 138 147
loop(\(x,i).(5 * ((2x * (1 + (2 * i))) div (2 + i))),(x + ~1),(x + 1))
A099046: 1 2 30 500 8750 157500 2887500 53625000 1005468750 18992187500 360851562500 6888984375000 132038867187500 2539208984375000 48970458984375000 946762207031250000
((2x + 1) - (((x + ~1) div (1 + (x div (2 + (if (x mod 3) <= 0 then 2 else 0))))) mod 2))
A227130: 0 3 5 7 8 10 13 14 16 19 20 22 25 26 28 30
((x + 1) * (2 + ((x + 1) * (1 + loop(\(x,i).(4x2 + 4x),2,3)))))
A031775: 9411 37640 84687 150552 235235 338736 461055 602192 762147 940920 1138511 1354920 1590147 1844192 2117055 2408736
((x + 1) * (2 + ((x + 1) * loop(\(x,i).(4x2 + 12x + 9),2,1))))
A031731: 2811 11240 25287 44952 70235 101136 137655 179792 227547 280920 339911 404520 474747 550592 632055 719136
((x + 1) * (2 + ((x + 1) * loop(\(x,i).(x2 + 2x + 1),2,7))))
A031743: 4227 16904 38031 67608 105635 152112 207039 270416 342243 422520 511247 608424 714051 828128 950655 1081632
((x + 1) * (2 + ((x + 1) * loop(\(x,i).(x2 + 4x + 4),2,7))))
A031761: 6891 27560 62007 110232 172235 248016 337575 440912 558027 688920 833591 992040 1164267 1350272 1550055 1763616
((x + 1) * (2 + ((x + 1) * loop(\(x,i).(4x3 + 4x2 + x),2,1))))
A031735: 3251 13000 29247 51992 81235 116976 159215 207952 263187 324920 393151 467880 549107 636832 731055 831776
((x + 1) * (2 + ((x + 1) * (~1 + loop(\(x,i).(2 + (x * (x + i))),2,8)))))
A031753: 5627 22504 50631 90008 140635 202512 275639 360016 455643 562520 680647 810024 950651 1102528 1265655 1440032
((x + 1) * (2 + ((x + 1) * (1 + loop(\(x,i).(6x2 + 2x),2,2)))))
A031747: 4763 19048 42855 76184 119035 171408 233303 304720 385659 476120 576103 685608 804635 933184 1071255 1218848
((~x + ~1) + ((loop(\(x,i).x2,1,(x + 19)) div 2) div 2))
A159026: 89 98 107 117 127 138 149 161 173 186 199 213 227 242 257 273
((~x + ~1) + ((loop(\(x,i).x2,1,(x + 25)) div 2) div 2))
A159258: 155 167 179 192 205 219 233 248 263 279 295 312 329 347 365 384
((2x + 2) * (4 + (3 * (if (x + ~1) <= 0 then 1 else 16))))
A019552: 14 28 312 416 520 624 728 832 936 1040 1144 1248 1352 1456 1560 1664
((x + 1) * ((if x <= 0 then 0 else (2 - (((x mod 2) - ((x2 + ~x) div 4)) div 2))) div 2))
A276560: 0 2 3 4 10 12 21 24 36 50 66 84 117 140 180 224
((2 + (if (x + ~2) <= 0 then x else (4x + ((x2 + ~x) div 4)))) div (x + 1))
A210691: 2 1 1 3 4 4 4 5 5 5 5 6 6 6 6 7
((4x + 4) + ((x + (((if (~2 + (x div 2)) <= 0 then 1 else 2) + (x div 2)) div 2)) div 2))
A190054: 4 8 13 18 22 27 32 36 41 46 50 55 60 64 69 73
((5x + 1) + (x2 div (1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2)))))
A315768: 1 6 12 18 24 30 35 40 46 52 58 64 70 76 82 88
((~x2 + ~3x + ~2) + (loop(\(x,i).((x2 + ~x) div 2),2,(x + 4)) div 3))
A227259: 3 9 23 50 96 168 274 423 625 891 1233 1664 2198 2850 3636 4573
((~x2 + ~3x + ~2) + (loop(\(x,i).((x2 + ~x) div 2),2,(2x + 4)) div 3))
A024386: 3 29 114 310 685 1323 2324 3804 5895 8745 12518 17394 23569 31255 40680 52088
loop(\(x,i).(7 * (x + (6x div (1 + i)))),x,(x + 1))
A050989: 1 56 1764 41160 792330 13311144 201885684 2826399576 37096494435 461645264080 5493578642552 62926446269232 697434779483988 7510836086750640 78863778910881720 809668130151718992
loop(\(x,i).(9 * (x + (8x div (1 + i)))),x,(x + 1))
A197194: 1 90 4455 160380 4691115 118216098 2659862205 54717165360 1046465787510 18836384175180 322102169395578 5270762771927640 83014513657860330 1264374900327411180 4611686018427387903 4611686018427387903
loop(\(x,i).(5 * (x + ((2x * (~1 + (2 * i))) div (1 + i)))),x,(x + 1))
A049382: 1 20 450 10500 249375 5985000 144637500 3512625000 85620234375 2092939062500 51277007031250 1258617445312500 30941012197265625 761624915625000000 4611686018427387903 4611686018427387903
((x + 1) * (x + (if x <= 0 then 1 else ((x + ~2) + (((x2 + ~x) div 2) + (x mod 3))))))
A128828: 1 2 15 28 65 120
((~x + ~1) + loop(\(x,i).((x + 1) - ((x + 1) mod (~1 + (x div ~5)))),2,x))
A199474: 1 2 3 2 4 3 5 4 3 6 5 4 7 6 5 4
((~x + 2) + ((x + 1) * loop(\(x,i).(11x + 7),2,x)))
A157443: 86 411 978 1787 2838 4131 5666 7443 9462 11723 14226 16971 19958 23187 26658 30371
((x + (if x <= 0 then 1 else (2 * (2x + ((x + (x2 div 3)) div 2))))) div (x + 1))
A091988: 1 2 4 5 5 6 6 7 7 8 8 8 9 9 9 10
loop(\(x,i).(~x + (54x div (1 + i))),x,(x + 1))
A017768: 1 52 1326 22100 270725 2598960 20358520 133784560 752538150 3679075400 15820024220 60403728840 206379406870 635013559600 1768966344600 4481381406320
loop(\(x,i).(x + (72x div (1 + i))),x,(x + 1))
A017737: 1 74 2775 70300 1353275 21111090 277962685 3176716400 32164253550 293052087900 2432332329570 18574174153080 131567066917650 870366750378300 5408707663065150 31731084956648880
loop(\(x,i).(~x + (72x div (1 + i))),x,(x + 1))
A017786: 1 70 2415 54740 916895 12103014 131115985 1198774720 9440350920 65033528560 396704524216 2163842859360 10638894058520 47465835030320 193253756909160 721480692460864
loop(\(x,i).(x + (60x div (1 + i))),x,(x + 1))
A017725: 1 62 1953 41664 677040 8936928 99795696 969443904 8361453672 65033528560 461738052776 3022285436352 18385569737808 104656320045984 560658857389200 2840671544105280
loop(\(x,i).(~x + (60x div (1 + i))),x,(x + 1))
A017774: 1 58 1653 30856 424270 4582116 40475358 300674088 1916797311 10648873950 52179482355 227692286640 891794789340 3155581562280 10142940735900 29752626158640
loop(\(x,i).(x + (52x div (1 + i))),x,(x + 1))
A017717: 1 54 1485 27720 395010 4582116 45057474 386206920 2944827765 20286591270 127805525001 743595781824 4027810484880 20448884000160 97862516286480 443643407165376
loop(\(x,i).(~x + (68x div (1 + i))),x,(x + 1))
A017782: 1 66 2145 45760 720720 8936928 90858768 778789440 5743572120 37014131440 210980549208 1074082795968 4922879481520 20448884000160 77413632286320 268367258592576
loop(\(x,i).(x + (66x div (1 + i))),x,(x + 1))
A017731: 1 68 2346 54740 971635 13991544 170230452 1799579064 16871053725 142466675900 1096993404430 7778680504140 51209646652255 315136287090800 1823288518168200 9967310565986160
loop(\(x,i).(~x + (62x div (1 + i))),x,(x + 1))
A017776: 1 60 1770 34220 487635 5461512 50063860 386206920 2558620845 14783142660 75394027566 342700125300 1399358844975 5166863427600 17345898649800 53194089192720
loop(\(x,i).((x + 1) + (((1 + ((x div 2) div 3)) div (1 + (x mod 4))) mod 2)),x,1)
A124391: 1 2 3 4 6 7 8 9 11 12 14 16 18 20 21 22
(x7 + loop(\(x,i).7x,x,1))
A001596: 1 8 177 2530 18785 94932 397585 1647086 7861953 45136576 292475249 1996813914 13877119009 96951758924 678328486353 4747732369318
(1 + (x * (x + ((1 + loop(\(x,i).10x2,x,2)) div 3))))
A140285: 1 15 10671
(1 + loop(\(x,i).(x + ((2x + 1) mod (1 + (2x mod (2 + (x div 4)))))),x,x))
A291934-A291785: 1 2 3 4 5 7 7 8 9 11 11 16 13 16 16 16
((1 + loop(\(x,i).((x + 1) + (2 * (x - ((~1 + (2 * (x mod 2))) * (1 + i))))),x,0)) div 2)
A076149: 0 3 5 20 54 169 499 1506 4508 13535 40593 121792 365362 1096101 3288287 9864878
(if x <= 0 then 1 else (2 * (1 + ((x + ~4) mod (1 + (x mod (1 + (x div 5))))))))
A318472: 1 2 2 2 2 4 2 4 2 4 2 4 2 4 4 8
((1 + (if (x + ~1) <= 0 then 0 else (1 + (7 * ((x + 1) mod 3))))) div 2)
A021679: 0 0 1 4 8 1 4 8 1 4 8 1 4 8 1 4
((if x <= 0 then 2 else (1 + (x mod (1 + (x div (3 + (x mod (2 + ((x div 2) mod 2))))))))) div 2)
A280716: 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 2
(if x <= 0 then 1 else (2 * (1 + (((x2 + 2x) div 2) mod (1 + ((1 + (x div 2)) div 3))))))
A342087: 1 2 2 2 2 4 2 4 2 4 2 6 2 4 4 4
(x mod (if (x + ~1) <= 0 then 1 else (2 * (1 + ((x mod 6) mod (1 + (x div 3)))))))
A079327: 0 0 0 3 0 1 0 3 2 1 0 3 0 1 2 7
(if x <= 0 then 1 else (2 * (1 + (x mod (1 + (((x + ~1) mod 6) mod (1 + (x div 2))))))))
A058263: 1 2 2 2 2 4 2 2 2 2 6 4 2 2 2 2
((x + 1) div ((2x + 2) div (2 + (x div (1 + (if (x mod 2) <= 0 then 6 else 1))))))
A293224: 1 1 1 2 1 2 1 2 1 3 1 4 1 4 2 5
(~2 + (if x <= 0 then 0 else (1 + ((5x + 6) mod 7))))
A194518: ~2 3 1 ~1 4 2 0 5 3 1 ~1 4 2 0 5 3
((loop(\(x,i).((x2 + ~x) div 2),2,(x + ~1)) div (1 + (x mod 7))) div 2)
A273923: 0 0 0 0 0 1 3 52
(if x <= 0 then 1 else (2 * (1 + ((x div 2) mod (1 + (((~x + 2) mod (2 + (x div 4))) div 2))))))
A083533: 1 2 2 2 2 2 4 2 2 2 2 4 2 2 4 4
(2 * (if x <= 0 then 0 else (1 + (x div (3 + ((~2x + 1) mod (4 + (x div 2))))))))
A276604: 0 2 2 4 2 2 4 4 6 2 2 4 4 4 4 6
((1 + loop(\(x,i).26x,x,9)) div 2)
A208387: 5 117 3042 79092 2056392 53466192 1390120992 36143145792 939721790592 24432766555392 635251930440192 16516550191444992 429430304977569792 4611686018427387903 4611686018427387903 4611686018427387903
(2 * loop(\(x,i).(x * i),2x,(1 + (x mod (1 + ((x2 + 2x) mod 8))))))
A279109: 2 8 48 5760 80640 14515200 958003200 1394852659200 41845579776000 25609494822912000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * (1 + ((6 * (x + (if (x + ~4) <= 0 then 1 else 2))) div 5)))
A103800: 4 6 8 10 14 18 20 22 26 28 30 32 34 38 40 42
(if x <= 0 then 1 else (2 + (((1 + (x div 3)) div 2) div (1 + (x mod (1 + (x mod 4)))))))
A292585: 1 2 2 2 3 2 3 2 3 3 3 2 4 3 2 2
((if (x mod 3) <= 0 then ((1 + (x div 5)) * (3 + (x mod 2))) else 1) div 2)
A280728: 1 0 0 2 0 0 3 0 0 4 0 0 4 0 0 8
(if x <= 0 then 1 else (x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))))
A136167: 1 0 0 1 0 1 0 2 1 1 0 2 0 1 1 3
((1 + loop(\(x,i).((2x + 2) * (1 + (x mod 2))),(x div 2),(1 + (2 * (x mod 2))))) div 2)
A222011: 1 2 4 8
A246347: 1 2 4 8 9 17 19 35 39 71 79 143 159 287 319 575
(if x <= 0 then 1 else (2 + ((x + 2) mod (1 + (((x + 1) mod 7) mod 3)))))
A334216-A082091: 1 2 2 3 2 2 2 3 3 2 2 3 2 2 2 4
(1 - ((1 + (if x <= 0 then 2 else (((x + 1) - ((x2 + ~x) div 4)) div 3))) div 2))
A026823: 0 1 0 0 1 1 1 1 2 2 3 3 4 5 6 7
(if x <= 0 then 1 else (x div (2 + ((x + 1) div (1 + ((x - ((x div 3) mod 2)) mod 3))))))
A039651: 1 0 0 1 0 1 0 1 1 1 0 1 0 1 2 2
loop(\(x,i).x6,1,(12x + 10))
A017646: 1000000 113379904 1544804416 9474296896 38068692544 117649000000 304006671424 689869781056 1418519112256 2699554153024 4826809000000 8198418170944 13339032325696 20924183895616
(22 * (x + loop(\(x,i).(x * (1 + i)),4,(x + 1))))
A157609: 2640 5302 7964 10626 13288 15950 18612 21274 23936 26598 29260 31922 34584 37246 39908 42570
((1 + ((loop(\(x,i).(~1 + (((x2 + ~x) div 2) + i)),x,(~x + 1)) div 2) div 3)) div 2)
A191938: 0 0 0 1 615
loop(\(x,i).x7,1,(12x + 2))
A017551: 128 105413504 8031810176 114415582592 781250000000 3521614606208 12151280273024 34792782221696 86812553324672 194871710000000 402271083010688 775771085481344 1414067010444416 2458100350228352
(3 + ((x + loop(\(x,i).((x + 1) + (x div 5)),(x + ~2),1)) div 3))
A120188: 3 3 4 4 5 6 6 7 8 9 11 12 14 16 18 21
(x - (2 * (x div (1 + (loop(\(x,i).2x,x,(1 + (x mod 3))) mod (2x + 1))))))
A144774: 0 1 2 1 4 5 6 1 4 9 10 7 12 13 14 1
((x + 2) - (if x <= 0 then 1 else ((x mod 2) - ((1 + (8 mod (1 + (x div 2)))) div 2))))
A233272: 1 2 4 4 7 7 8 8 12 12 13 13 15 15 16 16
((1 + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(3x + 1))) div 2)
A097613: 1 2 7 25 91 336 1254 4719 17875 68068 260338 999362 3848222 14858000 57500460 222981435
((1 + loop(\(x,i).(2 * (x - (~12x div (x + 2)))),x,1)) div 2)
A173034: 1 5 20 52 116 244 500 1012 2036 4084 8180 16372 32756 65524 131060 262132
((if x <= 0 then 2 else (~1 + ((1 + (x mod (1 + (2 * ((x + 1) mod 3))))) mod (x + 1)))) div 2)
A113429: 1 ~1 0 0 ~1 0 0 1 0 0 0 0 0 1 0 0
(2 * (1 + compr(\x.(~1 + (loop(\(x,i).(4x + 1),x,1) mod (2x + 1))),(x + 1))))
A243937: 6 8 12 14 18 20 24 30 32 36 38 42 44 48 54 60
(2 * (1 + compr(\x.(~1 + (loop(\(x,i).(4x + 9),x,1) mod (x + 1))),(x + 1))))
A050990: 4 6 8 10 12 14 22 24 26 30 34 38 46 56 58 62
((1 + (if (x mod 2) <= 0 then (1 + (x div 2)) else ((1 + (x mod 8)) mod (x + 1)))) div 2)
A029189: 1 0 1 0 2 0 2 0 3 1 3 2 4 3 4 4
((1 + ((12 * loop(\(x,i).(2x + 4),x,4)) div (x + 1))) div 2)
A003138: 24 36 56 90 149 252 435 765 1363 2455 4466 8190 15122 28085 52427 98303
loop(\(x,i).x7,1,(8x + 6))
A017143: 279936 105413504 2494357888 21870000000 114415582592 435817657216 1338925209984 3521614606208 8235430000000 17565568854912 34792782221696 64847759419264 114868566764928 194871710000000
((1 + (loop(\(x,i).((x + 2) + (5 * (x div 3))),x,2) div (x + 1))) div 2)
A003008: 1 1 2 4 8 17 39 90 213
((1 + ((x mod (~1 + (5 * (if (x mod 5) <= 0 then 2 else 1)))) div 2)) div 2)
A273302: 0 0 1 1 0 1 1 1 0 0 0 1 0 0 1 2
((1 + (if x <= 0 then 1 else (x div (2 + (x div (1 + ((x div 2) mod (1 + (x mod 4))))))))) div 2)
A170980: 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 2
((1 + ((if x <= 0 then 2 else (1 + ((6x + 3) mod (1 + (x div 2))))) div 2)) div 2)
A112222: 1 0 1 1 0 0 1 1 1 1 1 1 2 1 2 2
((1 + ((1 + ((1 + loop(\(x,i).(2x + ((i * i) div (x + 2))),x,1)) div 2)) div 2)) div 2)
A246878: 1 1 1 2 3 6 12 24 47 94 188 376 752 1504 3008 6016
(if (x mod 2) <= 0 then 1 else (2 * (1 + (x mod (2 * (1 + (x mod (2 * (1 + (x mod 4))))))))))
A297402: 1 4 1 8 1 4 1 16 1 4 1 8 1 4 1 32
((1 + ((1 + (loop(\(x,i).((x + 2) + (x div 2)),(x div 2),(1 + (x mod 2))) div 2)) div 2)) div 2)
A005686: 0 1 1 1 1 1 2 2 3 3 4 5 6 8 9 12
(2 * (1 + ((1 + (((2 + loop(\(x,i).(3x + ~3),x,2)) mod (x + 1)) div 2)) div 2)))
A102763: 2 2 4 2 4 4 4 2 6 4 4 4 4 4 6 6
(if x <= 0 then 1 else (2 * (1 + (((x + 1) mod (1 + (2 * ((1 + (x div 4)) div 2)))) div 2))))
A049716: 1 2 2 2 4 2 2 4 2 2 4 2 4 6 2 2
(3 + ((1 + ((((x2 + 3x) * (if (x mod 2) <= 0 then x else 1)) div 2) div 2)) div 2))
A053991: 3 4 6 5 17 8
(if (x + ~1) <= 0 then 1 else (2 * (1 + ((x mod (1 + (x div (2 + (x div 8))))) div 2))))
A096445: 1 1 2 2 2 4 4
A219654: 1 1 2 2 2 4 4 4 4 2 4 4 4 4 6 4
((1 + ((if x <= 0 then 2 else (1 + (((x2 mod (3x + 2)) div 2) div 2))) div 2)) div 2)
A137900: 1 0 1 1 0 1 1 0 1 2 1 1 2 1 2 3
(2 * (1 + (if x <= 0 then 1 else (2 + ((3 * ((x2 + x) div 2)) div 5)))))
A178549: 4 6 8 12 18 24 30 38 48 60 72 84 98 114 132 150
((x + 1) div (if x <= 0 then 1 else (2 * (1 + ((x2 + ~x + 2) mod 10)))))
A029388: 1 0 0 0 0 1 1 0 0 1 1 2 1 0 1 2
((1 + (x mod (2 + ((x + (if (~4 + (x div 2)) <= 0 then 1 else x)) mod 5)))) div 2)
A182071: 0 1 1 2 0 1 1 1 1 1 0 2 0 1 2 1
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 14)
A193063-A165132: 2 3 5 7 11 13
A039712: 2 3 5 7 11 13 3 5 9 1 3 9 13 1 5 11
(3 + (if x <= 0 then 1 else (2 * (6x - ((x div 3) + (x div 2))))))
A063129: 4 15 25 35 45 57 65 77 87 97 107 119 127 139 149 159
((1 + (((if ((1 + (x div 2)) mod 2) <= 0 then (x mod 2) else (x div 2)) + (x mod 3)) div 2)) div 2)
A053616: 0 0 1 0 1 1 0 1 2 1 0 1 2 2 1 0
(2 * ((if ((x + 1) mod (1 + (x div 4))) <= 0 then 1 else 2) * (1 + ((x mod 3) div 2))))
A100008: 2 2 4 2 4 4 4 2 4 4 4 4 4 4 8 2
((if x <= 0 then 2 else (1 + (((2 * (1 + (2 * (1 + (x mod 2))))) mod (1 + (x div 2))) div 2))) div 2)
A197945: 1 0 0 0 0 0 1 1 0 0 0 1 2 1 2 1
(1 - ((1 + (loop(\(x,i).((x + ~1) + ((x + (x div 2)) div 5)),x,1) div 2)) div 2))
A274200: 1 1 1 2 2 3 4 5 7 9 12 16 20 27 35 45
((1 + (loop(\(x,i).((x + 1) + (3 * (((1 + (x div 2)) div 2) div 2))),x,1) div 2)) div 2)
A003269: 0 1 1 1 1 2 3 4 5 7 10 14 19 26 36 50
(2 - (2 * (1 + (2 * loop(\(x,i).(2x + ~44),x,1)))))
A278124: ~4 168 512 1200 2576 5328 10832 21840 43856 87888 175952 352080 704336 1408848 2817872 5635920
(1 - ((1 + (loop(\(x,i).(1 + (8 * (x mod 2)) - (x div 2)),x,1) div 2)) div 2))
A118828: 1 ~1 0 ~1 ~1 1 0 1 1 ~1 0 ~1 ~1 1 0 1
((1 + ((loop(\(x,i).~10x,(x + 1),1) mod (x + 1)) div 2)) div 2)
A257992: 0 0 1 0 0 1 1 0 2 0 0 1 1 1 1 0
((1 + (((x + 1) * (~1 + (2 * loop(\(x,i).(x2 + 2),2,5)))) div 2)) div 2)
A033173: 365 731 1096 1461 1826 2192 2557 2922 3287 3653 4018 4383 4748 5114 5479 5844
(3 + ((loop(\(x,i).x5,1,(x mod 3)) mod (x + 1)) div 2))
A121937: 3 3 4 3 3 4 3 3 5 3 3 7 3 3 4 3
((1 + ((loop(\(x,i).2x,(x + ~1),(1 + ((x * (x div 2)) mod 2))) mod (x + 1)) div 2)) div 2)
A249071: 0 0 1 0 1 1 1 0 1 2 2 2 2 2 1 0
((1 + ((loop(\(x,i).2x,x,(0 - (4 * (x mod 4)))) mod (x + 1)) div 2)) div 2)
A213185: 0 0 0 0 0 1 2 0 0 1 1 0 0 2 3 0
((4x + 6) * loop(\(x,i).(13x + 13),2,x))
A240719: 1092 3510
(x div (2 + (2x div (1 + (2 * (if (16 mod (x + 1)) <= 0 then 0 else 2))))))
A303975: 0 0 1 0 1 1 1 0 1 1 1 1 2 1 2 0
(if x <= 0 then 1 else (2 * (1 + ((((x + 1) + (x div 2) - ((x div 2) mod 3)) div 2) div 2))))
A035114: 1 2 2 4 4 4 6 6 8 8 8 8 10 12 12 12
(x div (2 + ((x + 1) mod (5 + ((if (x mod 2) <= 0 then x else (~x + 2)) mod 3)))))
A234716: 0 0 0 0 0 1 1 1 2 1 1 2 2 3 4 3
(2 * (1 + (16 * loop(\(x,i).(2x + ~1),x,12))))
A277988: 386 738 1442 2850 5666 11298 22562 45090 90146 180258 360482 720930 1441826 2883618 5767202 11534370
(if x <= 0 then 1 else (2 * (x mod (1 + (2 * ((2x mod (4 + (x div 3))) mod 2))))))
A028605: 1 0 0 0 2 0 0 0 0 0 0 4 0 0 0 0
((1 + ((loop(\(x,i).(2x + 4),x,(4 + (x div 8))) div 2) div 2)) div 2)
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A290547: 1 2 4 8 16 32 64 128 288 576 1152 2304 4608 9216 18432 36864
((1 + (((((x + 4) * loop(\(x,i).(x + (x div 2)),(x + ~1),2)) div 2) div 2) div 2)) div 2)
A206139: 1 1 1 2 3 5 8 13 21 34 55 88 141 224 356 563
((1 + ((((loop(\(x,i).(x + (x2 div 4)),2,(x + ~2)) div 2) div 2) div 2) div 2)) div 2)
A319471: 0 0 0 0 0 0 1 1 2 3 5 7 11 14 20 25
((if x <= 0 then 2 else (1 + (x div (2 + (((~x + ((x + 1) * (x div 2))) div 4) mod 2))))) div 2)
A050373: 1 0 1 1 1 1 1 2 1 2 2 3 3 2 4 4
((if x <= 0 then 1 else 5x) - ((1 + ((x - ((x div 4) mod 2)) div 2)) div 2))
A314896: 1 5 9 14 19 24 29 33 38 43 47 52 57 62 67 71
((x div 2) - ((if x <= 0 then 0 else (1 + (((1 + (x div 2)) div (2 + ((x div 2) mod 2))) mod 2))) mod 2))
A055656: 0 ~1 0 0 2 2 3 3 3 3 4 4 6 6 6 6
loop(\(x,i).((x2 + x) div 2),1,(1 - (x div (~2 + (((~x + 2) div 2) div 5)))))
A013322: 1 3 3 3 6 6 6 10 10 10 15 15 15 15 15 15
((loop(\(x,i).10x,(x + 1),1) div (x + 1)) mod 10)
A061480: 0 0 3 0 0 6 1 0 1 0 0 3 0 7 6 0
((2 + compr(\x.(1 - ((~1 + loop(\(x,i).2x,x,2)) mod (x + 2))),x)) mod 10)
A088308: 2 4 6 8 9 0 2 4 5 6 8 0 1 2 4 5
((~2 - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 10)
A072003: 8 7 5 3 9 7 3 1 7 1 9 3 9 7 3 7
(1 - (((x + (if (2 - (x div 4)) <= 0 then (x div 3) else 1)) mod 5) div 2))
A259660: 1 0 0 ~1 1 1 0 0 1 0 0 ~1 1 0 0 1
(if x <= 0 then 1 else (2 * (2x - ((~x + ((x div 2) mod 5)) div 5))))
A315171: 1 6 10 14 18 22 26 30 34 38 44 50 54 58 62 66
(2 - ((if ((x + 1) mod (1 + (x div 4))) <= 0 then 1 else 2) mod (2 + (x mod 5))))
A035172: 1 1 1 1 0 1 0 1 1 0 2 1 0 0 0 1
(2 * (1 + (2 * (compr(\x.(~1 + (loop(\(x,i).4x,x,1) mod (2x + 1))),x) div 2))))
A082542: 2 2 6 6 10 14 18 18 22 30 30 38 42 42 46 54
(2 + ((~1 + ((loop(\(x,i).(2x + 2),x,0) mod (x + 1)) div 2)) div (1 + (2 * (x mod 2)))))
A330690: 1 1 1 2 1 2 1 2 4 2 1 2 1 2 4 4
(6 * (~1 + loop(\(x,i).(2x + 6),x,17)))
A304510: 96 234 510 1062 2166 4374 8790 17622 35286 70614 141270 282582 565206 1130454 2260950 4521942
((3 * (1 + ((x div 3) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))) div 2)
A157261: 1 1 1 3 1 1 1 4 1 1 1 3 1 1 1 9
(~2 + (3 * loop(\(x,i).(2x + 12),x,17)))
A304171: 49 136 310 658 1354 2746 5530 11098 22234 44506 89050 178138 356314 712666 1425370 2850778
(1 + (x div 2) - (if x <= 0 then 1 else ((3 * ((x + (x mod 2)) div 5)) div 2)))
A307092: 0 1 2 2 3 2 3 3 4 2 3 3 4 4 5 4
((3 * ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3)) div 2)
A076277: 0 0 0 1 0 1 0 3 1 1 0 4 0 1 1 7
(if x <= 0 then 1 else (2 * ((32x3 + 16x) div 3)))
A019560: 1 32 192 608 1408 2720 4672 7392 11008 15648 21440 28512 36992 47008 58688 72160
(x div (2 + (if x <= 0 then 0 else (1 - ((0 - ((x2 div 4) mod (x + 1))) div 3)))))
A154364: 0 0 0 0 0 1 1 1 1 3 2 2 1 4 2 2
(((if ((x * (x mod 3)) mod 5) <= 0 then 0 else 2) + ((x + 1) div 3)) div 2)
A057431: 0 1 1 0 1 1 1 2 2 1 1 3 2 3 3 2
(if x <= 0 then 1 else (2 * ((2 * (4x - (x div 7))) div 3)))
A310503: 1 4 10 16 20 26 32 36 40 46 52 56 62 68 72 76
((3 * ((1 + ((loop(\(x,i).x2,1,((x div 2) - (x mod 2))) div 2) div 2)) div 2)) div 2)
A340760: 0 0 0 0 1 0 1 1 3 1 4 3 7 4 9 7
(if x <= 0 then 1 else (2 * ((2 * (4x - ((x div 2) div 5))) div 3)))
A310504: 1 4 10 16 20 26 32 36 42 48 52 56 62 68 72 78
(loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),3) div 2)
A151787: 1 3 3 6 3 6 6 12 3 6 6 12 6 12 12 24
(if x <= 0 then 1 else (2 * (2x - (((~x + 1) + (2 * ((~x + 1) div 3))) div 3))))
A310502: 1 4 10 16 20 26 30 36 42 46 50 56 62 66 72 76
(x - ((3 * ((1 + (if ((x mod 3) div 2) <= 0 then (x mod 3) else x)) div 2)) div 2))
A082009: 0 0 1 3 3 1 6 6 2 9 9 2 12 12 4 15
((3 * ((loop(\(x,i).2x,x,(1 + (4 * (x mod 2)))) mod (x + 1)) div 2)) div 2)
A293903: 0 0 0 0 0 3 0 0 3 0 0 3 0 7 3 0
((loop(\(x,i).(x3 + 3x2 + 2x),1,((x2 + 3x + 2) div 2)) div 3) div 2)
A198833: 1 10 56 220 680 1771 4060 8436 16215 29260 50116 82160 129766 198485 295240 428536
(if x <= 0 then 1 else (2 + ((2 * (2x div (4 + (x div 8)))) div 3)))
A028829: 1 2 2 2 3 3 4 4 4 4 4 4 4 5 5 6
(if x <= 0 then 1 else (2 + ((2 * (((2x + 1) mod (2 + (x div 4))) div 2)) mod 3)))
A048669: 1 2 2 2 2 4 2 2 2 4 2 4 2 4 3 2
((if x <= 0 then 1 else 2x) - ((x - (((2x2 + 3x + ~2) div 2) div 3)) div 2))
A127762: 1 2 4 7 10 13 16 20 25 29 34 39 45 51 57 64
(2 * loop(\(x,i).(2x + (10x div (1 + i))),2x,3))
A054324: 6 224 4032 50688 512512 4472832 35094528 254017536 1725825024 11142168576 68975329280 412216197120 2390853943296 13514114596864 74693776244736 404792077713408
(loop(\(x,i).7x3,(2x + 1),1) div 6)
A022241: 1 16148168401 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 * (3x - ((x + ((x div 3) mod 3)) div 3))))
A315646: 1 6 12 16 22 26 32 36 42 48 54 60 64 70 74 80
loop(\(x,i).x7,1,(9x + 2))
A017191: 128 19487171 1280000000 17249876309 114415582592 506623120463 1727094849536 4902227890625 12151280273024 27136050989627 55784660123648 107213535210701 194871710000000 337931541778439
((if x <= 0 then 1 else 5x) - ((x - ((x + (x div 3)) div 3)) div 2))
A314894: 1 5 9 14 19 24 28 33 38 43 47 52 57 61 66 71
((loop(\(x,i).((x + 1) - (x div (~2 + ((~x + 2) div 4)))),x,0) + (x div 3)) div 2)
A025201: 0 0 1 3 4 6 8 10 12 15 17 19 22 25 27 30
((((if ((x + 1) mod 5) <= 0 then 2 else 1) * (1 + (x mod 2))) + (x mod 3)) div 2)
A156542: 0 1 1 1 1 2 0 1 1 2 1 2 0 1 2 1
(((2 * (if (~x + 2) <= 0 then ((x div 2) - ((x + ~1) div 3)) else 1)) - (x mod 3)) div 2)
A029298: 1 0 0 1 0 0 2 0 1 2 1 1 3 1 2 3
((if ((x + ((~x + 1) mod 3)) mod 5) <= 0 then 2 else 0) + ((x mod 3) div 2))
A291770: 0 0 1 0 0 1 0 0 3 2 2 1 0 0 1 0
((1 + ((x + (loop(\(x,i).((x + 2) + (x div (2 + (x mod 2)))),x,2) div (x + 2))) div 2)) div 2)
A100665: 0 1 1 1 2 2 3 4 5 6 7 9 12 15 19 25
(2 * loop(\(x,i).x2,1,(1 + (((2x + 1) + (x2 div 4)) div (x + 2)))))
A245508: 2 8 8 8 18 18 18 32 32 32 32 50 50 50 50 72
((1 + loop(\(x,i).((5 * (3 + (x mod 2))) div (x + 1)),2,2x)) div 2)
A083662: 1 2 3 3 5 5 5 5 8 8 8 8 8 8 8 8
((4x + 2) + (if x <= 0 then 1 else ((x + 2) + (2x div 9))))
A001968: 3 9 14 19 24 30 35 40 45 51 56 61 66 71 77 82
(if x <= 0 then 0 else (1 - (x mod (2 + ((2 * (1 + (x mod (2 + (x mod 2))))) mod (1 + (x div 2)))))))
A324692: 0 0 1 0 1 0 ~1 0 1 0 ~1 0 1 0 ~1 ~2
(loop(\(x,i).((2x + 1) - (7 * ((x div 4) mod 2))),x,1) div 2)
A215095: 0 1 3 4 8 17 35 68 136 273 547 1092 2184 4369 8739 17476
(2 * (1 + compr(\x.((x + 1) mod (1 + (x div (2 + (if (x mod 2) <= 0 then 1 else 8))))),x)))
A319796: 2 4 6 8 12 16 18 20 24 28 30 32 36 40 42 48
loop(\(x,i).x7,1,(10x + 2))
A017299: 128 35831808 2494357888 34359738368 230539333248 1028071702528 3521614606208 10030613004288 24928547056768 55784660123648 114868566764928 221068140740608 402271083010688 698260569735168
(1 - (loop(\(x,i).(x - ((2 - ((x div 2) div (1 + ((x + ~1) mod 3)))) div 2)),x,1) div 2))
A335766: 1 1 2 2 3 3 4 5 6 7 9 10 12 14 18 20
(((x + 1) + ((x + ((x + loop(\(x,i).2x,(~2 + (x div 3)),x)) div 2)) div 2)) div 2)
A259627: 0 1 2 3 4 5 6 7 8 10 11 12 17 18 19 28
(loop(\(x,i).((2x + 2) - ((4x + 4) mod 7)),x,1) div 2)
A222010: 0 1 3 7
A275788: 0 1 3 7 13 25 49 99 199 399 797 1593 3185 6371 12743 25487
(((1 + ((x + 1) div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))) mod (x + 1)) div 2)
A286471: 0 0 0 1 0 2 0 1 1 3 0 1 0 4 2 1
((if x <= 0 then 2 else ((1 + (x mod (1 + (x mod (2 * (2 + ((x div 2) mod 2))))))) mod (x + 1))) div 2)
A131802: 1 0 0 0 0 1 0 1 0 1 0 3 0 1 1 2
((x + 2) div (2 + (loop(\(x,i).2x,(2 - ((~x + 2) div 5)),1) mod (x + 1))))
A245195: 1 1 1 2 1 1 2 4 1 1 1 2 2 2 4 8
(loop(\(x,i).((6x * (~1 + (2 * i))) div (2 + i)),(x + 1),(x + 1)) div 2)
A101601: 1 9 81 756 7290 72171 729729 7505784 78298974 826489170 8811646074 94753804536 1026499549140 11192793160815 122744496427425 1352917116177840
(((x + 1) * (loop(\(x,i).((x + ((~1 + (2 * (i mod 2))) * i)) * (1 + i)),x,0) div 2)) div 2)
A145886: 0 1 0 12 50 405 3234 29680 300348 3337425 40382540 528644556 7445076990 112248853717 1803999433950 30788257007040
loop(\(x,i).3x,(x + 1),((x3 + 9x2 + 20x + 12) div 2))
A288836: 18 189 1296 7290 36450 168399 734832 3070548 12400290 48715425 187067232 704690766 2611501074 9542023155 34437376800 122941435176
(((x2 + 3x + 2) * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A196421: 2 9 30 70 165 273 476 684 1035 1595 2046 2886 3731 4515 5640 7208
loop(\(x,i).((~x + 2) + (5 * (x div 7))),2,(2x + 2))
A194529: 2 ~1 1 ~2 0 2 ~1 1 3 0 2 4 1 3 0 2
((x * (2 + (if (x mod 2) <= 0 then 2 else (10x + 5)))) div (2x + 2))
A019428: 0 4 1 13 1 23 1 33 1 43 1 53 1 63 1 73
(((x + ~1) * loop(\(x,i).x2,1,(((x3 + ~3x2 + 2x) div 2) div 3))) div 2)
A132458: 0 0 0 1 24 200 1000 3675 10976 28224 64800 136125 266200 490776 861224 1449175
(((1 + (x mod (1 + (x div 4)))) div (1 + ((x + 1) mod 4))) + (if x <= 0 then 1 else 2))
A328401: 1 2 2 3 2 2 2 4 3 2 2 5 2 2 2 6
(2 * (1 + loop(\(x,i).((x + 1) - (((2x + ~4) div (2 + (x div 4))) mod 2)),x,x)))
A078750: 2 4 8 8 10 16 16 16 18 20 32 32 32 32 32 32
(2 * ((1 + (x div (1 + (x div (2 + (if (x mod 10) <= 0 then 1 else 2)))))) div 2))
A309709: 0 2 2 4 2 2 4 4 2 4 2 4 4 4 4 4
(4 * (~1 + (34 * loop(\(x,i).(2x + 4),x,1))))
A305271: 132 812 2172 4892 10332 21212 42972 86492 173532 347612 695772 1392092 2784732 5570012 11140572 22281692
(((1 + ((if (x + ~2) <= 0 then 1 else (x div 3)) * (1 + ((x + ~1) mod 4)))) div 2) div 2)
A029265: 1 0 0 1 1 0 1 1 2 1 1 2 4 1 2 4
(~4 + (11 * (x + (if (~4 + (x div 2)) <= 0 then 1 else 2))))
A131191: 7 18 29 40 51 62 73 84 95 106 128 139 150 161 172 183
(((1 + (loop(\(x,i).x2,1,(2 - ((x2 + 3x) div 2))) div 3)) div 2) div 2)
A104385: 0 0 1 4 12 27 52 91 147 225 331 469 645 867 1141 1474
(((1 + ((x + 1) * (~1 + (2 * loop(\(x,i).(x2 + 2),2,5))))) div 2) div 2)
A033172: 365 730 1096 1461 1826 2191 2557 2922 3287 3652 4018 4383 4748 5113 5479 5844
(2 + (2 * (~1 + (2 * loop(\(x,i).(27x + i),x,0)))))
A198080: 0 4 116 3144 84904 2292428 61895580 1671180688 45121878608 1218290722452 32893849506244 888133936668632 23979616290053112 647449639831434076 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 * (((x + 1) mod (1 + (2 * ((x + 1) mod (1 + (x div 4)))))) div 2)))
A028613: 1 0 0 0 2 0 0 0 0 0 0 0 0 4 0 0
(2 * ((1 + (((2x + loop(\(x,i).2x,((x + ~1) div 2),1)) div 3) div 2)) div 2))
A214927: 0 0 0 2 2 2 2 4 4 6 6 10 10 16 16 26
(4 + loop(\(x,i).(24x2 + 1),(2x + 2),1))
A145275: 15005 4611686018427387903 4611686018427387903
(x - (2 * ((x - loop(\(x,i).(1 + (x div 2) - (2 * (x mod 2))),((x + 1) div 2),1)) div 2)))
A118822: 2 ~1 0 ~1 ~2 1 0 1 2 ~1 0 ~1 ~2 1 0 1
(if x <= 0 then 1 else (2 * (3x - ((1 + ((x - ((x div 4) mod 2)) div 2)) div 2))))
A315342: 1 6 10 16 22 28 34 38 44 50 54 60 66 72 78 82
(4 + loop(\(x,i).(10x + 5),(x + 2),9))
A108903: 959 9559 95559 955559 9555559 95555559 955555559 9555555559 95555555559 955555555559 9555555555559 95555555555559 955555555555559 9555555555555559 95555555555555559 955555555555555559
((if x <= 0 then 1 else 6x) - (x div (4 + ((x div 2) div 5))))
A315750: 1 6 12 18 23 29 35 41 46 52 58 64 70 76 82 87
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 20)
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A242120: 2 3 5 7 11 13 17 19 3 9 11 17 1 3 7 13
(1 - (2 * (((x + (if (x + ~10) <= 0 then 1 else 2)) mod 5) mod 2)))
A119664: ~1 1 ~1 1 1 ~1 1 ~1 1 1 ~1 ~1 1 1 ~1 1
(((3 * (1 + ((2 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 3))) div 2) div 2)
A335905: 0 0 1 0 2 1 2 0 3 2 3 1 3 2 4 0
(2 + ((compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + ((x + ~1) div 3)) div 2))
A089190: 1 2 3 4 7 8 10 11 13 16 18 21 23 24 26 29
((loop(\(x,i).(x - ((1 - (x div 2)) div 3)),x,18) div 2) div 2)
A120181: 4 5 6 7 8 9 11 12 14 17 20 23 27 31 36 42
(4 * (5 + loop(\(x,i).(2x + 40),x,1)))
A305166: 24 188 516 1172 2484 5108 10356 20852 41844 83828 167796 335732 671604 1343348 2686836 5373812
(2 + (if x <= 0 then 2 else (2 + ((2 * ((2x + 2) + ((x div 4) mod 2))) div 3))))
A123938: 4 6 8 9 11 12 14 15 16 17 18 20 22
loop(\(x,i).x7,1,(12x + 4))
A017575: 16384 268435456 13492928512 163840000000 1028071702528 4398046511104 14645194571776 40867559636992 100000000000000 221068140740608 450766669594624 860542568759296 1555363874947072
loop(\(x,i).x6,1,(~11x + ~4))
A017442: 4096 11390625 308915776 2565726409 12230590464 42180533641 117649000000 282429536481 606355001344 1194052296529 2194972623936 3814697265625 6327518887936 10090298369529 15557597153344
(if x <= 0 then 1 else (2 * (3x - ((x - ((x + (x div 3)) div 3)) div 2))))
A315340: 1 6 10 16 22 28 32 38 44 50 54 60 66 70 76 82
(((1 + ((x + (loop(\(x,i).2x,x,(2 + (x div 4))) div 3)) div 2)) div 2) div 2)
A283315: 0 0 0 1 2 4 9 17 43
((1 - (x mod (1 - (2 * (x mod (1 + ((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)))))))) div 2)
A206825: 0 0 1 0 0 0 3 2 0 0 1 0 0 0 7 0
((((x + 1) * loop(\(x,i).(6x2 + x),((x + 1) div 2),1)) div 2) div 2)
A309740: 0 3 5 301
((((x + 1) * (5 + (if (6 mod (x + 1)) <= 0 then 1 else 2))) div 2) div 2)
A187839: 1 3 4 7 8 9 12 14 15 17 19 21 22 24 26 28
((if x <= 0 then 1 else (2 + ((2 * ((1 + (x2 mod 5)) div 2)) mod (x + 1)))) div 2)
A165014: 0 1 1 1 2 1 2 3 3 2 1 2 3 3 2 1
((((x + 1) * (4 + (loop(\(x,i).(2x - (i mod 2)),(x + ~1),1) div 2))) div 2) div 2)
A018255: 1 2 3 5 6 10 15 30
(1 - (2 * (loop(\(x,i).~x6,1,(x2 + 1)) div 2)))
A091470: 3 65 15627
(2 - (if x <= 0 then 1 else ((x mod 2) - (((2x + 1) mod (1 - (x div ~4))) div 2))))
A318874-A301957-A001227: 1 1 2 1 2 2 2 1 3 2 2 2 2 2 4 1
(((loop(\(x,i).(x * (2 + i)),(13x + 13),1) div 2) div 2) div 2)
A172716-A172611: 81729648000 4611686018427387903 4611686018427387903 4611686018427387903
(2 + ((x - ((~1 + ((x + ~1) div (2 + (if (x mod 5) <= 0 then 2 else 0)))) div 2)) div 2))
A037037: 2 3 3 3 4 4 5 5 5 6 7 6 7 7 8 9
((2 + (loop(\(x,i).((x + 1) + (x div 4)),x,15) div 2)) div 2)
A146968: 4 5 7
A120163: 4 5 7 8 10 13 16 20 25 31 39 49 61 76 95 119
(if (x + ~4) <= 0 then (~2 + (((x + ~1) + (5 * (1 + (x div 2)))) div 2)) else 2)
A021292: 0 0 3 4 7 2 2 2 2 2 2 2 2 2 2 2
(2 + loop(\(x,i).(~x + 1),x,(2 * (((1 + (x * (x + (x div 2)))) div 5) mod 2))))
A106826: 2 3 4 3 4 1 4 3 4 1 2 1 4 1 4 3
(~2 + (((3 * (1 + (5 * (x + (if (x + ~2) <= 0 then 1 else 2))))) div 2) div 2))
A190695: 2 6 10 17 21 25 28 32 36 40 43 47 51 55 58 62
(~2 + (2 * ((3 * (if ((x + 1) mod 4) <= 0 then ((x + 1) div 3) else 1)) div 2)))
A060278: 0 0 0 0 0 0 0 4 0 0 0 10 0 0 0 12
(8 * ((1 + (4 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 3))
A056196: 8 24 32 40 56 72 88 96 104 120 128 136 152 160 168 184
((((3 * (loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1))) div 2) div 2) div 2)
A305736: 0 0 0 1 0 1 0 2 1 1 0 4 0 1 1 5
(2 + ((x2 - (if x <= 0 then 1 else (x + (((x + 1) div 3) mod 2) - (x div 2)))) div 2))
A081612: 1 2 3 5 8 13 18 24 31 39 49 59 71 83 96 110
(4 + (if x <= 0 then 1 else (98x + ~12)))
A336783: 5 90 188
(2 * loop(\(x,i).3x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),2))
A161411: 4 12 12 36 12 36 36 108 12 36 36 108 36 108 108 324
(if x <= 0 then 1 else (2 + ((((2 - (2x mod (2 + (x div 2)))) mod (x + 3)) div 2) div 2)))
A339049: 1 2 2 2 2 2 2 4 4 2 4 2 2 2 2 6
(8 * (1 + loop(\(x,i).(x + 1),(~4 + ((x + ((x div 2) mod 2)) div 2)),x)))
A085131: 8 16 24 32 40 48 56 64 72 80 96 112 120 128 144 160
(~2 + loop(\(x,i).(10x + 81),(2x + 2),2))
A274755: 1089 109989 10999989 1099999989 109999999989 10999999999989 1099999999999989 109999999999999989 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((1 + (x mod (1 + (if (x mod 2) <= 0 then 6 else 1)))) div (2 + (((x + 1) div 2) div 2)))
A285701: 0 1 1 0 1 0 2 0 0 0 1 0 1 0 0 0
(((2x + 2) * (if (x mod 4) <= 0 then 2 else 2x)) mod (2 + (((x + 1) div 2) div 2)))
A053201: 0 0 0 0 2 0 0 0 0 0 0 3 2 3 0 0
(16 * ((2 * loop(\(x,i).(x * (x - i)),2,(x + 3))) div 3))
A120054: 256 1280 3840 8960 17920 32256 53760 84480 126720 183040 256256 349440 465920 609280 783360 992256
(6 + (if x <= 0 then 1 else (4 * (5x - (x div 3)))))
A063159: 7 26 46 62 82 102 118 138 158 174 194 214 230 250 270 286
(~2 + (2 * ((2 + (loop(\(x,i).((x + 1) + (((~x + 2) mod 4) + i)),x,1) div 2)) div 2)))
A162762: 0 2 4 6 8 14 18 22 26 34 40 46 52 62 70 78
((4 + ((x mod (2 + ((~1 + loop(\(x,i).2x,x,4)) mod (x + 1)))) div 2)) div 2)
A074592: 2 2 2 2 3 2 2 3 2 2 2 2 2 3 2 5
((((loop(\(x,i).x2,1,(x - ((x2 + 2x) div 8))) div 2) div 2) div 2) div 2)
A320657: 0 0 0 0 0 0 0 0 0 0 1 2 5 7 12 16
((if x <= 0 then 1 else (2 * (2 + ((x + ((1 - (x div 3)) mod 3)) div 4)))) div 2)
A130855: 0 2 2 2 3 3 4 4 4 4 4 5 5 5 5 6
(((3 - (if x <= 0 then 1 else x)) mod (1 - (2 * (x div (~2 + ((~x + 2) div 4)))))) div 2)
A338971: 0 1 0 0 2 1 1 0 0 0 0 3 2 2 1 1
(2 + (if x <= 0 then 1 else ((x + 2) - (((((1 - (x div 2)) div 3) * (x div 2)) div 2) div 2))))
A336101-A267895: 3 5 6 7 9 10 11 12 13 14 17 18 19 20 22 23
((loop(\(x,i).(x2 + x),1,(~4x + ~44)) div 2) div 2)
A157434: 473 564 663 770 885 1008 1139 1278 1425 1580 1743 1914 2093 2280 2475 2678
((x + 1) div (4 + ((if (x mod 2) <= 0 then (x div 2) else (x2 + 2)) mod (x + 4))))
A236412-A236263: 0 0 0 0 0 1 1 0 1 1 1 1 1 2 1 0
((2 + ((x + 1) div (if (x mod 4) <= 0 then 5 else (2 - ((x div 2) mod 2))))) div 2)
A181803: 1 1 2 3 1 2 4 5 1 3 6 7 2 4 8 9
((1 + (if ((x * (x mod 3)) mod 5) <= 0 then 0 else 2)) * (x div 8))
A218825: 0 0 0 0 0 0 0 0 3 1 1 3 1 3 3 1
(((2x div 5) + (if x <= 0 then 1 else 4x)) - (x div 8))
A058759: 1 4 8 13
A311913: 1 4 8 13 17 22 26 30 34 38 43 47 51 56 60 65
(if x <= 0 then 1 else (2 * (3x - ((x + ((1 - (x div 2)) mod 4)) div 4))))
A315729: 1 6 12 18 22 26 32 38 44 50 56 62 66 70 76 82
((2x + 2) div loop(\(x,i).3x,(1 + (x mod 2)),(4 - (x mod 4))))
A308067: 0 0 1 0 0 0 2 1 1 0 3 2 2 1 5 3
((2 + ((x + loop(\(x,i).3x,((x div ~4) div ~2),1)) div 2)) div 2)
A107320: 1 1 1 2 2 3 3 3 3 4 4 4 4 6 6 7
loop(\(x,i).x7,1,(12x + 8))
A017623: 2097152 1280000000 34359738368 319277809664 1727094849536 6722988818432 20971520000000 55784660123648 131593177923584 282621973446656 562949953421312 1054135040000000 1874584905187328
loop(\(x,i).x6,1,(~11x + ~8))
A017490: 262144 47045881 729000000 4750104241 19770609664 62523502209 164206490176 377149515625 782757789696 1500730351849 2699554153024 4608273662721 7529536000000 11853911588401 18075490334784 26808753332089
((x + 2) - (2 * ((x + (x div (2 * loop(\(x,i).(x div (~2 + (x mod 2))),x,(x + 1))))) div 2)))
A094290: 2 3 2 5 2 3 2 7 2 3 2 5 2 3 2 11
(4 + (if x <= 0 then 1 else ((x + 2) + ((x + (((x mod 3) * (x div 2)) mod 2)) div 2))))
A184110: 5 7 9 10 12 13 15 17 18 19 21 22 24 25 27 28
(2 + (2 * (if (x + ~1) <= 0 then (22x + 11) else (x + 2))))
A087406: 24 68 10 12 14 16 18 20 22 24 26 28 30 32 34 36
((8x + 2) - ((~1 + loop(\(x,i).(x * (2 + i)),x,2)) mod 5))
A267329: 1 10 15 22 30 38 46 54 62 70 78 86
loop(\(x,i).x7,1,(7x + 2))
A017011: 128 4782969 268435456 3404825447 21870000000 94931877133 319277809664 897410677851 2207984167552 4902227890625 10030613004288 19203908986159 34792782221696 60170087060757 100000000000000 160578147647843
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(7x + 2))
A053369: 2 9 32 115 420 1554 5808 21879 82940 316030 1209312 4644094 17889032 69089700 267444000 1037348415
(9x + (if x <= 0 then 1 else (x + ((x + ~1) mod 9))))
A061470: 1 10 21 32 43 54 65 76 87 98 100 111 122 133 144 155
(2 * loop(\(x,i).2x,(((3 * (2x + (x div 4))) div 2) + (x div 2)),2))
A102557-A093581: 4 32 512 4096 131072 1048576 16777216 134217728 8589934592 68719476736 1099511627776 8796093022208 281474976710656 2251799813685248 36028797018963968 288230376151711744
((x + 1) div (2 + (x div (2 + (((x + (if (x mod 2) <= 0 then x else 2)) mod 3) + (x mod 2))))))
A328482-A267263-A060130: 0 1 1 2 1 2 1 2 2 3 2 3 1 2 2 3
((x + 1) div (2 + (x div (4 - (if ((x + 1) mod 8) <= 0 then 2 else (x mod 2))))))
A332999: 0 1 1 1 1 2 2 1 2 2 2 2 2 2 3 1
(1 - ((1 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) div 3)) mod 4))
A257834: 0 0 ~1 ~1 1 1 ~1 ~1 1 ~1 ~1 1 ~1 ~1 1 ~1
((if (2 - (x mod (1 + (x div (2 * (2 - (x mod 2))))))) <= 0 then (x2 + x) else 1) mod 4)
A281188: 1 1 1 1 1 2 1 0 0 2 1 0 1 2 2 0
(4 + ((1 + (loop(\(x,i).((x + 6) + (x div 3)),x,2) div 2)) div 2))
A120151: 5 6 8 11 15 20 26 35 47 62 83 111 148 197 263 350
(((3 * loop(\(x,i).x5,2x,3)) div 2) div 4)
A022263: 1 317733228541 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(((3 * (loop(\(x,i).x3,2,6) mod (x + 1))) div 2) mod 4)
A336118: 0 0 0 0 1 0 1 0 0 1 3 0 3 1 1 0
((x + (if (x mod 3) <= 0 then (1 + ((x2 + ~1) mod 5)) else 0)) div 4)
A029250: 1 0 0 1 1 1 1 1 2 2 2 2 4 3 3 5
((if x <= 0 then 1 else 6x) - ((x + ((1 - (x div 2)) mod 4)) div 4))
A315745: 1 6 12 18 23 28 34 40 46 52 58 64 69 74 80 86
((if x <= 0 then 1 else 5x) - ((x + ((1 - (x div 2)) mod 4)) div 4))
A313685: 1 5 10 15 19 23 28 33 38 43 48 53 57 61 66 71
((if x <= 0 then 1 else 5x) - ((x + ((x + (x div 2)) mod 4)) div 4))
A315020: 1 5 9 15 19 23 29 33 38 43 47 53 57 61 67 71
(1 + (((1 + (if (~2 + (x div 2)) <= 0 then x else (x + 4))) div 3) + (x div 4)))
A266113: 1 1 2 2 3 4 5 6 7 7 8 8 9 10 10 10
((if x <= 0 then 1 else ((x + 2) + ((((x div 2) div ~2) mod (x + 1)) div 2))) + (x div 4))
A308011: 1 3 5 6 9 10 11 13 15 17 18 19 22 23 24 26
((x + 4) + (if x <= 0 then 1 else (5 - ((x div 2) div ~5))))
A241145: 5 10 12 13 14 15 16 17 18 19 20 21 23 24 25 26
loop(\(x,i).x7,1,(10x + 4))
A017323: 16384 105413504 4586471424 52523350144 319277809664 1338925209984 4398046511104 12151280273024 29509034655744 64847759419264 131593177923584 250226879128704 450766669594624 775771085481344
((loop(\(x,i).((x2 + ~x) div 2),2,(x + 2)) div 3) * (2 + ((x2 + x) div 2)))
A215773: 0 3 25 120 420 1190 2898 6300 12540 23265 40755 68068 109200 169260 254660 373320
(2 * ((x + 2) + ((3 * (((if (~2 + (x div 2)) <= 0 then 1 else 2) + (x div 2)) div 2)) div 2)))
A284883: 4 6 10 12 14 16 22 24 28 30 32 34 40 42 44 46
(2 + loop(\(x,i).((x + 2) - (((x + 1) div (1 + (x mod 9))) mod 2)),x,2))
A299546: 4 5 6 7 8 9 10 11 13 15 17 19 21 23 24 26
(2 + (if x <= 0 then 1 else ((x + 2) + (((((2 - (x div 2)) div 2) * (x div 3)) div 2) div 2))))
A009004: 3 5 6 7 8 9 9 10 11 12 12 13 14 15 15 15
(2 + (if x <= 0 then 1 else ((x + 2) + ((x + (((x - (x div 3)) mod 3) div 2)) div 2))))
A324101: 3 5 7 9 10 11 13 15 16 17 19 21 22 23 25 26
((((x + 2) - ((x mod 2) + (x mod (1 + (2 * (if (x mod 3) <= 0 then 0 else 2)))))) div 2) div 2)
A049615: 0 0 0 1 0 1 2 1 1 2 3 2 3 2 3 4
(loop(\(x,i).2x,x,1) div ((2x + 4) * ((4x + 3) - (x mod 2))))
A309662: 0 0 0 0 0 0 0 0 0 0 0 1 2 5 8 15
(~2 + loop(\(x,i).(x3 mod 30),(x + 1),(x + 2)))
A222215: 6 1 2 3 4 5 0 7 8 9 16 11 12 13 14 15
((if x <= 0 then 1 else 6x) - (2x div (2 + (4x div (x + 2)))))
A315526: 1 6 11 17 22 28 34 40 45 51 56 62 68 73 79 84
(if x <= 0 then 1 else (2 * (2x + ((x - ((x div 2) mod ~4)) div 5))))
A310367: 1 4 10 14 18 22 26 30 34 38 44 48 52 58 62 66
(if x <= 0 then 1 else (2 * (2x + ((x + ((x div 2) mod 5)) div 5))))
A311601: 1 4 8 12 18 22 26 32 36 40 44 48 52 56 62 66
(if x <= 0 then 1 else (2 * (2x + ((1 + (2 * ((2x + 1) div 3))) div 3))))
A315207: 1 6 10 14 20 24 30 34 38 44 50 54 58 64 68 74
(if x <= 0 then 1 else (2 * (3x - ((2 * (x - ((x div 2) div 3))) div 3))))
A315208: 1 6 10 14 20 24 30 34 40 44 48 54 60 64 68 74
(if x <= 0 then 1 else (2 * (2x + ((x - (x mod (4 + (x div 3)))) div 3))))
A311384: 1 4 8 12 16 22 28 32 36 40 44 48 52 56 60 66
(if x <= 0 then 1 else (2 * (2x + ((2x + ((x div 3) mod 3)) div 3))))
A310521: 1 4 10 16 22 26 32 38 44 48 52 58 64 70 74 80
(if x <= 0 then 1 else (x - (2 * (~2x + ((x2 mod (x - ((~x + 2) div 2))) div (x + 1))))))
A313733: 1 5 10 15 20 25 30 33 38 45 50 55 60 63 68 75
(if x <= 0 then 1 else (2 * (2x + (((3 * (x - (x div 5))) div 2) div 2))))
A310518: 1 4 10 16 22 26 30 36 42 48 52 56 62 68 74 78
(if x <= 0 then 1 else (4x + ((x - ((x div 2) mod ~4)) div 5)))
A312891: 1 4 9 13 17 21 25 29 33 37 42 46 50 55 59 63
(4x + (if x <= 0 then 1 else (((2 - (x div 2)) mod (x + 4)) div 5)))
A311196: 1 4 8 12 16 20 25 30 34 38 42 46 50 54 58 62
(5x - ((0 - (if (~4 + (x div 2)) <= 0 then 1 else x)) div 5))
A315468: 1 6 11 16 21 26 31 36 41 46 52 58 63 68 73 78
(4x + (if x <= 0 then 1 else ((x + ((x div 2) mod 5)) div 5)))
A311440: 1 4 8 12 17 21 25 30 34 38 42 46 50 54 59 63
(4x + (if x <= 0 then 1 else ((x + (((~x + 2) div 2) mod 4)) div 5)))
A058759: 1 4 8 13
A311802: 1 4 8 13 17 21 25 29 33 37 42 46 51 55 59 63
(4x + (if x <= 0 then 1 else ((2 * (x - ((x div 2) div 5))) div 3)))
A313053: 1 4 9 14 18 23 28 32 37 42 46 50 55 60 64 69
(4x + (if x <= 0 then 1 else ((x - (x mod (4 + (x div 3)))) div 3)))
A311289: 1 4 8 12 16 21 26 30 34 38 42 46 50 54 58 63
(if x <= 0 then 1 else (4x + ((2 * (x - ((((x + 1) div 2) div 2) div 2))) div 3)))
A313051: 1 4 9 14 18 23 28 32 36 41 46 50 55 60 64 68
(4x + (if x <= 0 then 1 else ((2 * (x + (((x div 2) div 3) mod 2))) div 3)))
A313057: 1 4 9 14 18 23 28 33 38 42 47 52 56 60 65 70
(4x + (if x <= 0 then 1 else ((2x + ((x div 3) mod 3)) div 3)))
A313100: 1 4 9 14 19 23 28 33 38 42 46 51 56 61 65 70
((x div (1 + (2 * (2 + ((x div 3) mod 4))))) + (if x <= 0 then 1 else 4x))
A311125: 1 4 8 12 16 20 24 28 32 36 40 45 50 54 58 62
(x + (if x <= 0 then 1 else 4x) - ((~x + (2x div (2 + (x div 2)))) div 3))
A314117: 1 5 11 16 21 26 32 37 42 47 53 58 63 69 74 79
(x + (if x <= 0 then 1 else 4x) - (((x - ((x div 4) mod 2)) div 2) div ~2))
A314112: 1 5 11 16 21 26 31 37 42 47 53 58 63 68 73 79
((((x2 - ((x div 2) div 3)) mod 3) div 2) + (if x <= 0 then 1 else 4x))
A311183: 1 4 8 12 16 20 25 28 32 37 40 44 48 53 57 60
((((3 * (x - (x div 5))) div 2) div 2) + (if x <= 0 then 1 else 4x))
A313090: 1 4 9 14 19 23 27 32 37 42 46 50 55 60 65 69
(x + (if x <= 0 then 1 else 4x) - ((((x div 3) mod 2) + (x div 4)) div 2))
A313696: 1 5 10 15 19 24 30 35 39 44 49 54 59 64 69 73
(((x + ((0 - ((x div 2) div 3)) mod 3)) div 2) + (if x <= 0 then 1 else 4x))
A312935: 1 4 9 13 18 22 28 32 37 41 46 50 54 59 63 68
(x + (((x + ((x div 3) mod 3)) div 3) + (if x <= 0 then 1 else 4x)))
A313894: 1 5 10 16 21 27 32 38 43 48 53 58 64 69 75 80
(x + (((x + ((x div 4) mod 3)) div 3) + (if x <= 0 then 1 else 4x)))
A313891: 1 5 10 16 21 27 32 37 43 48 54 59 64 69 74 80
(x + (((((x div 3) mod 2) + (x div 4)) div 2) + (if x <= 0 then 1 else 4x)))
A313779: 1 5 10 15 21 26 30 35 41 46 51 56 61 66 71 77
(x + (((x + ((1 - (x div 2)) mod 4)) div 4) + (if x <= 0 then 1 else 4x)))
A313793: 1 5 10 15 21 27 32 37 42 47 52 57 63 69 74 79
(x + (((x + ((x + (x div 2)) mod 4)) div 4) + (if x <= 0 then 1 else 4x)))
A137002: 1 5 11 15
A314056: 1 5 11 15 21 27 31 37 42 47 53 57 63 69 73 79
(5x - ((0 - (if (~2 + (x div 4)) <= 0 then 2 else x)) div 6))
A315467: 1 6 11 16 21 26 31 36 41 46 51 56 62 68 73 78
(((1 + (((x * (if (x mod 5) <= 0 then 1 else 2)) div 2) div 3)) * (x mod 2)) div 2)
A174479: 0 0 0 1 0 0 0 1 0 2 0 2 0 2 0 1
(2 + loop(\(x,i).((10x + 21) - (x mod 2)),(x div 2),(x mod 2)))
A024773: 2 3 23 32 232
((if (2 - (2x mod (4 + (x div 3)))) <= 0 then (x + 2) else 1) mod (2 + (x mod 2)))
A259895: 1 0 1 1 0 1 1 0 0 2 0 1 1 0 0 2
(1 + ((x * (x div 2)) mod (1 + (if (x mod 8) <= 0 then 2 else 1))) - (2 * (x mod 2)))
A319993: 1 ~1 1 0 1 ~1 1 0 3 ~1 1 0 1 ~1 1 0
(~1 + (loop(\(x,i).4x,x,1) mod 13) - (2 * (x mod 2)))
A021081: 0 1 2 9 8 7 0 1 2 9 8 7 0 1 2 9
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),((x + 1) div 2),(1 - (2 * (x mod 2))))
A099363: 1 ~1 1 ~2 2 ~5 5 ~14 14 ~42 42 ~132 132 ~429 429 ~1430
(2 + ((x + loop(\(x,i).(1 + (((x2 + x) div 5) div 3)),2,x)) div 2))
A177876: 2 3 3 4
A182281: 2 3 3 4 4 5 5 6 7 8 9 11 12 15 17 20
(2 + compr(\x.(~1 + (x mod (1 + (2 * (if ((x + ~2) mod 7) <= 0 then 1 else 2))))),x))
A201363: 2 3 7
A329783: 2 3 7 8 11 12 13 17 18 22 23 27 28 32 33 37
(if x <= 0 then 1 else (2 + compr(\x.(1 - (x mod (1 + (3 * (x mod (3 + (x mod 2))))))),x)))
A080596: 1 4 5 7 9 10 11 12 13 15 17 19 21 22 23 24
(if x <= 0 then 1 else ((x + 2) + ((~x + 1) mod (1 + ((x - ((x div 3) mod 3)) div 2)))))
A088743: 1 3 5 5 7 9 9 9 11 13 15 15 15 17 17 17
(compr(\x.(if x <= 0 then 0 else (1 - (x mod (1 + ((~x2 + 2x + ~1) mod 8))))),x) div 2)
A320840: 0 1 1 2 3 3 5 5 6 7 9 9 10 11 11 13
(if x <= 0 then 1 else (2 * (~x + ((8x3 + 12x2 + 4x) div 3))))
A152100: 1 14 76 218 472 870 1444 2226 3248 4542 6140 8074 10376 13078 16212 19810
(2 * compr(\x.((2 + (x mod (1 + (2 * (if (x mod 6) <= 0 then 2 else 1))))) mod 3),x))
A277568: 2 8 12 14 20 26 32 38 44 48 50 56 62 68 72 74
(if x <= 0 then 1 else (2 * (x + ((2 * (2x - (x div ~7))) div 3))))
A315204: 1 6 10 14 20 24 28 34 40 44 48 54 58 62 68 74
((3x + 2) * loop(\(x,i).(13x + 13),2,(x mod 2)))
A305184: 364 1755
((x + 2) + (if (x div 3) <= 0 then 1 else (((x + 1) + ((~x + 1) mod 4)) div 3)))
A137905: 3 4 5 7 8 9 11 12 13 14 16 17 18 19 22 23
loop(\(x,i).((7x + 2) + ((x div 2) mod 2) - (x mod 3)),x,2)
A037635: 2 15 108 758 5307 37152 260066 1820463 12743244 89202710 624418971 4370932800 30596529602 214175707215 1499229950508 10494609653558
loop(\(x,i).x7,1,(10x + 8))
A017371: 2097152 612220032 13492928512 114415582592 587068342272 2207984167552 6722988818432 17565568854912 40867559636992 86812553324672 171382426877952 318547390056832 562949953421312
((x + 2) + ((x + 2) div (2 + (if ((2 - (x div 5)) mod 4) <= 0 then 2 else 1))))
A049692: 2 4 5 6 8 9 10 12 13 14 15 16 17 18 20 22
(loop(\(x,i).((x + ~1) - (2 * (~x + ((2 * (~2 + (x div 2))) div 5)))),2,x) div 2)
A187949: 2 5 10 13 15 18 23 26 31 34 36 39 44 47 49 52
(loop(\(x,i).(1 + compr(\x.(1 - ((x + 1) mod (1 + ((2 + (x div 2)) div 3)))),x)),2,x) div 2)
A196026: 5 6 7 9 10 11 12 13 14 14 15 16 17 18 18 19
(if x <= 0 then 1 else (2 + compr(\x.(1 - (x mod (2 + (13 mod (x + 1))))),x)))
A231407: 1 4 6
A171413: 1 4 6 7 8 10 11 12 13 15 16 18 19 20 21 22
((x + 2) + (((3 * (if (x + ~2) <= 0 then x else (2 - ((~x + 1) div 3)))) div 2) div 2))
A266347: 2 3 5 7 8 10 11 12 13 14 15 17 18 19 21 22
loop(\(x,i).(2x - (((x - (((x * (x div 3)) div 2) div 3)) div 2) mod 2)),x,2)
A262482: 2 3 5 10 20 40 79 158 316 631 1261 2521 5042 10083 20165 40330
loop(\(x,i).(2x - ((x - (((3 * ((~x2 + x) div 2)) div 2) div 2)) mod 2)),x,2)
A262236: 2 3 6 12 24 47 94 187 373 745 1490 2979 5958 11916 23832 47663
((x + 2) + ((((((loop(\(x,i).(x + (x div 2)),(x + ~1),2) div 2) div 2) div 2) div 2) div 2) div 2))
A096902: 2 3 4 5 6 7 8 9 10 11 12 14 16 18 20 24
((~x + ~2) + loop(\(x,i).(x + (7x div (1 + i))),x,8))
A063267: 6 33 116 325 786 1709 3424 6426 11430 19437 31812 50375 77506 116265 170528 245140
(((3x + 4) * loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,1)) div 2)
A024482: 2 7 25 91 336 1254 4719 17875 68068 260338 999362 3848222 14858000 57500460 222981435 866262915
((x + 2) + ((5 * (if (~2 + (x div 3)) <= 0 then x else (x + 2))) div (x + 2)))
A328077: 2 4 6 8 9 10 11 12 14 16 17 18 19 20 21 22
compr(\x.((x2 div 2) mod 3),(2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)))
A208296: 11 13 23 25 35 37 47 59 61 73 83 85 95 107 119 121
(((x2 + 3x + 2) div 2) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A156056: 1 0 1 3 4 8 11 17 22 26 4 4 9 19 26 30
((~x2 + ~2x + ~2) + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + 1),1))
A225692: 0 0 4 25 106 392 1380 4797 16714 58685 207890 742755 2674270 9694648 35357444 129644533
(((11x + 9) * loop(\(x,i).x3,2,x)) div 2)
A229152: 0 10 7936 413343 6946816 62500000 377913600 1735205101 6509559808 20920706406 59500000000 153266599915 363764514816 805941952348 1683875312896 3344572265625
(if x <= 0 then 1 else compr(\x.(~2 + ((x mod 2) + (x mod (4 + (x mod (2 + (x mod 2))))))),(x + 2)))
A231407: 1 4 6
A051234: 1 4 6 8 9 10 12 14 16 18 20 21 22 24 25 26
((x + 2) * (1 - (((x mod 2) - (x div ((if (x mod 3) <= 0 then 2 else 1) + (x mod 2)))) div 2)))
A062956: 2 3 8 5 18 14 24 18 50 22 72 39 56 60 128 51
(if (x + ~1) <= 0 then 1 else ((2x + 1) + ((x2 + (x2 div 4)) div 3)))
A333296: 1 1 6 10 15 21 28 35 43 52
((2x + 1) + (if (x + ~1) <= 0 then x else (2 + (((x3 + ~x) div 2) div 3))))
A058759: 1 4 8 13
A038793: 1 4 8 13 21 33 50 73 103 141 188 245 313 393 486 593
(2x + loop(\(x,i).(3 * ((18x + 1) + i)),x,1))
A065991: 1 62 3253
(2x + loop(\(x,i).((x + 2) + ((x div (3 + ((x div 2) div 3))) mod 2)),x,1))
A313683: 1 5 10 15 19 23 27 32 37 42 47 52 57 61 65 69
((2x + 2) + (if (x mod (2 + (5 mod (1 + (x div 4))))) <= 0 then 1 else 0))
A285346: 3 4 7 8 10 12 15 16 19 20 22 24 27 28 30 33
loop(\(x,i).(1 + ((2 * ((x + ((x div 2) mod 2)) div 2)) div 3) - (x mod 2)),2,2x)
A329143: 0 0 1 1 1 2 1 1 3 2 2 3 2 2 4 4
(4x + (if x <= 0 then 1 else (2 * ((x + (2 * (x mod 2))) mod (1 + (x div 2))))))
A008579: 1 4 8 14 18 22 28 30 38 38 48 46 58 54 68 62
((x + 1) + ((if x <= 0 then 0 else (1 + (((x + ~4) div (1 + (x div 2))) mod 2))) + (x div 2)))
A231407: 1 4 6
A299411: 1 4 6 7 8 9 11 12 14 16 18 19 21 22 24 25
((6 * ((x div 2) div (1 + (if (x mod 2) <= 0 then 6 else 0)))) + (x mod 2))
A331423: 0 1 0 7 0 13 0 19 0 25 0 31 0 37 6 43
(((x - (if ((((2x + ~1) * (x div 2)) div 2) mod 3) <= 0 then 1 else 0)) mod 2) - (x mod 2))
A328800: 1 ~1 0 0 0 ~1 0 0 1 0 0 0 1 ~1 0 0
(((x - (if (x mod (1 - (2 * ((~x + 1) div (2 + (x div 2)))))) <= 0 then 1 else 0)) mod 2) - (x mod 2))
A106459: 1 ~1 0 ~1 0 0 1 0 0 0 1 0 0 0 0 ~1
(((x mod (1 + (((x + (if (x mod 2) <= 0 then x else 1)) div 3) mod 3))) mod 2) - (x mod 2))
A059652: 0 ~1 0 0 1 ~1 0 0 0 ~1 0 0 0 0 0 ~1
((if x <= 0 then 0 else (2 - ((x div (2 + (2x mod 9))) mod 2))) - (x mod 2))
A287418: 0 1 2 1 2 0 1 0 2 1 2 0 1 0 2 0
((x + 1) mod (if x <= 0 then 1 else (x + (x mod 2) - (((x - ((~1 + (x div 2)) div 2)) div 2) mod 2))))
A117054: 0 0 0 1 1 0 1 1 2 0 1 0 2 1 2 0
((if x <= 0 then 1 else (2 + ((2x mod (4 + (x div 8))) mod 2))) - (x mod 2))
A237271: 1 1 2 1 2 1 2 1 3 2 2 1 2 2 3 1
((if (x mod 3) <= 0 then 1 else ((x mod (~3 - (x div 4))) mod 2)) - (x mod 2))
A214960: 1 ~1 1 0 0 0 1 0 0 0 0 ~1 1 0 0 0
((if x <= 0 then 1 else (2 + (((x2 + ~x) div (4 + (x * (x mod 2)))) mod 2))) - (x mod 2))
A307720: 1 1 2 1 3 1 3 2 2 2 2 2 3 2 3 2
(~2 + (loop(\(x,i).(10x + 4),(x div 2),(2 + (x mod 2))) + (x mod 2)))
A094625: 0 2 22 33 242 343 2442 3443 24442 34443 244442 344443 2444442 3444443 24444442 34444443
(loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x div 2),(x div 2)) div (2 - (x mod 2)))
A116385: 0 0 1 2 5 10 21 42 84 168 330 660 1287 2574 5005 10010
loop(\(x,i).(9x + 135),(x div 2),(x mod 2))
A038369: 0 1 135 144
((2x + 3) + (2 * (1 + loop(\(x,i).(x * (2 - (x mod ~4))),x,x))))
A260981: 5 17 41
A122035: 5 17 41 461
((3x + 3) + loop(\(x,i).x2,1,((x2 + 5x) div 2)))
A343994: 3 15 58 156 339 643 1110 1788 2731 3999 5658 7780 10443 13731 17734 22548
((x + loop(\(x,i).((x + 1) - (2 * ((x div 2) - (2 * (x div 5))))),2,x)) div 2)
A098382: 1 1 2 2 3 5 6 6 7 7 8 10 9 11 10 12
((x + loop(\(x,i).(x - (((x - (x2 div 4)) div 2) div 5)),2,x)) div 2)
A173552: 0 1 2 3 4 6 7 8 9 11 12 13 16 17 19 21
((x + 2) + loop(\(x,i).((x + ~1) + (((x - (x div ~2)) div 5) mod 2)),2,x))
A222011: 1 2 4 8
A206928: 1 2 4 8 10 12 14 15 16 18 22 24 26 27 28 30
(2 * (2x + (3 * (if (~2 + (x div 5)) <= 0 then 1 else 2)) - (x mod 2)))
A194399: 6 8 14 16 22 24 30 32 38 40 46 48 54 56 62 70
((~x + 1) + loop(\(x,i).((x + 1) + (((((~x + 2) * (x div 2)) div 2) div 3) mod 2)),x,0))
A063273: 1 1 1 1 2 3 4 5 5 5 6 6 7 7 7 7
compr(\x.(1 - (x mod (1 + (3 * (if (x mod (1 + (4 * (x mod 2)))) <= 0 then 0 else 2))))),x)
A235583: 1 3 9 11 13 17 19 23 27 29 31 33 37 39 41 43
((x + 1) + ((2 + ((if (x + ~1) <= 0 then 2 else (((x + ~1) div 2) * (x div 2))) div 2)) div 3))
A177876: 2 3 3 4
A301277: 2 3 3 4 6 7 8 10 11 13 15 16 18 20 22 24
loop(\(x,i).x7,1,11x)
A017395: 0 19487171 2494357888 42618442977 319277809664 1522435234375 5455160701056 16048523266853 40867559636992 93206534790699 194871710000000 379749833583241 698260569735168 1222791080775407
((~x + 1) + (loop(\(x,i).((4x + 2) + ((x2 + x) div 2)),2,x) div 3))
A024191: 5 19 47 95 170 280 434 642 915 1265 1705 2249 2912 3710 4660 5780
compr(\x.(2 - ((x + 1) mod (1 + (2 * (if (((x + 1) div 2) mod 6) <= 0 then 2 else 0))))),x)
A112063: 11 12 23 36 47 48 71 72 83 96 107 108 131 132 143 156
(x * loop(\(x,i).(75x + 49),2,1))
A004954-A004934: 0 9349 18698 28047 37396 46745 56094 65443 74792 84141 93490 102839 112188 121537 130886 140235
compr(\x.(2 - (2x mod (1 + (2 * ((if x <= 0 then 1 else x2) mod 9))))),x)
A189636: 1 2 4 5 7 10 11 13 14 16 19 20 22 25 28 29
compr(\x.(2 - ((1 + (loop(\(x,i).(x div (2 - (x mod 2))),x,x) div 2)) mod 7)),x)
A320698: 3 5 6 7 9 10 11 12 14 17 18 19 20 21 22 23
compr(\x.(if x <= 0 then 1 else ((2x * (x div 7)) mod 7)),x)
A032942: 1 2 3 4 5 6 7 14 21 28 35 42 49 50 51 52
compr(\x.(x mod (1 + (4 * (2x mod (1 + (2 * (if (x mod 3) <= 0 then 0 else 2))))))),x)
A241571: 0 3 5 6 9 10 12 15 17 18 20 21 24 25 27 30
(x + loop(\(x,i).i,(((3 * (1 + (2 * (2x div 5)))) div 2) div 2),1))
A166018: 1 2 3 5 6 8 9 10 13 14 16 17 18 21 22 24
((x + 1) + (x div (4 + ((~1 + loop(\(x,i).~2x,x,4)) mod (x + 1)))))
A306311: 1 2 3 4 5 6 7 8 9 11 12 13 14 15 18 16
(x + (9 * (if (~4 + (x div 2)) <= 0 then 0 else 9)))
A103303: 0 1 2 3 4 5 6 7 8 9
A280658: 0 1 2 3 4 5 6 7 8 9 91 92 93 94 95 96
(x + (9 * (1 + (if (~1 + (x div 4)) <= 0 then x else 8))))
A088923-A088479-A088478-A043525-A011539: 9 19 29 39 49 59 69 79 89 90 91 92 93 94 95 96
(x + (9 * (x - ((x mod 10) mod (if x <= 0 then 1 else x)))))
A011540: 0 10 20 30 40 50 60 70 80 90 100 101 102 103 104 105
loop(\(x,i).x6,1,(11x + 5))
A017454: 15625 16777216 387420489 3010936384 13841287201 46656000000 128100283921 304006671424 646990183449 1265319018496 2313060765625 4001504141376 6611856250609 10509215371264 16157819263041 24137569000000
loop(\(x,i).x6,1,(11x + 10))
A017514: 1000000 85766121 1073741824 6321363049 24794911296 75418890625 192699928576 433626201009 885842380864 1677100110841 2985984000000 5053913144281 8198418170944 12827693806929 19456426971136
(x * ((~x + loop(\(x,i).((x + 1) + (2 * ((x div 2) div 3))),x,1)) div 5))
A308926: 0 0 0 0 0 0 0 7 8 18 30 55 84 143 210 315
compr(\x.(loop(\(x,i).((x + 1) - ((~2x + 1) div 5)),2,x) mod 5),x)
A080914: 1 6 11 16 19 21 24 29 34 37 39 42 47 52 55 57
(x + (if x <= 0 then 1 else (~3 + ((4x3 + 12x2 + 8x) div 3))))
A273790: 1 6 31 80 161 282 451 676 965 1326 1767 2296 2921 3650 4491 5452
loop(\(x,i).x7,1,(7x + 3))
A017023: 2187 10000000 410338673 4586471424 27512614111 114415582592 373669453125 1028071702528 2488651484819 5455160701056 11047398519097 20971520000000 37725479487783 64847759419264
loop(\(x,i).x7,1,(7x + 6))
A017059: 279936 62748517 1280000000 10460353203 52523350144 194754273881 587068342272 1522435234375 3521614606208 7446353252589 14645194571776 27136050989627 47829690000000 80798284478113
(x + ((loop(\(x,i).(((x + ~1) * (x2 div 3)) div 2),2,(x + ~1)) div 2) div 3))
A123215: 0 1 2 3 4 13 112
(x + (3 * (((3 * (x + (if (~2 + (x div 4)) <= 0 then 2 else 1))) div 2) div 2)))
A096346: 3 7 11 12 16 20 24 25 29 33 37 38 39 43 47 51
compr(\x.(x - (12 * (if ((x + 2) mod 8) <= 0 then (x + 2) else 1))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A333598: 0 1 2 3 4 5 6 7 8 9 10 11 12 14 22 30
(~x + (if x <= 0 then 1 else (71x + ~23)))
A114646: 1 47 117 187 257 327 397 467 537 607 677 747 817 887 957 1027
(x + (loop(\(x,i).(x - ((~1 + (((x + ~1) div 2) div 2)) div 2)),2,x) + ((x + 2) div 3)))
A247421: 2 5 7 9 11 12 14 17 19 21 24 26 28 30 31 33
(x + ((2 * ((2x + 1) + (loop(\(x,i).2x,x,~1) mod (x + 2)))) div 3))
A219611: 1 3 5 9 11 14 14 21
(~x + (if x <= 0 then 1 else 4x) - ((2x + ~4) div (2 - ((~x + 1) div 3))))
A105527: 3 4 6 9 11 14 16 19 22 25 27 30 33 36 39 42
((x + 1) + ((x + loop(\(x,i).(x + i - (x div 11)),x,1)) div 2))
A214050: 1 3 6 9 12 16 20 24 29 34 39 44 49 55 60 66
loop(\(x,i).(x div 2),(1 + ((1 + (8 mod (1 + (x div 2)))) div 2) - (x mod 2)),x)
A209859: 0 1 1 3 1 2 3 7 1 2 2 5 3 6 7 15
(x + (if x <= 0 then 1 else (((3x3 + 6x2 + 2x) div 2) * (1 + (x mod 2)))))
A242941: 1 11 28 143
((x + 1) + loop(\(x,i).((x + 1) - ((x + 1) mod (~1 + (x div ~5)))),2,x))
A274428: 3 6 9 10 14 15 19 20 21 26 27 28 33 34 35 36
((2x + 1) + ((((x + 1) + ((x * (if (x + ~2) <= 0 then 1 else x)) div 3)) div 2) div 2))
A097911: 1 3 5 8
A278586: 1 3 5 8 11 14 17 21 24 28 32 36 40 44 49 53
(~x + loop(\(x,i).((x + 2) + ((x mod (1 + ((x div 4) + (x div 3)))) mod 2)),x,1))
A288217: 1 2 4 5 7 9 10 11 13 14 15 16 18 19 21 23
compr(\x.(2 - ((~1 + ((2 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 3)) mod (x + 1))),x)
A089970: 3 7 8 10 12 14 15 16 17 18 20 21 22 24 25 26
(x + ((3 * (if x <= 0 then 1 else (3 * (x + ((x div 2) div 3))))) div (x + 1)))
A065347: 3 5 8 9 11 12 15 16 17 18 19 20 21 22 23 24
loop(\(x,i).x7,1,(9x + 8))
A017263: 2097152 410338673 8031810176 64339296875 319277809664 1174711139837 3521614606208 9095120158391 20971520000000 44231334895529 86812553324672 160578147647843 282621973446656 476837158203125 775771085481344 1222791080775407
loop(\(x,i).(40x + 40),2,(5x + 4))
A157663: 8040 16040 24040 32040 40040 48040 56040 64040 72040 80040 88040 96040 104040 112040 120040 128040
loop(\(x,i).(7x3 + 14x2 + 7x + 1),1,(x2 + x))
A022523: 1 127 2059 14197 61741 201811 543607 1273609 2685817 5217031 9487171 16344637 26916709 42664987 65445871 97576081
((((1 + ((3 * ((x2 + 3x) div 2)) div 2)) div 2) div 2) + (if x <= 0 then 1 else x))
A231408: 1 2 4 6 9
A062048: 1 2 4 6 9 12 16 20 24 29 34 40 46 52 58 65
(x + (2 * (((2 * (x - (2 * (x div 5)))) div 3) + (if x <= 0 then 0 else 1))))
A081605: 0 3 6 9 10 11 12 15 18 19 20 21 24 27 28 29
(~x + (2 * (((x + (((~2x + 4) mod (2 + (x div 2))) div 2)) div 2) + (if x <= 0 then 0 else 1))))
A008342: 0 1 2 1 2 3 2 1 2 3 4 3 4 3 2 1
compr(\x.((x2 mod (~1 + (6 * (if (~2 + (x div 3)) <= 0 then 0 else 2)))) mod 2),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A296242: 0 1 2 3 4 5 6 7 8 9 11 13 20 22 24 31
loop(\(x,i).(1 + (2 * ((x div 2) div (1 + (x mod (1 + (x mod (3 + (x mod 2))))))))),2,x)
A336467: 1 1 1 1 3 1 1 1 1 3 3 1 7 1 3 1
compr(\x.((1 + ((1 + ((1 + (x div (if (x mod 4) <= 0 then 4 else 1))) div 2)) div 2)) mod 2),x)
A165564: 1 2 3 4 8 9 10 11 12 16 17 18 19 25 26 27
loop(\(x,i).(1 + ((x + 1) mod (1 - (x div (~2 + (((~x + 2) div 2) div 5)))))),2,x)
A307610: 1 1 2 1 1 1 2 1 2 1 2 1 3 1 1 2
compr(\x.(if (x mod 2) <= 0 then 2 else (((x + ~1) mod (3 + (x div (1 + (x mod 4))))) mod 2)),x)
A007665: 1 3 5 7 11 15 19 23 27 31 39 47 55 63 71 79
compr(\x.((if x <= 0 then 1 else ((x + 1) mod (1 + (x div (2 + ((1 + (x div 2)) mod 3)))))) mod 2),x)
A269870: 1 2 3 4 5 7 8 11 13 15 16 17 19 21 23 25
compr(\x.(2 - ((1 + (((1 + loop(\(x,i).((x * (x mod 2)) + (x div 2)),x,x)) div 2) div 2)) div 2)),x)
A039502: 17 21 23 25 31 33 34 37 41 42 45 46 49 50 55 61
compr(\x.(((if (x mod (1 + ((x + 2) mod 4))) <= 0 then 1 else x) div (1 + (x div 4))) mod 2),x)
A144043: 4 5 6 8 10 12 14 18 22 24 26 30 34 36 38 42
(x + (if x <= 0 then 1 else (2 * (x + ((x + ((x div 2) mod 2)) div 2) - ((x + 1) div 3)))))
A083462: 1 3 6 11
A316317: 1 3 6 11 14 15 20 25 26 29 34 37 40 43 46 51
loop(\(x,i).(((2x + 1) div 3) - (((x2 + ~x) div 2) div (x + 3))),2,x)
A254610-A045917: 0 1 1 1 2 1 2 2 2 2 3 3 3 2 3 2
(x * (2 + ((2 - (x mod (1 + (2 * (if (x mod 6) <= 0 then 2 else 1))))) mod (x + 1))))
A101404: 0 3 4 12 12 10 18 21 16 36 30 22 24 39 28 60
(~x + (2 * (2 + ((3 * (x + (if (x mod 3) <= 0 then 1 else 2))) div 5))))
A248864: 4 5 6 5 6 7 6 7 8 7 8 7 6 9 8 7
loop(\(x,i).x7,1,(9x + 4))
A017215: 16384 62748517 2494357888 27512614111 163840000000 678223072849 2207984167552 6060711605323 14645194571776 32057708828125 64847759419264 122987386542487 221068140740608 379749833583241
loop(\(x,i).x7,1,(7x + 4))
A017035: 16384 19487171 612220032 6103515625 34359738368 137231006679 435817657216 1174711139837 2799360000000 6060711605323 12151280273024 22876792454961 40867559636992 69833729609375
((x + 2) + (x div ((x + 2) div (2 + (loop(\(x,i).x3,2,2x) mod (x + 1))))))
A254734-A073353: 2 4 6 6 10 12 14 10 12 20 22 18 26 28 30 18
loop(\(x,i).((2 + (x div (1 + ((1 + (x div 2) - (x div 3)) mod 3)))) div 2),2,x)
A114294: 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 5
(x + (x2 div (6 + (if x <= 0 then 1 else (2 - ((~x + (x mod 2)) div 3))))))
A112671: 0 1 2 4 5 7 9 11 13 16 18 21 24 27 29 32
(x + (4 * (if x <= 0 then 2 else (x - (2 * (~2x + ((x + (x div 2)) div 4)))))))
A188026: 8 21 42 55 76 97 110 131 144 165 186 199 220 241 254 275
((if x2 <= 0 then 0 else (18x + 16)) div (x + 8))
A004220: 0 3 5 6 7 8 8 9 10 10 10 11 11 11 12 12
(0 - ((2 - (((x + 2) * (~1 + ((if (x mod 2) <= 0 then 2 else x) mod 4))) div 2)) div 2))
A131505: 0 ~1 0 2 1 ~1 1 4 2 ~1 2 6 3 ~1 3 8
(((x4 + 2x3 + ~x2 + ~2x) div 3) + loop(\(x,i).((x2 + x) div 2),2,x))
A264854: 0 1 14 61 175 400 791 1414 2346 3675 5500 7931 11089 15106 20125 26300
((3x + 2) - (((1 - loop(\(x,i).(~1 + (x * (1 + i))),x,0)) div (x + 2)) mod 2))
A287399: 2 5 7 10 14 17 20 23 25 29 32 34 37 41 44 47
(~x + (2 * (x + loop(\(x,i).(2 + (5 * i)),(x + ~7),1))))
A083158: 2 3 4 5 6 7 8 9 22 33 44 55 66 77 88 99
((2x + 2) + (loop(\(x,i).(2x - (x div 4)),3,x) div 5))
A190347: 2 5 8 12 14 17 21 24 26 29 33 36 39 42 45 48
(~x + ((x + ((loop(\(x,i).(5x + 2),x,2) div 3) div 3)) div 2))
A178750: 0 0 2 15 84 431 2167 10847 54249 271262 1356331 6781678 33908414 169542094 847710496 4238552509
(~x + ((x + loop(\(x,i).((x + 1) - (2 * (~x - ((x div 4) mod 2)))),x,1)) div 2))
A178706: 0 1 6 22 70 215 652 1964 5900 17709 53138 159426 478290 1434883 4304664 12914008
(~x + ((x + (loop(\(x,i).((x + 2) + (x div (2 + ((x div 2) mod 3)))),2,x) div 2)) div 2))
A145006: 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 ~1
((~x3 + 2x2 + ~2x) + (loop(\(x,i).((x2 + ~x) div 2),2,(x + 2)) div 3))
A319930: 0 0 1 0 ~5 ~15 ~30 ~49 ~70 ~90 ~105 ~110 ~99 ~65 0 105
loop(\(x,i).(~37x + ~37),2,(x2 + 2x))
A158743: 1332 5439 12284 21867 34188 49247 67044 87579 110852 136863 165612 197099 231324 268287 307988 350427
(x * ((x2 * loop(\(x,i).(x3 + x),1,x5)) div 2))
A170782: 0 1 131200 193713525 34359771136 1907348828125 50779979174016 814206801837625 9007199263129600 75047317670022921 500000000050000000 2779958656853295181 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 mod ((x + 1) - ((~2x + 1) div (4 + (x div 4))))),x,x)
A335262: 0 1 0 3 0 1 6 1 0 3 10 3 0 1 6 15
((2x + 1) - (((~x + 1) - (4 * (if (x + ~2) <= 0 then 0 else 2))) div 5))
A168045: 1 3 6 9 12 14 16 18 20 23 25 27 29 31 34 36
(2x + (if (x + ~1) <= 0 then 1 else (x - ((3 - ((x2 + ~x) div 2)) div 3))))
A076523: 1 3 6 9 13 18 22 27 33 38 44 51 57
(2x + (if x <= 0 then 1 else 4x) - (2 div (16 div (x + 1))))
A315763: 1 6 12 18 24 29 35 41 46 52 58 64 70 76 82 88
(x + loop(\(x,i).((x + 1) - (((x + 1) mod (1 - (x mod ~7))) mod 2)),2,x))
A240767: 2 3 4 7 8 11 12 16
A284937: 2 3 4 7 8 11 12 16 18 19 20 23 24 28 30 31
(2x + (if x <= 0 then 1 else (2 * (((((x + 1) div 2) div 2) * (x div 2)) div 5))))
A241071: 1 2 4 6 8 10 12
A093891: 1 2 4 6 8 10 12 16 18 20 24 28 30 32 36 40
((2x + 2) + (loop(\(x,i).((4x + 1) + ((x2 + x) div 2)),x,1) div 2))
A094475: 2 7 29 641
(~x + loop(\(x,i).(x + ((2x + 1) mod (1 + (2x mod (2 + (x div 4)))))),2,x))
A291786: 0 0 0 0 0 1 0 0 0 1 0 3 0 2 1 0
((x2 + 1) - (loop(\(x,i).2x,x,1) mod (1 - ((~x2 + x) mod 5))))
A157421: 1 2 5 11 17 26 37 50 67 82 101 122 145 171 197 226
loop(\(x,i).(~1 + (2 * ((~x + 2) mod (2 + (x mod (2 + (x div 5))))))),2,x2)
A262809: 1 1 1 1 1 1 1 3 1 1 1 13 13 1 1 1
(~x6 + loop(\(x,i).11x,x,1))
A024133: 1 10 57 602 10545 145426 1724905 19369522 214096737 2357416250 25936424601 285309899050 3138425390737 34522707317122 379749826053705 4177248158025026
(~x7 + loop(\(x,i).12x,x,1))
A024147: 1 11 16 ~459 4352 170707 2706048 35008265 427884544 5154997383 61907364224 742988883517 8916064616448 106993142630555 1283918359135360 15407021403726993
(~x7 + loop(\(x,i).10x,x,1))
A024121: 1 9 ~28 ~1187 ~6384 21875 720064 9176457 97902848 995217031 9990000000 99980512829 999964168192 9999937251483 99999894586496 999999829140625
(~x7 + loop(\(x,i).7x,x,1))
A024082: 1 6 ~79 ~1844 ~13983 ~61318 ~162287 0 3667649 35570638 272475249 1957839572 13805455393 96826261890 678117659345 4747390650568
((3x + 1) + (loop(\(x,i).((x + 4) + (x div 8)),x,1) mod 2))
A189362: 2 5 8 10 14 17 19 22 26 29 31 34 37 40 43 46
(x3 * (loop(\(x,i).(x5 + x2),1,x3) div 2))
A170791: 0 1 131328 193720086 34359869440 1907349609375 50779983373056 814206819132028 9007199321849856 75047317842209805 500000000500000000 2779958657925089586 4611686018427387903 4611686018427387903
(1 + (x div (1 + ((2x + 1) mod (1 + (2x mod (1 + ((x + 1) div 3))))))))
A345993: 1 2 3 4 5 3 7 8 9 5 11 4 13 7 3 16
(1 + (x div (1 + (x mod (1 + (x mod (1 + ((1 + ((x2 + ~x) div 2)) mod (x + 1)))))))))
A237109: 1 1 1 4 5 1 7 8 3 5 11 4 13 7 5 16
(1 + (x mod (1 + (x mod (1 + (x div (1 + (2 * ((x + 1) mod (1 + (x div 4)))))))))))
A066262-A065331: 1 2 3 4 1 6 1 8 9 2 1 12 1 2 3 16
(1 + (x div (1 + ((x2 + 2x) mod (1 + (x div (3 + ((x div 2) div 3))))))))
A073890: 1 2 3 2 5 3 7 4 3 10 11 4 13 14 5 4
(1 + (x div (1 + (x mod (1 + (x mod (1 + (x div (2 + ((x * (x div 2)) mod 3))))))))))
A284260: 1 2 3 2 5 3 7 2 3 2 11 3 13 2 5 2
(1 + (x div (1 + (x mod (1 + (x mod (1 + (x div (2 + ((1 - (x div 2)) mod 4))))))))))
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(1 + ((1 + ((x mod (1 + (2 * (16 mod (x + 1))))) mod 4)) div 2))
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(1 + ((1 + ((x * (1 - ((x3 div 8) mod 2))) div 4)) div 2))
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(1 + (2 * (x div (3 * (1 + (x3 mod 11))))))
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(1 + ((x mod (3 * (1 + (((2x + 1) mod (2 + (x div 4))) div 2)))) div 2))
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(1 + (2 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))
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A026174-A026170-A026138: 1 2 4 5 8 10 11 13 14 17 20 22 23 26 28 29
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A114035: 3 4 5 6 7 8 9 10 11 13 15 16 17 19 21 23
((x + 1) + ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2) - (x div 2))
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(x - (56 * ((x + 1) div ~8)))
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(686x + 672)
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(343x + 70)
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((5x + 5) + (((x div 2) div 3) + (x div 7)))
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(x + ((x mod ((x + ~1) - (x mod 12))) + (x div 7)))
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((x div (3 * (2 + (x mod 7)))) + (x mod 7))
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A070214: 1 2 5 8 11 14 19 23 28 32 38 43 49 55
(1 + ((3 * (x + (x div (4 + (8 mod (1 + (x div 2))))))) div 2))
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(1 + (((((1 + (x mod (2 + (x mod 2)))) * (x div 4)) div 2) + (x mod 3)) div 2))
A296977: 1 1 2 1 1 2 1 2 2 1 2 3 1 3 2 1
(1 + ((1 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 2)) div 2))
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(1 + (((1 mod (1 - (2x mod (4 + (x div 4))))) mod (x + 3)) div 2))
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(1 + (((x + 1) * ((x div (4 + (x div 2))) + ((((x + 1) div 2) div 2) div 2))) div 2))
A058365: 1 1 1 1 1 1 1 9 10 11 12 13 14 15 16 25
((1 + (4 * (x - (2x div ~7)))) div (1 + ((x + 1) div 2)))
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A110000: 1 4 6 5 8 7 8 7
(1 + (((1 + (x mod (1 + (31 mod (x + 1))))) div 2) div 2))
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A072219: 1 1 3 1 3 3 3 1 3 3 5 3 3 3 3 1
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(1 + (((1 + ((1 + ((x * (1 + ((2x + 4) div 3))) div 2)) div 2)) div 2) div 2))
A029051: 1 1 1 2 2 2 3 4 4 5 7 7 8 10 11 12
(1 + (((1 + (x div (2 - ((2 - (16 mod (x + 1))) div 2)))) div 2) div 2))
A246028: 1 1 1 2 1 1 2 3 1 1 1 2 2 2 3 5
(1 + (2 * ((1 + ((x + 1) div (2 + (((x2 + 1) div (2 + (x div 2))) mod 2)))) div 2)))
A070864: 1 1 3 3 3 5 3 5 5 5 7 5 7 5 7 7
(1 + (x div (2 * (2 + ((x + ((x2 + 2x) div 4)) mod 9)))))
A030422: 1 1 1 1 1 1 2 1 2 1 1 2 4 1 1 1
(1 + (((5 * (x + (x2 div (4x + 5)))) div 2) div 2))
A235933: 1 2 3 4 6 8 9 11 12 13 16 17 18 19 22 23
(~1 + (2 * ((3 * (1 + (2 div (1 + ((x + 2) mod 10))))) div 2)))
A336698: 1 1 1 1 1 1 1 1 7 5 1 1 1 1 1 1
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A230462: 1 11 13 17 19 29 31 41 43 47 49 59 61 71 73 77
(1 + (4 * (1 + (2 * (x + (x div (2 - (x div (~1 + ((~x + 2) div 4))))))))))
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(1 + (((1 + ((x + (x3 div 32)) div 2)) div 2) div 2))
A118301: 1 1 1 1 2 2 2 3 4 5 6 7 9 11 13 16
(1 + (x div (4 + ((1 + (9 * (x div 4))) mod (x + 1)))))
A320748-A320747-A305749: 1 1 1 1 2 1 1 2 2 1 1 2 3 4 1 1
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A175685: 1 1 1 1 1 1 2 2 1 1 1 3 2 1 1 3
(1 + (x div (2 * (2 + ((2 * (~1 + ((x2 + x) mod 5))) mod (x + 1))))))
A339788-A276696-A238453-A220777-A209805-A209612-A172479-A172453-A088855-A034851: 1 1 1 1 1 1 1 2 2 1 1 2 4 2 1 1
(1 + ((((2 * (x mod ((~x + 2) + (x mod 10)))) mod (x + 1)) div 2) div 2))
A110030: 1 1 1 1 1 1 1 1 1 1 3 1 2 3 3 4
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A131404: 1 1 1 1 5 1 1 7 7 1 1 11 13 11 1 1
(1 + ((x mod (2 + ((2 * (2 + ((x + ((x div 2) div 3)) div 2))) mod (x + 1)))) div 2))
A275471: 1 1 1 2 3 1 1 1 2 2 1 3 3 1 1 2
(((1 + (x div (2 + (x mod (2 + ((x div 2) mod 2)))))) mod 2) * (1 + (((x + 1) div 2) div 2)))
A050186: 1 1 1 0 2 0 0 3 3 0 0 4 4 4 0 0
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A230507: 0 0 1 1 1 1 1 2 2 1 2 3 4 2 3 3
(1 + (4 * ((1 + ((5 * ((x2 + x) div 2)) div 3)) div 2)))
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(2 div ((2x + 2) mod (1 + (2 * (2 + (((x + 1) mod 7) mod 2))))))
A308400-A025886: 1 0 0 0 0 1 0 1 0 0 1 0 2 0 1 1
(1 + (((((1 + ((2x + 1) div 5)) * (1 + (x div 2))) div 2) div 2) div 2))
A029095: 1 1 1 1 1 2 2 3 3 3 4 4 6 6 7 8
(1 + ((x div 2) div 3) - ((((x + 1) + (x div 8)) div 2) mod 2))
A025829: 1 0 0 1 1 0 1 2 1 1 2 2 2 2 3 3
(x mod (1 + (2 * ((((8 * (2 + (x mod 3))) mod (x + 1)) div 2) div 2))))
A306605: 0 0 0 0 1 0 0 0 2 0 0 1 0 3 0 0
(1 + (x div (2 - (((2 - (((((x + 1) div 2) div 2) div 2) * ((x + 1) div 2))) div 2) div 2))))
A099053: 1 1 2 2 3 3 4 3 3 4 4 4 5 4 4 3
(1 + ((((((x + 1) * (1 + (x div 4) - (2 * (x mod 2)))) div 2) div 2) div 2) div 2))
A029207: 1 0 1 0 1 1 1 1 2 1 3 1 4 2 4 3
(1 + (8 * ((x + 2) - ((~2x + 1) div (4 + (x div 4))))))
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(1 + (((x + 1) div 2) div 2) - ((1 - (x div (~2 + (((2 - (x div 2)) div 2) div 2)))) div 2))
A025833: 1 0 0 1 1 0 1 1 1 1 1 2 2 1 2 3
(1 + ((x mod ((x + ~1) - (x mod 12))) * (2 + (x mod 8))))
A323483: 1 1 1 1 1 1 1 1 1 1 1 1 7 15 25 37
(1 + ((x + 1) div (2 + ((((x - (x div 8)) mod 2) + (x div 4)) div 2))))
A264982: 1 2 2 3 3 3 4 3 4 4 4 5 4 5 4 6
((2 * (2 - ((x div 2) mod 2))) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))
A163259: 0 0 0 0 1 0 0 0 1 0 0 2 4 1 0 0
((x + 11) + (((x div 2) - ((~x + 2) div (2 + (x div 2)))) div 2))
A127957: 10 12 13 15 16 17 19 20 21 23 24 25 27 28 29 30
(9 * (1 + ((4 * (x + ((x div 2) div 3))) div 3)))
A195085: 9 18 27 45 54 63 90 99 117 126 135 153 171 189 198 207
(9 * (0 - ((2x - (x2 div 4)) div 5)))
A112440: 0 0 0 0 0 0 0 0 0 9 9 18 27 36 45 54
(9x3 + 117x2 + 423x + 459)
A224456: 459 1008 1845 3024 4599 6624 9153 12240 15939 20304 25389 31248 37935 45504 54009 63504
(((3x + 1) * (1 - (2 * ((x div 3) mod 2)))) mod 9)
A154687: 1 4 7 8 5 2 1 4 7 8 5 2 1 4 7 8
((4x3 + 15x2 + 18x + 9) div 9)
A238340: 1 5 15 34 64 108 169 249 351 478 632 816 1033 1285 1575 1906
(((x + 2) + (3 * (x2 mod 7))) div 9)
A079951: 0 0 1 1 1 2 1 1 1 2 2 2 2 2 1 2
(x - (x2 div ((2x + 1) + ((x2 + ~x) mod 9))))
A189705: 0 1 2 3 3 4 4 5 5 5 6 7 8 8 8 9
(1 + ((((x * (1 + compr(\x.(x mod (1 + (8 * (x mod 2)))),x))) div 2) div 2) div 2))
A126256: 1 1 2 3 5 7 9 12 16 20 24 29 35 41 48 53
(2 div (1 + ((1 + (x mod (1 - (x mod (~1 + (x div (~2 + (x mod ~2)))))))) mod 4)))
A260675: 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 2
((1 + (x div 7)) div (1 + (((x2 + 2) div 3) mod 4)))
A029422: 1 0 0 0 0 0 1 1 0 0 0 1 2 1 1 0
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A112344: 0 0 0 1 0 0 0 2 1 0 0 2 1 0 0 4
((1 + ((1 - (2x mod (4 + (x div 4)))) div 3)) mod 5)
A265421: 1 0 1 0 0 1 0 0 0 1 0 0 0 4 1 0
((8x3 + 12x2 + 14x + 6) div 5)
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((x div 3) mod ((~1 + ((4x + 4) * (1 + (x div 2)))) mod 5))
A038570: 0 0 0 0 1 0 0 0 2 3 0 1 1 0 0 0
(x7 mod 45)
A070725: 0 1 38 27 4 5 36 43 17 9 10 11 18 22 14 0
(x - ((~21 * (1 + (x div 3))) div 5))
A327301: 5 6 7 12 13 14 19 20 21 26 27 28 33 34 35 41
((6 * ((3x + 3) + (x div 8))) div 5)
A189460: 3 7 10 14 18 21 25 28 33 37 40 44 48 51 55 58
((6 * ((2x + 2) + (x div 12))) div 5)
A189939: 2 4 7 9 12 14 16 19 21 24 26 28 32 34 37 39
(120 * ((x + 1) + (x div 5)))
A232743: 120 240 360 480 600 840 960 1080 1200 1320 1560 1680 1800 1920 2040 2280
((2 * ((12x + 11) - (x mod 3))) div 5)
A206814: 4 8 13 18 23 27 33 37 42 47 52 56 62 66 70 76
((2 * (1 + (2 * (x - ((2x + ~1) div 7))))) div 5)
A194820: 1 1 2 2 2 3 4 5 5 6 6 6 7 8 9 9
((11x + 9) mod 30)
A064266: 9 20 1 12 23 4 15 26 7 18 29 10 21 2 13 24
(5 * ((27x2 + 33x + 8) div 2))
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((~2 + ((x + 1) * ((x + 3) + ((((x + 1) div 2) div 2) div 2)))) mod 5)
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((2 + ((1 - (2 * ((x2 + x) mod 8))) mod (x + 1))) div 5)
A035467: 0 0 0 0 1 0 1 0 0 1 0 1 1 1 2 0
((5 + ((x2 + 2x) mod 11)) div 5)
A080028: 1 1 2 1 1 1 1 2 1 1 3 1 1 2 1 1
((1 - (2 * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2))) mod 5)
A046569: 1 1 1 1 4 1 1 4 4 1 1 4 2 4 1 1
((122x + 80) div 5)
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((x + 5) + ((2 * (1 + (x div 2) - ((x div 4) mod 2))) div 3))
A201512: 5 6 8 9 10 11 13 14 16 17 19 20 21 22 23 24
((x * (1 + (2x * (x + ((x3 + 2x) div 3))))) div 5)
A069038: 0 1 10 51 180 501 1182 2471 4712 8361 14002 22363 34332 50973 73542 103503
(((((1 + (x div 3)) mod 3) + (x div 3)) div 2) * (x div 5))
A282894: 0 0 0 0 0 1 1 1 1 2 4 4 6 6 6 6
(1 + ((x + ((((x + 1) - (x * ((x div 2) div 5))) div 2) div 2)) mod 4))
A129968: 1 2 3 1 2 3 4 2 3 4 3 4 1 2 3 4
(1 + (((x + (14 * (x + (x div 8)))) div 2) div 2))
A190714: 1 4 8 12 16 19 23 27 34 38 42 45 49 53 57 60
(1 + (((x - (x3 div (~x + ~31))) div 2) div 2))
A332577: 1 1 1 2 2 3 4 5 6 8 9 11 14 16 19 23
(x6 + 12x5 + 54x4 + 120x3 + 141x2 + 84x + 20)
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((2x + 5) + (3 * (x - ((2x + 2) div 7))))
A188043: 5 10 15 17 22 27 29 34 39 44 46 51 56 58 63 68
((4x + 1) + ((2 * (2x - (x mod (2 * (2 - (x mod 2)))))) div 3))
A313914: 1 5 10 16 22 27 31 37 43 48 53 59 65 69 74 80
(1 + ((1 + ((1 + (6 mod (1 + (x div 2)))) div 3)) * ((x div 2) mod 2)))
A050603: 1 1 2 2 1 1 3 3 1 1 2 2 1 1 4 4
(((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x mod (2 + (x mod 2)))))
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((1 + ((((x + 1) - ((x div 2) mod 5)) div 2) div 2)) div (1 + (2 * (x mod 2))))
A029224: 1 0 1 0 1 0 2 0 2 0 3 1 4 1 4 1
(x - ((((x + 1) div 2) - ((3 * (x div 4)) div 2)) * (~1 + (2 * (x mod 2)))))
A227361: 0 0 3 1 5 3 8 4 9 7 12 8 14 10 17 11
((1 + ((x + 1) mod (1 + (4x mod (2 - ((x div 2) div ~2)))))) mod 3)
A144435: 1 1 1 1 2 1 1 1 1 1 1 0 2 0 1 1
(((x + 1) - (x mod ((x + ~2) + ((2x + 4) mod 7)))) mod 3)
A137865: 1 1 0 1 1 1 1 1 1 0 1 1 2 2 1 1
(((x + 1) + (((x + (x mod 2)) div 5) + ((x + 1) div 3))) mod 3)
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(((1 + (x mod (2 * (~2 + (x mod 2))))) * (1 + ((1 + (x div 3)) div 2))) mod 3)
A039973: 1 0 2 0 2 0 1 0 2 0 0 0 0 0 0 0
((1 + (2 * ((x + 1) mod (1 + (2 * (((x div 2) - (x mod 3)) div 2)))))) mod 3)
A261769: 1 1 1 1 1 1 0 2 1 1 0 1 1 0 1 2
((1 - (x mod (1 + (2 * (((x2 + 2x + 1) div 3) mod 3))))) mod 3)
A317240: 1 0 1 1 0 1 1 1 1 1 0 1 2 1 1 1
((1 + ((((2x + 4) + (x2 div 4)) * (1 + (x div 2))) div 2)) div 3)
A294085: 1 1 3 4 8 10 17 20 30 35 49 56 75 84 108 120
((1 + (2 * (x - ((x mod (2 + (6 mod (1 + (x div 2))))) div 2)))) div 3)
A279521: 0 1 1 2 3 3 3 4 5 6 7 7 7 7 7 8
((1 + (2 * (x - (((((x2 div 2) div 3) mod (x + 1)) div 2) div 2)))) div 3)
A014202: 0 1 1 2 3 3 3 5 5 6 6 6 7 9 9 9
(((((x2 + 3x + 2) div 2) * (2 + ((x div 2) mod 2))) div 5) mod 3)
A130068: 0 1 0 0 0 2 1 0 0 1 0 1 0 0 0 0
(6x - ((1 + (2 * (x - ((2 - (x div 2)) div (x + 2))))) div 3))
A314127: 1 5 11 16 21 27 31 37 42 47 53 58 63 69 74 79
(3 + ((2 * ((2x + 1) - ((~x + 1) div (2 + (x div 4))))) div 3))
A300737-A249433-A072668: 3 5 7 8 9 11 13 14 15 17 19 20 21 23 24 25
((2 - ((((x + 1) * ((~x + ~1) + (x div ~3))) div 2) div 3)) mod 3)
A169676: 0 0 1 0 2 1 1 2 2 0 0 1 0 2 1 1
(36 * (1 + (2 * (x - (3 * (x div ~2))))))
A237128: 36 324 396 684 756 1044 1116 1404 1476 1764 1836 2124 2196 2484 2556 2844
(1 - ((1 + ((x + 2) * (x - (32 div (x + 1))))) mod 3))
A167683: 1 0 ~1 1 0 0 ~1 0 1 0 0 0 1 0 0 1
((20x3 + 36x2 + 19x + 3) div 3)
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(((2x + 1) * (1 + (x div 4) - (x mod 10))) mod 3)
A248107: 1 0 1 1 0 0 2 0 2 0 0 1 2 0 0 2
(((x + 1) + (2 * ((x mod (2 + (6 mod (1 + (x div 2))))) div 2))) div 3)
A277267: 0 0 1 1 1 2 3 3 3 3 3 4 5 6 7 7
((3x2 + 6x + 3) + (((x3 + 3x2 + 2x) div 2) div 3))
A051939: 3 13 31 58 95 143 203 276 363 465 583 718 871 1043 1235 1448
(((x + 1) * ((x + 1) - ((x * (~2 + (((x + ~1) div 2) div 2))) div 3))) mod 3)
A098489: 1 0 0 0 1 0 0 1 0 1 1 0 1 2 0 2
(((x + 1) * (1 + ((x + 1) * ((3x2 + 7x + 4) div 2)))) div 3)
A213834: 1 10 46 140 335 686 1260 2136 3405 5170 7546 10660 14651 19670 25880 33456
(((x + 1) * (1 + (2 * ((((x div 2) * (x div 2)) div 2) + (x div 3))))) mod 3)
A112605: 1 2 0 0 2 0 1 2 0 2 2 0 0 0 0 2
(compr(\x.(1 - (x mod (5 + ((x div 2) mod 5)))),(x + 1)) div 3)
A076872: 0 1 1 1 2 2 2 3 4 5 5 6 7 7 7 8
(((x + 1) * (1 - ((x - (x div 12)) mod 5))) mod 3)
A219485: 1 0 0 1 0 0 0 1 0 0 2 0 0 1 0 0
((11x3 + 21x2 + 13x + 3) div 3)
A100186: 1 16 67 176 365 656 1071 1632 2361 3280 4411 5776 7397 9296 11495 14016
((17x3 + 33x2 + 19x + 3) div 3)
A100155: 1 24 103 272 565 1016 1659 2528 3657 5080 6831 8944 11453 14392 17795 21696
((16x3 + 39x2 + 32x + 9) div 3)
A213845: 3 32 119 296 595 1048 1687 2544 3651 5040 6743 8792 11219 14056 17335 21088
((32x3 + 192x2 + 352x + 192) div 3)
A141478: 64 256 640 1280 2240 3584 5376 7680 10560 14080 18304 23296 29120 35840 43520 52224
((3x + 3) + (4 * (x - ((2x + 2) div 7))))
A188396: 3 10 17 20 27 34 37 44 51 58 61 68 75 78 85 92
(((1 + (((x + 1) * (2 - ((x div 2) mod 2))) mod 9)) div 2) mod 3)
A168141: 1 2 2 2 1 2 1 1 0 1 1 2 1 1 0 1
(6 * (1 + ((2 * (1 + (2 * (x + (x div 8))))) div 3)))
A236864: 6 18 24 30 42 48 54 66 78 90 96 102 114 120 126 138
((2 * (1 + (((2x + 1) mod (1 + (2 * ((1 + (x div 2)) div 2)))) div 2))) div 3)
A035392: 0 0 1 0 0 1 1 0 1 2 0 1 2 2 1 2
((2 + ((x + 1) div (1 + (x mod (2 + (x div (2 + (3 * (x mod 2))))))))) div 3)
A132066: 1 1 1 1 2 1 1 2 1 4 1 1 1 3 1 6
(1 - ((2 * (((x + (x div 4)) div 2) + (x div 9))) mod 3))
A257196: 1 1 ~1 ~1 0 1 1 ~1 0 1 ~1 ~1 0 1 1 ~1
(3 * ((x mod (x - ((x + ~1) mod 8))) * (x mod 10)))
A069958: 0 0 0 0 0 0 0 0 0 0 0 6 18 36 60 90
((2 * (1 + ((((x + 2) + (x div (2 - ((x mod 3) mod 2)))) div 2) div 2))) div 3)
A290978: 0 1 1 1 2 2 2 3 2 2 4 3 4 5 4 4
(6x2 + 90x + 342)
A121205: 342 438 546 666 798 942 1098 1266 1446 1638 1842 2058 2286 2526 2778 3042
((((x + 3) * ((x3 + 9x2 + 8x) div 2)) div 2) div 3)
A166814: 0 6 25 66 140 260 441 700 1056 1530 2145 2926 3900 5096 6545 8280
(6 * ((2x + 1) + (((x div 2) div 7) + (x div 2))))
A328586: 6 18 36 48 66 78 96 108 126 138 156 168 186 198 222 234
((2 + ((1 + (2 * (2 - (x mod ~7)))) mod (1 + (x div 2)))) div 3)
A024361: 0 0 1 1 1 0 1 1 1 0 1 2 1 0 2 1
((((x + 1) * ((5x3 + 3x2 + ~2x) div 2)) div 2) div 3)
A185355: 0 1 12 52 150 345 686 1232 2052 3225 4840 6996 9802 13377 17850 23360
(((4x4 + 18x3 + 29x2 + 21x + 6) div 2) div 3)
A213843: 1 13 62 190 455 931 1708 2892 4605 6985 10186 14378 19747 26495 34840 45016
(((4x4 + 16x3 + 23x2 + 17x + 6) div 2) div 3)
A213840: 1 11 54 170 415 861 1596 2724 4365 6655 9746 13806 19019 25585 33720 43656
(1 + ((4 * (2x div 3)) div 3) - (((x + 1) div 2) div 3))
A143091: 1 1 2 3 3 4 5 5 6 8 8 8 9 9 11 12
(((x3 + 15x2 + 44x + 30) div 2) div 3)
A055831: 5 15 31 54 85 125 175 236 309 395 495 610 741 889 1055 1240
(3 + (((x2 + ~2x + 1) * (2 + ((x2 + ~x) div 5))) div 2))
A094177: 4 3 4 9 21 51
((2 * ((1 + (x mod (1 + ((x + ~1) mod (4 + (x div 3)))))) div 2)) mod 3)
A079693: 0 0 0 0 0 0 0 0 0 2 2 1 0 1 2 1
((4 * (1 + ((x + 1) mod (1 + (x div (2 * (2 + (x mod 4)))))))) div 3)
A205565: 1 1 1 1 2 1 1 1 1 1 2 1 2 4 2 1
(12 * ((2x + 1) - ((x - ((x div 2) mod 3)) div 3)))
A055926: 12 36 60 84 108 120 132 156 180 204 228 240 252 276 300 324
(3 + (4 * (1 + (((x + 1) mod (1 + (4 mod (1 + (x div 2))))) mod 2))))
A084503: 7 7 7 7 11 7 7 7 7 7 11 7 11 7 7 11
((2 * ((x + (2 * (2x div 3))) mod 14)) div 3)
A021411: 0 0 2 4 5 7 0 0 2 4 5 7 0 0 2 4
((4 * (1 + (2 * ((x + 8) + (x div 5))))) div 3)
A295799: 22 25 28 30 33 38
((4 * (1 + (((2x2 + 1) mod (2 + (x div 4))) div 2))) div 3)
A275122: 1 1 1 1 1 1 1 1 1 2 1 2 4 4 2 1
((4 * ((2x + 1) + (((x + 1) + (x div 8)) div 2))) div 3)
A278040: 1 5 8 12 14 18 21 25 29 32 36 38 42 45 49 52
((2 + ((x + 1) mod (2 + ((2 * (1 + (x div 5))) mod (x + 1))))) div 3)
A029232: 1 0 1 0 1 0 1 1 1 2 1 2 2 2 3 2
((2 + (((x + 1) * (((x * ((1 + (x div 2)) div 2)) div 3) mod 2)) div 2)) div 3)
A291900: 0 0 0 1 1 1 0 0 2 0 0 2 0 3 0 0
((2 + ((x mod (4 + (x div (1 + (x mod (2 * (1 + (x mod 2)))))))) div 2)) div 3)
A099302: 0 0 1 1 1 1 1 1 2 0 2 1 2 1 3 0
((2 * ((x + 2) - ((x mod (2 + (6 mod (1 + (x div 2))))) div 2))) div 3)
A078881: 1 2 2 3 4 4 4 5 6 7 8 8 8 8 8 9
(3 div ((2 * (2 + ((2x + 1) mod (4 + (x div 4))))) div 3))
A200472: 1 1 1 1 0 1 1 3 0 1 1 0 0 0 1 1
((1 - (((((x + ~2) * ((x div 3) * (1 - (x div 2)))) div 2) div 2) div 2)) div 3)
A165652: 0 0 0 0 0 0 1 1 2 3 4 5 8 9 12 16
((17 * ((x2 + 3x + 2) div 2)) div 12)
A088804: 1 4 8 14 21 29 39 51 63 77 93 110 128 148 170 192
((2 + ((x + (x3 div 31)) div 2)) div 3)
A237976: 0 0 1 1 1 2 2 3 4 6 7 9 11 14 17 21
(((2x2 + 4x + 4) + (x mod (x - ((x + ~1) mod 8)))) div 3)
A083462: 1 3 6 11
A025735: 1 3 6 11 17 24 33 43 54 67 81 97 114 132 152 173
(((x + 2) + ((5x3 + ~9x2) div 3)) div 3)
A212677: 0 0 1 7 21 46 86 144 223 327 459 622 820 1056 1333 1655
(((19x3 + 3x2 + ~16x) div 2) div 3)
A237618: 0 1 22 82 200 395 686 1092 1632 2325 3190 4246 5512 7007 8750 10760
(x + (((x3 + ~x) div 2) div 3) - ((x * ((~x2 + 2) div 2)) div 2))
A212578: 0 1 4 13 28 55 92 147 216 309 420 561 724 923 1148 1415
(~3 + (2 * (x + (2 * ((1 + ((x2 + 2x) div 4)) div 5)))))
A088749: ~3 ~1 1 3 9 11 17 23 29 35 41 47 53 59 69 75
((2x4 + 18x3 + 58x2 + 81x + 42) div 3)
A250141: 14 67 204 485 986 1799 3032 4809 7270 10571 14884 20397 27314 35855 46256 58769
(x - ((0 - compr(\x.(1 - (x mod (1 + ((~x2 + x) mod 8)))),x)) div 3))
A324143: 1 3 6 7 8 10 11 12 14 16 17 19 20 22 24 25
((x + (x3 mod 85)) mod 3)
A080884: 0 2 1 0 2 0 1 1 1 1 0 1 1 1 2 0
((3x + 3) - ((x + ((4 * (x div 3)) div 3)) mod 3))
A287437-A026603: 3 5 7 11 13 18 19 24 26 29 31 36 37 42 44 48
(x + ((x + ((4 * (x div 3)) div 3)) mod 3) - (x mod 3))
A159958: 0 1 2 4 5 3 8 6 7 10 11 9 14 12 13 15
((x + (2 * (x3 mod (1 + (3 * (2 + (x mod 4))))))) mod 3)
A243067: 0 0 0 1 0 0 1 0 1 0 1 2 0 0 1 0
((x + 3) + (2 * (1 + ((((~1 + ((x2 div 2) div 3)) div 2) div 2) div 2))))
A188003: 3 4 5 8 9 10 11 12 15 16 17 20 21 24 25 28
((x + (2 * (((x + 2) + (3 * (x div 2))) div (1 + (x div 4))))) mod 3)
A339839: 1 1 1 1 1 2 1 1 1 2 1 2 1 2 2 0
((2x + 3) - ((3 * (~x + ((~2x + 2) div 5))) div 2))
A189458: 3 7 12 15 20 24 27 32 36 41 44 48 53 56 61 65
(compr(\x.(((x - ((2x + 1) mod (1 + (x div 4)))) mod 2) - (x mod 2)),x) mod 3)
A219762: 0 1 2 0 2 1 2 0 1 2 1 0 2 0 1 0
(1 + (((2 * (2x - (x div ~7))) div 3) + (x div 3)))
A138097: 1 3 4 6 8 9 11 13 15 17 18 20 22 23 25 28
(1 + (((x + 1) div (2 + ((x2 div 4) div (x + 3)))) + (x div 3)))
A152850: 1 2 2 4 4 5 5 5 6 7 7 7 8 8 8 9
((5x + 4) + (x div 3) - ((2x + 2) div 5))
A184871: 4 9 13 19 23 28 34 38 43 48 53 58 63 68 72 78
((6x + 4) - ((x div 3) + ((2x + 4) div 5)))
A184916: 4 9 15 19 25 31 35 41 46 51 57 62 67 72 78 83
(2 * (((x + ~2) + ((~x + 2) div (1 + ((x mod (2 + (x mod 2))) div 2)))) * (x div 3)))
A336104: 0 0 0 0 0 2 0 0 0 0 0 24 0 0 0 0
compr(\x.(x mod (x - ((x + ~1) mod 8))),(10 - (x mod 3)))
A113779: 17 9 8 17 9 8 17 9 8 17 9 8 17 9 8 17
(~1 + (2 * compr(\x.(2 - ((x + 1) mod (1 + (6 * (2x mod 3))))),x)))
A111225: 1 3 7 9 13 15 19 21 31 33 37 43 45 51 55 57
(1 + (2 * (x + (5 * (10 + (x div 5))))))
A030474: 101 103 105 107 109 121 123 125 127 129 141 143 145 147 149 161
(1 + ((x + ((2 * (2 + ((4x2 + 2x) div 3))) div 3)) div 2))
A319159: 1 2 4 7 11 16 22 28 35 44 53 63 74 86
(1 + ((x + (((x * (2 + (((x2 + 2x) div 2) div 3))) div 2) div 3)) div 2))
A008770: 1 1 2 3 5 6 9 11 15 19 24 29 37 44 53 63
(1 + (((x + 1) + compr(\x.(~1 + (x mod ((x + 1) - (x mod 9)))),x)) div 2))
A169935: 1 2 3 4 5 6 7 8 9 11 12 16 17 22 23 27
(1 + (((x + 1) + compr(\x.(((x2 + 3) div (1 + (x div 3))) mod 2),x)) div 2))
A298746-A121232: 2 3 5 7 10 11 13 14 15 17 18 19 21 22 23 26
(1 + ((x + ((1 + (((x + 1) * (1 + (x2 div 4))) div 3)) div 2)) div 2))
A001401: 1 1 2 3 5 7 10 13 18 23 30 37 47 57 70 84
(1 + (2 * ((3x + 4) - ((((x + ~2) mod (1 + (x div 2))) mod 3) mod 2))))
A107987: 9 15 21 25 33 39 45 49 55 63 69 75 81 85 91 99
(~1 + (2 * ((3x + 4) - ((((x + ~2) mod (1 + (x div 2))) mod 3) mod 2))))
A209623-A176180-A049591: 7 13 19 23 31 37 43 47 53 61 67 73 79 83 89 97
(1 + ((x + ((3 * (x + (2x div (2 - ((~x + 1) div 3))))) div 2)) div 2))
A225647: 1 3 4 6 7
A087758: 1 3 4 6 7 8 10 12 13 14 16 17 19 20 21 22
(1 + ((x + (((1 + ((x * (2 + ((x2 + 2x) div 4))) div 2)) div 2) div 2)) div 2))
A008768: 1 1 2 3 5 6 9 12 16 20 26 32 40 48 58 69
(1 + ((x + ((x + ((x3 div 4) div 7)) div 2)) div 2))
A242216: 1 1 2 3 4 5 7 9 11 14 17 21 25 30 36 42
(1 + ((x + ((x + (((3 * (1 + ((x2 + x) div 2))) div 2) div 2)) div 2)) div 2))
A187102: 1 2 3 4 6 7 9 11
A248357: 1 2 3 4 6 7 9 11 13 16 19 21 24 28 31 34
(64x2 + 447x + 639)
A250661: 639 1150 1789 2556 3451 4474 5625 6904 8311 9846 11509 13300 15219 17266 19441 21744
(~1 + compr(\x.((x mod (x - ((x + ~1) mod 8))) - (x div 8)),(x + 2)))
A032905-A032871: 1 2 3 4 5 6 7 8 9 16 17 18 24 25 26 27
((2x2 + 8x + 6) + (((x3 + 3x2 + 2x) div 2) div 3))
A023545: 6 17 34 58 90 131 182 244 318 405 506 622 754 903 1070 1256
((2x + 1) + (((3 * ((2x + 2) - ((x div 2) div 3))) div 2) div 2))
A184821: 2 6 9 13 16 20 22 26 29 33 36 40 43 46 50 53
(10x5 + 37x4 + 52x3 + 34x2 + 10x + 1)
A109117: 1 144 1485 7168 23625 61776 138229 276480 508113 874000 1425501 2225664 3350425 4889808 6949125 9650176
(0 + (((x + ~2) mod (3 + ((x + (x mod 2)) div 3))) mod 2) - (x mod 2))
A112215: 1 ~1 0 0 0 0 0 ~1 1 0 0 ~1 1 ~1 1 0
(2 + (((x + 1) mod (1 + (4 * ((x div 4) mod 2)))) mod 2) - (x mod 2))
A085035: 2 1 2 1 2 2 2 2 2 1 2 1 3 1 2 2
(2 + (2 * (x - (((x div 2) - ((~1 + (x div 4)) div 2)) mod 2))) - (x mod 2))
A006364: 0 1 6 7 10 11 12 13 18 19 20 21 24 25 30 31
(x mod (2 + (((((x + 1) * ((~x + 2) mod 3)) div 2) div 2) div 2) - (x mod 2)))
A127325: 0 0 0 1 0 0 0 1 0 0 1 0 2 1 0 0
(1 + (x div (1 + (2 * (2 + (((((x + 1) div 2) div 2) * (x div 2)) mod 2))))) - (x mod 2))
A025808: 1 0 1 0 1 1 1 1 2 1 3 1 3 2 3 3
(1 + ((x div (2 + ((x div 2) div (1 + (x mod (2 + ((x mod 3) div 2))))))) + (x mod 2)))
A337454-A327527-A299701-A289849: 1 2 2 3 2 4 2 4 3 4 2 5 2 4 4 5
(1 + ((2 + (x div (2 + (x div (1 + ((x div 2) mod (1 + (x mod 4)))))))) * (x mod 2)))
A090740: 1 3 1 4 1 3 1 5 1 3 1 4 1 3 1 6
(1 + ((x div (2 + (x div (2 + (((x2 div 2) mod (2 + (x div 2))) div 2))))) + (x mod 2)))
A080226-A060741: 1 2 2 3 2 3 2 4 3 4 2 4 2 4 4 5
(1 + (x div (2 + (x div (2 + (((x2 div 2) mod (2 + (x div 2))) div 2))))) - (x mod 2))
A132881: 1 0 2 1 2 1 2 2 3 2 2 2 2 2 4 3
((1 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4)))) * (1 + (x mod 2)))
A335852: 1 2 1 4 1 2 1 6 2 2 1 4 1 2 1 8
((1 + (x div (2 * (2 + ((x * (x + (x div 2))) mod 6))))) div (1 + (x mod 2)))
A025805: 1 0 1 0 2 0 2 0 3 0 3 1 4 1 4 2
((1 - (2 * (((x mod 13) mod 3) mod 2))) div (1 + (x mod 2)))
A284881: 1 ~1 1 0 ~1 0 1 ~1 1 0 ~1 0 1 0 ~1 0
(1 + ((x2 * ((x + ((x5 + ~x3 + ~x2) div 2)) div 2)) div 2))
A229384: 1 1 13 239
(1 + (((3x + 1) + ((((2x + ~1) * (x div 2)) div 2) mod 3)) div 2))
A218979: 1 3 5 7 8 9 11 12 13 15 17 18 19 21 23 25
(1 + compr(\x.(~1 + (x mod (1 + ((9x + 1) mod (1 + (x div 2)))))),x))
A302594: 1 2 3 4 5 6 8 9 10 11 12 16 17 18 20 22
(~1 + compr(\x.(1 - (x mod (1 + ((x + 1) mod (1 + (2 * ((x + ~1) div 5))))))),x))
A062973: 6 8 9 10 12 14 16 18 20 21 22 24 25 26 27 28
(1 + compr(\x.(~1 + ((x + ((x - (((x + ~1) mod (2 + (x div 2))) div 2)) div 2)) mod 3)),x))
A325031-A093686: 1 2 3 4 6 7 8 9 10 12 14 16 18 19 20 21
(1 + compr(\x.(~1 + ((1 + ((x mod 10) mod 8)) mod (x + 1))),x))
A033074: 1 2 3 4 5 6 7 8 9 11 19 21 29 31 39 41
((x + 1) + (x2 div ((2x + 1) + ((x + 2) mod 7))))
A026431: 1 2 3 4 6 8 9 10 12 13 14 16 18 20 21 22
(1 + compr(\x.((x + 1) mod (1 + (2 * (((x + 1) div (2 + (x mod 5))) mod 2)))),x))
A342950-A337230-A238985: 1 2 3 4 5 6 7 8 9 12 14 15 16 18 21 24
((x + 1) + (9 * ((x mod (x - ((x + ~1) mod 8))) div 2)))
A330760: 1 2 3 4 5 6 7 8 9 10 11 21 22 32 33 43
(x2 mod ((x + ~1) + (9 * (x + (x mod 10)))))
A069940: 0 1 4 9 16 25 36 49 64 81 1 3 7 13 21 31
((x + 1) + ((x + ((x3 + 2x2 + 2x) div 4)) div 9))
A320593: 1 2 3 5 8 11 16 21 28 36 46 57 71 86 104 124
((x + 1) + (((4x2 + 12x + 8) div 5) div 5))
A024193: 1 2 4 7 9 12 15 19 23 27 32 36 42 47 53 59
((x + 1) + (3 * ((3 * (x div 8)) + ((x + 1) div 3))))
A080333: 1 2 6 7 8 12 13 14 27 28 29 33 34 35 39 40
(~1 + compr(\x.(1 - (((((x2 + ~2) * ((x + 1) div 2)) div 2) div 3) mod 3)),x))
A274374: 0 2 3 4 5 6 7 8 10 11 12 13 15 16 18 21
((x + 1) + ((2 * ((x + 1) - ((x mod (2 - ((x div 2) div ~2))) div 2))) div 3))
A026339: 1 3 4 6 8 9 11 12 15 16 18 20 21 22 24 26
((x + 1) + ((2 * (x + (x div 8) - (x div 5))) div 3))
A285140-A066507: 1 2 4 6 7 8 10 12 14 16 17 18 20 22 23 24
((x + 1) + (((7x3 + 15x2 + 8x) div 2) div 3))
A185787: 1 7 25 62 125 221 357 540 777 1075 1441 1882 2405 3017 3725 4536
((x + 1) + ((x - (2 * ((2x div (4 + (x div 4))) mod 2))) div 3))
A153350: 1 2 3 4 5 7 9 10 11 12 13 15 16 17 19 21
((~x + ~1) + ((4 * ((6x + 6) + (x div 4))) div 3))
A189931: 7 14 21 28 36 43 50 57 65 72 79 86 95 102 109 116
(1 + compr(\x.(2 - ((x2 + 4x + 4) mod (~x + 26))),x))
A164713: 1 2 3 4 5 6 7 8 9 10 12 14 15 16 17 21
((x + 1) + ((2 * ((x + 2) + (((x - (x div 3)) mod 3) div 2))) div 3))
A003254: 2 4 6 8 9 10 12 14 15 17 19 21 23 24 25 27
((x + 1) + ((2 * (x + ((3 * (2 + (((x + 1) div 2) div 2))) div 2))) div 3))
A206818: 3 4 6 8 10 12 13 16 18 20 21 24 25 27 29 32
(1 + compr(\x.(1 - ((x + ((x * ((1 + (x div 4)) div 2)) div 3)) mod 3)),x))
A092875: 2 3 5 7 9 11 12 13 15 16 17 18 20 21 23 24
(1 + compr(\x.(4 - (69 mod (x + 1))),x))
A078892: 5 7 8 9 10 12 13 14 15 16 18 19 20 21 24 25
((x + 1) + (2 * (((x + 2) - (((~x + ~1) + (x mod 2)) div 5)) mod (x + 1))))
A152769: 1 2 7 8 9 10 13 14 15 16 19 20 21 22 23 24
((x + 1) + ((x - ((5 * ((x + 2) div ~7)) div 2)) div 2))
A014248: 2 4 5 7 8 10 12 14 15 17 18 20 21 24 26 27
((x + 1) + (2 * ((3 * ((x mod (x - ((x + ~1) mod 8))) div 2)) div 2)))
A252494: 1 2 3 4 5 6 7 8 9 10 11 14 15 20 21 24
((x + 1) + (2 * ((3 * ((x + (1 mod (8 - (x div 2)))) div 2)) div 2)))
A102858-A102857: 1 4 5 10 11 14 15 20 21 24 25 30 31 34 35 36
((x + 1) + ((((x + ~1) * (x mod ((x + ~1) - (x mod 12)))) div 2) div 2))
A055471: 1 2 3 4 5 6 7 8 9 10 11 12 15 20 24 30
((x + ~1) + (2 * ((2 - ((3 * ((x div 2) - ((x mod 3) div 2))) div 2)) div 2)))
A259579: 1 2 3 2 1 4 3 4 5 4 3 6 3 4 5 6
((x + 1) + ((x mod (2 + (x div (2 + ((~2x + 1) mod (2 + (x div 4))))))) div 2))
A210253: 1 2 3 4 5 6 8 8 9 10 11 13 14 16 16 16
((x + 1) + ((x + (12x2 div 7)) div 2))
A022777: 1 3 7 13 20 29 40 53 67 83 101 121 142 165 190 216
((x + 1) + ((x + ((1 + ((3 * (x + ((x mod 3) mod 2))) div 2)) div 2)) div 2))
A187837: 1 3 5 6 9 10 12 14 16 18 20 21 23 26 27 29
((x + 1) + (2 * (x + ((6x + (x2 div 4)) div (x + 2)))))
A319879: 1 8 13 18 21 26 29 34 37 40 45 48 51 56 59 62
((x2 + 2x + 2) + ((4 * (x + ((x div 2) div 3))) div 3))
A161203: 2 6 12 21 31 43 59 75 94 114 136 161 188 217 247 279
((x + 1) * (1 + (x mod (1 + (2x div (1 + (x mod (1 + ((~x + 2) mod 4)))))))))
A304203: 1 4 9 8 25 36 49 32 27 100 121 72 169 196 225 128
((1 + ((x2 + x) div (1 + (x mod (1 + (x div (2 * (2 - (x mod 2))))))))) mod (x + 1))
A318828: 0 1 1 3 1 5 1 7 7 9 1 11 1 13 11 15
((x + 1) * (1 + (x mod (1 + ((4 * (2 + ((x mod 3) div 2))) mod (x + 1))))))
A099469: 1 2 3 4 5 6 7 8 9 10 22 12 52 70 30 112
((x + 1) * (1 + (x mod (1 + (x mod (1 - (x div (~2 + ((x + ~2) mod ~4)))))))))
A086938: 1 4 3 8 5 18 7 16 27 20 11 48 13 28 15 64
((x + 1) * ((x + 1) - (9 * (~x + (x mod 10)))))
A111704: 1 4 9 16 25 36 49 64 81 100 1111 1224 1339 1456 1575 1696
((x + 1) * (1 + (5 * ((3x3 + 3x2 + 2x) div 2))))
A095266: 1 42 303 1144 3105 6906 13447 23808 39249 61210 91311 131352 183313 249354 331815 433216
((x + 1) * (1 + ((3 * ((x2 + 3x + 2) div 2)) mod (1 + (x div 4)))))
A085701: 1 2 3 4 10 12 7 8 9 10 11 12 26 56 15 16
compr(\x.(~1 + ((1 + ((x div 2) div (1 + (x mod (3 - (x mod 2)))))) mod 3)),(x + 1))
A061910: 1 2 3 6 9 10 11 12 13 14 15 18 20 21 22 23
((x + 1) * (1 + (3 * ((7x2 + 5x) div 2))))
A100168: 1 38 174 472 995 1806 2968 4544 6597 9190 12386 16248 20839 26222 32460 39616
((1 + (3 * ((20x + 8) - (x mod 2)))) div (x + 1))
A309623: 25 41 48 50
compr(\x.(~1 + ((1 + (x mod (1 + (x mod (2 * (2 + ((x div 2) mod 2))))))) mod (x + 1))),(x + 1))
A325796-A279029: 1 2 3 4 6 8 10 12 16 18 20 24 28 30 32 36
compr(\x.(1 - (x mod (1 + ((1 + (5 * (2 + (x div 2)))) mod (x + 1))))),(x + 1))
A273786: 5 7 8 9 10 13 17 18 19 21 22 23 24 25 26 27
((x + 1) * (1 + (2 * ((x + 1) mod (1 + (x mod (2 * (2 + ((x + ~1) mod 3)))))))))
A161980: 1 2 3 4 5 6 7 8 9 10 55 12 91 14 15 16
((x + 1) * (1 + (2 * (2x div (5 + (x div (2 + (x mod 3))))))))
A154785: 1 2 3 12 15 18 21 40 45 50 55 84 65 70 105 80
((14x2 + 98x + 70) div (x + 1))
A295807: 70 91 107
((x + 1) * (1 + (2 * ((x + 1) + (2 * (x + ((x3 + 2x) div 3)))))))
A292001: 3 26 93 260 615 1278 2401 4168 6795 10530 15653 22476 31343 42630 56745 74128
compr(\x.((x + 1) mod (1 + (2 * ((2x div (~1 + ((~x + 2) div 3))) mod 2)))),(x + 1))
A099247: 1 2 4 5 6 8 11 13 14 16 17 18 19 20 21 22
((1 + (2 * (2 + (x mod (2 + ((4 * (x div 3)) div 3)))))) mod (x + 1))
A119994: 0 1 2 1 2 3 2 3 5 1 2 3 2 3 5 3
compr(\x.((x + 1) mod (1 + (x mod (2 * (2 + ((x2 div 2) mod 6)))))),(x + 1))
A196736: 1 2 3 4 5 7 8 9 11 12 13 15 16 17 19 23
compr(\x.(~1 + (2x2 mod (x + 60))),(x + 1))
A162826: 12 15 20 30 36 40 60 84 90 100 120 140 165 180 228 240
((9 * ((x + 2) - ((x + 1) mod 10))) div (x + 1))
A097326: 9 4 3 2 1 1 1 1 1 9 9 8 7 7 6 6
((~x + ~1) + (5 * ((x + 1) - (((~x + 2) - (x div 4)) div 4))))
A188293: 4 8 12 21 25 29 38 42 46 55 59 63 72 76 80 84
((x + 1) + ((2x div (5 + (x div 4))) + (x div 5)))
A187899: 1 2 3 5 6 8 10 11 12 13 15 17 18 19 20 22
compr(\x.(1 - (((x + 1) - ((((x div 4) mod 2) - (x div 2)) div 2)) mod 3)),(x + 1))
A288509: 1 2 3 5 6 8 10 12 13 15 17 19 20 22 23 24
((x + 1) * (((x2 + 4x + 1) * ((x3 + x2) div 2)) div 3))
A279437: 0 4 78 528 2200 6900 17934 40768 83808 159300 284350 482064 782808 1225588 1859550 2745600
((x + 1) * (1 + ((19x2 + 11x) div 2)))
A100172: 1 32 150 412 875 1596 2632 4040 5877 8200 11066 14532 18655 23492 29100 35536
compr(\x.(~1 + (5 * (2x mod 7)) - (x div 2)),(x + 1))
A168135: 7 11 14 18 21 22 25 28 29 32 33 35 36 39 40 42
((2 + ((x div (1 + ((x + 2) mod 8))) mod 2) - (x mod 2)) mod (x + 1))
A056171: 0 1 2 1 2 1 2 2 2 1 2 2 3 2 2 2
((1 + compr(\x.(1 - (((x + 1) div (2 + ((x * (x div 2)) mod 2))) mod 3)),x)) mod (x + 1))
A304431: 0 1 1 1 3 3 3 3 3 4 4 4 4 7 7 7
((2 + (x div (1 + (x mod (1 + ((3x mod (2 + (x div 2))) div 2)))))) mod (x + 1))
A306264: 0 1 1 1 1 4 1 1 1 6 1 5 1 8 6 1
((x + 1) + (2 * (1 + (x mod (2 * (1 + ((2 * (2x div 3)) div 3)))))))
A239487: 3 6 5 12 7 18 9 12 11 30 13 16 15 18 17 20
((x + 1) * (x - ((~1 + ((x mod (1 + ((2 - (x mod 4)) mod (x + 1)))) div 2)) div 2)))
A254520: 1 4 9 12 25 36 49 48 72 100 121 108 169 196 225 192
((2 + ((2 * (((2x + 1) mod (2 + (x div 4))) div 2)) mod 3)) mod (x + 1))
A049298: 0 0 2 2 2 4 2 2 2 4 2 4 2 4 3 2
((x + 1) * ((2x4 + 11x3 + 25x2 + 28x + 12) div 2))
A250388: 6 78 432 1560 4350 10206 21168 40032 70470 117150 185856 283608 418782 601230 842400 1155456
compr(\x.(2 * (((x div 2) - (x mod ((x + 1) - (x mod 10)))) div 2)),(x + 1))
A215121: 1 2 3 10 19 20 30
((x + 1) + ((2 * (2x div 15)) + (((x + 1) div 2) div 2)))
A120486: 1 2 3 5 6 7 8 10 13 14 15 17 18 19 20 24
((x + 1) * (1 - (2 * ((x - ((~x2 + x) div 32)) mod 2))))
A061019: 1 ~2 ~3 4 ~5 6 ~7 ~8 9 10 ~11 ~12 ~13 14 15 16
(1 - ((x div 2) mod (1 - ((2 - (2x mod (4 + (x div 4)))) mod (x + 1)))))
A214868: 1 1 1 1 2 1 1 3 3 1 1 5 6 5 1 1
((((x3 + 3x2 + 2x) div 2) div 3) + ((x + 1) * (x2 div 4)))
A272459: 0 1 7 18 40 71 119 180 264 365 495 646 832 1043 1295 1576
((x + 1) * ((33x2 + 25x + 2) div 2))
A100153: 1 60 276 748 1575 2856 4690 7176 10413 14500 19536 25620 32851 41328 51150 62416
((2x + 2) * (~x + ((x4 + 9x3 + 28x2 + 36x + 16) div 2)))
A268459: 16 176 852 2776 7160 15816 31276 56912 97056 157120 243716 364776 529672 749336 1036380 1405216
((x + 1) + ((((x3 + 3x2 + 2x) div 2) div 3) + (x2 div (x + 2))))
A054107: 1 3 8 15 27 44 67 97 135 182 239 307 387 480 587 709
((3x + 1) + ((x + ((~x + 2) mod (3 + (x div 4)))) div 4))
A327737: 1 4 7 11 14 17 20 24 28 31 34 37 40 43 46 51
(1 - ((1 + (((x2 + ~2x) div (4 + (x div 2))) mod 2) - (x mod 2)) mod (x + 1)))
A168394: 1 0 0 1 ~1 1 ~1 0 0 0 0 0 0 1 ~1 0
(x10 + x9 + x8 + x7 + x6 + x5 + x4 + x3 + x2 + x)
A228294: 0 10 2046 88572 1398100 12207030 72559410 329554456 1227133512 3922632450 11111111110 28531167060 67546215516 149346699502 311505013050 617839704240
compr(\x.(~x + (17 * (x mod 14))),(x + 1))
A297282-A296755: 14 28 29 42 43 44 56 57 58 59 70 71 72 73 74 84
((2x + 1) + (3 * ((x + 1) + (3 * ((x + (x div 2)) div 4)))))
A105503: 4 9 14 28 33 38 52 57 71 76 81 95 100 105 119 124
((3x + 1) + ((x - ((~2x + 4) div (2 - (x div ~4)))) mod 2))
A287444: 1 5 7 10 13 17 19 22 26 28 31 35 37 41 43 46
((~x + 1) + (5 * (x - ((~2x3 + 3x2 + ~x) div 3))))
A143131: 1 5 19 63 157 321 575 939 1433 2077 2891 3895 5109 6553 8247 10211
((4x3 + ~4x) + (((x3 + 3x2 + 2x) div 2) div 3))
A256647: 0 1 28 106 260 515 896 1428 2136 3045 4180 5566 7228 9191 11480 14120
(x mod (2 + (x div (1 + (x mod (1 + (x mod (1 + (x div (2 + (x div 5)))))))))))
A056737: 0 1 2 0 4 1 6 2 0 3 10 1 12 5 2 0
((1 + ((1 + (x div 5)) div (1 + (~2x mod 5)))) div 2)
A025884: 1 0 0 0 0 1 0 1 0 0 2 0 1 0 1 2
((1 + ((1 - ((1 + (x div (2 * (2 - (x mod 2))))) div 2)) mod (1 + (x div 3)))) div 2)
A199331: 0 0 0 0 0 0 0 1 0 2 0 1 2 2 2 2
((1 + ((x + 1) div (1 + (2 * (1 + (x mod (1 + (2 * (x div 5))))))))) div 2)
A088018: 0 0 1 1 1 0 1 1 1 2 2 1 1 1 1 2
((1 + (x2 mod (1 + (2 * (1 + (((x * (x div 2)) div (x + 4)) mod 2)))))) div 2)
A330961: 0 1 1 0 1 0 1 2 1 0 0 1 0 1 1 0
(2 * ((x + 1) - ((x + 1) mod (1 + (2 * (((x2 div 3) mod (x + 1)) div 2))))))
A060685: 2 4 6 6 10 12 10 16 18 14 22 20 18 28 30 22
((1 + ((x + 1) mod (1 + (2 * (((~x2 + 2) mod (2 - (x div ~2))) div 2))))) div 2)
A089605: 0 0 0 0 1 0 0 0 2 0 0 0 1 2 0 1
((x + 1) div (2 * (1 + (2x mod (1 + (2 * (2 - (x mod ~7))))))))
A076413: 0 0 0 0 0 1 0 0 0 1 0 6 0 1 1 0
(3 + (2x div (1 + (2x div (2 + (2x div (2 + (x div 4))))))))
A143082: 3 5 5 6 5 6 7 7 8 7 9 8 7 9 8 10
((1 + ((2x + 2) mod (1 + ((2x + ~1) mod (4 + (x div 4)))))) div 2)
A103633-A093323: 1 0 1 0 1 1 0 0 1 1 0 0 1 2 1 0
(x + (((x + 1) div (1 + (x mod 9))) mod 2) - (2 * (x div 3)))
A199323: 1 2 3 2 3 4 3 4 5 3 5 5 5 5 6 5
((1 + (3 * (((x + 1) mod (1 + (2 * ((1 + (x div 4)) div 2)))) div 2))) div 2)
A096142: 0 0 0 0 2 0 0 2 0 0 2 0 2 3 0 0
((x2 div ((2x + 1) - (3 * ((x div 2) - ((x mod 3) div 2))))) div 2)
A234306: 0 0 0 1 2 1 4 4 4 5 8 5 10 9 8 11
((((3x2 + 7x + 4) div 2) * (1 + (3 * ((x + 1) div 2)))) div 2)
A228124: 1 14 30 91 140 285 385 650 819 1240 1496 2109 2470 3311 3795 4900
((1 + (3 * ((2x + 2) - (x div (4 + ((x div 2) mod 4)))))) div 2)
A305495: 3 6 9 12 15 18 21 23 24 27 30 33 36 39 42 45
(3 + ((2 * (x - ((((((x + ~1) div 2) div 2) * (x div 2)) div 2) div 2))) div 3))
A196592: 3 3 4 5 5 6 7 7 7 7 8 9 9 9 9 9
(x7 mod 46)
A240129: 0 1 36
A070726: 0 1 36 25 8 17 26 5 12 27 14 7 16 9 42 11
(2 - ((1 + ((((x + 2) * ((~x + 4) + (x div 4))) div 2) div 3)) div 2))
A070048: 1 1 1 2 1 2 3 3 4 5 6 7 8 9 11 13
(2 - ((2 - (((x + 5) + (x div 4)) mod (1 + (x div 3)))) div 2))
A140192: 1 1 1 1 1 2 1 2 1 1 2 2 1 2 2 4
((x + 2) - (1 mod ((x + 1) - ((2x + 1) * (~1 + ((x2 + ~x) div 4))))))
A333547: 1 2 3 4 18 44
((1 + ((1 + ((2 + (x * (x div 3))) div 5)) mod (1 + (x div 2)))) div 2)
A302242: 0 0 1 0 1 1 2 0 2 1 1 1 2 2 2 0
((1 + ((1 + ((((2 + (x div 2)) * (x div 3)) div 2) div 2)) div (1 + (x mod 2)))) div 2)
A029198: 1 0 1 0 1 1 2 1 2 1 3 2 5 2 5 3
(2 * ((x + 1) - ((1 + (x mod (2 * (1 + (x mod 9))))) mod (x + 1))))
A117463: 2 4 6 8 10 12 14 16 18 16 16 12 16 20 24 28
((1 + (((~x + 1) + (x mod (1 + (x mod (2 * (2 + ((x div 2) mod 2))))))) mod (x + 1))) div 2)
A088433: 0 1 1 1 1 2 1 2 1 2 1 4 1 2 2 3
((1 + ((1 + ((x + 2) mod (1 + (x div (1 + (2 * (1 + (x mod 3)))))))) div 2)) div 2)
A001842: 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 2
((1 + ((1 + ((x * ((x + ~1) div 2)) div (1 + ((1 + (x div 2)) div 3)))) div 2)) div 2)
A307815: 0 0 0 1 1 2 2 3 3 5 4 5 5 7 7 9
(3 + ((x - ((2 * (x + (x div 3))) div (~1 + ((~x + 1) div 3)))) div 2))
A088243: 3 4 5 6 7 7 9 9 9 10 11 11 12 13 13 14
(((x + 1) mod (1 + (2 * ((1 + ((x2 + ~x) div 2)) mod (1 + (x div 3)))))) div 2)
A218786: 0 0 0 0 1 0 0 1 2 0 0 0 1 2 0 3
((1 + ((1 + (((2x2 + ~x) mod 9) mod (x + 1))) div 2)) div 2)
A180835: 0 1 0 1 1 0 1 1 1 0 1 2 2 1 0 1
(1 - ((1 + ((1 + (((x2 + ~2x) mod 11) div 2)) div 2)) div 2))
A014075: 1 ~1 1 0 0 0 0 0 0 0 0 1 ~1 1 0 0
(2 * (1 - (x div (~1 - (x div (2 + (x div (1 + (x mod (2 * (1 + (x mod 2))))))))))))
A247653: 2 4 6 6 10 8 14 8 18 12 22 10 26 16 30 10
((1 + ((1 + (((1 + (((x + 1) * (x div (1 + (x mod 2)))) div 2)) div 2) div 2)) div 2)) div 2)
A308307: 0 0 1 0 1 1 2 1 3 2 4 2 5 3 7 4
(((2x + 1) mod (3 + ((2x + 1) mod (3 + (x div 4))))) div 2)
A305435: 0 0 0 1 0 2 0 1 1 2 0 2 0 1 2 1
((~1 + ((14x3 + 21x2 + 14x + 7) div 2)) div 2)
A007202: 1 13 57 153 323 587 967 1483 2157 3009 4061 5333 6847 8623 10683 13047
((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~1) div 2))) div 2)
A327031-A271916-A226545-A014473: 0 0 0 0 1 0 0 2 2 0 0 3 5 3 0 0
((1 + (((1 + (((x + 1) * ((2 - ((x * (x mod 2)) div 2)) div 2)) div 2)) div 2) div 2)) div 2)
A246582: 0 0 0 0 0 0 1 0 1 0 1 ~1 1 ~2 1 ~3
((1 + ((x - ((x - ((~1 + (2x div 3)) mod 5)) div 2)) div 2)) div 2)
A134337: 1 1 0 1 1 1 1 1 2 1 1 2 2 2 2 3
((1 + (((((x + 1) - ((x + 1) div 5)) * (1 + (x div 2))) div 2) div 2)) div 2)
A340275: 0 0 1 1 2 2 3 4 5 5 7 8 10 11 12 13
((1 + ((((x + 1) * ((4 * (1 + (x div 2))) + (x div 3))) div 2) div 2)) div 2)
A212987: 1 1 3 5 8 10 16 18 25 29 37 41 52 56 68 74
(3 + (((((x + 1) * (~1 + (2 * ((x - (x div 4)) mod 2)))) div 2) div 2) div 2))
A124474: 2 3 2 3 3 2 3 2 1 4 1 4 4 1 4 1
(2 * (1 + (2 * (x - ((0 - ((x - (((x + 1) div 2) mod 6)) div 2)) div 2)))))
A039956: 2 6 10 14 22 26 30 34 38 42 46 58 62 66 70 74
((1 + (x div 3)) div (2 * (1 + (((x + 2) mod (2 + ((x + 1) mod 4))) div 2))))
A035438: 0 0 0 1 1 0 0 1 1 1 1 2 1 1 2 3
(2 + ((~1 + (x2 div 2)) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))))
A259578: 2 2 2 2 3 2 2 3 3 2 2 4 3 4 2 2
(1 - ((1 + (x mod 2) - (((x - (((~x + 1) * (x div 3)) div 2)) div 2) div 2)) div 2))
A029158: 1 0 1 1 1 1 2 2 2 3 4 3 5 5 6 6
(1 - ((1 + ((~1 + ((2x + 1) mod (4 + (x div 4)))) mod 4)) div 2))
A117449: 1 0 1 0 ~1 1 0 ~1 1 1 0 1 ~1 0 1 0
((1 + (((3 * ((x + 2) - (x mod 8))) mod (x + 1)) mod 4)) div 2)
A256572: 0 0 0 1 1 0 1 1 2 0 0 1 0 1 0 1
((((x + 1) div (1 + (3 * ((~x + 1) mod 5)))) mod 5) div 2)
A100699: 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 2
((x + 2) div (2 + ((((3 * (x div 4)) div 2) - (x div 2)) mod 5)))
A173911: 1 1 0 0 1 1 1 1 1 1 2 2 2 3 4 4
((x - ((2x + 2) mod 21)) mod 10)
A161813: 8 7 6 5 4 3 2 1 0 9 9 8 7 6 5 4
(((2x + 1) * (1 - (2 * ((x div 5) mod 2)))) mod 10)
A206543: 1 3 5 7 9 9 7 5 3 1 1 3 5 7 9 9
(10 + compr(\x.(x mod ((x + 1) - (x mod 10))),(x + 1)))
A261020: 11 12 13 14 15 16 17 18 19 21 31 41 51 61 71 81
((x + 10) - (4 * ((x div 2) - (2 * ((x div 4) mod 2)))))
A004451: 10 11 8 9 14 15 12 13 2 3 0 1 6 7 4 5
(compr(\x.(x mod ((x + 1) - (x mod 10))),x) + (x mod 10))
A345111-A056964-A052008: 0 2 4 6 8 10 12 14 16 18 11 22 33 44 55 66
(2 - ((1 + (((2x mod (2 + (x div 2))) div 2) mod 2)) mod (2 + (x mod 5))))
A121444: 1 1 1 1 1 2 0 1 1 1 2 1 1 0 1 2
((1 + (((x + (6 * ((1 + (x mod 5)) div 2))) div 2) div 2)) div 2)
A245574-A245573-A057536: 0 1 1 2 2 1 2 2 3 3 1 2 2 3 3 2
(~2 + (3 * (1 + (x mod (1 + (2x mod (~1 + (2 * ((x + ~1) mod 4)))))))))
A131301: 1 1 1 1 1 1 1 4 1 1 1 4 7 1 1 1
((3 * (1 + ((x + 2) mod (2 - ((1 - (x div 2)) div (1 + (2 mod (x + 1)))))))) div 2)
A107638: 1 1 1 3 1 3 4 1 3 4 1 3 4 6 1 3
(~2 + (3 * (1 + (((3x2 + x) div 2) mod 9))))
A070412: 1 7 22 19 25 13 10 16 4 1 7 22 19 25 13 10
(2 * ((1 + (((2x + 1) * ((x2 + x) div 3)) div 3)) div 3))
A307559: 0 0 2 6 12 24 40 60 90 126 168 224 288 360 450 550
(2 + (3 * (1 + ((4 * (x - (x div ~5))) div 3))))
A084088: 5 11 17 20 23 29 35 41 44 47 53 59 65 68 71 77
(2 * ((x - (x mod (~1 + (2 * ((~2x + 2) div 9))))) div 3))
A198332: 0 0 2 2 4 4 6 6 6 6 6 8 8 8 8 12
(((1 + (((x + 2) + (x div 7)) * ((x + 1) div 2))) div 3) div 2)
A049995: 0 0 0 1 2 3 4 6 7 10 11 14 15 18 21 25
((3 * (((8x + 8) + (x div 5)) div 3)) div 2)
A022805: 3 7 12 15 19 24 28 31 36 40 45 48 52 57 60 64
((3 * ((2 + ((x + 1) mod (2 + ((x mod (1 + (x div 2))) div 2)))) div 3)) div 2)
A291960-A245120: 1 0 1 0 1 0 1 1 0 1 1 0 1 3 0 1
(6 * (2 + ((x + 1) mod (1 + (x mod (8 - (x mod 3)))))))
A343194: 12 12 12 12 12 12 12 12 12 12 30 12 30 12 12 12
(3 - ((2 * (1 + ((1 + (x div (1 + ((x + 2) mod 4)))) div 2))) mod 3))
A136691: 1 1 2 2 2 2 1 3 2 2 3 1 3 3 2 2
((1 + (2 * ((x + 1) + (2 * (x + (x mod 2))))) - (((x + 1) div 2) div 3)) div 2)
A011990: 1 6 7 12
A327313: 1 6 7 12 13 18 19 24 25 30 31 35 36 41 42 47
(((((x2 + x) * ((x + ~1) + (2 * (2x + (x mod 2))))) div 2) div 3) div 2)
A220788: 0 1 4 16
A046001: 0 1 4 16 31 65
(~2 + (3 * (2 + ((x mod (2 + ((~1 + (x mod 5)) mod 3))) div 2))))
A023404: 4 4 7 7 4 4 4 4 4 4 7 4 4 4 4 7
((3 * (((2x2 + ~4x + 2) mod (4 + (x div 4))) div 2)) div 2)
A325268: 1 0 1 0 1 1 0 1 1 1 0 1 3 0 1 0
((~x + 4) + (3 * (2x - ((x - ((x + (x div 2)) div 4)) div 2))))
A190547: 4 9 11 16 21 23 28 33 38 40 45 50 52 57 62 64
(32 + ((3 * (x div 4)) div 2) - ((x + 1) div 2))
A131762: 32 31 31 30 31 30 30 29 31 30 30 29 30 29 29 28
(2x + ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2) - (x div 2))
A283208: 0 2 3 6 7 9 10 14 15 17 18 21 22 24 25 30
(2 + (3 * (2 + compr(\x.((((x2 div 3) * ((x + 1) div 2)) div 2) mod 2),x))))
A279776: 8 11 14 23 26 29 32 38 41 44 47 53 56 59 62 65
((((5x4 + 20x3 + 22x2 + 4x) div 2) div 3) div 2)
A187452: 0 4 28 96 244 516 968 1664 2680 4100 6020 8544 11788 15876 20944 27136
((((x2 + 2x + 1) * (x div 2)) - (((~x3 + x) div 2) div 3)) div 2)
A294286: 0 0 5 10 30 46 91 124 204 260 385 470 650 770 1015 1176
((3 * compr(\x.(1 - (x mod (1 + (2 * (2 - ((~1 + (x mod 4)) div 2)))))),x)) div 2)
A022304: 1 3 6 9 10 12 13 16 18 19 21 24 25 27 28 30
(6 * compr(\x.(2 - ((x2 - ((x div 4) mod 2)) mod 5)),x))
A112054: 12 18 30 42 48 72 78 90 102 108 120 132 138 162 168 180
(2 + (3 * (x + ((2 * (x - (x2 div (x - ((~x + 2) div 2))))) div 3))))
A031210: 2 5 8 11 14 20 23 29 32 35 38 41 44 50 53 56
((3 * (x + ((((x + 1) div (1 + (x mod 4))) mod 2) + (x div 3)))) div 2)
A026225: 1 3 4 7 9 10 12 13 16 19 21 22 25 27 28 30
((((2x + 2) + (x * (3 + ((x - ((x div 2) mod 2)) div 2)))) div 3) div 2)
A195060: 0 1 2 3 5 6 7 9 12 13 15 18 22 24 26 30
((1 + ((2 * ((2x + 2) - (((1 + (x div 2)) div 2) div 2))) + (x div 3))) div 2)
A184978: 2 4 6 9 11
A024978: 2 4 6 9 11 13 14 16 18 21 23 25 27 29 30 33
(((2 * (1 + ((((x + 2) div 3) mod 4) div 3))) + (x mod 3)) div 2)
A105202: 1 1 2 1 1 2 1 2 3 2 1 2 1 1 2 1
(((2 * ((2 - (x div (~5 + (x div 4)))) div 2)) - (x mod 3)) div 2)
A029272: 1 0 0 1 0 1 2 1 1 2 2 2 4 3 3 5
((((~1 + (2 * (x mod 4))) mod (1 + (x div 2))) div 3) + ((x mod 3) mod 2))
A128115: 0 1 0 0 1 0 1 1 1 0 2 1 2 1 1 1
((1 + ((x + (3 * (2 - ((~x + 2) div (2 - (x div ~4)))))) div 2)) div 2)
A067434: 1 2 2 3 3 4 4 5 5 5 6 6 6 6 7 8
((1 + ((~1 + ((x2 div 2) + (2x mod (1 + (x div 4))))) mod (x + 2))) div 2)
A337787: 1 1 1 2 1 2 1 3 1 3 2 4 1 5 1 6
(~2 + ((x + 3) * (1 + ((7x2 + 5x) div 2))))
A095796: 1 26 98 238 467 806 1276 1898 2693 3682 4886 6326 8023 9998 12272 14866
(((x3 + 2x2 + ~1) * (((x3 + 3x2 + 2x) div 2) div 3)) div 2)
A076389: 0 1 30 220 950 3045 8036 18480 38340 73425 131890 224796 366730 576485 877800 1300160
((2 + ((x - (((x + 1) div 2) mod 5)) div 3) - (x mod 2)) div 2)
A029230: 1 0 1 0 1 0 1 1 1 2 2 2 2 2 3 2
((2 + ((2 + ((x * (x div 5)) div 2)) div 3) - (x mod 2)) div 2)
A029206: 1 0 1 0 1 1 1 1 2 1 3 2 3 3 3 4
((2 + ((x + 1) div (2 + ((2x mod 3) + (x mod 2)))) - (x mod 2)) div 2)
A339660: 1 0 1 1 1 1 2 1 2 2 2 2 4 1 3 3
(((x + ~1) mod (2 + (2 * (((~x + 1) mod 3) + (x mod 2))) - (x mod 2))) div 2)
A319195: 1 0 0 1 0 2 0 0 0 1 0 1 1 0 0 2
(((x + ~1) mod (3 + (((x mod (1 + ((~x + 2) mod 4))) div 2) + (x mod 2)))) div 2)
A230264: 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 2
(x div (2 + (x div (1 + ((2 * ((2x div (1 + (x div 4))) mod 2)) + (x mod 2))))))
A334201-A323077: 0 0 0 1 0 1 0 2 2 1 0 2 0 1 2 3
((1 + compr(\x.(1 - (x mod (1 + (4 * (x mod (2 + ((~x + 2) mod 4))))))),x)) div 2)
A246372: 1 2 3 4 6 7 9 10 12 15 16 19 20 21 22 24
(((x + 1) + (9 * ((x + 1) - (x mod 10)))) div 2)
A106746: 5 5 6 6 7 7 8 8 9 9 55 55 56 56 57 57
((x + 3) + (9 * (1 - (((x div 3) mod 3) div 2))))
A004501: 12 13 14 15 16 17 9 10 11 21 22 23 24 25 26 18
(((x + 1) + (49x div (x + 3))) div 2)
A004235: 0 7 11 14 16 18 19 21 22 23 24 25 26 26 27 28
(3 + compr(\x.(1 - (((x mod (~2 + (x mod ~7))) mod 2) + (x mod 2))),x))
A121541: 4 5 6 7 8 10 12 14 16 18 19 20 22 23 24 26
(((x + 1) * (1 + (3 * ((1 + (x mod (~2 - (x div 3)))) mod 2)))) div 2)
A073675: 2 1 6 8 10 3 14 4 18 5 22 24 26 7 30 32
(((1 + (x mod ((1 + (x mod (1 + (x div 4)))) * (1 + (x mod 2))))) mod (x + 1)) div 2)
A028422: 0 0 0 1 0 1 0 2 1 1 0 3 0 1 1 4
(x div (2 + ((1 + (2 * (1 + (2 div (1 + (x mod (2 + (x mod 4)))))))) mod (x + 1))))
A212178: 0 0 1 0 1 1 1 1 0 1 2 1 1 1 2 1
((x + 2) div (2 + ((1 + ((((~2 + (x div 2)) * (x div 2)) mod (x + 1)) mod 2)) mod (x + 1))))
A049317: 1 1 1 1 2 2 2 2 3 3 4 3 3 5 4 4
(((1 + (2 * (2 + (x2 div 19)))) mod (x + 1)) div 2)
A027189: 0 0 1 0 0 0 0 0 1 1 2 2 3 3 5 5
(((1 + (x mod (2 + ((x + ~1) mod (4 + (((x + 1) div 2) div 2)))))) mod (x + 1)) div 2)
A243823: 0 0 0 0 0 0 0 1 1 1 0 1 0 3 3 4
(x div (2 + ((x - (3 * (((x div 3) mod 2) - (x mod 3)))) mod (x + 1))))
A292108: 0 0 0 1 0 1 0 1 1 1 0 2 0 3 2 1
(1 - (x div (2 + ((3 * (2 + ((1 + (x div 2)) mod 6))) mod (x + 1)))))
A089810: 1 1 0 0 ~1 0 0 0 0 ~2 0 0 0 0 0 0
(1 - (x div (~2 - ((18 + (x div 3)) mod (x + 1)))))
A341737: 1 2 2 2 2 3 2 3 3 4 2 2 3 3 3 3
(8x5 + 6x4 + ~8x3 + ~2x2 + 4x)
A187191: 0 8 288 2208 9200 27720 68208 146048 282528 505800 851840 1365408 2101008 3123848 4510800 6351360
(compr(\x.((1 + ((x div 2) mod (1 + (x div (1 + (2 * (2 + (x mod 2)))))))) mod 2),(x + 1)) div 2)
A195868: 3 5 7 7 9 11 11 13 13 15 16 17 17 19 19 21
(2 * compr(\x.(((1 + ((x + (3 * (x2 div 3))) div 2)) div 2) mod 2),(x + 1)))
A194379: 2 14 16 28 30 32 34 36 42 44 46 48 50 62 64 76
(((2 + ((2x + 1) mod (1 - (x div (~2 + (x mod ~4)))))) mod (x + 1)) div 2)
A305825: 0 0 0 1 1 1 1 2 2 1 1 2 3 2 3 1
(((2 * (2 - (((1 + ((x2 div 2) + (x div 4))) div 2) mod 2))) mod (x + 1)) div 2)
A212185: 0 0 1 0 1 1 2 1 1 1 2 1 2 2 1 2
(((x + 1) * (x - ((~7x3 + x2 + 6x) div 2))) div 2)
A172077: 0 1 33 168 520 1245 2541 4648 7848 12465 18865 27456 38688 53053 71085 93360
((10x4 + 58x3 + 121x2 + 107x + 34) div 2)
A076458: 17 165 678 1910 4335 8547 15260 25308 39645 59345 85602 119730 163163 217455 284280 365432
((9 * (1 + (2 * ((2x + 1) - (x mod 2))))) + ((x + 1) div 2))
A241407: 27 46 100 119 173 192 246 265 319 338 392 411 465 484 538 557
(((~x + 2) + (5 * (x - (3 * (x div ~2))))) * ((x + 1) div 2))
A219393: 0 21 25 88 96 201 213 360 376 565 585 816 840 1113 1141 1456
(1 + ((2 * (((x + 1) + (x div 2) - ((x div 4) mod 2)) div 2)) + ((x + 1) div 2)))
A231407: 1 4 6
A069909: 1 4 6 7 9 10 12 15 17 20 22 23 25 26 28 31
((2 * (~1 + (2 * ((12x + 6) + (x mod 2))))) + ((x + 1) div 2))
A241521: 22 75 119 172 216 269 313 366 410 463 507 560 604 657 701 754
(((1 + ((x + 1) div (1 + (x mod (2 + (x div (2 + (x mod 5)))))))) div 2) div 2)
A193759: 0 0 1 0 1 1 0 1 1 2 0 1 1 2 1 0
(((1 + ((7x + 7) mod 17)) div 2) div 2)
A190549: 2 3 1 3 0 2 4 1 3 0 2 4 1 3 1 2
(x7 mod 44)
A070724: 0 1 40 31 16 25 8 39 24 37 32 11 12 29 20 27
(x div (2 + ((x + 1) div (2 * (1 + (x2 mod (2 * (1 + (x div 5)))))))))
A343897: 0 0 0 1 1 1 1 1 1 2 3 2 1 2 4 2
((x + 1) div (4 + (((x + 4) * ((x + 1) div 2)) mod 7)))
A137171: 0 0 0 1 0 0 1 1 0 1 2 1 1 3 3 1
(2 + ((1 + (x div (2 + ((~x + 17) mod (1 + (x div 2)))))) div 2))
A262887: 2 2 2 3 3 3 3 3 3 3 4 5 3 3 3 4
(((1 + (((x + 1) * (1 + (2 * (2 - ((~x + 1) div 5))))) div 2)) div 2) div 2)
A201992: 0 1 2 3 4 5 6 9 10 11 12 13 18 19 20 22
(((1 + (x mod (2 + ((6 * (1 + (2 * (x mod 2)))) mod (x + 1))))) div 2) div 2)
A260728: 0 0 0 1 0 0 1 1 0 2 0 1 1 0 1 1
(((1 + (((x + 1) * ((5x2 + 5) div (x + 1))) div 2)) div 2) div 2)
A293407: 0 1 3 6 10 16 23 31 40 51 62 75 89 105 122 140
(((1 + (((((x + 1) * ((x * (~1 + ((x + ~1) div 2))) div 2)) div 2) div 2) div 2)) div 2) div 2)
A331443: 0 0 0 0 0 0 0 2 2 4 5 8 10 14 16 22
(x - (4x div (4 + (x div (5 + (((x + ~1) div 2) mod 2))))))
A303637: 0 0 0 0 0 1 2 2 2 2 4 3 4 5 5 5
(4 * (1 + (2 * (x - (((x - ((x2 + ~x) div 8)) div 2) div 2)))))
A316489: 4 12 20 28 36 44 52 60 68 76 92 100 108 124 132 148
((2 + ((3x * (2x - (x mod 4))) mod 9)) div 2)
A106641: 1 2 2 1 4 1 1 4 4 1 1 4 1 2 2 1
(1 - (((x - (5 * ((x2 + 2x) div 12))) div 2) div 2))
A008670: 1 1 1 2 3 3 5 6 7 9 11 12 16 18 20 24
((((5 * ((x2 + 3x + 2) div 2)) + (x div 5)) div 2) div 2)
A005228: 1 3 7 12 18 26 35 45 56 69 83 98 114 131 150 170
(((1 + (2x mod (2 - ((~x + 1) div 3)))) mod (2 + (x mod 5))) div 2)
A173920: 0 0 1 0 1 0 0 1 1 2 0 1 0 1 0 0
((x - (2 * ((2 * (x div (1 + (2 * (2 - ((x mod 3) mod 2)))))) div 3))) div 2)
A049822: 0 0 1 1 2 2 3 2 4 4 3 4 5 4 6 5
(2 + ((3 * (x div (2 + ((x + 1) div (1 + (x mod (2 + (x mod 4)))))))) div 2))
A248596: 2 2 2 3 2 3 3 3 2 2 5 3 2 3 5 2
(2 * ((x + 2) - (3 * ((((2 - (x div 3)) * (x div 3)) div 2) div 2))))
A134928: 4 6 8 10 12 14 16 18 20 28 30 32 40 42 44 58
((x + 2) - (2 * ((2 + ((2x + 1) mod (2 - (x mod ~4)))) div 3)))
A222253: 0 1 2 3 4 5 6 9 8 7 10 11 12 13 14 15
((2 + ((2 + ((x2 + ~x) div (4 + ((x div 4) mod 2)))) div 3)) div 2)
A029096: 1 1 1 1 1 2 2 2 3 4 5 5 5 6 7 8
(((3 * (2 + ((x + ((x2 div (x - ((~x + 2) div 2))) mod 2)) div 2))) div 2) div 2)
A283480: 1 2 2 2 3 3 3 3 4 4 5 6 6 6 6 6
(2 + ((3 * (x + (2 * ((1 + (x div 2) - ((x div 4) mod 2)) div 2)))) div 2))
A288740: 2 3 8 9 11 12 14 15 20 21 26 27 29 30 32 33
((((3 * ((x + 2) - ((x div 2) div 5))) + (x mod 3)) div 2) div 2)
A108789: 1 2 3 3 4 5 6 7 8 8 8 9 9 10 11 12
((((2 * (1 + ((2 + (x mod 8)) mod (x + 1)))) - (x mod 3)) div 2) div 2)
A238210: 0 0 0 1 0 0 1 0 1 2 2 2 3 3 4 5
(4 * (1 + ((x + (((2x3 + 5x2 + 2x) div 2) div 3)) div 2)))
A334706: 4 8 20 44 84 140 224 332 472 648 864 1120 1428 1784 2196 2668
(2 + ((1 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 2)) div 2))
A201375: 2 2 2 2 3 2 2 4 4 2 2 5 8 5 2 2
(32x3 + 80x2 + 184x + 76)
A167586: 76 372 1020 2212 4140 6996 10972 16260 23052 31540 41916 54372 69100 86292 106140 128836
(x div (2 + (x div (2 + ((1 + (4 * (2x + (x div 2)))) mod (1 + (x div 2)))))))
A030620: 0 0 1 1 1 1 1 1 2 3 3 2 2 3 3 3
(x mod (5 + (2x div (2 + (((x + 1) div 2) div 3))) - (x mod 2)))
A103303: 0 1 2 3 4 5 6 7 8 9
A103693: 0 1 2 3 4 5 6 7 8 9 10 2 1 3 2 4
(4 * ((x + 1) + (13 * ((x + 1) div 5))))
A194374: 4 8 12 16 72 76 80 84 88 144 148 152 156 160 216 220
(2 + (((x + 1) + (2 * ((3 * (2x - ((~x + 2) div 4))) div 2))) div 2))
A184836: 2 6 9 14 17 21 24 30 33 37 40 45 48 52 55 61
(~2 + (2 * compr(\x.((x + 2) - (3 * (~2 + ((x - (x div 4)) div 2)))),(x + 1))))
A272303: 114 120 124 126 130 132 136 138 140 142 144 146 148 150 152 154
(3 mod ((2 + ((3 - ((2x + ~1) mod 5)) mod (x + 1))) div 2))
A322512: 0 0 0 1 0 0 1 0 1 0 3 1 0 1 0 3
(2 + (((x + 1) * ((x3 + 3x2 + 18x + 16) div 2)) div 2))
A120478: 6 21 56 126 252 461 786 1266 1946 2877 4116 5726 7776 10341 13502 17346
((2 * ((x + 1) - ((2 * (((x + 1) div 2) div 2)) div 3))) + (((x + 1) div 2) div 2))
A184978: 2 4 6 9 11
A191194: 2 4 6 9 11 13 15 16 18 20 22 23 25 27 29 32
((1 - (x mod (1 - (2 * (x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4)))))))))) div 2)
A330018: 0 0 0 1 0 0 0 3 1 0 0 2 0 0 0 6
((((3 * ((7x2 + 18x + 8) div 2)) div 2) div 2) div 2)
A194126: 1 6 13 23 36 51 69 89 112 138 166 197 231 267 306 347
((x + 2) - (2 * ((2 + (x mod 3) - ((x mod (4 - (x mod 2))) div 2)) div 2)))
A222250: 0 1 2 3 4 5 8 7 6 9 10 11 12 13 14 15
(2 + (x mod (4 + ((1 + (9 * (1 + (x div 2)))) div (x + 1)))))
A079050: 2 3 4 5 6 7 8 9 10 3 3 5 6 7 8 9
(((2 + ((x - (4 * (2 - (x mod (~2 + (x mod ~2)))))) mod (x + 1))) div 2) div 2)
A175045: 0 0 0 1 0 1 1 2 0 0 1 3 1 3 2 2
(((12x + 12) div 5) + ((((x + 1) div 2) div 2) div 2))
A189470: 2 4 7 9 12 14 16 20 22 25 27 29 32 34 37 40
((3x + 2) + ((((x + 1) div 2) div 2) div 2) - (((x + 1) div 2) div 3))
A189525: 2 5 8 11 14 16 19 23 26 29 32 34 37 40 43 47
((((((x + 1) * (1 + (x div (4 + (x mod (2 + (x mod 2))))))) div 2) div 2) div 2) div 2)
A234361: 0 0 0 0 0 0 0 1 1 1 2 1 3 2 3 4
((((((x + 1) * (2 + ((x2 + 2x) div 9))) div 2) div 2) div 2) div 2)
A239142: 0 0 0 0 1 1 3 4 5 8 10 12 16 20 24 30
(((((x + (9 * (1 + (x div 2)))) * ((x + 1) div 2)) div 2) div 2) div 2)
A192225: 0 1 2 5
A129232: 0 1 2 5 7 12 15 21 26 33 40 48 56 66 75 87
(x div (2 * (2 + (x mod (2 + ((x + ~1) mod (4 + ((x div 2) div 5))))))))
A275494: 0 0 0 0 0 0 1 0 0 1 0 1 3 2 1 1
((2 + ((2 + ((0 - (x div (~2 + (x mod ~2)))) * (((x + ~1) div 2) div 2))) div 2)) div 2)
A187821: 1 1 1 1 1 2 2 2 2 3 4 3 4 5 6 5
((x + 1) div (4 + ((((x + 1) mod 10) + (x div 4)) div 2)))
A237523: 0 0 0 0 0 0 0 1 1 2 2 2 1 2 1 2
(9 div (1 - (8 mod (2 * (~8 + (x div 2))))))
A290300: 1 1 1 1 1 1 3 3 9 9 1 1 9 9 9 9
(4 + ((3x3 + 10x2 + 17x + 18) div 2))
A001291: 13 28 62 124
(((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2) + (x div 8))
A069812: 0 0 0 1 1 1 1 3 4 4 4 5 5 5 5 8
((2 + ((x + (((x3 div 2) div 3) div 9)) div 2)) div 2)
A069911-A008582: 1 1 1 1 2 2 3 4 5 6 8 9 12 14 17 20
((((5x + 2) * (((x3 + ~x) div 2) div 3)) div 2) div 2)
A212415: 0 0 3 17 55 135 280 518 882 1410 2145 3135 4433 6097 8190 10780
((2 + ((x + ((~1 + ((x * ((x + 2) + (3 * (x div 2)))) div 2)) div 2)) div 2)) div 2)
A049700: 0 1 2 3 4 6 8 10 13 16 20 22 27 30 36 40
((2 + ((x + ((((x + 1) * ((x + 2) + (x div 5))) div 2) div 2)) div 2)) div 2)
A251419: 1 1 2 3 3 5 6 7 9 10 13 15 17 19 21 24
(((2x + 1) mod (1 + (2x mod (2 + (x div 4))))) * (2 + ((x div 2) mod 2)))
A333783: 0 0 0 0 0 2 0 0 0 2 0 6 0 2 3 0
((1 + ((x2 + 4x + 4) div (~x + 26))) mod 4)
A257398: 1 1 1 2 2 3 0 1 2 0 2 0 3 2 2 3
((((5x4 + ~2x3 + ~5x2 + 2x) div 2) div 3) div 4)
A212501: 0 0 2 13 45 115 245 462 798 1290 1980 2915 4147 5733 7735 10220
((x + 4) + (((3 * (x + (x2 div ((x + 2) + (x div 2))))) div 2) div 2))
A146968: 4 5 7
A187479: 4 5 7 10 12 14 16 19 21 23 25 27 30 32 34 37
((2x + 4) + (((1 + ((x2 + (x2 div 4)) div 2)) div 2) div 2))
A343946: 4 6 8 11 14 18 21 25 30 34 39 45 50 56 62 69
((2 - ((x * ((x2 + ~1) - (((x3 + ~x) div 2) div 3))) div 2)) div 2)
A058923: 1 1 0 ~2 ~4 ~4 1 15 43 91 166 276 430 638 911 1261
((((x + 1) + (2 * (20x div (x + 3)))) div 2) div 2)
A004219: 0 3 4 6 6 7 8 9 9 10 10 10 11 11 11 12
(((x + 2) + ((((((x + 1) * (x2 div 4)) div 2) div 2) div 2) div 3)) div 2)
A137793: 1 1 2 2 3 4 5 6 8 9 11 14 16 19 23 27
((3x + 5) - ((x2 + 2x) div (2x - ((~x + 2) div 2))))
A336008: 5 7 9 12 15 18 20 23 25 28 30 33 36 38 41 44
(2 * ((3x + 6) - ((((x + ~2) mod (1 + (x div 2))) mod 3) mod 2)))
A297925: 12 18 24 28 36 42 48 52 58 66 72 78 84 88 94 102
(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2))
A339379-A339359-A329052-A306309-A303484-A302998-A299807-A296115-A275198-A273914-A242312-A223968-A214846-A212954-A197061-A183328-A180183-A180182-A180171-A144398-A140822-A140586-A140280-A140279-A128629-A123264-A108363-A107065-A096145-A095145-A095144-A095143-A095142-A089239-A076831-A061676-A051137-A034932-A034930-A034328-A034253-A008975-A008571-A007318: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1
(4 + compr(\x.(1 - (((2x div (1 + (2 * (x mod 4)))) mod 2) + (x mod 2))),x))
A342378: 5 7 9 11 13 15 17 18 19 21 22 23 25 27 29 31
((2x + 3) - ((2 * (~x + (x2 div 3))) div (x + 6)))
A186385: 3 6 8 9 11 13 14 16 18 19 21 22 23 25 26 28
(((3x + 2) - (((x - (x div 4)) div 2) mod (~4x + 1))) div 2)
A085303: 1 2 7 10 14 17 20 23 27 30 33 37 40 43 47 50
((4x + 1) + (2 * (x + ((10x + 1) * (x div 2)))))
A014637: 1 7 55 81 189 235 403 469 697 783 1071 1177 1525 1651 2059 2205
((5x + 1) + ((x - (x div (1 + ((1 + (x div 2)) div 3)))) div 2))
A315489: 1 6 11 16 22 27 32 38 43 48 54 60 65 70 76 81
((1 + (2 * ((x + 1) - (4 * (~x + (x div 5))))) - (x div 2)) div 2)
A287577: 1 6 11 16 20 21 26 31 35 40 41 46 50 55 60 61
(2 + ((3 * (x + (3 * (1 + (2 * (x - (x div ~2))))))) + (x div 2)))
A241406: 11 50 72 111 133 172 194 233 255 294 316 355 377 416 438 477
((1 + ((2 * (x mod (2 + (x mod (2 + (x mod 2)))))) + (x div 2)) - (x div 3)) div 2)
A238950: 0 1 1 1 1 2 1 2 1 2 1 4 1 2 2 2
((x + 8) + (x div 2) - (2x div (~2 - (x div 4))))
A184116: 8 10 13 15 17 19 21 23 24 26 28 30 31 33 35 36
(1 + ((((1 + (x mod 5)) mod (1 + (x div 3))) mod 2) + ((x div 2) mod 2)))
A306227: 1 1 2 2 2 2 2 2 2 2 3 2 2 1 2 3
(2 + ((1 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4)))) * (x mod 2)))
A085058: 2 3 2 4 2 3 2 5 2 3 2 4 2 3 2 6
(((x + 1) + (x mod 2) - (3 * (2x div (8 + (x mod 2))))) div 2)
A178677: 0 1 1 2 1 2 2 3 1 2 2 3 2 4 3 4
((1 + (((((2 * (~2 + ((x div 2) mod 3))) mod (x + 1)) div 2) div 2) + (x mod 2))) div 2)
A089614: 0 1 0 1 0 1 0 1 1 2 0 1 1 2 2 2
(2 * ((2 * ((2 * (2x - (x mod 8))) - (x mod 4))) - (x mod 2)))
A062880: 0 2 8 10 32 34 40 42 128 130 136 138 160 162 168 170
((x + 2) + (x div (1 + (x mod (1 + ((4 + (x div 2)) mod (1 + (x div 3))))))))
A254732: 2 4 6 6 10 12 14 12 12 20 22 18 26 28 30 20
((x + 2) + (x div (1 + (x mod (1 + (x mod (1 + (x div (2 + (x div 5))))))))))
A248835: 2 4 6 6 10 9 14 12 12 15 22 16 26 21 20 20
(2 + compr(\x.(x mod (1 + ((x4 + 4x3) mod 9))),x))
A138671: 2 5 7 8 11 14 16 17 20 22 23 25 26 29 32 34
(((x + 2) + (x div 3) - ((x2 + 2x) mod 7)) div 2)
A243271: 1 0 1 2 2 4 2 5 4 6
(2 + compr(\x.(x mod (1 + (2 * (((x2 + ~2) mod (x + 6)) mod 3)))),x))
A028770: 2 3 5 8 10 11 12 13 14 15 17 18 20 21 22 23
((x + 2) + (((3 * ((x2 div 2) div 3)) div 2) div 7))
A225804: 2 3 4 5 6 7 9 10 12 13 15 17 19 21 22 24
((7x + 50) + (x div 7))
A282112: 50 57 64 71 78 85 92 100 107 114 121 128 135 142 150 157
(((x + 1) + ((3 * (x + ((((2 - (x div 2)) mod (x + 1)) div 2) div 2))) div 2)) div 2)
A194081: 0 1 3 4 5 6 8 10 11 13 14 15 17 18 19 20
((x + 2) + ((25x + 25) div (2x + 3)))
A188643: 10 13 14 16 17 18 19 20 21 22 23 25 26 27 28 29
(2 * ((x + 1) + (2 * ((4x3 + 7x2 + 4x + 1) div 2))))
A199944: 2 36 142 376 778 1404 2294 3504 5074 7060 9502 12456 15962 20076 24838 30304
((x + 2) + ((2x + 1) div (1 + (2 * (2 + ((((x + 1) div 2) div 3) mod 2))))))
A198045: 2 3 5 6 7 8 9 11 12 13 15 17 19 20 21 23
(~2 + compr(\x.(2 - ((x + 1) mod (1 + (4 * ((2x mod (2 + (x div 2))) mod 2))))),x))
A072836: 0 9 16 20 21 24 25 29 36 40 41 44 45 49 56 60
((x + ~2) + ((31x + 31) div (2x + 5)))
A025357-A000414: 4 7 10 12 13 15 16 18 19 20 21 22 23 25 26 27
((x + 2) + ((4 * ((2x - (x mod 4)) div 5)) div 3))
A107912: 2 3 4 5 7 8 10 11 14 15 16 17 19 21 22 23
((x + ((((x + 2) * ((4x + 9) - (x mod 2))) div 2) div 3)) div 2)
A294476: 1 3 6 9 14 18 25 30 38 44 54 61 72 81 93 103
((~x + (((10x3 + 3x2 + ~4x) div 2) div 3)) div 2)
A212692: 0 0 6 22 54 106 184 292 436 620 850 1130 1466 1862 2324 2856
((x + 2) + (x2 div (~1 + (2 * ((x + 1) + (x mod 11))))))
A177989: 2 3 4 5 6 8 9 10 11 13 14 18 19 20 21 22
((x + ~2) + ((((x + 2) * (2 + ((x2 + x) div 2))) div 2) div (3x + 1)))
A060903: 0 0 1 3 4 6 8 11 13 16 19 22 25 28 31 35
((x + ((2 * ((9x + 6) + (x div 3))) div (x + 1))) div 2)
A190572: 6 8 9 10 10 11 11 12 12 13 14 14 15 15 16 16
((33x2 + ~44x) + ((x2 + ~x) div 2))
A263227: 0 ~11 45 168 358 615 939 1330 1788 2313 2905 3564 4290 5083 5943 6870
((x + 2) + (((3 * (x - ((x2 + x + 1) div (2 + (x div 2))))) div 2) div 2))
A085883: 2 3 4 4 5 5 6 6 7 6 8 7 8 8 9 8
((x + 2) + ((2 + ((3 + ((2x + 2) div 5)) mod (x + 1))) div 2))
A159973: 3 4 5 6 7 10 11 13 14 15 16 17 19 20 21 22
((x + (2 * ((x + 2) + ((2 * (x - (((x + 1) div 2) mod 3))) div 3)))) div 2)
A283768: 2 3 5 6 9 12 15 16 18 19 22 25 28 29 31 32
((x + 2) + ((x + ((x - ((((~x + 1) * (x div 2)) div 2) div 3)) mod 3)) div 2))
A026457: 2 4 5 7 9 10 11 13 14 15 17 19 21 22 23 25
((3x + 6) + (x div 2) - (~2x div (1 + (x div 2))))
A135708: 6 11 15 19 23 27 30 34 38 41 45 48 52 55 59 62
((x + 2) + ((x + ((x + ((3 * (x + (x2 mod 3))) div 2)) div 2)) div 2))
A187688: 2 4 6 8 10 13 14 17 19 21 23 25 27 30 32 33
compr(\x.((x + 1) mod (1 + ((x div 2) mod (1 + (x mod (2 + (x div 5))))))),(x + 2))
A140297: 2 3 4 5 6 7 9 11 12 13 15 16 17 19 23 24
((~1 + (2 * (1 - ((x mod (1 + ((2 - (x mod 4)) mod (x + 1)))) div 2)))) mod (x + 2))
A083730: 1 1 1 4 1 1 1 4 9 1 1 4 1 1 1 4
(((x + 1) + (15x div (x + 5))) mod (x + 2))
A242374: 1 1 3 4 5 6 7 7 8 8 9 9 9 9 10 10
((1 + (x * ((2x + 1) + (((x + 1) + (x2 div 4)) div 2)))) div (x + 2))
A185549: 0 1 3 6 8 12 15 19 23 27 32 37 42 47 53 59
((x2 + 4x + 4) * (1 + ((x + 1) mod (1 + (x div (2 + (x mod (2 + (x mod 2)))))))))
A071378: 4 9 32 25 108 49 256 243 500 121 864 169 1372 1125 2048 289
((((x - ((x * (2 + (x div 5))) div 4)) mod 2) - (x mod 2)) mod (x + 2))
A055672: 0 0 1 4 0 6 0 8 0 0 0 12 0 14 0 0
((2x + 1) + ((x - ((0 - ((2x + 1) mod (2 + (x div 4)))) div 2)) div 2))
A231407: 1 4 6
A285976: 1 4 6 9 11 14 16 18 21 24 26 29 31 34 37 39
((2x + 2) - ((1 + ((~x + 1) mod (1 + (2x mod (1 + (x div 2)))))) mod 3))
A024806: 1 3 5 7 9 11 13 15 16 19 21 23 24 27 30 31
(2x + ((1 + ((((x + 1) div (2 + (x div 8))) div 2) + (x mod 2))) div 2))
A245239: 0 3 4 7 9 11 13 16 17 19 21 24 25 28 29 32
(1 + ((x mod ((x + 1) - (((x - (x mod (2 + (x mod 4)))) div 2) mod 2))) + (x div 2)))
A026202: 1 2 4 5 7 3 10 11 13 14 16 6 19 20 22 8
(1 + (((x + ((x3 + 2x) div 16)) div 3) + (x div 2)))
A341912: 1 1 2 3 5 7 10 13 18 23 30 37 47 57 70 83
(1 + (((x mod (1 + (11 mod (x + 1)))) div 3) + (x mod 2)))
A181801: 1 2 1 3 1 3 1 3 1 2 1 5 1 2 1 3
(1 + ((((1 + (x div 3)) mod 3) + (x div 3)) div 3) - (x mod 2))
A287729: 1 0 1 1 2 1 1 0 1 1 2 1 3 2 3 1
(1 + (((2 + ((8x + 8) mod (1 + (x div 2)))) div 3) + (x mod 2)))
A297770: 1 2 1 2 2 2 1 2 2 2 3 2 3 2 1 2
(1 + ((2 * (((x + 1) * (1 + (x mod 2))) mod (1 + (x div 5)))) + (x mod 2)))
A054716: 1 2 1 2 1 2 3 2 3 2 5 2 3 4 1 2
(1 + ((x2 mod (1 + (2 * (3x div 5)))) div 2) - (x mod 2))
A001314: 1 0 1 0 1 2 1 2 1 2 5 2 5 2 5 8
(2 div (1 + ((((x + ~1) mod (1 + (2 * (2 + (x mod 6))))) div 2) + (x mod 2))))
A108069: 0 1 2 0 1 0 2 0 0 0 0 0 2 0 0 0
(~1 + (2 * (((1 + (x div 4)) * (1 + (x mod 2))) mod 5)) - (x mod 2))
A106576: 1 2 1 2 3 6 3 6 5 0 5 0 7 4 7 4
(1 + ((((x + 1) - ((1 + (x mod 3)) * (x mod 3))) div 2) div 2) - (x mod 2))
A029254: 1 0 0 1 1 0 2 1 1 2 3 1 4 3 3 4
(~1 + ((2 * ((1 + ((x2 + 2x) div (2 - (x div ~4)))) mod 2)) + (x mod 2)))
A098381: 1 0 1 0 1 2 1 0 1 0 1 2 ~1 2 ~1 2
(1 + (((x - ((((((x + 1) div 2) div 2) div 2) * (x div 3)) div 2)) div 2) + (x mod 2)))
A140828: 1 2 2 3 3 4 4 5 4 6 5 7 6 7 7 7
(1 + ((2 * ((22 mod (2 + (x div 2))) div 2)) + (x mod 2)))
A286579: 1 2 1 2 3 4 3 4 5 6 1 2 7 8 5 6
(1 + ((2 + (((~2x + 4) mod (2 + (x div 2))) div 2) - (x mod 2)) div 2) - (x mod 2))
A143232: 2 0 2 0 2 1 2 0 2 1 3 1 3 1 2 0
(((((x + 1) div 2) div 2) + (x mod 2)) - ((x div (1 + ((x div 3) mod 3))) mod 2))
A103151: 0 0 0 1 1 2 1 3 2 2 2 3 3 4 2 4
((x * (~x + (3 * ((x * ((2x + 1) - (x mod 5))) div 2)))) div 2)
A151717: 0 1 7 22 52 190
((x2 * ((x3 + x) + (((x3 + ~x) div 2) div 3))) div 2)
A245380: 0 1 22 153 624 1875 4626 9947 19328 34749 58750 94501 145872 217503 314874 444375
compr(\x.(1 - (x mod (1 + (((x2 + 3x + 2) div 2) mod 11)))),x)
A045745: 1 2 3 4 5 6 7 11 13 14 16 17 18 19 23 24
compr(\x.(1 - ((x + 1) mod (1 + ((3x + 2) mod 11)))),x)
A138083: 0 1 2 4 5 6
A345167-A333489: 0 1 2 4 5 6 8 9 12 13 16 17 18 20 22 24
((x + 1) + (x div (1 + ((x - ((x2 + ~1) mod 16)) mod (x + 1)))))
A302175: 1 2 3 4 5 7 8 8 11 10 12 14 14 16 16 16
compr(\x.(1 - (x2 mod (1 + ((x * (x mod 4)) mod 15)))),x)
A107040: 1 2 3 5 6 9 10 11 13 17 18 19 22 23 25 26
compr(\x.(1 - (x mod (1 + ((x * (1 + (2 * (x mod 3)))) mod 9)))),x)
A160685: 1 3 5 6 7 8 10 11 13 14 15 17 19 21 22 23
((x + 1) + (x div (5 - (x mod (1 + ((x + ~1) mod (4 + (x div 2))))))))
A307750: 1 2 3 4 5 7 8 9 10 11 13 14 15 17 19 23
compr(\x.(1 - (x mod (1 + (5 * ((x * (x mod 3)) mod 5))))),x)
A236217: 1 2 4 7 8 13 14 16 17 19 23 26 28 29 31 32
compr(\x.(~1 + (((x + 1) - ((x mod (2 - ((~x + 1) div 3))) div 3)) mod 3)),x)
A153763: 0 2 3 5 6 7 9 12 14 15 17 18 19 20 21 22
compr(\x.((~x + 1) mod (1 + ((1 + (((x + ~1) * (x + (x mod 2))) div 3)) mod 3))),x)
A325462: 1 3 4 5 7 9 12 13 15 16 17 19 21 22 23 25
compr(\x.((~x + 1) mod (1 + ((1 + ((4x2 + 8x) div 3)) mod 3))),x)
A263488: 1 3 4 7 9 10 12 13 19 21 22 25 27 28 30 31
compr(\x.(~1 + (((x + 1) - ((x mod (~1 - (x div 5))) mod 2)) mod 3)),x)
A003605: 0 2 3 6 7 8 9 12 15 18 19 20 21 22 23 24
compr(\x.(~1 + ((1 + (((1 + (((x + ~1) * (x div 3)) div 2)) div 2) div 2)) mod 3)),x)
A023760: 0 1 2 3 4 5 8 9 10 12 13 14 15 16 20 21
compr(\x.(1 - (x mod (1 + ((x mod (1 + (2 * (x mod (2 + (x mod 3)))))) mod 3)))),x)
A013660: 1 2 5 7 11
A177512: 1 2 5 7 11 13 17 19 23 25 29 31 37 41 43 47
(x + (19 * (x mod (x - ((x + ~1) mod 8)))))
A103303: 0 1 2 3 4 5 6 7 8 9
A118767: 0 1 2 3 4 5 6 7 8 9 29 49 69 89
compr(\x.(~1 + ((2 + ((x + 1) div (2 + (x div (2 + (3 * (x mod 2))))))) mod 3)),x)
A026507: 1 2 3 4 5 6 7 8 10 12 14 16 18 19 20 22
((x + 1) + ((x + (2 * ((12x + 3) div (x + 2)))) div 3))
A168146: 1 5 7 9 11 13 15 16 17 19 21 22 23 25 26 27
((x + 1) + ((1 + (x div (1 + (x div (1 + (x mod 9)))))) mod (x + 1)))
A275945: 1 2 3 4 5 6 7 8 9 11 13 15 17 19 20 22
compr(\x.(3 mod (1 + ((2 - ((x + 1) mod 11)) mod (x + 1)))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A292439-A215014: 0 1 2 3 4 5 6 7 8 9 10 12 21 23 32 34
compr(\x.(1 - (x mod (1 + (2 * (1 + ((x3 mod (x + 4)) mod 3)))))),x)
A035262: 1 2 4 5 8 9 10 11 13 16 17 18 19 20 22 23
compr(\x.(2 - (((6x + 3) * (2 - (x mod 2))) mod 7)),x)
A158850: 0 1 2 4 5 7 8 11 12 13 14 15 16 18 19 21
compr(\x.(1 - (((x2 - (2x mod 5)) div 2) mod 7)),x)
A114904: 1 3 4 5 6 7 8 9 10 11 14 16 17 19 20 21
((x + 1) + ((1 + (((x - (x mod 7)) div 2) + (x div 3))) div 2))
A050942: 1 2 3 5 6 7 8 11 12 13 14 15 17 18 21 22
((x + 1) + (((x + 1) + (((((x2 + 2x) div 2) + (x mod 3)) div 2) div 2)) div 2))
A248638: 1 3 5 6 9 11 13 16 18 21 24 27 30 33 36 39
((x + 1) + (((x + 1) + ((((2x2 + 3x + 1) + (x div 2)) div 2) div 2)) div 2))
A024190: 1 3 6 9 13 17 22 27 33 39 46 53 60 69 77 86
((x + 1) + ((x - (x div (2 + (x mod ((x + ~1) - (x mod 12)))))) div 2))
A284955: 1 2 3 5 6 7 8 10 11 12 13 15 17 19 21 22
compr(\x.(2 - ((x + 1) mod (1 + (4 * (4x mod 7))))),x)
A333909: 1 2 3 4 5 6 8 10 11 12 15 16 17 19 20 22
((x + 1) + ((x - ((x mod (1 + (2 * (2 + ((x div 2) div 5))))) div 2)) div 2))
A095976: 1 2 3 5 6 8 10 11 12 13 15 16 18 19 22 23
((5x + 1) - ((2x + 2) div (4 + ((x div 2) div 3))))
A313543: 1 5 10 14 19 23 29 33 38 42 47 52 57 62 66 71
(x + (51 * (x div 13)))
A103303: 0 1 2 3 4 5 6 7 8 9
A004863: 0 1 2 3 4 5 6 7 8 9 10 11 12 64 65 66
(29x + (x div 15))
A249079-A004942: 0 29 58 87 116 145 174 203 232 261 290 319 348 377 406 436
(x + (162 * (x div 8)))
A073789: 0 1 2 3 4 5 6 7 170 171 172 173 174 175 176 177
(144x2 + 161x + 45)
A156719: 45 350 943 1824 2993 4450 6195 8228 10549 13158 16055 19240 22713 26474 30523 34860
(x + (9 * ((2 + (x mod 11)) mod (x + 1))))
A307560: 0 10 11 12 13 14 15 16 17 18 19 29 39 49 59 69
(x + (71 * (x div 9)))
A024656: 0 1 2 3 4 5 6 7 8 80 81 82 83 84 85 86
compr(\x.(1 - (x mod (~1 + (2 * (1 + ((x mod (2 + (x mod 4))) + (x mod 4))))))),x)
A326537-A302798-A294472: 1 2 3 5 6 7 10 11 13 14 15 17 19 22 23 26
compr(\x.(2 - (((2x + 2) - ((2x + 2) div 5)) mod 5)),x)
A026313: 0 1 3 4 6 7 10 13 14 16 17 19 20 22 23 25
(x + (10 * ((x + 1) - (x mod (x - ((x + ~1) mod 8))))))
A104341: 10 21 32 43 54 65 76 87 98
A095778: 10 21 32 43 54 65 76 87 98 109 110 111 112 113 114 115
(~x + ((132x + 4) div 5))
A169861: 0 26 51 77 102 127 153 178 204 229 254 280 305 331 356 381
(x + (3 * (1 + (6 * (2 - (2 div (~8 + (x div 2))))))))
A217923: 57 58 59 60 61 62 63 64 65 66 67 68 69 70 89 90
compr(\x.(((x + 1) * (1 + (x3 mod 13))) mod 3),x)
A028726: 2 5 6 7 8 11
A028791-A028752: 2 5 6 7 8 11 14 15 17 18 19 20 21 23 24 26
compr(\x.(x - (3 * (2 + (x mod (5 * (1 + (x mod (2 + (x mod 2))))))))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A305933-A030700: 0 1 2 3 4 5 6 7 8 9 11 12 13 14 19 23
(x * (((x3 + 15x2 + 68x + 96) div 2) div 3))
A130863: 0 30 100 231 448 780 1260 1925 2816 3978 5460 7315 9600 12376 15708 19665
(24x4 + ~60x3 + 54x2 + ~17x)
A272379: 0 1 86 759 3100 8765 19986 39571 70904 117945 185230 277871 401556 562549 767690 1024395
(x + ((4 * (1 + ((2 * ((x + ((x div 2) mod 2)) div 2)) div 3))) div 3))
A110086: 1 2 3 5 6 7 10 11 12 13 15 17 18 19 20 23
(~x + ((2 * ((x + 2) + ((x + ((x * (x div 2)) div 4)) div 3))) div 3))
A112213: 1 1 0 1 1 1 1 1 2 2 2 3 4 3 4 5
((5x + 4) - ((2 * (~x + (x div 9))) div 3))
A190060: 4 10 16 21 27 33 38 44 50 55 60 66 72 77 83 89
((~x + 1) + compr(\x.(~1 + ((x - (((x mod 4) - (x div 2)) div 3)) mod 3)),x))
A104406: 1 1 2 3 3 3 3 3 4 5 5 6 7 7 7 7
((~x + 1) + compr(\x.(~1 + ((1 - (x div (2 + (x div (2 * (2 - (x mod 2))))))) mod 3)),x))
A287643: 1 1 1 1 1 1 2 3 4 5 6 7 7 7 8 8
((x2 + x + 1) + (((2x + 2) * (2 + ((~x + 1) mod 3))) div 3))
A201874: 3 5 15 21 27 47 57 67 97 111 125 165 183 201 251 273
compr(\x.((1 + (x5 mod 31)) mod 2),x)
A095042: 1 2 4 5 7 8 9 10 14 16 18 19 20 25 28
compr(\x.(1 - ((x + 1) mod (2 + ((x + (x div 8)) mod (1 + (x div 3)))))),x)
A029596: 0 2 3 4 6 7 8 9 10 12 13 14 15 16 18 21
compr(\x.(x - (2 * (1 + ((1 - ((x + 1) mod 11)) mod (x + 1))))),x)
A119799: 0 1 2 3 4 12 13 14 15 16 17 18 19 20 23 24
compr(\x.(((x + 1) div (1 + (2 * (((~x + 2) mod (3 + (x div 3))) mod 2)))) mod 2),x)
A064615: 1 5 6 7 11 13 17 19 23 25 29 30 31 35 36 37
(x * ((1 + (((((x + 1) * (1 + ((x * (x div 2)) div 4))) div 2) div 2) div 2)) div 2))
A308775: 0 0 0 0 4 5 12 21 40 54 90 121 180 234 322 405
(x + ((17 * (2x div 15)) div 2))
A004836: 0 1 2 3 4 5 6 7 16 17 18 19 20 21 22 32
((x + 1) - ((x - (((x3 div (2 - ((x div 2) mod 2))) div 2) div 3)) div 2))
A272776: 1 2 3 5 6 9 22 33
(x + (((2 * (2 - ((~x + (2 div (x + 1))) div 5))) + (x div 3)) div 2))
A096600: 2 3 5 6 7 8 11 12 13 14 15 17 19 20 21 22
compr(\x.(~2 + ((1 + (x mod (1 + (2 * (2 + ((x div 2) mod 5)))))) mod (x + 1))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A334145-A130576-A084383-A072543-A009996: 0 1 2 3 4 5 6 7 8 9 10 11 20 21 22 30
(x + (((1 + (((x + 1) * (((x + ~1) + (x mod 2)) div 5)) div 2)) div 2) div 2))
A014155: 0 1 2 3 4 6 7 8 9 10 11 14 15 16 18 21
((5 * ((x2 + 3x) div 2)) div (x + 20))
A127032: 0 0 1 1 2 4 5 6 7 9 10 12 14 15 17 19
(x + (((3 * (2 - ((x div 2) div (1 + (x mod 10))))) div 2) div 2))
A319345: 1 2 3 4 5 6 7 8 9 10 7 11 12 13 14 15
(x + ((2 + ((2 + ((x + 1) * ((2 * (x div 2)) div 5))) div 3)) div 2))
A243355: 1 2 3 4 5 6 8 9 10 12 15 16 17 19 20 21
(x + (4 * ((2x + 2) - (2 * (1 + (x mod (1 + (x div 8))))))))
A178895-A114386: 0 9 18 27 36 45 54 63 72 73 90 91 108 109 126 127
(x + (((((x + 1) * ((1 + ((x - ((x div 3) mod 2)) div 2)) div 2)) div 2) div 2) div 2))
A067570: 0 1 2 3 4 5 7
A191917: 0 1 2 3 4 5 7 9 10 11 12 15 16 18 21 23
(x + (((((x + 1) * (x + ((1 + (x mod 8)) mod (x + 1)))) div 2) div 2) div 2))
A194162: 0 1 2 4 6 8 11 14 18 22 27 33 39 46 53 61
compr(\x.(2 - (x mod (4 + ((2x + 1) mod (4 + ((x div 2) div 3)))))),x)
A053577: 2 3 4 5 6 7 8 11 12 13 14 16 17 19 23 24
(~x + (4 * (4x - (((x - ((2 - (x div 4)) div 2)) div 2) div 2))))
A188075: 4 15 30 45 56 71 86 101 112 127 142 157 168 183 198 209
((~1 + ((8x2 + 15x + 7) div 2)) div (x + 8))
A050504: 0 1 3 5 8 10 13 16 19 23 26 29 33 36 40 44
(x + ((x + ((((x + 1) * ((x + 2) + (x div 4))) div 2) div 5)) div 2))
A219087: 0 1 3 5 7 9 12 14 17 20 22 25 29 32 35 38
((2x + 2) + ((x + (((x2 + 4x + 4) div 5) mod 3)) div 2))
A187475: 2 5 7 10 12 14 17 20 23 24 27 29 32 34 37 39
(3x + (((x + 1) - ((2 - (x div 3)) mod 5)) mod 3))
A201363: 2 3 7
A092293: 2 3 7 9 13 17 19 23 24 27 31 35 37 41 42 47
(2x + ((x - ((((~x2 + x) div 2) - (x mod 3)) div 3)) div 3))
A211273: 0 2 5 7 10 13 15 19 22 25 28 32 35 39 43 46
(x2 - (3 * ((1 + (((x + 1) div 2) * (1 + (x div 2)))) div 3)))
A230276: 0 1 1 6 10 16 24 34 43 57 70 85 102 121 139 162
(x4 + 10x3 + 20x2 + 10x + 1)
A090198: 1 42 197 562 1257 2426 4237 6882 10577 15562 22101 30482 41017 54042 69917 89026
(2 - loop(\(x,i).loop(\(x,i).(2 + (if x <= 0 then 2 else loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x))),2,x),1,(x + 1)))
A113680: 1 0 1 ~2 0 1 ~2 ~2 0 1 ~2 ~2 ~2 0 1 ~2
((if x <= 0 then 2 else loop(\(x,i).((x + 1) + loop(\(x,i).loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0),2,x)),x,1)) div 2)
A134310: 1 1 1 2 2 3 4 4 5 7 8 8 9 11 15 16
(if (x + ~1) <= 0 then 1 else loop(\(x,i).(if x <= 0 then 1 else (loop(\(x,i).(x * i),i,(1 + i)) + (x * i))),(x + ~1),0))
A203799: 1 1 1 8 48 312 2280 18720 171360 1733760 19232640 232243200 3033676800 42631142400 641383142400 10287038361600
loop(\(x,i).x2,1,loop(\(x,i).(4 * ((if x <= 0 then 1 else 2x) - (x div (if i <= 0 then 1 else i)))),x,0))
A089156: 0 16 576 25600 1254400 65028096 3497066496 192980975616 10855179878400 619683355033600 35792910586740736 2087229562810269696 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(loop(\(x,i).(if x <= 0 then (loop(\(x,i).(x * i),(~1 + i),1) + (x * i)) else 0),i,1) + (x * i)),x,0)
A208493: 0 0 1 3 18
A092691: 0 0 1 3 18 90 660 4620 42000 378000 4142880 45571680 586776960 7628100480 113020427520 1695306412800
((if (x mod 8) <= 0 then 1 else loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)) + (if x <= 0 then 0 else 1))
A275723: 1 1 2 1 2 3 1 2 2 4 1 2 3 4 5 1
loop(\(x,i).2x,x,loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,i,1))),(x + ~1),1))
A028368: 1 2 8 192 21504 10321920 20478689280 165140150353920 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 0 else (1 + (if (x mod 2) <= 0 then 1 else (if (x div 2) <= 0 then x else (2 + (if (x mod 3) <= 0 then 2 else 0))))))
A108053: 0 2 2 5 2 3 2 3 2 5 2 3 2 3 2 5
(if x <= 0 then 1 else loop(\(x,i).loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 2 else 0)),x,(x + 2)),(x + 4),1))
A334391-A322274-A132077-A008365: 1 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71
(loop(\(x,i).x2,1,loop(\(x,i).(x * (1 + (if (i mod 2) <= 0 then i else 1))),x,1)) div loop(\(x,i).2x,x,1))
A297470: 1 2 9 18 225 450 11025 22050 893025 1786050 108056025 216112050 18261468225 36522936450 4108830350625 8217660701250
loop(\(x,i).x2,1,(if x <= 0 then 2 else loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then i else 0)),(x div 2),(x + 1))))
A069549: 4 4 9 25 25 49 49 121 121 121 121 169 169 289 289 289
(if x <= 0 then 1 else loop(\(x,i).(loop(\(x,i).2x,x,(if (x mod 4) <= 0 then x else (x div 2))) div 2),1,(x + ~1)))
A299783: 1 0 0 2 4 32 32 96
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).(x + loop(\(x,i).3x,i,(1 + i))),i,(x + 1)),i,1)),x,1)
A213164: 1 9 51 235 966 3702 13546 47994 166095 564679 1893285 6277677 20626588 67260540 217924068 702199684
loop(\(x,i).(~x + loop(\(x,i).x2,1,loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),i,1))),x,1)
A228002: 1 3 33 367 4533 58971 794805 10983819 154653081 2209251319 31925528217 465708778407 6846750893929 101325729466071 1508015866093929 22553429144856471
loop(\(x,i).(~x + loop(\(x,i).(x + loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),i,1)),i,1)),x,1)
A106188: 1 2 7 22 77 274 1001 3706 13871 52326 198627 757758 2902783 11158358 43019383 166275878
loop(\(x,i).(x div (2 - (x mod 2))),x,(1 + compr(\x.loop(\(x,i).loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0),2,x),x)))
A188509: 1 1 3 1 5 7 1 9 13 15 1 17 25 29 31 1
loop(\(x,i).x2,2,(if x <= 0 then 1 else (3 + loop(\(x,i).(x2 + x),1,loop(\(x,i).(x * i),x,1)))))
A143026: 1 625 6561 4100625
((loop(\(x,i).2x,x,1) - loop(\(x,i).(x - loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0)),3,x)) div 2)
A120739: 0 0 1 2 7 14 30 60 127 254 510 1020 2046 4092 8188 16376
compr(\x.(if x <= 0 then 1 else loop(\(x,i).((if x <= 0 then 2 else loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 2),x,x)),2x)
A328012: 1 3 7 9 15 19 21 25 31 33 39 43 45 51 53 57
loop(\(x,i).(if x <= 0 then 2 else loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then i else 0)),(x div 2),(x + 1))),1,(x div 2))
A308052: 2 2 2 2 3 3 5 5 5 5 7 7 7 7 11 11
(x + loop(\(x,i).(x - (if x <= 0 then 1 else loop(\(x,i).(~1 + (if x <= 0 then 2 else 0)),(x mod 2),(x div 2)))),x,(x + 1)))
A119477: 1 2 4 3 6 5 5 4 8 7 7 6 7 6 6 5
(if x <= 0 then 0 else loop(\(x,i).(loop(\(x,i).(2 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),2,x) div (1 + i)),2,x))
A277700: 0 1 1 2 1 1 2 3 1 2 1 3 2 1 3 4
(~x + loop(\(x,i).(if x <= 0 then 2 else loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then i else 0)),(x div 2),(x + 1))),2,x))
A105161: 3 2 3 4 3 6 5 6 5 4 3 6 5 6 5 4
compr(\x.loop(\(x,i).(if x <= 0 then 2 else (2 + loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),2,x))),2,x),x)
A043687: 2 4 5 6 8 9 11 12 13 14 16 17 19 23 24 25
(x + loop(\(x,i).(x - (if x <= 0 then 1 else (if (x mod 2) <= 0 then (if x <= 0 then 2 else ~1) else (1 + (x div 2))))),x,x))
A061313: 0 1 3 2 5 4 4 3 7 6 6 5 6 5 5 4
(x + loop(\(x,i).(x - (if x <= 0 then 1 else (if (x mod 2) <= 0 then (x div 2) else (2 + (if (~x + 2) <= 0 then x else 0))))),x,x))
A089263: 0 0 1 ~1 2 ~1 0 ~1 3 ~1 0 ~1 1 ~1 0 ~1
loop(\(x,i).(x - i),x,loop(\(x,i).(x + i),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),0))
A161624: 3 5 12 22 56 76 132 162 240 390 441 637 783 855 1023 1311
(loop(\(x,i).5x,x,1) - loop(\(x,i).(x * (x div 2)),1,loop(\(x,i).(2x + ~1),x,0)))
A083315: 1 4 19 97 505 2629 13609 69997 357985 1822309 9241849 46731997 235754065 1187152789 5969306089 29980723597
(loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).2x,x,1)) - loop(\(x,i).(3x + 1),x,0))
A134064: 1 2 6 23 96 407 1716 7163 29616 121487 495276 2009603 8124936 32761367 131834436 529712843
(if x <= 0 then 1 else loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),x,0))
A229127: 1 9 171 2439 30951 368559 4217031 46953279 512579511 5513215599 58618940391 617570463519 6458134171671 67123207545039 694108867905351 7146979811148159
(loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1) + loop(\(x,i).(3x + 2),x,0))
A081670: 1 4 14 46 150 494 1652 5618 19430 68302 243804 882578 3235596 11994922 44899568 169466426
(if x <= 0 then 2x else (loop(\(x,i).(4x + ~4),x,2) - loop(\(x,i).(3x + 2),x,0)))
A120664: 0 2 4 18 92 442 2004 8738 37132 155082 640004 2619058 10653372 43144922 174174004 701478978
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) + loop(\(x,i).(2 * (if x <= 0 then 1 else x)),x,0))
A141353: 1 3 6 13 30 74 196 557 1686 5374 17820 60834 212108 751092 2690824 9727613
(3 - loop(\(x,i).(x + loop(\(x,i).(x * loop(\(x,i).(x * (x - i)),2,(x + ~2))),1,(x + ~1))),x,0))
A219010: 3 123 28143753123 4611686018427387903
loop(\(x,i).(x + (loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i),1) div 2)),x,0)
A135482: 0 1 3 11 43 555 2603 35371 166443 2263595 136481323 673352235 35033090603 584788904491 2783812160043 37968184248875
loop(\(x,i).2x,x,(1 + (loop(\(x,i).(3x + ~1),x,2) * loop(\(x,i).(2x + 2),x,0))))
A019490: 1 22 340 4600 58576 724192 8822080 106672000 1284971776 15449370112 185571742720 2227940915200 26741787774976 320940501164032 3851520569589760 46219655242547200
loop(\(x,i).2x,(loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (1 + (((x + 1) div 2) div 2))),1)
A344110: 1 1 2 1 4 16 1 8 64 512 1 16 256 4096 65536 1
(if (x mod 2) <= 0 then (5 * (if (x mod 4) <= 0 then (2 * (2 + (if x <= 0 then 0 else 2))) else 1)) else 1)
A040414: 20 1 5 1 40 1 5 1 40 1 5 1 40 1 5 1
(if (x mod 2) <= 0 then (3 * (if (x mod 4) <= 0 then (8 * (if x <= 0 then 1 else 2)) else 1)) else 1)
A040590: 24 1 3 1 48 1 3 1 48 1 3 1 48 1 3 1
(if (x mod 5) <= 0 then (3 * (if (x mod 2) <= 0 then (2 * (2 + (if x <= 0 then 0 else 2))) else 1)) else 1)
A010208: 12 1 1 1 1 3 1 1 1 1 24 1 1 1 1 3
(if (x mod 3) <= 0 then (6 * (if (x mod 2) <= 0 then (2 * (2 + (if x <= 0 then 0 else 2))) else 1)) else 1)
A040577: 24 1 1 6 1 1 48 1 1 6 1 1 48 1 1 6
(~1 + ((2 + loop(\(x,i).(2 + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)),2,(x + 1))) mod 3))
A110247: 1 0 1 0 1 1 0 1 ~1 1 0 1 ~1 0 1 0
(1 + ((loop(\(x,i).3x,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1) div 2) div 3))
A341359-A125311: 1 1 1 1 1 2 1 1 2 5 1 1 2 5 14 1
(~1 + loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x)),2,6x))
A141427: 1 4 10 16 22 28 30 40 46 52 58 60 70 72 82 88
loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x)),1,(6x + 1))
A067774: 2 7 13 19 23 31 37 43 47 53 61 67 73 79 83 89
(loop(\(x,i).(2x + 2),x,0) div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))
A225101: 0 1 2 7 6 31 18 127 170 511 186 2047 630 8191 10922 32767
(loop(\(x,i).x2,3,(2x + 1)) div loop(\(x,i).x2,3,(1 + (if x <= 0 then 2 else 1))))
A219091: 0 25 1525 22518 168151 837339 3186448 10011291 27249052 66342043 147745544 305902286 596046447 1103240376 1954087550 3331605615
loop(\(x,i).(x + loop(\(x,i).(x * i),i,1)),(1 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x)),1)
A236399: 2 4 34 874 4037914 522956314 22324392524314 6780385526348314 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).3x,x,1))) * (1 + loop(\(x,i).2x,x,1)))
A034661: 6 39 455 6813 112931 1956669 34591115 617285253 11064693731 198756808749 3574014537275 64300154115093 1157115988280531 20825519793796029 374836322743499435 4611686018427387903
loop(\(x,i).x2,1,(loop(\(x,i).(3x + ~1),(x + ~1),1) - loop(\(x,i).2x,(x + ~1),1)))
A129839: 0 0 0 1 36 625 8100 90601 933156 9150625 87048900 812307001 7486748676 68447640625 622473660900 5641104760201
(1 + (if x <= 0 then 0 else (loop(\(x,i).6x,(x + ~1),1) + loop(\(x,i).3x,x,1))))
A275100: 1 5 16 64 298 1540 8506 48844 286498 1699300 10136746 60643324 363328498 2178376660 13065476986 78378513004
((1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1))) * (1 + loop(\(x,i).3x,x,1)))
A034660: 6 28 210 2044 22386 257908 3037530 36130444 431733666 5170140388 61978939050 743375541244 8918294543346 107006334784468 1283997101947770 15407492847694444
((x + 1) - loop(\(x,i).2x,x,(loop(\(x,i).(x * i),x,1) - loop(\(x,i).(x * (~1 + (2 * i))),x,1))))
A320329: 1 2 7 76 1301 26406 619207 16652168 508596489 17457431050 666726681611 28076838451212 1293333060096013 64713740778086414 3495868307630899215 4611686018427387903
((x + 1) - loop(\(x,i).(x + loop(\(x,i).((2x + 1) - loop(\(x,i).3x,i,1)),i,1)),x,1))
A298564: 0 1 10 53 218 789 2658 8581 26986 83477 255506 776709 2350554 7092565 21359554 64242437
(1 + ((1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (if (~2 + (x div 2)) <= 0 then 1 else 2))) div 2))
A273673: 1 1 2 1 2 2 1 2 3 4 1 2 3 4 5 1
(1 + (2 * (loop(\(x,i).loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 2 else 0)),i,(x + 2)),x,1) div 3)))
A323703: 1 3 3 5 7 9 11 13 15 19 21 25 27 29 31 35
(1 + (2 * (1 + loop(\(x,i).compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x),2,x))))
A104294: 3 5 7 13 17 23 29 37 47 53 67 73 79 89 103 113
(if (x mod 3) <= 0 then 1 else (1 + ((loop(\(x,i).2x,(if (x mod 2) <= 0 then x else 1),2) mod (x + 1)) div 2)))
A073300: 1 1 2 1 2 3 1 3 5 1 2 3 1 3 5 1
(1 + (2 * compr(\x.loop(\(x,i).((if x <= 0 then 2 else loop(\(x,i).(x div (2 - (x mod 2))),x,x)) div 2),2,x),(x + 1))))
A084468: 7 11 13 19 21 25 35 37 41 49 67 69 73 81 97 131
(if (x mod 2) <= 0 then ((1 + (if ((x div 2) mod 2) <= 0 then 10 else 1)) * (if x <= 0 then 1 else 2)) else 1)
A010199: 11 1 4 1 22 1 4 1 22 1 4 1 22 1 4 1
(if (x mod 3) <= 0 then ((1 + (if (x mod 2) <= 0 then 16 else 1)) * (if x <= 0 then 1 else 2)) else 1)
A040290: 17 1 1 4 1 1 34 1 1 4 1 1 34 1 1 4
(if (x mod 3) <= 0 then ((1 + (3 * (if (x mod 2) <= 0 then 4 else 1))) * (if x <= 0 then 1 else 2)) else 1)
A010225: 13 1 1 8 1 1 26 1 1 8 1 1 26 1 1 8
(if (x mod 2) <= 0 then ((1 + (4 * (if (x mod 4) <= 0 then 4 else 1))) * (if x <= 0 then 1 else 2)) else 1)
A040303: 17 1 10 1 34 1 10 1 34 1 10 1 34 1 10 1
(if (x mod 2) <= 0 then ((if (x mod 4) <= 0 then 17 else 2) * (if x <= 0 then 1 else 2)) else 1)
A040300: 17 1 4 1 34 1 4 1 34 1 4 1 34 1 4 1
(1 + ((loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).3x,x,1)) div 2))
A196836: 2 5 15 50 177 650 2445 9350 36177 141170 554325 2186750 8656377 34355690 136617405 544061750
(~1 + (4 * (1 + (2 * compr(\x.loop(\(x,i).loop(\(x,i).(~1 + (if x <= 0 then i else x)),x,0),2,x),(x + 1))))))
A224380: 11 19 27 35 51 59 67 99 115 123 131 195 227 243 251 259
(if (x mod 2) <= 0 then (4 * (if (x mod 4) <= 0 then (5 * (if x <= 0 then 1 else 2)) else 1)) else 1)
A040413: 20 1 4 1 40 1 4 1 40 1 4 1 40 1 4 1
(1 + ((loop(\(x,i).(2x2 + ~x),1,(1 + loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x))) div 2) div 2))
A096744: 1 1 1 1 1 1 1 3 1 1 1 6 3 1 1 1
(if (x mod 2) <= 0 then (8 * (if (x mod 4) <= 0 then (3 * (if x <= 0 then 1 else 2)) else 1)) else 1)
A040595: 24 1 8 1 48 1 8 1 48 1 8 1 48 1 8 1
(if x <= 0 then 1 else (1 + (2 * (loop(\(x,i).(1 + loop(\(x,i).(x2 + ~2),(x mod 3),x)),x,2) div 2))))
A016043: 1 3 5 15 17 255 257 65535 65537 4294967295 4294967297 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,(1 + (2 * loop(\(x,i).(2 + (if x <= 0 then 1 else 4x)),(x div 2),(x mod 2)))))
A266976: 1 6 28 104 464 1696 7488 27264 120064 436736 1922048 6989824 30756864 111845376 492126208 1789558784
(x - (if x <= 0 then 0 else (~1 + (x mod (2 + loop(\(x,i).2x,loop(\(x,i).(x div (1 + (x mod 2))),x,x),2))))))
A206773: 0 1 1 1 1 1 1 5 1 1 1 11 1 1 1 13
(3 + (if x <= 0 then 1 else (loop(\(x,i).(x + (x div (2 + (i mod 2)))),x,2) + loop(\(x,i).2x,x,1))))
A342761: 4 7 10 15 25 43 79 147 283 547 1075 2115 4195 8323 16579 33027
loop(\(x,i).x2,1,((loop(\(x,i).x2,2,loop(\(x,i).(x * (x + i)),2x,2)) div 2) div 3))
A066545: 4 782757789696 4611686018427387903 4611686018427387903
((loop(\(x,i).x2,1,compr(\x.loop(\(x,i).(x - (if (x mod (2 + i)) <= 0 then 0 else 1)),x,x),x)) div 2) div 3)
A242089: 0 0 0 2 10 16 32 42 66 112 130 192 240 266 322 416
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (1 + (x * (1 + loop(\(x,i).(x2 + x),2,2))))),x,3)
A037119: 3 130 65 2796 1398 699 30058 15029 646248 323124 161562 80781 3473584 1736792 868396 434198
(~1 + loop(\(x,i).loop(\(x,i).2x,loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),i,1),1),x,2))
A144964: 1 3 31 16383 4398046511103 4611686018427387903
(1 + loop(\(x,i).loop(\(x,i).2x,x,x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A098773: 9 25 161 897 22529 106497 2228225 9961473 192937985 15569256449 66571993089 5085241278465 90159953477633 378231999954945 6614661952700417 477381560501272577
(~1 + loop(\(x,i).loop(\(x,i).2x,x,x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A099051: 7 23 159 895 22527 106495 2228223 9961471 192937983 15569256447 66571993087 5085241278463 90159953477631 378231999954943 6614661952700415 477381560501272575
loop(\(x,i).3x,x,(1 + loop(\(x,i).(4x + 2),x,2) - loop(\(x,i).2x,x,2)))
A017954: 1 21 315 4185 52731 648081 7869555 94992345 1143260811 13739265441 164992058595 1980630120105 23771914474491 285289093487601 3423625845396435 41084450500377465
loop(\(x,i).x2,1,(1 + (2 * compr(\x.loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,2x),x))))
A062532: 1 81 225 441 625 729 1089 1225 1521 2025 2401 2601 3025 3249 3969 4225
(1 + (2 * loop(\(x,i).(if (loop(\(x,i).x2,4,2) mod (x + 1)) <= 0 then x else (x + 1)),(x div 2),x)))
A290649: 1 3 7 7 13 15 15 15 25 27 31 31 31 31 31 31
loop(\(x,i).loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)),1,((~x + ~3) + loop(\(x,i).2x,x,2)))
A036295: 0 1 1 11 13 57 15 247 251 1013 509 4083 4089 16369 2047 65519
loop(\(x,i).(x div (2 - (x mod 2))),x,loop(\(x,i).(2 * (~2x + (x div (if i <= 0 then 1 else i)))),2x,1))
A061548: 1 3 35 231 6435 46189 676039 5014575 300540195 2268783825 34461632205 263012370465 8061900920775 61989816618513 956086325095055 7391536347803839
(loop(\(x,i).2x,x,(1 + loop(\(x,i).3x,x,1))) + loop(\(x,i).3x,2x,1))
A074543: 3 17 121 953 7873 66857 578161 5063033 44726593 397498697 3547251601 31743858713 284606322913 2554926530537 22955156635441 206361317111993
(loop(\(x,i).(x3 + x2),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).3x,2x,1))
A074570: 3 21 161 1305 10913 92841 797681 6896505 59889473 521900361 4561574801 39975188505 351165790433 3091688751081 27275107401521 241076577925305
(loop(\(x,i).(x3 + x),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).3x,2x,1))
A074546: 3 19 149 1249 10673 91849 793649 6880249 59824193 521638729 4560527249 39970996249 351149017313 3091621650409 27274838982449 241075504216249
(loop(\(x,i).x2,1,loop(\(x,i).(x * (1 + (if (i mod 2) <= 0 then 4 else 1))),x,1)) * (1 + (x mod 2)))
A083227: 1 8 100 800 10000 80000 1000000 8000000 100000000 800000000 10000000000 80000000000 1000000000000 8000000000000 100000000000000 800000000000000
loop(\(x,i).x2,1,loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x div 2),(1 + (x mod 2))))
A092266: 1 4 4 16 36 144 400 1600 4900 19600 63504 254016 853776 3415104 11778624 47114496
loop(\(x,i).2x,x,loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x div 2),(1 + (x mod 2))))
A304940: 1 4 8 32 96 384 1280 5120 17920 71680 258048 1032192 3784704 15138816 56229888 224919552
(1 + (2 * (if x <= 0 then 2 else compr(\x.(1 - loop(\(x,i).(0 - (if (x mod (1 + i)) <= 0 then 0 else x)),(x div 2),x)),x))))
A294091: 5 11 27 35 59 75 83 107 123 147 179 195 203 219 227 275
(1 + loop(\(x,i).loop(\(x,i).(x + i),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)),x),x,2))
A085739: 3 9 24 52 118 209 362 552 828 1263 1759 2462 3323 4269 5397 6828
(loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1) * loop(\(x,i).(4x + ~1),x,1))
A124862: 1 6 66 860 11970 172116 2523444 37487736 562303170 8496977060 129153866556 1972531074696 30245473774516 465314970745800 7179145222818600 111037445957810160
loop(\(x,i).2x,x,loop(\(x,i).(6x + loop(\(x,i).(4x + 1),i,1)),x,1))
A016320: 1 22 348 4856 63728 808416 10050496 123402112 1503194880 18217295360 220039199744 2651923642368 31914709676032 383709523861504 4610378348347392 55371452676276224
(loop(\(x,i).(x3 + x2),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).6x,x,1))
A074566: 3 18 116 792 5648 41568 312896 2393472 18522368 144557568 1135256576 8956925952 70913036288 562883616768 4476679110656 35655630815232
(~1 + loop(\(x,i).(x + i),x,(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1)))))
A326714: 0 2 3 8 10 16 21 31 36 46 55 68 78 92 105 124
loop(\(x,i).(1 + loop(\(x,i).(x + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),i,1)),i,x)),x,1)
A119683: 1 4 12 34
A014143: 1 4 12 34 98 294 919 2974 9891 33604 116103 406614 1440025 5147876 18550572 67310938
((x + 1) + ((1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x)) * (if x <= 0 then 1 else 2)))
A087711: 2 4 5 8 7 8 11 10 11 14 13 18 17 16 17 22
loop(\(x,i).(8x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A016277: 1 13 123 1049 8603 69489 557971 4470073 35779755 286296065 2290543619 18324876297 146600596507 1172809538641 9382490625267 75059967983321
(loop(\(x,i).3x,x,(1 + loop(\(x,i).2x,x,1))) + loop(\(x,i).8x,x,1))
A074556: 3 17 109 755 5473 40787 309529 2379275 18463393 144315107 1134267049 8952908795 70896790513 562818102227 4476415458169 35654571422315
(loop(\(x,i).(x2 + x),1,loop(\(x,i).3x,x,1)) + loop(\(x,i).8x,x,1))
A074560: 3 20 154 1268 10738 92060 794314 6882308 59830498 521657900 4560585274 39971171348 351149544658 3091623236540 27274843749034 241075518532388
loop(\(x,i).2x,x,loop(\(x,i).(4 * (x + (6x div (if i <= 0 then 1 else i)))),x,1))
A140406: 1 56 1792 43008 860160 15138816 242221056 3598712832 50381979648 671759728640 8598524526592 106309030510592 1275708366127104 14915974742409216 170468282770391040 1909244767028379648
loop(\(x,i).2x,x,loop(\(x,i).(4 * (x + (5x div (if i <= 0 then 1 else i)))),x,1))
A173155: 1 48 1344 28672 516096 8257536 121110528 1660944384 21592276992 268703891456 3224446697472 37520834297856 425236122042368 4710307813392384 51140484831117312 545498504865251328
loop(\(x,i).2x,x,loop(\(x,i).(4x + loop(\(x,i).(5x + 1),i,1)),x,1))
A016317: 1 20 284 3520 40656 450240 4851904 51315200 535521536 5534172160 56773377024 579187015680 5883496124416 59567968993280 601543751942144 6062350015528960
loop(\(x,i).3x,x,loop(\(x,i).(4x + loop(\(x,i).(3x + 1),i,1)),x,1))
A018092: 1 24 405 5940 81081 1061424 13533885 169579980 2099526561 25775439624 314535422565 3821496571620 46281602898441 559192032726624 6744619579010445 81244271639092860
loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).2x,i,1)),i,1)),x,1)
A016282: 1 11 83 535 3171 17871 97483 520055 2731091 14179231 72992283 373347975 1900290211 9635660591 48715157483 245723238295
loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A016291: 1 15 163 1587 14779 135027 1223371 11042979 99517627 896182419 8067737899 72618027651 653595799195 5882496402291 52943004475147 476489187727203
loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).~3x,i,1)),i,1)),x,1)
A249994: 1 3 19 63 307 1095 4843 18111 76483 294327 1213147 4747119 19308979 76282599 308006731 1223430687
loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A000453: 1 10 65 350 1701 7770 34105 145750 611501 2532530 10391745 42355950 171798901 694337290 2798806985 11259666950
((x * loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,2)) - loop(\(x,i).4x,x,1))
A068552: ~1 0 8 56 304 1496 6992 31664 140384 613016 2646544 11325200 48122528 203306736 854829344 3579783776
loop(\(x,i).2x,x,loop(\(x,i).(5x + loop(\(x,i).(3x + 1),i,1)),x,1))
A016307: 1 18 232 2640 28336 295008 3020032 30620160 308720896 3102325248 31113951232 311683706880 3120102240256 31220613439488 312323680632832 3123942083788800
loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).(~2x + 1),i,1)),i,1)),x,1)
A002041: 1 6 35 180 921 4626 23215 116160 581141 2906046 14531595 72659340 363302161 1816516266 9082603175 45413037720
loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A016273: 1 10 69 410 2261 11970 61909 315850 1598421 8050130 40425749 202656090 1014866581 5079099490 25409813589 127092049130
loop(\(x,i).x2,1,loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).10x,x,1)))
A038544: 1 3025 25502500 250500250000 2500500025000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(if (x mod 4) <= 0 then 1 else x),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A177863: 1 2 1 6 10 1 1 18 22 1 30 1 1 42 46 1
loop(\(x,i).3x,2x,loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),x,1))
A076009: 1 54 2025 65610 1974861 57041334 1607609025 44625100770 1226874595221 33521945231214 912229968911625 24758714599712730 670798674525559581 4611686018427387903 4611686018427387903
loop(\(x,i).6x,x,loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),x,1))
A075916: 1 36 900 19440 390096 7511616 141134400 2611802880 47870735616 871982724096 15819463296000 286235993272320 5170077903015936 93275375604350976 1681524519443251200 4611686018427387903
loop(\(x,i).8x,x,loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),x,1))
A076003: 1 48 1600 46080 1232896 31653888 792985600 19566428160 478167433216 11613323132928 280917704704000 6777200695050240 163215697915150336 3926183399462535168 4611686018427387903
loop(\(x,i).5x,x,loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),x,1))
A075911: 1 30 625 11250 188125 3018750 47265625 728906250 11133203125 168996093750 2554931640625 38523925781250 579858642578125 8717878417968750 130968170166015625 1966522521972656250
loop(\(x,i).(2x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A016278: 1 14 145 1370 12541 113534 1023865 9221090 83008981 747138854 6724424785 60520350410 544684739821 4902167424974 44119521140905 397075733249330
(loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1) + loop(\(x,i).2x,x,1))
A074527: 3 10 38 160 722 3400 16418 80440 397442 1973320 9825698 49007320 244676162 1222305640 6108314978 30531959800
((loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1)) - loop(\(x,i).2x,x,1))
A135160: 1 6 30 144 690 3336 16290 80184 396930 1972296 9823650 49003224 244667970 1222289256 6108282210 30531894264
((loop(\(x,i).5x,x,1) + loop(\(x,i).2x,x,1)) - loop(\(x,i).3x,x,1))
A135159: 1 4 20 106 560 2914 14960 76066 384320 1933954 9707600 48653026 243613280 1219116994 6098749040 30503261986
(loop(\(x,i).5x,x,1) - (loop(\(x,i).2x,x,1) + loop(\(x,i).3x,x,1)))
A135158: ~1 0 12 90 528 2850 14832 75810 383808 1932930 9705552 48648930 243605088 1219100610 6098716272 30503196450
loop(\(x,i).4x,(x + 1),(loop(\(x,i).5x,x,2) + loop(\(x,i).2x,x,1)))
A212596: 12 192 3456 66048 1296384 25731072 513048576 10248388608 204867108864 4096536870912 81924294967296 1638434359738368 32768274877906944 655362199023255552 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),i,2x),x,1)
A051357: 1 6 180 37800 87318000 2622159540000 1338638666765400000 4611686018427387903 4611686018427387903 4611686018427387903
(2 - loop(\(x,i).((x div (1 + (if (x mod 3) <= 0 then 2 else 0))) + (if (x + ~2) <= 0 then 1 else 2)),1,(x + 1)))
A194880: 0 ~1 ~1 ~4 ~5 ~2 ~7 ~8 ~3 ~10 ~11 ~4 ~13 ~14 ~5 ~16
((x + 1) + loop(\(x,i).((x + 2) + loop(\(x,i).(0 - (loop(\(x,i).2x,x,2) mod (x + 1))),2,x)),x,1))
A066614: 2 5 8 12 20 23 33
((x + 1) + loop(\(x,i).x2,1,loop(\(x,i).(3x - (1 mod loop(\(x,i).x2,x,2))),x,1)))
A324126: 2 6 28 200 4611686018427387903
loop(\(x,i).(x * i),x,((x + 1) * loop(\(x,i).(x + ((x + loop(\(x,i).(x * i),i,1)) * (1 + i))),x,1)))
A129460: 1 10 156 3696 125280 5780160 349090560 26760222720 2540101939200 292579402752000 40213832085504000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).2x,x,1),(x div 2),(loop(\(x,i).x2,3,(2 + (x mod 2))) mod (x + 1)))
A264933: 0 1 2 2 4 256 4611686018427387903
compr(\x.loop(\(x,i).(if x <= 0 then 3 else (loop(\(x,i).(x div (2 - (x mod 2))),x,x) div 2)),3,x),(x + 1))
A014311: 7 11 13 14 19 21 22 25 26 28 35 37 38 41 42 44
((x + 1) + loop(\(x,i).((x + 1) - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + (i div 3)))),x,x)),2,x))
A184410: 3 5 8 11 12 15 16 20 21 25 26 27 31 32 33 38
(if ((if x <= 0 then 1 else x) mod 8) <= 0 then (x + ~2) else loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))
A341042: 1 1 3 1 5 3 7 1 6 5 11 3 13 7 15 1
(1 + loop(\(x,i).(x - (x div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))),x,x))
A323075: 1 2 3 3 5 3 7 5 7 3 11 7 13 5 11 7
loop(\(x,i).(x + loop(\(x,i).(2x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i))),(~1 + i),1)),x,1)
A072100: 1 2 3 5 8 14 24 44 79 149 275 527 989 1913 3629 7061
loop(\(x,i).(x * loop(\(x,i).(4x2 + ~x),1,loop(\(x,i).4x,(~1 + i),1))),x,1)
A053291: 1 3 180 181440 2961100800 775476766310400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).7x,x,1))
A074534: 3 13 69 415 2673 17863 121809 840055 5830593 40616263 283524849 1981523095 13858068513 96956127463 678491524689 4748635284535
(loop(\(x,i).3x,x,(1 + loop(\(x,i).2x,x,1))) + loop(\(x,i).5x,x,1))
A001579: 3 14 70 368 2002 11144 63010 360248 2076802 12050504 70290850 411802328 2421454402 14282991464 84472462690 500716911608
(loop(\(x,i).2x,x,(1 + loop(\(x,i).3x,x,1))) + loop(\(x,i).5x,x,1))
A074537: 3 13 65 349 1937 10933 62345 358189 2070497 12031333 70232825 411627229 2420927057 14281405333 84467696105 500702595469
(loop(\(x,i).(x3 + x2),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).5x,x,1))
A074563: 3 17 105 701 4977 36917 281865 2191661 17233377 136432997 1084556025 8642957021 68980394577 551043625877 4404418462185 35215963408781
(loop(\(x,i).(x3 + x),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).5x,x,1))
A074539: 3 15 93 645 4737 35925 277833 2175405 17168097 136171365 1083508473 8638764765 68963621457 550976525205 4404150043113 35214889699725
(loop(\(x,i).(x2 + x),1,loop(\(x,i).3x,x,1)) + loop(\(x,i).5x,x,1))
A074554: 3 17 115 881 7267 62417 547795 4863281 43443907 389393297 3496609075 31430064881 282674208547 2543088125777 22882900753555 205921664021681
(1 - loop(\(x,i).((x + 1) - ((1 + loop(\(x,i).2x,x,(if x <= 0 then 1 else (x * i)))) div 3)),x,1))
A218599: 0 0 0 1 0 2 1 0 4 3 2 1 0 8 7 6
(loop(\(x,i).((x2 + 3x) div 2),1,loop(\(x,i).2x,x,1)) - loop(\(x,i).3x,x,1))
A084869: 1 2 5 17 71 317 1415 6197 26591 112157 466775 1923077 7863311 31972397 129459335 522571157
((loop(\(x,i).2x,x,(1 + loop(\(x,i).2x,x,3))) div 2) - loop(\(x,i).3x,x,1))
A083330: 1 4 17 73 311 1309 5447 22453 91871 373789 1514327 6115333 24636431 99073069 397878407 1596280213
((loop(\(x,i).(2x + 2),x,(1 + loop(\(x,i).2x,x,1))) div 2) - loop(\(x,i).3x,x,1))
A220788: 0 1 4 16
A133789: 0 1 4 16 70 316 1414 6196 26590 112156 466774 1923076 7863310 31972396 129459334 522571156
loop(\(x,i).(x + (if x <= 0 then 1 else (~1 + (if (x + ~1) <= 0 then (x * i) else x5)))),x,1)
A112980: 1 1 2 33 39135425 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).20x,i,1))),x,1)
A028682: 1 380 60648000 3880986816000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).15x,i,1))),x,1)
A028677: 1 210 10584000 120522654000000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).18x,i,1))),x,1)
A028680: 1 306 32023512 1089004102288704 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).24x,i,1))),x,1)
A028686: 1 552 182822400 34935377382604800 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).x2,1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)))),x,1)
A024525: 1 5 14 39 88 209 378 667 1028 1557 2398 3359 4728 6409 8258 10467
loop(\(x,i).(x * loop(\(x,i).x2,1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)))),x,1)
A061742: 1 4 36 900 44100 5336100 901800900 260620460100 94083986096100 49770428644836900 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).2x,i,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)))),x,1)
A112044: 1 5 17 57 169 521 1353 3529 8393 20169 49865 113353 264905 600777 1305289 2845385
loop(\(x,i).(x + loop(\(x,i).((x + 1) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),i,1)),x,1)
A023538: 1 4 10 21 39 68 110 169 247 348 478 639 837 1076 1358 1687
loop(\(x,i).(~x + loop(\(x,i).((x + 1) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),i,1)),x,1)
A073738: 1 2 4 7 11 18 24 35 43 58 72 89 109 130 152 177
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).14x,i,1))),x,1)
A028676: 1 182 6956040 52356666223680 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).x2,1,loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),i,1))),x,1)
A167892: 1 5 30 226 1990 19414 203455 2248355 25887399 307993015 3763786811 47032778955 598933188955 7751562502555 101741582076580 1351906409905480
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).13x,i,1))),x,1)
A028675: 1 156 4429152 21368939889024 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).11x,i,1))),x,1)
A028673: 1 110 1597200 2827411356000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).17x,i,1))),x,1)
A028679: 1 272 22639104 546341708980224 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),i,1)),x,1)
A143293: 1 3 9 39 249 2559 32589 543099 10242789 233335659 6703028889 207263519019 7628001653829 311878265181039 13394639596851069 628284422185342479
loop(\(x,i).(x + loop(\(x,i).x2,1,loop(\(x,i).(2 * (2x - (x div (1 + i)))),(~1 + i),2))),x,1)
A115257: 1 5 41 441 5341 68845 922621 12701245 178338145 2542242545 36677022081 534311328705 7846771001041 116019251361041 1725360846921041 25786805857871441
loop(\(x,i).(x + loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),i,2)),x,1)
A217723: 1 7 37 247 2557 32587 543097 10242787 233335657 6703028887 207263519017 7628001653827 311878265181037 13394639596851067 628284422185342477 4611686018427387903
loop(\(x,i).(x2 + x),1,(1 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x)))
A024701: 2 6 12 30 42 72 90 132 210 240 342 420 462 552 702 870
loop(\(x,i).(2x + loop(\(x,i).((4x + ~2) + loop(\(x,i).3x,i,1)),i,1)),x,1)
A168584: 1 7 41 215 1041 4767 21001 90055 378881 1572527 6463161 26375895 107081521 433076287 1746588521 7029269735
loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then (4x + loop(\(x,i).3x,i,1)) else x)),x,1)
A018325: 1 2 4 47 94 188
(1 + (if (x + ~1) <= 0 then x else loop(\(x,i).(x + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,x)))
A024521: 1 2 6 11 18 29 42 59 78 101 130 161 198 239 282 329
loop(\(x,i).(x + loop(\(x,i).(1 + (2 * (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))),1,i)),x,1)
A080277: 1 4 5 12 13 16 17 32 33 36 37 44 45 48 49 80
loop(\(x,i).(x + loop(\(x,i).(x + (loop(\(x,i).(2 + ((x2 + x) div 2)),2,x) div 3)),1,i)),x,1)
A027660: 1 4 11 26 56 112 210 372 627 1012 1573 2366 3458 4928 6868 9384
loop(\(x,i).(x * loop(\(x,i).(x2 + 2x),1,compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),x,1)
A318766: 1 3 24 576 27648 3317760 557383680 160526499840 57789539942400 30512877089587200 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x2,loop(\(x,i).loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),i,x),x,1))
A247859: 1 2 32 5120 9175040 197300060160 53337309063413760 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).4x,x,loop(\(x,i).(x + (9x div (if i <= 0 then 1 else i))),x,1))
A054340: 1 40 880 14080 183040 2050048 20500480 187432960 1593180160 12745441280 96865353728 704475299840 4931327098880 33381291130880 219362770288640 1403921729847296
loop(\(x,i).7x,x,loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,1))
A139641: 1 35 735 12005 168070 2117682 24706290 271769190 2853576495 28852829005 282757724249 2699051004195 25191142705820 230595844768660 2075362602917940 18401548412539068
(2 * (loop(\(x,i).4x,x,1) - loop(\(x,i).4x,(x div 2),(1 - (if x <= 0 then 2 else 0)))))
A032087: 4 6 24 120 480 2016 8064 32640 130560 523776 2095104 8386560 33546240 134209536 536838144 2147450880
(loop(\(x,i).4x,x,(1 + (if x <= 0 then 2 else (if (x mod 2) <= 0 then 4 else ~3)))) div 2)
A091104: 1 ~4 40 ~64 640 ~1024 10240 ~16384 163840 ~262144 2621440 ~4194304 41943040 ~67108864 671088640 ~1073741824
(loop(\(x,i).2x,x,(1 + (loop(\(x,i).(3x + ~1),x,2) + loop(\(x,i).2x,x,1)))) div 2)
A266797: 2 8 38 200 1112 6368 37088 218240 1292672 7689728 45874688 274196480 1640978432 9829081088 58907353088 353175633920
(if (x mod 3) <= 0 then (if (x mod 2) <= 0 then (14 * (if x <= 0 then 1 else 2)) else 1) else 2)
A040193: 14 2 2 1 2 2 28 2 2 1 2 2 28 2 2 1
(2 * loop(\(x,i).2x,x,(~1 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).(2x + 2),2x,2)))))
A167440: 2 724 30248 1028176 33390752 1072431424 34349253248 1099427742976 35183701002752 1125894538138624 36028754069301248 1152921161009483776 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 * ((1 + loop(\(x,i).2x,(x + ~1),(if (x mod 3) <= 0 then 1 else 2))) div 3)))
A087628: 1 2 2 2 10 22 22 86 170 170 682 1366 1366 5462 10922 10922
(2 * (1 + (2 * compr(\x.loop(\(x,i).loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)),2,x),x))))
A079702: 14 26 34 38 62 74 86 94 118 122 134 142 146 158 194 202
(2 * (loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x)),2,2x) mod (x + 1)))
A303603: 0 0 0 2 4 2 8 10 8 14 16 14 20 18 16 26
loop(\(x,i).(x * loop(\(x,i).x2,1,compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),(x + 1),2)
A307124: 2 8 128 4608 460800 66355200 16986931200 5503765708800 2663822603059200 2088436920798412800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else loop(\(x,i).x2,1,loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(x + ~1),2)))
A284494: 1 4 4 16 100 784 7056 69696 736164 8179600 94556176 1128422464 13823175184 173075968576 2207601640000 28610517254400
((1 + (if (x mod 2) <= 0 then (2 * (if (x mod 4) <= 0 then 8 else 1)) else 0)) * (if x <= 0 then 1 else 2))
A040287: 17 2 6 2 34 2 6 2 34 2 6 2 34 2 6 2
((if (x div 2) <= 0 then 1 else ((4 * (2 + (x mod 2))) - ((if x <= 0 then 2 else x) div 2))) * (if x <= 0 then 1 else 2))
A073143: 1 2 14 22 12
((loop(\(x,i).(x2 + 3x),1,loop(\(x,i).2x,x,1)) - loop(\(x,i).3x,x,1)) div 2)
A134168: 1 3 9 30 111 438 1779 7290 29871 121998 496299 2011650 8129031 32769558 131850819 529745610
((if x <= 0 then 2 else (1 - ((2x + 1) mod (~1 + loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x))))) div 2)
A339737: 1 1 0 1 1 0 2 0 1 0 2 1 1 1 0 3
(x - ((if 2x <= 0 then x else (~1 + loop(\(x,i).(x + (if (~2 + (x div 4)) <= 0 then 1 else 0)),x,x))) div 2))
A209384: 0 1 1 1 1 1 1 2 3 4 5 6 7 7 8 8
(loop(\(x,i).(x + loop(\(x,i).(x * (1 + (if (x mod 2) <= 0 then 16 else 1))),1,i)),x,1) div 2)
A303298: 0 1 18 21 55 60 111 118 186 195 280 291 393 406 525 540
(4 * loop(\(x,i).loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 2 else 0)),x,(x + 2)),(x + 4),1))
A270298: 44 52 68 76 92 116 124 148 164 172 188 212 236 244 268 284
(loop(\(x,i).2x,x,2) - loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),((x + 1) div 2),2))
A180967: 0 0 4 4 20 24 88 116 372 520 1544 2248 6344 9520 25904 39796
(2 * loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),x,(if x <= 0 then 1 else 2)))
A272590: 2 8 24 120 840 9240 120120 2042040 38798760 892371480 25878772920 802241960520 29682952539240 1217001054108840 52331045326680120 2459559130353965640
(1 - ((((~x + 1) + loop(\(x,i).x2,1,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x))) div 2) div 2))
A193739: 1 1 1 2 2 1 3 3 2 1 4 4 3 2 1 5
(2 * (if x <= 0 then 2 else ((loop(\(x,i).x2,1,loop(\(x,i).x3,(x + ~1),4)) div 2) div 2)))
A057841: 4 8 2048 34359738368 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (x - (((x - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * (1 + i)))),x,2x)) div 2) div 2)))
A138585: 1 1 2 1 2 3 3 4 5 6 4 5 6 7 8 7
(2 * (if (x + ~2) <= 0 then x else loop(\(x,i).3x,x,loop(\(x,i).10x,x,2))))
A079236: 0 2 4 108000
(2 + (loop(\(x,i).(x2 + x),1,(1 + loop(\(x,i).2x,x,1))) + loop(\(x,i).3x,x,2)))
A254030: 10 20 50 146 470 1610 5750 21146 79430 303050 1169750 4554746 17852390 70322090 278050550 1102537946
(0 - loop(\(x,i).loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),x,x),1,(3x + 2)))
A087298: 1 4 7 10 11 16 18 22 23 26 31 34 35 39 41 46
(2 + compr(\x.(x - loop(\(x,i).loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),x,(2x + 1)),2,(x + 1))),x))
A124485: 2 3 6 12 15 21 27 42 45 57 66 87 90 96 117 120
(2 + compr(\x.loop(\(x,i).loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 0 else 2))),x,(x + 1)),2,(x + 1)),x))
A043321: 3 6 10 11 12 15 19 20 21 24 31 32 34 35 37 38
loop(\(x,i).(x + loop(\(x,i).(x * i),x,1)),1,(2 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x)))
A267898: 4 9 125 5047 39916811 6227020813 355687428096017 121645100408832019 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + loop(\(x,i).(x * i),x,1)),1,(2 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x)))
A267897: 0 3 115 5033 39916789 6227020787 355687428095983 121645100408831981 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * loop(\(x,i).loop(\(x,i).2x,x,(x + 2)),1,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A299795: 4 12 80 448 11264 53248 1114112 4980736 96468992 7784628224 33285996544 2542620639232 45079976738816 189115999977472 3307330976350208 238690780250636288
loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),2))
A141083: 2 12 240 4032 1047552 16773120 4294901760 68719214592 17592181850112 72057593769492480 1152921503533105152 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).2x,x,x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A098096: 16 72 800 6272 247808 1384448 37879808 189267968 4437573632 451508436992 2063731785728 188153927303168 3696558092582912 16263975998062592 310889111776919552 4611686018427387903
(2 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (3 + i)) <= 0 then 2 else 1)),x,(x + 2)),2,2x),x))
A067656: 7 13 17 19 24 25 27 31 32 34 37 38 43 45 47 49
((if x <= 0 then 1 else compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + (x div 2)))),x)) div 2)
A222010: 0 1 3 7
A111223: 0 1 3 7 9 13 19 21 25 27 31 33 39 45 51 55
loop(\(x,i).(2 * loop(\(x,i).x2,1,(x2 * (x2 + loop(\(x,i).x3,2,x))))),x,2)
A324440: 2 8520192 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(2x + 1),loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),2,x),1) mod (x + 2))
A344852: 1 1 1 1 1 1 3 1 1 1 3 1 3 3 15 1
loop(\(x,i).loop(\(x,i).(~x + (17x div (if i <= 0 then 1 else i))),x,1),1,2x)
A110839: 1 120 1820 8008 12870 8008 1820 120 1
(loop(\(x,i).x2,1,loop(\(x,i).(2 * (~2x + (x div (if i <= 0 then 1 else i)))),x,1)) div (~2x + 1))
A010370: 1 ~4 ~12 ~80 ~700 ~7056 ~77616 ~906048 ~11042460 ~139053200 ~1796567344 ~23696871744 ~317933029232 ~4326899214400 ~59605244280000 ~829705000377600
((if (x mod 3) <= 0 then (3 * (if (x mod 2) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1)) else 2) - (x mod 2))
A010135: 6 1 2 2 2 1 12 1 2 2 2 1 12 1 2 2
(loop(\(x,i).(4x - loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),i,1)),x,x) div 2)
A018218: 0 1 9 58 325 1686 8330 39796 185517 848830 3827230 17053356 75249954 329353948 1431575220 6185613032
((loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,x) + loop(\(x,i).4x,x,x)) div 2)
A100511: 0 3 22 126 652 3190 15060 69356 313624 1398438 6166660 26948548 116888232 503811516 2159864392 9216445080
(2 - ((~x + loop(\(x,i).(1 - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * (1 + i)))),x,2x)),2,x)) div 2))
A155124: 1 0 2 ~1 2 2 ~2 2 2 2 ~3 2 2 2 2 ~4
(2 + (if x <= 0 then 0 else compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),x)))
A175075-A094743: 2 5 7 13 19 31 43 61 73 103 109 139 151 181 193 199
loop(\(x,i).(x + loop(\(x,i).~x,x,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)))),x,2)
A066033: 2 5 0 7 ~4 9 ~8 11 ~12 17 ~14 23 ~18 25 ~22 31
loop(\(x,i).(x + loop(\(x,i).(x * (2 + i)),compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i),2)),x,2)
A111179: 2 8 128 5168 39921968 6266942768 355693695038768 122000794103870768 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).((x + 2) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)),i,2)),x,2)
A014148: 2 7 17 34 62 103 161 238 338 467 627 824 1062 1343 1671 2052
loop(\(x,i).(x + loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),i,2)),x,2)
A060389: 2 8 38 248 2558 32588 543098 10242788 233335658 6703028888 207263519018 7628001653828 311878265181038 13394639596851068 628284422185342478 4611686018427387903
(loop(\(x,i).(x2 + ~x),1,compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x)) div 2)
A030007: 0 0 1 6 10 21 28 45 78 91 136 171 190 231 300 378
loop(\(x,i).(2x + loop(\(x,i).(4x + loop(\(x,i).3x,(1 + i),1)),i,2)),x,2)
A095262: 2 21 137 735 3557 16191 70877 302295 1266437 5239311 21481517 87506055 354778517 1433405631 5776554557 23235129015
((~x + ~1) + (2 * loop(\(x,i).(x + loop(\(x,i).(x + loop(\(x,i).3x,(1 + i),i)),i,1)),x,1)))
A100190: 1 20 147 760 3317 13164 49255 177200 620073 2125828 7174523 23914920 78919069 258280412 839411151 2711943520
compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(x2 + 3)),x)
A111040: 1 2 4 5 7 8 11 13 14 16 17 20 22 25 26 31
compr(\x.(x - loop(\(x,i).loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),x,(2x + 1)),2,(2x + 1))),x)
A244087: 0 2 5 20 32 44 47 59 62 89 104 107 110 122 164 170
((x + 1) + (if x <= 0 then 2 else (x + (if x <= 0 then 1 else (loop(\(x,i).(x * i),(x + ~2),x) * (1 + (x mod 2)))))))
A079481: 3 5 7 13 17 71
((x + 1) + loop(\(x,i).(loop(\(x,i).(2x + 3),x,0) div loop(\(x,i).(x2 + x),2,2)),2,x))
A345900: 1 2 3 4 5 6 8 44
compr(\x.((~x + 2) + loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x)),2,(x + 1))),x)
A079364: 9 15 21 25 26 27 33 34 35 39 45 49 50 51 55 56
loop(\(x,i).(if x <= 0 then 1 else (x * (~2 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)))),(x + 1),x)
A059862: 1 1 2 8 64 640 8960 143360 2867200 74547200 2087321600 70968934400 2696819507200 107872780288000 4746402332672000 237320116633600000
(x * loop(\(x,i).(if x <= 0 then 1 else (2 * ((1 + loop(\(x,i).(3x * i),x,1)) div 2))),1,(x + ~1)))
A052690: 0 1 8 54 648 9720 174960 3674160 88179840 2380855680 71425670400 2357047123200 84853696435200 3309294160972800 138990354760857600 4611686018427387903
(loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,1) + loop(\(x,i).4x,(x + ~1),x))
A241524: 1 7 38 188 886 4052 18156 80152 349862 1513604 6501316 27759272 117935548 498920008 2102905496 8835174960
(loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1) + loop(\(x,i).4x,(x + ~1),x))
A241478: 1 3 14 68 326 1532 7068 32104 143942 638444 2806196 12239768 53035804 228504408 979640696 4181649360
compr(\x.(if ((x div 2) mod 2) <= 0 then 1 else ((x + ~1) - loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x))),x)
A201363: 2 3 7
A045326: 2 3 7 11 19 23 31 43 47 59 67 71 79 83 103 107
(~x + (loop(\(x,i).3x,x,(if (x + ~2) <= 0 then loop(\(x,i).(x * (2 + (i mod 2))),x,1) else 0)) div 2))
A234319: 0 3 25 ~3 ~4 ~5 ~6 ~7 ~8 ~9 ~10 ~11 ~12 ~13 ~14 ~15
compr(\x.(3 + loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 2 else 1)),x,x)),2,2x)),x)
A195613: 25 28 32 38 46 58 60 62 72 77 80 85 88 92 93 94
loop(\(x,i).(1 - ((x2 + 2x + 1) mod (~1 + loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)))),2,x)
A245570: 1 1 1 3 1 1 2 3 1 1 1 1 3 1 1 3
(x + (if x <= 0 then 1 else (2 * (x + loop(\(x,i).(x * (2 + (i mod 2))),x,1) - (if (x + ~2) <= 0 then 1 else 0)))))
A066009: 1 7 16 45 84
loop(\(x,i).(loop(\(x,i).2x,x,2) div (x + 2)),1,compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))
A007663: 1 3 9 93 315 3855 13797 182361 9256395 34636833 1857283155 26817356775 102280151421 1497207322929 84973577874915 4885260612740877
compr(\x.(loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (2 + i)) <= 0 then 2 else 1)),x,2x)),2,x) mod (x + 2)),x)
A243811: 0 1 4 7 13 19 28 34 49 52 67 73 88 94 97 112
(0 - loop(\(x,i).(x - loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then i else 0)),x,(x + 1))),1,2x))
A130140: 1 3 5 7 3 11 13
A326577-A090368: 1 3 5 7 3 11 13 3 17 19 3 23 5 3 29 31
(1 - loop(\(x,i).(x - (if x <= 0 then 0 else loop(\(x,i).((x + 1) + ((x + (x mod 2)) div 3)),i,1))),x,x))
A280514: 1 2 1 3 2 1 5 4 3 2 1 8 7 6 5 4
(if x <= 0 then 2 else compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 4x))),x))
A201363: 2 3 7
A172238: 2 3 7 13 19 37 43 67 79 97 103 109 127 163 193 223
loop(\(x,i).(if x <= 0 then 1 else (2 * (x + ((x + (if (~2 + (x div 4)) <= 0 then 1 else 2)) div 2)))),1,x2)
A342235: 1 4 12 28 50 76 110 148 194 244 302 364 434 508 590 676
(~x2 + (if x <= 0 then 1 else (x + (2 * (if (x + ~1) <= 0 then 1 else ((x + 1) + loop(\(x,i).2x,x,1)))))))
A281353: 1 2 12 18 30 56
loop(\(x,i).(x2 + 3x),1,compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))
A222963: 0 4 10 28 40 70 88 130 208 238 340 418 460 550 700 868
loop(\(x,i).3x,(2x + 2),loop(\(x,i).(10x + 5),(x + 1),0))
A220094: 45 4455 404595 36446355 3280467195 295244704755 26572047342795 2391484476085155 215233604784766395 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).10x,x,loop(\(x,i).(10x + 10),(x + 1),0))
A138147: 10 1100 111000 11110000 1111100000 111111000000 11111110000000 1111111100000000 111111111000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (~2 + (2x mod (4 + (x div 4)))) <= 0 then 1 else (if (x mod 8) <= 0 then 2 else 0))
A286564: 1 1 1 1 0 1 1 0 2 1 1 0 0 0 1 1
(1 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + (if ((x + ~1) mod 4) <= 0 then 2 else 0)))
A163976: 1 4 4 6 10 14 16 18 22 30 30 36 40 44 46 52
loop(\(x,i).(x + (i * i * i * i)),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),0)
A098997: 17 98 979 4676 39974 89271 327369 562666 1431244 4463999 6197520 14822755 24607093 31137590 48343448 87633963
(loop(\(x,i).11x,x,1) + loop(\(x,i).(3x + 2),2x,0))
A155670: 1 19 201 2059 21201 220099 2303001 24270139 257405601 2745368179 29424209001 316692730219 3420857913201 37064577972259 402626626038201 4383139301510299
(loop(\(x,i).11x,x,1) - loop(\(x,i).(3x + 2),2x,0))
A155672: 1 3 41 603 8081 102003 1240121 14704203 171312161 1970527203 22450640201 253930611003 2855998840241 31980846315603 356873041128281 3971357037321003
loop(\(x,i).(10x + 1),x,loop(\(x,i).(10x + 10),x,0))
A138148: 0 101 11011 1110111 111101111 11111011111 1111110111111 111111101111111 11111111011111111 1111111110111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(10x + ~1),x,loop(\(x,i).(10x + 10),x,0))
A244842: 0 99 10989 1109889 111098889 11110988889 1111109888889 111111098888889 11111110988888889 1111111109888888889 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).6x,x,1) - loop(\(x,i).(11x + ~10),x,0))
A155649: 1 16 156 1546 15936 168826 1818216 19767106 216038496 2368025386 25997890776 285674467666 3140605159056 34535772837946 379828197747336 4177718354400226
(loop(\(x,i).8x,x,1) - loop(\(x,i).(11x + ~10),x,0))
A155665: 1 18 184 1842 18736 193818 2033704 21584322 231136096 2492165418 27011166424 293901605202 3207147853456 35072467957818 384147880094344 4212432541504482
(loop(\(x,i).5x,x,1) - loop(\(x,i).(11x + ~10),x,0))
A155638: 1 15 145 1455 15265 164175 1787185 19565295 214749505 2359900815 25947190225 285360498735 3138672517345 34523932847055 379755937098865 4177278686993775
(loop(\(x,i).10x,x,1) - loop(\(x,i).(7x + ~6),x,0))
A155657: 1 16 148 1342 12400 116806 1117648 10823542 105764800 1040353606 10282475248 101977326742 1013841287200 10096889010406 100678223072848 1004747561509942
(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x div 2),1) + loop(\(x,i).(2x + 1),x,0))
A258143: 1 2 6 10 25 41 98 162 381 637 1485 2509 5811 9907 22818 39202
(x + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) - loop(\(x,i).(2x + 1),x,0))
A004303: 1 1 1 1 3 16 75 309 1183 4360 15783 56750 203929 734722 2658071 9662093
(~x + (loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) + loop(\(x,i).(2x + 1),x,0)))
A338726: 1 1 3 9 25 68 189 549 1677 5364 17809 60822 212095 751078 2690809 9727597
((3 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) - (if (x + ~1) <= 0 then x else 0))
A063534: 6 8 15 21 33 39 51 57 69 87 93 111 123 129 141 159
((x + ~1) + loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2) - loop(\(x,i).(2x + 4),x,0))
A013981: 1 2 9 44 195 804 3185 12368 47607 182720 701349 2695978 10384231 40083848 155052001 600949336
loop(\(x,i).(4x + loop(\(x,i).27x,(~1 + i),1)),x,0)
A180847: 0 1 31 853 23095 623821 16844191 454797253 12279542215 331547705341 8951788306351 241698285320053 6525853707835735 176198050128342061 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(~2 + i),1)),x,0)
A258431: 0 1 5 23 102 443 1898 8054 33932 142163 592962 2464226 10209620 42190558 173962532 715908428
loop(\(x,i).(10x + 1),x,loop(\(x,i).(10x + 8),x,0))
A184337: 0 81 8811 888111 88881111 8888811111 888888111111 88888881111111 8888888811111111 888888888111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).10x,x,1) - loop(\(x,i).(7x + 6),x,0))
A155661: 1 4 52 658 7600 83194 882352 9176458 94235200 959646394 9717524752 98022673258 986158712800 9903110989594 99321776927152 995252438490058
(loop(\(x,i).11x,x,1) - loop(\(x,i).(5x + 4),x,0))
A155644: 1 7 97 1207 14017 157927 1755937 19409047 213968257 2355994567 25927658977 285262842487 3138184236097 34521491440807 379743730067617 4177217651837527
(1 + (x mod (1 + (x mod (1 + (((x + ~1) + loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x)) mod (x + 1)))))))
A318459: 1 1 1 1 1 2 1 4 3 2 1 2 1 2 1 1
(loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,1) div (1 + (2 mod (1 + (x mod 3)))))
A067047: 1 5 5 35 70 42 210 330 165 715 1001 455 1820 2380 1020 3876
loop(\(x,i).x2,1,(1 + (x mod (1 + (loop(\(x,i).2x,x,(1 + (x mod 2))) mod (2x + 1))))))
A055491: 1 4 9 1 25 36 49 4 1 100 121 9 169 196 225 1
(1 + ((x + 1) div (1 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,(2x + 1)))))
A254046: 1 2 1 1 3 1 1 2 1 1 2 1 1 4 1 1
(~1 + loop(\(x,i).(3x2 + x),1,(1 + loop(\(x,i).10x,x,1))))
A171656: 13 373 30703 3007003 300070003 30000700003 3000007000003 300000070000003 30000000700000003 3000000007000000003 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).10x,x,(~1 + loop(\(x,i).10x,(x + 1),1)))
A083909: 9 990 99900 9999000 999990000 99999900000 9999999000000 999999990000000 99999999900000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 2) div loop(\(x,i).2x,(1 + ((loop(\(x,i).2x,(x div 2),1) + (x div 2)) div (x + 1))),1))
A242998: 0 1 1 2 1 1 2 2 1 1 0 0 0 0 0 0
((1 + (x div 2)) div (1 + (if x <= 0 then 0 else (if (x mod (3 + ((x div 2) mod 3))) <= 0 then 2 else 1))))
A060426: 1 0 1 1 1 1 1 2 1 2 2 3 2 3 4 4
(1 + (if x <= 0 then 0 else loop(\(x,i).(2 * i),(((x + ~1) div 2) - ((3 * (x div 4)) div 2)),1)))
A057334: 1 2 2 3 2 3 3 5 2 3 3 5 3 5 5 7
(if (x mod 10) <= 0 then (14 * (2 + (if x <= 0 then 0 else 2))) else 1)
A040790: 28 1 1 1 1 1 1 1 1 1 56 1 1 1 1 1
(if x <= 0 then 0 else (1 + ((x div 2) div (1 + (x div (2 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))))
A164879: 0 1 1 2 1 2 1 4 3 2 1 3 1 2 3 8
(~1 + loop(\(x,i).2x,x,1) - (loop(\(x,i).2x,x,1) div 33))
A222010: 0 1 3 7
A224521: 0 1 3 7 15 31 62 124 248 496 992 1985 3971 7943 15887 31775
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(10x + 6))
A017351: 362797056 17592186044416 3670344486987776 131621703842267136 1951354384207722496 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(10x + 9))
A017387: 31381059609 116490258898219 12200509765705829 317475837322472439 3909821048582988049 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else ((2x + 1) - (x div ~2))),x,5))
A070870: 6 15 8 20 50 125 63 32 80 200 500 1250 3125 1563 782 1955
(1 + ((1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (2 + (x div 4)))) div 3))
A209435: 1 1 2 1 2 3 1 2 4 5 1 2 4 6 8 1
(if x <= 0 then 0 else (1 + ((loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) div 5) mod 3)))
A332897: 0 1 1 1 2 1 2 1 2 2 3 1 3 2 1 1
(1 + (3 * (loop(\(x,i).2x,(x div 2),(2 + (x mod 2))) + loop(\(x,i).2x,x,3))))
A184031: 16 28 49 91 169 325 625 1225 2401 4753 9409 18721 37249 74305 148225 296065
(1 + (loop(\(x,i).(x * (2 + i)),compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x),1) div 3))
A139164: 2 21 841 6652801 1037836801 59281238016001 20274183401472001 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(12x + 11))
A017663: 285311670611 952809757913927 96549157373046875 2472159215084012303 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + ((3x + 3) * (if x <= 0 then 1 else ((x2 + 2) + loop(\(x,i).x2,2,x2)))))
A069151: 2 23 2357
(1 + (3 * loop(\(x,i).(x2 + x),1,loop(\(x,i).10x,x2,1))))
A160432: 7 331 300030001 3000000003000000001
((x + 1) div (1 + (3 * (if x <= 0 then 0 else (if ((x + (x div 4)) mod 3) <= 0 then 1 else 2)))))
A029281: 1 0 0 1 0 1 1 1 1 1 2 1 3 2 2 4
(1 + (3 * (if x <= 0 then 0 else (if (x mod (1 - (2 * ((~x + 1) div (2 + (x div 2)))))) <= 0 then 1 else 2))))
A254398: 1 4 7 4 7 7 4 7 7 7 4 7 7 7 7 4
(1 + (6 * (1 + (if x <= 0 then 0 else ((2 + loop(\(x,i).2x,((x + ~1) div 2),x)) div 2)))))
A272381: 7 13 19 31 37 73
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(12x + 7))
A017615: 1977326743 116490258898219 25408476896404831 929293739471222707 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(~11x + ~7))
A017482: 282475249 3570467226624 420707233300201 10485760000000000 119042423827613001 839299365868340224 4297625829703557649 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(~11x + ~7))
A017484: 13841287201 1156831381426176 353814783205469041 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(12x + 5))
A017591: 48828125 34271896307633 12200509765705829 550329031716248441 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((2 + (loop(\(x,i).2x,x,2) mod loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))) div 3))
A054992: 1 1 2 1 2 2 2 1 4 3 2 2 2 3 4 1
(1 + ((2 + (if x <= 0 then 1 else ((loop(\(x,i).(~2x + 6),x,1) mod (x + 1)) div 2))) div 3))
A230798: 2 1 1 2 1 2 1 2 2 2 1 3 1 2 3 2
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (5x + 1)),x,11)
A259193: 11 56 28 14 7 36 18 9 46 23 116 58 29 146 73 366
(11 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))
A097932: 11 12 13 15 16 18 19 21 24 25 28 30 31 33 36 39
(1 + (if x <= 0 then 1 else 4x) - ((2 * (~x + (if (~2 + (x div 2)) <= 0 then 2 else 1))) div 3))
A314890: 1 5 9 14 19 23 29 33 38 43 47 52 57 61 66 71
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(9x + 7))
A017255: 1977326743 17592186044416 2384185791015625 70188843638032384 929293739471222707 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(9x + 5))
A017231: 48828125 4049565169664 952809757913927 36028797018963968 550329031716248441 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((2 * (x + loop(\(x,i).(1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2))),2,(x + ~1)))) div 3))
A111801: 1 3 4 5 7 8 11 13 15 16 17 19 20 21 23 24
(1 + (loop(\(x,i).(x * (2 + i)),compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x),2) div 3))
A139161: 3 41 1681 13305601 2075673601 118562476032001 40548366802944001 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (loop(\(x,i).(x * (2 + i)),compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x),2) div 3))
A139191: 1 39 1679 13305599 2075673599 118562476031999 40548366802943999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((2 * (2x - loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),x,x))) div 3))
A184835: 1 3 4 7 8 10 11 15 16 18 19 22 23 25 27 31
(1 + (3 * compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(3x + 1))),x)))
A225227: 1 7 13
A123365: 1 7 13 19 31 37 43 61 67 73 79 97 103 109 127 139
(1 + (3 * compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(3x + 1))),x)))
A272409-A272406-A272384-A144921-A002476: 7 13 19 31 37 43 61 67 73 79 97 103 109 127 139 151
(x div ((x2 + ~x + 2) div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))))
A064891: 0 1 2 0 2 0 1 0 0 0 1 0 1 0 0 0
(~1 + loop(\(x,i).(x + ((~1 + i) * i)),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1))
A127919: 2 8 40 112 440 728 1632 2280 4048 8120 9920 16872 22960 26488 34592 49608
loop(\(x,i).10x,x,(1 + loop(\(x,i).10x,(x + 2),1)))
A164367: 101 10010 1000100 100001000 10000010000 1000000100000 100000001000000 10000000010000000 1000000000100000000 4611686018427387903
(loop(\(x,i).4x,x,1) div loop(\(x,i).2x,((x3 div 2) div (x + 3)),1))
A331055: 1 4 16 16 16 8 1
((1 + (x div 4)) div (1 + (if (x mod (1 + (if (x mod 2) <= 0 then 6 else 0))) <= 0 then x else 1)))
A292374: 1 0 0 0 1 0 1 0 1 0 1 0 2 0 0 0
(1 + loop(\(x,i).11x,x,1) - loop(\(x,i).6x,x,1))
A155654: 1 6 86 1116 13346 153276 1724906 19207236 212679266 2347869996 25876958426 284948873556 3136251594386 34509651449916 379671469419146 4176777984431076
(1 + loop(\(x,i).((x + 1) + (loop(\(x,i).(x2 + 4x + 2),2,3) mod (x + 1))),x,1))
A323395: 2 4 8 16 32 48 96 144 192
loop(\(x,i).(x * i),(1 + compr(\x.(loop(\(x,i).((x2 + x) div 2),5,2) mod (x + 1)),x)),1)
A088258: 1 2 6 24 720 5040 39916800 479001600 87178291200 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).11x,x,1) - loop(\(x,i).8x,x,1))
A155668: 1 4 58 820 10546 128284 1509418 17390020 197581666 2223729964 24863682778 276721736020 3069708899986 33972956330044 375351787072138 4142063797326820
(1 + loop(\(x,i).(3x2 + 5x + 2),1,loop(\(x,i).10x,x,1)))
A171630: 11 353 30503 3005003 300050003 30000500003 3000005000003 300000050000003 30000000500000003 3000000005000000003 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(3x2 + 2x + 2),1,loop(\(x,i).10x,x,1)))
A171248: 8 323 30203 3002003 300020003 30000200003 3000002000003 300000020000003 30000000200000003 3000000002000000003 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(3x2 + 8x + 4),1,loop(\(x,i).10x,x,1)))
A171718: 14 383 30803 3008003 300080003 30000800003 3000008000003 300000080000003 30000000800000003 3000000008000000003 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x2 + 7x),1,loop(\(x,i).10x,x,1)))
A225813: 9 171 10701 1007001 100070001 10000700001 1000007000001 100000070000001 10000000700000001 1000000007000000001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x2 + 9x),1,loop(\(x,i).10x,x,1)))
A171553: 11 191 10901 1009001 100090001 10000900001 1000009000001 100000090000001 10000000900000001 1000000009000000001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 - loop(\(x,i).(~3x2 + 2x),1,(1 + loop(\(x,i).10x,x,1))))
A171583: 10 343 30403 3004003 300040003 30000400003 3000004000003 300000040000003 30000000400000003 3000000004000000003 4611686018427387903 4611686018427387903
loop(\(x,i).(2x * (1 + (2 * i))),(1 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x)),1)
A075069: 6 60 15120 8648640 14079294028800 32382376266240000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x6 + x5 + x4 + x3 + x2 + x),1,loop(\(x,i).2x,x,1)))
A034670: 7 127 5461 299593 17895697 1108378657 69810262081 4432676798593
A020516: 7 127 5461 299593 17895697 1108378657 69810262081 4432676798593 282578800148737 18049651735527937 1154048505100108801 4611686018427387903 4611686018427387903 4611686018427387903
((~x + ~1) + (loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,1) + loop(\(x,i).2x,x,1)))
A181490: 1 2 6 18
A132790: 1 2 6 18 53 158 486 1550 5109 17298 59799 210048 746983 2682618 9711214 35390422
(x div (1 + ((~1 + loop(\(x,i).(x * i),x,loop(\(x,i).(2 * (x + (i mod 2))),(x div 2),1))) mod (x + 1))))
A292936: 0 1 1 0 2 0 2 0 0 0 3 0 1 0 0 0
(1 + ((1 + (2 * loop(\(x,i).loop(\(x,i).(2 + (x2 div (x + 4))),2,x),2,x))) mod (x + 1)))
A062406: 1 2 3 4 5 4 3 2 1 2 3 4 5 4 5 4
(1 + ((1 + (x mod (1 - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * (1 + i)))),x,2x)))) mod (x + 1)))
A306680: 1 1 2 1 1 3 1 1 2 4 1 1 1 3 5 1
(1 + compr(\x.(loop(\(x,i).(2x + 2),x,(if (x mod 8) <= 0 then 1 else 0)) mod (x + 1)),(x + 1)))
A193063-A165132: 2 3 5 7 11 13
A129944-A097375-A089189-A042987-A007459: 2 3 5 7 11 13 19 23 29 31 37 43 47 53 59 61
(~1 + (loop(\(x,i).2x,loop(\(x,i).(x div (1 + (x mod 2))),x,x),1) mod ((x + 1) * (2 - (x mod 2)))))
A078788: 0 0 3 0 5 3 7 0 3 5 11 3 13 7 3 0
loop(\(x,i).(x * (~1 + loop(\(x,i).(x3 + 7x2 + 14x + 8),1,x2))),(x + 1),1)
A144839: 29 17393796001 4611686018427387903
(1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))
A213642: 2 2 5 2 11 5 17 2 23 11 31 5 41 17 47 2
(~1 + loop(\(x,i).x2,1,((4x + 4) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A065915: 15 63 15 255 15 63 15 1023 15 63 15 255 15 63 15 4095
(~1 + loop(\(x,i).2x2,1,((2x + 2) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A065916: 7 31 7 127 7 31 7 511 7 31 7 127 7 31 7 2047
loop(\(x,i).(x - (x div 5)),2,(1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A068057: 1 2 1 4 1 2 1 6 1 2 1 4 1 2 1 11
loop(\(x,i).3x,3x,(1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A157094: 1 54 729 78732 531441 28697814 387420489 83682825624 282429536481 15251194969974 205891132094649 22236242266222092 150094635296999121 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).7x,x,(1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A156192: 1 14 49 1372 2401 33614 117649 6588344 5764801 80707214 282475249 7909306972 13841287201 193778020814 678223072849 75960984159088
(loop(\(x,i).(2 * (2x - (x div (1 + i)))),(x + ~1),2) - loop(\(x,i).4x,(x + ~1),1))
A127275: 1 1 2 4 6 ~4 ~100 ~664 ~3514 ~16916 ~77388 ~343144 ~1490148 ~6376616 ~26992264 ~113317936
loop(\(x,i).(x * loop(\(x,i).(4x * ((~1 + (2 * i)) * (1 + (2 * i)))),i,1)),(x + ~1),1)
A107254: 1 1 12 8640 870912000 22122558259200000 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * loop(\(x,i).(x + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),i,i)),(x + ~1),0)))
A281593: 1 1 3 11 41 153 573 2157 8163 31043 118559 454479 1747771 6740059 26055459 100939779
(1 + ((loop(\(x,i).(3x + 1),x,0) - loop(\(x,i).(5x + ~1),x,0)) div 2))
A233106: 1 2 6 23 99 452 2136 10313 50469 249062 1235466 6147803 30650439 152986472 764135196 3818284493
(1 + (loop(\(x,i).((x + 1) + (if (x mod 2) <= 0 then 2 else ((x + ~2) mod (1 + (x div 4))))),x,0) div 2))
A290492: 1 2 3 4 5 6 7 8 9 10 11 12 14
A180643: 1 2 3 4 5 6 7 8 9 10 11 12 14 17 18 22
(1 + (2 * (1 + (if x <= 0 then 1 else (if (x mod (3 * (1 + (x div 5)))) <= 0 then 2 else 0)))))
A120275: 5 3 3 7 3 3 7 3 3 3 3 3 3 3 3 3
(if (x mod 4) <= 0 then 0 else (1 + ((1 + (x mod (~1 + (loop(\(x,i).2x,x,x) mod (x + 1))))) div 2)))
A299485: 0 1 1 1 0 2 2 1 0 2 2 2 0 2 3 1
(1 + (2 * (if x <= 0 then 0 else (1 + ((1 + loop(\(x,i).(2x + 4),(x div 2),(x mod 2))) div 3)))))
A169969: 1 3 5 7 11 13 21 27 43 53 85 107 171 213 341 427
(3 - (if x <= 0 then 1 else ((0 - (x div (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))) div 2)))
A177876: 2 3 3 4
A077603-A077567: 2 3 3 4 3 3 3 5 4 3 3 5 3 3 3 6
(1 + (loop(\(x,i).2x,x,(~1 + loop(\(x,i).(2x + (2x div (1 + (x div 2)))),x,1))) div 2))
A256959: 1 4 19 89 385 1601 6529 26369 105985 424961 1701889 6811649 27254785 109035521 436174849 1744764929
(~1 + (2 * loop(\(x,i).x2,1,(1 + ((x + 1) * loop(\(x,i).(2x2 + 8x + 8),2,0))))))
A157664: 80801 321601 722401 1283201 2004001 2884801 3925601 5126401 6487201 8008001 9688801 11529601 13530401 15691201 18012001 20492801
(~1 + (2 * loop(\(x,i).x2,1,(~1 + ((x + 1) * loop(\(x,i).(2x2 + 8x + 8),2,0))))))
A157661: 79201 318401 717601 1276801 1996001 2875201 3914401 5113601 6472801 7992001 9671201 11510401 13509601 15668801 17988001 20467201
((if x <= 0 then 1 else x) div (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))))
A070777: 1 1 2 1 4 2 6 1 2 4 10 2 12 6 4 1
(~1 + (2 * loop(\(x,i).x2,1,(1 + ((x + 1) * (1 + loop(\(x,i).(x * (x + i)),2,4)))))))
A157741: 390727 1559377 3505951 6230449 9732871 14013217 19071487 24907681 31521799 38913841 47083807 56031697 65757511 76261249 87542911 99602497
(x div (1 + ((if x <= 0 then 2 else (1 + (loop(\(x,i).((x2 + 3x + 2) div 2),2,x) mod (x + 1)))) div 2)))
A331803: 0 1 1 1 2 2 3 1 4 2 5 3 6 6 7 1
(1 + (2 * loop(\(x,i).i,((1 + (x div (1 + ((~1 + loop(\(x,i).2x,x,2)) mod (x + 2))))) div 2),1)))
A076566: 3 3 3 5 3 7 3 3 5 11 3 13 7 5 3 17
(~1 + ((1 + ((~1 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 0 else 2))),x,x)) mod 4)) div 2))
A309048: 1 1 1 0 1 1 0 1 1 ~1 0 0 1 1 1 0
(2 div (1 + ((if x <= 0 then 2 else ((if (~2 + (x div 4)) <= 0 then 1 else 2) * (1 + (x mod 4)))) div 2)))
A115211: 1 1 1 0 2 1 1 0 2 1 1 0 1 0 0 0
(1 + (2 * (3 + loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),2))))
A241679: 11 15 39 135 2055 8199 131079 524295 8388615 536870919 2147483655 137438953479 2199023255559 8796093022215 140737488355335 9007199254740999
(1 + (2 * (3 + (loop(\(x,i).2x,(x div 2),(2 + (x mod 2))) + loop(\(x,i).2x,x,2)))))
A184041: 15 21 31 51 87 159 295 567 1095 2151 4231 8391 16647 33159 66055 131847
(1 + ((3 * ((x + 1) + (loop(\(x,i).3x,x,2) + loop(\(x,i).2x,x,1)))) div 2))
A169877: 7 16 38 100 275
(if x <= 0 then 1 else loop(\(x,i).((2x * (1 + (2 * i))) div (1 + i)),(x + ~1),7))
A146533: 1 7 21 70 245 882 3234 12012 45045 170170 646646 2469012 9464546 36402100 140408100 542911320
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (7x + 1)),x,7)
A271623: 7 50 25 176 88 44 22 11 78 39 274 137 960 480 240 120
(1 + ((1 + ((x + loop(\(x,i).(loop(\(x,i).(x * (2 + i)),i,1) + (x * (i * i))),x,1)) div 2)) div 2))
A320946: 1 2 9 80 1340
(~1 + (2 * (1 + (2 * compr(\x.loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,4x),x)))))
A091113: 1 9 21 25 33 45 49 57 65 69 77 81 85 93 105 117
(x div (1 + (2 * ((2 - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + (2 * i)))),x,x)) mod (x + 3)))))
A030398: 0 1 0 0 0 0 0 1 1 0 0 0 1 1 2 3
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(10x + 3))
A017315: 177147 1792160394037 952809757913927 50542106513726817 929293739471222707 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * (1 + compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(4x + 1))),x))))
A089255: 5 9 11 17 21 23 29 33 39 47 51 53 57 59 71 77
(1 + loop(\(x,i).(3x + 4),(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),2))
A098116: 11 35 323 2915 236195 2125763 172186883 1549681955 125524238435 91507169819843 823564528378595 600378541187996483 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,((((x3 + ~3x2 + 2x) div 3) + loop(\(x,i).2x,x,1)) div 2),1)
A122214: 1 2 4 32 4096 67108864 4503599627370496 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).(1 + (x div (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))),1,(x + 1)) div 2))
A088529: 1 1 2 1 1 1 3 2 1 1 3 1 1 1 4 1
(x mod (1 + (((~2 + loop(\(x,i).2x,(x + (if (~2 + (x div 2)) <= 0 then 1 else 2)),1)) mod (x + 1)) div 2)))
A215486: 0 0 0 1 0 1 0 3 2 1 0 3 0 1 6 7
loop(\(x,i).(x3 + ~x2 + x),1,loop(\(x,i).10x,(2x + 2),1))
A055617: 990100 999900010000 999999000001000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(~2 + i),1)),((x + 1) div 2),1)
A166588: 1 2 2 3 3 5 5 10 10 24 24 66 66 198 198 627
(1 + (if x <= 0 then 0 else loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(x div 2),((x + 1) mod 2))))
A329696: 1 1 2 1 3 1 6 1 15 1 43 1 133 1 430 1
(1 + (2 * compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1))))
A082496: 7 11 23 35 59 83 119 143 203 215 275 299 359 383 395 455
(1 + (compr(\x.(1 - loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1)) div 2))
A040040: 2 3 6 9 15 21 30 36 51 54 69 75 90 96 99 114
(1 + (((x + ~1) * ((x * (1 + loop(\(x,i).(if (x + ~2) <= 0 then 0 else x2),(x div 2),x))) div 2)) div 2))
A326216: 1 1 1 16 772
(if (x mod 2) <= 0 then ((~1 + (7 * ((x + ~1) mod 4))) * (if x <= 0 then 1 else 2)) else 1)
A040417: 20 1 12 1 40 1 12 1 40 1 12 1 40 1 12 1
(if (x mod 2) <= 0 then ((~1 + (7 * (2 - ((x div 2) mod 2)))) * (if x <= 0 then 1 else 2)) else 1)
A010236: 13 1 12 1 26 1 12 1 26 1 12 1 26 1 12 1
(if (x mod 2) <= 0 then ((~1 + (9 * ((x + ~1) mod 4))) * (if x <= 0 then 1 else 2)) else 1)
A040699: 26 1 16 1 52 1 16 1 52 1 16 1 52 1 16 1
(if (x mod 2) <= 0 then ((1 + (9 * ((~x + 2) mod 4))) * (if x <= 0 then 1 else 2)) else 1)
A040370: 19 1 2 1 38 1 2 1 38 1 2 1 38 1 2 1
(if (x mod 2) <= 0 then ((~1 + (9 * (2 - ((x div 2) mod 2)))) * (if x <= 0 then 1 else 2)) else 1)
A040304: 17 1 16 1 34 1 16 1 34 1 16 1 34 1 16 1
(if (x mod 2) <= 0 then ((~1 + (5 * (2 + ((~x + 2) mod 4)))) * (if x <= 0 then 1 else 2)) else 1)
A040378: 19 1 18 1 38 1 18 1 38 1 18 1 38 1 18 1
(if (x mod 2) <= 0 then ((1 + (10 * ((~x + 2) mod 4))) * (if x <= 0 then 1 else 2)) else 1)
A040451: 21 1 2 1 42 1 2 1 42 1 2 1 42 1 2 1
(if (x mod 2) <= 0 then ((~1 + (6 * (2 + ((~x + 2) mod 4)))) * (if x <= 0 then 1 else 2)) else 1)
A040550: 23 1 22 1 46 1 22 1 46 1 22 1 46 1 22 1
(if (x mod 2) <= 0 then ((1 + (12 * (2 - (x mod 4)))) * (if x <= 0 then 1 else 2)) else 1)
A040637: 25 1 2 1 50 1 2 1 50 1 2 1 50 1 2 1
(1 + (((((1 + loop(\(x,i).2x,x,2)) div 3) * (1 + loop(\(x,i).2x,x,1))) div 2) div 2))
A022016: 1 1 4 12 47 174
loop(\(x,i).4x,(x + 1),(~1 + (2 * (~2 + loop(\(x,i).8x,(x + 1),1)))))
A094506: 44 1968 65216 2095872 67103744 2147463168 68719394816 2199022927872 70368742866944 2251799808442368 72057594016956416 2305843009129807872 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (4 * (1 + (4 * (loop(\(x,i).3x,x,2) - loop(\(x,i).2x,x,2))))))
A305861: 5 37 165 613 2085 6757 21285 65893 201765 613477 1856805 5603173 16875045 50756197 152530725 458116453
(3 + ((5 * (x + loop(\(x,i).(x - (if (~2 + (x div 2)) <= 0 then 0 else 1)),2,x))) div 2))
A277600: 3 8 13 18 23 28 30 33 38 43 48 53 58 63 68 73
(1 + (2 * ((3 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),x)) div 2)))
A074938: 1 3 9 13 27 31 37 39 81 85 91 93 109 111 117 121
(1 + ((loop(\(x,i).(x * (2 + i)),compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x),1) div 2) div 2))
A139166: 16 631 4989601 778377601 44460928512001 15205637551104001 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + ((loop(\(x,i).(x * (2 + i)),compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x),1) div 2) div 2))
A139196: 14 629 4989599 778377599 44460928511999 15205637551103999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (4 * compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(4x + ~1)),(x + 1))))
A091236: 15 27 35 39 51 55 63 75 87 91 95 99 111 115 119 123
(1 + (((loop(\(x,i).7x,x,1) + loop(\(x,i).3x,x,1)) div 2) div 2))
A193661: 1 3 15 93 621 4263 29595 206433 1442841 10093323 70633575 494375973 3460454661 24222651183 169556963955 1186893964713
(1 + ((((loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (1 + ((x + 1) div 2))) div 2) div 2) div 2))
A259799-A208447-A047913: 1 1 1 1 1 2 1 1 2 3 1 1 2 4 5 1
(1 + (8 * loop(\(x,i).(8x + loop(\(x,i).3x,i,1)),x,2)))
A295932: 17 153 1289 10521 84809 680409 5449097 43610265 348934601 2791634265 22333546505 178669789209 1429362565193 11434913276121 91479344472713 731834870572953
((loop(\(x,i).5x,x,2) - loop(\(x,i).(2x + 1),x,0)) div 9)
A180928: 0 1 5 27
A084177: 0 1 5 27 137 691 3465 17347 86777 433971 2170025 10850467 54253017 271266451 1356334985 6781680387
((loop(\(x,i).(5x + ~2),x,1) - loop(\(x,i).2x,x,1)) div 9)
A084153: 0 0 1 6 33 170 861 4326 21673 108450 542421 2712446 13562913 67815930 339082381 1695417366
(loop(\(x,i).(x + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),x,x) mod 9)
A283556: 0 2 5 1 8 1 5 4 5 1 3 7 8 4 2 4
(~1 + loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),x,8))
A228698: 7 23 119 839 9239 120119 2042039 38798759 892371479 25878772919 802241960519 29682952539239 1217001054108839 52331045326680119 2459559130353965639 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(12x + 9))
A017639: 31381059609 350277500542221 50542106513726817 1532278301220703125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(~11x + ~9))
A017506: 3486784401 10240000000000 819628286980801 17080198121677824 174887470365513049 1152921504606846976 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(~11x + ~9))
A017508: 282429536481 4096000000000000 787662783788549761 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) div (if ((x + 1) mod (4 + (if (x mod 2) <= 0 then 1 else 8))) <= 0 then 4 else 1))
A001438: 1 2 3 4 1 6 7 8
A235380: 1 2 3 4 1 6 7 8 9 10 11 3 13 14 3 16
((1 + ((if (((if x <= 0 then 2 else x) div (2 + (x mod 2))) mod 2) <= 0 then x else 1) div 3)) mod 5)
A248473: 1 1 1 1 2 1 1 3 3 1 1 1 0 0 1 1
(loop(\(x,i).(x * (x div 2)),1,loop(\(x,i).(10x + 1),x,1)) div 5)
A274766: 0 11 1221 123321 12344321 1234554321 123456654321 12345677654321 1234567887654321 123456789987654321 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).(1 + loop(\(x,i).10x,(1 + i),x)),x,1) div 2) div 5)
A101305: 0 10 10100 101001000 10100100010000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).(2x2 + x),1,loop(\(x,i).(4x + 2),x,2)) div 2) div 5)
A006105: 1 21 357 5797 93093 1490853 23859109 381767589 6108368805 97734250405 1563749404581 25019996065701 400319959420837 6405119440211877 102481911401303973
(if x <= 0 then 1 else (5 * loop(\(x,i).(10x + 2),(x div 2),(x mod 2))))
A328332: 1 5 10 60 110 610 1110 6110 11110 61110 111110 611110 1111110 6111110 11111110 61111110
(loop(\(x,i).(x2 + ~x),1,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 5)
A086937: 0 0 1 0 2 0 0 2 0 2 2 0 2 0 0 0
(loop(\(x,i).(x * (x div 2)),1,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 5)
A051830: 0 0 3 0 1 0 0 1 0 1 1 0 1 0 0 0
(1 + (((x + (loop(\(x,i).(2x + 2),(x + ~2),(1 + loop(\(x,i).2x,x,1))) div 2)) div 2) div 2))
A253927: 1 1 2 4 11 37 136
(loop(\(x,i).2x2,1,(~1 + loop(\(x,i).10x,(x + 1),1))) div 3)
A178633: 54 6534 665334 66653334 6666533334 666665333334 66666653333334 6666666533333334 666666665333333334 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 - ((1 + (loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x) mod 7)) div 3))
A141679: 1 ~1 1 ~1 ~1 1 0 ~1 ~1 1 0 0 ~1 ~1 1 0
(((3 * (if (x mod 2) <= 0 then (if x <= 0 then 1 else 2) else ~1)) mod (1 + (x div 3))) mod 3)
A057594: 0 0 0 1 0 1 0 0 0 1 2 1 1 2 1 0
(3 * loop(\(x,i).2x2,2,(1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))))
A059157: 24 384 24 6144 24 384 24 98304 24 384 24 6144 24 384 24 1572864
((1 + ((1 + loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 6 else 0))),2,x)) div 2)) mod 3)
A003137: 1 2 1 0 1 1 1 2 2 0 2 1 2 2 1 0
((1 + (2 * (if x <= 0 then 1 else (2 * (4x + (if (~2 + (x div 2)) <= 0 then 0 else 1)))))) div 3)
A314133: 1 5 11 16 21 27 33 39 44 49 55 60 65 71 76 81
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (3x + 1)),x,27)
A008884: 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242
((loop(\(x,i).x3,1,loop(\(x,i).(x + (3x * i)),x,1)) div 3) div 3)
A249352: 0 7 2439 2439111 5358727111 21949346247111 150550565908935111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x + (i div 2)),(2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)),1) div 3)
A081115: 2 4 10 14 24 30 44 70 80 114 140 154 184 234 290 310
(((x + 3) * loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,4)) div 3)
A002012: 4 32 200 1120 5880 29568 144144
(((x + 3) * loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,(x + 2))) div 3)
A189769: 2 24 200 1400 8820 51744 288288 1544400 8022300 40646320 201753552 984312784 4732273000 22465296000 105479913600 490481598240
((if x <= 0 then 1 else 6x) - ((1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2))) div 3))
A315536: 1 6 11 17 23 28 33 39 45 50 56 62 67 73 79 84
(((2x + 1) * loop(\(x,i).(x + (if (~4 + (x div 2)) <= 0 then 1 else 2)),4,x)) mod 3)
A029321: 1 0 0 1 0 0 1 0 1 1 0 2 2 0 2 2
(3 * (loop(\(x,i).6x,x,1) - loop(\(x,i).6x,(x div 2),1)))
A320524: 0 15 90 630 3780 23220 139320 839160 5034960 30229200 181375200 1088367840 6530207040 39181942080 235091652480 1410554113920
loop(\(x,i).(2x2 + x),1,(3 * loop(\(x,i).(10x + 1),x,1)))
A319170: 21 2211 222111 22221111 2222211111 222222111111 22222221111111 2222222211111111 222222222111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(3 * loop(\(x,i).((5x2 + ~x) div 2),1,loop(\(x,i).4x,x,1)))
A121544: 6 114 1896 30624 491136 7862784 125822976 2013241344 32212156416 515395682304 8246335635456 131941389041664 2111062300164096 33776997104615424 540431954881806336 4611686018427387903
((loop(\(x,i).(2 * (2x - (3 * (i mod 2)))),x,2) + loop(\(x,i).2x,x,1)) div 3)
A214142: 1 1 4 11 40 147 568 2227 8824 35123 140152 559923 2238328 8950579 35796856 143176499
(1 - (((x + 1) * (1 + (x * (~1 + loop(\(x,i).loop(\(x,i).(x * i),i,x),x,~x))))) div 3))
A060595: 1 2 10 148 7686
(x - ((x - (if x <= 0 then 1 else (loop(\(x,i).(x2 + ~x),2,4x) mod (x + 1)))) div 3))
A140859: 1 1 2 2 3 4 5 6 6 6 9 10 9
((if (x mod 4) <= 0 then (x div (1 + (if (x mod 3) <= 0 then 2 else 0))) else 0) * ((x + 1) div 3))
A264769: 0 0 0 0 4 0 0 0 24 0 0 0 16 0 0 0
(loop(\(x,i).x2,1,((2x + 2) div loop(\(x,i).(x div (~2 + (x mod 2))),x,(x + 1)))) div 3)
A296306: 1 5 1 21 1 5 1 85 1 5 1 21 1 5 1 341
((2 + loop(\(x,i).(x div (2 - (x mod 2))),x,(x div (1 + (if (x mod 3) <= 0 then 2 else 0))))) div 3)
A126760: 0 1 1 1 1 2 1 3 1 1 2 4 1 5 3 2
((2 + ((1 + loop(\(x,i).(x * (1 + (if (i mod 2) <= 0 then 4 else 1))),x,1)) div 3)) div 3)
A081857: 0 1 1 3 11 23 111 223 1111 2223 11111 22223 111111 222223 1111111 2222223
(3 * (2 + (loop(\(x,i).3x,x,3) + loop(\(x,i).2x,(x + 2),3))))
A235878: 51 105 231 537 1311 3345 8871 24297 68271 195585 568311 1668057 4930431 14643825 43636551 130319817
(6 * compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(4x + ~1)),(x + 1)))
A162886: 24 42 54 60 78 84 96 114 132 138 144 150 168 174 180 186
((2 + loop(\(x,i).loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),(x + ~2),x),1,(x + 1))) mod 3)
A122807: 0 1 1 2 1 2 1 0 2 0 1 2 1 0 2 0
((1 - ((loop(\(x,i).2x,x,(2 + (if (x mod 4) <= 0 then 2 else 0))) mod (x + 1)) div 2)) mod 3)
A113414: 1 1 0 1 2 2 0 1 1 2 0 2 2 2 0 1
((2 * (loop(\(x,i).2x,((loop(\(x,i).(x * i),x,2) mod (x + 1)) div 2),2) mod (x + 1))) mod 3)
A319395: 0 0 1 1 2 1 2 1 1 1 2 1 0 1 1 1
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(7x + 5))
A017051: 48828125 743008370688 116490258898219 3670344486987776 50542106513726817 419430400000000000 2472159215084012303 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).3x,x,1) - loop(\(x,i).3x,(x div 2),((x + 1) mod 2))) div 3)
A122006: 0 1 2 9 24 81 234 729 2160 6561 19602 59049 176904 531441 1593594 4782969
((2 * (2 + (if x <= 0 then 1 else loop(\(x,i).(x + i - ((x + 1) div 5)),x,0)))) div 3)
A077075: 2 2 3 5 7 9 12 14 17 20 23 26 30 33 36 40
((2 + ((loop(\(x,i).(x - (x div (~2 + (x mod 2)))),x,2) + loop(\(x,i).2x,x,1)) div 2)) div 3)
A036557: 1 1 2 3 6 10 20 35 70 126 252 463 926 1730 3460 6555
(12 + (loop(\(x,i).2x,(x div 2),(2 + (x mod 2))) + loop(\(x,i).2x,x,1)))
A183981: 15 17 20 26 36 56 92 164 300 572 1100 2156 4236 8396 16652 33164
loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),x,12)
A001041: 12 24 72 360 2520 27720 360360 6126120 116396280 2677114440 77636318760 2406725881560 89048857617720 3651003162326520 156993135980040360 4611686018427387903
(3 * (loop(\(x,i).((x + 1) * loop(\(x,i).5x2,2,2x)),x,2) div 2))
A306594: 3 144000 4611686018427387903 4611686018427387903
((2 * loop(\(x,i).(9x + (if (i mod 3) <= 0 then 2 else 0)),x,2)) div 3)
A037602: 1 12 108 973 8760 78840 709561 6386052 57474468 517270213 4655431920 41898887280 377089985521 3393809869692 30544288827228 274898599445053
((loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x))) div 2) div 3)
A084922: 4 8 20 28 48 60 88 140 160 228 280 308 368 468 580 620
loop(\(x,i).3x,(2 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))),3)
A100627: 243 2187 177147 14348907 94143178827 7625597484987 50031545098999707 4052555153018976267 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).2x,x,(loop(\(x,i).2x,x,3) mod (x + 2))) mod (x + 4)) mod 3)
A239003: 1 0 0 1 0 1 0 0 2 0 0 1 0 2 0 0
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(11x + 1))
A017411: 1 743008370688 952809757913927 70188843638032384 1532278301220703125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(11x + 2))
A017423: 2048 1792160394037 1521681143169024 96549157373046875 1951354384207722496 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((if x <= 0 then 0 else (if x <= 0 then 1 else (2 + ((x + 2) div 7)))) + ((x div 2) div 3))
A029551: 0 2 2 2 2 3 4 4 4 4 4 4 6 6 6 6
loop(\(x,i).~x,x,(1 - (compr(\x.(if (x mod 2) <= 0 then ((x div 3) mod 3) else 0),x) mod 3)))
A089045: 1 0 ~1 ~1 ~1 0 1 0 ~1 0 1 1 1 0 ~1 ~1
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (25x + 1)),x,3)
A037110: 3 76 38 19 476 238 119 2976 1488 744 372 186 93 2326 1163 29076
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (27x + 1)),x,3)
A037111: 3 82 41 1108 554 277 7480 3740 1870 935 25246 12623 340822 170411 4601098 2300549
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (21x + 1)),x,3)
A037108: 3 64 32 16 8 4 2 1 22 11 232 116 58 29 610 305
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (19x + 1)),x,3)
A037107: 3 58 29 552 276 138 69 1312 656 328 164 82 41 780 390 195
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (23x + 1)),x,3)
A037109: 3 70 35 806 403 9270 4635 106606 53303 1225970 612985 14098656 7049328 3524664 1762332 881166
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (33x + 1)),x,3)
A037114: 3 100 50 25 826 413 13630 6815 224896 112448 56224 28112 14056 7028 3514 1757
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (31x + 1)),x,3)
A037113: 3 94 47 1458 729 22600 11300 5650 2825 87576 43788 21894 10947 339358 169679 5260050
loop(\(x,i).(x3 + ~x2),1,(3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A178398: 18 48 180 448 1584 2548 5508 7600 13248 26100 31744 53428 72324 83248 108288 154548
(loop(\(x,i).7x,x,4) - loop(\(x,i).5x,x,3))
A081033: 1 13 121 997 7729 57853 423721 3059797 21887329 155555053 1100604121 7762822597 54632726929 383893932253 2694581744521 18898693305397
(1 + (2 * ((x + 1) + (((x + 1) + (loop(\(x,i).(loop(\(x,i).(x * i),x,i) + i),x,0) div 2)) div 2))))
A172291: 3 7 13 1093
(1 + (2 * compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(3x + 1)),x)))
A125164: 11 21 25 31 39 41 47 51 53 61 67 69 71 73 81 91
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(10x + 7))
A017363: 1977326743 34271896307633 5559060566555523 177917621779460413 2472159215084012303 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (2 * compr(\x.(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then x else 5)),x,x)),x)))
A209839: 1 3 7 13 15 21 25 27 31 37 43 45 51 55 57 63
(x div (1 + (2 * loop(\(x,i).(1 + (x mod (1 + ((if (x mod 3) <= 0 then 0 else 2) * (1 + i))))),2,x))))
A262436: 0 0 0 0 0 1 1 2 0 1 2 1 2 1 1 3
loop(\(x,i).7x,(2 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x)),1)
A269327: 49 343 16807 823543 1977326743 96889010407 232630513987207 11398895185373143 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x3 + x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A181151: 13 37 151 393 1453 2367 5203 7221 12697 25231 30753 52023 70603 81357 106033 151687
(1 + loop(\(x,i).(x3 + x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A181150: 11 31 131 351 1343 2211 4931 6879 12191 24419 29823 50691 68963 79551 103871 148931
(2 - loop(\(x,i).((2x + ~4) + i),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1))
A243139: 6 11 37 135 2059 8205 131089 524307 8388631 536870941 2147483679 137438953509 2199023255593 8796093022251 140737488355375 9007199254741045
(loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x div 2),1) div (1 + ((x * (x mod 2)) div 2)))
A089849: 1 1 2 1 6 2 20 5 70 14 252 42 924 132 3432 429
loop(\(x,i).10x,x,loop(\(x,i).(10x + 1),2x,1))
A147589: 1 1110 1111100 1111111000 1111111110000 1111111111100000 1111111111111000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div (2 - (x mod 2))),x,loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),2x,1))
A063079: 1 5 63 429 12155 88179 1300075 9694845 583401555 4418157975 67282234305 514589420475 15801325804719 121683714103007 1879204156221315 14544636039226909
loop(\(x,i).(x div (2 - (x mod 2))),x,loop(\(x,i).((2 * (x - (2x * i))) div (1 + i)),2x,1))
A001795: 1 1 7 33 715 4199 52003 334305 17678835 119409675 1641030105 11435320455 322476036831 2295919134019 32968493968795 238436656380769
loop(\(x,i).(10x + (if ((x + 1) mod 8) <= 0 then 0 else 1)),2x,1)
A265688: 1 111 11101 1110111 111011101 11101110111 1110111011101 111011101110111 11101110111011101 1110111011101110111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((2x + 1) * (1 + (2 * compr(\x.loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,2x),x))))
A163506: 1 27 75 147 225 297 429 525 663 855 1029 1173 1375 1539 1827 2015
((1 + (2 * compr(\x.loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,2x),x))) mod (2x + 1))
A163505: 0 0 0 0 7 5 7 5 5 7 7 5 5 3 5 3
((x + loop(\(x,i).(x + (6x div (if i <= 0 then 1 else i))),2x,1)) div (2x + 1))
A000971: 1 9 42 132 334 728 1428 2584 4389 7084 10963 16380 23751 33563 46376 62832
loop(\(x,i).x2,1,(if (~x + 2) <= 0 then (1 + (((x mod (1 + (x div 4))) div 2) + (x mod 2))) else 1))
A330571: 1 1 1 4 1 4 1 4 4 4 1 9 1 4 4 9
loop(\(x,i).i,((x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))) - (x mod 2)),1)
A319694: 1 1 1 1 1 1 1 2 2 1 1 2 1 1 2 6
(((if (x mod 3) <= 0 then 13 else 1) * (if x <= 0 then 1 else 2)) div (1 + (x mod 2)))
A010229: 13 1 2 13 2 1 26 1 2 13 2 1 26 1 2 13
(((1 + (if (x mod 3) <= 0 then 10 else 1)) * (if x <= 0 then 1 else 2)) div (1 + (x mod 2)))
A010191: 11 2 4 11 4 2 22 2 4 11 4 2 22 2 4 11
((2x + ~1) + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (1 + (x mod 2))))),x,(x + 1)) - (x mod 2))
A093050: 0 0 3 2 6 4 7 6 11 8 11 10 14 12 15 14
loop(\(x,i).(10x - loop(\(x,i).(10x + 1),i,0)),x,1)
A294344: 1 9 79 679 5679 45679 345679 2345679 12345679 12345679 ~987654321 ~20987654321 ~320987654321 ~4320987654321 ~54320987654321 ~654320987654321
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (35x + 1)),x,1)
A033973: 1 36 18 9 316 158 79 2766 1383 48406 24203 847106 423553 14824356 7412178 3706089
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (45x + 1)),x,1)
A033978: 1 46 23 1036 518 259 11656 5828 2914 1457 65566 32783 1475236 737618 368809 16596406
(1 + compr(\x.(~1 + ((1 + compr(\x.loop(\(x,i).(x - (if (x mod (2 + i)) <= 0 then 0 else 1)),x,x),x)) mod 3)),x))
A091177: 1 3 5 7 9 10 13 15 16 17 20 23 24 26 28 30
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (39x + 1)),x,1)
A033975: 1 40 20 10 5 196 98 49 1912 956 478 239 9322 4661 181780 90890
(1 + compr(\x.(~1 + (compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x) mod 3)),x))
A138969: 1 2 4 6 8 9 12 14 15 16 19 22 23 25 27 29
loop(\(x,i).5x,compr(\x.(~1 + (loop(\(x,i).4x,x,1) mod (2x + 1))),x),1)
A062875: 1 5 25 125 3125 15625 390625 1953125 48828125 6103515625 30517578125 3814697265625 95367431640625 476837158203125 11920928955078125 1490116119384765625
(if x <= 0 then 1 else (1 + compr(\x.(1 - (x mod (1 + (loop(\(x,i).(3x + 2),x,0) mod (x + 1))))),x)))
A195101: 1 6 8 9 12 14 15 16 18 20 21 24 26 27 30 32
(1 + compr(\x.(~1 + (loop(\(x,i).(2x + 2),x,2) mod loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))),x))
A241071: 1 2 4 6 8 10 12
A090778: 1 2 4 6 8 10 12 16 18 20 24 32 36 40 42 48
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (29x + 1)),x,1)
A033971: 1 30 15 436 218 109 3162 1581 45850 22925 664826 332413 9639978 4819989 139779682 69889841
loop(\(x,i).((2x + 2) - (if ((x + 1) mod (4 + (x mod (2 + (x mod 2))))) <= 0 then 2 else 1)),x,1)
A112306: 1 3 6 13 27 54 109 218 437 874 1749 3499 6998 13997 27994 55989
(if x <= 0 then 0 else ((x + 1) + (9 * loop(\(x,i).i,(x + ~9),1))))
A216589: 0 11 12 13 14 15 16 17 18 19 20 30 40 50 60 70
loop(\(x,i).(9 * (x + (7x div (if i <= 0 then 1 else i)))),x,1)
A173192: 1 72 2916 87480 2165130 46766808 911952756 16415149608 277005649635 4432090394160 67810983030648 998670840996816 14231059484204628 197045439012064080 2660113426662865080 4611686018427387903
loop(\(x,i).((9x + 1) + (if (~2 + (x div 5)) <= 0 then 1 else x)),x,1)
A290112: 1 11 101 1011 10111 101111 1011111 10111111 101111111 1011111111 10111111111 101111111111 1011111111111 10111111111111 101111111111111 1011111111111111
loop(\(x,i).(loop(\(x,i).((x2 + ~x) div 2),2,(x + 2)) div 3),1,(5x + 1))
A151989: 1 126 1001 3876 10626 23751 46376 82251 135751 211876 316251 455126 635376 864501 1150626 1502501
(1 + compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(4x + 1))),x))
A005125: 1 2 4 5 7 8 13 14 19 20 22 23 25 29 34 35
loop(\(x,i).((2x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i))) * (1 + ((x div 2) mod 2))),x,1)
A257546: 1 1 2 6 24 40 80 140 280 504 1008 1848 3696 6864 13728 25740
(1 + compr(\x.((1 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x)) mod 3),x))
A138968: 3 5 7 10 11 13 17 18 20 21 24 26 28 30 33 35
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (47x + 1)),x,1)
A033979: 1 48 24 12 6 3 142 71 3338 1669 78444 39222 19611 921718 460859 21660374
loop(\(x,i).(12x + loop(\(x,i).(9x + 1),i,1)),x,1)
A016263: 1 22 355 5080 68341 886522 11236135 140214460 1731001081 21207861022 258416964715 3136307268640 37953420452221 458300644483522 5525344125314095 66535757027375620
loop(\(x,i).(12x + loop(\(x,i).(10x + 1),i,1)),x,1)
A016267: 1 23 387 5755 80171 1073163 13989067 178979915 2258870091 28217552203 349721737547 4307771961675 52804374651211 644763606925643 7848274394218827 95290403841737035
loop(\(x,i).(12x + loop(\(x,i).(7x + 1),i,1)),x,1)
A016255: 1 20 297 3964 50369 624036 7625689 92469068 1116354417 13443332212 161649541001 1942101373212 23321364646945 279969412942148 3360424215557433 40330629408450796
loop(\(x,i).(6x + loop(\(x,i).(11x + 1),i,1)),x,1)
A016247: 1 18 241 2910 33565 378546 4219993 46755846 516329845 5691721530 62681496241 689931815118 7591862105101 83526155988930 918881752875145 10108263503608086
loop(\(x,i).(6x + loop(\(x,i).(8x + (x mod 3)),i,1)),x,1)
A081034: 1 15 162 1548 13896 120240 1016352 8457408 69618816 568707840 4620206592 37384915968 301618907136 2428188733440 19516934725632 156684026953728
loop(\(x,i).(7x + loop(\(x,i).(9x + 1),i,1)),x,1)
A016250: 1 17 210 2290 23411 230307 2210020 20850980 194384421 1796538997 16498405430 150792530070 1373280939031 12472565630087 113044350922440 1022937980063560
loop(\(x,i).(7x + loop(\(x,i).(10x + 1),i,1)),x,1)
A016252: 1 18 237 2770 30501 324618 3383437 34795170 354677301 3593852218 36268076637 364987647570 3666024644101 36773283619818 368524096449837 3690779786259970
loop(\(x,i).(7x + loop(\(x,i).11x,i,1)),x,1)
A016183: 1 18 247 3060 36061 413478 4665907 52148520 579398521 6413737338 70833585967 781146772380 8606455783381 94767902627598 1043125151976427 11479124233250640
loop(\(x,i).(9x + loop(\(x,i).(10x + 1),i,1)),x,1)
A016261: 1 20 291 3730 44681 513240 5730271 62683550 675263061 7188478660 75807419051 793377882570 8251512054241 85374719599280 879483587504631 9026463398652790
(1 + compr(\x.(2 - ((~1 + loop(\(x,i).2x,x,2)) mod (1 + (if (~1 + (x mod 3)) <= 0 then x else 2)))),x))
A157695: 4 8 10 14 16 20 22 25 26 28 32 34 35 38 40 44
loop(\(x,i).10x,2x,loop(\(x,i).(10x + 1),x,1))
A147816: 1 1100 1110000 1111000000 1111100000000 1111110000000000 1111111000000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((2x + 1) + ((~1 + loop(\(x,i).2x,(2 + (x mod 2)),(x div 2))) div (x + 2))),x,1)
A290198: 1 2 5 13 30 62 126 254 510 1022 2046 4094 8190 16382 32766 65534
loop(\(x,i).(x * (1 + (2 * i))),2x,loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1))
A290819: 1 45 9450 4729725 4341887550 6352181485650 13566444744352500 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * ((2x - (x div (if i <= 0 then 1 else i))) * (~1 + (2 * i)) * (~1 + (2 * i)))),x,1)
A283678: 1 2 54 4500 771750 225042300 99843767100 62673358948200 52880646612543750 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (41x + 1)),x,1)
A033976: 1 42 21 862 431 17672 8836 4418 2209 90570 45285 1856686 928343 38062064 19031032 9515516
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (37x + 1)),x,1)
A033974: 1 38 19 704 352 176 88 44 22 11 408 204 102 51 1888 944
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (49x + 1)),x,1)
A033980: 1 50 25 1226 613 30038 15019 735932 367966 183983 9015168 4507584 2253792 1126896 563448 281724
(loop(\(x,i).(10x + 2),x,2) - loop(\(x,i).(5x + 1),x,1))
A016237: 1 16 191 2066 21441 218316 2202691 22124566 221733941 2219780816 22210015191 222161187066 2221917046441 22220696343316 222214592827691 2222184075249566
(1 + compr(\x.(loop(\(x,i).(2x + 2),x,(if ((x + 2) mod 5) <= 0 then 1 else 0)) mod (x + 1)),x))
A143390: 1 2 3 5 7 11 13 17 23 31 37 41 43 47 53 61
(if (x div 4) <= 0 then (x + 3) else (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x)))
A137922: 3 4 5 6 7 11 13 17 19 23 29 31 37 41 43 47
(1 + compr(\x.(loop(\(x,i).4x,1,(~1 + loop(\(x,i).~4x,x,1))) mod (x + 1)),x))
A123091: 1 2 3 4 5 7 10 11 13 15 17 19 20 23 29 31
(1 + compr(\x.(2 - ((~1 + loop(\(x,i).2x,loop(\(x,i).(x div (1 + (x mod 2))),x,x),2)) mod (x + 1))),x))
A119486: 9 12 15 18 20 21 24 25 27 28 30 33
(1 + compr(\x.(loop(\(x,i).(x2 + x),1,(loop(\(x,i).(2 * (x - i)),x,2) mod (x + 1))) mod (x + 1)),x))
A187731: 1 2 3 5 7 11 13 15 17 19 23 29 31 37 41 43
(1 + compr(\x.(loop(\(x,i).(2x + 2),x,(loop(\(x,i).(2 * (x - i)),x,2) mod (x + 1))) mod (x + 1)),x))
A325623: 1 2 3 5 7 9 11 13 17 19 23 25 29 31 37 41
loop(\(x,i).((x2 + ~x) div 2),1,(1 + compr(\x.(loop(\(x,i).(x * (1 + (i div 2))),x,1) mod (x + 1)),x)))
A161777: 0 6 15 28 36 45 66 91 105 120 153 190 210 231 276 300
loop(\(x,i).x2,1,(1 + compr(\x.(loop(\(x,i).x2,2,(4 * (2 + (x mod 2)))) mod (x + 1)),x)))
A063755: 1 4 16 36 64 144 256 324 576 1024 1296 2304 2916 4096 5184 9216
(1 + compr(\x.(loop(\(x,i).(x * (2 + (x * loop(\(x,i).(2x2 + x),2,2)))),2,x) mod (x + 1)),x))
A222011: 1 2 4 8
A018442: 1 2 4 8 13 16 26 32 52 104 208 416
loop(\(x,i).((x + 1) + loop(\(x,i).(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1,i)),x,1)
A097911: 1 3 5 8
A330038: 1 3 5 8 10 13 16 20 22 25 28 32 35 39 43 48
loop(\(x,i).((4 * ((2x - (x div (if i <= 0 then 1 else i))) * (1 + (2 * i)))) div (1 + i)),x,1)
A000894: 1 6 60 700 8820 116424 1585584 22084920 312869700 4491418360 65166397296 953799087696 14062422446800 208618354980000 3111393751416000 46619049708716400
loop(\(x,i).(2 * ((x + 1) - ((x div (1 + (if (x mod 2) <= 0 then 6 else 1))) mod 3))),x,1)
A168673: 1 4 10 20 38 74 148 298 598 1196 2390 4778 9556 19114 38230 76460
(1 + compr(\x.((x - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x + 1))) mod 2),x))
A124934: 2 5 8 11 12 14 17 19 20 23 26 29 30 32 33 35
((x + ~1) + (2 * ((1 + ((if (x div 2) <= 0 then 1 else ((if (x mod 2) <= 0 then 2 else x) div 2)) mod 4)) div 2)))
A199426: 1 2 3 4 5 6 7 10 9 8 11 12 13 14 15 18
loop(\(x,i).(2 * ((1 + (((x + 2) * (if (x + ~2) <= 0 then x else (x + 5))) div 2)) div 2)),x,1)
A248872: 1 2 4 28 496
loop(\(x,i).(8x + loop(\(x,i).~9x,(~1 + i),1)),x,1)
A165510: 1 9 63 585 3951 38169 246303 2501865 15231951 164902329 931798143 10941169545 56148296751 731615910489 3311061455583 49365284099625
loop(\(x,i).(8x + loop(\(x,i).(11x + 1),i,1)),x,1)
A016259: 1 20 293 3808 46569 549708 6346381 72206936 813450257 9101344516 101341923189 1124578223184 12448896999865 137566159357244 1518254091799517 16741005720753352
loop(\(x,i).(4x + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),i,(1 + i))),x,1)
A029760: 1 8 47 244 1186 5536 25147 112028 491870 2135440 9188406 39249768 166656772 704069248 2961699667 12412521388
((x + 1) + (if x <= 0 then 1 else (4x + ((x div (if (x mod 4) <= 0 then 4 else 1)) mod 2))))
A297469: 2 7 11 17 22 27 31 37 41 47 51 57 62 67 71 77
(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,(x + 2)) - loop(\(x,i).4x,x,1))
A112613: 1 5 24
A296770: 1 5 24 111 500 2210 9632 41531 177564 754014 3184016 13382710 56026984 233765636 972504704 4035441491
loop(\(x,i).(5x + loop(\(x,i).(11x + 1),i,1)),x,1)
A016238: 1 17 218 2554 28875 321531 3556372 39217748 431883509 4753160005 52296967086 575327673102 6328909579903 69619531257839 765822473230760 8424085352511016
loop(\(x,i).(5x + loop(\(x,i).(2 * (2x - (x div (1 + i)))),(~1 + i),2)),x,1)
A144635: 1 7 41 225 1195 6227 32059 163727 831505 4206145 21215481 106782837 536618341 2693492305 13507578125 67693008145
loop(\(x,i).(4x + (34x div (if i <= 0 then 2 else i))),x,1)
A020930: 1 38 798 12236 152950 1651860 15967980 141430680 1166803110 9075135300 67156001220 476197099560 3254013513660 21526550936520 138384970306200 867212480585520
(loop(\(x,i).15x,x,1) mod loop(\(x,i).10x,x,1))
A204544: 0 5 25 375 625 59375 390625 859375 62890625 443359375 6650390625 49755859375 746337890625 6195068359375 92926025390625 893890380859375
(loop(\(x,i).11x,x,1) + loop(\(x,i).10x,x,1))
A155872: 2 21 221 2331 24641 261051 2771561 29487171 314358881 3357947691 35937424601 385311670611 4138428376721 44522712143931 479749833583241 5177248169415651
(loop(\(x,i).11x,x,1) - loop(\(x,i).10x,x,1))
A016195: 0 1 21 331 4641 61051 771561 9487171 114358881 1357947691 15937424601 185311670611 2138428376721 24522712143931 279749833583241 3177248169415651
(loop(\(x,i).11x,x,1) mod loop(\(x,i).10x,x,1))
A091947: 0 1 21 331 4641 61051 771561 9487171 14358881 357947691 5937424601 85311670611 138428376721 4522712143931 79749833583241 177248169415651
loop(\(x,i).(10x + 1),(x + 2),loop(\(x,i).10x,x,1))
A244663: 111 10111 1001111 100011111 10000111111 1000001111111 100000011111111 10000000111111111 1000000001111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,10x)),x))
A024913: 1 2 3 5 6 8 9 11 12 17 18 20 23 24 27 29
(loop(\(x,i).3x,x,1) - loop(\(x,i).2x,(x + ((x + ((x div 2) div 3)) div 2)),1))
A056577: 0 1 1 11 17 115 217 139 2465 3299 26281 46075 7153 545747 588665 5960299
loop(\(x,i).(x - (2 * (x + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(~2 + i),1)))),x,1)
A181641: 1 ~3 1 ~5 ~5 ~23 ~61 ~203 ~655 ~2205 ~7519 ~26073 ~91499 ~324525 ~1161275 ~4187605
loop(\(x,i).(x + (loop(\(x,i).(2x * (~1 + (2 * i))),i,1) + (2x * (1 + (2 * i))))),x,1)
A143167: 1 9 111 1785 35595 848925 23586255 748471185 26715409875 1059544210725 46230843633975 2201008238854425 113546715232225275 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x7 + x6 + x5 + x4 + x3 + x2 + x + 1),1,loop(\(x,i).2x,x,1))
A034674: 8 255 21845 2396745 286331153 35468117025 4467856773185 567382630219905 72340172838076673 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(((((x2 div 2) mod 3) + loop(\(x,i).2x,x,1)) div 3) + loop(\(x,i).2x,x,1))
A083322: 1 2 6 11 22 42 85 170 342 683 1366 2730 5461 10922 21846 43691
(loop(\(x,i).(x + ((x + ((x * i) div (1 + i))) * i * (~1 + i))),x,1) + loop(\(x,i).2x,x,1))
A201363: 2 3 7
A119662: 2 3 7 41 757
loop(\(x,i).(6x + ((if (x div 2) <= 0 then 2 else 5x) + (x mod 2))),x,1)
A056002: 1 9 100 1100 12100 133100 1464100 16105100 177156100 1948717100 21435888100 235794769100 2593742460100 28531167061100 313842837672100 3452271214393100
loop(\(x,i).(x * ((1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)) * (2 - (x mod 2)))),x,1)
A303557: 1 2 12 120 1680 36960 960960 32672640 1241560320 57111774720 3312482933760 205373941893120 15197671700090880 1246209079407452160 4611686018427387903 4611686018427387903
(loop(\(x,i).4x,x,4) - loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,1))
A038679: 3 14 59 242 982 3964 15955 64106 257282 1031780 4135518 16569204 66365964 265761016 1064046979 4259609626
((1 + ((~2x + 1) mod loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1))) div (x + 1))
A289653: 1 1 1 4 12 40 130 427 1428 4860 16794 58784 208010 742898 2674438 9694843
loop(\(x,i).(if x <= 0 then 1 else (x - (x div (11 - (x div 2))))),3,(x + 1))
A132125: 1 2 3 4 5 6 7 7 7 7 8 8 9 9 9 9
compr(\x.(x mod (1 + (2 * (x mod loop(\(x,i).(1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),2,x))))),(x + 1))
A034884: 2 3 4 6 8 10 12 14 15 16 18 20 24 28 30 32
loop(\(x,i).((x2 + x) div 2),1,((x + 1) * loop(\(x,i).(10x + 1),x,1)))
A077695: 1 253 55611 9876790 1543206790 222222111111 30246911419753 3950617249382716 499999999500000000 4611686018427387903 4611686018427387903
((x + 1) * loop(\(x,i).x3,1,loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1)))
A186414: 1 2 24 500 13720 444528 16099776 631628712 26317863000 1149330319280 52120705189696 2437827529099872 117006104720150464 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).4x,(x + ~2),((1 + loop(\(x,i).10x,x,x)) div (x + 1)))
A291807: 1 5 67 3000
((x + 1) + ((if x <= 0 then 2 else (x + (if (x mod 2) <= 0 then 1 else (~x + ~1)) - (x div 3))) div 2))
A054082: 2 1 4 3 7 5 9 6 12 8 15 10 17 11 20 13
((x + 1) * (((x + 1) * loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,(x + 2))) div 2))
A259455: 1 30 270 1400 5250 15876 41160 95040 200475 393250 726726 1277640 2153060 3498600 5508000 8434176
loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),8,(x + 1))
A147575: 9699690 19399380 29099070 38798760 48498450 58198140 67897830 77597520 87297210 96996900 106696590 116396280 126095970 135795660 145495350 155195040
(loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,1) + ((x + 1) * ((x2 + x) div 2)))
A008779: 1 7 24 59 120 216 357 554 819 1165 1606 2157 2834 3654 4635 5796
((x + 1) * (loop(\(x,i).4x,x,2) - loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,2)))
A018217: 0 4 36 232 1300 6744 33320 159184 742068 3395320 15308920 68213424 300999816 1317415792 5726300880 24742452128
((2x + 2) * loop(\(x,i).(x + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),(x + 2),x))
A177082: 6 32 90 208 390 672 1050 1568 2286 3160 4290 5664 7254 9128 11370 14016
((x2 + 3x + 3) + (loop(\(x,i).3x,x,3) + loop(\(x,i).2x,x,2)))
A169878: 8 20 48 118 306
(2x mod (x - loop(\(x,i).(x - (if x <= 0 then 1 else (11 * i))),2,(x + 1))))
A004521: 0 2 4 6 8 10 1 3 5 7 9 22 24 26 28 30
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,7x),(x + 1))
A153307: 3 6 8 9 10 12 13 15 18 21 23 24 27 28 30 31
((x + 1) div loop(\(x,i).(x * (2 - (x mod 4))),1,loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))
A055975: 1 2 ~1 4 1 ~2 ~1 8 1 2 ~1 ~4 1 ~2 ~1 16
loop(\(x,i).(x div (2 - (x mod 2))),x,compr(\x.loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,x),(x + 1)))
A207873: 1 1 1 5 1 9 5 1 17 9 5 21 1 33 17 9
((1 + ((2x + 2) div 5)) div (1 + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)))
A194543: 1 1 1 2 1 1 3 2 1 1 5 2 2 1 1 7
loop(\(x,i).(x + (if (x mod 9) <= 0 then (9x + 9) else 1)),x,1)
A239138: 1 2 3 4 5 6 7 8 9 99 999 9999 99999 999999 9999999 99999999
(loop(\(x,i).12x,x,1) - loop(\(x,i).11x,x,1))
A016197: 0 1 23 397 6095 87781 1214423 16344637 215622815 2801832661 35979939623 457696700077 5777672071535 72470493235141 904168630965623 11229773405170717
(loop(\(x,i).12x,x,1) mod loop(\(x,i).11x,x,1))
A245805: 0 1 23 397 6095 87781 1214423 16344637 1263934 443884970 10042515022 172385029466 2639243694814 3425068947279 144668963799141 2875277066339415
(loop(\(x,i).11x,x,1) - loop(\(x,i).7x,x,1))
A139745: 0 4 72 988 12240 144244 1653912 18663628 208594080 2317594084 25654949352 283334343868 3124587089520 34425823133524 379071610510392 4172500607905708
(2x + loop(\(x,i).7x,x,1) - loop(\(x,i).5x,x,1))
A121203: 0 4 28 224 1784 13692 102036 745432 5374192 38400500 272709644 1928498640 13597146600 95668307308 672119557252 4717043931848
(~2x + (loop(\(x,i).5x,x,1) + loop(\(x,i).7x,x,1)))
A121201: 2 10 70 462 3018 19922 133262 901654 6155410 42306714 292240854 2026154846 14085427802 98109713506 684326588446 4778079088038
(loop(\(x,i).7x,(x + ~1),x) + loop(\(x,i).7x,x,1))
A081107: 1 8 63 490 3773 28812 218491 1647086 12353145 92236816 686011319 5084554482 37569208117 276825744020 2034669218547 14920907602678
(8x + loop(\(x,i).5x,x,1) - loop(\(x,i).3x,x,1))
A120969: 0 10 32 122 576 2922 14944 75994 384128 1933514 9706656 48651066 243609280 1219108906 6098732768 30503229338
(2x + (loop(\(x,i).7x,x,1) + loop(\(x,i).5x,x,1)))
A121200: 2 14 78 474 3034 19942 133286 901682 6155442 42306750 292240894 2026154890 14085427850 98109713558 684326588502 4778079088098
(~2x + loop(\(x,i).7x,x,1) - loop(\(x,i).5x,x,1))
A121204: 0 0 20 212 1768 13672 102012 745404 5374160 38400464 272709604 1928498596 13597146552 95668307256 672119557196 4717043931788
loop(\(x,i).((x + 1) + ((x + (if ((x mod 5) mod 2) <= 0 then 1 else (x mod 3))) mod 2)),x,1)
A229785: 1 2 4 6 7 8 9 10 12 14 16 18 19 20 22 24
loop(\(x,i).(x + loop(\(x,i).(5 * ((2x * (~1 + (2 * i))) div (1 + i))),i,1)),x,1)
A112699: 1 6 56 681 9431 140681 2203181 35718806 594312556 10090406306 174113843806 3044524000056 53828703687556 960689055250056 17284175383375056 313147365080640681
loop(\(x,i).(x + loop(\(x,i).(3 * ((4x * (~1 + (2 * i))) div (1 + i))),i,1)),x,1)
A112700: 1 7 79 1159 19303 345895 6504487 126597031 2528447911 51526205863 1067116097959 22394503831975 475191351108007 10177980935594407 219758235960500647 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(2 * ((8x * (~1 + (2 * i))) div (1 + i))),i,1)),x,1)
A112702: 1 9 137 2697 60041 1436297 36039305 935717513 24927136393 677493729929 18712061405833 523679956331145 14818155751139977 423231749888535177 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (2 * (x - loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(~2 + i),1)))),x,1)
A137720: 1 1 1 ~1 ~13 ~67 ~285 ~1119 ~4215 ~15505 ~56239 ~202309 ~724499 ~2589521 ~9254363 ~33111969
((4x + ~1) + (if x <= 0 then 2 else loop(\(x,i).(x - (x div 12)),2,x)))
A313117: 1 4 9 14 19 24 29 34 39 44 49 54 58 62 67 72
loop(\(x,i).(x + (63x div (if i <= 0 then 1 else i))),x,1)
A017727: 1 64 2080 45760 766480 10424128 119877472 1198774720 10639125640 85113005120 621324937376 4179822305984 26123889412400 152724276564800 839983521106400 4367914309753280
loop(\(x,i).(x + (65x div (if i <= 0 then 1 else i))),x,1)
A017729: 1 66 2211 50116 864501 12103014 143218999 1473109704 13442126049 110524147514 828931106355 5727160371180 36749279048405 220495674290430 1244225590638855 6635869816740560
loop(\(x,i).(x + (55x div (if i <= 0 then 1 else i))),x,1)
A017719: 1 56 1596 30856 455126 5461512 55525372 491796152 3872894697 27540584512 179013799328 1074082795968 5996962277488 31368725759168 154603005527328 721480692460864
loop(\(x,i).(~x + (55x div (if i <= 0 then 1 else i))),x,1)
A017770: 1 54 1431 24804 316251 3162510 25827165 177100560 1040465790 5317936260 23930713170 95722852680 343006888770 1108176102180 3245372870670 8654327655120
loop(\(x,i).(x + (99x div (if i <= 0 then 1 else i))),x,1)
A017763: 1 100 5050 171700 4421275 91962520 1609344100 24370067800 325949656825 3911395881900 42634215112710 426342151127100 3943664897925675 33976189889821200 274236389824985400
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(1 + (x div 2)),(if (x mod 2) <= 0 then 1 else ~2))
A099364: 1 ~2 2 ~4 5 ~10 14 ~28 42 ~84 132 ~264 429 ~858 1430 ~2860
(loop(\(x,i).(2x + (loop(\(x,i).(x + 1),(x div (~1 + (4 * i))),(x + 1)) mod 2)),x,0) div 2)
A215411: 0 0 1 2 5 10 21 42 84 169 338 677 1355 2710 5420 10841
(2 * loop(\(x,i).(x + loop(\(x,i).(((3 * (x + (x div 4))) - (x mod 2)) div 2),1,i)),x,0))
A077071: 0 2 8 16 30 46 66 88 118 150 186 224 268 314 364 416
(2 * (1 + (if (x mod 4) <= 0 then 0 else (if (x mod (1 + (2 * (2x mod 3)))) <= 0 then 2 else 0))))
A240501: 2 2 2 6 2 2 6 2 2 6 6 2 2 2 2 6
((if (x mod 4) <= 0 then 2 else (1 + ((x div 2) div (1 + (if (x mod 2) <= 0 then 6 else 1))))) div 2)
A144477: 1 0 0 0 1 1 0 1 1 1 0 1 1 2 1 2
((if x <= 0 then 2 else (1 + (x div (1 + (3 * ((if (x mod 3) <= 0 then 2 else 1) + (x mod 2))))))) div 2)
A277210: 1 0 0 0 1 0 0 1 1 0 1 1 1 1 2 1
((1 + loop(\(x,i).2x,x,1) - loop(\(x,i).((x * (1 + i)) div (1 + (i div 2))),(x + ~1),1)) div 2)
A007008: 0 1 1 3 5 11 22 47 93 193 386 793 1586 3238 6476 13167
((1 + ((loop(\(x,i).~3x,x,2) + loop(\(x,i).4x,x,1)) div 3)) div 2)
A192355: 1 0 6 2 70 90 926 2002 13110 37130 194446 640002 2973350 10653370 46333566 174174002
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(12x + 10))
A017651: 100000000000 584318301411328 70188843638032384 1951354384207722496 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 + (if (x div 2) <= 0 then x else (1 + (3 * (x + loop(\(x,i).2x,(x + ~5),1))))))
A173903: 2 3 12 15 18 21 27
((1 + loop(\(x,i).(4 * ((2x - (x div (if i <= 0 then 1 else i))) * (~1 + (2 * i)))),x,1)) div 2)
A187535: 1 2 36 1200 58800 3810240 307359360 29682132480 3339239904000 428906814336000 61934143990118400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(1 + ((if (~x + (2 * (2 + ((x + 2) mod 4)))) <= 0 then 2 else 1) mod (x + 1))),2)
A054006: 4 8 8 8 8 8 16 16 16 8 16 16 16 16 16 16
(2 * loop(\(x,i).(3x + loop(\(x,i).(7x + 6),i,1)),(x + 1),1))
A337418: 32 290 2240 16322 116192 819170 5751680 40314242 282357152 1976972450 13840224320 96885821762 678213506912 4747532812130 33232844476160 232630255706882
(2 * (1 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1))))
A088525-A054735: 8 12 24 36 60 84 120 144 204 216 276 300 360 384 396 456
(2 * loop(\(x,i).4x,(x + 1),(1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))))
A255932: 8 64 128 2048 2048 16384 32768 1048576 524288 4194304 8388608 134217728 134217728 1073741824 2147483648 137438953472
((1 + (((x + 1) - (5 * loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x))) div 2)) div 2)
A294317: 0 2 1 4 3 2 6 5 4 3 8 7 6 5 4 10
(x div (2 * (1 + ((1 + (x div (1 + (2 * loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x))))) div 2))))
A109754: 0 0 1 0 1 1 0 1 2 2 0 1 3 3 3 0
((1 + (if x <= 0 then 1 else (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))))) div 2)
A070821: 1 0 0 1 0 1 0 2 1 1 0 2 0 1 1 4
(if x <= 0 then 1 else (2 * (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))))))
A278525: 1 2 2 4 2 4 2 8 6 4 2 8 2 4 6 16
(if x <= 0 then 1 else (2 * (1 + (((x + 1) - ((loop(\(x,i).(2x + i),(x + ~2),1) div 2) mod 2)) div 2))))
A256416: 1 4 4 4 6 6 8 10 10 10 12 14 14 14 16 18
((1 + ((1 + ((loop(\(x,i).(x - ((~x + (x div (if i <= 0 then 1 else i))) div 2)),x,1) div 2) div 2)) div 2)) div 2)
A173693: 0 0 0 0 1 1 1 1 2 2 3 5 7 10 14 20
((1 + ((5 * loop(\(x,i).(x + loop(\(x,i).3x,(~1 + i),x)),x,1)) div 2)) div 2)
A188545: 1 3 10
A015487: 1 3 10 100 2800 229600 56022400 40896352000 89481218176000 587175753670912000 4611686018427387903 4611686018427387903 4611686018427387903
((1 + (loop(\(x,i).(loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)),1,(x + 1)) div 2)) div 2)
A064577: 0 0 1 0 1 0 2 1 1 0 3 0 1 1 4 0
(if x <= 0 then 1 else (2 * (1 + (((~1 + loop(\(x,i).2x,x,(x - ((x div 2) mod 2)))) mod (x + 1)) div 2))))
A062570: 1 2 2 4 4 4 6 8 6 8 10 8 12 12 8 16
((x + 2) - loop(\(x,i).i,((loop(\(x,i).(2x + 2),x,(1 - (2 * (x mod 2)))) mod (x + 1)) div 2),1))
A141258: 1 2 3 4 5 6 7 6 9 10 11 10 13 14 11 10
(2 * (if (x mod 2) <= 0 then ((1 + (5 * ((~x + 2) mod 4))) * (if x <= 0 then 1 else 2)) else 1))
A040481: 22 2 4 2 44 2 4 2 44 2 4 2 44 2 4 2
((1 + (((loop(\(x,i).(x3 + x2),1,loop(\(x,i).(2x + 2),x,0)) div 2) div 2) div 2)) div 2)
A288720: 0 1 16 184 1744 15136 126016 1028224 8306944 66781696 535561216 4289726464 34338770944 274794029056 2198687727616 17590843899904
(19 + (loop(\(x,i).2x2,(if x <= 0 then 1 else 2x),2) div 2))
A104068: 23 83 1073741843 4611686018427387903 4611686018427387903
((1 + (((loop(\(x,i).(x2 + 2x),1,((if (x mod 2) <= 0 then 2 else 0) + (x div 2))) div 2) div 2) div 2)) div 2)
A025802: 1 0 1 0 2 1 2 1 3 2 4 2 5 3 6 4
((1 + (loop(\(x,i).(2x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i))),(x + 2),2) div 2)) div 2)
A002661: 1 2 3 5 10 18 35 63 126 231 462 858 1716 3218 6435 12155
(2 + ((~1 + loop(\(x,i).(loop(\(x,i).2x,x,2) mod (x + 1)),1,(2x + 2))) div 5))
A195352: 2 2 2 3 2 2 3 2 2 3 2 3 7 2 2 3
loop(\(x,i).2x,(5 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))),2)
A100629: 2048 65536 67108864 68719476736 72057594037927936 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~10 + loop(\(x,i).(10x + 1),(if (x mod 2) <= 0 then 1 else x),1))
A277864: 1 1 1 1101 1 111101 1 11111101 1 1111111101 1 111111111101 1 11111111111101 1 1111111111111101
(if x <= 0 then 1 else (2 + ((1 + (if (2 - (x mod (1 + ((~x + 2) mod 4)))) <= 0 then x else 1)) div 3)))
A305980: 1 2 2 3 2 2 2 4 5 2 2 6 2 2 2 7
(if x <= 0 then 1 else (2 * (3x - ((1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2))) div 3))))
A315327: 1 6 10 16 22 26 30 36 42 46 52 58 62 68 74 78
(2 + (if x <= 0 then 1 else (3 * (if (x mod (1 + (2 * (x div (2 * (2 + (x mod 2))))))) <= 0 then 1 else 2))))
A278545: 3 5 5 5 8 5 5 8 8 5 5 8 8 8 5 5
(((loop(\(x,i).(x * (x2 div 2)),1,loop(\(x,i).(~2x + 1),x,3)) div 2) div 3) div 2)
A015266: 1 ~5 55 ~385 3311 ~25585 208335 ~1652145 13275471 ~105970865 848699215 ~6785865905 54301841231 ~434355079345 3475079247695 ~27799679551665
(if x <= 0 then 1 else (2 + ((x + loop(\(x,i).(2x + 2),(((x + 1) div 2) div 3),1)) div 3)))
A308172: 1 2 3 3 3 5 5 5 6 6 6 9 9 9 10 10
(if x <= 0 then 1 else (2 + (3 * compr(\x.(~1 + (loop(\(x,i).4x,x,1) mod (2x + 1))),x))))
A162939: 1 5 8 11 17 20 26 29 35 44 47 56 62 65 71 80
((if (x mod 2) <= 0 then (3 * (if (~2 + (x div 3)) <= 0 then 1 else 2)) else 1) div (2 + (x mod 3)))
A341980-A219202: 1 0 0 0 1 0 1 0 0 0 2 0 3 0 1 0
((1 + ((x + 1) mod (2 + (if x <= 0 then 2 else loop(\(x,i).(((x + 1) - ((x div 2) mod 2)) div 2),2,x))))) div 2)
A293112-A292085-A286653-A262163-A255636: 1 1 0 1 1 0 1 1 1 0 1 1 2 2 0 1
(loop(\(x,i).(x + ((~1 + i) * i)),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1) div 2)
A127920: 1 4 20 56 220 364 816 1140 2024 4060 4960 8436 11480 13244 17296 24804
(((x + 3) * loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,(x + 4))) div 2)
A001303: 6 50 225 735 1960 4536 9450 18150 32670 55770 91091 143325 218400 323680 468180 662796
((loop(\(x,i).11x,x,1) + loop(\(x,i).3x,2x,1)) div 2)
A081192: 1 10 101 1030 10601 110050 1151501 12135070 128702801 1372684090 14712104501 158346365110 1710428956601 18532288986130 201313313019101 2191569650755150
(if x <= 0 then 1 else loop(\(x,i).x3,1,((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)))
A342980: 1 0 0 0 1 0 0 1 1 0 0 1 8 1 0 0
(((x + 2) div (1 + loop(\(x,i).(1 + (if (x mod 2) <= 0 then 6 else 1)),(x div 2),(x mod 2)))) div 2)
A029368: 1 0 0 0 1 0 0 1 1 0 0 2 2 0 1 2
((loop(\(x,i).6x,((x + 1) div 2),1) + loop(\(x,i).6x,x,1)) div 2)
A056308: 1 6 21 126 666 3996 23436 140616 840456 5042736 30236976 181421856 1088414496 6530486976 39182222016 235093332096
((loop(\(x,i).10x,x,3) - loop(\(x,i).6x,x,1)) div 2)
A165150: 1 12 132 1392 14352 146112 1476672 14860032 149160192 1494961152 14969766912 149818601472 1498911608832 14993469652992 149960817917952 1499764907507712
(loop(\(x,i).(x div (1 + (x mod 2))),2x,loop(\(x,i).(10x + 1),x,1)) div 2)
A086223: 0 1 3 69 694 6944 69444 694444 6944444 69444444 694444444 6944444444 69444444444 694444444444 6944444444444 69444444444444
(2 * loop(\(x,i).(x div (2 - (x mod 2))),x,loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1)))
A322756: 2 6 10 70 126 462 858 12870 24310 92378 176358 1352078 2600150 10029150 19389690 601080390
((loop(\(x,i).((4x + 1) + (x mod 2)),x,1) - loop(\(x,i).(3x + 1),x,1)) div 2)
A099621: 0 1 6 31 144 637 2730 11467 47508 194953 794574 3222583 13023192 52491349 211161138 848231779
(2 * (1 + compr(\x.(loop(\(x,i).x2,2,(~1 + (loop(\(x,i).2x,x,1) mod (x + 1)))) mod (x + 1)),x)))
A278568: 2 6 10 14 18 22 26 34 38 46 50 54 58 62 74 82
(2 * (1 + compr(\x.(2 - (loop(\(x,i).2x,x,(if (~2 + (x div 3)) <= 0 then 2 else 1)) mod (x + 1))),x)))
A334166: 6 10 12 14 18 20 24 28 30 36 40 42 44 48 50 52
((loop(\(x,i).12x,x,3) - loop(\(x,i).8x,x,1)) div 2)
A165152: 1 14 184 2336 29056 356864 4347904 52699136 636583936 7672561664 92339175424 1110217588736 13339790934016 160214930161664 1923678673567744 23092940175835136
((loop(\(x,i).(2 * (2x - (x div (1 + i)))),(x + ~1),2) + loop(\(x,i).4x,x,1)) div 2)
A032443: 1 3 11 42 163 638 2510 9908 39203 155382 616666 2449868 9740686 38754732 154276028 614429672
(2 * loop(\(x,i).(5x2 + ~5x),1,loop(\(x,i).10x,x,1)))
A093798: 0 900 99000 9990000 999900000 99999000000 9999990000000 999999900000000 99999999000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
A093230: 0 900 99000 9990000 999900000 99999000000 9999990000000 999999900000000 99999999000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 * loop(\(x,i).((x + 2) + ((x div (3 + ((x div 2) div 3))) mod 2)),x,1)))
A315727: 1 6 12 18 22 26 30 36 42 48 54 60 66 70 74 78
loop(\(x,i).(2x * (1 + (2 * i))),(1 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x)),2)
A262204: 12 120 30240 17297280 28158588057600 64764752532480000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(((1 + (loop(\(x,i).2x,(loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2),1) div 2)) mod (x + 1)) div 2)
A292377: 0 0 1 0 1 1 2 0 0 1 3 1 3 2 2 0
loop(\(x,i).x2,1,(loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + 1),(x + 1)) div 2))
A337901: 1 25 441 7056 108900 1656369 25050025 378224704 5712638724 86394844900 1308887012356 19868414760000 302198588499600 4605510959127225 70321771565375625 1075697380745222400
(2 + compr(\x.((compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x) div 2) mod 2),(x + 1)))
A024705: 3 5 6 8 10 12 14 16 17 18 19 23 26 28 29 32
(((x + 1) * loop(\(x,i).(x + (7x div (if i <= 0 then 1 else i))),x,(x + 2))) div 2)
A104670: 1 24 216 1200 4950 16632 48048 123552 289575 629200 1283568 2482272 4585308 8139600 13953600 23193984
(2 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 4x))),(x + 1)))
A087679: 5 9 15 21 39 45 69 81 99 105 111 129 165 195 225 231
(2 * compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 4x))),(x + 1)))
A165986: 6 14 26 38 74 86 134 158 194 206 218 254 326 386 446 458
(compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 4x))),(x + 1)) div 2)
A047847: 1 3 6 9 18 21 33 39 48 51 54 63 81 96 111 114
(2 + compr(\x.(1 - loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),(x div 2),(x2 + 4x))),(x + 1)))
A029708: 9 15 21 39 45 69 81 99 105 111 129 165 195 225 231 279
(2 + (if (x mod (1 + (2 * (x mod 4)))) <= 0 then 1 else loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))
A162277: 3 3 5 3 3 5 9 3 3 3 3 5 3 9 17 3
((loop(\(x,i).5x,((x + 1) div 2),1) + loop(\(x,i).5x,x,1)) div 2)
A032122: 1 5 15 75 325 1625 7875 39375 195625 978125 4884375 24421875 122078125 610390625 3051796875 15258984375
((loop(\(x,i).11x,x,1) + loop(\(x,i).5x,x,1)) div 2)
A152429: 1 8 73 728 7633 82088 893593 9782648 107374753 1179950408 12973595113 142680249368 1569336258673 17261966423528 189877968549433 2088639343496888
((loop(\(x,i).(13x + ~8),x,1) + loop(\(x,i).3x,x,1)) div 2)
A198900: 1 4 33 380 4801 62004 804833 10459180 135958401 1767426404 22976444833 298693487580 3883014452801 50479185229204 656229400008033 8530982176189580
(loop(\(x,i).((~x + 1) + (3 * loop(\(x,i).4x,(~1 + i),1)) - (x mod 2)),x,1) div 2)
A227451: 0 1 5 18 77 306 1229 4914 19661 78642 314573 1258290 5033165 20132658 80530637 322122546
(2 * ((3 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),(x + 1))) div 2))
A107755: 2 8 12 26 30 36 38 80 84 90 92 108 110 116 120 242
((2 + (loop(\(x,i).(x2 + 2x + ~2),1,loop(\(x,i).4x,(x div 2),1)) mod (x + 1))) div 2)
A332294: 1 1 1 2 1 3 1 4 3 4 1 6 1 5 4 8
(2 * (2 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1))))
A176810: 10 14 26 38 62 86 122 146 206 218 278 302 362 386 398 458
(if x <= 0 then 1 else (2 * (if (x mod 5) <= 0 then 0 else (1 - (2 * ((x div 5) mod 2))))))
A305029: 1 2 2 2 2 0 ~2 ~2 ~2 ~2 0 2 2 2 2 0
(((((x + ~1) * ((x * loop(\(x,i).2x,x,loop(\(x,i).x2,(x + ~1),2))) div 2)) div 2) div 2) div 2)
A087085: 0 0 2 48 3072 2621440 515396075520 4611686018427387903 4611686018427387903
loop(\(x,i).2x,(x div 2),(2 - ((if x <= 0 then 1 else (((x - ((x mod 3) div 2)) div 2) div 2)) mod 2)))
A236680: 1 2 4 4 4 4 8 8 16 32 64 64 64 64 128 128
(2x - (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (4 + (((x + 1) div 2) div 2))))
A095834: 0 2 0 6 3 0 12 8 4 0 20 15 10 5 0 30
((2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)) * loop(\(x,i).4x2,2,2))
A137485: 3072 5120 7168 11264 13312 17408 19456 23552 29696 31744 37888 41984 44032 48128 54272 60416
(loop(\(x,i).11x,x,1) mod (~2 + loop(\(x,i).(x3 + 2),2,2)))
A216131: 1 11 121 331 641 51 561 171 881 691 601 611 721 931 241 651
(~8 + loop(\(x,i).x2,2,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A153482: 8 73 617 2393 14633 28553 83513 130313 279833 707273 923513 1874153 2825753 3418793 4879673 7890473
((2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)) * loop(\(x,i).x2,2,8))
A137489: 12288 20480 28672 45056 53248 69632 77824 94208 118784 126976 151552 167936 176128 192512 217088 241664
(1 + (compr(\x.loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 0 else 2))),x,x),x) + (x div 8)))
A063756: 1 2 3 5 6 8 9 14 16 18 19 24 25 27 28 42
(x mod (2 + ((x + (if (x mod 3) <= 0 then (if (~2 + (x div 4)) <= 0 then 1 else 2) else 0)) mod 4)))
A337005: 0 1 2 1 0 2 1 2 0 1 2 1 0 1 2 0
((x + 6) + (loop(\(x,i).(x + (if (~2 + (x div 3)) <= 0 then 1 else 2)),x,(x + 1)) div 2))
A026286: 6 8 10 12 14 17 20 23 26 29 31 34 36 39 41 44
(1 - (2 * (2 + loop(\(x,i).(2x + ~4),compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),2))))
A098231: ~7 ~3 21 117 2037 8181 131061 524277 8388597 536870901 2147483637 137438953461 2199023255541 8796093022197 140737488355317 9007199254740981
((loop(\(x,i).2x,x,((2x + 4) + (loop(\(x,i).(2 * (x + i)),x,x) div 2))) div 2) div 2)
A082307: 1 4 16 66 280 1208 5248 22816 98944 427392 1838080 7870976 33568768 142637056 604045312 2550276096
(8x + (loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1)))
A120948: 2 16 50 176 738 3408 16402 80368 397250 1972880 9824754 49005360 244672162 1222297552 6108298706 30531927152
(4 + loop(\(x,i).((x + 1) + ((x + (if (i mod 2) <= 0 then 2 else 0)) div 3)),(x div 2),(x mod 2)))
A120189: 4 5 5 6 7 8 9 10 12 13 15 17 20 23 26 30
(2 * ((if (x mod 4) <= 0 then (7 * (if x <= 0 then 1 else 2)) else 1) * (2 + (x mod 2))))
A040764: 28 6 4 6 56 6 4 6 56 6 4 6 56 6 4 6
(~1 + ((if x <= 0 then 1 else compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x)) + (4 * (x mod 2))))
A082455: 0 4 1 7 5 13 11 19 17 25 27 33 35 43 41 49
(4 * (1 + compr(\x.(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then x else (1 + i))),x,x)),x)))
A186293: 8 20 36 44 48 56 68 96 116 120 128 140 156 168 176 200
((~1 + (if x <= 0 then 1 else (x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))) mod 4)
A340867: 0 2 1 0 3 0 1 0 3 0 1 2 3 2 1 2
((2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)) * loop(\(x,i).x3,2,4))
A175747: 786432 1310720 1835008 2883584 3407872 4456448 4980736 6029312 7602176 8126464 9699328 10747904 11272192 12320768 13893632 15466496
(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1) + loop(\(x,i).4x,x,4))
A212403: 5 19 74 291 1150 4558 18100 71971 286454 1140954 4547020 18129294 72309164 288493756 1151300584 4595507491
((((x + ~1) + loop(\(x,i).(x + ((if (x + ~4) <= 0 then 1 else 2) + (x div 4))),x,1)) div 2) div 2)
A239468: 0 0 1 1 2 3 4 6 7 10 12 16 20 25 31 39
(2 + ((x + (if x <= 0 then 1 else (x - ((x + 1) mod (2 * (1 + (if (x + ~4) <= 0 then 0 else 2))))))) div 2))
A093841: 2 3 3 5 5 7 7 8 8 9 9 13 13 14 14 15
(2 * (loop(\(x,i).20x,x,1) + loop(\(x,i).8x,x,2)))
A332705: 6 72 1056 18048 336384 6531072 129048576 2568388608 51267108864 1024536870912 20484294967296 409634359738368 8192274877906944 163842199023255552 3276817592186044416 4611686018427387903
(loop(\(x,i).(x3 + ~x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A138416: 2 9 50 147 605 1014 2312 3249 5819 11774 14415 24642 33620 38829 50807 73034
(loop(\(x,i).(x3 + x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A066886: 5 15 65 175 671 1105 2465 3439 6095 12209 14911 25345 34481 39775 51935 74465
(loop(\(x,i).(x3 + ~x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A127918: 3 12 60 168 660 1092 2448 3420 6072 12180 14880 25308 34440 39732 51888 74412
(loop(\(x,i).(x * ((x + 1) - i)),2,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A138418: 6 36 300 1176 7260 14196 41616 64980 139656 353220 461280 936396 1412040 1708476 2438736 3943836
(4 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(x2 + ~2))),x))
A110558: 8 12 16 24 28 32 40 44 52 60 68 72 84 88 96 100
(2 + (compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) + (loop(\(x,i).(~x + 1),x,(x + 2)) div 2)))
A014694: 4 4 9 9 16 14 23 19 34 26 43 35 50 40 61 51
(2 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + (loop(\(x,i).(~x + 1),x,(x + 2)) div 2)))
A014693: 3 2 7 5 14 10 21 15 28 24 37 31 48 36 55 45
(if x <= 0 then 1 else (2 * (2x + (loop(\(x,i).(x * (~2 + (i mod 2))),x,1) mod (1 + (x div 4))))))
A311153: 1 4 8 12 16 20 24 28 34 40 44 46 48 52 56 60
(if x <= 0 then 1 else (2 * (2x + ((1 + (if (~2 + (x div 2)) <= 0 then x else (x + 4))) div 3))))
A310380: 1 4 10 14 18 24 30 36 40 44 50 54 58 64 68 72
(if x <= 0 then 1 else (2 * (2x + ((2 * ((x + (if (~2 + (x div 2)) <= 0 then 1 else 0)) div 2)) div 3))))
A312549: 1 4 8 14 18 24 28 32 36 40 46 50 56 60 64 68
(if x <= 0 then 1 else (2 * (2x + ((2 + (if (~4 + (x div 2)) <= 0 then x else (x + 2))) div 3))))
A315203: 1 6 10 14 20 24 28 34 38 42 48 54 58 62 68 72
(if x <= 0 then 1 else (2 * (2x + ((2 * (x + (if (~2 + (x div 4)) <= 0 then 1 else 2))) div 3))))
A315650: 1 6 12 16 22 28 32 38 44 48 54 60 66 72 76 82
(4x + (if x <= 0 then 1 else ((2 * ((x + (if (~2 + (x div 2)) <= 0 then 1 else 0)) div 2)) div 3)))
A058759: 1 4 8 13
A311914: 1 4 8 13 17 22 26 30 34 38 43 47 52 56 60 64
(4x + (if x <= 0 then 1 else (x - ((1 - (if (~2 + (x div 2)) <= 0 then x else (x + 2))) div 3))))
A301726: 1 5 11 16 21 27 33 38 43 49 54 59 65 70 75 81
((x + 2) + (if x <= 0 then 1 else 4x) - (4 div (if (~2 + (x div 2)) <= 0 then 2 else (x + ~2))))
A313739: 1 5 10 15 20 25 31 37 42 47 52 57 62 67 72 77
(x + (((x - (if (~2 + (x div 4)) <= 0 then 0 else 2)) div 3) + (if x <= 0 then 1 else 4x)))
A313876: 1 5 10 16 21 26 32 37 42 48 53 58 63 68 74 79
(4x + (if x <= 0 then 1 else ((x + ~1) + loop(\(x,i).(x - (x div 12)),2,x))))
A314254: 1 5 11 17 23 29 35 41 47 53 59 65 70 75 81 87
(if x <= 0 then 1 else (2 * ((if (x mod (1 + ((~2x + 2) mod (1 + (x div 2))))) <= 0 then 1 else 2) + (x div 2))))
A007843: 1 2 4 4 6 8 8 8 10 12 12 14 16 16 16 16
((if (x mod 4) <= 0 then (13 * (if x <= 0 then 1 else 2)) else 1) + (2 * (x mod 2)))
A010220: 13 3 1 3 26 3 1 3 26 3 1 3 26 3 1 3
(4 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 4x))),x))
A067830: 5 7 11 17 23 41 47 71 83 101 107 113 131 167 197 227
(2 + compr(\x.(~1 + (((x + 1) + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x)) mod 3)),x))
A116000: 2 3 4 5 6 7 10 11 13 16 17 19 22 23 25 27
((x + 1) + (1 mod ((~x + 1) + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))))
A135680: 1 2 3 4 5 4 7 4 5 4 11 4 13 4 5 4
((x + 3) + loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,(6x + 2)))
A107745: 5 11 17 23 29 5 41 47 53 59 5 71 7 83 89 5
(2 + compr(\x.(1 - (loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x + 2)) mod 7)),x))
A072538: 2 3 5 11 13 17 19 23 29
(2 + compr(\x.((1 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x)) mod 3),x))
A091178: 4 6 8 11 12 14 18 19 21 22 25 27 29 31 34 36
loop(\(x,i).x2,1,((~x + ~2) + (loop(\(x,i).(2 + ((x2 + x) div 2)),2,(x + 2)) div 3)))
A223719: 9 81 484 2116 7396 21904 57121 134689 292681 594441 1140624 2085136 3655744 6180196 10118761 16104169
((~3x + ~2) + loop(\(x,i).2x,2,compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)))
A122264: 2 7 12 25 30 43 48 61 82 87 108 121 126 139 160 181
(2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x2 + 1))),x))
A078402: 0 6 12 36 48 72 78 96 114 126 162 168 198 204 246 258
loop(\(x,i).(((2 * (x + (2 * (2x div (if i <= 0 then 1 else i))))) div (1 + i)) * (1 + (2 * i))),x,2)
A189770: 2 30 300 2450 17640 116424 720720 4247100 24066900 132100540 706137432 3691172940 18929092000 95477508000 474659611200 2329787591640
loop(\(x,i).(10x + 1),x,loop(\(x,i).(10x + ~8),x,2))
A332112: 2 121 11211 1112111 111121111 11111211111 1111112111111 111111121111111 11111111211111111 1111111112111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(4x + (2x div (1 + i))),x,3) - loop(\(x,i).4x,x,2))
A296769-A000531: 1 7 38 187 874 3958 17548 76627 330818 1415650 6015316 25413342 106853668 447472972 1867450648 7770342787
(~2 + compr(\x.(1 - loop(\(x,i).(if x <= 0 then 1 else (x + ~11)),x,4x)),x))
A275672: 0 1 3 4 6 7 9
A026315: 0 1 3 4 6 7 9 10 13 16 19 22 23 25 26 28
(2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x2 + 4))),x))
A114274: 0 6 24 30 36 54 90 96 114 120 126 144 150 180 186 204
(2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,10x)),x))
A087505: 0 2 4 8 10 14 16 20 22 32 34 38 44 46 52 56
(2 + compr(\x.((~1 + loop(\(x,i).2x,x,(if (x mod 7) <= 0 then 1 else 2))) mod (x + 2)),x))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A176164-A133956: 2 3 5 7 11 13 17 19 29 31 41 43 47 53 59 61
loop(\(x,i).(x3 + x2 + x + 1),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A131991: 15 40 156 400 1464 2380 5220 7240 12720 25260 30784 52060 70644 81400 106080 151740
((1 + loop(\(x,i).x2,2,(x + 1))) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A246864: 0 2 2 5 10 10 5 12 7 25 10 17 26 18 7 29
loop(\(x,i).((x2 + x) * (x div 2)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A117762: 6 12 60 168 660 1092 2448 3420 6072 12180 14880 25308 34440 39732 51888 74412
loop(\(x,i).(x4 + ~x3),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A138403: 8 54 500 2058 13310 26364 78608 123462 267674 682892 893730 1823508 2756840 3339294 4775858 7741604
(loop(\(x,i).3x,x,3) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A297966: 1 0 2 4 1 1 11 6 18 5 13 10 38 36 42 15
loop(\(x,i).(x3 + ~x2 + x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A083558: 6 21 105 301 1221 2041 4641 6517 11661 23577 28861 49321 67281 77701 101661 146121
loop(\(x,i).(x3 + x2 + x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A181149: 14 39 155 399 1463 2379 5219 7239 12719 25259 30783 52059 70643 81399 106079 151739
loop(\(x,i).(x4 + ~x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A138401: 14 78 620 2394 14630 28548 83504 130302 279818 707252 923490 1874124 2825720 3418758 4879634 7890428
loop(\(x,i).(x + (x mod 6)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A263483: 4 6 10 8 16 14 22 20 28 34 32 38 46 44 52 58
loop(\(x,i).(x * (2 - (x mod 4))),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A073579: 0 ~3 5 ~7 ~11 13 17 ~19 ~23 29 ~31 37 41 ~43 ~47 53
loop(\(x,i).(3x2 + ~2x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A267144: 8 21 65 133 341 481 833 1045 1541 2465 2821 4033 4961 5461 6533 8321
loop(\(x,i).x5,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A050997: 32 243 3125 16807 161051 371293 1419857 2476099 6436343 20511149 28629151 69343957 115856201 147008443 229345007 418195493
loop(\(x,i).(2x + ((x div 2) mod 2)),2,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A075520: 10 15 21 31 47 53 69 79 95 117 127 149 165 175 191 213
compr(\x.(((~x + 1) - loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,x)) mod 3),(x + 2))
A332245: 5 8 9 11 12 14 17 20 21 23 26 29 30 32 35 36
((x + 2) + loop(\(x,i).(~1 + loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,x)),(x + 1),(x + 1)))
A038374: 1 1 2 1 1 2 3 1 1 1 2 2 2 3 4 1
((2x + 1) + (2 * loop(\(x,i).(4 * (if (x mod 2) <= 0 then 12 else 1)),x,1)))
A154299: 3 11 101 103
((3x + 2) + (if (if (x mod 5) <= 0 then (x mod 2) else 0) <= 0 then 1 else (x mod 3)))
A156242: 3 6 9 12 15 19 21 24 27 30 33 36 39 42 45 47
(3x + loop(\(x,i).((~1 + loop(\(x,i).2x,x,10)) mod (x + 2)),2,x))
A287338: 1 4 10 12 16 18 19 22 28 30 34 36 40 42 46 48
loop(\(x,i).(if x <= 0 then 1 else (x + (x mod 2) - ((x div (~2 + (x mod ~2))) mod 2))),(x mod 2),(x div 2))
A123621: 0 1 1 1 2 1 3 3 4 4 5 6 6 5 7 7
((x + 1) + (x mod 2) - (if (x2 mod 7) <= 0 then (if x <= 0 then 0 else 3) else 0))
A078936: 1 3 3 5 5 7 7 6 9 11 11 13 13 15 12 17
(loop(\(x,i).(10x + 1),loop(\(x,i).~x,(x + 1),2x),1) - (x mod 2))
A266301: 1 110 1 1111110 1 11111111110 1 111111111111110 1 1111111111111111110 1 4611686018427387903 1 4611686018427387903 1 4611686018427387903
((if (x mod 4) <= 0 then (27 * (if x <= 0 then 1 else 2)) else 2) - (x mod 2))
A040742: 27 1 2 1 54 1 2 1 54 1 2 1 54 1 2 1
(((if (x mod 4) <= 0 then 23 else 1) * (if x <= 0 then 1 else 2)) - (x mod 2))
A040540: 23 1 2 1 46 1 2 1 46 1 2 1 46 1 2 1
(((if (x mod (1 + ((~2x + 2) mod (1 + (x div 2))))) <= 0 then 0 else 2) + (if x <= 0 then 1 else 2)) - (x mod 2))
A088696: 1 1 2 1 2 3 2 1 2 3 2 3 4 3 2 1
((if (x mod 3) <= 0 then (11 * (if x <= 0 then 1 else 2)) else 1) * (2 - (x mod 2)))
A040491: 22 1 2 22 2 1 44 1 2 22 2 1 44 1 2 22
((if (x mod 3) <= 0 then (14 * (if x <= 0 then 1 else 2)) else 1) * (2 - (x mod 2)))
A040793: 28 1 2 28 2 1 56 1 2 28 2 1 56 1 2 28
(5x - loop(\(x,i).~x,(x div 2),(x - (if x <= 0 then 1 else (x div (2 - (x mod 2)))))))
A137002: 1 5 11 15
A164355: 1 5 11 15 18 25 33 35 36 45 55 55 54 65 77 75
loop(\(x,i).(x + ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)) * (1 + (2 * i)))),x,2)
A316322: 2 11 36 85 184 327 548 833 1224 1775 2426 3277 4302 5463 6826 8469
(2 * loop(\(x,i).(x + loop(\(x,i).(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1,i)),x,x))
A067699: 0 4 8 14 18 24 30 38 42 48 54 62 68 76 84 94
((x + 1) + ((1 - (if (if (2x mod (x + 5)) <= 0 then 2 else 0) <= 0 then x else 1)) mod 3))
A235452: 1 2 5 5 5 6 8 8 11 11 11 14 14 14 17 17
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(6x + 1))),x)
A167055: 0 1 2 3 4 7 8 9 11 12 14 16 19 21 22 23
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(6x + ~1))),x)
A110801: 1 3 5 6 8 9 13 15 16 19 20 23 26 28 29 31
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(9x + ~1)),x)
A153400: 0 3 5 8 12 13 14 16 18 19 20 23 25 26 28 31
(x + loop(\(x,i).2x,((1 + (x div (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))) div 2),1))
A069208: 1 2 3 5 5 6 7 11 10 10 11 15 13 14 15 23
((x + 1) + (2 * (loop(\(x,i).loop(\(x,i).(2x * (1 + (2 * i))),(i * i),x),2,x) mod (x + 1))))
A161978: 1 2 3 4 5 6 7 8 9 10 27 12 27 14 15 16
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(8x + 1))),x)
A127590: 0 2 3 6 9 11 12 14 17 18 23 24 26 38 41 42
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(8x + ~1))),x)
A011990: 1 6 7 12
A155942: 1 6 7 12 15 16 21 22 25 27 28 36 37 40 42 48
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(11x + 5))
A017459: 48828125 17592186044416 5559060566555523 238572050223552512 3909821048582988049 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(0 - ((0 - loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,1)) div 5))
A008646: 1 1 3 7 14 26 42 66 99 143 201 273 364 476 612 776
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(11x + 10))
A017519: 100000000000 350277500542221 36028797018963968 929293739471222707 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(11x + 3))
A017435: 177147 4049565169664 2384185791015625 131621703842267136 2472159215084012303 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.((1 + loop(\(x,i).2x,(1 + (loop(\(x,i).(x div (2 - (x mod 2))),x,x) div 2)),x)) mod 3),x)
A074226: 1 4 10 11 13 14 16 23 25 34 35 37 38 40 44 47
(~x + loop(\(x,i).2x,x,1) - (loop(\(x,i).(2 + ((x2 + x) div 2)),2,(x + ~1)) div 3))
A002664: 0 0 0 0 0 1 7 29 93 256 638 1486 3302 7099 14913 30827
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(11x + 6))
A017471: 362797056 34271896307633 8293509467471872 317475837322472439 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x * (((1 + (loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,x) div 2)) div 2) div 3))
A300850: 0 0 10 105 840 5775 36036 210210 1166880 6235515 32332300 163601438 811246800 3954828150 19001896200 90162058500
compr(\x.(1 - (x mod (1 + (2 * (x mod loop(\(x,i).(1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),2,x)))))),x)
A005763: 1 5 7 9 11 13 17
A035034: 1 5 7 9 11 13 17 19 21 22 23 25 26 27 29 31
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x + (2 mod (1 + (x div 2)))))
A215658-A192579: 2 3 5 7 17
A072885: 2 3 5 7 17 19 23
A178209: 2 3 5 7 17 19 23 29 31 37 41 43 47 53 59 61
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(5x + ~1))),x)
A225647: 1 3 4 6 7
A024912: 1 3 4 6 7 10 13 15 18 19 21 24 25 27 28 31
(x + (if (x + ~2) <= 0 then 1 else (loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) div (x + 1))))
A185092: 1 2 3 4 6 12
A306348: 1 2 3 4 6 12 24 60
loop(\(x,i).(if x <= 0 then 1 else (~1 + (2x mod (~1 + (2 * (((~x + 2) div 2) mod 4)))))),(x + ~1),x)
A011606-A011594: 0 1 ~1 1 1 1 ~1 1 ~1 1 ~1 ~1 1 ~1 ~1 1
loop(\(x,i).(1 + (x mod (1 + (loop(\(x,i).2x,(2 + (3 * (x mod 2))),1) mod (x + 1))))),2,x)
A339899: 1 1 1 1 3 1 1 1 5 1 1 1 1 5 3 1
(x + (if x <= 0 then 1 else (2 * loop(\(x,i).((x + 1) + (2 * (x div 4))),(((x + 1) div 2) div 2),1))))
A057811: 1 3 4 7 8 9 10 13 14 15 16 19 20 21 22 29
loop(\(x,i).x2,1,(x + (if (x + ~1) <= 0 then 1 else ((x div 2) - (((x + ~1) div 5) mod 2)))))
A000548: 1 4 9 16 36 49 64 81 121 144 196 256 324 361 441 484
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(6x + 2))),x)
A167056: 0 1 2 3 5 6 8 10 11 12 13 16 17 18 22 23
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(6x + ~2))),x)
A138620: 1 2 4 5 6 7 9 11 14 15 16 19 20 21 22 26
compr(\x.(((if x <= 0 then 2 else loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x + ~1),1)) div 2) mod 2),x)
A072823: 1 7 11 13 14 15 19 21 22 23 25 26 27 28 29 30
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(11x + 4))
A017447: 4194304 8649755859375 3670344486987776 177917621779460413 3116402981210161152 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(11x + 8))
A017495: 8589934592 116490258898219 17714700000000000 550329031716248441 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(12x + 8)),x)
A240531: 3 4 7 9 10 14 16 17 18 19 24 27 29 31 34 38
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(6x + 4))),x)
A167057: 0 1 3 4 5 6 8 10 13 14 15 18 19 20 21 25
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(5x + ~2))),x)
A105042: 2 3 6 8 9 11 14 15 18 20 23 24 27 35 36 38
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(5x + 2))),x)
A102342: 0 1 3 4 6 9 10 12 13 15 16 19 22 25 27 30
compr(\x.((if x <= 0 then 1 else loop(\(x,i).(x5 mod 9),x,x)) mod 2),x)
A107743: 2 3 4 5 6 7 8 9 12 15 17 18 20 21 22 23
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,7x)),x)
A090614: 0 1 2 4 5 7 11 14 16 17 19 20 22 25 26 29
compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(7x + 6)),x)
A331386: 3 5 6 9 10 11 12 15 17 18 20 21 22 24 25 27
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(5x + 4))),x)
A126785: 0 2 3 5 6 9 12 14 17 18 20 23 24 26 27 30
(2x + loop(\(x,i).((x div (2 + (x div (1 + (x mod 4))))) - (if x <= 0 then 0 else 1)),x,(x + 1)))
A191535-A100598: 1 2 4 5 8 10
A131391: 1 2 4 5 8 10 11 13 16 17 19 21 24 25 28 29
(loop(\(x,i).11x,x,1) + (x2 * loop(\(x,i).x3,2,x)))
A177069: 1 12 2169 178478 4208945 48989176 364568617 1996813914 8804293473 33739007300 125937424601 570623341222 3881436747409 36314872537968 383799398752905 4185897925275026
(loop(\(x,i).11x,x,1) - (x2 * loop(\(x,i).x3,2,x)))
A024138: 1 10 ~1927 ~175816 ~4179663 ~48667074 ~361025495 ~1957839572 ~8375575711 ~29023111918 ~74062575399 0 2395420006033 32730551749894 375700268413577 4168598413556276
loop(\(x,i).(x + loop(\(x,i).(((1 + (8 mod (1 + (x div 2)))) div 2) - (x mod 2)),1,i)),x,x)
A181132: 0 0 1 1 3 4 5 5 8 10 12 13 15 16 17 17
loop(\(x,i).(4x + 2),((2x + 1) mod (1 + (2x mod (2 + (x div 4))))),0)
A305566: 0 0 0 0 0 2 0 0 0 2 0 10 0 2 2 0
(if (2x mod (4 + (x div 4))) <= 0 then ((2x + 8) div 5) else 0)
A132825: 1 0 2 0 0 3 0 0 0 5 0 0 0 0 7 0
((x + 1) + loop(\(x,i).(2 * (x + i)),x,0) - (((x3 + 3x2 + 2x) div 2) div 3))
A124671: 1 3 7 16 37 85 191 418 893 1871 3863 7892 16005 32297 64959 130374
((x + 1) div (1 + (if (x mod (1 + ((x2 + ~x) mod 8))) <= 0 then (x mod 3) else 0)))
A280488: 1 1 3 4 5 2 7 8 3 10 11 12 13 14 5 16
((x + 1) - ((x + 1) mod (1 + (if (x mod 2) <= 0 then ((1 + (x mod 8)) mod (x + 1)) else 0))))
A274016: 1 2 3 4 5 6 7 8 8 10 8 12 12 14 8 16
(1 + ((3 mod (1 + ((x div 2) mod (1 + (x mod (1 + (x div 3))))))) + (if x <= 0 then 0 else 1)))
A100549: 1 2 2 3 2 2 2 3 3 2 2 3 2 2 2 5
((x div (1 + (x mod (1 + ((4 + (x div 2)) mod (1 + (x div 3))))))) + (if x <= 0 then 0 else 1))
A019530: 0 2 3 2 5 6 7 4 3 10 11 6 13 14 15 4
(x - (((x + 2) mod (1 + (((x + 1) mod 7) mod 3))) + (if x <= 0 then 0 else 1)))
A338233: 0 0 1 1 3 4 5 5 6 8 9 9 11 12 13 12
(((1 + (((2x + 1) mod (4 + (x div 4))) div 2)) mod 3) - (if x <= 0 then 0 else 1))
A128431: 1 1 0 1 ~1 0 1 0 ~1 0 1 ~1 ~1 0 0 1
((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1))
A326191-A326190-A326189-A324190-A305822-A302037-A277013-A257091-A253557-A098893-A069248-A001222: 0 1 1 2 1 2 1 3 2 2 1 3 1 2 2 4
(1 + loop(\(x,i).((x + 1) + (((2x + 1) div 7) + (x div 3))),x,0))
A169985: 1 2 3 4 7 11 18 29 47 76 123 199 322 521 843 1364
(1 + (x div (1 + (x mod (1 + (x div (1 + (2 * (loop(\(x,i).(2x + 2),x,0) mod (x + 1))))))))))
A326690: 1 1 1 4 1 3 1 8 9 5 1 4 1 7 15 16
loop(\(x,i).x2,1,(~1 + (x div (1 + (x mod (1 + (x mod (1 + (x div (2 * (2 - (x mod 2))))))))))))
A167354: 1 0 1 0 9 0 25 0 1 0 81 0 121 0 9 0
(1 + (if x <= 0 then 0 else (1 + ((x + 1) mod (1 + ((x + ((x + ~2) div (2 + (x div 2)))) mod 3))))))
A099774: 1 2 2 2 3 2 2 4 2 2 4 2 3 4 2 2
(1 + (x mod (1 + (x div (1 + (2 * (2 mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1))))))))
A034684: 1 2 3 4 5 2 7 8 9 2 11 3 13 2 3 16
(2 div (1 + (if x <= 0 then 1 else (x mod (1 + (x div (1 + (2 * (x mod (2 * (1 + (2 * (x mod 2)))))))))))))
A134269: 1 2 0 2 0 2 0 1 0 1 0 1 0 0 0 2
(~1 + loop(\(x,i).2x2,1,(72x + 17)))
A157264: 577 15841 51841 108577 186049 284257 403201 542881 703297 884449 1086337 1308961 1552321 1816417 2101249 2406817
(x div (1 + ((if (~2 + (2x mod (2 + (x div 2)))) <= 0 then 2 else 1) * (1 + (x div 5)))))
A342263: 0 0 0 1 1 1 1 2 2 1 2 1 1 1 2 3
(1 + (5 mod (1 + (((x + 1) * (if (~4 + (x div 2)) <= 0 then 1 else 2)) div 3))))
A080967: 1 1 2 2 2 3 3 3 2 2 6 6 6 6 6 6
(~1 + loop(\(x,i).2x2,1,(49x + 50)))
A157367: 4999 19601 43807 77617 121031 174049 236671 308897 390727 482161 583199 693841 814087 943937 1083391 1232449
(1 + (x mod (1 + ((0 - loop(\(x,i).((x + 1) + (2 * (2x + (x mod 2)))),x,1)) mod (x + 1)))))
A300711: 1 1 1 1 5 1 7 1 1 1 11 1 13 7 5 1
(1 + (x mod (~1 + (x mod 2) - (if (x mod (1 + (2 * (x div (2 * (2 + (x mod 2))))))) <= 0 then 1 else 2))))
A204183: 1 1 1 1 ~1 1 1 0 0 1 1 0 1 0 1 1
((x + 1) div (1 + (if x <= 0 then 0 else (1 + ((x div (1 + ((x2 + (x div 2)) mod 3))) div 2)))))
A106806: 1 1 1 2 1 1 1 2 3 2 1 1 1 2 3 3
(1 + (if x <= 0 then 0 else (1 + ((1 + (x div 3)) div (2 * (1 + ((x + 2) mod 6)))))))
A175064: 1 2 2 2 3 2 2 2 2 2 4 3 2 2 2 2
(if x <= 0 then 0 else (1 + (x div (1 + (2 * (1 + (((x2 + ~x + 2) mod (x + 4)) div 2)))))))
A272604-A126387: 0 1 1 2 1 1 2 3 1 1 1 2 2 2 3 4
(1 + (7 * (if ((x + 1) mod 7) <= 0 then 8 else 1)))
A088841: 8 8 8 8 8 8 57 8 8 8 8 8 8 57 8 8
(1 + (7 * (3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A129073: 22 29 43 57 85 99 127 141 169 211 225 267 295 309 337 379
((x + 1) div (1 + (7 * (if (((x + 1) div 3) mod 4) <= 0 then x else 1))))
A017859: 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 2
loop(\(x,i).2x,(1 + ((1 + (x div 3)) div (2 + (2x2 mod (1 + (x div 2)))))),1)
A066671: 2 2 2 4 2 2 4 2 2 4 4 4 4 4 8 4
loop(\(x,i).(x * i),(1 + ((x - (x div (2 - ((x3 div 8) mod 2)))) div 2)),1)
A155795: 1 1 1 1 2 1 1 6 6 1 1 24 24 24 1 1
(1 + ((~1 + (if (x mod 2) <= 0 then x else 0)) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))))
A125778-A050176-A047130-A047110: 1 1 1 1 1 1 1 2 2 1 1 3 2 3 1 1
loop(\(x,i).(2 * i),((~2 + (x mod 2)) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))),1)
A278218: 1 1 1 1 2 1 1 2 2 1 1 4 6 4 1 1
(1 + (((x2 + 3x + 2) div (1 + (if (x mod 3) <= 0 then 2 else 0))) mod 9))
A153186: 1 7 4 7 4 7 1 1 1 1 7 4 7 4 7 1
(1 + ((~1 + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1)) mod 9))
A130856: 1 1 2 5 5 6 6 6 8 2 2 7 4 4 9 9
(1 + (9 * (loop(\(x,i).10x,(x + 1),(x + 1)) div 2)))
A078427: 46 901 13501 180001 2250001 27000001 315000001 3600000001 40500000001 450000000001 4950000000001 54000000000001 585000000000001 6300000000000001 67500000000000001 720000000000000001
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod (1 + (x mod 9)))
A141071: 0 1 2 3 1 1 3 3 5 0 1 1 1 3 5 4
loop(\(x,i).5x,2x,(1 + (x mod (1 + ((x2 + 2x) mod 8)))))
A156965: 1 50 625 62500 390625 19531250 244140625 48828125000 152587890625 7629394531250 95367431640625 9536743164062500 59604644775390625 2980232238769531250 4611686018427387903 4611686018427387903
(3 mod (1 + (if x <= 0 then 1 else ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4))))))
A320659: 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 3
(3 - (2 div ((1 - (if ((x + 2) mod (2 + ((x div 2) mod 2))) <= 0 then x else 0)) mod 5)))
A090402: 1 1 1 1 2 1 1 3 3 1 1 1 3 1 1 1
(1 + ((6 * (if (~4 + (x div 2)) <= 0 then x else (x + 3))) div 5))
A324766: 1 2 3 4 5 7 8 9 10 11 16 17 19 20 21 22
loop(\(x,i).x7,1,(10x + 6))
A017347: 279936 268435456 8031810176 78364164096 435817657216 1727094849536 5455160701056 14645194571776 34792782221696 75144747810816 150363025899136 282621973446656 504189521813376 860542568759296
loop(\(x,i).x7,1,(10x + 9))
A017383: 4782969 893871739 17249876309 137231006679 678223072849 2488651484819 7446353252589 19203908986159 44231334895529 93206534790699 182803912081669 337931541778439 594467302491009
(1 + ((2 * (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))) div 5))
A253558: 1 1 2 1 3 2 4 1 2 3 5 2 6 4 3 1
loop(\(x,i).(x2 + x),(2 - ((2x + 1) mod ((x + 5) + (x div 4)))),1)
A174215: 2 1 1 1 1 6 2 1 1 1 1 1 1 1 1 1
(1 + (x mod (~1 + (2 * ((if ((2x mod 5) mod 3) <= 0 then 2 else 0) + (x mod 2))))))
A307372: 1 1 1 1 2 1 1 1 1 5 2 1 1 1 3 1
(if x <= 0 then 1 else (~1 + ((1 - ((x + 1) mod (1 + (x div (1 + ((x + 2) mod 4)))))) mod 3)))
A298601: 1 0 0 0 ~1 0 0 0 0 ~1 0 0 0 1 0 0
(~1 + (((2 + loop(\(x,i).i,(x + ~8),1)) * (1 + (x div 5))) div 3))
A099562: 0 0 0 0 0 1 1 1 1 1 3 4 5 6 7 11
((x + 3) mod (1 + ((1 + (loop(\(x,i).(~2x + 1),x,(x + 1)) div 3)) mod 3)))
A138088: 1 0 1 0 1 0 0 0 2 0 0 0 0 1 0 0
(loop(\(x,i).7x,x,1) mod 71)
A036132: 1 7 49 59 58 51 2 14 27 47 45 31 4 28 54 23
(35 * (~1 + loop(\(x,i).10x,x,2)))
A175774: 35 665 6965 69965 699965 6999965 69999965 699999965 6999999965 69999999965 699999999965 6999999999965 69999999999965 699999999999965 6999999999999965 69999999999999965
(~1 + (((if x <= 0 then 1 else (x - ((x div ~4) div ~2))) + (x div 3)) mod 3))
A296030: 0 0 1 0 1 1 0 1 ~1 1 ~1 0 ~1 ~1 0 ~1
(1 + (((4 * (x + (if (~4 + (x div 2)) <= 0 then 1 else 2))) - (x div 3)) div 3))
A068998: 2 3 5 6 7 8 9 11 12 13 16 17 18 19 21 22
(1 + ((x - compr(\x.(1 - (x mod (2 + (if (x mod 5) <= 0 then 2 else 0)))),(x + 1))) mod 3))
A339584: 1 3 2 1 1 1 3 2 1 3 2 1 3 2 1 1
(1 + ((6x + 6) * (1 + (if (~x + 4) <= 0 then 16 else 1))))
A309809: 13 25 37 49 511 613 715 817 919 1021 1123 1225 1327 1429 1531 1633
loop(\(x,i).2x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A299906-A117401: 1 1 1 1 2 1 1 4 4 1 1 8 16 8 1 1
loop(\(x,i).(2 * i),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A157528: 1 1 1 1 2 1 1 4 4 1 1 6 8 6 1 1
loop(\(x,i).(x * i),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A155794: 1 1 1 1 1 1 1 2 2 1 1 6 24 6 1 1
loop(\(x,i).x7,1,(12x + 11))
A017659: 19487171 3404825447 64339296875 506623120463 2488651484819 9095120158391 27136050989627 69833729609375 160578147647843 337931541778439 662062621900811 1222791080775407 2149422977421875
(1 + (loop(\(x,i).(x * (1 - ((x3 div 8) mod 2))),1,(x + ~1)) div 3))
A208342: 1 1 1 1 1 2 1 1 3 3 1 1 4 5 5 1
(1 + ((loop(\(x,i).((5x + 1) - (x mod 3)),(x + 1),1) div 2) div 3))
A046633: 1 5 21 101 505 2521 12601 63005 315021 1575101 7875505 39377521 196887601 984438005 4922190021 24610950101
(1 + ((2 * (1 + ((1 + (loop(\(x,i).(x div (1 + (2 * (x mod 2)))),2,x) div 2)) div 2))) div 3))
A060682: 1 1 2 1 2 1 3 2 3 1 3 1 3 2 4 1
(1 + ((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3))
A325765: 1 1 1 2 1 3 1 3 2 3 1 5 1 3 3 4
(loop(\(x,i).5x,x,1) mod 103)
A036139: 1 5 25 22 7 35 72 51 49 39 92 48 34 67 26 27
(1 + (((5 * (1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2))) div 2) div 3))
A336920-A336473-A336159: 1 1 2 1 3 2 4 1 5 3 6 2 6 4 7 1
(1 + ((loop(\(x,i).(x2 + x),1,(5 * ((x2 + x) div 2))) div 2) div 3))
A257602: 1 6 41 156 426 951 1856 3291 5431 8476 12651 18206 25416 34581 46026 60101
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 19)
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A033633: 2 3 5 7 11 13 17 0 4 10 12 18 3 5 9 15
loop(\(x,i).(x2 + 2x),(2 - ((5x + 4) mod 18)),1)
A285865: 1 1 1 3 1 1 1 1 1 1 15 1 1 1 1 1
loop(\(x,i).x7,1,(12x + 7))
A017611: 823543 893871739 27512614111 271818611107 1522435234375 6060711605323 19203908986159 51676101935731 122987386542487 266001988046875 532875860165503 1002544368429379 1789940649848551
loop(\(x,i).x6,1,(~11x + ~7))
A017478: 117649 34012224 594823321 4096000000 17596287801 56800235584 151334226289 351298031616 735091890625 1418519112256 2565164201769 4398046511104 7212549413161 11390625000000 17416274304961 25892303048704
loop(\(x,i).x7,1,(12x + 5))
A017587: 78125 410338673 17249876309 194754273881 1174711139837 4902227890625 16048523266853 44231334895529 107213535210701 235260548044817 476837158203125 905824306333433 1630436461403549
(1 + ((2 * (1 + (2 * (x + loop(\(x,i).(x - (x div 12)),2,x))))) div 3))
A260395: 1 4 7 9 12 15 17 20 23 25 28 31 32 33 36 39
(~1 + ((2 * (2 + ((1 + loop(\(x,i).((x + 2) + (x div 4)),x,2)) div 3))) div 3))
A121659: 1 1 1 2 3 4 5 7 9 12 15 20 25 32 40 51
(~1 + ((2 * (2 + ((2 + ((if x <= 0 then 2 else (x * (x div 3))) div 2)) div 3))) div 3))
A025148: 1 0 0 1 1 1 1 2 2 3 3 4 5 6 7 9
(1 + (12 * (3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A129072: 37 49 73 97 145 169 217 241 289 361 385 457 505 529 577 649
(~1 + ((2 * (2 + loop(\(x,i).(x + i - (x div ~12)),x,1))) div 3))
A179385: 1 2 4 7 10 15 20 27 35 44 55 67 81 97 115 135
(1 + ((x - (2 * (((3 * (if ((x div 2) mod 3) <= 0 then 1 else x)) div 2) div 2))) mod 3))
A101608: 1 2 1 3 2 3 1 2 3 1 3 2 1 2 1 3
(1 + ((if x <= 0 then 1 else (2 + ((~2x + 3) mod (4 + (x div 4))))) div 3))
A204018: 1 2 2 2 1 2 2 3 3 2 2 3 1 3 2 2
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 25)
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A242123: 2 3 5 7 11 13 17 19 23 4 6 12 16 18 22 3
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 23)
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A229786: 2 3 5 7 11 13 17 19 0 6 8 14 18 20 1 7
(11 * loop(\(x,i).7x,5x,1))
A324267: 11 184877 3107227739 52223176609373 877714929273732011 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x2 + 2x + 1) - loop(\(x,i).x2,1,(x mod ((x + ~1) - (x mod 12)))))
A162497: 1 4 9 16 25 36 49 64 81 100 121 144 168 192 216 240
(1 + ((loop(\(x,i).(2x + 1),((x + 1) div 2),(1 + (x div 2))) div (2 + (x mod 2))) div 3))
A319645: 1 1 1 2 3 4 7 9 16 22 38
loop(\(x,i).x7,1,(9x + 7))
A017251: 823543 268435456 6103515625 52523350144 271818611107 1028071702528 3142742836021 8235430000000 19203908986159 40867559636992 80798284478113 150363025899136 266001988046875 450766669594624
loop(\(x,i).x7,1,(9x + 5))
A017227: 78125 105413504 3404825447 34359738368 194754273881 781250000000 2488651484819 6722988818432 16048523266853 34792782221696 69833729609375 131593177923584 235260548044817 402271083010688
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(9x + 5))
A081496: 5 14 46 160 574 2100 7788 29172 110110 418132 1595620 6113744 23505356 90633800 350351640 1357278300
((x + 1) div (loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) + (x div (1 + ((x div 2) mod 3)))))
A157187: 1 1 0 2 0 1 0 1 0 1 0 2 0 0 0 2
(1 + (((x * loop(\(x,i).((x3 + ~3x2 + 2x) div 5),2,x)) div 2) div 3))
A140441: 1 1 1 1 3 221
(~1 + ((2x + 2) * (if x <= 0 then 1 else (x + 2))) - (((~x3 + x) div 2) div 3))
A055820: 1 11 24 43 69 103 146 199 263 339 428 531 649 783 934 1103
(1 + (if x <= 0 then 0 else ((((x + 1) div (1 + (x mod 9))) mod 2) + (x div 3))))
A194303: 1 2 2 3 3 3 4 4 4 4 5 4 6 5 5 6
(1 - ((1 + (if (2x mod (4 + (x div 3))) <= 0 then 0 else 1)) mod (1 + (x div 3))))
A016414: 1 1 1 1 1 0 0 ~1 ~1 ~1 ~1 ~1 0 ~1 ~1 ~1
(1 + ((1 + (if ((x + 3) mod (2 + (x div 5))) <= 0 then 2 else 0)) mod (1 + (x div 2))))
A081755: 1 1 2 2 2 2 4 2 2 4 2 2 2 4 2 2
(~1 + (if (x + ~1) <= 0 then x else (1 + (((x2 mod (x - ((~x + 2) div 2))) div (x + 1)) + (x mod 2)))))
A225721: ~1 0 0 1 0 1 0 2 1 1 0 1 0 2 1 1
(~1 + ((1 + (if ((1 + (x div 4)) mod (2 + (x mod 4))) <= 0 then 2 else 0)) * (1 + (x mod 2))))
A092147: 0 1 0 1 2 1 0 1 0 5 0 1 2 1 2 1
(1 + ((1 + (x div (1 + (if ((x + 2) mod (2 + (x div 5))) <= 0 then 2 else 0)))) mod (x + 1)))
A263646: 1 1 2 1 3 1 1 4 1 1 5 1 1 1 6 1
(1 + ((~1 + loop(\(x,i).2x,((x + 1) - ((x mod (1 + (x div 4))) div 2)),1)) mod (x + 1)))
A061142: 1 2 2 4 2 4 2 8 4 4 2 8 2 4 4 16
(1 + ((1 + ((if ((x + ~1) mod 3) <= 0 then (2 + (x div 4)) else 1) mod 3)) mod (x + 1)))
A102313: 1 2 3 3 2 3 3 2 3 3 3 3 3 4 3 3
((2x + 1) - ((if ((1 + (x div 2)) mod 5) <= 0 then (x div 3) else 1) mod (x + 1)))
A241071: 1 2 4 6 8 10 12
A302696: 1 2 4 6 8 10 12 14 15 16 20 22 24 26 28 30
((x + 1) mod (1 + ((1 - ((x + 1) mod (1 + (2 * (if (x mod 4) <= 0 then 0 else 2))))) mod (x + 1))))
A060953: 0 0 1 0 1 0 0 1 1 0 0 0 1 2 1 0
(1 + ((1 + (4 * ((x mod (1 + (2 * (if (x mod 4) <= 0 then 0 else 2)))) mod 2))) mod (x + 1)))
A278247: 1 2 2 2 2 2 6 2 2 2 2 6 2 6 2 2
((x + 1) mod (1 + (((7 * (if x <= 0 then 1 else 2)) + (x mod 3)) mod (x + 1))))
A044933: 0 0 1 1 0 1 0 0 1 0 1 2 1 0 1 1
(1 + (loop(\(x,i).((x + 1) + ((2x + 1) div (1 + (x mod 12)))),x,0) div 2))
A297182: 1 2 3 4 5 6 7 20 33 46 59 72 85 254 423 592
(1 + ((1 + ((loop(\(x,i).(2x2 div (x + 1)),2,x) div 2) mod 9)) div 2))
A105932: 1 1 2 3 4 5 1 2 3 4 5 2 3 4 5 1
loop(\(x,i).2x,(x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))),1)
A319004: 1 1 1 2 1 2 1 4 2 2 1 4 1 2 2 8
(1 + ((1 + (((loop(\(x,i).x2,1,((x + 1) + (x div 3))) div 2) div 2) div 3)) div 2))
A029035: 1 1 1 2 3 3 4 5 6 8 9 10 13 15 16 19
((if (x mod (3 + ((x div 2) div 3))) <= 0 then 0 else 1) * (1 + ((1 + (x div 3)) div 2)))
A320471: 0 1 1 0 2 2 2 2 0 3 3 3 3 3 3 0
(~1 + (2 * loop(\(x,i).x2,1,(50x + 49))))
A157516: 4801 19601 44401 79201 124001 178801 243601 318401 403201 498001 602801 717601 842401 977201 1122001 1276801
(1 + loop(\(x,i).x2,1,(((x + 1) mod (1 + ((2 * (1 + (x mod 3))) mod (x + 1)))) div 2)))
A337278: 1 1 1 1 1 1 1 2 2 1 1 5 1 5 1 1
(1 + (2 * (1 + ((5 * (loop(\(x,i).2x,x,3) div 5)) div 2))))
A100720: 3 7 13 23 47 97 193 383 767 1537 3073 6143 12287 24577 49153 98303
(~1 + (2 * (1 + ((if (~2 + (x div 5)) <= 0 then x else (x + 2)) + ((1 + (x div 2)) div 2)))))
A069254: 1 3 7 9 11 13 17 19 21 23 27 29 31 33 37 43
(x div (1 + (2 * (x div (1 + (2 * (2 mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1))))))))
A260737: 0 0 0 0 0 1 0 0 0 3 0 2 0 2 2 0
(1 + (2 * (1 + (2 * loop(\(x,i).((10x + 1) + (x mod 2)),(~x + 2),1)))))
A178812: 487 51
(1 + (((x + 2) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 10))
A089103: 3 5 8 1 6 9 4 7 2 9 2 9 4 7 2 9
(loop(\(x,i).(10x + 1),2x,1) * (1 + (2 * (x mod 5))))
A158859: 1 333 55555 7777777 999999999 11111111111 3333333333333 555555555555555 77777777777777777 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((1 + (((if x <= 0 then 1 else ((1 + (x div 4)) * (x div 3))) - (x mod 2)) div 2)) div 2))
A259357: 1 1 1 1 2 1 2 2 3 3 3 3 5 5 5 6
((x + 1) div (1 + ((x + 1) div (2 + (if (x mod 4) <= 0 then 0 else (1 + (x mod (2 + (x mod 2)))))))))
A340382: 1 2 1 2 1 3 2 2 1 2 2 4 1 3 2 2
(1 - (x mod (~3 + (if x <= 0 then 2 else ((1 + (x3 div (x + 3))) mod 3)))))
A330739: 1 2 1 1 1 2 1 1 1 2 1 2 1 3 2 1
(1 + ((loop(\(x,i).x2,1,((x + ~1) - (4 * (x div 5)))) div 3) div 2))
A097886: 1 1 1 1 2 1 1 1 2 3 1 1 2 3 5 1
(1 + ((3 * ((loop(\(x,i).5x,(x + 1),2) div 3) div 3)) div 2))
A337753: 2 8 41 208 1042 5209 26042 130208 651041 3255208 16276042 81380209 406901042 2034505208 10172526041 50862630208
(1 + ((3 * ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3)) div 2))
A319002-A317545-A308063-A050363: 1 1 1 2 1 2 1 4 2 2 1 5 1 2 2 8
(1 + ((3 * ((2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)) div 3)) div 2))
A207336: 2 4 5 7 8 10 11 14 16 19 20 22 23 26 29 31
loop(\(x,i).(2 * (x - (x div ~2))),(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)
A147582: 1 4 4 12 4 12 12 36 4 12 12 36 12 36 36 108
loop(\(x,i).10x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)
A102377: 1 10 10 100 10 100 100 1000 10 100 100 1000 100 1000 1000 10000
loop(\(x,i).7x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)
A161343: 1 7 7 49 7 49 49 343 7 49 49 343 49 343 343 2401
(loop(\(x,i).10x,(6x + 6),1) div 7)
A146754: 142857 142857142857 142857142857142857 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x - (7 * (1 - (if (2 - (x div 4)) <= 0 then (x mod 8) else 1))))
A255693-A255593-A030107: 0 1 2 3 4 5 6 7 1 9 17 25 33 41 49 57
(((4x + 1) * loop(\(x,i).(4x + 4),(x + 1),2)) mod 7)
A254247: 5 1 4 2 2 0 6
(7 * loop(\(x,i).(10x + 81),x,1))
A175601: 7 637 6937 69937 699937 6999937 69999937 699999937 6999999937 69999999937 699999999937 6999999999937 69999999999937 699999999999937 6999999999999937 69999999999999937
(7 * (1 + loop(\(x,i).(x + 1),(~4 + ((x + ((x div 2) mod 2)) div 2)),x)))
A085130-A080194: 7 14 21 28 35 42 49 56 63 70 84 98 105 112 126 140
((2 * (2 + ((2 + loop(\(x,i).(5x + 1),x,1)) div 2))) div 7)
A178873: 0 1 5 23 112 558 2790 13951 69755 348773 1743862 8719308 43596540 217982701 1089913505 5449567523
(((if x <= 0 then 1 else 4x) + (x div 7)) - ((~x + 2) div 5))
A058759: 1 4 8 13
A311822-A311821: 1 4 8 13 17 21 25 30 35 39 43 47 51 56 61 65
(((if x <= 0 then 1 else 4x) + (x div 7)) - (x div ~7))
A314674: 1 5 9 13 17 21 25 30 35 39 43 47 51 55 60 65
(~1 + (((2 * (2 + ((x mod (~2 + (if (x mod 4) <= 0 then x else 0))) div 2))) - (x mod 3)) div 2))
A128519: 1 ~1 0 0 0 ~1 1 ~1 1 0 0 ~1 2 ~1 0 0
loop(\(x,i).(2x3 + x2),((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2),1)
A174546: 1 1 1 1 3 1 1 3 3 1 1 3 63 3 1 1
(1 + ((1 + (loop(\(x,i).(x3 mod 30),x,x) div 2)) div 2))
A307450: 1 1 2 8 2 2 3 4 3
(1 + (loop(\(x,i).((2x + 1) - ((~x + ((x + ~2) * (x div 3))) div 3)),x,1) div 2))
A329513: 1 3 6 9 9 8 8 8 8 8 8 8 8 8 8 8
(1 + (loop(\(x,i).(9 * (x - ((3 * (x div 4)) div 2))),x,1) div 2))
A243669: 1 5 28 158 892
loop(\(x,i).x7,1,(10x + 3))
A017311: 2187 62748517 3404825447 42618442977 271818611107 1174711139837 3938980639167 11047398519097 27136050989627 60170087060757 122987386542487 235260548044817 425927596977747 736141813551277
(1 + (((x + 1) + loop(\(x,i).x2,1,((1 + (8 mod (1 + (x div 2)))) div 2))) div 2))
A284511: 1 2 2 3 4 4 4 5 7 8 7 7 8 8 8 9
(1 + (2 * ((x + 1) + (2 * (x2 div (1 + (2 * (if (x mod 5) <= 0 then 0 else 2))))))))
A267549: 3 5 7 13 23 113
((x + 2) - (2 * ((x + 1) - loop(\(x,i).(x - (x div 8)),6,x))))
A287655: 0 1 2 3 4 5 6 7 6 5 4 3 2 1 2 3
(~1 + (if x <= 0 then 2 else (((1 + (x mod (1 + (x mod (2 * (2 + ((x div 2) mod 2))))))) mod (x + 1)) div 2)))
A334744: 1 ~1 ~1 ~1 ~1 0 ~1 0 ~1 0 ~1 2 ~1 0 0 1
(1 + (((x + 1) * (~1 + loop(\(x,i).(2x2 + ~x),1,(5x + 5)))) div 2))
A167467: 23 190 652 1559 3061 5308 8450 12637 18019 24746 32968 42835 54497 68104 83806 101753
loop(\(x,i).i,(x div (2 + (((2x + ~3) * (4 + (x div 4))) mod (x + 1)))),1)
A337131: 1 1 1 1 2 1 1 1 1 4 2 1 2 1 1 1
(if x <= 0 then 1 else ((2x + 3) + ((10x + 8) div (x + 3))))
A138945: 1 9 12 15 17 20 22 24 27 29 31 33 35 37 39 41
((x + 1) * ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (1 + ((x + 1) div 2))))
A083175: 2 12 30 84 165 312 476 760 1035 1740 2046 3108 3731 4816 5640 7632
(1 + (2 * loop(\(x,i).((x + 1) + ((x div (2 + (((x - (x div 4)) div 2) mod 2))) mod 2)),x,1)))
A309203: 3 5 7 11 13 17 19 23 27 29 31 35 37 39 41 43
(x - ((2x + 1) div (3 + (if (((x + 2) mod 8) mod 3) <= 0 then 0 else 2))))
A227859-A193564: 0 0 1 2 1 3 2 4 5 3 6 7 4 8 5 9
(3 + loop(\(x,i).(~1 + (2 * (1 + (2 * (x - (2 * (x mod ~3))))))),x,0))
A189738: 3 4 24 88 360 1432 5736 22936 91752 367000 1468008 5872024 23488104 93952408 375809640 1503238552
(1 + (((1 + (x mod (2 + ((4 + loop(\(x,i).3x,x,1)) mod (x + 1))))) div 2) div 2))
A333765: 1 1 1 2 1 1 2 3 1 1 2 1 2 2 4 5
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 21)
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A242121: 2 3 5 7 11 13 17 19 2 8 10 16 20 1 5 11
(1 + (((1 + ((x + (loop(\(x,i).2x,x,(2 + (x div 4))) div 3)) div 2)) div 2) div 2))
A283314: 1 1 1 2 3 5 10 18 44
(1 + ((((2 - ((if (x mod 2) <= 0 then (~x + 2) else x) mod 7)) mod (x + 1)) div 2) div 2))
A129176: 1 1 1 1 1 1 2 1 1 1 2 3 3 3 1 1
(1 + ((((5 * (2 + (2 * (if (x mod 3) <= 0 then 0 else 2)))) mod (x + 1)) div 2) div 2))
A132844: 1 1 1 1 1 1 1 2 1 1 3 2 3 1 1 3
(1 + ((((x + 1) * ((2x + 2) + (if (~2 + (x div 5)) <= 0 then 2 else 1))) div 2) div 2))
A254835: 2 4 7 11 16 22 29 37 46 56 67 79 92 106 121 133
((if x <= 0 then 1 else (x - (((~2x + 1) + (x mod 2)) div 3))) mod (1 + (((x + 1) div 2) div 2)))
A334153: 0 0 0 1 1 0 0 2 1 0 2 2 0 1 3 0
(~1 + (8 * ((1 + (4 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 3)))
A225822: 7 23 31 39 55 71 87 95 103 119 127 135 151 159 167 183
((x + 1) - ((((3 * (1 + (if (x mod 9) <= 0 then 0 else x))) div 2) div 2) div 2))
A168560: 1 2 2 3 4 4 5 5 6 10 7 8 9 9 10 10
(1 + ((((3 * (loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1))) div 2) div 2) div 2))
A342085-A050379: 1 1 1 2 1 2 1 3 2 2 1 5 1 2 2 6
((x + 1) - (2 * loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),2)))
A076535: ~3 ~6 ~5 ~12 ~3 ~10 ~9 ~24 1 ~6 ~5 ~20 ~3 ~18 ~17 ~48
((if x <= 0 then 1 else 4x) - ((~x + 1) div (1 + (2 * (2 + (((x div 2) div 3) mod 2))))))
A312892: 1 4 9 13 17 21 25 29 33 38 42 46 51 55 59 63
(1 + (((loop(\(x,i).((x + 2) + ((((x + 1) + (x div 4)) div 2) div 2)),x,1) div 2) div 2) div 2))
A115593: 1 1 1 2 2 3 4 6 7 10 13 17 22 29 38 50
(1 + (if x <= 0 then 1 else (2 * (x - ((0 - ((x - (((x + 1) div 2) mod 6)) div 2)) div 2)))))
A193063-A165132: 2 3 5 7 11 13
A072697: 2 3 5 7 11 13 15 17 19 21 23 29 31 33 35 37
(loop(\(x,i).3x,(x2 mod 7),1) mod 15)
A331065: 1 3 6 9 9 6 3 1
(((2x2 + ~x) * loop(\(x,i).((x2 + ~x) div 2),2,(x + ~2))) div 9)
A055504: 0 0 0 0 0 15 110 455 1400 3570 7980 16170 30360 53625 90090 145145
(9 * loop(\(x,i).(10x + 2),(x div 2),(1 + (x mod 2))))
A050250: 9 18 108 198 1098 1998 10998 19998 109998 199998 1099998 1999998 10999998 19999998 109999998 199999998
(loop(\(x,i).x6,1,(3x + 1)) div 9)
A282232: 0 455 13072 111111 536312 1864135 5227320 12597767 27126736 53543367 98611520 171644935 285080712 455111111 702373672 1052699655
(9 * (1 + loop(\(x,i).(x + 1),(~4 + ((x + ((x div 2) mod 2)) div 2)),x)))
A085132: 9 18 27 36 45 54 63 72 81 90 108 126 135 144 162 180
(if x <= 0 then 1 else (9 + compr(\x.(x mod ((x + 1) - (x mod 10))),x)))
A115844: 1 10 11 12 13 14 15 16 17 18 20 30 40 50 60 70
((x * loop(\(x,i).(10x + 1),8,1)) div 9)
A070189: 0 12345679 24691358 37037037 49382716 61728395 74074074 86419753 98765432 111111111 123456790 135802469 148148148 160493827 172839506 185185185
loop(\(x,i).x7,1,(12x + 9))
A017635: 4782969 1801088541 42618442977 373669453125 1954897493193 7446353252589 22876792454961 60170087060757 140710042265625 300124211606973 594467302491009 1107984764452581 1962637152460137 3329565857578125 5442680797299153 8614550657858229
loop(\(x,i).x6,1,(~11x + ~9))
A017502: 531441 64000000 887503681 5489031744 22164361129 68719476736 177978515625 404567235136 832972004929 1586874322944 2839760855281 4826809000000 7858047974841 12332795428864 18755369578009
(1 + (loop(\(x,i).((x + 2) - (((x2 div 3) mod (2x + 1)) mod 2)),x,1) mod 4))
A106645: 2 4 1 2 4 1 3 1 2 4 1 2 4 1 3 1
(1 + (((x * (~1 + (2 * (1 + (x div (if (x mod 2) <= 0 then 3 else ~2)))))) div 2) mod 4))
A083954: 1 4 2 4 3 4 4 4 1 4 4 4 3 4 4 4
((~1 + (2 * (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))) div 5)
A328167: 0 0 1 0 2 1 3 0 1 2 4 1 5 3 1 0
((if x <= 0 then 1 else 6x) - ((3 * ((x + 1) + (x mod 2))) div 5))
A137002: 1 5 11 15
A314053: 1 5 11 15 21 26 32 37 43 48 54 59 65 69 75 80
(((2 * loop(\(x,i).(2x + 1),(x + 4),6)) div 3) div 5)
A263119: 14 29 59 119 238 477 955 1911 3822 7645 15291 30583 61166 122333 244667 489335
((((loop(\(x,i).(x3 + ~x),1,(x + 4)) div 2) div 2) div 3) div 5)
A084624: 1 2 3 5 8 12 16 22 28 36 45 56 68 81 96 114
(5 * (1 + compr(\x.(loop(\(x,i).4x2,2,5) mod (x + 1)),x)))
A086761: 5 10 20 25 40 50 80 100 125 160 200 250 320 400 500 625
((loop(\(x,i).(7x + ~3),(x + 1),5) div 2) div 5)
A037775: 3 22 154 1080 7563 52942 370594 2594160 18159123 127113862 889797034 6228579240 43600054683 305200382782 2136402679474 14954818756320
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 30)
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A095959: 2 3 5 7 11 13 17 19 23 29 1 7 11 13 17 23
((loop(\(x,i).10x,x,(x + 10)) div 2) div 5)
A081122: 1 11 120 1300 14000 150000 1600000 17000000 180000000 1900000000 20000000000 210000000000 2200000000000 23000000000000 240000000000000 2500000000000000
((if x <= 0 then 1 else 6x) - ((x + ((x div 2) mod 5)) div 5))
A315749: 1 6 12 18 23 29 35 40 46 52 58 64 70 76 81 87
((if x <= 0 then 1 else 5x) - ((x + ((x div 2) mod 5)) div 5))
A313692: 1 5 10 15 19 24 29 33 38 43 48 53 58 63 67 72
(x + ((if (x div 7) <= 0 then 1 else (3x + 3)) + (x div 5)))
A212317: 1 2 3 4 5 7 8 32
(~1 + (((x + (14 * (x + (if (~2 + (x div 2)) <= 0 then 1 else 2)))) div 2) div 2))
A190701: 2 6 10 13 17 21 28 32 36 39 43 47 51 54 58 62
(~1 + ((loop(\(x,i).((4x + 4) - ((~2x + 2) div 5)),2,x) div 2) div 2))
A189396: 4 8 14 18 24 28 33 38 43 48 52 57 62 67 72 77
((x + 5) + (if x <= 0 then 1 else ((4x + 2) + ((1 + (x div 2)) div 3))))
A212449: 6 12 17 22 28 33 38 43 48 53 59 64 69 74 79 84
(1 + ((((x + 2) + (loop(\(x,i).(x * (1 + i)),(2 + (x div 4)),1) mod (x + 1))) div 2) div 2))
A107452: 1 1 2 2 3 2 3 3 4 3 6 4 5 6 5 5
(x mod (~1 + (2 * ((if (~x + 2) <= 0 then (1 - (x mod (1 + (4 * (x mod 2))))) else 1) + (x mod 2)))))
A248395: 0 1 0 0 0 2 0 0 0 ~1 0 0 0 ~2 0 0
((x + 1) div (~1 + (2 * (if x <= 0 then 1 else ((3 * (1 + (x mod (2 + (x mod 2))))) + (x mod 2))))))
A204389-A101048: 1 0 0 0 1 0 1 0 1 1 2 0 2 1 3 2
(loop(\(x,i).2x,((x div 2) - ((3 * (x div 4)) div 2)),1) * (1 + (2 * (x mod 2))))
A071044: 1 3 2 6 2 6 4 12 2 6 4 12 4 12 8 24
(loop(\(x,i).14x,(x div 2),(1 + (x mod 2))) * (1 + (2 * (x mod 2))))
A182752: 1 6 14 84 196 1176 2744 16464 38416 230496 537824 3226944 7529536 45177216 105413504 632481024
((1 + ((loop(\(x,i).x2,1,(4x + ~1)) div 5) div 3)) mod 3)
A081285: 1 1 1 0 1 1 0 1 2 1 0 1 1 0 1 2
((1 + (loop(\(x,i).x2,1,((2x + 8) div 5)) div 3)) mod 3)
A160096: 1 2 2 2 1 1 0 0 0 0 0 1 1 1 2 2
((1 + ((loop(\(x,i).(x3 div 2),1,(x2 + 2x + 1)) div 2) div 3)) div 3)
A061004: 0 2 20 114 434 1296 3268 7282 14762 27778 49210 82944 134078 209154 316406 466034
((1 + ((((x + 1) * (x + loop(\(x,i).x2,1,(2x + 4)))) div 2) div 3)) div 3)
A131177-A092498: 1 4 11 23 41 67 102 147 204 274 358 458 575 710 865 1041
((1 + (2 * loop(\(x,i).3x,(~1 + ((x * (~1 + (x mod 3))) div 2)),1))) div 3)
A090163: 1 1 1 1 1 2 1 1 18
((1 - (if x <= 0 then 0 else (1 + ((x mod (1 + ((2 - (x mod 4)) mod (x + 1)))) div 2)))) mod 3)
A171919: 1 0 0 2 0 0 0 0 2 0 0 1 0 0 0 2
((1 + (2 * (if x <= 0 then 1 else (8x - ((x + 2) div 5))))) div 3)
A137002: 1 5 11 15
A314049: 1 5 11 15 21 26 31 37 41 47 52 57 63 67 73 78
((1 + (2 * (if x <= 0 then 1 else (2 * (4x - ((~x + 2) div 5)))))) div 3)
A301718: 1 5 11 17 23 28 33 39 45 51 56 61 67 73 79 84
((1 + (2 * (if x <= 0 then 1 else (2 * ((x + 1) + (2 div (~x + 16))))))) div 3)
A187885: 1 3 4 5 7 8 9 11 12 13 15 16 17 19 21 24
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 27)
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A242125: 2 3 5 7 11 13 17 19 23 2 4 10 14 16 20 26
((loop(\(x,i).(2x + 2),x,1) mod (30x + 10)) mod 3)
A240021: 1 1 1 1 1 1 0 0 1 2 1 1 1 0 1 1
((if x <= 0 then 1 else 6x) - ((1 + (2 * ((x + ((x div 2) mod 2)) div 2))) div 3))
A315540: 1 6 11 17 23 29 34 39 45 51 57 62 68 74 79 85
((if x <= 0 then 1 else 5x) - ((1 + (2 * ((x + ((x div 2) mod 2)) div 2))) div 3))
A314893: 1 5 9 14 19 24 28 32 37 42 47 51 56 61 65 70
((1 + (2 * (if x <= 0 then 1 else (6x - ((~x + ((x div 2) mod 2)) div 2))))) div 3)
A314683: 1 5 9 13 17 22 26 30 35 39 43 47 52 57 61 65
((loop(\(x,i).9x,x,(x + 9)) div 3) div 3)
A081109: 1 10 99 972 9477 91854 885735 8503056 81310473 774840978 7360989291 69735688020 659002251789 6213449802582 58462914051567 549043018919064
(((2 + ((x + 1) div (1 + (if (x mod (2 + (x mod 4))) <= 0 then 2 else 1)))) div 3) mod 3)
A217463-A216501: 0 1 1 1 1 1 1 2 1 1 2 2 2 0 0 2
(~2 + ((x div 2) + (3 * ((4 * (x + (if (~2 + (x div 2)) <= 0 then 1 else 2))) div 3))))
A285979: 1 4 11 14 18 24 31 37 41 44 51 54 58 64 68 71
(((x2 + 4x + 3) * loop(\(x,i).x2,1,((x2 + 3x + 2) div 2))) div 3)
A165187: 1 24 180 800 2625 7056 16464 34560 66825 121000 207636 340704 538265 823200 1224000 1775616
(((x + ((x div 2) mod 2)) div 2) + (if x <= 0 then 1 else 4x) + ((2x + 1) div 3))
A313862: 1 5 10 16 21 25 31 37 41 46 52 57 62 67 72 78
(4x + ((2x + 1) div 3) - ((((x div 2) mod 2) - (if x <= 0 then 1 else x)) div 2))
A315274: 1 6 10 15 21 26 31 36 41 47 52 56 62 68 72 77
((x + 1) + (((x + (if (~2 + (x div 2)) <= 0 then 1 else 2)) div 4) + ((1 + (x div 2)) div 3)))
A288378: 1 2 3 5 7 8 10 11 12 13 16 17 18 19 21 22
(((x + 1) * (1 + (2 * ((2x + (if (x + ~3) <= 0 then x else 0)) div 3)))) mod 3)
A135298: 1 0 0 1 1 0 0 0 0 1 2 0 2 1 0 0
((x2 + 3x + 5) + (loop(\(x,i).((x2 + ~x) div 2),2,(x + 1)) div 3))
A188555: 5 9 16 28 48 80 129 201 303 443 630 874 1186 1578 2063 2655
(6 * (1 + (2 * (1 + (5 * loop(\(x,i).(2x + 4),x,3))))))
A304614: 198 618 1458 3138 6498 13218 26658 53538 107298 214818 429858 859938 1720098 3440418 6881058 13762338
((2 * (1 + ((1 + ((loop(\(x,i).((2x + 1) * i),x,1) mod (x + 1)) div 2)) div 2))) div 3)
A064875: 0 0 1 1 0 1 1 1 2 0 1 1 2 2 2 2
((2 * (1 + ((1 + ((loop(\(x,i).(x + (x div 2)),x,3) - (x mod 2)) div 2)) div 2))) div 3)
A057591: 1 1 2 2 2 4 5 7 11 16 24
(3 + (if x <= 0 then 1 else (2 + ((~x + 1) mod (1 + ((x - ((x div 3) mod 3)) div 2))))))
A136004: 4 5 6 5 6 7 6 5 6 7 8 7 6 7 6 5
((2 * ((2 * (if x <= 0 then 1 else 4x)) - (2x div 7))) div 3)
A313836: 1 5 10 16 20 26 31 36 41 46 52 56 62 67 72 77
(3 * (2 + (5 * loop(\(x,i).(6x + 2),(x div 2),(x mod 2)))))
A056488: 6 21 36 126 216 756 1296 4536 7776 27216 46656 163296 279936 979776 1679616 5878656
((if x <= 0 then 1 else 4x) - ((1 - (2 * (x - ((~x + 2) div 5)))) div 3))
A250120: 1 5 9 15 19 24 29 33 39 43 48 53 57 63 67 72
((2 + ((1 + (((if (x mod 2) <= 0 then 2 else 0) + (x div 2)) * (1 + (x div 2)))) div 3)) div 3)
A266755: 1 0 1 1 2 1 3 2 4 3 5 4 7 5 8 7
(6 * (3 + loop(\(x,i).(2x + 40),(x + 1),1)))
A278130: 270 762 1746 3714 7650 15522 31266 62754 125730 251682 503586 1007394 2015010 4030242 8060706 16121634
(18 * ((x + ~1) + loop(\(x,i).(x - ((~2 + (x div 2)) div 3)),2,x)))
A044120: 18 54 90 108 126 162 198 234 270 306 324 342 378 414 450 486
((loop(\(x,i).(x2 + x),1,(x3 + 7x2 + 15x + 9)) div 2) div 3)
A024197: 15 176 950 3480 10045 24640 53676 106800 197835 345840 576290 922376 1426425 2141440 3132760 4479840
((loop(\(x,i).x2,1,(1 + ((x2 + 6x + 8) div 2) - (x mod 2))) div 2) div 3)
A338429: 4 8 28 48 104 160 280 400 620 840 1204 1568 2128 2688 3504 4320
((((x2 + 3x + 2) * loop(\(x,i).((x2 + ~x) div 2),2,(x + 4))) div 2) div 3)
A027801: 5 45 210 700 1890 4410 9240 17820 32175 55055 90090 141960 216580 321300 465120 658920
loop(\(x,i).x7,1,(7x + 5))
A017047: 78125 35831808 893871739 8031810176 42618442977 163840000000 506623120463 1338925209984 3142742836021 6722988818432 13348388671875 24928547056768 44231334895529 75144747810816
((2 + (loop(\(x,i).(2 * ((~2x + 2) div 5)),x,~x) mod (x + 1))) div 3)
A343333: 0 0 1 1 1 2 1 2 2 2 3 2 3 2 4 2
((4 * (1 + ((x div 3) div (1 + (if (~2 + (x div 4)) <= 0 then 2 else 0))))) div 3)
A032558: 1 1 1 1 1 1 1 1 1 2 2 2 6 6 6 8
((4 * (1 + (x div (1 + (if ((x * (x div 2)) mod 2) <= 0 then x else (x mod 3)))))) div 3)
A323921: 1 1 1 5 1 1 1 5 1 1 1 5 1 1 1 21
((4 * loop(\(x,i).10x2,(3x + 1),1)) div 3)
A093671: 13 1333333333333333 4611686018427387903 4611686018427387903
((2 * ((5 * (1 + (if ((x + ~1) mod 3) <= 0 then 2x else 0))) div 2)) div 3)
A267318: 1 4 1 1 14 1 1 24 1 1 34 1 1 44 1 1
(x2 div (5 + (if x <= 0 then 1 else (x - (2 * ((x mod (2 + (x div 2))) div 3))))))
A248517: 0 0 0 1 1 2 3 4 4 6 7 8 9 10 11 14
((if x <= 0 then 1 else 6x) - ((x - (x mod (4 + (x div 3)))) div 3))
A315761: 1 6 12 18 24 29 34 40 46 52 58 64 70 76 82 87
((if x <= 0 then 1 else 5x) - ((x - (x mod (4 + (x div 3)))) div 3))
A313719: 1 5 10 15 20 24 28 33 38 43 48 53 58 63 68 72
((2 * (2 + (loop(\(x,i).2x,x,(1 + (x mod (2 + (x mod 4))))) mod (x + 1)))) mod 3)
A143111: 1 1 1 1 0 1 1 1 0 2 1 0 0 0 1 1
((2 * (2 + ((1 - (loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 3)) mod (x + 1)))) mod 3)
A064692: 1 0 0 0 1 0 1 0 2 1 1 0 0 0 1 0
loop(\(x,i).((11x2 + 52x + 41) div 2),2,3)
A263081: 124340 124340 124340 124340 124340 124340 124340 124340 124340 124340 124340 124340 124340 124340 124340 124340
(9 + (if (~x + 2) <= 0 then (2 + ((x + ~1) mod 9)) else 1))
A063660: 10 10 12 13 14 15 16 17 18 19 11 12 13 14 15 16
((4 * ((3 * (x + (if (~x + 2) <= 0 then (2 + (x div 4)) else 1))) div 2)) div 3)
A308416: 1 4 8 9 13 16 17 20 24 25 28 29 33 36 37 40
((2 * (2 + ((loop(\(x,i).(3x + 12),(x + 1),0) mod (x + 1)) div 2))) mod 3)
A225245: 1 1 1 1 0 1 2 1 0 0 1 1 1 1 1 1
((2 * (4 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3)
A307408: 2 2 2 3 2 4 2 4 3 4 2 6 2 4 4 5
((if x <= 0 then 1 else 6x) - ((2 * (x - ((((x + 1) div 2) div 2) div 2))) div 3))
A315490: 1 6 11 16 22 27 32 38 44 49 54 60 65 70 76 82
((2 * (2 + (((((x + loop(\(x,i).3x,(x + ~2),x)) div 2) div 2) div 2) div 2))) mod 3)
A141647: 1 1 1 1 2 2 1 0 2 1 1 2 0 0 2 1
((loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) mod (4 * (2 + (x mod 4)))) mod 3)
A035196: 1 1 0 1 2 0 1 1 1 2 2 0 2 1 0 1
(1 - (if (x + ~1) <= 0 then 2x else ((2 - (2x mod (4 + (x div 4)))) div 3)))
A143209: 1 ~1 1 1 2 1 1 2 2 1 1 2 2 2 1 1
(5 + ((x + loop(\(x,i).(x - (((~x + ~1) + (x mod 2)) div 5)),x,1)) div 2))
A120190: 5 6 7 8 9 10 12 13 15 17 20 23 26 30 34 39
((if x <= 0 then 1 else 5x) - ((1 - (2 * ((x + ((x div 2) mod 2)) div 2))) div 3))
A314124: 1 5 11 16 21 26 32 38 43 48 53 59 64 69 75 80
((4 + (x * (2 + (x * (2 + (loop(\(x,i).x2,4,2) mod (x + 1))))))) div 3)
A337639: 1 2 6 9 20 54
loop(\(x,i).x7,1,(11x + 1))
A017407: 1 35831808 3404825447 52523350144 373669453125 1727094849536 6060711605323 17565568854912 44231334895529 100000000000000 207616015289871 402271083010688 736141813551277 1283918464548864
loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(11x + 1))
A050490: 1 12 46 170 630 2352 8844 33462 127270 486200 1864356 7171892 27665596 106977600 414538200 1609344270
loop(\(x,i).x7,1,(11x + 2))
A017419: 128 62748517 4586471424 64339296875 435817657216 1954897493193 6722988818432 19203908986159 47829690000000 107213535210701 221068140740608 425927596977747 775771085481344 1347646586640625
((x + 1) - (((x + 2) + (((if x <= 0 then 1 else x) + (x div 2)) mod (1 + (x div 3)))) div 3))
A005185: 1 1 2 3 3 4 5 5 6 6 6 8 8 8 10 9
((2 * (x + (if ((x2 + ~x) mod 5) <= 0 then (x mod 8) else 1))) mod 3)
A229764: 0 1 0 2 1 2 0 1 0 2 0 1 2 1 0 2
((if x <= 0 then 1 else 6x) - ((2 * (x + (((x div 2) div 3) mod 2))) div 3))
A315488: 1 6 11 16 22 27 32 37 42 48 53 58 64 70 75 80
((if x <= 0 then 1 else 5x) - ((2 * (x + (((x div 2) div 3) mod 2))) div 3))
A314706: 1 5 9 13 18 22 26 30 34 39 43 47 52 57 61 65
((if x <= 0 then 1 else 5x) - ((2 * (~x + (((x div 2) div 3) mod 2))) div 3))
A315703: 1 6 12 17 23 29 34 39 45 51 56 62 68 74 80 85
(6x + (if x <= 0 then 1 else ((~x + ((x div 2) mod 5)) div 5)))
A314252: 1 5 11 17 23 29 35 41 47 53 58 63 69 75 81 87
(6x + (if x <= 0 then 1 else ((2 * (~x + (((x div 2) div 3) mod 2))) div 3)))
A313879: 1 5 10 16 21 26 32 38 43 48 54 59 64 69 74 80
(6x + (if x <= 0 then 1 else (~4 + ((2x + 1) div 7))))
A272930: 1 2 8 15
A213082: 1 2 8 15 21 27 33 40 46 52 59 65 71 77 84 90
(6x + ((11x2 + 1) * (if x <= 0 then 1 else x)))
A008528: 1 18 102 318 732 1410 2418 3822 5688 8082 11070 14718 19092 24258 30282 37230
(~3 + (2 * (x + loop(\(x,i).((x + 3) + ((x - ((x div 2) div 3)) div 2)),2,x))))
A209624-A175888: 11 17 23 29 37 41 47 53 59 67 71 79 83 89 97 101
(((2x + 2) + (if x <= 0 then 1 else (2 * (x + (2 * (x2 div 8)))))) div 3)
A127758: 1 2 3 6 8 11 14 18 22 26 30 35 40 46 51 58
((if x <= 0 then 1 else 5x) - ((x + ((x + (x div 3)) mod 3)) div 3))
A314848: 1 5 9 14 18 24 28 33 37 42 47 51 56 60 66 70
((x + (2 * (1 + (16 * (~1 + loop(\(x,i).(2 * (x + i)),x,2)))))) div 3)
A059135: 11 54 161 396 887 1890 3917 7992 16163 32526 65273 130788 261839 523962 1048229
((if x <= 0 then 1 else 4x) - (((~x + 1) - (2 * ((x + ((x div 2) mod 2)) div 2))) div 3))
A313099: 1 4 9 14 19 23 28 33 37 42 47 52 56 60 65 70
((3x + 3) + (((x + (if (~2 + (x div 4)) <= 0 then 1 else 2)) div 2) + (x div 3)))
A190306: 3 7 10 15 18 22 26 30 33 38 41 45 50 53 57 61
(((if x <= 0 then 2 else (x - (((x mod 6) + (x div 4)) div 2))) div 2) - (x div 3))
A029415: 1 0 0 0 0 0 1 1 1 0 0 1 1 1 2 1
((2x + 3) + (if x <= 0 then 1 else (2 * ((2x + 1) + ((x div 2) + (x div 3))))))
A063215: 4 11 19 27 35 41 51 57 65 73 81 87 97 103 111 119
(1 + (2 * (x + loop(\(x,i).(x2 + x),1,(~1 + (x mod (x - ((x + ~1) mod 8))))))))
A143452: 1 3 5 7 9 11 13 15 17 19 21 27 37 51 69 91
loop(\(x,i).x7,1,(10x + 7))
A017359: 823543 410338673 10460353203 94931877133 506623120463 1954897493193 6060711605323 16048523266853 37725479487783 80798284478113 160578147647843 300124211606973 532875860165503
((2x + 1) + ((x + (if (~2 + (x div 4)) <= 0 then 1 else 2)) div 2) - (((x + 1) div 2) div 2))
A231407: 1 4 6
A189473: 1 4 6 8 10 13 15 17 19 22 24 26 29 31 34 35
(x mod (1 + ((x + ((3 * ((x + (if (x mod 2) <= 0 then x else 1)) div 5)) div 2)) div 2)))
A161229: 0 0 0 1 1 1 1 2 1 2 1 3 2 4 3 5
(1 + (2 * ((x + 4) + (if x <= 0 then 1 else (10x + 48)))))
A174270: 11 127 149
(1 + ((x + (if x <= 0 then 1 else (2 + compr(\x.((1 + ((x + ((x div 2) div 3)) div 2)) mod 2),x)))) div 2))
A231407: 1 4 6
A299540: 1 4 6 8 9 10 11 13 14 16 17 19 21 22 24 26
((2x2 + 4x + 1) * loop(\(x,i).((2 * (x - (2x * i))) div (1 + i)),2x,1))
A256462: 1 14 238 4092 70070 1192516 20177164 339653880 5692584870 95050101300 1581953021220 26255495764680 434697697648188 7181635051211432 118422830335911640 1949458102569167344
(loop(\(x,i).2x,x,1) mod compr(\x.(x mod (1 + (4 * (x mod (2 + (x mod 2)))))),(x + 3)))
A222011: 1 2 4 8
A175156: 1 2 4 8 6 8 8 8 0 8 4 11 4 8 9 8
(loop(\(x,i).2x,x,2) mod compr(\x.(x mod (1 + (4 * (x mod (2 + (x mod 2)))))),(x + 3)))
A073800: 2 4 0 7 2 4 2 1 0 16 8 1 8 16 18 16
((x3 + 8x2 + 19x + 12) * loop(\(x,i).5x,x,(x + 2)))
A154128: 24 600 9000 105000 1050000 9450000 78750000 618750000 4640625000 33515625000 234609375000 1599609375000 10664062500000 69726562500000 448242187500000 2838867187500000
((x + 3) * (2 + ((1 + (if (x mod 3) <= 0 then (2 - ((x div 2) mod 2)) else 0)) * (x mod 2))))
A114797: 6 12 10 24 14 24 18 30 22 60 26 42 30 48 34 72
(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) - ((~2x + 2) div (x + 3)))
A098393: 2 3 6 8 12 14 19 21 25 31 33 39 43 45 49 55
(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) - (3x div (x + 3)))
A163292: 1 2 3 5 9 11 14 16 20 26 28 34 38 40 44 50
((2x + 1) + ((2x + loop(\(x,i).(x + i - (x div 7)),x,1)) div 2))
A181625: 1 5 9 13 18 23 28 33 39 44 50 56 62 68 74 80
(loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x div 2),(1 + (x mod 2))) * (1 + (x div 2)))
A222011: 1 2 4 8
A026023: 1 2 4 8 15 30 56 112 210 420 792 1584 3003 6006 11440 22880
(1 + (2 * (((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2) + (if x <= 0 then 0 else 1))) - (x mod 2))
A288569: 1 2 3 2 3 4 3 2 3 4 3 4 3 4 5 2
(if (x mod 2) <= 0 then 1 else (1 + ((x div (2 + (x div (1 + ((2 - (x div 2)) mod 4))))) + (x mod 2))))
A308551-A285324: 1 2 1 3 1 2 1 4 1 3 1 3 1 2 1 5
(loop(\(x,i).3x,((x div 2) - ((3 * (x div 4)) div 2)),1) * (1 + (x mod 2)))
A323642: 1 2 3 6 3 6 9 18 3 6 9 18 9 18 27 54
(1 + compr(\x.(~1 + ((1 + (if (x mod 7) <= 0 then 0 else x)) mod (1 + (x div 3)))),x))
A334929: 1 2 3 4 5 6 7 8 9 12 15 18 21 22 24 27
(1 + compr(\x.(~1 + (x mod (1 + ((~1 + loop(\(x,i).(~2x + 1),x,6)) mod (x + 1))))),x))
A247397: 1 2 3 4 5 6 7 8 9 10 12 13
A082918: 1 2 3 4 5 6 7 8 9 10 12 13 14 19 21 24
(1 + compr(\x.(~1 + ((1 + (loop(\(x,i).(5x + 2),x,1) div (x + 1))) mod 3)),x))
A201363: 2 3 7
A246448: 2 3 7 8 10 11 12 13 14 15 17 18 19 20 22 23
((x + 1) + ((~x + 1) mod (1 + ((1 - loop(\(x,i).(2x + ~4),(x + ~2),0)) mod (2x + 1)))))
A222011: 1 2 4 8
A258096: 1 2 4 8 7 10 12 8 18 18 16 24 21 20 28 32
(1 + compr(\x.((x + 1) mod (1 + (x div (1 + ((if (~2 + (x div 4)) <= 0 then 1 else 2) + (x mod 2)))))),x))
A141113: 1 2 4 6 12 15 16 20 21 24 27 28 32 33 36 39
(1 + compr(\x.(x mod (1 + ((~1 + loop(\(x,i).(2 * (x - (i mod 2))),x,(2x + 1))) mod (x + 1)))),x))
A340077-A179458: 1 3 5 7 11 13 15 17 19 23 29 31 37 41 43 47
(1 + compr(\x.(~1 + ((1 + loop(\(x,i).(6x2 + ~12),2,(x + 1))) mod (x + 1))),x))
A185092: 1 2 3 4 6 12
A018683: 1 2 3 4 6 12 71 142 213 284 426 852
(1 + compr(\x.(~1 + (9x mod loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))),x))
A052347: 1 2 3 4 5 6 8 9 10 12 16 18 20 24 32 36
(1 + compr(\x.((x + ~1) - ((4x + 4) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))),x))
A067319: 1 2 3 4 5 6 8 10 12
A233205: 1 2 3 4 5 6 8 10 12 16 24 32 48 64 96 128
loop(\(x,i).x3,1,(1 + compr(\x.(x mod (1 + ((x mod ((x + ~1) - (x mod 4))) div 2))),x)))
A125496: 1 8 27 64 125 343 512 729 1331 2197 3375 4096 4913 6859 9261 12167
(1 + compr(\x.(1 - ((x div 2) mod (1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 6)))),x))
A237417: 3 5 6 9 10 12 15 17 18 20 21 23 24 27 29 30
(1 + compr(\x.(x mod (1 + (4 * (2x mod (1 + (2 * (if (x mod 3) <= 0 then 0 else 2))))))),x))
A231407: 1 4 6
A133483: 1 4 6 7 10 11 13 16
A153082: 1 4 6 7 10 11 13 16 18 19 21 22 25 26 28 31
(if x <= 0 then 0 else ((x + 1) + (9 * ((x + 1) - (x mod 10)))))
A162672: 0 11 12 13 14 15 16 17 18 19 110 111 112 113 114 115
loop(\(x,i).(5 * (2x + (18x div (1 + i)))),x,1)
A053113: 1 55 2200 71500 2002000 50050000 1144000000 24310000000 486200000000 9237800000000 167960000000000 2939300000000000 49742000000000000 817190000000000000 4611686018427387903 4611686018427387903
(1 + compr(\x.(2 - ((1 + ((1 + ((loop(\(x,i).2x,x,2) mod (x + 1)) div 2)) div 2)) mod 3)),x))
A154663: 3 5 6 7 10 11
A335657-A038550: 3 5 6 7 10 11 12 13 14 17 19 20 22 23 24 26
((~x + ~1) + (6 * ((x + 1) div (if ((x + 1) mod 5) <= 0 then 4 else 1))))
A307151: 5 10 15 20 1 30 35 40 45 2 55 60 65 70 3 80
(1 + compr(\x.((0 - ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 2)) mod 3),x))
A171561: 1 2 3 5 7 8 11 13 17 19 23 27 29 31 32 37
((x + 1) + (12 * (1 + ((x + 1) * (2 + loop(\(x,i).x2,2,3))))))
A100776: 1009 2006 3003 4000 4997 5994 6991 7988 8985 9982 10979 11976 12973 13970 14967 15964
((x + 1) + ((2 * (2x + (if ((x + ~1) mod 7) <= 0 then 1 else 2))) div 3))
A187686: 2 4 7 9 11 14 16 18 20 23 25 28 30 32 35 36
loop(\(x,i).(((2x * ((1 + (2 * i)) * (1 + (2 * i)))) div (1 + i)) * (1 + (2 * i))),x,1)
A060629: 1 27 2250 385875 112521150 49921883550 31336679474100 26440323306271875 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((((4x div (1 + i)) * (~1 + (2 * i))) div (1 + i)) * (1 + (2 * i))),x,1)
A000891: 1 3 20 175 1764 19404 226512 2760615 34763300 449141836 5924217936 79483257308 1081724803600 14901311070000 207426250094400 2913690606794775
(1 + compr(\x.(loop(\(x,i).x3,2,39) mod (x + 1)),x))
A107364: 1 3 9 13 27 39 81 117 169 243 351 507 729 1053 1521 2187
(1 + compr(\x.(2 - (loop(\(x,i).x2,2,35) mod (x + 1))),x))
A219256: 10 11 13 14 15 19 20 21 22 23 26 27 28 29 30 31
(1 + compr(\x.(loop(\(x,i).x3,2,65) mod (x + 1)),x))
A107466: 1 5 13 25 65 125 169 325 625 845 1625 2197 3125 4225 8125 10985
(1 + compr(\x.(loop(\(x,i).(x2 + 10x + 16),2,9) mod (x + 1)),x))
A218584: 1 3 5 7 9 13 15 21 27 35 39 45 63 65 81 91
(1 + compr(\x.(loop(\(x,i).(x2 + 2x),2,(6 * (1 + (2 * (x mod 2))))) mod (x + 1)),x))
A067319: 1 2 3 4 5 6 8 10 12
A336505: 1 2 3 4 5 6 8 10 12 15 16 18 20 24 25 30
(1 + compr(\x.(x - ((1 + loop(\(x,i).(x * (4x + (i mod 2))),2,2x)) mod (x + 1))),x))
A018646: 1 2 3 6 131 262 393 786
(1 + compr(\x.((1 + (x * loop(\(x,i).x2,2,20x))) mod (x + 1)),x))
A018432: 1 3 7 19 21 57 133 399
(1 + compr(\x.((1 + loop(\(x,i).4x,22,x)) mod (x + 1)),x))
A003549: 1 3 5 15 23 69 89 115 267 345 397 445 683 1191 1335 1985
(1 + compr(\x.((1 + loop(\(x,i).10x,10,x)) mod (x + 1)),x))
A027895: 1 3 9 11 33 41 99 123 271 369 451 813 1353 2439 2981 4059
(1 + compr(\x.((1 + (x * loop(\(x,i).x2,2,(10x + ~16)))) mod (x + 1)),x))
A018586: 1 3 5 9 15 25 27 45 75 135 225 675
(1 + compr(\x.((1 + (x * loop(\(x,i).(~3x2 + x + ~1),2,2x))) mod (x + 1)),x))
A018595: 1 2 4 173 346 692
(1 + compr(\x.((1 + (x * loop(\(x,i).(5x2 + 5x),2,2x))) mod (x + 1)),x))
A018513: 1 3 9 61 183 549
(1 + compr(\x.(x - ((1 + (x * loop(\(x,i).(4x2 + ~1),2,2x))) mod (x + 1))),x))
A318165: 1 3 13
A018709: 1 3 13 23 39 69 299 897
(1 + compr(\x.((1 + (x * loop(\(x,i).(4x2 + x + 1),2,2x))) mod (x + 1)),x))
A018719: 1 3 5 15 61 183 305 915
(1 + compr(\x.((1 + (x * loop(\(x,i).(3x2 + x + 1),2,2x))) mod (x + 1)),x))
A018420: 1 2 11 17 22 34 187 374
(1 + compr(\x.((1 + (x * loop(\(x,i).(3x2 + ~2x + 1),2,2x))) mod (x + 1)),x))
A018672: 1 7 17 49 119 833
(1 + compr(\x.((1 + (x * loop(\(x,i).x5,1,3x))) mod (x + 1)),x))
A018352: 1 2 4 61 122 244
(1 + compr(\x.((1 + (x * loop(\(x,i).(~6x2 + 2x + ~1),2,x))) mod (x + 1)),x))
A018491: 1 2 11 22 23 46 253 506
(1 + compr(\x.((1 + (x * loop(\(x,i).(~4x2 + 4x + ~3),2,x))) mod (x + 1)),x))
A018505: 1 2 4 7 14 19 28 38 76 133 266 532
(1 + compr(\x.((1 + (x * loop(\(x,i).(5x2 + 10x + ~10),2,x))) mod (x + 1)),x))
A018747: 1 2 4 241 482 964
(1 + compr(\x.((1 + (x * loop(\(x,i).~10x2,2,x))) mod (x + 1)),x))
A018768: 1 7 11 13 77 91 143 1001
(1 + compr(\x.((1 + (x * loop(\(x,i).(5 * (2 + (x * (x + i)))),2,x))) mod (x + 1)),x))
A018548: 1 3 7 21 29 87 203 609
(1 + compr(\x.((1 + (x * loop(\(x,i).(5x2 + 20x),2,x))) mod (x + 1)),x))
A222011: 1 2 4 8
A018666: 1 2 4 8 103 206 412 824
(1 + compr(\x.((1 + (x * loop(\(x,i).(6x2 + ~6x + ~3),2,x))) mod (x + 1)),x))
A018449: 1 2 4 107 214 428
(1 + compr(\x.((1 + (x * loop(\(x,i).(9x2 + ~18),2,x))) mod (x + 1)),x))
A172411: 1 2 5 10
A018603: 1 2 5 10 71 142 355 710
(1 + compr(\x.((1 + (x * loop(\(x,i).~9x2,2,x))) mod (x + 1)),x))
A172411: 1 2 5 10
A018615: 1 2 5 10 73 146 365 730
(1 + compr(\x.((1 + (x * loop(\(x,i).(6x2 + ~3x + 3),2,x))) mod (x + 1)),x))
A172411: 1 2 5 10
A018670: 1 2 5 10 83 166 415 830
(1 + compr(\x.((1 + (x * loop(\(x,i).(12x2 + ~6),2,x))) mod (x + 1)),x))
A018447: 1 5 17 25 85 425
(1 + compr(\x.((1 + (x * loop(\(x,i).(~12x2 + 3),2,x))) mod (x + 1)),x))
A172411: 1 2 5 10
A018751: 1 2 5 10 97 194 485 970
(1 + compr(\x.((1 + (x * loop(\(x,i).(6x2 + ~5x),2,x))) mod (x + 1)),x))
A172411: 1 2 5 10
A018584: 1 2 5 10 67 134 335 670
(1 + compr(\x.((1 + (x * loop(\(x,i).(8x2 + ~4x + ~4),2,x))) mod (x + 1)),x))
A018475: 1 5 19 25 95 475
(1 + compr(\x.((1 + (x * loop(\(x,i).(16x2 + ~8),2,x))) mod (x + 1)),x))
A018776: 1 5 7 29 35 145 203 1015
(1 + compr(\x.((1 + (x * loop(\(x,i).(~6x2 + ~11x + 2),2,x))) mod (x + 1)),x))
A172411: 1 2 5 10
A018418: 1 2 5 10 37 74 185 370
(1 + compr(\x.((1 + (x * loop(\(x,i).(x * (1 + (3x * (2 + i)))),2,x))) mod (x + 1)),x))
A018639: 1 5 25 31 155 775
(1 + compr(\x.((1 + (x * loop(\(x,i).(x * (~1 + (4x * (1 + i)))),2,x))) mod (x + 1)),x))
A018745: 1 2 13 26 37 74 481 962
(1 + compr(\x.((1 + (x * loop(\(x,i).(7x2 + ~2x),2,x))) mod (x + 1)),x))
A018512: 1 2 4 137 274 548
(1 + compr(\x.((1 + (x * loop(\(x,i).(x * (~1 + (2 * (4x + i)))),2,x))) mod (x + 1)),x))
A018440: 1 2 4 103 206 412
(1 + compr(\x.(loop(\(x,i).(3x3 + 3),2,10) mod (x + 1)),x))
A185092: 1 2 3 4 6 12
A018616: 1 2 3 4 6 12 61 122 183 244 366 732
(1 + compr(\x.((~2 + loop(\(x,i).(x2 + x),2,(12x + 6))) mod (x + 1)),x))
A222011: 1 2 4 8
A018726: 1 2 4 8 16 29 32 58 116 232 464 928
(1 + compr(\x.(loop(\(x,i).(4x2 + 8x + 4),2,8x) mod (x + 1)),x))
A018647: 1 2 4 197 394 788
(1 + compr(\x.((2 + (x * loop(\(x,i).(x4 + ~x3),1,4x))) mod (x + 1)),x))
A018390: 1 2 3 6 53 106 159 318
(1 + compr(\x.(x - ((2 + (x * loop(\(x,i).(4x2 + x),2,2x))) mod (x + 1))),x))
A018650: 1 3 5 15 53 159 265 795
(1 + compr(\x.(loop(\(x,i).(8x2 + 15x + 7),2,2x) mod (x + 1)),x))
A172411: 1 2 5 10
A018648: 1 2 5 10 79 158 395 790
((x + 1) + ((loop(\(x,i).2x,x,(1 + (x mod (2 * (1 + (x mod 2)))))) - (x mod 2)) mod (x + 1)))
A332994: 1 3 4 7 6 9 8 15 13 13 12 19 14 17 19 31
(1 + compr(\x.((2 + (x * loop(\(x,i).(10x2 + 5x),2,x))) mod (x + 1)),x))
A018367: 1 3 7 13 21 39 91 273
(1 + compr(\x.((2 + (x * loop(\(x,i).(8x2 + ~4x + ~4),2,x))) mod (x + 1)),x))
A018474: 1 2 3 6 79 158 237 474
(1 + compr(\x.((2 + (x * loop(\(x,i).(9x2 + 2),2,x))) mod (x + 1)),x))
A057245-A018282: 1 3 9 11 33 99
A004668: 1 3 9 11 33 99 121 363
A239661: 1 3 9 11 33 99 121 363 1089
(1 + compr(\x.((2 + (x * loop(\(x,i).(16x2 + ~8),2,x))) mod (x + 1)),x))
A018274: 1 2 3 6 13 26 39 78
A018775: 1 2 3 6 13 26 39 78 169 338 507 1014
(1 + compr(\x.((2 + (x * loop(\(x,i).((x2 + 4x) * (4 + i)),2,x))) mod (x + 1)),x))
A018761: 1 2 4 13 19 26 38 52 76 247 494 988
(1 + compr(\x.((2 + (x * loop(\(x,i).(9x2 + x),2,x))) mod (x + 1)),x))
A018531: 1 2 3 6 97 194 291 582
(1 + compr(\x.((2 + (x * loop(\(x,i).(7x2 + ~3x),2,x))) mod (x + 1)),x))
A018583: 1 2 4 167 334 668
(1 + compr(\x.((2 + (x2 * loop(\(x,i).(4x2 + 4x),2,2x))) mod (x + 1)),x))
A172411: 1 2 5 10
A018377: 1 2 5 10 29 58 145 290
(1 + compr(\x.(loop(\(x,i).(2x5 + 4x),1,3x) mod (x + 1)),x))
A018488: 1 2 3 6 83 166 249 498
(1 + compr(\x.(loop(\(x,i).(2x5 + ~x4),1,3x) mod (x + 1)),x))
A018522: 1 3 7 9 21 27 63 81 189 567
(1 + compr(\x.(loop(\(x,i).(2x5 + ~x3),1,3x) mod (x + 1)),x))
A018466: 1 3 9 17 27 51 153 459
(1 + compr(\x.(loop(\(x,i).(x5 + 4x3),1,3x) mod (x + 1)),x))
A018407: 1 3 9 13 27 39 117 351
(1 + compr(\x.(loop(\(x,i).(7x2 + 28x + 7),2,x) mod (x + 1)),x))
A018760: 1 3 7 21 47 141 329 987
(1 + compr(\x.(loop(\(x,i).(40x2 + 5x),2,x) mod (x + 1)),x))
A018319: 1 5 7 25 35 175
(1 + compr(\x.(loop(\(x,i).(24x2 + ~24x + 6),2,x) mod (x + 1)),x))
A018566: 1 2 3 6 107 214 321 642
(1 + compr(\x.(loop(\(x,i).(18x2 + 18x + 6),2,x) mod (x + 1)),x))
A018632: 1 2 3 6 127 254 381 762
(1 + compr(\x.(loop(\(x,i).(18x2 + 18x + ~6),2,x) mod (x + 1)),x))
A018506: 1 2 3 6 89 178 267 534
(1 + compr(\x.(loop(\(x,i).(12 * (2x - (x mod 4))),2,x) mod (x + 1)),x))
A344470-A053640: 1 2 3 4 6 8 9 12 16 18 20 24 32 36 40 48
(1 + compr(\x.(loop(\(x,i).(~24x2 + 24x + ~6),2,x) mod (x + 1)),x))
A018574: 1 2 3 6 109 218 327 654
(1 + compr(\x.(loop(\(x,i).(4 * (1 + ((3x + 6) * (x + i)))),2,x) mod (x + 1)),x))
A018455: 1 2 4 109 218 436
(1 + compr(\x.(loop(\(x,i).(14x2 + 6x + 4),2,x) mod (x + 1)),x))
A225841: 1 2 4 523 1046 2092
(1 + compr(\x.(loop(\(x,i).(x * (1 + (2 * (5x + (x div 2))))),2,x) mod (x + 1)),x))
A018516: 1 3 5 15 37 111 185 555
(1 + ((x2 + x) * loop(\(x,i).(x5 + x4 + x3 + x2 + x + 1),1,x2)))
A060887: 1 13 8191 797161 22369621 305175781 2612138803 16148168401 78536544841 317733228541 1111111111111 3452271214393 9726655034461 25239592216021 61054982558011 139013933454241
loop(\(x,i).((2 * (((2x * (1 + (2 * i))) div (2 + i)) * (~1 + (2 * i)))) div (1 + i)),x,1)
A005568: 1 2 10 70 588 5544 56628 613470 6952660 81662152 987369656 12228193432 154532114800 1986841476000 25928281261800 342787130211150
((x + 1) + (4 * (if (x mod 3) <= 0 then 0 else (1 - (2 * ((x div 5) mod 2))))))
A230848: 1 6 7 4 9 2 7
(1 + compr(\x.((x + 1) mod (if x <= 0 then 1 else (2 * (2 + (x mod (x - ((x + ~1) mod 8))))))),x))
A048168: 1 4 8 16 32 48 64 80 96 112 128 144 160 176 192 208
((x2 + 2x + 1) * (1 + (11 * (if x <= 0 then 1 else 2)) - (x mod 2)))
A082814: 12 88 207
((2x + 1) - loop(\(x,i).((x + 1) + (((2x + ~4) div (2 + (x div 4))) mod 2)),x,0))
A285763: 1 2 2 2 3 4 4 4 5 6 7 8 8 8 8 8
((x + 1) * (((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4))) + (if x <= 0 then 0 else 1)))
A188385: 0 2 3 8 5 6 7 24 18 10 11 24 13 14 15 64
compr(\x.(~1 + ((x + 1) mod (1 + ((x + 1) div (1 + (if (x mod 2) <= 0 then 6 else 1)))))),(x + 1))
A122957: 1 2 3 4 6 8 10 12 14 18 20 24 30 36 42 48
((x + 1) * (1 + ((x div 2) div (1 + (x mod (1 + (if (~1 + (x mod 3)) <= 0 then (x div 2) else 2)))))))
A334463: 1 2 3 4 10 6 14 8 18 10 22 24 26 14 45 16
((x + 1) * (~1 + (if x <= 0 then 2 else (((x2 + 2x) div 2) mod (1 + ((1 + (x div 2)) div 3))))))
A224892: 1 ~2 ~3 ~4 ~5 0 ~7 0 ~9 0 ~11 12 ~13 0 0 0
((1 + (x mod (1 + ((1 + (if (x mod 6) <= 0 then 2x else 1)) mod (x + 1))))) mod (x + 1))
A308896: 0 1 0 1 2 3 0 2 3 1 2 3 0 2 3 1
((if x <= 0 then 0 else (1 + (2 * ((x + 1) - (((~x2 + x) div 2) div 5))))) div (x + 1))
A339085: 0 2 3 2 3 2 3 3 3 3 3 3 4 4 4 4
((x + 1) * (1 + (x div ((x + 2) div (2 + (loop(\(x,i).x3,2,2x) mod (x + 1)))))))
A064549: 1 4 9 8 25 36 49 16 27 100 121 72 169 196 225 32
(loop(\(x,i).2x,((((1 + (x mod 4)) * (1 + (x div 3))) div 2) div 2),1) div (x + 1))
A321188: 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 4
compr(\x.(x mod (1 + (4 * (2x mod (1 + (2 * (if (x mod 3) <= 0 then 0 else 2))))))),(x + 1))
A080307: 3 5 6 9 10 12 15 17 18 20 21 24 25 27 30 33
(((1 + (((loop(\(x,i).2x,(x + 1),~2) mod (x + 1)) div 2) div 2)) mod 3) mod (x + 1))
A062831: 0 1 1 1 1 2 1 1 1 1 2 2 0 2 1 1
((3x + 3) * (if x <= 0 then 1 else (3x6 + 3x)))
A272660: 3 36 1782
((x + 1) * ((((x + 3) * loop(\(x,i).(x * (4 + i)),x,(x + 2))) div 2) div 3))
A001755: 1 20 300 4200 58800 846720 12700800 199584000 3293136000 57081024000 1038874636800 19833061248000 396661224960000 8299373322240000 181400588328960000 4135933413900288000
((x + 1) * (3 + (2 * (2 + (3 * (if (x + ~2) <= 0 then 1 else 16))))))
A019551: 13 26 39 412 515 618 721 824 927 1030 1133 1236 1339 1442 1545 1648
((1 + ((x * (1 + ((1 + loop(\(x,i).(x - (x div ~3)),x,1)) div 2))) div 2)) div (x + 1))
A322340: 1 1 1 1 1 2 3 4 5 6 8 11 15 20 27 36
loop(\(x,i).(2x + (14x div (1 + i))),(2x + 1),(x + 1))
A054327: 9 660 20592 411840 6223360 77395968 833495040 8033304576 70882099200 581979340800 4500640235520 33087710822400 232937484189696 1579462143508480 10363761453957120 66060621396836352
((2 + (if ((x + 2) mod 6) <= 0 then (x div 4) else 0) - (x mod 2)) mod (x + 1))
A184166: 0 1 2 1 3 1 2 1 2 1 4 1 2 1 2 1
((x + 1) * loop(\(x,i).(3 * ((x * (~1 + (9 * i))) div (1 + i))),x,1))
A097192: 1 24 612 15912 417690 11027016 292215924 7764594552 206732329947 5512862131920 147193418922264 3934078651195056 105236603919467748 2817102935690367408 4611686018427387903 4611686018427387903
compr(\x.(~1 + loop(\(x,i).(x3 mod 37),2,x)),(x + 1))
A095034: 1 7 9 10 12 16 26 33 34
(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1) mod (x3 + 3x2 + 3x + 1))
A099907: 0 3 10 35 1 30 1 291 253 378 1 782 1 2404 1260 291
((x3 + 3x2 + 3x + 3) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A089620: 3 11 32 71 136 229 360 531 752 1029 1362 1765 2238 2787 3422 4149
((x + 1) * loop(\(x,i).(x + (96x div (1 + i))),x,1))
A017761: 1 98 4851 161700 4082925 83291670 1429840335 21243342120 278818865325 3283866636050 35137373005735 344985116783580 3133614810784185 26515202245096950 210227674943268675 1569699972909739440
((x + 1) * (1 + loop(\(x,i).(x6 + x5 + x4 + x3 + x2 + x),1,x2)))
A104376: 1 14 16383 2391484 89478485 1525878906 15672832819 113037178808 628292358729 2859599056870 11111111111111 37974983358324 116719860413533 328114698808274 854769755812155 2085209001813616
((2 + ((x div (1 + (2 * (2 + (x mod 2))))) + (if x <= 0 then 0 else 1)) - ((x div 2) mod 2)) mod (x + 1))
A072660: 0 1 2 2 3 3 3 3 4 4 4 3 5 4 4 4
((x + 1) + (2 * (1 + (((x + 1) * (1 + loop(\(x,i).(x2 + x + 1),2,x))) div 3))))
A036235: 5 22 121 496
(((x + 2) - ((0 - (loop(\(x,i).(2x + 2),x,0) mod (x + 1))) div 5)) mod (x + 1))
A270096: 0 1 1 2 1 2 1 3 3 2 1 2 1 2 3 4
((x + 1) * (2 + ((3x + 3) * loop(\(x,i).(3x2 + 12x + 12),2,1))))
A031765: 7571 30280 68127 121112 189235 272496 370895 484432 613107 756920 915871 1089960 1279187 1483552 1703055 1937696
((x + 1) * (2 + ((x + 1) * (1 + loop(\(x,i).((2x + 1) * ((x2 + x) div 2)),2,2)))))
A031739: 3723 14888 33495 59544 93035 133968 182343 238160 301419 372120 450263 535848 628875 729344 837255 952608
((x + 1) * (2 + ((x + 1) * loop(\(x,i).(x2 + 6x + 9),2,5))))
A031745: 4491 17960 40407 71832 112235 161616 219975 287312 363627 448920 543191 646440 758667 879872 1010055 1149216
((x + 1) * (2 + ((x + 1) * loop(\(x,i).(x2 + 8x + 16),2,5))))
A031763: 7227 28904 65031 115608 180635 260112 354039 462416 585243 722520 874247 1040424 1221051 1416128 1625655 1849632
((x + 1) * (2 + ((x + 1) * loop(\(x,i).(4x2 + 12x + 9),2,3))))
A157820: 27227 108904 245031 435608 680635 980112 1334039 1742416 2205243 2722520 3294247 3920424 4601051 5336128 6125655 6969632
((x + 1) * (~2 + ((x + 1) * loop(\(x,i).(4x2 + 12x + 9),2,3))))
A157814: 27223 108896 245019 435592 680615 980088 1334011 1742384 2205207 2722480 3294203 3920376 4600999 5336072 6125595 6969568
((x + 1) * (2 + loop(\(x,i).93x,2,(x + 1))))
A031771: 8651 34600 77847 138392 216235 311376 423815 553552 700587 864920 1046551 1245480 1461707 1695232 1946055 2214176
((x + 1) * (2 + loop(\(x,i).59x,2,(x + 1))))
A031737: 3483 13928 31335 55704 87035 125328 170583 222800 281979 348120 421223 501288 588315 682304 783255 891168
((x + 1) * (2 + loop(\(x,i).95x,2,(x + 1))))
A031773: 9027 36104 81231 144408 225635 324912 442239 577616 731043 902520 1092047 1299624 1525251 1768928 2030655 2310432
((x + 1) + (4 * (x mod (1 + (2 * (if ((x2 + x) mod 8) <= 0 then 2 else 0))))))
A285724: 1 2 3 4 5 6 7 16 21 10 11 12 13 14 15 16
((~x + ~1) + ((loop(\(x,i).x2,1,(x + 29)) div 2) div 2))
A159274: 209 223 237 252 267 283 299 316 333 351 369 388 407 427 447 468
(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) - ((x + 1) * (1 - (2 * (x mod 2)))))
A176624: 1 5 2 11 6 19 10 27 14 39 20 49 28 57 32 69
((~x + ~1) + (if x <= 0 then 1 else ((~x + 1) + (4 * (1 + ((3x2 + ~2x) div 2))))))
A211620: 0 2 16 38 76 122 184 254 340 434 544 662 796 938 1096 1262
((x + ((2 * (x + loop(\(x,i).2x,((x + ~2) div 5),1))) div 3)) mod (x + 1))
A335599: 0 0 1 1 2 3 3 5 5 6 7 7 9 10 11 11
((x + (if (x mod 2) <= 0 then (x div 2) else (10x2 + 7x + 1))) div (x + 1))
A019433: 0 9 1 28 1 48 1 68 1 88 1 108 1 128 1 148
loop(\(x,i).(4 * (2x + (14x div (1 + i)))),x,(x + 1))
A141054: 1 72 2880 84480 2027520 42172416 787218432 13495173120 215922769920 3262832967680 46984794734592 649244436332544 8656592484433920 111869810568069120 1406363332855726080 4611686018427387903
loop(\(x,i).(4x + (34x div (1 + i))),x,(x + 1))
A020932: 1 42 966 16100 217350 2521260 26053020 245642760 2149374150 17672631900 137846528820 1027583214840 7364346373020 50983936428600 342320716020600 2236495344667920
loop(\(x,i).(~x + (90x div (1 + i))),x,(x + 1))
A017804: 1 88 3828 109736 2331890 39175752 541931236 6348337336 64276915527 571350360240 4513667845896 32006008361808 205371886988268 1200635647008336 6431976680401800 31731084956648880
loop(\(x,i).(~x + (98x div (1 + i))),x,(x + 1))
A017812: 1 96 4560 142880 3321960 61124064 927048304 11919192480 132601016340 1296543270880 11279926456656 88188515933856 624668654531480 4036320536972640 23929614612052080 130815226545884704
((x + 1) * loop(\(x,i).(x7 + x6 + x5 + x4 + x3 + x2 + x + 1),1,x2))
A105312: 1 16 65535 21523360 1431655765 38146972656 564221981491 5538821761600 40210710958665 231627523606480 1111111111111111 4594972986357216 16807659899548765 55451384098598320 167534872139182395 469172025408063616
loop(\(x,i).(1 + (x div (1 + ((x div 2) mod (1 + (x mod (1 + ((~x + 2) mod 4)))))))),1,(x + ~1))
A090078: 0 1 2 3 2 5 6 7 2 5 10 11 6 13 14 15
loop(\(x,i).(1 + (x mod (1 + ((1 + (x div 3)) mod (1 + ((x + 1) mod 4)))))),1,(x + ~1))
A079115: 1 1 2 1 1 1 3 3 1 1 2 1 1 1 2 1
(loop(\(x,i).((x + 1) + (((2x + 1) div 7) + (x div 3))),x,0) div 2)
A245968: 0 0 1 1 3 5 8 14 23 37 61 99 160 260 421 681
((1 + loop(\(x,i).(1 + (2 * ((24x + 1) div (x + 1)))),x,0)) div 2)
A186682: 0 2 19 24 24 24 24 24 24 24 24 24 24 24 24 24
(2 * (((x + 1) mod (1 + (x div (1 + (2 * (2 - ((x mod 3) div 2))))))) + (if x <= 0 then 0 else 1)))
A211449: 0 2 2 2 2 2 4 2 2 2 6 2 4 6 2 2
((1 + ((x + 1) mod (1 + (if x <= 0 then 0 else (1 + (x div (1 + (2 * (1 + ((x div 2) mod 2)))))))))) div 2)
A066360: 0 0 1 0 1 0 1 1 1 0 2 0 1 1 2 1
(2 - ((~x + 2) div (2 + ((x div 2) div (1 + (x mod (1 + (if (x mod 2) <= 0 then 6 else 1))))))))
A194335: 1 2 2 3 3 3 4 4 4 4 5 5 6 5 4 5
(2 + (x mod (1 + (x mod (1 + (((x + 1) - (loop(\(x,i).2x,x,2) mod (x + 2))) mod (x + 1)))))))
A091963: 2 3 2 5 2 7 2 3 2 11 3 13 2 3 2 17
((1 + ((1 + (x div 2)) mod (1 + ((x + ~1) mod (2 + (if (x mod (2 + (x mod 2))) <= 0 then 2 else 0)))))) div 2)
A338690: 1 0 0 1 2 0 0 0 1 0 0 0 2 0 0 1
(loop(\(x,i).3x,(2 - ((x + 1) mod (1 + (2 * (2 - (x mod ~4)))))),1) div 2)
A156393: 1 0 0 0 4 0 0 1 0 0 0 0 0 0 0 0
(2 * (~1 + (10 * (1 + (2 * loop(\(x,i).(2x + 16),x,1))))))
A305263: 58 738 2098 4818 10258 21138 42898 86418 173458 347538 695698 1392018 2784658 5569938 11140498 22281618
((1 + (if x <= 0 then 1 else (x div (3 * (1 + ((x2 + 2x) mod 7)))))) div 2)
A029399: 1 0 0 0 0 1 0 1 0 1 1 0 2 0 2 1
((if x <= 0 then 2 else (1 + (((x + 1) - (((x + ~1) * ((~x + 1) div 3)) div 2)) div 3))) div 2)
A029146: 1 0 1 1 1 2 2 2 3 4 4 5 6 6 8 9
((1 + (3 * ((2x + 4) mod (1 + (if (x + ~1) <= 0 then 6 else 4))))) div 2)
A254276: 6 9 5 0 3
loop(\(x,i).x7,1,(12x + 10))
A017647: 10000000 2494357888 52523350144 435817657216 2207984167552 8235430000000 24928547056768 64847759419264 150363025899136 318547390056832 627485170000000 1164175380274048 2054210978157184
(if x <= 0 then 1 else (2 * (1 + ((x2 + 4x + 4) div (~x + 26)))))
A087135: 1 2 2 4 4 6 8 10 12 16 20 24 30 36 44 54
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 26)
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A242124: 2 3 5 7 11 13 17 19 23 3 5 11 15 17 21 1
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 22)
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A242122: 2 3 5 7 11 13 17 19 1 7 9 15 19 21 3 9
((1 + ((~x + loop(\(x,i).((x + 2) + (2x div 7)),x,1)) div 3)) div 2)
A237751: 0 0 1 1 1 2 3 4 6 8 10 14 18 24 32 41
((1 + (loop(\(x,i).(1 + ((2x2 + 4x + 4) div 5)),2,x) div 3)) div 2)
A265317: 1 1 3 5 10 17 33 53
((2x + 2) - (if x <= 0 then 1 else ((x mod 2) - ((1 + (8 mod (1 + (x div 2)))) div 2))))
A120511: 1 3 6 7 11 12 14 15 20 21 23 24 27 28 30 31
((1 + ((1 + (x div (1 + (2 * (if (~4 + (x div 2)) <= 0 then 2 else 1))))) div (1 + (x mod 2)))) div 2)
A025812: 1 0 1 0 1 1 1 1 1 1 2 1 3 1 3 2
(1 - (((x + 1) mod (1 + ((1 + ((1 + (if x <= 0 then 1 else x)) mod 3)) * (1 + (x mod 2))))) div 2))
A013596: 1 0 1 ~1 1 1 1 1 1 1 0 1 1 1 1 1
((x + 1) div (2 + ((x div 2) div (1 + (2 mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1))))))
A316314-A183096-A183093-A095960: 0 1 1 1 1 3 1 1 1 3 1 4 1 3 3 1
(2 * (1 + compr(\x.(loop(\(x,i).(x * i),(1 + (x mod (1 + (x div 3)))),1) mod (x + 1)),(x + 1))))
A122181: 24 30 36 40 42 48 54 56 60 64 66 70 72 78 80 84
((1 + ((1 - (2 * (((if (x mod 4) <= 0 then 0 else 1) * (1 + (x div 2))) div 2))) mod (x + 1))) div 2)
A071912: 0 1 1 2 1 3 2 3 1 4 3 4 1 5 4 5
((1 + (((x * (2x div 3)) div 2) mod loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))) div 2)
A277322: 0 0 1 0 2 1 3 0 1 1 4 1 5 2 2 0
((1 + loop(\(x,i).((x + 1) + ((2x div 7) + (x div 3))),x,1)) div 2)
A254729: 1 1 2 3 4 7 11 18 29 47 76 123 199 322 521 843
((x + ~3) + (2 * (1 + ((1 + (if (x mod 2) <= 0 then ((1 + (x div 2)) mod 4) else 1)) div 2))))
A267299: 1 2 3 4 7 6 5 8 9 10 11 12 15 14 13 16
((1 + ((1 + ((1 + (loop(\(x,i).(x + i - (x div ~4)),x,1) div 2)) div 2)) div 2)) div 2)
A239833: 0 1 1 1 2 2 3 4 6 7 10 13 17 22 28 36
((1 + (((if (x div 2) <= 0 then 2 else ((x + ~2) * (x div 3))) mod 7) div 2)) div 2)
A261612: 1 1 0 0 1 1 0 1 1 0 1 2 1 1 2 1
((1 + ((1 + ((loop(\(x,i).2x,x,(1 + (x div 4))) mod (x + 3)) div 2)) div 2)) div 2)
A294019: 0 1 1 1 1 0 1 1 1 0 1 2 1 0 0 2
((1 + ((3 * (1 + (3 * (x - loop(\(x,i).(x div (1 + (x mod 2))),x,x))))) div 2)) div 2)
A165498: 1 3 1 8 1
A319045: 1 3 1 8 1 8 1 17 1
(if x <= 0 then 1 else (2 * (2x + (x div 7) - (x div ~7))))
A315175: 1 6 10 14 18 22 26 32 38 42 46 50 54 58 64 70
((1 + ((1 + (((x + 1) + loop(\(x,i).(x + ((x div 2) div 3)),(x + ~1),x)) div 2)) div 2)) div 2)
A026838: 0 1 1 1 1 2 3 3 4 5 6 7 9 11 14 16
((1 + (((~1 + loop(\(x,i).2x,2x,(1 + (x div (2 + (x mod 2)))))) mod (x + 1)) div 2)) div 2)
A333124: 0 0 0 1 1 0 1 2 2 1 1 1 2 1 2 4
((1 + (((x + 1) * (1 + (2 * (if (~2 + ((x + (x div 2)) mod 4)) <= 0 then 1 else 0)))) div 2)) div 2)
A026366: 1 2 1 3 4 2 5 6 7 8 3 9 10 4 11 12
((1 + ((x + 1) div (2 + ((1 + (if ((x + ~2) mod 6) <= 0 then x else 2)) mod (x + 1))))) div 2)
A115878: 0 0 1 0 1 1 1 1 2 1 1 1 1 1 4 2
((1 + (x div (2 + ((2 * ((if (x mod 3) <= 0 then 1 else 2) + (x mod 4))) mod (x + 1))))) div 2)
A063993: 0 0 0 1 0 1 0 1 1 1 1 0 2 1 1 1
((1 + (((1 + loop(\(x,i).((x + 2) + (2x div 7)),x,2)) div 2) div 2)) div 2)
A064651: 0 1 1 2 2 3 4 5 7 9 12 15 20 25 33 42
((if x <= 0 then 2 else (1 + ((x - (((1 + (~x mod 4)) * (1 + (x div 2))) div 2)) div 2))) div 2)
A025867: 1 0 0 0 1 0 0 1 2 0 0 1 2 0 1 2
((1 + ((loop(\(x,i).((x + 2) + (x div (4 + ((x mod 3) div 2)))),x,1) div 2) div 2)) div 2)
A240200: 0 0 1 1 1 2 3 3 4 5 7 9 11 14 17 21
(1 - ((1 + ((x mod (2 + (loop(\(x,i).2x,((x + 1) mod 4),2) mod (x + 1)))) div 2)) div 2))
A279255: 1 1 0 0 0 1 0 0 0 ~1 0 0 1 0 0 0
(3 + (loop(\(x,i).(2 * (x - ((x + (x div 3)) div 5))),(x + ~1),2) div 2))
A019527: 4 4 5 6 8 11 15 21 30 43 62 90 131 191 279 408
(if x <= 0 then 1 else (2 * (2x - ((~x + 1) div (1 + (2 * (2 + (((x div 2) div 3) mod 2))))))))
A310368: 1 4 10 14 18 22 26 30 34 40 44 48 54 58 62 66
((1 + (((loop(\(x,i).(2x + 2),x,(~x + 17)) div 2) div 2) div 2)) div 2)
A222011: 1 2 4 8
A008936: 1 2 4 8 15 28 52 96 176 320 576 1024 1792 3072 5120 8192
((1 + (((loop(\(x,i).((x + 1) + (2 * (x div 5))),(x + 1),2) div 2) div 2) div 2)) div 2)
A289432: 0 0 0 1 1 1 1 2 3 4 6 8 11 15 21 30
(if (x div 3) <= 0 then 1 else (2 * (1 + ((x + 2) div (8 + (x div ~4))))))
A140839: 1 1 1 2 2 4
A098667: 1 1 1 2 2 4 4 4 4 6 6 6 6 8 10 10
(2 + (9 * loop(\(x,i).(10x + 2),(x div 2),(x mod 2))))
A094629: 2 11 20 110 200 1100 2000 11000 20000 110000 200000 1100000 2000000 11000000 20000000 110000000
(((loop(\(x,i).(x3 + 2x2 + 2x),1,(x2 + 3x + 2)) div 2) div 5) div 2)
A085465: 1 15 102 442 1443 3885 9100 19188 37269 67771 116754 192270 304759 467481 696984 1013608
(20 * (~2 + loop(\(x,i).20x,2,(x + 1))))
A157660: 7960 15960 23960 31960 39960 47960 55960 63960 71960 79960 87960 95960 103960 111960 119960 127960
(compr(\x.(x mod ((x + 1) - (x mod 10))),x) + (if x <= 0 then 1 else 10))
A284062: 1 11 12 13 14 15 16 17 18 19 21 31 41 51 61 71
(if x <= 0 then 1 else (2 * (3x - ((x + ((x div 2) mod 5)) div 5))))
A315732: 1 6 12 18 22 28 34 38 44 50 56 62 68 74 78 84
(((~1 + (if ((x * (x mod 3)) mod 5) <= 0 then 2 else 0)) * (1 + (2 * (x div 2)))) div 2)
A285779: 0 ~1 ~2 1 ~3 2 3 ~4 ~5 4 5 ~6 6 ~7 ~8 7
(~2 + (3 * (1 + ((1 + ((x mod (1 + (2 * (if (x mod 2) <= 0 then x else 2)))) div 2)) div 3))))
A318281: 1 1 1 1 4 1 4 1 4 4 7 1 7 1 7 1
((9 * ((x * (x div 2)) mod (1 + (if (x mod 8) <= 0 then 2 else 1)))) div 2)
A071327: 0 0 0 4 0 0 0 4 9 0 0 4 0 0 0 4
(if x <= 0 then 1 else (2 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))
A142240: 1 2 2 2 3 2 2 4 4 2 2 5 6 5 2 2
(~2 + (3 * (2 + (3 * ((x mod (2 + (if (x mod 8) <= 0 then x else 1))) div 2)))))
A088838: 4 4 13 4 4 13 4 4 40 4 4 13 4 4 13 4
(if x <= 0 then 1 else (2 * (2x - (((~x + 1) + (2 * ((~2x + 1) div 3))) div 3))))
A315343: 1 6 10 16 22 28 34 40 44 50 56 60 66 72 78 84
(2 + ((2 + (loop(\(x,i).((x + 3) + (x div 5)),(x + 1),2) div 2)) div 3))
A120172: 3 4 4 5 6 7 9 11 13 15 18 22 26 32 38 46
(((2 + (loop(\(x,i).(x2 + x),1,(x - (x2 div 8))) div 2)) div 3) div 2)
A334246: 0 0 0 0 0 0 0 0 0 0 0 1 2 5 7 13
(((2 + (loop(\(x,i).(x2 + 2x),1,(x5 + 2)) div 2)) div 3) div 2)
A274252: 1 1 102 5043 87894 815365 5042737 23548008 89494870 290594892 833383334 2161532576 5159904769 11488393301 24104823494 48054578907
(if ((x + ~1) mod 8) <= 0 then 1 else (((x + 1) div 2) - ((3 * (x div 4)) div 2)))
A330004: 0 1 1 2 1 2 2 3 1 1 2 3 2 3 3 4
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(5x + 3)) div 2)
A165205: 1 4 13 45 161 588 2178 8151 30745 116688 445094 1704794 6552378 25258600 97617060 378098955
(~2 + loop(\(x,i).(4 * (1 + ((32 mod (x + 1)) div 2))),x,3))
A082816: 1 2 6 10 14 30 66
(((2 * (1 + ((loop(\(x,i).2x,x,1) mod 9) div 2))) - (x mod 3)) div 2)
A076840: 1 1 2 5 3 2 1 1 2 5 3 2 1 1 2 5
(2 * ((loop(\(x,i).((5x + 1) - (x mod 3)),x,2) div 2) + (x mod 3)))
A320521: 2 10 50 230 1150
((1 + ((if x <= 0 then 2 else (x + (((x3 + ~3x2 + 2x) div 2) div 5))) div 2)) div 2)
A321176: 1 0 1 1 2 3 5 7 10 15 21 28
(2 * (1 + ((x + (((x + 2) div (if ((x + 2) mod 16) <= 0 then 2 else 1)) div 2)) div 2)))
A085271: 2 4 6 6 8 10 12 12 14 16 18 18 20 22 20 24
loop(\(x,i).x2,1,(((1 + ((x3 + 3x2 + 2x) div 3)) * (1 + (x div 2))) div 2))
A270538: 0 1 81 441 3721
(x div (2 + ((1 + (4 * (2x + (if (~2 + (x div 2)) <= 0 then 0 else 1)))) mod (1 + (x div 2)))))
A242425: 0 0 0 1 2 1 2 2 1 2 3 2 2 2 2 2
((1 + loop(\(x,i).((2x + 2) + (3 * (2x + (x mod 2)))),(x div 2),(x mod 2))) div 2)
A299913: 0 1 1 7 9 55 73 439 585 3511 4681 28087 37449 224695 299593 1797559
((1 + ((x * (x + (loop(\(x,i).((3x * (i * i)) div 2),x,1) div (x + 1)))) div 2)) div 2)
A085617: 0 0 2 17 392
(2 * (~1 + (2 * (x + loop(\(x,i).((x + 1) - ((((2 - (x div 2)) mod (x + 1)) div 2) div 2)),2,x)))))
A062316: 6 14 22 30 38 42 46 54 62 66 70 78 86 94 102 110
(((x + 1) + (loop(\(x,i).(2x + 2),(2 * (x div 7)),1) div (x + 1))) div 2)
A238884: 1 1 1 2 2 3 3 4 5 5 5 6 6 7 9 9
(loop(\(x,i).(2x + ((((((x3 + ~3x2 + 2x) div 2) div 2) div 2) div 2) mod 2)),x,1) div 2)
A293322: 0 1 2 4 9 19 39 79 158 316 632 1265 2531 5062 10125 20251
((x + ~1) mod (2 + ((if (x mod 2) <= 0 then (1 + (x mod (2 + ((x + ~1) mod 3)))) else 0) mod (x + 1))))
A219204: 1 0 1 0 0 0 0 0 2 0 0 0 2 0 3 0
(((x + 1) * (1 + ((if x <= 0 then 1 else (18x2 + ~9)) div 2))) div 2)
A215543: 0 5 48 154 350 663 1120 1748 2574 3625 4928 6510 8398 10619 13200 16168
((2x + 2) * (~1 + (2 * loop(\(x,i).(x + ((4x + 8) div (1 + i))),x,3))))
A086115: 10 100 390 1080 2470 4980 9170 15760 25650 39940 59950 87240 123630 171220 232410 309920
(x div (2 + ((1 + (2 * loop(\(x,i).(2 * ((x + ~4) - (x div 4))),x,1))) mod (x + 1))))
A126306: 0 0 0 1 0 1 1 1 2 0 1 1 1 2 1 2
(((x + 1) * loop(\(x,i).(x + ((x3 + 2x) div 3)),1,(x2 + 2x + 1))) div 2)
A331353: 1 28 387 2784 13125 46836 137543 349952 797769 1667500 3248971 5973408 10459917 17571204 28479375 44742656
(2 * compr(\x.(((0 - (x mod (1 + (2 * (if (x mod 3) <= 0 then 0 else 2))))) mod (x + 1)) div 2),(x + 1)))
A101814: 2 4 6 8 10 12 18 20 24 30 36 40 42 48 50 54
(((x + 1) * (2 + ((x - ((x + 1) mod (if x <= 0 then 1 else (2 * (1 + (2 * (x mod 2))))))) div 2))) div 2)
A212189: 1 1 3 2 7 12 14 16
(((x + 1) * (4 + loop(\(x,i).((x + 2) + (x div (4 + (x div 2)))),(x + ~1),2))) div 2)
A066140: 3 6 12 20 30 45 63 84
(((x + 1) * ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (2 + (x mod 2)))) div 2)
A083174: 2 9 15 42 55 117 119 228 207 435 341 666 533 903 705 1272
((1 + (15 * (2 + (if x <= 0 then 0 else 2))) - (x mod 2)) * ((x + 1) div 2))
A256749: 0 60 61 120 122 180 183 240 244 300 305 360 366 420 427 480
((if x <= 0 then 1 else (2 * (x - (((2 + (x * (x + (x div 2)))) div (x + 2)) div 2)))) + ((x + 1) div 2))
A110261: 1 3 3 6 6 9 9 10 12 13 13 16 16 17 17 20
((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 1 else 2))
A326196-A222084-A073093: 1 2 2 3 2 3 2 4 3 3 2 4 2 3 3 5
((((1 + (x mod (1 + (x mod (2 * (2 + ((x div 2) mod 2))))))) mod (x + 1)) div 2) + (if x <= 0 then 1 else 2))
A108502: 1 2 2 2 2 3 2 3 2 3 2 5 2 3 3 4
((loop(\(x,i).((x + 2) + ((2x + 4) div (4 + (x div 8)))),x,0) div 2) div 2)
A003070: 0 0 1 3 5 7 10 13 16 19 22 26 29 33 37 41
(((x2 - (if x <= 0 then 1 else (~1 + (3 * ((~x2 + 1) mod 8))))) div 2) div 2)
A214297: ~1 0 ~3 2 3 6 5 12 15 20 21 30 35 42 45 56
(2 - (if x <= 0 then 1 else (2 * (((2 + (x mod (2 + (x mod 3)))) mod (1 + (x div 3))) mod 2))))
A054978: 1 2 2 0 0 0 2 2 2 0 0 0 2 0 2 0
((if (x + ~1) <= 0 then 1 else (2 * (1 + ((2 * (1 + (x mod (2 + (x mod 4))))) div (x + 1))))) div 2)
A244328: 0 0 3 3 1 2 1 1 1 1 1 1 1 1 1 1
(2 * (if (x mod 2) <= 0 then 1 else (2 * (1 + (x mod (2 * (1 + (x mod (2 * (1 + (x mod 4)))))))))))
A074723: 2 8 2 16 2 8 2 32 2 8 2 16 2 8 2 64
(2 + ((7 * (4x + (if ((x + 2) mod 4) <= 0 then 2 else 1))) div 2))
A232057: 5 19 37 47 61 75
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 28)
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A242126: 2 3 5 7 11 13 17 19 23 1 3 9 13 15 19 25
(2 * (3 - (2 * (1 + (loop(\(x,i).(2 * (2x - (2x * (x div 2)))),x,1) div 2)))))
A228931: 2 ~6 34 1154 1331714 1773462177794 4611686018427387903 4611686018427387903
((x + 1) mod (4 * (1 + (x div (2 + (loop(\(x,i).(x * (2 + i)),4,2) mod (x + 1)))))))
A097751: 1 2 3 4 5 6 3 8 9 10 3 12 5 6 15 16
(2 + (2 * (1 + (((2 + (x div (1 + (loop(\(x,i).(2x + i),x,0) mod (x + 1))))) div 2) div 2))))
A139324: 4 4 4 4 6 4 6 4 4 6 6 6 8 6 4 4
loop(\(x,i).(1 + (x div 2)),(x div 2),(2 * ((1 + (x mod (2 + ((x mod (2 + (x div 2))) div 2)))) mod 2)))
A039701: 2 0 2 1 2 1 2 1 2 2 1 1 2 1 2 2
(((5 * (1 + (x div (2 + (loop(\(x,i).(2x + 2),x,1) mod (x + 1)))))) div 2) div 2)
A007735: 1 1 1 1 2 1 3 1 3 2 5 1 6 3 2 1
((~2 - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 20)
A074972: 18 17 15 13 9 7 3 1 17 11 9 3 19 17 13 7
(((1 + (((x + 2) * (loop(\(x,i).2x,x,(x + 7)) div 2)) div 2)) div 2) div 2)
A058396: 1 3 9 25 66 168 416 1008 2400 5632 13056 29952 68096 153600 344064 765952
(~2 + ((3 * (1 + ((x + 1) div (1 + (3 * (if (~2 + (x div 2)) <= 0 then 0 else 2)))))) div 2))
A255873: 1 2 4 5 7 8 1 1 1 1 1 1 1 2 2 2
((if x <= 0 then 1 else 6x) - (((3 * (x - (x div 5))) div 2) div 2))
A315477: 1 6 11 16 21 27 33 38 43 48 54 60 65 70 75 81
((if x <= 0 then 1 else 5x) - (((3 * (x - (x div 5))) div 2) div 2))
A314685: 1 5 9 13 17 22 27 31 35 39 44 49 53 57 61 66
(4 + ((((x2 + 7x + 6) * (2 + (if x <= 0 then 1 else x))) div 2) div 3))
A184063: 7 11 20 34 54 81 116 160 214 279 356 446 550 669 804 956
(2 * (2 + ((((x + 1) * (x + (3 * (if (~2 + (x div 2)) <= 0 then 1 else 2)))) div 2) div 3)))
A046458: 4 6 8 12 14 20 32 38
(if ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) <= 0 then 1 else (2 * ((1 + (x div 2)) div 2)))
A283796: 1 1 1 1 2 1 1 4 4 1 1 6 6 6 1 1
((2 + ((3 * (if (x mod 3) <= 0 then 14 else 1)) mod (x + 1))) div 2)
A032539: 1 1 1 2 2 2 1 2 2 2 2 2 2 2 2 6
((x + 2) - (((x + 1) * (x - (if x <= 0 then 1 else (2 * (x - (1 div (x2 + ~3))))))) div 2))
A162523: 3 6 4 11 16 22
(if (x mod 4) <= 0 then 1 else ((((2 - ((x + 2) mod ~7)) mod (x + 1)) div 2) div 2))
A165125: 1 0 0 0 1 0 0 1 1 1 1 0 1 2 1 1
(2 - ((~x + 2) div (2 + (x div (2 * (if (x mod (1 + (((x + 1) div 2) div 3))) <= 0 then 1 else 2))))))
A097747: 1 2 2 3 3 3 3 4 3 4 4 5 4 5 5 4
(if (x mod 2) <= 0 then 1 else (4 + (x div (2 + (x div (1 + ((x div 2) mod (1 + (x mod 4)))))))))
A195986: 1 4 1 5 1 4 1 6 1 4 1 5 1 4 1 7
(4 * (((if ((x + ~1) mod 8) <= 0 then x else 1) + (x div 9)) div 2))
A018816: 0 0 0 0 0 0 0 0 0 20 4 4 4 4 4 4
(4 * (~2 + (3 * (~4 + loop(\(x,i).(2x + 16),(x + 1),1)))))
A278122: 160 568 1384 3016 6280 12808 25864 51976 104200 208648 417544 835336 1670920 3342088 6684424 13369096
(4 + (if x <= 0 then 1 else (2 * (7x - ((x div 3) + (x div 2))))))
A063141: 5 18 30 42 54 68 78 92 104 116 128 142 152 166 178 190
(~2 + (2 * ((3 * (x + loop(\(x,i).((x + 1) - (((x + 1) div 2) div 3)),2,x))) div 2)))
A277570: 4 10 16 22 24 28 34 40 46 52 58 60 64 70 76 82
((2 + (if x <= 0 then 1 else (3 + (31x2 div 2)))) div 2)
A299287: 1 10 33 72 126 196 281 382 498 630 777 940 1118 1312 1521 1746
(2 + ((((x + 1) * (~1 + (2 * (loop(\(x,i).(2x - (i mod 2)),(x + ~1),1) div 2)))) div 2) div 2))
A089892: 1 1 1 3 3 9 17 44
((if x <= 0 then 2 else ((((x + 1) * (1 + ((2x mod (2 + (x div 3))) mod 2))) div 2) div 2)) div 2)
A073700: 1 0 0 0 0 1 0 1 1 2 1 1 1 1 1 2
(((2 + ((3 * (1 + ((if (x mod 3) <= 0 then 2 else 0) + (x mod 2)))) mod (x + 1))) div 2) div 2)
A340996-A072530: 0 0 0 0 1 0 1 2 1 1 1 2 2 2 1 3
((2 + ((x + 1) mod (2 + ((1 + (x div 2)) div (2 + (if (x mod 5) <= 0 then 2 else 0)))))) div 2)
A336005: 1 1 1 1 2 1 2 1 1 2 2 2 2 3 2 1
(2 * (2 - (if x <= 0 then 1 else ((x mod 2) - (((2x + 1) mod (1 - (x div ~4))) div 2)))))
A054844: 2 2 4 2 4 4 4 2 6 4 4 4 4 4 8 2
(2 + (if x <= 0 then 1 else (2 + ((((1 + (x mod 5)) * (x div 5)) div 2) div 2))))
A288177: 3 4 4 4 4 4 4 4 5 5 4 5 5 6 6 4
(4 + (loop(\(x,i).(2 * (x - ((x - (x div 5)) div 3))),(x + 1),2) div 2))
A048585: 6 7 9 12 16 22 31 44 63 91 132 192 280 409 598 875
(2 + (2 * (4 + (if x <= 0 then 1 else ((x + 2) - ((1 + (x2 div 2)) div (x + 3)))))))
A189685: 12 16 18 20 20 22 22 24 24 26 28 28 30 30 32 32
((if x <= 0 then 0 else 1) div (1 - (2 * ((~2 + ((~2x + 2) mod (4 + (x div 4)))) div 2))))
A279907: 0 0 1 0 ~1 1 0 1 ~1 1 0 ~1 ~1 ~1 1 0
(2 * (2 + (if x <= 0 then 1 else ((x + 2) - (((((1 - (x div 2)) div 3) * (x div 2)) div 2) div 2)))))
A100367-A098902: 6 10 12 14 18 20 22 24 26 28 34 36 38 40 44 46
(32 * (x + loop(\(x,i).(x - ((~1 + (x div 4)) div 2)),2,(x + ~1))))
A044219: 32 96 160 224 256 288 352 416 480 544 608 672 736 768 800 864
((((5 * (x + (if (~2 + (x div 2)) <= 0 then 1 else 2))) div 2) + ((x div 4) mod 2)) div 2)
A187897: 1 2 3 5 6 8 10 11 12 13 15 16 18 19 20 21
((2 + (((2x + ~1) + loop(\(x,i).x2,1,(3 * (x + (x div 4))))) div 2)) div 2)
A171686: 0 3 10 22 59 84
(4 * loop(\(x,i).(2x + (14x div (1 + i))),2x,2))
A054326: 8 480 12672 219648 2928640 32587776 317521920 2794192896 22682271744 172438323200 1241555927040 8538764083200 56469693136896 361019918516224 2240813287342080 13550896696786944
(((loop(\(x,i).(x + ((x div 7) + ((x + 1) div 3))),x,2) div 2) div 2) div 2)
A111388: 0 0 0 0 0 1 1 2 3 5 8 12 17 26 38 56
(8 + (if x <= 0 then 1 else (2 * (11x - (x div 3)))))
A063161: 9 30 52 72 94 116 136 158 180 200 222 244 264 286 308 328
((12x + 10) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A245071: 10 21 31 41 49 59 67 77 85 91 101 107 115 125 133 139
((x + 6) + (if x <= 0 then 1 else ((4x + 2) + ((1 + (x div 2)) div 3))))
A212454: 7 13 18 23 29 34 39 44 49 54 60 65 70 75 80 85
(2 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + (x2 div (2x + 8))))
A004683: 2 3 5 7 12 14 18 21 25 32 34 41 45 47 52 58
((((3 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) - (x div 2)) div 2) div 2)
A293262: 1 2 3 5 7 9 12 13 16 20 22 26 29 30 33 38
((if x <= 0 then 2 else ((1 + ((x div (2 + (x mod (2 * (1 + (2 * (x mod 2))))))) + (x mod 2))) div 2)) div 2)
A029414: 1 0 0 0 0 0 1 1 1 0 1 0 1 1 2 1
(((2 * (if (((x2 + 2x) div 2) mod 3) <= 0 then 1 else 2)) mod (1 + (x div 3))) mod 4)
A054009: 0 0 0 0 0 0 2 1 1 0 2 0 2 0 0 0
(((1 + (((3 * (1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x))) div 2) div 2)) div 2) mod 4)
A140086: 0 1 1 2 1 2 2 3 1 0 2 1 2 1 3 2
((x + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + (((x + ~1) div 2) mod 2))) div 4)
A097428: 0 0 1 2 3 4 5 6 7 9 9 11 13 13 14 16
(2 + (if x <= 0 then 1 else (2 + compr(\x.(~1 + ((2 * (((x div 3) * (x div 2)) div 2)) mod 3)),x))))
A154663: 3 5 6 7 10 11
A067351: 3 5 6 7 10 11 13 16 17 18 19 20 21 22 23 24
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(x2 + 5x + 2)) div 2)
A132820: 1 4 16 65 266 1092 4488 18447 75790 311168 1276496 5231954 21425236 87662200 358374960 1463921595
(if x <= 0 then 1 else (2 + ((x + ((3 * (2 - ((~x + 1) div (2 + (x div 4))))) div 2)) div 2)))
A061508: 1 4 5 5 6 7 8 8 9 9 10 11 11 12 12 13
(((3x + 3) * (if (16 mod (x + 1)) <= 0 then 2 else 0)) div (x + 4))
A104117: 1 2 0 3 0 0 0 4 0 0 0 0 0 0 0 5
((x3 + 8x2 + 19x + 12) * loop(\(x,i).(x * (4 + i)),x,(x + 2)))
A001806: 24 600 10800 176400 2822400 45722880 762048000 13172544000 237105792000 4452319872000 87265469491200 1784975512320000 38079477596160000 846536078868480000 4611686018427387903 4611686018427387903
(((x + 1) * loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + 1),2)) div (x + 4))
A002057: 1 4 14 48 165 572 2002 7072 25194 90440 326876 1188640 4345965 15967980 58929450 218349120
((1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * ((x2 + ~x) div (2x + 4)))
A270819: 0 0 0 0 10 12 16 36 44 84 90 144 160 210 230 312
(if x <= 0 then 1 else (2 * (2x + ((x + 2) div (1 + (2 * (2 + (((x div 2) div 3) mod 2))))))))
A312466: 1 4 8 14 18 22 26 30 34 38 42 46 52 58 62 66
(if x <= 0 then 1 else (2 * (2x + ((x mod (2 + ((x - ((~x + 1) div 3)) mod 3))) div 2))))
A311337: 1 4 8 12 16 22 26 28 32 36 40 44 48 52 58 62
(if x <= 0 then 1 else (4x + ((x + 2) div (1 + (2 * (2 + (((x div 2) div 3) mod 2)))))))
A058759: 1 4 8 13
A311798: 1 4 8 13 17 21 25 29 33 37 41 45 50 55 59 63
(if x <= 0 then 1 else (4x + ((1 + (2 * (x - (2 * ((~x + 1) div 3))))) div 3)))
A137002: 1 5 11 15
A314034: 1 5 11 15 20 26 31 35 41 46 51 57 61 66 72 77
(4x + (if x <= 0 then 1 else ((2 * (x - (x div 13))) div 3)))
A313054: 1 4 9 14 18 23 28 32 37 42 46 51 56 60 64 69
(4x + (if x <= 0 then 1 else ((2 * (x - (2x div ~7))) div 3)))
A313613: 1 5 10 14 20 24 29 34 39 44 48 54 58 63 68 73
(if x <= 0 then 1 else (4x + ((2 * (x + ((x + ((x div 2) mod 4)) div 2))) div 3)))
A310458: 1 4 10 15 20 25 30 36 40 44 50 55 60 65 70 76
(4x + (if x <= 0 then 1 else ((x + ~1) + ((x + 2) div (2 - (((x div 2) div ~2) div 2))))))
A313782: 1 5 10 15 21 26 31 37 42 47 52 57 62 67 73 78
(x + (((~x + ((x div 2) mod 5)) div 5) + (if x <= 0 then 1 else 4x)))
A313116: 1 4 9 14 19 24 29 34 39 44 48 52 57 62 67 72
(x + (((2 * (x - ((x div 2) div 5))) div 3) + (if x <= 0 then 1 else 4x)))
A314220: 1 5 11 17 22 28 34 39 45 51 56 61 67 73 78 84
(x + (((x - (x mod (4 + (x div 3)))) div 3) + (if x <= 0 then 1 else 4x)))
A313752: 1 5 10 15 20 26 32 37 42 47 52 57 62 67 72 78
(x + (((2 * (x + (((x div 2) div 3) mod 2))) div 3) + (if x <= 0 then 1 else 4x)))
A314222: 1 5 11 17 22 28 34 40 46 51 57 63 68 73 79 85
(x + (((2 * (~x + (((x div 2) div 3) mod 2))) div 3) + (if x <= 0 then 1 else 4x)))
A058759: 1 4 8 13
A311861: 1 4 8 13 17 21 26 31 35 39 44 48 52 56 60 65
(x + (((x + ((x + (x div 3)) mod 3)) div 3) + (if x <= 0 then 1 else 4x)))
A314141: 1 5 11 16 22 26 32 37 43 48 53 59 64 70 74 80
(5x + (if x <= 0 then 1 else ((5x + 5) mod 9)))
A101239: 1 6 16 17 27 28 38 39 40 50 51 61 62 72 73 83
(if x <= 0 then 1 else (2 * (3x + ((~x + ((x div 2) mod 5)) div 5))))
A310532: 1 4 10 16 22 28 34 40 46 52 56 60 66 72 78 84
(loop(\(x,i).2x,(((x + ~1) * ((x3 + ~3x2 + 2x) div 2)) div 2),1) + ((x div 2) mod 2))
A049384: 1 1 2 9 262144
(~3 + ((2 * (1 + ((x + 2) * ((1 + loop(\(x,i).2x,x,2)) div 3)))) + (x mod 2)))
A341549: 3 6 23 50 131 294 687 1530 3419 7502 16391 35490 76467 163830 349535 742730
(((x + 1) + ((x + ~1) mod (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))) div 2)
A202479: 1 1 2 2 4 3 6 4 6 6 10 6 12 9 9 8
((x + 2) + (x div (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))))))
A070229: 2 4 6 6 10 9 14 10 12 15 22 15 26 21 20 18
((x + 2) + (((x + 1) * (2 + (if (~2 + (x div 3)) <= 0 then 1 else 2))) div 7))
A026428: 2 3 5 6 8 9 11 12 13 16 18 19 21 23 24 26
loop(\(x,i).(1 + (2 * (((x + ~2) + ((1 - (x div 4)) mod 3)) mod (2x + 1)))),x,2)
A046689: 2 3 5 7 11 23
A165802: 2 3 5 7 11 23 47
(2 * compr(\x.(2 - (x mod (1 + (2 * (loop(\(x,i).(x2 + x),2,8) mod (x + 1)))))),x))
A270660: 12 18 20 24 30 32 36 38 40 42 44 48 50 52 54 56
(2 + compr(\x.(x mod (1 + (4 * (2x mod (1 + (2 * (if (x mod 3) <= 0 then 0 else 2))))))),x))
A153083: 2 5 7 8 11 12 14 17 19 20 22 23 26 27 29 32
((x + 4) - ((x2 div 2) mod (3 * (1 + (if (x mod 2) <= 0 then 6 else 0)))))
A303275: 4 5 4 6 0 9
((x + 2) + ((2 * (1 + (((x + 1) * (if (x + ~4) <= 0 then 1 else 2)) div 3))) div 3))
A248792: 2 3 5 6 7 10 11 13 14 15 17 19 20 21 23 24
(if x <= 0 then 1 else (2 * (x + ((2 * (2x - (2x div 7))) div 3))))
A312289: 1 4 8 14 16 22 26 30 34 38 44 46 52 56 60 64
loop(\(x,i).((((4x div (1 + i)) * (~1 + (2 * i))) div (1 + i)) * (1 + (2 * i))),x,2)
A267981: 2 6 40 350 3528 38808 453024 5521230 69526600 898283672 11848435872 158966514616 2163449607200 29802622140000 414852500188800 5827381213589550
((loop(\(x,i).((x2 + ~x) div 2),2,(x + 1)) div 3) + ((x3 + 2x2 + ~x) div 2))
A252870: 0 1 8 26 61 120 211 343 526 771 1090 1496 2003 2626 3381 4285
(2 - ((1 - (2 * ((2x div (4 + (x div 4))) mod 2))) * ((if x <= 0 then 1 else x) mod 2)))
A026490: 1 1 2 3 2 1 2 1 2 3 2 3 2 3 2 1
(2 * (x + (if x <= 0 then 1 else (2 * (1 + (((2x2 + ~x + ~1) * (x + (x div 2))) div 2))))))
A120824: 2 6 36 122 336
((x + 2) + loop(\(x,i).(5x2 + 10x + 5),(x + ~1),10))
A099415: 12 13 609
(if x <= 0 then 1 else (2 * (x + ((3 * (x + ((x mod ((x + 1) - (x mod 4))) mod 2))) div 2))))
A310416: 1 4 10 14 20 24 32 34 40 44 52 54 60 64 72 74
(((x + 2) + ((1 + (2 * (2 + (if (x + ~6) <= 0 then 0 else 2)))) mod (1 + (x div 2)))) div 2)
A087875: 1 1 2 3 4 4 4 5 7 7 7 8 8 8 8 9
(if x <= 0 then 1 else (2 * (3x - (x div (4 + ((x div 2) div 5))))))
A315733: 1 6 12 18 22 28 34 40 44 50 56 62 68 74 80 84
((x + 2) + (((x - (2 * (loop(\(x,i).(x + 2),(x + ~8),x) div 3))) div 2) div 2))
A121603: 2 3 4 5 6 7 8 9 11
A123241: 2 3 4 5 6 7 8 9 11 11 12 13 14 14 15 16
(if x <= 0 then 1 else ((x + 2) + ((x + ((~1 + (x div 2)) mod (1 + ((1 + (x div 2)) div 3)))) div 2)))
A288934: 1 3 5 6 8 10 11 12 14 16 17 19 21 22 23 24
((x + ((x + loop(\(x,i).((x + 1) + ((x * (4 + i)) div (x + 3))),x,1)) div 2)) div 2)
A195311: 0 1 3 5 7 10 13 17 21 25 29 33 38 43 48 54
((x + 2) + ((x + ((x + ((x + (loop(\(x,i).(x * (x div 2)),(x + ~2),x) div 2)) div 2)) div 2)) div 2))
A103850: 2 3 5 7 11 89
(2 + compr(\x.(loop(\(x,i).(x3 + x2),2,48) mod (x + 2)),x))
A269804: 2 3 4 6 7 8 9 12 14 16 17 18 21 24 27 28
((x3 + 3x2 + 3x + 1) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A167622: 1 2 2 1 4 8 3 18 16 14 29 26 24 35 38 15
((x + 3) + (if (x + ~1) <= 0 then 8x else 23))
A260815: 3 12 28 29 30 31 32 33 34 35 36 37 38 39 40 41
((1 + (2 * ((x + ~1) mod (if ((x2 + x) mod 8) <= 0 then 4 else 1)))) mod (x + 2))
A329346: 1 1 1 1 1 1 1 5 7 1 1 1 1 1 1 5
((loop(\(x,i).(x + (5x div (1 + i))),x,6) div 3) div (x + 2))
A222011: 1 2 4 8
A084626: 1 2 4 8 14 22 33 47 66 91 121 158 204 258 323 399
(((x2 + x + 1) * loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,x)) div (x + 2))
A034267: 0 1 7 39 196 930 4257 19019 83512 361998 1553630 6615686 27992472 117823940 493768485 2061580275
((x3 + 2x2 + ~1) + loop(\(x,i).(x3 + 2x),1,((x2 + 3x + 2) div 2)))
A193576: 2 35 243 1064 3500 9477 22295 47168 91854 167375 288827 476280 755768 1160369 1731375 2519552
(2x + (if x <= 0 then 1 else (x mod (1 + ((1 - ((x2 + 2x) mod 8)) mod (x + 1))))))
A241071: 1 2 4 6 8 10 12
A255385: 1 2 4 6 8 10 12 15 16 18 20 26 24 26 28 34
(3x + (if ((x + ((4 * (x div 3)) div 3)) mod 3) <= 0 then 2 else 1))
A287420: 2 4 7 10 13 17 19 23 25 28 31 35 37 41 43 47
(3x + (5 * ((if x <= 0 then 1 else 2x) - ((x + (x div 2)) div 4))))
A188471: 5 13 26 34 47 60 68 81 89 102 115 123 136 149 157 170
(1 + ((2 * (loop(\(x,i).((x + 1) + (x div 5)),x,1) div 2)) div 3) - (x mod 2))
A069910: 1 0 1 1 2 2 3 3 5 5 7 8 11 12 16 18
(~1 + ((loop(\(x,i).2x,(3x div (1 + (x mod 4))),1) mod (x + 1)) + (x mod 2)))
A326067: ~1 0 0 0 0 2 0 0 0 2 0 4 0 2 3 0
(1 + ((2 * ((1 + ((2 + (if (x mod 4) <= 0 then x else (x div 2))) div 3)) div 2)) + (x mod 2)))
A099034: 1 2 3 4 3 4 3 4 5 4 3 4 5 4 5 6
(((1 + ((loop(\(x,i).((x * ((x + ~1) div 2)) div 2),2,x) div 2) div 3)) div 3) * (x mod 2))
A164735: 0 0 0 0 0 0 0 1 0 4 0 10 0 20 0 36
((if x <= 0 then 1 else (2 * (1 + ((x div (3 * (2 + ((x + ~1) mod 4)))) mod 2)))) - (x mod 2))
A331541: 1 1 2 1 2 1 2 1 2 3 4 1 2 1 4 3
((4 * ((1 + (4 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 3)) - (x mod 2))
A248104: 4 11 16 19 28 35 44 47 52 59 64 67 76 79 84 91
((if x <= 0 then 1 else (x + ((x - ((x2 mod (x - ((~x + 2) div 2))) div (x + 1))) mod 2))) + (x mod 2))
A135762: 1 3 2 5 4 7 6 8 9 11 10 13 12 14 15 17
((3x + 4) + ((x + loop(\(x,i).(x + ((x - (x div 4)) div 2)),2,x)) div 2))
A207673: 4 8 13 17 21 26 30 35 39 43 48 53 57 62 66 71
compr(\x.(~1 + ((x2 * loop(\(x,i).x3,2,x)) mod 23)),x)
A010385: 0 1 2 3 4 6 8 9 12 13 16 18
A010407: 0 1 2 3 4 6 8 9 12 13 16 18 23 24 25 26
((x + 1) + (loop(\(x,i).(4x + 4),(x + 1),(4x + 4)) div 5))
A180635: 5 31 173 891 4373
((x + 1) + ((2 * ((x + 1) - (x mod (1 - (2 * (if (x mod 4) <= 0 then 0 else 2)))))) div 3))
A328983: 1 4 5 6 8 10 11 14 15 16 19 20 21 24 25 26
compr(\x.(2 - ((x2 * loop(\(x,i).x3,2,x)) mod 23)),x)
A028736: 5 7 10 11 14 15 17 19 20 21 22
A278579-A028759: 5 7 10 11 14 15 17 19 20 21 22 28 30 33 34 37
((x + 1) + ((x + loop(\(x,i).(x2 + ~x),1,(2 - ((~x + 2) div (2 + (x div 2)))))) div 3))
A120515: 1 3 4 7 8 9 11 12 13 17 18 19 21 22 23 25
(x + (if x <= 0 then 1 else (1 + (2 * ((x + 1) - ((x mod (2 + (((x + 1) div 2) div 3))) div 2))))))
A189728: 1 6 9 12 15 16 21 24 25 30 33 34 39 42 43 46
((x + 1) + (2 * (1 + ((if (x + ~6) <= 0 then 0 else 2) + (x div 9)))))
A154660: 3 4 5 6 7 8
A096828: 3 4 5 6 7 8 9 14 15 18 19 20 21 22 23 24
((x + ~1) + (2 * ((1 + (if (x mod 2) <= 0 then ((~x + 2) mod (1 + (x div 4))) else 0)) mod 3)))
A332808-A108548: 1 2 3 4 5 6 7 8 9 10 13 12 11 14 15 16
(x + (((x * (loop(\(x,i).x2,2,(2 * (x mod 2))) mod (x + 1))) div 2) div 7))
A233569: 0 1 2 3 4 6 6 7 8 12 10 14 12 14 14 15
compr(\x.(1 - (x mod (1 + (2 * (if (x mod (1 + (10 * (x mod 2)))) <= 0 then 0 else 2))))),x)
A236208: 1 3 7 9 13 17 19 21 23 27 29 31 37 39 41 43
compr(\x.((x + 1) mod (1 + (4 * (if (x mod 5) <= 0 then 10 else 1)))),x)
A277601: 4 9 14 19 24 29 34 39 40 44 49 54 59 64 69 74
compr(\x.(1 - (x mod (1 + (4 * (2x mod (1 + (2 * (if (x mod 3) <= 0 then 0 else 2)))))))),x)
A080308: 1 2 4 7 8 11 13 14 16 19 22 23 26 28 29 31
(x + (1 mod (~1 + (2 * (((~x + 1) + (2 * (6 + (x mod 2)))) * (if x <= 0 then 1 else 2))))))
A318891-A318890: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 10 15
loop(\(x,i).x7,1,(11x + 5))
A017455: 78125 268435456 10460353203 114415582592 678223072849 2799360000000 9095120158391 24928547056768 60170087060757 131593177923584 266001988046875 504189521813376 905824306333433 1555363874947072 2569093262823519 4103386730000000
loop(\(x,i).x7,1,(11x + 10))
A017515: 10000000 1801088541 34359738368 271818611107 1338925209984 4902227890625 14645194571776 37725479487783 86812553324672 182803912081669 358318080000000 662062621900811 1164175380274048
(x * ((loop(\(x,i).(2 + ((x + (x2 div 3)) div 2)),2,(x + ~1)) div 2) div 5))
A308822: 0 0 0 0 0 5 6 14 24 45 70 110 156 234 322 450
((x5 + 5x) + loop(\(x,i).5x,x,1))
A220511: 1 11 67 383 1669 6275 23431 94967 423433 2012219 9865675 48989231 244389517 1221074483 6104053519 30518337575
((~x + 1) + (2 * (((x + 1) + (3 * ((x + (if (x mod 2) <= 0 then x else 2)) mod 3))) div 2)))
A154127: 1 2 5 8 7 4 1 2 5 8 7 4 1 2 5 8
((x + ~1) + (2 * (if (x div 4) <= 0 then ((x + 1) mod (4 - (x mod 4))) else (x div 2))))
A067016: 1 4 3 2 7 8 11 12 15 16 19 20 23 24 27 28
loop(\(x,i).x7,1,(11x + 3))
A017431: 2187 105413504 6103515625 78364164096 506623120463 2207984167552 7446353252589 20971520000000 51676101935731 114868566764928 235260548044817 450766669594624 817215093984375 1414067010444416
(x + ((2 * (1 + ((2 * (x + (if (x mod 5) <= 0 then 2 else 1))) div 3))) div 3))
A289166: 1 2 4 5 6 8 9 11 12 13 16 17 18 19 21 23
loop(\(x,i).x7,1,(11x + 6))
A017467: 279936 410338673 13492928512 137231006679 781250000000 3142742836021 10030613004288 27136050989627 64847759419264 140710042265625 282621973446656 532875860165503 953133216331392 1630436461403549 2684354560000000 4275360817613091
(~x + (((x + 1) + (2 * loop(\(x,i).(x - ((~x + (x mod 2)) div 3)),x,2))) div 3))
A219282: 1 1 1 2 3 4 6 9 13 18 25 35 49 68 93 126
((3x + 1) + (if (x mod (1 + (2 * (3 - ((x div 3) mod 2))))) <= 0 then 2 else 0))
A287410: 3 4 7 10 13 18 19 24 25 28 33 34 37 40 45 48
((2x + 3) + (loop(\(x,i).(x + ((x + (i * i)) div (1 + (x div 2)))),x,1) div 3))
A336803: 3 6 9 12 15 19 22 26 30 34 38 43 47 51 56 60
((~x + 1) + (((~1 + loop(\(x,i).((x2 + 3x + 2) div 2),x,4)) div 3) + (x mod 2)))
A307147: 2 5 44 3149
((~x + 1) + compr(\x.(~1 + (loop(\(x,i).2x,x,1) mod (1 + (2x mod (2 + (x div 4)))))),x))
A195850: 1 1 1 1 1 1 1 2 3 4 4 4 4 4 5 7
(~x + loop(\(x,i).((x + 3) + (((2x * (1 + (2 * i))) div (2 + i)) div (1 + i))),x,1))
A034223: 1 4 10 20 35 57 87 127 179 245 327 428 550 696 869
((x + 1) + loop(\(x,i).((x + 1) - ((((x - ((x mod 3) div 2)) div 2) + (x mod 2)) div 2)),2,x))
A229089: 3 5 6 7 9 11 13 14 17 18 19 20 22 23 25 26
(~x + (2 * (4x div (1 + (if (x mod 7) <= 0 then 6 else 0)))))
A283444: 0 7 14 21 28 35 42 1 56 63 70 77 84 91 2 105
compr(\x.((1 + (if x <= 0 then 0 else (1 + (((3x + ~6) mod (1 + (x div 2))) div 3)))) mod 2),x)
A208982: 1 2 3 4 5 6 9 10 12 15 16 17 18 19 21 22
loop(\(x,i).(1 + (x mod (1 + (x mod (2 + ((x + 1) div (1 + (2 * (x mod 5))))))))),2,x)
A214069: 2 1 2 1 2 1 2 1 2 2 6 1 2 1 2 2
compr(\x.((1 + (((if ((x + 1) mod 8) <= 0 then 3 else x) mod 5) div 2)) mod 2),x)
A201363: 2 3 7
A055053: 2 3 7 8 12 13 15 17 18 22 23 27 28 31 32 33
compr(\x.(1 - (x mod (2 + ((x + (if (x mod 2) <= 0 then x2 else (x + 1))) mod 9)))),x)
A336360: 1 2 3 5 6 7 10 11 12 13 14 15 17 19 20 21
(x + ((1 + ((if (~1 + (x div 4)) <= 0 then x else 8) + (x div 5))) div 2))
A138390: 0 2 3 5 6 8 10 11 13 14 15 16 17 18 19 21
((x + 2) + (x div 2) - (((2 * (if (~2 + (x div 4)) <= 0 then 0 else 2)) - (x div 2)) div 3))
A285567: 2 3 6 7 9 10 12 13 16 17 19 20 21 22 24 25
(x + (((x + 1) + (2 * (loop(\(x,i).(~2 + (x div 2)),(x + ~1),(x + 4)) div 3))) div 2))
A003860: 1 3 3 4 5
A011977: 1 3 3 4 5 6 7 9 10 12 13 15 16 18 19 21
compr(\x.((loop(\(x,i).2x,((x - (x div 5)) mod 5),1) mod (x + 1)) div 2),x)
A048302: 0 1 2 3 4 6 12 18 24 25 31 37 43 49 50 56
compr(\x.(loop(\(x,i).((x + 1) + (((x + ((x + ~1) mod 3)) mod 5) mod 2)),x,1) mod 2),x)
A327138: 2 5 8 11 12 14 15 17 18 20 21 24 27 30 33 34
(0 - ((((x + 1) - loop(\(x,i).((x + 1) + ((x + (x div 2)) div 4)),x,0)) div 2) div 2))
A232482: 0 0 0 0 0 1 1 2 3 5 7 11 16 23 33 46
((x + 1) - (((3 * (1 + (if x <= 0 then 0 else ((x + 1) + ((x mod 3) div 2))))) div 2) div 2))
A029258: 1 0 0 1 1 0 1 2 1 2 2 2 3 3 3 4
loop(\(x,i).x7,1,(11x + 4))
A017443: 16384 170859375 8031810176 94931877133 587068342272 2488651484819 8235430000000 22876792454961 55784660123648 122987386542487 250226879128704 476837158203125 860542568759296 1483273860320763
loop(\(x,i).x7,1,(11x + 8))
A017491: 2097152 893871739 21870000000 194754273881 1028071702528 3938980639167 12151280273024 32057708828125 75144747810816 160578147647843 318547390056832 594467302491009 1054135040000000 1789940649848551 2928229434235008 4637914326451397
(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) - (x2 div (3x + 4)))
A004684: 2 3 5 7 10 12 16 18 21 27 29 34 38
(x + (if x <= 0 then 1 else 4x) - ((~x + ((0 - ((x div 2) div 3)) mod 3)) div 2))
A315521: 1 6 11 17 22 28 32 38 43 49 54 60 66 71 77 82
(x + (if x <= 0 then 1 else (2 * (x + ((((x + 1) - ((x div 2) mod 2)) div 2) + ((x + 1) div 3))))))
A313416: 1 5 10 13 18 25 28 31 38 43 46 51 56 61 66 69
(x + ((x + ((loop(\(x,i).23x,2,x) div 2) div 3)) div 2))
A121925: 0 45 91 136 182 227 273 319 364 410 455 501 547 592 638 683
loop(\(x,i).(x + (2 * (x mod (1 + ((3 * ((x + 1) div 2)) mod (1 + (x div 3))))))),2,x)
A340632: 0 1 2 3 4 7 6 7 8 15 14 15 12 15 14 15
((~x + 2) + compr(\x.((((x + 1) div (2 + (if (~2 + (x div 4)) <= 0 then 1 else 2))) mod 2) - (x mod 2)),x))
A066997: 2 2 3 4 4 4 5 6 7 8 8 8 8 8 9 10
(~x + loop(\(x,i).((2x + 3) - (((2x + ~4) div (2 + (x div 4))) mod 2)),2,x))
A083134: 8 9 14 15 19 24 26
(2x + (if x <= 0 then 1 else (2 * (2x - (2x div (2 + (4x div (x + 2))))))))
A315312: 1 6 10 16 20 26 32 38 42 48 52 58 64 68 74 78
(2x + (if x <= 0 then 1 else (2 * (x + ((x + (5 mod (1 + (x div 4)))) div 2)))))
A310420: 1 4 10 14 20 26 30 36 42 46 52 56 60 66 70 76
(x4 + ((x * loop(\(x,i).x3,1,(~x + (x div (2 - (x mod 2)))))) div 2))
A309336: 0 1 15 81 240 625 1215 2401 3840 6561 9375 14641 19440 28561 36015 50625
(~x7 + loop(\(x,i).11x,x,1))
A024134: 1 10 ~7 ~856 ~1743 82926 1491625 18663628 212261729 2353164722 25927424601 285292183440 3138392544913 34522649395414 379749728169737 4177247998556276
(3x + (if x <= 0 then 2 else (1 + (((x2 + ~x) div 3) div 7))))
A135678: 2 4 7 10 13 16 20 24 27 31 35 39 43 47 51 56
(1 + (x div (1 + (x mod (1 + (x mod (1 + (x mod (1 + (x div (2 + (x div 8))))))))))))
A088444: 1 2 3 2 5 2 7 2 3 5 11 3 13 7 3 4
(1 + ((x + 1) mod (1 + ((x + ~1) mod (1 + (x mod (1 + ((3x + ~6) mod (x + 1)))))))))
A220464: 1 1 1 2 1 1 1 2 1 1 2 1 2 1 1 3
(1 + (x div (1 + (x mod (1 + (x mod (1 + (x div (2 + ((x div 2) mod (3 - (x mod 2))))))))))))
A096776: 1 2 3 2 5 2 7 4 3 2 11 3 13 2 3 4
(1 + (x div (2 - ((~x + 1) div (1 + (x mod (1 + (x mod (1 + (x div (2 * (2 - (x mod 2)))))))))))))
A322873: 1 1 1 2 1 2 1 2 2 3 1 3 1 4 3 4
(1 + (x div (1 + (x mod (1 + ((x mod (2 + ((x2 div 4) mod (x + 1)))) div 3))))))
A135875: 1 2 3 2 5 6 7 8 3 10 11 6 13 14 15 8
(1 + (x mod (1 + (x mod (1 + ((1 + (6 * (0 - (x mod 4)))) mod (x + 1)))))))
A322362-A087258: 1 2 1 4 1 2 1 8 1 2 1 4 1 2 5 16
(1 + (x mod (1 + (x mod (~1 + (2 * (1 + ((x mod (1 + (x div (2 + ((x div 2) mod 2))))) div 2))))))))
A093803: 1 1 1 1 1 3 1 1 3 5 1 3 1 7 5 1
(1 + (x div (1 + (x mod (1 + (x mod (2 + ((1 + (~x mod 4)) mod (1 + (x div 2))))))))))
A086956: 1 1 1 2 5 2 7 2 3 5 11 3 13 7 3 4
(1 + (x mod (1 + ((2 * (1 + (x div (2 - ((x * (x div 2)) mod 2))))) mod (1 + ((x + 1) div 2))))))
A059807: 1 1 1 1 1 3 1 2 1 5 1 4 1 7 1 4
((x + 1) div (1 + (x mod (1 + ((x mod 13) mod 9)))))
A235600: 1 1 1 1 1 1 1 1 1 10 11 4 13 14 15 16
(1 + (x div (1 + (x mod (3 * (1 + ((x2 + 2x) mod 13)))))))
A344970: 1 1 1 1 1 1 1 1 1 1 1 4 1 7 5 1
(2 - ((~x + 1) div (1 + ((x + 2) mod (1 + (((1 + (x * (x div 2))) div 3) mod 3))))))
A331299: 1 2 3 3 5 6 7 5 6 10 11 12 13 14 15 7
(1 + (x mod (1 + ((1 - ((2 + (((x div 3) * (x div 2)) div 2)) div 3)) mod 3))))
A030338: 1 2 1 2 1 1 1 1 3 1 1 2 1 1 3 2
(1 + (x mod (1 + (3 * (((x + ~1) mod (3 + (x div (1 + (x mod 4))))) mod 2)))))
A001165: 1 1 3 1 1 1 1 1 1 2 3 1 1 2 1 1
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((x div 2) div 3))))
A027948: 1 1 1 1 2 1 1 3 3 1 1 3 7 4 1 1
(1 + ((x + 1) div (1 + ((1 + (2 mod (1 + (x mod (1 + (x mod 4)))))) mod (1 + (x div 2))))))
A204905: 2 3 2 3 3 4 4 3 5 6 6 4 7 8 4 5
(1 + (x div (1 + ((x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4)))))) mod (1 + (x div 2))))))
A109395: 1 2 3 2 5 3 7 2 3 5 11 3 13 7 15 2
(1 + ((x + ~1) mod (1 + ((1 + (((x + 3) mod 7) mod 2)) mod (x + 1)))))
A099910: 1 1 2 1 2 2 2 1 2 3 2 1 3 1 2 1
(1 + (x mod (1 + ((x5 mod 32) mod (x + 1)))))
A076775: 1 2 1 4 1 2 1 8 1 10 1 4 1 2 1 16
(1 + ((~1 + (x mod 3)) mod (1 + ((x mod (1 + ((2 - (x mod 4)) mod (x + 1)))) div 2))))
A318498: 1 1 1 2 1 1 1 1 2 1 1 2 1 1 1 8
(1 + ((x + 1) div (1 + (2 * (1 + (((2x + 1) mod (2 + (x div (2 + (x mod 2))))) div 2))))))
A046663: 1 1 1 2 2 2 2 2 2 2 4 3 5 3 4 4
(1 + ((1 + (3 * ((3x2 + 5x + 2) div 2))) div 7))
A025744: 1 3 6 10 16 23 31 40 51 63 76 91 107 124 142 162
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((1 + (x div 2)) div 2))))
A050177-A013580: 1 1 1 1 3 1 1 4 4 1 1 5 9 5 1 1
(1 + ((1 div ((2x + ~1) mod (4 + (x div 4)))) * (1 + ((1 + (x div 2)) div 2))))
A130296: 1 2 1 3 1 1 4 1 1 1 5 1 1 1 1 6
(1 + (x div (~1 + (2 * (2 + ((x div 2) div (1 + (x mod (1 + (x mod (3 + (x mod 2))))))))))))
A056692: 1 1 1 2 1 2 1 3 2 2 1 3 1 2 3 4
(1 + ((2x + 1) mod (1 + (((x + 1) div (2 * (1 + (x mod (2 * (2 - (x mod 2))))))) div 2))))
A267134: 1 1 1 1 2 1 1 2 3 2 1 2 2 2 2 2
(1 + ((x * (2 - ((x div 2) mod 2))) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))))
A176346: 1 1 1 1 3 1 1 2 2 1 1 3 5 3 1 1
(216x2 + 720x + 503)
A179172: 503 1439
((9x + 82) + (x div 9))
A282114: 82 91 100 109 118 127 136 145 154 164 173 182 191 200 209 218
(5 div (3 - ((2x + 1) mod (1 + (2x mod (2 + (x div 4)))))))
A318670-A114717: 1 1 1 1 1 2 1 1 1 2 1 5 1 2 2 1
(1 + ((x * (1 - ((x3 div 8) mod 2))) mod (1 + (2 * (x div 4)))))
A136788: 1 1 1 1 2 1 1 2 4 1 1 2 6 7 1 1
(1 + ((2 * ((12x + 11) - (x mod 3))) div 5))
A226724: 5 9 14 19 24 28 34 38 43 48 53 57 63 67 71 77
(420x + 301)
A256101: 301 721 1141 1561 1981 2401 2821 3241 3661 4081 4501 4921 5341 5761 6181 6601
(1 + ((2 + ((2 + (((x + 1) * (x + (x div 5))) div 2)) div 2)) div 5))
A097920-A029042: 1 1 1 2 2 3 4 4 5 6 8 9 10 12 13 16
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (~x mod 5)))
A320796: 1 1 1 1 2 1 1 4 3 1 1 5 7 3 1 1
(1 + (((~x + 1) mod (1 + ((4x + ~4) mod (1 + (x div 2))))) * (x div 5)))
A076037: 1 1 1 1 1 1 1 1 2 2 1 1 3 5 5 1
(1 + (((x + 1) * ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2)) div (1 + (x mod 4))))
A326135: 1 1 1 1 1 4 1 1 1 6 1 4 1 8 6 1
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x mod (2 + (x mod 2))))))
A343658-A343656-A194005-A077592: 1 1 1 1 2 1 1 3 2 1 1 4 3 3 1 1
(~1 + (((x + 1) - ((~x + 1) div (1 + (2 * (2 + (((x div 2) div 3) mod 2)))))) mod 3))
A281772: 0 1 0 1 ~1 0 1 ~1 0 ~1 0 1 0 1 ~1 0
(~1 + ((1 + (x mod (1 + (2 * (((((~x + 1) * (x div 2)) div 2) mod (x + 2)) div 2))))) mod 3))
A072784: 0 0 ~1 0 1 ~1 0 0 1 ~1 0 0 0 1 ~1 0
(1 + (((~4 + ((x + 1) * (1 - (2 * (x mod 2))))) mod (1 + (x div 3))) mod 3))
A341052: 1 1 1 1 2 1 1 1 3 3 1 1 2 3 2 2
(~1 + ((1 + ((1 + ((x + 2) div 5)) mod (2 + (x div 5)))) mod 3))
A016416-A016410-A016388-A016372-A016366-A014024: 1 1 1 0 0 ~1 ~1 ~1 0 0 0 0 0 0 0 1
(1 + (((1 + (x mod (2 * (1 + (x mod 2))))) * (1 + ((1 + (x div 4)) div 2))) div 3))
A072347: 1 1 1 2 1 2 1 3 1 2 1 3 2 3 2 5
(x div ((x + 2) div (1 + ((1 + ((~2x + 2) mod (4 + (x div 4)))) div 3))))
A238010: 0 0 1 0 1 1 0 1 1 1 0 1 3 1 1 0
(1 + (3 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))
A296180: 1 1 1 1 4 1 1 7 7 1 1 10 13 10 1 1
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((2x + ~1) div 3)))
A121522: 1 1 1 1 3 1 1 5 6 1 1 8 15 9 1 1
(1 + (((1 + (((x div 2) - ((((x + 1) div 2) div 2) mod 2)) mod 3)) mod (x + 1)) mod 3))
A245553: 1 2 3 2 3 3 1 2 3 3 1 3 1 1 2 3
(1 + (((x + 1) + ((((x + 2) * ((x2 + 4x + 4) div 2)) div 2) div 3)) div 3))
A275580: 1 2 3 5 8 12 17 23 31 41 52 65 81 99 119 142
((x + 1) mod (1 + (((10 * (1 + (2 * (x mod 2)))) mod (x + 1)) mod 3)))
A124060: 0 0 1 1 0 0 0 0 1 0 1 0 1 2 1 1
((3x + 4) + (37 * (1 + (x div 2))))
A185657: 41 44 84 87 127 130 170 173 213 216 256 259 299 302 342 345
(1 + ((2 * (1 + (x mod (1 + (((~x + ((~x + 2) div 4)) div 2) mod 4))))) div 3))
A191770: 1 2 3 1 1 2 1 3 1 1 2 2 1 1 3 1
(~1 + ((1 - ((1 + (((x + 1) * (1 - (2 * (x mod 2)))) mod 5)) div 2)) mod 3))
A292301: ~1 1 1 ~1 0 1 ~1 ~1 1 0 ~1 1 1 ~1 0 1
(1 + ((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) mod 3))
A116479: 1 1 1 2 1 2 1 3 2 2 1 3 1 2 2 1
(~1 + ((2 + ((x + 2) mod (1 + (((x + 1) mod 7) mod 3)))) mod 3))
A166234: 1 1 1 ~1 1 1 1 ~1 ~1 1 1 ~1 1 1 1 0
(1 + ((2 * (1 + ((2 * (1 + (x2 div 3) - (x mod 2))) div 3))) div 3))
A029002-A008751: 1 1 2 3 4 5 7 8 11 13 16 19 23 26 31 35
((x + 1) div (1 + (3 * (((x + 1) - ((1 + ((x * (x div 2)) div 4)) div 2)) div 2))))
A017851: 1 0 0 0 0 0 1 1 1 1 1 1 1 2 3 4
(2 div (1 + ((2 + ((2x + 1) mod (5 * (1 + (x mod 3))))) div 3)))
A179519-A179317-A109502: 1 1 0 1 0 0 1 0 1 0 1 0 2 0 0 1
(1 + ((x - (2 * (((x + 1) div 3) - ((1 - (x div 3)) div 3)))) mod 3))
A105203: 1 2 1 2 3 2 1 2 1 2 3 2 3 1 3 2
(~1 + ((((x3 + 6x2 + 11x + 6) * (1 - (2 * (x mod 2)))) div 2) div 3))
A216414: 0 ~5 9 ~21 34 ~57 83 ~121 164 ~221 285 ~365 454 ~561 679 ~817
(1 + (3 * (((1 + (x mod (1 + (x mod (2 * (2 + ((x div 2) mod 2))))))) mod (x + 1)) div 2)))
A050347: 1 1 1 1 1 4 1 4 1 4 1 10 1 4 4 7
(~1 + (((x3 + 24x2 + 65x + 42) div 2) div 3))
A087863: 6 21 45 79 124 181 251 335 434 549 681 831 1000 1189 1399 1631
(1 + ((((x2 + x) * (9 - ((~x2 + x) div 2))) div 2) div 3))
A136395: 1 4 11 25 51 96 169 281 445 676 991 1409 1951 2640 3501 4561
(1 + ((4 * (1 + ((x mod (2 + (((x div 2) mod 2) + (x mod 3)))) div 2))) div 3))
A078545: 2 2 3 2 2 2 2 3 2 2 3 2 2 2 5 2
(1 + ((4 * (x + ((x div 5) + ((x + 1) div 5)))) div 3))
A193622: 1 2 3 5 7 10
A325160: 1 2 3 5 7 10 11 13 14 17 19 21 22 23 26 29
(1 + ((4 * ((2x + 1) + (((x + 1) + (x div 8)) div 2))) div 3))
A003145: 2 6 9 13 15 19 22 26 30 33 37 39 43 46 50 53
(~1 + ((4 * ((2x + 1) + (((x + 1) + (x div 8)) div 2))) div 3))
A308199: 0 4 7 11 13 17 20 24 28 31 35 37 41 44 48 51
(~1 + ((4 * ((x + 1) + (3 * ((1 + (x div 3)) div 3)))) div 3))
A023713: 0 1 3 4 5 7 12 13 15 16 17 19 20 21 23 28
(1 + ((1 - (((((x + ~2) * ((x div 3) * (1 - (x div 2)))) div 2) div 2) div 2)) div 3))
A008925: 1 1 1 1 1 1 2 2 3 4 5 6 9 10 13 17
(1 + ((2 * ((2x + 2) + ((x - ((x + (x mod 2)) div 5)) mod 2))) div 3))
A112233: 2 4 5 7 7 9 11 11 13 15 15 17 18 20 21 22
((15x2 + 40x + 25) div 11)
A194140: 2 7 15 25 38 54 73 94 118 145 175 207 242 280 320 363
(~1 + ((16x3 + 84x2 + 146x + 84) div 3))
A143938: 27 109 279 569 1011 1637 2479 3569 4939 6621 8647 11049 13859 17109 20831 25057
(1 + ((x + (4 * ((x + 1) + ((x + (x div 12)) div 2)))) div 3))
A316326: 2 4 7 8 11 13 16 18 21 22 25 27 30 33 35 38
(1 + ((x + (2 * ((((1 + (x mod (1 + (x div 3)))) * (x div 2)) div 2) div 2))) div 3))
A325393-A320388: 1 1 1 2 2 3 3 4 5 5 6 8 7 9 11 10
(1 + (compr(\x.(((x - ((2x + 1) mod (1 + (x div 4)))) mod 2) - (x mod 2)),x) mod 3))
A099054-A003270: 1 2 3 1 3 2 3 1 2 3 2 1 3 1 2 1
(3 div (1 + ((~1 + (2x2 mod (4 + (x div 4)))) mod (x + 3))))
A346061-A305161-A294250-A293960-A250484-A226873-A183134: 1 1 0 1 1 0 1 1 1 0 1 1 3 1 0 1
(x - (x div (1 + ((x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4)))))) mod (1 + (x div 2))))))
A331176: 0 0 0 2 0 3 0 6 6 5 0 9 0 7 0 14
((x + 1) div (1 + ((3 * (x + (24 * (x mod 2)))) div (x + 1))))
A029219: 1 0 1 0 1 0 2 0 3 1 3 1 4 1 5 2
(1 + ((2 + ((x div (1 + ((x + 2) mod 8))) mod 2) - (x mod 2)) mod (x + 1)))
A076225: 1 2 3 2 3 2 3 3 3 2 3 3 4 3 3 3
((x3 + 3x2 + 4x + 1) * (((x3 + 3x2 + 2x) div 2) div 3))
A292350: 0 9 116 670 2580 7735 19544 43596 88440 166485 295020 497354 804076 1254435 1897840 2795480
(x10 + x9 + x8 + x7 + x6 + x5 + x4 + x3 + x2 + x + 1)
A060885: 1 11 2047 88573 1398101 12207031 72559411 329554457 1227133513 3922632451 11111111111 28531167061 67546215517 149346699503 311505013051 617839704241
(~1 + (2 * (1 + ((x + ~4) mod (1 + ((x mod 6) mod (1 + (x div 3))))))))
A163378: 1 1 1 3 1 3 1 3 3 3 1 3 1 3 3 7
(1 + ((1 + (x mod (1 + (x mod (1 + (x div (2 + ((1 - (x div 4)) mod 3)))))))) div 2))
A322872: 1 1 1 2 1 2 1 3 2 1 1 2 1 2 3 3
(3 mod (1 + ((1 + ((x + 1) div (1 + ((1 + (x2 div 3)) mod (x + 1))))) div 2)))
A124921: 1 1 1 0 1 1 1 0 1 1 3 1 1 3 1 1
(1 + (x div (2 + (x div (1 + ((x mod (~1 + (x mod (~1 + ((~x + 2) div 3))))) mod 3))))))
A249973: 1 1 1 2 1 2 1 2 1 1 2 3 1 2 1 3
(1 + (((1 + (x div 3)) div (1 + ((x - (x div 12)) mod 3))) div 2))
A335438: 1 1 1 2 1 1 2 1 1 3 2 1 1 3 2 2
(x mod (1 + (2 * ((2 - (((x + ~2) - (x div 3)) mod 3)) mod (1 + (x div 3))))))
A103822: 0 0 0 0 1 0 0 2 2 0 0 1 2 1 0 0
(~1 + ((1 + ((1 + (x2 div (1 + (3 * (((x + 1) * (x div 2)) mod 2))))) div 2)) div 2))
A214630: ~1 0 0 2 3 6 2 12 15 20 6 30 35 42 12 56
(1 + (2 * ((x div 2) div (1 + (x mod (2 * (1 + (x mod (1 + ((2 - (x div 2)) mod 4))))))))))
A299766: 1 1 3 1 5 3 7 1 3 5 11 3 13 7 5 1
(1 + ((1 + (((x + 1) mod (1 + (3 * ((x2 + ~x) mod 5)))) div 2)) div 2))
A244840: 1 1 2 1 2 1 1 1 1 2 1 1 3 2 1 1
(1 + (x div (2 + (x div (1 + (x mod (2 * (1 + ((2 - (x mod 8)) mod 3)))))))))
A078899: 1 1 1 2 1 2 1 3 3 2 1 4 1 2 3 4
(1 + ((1 + ((1 + ((2 + (x2 * (x + ((x * (x div 2)) mod 2)))) div 3)) div 2)) div 2))
A179183: 1 2 2 4 7 12 19 34
(1 + (x div (2 * (1 + (x mod (2 * (1 + (x mod (2 * (1 + ((~1 + (x div 2)) mod 4)))))))))))
A336933: 1 1 2 1 3 2 4 1 5 3 6 2 7 4 3 1
(1 + ((2x mod (1 + (2 * (2x mod (1 + (2 * ((1 + (x div 4)) div 2))))))) div 2))
A337266: 1 1 1 1 2 1 1 3 1 1 1 1 4 2 1 1
(2 div (1 + ((1 + (x mod (2 + (x mod (5 * (1 + (2 * (x mod 3)))))))) div 2)))
A263250: 2 1 1 0 0 0 2 0 0 0 0 0 2 0 0 1
((2x + 5) - ((x - ((3x2 + 3) div 7)) div 2))
A159018: 5 7 9 12 15 18 22 26 31 36 42 48 54 61 68 76
(1 + (((x2 div 2) mod (1 + (2 * (((x + ~2) * (x div 3)) mod (1 + (x div 2)))))) div 2))
A164953: 1 1 1 1 2 1 1 3 2 1 1 3 4 3 1 1
(1 + ((1 + (x div (2 + ((3 * (1 + (x mod (2 + (x mod 3))))) mod (x + 1))))) div 2))
A343240: 1 1 2 1 2 2 2 1 2 2 2 4 2 2 2 2
(1 + ((1 + ((((~1 + ((~2x + 2) mod 9)) div 2) mod (x + 1)) div 2)) div 2))
A106476: 1 1 1 2 1 1 2 2 1 1 4 2 2 1 1 2
(1 + (2 * (1 + (((1 + (x mod (3 + ((x2 div 3) mod (x + 1))))) div 2) div 2))))
A162022: 3 3 3 5 3 3 5 3 3 7 3 5 3 3 5 3
(1 + (x div (2 + (x div (1 + (2 * (((2x + ~6) div (1 + (x div 3))) mod 2)))))))
A300655: 1 1 1 1 2 1 1 1 3 2 3 1 3 1 1 1
(1 + ((x mod (~1 + (4 * (2 + ((1 + ((x - (x div 8)) div 2)) mod 2))))) div 2))
A071508-A071505: 1 1 2 2 3 3 4 1 1 5 6 3 3 2 2 1
(1 + (2 * (1 + (2 * (x - ((0 - ((x - (((x + 1) div 2) mod 6)) div 2)) div 2))))))
A160785: 3 7 11 15 23 27 31 35 39 43 47 59 63 67 71 75
(96x2 + 208x + 141)
A228597: 141 445 941 1629 2509 3581 4845 6301 7949 9789 11821 14045 16461 19069 21869 24861
(1 + (2 * ((~1 + (x2 div 2)) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))))
A176149: 1 1 1 1 3 1 1 3 3 1 1 5 3 5 1 1
(1 + ((1 + (x div 3)) div (2 * (1 + (x mod (1 - (2 * ((~x + 1) div (2 + (x div 2))))))))))
A079211-A026835: 1 1 1 2 1 1 2 1 1 1 3 2 1 1 1 4
(2 div (1 + ((1 + (((1 - (x div (1 + (x mod 4)))) mod (1 + (x div 2))) mod 4)) div 2)))
A157865: 2 2 1 1 2 1 0 2 0 1 2 1 0 1 1 1
(1 + ((5 * ((2x + 1) mod (1 + (2x mod (2 + (x div 4)))))) div 2))
A191278: 1 1 1 1 1 3 1 1 1 3 1 6 1 3 3 1
(1 + (compr(\x.(x mod ((x + 1) - (x mod 10))),x) + (x mod 10)))
A160927: 1 3 5 7 9 11 13 15 17 19 12 23 34 45 56 67
(1 + (2 * ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 5)))
A196493-A132729: 1 1 1 1 1 1 1 3 3 1 1 5 9 5 1 1
(1 + ((1 + (((x + 1) + ((((x + ~1) div 2) div 2) * (x div 5))) mod 4)) div 2))
A325518: 2 2 3 1 2 3 1 2 2 1 3 1 2 1 2 2
(1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (3 + (x div 2))) div 2))
A147290: 1 1 1 1 3 1 1 4 4 1 1 5 10 5 1 1
(1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (~3 + (x div 2))) div 2))
A132823: 1 1 1 1 0 1 1 1 1 1 1 2 4 2 1 1
(1 + (x div (2 + ((1 + (x div 3) - (x div (~1 + ((~x + 1) div 3)))) mod 3))))
A110884: 1 1 1 2 2 2 2 4 3 4 4 4 4 4 4 8
(1 + ((3 * ((2 + (x div 2)) div (3 + ((x2 + 2x) mod 6)))) div 2))
A327790-A206941: 1 1 1 1 2 1 2 1 2 2 4 1 4 2 2 2
(4 mod (1 + (2 * ((1 + ((~2x + 2) mod (4 + (x div 4)))) div 3))))
A135302: 1 0 1 0 1 1 0 1 1 1 0 1 4 1 1 0
(1 + ((3 * ((((3 * (x2 mod 6)) mod (x + 1)) div 2) div 2)) div 2))
A046591-A046563: 1 1 1 1 1 1 1 1 1 4 1 1 1 1 5 4
((x + 1) div (1 + (x div 2) - ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2)))
A135941: 1 2 1 4 2 3 2 8 4 5 3 6 4 4 3 16
(35x4 + 210x3 + 455x2 + 420x + 140)
A317984: 140 1260 5040 14000 31500 61740 109760 181440 283500 423500 609840 851760 1159340 1543500 2016000 2589440
(686x + 700)
A157366: 700 1386 2072 2758 3444 4130 4816 5502 6188 6874 7560 8246 8932 9618 10304 10990
(((19x2 + 51x + 32) div 2) div 7)
A184976: 2 7 15 25 38 54 73 94 118 145 174 206 241 279 319 362
(343x + 273)
A157374: 273 616 959 1302 1645 1988 2331 2674 3017 3360 3703 4046 4389 4732 5075 5418
(1 + ((((1 + (x div 2)) div (1 + (x mod (1 + (x div 5))))) + (x div 3)) div 2))
A339147-A062821: 1 1 2 2 3 2 4 3 4 3 4 3 6 4 4 4
((1 + (x mod 5)) mod ((1 + (x div 8)) * (1 + ((x div 3) mod 2))))
A035440: 0 0 0 0 1 1 0 0 0 1 1 2 1 0 1 1
(1 + (((3 * ((((x2 div 3) mod (x + 1)) div 2) div 2)) - (x mod 3)) div 2))
A029305: 1 0 0 1 0 0 2 0 0 2 0 1 4 0 1 4
(1 + ((1 + ((x + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2)))))) div 2)) div 2))
A057022: 1 1 2 2 3 3 4 3 4 4 6 4 7 6 6 6
(~1 + (2 * (1 + (((((x + 1) * (x + (x div 3))) div 2) div 5) + (x div 2)))))
A225523: 1 1 3 5 9 11 17 21 27 33 39 43 53 59 69 79
(1 + (((2 + (x mod 2) - (x mod (4 * (2 - (x mod 2))))) mod (1 + (x div 2))) div 2))
A285521: 1 1 1 1 1 2 1 1 2 2 1 1 3 2 3 1
(1 + (x div (2 + (x div (1 + ((2 * ((2x div (1 + (x div 4))) mod 2)) + (x mod 2)))))))
A322866: 1 1 1 2 1 2 1 3 3 2 1 3 1 2 3 4
(12x4 + 16x3 + 10x2 + 4x + 1)
A272124: 1 43 369 1507 4273 9771 19393 34819 58017 91243 137041 198243 277969 379627 506913 663811
(1 + (((x + 1) + (((1 + (((x + 2) * (x + ((x * (x div 2)) mod 2))) div 2)) div 2) div 2)) div 2))
A082463: 1 2 3 4 5 6 7 9 10
A284831: 1 2 3 4 5 6 7 9 10 12 14 16 18 20 22 26
(1 + (((1 + (x mod (1 + (x mod (2 * (1 + (x mod (1 + (x div 3))))))))) mod (x + 1)) div 2))
A306467: 1 1 1 1 1 2 1 3 2 2 1 3 1 2 3 5
(1 + (((1 + (x div (1 + (((2x + 1) mod (2 + (x div 4))) div 2)))) mod (x + 1)) div 2))
A345062: 1 1 1 1 1 2 1 1 1 3 1 4 1 4 3 1
(1 + (((1 + (x mod ((1 + (x mod (1 + (x div 4)))) * (1 + (x mod 2))))) mod (x + 1)) div 2))
A337093-A326334-A323438-A318559-A317791-A317508-A317141-A305254-A252665-A218320-A001055: 1 1 1 2 1 2 1 3 2 2 1 4 1 2 2 5
(1 + (2 * (((x + 1) - (2 * ((1 + ((3 * ((x + 1) div 2)) div 2)) div 2))) mod (x + 1))))
A234587: 1 1 3 1 3 5 7 5 7 5 7 5 7 9 11 9
(1 + (x div (2 + ((1 + ((x div (1 + (2 * ((x div 2) mod 2)))) mod 2) - (x mod 2)) mod (x + 1)))))
A187181: 1 1 1 2 2 2 3 4 3 4 3 4 5 5 5 6
(1 + ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) - (x div (~2 + (x div ~2))))
A178994: 1 2 2 2 3 2 3 4 4 3 3 4 5 4 3 3
(1 + (((1 + (x div (1 + (((2x + ~4) div (4 + (x div 4))) mod 2)))) div 2) div 2))
A176816: 1 1 1 2 2 1 2 3 3 3 3 2 4 2 3 3
(1 + (2 * ((1 + (x mod (1 + (2 * (x div (2 * (2 + ((x + 2) mod (2 + (x mod 2)))))))))) div 2)))
A131248: 1 1 1 1 3 1 1 3 5 1 1 3 7 7 1 1
(1 + (((x - (x3 div (x + ~49))) div 2) div 2))
A179241: 1 1 1 2 2 3 4 5 6 8 10 12 15 19 24 29
((x + 1) - (2 * ((1 + ((x - (3 * ((~x + 1) div 7))) div 2)) div 2)))
A245615: 1 2 1 0 1 2 3 2 3 2 3 4 3 4 5 6
(1 + (2 * ((7 * (x div (4 * (8 - (x div 2))))) div 2)))
A147056-A146804-A146735-A146711-A146703-A146671-A146639-A146631-A146615-A146466-A146410-A146402: 1 1 1 1 1 1 1 1 1 1 1 1 7 7 21 21
(1 + (x div (2 + (x mod (2 + (x div (1 + (2 * ((x mod (~1 + (2 * (x div 3)))) mod 2)))))))))
A330942: 1 1 1 1 1 1 1 2 1 1 1 4 7 1 1 1
((x2 + 2x) div (1 + (2 * (((4x2 + 8x + 4) mod 5) div 2))))
A146975: 0 3 8 3 24 7 48 63 16 99
(~1 + ((((5 * ((x2 + 3x + 2) div 2)) + (x div 5)) div 2) div 2))
A081689: 0 2 6 11 17 25 34 44 55 68 82 97 113 130 149 169
(1 + (((1 + ((21x2 + 58x + 32) div 2)) div 2) div 2))
A194150: 5 15 30 50 76 107 143 184 231 283 340 402 470 543 621 704
(64x2 + 168x + 119)
A243581: 119 351 711 1199 1815 2559 3431 4431 5559 6815 8199 9711 11351 13119 15015 17039
(1 + (((12x3 + 54x2 + 87x + 45) div 2) div 2))
A248230: 12 50 133 280 507 833 1276 1855 2586 3488 4579 5878 7401 9167 11194 13501
(5 + ((2 * ((2x + 4) - ((~x + 2) div (2 + (x div 4))))) div 3))
A248636: 7 9 10 12 13 15 17 18 19 21 22 24 25 27 28 29
(1 + (2 * ((3 * (x - ((((x * ((1 - (x div 2)) div 3)) div 2) div 2) div 2))) div 2)))
A026175-A026139: 1 3 7 9 15 19 21 25 27 33 39 43 45 51 55 57
(~1 + (2 * ((3 * ((x + 2) + (((3 * ((~1 + (x div 2)) div 2)) div 2) div 2))) div 2)))
A206547: 1 5 11 13 17 19 23 25 29 31 37 41 43 47 53 55
(x mod (1 + (((1 + ((x * (2 - ((~x + 1) div (1 + ((x div 2) div 3))))) div 2)) div 2) div 2)))
A099314: 0 0 0 1 1 0 1 2 1 1 0 1 2 2 1 1
(1 + (2 * ((1 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 2)) div 2)))
A302997-A238339-A026714-A008288: 1 1 1 1 3 1 1 5 5 1 1 7 13 7 1 1
(1 + (2 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)))
A338934: 1 1 1 1 3 1 1 5 5 1 1 7 15 7 1 1
(1 + ((((x + 1) * (~1 + (3 * (2 + ((x + 2) * (1 - (2 * (x mod 2)))))))) div 2) div 2))
A142888: 3 ~1 13 ~9 29 ~23 51 ~43 79 ~69 113 ~101 153 ~139 199 ~183
(1 + ((x mod (2 + ((0 - (3 * (1 + (x mod (1 + (x mod 4)))))) mod (x + 1)))) div 2))
A122085: 1 1 1 1 1 1 1 1 1 2 2 1 1 2 4 2
(1 + (2 * ((x - ((0 - (3 * ((x + 1) mod 12))) div (x + 1))) div 2)))
A079886: 3 5 5 7 7 9 9 11 11 13 13 11 13 15 15 17
(1 + (((2x + 2) mod (2 + (46 mod (x + 1)))) div 2))
A049998: 1 1 1 1 1 1 2 1 1 3 2 1 5 3 1 1
(1 + ((x + 1) div (2 * (2 + ((2 * (2 - (x div (~1 + ((~x + 2) div 4))))) mod (x + 1))))))
A240837: 1 1 1 2 1 1 1 2 2 3 2 1 1 1 1 1
(1 + (((18x + 12) div 5) + (((x + 1) div 2) div 2)))
A189530: 3 7 10 15 18 22 26 30 34 37 41 46 49 53 56 61
(1 + (2 * (((x + ~1) mod (2 + (x mod (1 + (x mod (2 - ((x div 4) div ~2))))))) div 2)))
A212181: 1 1 1 3 1 1 1 1 3 1 1 3 1 1 1 5
(1 + (4 * ((3 * (x - ((~1 + (2 * ((~x + 2) div 4))) div 3))) div 2)))
A162597-A008846: 5 13 17 25 29 37 41 53 61 65 73 85 89 97 101 109
compr(\x.((x div 2) mod 2),(1 + ((x - (x div (2 - ((x3 div 8) mod 2)))) div 2)))
A143334: 1 1 1 1 4 1 1 5 5 1 1 8 8 8 1 1
((20x2 + 54x + 34) div 17)
A194143: 2 6 13 22 33 47 63 81 102 125 151 179 209 242 277 314
(1 + ((x mod (1 + ((x2 + 2x) mod 8))) + (x div 15)))
A003484: 1 2 1 4 1 2 1 8 1 2 1 4 1 2 1 9
compr(\x.((x div 2) mod 2),((~2 + (x mod 2)) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))))
A258197: 0 0 0 0 1 0 0 1 1 0 0 4 5 4 0 0
(9 * (1 + (9 * (x + (x div 9)))))
A044641: 9 90 171 252 333 414 495 576 657 819 900 981 1062 1143 1224 1305
((1 + ((x4 + 9x3 + 28x2 + 36x + 16) div 2)) div 9)
A216173: 1 5 16 39 80 147 249 396 600 874 1232 1690 2265 2975 3840 4881
(378x2 + 702x + 324)
A305070: 324 1404 3240 5832 9180 13284 18144 23760 30132 37260 45144 53784 63180 73332 84240 95904
(9 * ((10x + 10) + (x mod 10)))
A282473: 90 189 288 387 486 585 684 783 882 981 990 1089 1188 1287 1386 1485
(9 * ((((1 + (x mod 5)) * (x div 5)) div 2) div 2))
A229758: 0 0 0 0 0 0 0 0 9 9 0 9 9 18 18 0
(1 + (((x + 1) div (2 + (x mod 11))) + (x div 9)))
A061828: 1 1 1 1 1 1 1 1 1 2 2 8 6 5 5 4
(~1 + (2 * ((2 + compr(\x.((2x + 1) mod (1 + (2x mod (2 + (x div 4))))),x)) div 2)))
A050826: 1 1 3 3 5 7 7 9 11 13 15 17 17 19 19 21
(1 + ((~1 + ((~2x + 2) mod (4 + (x div 4)))) div (2 + (x mod (2 + (x mod 2))))))
A168316: 1 0 1 0 2 1 0 1 2 1 0 1 3 2 1 0
(2 div (1 + ((1 + ((~1 + (x div 2)) mod (1 + ((x div 2) div (1 + (2 * (x mod 2))))))) mod 4)))
A216282: 1 1 1 1 0 1 0 1 2 0 1 1 0 0 0 1
(1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) mod 4))
A095140: 1 1 1 1 2 1 1 3 3 1 1 4 1 4 1 1
((1 + (6 * ((16x + 16) div 3))) div 5)
A190265: 6 12 19 25 31 38 44 50 57 63 69 77 83 89 96 102
(2 - ((1 + (((3 * ((x + 1) - ((x + 1) mod 3))) div 2) div 2)) mod 5))
A037865: 1 1 ~1 ~1 ~1 2 2 2 0 0 0 2 2 2 0 0
((3 * (1 + ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2))) mod 5)
A138070: 3 3 3 3 1 3 3 1 1 3 3 1 4 1 3 3
(5 + ((2 * ((2x + 1) - ((~x + 1) div (2 + (x div 4))))) div 3))
A079696: 5 7 9 10 11 13 15 16 17 19 21 22 23 25 26 27
((6 * ((2x + 2) - ((x + 1) mod 10))) div 5)
A059589: 1 2 3 4 6 7 8 9 10 24 25 26 27 28 30 31
(360x2 + 1440x + 1560)
A069475: 1560 3360 5880 9120 13080 17760 23160 29280 36120 43680 51960 60960 70680 81120 92280 104160
((((x3 + 12x2 + 35x + 30) div 2) div 3) div 5)
A026053: 1 2 5 9 14 21 29 40 53 68 86 106 130 157 187 221
(7 + compr(\x.((x mod 10) * (x mod 7)),x))
A092433: 7 14 17 21 27 28 35 37 42 47 49 56 57 63 67 70
(((x + 2) + (2 * (1 + (2 * ((x - (x div 12)) mod 2))))) div 5)
A260617: 0 1 1 2 1 2 2 3 2 3 2 3 4 3 4 3
(1 + (((x + (((x + 4) * (2x + (x2 div 4))) div 3)) div 2) div 2))
A008804: 1 2 4 6 10 14 20 26 35 44 56 68 84 100 120 140
(1 + (2 * ((1 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4)))) * (x mod 2))))
A037227: 1 3 1 5 1 3 1 7 1 3 1 5 1 3 1 9
(~1 + (2 * ((44x2 + 44x + 1) + (x mod 2))))
A120821: 1 179 529
(1 + (2 * ((2 * ((2 * (2x - (x mod 8))) - (x mod 4))) - (x mod 2))))
A145812: 1 3 9 11 33 35 41 43 129 131 137 139 161 163 169 171
((x2 div (1 + (x mod (1 + ((1 + (x div 2)) mod (1 + (x div 5))))))) mod 3)
A060950: 0 1 1 0 1 0 0 1 1 1 1 1 0 0 2 0
(((x + 1) div (1 + (x mod (1 + ((x - ((2 + (x div 2)) div 3)) mod 3))))) div 3)
A264010: 0 0 1 1 1 1 2 2 3 1 1 4 4 2 1 5
((1 + (x div (1 + ((1 + (x div (1 + (4 * (1 + (2 * (x mod 2))))))) mod 2)))) div 3)
A154263: 0 0 0 0 1 1 2 1 3 1 2 2 2 4 2 5
((1 + ((16x3 + 24x2 + 24x + 8) div 3)) div 3)
A299261: 1 8 31 81 168 303 497 760 1103 1537 2072 2719 3489 4392 5439 6641
((1 + (((x + 1) * (1 + (((x + 1) * (x - (x div ~2))) div 2))) div 3)) mod 3)
A059963: 1 0 0 0 0 0 0 1 1 0 2 2 2 2 2 0
((1 + ((2 * ((2x + 1) - ((~x + 1) div (2 + (x div 4))))) div 3)) mod 3)
A111397: 1 0 2 0 1 0 2 0 1 0 2 0 1 0 1 2
(((11x + 33) * ((x2 + 3x + 2) div 2)) div 3)
A111080: 11 44 110 220 385 616 924 1320 1815 2420 3146 4004 5005 6160 7480 8976
(2 - ((1 + ((x + 1) div (2 + (((~x + 2) mod 5) + (x div 3))))) mod 3))
A216228: 1 1 0 1 1 0 0 2 0 0 0 2 2 0 0 0
((1 + ((x + 2) mod (2 * (1 + (x mod (1 + ((x2 + 2x) mod 8))))))) div 3)
A346070-A254990-A191258: 0 1 0 2 0 1 0 3 0 1 0 2 0 1 0 0
(((2x3 + 4x2 + 5x + 3) * ((x2 + 3x + 2) div 2)) div 3)
A077538: 1 14 90 360 1075 2646 5684 11040 19845 33550 53966 83304 124215 179830 253800 350336
(6x - ((1 + (4 * (x - ((2 - (x div 2)) div (x + 2))))) div 3))
A314885: 1 5 9 14 19 23 27 31 36 41 45 50 55 59 64 69
((1 + (((~1 + (2 * (((x div 4) - (x mod 4)) div 2))) mod (x + 2)) div 2)) div 3)
A181676-A181674: 0 0 0 0 1 1 1 1 0 2 2 2 0 0 2 3
((((16x + 8) mod 13) div 3) mod 3)
A287240: 2 0 0 1 2 0 0 1 2 0 1 0 1 2 0 0
((1 - (x div (3 * (1 + (x mod (2 * (1 + (x mod (3 + (x mod 2)))))))))) mod 3)
A035200: 1 1 1 1 0 1 2 1 1 0 0 1 0 2 0 1
((2 - ((1 + (2 * (x - ((x + 1) mod (1 + ((~x + 2) mod 4)))))) div 3)) mod 3)
A125070: 0 1 1 0 1 2 1 0 0 2 1 1 1 2 2 1
(1 - (3 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))
A176625: 1 1 1 1 ~2 1 1 ~5 ~5 1 1 ~8 ~11 ~8 1 1
(~3 + ((1 + (2 * ((x2 + ~2) mod 13))) div (1 + (x mod 2))))
A216289: 20 9 2 4 0
((3x2 + 12x + 3) + (((x3 + 3x2 + 2x) div 2) div 3))
A103145: 3 19 43 76 119 173 239 318 411 519 643 784 943 1121 1319 1538
(1 - (((1 + (3 * ((2x + 1) mod 7))) mod (x + 1)) mod 3))
A074711: 1 1 0 0 ~1 0 ~1 0 0 1 0 0 1 ~1 0 0
(((x + 1) * (1 - (x mod (~1 + (3 * (16 div (x + 1))))))) mod 3)
A171368: 1 0 0 1 0 0 0 1 0 0 2 0 1 0 0 0
(((2 - (2 * ((x + (x div 8)) mod 5))) mod (x + 1)) div 3)
A221515: 0 0 0 0 1 0 0 2 1 0 0 3 3 2 0 0
(((x + 1) * (1 + ((13x2 + 17x + 4) div 2))) div 3)
A100183: 1 12 46 116 235 416 672 1016 1461 2020 2706 3532 4511 5656 6980 8496
(((x + 1) * (~1 + ((11x2 + 19x + 8) div 2))) div 3)
A100156: 1 12 44 108 215 376 602 904 1293 1780 2376 3092 3939 4928 6070 7376
((40x3 + 69x2 + 32x + 3) div 3)
A100146: 1 48 221 600 1265 2296 3773 5776 8385 11680 15741 20648 26481 33320 41245 50336
((5x + 1) + (x div (~2 + ((~x + 2) div 4))) - ((x + 1) div 3))
A314830: 1 5 9 14 18 22 27 32 36 40 45 49 54 59 63 68
(6 * (1 + (3 * (x - (9 * ((~x2 + x) div 2))))))
A277985: 6 24 204 546 1050 1716 2544 3534 4686 6000 7476 9114 10914 12876 15000 17286
((2 * (1 + ((4x3 + 6x2 + 12x + 5) div 3))) div 3)
A299265: 1 6 19 45 90 159 257 390 563 781 1050 1375 1761 2214 2739 3341
(1 - ((2 * ((x + 1) - ((2 * (1 + (((x + 1) * (x div 2)) div 2))) div 3))) div 3))
A321404: 1 0 0 0 1 0 1 1 3 4 6
((2 * (1 + ((2 * (2 + ((~3x + 3) mod (1 + (x div 2))))) div 3))) mod 3)
A321854: 1 1 0 1 1 1 0 0 1 0 2 1 0 0 0 0
((2 * (1 + ((2 * (2 + (x3 div (x + 8)))) div 3))) div 3)
A125811: 1 1 1 2 3 5 8 11 15 20 26 32 39 47 56 66
((2 * (1 + (2 * ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4)))))) div 3)
A275812-A212172: 0 0 0 2 0 0 0 3 2 0 0 2 0 0 0 4
((2 * (1 + (2 * ((2x + 2) + ((x + (x div 12)) div 2))))) div 3)
A287176: 3 6 10 12 16 19 23 26 30 32 36 39 43 47 50 54
(3 * ((3 * (1 + (x mod (1 - (x mod (~1 + (x div ~8))))))) div 2))
A179802: 3 9 3 9 3 9 3 9 3 3 9 9 3 9 3 3
((4 + ((x + 1) div 3) - ((~x + 2) div (2 - (x div ~4)))) mod 3)
A079632: 0 1 2 0 0 1 1 2 0 0 0 1 1 1 2 0
((2 + (((11x2 + 21x + 10) div 2) div 3)) div 3)
A025736-A022784: 1 3 6 10 15 22 30 39 49 61 74 88 103 119 137 156
(((x2 + 2x) * (1 + (x div 2))) - (((x3 + 3x2 + ~x + ~3) div 2) div 3))
A024598: 1 3 14 22 55 73 140 172 285 335 506 578 819 917 1240 1368
((2 * ((x + 1) + (2 * ((2x + 2) + ((x - (x div 3)) div 3))))) div 3)
A189368: 3 6 10 13 18 21 24 28 32 36 39 42 46 50 54 57
((2 + ((1 + (2 * ((1 + ((x mod 4) + (x mod 3))) div 2))) mod (x + 1))) div 3)
A332997: 0 1 1 1 1 2 1 2 1 1 2 3 1 1 2 2
((x mod (2 + (~89 mod (x + 1)))) div 3)
A284269: 0 0 0 1 0 0 0 2 0 0 3 0 0 0 0 2
((2 + ((x - (2 * ((2 * (~8 + (x div 2))) div 3))) mod (x + 1))) div 3)
A336929: 0 1 0 1 1 1 0 3 2 2 1 1 1 1 1 1
(((17x3 + 3x2 + ~14x) div 2) div 3)
A237617: 0 1 20 74 180 355 616 980 1464 2085 2860 3806 4940 6279 7840 9640
(((((x + 7) * ((x3 + 3x2 + 2x) div 2)) div 2) div 2) div 3)
A005582: 0 2 9 25 55 105 182 294 450 660 935 1287 1729 2275 2940 3740
((4 * ((2 - ((x + 1) mod (~1 + (2 * ((~x + 1) div (2 + (x div 2))))))) div 2)) div 3)
A101566: 1 1 1 2 1 1 2 2 1 1 4 2 2 1 1 4
((4 * ((2 - (x mod (~2 + ((x div 2) mod (~2 - (x div 4)))))) div 2)) div 3)
A036065: 1 1 1 1 2 1 1 1 1 1 1 4 1 4 1 1
((3 - (x mod ((~x + ~2) + (2x mod (4 + (x div 4)))))) div 3)
A146565-A115594-A086623-A086461-A072405-A047089: 1 1 1 1 1 1 1 2 2 1 1 3 4 3 1 1
(3 + (2 * (4 + (((x + 2) * ((4x + 9) - (x mod 2))) div 2))))
A138052: 29 47 79 111
((((x + 4) * ((x + 2) - (((~x + ~1) + (x mod 2)) div 5))) div 2) mod 3)
A082786: 0 1 0 0 1 0 2 0 0 0 0 0 1 0 0 1
((2 * ((x + 2) + ((x - (((x div 2) - ((x2 + ~x) div 4)) div 2)) div 2))) div 3)
A164043: 1 2 3 4 5 6 8 9 10 12 14 16 18 20 21 24
(~3 + ((3 * ((10x + 10) + (x div 2))) + ((x div 2) mod 2)))
A260440: 27 57 91 121 153 183 217 247 279 309 343 373 405 435 469 499
(((x + 2) + (4 * ((x + 2) + ((x + (x div 12)) div 2)))) div 3)
A107792: 3 5 8 9 12 14 17 19 22 23 26 28 31 34 36 39
((2 * ((x + 2) + ((x + ((x * ((x + 1) div 7)) div 2)) div 2))) div 3)
A102799: 1 2 3 4 5 6 8 9 10 11 12 14 15 18 20 21
(((x * ((x * (x - (x4 div (~1 + (x div ~2))))) div 2)) div 2) mod 3)
A340728: 0 0 1 1 0 1 0 2 0 1 0 1 0 2 1 0
((((4x3 + 12x2 + 8x) div 3) + ((x2 + 2x) div 2)) div 3)
A001860: 0 3 12 29 57 99 157 234 333 456 606 786 998 1245 1530 1855
(1 - (((((x + 1) mod (1 + (2 * ((1 + (x div 4)) div 2)))) div 2) - (x mod 2)) mod 3))
A077009: 1 ~1 1 ~1 0 ~1 1 1 1 ~1 0 ~1 0 0 1 ~1
(3 * ((2 * ((2 * (2x - (x mod 8))) - (x mod 4))) - (x mod 2)))
A001196: 0 3 12 15 48 51 60 63 192 195 204 207 240 243 252 255
(((x + 1) + (2 * ((((2 + (x div 4)) * ((x + 1) div 3)) div 2) div 2))) div 3)
A053046: 0 0 1 1 1 2 3 3 5 5 5 6 7 8 9 9
((x + 1) - (((x + 2) + (x div (2 + (16 mod (1 + (x div 2)))))) div 3))
A006165: 1 1 2 2 3 4 4 4 5 6 7 8 8 8 8 8
(2x - (((x + 2) + (x div (2 + (16 mod (1 + (x div 2)))))) div 3))
A294456: 0 1 3 4 6 8 9 10 12 14 16 18 19 20 21 22
((x + ~3) + (4 * (x - (2 * ((~2x + ~2) + ((x - (x div 4)) div 2))))))
A134864: 13 34 47 68 89 102 123 136 157 178 191 212 233 246 267 280
(2 + (((2 * (2 + ((x div 2) div 5))) mod (1 + (x div 3))) + (x div 3)))
A076973: 2 2 2 3 3 3 5 5 5 5 7 7 7 7 7 7
((2x + 5) + ((2 + (((x + 1) mod (1 + (x mod 4))) div 2)) mod (x + 1)))
A280199: 5 7 11 13 15 17 19 21 23 25 28 29 31 33 35 37
((x + 1) div (1 + ((x * (1 + (3x2 mod 11))) div 2)))
A219484: 1 0 1 0 0 0 0 0 0 1 0 2 0 1 0 0
(3 + compr(\x.(x mod (1 + ((x4 + 4x3) mod 9))),x))
A189637: 3 6 8 9 12 15 17 18 21 23 24 26 27 30 33 35
(1 + (2 * ((x + 1) + (((x + 1) + ((x - (x mod (4 + (x div 2)))) div 3)) div 2))))
A340933: 3 7 9 13 15 19 21 27 29 33 37 39 43 45 49 51
(1 + ((x + (((4x3 + 12x2 + 12x + 8) div 3) div 3)) div 2))
A188123: 1 3 8 16 31 51 80 118 167 227 302 390 495 617 758 918
(1 + (((x2 + 2x + 1) - (x2 div (x + 24))) div 2))
A118028: 1 3 5 9 13 19 25 32 40 50 60 71 83 97 111 126
(1 + ((x + (((1 + (((x + 1) * ((x2 + 2x) div 5)) div 2)) div 2) div 2)) div 2))
A003107: 1 1 2 3 4 6 8 10 14 17 22 27 33 41 49 59
(1 + ((x + ((((1 + ((x + ((x2 div 2) div 3)) div 2)) * (x div 2)) div 2) div 2)) div 2))
A136343: 1 1 2 2 4 4 6 7 10 11 14 16 21 23 29 32
(1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (x + (x div 4))) div 2))
A114172: 1 1 1 1 3 1 1 5 6 1 1 7 16 9 1 1
(1 + ((x + ((x + (((x3 + x2) div 2) div 11)) div 2)) div 2))
A067996-A020702: 1 1 2 3 4 6 8 10 13 16 21 25 31 37 44 53
(1 + ((x + ((x + (x3 div (12 + ((x + 1) div 2)))) div 2)) div 2))
A242717-A001400: 1 1 2 3 5 6 9 11 15 18 23 27 34 39 47 54
(~1 + compr(\x.(~1 + ((1 + (x mod (1 + (x mod (2 * (2 + ((x div 2) mod 2))))))) mod (x + 1))),(x + 2)))
A323648: 1 2 3 5 7 9 11 15 17 19 23 27 29 31 35 39
(((x * (2 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))) + (x mod 2)) div (x + 3))
A319685-A076526-A069157: 0 1 1 2 1 2 1 3 2 2 1 4 1 2 2 4
((2x + 1) + ((2 * ((2x + 4) - ((1 - (x div 2)) div 5))) div 3))
A285359: 3 7 10 13 17 21 24 27 31 34 37 41 44 47 51 55
((2x + 1) + ((((x2 mod 15) mod 2) - (x div 2)) div 3))
A184820: 1 3 4 7 8 10 12 14 15 17 19 21 23 25 27 28
((~x + 1) mod (1 + (((x + (((x div 2) - (x div 5)) mod 3)) mod 2) * (x div 2))))
A294614: 0 0 1 0 0 0 0 2 0 2 0 2 3 0 0 0
((x + 1) div (2 + ((((x - ((x2 + (x div 2)) div 3)) div 2) mod 2) + (x mod 2))))
A102351: 0 0 1 1 1 2 3 2 3 3 3 4 4 3 5 4
(1 + ((x div (2 + ((x div 2) div (1 + ((x mod (2 + ((~x + 1) mod 4))) div 2))))) + (x mod 2)))
A327394: 1 2 2 3 2 3 2 4 3 3 2 4 2 3 4 5
(x div (3 + (((2 + ((x * (2 + ((x + 1) mod 4))) div 2)) mod 3) + (x mod 2))))
A302481: 0 0 0 0 0 1 1 1 1 1 3 2 2 2 3 2
((~1 + ((2 * (3 + (2 * (x div 4)))) div 3) - (x mod 2)) div (1 + (x mod 2)))
A029190: 1 0 1 0 2 0 2 0 3 1 3 1 5 2 5 2
(1 - (2 mod (~x + (x div 3) - ((x + 1) mod (1 + ((x + ~1) mod 3))))))
A301337: 1 1 2 2 2 3 4 4 6 6 6 7 8 8 10 10
(1 + compr(\x.(x mod (1 + ((5x2 + 10x + 5) mod 9))),x))
A026227: 1 3 6 7 9 12 15 16 18 19 21 24 25 27 30 33
(1 + compr(\x.((x + 1) mod (1 + ((~1 + (2 * ((1 + (x div 2)) div 2))) mod (1 + (x div 4))))),x))
A143896: 1 2 3 4 6 8 9 10 12 14 16 18 20 24 25 28
(1 + compr(\x.(~1 + (((2 * (x + (x div 3))) - (x div 7)) mod 3)),x))
A333227: 1 3 5 6 7 9 11 12 13 14 15 17 18 19 20 23
(1 + compr(\x.(2 - ((2x3 + 7x2 + 6x) mod 11)),x))
A284958: 2 4 6 7 8 9 11 13 15 17 18 19 20 22 24 26
(~1 + compr(\x.(1 - (x mod (1 + ((1 + ((x + ((x div 2) div 3)) mod 3)) mod (x + 1))))),x))
A026439: 2 3 4 6 9 10 12 13 14 16 18 20 21 22 24 28
(1 + compr(\x.((x + 1) mod (1 + (x div (1 - (x div (~2 + (((~x + 2) div 2) div 5))))))),x))
A241562-A071562: 1 2 4 6 8 9 12 15 16 18 20 24 25 28 30 32
((x + 1) + (9 * ((x + 1) - (x mod (x - ((x + ~1) mod 8))))))
A209932-A057169: 10 20 30 40 50 60 70 80 90 100 101 102 103 104 105 106
((x + 1) + (3 * (x + ((~x + 3) div 9) - (x div 3))))
A111102: 1 5 9 10 11 15 16 20 24 25 29 33 34 35 39 40
((x + 1) + ((4 * ((5x + 5) + (x div 5))) div 3))
A206906: 7 15 23 30 38 47 55 62 70 78 87 94 102 110 117 126
((x + 1) + ((4 * ((x + 1) div (8 - ((x + 2) div 3)))) div 3))
A099849: 1 2 3 4 5 7 8 9 10 12 13 16 17 19 21 22
((~x + ~1) + ((2x2 + 4x + 1) * (((x3 + 3x2 + 2x) div 2) div 3)))
A071902: ~1 5 65 306 975 2479 5425 10660 19311 32825 53009 82070 122655 177891 251425 347464
((x + 1) + ((1 + (((x3 + ~3x2 + 2x) div 2) div 15)) div 2))
A039853: 1 2 3 4 5 7 9 12 15 18 23 29 35 43 51 62
((x + 1) + (x div (2 + (x div (1 + ((x mod (1 + ((2 - (x mod 4)) mod (x + 1)))) div 2))))))
A076752: 1 2 3 5 5 6 7 10 10 10 11 15 13 14 15 21
((x + 1) + (((1 + (((x + 1) * (x mod (x - ((x + ~1) mod 8)))) div 2)) div 2) div 2))
A246084: 1 2 3 4 5 6 7 8 9 10 12 15 18 21 24 28
((x + 1) + (((5 * ((2x + 2) + (((x + 1) div 2) div 3))) div 2) div 2))
A189999: 3 7 10 14 17 22 25 29 32 36 39 44 48 51 55 58
((x + 1) + (((1 + ((x * ((2x + 2) + ((x + (x div 2)) div 4))) div 2)) div 2) div 2))
A076268: 1 2 4 7 10 14 19 24 30 36 42 50 58 66 76 85
((x + 1) + (2 * ((2 * (2x div 15)) + (((x + 1) div 2) div 2))))
A132188: 1 2 3 6 7 8 9 12 17 18 19 22 23 24 25 32
((x + 1) + ((x + ((3 * (2 + (x2 div 15))) div 2)) div 2))
A295579: 2 4 5 7 9 10 13 15 17 19 22 25 27
((x + 1) + (2 * (x + (((x + ((4 * (x div 3)) div 3)) mod 3) mod 2))))
A011990: 1 6 7 12
A287412: 1 6 7 12 13 16 19 22 27 30 31 34 37 40 45 46
((x + 1) * (1 + (x mod (1 + (((x + 2) * (2 - ((x div 2) mod 2))) mod (1 + (x div 3)))))))
A131959: 1 2 3 8
A135874: 1 2 3 8 5 6 7 8 27 10 11 24 13 14 15 64
((1 + (x mod (1 + ((x mod (1 + (2 * (1 + (x mod 5))))) div 3)))) mod (x + 1))
A124010: 0 1 1 2 1 1 1 1 3 2 1 1 1 2 1 1
compr(\x.((x + 1) - (9 * ((2x + 1) mod 7))),(x + 1))
A289105: 1 2 4 5 6 7 8 9 11 12 13 15 16 19 20 22
(((x + 1) - ((4x + (x2 div 4)) mod (x + 5))) div (x + 1))
A132976: 1 ~1 0 ~1 0 0 1 0 0 1 0 0 ~1 0 0 0
((1 + ((x + (2 * (4 - ((~x + 1) div (2 + (x div 4)))))) div 3)) mod (x + 1))
A065860: 0 0 2 1 0 0 0 7 7 8 9 9 9 10 10 10
((x + 1) * (1 + (2 * ((x div 2) div (1 + (x mod (1 + (x mod (1 + ((~x + 2) mod 4))))))))))
A318680: 1 2 9 4 25 18 49 8 27 50 121 36 169 98 225 48
((1 + (((1 + (x div 3)) div (1 + (x mod (2 - (x mod ~3))))) mod 2)) mod (x + 1))
A065203: 0 1 1 2 1 1 2 1 2 1 2 2 2 1 2 2
((1 + ((1 + (x div (2 + ((2 * (1 + (2 * (x mod 2)))) mod (1 + (x div 2)))))) div 2)) mod (x + 1))
A066088: 0 1 2 2 2 2 2 2 2 3 2 4 3 2 3 2
compr(\x.((x + 1) mod (1 + (x div (1 - (x div (~2 + (((~x + 2) div 2) div 5))))))),(x + 1))
A276112: 1 3 5 7 8 11 14 15 17 19 23 24 27 29 31 34
(2x - ((~1 + (2 * ((3 * (x + ((x - ((x div 2) mod 2)) div 2))) div 2))) div (x + 1)))
A013930: 1 2 3 4 5 7 9 11 13 15 17 19 20 23 25 26
((1 + (((((x + 1) mod 4) + (x div 4) + (x mod 3)) div 2) div 2)) mod (x + 1))
A087974: 0 1 2 1 1 2 2 1 2 2 2 2 2 2 3 1
((1 + (2 * ((1 + ((x * (1 + (2x mod (2 + (x div 4))))) div 2)) div 2))) div (x + 1))
A271592-A204459: 1 0 1 0 1 1 0 1 0 1 0 1 2 1 1 0
((18 * ((2x mod (~1 + (2 * (x div 4)))) mod 2)) mod (x + 1))
A344973: 0 0 0 0 0 0 0 0 0 0 0 6 0 4 3 0
((1 + (2 * compr(\x.((x + 1) mod (1 + ((x + (2 * (x mod 2))) div 5))),x))) div (x + 1))
A035453: 1 1 1 1 1 1 2 2 3 3 3 3 3 4 5 6
((2 + ((x + 1) div (1 + ((((~1 + (x div 2)) * (x div 3)) div 2) mod 3)))) div (x + 1))
A251482: 3 2 1 1 1 1 0 0 1 0 1 1 0 0 1 1
((x + 1) + (2 * (1 + ((1 + ((x * ((1 + (x div 3)) div 2)) div 5)) div 2))))
A092860: 3 4 5 6 7 10 11 12 13 16 17 18 19 22 23 28
((2 + ((x div 2) div (1 + (x mod (2 + ((~2x + 1) mod (2 + (x div 4)))))))) mod (x + 1))
A201443: 0 0 2 3 4 3 5 2 3 2 4
((2 + ((((~x + 2) mod 11) mod 2) + (x div 5))) mod (x + 1))
A124831: 0 1 2 2 3 3 4 3 4 3 5 4 5 4 4 6
compr(\x.(1 - (x mod (2 + ((x - (2 * ((~1 + (((x + ~1) div 2) div 2)) div 2))) mod 3)))),(x + 1))
A302403: 2 3 5 7 9 10 11 13 17 19 21 23 25 26 27 29
((~x + ~1) + (2 * (3 + (2 * (2 + (3 * (x + ((((x + 1) div 2) div 2) div 2))))))))
A104342: 13 24 35 46 57 68 79
A266912: 13 24 35 46 57 68 79 102 113 124 135 146 157 168 179 202
compr(\x.(~2 + ((1 + (x mod (1 + (2 * (2 + ((x div 2) mod 5)))))) mod (x + 1))),(x + 1))
A032907-A032873: 1 2 3 4 5 6 7 8 9 10 11 20 21 22 30 31
compr(\x.(~2 + ((x + 1) mod (2 * (1 + (x div (3 * (2 + (x2 mod 3)))))))),(x + 1))
A326841-A274222-A219301: 1 2 3 4 5 7 8 9 11 12 13 16 17 19 23 25
(1 - ((1 + (x div 2)) mod (1 - ((2 - (2x mod (4 + (x div 4)))) mod (x + 1)))))
A322190: 1 1 1 1 1 1 1 2 2 1 1 4 5 4 1 1
((~2 + ((x2 + ~1) mod (2 * (2 + ((x + ((x mod (1 + (x div 2))) div 2)) div 2))))) div (x + 1))
A077606: 1 ~1 0 0 1 0 0 ~1 0 0 0 0 1 0 0 0
(compr(\x.(1 - ((2 * ((2x + 1) - ((x + (x div 2)) div 4))) mod 3)),x) mod (x + 1))
A087177: 0 0 1 1 1 1 1 1 2 3 4 5 5 5 5 6
((1 + ((x + 1) div (1 + (x mod (1 + (2 * (1 + ((x + ~1) mod (1 + (x mod 3)))))))))) div 2)
A248514: 1 1 1 2 1 3 4 2 1 5 6 3 7 4 2 8
(((x + 1) - (x div (1 + (((x2 + 2x) div 2) mod (1 + (x div (2 + (x div 3)))))))) div 2)
A144741: 0 0 0 1 0 2 0 2 2 3 0 4 0 4 4 4
((1 + ((1 + (4x mod 13)) mod (1 + (x div 3)))) div 2)
A276007: 0 0 0 1 0 0 0 0 1 2 1 1 0 1 0 2
((1 + ((~1 + (3 * ((x + ~1) mod (2 + (x div 4))))) mod (1 + (x div 3)))) div 2)
A089339: 0 0 0 1 1 0 1 1 1 2 1 1 1 0 2 3
((1 + ((x + 1) mod (1 + (2 * (1 + ((x div (1 + (x mod 9))) mod 2)))))) div 2)
A293461: 1 1 0 1 1 0 1 1 0 0 1 1 2 1 0 1
((1 + ((x + 1) div (1 + ((1 + (((x * ((1 + (x div 2)) div 2)) div 3) div 2)) div 2)))) div 2)
A271099: 1 1 2 2 3 3 2 2 2 2 1 2 2 2 1 1
((1 + ((x + 1) mod (1 + (8 * (2 div (6 - (x div 3))))))) div 2)
A308925: 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3 8
((1 + ((((3 * ((x + 2) mod 5)) mod (x + 1)) div 2) mod 5)) div 2)
A309416-A296239: 0 0 0 0 1 0 1 1 0 1 2 2 1 0 1 2
(x div (2 + (x div (1 + ((x - (x div (11 - (x div 2)))) mod 3)))))
A192062-A172371: 0 0 1 0 1 1 0 1 1 1 0 1 1 2 2 0
(30x4 + 120x3 + 210x2 + 180x + 62)
A069473: 62 602 2702 8162 19502 39962 73502 124802 199262 303002 442862 626402 861902 1158362 1525502 1973762
(3 + ((((2x2 + 4x + 2) * (2 - ((x * (x div 2)) mod 2))) div 2) mod 3))
A291040: 5 5 3 4 5 3 5 4 3 5 5 3 5 5 3 4
(3 + ((x - (2 * ((x mod (3 + ((~x + 1) mod (2 + (x div 2))))) div 2))) mod 3))
A052384: 3 4 3 4 4 3 3 4 5 4 5 4 5 4 5 3
(3 + ((4 * (x - ((x - ((x div 2) mod 4)) div 5))) div 3))
A024355: 3 4 5 7 8 9 11 12 12 13 15 15 16 17 19 20
(5 mod ((~1 + (3 * ((~2x + 2) mod (4 + (x div 4))))) div 2))
A339209: 1 0 1 0 0 1 0 1 0 1 0 0 5 0 1 0
((1 + ((((x * (1 + ((x + ((x * (x div 2)) div 3)) div 2))) div 2) div 2) div 3)) div 2)
A026928: 0 0 0 0 1 1 2 2 3 4 6 7 10 11 14 16
((1 + ((((x + 2) * ((x + 3) - (((2 - (x div 2)) div 2) div 2))) div 2) div 3)) div 2)
A008757: 1 1 2 3 4 5 7 8 10 12 14 16 19 21 25 28
((9x8 + 7x7) div 2)
A229150: 0 8 1600 37179 352256 2031250 8538048 28824005 82837504 210450636 485000000 1032820063 2060328960 3890408054 7009998016 12131015625
(((3x2 + 12x + 13) + (((x3 + ~x) div 2) div 3)) div 2)
A026055: 6 14 25 40 59 84 114 150 192 242 299 364 437 520 612 714
((3x2 + 12x + 9) + (((x3 + ~x) div 2) div 3))
A023551: 9 24 46 76 115 164 224 296 381 480 594 724 871 1036 1220 1424
((~1 + (((x + ~2) * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 3)) div 2)
A172971-A172970: ~1 ~1 ~1 ~1 ~1 ~1 ~1 0 0 ~1 ~1 1 2 1 ~1 ~1
((1 + ((1 + (x div (3 + (2x mod 7)))) div (1 + (x mod 2)))) div 2)
A109698-A025820: 1 0 1 0 1 0 1 1 1 1 1 1 2 1 3 1
(2 * (1 + compr(\x.((x + 1) mod (1 + (x mod (1 + (x div (2 + (x div 8))))))),(x + 1))))
A097619: 4 6 8 12 16 18 20 24 30 32 36 40 42 48 50 52
((((x + 1) div (1 + (2 * ((1 + (x div 4)) div 2)))) mod 2) + ((x div ~3) mod 2))
A191336: 1 1 2 1 1 0 0 1 2 2 1 0 0 1 2 2
(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (~1 + (x div ~2))) div 2))
A173117-A028262: 1 1 1 1 3 1 1 4 4 1 1 5 8 5 1 1
((1 + ((1 + ((x + 1) div (1 + ((x - ((x div 2) mod 5)) mod 3)))) div 2)) div 2)
A337763: 1 1 1 1 1 2 2 1 1 1 2 1 1 4 4 2
((1 + ((1 + ((x + 1) div (1 + (x mod (2 + (x mod (~1 + (2 * (x div 4))))))))) div 2)) div 2)
A226378: 1 1 1 1 2 1 2 1 3 2 2 1 4 1 2 2
(2 * (1 + (((x + 1) mod (1 + (3 * (((x + 1) mod 8) mod 3)))) div 2)))
A255671: 2 4 2 2 6 2 4 2 2 4 2 2 8 2 4 2
(((x + 1) mod (1 + (2 * (1 + ((x + ((1 - (x2 div 2)) mod 3)) mod 3))))) div 2)
A322338: 0 1 1 0 1 0 1 0 2 0 1 0 1 0 0 0
(2 * (1 + (2 * ((x div 2) div (1 + (x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4)))))))))))
A099985: 2 2 6 2 10 6 14 2 6 10 22 6 26 14 30 2
((x + ((2 * ((x + 4) + (x div 8))) + (x div 7))) div 2)
A146968: 4 5 7
A219958: 4 5 7 8 10 11 13 15 17 19 20 22 23 25 27 28
((1 + ((~1 + ((2x + ~2) mod (4 + (x div 4)))) mod (2 + (x div 3)))) div 2)
A284593: 1 1 1 1 0 1 2 1 1 2 2 1 0 1 2 3
((1 + ((2 + ((1 + (((x div 3) * (x div 2)) div 2)) div 2) - (x mod 2)) div 2)) div 2)
A282970: 1 0 1 0 1 1 1 1 1 1 2 1 2 2 2 3
((1 + (x mod (2 + ((1 + (2 * ((x + 1) div (2 * (2 + ((x div 2) mod 2)))))) mod (x + 1))))) div 2)
A078821: 0 1 1 0 2 0 1 1 1 1 0 2 2 2 0 1
(1 - ((1 + (x div (2 + ((2 + (x2 mod (4 * (2 + (x mod 2))))) mod (x + 1))))) div 2))
A143840: 1 1 0 1 0 0 1 0 0 ~1 0 0 ~1 0 0 0
((4x + 6) * ((1 + (2 * ((2x + 2) - (x mod 2)))) * (1 + (x div 2))))
A218327: 30 70 364 540 1386 1794 3480 4216 7030 8190 12420 14100 20034 22330 30256 33264
((1 + (((1 + ((((x2 div 4) * (1 + ((x + 1) div 2))) div 2) div 2)) div 2) div 2)) div 2)
A062890: 0 0 0 0 1 1 1 2 3 4 5 7 8 11 12 16
(3 + (x div (2 * (2 + ((2 * (~1 + ((x2 + x) mod 5))) mod (x + 1))))))
A259581: 3 3 3 3 3 3 3 4 4 3 3 4 6 4 3 3
((1 + ((((x + 1) * ((x + 4) - (x div ~14))) div 2) div 2)) div 2)
A139542: 1 2 3 4 6 8 10 12 15 18 21 24 28 32 36 42
(2 * ((1 + (x div (2 + (x div (2 + ((x div 2) mod 3)))))) mod (1 + (((x + 1) div 2) div 2))))
A241658: 0 0 0 0 0 0 0 4 0 4 0 6 4 4 6 6
((1 + (((((x + 1) * (2 + (((~x + 3) div 3) mod (x + 1)))) div 2) div 2) div 2)) div 2)
A268084: 0 0 0 1 2 3 4 4 5 6 7 8 10 11 12 14
(3 + (((2 + ((((x + 2) * (x - (2 mod (1 + (x div 4))))) div 2) div 2)) div 2) div 2))
A120196: 3 3 4 4 5 5 6 7 7 8 9 10 12 13 15 17
((64x + 62) - (x div 15))
A103584: 62 126 190 254 318 382 446 510 574 638 702 766 830 894 958 1021
((((31x2 + ~x) div 2) div 9) div 2)
A235532: 0 0 3 7 13 21 30 42 54 69 85 103 123 145 168 193
(((x + 7) * ((x3 + 9x2 + 20x + 12) div 2)) div 2)
A104676: 21 84 216 450 825 1386 2184 3276 4725 6600 8976 11934 15561 19950 25200 31416
(10 * ((x + 1) - (9 * (~x + (x mod 8)))))
A044835: 10 20 30 40 50 60 70 80 810 820 830 840 850 860 870 880
(2 + ((((x + 1) * (~1 + (2 * (4 + (((x + 1) div 2) div 2))))) div 2) div 5))
A334142: 2 3 4 5 6 7 8 10 11 13 14 17 18 20 21 26
(((7x + 7) - (x div 9)) mod 10)
A237042: 7 4 1 8 5 2 9 6 3 9 6 3 0 7 4 1
(compr(\x.(x mod (1 + (4 * (x mod (2 + (x mod 2)))))),(x + 3)) mod 10)
A083786: 4 6 8 9 0 2 4 5 6 8 0 1 2 4 5 6
(((4x + 4) + ((2x + 2) div ~7)) mod 10)
A071792: 3 7 1 4 8 2 6 9 3 7 0 4 8 2 5 9
(~x + (compr(\x.(x mod ((x + 1) - (x mod 10))),x) + (x mod 10)))
A103303: 0 1 2 3 4 5 6 7 8 9
A345110-A004086: 0 1 2 3 4 5 6 7 8 9 1 11 21 31 41 51
((1 + (((x mod (2 + ((x2 div 4) mod (x + 1)))) div 2) + (x div 5))) div 2)
A318440: 0 0 1 1 1 1 1 1 3 1 1 2 1 1 2 3
((1 + ((((x + 1) + (2 * ((((x + 2) * (x - (x div ~2))) div 2) div 2))) div 2) div 2)) div 2)
A262249: 0 1 1 2 3 4 5 7 9 11 13 15 17 21 23 26
(~1 + ((x div 2) + (((x div 4) - ((1 + ((x mod 5) div 2)) mod 3)) mod 2)))
A306878: 0 0 0 0 2 1 2 3 3 3 5 5 6 6 7 6
((3 * (1 + (((x + 1) div (2 - (16 mod (~x + ~1)))) div 2))) div 2)
A346403: 1 1 1 3 1 1 1 4 3 1 1 1 1 1 1 7
((3 * ((7x + 6) - ((x + 1) div 7))) div 2)
A189798: 9 19 30 40 51 61 70 81 91 102 112 123 133 142 153 163
((~x + 6) + (2 * (((x + 1) div 3) - ((1 - (x div 3)) div 3))))
A106154: 6 5 6 5 4 5 6 5 6 5 4 5 4 3 4 5
((24x + 12) * (x + ((x3 + 3x2 + 2x) div 3)))
A129027: 0 108 600 1932 4752 9900 18408 31500 50592 77292 113400 160908 222000 299052 394632 511500
(x - ((x - (((x + 1) + ((x3 + 2x) div 9)) div 3)) div 2))
A175864: 0 1 2 3 4 6 8 11 15 20 26 33 41 50 61 73
(1 - (2 * (((0 - (x mod (1 + (2 * (x div (2 * (2 + (x mod 2)))))))) mod (x + 1)) div 3)))
A123562: 1 1 1 1 ~1 1 1 ~3 ~3 1 1 ~5 ~3 ~5 1 1
((3 * ((5x + 4) - ((2x + 1) div 9))) div 2)
A330177: 6 13 21 28 34 42 49 57 64 70 78 85 93 99 106 114
(2 * ((5x4 + 20x3 + 31x2 + 28x + 12) div 3))
A167239: 8 64 288 880 2120 4368 8064 13728 21960 33440 48928 69264
((3x + 5) + (5 * (x - ((x + (x div 4)) div ~2))))
A035338: 5 18 26 39 52 60 73 81 94 107 115 128 141 149 162 170
(2 * (((3x4 + 13x3 + 21x2 + 14x + 3) div 2) div 3))
A215191: 0 18 88 276 664 1366 2512 4264 6800 10330 15080 21308 29288 39326 51744 66896
((((3x5 + 10x4 + 13x3 + 8x2 + 2x) div 2) div 3) div 2)
A132122: 0 3 33 164 550 1455 3283 6608 12204 21075 34485 53988 81458 119119 169575 235840
(((((x + 1) * ((5x3 + 9x2 + ~2x) div 2)) div 2) div 3) div 2)
A002418: 0 1 9 35 95 210 406 714 1170 1815 2695 3861 5369 7280 9660 12580
((((x4 + 14x3 + 53x2 + 76x + 36) div 2) div 3) div 2)
A127407: 3 15 44 100 195 343 560 864 1275 1815 2508 3380 4459 5775 7360 9248
(2 + ((2 * ((x + 2) + ((x + ((x + (x2 div 4)) div 3)) div 2))) div 3))
A100966: 3 4 5 6 8 9 10 12 14 15 16 18 20 22 24 26
(x - ((3 * (~1 + (2 * ((x2 div (x - ((~x + 2) div 2))) mod 2)) - (x mod 2))) div 2))
A105364: 2 1 4 6 3 5 8 10 7 12 9 11 14 16 13 18
(6 * (x + ((((x + 1) - (2 * (~x + (x mod 10)))) div 2) div 2)))
A061822: 0 6 12 24 30 36 42 54 60 66 102 114 120 126 132 144
(((2 * (1 + ((2 + (((x div 3) * (x div 2)) div 2)) div 3))) - (x mod 3)) div 2)
A008681: 1 0 0 1 1 1 2 1 2 3 3 3 5 4 5 7
(((2 * (1 + (((1 + (x div 4)) mod (1 + (x div 3))) div 2))) - (x mod 3)) div 2)
A029295: 1 0 0 1 0 0 2 1 0 2 1 1 3 2 2 3
(((2 * (1 + (x div (4 + (8 mod (1 + (x div 2))))))) - (x mod 3)) div 2)
A029292: 1 0 0 1 0 0 2 1 1 2 1 1 3 2 3 4
(3 + ((x + ((((x2 + ~1) div 2) div 5) + (((x + 1) div 2) div 2))) div 2))
A121603: 2 3 4 5 6 7 8 9 11
A072495: 2 3 4 5 6 7 8 9 11 12 13 16 17 19 21 23
((x div (3 + (x div 4))) - ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2))
A239287: 0 0 0 1 0 1 1 0 0 1 2 1 0 1 2 2
(2x div (2 + (x div (1 + ((((~x + 1) div (2 - (x mod ~4))) mod 2) + (x mod 2))))))
A187808: 0 1 1 2 1 3 1 2 1 3 2 3 1 4 1 4
(((x + 1) + ((20x2 + ~10x) div 7)) div 2)
A293502: 0 1 5 12 22 35 50 69 90 114 141 171 203 239 277 318
(((x + 1) + ((12x2 + 24x + 12) div 7)) div 2)
A194106: 1 4 9 15 23 33 45 58 73 90 109 129 151 175 200 227
((x + 3) + ((9 * ((x + 1) + (2 * (2x + (x mod 2))))) div 2))
A164135: 7 40 54 87 101 134 148 181 195 228 242 275 289 322 336 369
((8x4 + 46x3 + 95x2 + 83x + 26) div 2)
A076457: 13 129 534 1510 3435 6783 12124 20124 31545 47245 68178 95394 130039 173355 226680 291448
(((1 + (2 * (1 + ((3x mod 7) mod 3)))) mod (x + 1)) div 2)
A025485: 0 0 0 1 1 2 2 1 1 1 3 3 2 2 1 1
(((1 + (2 * (((x2 div ~4) mod 5) mod 3))) mod (x + 1)) div 2)
A075685: 0 0 0 0 1 0 1 2 1 1 0 1 1 2 1 0
(2 + ((1 + (2 * ((4 * ((x - (x div 3)) div 3)) div 3))) mod (x + 1)))
A087418: 2 3 3 3 5 5 5 5 7 7 7 7 7 11 11 11
((4x2 + 10x + 6) + (((x3 + 3x2 + 2x) div 2) div 3))
A051941: 6 21 46 82 130 191 266 356 462 585 726 886 1066 1267 1490 1736
(((x + 1) * (1 + (((x + ~1) mod (3 + (x div (1 + (x mod 2))))) mod 2) - (x mod 2))) div 2)
A341310: 0 0 3 0 5 0 7 0 9 5 11 0 13 7 15 0
(2 + ((~2 + (2 * ((2 - (2x mod (4 + (x div 4)))) mod (x + 1)))) div (x + 1)))
A275015: 0 1 2 1 3 2 1 3 3 2 1 3 3 3 2 1
(1 - (x div (2 + ((2 * (2 + (((x mod (~2 + ((~x + 2) div 4))) div 2) mod 2))) mod (x + 1)))))
A206959: 1 1 1 0 0 ~1 0 1 0 0 0 0 ~1 0 0 ~1
(x div (2 + (((4 div (4 - ((x mod (1 + (x div 2))) div 2))) - (x mod 2)) mod (x + 1))))
A319396: 0 0 0 1 1 2 2 3 2 3 2 3 3 2 2 3
((3x + 3) - ((x - ((2 - (x div 3)) mod 5)) mod 3))
A287436-A026602: 2 4 9 10 15 17 21 23 25 28 33 35 39 41 43 47
((2x + 2) + ((11x2 + 11x) div 9))
A194137: 2 6 13 22 34 48 65 84 106 130 156 185 216 250 286 325
((2x + 2) + (5 * ((12x + 12) div 5)))
A187975: 12 24 41 53 70 82 94 111 123 140 152 164 181 193 210 222
((~2x + ~2) + (5 * ((2x + 2) + (((x + 1) + (x div 4)) div 2))))
A134862: 8 21 29 42 55 63 76 84 97 110 118 131 144 152 165 173
(3 - (((x + 1) * ((~x + 1) - (2 * (24 + (x div 2))))) div 2))
A217235: 27 51 80 107
((2 + (x mod (1 + ((1 + (x mod (2 * (2 + (((x + 1) div 2) mod 3))))) mod (x + 1))))) div 2)
A274888: 1 1 1 1 1 2 2 1 1 1 2 1 1 1 2 4
(((1 + (((x + 1) * (1 + ((x - ((x + (x div 2)) div 5)) div 2))) div 2)) div 2) div 2)
A340276: 0 0 1 1 1 2 2 3 4 5 5 7 8 10 11 12
(((1 + (((x + 1) * (x + ((2 * (x + (x div 3))) div 5))) div 2)) div 2) div 2)
A239517: 0 0 1 2 4 5 8 10 13 16 20 24 29 33 39 46
(((1 + ((((x + 1) * (2 + ((2 + (x mod 8)) mod (x + 1)))) div 2) div 2)) div 2) div 2)
A033102: 0 0 0 1 1 1 1 1 2 3 4 5 6 8 9 11
(4 * (1 + (2 * (x - ((0 - ((x - (((x + 1) div 2) mod 6)) div 2)) div 2)))))
A081770: 4 12 20 28 44 52 60 68 76 84 92 116 124 132 140 148
(~2 + ((5 * ((x + 2) - ((2 * (~x + ((x div 3) mod 2))) div 3))) div 2))
A277555: 3 8 13 15 18 23 28 33 38 40 43 48 53 58 63 65
(((5 * ((2x + 2) + ((x - (x div ~7)) div 2))) div 2) div 2)
A189515: 2 6 8 12 15 18 21 25 28 31 35 37 41 43 47 51
(((5 * compr(\x.(2 - (3x mod 13)),x)) div 2) div 2)
A076437: 1 2 3 5 6 7 8 10 12 13 15 17 18 20 21 22
(4 * ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 5))
A190113: 0 0 0 0 0 0 0 4 4 0 0 8 16 8 0 0
(2 * ((1 + (((x + 2) * ((2x + 4) + ((x * (x div 3)) mod 2))) div 2)) div 2))
A343907: 4 10 16 28 36 52 64 82 100
(x - (2 * (((2x + 1) mod (3 * (1 + (2 * ((x div 5) mod 2))))) div 2)))
A167877: 0 1 0 3 4 3 2 1 0 9 10 9 12 13 12 11
(2 * (x - (((2x + 1) mod (3 * (1 + (2 * ((x div 5) mod 2))))) div 2)))
A167878: 0 2 2 6 8 8 8 8 8 18 20 20 24 26 26 26
(((x + 1) div (2 + ((x2 div (2 - (x mod (1 + (x div 8))))) mod 3))) div 2)
A219254: 0 0 0 0 0 1 1 2 1 2 1 2 3 2 1 4
(x - (((3 * (x - (2 * (x div (3 + ((x div 3) mod 3)))))) div 2) div 2))
A333536: 0 1 1 1 3 3 3 4 4 7 7 8 8 8 8 9
(x - (((3 * (2 + ((((x + 1) * (~1 - (x div 4))) div 2) div 2))) div 2) div 2))
A096276: 0 1 2 3 5 6 8 9 12 14 16 17 21 22 24 26
((x + 1) div (2 * (2 + (x div (3 * (2 + ((x2 + 4x + 4) mod 8)))))))
A143974: 0 0 0 1 1 1 1 2 2 1 1 2 3 2 1 2
(2 + (((2x mod (4 + (x div 4))) - ((2 + (x div 4)) mod 3)) div 2))
A233420: 1 2 1 2 3 2 3 4 3 1 2 3 2 3 1 2
((((x + 1) + (3 * (2x - ((x + 1) mod (1 + ((x div 2) div 3)))))) div 2) div 2)
A076355: 0 2 3 5 7 9 10 12 13 16 17 19 20 21 24 25
(((9x4 + 18x3 + 23x2 + 14x + 5) div 2) div 2)
A160767: 1 17 103 367 971 2131 4117 7253 11917 18541 27611 39667 55303 75167 99961 130441
((x mod (2 + ((1 + (2 * ((x mod (1 + (2 * (1 + (2 * (x mod 2)))))) div 2))) mod (x + 1)))) div 2)
A304650: 0 0 0 1 0 2 0 0 1 2 0 2 0 2 2 0
(2 * ((((5 * ((x2 + 3x + 2) div 2)) + (x div 5)) div 2) div 2))
A109592: 2 6 14 24 36 52 70 90 112 138 166 196 228 262 300 340
((2 + ((3 * ((2 + ((x2 + 2x) div 9)) div 3)) div 2)) div 2)
A029107: 1 1 1 1 1 1 2 3 3 4 4 4 5 6 7 8
(2 + ((x mod (2 + ((3 * (2 + (x2 mod (x + 5)))) mod (x + 1)))) div 2))
A252375: 2 2 2 2 2 2 2 2 2 6 2 2 2 8 3 2
(x div (4 + (x mod (2 + ((3 * ((x + 2) - (x2 div 4))) mod (x + 1))))))
A079066: 0 0 0 0 0 1 1 0 2 1 1 2 0 1 1 2
(2 * ((2 + ((3 * (2 - ((x3 mod (2 + (x div 2))) mod 2))) mod (x + 1))) div 2))
A330772: 2 2 2 4 2 4 4 4 8 4 8 4 8 4 8 8
((2 + (x2 mod (6 - (x mod (1 + ((x + ~1) mod 9)))))) div 2)
A107335: 1 1 3 2 3 1 1 1 3 2 3 1 1 3 1 1
((((((x + 1) - (2 * ((x - ((~1 + (x div 2)) div 2)) div 2))) * ((x + 1) div 2)) div 2) div 2) div 2)
A098822: 0 0 0 0 0 0 1 1 1 1 1 3 2 3 4 4
(x div (2 + ((x + 1) div (2 * (2 + (x mod (2 + (x mod (2 - ((x div 4) div ~2))))))))))
A232194: 0 0 1 1 2 1 2 2 2 3 3 3 2 3 4 2
(8 * ((x div 9) - (x mod (x - ((x + ~1) mod 8)))))
A055959: 0 0 0 0 0 0 0 0 0 8 0 ~8 ~16 ~24 ~32 ~40
((2 + (((x - (5 * (2 - ((x div 2) mod 5)))) mod (x + 2)) div 2)) div 2)
A037162: 1 1 1 1 2 2 1 1 3 3 1 1 2 3 4 4
((((28x2 + 105x + 98) div 2) div 2) div 2)
A126195: 12 28 52 83 120
((2 + ((x + (3 * ((x mod 10) mod 9))) div 2)) div 2)
A061499: 1 2 3 4 5 6 7 8 9 3 3 4 5 6 7 8
((x + 6) + ((x2 + 2x + 2) div (~x + 25)))
A120191: 6 7 8 9 11 12 14 16 18 21 24 27 31 35 40 46
((2 + ((~x + (3 * ((x + (x2 div 14)) div 2))) div 2)) div 2)
A320614: 1 0 1 1 1 2 2 3 3 4 4 5 6 6 8 8
((x + 6) + ((x + (2 * (2 + (((x + ~1) mod (2 + (x div 2))) div 2)))) div 3))
A125134: 7 8 10 12 13 14 15 16 18 20 21 22 24 26 27 28
(4 * ((2x + 3) + (2 * (x div (1 + (x div (2 + (x div 5))))))))
A255136: 12 28 36 44 52 68 76 84 92 100 116 124 132 140 148 156
(2 * (1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))
A028326: 2 2 2 2 4 2 2 6 6 2 2 8 12 8 2 2
(1 - (2 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))
A113245-A109128: 1 1 1 1 3 1 1 5 5 1 1 7 11 7 1 1
(1 - ((((x + 2) * ((2 - (2x mod (4 + (x div 4)))) div (x + 1))) div 2) div 2))
A049687: 0 1 1 1 3 1 1 4 4 1 1 5 5 5 1 1
(2 - ((((x + 2) * ((2 - (2x mod (4 + (x div 4)))) div (x + 1))) div 2) div 2))
A049627: 1 2 2 2 4 2 2 5 5 2 2 6 6 6 2 2
((1 + ((1 + (x mod (2 * (2 + ((x2 + 2x) mod 6))))) mod (x + 1))) mod 4)
A330466: 1 1 1 1 2 1 0 1 2 1 0 1 2 1 0 3
((1 + (((1 mod (1 - (2x mod (4 + (x div 4))))) mod (x + 1)) div 2)) mod 4)
A211313: 1 1 1 1 3 1 1 0 0 1 1 2 3 2 1 1
((1 - ((x - (x mod (1 + (2 * ((x - (x div 3)) mod 3))))) mod 3)) mod 4)
A143333: 1 1 1 1 0 1 1 3 3 1 1 0 0 0 1 1
((0 + (2 * (((2x2 + x) div 3) mod 3)) - (x mod 2)) mod 4)
A221168: 0 1 0 1 0 3 0 3 0 3 2 3 2 3 0 3
((1 - ((1 + (x mod (1 + ((x2 + ~x) mod (4 + (x div 4)))))) div 2)) mod 4)
A103306: 1 1 0 1 0 1 1 0 0 1 1 0 2 0 1 1
((x + 5) + (((x2 + x + 1) * ((x2 + x) div 4)) div 3))
A066901: 5 6 9 21 44
(x - (x mod (1 - (2 * (((x + 1) + ((32 mod (x + 1)) div 2)) div 2)))))
A206914-A175298: 0 1 3 3 5 5 7 7 9 9 15 15 15 15 15 15
((x + 4) + ((2 * ((2x + 1) + (((1 + (x div 2)) div 3) mod 2))) div 3))
A025054: 4 7 9 11 14 17 19 21 24 26 28 30 32 35 37 39
(((x + (((10x3 + ~3x2 + ~4x) div 2) div 3)) div 2) div 2)
A212068: 0 0 3 10 25 49 86 137 206 294 405 540 703 895 1120 1379
(2 + ((x + (((17x2 + 38x + 8) div 2) div 3)) div 2))
A194112: 2 7 15 26 40 56 75 97 122 150 181 214 250 289 331 376
((x + 4) + ((x + (x div (2 + ((x div (2 + (x mod (2 + (x mod 2))))) mod 2)))) div 3))
A272054: 4 5 6 8 10 11 12 14 16 17 18 20 22 23 24 25
((x + 2) - (2 * (~x + ((x - (((x + ~1) div 2) mod (1 + ((1 + (x div 2)) div 3)))) div 2))))
A055938: 2 5 6 9 12 13 14 17 20 21 24 27 28 29 30 33
(((x + 2) + ((3 * ((x + 2) + (x div (9 - (x div 2))))) div 2)) div 2)
A229992: 2 3 5 6 7 8 10 12 13 14 16 17 20 21 25 26
((x + 4) + (((3 * (2x + ((2 + (x2 div 2)) div (x + 2)))) div 2) div 2))
A191407: 4 6 9 12 14 18 20 23 26 28 32 34 37 40 43 46
((((x3 + 3x2 + 2x) div 2) div 3) + (((x + 2) * ((x2 + 1) div 2)) div 2))
A212970: 0 2 8 22 44 80 128 196 280 390 520 682 868 1092 1344 1640
(2 + compr(\x.((x + 1) mod (1 + (x mod (1 + (x div (2 + (x mod (2 * (1 + (2 * (x mod 2))))))))))),x))
A000430: 2 3 4 5 7 9 11 13 17 19 23 25 29 31 37 41
((x + ~1) + ((2 + ((x mod ((x div 2) - ((1 + (x div 2)) mod 3))) div 2)) mod 4))
A290492: 1 2 3 4 5 6 7 8 9 10 11 12 14
A191431: 1 2 3 4 5 6 7 8 9 10 11 12 14 15 13 16
((x + ((x + (((2x3 + 7x2 + ~4x) div 2) div 3)) div 3)) div 2)
A025196: 0 0 2 4 8 14 22 32 45 61 80 103 130 162 198 239
(2 * ((x + 1) + (2 * ((x + 1) + ((x3 + 9x2 + 8x) div 3)))))
A207106: 6 36 98 200 350 556 826 1168 1590 2100 2706 3416 4238 5180 6250 7456
(2 * (x + ((x + (3 * ((5x + 4) + (x div 4)))) div (x + 1))))
A048260: 24 30 32 36 38 40 42 44 48 50 52 54 56 58 60 62
((x + ((1 + (((2x - (x mod 2)) * (1 + (x div 2))) mod 7)) div 2)) div 2)
A194817: 0 1 1 2 3 4 4 4 5 5 5 5 6 6 7 8
((x + ((1 + (((x + 1) + (2 mod (1 + (x div 4)))) mod 9)) div 2)) div 2)
A337774: 0 1 2 2 3 4 5 5 4 5 6 7 7 8 9 7
((x + ((1 + (((x + 2) + (x3 div 9)) div 3)) div 2)) div 2)
A062188: 0 1 1 2 3 4 5 7 9 12 15 19 23 28 33 40
((x + 2) + ((3 * (2 + ((4x + (x2 div 4)) div (x + 2)))) div 2))
A161827: 5 7 10 11 13 14 17 18 19 21 22 23 26 27 28 29
((x + ~2) + (((5 * ((x + 2) - (x2 div (x + 6)))) div 2) div 2))
A090946: 0 2 5 6 8 9 10 12 13 14 15 16 17 19 20 21
((x + 2) + (((3 * (x - ((2 * (~x + (x div 5))) div 3))) div 2) div 2))
A187838: 2 4 7 8 11 13 15 17 19 22 24 25 28 30 32 34
((x + 2) + (((3 * (3x - ((~x + 1) div (2 + (x div 4))))) div 2) div 2))
A184926: 2 5 9 12 15 19 23 26 29 32 36 40 43 46 49 53
((x + 6) + ((5 * (1 - ((~x + 1) div 7))) div 2))
A079525: 8 9 13 14 15 16 17 18 19 22
((x + 2) + (((((x2 + ~x + ~1) - ((x2 + 2x) div 5)) div 2) div 2) div 2))
A331903: 1 2 4 5 6 8 10 12 14 17 20 23 26 29 33 36
(2 + (x * (2 + (x * ((x + 1) + (((x4 + x3 + 2x2 + 2x) div 2) div 3))))))
A131682: 2 7 42 242 1050 3537 9842 23732 51282 101675 188122 328902 548522 878997 1361250 2046632
(x - ((x + ((x + (((((x * ((~x2 + 2x) div 4)) div 2) div 2) div 2) div 2)) div 2)) div 2))
A096792: 0 1 1 1 2 2 3 3 4 5 6 8 9 11 13 16
(2x * (2 + (x * (2 + ((x8 + x3) div 2)))))
A054609: 0 10 1080 59340 1049680 9768870 60474120 282492280 1073774880 3486843810 10000100440 25937586180 61917613680 137858863870 289255193640 576651150960
(((5x3 + 25x2 + 21x + 1) div 2) div (x2 + 2x + 2))
A182617: 0 5 9 12 15 18 21 23 26 29 31 34 36 39 41 44
((1 + (2 * compr(\x.(1 - (x mod (1 + ((x - (x div ~4)) mod 3)))),x))) div (x + 2))
A316844: 1 2 2 2 3 3 3 3 3 4 4 4 4 3 4 4
((x3 + 3x2 + 4x + 4) + (((x4 + ~x3 + ~x2 + x) div 2) div 3))
A225894: 4 12 33 78 162 304 527 858 1328 1972 2829 3942 5358 7128 9307 11954
((2x + 1) + ((1 + (2x mod (4 + (x div 2)))) mod (1 + (x div 5))))
A131628: 1 3 5 7 9 12 13
A191749: 1 3 5 7 9 12 13 16 18 20 21 25 27 28 30 32
((2x + 1) + ((1 - ((x + 1) mod (1 + ((x + ~1) mod (1 + (x div 3)))))) mod 3))
A189010: 2 4 6 8 9 12 13 16 17 20 21 24 25 29 30 31
((2x + 1) + ((1 - ((x + 1) mod (1 - ((~x + 1) div (2 + (x div 3)))))) mod 3))
A189205: 2 4 5 8 9 12 13 17 18 19 23 24 25 29 30 31
((2x + ~1) + ((2 * ((2x + 4) - (x mod (~1 + ((~x + 1) div 2))))) div 3))
A287114: 1 5 8 12 16 19 23 25 29 32 36 39 43 45 49 52
(2x + (((6x2 + 9x + 3) div 5) div 5))
A161569: 0 2 5 9 13 17 22 28 34 40 47 55 63 71 80 89
(1 + (((1 + (x mod (1 + (x mod (2 * (1 + (x div 5))))))) mod (x + 1)) + (x mod 2)))
A306652: 1 2 2 4 2 4 2 6 2 4 2 8 2 4 4 10
(1 + ((((((x + ~1) div 2) mod (~4 - (x div 4))) mod 3) div 2) + (x mod 2)))
A230259: 2 2 1 2 2 2 1 2 1 2 1 3 1 3 2 2
(1 - ((2 * ((1 - (2 * ((x div 5) mod 2))) * ((x div ~2) mod 2))) + (x mod 2)))
A065364: 1 ~2 ~1 0 1 2 3 0 1 2 ~1 0 1 ~2 ~1 0
((2x + 3) + (2 * (1 + (x * ((x * (1 + ((x * (x div 2)) div 4))) div 2)))))
A336581: 5 7 13 17 61
((2x + 2) + ((2 * ((4x + 1) - (((x + 1) * (x div 2)) mod 2))) div 3))
A190518: 2 7 11 16 21 26 30 35 40 44 48 54 58 63 67 72
compr(\x.(~1 + ((1 + ((x + 1) div (3 * (2 + ((x div 2) mod 5))))) mod 3)),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A247753: 0 1 2 3 4 5 6 7 8 9 11 20 21 22 23 24
((x + 1) + ((2 * (2 + (x2 div ((x + 1) + (2 * ((x div 2) div 3)))))) div 3))
A024609: 2 3 5 6 8 10 11 12 13 15 17 18 19 21 23 24
compr(\x.(~1 + ((1 + ((x - (x div 7)) mod 7)) mod (x + 1))),x)
A048304: 0 1 2 3 4 5 6 8 16 24 32 40 48 49 57 65
compr(\x.(1 + (((x + 1) mod (1 + (2 * ((x mod ~21) div 2)))) div 2)),x)
A330982: 1 2 3 4 5 6 7 8 9 11 12 14 15 16 18 22
((x + 1) + ((((x + 1) * (x div (3 * (8 - (x div 2))))) div 3) div 2))
A180648: 1 2 3 4 5 6 7 8 9 10 12 14 17 18 25 29
((x + 1) + (x div (2 + ((1 + (((x div 2) - ((x div 4) mod 2)) mod 3)) mod (x + 1)))))
A176253: 1 2 3 4 6 7 8 9 11 12 13 14 15 16 19 21
compr(\x.(x mod (1 + (2 * (((~x + 17) mod (1 + (x div 3))) div 2)))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A171827: 0 1 2 3 4 5 6 7 8 9 12 15 16 17 20 24
((x + 1) + (((3 * (1 + (3 * (2x div 7)))) div 2) div 2))
A230998: 1 2 3 4 8 9 10 13 14 15 16 19 20 21 24 25
((x + 1) + (((1 + compr(\x.(((((1 + (x div 2)) div 2) * (x div 2)) div 2) mod 3),x)) div 2) div 2))
A085921-A005243: 1 2 3 5 6 8 10 11 14 16 17 18 19 21 22 24
((x + 1) + ((((2 * (x mod ((~x + 2) + (x mod 10)))) mod (x + 1)) div 2) div 2))
A110029: 1 2 3 4 5 6 7 8 9 10 13 12 14 16 17 19
((x + 1) + ((x - (((3 * (1 + (2x div (1 + (x div 4))))) div 2) div 2)) div 2))
A341534: 1 1 2 3 5 6 7 8 11 12 13 14 16 18 19 20
compr(\x.(2 - (x2 div ((~x + 1) + (9 * (x mod 10))))),x)
A297272-A297146-A296713-A071589: 12 13 14 15 16 17 18 19 23 24 25 26 27 28 29 34
(x + (5 * ((~x + (x mod 9)) mod 20)))
A004859: 0 1 2 3 4 5 6 7 8 64 65 66 67 68 69 70
((5x2 + ~6x) + (((x3 + 3x2 + 2x) div 2) div 3))
A266398: 0 0 12 37 76 130 200 287 392 516 660 825 1012 1222 1456 1715
((5x + 1) + (((x - (((~x + 2) * (x div 2)) div 8)) div 2) div 2))
A315519: 1 6 11 17 22 27 33 38 43 49 54 60 66 71 77 82
compr(\x.((1 + ((4 * (2x - (x mod 7))) div 3)) mod 3),x)
A283769: 2 4 6 8 13 15 17 19 21 26 28 30 32 39 41 43
compr(\x.(1 - (((x + 1) * (1 + (x3 mod 13))) mod 3)),x)
A010376: 0 1 3 4 9 10 12
A010400: 0 1 3 4 9 10 12 13 16 22 25 27 30 36
A010439: 0 1 3 4 9 10 12 13 16 22 25 27 30 36 39 40
(x + ((((x + 1) * ((2x + 1) + ((x mod 2) + (x mod ~3)))) div 2) div 3))
A010390: 0 1 4 8 9 16 21 25
(x + ((2 * ((2x + 4) - (((x mod 2) - (x div 5)) div 2))) div 3))
A029901: 2 5 7 9 12 14 17 19 22 23 26 29 31 33 36 38
(x + (6 * ((x + 2) + ((x - ((3 * ((x div 2) div 3)) div 2)) div 2))))
A136770: 12 19 32 39 52 59 66 79 86 99 106 119 120 133 140 153
((~x + 1) + compr(\x.(~1 + ((1 - (2x2 div (x + 7))) mod 3)),x))
A078474: 1 1 1 1 2 3 4 5 5 5 5 6 6 6 6 7
((~x + 1) + compr(\x.(~1 + ((2 * (x + ((x + ((x * (x div 2)) mod 2)) div 3))) mod 3)),x))
A285764: 1 2 3 3 3 3 4 5 6 6 6 6 7 8 9 10
(x + ((2 + (x div (1 + (x mod (1 + ((3x mod (2 + (x div 2))) div 2)))))) mod (x + 1)))
A334023: 0 2 3 4 5 9 7 8 9 15 11 16 13 21 20 16
compr(\x.((1 + ((1 - (x mod (x - ((x + ~1) mod 8)))) mod (1 + (x div 3)))) mod 2),x)
A154660: 3 4 5 6 7 8
A026458: 3 4 5 6 7 8 9 11 12 14 15 17 20 21 23 24
(x + ((1 + ((1 + (((x + 1) * (2 + ((x + (x mod 2)) div 5))) div 2)) div 2)) div 2))
A196277: 1 2 3 4 6 8 9 10 12 14 16 17 19 20 22 25
(x + (((x + 1) mod (1 + (8 * (x div (~2x + 32))))) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A281943-A215009: 0 1 2 3 4 5 6 7 8 9 10 12 14 20 21 23
compr(\x.(2 * (((2x + 1) mod 29) mod 5)),x)
A190486: 2 7 12 14 19 24 31 36 41 43 48 53 60 65 70 72
(x + ((5 * (1 + ((2 * ((2x + 1) - (x mod 2))) + ((x div 2) mod 2)))) div 2))
A026318: 7 13 32 38 51 57 76 82 95 101 120 126 139 145 164 170
(x + ((3 * ((1 + ((((x + 1) * ((1 + (x div 2)) div 3)) div 2) div 2)) div 2)) div 2))
A268231: 0 1 2 3 5 6 7 8 9 10 14 15 16 19 20 21
compr(\x.(((2 + ((~4x + ~4) mod 17)) div 3) mod 2),x)
A190764: 2 5 6 9 12 13 15 16 19 22 23 26 29 30 32 33
compr(\x.(((x5 mod 41) div 2) mod 2),x)
A233524: 0 1 2 4 5 8
A010443-A010402: 0 1 2 4 5 8 9 10 16 18 20 21 23 25 31 32
compr(\x.(((3 * compr(\x.(2 - (x mod (1 + (2 * (1 + (4 * (x mod 2))))))),x)) div 2) mod 2),x)
A152520: 1 3 4 8 10 11
A327185: 1 3 4 8 10 11 15 17 18 19 22 24 25 26 29 31
compr(\x.((x + 2) - (((7 * (x - (2x div 5))) div 2) div 2)),x)
A162918: 12 17 19 22 24 26 27 29 31 32 33 34 36 37 38 39
((x + 4) - (((3 * (2 + (x2 div 32))) div 2) div 2))
A154660: 3 4 5 6 7 8
A009041: 3 4 5 6 7 8 8 9 9 10 11 12 12 12 12 13
compr(\x.(((2 + ((5 * (x + ((x + (x div 8)) div 2))) div 2)) div 2) mod 2),x)
A102701: 1 2 3 4 6 8 9 11 13 16 18 23
(x + (((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2) + (x div 8)))
A138083: 0 1 2 4 5 6
A129132: 0 1 2 4 5 6 7 10 12 13 14 16 17 18 19 23
(x + ((~x + 1) div (1 + ((((3 * (x + ((~x + 1) mod 3))) div 2) div 2) + (x mod 2)))))
A128557: 1 1 1 2 3 4 5 6 7 8 8 10 10 11 13 14
((2x + 1) + (2 * ((1 + ((((x + ~1) * ((x + 2) div 5)) div 2) div 2)) div 2)))
A307001: 1 3 5 7 9 13 15 17 21 23 25 29 31 37 39 41
(49x2 + 70x + 1)
A118058: 1 120 337 652 1065 1576 2185 2892 3697 4600 5601 6700 7897 9192 10585 12076
loop(\(x,i).(x + (if (if x <= 0 then 1 else loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x + ~2),x)) <= 0 then (x + 1) else x)),x,1)
A125050: 1 2 4 9 19 38 77 155 311 622 1245 2491 4983 9967 19934 39869
(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x - (if x <= 0 then 1 else loop(\(x,i).(if (x * i) <= 0 then 1 else (x + ~1)),i,x))))),x,x))
A140358: 0 1 3 2 3 5 3 5 4 5 4 5 7 5 7 5
(if (x mod 3) <= 0 then (if x <= 0 then 1 else loop(\(x,i).(if (x mod 2) <= 0 then x else (2 + (x mod 2))),(x mod 2),(x div 2))) else 0)
A160540: 1 0 0 3
A341794: 1 0 0 3 0 0 3 0 0 4 0 0 6 0 0 3
((x + 1) div (1 + (if x <= 0 then 0 else loop(\(x,i).(2x + 2),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1))))
A202452: 1 1 0 2 1 0 3 1 0 0 5 2 1 0 0 8
(1 + ((1 + loop(\(x,i).x2,1,loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).(x * (i * i)),i,x),i,1)),x,1))) div 2))
A254380: 2 3 19 11251
((2 * (if x <= 0 then 2 else loop(\(x,i).(if x <= 0 then 2 else (loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2)),2,x))) mod 3)
A035144: 1 1 0 1 2 0 0 1 1 2 2 0 0 0 0 1
(if x <= 0 then 1 else loop(\(x,i).(x2 + ~x),1,(2 - (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))))
A167356: 1 0 0 0 6 0 20 0 0 0 72 0 110 0 0 0
loop(\(x,i).(x + loop(\(x,i).(x - (if x <= 0 then 1 else loop(\(x,i).(x mod 2),(x mod 2),(x div 2)))),x,x)),x,(1 + (x mod 2)))
A087756: 1 3 3 5 5 15 15 17 17 51 51 85 85 255 255 257
(~1 + (2 * compr(\x.loop(\(x,i).(if x <= 0 then 1 else loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + ~1))),2,x),x)))
A307390: 5 11 13 17 23 29 41 43 47 53 59 61 67 71 73 83
((x + 1) mod (1 + loop(\(x,i).(if x <= 0 then 0 else (1 + (2 * loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)))),2,x)))
A068494: 0 0 1 0 1 0 1 0 3 2 1 0 1 2 7 0
(loop(\(x,i).(1 - loop(\(x,i).loop(\(x,i).(x - (if (x mod (2 + i)) <= 0 then 1 else 2)),x,x),1,2x)),x,1) div (x + 1))
A128023: 1 1 1 2 3 5 9 16 28 51 92 169 312 580 1082 2029
loop(\(x,i).(~x + loop(\(x,i).x3,1,loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),i,1))),x,1)
A275822: 1 7 209 7791 335209 15667799 773221225 39651016343 2092095886657 112840936041343 6193764391911873 344853399798469695 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.loop(\(x,i).(if x <= 0 then 2 else (2 + loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),2,x))),2,x),x))
A238246: 3 5 6 7 9 10 12 13 14 15 17 18 20 24 25 26
loop(\(x,i).(loop(\(x,i).(loop(\(x,i).(loop(\(x,i).2x,i,1) + (x * i)),i,1) + (x * i)),i,1) + (x * i)),x,1)
A082031: 1 5 28 176 1240 9752 85120 819296 8639872 99209600 1233416704 16517058560 237137769472 3634932675584 59263206154240 1024222802014208
loop(\(x,i).loop(\(x,i).loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),i,x),i,x),x,1)
A066120: 1 2 24 8640 653184000 114069441024000000 4611686018427387903 4611686018427387903
(loop(\(x,i).(1 + loop(\(x,i).(if x <= 0 then 1 else (x * (if (x mod 2) <= 0 then 10 else 1))),2,x)),x,0) div 2)
A094027: 0 1 100 101 10100 10101 1010100 1010101 101010100 101010101 10101010100 10101010101 1010101010100 1010101010101 101010101010100 101010101010101
(loop(\(x,i).loop(\(x,i).loop(\(x,i).(loop(\(x,i).(1 + (x * i)),i,1) - (x * i)),x,1),1,(x + 1)),1,(x + 1)) div 2)
A114633: 1 3 18 70 555 2961 31108 213228 2799765 23455135 369569046 3659001138 67261566463 768390239085 16142775951240 209002145031256
loop(\(x,i).x2,1,loop(\(x,i).(1 - loop(\(x,i).(x - (if x <= 0 then 0 else (i - (x mod 2)))),x,x)),1,(2x + 2)))
A152205: 1 4 9 1 16 4 25 9 1 36 16 4 49 25 9 1
loop(\(x,i).loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x)),2,(x + 1)),x,(2x + 2))
A120303: 2 5 7 7 11 13 13 17 19 19 23 23 23 29 31 31
(2 * (~1 + compr(\x.loop(\(x,i).(if x <= 0 then 1 else loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + ~1))),2,x),x)))
A109274: 4 10 12 16 22 28 40 42 46 52 58 60 66 70 72 82
(x + loop(\(x,i).(x - (if x <= 0 then 1 else (if (x mod 2) <= 0 then (x div 2) else (1 + (if (~x + 2) <= 0 then x else 0))))),x,(x + 1)))
A135523: 1 2 0 3 0 1 0 4 0 1 0 2 0 1 0 5
(x + loop(\(x,i).(x - (if x <= 0 then 1 else loop(\(x,i).(2 - ((if x <= 0 then 1 else x) mod 2)),(x mod 2),(x div 2)))),x,(x + 1)))
A300118: 1 2 3 3 4 4 5 4 6 5 6 5 7 6 7 5
loop(\(x,i).loop(\(x,i).2x,x,x),1,(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1))))
A183037: 2 8 2 24 2 8 2 64 2 8 2 24 2 8 2 160
(x * loop(\(x,i).(x * (if (x + ~2) <= 0 then 0 else loop(\(x,i).loop(\(x,i).(x * i),(x + ~2),x),1,(x + ~1)))),1,(x + ~1)))
A052759: 0 0 0 0 24 60 240 1260 8064 60480 518400 4989600 53222400 622702080 7925299200 108972864000
compr(\x.(0 - loop(\(x,i).loop(\(x,i).loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,2x),1,(x + 1)),2,x)),x)
A116958: 0 3 6 12 18 27 33 48 51 66 72 87 93 96 111 117
(x + loop(\(x,i).(x - (if x <= 0 then 1 else (1 + loop(\(x,i).(x - (if (x mod (2 * (1 + i))) <= 0 then 1 else 0)),x,i)))),x,x))
A229878: 0 0 1 0 1 2
A336684: 0 0 1 0 1 2 0 1 2 3 1 2 3 4 0 1
compr(\x.(x * loop(\(x,i).loop(\(x,i).(if x <= 0 then 3 else (loop(\(x,i).(x div (2 - (x mod 2))),x,x) div 2)),2,x),2,x)),x)
A084561-A084345: 0 1 2 4 8 15 16 23 27 29 30 32 39 43 45 46
compr(\x.loop(\(x,i).loop(\(x,i).((if x <= 0 then 2 else loop(\(x,i).(x div (2 - (x mod 2))),x,x)) div 2),x,(x + 1)),1,x2),x)
A235331: 1 2 4 5 7 8 9 10 11 14 16 17 18 19 20 22
loop(\(x,i).(x + loop(\(x,i).x2,2,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)))),(x + 1),0)
A122102: 16 97 722 3123 17764 46325 129846 260167 540008 1247289 2170810 4044971 6870732 10289533 15169214 23059695
loop(\(x,i).(x + loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)))),(x + 1),0)
A133547: 9 34 83 204 373 662 1023 1552 2393 3354 4723 6404 8253 10462 13271 16752
loop(\(x,i).(x + loop(\(x,i).x2,2,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)))),(x + 1),0)
A133549: 81 706 3107 17748 46309 129830 260151 539992 1247273 2170794 4044955 6870716 10289517 15169198 23059679 35177040
loop(\(x,i).(x + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),i)),(x + 1),0)
A086167: 3 8 19 36 65 106 165 236 337 444 581 730 909 1100 1297 1524
(loop(\(x,i).5x,x,1) - (loop(\(x,i).(2x + 1),x,0) + loop(\(x,i).3x,x,1)))
A090020: 0 1 13 91 529 2851 14833 75811 383809 1932931 9705553 48648931 243605089 1219100611 6098716273 30503196451
(loop(\(x,i).(2x2 + x),1,loop(\(x,i).(2x + 1),x,0)) * loop(\(x,i).(3x + 1),x,0))
A160875: 0 3 84 1365 18600
loop(\(x,i).(3x + 3),(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1))),0)
A085296: 3 12 3 39 3 12 3 120 3 12 3 39 3 12 3 363
loop(\(x,i).loop(\(x,i).(x + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(~1 + i),1)),(~1 + i),x),x,0)
A143954: 0 0 1 5 19 68 243 880 3233 12021 45119 170595 648787 2479057 9509627 36598497
loop(\(x,i).4x,(x + ~1),loop(\(x,i).(loop(\(x,i).(x * (i * i)),(~1 + i),1) + (x * (i * i))),x,0))
A002455: 0 1 20 784 52480 5395456 791691264 157294854144 40683662475264 13288048674471936 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 2x else (~1 + loop(\(x,i).2x,(1 + (loop(\(x,i).(2 * (x - (i mod 2))),x,2) div 3)),1)))
A222010: 0 1 3 7
A277028: 0 1 3 7 31 255 32767
(~1 + loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x)),1,(6x + 1)))
A141515: 1 6 12 18 22 30 36 42 46 52 60 66 72 78 82 88
(1 + loop(\(x,i).2x,x,(3 * (1 + (loop(\(x,i).3x,x,2) + loop(\(x,i).2x,x,1))))))
A290396: 13 55 277 1513 8593 49825 292417 1729153 10275073 61254145 365945857 2189371393 13111037953 78565515265 470990340097 2824331231233
(if (x mod 2) <= 0 then (3 * (if (x mod 4) <= 0 then (9 * (if x <= 0 then 1 else 2)) else 2)) else 1)
A040749: 27 1 6 1 54 1 6 1 54 1 6 1 54 1 6 1
(if (x mod 2) <= 0 then (3 * ((1 + (if (x mod 4) <= 0 then 8 else 1)) * (if x <= 0 then 1 else 2))) else 1)
A040752: 27 1 12 1 54 1 12 1 54 1 12 1 54 1 12 1
(if x <= 0 then 1 else (loop(\(x,i).2x,x,(if (x mod 7) <= 0 then 2 else 1)) mod (1 + (x div 3))))
A017848: 1 0 0 0 0 0 1 1 1 0 0 0 1 2 3 2
((x + ~1) mod (if (x mod 2) <= 0 then (1 + ((if (~1 + (x mod 3)) <= 0 then x else 2) + (if (~x + 2) <= 0 then 2 else 1))) else 1))
A003966: 1 0 1 0 3 0 5 0 2 0 9 0 11 0 3 0
(if 2x <= 0 then x else (1 + loop(\(x,i).(x * i),((((x div 2) * (x div 2)) div 2) + (if x <= 0 then 1 else 2x)),1)))
A062411: 0 3 25 721 3628801 479001601 20922789888001 6402373705728001 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(2x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i))),i,1)),(2x + 1),1)
A274104: 2 7 23 78 274 988 3628 13495 50675 191673 729145 2786655 10691111 41150011 158825371 614483086
(1 + loop(\(x,i).(x + loop(\(x,i).(x * i),x,1)),1,(1 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x))))
A100856: 3 5 29 727 3628811 479001613 20922789888017 6402373705728019 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (1 + compr(\x.(~1 + (loop(\(x,i).(2x + 2),(if (x mod 2) <= 0 then x else 1),1) mod (x + 1))),(x + 1))))
A193339: 1 3 4 5 7 9 11 13 17 19 23 29 31 37 41 43
loop(\(x,i).(x + loop(\(x,i).(x + loop(\(x,i).11x,i,(1 + i))),i,1)),(x + 1),1)
A221619: 24 410 6120 85035 1130256 14576404 183919920 2282493365 27960543720 338950264686 4073680032984 48607978698655 576460247379360 6800560019808680 79860630502888416 934066108666694889
(1 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 1))),1,loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))
A003960: 1 1 2 1 3 2 4 1 4 3 6 2 7 4 6 1
((1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1))) * (1 + loop(\(x,i).5x,x,1)))
A034662: 6 42 546 9198 170898 3304182 65019786 1290094638 25700456418 513002215782 10250010815226 204900053024478 4097000260921938 81930001287820182 1638500006371967466 4611686018427387903
(1 + loop(\(x,i).(x3 + 2x2),1,loop(\(x,i).(2x + 1),x,0)) - loop(\(x,i).3x,x,1))
A090023: 0 1 37 415 3745 31471 257257 2078455 16704865 133935391 1072633177 8585561095 68702163985 549687102511 4397773276297 35183283965335
(loop(\(x,i).(x3 + x2 + x + 1),1,loop(\(x,i).2x,x,1)) * (1 + loop(\(x,i).3x,x,1)))
A034664: 8 60 850 16380 358258 8253300 194402650 4624699020 110523825058 2647111898340 63466433646250 1522433108644860 36529334450076658 876595894555956180 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x * loop(\(x,i).x2,1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)))),x,1))
A189409: 2 5 37 901 44101 5336101 901800901 260620460101 94083986096101 49770428644836901 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 3) <= 0 then (if (x mod 2) <= 0 then (14 * (2 + (if x <= 0 then 0 else 2))) else 2) else 1)
A040788: 28 1 1 2 1 1 56 1 1 2 1 1 56 1 1 2
(if (x mod 3) <= 0 then (2 * (if (x mod 2) <= 0 then (11 * (if x <= 0 then 1 else 2)) else 1)) else 1)
A040487: 22 1 1 2 1 1 44 1 1 2 1 1 44 1 1 2
(1 + (2 * (1 + (2 * compr(\x.loop(\(x,i).loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)),2,x),x)))))
A053177: 15 27 35 39 63 75 87 95 119 123 135 143 147 159 195 203
(loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),x,1) * (if (x + ~1) <= 0 then 2 else 1))
A121069: 2 4 6 30 210 2310 30030 510510 9699690 223092870 6469693230 200560490130 7420738134810 304250263527210 13082761331670030 614889782588491410
(if (x mod 2) <= 0 then ((~1 + (5 * (if (x mod 4) <= 0 then 4 else 1))) * (if x <= 0 then 1 else 2)) else 1)
A040376: 19 1 8 1 38 1 8 1 38 1 8 1 38 1 8 1
(if (x mod 2) <= 0 then ((~1 + (6 * (if (x mod 4) <= 0 then 4 else 1))) * (if x <= 0 then 1 else 2)) else 1)
A040548: 23 1 10 1 46 1 10 1 46 1 10 1 46 1 10 1
(if (x mod 2) <= 0 then ((1 + (2 * (if (x mod 4) <= 0 then 9 else 1))) * (if x <= 0 then 1 else 2)) else 1)
A040375: 19 1 6 1 38 1 6 1 38 1 6 1 38 1 6 1
(if (x mod 2) <= 0 then ((if (x mod 4) <= 0 then 23 else 2) * (if x <= 0 then 1 else 2)) else 1)
A040544: 23 1 4 1 46 1 4 1 46 1 4 1 46 1 4 1
(if (x mod 2) <= 0 then (2 * ((if (x mod 4) <= 0 then 13 else 1) * (if x <= 0 then 1 else 2))) else 1)
A040693: 26 1 4 1 52 1 4 1 52 1 4 1 52 1 4 1
loop(\(x,i).x2,1,(1 + loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),4)))
A174623: 25 81 1089 16641 4198401 67125249 17180131329 274878955521 70368760954881 288230377225453569 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(~1 + loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),4)))
A174744: 9 49 961 16129 4190209 67092481 17179607041 274876858369 70368727400449 288230375077969921 4611686014132420609 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(4 + compr(\x.loop(\(x,i).loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x + 4)),2,x),(x + 1)))
A105575: 5 11 17 23 29 31 41 47 53 59 61 71 73 83 89 101
loop(\(x,i).(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 2))),1,(3x + 3))
A087230: 1 4 1 2 1 3 1 2 1 6 1 2 1 3 1 2
(3 * (if x <= 0 then 1 else ((loop(\(x,i).3x,x,1) - loop(\(x,i).3x,(x div 2),1)) div 2)))
A032086: 3 3 9 36 108 351 1053 3240 9720 29403 88209 265356 796068 2390391 7171173 21520080
(3 + loop(\(x,i).(if loop(\(x,i).x3,2,x) <= 0 then 1 else (8x + 2)),x,4))
A075996: 7 37 277 4611686018427387903 4611686018427387903
((2 + loop(\(x,i).(x - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * i))),x,x)),1,(3x + 2))) div 3)
A189018-A189015: 1 3 6 7 10 11 12 16 17 18 23 24 25 26 31 32
loop(\(x,i).(x + (if x <= 0 then 0 else (loop(\(x,i).(x * (~1 + (2 * i))),i,1) + (x * (~1 + (2 * i)))))),x,3)
A123332: 3 7 31 201 1713 18075 227295 3317265 55103265 1026318195 21181092975 479733356025 11829834687825 315481555464075 9046941599670975 277598531343758625
(1 + (2 * (x + (if x <= 0 then 0 else (1 + compr(\x.loop(\(x,i).(if ((x + 1) mod (1 + i)) <= 0 then 0 else x),x,2x),x))))))
A165955: 1 13 21 29 35 39 47 51 57 65 71 75 81 85 93 97
loop(\(x,i).(if x <= 0 then 0 else (2x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i)))),((x2 + x) div 2),1)
A331504: 1 1 3 20 252 6435 352716 40116600 9075135300 4116715363800 3824345300380220 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (2 * compr(\x.(x - loop(\(x,i).loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),x,(2x + 1)),2,(x + ~1))),x)))
A161896: 5 11 23 29 41 53 83 89 113 131 173 179 191 233 239 251
(~1 + (2 * compr(\x.(if x <= 0 then 1 else (~2 + (loop(\(x,i).2x,x,(if (x mod 3) <= 0 then 0 else 2)) mod (x + 1)))),x)))
A330225: 1 3 5 7 11 13 17 19 23 29 31 35 41 43 47 53
(~1 + loop(\(x,i).loop(\(x,i).4x,x,x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A100689: 31 191 5119 114687 46137343 872415231 292057776127 5222680231935 1618481116086271 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).loop(\(x,i).3x,x,x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A100688: 17 80 1214 15308 1948616 20726198 2195382770 22082967872 2165293113020 1990280943581606 19147875284802356 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),i,2x),x,2))
A066266: 3 13 361 75601 174636001 5244319080001 2677277333530800001 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),i,2x),x,2))
A066268: 1 11 359 75599 174635999 5244319079999 2677277333530799999 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).x2,1,loop(\(x,i).((x + 2) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)),x,2)))
A092780: 3 24 99 288 783 1680 3363 5928 9999 16640 25599 38808 56643 78960 107583 145160
((2x + 1) + ((1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x)) * (if x <= 0 then 1 else 2)))
A020484: 2 5 7 11 11 13 17 17 19 23 23 29 29 29 31 37
(loop(\(x,i).5x,x,1) + loop(\(x,i).2x,x,1) + loop(\(x,i).3x,2x,1))
A074540: 3 16 110 862 7202 62206 547130 4861222 43437602 389374126 3496551050 31429889782 282673681202 2543086539646 22882895986970 205921649705542
(loop(\(x,i).2x,x,1) - loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x div 2),(1 + (x mod 2))))
A307768: 0 0 2 4 10 20 44 88 186 372 772 1544 3172 6344 12952 25904
((x + 1) - ((x + loop(\(x,i).(1 - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * (1 + i)))),x,2x)),2,x)) div 2))
A167407: 0 ~1 1 ~2 1 1 ~3 1 1 1 ~4 1 1 1 1 ~5
loop(\(x,i).(12x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A016281: 1 17 223 2741 33103 397901 4776871 57328757 687964255 8255629085 99067724119 1188813216773 14265760187407 171189127015469 2054269538501767 24651234505002389
loop(\(x,i).(6x + loop(\(x,i).(~1 + (2 * (2x + loop(\(x,i).2x,i,1)))),i,1)),x,1)
A021076: 1 13 113 833 5649 36561 230161 1424401 8720657 53021969 320925969 1936736529 11665150225 70169841937 421734846737 2533272326417
loop(\(x,i).2x,x,loop(\(x,i).(6x + loop(\(x,i).(5x + 1),i,1)),x,1))
A016326: 1 24 412 6192 86800 1166592 15249088 195489024 2470868224 30900418560 383305022464 4724660269056 57945923227648 707851078729728 8619212944752640 104680555337023488
loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).2x,i,1)),i,1)),x,1)
A016295: 1 13 117 905 6461 43953 289717 1868425 11861421 74423393 462815717 2858273145 17556537181 107373722833 654414852117 3977351721065
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A016765: 1 13 115 865 5971 39193 249355 1555105 9573091 58428073 354585595 2143759345 12928070611 77832076153 468051849835 2812563019585
loop(\(x,i).(6x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A016306: 1 17 205 2165 21421 204437 1909885 17608805 160998541 1464103157 13267627165 119952839045 1082840722861 9765157542677 88003964122045 792740954558885
loop(\(x,i).(6x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021029: 1 12 97 672 4333 26964 164809 998184 6017605 36192156 217414561 1305276336 7834033117 47011340388 282089500153 1692601439928
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).2x,i,1)),i,1)),x,1)
A016285: 1 13 119 953 7167 52185 373423 2646601 18657023 131122937 919956687 6448083369 45170133919 316325146969 2214812883311 15505837634057
loop(\(x,i).(7x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A016276: 1 12 103 786 5713 40656 286651 2012862 14109205 98822460 691932319 4844053578 33909961177 237374494824 1661635779907 11631493440534
loop(\(x,i).~x,x,loop(\(x,i).(x - loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(~2 + i),1)),x,1))
A099324: 1 0 ~1 3 ~8 22 ~64 196 ~625 2055 ~6917 23713 ~82499 290511 ~1033411 3707851
((loop(\(x,i).(2x + 2),x,(1 + loop(\(x,i).2x,x,1))) div 2) - loop(\(x,i).(3x + 1),x,1))
A032263: 0 0 0 3 30 195 1050 5103 23310 102315 437250 1834503 7597590 31175235 127067850 515396703
loop(\(x,i).2x,x,(loop(\(x,i).(6x + 2),x,2) - loop(\(x,i).(3x + 1),x,1)))
A016309: 1 20 292 3824 47824 585536 7096384 85576448 1029436672 12368356352 148510974976 1782675894272 21395375902720 256764101869568 3081286768672768 36976146501533696
(1 + compr(\x.(~1 + loop(\(x,i).loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)),1,(x2 + 2x))),x))
A143834: 1 5 9 12 14 16 19 20 23 26 27 29 30 31 32 33
(if x <= 0 then 2 else (1 + compr(\x.(loop(\(x,i).x2,2,(~1 + (loop(\(x,i).2x,x,1) mod (x + 1)))) mod (x + 1)),x)))
A319151-A305081: 2 3 5 7 9 11 13 17 19 23 25 27 29 31 37 41
loop(\(x,i).(loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),i,x) div (1 + i)),x,1)
A071627: 1 1 2 15 630 242550 1040539500 66400727518125 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).4x,x,1) + loop(\(x,i).(2x + 2),x,1)) - loop(\(x,i).(3x + 2),x,2))
A028244: 0 0 0 6 60 390 2100 10206 46620 204630 874500 3669006 15195180 62350470 254135700 1030793406
loop(\(x,i).(16x + loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),i,1)),x,1)
A167713: 1 18 294 4724 75654 1210716 19372380 309961512 4959397062 79350401612 1269606610548 20313706474200 325019306291356 5200308911062296 83204942617113336 1331279082028930896
loop(\(x,i).(8x + loop(\(x,i).(~1 + (2 * (2x + loop(\(x,i).2x,i,1)))),i,1)),x,1)
A006096: 1 15 155 1395 11811 97155 788035 6347715 50955971 408345795 3269560515 26167664835 209386049731 1675267338435 13402854502595 107225699266755
loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).2x,i,1)),i,1)),x,1)
A016297: 1 15 159 1475 12831 107835 888679 7239555 58567311 471793355 3790622199 30406356435 243657749791 1951296498075 15620544499719 125015218606115
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A016849: 1 15 157 1431 12229 101199 823789 6649287 53436757 428483583 3431885821 27471332343 219836173285 1758953038767 14072683703053 112585721544999
loop(\(x,i).(8x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A016316: 1 19 255 2975 32231 333759 3353335 32976175 319155111 3051352799 28893830615 271497720975 2535105456391 23548956856639 217804673719095 2007154559579375
loop(\(x,i).(8x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021044: 1 14 137 1186 9789 79278 637249 5107322 40887077 327183142 2617726761 20942603058 167543199565 1340352738206 10722843363473 85782811346794
loop(\(x,i).(9x + loop(\(x,i).(1 + (x * loop(\(x,i).x2,2,3))),i,1)),x,1)
A022253: 1 91 7462 605242 49031983 3971657053 321704819164 26058095733124 2110705802810605 170967170463507055 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,loop(\(x,i).(4 * (x + (7x div (if i <= 0 then 1 else i)))),x,1))
A053107: 1 64 2304 61440 1351680 25952256 449839104 7197425664 107961384960 1535450808320 20882130993152 273366078455808 3462636993773568 42617070692597760 511404848311173120 4611686018427387903
loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A016753: 1 12 97 660 4081 23772 133057 724260 3863761 20308332 105558817 544039860 2785713841 14192221692 72020501377 364354427460
loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A021074: 1 12 95 630 3801 21672 119155 639210 3370301 17549532 90541815 463889790 2364180001 11999840592 60714998075 306438236370
loop(\(x,i).(4x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A016909: 1 16 181 1804 17017 156520 1422877 12864868 116026273 1045225984 9411051013 84715704892 762506858569 6862825379608 61766487809389 555902642205076
(((x + 1) * loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,2)) - loop(\(x,i).4x,x,1))
A296665: 1 4 20 96 444 2000 8840 38528 166124 710256 3016056 12736064 53530840 224107936 935062544 3890018816
(loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1) + loop(\(x,i).4x,x,1))
A074547: 3 12 50 216 962 4392 20450 96696 462722 2234952 10873250 53199576 261449282 1289406312 6376734050 31605668856
((loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1)) - loop(\(x,i).4x,x,1))
A083325: 1 4 18 88 450 2344 12258 63928 331650 1710664 8776098 44810968 227894850 1155188584 5839863138 29458185208
((loop(\(x,i).5x,x,1) + loop(\(x,i).4x,x,1)) - loop(\(x,i).3x,x,1))
A083320: 1 6 32 162 800 3906 18992 92322 449600 2195586 10755152 52845282 260386400 1286217666 6367168112 31576971042
(loop(\(x,i).5x,x,1) - (loop(\(x,i).4x,x,1) + loop(\(x,i).3x,x,1)))
A193052: ~1 ~2 0 34 288 1858 10800 59554 318528 1671298 8658000 44456674 226831968 1151999938 5830297200 29429487394
loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A016298: 1 16 183 1850 17681 164316 1504843 13673710 123714261 1116683216 10066424303 90679197570 816519676441 7350711587716 66166576804563 595550053849430
loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021024: 1 11 80 490 2751 14721 76630 392480 1990901 10041031 50466780 253122870 1267989451 6347088941 31756902530 158848951660
loop(\(x,i).(10x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A016279: 1 15 169 1755 17761 178275 1784809 17854395 178563121 1785689235 17857067449 178571201835 1785713604481 17857140811395 178571422430089 1785714267282075
loop(\(x,i).x2,1,(1 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + 2x + 2))),x)))
A075408: 1 4 16 36 100 196 256 400 576 676 1296 1600 2916 3136 4356 5476
loop(\(x,i).(loop(\(x,i).(x * i),x,1) div (x + 1)),1,(1 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x)))
A091330: 0 0 4 102 329890 36846276 1230752346352 336967037143578 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(loop(\(x,i).(x * i),x,2) div (x + 2)),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A130775: 0 1 8 180 604800 68428800 2324754432000 640237370572800 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(if (x mod 4) <= 0 then (x div 2) else x),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A081728: 1 2 2 6 10 6 8 18 22 14 30 18 20 42 46 26
loop(\(x,i).7x,x,loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),x,1))
A075922: 1 42 1225 30870 722701 16235562 355888225 7683656190 164302593301 3491636199282 73902587019625 1560051480424710 32874455072382301 691950889177526202 4611686018427387903 4611686018427387903
(loop(\(x,i).(4x + 1),x,(~1 + loop(\(x,i).2x,(x * (x mod 2)),2))) div loop(\(x,i).2x,x,1))
A266980: 1 6 5 122 21 2026 85 32682 341 523946 1365 8387242 5461 134212266 21845 2147461802
(((x + 1) * (loop(\(x,i).3x,x,3) - loop(\(x,i).2x,x,2))) div loop(\(x,i).2x,x,1))
A139754: 1 5 14 32 65 124 225 394 673 1133 1880 3089 5034 8146 13106 20986
(loop(\(x,i).7x,x,1) + loop(\(x,i).3x,x,1) + loop(\(x,i).2x,x,1))
A074529: 3 12 62 378 2498 17082 118442 825858 5771618 40373802 282535322 1977505938 13841822738 96890612922 678227872202 4747575891618
(loop(\(x,i).(2x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i))),x,(x + 2)) - loop(\(x,i).2x,x,1))
A296663: 1 1 4 7 20 38 96 187 444 874 2000 3958 8840 17548 38528 76627
loop(\(x,i).(3x + (if (~2 + (x div 2)) <= 0 then 1 else (if x <= 0 then 1 else 7x))),x,1)
A067634: 1 4 13 130 1300 13000 130000 1300000 13000000 130000000 1300000000 13000000000 130000000000 1300000000000 13000000000000 130000000000000
compr(\x.(~1 + loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),x,2x)),2,x)),(x + 1))
A073216: 1 2 3 5 6 9 14 15 18 27 41 42 45 54 81 122
((loop(\(x,i).x2,1,(1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x))) div (x + 1)) mod (x + 1))
A076981: 0 0 1 2 1 4 3 6 5 4 4 10 9 12 11 10
(if (x mod 10) <= 0 then 1 else loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,(x + 1)))
A172500: 1 2 1 4 5 2 7 8 1 10 1 4 13 14 5 16
((x + 1) div loop(\(x,i).(loop(\(x,i).(x * loop(\(x,i).(2x2 + ~1),2,2)),2,x) mod (x + 1)),2,(x + 1)))
A056623: 1 1 1 4 1 1 1 1 9 1 1 4 1 1 1 16
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(if (x + ~3) <= 0 then x else (x + 1)))
A106118-A059168-A050757-A032758-A029743: 2 3 5 7 13 17 19 23 29 31 37 41 43 47 53 59
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(if (~2 + (x div 2)) <= 0 then x else (x + 1)))
A193063-A165132: 2 3 5 7 11 13
A095074-A057447: 2 3 5 7 11 13 19 23 29 31 37 41 43 47 53 59
compr(\x.loop(\(x,i).(x * (loop(\(x,i).(1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),2,x) div (1 + i))),2,x),(x + 1))
A268415: 1 2 3 4 6 7 8 12 14 15 16 21 24 28 30 31
loop(\(x,i).x2,1,compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1)))
A108570: 9 25 121 289 841 1681 3481 5041 10201 11449 18769 22201 32041 36481 38809 51529
(if x <= 0 then 0 else loop(\(x,i).((x + ~1) * loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,x)),1,(x + ~1)))
A217213: 0 0 0 4 30 168 840 3960 18018 80080 350064 1511640 6466460 27457584 115892400 486748080
(1 + loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then (if ((x + 2) mod (2 + ((x div 2) mod 2))) <= 0 then 2 else 0) else 1))),x,x))
A161788: 1 1 3 1 1 3 7 1 3 1 1 3 1 7 15 1
(if (1 - (2 * (x mod 2))) <= 0 then (2 + (x div 2)) else loop(\(x,i).(x * (1 + (if (i mod 2) <= 0 then 4 else 1))),x,1))
A332701: 1 2 10 3 100 4 1000 5 10000 6 100000 7 1000000 8 10000000 9
loop(\(x,i).(x + loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),(~1 + i),1)),x,1)
A084737: 1 2 4 10 40 250 2560 32590 543100 10242790 233335660 6703028890 207263519020 7628001653830 311878265181040 13394639596851070
(loop(\(x,i).3x,x,(1 + loop(\(x,i).2x,x,1))) + loop(\(x,i).7x,x,1))
A074555: 3 16 94 586 3778 24826 165034 1105666 7450978 50450986 343000474 2340300946 16018600978 109951298746 756592019914 5217760843426
(loop(\(x,i).2x,x,(1 + loop(\(x,i).3x,x,1))) + loop(\(x,i).7x,x,1))
A074541: 3 15 89 567 3713 24615 164369 1103607 7444673 50431815 342942449 2340125847 16018073633 109949712615 756587253329 5217746527287
(loop(\(x,i).(x3 + x2),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).7x,x,1))
A074568: 3 19 129 919 6753 50599 383889 2937079 22607553 174833479 1357265649 10571455639 82577541153 646711933159 5076538019409 39933007340599
(loop(\(x,i).(x3 + x),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).7x,x,1))
A074544: 3 17 117 863 6513 49607 379857 2920823 22542273 174571847 1356218097 10567263383 82560768033 646644832487 5076269600337 39931933631543
(loop(\(x,i).(x2 + x),1,loop(\(x,i).3x,x,1)) + loop(\(x,i).7x,x,1))
A074559: 3 19 139 1099 9043 76099 649819 5608699 48818083 427793779 3769318699 33358563499 296271355123 2638756433059 23555020310779 210638707953499
loop(\(x,i).(x * ((1 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).3x,(1 + i),1))) div 3)),x,1)
A003787: 1 24 5616 12130560 237783237120 42064805779476480 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,(x + 2)),1,3x),x))
A060461: 20 24 31 34 36 41 48 50 54 57 69 71 79 86 88 89
((loop(\(x,i).(2x + 1),x,(4 + loop(\(x,i).2x,x,1))) div 2) - loop(\(x,i).3x,x,1))
A134165: 1 3 8 24 86 348 1478 6324 26846 112668 467798 1925124 7867406 31980588 129475718 522603924
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).21x,i,1))),x,1)
A028683: 1 420 81496800 6988909668048000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).22x,i,1))),x,1)
A028684: 1 462 108002664 12244181663697984 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).x3,1,loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),i,1))),x,1)
A167893: 1 9 134 2878 76966 2376934 81330523 3005537523 117938569451 4856184495787 208008478587443 9208478072445171 419215292661445171 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).19x,i,1))),x,1)
A028681: 1 342 44446320 2090711424299040 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,loop(\(x,i).23x,i,1))),x,1)
A028685: 1 506 141331872 20920469730667584 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + loop(\(x,i).(x + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(~1 + i),1)),i,1)),x,1)
A106269: 1 1 4 11 39 137 501 1853 6936 26163 99314 378879 1451392 5579179 21509692 83137939
loop(\(x,i).(x + loop(\(x,i).(0 - (x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)))),i,1)),x,1)
A265184: 1 ~1 5 ~25 185 ~2125 27905 ~482605 9217085 ~213875785 6255817445 ~194304672685 7226433462125 ~297023830065085 12785737501604945 ~602104045086886465
loop(\(x,i).(x + loop(\(x,i).x3,1,loop(\(x,i).(2 * (2x - (x div (1 + i)))),(~1 + i),2))),x,1)
A079727: 1 9 225 8225 351225 16354233 805243257 41229480825 2172976383825 117106008311825 6423711336265041 357470875526646609 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.(1 - loop(\(x,i).loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x + 2)),1,(x2 + 4x))),x))
A089623: 1 2 4 6 8 12 14 18 20 26 28 32 34 36 42 46
loop(\(x,i).(x * loop(\(x,i).(x2 + ~x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)))),x,1)
A335334: 1 6 120 5040 554400 86486400 23524300800 8045310873600 4070927302041600 3305592969257779200 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).((1 + (4 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 3),1,i)),x,1)
A058759: 1 4 8 13
A071994: 1 4 8 13 20 29 40 52 65 80 96 113 132 152 173 196
loop(\(x,i).2x,3x,loop(\(x,i).(x + (9x div (if i <= 0 then 1 else i))),x,1))
A196280: 1 80 3520 112640 2928640 65601536 1312030720 23991418880 407854120960 6525665935360 99190122217472 1442765414072320 20198715797012480 273459536944168960 3594039628409077760 4611686018427387903
loop(\(x,i).(x * (9 + i)),x,loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,1))
A062151: 1 50 1650 46200 1201200 30270240 756756000 19027008000 485188704000 12614906304000 335556507686400 9151541118720000 256243151324160000 4611686018427387903 4611686018427387903
loop(\(x,i).3x,2x,loop(\(x,i).(x + (10x div (if i <= 0 then 1 else i))),x,1))
A196221: 1 99 5346 208494 6567561 177324147 4255779528 93019181112 1883638417518 35789129932842 644204338791156 11068601821048044 182631930047292726 2908062270753045714 4611686018427387903 4611686018427387903
(loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),x,1) div loop(\(x,i).(x * i),x,1))
A135568: 1 2 3 5 8 19 41 101 240 614 1782 5024 15492 48859 150069 470216
(loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),x,1) mod loop(\(x,i).(x * i),x,1))
A182254: 0 0 0 0 18 30 510 1470 22890 284550 3171630 18486930 45347610 4254260010 2349577230 371965003410
((1 + ((2 + loop(\(x,i).2x,(0 - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)),1)) div 3)) div 2)
A332954-A316074: 1 1 1 1 1 1 2 1 1 1 3 2 1 1 1 6
(2 + loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x)),1,(6x + 1)))
A107986: 4 9 15 21 25 33 39 45 49 55 63 69 75 81 85 91
((loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x div 2),1) + loop(\(x,i).2x,(x + ~1),1)) div 2)
A116406: 1 1 2 3 7 11 26 42 99 163 382 638 1486 2510 5812 9908
((1 + loop(\(x,i).(if x <= 0 then 0 else (2x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i)))),x,(x + ~1))) div 2)
A191527: 0 0 1 3 9 20 50 105 245 504 1134 2310 5082 10296 22308 45045
((1 + ((if x <= 0 then 2 else (1 + ((2 * (1 + loop(\(x,i).(if x <= 0 then i else (x div 2)),x,0))) mod (x + 1)))) div 2)) div 2)
A107110: 1 0 1 0 1 1 0 0 1 1 0 0 2 1 1 0
((loop(\(x,i).2x,x,1) - loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),((x + 1) div 2),1)) div 2)
A294175: 0 0 1 1 5 6 22 29 93 130 386 562 1586 2380 6476 9949
(if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).2x,x,(if (x mod 2) <= 0 then ((x div 2) mod 2) else x)) mod (x + 1)) div 2))))
A273258: 1 2 2 2 2 6 2 2 2 10 2 6 2 14 6 2
(2 * (if (x mod 2) <= 0 then ((1 + (if ((x div 2) mod 2) <= 0 then 10 else 1)) * (if x <= 0 then 1 else 2)) else 1))
A040482: 22 2 8 2 44 2 8 2 44 2 8 2 44 2 8 2
(if (x mod 2) <= 0 then (if (x mod 3) <= 0 then (23 * (if x <= 0 then 1 else 2)) else 1) else 2)
A040522: 23 2 1 2 1 2 46 2 1 2 1 2 46 2 1 2
(loop(\(x,i).2x,(x + ~1),(1 + loop(\(x,i).2x,x,1) - ((if (x mod 2) <= 0 then 2 else x) mod 4))) div 2)
A073996: 0 1 3 12 60 256 1008 4032 16320 65536 261888 1047552 4193280 16777216 67104768 268419072
(if x <= 0 then 0 else ((5x + 2) + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,x)))
A210254: 0 7 12 15 21 23 28 31 38 39 44 47 53 55 60 63
(3 div (2 * (1 + (2 * loop(\(x,i).(x2 + 2x),1,loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x))))))
A185018: 1 ~2 1 1 ~2 1 0 1 ~2 1 0 0 1 ~2 1 0
((loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,(x + 1)) - loop(\(x,i).4x,x,1)) div 2)
A139262: 0 0 1 8 47 244 1186 5536 25147 112028 491870 2135440 9188406 39249768 166656772 704069248
(if x <= 0 then 1 else (2 * ((4x + 1) - loop(\(x,i).(x + (if (~2 + (x div 4)) <= 0 then 1 else 2)),2,x))))
A310533: 1 4 10 16 22 28 34 40 46 52 58 62 66 72 78 84
(2 * (loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),x,1) - loop(\(x,i).2x,x,1)))
A130072: 0 12 90 528 2850 14832 75810 383808 1932930 9705552 48648930 243605088 1219100610 6098716272 30503196450 152544778368
(((loop(\(x,i).(4x + 1),x,2) + loop(\(x,i).3x,x,1)) - loop(\(x,i).2x,x,1)) div 2)
A246986: 1 5 21 84 331 1300 5111 20144 79611 315420 1252351 4980904 19837091 79086740 315557991 1259856864
((loop(\(x,i).4x,x,3) - loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1)) div 2)
A265939: 1 5 21 86 349 1410 5682 22860 91869 368906 1480486 5938740 23813746 95462996 382594884 1533053976
((1 + ((~x + 1) mod loop(\(x,i).(compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x + 2)),x) + i),2,x))) div 2)
A076236: 1 0 7 7 8 9 10 10 10 10 12 12 12 12 13 13
(if x <= 0 then 1 else (if (x mod (2 + (x mod 2))) <= 0 then (x div (1 + (if (x mod 3) <= 0 then 2 else 0))) else ((x + 1) div 2)))
A214918: 1 1 2 1 4 3 2 4 8 3 10 6 4 7 14 5
((loop(\(x,i).3x,x,(1 + loop(\(x,i).2x,x,2))) - loop(\(x,i).5x,x,1)) div 2)
A083316: 1 5 28 167 1024 6335 39208 241967 1487584 9110975 55612888 338471567 2054977744 12451139615 75314797768 454933369967
((loop(\(x,i).(5x - loop(\(x,i).2x,i,1)),x,1) + loop(\(x,i).3x,x,1)) div 2)
A188545: 1 3 10
A086444: 1 3 10 37 150 653 2990 14157 68470 335533 1657470 8227277 40957190 204250413 1019649550 5093448397
(2 + (loop(\(x,i).(~1 + loop(\(x,i).(3 * (x + loop(\(x,i).2x,i,1))),(x + 1),1)),1,(x + 2)) div 2))
A250749: 72 237 756 2361 7272 22197 67356 203601 613872 1847757 5555556 16691241 50122872 150466917 451597356 1355185281
(2 + (2 * loop(\(x,i).(2 - loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,(x + 2))),1,(x + 2))))
A212595: 2 2 4 2 2 4 2 4 6 2 2 4 6 2 4 2
(4 + loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x)),2,6x))
A164383: 6 9 15 21 27 33 35 45 51 57 63 65 75 77 87 93
(loop(\(x,i).((2x + 2) + (x div 4)),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1) div 4)
A229878: 0 0 1 0 1 2
A180662: 0 0 1 0 1 2 0 1 2 6 0 1 2 6 15 0
loop(\(x,i).(x + loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)))),x,4)
A024450: 4 13 38 87 208 377 666 1027 1556 2397 3358 4727 6408 8257 10466 13275
((2 + (if x <= 0 then 1 else compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + (x div 2)))),x))) div 2)
A222011: 1 2 4 8
A024895: 1 2 4 8 10 14 20 22 26 28 32 34 40 46 52 56
(if (if (x mod 8) <= 0 then x else 0) <= 0 then loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) else (x + 4))
A336652: 1 1 3 1 5 3 7 1 12 5 11 3 13 7 15 1
(loop(\(x,i).(x + loop(\(x,i).2x,i,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)))),x,2) div 2)
A135483: 1 4 14 42 130 338 882 2098 5042 12466 28338 66226 150194 326322 711346 1579698
(2 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,(x + 2)),1,(2x + 1)),x))
A217707: 14 16 19 23 29 30 31 36 40 44 46 47 51 52 54 55
(loop(\(x,i).(x2 + x),1,compr(\x.(1 + loop(\(x,i).(0 - (if (x mod (1 + i)) <= 0 then 0 else x)),(x div 2),x)),x)) div 2)
A034955: 6 28 66 190 276 496 946 1128 1770 2278 2556 3160 3486 5356 5778 8128
loop(\(x,i).loop(\(x,i).x3,2,x2),1,(2 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x)))
A030637: 262144 387420489 3814697265625 1628413597910449 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x2 + ~x),1,loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),2))
A060286: 6 28 496 8128 2096128 33550336 8589869056 137438691328 35184367894528 144115187807420416 2305843008139952128 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x2,4,x)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A138032: 131072 129140163 762939453125 232630513987207 505447028499293771 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x3,2,x)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A030629: 1024 59049 9765625 282475249 25937424601 137858491849 2015993900449 6131066257801 41426511213649 420707233300201 819628286980801 4808584372417849 13422659310152401
loop(\(x,i).(x2 + loop(\(x,i).2x,x,1)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A097058: 8 17 57 177 2169 8361 131361 524649 8389137 536871753 2147484609 137438954841 2199023257233 8796093024057 140737488357537 9007199254743801
loop(\(x,i).(~x2 + loop(\(x,i).2x,x,1)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A098105: 0 ~1 7 79 1927 8023 130783 523927 8388079 536870071 2147482687 137438952103 2199023253871 8796093020359 140737488353119 9007199254738183
loop(\(x,i).loop(\(x,i).x2,2,x3),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A030631: 4096 531441 244140625 13841287201 3138428376721 23298085122481 582622237229761 2213314919066161 21914624432020321 353814783205469041 787662783788549761 4611686018427387903
loop(\(x,i).(x + (if (loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) <= 0 then 2 else 1)),(x + 1),(x + 2))
A219786: 4 6 9 10 14 15 18 21 24 25 27 28 32 34 36 38
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(if (~2 + (x div 2)) <= 0 then x else (x + 2)))
A193063-A165132: 2 3 5 7 11 13
A181172: 2 3 5 7 11 13 23 29 31 37 41 43 47 53 59 61
(if x <= 0 then 3 else compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 2)))
A172070: 3 11 17 29 41 59 71 101 107 137 149 179 191 197 227 239
((2x + 2) - (loop(\(x,i).(if x <= 0 then 0 else (1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2)))),2,x) mod 3))
A287332: 2 4 5 6 10 12 14 15 16 20 21 22 26 27 28 32
(3x + loop(\(x,i).loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),x,x),1,3x))
A240883: 0 0 2 1 2 0 2 2 2 2 4 1 2 1 3 3
((if (x mod 3) <= 0 then (if (x mod 2) <= 0 then (9 * (if x <= 0 then 1 else 2)) else 0) else 1) + (x mod 2))
A010160: 9 2 1 1 1 2 18 2 1 1 1 2 18 2 1 1
(2 * loop(\(x,i).((x + 1) - (if x <= 0 then 1 else (if (x mod (2 + ((x2 div 2) mod (x + 2)))) <= 0 then 2 else 0))),x,x))
A304651: 0 4 8 8 8 16 16 16 16 16 24 24 24 32 32 32
loop(\(x,i).x3,1,loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),x,2))
A115964: 8 216 27000 9261000 12326391000 27081081027000 133049351085651000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) + loop(\(x,i).((x + 2) + (if x <= 0 then 0 else ((if (x mod (2 + (x mod 2))) <= 0 then 1 else x) mod 4))),x,0))
A311356: 1 4 8 12 16 22 26 32 36 40 44 48 52 56 60 64
compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(x2 + 3x + 3)),x)
A224870: 1 2 5 7 10 11 16 20 22 25 37 40 41 46 50 55
compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (2 + i)) <= 0 then 0 else 1)),x,x),1,(7x + ~1)),x)
A105772: 0 3 5 11 15 21 23 27 33 45 47 51 53 57 63 65
(if x <= 0 then 1 else compr(\x.(x mod (1 + (2 * (x mod loop(\(x,i).(1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),2,x))))),x))
A175495: 1 2 3 4 6 8 10 12 14 15 16 18 20 24 28 30
loop(\(x,i).(loop(\(x,i).(2x + 2),x,0) div (x + 1)),1,compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))
A064535: 0 1 2 6 18 186 630 7710 27594 364722 18512790 69273666 3714566310 53634713550 204560302842 2994414645858
compr(\x.(loop(\(x,i).x2,2,(~2 + loop(\(x,i).(1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),2,x))) mod (x + 1)),x)
A328607-A258209-A257250: 0 1 2 3 4 6 7 8 12 14 15 16 24 26 28 30
(0 - (if x <= 0 then 0 else loop(\(x,i).(~1 + loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,x)),x,(x + 1))))
A283972: 0 1 1 3 4 4 4 7 8 9 9 10 11 11 11 15
loop(\(x,i).(loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,(x + 1)) mod 5),(x + ~1),x)
A048138: 0 1 1 0 2 1 2 1 1 1 1 2 2 2 2 2
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x + (if (x + ~4) <= 0 then 1 else 2)))
A216285: 3 5 7 11 13 19 23 29 31 37 41 43 47 53 59 61
compr(\x.(loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),x,2x)),2,(x + 1)) div 2),x)
A233524: 0 1 2 4 5 8
A031988-A023745: 0 1 2 4 5 8 13 14 17 26 40 41 44 53 80 121
compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(2 + ((x2 + x) div 2))),x)
A027756: 0 2 3 5 8 9 11 12 17 18 24 26 29 30 32 33
(0 - loop(\(x,i).loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),x,x),1,(2x2 + 4x)))
A281264: 0 4 15 26 46 67 94 120 158 194 236 281 333 386 445 502
compr(\x.(loop(\(x,i).(x div (2 - ((1 + (if (x + ~2) <= 0 then x else (if (x mod 4) <= 0 then 0 else 1))) mod 2))),x,x) div 2),x)
A280873: 0 1 3 6 7 13 14 15 26 27 29 30 31 53 54 55
loop(\(x,i).(x + loop(\(x,i).(x - (if x <= 0 then 1 else (i - ((x + (x div 3)) div 5)))),x,x)),2,x)
A078349: 0 1 1 1 2 1 2 1 1 2 3 1 2 2 2 1
compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (2 + i)) <= 0 then 0 else 1)),x,x),1,11x),x)
A102686: 0 4 10 14 16 20 28 38 40 44 46 56 58 68 70 76
compr(\x.(1 - loop(\(x,i).(~2 + (loop(\(x,i).(1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),2,x) mod (x + 1))),2,x)),x)
A043683: 21 37 41 42 43 45 53 69 73 74 75 77 81 82 83 84
(3x + loop(\(x,i).loop(\(x,i).(~1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),x,x),1,3x))
A036555: 0 2 2 2 2 4 2 3 2 4 4 2 2 4 3 4
(if (x mod 2) <= 0 then (1 + ((2 * (1 + ((1 + (loop(\(x,i).(x + i),(x + ~2),1) div 2)) div 2))) div 3)) else 0)
A240146-A240145-A240144-A240143-A035363: 1 0 1 0 2 0 3 0 5 0 7 0 11 0 15 0
loop(\(x,i).10x,x,loop(\(x,i).(10x + 10),(2x + 1),0))
A138118: 10 11100 11111000 11111110000 11111111100000 11111111111000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).10x,2x,loop(\(x,i).(10x + 10),(x + 1),0))
A138119: 10 11000 11100000 11110000000 11111000000000 11111100000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (~x + 2) <= 0 then (if (x mod 3) <= 0 then 2 else (((x + 1) div 2) - ((3 * (x div 4)) div 2))) else 0)
A180094: 0 0 1 2 1 2 2 3 1 2 2 3 2 3 3 2
loop(\(x,i).(10x + 2),x,(1 - loop(\(x,i).(10x + ~20),x,0)))
A332121: 1 212 22122 2221222 222212222 22222122222 2222221222222 222222212222222 22222222122222222 2222222221222222222 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).10x,x,1) - loop(\(x,i).(11x + ~10),x,0))
A155673: 1 20 220 2330 24640 261050 2771560 29487170 314358880 3357947690 35937424600 385311670610 4138428376720 44522712143930 479749833583240 5177248169415650
(loop(\(x,i).7x,x,1) - loop(\(x,i).(11x + ~10),x,0))
A155658: 1 17 169 1673 17041 177857 1889209 20310713 220123681 2398301297 26219899849 287288997353 3152269663921 34619601154337 380428056656089 4181995730925593
(loop(\(x,i).11x,x,1) + loop(\(x,i).(7x + ~6),x,0))
A155662: 1 5 73 989 12241 144245 1653913 18663629 208594081 2317594085 25654949353 283334343869 3124587089521 34425823133525 379071610510393 4172500607905709
loop(\(x,i).((x + 1) + (3 * ((2x + 2) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))),x,0)
A097254: 0 7 56 63 448 455 504 511 3584 3591 3640 3647 4032 4039 4088 4095
((loop(\(x,i).(9x + 2),x,0) div 3) * loop(\(x,i).(3x + 1),x,0))
A275635: 0 0 24 780 21840 595320 16120104 435647940 11766101280 317717078640 8578651865784 231626215995900 6253931369278320 168856358797449960 4559123593944869064 4611686018427387903
(if x <= 0 then 1 else (if ((x - ((((3 * (x div 4)) div 2) - ((x + ~1) div 2)) div 2)) mod 2) <= 0 then x else 0))
A063973: 1 0 2 3 4 5 0 7 8 9 0 11 0 13 0 0
(1 + loop(\(x,i).((9x + ~1) + loop(\(x,i).10x,i,1)),x,0))
A095807: 1 10 181 2620 33571 402130 4619161 51572440 564151951 6077367550 64696307941 682266771460 7140400943131 74263608488170 768372476393521 7915352287541680
(1 + loop(\(x,i).10x,x,1) - loop(\(x,i).(9x + 9),x,0))
A217094: 2 2 11 182 2621 33572 402131 4619162 51572441 564151952 6077367551 64696307942 682266771461 7140400943132 74263608488171 768372476393522
(loop(\(x,i).(2x + 2),(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1) - (if x <= 0 then 0 else 1))
A266533: 1 3 3 9 3 9 9 21 3 9 9 21 9 21 21 45
(((1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))) div 2) + (if x <= 0 then 0 else 1))
A318473-A008481: 0 1 1 2 1 2 1 3 2 2 1 3 1 2 2 5
loop(\(x,i).2x,(((~x + 1) mod (1 + ((x - ((x div 3) mod 3)) div 2))) + (if x <= 0 then 0 else 1)),1)
A166242: 1 2 4 2 4 8 4 2 4 8 16 8 4 8 4 2
loop(\(x,i).2x,((((1 + (8 mod (1 + (x div 2)))) div 2) + (if x <= 0 then 0 else 1)) - (x mod 2)),1)
A080100: 1 1 2 1 4 2 2 1 8 4 4 2 4 2 2 1
(1 + (if x <= 0 then 0 else (1 + (x mod (1 + ((4 * (loop(\(x,i).2x,x,x) mod (x + 1))) div 3))))))
A325971: 1 2 4 2 6 7 8 2 3 11 12 7 14 15 16 2
(1 + (x div (1 + (x mod (1 + (loop(\(x,i).2x,x,(if (x + ~4) <= 0 then 1 else 2)) mod (2x + 1)))))))
A322020: 1 1 1 2 1 1 1 4 3 1 1 4 1 1 1 16
(1 + (x div (1 + (x mod (1 + ((~1 + loop(\(x,i).2x,x,loop(\(x,i).(2 + (x * i)),x,2))) mod (x + 1)))))))
A097706: 1 1 3 1 1 3 7 1 9 1 11 3 1 7 3 1
(1 + (x mod (1 + (x mod (1 + (loop(\(x,i).(x + (if (x + ~4) <= 0 then 3 else x)),x,1) mod (x + 1)))))))
A180172: 1 1 1 1 1 3 1 1 1 1 11 3 1 1 1 1
(~1 + loop(\(x,i).10x,x,(~1 + loop(\(x,i).10x,(x + 1),1))))
A181965: 8 989 99899 9998999 999989999 99999899999 9999998999999 999999989999999 99999999899999999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x - (if x <= 0 then 0 else (1 + (x mod (1 + ((4 * (loop(\(x,i).2x,x,x) mod (x + 1))) div 3))))))
A325970: 0 0 ~1 2 ~1 ~1 ~1 6 6 ~1 ~1 5 ~1 ~1 ~1 14
(1 + (if (~x + 2) <= 0 then (1 - (compr(\x.(if (x mod 2) <= 0 then ((x div 3) mod 3) else 0),x) mod 3)) else 1))
A316344: 2 2 0 2 0 1 2 1 0 1 2 0 2 1 0 2
(if (x mod 2) <= 0 then (1 + ((1 + (if (x mod 5) <= 0 then 0 else (x div 5))) mod (x + 1))) else 1)
A278538: 1 1 2 1 2 1 3 1 3 1 2 1 4 1 4 1
(~1 + loop(\(x,i).(9x + loop(\(x,i).10x,i,1)),(x + 1),1))
A083445: 18 270 3438 40950 468558 5217030 56953278 612579510 6513215598 68618940390 717570463518 7458134171670 77123207545038 794108867905350 8146979811148158 83322818300333430
(1 + ((if x <= 0 then 1 else x) div (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))))))
A111089: 2 2 3 2 5 3 7 2 3 5 11 3 13 7 5 2
((2x + 1) - (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (3 + (((x + 1) div 2) div 2))))
A128140: 1 3 2 7 5 3 13 10 7 4 21 17 13 9 5 31
(~1 + (9 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),(x + 1))))
A265104: 8 26 35 80 89 107 116 242 251 269 278 323 332 350 359 728
(1 + (loop(\(x,i).(x * i),(2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)),1) div 5))
A139163: 25 1009 7983361 1245404161 71137485619201 24329020081766401 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (loop(\(x,i).(x * i),(2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)),1) div 5))
A139193: 23 1007 7983359 1245404159 71137485619199 24329020081766399 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (5 * loop(\(x,i).(2x2 + ~x),1,loop(\(x,i).10x,x,1))))
A332194: 4 949 99499 9994999 999949999 99999499999 9999994999999 999999949999999 99999999499999999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).(x * (2 + i)),compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x),1) div 5))
A139168: 13 505 3991681 622702081 35568742809601 12164510040883201 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (loop(\(x,i).(x * (2 + i)),compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x),1) div 5))
A139198: 11 503 3991679 622702079 35568742809599 12164510040883199 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (x div (3 + ((if (x mod 4) <= 0 then 0 else (if (x mod (2 + (x mod 2))) <= 0 then 1 else x)) + (x mod 2)))))
A323524: 1 1 1 1 2 1 2 1 3 2 3 1 5 1 4 4
(if (x mod 3) <= 0 then (3 * (1 + (if (2x mod (4 + (x div 4))) <= 0 then 2 else 0))) else 1)
A109012: 9 1 1 3 1 1 3 1 1 9 1 1 3 1 1 3
(1 + ((1 + (if ((x div 2) mod 3) <= 0 then 0 else loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))) div 3))
A295665: 1 1 2 1 3 2 1 1 4 3 5 2 1 1 6 1
(1 + ((1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (2 + (x div 5)))) div 3))
A318806: 1 1 2 1 2 3 1 2 3 4 1 2 4 5 6 1
(x mod (1 + ((1 + loop(\(x,i).loop(\(x,i).3x,((x + ~1) div 2),1),(x mod 2),(x div 2))) div 3)))
A067166: 0 0 0 0 0 0 0 1 0 1 1 3 0 1 2 5
((if (((x * (x div 3)) div 2) mod 3) <= 0 then (if x <= 0 then 0 else 1) else 0) * (1 + ((x + 1) div 3)))
A091227: 0 1 2 0 0 0 3 0 0 0 4 0 5 0 0 0
(1 + ((2 + loop(\(x,i).(x div (2 - (x mod 2))),x,(x div (1 + (if (x mod 3) <= 0 then 2 else 0))))) div 3))
A126759: 1 2 2 2 2 3 2 4 2 2 3 5 2 6 4 3
((x + 1) - ((2 * (1 + ((2 * loop(\(x,i).(x + (if (x - i) <= 0 then x else 0)),x,1)) div 3))) div 3))
A119671: 1 1 1 2 1 2 3 4 2 3 4 5 6 7 8 9
(1 + ((2 * loop(\(x,i).x2,1,(1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))) div 3))
A276391: 1 3 1 11 1 3 1 43 1 3 1 11 1 3 1 171
(~1 + (3 * (2 + (3 * compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),x)))))
A265100: 5 14 32 41 86 95 113 122 248 257 275 284 329 338 356 365
((x + 1) div (if x <= 0 then 1 else (~1 + (6 * (if (x mod (1 + ((x + ~1) mod 4))) <= 0 then 1 else 2)))))
A029328: 1 0 0 0 1 1 1 0 1 2 2 1 2 2 3 3
(1 + ((2 * loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)))) div 3))
A286679: 17 33 81 113 193 241 353 561 641 913 1121 1233 1473 1873 2321 2481
(~1 + ((loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x))) div 2) div 3))
A171140: 3 7 19 27 47 59 87 139 159 227 279 307 367 467 579 619
(1 + (((x + 1) - loop(\(x,i).(x - ((x + (if (x mod 3) <= 0 then 2 else 1)) div 4)),2,x)) mod 3))
A288724: 2 2 2 3 1 1 2 2 3 3 3 1 1 1 2 3
(1 + ((1 + (if ((x + loop(\(x,i).(x div (2 - (x mod 2))),x,x)) mod 3) <= 0 then 2 else 1)) mod (1 + (x div 2))))
A157790: 1 1 2 2 3 3 4 3 4 4 4 3 4 3 4 4
(1 + ((~1 + loop(\(x,i).2x,x,(1 - loop(\(x,i).(2 * (x - (i mod 2))),x,(x mod 2))))) * (1 + (x mod 2))))
A267055: 1 3 20 47 336 703 5440 11007 87296 175103 1397760 2797567 22368256 44744703 357908480 715849727
(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x + ~1),1) * (~1 + loop(\(x,i).4x,x,1)))
A131568: 0 3 45 630 8925 128898 1891890
(1 + loop(\(x,i).11x,x,1) - loop(\(x,i).10x,x,1))
A155674: 1 2 22 332 4642 61052 771562 9487172 114358882 1357947692 15937424602 185311670612 2138428376722 24522712143932 279749833583242 3177248169415652
loop(\(x,i).(10x + 1),(1 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x)),1)
A031974: 11 111 11111 1111111 11111111111 1111111111111 11111111111111111 1111111111111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(9x + 1),(1 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)),1)
A210461: 91 7381 597871 3922632451 317733228541 2084647712458321 168856464709124011 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.(loop(\(x,i).(2x + 2),x,(if (x mod 7) <= 0 then 1 else 0)) mod (x + 1)),(x + 1)))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A216882-A216881-A042966: 2 3 5 7 11 13 17 19 23 31 37 41 47 53 59 61
(1 + compr(\x.(loop(\(x,i).(2x + 2),x,(if (x mod 9) <= 0 then 1 else 0)) mod (x + 1)),(x + 1)))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A299956: 2 3 5 7 11 13 17 23 29 31 41 43 47 53 59 61
(1 + compr(\x.(loop(\(x,i).(x2 + x),1,(loop(\(x,i).(2 * (x - i)),x,2) mod (x + 1))) mod (x + 1)),(x + 1)))
A193063-A165132: 2 3 5 7 11 13
A240960-A182140: 2 3 5 7 11 13 15 17 19 23 29 31 37 41 43 47
(1 + compr(\x.(loop(\(x,i).(2x + 2),x,(loop(\(x,i).(2 * (x - i)),x,2) mod (x + 1))) mod (x + 1)),(x + 1)))
A136327-A070566: 2 3 5 7 9 11 13 17 19 23 25 29 31 37 41 43
(loop(\(x,i).10x,(x div 2),1) + loop(\(x,i).10x,(x + 1),1))
A164046: 11 101 1010 10010 100100 1000100 10001000 100001000 1000010000 10000010000 100000100000 1000000100000 10000001000000 100000001000000 1000000010000000 10000000010000000
loop(\(x,i).(x * ((x2 + x + 1) div 3)),1,loop(\(x,i).10x,(x + 1),1))
A281858: 370 336700 333667000 333366670000 333336666700000 333333666667000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (x div (if (x mod (1 + (2 * (x mod 4)))) <= 0 then 1 else loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A161399: 1 2 1 4 5 2 1 8 9 10 11 4 13 2 1 16
loop(\(x,i).15x,x,(1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A156372: 1 30 225 13500 50625 1518750 11390625 1366875000 2562890625 76886718750 576650390625 34599023437500 129746337890625 3892390136718750 29192926025390625 4611686018427387903
loop(\(x,i).11x,x,(1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A156293: 1 22 121 5324 14641 322102 1771561 155897368 214358881 4715895382 25937424601 1141246682444 3138428376721 69045424287862 379749833583241 66835970710650416
(~1 + loop(\(x,i).(x + (if (x mod 11) <= 0 then (8x + 2) else 1)),x,1))
A103303: 0 1 2 3 4 5 6 7 8 9
A055649: 0 1 2 3 4 5 6 7 8 9 10 100 101 102 103 104
(1 + loop(\(x,i).(x + (3 * (if (~2x mod 5) <= 0 then 3x else 1))),x,1))
A135050: 2 5 8 11 101 1001 10001 100001 1000001 10000001 100000001 1000000001 10000000001 100000000001 1000000000001 10000000000001
(if x <= 0 then 1 else (x - (x mod (1 + (2 * (2x mod (1 + (if (x mod 2) <= 0 then 12 else 0))))))))
A325962: 1 1 0 3 0 5 0 7 7 9 0 11 0 13 10 15
(1 + ((if x <= 0 then 2 else (1 + ((1 + (loop(\(x,i).4x,x,1) mod (2x + 1))) div 3))) div 2))
A103961: 2 1 1 1 2 1 1 2 1 1 2 1 4 3 1 1
(1 + ((1 + (loop(\(x,i).(1 + (x * (1 + (if (x mod 3) <= 0 then 2 else 0)))),2x,1) div 3)) div 2))
A137823: 1 2 3 7 8 21 61 62 183 547 548 1641 4921 4922 14763 44287
(~1 + ((1 + (loop(\(x,i).2x,x,loop(\(x,i).2x,(x div 2),(3 + (x mod 2)))) div (x + 1))) div 2))
A000633: 1 1 3 7 18 42 109
(~1 + loop(\(x,i).10x,x,(~2 + loop(\(x,i).10x,(x + 1),1))))
A332197: 7 979 99799 9997999 999979999 99999799999 9999997999999 999999979999999 99999999799999999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (2 * (if x <= 0 then 2 else (~1 + (2 * ((4 * (x + (if (~2 + (x div 2)) <= 0 then 1 else 2))) div 3))))))
A260191: 3 5 13 17 21 29 37 45 49 53 61 65 69 77 81 85
(1 + ((1 + (loop(\(x,i).(loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)),1,(x + 1)) div 2)) div 2))
A335079: 1 1 2 1 2 1 3 2 2 1 4 1 2 2 5 1
(1 + (2 * (1 + (2 * (2 + loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),1))))))
A241680: 15 19 43 139 2059 8203 131083 524299 8388619 536870923 2147483659 137438953483 2199023255563 8796093022219 140737488355339 9007199254741003
(loop(\(x,i).2x,x,2) - loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1))
A166456: 1 2 6 12 30 60 124 248 510 1020 2044 4088 8188 16376 32760 65520
((3 * (2 + (if x <= 0 then 0 else (1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x))))) div 7)
A340717: 0 1 1 2 1 3 2 4 1 5 3 6 2 6 4 7
(~1 + loop(\(x,i).(x2 + x),1,(2 * (1 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) div 2)))))
A039914: 5 5 19 41 109 155 271 341 505 811 929 1331 1639 1805 2161 2755
(1 + (loop(\(x,i).(6x + loop(\(x,i).(10x + 2),2,x)),x,1) div 2))
A282839: 1 65 6796
(~1 + (2 * loop(\(x,i).(5x2 + ~2x),1,loop(\(x,i).10x,x,1))))
A332195: 5 959 99599 9995999 999959999 99999599999 9999995999999 999999959999999 99999999599999999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (((1 + (loop(\(x,i).2x,(loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2),1) div 2)) mod (x + 1)) div 2))
A292583: 1 1 2 1 2 2 3 1 1 2 4 2 4 3 3 1
loop(\(x,i).x2,1,(1 + (x div ((x + 2) div (2 + (loop(\(x,i).x3,2,2x) mod (x + 1)))))))
A078615: 1 4 9 4 25 36 49 4 9 100 121 36 169 196 225 4
(1 + (compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 4x))),(x + 1)) div 2))
A088762: 2 4 7 10 19 22 34 40 49 52 55 64 82 97 112 115
(1 + (loop(\(x,i).(x - (x div 12)),x,loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))) div 2))
A334867: 1 1 2 1 3 2 4 1 5 3 6 2 6 4 6 1
(if (x mod 2) <= 0 then ((~1 + (7 * (1 + ((x + ~1) mod 4)))) * (if x <= 0 then 1 else 2)) else 1)
A040754: 27 1 26 1 54 1 26 1 54 1 26 1 54 1 26 1
(if (x mod 2) <= 0 then ((1 + (14 * ((~x + 2) mod 4))) * (if x <= 0 then 1 else 2)) else 1)
A040855: 29 1 2 1 58 1 2 1 58 1 2 1 58 1 2 1
(if (x mod 2) <= 0 then ((~1 + (6 * (1 + (2 * ((~x + 2) mod 4))))) * (if x <= 0 then 1 else 2)) else 1)
A040865: 29 1 10 1 58 1 10 1 58 1 10 1 58 1 10 1
(1 + (4 * (3 + ((loop(\(x,i).x2,1,(2 + loop(\(x,i).4x,x,2))) div 2) div 2))))
A225928: 29 113 1169 16913 264209 4202513 67141649 1073872913 17180393489 274880004113 4398054899729 70368777732113 1125900041060369 18014399046352913 288230378299195409 4611686018427387903
((x + 1) - (((2 + (loop(\(x,i).loop(\(x,i).(x div (~2 + (x mod 2))),x,(x + 1)),2,x) mod (x + 1))) div 2) div 2))
A288773: 1 2 2 4 4 5 5 8 8 8 9 9 11
(1 + (((loop(\(x,i).(x2 + 2x),1,loop(\(x,i).(((x + 1) - (2 * (i mod 2))) * i),x,1)) div 2) div 2) div 2))
A001121: 1 1 2 2 37 722
((2x + 1) - (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (4 + (((x + 1) div 2) div 2))))
A323956: 1 3 1 7 4 1 13 9 5 1 21 16 11 6 1 31
(1 + (2 * (6 + (if x <= 0 then 2 else loop(\(x,i).x3,1,14)))))
A062659: 17 5501
(1 + ((x - ((((if (x mod 2) <= 0 then (if (x mod 3) <= 0 then 1 else x) else 3) + (x div 2)) div 2) div 2)) div 2))
A077105: 1 1 2 2 2 3 3 4 3 5 4 5 6 6 5 7
((x * loop(\(x,i).(x * loop(\(x,i).((x2 + ~x) div 2),2,(x + ~2))),1,(x + ~1))) div 9)
A271040: 0 0 0 0 0 0 10 70 280 840 2100 4620 9240 17160 30030 50050
(1 + (4 * (1 + compr(\x.(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then x else (1 + i))),x,x)),x))))
A186294: 9 21 37 45 49 57 69 97 117 121 129 141 157 169 177 201
(if x <= 0 then 1 else (5 * (1 + (2 * (2 mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1))))))
A082476: 1 5 5 5 5 25 5 5 5 25 5 25 5 25 25 5
(5 * loop(\(x,i).x2,1,(3 * loop(\(x,i).(10x + 1),x,1))))
A178632: 45 5445 554445 55544445 5555444445 555554444445 55555544444445 5555555444444445 555555554444444445 4611686018427387903 4611686018427387903 4611686018427387903
(5 * (1 + loop(\(x,i).x2,1,(2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)))))
A093194: 50 130 250 610 850 1450 1810 2650 4210 4810 6850 8410 9250 11050 14050
(5 * (loop(\(x,i).5x,x,1) - loop(\(x,i).5x,(x div 2),1)))
A240437: 0 20 100 600 3000 15500 77500 390000 1950000 9762500 48812500 244125000 1220625000 6103437500 30517187500 152587500000
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(11x + 9))
A017507: 31381059609 204800000000000 25408476896404831 717368321110468608 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (4 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,8x)),x)))
A186297: 1 5 9 21 29 33 41 53 65 69 81 89 105 113 125 141
((4x + 1) * loop(\(x,i).x2,1,loop(\(x,i).((2 * (x - (2x * i))) div (1 + i)),x,1)))
A267980: 1 5 36 325 3332 37044 435600 5337189 67481700 874644628 11566330256 155510720820 2120180615056 29250721730000 407699870875200 5733391194015525
(if (x mod 4) <= 0 then (14 * (2 + (if x <= 0 then 0 else 2))) else (1 + (2 * (x mod 2))))
A040770: 28 3 1 3 56 3 1 3 56 3 1 3 56 3 1 3
((if x <= 0 then 1 else (~1 + (2 * (~1 + (x mod (2 * (1 + (if (x mod 2) <= 0 then 6 else 1)))))))) mod 3)
A228817: 1 2 1 0 2
A000925: 1 2 1 0 2 2 0 0 1 2 2 0 0 2 0 0
((loop(\(x,i).x2,2,(2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x))) div 3) mod 3)
A024712: 1 2 2 1 0 0 1 2 1 0 1 2 2 0 1 2
(((x + 3) * (loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,(x + 2)) div 2)) div 3)
A085374: 1 12 100 700 4410 25872 144144 772200 4011150 20323160 100876776 492156392 2366136500 11232648000 52739956800 245240799120
((1 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 2))) div 3)
A167379: 2 4 6 10 14 20 24 34 36 46 50 60 64 66 76 80
(if x <= 0 then 1 else (3 * (1 + compr(\x.(loop(\(x,i).x2,2,(4 * (2 + (x mod 2)))) mod (x + 1)),x))))
A187778: 1 6 12 18 24 36 48 54 72 96 108 144 162 192 216 288
(3 * loop(\(x,i).x2,1,(1 + compr(\x.(loop(\(x,i).(x3 + 2x),2,2x) mod (x + 1)),x))))
A018230: 3 12 27 48 108 192 432 1728
(((x + 1) * (1 + loop(\(x,i).(if x <= 0 then 1 else ((2x * (~1 + (2 * i))) mod (1 + i))),x,0))) mod 3)
A033762: 1 1 0 2 1 0 2 0 0 2 2 0 1 1 0 2
(loop(\(x,i).3x,x,(loop(\(x,i).(x + ((5 + i) * i)),(x + 1),0) div 2)) div 3)
A080421: 1 10 66 360 1755 7938 34020 139968 557685 2165130 8227494 30705480 112842639 409209570 1466777160 5203870272
(3 * (2 + (3 * (x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1))))))
A059144: 15 24 15 33 15 24 15 42 15 24 15 33 15 24 15 51
((((x + 3) * loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,(x + 2))) div 2) div 3)
A006542: 1 10 50 175 490 1176 2520 4950 9075 15730 26026 41405 63700 95200 138720 197676
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(11x + 7))
A017483: 1977326743 64268410079232 12200509765705829 419430400000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,((2 * (1 + (x div 2))) div 3))
A033302: 2 2 3 3 5 5 5 5 7 7 11 11 11 11 13 13
((2 * (1 + (if x <= 0 then 1 else loop(\(x,i).((2x * (~1 + (2 * i))) div 3),(x + ~2),x)))) mod 3)
A073265: 1 1 0 0 1 0 1 2 0 0 0 1 1 0 0 0
(3 + (2 * compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),8x)))
A031912: 3 29 61 101 139 181 229 271 317 373 421 463 521 577 619 673
((if x <= 0 then 1 else 6x) - ((2 * ((x + (if (~2 + (x div 2)) <= 0 then 1 else 0)) div 2)) div 3))
A315701: 1 6 12 17 23 28 34 40 46 52 57 63 68 74 80 86
(((x * loop(\(x,i).((x + ~1) * loop(\(x,i).5x,(x + ~2),x)),1,(x + ~1))) div 2) div 3)
A081143: 0 0 0 1 20 250 2500 21875 175000 1312500 9375000 64453125 429687500 2792968750 17773437500 111083984375
(loop(\(x,i).(x * ((x + 1) - i)),2,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 3)
A138419: 4 24 200 784 4840 9464 27744 43320 93104 235480 307520 624264 941360 1138984 1625824 2629224
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (35x + 1)),x,3)
A037115: 3 106 53 1856 928 464 232 116 58 29 1016 508 254 127 4446 2223
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (45x + 1)),x,3)
A037120: 3 136 68 34 17 766 383 17236 8618 4309 193906 96953 4362886 2181443 98164936 49082468
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (39x + 1)),x,3)
A037117: 3 118 59 2302 1151 44890 22445 875356 437678 218839 8534722 4267361 166427080 83213540 41606770 20803385
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (29x + 1)),x,3)
A037112: 3 88 44 22 11 320 160 80 40 20 10 5 146 73 2118 1059
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (47x + 1)),x,3)
A037121: 3 142 71 3338 1669 78444 39222 19611 921718 460859 21660374 10830187 509018790 254509395 11961941566 5980970783
(compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x2 + 1))),x) div 3)
A056906: 0 1 2 6 8 12 13 16 19 21 27 28 33 34 41 43
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (41x + 1)),x,3)
A037118: 3 124 62 31 1272 636 318 159 6520 3260 1630 815 33416 16708 8354 4177
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (37x + 1)),x,3)
A037116: 3 112 56 28 14 7 260 130 65 2406 1203 44512 22256 11128 5564 2782
loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (49x + 1)),x,3)
A037122: 3 148 74 37 1814 907 44444 22222 11111 544440 272220 136110 68055 3334696 1667348 833674
(compr(\x.(1 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x2 + 2x))),x) div 3)
A056900: 0 1 2 3 5 6 7 9 13 16 17 18 19 20 24 28
loop(\(x,i).(x div (2 - (x mod 2))),(x + 1),(3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A057024: 3 1 3 1 3 7 9 5 3 15 1 19 21 11 3 27
(((1 + (loop(\(x,i).2x,x,loop(\(x,i).(x + (x div 2)),x,4)) div 2)) div 3) + (x div 3))
A181490: 1 2 6 18
A156989: 1 2 6 18 52 150 450
loop(\(x,i).(x + ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)) * (1 + (2 * i)))),x,3)
A083215: 3 12 37 86 185 328 549 834 1225 1776 2427 3278 4303 5464 6827 8470
(1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(4x + 1))),x)))
A230076: 1 3 7 9 13 15 25 27 37 39 43 45 49 57 67 69
(1 + (2 * ((x + 1) + loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(3x + 2)))))
A107744: 7 13 19 5 31 37 43 7 5 61 67 73 79 5 7 97
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x - (x div (~1 + ((~x + 1) div 2)))))
A261123: 2 5 7 13 17 19 23 29 31 37 41 43 47 53 59 61
(1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(x2 + x + ~1))),x)))
A002731: 3 5 9 11 15 19 25 29 35 39 45 49 51 59 61 65
(~1 + (2 * compr(\x.(1 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x2 + 2x))),x)))
A225227: 1 7 13
A129389: 1 7 13 19 31 37 43 55 79 97 103 109 115 121 145 169
loop(\(x,i).x3,1,(1 + loop(\(x,i).(10x3 + 10x + 2),x,2)))
A050650: 27 1092727 4611686018427387903 4611686018427387903
(1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,10x)),x)))
A024896: 1 3 5 9 11 15 17 21 23 33 35 39 45 47 53 57
(1 + ((x * (2 + (x * ((~1 + loop(\(x,i).2x,1,loop(\(x,i).(x * i),(x + ~1),1))) div (x + 1))))) div 2))
A109302: 1 2 3 4 21 93
loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1)
A161744: 1 2 44 1854 14684570 2290792932 130850092279664 44750731559645106 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + (((2 + i) * (1 + i)) div 2)),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1)
A271512: 10 20 56 120 364 560 1140 1540 2600 4960 5984 9880 13244 15180 19600 27720
(loop(\(x,i).(7x + 6),(x + 2),2) - loop(\(x,i).(3x + 2),(x + 2),1))
A341552: 129 975 7041 49935 351489 2466255 17281281 121021455 847307649 5931625935 41522798721 290663842575 2034659652609 14242655832015 99698705615361 697891283681295
((3 * ((x + 1) + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))) div (x + 3))
A333600: 1 2 3 2 3 2 4 2 3 2 4 2 5 2 3 2
((x2 + 6x + 9) * loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x + 2),2))
A202194: 108 640 3500 18144 90552 439296 2084940 9724000 44710952 203164416 914004728 4077035200 18052470000 79420170240 347424465420 1512176830560
(loop(\(x,i).(4x - (x div (1 + (if (x mod 3) <= 0 then 2 else 0)))),(x div 2),1) * (1 + (x mod 2)))
A018268: 1 2 3 6 11 22 33 66
A018613: 1 2 3 6 11 22 33 66 121 242 363 726
((if (x mod 3) <= 0 then (25 * (if x <= 0 then 1 else 2)) else 2) div (1 + (x mod 2)))
A040633: 25 1 2 25 2 1 50 1 2 25 2 1 50 1 2 25
(((if (x mod 3) <= 0 then 19 else 1) * (if x <= 0 then 1 else 2)) div (1 + (x mod 2)))
A040367: 19 1 2 19 2 1 38 1 2 19 2 1 38 1 2 19
((if (x mod 4) <= 0 then 31 else 1) * (if x <= 0 then 1 else 2) * (1 + (x mod 2)))
A040943: 31 4 2 4 62 4 2 4 62 4 2 4 62 4 2 4
(1 + compr(\x.(1 - ((x + 1) mod (1 + ((~1 + loop(\(x,i).(x - (if x <= 0 then 1 else (2 * i))),x,x)) mod (x + 1))))),x))
A194470: 3 7 8 11 13 14 15 19 21 22 23 24 27 28 29 31
(1 + compr(\x.(2 - ((if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).2x,x,1) mod (x + 1)) div 2)))) mod 3)),x))
A162721: 2 3 4 5 7 8 11 13 16 17 19 23 27 29 31 32
loop(\(x,i).(12x + loop(\(x,i).(11x + 1),i,1)),x,1)
A016268: 1 24 421 6516 94297 1308720 17653357 233276172 3035108833 39015048456 496711748533 6274383820068 78744877055209 982913508020832 12212686913191549 151147215944655804
loop(\(x,i).(7x + loop(\(x,i).(11x + 1),i,1)),x,1)
A016254: 1 19 266 3326 39387 452865 5118772 57267292 636665813 7050403151 77883989118 859030761498 9465486544879 104233389172477 1147358541148904 12626482774399544
loop(\(x,i).(7x + loop(\(x,i).(2 * (4x - (x div ~2))),i,1)),x,1)
A081035: 1 17 209 2273 23201 228017 2186609 20620673 192174401 1775688017 16304021009 148995991073 1356782533601 12321773100017 111671069983409 1010465414433473
loop(\(x,i).(10x2 + x),1,loop(\(x,i).(10x + 1),x,1))
A259937: 11 1221 123321 12344321 1234554321 123456654321 12345677654321 1234567887654321 123456789987654321 4611686018427387903 4611686018427387903 4611686018427387903
A261138: 11 1221 123321 12344321 1234554321 123456654321 12345677654321 1234567887654321 123456789987654321 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x + 1) + ((1 + (2 * (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))) div 3)),x,1)
A033053: 1 3 6 7 13 15 26 27 30 31 53 55 61 63 106 107
(if (2 * (x div 5)) <= 0 then 2x else (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x)))
A331417: 0 2 4 6 8 11 13 17 19 23 29 31 37 41 43 47
(1 + compr(\x.((~1 + loop(\(x,i).x3,1,loop(\(x,i).x2,2,10))) mod (x + 1)),x))
A027897: 1 3 7 9 11 13 21 27 33 37 39 63 77 91 99 101
(1 + compr(\x.((~1 + loop(\(x,i).x3,1,loop(\(x,i).4x2,2,4))) mod (x + 1)),x))
A003547: 1 3 7 9 21 43 49 63 127 129 147 301 337 381 387 441
(1 + compr(\x.(loop(\(x,i).(x * loop(\(x,i).3x,3,(x2 + x + 2))),2,1) mod (x + 1)),x))
A128170: 1 2 3 4 6 7 8 9 12 14 18 21 24 27 28 29
(1 + compr(\x.(loop(\(x,i).(2x2 + x),1,(loop(\(x,i).(2x + 2),x,0) mod (x + 1))) mod (x + 1)),x))
A193622: 1 2 3 5 7 10
A117286: 1 2 3 5 7 10 11 13 17 19 23 29 31 37 39 41
(1 + compr(\x.((2 + (x * loop(\(x,i).(x2 + x),1,loop(\(x,i).x2,2,5)))) mod (x + 1)),x))
A335878: 1 2 3 4 6 8 9 11 12 13 16 18 19 22 24 26
(1 + compr(\x.(loop(\(x,i).(x * (1 + loop(\(x,i).10x,(1 + i),x))),2,x) mod (x + 1)),x))
A018596: 1 3 7 9 11 21 33 63 77 99 231 693
loop(\(x,i).(36x + loop(\(x,i).(6x + 1),i,1)),x,1)
A022220: 1 43 1591 57535 2072815 74630671 2686760143 96723701071 3482055254095 125354001240655 4512744117222991 162458788655384143 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(64x + loop(\(x,i).(8x + 1),i,1)),x,1)
A022242: 1 73 4745 304265 19477641 1246606473 79783113865 5106121684105 326791806956681 20914675798619273 1338539252338766985 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).2x,((x2 + ~x) div 2),1) - loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1))
A326250: 0 0 0 3 50 982 32636 2096723
(loop(\(x,i).(2x * (~1 + (2 * i))),x,1) - loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1))
A089833: 0 1 10 115 1666 30198 665148 17296851 518916970 17643220738 670442556004 28158587998814 1295295050441588 64764752531737100 3497296636751245560 4611686018427387903
(1 + compr(\x.(loop(\(x,i).(x + ((x + loop(\(x,i).4x,i,1)) div (2x + 1))),(x + 1),1) mod 2),x))
A231407: 1 4 6
A320985: 1 4 6 8 9 10 11 12 14 15 20 21 24 25 28 29
(~1 + compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(8x + ~2))),x))
A127575: 1 2 4 7 11 13 14 16 22 23 26 28 29 37 44 46
(1 + compr(\x.(~2 + (loop(\(x,i).(~1 + ((x + 1) * loop(\(x,i).(x2 + 1),2,3))),2,1) mod (x + 1))),x))
A067319: 1 2 3 4 5 6 8 10 12
A295298: 1 2 3 4 5 6 8 10 12 15 16 17 20 23 24 25
loop(\(x,i).(~8x + loop(\(x,i).(64x + 1),i,1)),x,1)
A015259: 1 57 3705 236665 15150201 969583737 62053592185 3971428035705 254171409198201 16266970069380217 1041086085394771065 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(9x + loop(\(x,i).(11x + 1),i,1)),x,1)
A016262: 1 21 322 4362 55363 675423 8027524 93683604 1078947205 12304267305 139269572806 1567268992926 17557692150727 195994212714867 2181672731375368 24230027568735528
(~1 + compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(5x + ~2))),x))
A102700: 1 2 5 7 8 10 13 14 17 19 22 23 26 34 35 37
loop(\(x,i).(5x + loop(\(x,i).(25x + 1),i,1)),x,1)
A006111: 1 31 806 20306 508431 12714681 317886556 7947261556 198682027181 4967053120931 124176340230306 3104408566792806 77610214474995931 1940255363400777181 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x + (if ((x2 + 2x) mod (1 + (8 * (x mod 2)))) <= 0 then (x + 1) else 0)),2,x))
A085050: 2 2 6 4 20 6 14 16 18 20 22 12 52 14 30 16
(1 + compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(5x + 2))),x))
A024914: 1 2 4 5 7 10 11 13 14 16 17 20 23 26 28 31
loop(\(x,i).(10x + loop(\(x,i).(11x + 1),i,1)),x,1)
A016265: 1 22 353 4994 66045 837606 10324777 124683658 1482631349 17420055950 202731726561 2341160103282 26863872247213 306613705830454 3483861875246105 39433591738818266
loop(\(x,i).(10x + loop(\(x,i).(8x + (x mod 3)),i,1)),x,1)
A081036: 1 19 262 3196 36568 402544 4320352 45562816 474502528 4896020224 50168161792 511345294336 5190762354688 52526098837504 530208790700032 5341670325600256
loop(\(x,i).(10x2 + 11x + 1),1,loop(\(x,i).10x,x,1))
A319667: 22 1111 101101 10011001 1000110001 100001100001 10000011000001 1000000110000001 100000001100000001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(10x + 2),2x,2) + loop(\(x,i).10x,x,1))
A332123: 3 232 22322 2223222 222232222 22222322222 2222223222222 222222232222222 22222222322222222 2222222223222222222 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((x2 div 4) mod (x + 1)),1,(1 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)))
A292411: 1 4 2 3 10 13 5 6 22 8 28 31 11 12 40 15
loop(\(x,i).(4x2 + 5x + 1),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A267217: 10 27 85 175 451 637 1105 1387 2047 3277 3751 5365 6601 7267 8695 11077
loop(\(x,i).(x4 + 3x3 + 2x2),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A244509: 6 48 480 2016 13200 26208 78336 123120 267168 682080 892800 1822176 2755200 3337488 4773696 7738848
loop(\(x,i).((x + ~1) * (x2 div 4)),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A331764: 0 1 12 45 225 396 960 1377 2541 5292 6525 11340 15600 18081 23805 34476
((x2 + 2x + 1) + loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A106587: 5 13 34 65 146 205 338 425 610 941 1082 1513 1850 2045 2434 3065
((~x2 + ~2x + ~1) + loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A106588: 3 5 16 33 96 133 240 297 448 741 840 1225 1512 1653 1984 2553
((x2 + 2x + 1) * loop(\(x,i).x2,2,loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1)))
A186418: 1 4 144 10000 960400 112021056 14876193024 2167749739584 338710896810000 55880440123393600 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) mod (x2 + 2x + 1))
A178445: 0 1 7 1 21 25 44 41 43 41 114 73 160 85 184 249
(2 - loop(\(x,i).loop(\(x,i).(((3 * (x div 4)) div 2) + ((x + ~1) div 3)),1,2x),x,1))
A175539: 1 2 3 5 8 12 17 25 36 51 73 104 148 210 297 421
(1 + (if x <= 0 then 0 else (x + (if ((1 + ((x + (x div 2)) div 2)) mod 5) <= 0 then 2 else 1) - (x mod 2))))
A161765: 1 2 4 4 6 6 9 8 10 10 12 12 15 15 16 16
((1 + loop(\(x,i).(if x <= 0 then 1 else (2 * (x - ((x + (x div 3)) div 5)))),x,0)) div (x + 1))
A286225: 1 1 1 1 1 1 2 3 4 5 7 9 13 18 25 34
((x + 1) * (1 + (loop(\(x,i).(if (x mod (3 + (i mod 2))) <= 0 then 1 else x),x,(x + 1)) div 5)))
A241083: 1 2 3 4 10 6 14 8 9 30 33 12 39 42 15 16
((~1 + loop(\(x,i).2x,x,1) - (if x <= 0 then 0 else (~1 + ((x * (~1 + (x mod 3))) div 2)))) div (x + 1))
A056303: 0 1 1 2 3 5 9 16 28 51 93 170 315 585 1091 2048
((x + 1) * loop(\(x,i).4x,x,(~1 + (2 * loop(\(x,i).(12x + 8),x,1)))))
A015704: 1 312 23760
((1 + ((loop(\(x,i).x2,2,(x4 + 1)) div loop(\(x,i).2x,x,1)) div 2)) mod (x + 1))
A275377: 0 1 1 2 1 1 1 5 4 6
((x + 1) * (loop(\(x,i).4x,x,2) - loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1)))
A033504: 1 10 66 372 1930 9516 45332 210664 960858 4319100 19188796 84438360 368603716 1598231992 6889682280 29551095248
((~x + ~1) + (loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1) + loop(\(x,i).(2x + 2),x,1)))
A242429: 1 5 17 53 167 550 1899 6809 25067 93902 355775 1358208 5212573 20082860 77607895 300638481
(2 - ((2 * (if x <= 0 then 0 else (1 + ((1 + loop(\(x,i).(2x + 4),(x + ~1),0)) mod (x + 1))))) div (x + 1)))
A345079: 2 0 0 1 0 2 0 1 1 2 0 2 0 2 2 1
((x + 1) * loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),6,2))
A147574: 510510 1021020 1531530 2042040 2552550 3063060 3573570 4084080 4594590 5105100 5615610 6126120 6636630 7147140 7657650 8168160
((x2 + 3x + 2) * loop(\(x,i).x2,1,loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,1)))
A135389: 2 24 300 3920 52920 731808 10306296 147232800 2127513960 31031617760 456164781072 6749962774464 100445874620000 1502052155856000 22557604697766000 340044833169460800
loop(\(x,i).(x * (2 - (x * (x mod 2)))),((x * (x div 2)) mod 2),loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))
A040026: 1 1 3 1 5 3 7 1 9 5 11 ~3 13 7 15 1
((x + ~1) + (if x <= 0 then 1 else (~1 + loop(\(x,i).((x + 1) + (x div (3 + ((x div 2) div 3)))),x,1))))
A260706: 0 1 3 6 9 12 16 20 25 30 35 40 45 51 57 63
loop(\(x,i).loop(\(x,i).(((x3 + ~3x2 + 2x) div 2) div 3),1,((x2 + ~x) div 2)),1,(x + ~1))
A093566: 0 0 0 0 1 20 120 455 1330 3276 7140 14190 26235 45760 76076 121485
((x + ~1) * (if x <= 0 then 0 else (loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + ~2),(x + ~2)) div 2)))
A002740: 0 0 0 2 15 84 420 1980 9009 40040 175032 755820 3233230 13728792 57946200 243374040
loop(\(x,i).(x * (1 + ((1 + loop(\(x,i).((x2 + x) div 2),2,7)) mod (x + 1)))),x,1)
A106037: 1 2 6 12 60 2520
(((((x + ~1) * loop(\(x,i).3x,(x + ~1),x)) div 2) div 3) + loop(\(x,i).3x,x,1))
A188545: 1 3 10
A081909: 1 3 10 36 135 513 1944 7290 26973 98415 354294 1259712 4428675 15411789 53144100 181752822
loop(\(x,i).x5,1,(12x + loop(\(x,i).3x,x,1)))
A137468: 1 759375 39135393
loop(\(x,i).(x + loop(\(x,i).(7 * ((2x * (~1 + (2 * i))) div (1 + i))),i,1)),x,1)
A112701: 1 8 106 1821 35435 741329 16270997 369570944 8613236374 204812473608 4949266755812 121188396669810 3000342229924222 74979188061284522 1888846103011564082 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(9 * ((2x * (~1 + (2 * i))) div (1 + i))),i,1)),x,1)
A112703: 1 10 172 3817 95671 2575729 72725941 2124619642 63681430672 1947319848190 60511350647386 1905278320822060 60654011063307832 1949006134928921932 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(5 * ((4x * (~1 + (2 * i))) div (1 + i))),i,1)),x,1)
A112704: 1 11 211 5211 145211 4345211 136345211 4426345211 147426345211 5009426345211 172969426345211 6051569426345211 214063569426345211 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((10x + ~1) + (if ((x + 2) mod 6) <= 0 then 0 else 1)),x,1)
A105694: 1 10 99 990 9900 99000 990000 9900000 99000000 990000000 9900000000 99000000000 990000000000 9900000000000 99000000000000 990000000000000
loop(\(x,i).(x + loop(\(x,i).(1 + (x mod (1 + (x mod (1 + (x div (2 + (x div 5)))))))),1,i)),x,1)
A219729: 1 2 3 5 6 8 9 11 14 16 17 20 21 23 26 30
(2 * loop(\(x,i).(10x + 1),x,loop(\(x,i).(10x + 10),x,0)))
A332120: 0 202 22022 2220222 222202222 22222022222 2222220222222 222222202222222 22222222022222222 2222222220222222222 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).(11x + ~5),x,2) + loop(\(x,i).(3x + 1),x,0)) div 2)
A082724: 1 9 93 1005 11001 120849 1328853 14615925 160770801 1768465689 19453083213 213983797245 2353821415401 25892034506529 284812376383173 3132936130648965
(loop(\(x,i).2x,(1 + ((((x - (x mod (~3 + (x mod 2)))) div 2) div 2) + (if x <= 0 then 0 else 1))),1) div 2)
A039593: 1 2 2 4 4 4 4 8 8 8 16 16 16 16 16 32
((~1 + loop(\(x,i).2x,x,(1 + (2 * (1 + loop(\(x,i).(2x + 4),(x + ~1),0) - (x mod 2)))))) div 2)
A267681: 1 0 21 99 471 1935 8031 32319 130431 522495 2094591 8381439 33544191 134189055 536829951 2147368959
((1 + ((1 + loop(\(x,i).2x,(~1 + (2 * (x - (3 * (if x <= 0 then 0 else 2))))),1)) div 3)) div 2)
A107247-A107246: 0 0 0 0 0 0 0 1 2 6 22 86 342 1366 5462 21846
(2 * (1 + (3 * loop(\(x,i).x2,1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))))
A261971: 8 26 98 218 602 866 1538 1946 2906 4706 5402 7778 9602 10586 12698 16226
(2 * (1 + (((x + 1) + (loop(\(x,i).2x,x,(~1 + loop(\(x,i).2x,x,2))) div 3)) div 3)))
A280432: 2 4 10 30 114 454
(3 + (((x + 1) * (1 + (x * loop(\(x,i).(x2 + ~2x),1,loop(\(x,i).2x,x,2))))) div 3))
A245646: 3 9 100 900
(2 + (if x <= 0 then 0 else (1 + ((2 * (1 + (((loop(\(x,i).2x,x,x) mod (x + 1)) div 2) div 2))) div 3))))
A323466: 2 3 3 3 4 4 4 3 4 5 5 4 5 5 5 3
((if x <= 0 then 2 else (1 + ((2 * (if x <= 0 then 1 else (2 * (x mod (~1 + (2 * (x div 4))))))) div 3))) div 2)
A294141: 1 0 0 0 0 0 0 0 1 0 1 1 1 2 3 0
(2 * (1 + (3 * compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(3x + 1))),x))))
A112772: 14 26 38 62 74 86 122 134 146 158 194 206 218 254 278 302
((loop(\(x,i).(2 * (2x - (x div (1 + i)))),(x + ~1),2) + loop(\(x,i).2x,(2x + ~1),1)) div 2)
A114121: 1 2 7 26 99 382 1486 5812 22819 89846 354522 1401292 5546382 21977516 87167164 345994216
(1 - ((1 + ((1 + loop(\(x,i).(if (x mod 2) <= 0 then (~4x + 9) else (x div 2)),x,0)) div 2)) div 2))
A078052: 1 ~2 0 2 2 ~6 ~2 10 6 ~22 ~10 42 22 ~86 ~42 170
((1 + ((1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (1 + ((x + 1) mod 3)))) div 2)) div 2)
A321258: 0 0 1 0 1 1 0 1 1 2 0 1 1 3 1 0
((if x <= 0 then 2 else (1 + ((x mod (1 + (x div (1 + (if (x mod 2) <= 0 then ((x div 2) mod 2) else 3))))) div 2))) div 2)
A029353: 1 0 0 0 1 0 1 0 2 0 1 1 3 0 2 1
((1 + ((1 + (if x <= 0 then 0 else (1 + ((loop(\(x,i).(x - ((~x + (i mod 2)) div 2)),x,1) div 2) div 2)))) div 2)) div 2)
A316076: 0 1 1 1 1 1 1 2 2 3 4 6 8 12 18 26
(if x <= 0 then 1 else (2 * (1 + ((1 + (loop(\(x,i).(x * i),x,(7x + ~3)) div 2)) div 2))))
A309514: 1 4 14 56 302
(x div (3 + ((((1 + (if (x mod 2) <= 0 then 2x else 1)) * (if x <= 0 then 1 else 2)) mod (1 + (x div 2))) div 2)))
A241472: 0 0 0 1 1 1 1 2 1 1 3 2 4 2 3 3
((if x <= 0 then 1 else (~1 + ((loop(\(x,i).2x,(16 mod (x + 1)),1) mod (x + 1)) div 2))) div 2)
A283497: 0 ~1 0 ~1 0 0 0 ~1 0 0 2 0 1 0 0 ~1
(x div (2 * (1 + ((loop(\(x,i).4x,(if (x mod 3) <= 0 then 1 else 0),3) mod (x + 1)) div 2))))
A305629: 0 0 1 1 1 1 1 1 2 2 2 2 0 3 3 1
(2 * (3 + ((5 * (x + loop(\(x,i).(x - (if (~2 + (x div 2)) <= 0 then 0 else 1)),2,x))) div 2)))
A277593: 6 16 26 36 46 56 60 66 76 86 96 106 116 126 136 146
((1 - (if x <= 0 then 0 else (if (x mod 4) <= 0 then (2x2 + 3x + 1) else 0))) mod 10)
A320832: 1 1 1 1 6 1 1 1 8 1 1 1 6 1 1 1
(loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) mod 10)
A137807: 4 9 5 9 1 9 9 1 9 1 1 9 1 9 9 9
(loop(\(x,i).((x + 2) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)),x,2) mod 10)
A096319: 2 5 0 7 8 1 8 7 0 9 0 7 8 1 8 1
(if x <= 0 then 1 else (2 * (3x - ((1 + (if (~2 + (x div 2)) <= 0 then x else (x + 4))) div 3))))
A315326: 1 6 10 16 22 26 30 34 40 46 50 56 62 66 72 78
(~2 + (3 * ((1 + (2 mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1))) * (if x <= 0 then 1 else 2))))
A285052: 1 4 4 4 4 16 4 4 4 16 4 16 4 16 16 4
(~2 + (3 * compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(3x + 1)),x)))
A138685: 13 28 34 43 55 58 67 73 76 88 97 100 103 106 118 133
(loop(\(x,i).(17 * ((if x <= 0 then 1 else 2) * (1 + (x mod 2)))),1,(x mod 3)) div 2)
A091720: 8 34 17 8 34 17 8 34 17 8 34 17 8 34 17 8
(((if (x mod 2) <= 0 then 6 else ~4) + loop(\(x,i).5x,x,3)) div 2)
A189744: 4 5 40 185 940 4685 23440 117185 585940 2929685 14648440 73242185 366210940 1831054685 9155273440 45776367185
(loop(\(x,i).(x div 2),(x mod 2),(if (x mod 7) <= 0 then (5x + 2) else 1)) div 2)
A340982: 1 0 0 0 0 0 0 9 0 0 0 0 0 0 36 0
(1 - ((1 + (if (2x mod (4 + (x div 4))) <= 0 then 0 else (if (x + ~3) <= 0 then x else 2))) div 2))
A127253-A117945: 1 0 1 ~1 0 1 0 0 0 1 0 0 0 0 1 0
((1 + ((x + (((x + 1) + loop(\(x,i).x2,1,loop(\(x,i).((x + ~1) - (x * i)),x,2))) div 2)) div 2)) div 2)
A231074: 1 1 1 1 2 12 244
(2 * (1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,8x)),x))))
A186296: 2 6 10 22 30 34 42 54 66 70 82 90 106 114 126 142
(if (~1 + (x div 2)) <= 0 then loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) else (4x + ~2))
A089410: 1 1 2 5 14 18 22 26 30 34 38 42 46 50 54 58
loop(\(x,i).(if x <= 0 then 1 else (4x + 8)),1,((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2))
A174096: 1 1 1 1 12 1 1 12 12 1 1 12 16 12 1 1
(if x <= 0 then 1 else loop(\(x,i).2x,(1 + ((1 + (8 mod (1 + (x div 2)))) div 2) - (x mod 2)),2))
A267584: 1 2 4 2 8 4 4 2 16 8 8 4 8 4 4 2
(2 * (1 + loop(\(x,i).(x + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(1 + (2 * i)),1)),x,2)))
A066797: 6 76 1000 13870 198626 2902782 43019382 644099772 9719235072 147565763892 2251664727612 34499268410712 530417801358816 8179108402119256 126443689966980680 1959067830909571214
(if x <= 0 then 1 else (2 * loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(x + ~1),(3x + ~1))))
A028283: 1 4 10 32 110 392 1428 5280 19734 74360 281996 1074944 4115020 15808912 60917800 235350720
(2 * (1 + compr(\x.(2 - ((~1 + loop(\(x,i).2x,loop(\(x,i).(x div (1 + (x mod 2))),x,x),2)) mod (x + 1))),x)))
A076771: 18 24 30 36 40 42 48 50 54 56 60 66 70 72 78 80
(2 * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,(loop(\(x,i).(2 * (x - i)),x,2) mod (x + 1))) mod (x + 1)),x)))
A062091: 2 4 6 10 14 18 22 26 34 38 46 50 58 62 74 82
(2 * (loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,(x + 2)) - loop(\(x,i).4x,x,1)))
A065982: 2 10 48 222 1000 4420 19264 83062 355128 1508028 6368032 26765420 112053968 467531272 1945009408 8070882982
(2 * (1 + compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,10x)),x)))
A309374: 2 4 6 10 12
A107304: 2 4 6 10 12 16 18 22 24 34 36 40 46 48 54 58
(((x + 1) * (loop(\(x,i).2x,x,1) - loop(\(x,i).((x * (1 + i)) div (1 + (i div 2))),(x + ~1),1))) div 2)
A130783: 0 1 3 10 25 66 154 372 837 1930 4246 9516 20618 45332 97140 210664
(if ((x + ~1) mod 3) <= 0 then 1 else ((x + 2) div (2 + (loop(\(x,i).x3,2,2x) mod (x + 1)))))
A331738: 1 1 1 2 1 1 1 1 3 1 1 2 1 1 1 8
((loop(\(x,i).11x,x,1) + loop(\(x,i).7x,x,1)) div 2)
A152106: 1 9 85 837 8521 88929 944605 10155357 110061841 1199150649 13109949925 143644498677 1576134831961 17309800577169 190214028328045 2090997865462797
(2 * (1 + compr(\x.((x2 + 2x + 1) mod loop(\(x,i).(1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),2,x)),x)))
A066192: 4 8 12 16 24 32 48 56 64 96 112 120 128 192 224 240
(((~1 + (6 * (1 + loop(\(x,i).(x + (if (i mod (2 + (x mod 2))) <= 0 then 1 else x)),x,0)))) div 2) div 2)
A128216: 1 1 2 4 5 10 11 22 23 25 26 52 53 106 107 109
((loop(\(x,i).x2,1,((x + 1) + ((if ((x div 2) mod 3) <= 0 then 0 else 1) + (x div 3)))) div 2) div 2)
A010386: 0 1 4 9 12 16
A210607: 0 1 4 9 12 16 20 25 36
(4 * (1 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1))))
A111046: 16 24 48 72 120 168 240 288 408 432 552 600 720 768 792 912
(if x <= 0 then 1 else (2 * ((if x <= 0 then 2 else (1 + (((1 - (2x div 3)) mod (1 + (x div 2))) div 2))) div 2)))
A028621: 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 4
(4 * (1 + compr(\x.(~1 + (loop(\(x,i).2x,x,2) mod (1 + (if (~1 + (x mod 3)) <= 0 then x else 2)))),x)))
A335668: 4 8 16 24 32 48 64 72 96 120 128 144 168 192 216 240
(2 * ((loop(\(x,i).8x,x,(~1 + loop(\(x,i).2x,(x * (x mod 2)),2))) mod (x + 1)) div 2))
A074037: 0 0 0 0 0 0 0 0 0 4 0 0 0 10 4 0
(4 + ((x + 1) * ((x + ~1) + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 2)))))
A088482: 5 4 10 4 9 4 25 4 13 4 26 4 17 4 64 4
((x mod (2 + ((loop(\(x,i).2x,(x mod 8),1) + loop(\(x,i).2x,x,1)) mod (x + 1)))) div 2)
A343220: 0 0 1 0 0 2 1 0 0 1 1 2 0 2 2 0
(4 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 4x))),(x + 1)))
A046132: 7 11 17 23 41 47 71 83 101 107 113 131 167 197 227 233
(2 * (2 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 4x))),(x + 1))))
A167607: 10 18 30 42 78 90 138 162 198 210 222 258 330 390 450 462
(4 + compr(\x.(1 - loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),(x div 2),(x2 + 4x))),(x + 1)))
A031505: 11 17 23 41 47 71 83 101 107 113 131 167 197 227 233 281
((2 + compr(\x.(1 - loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),(x div 2),(x2 + 4x))),(x + 1))) div 2)
A111981: 4 7 10 19 22 34 40 49 52 55 64 82 97 112 115 139
(if x <= 0 then 1 else (7 + (((x + 1) * (1 + loop(\(x,i).2x,x,3))) div 3)))
A076851: 1 11 20 40 88
(((loop(\(x,i).x2,1,(1 + loop(\(x,i).(2 * ((5x + 1) + i)),x,2))) div 2) div 2) div 2)
A077694: 1 78 7626 761995 76205685 7620753696 762078456028 76207888812681 7620789436823655 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((2 + (loop(\(x,i).((~2x + ~5) + loop(\(x,i).4x,x,1)),x,1) div 2)) div 2)
A048831: 1 0 1 2 4092
(x div (1 + ((if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1) + ((((x + 1) div 2) div 2) div 2))))
A334203: 0 0 0 1 0 2 0 2 2 3 0 3 0 4 3 3
(8 * (3 + loop(\(x,i).2x,x,(1 + (2 * (4 + loop(\(x,i).2x,x,1)))))))
A235887: 112 232 568 1624 5272 18712 70168 271384 1067032 4231192 16850968 67256344 268730392 1074331672 4296146968 17182228504
(16 + loop(\(x,i).x2,2,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A287925: 32 97 641 2417 14657 28577 83537 130337 279857 707297 923537 1874177 2825777 3418817 4879697 7890497
((((x + 4) * loop(\(x,i).x2,1,loop(\(x,i).(x + (((2 + i) * (1 + i)) div 2)),x,1))) div 2) div 2)
A108647: 1 20 150 700 2450 7056 17640 39600 81675 157300 286286 496860 828100 1332800 2080800 3162816
((x + 1) div (if (x mod 2) <= 0 then 1 else (loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) + (2 * (x div 4)))))
A059806: 1 2 3 4 5 1 7 2 9 1 11 1 13 1 15 2
((2 + (((x + 2) + (loop(\(x,i).2x,x,(1 + (if (x mod 3) <= 0 then x else 0))) mod (x + 1))) div 2)) div 2)
A045864: 1 1 2 2 2 3 3 3 4 3 4 6 4 5 6 5
((loop(\(x,i).(x * ((x + 1) - i)),2,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 2)
A138420: 3 18 150 588 3630 7098 20808 32490 69828 176610 230640 468198 706020 854238 1219368 1971918
((2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)) * loop(\(x,i).2x3,2,4))
A175753: 12582912 20971520 29360128 46137344 54525952 71303168 79691776 96468992 121634816 130023424 155189248 171966464 180355072 197132288 222298112 247463936
(1 + ((if x <= 0 then 0 else (if (x mod (1 + (x mod 6))) <= 0 then 2 else 1)) + (x mod 2) + (x div 4)))
A061266: 1 3 2 3 3 4 4 4 4 5 5 5 6 6 5 6
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) * (loop(\(x,i).(3x + ~1),x,2) div 2))
A185010: 1 2 14 100 854 7644 72204 703560 7037030 71772844 743844452 7810307960 82909630972 888316731800 9593823377880 104332819539600
(2 * loop(\(x,i).(10x + 1),x,loop(\(x,i).(10x + ~8),x,2)))
A332124: 4 242 22422 2224222 222242222 22222422222 2222224222222 222222242222222 22222222422222222 2222222224222222222 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(((x + 2) + ((((if x <= 0 then 2 else (1 + loop(\(x,i).(x * (x + i)),2,3))) mod (x + 2)) div 2) div 2)) div 2)
A037458: 1 1 2 3 3 3 4 5 6 6 6 6 7 8 9 10
(loop(\(x,i).(10x + 2),x,2) * (2 + loop(\(x,i).10x,x,2)))
A332148: 8 484 44844 4448444 444484444 44444844444 4444448444444 444444484444444 44444444844444444 4444444448444444444 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x4 + ~x3),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A138423: 4 27 250 1029 6655 13182 39304 61731 133837 341446 446865 911754 1378420 1669647 2387929 3870802
(loop(\(x,i).((x + ~2) * (x2 div 2)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A078837: 0 2 18 60 270 462 1080 1530 2772 5670 6960 11970 16380 18942 24840 35802
(loop(\(x,i).(3x2 + ~x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A116995: 5 12 35 70 176 247 425 532 782 1247 1426 2035 2501 2752 3290 4187
(loop(\(x,i).(x4 + ~x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A138417: 7 39 310 1197 7315 14274 41752 65151 139909 353626 461745 937062 1412860 1709379 2439817 3945214
(loop(\(x,i).(x3 + 3x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A179546: 10 27 100 245 847 1352 2890 3971 6877 13456 16337 27380 36982 42527 55225 78652
(x + ((((if (~2 + (x div 3)) <= 0 then 2 else (x div 2)) mod (x + 1)) div 2) + (if x <= 0 then 1 else 4x)))
A314111: 1 5 11 16 21 26 31 36 41 47 52 57 63 68 73 78
(2 * (if x <= 0 then 2 else ((x + 1) mod ((if ((x mod 7) mod 3) <= 0 then 1 else 2) + (x mod 2)))))
A058888: 4 4 2 0 2 0 0 0 2 2 0 0 2 0 0 2
(2 * (loop(\(x,i).2x,x,1) - loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x div 2),(x mod 2))))
A202736: 2 2 8 10 32 44 128 186 512 772 2048 3172 8192 12952 32768 52666
(if (x mod 4) <= 0 then (29 * (if x <= 0 then 1 else 2)) else (2 + (x mod 2)))
A040828: 29 3 2 3 58 3 2 3 58 3 2 3 58 3 2 3
(2 + compr(\x.(~1 + ((1 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x)) mod 3)),x))
A171820: 2 4 6 8 11 12 14 18 19 21 22 25 27 29 31 34
(2 + loop(\(x,i).compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),1,(x + (x div 9))))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A102348: 2 3 5 7 11 13 17 19 23 31 37 41 43 47 53 59
(2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(5x + ~1))),x))
A024894: 2 6 8 12 14 20 26 30 36 38 42 48 50 54 56 62
(2 * loop(\(x,i).x2,1,(x + (if (x + ~1) <= 0 then 1 else ((x div 2) - (((x + ~1) div 5) mod 2))))))
A050804: 2 8 18 32 72 98 128 162 242 288 392 512 648 722 882 968
(2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(5x + ~2))),x))
A153355: 4 6 12 16 18 22 28 30 36 40 46 48 54 70 72 76
(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,(x + 3)) - loop(\(x,i).4x,x,2))
A194460: 1 4 18 82 370 1648 7252 31582 136338 584248 2488156 10540484 44450068 186715072 781628008 3262239862
(2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(5x + 2))),x))
A111224: 0 2 6 8 12 18 20 24 26 30 32 38 44 50 54 60
(loop(\(x,i).(10x + 1),2x,1) + loop(\(x,i).10x,x,2))
A332113: 3 131 11311 1113111 111131111 11111311111 1111113111111 111111131111111 11111111311111111 1111111113111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((2x + 4) + (if (x div 4) <= 0 then 1 else ((1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2))) div 2)))
A026282: 5 7 9 11 14 17 20 23 25 28 30 33 35 38 40 43
(2 + compr(\x.((~1 + loop(\(x,i).2x,x,(if (x mod 13) <= 0 then 1 else 2))) mod (x + 2)),x))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A256484-A238242: 2 3 5 7 11 13 17 19 23 29 31 37 43 47 53 59
(2 + compr(\x.((~1 + loop(\(x,i).2x,x,(if (x mod 11) <= 0 then 1 else 2))) mod (x + 2)),x))
A322477-A076805: 2 3 5 7 11 17 19 23 29 31 37 41 43 47 53 59
loop(\(x,i).((2x * (1 + (2 * i))) div (1 + i)),compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),2)
A136268: 2 6 70 924 184756 2704156 601080390 9075135300 2104098963720 7648690600760440 118264581564861424 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x3 + 3x2 + x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A098996: 30 84 330 840 3036 4914 10710 14820 25944 51330 62496 105450 142926 164604 214320 306234
(loop(\(x,i).5x,(x + 1),1) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A297967: 1 1 0 2 1 12 10 4 11 20 25 10 39 36 41 13
loop(\(x,i).(x5 + ~x4),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A138407: 16 162 2500 14406 146410 342732 1336336 2345778 6156502 19803868 27705630 67469796 113030440 143589642 224465326 410305012
loop(\(x,i).(x5 + ~x3),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A138406: 24 216 3000 16464 159720 369096 1414944 2469240 6424176 20486760 28599360 69293304 115787280 146928936 229241184 418046616
loop(\(x,i).(x + ((x div 2) div 5)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A031216: 2 3 5 7 12 14 18 20 25 31 34 40 45 47 51 58
loop(\(x,i).(x5 + ~x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A138404: 30 240 3120 16800 161040 371280 1419840 2476080 6436320 20511120 28629120 69343920 115856160 147008400 229344960 418195440
loop(\(x,i).(x + (x mod 10)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A268185: 4 6 10 14 12 16 24 28 26 38 32 44 42 46 54 56
loop(\(x,i).(x * (x mod 10)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A063482: 4 9 25 49 11 39 119 171 69 261 31 259 41 129 329 159
loop(\(x,i).(x5 + ~x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A138405: 28 234 3100 16758 160930 371124 1419568 2475738 6435814 20510308 28628190 69342588 115854520 147006594 229342798 418192684
loop(\(x,i).(x2 + (x2 div 4)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A246010: 5 11 31 61 151 211 361 451 661 1051 1201 1711 2101 2311 2761 3511
loop(\(x,i).x6,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A092758: 64 729 15625 117649 1771561 4826809 24137569 47045881 148035889
A030516: 64 729 15625 117649 1771561 4826809 24137569 47045881 148035889 594823321 887503681 2565726409 4750104241 6321363049 10779215329 22164361129
compr(\x.((x div 2) - (if (x mod 2) <= 0 then x else 4)),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A105930: 2 3 5 7 12 16 24 28 36 48 52 64 72 76 84 96
((loop(\(x,i).(4x - (x div 2)),x,1) + loop(\(x,i).(2x + 2),x,1)) div (x2 + 2x + 2))
A185178: 1 1 2 4 8 18
A338729: 1 1 2 4 8 18 45 119
compr(\x.(~1 + (x mod (1 + (((x + ~2) + loop(\(x,i).(2 + (if (~x + i) <= 0 then 0 else x)),x,1)) mod (x + 1))))),(x + 2))
A258159: 3 5 7 9 15 17 19 21 31 33 63 65 67 71 73 85
((3x + 1) - (if (x + ~1) <= 0 then x else (1 + ((1 + (8 mod (if x <= 0 then 1 else x))) mod 2))))
A097911: 1 3 5 8
A022433: 1 3 5 8 11 15 17 21 23 26 29 32 35 38 41 44
((3x + 1) + (2 * loop(\(x,i).(2x + ~2),x,(~1 + loop(\(x,i).4x,x,4)))))
A290756: 7 60 499 4062 32689 261972 2096791 16776474 134216221 1073738784 8589928483 68719464486 549755789353 4398046461996 35184371990575 281474976514098
(loop(\(x,i).(x + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),i,1)),((x + 1) div 2),1) - (x mod 2))
A276032: 1 2 3 7 8 21 22 63 64 195 196 624 625 2054 2055 6916
(if (((~1 + loop(\(x,i).4x,x,2)) mod 19) mod 2) <= 0 then 2 else (x mod 2))
A287528: 0 1 2 1 0 2 2 1 0 1 0 2 0 1 2 2
(2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,7x)),x))
A089033: 0 2 4 8 10 14 22 28 32 34 38 40 44 50 52 58
(2 + compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x2 + 3x))),x))
A073338: 2 3 4 9 10 12 15 18 22 30 31 36 37 39 40 46
(2 + compr(\x.(1 - loop(\(x,i).(x - (loop(\(x,i).((x2 + x) div 2),2,3x) mod (x + 1))),x,x)),x))
A275340: 4 7 10 11 13 16 19 21 22 25 28 29 31 34 37 40
(0 - (if x <= 0 then 1 else (if (~x + 2) <= 0 then (1 - (2 * ((x mod (1 + (((x + 1) div 2) div 2))) mod 2))) else 0)))
A134323: ~1 0 ~1 1 ~1 1 ~1 1 ~1 ~1 1 1 ~1 1 ~1 ~1
((x + 1) + loop(\(x,i).(x + (if x <= 0 then 1 else (i - ((x2 mod (x - ((~x + 2) div 2))) div (x + 1))))),x,0))
A061791: 1 3 6 10 15 21 28 36 45 55 66 77 90 104 119 134
(x + loop(\(x,i).((x + 1) + (if ((x div 2) mod 3) <= 0 then 2 else 1) - (x mod 2)),((x + 1) div 3),1))
A187578: 1 2 5 6 7 9 10 11 14 15 16 20 21 22 24 25
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(12x + 1))),x)
A139527: 0 1 2 4 6 7 8 11 12 13 16 19 21 23 27 28
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(9x + ~1))),x)
A111094: 1 2 4 6 7 9 10 11 15 17 21 22 24 27 29 30
(1 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + (if (~2 + (x div 5)) <= 0 then 1 else x)))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A154363: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 67
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(16x + ~1))),x)
A133869: 3 6 8 11 14 18 20 21 24 29 36 38 39 44 50 53
(if x <= 0 then 1 else loop(\(x,i).x6,1,(11x + 5)))
A177081: 1 16777216 387420489
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x + ((x div 2) div 5)))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A100370-A095323: 2 3 5 7 11 13 17 19 23 29 37 41 43 47 53 59
((x + 1) + (2 * loop(\(x,i).(9 * (if x <= 0 then 1 else (2 + (x mod 2)))),(x div 2),(x mod 2))))
A135559: 1 4 21 58 59 60 61 62 63 64 65 66 67 68 69 70
((x + 1) + ((loop(\(x,i).(x + (if ((x + 1) mod 10) <= 0 then (x + 2) else 1)),x,x) div 2) div 2))
A082741: 1 2 4 5 7 11 12 14 15 17 21 22 24 25 27 41
compr(\x.((1 + loop(\(x,i).(x div (2 - (x mod 2))),x,(x div (1 + (if (x mod 3) <= 0 then 2 else 0))))) mod 3),x)
A225838: 5 10 11 15 17 20 22 23 29 30 33 34 35 40 41 44
(x + (3 * (if ((1 + (x div 3)) mod 3) <= 0 then (if (x div 4) <= 0 then 2 else ~2) else 1)))
A154660: 3 4 5 6 7 8
A004492: 3 4 5 6 7 8 0 1 2 12 13 14 15 16 17 9
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x + (((x + 1) div 2) div 3)))
A042988: 2 3 5 7 11 17 19 23 29 31 37 43 47 53 59 61
(~x + (if x <= 0 then 1 else (3 * (2 + (loop(\(x,i).(2 * (x - (x div ~7))),x,1) div 2)))))
A076853: 1 11 19 39 86
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(7x + ~2))),x)
A138622: 1 3 6 7 10 12 13 16 18 21 22 25 30 31 33 36
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(10x + ~1))),x)
A124204: 2 3 5 9 12 14 20 21 23 26 27 30 32 33 35 38
((~2x2 + ~x) + loop(\(x,i).(x + i),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),0))
A161626: 3 3 5 7 30 36 75 85 140 264 286 450 561 595 722 966
((~x + 1) + (loop(\(x,i).(x - (if x <= 0 then 0 else (~1 + (2 * (((1 + (x div 2)) div 2) mod 2))))),2,x) + (x mod 2)))
A072175: 1 2 1 0 ~1 0 3 4 3 2 1 0 ~1 0 3 4
loop(\(x,i).loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,(x + 1)),1,(x3 + x2 + x))
A101355: 1 56 145422675 4611686018427387903 4611686018427387903
compr(\x.(2 - ((0 - loop(\(x,i).2x,x,(if (x mod (2 + ((~x + 1) mod 3))) <= 0 then 1 else 0))) mod (x + 1))),x)
A275722: 4 6 8 9 10 12 16 18 20 21 22 24 27 28 30 32
((x3 + x2 + ~1) + (loop(\(x,i).(2x + 2),x,2) * (if (x + ~1) <= 0 then 3 else 0)))
A106229: 5 19 11 35 79 149 251 391 575 809 1099 1451 1871 2365 2939 3599
compr(\x.(1 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(8x2 + 8x))),x)
A123986: 1 4 7 10 25 34 37 49 67 70 115 130 142 154 160 202
(x + loop(\(x,i).(x + loop(\(x,i).(((1 + (8 mod (1 + (x div 2)))) div 2) - (x mod 2)),1,i)),x,1))
A059015: 1 1 2 2 4 5 6 6 9 11 13 14 16 17 18 18
loop(\(x,i).(x div 2),(x mod 2),loop(\(x,i).i,((x + 1) mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4)))))),x))
A239062: 1 1 1 2 1 1 1 3 3 1 1 2 1 1 1 7
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(12x + 2))),x)
A139483: 0 1 3 4 5 6 8 9 11 15 18 19 20 25 26 30
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(12x + ~2))),x)
A131210: 1 2 3 7 8 10 11 13 15 16 18 20 21 25 27 30
(x + ((1 + loop(\(x,i).(x + (2x div 7)),2,(if x <= 0 then 1 else 4x))) div 2))
A058759: 1 4 8 13
A311817: 1 4 8 13 17 21 25 30 34 39 43 47 51 55 60 65
compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(12x + 8))),x)
A192225: 0 1 2 5
A139532: 0 1 2 5 6 8 11 12 13 15 20 21 22 23 25 26
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x + (x div (4 + (x div 2)))))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A316787: 2 3 5 7 11 13 17 23 29 31 37 41 43 47 53 59
(x + (if x <= 0 then 1 else (2 * (2x + ((2 * ((x + (if (~2 + (x div 2)) <= 0 then 1 else 0)) div 2)) div 3)))))
A313982: 1 5 10 17 22 29 34 39 44 49 56 61 68 73 78 83
compr(\x.((loop(\(x,i).(1 + ((x + 1) * i)),(2 * (if (~2 + (x div 3)) <= 0 then 0 else 2)),1) - (x div 2)) div 2),x)
A004881: 0 1 2 3 4 5 6 7 8 256 257 258 259 260 261 262
((2x + 2) + (loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,3) div 5))
A003041: 2 7 24 92 388
(x + ((3 + loop(\(x,i).2x,x,1) - loop(\(x,i).3x,x,1)) mod (3x + 2)))
A066494: 1 3 8 9 12 18 24
(compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A255311-A001223: 1 2 2 4 2 4 2 4 6 2 6 4 2 4 6 6
(compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A033957-A031131: 3 4 6 6 6 6 6 10 8 8 10 6 6 10 12 8
(~x2 + loop(\(x,i).x2,1,((~2 - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) div 2)))
A163637: 1 3 5 7 20 24 45 51 80 144 156 240 297 315 380 504
(if (x mod 2) <= 0 then (1 + ((1 + ((x + (((~1 + (2 * (x mod 4))) * (x div 2)) div 2)) div 2)) div 2)) else 0)
A167156: 1 0 2 0 2 0 4 0 3 0 5 0 3 0 7 0
((((1 + (x mod (1 + (31 mod (x + 1))))) div 2) div 2) + (if x <= 0 then 0 else 1))
A321271-A305193: 0 1 1 2 1 1 1 3 2 1 1 2 1 1 1 5
(x + ((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)))
A222312: 0 2 3 5 5 7 7 10 10 11 11 14 13 15 16 19
(~1 + ((1 + (x div 3)) mod (1 + (if ((2x + 4) mod (4 + (x div 4))) <= 0 then 2 else 0))))
A080301: 0 ~1 0 ~1 ~1 ~1 ~1 ~1 ~1 ~1 0 ~1 1 ~1 ~1 ~1
(1 + (if x <= 0 then 0 else (1 + (((x2 + 2x) div 2) mod (1 + (x mod (1 + (((x + 1) div 2) div 3))))))))
A010553: 1 2 2 2 2 3 2 3 2 3 2 4 2 3 3 2
(1 + (x mod (1 + (x mod ((x + 1) - (compr(\x.(loop(\(x,i).(2x + 1),x,0) mod (x + 1)),x) mod (x + 1)))))))
A084309: 1 2 1 2 5 6 1 2 1 2 1 12 1 14 1 4
(1 + (x mod (1 + (if x <= 0 then 0 else (1 + (2 * (((2x + 2) * (x mod 2)) mod 7)))))))
A281071: 1 2 1 4 1 6 1 2 1 10 1 4 1 2 1 6
((x + 1) - loop(\(x,i).x2,1,(1 + (x mod (1 + (x mod (1 + (x div (2 + (x div 5))))))))))
A139716: 0 1 2 0 4 2 6 4 0 6 10 3 12 10 6 0
loop(\(x,i).2x,(~1 + (x mod (~1 + (2 * ((x * ((x + 1) mod 5)) div 8))))),1)
A300138: 1 1 1 1 1 1 1 1 1 1 1 2 16 2 1 1
(~1 + loop(\(x,i).2x2,1,(72x + 55)))
A157267: 6049 32257 79201 146881 235297 344449 474337 624961 796321 988417 1201249 1434817 1689121 1964161 2259937 2576449
(1 + (if x <= 0 then 0 else (1 + (((1 - ((x mod 3) + (2 * (x mod 2)))) mod (2x + ~1)) div 3))))
A344025-A329381-A329353-A329351-A328767-A328315-A327970-A327931-A320014-A319709-A319693-A319682-A319348-A317943-A305895-A305800-A305793-A300835-A300833-A300249-A300245-A300243-A300241-A300235-A300233-A300232-A300231-A296073-A293232-A293226-A293217-A293215: 1 2 2 3 2 4 2 5 6 7 2 8 2 9 10 11
(1 + (x mod (1 + ((x2 + 2x) mod (3 * (if (16 mod (x + 1)) <= 0 then 1 else 2))))))
A324284: 1 1 3 1 1 6 1 1 3 2 1 6 1 2 3 1
(x div (1 + (x mod (1 + (loop(\(x,i).4x,((x - (x div 4)) div 2),2) mod (2x + 1))))))
A249421: 0 0 0 1 0 0 0 0 0 0 5 2 0 0 0 2
(1 + (x mod (1 + (loop(\(x,i).(2x + 1),x,54) mod (x + 1)))))
A343430-A247503: 1 2 1 4 5 2 1 8 1 10 11 4 1 2 5 16
(1 + ((x2 + 2x) div (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))))))
A253560: 1 4 9 8 25 18 49 16 27 50 121 36 169 98 75 32
loop(\(x,i).x2,1,(1 + (x div (1 + (2 * (1 + (((x2 + ~x + 2) mod (x + 4)) div 2)))))))
A246595: 1 1 1 4 1 1 4 9 1 1 1 4 4 4 9 16
(1 + (if x <= 0 then 0 else (1 + (((2 + ((x + 2) mod (2 * (2 + ((x div 4) mod 2))))) div 3) mod 2))))
A264843: 1 3 2 3 2 3 3 3 3 3 2 3 3 3 2 2
((x + 1) - ((2x + 1) div (3 + (if (((x + 2) mod 8) mod 3) <= 0 then 0 else 2))))
A026242: 1 1 2 3 2 4 3 5 6 4 7 8 5 9 6 10
((1 + (x div 4)) div (1 + (if x <= 0 then 0 else (1 + ((((~x + 2) mod 7) div 2) mod 2)))))
A029346: 1 0 0 0 1 1 0 0 1 1 1 1 2 1 1 2
(1 + (if x <= 0 then 0 else (1 + (((1 + (((x + 1) * (1 + ((x + ~1) div 5))) div 2)) div 2) div 2))))
A085003: 1 2 2 2 2 3 4 4 4 4 5 6 7 7 7 8
(1 + (if x <= 0 then 0 else (1 + (((2 + ((2 * (1 + (8 * (x mod 2)))) mod (x + 1))) div 2) div 2))))
A084966: 1 2 3 3 3 2 3 3 3 4 3 4 3 3 3 3
loop(\(x,i).x2,1,(1 + (x mod (~1 + (2 * ((x * ((x + 1) mod 5)) div 8))))))
A174126: 1 1 1 1 1 1 1 4 4 1 1 9 36 9 1 1
(1 + (9 * loop(\(x,i).(10x + 2),(x div 2),(1 + (x mod 2)))))
A070199: 10 19 109 199 1099 1999 10999 19999 109999 199999 1099999 1999999 10999999 19999999 109999999 199999999
loop(\(x,i).17x,x,(1 + (x mod (1 + ((x2 + 2x) mod 8)))))
A156531: 1 34 289 19652 83521 2839714 24137569 3282709384 6975757441 237175752994 2015993900449 137087585230532 582622237229761 19809156065811874 168377826559400929 4611686018427387903
(loop(\(x,i).6x,x,1) mod 151)
A036148: 1 6 36 65 88 75 148 133 43 107 38 77 9 54 22 132
(1 + (loop(\(x,i).((x + 1) + ((x - ((x + (x div 3)) div 3)) div 2)),x,1) div 5))
A240735: 1 1 1 2 2 3 4 5 6 8 10 13 17 21 27 35
(~1 + (10 * (1 + (2 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))))
A137558: 49 69 109 149 229 269 349 389 469 589 629 749 829 869 949 1069
(1 + (((3 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 5))
A227683: 1 1 2 3 4 4 6 6 7 9 10 12 13 13 15 16
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 29)
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A242127: 2 3 5 7 11 13 17 19 23 0 2 8 12 14 18 24
loop(\(x,i).2x,((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 5),1)
A209543: 1 1 1 1 1 1 1 2 2 1 1 4 16 4 1 1
(1 + ((if x <= 0 then 1 else (~2 + (2 * ((x + ~1) mod (6 + (x div 4)))))) mod 3))
A026146: 2 2 1 3 2 1 3 2 1 2 1 3 3 2 1 3
(1 + (3 * (1 + (3 * loop(\(x,i).(10x + 4),(x div 2),(x mod 2))))))
A094628: 4 13 40 130 400 1300 4000 13000 40000 130000 400000 1300000 4000000 13000000 40000000 130000000
((2x + ~1) mod (1 + ((1 + ((2 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 3)) mod 3)))
A035168: 1 1 0 1 0 0 0 1 1 0 1 0 2 0 0 1
(~1 + ((1 + ((if (~1 + (2x mod (4 + (x div 2)))) <= 0 then 1 else 0) * (1 + (x div 2)))) mod 3))
A307424: 1 0 0 ~1 0 0 0 1 ~1 0 0 0 0 0 0 0
(~1 + ((1 + ((x + 1) div (2 + ((x + 1) div (1 + (if (x mod 5) <= 0 then 0 else 2)))))) mod 3))
A332828: 0 1 1 1 1 0 1 ~1 1 ~1 0 ~1 ~1 ~1 ~1 0
(1 + (loop(\(x,i).3x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1) div 3))
A079314: 1 2 2 4 2 4 4 10 2 4 4 10 4 10 10 28
(1 + (((x + 1) * (if x <= 0 then 1 else ((x + ~1) + ((1 + (x mod 5)) * (x mod 2))))) mod 3))
A286634: 2 2 1 1 1 1 3 1 1 2 1 1 3 3 1 1
loop(\(x,i).(2x + 1),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A136126: 1 1 1 1 3 1 1 7 7 1 1 15 31 15 1 1
loop(\(x,i).((x + 1) + i),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A299146: 1 1 1 1 3 1 1 6 6 1 1 10 15 10 1 1
loop(\(x,i).(2x + 4),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A152602: 1 1 1 1 6 1 1 16 16 1 1 36 76 36 1 1
loop(\(x,i).4x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A118185: 1 1 1 1 4 1 1 16 16 1 1 64 256 64 1 1
loop(\(x,i).x2,1,(1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))
A082043: 1 1 1 1 4 1 1 9 9 1 1 16 25 16 1 1
loop(\(x,i).3x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A118180: 1 1 1 1 3 1 1 9 9 1 1 27 81 27 1 1
loop(\(x,i).(x + (2 * i)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A082039: 1 1 1 1 3 1 1 7 7 1 1 13 21 13 1 1
loop(\(x,i).(2x + i),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A157210: 1 1 1 1 3 1 1 8 8 1 1 19 42 19 1 1
(1 + ((loop(\(x,i).((x + 2) + (((x div 2) div 3) + (x div 5))),x,0) div 2) div 3))
A173508: 1 1 1 2 2 3 4 6 8 11 15 20 28 38 52 71
(if x <= 0 then 0 else (1 + ((2 * (1 + ((x div 4) div (1 + (x mod (2 * (1 + (x mod 2)))))))) div 3)))
A238845: 0 1 1 1 2 1 2 1 3 2 3 1 3 2 3 1
(~1 + ((2 * (1 + ((1 + (if (((x + 1) div (2 + (x mod 2))) mod 2) <= 0 then x else 1)) div 3))) mod 3))
A323378: 1 1 1 1 0 ~1 1 ~1 1 1 1 0 0 0 1 1
(if x <= 0 then 0 else (1 + ((2 * (1 + ((((x + 1) mod 6) + (x div 2)) div 3))) div 3)))
A200747: 0 1 2 2 3 1 2 2 3 3 3 2 3 3 3 3
(~1 + (loop(\(x,i).(5x + 1),(x + 1),(8x + 6)) div 3))
A022607: 9 117 926
(1 + ((2 * (1 + loop(\(x,i).(x - (x div ~5)),x,10))) div 3))
A120176: 8 9 11 13 16 19 23 28 33 40 48 57 69 83 99 119
(1 + (6 * (1 + (4 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))))
A135984: 55 79 127 175 271 319 415 463 559 703 751 895 991 1039 1135 1279
(~1 + (18 * ((x + ~1) + loop(\(x,i).(x - ((~2 + (x div 2)) div 3)),2,x))))
A044500: 17 53 89 107 125 161 197 233 269 305 323 341 377 413 449 485
(1 + ((2 * (2 + ((1 - (loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 3)) mod (x + 1)))) mod 3))
A064693: 2 1 1 1 2 1 2 1 3 2 2 1 1 1 2 1
(~1 + ((2 * (2 + ((x - (2 * (if (~2 + (x div 3)) <= 0 then 2 else (x + ~2)))) mod (x + 1)))) div 3))
A316827: 0 1 1 2 0 1 1 2 3 3 3 3 3 3 3 3
(1 + ((2 * ((2x + 2) + (x div (1 + (2 * (if (~4 + (x div 2)) <= 0 then 2 else 1)))))) div 3))
A114148: 2 3 5 6 7 9 11 12 13 15 17 19 21 22 23 25
(1 + ((2 * (4 + (if x <= 0 then 1 else (x - (2 * ((x div 5) div ~2)))))) div 3))
A257291: 4 4 5 5 6 8 9 9 10 11 11 12 13 13 14 16
(13 * loop(\(x,i).7x,7x,1))
A324270: 13 10706059 8816899947037 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((2 + (loop(\(x,i).21x,x,x) div 2)) mod 13)
A113491: 2 12 1 9 4
(11 * (1 + compr(\x.(loop(\(x,i).(2x3 + 2x2),2,2) mod (x + 1)),x)))
A070022: 11 22 33 44 55 66 88 99 110 132 165 176 198 220 264 275
(1 + ((2 * ((x + 2) + (if x <= 0 then 1 else (4x - (((1 + (x div 2)) div 2) div 2))))) div 3))
A191403: 3 5 9 12 15 19 21 25 28 31 35 38 41 45 47 51
(1 + ((2 * (x + ((2 * (x + loop(\(x,i).2x,((x + ~2) div 3),1))) div 3))) div 3))
A133813: 1 2 3 4 5 7 8 9 11 12 13 16 17 19 23 24
(x - ((1 + (x div 3)) div (1 + (2 * (1 + (if (x + ~4) <= 0 then 0 else 2))) - (x div 3))))
A227191: 0 1 2 2 3 5 6 7 8 8 9 10 11 12 13 12
((2x3 + 5x2 + 2x + 1) + (loop(\(x,i).((x2 + ~x) div 2),2,(x + 2)) div 3))
A143059: 1 11 46 121 252 456 751 1156 1691 2377 3236 4291 5566 7086 8877 10966
(if x <= 0 then 0 else (1 + (x div (2 + (((3 * (((x + 1) div 2) div 3)) div 2) + (x mod 2))))))
A185816: 0 1 2 2 3 2 3 2 3 3 4 2 3 3 3 3
(1 + (9 mod (1 + compr(\x.(loop(\(x,i).x2,2,10) mod (x + 1)),x))))
A083456: 1 2 2 5 2 10 10 10 10 10 10 10 10 10 10 10
(1 + compr(\x.(~1 + (x mod (1 + ((~1 + loop(\(x,i).2x,x,(~1 + (x mod 4)))) mod (x + 1))))),(x + 1)))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A079603: 2 3 5 7 11 13 17 19 23 27 29 31 37 41 43 47
(1 + ((1 + (x mod (1 + ((1 + (if (x mod 6) <= 0 then 2x else 1)) mod (x + 1))))) mod (x + 1)))
A308897: 1 2 1 2 3 4 1 3 4 2 3 4 1 3 4 2
(x div (1 + ((~1 + ((x mod (2 * (1 + (if (x mod 2) <= 0 then 6 else 1)))) mod 3)) mod (x + 1))))
A143574: 0 1 1 0 4 5 0 0 4 9 10 0 0 13 0 0
(1 + ((~1 + (2 * (1 + (((x + 1) * (if (x mod 4) <= 0 then 2 else (x mod 2))) div 3)))) mod (x + 1)))
A076435: 1 2 2 4 3 6 2 6 5 8
(1 + ((1 + (2 * (x mod (1 + (2 * (2 + (if (x mod 10) <= 0 then 0 else 2))))))) mod (x + 1)))
A276716: 1 2 3 4 5 6 7 8 9 2 2 6 8 10 12 14
(1 + loop(\(x,i).(((1 + (x mod (1 + (x mod (2 * (2 + ((x div 2) mod 2))))))) mod (x + 1)) div 2),1,(x + 1)))
A303386-A295636: 1 1 1 1 2 1 2 1 2 1 4 1 2 2 3 1
(1 + ((x + 1) * (1 + (x div ((x + 2) div (2 + (loop(\(x,i).x3,2,2x) mod (x + 1))))))))
A078310: 2 5 10 9 26 37 50 17 28 101 122 73 170 197 226 33
((x + 1) - ((6 * (x div (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))) mod (x + 1)))
A336965: 1 2 3 2 5 6 7 6 6 10 11 6 13 14 15 2
(1 + compr(\x.(loop(\(x,i).(8x3 + 12x2),2,3) mod (x + 1)),(x + 1)))
A219174: 2 3 4 6 7 8 9 12 14 16 18 21 24 27 28 31
(1 + ((x + (3 * (~2x + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))) div (x + 1)))
A163127: 1 0 0 1 2 2 3 3 3 4 4 5 5 5 5 5
loop(\(x,i).(2 * ((((2x * (1 + (2 * i))) div (2 + i)) div (1 + i)) * (1 + (2 * i)))),(x + ~1),1)
A125558: 1 1 6 50 490 5292 60984 736164 9202050 118195220 1551580888 20734762776 281248448936 3863302870000 53644719852000 751920156592200
(1 + (loop(\(x,i).((x + 1) + (((2x + 1) div 7) + (x div 3))),x,0) div 2))
A173495: 1 1 2 2 4 6 9 15 24 38 62 100 161 261 422 682
(1 + (2 * (x div (2 - ((~x + 1) div (1 + (if (x mod (3 + ((x div 2) div 3))) <= 0 then 2 else 0)))))))
A336839: 1 1 1 3 1 1 1 1 3 1 1 1 1 1 1 5
(1 + ((1 + (x mod (1 + (x mod ((if ((x + 1) mod 5) <= 0 then 2 else 1) + (x div 3)))))) div 2))
A257695-A257694: 1 1 1 2 1 2 1 2 2 3 2 3 1 2 2 3
(if (x mod 3) <= 0 then 0 else (1 + ((1 + ((x div 4) mod (1 + (x mod 10)))) div 2)))
A215879: 0 1 1 0 2 2 0 2 2 0 1 1 0 3 3 0
(1 + (loop(\(x,i).(~x + 1),x,(1 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4))))) div 2))
A344299: 1 1 1 0 1 1 1 0 2 1 1 0 1 1 1 ~1
loop(\(x,i).(x * (1 + i)),(x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))),1)
A130675: 1 1 1 2 1 2 1 6 2 2 1 6 1 2 2 24
(1 + (x div (2 + (x div (1 + ((x - ((~1 + (if (x mod 4) <= 0 then x else 0)) div 3)) mod 3))))))
A305875: 1 1 1 2 1 1 2 2 1 2 3 1 1 3 1 2
(1 + ((1 + (x div (3 * (if ((x + 1) mod (1 + (x div (2 + ((x div 2) mod 2))))) <= 0 then 1 else 2)))) div 2))
A306468: 1 1 1 2 1 2 2 2 2 3 2 3 2 3 3 2
((2x + 3) - (if x <= 0 then 1 else ((x mod 2) - ((1 + (8 mod (1 + (x div 2)))) div 2))))
A233273: 2 4 7 8 12 13 15 16 21 22 24 25 28 29 31 32
(1 + ((x + 1) div (2 + ((x div 2) div (1 + (2 mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1)))))))
A316398-A304817-A183095-A073180: 1 2 2 2 2 4 2 2 2 4 2 5 2 4 4 2
(1 + ((1 + (loop(\(x,i).((x + 2) + ((4 * (x div 5)) div 3)),x,1) div 2)) div 2))
A063827: 1 2 2 3 4 5 6 8 10 13 16 21 26 33 42 53
(1 + ((1 + (((1 + loop(\(x,i).2x,x,(1 + (((1 + (x div 2)) div 2) div 2)))) mod (x + 1)) div 2)) div 2))
A123926-A082902: 1 1 2 1 2 2 2 1 1 2 2 2 2 2 4 1
(1 + ((1 + ((loop(\(x,i).(2 * (x - (2 * (~2 + (x mod 4))))),(x + ~1),1) mod (x + 1)) div 2)) div 2))
A023582: 1 1 1 1 2 1 2 1 2 2 1 1 1 2 2 3
(1 + ((1 + ((x + 1) div (2 + ((1 + (if ((x + ~2) mod 6) <= 0 then x else 2)) mod (x + 1))))) div 2))
A176835: 1 1 2 1 2 2 2 2 3 2 2 2 2 2 5 3
(1 + ((1 + (x div (2 + ((~1 + (if (~1 + (x mod 3)) <= 0 then x else 2) - (x mod 2)) mod (x + 1))))) div 2))
A115751: 1 1 1 2 1 2 1 2 2 2 1 4 1 2 3 2
(1 + ((1 + (x div (2 + (((x mod 2) - (if ((x + ~1) mod 5) <= 0 then 1 else x)) mod (x + 1))))) div 2))
A289494: 1 1 1 1 2 2 1 2 2 2 3 4 3 3 3 3
(1 + ((1 + (((1 + loop(\(x,i).((x + 2) + (2x div 7)),x,2)) div 2) div 2)) div 2))
A064650: 1 2 2 3 3 4 5 6 8 10 13 16 21 26 34 43
(1 + ((1 + ((x mod (2 + ((4 + (if (x mod 2) <= 0 then 1 else 8)) mod (x + 1)))) div 2)) div 2))
A115621: 1 1 2 1 1 1 3 1 1 1 2 1 2 4 1 1
(1 + (2 * ((~1 + (if (x mod 2) <= 0 then x else 0)) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))))
A046221-A046218: 1 1 1 1 1 1 1 3 3 1 1 5 3 5 1 1
(4 - ((1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 10))
A277097: 3 2 0 ~2 4 2 ~2 ~4 2 ~4 4 ~2 4 2 ~2 2
(~1 + ((3 * (1 + ((2 + (if ((x2 + x) mod 8) <= 0 then x else 0)) div 3))) div 2))
A144776: 0 0 0 0 0 0 0 5 5 0 0 0 0 0 0 8
(~1 + (2 * ((1 + (2 * ((loop(\(x,i).(x2 div 3),2,x) div (x + 1)) mod 3))) mod 3)))
A177693: 1 1 1 1 ~1 1 1 ~1 ~1 1 1 3 3 3 1 1
(~1 + (2 * loop(\(x,i).x2,1,(~8x + ~87))))
A157436: 15137 18049 21217 24641 28321 32257 36449 40897 45601 50561 55777 61249 66977 72961 79201 85697
(1 + (if ((x + 2) mod 6) <= 0 then 1 else (((x + 1) div 2) - ((3 * (x div 4)) div 2))))
A329326: 1 2 2 3 2 3 3 4 2 3 2 4 3 4 4 5
loop(\(x,i).(2 * (2x - (x div ~2))),(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)
A151779: 1 6 6 30 6 30 30 150 6 30 30 150 30 150 150 750
loop(\(x,i).4x,((x div 2) - ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2)),1)
A151783: 1 1 4 1 4 4 16 1 4 4 16 4 16 16 64 1
loop(\(x,i).3x,((x div 2) - ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2)),1)
A147610: 1 1 3 1 3 3 9 1 3 3 9 3 9 9 27 1
(7 * loop(\(x,i).13x,(x + 1),7))
A203880: 637 8281 107653 1399489 18193357 236513641 3074677333 39970805329 519620469277 6755066100601 87815859307813 1141606171001569 14840880223020397 192931442899265161 2508108757690447093
(42 * (x + ((x + 1) * loop(\(x,i).(x * (x + i)),2,4))))
A157738: 18480 37002 55524 74046 92568 111090 129612 148134 166656 185178 203700 222222 240744 259266 277788 296310
(7 * (1 + compr(\x.(loop(\(x,i).4x2,2,5) mod (x + 1)),x)))
A178335: 7 14 28 35 56 70 112 140 175 224 280 350 448 560 700 875
(14 * (1 + (9 * (1 + loop(\(x,i).2x,x,4)))))
A304607: 644 1148 2156 4172 8204 16268 32396 64652 129164 258188 516236 1032332 2064524 4128908 8257676 16515212
(14 * (1 + compr(\x.(loop(\(x,i).((x + 1) * (x + i)),4,2) mod (x + 1)),x)))
A033847: 14 28 56 98 112 196 224 392 448 686 784 896 1372 1568 1792 2744
(3 - (loop(\(x,i).(3x + 1),(x + ~1),16) mod 7))
A138034: 1 1 3 2 ~1 ~3 ~2 1 3 2 ~1 ~3 ~2 1 3 2
(1 + ((1 + ((if x <= 0 then 2 else (x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2))) div 2)) div 2))
A155798: 2 1 1 1 2 1 1 3 3 1 1 4 7 4 1 1
(1 + (if x <= 0 then 1 else ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)))
A055652: 2 1 1 1 2 1 1 3 3 1 1 4 8 4 1 1
(1 + (2 * (if x <= 0 then 1 else (1 + compr(\x.(1 - (x mod (2 + ((2x + 1) mod 7)))),x)))))
A235387: 3 7 9 13 15 17 19 21 25 29 31 35 37 39 41 43
(1 + (loop(\(x,i).((x + 2) + (4 * ((2x div (4 + (x div 4))) mod 2))),x,1) div 2))
A288730: 1 2 5 8 9 10 11 12 15 18 21 24 25 26 27 28
(1 + (loop(\(x,i).(2x + ((((((x3 + ~3x2 + 2x) div 2) div 2) div 2) div 2) mod 2)),x,1) div 2))
A293323: 1 2 3 5 10 20 40 80 159 317 633 1266 2532 5063 10126 20252
(1 + (((x + 1) * (1 + (3 * (if (x + ~1) <= 0 then 1 else (6x2 + 3x))))) div 2))
A225672: 3 5 137 381
(2 div ((x + 1) div (1 + (((~1 + (loop(\(x,i).(2x + 2),x,0) mod (2x + 1))) mod (x + 1)) div 2))))
A257265: 2 1 0 1 1 0 0 1 2 0 1 1 0 0 0 1
(1 + (x div (2 + ((1 + (2 * loop(\(x,i).(2 * ((x + ~4) - (x div 4))),x,1))) mod (x + 1)))))
A067995: 1 1 1 2 1 2 2 2 3 1 2 2 2 3 2 3
((x + 1) - (2 * ((1 + (x mod (2 + (loop(\(x,i).(2 * (x + i)),x,1) mod (x + 1))))) mod (x + 1))))
A091564: 1 2 1 4 5 2 3 8 7 10 9 4 7 6 5 16
(if (x div 9) <= 0 then (11x + 11) else (2x + 3))
A060314: 11 22 33 44 55 66 77 88 99 21 23 25 27 29 31 33
(1 + ((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 1 else 2)))
A177876: 2 3 3 4
A305716: 2 3 3 4 3 4 3 5 4 4 3 5 3 4 4 6
(1 + (2 * ((1 + (x div (1 + (x mod (1 + ((~1 + loop(\(x,i).2x,(x div 2),2)) mod (x + 1))))))) div 2)))
A163381: 1 1 3 1 3 3 7 1 3 5 7 3 7 7 15 1
(~1 + (4 * (1 + (2 * (~2 + loop(\(x,i).(2x + ((x + (x2 div 3)) div 2)),x,2))))))
A261716: 3 27 115 643
(1 + (((3 * (1 + (x div (if (x mod 4) <= 0 then (2 + ((x mod 3) div 2)) else 1)))) div 2) div 2))
A324533: 1 2 3 4 3 5 6 7 3 8 9 10 6 11 12 13
(1 + (((3 * (1 + ((if ((x div 4) mod 2) <= 0 then x else ~x) mod 8))) div 2) div 2))
A030241: 1 2 3 4 4 4 3 2 1 2 3 4 4 4 3 2
(1 + (((3 * (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))) div 2) div 2))
A083716: 1 1 1 1 1 1 1 3 2 1 1 3 1 1 2 6
((x + 2) div (1 + ((x + 2) div (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2)))))
A319149: 1 1 1 2 1 3 1 3 2 3 1 6 1 3 3 5
(~1 + (2 * (2 + (if x <= 0 then 1 else (30x3 + 30x + 2)))))
A157438: 5 127 607
((x + 1) div (1 + (((2 + ((1 - (loop(\(x,i).(2x + 1),x,0) mod (x + 1))) mod (x + 1))) div 2) div 2)))
A062789: 1 2 3 2 5 6 7 4 3 10 11 4 13 14 3 8
(1 + (((2 + (x mod (2 + ((1 + (4 * loop(\(x,i).2x,(x div 2),2))) mod (x + 1))))) div 2) div 2))
A275344: 1 1 2 1 2 1 2 1 2 3 2 2 2 2 1 1
(5 + (loop(\(x,i).(2 * (x - ((x - (x div 5)) div 3))),(x + 1),2) div 2))
A048588: 7 8 10 13 17 23 32 45 64 92 133 193 281 410 599 876
(~1 + (32 * (x + loop(\(x,i).(x - ((~1 + (x div 4)) div 2)),2,(x + ~1)))))
A044599: 31 95 159 223 255 287 351 415 479 543 607 671 735 767 799 863
(17 + loop(\(x,i).8x,x,19))
A330770: 36 169 1233 9745 77841 622609 4980753 39845905 318767121 2550136849 20401094673 163208757265 1305670058001 10445360463889 83562883710993 668503069687825
(17 * (1 + compr(\x.(loop(\(x,i).(x * (x + i)),2,5) mod (x + 1)),x)))
A070814: 17 34 51 68 85 102 136 170 204 255 272 340 408 510 544 680
((((x * loop(\(x,i).((x2 + ~x) div 2),2,(x + ~2))) div 2) div 3) div 15)
A011843: 0 0 0 0 0 0 1 3 9 21 42 77 132 214 333 500
loop(\(x,i).((1 + (x2 div 2)) mod (x + 2)),1,(~1 + ((~2x + 2) mod (4 + (x div 4)))))
A292835: 1 0 1 0 0 1 0 3 0 1 0 0 6 0 1 0
(1 + ((((x + (((x + 2) * ((x + 2) + loop(\(x,i).i,(x + ~8),1))) div 2)) div 2) div 2) div 2))
A266480: 1 1 2 3 4 5 6 7 8 10 12 15 18 21 24 28
(2 div (1 + ((loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) mod 13) mod 4)))
A053694: 1 1 0 1 1 0 0 1 1 1 0 0 2 0 0 1
((1 + ((1 + ((x + (if (~2 + (x div 3)) <= 0 then 1 else 2)) * ((x + 1) div 2))) div 2)) div 5)
A229950: 0 0 0 1 1 2 2 3 3 5 6 8 8 10 11 13
(2 - (loop(\(x,i).(x div ~2),(~2 + (2x mod (4 + (x div 4)))),1) mod 5))
A156593: 1 1 1 1 ~2 1 1 2 2 1 1 2 ~2 2 1 1
(((x * loop(\(x,i).((x2 + ~x) div 2),2,(x + ~2))) div 15) div 5)
A011851: 0 0 0 0 0 0 1 4 11 25 50 92 158 257 400 600
((((loop(\(x,i).(x3 + ~x),1,(x2 + 4x + 4)) div 2) div 2) div 3) div 5)
A213547: 1 12 68 260 777 1960 4368 8856 16665 29524 49764 80444 125489 189840 279616 402288
(10 * (1 + compr(\x.(loop(\(x,i).4x2,2,5) mod (x + 1)),x)))
A033846: 10 20 40 50 80 100 160 200 250 320 400 500 640 800 1000 1250
loop(\(x,i).x7,1,(11x + 9))
A017503: 4782969 1280000000 27512614111 230539333248 1174711139837 4398046511104 13348388671875 34792782221696 80798284478113 171382426877952 337931541778439 627485170000000 1107984764452581 1874584905187328 3057125241215467 4828861374436224
(20 * (~2 + loop(\(x,i).47x,x,2)))
A257319: 0 1840 88320 4152880 195187200 9173800240 431168613120 20264924818480 952451466470400 44765218924110640 2103965289433201920 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (4 * compr(\x.(2 - ((x + 1) mod (1 + (2 * (if ((x + 1) mod 8) <= 0 then 2 else 1))))),x)))
A080065: 3 15 27 39 51 63 75 87 91 99 111 123 135 147 159 171
(if x <= 0 then 1 else ((5x + ~1) - ((2 * (x + (((x div 2) div 3) mod 2))) div 3)))
A311429: 1 4 8 12 17 21 25 29 33 38 42 46 51 56 60 64
loop(\(x,i).32x,(((3 * (x + (x div 4))) - (x mod 2)) div 2),1)
A074800: 1 32 32768 1048576 34359738368 1099511627776 1125899906842624 36028797018963968 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((1 + (if x <= 0 then 0 else (1 + ((x + 1) mod (2 * (1 + (4 * (x mod (2 + (x mod 2)))))))))) div 3)
A160550: 0 1 1 0 1 2 1 3 1 0 1 4 1 2 1 0
((1 + (x mod (~1 + (2 * (if x <= 0 then 1 else (x - (x2 mod 20))))))) mod 3)
A104607: 1 1 1 0 1 1 1 1 2 1 2 0 1 1 0 1
((~1 + (loop(\(x,i).10x,x,1) mod 31)) div 3)
A021035: 0 3 2 2 5 8 0 6 4 5 1 6 1 2 9 0
(3 * (1 + (9 * loop(\(x,i).(2 * (1 + (x div 2))),x,7))))
A039667: 192 219 273 327
((loop(\(x,i).10x,x,1) mod 29) div 3)
A021033: 0 3 4 4 8 2 7 5 8 6 2 0 6 8 9 6
((1 + (((loop(\(x,i).(x3 div 2),1,(x2 + 2x + 1)) div 2) div 2) div 3)) div 3)
A061005: 0 1 10 57 217 648 1634 3641 7381 13889 24605 41472 67039 104577 158203 233017
(1 - ((1 + ((1 + (((if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1) div 2) div 2)) div 2)) mod 3))
A079872: 0 0 0 0 0 ~1 0 0 0 ~1 0 ~1 0 1 1 0
((1 + (2 * (if x <= 0 then 1 else (2 * (x3 mod (1 + (3 * (2 - (x mod 2))))))))) mod 3)
A285110: 0 2 2 1 2 2 1 1 2 2 1 1 1 2 1 1
((if x <= 0 then 1 else 6x) - ((1 + (2 * (((x + 1) - ((x div 2) mod 2)) div 2))) div 3))
A314240: 1 5 11 17 23 28 34 40 45 51 57 63 68 73 79 85
((1 + (2 * (((2 - (if (x mod 5) <= 0 then 1 else (x div 3))) mod (x + 1)) div 2))) mod 3)
A267632: 1 1 0 1 1 1 1 1 1 0 1 2 2 1 1 1
((~1 + (2 * (((x + 1) + ((loop(\(x,i).(x - (2 * (~x + (i mod 2)))),x,1) div 2) div 2)) div 2))) mod 3)
A004610: 2 1 1 0 0 1 0 2 0 0 0 2 2 0 2 1
((if x <= 0 then 1 else (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) mod 3)
A196078: 1 0 0 0 1 0 0 2 2 0 0 0 1 0 0 0
(if x <= 0 then 1 else (((~1 + ((~2x + 2) mod (4 + (x div 4)))) mod (1 + (x div 2))) mod 3))
A264394-A263234: 1 0 1 1 0 1 0 2 0 1 2 0 2 0 1 1
(7 mod (3 * (1 + (if (x mod 2) <= 0 then ((1 + (x div 2)) mod 6) else x))))
A031182: 1 1 7 7 7 7 7 7 7 7 1 7 1 7 7 7
(3 * loop(\(x,i).(2 * ((2x * ((~1 + (2 * i)) * (1 + (2 * (1 + i))))) div (1 + i))),x,1))
A113677: 3 30 840 37800 2328480 181621440 17124307200 1892235945600 239683219776000 34226763784012800 4611686018427387903 4611686018427387903 4611686018427387903
((if x <= 0 then 1 else 6x) - (((x + 1) + (2 * ((x + ((x div 2) mod 2)) div 2))) div 3))
A315476: 1 6 11 16 21 27 32 37 43 48 53 58 64 70 75 80
(((x + 1) * (1 + (2 * loop(\(x,i).((x + 2) + (x div (6 + (x mod 2)))),x,0)))) mod 3)
A119395: 1 1 0 1 2 0 0 1 0 1 0 0 2 1 0 0
(1 + ((if (x mod 3) <= 0 then (1 - (x div (~2 + ((~x + 2) div 4)))) else 1) + ((x + 1) div 3)))
A205153: 2 2 3 4 3 4 6 4 5 8 5 6 9 6 7 10
(4x + ((x + 1) div 3) - ((~x2 + 2x + ~1) div loop(\(x,i).x2,2,3)))
A310373: 1 4 10 14 18 23 27 31 36 40 44 50 54 58 64 68
(((x + (((x div 2) div 3) mod 2)) div 2) + (if x <= 0 then 1 else 4x) + ((x + 1) div 3))
A310400: 1 4 10 14 19 24 29 34 39 44 48 54 58 62 68 72
(4x + ((x + 1) div 3) - (((((x div 2) div 3) mod 2) - (if x <= 0 then 1 else x)) div 2))
A313702: 1 5 10 15 19 25 29 33 39 43 48 53 58 63 68 73
(loop(\(x,i).(x div (2 - ((1 + ((x + ((x2 div 2) div 3)) div 2)) mod 2))),x,(x + 1)) mod 3)
A035208: 1 1 0 1 2 0 0 1 1 2 2 0 1 0 0 1
(1 - (((if x <= 0 then 2 else (x5 mod 11)) div 2) mod 3))
A165591-A011627: 0 1 ~1 1 1 1 ~1 ~1 ~1 1 ~1 1 1 ~1 1 1
((2 * (1 + ((1 + (x div (1 + (loop(\(x,i).((x + 1) * i),(x div 2),2) mod (x + 1))))) div 2))) div 3)
A232353: 0 1 1 0 1 1 0 1 1 2 1 2 2 1 1 2
((2 * (1 + ((1 + (x2 div (1 + (loop(\(x,i).(x div (2 - (x mod 2))),x,x) div 2)))) div 2))) mod 3)
A344858: 2 1 0 0 0 1 2 2 0 0 0 1 2 2 1 0
(if x <= 0 then 1 else ((2 * (1 + ((((~1 + (2 * (x mod 5))) mod (x + 1)) div 2) div 2))) div 3))
A029403: 1 0 0 0 0 1 0 0 1 1 2 0 0 1 1 2
((2 * ((2 * (if x <= 0 then 1 else 4x)) - ((2x + 1) div 9))) div 3)
A313837: 1 5 10 16 20 26 31 36 42 46 52 57 62 67 72 78
((2 + ((1 + (2 * loop(\(x,i).((x + 2) + ((x div 2) div 3)),(x + ~1),1))) div 3)) div 3)
A281744: 1 1 1 1 2 3 3 4 5 6 7 9 11 13 15 18
(3 + (2 * ((x + (if (x mod 3) <= 0 then (2 + (((x + 1) * (x div 2)) mod 2)) else 1)) div 3)))
A075260: 3 3 5 5 5 7 9 7 9 9 9 11 11 11 13 13
(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) - ((x mod (2 + (x div 3))) div 3))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A171057: 2 3 5 7 11 13 17 18 23 28 31 37 41 43 47 53
((2 * (1 + (if x <= 0 then 1 else (2 * (x + ((3 * ((((x + 1) div 2) div 2) div 2)) div 2)))))) div 3)
A242925: 1 2 3 4 6 7 8 11 12 14 15 16 18 19 20 24
((((x2 + 4x + 3) * loop(\(x,i).(x * (1 + (2 * (2 + i)))),x,(x + 2))) div 2) div 3)
A038121: 1 28 630 13860 315315 7567560 192972780 5237832600 151242416325 4638100767300 150738274937250 5179915266025500 187771928393424375 4611686018427387903 4611686018427387903 4611686018427387903
((((x2 + 5x + 6) * loop(\(x,i).x2,1,((x2 + 3x + 2) div 2))) div 2) div 3)
A108648: 1 18 120 500 1575 4116 9408 19440 37125 66550 113256 184548 289835 441000 652800 943296
loop(\(x,i).x7,1,(11x + 7))
A017479: 823543 612220032 17249876309 163840000000 897410677851 3521614606208 11047398519097 29509034655744 69833729609375 150363025899136 300124211606973 562949953421312 1002544368429379 1708593750000000 2804020163098721 4453476124377088
((((x2 + 5x + 4) * loop(\(x,i).((x2 + ~x) div 2),2,(x + 4))) div 2) div 3)
A027778: 10 75 315 980 2520 5670 11550 21780 38610 65065 105105 163800 247520 364140 523260 736440
(1 - (((1 + ((x + ((1 - (x div 3)) mod 3)) div 3)) * (if x <= 0 then 1 else 2)) mod 3))
A342563: 0 ~1 0 0 0 0 1 ~1 ~1 ~1 ~1 0 0 0 0 1
(6 * ((5 * (2x + (if (~2 + (x div 5)) <= 0 then 2 else 1))) div 2))
A226944: 30 60 90 120 150 180 210 240 270 300 330 360 390 420 450 462
((2 * (2 + ((((x + 1) * loop(\(x,i).(x + ((3 + i) * i)),x,0)) div 2) div 3))) mod 3)
A035193: 1 0 0 1 2 0 2 0 1 0 1 0 0 0 0 1
((loop(\(x,i).((9x + 1) + ((x + 1) mod 3)),(x + 1),2) div 2) div 3)
A037672: 3 29 261 2352 21170 190530 1714773 15432959 138896631 1250069682 11250627140 101255644260 911300798343 8201707185089 73815364665801 664338281992212
(((((x + 1) * (((x + 2) * loop(\(x,i).x3,1,(x + 3))) div 2)) div 2) div 2) div 3)
A061608: 2 16 62 180 428 896
((2 * (2 + (loop(\(x,i).((3 * ((x2 + x) div 2)) div 2),3,x) mod (x + 1)))) mod 3)
A117479: 1 0 1 0 1 1 0 2 1 1 1 0 2 2 1 2
(5 - ((x + 1) mod (4 + ((if (x mod 2) <= 0 then (x div 2) else 2x) mod (x + 4)))))
A030586: 4 3 2 1 0 4 5 4 4 4 3 4 2 4 1 4
((2 * ((x + 2) + (((5 * (x + (if (x + ~4) <= 0 then 1 else 2))) div 2) div 2))) div 3)
A285302: 2 3 4 6 8 10 12 13 14 16 18 19 20 22 24 25
(((x * (1 + (loop(\(x,i).(~6x2 + 3x),2,x) div (x + 1)))) div 2) mod 3)
A166712: 0 2 1 1 0 2 0 2 1 0 1 1 0 1 2 1
(((x * ((x + ~1) + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + ~2),x))) div 2) mod 3)
A338203: 0 0 0 0 1 2 0 0 1 0 1 2 0 2 0 0
((2 * ((x + 4) + (if x <= 0 then 1 else (2 * (3x - ((x div 2) div 3)))))) div 3)
A184917: 3 7 12 16 21 26 29 34 38 43 48 52 56 60 65 70
((if x <= 0 then 1 else 6x) - ((2 * (x + ((x + ((x div 2) mod 4)) div 2))) div 3))
A315259: 1 6 10 15 20 25 30 34 40 46 50 55 60 65 70 74
(((x + 1) * ((x3 + x) div 2)) - (loop(\(x,i).((x2 + ~x) div 2),2,(x + 2)) div 3))
A179095: 0 1 10 45 135 320 651 1190 2010 3195 4840 7051 9945 13650 18305 24060
(if x <= 0 then 1 else (6x + (x div ~7) - (x div 7)))
A314249: 1 5 11 17 23 29 35 40 45 51 57 63 69 75 80 85
(6x + (if x <= 0 then 1 else ((~x + 1) div (1 + (2 * (2 + (((x div 2) div 3) mod 2)))))))
A315547: 1 6 11 17 23 29 35 41 47 52 58 64 69 75 81 87
(x + (((x + (x div 3)) div 3) + (if x <= 0 then 1 else 4x)) - ((x div 2) div 3))
A313887: 1 5 10 16 21 27 31 37 42 48 53 58 63 68 74 79
(x - ((x2 + ~x) div ((x + 3) + (loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) div 3))))
A319856-A161511: 0 1 2 2 3 3 4 3 4 4 5 4 6 5 6 4
(loop(\(x,i).(4 * (1 + ((32 mod (x + 1)) div 2))),3,x) mod 3)
A049115: 0 0 1 0 1 1 2 0 2 1 2 1 2 2 1 0
(((x + 2) - loop(\(x,i).((~2x + ~1) + (((x + 1) div 2) div 3)),3,x)) div 3)
A231407: 1 4 6
A189363: 1 4 6 9 11 13 16 18 21 23 25 27 30 33 35 38
(1 + (2 * compr(\x.(2 - ((x + 1) mod (1 + (2 * (if (((x + 1) div 2) mod 6) <= 0 then 2 else 0))))),x)))
A112073: 23 25 47 73 95 97 143 145 167 193 215 217 263 265 287 313
(2 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + (x2 div ((2x + ~1) + (x div 2)))))
A338361: 2 4 6 8 12 15 19 22 26 32 35 41 45 48 52 59
(if (~1 + (x div 5)) <= 0 then x else (74x + 37))
A103303: 0 1 2 3 4 5 6 7 8 9
A145461: 0 1 2 3 4 5 6 7 8 9 777
(if (x + ~1) <= 0 then x else (1 + (((2x + 1) mod (1 + (2x mod (2 + (x div 4))))) + (x mod 2))))
A157226: 0 1 1 2 1 3 1 2 1 3 1 4 1 3 2 2
(if x <= 0 then 0 else (1 + ((x div (2 + ((x div 2) div (1 + (x mod (2 + ((x mod 3) div 2))))))) + (x mod 2))))
A079243: 0 2 2 3
A080256: 0 2 2 3 2 4 2 4 3 4 2 5 2 4 4 5
(~1 + ((4 * ((1 + (4 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 3)) + (x mod 2)))
A248105: 3 12 15 20 27 36 43 48 51 60 63 68 75 80 83 92
(loop(\(x,i).4x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1) * (1 + (x mod 2)))
A213178: 1 8 4 32 4 32 16 128 4 32 16 128 16 128 64 512
(2 + ((2 * ((x mod (2 + (if ((x2 + 2x) mod 6) <= 0 then x else 1))) div 2)) + (x mod 2)))
A126801: 2 3 4 3 6 5 8 3 4 3 12 5 14 3 4 3
(((x + 1) * loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),((x + ~1) div 2),1)) div (1 + (x mod 2)))
A047074: 1 1 3 2 5 6 14 20 45 70 154 252 546 924 1980 3432
(1 + compr(\x.(~1 + (x mod (1 + (((1 - loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))) div 2) mod (x + 1))))),x))
A029749: 1 2 4 5 7 8 10 14 16 20 28 32 40 56 64 80
(1 + compr(\x.(~1 + ((~1 + ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 2)) mod 3)),x))
A174896: 4 6 9 10 12 14 15 16 18 20 21 22 24 25 26 28
((x + 1) + ((((x + 1) * loop(\(x,i).((x2 + ~x) div 2),2,(x + ~1))) div 3) div 5))
A185092: 1 2 3 4 6 12
A161701: 1 2 3 4 6 12 28 64 135 262 473 804 1300 2016 3018 4384
((x + 1) + ((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3))
A134871: 1 2 3 5 5 8 7 10 10 12 11 16 13 16 17 19
(1 + compr(\x.(loop(\(x,i).x3,2,55) mod (x + 1)),x))
A003598: 1 5 11 25 55 121 125 275 605 625 1331 1375 3025 3125 6655 6875
(1 + compr(\x.(loop(\(x,i).(x2 + 2x),2,(~1 + (x mod (9 + (x mod 2))))) mod (x + 1)),x))
A276393: 1 2 3 4 5 6 7 8 9 10 11 12 16 20 22 26
(1 + compr(\x.(loop(\(x,i).(x2 + 2x),3,(6 * (x div 5))) mod (x + 1)),x))
A067319: 1 2 3 4 5 6 8 10 12
A162002: 1 2 3 4 5 6 8 10 12 14 15 16 17 18 20 24
(1 + compr(\x.(x - ((1 + loop(\(x,i).(x4 + 3x3 + 2x2),1,(x2 + 2))) mod (x + 1))),x))
A018322: 1 2 7 13 14 26 91 182
(1 + compr(\x.((1 + loop(\(x,i).10x,15,x)) mod (x + 1)),x))
A111117: 1 3 9 27 31 37 41 93 111 123 271 279 333 369 813 837
(1 + compr(\x.((1 + loop(\(x,i).(20x2 + 30x),2,x)) mod (x + 1)),x))
A133027: 1 3 7 9 21 27 63 81 189 243 567 1701
(1 + compr(\x.((1 + loop(\(x,i).(9 + ((x3 + x) div 2)),2,x)) mod (x + 1)),x))
A018298: 1 3 5 9 15 27 45 135
(1 + compr(\x.((1 + loop(\(x,i).17x,(2 * (1 + (x mod 2))),x)) mod (x + 1)),x))
A188591-A002183: 1 2 3 4 6 8 9 10 12 16 18 20 24 30 32 36
(1 + compr(\x.((1 + (x * loop(\(x,i).(6x2 + 12x + ~7),2,x))) mod (x + 1)),x))
A172411: 1 2 5 10
A018682: 1 2 5 10 17 25 34 50 85 170 425 850
(1 + compr(\x.((1 + (x * loop(\(x,i).(15x2 + 10x),2,x))) mod (x + 1)),x))
A222011: 1 2 4 8
A018446: 1 2 4 8 53 106 212 424
(1 + compr(\x.((1 + (x * loop(\(x,i).(16x2 + 10x + 1),2,x))) mod (x + 1)),x))
A018684: 1 2 7 14 61 122 427 854
(1 + compr(\x.((1 + (x * loop(\(x,i).(10x2 + 2x + ~2),2,x))) mod (x + 1)),x))
A018417: 1 3 9 41 123 369
(1 + compr(\x.((1 + (x * loop(\(x,i).(11x2 + 2x),2,x))) mod (x + 1)),x))
A018715: 1 2 4 227 454 908
(1 + compr(\x.((1 + (x * loop(\(x,i).(~10x2 + ~3x),2,x))) mod (x + 1)),x))
A172411: 1 2 5 10
A018472: 1 2 5 10 47 94 235 470
(1 + compr(\x.(loop(\(x,i).(6x2 + 14x + 4),2,8x) mod (x + 1)),x))
A018517: 1 2 4 139 278 556
(1 + compr(\x.((2 + (x * (1 + (x * loop(\(x,i).(6x2 + 2),2,x))))) mod (x + 1)),x))
A018427: 1 3 9 43 129 387
(1 + compr(\x.(loop(\(x,i).(x7 + x5 + x3 + x),1,2x) mod (x + 1)),x))
A172411: 1 2 5 10
A018315: 1 2 5 10 17 34 85 170
(1 + compr(\x.(loop(\(x,i).(24x2 + 16x + 2),2,2x) mod (x + 1)),x))
A018363: 1 2 7 14 19 38 133 266
((1 + loop(\(x,i).(x2 + x),1,x7)) div (x2 + x + 1))
A269483: 1 1 2359 368089 12783421 196890121 1822428931 11898664849 60247241209 251393376241 900900990991 2855262053161 8177824843189 21515718297529 52663539957211 121132473843361
(1 + compr(\x.(loop(\(x,i).((x mod 2) - ((x2 + 6x + 9) div 2)),3,x) mod (x + 1)),x))
A018381: 1 3 9 11 27 33 99 297
(1 + compr(\x.(loop(\(x,i).(15x2 + 33x + 9),2,x) mod (x + 1)),x))
A018725: 1 3 9 103 309 927
(1 + compr(\x.(loop(\(x,i).(30x2 + 30x + ~6),2,x) mod (x + 1)),x))
A018707: 1 2 3 6 149 298 447 894
(1 + compr(\x.(loop(\(x,i).(24x2 + 20x + 2),2,x) mod (x + 1)),x))
A018759: 1 2 17 29 34 58 493 986
(1 + compr(\x.(loop(\(x,i).(48x2 + 96x + 4),2,x) mod (x + 1)),x))
A018364: 1 2 4 67 134 268
(1 + compr(\x.(loop(\(x,i).(96x2 + x),2,x) mod (x + 1)),x))
A018581: 1 5 7 19 35 95 133 665
loop(\(x,i).((10x + 4) - ((2x + 2) mod 5)),x,1)
A037680: 1 10 102 1023 10231 102310 1023102 10231023 102310231 1023102310 10231023102 102310231023 1023102310231 10231023102310 102310231023102 1023102310231023
loop(\(x,i).(2 * ((1 + (((x2 + 2x + 1) * ((x3 + x2) div 2)) div 3)) div 2)),x,1)
A067765: 1 2 18 370386 4611686018427387903
((x + ~1) + (2 * (if x <= 0 then 1 else (2 + ((6x + (x2 div 4)) div (x + 2))))))
A265412: 1 8 11 14 15 18 19 22 23 24 27 28 29 32 33 34
((x + ~1) + loop(\(x,i).((3x + 2) + (x div 5)),7,4))
A177949: 15684 15685 15686 15687 15688 15689 15690 15691 15692 15693 15694 15695 15696 15697 15698 15699
loop(\(x,i).(2 * (x + ((x mod (2 + (2x2 mod 30))) div 2))),x,1)
A181490: 1 2 6 18
A214799: 1 2 6 18 54 120 240 480 960 1920
(1 + compr(\x.(1 - (loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,1) mod (2 + (x * (x mod 2))))),x))
A336488-A080389: 1 2 3 4 6 7 8 10 12 15 16 18 20 22 24 26
((x + 1) * (~1 + (if x <= 0 then 2 else (x div (1 + (x mod (1 + (x mod (1 + (x div (2 * (2 - (x mod 2)))))))))))))
A167339: 1 0 3 0 15 0 35 0 9 0 99 0 143 0 45 0
((x + 1) * (1 + (x mod ((x + 1) - ((if (x mod 4) <= 0 then 2 else (x mod 2)) mod (1 + (x div 3)))))))
A210966: 1 4 9 4 25 6 49 8 18 10 121 12 26 14 225 16
((1 + (x mod (1 + ((2x + 1) mod ((x + 1) - (loop(\(x,i).2x,x,1) mod (x + 1))))))) mod (x + 1))
A229878: 0 0 1 0 1 2
A176095: 0 0 1 0 1 2 1 0 3 2 1 4 1 2 7 0
compr(\x.(~1 + ((x2 * loop(\(x,i).x3,2,x)) mod 23)),(x + 1))
A095037: 1 2 3 4 6 8 9 12 13 16 18
A035240: 1 2 3 4 6 8 9 12 13 16 18 23 24 25 26 27
compr(\x.(~1 + ((1 + (x mod (1 + (3 * (if (x mod 8) <= 0 then 1 else 2))))) mod (x + 1))),(x + 1))
A245802: 1 2 3 4 5 6 7 8 14 16 21 24 28 32 35 40
((~1 + (2 * (1 + ((2 * (1 + (loop(\(x,i).x2,2,(x + 1)) div 3))) div 3)))) div (x + 1))
A184633: 1 4 12 28 55 96 152 227 324 444 591 768 976 1219 1500 1820
((x + 1) + ((7x + 7) * (1 + (3 * (if (~2 + (x div 2)) <= 0 then 0 else 2)))))
A020335: 8 16 24 32 40 48 350 400 450 500 550 600 650 700 750 800
((~1 + (2 * ((x + 1) + ((2 * (x + (loop(\(x,i).2x,x,2) mod (x + 1)))) div 3)))) div (x + 1))
A275663: 1 1 3 2 3 3 3 2 4 3 3 3 3 3 3 3
(1 - ((1 + ((1 + (loop(\(x,i).2x,((x + ~1) div 2),1) mod (x + 2))) mod 2) - (x mod 2)) mod (x + 1)))
A178948: 1 1 0 0 ~1 0 ~1 0 ~1 1 ~1 0 ~1 0 ~1 1
(loop(\(x,i).(x - (((~2x + ~1) + (x div 7)) div 3)),x,1) div (x + 1))
A078620: 1 1 1 1 2 3 4 6 9 14 21 31 46 70 106 161
((x + 1) * loop(\(x,i).(0 - (((4x * (~1 + (2 * i))) div (1 + i)) * (~1 + (2 * i)))),x,1))
A295383: 1 ~4 72 ~2400 117600 ~7620480 614718720 ~59364264960 6678479808000 ~857813628672000 123868287980236800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).((x + 1) + (((2x + 1) div 7) + (x div 3))),x,1) div (x + 1))
A172128: 1 1 1 1 2 2 4 5 8 12 18 26 40 60 90 137
compr(\x.((1 + ((x + 1) div (1 + ((x - (if (x mod 9) <= 0 then 0 else 1)) mod 2)))) mod 2),(x + 1))
A276936: 2 6 9 10 14 18 22 26 30 34 36 38 42 45 46 50
((2 * (1 + (2 * (1 + ((if ((x + ~1) mod 4) <= 0 then 2 else 1) * (1 + (2 * (x mod 2)))))))) mod (x + 1))
A341410: 0 0 1 2 0 0 3 2 1 0 10 6 10 2 10 2
((loop(\(x,i).((x2 + ~x) div 2),2,(x + 2)) div 3) + ((x + 1) * ((x2 + 3x + 2) div 2)))
A022815: 1 7 23 55 110 196 322 498 735 1045 1441 1937 2548 3290 4180 5236
((4x + 4) * (1 + (2 * (2 + (3 * (if (x + ~1) <= 0 then 1 else 16))))))
A248365: 44 88 1212 1616 2020 2424 2828 3232 3636 4040 4444 4848 5252 5656 6060 6464
((x + 1) * (2 - (if x <= 0 then 1 else ((x mod 2) - (((2x + 1) mod (1 - (x div ~4))) div 2)))))
A245579: 1 2 6 4 10 12 14 8 27 20 22 24 26 28 60 16
((2x2 + 2x) + loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1))
A128806: 1 6 14 28 42 64 88 120 146 184 224 272 316 372 428 496
loop(\(x,i).((2 * (((2x * (1 + (2 * i))) div (2 + i)) * (~1 + (2 * i)))) div (1 + i)),x,(x + 1))
A172392: 1 4 30 280 2940 33264 396396 4907760 62573940 816621520 10861066216 146738321184 2008917492400 27815780664000 388924218927000 5484594083378400
compr(\x.(x - loop(\(x,i).(x5 mod 31),2,x)),(x + 1))
A072600: 1 3 5 6 7 11 13 14 15 19 21 22 23 25 26 27
loop(\(x,i).((x + 1) + ((x div (1 + (((1 + ((x + (x div 2)) div 4)) mod 2) + (x mod 2)))) mod 2)),x,1)
A160992: 1 2 4 5 6 8 9 10 11 13 14 15 17 19 21 22
loop(\(x,i).(200x3 + ~3x),x,1)
A145452: 1 197 1529074009 4611686018427387903 4611686018427387903
loop(\(x,i).((((4x div (1 + i)) * (~1 + (2 * i))) div (1 + i)) * (1 + (2 * i)) * i),x,1)
A204515: 1 3 40 1050 42336 2328480 163088640 13913499600 1401656256000 162984589447680 21497802046156800 3172717285311974400 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * ((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)))
A255201: 0 2 2 4 2 4 2 6 4 4 2 6 2 4 4 8
((1 + ((x + 1) div (1 + (x mod (1 + (x div (if (x mod 2) <= 0 then 2 else (x mod 10)))))))) div 2)
A134838: 1 1 2 1 1 2 1 2 1 3 1 1 1 2 1 2
(2 + (if x <= 0 then 0 else ((x + 1) - (((x + 1) * (1 + (x div 8))) div 7))))
A195994: 2 4 5 6 7 8 8 9 9 10 10 11 12 12 13 14
((1 + ((1 + (x div 5)) div (1 + (x mod (2 + (2 * (if (x mod 3) <= 0 then 0 else 2))))))) div 2)
A029419: 1 0 0 0 0 0 1 1 0 1 0 0 2 1 1 1
(if x <= 0 then 0 else (((x div 3) + (((x + 1) div (1 + (x mod 9))) mod 2)) - (x mod 2)))
A070804: 0 0 1 1 2 1 3 2 3 2 4 2 5 3 4 4
((1 + ((((x * (((x + 1) * (if x <= 0 then 2 else ((x + 1) div 2))) div 2)) div 2) div 3) div 3)) div 2)
A340589: 0 0 0 0 1 1 2 3 4 6 8 11 13 18 20 27
((1 + (3 * loop(\(x,i).((9x + 1) + ((x + 1) mod 3)),x,1))) div 2)
A037623: 2 18 165 1487 13383 120450 1084052 9756468 87808215 790273937 7112465433 64012188900 576109700102 5184987300918 46664885708265 419983971374387
((1 + (if x <= 0 then 0 else (1 + (x * ((1 + ((~x + 1) mod 21)) div 2))))) div 2)
A106673: 0 1 11 16 19 23 25
(2 * (1 + compr(\x.(2 - (((x + 1) * (2 + (if (x mod 3) <= 0 then 0 else 2))) mod 5)),(x + 1))))
A028876: 4 6 8 12 14 16 22 24 32 34 36 38 42 44 46 52
(loop(\(x,i).((x + 1) + (3 * ((x2 div 4) mod 7))),(x + 1),1) div 2)
A152083: 1 3 6 7 7 8 10 13 14 14 15 17 20 21 21 22
(1 - ((1 + ((1 + ((1 + (loop(\(x,i).(~x + 1),(x div (2 + (x mod 2))),(x + 1)) div 2)) div 2)) div 2)) div 2))
A026821: 1 0 1 1 0 1 1 0 0 1 1 1 0 0 1 2
((1 + ((1 + (((~1 + loop(\(x,i).2x,(2 - ((~x + 1) div 3)),2)) mod (x + 1)) div 2)) div 2)) div 2)
A331195: 0 0 0 1 0 0 1 1 0 1 1 1 2 0 0 2
(0 + ((x div 2) + ((if x <= 0 then 2 else (1 - ((x + 1) mod (1 + (2 * ((x div 2) div 3)))))) div 2)))
A332436: 1 0 1 1 2 2 3 2 4 4 4 5 5 4 7 7
((1 + (((1 + ((x + 1) div (2 - (if (x mod 5) <= 0 then (x mod 2) else 0)))) mod (x + 1)) div 2)) div 2)
A127322: 0 0 1 1 1 0 1 1 1 2 2 2 2 2 2 0
(2 + (if x <= 0 then 1 else (2 * (1 + ((((x + ~2) * (x div 3)) mod (x + 1)) div 2)))) - (2 * (x mod 2)))
A013633: 3 2 4 2 6 4 4 4 6 2 6 4 4 4 6 2
(3 + ((loop(\(x,i).((x + 2) + (((x + 1) div 2) div 3)),(x + 5),1) div 2) div 2))
A120183: 6 7 9 10 12 14 16 19 22 26 30 35 41 48 56 65
(~1 - ((loop(\(x,i).x3,1,((2x + 1) * (1 - (2 * (x mod 2))))) div 2) div 2))
A305291: ~1 6 ~32 85 ~183 332 ~550 843 ~1229 1714 ~2316 3041 ~3907 4920 ~6098 7447
((1 + ((loop(\(x,i).(2 * ((2x * (1 + (2 * i))) div (2 + i))),(x + 1),(x + 1)) div 2) div 2)) div 2)
A082145: 1 5 42 336 2640 20592 160160 1244672 9674496 75246080 585761792 4564377600 35602145280 277970595840 2172375244800 16992801914880
((1 + ((if x <= 0 then 2 else (x - (((x - (x3 div 16)) div 2) div 2))) div 2)) div 2)
A199122: 1 0 1 1 1 2 2 3 4 5 6 7 9 11 14 16
((1 + ((if x <= 0 then x else ((1 + (x mod (1 + (x div 5)))) * (1 + (x mod 2)))) mod 4)) div 2)
A333809: 0 1 1 1 1 0 1 0 1 0 1 1 1 0 2 0
(((2 - ((2 * (1 + (4 * (if (x mod 3) <= 0 then 0 else 2)))) mod (x + 1))) mod 5) div 2)
A304685: 1 1 1 0 2 1 0 0 1 0 0 0 0 1 2 0
((3 - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 10)
A048199: 3 2 0 8 4 2 8 6 2 6 4 8 4 2 8 2
((3 * (1 + (((loop(\(x,i).(x2 + 2x),1,((x div 2) - (x mod 2))) div 2) div 2) div 3))) div 2)
A029151: 1 0 1 1 1 1 3 1 4 3 4 4 7 4 9 7
((3 * ((if ((x mod (~1 + (2 * (x div 4)))) mod 2) <= 0 then 1 else x) mod 7)) div 2)
A232530: 1 1 1 1 1 1 1 1 1 1 4 1 1 9 1 1
((3 * (loop(\(x,i).(10x + 1),(x div 2),1) * (1 + (2 * (x mod 2))))) div 2)
A173712: 1 4 16 49 166 499 1666 4999 16666 49999 166666 499999 1666666 4999999 16666666 49999999
((3 * (1 - ((1 + (x mod (1 + (2 * (if (x mod 2) <= 0 then 1 else (x div 4)))))) div 3))) div 2)
A307039: 1 1 0 1 1 0 1 1 0 0 1 1 1 ~2 0 1
((9 * ((x div (1 + (2 * (if (x mod 10) <= 0 then 0 else 2)))) div 2)) div 2)
A018817: 0 0 0 0 0 0 0 0 0 0 22 4 4 4 4 4
(~2 + (3 * ((x + 1) + (loop(\(x,i).(x + 4),(~2 + ((x + ~1) div 3)),x) div 3))))
A202822: 1 4 7 13 16 19 25 28 31 37 43 49 52 61 64 67
(2 + ((2 * loop(\(x,i).((x + 2) + (((2x + ~1) div (2 + (x div 4))) mod 2)),x,1)) div 3))
A112235: 2 4 5 7 9 11 13 15 17 18 20 21 22 24 25 26
(((2 + ((5 * (2 - (loop(\(x,i).((x + ~2) + (x div 2)),x,0) div 2))) div 2)) div 3) div 2)
A329758: 1 1 2 3 4 7 10 15 22 34 51 76 114 171 257 385
((x + 1) div (if x <= 0 then 1 else (2 + ((2 * ((~2x + 2) mod (4 + (x div 4)))) div 3))))
A283845: 1 1 1 2 1 2 3 2 2 3 5 3 2 3 5 8
(if x <= 0 then 1 else (2 * ((x + (2 * (4x - ((2x + 2) div 5)))) div 3)))
A315313: 1 6 10 16 20 26 32 38 44 48 54 60 64 70 76 82
(if x <= 0 then 1 else (2 * ((x + (2 * (4x - ((x + (x div 4)) div 3)))) div 3)))
A315647: 1 6 12 16 22 26 32 38 44 50 54 60 64 70 76 82
((((3 * (1 + ((loop(\(x,i).2x,x,1) mod (1 + (x div 2))) div 2))) div 2) + (x mod 3)) div 2)
A287475: 0 1 1 0 1 2 0 1 1 1 2 2 0 2 1 0
(((x2 + 4x + 5) * loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + 1),1)) div 2)
A034274: 5 25 119 546 2442 10725 46475 199342 848198 3585946 15080870 63146500 263432340 1095517485 4543460595 18798494550
(((3 + loop(\(x,i).(7x + 7),(x div 2),(x mod 2))) div (2x + 1)) div 2)
A086826: 1 0 1 1 3 4 15 24 82
(2 * (1 + compr(\x.(2 - ((1 + ((1 + ((loop(\(x,i).2x,x,2) mod (x + 1)) div 2)) div 2)) mod 3)),x)))
A128691-A100368-A036348: 6 10 12 14 20 22 24 26 28 34 38 40 44 46 48 52
(((x + 1) + (6 * (x + (((x + (x mod 2)) div 5) + (if x <= 0 then 1 else 2))))) div 2)
A188373: 3 10 13 17 20 27 30 34 37 44 47 51 54 58 61 68
(2 * ((x + 1) + (((3 * (if x <= 0 then 1 else (2 + ((x - ((x div 3) mod 2)) div 2)))) div 2) div 2)))
A139710: 2 6 10 12 14 18 20 22 26 28 30 34 38 40 42 44
(compr(\x.((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) mod 10),(x + 1)) div 2)
A082583: 1 2 3 5 6 8 9 11 14 15 18 20 21 22 23 26
(((x + 1) * (loop(\(x,i).((x3 + 7x2 + 14x + 8) div 2),1,(x2 + 2x)) div 2)) div 2)
A075664: 1 35 405 2584 11375 38961 111475 278720 627669 1300375 2516921 4604040 8030035 13446629 21738375 34080256
(((x + 1) * loop(\(x,i).(x + (37x div (1 + i))),x,2)) div 2)
A010991: 1 39 780 10660 111930 962598 7059052 45379620 260932815 1362649145 6540715896 29135916264 121399651100 476260169700 1768966344600 6250347750920
(x + ((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 1 else 2)))
A064800: 1 3 4 6 6 8 8 11 11 12 12 15 14 16 17 20
((if x <= 0 then 2 else ((1 + ((x + 1) div (1 + (x mod (2 + (x div (2 + (x mod 5)))))))) div 2)) div 2)
A108455: 1 0 1 0 1 1 0 1 1 2 0 1 1 2 1 0
(4 * (1 + (3 * loop(\(x,i).(2x + 16),x,13))))
A278129: 160 508 1204 2596 5380 10948 22084 44356 88900 177988 356164 712516 1425220 2850628 5701444 11403076
(((1 + (((x + ~1) * loop(\(x,i).(1 + (x2 div 2) - (x mod 2)),1,(x + ~1))) div 3)) div 2) div 2)
A032801: 0 0 0 0 1 3 5 9 14 22 30 42 55 73 91 115
((loop(\(x,i).x2,1,(1 + ((x + 2) div 3) - ((2 * (x div 3)) div 3))) div 2) div 2)
A178305: 0 1 1 1 2 2 1 2 2 1 2 2 2 4 4 2
(((1 + ((x * (1 + (x div (2 + (loop(\(x,i).(1 - (x * i)),x,1) mod (x + 1)))))) div 3)) div 2) div 2)
A241165: 0 0 0 0 0 0 0 1 2 1 3 1 2 2 3 2
((x + 1) div (2 + (x div 2) - (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))))
A328892: 0 1 1 2 1 2 1 4 2 2 1 3 1 2 2 8
((2 + (x div (1 + ((~1 + loop(\(x,i).2x,x,(4 + ((x div 2) div 3)))) mod (x + 1))))) div 2)
A072038: 1 1 2 1 1 2 1 1 3 1 2 2 2 1 1 1
(~2 + (2 * (1 + loop(\(x,i).(2x2 + 8x),1,((1 + (x mod 8)) mod (x + 1))))))
A177725: 0 0 0 0 0 0 0 0 20 48 84 128 180 240 308 384
(if x <= 0 then 1 else (2 + (x div (2 + (x div (1 + (((1 + ((x * (x mod 2)) div 2)) mod 5) mod 2)))))))
A078570: 1 2 2 2 3 3 3 2 3 2 3 3 3 2 3 3
(((1 + (((x + 1) * (loop(\(x,i).2x,(x + ~10),1) div 3)) div 2)) div 2) div 2)
A210634: 0 0 0 0 0 0 0 0 0 0 0 0 1 3 9 20
(((3 * (1 + (x div (1 + ((~1 + loop(\(x,i).2x,x,(2 + (x mod 2)))) mod (x + 1)))))) div 2) div 2)
A079067: 0 0 1 0 2 0 3 0 1 1 4 0 5 2 1 0
(2 + ((3 * (1 + loop(\(x,i).(x + (3 * (x + (i mod 2)))),x,1) - (2 * (x mod 2)))) div 2))
A276300: 5 11 45 173 693 2765 11061 44237 176949 707789 2831157 11324621 45298485 181193933 724775733 2899102925
((2 + (((((x + 2) * (1 + loop(\(x,i).(x + (x div (2 + (x mod 2)))),x,2))) div 2) div 2) div 3)) div 2)
A337495: 1 1 1 2 3 4 7 11 16 26 42
(~2 + ((3 * compr(\x.(2 - (x mod (3 * (2 + (if ((x + ~1) mod 4) <= 0 then 2 else 1))))),x)) div 2))
A213539: 1 2 4 5 7 8 10 11 14 16 19 20 22 23 28 29
(2 + ((3 * (x + ((x + loop(\(x,i).(1 - (x2 div (x - ((~x + 2) div 2)))),2,x)) div 2))) div 2))
A183234: 2 5 8 9 12 14 17 20 23 26 27 30 33 35 38 41
((loop(\(x,i).2x,x,compr(\x.(x mod (1 + (4 * (x mod (2 + (x mod 2)))))),(x + 3))) div 2) div 2)
A240135: 1 3 8 18 40 96 224 480 1024 2304 5120 10752 22528 49152 102400 212992
(4 * (1 + compr(\x.((x + 1) mod (1 + (x div (2 + (loop(\(x,i).(2x + 2),x,1) mod (x + 1)))))),x)))
A322136: 4 8 12 16 24 32 36 40 48 64 72 80 96 108 112 120
((x - ((loop(\(x,i).2x,x,(1 + (x mod (1 + (x mod (1 + (x mod 4))))))) mod (x + 1)) div 2)) div 2)
A085599: 0 0 1 1 2 1 3 3 3 3 5 3 6 5 4 7
((((~1 + loop(\(x,i).2x,x,((x mod 6) - (x mod 5)))) mod (x + 1)) div 2) div 2)
A333707: 0 0 0 0 1 0 1 1 1 1 0 1 2 2 1 3
(1 - ((x mod (2 + ((1 + (2 * (if (~4 + (x div 2)) <= 0 then 1 else (x div 3)))) mod (x + 1)))) div 2))
A321895-A321758: 1 1 1 0 ~1 1 1 0 0 ~1 1 0 1 0 0 0
(x + (((x + (x mod 2)) div 5) + (if x <= 0 then 1 else 4x)) - (((x + 1) div 2) div 2))
A313581: 1 5 10 14 19 25 30 34 39 45 50 54 59 64 69 74
(~2 + (((3 * (2 + (if (x mod (1 - (2 * ((~x + 1) div (2 + (x div 2)))))) <= 0 then 1 else x))) div 2) div 2))
A271439: 0 0 1 0 2 3 0 4 5 6 0 7 8 9 10 0
((((loop(\(x,i).8x,x,(9x + 7)) div 2) div 2) div 2) div 2)
A229282: 0 8 100 1088 11008 106496 999424 9175040 82837504 738197504 6509559808 56908316672 493921239040 4260607557632 36558761623552 312261302288384
((loop(\(x,i).x2,1,(2 * (x div (1 - ((~x + 1) div (3 + (x mod 6))))))) div 2) div 2)
A262690: 0 1 1 1 4 4 4 4 4 9 9 9 4 9 9 9
(2 + (16 * (~1 + (6 * (2 + (3 * loop(\(x,i).2x,x,2)))))))
A304608: 754 1330 2482 4786 9394 18610 37042 73906 147634 295090 590002 1179826 2359474 4718770 9437362 18874546
((((((loop(\(x,i).x3,1,(4x2 + 4x + 1)) div 2) div 2) div 2) div 2) div 2) div 2)
A219089: 0 11 244 1838 8303 27680 75418 177978 377149 735091 1340095 2313060 3814697 6053445 9294114 13867245
(1 - ((x + 1) div (2 + (x div (if (~2 + (2x mod (4 + (x div 4)))) <= 0 then 1 else 4)))))
A335977: 1 1 1 1 0 1 1 ~1 ~1 1 1 ~2 ~1 ~1 1 1
loop(\(x,i).(50x2 + 129x + 79),x,8)
A100351: 8 4311
(~2 + (2 * ((x + 2) + ((2x + ((~x + (if x <= 0 then 2 else 1)) mod 9)) div 3))))
A194388: 2 4 14 16 18 22 24 26 30 32 34 44 46 48 52 54
((x div 2) - ((x - ((loop(\(x,i).(1 + ((x + (x2 div 4)) div 3)),2,x) div 2) div 2)) div 2))
A067772: 0 0 0 0 0 0 1 0 1 1 2 2 4 4 6 7
(if ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) <= 0 then 1 else ((x div 2) - (2 * ((x div 2) mod 2))))
A205552: 1 1 1 1 2 1 1 1 4 1 1 3 6 6 1 1
((1 + ((6x + 24) mod loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))) mod 4)
A035148: 1 1 1 1 0 1 1 1 1 0 0 1 2 1 0 1
(2 + (if x <= 0 then 1 else ((x + 2) + ((((1 + (x div 2)) div 3) * (1 + (((x + 1) div 2) div 2))) div 2))))
A216189: 3 5 6 7 9 10 11 12 13 14 17 19 20 21 22 24
(2 + ((x + (x2 div loop(\(x,i).(x + 1),(2 + (2x div (4 + (x div 4)))),2))) div 2))
A060620: 2 2 3 4 5 6 8 9 11 12 14 16 18 20 21 23
(((x + 1) * loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + 1),(x + 2))) div (x + 4))
A002694: 1 6 28 120 495 2002 8008 31824 125970 497420 1961256 7726160 30421755 119759850 471435600 1855967520
((2x + ~1) + (2 * loop(\(x,i).(3x2 + 16x + 16),2x,3)))
A242833: 5 52631 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 * (2x + ((2 * (2x div (4 + (x div 8)))) div 3))))
A311612: 1 4 8 12 18 22 28 32 36 40 44 48 52 58 62 68
(if x <= 0 then 1 else (2 * (2x + (((~x + (3 * (x - (2x div 5)))) div 2) div 2))))
A310342: 1 4 10 12 18 22 26 32 34 40 44 48 54 56 62 66
(4x + (if x <= 0 then 1 else ((2 * (2x div (4 + (x div 8)))) div 3)))
A311458: 1 4 8 12 17 21 26 30 34 38 42 46 50 55 59 64
(if x <= 0 then 1 else (4x + ((2 * (x + ((x + ((1 - (x div 2)) mod 4)) div 2))) div 3)))
A313635: 1 5 10 14 20 26 30 35 40 45 50 54 60 66 70 75
(((2 * (1 + ((x - (((x div 2) div 3) mod 2)) div 2))) div 3) + (if x <= 0 then 1 else 4x))
A312926: 1 4 9 13 18 22 26 30 34 39 43 48 52 56 61 65
compr(\x.((x - (x2 mod (11x + 12))) div 2),(if x <= 0 then 1 else 4x))
A058759: 1 4 8 13
A311797: 1 4 8 13 17 21 25 29 33 37 41 45 50 54 59 63
(((x + ((x + ((2 - (x div 2)) mod 6)) div 3)) div 2) + (if x <= 0 then 1 else 4x))
A314841: 1 5 9 14 18 23 28 33 38 42 47 51 56 61 65 70
(x + (((~x + 1) div (1 + (2 * (2 + (((x div 2) div 3) mod 2))))) + (if x <= 0 then 1 else 4x)))
A314898: 1 5 9 14 19 24 29 34 39 43 48 53 57 62 67 72
(2 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + (((((x + 1) div 2) div 2) * (x div 2)) mod 2)))
A171048: 2 3 5 8 11 13 18 19 23 29 31 38 41 43 48 53
(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) - (((((x + 1) div 2) div 2) * (x div 2)) mod 2))
A171040: 2 3 5 6 11 13 16 19 23 29 31 36 41 43 46 53
((x + 6) + ((if x <= 0 then 1 else (2 * (8x - (x div 3)))) + (x mod 2)))
A063165: 7 24 40 56 72 90 104 122 138 154 170 188 202 220 236 252
(2 + compr(\x.(~1 + ((loop(\(x,i).((2x + 1) - ((1 - (x div 2)) div 3)),x,1) div 2) mod 3)),x))
A286057: 2 3 4 6 7 9 10 11 12 13 14 15 18 19 20 22
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod (2 + (x * (1 + (x mod 8)))))
A171014: 0 3 5 7 11 13 17 19 3 9 31 37 41 43 47 53
(((7x + 3) * loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1)) div 2)
A026619: 1 5 17 60 217 798 2970 11154 42185 160446 613054 2351440 9048522 34916300 135059220 523521630
(if x <= 0 then 1 else (2 * (x + ((x - (2 * ((2x div (4 + (x div 4))) mod 2))) div 3))))
A058825: 1 2 4 6 8 12 16 18 20 22 24 28 30 32 36 40
loop(\(x,i).x2,1,((x + 2) + ((1 + ((((x + 1) div 5) * (x div 3)) div 2)) div 2)))
A340674: 4 9 16 25 36 49 81 100 121 169 196 225 256 289 361 441
(if x <= 0 then 1 else (2 * (x + ((x + ((x - ((((~x + 1) * (x div 2)) div 2) div 3)) mod 3)) div 2))))
A231407: 1 4 6
A171945: 1 4 6 10 14 16 18 22 24 26 30 34 38 40 42 46
(2 + compr(\x.(1 - (loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,1) mod (2 + (x * (x mod 2))))),x))
A273200: 2 3 4 5 7 8 9 11 13 16 17 19 21 23 25 27
compr(\x.(2 - ((x + 2) mod 12)),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A031344: 2 3 5 7 13 15 19 21 27 33 37 43 49 51 55 63
(~2 + ((x + 1) * (2 + (x div 8))) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A082899: 0 1 1 1 ~1 ~1 ~3 ~3 4 1 2 ~1 ~2 ~1 ~2 ~5
compr(\x.(2 - ((x + 2) mod 10)),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A004682: 2 3 5 7 13 15 21 23 27 35 37 45 51 53 57 65
(1 - ((1 + ((x + 1) mod (1 + (loop(\(x,i).2x,x,(1 + (x mod 2))) mod (2x + 1))))) mod (x + 2)))
A295306-A295303: 0 0 1 ~1 1 1 1 0 ~1 1 1 0 1 1 1 ~1
((~x + ~3) + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(1 + (x div 2)),(1 + (x mod 2))))
A194124: 0 2 5 14 28 62 117 242 451 912 1703 3418 6420 12854 24293 48602
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(7x + 2)) div (x + 2))
A000782: 1 3 8 23 70 222 726 2431 8294 28730 100776 357238 1277788 4605980 16715250 61020495
((2x + 1) + ((2 * (1 + (x div (1 + (if (x mod 2) <= 0 then ((x div 2) mod 2) else 3))))) mod 3))
A325428: 3 5 6 9 10 12 15 16 17 19 21 23 27 29 30 33
(3x + (if x <= 0 then 1 else (x + (((x - (((x mod 6) - (x div 2)) div 2)) div 2) div 2))))
A311292: 1 4 8 12 16 21 26 30 34 38 42 46 51 56 60 64
((2x + 1) - ((x div 2) + ((1 - (4 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 3)))
A285971: 2 6 8 11 14 18 21 24 26 30 32 35 38 41 43 47
((if x <= 0 then 0 else (~1 + ((x mod 2) + (x mod (1 + (((x div 2) - (x mod 2)) mod (1 + (x div 2)))))))) + (x div 2))
A117248: 0 0 0 1 2 3 4 4 6 5 8 6 10 7 12 8
(((x + (loop(\(x,i).(1 + ((x + ((x2 div 2) div 3)) div 2)),2,x) div 3)) div 2) - (x div 2))
A238708: 0 0 0 1 0 1 1 2 2 3 4 5 6 8 10 13
((x + 1) + (((4 * (x + (if (~2 + (x div 2)) <= 0 then 1 else 2))) div 3) + (x div 2)) - (x mod 2))
A284791: 2 3 8 9 13 15 20 22 26 27 32 33 37 39 43 44
(1 + ((x mod (1 + (x div (1 + (loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)))))) + (x mod 2)))
A276632-A134332-A079866: 1 2 3 2 5 2 7 2 3 3 11 2 13 3 3 2
(1 + ((if (x + ~1) <= 0 then 0 else (1 + ((x + ~1) mod (1 + (x mod (2 + (x div 5))))))) + (x mod 2)))
A196437: 1 2 2 3 2 4 2 3 3 3 2 5 2 3 3 3
(1 + (((x * (x div 2)) mod (1 + (if ((x + 1) mod 8) <= 0 then 8 else 1))) + (x mod 2)))
A268361: 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 8
(1 + (9 * loop(\(x,i).(10x + (i mod 2)),x,1)) - (x mod 2))
A179557: 10 99 991 9909 99091 990909 9909091 99090909 990909091 9909090909 99090909091 990909090909 9909090909091 99090909090909 990909090909091 9909090909090909
(1 + ((x + 1) div (1 + ((if (16 mod (x + 1)) <= 0 then 1 else 2) * (x mod 2)))) - (x mod 2))
A109170: 2 1 4 2 6 2 8 4 10 3 12 4 14 4 16 8
(1 + (((1 + (~x mod (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))) mod (x + 1)) + (x mod 2)))
A327730: 1 2 2 4 2 4 2 4 2 4 2 8 2 4 4 4
(1 + (2 * ((((2x + 1) mod (1 - (x div ~4))) div 2) + (if x <= 0 then 0 else 1))) - (x mod 2))
A086374: 1 2 3 2 3 4 3 2 5 4 3 4 3 4 7 2
(((x + 1) div (if x <= 0 then 1 else (2 * (1 + ((1 - (2 * ((x div 2) mod 2))) mod (1 + (x div 2))))))) - (x mod 2))
A280605: 1 0 0 0 1 0 0 0 2 1 0 0 3 2 0 0
((if x <= 0 then 1 else (2 + ((1 + ((x div 2) div (1 + (x mod (2 * (1 + (x mod 2))))))) div 3))) - (x mod 2))
A073407: 1 1 2 1 3 1 3 1 3 2 4 1 4 2 4 1
((if (x + ~1) <= 0 then 1 else (2 * (((x2 mod (x - ((~x + 2) div 2))) div (x + 1)) + (x mod 2)))) - (x mod 2))
A204065-A056898: 1 0 0 1 0 1 0 3 2 1 0 1 0 3 2 1
(loop(\(x,i).(2 * ((((2x * (1 + (2 * i))) div (2 + i)) * (~1 + (2 * i))) div (1 + i))),x,x) div 2)
A046715: 0 1 10 105 1176 13860 169884 2147145 27810640 367479684 4936848280 67255063876 927192688800 12914469594000 181497968832600 2570903476583625
((4x + 2) + (if (x div 8) <= 0 then 1 else (x div (~2 + ((~x + 2) div 4)))))
A254311: 3 7 11 15 19 23 27 31 32 35 39 43 47 51 55 59
((x + 1) + (6 * (if x <= 0 then 1 else (4 * ((x + 1) + (3 * (x + (x mod 2))))))))
A308610: 7 194 219
((x + 1) + (((x + 1) + (if x <= 0 then 0 else (1 - ((0 - ((~x + 1) mod 5)) div 2)))) div 3))
A288224: 1 3 5 6 7 8 9 11 13 14 15 16 18 19 20 22
(x + (if x <= 0 then 1 else ((3x2 + 6x + ~1) + (((x3 + ~x) div 2) div 3))))
A330395: 1 9 26 51 85 129 184 251 331 425 534 659 801 961 1140 1339
compr(\x.(1 - (x mod (1 + (2 * (3 - ((x div 2) mod (1 + (if (x mod 2) <= 0 then 6 else 1)))))))),x)
A345944: 1 2 3 4 5 7 9 11 13 16 17 19 23 25 27 29
((~x + 1) + (2 * ((2x + 1) div (1 + (2 * ((x mod (1 + (if (x mod 4) <= 0 then 0 else 2))) div 2))))))
A120229: 3 6 1 12 15 2 21 24 27 30 33 4 39 42 5 48
(5x + (loop(\(x,i).(2 + (x div 2)),(x + ~8),1) + ((x + 1) div 3)))
A315690: 1 6 12 17 22 28 33 38 44 50 56 62 67 72 78 83
(x + (x2 div (5 + (if x <= 0 then 1 else (x - (2 * ((x mod (2 + (x div 2))) div 3)))))))
A060831: 0 1 2 4 5 7 9 11 12 15 17 19 21 23 25 29
(~x + ((2 * ((2x + 2) + ((x + 2) div (2 + (if (~2 + (x div 4)) <= 0 then 1 else 2))))) div 3))
A324473: 1 2 2 3 4 4 4 5 6 6 7 7 7 7 8 9
(x + (if (x + ~1) <= 0 then 1 else (2 - (((~x + 1) - (6 * (x div 8))) div 3))))
A193260: 1 2 5 6 7 9 10 11 15 16 17 19 20 21 23 24
((~x + 1) + ((x + loop(\(x,i).((x + 1) - (((~x + ~1) + (2 * (x mod 2))) div 5)),x,1)) div 2))
A066447: 1 1 2 2 3 4 6 8 10 13 16 20 26 32 40 50
((~x + 1) + (((x2 + ~x) + (loop(\(x,i).x2,1,(~2x2 + 2x + ~1)) div 3)) div 2))
A345897: 1 0 4 29 107 286 630 1219 2149 3532 5496 8185 11759 16394 22282 29631
((2x + 1) + (loop(\(x,i).(0 - (3 * ((~x + ((~x + 2) div 4)) div 2))),2,x) div 2))
A190546: 1 6 8 13 18 20 25 30 32 35 37 42 47 49 54 59
(x + ((6 * (x + (if x <= 0 then 1 else (x + (2 * ((x + 1) div 5)))))) div (x + 1)))
A083133: 6 7 10 12 16 17 18
((x2 + x + 1) + loop(\(x,i).(x7 + x5 + x3 + x),1,(x + 1)))
A123111: 5 173 2467 17489 81401 287965 840743 2130497 4842829 10101101 19649675 36082513 63122177 105954269 171622351 269488385
loop(\(x,i).(x + (((x + 2) + ((x - (((1 + ((x2 + ~x) div 2)) div 2) div 2)) div 2)) div 2)),(x + ~1),x)
A079287: 0 1 4 10 18 23 25
(~x - (((x - ((x3 + 3x2 + 2x + 6) div 3)) div 2) + (if x <= 0 then 1 else x)))
A306262: 0 0 0 4 11 24 42 68 101 144 196 260 335 424 526 644
compr(\x.(if x <= 0 then 1 else (2 * (x mod (1 + (x div (1 + (2 * (1 + (2x mod 7))))))))),x)
A128168: 1 2 3 4 5 6 8 9 10 12 15 16 20 24 27 30
(2x * (1 + ((1 + ((1 + ((x * loop(\(x,i).(2 * ((x + 1) + (x div 2))),x,1)) div 2)) div 2)) div 2)))
A265084: 0 4 20 108 544 2540
loop(\(x,i).(~1 + (x mod 9)),(((x + 1) div 2) - ((3 * (x div 4)) div 2)),x)
A180018: 0 0 1 1 3 3 4 4 7 7 ~1 ~1 1 1 2 2
((x + 1) - loop(\(x,i).(((2x + 1) div 3) - (((x2 + ~x) div 2) div (x + 3))),2,x))
A227065: 1 1 2 3 3 5 5 6 7 8 8 9 10 12 12 14
((x + 2) + ((x + 1) * (2 + ((x + 1) * (1 + loop(\(x,i).(4x * i),5,x))))))
A123693: 5 491531
compr(\x.(((x + ~1) + (x mod (1 + (x div (1 + (if (x mod 2) <= 0 then 6 else 1)))))) mod 8),x)
A319281: 1 16 17 33 49 65 81 97 113 129 145 161 177 193 209 225
(if (2 - ((x + 1) div (1 + (2 * (((x + 1) * (x div 2)) mod 3))))) <= 0 then (2 + (x div 4)) else x)
A079243: 0 2 2 3
A229989: 0 2 2 3 4 3 3 3 4 4 4 4 5 5 5 5
((2x + 2) + ((3x + ((if (x mod 4) <= 0 then 2 else 1) + (x div 3))) div 3))
A184872: 2 5 8 11 15 17 21 24 27 30 33 36 40 42 45 49
(~x + (if x <= 0 then 1 else (x + (2 * ((x mod (3 + (((1 + (x div 4)) mod 2) * (x div 2)))) div 2)))))
A103272: 1 0 2 2 0 2 0 0 0 2 2 2 0 0 2 0
(x + loop(\(x,i).(2 + ((x - ((2 - ((x + 1) mod (1 - (x mod ~7)))) div 2)) div 2)),2,x))
A299491: 2 4 6 7 8 9 10 11 13 14 15 16 18 19 20 22
loop(\(x,i).(15x + 84),1,x5)
A113931: 84 99 564
(3x + (((x + 1) + (((x + 1) * (if ((x + ~1) mod 4) <= 0 then 1 else 2)) div 3)) mod 2))
A190742: 1 3 7 9 12 15 19 22 25 28 30 33 37 39 43 45
(3x + (if x <= 0 then 1 else (2x + ((x div (5 * (1 + (x mod 3)))) mod 2))))
A313736: 1 5 10 15 20 25 31 35 40 46 51 55 60 66 70 76
(x4 * ((x3 * (x + ((x + loop(\(x,i).x3,2,x)) div 2))) div 2))
A283028: 0 1 16576 10766601 1073790976 38147265625 705278736576 8308236966001 70368756760576 463255079498001 2500000075000000 11487432626662201 46221065046245376 166354152907593001 544488335559184576 1642102090850390625
(1 + (x div (1 + (x mod (1 + (x mod (1 + (x div (2 + (2 div (1 + (x mod (2 * (1 + (x mod 2)))))))))))))))
A346152-A088387: 1 2 3 2 5 3 7 2 3 5 11 2 13 7 5 2
(1 + (x div (1 + (x mod (1 + (x mod (1 + (x div (2 + ((2x mod (1 + (x div 3))) mod 2))))))))))
A071889: 1 2 3 2 5 2 7 2 3 2 11 2 13 7 3 2
(1 + (x div (1 + (x mod ((x + 1) - ((2x + 1) mod (1 + (2x mod (2 + (x div 4))))))))))
A340679-A340677-A290479-A166142: 1 1 1 1 1 6 1 1 1 10 1 6 1 14 15 1
compr(\x.((x div 2) mod 2),(1 + ((x div 2) mod (1 + (x mod (1 + (7 mod (1 + (x div 2)))))))))
A212173: 1 1 1 4 1 1 1 8 4 1 1 4 1 1 1 16
(1 + (x mod (1 + (x mod (1 + ((1 + (7 * ((~x + 1) mod 4))) mod (x + 1)))))))
A235872: 1 2 1 4 1 2 1 8 9 2 1 4 1 2 1 16
(1 + (x mod (1 + (x mod (1 + ((1 + (x mod (1 + (2 * (2 + (x div 8)))))) mod (x + 1)))))))
A303781: 1 1 1 1 1 2 1 4 3 2 1 6 1 2 1 1
(1 + (x mod (1 + (x mod (1 + (x div (2 + ((1 + (((1 + (x div 4)) * (x div 2)) div 2)) mod 2))))))))
A098372: 1 1 1 2 1 2 1 4 3 2 1 6 1 2 5 4
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (~1 + (~x mod 5))))
A259341: 1 1 1 1 1 1 1 3 2 1 1 4 5 2 1 1
(1 + (x2 mod (1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))))
A245185-A242093-A131373-A034853: 1 1 1 1 1 1 1 2 2 1 1 2 5 2 1 1
(1 + ((x + 1) mod (1 + ((2 * (1 + ((1 + (x2 div (2 + (x div 3)))) div 2))) div 3))))
A200648: 1 1 2 2 3 3 3 4 3 4 4 4 5 4 4 5
(1 + ((~2x + 1) mod (1 + ((x * (1 - ((x3 div 8) mod 2))) div 3))))
A108888: 1 1 1 1 2 1 1 3 1 1 1 4 3 1 1 1
(1 + ((3 * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) mod (1 + (x div 3))))
A146532-A082907: 1 1 1 1 2 1 1 1 1 1 1 4 2 4 1 1
((x + 1) - ((1 - (2 * ((x div 5) mod 2))) mod (1 + (2 * (1 + (x mod 5))))))
A167831: 0 1 2 3 4 4 3 2 1 0 10 11 12 13 14 14
((x + 1) div (1 + (x mod (1 + ((1 + (x div 2)) mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4))))))))))
A090395: 1 1 3 4 5 3 7 2 3 5 11 2 13 7 15 16
(1 + (3 mod (1 + (x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))))))
A329618: 1 1 1 2 1 2 1 1 2 2 1 1 1 2 2 4
(1 + (x mod (1 + (2 * ((2 - (((x + ~2) - (x div 3)) mod 3)) mod (1 + (x div 3)))))))
A098802-A048804: 1 1 1 1 2 1 1 3 3 1 1 2 3 2 1 1
(1 + (x2 mod (1 + (2 * ((4x + ~1) mod (1 + (2x mod (2 + (x div 4)))))))))
A165194: 1 1 1 1 1 2 1 1 1 2 1 2 5 2 1 1
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (2 * (x div 5)))))
A274310-A172991: 1 1 1 1 2 1 1 4 4 1 1 6 11 6 1 1
(1 + ((x + 1) div (1 + (x div 2) - ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2))))
A131470: 2 3 2 5 3 4 3 9 5 6 4 7 5 5 4 17
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (~1 + (2 * (((x + ~1) div 2) mod 2)))))
A307079: 1 1 1 1 2 1 1 2 2 1 1 2 3 0 1 1
(1 + (((6x + 5) - (x div 7)) mod 9))
A037905: 6 3 9 6 3 9 6 2 8 5 2 8 5 2 7 4
(1 + ((1 + ((1 + ((((x + 1) div 2) div 2) mod 4)) * (1 + (x div 3)))) div 5))
A194621: 1 1 1 2 2 2 2 3 3 3 3 4 5 5 5 2
((~1 + ((~2x + 2) mod (4 + (x div 4)))) div (1 + (x2 mod (x + 5))))
A176918: 1 ~1 0 ~1 0 0 ~1 1 0 0 ~1 0 0 0 0 ~1
(1 + (((x + 1) - (x div (1 + ((x div 2) mod (1 + (x mod (1 + ((~x + 2) mod 4)))))))) div 3))
A336424: 1 1 1 2 1 1 1 3 2 1 1 3 1 1 1 5
(~1 + ((1 + ((x + 1) div (~1 + (2 * (((~1 + (2x mod (2 + (x div 2)))) div 2) mod 2))))) mod 3))
A091338: 1 ~1 0 1 ~1 0 ~1 ~1 0 1 1 0 1 1 0 1
(~1 + ((~1 + ((~2 + (x mod 2)) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))) mod 3))
A103447: 1 1 1 1 ~1 1 1 ~1 ~1 1 1 0 1 0 1 1
(1 + ((1 + ((x + 2) mod (2 * (1 + (x mod (1 + ((x2 + 2x) mod 8))))))) div 3))
A317954: 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 1
((((x + 1) div 2) div 2) div (1 + ((1 + ((2x + ~1) mod (4 + (x div 4)))) mod 3)))
A093555: 0 0 0 0 1 0 0 1 1 2 0 1 3 1 1 1
(1 + (((((2x + ~1) mod (4 + (x div 4))) div 2) * (1 + (x div 4))) div 3))
A179009: 1 1 1 1 1 2 1 1 2 3 1 2 2 3 5 1
(~1 + (((x + ~1) + ((1 + (x mod (1 + (2 * (1 + (x mod 5)))))) div 3)) mod 3))
A174854: 1 ~1 1 ~1 0 1 1 ~1 0 1 ~1 0 0 0 1 1
(1 + (3 * (((x * (1 - ((x3 div 8) mod 2))) + (x mod 2)) div 3)))
A316620-A316123-A305360-A304952-A304676-A304010: 1 1 1 1 4 1 1 7 7 1 1 13 13 13 1 1
(1 + (((2 - (2 * ((x + (x div 8)) mod 5))) mod (x + 1)) div 3))
A186807-A114282-A093628: 1 1 1 1 2 1 1 3 2 1 1 4 4 3 1 1
(1 + (3 * ((1 + (3 * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2))) div 2)))
A174095: 1 1 1 1 7 1 1 7 7 1 1 7 10 7 1 1
(1 div ((x + 1) mod (~1 + (6 * (~1 + (2 * ((2x + ~1) mod 7)))))))
A284502: 1 0 0 0 ~1 0 0 0 0 0 0 ~1 0 0 0 1
(1 + ((2 * (1 + (((2x + 1) mod (1 + (2 * (2 + (x div 8))))) div 2))) div 3))
A106036: 1 2 1 2 3 1 2 1 2 3 1 2 3 3 1 2
(1 + ((2 * (1 + (((x + 1) div (2 - (16 mod (~x + ~1)))) div 2))) div 3))
A306694-A296134: 1 1 1 2 1 1 1 3 2 1 1 1 1 1 1 4
(1 + ((2 * (1 + (((((2x + 1) div 3) * (1 + (x div 3))) div 2) div 2))) div 3))
A029058: 1 1 1 2 2 2 3 3 3 5 6 6 8 9 9 11
(1 + ((2 * (1 + ((((~x + 3) * (~1 - ((x div 2) div 3))) div 2) div 2))) div 3))
A029109: 1 1 1 1 1 1 2 3 3 3 3 4 5 6 7 7
(1 + ((2 * ((2x + 2) + (x div 5) - (x div 12))) div 3))
A242482-A085784-A085783: 2 3 5 6 7 9 11 12 13 15 17 18 19 20 21 23
(1 + (6 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))
A287326: 1 1 1 1 7 1 1 13 13 1 1 19 25 19 1 1
(1 + (3 * ((1 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 2)) div 2)))
A124376-A047671: 1 1 1 1 4 1 1 7 7 1 1 10 19 10 1 1
(1 + (3 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)))
A081577: 1 1 1 1 4 1 1 7 7 1 1 10 22 10 1 1
((6x + 5) + (x div 9) - (((x + 1) div 2) div 3))
A189751: 5 11 17 23 29 34 40 46 52 59 65 70 76 82 88 94
(1 + ((x - (2 * (((2 - ((~x + 2) div 8)) mod (1 + (x div 3))) div 2))) mod 3))
A106590: 1 2 3 1 2 3 1 2 3 2 3 3 3 1 2 3
((x + 1) mod (1 + ((4 * (1 + ((x2 + 2x) div ((x + 4) + (x div 2))))) div 3)))
A029315: 1 0 0 1 0 0 1 1 0 1 1 1 2 1 2 2
(11 * (x - (9 * (~x + (x mod 10)))))
A338754: 0 11 22 33 44 55 66 77 88 99 1100 1111 1122 1133 1144 1155
(1 + (((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (2 - (x div 2))) div 2) mod 3))
A178395-A098505: 1 1 1 1 1 1 1 3 3 1 1 2 3 2 1 1
(~1 + ((2 * ((x + 1) + (4 * (x - ((2x + ~4) div 7))))) div 3))
A094350: 2 5 6 9 13 16 17 20 23 24 27 31 34 35 38 41
(~1 + ((2 * ((2x + 2) + (15 * (x2 div 3)))) div 3))
A292472: 0 1 13 34 55
(1 + ((x + (4 * ((x + 1) + (x div (2 - (x div (~1 + ((~x + 2) div 4)))))))) div 3))
A187951: 2 4 5 7 10 12 13 15 17 18 20 23 25 26 28 31
(1 + ((x + (2 * ((2x + 2) + ((~x + 1) div (2 + (((x + 1) div 2) div 3)))))) div 3))
A184867: 2 4 5 6 7 9 11 12 13 15 17 18 20 22 23 24
(2 div (1 + ((1 + (3 * ((~2x + 2) mod (4 + (x div 4))))) mod (x + 3))))
A176891: 1 1 0 1 0 0 1 2 0 0 1 0 0 0 0 1
((1 + (x mod 2)) div (1 + (x mod (2 + ((((x + 2) mod 7) mod 2) + (x mod 2))))))
A257217: 1 1 1 0 1 0 1 1 0 2 0 0 1 1 1 0
(1 + (x mod (1 + ((2 * (2x mod (3 * (1 + (8 * (x mod 2)))))) + (x mod 2)))))
A064830: 1 2 3 4 5 6 1 8 3 10 1 12 1 14 3 8
((x + 1) - ((1 + (x div (1 + ((x2 + 2x) mod (1 + ((2 - (x div 2)) mod 4)))))) mod (x + 1)))
A293303: 1 2 3 2 5 6 7 6 6 10 11 6 13 14 15 12
(1 + ((~1 + ((1 + (x mod (2 + ((x mod (1 + ((~x + 2) mod 4))) div 2)))) mod 3)) mod (x + 1)))
A331287: 1 2 1 1 1 2 1 2 9 2 1 12 1 2 1 1
((x + 1) - ((1 + (x mod (2 * (1 + (x mod (2 * (1 + (x mod (1 + (x div 3)))))))))) mod (x + 1)))
A108514: 1 2 2 4 4 4 6 8 6 8 10 8 12 12 10 16
(1 + ((1 - ((~1 + ((~2x + 2) mod (4 + (x div 4)))) mod 5)) div (x + 1)))
A128189: 1 ~1 1 0 0 1 0 0 0 1 0 0 1 0 1 0
((x + 1) - (x mod (2 + (x div (1 + (x mod (1 + (x mod (1 + (x div (2 + (x div 5))))))))))))
A101322: 1 1 1 4 1 5 1 6 9 7 1 11 1 9 13 16
(((x2 + x) div 5) mod (1 + (x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4))))))))
A123391: 0 0 0 2 0 0 0 3 2 0 0 2 0 0 0 0
(1 + ((x + 1) div (3 + (x div (3 * ((1 + (x div 8)) * (1 + (x mod 2))))))))
A078705: 1 1 2 2 2 3 2 3 3 4 3 5 3 4 4 5
(1 + (((x + 1) - ((2 * (1 + ((1 + (((x + ~2) div 3) * (x div 2))) div 2))) div 3)) div 2))
A238407: 1 2 2 3 3 3 3 4 4 4 4 4 4 5 3 4
(1 + ((x mod (2 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 2))) div 2))
A331485: 1 1 1 1 1 1 1 2 2 1 1 3 7 3 1 1
(1 + ((1 + ((1 + (x div (1 + ((x + ~1) mod (1 + (2 * (1 + ((x div 3) mod 2)))))))) div 2)) div 2))
A141256: 1 2 2 2 2 2 2 3 2 2 2 4 2 5 3 2
(1 + ((1 + ((1 + (x div (1 + (((3 + ((~x + 1) mod 8)) div 2) div 2)))) div 2)) div 2))
A072628: 1 2 1 2 2 2 2 2 2 4 2 2 2 3 3 3
(~1 + (2 * (1 + (((x + 1) - ((1 + (x div 5)) mod (1 + (((x + 1) div 2) div 2)))) mod 2))))
A122567: 3 1 3 3 1 1 3 1 3 1 3 3 1 3 1 1
(~1 + (2 * (1 + (((x + 1) mod (1 + (3 * (((x + 1) mod 8) mod 3)))) div 2))))
A255670: 1 3 1 1 5 1 3 1 1 3 1 1 7 1 3 1
(1 + ((1 + ((1 + ((1 + ((((x + 2) * (x - ((~1 + (x div 2)) div 2))) div 2) div 2)) div 2)) div 2)) div 2))
A018119: 1 2 2 2 2 2 3 3 4 4 4 5 6 7 7 8
(1 + ((1 + ((1 + (((x2 + ~x) + (2 * (((x2 div 2) mod (x + 1)) div 2))) div 2)) div 2)) div 2))
A029011: 1 1 2 2 3 4 6 7 9 10 13 15 19 21 25 28
((((x + 1) div 2) - ((3 * (x div 4)) div 2)) mod (1 + (2 * (x mod 7))))
A140084: 0 1 1 2 1 2 2 0 1 2 2 3 2 3 0 1
(1 + (((1 + (x div 2)) div (1 + (2 * ((1 + (3 * (2 - (x mod 2)))) mod (1 + (x div 2)))))) div 2))
A135222: 1 1 1 2 1 1 1 3 1 1 2 1 4 1 1 1
(2 - ((2x + 1) mod (~1 - ((1 + ((32 mod (x + 1)) div 2)) div 2))))
A136510: 2 2 3 2 3 3 3 2 3 3 5 3 4 3 3 2
(1 + ((1 + ((x + 1) div (2 + ((1 + (x div (1 + (2 * (2 - ((x * (x div 2)) mod 2)))))) mod 2)))) div 2))
A344150: 1 1 2 2 2 3 3 2 3 4 3 4 3 3 4 5
(1 + ((1 + ((x mod (2 + ((1 + (x mod (2 + (x div (2 + (x mod 3)))))) mod (x + 1)))) div 2)) div 2))
A270928: 1 1 2 1 1 1 2 1 2 2 1 2 2 1 1 3
(1 + ((1 + ((((x + 1) * ((x + 2) - (x2 div (x + 16)))) div 2) div 2)) div 2))
A044919: 1 2 3 4 5 6 7 8 10 11 13 15 16 19 20 21
(1 + ((1 + (((2 + ((1 - ((x2 + 2x) mod 7)) mod (x + 1))) div 2) div 2)) div 2))
A167404: 1 1 1 1 2 1 2 1 2 1 1 3 1 2 1 3
(1 + ((1 + (((((x + 1) * ((x - (2x2 mod 5)) div 2)) div 2) div 2) div 2)) div 2))
A103372: 1 1 1 1 1 2 2 2 2 3 4 4 4 5 7 8
(((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((x - (x mod 5)) div 2)))
A129533: 0 0 0 0 1 0 0 3 3 0 0 6 12 6 0 0
(1 + (2 * (3 + ((2 * ((2x + 1) - ((~x + 1) div (2 + (x div 4))))) div 3))))
A192992: 7 11 15 17 19 23 27 29 31 35 39 41 43 47 49 51
(1 + ((((1 - ((2x + ~1) mod (4 + (x div 4)))) mod (2x + 1)) div 3) div 2))
A294453: 1 1 1 1 2 2 1 3 3 3 1 4 5 5 5 1
(1 + ((3 * (x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2)))))))) div 2))
A296131: 1 1 1 2 1 2 1 4 2 2 1 4 1 2 2 5
(1 + ((3 * ((1 + (((1 + ((x * (x mod (2 + (x mod 4)))) div 2)) div 2) div 2)) div 2)) div 2))
A248597: 1 1 1 2 1 2 2 2 1 1 2 2 1 2 4 1
(1 + ((3 * (((1 mod (1 - (2x mod (4 + (x div 4))))) mod (x + 1)) div 2)) div 2))
A156050-A136489: 1 1 1 1 4 1 1 5 5 1 1 8 10 8 1 1
(3 div (1 + (2 * ((2 + ((2x2 + ~1) mod (4 + (x div 4)))) div 3))))
A328747: 1 1 1 1 1 0 1 1 1 0 1 1 3 1 0 1
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x - ((x div 2) div 3)) div 2)))
A026374: 1 1 1 1 3 1 1 4 4 1 1 6 11 6 1 1
((153x + 152) div 7)
A135391: 21 43 65 87 109 131 152 174 196 218 240 262 284 305 327 349
((1 + (9 * ((5x + 4) - (x div 2)))) div 7)
A190323: 5 11 16 23 28 34 40 46 51 58 63 69 74 81 86 92
(x - ((x2 - ((x3 + ~3x2 + 2x) div 9)) div 7))
A074732: 0 1 2 2 2 3 3 4 5 6 8 10 13 16 21 27
((1 + (x div 4)) div ((1 - (2x mod (4 + (x div 4)))) mod 7))
A325458: 1 0 1 0 0 2 0 0 0 3 0 0 0 1 4 0
(2 div ((2 - (x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2))) mod 7))
A250211-A093662: 1 1 1 1 0 1 1 1 2 1 1 0 0 0 1 1
(1 + ((1 + ((x + ((((x + 1) * (x + ((x2 + 2x) div 4))) div 2) div 3)) div 2)) div 2))
A028290: 1 1 2 3 4 6 8 10 14 17 22 27 33 40 48 57
(1 + (2 * (1 + compr(\x.(x - (3 * (1 + (x3 mod 11)))),x))))
A082720: 3 5 7 9 11 13 15 17 19 21 23 29 31 33 37 41
(~1 + (2 * ((1 + (2 * ((x + 1) - ((x mod (1 + ((x div 4) + (x mod 2)))) div 2)))) mod (x + 1))))
A128060: ~1 1 1 1 1 9 1 1 15 1 1 21 1 25 27 1
(1 + ((x + 1) div (2 + ((1 + (2 * ((8x + 8) div 5))) mod (x + 1)))))
A104307: 1 1 2 2 2 3 2 3 3 3 3 3 4 3 3 4
(1 + (((2 + ((1 - (2x mod (1 + (3 * (2 - (x mod 2)))))) mod (x + 1))) mod (x + 1)) div 2))
A265575: 1 1 2 1 2 1 3 1 1 1 5 1 1 1 2 1
(1 + (((2 + (x mod (2 * (1 + (x mod (2 * (1 + (x mod (1 + (x div 3)))))))))) mod (x + 1)) div 2))
A060764: 1 1 2 1 2 2 2 1 3 2 2 3 2 2 4 1
(10 mod (1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 2)))
A301400-A300776: 0 0 0 0 1 0 0 2 2 0 0 4 3 4 0 0
((3x + 3) + (5 * ((x + 2) - ((x + (x div 4)) div ~2))))
A101870: 13 26 34 47 60 68 81 89 102 115 123 136 149 157 170 178
((x + 1) - (2 * ((x - (x div (1 + (x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4))))))))) div 2)))
A195637: 1 2 3 2 5 4 7 2 3 6 11 4 13 8 15 2
(1 + (((5 * compr(\x.(1 - (x mod (1 + (4 * (x mod 5))))),x)) div 2) div 2))
A020900: 2 3 4 6 8 9 11 12 14 16 18 21 22 23 24 27
(1 + (((1 + (((x + 2) * ((x + (x2 div 4)) div 7)) div 2)) div 2) div 2))
A002723: 1 1 1 1 2 2 3 3 5 6 8 9 11 14 19 22
(1 + ((x mod (2 + ((1 + (x mod (1 + (2 * (2 + (((x div 2) div 3) mod 2)))))) mod (x + 1)))) div 2))
A227543: 1 1 1 1 1 2 1 1 1 3 3 3 2 1 1 1
(1 + (2 * (x div (2 + (x mod (2 + (x div (1 + (2 * ((x mod (~1 + (2 * (x div 3)))) mod 2))))))))))
A263159-A229142: 1 1 1 1 1 1 1 3 1 1 1 7 13 1 1 1
(1 + (8 * ((x * (1 - ((x3 div 8) mod 2))) div 5)))
A197401: 1 1 1 1 1 1 1 9 9 1 1 17 17 17 1 1
(1 + (((((x + 1) * (2 + ((2 + (((x div 3) * (x div 2)) div 2)) div 3))) div 2) div 2) div 2))
A145933: 1 1 1 2 2 3 3 4 5 6 7 8 10 11 14 17
(1 + ((((((x + 1) * (~1 + ((~2x + 2) mod (4 + (x div 4))))) div 2) div 2) div 2) div 2))
A155161: 1 0 1 0 1 1 0 2 2 1 0 3 5 3 1 0
(1 - (((2 - (x2 div 2)) div 3) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))))
A164381: 1 1 1 1 0 1 1 1 ~1 1 1 0 0 ~1 1 1
(1 + (((((x + 2) * (1 + ((2 + (((x div 3) * (x div 2)) div 2)) div 3))) div 2) div 2) div 2))
A286219: 1 1 1 1 2 2 3 3 4 5 7 7 9 10 13 15
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + 1) div (2 + (x div 4)))))
A255741-A132892: 1 1 1 1 2 1 1 3 3 1 1 4 5 3 1 1
(1 + (4 * ((x + 2) + ((4 * ((2x + 1) div 9)) div 3))))
A227062: 9 13 17 21 29 33 37 41 45 53 57 61 65 77 81 85
(1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (x div (2 - ((x div 2) mod 2)))) div 2))
A026769: 1 1 1 1 2 1 1 4 3 1 1 6 7 4 1 1
(1 + ((((3x + 3) + (x div 3) - (x mod 10)) div 2) div 2))
A175858: 1 2 2 3 4 4 5 5 6 7 10 10 11 11 12 13
((1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) mod 5)
A177974-A095141: 1 1 1 1 2 1 1 3 3 1 1 4 0 4 1 1
((1 - (x mod (1 + (2 * ((x + ~1) mod (1 + (x div (2 + ((x div 2) mod 3))))))))) mod 5)
A060036: 1 1 1 1 0 1 1 4 4 1 1 4 3 4 1 1
((1 + (x div (2 + ((6 * (1 + (x div 8))) mod (x + 1))))) mod 5)
A181631: 1 1 2 1 2 3 1 1 2 3 4 1 1 1 2 2
((6x + 654) div 5)
A043604: 130 132 133 134 135 136 138 139 140 141 142 144 145 146 147 148
(((1 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 2)) div 2) mod 5)
A341288-A325820-A323473: 0 0 0 0 1 0 0 2 2 0 0 3 1 3 0 0
((x + 5) + ((2 * ((2x + 1) - ((~x + 1) div (2 + (x div 4))))) div 3))
A161537: 5 8 11 13 15 18 21 23 25 28 31 33 35 38 40 42
(((2x + 1) + (2 * (19x div (x + 2)))) div 5)
A202307: 0 3 4 5 6 7 8 8 9 9 10 11 11 11 12 12
(1 + ((((x + 1) + ((13x + 6) mod 9)) div 2) div 2))
A240450: 2 1 3 2 3 4 3 4 3 5 4 5 4 5 6 5
(1 + (((x + (((x + 1) * (2 - ((2 + (x div 2) - (x * (x mod 2))) div (x + 1)))) div 2)) div 2) div 2))
A046700: 1 1 1 2 3 4 4 5 5 7 6 8 7 9 8 10
(1 + (2 * (1 + (((x mod (1 + ((2 - (x mod 8)) mod (x + 1)))) div 3) + (x mod 2)))))
A095366: 3 5 3 7 3 5 3 7 3 5 3 11 3 5 3 7
((1 + ((2 + (((x div 3) * (x div 2)) div 2)) div 3) - (x mod 2)) div (1 + (2 * (x mod 2))))
A029191: 1 0 1 0 2 0 2 0 3 0 4 1 5 1 6 2
((1 - (((x + 1) div 5) div (1 + (x mod (1 + (x mod (3 + (x mod 2)))))))) mod 3)
A035194: 1 1 1 1 0 1 0 1 1 0 2 1 2 0 0 1
(1 - ((1 + (x mod (1 + (2 * (1 + (x mod (1 + ((~x + 2) mod (2 + (x div 3)))))))))) div 3))
A345416: 1 1 0 1 1 0 1 ~1 1 0 1 1 1 0 0 1
((1 + (((49x2 + ~x) div 2) div 3)) div 3)
A293414: 0 3 11 24 43 68 98 133 174 220 272 329 391 459 533 612
((x mod (1 + (x div (1 + (((x mod (~1 + (4 * (~2 + (x mod 2))))) mod 2) + (x mod 2)))))) div 3)
A210722: 0 0 0 0 0 0 0 0 1 0 3 1 4 2 4 2
((1 + (2 * (x mod (1 + ((x + 1) mod (~1 + (2 * ((2x + 2) mod 5)))))))) mod 3)
A271606: 1 0 1 1 1 1 1 1 1 1 0 2 1 1 1 0
((1 + ((2x + 2) * (1 + (2 * (((x mod (~2 + ((~x + 2) div 4))) div 2) mod 2))))) div 3)
A026216-A026196-A026177: 1 4 2 3 10 12 5 16 6 7 22 8 9 28 30 11
((1 + (((x + 2) mod ((x + 3) - (2x mod (4 + (x div 4))))) div 2)) div 3)
A123262: 0 0 1 0 0 1 0 0 0 2 0 0 0 1 3 0
(((x + 1) + ((56x + 1) div (x + 3))) div 3)
A344443: 0 5 8 10 12 13 14 15 16 17 18 18 19 19 20 20
(1 - (((~1 + ((x + ((x - (x div 4)) mod 2) - (x mod 2)) mod 3)) mod (x + 1)) mod 3))
A070965: 1 1 0 1 0 1 1 0 0 1 1 0 1 0 ~1 0
((3x + 3) * (1 + ((9x2 + 9x + 1) div (1 + (x mod 2)))))
A061495: 6 60 504 660 2730 2448 7980 6072 17550 12180 32736 21420 54834 34440 85140 51888
(((x + 1) * (1 + (2 * (1 + ((x + 1) div (2 + (x div (2 + ((~x + 2) mod 4))))))))) mod 3)
A124210: 0 1 0 1 1 0 2 2 0 1 1 0 1 2 0 0
((22x3 + 36x2 + 17x + 3) div 3)
A100163: 1 26 119 324 685 1246 2051 3144 4569 6370 8591 11276 14469 18214 22555 27536
((3x2 + 9x + 6) * (1 + (3 * ((3x2 + 7x + 4) div 2))))
A224455: 42 396 1656 4740 10890 21672 38976 65016 102330 153780 222552 312156 426426 569520 745920 960432
((6x + 4) - (((x + 1) div 3) + ((2x + 1) div 7)))
A189399: 4 10 15 20 26 31 37 42 47 53 58 63 69 75 79 85
((2 * (1 + (x div (3 * (1 + (x mod (2 * (1 + (x mod (3 + (x mod 2))))))))))) div 3)
A064559: 0 0 0 0 1 0 2 0 0 1 1 0 3 2 1 0
(3 + (2 * (1 + (((1 + (x * (2 + (x mod (2 + (x mod 2)))))) * (1 + (x div 2))) div 3))))
A263467: 5 7 11 13 23 47
(3 + (2 * (1 + compr(\x.(2 - (x mod (1 + (4 * (2x mod 5))))),(x + 1)))))
A061116: 11 13 17 19 21 23 27 29 31 37 41 43 47 49 51 53
((2 * (1 + ((1 + (x div (2 + ((6 * (2 - (x div 2))) mod (x + 1))))) div 2))) div 3)
A308117: 0 0 1 0 1 1 1 1 1 0 1 1 2 1 3 2
((x + 3) - (2 * (1 + ((1 + ((((x + 1) * ((1 + (x div 4)) div 2)) div 2) div 2)) div 2))))
A268233: 1 2 3 4 3 4 5 6 7 8 9 8 7 6 7 8
(((1 + (((x + 1) * (1 - ((32 mod (x + 1)) div 2))) div 2)) div 2) mod 3)
A060154: 0 1 0 1 0 0 1 2 1 0 1 0 0 0 0 1
((2 + ((10x2 + 48x + 38) div 5)) div 3)
A024388: 3 7 12 18 26 35 46 58 71 86 101 119 137 157 178 201
(~3 + ((3 * (1 + compr(\x.((x + 2) mod (1 + (8 * (x mod 2)))),(x + 1)))) div 2))
A055047: 1 4 7 9 10 13 16 19 22 25 28 31 34 36 37 40
((2 * ((2x + 4) - ((~x + 1) div (3 + (2 * (x - (x mod 8))))))) div 3)
A138204: 2 4 6 7 8 10 12 13 14 15 16 18 19 20 22 23
(3 * ((3x + 2) - ((x + ((4 * (x div 3)) div 3)) mod 3)))
A198682: 6 12 18 30 36 51 54 69 75 84 90 105 108 123 129 141
(3 * ((3 * (x + ((((x + 1) div (1 + (x mod 4))) mod 2) + (x div 3)))) div 2))
A155504: 3 9 12 21 27 30 36 39 48 57 63 66 75 81 84 90
((((x + 3) * (((x2 + 3x + 2) * (2 + ((x2 + x) div 2))) div 2)) div 2) div 3)
A256859: 1 6 25 80 210 476 966 1800 3135 5170 8151 12376 18200 26040 36380 49776
((((x + 3) * ((5x3 + 17x2 + 16x + 4) div 2)) div 2) div 3)
A051799: 1 14 60 170 385 756 1344 2220 3465 5170 7436 10374 14105 18760 24480 31416
((2 * (1 + compr(\x.(1 - ((x + 1) mod (1 + ((x - ((x div 3) mod 3)) div 2)))),x))) mod 3)
A108964: 0 1 2 1 0 1 2 0 2 1 0 2 0 1 2 1
((((x + 1) * ((5x3 + 21x2 + 28x + 12) div 2)) div 2) div 3)
A117066: 1 11 48 140 325 651 1176 1968 3105 4675 6776 9516 13013 17395 22800 29376
(((28x3 + 3x2 + ~25x) div 2) div 3)
A256650: 0 1 31 118 290 575 1001 1596 2388 3405 4675 6226 8086 10283 12845 15800
((((x2 + 3x + 2) * (x - (9 * ((~x2 + x) div 2)))) div 2) div 3)
A264852: 0 1 22 100 290 665 1316 2352 3900 6105 9130 13156 18382 25025 33320 43520
(((22x3 + 3x2 + ~19x) div 2) div 3)
A256716: 0 1 25 94 230 455 791 1260 1884 2685 3685 4906 6370 8099 10115 12440
(3 * ((x + (((x3 + 3x2 + 2x) div 2) div 3) - (x2 div ~2)) div 2))
A213486: 0 3 12 27 48 78 120 174 240 321 420 537 672 828 1008 1212
(~3 + (4 * (1 + ((3 * (x + ((x + (x2 mod 3)) div 4))) div 2))))
A231754: 1 5 13 17 29 37 41 53 61 65 73 85 89 97 101 109
((4 * (1 + ((1 + ((x + ((2x * (x div 2)) div 5)) div 2)) div 2))) div 3)
A342498: 1 1 2 2 4 4 5 6 8 9 12 12 14 16 18 20
((2 + ((((x3 + 16x2 + 15x) div 2) div 3) div 2)) div 3)
A320272: 0 1 3 6 11 17 25 34 46 60 77 96 117 142 169 200
(((((x + 3) * ((x4 + 7x3 + 18x2 + 20x + 8) div 2)) div 2) div 2) div 3)
A006414: 1 9 40 125 315 686 1344 2430 4125 6655 10296 15379 22295 31500 43520 58956
(324x2 + 492x + 156)
A304619: 156 972 2436 4548 7308 10716 14772 19476 24828 30828 37476 44772 52716 61308 70548 80436
((2 * (2 + (((x mod 2) - ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2)) mod (x + 1)))) div 3)
A080215: 1 2 1 2 1 1 1 2 1 1 1 1 1 1 10 2
((2 * ((x + 2) + ((2 * (x - ((2x2 + ~x) div (x + 3)))) div 3))) div 3)
A161205: 1 2 2 3 4 4 4 4 5 6 6 6 6 6 6 7
((2 * ((2x + 6) - ((~x + 1) div (1 + ((x + 1) div 5))))) div 3)
A186381: 3 5 7 9 10 12 14 15 17 18 19 21 22 24 25 26
(1 - ((2 * (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2))) div 3))
A128545: 1 1 1 1 2 1 1 3 3 1 1 5 8 5 1 1
(1 - (3 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))
A131060: 1 1 1 1 4 1 1 7 7 1 1 10 16 10 1 1
((x + 3) - (2 * (~x + ((x - (((x + ~1) div 2) mod (1 + ((1 + (x div 2)) div 3)))) div 2))))
A045412: 3 6 7 10 13 14 15 18 21 22 25 28 29 30 31 34
(((x + 2) + (2 * ((x + (2 * ((x + (x2 div 3)) div 3))) div 3))) div 3)
A249724: 0 1 2 3 4 5 6 7 8 11 12 14 16 17 20 22
((x + 10) + (((x + 2) div (~2x + 32)) div 2))
A322322: 10 11 12 13 14 15 16 17 18 19 20 21 22 24 26 29
(((x + 1) + ((2 * (1 + ((x3 + 3x2 + 2x) div 5))) div 3)) mod 3)
A254011-A025878: 1 0 0 0 0 1 1 0 0 1 1 1 1 0 1 2
((2x + 2) - (((x + 2) + (x div (2 + (16 mod (1 + (x div 2)))))) div 3))
A275202: 2 3 5 6 8 10 11 12 14 16 18 20 21 22 23 24
(3 * compr(\x.(2 - ((x mod 2) + (x mod (1 + (3 * (2x mod 7)))))),x))
A276381: 3 6 9 15 18 27 30 33 36 39 45 48 51 54 57 60
((5x + 4) + (((x + 1) div 7) + (x div 3)) - (x div 2))
A184912: 4 9 13 19 23 28 34 39 43 49 53 58 63 69 73 79
((3x + ~3) + (5 * ((x + 2) - ((x + (x div 4)) div ~2))))
A134863: 7 20 28 41 54 62 75 83 96 109 117 130 143 151 164 172
(~1 + (2 * ((x + 1) + (((5 * (1 - ((~x + (x mod 3)) div 4))) div 2) div 2))))
A165887: 3 5 7 11 13 15 19 21 23 29 31 33 35 37 39 43
(~1 + (2 * ((x + 1) + (((1 + (((x * ((x + (2 mod (x + 1))) div 3)) div 2) div 2)) div 2) div 2))))
A256862: 1 3 5 7 9 11 15 17 19 21 25 29 31 35 37 39
((x + 3) div ((x + 3) - ((x + (x2 div (5 + (x div 2)))) div 2)))
A274144: 1 1 1 1 1 2 2 2 2 4 4 4 5 8 8 9
(1 + ((x + ((1 + (((((x + 1) * (x + ((x2 + 2x) div 4))) div 2) div 2) div 2)) div 2)) div 2))
A055104: 1 1 2 3 4 6 8 10 13 16 20 24 29 34 41 47
(1 + ((x + ((1 + (((((x + ~1) * (x + ((x * (x div 2)) div 4))) div 2) div 2) div 2)) div 2)) div 2))
A029012: 1 1 2 2 3 4 5 7 8 10 12 14 17 19 23 26
(1 + ((x + ((1 + ((((x * (2 + ((x + (x2 div 3)) div 2))) div 2) div 2) div 2)) div 2)) div 2))
A330500: 1 1 2 3 4 5 6 7 9 11 13 16 19 22 26 30
(1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (x + ((~x + 1) mod 4))) div 2))
A108359-A106597-A100936-A086620: 1 1 1 1 3 1 1 5 5 1 1 7 14 7 1 1
(1 + ((x + ((x + ((((x + ~1) * ((x3 + x) div 2)) div 2) div 5)) div 2)) div 2))
A115992: 1 1 2 4 6 11 19 32 52
(1 + ((x + ((x + (((((x + ~1) * (x + ((x * (x div 2)) div 4))) div 2) div 2) div 2)) div 2)) div 2))
A085756-A029006-A008755: 1 1 2 3 4 5 7 8 10 12 14 16 20 22 26 30
((2x + 1) * (1 + (2 * (2 + ((17x2 + 17x) div 2)))))
A006221: 5 117 535 1463 3105 5665 9347 14355 20893 29165 39375 51727 66425 83673 103675 126635
(0 + (((2 * (1 + ((3x2 + 10x + 8) div 3))) div 3) + (x mod 2)))
A181025: 2 6 9 15 22 31 39
((x + 1) div (1 + ((x div (2 + ((x div 2) div (1 + (x mod (2 + ((x mod 3) div 2))))))) + (x mod 2))))
A078709: 1 1 1 1 2 1 3 2 3 2 5 2 6 3 3 3
(1 + ((x div (2 + ((x + 1) div (2 * (1 + (x mod (1 + (x mod (3 + (x mod 2)))))))))) + (x mod 2)))
A125747: 1 2 2 3 2 3 2 4 3 4 2 5 2 4 4 5
((1 + ((2 * (1 + (((((1 + (x div 2)) div 2) * (x div 2)) div 2) div 2))) div 3)) div (1 + (x mod 2)))
A029214: 1 0 1 0 1 0 2 1 3 1 3 1 4 2 6 3
((2x + 1) - compr(\x.(1 - (x mod (1 + (x mod (1 + (x2 mod (x + 5))))))),x))
A244230: 0 1 2 3 4 4 5 6 7 8 8 8 8 8 8 9
(1 + compr(\x.(~1 + ((1 + ((x + 1) div (2 + ((2 + (x mod 8)) mod (x + 1))))) mod 3)),x))
A184939: 1 2 6 7 8 9 10 18 19 20 21 22 23 24 25 26
(1 + compr(\x.(~1 + ((2 + ((2 * ((x + 1) - (2 * (((x + ~1) div 2) mod 2)))) div 3)) mod 3)),x))
A062895: 1 2 3 4 5 6 7 8 9 11 13 15 17 22 24 26
((x + 1) + (5 mod (1 + ((x * ((x mod (1 + ((~x + 2) mod 4))) div 2)) div 3))))
A058189: 1 2 3 5 5 6 7 10 11 10 11 13 13 14 15 21
(1 + compr(\x.(~1 + ((1 + ((x mod 11) mod 9)) mod (x + 1))),x))
A033075: 1 2 3 4 5 6 7 8 9 10 12 21 23 32 34 43
(1 + compr(\x.(1 - ((x + 1) mod (1 + (x div (1 - (x div (~2 + (((~x + 2) div 2) div 5)))))))),x))
A241561-A241008-A071561: 3 5 7 10 11 13 14 17 19 21 22 23 26 27 29 31
(1 + compr(\x.((x + 1) mod (1 + (4 * (x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4))))))))),x))
A103848: 1 3 5 7 9 10 11 13 15 17 19 23 25 27 29 30
((x + 1) + (((1 + (((x + 1) * (1 + (2 * ((1 + (x div 4)) div 2)))) div 2)) div 2) div 3))
A119931: 1 2 3 4 6 7 8 10 11 12 13 15 18 20 21 22
((x + 1) + ((4 * ((2x + 2) + (((x + 1) + (x div 8)) div 2))) div 3))
A189758: 3 8 12 17 21 26 29 34 39 43 48 52 57 60 65 69
((x + 1) + ((2 * ((x + 2) - ((x mod (2 + (6 mod (1 + (x div 2))))) div 2))) div 3))
A159615: 2 4 5 7 9 10 11 13 15 17 19 20 21 22 23 25
((x + 1) + ((2 * ((x + 2) + ((x + ((2 * (x2 div 2)) div 5)) div 2))) div 3))
A070978: 2 4 6 8 11 13 16 19 22 25 29 32 35 39 43 46
((x + 1) + ((1 + (x mod (1 + (2x div (1 + (x mod (1 + ((~x + 2) mod 4)))))))) mod (x + 1)))
A336465: 1 2 3 6 5 6 7 12 12 10 11 18 13 14 15 24
(x2 mod ((x + 1) + (x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2)))))))))
A277027: 0 1 1 4 1 4 1 9 4 4 1 9 1 4 4 16
((x + 1) + (2 * ((2 * ((x + 1) - ((x div 2) mod (1 + (x mod (1 + (x div 3))))))) div 3)))
A080578: 1 4 7 8 11 14 15 16 19 22 23 26 29 30 31 32
((x + 1) + (2 * ((1 + (9 * (x mod (x - ((x + ~1) mod 8))))) div 2)))
A068860: 1 2 3 4 5 6 7 8 9 10 21 30 41 50 61 70
((x + 1) + (((1 + (((x + ~1) * (1 + (((x2 + 3x + 2) div 2) div 3))) div 2)) div 2) div 2))
A193622: 1 2 3 5 7 10
A062684: 1 2 3 5 7 10 13 18 23 29 37 46 55 68 81 96
((~x + 1) + (2 * ((x - ((x - (3 * (3x div 7))) div 2)) div 2)))
A130911: 1 0 ~1 0 1 2 1 2 1 0 1 2 3 2 3 2
((x + 1) + ((x + ((1 + ((x + ((x3 + ~3x2 + 2x) div 5)) div 2)) div 2)) div 2))
A220850: 1 2 4 6 8 10 14 17 22 28 35 43 53 65 78 93
compr(\x.(~1 + ((5x2 + 10x + 4) mod (1 + (x div 5)))),(x + 1))
A247397: 1 2 3 4 5 6 7 8 9 10 12 13
A091401: 1 2 3 4 5 6 7 8 9 10 12 13 16 18 25
((x + 1) * (1 + (5 * ((11x2 + 7x) div 2))))
A100169: 1 92 438 1204 2555 4656 7672 11768 17109 23860 32186 42252 54223 68264 84540 103216
((1 + (3 * (1 + (((x + ~1) * (1 + (2 * (x - ((~x + 1) div 3))))) div 2)))) div (x + 1))
A306221: 1 2 4 7 10 15 18 21 27
((1 + (3 * ((x2 + 4x + 4) div (~x + 26)))) div (x + 1))
A280151: 1 0 0 1 0 1 1 1 1 2 2 2 3 3 4 4
compr(\x.(~1 + ((1 + (x mod (3 * (2 + (2x mod 7))))) mod (x + 1))),(x + 1))
A064390: 1 2 3 4 5 6 8 9 10 12 13 16 17 18 20 24
compr(\x.(1 - ((x + 1) mod (1 + (2 * ((1 + (x div 4)) div (1 + (x mod 5))))))),(x + 1))
A037359: 5 6 10 12 13 15 16 18 19 20 21 22 24 25 26 27
((x + 2) + (2 * (1 + (2 * (1 + (2 * (x - ((x + 1) mod ~9))))))))
A133899: 72 73 74 75 76 77 78 79 80 153 154 155 156 157 158 159
compr(\x.(1 - ((x + 1) mod (1 + (2 * (1 + ((x mod (1 + (2 * (x mod 6)))) mod 2)))))),(x + 1))
A026432: 1 3 4 5 6 7 8 9 10 12 13 15 16 18 21 22
(((2 * ((2x + 1) + ((((x div 2) div 3) mod 2) + (x div 3)))) div 3) mod (x + 1))
A071940: 0 0 0 1 1 2 3 4 4 5 5 6 6 6 7 8
((2 + (2 * ((x mod (~2 - (x mod 7))) mod 2)) - (x mod 2)) mod (x + 1))
A234022: 0 1 2 1 2 1 2 3 4 3 2 3 2 3 2 1
((1 + ((((x + 1) div (1 + ((2x + ~1) mod 9))) mod 2) + (x mod 2))) mod (x + 1))
A265893: 0 1 1 2 1 2 1 3 2 3 2 3 1 3 2 3
(~x + compr(\x.(1 - (x mod (1 + ((((2x + 1) mod (2 + (x div 2))) div 2) + (x mod 2))))),x))
A199332: 1 2 3 4 4 4 5 6 7 8 9 9 9 9 9 10
((x + 1) + ((x mod 2) + ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2)) - (x div 2))
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((2 * (2 + ((1 + (2 * ((x mod (2 * (1 + (x mod 3)))) mod 3))) mod (x + 1)))) div (x + 1))
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((x + 1) + (((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2) + (x div 8)))
A140661: 1 2 3 5 6 7 8 11 13 14 15 17 18 19 20 24
((x + 1) div (2 + ((x div 2) mod (1 + (x mod (1 + (x mod (1 + (x div (2 + (x div 5)))))))))))
A105612: 0 1 1 1 2 3 3 2 3 5 5 3 6 7 5 3
((1 + ((x + 1) div (1 + ((2 - ((x + (x div 5)) mod 5)) mod (x + 1))))) div 2)
A181802: 1 1 2 1 1 2 4 1 1 2 6 1 1 2 4 1
((1 + ((x + 1) mod (1 + (2 * (1 + (x mod (1 + (2 * (((2x + ~4) mod (x + 2)) mod 2))))))))) div 2)
A157897: 1 1 0 1 1 0 1 2 0 1 1 3 1 2 0 1
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A212981: 0 2 8 21 43 77 125 190 274 380 510 667 853 1071 1323 1612
((1 + ((2 * (x + ((x + ((x - (4 * (x + (x mod 2)))) div 2)) div 2))) + (x mod 3))) div 2)
A071046: 0 0 2 1 4 3 4 5 7 5 8 8 9 9 11 10
(x div (2 + (x mod (1 + ((x + 1) div (1 + (((2x div (1 + (x div 4))) mod 2) + (x mod 2))))))))
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((1 + ((2 + (x mod (2 * (1 + (x mod (2 * (1 + (x mod (1 + (x div 3)))))))))) mod (x + 1))) div 2)
A086598: 0 1 1 1 1 2 1 1 2 2 1 3 1 2 3 1
((1 + ((1 + ((x + 1) div (1 + ((x2 + 2x) mod (1 + (x div (2 + (x div 4)))))))) div 2)) div 2)
A116482: 1 1 1 1 2 1 2 2 1 3 3 1 4 4 2 1
(((x + 1) - ((1 + (x div (1 + (31 mod (2x + 1))))) div 2)) div 2)
A125186: 0 1 1 2 2 3 3 3 4 5 5 5 6 6 6 4
((1 + ((1 + ((x + 1) div (1 + ((~1 + ((x mod 5) mod 3)) mod (x + 1))))) div 2)) div 2)
A146290: 1 1 1 1 2 1 2 1 1 3 1 3 2 1 4 1
((1 + ((1 + ((x + 1) mod (1 + (2 * (1 + (x mod (1 + (2 * ((x div 2) div 3))))))))) div 2)) div 2)
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((1 + ((1 + ((x + 1) div (1 + (2 * ((x + 1) mod (1 + ((1 + (x div 4)) div 2))))))) div 2)) div 2)
A232440: 1 1 1 1 1 2 1 2 1 3 1 3 1 1 4 2
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A277824: 0 1 1 1 1 2 1 1 1 1 2 2 1 3 1 1
((1 + ((1 + ((1 + ((1 + (((x2 + x) * (x div 2)) div 5)) div 2)) div 2)) div 2)) div 2)
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((1 + ((1 + (((1 + (((x + 1) * ((x + 1) div (2 - (x mod 2)))) div 3)) div 2) div 2)) div 2)) div 2)
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(2 * (1 + ((x mod (1 + (2 * ((x + ~2) mod (2 * (1 + (((x + 1) mod 5) mod 2))))))) div 2)))
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((1 + ((1 + (((1 + (((x + 1) * (((1 + (x div 2)) * (x div 2)) div 2)) div 2)) div 2) div 2)) div 2)) div 2)
A309712: 0 0 0 0 1 1 2 2 3 3 5 6 9 10 13 14
((1 + ((1 + ((x + 1) mod (2 * (2 + ((2 * (2 - ((x * (x div 2)) mod 2))) mod (x + 1)))))) div 2)) div 2)
A071441: 1 1 1 1 2 2 2 0 3 3 3 1 1 1 1 0
((1 + ((((~2x + 2) mod (4 + (x div 4))) div 2) mod (2 + (x div 5)))) div 2)
A124790: 1 0 1 0 0 1 0 1 1 1 0 1 2 1 1 0
(4 div (2 + ((4 * (2 + (16 mod (x + 1)))) mod 7)))
A035162: 1 1 0 1 0 0 1 1 1 0 2 0 0 1 0 1
((1 + ((2 + (((x + 1) div 5) * (1 + (x div 4))) - (x mod 2)) div 2)) div 2)
A035433-A029210: 1 0 1 0 1 1 1 1 1 2 2 2 3 2 4 3
((1 + (x mod (2 + (((4x + 8) * (2 + (x mod ~7))) mod (x + 1))))) div 2)
A071086: 0 1 0 1 1 1 0 1 0 5 0 1 0 1 2 1
(3 + (((15 * (x - (x div ~14))) div 2) div 2))
A190706: 3 10 14 18 21 25 29 33 36 40 44 48 51 55 59 66
((1 + (((5x4 + 20x3 + 32x2 + 24x + 7) div 2) div 2)) div 2)
A093198: 1 11 53 164 397 819 1513 2576 4121 6275 9181 12996 17893 24059 31697 41024
(1 - ((1 + ((((x + 1) * (0 + (2 * (x mod 2)) - (((x + 1) div 2) div 2))) div 2) div 2)) div 2))
A213423: 1 0 1 0 2 0 2 1 3 1 4 2 6 3 7 5
(2 - (2 * (1 + (((((x2 + ~x) - (((x3 + ~x) div 2) div 3)) div 2) div 2) div 2))))
A049322-A014557: 0 0 0 0 0 0 2 4 8 12 20 28 40 52 70 88
((1 + (((2 + ((1 + (4 * (2 + (x mod (2 + (x mod 4)))))) mod (x + 1))) div 2) div 2)) div 2)
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(((x + 1) - (((2 + ((1 - (x mod (1 + ((2 - (x div 2)) mod 4)))) mod (x + 1))) div 2) div 2)) div 2)
A285734: 0 1 1 2 2 3 2 3 3 5 5 6 6 7 5 6
(2 * (1 + ((1 - ((x + 1) mod (1 + (4x mod (2 - ((x div 2) div ~2)))))) mod 4)))
A046587: 4 4 4 4 2 4 4 4 4 4 4 8 2 8 4 4
((((3x + 3) * (1 + (x mod (2 * (2 + (3 * (x mod 2))))))) mod 5) div 2)
A035224: 1 1 1 1 0 1 1 1 1 0 2 1 2 1 0 1
((x3 mod (11 * (1 + (x mod 3)))) mod 10)
A096340: 0 1 8 5 0 6 7
(2 * (((2x + 1) + (2 * ((x + ((~x + 1) mod 3)) mod 5))) div 5))
A287394: 0 2 4 6 6 6 6 6 6 6 8 10 12 12 12 12
(((1 + (x div (2 + ((x div 2) div (1 + (((1 + (x div 2)) div 2) div 2)))))) * (1 + (x div 4))) div 2)
A278959: 0 0 0 1 2 2 3 3 4 4 4 4 6 6 8 8
(~2 + (3 * (1 + (3 * ((6x2 + ~6x) + ((x2 + x) div 2))))))
A050408: 1 10 136 379 739 1216 1810 2521 3349 4294 5356 6535 7831 9244 10774 12421
(x - ((x - (3 * ((3x + 2) - ((2x + 1) div 7)))) div 2))
A292655: 3 8 13 17 22 27 32 35 40 45 49 54 59 64 67 72
((3 * (1 + (((1 + (x mod (1 + (x mod (2 * (2 + ((x div 2) mod 2))))))) mod (x + 1)) div 2))) div 2)
A296120-A050345: 1 1 1 1 1 3 1 3 1 3 1 6 1 3 3 4
((3 * (((x * (1 - ((x3 div 8) mod 2))) + (x mod 2)) div 3)) div 2)
A335682: 0 0 0 0 1 0 0 3 3 0 0 6 6 6 0 0
((3 * ((x + (2 * (x + (x2 div (x + 17))))) div 3)) div 2)
A275672: 0 1 3 4 6 7 9
A089038: 0 1 3 4 6 7 9 12 13 16 18 19 21 24 27 28
(2 + (3 * (1 + (2 * (x + ((x * (1 + (x div 5))) div 9))))))
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(1 - (2 mod (1 - (2 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))))
A340910: 1 1 1 1 1 1 1 2 2 1 1 4 6 4 1 1
((3 * (x div (2 + (x div (1 + ((x mod (1 + ((2 - (x mod 4)) mod (x + 1)))) div 2)))))) div 2)
A244963: 0 0 0 1 0 0 0 3 1 0 0 4 0 0 0 7
((3 * ((3 * ((x2 mod (4 + (((x + 1) div 2) div 2))) mod 3)) div 2)) div 2)
A278987: 0 1 0 1 1 0 1 1 1 0 1 4 1 1 0 1
(2 + (3 * ((3 * (x - ((((x * ((1 - (x div 2)) div 3)) div 2) div 2) div 2))) div 2)))
A026228: 2 5 11 14 23 29 32 38 41 50 59 65 68 77 83 86
(((((x + 3) * ((x3 + ~5x2 + ~22x + ~16) div 2)) div 2) div 3) div 2)
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(0 - (((~20x3 + ~3x2 + 17x) div 2) div 3))
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((((7x4 + 16x3 + ~x2 + ~10x) div 2) div 3) div 2)
A264850: 0 1 18 80 230 525 1036 1848 3060 4785 7150 10296 14378 19565 26040 34000
(x + ((x + 1) div 2) - ((4 * (x div 5)) + ((3 * (x div 4)) div 2)))
A096289: 0 2 3 5 5 3 4 6 5 7 4 6 6 8 9 7
((3 * compr(\x.(1 - (x mod (2 + ((1 + ((x - ((x div 2) mod 2)) div 2)) mod 5)))),x)) div 2)
A005122: 1 3 4 6 9 10 13 16 19 21 24 25 28 30 33 34
(((2 * (1 + (x div (2 + (((x2 + x) div 4) mod (2x + 1)))))) + (x mod 3)) div 2)
A291771: 1 1 2 1 1 2 1 1 4 2 2 2 1 1 2 1
(((2 * (1 + ((x + 1) div (2 + (x div (2 + (((x div 2) mod 3) mod 2))))))) - (x mod 3)) div 2)
A333516: 1 1 1 2 1 1 2 1 2 3 1 1 2 1 2 3
(((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4))) + (x mod 2) + ((x mod 3) div 2))
A169611: 0 1 1 2 0 2 0 3 2 1 0 3 0 1 1 4
(2x div (2 + (x7 mod (10x + 1))))
A096693: 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 3
((1 + ((x + (((10x3 + 3x2 + ~4x) div 2) div 3)) div 2)) div 2)
A212247: 0 1 4 13 29 56 95 150 222 315 430 571 739 938 1169 1436
((2 + (x div (2 + (x div (1 + (x mod (1 + ((2 - (x div 2)) mod 4))))))) - (x mod 2)) div 2)
A034178: 1 0 1 1 1 0 1 1 2 0 1 1 1 0 2 2
((2 + (((((1 + (x div 2)) div (1 + (x mod 2))) * (1 + (x div 2))) div 2) div 2) - (x mod 2)) div 2)
A029178: 1 0 1 0 2 0 3 1 4 1 5 2 7 3 9 4
(((x + 1) + (3 * ((4x + 2) - ((~2x + 2) div 9)))) div 2)
A035488: 3 10 18 24 31 37 45 52 58 65 71 79 86 92 99 107
(2 * ((~1 + ((1 + (x mod (~1 + (3 * (((x + ~1) div 2) mod 3))))) mod 3)) mod (x + 1)))
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(((1 + (6 * ((x + 1) - (x mod (1 - (2 * (2 + (x mod 3)))))))) mod (x + 1)) div 2)
A268142: 0 0 0 0 1 0 0 1 0 0 0 3 0 6 0 0
((x - ((1 + (x mod (2 * (1 + (x mod (2 * (1 + (x mod (1 + (x div 3)))))))))) mod (x + 1))) div 2)
A072106: 0 0 0 1 1 1 2 3 2 3 4 3 5 5 4 7
(2 + ((1 + (2 * ((4 * ((2x + 2) div 7)) div 3))) mod (x + 1)))
A280740: 2 3 3 5 5 5 7 7 7 7 11 11 11 13 13 13
(2 + ((1 + (2 * ((4 * ((2x + 1) div 9)) div 3))) mod (x + 1)))
A137847: 2 3 3 3 5 5 5 5 5 7 7 7 7 11 11 11
(((1 + (2 * ((((x + 1) div (1 + (x div 5))) + (x div 3)) div 2))) mod (x + 1)) div 2)
A322006: 0 0 0 0 1 2 2 3 3 4 3 3 4 4 4 4
(((2 * (1 + (((1 - (x mod (3 + (x mod 2)))) mod (x + 1)) div 5))) mod (x + 1)) div 2)
A338117: 0 0 1 1 1 1 1 2 2 1 1 3 1 1 3 3
(((2 * (1 + ((1 + ((x + 1) mod (1 + (x div (2 + (x mod 5)))))) div 2))) mod (x + 1)) div 2)
A280726: 0 0 1 1 1 1 2 1 2 1 4 1 2 2 1 1
(((x + 1) * ((4x + 6) + (((x3 + 3x2 + 2x) div 2) div 3))) div 2)
A219621: 3 11 27 56 105 183 301 472 711 1035 1463 2016 2717 3591 4665 5968
((~1 + (2 * ((x + 1) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))))) mod (2x + 2))
A130140: 1 3 5 7 3 11 13
A099984: 1 3 5 7 3 11 13 15 17 19 21 23 5 3 29 31
((~2 + (5 * (1 + (((x + 1) * (1 + (x mod 2))) mod (1 + (x div 5)))))) div 2)
A193454-A193254: 1 1 1 1 1 1 4 1 4 1 6 1 4 4 1 1
((6x + 4) - ((4x + ((x + 1) mod 4)) div 5))
A184515: 4 9 14 20 25 30 35 41 46 51 56 62 67 72 77 82
((x * (1 + (2 * ((2x + 2) + ((x div 2) div 5))))) div 20)
A194224: 0 0 1 2 4 6 8 11 14 18 23 28 33 38 44 50
(2 * ((3 * ((~2 + (x mod 2)) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))) div 2))
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(2 * ((3 * ((2 + (x div 3)) mod (~1 + (2x mod (4 + (x div 4)))))) div 2))
A216800: 0 0 0 0 2 0 0 2 2 0 0 6 0 6 0 0
((x + 1) div (2 + (x div (2 + ((x - ((x - ((x div 5) mod 2)) div 3)) mod 3)))))
A164995: 0 1 1 2 1 2 2 2 1 2 2 3 2 1 2 3
((x + 1) div (2 * (2 + ((2 + (x mod (1 + (2 * (16 mod (x + 1)))))) div 3))))
A139353: 0 0 0 1 0 0 1 2 0 1 0 2 1 2 2 4
(((3 * (2 + ((x2 + 4x + 4) div (~x + 26)))) div 2) div 2)
A015753: 1 1 1 2 2 3 3 4 5 6 8 9 12 14 17 21
((2 + ((((x + 1) * ((x + 1) - (2 * (1 + ((x + ~2) div (2 + (x div 2))))))) div 2) div 3)) div 2)
A327720-A327716: 1 1 1 1 2 3 3 3 4 6 7 9 10 12 14 17
(((3 * ((x + 2) + (((3x2 + 16x + 16) div 2) div 3))) div 2) div 2)
A027920: 3 6 10 15 20 26 33 40 49 58 68 78 90 102 115 129
((2 + (((2x + 1) + (x3 div (x + 32))) div 3)) div 2)
A104648: 1 1 1 2 2 3 4 4 5 7 8 9 11 13 15 18
((2 + ((1 + (2 * (((x + 2) - ((~x + 1) div (2 + (x div 4)))) mod 3))) mod (x + 1))) div 2)
A105265: 1 1 2 1 2 1 2 3 1 2 1 2 3 1 2 3
((x mod (2 + ((3 * (1 + (4x mod 13))) mod (x + 1)))) div 2)
A276004: 0 0 0 1 0 0 0 0 1 2 1 1 0 1 0 1
(2 + (((x + 1) * (x - (2 * ((x - (((x - (x div 5)) mod 3) div 2)) div 2)))) div 2))
A284278: 2 3 5 4 2 5 9 6 2 7 13 8 2 9 2 10
((((x2 + 3x + 2) * (~1 + (9 * ((x2 + 3x + 2) div 2)))) div 2) div 2)
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(2 + (((x + ~1) * (2 + (((x3 + ~2x2) div 17) + (x mod 2)))) div 2))
A126250: 1 2 3 5 6 16 27
((2x + 2) - ((x - (((9 * (x + (x div 5))) div 2) div 2)) div 2))
A189757: 2 5 7 10 13 16 19 22 24 27 31 33 36 38 41 45
(((2 + ((3 * (1 + (((x + 1) mod 13) div 2))) mod (x + 1))) div 2) div 2)
A159700: 0 0 0 0 1 0 1 2 2 2 2 2 1 1 2 2
(((((37x2 + 74x + 36) div 2) div 2) div 2) div 2)
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(1000x + 736)
A067866: 736 1736 2736 3736 4736 5736 6736 7736 8736 9736 10736 11736 12736 13736 14736 15736
(8 + ((2 + (5 * ((x + 2) + (2 * (x div 4))))) div 3))
A226099: 12 13 15 17 22 23 25 27 32 33 35 37 42 43 45 47
((2 + ((1 + ((2 * (1 + (2 * (2x - (x mod 8))))) + ((x + 1) div 2))) div 2)) div 2)
A051415: 1 3 4 5 6 7 8 9 18 20 21 22 23 24 25 26
(x - (8 * ((x div 9) - (x mod (x - ((x + ~1) mod 8))))))
A255594-A030108: 0 1 2 3 4 5 6 7 8 1 10 19 28 37 46 55
(2 * (x - (4 * ((x div 9) - (x mod (x - ((x + ~1) mod 8)))))))
A319747-A055958: 0 2 4 6 8 10 12 14 16 10 20 30 40 50 60 70
(((2 - (x mod (4 - ((x2 div 2) + (2x mod (4 + (x div 4))))))) div 2) div 2)
A147609: 0 0 0 0 1 1 3 4 6 7 10 12 15 18 20 24
((((x2 + 2) - (2 * ((2 * (2x - (x mod 8))) - (x mod 4)))) div 2) div 2)
A213673: 0 0 0 1 0 2 4 7 0 4 8 13 16 22 28 35
(1 - (4 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))
A131061: 1 1 1 1 5 1 1 9 9 1 1 13 21 13 1 1
(((x + 1) * ((x + 8) + ((x2 + 2x) div 8))) div 8)
A231408: 1 2 4 6 9
A090631-A064985: 1 2 4 6 9 12 17 22 29 36 45 54 66 78 93 108
(8 + (2 * ((2 * (2x - (x mod 8))) - (x mod 4))) - (x mod 2))
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((1 + (((x + 1) mod (1 + ((2 * (1 + (x mod 3))) mod (x + 1)))) div 2)) mod (2 + (x mod 4)))
A331510: 1 1 1 1 1 1 1 2 0 1 1 3 1 0 1 1
((2 + ((x + ((1 + (((((x + 2) * (2 + (x2 div 3))) div 2) div 2) div 2)) div 2)) div 2)) div 2)
A008675: 1 1 1 2 2 3 4 5 6 8 10 12 15 17 21 25
(x mod (4 + ((x + ((3 * (1 + (x mod (2 + (x mod 10))))) div 2)) div 2)))
A103303: 0 1 2 3 4 5 6 7 8 9
A247149: 0 1 2 3 4 5 6 7 8 9 1 0 2 0 1 2
(2 * (2 + (((x + 2) + (((x + ((x div 2) div 7)) mod 4) + (x div 2))) div 2)))
A079772: 6 8 10 12 12 14 16 18 18 20 22 24 24 26 30 28
(2 + (((x + 2) * ((5x + 1) + (((x3 + ~x) div 2) div 3))) div 2))
A220147: 3 11 26 52 95 163 266 416 627 915 1298 1796 2431 3227 4210 5408
((1 + (x mod (1 + ((18x + 1) mod (x + 5))))) div 4)
A326819: 0 0 0 1 0 0 1 2 0 2 0 1 3 0 0 1
((1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)) mod 4)
A285117: 1 1 1 1 0 1 1 3 3 1 1 2 0 2 1 1
((1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)) mod 4)
A034931: 1 1 1 1 2 1 1 3 3 1 1 0 2 0 1 1
(1 - (((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2) mod 4))
A173120: 1 1 1 1 ~2 1 1 ~1 ~1 1 1 0 ~2 0 1 1
(4 + (((x + 1) + ((x2 div (16 - (x div 3))) mod 3)) div 2))
A178400: 4 5 5 6 7 7 8 8 9 9 10 10 10 12 12 13
(((x + 1) + ((2 * (4 + ((x mod 8) + (x mod 3)))) div 3)) div 4)
A078342: 0 1 2 2 2 3 3 4 3 3 3 4 4 5 5 5
((((x + 2) + (x div (2 + (16 mod (1 + (x div 2)))))) div 3) + (x div 4))
A074753: 0 1 1 2 3 3 4 5 6 6 6 6 8 9 10 11
((1 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4)))) * (x mod 2) * (x div 4))
A061064: 0 0 0 0 0 1 0 3 0 2 0 4 0 3 0 12
((((x + 1) + ((2 * (x + (x div 13))) mod 7)) div 2) div 2)
A342385: 0 1 1 2 1 2 3 2 2 3 4 3 4 3 4 5
(2 * ((x + 2) + (((x + 1) * (1 + ((x + 1) div 7))) div 9)))
A061344: 4 6 8 10 12 14 18 20 24 26 28 30 32 38 42 44
(2 + ((x + (3 * ((4x + 2) - ((x - (x div 5)) div 3)))) div 2))
A189406: 5 11 18 23 29 36 42 47 54 60 67 72 78 85 90 96
(2 * ((x + 3) + ((x + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4)))) div 2)))
A177085: 6 8 12 16 18 20 24 28 30 32 36 40 42 44 48 54
((2 + (x7 mod (17x + 8))) div 2)
A191648: 1 1 2 3 23 3
((x + 4) + ((x + ((3 * ((1 + (2 * (1 - (x div 4)))) div 3)) div 2)) div 2))
A242286: 4 6 7 9 10 11 13 14 15 16 18 19 21 22 24 25
((1 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4))) - (x mod 2)) mod (2 + (x mod 2)))
A114643: 1 0 1 1 1 0 1 2 0 0 1 1 1 0 1 0
(2 * ((x + 1) + ((2 * (1 + ((((x + ~1) * (x + (x div 3))) div 2) div 3))) div 3)))
A234941: 2 4 6 10 14 18 22 28 34 42 48 56 66 74 82 94
((x + 3) + ((1 + ((x + 1) div (2 - (x div ~12)))) mod (x + 1)))
A020884: 3 5 7 8 9 11 12 13 15 16 17 19 20 20 21 23
(2 + compr(\x.(1 - ((x + 1) mod (1 + (x div (2 + (((x + ~2) div 3) mod (1 + (x mod 4)))))))),x))
A063806: 4 6 8 9 10 12 14 15 18 20 21 22 24 25 26 27
((x + 3) + (((x + 1) + (((x + (((~x + 1) mod (4 + (x div 2))) div 2)) div 2) div 2)) div 2))
A225554: 3 5 7 8 10 11 13 14 16 18 19 21 23 25 26 28
((2x + 2) - (((~x + ~1) + (2 * (x + (1 mod (8 - (x div 2)))))) mod 5))
A037325: 1 2 3 4 10 11 12 13 14 20 21 22 23 24 27 28
((x + ((2 * ((x + (2 * (2 + ((x + 2) mod 7)))) div 3)) div 3)) div 2)
A325953: 0 1 2 3 4 3 4 5 6 6 7 8 7 8 9 10
((x + 2) + ((4 * ((2x + 1) + (((x + 1) + (x div 8)) div 2))) div 3))
A140103: 3 8 12 17 20 25 29 34 39 43 48 51 56 60 65 69
((x + 2) + ((4 * ((2x + 1) + ((x + (x div 12)) div 2))) div 3))
A107790: 3 7 12 15 20 24 29 33 38 41 46 50 55 60 64 69
(((x + 1) + (((x + 1) + (49x div (x + 2))) div 2)) div 2)
A121901: 0 5 8 10 11 13 14 15 16 17 18 19 20 21 21 22
((x + ((1 + (x mod (2 + ((x + 1) div (1 + (((x2 + 2x) div 2) mod 3)))))) mod (x + 1))) div 2)
A304183: 0 0 1 1 2 3 3 4 5 6 5 8 6 9 10 10
((2x + 4) - (x2 div ((x + 3) - ((x - (x div 5)) div 3))))
A091984: 4 6 8 9 10 11 12 12 13 14 15 15 16 17 17 18
((x + (((5 * (x + (2 * (2 - ((~2x + 1) div 5))))) div 2) div 2)) div 2)
A050099: 2 4 6 7 9 10 13 14 15 17 18 21 22 23 25 26
(((x + 2) + (((2 + ((1 - (x mod (1 + ((2 - (x div 2)) mod 4)))) mod (x + 1))) div 2) div 2)) div 2)
A285735: 1 1 2 2 3 3 5 5 6 5 6 6 7 7 10 10
((x + 2) + ((x + ((x - ((x + ((x2 + 3x + 2) div 2)) div 7)) div 2)) div 2))
A232532: 2 3 5 7 8 10 11 12 14 15 17 18 19 20 21 23
((x + 2) + ((x + ((x + ((x + ((x2 * (x2 div 2)) div 5)) div 2)) div 2)) div 2))
A086676: 2 3 5 8 12 18 29 44 68
((~1 + (2 * (1 + ((x - ((2x2 + 4x + 1) div 7)) div 2)))) mod (x + 2))
A194738: 1 1 1 4 3 2 1 7 5 3 1 10 7 4 15 11
((2x + 1) + ((((x + ~1) div (1 + (x mod (1 + (((x + 1) div 2) div 3))))) mod 2) + (x mod 2)))
A024807: 2 4 6 8 10 12 14 17 18 20 22 25 26 28 29 32
(1 + (((1 + (x mod ((1 + (x mod (1 + (x div 4)))) * (1 + (x mod 2))))) mod (x + 1)) + (x mod 2)))
A101113: 1 2 2 4 2 4 2 6 4 4 2 8 2 4 4 10
(1 + (((x mod ((x + ~1) - (x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4)))))))) div 2) + (x mod 2)))
A081373: 1 2 1 2 1 3 1 2 2 3 1 4 1 3 1 2
(1 + (x div (2 + ((x + 1) div (1 + (2 * ((3 * (x div 5)) div 2)))))) - (x mod 2))
A344246: 1 0 1 0 1 1 2 1 2 1 4 3 5 3 4 5
(1 + (((2 + ((1 - (x mod (1 + ((2 - (x div 2)) mod 4)))) mod (x + 1))) div 2) div 2) - (x mod 2))
A285736: 1 0 1 0 1 0 3 2 3 0 1 0 1 0 5 4
(x - ((x * (2x - (((x + ~1) * (4x + ((x2 + ~x) div 2))) div 3))) div 2))
A326247: 0 0 1 9 32 80 165 301 504 792 1185 1705 2376 3224 4277 5565
((3x + ~2) + (5 * ((x + 2) + ((x + ((x mod (1 + (x div 2))) div 2)) div 2))))
A047925: 8 16 29 37 50 63 71 84 92 105 118 126 139 152 160 173
((x + 1) + ((1 div ((2x + ~1) mod (4 + (x div 4)))) * (1 + ((1 + (x div 2)) div 2))))
A132119: 1 3 3 6 5 6 10 8 9 10 15 12 13 14 15 21
compr(\x.(1 - ((x div 2) mod (1 + (((x - (x mod 3)) * (x div 3)) mod 9)))),x)
A133896: 3 4 5 6 7 12 13 14 15 21 22 23 26 30 31 34
((~x + 1) + ((2 * ((x + 1) + ((x + (((1 + ((x2 + x) div 2)) div 2) div 2)) div 2))) div 3))
A325358: 1 1 1 2 2 2 3 4 4 5 6 6 7 9 10 11
((x + 1) + ((2 * (x - ((1 + (((x * ((1 + (x div 2)) div 2)) div 3) div 2)) div 2))) div 3))
A289243: 1 2 4 6 7 9 10 12 13 14 15 17 19 20 21 22
((x + 1) + ((4 * ((4 * (2x div 7)) div 3)) div 3))
A129989: 1 2 3 4 6 7 8 10 11 12 13 17 18 19 21 22
((x + ~1) + ((2 * (2 + ((2 + (((x + 1) * ((x + ~1) div 3)) div 2)) div 3))) div 3))
A158746: 0 1 2 3 5 6 7 9 10 12 14 15 17 20 21 22
((~x + 1) + ((2 * (x + ((x + ((((1 + (x div 3)) div 2) * (x div 2)) div 2)) div 2))) div 3))
A058769: 1 0 1 0 1 1 1 1 1 2 2 2 3 2 3 4
compr(\x.(1 - (x mod (1 + ((1 + ((x - (((x + ~1) div 3) * (x div 2))) mod 3)) mod (x + 1))))),x)
A286607: 3 5 7 10 11 13 14 15 17 19 21 22 23 25 28 29
((x + 1) + ((1 + (((x + 1) - ((x mod (x - ((x + ~1) mod 8))) div 2)) div 2)) mod (x + 1)))
A233745: 1 2 5 7 8 10 11 13 14 16 17 18 20 21 22 23
((x + 1) + ((2 + ((x div (1 + ((x + 2) mod 8))) mod 2) - (x mod 2)) mod (x + 1)))
A338363: 1 3 5 5 7 7 9 10 11 11 13 14 16 16 17 18
((x + 1) + (((x + 1) - ((1 + ((x - ((x div 2) mod 2)) div 2)) mod (1 + (x div 5)))) div 2))
A225647: 1 3 4 6 7
A274829: 1 3 4 6 7 8 10 12 13 14 15 18 19 20 22 24
compr(\x.((x + 2) mod (1 + (2 * ((x * (1 - ((x3 div 8) mod 2))) div 3)))),x)
A324689: 0 1 2 3 4 5 6 8 9 10 14 15 18 19 21 22
((x + 1) + (((x + 1) + ((9x + (x div 3)) div (x + 4))) div 2))
A335155: 1 3 6 8 9 11 13 14 16 18 19 21 23 24 26 27
compr(\x.(~1 + (x div (2 + ((15 * (1 + ((x div 4) mod 2))) mod (x + 1))))),x)
A336205: 0 1 2 3 6 7 8 9 10 15 16 17 18 19 20 24
((x + 1) + ((((x2 + 10x) + (x mod 10)) div (x + 1)) div 2))
A184108: 1 5 7 9 11 12 14 15 17 19 20 21 23 24 26 27
((x + 1) + (4 * (1 + (((2x3 + 9x2 + 11x + 2) div 2) div 3))))
A209116: 5 22 55 120 221 362 559 816 1137 1538 2023 2596 3273 4058 4955 5980
(x * (1 + (2 * (x - (2x div (2 + (x mod (1 + (2 * (x mod (1 + (x div 8))))))))))))
A103303: 0 1 2 3 4 5 6 7 8 9
A326302: 0 1 2 3 4 5 6 7 8 9 10 143 12 143 14 15
((x + 1) + (((1 + (((2 * (((x - ((x div 2) mod 2)) div 2) * ((x + 1) div 2))) div 2) div 2)) div 2) div 2))
A334298-A304686: 1 2 3 4 5 7 8 9 11 12 13 16 17 19 20 23
((x + 1) + (2 * ((1 + ((x + ((x2 mod ((x + 1) + (2 * (x div 4)))) div 2)) div 2)) div 2)))
A080727: 1 2 5 6 7 8 11 14 17 18 19 20 21 22 23 24
(2x - (9 * ((2 * (x mod 10)) div 9)))
A169909: 0 2 4 6 8 1 3 5 7 0 20 22 24 26 28 21
compr(\x.(1 - (((x + 1) * (1 + (2 * (2x2 mod 17)))) mod 3)),x)
A010412: 0 1 4 9 13 15 16 18 19 21 25 30 33 34 36 42
(~x + ((((x + 5) * ((x3 + 7x2 + 6x) div 2)) div 2) div 3))
A166796: 0 6 26 69 146 270 456 721 1084 1566 2190 2981 3966 5174 6636 8385
(486x2 + ~138x)
A304837: 0 348 1668 3960 7224 11460 16668 22848 30000 38124 47220 57288 68328 80340 93324 107280
(x + ((2 * ((2x + 4) + ((2x * (2 + (2 div (x + 1)))) div 3))) div 3))
A190344: 2 6 8 12 15 18 22 25 28 31 34 37 41 44 47 51
((3x + 1) + ((2 * (x - (2 * ((4 * (x div 3)) div 3)))) mod 3))
A287435-A026601: 1 6 8 12 14 16 20 22 27 30 32 34 38 40 45 46
((3x2 + 16x) + (((x3 + 3x2 + 2x) div 2) div 3))
A264444: 0 20 48 85 132 190 260 343 440 552 680 825 988 1170 1372 1595
(x + ((x + (2 * (((1 + ((x div 2) div 3)) * (1 + (x div 5))) div 2))) div 3))
A087063: 0 1 2 4 5 7 9 10 12 13 15 16 18 20 21 24
((x + 1) + (((x + 1) + ((((1 - (2 * (x mod 5))) mod (x + 3)) div 2) div 2)) div 2))
A225647: 1 3 4 6 7
A018825: 1 3 4 6 7 9 11 12 14 15 16 19 21 22 23 24
((~x + ~1) + compr(\x.(1 - (x mod (1 + (((x mod (~1 + (2 * ((x + ~1) div 3)))) div 2) + (x mod 2))))),x))
A103303: 0 1 2 3 4 5 6 7 8 9
A340835: 0 1 2 3 4 5 6 7 8 9 11 11 12 12 12 12
(x * (~x + (compr(\x.(x mod ((x + 1) - (x mod 10))),x) + (x mod 10))))
A061205: 0 1 4 9 16 25 36 49 64 81 10 121 252 403 574 765
compr(\x.(x - ((((x + 1) div 2) - ((3 * (x div 4)) div 2)) * (2 + (x div 5)))),x)
A023798: 0 1 2 3 5 6 7 11 15 19 21
((x + 2) + ((1 + (2 * ((1 + (x div 8)) * (x div 7)))) mod (x + 1)))
A167493: 2 4 5 6 7 8 9 12 15 16 17 18 19 20 25 26
(x + (((~1 + (6 * (2 + ((3 * ((x + 1) - ((x div 2) mod 2))) div 2)))) div 2) div 2))
A229004: 4 8 9 11 17 21 22 24 30 34 35 37 43 47 48 50
(~x + (((5 * compr(\x.(1 - (x mod (1 + (4 * (x mod 5))))),x)) div 2) div 2))
A070046: 1 1 1 2 3 3 4 4 5 6 7 9 9 9 9 11
compr(\x.(((1 + ((x * ((3x + ~1) - (2x mod (2 + (x div 4))))) div 2)) div 2) mod 2),x)
A254130: 0 3 5 6 7 8 9 13 16
compr(\x.(2 - ((x + 2) mod (2 * (2 + ((1 - (2 * ((~x + 1) div 7))) mod (x + 1)))))),x)
A253200: 0 1 3 4 5 6 7 9 10 11 14 15 18 19 20 21
(x div (x + (2 * (1 - (2 * ((x mod (1 + ((2 * (x + ((x * (x div 2)) mod 2))) div 3))) mod 2))))))
A085975: 0 0 0 0 2 1 1 1 0 0 1 0 1 0 0 0
(x + ((2 + ((2 + ((3 * ((x + 1) - (2 * (~x + ((x div 4) mod 2))))) div 2)) div 2)) div 2))
A231407: 1 4 6
A190485: 1 4 6 8 9 11 13 16 18 21 23 25 26 28 30 33
(x + (2 * (((((x3 + ~x) div 2) div 3) + ((x3 + x2 + x) div 2)) div 2)))
A137930: 0 1 10 25 56 101 170 261 384 537 730 961 1240 1565 1946 2381
((3x + 2) + (((x + 1) + (x div (1 + ((2x + 1) mod 9)))) mod 2))
A287421: 3 5 9 11 15 18 20 24 27 29 33 36 38 42 45 48
(169x2 + 140x + 29)
A156640: 29 338 985 1970 3293 4954 6953 9290 11965 14978 18329 22018 26045 30410 35113 40154
(1 + loop(\(x,i).(x + (if (if x <= 0 then 2 else loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1))) <= 0 then x else 1)),x,1))
A081869: 2 3 4 5 9 10 11 21 22 23 45 46 91 92 183 365
(1 + (loop(\(x,i).(x + loop(\(x,i).(x + (if x <= 0 then 1 else loop(\(x,i).(x - (if x <= 0 then 1 else (2 * i))),x,x))),1,i)),x,1) div 2))
A004737: 1 1 2 1 1 2 3 2 1 1 2 3 4 3 2 1
loop(\(x,i).(1 + loop(\(x,i).(x - (if x <= 0 then 1 else loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,x))),x,x)),x,1)
A215523: 1 2 3 6 9 14 15 18 21 26 29 30 33 36 39 44
loop(\(x,i).(if x <= 0 then 2 else (if x <= 0 then 1 else (x * (if (loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2) <= 0 then x else 1)))),x,(x + 2))
A281384: 2 9 4 5 6 49 8 9 10 11 12 13 14 225 16 17
loop(\(x,i).(x + loop(\(x,i).((loop(\(x,i).3x,x,1) - loop(\(x,i).3x,(x div 2),1)) div 2),1,i)),x,0)
A220788: 0 1 4 16
A107767: 0 1 4 16 52 169 520 1600 4840 14641 44044 132496 397852 1194649 3585040 10758400
(if (x mod 2) <= 0 then ((3 * (if (x mod 4) <= 0 then (2 * (2 + (if x <= 0 then 0 else 2))) else 1)) + (if x <= 0 then 1 else 2)) else 1)
A010234: 13 1 5 1 26 1 5 1 26 1 5 1 26 1 5 1
loop(\(x,i).(2x2 + ~x),1,loop(\(x,i).4x,(if x <= 0 then 1 else (loop(\(x,i).2x,x,2) - (x mod 2))),1))
A099058: 28 8128 8589869056 2305843008139952128 4611686018427387903 4611686018427387903
(if x <= 0 then 2 else (1 + (2 * compr(\x.(x - loop(\(x,i).loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),x,(2x + 1)),2,x)),x))))
A118332: 2 3 5 11 23
A246857-A005384: 2 3 5 11 23 29 41 53 83 89 113 131 173 179 191 233
(1 + (2 * compr(\x.loop(\(x,i).(if x <= 0 then 2 else (2 + loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),2,x))),2,x),x)))
A043766-A043757-A043749-A043742-A043736-A043731-A043727-A043570: 5 9 11 13 17 19 23 25 27 29 33 35 39 47 49 51
((x + 1) + loop(\(x,i).(x - (if x <= 0 then 1 else (if (x mod 2) <= 0 then (x div 2) else (1 + (if (~x + 2) <= 0 then x else 0))))),x,(x + 1)))
A135560: 2 3 1 4 1 2 1 5 1 2 1 3 1 2 1 6
((x + 1) div (1 + (if x <= 0 then 0 else (x + loop(\(x,i).(~2x + 1),loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1)))))
A121467: 1 0 1 0 1 0 0 1 0 2 0 1 0 1 0 0
loop(\(x,i).(4x + loop(\(x,i).x2,1,loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),i,1))),x,1)
A167859: 1 8 68 672 7588 93856 1229200 16695424 232418596 3293578784 47309094672 686870685312 10059942413584 148412250014336 2202990595617344 32873407393419776
loop(\(x,i).(2x + loop(\(x,i).x3,1,loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),i,1))),x,1)
A167867: 1 10 236 8472 359944 16722896 822334816 42068907200 2215884717400 119364801362800 6545334930678816 364137834051739200 4611686018427387903 4611686018427387903 4611686018427387903
(2 - loop(\(x,i).(x - (if x <= 0 then 1 else (x - ((if x <= 0 then 2 else loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 2)))),x,(x + 1)))
A117123: 1 1 3 2 4 5 7 5 7 8 10 10 12 13 15 12
loop(\(x,i).(x + (if x <= 0 then 1 else (~1 + loop(\(x,i).(x * (if (x mod 5) <= 0 then 2 else 1)),(x + 1),(x + 1))))),x,1)
A018573: 1 2 4 163 326 652
loop(\(x,i).(~x + loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A099110: 1 8 47 238 1113 4956 21379 90266 375485 1545544 6313671 25650534 103792417 418745972 1685723723 6775136242
loop(\(x,i).x2,1,loop(\(x,i).loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),i,x),x,1))
A239350: 1 4 144 129600 5715360000 30497732496000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 + loop(\(x,i).3x,x,(~1 + loop(\(x,i).2x,x,(if (x mod 2) <= 0 then 1 else loop(\(x,i).(2x + 2),x,0))))))
A103830-A062802: 2 11 29 2999
((1 + loop(\(x,i).2x,x2,(if x <= 0 then 1 else (if (x + ~2) <= 0 then x else loop(\(x,i).x3,x,3))))) div 2)
A330716: 1 1 16 1952152956156672
(loop(\(x,i).(x + loop(\(x,i).(x - (if x <= 0 then 1 else (if (x mod (1 + (2 * i))) <= 0 then x else 0))),x,x)),1,(2x + 1)) div 2)
A341585: 1 0 1 1 0 2 3 0 4 4 0 5 1 0 7 7
(2 * (loop(\(x,i).(x * i),x,(1 + (if (if x <= 0 then 1 else (x * loop(\(x,i).((~1 + i) * i),(x + ~2),1))) <= 0 then x else 0))) div 2))
A052686: 0 0 2 24 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000
loop(\(x,i).(x + loop(\(x,i).(x - (if x <= 0 then 1 else i)),x,x)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A057060: 1 2 2 1 1 3 2 4 2 1 3 1 5 7 2 8
(0 - loop(\(x,i).loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A243111: 1 0 1 3 4 2 4 2 5 7 5 8 4 2 8 2
(1 - loop(\(x,i).loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A057061: 2 1 2 4 5 3 5 3 6 8 6 9 5 3 9 3
(if x <= 0 then 1 else loop(\(x,i).loop(\(x,i).x2,1,(2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))),1,(x + 2)))
A240775: 1 121 169 289 361 529
loop(\(x,i).(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (1 + (if (x mod 3) <= 0 then 0 else 2))))),x,(x + 1))),1,(x + 2))
A087088: 1 2 3 1 4 2 1 5 3 1 2 6 1 4 2 1
(3x + loop(\(x,i).(x - (if x <= 0 then 1 else loop(\(x,i).(~1 + (if x <= 0 then 2 else 0)),(x mod 2),(x div 2)))),x,(x + 1)))
A120512: 1 4 8 9 14 15 17 18 24 25 27 28 31 32 34 35
((x + 1) - loop(\(x,i).(if x <= 0 then 2 else loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then i else 0)),(x div 2),(x + 1))),1,(x div 2)))
A308048: ~1 0 1 2 2 3 2 3 4 5 4 5 6 7 4 5
((x + 2) + loop(\(x,i).(x - (if x <= 0 then 1 else (if (x mod 2) <= 0 then (x div 2) else (if (~x + 2) <= 0 then (2 + (x div 2)) else 1)))),x,x))
A327565: 2 3 4 3 5 4 4 5 6 4 5 6 5 5 6 5
(x * (loop(\(x,i).2x,x,loop(\(x,i).loop(\(x,i).2x,x,(if x <= 0 then 2 else (2x + ~1))),1,3x)) div 2))
A268151: 0 40 2816 104448 3014656 76021760 1761607680 38520487936 807453851648 16389595201536 324355930193920 6289206510878720 119908340078739456 2254051613498933248 4611686018427387903 4611686018427387903
(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x - ((if x <= 0 then 2 else loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 2)))),x,(x + 2)))
A080801: 2 1 3 2 2 1 4 3 3 2 3 2 2 1 5 4
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x))
A037126: 2 2 3 2 3 5 2 3 5 7 2 3 5 7 11 2
(if (x + ~1) <= 0 then 1 else (if (x mod 5) <= 0 then 1 else loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x)))
A337126: 1 1 0 1 0 1 1 0 0 1 1 2 1 0 0 1
loop(\(x,i).(x + loop(\(x,i).x2,3,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)))),(x + 1),0)
A236214: 256 6817 397442 6162243 220521124 1036251845 8012009286 24995572327 103306557608 603552970569 1456444008010 4968923461931 12953848691052 24642048968653 48453335630414 110713026041775
loop(\(x,i).(x + loop(\(x,i).x3,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i)))),(x + 1),0)
A133548: 27 152 495 1826 4023 8936 15795 27962 52351 82142 132795 201716 281223 385046 533923 739302
(loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) - loop(\(x,i).(1 + (if (x + ~1) <= 0 then x else i)),(x + ~1),0))
A289615: 1 1 1 3 10 37 126 422 1422 4853 16786 58775 208000 742887 2674426 9694830
((loop(\(x,i).5x,x,1) - loop(\(x,i).3x,x,1)) * loop(\(x,i).(3x + 1),x,0))
A134939: 0 2 64 1274 21760 348722 5422144 83000234 1259729920 19027002722 286576949824 4309163074394 64731832372480 971825991711122 14585021567101504 218843984372767754
loop(\(x,i).x2,1,loop(\(x,i).(x + loop(\(x,i).(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1,i)),x,0))
A220788: 0 1 4 16
A163095: 0 1 4 16 25 49 81 144 169 225 289 400 484 625 784 1024
loop(\(x,i).loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,x),1,(10x + 9))
A268488: 1 19 29 13 49 59 23 79 89 11 109 119 43 139 149 53
(if x <= 0 then 1 else (~1 + ((1 + (loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x) mod 7)) mod 3)))
A142475: 1 0 0 ~1 0 0 1 ~1 0 0 0 1 ~1 0 0 ~1
(1 + loop(\(x,i).(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1))),1,(3x + 3)))
A087229: 4 2 3 2 6 2 3 2 4 2 3 2 5 2 3 2
(1 + (loop(\(x,i).3x,(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,x)),1) div 3))
A061393: 1 2 4 2 10 2 4 2 28 2 4 2 10 2 4 2
(1 + loop(\(x,i).(2x2 + x),1,loop(\(x,i).(2x + 1),x,0)) - loop(\(x,i).(3x + 1),x,1))
A051375: 0 0 9 66 345 1590 6909 29106 120465 493230 2005509 8116746 32744985 131801670 529647309 2125861986
(1 + loop(\(x,i).(loop(\(x,i).(x * i),x,1) div (x + 1)),1,(1 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x))))
A007619: 1 1 5 103 329891 36846277 1230752346353 336967037143579 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1)
A135171: 5 19 211 2059 175099 1586131 129009091 1161737179 94134790219 68629840493971 617671248800299 450283768452043891 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(1 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1))))
A075369: 16 36 144 324 900 1764 3600 5184 10404 11664 19044 22500 32400 36864 39204 51984
loop(\(x,i).(x + (x * loop(\(x,i).x2,1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))))),(x + 1),1)
A082100: 5 50 1300 65000 7930000 1348100000 390949000000 141523538000000 75007475140000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1))) * (1 + loop(\(x,i).7x,x,1)))
A241031: 6 56 1050 25112 655746 17766056 489541650 13599182072 379283617986 10599157616456 296486304875250 8297561014164632 232274972859656226 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (loop(\(x,i).(3x + 1),x,(1 + loop(\(x,i).2x,x,1))) div loop(\(x,i).5x,x,1)))
A096791: 1 1 0 1 1 1 2 2 3 4 5 6 7 9 11 14
(1 + ((3 * loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).2x,x,1))) + loop(\(x,i).3x,x,1)))
A283456: 5 13 40 136 490 1828 6970 26956 105250 413668 1633450 6471676 25703410 102269908 407460730 1625010796
(1 + (loop(\(x,i).2x,x,(5 + (loop(\(x,i).3x,x,2) + loop(\(x,i).2x,x,1)))) div 2))
A281698: 5 14 55 269 1465 8369 48865 288449 1713025 10210049 60993025 364899329 2185181185 13094268929 78498422785 470721937409
(if (x mod 5) <= 0 then (if (x mod 2) <= 0 then (25 * (if x <= 0 then 1 else 2)) else 2) else 1)
A040630: 25 1 1 1 1 2 1 1 1 1 50 1 1 1 1 2
(1 + (2 * (if x <= 0 then 0 else (1 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),(x + 4))))))
A322275-A008366: 1 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73
(~1 + (2 * loop(\(x,i).(2x + loop(\(x,i).(4x + loop(\(x,i).3x,i,1)),i,1)),x,3)))
A126642: 5 25 125 601 2765 12265 52925 223801 932525 3844105 15722525 63936601 258902285 1045109545 4209004925 16921851001
(~1 + (2 * ((x + 1) - (loop(\(x,i).(x2 + 3x),1,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)) div 2))))
A185877: 1 3 1 7 5 1 13 11 7 1 21 19 15 9 1 31
(~1 + (2 * loop(\(x,i).loop(\(x,i).x2,1,(x2 + x + 1)),1,loop(\(x,i).10x,x,1))))
A171687: 17 24641 204060401 2004006004001 20004000600040001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (x mod 3) <= 0 then ((1 + (if (x mod 2) <= 0 then 26 else 1)) * (if x <= 0 then 1 else 2)) else 1)
A040731: 27 1 1 4 1 1 54 1 1 4 1 1 54 1 1 4
(if (x mod 2) <= 0 then ((1 + (if ((x div 2) mod 2) <= 0 then 28 else 1)) * (if x <= 0 then 1 else 2)) else 1)
A040860: 29 1 4 1 58 1 4 1 58 1 4 1 58 1 4 1
(if (x mod 2) <= 0 then ((~1 + (5 * (if (x mod 4) <= 0 then 6 else 1))) * (if x <= 0 then 1 else 2)) else 1)
A040864: 29 1 8 1 58 1 8 1 58 1 8 1 58 1 8 1
(if (x mod 3) <= 0 then ((1 + (3 * (1 + (if (x mod 2) <= 0 then 6 else 1)))) * (if x <= 0 then 1 else 2)) else 1)
A040484: 22 1 1 14 1 1 44 1 1 14 1 1 44 1 1 14
(if (x mod 3) <= 0 then ((1 + (3 * (if (x mod 2) <= 0 then 10 else 1))) * (if x <= 0 then 1 else 2)) else 1)
A040962: 31 1 1 8 1 1 62 1 1 8 1 1 62 1 1 8
(if (x mod 3) <= 0 then ((1 + (3 * (2 + (if (x mod 2) <= 0 then 8 else 1)))) * (if x <= 0 then 1 else 2)) else 1)
A040961: 31 1 1 20 1 1 62 1 1 20 1 1 62 1 1 20
(1 + (2 * (1 + compr(\x.(if (x mod 4) <= 0 then 1 else loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x)),x))))
A216777-A216747-A216739-A216735-A045442: 5 7 13 17 23 29 31 37 41 47 53 61 71 73 79 89
(5 + (loop(\(x,i).(x2 + x),1,(1 + loop(\(x,i).2x,x,1))) + loop(\(x,i).3x,x,1)))
A229355: 12 20 44 122 392 1370 5024 18962 72872 283370 1110704 4377602 17320952 68727770 273267584 1088189042
(~1 + (4 * loop(\(x,i).(2x + loop(\(x,i).(4x + loop(\(x,i).3x,i,1)),i,1)),x,2)))
A126718: 7 43 235 1171 5467 24403 105595 447091 1864027 7686163 31440955 127865011 517788187 2090186323 8417944315 33843570931
(if (loop(\(x,i).2x,x,(2 * (if (x mod 2) <= 0 then 10 else 1))) mod (x + 1)) <= 0 then 0 else 5)
A237660: 0 0 5 0 0 5 5 0 5 5 5 5 5 5 5 0
(3 - loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,(x + 2)),1,(x + 5)))
A322984: 1 1 2 1 2 3 1 1 2 3 1 2 1 1 2 1
((1 + ((loop(\(x,i).2x,(x - loop(\(x,i).(~1 + (if x <= 0 then (2 * i) else x)),x,0)),1) mod (x + 1)) div 2)) mod 3)
A052343: 1 1 1 1 1 0 2 1 0 1 1 1 1 1 0 1
((2 * compr(\x.(x - loop(\(x,i).loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),x,(2x + 1)),2,(x + ~1))),x)) div 3)
A317626: 2 4 8 10 14 18 28 30 38 44 58 60 64 78 80 84
(6x + (if x <= 0 then 1 else ((x + 1) - loop(\(x,i).(x + (if (~2 + (x div 4)) <= 0 then 1 else 2)),2,x))))
A314253: 1 5 11 17 23 29 35 41 47 53 59 64 69 75 81 87
loop(\(x,i).x2,1,(1 + (2 * compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + x + 1))),x))))
A110284: 9 25 49 121 169 289 625 841 961 1225 1681 1849 2401 3025 4489 5929
loop(\(x,i).x2,1,(1 + (2 * compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + x + ~1))),x))))
A110013: 25 49 81 121 169 289 361 441 529 729 961 1089 1521 1681 1849 2401
(~1 + loop(\(x,i).loop(\(x,i).5x,x,x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A100690: 49 374 15624 546874 537109374 15869140624 12969970703124 362396240234374 274181365966796874 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(loop(\(x,i).14x,x,1) + loop(\(x,i).3x,x,1)),1,(2x + 1))
A138199: 17 2771 538067 105415691 20661066467 4049565346811 793714774848467 155568095572161131 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((3x + 1) + loop(\(x,i).(x - (if x <= 0 then 1 else (if (x mod 2) <= 0 then (x div 2) else (2x + ~1)))),x,(x + 1)))
A084432: 2 5 4 10 6 11 8 19 10 17 12 24 14 23 16 36
(loop(\(x,i).6x,x,1) + loop(\(x,i).4x,x,1) + loop(\(x,i).3x,2x,1))
A074567: 3 19 133 1009 8113 67849 582193 5079289 44791873 397760329 3548299153 31748050969 284623096033 2554993631209 22955425054513 206362390821049
(loop(\(x,i).5x,x,1) + loop(\(x,i).4x,x,1) + loop(\(x,i).3x,2x,1))
A074564: 3 18 122 918 7442 63198 551162 4877478 43502882 389635758 3497598602 31434082038 282690454322 2543153640318 22883164406042 205922723414598
(loop(\(x,i).7x,x,1) + loop(\(x,i).2x,x,1) + loop(\(x,i).3x,2x,1))
A074545: 3 18 134 1080 8978 75888 649154 5606640 48811778 427774608 3769260674 33358388400 296270827778 2638754846928 23555015544194 210638693637360
(1 + (2 * compr(\x.loop(\(x,i).loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(4x + ~1)),1,(x2 + x)),x)))
A106563: 1 11 17 23 25 31 39 41 45 51 53 57 59 65 67 73
(1 + (if x <= 0 then 1 else compr(\x.(~1 + ((1 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,x)) mod 3)),x)))
A246647: 2 3 6 7 9 12 15 16 18 19 21 24 25 27 28 30
loop(\(x,i).(1 + (6 * (2 + (if x <= 0 then 0 else (1 + (x * loop(\(x,i).((x2 + ~x) div 2),2,x))))))),x,1)
A070632: 1 19 1657009 4611686018427387903 4611686018427387903
loop(\(x,i).(12x + loop(\(x,i).(~1 + (2 * (2x + loop(\(x,i).2x,i,1)))),i,1)),x,1)
A021104: 1 19 263 3311 40383 487263 5857951 70338847 844240415 10131583007 121581790239 1458992663583 17507956694047 210095659269151 2521148627024927 30253786387545119
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).2x,i,1)),i,1)),x,1)
A016302: 1 19 267 3407 41915 508167 6124003 73618159 884068779 10612080215 127361237939 1528416234111 18341401707643 220098854991463 2641196432412675 31694408051560463
loop(\(x,i).(12x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A016324: 1 23 379 5483 74227 966635 12282883 153544091 1897874803 23272609547 283754322787 3445398949499 41707911082579 503763046196459 6074569573223491 73159552048508507
loop(\(x,i).(12x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021064: 1 18 241 2982 36085 433986 5210857 62539614 750503869 9006132954 108073857073 1296887073846 15562647261253 186751774276722 2241021312778489 26892255817780878
(1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (2 + i)) <= 0 then 0 else 1)),x,x),1,(7x + ~1)),x))
A231407: 1 4 6
A024904: 1 4 6 12 16 22 24 28 34 46 48 52 54 58 64 66
loop(\(x,i).(6x + loop(\(x,i).(~1 + (2 * (4x + loop(\(x,i).2x,i,1)))),i,1)),x,1)
A021184: 1 17 197 1957 17973 157749 1345909 11271029 93191285 763669621 6218195061 50398593141 407106949237 3280364834933 26383974158453 211918126207093
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).2x,i,1)),i,1)),x,1)
A016304: 1 15 157 1419 11869 94731 733069 5551323 41378557 304766187 2224062061 16112628987 116053574365 831966057483 5941308640333 42294437942811
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).4x,i,1)),i,1)),x,1)
A019333: 1 18 220 2280 21616 194208 1685440 14290560 119232256 983566848 8047836160 65462691840 530198327296 4280634482688 34479631482880 277245459333120
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A017932: 1 17 199 1997 18487 163205 1398223 11743469 97300423 798539093 6509186047 52798905341 426744275959 3440074001381 27677315556271 222358880070413
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A019443: 1 19 247 2743 28063 273847 2596399 24174631 222479455 2032023895 18467516431 167287650439 1512085646527 13647818683063 123064923768943 1108992721390567
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021354: 1 14 129 994 6965 46158 295513 1850618 11423709 69851782 424437377 2568196722 15496267333 93328343486 561380193321 3373943212906
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).5x,i,1)),i,1)),x,1)
A016103: 1 15 151 1275 9751 70035 481951 3216795 20991751 134667555 852639151 5343198315 33212784151 205111785075 1260114546751 7708980203835
loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A017269: 1 14 133 1070 7861 54614 365653 2385950 15282421 96547814 603612373 3743478830 23070427381 141471930614 864083198293 5260771611710
loop(\(x,i).(6x + loop(\(x,i).(2x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A021114: 1 14 131 1036 7497 51450 341167 2209592 14071013 88494406 551310123 3409583268 20966120449 128339843282 782754695399 4760106416464
(loop(\(x,i).5x,x,1) + loop(\(x,i).4x,x,1) + loop(\(x,i).6x,x,1))
A074561: 3 15 77 405 2177 11925 66377 374445 2135777 12292965 71280377 415819485 2437700177 14348506005 84736115177 501776304525
((loop(\(x,i).4x,x,1) + loop(\(x,i).6x,x,1)) - loop(\(x,i).5x,x,1))
A083326: 1 5 27 155 927 5675 35127 218195 1354527 8386715 51749127 318163235 1949418927 11907099755 72529083927 440741148275
loop(\(x,i).(7x + loop(\(x,i).(~1 + (2 * (2x + loop(\(x,i).2x,i,1)))),i,1)),x,1)
A021079: 1 14 133 1086 8253 60438 433861 3080462 21737485 152860422 1072817109 7520900478 52691034397 369016181366 2583829064677 18089666698734
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).2x,i,1)),i,1)),x,1)
A016296: 1 14 137 1162 9165 69342 511393 3709874 26619989 189594790 1343438889 9485451066 66805055773 469669890158 3297861746225 23135894831938
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A016801: 1 14 135 1120 8621 63714 460195 3280340 23204841 163423414 1147981055 8052113160 56430306661 395275799114 2767989986715 19380181827580
loop(\(x,i).(7x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A016312: 1 18 229 2538 26197 259290 2498293 23637546 220808533 2043771642 18789409717 171872944074 1566234297109 14231753285274 129035291862901 1167964212866922
loop(\(x,i).(7x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021034: 1 13 116 902 6615 47271 333922 2346784 16455989 115278449 807210768 5651264346 39561225523 276935720347 1938571500254 13570064940788
loop(\(x,i).(7x + loop(\(x,i).(2x + loop(\(x,i).8x,i,1)),i,1)),x,1)
A016311: 1 17 203 2101 20163 184821 1643251 14298917 122461955 1036190485 8684988819 72248167173 597363137827 4914549713909 40265910006707 328773866154469
(if (x mod 2) <= 0 then loop(\(x,i).10x,x,1) else loop(\(x,i).(10x + 1),x,1))
A285474: 1 11 100 1111 10000 111111 1000000 11111111 100000000 1111111111 10000000000 111111111111 1000000000000 11111111111111 100000000000000 1111111111111111
((loop(\(x,i).(2x + 1),x,(4 + loop(\(x,i).2x,x,1))) div 2) - loop(\(x,i).(3x + 1),x,1))
A134019: 1 2 4 11 46 227 1114 5231 23566 102827 438274 1836551 7601686 31183427 127084234 515429471
loop(\(x,i).x2,1,(1 + compr(\x.(loop(\(x,i).x2,2,(~1 + (loop(\(x,i).2x,x,1) mod (x + 1)))) mod (x + 1)),x)))
A259417: 1 9 25 49 81 121 169 289 361 529 625 729 841 961 1369 1681
(loop(\(x,i).(x + loop(\(x,i).(1 + (2 * (2x - (x div (if i <= 0 then 1 else i))))),i,1)),x,1) div (x2 + x + 1))
A321994: 1 1 2 4 9 22 59 165
(1 + compr(\x.(loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,2x)),2,x) mod (x + 1)),x))
A045753: 1 3 15 18 27 45 48 57 60 78 87 105 108 150 165 207
(1 + compr(\x.(loop(\(x,i).x2,1,loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,(x mod 4),x))) mod (x + 1)),x))
A322492: 1 2 4 6 8 12 16 18 24 32 36 48 64 72 96 108
(4 mod (1 + (if x <= 0 then 2 else (x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - ((x div 2) mod 2))))),x,(x + 1))))))
A260189: 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 4
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A019664: 1 21 301 3669 40957 433125 4418317 43942773 428973853 4128937989 39306876973 370937567637 3475860284989 32382187083813 300235508341069 2772487245505461
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021374: 1 16 173 1604 13833 115032 938821 7588108 61024865 489508448 3921394269 31392726612 251228899897 2010181938664 16082865641717 128668587186716
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).5x,i,1)),i,1)),x,1)
A018250: 1 17 197 1945 17661 152817 1284277 10599305 86485421 700600417 5649437157 45422860665 364536479581 2922126916817 23406459170837 187399966290025
loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A017521: 1 16 177 1688 14945 127008 1054033 8624296 69961089 564542000 4540661489 36447096504 292186326433 2340539977792 18739571436945 149992843917512
loop(\(x,i).(8x + loop(\(x,i).(2x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A021129: 1 16 175 1650 14481 122316 1010995 8250550 66817861 538611216 4329233415 34735589850 278393339641 2229689837716 17850234337435 142865452943550
loop(\(x,i).(8x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A018056: 1 20 277 3296 36169 377804 3819229 37727192 366384337 3512195588 33327711781 313693195088 2933189599705 27278314742972 252541704234733 2329170324845384
(loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1) + loop(\(x,i).8x,x,1))
A074553: 3 16 98 664 4802 36136 278498 2177464 17174402 136190536 1083566498 8638939864 68964148802 550978111336 4404154809698 35214904015864
loop(\(x,i).(9x + loop(\(x,i).(~1 + (2 * (2x + loop(\(x,i).2x,i,1)))),i,1)),x,1)
A021084: 1 16 179 1766 16545 151572 1374943 12417922 111935549 1008117968 9075855867 81693883518 735289682713 6617786085004 59560790560151 536049978287354
loop(\(x,i).(9x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021048: 1 15 160 1530 14071 127605 1151470 10372560 93381541 840520395 7564945180 68085295590 612770035411 5514937460385 49634458601290 446710191850620
loop(\(x,i).(4x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),x,1)
A016293: 1 17 215 2485 27831 308157 3397855 37409045 411630311 4528457197 49815125295 547974764805 6027755963191 66305449804637 729360484705535 8022967479211765
loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A018911: 1 18 223 2376 23485 222894 2067787 18935172 172107529 1557684810 14063797111 126801537408 1142367430933 10287141958566 92613721463395 833671786093884
loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021344: 1 13 110 770 4851 28623 161680 885940 4749701 25058033 130616850 674656710 3460370551 17652592243 89673093620 454027521080
loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A021092: 1 17 205 2205 22701 229677 2307565 23119085 231365101 2314349037 23146284525 231474025965 2314784990701 23148028847597 231481004271085 2314812905956845
loop(\(x,i).(4x + loop(\(x,i).(3x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A016981: 1 17 207 2245 23231 235677 2370967 23768645 237928911 2380278637 23806803527 238084281045 2380908324991 23809346902397 238094528416887 2380949536089445
(loop(\(x,i).7x,x,1) + loop(\(x,i).3x,x,1) + loop(\(x,i).4x,x,1))
A074549: 3 14 74 434 2738 18074 122474 842114 5836898 40635434 283582874 1981698194 13858595858 96957713594 678496291274 4748649600674
loop(\(x,i).(5x + loop(\(x,i).(2 * (4x + loop(\(x,i).4x,i,1))),i,1)),x,1)
A092794: 1 21 265 2733 25441 223461 1895545 15736413 128882641 1046542101 8451838825 68020609293 546227922241 4380272835141 35094966838105 281025802973373
loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A016299: 1 17 209 2293 23961 244797 2473969 24869813 249349001 2496744877 24983724129 249918620133 2499593099641 24997965496157 249989827476689 2499949137375253
loop(\(x,i).(5x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A017897: 1 17 202 2090 20251 189707 1745332 15900020 144066901 1301455397 11737424062 105758621150 952437144751 8574983669087 77190104636392 694787214149480
((x + 1) mod (1 + loop(\(x,i).(if x <= 0 then 0 else (x + (x mod 2) - (if ((x + (x div 2)) mod 4) <= 0 then 2 else 1))),2,x)))
A298972: 0 0 1 0 2 0 1 0 3 0 1 2 2 0 1 0
loop(\(x,i).(2 * (x + (if x <= 0 then 1 else (if (x mod (1 + (2 * (2x mod 3)))) <= 0 then (x div 3) else 1)))),x,1)
A322060: 1 4 10 26 54 144
loop(\(x,i).(10x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A016321: 1 21 313 4065 49081 566721 6350473 69654225 751887961 8016991521 84652923433 886876310385 9231886792441 95586981129921 985282830165193 10117545471478545
loop(\(x,i).(10x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021049: 1 16 185 1940 19701 197976 1982785 19837180 198400301 1984089536 19841156985 198412358820 1984125963301 19841266774696 198412689204785 1984126956486860
loop(\(x,i).(11x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A016280: 1 16 195 2210 24521 270396 2976415 32746870 360234741 3962640176 43589217035 479481914730 5274302648161 58017333896356 638190687176055 7020097601917790
loop(\(x,i).((loop(\(x,i).(x * i),x,1) div (x + 1)) div 2),1,(1 + compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x)))
A129742: 0 0 2 51 164945 18423138 615376173176 168483518571789 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(loop(\(x,i).4x,x,1) div (x + 1)),1,(1 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)))
A180511: 5 51 585 95325 1290555 252645135 3616814565 764877654105 2484744621997515 37191016277640225 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A236959: 1 2 4 2 10 4 16 6 22 28 10 12 40 14 46 52
loop(\(x,i).((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A136035: 0 3 1 7 7 1 13 7 7 1 31 1 31 7 31 13
loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A099585: 1 2 4 2 10 4 16 2 22 28 10 4 40 14 46 52
(1 + compr(\x.(loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,2x)),2,x) mod (x + 2)),x))
A174237: 1 2 5 11 17 20 26 32 41 56 77 95 110 116 122 125
((x + 1) + compr(\x.(~1 + loop(\(x,i).(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,x)),2,x)),2x))
A285973: 1 5 8 13 17 21 24 28 32 37 40 45 49 53 58 61
loop(\(x,i).(2x + (loop(\(x,i).4x,x,(if (x mod (4 - (x mod 2))) <= 0 then 1 else 0)) div (x + 1))),x,1)
A018348: 1 2 4 59 118 236
(~1 + (loop(\(x,i).(~2x + 1),x,loop(\(x,i).(x mod 2),(x div 2),(1 - (2 * (x mod 2))))) + loop(\(x,i).2x,x,1)))
A231407: 1 4 6
A087231: 1 4 6 2 26 10 106 42 426 170 1706 682 6826 2730 27306 10922
(loop(\(x,i).(x * (2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),i))),x,3) - loop(\(x,i).2x,x,1))
A330349: 2 13 101 1147 14999 255223 4849781 111546307 3234846359 100280244553 3710369066381 152125131761557 6541380665830919 307444891294237513 4611686018427387903 4611686018427387903
(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1) + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).2x,x,1)))
A085812: 1 5 22 91 366 1454 5748 22691 89590 354010 1400268 5544334 21973420 87158972 345977832 1374249251
(loop(\(x,i).(x + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(~1 + i),1)),x,1) - loop(\(x,i).2x,x,1))
A306376: 0 0 1 7 34 144 574 2226 8533 32587 124453 476145 1826175 7022379 27072487 104614863
(loop(\(x,i).7x,x,1) + loop(\(x,i).5x,x,1) + loop(\(x,i).2x,x,1))
A074538: 3 14 78 476 3042 19964 133338 901796 6155682 42307244 292241898 2026156916 14085431922 98109721724 684326604858 4778079120836
((loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,(x + 1)) - loop(\(x,i).4x,x,1)) div (x + 1))
A282708: 0 0 0 4 18 81 338 1384 5588 22405 89430 355906 1413600 5607109 22220902 88008656
((x + 1) + loop(\(x,i).(x + loop(\(x,i).(1 + (2 * (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))),1,i)),x,1))
A326300: 2 6 8 16 18 22 24 40 42 46 48 56 58 62 64 96
loop(\(x,i).(x2 + 2x),1,compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1)))
A037074: 15 35 143 323 899 1763 3599 5183 10403 11663 19043 22499 32399 36863 39203 51983
((2x + 1) + (if x <= 0 then 1 else (2 * (x + (if (x mod 3) <= 0 then 0 else (if (x mod (2 + (x mod 2))) <= 0 then 1 else x))))))
A020583: 2 7 11 13 19 31
((3x + 1) + loop(\(x,i).loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),x,x),1,3x))
A046818: 1 1 3 2 3 1 3 3 3 3 5 2 3 2 4 4
(loop(\(x,i).(x * (2 + i)),compr(\x.((~1 + loop(\(x,i).(x * i),x,1)) mod (x + 2)),x),2) - loop(\(x,i).(x * i),x,(x + 1)))
A261457: 1 4 114 5016 39916680 6227020080 355687428090960 121645100408791680 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else loop(\(x,i).loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),2),1,(x + ~1)))
A131136: 1 2 4 4 8 4 8 8 16 4 8 8 16 8 16 16
(1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (2 + i)) <= 0 then 0 else 1)),x,x),1,(9x + 4)),x))
A024910: 1 5 7 9 11 17 25 27 31 35 37 39 41 47 49 51
loop(\(x,i).(x + loop(\(x,i).(1 + (x div (1 + (x mod (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))))),1,i)),x,1)
A268398: 1 2 3 7 8 9 10 14 17 18 19 23 24 25 26 42
loop(\(x,i).(x * loop(\(x,i).(7x + loop(\(x,i).10x,i,1)),1,i)),x,1)
A053106: 1 17 408 12648 480624 21628080 1124660160 66354949440 4379426663040 319698146401920 25575851712153600 2225099098957363200 4611686018427387903 4611686018427387903
loop(\(x,i).7x,x,loop(\(x,i).(x + (10x div (if i <= 0 then 1 else i))),x,1))
A197193: 1 77 3234 98098 2403401 50471421 942133192 16016264264 252256162158 3727785507446 52188997104244 697434779483988 8950413003377846 110847422580294862 1330169070963538344 4611686018427387903
((if x <= 0 then 2 else loop(\(x,i).(2 * (x - loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(~2 + i),1))),x,0)) div 2)
A158495: 1 ~1 ~3 ~8 ~21 ~56 ~154 ~440 ~1309 ~4048 ~12958 ~42712 ~144210 ~496432 ~1735764 ~6145968
(2 * (1 + loop(\(x,i).(x + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x)),1,(3x + 3))))
A136799: 10 16 22 28 36 40 46 52 58 66 70 78 82 88 96 100
((1 + ((1 + ((1 + (if x <= 0 then 1 else ((x * loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)) div 2))) div 2)) div 2)) div 2)
A238794: 1 0 1 0 1 1 0 1 1 2 0 1 2 3 4 0
((loop(\(x,i).2x,x,3) - loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),((x + 1) div 2),1)) div 2)
A117186: 1 2 5 9 21 38 86 157 349 642 1410 2610 5682 10572 22860 42717
((if x <= 0 then 2 else (1 + (((1 + ((loop(\(x,i).(x * (if (x mod 2) <= 0 then 1 else x)),1,(x + ~2)) div 2) div 2)) div 2) div 2))) div 2)
A263395: 1 0 0 0 0 0 0 1 0 2 0 3 0 4 1 5
((1 + ((if x <= 0 then 2 else (loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,x) div (2 + (x mod 2)))) div 2)) div 2)
A141099: 1 0 0 0 1 0 0 1 1 0 1 1 1 1 2 0
(loop(\(x,i).loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 2 else 0)),x,(x + 2)),(x + 4),1) mod 10)
A093336: 1 3 7 9 3 9 1 7 1 3 7 3 9 1 7 1
((loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) - (if (x + ~2) <= 0 then 2 else 1)) div 2)
A112051: 1 3 11 24 60 84 144 180 264 420 480 684 840 924 1104 1404
(1 - ((loop(\(x,i).x3,1,(loop(\(x,i).(x * i),(x div 2),1) - loop(\(x,i).(x * i),x,1))) div 3) div 2))
A330124: 1 1 2 22 1776
(1 - ((1 + ((x + (if x <= 0 then 2 else (loop(\(x,i).(x * (~2 + (i mod 2))),x,1) - loop(\(x,i).2x,x,1)))) div 2)) div 2))
A091328: 0 1 1 3 3 9 13 33 59
((1 + (if x <= 0 then 1 else compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 2)))) div 2)
A168544: 1 6 9 15 21 30 36 51 54 69 75 90 96 99 114 120
(2 - ((1 + loop(\(x,i).(1 + loop(\(x,i).(x - (if x <= 0 then 1 else (1 + (2 * (1 + i))))),x,2x)),1,2x)) div 2))
A271647: 1 2 4 3 6 5 9 8 7 12 11 10 16 15 14 13
((loop(\(x,i).(2x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i))),x,(x + 1)) + loop(\(x,i).2x,x,1)) div 2)
A172411: 1 2 5 10
A323988: 1 2 5 10 23 46 102 204 443 886 1898 3796 8054 16108 33932 67864
((loop(\(x,i).(2x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i))),x,(x + 1)) - loop(\(x,i).2x,x,1)) div 2)
A107373: 0 0 1 2 7 14 38 76 187 374 874 1748 3958 7916 17548 35096
((loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x div 2),((x + 1) mod 2)) + loop(\(x,i).2x,x,1)) div 2)
A027306: 1 1 3 4 11 16 42 64 163 256 638 1024 2510 4096 9908 16384
(2 * compr(\x.(~1 + loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),x,2x)),2,x)),(x + 1)))
A309374: 2 4 6 10 12
A055235: 2 4 6 10 12 18 28 30 36 54 82 84 90 108 162 244
(2 * compr(\x.loop(\(x,i).(x * (loop(\(x,i).(1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),2,x) div (1 + i))),2,x),(x + 1)))
A043726: 2 4 6 8 12 14 16 24 28 30 32 42 48 56 60 62
(~2 + loop(\(x,i).x2,1,compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1))))
A137367: 7 23 119 287 839 1679 3479 5039 10199 11447 18767 22199 32039 36479 38807 51527
loop(\(x,i).x2,1,(2 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1))))
A108604: 25 49 169 361 961 1849 3721 5329 10609 11881 19321 22801 32761 37249 39601 52441
((2 * ((if (x mod 4) <= 0 then 8 else 1) * (if x <= 0 then 1 else 2) * (2 - (x mod 2)))) - (if x <= 0 then 1 else 2))
A040958: 31 2 6 2 62 2 6 2 62 2 6 2 62 2 6 2
(2 * (1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,(x + 2)),1,3x),x)))
A120382: 40 48 62 68 72 82 96 100 108 114 138 142 158 172 176 178
(2 * loop(\(x,i).2x,((3x + 6) - loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),x,x)),1))
A093528: 128 2048 16384 524288 4194304 67108864 536870912 34359738368 274877906944 4398046511104 35184372088832 1125899906842624 9007199254740992 144115188075855872 1152921504606846976
((loop(\(x,i).2x,x,(1 + (loop(\(x,i).2x,(x div 2),(2 + (x mod 2))) + loop(\(x,i).2x,x,1)))) div 2) div 2)
A096222: 1 3 9 30 100 360 1296 4896 18496 71808 278784 1098240 4326400 17172480 68161536 271589376
((if (x mod 2) <= 0 then (7 * (if (x mod 4) <= 0 then (2 * (2 + (if x <= 0 then 0 else 2))) else 1)) else 2) div 2)
A040204: 14 1 3 1 28 1 3 1 28 1 3 1 28 1 3 1
(loop(\(x,i).(x2 + x),1,(if x <= 0 then 1 else (2 + (2 mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1))))) div 2)
A122916: 1 3 3 3 3
A337328: 1 3 3 3 3 10 3 3 3 10 3 10 3 10 10 3
((loop(\(x,i).(1 - loop(\(x,i).(~1 + (2 * loop(\(x,i).(x div (1 + (x mod 2))),x,x))),2x,x)),1,(x + 1)) div 2) div 2)
A120069: 1 2 16 32 128 256 4096 8192 32768 65536 524288 1048576 4194304 8388608 268435456 536870912
((loop(\(x,i).2x,x,1) - loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x div 2),((x + 1) mod 2))) div 2)
A058622: 0 1 1 4 5 16 22 64 93 256 386 1024 1586 4096 6476 16384
(8 * loop(\(x,i).loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 2 else 0)),x,(x + 2)),(x + 6),1))
A270301: 136 152 184 232 248 296 328 344 376 424 472 488 536 568 584 632
((if x <= 0 then 0 else (2 + compr(\x.(~1 + (loop(\(x,i).2x,x,(1 + (if (x mod 2) <= 0 then 2x else 1))) mod (x + 2))),x))) div 2)
A143738: 0 1 2 2 3 3 4 5 6 6 8 8 9 11 12 14
(loop(\(x,i).(loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1)),1,(x2 + x + 2)) div 2)
A121824: 17 353 198593
(loop(\(x,i).3x,(x div 2),loop(\(x,i).(2x - ((if (i mod 2) <= 0 then 1 else 2x) div (1 + i))),x,2)) div 2)
A098662: 1 1 6 9 54 90 540 945 5670 10206 61236 112266 673596 1250964 7505784 14073345
(if (x mod 3) <= 0 then (2 * ((if (x mod 2) <= 0 then 12 else 1) * (if x <= 0 then 1 else 2))) else (2 + (x mod 2)))
A040565: 24 3 2 4 2 3 48 3 2 4 2 3 48 3 2 4
loop(\(x,i).2x,x,(if x <= 0 then 1 else (2 * loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(x + ~1),~x))))
A098580: 1 ~4 ~16 ~96 ~640 ~4480 ~32256 ~236544 ~1757184 ~13178880 ~99573760 ~756760576 ~5778898944 ~44304891904 ~340806860800 ~2629081497600
(2 + loop(\(x,i).loop(\(x,i).5x,(2x + ~1),1),1,(x * (1 + (if (x mod 3) <= 0 then 2 else 0)))))
A182330: 3 7 127 762939453127
loop(\(x,i).x2,1,((if x <= 0 then 2 else loop(\(x,i).((2x * (~1 + (2 * i))) div (2 + i)),x,3x)) div 2))
A338727: 1 1 9 81 784 8100 88209 1002001 11778624 142420356 1763160100 22268399076 286105172544 3730846771600 49286086364025 658580586980625
loop(\(x,i).loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),x,1),1,((x2 + x) div 2))
A113511: 1 2 30 30030 6469693230 614889782588491410 4611686018427387903 4611686018427387903 4611686018427387903
((x + (2 * (x div (1 + (2 * (if loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 0 else 2))),x,x) <= 0 then 2 else 1)))))) div 2)
A334043: 0 0 1 2 2 3 5 4 5 7 8 8 10 8 9 12
(2 * compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(2x2 + 6)),x))
A121982: 2 4 8 14 16 22 26 32 34 38 44 46 52 64 68 76
loop(\(x,i).loop(\(x,i).(x * (~1 + (2 * i))),(x div 2),1),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A207332: 1 1 3 15 945 10395 2027025 34459425 13749310575 213458046676875 6190283353629375 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * ((if (x mod 2) <= 0 then 2 else 0) + (x div 2))),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A112456: 6 3 10 21 55 78 136 171 253 406 465 666 820 903 1081 1378
loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A079395: 2048 177147 48828125 1977326743 285311670611 1792160394037 34271896307633 116490258898219 952809757913927 12200509765705829 25408476896404831 177917621779460413 550329031716248441
loop(\(x,i).(x2 * loop(\(x,i).3x,x,x)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A097205: 72 729 30375 750141 235782657 3502727631 634465620819 7971951402153 1145440056788109 1673826273552131487 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).x2,2,x3)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A138031: 8192 1594323 1220703125 96889010407 34522712143931 302875106592253 9904578032905937 42052983462257059 504036361936467383 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x + ~2),x),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A065858: 6 8 10 14 20 22 27 30 35 44 46 54 58 62 66 75
compr(\x.loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A078782: 4 6 9 12 18 21 26 28 34 42 45 52 57 60 65 74
((~1 + ((loop(\(x,i).((x2 + ~x) div 2),1,loop(\(x,i).4x,x,1)) div 2) div 2)) mod loop(\(x,i).2x,x,2))
A284405: 1 0 5 7 31 63 127 255 511 1023 2047 4095 8191 16383 32767 65535
(loop(\(x,i).5x,(x + 1),1) div (loop(\(x,i).3x,x,3) - loop(\(x,i).2x,x,2)))
A191695: 5 5 6 9 14 23 37 61 101 168 278 462 769 1280 2131 3550
(loop(\(x,i).~3x,x,loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1)) div (~2x + 1))
A108735: 1 6 ~18 108 ~810 6804 ~61236 577368 ~5629338 56293380 ~574192476 5950722024 ~62482581252 663276631752 ~7106535340200 76750581674160
(2x + (if x <= 0 then 1 else loop(\(x,i).(if x <= 0 then 0 else (1 + (5 * ((x2 + ~x) div 2)))),1,(x + ~1))))
A116733: 1 2 5 12 24 41 63 90 122 159 201 248 300 357 419 486
(1 + ((2 * ((1 + loop(\(x,i).2x,x,(if (x mod 3) <= 0 then 1 else 2))) div 3)) + (if x <= 0 then 1 else 2x)))
A020629: 2 5 11 13 31 53
((3 * (if (x mod 3) <= 0 then ((1 + (if (x mod 2) <= 0 then 4 else 0)) * (if x <= 0 then 1 else 2)) else 1)) + (x mod 2))
A040216: 15 4 3 7 3 4 30 4 3 7 3 4 30 4 3 7
((2 * (if (x mod 3) <= 0 then ((1 + (if (x mod 2) <= 0 then 6 else 0)) * (if x <= 0 then 1 else 2)) else 1)) - (x mod 2))
A040201: 14 1 2 3 2 1 28 1 2 3 2 1 28 1 2 3
((if (x mod 3) <= 0 then (3 * (if (x mod 2) <= 0 then (3 * (2 + (if x <= 0 then 0 else 2))) else 1)) else 2) - (x mod 2))
A040331: 18 1 2 2 2 1 36 1 2 2 2 1 36 1 2 2
(loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (1 + (2 * loop(\(x,i).(2x - (x mod 4)),2,2x)))),x,x) div 2)
A079237: 0 2 2 4642
loop(\(x,i).(1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x)),1,(loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2))
A181363: 1 1 2 1 3 2 5 1 7 3 11 2 13 5 17 1
(2 * compr(\x.(1 - loop(\(x,i).(~2 + (loop(\(x,i).(1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),2,x) mod (x + 1))),2,x)),x))
A043769-A043760-A043752-A043745-A043733-A043573: 42 74 82 84 86 90 106 138 146 148 150 154 162 164 166 168
compr(\x.loop(\(x,i).(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(4x + 1))),1,6x),x)
A114913-A111174: 3 4 8 10 13 14 17 18 19 24 25 28 32 39 42 43
((x + ~1) + loop(\(x,i).(1 + (if x <= 0 then x else (x - (if x <= 0 then 1 else (~1 + (x div (2 + ((x div 2) div 3)))))))),2,x))
A026420: 2 4 5 6 7 9 11 13 15 16 17 19 21 23 25 27
(x + loop(\(x,i).(x - (if x <= 0 then 1 else (~1 + ((1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)) mod 3)))),x,(x + 1)))
A244731: 1 2 5 6 10 11 12 13 17 21 22 23 24 25 29 30
compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(12x + 4)),x)
A139528: 0 2 3 4 5 7 9 10 14 17 18 19 20 23 24 27
compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(2 + ((x2 + 3x + 2) div 2))),x)
A175282: 1 2 4 7 8 10 11 16 17 23 25 28 29 31 32 37
compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (2 + i)) <= 0 then 0 else 1)),x,x),1,(13x + 2)),x)
A154610: 0 2 6 8 18 24 32 38 44 56 62 66 72 74 78 84
compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (2 + i)) <= 0 then 0 else 1)),x,x),1,(17x + 2)),x)
A138624: 0 4 6 16 18 22 36 42 46 48 58 64 72 76 82 84
((x + 3) + (if x <= 0 then 1 else loop(\(x,i).(~1 + (if x <= 0 then ((1 + ((1 + i) * i)) * i) else x)),x,0)))
A087573: 4 6 6 6 90 90
((3x + 2) - (loop(\(x,i).(if x <= 0 then 0 else (1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2)))),2,x) mod 3))
A287363: 2 5 7 9 14 17 20 22 24 29 31 33 38 40 42 47
compr(\x.(1 - loop(\(x,i).(~1 + loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),(x div 2),(2x + ~1))),1,(x2 div 2))),x)
A028870: 2 3 5 7 9 13 15 19 21 27 29 33 35 37 43 47
compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (2 + i)) <= 0 then 0 else 1)),x,x),1,(11x + 10)),x)
A102721: 0 6 8 14 18 20 24 36 38 48 50 54 60 66 68 74
compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (2 + i)) <= 0 then 0 else 1)),x,x),1,(17x + 4)),x)
A138630: 0 2 6 12 18 20 26 36 38 48 50 62 66 68 72 80
compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (2 + i)) <= 0 then 0 else 1)),x,x),1,(13x + 8)),x)
A111369: 0 2 6 12 14 20 26 30 36 42 50 56 72 80 84 86
(loop(\(x,i).x3,1,loop(\(x,i).(10x + 1),x,1)) * loop(\(x,i).x3,x,x))
A052072: 0 1331 700227072 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + i),((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3),0)
A343877: 0 0 0 1 0 3 0 3 1 3 0 10 0 3 3 6
(loop(\(x,i).(10x + 1),2x,1) - (if (x + ~1) <= 0 then 10x else 0))
A267937: 1 101 11111 1111111 111111111 11111111111 1111111111111 111111111111111 11111111111111111 1111111111111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x - ((~1 - (2 * (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))) div 5)),x,0)
A345297: 0 1 2 3 5 6 7 10 11 13 14 15 22 23 26 27
loop(\(x,i).(10x + 1),(x + 3),loop(\(x,i).(10x + 10),x,0))
A244845: 111 101111 11011111 1110111111 111101111111 11111011111111 1111110111111111 111111101111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(10x + 1),(x + 1),loop(\(x,i).(10x + 10),x,0)))
A173521: 0 1010 110110 11101110 1111011110 111110111110 11111101111110 1111111011111110 111111110111111110 4611686018427387903 4611686018427387903 4611686018427387903
(((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1))
A325770-A305611-A294928-A239707: 0 1 1 2 1 3 1 3 2 3 1 5 1 3 3 4
loop(\(x,i).4x,((((1 + (8 mod (1 + (x div 2)))) div 2) + (if x <= 0 then 0 else 1)) - (x mod 2)),1)
A309074: 1 1 4 1 16 4 4 1 64 16 16 4 16 4 4 1
loop(\(x,i).3x,((((1 + (8 mod (1 + (x div 2)))) div 2) + (if x <= 0 then 0 else 1)) - (x mod 2)),1)
A309057: 1 1 3 1 9 3 3 1 27 9 9 3 9 3 3 1
(1 + (x mod (1 + (x mod (1 + (loop(\(x,i).2x,x,(1 + (if (x mod (2 + (x mod 2))) <= 0 then 1 else x))) mod (x + 1)))))))
A069226: 1 1 3 1 1 1 1 1 9 5 1 1 1 1 3 1
loop(\(x,i).(x * i),(1 + (x div (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))))),1)
A102068: 1 2 6 2 120 6 5040 2 6 120 39916800 6 6227020800 5040 120 2
(~1 + loop(\(x,i).2x,(~1 + (2 * ((if x <= 0 then 2 else (((x + ~2) * (x div 3)) mod (1 + (x div 2)))) div 2))),1))
A271697: 1 0 0 0 1 0 0 1 1 0 0 1 7 1 0 0
(1 + (2x div (1 + ((1 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),x,2x)) mod 3))))
A026210-A026186-A026172-A026136: 1 3 2 7 9 4 5 15 6 19 21 8 25 27 10 11
(1 + loop(\(x,i).(x * ((x2 + x + 1) div 3)),1,loop(\(x,i).10x,(x + 1),1)))
A281860: 371 336701 333667001 333366670001 333336666700001 333333666667000001 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (x mod (1 + ((loop(\(x,i).(2x + 2),loop(\(x,i).(x div (1 + (x mod 2))),x,x),1) - (x mod 2)) mod (x + 1)))))
A340082: 1 1 1 1 1 2 1 1 1 4 1 2 1 6 4 1
(~1 + (3 * ((1 - (if (2 - (x div 4)) <= 0 then (x mod 8) else 1)) * (1 + (if x <= 0 then 0 else 2)))))
A160925: ~1 ~1 ~1 ~1 ~1 ~1 ~1 ~1 8 ~1 ~10 ~19 ~28 ~37 ~46 ~55
(~1 + loop(\(x,i).10x,x,(~3 + loop(\(x,i).10x,(x + 1),1))))
A332196: 6 969 99699 9996999 999969999 99999699999 9999996999999 999999969999999 99999999699999999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((3 * (2 + (if x <= 0 then 0 else (1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x))))) div 7))
A323889: 1 2 2 3 2 4 3 5 2 6 4 7 3 7 5 8
(1 + (if (x + ~1) <= 0 then 0 else (1 + ((x div (1 + ((if (((x + ~1) div 2) mod 4) <= 0 then 2 else 1) + (x mod 2)))) mod 2))))
A332297: 1 1 2 3 2 3 3 2 2 2 3 3 2 2 3 3
(1 + (x mod (1 + (x div (2 + (loop(\(x,i).2x,(x + ~1),(if (x mod (2 + (x mod 2))) <= 0 then 1 else 0)) mod (x + 1)))))))
A094522: 1 1 1 2 1 3 1 4 3 2 1 6 1 7 3 8
(2 + (((x + 1) * (~1 + loop(\(x,i).(x + (if x <= 0 then 1 else (2x * ((~1 + i) * (~2 + i))))),x,x))) div 2))
A326224: 1 2 3 30 649
(if x <= 0 then 0 else (1 + ((2 * (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))) div 5)))
A061395: 0 1 2 1 3 2 4 1 2 3 5 2 6 4 3 1
(1 + (loop(\(x,i).(x3 + 2x2 + 2x),1,loop(\(x,i).10x,(x + 1),1)) div 3))
A281859: 407 340067 334000667 333400006667 333340000066667 333334000000666667 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (((if x <= 0 then 1 else x) mod (3 + (if (((x + 2) mod 8) mod 3) <= 0 then 0 else 2))) mod 3))
A241815: 2 2 3 1 2 1 1 3 1 1 1 2 1 1 3 1
(if x <= 0 then 1 else (~1 + ((0 - ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3)) mod 3)))
A307420: 1 ~1 ~1 1 ~1 1 ~1 0 1 1 ~1 ~1 ~1 1 1 0
(1 + ((1 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 2))) div 3))
A177139: 3 5 7 11 15 21 25 35 37 47 51 61 65 67 77 81
(if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + ((loop(\(x,i).2x,(x div 2),2) mod (x + 1)) div 2)) div 2))) div 3)))
A309981: 0 1 1 1 2 2 2 1 2 2 3 2 3 2 1 1
(1 + ((2 * (1 + ((1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * ((x + 1) div 2))) div 2))) div 3))
A221640: 1 1 2 1 2 3 1 3 4 7 1 3 5 9 11 1
loop(\(x,i).(2 * i),((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3),1)
A216864: 1 1 1 2 1 4 1 4 2 4 1 8 1 4 4 6
(~1 + ((if x <= 0 then 1 else (2 + ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3))) mod 3))
A317146: 0 1 1 ~1 1 ~1 1 0 ~1 ~1 1 1 1 ~1 ~1 0
(~1 + (3 * loop(\(x,i).5x,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),2)))
A098117: 29 149 3749 93749 58593749 1464843749 915527343749 22888183593749 14305114746093749 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + ((loop(\(x,i).(x * (2 - (x div 4))),1,loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))) div 2) mod 3))
A005094: 0 0 ~1 0 1 ~1 ~1 0 ~1 1 ~1 ~1 1 ~1 0 0
(1 + (6 * compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(3x + ~1)),x)))
A216869: 1 25 49
A091300: 1 25 49 55 85 91 115 121 133 145 169 175 187 205 217 235
(if (~x + 2) <= 0 then loop(\(x,i).(10x + 1),2x,1) else (9x + 1))
A267887: 1 10 11111 1111111 111111111 11111111111 1111111111111 111111111111111 11111111111111111 1111111111111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (compr(\x.(1 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x2 + 2x))),x) div 3))
A091199: 1 2 3 4 6 7 8 10 14 17 18 19 20 21 25 29
(~1 + (2 * (1 + (if (x mod 3) <= 0 then 0 else (if ((x + 1) mod 5) <= 0 then 2 else 1)))) - (x mod 3))
A249694: 1 2 1 1 4 1 1 2 1 1 2 1 1 2 3 1
loop(\(x,i).(6x + 1),(1 + compr(\x.(loop(\(x,i).(2x + 2),x,8) mod (x + 1)),x)),1)
A165210: 7 43 55987 4611686018427387903 4611686018427387903
((1 + loop(\(x,i).10x,(x + 1),1)) * (~1 + loop(\(x,i).10x,x,1)))
A332190: 0 909 99099 9990999 999909999 99999099999 9999990999999 999999909999999 99999999099999999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1)
A290059: 3 10 126 1716 352716 5200300 1166803110 17672631900 4116715363800 15033633249770520 232714176627630544 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1)
A246669: 2 5 42 429 58786 742900 129644790 1767263190 343059613650 1002242216651368 14544636039226909 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(x - (if (x mod 5) <= 0 then (5 * (1 - (2 * (x mod 2)))) else 0)),1,(x + 1)))
A222244: 0 1 2 3 9 5 6 7 8 4 10 11 12 13 19 15
(1 + ((1 + (((loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,1) mod (x + 2)) div 2) div 2)) mod (x + 1)))
A129654: 1 2 2 2 3 2 2 3 3 2 3 2 2 4 3 2
(~1 + ((x + 1) * (2 + ((x + 1) * loop(\(x,i).(4x + 2),(if x <= 0 then 2 else ~1),4x)))))
A106231: 11 19 77 199 409 731 1189 1807 2609 3619 4861 6359 8137 10219 12629 15391
((4x + 3) * loop(\(x,i).x2,1,loop(\(x,i).((2 * (x - (2x * i))) div (1 + i)),x,1)))
A267844: 3 7 44 375 3724 40572 470448 5705271 71571500 921922716 12130541488 162422308412 2206718599344 30354522550000 422005129502400 5921371233163575
(2 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + loop(\(x,i).10x,(x + 1),1)))
A262778: 12 103 1005 10007 100011 1000013 10000017 100000019 1000000023 10000000029 100000000031 1000000000037 10000000000041 100000000000043 1000000000000047 10000000000000053
(if x <= 0 then 2 else (1 + (2 * (1 + (if (~x + 2) <= 0 then (1 - (2 * ((x mod (1 + (((x + 1) div 2) div 2))) mod 2))) else 0)))))
A039704: 2 3 5 1 5 1 5 1 5 5 1 1 5 1 5 5
(~1 + (2 * loop(\(x,i).x2,1,(1 + ((3x + 3) * loop(\(x,i).(x2 + 2x),2,6))))))
A157863: 103708801 414777601 933206401 1658995201 2592144001 3732652801 5080521601 6635750401 8398339201 10368288001 12545596801 14930265601 17522294401 20321683201 23328432001 26542540801
(~1 + (2 * loop(\(x,i).x2,1,(~1 + ((3x + 3) * loop(\(x,i).(x2 + 2x),2,6))))))
A157859: 103651201 414662401 933033601 1658764801 2591856001 3732307201 5080118401 6635289601 8397820801 10367712001 12544963201 14929574401 17521545601 20320876801 23327568001 26541619201
(1 + ((1 + (loop(\(x,i).(12x + 1),x,1) div loop(\(x,i).(4x + ~1),x,1))) div 2))
A263459: 2 3 8 23 67 200 597 1790 5369 16105 48314 144939 434816 1304447 3913339 11740016
((if x <= 0 then 1 else x) div (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1))))))))
A268336: 1 1 2 1 4 1 6 1 2 2 10 1 12 3 4 1
(1 + ((1 + ((1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (1 + ((x + 1) mod 3)))) div 2)) div 2))
A308694: 1 1 2 1 2 2 1 2 2 3 1 2 2 4 2 1
(7 * loop(\(x,i).x2,1,(3 * loop(\(x,i).(10x + 1),x,1))))
A178634: 63 7623 776223 77762223 7777622223 777776222223 77777762222223 7777777622222223 777777776222222223 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * ((2 - ((x + 1) mod (1 + (2 * (if ((if x <= 0 then 1 else x) mod 6) <= 0 then 2 else 0))))) mod (x + 1))))
A125563: 1 1 5 5 5 5 1 5 5 5 5 5 25 5 5 5
(1 + (((1 + (((1 + loop(\(x,i).(x + (if (x + ~2) <= 0 then 1 else ((x2 + ~x) * i))),x,0)) div 2) div 2)) div 2) div 2))
A071881: 1 1 1 1 3 222
(1 + (((3 * (1 + (x div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))))) div 2) div 2))
A323906: 1 1 1 2 1 3 1 4 3 4 1 5 1 6 4 7
(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) - (if (((x + 1) div 2) mod 6) <= 0 then 2 else 1))
A249425: 0 2 4 6 10 12 16 18 22 28 30 35 39 42 46 52
loop(\(x,i).2x,((2 + ((1 + (5 * (loop(\(x,i).2x,(x + ~1),1) div 3))) div 2)) div 2),1)
A160179: 2 2 2 4 8 128 8192 134217728 9007199254740992
(1 + (8 * (1 + compr(\x.(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then x else (1 + i))),x,x)),x))))
A141174-A007519: 17 41 73 89 97 113 137 193 233 241 257 281 313 337 353 401
(~1 + (8 * (1 + compr(\x.(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then x else (1 + i))),x,x)),x))))
A186295: 15 39 71 87 95 111 135 191 231 239 255 279 311 335 351 399
(if x <= 0 then 1 else (9 * ((~1 + (3 * (2 + (if (x + ~4) <= 0 then 0 else 2)))) div (x + 1))))
A169736: 1 18 9 9 9 9 9 9 9 9 9 0 0 0 0 0
(((x * loop(\(x,i).(x * loop(\(x,i).((x2 + ~x) div 2),2,(x + ~2))),1,(x + ~1))) div 2) div 9)
A000910: 0 0 0 0 0 0 5 35 140 420 1050 2310 4620 8580 15015 25025
(1 + (8 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,8x)),x)))
A186298: 1 9 17 41 57 65 81 105 129 137 161 177 209 225 249 281
(loop(\(x,i).2x,(x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))),1) mod 5)
A323903: 1 1 1 2 1 2 1 3 4 2 1 3 1 2 4 3
((1 + (2 * loop(\(x,i).(x2 + ~x),1,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))) mod 5)
A051834: 1 1 3 1 0 1 1 0 1 0 0 1 0 1 1 1
(loop(\(x,i).(3x2 + 2x),1,loop(\(x,i).(10x + 1),x,1)) div 5)
A099638: 1 77 7437 741037 74077037 7407437037 740741037037 74074077037037 7407407437037037 740740741037037037 4611686018427387903 4611686018427387903 4611686018427387903
(5 * loop(\(x,i).(6x2 + x),1,loop(\(x,i).10x,x,1)))
A343586: 35 3050 300500 30005000 3000050000 300000500000 30000005000000 3000000050000000 300000000500000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + loop(\(x,i).(2x2 + 2x),2,5)))
A295004: 7322 7323 7325 7327 7331 7333 7337 7339 7343 7349 7351 7357 7361 7363 7367 7373
(((loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 2) div 5)
A137831: 0 0 1 2 6 8 14 18 26 42 48 68 84 92 110 140
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x - ((1 - (x div 2)) div 5)))
A042990: 2 3 5 7 13 17 19 23 29 31 37 41 43 47 59 61
(3 * loop(\(x,i).(10x + 1),x,loop(\(x,i).(10x + 10),x,0)))
A332130: 0 303 33033 3330333 333303333 33333033333 3333330333333 333333303333333 33333333033333333 3333333330333333333 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.((x div 2) mod 2),(if x <= 0 then 1 else ((1 + (x mod (1 + (2 * (if (x mod 2) <= 0 then 1 else (x div 4)))))) div 3)))
A137252-A098172: 1 0 1 0 0 1 0 0 1 1 0 0 0 4 1 0
(((2x + 3) * (loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,(x + 2)) div 2)) div 3)
A002803: 1 15 140 1050 6930 42042 240240 1312740 6928350 35565530 178474296 878850700 4259045700 20359174500 96172862400 449608131720
(1 - ((loop(\(x,i).2x,x,loop(\(x,i).2x,((x + 1) div 7),1)) div 3) mod 3))
A011635: 1 1 0 ~1 ~1 0 1 0 ~1 ~1 0 1 1
A014555: 1 1 0 ~1 ~1 0 1 0 ~1 ~1 0 1 1 ~1 ~1 0
(((2 * (loop(\(x,i).(6x + 2),x,1) - loop(\(x,i).3x,x,1))) div 3) div 3)
A200674: 0 1 9 61 385 2365 14353 86605 521089 3130909 18798577 112830829 677103073 4062972733 24378899281 146276584333
((2 * (1 + ((1 + (loop(\(x,i).2x,((if (x mod 2) <= 0 then 1 else x) - (x div 2)),1) div (x + 1))) div 2))) div 3)
A052120: 1 1 0 1 0 1 0 1 0 2 0 2 0 4 0 6
((if x <= 0 then 1 else x) - ((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3))
A062968: 1 1 2 2 4 3 6 5 7 7 10 7 12 11 12 12
((1 - ((1 + (x div (2 + ((~1 + loop(\(x,i).2x,x,(if (x + ~2) <= 0 then 1 else 2))) mod (x + 1))))) div 2)) mod 3)
A035220: 1 1 0 1 0 0 0 1 1 0 2 0 2 0 0 1
(3 + (2 * compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),(8x + 1))))
A031908: 5 31 67 103 149 191 233 277 331 379 431 467 523 587 631 677
((2 * loop(\(x,i).(2x + 1),x,(1 + (2 * (x + (loop(\(x,i).4x,x,2) div (x + 1))))))) mod 3)
A255648: 1 1 2 1 0 2 2 1 2 0 0 2 2 2 0 1
(3 + (2 * compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),(5x + 1))))
A031379: 5 19 41 61 83 107 137 163 191 223 241 271 307 337 367 397
((loop(\(x,i).(2x3 + 3x2 + x),1,loop(\(x,i).10x,x,1)) div 2) div 3)
A130612: 1 385 338350 333833500 333383335000 333338333350000 333333833333500000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).(x3 + ~x),1,(1 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) div 2) div 3)
A126995: 1 10 35 165 286 680 969 1771 3654 4495 7770 10660 12341 16215 23426 32509
((2 + compr(\x.(1 - loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),(x div 2),(x2 + 4x))),(x + 1))) div 3)
A157834: 3 5 7 13 15 23 27 33 35 37 43 55 65 75 77 93
((2 * (if (x mod 2) <= 0 then ((~1 + (5 * (2 - ((x div 2) mod 2)))) * (if x <= 0 then 1 else 2)) else 2)) div 3)
A010137: 6 1 5 1 12 1 5 1 12 1 5 1 12 1 5 1
((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3)
A335519-A325560-A322986-A318412-A302051-A184395-A179942-A179941-A167447-A134687-A122668-A122667-A073668-A000005: 1 2 2 3 2 4 2 4 3 4 2 6 2 4 4 5
(12 * (2 + (if x <= 0 then 0 else (2 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))))
A055669: 24 96 144 192 288 336 432 480 576 720 768 912 1008 1056 1152 1296
((((loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x))) div 2) div 2) div 2) div 3)
A024702: 1 2 5 7 12 15 22 35 40 57 70 77 92 117 145 155
(3 + (2 * compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),(5x + 2))))
A031371: 7 23 43 67 89 109 139 167 193 227 251 277 311 347 373 401
((if x <= 0 then 1 else 4x) - ((1 - (2 * ((x + (if (~2 + (x div 4)) <= 0 then 1 else 2)) div 2))) div 3))
A314684: 1 5 9 13 17 22 26 31 35 39 43 48 53 57 61 65
((loop(\(x,i).(x * (x2 div 2)),1,(2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) div 2) div 3)
A127921: 2 10 28 110 182 408 570 1012 2030 2480 4218 5740 6622 8648 12402 17110
(3 + (2 * compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),7x)))
A031907: 3 23 53 83 113 157 193 233 271 313 359 401 443 487 541 587
((2 * (x + (if x <= 0 then 2 else (2 * (1 + (((x + ~1) * loop(\(x,i).(2x - (i mod 2)),x,1)) div 2)))))) div 3)
A259545: 1 2 4 7 16 34 78 178
(3 * loop(\(x,i).(10x + 1),x,loop(\(x,i).(10x + ~8),x,2)))
A332136: 6 363 33633 3336333 333363333 33333633333 3333336333333 333333363333333 33333333633333333 3333333336333333333 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x2 * (x2 div 2)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 3)
A138421: 2 12 100 392 2420 4732 13872 21660 46552 117740 153760 312132 470680 569492 812912 1314612
(5x - (loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (3x + ~1)),3,x) mod 3))
A075326: 0 3 9 13 18 23 29 33 39 43 49 53 58 63 69 73
((x + (loop(\(x,i).2x,x,(1 - ((~1 + loop(\(x,i).4x,x,2)) mod (x + 1)))) div (x + 1))) mod 3)
A074942: 1 1 2 2 1 2 0 1 0 1 1 1 0 0 2 2
(loop(\(x,i).(10x + 1),2x,1) + loop(\(x,i).10x,x,3))
A332114: 4 141 11411 1114111 111141111 11111411111 1111114111111 111111141111111 11111111411111111 1111111114111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(10x + 2),2x,2) + loop(\(x,i).10x,x,3))
A332125: 5 252 22522 2225222 222252222 22222522222 2222225222222 222222252222222 22222222522222222 2222222225222222222 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(((1 + (if x <= 0 then 2 else loop(\(x,i).((4x2 + 2x) div 3),x,1))) div 3) - (x div 3))
A326974: 1 1 2 16 1212
(1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x2 + 2x + 1))),x)))
A007591: 1 3 5 7 13 15 17 27 33 35 37 45 47 57 65 67
(if (~x + 2) <= 0 then loop(\(x,i).(10x + 1),2x,1) else (10x + 1))
A267940: 1 11 11111 1111111 111111111 11111111111 1111111111111 111111111111111 11111111111111111 1111111111111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).(10x + 1),(x + ~2),0),(x + ~1),(10x + 1))
A243534: 1 11 1111111111111111111 4611686018427387903
(1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x2 + 2x + 2))),x)))
A114269: 1 5 11 19 25 31 35 61 65 79 89 91 109 131 145 151
(1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x2 + 2x + 4))),x)))
A114273: 1 3 7 11 13 27 31 39 49 53 57 59 71 77 81 83
(~1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(5x + ~2))),x)))
A024897: 3 5 11 15 17 21 27 29 35 39 45 47 53 69 71 75
(1 + loop(\(x,i).(x4 + x3 + x2 + x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A131992: 31 121 781 2801 16105 30941 88741 137561 292561 732541 954305 1926221 2896405 3500201 4985761 8042221
(~1 + loop(\(x,i).(2x3 + ~3x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A297491: 9 44 234 664 2628 4354 9774 13660 24264 48690 59488 101194 137718 158884 207504 297594
(1 + loop(\(x,i).(10x + 4),2,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A137521: 245 345 545 745 1145 1345 1745 1945 2345 2945 3145 3745 4145 4345 4745 5345
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x - ((x * (x div 2)) div (x + 3))))
A039734: 2 3 5 7 7 11 11 13 17 17 19 23 23 29 29 31
(if x <= 0 then 1 else ((2x + ~1) + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(3x + 1))))
A081495: 1 5 17 55 189 681 2519 9451 35765 136153 520695 1998745 7696467 29716025 115000947 445962899
(loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),x,1)) div (2x + 1))
A138552: 1 2 11 90 889 9723 113322 1380522 17382365 224573349 2962117366 39741658047 540862505806 7450655906450 103713126384420 1456845308244810
((~2x + ~1) + (loop(\(x,i).4x,x,1) div loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1)))
A152737: 0 1 3 5 9 13 18 23 28 34 41 48 55 63 71 79
(if x <= 0 then 0 else (2 + (x div (1 + (if (x mod 2) <= 0 then (2 * (1 + ((x mod 3) div 2))) else 1))) - (x mod 2)))
A252759: 0 1 2 2 3 3 4 4 3 5 5 6 6 7 4 8
(0 + (if x <= 0 then 0 else (1 + (x div (3 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))) - (x mod 2))
A318995: 0 0 1 0 2 1 3 0 2 2 4 1 5 3 3 0
(1 + ((loop(\(x,i).2x,x,(1 + (if ((x + 1) mod 3) <= 0 then 2x else 1))) mod (x + 1)) div 2) - (x mod 2))
A329321: 1 0 2 0 2 2 2 0 3 2 2 2 2 2 6 0
((if x <= 0 then 1 else (2 * loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),((x + ~1) div 2),1))) div (1 + (x mod 2)))
A089408: 1 1 2 1 2 2 4 5 10 14 28 42 84 132 264 429
(((if (x mod 5) <= 0 then 23 else 1) * (if x <= 0 then 1 else 2)) div (1 + (x mod 2)))
A040539: 23 1 2 1 2 23 2 1 2 1 46 1 2 1 2 23
(1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,7x)),x)))
A024903: 1 3 5 9 11 15 23 29 33 35 39 41 45 51 53 59
(~1 + (2 * compr(\x.(1 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,7x)),x)))
A111250: 1 3 7 9 13 21 27 31 33 37 39 43 49 51 57 67
(1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(5x + 4))),x)))
A081759: 1 5 7 11 13 19 25 29 35 37 41 47 49 53 55 61
(1 + compr(\x.(~1 + ((1 - loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 0 else 2))),x,(2x + 2))) mod (x + 1))),x))
A119930: 1 2 3 4 6 7 8 9 11 12 13 15 18 20 21 22
(loop(\(x,i).(10x + 1),2x,1) * loop(\(x,i).(10x + 1),x,1))
A053655: 1 1221 1233321 1234444321 1234555554321 1234566666654321 1234567777777654321 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * loop(\(x,i).(10x + 1),x,1))
A064008: 2 33 555 7777 122221 1444443 18888887 211111109 2555555553 32222222219 344444444441 4111111111107 45555555555551 477777777777773 5222222222222217 58888888888888883
(1 + compr(\x.(2 - ((0 - loop(\(x,i).2x,x,(if (x mod (2 + ((~x + 1) mod 3))) <= 0 then 1 else 0))) mod (x + 1))),x))
A275718: 5 7 9 10 11 13 17 19 21 22 23 25 28 29 31 33
(compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x) mod (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x)))
A159461: 0 1 2 4 4 4 4 4 8 6 6 8 4 4 8 10
(1 + compr(\x.(2 - (loop(\(x,i).2x,x,(~1 + (if ((x + 1) mod (3 - (x mod 2))) <= 0 then x else 1))) mod (x + 1))),x))
A324455: 6 10 12 14 15 18 20 21 22 24 26 28 30 33 34 36
(1 + compr(\x.(loop(\(x,i).(x2 + x),1,(1 - (loop(\(x,i).(2x + 1),2x,2) mod (x + 1)))) mod (x + 1)),x))
A121912: 1 2 3 5 6 7 9 10 11 13 15 17 18 19 23 29
((x + 1) + (compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1)) div (x + 1)))
A090682: 4 4 6 8 10 12 15 16 20 20 23 24 26 27 28 30
loop(\(x,i).32x,x,loop(\(x,i).((2x * (~1 + (4 * i))) div (1 + i)),x,1))
A254286: 1 96 14336 2523136 484442112 98180268032 20645907791872 4459516083044352 983075545417777152 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (1 + ((2x + ~2) * ((x + 2) + (loop(\(x,i).2x,x,1) mod 9))))),x,1)
A002782: 1 2 34 5678 4611686018427387903
loop(\(x,i).((2x + 3) - (((2x + 1) * (1 + (if x <= 0 then 1 else 2))) mod 7)),x,1)
A202349: 1 3 9 20 39 75 148 297 597 1196 2391 4779 9556 19113 38229 76460
loop(\(x,i).(9x + loop(\(x,i).(25x + 1),i,1)),x,1)
A002453: 1 35 966 24970 631631 15857205 397027996 9931080740 248325446061 6208571999575 155218222621826 3880490869237710 97012589464171291 2425317596203339145 4611686018427387903 4611686018427387903
(~1 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x) - compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))
A176246: 1 1 3 1 3 1 3 5 1 5 3 1 3 5 5 1
(1 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x) - compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))
A178984: 3 3 5 3 5 3 5 7 3 7 5 3 5 7 7 3
(compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x) mod (1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A046933: 0 1 1 3 1 3 1 3 5 1 5 3 1 3 5 5
(1 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A119912: 2 3 3 5 3 5 3 5 7 3 7 5 3 5 7 7
(~1 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x))
A135732: 2 1 3 1 3 1 3 5 1 5 3 1 3 5 5 1
((x2 + 2x + 1) * loop(\(x,i).x3,1,loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1)))
A186415: 1 4 72 2000 68600 2667168 112698432 5053029696 236860767000 11493303192800 573327757086656 29253930349198464 1521079361361956032 4611686018427387903 4611686018427387903 4611686018427387903
((((1 + (((x + ~1) * loop(\(x,i).(3x + (i div 2)),x,0)) div 2)) div 2) div 2) div loop(\(x,i).2x,x,1))
A179111: 0 0 0 0 0 0 1 2 4 7 12 20 33 54 88 143
((~1 + ((~1 + (loop(\(x,i).(if (~x + i) <= 0 then 1 else (x + 2)),x,1) mod (x + 1))) mod (3x + 3))) div (x + 1))
A106347: 1 ~1 2 ~1 0 0 2 ~1 0 0 0 0 0 0 2 ~1
((x + 1) * (~1 + (3 * loop(\(x,i).((x + 6) * loop(\(x,i).(2x + 2),x,2)),x,4))))
A134806: 11 3718 4611686018427387903
((1 + (2 * ((1 + loop(\(x,i).2x,x,1) - loop(\(x,i).2x,(x div 2),(x mod 2))) div 3))) div (x + 1))
A165920: 1 0 1 1 2 3 6 10 19 33 62 112 210 387 728 1360
compr(\x.((1 + (((x + 1) * (1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x))) div 2)) mod 3),(x + 1))
A090466: 6 9 10 12 15 16 18 21 22 24 25 27 28 30 33 34
compr(\x.(1 - (((loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)) mod (x + 1)) div 2) mod 3)),(x + 1))
A034784: 3 5 8 9 11 14 15 20 21 23 26 29 33 35 39 41
((1 + ((x + (x2 div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))) div 2)) mod (x + 1))
A204187: 0 1 2 0 4 3 6 0 6 5 10 0 12 7 10 0
(loop(\(x,i).(9x + 9),2,loop(\(x,i).(10x + 1),x,1)) mod (x + 1))
A114795: 0 1 0 1 1 3 3 1 0 1 6 9 2 1 6 1
loop(\(x,i).loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),2x,1),1,(x3 + 4x2 + 5x + 2))
A173866: 42 4861946401452 4611686018427387903
((x + 1) * (if x <= 0 then 1 else (2 * (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))))))
A231407: 1 4 6
A129597: 1 4 6 16 10 24 14 64 54 40 22 96 26 56 90 256
((~x + ~1) + (2 * (1 + (if x <= 0 then 0 else (if (x mod (x - ((x + ~1) mod 8))) <= 0 then 5 else x)))))
A249591: 1 10 9 8 7 6 5 4 3 2 11 12 13 14 15 16
((x + 1) * (2 + (if (x mod (1 + (2 * (x mod 4)))) <= 0 then 1 else loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))
A162276: 3 6 15 12 15 30 63 24 27 30 33 60 39 126 255 48
((4 * (1 + ((((x + 1) * loop(\(x,i).(x + (if x <= 0 then (1 + i) else 0)),x,(~x + 1))) div 2) div 2))) div (x + 1))
A030788: 4 4 1 4 2 1 4 3 2 1 5 4 3 2 1 6
((2 + ((x + (x2 div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))) div 2)) mod (x + 1))
A201560: 0 0 0 1 0 4 0 1 7 6 0 1 0 8 11 1
(((x + 2) * (1 + ((x2 + 2x + 1) * loop(\(x,i).(x + 1),(if x <= 0 then 3 else x),3)))) div (x + 1))
A079505: 14 25 61 121 211 337 505 721 991 1321 1717 2185 2731 3361 4081 4897
((x + 1) * (loop(\(x,i).4x,x,1) - loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,2x)))
A153337: 1 4 24 136 720 3624 17584 83024 383904 1746280 7839216 34812144 153204064 669108496 2903267040 12526343584
(1 + ((x + 1) div (2 + (((x + 1) div 2) div 2) - loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x))))
A070081: 1 2 2 3 2 3 4 3 3 4 3 5 4 3 4 5
(loop(\(x,i).3x,(x + ((4 * (x div 3)) div 3)),1) * loop(\(x,i).3x,x,1))
A344402: 1 9 81 2187 19683 177147 4782969 43046721 387420489 31381059609 282429536481 2541865828329 68630377364883 617673396283947 5559060566555523 150094635296999121
loop(\(x,i).4x,x,loop(\(x,i).(x + ((x * (1 + (15 * i))) div (1 + i))),x,1))
A034996: 1 36 1632 81600 4308480 235530240 13189693440 751812526080 43438057062400 2536782532444160 149439552820346880 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).loop(\(x,i).((((4x div (1 + i)) * (~1 + (2 * i))) div (1 + i)) * (1 + (2 * i))),i,x),x,1)
A120307: 1 3 60 10500 18522000 359400888000 81408613942656000 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(10x + 1),(x + 1),loop(\(x,i).(10x + 10),x,0)) div 2)
A332150: 0 505 55055 5550555 555505555 55555055555 5555550555555 555555505555555 55555555055555555 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 * loop(\(x,i).(10x + 2),x,(1 - loop(\(x,i).(10x + ~20),x,0))))
A332142: 2 424 44244 4442444 444424444 44444244444 4444442444444 444444424444444 44444444244444444 4444444442444444444 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((1 + (if (2x mod (4 + (x div 4))) <= 0 then loop(\(x,i).(2x + 1),(x div 4),1) else 0)) div 2)
A134309: 1 0 1 0 0 2 0 0 0 4 0 0 0 0 8 0
((1 + (loop(\(x,i).(3x + 1),x,1) div (1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))) div 2)
A329008: 1 1 7 5 61 91 547 205 4921 7381 44287 33215 398581 597871 3587227 672605
(20 div (if (x mod 3) <= 0 then (if (x mod 2) <= 0 then 15 else 1) else 2))
A331057: 1 10 10 20 10 10 1
(2 + (if x <= 0 then 0 else (1 + ((2 * (1 + loop(\(x,i).(x * (1 + (2 * (2 + (2 mod (x + 1)))))),x,1))) div 3))))
A222940: 2 7 33 273 2433 21873 196833 1771473 15943233 143489073 1291401633 11622614673 104603532033 941431788273 8472886094433 76255974849873
((1 + ((loop(\(x,i).x2,1,(3 + (x2 * loop(\(x,i).x3,2,x)))) div 2) div 3)) div 2)
A274254: 1 1 350550 2615176875 1466017600854 198682173665365 10968475501587457 325818421703912376 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((1 + ((x + 1) div 2) - ((2 * (1 + (2 * loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)))) div 3)) div 2)
A335607: 0 1 1 2 2 2 4 3 3 3 5 5 4 4 4 7
((1 + ((if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).(2 * (x - i)),x,2) mod (x + 1)) div 2)))) div (1 + (x mod 2)))) div 2)
A153452: 1 1 1 1 1 2 1 1 2 3 1 3 1 4 5 1
((1 + ((1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (1 + (((x + ~1) div 2) div 3)))) div 2)) div 2)
A172237: 0 0 1 0 1 1 0 1 1 2 0 1 1 3 3 0
(1 - ((1 + ((1 + ((1 + (((x + 1) * loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)) div 2)) div 2)) div 2)) div 2))
A191781-A155092-A095133: 1 1 1 1 1 1 2 2 1 1 3 3 2 1 1 6
((1 + ((1 + ((loop(\(x,i).((x + 2) + (x div (2 + (i mod 2)))),x,2) + loop(\(x,i).2x,x,1)) div 2)) div 2)) div 2)
A290075: 1 1 2 3 5 8 14 24 44 80 152 288 560 1088 2144 4224
(1 - ((1 + ((if x <= 0 then 1 else (3 * (if ((x + ~1) mod 3) <= 0 then (2 + (x div 4)) else 1))) div 2)) div 2))
A290976: 1 ~1 0 0 ~1 0 0 ~1 0 0 ~2 0 0 ~3 0 0
loop(\(x,i).(~x + 1),x,(x div (2 + (x div (1 + (((if (x mod 2) <= 0 then 1 else x) mod 4) + ((x mod 3) div 2)))))))
A317531: 0 1 1 0 1 0 1 ~1 2 0 1 ~1 1 0 2 ~2
((1 + ((loop(\(x,i).12x,(x + 1),1) div loop(\(x,i).3x,2x,1)) div 2)) div 2)
A227391: 3 4 5 7 9 13 17 22 30 40 53 71 95 126 168 224
((if x <= 0 then 2 else (1 + ((((2 - ((if (x mod 4) <= 0 then 0 else 2) + (x div 4))) mod (x + 1)) div 2) div 2))) div 2)
A029379: 1 0 0 0 0 1 1 1 0 1 1 1 2 1 2 2
(2 * (loop(\(x,i).2x,x,(loop(\(x,i).((x2 + ~x) div 2),2,(x + 4)) div 3)) div 5))
A124723: 2 12 56 224 806 2688 8448 25344 73216 205004 559104 1490944 3899392 10027008 25401752 63504384
(if x <= 0 then 1 else (2 + ((2 * (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))) div 5)))
A159081: 1 2 3 2 4 3 5 2 3 4 6 3 7 5 4 2
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) div (if (x + ~3) <= 0 then 1 else 10))
A077648: 2 3 5 7 1 1 1 1 2 2 3 3 4 4 4 5
(((x + 5) * loop(\(x,i).(x + (3 * (2x div (if i <= 0 then 1 else i)))),x,6)) div 2)
A027779: 15 126 588 2016 5670 13860 30492 61776 117117 210210 360360 594048 946764 1465128 2209320 3255840
(((1 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 2))) div 3) div 2)
A193622: 1 2 3 5 7 10
A002822: 1 2 3 5 7 10 12 17 18 23 25 30 32 33 38 40
(2 * (((x + 1) * (1 + loop(\(x,i).(if x <= 0 then 1 else ((2x * (~1 + (2 * i))) mod (1 + i))),x,0))) mod 3))
A005881: 2 2 0 4 2 0 4 0 0 4 4 0 2 2 0 4
(if x <= 0 then 1 else (2 + ((2 + (x div (1 + (x mod (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))) div 3)))
A324183: 1 2 3 2 4 3 4 2 5 4 6 3 6 4 4 2
(6 * ((loop(\(x,i).((x * (x + (x mod 3))) div 2),1,loop(\(x,i).2x,x,1)) div 3) div 2))
A321579: 0 0 6 36 132 540 2076 8316 32892 131580 524796 2099196 8390652 33562620 134225916 536903676
(if x <= 0 then 1 else (2 * (2x - ((1 - (2 * ((x + (if (~2 + (x div 4)) <= 0 then 1 else 2)) div 2))) div 3))))
A315186: 1 6 10 14 18 24 28 34 38 42 46 52 58 62 66 70
loop(\(x,i).2x,x,(if x <= 0 then 1 else (2 * (((x3 + 9x2 + 14x) div 2) div 3))))
A100313: 1 16 96 400 1408 4480 13312 37632 102400 270336 696320 1757184 4358144 10649600 25690112 61276160
(x div ((3 * (2 + ((if (x mod 4) <= 0 then 0 else (if (x mod (2 + (x mod 2))) <= 0 then 1 else x)) + (x mod 2)))) div 2))
A340732: 0 0 0 0 1 0 1 0 2 1 2 0 4 0 3 2
(~2 + (3 * compr(\x.(2 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(3x + 1))),x)))
A138694: 1 4 7 10 16 19 22 25 31 37 40 46 49 52 61 64
(2 * (1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(4x + 1))),x))))
A186299: 2 6 14 18 26 30 50 54 74 78 86 90 98 114 134 138
((if x <= 0 then 0 else ((2 - (2x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))) div 2)) mod (4x + 2))
A307170: 0 0 0 12 0 21 0 24
(2 * ((~x + ~1) + loop(\(x,i).(x + loop(\(x,i).(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1,i)),x,1)))
A076178: 0 0 0 2 2 4 6 10 10 12 14 18 20 24 28 34
(2 * (loop(\(x,i).(10x + 2),2x,2) + loop(\(x,i).10x,x,1)))
A332146: 6 464 44644 4446444 444464444 44444644444 4444446444444 444444464444444 44444444644444444 4444444446444444444 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x4 + 3x3 + 2x2),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A230325: 3 24 240 1008 6600 13104 39168 61560 133584 341040 446400 911088 1377600 1668744 2386848 3869424
((loop(\(x,i).((x2 + x) div 2),1,(1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))) mod (x + 1)) div 2)
A238618: 0 0 0 1 0 1 0 2 0 1 0 5 0 1 0 4
((x + 1) div (2 + ((~1 + loop(\(x,i).2x,x,loop(\(x,i).2x,((x mod (1 + (x div 2))) div 2),2))) mod (x + 1))))
A229878: 0 0 1 0 1 2
A324827: 0 0 1 0 1 2 1 0 1 1 1 2 1 2 3 0
loop(\(x,i).(loop(\(x,i).((x2 + ~x) div 2),2,(x + 2)) div 3),1,((x2 + 7x + 6) div 2))
A234249: 15 210 1365 5985 20475 58905 148995 341055 720720 1426425 2672670 4780230 8214570 13633830 21947850 34389810
(loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,1) + ((x3 + 7x2 + 14x + 8) div 2))
A006504: 5 20 51 105 190 315 490 726 1035 1430 1925 2535 3276 4165 5220 6460
((loop(\(x,i).11x,x,3) - loop(\(x,i).7x,x,1)) div 2)
A165151: 1 13 157 1825 20761 233173 2598517 28818985 318655921 3516744733 38764899277 426978842545 4700721921481 51735623710693 569285638838437 6263498473368505
(2 * (1 + compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,7x)),x)))
A309374: 2 4 6 10 12
A033868: 2 4 6 10 12 16 24 30 34 36 40 42 46 52 54 60
(2 * (1 + compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x2 + 3x))),x)))
A096174: 2 4 6 16 18 22 28 34 42 58 60 70 72 76 78 90
(4 * loop(\(x,i).(10x + 1),x,loop(\(x,i).(10x + 10),x,0)))
A332140: 0 404 44044 4440444 444404444 44444044444 4444440444444 444444404444444 44444444044444444 4444444440444444444 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(4 + (7 * (x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1)))))
A059141: 11 18 11 25 11 18 11 32 11 18 11 25 11 18 11 39
(1 - (2 * ((1 + (((1 + loop(\(x,i).((2x + 2) - loop(\(x,i).2x,x,1)),1,(x div 2))) div 2) div 2)) div 2)))
A147048: 1 1 1 1 1 1 1 1 3 3 5 5 13 13 29 29
(~4 + loop(\(x,i).loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),2),2,(x + 1)))
A288775: 0 0 0 0 0 0 4 0 0 0 4 0 4 4 28 0
(x div (if (x + ~1) <= 0 then 1 else (2 * ((x + 1) div (2 * (if (x mod (1 + (((x + 1) div 2) div 3))) <= 0 then 1 else 2))))))
A136177: 0 1 1 0 1 2 1 1 1 2 1 1 1 2 2 0
(8 * (1 + (loop(\(x,i).10x,(x + 1),1) + loop(\(x,i).3x,x,1))))
A326576: 96 832 8080
(4 * ((1 + (((loop(\(x,i).(x2 + 2x),1,loop(\(x,i).(2x + (i mod 2)),x,0)) div 2) div 2) div 2)) div 2))
A241684: 0 0 4 8 32 120 464 1848 7312 29240 116624 466488 1864592 7458360 29827984 119311928
((loop(\(x,i).x2,1,(2 + ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3))) div 2) div 2)
A281118: 1 1 1 2 1 2 1 4 2 2 1 6 1 2 2 12
(6 + (if x <= 0 then 1 else (2 + ((2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)) div 3))))
A192268: 7 10 11 12 13 14 15 17 18 20 21 22 23 25 27 28
(~32 + loop(\(x,i).x2,2,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A153483: ~16 49 593 2369 14609 28529 83489 130289 279809 707249 923489 1874129 2825729 3418769 4879649 7890449
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (if (x div 2) <= 0 then (2x + 1) else 8))
A120700: 2 9 40 56 88 104 136 152 184 232 248 296 328 344 376 424
((2 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1))) mod 8)
A165242: 5 7 5 3 7 3 5 1 7 5 3 7 5 1 7 5
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x - (x2 div (x + 6))))
A115732: 2 3 5 5 7 7 7 11 11 11 11 11 11 13 13 13
((2 + (loop(\(x,i).(3x + ~2),(x + ~1),5) * loop(\(x,i).4x,x,2))) div 4)
A233257: 3 10 104 1184 13952 166400 1992704 23896064 286687232 3439984640 41278767104 495341010944 5944075354112 71328837140480 855945777250304 10271348253261824
(2 - ((x + loop(\(x,i).(((x + 1) - (loop(\(x,i).2x,x,2) mod (x + 2))) mod (x + 1)),1,(x + 1))) mod 4))
A049340: 1 1 1 0 1 1 0 0 1 2 1 0 0 1 1 0
(loop(\(x,i).(10x + 1),2x,1) + loop(\(x,i).10x,x,4))
A332115: 5 151 11511 1115111 111151111 11111511111 1111115111111 111111151111111 11111111511111111 1111111115111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(10x + 2),2x,2) + loop(\(x,i).10x,x,4))
A332126: 6 262 22622 2226222 222262222 22222622222 2222226222222 222222262222222 22222222622222222 2222222226222222222 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x5 + ~x4),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A138439: 8 81 1250 7203 73205 171366 668168 1172889 3078251 9901934 13852815 33734898 56515220 71794821 112232663 205152506
(loop(\(x,i).(x5 + ~x3),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A138432: 12 108 1500 8232 79860 184548 707472 1234620 3212088 10243380 14299680 34646652 57893640 73464468 114620592 209023308
(loop(\(x,i).(x5 + ~x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A138424: 15 120 1560 8400 80520 185640 709920 1238040 3218160 10255560 14314560 34671960 57928080 73504200 114672480 209097720
(loop(\(x,i).(x4 + 2x3 + ~x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A229738: 14 63 425 1519 8591 16393 46529 71839 151823 377609 491071 987049 1480961 1787983 2542559 4092713
(loop(\(x,i).(x5 + x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A297027: 18 126 1575
(loop(\(x,i).(x5 + ~x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A138431: 14 117 1550 8379 80465 185562 709784 1237869 3217907 10255154 14314095 34671294 57927260 73503297 114671399 209096342
((1 + (if x <= 0 then 0 else (1 + (x div (3 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))) - (x mod 2)) div 2)
A339823: 0 0 1 0 1 1 2 0 1 1 2 1 3 2 2 0
((1 + (((if x <= 0 then 2 else (1 + (x mod (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))) div 2) + (x mod 2))) div 2)
A320439: 1 1 0 2 0 1 0 3 0 1 0 2 0 1 1 5
((if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2)))) div (2 + (x mod 2)))
A023645: 0 0 1 1 1 2 1 2 2 2 1 4 1 2 3 3
(2 + compr(\x.(~1 + ((1 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x)) mod 5)),x))
A244737: 2 5 6 9 11 13 14 16 18 20 21 23 26 27 30 32
(2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(9x + ~1))),x))
A024911-A024906: 2 4 8 12 14 18 20 22 30 34 42 44 48 54 58 60
(2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(7x + ~1))),x))
A024905: 4 6 10 16 18 28 30 34 40 48 54 60 64 66 70 78
(2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(7x + 1))),x))
A111367: 0 2 6 8 12 14 18 24 32 36 38 44 54 56 62 66
(8x mod (loop(\(x,i).(1 + (loop(\(x,i).(3x + 1),x,1) mod (2x + 1))),2,x) div 2))
A110620: 0 0 0 0 0 0 0 0 0 0 3 0 0 6 8 0
(if x <= 0 then 1 else (2 * (3x - (((if (~2 + (x div 3)) <= 0 then 2 else (x div 2)) mod (x + 1)) div 2))))
A315344: 1 6 10 16 22 28 34 40 46 50 56 62 66 72 78 84
(1 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + ((if (~2 + (x div 5)) <= 0 then 2 else x) div 2)))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A329191-A167773-A127566-A103146-A049545: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 59
(2 + compr(\x.(((3 * (1 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))) div 2) mod 2),x))
A024704: 4 7 9 11 13 15 20 21 22 24 25 27 30 31 33 36
(((x + 2) + (x * ((x + 2) + loop(\(x,i).(x + (4x div (if i <= 0 then 1 else i))),x,(x + 3))))) div 2)
A133718: 1 13 81 325 995 2541 5698 11586 21825 38665 65131 105183 163891 247625 364260 523396
loop(\(x,i).x7,1,(2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)))
A086874: 2187 78125 823543 19487171 62748517 410338673 893871739 3404825447 17249876309 27512614111 94931877133 194754273881 271818611107 506623120463 1174711139837 2488651484819
((compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x) - compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)) div 2)
A028334: 1 1 2 1 2 1 2 3 1 3 2 1 2 3 3 1
(~2 + loop(\(x,i).10x,(x + 1),1) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A262777: 8 97 995 9993 99989 999987 9999983 99999981 999999977 9999999971 99999999969 999999999963 9999999999959 99999999999957 999999999999953 9999999999999947
loop(\(x,i).(x6 + ~x5),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A138412: 32 486 12500 100842 1610510 4455516 22717712 44569782 141599546 574312172 858874530 2496382452 4634248040 6174354606 10549870322 21746165636
loop(\(x,i).(x6 + ~x4),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A138411: 48 648 15000 115248 1756920 4798248 24054048 46915560 147756048 594116040 886580160 2563852248 4747278480 6317944248 10774335648 22156470648
loop(\(x,i).(x - (2 * (x mod 10))),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A274698: ~2 ~3 ~5 ~7 9 7 3 1 17 11 29 23 39 37 33 47
loop(\(x,i).(x6 + ~x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A138408: 62 726 15620 117642 1771550 4826796 24137552 47045862 148035866 594823292 887503650 2565726372 4750104200 6321363006 10779215282 22164361076
((0 - loop(\(x,i).10x,x,1)) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A091803: 1 2 0 1 10 9 8 4 21 11 26 11 23 5 43 6
loop(\(x,i).(x5 + x3 + x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A135182: 44 279 3275 17199 162503 373659 1425059 2483319 6449039 20536379 28659903 69395979 115926803 147089799 229451039 418347179
loop(\(x,i).(x5 + x3 + ~x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A135181: 36 261 3225 17101 162261 373321 1424481 2482597 6447981 20534697 28657981 69393241 115923441 147086101 229446621 418341561
loop(\(x,i).(x5 + ~x3 + x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A135180: 28 225 3025 16513 159841 369265 1415233 2469601 6424705 20487601 28600321 69294673 115788961 146930785 229243393 418049425
loop(\(x,i).(x5 + ~x3 + ~x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A135179: 20 207 2975 16415 159599 368927 1414655 2468879 6423647 20485919 28598399 69291935 115785599 146927087 229238975 418043807
loop(\(x,i).(x6 + ~x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A138409: 60 720 15600 117600 1771440 4826640 24137280 47045520 148035360 594822480 887502720 2565725040 4750102560 6321361200 10779213120 22164358320
loop(\(x,i).(x6 + ~x3),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A138410: 56 702 15500 117306 1770230 4824612 24132656 47039022 148023722 594798932 887473890 2565675756 4750035320 6321283542 10779111506 22164212252
loop(\(x,i).x7,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A092759: 128 2187 78125 823543 19487171 62748517 410338673 893871739 3404825447 17249876309 27512614111 94931877133 194754273881 271818611107 506623120463 1174711139837
(loop(\(x,i).(2 * (2 + (x * (~1 + (2 * i))))),x,2) div (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A245901: 1 2 10 74 667
loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A028302: 2 6 25 98 462 1716 7293 27170 111826 487084 1822366 7696444 30458900 115000920 455657715 1873956510
(compr(\x.(2 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(8x - (x div 2)))),x) div 2)
A158806: 0 2 3 4 6 7 11 12 13 14 16 20 23 24 25 27
((if (x mod 2) <= 0 then ((~1 + (9 * (x mod 6))) * (if x <= 0 then 1 else 2)) else 1) mod (x + 2))
A340081: 1 1 2 1 4 1 6 1 4 1 10 1 12 1 2 1
(((x + 5) * loop(\(x,i).(x + (5x div (if i <= 0 then 1 else i))),x,(x + 2))) div (x + 2))
A027765: 5 36 147 448 1134 2520 5082 9504 16731 28028 45045 69888 105196 154224 220932 310080
loop(\(x,i).loop(\(x,i).(2x + (18x div (1 + i))),x,5),1,2x)
A054332: 5 440 16016 366080 6223360 85995520 1018716160 10711072768 102385254400 905301196800 7501067059200 58822597017600 439993025691648 3158924287016960 21879051958353920 146801380881858560
((2x + 1) + (compr(\x.(1 - loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1)) div 2))
A163059: 2 5 10 15 23 31 42 50 67 72 89 97 114 122 127 144
compr(\x.((1 + loop(\(x,i).loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)),1,(x - ((~x + 2) div 2)))) mod 3),2x)
A331831: 3 11 15 23 29 35 43 47 53 59 63 71 77 83 91 95
(x - loop(\(x,i).((x + 1) - (2 * ((4 * (x + (if (~2 + (x div 2)) <= 0 then 1 else 2))) div 3))),1,(x div 2)))
A284389: 1 2 4 5 9 10 12 13 15 16 20 21 25 26 30 31
(1 + (if x <= 0 then 0 else (if (x mod (2 + ((1 + (6 mod (1 + (x div 2)))) mod 2))) <= 0 then 2 else 1)) - (x mod 2))
A078314: 1 1 2 2 2 1 3 1 3 1 2 1 3 1 2 2
(1 + (((1 + (if (if ((x + 2) mod (1 + ((x + ~1) mod 3))) <= 0 then 1 else 0) <= 0 then x else 0)) div 3) + (x mod 2)))
A293247: 1 2 1 3 1 4 3 2 1 5 1 6 5 2 1 7
(1 + ((2 * ((1 + (((loop(\(x,i).2x,x,2) - loop(\(x,i).(x * i),(x div 2),1)) div 2) div 2)) div 2)) + (x mod 2)))
A018251: 1 2 3 6 9 18
A091326: 1 2 3 6 9 18 31 64 123
((2 + (if x <= 0 then 3 else (1 + ((if (~1 + (x mod (2 + (x mod 2)))) <= 0 then 1 else 2x) div 3)))) * (x mod 2))
A132748: 0 3 0 3 0 6 0 3 0 3 0 10 0 3 0 3
((if (x mod 4) <= 0 then (25 * (if x <= 0 then 1 else 2)) else 6) + (x mod 2))
A040606: 25 7 6 7 50 7 6 7 50 7 6 7 50 7 6 7
(((1 + (if (x mod 2) <= 0 then (9 * (2 - (x mod 4))) else 1)) * (if x <= 0 then 1 else 2)) + (x mod 2))
A040348: 19 5 2 5 38 5 2 5 38 5 2 5 38 5 2 5
(((if (x mod 8) <= 0 then 29 else 1) * (if x <= 0 then 1 else 2)) - (x mod 2))
A040854: 29 1 2 1 2 1 2 1 58 1 2 1 2 1 2 1
(2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,13x)),x))
A155853: 0 2 8 16 20 28 32 40 46 50 58 62 68 76 82 98
((x + 1) + (if x <= 0 then 0 else (1 + (x div ((x + 2) div (2 + (loop(\(x,i).x3,2,2x) mod (x + 1))))))))
A231407: 1 4 6
A075656: 1 4 6 6 10 12 14 10 12 20 22 18 26 28 30 18
((~x + 1) + loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),8x,1))
A053823: 2 111546435 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x + (x div 13)))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A219669-A109611-A086472: 2 3 5 7 11 13 17 19 23 29 31 37 41 47 53 59
(x * (loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x + ~1),1) + loop(\(x,i).4x,(x + ~1),1)))
A339240: 0 2 14 78 396 1910 8916 40684 182552 808614 3545220 15414212 66556584 285707708 1220340296 5189913240
((x + 1) + ((1 + ((1 + loop(\(x,i).(x + (if x <= 0 then 1 else ((x * (x mod 2)) + (x div 2)))),x,0)) div (x + 1))) div 2))
A211385: 2 3 4 5 6 8 10 12 18 30
loop(\(x,i).(2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)),1,(x + ((x div 2) div 7)))
A191376-A179429: 3 5 7 11 13 17 19 23 29 31 37 41 43 47 59 61
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x + ((x div 2) div 7)))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A049555: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 53 59
compr(\x.(if (x mod 2) <= 0 then 1 else (1 - (x mod (1 + (4 * (x mod (1 + (2 * (if (x mod 3) <= 0 then 0 else 2))))))))),x)
A147956: 1 7 11 17 19 23 29 31 37 41 43 47 49 53 59 61
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x + ((2 * (x div 2)) div 5)))
A193063-A165132: 2 3 5 7 11 13
A176162: 2 3 5 7 11 13 19 23 29 31 41 43 47 53 59 61
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x + ((x mod (1 + (x div 2))) div 3)))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A165671: 2 3 5 7 11 13 17 23 29 31 37 41 43 53 59 61
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x + ((x mod (2 + (x div 2))) div 3)))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A161929: 2 3 5 7 11 13 17 19 23 31 37 41 43 47 53 61
(x + (((2x + 2) + (if x <= 0 then 1 else (2 * (x + ((if (~2 + (x div 2)) <= 0 then 1 else 2) + (x mod 2)))))) div 3))
A231407: 1 4 6
A284654: 1 4 6 9 10 13 16 19 20 23 25 28 30 33 34 37
(3x + ((2 + (if x <= 0 then 1 else (x * (if (x mod 2) <= 0 then x else ((x2 + ~x) div 4))))) div 3))
A079541-A064435-A020488: 1 3 8 10 18 24 30
compr(\x.((3x + 2) - (loop(\(x,i).3x,x,1) mod loop(\(x,i).(2x2 + x),2,2))),x)
A293715: 2 3 4 5 6 7 8 9 10 11 12 16 18 19 21 23
(~x + ((3 * loop(\(x,i).(8x + 2),(x div 2),(x mod 2))) + loop(\(x,i).(2x + 4),x,1)))
A066011: 1 8 20 63 126
(1 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))
A075527: 2 3 4 6 6 6 6 6 10 8 8 10 6 6 10 12
(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))
A075526: 1 1 2 2 4 2 4 2 4 6 2 6 4 2 4 6
(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))
A230846: 2 2 3 3 5 3 5 3 5 7 3 7 5 3 5 7
(x + loop(\(x,i).x2,1,((x + 1) * (15 + loop(\(x,i).x3,x2,x)))))
A272674: 225 1025 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.(2 * loop(\(x,i).(~1 + (x mod 3)),(x + ~2),(if ((x + 2) mod (1 + (2 * (2 + (x mod 2))))) <= 0 then 0 else 1))),x)
A154660: 3 4 5 6 7 8
A026436: 3 4 5 6 7 8 9 10 12 13 15 16 18 21 22 24
compr(\x.(if (x mod 2) <= 0 then 1 else (2 - ((1 + (((1 + loop(\(x,i).((x * (x mod 2)) + (x div 2)),x,x)) div 2) div 2)) div 2))),x)
A039505: 17 21 23 25 31 33 37 41 45 49 55 61 67 73 83 91
compr(\x.(2 - ((x + 1) mod (2 + (if (x mod (1 + (3 * (if (x mod (2 + (x mod 2))) <= 0 then 0 else 2)))) <= 0 then 0 else 2)))),x)
A004613: 1 5 13 17 25 29 37 41 53 61 65 73 85 89 97 101
(if (x + ~3) <= 0 then (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) else (x + 16))
A320584: 2 3 5 7 20 21 22 23 24 25 26 27 28 29 30 31
(~x + (2 * (((x + 2) + (loop(\(x,i).(x + (if ((x div 3) mod 2) <= 0 then 3 else 2x)),x,1) div 2)) div 2)))
A085453: 2 3 8 9 24 69
(x + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A147966: 1 3 4 7 6 9 8 11 14 11 16 15 14 17 20 21
loop(\(x,i).(if x <= 0 then 1 else (2 * (1 + ((1 + (5 * ((x2 + 3x) div 2))) div 2)))),1,x2)
A008533: 1 12 72 272 762 1752 3512 6372 10722 17012 25752 37512 52922 72672 97512 128252
compr(\x.loop(\(x,i).(~1 + loop(\(x,i).(x3 mod 37),2,x)),1,x2),x)
A010435-A010398: 0 1 3 4 7 9 10 11 12 16 21 25 26 27 28 30
loop(\(x,i).(2 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) + (x mod 5))),(x + ~1),0)
A021408: 0 0 2 4 7 5 2 4 7 5 2 4 7 5 2 4
loop(\(x,i).(x + i),(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)),0)
A107105-A100862-A098568-A088925: 1 1 1 1 3 1 1 6 6 1 1 10 21 10 1 1
(((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) mod 4) + (if x <= 0 then 0 else 1))
A225043: 0 1 1 1 2 1 1 3 3 1 1 4 1 4 1 1
(1 + (x div (1 + (x mod (1 + (x mod (1 + (8 mod loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))))))))
A343250: 1 2 1 4 5 2 7 8 1 5 11 4 13 7 5 16
(~1 + loop(\(x,i).2x,(1 + (x div (1 + (2 * (1 + (((x2 + ~x + 2) mod (x + 4)) div 2)))))),1))
A246674: 1 1 1 3 1 1 3 7 1 1 1 3 3 3 7 15
(1 + (x div (1 + (x mod (1 + ((~1 + loop(\(x,i).2x,x,(((~x + 1) mod 3) - (x mod 2)))) mod (x + 1)))))))
A248101: 1 1 3 1 1 3 7 1 9 1 1 3 13 7 3 1
(~1 + loop(\(x,i).((x + 1) + i),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1))
A285192: 0 0 0 0 2 0 0 5 5 0 0 9 14 9 0 0
(1 + (x mod (2 - (x div (~1 + (((2 - (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1)) div 2) div 3))))))
A201059: 1 2 3 4 5 1 7 8 9 5 11 6 13 7 1 16
(1 + (x mod (1 + ((1 + (x div (1 + (2 * (x div (1 + (3 * (if (x mod 2) <= 0 then x else 2)))))))) mod (x + 1)))))
A132588: 1 1 1 1 1 1 1 4 1 5 1 2 1 2 1 1
(1 + (x div (1 + ((~1 + (3 * (if x <= 0 then 1 else (x mod (1 + (((x + 1) div 2) div 3)))))) mod (x + 1)))))
A302788: 1 1 1 1 1 2 1 3 1 4 1 2 1 5 3 1
(1 + (x mod (1 + ((1 + loop(\(x,i).((x + 1) - ((1 + (2 * (x div 3))) div 3)),2,x)) mod (x + 1)))))
A096089: 1 1 1 1 1 1 1 1 1 10 1 1 2 2 3 3
(1 + (loop(\(x,i).(~2 + i),((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2),1) mod 7))
A138068: 2 2 2 2 7 2 2 7 7 2 2 7 1 7 2 2
((1 + ((x + 1) div 2)) div (1 + (if x <= 0 then 0 else (1 + ((x mod (2 + (6 mod (1 + (x div 2))))) div 2)))))
A124772: 1 1 1 1 1 2 1 1 1 3 3 3 1 2 1 1
loop(\(x,i).23x,x,(1 + (x mod (1 + ((x2 + 2x) mod 8)))))
A156892: 1 46 529 48668 279841 12872686 148035889 27238603576 78310985281 3602305322926 41426511213649 3811239031655708 21914624432020321 1008072723872934766 4611686018427387903 4611686018427387903
loop(\(x,i).31x,x,(1 + (x mod (1 + ((x2 + 2x) mod 8)))))
A157499: 1 62 961 119164 923521 57258302 887503681 220100912888 852891037441 52879244321342 819628286980801 101633907585619324 787662783788549761 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).6x,x,1) mod 229)
A036162: 1 6 36 216 151 219 169 98 130 93 100 142 165 74 215 145
(1 + ((1 + (x mod (1 + (2 * (1 + (if (x mod 3) <= 0 then (2 * ((x div 4) mod 2)) else 1)))))) div 3))
A256106: 1 1 2 1 2 1 3 2 2 1 1 1 3 2 2 1
loop(\(x,i).2x,((1 + ((4 * (1 + (2 * (2x - (x div 3))))) div 3)) div 3),1)
A101653: 1 4 16 32 128 256 512 2048 8192 16384 32768 131072 262144 1048576 4194304 8388608
(1 + (3 * (if x <= 0 then 0 else (1 + ((x + ((1 - (x div 2)) mod (1 + ((1 + (x div 2)) div 3)))) div 2)))))
A088744: 1 4 7 7 10 13 13 13 16 19 22 22 22 25 25 25
(8 mod (1 + (((2x + 1) * (if (x mod 4) <= 0 then 1 else (x mod (2 + (x mod 2))))) div 3)))
A069971: 0 0 0 0 0 0 0 2 2 0 0 8 8 8 0 0
(1 + ((3x + 3) * (~1 + loop(\(x,i).x3,1,(7x + 5)))))
A134161: 373 10363 61723 210901 539041 1151983 2180263 3779113 6128461 9432931 13921843 19849213 27493753 37158871 49172671 63887953
loop(\(x,i).6x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A158116: 1 1 1 1 6 1 1 36 36 1 1 216 1296 216 1 1
loop(\(x,i).8x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A176642: 1 1 1 1 8 1 1 64 64 1 1 512 4096 512 1 1
loop(\(x,i).((x + 2) + (2 * i)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A082046: 1 1 1 1 5 1 1 11 11 1 1 19 29 19 1 1
loop(\(x,i).(2x + (x div 2)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A176420-A139332-A099927: 1 1 1 1 2 1 1 5 5 1 1 12 30 12 1 1
loop(\(x,i).(2 + ((x div 2) * i)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A268079-A268056-A202549: 1 1 1 1 2 1 1 4 4 1 1 8 18 8 1 1
loop(\(x,i).((x + 2) mod (2 + i)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A157654: 1 1 1 1 0 1 1 2 2 1 1 4 0 4 1 1
loop(\(x,i).5x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A118190: 1 1 1 1 5 1 1 25 25 1 1 125 625 125 1 1
loop(\(x,i).(x + (2 * (2 + i))),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A082110: 1 1 1 1 7 1 1 15 15 1 1 25 37 25 1 1
loop(\(x,i).(((~x + 2) div 2) * i),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A342936: 1 1 1 1 0 1 1 2 2 1 1 0 4 0 1 1
(2 - loop(\(x,i).((2 - i) * i),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1))
A092450: 1 1 1 1 1 1 1 2 2 1 1 5 10 5 1 1
(1 + ((1 - ((1 + (((x + 1) * (1 + (if (~x + 2) <= 0 then x else 0))) mod 9)) div 2)) mod 3))
A332089: 1 1 2 1 1 2 3 1 2 1 3 2 1 1 2 3
(if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (x div (2 + (x mod (x - ((x + 1) mod 4)))))) div 2))) div 3)))
A196046: 0 1 2 2 2 2 3 3 2 2 2 3 3 3 2 4
(1 + ((2 * (1 + (2 * (loop(\(x,i).2x,x,1) - ((1 + (x div (~2 + (x mod 2)))) mod 3))))) div 3))
A130625: 1 4 7 11 20 41 85 172 343 683 1364 2729 5461 10924 21847 43691
(if x <= 0 then 1 else ((2x + 3) - ((~1 - (4x2 div 5)) div 3)))
A084806: 1 6 9 12 16 20 25 31 37 43 50 58 66 75 84 94
(1 + ((((x + 1) * (~1 + loop(\(x,i).i,(((x + ~2) * (x div 3)) mod (1 + (x div 2))),1))) div 2) div 3))
A219727: 1 1 1 1 1 1 1 2 2 1 1 5 9 3 1 1
(1 + ((2 + ((1 - (loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 12)) mod (x + 1))) div 3))
A327163-A326193: 1 2 2 2 2 3 2 2 2 4 2 5 2 4 6 2
(1 + ((2 + (if x <= 0 then 1 else (2 * (2x - ((x + ((x div 3) mod 3)) div 3))))) mod 3))
A103682: 1 1 2 1 2 1 2 1 2 3 1 2 1 2 1 2
(1 + ((8 * ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3)) div 3))
A317144-A050336: 1 1 1 3 1 3 1 6 3 3 1 9 1 3 3 14
(1 + (6 * (4 + (((1 + loop(\(x,i).x3,x,5)) div 3) div 2))))
A104049: 31 151 1953151 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (x div ((2 * (4 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3)))
A334762: 1 1 2 2 3 2 4 2 3 3 6 2 7 4 4 4
(((3 * loop(\(x,i).(9x + 2),(x + 1),2)) div 2) div 13)
A037630: 2 21 189 1703 15330 137970 1241732 11175591 100580319 905222873 8147005860 73323052740 659907474662 5939167271961 53452505447649 481072549028843
(1 + ((x + (2 * (1 + (if (x + ~1) <= 0 then 0 else (1 + ((x mod (1 + ((1 + (x div 2)) div 2))) div 2)))))) div 3))
A039728: 1 2 3 3 3 4 4 4 5 5 6 6 6 6 8 7
(1 + ((2 + ((1 + ((1 + loop(\(x,i).(x - (x div (~2 + (x mod ~2)))),x,1)) div 2)) div 2)) div (x + 1)))
A285001: 4 2 2 1 1 1 1 1 2 2 2 2 3 4 5 6
(1 + (loop(\(x,i).(2x + 1),(((x2 + 2x) div 2) mod (1 + (x div (2 + (x div 4))))),1) mod (x + 1)))
A303809: 1 2 2 4 2 4 2 4 4 4 2 8 2 4 4 16
(1 + compr(\x.(x mod (1 + ((x + loop(\(x,i).2x,(x div (2 + (x mod (2 + (x mod 2))))),1)) mod (x + 1)))),(x + 1)))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A092579-A054403: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 49
(1 + ((~1 + (2 * (1 + ((~2x + 1) mod (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))) mod (x + 1)))
A318316: 1 2 2 4 2 4 2 8 4 4 2 8 2 4 4 8
(~1 + (2 * loop(\(x,i).x2,1,(200x + 49))))
A157628: 4801 124001 403201 842401 1441601 2200801 3120001 4199201 5438401 6837601 8396801 10116001 11995201 14034401 16233601 18592801
((x + 1) div (1 + (2 * (if x <= 0 then 0 else (1 + ((2 * (x + ((((x + ~1) div 2) * (x div 2)) div 2))) mod 3))))))
A029255: 1 0 0 1 1 0 2 1 1 2 2 2 4 2 3 5
(1 + ((1 + ((1 + (x mod (1 + (6 * (if (x mod 8) <= 0 then 1 else (x mod 2)))))) div 2)) div 2))
A303755: 1 2 1 2 1 3 1 1 2 2 1 2 1 3 1 2
(1 + ((1 + ((1 + (x mod (1 + (loop(\(x,i).(2x + 1),3,(2 * (x mod 2))) mod (x + 1))))) div 2)) div 2))
A261787: 1 2 1 2 2 3 1 3 1 2 2 4 2 2 3 3
(~1 + ((1 + ((1 + (((x + 1) * (1 + (if (x mod 10) <= 0 then (x + 2) else 0))) div 2)) div 2)) div 2))
A088469: 0 0 0 0 0 0 0 0 0 1 17 1 1 1 1 1
(if x <= 0 then 0 else (1 + ((x + 1) div (2 * (1 + ((1 + ((x + 1) div (2 + (x div (4 + (x mod 2)))))) div 2))))))
A096198: 0 1 1 2 2 2 2 3 3 2 3 3 4 3 3 3
loop(\(x,i).(x + i),((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~1) div 2))) div 2),1)
A156184-A126770: 1 1 1 1 2 1 1 4 4 1 1 7 16 7 1 1
(1 + ((1 + (((1 + (((x + 1) * loop(\(x,i).((x + 2) + ((x div 2) div 3)),x,1)) div 2)) div 2) div 2)) div 2))
A186964: 1 2 2 3 4 6 9 12 16 21 28 36 47 60 76 96
(1 + (loop(\(x,i).(x * (x div (1 + (x mod 2)))),1,(~1 + ((~2x + 2) mod (4 + (x div 4))))) div 2))
A172279: 1 1 1 1 2 1 1 3 2 1 1 2 6 2 1 1
(x div ((if (x mod (1 + (2 * (x div (2 * (2 + (x mod 2))))))) <= 0 then 1 else 2) * (1 + (x mod 10))))
A343103: 0 0 0 0 0 0 0 0 0 0 10 2 2 1 2 2
loop(\(x,i).(4 * (1 + (2 * (x div 4)))),(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)
A160721: 1 4 4 12 4 12 12 28 4 12 12 28 12 28 28 60
loop(\(x,i).(x * (6 + (2 div (x + 1)))),(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)
A151791: 1 7 7 42 7 42 42 252 7 42 42 252 42 252 252 1512
loop(\(x,i).6x,((x div 2) - ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2)),1)
A151784: 1 1 6 1 6 6 36 1 6 6 36 6 36 36 216 1
loop(\(x,i).8x,((x div 2) - ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2)),1)
A151786: 1 1 8 1 8 8 64 1 8 8 64 8 64 64 512 1
loop(\(x,i).5x,((x div 2) - ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2)),1)
A151780: 1 1 5 1 5 5 25 1 5 5 25 5 25 25 125 1
((1 + (((x + 1) * loop(\(x,i).(x + (x div 5)),x,5)) div 2)) div 7)
A239100: 0 1 1 2 3 4 6 8 10 13 17 22 28 37 47 59
(7 * ((x * loop(\(x,i).((x2 + ~x) div 2),2,(x + ~2))) div 15))
A266387: 0 0 0 0 0 7 42 147 392 882 1764 3234 5544 9009 14014 21021
((1 - ((1 + (x mod (1 + (2 * (if (x mod 2) <= 0 then 1 else (x div 4)))))) div 3)) mod 7)
A293486: 1 1 0 1 1 0 1 1 0 0 1 1 1 6 0 1
(42 * (1 + ((x + 1) * (1 + loop(\(x,i).(x * (x + i)),2,4)))))
A157740: 18564 37086 55608 74130 92652 111174 129696 148218 166740 185262 203784 222306 240828 259350 277872 296394
(loop(\(x,i).x7,(x + 1),10) div 7)
A242824: 1428571 4611686018427387903
((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (if (x mod 3) <= 0 then 2 else 1))
A329331: 0 0 0 0 1 0 0 2 2 0 0 3 8 3 0 0
loop(\(x,i).(3 * i),((1 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 2)) div 2),1)
A054120: 1 1 1 1 3 1 1 6 6 1 1 9 18 9 1 1
(1 + ((if x <= 0 then 1 else (2 + (x div (2 + ((1 + ((~x + 2) mod 4)) mod (x + 1)))) - (x mod 2))) div 2))
A062843: 1 1 2 2 2 2 3 2 2 2 3 2 3 3 4 2
((x + 1) - (((~1 + (loop(\(x,i).4x,x,5) mod (2x + 3))) mod (x + 1)) div 2))
A084841: 1 2 2 4 4 4 5 6 7 8 8 9 9 10 11 14
(1 + (((~1 + loop(\(x,i).2x,x,(1 - (2 * ((x mod (2 + (x mod 5))) mod 2))))) mod (x + 1)) div 2))
A247074: 1 1 1 2 1 2 1 4 3 4 1 4 1 6 2 8
(1 + (((1 + (((((x + 1) * loop(\(x,i).((x + 2) + (x div 8)),x,1)) div 2) div 2) div 2)) div 2) div 2))
A122130: 1 1 1 2 2 3 4 5 7 9 11 14 18 22 27 34
(1 + (4 * ((~1 + (if (x mod 2) <= 0 then x else 0)) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))))
A046571-A046568: 1 1 1 1 1 1 1 5 5 1 1 9 5 9 1 1
(21 * (1 + compr(\x.(loop(\(x,i).(x * (x - i)),2,8) mod (x + 1)),x)))
A086794: 21 42 63 84 126 147 168 189 252 294 336 378 441 504 567 588
(1 + (2 * ((5 * (2x - (if (~2 + (x div 2)) <= 0 then (~1 + (x div 5)) else 1))) div 2)))
A323354: 5 15 25 35 45 51 55 65 75 85 95 105 115 125 135 145
(1 + ((loop(\(x,i).((2x + 1) - ((x - ((3 * ((x div 2) div 3)) div 2)) div 2)),x,1) div 2) div 2))
A147659: 1 1 2 3 5 8 13 21 34 55 90 146 237 385 625 1015
(1 + ((loop(\(x,i).(7x + (((x + 1) div ~7) mod 2)),x,1) div 2) div 2))
A046635: 1 3 15 99 689 4817 33713 235987 1651903 11563315 80943201 566602401 3966216801 27763517603 194344623215 1360412362499
(1 + (((~x2 + x + 1) - (((x + 1) * ((~x + 1) - loop(\(x,i).3x,(x div 2),2))) div 2)) div 2))
A129881: 2 2 6 6 22 24 90 100
(31 * loop(\(x,i).11x,5x,1))
A324268: 31 4992581 804060162631 129494693251885181 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).2x,x,29) div 3) div 17)
A119027: 0 1 2 4 9 18 36 72 145 291 582 1164 2329 4658 9316 18632
(((1 + loop(\(x,i).8x,(x div 2),(1 + (2 * (x mod 2))))) div 3) mod 9)
A156227: 0 1 3 8 3 1 0 8 6 1 6 8 0 1 3 8
(loop(\(x,i).4x,((x div 2) - ((3 * (x div 4)) div 2)),1) * (1 + (4 * (x mod 2))))
A269695: 1 5 4 20 4 20 16 80 4 20 16 80 16 80 64 320
((x mod 2) - ((~1 + (2 * (1 + (2 * (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))))) div 5))
A228368: 0 0 0 ~1 0 0 0 ~4 0 0 0 ~1 0 0 0 ~11
(((6 * (x div (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))) mod (x + 1)) mod 5)
A057108: 0 0 0 2 0 0 0 2 3 0 0 1 0 0 0 4
((if (x mod 2) <= 0 then 1 else (2 * (1 + (x mod (2 * (1 + (x mod (2 * (1 + (x mod 4)))))))))) mod 5)
A089612: 1 4 1 3 1 4 1 1 1 4 1 3 1 4 1 2
(((1 + (x mod (1 + (if (x mod (2 + (x mod 2))) <= 0 then 1 else (x div 4))))) mod (x + 1)) + (x div 5))
A007828: 0 1 1 2 1 3 2 3 2 3 3 5 3 4 3 5
loop(\(x,i).(x * i),(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)),1)
A321789: 1 1 1 1 2 1 1 6 6 1 1 24 720 24 1 1
loop(\(x,i).x2,1,(~1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))
A008459: 1 1 1 1 4 1 1 9 9 1 1 16 36 16 1 1
loop(\(x,i).x2,2,(~1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))
A202750: 1 1 1 1 16 1 1 81 81 1 1 256 1296 256 1 1
(((x + 2) * loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + 2),(x + 1))) div (x + 5))
A002058: 2 14 72 330 1430 6006 24752 100776 406980 1634380 6537520 26075790 103791870 412506150 1637618400 6495886320
((1 + (((2x + 2) * ((x div 2) div (1 + (if (x mod 2) <= 0 then 6 else 1)))) div 3)) mod 3)
A344652-A335451: 1 1 1 1 1 2 1 0 1 2 1 2 1 2 2 0
((1 - (x mod (1 + ((1 + (3 * (2 + (if (x mod 2) <= 0 then 1 else 8)))) mod (x + 1))))) mod 3)
A035145: 1 0 1 1 1 0 2 0 1 0 0 1 0 0 1 1
((1 + (x mod 2) - (loop(\(x,i).(2 * (6x + (2x div (1 + i)))),x,1) div 2)) mod 3)
A108921: 1 1 1 2 0 0 0 2 1 2 0 1 0 0 1 1
((1 + (2 * (if x <= 0 then 1 else (2 * (4x - ((x - (x div 12)) div 2)))))) div 3)
A315024: 1 5 9 15 19 24 28 33 37 43 47 52 57 61 67 71
((1 + (2 * (if x <= 0 then 1 else (2 * (4x - ((((x + 1) - (x div 4)) div 2) div 2)))))) div 3)
A137002: 1 5 11 15
A314029: 1 5 11 15 20 25 31 36 41 45 51 56 61 67 71 76
((1 + (2 * (if x <= 0 then 1 else (2 * (4x - ((x - (x div ~7)) div 2)))))) div 3)
A312974: 1 4 9 13 19 23 28 32 36 41 45 51 55 60 64 68
((1 + (2 * (if x <= 0 then 1 else (2 * (4x - ((x + ((x div 2) mod 4)) div 4)))))) div 3)
A137002: 1 5 11 15
A314026: 1 5 11 15 20 25 29 35 40 45 51 55 60 65 69 75
((1 + (2 * (((x - (x div 12)) div 2) + (2 * (if x <= 0 then 1 else 4x))))) div 3)
A314239: 1 5 11 17 23 28 34 39 45 51 57 62 67 73 79 85
((loop(\(x,i).2x,1,(1 + ((1 - (x2 mod (3x + 2))) div 3))) div 3) mod 3)
A089617: 0 0 0 1 0 1 0 0 1 1 0 0 0 2 2 1
(((x + (((x div 2) div 3) mod 2)) div 2) + (if x <= 0 then 1 else 4x) + ((2x + 1) div 3))
A313774: 1 5 10 15 21 25 31 37 41 47 52 57 62 67 72 77
((if x <= 0 then 1 else 4x) - (((1 + (x div 2)) div 3) + ((~2x + 4) div 9)))
A058759: 1 4 8 13
A311685: 1 4 8 13 16 20 24 29 33 37 40 44 49 53 57 61
(((1 + (x mod (1 + (3 * ((loop(\(x,i).(2x + 2),x,0) mod (x + 1)) div 2))))) mod (x + 1)) mod 3)
A341595-A056169: 0 1 1 0 1 2 1 0 0 2 1 1 1 2 2 0
(((x + 1) * (1 + ((1 + (if ((x + 1) mod 5) <= 0 then 2x else (x div 2))) mod (x + 1)))) mod 3)
A069850: 1 1 0 0 1 0 2 1 0 1 2 0 2 1 0 0
loop(\(x,i).(x * (2 + (x mod 2))),1,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))
A316801-A305223-A304263: 0 0 0 0 3 0 0 4 4 0 0 9 8 9 0 0
((if x <= 0 then 1 else ((5x + ~1) - (x div (~2 + ((~x + 2) div 4))))) + ((x + 1) div 3))
A314159: 1 5 11 16 22 28 33 38 44 50 55 61 66 71 77 82
((4x + 1) + (x2 div (1 + (if (~2 + (x div 2)) <= 0 then x else (x + 2)))) - ((x + 1) div 3))
A314884: 1 5 9 14 19 23 27 31 35 40 45 49 54 59 63 68
(x + (if x <= 0 then 1 else 4x) - (((x + 1) div 3) + ((~x + (((x div 2) div 3) mod 2)) div 2)))
A315318: 1 6 10 16 21 26 31 36 41 46 52 56 62 68 72 78
((2 * (1 + (if (x + ~1) <= 0 then 0 else (1 + ((x div 2) div (1 + (x mod (2 + ((x mod 3) div 2))))))))) div 3)
A297167: 0 0 1 1 2 1 3 2 2 2 4 2 5 3 2 3
((2 * (1 + ((1 + loop(\(x,i).(x2 + x),1,(1 + (x div 2) - (2 * (x mod 2))))) div 3))) div 3)
A008798: 1 0 2 0 3 1 5 2 7 3 10 5 13 7 16 10
((2 * (1 + ((1 + ((loop(\(x,i).(((x2 + x) div 2) div 3),2,(x + ~2)) div 2) div 2)) div 2))) div 3)
A308954: 0 0 0 0 0 0 0 1 1 2 2 4 5 8 10 13
((if x <= 0 then 1 else 6x) - ((2 * (1 + ((x - (((x div 2) div 3) mod 2)) div 2))) div 3))
A315527: 1 6 11 17 22 28 34 40 46 51 57 62 68 74 79 85
((x - ((if (x mod (1 - (((x mod 4) - (x div 2)) div 3))) <= 0 then x else 5) div 2)) div 3)
A071285: 0 0 0 0 0 1 1 1 2 2 1 3 2 3 4 2
((2 + ((loop(\(x,i).(2x4 + 6x3 + 5x2 + 3x + 2),1,(x + 1)) div 2) div 3)) div 3)
A238702: 1 6 21 55 119 227 396 645 996 1474 2106 2922 3955 5240 6815 8721
((2 * ((x + 1) + ((2 * ((x + 2) + (if ((x + ~2) mod 5) <= 0 then 1 else 2))) div 3))) mod 3)
A230417: 0 1 0 1 2 0 2 1 1 0 1 2 1 2 0 2
((4 * (1 + ((1 + ((loop(\(x,i).(x - (2 * (~x + (x div 3)))),x,1) div 2) div 2)) div 2))) div 3)
A003007: 1 1 2 4 8 17 38 89 208
((2 + ((loop(\(x,i).(2x + 2),((1 + (x mod 8)) mod (x + 1)),1) mod (x + 1)) div 2)) div 3)
A079135: 0 0 0 0 0 0 0 0 1 0 0 2 1 2 1 3
((if x <= 0 then 1 else (2 - (x mod (4 + ((1 - (2 * (x mod 7))) mod (x + 1)))))) mod 3)
A033798: 1 1 0 2 1 0 2 0 0 2 2 0 1 2 1 2
((if x <= 0 then 1 else 6x) - ((2 * (2x div (4 + (x div 8)))) div 3))
A315748: 1 6 12 18 23 29 34 40 46 52 58 64 70 75 81 86
(9 + (if x <= 0 then 1 else ((x + 2) + ((x * (x div 8)) div 5))))
A065206: 10 12 13 14 15 16 17 18 20 21 23 24 25 26 27 29
(((x * ((x + ~1) + (2 * ((x + ((loop(\(x,i).(x2 + x),2,x) div 2) div 3)) div 2)))) div 2) mod 3)
A340683: 0 1 0 0 1 2 0 2 0 0 2 0 0 1 1 0
((if x <= 0 then 1 else 6x) - ((2 * (x + ((x + ((1 - (x div 2)) mod 4)) div 2))) div 3))
A313826: 1 5 10 16 20 24 30 35 40 45 50 56 60 64 70 75
(x + (if x <= 0 then 1 else (4x + ((x - (x div 5)) div 3))) - (2x div 3))
A314887: 1 5 9 14 19 23 27 33 37 41 46 51 55 60 65 69
(((x + ~1) + (2 * (loop(\(x,i).(11x + 10),x,4) div (x + 1)))) mod 3)
A171774-A074941-A002324: 1 0 1 1 0 0 2 0 1 0 0 1 2 0 0 1
((if x <= 0 then 1 else 5x) - ((x + ((x - ((1 - (x div 2)) div 3)) mod 3)) div 3))
A314847: 1 5 9 14 18 24 28 32 38 42 47 51 56 61 65 70
(3 * ((2x + 1) + (2 * (2x + (if (x + ~2) <= 0 then 1 else (8x + 6))))))
A062231: 9 27 45 237
(1 + ((x + (6 * ((1 + (4 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 3))) div 2))
A285965: 4 10 14 17 24 30 37 40 44 50 54 57 64 67 71 77
(~1 + (2 * (x + ((2 * (2 + ((if (~2 + (x div 3)) <= 0 then x else (x + 4)) div 3))) div 3))))
A325129: 1 3 5 9 11 13 15 17 19 25 27 29 31 33 37 39
(1 + (((x + 1) + (((x + 1) + ((x + loop(\(x,i).2x,(~1 + (((x + ~1) div 2) div 2)),x)) div 2)) div 2)) div 2))
A318736: 1 2 3 4 5 6 7 8 9 11 13 14 15 19 21 22
(1 + ((x + ((1 + ((((x2 + 2x + 1) * loop(\(x,i).(x * (1 + i)),x,(x + 1))) div 2) div 2)) div 2)) div 2))
A245897: 1 2 12 98 940
((x + 1) div (1 + (loop(\(x,i).(2x + 2),((5x + 13) div 2),1) mod (x + 2))))
A335324: 1 1 1 4 1 1 1 4 9 1 1 4 1 1 1 1
(loop(\(x,i).2x,x,((x + 3) + ((1 + ((x + 1) * (x - (x div ~2)))) div 2))) div (x + 3))
A322059: 1 3 8 21 50 128
compr(\x.(1 - (x mod (1 + (if x <= 0 then 1 else ((3 * (1 + (x mod (2 + (x mod 2))))) + (x mod 2)))))),(2x + 1))
A161580: 2 5 7 10 14 18 21 23 26 29 31 34 37 39 42 46
((loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(1 + (2 * (x mod 2))),(x + 2)) div 2) * (1 + (x div 2)))
A085047: 1 7 4 24 9 51 16 88 25 135 36 192 49 259 64 336
(0 + (loop(\(x,i).(2 * i),((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4))),1) + (x mod 2)))
A101872: 1 2 1 3 1 2 1 5 2 2 1 3 1 2 1 7
((x + 1) div (1 + ((if x <= 0 then 0 else (2 * ((1 + (4 * (x mod 2))) * (1 + (x mod 3))))) + (x mod 2))))
A341978-A219200: 1 0 0 0 1 0 2 0 1 0 2 0 4 0 2 1
(1 + (((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (x mod 2)))
A340273: 1 2 1 3 1 4 1 4 2 4 1 6 1 4 3 5
((1 + ((2 * (1 + ((1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2)) div 2))) div 3)) * (1 + (x mod 2)))
A023159-A023153: 1 2 2 2 2 4 3 2 3 4 3 4 3 6 4 2
((2 - (if x <= 0 then 1 else ((x mod 2) - (((2x + 1) mod (1 - (x div ~4))) div 2)))) * (1 + (x mod 2)))
A069733: 1 2 2 2 2 4 2 2 3 4 2 4 2 4 4 2
(if x <= 0 then 1 else (1 + compr(\x.(1 - (x mod (1 + (x mod (2 + (4x mod (4 + (x div 4)))))))),x)))
A231407: 1 4 6
A228358: 1 4 6 8 10 12 13 14 16 18 20 22 23 24 26 27
loop(\(x,i).(1 + compr(\x.(1 - (x mod (2 + ((1 + (3 * ((1 + (x div 4)) div 2))) mod (x + 1))))),x)),x,1)
A083505: 1 3 6 10 14
A269745: 1 3 6 10 14 18 23 29 36 44 52 60 68 76
(1 + compr(\x.(loop(\(x,i).(~11x2 + x),2,6x) mod (x + 1)),x))
A018434: 1 2 3 6 67 134 201 402
(1 + compr(\x.((1 + (x * loop(\(x,i).(16x2 + 14x + 3),2,x))) mod (x + 1)),x))
A222011: 1 2 4 8
A018473: 1 2 4 8 59 118 236 472
(1 + ((x2 + x) * (1 + loop(\(x,i).(x6 + x5 + x4 + x3 + x2 + x),1,x2))))
A104682: 1 15 32767 7174453 357913941 7629394531 94036996915 791260251657 5026338869833 25736391511831 111111111111111 417724816941565 1400638324962397 4265491084507563 11966776581370171 31278135027204241
(1 + compr(\x.(loop(\(x,i).(2x7 + x6 + 2x2 + x),1,2x) mod (x + 1)),x))
A018324: 1 2 3 6 31 62 93 186
(1 + compr(\x.(loop(\(x,i).(6 * (8x2 + (x mod 3))),2,x) mod (x + 1)),x))
A097273: 1 2 3 4 6 8 9 12 15 16 18 24 27 30 32 36
(1 + compr(\x.(loop(\(x,i).(80x2 + 8x + 4),2,x) mod (x + 1)),x))
A018500: 1 2 4 131 262 524
(1 + ((x2 + x) * loop(\(x,i).(x7 + x6 + x5 + x4 + x3 + x2 + x + 1),1,x2)))
A269442: 1 17 131071 64570081 5726623061 190734863281 3385331888947 38771752331201 321685687669321 2084647712458321 11111111111111111 50544702849929377 201691918794585181 720867993281778161 2345488209948553531 4611686018427387903
loop(\(x,i).(2 * (1 + ((x + (x6 div (5x + 1))) div 2))),x,1)
A179056: 1 2 8 6402
(1 + compr(\x.(~2 + ((1 + (x mod (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))) mod (x + 1))),x))
A225657: 1 2 3 4 5 6 7 8 9 11 13 16 17 19 23 25
loop(\(x,i).(16x + ((10x * (~1 + (2 * i))) div (1 + i))),x,1)
A034789: 1 21 546 15561 466830 14471730 458960580 14801478705 483514971030 15955994043990 530899438190940 17785131179396490 599222112044281740 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 * (2 + (((x + 1) + ((x mod (1 + (2 * (16 mod (x + 1))))) mod 2)) div 2))),x,1)
A315726: 1 6 12 18 22 26 30 34 40 46 52 58 64 70 74 78
((x + 1) * ((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)))
A066959: 0 2 3 8 5 12 7 24 18 20 11 36 13 28 30 64
compr(\x.(~1 + (x mod (1 + ((loop(\(x,i).2x,x,2) - ((3 * (x mod 3)) div 2)) mod (x + 1))))),(x + 1))
A059877: 1 3 4 5 6 10 11 12 13 15 16 17 18 21 22 24
((~1 + ((~1 + (9 * (if (~2 + (x div 4)) <= 0 then 1 else 2))) mod (x + 3))) div (x + 1))
A298249: 1 ~1 0 0 0 ~1 1 0 0 0 0 0 0 0 ~1 1
((x + 1) * (1 + ((~1 + loop(\(x,i).2x,((x + 1) - ((x mod (1 + (x div 4))) div 2)),1)) mod (x + 1))))
A231407: 1 4 6
A123667: 1 4 6 16 10 24 14 64 36 40 22 96 26 56 60 256
(loop(\(x,i).(2 * i),(x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))),1) mod (x + 1))
A345344: 0 1 1 2 1 2 1 4 2 2 1 4 1 2 2 6
((1 + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) - ((x div 2) + (x * (x mod 2)))) mod (x + 1))
A137345: 0 1 2 2 3 0 4 4 5 0 6 7 7 0 9 8
loop(\(x,i).((2 * (((2x * (1 + (2 * i))) div (2 + i)) * (~1 + (2 * i)))) div (1 + i)),(x + 1),(x + 1))
A067636: 2 20 210 2352 27720 339768 4294290 55621280 734959368 9873696560 134510127752 1854385377600 25828939188000 362995937665200 5141806953167250 73343003232628800
compr(\x.loop(\(x,i).(2x + 2),1,(1 - (x mod (2 * (1 + (x mod (2 * (2 + ((x + ~1) mod 3))))))))),(x + 1))
A343217: 3 5 6 7 8 10 11 12 14 15 17 19 20 21 22 23
compr(\x.(2 * (x mod (1 + (((loop(\(x,i).2x,x,(2 - ((x div 2) mod 2))) mod (x + 1)) div 2) + (x mod 2))))),(x + 1))
A309374: 2 4 6 10 12
A132631: 2 4 6 10 12 16 18 20 22 24 28 30 36 40 42 46
((2 * (if x <= 0 then 0 else (1 - ((1 + (x mod (1 + (2 * (2 + (x2 mod 3)))))) mod (x + 1))))) div (x + 1))
A031283: 0 1 0 0 0 0 ~1 0 ~1 ~1 ~1 ~1 ~1 ~1 0 0
compr(\x.(x - (2 * (2 + (x div (1 + (((if (x mod 2) <= 0 then 1 else x) mod 4) + ((x mod 3) div 2))))))),(x + 1))
A229461: 1 2 3 4 5 6 8 9 10 12 13 16 18 21 22 24
compr(\x.(((1 + (if (1 - (x mod (1 + ((x + ~1) mod 7)))) <= 0 then x else 0)) div 2) mod 4),(x + 1))
A032904-A032870: 1 2 3 4 5 6 7 8 14 15 16 21 22 23 24 28
((4x + 1) + (x div (2 + (if (x + ~10) <= 0 then 2 else 1))))
A314707: 1 5 9 13 18 22 26 30 35 39 43 48 53 57 61 66
compr(\x.(x - (2 * loop(\(x,i).(x5 mod 31),2,x))),(x + 1))
A072601: 1 2 3 5 6 7 9 10 11 12 13 14 15 19 21 22
((x + 1) * ((x * ((1 + ((x * (1 + loop(\(x,i).(x3 + x),1,(x2 + ~1)))) div 2)) div 2)) div 2))
A079240: 0 0 48 2344
((2x + 2) * loop(\(x,i).(((2x + 1) div 3) - (((x2 + ~x) div 2) div (x + 3))),2,x))
A226237: 0 4 6 8 20 12 28 32 36 40 66 72 78 56 90 64
((2x + 1) + ((2 * ((x + 1) + loop(\(x,i).(x - (x div (~2 + ((~x + 2) div 4)))),x,1))) div 3))
A276217: 2 5 9 12 16 20 24 29 33 38 43 48 53 59 64 69
((~x + 1) + loop(\(x,i).(x + ((~x2 + 2) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))),2,x))
A318805-A180360-A175331: 1 1 1 1 2 1 1 3 2 1 1 5 4 2 1 1
(loop(\(x,i).(1 + (x * i)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),0) div 2)
A283522: 0 0 0 0 0 0 0 1 1 0 0 5 20 5 0 0
((if x <= 0 then 2 else (1 + (x mod (1 + ((x div 2) div (1 + (x mod (1 + (x div (2 + (x div 5))))))))))) div 2)
A029382: 1 0 0 0 0 1 1 1 0 0 1 1 3 1 1 1
((1 + loop(\(x,i).((x + 1) * i),(1 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4)))),1)) div 2)
A256692: 1 1 1 3 1 1 1 11 3 1 1 3 1 1 1 44
((if x <= 0 then 2 else (1 + ((x - (2 * ((4 * (x div 3)) div 3))) mod (1 + (x div 3))))) div 2)
A035460: 1 0 0 1 0 1 1 0 1 1 1 2 1 2 2 2
(((if (2x mod (4 + (x div 4))) <= 0 then (x + 3) else 0) div (1 + (x div 5))) div 2)
A130209: 1 0 2 0 0 2 0 0 0 3 0 0 0 0 2 0
((1 + ((loop(\(x,i).x2,1,(x7 + 3)) div 2) div 3)) div 2)
A274253: 1 1 1430 399675 22377814 508665365 6530486977 56519001176 366504924502 1906401762732 8333338333334 31645829208856 106993223294977 328114730182533 926000621503254 2432743920878907
(loop(\(x,i).((2 * (((2x * (1 + (2 * i))) div (2 + i)) * (~1 + (2 * i)))) div (1 + i)),(x + 1),1) div 2)
A000356: 1 5 35 294 2772 28314 306735 3476330 40831076 493684828 6114096716 77266057400 993420738000 12964140630900 171393565105575 2291968851019650
((~x + 2) + (2 * ((2x2 + 2x + 1) + (loop(\(x,i).((x2 + ~x) div 2),2,(x + 1)) div 3))))
A239031: 4 11 28 59 110 189 306 473 704 1015 1424 1951 2618 3449 4470 5709
((1 + (loop(\(x,i).((x + 1) + (((2x + 1) div 7) + (x div 3))),x,0) div 2)) div 2)
A227047: 0 0 1 1 2 3 4 7 12 19 31 50 80 130 211 341
((1 + ((1 + (loop(\(x,i).2x,x,1) mod (2 + ((x + ((x div 2) mod 2)) div 2) - (x mod 2)))) div 2)) div 2)
A094215: 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 2
((1 + ((1 + (loop(\(x,i).((x + 1) + ((x + 2) div (2 + ((~x + 2) mod 8)))),x,1) div 2)) div 2)) div 2)
A239880: 0 1 1 1 1 1 2 2 3 3 5 5 7 7 10 11
((1 + (((x + 1) * (x + (if x <= 0 then 1 else (~1 + (2 * (12x + (x mod 2))))))) div 2)) div 2)
A222964: 0 13 37 76 124 189 261 352 448 565 685 828 972 1141 1309 1504
((if x <= 0 then 2 else (1 + ((((x + 1) - ((x + 1) div (1 + (10 mod (x + 1))))) div 2) div 2))) div 2)
A029378: 1 0 0 0 0 1 1 1 1 0 1 1 2 2 2 2
((x + 1) div (if x <= 0 then 1 else (2 * (1 + ((x + 1) div (4 + (((x2 + x) div 2) mod 5)))))))
A043277: 1 1 1 2 1 1 1 2 2 1 1 2 3 2 1 1
(30 * (1 + compr(\x.(loop(\(x,i).(2x3 + 2x2),2,2) mod (x + 1)),x)))
A143207-A069819: 30 60 90 120 150 180 240 270 300 360 450 480 540 600 720 750
((loop(\(x,i).(2x + 2),x,(12 * (x div 7))) mod 5) div 2)
A080843: 0 1 0 2 0 1 0 0 1 0 2 0 1 0 1 0
(2 * ((x + (2 * (1 + (if (x mod (2 * (2 - (x mod 2)))) <= 0 then (x mod 8) else 1)))) div 5))
A005137: 0 2 2 2 4 2 4 4 4 4 4 6 8 6 6 6
(2 + (3 * ((3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) div 7)))
A244480: 2 2 2 5 5 8 8 8 11 14 14 17 20 20 20 23
((3 * (1 + compr(\x.(loop(\(x,i).(2x + 2),36,0) mod (x + 1)),x))) div 2)
A002977: 1 3 4 7 9 10 13 15 19 21 22 27 28 31 39 40
(((((x2 + 6x + 9) * loop(\(x,i).(x * ((x + 1) - i)),2,(x + 2))) div 2) div 3) div 2)
A090448: 9 96 500 1800 5145 12544 27216 54000 99825 174240 290004 463736 716625 1075200 1572160 2247264
(2 + ((2 + ((2 + (x mod 2) - (if (x mod (2 + ((~x + 1) mod 3))) <= 0 then 1 else 0)) mod (x + 1))) mod 3))
A177864: 4 2 3 3 2 4 2 4 2 3 2 4 2 4 3 3
(2 + (x div 2) - ((if (x + ~2) <= 0 then 1 else 2) + ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2)))
A265262: 1 1 2 0 1 1 2 0 1 1 2 1 2 2 3 0
(((2 * (1 + (x div (2 * (2 + ((x + (if (~x + 2) <= 0 then x else 2)) mod 5)))))) - (x mod 3)) div 2)
A029290: 1 0 0 1 0 1 1 0 1 1 2 1 2 2 1 4
(2 + (((2x + 1) + (2 * ((3 * (x + loop(\(x,i).i,(x + ~5),1))) div 2))) div 3))
A295581: 3 5 6 8 9 11 13 15 18 21 23 26 29
((1 + ((x + ((x + (x3 div (~1 + (2 * (loop(\(x,i).2x,x,1) div (x + 1)))))) div 2)) div 2)) div 2)
A095395: 0 1 2 2 3 4 4 4 4 4 4 5 5 5 5 6
(((x2 + 5x + 6) * loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + 2),(x + 1))) div 2)
A055660: 15 168 1260 7920 45045 240240 1225224 6046560 29099070 137287920 637408200 2920488480 13233463425 59400885600 264475371600 1169259537600
(1 + (x div (2 + (if (x mod (1 + (2 * (x div (2 * (2 + (x mod 2))))))) <= 0 then 1 else 2))) - ((1 + (x div 2)) div 2))
A264997: 1 1 0 1 1 1 1 0 1 2 1 0 1 1 1 2
(2 * (~1 + ((4 * ((1 + (4 * (x + (if (x + ~4) <= 0 then 1 else 2)))) div 3)) + (x mod 2))))
A234648: 6 24 30 40 54 72 86 96 102 120 126 136 150 160 166 184
(3 + compr(\x.((x + 1) mod (1 + (4 * (x mod (1 + (4 * (if (x mod 3) <= 0 then 0 else 2))))))),x))
A119888: 3 6 9 12 15 18 21 22 24 27 30 33 36 39 42 44
(((x + 1) + (loop(\(x,i).((4x + 3) - ((~2x + 2) div 5)),2,x) div 2)) div 2)
A189459: 4 9 15 20 26 31 36 42 47 53 58 62 68 73 79 84
(((x3 + 3x2 + 3x + 1) * loop(\(x,i).((3x + 2) + i),6,3)) div 2)
A280428: 1729 13832 46683 110656 216125 373464 593047 885248 1260441 1729000 2301299 2987712 3798613 4744376 5835375 7081984
((2x + 2) * (1 + (2 * (1 + (((x + 1) * (2 + loop(\(x,i).x2,2,2x2))) div 3)))))
A288629: 6 108 49194
(2 + ((1 + (2 * ((1 + loop(\(x,i).(((3 * (x div 4)) div 2) + (x div 2)),2,x)) div 2))) mod (x + 1)))
A338451: 2 3 3 3 5 5 7 7 7 7 11 11 11 11 11 11
(2 + ((1 + (2 * ((2x mod (2 - (x div (~1 - (if (x + ~4) <= 0 then 0 else 2))))) div 2))) mod (x + 1)))
A184995: 2 3 3 3 5 5 3 7 3 5 5 7 3 7 3 5
(((x + 1) * loop(\(x,i).(x + (85x div (1 + i))),x,2)) div 2)
A017750: 1 87 3828 113564 2555190 46504458 713068356 9473622444 111315063717 1174992339235 11279926456656 99468442390512 812325612855848 6186171974825304 44186942677323600 297525414027312240
(((x + 1) * loop(\(x,i).(x + (57x div (1 + i))),x,2)) div 2)
A017722: 1 59 1770 35990 557845 7028847 74974368 696190560 5743572120 42757703560 290752384208 1823810410032 10638894058520 58104729088840 298824321028320 1454278362337824
(((x + 1) * loop(\(x,i).(x + (93x div (1 + i))),x,2)) div 2)
A017758: 1 95 4560 147440 3612280 71523144 1192052400 17199613200 219295068300 2509710226100 26100986351440 249145778809200 2200787712814600 18114175790089400 139737927523546800 1015428940004440080
(((x + 1) * loop(\(x,i).(x + (58x div (1 + i))),x,2)) div 2)
A017723: 1 60 1830 37820 595665 7624512 82598880 778789440 6522361560 49280065120 340032449328 2163842859360 12802736917880 70907466006720 369731787035040 1824010149372864
(((x + 1) * loop(\(x,i).(x + (73x div (1 + i))),x,2)) div 2)
A017738: 1 75 2850 73150 1426425 22537515 300500200 3477216600 35641470150 328693558050 2761025887620 21335200040700 152902266958350 1023269017336650 6431976680401800 38163061637050680
((loop(\(x,i).(2x + 1),(x + 1),(6x2 + 12x + 6)) div 3) div (2x + 2))
A333186: 2 8 24 64 161 385 899 2053 4617 10257 22559 49208 106601 229571 491884 1049258
((2x + 2) + ((2 * ((x + 1) + loop(\(x,i).(x - (x div (~2 + ((~x + 2) div 4)))),x,1))) div 3))
A276219: 3 6 10 13 17 21 25 30 34 39 44 49 54 60 65 70
((1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)) * (if x <= 0 then 1 else 2))
A134058: 1 2 2 2 4 2 2 6 6 2 2 8 12 8 2 2
(if x <= 0 then 1 else (2 + ((x + 1) div (2 * (1 + ((1 + ((x + 1) div (2 + (x div (4 + (x mod 2)))))) div 2))))))
A072768-A071673: 1 2 2 3 3 3 3 4 4 3 4 4 5 4 4 4
(2 + ((1 + (((1 + ((x + 1) div (2 - (if (x mod 5) <= 0 then (x mod 2) else 0)))) mod (x + 1)) div 2)) div 2))
A194883: 2 2 3 3 3 2 3 3 3 4 4 4 4 4 4 2
((if x <= 0 then 1 else (2 * (1 + (((1 + (x mod (2 + (x mod (1 + (2 * (2 - (x mod 2)))))))) mod (x + 1)) div 2)))) div 2)
A345266: 0 1 1 2 1 2 1 2 3 2 1 3 1 2 2 2
(((1 + (((1 + ((loop(\(x,i).x2,1,((x * ((x + ~1) div 2)) div 3)) div 2) div 2)) div 2) div 2)) div 2) div 2)
A035548: 0 0 0 0 0 0 0 1 1 2 2 5 6 10 12 19
(((9 * (if (2x mod (4 + (x div 4))) <= 0 then (x + 3) else 0)) div 2) div 2)
A158897: 6 0 11 0 0 18 0 0 0 27 0 0 0 0 38 0
((1 + (x div 2)) div (2 + ((x + 1) div (2 * (1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 8))))))
A292598: 0 0 1 0 1 1 2 0 0 1 2 1 2 2 2 0
((loop(\(x,i).4x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),5) div 2) div 2)
A151789: 1 5 5 20 5 20 20 80 5 20 20 80 20 80 80 320
(if 2x <= 0 then 2 else ((((5 * ((x2 + 3x + 2) div 2)) + (x div 5)) div 2) div 2))
A201363: 2 3 7
A061577: 2 3 7 12 18 26 35 45 56 69 83 98 114 131 150 170
loop(\(x,i).((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2),1,(x - (2 * (~2 + (x div 5)))))
A203947: 1 0 0 1 1 1 1 0 0 1 0 1 2 1 0 1
(if ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) <= 0 then 1 else (2 + (x div (2 + (x mod 5)))))
A235803-A174802: 1 1 1 1 2 1 1 3 3 1 1 5 5 4 1 1
(x - (((3 * (if x <= 0 then 1 else (9 * (~x + (x mod 9))))) div 2) div 2))
A024655: 0 1 2 3 4 5 6 7 8 70 71 72 73 74 75 76
(4 + ((2 * (if x <= 0 then 1 else (2 * (1 + ((2x + 1) div (3 + (x div 4))))))) div 3))
A111653: 4 6 6 8 8 8 9 9 9 9 10 10 10 10 10 12
(4 + ((4 * ((3 * (x + (if (~x + 2) <= 0 then (2 + (x div 4)) else 1))) div 2)) div 3))
A079896: 5 8 12 13 17 20 21 24 28 29 32 33 37 40 41 44
((loop(\(x,i).2x,((x div (2 + (x div (2 + ((x2 + 2x) mod 6))))) + (x mod 2)),1) div 2) div 2)
A053470: 0 0 0 1 0 2 0 2 1 4 0 4 0 4 1 4
((loop(\(x,i).((x + 1) + ((x + (2 * (3x div 7))) div 3)),x,1) div 2) div 2)
A201864: 0 0 0 1 2 3 6 10 16 27 44 71 116 188 304 493
((x mod (2 + ((1 + (2 * ((2 * ((loop(\(x,i).2x,x,1) mod (x + 1)) div 2)) + (x mod 2)))) mod (x + 1)))) div 2)
A328515: 0 0 1 1 0 1 0 1 0 0 0 1 0 2 1 0
((2 + ((3 * ((if (x mod (3 + ((x div 2) div 3))) <= 0 then 1 else 0) - (x mod 2))) mod (x + 1))) div 2)
A243561: 1 1 1 1 1 2 1 3 2 4
A300980: 1 1 1 1 1 2 1 3 2 4 1 5 1 6 1 1
((2 + (((2 * (1 + (if ((x div 3) mod 3) <= 0 then (x mod 2) else 0))) - (x mod 3)) mod (x + 1))) div 2)
A218799-A078770: 1 1 1 2 1 1 2 1 1 3 1 2 2 1 1 2
((((3 * (1 + (((if (~2 + (x div 2)) <= 0 then 1 else 2) + (x div 2)) div 2))) div 2) div 2) + (((x + 1) div 2) div 2))
A194813: 0 0 1 2 2 2 3 4 5 5 5 6 6 6 6 7
((x + 2) div (4 + ((3 * ((1 + (x mod (2 * (if (x mod 4) <= 0 then 4 else 1)))) div 2)) div 2)))
A290983: 0 0 1 1 0 1 2 1 2 2 3 2 2 3 4 3
(4 * loop(\(x,i).7x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),2))
A160429: 8 56 56 392 56 392 392 2744 56 392 392 2744 392 2744 2744 19208
((((((((loop(\(x,i).x2,3,(2x + 1)) div (2x + 1)) div 2) div 2) div 2) div 2) div 2) div 2) div 2)
A219090: 0 17 610 6433 37366 152243 490222 1334838 3205770 6983372 14071004 26600198 47683715 81721509 134764658 214942297
((1 + (((x + 1) div 2) div 2)) div (if x <= 0 then 1 else (2 + (((2x + 1) mod (4 + (x div 4))) div 2))))
A029398: 1 0 0 0 0 1 0 1 0 1 1 1 1 0 2 1
((4x + (loop(\(x,i).((x + 2) + (2x div (4 + (x div 4)))),x,1) div 3)) div 2)
A094065: 0 2 5 7 10 13 16 19 22 26 29 32 36 39 42 46
(((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)) mod 4)
A125030: 0 1 1 2 1 2 1 3 2 2 1 3 1 2 2 0
((~1 + ((x + 1) * (1 + (2 * loop(\(x,i).(12x + 8),2,3))))) div 4)
A096613: 268 536 804 1072 1341 1609 1877 2145 2414 2682 2950 3218 3487 3755 4023 4291
(4 + compr(\x.((if x <= 0 then 1 else 2) - ((x mod 2) + ((1 + (8 mod (1 + (x div 2)))) div 2))),(x + 1)))
A076979: 12 13 15 17 20 21 22 23 24 25 26 27 28 29 30 31
(((1 + (((loop(\(x,i).x2,1,(((x + 1) * (x3 div 2)) div 2)) div 2) div 2) div 2)) div 2) div 4)
A092707: 0 0 0 10 100 540
(((2x + 2) + (if x <= 0 then 2 else (1 + (2 * ((x + 1) div (~x + 17)))))) div 4)
A334742: 1 1 1 2 2 3 3 4 5 5 6 7 7 8 10 12
(loop(\(x,i).(x2 + x),1,(2 * (x + ((((x + 1) div (1 + (x mod 4))) mod 2) + (x div 3))))) div 2)
A298856: 3 10 21 55 78 105 136 171 253 351 406 465 595 666 741 820
((((~x + 4) + ((x + (loop(\(x,i).((x + 2) + ((x - (x div 4)) div 2)),x,2) div 2)) div 2)) div 2) div 2)
A206737: 1 1 1 1 1 2 3 4 5 7 10 14 20 28 39 54
(if (x + ~2) <= 0 then 0 else (1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))
A094495: 0 0 0 1 2 1 1 3 3 1 1 4 6 4 1 1
((x + 4) + ((2x2 + 4x + ~1) div (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A065940: 3 6 9 11 12 14 15 17 18 19 21 22 24 26 27 28
(((x2 + 3x + 2) * loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + 1),2)) div (x + 4))
A006659: 2 12 56 240 990 4004 16016 63648 251940 994840 3922512 15452320 60843510 239519700 942871200 3711935040
(if x <= 0 then 1 else (2 * (2x + (((x + 1) + (2 * ((x - (x div 12)) div 2))) div 3))))
A310520: 1 4 10 16 22 26 32 36 42 48 54 58 62 68 74 80
(if x <= 0 then 1 else (2 * (3x - ((2 * (2x div (4 + (x div 8)))) div 3))))
A315731: 1 6 12 18 22 28 32 38 44 50 56 62 68 72 78 82
((4x + 1) + compr(\x.(loop(\(x,i).((x2 + x) * (2 - (x mod 2))),2,(1 + (x div 2))) mod (x + 1)),x))
A315498: 1 6 11 16 22 28 34 40 46 51 56 62 68 73 78 84
(x + (((x + ((x - ((1 - (x div 2)) div 3)) mod 3)) div 3) + (if x <= 0 then 1 else 4x)))
A314142: 1 5 11 16 22 26 32 38 42 48 53 59 64 69 75 80
(2 * ((if (x + ~1) <= 0 then 1 else (2 * (((x2 mod (x - ((~x + 2) div 2))) div (x + 1)) + (x mod 2)))) - (x mod 2)))
A308046: 2 0 0 2 0 2 0 6 4 2 0 2 0 6 4 2
(((x + 1) + (((x + 1) * (if ((x + ~1) mod 4) <= 0 then 4x else 1)) div (1 + (2 * (x mod 2))))) div 2)
A120716: 1 2 3 2 5 23 7
(((x + 1) + loop(\(x,i).((x + 1) + (x div (2 + (x div (2 + (x mod (1 + ((~x + 2) mod 4)))))))),x,1)) div 2)
A333309: 1 2 3 4 6 8 9 11 12 14 17 19 22 24 27 30
(((x + 1) + ((2 * (x + ((x + (if (~2 + (x div 3)) <= 0 then 2 else 1)) div 2))) + (((x + 1) div 2) div 2))) div 2)
A189372: 1 3 5 7 10 11 14 16 18 20 21 24 26 28 30 33
((x + 2) + (((3 * ((x + 1) + loop(\(x,i).(x + (x div (~1 + (4 * (1 + i))))),2,x))) div 2) div 2))
A190087: 2 5 7 10 12 15 17 21 23 26 29 31 34 36 40 42
(if x <= 0 then 1 else (2 * (x + ((x + ((x + ((5 * (x + ((x div 3) mod 2))) div 2)) div 2)) div 2))))
A312656: 1 4 8 14 20 24 28 32 38 44 48 52 56 60 66 72
(loop(\(x,i).(x * i),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) mod (x + 2))
A174640: 1 1 1 1 1 1 1 2 2 1 1 6 10 6 1 1
((1 + ((x + 1) * loop(\(x,i).(2x5 + 8x4 + 10x3 + 4x2),2,3))) mod (x + 2))
A316786: 1 1 1 1 1 1 1 1 1 1 1 8 1 1 1 4
((~2x + ~1) + (2 * (loop(\(x,i).((x + ~1) - (3 * ((~2x + 1) div 5))),x,2) div 2)))
A033943: 1 1 3 13 33 81 189
loop(\(x,i).(1 + (((3 * (1 + ((((x + 2) div 3) * (x div 4)) div 2))) div 2) div 2)),2,2x)
A010578: 1 1 1 1 2 2 2 2 4 4 7 10
(2x + (if x <= 0 then 1 else (2 * (2x + (x div ~7) - (x div 7)))))
A310529: 1 4 10 16 22 28 34 38 42 48 54 60 66 72 76 80
((4x + 4) + (if x <= 0 then 1 else (2 * ((2x + 1) + ((x div 2) + (x div 3))))))
A063223: 5 14 24 34 44 52 64 72 82 92 102 110 122 130 140 150
(1 + ((((x + ~1) mod (~1 + (5 * (if ((x + 1) mod 5) <= 0 then 2 else 0)))) div 2) + (x mod 2)))
A070304: 1 2 1 2 2 2 1 2 1 6 1 2 1 2 3 2
((2x + ~1) + ((((x3 + ~x) div 2) div 3) + loop(\(x,i).x2,1,(2x + 4))))
A059605: 15 37 68 109 161 225 302 393 499 621 760 917 1093 1289 1506 1745
compr(\x.(~1 + ((2 * ((~1 + loop(\(x,i).2x,x,2)) mod 41)) mod 3)),x)
A169968: 1 3 7 9 10 11 12 13 14 15 16 17 18 19 21 23
((x + ~1) + ((2 * ((x + 2) + (if x <= 0 then 1 else (2 * (2 + ((x + 2) div 7)))))) div 3))
A231407: 1 4 6
A327204: 1 4 6 8 9 12 14 16 17 19 21 22 25 27 29 30
((x + 1) + ((1 + (loop(\(x,i).2x,x,1) mod (1 + (x mod (1 + (6 * (x mod 2))))))) mod (x + 1)))
A333694: 1 3 4 5 6 9 8 9 10 13 12 16 14 17 16 17
compr(\x.(1 - (x mod (1 + (((x div 2) - (21 * (if x <= 0 then 1 else 2))) mod (x + 1))))),x)
A154663: 3 5 6 7 10 11
A295307-A073803: 3 5 6 7 10 11 13 14 15 17 19 20 21 22 23 24
((~x + 1) + (2 * loop(\(x,i).((x + 1) + ((x mod (1 + (3 * (x mod 7)))) mod 2)),x,1)))
A285402: 3 6 9 12 13 14 15 16 19 22 25 28 31 32 33 34
(((2 * (1 + ((x - (((x div 2) div 3) mod 2)) div 2))) div 3) + (if x <= 0 then 1 else 5x))
A314144: 1 5 11 16 22 27 32 37 42 48 53 59 64 69 75 80
((x + 1) + (2 * (((x + 1) + (2 * (x + ((1 + (if (x mod 9) <= 0 then 0 else x)) div 2)))) div 2)))
A118549: 1 8 11 18 21 28 31 38 41 38 51 58 61 68 71 78
(~x + ((1 + ((2 * (1 + (2 * loop(\(x,i).((x + 3) + (x div 4)),x,1)))) div 3)) div 3))
A105780: 1 1 2 3 5 7 10 14 19 26 35 46 61 79 102 131
compr(\x.(1 - ((((x + 1) * (~1 + loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1))) div 2) mod 3)),x)
A161577: 2 3 4 6 7 8 9 10 12 14 15 18 19 20 21 24
(~x + (((x * loop(\(x,i).((x3 + 7x2 + 14x + 8) div 2),1,(x + 3))) div 2) div 3))
A092327: 0 19 61 137 260 445 709 1071 1552 2175 2965 3949 5156 6617 8365 10435
compr(\x.(((x + 3) + compr(\x.(~1 + ((x div 2) mod (1 + (if (x mod 2) <= 0 then 6 else 1)))),x)) mod 3),x)
A039084: 0 3 4 5 6 7 8 11 19 27 30 31 32 33 34 35
((~x + 1) + ((x + (if (x mod 2) <= 0 then (1 + (2 * ((x + 1) - (x div ~5)))) else ~2)) div 2))
A270439: 2 ~1 4 ~2 5 ~3 7 ~4 8 ~5 9 ~6 11 ~7 12 ~8
compr(\x.((loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(x + ~1),(x2 div 2)) div 5) mod 2),x)
A267414: 0 1 2 4 9 10 11 12 14 15 16 17 18 19 20 21
((x + 6) + (x3 div loop(\(x,i).x3,1,6)))
A120199: 6 7 8 9 10 11 13 14 16 18 20 23 26 29 32 36
(x + (if x <= 0 then 1 else (2 * ((x + 1) + ((3 * (x + ((x3 + x) div 5))) div 2)))))
A318790: 1 7 20 37 64 109
((2x + 2) + ((x + (((1 + (((x + 2) * (x + (if (x + ~4) <= 0 then 1 else 2))) div 2)) div 2) div 2)) div 2))
A094019: 2 5 7 10 14 17 21 24 28 32 36 40 44 48 53 57
compr(\x.(x * (if (x mod 2) <= 0 then 1 else (((x + 1) div (1 + (2 * (((~x + 2) mod (2 + (x div 4))) div 2)))) mod 2))),x)
A082916: 0 1 3 5 7 9 11 13 17 19 23 25 27 29 31 37
(2x + (if x <= 0 then 1 else (2 * (x - (2 * ((x + ((x2 div 2) div 15)) div 2))))))
A071339: 1 4 4 8 8 12 12 12 12 16 16 16 16 16 16 16
(1 + (x mod (1 + (x mod (1 + ((~1 + (9 * (x mod 10))) mod (x + 1)))))))
A139378: 1 1 3 1 1 3 1 1 9
A109848: 1 1 3 1 1 3 1 1 9 1 11 3 1 1 3 1
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + 2) div (1 + (x mod 5)))))
A307133: 1 1 1 1 2 1 1 4 3 1 1 7 9 4 1 1
(1 + ((((x + 1) div 2) div 2) div (1 + ((1 + ((2x + ~1) mod (4 + (x div 4)))) mod 3))))
A057820: 1 1 1 1 2 1 1 2 2 3 1 2 4 2 2 2
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (3 * (x div 5)))))
A197242: 1 1 1 1 2 1 1 5 5 1 1 8 15 8 1 1
(1 + ((0 - ((2 - (2x mod (4 + (x div 4)))) mod (x + 1))) mod (1 + ((x + 1) div 3))))
A260876: 1 1 1 1 1 2 1 1 2 3 1 1 4 5 5 1
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((2 * ((~x + 2) div 2)) div 3))))
A180957: 1 1 1 1 1 1 1 0 0 1 1 ~2 ~5 ~2 1 1
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (((2 - (x div 2)) div 2) mod 3))))
A176388: 1 1 1 1 2 1 1 4 4 1 1 3 5 3 1 1
((x + 1) - ((x + 1) mod (1 + (x mod (1 + ((x + (x mod ((x + ~1) - (x mod 12)))) div 2))))))
A329004: 1 2 3 4 4 6 6 8 8 10 10 12 12 12 12 12
(1 + (x mod (1 + (x div (2 + (2 * (((2x + 1) mod (2 + (x div 4))) div 2)) - (x mod 2))))))
A343998: 1 2 1 4 2 2 3 8 4 2 5 4 6 4 3 16
(1 + ((x + 1) mod (1 + (x div (1 + ((((x + 1) div (~1 + (((~x + 2) div 2) div 3))) mod 2) + (x mod 2)))))))
A152443: 1 1 2 1 3 1 1 1 5 1 1 1 7 5 8 1
(1 + ((0 - (2x mod (4 + (x div 4)))) div (1 + ((x2 div 2) mod (3x + 1)))))
A115359: 1 ~1 1 0 0 1 0 ~1 0 1 0 0 0 0 1 0
(1 + (x mod (1 + ((x mod (1 + ((~1 + ((~2x + 2) mod (4 + (x div 4)))) mod (x + 1)))) div 2))))
A098824: 1 1 1 2 1 1 3 1 1 1 5 2 1 1 1 8
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((x - (x mod 5)) div 2))))
A086629: 1 1 1 1 2 1 1 4 4 1 1 7 13 7 1 1
(1 + ((3 * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) mod (1 + ((1 + (x div 2)) div 2))))
A305720: 1 1 1 1 2 1 1 1 1 1 1 4 3 4 1 1
(~1 + (5 mod (1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~1) div 2)))))
A172088: ~1 ~1 ~1 ~1 0 ~1 ~1 0 0 ~1 ~1 4 4 4 ~1 ~1
(1 + (((1 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 2)) div 2) mod 5))
A335174-A125605-A110570-A082905: 1 1 1 1 2 1 1 3 3 1 1 4 2 4 1 1
(1 + ((x * ((~x2 + 2) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))) div 5))
A342061-A045995: 1 1 1 1 1 1 1 2 2 1 1 3 8 3 1 1
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((x div 2) div (2 - ((x div 2) mod 2))))))
A208510: 1 1 1 1 3 1 1 5 4 1 1 7 9 5 1 1
(1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) div (1 + ((x div 2) mod 2))))
A224698-A179749-A117935-A103462: 1 1 1 1 2 1 1 2 3 1 1 2 5 4 1 1
compr(\x.((x div 4) mod 2),(1 + ((x mod (1 + (31 mod (x + 1)))) div 3)))
A293515: 1 1 1 2 1 1 1 3 2 1 1 2 1 1 1 10
(~1 + ((1 + ((x + 1) div (2 + ((x div 2) div (1 + (x mod (1 + (x mod (3 + (x mod 2)))))))))) mod 3))
A304438: 0 1 1 ~1 1 ~1 1 1 0 ~1 1 1 1 ~1 0 ~1
(1 + (x div (3 * (2 + (((1 + (x mod 5)) mod 2) + ((x div 2) mod 2)) - (x mod 2)))))
A216612: 1 1 1 1 1 1 1 1 2 2 1 2 2 5 2 2
(1 + ((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (x + ((x div 2) mod 2)))) div 3))
A147532: 1 1 1 1 2 1 1 4 4 1 1 5 9 5 1 1
(~1 + ((2 * (1 + ((x + 1) div (1 + (x div (3 + ((x2 + 2x) mod 6))))))) div 3))
A293435: 0 1 1 2 1 3 1 2 2 3 1 3 1 2 3 3
(1 + ((2 * (1 + (((1 + (((x + 1) * (((x + 1) - ((x div 2) mod 2)) div 2)) div 2)) div 2) div 2))) div 3))
A029069: 1 1 1 1 2 3 3 3 4 5 6 6 8 9 10 11
(1 + ((2 * (1 + (((3 * (1 + ((x2 + x) mod 7))) div 2) div 2))) div 3))
A272647: 1 3 5 4 5 3 1 1 3 5 4 5 3 1 1 3
(1 + ((((x + 3) * ((x3 + 13x2 + 44x + 32) div 2)) div 2) div 3))
A224000: 9 31 76 155 281 469 736 1101 1585 2211 3004 3991 5201 6665 8416 10489
((x + 3) - ((2 * ((x + 3) + ((x mod (4 - (x mod 2))) + (x div 3)))) div 3))
A344961: 1 1 1 2 2 1 1 2 3 2 1 2 3 2 2 3
(1 - (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((2 * ((~x + 2) div 2)) div 3))))
A254414: 1 1 1 1 1 1 1 2 2 1 1 4 7 4 1 1
(1 + ((2 * (x + ((2 + ((1 + (((x + 1) * ((x + 1) + (x div 2))) div 2)) div 2)) div 3))) div 3))
A325461-A051532: 1 2 3 4 5 7 9 11 13 15 17 19 23 25 29 31
((x + 3) mod (1 + (((x + 2) + (x div (2 + (16 mod (1 + (x div 2)))))) div 3)))
A229878: 0 0 1 0 1 2
A080776-A053646: 0 0 1 0 1 2 1 0 1 2 3 4 3 2 1 0
(1 + ((x * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) div (1 + (x div 2))))
A156580: 1 1 1 1 2 1 1 4 4 1 1 6 7 6 1 1
((x + 1) - ((1 + (x div (1 + (x mod (1 + (((x2 + x) div 2) mod (2 * (1 + (x mod 2))))))))) mod (x + 1)))
A094758: 1 1 3 4 5 3 7 8 9 5 11 8 13 7 15 16
(x div (1 + ((1 + (((x + 1) div (1 + ((x mod (1 + (2 * (x mod 6)))) div 2))) div 2)) mod (x + 1))))
A241918: 0 1 1 1 2 1 1 1 2 2 1 1 1 1 3 1
(1 + ((2 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)) mod (x + 1)))
A211315: 1 1 1 1 3 1 1 5 5 1 1 7 2 7 1 1
(1 + ((1 + ((x + 1) div (1 + ((2 - ((x + (x div 5)) mod 5)) mod (x + 1))))) div 2))
A108939: 2 2 3 2 2 3 5 2 2 3 7 2 2 3 5 2
((2x + 3) - ((1 + ((1 + ((x3 + 2) div 3)) mod 7)) div 2))
A188029: 2 4 5 7 10 12 13 15 17 18 20 23 25 26 28 30
(~1 + ((1 + (((14x2 + 45x + 36) div 2) div 5)) div 2))
A027924: 1 4 8 14 21 30 40 51 64 78 93 110 129 148 170 192
(1 + ((1 + ((((~2x + 2) mod (4 + (x div 4))) * (1 + (x div 3))) div 3)) div 2))
A345032: 1 1 1 1 2 2 1 3 3 2 1 4 6 4 3 1
(1 + (x div (2 + (x mod (1 + ((x + 1) div (1 + (((2x div (1 + (x div 4))) mod 2) + (x mod 2)))))))))
A343652-A316365-A294894-A292886-A034836-A033273: 1 1 1 2 1 2 1 3 2 2 1 4 1 2 2 4
(1 + (((x + 1) - ((1 + (x mod (1 + (4 * (2x mod 7))))) mod (x + 1))) div 2))
A181988: 1 2 2 3 3 4 4 4 5 6 6 6 7 8 8 5
(1 + ((1 + ((1 + (((x + 1) + (x div (2 + (((x + ~1) mod 3) + (x mod 2))))) div 2)) mod (x + 1))) div 2))
A087842: 1 1 2 3 3 3 4 4 4 4 6 5 6 6 6 6
((x + 1) div (1 + (x div (2 + (x div (1 + (x mod (2 * (1 + (x mod (1 + ((2 - (x div 2)) mod 4))))))))))))
A285708: 1 2 3 2 5 3 7 2 3 5 11 4 13 7 5 2
(1 + ((1 + ((1 + ((1 + ((((x + 1) * ((~1 + (x2 div 2)) div 3)) div 2) div 2)) div 2)) div 2)) div 2))
A098527: 1 1 1 2 2 2 2 3 4 5 7 9 11 13 16 20
((x + 1) div (~1 + (2 * ((x + 2) mod (1 + (2 * (1 + (2 * (2 + ((x2 + 2x) mod 6))))))))))
A342123: 0 0 0 0 0 0 0 0 0 0 11 0 2 0 0 0
(1 + ((1 + ((1 + (((1 + (2 * (x + (x div 15)))) * (x div 2)) div 2)) div 2)) div 2))
A029008: 1 1 2 2 4 4 6 7 10 11 14 16 20 22 27 30
(2 div (1 + ((1 + ((1 + (((1 + (x div 2)) mod (4 * (2 - (x mod 2)))) + (x mod 3))) div 2)) div 2)))
A277085: 1 1 1 1 1 0 1 1 0 1 0 1 0 1 1 2
(1 + ((1 + (x div (2 + ((1 + (4 * (2 - (x div (~1 + ((~x + 1) div 3)))))) mod (x + 1))))) div 2))
A227156: 1 1 1 2 2 1 2 2 1 3 1 2 2 2 2 2
(x div (1 + (((x + 1) - ((x mod ((x + 2) - (x mod ((x + 1) - (x mod 10))))) div 2)) div 2)))
A057768: 0 0 1 1 2 1 2 2 2 2 1 2 3 1 1 1
(1 + ((1 + (((1 + ((((2x + 1) * ((x + ~1) + ((x * (x div 2)) mod 2))) div 2) div 2)) div 2) div 2)) div 2))
A027583: 1 1 1 2 2 3 3 4 5 6 7 9 10 11 13 16
(1 + ((1 + (((x + 1) mod (2 + ((6 * (1 + ((x div 2) div 3))) mod (x + 1)))) div 2)) div 2))
A067390: 1 1 1 1 2 1 1 2 2 2 2 1 3 2 1 1
(1 + ((1 + ((((x + 1) * (7 + ((((x + ~1) + (x div 2)) div 2) div 2))) div 2) div 2)) div 2))
A071557: 2 3 4 5 6 7 9 10 11 14 15 16 19 20 24 25
(1 + ((1 + ((x mod (2 + (x mod 3) - ((~x + 1) div (2 + (((x + 1) div 2) div 3))))) div 2)) div 2))
A230643: 1 1 2 1 2 2 2 2 1 2 2 2 2 1 3 2
(1 + ((1 + (((((x + 1) * (1 + ((x + (x2 div 7)) div 2))) div 2) div 2) div 2)) div 2))
A309999: 1 1 1 2 2 3 4 5 6 8 10 12 15 18 22 25
((~x + ~1) + (compr(\x.(x mod ((x + 1) - (x mod 10))),(x + 1)) + (x mod 10)))
A265556: 0 1 2 3 4 5 6 7 8 10 10 20 30 40 50 60
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + 2) div (2 + (x mod 5)))))
A258708-A113983: 1 1 1 1 2 1 1 3 3 1 1 5 7 4 1 1
(~1 + ((3 * ((x + (2 * (x + (x2 div (x + 17))))) div 3)) div 2))
A161720: ~1 0 2 3 5 6 8 11 12 15 17 18 20 23 26 27
(1 + (2 * (((2 - (2 * ((x + (x div 8)) mod 5))) mod (x + 1)) div 3)))
A114278: 1 1 1 1 3 1 1 5 3 1 1 7 7 5 1 1
(x div (1 + ((x + 2) div (2 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))))
A122218: 0 0 0 1 1 1 1 2 2 1 1 3 4 3 1 1
(2 - (2 mod (1 - (2 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))))
A174373: 2 2 2 2 2 2 2 3 3 2 2 5 7 5 2 2
((x + 1) div (1 + (2 * ((2x + 1) div (3 + ((~2x + 2) mod (4 + (x div 4))))))))
A172101: 1 0 1 0 1 1 0 1 1 1 0 1 2 2 1 0
(1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~1) + ((x div 2) div 3))) div 2))
A339285: 1 1 1 1 2 1 1 4 5 1 1 6 14 8 1 1
((2 - (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) mod 7)
A036238: 2 2 2 2 1 2 2 0 0 2 2 6 5 6 2 2
(1 + ((3 * compr(\x.(1 - (x mod (2 + ((1 + ((x - ((x div 2) mod 2)) div 2)) mod 5)))),x)) div 2))
A153766: 2 4 5 7 10 11 14 17 20 22 25 26 29 31 34 35
(~1 + ((3 * compr(\x.(1 - (x mod (2 + ((1 + ((x - ((x div 2) mod 2)) div 2)) mod 5)))),x)) div 2))
A139487: 0 2 3 5 8 9 12 15 18 20 23 24 27 29 32 33
(1 + ((1 + ((x * ((~x2 + 2) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))) div 2)) div 2))
A309876-A123610-A059922: 1 1 1 1 2 1 1 3 3 1 1 4 10 4 1 1
(1 + ((1 + ((x + ((x + (((x + 1) * (x + ((x2 + 2x) div 4))) div 3)) div 2)) div 2)) div 2))
A008772: 1 1 2 3 5 6 9 11 15 18 23 28 35 41 50 59
((x + 2) mod ((x + 1) - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)))
A341314: 0 1 1 1 2 1 1 3 3 1 1 4 2 4 1 1
(~1 + (2 * (3 + ((((~2 + (x div 2)) * (x div 2)) mod (x + 1)) mod 2) - ((x mod 2) + (x mod 2)))))
A122002: 5 1 5 3 5 1 7 3 5 1 5 3 7 1 7 3
(1 + (2 * ((x + 1) + (((x + 1) * (1 + ((x + 1) div 7))) div 9))))
A325372-A098903: 3 5 7 9 11 13 17 19 23 25 27 29 31 37 41 43
(1 + (((x + 1) + (((3 * compr(\x.(1 - (x mod (1 + (2 * (x mod (2 + (x mod 2))))))),x)) div 2) div 2)) div 2))
A231407: 1 4 6
A256792: 1 4 6 7 9 11 13 14 16 17 20 22 23 25 26 28
(1 + (2 * ((1 + (x mod (1 + (2 * (2 + (4x mod 17)))))) mod (x + 1))))
A137795: 1 1 1 1 1 1 1 1 1 3 1 1 1 15 1 1
(1 + (((2 * (x mod (1 - ((2 - (2x mod (4 + (x div 4)))) mod (x + 1))))) mod (x + 1)) div 2))
A227655-A225816: 1 1 1 1 1 1 1 2 1 1 1 6 4 1 1 1
(1 + (((~1 + (6 * (1 + ((x * (x div 2)) mod (1 - ((~x + 2) div 8)))))) div 2) div 2))
A056608: 2 2 2 3 2 2 2 3 2 2 2 3 2 2 5 2
(1 + (((1 + ((~1 + (x mod 2) - ((1 + (8 mod (1 + (x div 2)))) div 2)) mod (x + 1))) div 2) div 2))
A266348: 1 1 1 1 2 2 2 1 2 3 3 4 4 4 4 1
(1 + (((1 + ((((x + 1) * (2 + ((4 * (2x div 3)) div 3))) div 2) div 2)) div 2) div 2))
A259201: 1 1 1 2 2 3 4 4 5 7 8 9 11 11 14 16
(1 + (((1 + ((((x + 1) * (2 + ((1 + ((x + (x2 div 3)) div 2)) div 2))) div 2) div 2)) div 2) div 2))
A058706-A027581: 1 1 1 2 2 3 4 5 6 8 10 12 15 17 21 26
(1 + (((1 + ((((2 + ((x2 + 2x) div 9)) * ((x + 1) div 2)) div 2) div 2)) div 2) div 2))
A274146: 1 1 1 1 1 2 2 3 3 5 5 7 8 11 12 16
(1 + ((((((x + 1) div 2) - ((3 * (x div 4)) div 2)) * (~1 + (2 * (x div 4)))) div 2) div 2))
A025149: 1 0 0 0 1 1 1 1 1 2 2 3 3 4 4 6
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (2 + (x div (2 + (x mod 5))))))
A026747: 1 1 1 1 3 1 1 4 4 1 1 6 11 5 1 1
(1 + (((1 + (((x * ((14x + 9) + (x div 2))) div 2) div 2)) div 2) div 2))
A201993: 1 2 6 11 18 26 37 49 63 79 97 116 138 161 186 213
(1 + (2 * ((3 * (((1 + (x mod (1 + (x mod (2 * (2 + ((x div 2) mod 2))))))) mod (x + 1)) div 2)) div 2)))
A319137: 1 1 1 1 1 3 1 3 1 3 1 9 1 3 3 7
(1 + ((x mod (2 + ((1 + (2 * ((1 + (x div (1 + (x mod (4 + (x div 2)))))) mod 2))) mod (x + 1)))) div 2))
A094006: 1 1 1 2 3 1 1 1 2 3 1 2 2 1 2 1
(1 + ((x + 1) div (4 + ((2 * (1 + (x3 mod 11))) mod (x + 1)))))
A216665: 1 1 1 2 2 1 2 1 2 1 3 3 2 2 1 3
(1 + (8 * ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 5)))
A197364: 1 1 1 1 1 1 1 9 9 1 1 17 33 17 1 1
(1 + (((2 + (x2 mod ((x + 1) + (3 * ((x mod (1 + ((~x + 2) mod 4))) div 2))))) div 2) div 2))
A316790-A294338: 1 1 1 2 1 1 1 2 2 1 1 1 1 1 1 5
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + 1) div (2 + (((x + ~1) div 2) mod 2)))))
A210341: 1 1 1 1 2 1 1 3 4 1 1 5 9 8 1 1
(1 + (((((((x + 1) * (~1 + ((~2x + 2) mod (4 + (x div 4))))) div 2) div 2) div 2) div 2) div 2))
A110540: 1 0 1 0 1 1 0 1 1 1 0 2 3 2 1 0
((41x2 + 82x + 40) div 15)
A224837: 2 10 24 43 68 98 133 174 221 273 330 393 461 535 614 699
((((2 + (x div (2 + (x mod 2)))) mod 3) div 2) div (~1 + ((~2x + 2) mod (4 + (x div 4)))))
A232714: 1 ~1 0 0 0 0 ~1 0 0 1 0 0 0 0 0 0
(1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (2 + (x div (2 * (2 - (x mod 2)))))) div 2))
A050447-A022818: 1 1 1 1 2 1 1 3 3 1 1 4 6 5 1 1
(((x * (11x + (x div 7))) div 2) div 9)
A152738: 0 0 2 5 9 15 22 30 39 50 61 74 88 104 121 139
(1 + ((9 * (x mod (x - ((x + ~1) mod 8)))) + (x mod 9)))
A121760-A084011: 1 2 3 4 5 6 7 8 9 1 11 21 31 41 51 61
(((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + 1) div (1 + (2 * (2 - ((x div 2) mod 2))))))
A192396: 0 0 0 0 1 0 0 2 1 0 0 4 4 2 0 0
(2 - ((1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) mod 5))
A144431: 1 1 1 1 0 1 1 ~1 ~1 1 1 ~2 2 ~2 1 1
(5 * (~1 + (2 * ((3x + 4) - ((((x + ~2) mod (1 + (x div 2))) mod 3) mod 2)))))
A297150: 35 65 95 115 155 185 215 235 265 305 335 365 395 415 445 485
(1 - (5 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))
A131063: 1 1 1 1 6 1 1 11 11 1 1 16 26 16 1 1
(1 + ((x div (2 + ((x - ((x2 + ~2) div (x + 6))) mod 3))) + (x div 5)))
A194816: 1 1 1 2 3 4 4 4 4 5 6 6 6 6 6 7
(2 - ((1 + ((x div 3) div (1 + (x div (2 * (2 + ((1 - (x div 3)) mod 3))))))) mod 3))
A228552: 1 1 1 0 1 1 2 2 0 0 0 0 0 0 0 2
((1 + (((x + 1) * (~1 + (2 * ((16x + 16) div 3)))) div 3)) mod 3)
A337518: 1 1 2 1 2 1 0 0 1 0 2 2 0 0 1 2
((1 + ((((x + 2) * ((x4 + 3x3 + 3x2 + 2x + 1) div 2)) div 2) div 3)) mod 3)
A128521: 1 0 1 1 1 1 0 1 1 1 1 2 2 1 1 0
((1 + ((1 + (((1 + ((((x * ((x2 + 4x + 4) div 2)) div 2) div 2) div 2)) div 2) div 2)) div 2)) mod 3)
A317675: 1 1 1 2 2 0 1 0 1 1 0 1 2 0 2 2
((1 + (((1 + (x mod (1 + (x mod (2 * (2 + ((x div 2) div 5))))))) mod (x + 1)) div 2)) mod 3)
A344606-A341592: 1 1 1 1 1 2 1 0 1 2 1 1 1 2 2 0
((1 + (2 * (1 - (x mod (1 - ((2 - (2x mod (4 + (x div 4)))) mod (x + 1))))))) div 3)
A199333-A181031-A089980: 1 1 1 1 2 1 1 3 3 1 1 5 7 5 1 1
(1 - (1 mod (1 - (3 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))))
A197342: 1 1 1 1 2 1 1 5 5 1 1 8 11 8 1 1
(1 - (2 mod (2 - (3 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))))
A086626: 1 1 1 1 1 1 1 3 3 1 1 6 9 6 1 1
((1 + ((x * ((x + 1) + (((x + 1) * (1 + (3 * ((x2 + x) div 2)))) div 2))) div 2)) div 3)
A259474: 0 1 6 21 55 120 231 406 665 1035 1540 2211
(6x - ((1 + (2 * (x + ((2x + ~1) div (4 + (x div 4)))))) div 3))
A137002: 1 5 11 15
A314048: 1 5 11 15 21 26 31 36 41 47 51 57 62 67 73 77
((2 * (1 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) mod (1 + (x div 2))))) div 3)
A300646-A300465: 0 0 0 0 1 0 0 2 2 0 0 4 2 4 0 0
((2 * (1 + ((1 + ((1 + ((~2 - (x2 div 3)) mod (x + 1))) div 2)) div 2))) div 3)
A254688: 0 0 0 1 1 1 0 2 1 1 2 2 1 2 2 1
((x - (2 * (~1 + (x div 3) - ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)))) div 3)
A144001: 0 1 1 1 2 1 1 2 2 1 2 3 3 3 2 2
((2 * (1 + (2 * (x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2)))))))))) div 3)
A144494-A136166: 0 0 0 2 0 2 0 3 2 2 0 3 0 2 2 4
((2 * (1 + ((((1 + (x mod (2 + ((x + ~1) mod 3)))) * (1 + (x div 4))) div 2) div 2))) div 3)
A246369: 0 0 0 1 0 1 1 1 2 1 0 2 1 2 2 3
((2 * ((x + 1) + (2 * ((3x + 2) - ((2x + 1) div 7))))) div 3)
A022806: 3 8 12 16 20 25 30 33 38 42 46 50 55 60 63 68
((2 + ((1 + (5 * ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2))) mod (x + 1))) div 3)
A327164-A326194: 0 1 1 1 1 0 1 1 1 2 1 2 1 2 2 1
((((17x2 + 34x + 17) * (x mod 7)) div 2) mod 3)
A072612: 0 1 0 0 1 0 0 0 1 2 1 0 0 0 0 1
(((x + 3) + (((3x2 + 57x + 102) div 2) div 2)) div 3)
A006624: 9 14 20 27 33 41 49 57
(((11x4 + 64x3 + 136x2 + 125x + 42) div 2) div 3)
A007291: 7 63 254 710 1605 3157 5628 9324 14595 21835 31482 44018 59969 79905 104440 134232
(((12x4 + 68x3 + 135x2 + 109x + 30) div 2) div 3)
A024378: 5 59 254 730 1675 3325 5964 9924 15585 23375 33770 47294 64519 86065 112600 144840
(3 * (((x2 + 3x + 2) * ((4x + 3) + ((x2 + 3x) div 2))) div 2))
A207064: 9 81 288 720 1485 2709 4536 7128 10665 15345 21384 29016 38493 50085 64080 80784
(1 - ((2 * (x div (2 + (x div (1 + ((x mod (1 + ((2 - (x mod 4)) mod (x + 1)))) div 2)))))) mod 3))
A053864: 1 1 1 ~1 1 1 1 0 ~1 1 1 1 1 1 1 0
((2 * (2 + ((x + 1) mod (1 + (2 * ((3 * (2x div 9)) div 2)))))) mod 3)
A255315: 1 1 1 1 1 1 0 2 1 1 0 2 1 1 1 0
((2 * (2 + ((2x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 3))) div 3)
A161126-A128562: 1 1 1 1 2 1 1 4 4 1 1 6 12 6 1 1
((2 * (2 + ((1 + ((((x + ~1) * (3 + (x div (1 + (x mod 4))))) div 2) div 2)) div 2))) mod 3)
A106823: 1 1 1 0 1 1 1 1 0 0 0 1 1 2 2 2
(1 - (6 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))
A131065: 1 1 1 1 7 1 1 13 13 1 1 19 31 19 1 1
(((1 + ((x div 2) div (1 + (x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4))))))))) mod 4) mod 3)
A091392: 1 1 2 1 0 2 0 1 2 0 2 2 0 0 0 1
((2 * ((x + 2) + ((2 * (x + ((4x2 + 10x + 4) div 3))) div (x + 1)))) div 3)
A171504: 2 6 9 12 14 16 19 22 24 26 29 32 34 36 39 41
(((x + 2) + ((2 * (1 + (((x + 2) * (1 + (2 * (x - (x div ~2))))) div 2))) div 3)) div 3)
A022939: 1 2 4 7 10 15 19 26 31 39 45 55 62 73 82 94
(((x + 2) + (((4x3 + 27x2 + 51x + 28) div 2) div 3)) div 3)
A241526: 2 7 16 31 53 83 123 174 237 314 406 514 640 785 950 1137
(((24x5 + 60x4 + 50x3 + 15x2 + x) div 2) div 3)
A059255: 0 25 365 2030 7230 19855 45955 94220 176460 308085 508585 802010 1217450 1789515 2558815 3572440
(((2x + 5) + (((3x + 4) - (x div 2)) * ((x + 1) div 2))) div 3)
A231407: 1 4 6
A158138: 1 4 6 11 13 22 24 35 39 52 56 73 77 96 102 123
((2x + 9) - (x2 div ((x + 10) + (x div 4))))
A334688: 9 11 13 15 16 18 19 21 22 24 25 26 28 29 30 31
(x + (x div 3) - ((~21 * (1 + (x div 3))) div 5))
A273929: 5 6 7 13 14 15 21 22 23 29 30 31 37 38 39 46
(1 + (((x + 1) + (x mod (1 + (x mod (1 + (x div (1 + ((x mod (1 + ((~x + 2) mod 4))) div 2)))))))) div 2))
A277886: 1 2 3 3 5 6 7 6 5 10 11 9 13 14 15 12
(1 + (((x + 1) + (x mod (1 + (x mod (1 + (x div (1 + (2 * ((x + 1) mod (1 + (x div 4))))))))))) div 2))
A290732: 1 2 3 4 3 6 4 8 9 6 6 12 7 8 9 16
(~1 + (2 * ((x + 1) + ((2 * (1 + ((((x + ~1) * (x + (x div 3))) div 2) div 3))) div 3))))
A342474: 1 3 5 9 13 17
A123509: 1 3 5 9 13 17 21 27 33 41 47 55
A196094: 1 3 5 9 13 17 21 27 33 41 47 55 65 73 81 93
(1 + (((x2 + x) + (((1 + ((((2 + ((x3 + x2) div 2)) div 2) div 2) div 2)) div 2) div 2)) div 2))
A095233: 1 2 4 7 11 17 24 32 41 52 64 78 93 110 129 149
(1 + ((x + ((1 + (((((x + 2) * (x + ((x2 + 2x) div 4))) div 2) div 3) div 2)) div 2)) div 2))
A280241: 1 1 2 3 4 5 7 8 11 13 16 19 23 26 31 36
(2 + (((x - (x3 div (~x + ~31))) div 2) div 2) - (x mod 2))
A003113: 2 1 2 2 3 3 5 5 7 8 10 11 15 16 20 23
(1 + ((x div (2 + (x div (1 + (2 * ((x div 2) mod (1 + (x mod (1 + ((~x + 2) mod 4)))))))))) + (x mod 2)))
A331179: 1 2 1 3 1 2 1 4 3 2 1 4 1 2 1 5
(1 + compr(\x.((1 + (2 * ((2x + 1) - ((x + (x mod 3)) div 7)))) mod 3),x))
A231407: 1 4 6
A089960: 1 4 6 7 9 12 14 17 20 22 25 27 28 30 33 35
((~x + 1) + (((5 * compr(\x.(1 - (x mod (1 + (4 * (x mod 5))))),x)) div 2) div 2))
A063124: 2 2 2 3 4 4 5 5 6 7 8 10 10 10 10 12
(1 + compr(\x.(((((x + ~1) * (1 - (((x - ((x2 + ~x) div 4)) div 2) div 3))) div 2) div 2) mod 2),x))
A285276: 2 3 4 5 7 10 11 12 14 15 16 18 19 20 21 24
(14x4 + 27x3 + 19x2 + 7x + 1)
A027850: 1 68 531 2056 5645 12636 24703 43856 72441 113140 168971 243288 339781 462476 615735 804256
((x + 1) * (1 + (x div (1 + ((x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4)))))) mod (1 + (x div 2)))))))
A072995-A050399: 1 4 9 8 25 18 49 16 27 50 121 36 169 98 225 32
compr(\x.(~1 + ((1 + (x mod (1 + (2 * ((3x + 3) mod 7))))) mod 3)),(x + 1))
A028803-A028758: 2 3 5 6 7 8 11 12 13 14 15 17 18 20 21 22
((x + 1) * (1 + (((1 + (x mod ((1 + (x mod (1 + (x div 4)))) * (1 + (x mod 2))))) mod (x + 1)) div 2)))
A131959: 1 2 3 8
A344368: 1 2 3 8 5 12 7 24 18 20 11 48 13 28 30 80
((2x + 1) - (compr(\x.(x mod ((x + 1) - (x mod 10))),x) + (x mod 10)))
A160928: 1 1 1 1 1 1 1 1 1 1 10 1 ~8 ~17 ~26 ~35
((x + 1) * (~x + (compr(\x.(x mod ((x + 1) - (x mod 10))),x) + (x mod 10))))
A160929: 0 2 6 12 20 30 42 56 72 90 11 132 273 434 615 816
((1 - ((1 - ((1 + ((1 - (((x2 + ~x) div 3) mod 3)) mod (x + 1))) div 2)) div 2)) mod (x + 1))
A107682: 0 1 1 2 1 1 1 3 1 1 1 1 4 1 1 1
((2 * (2 + ((1 + (2 * ((2x + 2) mod (1 + (3 * (x mod 3)))))) mod (x + 1)))) div (x + 1))
A182425: 4 3 2 1 0 2 0 0 0 0 1 1 0 0 0 0
((x + 1) + (2 * ((((x + 2) + ((2 * (2 - ((x div 4) mod 2))) mod (x + 1))) div 2) + (x div 4))))
A285662: 3 4 7 8 15 16 19 20 27 28 31 32 35 36 39 40
((3x + 1) + ((x + (((7 * (x + ((x div 2) div 3))) div 2) div 2)) div 2))
A314832: 1 5 9 14 18 22 28 32 36 41 45 50 55 59 64 68
((x + 1) - (2 * (x mod (1 + (((x div (3 + (x div 3))) mod 2) + (x div 2))))))
A232113: 1 2 3 2 5 4 5 4 5 4 5 4 5 4 3 4
((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (2 - ((x div 2) div ~2)))
A068606: 0 0 0 0 3 0 0 8 8 0 0 15 20 15 0 0
((x + 1) div (2 + (x mod (1 + (x div 2) - ((2x + 1) mod (1 + (2x mod (2 + (x div 4)))))))))
A076511: 0 1 1 1 1 2 1 1 1 3 1 2 1 4 7 1
((1 + ((2 + ((1 + (4 * (1 + (x mod (2 * (2 + (x mod 4))))))) mod (x + 1))) div 3)) div 2)
A089611: 0 1 1 1 0 1 1 1 1 2 1 2 1 2 3 2
((1 + ((2 + ((1 + ((((x + 1) * (2 + ((x + 2) div (2 - (x mod 2))))) div 2) div 2)) div 2)) div 3)) div 2)
A127682: 0 1 1 1 1 2 1 2 2 3 2 4 3 5 4 7
((1 + ((1 + (((x + 1) * (x2 mod 11)) mod 9)) div 2)) div 2)
A164067: 0 1 1 0 2 0 1 1 0 1 1 0 1 1 0 2
((1 + ((1 + ((1 + ((1 + ((8x3 + 3x) div 2)) div 2)) div 2)) div 2)) div 2)
A222010: 0 1 3 7
A176690: 0 1 3 7 17 32 55 87 129 184 251
((1 + ((1 + ((1 + ((x * (x - (((~2x + 1) - (x2 div 3)) div 2))) div 2)) div 2)) div 2)) div 2)
A309408: 0 1 1 2 3 5 7 10 13 18 23 29 36 44 53 63
((1 + ((1 + (x div (2 + ((2 - (x mod (1 + (2 * (1 + ((~x + 2) mod 4)))))) mod (x + 1))))) div 2)) div 2)
A333948: 0 0 1 0 0 1 1 1 1 0 1 2 1 0 2 1
((1 + (((x + 1) + ((x + (((x + 1) * ((x2 + ~x) div 4)) div 8)) div 2)) div 2)) div 2)
A153178: 0 1 1 1 2 3 3 4 5 6 8 9 11 14 16 19
(((x + 1) - (2 * ((x - (2 * ((x div (2 * (~2 + ((x * (x div 2)) mod 2)))) div 3))) mod (x + 1)))) div 2)
A102563: 0 0 0 1 1 2 2 1 3 4 4 3 5 4 4 3
(((2x + 3) mod (~1 + (4 * (1 + (((x2 mod (x + 5)) div 2) mod 2))))) div 2)
A341354: 0 1 0 0 2 0 0 1 0 0 1 0 0 0 1 0
((1 + (((1 + ((((x + 1) * (1 + (2 * (2x + ((x * (x div 2)) mod 2))))) div 2) div 2)) div 2) div 2)) div 2)
A145807: 0 0 1 2 3 4 6 8 9 12 14 18 20 23 27 32
((1 + ((((x + 1) * (1 + (x mod 2) - (((1 - (((x mod 2) - (x div 2)) div 2)) div 2) mod 2))) div 2) div 2)) div 2)
A045841: 0 1 0 1 0 1 0 1 0 1 1 2 2 4 2 4
(1 - ((1 + (((((x + 1) * (~1 + ((0 - ((((x + ~1) div 2) * (x div 2)) div 2)) div 2))) div 2) div 2) div 2)) div 2))
A193942: 1 1 1 1 2 2 2 2 3 4 5 6 8 10 12 14
(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (4 * (1 - (x div 2))))) div 2))
A047812: 1 1 1 1 3 1 1 5 7 1 1 9 20 11 1 1
(((4x + 1) * ((6x4 + 11x3 + 6x2 + x) div 3)) div 2)
A011197: 0 20 315 1820 6630 18480 43225 89320 168300 295260 489335 774180 1178450 1736280 2487765 3479440
(x div (2 * (1 + (x div (3 + ((x + 1) mod (1 + (x div (2 + (x mod (2 + (x mod 2))))))) - (x mod 2))))))
A342652: 0 0 1 0 2 0 1 1 2 0 2 0 3 2 3 0
(9 mod (2 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))
A066340: 1 1 1 1 0 1 1 1 1 1 1 4 3 4 1 1
((3 * ((x + 1) div (2 + ((x div 2) div (1 + (((2x + 1) mod (2 + (x div 4))) div 2)))))) div 2)
A334019: 0 1 1 1 1 3 1 1 1 3 1 4 1 3 4 1
(((((x + 3) * ((x3 + 15x2 + 38x + 24) div 2)) div 2) div 3) div 2)
A095661: 3 13 35 75 140 238 378 570 825 1155 1573 2093 2730 3500 4420 5508
(((((x + 3) * ((x3 + 19x2 + 50x + 32) div 2)) div 2) div 3) div 2)
A095667: 4 17 45 95 175 294 462 690 990 1375 1859 2457 3185 4060 5100 6324
((3 * (((1 + (x mod ((1 + (x mod (1 + (x div 4)))) * (1 + (x mod 2))))) mod (x + 1)) div 2)) div 2)
A337525: 0 0 0 1 0 1 0 3 1 1 0 4 0 1 1 6
((3 * ((1 - (x mod (1 - ((2 - (2x mod (4 + (x div 4)))) mod (x + 1))))) div 2)) div 2)
A335681: 0 0 0 0 1 0 0 3 3 0 0 6 7 6 0 0
(((((x2 + 3x + 2) * (1 + (5 * ((x2 + 3x + 2) div 2)))) div 2) div 3) div 2)
A006322: 1 8 31 85 190 371 658 1086 1695 2530 3641 5083 6916 9205 12020 15436
((3 * (1 - (((1 + (x mod (1 + (31 mod (x + 1))))) div 2) div 2))) div 2)
A326815: 1 1 1 0 1 1 1 ~2 0 1 1 0 1 1 1 ~5
((2 - (3 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2))) div 2)
A026659-A026637-A026386: 1 1 1 1 2 1 1 4 4 1 1 5 8 5 1 1
(7 + (((2x + 2) * (2 + ((4x + 2) div 5))) div 3))
A256073: 8 11 15 17 23 31
(2 + ((x + ((8 * ((2x + 1) - ((x div 3) mod 3))) div 3)) div 3))
A285413: 2 5 7 8 10 12 13 15 18 21 24 26 27 29 31 32
((1 + (((x mod ((x + 1) - (6 * (x div 7)))) div 2) + (x mod 3))) div 2)
A164885: 0 1 2 1 2 2 2 1 2 0 1 2 1 2 2 1
(((((1 + ((1 + ((x * (1 + (((x + 1) div 2) div 2))) div 2)) div 2)) div 2) mod 3) + (x mod 3)) div 2)
A229878: 0 0 1 0 1 2
A037889: 0 0 1 0 1 2 1 0 1 0 1 1 0 1 1 0
((((1 + (x mod (1 + ((x2 + 2x) mod 8)))) * (1 + (x div 2))) div 2) * ((x mod 3) div 2))
A193291: 0 0 1 0 0 3 0 0 2 0 0 12 0 0 4 0
((x - (x mod (1 + ((x + (x div (1 + (23 mod (2x + 1))))) div 2)))) div 2)
A342881: 0 0 1 1 1 2 2 2 2 3 3 0 3 3 4 4
(3 + ((x + ((1 + ((((x * (2 + (((x2 + ~x) div 2) div 3))) div 2) div 2) div 2)) div 2)) div 2))
A120180: 3 3 4 5 5 6 7 8 10 11 13 15 18 21 24 28
(((2x + 1) div (3 + (x div 4))) - ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2))
A344838-A344835-A087061-A082860-A003984: 0 1 1 2 1 2 3 2 2 3 4 3 2 3 4 5
(((x + 1) + (2 * ((3 * (((5x + 5) + ((x div 2) div 3)) div 2)) div 2))) div 2)
A184925: 3 8 11 17 20 25 30 34 38 42 47 51 55 61 64 69
(1 - (x div (2 + ((~1 + (2 * (2 + ((2x mod (1 + (2 * (x mod 3)))) + (x mod 2))))) mod (x + 1)))))
A199918: 1 1 1 0 0 1 0 ~1 0 0 0 0 ~1 0 0 ~1
(((x + 1) * ((x3 + 3x2 + 4x + 2) + (((x3 + 3x2 + 2x) div 2) div 3))) div 2)
A185505: 1 11 51 156 375 771 1421 2416 3861 5875 8591 12156 16731 22491 29625 38336
(((2 * (1 + (x div (2 + (((1 + ((x mod 3) div 2)) * (1 + (x mod 2))) mod (x + 1)))))) mod (x + 1)) div 2)
A317243: 0 0 1 1 2 1 3 2 3 3 4 2 5 4 4 4
(((2 * (x - (2 * (x mod (1 + ((3 * ((x + 1) div 2)) mod (1 + (x div 3)))))))) mod (x + 1)) div 2)
A279645: 0 0 0 1 1 0 2 3 3 2 0 1 5 4 6 7
(((x + 1) * (2 + ((1 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4)))) * (x mod 2)))) div 2)
A267092: 1 3 3 8 5 9 7 20 9 15 11 24 13 21 15 48
((2x + 2) + (((5 * ((3x + 3) + ((x - (x div 4)) div 2))) div 2) div 2))
A184822: 5 11 18 24 30 37 42 49 55 61 68 74 79 86 92 99
(((~1 + (6 * (1 + (x div (2 + (x div (2 + (((x + 2) mod 5) div 2)))))))) div 2) div 2)
A086876: 1 1 2 2 2 2 2 4 2 2 4 4 4 2 2 4
((2 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (2 - (x mod ~5)))) div 2)
A055216: 1 1 1 1 2 1 1 3 3 1 1 4 6 3 1 1
(((1 + ((((x + 1) * ((x + 1) - (((~x + ~1) + (x2 div 4)) div 3))) div 2) div 2)) div 2) div 2)
A319468: 0 0 1 1 2 2 3 3 4 4 5 4 5 4 4 3
(((1 + ((((x + 1) * ((x + 1) + (2 * (2x + ((x mod (1 + (x div 2))) div 2))))) div 2) div 2)) div 2) div 2)
A260732: 0 1 2 4 6 10 14 19 24 31 38 45 53 63 72 82
(2 * ((1 + (((((x + 6) * (1 + ((1 + (x2 div 2)) div 3))) div 2) div 2) div 2)) div 2))
A162776: 0 0 2 2 6 6 10 14 22 26
(128x2 + 416x + 204)
A292346: 204 748 1548 2604 3916 5484 7308 9388 11724 14316 17164 20268 23628 27244 31116 35244
(~2 + ((5 * (1 + ((x - (x div (2 - ((x3 div 8) mod 2)))) div 2))) div 2))
A135090: 0 0 0 0 3 0 0 5 5 0 0 8 8 8 0 0
(2x - (((5 * compr(\x.(1 - (x mod (1 + (4 * (x mod 5))))),x)) div 2) div 2))
A331677: ~1 0 1 1 1 2 2 3 3 3 3 2 3 4 5 4
(((3 * ((x + 1) - (2 * ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2)))) div 2) div 2)
A035531: 0 1 2 1 2 3 3 1 2 3 3 3 3 4 5 1
(2 * (2 + (3 * (1 + (2 * (x + ((x * (1 + (x div 5))) div 9)))))))
A232540: 10 22 34 46 58 82 94 106 118 142 166 178 202 214 226 262
(2 * (2 + (3 * ((1 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4)))) * (x mod 2)))))
A059132: 4 10 4 16 4 10 4 22 4 10 4 16 4 10 4 28
(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (~6 + ((~x + 2) div 2))) div 2))
A173119-A028313: 1 1 1 1 5 1 1 6 6 1 1 7 12 7 1 1
((2x + 33) + (2 * (2 + (6 * (x div 3)))) - (x mod 2))
A071887: 37 38 41 54 57 58
(2 + ((1 + ((x * ((~x2 + 2) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))) div 2)) div 2))
A309865: 2 2 2 2 3 2 2 4 4 2 2 5 11 5 2 2
((((x + 1) + ((x + ((1 + (((((x3 + ~3x2 + 2x) div 2) div 2) div 2) div 2)) div 2)) div 2)) div 2) div 2)
A118302: 0 0 1 1 1 2 3 3 4 5 6 8 9 11 14 16
((2 + ((2 * (1 + (((1 - (x mod (3 + (x mod 2)))) mod (x + 1)) div 5))) mod (x + 1))) div 2)
A320111: 1 1 2 2 2 2 2 3 3 2 2 4 2 2 4 4
((2 + ((1 + ((2 * (2 + ((x * (1 + (x2 div (x + 5)))) div 2))) div 3)) div 2)) div 2)
A096938: 1 1 1 2 2 2 3 4 4 6 7 8 10 12 14 16
((((3 * ((x mod (x - ((x + ~1) mod 8))) * (2 + (x div 5)))) div 2) div 2) div 2)
A108797: 0 0 0 0 0 0 0 0 0 0 1 3 4 6 7 11
(2 + ((1 + ((2 * ((x + 2) + ((x - ((x + (x div 3)) div 3)) div 2))) + ((x + 1) div 2))) div 2))
A077094: 4 6 8 9 10 12 14 15 16 18 20 21 22 25 26 27
((1 + (((1 + ((2x + ~1) mod (4 + (x div 4)))) mod 3) + (((x + 1) div 2) div 2))) div 2)
A057226: 1 1 1 2 1 2 2 2 2 1 2 2 2 3 2 3
(((((5x2 + 12x + 7) div 2) + (4 * (1 + (x div 3)))) div 2) div 2)
A266811: 1 4 7 13 18 26 35 45 55 69 82 97 113 131 149 170
(1 - (8 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))
A168625: 1 1 1 1 9 1 1 17 17 1 1 25 41 25 1 1
(~2 + ((2 + (((1 + (2 * ((~1 + (2 * ((1 + (x div 2)) div 2))) mod (x + 1)))) mod (x + 1)) div 2)) mod 4))
A343642: 0 0 0 1 1 1 0 ~1 ~1 ~1 0 1 1 1 0 ~1
((((x + 1) * (1 + (3 * ((5x2 + 13x + 8) div 2)))) div 2) mod 8)
A289487: 6 0 3 6 7 6 0
(((1 + (((10 * (x + (2 * (x mod 2)))) mod 7) + (x mod 2))) div 2) div 2)
A133300: 0 1 1 0 1 0 1 2 1 1 0 1 0 1 0 1
(((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (2 * ((x div 2) mod 2))) * (x div 4))
A062707: 0 0 0 0 1 0 0 3 2 0 0 6 6 3 0 0
((2 + compr(\x.((x2 + 2x + 2) mod (5 * (~1 + (2 * (6 + (x mod 2)))))),x)) div 2)
A203464: 4 9 56 61 69 74 121 126 134 139 186 191 199 204 251 256
(2 * ((x + 2) + (((2x3 + 18x2 + 43x + 27) div 2) div 3)))
A152135: 12 36 74 134 216 328 470 650 868 1132 1442 1806 2224 2704 3246 3858
(2 * ((2x + 4) - ((((x + 1) div 2) div 3) + (5 * ((~x + ~2) + (x mod 2))))))
A230855: 28 32 56 60 84 86 110 114 138 142 166 168 192 196 220 224
compr(\x.((x div 2) mod 2),(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))
A166455: 1 1 1 1 4 1 1 5 5 1 1 8 12 8 1 1
(((x + 2) + ((x + ((2 + ((x * (2 + (((x2 + 3x + 2) div 2) div 2))) div 2)) div 3)) div 2)) div 2)
A306385: 1 2 3 4 5 7 9 12 15 18 23 28 33 40 47 56
((~4x + ~1) + ((((x + 3) * ((x3 + 5x2 + 8x + 4) div 2)) div 2) div 3))
A124479: 0 1 11 37 88 175 311 511 792 1173 1675 2321 3136 4147 5383 6875
(2 + ((2 * (((1 + (x mod (1 + (31 mod (x + 1))))) div 2) div 2)) + (x mod 2)))
A101876: 2 3 2 5 2 3 2 7 4 3 2 5 2 3 2 11
((1 + (x div (2 + (x mod (1 + ((x + 1) mod (1 + (x div (2 + (x div 5)))))))))) div (2 + (x mod 2)))
A291598: 0 0 1 0 1 1 2 1 2 1 2 2 3 1 2 2
(x div (((x + 1) + (((x + 1) * (4 - (2x mod (4 + (x div 4))))) div 3)) div 2))
A254606: 0 1 0 1 1 0 1 1 2 0 1 1 1 3 0 1
(((x + 1) + (2 * (((x + 40) + (x div 9)) div 2))) div 2)
A270045: 20 21 22 23 24 25 26 27 28 30 30 32 32 34 34 36
((x + ((2 + ((66x + 33) div (x + 3))) div (x + 1))) div 2)
A343436: 6 7 6 6 6 6 6 6 6 7 7 7 8 8 8 9
((x + ((3 * ((4x + 5) - ((~x + 2) div (4 + (x mod 2))))) div 2)) div 2)
A288175: 3 7 10 15 18 22 25 29 33 36 40 43 48 51 55 58
((x + 2) + (((5 * compr(\x.(1 - (x mod (1 + (4 * (x mod 5))))),x)) div 2) div 2))
A298862: 3 5 7 10 13 15 18 20 23 26 29 33 35 37 39 43
((x + (((x + 2) + ((((3x + 2) * (x div (~2 + ((~x + 2) div 4)))) div 2) div 2)) div 2)) div 2)
A131840: 0 0 1 2 1 2 2 2 3 1 2 2 2 2 2 2
((x + 2) + (((x + 1) + ((2 * (x + ((x - ((x + (x div 2)) div 5)) div 2))) + (x div 2))) div 2))
A189472: 2 5 9 11 14 18 21 23 27 30 33 36 39 43 46 48
((~x + ~2) + (((2x3 + 27x2 + 91x) div 2) div 3))
A073775: ~2 17 47 90 148 223 317 432 570 733 923 1142 1392 1675 1993 2348
(~1 + (2 * ((x + 1) + ((2 * (1 + (((x + (2 mod (1 + (x div 2)))) div 2) div 2))) div 3))) - (x div 2))
A285412: 1 3 4 6 9 11 14 16 17 19 20 22 23 25 28 30
((~x + 1) + ((1 + ((5 * ((2x + 1) - ((x div 4) mod 2))) div 3)) div 3))
A338409: 1 2 2 2 1 1 2 2 2 2 3 3 2 2 2 3
compr(\x.(~1 + ((2 * (1 + (((2 + ((1 - (x mod 9)) mod (x + 1))) div 2) div 2))) mod 3)),x)
A037343: 2 3 4 5 6 7 8 20 21 22 23 24 25 26 29 30
compr(\x.(~1 + ((1 + (((x + 1) - (2 * ((x + (x div 3)) div 5))) mod 3)) mod (x + 1))),x)
A090893: 0 1 2 4 7 9 14 16 21 23 26 28 30 33 35 40
((x + 1) + ((1 + (x mod (2 * (2 + (x3 mod 25))))) mod (x + 1)))
A098098: 1 2 3 4 5 8 7 8 9 10 14 12 16 14 15 20
((x + 1) + (((1 + ((((x + 1) * ((x + 1) + ((x - ((x mod 3) div 2)) div 2))) div 2) div 2)) div 2) div 2))
A097046: 1 2 3 5 7 9 11 13 16 19 22 25 28 31 34 39
compr(\x.(2 - (((x + 1) + (((x + 1) - (2 * ((~2x + 1) div 3))) div 3)) mod 5)),x)
A213356: 1 2 4 6 7 9 10 12 13 15 18 21 23 24 26 27
(5x + (((~2x + 4) div (4 + ((x div 2) div 3))) + ((x + 1) div 3)))
A137002: 1 5 11 15
A314028: 1 5 11 15 20 25 30 35 40 45 49 55 60 65 71 75
((x + 1) - ((((3 - (x mod (1 + ((x2 + 2x) mod 8)))) mod (x + 1)) div 2) mod 3))
A306890: 1 2 3 4 4 5 6 6 8 9 10 12 12 13 14 16
(~x + ((2 * ((x + 2) + ((((x + 1) div 5) * (1 + (((x + 1) div 2) div 2))) div 2))) div 3))
A016348: 1 1 0 0 0 0 0 ~1 ~1 0 0 0 0 ~1 0 1
((~x + 1) + ((x + (((3 * (x + ((x + (x2 div 4)) div 5))) div 2) div 2)) div 2))
A280169: 1 0 0 1 0 1 1 1 1 1 2 2 2 3 3 4
((~x + 6) + (((5 * (~2 + (3 * (x - ((~x + 1) * (x div 2)))))) div 2) div 2))
A226220: 3 6 12 19 37 47
(~x + (((x + 2) + ((x + ((1 + ((((x + 1) * (x + ((x + ~1) mod 3))) div 2) div 2)) div 2)) div 2)) div 2))
A087897: 1 0 0 1 0 1 1 1 1 2 2 2 3 3 4 5
((2x + 1) + ((2 * ((x + 1) + (2 * (x - ((~x2 + 1) div (x + 4)))))) div 3))
A314096: 1 5 11 16 20 25 31 36 41 47 52 56 61 67 72 77
(x + ((x + ((1 + (((((x + 1) * (2 + (3 * (x + (x div 4))))) div 2) div 2) div 2)) div 2)) div 2))
A237886: 0 2 4 6 8 11 14 17 21 24 28 32 37 41 46 50
((x2 + 1) + ((x + ((x + ((7x2 + 17x + 6) div 3)) div 2)) div 2))
A025734: 1 5 12 22 35 51 71 94 120 149 181 216 255 297 342 390
((x2 + 2x + 4) + ((24x + 24) div 7))
A236312: 7 13 22 32 45 59 76 94 114 137 161 188 216 247 279 313
((5x + 3) + (7 * (0 - ((x - (x div 4)) div 2))))
A080939: 3 8 6 11 16 14 19 17 22 27 25 30 35 33 38 36
(if x <= 0 then 1 else loop(\(x,i).2x,(x + (if x <= 0 then 1 else loop(\(x,i).(x - (if (x mod 2) <= 0 then ((if x <= 0 then 2 else x) div 2) else 1)),x,x))),2))
A189007: 1 4 8 16 16 32 32 64 32 64 64 128 64 128 128 256
(loop(\(x,i).(x * loop(\(x,i).x2,1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)))),x,1) - (if x <= 0 then 0 else 1))
A135516: 1 3 35 899 44099 5336099 901800899 260620460099 94083986096099 49770428644836899 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).(2x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),i,1)),(x + 1),1)
A222993: 9 50 222 867 3123 10660 35064 112373 353517 1097430 3374226 10302919 31301991 94757960 286108908 862258905
loop(\(x,i).3x,x,(1 + (loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).3x,x,1))))
A220442: 4 30 270 2700 28674 315900 3564810 40896900 474714594 5557298220 65464673850 774752404500 9200707298514 109548133495740 1306873625950890 15613382906014500
(1 + (2 * (1 + loop(\(x,i).(x + (if x <= 0 then 1 else loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,2x))),x,1))))
A227770: 5 7 11 19 31 59 113 223 443 883 1759 3511 7019 14033 28057 56101
(1 + (2 * (1 + ((1 + loop(\(x,i).(x + (if x <= 0 then 1 else loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,x))),2,x)) div 2))))
A076568: 5 5 5 5 7 5 5 5 11 5 13 7 5 5 17 5
(if (x mod 2) <= 0 then ((if (x mod 4) <= 0 then (9 * (2 + (if x <= 0 then 0 else 2))) else 1) + (if x <= 0 then 1 else 2)) else 1)
A040372: 19 1 3 1 38 1 3 1 38 1 3 1 38 1 3 1
(compr(\x.(0 - loop(\(x,i).loop(\(x,i).loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,2x),1,(x + 1)),2,x)),x) div 3)
A153196: 0 1 2 4 6 9 11 16 17 22 24 29 31 32 37 39
(if x <= 0 then 2 else (1 + (2x * (if ((1 + loop(\(x,i).x2,x,loop(\(x,i).(x * i),x,1))) div 3) <= 0 then 1 else 2x))))
A067976: 2 3 17 37 4611686018427387903
loop(\(x,i).2x,x,loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1))
A025966: 1 20 260 2800 27216 248640 2182720 18656000 156544256 1296655360 10641146880 86744985600 703688298496 5688011079680 45855653642240 368956766617600
loop(\(x,i).3x,x,loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),x,1))
A020724: 1 27 495 7695 109431 1474767 19198215 244167615 3055792311 37811613807 464078786535 5662363023135 68791291322391 833094971965647 10065613312624455 121404092777808255
loop(\(x,i).(4x + loop(\(x,i).x3,1,loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),i,1))),x,1)
A167869: 1 12 264 9056 379224 17519904 858968640 43860112128 2307187351512 124161781334048 6803252453289408 378260174003539200 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(loop(\(x,i).2x,x,1) - loop(\(x,i).((x * (1 + i)) div (1 + (i div 2))),(x + ~1),1)),1,loop(\(x,i).2x,x,1))
A037267: 1 2 10 186 52666 3693886906 4611686018427387903
((2x + 1) + (if x <= 0 then 1 else (2 * (2 + (if x <= 0 then 1 else (2 * (1 + loop(\(x,i).loop(\(x,i).(x * (2 + i)),x,x),x,1))))))))
A273976: 2 23 733 4611686018427387903
loop(\(x,i).2x,x,(loop(\(x,i).4x,x,(1 + loop(\(x,i).3x,x,1))) - loop(\(x,i).3x,x,1)))
A057010: 1 26 604 14120 334576 7987616 191318464 4588288640 110090411776 2641931680256 63404394241024 1521689370306560 36520413978750976 876488875160477696 4611686018427387903 4611686018427387903
loop(\(x,i).(x * loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),i,1)),x,1)
A126680: 1 10 650 227500 386977500 3006815175000 102547431543375000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).x2,1,loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),i,1))),x,1)
A189997: 1 5 41 941 45041 5381141 907182041 261527642141 94345513738241 49864774158575141 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,loop(\(x,i).(2x + 2),4,x)),x))
A127577: 3 5 6 11 14 18 26 30 33 35 39 44 45 48 51 54
(if x <= 0 then 1 else (loop(\(x,i).loop(\(x,i).(x + (loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),i,1) + (x * i))),x,1),x,1) div 2))
A297023: 1 1 3 29931
loop(\(x,i).(1 + (loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).3x,x,1))),1,(2x + 2))
A091775: 30 354 4890 72354 1108650 17312754 273234810 4338079554 69107159370 1102999460754 17623571298330 281757423024354 4506141560307690 72080471098818354 1153127396812683450 4611686018427387903
((3 * (if (x mod 2) <= 0 then (3 * (if (x mod 4) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1)) else 1)) - (if x <= 0 then 1 else 2))
A040302: 17 1 7 1 34 1 7 1 34 1 7 1 34 1 7 1
(if (x + ~2) <= 0 then loop(\(x,i).2x,x,2) else loop(\(x,i).x2,2,(2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))))
A062286: 2 4 8 14641
compr(\x.(~1 + ((~1 + (if loop(\(x,i).((if x <= 0 then 2 else loop(\(x,i).(x div (2 - (x mod 2))),x,x)) div 2),2,x) <= 0 then 0 else x)) mod 3)),x)
A140137: 1 2 4 7 8 11 13 14 16 19 22 23 25 26 28 29
((x + 1) + (if x <= 0 then 0 else loop(\(x,i).(3 * (~x + (if x <= 0 then 1 else (~1 + loop(\(x,i).(x3 + x),x,1))))),x,1)))
A116899: 1 2 6 3022
(x + loop(\(x,i).(x - (if x <= 0 then 1 else (if (x mod 2) <= 0 then (x div 2) else loop(\(x,i).i,((~1 + (x div 2)) div 2),1)))),(x + 1),(x + 1)))
A302039-A056239: 0 1 2 2 3 3 4 3 4 4 5 4 6 5 5 4
(if (x + ~1) <= 0 then 1 else loop(\(x,i).(10x + 1),x,loop(\(x,i).(10x + 10),x,0)))
A267811: 1 1 11011 1110111 111101111 11111011111 1111110111111 111111101111111 11111111011111111 1111111110111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(10x + 1),2x,1) - loop(\(x,i).(if x <= 0 then 1 else 10x),x,0))
A267775: 1 110 11101 1111011 111110111 11111101111 1111111011111 111111110111111 11111111101111111 1111111111011111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).7x,x,1) - (loop(\(x,i).(3x + 2),x,0) + loop(\(x,i).4x,x,1)))
A090022: 0 1 25 253 2065 15541 112825 804973 5692705 40071781 281367625 1972955293 13823978545 96820307221 677949854425 4746473419213
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).3x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1),1,i)),x,0)
A160724: 0 3 6 15 18 27 36 63 66 75 84 111 120 147 174 255
((1 + loop(\(x,i).12x,x2,1)) * loop(\(x,i).(4x + 1),(if (x + ~1) <= 0 then 1 else 0),1))
A140362: 10 65 20737
(loop(\(x,i).(10x + 1),2x,1) - loop(\(x,i).10x,2,(if x <= 0 then 0 else 1)))
A267923: 1 11 11011 1111011 111111011 11111111011 1111111111011 111111111111011 11111111111111011 1111111111111111011 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).(x * i),(1 + compr(\x.(loop(\(x,i).(x3 + ~x2),2,x) mod (x + 1)),x)),1)))
A162455: 3 7 43 601 519121
(~1 + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1))
A242083: 4 18 210 2058 175098 1586130 129009090 1161737178 94134790218 68629840493970 617671248800298 450283768452043890 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else ((2x + 2) div ((2x + 1) div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))))
A231407: 1 4 6
A095196-A074828: 1 4 6 2 10 2 14 2 3 2 22 2 26 2 3 2
(1 - (if x <= 0 then 0 else (1 + (if (x + ~1) <= 0 then 2x else loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + ~2),1)))))
A115141: 1 ~2 ~1 ~2 ~5 ~14 ~42 ~132 ~429 ~1430 ~4862 ~16796 ~58786 ~208012 ~742900 ~2674440
(1 + ((x + 1) mod (1 + loop(\(x,i).(if x <= 0 then 0 else (x + (x mod 2) - (if ((x + (x div 2)) mod 4) <= 0 then 2 else 1))),2,x))))
A244569: 1 1 2 1 3 1 2 1 4 1 2 3 3 1 2 1
(1 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A323704: 2 3 5 3 11 5 17 7 23 29 11 13 41 15 47 53
(~1 + loop(\(x,i).(loop(\(x,i).(2x + 2),x,0) div (x + 1)),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A092679: 0 1 5 17
A164740: 0 1 5 17 185 629 7709 27593 364721 18512789 69273665 3714566309 53634713549 204560302841 2994414645857 169947155749829
(1 + loop(\(x,i).(loop(\(x,i).(2x * i),x,1) div (x + 1)),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A091825: 2 3 77 6583 337808291 150922350277 80658585770586353 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(x2 + 2x),1,compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1))))
A120875: 14 34 142 322 898 1762 3598 5182 10402 11662 19042 22498 32398 36862 39202 51982
((1 + loop(\(x,i).(x4 + x3 + x2 + x),1,loop(\(x,i).2x,x,1))) * (1 + loop(\(x,i).3x,x,1)))
A034668: 10 124 3410 131068 5732210 264105844 12441770330 591961476748 28294099221410 1355321291969764 64989628053819050 3117943006504850428 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * (if x <= 0 then 0 else (1 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),(x + 5))))))
A166061: 1 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79
(if (x mod 2) <= 0 then (if x <= 0 then 1 else (2 * (1 + (((~1 + loop(\(x,i).2x,x,(2 - ((x div 2) mod 2)))) mod (x + 1)) div 2)))) else 1)
A318658-A318512: 1 1 2 1 2 1 2 1 8 1 2 1 2 1 4 1
(1 + (2 * (if x <= 0 then 0 else (1 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),(x + 6))))))
A166063: 1 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83
(if (x mod 2) <= 0 then (if (x mod 4) <= 0 then (23 * (if x <= 0 then 1 else 2)) else 6) else 1)
A040546: 23 1 6 1 46 1 6 1 46 1 6 1 46 1 6 1
(~1 + (2 * (1 + compr(\x.(~1 + loop(\(x,i).loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)),1,(x2 + x))),x))))
A225227: 1 7 13
A180263: 1 7 13 17 21 23 27 31 33 37 41 43 47 53 55 57
(~1 + ((loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x div 2),((x + 1) mod 2)) + loop(\(x,i).2x,x,1)) div 2))
A226881: 0 0 2 3 10 15 41 63 162 255 637 1023 2509 4095 9907 16383
(1 + (2 * loop(\(x,i).(1 + (3 * (loop(\(x,i).(3x + ~3),x,2) + loop(\(x,i).2x,x,2)))),1,(x + 1))))
A183625: 45 87 189 447 1125 2967 8109 22767 65205 189447 556029 1643487 4881285 14545527 43439949 129926607
(1 + (2 * (1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(x2 + 3x)),x))))
A109358: 3 5 7 11 13 19 23 25 29 31 37 41 47 55 65 67
(1 + (2 * (1 + compr(\x.(if ((x + 2) mod 4) <= 0 then 1 else loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x)),x))))
A045403: 3 5 11 13 17 19 29 37 41 43 53 59 61 67 73 83
((x + 2) - (2 * (loop(\(x,i).((x + 2) + (if x <= 0 then 1 else (2 * loop(\(x,i).(3x + ~6),x,0)))),x,0) div 2)))
A258819: 2 1 156 153
((if x <= 0 then 0 else (7 + loop(\(x,i).((x2 + 2x) div 2),1,loop(\(x,i).2x,x,1)))) div 5)
A322752: 0 2 3 9 30 110 423
(loop(\(x,i).(2x + 2),(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),(x + ~1),x)),1) mod 5)
A110914: 1 0 2 0 1 0 2 0 4 0 2 0 1 0 2 0
((if (x mod 2) <= 0 then (if x <= 0 then 1 else ((x - (if ((x mod 3) mod (1 + (x mod 4))) <= 0 then 1 else 0)) div 2)) else 0) mod 3)
A297115: 1 0 1 0 1 0 2 0 0 0 2 0 2 0 1 0
loop(\(x,i).3x,(x + ~1),loop(\(x,i).x2,1,(3 * loop(\(x,i).12x,(x + ~1),1))))
A058200: 9 9 3888 1679616 725594112 313456656384 135413275557888 58498535041007616 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(loop(\(x,i).2x,x,2) div (x + 1)),1,(1 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x))) div 3)
A145756: 2 6 62 210 2570 9198 121574 6170930 23091222 1238188770 17878237850 68186767614 998138215286 56649051916610 3256840408493918 12600235023025650
(1 - ((2 * ((1 + loop(\(x,i).2x,x,(if x <= 0 then 1 else (x + (loop(\(x,i).2x,x,1) div (x + 2)))))) div 2)) mod 3))
A144475: ~1 ~1 1 ~1 1 1 ~1 1 1 ~1 ~1 1 0 ~1 1 ~1
(3 + (2 * loop(\(x,i).compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x),1,((x2 + x) div 2))))
A078722: 3 5 11 19 37 59 83 113 163 211 269 337 409 487 587 673
(loop(\(x,i).((~1 + loop(\(x,i).2x,x,2)) div (x + 2)),1,compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)) div 3)
A096060: 1 3 31 105 1285 4599 60787 3085465 11545611 619094385 8939118925 34093383807 499069107643 28324525958305 1628420204246959 6300117511512825
(1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(4x + (x div 2))),x))
A024907: 1 2 4 6 10 12 16 20 22 26 30 32 36 40 44 50
(2 div (1 + ((~1 + loop(\(x,i).2x,x,(if (loop(\(x,i).2x,x,3) mod (x + 3)) <= 0 then 2 else 1))) mod (x + 2))))
A039974: 1 1 0 2 0 2 0 1 0 2 0 0 0 0 0 0
((2x + 1) * ((loop(\(x,i).4x,x,1) - loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1)) div 2))
A303602: 0 3 25 154 837 4246 20618 97140 447661 2028478 9070110 40122028 175913250 765561564 3310623412 14238676712
loop(\(x,i).((if x <= 0 then 2 else loop(\(x,i).((2x * (~1 + (2 * i))) div (2 + i)),x,3x)) div 2),1,(2x + ~1))
A127769: 1 1 9 90 1001 11934 149226 1931540 25662825 347993910 4796857230 67016296620 946844533674 13505406670700 194214400834356 2812744285440936
(loop(\(x,i).8x,x,1) + loop(\(x,i).6x,x,1) + loop(\(x,i).3x,2x,1))
A074579: 3 23 181 1457 11953 99593 840241 7160057 61503553 531715913 4620992401 40333791257 353325795553 3104682336233 27353203130161 241545689168057
(loop(\(x,i).5x,x,1) + loop(\(x,i).6x,x,1) + loop(\(x,i).3x,2x,1))
A074573: 3 20 142 1070 8482 69950 593722 5141030 45116962 399451310 3557016202 31792684790 284850459442 2556147225470 22961260134682 206391834657350
(loop(\(x,i).5x,x,1) + loop(\(x,i).8x,x,1) + loop(\(x,i).3x,2x,1))
A074576: 3 22 170 1366 11282 94942 809210 6958246 60214562 523591342 4570291850 40019822326 351393153842 3092842345342 27280942481690 241106021761606
(loop(\(x,i).7x,x,1) + loop(\(x,i).4x,x,1) + loop(\(x,i).3x,2x,1))
A074569: 3 20 146 1136 9218 76880 653186 5622896 48877058 428036240 3770308226 33362580656 296287600898 2638821947600 23555283963266 210639767346416
((if (x mod 3) <= 0 then ((1 + (2 * (if (x mod 2) <= 0 then 6 else 1))) * (if x <= 0 then 1 else 2)) else 1) * (1 + (x mod 2)))
A010222: 13 2 1 12 1 2 26 2 1 12 1 2 26 2 1 12
(2x div (1 + (2 * loop(\(x,i).(x - (x div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))),x,x))))
A323076: 0 0 0 1 0 2 0 1 1 3 0 1 0 2 1 2
loop(\(x,i).x3,(x + ~2),(1 + (if (x * loop(\(x,i).x2,(x + ~2),x5)) <= 0 then x else 2)))
A271938: 1 3 3 27 19683 4611686018427387903
(1 + compr(\x.(~1 + loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(3x2 + 6x))),x))
A143826: 1 2 3 5 7 8 10 12 13 17 20 22 27 28 30 32
(1 + compr(\x.((1 + loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,3x)) mod 3),x))
A121765: 6 11 13 16 21 26 27 35 37 46 51 55 56 61 62 63
loop(\(x,i).(12x + loop(\(x,i).(~1 + (2 * (4x + loop(\(x,i).2x,i,1)))),i,1)),x,1)
A021279: 1 23 371 5227 68955 877371 10927867 134329979 1637524859 19854820219 239894019963 2891817662331 34806527338363 418516051199867 5028894399547259 60400347075823483
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).2x,i,1)),i,1)),x,1)
A016315: 1 21 319 4305 55015 683697 8369047 101581473 1227048295 14781074385 177768357559 2135988547329 25651240368391 307950529031985 3696355860679255 44362916914251873
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A018071: 1 23 373 5279 69853 890519 11105221 136616783 1666241005 20209628615 244233494869 2944545727487 35444499573757 426213603230711 5121600110316517 61515496310530991
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A019722: 1 25 433 6457 89089 1174537 15047761 189169369 2347464097 28866716329 352675969009 4288594179961 51971489903425 628233183645001 7579976215410577 91330317763703833
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021404: 1 20 285 3640 44681 540540 6505045 78138080 937976961 11257033060 135089723405 1621098253320 19453266126841 233439544261580 2801275941271365 33615316957309360
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).5x,i,1)),i,1)),x,1)
A019041: 1 21 313 4125 51601 630741 7630633 91892685 1104403201 13261555461 159183299353 1910426955645 22926277062001 275121159824181 3301483361726473 39617948633641005
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A017918: 1 20 289 3740 46321 563300 6797569 81762860 982121041 11790305780 141507994849 1698217742780 20379222467761 244553718979460 2934659879368129 35215994824839500
loop(\(x,i).(12x + loop(\(x,i).(2x + loop(\(x,i).(6x + 1),i,1)),i,1)),x,1)
A021214: 1 21 313 4137 51961 637497 7733881 93310329 1122747001 13491103353 162002078329 1944677972601 23340053875321 280104155744889 3361390924417657 40337537425951353
loop(\(x,i).(12x + loop(\(x,i).(2x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A021164: 1 20 287 3694 45609 553776 6677779 80295938 964364717 11576444932 138937682871 1667353916982 20008755624625 240107610616088 2881304043028763 34575712094589226
loop(\(x,i).(6x + loop(\(x,i).((9x + ~1) + loop(\(x,i).2x,i,2)),i,1)),x,1)
A021194: 1 18 223 2388 23809 228246 2138131 19746936 180745477 1644848634 14912475799 134865314844 1217706037705 10982863580382 98986827702427 891727782261312
loop(\(x,i).(6x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),x,1)
A016308: 1 19 261 3191 37037 419055 4679557 51894967 573363933 6322119551 69634013813 766518346503 8434966982989 92804227849807 1020964052585829 11231309855904599
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).4x,i,1)),i,1)),x,1)
A019316: 1 17 195 1885 16571 137277 1092715 8456045 64100091 478409437 3528167435 25777174605 186937014811 1347606967997 9667804397355 69083038251565
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A017931: 1 16 175 1630 13921 112756 881875 6730810 50468341 373414096 2734771975 19868820790 143434778761 1030163245036 7367866260475 52515419443570
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A020579: 1 23 355 4595 53851 592403 6240235 63710915 635468251 6225852083 60146237515 574587484835 5439634923451 51116555484563 477406092913195 4435981769620355
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(4x + 1),i,1)),i,1)),x,1)
A021814: 1 19 239 2519 24135 218343 1903783 16194343 135426599 1118993447 9166829607 74629521447 604827848743 4885462331431 39365093814311 316610553147431
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021503: 1 18 217 2214 20701 183906 1582129 13325598 110626021 909165114 7418351161 60217256502 486961532461 3927035533842 31604351090113 253963231160526
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).5x,i,1)),i,1)),x,1)
A019783: 1 19 243 2615 25571 235599 2086603 17981815 151979091 1266533279 10446235163 85502523015 695860175011 5639142048559 45552803794923 367090952376215
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A021744: 1 16 167 1442 11193 81228 563179 3779974 24771725 159439280 1012078431 6355276746 39568060897 244679845972 1504794392723 9213774596558
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A019483: 1 20 276 3280 36176 383040 3962176 40428800 409195776 4121666560 41395966976 415039672320 4156893515776 41607983022080 416314385842176 4164552265891840
loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A019793: 1 20 271 3110 32641 324800 3125011 29414090 272851381 2506362980 22871235751 207773763470 1881803862121 17008495407560 153516126074491 1384313656687250
loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021414: 1 15 148 1218 9079 63693 429346 2815296 18097717 114645531 718257904 4461736734 27532164115 169004094729 1033087293022 6293858904732
loop(\(x,i).(6x + loop(\(x,i).(2x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A021202: 1 19 251 2891 31227 326235 3346267 33966427 342687323 3445012571 34558963803 346242670683 3466344910939 34686958350427 347010638983259 3470952722772059
loop(\(x,i).(6x + loop(\(x,i).(2x + loop(\(x,i).(7x + 1),i,1)),i,1)),x,1)
A021174: 1 16 173 1592 13461 108192 841261 6392584 47771141 352537328 2576599389 18689228376 134742802741 966708860224 6908017500557 49202455443368
loop(\(x,i).(6x + loop(\(x,i).(3x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A017952: 1 19 253 2935 31861 333919 3431773 34875415 352106821 3541203919 35532912493 356054541895 3564898452181 35675104315519 356907766700413 3570018022624375
(loop(\(x,i).5x,x,1) + loop(\(x,i).8x,x,1) + loop(\(x,i).6x,x,1))
A074572: 3 19 125 853 6017 43669 324425 2455213 18847457 146248549 1143973625 9001559773 71140399697 564037211029 4482514190825 35685074651533
(loop(\(x,i).7x,x,1) + loop(\(x,i).4x,x,1) + loop(\(x,i).6x,x,1))
A074565: 3 17 101 623 3953 25607 168401 1119863 7509953 50693447 343990001 2344318103 16034846753 110016813287 756855672401 5218820236343
loop(\(x,i).(7x + loop(\(x,i).(~1 + (2 * (4x + loop(\(x,i).2x,i,1)))),i,1)),x,1)
A021224: 1 18 221 2322 22485 207306 1850557 16149474 138611429 1174801914 9859790733 82107957906 679471095733 5594020809642 45859930816349 374633796970818
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).4x,i,1)),i,1)),x,1)
A019512: 1 19 245 2675 26661 251139 2278165 20125075 174364421 1488724259 12567504885 105148209075 873459639781 7213661997379 59291458568405 485407880414675
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A017997: 1 18 223 2364 23053 213654 1914571 16756128 144132505 1223664090 10283600119 85728989892 710053773157 5849984757726 47986764852067 392202340697256
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A019613: 1 20 273 3172 33809 342132 3348241 32033924 301669137 2808831124 25937190929 238042888356 2174659962385 19797924540596 179763483454737 1628947562960068
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021364: 1 15 150 1270 9891 73605 533800 3814140 27018981 190442395 1338423450 9390536610 65820843271 461096642385 3229086629100 22609268456680
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).5x,i,1)),i,1)),x,1)
A018209: 1 16 173 1580 13161 103656 787333 5836420 42545921 306538496 2190403293 15560186460 110074899481 776359376536 5463959472053 38396009227700
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A017389: 1 15 154 1350 10891 83685 623764 4558380 32875381 234980955 1669192174 11806149810 83252603071 585817587825 4115974729384 28888095527640
loop(\(x,i).(7x + loop(\(x,i).(2x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A021124: 1 15 152 1314 10479 79821 591214 4301088 30921077 220515867 1563954756 11049405822 77854461595 547524351753 3845386097978 26981280929916
loop(\(x,i).(7x + loop(\(x,i).(2x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A016313: 1 19 257 3047 33825 361767 3782353 38976439 397835009 4034844935 40743914289 410207399511 4121451795553 41350162566823 414451137963665 4151157965737463
loop(\(x,i).(7x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A017998: 1 19 250 2830 29611 295729 2866900 27241660 255258421 2367929839 21805655950 199711092490 1821621686431 16564149750349 150264234543400 1360686332771320
(1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(2x2 + 5x + 1)),x))
A155736: 1 2 3 4 5 8 10 12 13 14 15 19 22 23 24 25
(1 + compr(\x.(loop(\(x,i).x3,1,(1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))) mod (x + 1)),x))
A322546: 1 2 3 4 5 7 8 9 11 13 17 19 23
A339841-A334393-A115975: 1 2 3 4 5 7 8 9 11 13 17 19 23 25 27 29
(1 + compr(\x.(1 - (loop(\(x,i).x2,2,(1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))) mod (x + 1))),x))
A105642: 6 10 12 14 15 18 20 21 22 24 26 28 30 32 33 34
(1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,((3x2 + 6x) div 2)),x))
A089681: 1 2 4 6 8 12 14 18 22 26 28 30 34 40 44 48
(1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(4x2 + 8x + 2)),x))
A143827: 1 2 3 4 5 9 11 12 14 17 18 19 21 23 25 26
loop(\(x,i).(8x + loop(\(x,i).((9x + ~1) + loop(\(x,i).2x,i,2)),i,1)),x,1)
A021264: 1 20 275 3250 35481 369240 3722575 36698750 355853861 3407206660 32301037275 303798758250 2838904214641 26387861071280 244192534790375 2251347094369750
loop(\(x,i).(8x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),x,1)
A016318: 1 21 315 4145 51051 605241 7007155 79874865 900993051 10089880361 112420339395 1248076978785 13820472734251 152758207825881 1686204348094035 18595160325141905
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A021764: 1 18 215 2160 19821 172638 1456915 12056220 98541641 799142058 6448579215 51871439880 416407919461 3338534836278 26744994007115 214144960297140
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A019671: 1 22 332 4280 50736 571872 6238912 66567040 699159296 7259766272 74744097792 764616652800 7783588704256 78935331561472 798149140201472 8051859072450560
loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A020343: 1 22 327 4100 46781 503202 5201827 52278640 514595961 4986022382 47721236927 452316244380 4253691236341 39747202125562 369442770633627 3418759065309320
loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021434: 1 17 194 1882 16827 143835 1197868 9822164 79783253 644325253 5184986742 41632083246 333818409679 2674358387471 21413929824416 171406773741928
loop(\(x,i).(8x + loop(\(x,i).(2x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A021268: 1 21 305 3825 44481 494721 5346625 56661825 592183361 6126355521 62899732545 642086748225 6525582872641 66093551865921 667637303808065 6729987319337025
loop(\(x,i).(8x + loop(\(x,i).(3x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A018069: 1 21 307 3873 45235 504633 5465323 58007361 606913219 6283868745 64556638939 659310178449 6703052628403 67910134629657 686138217844555 6917677165178337
(loop(\(x,i).7x,x,1) + loop(\(x,i).3x,x,1) + loop(\(x,i).8x,x,1))
A074558: 3 18 122 882 6578 49818 380522 2922882 22548578 174591018 1356276122 10567438482 82561295378 646646418618 5076274366922 39931947947682
loop(\(x,i).(9x + loop(\(x,i).(4x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021379: 1 17 198 2002 19019 175539 1598416 14463284 130489557 1175715541 10586766554 95302471446 857809330015 7720634709623 69487122519012 625389764724088
loop(\(x,i).(9x + loop(\(x,i).(2x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A021134: 1 17 200 2050 19731 184047 1688890 15362600 139076861 1255760077 11322184380 102001381950 918521058391 8269232646107 74435809450670 669985863300100
(~1 + compr(\x.(1 - loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(5x + ~2))),x))
A153380: 0 3 4 6 9 11 12 15 16 18 20 21 24 25 27 28
loop(\(x,i).6x,x,loop(\(x,i).(4x + loop(\(x,i).(10x + 1),i,1)),x,1))
A089513: 1 90 6156 387720 23705136 1432922400 86230132416 5179923146880 310942155338496 18660051727004160 1119687641441381376 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A018912: 1 19 251 2879 30891 320439 3266131 32986399 331554971 3324266759 33287301411 333100377519 3332157369451 33327408774679 333303531583091 3333183608754239
loop(\(x,i).(4x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A019682: 1 23 363 4891 60515 710619 8059507 89191307 969344739 10390594555 110181318611 1158295737963 12091317123523 125488476039131 1296062772061875 13331230899395659
loop(\(x,i).(4x + loop(\(x,i).(10x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021384: 1 18 225 2470 25701 261378 2632345 26400990 264329901 2644608538 26451412065 264535693110 2645444018101 26454790920498 264549319337385 2645498855426830
loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021094: 1 18 233 2718 30549 338706 3736561 41145606 452775917 4981233114 54796358409 602771123214 6630527086405 72935976891042 802296461596577 8825263940808342
loop(\(x,i).(4x + loop(\(x,i).(3x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A017065: 1 18 235 2760 31141 345918 3819295 42071220 463025881 5094274218 56041033555 616467614880 6781209278221 74593565712918 820530282235015 9025837356505740
(loop(\(x,i).((4x + 3) + loop(\(x,i).3x,(2 * i),1)),x,1) div loop(\(x,i).4x,x,1))
A108870: 1 4 9 20 46 103 233 525 1182 2660 5985 13467 30301 68178 153401 345152
(loop(\(x,i).7x,x,1) + loop(\(x,i).5x,x,1) + loop(\(x,i).4x,x,1))
A074562: 3 16 90 532 3282 20956 137370 918052 6220962 42568876 293289450 2030349172 14102205042 98176822396 684595023930 4779152829892
loop(\(x,i).(5x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),x,1)
A016301: 1 18 237 2810 31941 356538 3947917 43557210 479780181 5280836858 58105480797 639241667610 7032065242021 77354752161978 850912446296877 9360087771874010
loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A021144: 1 18 227 2520 26481 271278 2745247 27615060 276964061 2773708938 27757433067 277676053200 2777269152841 27775234648998 277765062125687 2777714199500940
loop(\(x,i).(5x + loop(\(x,i).(3x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A017916: 1 18 229 2562 27061 278058 2818549 28377522 284741941 2852272698 28547052469 285592329282 2856532847221 28568377838538 285699029999989 2857066572421842
loop(\(x,i).(10x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A018090: 1 22 337 4450 54301 631462 7111417 78287530 847442101 9055541902 95785566097 1004927161810 10472915657101 108541954516342 1119734731454377 11506184005511290
loop(\(x,i).(11x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A016322: 1 22 345 4730 60461 740982 8834065 103324210 1191912021 13609144142 154183593785 1736366607690 19463156373181 217362833310502 2420404185281505 26889163207923170
loop(\(x,i).(11x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021054: 1 17 212 2422 26943 297339 3273754 36020624 396255365 4358895541 47948112576 527430027306 5801732675467 63819066571823 702009753747878 7722107355665668
(loop(\(x,i).loop(\(x,i).x2,(x + ~1),(if x <= 0 then 1 else x5)),1,(x + 1)) div (x2 + 2x + 1))
A008972: 1 256 387420489 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(9x + ~2)),(x + 1))
A138918: 1 3 4 5 6 10 11 13 14 15 20 24 25 26 28 29
((~1 + (loop(\(x,i).2x,loop(\(x,i).(x div (1 + (x mod 2))),x,x),1) + loop(\(x,i).2x,x,1)) - (x mod 2)) mod (x + 1))
A318841: 0 1 1 3 1 4 1 7 7 6 1 10 1 8 7 15
loop(\(x,i).(if x <= 0 then 1 else (loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,x) * (~1 + (2 * (x mod 2))))),1,(x + ~1))
A158500: 1 1 1 ~4 15 ~56 210 ~792 3003 ~11440 43758 ~167960 646646 ~2496144 9657700 ~37442160
(loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1) + loop(\(x,i).7x,x,1))
A074552: 3 15 83 495 3107 20175 134003 903855 6161987 42326415 292299923 2026332015 14085959267 98111307855 684331371443 4778093436975
loop(\(x,i).x5,1,loop(\(x,i).(x * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i))),x,1))
A342455: 1 32 7776 24300000 408410100000 65774855015100000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).3x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1),1,i)),x,1)
A130665: 1 4 7 16 19 28 37 64 67 76 85 112 121 148 175 256
((1 + loop(\(x,i).2x,x,2) - loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x div 2),(1 + (x mod 2)))) div 2)
A164991: 1 1 3 6 13 26 54 108 221 442 898 1796 3634 7268 14668 29336
(loop(\(x,i).5x,(x + ~1),loop(\(x,i).2x,x,(1 + loop(\(x,i).10x,x,1)))) div 2)
A163449: 1 11 1010 100100 10001000 1000010000 100000100000 10000001000000 1000000010000000 100000000100000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((3 * (1 + ((loop(\(x,i).2x,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1) div 2) mod 5))) div 2)
A245093: 1 1 3 1 3 4 1 3 4 7 1 3 4 7 6 1
(6 + (loop(\(x,i).2x,(x + ~1),2) + loop(\(x,i).(2x + 2),x,1) + loop(\(x,i).3x,x,1)))
A271743: 10 15 29 63 149 375 989 2703 7589 21735 63149 185343 547829 1627095 4848509 14479983
(loop(\(x,i).8x,(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1))),3) div 2)
A059154: 12 96 12 768 12 96 12 6144 12 96 12 768 12 96 12 49152
(~2 + loop(\(x,i).((x2 + 5x) div 2),1,loop(\(x,i).2x,x,1)) - loop(\(x,i).(3x + 1),x,1))
A134018: 0 1 3 10 45 226 1113 5230 23565 102826 438273 1836550 7601685 31183426 127084233 515429470
(~2 + loop(\(x,i).(x2 + 2x),1,compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1))))
A124659: 13 33 141 321 897 1761 3597 5181 10401 11661 19041 22497 32397 36861 39201 51981
(2 * loop(\(x,i).(x2 + 2x),1,compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1))))
A071142: 30 70 286 646 1798 3526 7198 10366 20806 23326 38086 44998 64798 73726 78406 103966
(loop(\(x,i).(x2 + 2x),1,compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1))) div 2)
A120876: 7 17 71 161 449 881 1799 2591 5201 5831 9521 11249 16199 18431 19601 25991
(2 + ((x + ~1) * (x + (if x <= 0 then 1 else loop(\(x,i).((x * (1 + loop(\(x,i).(x * i),x,1) - (x mod 2))) div 2),1,(x + ~1))))))
A169982: 1 2 4 14 41 222
((3 * (if (x mod 2) <= 0 then (5 * ((2 - ((x div 2) mod 2)) * (if x <= 0 then 1 else 2))) else 1)) - (if x <= 0 then 1 else 2))
A040868: 29 1 28 1 58 1 28 1 58 1 28 1 58 1 28 1
(loop(\(x,i).3x,x,(loop(\(x,i).((x + (x div 2)) * (x div 2)),1,loop(\(x,i).3x,x,3)) div 2)) div 2)
A227524: 1 39 1170 32670 891891 24169509 653373540 17648258940 476567558181 12867905191779 347438670325110 9380891170278810 253284485241566871 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).x2,1,compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1))) div 2) div 2)
A117849: 2 6 30 72 210 420 870 1260 2550 2862 4692 5550 8010 9120 9702 12882
(loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) + loop(\(x,i).((x + 1) * (x + i)),2,2))
A138693: 114 119 135 159 231 279 399 471 639 951 1071 1479 1791 1959 2319 2919
(if x <= 0 then 1 else (2 * (2 + loop(\(x,i).(1 + (if x <= 0 then 1 else (10x + 21))),(x div 2),(x mod 2)))))
A250256: 1 6 8 68 88 688 888 6888 8888 68888 88888 688888 888888 6888888 8888888 68888888
(if x <= 0 then 0 else (loop(\(x,i).2x,(x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))),1) mod 4))
A105661: 0 1 1 2 1 2 1 0 0 2 1 0 1 2 0 0
(2 + compr(\x.(~1 + ((1 + (if (1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 2 else 1)),x,x)) <= 0 then 1 else x)) mod 5)),x))
A045372: 2 7 11 17 31 37 41 47 61 67 71 97 101 107 127 131
loop(\(x,i).loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),x,2),1,(5x + 2))
A140762: 30 9699690 304250263527210 4611686018427387903 4611686018427387903 4611686018427387903
(2 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(2x2 + 8x + 1)),x))
A091271: 2 4 5 9 10 14 16 19 21 24 26 31 35 39 40 45
((x * (loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),(x div 2),(1 + (x mod 2))) + loop(\(x,i).2x,x,1))) div 2)
A230137: 0 2 6 18 44 110 252 588 1304 2934 6380 14036 30120 65260 138712 297240
loop(\(x,i).(x + loop(\(x,i).10x,x,1)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A088805: 102 1003 100005 10000007 100000000011 10000000000013 100000000000000017 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(~x + loop(\(x,i).10x,x,1)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A088736: 98 997 99995 9999993 99999999989 9999999999987 99999999999999983 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x3 + loop(\(x,i).3x,x,1)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A097059: 17 54 368 2530 178478 1596520 129145076 1162268326 94143190994 68630377389272 617673396313738 450283905891048016 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.(x - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x + ~2),x)),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A201363: 2 3 7
A055003: 2 3 7 13 29 37 53 61 79 107 113 151 173 181 199 239
compr(\x.(x - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),x)),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A006450: 3 5 11 17 31 41 59 67 83 109 127 157 179 191 211 241
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(if (x + ~10) <= 0 then x else (x + 2)))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A283225: 2 3 5 7 11 13 17 19 23 29 31 43 47 53 59 61
((~2x + ~1) + loop(\(x,i).2x,(if (loop(\(x,i).2x2,2x,2) div 2) <= 0 then 1 else (4x + 1)),2))
A224451: 3 61 1019 4611686018427387903 4611686018427387903
((if (x mod 3) <= 0 then (3 * (if (x mod 2) <= 0 then (7 * (if x <= 0 then 1 else 2)) else 1)) else 1) + (x mod 2))
A040434: 21 2 1 4 1 2 42 2 1 4 1 2 42 2 1 4
((if (x mod 3) <= 0 then (5 * (if (x mod 2) <= 0 then (5 * (if x <= 0 then 1 else 2)) else 1)) else 2) - (x mod 2))
A040634: 25 1 2 4 2 1 50 1 2 4 2 1 50 1 2 4
((if (x mod 3) <= 0 then (3 * (if (x mod 2) <= 0 then (5 * (2 + (if x <= 0 then 0 else 2))) else 1)) else 2) - (x mod 2))
A040912: 30 1 2 2 2 1 60 1 2 2 2 1 60 1 2 2
((if (x mod 3) <= 0 then ((1 + (2 * (if (x mod 2) <= 0 then 6 else 1))) * (if x <= 0 then 1 else 2)) else 1) * (2 - (x mod 2)))
A040685: 26 1 2 6 2 1 52 1 2 6 2 1 52 1 2 6
compr(\x.(~1 + loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(12x + 6))),x)
A010375: 0 1 3 4 5 9
A139531: 0 1 3 4 5 9 10 11 14 16 18 21 23 24 25 26
compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(12x + 5)),x)
A139529: 0 1 2 4 6 7 9 11 14 15 16 17 22 25 27 29
compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(16x + 7)),x)
A105135: 0 3 7 10 12 13 18 27 30 31 37 40 42 46 48 55
(x + ((1 + ((x + 1) * loop(\(x,i).2x,x,(if x <= 0 then 1 else loop(\(x,i).((x2 + ~x) div 2),3,x))))) div 3))
A327129: 0 1 2 35 2804
((x + 1) + ((x + ((loop(\(x,i).(x + loop(\(x,i).(loop(\(x,i).(x + (i * i)),x,0) mod (x + 1)),1,i)),x,0) div 2) div 2)) div 2))
A022301: 1 2 4 6 7 9 10 12 15 17 18 20 21 24 27 29
compr(\x.loop(\(x,i).(2 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(4x + ~1))),1,(2x + 1)),x)
A105134: 2 4 5 8 14 17 19 25 28 32 35 37 38 47 50 53
(if x <= 0 then 17 else (x * loop(\(x,i).x3,1,loop(\(x,i).x3,2,(2x + 1)))))
A271562: 17 7625597484987 4611686018427387903
(2 - (if (x mod 9) <= 0 then 1 else (x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1)))))
A330261: 1 0 1 ~1 1 0 1 ~2 1 1 1 ~1 1 0 1 ~3
compr(\x.(1 - loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(8x + 6))),x)
A153264: 0 3 5 6 8 9 10 12 15 17 18 19 20 21 24 25
(if x <= 0 then 1 else (x - loop(\(x,i).(x - ((1 + (x mod (1 + (2 * (if (x mod 2) <= 0 then 1 else (x div 4)))))) div 3)),2,x)))
A343873-A054923: 1 0 1 0 0 1 0 0 1 2 0 0 0 2 3 0
(4x * ((1 + (loop(\(x,i).(x * i),(x + ~1),loop(\(x,i).loop(\(x,i).(~2 + i),((x + i) div 2),1),x,1)) div 2)) div 2))
A052521: 0 0 0 0 0 0 720 10080 120960 1451520 18144000 239500800 3353011200 49816166400 784604620800 13076743680000
compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(15x + 4)),x)
A158614: 0 1 2 3 4 6 8 9 10 13 14 15 16 17 21 23
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (1 - (if ((x + 1) mod 12) <= 0 then 2 else 0)))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A226159: 2 3 5 7 11 13 17 19 23 29 31 ~37 41 43 47 53
(loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x div 2),(1 + (2 * (x mod 2)))) + loop(\(x,i).(2x + 1),x,0))
A231407: 1 4 6
A261682: 1 4 6 16 25 61 98 232 381 889 1485 3433 5811 13339 22818 52072
(~1 + loop(\(x,i).10x,x,(1 - loop(\(x,i).(10x + ~60),x,0))))
A246880: 0 609 66099 6660999 666609999 66666099999 6666660999999 666666609999999 66666666099999999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x - (((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1)))
A049820: 0 0 1 1 3 2 5 4 6 6 9 6 11 10 11 11
(((2 * (4 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1))
A177876: 2 3 3 4
A334954: 2 3 3 4 3 5 3 5 4 5 3 7 3 5 5 6
(1 + loop(\(x,i).(x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))),1,(x - (if x <= 0 then 0 else 1))))
A323436: 1 1 1 1 2 1 2 1 3 2 2 1 3 1 2 2
(1 + ((~1 + loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))) mod 9))
A166923: 4 9 7 4 4 7 1 1 7 4 7 1 7 4 4 1
((x + 1) div (1 + ((1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)) * (1 + (x div 8)))))
A324120: 0 0 0 1 0 2 0 2 1 2 0 2 0 2 2 3
(~1 + ((loop(\(x,i).x2,1,(~3 + loop(\(x,i).10x,(x + 1),1))) div 2) div 5))
A332193: 3 939 99399 9993999 999939999 99999399999 9999993999999 999999939999999 99999999399999999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x - (2 mod (~1 - (x div 5)))))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A233393-A233265: 2 3 5 7 11 13 17 19 23 29 37 41 43 47 53 61
(1 + (3 * loop(\(x,i).(10x + 4),x,loop(\(x,i).(10x + 10),x,0))))
A332131: 1 313 33133 3331333 333313333 33333133333 3333331333333 333333313333333 33333333133333333 3333333331333333333 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (3 * loop(\(x,i).10x,x,loop(\(x,i).(10x + 21),x,1))))
A332192: 2 929 99299 9992999 999929999 99999299999 9999992999999 999999929999999 99999999299999999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (3 * loop(\(x,i).(10x + 4),x,loop(\(x,i).(10x + 1),x,1))))
A332134: 4 343 33433 3334333 333343333 33333433333 3333334333333 333333343333333 33333333433333333 3333333334333333333 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 2 else ((x + 1) - ((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3)))
A059292: 2 2 3 3 5 4 7 6 8 8 11 8 13 12 13 13
((x + 1) div (if x <= 0 then 1 else (~1 + (6 * (1 + (((x + (if (~2 + (x div 4)) <= 0 then 1 else 2)) div 2) mod 2))))))
A127838: 1 0 0 0 1 0 0 1 1 0 1 2 1 1 3 3
(~1 + (6 * (1 + compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(3x + 1)),x))))
A092256: 35 65 77 95 119 125 143 155 161 185 203 209 215 221 245 275
((loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x))) div 2) mod 11)
A024715: 1 2 5 7 1 4 0 2 7 2 4 0 4 7 2 1
(1 + ((2 * compr(\x.(1 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x2 + 2x))),x)) div 3))
A232011: 1 3 5 7 11 13 15 19 27 33 35 37 39 41 49 57
(2 div (if x <= 0 then 2 else (1 + ((x + loop(\(x,i).((x + ~1) + (2x mod (2 - (x mod ~4)))),2,x)) mod 3))))
A035169: 1 0 1 1 2 0 1 0 1 0 2 1 0 0 2 1
(~1 + loop(\(x,i).(10x + ~5),(2x + 1),1) - loop(\(x,i).10x,x,1))
A332143: 3 434 44344 4443444 444434444 44444344444 4444443444444 444444434444444 44444444344444444 4444444443444444444 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (loop(\(x,i).(10x + ~1),(2x + 1),1) + loop(\(x,i).10x,x,1)))
A332189: 9 898 88988 8889888 888898888 88888988888 8888889888888 888888898888888 88888888988888888 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + loop(\(x,i).(10x + ~1),(2x + 1),1) - loop(\(x,i).10x,x,1))
A332187: 7 878 88788 8887888 888878888 88888788888 8888887888888 888888878888888 88888888788888888 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + loop(\(x,i).(10x + 12),2x,2) - loop(\(x,i).10x,x,1))
A332132: 2 323 33233 3332333 333323333 33333233333 3333332333333 333333323333333 33333333233333333 3333333332333333333 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.(1 - (((loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(2x + 1)) mod (x + 1)) div 2) mod 3)),(x + 1)))
A174166: 4 6 9 10 12 15 16 21 22 24 27 30 34 36 40 42
loop(\(x,i).(x * loop(\(x,i).(2 * (((2x * ((1 + (2 * i)) * (~1 + (2 * i)))) div (1 + i)) * i)),i,1)),(x + ~1),1)
A107252: 1 1 6 1440 36288000 184354652160000 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,((x + 1) div (2 + ((x div 2) div (1 + (2 mod (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1)))))),1)
A295557: 1 2 2 2 2 8 2 2 2 8 2 16 2 8 8 2
(~1 + (2 * loop(\(x,i).x2,1,(1 + ((x + 1) * loop(\(x,i).(7x2 + x + ~6),2,2))))))
A157081: 32821201 131252401 295293601 524944801 820206001 1181077201 1607558401 2099649601 2657350801 3280662001 3969583201 4724114401 5544255601 6430006801 7381368001 8398339201
(~1 + (2 * loop(\(x,i).x2,1,(~1 + ((x + 1) * loop(\(x,i).(7x2 + x + ~6),2,2))))))
A157080: 32788801 131187601 295196401 524815201 820044001 1180882801 1607331601 2099390401 2657059201 3280338001 3969226801 4723725601 5543834401 6429553201 7380882001 8397820801
(1 + ((1 + (if (x + ~1) <= 0 then x else (2 * (1 + ((1 + (if ((x + 1) mod (3 - (x mod 2))) <= 0 then x else 1)) div 2))))) div 2))
A322809: 1 2 3 4 3 5 3 6 6 7 3 8 3 9 9 10
((x + 1) div (~1 + (2 * (1 + ((1 + (((~1 + loop(\(x,i).2x,x,(if (x mod 2) <= 0 then 2 else 0))) mod (x + 1)) div 2)) div 2)))))
A126773: 1 2 3 1 5 2 7 1 1 2 11 1 13 2 3 1
(loop(\(x,i).2x,x,1) mod (2 - loop(\(x,i).((x3 + ~1) - (2 * ((2x + 1) mod 5))),2,1)))
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A036161: 1 2 4 8 16 32 64 128 29 58 116 5 10 20 40 80
(1 + ((1 + (((~1 + loop(\(x,i).2x,x,(1 + (if (x mod 3) <= 0 then 2 else 0) - (x mod 2)))) mod (x + 1)) div 2)) div 2))
A304486: 1 1 1 2 1 2 2 3 2 2 1 4 2 4 2 5
(1 + (((1 + (if x <= 0 then 0 else (if (x mod (1 + (x mod 6))) <= 0 then 2 else 1))) * (1 + (((x + 1) div 2) div 2))) div 2))
A132073: 1 2 2 3 3 3 4 4 4 4 5 5 7 5 5 6
(1 + (2 * (1 + (4 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,8x)),x)))))
A252802: 3 11 19
A294912-A007520: 3 11 19 43 59 67 83 107 131 139 163 179 211 227 251 283
(1 + (2 * (1 + (4 * compr(\x.(1 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,8x)),x)))))
A294993: 11 19 43 59 67 83 107 131 139 163 179 211 227 251 283 307
(7 * loop(\(x,i).10x,x,loop(\(x,i).(10x + 10),x,0)))
A093270: 0 700 77000 7770000 777700000 77777000000 7777770000000 777777700000000 77777777000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 div ((1 + ((loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) + loop(\(x,i).2x,x,2)) div 2)) mod 7))
A035147: 1 0 0 1 0 0 0 0 1 0 2 0 2 0 0 1
((loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x))) div 3) mod 7)
A024714: 1 2 5 0 5 1 1 0 5 1 0 0 1 5 5 1
((loop(\(x,i).(x * loop(\(x,i).x2,2,x5)),1,x2) div 3) div 7)
A108496: 0 0 209430786243 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((if ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) <= 0 then (if x <= 0 then 1 else 0) else 2x) mod 7)
A259784: 1 0 0 0 1 0 0 0 2 0 0 1 3 5 0 0
(1 + (2 * (1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(4x + 1))),x)))))
A186300: 3 7 15 19 27 31 51 55 75 79 87 91 99 115 135 139
((x + ~1) - (2 * loop(\(x,i).2x,(x + ~1),(~1 - ((x + loop(\(x,i).(3x + ~1),2x,1)) div 2)))))
A131655: 1 8 89 1482
(1 + (2 * (1 + compr(\x.(loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x) + (x mod 7)),x))))
A045437: 3 17 31 59 73 101 157 199 227 241 269 283 311 353 367 409
(1 + (2 * (1 + compr(\x.(loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x) + (x mod 10)),x))))
A105854: 3 23 43 83 103 163 223 263 283 383 443 463 503 523 563 643
(1 + (2 * (1 + compr(\x.(loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x) + ((x + 1) mod 6)),x))))
A141122: 13 37 61 73 97 109 157 181 193 229 241 277 313 337
A068228: 13 37 61 73 97 109 157 181 193 229 241 277 313 337 349 373
(~1 + (2 * (~1 + compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(5x + ~2))),x))))
A111230: 1 3 9 13 15 19 25 27 33 37 43 45 51 67 69 73
(1 + (((loop(\(x,i).2x,x,1) - loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x + ~1),1)) mod (x + 1)) div 2))
A318362: 1 1 1 2 1 2 1 3 3 2 1 5 1 2 3 5
(1 + ((x + 1) div (2 + ((~1 + loop(\(x,i).2x,x,loop(\(x,i).2x,((x mod (1 + (x div 2))) div 2),2))) mod (x + 1)))))
A338170: 1 1 2 1 2 3 2 1 2 2 2 3 2 3 4 1
(~1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(5x + 2))),(x + 1))))
A111226: 1 5 7 11 17 19 23 25 29 31 37 43 49 53 59 61
(0 + (loop(\(x,i).5x,x,1) + (((x + ~1) * loop(\(x,i).5x,(x + ~2),x)) div 2)))
A081911: 1 5 26 140 775 4375 25000 143750 828125 4765625 27343750 156250000 888671875 5029296875 28320312500 158691406250
(1 + (2 * ((1 + ((1 + loop(\(x,i).2x,x,(1 + (x * (~1 + loop(\(x,i).(x * i),2x,1)))))) div 3)) div 2)))
A295169: 1 3 65 5757
(~1 + (2 * (9 + (loop(\(x,i).2x,(x div 2),(2 + (x mod 2))) + loop(\(x,i).2x,x,2)))))
A184042: 25 31 41 61 97 169 305 577 1105 2161 4241 8401 16657 33169 66065 131857
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,((2x + 1) div (3 + (x div 4))))
A005145: 2 3 3 5 5 5 7 7 7 7 11 11 11 11 11 13
((loop(\(x,i).(x2 + x),1,(1 + loop(\(x,i).10x,(x + 1),1))) div 3) div 5)
A332168: 8 686 66866 6668666 666686666 66666866666 6666668666666 666666686666666 66666666866666666 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).(x2 + ~x),1,(~1 + loop(\(x,i).10x,(x + 1),1))) div 3) div 5)
A332164: 4 646 66466 6664666 666646666 66666466666 6666664666666 666666646666666 66666666466666666 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(10x + 1),2x,1) + loop(\(x,i).10x,x,5))
A332116: 6 161 11611 1116111 111161111 11111611111 1111116111111 111111161111111 11111111611111111 1111111116111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(10x + 2),2x,2) + loop(\(x,i).10x,x,5))
A332127: 7 272 22722 2227222 222272222 22222722222 2222227222222 222222272222222 22222222722222222 2222222227222222222 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x div (1 + ((((x + 2) + (loop(\(x,i).(2x + (if (i mod 3) <= 0 then 3 else 0)),x,0) mod (x + 1))) div 2) div 2)))
A206829: 0 1 1 1 2 2 1 1 2 1 1 2 3 1 2 1
(1 + ((if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2)))) div (2 + (x mod 2))))
A076984: 1 1 2 2 2 3 2 3 3 3 2 5 2 3 4 4
((if (x mod 4) <= 0 then 29 else 1) * (if x <= 0 then 1 else 2) * (1 + (2 * (x mod 2))))
A040820: 29 6 2 6 58 6 2 6 58 6 2 6 58 6 2 6
(3 * loop(\(x,i).(10x + 2),x,(1 - loop(\(x,i).(10x + ~20),x,0))))
A332163: 3 636 66366 6663666 666636666 66666366666 6666663666666 666666636666666 66666666366666666 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((1 + (((x + 1) * loop(\(x,i).2x,(x + ~1),loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))) div 3)) mod 3)
A249223: 1 1 1 0 1 1 1 0 1 1 2 1 0 0 1 1
(if (x + ~2) <= 0 then 1 else (loop(\(x,i).4x,((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2),1) div 3))
A180977: 1 1 1 0 1 0 0 1 1 0 0 1 5 1 0 0
(((1 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 2))) div 3) div 3)
A257121: 0 1 2 3 4 6 8 11 12 15 16 20 21 22 25 26
(3 * ((loop(\(x,i).(2x2 + ~x),1,(~1 + loop(\(x,i).10x,x,1))) div 2) div 3))
A093275: 0 75 9750 997500 99975000 9999750000 999997500000 99999975000000 9999999750000000 999999997500000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(3 + (x mod 2) - (if (x mod 3) <= 0 then ((if (x mod (1 + (4 * (x mod 2)))) <= 0 then 1 else 0) - (x mod 2)) else 1))
A217607: 2 3 2 5 2 3 2 3 2 5 2 3 2 3 2 4
(3 * (loop(\(x,i).(10x + 2),2x,2) + loop(\(x,i).10x,x,1)))
A332169: 9 696 66966 6669666 666696666 66666966666 6666669666666 666666696666666 66666666966666666 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(x + ((x div (3 + (if (x + ~4) <= 0 then 0 else 2))) + (if x <= 0 then 1 else 4x) + ((x + 1) div 3)))
A314216: 1 5 11 17 22 28 33 38 44 49 55 61 66 71 77 83
(6 * loop(\(x,i).(10x + 1),x,loop(\(x,i).(10x + 10),x,0)))
A332160: 0 606 66066 6660666 666606666 66666066666 6666660666666 666666606666666 66666666066666666 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((2 * (if x <= 0 then 2 else (1 + (if (2x mod (4 + (x div 4))) <= 0 then ((x + 2) div 3) else 0)))) div 3)
A130207: 1 0 1 0 0 2 0 0 0 2 0 0 0 0 4 0
((~2 + (if x <= 0 then 2 else (1 + ((2 * (1 + ((2 * (2 + loop(\(x,i).(x * i),x,1))) div 3))) div 3)))) mod 3)
A326786: 0 1 1 0 2 2 2 2 1 0 0 0 0 0 0 0
((2 * (1 + ((1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (1 + (((x + 1) div 2) div 2)))) div 2))) div 3)
A229878: 0 0 1 0 1 2
A238158: 0 0 1 0 1 2 0 2 2 4 0 2 3 4 6 0
((2 * (1 + ((1 + loop(\(x,i).(2x + loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),i,1)),x,1)) div 2))) div 3)
A139627: 1 1 2 4 12 37 162
((if x <= 0 then 1 else 2x) - ((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3))
A286002: 1 2 4 5 8 8 12 12 15 16 20 18 24 24 26 27
(((1 + (loop(\(x,i).(1 + (loop(\(x,i).(x * i),x,(5x + 1)) div 2)),1,(x + 2)) div 2)) div 2) div 3)
A141052: 1 4 21 130 930 7560 68880 695520 7711200 93139200 1217462400 17124307200 257902444800 4140968832000 70614415872000 1274546617344000
(22 + (loop(\(x,i).2x,(x div 2),(2 + (x mod 2))) + loop(\(x,i).2x,x,1)))
A183982: 25 27 30 36 46 66 102 174 310 582 1110 2166 4246 8406 16662 33174
((if x <= 0 then 0 else ((x + 2) - (loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) mod (2x + ~1)))) mod 3)
A059018: 0 0 2 2 0 1 2 0 2 2 0 0 2 0 1 2
(3 + (2 * compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),(7x + 1))))
A031394: 5 29 59 89 127 163 197 239 277 317 367 409 449 491 547 593
(3 + (2 * (1 + compr(\x.(2 - ((~1 + loop(\(x,i).2x,x,(if (x mod 4) <= 0 then 2 else (x mod 2)))) mod (x + 1))),x))))
A075824: 9 11 17 19 21 25 27 33 35 39 41 43 45 49 51 53
((((loop(\(x,i).(x * (x - i)),2,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 2) div 2) div 3)
A262248: 0 0 5 35 330 715 2380 3876 8855 23751 31465 66045 101270 123410 178365 292825
(26 + loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A138689: 30 35 51 75 147 195 315 387 555 867 987 1395 1707 1875 2235 2835
(((x + (if x <= 0 then 1 else (if (16 mod (x + 1)) <= 0 then 8 else 1))) mod 8) mod 3)
A280634: 1 1 0 0 2 0 1 1 1 2 0 1 2 0 1 1
(((loop(\(x,i).(x * (x2 div 2)),1,(2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) div 2) div 2) div 3)
A127922: 1 5 14 55 91 204 285 506 1015 1240 2109 2870 3311 4324 6201 8555
((loop(\(x,i).(x2 * (x2 div 2)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 3)
A138422: 1 6 50 196 1210 2366 6936 10830 23276 58870 76880 156066 235340 284746 406456 657306
(12x + (loop(\(x,i).7x,x,1) + loop(\(x,i).5x,x,1)))
A121199: 2 24 98 504 3074 19992 133346 901752 6155522 42306840 292240994 2026155000 14085427970 98109713688 684326588642 4778079088248
(12x + loop(\(x,i).7x,x,1) - loop(\(x,i).5x,x,1))
A121202: 0 14 48 254 1824 13742 102096 745502 5374272 38400590 272709744 1928498750 13597146720 95668307438 672119557392 4717043931998
(3 * (loop(\(x,i).(10x + 1),2x,1) + loop(\(x,i).10x,x,2)))
A332139: 9 393 33933 3339333 333393333 33333933333 3333339333333 333333393333333 33333333933333333 3333333339333333333 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(10x + 1),2x,1) + (3 * loop(\(x,i).10x,x,2)))
A332117: 7 171 11711 1117111 111171111 11111711111 1111117111111 111111171111111 11111111711111111 1111111117111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(10x + 2),2x,2) + (3 * loop(\(x,i).10x,x,2)))
A332128: 8 282 22822 2228222 222282222 22222822222 2222228222222 222222282222222 22222222822222222 2222222228222222222 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).(x5 + ~x3),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 3)
A138433: 8 72 1000 5488 53240 123032 471648 823080 2141392 6828920 9533120 23097768 38595760 48976312 76413728 139348872
(loop(\(x,i).(x5 + ~x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 3)
A138425: 10 80 1040 5600 53680 123760 473280 825360 2145440 6837040 9543040 23114640 38618720 49002800 76448320 139398480
(loop(\(x,i).(x * (x4 div 2)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 3)
A138427: 5 40 520 2800 26840 61880 236640 412680 1072720 3418520 4771520 11557320 19309360 24501400 38224160 69699240
(compr(\x.(1 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(8x2 + 8x))),x) div 3)
A201541: 0 1 2 3 8 11 12 16 22 23 38 43 47 51 53 67
((compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 3)
A137264: 1 2 2 1 2 1 2 1 0 2 0 1 2 1 0 0
(1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(9x + 1))),x)))
A024909: 1 3 5 7 13 15 17 19 27 29 33 35 39 43 45 47
(1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x2 + 2x + 5))),x)))
A114275: 1 5 7 13 19 23 29 35 37 41 43 47 55 61 85 89
(~1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(7x + ~3))),x)))
A024902: 1 7 9 15 19 21 25 27 37 39 49 55 61 69 79 81
(~1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(7x + ~1))),x)))
A111249: 3 5 9 15 17 27 29 33 39 47 53 59 63 65 69 77
(~1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(7x + ~2))),x)))
A024900: 1 5 11 13 19 23 25 31 35 41 43 49 59 61 65 71
(1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(7x + 1))),x)))
A024901: 1 3 7 9 13 15 19 25 33 37 39 45 55 57 63 67
(~1 + loop(\(x,i).(10x + ~1),(2x + 1),1) - loop(\(x,i).10x,x,2))
A332186: 6 868 88688 8886888 888868888 88888688888 8888886888888 888888868888888 88888888688888888 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + (2 * (compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A100803: 1 3 3 7 3 7 3 7 11 3 11 7 3 7 11 11
loop(\(x,i).(1 + (if x <= 0 then 1 else 2x) - ((1 + ((32 mod (x + 1)) div 2)) div 2)),2x,1)
A147597: 1 7 31 119 455 1799 7175 28679 114695 458759 1835015 7340039 29360135 117440519 469762055 1879048199
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x - (x2 div ((2x + ~1) + (x div 2)))))
A079953: 2 2 3 5 7 7 11 11 13 17 17 19 23 23 29 29
compr(\x.(~1 + ((if (x mod 2) <= 0 then 2 else (1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))) mod 3)),(2x + 1))
A233388: 11 19 35 47 59 67 79 91 107 115 131 143 155 171 179 191
((if x <= 0 then 1 else (2 * (1 + (((~1 + loop(\(x,i).2x,x,(x - ((x div 2) mod 2)))) mod (x + 1)) div 2)))) div (1 + (x mod 2)))
A293484-A000010: 1 1 2 2 4 2 6 4 6 4 10 4 12 6 8 8
(1 + compr(\x.(~1 + (x mod (1 + ((~1 + loop(\(x,i).2x,x,(1 - loop(\(x,i).(2 * (x - (i mod 2))),x,0)))) mod (x + 1))))),x))
A325100: 1 2 3 5 6 7 11 13 14 17 19 21 23 26 29 31
(1 + loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x + (x div 13))))
A214583: 3 4 6 8 12 14 18 20 24 30 32 38 42 48 54 60
(~1 + compr(\x.(1 - (x mod (1 + ((~1 + (3 * (if (x mod 2) <= 0 then (2 * (2 + (if x <= 0 then 0 else 2))) else 1))) mod (x + 1))))),x))
A231407: 1 4 6
A286494: 1 4 6 7 10 11 12 13 15 16 17 18 19 22 24 25
(1 + compr(\x.(1 - (((x + 1) - ((loop(\(x,i).2x,(if (x mod 3) <= 0 then x else 1),2) mod (x + 1)) div 2)) mod 3)),x))
A231408: 1 2 4 6 9
A288623: 1 2 4 6 9 10 12 15 16 18 21 22 24 25 27 28
(1 + compr(\x.(1 - (((loop(\(x,i).(x * (x div 2)),1,loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))) div 2) div 2) mod 3)),x))
A028786: 5 7 10 11 13 14 15 17 20 21 22 26 28 29 30 31
loop(\(x,i).(7x + loop(\(x,i).(49x + 1),i,1)),x,1)
A022231: 1 57 2850 140050 6865251 336416907 16484565700 807744680100 39579496050501 1939395353553757 95030372653688550 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.(loop(\(x,i).((x + 1) * (2 + ((x + 1) * loop(\(x,i).(2x2 + x),2,2)))),2,3) mod (x + 1)),x))
A185092: 1 2 3 4 6 12
A018765: 1 2 3 4 6 12 83 166 249 332 498 996
((17x + (x div 2)) mod (1 + loop(\(x,i).loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)),2,x)))
A101979: 0 1 1 0 2 1 1 0 2 1 3 0 2 1 1 0
((1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (1 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)))
A083553: 2 8 24 60 120 192 288 396 616 840 1080 1440 1680 1932 2392 3016
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (1 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)))
A037166: 4 12 30 70 132 208 306 418 644 870 1116 1480 1722 1978 2444 3074
((x + 1) + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A123128: 2 4 5 8 7 10 9 12 15 12 17 16 15 18 21 22
((2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)) * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A037167: 3 10 28 66 130 204 304 414 638 868 1110 1476 1720 1974 2438 3068
((x3 + 3x2 + 3x + 1) * loop(\(x,i).x2,2,loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1)))
A186419: 1 8 432 40000 4802000 672126336 104133351168 17341997916672 3048398071290000 558804401233936000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(2x + (((1 + ((if x <= 0 then 1 else (3 * ((x + 1) + (x div 8)))) div 2)) div 2) mod 2)),x,1)
A222011: 1 2 4 8
A160686: 1 2 4 8 16 32 64
A117302: 1 2 4 8 16 32 64 129 258 516 1032 2064 4128 8256 16513 33026
((0 - loop(\(x,i).x2,1,(1 + (x mod (1 + (x div (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))))))) mod (x + 1))
A326186: 0 1 2 0 4 5 6 0 0 9 10 8 12 13 14 0
((x + 1) * (1 + ((if x <= 0 then 1 else x) div (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))))))
A129598: 2 4 9 8 25 18 49 16 27 50 121 36 169 98 75 32
((1 + loop(\(x,i).(x * (x div 2)),1,((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3))) mod (x + 1))
A318577: 0 1 1 1 1 1 1 3 1 1 1 4 1 1 1 11
((x mod 8) mod (if x <= 0 then 2 else (loop(\(x,i).x3,2,19) mod (x + 1))))
A165072: 0 0 0 0 0 0 0 1 0 1 2 3 4 5 2 1
((1 + (3 * ((x * (x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1)))) div 2))) div (x + 1))
A340785: 1 2 1 3 1 2 1 5 1 2 1 4 1 2 1 7
compr(\x.(~1 + ((1 + ((1 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,x)) mod 3)) mod (x + 1))),(x + 1))
A026179: 1 2 5 6 8 11 14 15 17 18 20 23 24 26 29 32
loop(\(x,i).loop(\(x,i).(10x + 11),(2x + 1),1),1,(x3 + 3x2 + 3x + 1))
A091189: 2221 222222222222222221 4611686018427387903
(((~1 + loop(\(x,i).2x,(1 + (x div (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))),1)) mod (x + 2)) mod (x + 1))
A124372: 0 1 1 3 1 1 1 6 7 1 1 2 1 1 1 12
((x + 1) * (compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A231407: 1 4 6
A141042: 1 4 6 16 10 24 14 32 54 20 66 48 26 56 90 96
(if x <= 0 then 0 else ((2x + 1) + (if x <= 0 then 1 else (2 * ((x + ~2) - ((~2x3 + 6x2 + ~4x) div 3))))))
A092679: 0 1 5 17
A174794: 0 1 5 17 45 97 181 305 477 705 997 1361 1805 2337 2965 3697
((if (~1 + (x mod 15)) <= 0 then (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) else 0) div 2)
A291551: 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 26
((1 + (compr(\x.(1 - loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1)) div 5)) div 2)
A120440: 0 1 1 2 3 4 6 7 10 11 14 15 18 19 20 23
(2 * (1 + (3 * (1 + compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(3x + 1)),x)))))
A343974: 38 68 80 98 122 128 146 158 164 188 206 212 218 224 248 278
(2 * (~1 + (3 * (2 + compr(\x.loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(3x + 1)),x)))))
A064635: 40 70 82 100 124 130 148 160 166 190 208 214 220 226 250 280
(2 * (~1 + ((x + 1) div (if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 2)))))))
A279228: 0 0 0 0 2 0 4 0 2 0 8 0 10 2 4 0
((1 + ((3 * ((loop(\(x,i).2x,x,(if ((x + (x div 2)) mod 4) <= 0 then 1 else 2)) mod (x + 1)) div 2)) div 2)) div 2)
A229878: 0 0 1 0 1 2
A326987: 0 0 1 0 1 2 1 0 2 2 1 3 1 2 3 0
(if x <= 0 then 1 else (2 * (1 + (x div (2 + ((1 + (2 * (if x <= 0 then 1 else (2 + (x mod (2 + (x div 4))))))) mod (x + 1)))))))
A179651: 1 2 2 2 4 4 2 2 4 4 2 2 4 4 2 6
((2x + 2) - (if x <= 0 then 1 else (2 * (1 + (((~1 + loop(\(x,i).2x,x,(x - ((x div 2) mod 2)))) mod (x + 1)) div 2)))))
A053196: 1 2 4 4 6 8 8 8 12 12 12 16 14 16 22 16
((x + 2) - ((x + 1) div (if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 2))))))
A244361: 1 2 3 4 4 6 5 8 8 10 7 12 8 13 13 16
(7 + loop(\(x,i).((x + 2) + (2x div (2 + (3 * (if (~2 + (x div 2)) <= 0 then 1 else 2))))),x,1))
A120166: 8 10 13 16 20 25 31 39 49 61 76 95 119 149 186 232
((1 + ((1 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2)))) mod 4)) div 2)
A074943: 1 2 2 0 2 1 2 1 0 1 2 0 2 1 1 2
(~2 + ((~2 + compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1))) mod 5))
A120439: ~1 1 2 ~2 0 2 0 2 2 ~2 ~2 0 0 2 ~2 ~2
((if ((1 + (x div 4)) mod 4) <= 0 then loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) else x) mod 10)
A103303: 0 1 2 3 4 5 6 7 8 9
A081286-A080867: 0 1 2 3 4 5 6 7 8 9 0 1 3 7 5 1
(10 + compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,10x)),x))
A108584: 10 11 12 14 15 17 18 20 21 26 27 29 32 33 36 38
(if x <= 0 then 1 else (2 * ((1 + (2 * (if x <= 0 then 2 else (4x - (((x + ~1) mod (2 + (x div 2))) div 2))))) div 3)))
A315215: 1 6 10 14 20 26 32 38 42 46 52 58 62 66 72 78
(2 + (if (x + ~1) <= 0 then x else ((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3)))
A096737: 2 3 2 3 2 4 2 4 3 4 2 6 2 4 4 5
(((2 + compr(\x.(1 - loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),(x div 2),(x2 + 4x))),(x + 1))) div 3) div 2)
A056956: 1 2 3 6 7 11 13 16 17 18 21 27 32 37 38 46
(2 * ((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3))
A062011: 2 4 4 6 4 8 4 8 6 8 4 12 4 8 8 10
(if x <= 0 then 1 else (2 * ((2 * (4 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3)))
A131089: 1 4 4 6 4 8 4 8 6 8 4 12 4 8 8 10
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,((1 + (x2 div (x - ((~x + 2) div 2)))) div 2))
A087731: 2 3 3 3 5 5 5 5 7 7 11 11 11 11 13 13
(2 * (1 + compr(\x.((x + 1) mod (1 + ((if x <= 0 then 1 else (2 - (loop(\(x,i).(2x + 2),x,0) mod (x + 1)))) mod 3))),x)))
A280270: 6 8 12 18 20 24 28 30 32 36 40 42 44 48 50 52
(2 * (~1 + compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(7x + ~3))),x)))
A101123: 0 6 8 14 18 20 24 26 36 38 48 54 60 68 78 80
((loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(3x + 1)) + loop(\(x,i).4x,x,1)) div 2)
A277924: 1 4 15 57 219 848 3302 12911 50643 199140 784626 3096514 12236830 48412432 191718188 759852347
(2 + (loop(\(x,i).(10x + 22),2x,2) + loop(\(x,i).10x,x,1)))
A332145: 5 454 44544 4445444 444454444 44444544444 4444445444444 444444454444444 44444444544444444 4444444445444444444 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((2x + 2) div (2 + loop(\(x,i).(x div (2 - (x mod 2))),x,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))))
A023506: 0 1 2 1 1 2 4 1 1 2 1 2 3 1 1 2
((if x <= 0 then 1 else (2 * (1 + (((~1 + loop(\(x,i).2x,x,(x - ((x div 2) mod 2)))) mod (x + 1)) div 2)))) * ((x + 1) div 2))
A079242: 0 2 2 8
A268342: 0 2 2 8 8 12 18 32 24 40 50 48 72 84 56 128
(2 - ((~1 + ((x div 2) mod (1 + (if (x mod 2) <= 0 then 6 else 1))) - ((x mod 2) + (x mod 2))) * (if x <= 0 then 1 else 2)))
A327951: 3 8 2 6 0 8
(x + (((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 1 else 2)))
A158907: 1 3 4 6 6 9 8 11 11 13 12 17 14 17 18 20
(3 + ((x + 1) div (2 + (((x + 1) div 2) div 2) - loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x))))
A107574: 3 4 4 5 4 5 6 5 5 6 5 7 6 5 6 7
(4 * loop(\(x,i).(10x + 2),x,(1 - loop(\(x,i).(10x + ~20),x,0))))
A332184: 4 848 88488 8884888 888848888 88888488888 8888884888888 888888848888888 88888888488888888 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~2 + (loop(\(x,i).(x * (x div 5)),1,(~3 + loop(\(x,i).10x,(x + 1),1))) div 2))
A332191: 1 919 99199 9991999 999919999 99999199999 9999991999999 999999919999999 99999999199999999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) div (if x <= 0 then 1 else (2 * (2 + (loop(\(x,i).x2,2,(x + 9)) mod 7)))))
A017838: 1 0 0 0 0 1 1 1 0 0 1 2 3 2 1 1
(2 * ((1 + (((loop(\(x,i).x3,1,loop(\(x,i).8x2,x,3)) div 2) div 2) div 2)) div 2))
A132638: 4 46656 8916100448256 4611686018427387903
(loop(\(x,i).(x2 + x),1,((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 10)) div 2)
A161625: 3 6 15 28 1 6 28 45 6 45 1 28 1 6 28 6
(if x <= 0 then 0 else (if ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) <= 0 then 1 else (2 * (2 + (x div 5)))))
A049702: 0 1 1 1 4 1 1 6 6 1 1 8 8 8 1 1
(((3 * (2 + ((loop(\(x,i).2x,x,(if ((x + (x div 2)) mod 4) <= 0 then 1 else 2)) mod (x + 1)) div 2))) div 2) div 2)
A111944: 1 1 2 1 2 3 2 1 3 3 2 4 2 3 4 1
(2 + (compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) + (4 * (if (~2 + (x div 5)) <= 0 then 0 else 2))))
A191378: 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 67
(8 * loop(\(x,i).(10x + 1),x,loop(\(x,i).(10x + 10),x,0)))
A332180: 0 808 88088 8880888 888808888 88888088888 8888880888888 888888808888888 88888888088888888 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(4 * ((1 + (((loop(\(x,i).(x2 + 2x + ~2),1,loop(\(x,i).(2x + (i mod 2)),x,0)) div 2) div 2) div 2)) div 2))
A241893: 0 0 0 8 28 120 460 1848 7308 29240 116620 466488 1864588 7458360 29827980 119311928
((loop(\(x,i).(x5 + ~x3),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 2)
A138434: 6 54 750 4116 39930 92274 353736 617310 1606044 5121690 7149840 17323326 28946820 36732234 57310296 104511654
(2 + ((if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2)))) div (2 + (x mod 2))))
A062558: 2 2 3 3 3 4 3 4 4 4 3 6 3 4 5 5
(4 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)))
A001043: 5 8 12 18 24 30 36 42 52 60 68 78 84 90 100 112
(2 * (2 + compr(\x.(loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x) - (x div 11)),x)))
A275671: 4 6 8 12 14 18 20 24 28 30 32 36 38 40 42 44
(2 * (2 + compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(7x + 1))),x)))
A089079: 4 6 10 12 16 18 22 28 36 40 42 48 58 60 66 70
((x + 4) + (if x <= 0 then 1 else (2 * (1 + ((1 + ((x + loop(\(x,i).((x + 1) * (i * i)),(x + ~1),1)) div 2)) div 2)))))
A117771: 5 9 10 17 70
(loop(\(x,i).2x,x,(((3x + 4) * loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,1)) div 2)) div 2)
A275827: 1 7 50 364 2688 20064 151008 1144000 8712704 66646528 511673344 3940579328 30429184000 235521884160 1826663915520 14192851599360
((loop(\(x,i).(10x + 10),(2x + 1),0) + loop(\(x,i).10x,x,2)) div 2)
A332156: 6 565 55655 5556555 555565555 55555655555 5555556555555 555555565555555 55555555655555555 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).(10x + 10),(2x + 1),0) - loop(\(x,i).10x,x,2)) div 2)
A332154: 4 545 55455 5554555 555545555 55555455555 5555554555555 555555545555555 55555555455555555 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).(10x + 5),(2x + 1),1) + loop(\(x,i).10x,x,2)) div 2)
A332178: 8 787 77877 7778777 777787777 77777877777 7777778777777 777777787777777 77777777877777777 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 + (loop(\(x,i).(10x + 21),2x,1) + loop(\(x,i).10x,x,2)))
A332135: 5 353 33533 3335333 333353333 33333533333 3333335333333 333333353333333 33333333533333333 3333333335333333333 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 + ((compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x) + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)) div 2))
A024675: 4 6 9 12 15 18 21 26 30 34 39 42 45 50 56 60
(loop(\(x,i).(x6 + ~x5),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A138460: 16 243 6250 50421 805255 2227758 11358856 22284891 70799773 287156086 429437265 1248191226 2317124020 3087177303 5274935161 10873082818
(loop(\(x,i).(x6 + ~x4),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A138453: 24 324 7500 57624 878460 2399124 12027024 23457780 73878024 297058020 443290080 1281926124 2373639240 3158972124 5387167824 11078235324
(loop(\(x,i).(x6 + ~x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A138440: 31 363 7810 58821 885775 2413398 12068776 23522931 74017933 297411646 443751825 1282863186 2375052100 3160681503 5389607641 11082180538
(loop(\(x,i).(x6 + ~x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A138441: 30 360 7800 58800 885720 2413320 12068640 23522760 74017680 297411240 443751360 1282862520 2375051280 3160680600 5389606560 11082179160
(loop(\(x,i).(x6 + ~x3),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)
A138452: 28 351 7750 58653 885115 2412306 12066328 23519511 74011861 297399466 443736945 1282837878 2375017660 3160641771 5389555753 11082106126
((2x + 4) * (loop(\(x,i).(4x + (2x div (1 + i))),x,3) - loop(\(x,i).4x,x,2)))
A118447: 4 42 304 1870 10488 55412 280768 1379286 6616360 31144300 144367584 660746892 2991902704 13424189160 59758420736 264191654758
(if x <= 0 then 1 else (4x + (((x + 1) + (2 * ((1 + (if (x mod 3) <= 0 then 0 else x)) div 3))) div 3)))
A312938: 1 4 9 13 18 23 26 32 37 39 45 50 52 59 64 65
(if x <= 0 then 1 else (4x + (((x + 1) + (2 * ((x + (if (~2 + (x div 2)) <= 0 then 1 else 2)) div 3))) div 3)))
A313046: 1 4 9 14 18 23 27 32 37 41 46 50 55 60 64 68
(2 + loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x + (x div 13))))
A146968: 4 5 7
A139690: 4 5 7 9 13 15 19 21 25 31 33 39 43 49 55 61
((3x + 2) + ((loop(\(x,i).(x2 + x),1,(~1 + loop(\(x,i).x2,1,(2x + 4)))) div 2) div 3))
A193390: 42 215 680 1661 3446 6387 10900 17465 26626 38991 55232 76085 102350 134891 174636 222577
((x + 2) + (((1 + ((x * (1 + loop(\(x,i).(x * (2x + loop(\(x,i).x3,2,x))),x,1))) div 2)) div 2) div 2))
A197635: 2 3 14771
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)))
A006094: 6 15 35 77 143 221 323 437 667 899 1147 1517 1763 2021 2491 3127
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)))
A090076: 10 21 55 91 187 247 391 551 713 1073 1271 1591 1927 2279 2773 3233
loop(\(x,i).(x mod (1 + ((x + ~1) mod 9))),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A179656: 0 0 0 0 1 1 1 0 3 1 3 0 1 1 1 5
loop(\(x,i).(x5 + x4 + x3 + x2 + x + 1),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A131993: 63 364 3906 19608 177156 402234 1508598 2613660 6728904 21243690 29583456 71270178 118752606 150508644 234330768 426237714
(loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,1) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A246714: 1 2 0 0 9 2 4 5 9 5 10 35 21 12 14 45
((x3 + 3x2 + 3x + 1) mod loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A167623: 1 8 2 15 4 47 54 151 200 159 370 359 516 895 1166 1287
((~2 - (if (x + ~2) <= 0 then 1 else 8)) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A338530: 1 0 2 4 1 3 7 9 13 19 21 27 31 33 37 43
((2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A261468: 1 1 1 6 6 6 6 10 8 8 10 6 6 10 12 8
((x + 2) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) - compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))
A147965: 1 1 2 1 4 3 6 5 4 9 6 9 12 11 10 11
((1 + (((loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,(x + ~1)) div 2) div 2) div 2)) div loop(\(x,i).2x,x,2))
A001949: 0 0 0 0 0 1 2 4 8 16 32 63 124 244 480 944
((2x + 2) + loop(\(x,i).(x + ~1),(1 - (((x * loop(\(x,i).(x2 div 3),2,x)) div 3) mod 3)),1))
A051244: 2 4 6 8 11 13 14 16 19 20 23 25 26 29 30 32
(2x + (if x <= 0 then 1 else (2x + (loop(\(x,i).(x - (x div 8)),2,(x + ~1)) + ((x + 1) div 3)))))
A310462: 1 4 10 15 20 26 31 36 42 46 50 56 61 66 72 77
compr(\x.loop(\(x,i).x2,1,(~1 + ((x2 * loop(\(x,i).x3,2,x)) mod 23))),x)
A095037: 1 2 3 4 6 8 9 12 13 16 18
A278580: 1 2 3 4 6 8 9 12 13 16 18 24 25 26 27 29
((x + 1) + (x div ((if x <= 0 then 1 else x) div (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))))))
A132009: 1 3 4 7 6 8 8 15 13 12 12 17 14 16 18 31
((~x + 1) + (if (2 * (x div 5)) <= 0 then 2x else (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))))
A331418: 1 2 3 4 5 7 8 11 12 15 20 21 26 29 30 33
compr(\x.(~1 + ((loop(\(x,i).2x,x,1) - loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x div 2),1)) mod (x + 1))),x)
A010378: 0 1 4 6 9 10
A171401: 0 1 4 6 9 10 12 16 18 21 22 25 28 30 33 36
(~x + ((compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x) + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)) div 2))
A024678: 2 3 5 7 9 11 13 17 20 23 27 29 31 35 40 43
(x * (x + (if x <= 0 then 1 else (2 * (x + ((((3x + ~3) * (loop(\(x,i).2x,(x + ~2),x) div 2)) div 2) div 2))))))
A265083: 0 3 12 51 192 675
compr(\x.(1 - loop(\(x,i).(~1 + loop(\(x,i).(x3 mod 37),2,x)),1,x2)),x)
A028787-A028750: 2 5 6 8 13 14 15 17 18 19 20 22 23 24 29 31
(if ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) <= 0 then ((2x + 1) div (3 + (x div 4))) else 0)
A144217: 0 1 1 2 0 2 3 0 0 3 4 0 0 0 4 5
((x div (2 + (x mod (1 + (x div (1 + (((2x mod (1 + (x mod 4))) div 2) + (x mod 2)))))))) + (if x <= 0 then 0 else 1))
A329313: 0 1 1 2 1 2 1 3 1 2 2 3 1 2 1 4
(((1 + (x div (2 + (x div (1 + (x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4))))))))))) div 2) + (if x <= 0 then 0 else 1))
A059829: 0 1 1 2 1 2 1 3 2 2 1 2 1 2 1 4
(1 + (x div (1 + (x mod (1 + (x div (2 + (loop(\(x,i).2x,(x + ~1),(1 + (~x mod 4))) mod (x + 1)))))))))
A208644: 1 2 3 2 5 6 7 2 3 5 11 6 13 7 15 2
(3 mod (1 + (if ((1 + ((x - ((x div 2) mod 3)) mod 5)) mod 3) <= 0 then (x div 3) else 1)))
A298667: 1 1 1 1 1 1 1 0 0 1 1 1 3 1 1 1
(1 + (x mod (1 + ((~1 + loop(\(x,i).2x,x,(1 + (x mod (2 * (1 + (x mod 2)))))) - (x mod 2)) mod (2x + 1)))))
A304339-A304328-A160400-A055231: 1 2 3 1 5 6 7 1 1 10 11 3 13 14 15 1
(1 + (x div (1 + ((~2 + loop(\(x,i).2x,x,(1 + (x mod (2 * (1 + (x mod 2)))))) - (x mod 2)) mod (x + 1)))))
A014673: 1 1 1 2 1 3 1 2 3 5 1 2 1 7 5 2
(1 + (if x <= 0 then 0 else (1 + (((x + ~1) + ((~x + 1) div (1 + (((2x + 1) mod (2 + (x div 4))) div 2)))) div 2))))
A327162: 1 2 2 2 2 3 2 2 2 4 2 4 2 5 6 2
(1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (if (x mod 3) <= 0 then 2 else 1)))
A099597: 1 1 1 1 2 1 1 3 3 1 1 4 9 4 1 1
(1 + (if x <= 0 then 0 else (1 + (x div (4 + ((1 - (9 * (x mod 6))) mod (x + 1)))))))
A079085: 1 2 2 2 3 2 3 3 3 3 2 3 4 3 2 3
(1 + (x2 div (~1 + (2 * (x - ((1 - ((x + ((2 + loop(\(x,i).2x,(x + ~1),1)) div (x + 1))) div 2)) div 2))))))
A343437: 1 2 2 2 2 2 3 3 3 3 3 2 2 1 1 1
((2x + 1) - (loop(\(x,i).2x,((x div 2) - ((3 * (x div 4)) div 2)),1) * (1 + (2 * (x mod 2)))))
A071043: 0 0 3 1 7 5 9 3 15 13 17 11 21 15 21 7
(if (x + ~1) <= 0 then 1 else (~1 + (3 * ((~x2 + 2) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))))))
A141591: 1 1 ~1 ~1 2 ~1 ~1 2 2 ~1 ~1 2 8 2 ~1 ~1
(1 + ((loop(\(x,i).((x2 + 5x) div 2),2,(5x + 1)) div 5) div 3))
A234043: 1 42 273 969 2530 5481 10472 18278 29799 46060 68211 97527 135408 183379 243090 316316
loop(\(x,i).12x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A176627: 1 1 1 1 12 1 1 144 144 1 1 1728 20736 1728 1 1
loop(\(x,i).((2x + 1) - (x mod 2)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A196641-A196636: 1 1 1 1 2 1 1 5 5 1 1 10 21 10 1 1
(1 + loop(\(x,i).(x2 + 4x),1,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))
A082105: 1 1 1 1 6 1 1 13 13 1 1 22 33 22 1 1
loop(\(x,i).(1 + ((1 + (x div 2)) * i)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A197090: 1 1 1 1 2 1 1 5 5 1 1 10 25 10 1 1
loop(\(x,i).10x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A158117: 1 1 1 1 10 1 1 100 100 1 1 1000 10000 1000 1 1
loop(\(x,i).(x + (x div 3)),2,(1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))
A147649: 1 1 1 1 2 1 1 5 5 1 1 6 8 6 1 1
loop(\(x,i).(x + (x mod 5)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A137854: 1 1 1 1 2 1 1 4 4 1 1 8 11 8 1 1
(1 + ((2 * loop(\(x,i).x2,1,(1 + (x mod (1 + ((4 + (x div 2)) mod (1 + (x div 3)))))))) div 3))
A055210: 1 1 1 3 1 1 1 3 7 1 1 3 1 1 1 11
(~1 + ((2 * (1 + (2 * loop(\(x,i).i,((x div 2) div (1 + (x mod (1 + (x mod (3 + (x mod 2))))))),1)))) div 3))
A065371: 1 1 1 1 2 1 3 1 1 2 6 1 7 3 2 1
(1 + ((2 * (1 + ((1 + (((~1 + loop(\(x,i).2x,x,(2 - ((x div 2) mod 2)))) mod (x + 1)) div 2)) div 2))) div 3))
A039636: 1 1 1 2 1 2 1 3 3 2 1 3 1 2 2 4
(if x <= 0 then 0 else (1 + ((2 * (1 + (((x + 1) div (2 - (16 mod (~x + ~1)))) div 2))) div 3)))
A327503-A158378-A071178-A052409-A051904: 0 1 1 2 1 1 1 3 2 1 1 1 1 1 1 4
(1 + ((((x + 1) * (~1 + (loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) mod 9))) div 2) mod 3))
A272084: 1 1 1 1 2 1 1 1 2 3 3 1 2 1 2 1
((~x + 1) mod (1 + ((2 * (2 + (if x <= 0 then 0 else (2 - ((x + 1) mod (2 + (x div (4 + (x mod 2))))))))) mod 3)))
A133827: 1 0 0 1 1 2 0 0 0 0 0 2 1 0 2 0
(~1 + ((2 * ((x + 2) + (if x <= 0 then 1 else (6x - (((x + ~1) mod (2 + (x div 2))) div 2))))) div 3))
A314725: 1 5 9 13 18 23 28 33 37 41 46 51 55 59 64 69
(loop(\(x,i).3x,((x div 2) - ((3 * (x div 4)) div 2)),1) * (1 + (6 * (x mod 2))))
A160797: 1 7 3 21 3 21 9 63 3 21 9 63 9 63 27 189
(if x <= 0 then 0 else (1 + (x div (5 + (x mod 2) - (((x + ~1) mod (4 + ((x div 2) div 3))) div 2)))))
A172245: 0 1 1 1 2 1 2 2 3 2 4 2 5 3 3 4
(1 + compr(\x.(~1 + (x mod (~1 + (6 * (loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)))))),(x + 1)))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A327783-A319333: 2 3 5 7 11 13 17 19 23 29 30 31 37 41 43 47
(1 + (loop(\(x,i).(2 * i),(x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))),1) mod (x + 1)))
A105560: 1 2 2 3 2 3 2 5 3 3 2 5 2 3 3 7
(1 + compr(\x.((x + 1) mod (1 + (2 * ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3)))),(x + 1)))
A106843: 2 3 5 6 7 9 11 13 15 17 18 19 21 23 27 29
(1 + ((1 + (x mod (1 + (x div (1 + ((if ((x * (x mod 3)) mod 5) <= 0 then 1 else 2) + (x mod 2))))))) div 2))
A243866: 1 1 1 2 1 2 2 2 2 2 3 2 4 2 3 3
(~1 + (2 * loop(\(x,i).x2,1,(200x + 151))))
A157653: 45601 246401 607201 1128001 1808801 2649601 3650401 4811201 6132001 7612801 9253601 11054401 13015201 15136001 17416801 19857601
(1 + ((1 + ((1 + (x mod (2 + (loop(\(x,i).(2x + 1),x,(4 * (x mod 2))) mod (x + 1))))) div 3)) div 2))
A198339: 1 1 1 2 1 1 1 2 2 3 1 1 1 2 2 4
(1 + ((1 + ((1 + ((((x + 1) * loop(\(x,i).((x + 2) + (x div 8)),x,1)) div 2) div 2)) div 3)) div 2))
A241772: 1 1 2 2 3 4 6 7 9 12 15 19 24 30 37 45
((x + 2) - (2 * (1 + (if x <= 0 then 0 else ((x + 1) mod (2 * (1 + ((x + ~2) mod (1 + (x div 5))))))))))
A105033: 0 1 0 3 2 1 4 7 6 5 0 11 10 9 12 15
((x + 1) div (~1 + (2 * (1 + ((1 + ((((x + 1) * (1 + (if (x mod 5) <= 0 then 0 else 2))) div 2) div 2)) div 2)))))
A107454: 1 0 1 0 1 2 1 1 1 1 3 1 1 1 1 3
(1 + ((1 + ((1 + (((loop(\(x,i).x2,1,((3 * (x div 2)) + (x div 3))) div 2) div 2) div 2)) div 2)) div 2))
A126793: 1 1 2 2 3 3 5 5 7 8 11 11 16 16 21 22
(1 + ((1 + ((loop(\(x,i).2x,x,(1 + ((x mod (2 + ((x div 2) div (1 + (x mod 2))))) div 2))) mod (x + 1)) div 2)) div 2))
A184241: 1 1 2 1 1 2 1 1 3 2 2 2 2 2 4 1
(1 + ((1 + (((if x <= 0 then 1 else (2 * (1 + ((1 + ((x * (1 + (x mod 3))) div 2)) div 2)))) mod (x + 1)) div 2)) div 2))
A054988: 1 1 1 1 1 2 3 2 2 3 1 3 3 2 3 4
loop(\(x,i).(2x + 1),((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~1) div 2))) div 2),1)
A059328: 1 1 1 1 3 1 1 7 7 1 1 15 63 15 1 1
(1 + ((1 + ((((x + 1) * (1 - (((x div 2) - (if ((x + 1) mod 8) <= 0 then 0 else 1)) mod 2))) div 2) div 2)) div 2))
A034003: 1 1 1 2 1 1 2 1 1 1 2 3 1 1 3 1
(1 + ((1 + (((2 + ((1 - (2 * ((if (x mod 3) <= 0 then 1 else x) mod 5))) mod (x + 1))) div 2) div 2)) div 2))
A275992: 1 1 1 2 2 1 2 2 2 2 1 3 3 2 2 3
(1 + ((loop(\(x,i).(2x + 2),x,(12 * (x div 7))) mod 5) div 2))
A119647-A092782: 1 2 1 3 1 2 1 1 2 1 3 1 2 1 2 1
(1 + ((3 * ((~1 + (if (x mod 2) <= 0 then x else 0)) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))) div 2))
A202735: 1 1 1 1 1 1 1 2 2 1 1 4 2 4 1 1
loop(\(x,i).(7x + (x mod 4)),(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)
A151782: 1 8 8 56 8 56 56 392 8 56 56 392 56 392 392 2744
loop(\(x,i).7x,((x div 2) - ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2)),1)
A151785: 1 1 7 1 7 7 49 1 7 7 49 7 49 49 343 1
(1 + ((1 + ((x * ((x + 4) + ((if (16 mod (x + 1)) <= 0 then 1 else 0) + (x mod 2)))) div 2)) div 2))
A341578: 1 3 4 8 9 14 16 24 25 33 36 45 49 60 64 80
(1 + (((~2 + (2 * (1 + (x div (1 + (loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1))))))) mod (x + 1)) div 2))
A309786: 1 1 1 1 2 1 3 1 3 2 5 1 6 3 4 1
(1 + (((x + 1) div (if x <= 0 then 1 else (2 * (1 + ((1 + ((20 mod (x + 1)) div 2)) div 2))))) div 2))
A329462: 1 1 1 2 2 1 1 2 2 3 1 2 2 2 2 3
(21 * (1 + compr(\x.((1 + loop(\(x,i).(x3 + ~1),2,4)) mod (x + 1)),x)))
A033850: 21 63 147 189 441 567 1029 1323 1701 3087 3969 5103 7203 9261 11907 15309
loop(\(x,i).i,(((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (2 + (x div (2 + (x mod 5))))),1)
A194672: 1 1 1 1 2 1 1 3 3 1 1 5 10 4 1 1
((x + 1) - (((3 * (1 + ((x + 1) div (1 + (2 * (if ((x + 1) mod 5) <= 0 then 0 else 2)))))) div 2) div 2))
A117386: 1 2 3 4 1 5 6 7 8 2 9 10 11 12 3 13
(1 + (((3 * (1 + ((x + 1) div (2 + (loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)))))) div 2) div 2))
A335286-A064839: 1 1 2 1 3 1 4 1 2 2 5 1 6 3 4 1
(15 * (1 + compr(\x.(loop(\(x,i).x3,2,15) mod (x + 1)),x)))
A033849: 15 45 75 135 225 375 405 675 1125 1215 1875 2025 3375 3645 5625 6075
(~1 + (((((x + 2) * (4 + (if x <= 0 then 1 else ((x + 2) + ((x + (x div 3)) div 3))))) div 2) div 2) div 2))
A029899: 0 1 3 5 7 10 13 17 20 25 29 33 39 44 51 56
(loop(\(x,i).4x,((x div 2) - ((3 * (x div 4)) div 2)),1) * (1 + (8 * (x mod 2))))
A164032: 1 9 4 36 4 36 16 144 4 36 16 144 16 144 64 576
((~1 + (2 * (~1 + (2 * (~1 + ((x + 1) * (2 + (if (~2 + (x div 4)) <= 0 then 1 else 2)))))))) div 9)
A039065: 0 1 3 4 5 7 8 9 11 12 13 15 22 24 25 27
loop(\(x,i).i,((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2),((2x + 1) div (3 + (x div 4))))
A159335-A109004: 0 1 1 2 1 2 3 1 1 3 4 1 2 1 4 5
(5 * ((((loop(\(x,i).x2,2,(10x + 3)) div 2) div 2) div 3) div 2))
A251820: 15 5950
((~1 + ((2 * (2 + (x div (1 + ((x div 2) mod (1 + (if (x mod 2) <= 0 then 6 else 1))))))) div 3)) mod 3)
A338757: 0 1 1 1 1 0 1 2 1 0 1 0 1 0 0 2
((1 + (2 * (if x <= 0 then 1 else (8x - ((x + ((x div 3) mod 3)) div 3))))) div 3)
A137002: 1 5 11 15
A314039: 1 5 11 15 21 25 31 35 41 46 51 57 61 67 71 77
((1 + (2 * (if x <= 0 then 1 else (2 * (4x - ((x + ((x div 3) mod 3)) div 3)))))) div 3)
A137002: 1 5 11 15
A314021: 1 5 11 15 20 24 29 33 39 44 49 55 59 64 68 73
((1 + (2 * (if x <= 0 then 1 else (2 * (4x - ((1 + ((x - ((x div 4) mod 2)) div 2)) div 2)))))) div 3)
A315061: 1 5 9 15 20 25 31 35 40 45 49 55 60 65 71 75
((1 + (2 * (if x <= 0 then 1 else (2 * (4x - (x div (4 + ((x div 2) div 5)))))))) div 3)
A314095: 1 5 11 16 20 25 31 36 40 45 51 56 61 67 72 76
((1 + (2 * (if x <= 0 then 1 else (2 * (4x - ((x + ((1 - (x div 2)) mod 4)) div 4)))))) div 3)
A314090: 1 5 11 16 20 24 29 35 40 45 51 56 60 64 69 75
((1 + (2 * (if x <= 0 then 1 else (2 * (3x + ((2 * (x - ((x div 2) div 3))) div 3)))))) div 3)
A313212: 1 4 9 15 19 24 28 33 37 43 48 52 56 61 67 71
((1 + (2 * (if x <= 0 then 1 else (2 * (3x + ((x + ((x div 3) mod 3)) div 3)))))) div 3)
A058759: 1 4 8 13
A311993: 1 4 8 13 17 23 27 32 36 40 44 48 53 57 63 67
((1 + (2 * (if x <= 0 then 1 else (2 * (3x + ((x - ((x + (x div 3)) div 3)) div 2)))))) div 3)
A312897: 1 4 9 13 17 21 27 31 35 39 44 48 52 57 61 65
(3 + (30 * compr(\x.(1 - (x mod (1 + (if (x mod 2) <= 0 then 6 else 0)))),x)))
A096023: 63 123 183 243 303 363 483 543 603 663 723 783 903 963 1023 1083
(1 - (((1 + (loop(\(x,i).7x,x,1) * (1 + (x div 5)))) div 3) mod 3))
A010890: 1 ~1 0 1 ~1 1 0 ~1 1
A015254-A015194-A015104-A015074-A015014-A014924-A014894-A014804-A014714-A014654-A014624-A014564-A014474-A014444-A014354-A014294-A014264: 1 ~1 0 1 ~1 1 0 ~1 1 0 0 0 0 0 0 0
((1 - ((1 + (loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) mod 11)) div 3)) mod 3)
A035226: 1 1 0 1 2 0 2 1 1 2 1 0 0 2 0 1
(if x <= 0 then 1 else ((x div (1 + (((1 + ((32 mod (x + 1)) div 2)) mod 2) + (x mod 2)))) mod 3))
A039980: 1 0 2 1 1 2 0 2 1 1 1 0 0 1 2 2
(((2x + 2) * (((x + 3) * loop(\(x,i).((x2 + ~x) div 2),2,(x + 4))) div 3)) div 3)
A027790: 10 80 350 1120 2940 6720 13860 26400 47190 80080 130130 203840 309400 456960 658920 930240
(4x + ((x + 1) div 3) - ((2 * ((((x div 2) div 3) mod 2) - (if x <= 0 then 1 else x))) div 3))
A137002: 1 5 11 15
A314031: 1 5 11 15 20 26 30 34 40 45 49 55 60 65 71 75
((((~x + ((x div 3) mod 3)) div 3) + (if x <= 0 then 1 else 6x)) - ((x + 1) div 3))
A313909: 1 5 10 16 22 26 32 38 43 48 53 58 64 70 74 80
(4x + ((if x <= 0 then 1 else ((2 * (x + (((x div 2) div 3) mod 2))) div 3)) + ((x + 1) div 3)))
A310444: 1 4 10 15 19 25 30 35 41 45 50 56 60 64 70 75
(x + (((x + ((x div 4) mod 3)) div 3) + (if x <= 0 then 1 else 4x)) - ((x + 1) div 3))
A315058: 1 5 9 15 20 25 30 35 40 45 51 55 60 65 69 75
((2 * (1 + ((2 * (2 + (loop(\(x,i).2x2,3,6) mod (x + 1)))) div 3))) mod 3)
A035154: 1 1 1 1 2 1 0 1 1 2 0 1 2 0 2 1
((2 * (1 + ((1 + (x div (1 + (loop(\(x,i).(2x + 1),(2x div 3),1) mod (x + 1))))) div 2))) div 3)
A318451: 0 0 1 0 1 1 1 0 3 1 1 1 1 1 2 0
(3 + (2 * (~1 + (2 * (~1 + loop(\(x,i).(2x + 24),x,17))))))
A305157: 65 229 557 1213 2525 5149 10397 20893 41885 83869 167837 335773 671645 1343389 2686877 5373853
((((x + 1) * (~1 + loop(\(x,i).((3x2 + 7x + 4) div 2),1,(x2 + 2x + 1)))) div 2) div 3)
A072474: 1 13 77 294 855 2071 4403 8492 15189 25585 41041 63218 94107 136059 191815 264536
((2 + (if x <= 0 then 1 else ((1 + (x mod (2 + (x div (1 + ((x div 2) mod (1 + (x mod 4)))))))) mod (x + 1)))) div 3)
A170978: 1 0 0 1 0 0 0 1 0 0 1 2 0 0 2 1
(72 * loop(\(x,i).(6 * (3x + (x div 2))),(x + 1),1))
A203820: 1296 27216 571536 12002256 252047376 5292994896 111152892816 2334210749136 49018425731856 1029386940368976 21617125747748496 453959640702718416 4611686018427387903 4611686018427387903
((x + 9) + (loop(\(x,i).((x + 1) + (2 * (6 - (x div 3)))),2,x) div 2))
A270044: 18 19 20 21 22 23 24 25 27 27 29 29 31 31 33 33
((x + ~1) + ((2 * ((x + 2) + (if x <= 0 then 1 else (4x + (((x + ~1) mod (2 + (x div 2))) div 2))))) div 3))
A313025: 1 4 9 14 18 22 26 30 35 40 44 48 53 58 62 66
(if x <= 0 then 1 else (3 * (1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2))))
A134059: 1 3 3 3 6 3 3 9 9 3 3 12 18 12 3 3
(1 + compr(\x.(~1 + ((1 + (x mod (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))) mod (x + 1))),(x + 2)))
A050150: 3 5 7 9 11 13 17 19 23 25 29 31 37 41 43 47
(loop(\(x,i).x2,1,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) mod (x + 3))
A165727: 0 0 0 0 1 0 0 4 4 0 0 9 1 9 0 0
(x mod (1 + (((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (x div 2))))
A003165: 0 0 0 0 1 0 2 1 2 2 4 1 5 4 4 4
(2 div (2 + (x mod (1 + (x mod (1 + (x mod (1 + (loop(\(x,i).4x,x,2) mod (x + 2)))))))) - (x mod 2)))
A077618: 1 1 1 0 1 2 1 0 0 2 1 0 1 1 1 0
(~1 + (if x <= 0 then 1 else (2 * (1 + ((1 + ((~7 + (x div 2)) mod (1 + (x div 2)))) div 2)))) - (x mod 2))
A319666: 0 0 1 0 3 2 1 0 3 2 5 4 7 6 1 0
((1 + ((1 + (x div (1 + (x mod (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))) mod (x + 1))) div (1 + (x mod 2)))
A319567: 1 1 1 1 1 2 1 1 1 3 1 2 1 4 6 1
(1 + compr(\x.(1 - (x mod (1 + (loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),x,1) mod 9)))),x))
A121603: 2 3 4 5 6 7 8 9 11
A257671: 2 3 4 5 6 7 8 9 11 12 13 17 18 19 20 22
(1 + (x * (1 + ((2 * (4 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3))))
A345741: 1 4 7 13 13 26 19 36 33 46 31 78 37 66 71 91
(1 + compr(\x.(x mod (1 + ((1 + (x mod (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))) mod (x + 1)))),x))
A084400-A079852-A026477: 1 2 3 4 5 7 9 11 13 16 17 19 23 25 29 31
(1 + compr(\x.(((x + 1) + (((x + 1) + ((x + loop(\(x,i).(x + (x div 3)),2,(x + ~1))) div 2)) div 2)) mod 3),x))
A190686: 1 2 5 9 13 16 17 20 24 28 31 32 35 39 42 43
(1 + compr(\x.((1 + (x * loop(\(x,i).(16x2 + 56x + 46),2,x))) mod (x + 1)),x))
A018743: 1 3 11 29 33 87 319 957
(1 + compr(\x.(loop(\(x,i).(120x2 + 12x + 6),2,x) mod (x + 1)),x))
A018734: 1 2 3 6 157 314 471 942
(1 + ((~2 + (6 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))) div (x + 8)))
A246778: 2 2 3 4 6 6 8 8 9 11 11 12 13 13 13 14
loop(\(x,i).(2 * (x + ((1 + (((1 + (((x + 1) * (x3 div 8)) div 2)) div 2) div 2)) div 2))),x,1)
A064773: 1 2 4 14 672
((~x + ~1) + loop(\(x,i).x2,1,(1 + (x div (1 + (x mod (1 + (x mod (1 + (x div (2 + (x div 5))))))))))))
A139717: 0 2 6 0 20 3 42 8 0 15 110 4 156 35 10 0
((1 + (x mod (1 + (x mod (1 + (x div (1 + (2 * (if (16 mod (x + 1)) <= 0 then 0 else 2))))))))) mod (x + 1))
A229878: 0 0 1 0 1 2
A345221: 0 0 1 0 1 2 1 0 1 2 1 3 1 2 3 0
loop(\(x,i).(1 + (x div (2 + (x div (1 + ((x div 2) mod (1 + (x mod (1 + (x mod (3 + (x mod 2)))))))))))),1,(x + 1))
A326622: 1 1 2 1 1 1 3 2 1 1 2 1 1 2 4 1
((~1 + ((x + (if ((x + 1) mod 10) <= 0 then 2 else 1) - (x div 2)) mod 9)) mod (x + 1))
A083802: 0 1 1 2 2 3 3 4 4 6 5 6 6 7 7 15
((1 + (((~x + 1) mod (1 + (2 * ((if (~2 + (x mod 5)) <= 0 then 1 else 2) + (x mod 2))))) div 3)) mod (x + 1))
A257696: 0 1 1 2 1 1 1 2 2 3 1 1 1 1 1 1
loop(\(x,i).(6x + (((x3 + 9x2 + 26x + 24) div 2) div 3)),1,(x + 1))
A255994: 16 32 53 80 114 156 207 268 340 424 521 632 758 900 1059 1236
((1 + (x div (2 + ((x + 1) div (2 + (5 * (if (8 mod (x + 1)) <= 0 then 2 else 1))))))) mod (x + 1))
A126302: 0 1 2 2 3 3 3 4 3 4 4 4 5 4 4 4
((1 + (((~1 + (3 * loop(\(x,i).10x,x,(x + 1)))) div 2) div 2)) mod (4x + 4))
A182688: 1 7 9 8 0 0 0 0 0 0 0 0 0 0 0 0
((x + ((2x + 1) * loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1))) div (x + 1))
A071051: 1 3 4 7 4 8 8 15 4 8 8 16 8 16 16 31
((1 + ((((x + 1) * (loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1))) div 2) div 7)) div 2)
A322337: 0 0 0 0 0 1 0 1 1 2 0 4 0 4 3 5
(if ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) <= 0 then 1 else ((x + ~2) - (x div (1 + (x mod 5)))))
A179743: 1 1 1 1 2 1 1 3 4 1 1 4 6 8 1 1
((1 + (((x + 1) * (4 + (if x <= 0 then 0 else (1 + (2x div (4 + (x div 4))))))) div 3)) div 2)
A257144: 1 2 3 4 5 7 8 9 11 13 15 16 17 19 23 24
(~3 + (6 * (1 + ((if x <= 0 then 2 else ((x + 1) - ((x mod 6) mod (1 + (x div 2))))) div 2))))
A251559: 9 9 9 9 15 15 21 21 21 21 21 21 39 39 39 39
((1 + ((2 + ((x * loop(\(x,i).((x2 + ~x) div 2),2,(x + ~2))) div 15)) div 3)) div 2)
A053643: 0 0 0 0 0 1 1 4 10 21 42 77 132 215 334 501
(~3 + (6 * ((~3 + loop(\(x,i).(2x + 40),(x + 1),1)) div 2)))
A304831: 111 357 849 1833 3801 7737 15609 31353 62841 125817 251769 503673 1007481 2015097 4030329 8060793
(50 * (2x - (if (~2 + (x div 2)) <= 0 then (~1 + (x div 5)) else 1)))
A044382: 50 150 250 350 450 500 550 650 750 850 950 1050 1150 1250 1350 1450
(2 * (1 + ((x + (2 * (1 + (if (x + ~1) <= 0 then 0 else (1 + ((x mod (1 + ((1 + (x div 2)) div 2))) div 2)))))) div 3)))
A050823: 2 4 6 6 6 8 8 8 10 10 12 12 12 12 16 14
(1 - ((if x <= 0 then 2 else (1 + ((1 - ((x + 1) mod (5 * (1 + (x mod 5))))) mod (x + 1)))) div 2))
A229656: 0 0 0 0 0 1 0 0 0 0 1 ~5 0 0 0 1
((1 + ((1 + ((x + 1) mod (1 + (2 * (loop(\(x,i).(2x + 1),x,6) mod 5))))) div 2)) div 2)
A321750: 1 1 1 0 1 2 1 0 0 1 1 0 1 0 0 0
((1 + ((if x <= 0 then 2 else (1 + ((1 + (x mod (~1 + (5 * (~x mod 4))))) mod (x + 1)))) div 2)) div 2)
A025869: 1 0 0 0 1 0 0 1 1 0 1 1 1 0 2 1
(if x <= 0 then 1 else (2 * (1 + ((1 + (((5 * (4x2 div (2 - (x mod 2)))) div 2) div 2)) div 2))))
A009926: 1 8 12 48 42 128 92 248 162 408 252 608 362 848 492 1128
((1 + ((1 + (((((x + 1) * (2 + (loop(\(x,i).(x * ((1 + i) div 2)),x,1) div 3))) div 2) div 2) div 2)) div 2)) div 2)
A308349: 0 0 0 1 1 1 3 13 55
((~1 + loop(\(x,i).2x,x,1) - (2 * ((x2 + 4x + 4) div (~x + 26)))) div 2)
A337698: 0 0 1 2 6 13 28 59 122 248 502 1012 2033 4078 8170 16357
(((~1 + (2 * (if x <= 0 then 1 else (2 * (x3 mod 13))))) mod 7) div 2)
A089643: 0 1 1 1 2 1 1 2 2 1 2 2 2 3 1 1
(if x <= 0 then 1 else (2 * (1 + (((1 + (x mod (1 + (x mod (2 * (1 + ((1 + (x div 2)) div 3))))))) mod (x + 1)) div 2))))
A147848: 1 2 2 4 2 4 2 6 2 4 2 8 2 4 4 6
((1 + (x mod (2 + ((1 + (2 * ((x + ~1) mod (1 + (x div (2 + (if (x mod 3) <= 0 then 2 else 0))))))) mod (x + 1))))) div 2)
A185279: 0 1 0 0 1 0 1 0 1 1 1 0 2 0 1 1
((1 + ((x mod (2 + ((1 + (2 * (x mod (1 + (loop(\(x,i).(x2 + 2x),2,2) mod (x + 1)))))) mod (x + 1)))) div 2)) div 2)
A319227: 0 0 1 0 0 1 2 0 2 0 1 1 0 2 0 0
(1 - ((1 + ((((x + 1) * ((~x + 2) + loop(\(x,i).(2 + ((x2 + ~2) div (x + 4))),2,x))) div 2) div 2)) div 2))
A017840: 1 0 0 0 0 1 1 1 1 1 1 2 3 4 5 5
(1 - ((loop(\(x,i).(2x + 2),x,(12 * (x div 7))) mod 5) div 2))
A317198: 1 0 1 ~1 1 0 1 1 0 1 ~1 1 0 1 0 1
(loop(\(x,i).(x + i),(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)),1) div 2)
A304942-A090011: 1 1 1 1 2 1 1 3 3 1 1 5 11 5 1 1
(x div (2 + ((~1 + (2 * (if (x mod 4) <= 0 then 2 else ((1 - (2 * (x mod 2))) * (1 + (x div 3)))))) mod (x + 1))))
A304081: 0 0 0 0 0 1 0 2 1 3 1 2 2 2 1 3
(loop(\(x,i).(compr(\x.(x mod ((x + 1) - (x mod 10))),x) + (x mod 10)),1,(x + 1)) div 2)
A079827: 1 2 3 4 5 6 7 8 9 5 11 16 22 27 33 38
(((x + 1) * (3 + (((x + 4) + (loop(\(x,i).2x,x,(2 + (x mod 2))) div (x + 1))) mod (x + 1)))) div 2)
A136136: 1 3 7 8 17 12 10
(((x + 1) * ((2x + 2) + (if x <= 0 then 1 else (3 * (((x + 1) - (2 * (~1 + (x mod 4)))) div 2))))) div 2)
A145830: 1 7 9 16 47 63
((loop(\(x,i).(2x * i),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2) div 2)
A282441-A281034: 0 0 0 0 0 0 0 2 2 0 0 12 96 12 0 0
(((~1 + (6 * (1 + (if ((x mod 7) mod 3) <= 0 then (x mod 3) else 1)))) div 2) div 2)
A129706: 1 2 2 1 2 2 1 2 2 2 2 2 2 2 4 2
((if x <= 0 then 1 else (2 * (1 + ((1 + ((5x2 + 10x + 5) div 7)) div 2)))) div 2)
A117634: 0 2 4 7 10 14 19 24 30 37 44 52 61 71 81 92
((if x <= 0 then 1 else (2 * (1 + ((1 + ((((x + 1) * (((~2x + 4) mod (2 + (x div 2))) div 2)) div 2) div 2)) div 2)))) div 2)
A301895: 0 1 1 1 1 2 2 1 1 4 4 3 4 3 3 1
(((1 + ((((x * (1 + ((loop(\(x,i).((x + 1) - ((~x + 1) div 3)),x,1) div 2) div 2))) div 2) div 2) div 2)) div 2) div 2)
A024791: 0 0 0 0 0 0 1 1 2 3 5 7 11 16 23 32
((x + 1) div (4 + ((loop(\(x,i).4x,x,1) mod 29) div 3)))
A035636: 0 0 0 0 0 0 1 0 0 1 1 2 1 1 3 3
(2 + ((1 + ((x * ((x + 1) + ((((x + ~1) * loop(\(x,i).(x * (x - i)),2,(x + ~1))) div 2) div 3))) div 2)) div 2))
A261639: 2 3 4 5 19 110
((2 + ((~1 + loop(\(x,i).(x3 + 2x2 + ~x),1,29)) mod (x + 1))) div 2)
A003636: 1 1 1 1 1 1 1 1 3 1 3 1 2 1 1 5
((2 + ((1 + (2 * ((x mod (1 + (4 * loop(\(x,i).i,(x + ~8),1)))) mod 3))) mod (x + 1))) div 2)
A248141: 1 1 2 1 2 1 2 3 1 2 2 3 1 2 3 1
((2 + ((1 - (x mod (1 - (2 * ((x + 1) mod (1 + (2 * (if (x mod 5) <= 0 then 0 else 2)))))))) mod (x + 1))) div 2)
A131107: 1 1 1 1 1 1 1 3 4 1 1 2 3 2 1 1
(16 * (~1 + (8 * (3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))))
A098823: 368 496 752 1008 1520 1776 2288 2544 3056 3824 4080 4848 5360 5616 6128 6896
(((loop(\(x,i).2x,x,(8 + (((x3 + ~3x2 + 2x) div 2) div 3))) div 2) div 2) div 2)
A081913: 1 2 4 9 24 72 224 688 2048 5888 16384 44288 116736 301056 761856 1896448
(if x <= 0 then 1 else (4 * (1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2))))
A132200: 1 4 4 4 8 4 4 12 12 4 4 16 24 16 4 4
(x - ((2 - (((x + ~1) + loop(\(x,i).((x2 + 3x + 2) div 2),2,9)) div 2)) div 8))
A301516-A204581-A134999: 100 101 102 103 104 105 106 107 108 109 110 112 113 114 115 116
((2 + ((1 + (3 * (x2 mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))) div (x + 2))) div 2)
A229945: 1 1 2 1 2 3 1 2 3 4 1 2 3 5 1 2
loop(\(x,i).x3,1,(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))
A181543: 1 1 1 1 8 1 1 27 27 1 1 64 216 64 1 1
(2 + (((2x + 2) + ((x + (if (x + ~1) <= 0 then 1 else (x - ((x + 1) mod 13)))) div 2)) div 2))
A288228: 3 4 5 6 7 9 10 11 12 14 15 16 21 22 23 24
(if x <= 0 then 1 else (4x + ((1 + (2 * (x + ((2x + ~1) div (4 + (x div 4)))))) div 3)))
A315026: 1 5 9 15 19 24 29 34 39 43 49 53 58 63 67 73
(4x + ((2 * ((2x + 2) + (x div (1 + (2 * (if (~4 + (x div 2)) <= 0 then 2 else 1)))))) div 3))
A315691: 1 6 12 17 22 28 34 39 44 50 56 62 68 73 78 84
((x + ((1 + ((loop(\(x,i).(x2 + x),1,((1 + ((x2 + ~x) div 2)) div 2)) div 2) div 3)) div 3)) div 2)
A321728: 0 0 1 1 2 3 5 7 10 14 20 28 37 50
(if x <= 0 then 1 else (2 * (x + (((x + 1) + (2 * (2x - (((x + 1) + (x mod 2)) div 5)))) div 3))))
A315212: 1 6 10 14 20 26 30 36 42 46 50 56 62 66 70 76
((x + 1) div (2 + (if (((x + 1) div 2) mod 4) <= 0 then ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) else x)))
A078771: 0 0 0 0 0 0 0 2 3 0 0 0 0 0 0 8
((x + (((~x + 4) + (((x + 2) + (loop(\(x,i).(5x + 4),x,0) mod (x + 1))) div 2)) div 2)) div 2)
A166079: 1 1 2 2 3 3 3 4 5 5 5 5 5 6 7 8
((x + 2) + ((x + (((((x + 1) * (2 + compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x))) div 2) div 2) div 2)) div 2))
A278299: 2 4 6 9 12 15 19 24 30 34
(loop(\(x,i).(x * i),((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 5),1) mod (x + 2))
A299581: 1 1 1 1 1 1 1 1 1 1 1 2 10 2 1 1
((2 * (x + (2 * ((loop(\(x,i).2x,x,(2 - ((2x + 2) mod 5))) mod (x + 1)) div 2)))) div (x + 2))
A080573: 0 0 1 1 2 1 2 1 2 2 1 2 1 3 2 1
((2x + ~1) + ((2 * (2 + (if x <= 0 then 1 else (4x - (((~x + 1) - (x mod 2)) div 3))))) div 3))
A313704: 1 5 10 15 19 25 29 35 39 44 49 54 59 64 69 73
(2x + ((1 + (2 * (if x <= 0 then 1 else (2 * (2x - ((~x + ((x div 2) mod 4)) div 4)))))) div 3))
A315411: 1 6 11 15 20 25 29 34 40 46 51 55 60 65 69 74
(2x + ((1 + (2 * (if x <= 0 then 1 else (2 * (2x + ((x - (x div 12)) div 2)))))) div 3))
A137002: 1 5 11 15
A314052: 1 5 11 15 21 26 32 37 43 47 53 58 63 69 73 79
(2x + ((1 + (2 * (if x <= 0 then 1 else (2 * (2x + ((((x + 1) - (x div 4)) div 2) div 2)))))) div 3))
A315056: 1 5 9 15 20 25 29 34 39 45 49 54 59 63 69 74
(2x + ((1 + (2 * (if x <= 0 then 1 else (2 * (2x + ((x - (x div ~7)) div 2)))))) div 3))
A315511: 1 6 11 17 21 27 32 38 44 49 55 59 65 70 76 82
(2x + ((1 + (2 * (if x <= 0 then 1 else (2 * (2x + ((x + (((x div 2) div 3) mod 2)) div 2)))))) div 3))
A137002: 1 5 11 15
A314054: 1 5 11 15 21 26 32 38 43 49 53 59 64 69 75 79
(3x + ((2 * ((2x + 2) + (x div (1 + (2 * (if (~4 + (x div 2)) <= 0 then 2 else 1)))))) div 3))
A313506: 1 5 10 14 18 23 28 32 36 41 46 51 56 60 64 69
((~x + 1) + (3 * (2x + (45 * (if x <= 0 then 0 else 2)))) - (x div 2))
A084802: 1 276 280 285 289 294 298 303 307 312 316 321 325 330 334 339
(1 + (3 * (loop(\(x,i).(10x + 1),(x div 2),(x mod 2)) * (1 + (x mod 2)))) - (x mod 2))
A308900: 1 6 4 66 34 666 334 6666 3334 66666 33334 666666 333334 6666666 3333334 66666666
((2x + 6) + (if x <= 0 then 1 else (2 * ((5x + 1) + ((x div 2) + (x div 3))))))
A063235: 7 20 34 48 62 74 90 102 116 130 144 156 172 184 198 212
(2 + ((x mod 2) + (x2 div 2)) - (2 * (if (x mod (1 + (2 * (x div (2 * (2 + (x mod 2))))))) <= 0 then 1 else 2)))
A192225: 0 1 2 5
A038191: 0 1 2 5 6 13 18 23 30 41 50 59 70
((~x + ~1) + ((2 * ((x + 2) + loop(\(x,i).(x - ((~1 + ((~x + ((x div 4) mod 2)) div 2)) div 2)),x,1))) div 3))
A115671-A105782: 1 1 1 2 3 4 6 8 11 15 20 26 34 44 56 72
((x + 1) + (((1 + ((((x + 1) * ((if (~2 + (x div 4)) <= 0 then 1 else 2) + (x div 3))) div 2) div 2)) div 2) div 2))
A094210: 1 2 3 4 5 7 8 9 10 12 14 15 18 19 20 23
loop(\(x,i).i,((1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) mod 5),x)
A159623: 1 1 1 1 2 1 1 3 3 1 1 4 12 4 1 1
(x + ((1 + (2 * ((if x <= 0 then 1 else 6x) - ((x + ((~x + 1) mod 3)) div 4)))) div 3))
A314899: 1 5 9 14 19 24 29 34 39 44 49 53 58 63 67 72
compr(\x.(((x + ((x + loop(\(x,i).((~x + 2) + (3 * ((2 + (x div 2)) div 3))),2,x)) div 2)) div 3) mod 2),x)
A268678: 0 1 3 4 5 7 8 11 15 16 18 19 20 22 23 26
(~x + ((2 + (((x + ~1) + loop(\(x,i).((x + 1) - ((~2x + 2) div 7)),2x,1)) div 2)) div 2))
A320921: 1 1 1 3 5 10 19 35 60
((2x + 1) + (((x + 1) + (((x + 1) + (x2 div (x + (if x <= 0 then 1 else (x div 3))))) mod 3)) div 2))
A190324: 2 4 7 9 12 14 17 19 21 24 26 30 32 35 37 39
(2x + (if x <= 0 then 1 else (2 * (x + (((x + 1) + (2 * (((x + 1) + (x mod 2)) div 5))) div 3)))))
A310496: 1 4 10 16 20 24 30 34 38 44 50 54 58 64 70 74
(1 + (x mod (1 + (x mod (1 + ((x + 1) div (1 + (x mod ((1 + (x mod (1 + (x div 4)))) * (1 + (x mod 2)))))))))))
A277708: 1 2 3 1 5 2 7 2 1 2 11 3 13 2 3 1
(1 + (x mod (1 + (x mod (1 + (((x + 1) - (9 * (x mod 10))) mod (x + 1)))))))
A068822: 1 2 1 2 5 2 1 2 1 10 1 4 1 2 5 4
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div (1 + (2 * (2 - ((x div 2) mod 2))))))))
A026758-A026725: 1 1 1 1 2 1 1 4 3 1 1 5 7 4 1 1
(1 + (7 mod (1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))))
A342767-A176653: 1 1 1 1 2 1 1 2 2 1 1 4 3 4 1 1
(1 + ((x2 + x + 1) mod (1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))))
A276162: 1 1 1 1 2 1 1 1 2 1 1 2 3 4 1 1
(1 + (~7 mod (1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))))
A158565: 1 1 1 1 2 1 1 3 3 1 1 2 4 2 1 1
(1 + ((x + 1) mod (1 + (x div (1 + ((((1 + (x div 3)) div (1 + (x mod (2 + (x mod 2))))) mod 2) + (x mod 2)))))))
A219094: 1 1 2 1 1 1 4 3 5 1 1 1 7 1 8 1
(1 - (1 mod (1 - (x div (1 + (x mod (1 + ((1 + (x mod (1 + (x mod (~1 + (2 * (x mod 4))))))) mod (x + 1)))))))))
A345990: 1 1 1 2 3 1 5 2 7 3 9 2 11 5 3 6
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div (2 + (2x mod 5))))))
A113749-A112564-A109225: 1 1 1 1 2 1 1 3 4 1 1 4 7 6 1 1
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((x + 1) div (2 + (x mod 5))))))
A110470-A058717-A055080-A034371-A034367: 1 1 1 1 2 1 1 4 3 1 1 6 9 4 1 1
(1 + (5 mod (1 + ((1 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 2)) div 2))))
A307239-A204087-A080396-A080381: 1 1 1 1 2 1 1 3 3 1 1 2 6 2 1 1
(1 + ((1 + (x div 2)) mod (1 + (x div (4 + ((x + ((4 * (x div 3)) div 3)) mod 3))))))
A214257-A214248-A214246: 1 1 1 1 1 2 1 1 2 2 1 1 2 4 3 1
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) + ((2x + 1) div (3 + (x div 4)))))
A204006: 1 2 2 3 4 3 4 5 5 4 5 6 7 6 5 6
(1 + ((3 * (1 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 2))) div 5))
A197957: 1 1 1 1 2 1 1 3 4 1 1 4 8 5 1 1
(1 + ((1 + (x * ((~x2 + 2) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))))) div 5))
A318045: 1 1 1 1 2 1 1 2 2 1 1 3 8 3 1 1
(~1 + ((1 + (((1 + (x mod (1 + (x mod (2 * (2 + ((x div 2) div 5))))))) mod (x + 1)) div 2)) mod 3))
A231122: 0 0 0 0 0 1 0 ~1 0 1 0 0 0 1 1 ~1
(1 + ((x - (3 * (x div (4 + ((x + 1) mod (1 + (2 * ((1 + (x div 4)) div 2)))))))) div 3))
A117535: 1 1 1 2 2 1 2 2 1 3 3 2 4 4 2 3
compr(\x.((x div (2 + (x mod 2))) mod 2),(1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))
A152236: 1 1 1 1 4 1 1 7 7 1 1 8 12 8 1 1
(1 + ((2 * (1 + ((2 * (1 + (2 * (((x2 + ~x) div 2) mod (1 + (x div 4)))))) div 3))) div 3))
A080311: 1 1 1 1 1 1 3 3 3 1 1 3 3 3 4 3
(1 + ((2 + ((x + 1) div (1 + ((x - (((((x + ~1) div 2) * (x div 3)) div 2) div 2)) mod 3)))) mod 3))
A112505: 1 1 1 1 2 2 2 2 1 1 2 1 3 1 2 2
(1 + ((2 * (1 + ((1 + (x div (2 * (1 + ((x mod (~2 + (((~x + 2) div 2) div 3))) mod 2))))) div 2))) div 3))
A152724: 1 1 2 2 2 2 3 3 2 2 3 2 3 3 4 4
(1 + ((2 * (1 + (2 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))) div 3))
A132735: 1 1 1 1 3 1 1 4 4 1 1 5 7 5 1 1
(1 + ((2 * (1 + (2 * (x + (((x - ((2 - (16 mod (x + 1))) div 2)) div 2) div 2))))) div 3))
A029675: 0 3 4 5 8 9 11 12 15 16 19 20 21 23 24 25
(~1 + ((2 + ((~1 + (2 * (1 + ((x + 2) mod (1 + (x div (4 + (x div 4)))))))) mod (x + 1))) mod 3))
A307445: 1 ~1 ~1 ~1 ~1 1 ~1 1 ~1 1 ~1 1 ~1 1 1 0
(x div (1 + ((2 + ((x - (6 * (x - ((x - (x div 3)) div 3)))) mod (x + 1))) div 3)))
A049819: 0 0 1 1 2 1 2 3 2 2 3 3 4 3 3 3
(1 + ((2 * (2 + ((2x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 3))) div 3))
A074589: 2 2 2 2 3 2 2 5 5 2 2 7 13 7 2 2
(1 + ((4 * (((x * (1 - ((x3 div 8) mod 2))) + (x mod 2)) div 3)) div 3))
A215297-A181039: 1 1 1 1 2 1 1 3 3 1 1 6 6 6 1 1
(~1 + ((2 + (((1 + ((x + 1) div (1 + (x mod (2 + (x div (2 + (x mod 5)))))))) div 2) div 2)) mod 3))
A054527: 1 1 ~1 1 ~1 ~1 1 ~1 ~1 0 1 ~1 ~1 0 ~1 1
((1 + (x div 3)) div (1 + (x div (3 * (2 + ((x mod (2 + ((x - (x div 3)) mod 3))) div 2))))))
A214707: 1 1 1 2 2 2 1 3 1 2 2 2 1 1 2 2
(1 + ((1 + ((2 * ((x div (3 * (2 + ((x + 1) mod 8)))) + (x mod 2))) mod 3)) mod (x + 1)))
A102641: 1 2 2 4 2 4 2 3 2 4 2 4 2 4 2 2
((x + 1) div (1 + ((~1 + (6 * (1 + ((x2 + x) mod 17)))) mod (x + 1))))
A175069: 1 1 1 2 1 1 1 2 3 1 1 1 1 1 1 8
(1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (2 - ((x div 2) div ~2))))
A176282: 1 1 1 1 4 1 1 9 9 1 1 16 21 16 1 1
(1 + ((1 + (x mod (1 + (x div (2 + (((x div (4 * (1 + (2 * (x mod 2))))) mod 2) + (x mod 2))))))) div 2))
A325622: 1 1 1 2 1 2 1 2 3 2 3 3 2 2 3 3
(1 + ((1 + ((x + 1) div (1 + (2 * (1 + (x mod (2 + ((2x + 1) mod (3 + (x div 4)))))))))) div 2))
A105068: 1 1 1 2 2 2 2 2 3 2 2 2 3 2 4 4
((x + 1) mod (1 + (2 * ((x + ~1) - ((2 * ((2x + 1) - (x2 div (3x + 4)))) div 3)))))
A292160: 0 ~1 0 ~2 ~1 0 ~3 ~2 ~1 0 ~4 ~3 ~2 0 0 ~5
(1 + ((1 + ((1 + ((2 * (1 + ((((x + 1) * (2 - ((x div 2) mod 2))) div 2) div 2))) div 3)) mod (x + 1))) div 2))
A245908: 1 1 2 2 3 3 2 3 3 4 3 3 4 4 3 3
(1 + ((1 + ((x mod (1 + ((1 - (x mod (1 + (x2 mod 14)))) mod (x + 1)))) div 2)) div 2))
A023586-A023584: 1 1 2 1 1 2 1 1 2 1 1 1 4 1 1 1
(1 + ((1 + ((x mod (1 + ((1 - (2 * ((x + (x div 8)) mod 5))) mod (x + 1)))) div 2)) div 2))
A309914: 1 1 1 2 1 1 3 1 2 1 4 1 2 2 1 5
(1 + ((1 + ((1 + ((x mod (2 + ((5 * (2 + (x mod 6))) mod (x + 1)))) div 2)) div 2)) div 2))
A253051: 1 1 2 1 1 2 1 2 1 2 1 3 1 1 1 2
(1 + ((1 + (((x + 1) * ((~x2 + 2) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))) div 2)) div 2))
A229556: 1 1 1 1 2 1 1 3 3 1 1 4 11 5 1 1
(1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (2 * (2 - ((x div 2) div ~2))))) div 2))
A147289: 1 1 1 1 4 1 1 5 5 1 1 6 12 6 1 1
(1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (4 * (x div 5)))) div 2))
A196989: 1 1 1 1 1 1 1 3 3 1 1 5 10 5 1 1
(1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (2 * (2 + ((x div 2) div 3))))) div 2))
A077228: 1 1 1 1 3 1 1 4 4 1 1 4 10 5 1 1
(1 + ((1 + ((x mod (2 + ((1 + (2 * (((x2 + ~x) div 2) mod (1 + (x div 4))))) mod (x + 1)))) div 2)) div 2))
A337633: 1 1 2 1 1 2 1 2 2 1 1 1 2 3 2 1
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((1 + ((x div 2) div (2 - ((x div 2) mod 2)))) div 2)))
A308813: 1 1 1 1 2 1 1 3 2 1 1 4 5 3 1 1
(1 + (2 * ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) div (1 + ((x div 2) mod 2)))))
A110291: 1 1 1 1 3 1 1 3 5 1 1 3 9 7 1 1
((x + 1) - ((3 * (x div (2 + (x div (1 + ((x mod (1 + ((2 - (x mod 4)) mod (x + 1)))) div 2)))))) div 2))
A344705: 1 2 3 3 5 6 7 5 8 10 11 8 13 14 15 9
(1 + ((3 * ((3 * ((x div 2) div (2 + ((2x2 + x) mod 12)))) div 2)) div 2))
A184097: 1 1 1 1 2 1 1 1 1 1 1 2 7 2 1 1
((((11x3 + 33x2 + 33x + 11) div 2) div 3) div 7)
A228189: 0 2 7 16 32 56 89 134 190 261 348 452 575 718 883 1072
(1 - (7 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))
A131067: 1 1 1 1 8 1 1 15 15 1 1 22 36 22 1 1
((x + (9 * ((12x + 12) div 5))) div 7)
A189384: 2 5 9 12 16 18 21 25 28 32 34 37 41 44 48 51
(1 + ((1 + ((x * ((3 * ((2x + 1) mod (1 + (2x mod (2 + (x div 4)))))) div 2)) div 2)) div 2))
A074761: 1 1 1 1 1 2 1 1 1 3 1 9 1 4 5 1
(1 + ((2x + 1) div (3 + (x div 4))) - ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2))
A342765-A321126-A051125: 1 2 2 3 2 3 4 3 3 4 5 4 3 4 5 6
((1 + (x div 3)) div ((1 + (x div 3)) div (1 + ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2))))
A343033: 1 1 1 1 2 1 1 3 3 1 1 2 5 2 1 1
((2x + 1) - (((2 * (1 + ((1 + ((x div 2) mod (1 + (x mod (1 + (x div 3)))))) div 2))) mod (x + 1)) div 2))
A024515: 1 3 4 7 8 10 12 13 15 18 19 21 24 25 27 28
(2 - ((2x + 1) mod (2 - (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~1) div 2)))))
A240656: 1 1 1 1 2 1 1 2 2 1 1 3 9 3 1 1
(1 + (((1 + (((1 + (((x + 1) * (1 + ((x + 3) mod 9))) div 2)) div 2) div 2)) div 2) div 2))
A213194: 1 1 1 2 2 3 1 1 2 2 3 3 4 4 5 1
(1 + (2 * ((5 * (((1 + (x mod (1 + (x mod (2 * (2 + ((x div 2) mod 2))))))) mod (x + 1)) div 2)) div 2)))
A050349: 1 1 1 1 1 5 1 5 1 5 1 15 1 5 5 11
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (2 + (x div (2 + (2x mod 5))))))
A135226: 1 1 1 1 3 1 1 4 5 1 1 5 9 7 1 1
((2x + 1) - (((5 * compr(\x.(1 - (x mod (1 + (4 * (x mod 5))))),x)) div 2) div 2))
A334051: 0 1 2 2 2 3 3 4 4 4 4 3 4 5 6 5
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~2) - (x div (2 + (x mod 5))))))
A054142: 1 1 1 1 3 1 1 5 6 1 1 7 15 10 1 1
(1 + (((3 * (1 + ((x div 2) div (1 + (x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4)))))))))) div 2) div 2))
A336395-A336393-A295877: 1 1 2 1 3 2 4 1 2 3 5 2 6 4 7 1
(~1 + (((1 + ((2 * (1 + (2 * ((x + 2) + ((x + (x mod 2)) div 3))))) + ((x + 1) div 3))) div 2) div 2))
A289012: 1 2 4 6 7 9 10 11 12 14 15 17 18 19 21 23
(1 + (2 * ((((~x2 + 2) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))) * (1 + (x div 2))) div 2)))
A253670: 1 1 1 1 3 1 1 5 5 1 1 7 21 7 1 1
(1 + (2 * (((2 * (x mod (1 - ((2 - (2x mod (4 + (x div 4)))) mod (x + 1))))) mod (x + 1)) div 2)))
A152795: 1 1 1 1 1 1 1 3 1 1 1 11 7 1 1 1
(1 + (((((1 + (2 * (x2 div (1 + (3 * (2 + (x mod 2))))))) mod (x + 1)) div 2) + (x div 4)) div 2))
A131909: 1 1 1 1 1 2 2 1 2 3 3 2 3 3 5 5
(1 + (~2 mod (1 - (2 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))))
A274643-A259698-A132731: 1 1 1 1 2 1 1 4 4 1 1 6 10 6 1 1
(((1 + ((x - (((x + 2) - ((((x + 2) * ((~x + 2) div 2)) div 2) div 2)) div 2)) div 2)) mod (x + 1)) mod 5)
A031268: 0 1 1 1 1 1 1 0 0 0 0 1 2 2 3 3
compr(\x.(((1 + (x div 2)) div 2) mod 2),((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 5))
A201195: 0 0 0 0 0 0 0 1 1 0 0 6 8 6 0 0
(1 + ((((2 * (1 + ((x div (1 + (2 * (1 + (2 * (x mod 2)))))) mod 2))) mod (x + 1)) div 2) + (x div 5)))
A230022: 1 1 2 2 3 3 3 4 3 4 5 5 4 5 4 5
(1 - (((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2) * (x div 5)))
A333513: 1 1 1 1 1 1 1 3 3 1 1 7 11 7 1 1
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (2 * ((x div 2) mod 2))) * (x div 4)))
A101321: 1 1 1 1 2 1 1 4 3 1 1 7 7 4 1 1
(2 - ((1 + (x div (1 + (x mod (1 + ((~2x + 36) mod (1 + (x div 2)))))))) mod 3))
A219840: 1 0 2 1 0 0 1 1 2 0 0 1 1 1 2 0
((1 + (x mod (1 + (x mod (1 + (x div (1 + (((1 + ((x + (x div 2)) div 4)) mod 2) + (x mod 2))))))))) mod 3)
A122190: 1 1 1 2 2 0 1 2 0 2 2 1 1 2 0 2
((2 * ((x + (((x div (~4 - (x mod 4))) mod 2) + (x div 2))) * (1 + (x2 div 2)))) mod 3)
A101662: 0 1 0 2 0 1 2 1 0 1 0 2 2 1 0 2
(7 mod (1 - (((2 - (2x mod (4 + (x div 4)))) mod (~x + ~1)) div 3)))
A343858: 0 0 1 0 1 1 0 1 1 3 0 1 1 1 1 0
((1 - ((~1 + (2 * compr(\x.(1 - ((((1 - (x mod 4)) mod (x + 1)) mod 3) mod 2)),x))) mod (x + 1))) mod 3)
A029367: 1 0 0 0 1 0 0 1 1 0 1 1 2 0 2 1
((2 * (1 + ((1 + ((1 + ((x + 1) div (1 + (x mod (4 - (x mod 4)))))) div 2)) div 3))) div 3)
A087010: 0 0 1 1 1 0 1 1 2 2 2 2 2 1 2 2
((2 * (1 + ((1 + (2 * ((x + 2) div ((2 + (x div 5)) * (1 + (x mod 2)))))) div 3))) mod 3)
A138253: 1 2 1 1 0 1 1 1 0 1 0 1 0 1 2 1
((2 * (1 + (((5 * ((3x2 + 7x + 4) div 2)) div 3) div 3))) mod 3)
A039977: 1 2 0 0 1 1 2 1 1 0 1 2 2 0 0 1
((2 * (1 + (((x + 1) mod ((x + 3) - (2x mod (4 + (x div 4))))) div 3))) div 3)
A087623: 0 0 1 0 0 2 0 0 0 2 0 0 0 1 4 0
((2 + ((48x2 + 146x + 100) div 9)) div 3)
A226183: 4 11 22 36 54 75 100 129 161 197 236 278 325 375 428 485
(3 * ((3 * ((~1 + (x2 div 2)) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))) div 2))
A230652: 0 0 0 0 3 0 0 3 3 0 0 9 3 9 0 0
((2 * (x - (((x * (~1 + compr(\x.(1 - ((~x2 + x) mod 8)),(x + 1)))) div 2) div 3))) mod 3)
A217864: 0 2 2 2 0 2 1 2 2 1 1 2 0 1 2 1
((4 * (1 + (2 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))) div 3)
A131399: 1 1 1 1 4 1 1 6 6 1 1 9 12 9 1 1
((2 * (2 + (x mod (1 + (2 * ((x * (1 - ((x3 div 8) mod 2))) div 3)))))) div 3)
A282748: 1 1 1 1 2 1 1 2 3 1 1 4 3 4 1 1
((2 * (2 + ((((x + 2) * ((x4 + 3x3 + 3x2 + 2x + 1) div 2)) div 2) div 3))) mod 3)
A128184: 1 2 1 1 1 1 2 1 1 1 1 0 0 1 1 2
((2 + ((((x + 1) * ((2x + 2) + ((2x2 + 9x + 10) div 3))) div 2) div 2)) mod 3)
A210255: 0 1 0 1 2 0 0 1 2 1 1 2 0 0 0 1
((2 * (2 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (2 + ((x + (x div 2)) div 2))))) div 3)
A102413: 1 1 1 1 4 1 1 6 6 1 1 8 16 8 1 1
(x mod ((2 + compr(\x.(~1 + ((3 * ((2x + 1) - ((x div 4) mod 2))) mod 5)),x)) div 3))
A035389: 0 0 0 1 1 0 0 1 1 2 1 1 1 2 3 3
((x + 4) + ((2 * (1 + ((1 + ((3 * (x + ((x div 3) mod 2))) div 2)) div 2))) div 3))
A067611: 4 6 8 9 11 13 14 15 16 19 20 21 22 24 26 27
(((3 * (1 + ((x2 + 4x + 4) div (~x + 26)))) div 2) - (x div 3))
A052336: 1 1 1 2 2 3 4 5 7 9 12 15 18 23 29 35
(((2x + 1) + (2 * ((x + 1) + ((2 * (1 + (6 mod (1 + (x div 2))))) div 3)))) div 3)
A166111: 1 2 3 5 6 7 10 11 12 13 14 15 19 21 22 23
(1 + (2 * ((x + 1) + (((~1 + ((x + 1) * (2 + ((3x + ~3) * ((x2 + x) div 2))))) div 2) div 2))))
A155778: 3 5 23 83 239
(1 + (((x + 1) + (((1 + (((x + 1) * (1 + ((x2 + ~2x + 1) div 5))) div 2)) div 2) div 2)) div 2))
A052816: 1 2 2 3 4 5 7 9 11 14 18 22 27 33 40 49
((x + 4) div (1 + (4 * (1 + (x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4)))))))) - (x mod 2)))
A303051: 0 0 1 0 1 1 2 0 0 1 2 0 3 2 3 0
(1 + compr(\x.(~1 + ((2 * (x + (((1 + (((x + 1) div 2) mod 3)) * ((~1 + (x div 2)) div 2)) div 2))) mod 3)),x))
A140181: 1 2 3 4 6 7 8 9 12 14 15 17 18 19 20 21
(~1 + compr(\x.(1 - (x mod (1 + ((1 + (((x + 2) mod 10) mod 9)) mod (x + 1))))),x))
A325440: 1 3 4 6 9 10 12 13 14 15 16 18 20 21 22 24
(121x2 + 38x + 3)
A157440: 3 162 563 1206 2091 3218 4587 6198 8051 10146 12483 15062 17883 20946 24251 27798
((1 + ((1 + (2x div (1 + ((x + 2) div (2 + (x div 4)))))) mod (1 + (x div 5)))) mod (x + 1))
A327522: 0 1 1 1 1 1 2 1 1 2 1 1 1 2 3 1
compr(\x.(~1 + (x mod (1 + ((~2 + (9 * (~x + (x mod 9)))) mod (x + 1))))),(x + 1))
A185660: 1 2 3 4 5 6 7 8 9 11 13 15 16 17 20 22
compr(\x.(~1 + ((1 + ((x + 1) div (~1 + (2 * ((x + (x div 8)) mod 5))))) mod 3)),(x + 1))
A183172: 1 3 4 5 7 9 10 12 13 14 16 17 18 19 22 23
((x2 mod (~1 + (6 * (1 + (((x + (x div 8)) mod 5) div 2))))) div (x + 1))
A095750: 0 0 1 2 3 0 0 0 1 0 0 0 0 1 0 0
((1 + (((1 + (((x + 1) * (1 + (((x2 + 4x + 4) div 2) div (2 + (x mod 2))))) div 2)) div 2) div 2)) div (x + 1))
A008584: 1 0 1 0 1 1 2 1 3 2 4 3 6 4 8 6
((0 + (((x + 1) - (2 * (x mod (x - ((x + ~1) mod 8))))) div 3) - (x mod 2)) mod (x + 1))
A287730: 0 1 1 0 1 1 2 1 3 2 3 1 2 1 1 0
((1 + (x div (1 + (((1 + ((x + 1) mod (1 + (x div (2 + ((x div 2) mod 2)))))) mod (x + 1)) + (x mod 2))))) mod (x + 1))
A198897: 0 1 2 2 2 2 3 2 2 4 3 4 2
((x + 1) * ((x + ~1) + (2 * (1 + (((4x3 + 8x2 + 9x + 5) div 2) div 3)))))
A071092: 1 20 93 296 725
((3 - (2 * (1 + ((((x + 2) * ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2)) div 2) div 2)))) mod (x + 1))
A066504: 0 1 1 1 1 5 1 1 1 7 1 7 1 9 8 1
compr(\x.(1 - (x mod (2 + (((2 + ((5 * (1 + (x mod 3))) mod (x + 1))) div 2) mod 3)))),(x + 1))
A026451: 2 4 5 7 8 9 11 13 14 15 17 19 21 23 25 26
((x + 9) + ((2 * (1 + ((x2 + 7x + 10) div 3))) div 3))
A159020: 11 14 17 21 25 30 35 40 46 52 59 66 74 82 91 100
((1 + ((x + 1) div (1 + (x div (1 + (2 * ((1 + (x mod (1 + (x mod (3 - (x mod 2)))))) mod (x + 1)))))))) div 2)
A097848: 1 1 1 2 1 2 1 2 2 3 1 2 1 2 3 2
(2 * (1 + (x mod (1 + (x div (2 + (2 * (((2x + 1) mod (2 + (x div 4))) div 2)) - (x mod 2)))))))
A343997: 2 4 2 8 4 4 6 16 8 4 10 8 12 8 6 32
((1 + (((16x3 + 48x2 + 47x + 15) div 2) div 7)) div 2)
A184631: 1 5 15 36 71 123 196 292 416 571 760 987 1255 1568 1928 2340
(1 - ((x + 1) mod (1 - (2 * (1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x mod 2))))))))
A109626: 1 1 1 1 2 1 1 3 1 1 1 4 3 2 1 1
((1 + ((1 + ((x + 1) mod (1 + (2 * (1 + (((2x2 + 1) mod (2 + (x div 4))) div 2)))))) div 2)) div 2)
A277537-A052154: 1 1 0 1 1 0 1 1 0 0 1 1 2 0 0 1
((1 + ((1 + ((1 + (x div (1 + ((0 - (2 * ((x + ~1) mod 4))) mod (2x + 1))))) div 2)) div 2)) div 2)
A031123: 0 1 0 0 1 1 0 0 0 2 0 0 0 2 0 0
(1 - ((1 + ((1 + ((1 + ((((x + ~1) * (2 - (2x mod 9))) div 2) div 2)) div 2)) div 2)) div 2))
A287417: 1 1 1 1 1 0 1 1 2 0 1 1 2 3 0 1
(2 div (2 * (1 + (2 * (2 - (x mod (1 + (2 * ((x + 5) div (6 * (1 + (x mod 2))))))))))))
A243841: 0 0 1 0 0 0 0 0 ~1 0 0 1 1 0 0 0
((1 + ((1 + ((x mod (2 + ((1 + (2 * ((x mod (~2 + ((~x + 1) div 3))) div 2))) mod (x + 1)))) div 2)) div 2)) div 2)
A174656: 0 0 1 0 1 0 1 1 1 1 0 2 0 1 1 1
((1 + ((1 + ((((x + 1) * (3 + (2 * ((x + 2) - ((~x + ((x div 2) mod 2)) div 2))))) div 2) div 2)) div 2)) div 2)
A022956: 1 2 3 4 6 9 11 14 18 22 26 30 35 41 46 51
((1 + ((1 + ((((x + 1) * (2 + ((((x + 1) div (2 - ((x * (x div 2)) mod 2))) div 2) div 2))) div 2) div 2)) div 2)) div 2)
A097576: 0 1 1 1 1 1 1 2 2 2 2 4 3 3 3 6
(((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + ((1 + (x div 2)) div 2))) div 2)
A299334-A298629-A298461-A297978: 0 0 0 0 1 0 0 3 3 0 0 6 8 6 0 0
compr(\x.(((x + ~1) div 2) mod 2),((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~1) div 2))) div 2))
A147644: 1 1 1 1 2 1 1 5 5 1 1 6 10 6 1 1
(((x2 + ~1) - ((((x2 + ~1) - ((((x3 + ~3x2 + 2x) div 2) div 2) div 3)) div 2) div 2)) div 2)
A025206: 0 0 1 3 6 10 14 20 27 35 45 55 67 81 96 112
(1 - ((1 + (((1 + (((x + 1) * (0 - ((x + ((~1 + (x div 2)) mod 3)) div 2))) div 2)) div 2) div 2)) div 2))
A029090: 1 1 1 1 1 2 3 3 3 3 4 5 7 7 7 8
((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) + ((2x + 1) mod (3 + (x div 4)))) div 2)
A115862: 0 0 1 0 1 1 0 2 1 2 0 2 1 2 2 0
(1 - ((5 * (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 4))) div 2))
A069322: 1 1 1 1 4 1 1 6 6 1 1 9 16 9 1 1
((1 + (((x + ((((x + 1) * (2 + (5 * ((x2 + x) div 2)))) div 2) div 3)) div 2) div 2)) div 2)
A025222: 0 0 1 3 6 10 16 25 35 48 65 84 108 135 166 203
(~2 + (3 * (1 + compr(\x.(x mod (1 + ((5x2 + 10x + 5) mod 9))),x))))
A026226: 1 7 16 19 25 34 43 46 52 55 61 70 73 79 88 97
(((((x + 3) * ((x3 + 27x2 + 74x + 48) div 2)) div 2) div 3) div 2)
A096958: 6 25 65 135 245 406 630 930 1320 1815 2431 3185 4095 5180 6460 7956
(((((x + 3) * ((9x3 + 31x2 + 30x + 8) div 2)) div 2) div 3) div 2)
A051798: 1 13 55 155 350 686 1218 2010 3135 4675 6721 9373 12740 16940 22100 28356
(((((x2 + 3x + 2) * (~1 + (7 * ((x2 + 3x + 2) div 2)))) div 2) div 3) div 2)
A006323: 1 10 41 115 260 511 910 1506 2355 3520 5071 7085 9646 12845 16780 21556
((3 * ((x + 1) + (((3 * (1 + (((x2 + ~4x + 4) div 2) div (x + 3)))) div 2) div 2))) div 2)
A225647: 1 3 4 6 7
A068675: 1 3 4 6 7 9 10 13 15 18 19 21 24 25 27 28
((x + 1) mod (4 + ((6x + 84) mod 11)))
A031076: 1 2 3 4 5 6 7 8 1 0 1 1 1 2 1 3
(~2 + (2 * (1 + ((1 + (x div (1 + (2 * ((2 + ((4 * (3 - (x mod 2))) mod (x + 1))) div 2))))) div 2))))
A276812: 0 0 0 2 0 2 0 2 2 0 4 2 0 2 0 2
(((1 + (((x + 1) * (1 + ((1 + (x mod (2 - (x div (~1 + ((~x + 2) div 4)))))) div 3))) div 2)) div 2) div 2)
A233567: 0 0 1 1 0 1 1 2 2 2 3 1 3 2 4 2
(((5 * (1 + (((1 mod (1 - (2x mod (4 + (x div 4))))) mod (x + 1)) div 2))) div 2) div 2)
A096583: 1 1 1 1 3 1 1 5 5 1 1 7 8 7 1 1
((((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (3 + (x div 2))) div 2) div 2)
A300175-A299602-A299554-A298841: 0 0 0 0 1 0 0 3 3 0 0 6 9 6 0 0
((((2 + (((14x2 + 27x + 9) div 2) div 3)) div 3) div 2) div 2)
A248358: 0 0 1 3 4 7 9 12 15 19 23 27 32 38 43 49
(4 + ((2 * ((2x + 4) + (x2 div ((x + 1) + (2 * (x div 5)))))) div 3))
A050199: 6 8 10 12 14 15 17 18 20 22 24 26 28 30 32 33
((2 + ((3 * (2 + ((33x + 11) mod (x + 1)))) div (x + 1))) div 2)
A182199: 4 2 3 2 2 2 2 1 2 2 1 1 1 1 2 2
((2 * ((x + ((x + (4 * ((x + 1) + (5 * (x + (x mod 2)))))) div 2)) * ((x + 1) div 2))) div 2)
A219258: 0 25 29 104 112 237 249 424 440 665 685 960 984 1309 1337 1712
(4 * ((3 * compr(\x.(1 - (x mod (2 + ((1 + ((x - ((x div 2) mod 2)) div 2)) mod 5)))),x)) div 2))
A186303: 4 12 16 24 36 40 52 64 76 84 96 100 112 120 132 136
((1 + ((2x + ~4) * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2))) mod (2 + (((x + 1) div 2) div 2)))
A167269: 1 1 1 1 2 1 1 3 1 1 1 4 1 3 1 1
(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 - (4 * ((1 + (x div 2)) div 2)))) div 2))
A128254-A103450: 1 1 1 1 3 1 1 5 5 1 1 7 12 7 1 1
(1 - (16 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))
A176203: 1 1 1 1 17 1 1 33 33 1 1 49 81 49 1 1
(2 * (2 + ((((x + 2) * (4 + (((x + 1) + ((((x + ~1) div 2) div 2) + (x mod 4))) div 2))) div 2) div 2)))
A165143: 8 10 16 20 22 32 40 48
(((49x2 + 99x + 50) div 5) div 8)
A101418: 1 4 11 19 30 44 60 78 99 122 148 176 207 240 276 314
(1 - (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * ((~x + 2) div 4)) div 2))
A225910: 1 1 1 1 2 1 1 3 3 1 1 6 7 6 1 1
(4 * ((2x + 3) + (2 * (x + (2 * ((x + 1) div (8 - ((x + 2) div 3))))))))
A223454: 12 28 44 60 76 108 124 140 156 188 204 236 252 284 316 332
(2 * ((x + 3) + ((4 * ((3 * (1 + (x div 2) - ((x div 4) mod 2))) div 2)) div 3)))
A287270: 8 10 18 20 22 24 28 30 40 42 50 52 54 56 60 62
(2 + (((x + 1) + compr(\x.((x mod (2 + ((2 * (x mod (~1 + (2 * (x mod 5))))) mod (x + 1)))) div 2),x)) div 2))
A028789: 2 3 6 7 8 10 11 12 13 14 15 18 19 21 22 23
((4x + 9) + (((6x + 5) div (x + 2)) mod 2))
A011767: 9 14 17 21 25 30 34 38 42 46 50
(((2x + 1) + compr(\x.(1 - (x mod (1 + (((x2 + 3x + 2) div 2) mod 9)))),(x + 1))) div 2)
A288463: 1 3 4 6 9 10 12 14 15 17 20 21 23 24 26 29
((4x + 1) + compr(\x.((((x + 1) div (1 + ((2x + 1) mod 9))) mod 2) - (x mod 2)),x))
A315495: 1 6 11 16 22 28 34 39 44 50 56 61 66 72 78 84
((x + ~3) + ((2 * ((2x + 6) + (2x div (8 + (x mod 2))))) div 3))
A097911: 1 3 5 8
A288474: 1 3 5 8 11 13 15 18 21 23 25 28 31 32 35 38
(((~x + 1) + (3 * ((2 * ((2 * (2x - (x mod 8))) - (x mod 4))) - (x mod 2)))) div 2)
A224915: 0 1 5 6 22 23 27 28 92 93 97 98 114 115 119 120
((x + 2) + ((((x + 3) * ((x3 + 19x2 + 50x + 32) div 2)) div 2) div 3))
A200872: 10 37 94 195 356 595 932 1389 1990 2761 3730 4927 6384 8135 10216 12665
((x + ((2 * ((x + 1) + (2 * ((2 * (2x - (x mod 8))) - (x mod 4))))) div 3)) div 2)
A010376: 0 1 3 4 9 10 12
A276986: 0 1 3 4 9 10 12 13 28 29 31 32 37 38 40 41
((x + ((2 * ((x + 2) + (((9x2 + 26x + 16) div 2) div 3))) div 3)) div 2)
A111201: 1 4 8 12 18 25 33 41 51 62 74 86 100 115 131 148
((x + ((1 + (((1 + (((x + 1) * (1 + ((1 - (x mod 3)) mod (x + 1)))) div 3)) div 2) div 2)) div 2)) div 2)
A049982: 0 0 1 1 2 3 3 3 6 5 5 8 6 7 12 8
((x + 2) + ((3 * (x + ((x + ((x + (((x4 + ~x3) div 2) div 3)) div 2)) div 2))) div 2))
A006808: 2 4 8 15 28 50 90 156
((x + ((2 + (((x * (1 + (3 * ((x3 div 5) mod 2)))) div 2) div 3)) div 2)) div 2)
A309965: 0 1 1 2 2 3 4 4 4 6 5 6 8 9 8 10
((x + ((x + ((1 + ((x * (2x + (((x2 + x) div 2) div 7))) div 2)) div 2)) div 2)) div 2)
A194238: 0 1 2 3 5 7 10 13 16 20 24 29 35 41 48 55
(1 + (compr(\x.(1 - ((~1 + (2 * ((2x + 2) - ((x mod ~4) div 2)))) mod 5)),x) + (x div 2)))
A237590: 1 2 4 5 7 8 10 11 14 16 18 19 21 23 26 27
(1 + ((1 + ((2 * (1 + ((1 + (x2 div 7)) div 2))) div 3)) mod (x + 1)) - (x mod 2))
A326668: 1 1 2 2 3 3 4 4 6 5 7 7 9 9 12 12
(1 + ((1 + ((x - ((3 * (2 - ((~x + 1) div (2 + (x div 4))))) div 2)) div 2)) mod (x + 1)) - (x mod 2))
A029182: 1 0 1 0 2 0 2 1 3 2 3 3 4 4 5 5
(((3x + 3) + ((2 * (x - ((x - (x div 3)) div 3))) + (((x + 1) div 2) div 2))) div 2)
A231407: 1 4 6
A184814: 1 4 6 9 11 13 16 19 20 23 25 28 31 32 35 38
(45x3 + 89x2 + 36x + 23)
A062640: 23 193 811
((4x + 5) + ((x * ((x + 2) + ((x3 + 2x) div 3))) div 4))
A215449: 5 10 17 29 51 90
compr(\x.(~1 + (((1 + ((x - ((x div 2) div 5)) mod 2) - (x mod 2)) * (1 + (x div 3))) div 3)),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A289351: 0 1 2 3 4 5 6 7 8 9 11 13 15 17 19 31
((x + 1) + ((2 * ((x + ~1) - (2 * ((x div (1 + (4 * (1 + (2 * (x mod 2)))))) + (x mod 2))))) div 3))
A180020: 0 0 3 4 7 7 9 10 12 14 14 17 17 19 21 22
((~x + 1) + ((2 * ((x + 1) + ((2 * (1 + ((((x2 + 3x + 2) div 2) div 2) div 2))) div 3))) div 3))
A323089: 1 1 1 2 1 2 3 3 4 4 5 6 7 9 10 12
compr(\x.(1 - (x mod (1 + ((2 + (x mod (1 + ((~2x + 1) mod 5))) - (x mod 2)) mod (x + 1))))),x)
A154660: 3 4 5 6 7 8
A207966: 3 4 5 6 7 8 10 11 13 14 17 19 20 22 23 25
((x + 1) + (2 * (((~1 + (6 * (3 + ((x + (x div 2)) div (4 + (x div 2)))))) div 2) div 2)))
A258469: 9 10 11 12 15 16 17 18 19 20 21 22 23 24 25 30
((x + 1) + ((x - ((~x + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) div 2)) div 2))
A342740: 1 3 4 6 8 10 11 13 14 17 18 19 21 23 25 27
compr(\x.(1 - ((2 * (1 + ((1 + (x3 div (3 * (1 + (2 * (x mod 3)))))) div 2))) mod 3)),x)
A138083: 0 1 2 4 5 6
A276005: 0 1 2 4 5 6 7 12 14 16 18 19 20 22 23 24
(~x + ((2 * ((2 + ((3 * (x + (2 * (x - ((3 * (x div 4)) div 2))))) div 2)) div 2)) div 3))
A330957: 0 1 1 1 1 1 2 3 1 1 2 3 2 3 3 3
(~x + ((2 * ((x + 2) + ((2 * ((x + 1) + (((x + 1) div 3) * (x div 3)))) div 3))) div 3))
A067357-A051059: 1 1 2 2 2 3 4 4 5 6 6 8 10 10 12 14
compr(\x.(2 - (x mod (2 + ((2 * ((1 + (x mod (1 + (x mod (3 - (x mod 2)))))) mod (x + 1))) + (x mod 2))))),x)
A269390: 3 5 6 9 10 11 13 14 17 18 19 20 22 23 25 26
((2x + 1) + ((1 + ((1 + (3x mod (1 + ((2x + 4) div 9)))) div 2)) mod 2))
A189214: 2 4 6 7 10 11 14 16 18 20 22 24 26 28 29 31
((3x + 3) + ((1 + ((17x2 + 17x) div 2)) div 5))
A194139: 3 9 19 32 49 69 92 119 149 183 220 260 304 351 402 456
(~x + (2 * (1 + (((x + 1) - ((2 * (1 + ((x mod 10) mod (1 + (x div 2))))) mod 3)) div 2))))
A165592-A165578: 0 1 0 1 2 3 2 1 0 1 0 1 2 1 2 3
((x + 1) - ((1 + ((1 + ((((x + 1) * (~1 + (2 * ((x mod (3 + (x mod 2))) mod 2)))) div 2) div 2)) div 2)) div 2))
A125616: 1 2 3 3 4 5 7 7 9 9 10 11 14 13 16 15
compr(\x.(x - (2 * ((x + 1) mod (1 + (2 * ((~1 + (6 * (x mod 10))) mod (x + 1))))))),x)
A233524: 0 1 2 4 5 8
A095031: 0 1 2 4 5 8 10
A323976: 0 1 2 4 5 8 10 12 14 15 19
(x + ((1 + (((1 + (((x + 1) * (1 + (2 * ((3 * ((x div 2) div 3)) div 2)))) div 2)) div 2) div 2)) div 2))
A051382: 0 1 2 3 4 6 7 9 10 11 12 13 18 19 21 22
((~x2 + ~2x) + ((x + 3) * (((x3 + 15x2 + 38x + 24) div 2) div 3)))
A252178: 12 49 132 285 536 917 1464 2217 3220 4521 6172 8229 10752 13805 17456 21777
(1 + loop(\(x,i).(loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).3x,x,1)),1,loop(\(x,i).2x,x,1)))
A247207: 10 30 354 72354 4338079554 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (2 * loop(\(x,i).(1 + loop(\(x,i).(x - (if x <= 0 then 1 else loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,x))),x,x)),x,1)))
A100859: 3 5 7 13 19 29 31 37 43 53 59 61 67 73 79 89
(1 + (if x <= 0 then 2 else (x + loop(\(x,i).(x - (if x <= 0 then 1 else (if (x mod 2) <= 0 then (x div 2) else (1 + (if (~x + 2) <= 0 then x else 0))))),x,(x + 1)))))
A241235: 3 3 1 4 1 2 1 5 1 2 1 3 1 2 1 6
loop(\(x,i).(loop(\(x,i).2x,x,loop(\(x,i).(3x + 2),x,0)) - loop(\(x,i).3x,x,1)),1,loop(\(x,i).2x,x,1))
A061063: 1 23 1199 1672799 2821066795199 4611686018427387903 4611686018427387903
((~x + ~1) + loop(\(x,i).(1 - loop(\(x,i).(x - (if x <= 0 then 0 else (~1 + loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x)))),x,x)),2,(x + 1)))
A085931: 2 4 12 17 23 39 48 58 69 95 109 124 140 157 195 215
loop(\(x,i).compr(\x.(1 - (x mod (2 + (if x <= 0 then 1 else loop(\(x,i).((if x <= 0 then 2 else loop(\(x,i).(x div (2 - (x mod 2))),x,x)) div 2),2,x))))),x),2,x)
A050198: 2 3 4 5 7 9 11 13 16 19 21 23 25 27 29 31
compr(\x.loop(\(x,i).(if x <= 0 then 1 else (~2 + (if x <= 0 then 2 else (loop(\(x,i).(1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),2,x) mod (x + 1))))),2,x),x)
A268412: 0 5 9 10 11 13 17 18 19 20 22 23 25 26 27 29
(x + (if (x + ~1) <= 0 then 1 else loop(\(x,i).(x - (if x <= 0 then 1 else (if (x div 3) <= 0 then x else (if (x mod (2 + (x mod 2))) <= 0 then 1 else x)))),x,x)))
A082691: 1 2 1 2 3 1 2 1 2 3 4 1 2 1 2 3
loop(\(x,i).2x,(x + ~1),((loop(\(x,i).2x,x,1) + loop(\(x,i).(4x + 1),x,0)) - loop(\(x,i).3x,x,1)))
A228700: 0 0 0 8 160 2080 22400 217728 1989120 17461760 149248000 1252354048 10373242880 85129175040 693959884800 5629506387968
(~1 + loop(\(x,i).(loop(\(x,i).(x * i),x,1) + loop(\(x,i).2x,x,1)),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))))
A186450: 2 5 13 151 5167 39918847
loop(\(x,i).2x,(x + ~1),(if x <= 0 then 0 else loop(\(x,i).x2,1,loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),(x + ~1),1))))
A116421: 0 1 18 400 9800 254016 6830208 188457984 5300380800 151289881600 4369251780608 127394382495744 3743979352236032 110768619888640000 3295931587706880000 4611686018427387903
(if (x mod 2) <= 0 then ((if (x mod 4) <= 0 then (14 * (2 + (if x <= 0 then 0 else 2))) else 1) + (if x <= 0 then 1 else 2)) else 1)
A040858: 29 1 3 1 58 1 3 1 58 1 3 1 58 1 3 1
(if (x mod 2) <= 0 then ((5 * (if (x mod 4) <= 0 then (5 * (if x <= 0 then 1 else 2)) else 1)) + (if x <= 0 then 1 else 2)) else 1)
A040696: 26 1 7 1 52 1 7 1 52 1 7 1 52 1 7 1
loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))
A105574: 2 3 5 3 11 3 17 3 5 3 31 3 41 3 5 3
(1 + loop(\(x,i).(x - loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,(x + 1))),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A147849: 3 6 6 10 15 15 21 21 28 36 36 45 45 45 55 55
(if (if x <= 0 then 1 else (loop(\(x,i).(2x + 2),x,0) mod (x + 1))) <= 0 then (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) else 1)
A259182: 1 3 5 1 11 1 17 1 1 1 31 1 41 1 1 1
loop(\(x,i).2x,x,loop(\(x,i).(6x + loop(\(x,i).(~1 + (2 * (2x + loop(\(x,i).2x,i,1)))),i,1)),x,1))
A025979: 1 26 452 6664 90384 1169952 14730304 182323328 2232488192 27147248128 328628192256 3966436411392 47780455321600 574831345147904 6909703728939008 83010267592032256
loop(\(x,i).2x,x,loop(\(x,i).(6x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1))
A025970: 1 24 388 5376 69328 862848 10547776 127767552 1540506880 18530383872 222632510464 2673205936128 32088199647232 385116900458496 4621754370506752 55463163983560704
loop(\(x,i).2x,((2x + 2) - (if x <= 0 then 2 else (x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (1 + (x mod 2))))),x,(x + 1))))),1)
A278312: 1 8 16 128 128 2048 4096 32768 16384 524288 1048576 8388608 8388608 134217728 268435456 2147483648
loop(\(x,i).2x,x,loop(\(x,i).(8x + loop(\(x,i).(~1 + (2 * (2x + loop(\(x,i).2x,i,1)))),i,1)),x,1))
A028258: 1 30 620 11160 188976 3108960 50434240 812507520 13044728576 209073047040 3348029967360 53591377582080 857645259698176 13723790036459520 219592368170516480 3513571713573027840
loop(\(x,i).2x,x,loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1))
A025977: 1 24 380 5040 60816 693504 7625920 81818880 862797056 8985360384 92714818560 950046289920 9683681284096 98302694129664 994754528460800 10041368129372160
loop(\(x,i).4x,x,loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1))
A075907: 1 40 1040 22400 435456 7956480 139694080 2387968000 40075329536 663887544320 10896534405120 177653730508800 2882307270639616 46596186764738560 751299029274460160 4611686018427387903
loop(\(x,i).3x,x,loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1))
A028085: 1 30 585 9450 137781 1888110 24862545 318755250 4012058061 49847787990 613622150505 7503229474650 91300979746341 1106997911204670 13386607046238465 161563913916523650
loop(\(x,i).2x,x,loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1))
A025968: 1 22 320 3920 44016 471072 4904320 50237440 509670656 5141007872 51677982720 518395637760 5193684791296 51995352604672 520305091051520 5205162447994880
(loop(\(x,i).loop(\(x,i).(x * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),i))),i,2x),x,1) div loop(\(x,i).2x,x,1))
A302156: 1 3 45 4725 5457375 81942485625 20916229168209375 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) + loop(\(x,i).(~1 + loop(\(x,i).(x - (x div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))),x,x)),x,x))
A297616: 1 2 3 3 4 3 4 4 4 3 4 4 5 4 4 4
((loop(\(x,i).3x,x,1) + loop(\(x,i).5x,x,1)) - loop(\(x,i).(2x + 1),x,loop(\(x,i).2x,x,1)))
A198628: 1 3 15 81 435 2313 12195 63801 331395 1710153 8775075 44808921 227890755 1155180393 5839846755 29458152441
(loop(\(x,i).5x,x,1) - (loop(\(x,i).3x,x,1) + loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1))))
A137787: ~2 ~4 ~4 26 272 1826 10736 59426 318272 1670786 8656976 44454626 226827872 1151991746 5830280816 29429454626
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).10x,x,loop(\(x,i).(10x + 1),x,1)),1,i)),x,1)
A109242: 1 111 11211 1122211 112232211 11223332211 1122334332211 112233444332211 11223344544332211 1122334455544332211 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~2 + loop(\(x,i).loop(\(x,i).(x + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(~2 + i),1)),x,1),1,loop(\(x,i).2x,x,1)))
A083942: 0 1 8 625 13402696 19720133460129649 4611686018427387903 4611686018427387903
loop(\(x,i).4x,x,((loop(\(x,i).4x,x,1) - loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1)) div 2))
A055787: 0 4 80 1408 23808 395264 6496256 106102784 1725759488 27987017728 452890460160 7316694892544 118053383700480 1902813588226048 30644438111879168 493182667873845248
((3 * (if (x mod 2) <= 0 then (5 * (if (x mod 4) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1)) else 1)) - (if x <= 0 then 1 else 2))
A040866: 29 1 13 1 58 1 13 1 58 1 13 1 58 1 13 1
((3 * (if (x mod 2) <= 0 then (3 * (if (if (x mod (2 + (x mod 4))) <= 0 then x else 0) <= 0 then 1 else 2)) else 1)) - (if x <= 0 then 1 else 2))
A010157: 8 1 7 1 16 1 7 1 16 1 7 1 16 1 7 1
(loop(\(x,i).(1 + loop(\(x,i).(1 + loop(\(x,i).2x,x,2) - loop(\(x,i).(4x + ~8),x,0)),1,2x)),1,(x + 2)) div 2)
A166916: 357 5525 87637 1399125 22373717 357930325 5726688597 91626231125 1466016552277 23456252253525 375299985724757 6004799570269525 96076792319006037 1537228673882871125 4611686018427387903
loop(\(x,i).loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),x,(2x + 1)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A119653: 5 7 11 1 23 1 1 1 47 59 1 1 83 1 1 107
loop(\(x,i).(loop(\(x,i).3x,x,1) + loop(\(x,i).2x,x,1)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A135172: 13 35 275 2315 179195 1602515 129271235 1162785755 94151567435 68630914235795 617675543767595 450284043329950835 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if (if x <= 0 then 1 else (loop(\(x,i).(2x + 2),x,0) mod (x + 1))) <= 0 then 1 else (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A259175: 2 1 1 7 1 13 1 19 23 29 1 37 1 43 47 53
loop(\(x,i).loop(\(x,i).(x + (if (x mod (1 + i)) <= 0 then 1 else 0)),x,2x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A059786: 5 7 11 17 23 29 37 41 47 59 67 79 83 89 97 107
(1 - loop(\(x,i).loop(\(x,i).(x - (if x <= 0 then 0 else (1 + (2 * i)))),x,x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A106044: 2 1 4 2 5 3 8 6 2 7 5 12 8 6 2 11
(((loop(\(x,i).2x,x,1) + loop(\(x,i).3x,x,1)) - loop(\(x,i).3x,(x + ~2),1)) div loop(\(x,i).2x,x,2))
A179523: 0 1 1 2 2 3 5 8 11 17 26 38 58 86 130 195
(3x + loop(\(x,i).(x - (if x <= 0 then 1 else (x - ((if x <= 0 then 2 else loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 2)))),x,(x + 1)))
A193259: 1 4 5 9 10 12 13 18 19 21 22 25 26 28 29 35
(x + loop(\(x,i).(x - (if x <= 0 then 1 else (if (x mod 2) <= 0 then (x div 2) else (1 + ((if ((x + ~1) mod 3) <= 0 then 1 else x) * (x mod 2)))))),x,x))
A064918: 0 0 1 0 2 0 1 1 3 0 1 0 2 1 2 0
loop(\(x,i).2x,(((1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))) div 2) + (if x <= 0 then 0 else 1)),1)
A318474-A318312: 1 2 2 4 2 4 2 8 4 4 2 8 2 4 4 32
(~1 + loop(\(x,i).(4x + loop(\(x,i).3x,i,1)),(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1))
A244841: 6 36 780 14196 4017156 65514540 17050729020 273715645476 70274600998836 288161745774346860 4611068345031103956 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (1 + (9 * ((1 + loop(\(x,i).loop(\(x,i).((x + 1) + (x2 div 3)),x,1),x,1)) div 2))))
A045646: 1 10 19 199 4611686018427387903
(~1 + ((3x + 3) * loop(\(x,i).(if x <= 0 then (x + 1) else (2 - loop(\(x,i).(x - (2 * (~2x + (i mod 2)))),x,0))),x,1)))
A069151: 2 23 2357
A124513: 2 23 2357 4611686018427387903
(if (x + ~1) <= 0 then 1 else (~1 + (loop(\(x,i).2x,x,((1 + loop(\(x,i).(2 * ((x + 2) - (x * (i mod 2)))),x,1)) div 2)) div 3)))
A282802: 1 1 7 4 31 20 127 84 511 340 2047 1364 8191 5460 32767 21844
(1 + ((loop(\(x,i).3x,(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1))),1) div 2) div 3))
A236313: 1 2 1 5 1 2 1 14 1 2 1 5 1 2 1 41
(1 + compr(\x.(loop(\(x,i).x3,1,(1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))) mod (x + 1)),(x + 1)))
A283262-A277187-A087797: 2 3 4 5 7 8 9 11 13 17 19 23 25 27 29 31
(if x <= 0 then 1 else (loop(\(x,i).(10x + 1),2x,1) - loop(\(x,i).10x,(x + 1),1)))
A267815: 1 11 10111 1101111 111011111 11110111111 1111101111111 111111011111111 11111110111111111 1111111101111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).3x,x,loop(\(x,i).7x,x,(1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))))
A156762: 1 42 441 37044 194481 8168202 85766121 14408708328 37822859361 1588560093162 16679880978201 1401110002168884 7355827511386641 308944755478238922 3243919932521508681 4611686018427387903
(1 + (loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1) + loop(\(x,i).7x,x,1)))
A134006: 4 16 84 496 3108 20176 134004 903856 6161988 42326416 292299924 2026332016 14085959268 98111307856 684331371444 4778093436976
(1 + (2 * (1 + (2 * compr(\x.(x - loop(\(x,i).loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),x,(2x + 1)),2,(2x + 1))),x)))))
A002515: 3 11 23 83 131 179 191 239 251 359 419 431 443 491 659 683
(1 + (x div (2 + (x mod (1 + (loop(\(x,i).2x,x,(if x <= 0 then 1 else (if (x mod 2) <= 0 then (~1 + (2 * (x mod 2))) else x))) mod (x + 2)))))))
A094521: 1 1 2 1 2 1 4 3 2 1 4 1 2 5 8 1
(1 + (2 * (1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(2x2 + 6x)),x))))
A028879: 3 5 7 13 17 23 25 47 53 55 65 67 73 77 83 85
(1 + (((1 + (((((x + 1) * loop(\(x,i).x2,1,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x))) div 2) div 2) div 2)) div 2) div 2))
A274859-A113143: 1 1 1 1 1 2 1 1 2 4 1 1 2 5 8 1
(5 + (if x <= 0 then 2 else (2 - (if x <= 0 then 2 else (1 + (if ((x - ((x div 5) mod 2)) mod 3) <= 0 then 2 else 1))))))
A098842: 7 5 5 4 5 5 5 4 5 5 5 5 4 5 5 5
(loop(\(x,i).(5x + (if (x mod 2) <= 0 then 1 else (3 + (if (x mod 3) <= 0 then 0 else 2)))),(x + 1),1) div 3)
A037794: 3 17 86 430 2153 10767 53836 269180 1345903 6729517 33647586 168237930 841189653 4205948267 21029741336 105148706680
(6 * (1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,(x + 2)),1,3x),x)))
A259826: 120 144 186 204 216 246 288 300 324 342 414 426 474 516 528 534
((if (x mod 3) <= 0 then ((1 + (if (x mod 2) <= 0 then 16 else 1)) * (if x <= 0 then 1 else 2)) else 1) + (3 * (x mod 2)))
A040278: 17 4 1 7 1 4 34 4 1 7 1 4 34 4 1 7
compr(\x.(x + (if x <= 0 then 1 else loop(\(x,i).(x - (if x <= 0 then 1 else (x2 mod (1 + (4x * (x mod 2)))))),x,x))),(2x + 1))
A331830: 7 13 19 27 31 39 45 51 55 61 67 75 79 87 93 99
(loop(\(x,i).7x,x,1) + loop(\(x,i).6x,x,1) + loop(\(x,i).3x,2x,1))
A074578: 3 22 166 1288 10258 83632 695746 5886448 50491138 437851792 3829725826 33721183408 298447606018 2651815532752 23633379691906 211108878589168
(loop(\(x,i).7x,x,1) + loop(\(x,i).8x,x,1) + loop(\(x,i).3x,2x,1))
A074580: 3 24 194 1584 13058 108624 911234 7703664 65588738 561991824 4843001474 41948320944 364990300418 3188510652624 27953062038914 245823065693424
(loop(\(x,i).7x,x,1) + loop(\(x,i).5x,x,1) + loop(\(x,i).3x,2x,1))
A074575: 3 21 155 1197 9587 78981 664715 5684637 49202147 429727221 3779025275 33407214477 296514964307 2639975541861 23561119043435 210669211182717
(1 + loop(\(x,i).compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x),1,(x + (x div 11))))
A027563: 1 2 3 5 6 8 9 11 14 15 18 21 23 26 29 30
(~1 + compr(\x.((1 + ((loop(\(x,i).2x,loop(\(x,i).(loop(\(x,i).(x div (2 - (x mod 2))),x,x) div 2),2,x),2) div 2) div 2)) mod 3),x))
A004752: 10 18 20 21 26 34 36 37 40 41 42 43 50 52 53 58
loop(\(x,i).(12x + loop(\(x,i).((9x + ~1) + loop(\(x,i).2x,i,2)),i,1)),x,1)
A021304: 1 24 403 5886 80113 1046748 13329631 166873722 2064748525 25337358072 309091680859 3754490630358 45462401712937 549225447909396 6623795021132887 79783347069641394
loop(\(x,i).(12x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),x,1)
A016633: 1 25 447 6989 101759 1417941 19180519 253983853 3309800367 42599540357 542895780791 6863463633117 86197420501375 1076563471968373 13382900349107463 165700329729679181
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(4x + 1),i,1)),i,1)),x,1)
A021844: 1 23 363 4963 63539 787731 9609811 116281811 1401253587 16850623699 202422366419 2430363281619 29172151056595 350112652220627 4201633221810387 50421288464357587
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021534: 1 22 337 4522 57253 705334 8574889 103567234 1246828045 14986093486 179978152081 2160608272186 25932522746677 311221616234278 3734847461630713 44819297962008178
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).8x,i,1)),i,1)),x,1)
A020594: 1 26 460 6920 95536 1254176 15958720 199053440 2450711296 29915173376 363095649280 4390419138560 52953377222656 637600367845376 7668561507696640 92162065025761280
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).5x,i,1)),i,1)),x,1)
A019869: 1 23 367 5075 65551 817643 10013527 121451315 1465540351 17637184763 211960186087 2545454874755 30557298487951 366759842503883 4401557777453047 52821361851453395
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).4x,i,1)),i,1)),x,1)
A019628: 1 23 369 5143 66977 841575 10367953 126315191 1529146113 18443562247 221980457777 2668373663319 32052757927009 384859080003239 4619891122628241 55449769683406327
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).3x,i,1)),i,1)),x,1)
A018055: 1 22 343 4696 60493 755146 9267091 112644652 1361819305 16412435710 197443515919 2372782379968 28497610413637 342140879536114 4106877441223627 49290837516564244
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A020978: 1 29 565 9245 137221 1915949 25677205 334395965 4265954341 53604494669 666045061045 8206250792285 100467119521861 1224084180206189 14859716922480085 179888148281902205
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(4x + 1),i,1)),i,1)),x,1)
A021944: 1 25 425 6185 83241 1072425 13462825 166325545 2034167081 24716438825 299050134825 3608230161705 43455812660521 522726247165225 6282767285808425 75473627419962665
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021674: 1 24 397 5676 75529 966048 12071269 148688052 1814929057 22024557672 266258052541 3210803780028 38655303353785 464868906584496 5586469016901013 67101965327432004
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).5x,i,1)),i,1)),x,1)
A020448: 1 25 429 6305 85541 1108665 13976989 173186065 2122320981 25822510505 312717161549 3775431050625 45488017644421 547320192731545 6579560264282109 79048497300991985
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A021794: 1 22 335 4460 56061 686802 8317435 100210120 1204613321 14466168782 173649468135 2084076423780 25010353485781 300131513309962 3601614875036435 43219563508677440
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A019747: 1 26 468 7240 103376 1406496 18541888 239158400 3036523776 38104777216 473923294208 5853743400960 71911576293376 879605537447936 10721932937084928 130329861195857920
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A020566: 1 26 463 7040 98461 1310486 16902043 213488540 2658229321 32768006546 401049136423 4883135986040 59232793113781 716511189600206 8649599428831603 104258410046219540
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021484: 1 21 310 4050 50371 613671 7411240 89174100 1071295141 12861600921 154369595770 1852587338550 22231809806311 266785528785771 3201445408153900 38417440232993400
loop(\(x,i).(12x + loop(\(x,i).(2x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A021324: 1 25 437 6629 93429 1260021 16509109 211998133 2682866357 33583284917 416888307381 5141548576437 63087471804085 770938550533813 9390151495286453 114070706832309941
loop(\(x,i).(12x + loop(\(x,i).(2x + loop(\(x,i).(7x + 1),i,1)),i,1)),x,1)
A021254: 1 22 341 4646 59661 743358 9112405 110693878 1337742173 16118816558 193887174117 2329875721446 27981116089837 335931645121822 4032287505801077 48395204420052950
loop(\(x,i).(12x + loop(\(x,i).(3x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A018207: 1 25 439 6685 94471 1276405 16745119 215226205 2725568791 34135388485 423910350799 5229781276525 64185946519111 784517071831765 9557062002788479 116113315455883645
loop(\(x,i).(11x + loop(\(x,i).(~1 + (2 * (4x + loop(\(x,i).2x,i,1)))),i,1)),x,1)
A021274: 1 22 337 4482 55533 660774 7667929 87542794 988535845 11078416206 123498755601 1371575734386 15192048468637 167950256294518 1854154604388553 20449314929530458
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A020571: 1 22 325 4030 45301 478702 4851925 47752510 460048501 4362445582 40876539925 379553364190 3499808594101 32098136255662 293160602826325 2668857246099070
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(4x + 1),i,1)),i,1)),x,1)
A021804: 1 18 213 2098 18669 155946 1248661 9704706 73804797 552214234 4080381669 29857556274 216794571085 1564401539082 11232205936437 80315244188002
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021494: 1 17 192 1822 15743 128499 1010374 7741184 58209525 431623621 3166395596 23035216386 166469995147 1196633240183 8564499500658 61079918944228
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).5x,i,1)),i,1)),x,1)
A019757: 1 18 217 2190 19981 170898 1398097 11075670 85654261 650280378 4865931577 35994162750 263799130141 1918854559458 13871649322657 99770067275430
loop(\(x,i).(6x + loop(\(x,i).(9x + loop(\(x,i).(4x + 1),i,1)),i,1)),x,1)
A021824: 1 20 267 3010 31073 304920 2901319 27075950 249555405 2281579300 20749095731 188036746170 1700122392697 15347941075760 138412864844703 1247405586235270
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A022111: 1 20 263 2878 28449 264048 2350651 20332466 172311557 1438844836 11885079999 97387603014 793247778025 6432389826584 51985193621507 419076145997722
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A020584: 1 24 388 5280 65296 760704 8515648 92705280 989122816 10397865984 108092228608 1114193633280 11410283892736 116262680100864 1179983894560768 11939165879009280
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).7x,i,1)),i,1)),x,1)
A020570: 1 21 295 3465 36751 365001 3463615 31794105 284628751 2499039081 21606842335 184519243545 1559982264751 13079717026761 108915112739455 901732722577785
loop(\(x,i).(6x + loop(\(x,i).(9x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021504: 1 19 244 2674 27055 261793 2467018 22871728 209866789 1912958047 17361652672 157125321262 1419351371803 12805505620381 115437617402806 1040066979064876
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A021829: 1 21 297 3577 39753 422793 4384969 44813769 454009545 4575676105 45971643081 461011315401 4617904831177 46225887853257 462540273695433 4627092539587273
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A019488: 1 21 307 3897 46243 529953 5961259 66380889 735097555 8115781905 89452902331 985061928201 10842178002787 119303005894977 1312567620466123 14439652232597433
loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A019839: 1 21 301 3681 41461 445641 4658221 47871201 486836581 4919066361 49504632541 496978967121 4981629662101 49888557269481 499325240101261 4995920923029441
loop(\(x,i).(6x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A020595: 1 25 421 5965 76741 929005 10791061 121699645 1342777381 14569879885 156038219701 1653799781725 17380932862021 181408804717165 1882561696208341 19442349988398205
loop(\(x,i).(6x + loop(\(x,i).(10x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021514: 1 20 273 3208 35069 368988 3800761 38676176 390782997 3931986916 39464899409 395519441304 3960417893485 39635522209004 396543288909417 3966561311533792
loop(\(x,i).(6x + loop(\(x,i).(2x + loop(\(x,i).(24x + 1),i,1)),i,1)),x,1)
A299074: 1 33 853 20853 502789 12080901 290025541 6961116741 167069824837 4009693935429 96232763288389 2309586971953989 55430091245099845 1330322213391637317 4611686018427387903 4611686018427387903
loop(\(x,i).(6x + loop(\(x,i).(2x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021204: 1 20 281 3472 40509 459564 5139121 57034088 630398021 6952517572 76586531385 843104877888 9278071860877 102082299710684 1123046352296513 12354356208201112
loop(\(x,i).(6x + loop(\(x,i).(3x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A017953: 1 20 283 3518 41209 468608 5247271 58277666 644406997 7108612676 78315612739 862197157094 9488521761265 104399859167624 1148555174389087 12635047273900202
(loop(\(x,i).(~1 + (2 * (2x + loop(\(x,i).10x,i,1)))),x,1) * loop(\(x,i).6x,x,1))
A089518: 1 138 10476 683208 42315696 2570768928 155010407616 9318969502848 559578466388736 33585275183251968 2015370124337581056 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).7x,x,1) + loop(\(x,i).8x,x,1) + loop(\(x,i).6x,x,1))
A074577: 3 21 149 1071 7793 57351 426449 3200631 24221633 184649031 1416683249 10930058391 84737546273 659705518311 5154633748049 40402118583351
(loop(\(x,i).7x,x,1) + loop(\(x,i).5x,x,1) + loop(\(x,i).6x,x,1))
A074571: 3 18 110 684 4322 27708 179930 1181604 7835042 52384428 352707050 2388951924 16262210162 111170407548 762690752570 5248264072644
loop(\(x,i).(7x + loop(\(x,i).((9x + ~1) + loop(\(x,i).2x,i,2)),i,1)),x,1)
A021229: 1 19 248 2786 28983 288273 2786566 26424112 247232645 2291004287 21080414004 192953358078 1759187655187 15990940940461 145026232803362 1312990445670284
loop(\(x,i).(7x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),x,1)
A016314: 1 20 287 3634 43329 500136 5666179 63480878 706360277 7826457892 86486501751 954119775882 10514695335145 115797293297888 1274719738572203 14028563710395046
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A020782: 1 24 385 5160 62401 706104 7628545 79669320 810888001 8089258584 79415935105 769621605480 7379461252801 70134974713464 661651583000065 6203106293141640
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(4x + 1),i,1)),i,1)),x,1)
A021854: 1 20 265 2940 29601 280740 2558905 22683980 197048401 1685772660 14253277545 119401486620 992861126401 8206523123780 67497981692185 552905862106860
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021544: 1 19 242 2606 25659 239313 2153884 18910012 163042517 1386706607 11670306726 97399296618 807453069775 6657437827501 54644202679568 446846543376824
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).5x,i,1)),i,1)),x,1)
A019928: 1 20 269 3040 31161 300300 2775109 24887960 218303921 1882786180 16026538749 135010883280 1127921219881 9359429537660 77233958267189 634411837477000
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A021754: 1 17 190 1770 14931 118587 905920 6742340 49288261 355826757 2546230050 18106416510 128181315991 904540692527 6368500164580 44764509392280
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A019618: 1 21 303 3745 42711 464961 4918663 51086385 524227671 5336085601 54018566823 544793838225 5480212349431 55028108373441 551863246323783 5529708675105265
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A019943: 1 21 298 3570 38971 401751 3988468 38583300 366449941 3434404281 31873887838 293663563830 2690806228111 24553315831611 223338364450408 2026585451393160
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021424: 1 16 170 1520 12411 96096 719860 5278240 38153621 273134576 1942326750 13748476560 97001079631 682818667456 4798793396840 33686888924480
loop(\(x,i).(7x + loop(\(x,i).(2x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A021234: 1 20 277 3324 37149 398916 4181269 43157708 440992717 4475837652 45219751941 455427151452 4576878947005 45927041513828 460378179477493 4611536145214956
loop(\(x,i).(7x + loop(\(x,i).(3x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A017999: 1 20 279 3370 37841 407640 4281739 44256950 452652981 4597133860 46465625999 468116448930 4705386343321 47223418005680 473421066847059 4742518890351310
(if x <= 0 then 1 else (compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x) mod (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))))
A046930: 1 1 2 4 4 4 4 4 8 6 6 8 4 4 8 10
(1 + compr(\x.(loop(\(x,i).(2x2 + ~x),1,(1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))) mod (x + 1)),x))
A098962: 1 2 3 5 6 7 11 13 15 17 19 23 25 29 31 35
(1 + compr(\x.(1 - (loop(\(x,i).x3,1,(1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))) mod (x + 1))),x))
A325265: 6 10 12 14 15 16 18 20 21 22 24 26 28 30 32 33
loop(\(x,i).(8x + loop(\(x,i).(9x + loop(\(x,i).(4x + 1),i,1)),i,1)),x,1)
A021904: 1 22 323 3992 44949 478074 4896391 48839164 477813017 4606751006 43913627979 414851195616 3890711480605 36272898564418 336508406905487 3108995652410948
loop(\(x,i).(8x + loop(\(x,i).(9x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021634: 1 21 298 3594 39763 417567 4236796 41963988 408348325 3920543913 37248255694 350941450782 3284131050487 30562445793459 283104150028192 2612274474873576
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A021914: 1 23 355 4635 55371 627243 6866155 73433195 772592491 8032358763 82776456555 847393109355 8630981813611 87566313375083 885715453576555 8937574526027115
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A019672: 1 23 365 4975 62661 753783 8811805 101107775 1145674421 12870591943 143722946445 1598128085775 17716831119781 195984586836503 2164626279788285 23881256748106975
loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A229026: 1 19 238 2490 23631 211509 1823908 15348100 127057261 1040261799 8453319978 68343722910 550640774491 4426107030889 35521389816448 284771933350920
loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A020346: 1 23 359 4747 57351 655683 7229839 77760587 821694071 8571599443 88563029919 908455411227 9267399149191 94137972490403 953097676407599 9624750893682667
loop(\(x,i).(8x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A020976: 1 27 487 7335 99631 1265607 15341887 179688375 2050086511 22913907687 251930201887 2733012078615 29322230800591 311701053949767 3287717299503487 34448718207176055
loop(\(x,i).(8x + loop(\(x,i).(10x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021644: 1 22 329 4202 49437 554070 6019393 64026754 670939973 6954808718 71511447657 730821626106 7433874254509 75344008884166 761482226728721 7679159391907058
loop(\(x,i).(8x + loop(\(x,i).(3x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A018070: 1 22 339 4532 56357 672210 7813303 89300464 1009144713 11315328398 126186563867 1401795991596 15529706751469 171706382611786 1895807080277631 20910172869786728
(loop(\(x,i).7x,x,1) + loop(\(x,i).5x,x,1) + loop(\(x,i).8x,x,1))
A074574: 3 20 138 980 7122 52700 395418 2998820 22932642 176524460 1365982698 10616089460 82804904562 647865527420 5082373099578 39962451176900
loop(\(x,i).(9x + loop(\(x,i).(4x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A021772: 1 19 242 2618 26103 248997 2316784 21251956 193359485 1751044295 15814841406 142616378814 1284983809747 11572125768313 104185847231708 937857633325592
loop(\(x,i).(9x + loop(\(x,i).(5x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021454: 1 18 220 2310 22561 212268 1957600 17857620 161924521 1463379918 13200803980 118959425130 1071396569881 9646380238968 86836484875360 781623699024840
loop(\(x,i).(9x + loop(\(x,i).(2x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A021284: 1 22 335 4400 53481 620202 6970675 76624900 828512861 8845504382 93498427815 980374738200 10212261530641 105799242660562 1091082072825755 11208627544304300
loop(\(x,i).(4x + loop(\(x,i).(4x + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),i,1)),i,1)),x,1)
A029887: 1 11 82 515 2934 15694 80324 397923 1922510 9105690 42438076 195165646 887516252 3997537980 17857602568 79200753059
loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A021774: 1 20 271 3150 34041 354480 3620611 36607010 368161981 3692428740 36979730151 370080107670 3702237477121 37029646251800 370333177834891 3703516786589130
loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A019040: 1 20 281 3460 40161 453300 5048041 55853540 616079921 6785596180 74686191801 821775473220 9040683799681 99453356876660 1094016369479561 12034328357198500
loop(\(x,i).(4x + loop(\(x,i).(3x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021394: 1 19 254 3014 34155 380073 4199368 46270588 509296469 5603570687 61644604242 678112219122 7459321497343 82052887210261 902583169445276 9928420525951016
loop(\(x,i).(5x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A020494: 1 24 391 5394 67921 808164 9257851 103242534 1128792181 12157176504 129404822911 1364594578074 14281107062041 148528742855244 1536752582181571 15830742722056014
loop(\(x,i).(5x + loop(\(x,i).(10x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021464: 1 19 248 2810 29871 307929 3126478 31504000 316245941 3168518639 31715571108 317307900390 3173840747611 31742218586149 317441248586138 3174507821007980
loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021154: 1 19 256 3066 35007 391545 4339462 47896672 527676853 5808513711 63913994508 703155662118 7735220904139 85089973066117 936002419362994 10296090191237004
loop(\(x,i).(5x + loop(\(x,i).(3x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A017917: 1 19 258 3110 35651 399609 4433668 48962380 539552901 5939935199 65363612678 719121544050 7910946538951 87023461294789 957273325857288 10530082856852120
loop(\(x,i).(10x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),x,1)
A016325: 1 23 377 5395 71841 915243 11317657 136994195 1631936081 19201296763 223714264137 2585856904995 29694425953921 339138685491083 3855525540397817 43660780944367795
loop(\(x,i).(11x + loop(\(x,i).(4x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A019687: 1 24 397 5628 73513 914112 11008549 129690276 1504024705 17241418920 195930981181 2211723344844 24837316537177 277785786712848 3096821665511893 34435641499407732
loop(\(x,i).2x,(compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1)
A218075: 2 4 4 16 4 16 4 16 64 4 64 16 4 16 64 64
((loop(\(x,i).x3,1,25) - loop(\(x,i).(2x + 2),x,0)) mod loop(\(x,i).2x,x,1))
A321082: 0 1 3 3 11 11 11 11 11 267 267 1291 3339 7435 15627 15627
((~1 + (2 * (2 + loop(\(x,i).2x,x,(3 + (loop(\(x,i).4x,x,2) + loop(\(x,i).2x,x,1))))))) mod (x + 1))
A341411: 0 1 0 3 0 1 1 3 0 5 4 7 2 13 0 3
(1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(11x + 10)),x))
A215667: 1 3 4 9 15 16 18 19 21 28 30 31 33 39 40 43
((1 + (if x <= 0 then 0 else (1 + ((loop(\(x,i).2x,x,((~1 + loop(\(x,i).2x,(x + ~2),2)) div (x + 1))) mod (x + 1)) div 2)))) div 2)
A099245: 0 1 1 1 1 2 2 1 1 1 1 3 1 3 3 1
(2 * (1 + ((x + 1) div (1 + (2 * loop(\(x,i).(2x + 1),1,loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,x)))))))
A144412: 2 2 4 0 ~8 0 0 0 0 0 0 0 0 0 0 0
(2 + ((~2 + (x mod 2)) mod (if (x mod 3) <= 0 then ((1 + (if (x mod 2) <= 0 then 16 else 1)) * (if x <= 0 then 1 else 2)) else 1)))
A040285: 17 2 2 5 2 2 34 2 2 5 2 2 34 2 2 5
((1 + ((((x + 1) * (6 + loop(\(x,i).(x * i),x,loop(\(x,i).(x + loop(\(x,i).(x * i),i,2)),x,1)))) div 2) div 2)) div 2)
A322012: 1 2 8 60 1009
((1 + ((if (x mod 3) <= 0 then ((1 + (if (x mod 2) <= 0 then 6 else 1)) * (if x <= 0 then 1 else 2)) else 1) * (2 + (x mod 2)))) div 2)
A010140: 7 2 1 6 1 2 14 2 1 6 1 2 14 2 1 6
((3 * (if x <= 0 then 2 else (1 + (2 * compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(3x + 1))),x))))) div 2)
A144919-A007645: 3 7 13 19 31 37 43 61 67 73 79 97 103 109 127 139
(2 + ((1 + loop(\(x,i).(x + loop(\(x,i).(x * i),(2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),i)),1)),x,2)) div 3))
A114337: 3 43 1723 13307323
(if x <= 0 then 1 else loop(\(x,i).2x,((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3),2))
A100577: 1 2 2 4 2 8 2 8 4 8 2 32 2 8 8 16
((loop(\(x,i).(~x2 + loop(\(x,i).2x,x,1)),1,(2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x))) div 3) div 2)
A166743: 1 13 321 1337 21797 87321 1398013 89478345 357913781 22906492017 366503875645 1466015503393 23456248058853 1501199875789697 96076792050570001 384307168202281705
(((loop(\(x,i).6x,x,2) + loop(\(x,i).8x,x,1)) - loop(\(x,i).4x,x,3)) div 2)
A178294: 0 4 44 376 2960 22624 171584 1303936 9969920 76793344
(2 * (1 + compr(\x.(~1 + loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(3x2 + 6x))),x)))
A089238: 2 4 6 10 14 16 20 24 26 34 40 44 54 56 60 64
loop(\(x,i).4x,x,((loop(\(x,i).(2 * (2x - (x div (1 + i)))),(x + ~1),2) + loop(\(x,i).4x,x,1)) div 2))
A045952: 1 12 176 2688 41728 653312 10280960 162332672 2569207808 40732459008 646621167616 10275491151872 163421593010176 2600786039144448 41413155926048768 659738836733001728
(loop(\(x,i).2x,x,1) - ((loop(\(x,i).(2 * (2x - (x div (1 + i)))),(x + ~1),2) - loop(\(x,i).4x,x,1)) div 2))
A246472: 1 3 9 30 109 418 1650 6604 26589 107274 432934 1746484 7040626 28362324 114175812 459344920
(~2 + loop(\(x,i).(2 * (1 + (2 * (1 + (loop(\(x,i).(3x + ~1),x,2) * loop(\(x,i).(2x + 2),x,0)))))),1,(x + 1)))
A183633: 44 340 2300 14644 90524 551380 3333500 20077684
(2 * compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(9x + ~2)),(x + 1)))
A258663: 2 6 8 10 12 20 22 26 28 30 40 48 50 52 56 58
((if (x mod 4) <= 0 then (27 * (if x <= 0 then 1 else 2)) else 2) + ((2 - (x mod 2)) * (if x <= 0 then 1 else 2)))
A040825: 29 4 6 4 58 4 6 4 58 4 6 4 58 4 6 4
(2 + (if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + (loop(\(x,i).(2 * (x + (if (i mod 2) <= 0 then 2 else 0))),x,1) div 3)) div 2)) div 2)))))
A343883: 3 4 6 8 10 16 30 54
((2 + (3 * (if (x mod 2) <= 0 then ((~1 + (5 * (if (x mod 4) <= 0 then 2 else 1))) * (if x <= 0 then 1 else 2)) else 0))) div 2)
A040208: 14 1 13 1 28 1 13 1 28 1 13 1 28 1 13 1
(2 + (loop(\(x,i).x2,1,(1 + (2 * compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + x + 1))),x)))) div 2))
A107317: 6 14 26 62 86 146 314 422 482 614 842 926 1202 1514 2246 2966
(2 * (2 + loop(\(x,i).(x2 + 2x),1,compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1)))))
A063533: 34 74 290 650 1802 3530 7202 10370 20810 23330 38090 45002 64802 73730 78410 103970
(2 + (loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) + loop(\(x,i).((x2 + x) * i),2,2)))
A138692: 90 95 111 135 207 255 375 447 615 927 1047 1455 1767 1935 2295 2895
((2 + ((((x + 1) * ((x + 4) + (if x <= 0 then 1 else (2 + loop(\(x,i).((x + ~1) - (if x <= 0 then 0 else i)),x,x))))) div 2) div 2)) div 2)
A283734-A247714-A087465: 1 2 3 4 5 7 6 8 10 12 9 11 14 16 19 13
(8 * ((loop(\(x,i).(2x + 2),x,(1 + loop(\(x,i).2x,x,1))) div 2) - loop(\(x,i).(3x + 1),x,1)))
A000919: 0 0 0 24 240 1560 8400 40824 186480 818520 3498000 14676024 60780720 249401880 1016542800 4123173624
(2 * (2 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(2x2 + 8x + 1)),x)))
A090696: 4 8 10 18 20 28 32 38 42 48 52 62 70 78 80 90
(2 + compr(\x.(~1 + loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(9x + 6))),x))
A246965: 2 4 5 6 7 11 12 14 15 16 21 25 26 27 29 30
(2 * compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(11x + 1)),x))
A108233: 0 6 12 16 24 28 34 36 42 52 54 58 64 72 78 82
(2 * compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(11x + 10)),x))
A102731: 0 4 6 16 28 30 34 36 40 54 58 60 64 76 78 84
(2 * compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(17x + 8)),x))
A108976: 0 2 12 14 20 26 32 36 42 54 56 60 74 84 86 90
compr(\x.(~1 + loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(15x + 6))),x)
A158648: 0 1 3 4 5 6 7 8 10 11 15 18 19 20 21 22
compr(\x.(~1 + loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,21x)),x)
A163627: 0 1 2 3 4 6 9 11 12 14 16 17 18 21 22 23
compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(32x + 9)),x)
A127591: 2 4 10 13 17 19 20 22 23 25 29 32 37 44 50 53
compr(\x.(1 - (((x + 1) * (1 + loop(\(x,i).loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),1,(x + 1)))) mod 3)),x)
A014419: 0 1 3 4 6 9 10 12 13 15 18 19 21 22 27 28
compr(\x.(~1 + loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,33x)),x)
A157202: 0 1 2 4 6 7 9 12 13 14 16 18 19 23 26 27
(if x <= 0 then 2 else (1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x)))
A054541: 2 1 2 2 4 2 4 2 4 6 2 6 4 2 4 6
(if x <= 0 then 1 else (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x)))
A076368: 1 2 3 3 5 3 5 3 5 7 3 7 5 3 5 7
loop(\(x,i).loop(\(x,i).10x,x,loop(\(x,i).(10x + 10),(x + 1),0)),1,(x2 + x))
A080319: 10 111000 11111110000000 4611686018427387903 4611686018427387903 4611686018427387903
((~x + 2) + (loop(\(x,i).5x,x,1) + loop(\(x,i).4x,x,1) + (loop(\(x,i).4x,x,1) div 2)))
A152123: 4 12 49 220 1007
(if x2 <= 0 then 1 else (x * (loop(\(x,i).x6,(x + ~1),(x * (1 + loop(\(x,i).2x,x,2)))) div 2)))
A135235: 1 2 34012224
(x + (2 * ((x + 1) + loop(\(x,i).(if x <= 0 then 0 else (1 + (x * ((x + 1) + loop(\(x,i).(2x2 + ~x),2,x))))),2x,x))))
A082912: 2 12367 4611686018427387903
loop(\(x,i).x2,1,(compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) - compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)))
A076821: 1 4 4 16 4 16 4 16 36 4 36 16 4 16 36 36
compr(\x.(x + (if x <= 0 then 1 else (2 * (1 + ((1 + (loop(\(x,i).(~2x + (if (x mod (1 + i)) <= 0 then 0 else x)),x,x) div (x + 1))) div 2))))),x)
A226025: 15 21 27 33 35 39 45 51 55 57 63 65 69 75 77 81
(((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (x div 2) + (if x <= 0 then 0 else 1))
A088922: 0 1 2 3 3 5 4 6 6 7 6 10 7 9 10 11
loop(\(x,i).4x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165825: 1 4 4 16 4 16 4 64 16 16 4 64 4 16 16 256
loop(\(x,i).~2x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165872: 1 ~2 ~2 4 ~2 4 ~2 ~8 4 4 ~2 ~8 ~2 4 4 16
loop(\(x,i).3x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165824: 1 3 3 9 3 9 3 27 9 9 3 27 3 9 9 81
(1 + (x div (1 + ((5 + (x div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))) div 3))))
A107324: 1 1 2 2 3 2 4 3 3 3 6 3 7 4 4 4
(1 + (x mod (1 + ((~1 + (2 * loop(\(x,i).x2,1,loop(\(x,i).((2 * (x - (2x * i))) div (1 + i)),x,1)))) mod (x + 1)))))
A071416: 1 2 1 2 1 6 1 2 1 2 1 4 1 2 15 2
(1 + ((2x + 1) mod (1 + ((1 + (x mod (1 - loop(\(x,i).(x - (if x <= 0 then 1 else (2 * (1 + i)))),x,2x)))) mod (x + 1)))))
A175892: 1 1 2 1 1 3 1 1 2 4 1 1 1 1 5 1
(1 + ((x + 1) mod (1 + (2 * ((loop(\(x,i).(2x + 2),x,(if (x mod (2 + (x mod 4))) <= 0 then 1 else 0)) mod (x + 1)) div 2)))))
A321649: 1 1 1 2 1 1 1 2 1 1 1 1 1 3 2 2
(1 + ((~1 + loop(\(x,i).x3,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))) mod 9))
A073637: 8 9 8 1 8 1 8 1 8 8 1 1 8 1 8 8
(~1 + ((loop(\(x,i).x2,1,(~3 + loop(\(x,i).10x,(x + 1),1))) div 3) div 5))
A332162: 2 626 66266 6662666 666626666 66666266666 6666662666666 666666626666666 66666666266666666 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((1 + loop(\(x,i).2x,x,(~1 + (loop(\(x,i).2x,x,1) mod (~1 + (2 * (((~x + 2) div 2) mod 4))))))) mod 3))
A102668: 1 3 1 3 2 1 2 3 1 3 1 3 2 1 2 3
(~1 + (((2x + 2) * (2 + ((~1 + (2 * (if x <= 0 then 1 else (if (x mod 4) <= 0 then (x div 2) else x)))) mod (x + 1)))) mod 3))
A106549: 0 ~1 ~1 ~1 1 ~1 ~1 0 ~1 ~1 0 ~1 1 0 ~1 ~1
(1 + (((1 + (loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) div (if x <= 0 then 2 else (1 + (x mod 8))))) div 2) mod 3))
A085029: 1 1 2 1 2 1 2 1 3 2 3 1 2 2 2 1
(1 + ((2 * (1 + ((1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (1 + (((x + 1) div 2) div 2)))) div 2))) div 3))
A225597: 1 1 2 1 2 3 1 3 3 5 1 3 4 5 7 1
(1 + ((2 * (1 + ((1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (1 + ((x + 1) mod 4)))) div 2))) div 3))
A079723-A079722: 1 1 3 1 2 3 1 2 3 5 1 2 3 5 7 1
(if 2x <= 0 then 1 else (1 + ((2 * (1 + ((1 + (if (1 - ((x2 + x) mod 5)) <= 0 then x else 1)) div 2))) div 3)))
A254618: 1 2 2 3 2 2 3 4 4 2 2 5 5 6 2 2
(if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + ((loop(\(x,i).(1 + (2 * (x mod (1 + i)))),x,1) mod (x + 1)) div 2)) div 2))) div 3)))
A325121: 0 1 1 2 2 2 1 3 2 3 2 3 2 2 3 4
(1 + (if (x + ~1) <= 0 then x else ((2 * (4 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3)))
A212356: 1 2 3 4 3 5 3 5 4 5 3 7 3 5 5 6
(loop(\(x,i).2x,((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3),1) mod 11)
A111588: 1 1 1 2 1 2 1 4 2 2 1 8 1 2 2 10
(1 + ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))))
A023523: 3 7 16 36 78 144 222 324 438 668 900 1148 1518 1764 2022 2492
(~1 + ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))))
A023515: 1 5 14 34 76 142 220 322 436 666 898 1146 1516 1762 2020 2490
(~1 + ((1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (1 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))))
A037165: 1 7 23 59 119 191 287 395 615 839 1079 1439 1679 1931 2391 3015
(1 + ((~1 + loop(\(x,i).x2,1,(1 + (x mod (1 + (x div (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))))))) mod (x + 1)))
A274006-A203025-A057521: 1 1 1 4 1 1 1 8 9 1 1 4 1 1 1 16
(if (x mod 2) <= 0 then 1 else (1 + ((1 - ((1 + ((2 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 3)) mod 3)) mod (x + 1))))
A237835: 1 1 1 1 1 6 1 1 1 2 1 12 1 2 1 1
(1 + (2 * (((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1))))
A114003: 1 3 3 5 3 7 3 7 5 7 3 11 3 7 7 9
(1 + (2 * (1 + (((x + 1) * (1 + loop(\(x,i).loop(\(x,i).(3x + ((~1 + (2 * i)) * i)),x,1),x,0))) div 3))))
A177007: 3 5 13 631 4611686018427387903
(1 + ((if x <= 0 then 2 else (1 + ((2 * ((2 + ((if ((x + ~1) mod 3) <= 0 then 1 else x) + (x mod 2))) div 3)) div 3))) div 2))
A245077: 2 1 1 2 1 2 2 1 2 2 1 2 2 1 3 3
(loop(\(x,i).2x,x,1) mod (~1 + (2 * (1 + ((1 + ((1 + ((x + loop(\(x,i).(x * i),(x + ~1),1)) div 2)) div (x + 1))) div 2)))))
A260019: 1 2 0 0 1 2 9 34
(1 + (2 * (1 + (4 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(4x + 1))),x)))))
A186301: 3 11 27 35 51 59 99 107 147 155 171 179 195 227 267 275
(1 + (6 * (1 + loop(\(x,i).(~1 + (2 * (~1 + loop(\(x,i).(x2 + ~x + ~1),x,8)))),(x + 1),2))))
A172712: 35617 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(7 * loop(\(x,i).(10x + 1),x,loop(\(x,i).(10x + 10),x,0)))
A332170: 0 707 77077 7770777 777707777 77777077777 7777770777777 777777707777777 77777777077777777 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + ((1 + loop(\(x,i).(x - (3 * (x div 4))),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))) div 2))
A208882: 0 1 0 1 2 1 2 3 3 3 4 4 5 6 6 6
(if x <= 0 then 0 else (1 + (x div (2 + (x div (1 + (((x + ~1) mod (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))) + (x mod 2))))))))
A171453: 0 1 1 2 1 2 1 4 3 2 1 3 1 2 2 8
(1 + (2 * (1 + compr(\x.(loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x) + ((x + 1) mod 9)),x))))
A061237: 19 37 73 109 127 163 181 199 271 307 379 397 433 487 523 541
(1 + (2 * loop(\(x,i).((x + 1) + loop(\(x,i).(5x mod 17),1,(2x + 2))),x,1)))
A277167: 3 11 31 47 53
(1 + (2 * (1 + compr(\x.(loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x) + ((1 + (x div 2)) mod 6)),x))))
A130063: 23 47 71 73 97 167 191 193 239 241 263 311 313 337 359 383
(1 + ((1 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) div 2))
A078444: 2 3 5 8 11 14 17 20 25 29 33 38 41 44 49 55
(6x mod (1 + (if x <= 0 then 2 else (loop(\(x,i).x3,2,11) mod (x + 1)))))
A126164: 0 0 0 2 0 0 0 2 3 0 0 6 0 0 0 6
((x + 1) + (((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 1 else 2)))
A062249: 2 4 5 7 7 10 9 12 12 14 13 18 15 18 19 21
(1 + ((loop(\(x,i).(x2 + x),1,(1 + ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3))) div 2) div 2))
A292504: 1 1 1 2 1 2 1 4 2 2 1 6 1 2 2 11
(1 + (4 * (1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(4x + 1))),x)))))
A294919-A007521: 5 13 29 37 53 61 101 109 149 157 173 181 197 229 269 277
(1 + (((1 + ((x * (2 + (x * ((~1 + (loop(\(x,i).(x + loop(\(x,i).(x * i),(x + ~2),1)),x,0) div 2)) div 2)))) div 2)) div 2) div 2))
A218122: 1 1 1 2 2 5 34 4611686018427387903
((1 + (compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x) + (x div 4))) mod (1 + (((x + 1) div 2) div 2)))
A138319: 0 0 0 1 1 1 0 0 1 2 2 2 0 2 1 2
(loop(\(x,i).(x5 + ~x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 5)
A138426: 6 48 624 3360 32208 74256 283968 495216 1287264 4102224 5725824 13868784 23171232 29401680 45868992 83639088
(loop(\(x,i).(x * (x4 div 2)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 5)
A138428: 3 24 312 1680 16104 37128 141984 247608 643632 2051112 2862912 6934392 11585616 14700840 22934496 41819544
(5 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)))
A092949: 6 9 13 19 25 31 37 43 53 61 69 79 85 91 101 113
(5 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)))
A111254: 8 11 17 21 29 33 41 49 55 67 73 81 89 97 107 115
(1 + (4 * compr(\x.(1 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(8x2 + 8x))),x)))
A071695: 5 17 29 41 101 137 149 197 269 281 461 521 569 617 641 809
((1 + ((1 + loop(\(x,i).2x,x,(if ((x + 1) mod (2 + ((~x + 2) mod 5))) <= 0 then 2 else 0))) div 3)) mod 3)
A121361: 1 1 1 1 0 1 1 2 1 0 1 1 1 1 1 0
((1 + ((loop(\(x,i).2x,x,(1 + (loop(\(x,i).6x,x,(x + 1)) mod (2x + 1)))) div 2) div 2)) mod 3)
A033687: 1 1 2 0 2 1 2 0 1 2 2 0 2 0 2 0
((1 + (4 * (if (x mod 2) <= 0 then ((~1 + (5 * (2 - ((x div 2) mod 2)))) * (if x <= 0 then 1 else 2)) else 1))) div 3)
A010215: 12 1 11 1 24 1 11 1 24 1 11 1 24 1 11 1
((1 + (2 * (if x <= 0 then 1 else (2 * (3x + ((x - (if (~2 + (x div 4)) <= 0 then 0 else 2)) div 3)))))) div 3)
A058759: 1 4 8 13
A311889: 1 4 8 13 17 21 27 31 35 40 44 48 52 56 61 65
((loop(\(x,i).10x,(2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)),1) div 3) div 3)
A259102: 111 11111 1111111 11111111111 1111111111111 11111111111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).2x,x,(1 + (if (2x mod (4 + ((x + 1) mod 4))) <= 0 then 4 else 0))) mod (x + 1)) mod 3)
A229878: 0 0 1 0 1 2
A318463: 0 0 1 0 1 2 1 0 1 0 1 2 1 2 2 0
(((2 + loop(\(x,i).(4 * ((2 - (x mod 2)) * (if x <= 0 then 1 else 2))),(x mod 4),1) - (x mod 2)) mod (x + 1)) mod 3)
A228360: 0 1 0 1 0 0 1 1 0 0 1 2 0 0 0 1
((2 * loop(\(x,i).2x,(((~x + 1) mod (1 + ((x - ((x div 3) mod 3)) div 2))) + (if x <= 0 then 0 else 1)),1)) div 3)
A090079: 0 1 2 1 2 5 2 1 2 5 10 5 2 5 2 1
(if x <= 0 then 1 else (((x + 1) div 2) - ((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3)))
A319318: 1 1 1 1 2 1 3 2 3 3 5 2 6 5 5 5
((2 + loop(\(x,i).(x + (if x <= 0 then 1 else (x - (3 * ((x + ~1) div 5))))),(x div 2),((x + 1) mod 2))) div 3)
A262090: 1 0 1 1 2 1 3 2 5 3 7 5 11 7 15 11
((x + 1) mod ((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3))
A054008: 0 0 1 1 1 2 1 0 0 2 1 0 1 2 3 1
((loop(\(x,i).(x4 + 3x3 + 2x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 3)
A098741: 8 30 175 588 3146 5915 16473 25270 52900 130355 169136 338143 505981 610170 865928 1390455
((loop(\(x,i).(x5 + ~x3),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 3)
A138435: 4 36 500 2744 26620 61516 235824 411540 1070696 3414460 4766560 11548884 19297880 24488156 38206864 69674436
((loop(\(x,i).(x3 * (x2 div 2)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 3)
A138437: 2 18 250 1372 13310 30758 117912 205770 535348 1707230 2383280 5774442 9648940 12244078 19103432 34837218
(loop(\(x,i).(x6 + ~x4),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 3)
A138454: 16 216 5000 38416 585640 1599416 8018016 15638520 49252016 198038680 295526720 854617416 1582426160 2105981416 3591445216 7385490216
(loop(\(x,i).(x6 + ~x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 3)
A138442: 20 240 5200 39200 590480 1608880 8045760 15681840 49345120 198274160 295834240 855241680 1583367520 2107120400 3593071040 7388119440
(loop(\(x,i).(x2 * (x4 div 2)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 3)
A138445: 10 120 2600 19600 295240 804440 4022880 7840920 24672560 99137080 147917120 427620840 791683760 1053560200 1796535520 3694059720
(1 + (((x + 1) + (((x + 1) + ((x + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * ((x + 1) div 2))) div 2)) div 2)) div 2))
A283962: 1 2 3 4 5 6 7 8 9 11 10 12 13 15 17 14
(1 + ((1 + (compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))) div 2))
A097911: 1 3 5 8
A062839: 1 3 5 8 10 14 16 20 24 27 33 36 40 44 48 53
(1 + ((x + (((5 * (1 + compr(\x.loop(\(x,i).(x div (1 + (if (x mod 2) <= 0 then 2 else 0))),x,2x),x))) div 2) div 2)) div 2))
A036795: 1 2 4 5 9 10 12 13 22 23 25 26 30 31 33 34
(1 + ((~1 + loop(\(x,i).10x,(x + 1),1)) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A091802: 2 1 5 4 10 1 5 17 20 6 19 1 16 36 40 46
((~2x + 1) + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)))
A108568: 2 3 5 9 13 17 21 25 33 39 45 53 57 61 69 79
(if ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) <= 0 then 1 else (if (x mod 3) <= 0 then 8 else (1 + (x div 2))))
A275204: 1 1 1 1 3 1 1 4 5 1 1 6 8 7 1 1
(if x <= 0 then 1 else (2 + (((1 + (x div 3)) div (1 + (if (x mod (4 - (x mod 2))) <= 0 then 2 else 0))) div 2) - (x mod 2)))
A188550: 1 1 2 1 2 2 3 2 2 1 4 3 2 3 4 2
(x div (2 + ((if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1) + (x div 7)) - (x mod 2)))
A324285: 0 0 0 1 0 2 0 2 1 3 0 3 0 4 2 3
(1 + compr(\x.(2 - ((if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 2)))) mod 3)),x))
A268391-A246551: 2 3 5 7 8 11 13 17 19 23 27 29 31 32 37 41
(2 + (compr(\x.(loop(\(x,i).(x * (1 + (i div 2))),x,1) mod (x + 1)),x) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x)))
A171639: 2 6 9 13 16 21 25 31 34 39 47 51 58 63 67 72
(1 + compr(\x.((2 + (x * loop(\(x,i).loop(\(x,i).(x4 + x),1,(2x + 1)),1,3x))) mod (x + 1)),x))
A018553: 1 2 3 6 103 206 309 618
loop(\(x,i).(10x + (if (2 - ((~4x + 2) mod (4 + (x div 4)))) <= 0 then 1 else 0)),x,1)
A266680: 1 11 110 1101 11011 110111 1101111 11011111 110111111 1101111111 11011111111 110111111111 1101111111111 11011111111111 110111111111111 1101111111111111
((3 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (1 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)))
A087105: 12 24 60 96 192 252 396 560 720 1080 1280 1596 1932 2288 2784 3240
((x + 1) * (((2x + 3) * (loop(\(x,i).(2 * (2x + (x div (if i <= 0 then 1 else i)))),x,(x + 2)) div 2)) div 3))
A106440: 1 30 420 4200 34650 252252 1681680 10501920 62355150 355655300 1963217256 10546208400 55367594100 285028443000 1442592936000 7193730107520
((x + 1) * ((if x <= 0 then 1 else x) - ((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3)))
A069553: 1 2 6 8 20 18 42 40 63 70 110 84 156 154 180 192
((x + 1) * ((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3))
A231407: 1 4 6
A038040: 1 4 6 12 10 24 14 32 27 40 22 72 26 56 60 80
((x + 1) * (compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x) mod (1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A147967: 0 2 3 12 5 18 7 24 45 10 55 36 13 42 75 80
((~x3 + ~3x2 + ~3x + ~1) + loop(\(x,i).x3,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A262186: 7 19 98 279 1206 1981 4570 6347 11438 23389 28460 48925 66724 76763 100448 144781
((x + 1) * ((if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2)))) div (2 + (x mod 2))))
A296966: 0 0 3 4 5 12 7 16 18 20 11 48 13 28 45 48
((x + (if x <= 0 then 1 else (2 * (((~1 + ((x + 1) * loop(\(x,i).(2 * (x + (x div (4 + i)))),x,1))) div 2) div 2)))) div (x + 1))
A034007: 1 0 2 4 9 20 44 96 208 448 960 2048 4352 9216 19456 40960
loop(\(x,i).(x + loop(\(x,i).((((4x div (1 + i)) * (~1 + (2 * i))) div (1 + i)) * (1 + (2 * i))),i,(1 + i))),x,1)
A082578: 1 7 67 767 9587 126011 1711595 23796515 336666215 4828084575 69994481871 1023793569567 15086216016367 223704570996367 3335098322412367 49954148031128767
loop(\(x,i).(x + loop(\(x,i).(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)),1,i)),x,1)
A163866: 1 2 3 4 6 7 8 11 14 15 16 20 26 30 31 32
(loop(\(x,i).(10x + loop(\(x,i).(x + ((1 + i) * i)),i,0)),x,0) div 2)
A262183: 0 1 14 150 1520 15235 152406 1524144 15241560 152415765 1524157870 15241578986 152415790224 1524157902695 15241579027510 152415790275780
((~1 + (6 * (1 + compr(\x.((1 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,x)) mod 3),x)))) div 2)
A026231: 8 17 20 26 35 44 47 53 56 62 71 74 80 89 98 101
(2 * (1 + compr(\x.(1 - (x mod (2 + ((1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)) mod (x + 1))))),(x + 1))))
A083348: 8 12 16 18 20 24 28 30 32 36 40 44 48 52 54 56
((1 + ((loop(\(x,i).2x,x,(~1 + ((if (x mod 4) <= 0 then 2 else (x mod 2)) * (1 + (x div 4))))) mod (x + 1)) div 2)) div 2)
A288002: 0 0 1 0 1 1 2 0 1 1 3 1 2 2 3 0
((1 + (((3 * loop(\(x,i).3x,(if x <= 0 then 1 else ((3 * (x div 4)) div 2)),1)) mod (x + 1)) div 2)) div 2)
A335230: 0 0 0 1 1 1 1 0 0 0 1 2 2 1 1 1
((1 + (((1 + loop(\(x,i).(4x + (((x + ((x div 2) mod 2)) div 2) + (if x <= 0 then 1 else 2x))),2,x)) div 2) div 2)) div 2)
A314120: 1 5 11 16 21 26 32 38 42 47 53 59 64 68 74 80
((1 + ((loop(\(x,i).((x + 2) + ((x + (if (x + ~2) <= 0 then 1 else ((x + 1) div 7))) div 2)),x,1) div 2) div 2)) div 2)
A023437: 0 1 1 2 3 5 8 13 20 32 50 79 124 195 306 481
(~2 + (5 * ((loop(\(x,i).(x2 + x),1,(1 + loop(\(x,i).10x,x,2))) div 2) div 3)))
A332138: 8 383 33833 3338333 333383333 33333833333 3333338333333 333333383333333 33333333833333333 3333333338333333333 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((3 * (((1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))) div 2) + (if x <= 0 then 0 else 1))) div 2)
A290080-A289617: 0 1 1 3 1 3 1 4 3 3 1 4 1 3 3 7
((compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 6)
A054763: 1 2 2 4 2 4 2 4 0 2 0 4 2 4 0 0
(2 * (1 + (2 * compr(\x.(1 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(8x2 + 8x))),x))))
A335908: 6 18 30 42 102 138 150 198 270 282 462 522 570 618 642 810
(3 + (2 * compr(\x.(2 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),28,x)),x)))
A073523: 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139
(((1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (1 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) div 2)
A099407: 1 4 12 30 60 96 144 198 308 420 540 720 840 966 1196 1508
(((2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)) * (1 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) div 2)
A014302: 5 14 33 65 102 152 207 319 434 555 738 860 987 1219 1534 1769
(((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (1 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) div 2)
A014303: 2 6 15 35 66 104 153 209 322 435 558 740 861 989 1222 1537
((3 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x))) div 2)
A073273: 3 4 7 9 13 15 19 23 26 32 35 39 43 47 52 56
((((x + 1) - (3 * (if x <= 0 then 2 else ((if x <= 0 then 2 else (1 + ((1 + (x div (2 + (x mod 2)))) div 2))) div 2)))) mod (x + 1)) div 2)
A154258: 0 0 0 0 1 1 2 2 3 3 2 4 3 5 4 5
(((2 * (1 + ((if x <= 0 then 2 else (2 - ((x + 1) mod (1 + (2 * (if ((x + ~1) mod 4) <= 0 then 2 else 1)))))) div 2))) mod (x + 1)) div 2)
A284478: 0 0 0 1 1 1 1 1 2 2 1 2 1 0 2 1
((x + 2) mod (2 + ((2 * (x + (if x2 <= 0 then 1 else (1 + (2 * loop(\(x,i).4x,(x + ~2),3)))))) mod (x + 1))))
A330167: 0 1 0 1 2 1 0 1 0 1 1 1 2 3 2 1
((3 + ((3 * (if (x mod 2) <= 0 then (9 * (if x <= 0 then 1 else 2)) else 1)) mod (1 + (x div 3)))) div 2)
A198898: 1 1 1 2 1 2 1 1 1 3 2 3 3 3 3 3
(((~1 + (6 * (1 + (x div (3 + ((~1 + loop(\(x,i).(if x <= 0 then i else (x div 2)),x,2)) mod (x + 1))))))) div 2) div 2)
A140993-A137940-A027935: 1 1 1 1 2 1 1 2 4 1 1 2 5 7 1 1
(2 * ((x + 2) - ((x + 1) div (if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 2)))))))
A244363: 2 4 6 8 8 12 10 16 16 20 14 24 16 26 26 32
(68 + loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A138691: 72 77 93 117 189 237 357 429 597 909 1029 1437 1749 1917 2277 2877
(2 + (((x + 1) mod (2 + ((1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)) mod (x + 1)))) div 2) - (x mod 2))
A048684: 2 1 2 1 2 2 2 1 4 2 2 1 2 2 2 1
(56 + loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A138690: 60 65 81 105 177 225 345 417 585 897 1017 1425 1737 1905 2265 2865
(2 + ((((x + 1) * (1 + ((loop(\(x,i).2x,x,loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))) div 2) + (x mod 2)))) div 2) div 2))
A201363: 2 3 7
A103173: 2 3 7 8 53 77
(loop(\(x,i).(x2 + x),1,(2 - (if x <= 0 then 1 else ((x mod 2) - (((2x + 1) mod (1 - (x div ~4))) div 2))))) div 2)
A337333: 1 1 3 1 3 3 3 1 6 3 3 3 3 3 10 1
(2 + (if x <= 0 then 2 else (((2 + ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 12)) div 2) div 2)))
A180217: 4 3 3 4 5 2 3 4 5 3 4 2 3 4 5 3
((2 + ((loop(\(x,i).loop(\(x,i).(8x + 4),(x + 1),0),1,(x3 + 3x2 + 4x + 2)) div 2) div 2)) div 2)
A171407: 37 613566757 4611686018427387903
(((loop(\(x,i).(x5 + ~x3),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 2) div 2)
A138436: 3 27 375 2058 19965 46137 176868 308655 803022 2560845 3574920 8661663 14473410 18366117 28655148 52255827
((loop(\(x,i).(10x + 1),(2x + 1),1) + loop(\(x,i).10x,x,4)) div 2)
A332157: 7 575 55755 5557555 555575555 55555755555 5555557555555 555555575555555 55555555755555555 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).(10x + 1),(2x + 1),1) - loop(\(x,i).10x,x,4)) div 2)
A332153: 3 535 55355 5553555 555535555 55555355555 5555553555555 555555535555555 55555555355555555 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((loop(\(x,i).(x6 + ~x4),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 2)
A138455: 12 162 3750 28812 439230 1199562 6013512 11728890 36939012 148529010 221645040 640963062 1186819620 1579486062 2693583912 5539117662
((loop(\(x,i).(x6 + ~x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 2)
A138443: 15 180 3900 29400 442860 1206660 6034320 11761380 37008840 148705620 221875680 641431260 1187525640 1580340300 2694803280 5541089580
((((if x <= 0 then 1 else (2 * (1 + ((1 + (loop(\(x,i).2x,(x + ~7),1) div 2)) div 2)))) - (x mod 2)) div 2) div 2)
A251759: 0 0 0 0 0 0 0 0 1 0 1 2 4 8 16 32
((1 + (((loop(\(x,i).((2x + ~1) * (x div 2)),1,loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))) div 2) div 2) div 2)) mod 4)
A271714: 1 1 1 1 3 1 1 1 1 3 2 1 3 1 2 1
(((2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)) * (2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) div 2)
A102770: 7 17 38 71 110 161 218 333 449 573 758 881 1010 1245 1563 1799
(~2 + ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))))
A124669: 4 13 33 75 141 219 321 435 665 897 1145 1515 1761 2019 2489 3125
(2 * ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))))
A069486: 12 30 70 154 286 442 646 874 1334 1798 2294 3034 3526 4042 4982 6254
(2 - ((if x <= 0 then 2 else (~2 + ((x + 1) * (~1 + (2 * (x mod 2)))) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2))
A163294: 1 3 6 4 10 6 14 8 18 12 23 15 29 17 33 21
(((x + 2) * (compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x) - compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) div 2)
A162775: 2 3 8 5 12 7 16 27 10 33 24 13 28 45 48 17
(((2 * (2x + (x div (3 + (if (~2 + (x div 4)) <= 0 then 0 else 2))))) div 3) + (if x <= 0 then 1 else 4x))
A313918: 1 5 10 16 22 27 33 38 44 50 55 60 65 70 76 82
(if (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) <= 0 then 1 else (if ((x div 2) mod 2) <= 0 then (x div 2) else 2))
A110971: 1 1 1 1 2 1 1 2 4 1 1 2 6 6 1 1
((x + ~1) + loop(\(x,i).(if x <= 0 then 1 else ((3x + 3) - ((x - (x div 3)) div 3))),1,((x + 1) div 2)))
A164018: 0 6 7 11 12 16 17 20 21 25 26 30 31 35 36 39
(if x <= 0 then 1 else (2 * (x + ((2 * ((2x + 2) + (x div (1 + (2 * (if (~4 + (x div 2)) <= 0 then 2 else 1)))))) div 3))))
A315637: 1 6 12 16 20 26 32 36 40 46 52 58 64 68 72 78
(if x <= 0 then 1 else (2 * (x + ((x + ((3 * ((3 * (x + (if (~2 + (x div 4)) <= 0 then 1 else 2))) div 2)) div 2)) div 2))))
A315730: 1 6 12 18 22 28 32 38 42 48 54 60 66 72 78 82
((2x + ~1) + ((2 * (2 + (if x <= 0 then 1 else (2 * (x + loop(\(x,i).(~x - (x div (4 + i))),2,x)))))) div 3))
A315418: 1 6 11 15 20 26 32 37 41 46 52 58 63 67 72 78
(1 + ((2 * ((x + 2) + ((if x <= 0 then 0 else ((3x + 1) + (x div 3))) + (x div 2)))) + (if x <= 0 then 1 else 2x)))
A063230: 6 17 29 41 53 63 77 87 99 111 123 133 147 157 169 181
(1 + ((2 * (((~1 + loop(\(x,i).2x,x,(1 + (2 * (if (x mod 5) <= 0 then 0 else 2))))) mod (x + 1)) div 2)) + (x mod 2)))
A072014: 1 2 1 4 5 2 5 8 1 10 1 4 5 10 5 16
loop(\(x,i).x2,1,((if (x + ~1) <= 0 then 1 else (2 * (((x2 mod (x - ((~x + 2) div 2))) div (x + 1)) + (x mod 2)))) - (x mod 2)))
A056897: 1 0 0 1 0 1 0 9 4 1 0 1 0 9 4 1
((3x + 2) + loop(\(x,i).(x + loop(\(x,i).(4x - ((x - (x div 5)) div 3)),1,i)),x,1))
A194141: 3 10 21 35 53 75 101 130 163 200 241 285 333 385 440 499
((x + ~1) + ((2 * (2 + (if (x + ~1) <= 0 then 1 else (2 + (loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)))))) div 3))
A145110: 1 2 3 6 5 10 7 13 11 14
((~x + 1) + (2 * ((loop(\(x,i).(~1 + loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,x)),x,(x + 1)) mod (2x + 2)) div 2)))
A124071: 1 2 3 2 3 4 5 2 3 2 3 4 3 4 5 2
(0 + (loop(\(x,i).(x - (x div 8)),2,(x + ~1)) + (if x <= 0 then 1 else 4x)) - ((x + 1) div 3))
A058759: 1 4 8 13
A312100: 1 4 8 13 18 22 27 32 36 40 44 48 53 58 62 67
(if (x div 7) <= 0 then (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) else (x + 12))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A331046: 2 3 5 7 11 13 17 19 20 21 22 23 24 25 26 27
compr(\x.(((x + 2) + ((x - (if (x mod (1 + ((x + 2) div 5))) <= 0 then (if x <= 0 then 0 else 1) else 2)) div 4)) mod 3),x)
A231407: 1 4 6
A190499: 1 4 6 11 16 18 21 23 28 30 33 35 40 42 45 47
((x + 1) + (((x + 1) + ((x + loop(\(x,i).(1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),i)),(x + ~1),1)) div 2)) div 2))
A139130: 1 3 5 7 9 12 14 17 19 22 24 28 30 33 36 38
((~x + 1) + (((x + 1) + loop(\(x,i).(x + ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3)),2,x)) div 2))
A039637: 1 1 1 2 1 2 1 3 2 2 1 3 1 2 4 4
(x * ((1 + (((x + 1) * loop(\(x,i).2x,(x + ~1),(~1 + (if x <= 0 then 2 else ((x2 + 5x) div 2))))) div 2)) div 2))
A058649: 0 1 18 132 680 2880 10752 36736 117504 357120 1041920 2939904 8067072 21618688 56770560 146472960
compr(\x.(1 - (((~x + 1) + (2 * ((if x <= 0 then 1 else (x - (loop(\(x,i).2x,x,1) mod 9))) mod (x + 1)))) div 2)),x)
A292046: 1 3 6 7 11 12 13 14 16 17 18 19 20 21 22 23
((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) - loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x))
A094053: 0 1 0 2 2 0 3 4 3 0 4 6 6 4 0 5
(x2 * (if x <= 0 then 1 else (x * (x - ((x - ((x * loop(\(x,i).(x3 + x),1,x4)) div 2)) div 2)))))
A283027: 0 1 16456 10763361 1073758336 38147070625 705277897416 8308234084801 70368748374016 463255057977921 2500000025005000 11487432519490081 46221064831264896 166354152499741921 544488334821309256 1642102089568970625
(1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x)))
A295181: 1 1 0 1 0 0 1 0 1 0 1 0 2 2 0 1
(if ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) <= 0 then (1 + ((2x + 1) div (3 + (x div 4)))) else 0)
A103516: 1 2 2 3 0 3 4 0 0 4 5 0 0 0 5 6
(1 - loop(\(x,i).((2x + ~2) + ((1 + (((2x + 2) * (2 - ((x div 4) mod 2))) div 5)) mod 2)),x,0))
A118255: 1 2 4 9 18 37 74 149 299 599 1198 2397 4794 9589 19179 38359
(1 + (if ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) <= 0 then ((2x + 1) div (3 + (x div 4))) else 0))
A131821: 1 2 2 3 1 3 4 1 1 4 5 1 1 1 5 6
(((3 * ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 5)) div 2) + (if x <= 0 then 0 else 1))
A132311: 0 1 1 1 1 1 1 2 2 1 1 4 7 4 1 1
(1 + (x mod (1 + (2x div (1 + ((loop(\(x,i).2x,x,(1 + (x mod (2 * (1 + (x mod 2)))))) - (x mod 2)) mod (x + 1)))))))
A078834: 1 2 3 2 5 3 7 2 1 5 11 3 13 7 3 2
(1 + (x mod (1 + (x mod (1 + (x div (2 + (if x <= 0 then 0 else (1 + ((x div (1 + (2x mod 3))) mod 2) - (x mod 2))))))))))
A280696: 1 1 1 2 1 3 1 4 3 2 1 4 1 7 3 4
(1 + (if x <= 0 then 0 else (1 + ((2 * (1 + (((x + 1) div (2 - (16 mod (~x + ~1)))) div 2))) div 3))))
A328162: 1 2 2 3 2 2 2 4 3 2 2 2 2 2 2 5
(1 + ((x + 2) mod (1 + ((1 + (((x + 1) div (if ((x + 1) mod 5) <= 0 then 4 else 1)) mod 3)) mod (x + 1)))))
A277427: 1 2 1 3 1 2 3 2 1 4 1 2 3 4 1 3
(if ((x + 1) mod 4) <= 0 then 0 else (1 + (x div (1 + (x mod (2 * (1 + (x mod (2 * (1 + (x mod (1 + (x div 3)))))))))))))
A336597: 1 1 3 0 5 3 7 0 3 5 11 0 13 7 3 0
((x + 1) mod (1 + ((x + 1) div (if (x mod (3 * (1 + ((x div 2) div (1 + (x mod (2 * (1 + (x mod 2))))))))) <= 0 then 2 else 1))))
A182659: 0 2 3 1 5 6 7 8 9 4 11 12 13 14 15 16
loop(\(x,i).(x + 1),(~1 + ((x div 9) + (x div 7)) - (x div ~7)),1)
A029117: 1 1 1 1 1 1 1 2 3 4 4 4 4 4 5 6
loop(\(x,i).i,((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + ((1 + (x div 2)) div 2))),1)
A157635-A075798: 1 1 1 1 2 1 1 6 6 1 1 12 16 12 1 1
(~1 + ((1 + (5 * loop(\(x,i).2x,(((x + ~1) div 2) - ((3 * (x div 4)) div 2)),1))) div 3))
A284002: 1 1 1 2 1 2 2 6 1 2 2 6 2 6 6 12
(1 + ((x + 1) div (3 * (1 + (x mod (3 * (1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 8))))))))
A037226: 1 1 1 2 1 1 1 2 2 1 2 2 1 1 1 6
(~1 + ((1 + ((2 * (2 + (x div (1 + ((x div 2) mod (1 + (if (x mod 2) <= 0 then 6 else 1))))))) div 3)) mod 3))
A129667: 1 ~1 ~1 ~1 ~1 1 ~1 0 ~1 1 ~1 1 ~1 1 1 0
loop(\(x,i).15x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A176639: 1 1 1 1 15 1 1 225 225 1 1 3375 50625 3375 1 1
loop(\(x,i).(3x + (x div 3)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A172339: 1 1 1 1 3 1 1 10 10 1 1 33 110 33 1 1
loop(\(x,i).((x + (x div 2)) * (1 + (x mod 2))),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A129439: 1 1 1 1 2 1 1 3 3 1 1 8 12 8 1 1
loop(\(x,i).(2 * (x - (x div 5))),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A255256-A099594: 1 1 1 1 2 1 1 4 4 1 1 8 14 8 1 1
loop(\(x,i).((2x + 2) + (x div 4)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A168287: 1 1 1 1 4 1 1 11 11 1 1 26 60 26 1 1
loop(\(x,i).((x + 2) + (x div 5)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A296327: 1 1 1 1 3 1 1 5 5 1 1 8 11 8 1 1
loop(\(x,i).(2 * (x + ((x mod 3) div 2))),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A223257-A155864-A145903: 1 1 1 1 2 1 1 6 6 1 1 12 24 12 1 1
loop(\(x,i).(2x + (x div 5)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A331406: 1 1 1 1 2 1 1 4 4 1 1 8 17 8 1 1
loop(\(x,i).(x * (1 + (x mod 5))),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A173881: 1 1 1 1 2 1 1 6 6 1 1 12 36 12 1 1
loop(\(x,i).17x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A156581: 1 1 1 1 17 1 1 289 289 1 1 4913 83521 4913 1 1
loop(\(x,i).((1 + ((1 + (x div 2)) div 2)) * i),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A173886-A139331-A090441: 1 1 1 1 1 1 1 2 2 1 1 6 12 6 1 1
(1 + (((x + 1) * ((if x <= 0 then 1 else (x - (2 * (x div (~3 + (2 * (~1 + (x mod 3)))))))) - (x mod 2))) div 3))
A265495: 1 2 7 6 14 29
((x + 3) - ((2 * (1 + ((2 * (x - (if (16 mod (x + 1)) <= 0 then 0 else 1))) div 3))) div 3))
A309704: 3 4 5 4 5 6 7 7 8 8 9 10 10 10 11 11
(1 + ((2 * (if x <= 0 then 1 else (2 * (1 + ((1 + (x mod (1 + (x div 4)))) div (1 + ((x + 1) mod 4))))))) div 3))
A329601: 1 2 2 3 2 2 2 5 3 2 2 6 2 2 2 7
(1 + ((x2 + 2x) mod ((2 * (4 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3)))
A306671: 1 2 1 1 1 4 1 4 3 4 1 6 1 4 1 1
(1 + (x3 mod ((2 * (4 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3)))
A009191: 1 2 1 1 1 2 1 4 3 2 1 6 1 2 1 1
(~1 + ((2 * (2 + (if x <= 0 then 1 else (2 * (4x + ((~x + ((x div 2) mod 4)) div 4)))))) div 3))
A313258: 1 4 9 15 20 25 31 36 40 44 49 55 60 65 71 76
(~1 + ((2 * ((x + 2) + (if x <= 0 then 1 else (6x - (((x + 1) + (x mod 2)) div 5))))) div 3))
A314720: 1 5 9 13 18 23 27 32 37 41 45 50 55 59 63 68
(~1 + ((2 * ((x + 2) + (if x <= 0 then 1 else (8x - ((x + ((~x + 1) mod 3)) div 4))))) div 3))
A315549: 1 6 11 17 23 29 35 41 47 53 59 64 70 76 81 87
(~1 + ((2 * ((2x + 2) + (if x <= 0 then 1 else (6x + (((~x + 1) - (x mod 2)) div 3))))) div 3))
A313772: 1 5 10 15 21 25 31 35 41 46 51 56 61 66 71 77
(~1 + ((2 * ((2x + 2) + (if x <= 0 then 1 else (6x + (((x + ~1) mod (2 + (x div 2))) div 2))))) div 3))
A314209: 1 5 11 17 22 27 32 37 43 49 54 59 65 71 76 81
(1 + (((x + 3) - (((1 + (x2 mod (3 * (if (x + ~6) <= 0 then 1 else 2)))) div 2) div 2)) mod 3))
A082846: 1 2 3 1 2 3 1 2 2 3 1 3 1 2 2 3
(if x <= 0 then 0 else ((x + 1) - ((x + 1) mod (1 + ((x div (3 * (2 + ((x2 + x) mod 8)))) + (x mod 2))))))
A161658: 0 2 3 4 5 6 7 6 8 10 11 12 13 14 14 16
(1 + (if (x + ~1) <= 0 then x else (1 + ((((1 + (x mod (1 + (x mod (2 * (2 + ((x div 2) mod 2))))))) mod (x + 1)) div 2) + (x mod 2)))))
A320538-A093640: 1 2 2 3 2 4 2 4 2 4 2 6 2 4 3 5
(if x <= 0 then 1 else (~1 + ((~1 + (2 * compr(\x.(1 - ((x + 1) mod (1 + (x div (2 + ((x div 4) mod 3)))))),x))) mod (x + 1))))
A179764: 1 0 1 0 1 0 1 2 3 4 3 2 1 0 1 2
(~1 + (2 * loop(\(x,i).(2 + ((x div 2) * i)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)))
A022166: 1 1 1 1 3 1 1 7 7 1 1 15 35 15 1 1
(1 + ((if x <= 0 then 2 else (1 + ((2 * (1 + (x mod (1 + (x mod (1 + (x div (2 + ((x div 2) mod 3))))))))) div 3))) div 2))
A321944: 2 1 1 2 1 2 1 2 2 2 1 2 1 3 3 2
(1 + ((1 + ((x mod (1 + (2 * ((x - (2 * loop(\(x,i).(x div (2 - (x mod 2))),x,x))) mod 7)))) div 2)) div 2))
A275648: 1 1 1 2 2 1 1 1 3 3 1 2 4 1 1 2
(1 + (x mod (2 * (1 + ((1 + ((1 + ((x * ((if (x mod 5) <= 0 then 1 else 2) + (x mod 4))) div 2)) div 2)) div 2)))))
A001438: 1 2 3 4 1 6 7 8
A076388: 1 2 3 4 1 6 7 8 3 10 1 12 5 2 15 16
((3 + (x mod 2)) div (1 + (x div (2 + (x div (1 + (((if (x mod 2) <= 0 then 1 else x) mod 4) + ((x mod 3) div 2))))))))
A204999: 3 4 1 2 1 2 1 1 1 2 1 1 1 2 1 1
(~1 + loop(\(x,i).(x2 + x),1,((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~1) div 2))) div 2)))
A144403: ~1 ~1 ~1 ~1 1 ~1 ~1 5 5 ~1 ~1 11 29 11 ~1 ~1
(1 + ((1 + (((1 + ((loop(\(x,i).x2,1,((x + 1) + ((x div 5) + (x div 2)))) div 2) div 2)) div 2) div 2)) div 2))
A339094-A182086-A057537-A001313-A001312-A001302-A001301-A000008: 1 1 2 2 3 4 5 6 7 8 11 12 15 16 19 22
(1 + ((1 + (((3 * (1 + ((x + (loop(\(x,i).8x,(x + 1),1) mod (x + 1))) div 2))) div 2) div 2)) div 2))
A331854: 1 1 2 2 3 3 3 3 4 4 5 4 5 5 4 4
(1 + ((1 + ((((~1 + (if (2 - (2x mod (4 + (x div 4)))) <= 0 then 0 else (x2 + ~x))) div 2) div 2) div 2)) div 2))
A216645-A216635: 1 1 1 1 1 2 1 1 1 5 1 1 1 1 12 1
loop(\(x,i).i,(((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (2 + (x div (1 + (2 * (2 - ((x div 2) mod 2))))))),1)
A130523-A034363: 1 1 1 1 2 1 1 4 3 1 1 5 8 4 1 1
(1 + (10 * (1 + compr(\x.((1 + (x * loop(\(x,i).(5x * (x - i)),2,x))) mod (x + 1)),x))))
A293659: 11 31 71 191 211
((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) div (if ((x + 2) mod 5) <= 0 then 2 else 1))
A071920: 0 0 0 0 1 0 0 2 1 0 0 3 4 1 0 0
(~1 + (2 * loop(\(x,i).x2,1,(~1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))))
A141597: 1 1 1 1 7 1 1 17 17 1 1 31 71 31 1 1
(1 + (loop(\(x,i).(x * (x2 div 2)),1,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) div 2))
A196786: 1 1 1 1 1 1 1 3 3 1 1 7 17 7 1 1
(1 + ((1 + ((x + loop(\(x,i).(2 * (2 + (x div 3))),(~1 + (2x mod (4 + (x div 4)))),1)) div 2)) div 2))
A063712: 1 2 2 3 4 3 4 5 5 4 5 6 6 6 5 6
(~1 + ((2 + ((2 * (1 + (loop(\(x,i).(x + (x div (2 + (x mod 2)))),x,2) div (x + 2)))) div 3) - (x mod 2)) div 2))
A206557: 0 0 0 0 0 0 1 0 1 1 2 2 4 5 7 9
(2 div (1 + (((1 + (loop(\(x,i).(2 * ((x + 1) - (2 * (i mod 2)))),x,1) * (1 + (4 * (x mod 2))))) mod (x + 1)) div 2)))
A086137: 2 2 2 1 1 1 1 1 0 2 1 1 1 2 1 1
((1 + loop(\(x,i).5x,((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2),1)) div (1 + ((x + 1) div 2)))
A180997: 2 1 1 0 2 0 0 1 1 0 0 0 3 0 0 0
((1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)) * (1 + (2 * (if x <= 0 then 0 else 2))))
A135089: 1 5 5 5 10 5 5 15 15 5 5 20 30 20 5 5
((x + 1) - (2 * (((x + 1) - ((1 + ((x * (1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x))) div 2)) mod 5)) div 2)))
A105969: 1 2 3 2 1 2 3 4 5 2 1 2 1 2 3 2
(~1 + (((~1 + (6 * (1 + ((if x <= 0 then 2 else (1 + ((x + 3) mod (1 + (x div 4))))) div 2)))) div 2) div 2))
A029358: 1 0 0 0 1 0 1 0 1 0 1 1 3 0 1 1
(1 + (((1 + (((2x + 2) * ((1 + ((loop(\(x,i).(x + (x div (2 + (x mod 2)))),x,2) div 2) div 2)) div 2)) div 2)) div 2) div 2))
A096445: 1 1 2 2 2 4 4
A010238: 1 1 2 2 2 4 4 7 12 18
(1 + (((1 + (((1 + (((x + 1) * (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))) div 3)) div 2) div 2)) div 2) div 2))
A318810: 1 1 1 1 1 1 1 2 2 1 1 3 1 1 2 6
(~1 + (2 * ((3 * ((~1 + (if (x mod 2) <= 0 then x else 0)) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))) div 2)))
A144432: ~1 ~1 ~1 ~1 ~1 ~1 ~1 1 1 ~1 ~1 5 1 5 ~1 ~1
(~1 + (((3 * (2 + ((2 + ((((if (x mod 2) <= 0 then 2 else 0) + (x div 2)) * (1 + (x div 2))) div 2)) div 3))) div 2) div 2))
A029142: 1 0 1 1 2 1 3 2 4 3 5 4 8 5 9 8
((x + ~1) - (if x <= 0 then 2 else (x - ((((~1 + (x div 2)) div 2) - ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 2))))
A140056: ~3 ~2 ~1 ~1 ~2 ~1 ~1 ~1 ~1 ~1 0 ~1 ~1 ~1 0 0
(~1 + (2 * ((1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)) * (if x <= 0 then 1 else 2))))
A135087: 1 3 3 3 7 3 3 11 11 3 3 15 23 15 3 3
(1 + ((((loop(\(x,i).(x * (1 + (x div 5))),1,(13x + 13)) div 2) div 2) div 2) div 2))
A338631: 3 10 20 36 57 79
(1 + ((((5 * (2 + compr(\x.(1 - (x mod (1 + (if (x mod 8) <= 0 then 2 else 1)))),x))) mod (x + 2)) div 2) div 2))
A072811-A048996: 1 1 1 1 1 2 1 1 2 1 3 1 1 2 2 3
((1 + ((2 * (1 + ((((x2 + 3x + 2) div 2) + loop(\(x,i).2x,x,1)) * (2 + (x mod 2))))) div 3)) div 3)
A260818: 1 3 5 12 14 35 41
((1 + (2 * (loop(\(x,i).2x,x,1) mod (1 + (3 * (4x mod 13)))))) mod 3)
A194305: 1 2 0 2 1 0 1 2 1 0 1 1 2 1 0 1
((1 + (2 * (if x <= 0 then 1 else (2 * (4x - ((x + ((x + (x div 3)) mod 3)) div 3)))))) div 3)
A315033: 1 5 9 15 19 25 29 35 39 44 49 53 59 63 69 73
((1 + (2 * (if x <= 0 then 1 else (6x - ((~2x + 4) div (4 + ((x div 2) div 3))))))) div 3)
A058759: 1 4 8 13
A311809: 1 4 8 13 17 21 25 29 34 38 43 47 51 55 59 63
((1 + (2 * (if x <= 0 then 1 else (2 * (3x + ((2x + ((x div 3) mod 3)) div 3)))))) div 3)
A313241: 1 4 9 15 20 24 29 35 40 44 48 53 59 64 68 73
(((2x + 1) * (1 + ((2 * (1 + ((1 + (loop(\(x,i).2x,(x + ~1),x) div (x + 1))) div 2))) div 3))) mod 3)
A256852: 1 0 1 0 0 0 2 0 0 0 0 1 1 0 0 0
(((2x + 1) * (~1 + (2 * (loop(\(x,i).x3,1,(10x + 2)) div (x + 1))))) mod 3)
A023555: 0 0 1 0 0 2 0 0 1 2 0 0 2 0 2 0
(((if x <= 0 then 1 else 4x) + ((2x + 1) div 3)) - ((1 - (2 * ((x + ((x div 2) mod 2)) div 2))) div 3))
A313726: 1 5 10 15 20 24 30 36 40 45 50 55 60 65 70 75
(if ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) <= 0 then 1 else (((2 - ((x div 2) mod 2)) * (1 + (x div 2))) div 3))
A047150-A047140: 1 1 1 1 2 1 1 1 3 1 1 2 4 4 1 1
loop(\(x,i).((3x2 + 3) div 2),1,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))
A108470: 1 1 1 1 3 1 1 7 7 1 1 15 25 15 1 1
(((if x <= 0 then 1 else 5x) + ((x + 1) div 3)) - ((1 + (2 * ((x + ((x div 2) mod 2)) div 2))) div 3))
A313744: 1 5 10 15 20 26 30 34 40 45 50 55 60 65 70 75
((if x <= 0 then 1 else 6x) - (((x + 1) div 3) + ((2 * (x + (((x div 2) div 3) mod 2))) div 3)))
A315271: 1 6 10 15 21 25 30 35 39 45 50 54 60 66 70 75
(6x + (if x <= 0 then 1 else ((2 * (~x + (((x div 2) div 3) mod 2))) div 3)) - ((x + 1) div 3))
A315053: 1 5 9 15 20 24 30 36 40 45 51 55 60 65 69 75
(((if x <= 0 then 1 else 4x) + ((x + 1) div 3)) - (((~x + 1) - (2 * ((x + ((x div 2) mod 2)) div 2))) div 3))
A310457: 1 4 10 15 20 25 30 35 40 45 50 56 60 64 70 75
((2 * (1 + ((1 + (x div (2 + (loop(\(x,i).2x,(1 + (((1 + (x div 2)) div 2) div 2)),2) mod (x + 1))))) div 2))) div 3)
A124764: 0 0 0 1 0 0 1 2 0 0 1 1 1 1 2 3
((2 + ((1 + ((1 + (if (x mod 4) <= 0 then 2x else (x div 2))) * (1 + (4 * (x mod 2))))) div 3)) div 3)
A317988: 0 1 1 1 1 2 1 3 2 3 1 4 3 4 1 5
((((x2 + 5x + 6) * loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + 2),(x + 1))) div 2) div 3)
A030060: 5 56 420 2640 15015 80080 408408 2015520 9699690 45762640 212469400 973496160 4411154475 19800295200 88158457200 389753179200
(~3 + (2 * (1 + compr(\x.(2 - (loop(\(x,i).((x + 1) * (1 + ((~x + 2) mod 4))),x,5) mod (x + 1))),x))))
A217460: 7 9 15 17 21 23 25 27 31 33 35 39 41 43 45 47
((4 * (1 + ((2 * (1 + ((2 * loop(\(x,i).(3x + 4),x,(x + 2))) div 3))) div 3))) div 3)
A292482: 2 9 32 112 384 1296 4320 14256 46656 151632 489888 1574640 5038848 16061328 51018336 161558064
((2 * (2 + ((2 + ((2 + loop(\(x,i).(x - (3 * (x div (~2 + (x mod ~2))))),x,1)) div 2)) div 3))) mod 3)
A287320: 0 0 2 2 1 0 0 0 2 2 1 0 2 2 1 0
((4 * (1 + compr(\x.((x + 1) mod (1 + (x mod (2 + (loop(\(x,i).x3,2,2x) mod (x + 1)))))),x))) div 3)
A184967: 1 2 4 5 6 8 9 10 12 13 16 20 21 22 24 25
(if x <= 0 then 1 else (1 - ((2 * (2 + ((~1 + (2 * (1 + (x mod (4 * (1 + (2 * (x mod 2)))))))) mod (x + 1)))) mod 3)))
A253414: 1 1 ~1 0 1 ~1 ~1 1 1 0 ~1 ~1 1 0 ~1 1
((2x + ~1) + ((2 * (2 + (if x <= 0 then 1 else (2 * (2x - ((~x + 3) div 7)))))) div 3))
A314954: 1 5 9 14 20 25 29 34 39 43 48 54 59 63 68 73
((2 * ((x + 1) + ((2 * ((2x + 2) + (if ((1 + (x div 2)) mod 6) <= 0 then 2 else 0))) div 3))) div 3)
A213733: 1 2 4 6 7 9 10 12 14 15 18 19 20 21 23 24
(((2x + 2) + (if x <= 0 then 1 else (2 * (6x + ((2x + 1) div 9))))) div 3)
A313611: 1 5 10 14 20 24 29 34 38 44 48 53 58 63 68 72
(1 + ((x + (loop(\(x,i).((x2 + x) div 2),1,(1 + (x mod (1 + (x mod (2 * (1 + (2 * (x mod 2))))))))) mod (x + 1))) div 2))
A300271: 1 2 2 3 3 5 4 6 5 7 6 11 7 9 8 13
(loop(\(x,i).(x * i),((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 5),1) mod (x + 3))
A298589: 1 1 1 1 1 1 1 1 1 1 1 2 9 2 1 1
loop(\(x,i).2x,(4x + ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2) - (x div 2)),1)
A120785: 1 16 128 4096 32768 524288 4194304 268435456 2147483648 34359738368 274877906944 8796093022208 70368744177664 1125899906842624 9007199254740992 1152921504606846976
(1 + compr(\x.(~1 + (x mod (1 + ((1 + (x mod (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))) mod (x + 1))))),x))
A334965-A166401-A133811: 1 2 3 4 5 7 8 9 11 13 16 17 18 19 23 25
loop(\(x,i).(1 + ((2 * (1 + (((x + 1) * (1 + (2 * ((x + 1) div (3 - (x mod 2)))))) div 3))) div 3)),x,1)
A307140: 1 3 5 11 36 207
(1 + compr(\x.(1 - (x mod (1 + ((((4x + ~4) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))) div 2) mod 3)))),x))
A263636: 4 6 16 20 24 28 36 44 52 60 64 68 76 80 84 92
(1 + compr(\x.(~1 + ((1 + (x mod (1 + (x mod (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))))) mod (x + 1))),x))
A180934: 1 2 3 5 7 9 11 13 17 19 23 25 28 29 31 37
loop(\(x,i).(3 * ((3 * (~1 + (3 * (1 + ((x div 2) mod (1 + (6 * (x mod 2)))))))) div 2)),x,1)
A181403: 1 9 63 48
(1 + compr(\x.((x - loop(\(x,i).(3x + 2),(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1)) mod (x + 1)),x))
A294455: 1 2 3 6 18 27 54 81 162
(1 + compr(\x.(loop(\(x,i).(18x2 + 306x + 282),2,x) mod (x + 1)),x))
A018714: 1 2 3 6 151 302 453 906
loop(\(x,i).(1 + (x div (2 + (x mod (1 + (x div (1 + (((2x mod (1 + (x mod 4))) div 2) + (x mod 2))))))))),1,(x + 1))
A329312: 1 1 2 1 2 1 3 1 2 2 3 1 2 1 4 1
compr(\x.(~1 + ((1 + (x mod (5 * (2 + (if (x mod 12) <= 0 then (x div 2) else 0))))) mod (x + 1))),(x + 1))
A342650-A342262-A328273: 1 2 3 4 5 6 7 8 9 10 12 20 24 30 36 40
((1 + (2 * (((~x + 2) + ((if (x + ~2) <= 0 then 1 else ((x + 2) div 5)) mod 2)) mod (1 + (x div 3))))) mod (x + 1))
A329984: 0 1 1 1 3 1 1 5 1 3 1 7 1 1 9 1
((x + 1) * loop(\(x,i).(8 * ((((2x * (1 + (2 * i))) div (2 + i)) * (~1 + (2 * i))) div (1 + i))),x,1))
A254633: 1 16 480 17920 752640 34062336 1623638016 80408739840 4100845731840 214072431738880 11388653368508416 615465127495335936 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) * (loop(\(x,i).(2 * ((((2x * (1 + (2 * i))) div (2 + i)) div (1 + i)) * (1 + (2 * i)))),(x + 1),1) div 2))
A337902: 3 50 735 10584 152460 2208492 32207175 472780880 6982113996 103673813880 1546866469148 23179817220000 348690679038000 5263441096145400 79698007774092375 1210159553338375200
((x + 1) + (2 * ((x + 1) + (x mod 2) - ((loop(\(x,i).2x,x,1) mod (1 + (4 * (x mod 4)))) mod 3))))
A287458: 3 4 7 10 15 16 19 22 27 28 31 36 39 40 43 46
(1 - ((1 + (x mod (1 + ((1 + ((x + 1) mod (1 + ((1 + (if (x mod 3) <= 0 then 0 else x)) div 3)))) mod (x + 1))))) div 2))
A111412: 1 0 0 0 0 0 1 ~1 0 0 1 ~1 1 0 ~1 0
((1 + (((x + 2) * loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + 2),(x + 1))) div (x + 5))) div 2)
A003516: 1 7 36 165 715 3003 12376 50388 203490 817190 3268760 13037895 51895935 206253075 818809200 3247943160
((1 + (loop(\(x,i).3x,(1 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4)))),1) div 3)) div 2)
A069739-A066060: 1 1 1 2 1 1 1 5 2 1 1 2 1 1 1 14
((1 + ((2 * (2 + (x div (1 + (loop(\(x,i).(x2 + x + 2),2,12) mod (x + 1)))))) div 3)) div 2)
A143258: 1 1 1 2 1 1 2 1 1 1 4 1 1 1 1 2
(26 * (1 + compr(\x.(loop(\(x,i).(~x4 + 3x2),3,2) mod (x + 1)),x)))
A288162: 26 52 104 208 338 416 676 832 1352 1664 2704 3328 4394 5408 6656 8788
(22 * (1 + compr(\x.(loop(\(x,i).((x + 1) * (x + i)),4,5) mod (x + 1)),x)))
A033848: 22 44 88 176 242 352 484 704 968 1408 1936 2662 2816 3872 5324 5632
(2 * (1 + ((1 + (((x + 2) + ((x + ((x + ((x + loop(\(x,i).2x,x,1)) div (x + 1))) div 2)) div 2)) div 3)) div 2)))
A033825: 2 4 4 4 6 6 8 8 10 12 16 24
((1 + ((1 + ((1 + (loop(\(x,i).2x,x,2) div (1 + (6 * (1 + (4 * (x mod 2))))))) div 2)) div 2)) div 2)
A316193: 0 0 1 0 1 1 3 1 10 5
((1 + ((1 + (((3 * ((1 - loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,x)) mod (x + 1))) div 2) div 2)) div 2)) div 2)
A301572: 0 0 0 1 0 0 1 1 0 0 0 1 2 3 2 1
((1 + ((1 + ((1 + ((((x + 1) + (((if (x mod 2) <= 0 then x else 0) * (1 + (x div 2))) div 2)) div 2) + (x mod 2))) div 2)) div 2)) div 2)
A326850: 0 1 1 1 1 1 2 1 2 1 3 1 4 1 5 2
(loop(\(x,i).x2,1,(~1 + (2 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)))) div 2)
A282593: 0 0 0 0 0 0 0 4 4 0 0 12 84 12 0 0
((1 + (((((loop(\(x,i).8x,x,49) div 2) div 2) div 2) div 2) div 2)) div 2)
A055847: 1 6 49 392 3136 25088 200704 1605632 12845056 102760448 822083584 6576668672 52613349376 420906795008 3367254360064 26938034880512
(4 - ((loop(\(x,i).(2x + 2),x,(12 * (x div 7))) mod 5) div 2))
A276789: 4 3 4 2 4 3 4 4 3 4 2 4 3 4 3 4
(~2 + (3 * (1 + ((loop(\(x,i).((x + 1) + ((x mod (2 + (6 mod (1 + (x div 2))))) div 2)),x,1) div 2) div 2))))
A244481: 1 1 1 4 4 4 7 7 7 10 10 13 16 19 19 19
(2 + ((x + (2 * (((x4 mod 31) mod 2) + (if x <= 0 then 0 else 1)))) div 3))
A177876: 2 3 3 4
A341053: 2 3 3 4 4 5 5 5 5 5 6 7 6 7 8 7
(1 - ((x + 1) div (2 + ((~1 + loop(\(x,i).(2x + ~2),(1 + ((x div 3) mod 2)),(1 + (x div 4)))) mod (x + 1)))))
A016353: 1 1 1 0 0 ~1 ~1 ~1 0 0 0 0 0 ~1 ~1 0
(1 - (((2 * (1 + ((1 + ((x mod (2 + (loop(\(x,i).3x,x,3) mod (x + 1)))) div 2)) div 2))) mod (x + 1)) div 2))
A226350: 1 1 0 0 ~1 0 0 0 0 ~2 0 0 ~1 ~1 0 0
(((1 + (2 * ((1 + ((loop(\(x,i).x2,1,((x + 4) + (x div 2))) div 2) div 2)) div 2)) - (x mod 2)) mod (x + 1)) div 2)
A238211: 0 0 0 0 1 0 0 1 1 1 1 2 3 3 3 5
((x div (2 + (x mod (1 + ((x + 1) div (1 + (((2x div (1 + (x div 4))) mod 2) + (x mod 2)))))))) + (if x <= 0 then 1 else 2))
A335549-A335516-A326082-A319686-A181796-A088873-A085082: 1 2 2 3 2 3 2 4 3 3 2 5 2 3 3 5
(((~1 + (6 * (1 + (((x + 1) mod (2 + ((((x + 1) div 2) div 3) + (if x <= 0 then 0 else 1)))) div 2)))) div 2) div 2)
A060778: 1 2 1 1 2 2 2 1 1 2 2 2 2 4 1 1
((x + 3) - (2 * (1 + ((1 + ((1 + (((x + (loop(\(x,i).(x + (x div 2)),x,2) div (x + 1))) div 2) div 2)) div 2)) div 2))))
A175266: 1 2 3 2 3 4 5 6 7 8 9 8 9 10 9 8
(((5 * loop(\(x,i).(i div 3),((2 - (2x mod (4 + (x div 4)))) mod (x + 1)),1)) div 2) div 2)
A296068-A144064: 1 1 0 1 1 0 1 2 2 0 1 3 5 3 0 1
(((3 * ((x + 2) + ((2 * (4 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 3))) div 2) div 2)
A071259: 3 4 6 8 10 12 15 17 19 23 25 29 31 33 36 39
(((1 + (((loop(\(x,i).(x * (2 + i)),(16x + 16),1) div 2) div 2) div 2)) div 2) div 16)
A172719-A172615: 12504636144000 4611686018427387903 4611686018427387903 4611686018427387903
(2 * (2 + (((x + 3) + (if (x + ~1) <= 0 then 1 else (((1 + (8 mod (1 + (x div 2)))) div 2) - (x mod 2)))) div 2)))
A166082: 8 8 8 8 12 12 12 12 16 16 18 18 20 20 20 20
(if x <= 0 then 1 else ((x + 4) + ((((5 * ((x2 + 3x + 2) div 2)) + (x div 5)) div 2) div 2)))
A022954: 1 8 13 19 26 35 45 56 68 82 97 113 130 148 168 189
loop(\(x,i).(x * ((x + 1) div 2)),1,(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))
A168641: 1 1 1 1 2 1 1 6 6 1 1 8 18 8 1 1
(2 * (loop(\(x,i).(x * i),(1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)),1) div (x + 2)))
A230513: 0 0 0 0 0 0 0 0 0 0 0 2 16 2 0 0
(8x * ((10x + 2) + (loop(\(x,i).x2,2,(3x + 2)) div 2)))
A326747: 0 2592 33120
(((if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + (((3 * (x div 4)) div 2) * (x div 2))) div 2)) div 2)))) - (x mod 2)) div 2)
A088931: 0 0 1 0 2 1 2 1 4 3 5 4 7 6 8 7
(((x + 1) + (((1 + (((1 + ((loop(\(x,i).x2,1,(1 + (x2 div 3))) div 2) div 2)) div 2) div 2)) div 2) div 2)) div 2)
A098492: 0 1 1 2 2 3 4 6 8 11 14 19 25 32 41 53
((x + ((5 * ((1 + (2 * (if x <= 0 then 1 else (2 * (x - ((~1 + (x div 2)) div 3)))))) div 3)) div 2)) div 2)
A011982: 1 4 4 6 8 11 13 14 15
((x + 8) + ((x + (2 * (if x <= 0 then 1 else (2 + ((x - ((x div 2) mod 5)) div 2))))) div 3))
A033872: 8 10 12 14 15 16 18 20 21 22 26 27 28 30 32 33
(if x2 <= 0 then 1 else ((x + ((x + ((1 + (((x + 1) * (x - (((~x2 + x) div 2) div 3))) div 2)) div 2)) div 2)) div 2))
A062438: 1 1 2 3 5 7 9 12 16 20 24 30 36 44 52 61
(~2 - loop(\(x,i).(1 - (((x + 2) * (1 + ((x2 + 4x + 4) div 2) - (x mod 2))) div 3)),1,(x + 2)))
A097478: 9 17 35 53 85 117
((2x + ~1) + ((2 * (2 + ((1 + (2 * (if x <= 0 then 1 else (2 * (2x - ((x div 2) mod 2)))))) div 3))) div 3))
A310737: 1 4 7 11 15 19 22 25 30 34 37 41 45 49 52 56
(2x + ((1 + (2 * (if x <= 0 then 1 else (2 * (2x - ((~x + ((x div 3) mod 3)) div 3)))))) div 3))
A315416: 1 6 11 15 20 26 31 35 40 46 52 57 61 66 72 77
(2x + ((1 + (2 * (if x <= 0 then 1 else (2 * (2x + ((x + ((x div 3) mod 3)) div 3)))))) div 3))
A315068: 1 5 9 15 20 26 31 37 41 46 51 55 61 66 72 77
(2x + ((1 + (2 * (if x <= 0 then 1 else (2 * (2x + (x div (4 + ((x div 2) div 5)))))))) div 3))
A314955: 1 5 9 14 20 25 29 34 40 45 49 54 59 63 68 74
(2x + ((1 + (2 * (if x <= 0 then 1 else (2 * (2x + ((x + ((1 - (x div 2)) mod 4)) div 4)))))) div 3))
A314969: 1 5 9 14 20 26 31 35 40 45 49 54 60 66 71 75
(1 + (((2 * (1 + ((1 + (((~1 + loop(\(x,i).4x,(x div 2),2)) mod (x + 1)) div 2)) div 2))) div 3) + (x mod 2)))
A026100: 1 2 1 3 1 2 1 4 3 2 1 4 1 2 3 5
(if (x + ~1) <= 0 then 1 else (1 + (((x mod ((x + ~1) - (x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4)))))))) div 2) + (x mod 2))))
A303757: 1 1 1 2 1 3 1 2 2 3 1 4 1 3 1 2
(1 + (x div (2 + ((x + 1) div (1 + (2 * ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 2)))))) - (x mod 2))
A068322: 1 0 1 1 1 1 1 2 2 2 1 3 1 3 3 5
loop(\(x,i).(2 * (3 + (x3 mod (1 + (6 * (1 + (4 * (x mod 2)))))))),(x div 2),(x mod 2))
A093479: 0 1 6 8 18 8 8 8 8 8 8 8 8 8 8 8
((2x + 3) + (2 * ((1 + ((x * (1 + (loop(\(x,i).3x,(x3 + 2x),1) div 2))) div 2)) div 2)))
A092830: 3 13 265729
((x + 1) + ((2 * (1 + (((1 + (((x * (if (~4 + (x div 2)) <= 0 then 1 else x)) div 3) div 2)) div 2) div 2))) div 3))
A136040: 1 2 3 4 5 6 7 8 9 10 14 16 17 19 21 22
((x + ~1) + ((2 * ((x + 2) + (if x <= 0 then 1 else (6x - (((x + ~1) mod (2 + (x div 2))) div 2))))) div 3))
A315496: 1 6 11 16 22 28 34 40 45 50 56 62 67 72 78 84
compr(\x.(1 - (x mod (1 + (loop(\(x,i).2x,x,(1 + (3x mod (2 * (1 + (x mod 6)))))) mod (x + 1))))),x)
A294675: 5 8 11 13 14 16 17 19 21 22 23 24 25 26 27 28
((x + 1) + ((1 + ((1 + ((1 + ((1 + (loop(\(x,i).(2x * i),(x + ~1),1) div 3)) div 3)) div 2)) div 2)) div 2))
A191783: 1 2 3 5 6 12 61
((x7 + 7x) + loop(\(x,i).7x,x,1))
A220528: 1 15 191 2551 18813 94967 397627 1647135 7862009 45136639 292475319 1996813991 13877119093 96951759015 678328486451 4747732369423
(x + (if (x + ~12) <= 0 then 1 else (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))
A102450: 1 2 3 4 5 6 7 8 9 10 11 12 13 16 14 15
(x + ((4 * ((2 + ((3 * (x + (4 * (if (~2 + (x div 4)) <= 0 then 0 else 2)))) div 2)) div 2)) div 3))
A308496: 1 2 4 7 9 10 12 15 17 18 20 23 33 34 36 39
((2x + 4) + (if x <= 0 then 0 else (7 + ((x + ((x mod (1 + (x div 2))) div 2)) div 2))))
A022416: 4 13 16 18 21 24 26 29 31 34 37 39 42 45 47 50
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((((x + 1) div 2) div 2) * (x div 5)))))
A328887: 1 1 1 1 2 1 1 4 4 1 1 8 15 8 1 1
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((2 - ((x div 2) mod 2)) * (x div 5)))))
A256161: 1 1 1 1 2 1 1 3 4 1 1 4 11 6 1 1
(1 + ((1 + (2 * (x div 4))) mod (1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))))
A309939-A309931-A164306-A111603: 1 1 1 1 2 1 1 1 3 1 1 2 3 4 1 1
(~1 + (2 div (1 + ((1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) mod 7)) div 2))))
A294254: 1 1 0 1 ~1 0 1 ~1 1 0 1 ~1 ~1 ~1 0 1
(~1 + ((x + 1) div (1 + (((~1 + (6 * (1 + (x div (2 + (x div (2 + ((x * (x div 2)) mod 2)))))))) div 2) div 2))))
A063276: ~1 0 0 0 0 1 1 1 2 2 2 1 3 3 4 2
(1 + ((3 + ((2 * ((2x + 1) - ((~x + 1) div (2 + (x div 4))))) div 3)) mod 9))
A308375: 4 6 8 9 1 3 5 6 7 9 2 3 4 6 7 8
(1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 3) - (x mod (2 - ((x div 2) mod 2))))))
A026670: 1 1 1 1 3 1 1 4 4 1 1 5 11 5 1 1
(1 + ((1 + (5 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))) div 3))
A238498-A136482-A026648-A026626: 1 1 1 1 3 1 1 4 4 1 1 6 8 6 1 1
(1 + (((x + 1) div (1 + (x mod (2 + (x div (1 + ((x div 2) mod (1 + (x mod (1 + ((~x + 2) mod 4))))))))))) div 3))
A316789: 1 1 1 2 1 1 1 2 2 1 1 1 1 1 1 6
compr(\x.(~1 + (x mod (1 + (x mod 4)))),(1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))
A173740: 1 1 1 1 4 1 1 5 5 1 1 6 8 6 1 1
compr(\x.(x mod (1 + (2 * (x div 4)))),(1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))
A215292: 1 1 1 1 2 1 1 3 3 1 1 6 10 6 1 1
compr(\x.((x mod 4) * (x div 3)),(1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))
A154867-A100631-A064298: 1 1 1 1 2 1 1 4 4 1 1 8 12 8 1 1
(1 + ((2 * (1 + ((1 + ((1 + ((1 - (2x mod 9)) mod (x + 1))) div 3)) div 2))) div 3))
A168258: 1 1 1 2 2 1 2 2 2 1 3 3 3 2 1 3
(1 + ((2 * (1 + ((x mod (1 + ((~1 + ((~2x + 2) mod (4 + (x div 4)))) mod (x + 1)))) div 2))) div 3))
A160182: 1 1 1 2 1 1 3 1 1 1 5 2 1 1 1 6
((6x + 1) div (1 + ((2 * (1 + ((1 + (3x div (2 + (x div 3)))) div 2))) div 3)))
A027440: 1 3 4 6 8 10 12
A334905: 1 3 4 6 8 10 12 14 16 18 20 22 24 26 21 30
(1 + ((2 * (1 + ((1 + ((((x + 1) * (1 - ((~x + 1) div (2 + ((x div 2) div 3))))) div 2) div 2)) div 2))) div 3))
A157524: 1 1 2 2 3 3 3 3 5 5 5 7 6 6 7 8
(1 + ((2 * ((x + 1) + ((2 * (1 + ((2x2 + x + 1) div 7))) div 3))) div 3))
A129895: 1 2 3 5 7 9 11 13 15 18 21 25 29 33 37 41
(1 - ((x + 1) mod (~1 - ((x + 1) * ((~x2 + 2) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))))))
A174545: 1 1 1 1 2 1 1 2 2 1 1 2 28 2 1 1
(1 + ((1 + (x mod (1 + ((x + 1) div (2 * (1 + ((1 + (x mod (1 + ((2 - (x div 2)) mod 6)))) div 2))))))) div 2))
A271778: 1 1 1 2 2 2 2 2 1 2 2 2 4 2 4 1
(1 + ((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (2 * (1 + (((x + 1) div 2) div 2)))))) div 2))
A173118-A028275: 1 1 1 1 4 1 1 5 5 1 1 6 10 6 1 1
((2x + 1) - (((x + 1) - ((1 + (x mod (1 + (11 mod (x + 1))))) mod (x + 1))) div 2))
A206285: 1 2 4 5 7 8 11 13 14 15 16 17 19 21 23 25
(1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (3 + (x div (1 + (x mod 5))))) div 2))
A214987: 1 1 1 1 2 1 1 3 3 1 1 5 8 4 1 1
(1 + (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + ((1 + (x div 2)) div 2))) div 2))
A296157: 1 1 1 1 2 1 1 4 4 1 1 7 9 7 1 1
(1 + ((1 + (((1 + (((((x + 1) * (1 + (((x + 2) div 3) * ((x + ~1) div 2)))) div 2) div 2) div 2)) div 2) div 2)) div 2))
A036847: 1 1 1 1 1 2 2 2 3 3 4 5 5 8 8 10
(1 + ((1 + (((3 * (1 + (x div (1 + (x mod (1 + (x mod (2 + (x div (3 - (x mod 2))))))))))) div 2) div 2)) div 2))
A139169: 1 1 2 3 3 2 4 3 4 3 5 3 6 4 3 4
(1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (8 * ((1 + (x div 2)) div 2)))) div 2))
A157169: 1 1 1 1 5 1 1 9 9 1 1 13 26 13 1 1
(3 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) + ((2x + 1) div (3 + (x div 4)))))
A204002: 3 4 4 5 6 5 6 7 7 6 7 8 9 8 7 8
(1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (2 * ((x div 2) div (2 - ((x div 2) mod 2)))))) div 2))
A257365-A177976-A161492-A060098-A034781: 1 1 1 1 2 1 1 4 3 1 1 6 8 4 1 1
(1 + (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + ((x + 2) mod 4))) div 2))
A244911: 1 1 1 1 2 1 1 3 4 1 1 4 7 7 1 1
(~1 + ((5 * (1 + (((x + ~1) mod (2 + (x mod (1 + (x mod (2 - ((x div 4) div ~2))))))) div 2))) div 2))
A193349: 1 1 1 4 1 1 1 1 4 1 1 4 1 1 1 6
(1 + (2 * ((2 * (1 + (2 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))) div 3)))
A132737: 1 1 1 1 5 1 1 7 7 1 1 9 13 9 1 1
(~1 + (((((x + 3) * ((9x3 + 31x2 + 30x + 8) div 2)) div 2) div 3) div 2))
A088941: 0 12 54 154 349 685 1217 2009 3134 4674 6720 9372 12739 16939 22099 28355
((1 + (2 * ((1 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 2)) div 2))) mod 7)
A211314: 1 1 1 1 3 1 1 5 5 1 1 0 6 0 1 1
((1 + (2 * ((x + 2) - (2 * ((~2 + ((~2x + 2) mod (4 + (x div 4)))) div 2))))) div 7)
A342859: 0 1 1 2 1 2 3 2 2 3 4 3 3 3 4 5
((2x + ~1) - (2 * ((3x + 1) - (2 * ((x + 1) + (((x - (x div ~2)) * (x div 2)) + (x mod 2)))))))
A272705: 1 5 13 25 49 69 109 137 193 229 301 345 433 485 589 649
(1 + (2 * ((1 + (((1 + (((x + 1) * (1 + (2 * ((x - (x div 8)) mod 2)))) div 3)) div 2) div 2)) div 2)))
A109599: 1 1 1 3 1 3 1 3 3 3 5 3 5 3 5 3
(1 + (((9 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) div 2) div 2))
A134398-A026681-A026615: 1 1 1 1 3 1 1 5 5 1 1 7 10 7 1 1
(1 + ((((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (3 + (x div 2))) div 2) div 2))
A295213-A113582: 1 1 1 1 2 1 1 4 4 1 1 7 10 7 1 1
(~1 + (2 * ((3 * (3 + ((x2 + x + 94) div 2))) div 2)))
A268428: 149 151 157 167 179 193 211 233 257 283 313 347 383 421 463 509
(x div (~1 + (2 * (2 + ((1 + (2 * ((x + 1) mod (1 + (2 * ((3 * (x div 5)) div 2)))))) mod (x + 1))))))
A309784: 0 0 0 0 0 1 0 0 1 1 0 0 4 2 1 0
(~1 + (4 * ((3 * compr(\x.(1 - (x mod (2 + ((1 + ((x - ((x div 2) mod 2)) div 2)) mod 5)))),x)) div 2)))
A186302: 3 11 15 23 35 39 51 63 75 83 95 99 111 119 131 135
(1 + (((2x + 3) * (x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2)))))))) mod 4))
A329382: 1 1 1 2 1 2 1 3 4 2 1 3 1 2 4 4
((1 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 5)) div (1 + ((x + 1) mod 4)))
A037872-A037854: 0 0 0 1 0 0 0 2 1 0 0 3 2 1 0 1
(1 + (((3 * ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 5)) div 2) mod 4))
A123566: 1 1 1 1 1 1 1 2 2 1 1 4 3 4 1 1
((1 + ((1 + (((3 * (1 + (x mod (1 + (3 * ((x + 2) mod 5)))))) div 2) div 2)) div 2)) mod 3)
A285194: 1 2 2 1 1 0 1 1 1 2 0 2 0 1 2 2
((5 * (1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2))) div 3)
A026703: 1 1 1 1 3 1 1 5 5 1 1 6 13 6 1 1
compr(\x.((x + 2) mod (2 + (((x + ~1) div 2) mod 2))),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))
A097859: 2 2 2 2 4 2 2 6 6 2 2 7 10 7 2 2
((2 - (x mod 2)) div (2 + (x div 4) - (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))
A187080: 1 0 1 0 1 0 0 1 1 0 0 1 2 0 0 0
((2 * (1 + ((1 + (x mod (1 + (2 * (1 + (x mod (1 + (2 * (2 - ((x * (x div 2)) mod 2)))))))))) div 3))) div 3)
A216789: 0 0 1 0 1 1 0 1 2 2 0 1 2 1 1 0
((2 * (1 + ((1 + (x div (1 + (((x + 1) - (2 * ((x div 2) div (1 + (x mod 4))))) mod (x + 1))))) div 2))) div 3)
A136568: 0 1 1 2 1 1 1 3 2 1 1 1 2 1 1 1
((2 * (1 + (((2 * (1 + ((2 + (((x div 3) * (x div 2)) div 2)) div 3))) - (x mod 3)) div 2))) div 3)
A058762: 1 0 0 1 1 1 2 1 2 2 2 2 4 3 4 5
((2 * (1 + (((1 + ((((15x2 + 10x) div 2) div 3) div 2)) div 2) div 2))) div 3)
A214294: 0 0 1 2 4 6 8 12 14 18 22 27 32 37 43 49
(3 * (((x + 1) + (3 * ((1 + (2 * (x - (2 div (~8 + (x div 2)))))) div 5))) mod 2))
A084055: 3 3 0 3 3 0 0 3 0 0 3 3 0 3 3 3
((2 * (2 + (x mod (1 + (2 * ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 3)))))) div 3)
A152650: 1 1 1 1 2 1 1 2 3 1 1 4 9 4 1 1
((2 * (2 + ((1 + (x mod (2 + ((1 + (x mod (3 * (1 + (x mod 4))))) mod (x + 1))))) mod (x + 1)))) div 3)
A118177: 1 1 2 2 2 2 2 2 4 4 3 2 2 2 6 4
((1 - ((x mod (2 + ((1 + (2 * ((1 - (x mod (4 * (2 - (x mod 2))))) mod (x + 1)))) mod (x + 1)))) div 2)) mod 3)
A024940: 1 1 0 1 1 0 1 1 0 1 2 1 0 1 1 1
(6 + (2 * (1 + (2 * (2 + (2 * (1 + (2 * ((2x + 2) - (x mod 2))))))))) - (x mod 2))
A043938: 56 71 120 135 184 199 248 263 312 327 376 391 440 455 504 519
(1 + ((x + ((2 + (((49x2 + 49x) div 2) div 3)) div 3)) div 2))
A022785: 1 4 10 19 30 44 61 81 103 128 156 186 219 255 294 335
(1 + ((x + ((2 * ((x + 1) + (2 * ((2 * (2x - (x mod 8))) - (x mod 4))))) div 3)) div 2))
A004792: 1 2 4 5 10 11 13 14 29 30 32 33 38 39 41 42
(1 + ((x + ((1 + (((1 + (((x + 1) * (1 + ((1 - (x mod 3)) mod (x + 1)))) div 3)) div 2) div 2)) div 2)) div 2))
A049980: 1 1 2 2 3 4 4 4 7 6 6 9 7 8 13 9
((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div (2 + ((x div 2) mod 2)))))) div (1 + (x div 2)))
A339829-A301345: 1 1 0 0 1 0 0 1 1 0 0 0 2 1 0 0
(0 + (((2 * (1 + ((1 + (((2 - (2x mod (2 + (x div 2)))) mod (x + 1)) div 2)) div 2))) div 3) + (x mod 2)))
A124748: 0 1 0 2 1 1 0 3 2 2 2 1 1 1 0 4
(1 + ((x div (2 + (x mod (1 + ((x + 1) div (1 + (((2x div (1 + (x div 4))) mod 2) + (x mod 2)))))))) + (x mod 2)))
A344774: 1 2 1 3 1 3 1 4 2 3 1 5 1 3 2 5
(1 + compr(\x.(~1 + ((x + (2 * (1 + (2 * (x - ((x mod (2 + (6 mod (1 + (x div 2))))) div 2)))))) mod 3)),x))
A028778: 2 3 5 6 7 8 11 12 13 15 17 18 19 20 21 22
(1 + compr(\x.(2 - (((x + 1) + (((x + 1) + (x div (1 - (2 * ((~x + 1) div (2 + (x div 2))))))) div 2)) mod 5)),x))
A117672: 2 3 5 6 8 9 11 12 14 15 17 18 21 24 25 27
(1 + compr(\x.(1 - ((1 + ((4 * ((2x + 1) - ((~x + ((~x + 2) div 4)) div 2))) div 3)) mod 3)),x))
A284790: 1 4 5 6 7 10 11 12 14 16 17 18 19 21 23 24
(1 + compr(\x.(1 - ((2 * (1 + (((2 + ((9 * (1 + (x div 2))) mod (x + 1))) div 2) div 2))) mod 3)),x))
A051534: 1 2 3 4 5 6 7 8 9 10 11 13 15 17 19 20
((x + 1) + ((2 * ((x + 2) + ((2 * ((x + 1) + (2 * ((x + (x div 2)) div 8)))) div 3))) div 3))
A187575: 2 4 7 8 11 13 16 18 20 22 24 27 29 32 33 36
(1 + compr(\x.(((5x + (((~x + 1) div (2 + (x div 2))) + (x div 5))) mod (1 + (x div 2))) mod 2),x))
A342777: 1 2 4 7 8 9 10 11 13 14 15 16 17 20 22 23
((x + 1) + (((3 * (1 + (((x mod (x - ((x + ~1) mod 8))) * (1 + (x div 4))) div 2))) div 2) div 2))
A102576: 1 2 3 4 5 6 7 8 9 10 12 15 18 20 23 25
((x + 2) + ((2 * (1 + (((1 + ((2 + (x div 2)) div 3)) * (1 + ((1 + (x div 2)) div 2))) div 2))) div 3))
A050023: 2 3 6 7 8 9 10 11 13 14 16 17 18 19 23 24
((x + 1) * (1 + (2 * ((1 + (x mod (1 + (2 * (2 + (4x mod 17)))))) mod (x + 1)))))
A072941: 1 2 3 4 5 6 7 8 9 30 11 12 13 210 15 16
(9 + ((11x + 11) div (x + 6)))
A109394: 10 12 13 13 14 15 15 15 16 16 16 16 16 17 17 17
compr(\x.(((2 * (x div 7)) + ((3 * (x div 4)) div 2)) - ((x mod 2) + ((x + 1) div 2))),(x + 1))
A082463: 1 2 3 4 5 6 7 9 10
A283970: 1 2 3 4 5 6 7 9 10 11 12 13 15 17 19 23
((2x + 4) + (2 * ((3x + 3) - ((1 + (x mod (~2 - (x div 3)))) mod 2))))
A043101: 8 18 24 32 40 50 56 66 72 82 88 96 104 114 120 128
((1 + (((1 + ((~2x + 2) mod (4 + (x div 4)))) div 3) * (1 + (x div 7)))) div 2)
A333310: 1 0 1 0 1 1 0 1 1 1 0 1 2 1 2 0
(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (~1 + (x div (~1 - (x mod 5))))) div 2))
A213086-A050446-A026736: 1 1 1 1 2 1 1 3 3 1 1 5 6 4 1 1
(3 + (x div (3 * (1 + (((x + 1) * ((x + 1) + (2 * (x div 5)))) mod 9)))))
A216944: 3 3 3 3 3 3 5 3 5 3 3 3 3 7 3 5
(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (~1 + (3 * ((1 - (x div 2)) div 3)))) div 2))
A091442: 1 1 1 1 3 1 1 3 3 1 1 5 8 5 1 1
(x div ((~1 + (6 * (1 + ((1 + (((1 + (x mod (1 + ((~x + 2) mod 4)))) * (x div 2)) div 2)) div 2)))) div 2))
A213726-A213725: 0 0 1 0 0 1 1 0 0 1 2 0 1 1 1 0
((1 + ((2 + (((x + 1) * (1 - ((x3 div 8) mod 2))) mod 9)) div 3)) div 2)
A228601: 1 1 0 0 1 0 0 2 0 0 0 1 1 1 0 0
((1 + ((1 + ((3 * (~1 + ((2x + 1) mod (4 + (x div 4))))) mod 7)) div 2)) div 2)
A096810: 0 2 0 2 1 0 2 1 2 0 2 2 1 1 0 2
(1 - ((1 + ((1 + ((1 + ((1 + ((1 + ((x * (2 - (((x + ~1) div 2) * (x div 2)))) div 2)) div 2)) div 2)) div 2)) div 2)) div 2))
A017830: 1 0 0 0 1 1 1 1 2 2 3 4 6 7 9 12
((1 + ((1 + ((1 + (x mod (2 + ((1 + (2 * ((x - ((x div 2) mod 2)) mod 5))) mod (x + 1))))) div 2)) div 2)) div 2)
A070000: 0 1 0 0 1 1 0 1 1 2 2 1 1 1 1 1
((1 + ((1 + (x div (2 + ((2 - (x mod (1 + (2 * ((x mod 7) mod 3))))) mod (x + 1))))) div 2)) div 2)
A280134: 0 0 1 0 1 1 1 1 1 0 1 2 2 1 1 1
((1 + ((1 + (((((x + 5) * ((~2x + 2) mod (4 + (x div 4)))) div 2) div 2) div 2)) div 2)) div 2)
A167749: 1 0 1 0 1 1 0 1 2 1 0 2 3 3 1 0
((1 + (((x + 1) * ((x3 + 4x2 + 6x + 4) - (((x3 + 3x2 + 2x) div 2) div 3))) div 2)) div 2)
A007715: 1 7 27 75 170 336 602 1002 1575 2365 3421 4797 6552 8750 11460 14756
(x - ((1 + (((1 + (((x + 1) * (1 + (x div (2 + (x div (2 + (x mod 10))))))) div 2)) div 2) div 2)) div 2))
A337020: 0 1 1 2 3 4 4 5 5 6 8 9 9 9 10 11
(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (2 * (2 - (2 * (x div 5)))))) div 2))
A111028: 1 1 1 1 ~1 1 1 1 1 1 1 3 4 3 1 1
(1 + (2 * ((2x + 1) div (3 + (x div 4)))) - ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2))
A204004: 1 3 3 5 4 5 7 6 6 7 9 8 7 8 9 11
(1 - (1 mod (~2 + (3 * (1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2))))))
A197217: 1 1 1 1 2 1 1 5 5 1 1 8 14 8 1 1
((3 * (1 - ((2 * (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2))) div 3))) div 2)
A102716: 1 1 1 1 3 1 1 4 4 1 1 7 12 7 1 1
(((((x3 + 4x2 + 5x + 2) * (1 + (5 * ((x2 + 3x + 2) div 2)))) div 2) div 3) div 2)
A108676: 1 16 93 340 950 2226 4606 8688 15255 25300 40051 60996 89908 128870 180300 246976
(((((x2 + 3x + 2) * (1 + (5 * ((3x2 + 5x + 2) div 2)))) div 2) div 3) div 2)
A302560: 1 13 61 185 440 896 1638 2766 4395 6655 9691 13663 18746 25130 33020 42636
(2 * ((8 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)) div 3))
A271910: 0 0 0 0 4 0 0 10 10 0 0 16 36 16 0 0
((((x + 4) + ((2 * (1 + ((x + 1) div (1 + (x div (2 + (x mod (2 + (x mod 2))))))))) mod (x + 1))) div 3) div 2)
A319821: 0 0 1 1 2 1 2 2 2 3 3 4 3 3 3 4
(((2 * (1 + ((1 + ((2 + ((8 * (1 + (x mod 2))) mod (x + 1))) div 3)) div 2))) - (x mod 3)) div 2)
A000360: 1 0 1 1 1 1 2 0 2 2 2 1 3 1 2 1
(2 + (((2x + 1) + (2 * (((x + 1) + (2 * ((((x2 div 2) - (x div 3)) div 2) div 2))) div 2))) div 3))
A135785: 2 3 4 5 7 9 11 13 15 17 19 23 25 29 31 35
(1 + ((2 * ((x mod (~1 + (2 * ((x + ~1) div 3)))) div 2)) + ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)))
A137855: 1 1 1 1 2 1 1 2 4 1 1 2 5 8 1 1
((9x + 7) + (((x + 1) div 2) div 2) - ((x + (x div 3)) div 5))
A326664: 7 16 25 35 43 52 61 71 79 88 97 107 115 124 133 142
(2 + ((1 + (((x + 1) * (x - (2 * ((((x2 div 4) mod (x + 1)) mod 3) mod 2)))) mod 3)) mod (x + 1)))
A098201: 2 3 3 3 4 3 3 4 3 3 5 3 4 5 3 3
(~1 + ((9 * (2 + (2 * (x + (3 * (1 + (x div 2))))) - (x div 2))) + ((x + 1) mod 2)))
A043967: 72 89 153 170 234 251 315 332 396 413 477 494 558 575 639 656
(((1 + ((x + 1) div (1 + (x mod (1 + (x div (2 + ((1 mod (~2x + 1)) mod (4 + (x div 4)))))))))) div 2) div 2)
A104245: 0 0 1 0 1 1 0 1 2 2 0 1 3 2 1 0
(((~1 + (6 * (1 + ((1 + (x mod (1 + (2 * ((x + 2) mod (2 * (1 + (x mod 2)))))))) div 3)))) div 2) div 2)
A336722: 1 1 1 1 1 4 1 1 1 2 1 2 1 4 1 1
(((~1 + (6 * (1 + ((1 + (x mod (1 + (((x mod 5) * (x div 4)) div 2)))) div 2)))) div 2) div 2)
A113926: 1 1 1 1 2 1 1 2 1 4 1 2 1 4 1 1
((2 + (x mod (1 + ((1 + ((x + 1) mod (2 * (2 + (x div (3 + ((x div 2) mod 5))))))) mod (x + 1))))) div 2)
A240128: 1 1 1 1 1 1 1 2 2 2 1 2 2 1 3 4
(1 - (((1 + (((1 + (((x + 1) * (1 - ((2x + ~1) mod (4 + (x div 4))))) div 2)) div 2) div 2)) div 2) div 2))
A330617: 1 1 1 1 1 2 1 2 2 2 1 2 2 2 4 1
((2 + ((x * (1 + (2 * (2 + (2 * (((x + 1) mod (1 + (2 * (x mod 5)))) mod 2)))))) mod 5)) div 2)
A242012: 1 1 2 1 1 1 3 2 1 1 1 1 2 1 1 1
(((1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (x - (x div 4)))) div 2) div 2)
A338034: 0 0 0 0 1 0 0 3 3 0 0 7 9 7 0 0
((((x + 1) + (4 * ((2 + ((1 + ((1 + ((x3 div 4) div 3)) div 2)) div 2)) div 2))) div 2) div 2)
A218947: 1 1 1 2 3 3 4 6 8 10 13 18 22
((((2 * (x + (2 * ((3 * (x3 mod 17)) div (x + 1))))) mod (x + 1)) div 2) div 2)
A132213: 0 0 0 0 0 1 1 0 1 1 2 0 1 3 0 0
(2 - (1 mod (2 - (4 * ((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~1) div 2))) div 2)))))
A132733: 1 1 1 1 3 1 1 7 7 1 1 11 19 11 1 1
(((1 + ((2 * ((3 * (x + ((5 * ((x2 + x) div 2)) div 3))) div 2)) + (x mod 2))) div 2) div 2)
A267454: 0 2 5 10 15 23 30 40 51 63 75 91 106 123 141 161
((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (~1 + (2 * (x mod 7))))) mod 4)
A127967: 1 1 1 1 0 1 1 0 2 1 1 0 3 0 1 1
((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (2 * ((((x + 1) div 2) div 2) div 2))))) mod 4)
A204179: 1 1 1 1 2 1 1 0 0 1 1 0 3 0 1 1
(((((x3 + 15x2 + 74x + 120) div 2) div 3) div 5) div 4)
A084627: 1 1 2 4 6 8 11 14 18 22 28 34 40 48 57 66
(((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div (2 - ((x div 2) mod 2)))))) div 2) mod 4)
A143655: 0 0 0 0 2 0 0 0 3 0 0 2 3 0 0 0
(2 + (((x + 2) + (2 * (4x - ((2x + 1) div 7))) - (((x + 1) div 2) div 2)) div 2))
A189403: 3 7 12 15 19 24 28 31 36 40 44 48 52 57 60 64
(~1 + (((2 * ((3x + 4) + ((~x + 1) mod (2 + (x div (2 + (x mod 2))))))) div 3) + ((x div 2) mod 2)))
A217682: 2 3 8 9 10 13 14 18 21
((1 + (((2 * (1 + ((1 + (((x2 + 2x) div 2) mod 11)) div 2))) div 3) + (x mod 2))) div 2)
A193330: 0 1 1 2 1 2 1 3 2 2 1 2 2 3 1 2
((x + ((2 * ((x + 1) + (2 * ((3x + 3) + ((x - ((~2 + (x div 2)) div 3)) div 2))))) div 3)) div 2)
A184813: 2 5 8 12 15 17 21 24 27 30 33 36 39 43 46 49
((x + 2) + (((x + 2) + ((x + (((x2 + (((x + ~2) * (x2 div 2)) div 3)) div 2) div 2)) div 2)) div 3))
A058577: 2 4 5 7 9 11 14 16 20 23 27 31 36 42 48 54
(((x + 1) + (((x + 1) + ((2 * (1 + ((2x + 1) mod 31))) div 3)) div 2)) div 2)
A302839: 1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 12
(2 * (x + ((1 + (((1 + (((x + 1) * (1 + (2 * ((3 * ((x div 2) div 3)) div 2)))) div 2)) div 2) div 2)) div 2)))
A249721: 0 2 4 6 8 12 14 18 20 22 24 26 36 38 42 44
((x + ~2) + ((3 * ((4x + 6) + ((x - (x div 9)) div 2))) div 2))
A190367: 7 14 22 29 38 45 53 60 69 76 83 91 98 107 114 122
((x + (((x + 3) + ((x + ((((x + 1) * (2 + ((~1 + (x div 4)) * (x div 2)))) div 2) div 2)) div 2)) div 2)) div 2)
A084689: 0 1 2 3 4 5 6 7 9
A174328: 0 1 2 3 4 5 6 7 9 10 11 13 16 18 20 21
((1 + ((2 * (1 + (((8x2 + 19x + 6) div 2) div 3))) div 5)) mod (x + 2))
A008802: 1 0 2 0 3 0 4 0 5 1 7 2 9 3 11 4
(1 + ((((x + 1) - ((1 + (x div (1 + (((2x + 1) mod (2 + (x div 4))) div 2)))) mod (x + 1))) div 2) + (x div 2)))
A074882: 1 2 3 4 5 4 7 8 9 7 11 9 13 10 13 16
(1 + ((2 * (1 + ((1 + ((1 + ((x + ~1) * (x2 div 4))) div 5)) div 2))) div 3) - (x mod 2))
A321185: 1 0 1 1 2 2 5 5 9 11 17 20
(1 + (((2 * (1 + ((1 + (x div (2 + ((x - ((x div 2) mod 5)) mod 3)))) div 2))) div 3) + (x mod 2)))
A126237: 1 2 1 2 2 3 3 3 2 3 3 3 3 4 4 4
(((3 * (1 + (((1 + (x mod (1 + (31 mod (x + 1))))) div 2) div 2))) div 2) * (x mod 2))
A318455: 0 1 0 3 0 1 0 4 0 1 0 3 0 1 0 7
compr(\x.(1 - (x mod (1 + (x mod (1 + ((1 + (x mod ((1 + (x mod (1 + (x div 4)))) * (1 + (x mod 2))))) mod (x + 1))))))),x)
A113837: 5 7 11 13 14 15 17 19 22 23 26 27 29 31 33 34
((x + 1) + ((1 + (((32x2 + ~31x + ~1) * ((x + ~1) div 3)) div 2)) div 3))
A066776: 1 2 3 4 69 113
((x + 1) + ((2 * (1 + ((1 + (((1 + ((((x + 1) * (x + (x mod 3))) div 2) div 2)) div 2) div 2)) div 2))) div 3))
A146215: 1 2 4 5 6 7 8 10 11 12 14 16 17 18 21 22
compr(\x.(~1 + ((2 + ((1 + (2 * (x mod (1 + ((x + ~1) mod (1 + (2 * (2 + (x mod 3))))))))) mod (x + 1))) mod 3)),x)
A211202: 1 2 3 4 5 6 7 8 12 15 16 18 20 21 22 23
((~x + 1) + ((2 * (x + ((1 + (((1 + (((x + 1) * ((x + 1) + (x div 3))) div 2)) div 2) div 2)) div 2))) div 3))
A339395: 1 0 1 0 1 1 1 2 2 3 4 4 6 7 8 10
((~x + 1) + ((2 * (x + (((x + 2) + (((((x + ~1) * (x + (x div 5))) div 2) div 2) div 2)) div 2))) div 3))
A108932: 1 1 1 1 1 2 3 3 3 4 5 6 7 8 10 12
compr(\x.(2 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) - ((x + (x div 2)) div 4)),x)
A169692: 6 9 10 14 15 16 17 19 22 23 24 25 26 27 28 30
((~x + 1) + ((x + (2 * (x + ((x + ((x + ((3 * ((3x2 + x) div 2)) div 2)) div 2)) div 2)))) div 2))
A294864: 1 2 6 9 15 21 29 38 48 59 71 84 99 114 131 148
((~x + 1) + compr(\x.(1 - ((2 * (1 + ((2 * ((x + 1) + (2 * ((x + ((x div 2) mod 2)) div 2)))) div 3))) mod 3)),x))
A305557: 1 1 1 2 2 3 4 5 5 6 6 6 6 6 7 7
((~x + 1) + compr(\x.(1 - ((2 * ((x + 2) + ((x + (((2 * (~1 + (x div 4))) mod (x + 1)) div 2)) div 2))) mod 3)),x))
A284520: 1 2 2 2 3 4 4 4 4 5 6 7 8 8 8 8
(x + ((2 - ((1 + (x mod (2 + (x div (1 + ((x div 2) mod (1 + (x mod (1 + ((~x + 2) mod 4)))))))))) mod (x + 1))) div 2))
A081210: 1 2 3 3 5 6 7 7 7 10 11 9 13 14 15 15
compr(\x.(2 * (((x + 1) mod (1 + (2 * ((1 - (((2x + ~2) mod (2 + (x div 4))) mod 3)) mod 3)))) mod 2)),x)
A269389: 1 2 4 6 7 8 11 13 14 16 18 19 20 21 22 23
compr(\x.(1 - ((x mod (2 + ((1 + (2 * ((1 + (x div 3)) mod (1 + (x mod (1 + (x div 3))))))) mod (x + 1)))) div 2)),x)
A242401: 2 5 7 8 11 12 13 14 17 18 19 20 22 23 24 26
((2x + 1) + ((2 * (1 + ((4x3 + 6x2 + 5x + 1) div 5))) div 3))
A299276: 1 5 14 31 59 101 161 242 347 479 641 837 1070 1343 1659 2021
(1 + compr(\x.(~1 + loop(\(x,i).(x + (if x <= 0 then 1 else (if (x mod 2) <= 0 then x else loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),x,x)))),2,x)),x))
A241071: 1 2 4 6 8 10 12
A239063-A151999: 1 2 4 6 8 10 12 16 18 20 24 30 32 34 36 40
loop(\(x,i).(3x + (if x <= 0 then 1 else loop(\(x,i).x3,1,loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),i,1)))),x,1)
A167868: 1 11 249 8747 369241 17110731 840221217 42944901219 2260581606657 121714776747971 6671749658197129 371062413164972955 4611686018427387903 4611686018427387903 4611686018427387903
compr(\x.loop(\(x,i).(if x <= 0 then 1 else (~2 + (if x <= 0 then 2 else (loop(\(x,i).(1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),2,x) mod (x + 1))))),2,x),(x + 1))
A043682: 5 9 10 11 13 17 18 19 20 22 23 25 26 27 29 33
((if (x mod 2) <= 0 then ((if (x mod 4) <= 0 then (9 * (if x <= 0 then 1 else 2)) else 1) + (if x <= 0 then 1 else 2)) else 1) + (if x <= 0 then 1 else 2))
A010189: 11 3 5 3 22 3 5 3 22 3 5 3 22 3 5 3
compr(\x.loop(\(x,i).(~x + 1),x,(if x <= 0 then 1 else (~2 + (if x <= 0 then 2 else (loop(\(x,i).(1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),2,x) mod (x + 1)))))),x)
A280998: 2 4 5 6 8 9 11 12 13 14 16 17 19 21 23 24
compr(\x.loop(\(x,i).((x + 1) * loop(\(x,i).((x + 1) - (if x <= 0 then 2 else (1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x)))),2,x)),2,x),x)
A174219: 2 3 4 5 6 7 11 12 13 17 18 19 23 29 30 31
(x + loop(\(x,i).(x - (if x <= 0 then 1 else loop(\(x,i).(x - (x div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))),2,x))),x,x))
A304091: 0 1 1 2 1 3 1 3 2 2 1 4 1 3 2 3
(1 + (if (if x <= 0 then 1 else (loop(\(x,i).(2x + 2),x,0) mod (x + 1))) <= 0 then x else (1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A068519: 2 2 3 7 5 13 7 19 23 29 11 37 13 43 47 53
(1 + (loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1)) + loop(\(x,i).3x,x,1) + loop(\(x,i).5x,x,1)))
A001552: 5 15 55 225 979 4425 20515 96825 462979 2235465 10874275 53201625 261453379 1289414505 6376750435 31605701625
(~1 + loop(\(x,i).5x,x,1) - (loop(\(x,i).3x,x,1) + loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1))))
A147976: ~3 ~5 ~5 25 271 1825 10735 59425 318271 1670785 8656975 44454625 226827871 1151991745 5830280815 29429454625
(1 - ((if x <= 0 then 0 else (1 + ((loop(\(x,i).2x,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1) div 2) mod 5))) mod 3))
A227985: 1 0 ~1 0 ~1 1 0 ~1 1 ~1 0 ~1 1 ~1 0 0
((3x + 1) + loop(\(x,i).(x - (if x <= 0 then 1 else (x - ((if x <= 0 then 2 else loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 2)))),x,(x + 2)))
A193532: 3 4 8 9 11 12 17 18 20 21 24 25 27 28 34 35
(1 + (2 * compr(\x.loop(\(x,i).(x - loop(\(x,i).(x - (x div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))),x,x)),2,x),x)))
A182058: 1 3 5 7 9 13 17 21 25 29 33 37 41 45 49 57
loop(\(x,i).2x,x,loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1))
A026738: 1 28 516 7952 111440 1477056 18912832 236879104 2924469504 35764112384 434623874048 5259666886656 63472710995968 764545789837312 9197653087371264 110557371200503808
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025440: 1 15 145 1155 8281 55755 360865 2276835 14126761 86681595 527948785 3199656915 19327384441 116486845035 701025539905 4214614099395
loop(\(x,i).2x,x,loop(\(x,i).(6x + loop(\(x,i).(2x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1))
A025984: 1 28 524 8288 119952 1646400 21834688 282827776 3602179328 45309135872 564541565952 6982826532864 85877229359104 1051359996166144 12824652929417216 155979167054692352
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025467: 1 17 191 1813 15855 132909 1089607 8828501 71093759 570671101 4573228023 36617788389 293071750063 2345096538893 18762876780839 150111475106677
loop(\(x,i).(4x + loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),i,1)),x,1)
A163942: 1 14 121 834 5037 27918 145777 728858 3526933 16640262 76952793 350167122 1572467389 6984206846 30735634369 134202204426
loop(\(x,i).2x,x,loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1))
A026562: 1 26 440 6160 77616 915936 10347520 113400320 1215923456 12829712896 133751654400 1381696942080 14173677776896 144610035654656 1469203965870080 14877573810749440
loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025211: 1 14 125 910 5901 35574 204205 1132670 6129101 32566534 170691885 885423630 4556561101 23305343894 118631189165 601616805790
loop(\(x,i).3x,2x,loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1))
A076010: 1 90 5265 255150 11160261 458810730 18124795305 697117731750 26323112938221 981154011007170 36233774365169745 1329174591745823550 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).6x,x,loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1))
A075917: 1 60 2340 75600 2204496 60419520 1591202880 40800672000 1027086863616 25522067450880 628349082117120 15366613964083200 373968813041012736 4611686018427387903 4611686018427387903
loop(\(x,i).8x,x,loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1))
A076004: 1 80 4160 179200 6967296 254607360 8940421120 305659904000 10259284361216 339910422691840 11158051230842880 363834840082022400 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).5x,x,loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1))
A075912: 1 50 1625 43750 1063125 24281250 532890625 11386718750 238867578125 4946347656250 101481884765625 2068161621093750 41943091064453125 847579699707031250 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A025470: 1 18 217 2238 21493 199506 1821889 16508646 149043565 1343313114 12097677241 108911059374 980328977317 8823483334242 79413454477873 714729551160822
(0 - loop(\(x,i).loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),x,x),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A080085: 1 1 3 4 8 10 15 16 19 25 26 34 38 39 42 49
(2 + loop(\(x,i).5x,x,1) - (loop(\(x,i).3x,x,1) + loop(\(x,i).(2x + 1),x,loop(\(x,i).2x,x,1))))
A081684: 1 ~1 ~1 29 275 1829 10739 59429 318275 1670789 8656979 44454629 226827875 1151991749 5830280819 29429454629
(2 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).3x,x,1)) - (loop(\(x,i).5x,x,1) + loop(\(x,i).2x,x,1)))
A090024: 0 1 45 571 5841 55651 515025 4702531 42649281 385447171 3476958705 31332052291 282184860321 2540643522691 22870684139985 205860600134851
(if x2 <= 0 then 1 else ((1 + ((loop(\(x,i).2x,x,(loop(\(x,i).(2x + 2),x,1) div 2)) div loop(\(x,i).3x,x,1)) div 2)) div 2))
A182097: 1 0 1 1 1 2 2 3 4 5 7 9 12 16 21 28
(loop(\(x,i).3x,(x + ~1),(loop(\(x,i).4x,x,1) - loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),x,1))) div 2)
A322914: 0 1 15 198 2511 31266 385398 4721004 57590271 700465482 8501284530 103007201364 1246500179910 15068548264212 182007001727244 2196875784339288
(((loop(\(x,i).3x,x,1) + loop(\(x,i).5x,x,1)) - loop(\(x,i).(x2 + x),1,loop(\(x,i).2x,x,1))) div 2)
A083327: 0 1 7 40 217 1156 6097 31900 165697 855076 4387537 22404460 113945377 577590196 2919923377 14729076220
(if 2x <= 0 then 1 else (((~x + (if x <= 0 then 1 else (2 * (if x <= 0 then 1 else ((x2 + 2) + loop(\(x,i).(2 * (x + (x div 2))),x,1)))))) div 2) div 2))
A335725: 1 2 5 13 35 93 260
loop(\(x,i).x3,1,loop(\(x,i).(2x2 + ~x),1,loop(\(x,i).2x,compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x),2)))
A133052: 216 21952 122023936 536971313152 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,loop(\(x,i).(x2 * loop(\(x,i).x3,2,x)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A137486: 4194304 31381059609 2384185791015625 3909821048582988049 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(((if (x mod 3) <= 0 then (5 * (if (x mod 2) <= 0 then (3 * (if x <= 0 then 1 else 2)) else 1)) else 1) + (if x <= 0 then 1 else 2)) - (x mod 2))
A040253: 16 2 3 6 3 2 32 2 3 6 3 2 32 2 3 6
compr(\x.(2 * loop(\(x,i).(~2x + 1),(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (1 + (if (x mod 3) <= 0 then 0 else 2))))),x,(x + 1))),1)),x)
A233524: 0 1 2 4 5 8
A072756: 0 1 2 4 5 8 9 10 11 14 17 18 19 20 22 23
loop(\(x,i).(x + i),(((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1)),0)
A066446: 0 1 1 3 1 6 1 6 3 6 1 15 1 6 6 10
loop(\(x,i).(x + loop(\(x,i).(loop(\(x,i).3x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1) div 3),1,i)),x,0)
A192225: 0 1 2 5
A160714: 0 1 2 5 6 9 12 21 22 25 28 37 40 49 58 85
loop(\(x,i).(x + loop(\(x,i).((2 * (4 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3),1,i)),x,0)
A077597: 0 2 4 7 9 13 15 19 22 26 28 34 36 40 44 49
(2 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x) + (if x <= 0 then 0 else 1)))
A011974: 2 5 8 12 18 24 30 36 42 52 60 68 78 84 90 100
(loop(\(x,i).5x,x,1) mod loop(\(x,i).(~1 + (2 * (~3 + loop(\(x,i).10x,(x + 1),1)))),1,1))
A036156: 1 5 25 125 46 37 185 153 186 158 18 90 64 127 56 87
(1 + ((0 - (if (x mod 3) <= 0 then ((loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,x) div 2) mod 3) else 1)) mod 3))
A111629: 1 3 3 1 3 3 3 3 3 1 3 3 2 3 3 2
(x div (1 + ((2 * (1 + (5 * (loop(\(x,i).2x,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1) div 2)))) div 3)))
A220692: 0 1 0 3 0 0 6 1 1 0 10 2 1 0 0 15
loop(\(x,i).(x * i),((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3),1)
A130674: 1 2 2 6 2 24 2 24 6 24 2 720 2 24 24 120
(1 + loop(\(x,i).2x,(compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1))
A137780: 3 5 5 17 5 17 5 17 65 5 65 17 5 17 65 65
((x + 1) - ((~1 + (loop(\(x,i).2x,loop(\(x,i).(x div (1 + (x mod 2))),x,x),1) + loop(\(x,i).2x,x,1)) - (x mod 2)) mod (x + 1)))
A173557: 1 1 2 1 4 2 6 1 2 4 10 2 12 6 8 1
(1 + (2 * (if 1 <= 0 then (x * (loop(\(x,i).2x2,x2,2) div 2)) else (~1 + loop(\(x,i).10x,(x + 1),1)))))
A160452: 19 199 1999 4611686018427387903
(1 + (2 * ((1 + loop(\(x,i).2x,(if x <= 0 then 2 else (1 + (2 * (x mod 2)))),loop(\(x,i).6x,x,1))) div 5)))
A339545: 3 19 29 691
(~1 + (2 * ((4 * compr(\x.(x - loop(\(x,i).loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),x,(2x + 1)),2,(x + ~1))),x)) div 3)))
A317510: 7 15 31 39 55 71 111 119 151 175 231 239 255 311 319 335
(~1 + (2 * (3 + (loop(\(x,i).2x,x,(1 + loop(\(x,i).3x,x,2))) + loop(\(x,i).(3x + 2),2x,2)))))
A206170: 15 85 641 5257 44585 385465 3375401 29817817 264999305 2364834745 21162573161 189737549977 1703284356425 15303437762425 137574211418921 1237227532571737
(1 + (2 * (if x <= 0 then 2 else (6 * (2x + ((2 * (2 + loop(\(x,i).loop(\(x,i).((x + 1) * i),x,2),x,1))) div 3))))))
A092838: 5 61 277 4611686018427387903 4611686018427387903
(loop(\(x,i).8x,(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1))),1) div 7)
A318935: 1 9 1 73 1 9 1 585 1 9 1 73 1 9 1 4681
(~1 + (2 * (1 + compr(\x.(1 - loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(2x2 + 2x + 1))),x))))
A263722: 9 11 19 21 23 25 29 31 39 41 43 49 51 53 55 59
(1 + (loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),3),1,i)),x,1) div 2))
A151788: 1 4 7 13 16 22 28 40 43 49 55 67 73 85 97 121
(1 + (4 * (1 + compr(\x.(loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,2x)),2,x) mod (x + 1)),x))))
A071699: 5 13 61 73 109 181 193 229 241 313 349 421 433 601 661 829
(~1 + (4 * (1 + compr(\x.(loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,2x)),2,x) mod (x + 1)),x))))
A089188-A071698: 3 11 59 71 107 179 191 227 239 311 347 419 431 599 659 827
(1 + ((((~1 + (2 * (if x <= 0 then 1 else (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (1 + (x div 5)))))) div 2) div 2) div 2))
A318601-A214568: 1 0 1 0 1 1 0 1 1 2 0 1 2 3 3 0
(~1 + (4 * (if x <= 0 then 1 else (2 + (3 * ((1 + loop(\(x,i).2x,x,(1 + loop(\(x,i).3x,x,1)))) div 3))))))
A306970: 3 43 163 907
((1 + (2 * (if x <= 0 then 1 else ((8x + 1) - loop(\(x,i).(x + (if (~2 + (x div 4)) <= 0 then 1 else 2)),2,x))))) div 3)
A312944: 1 4 9 13 18 23 27 32 37 41 46 50 54 59 63 68
(~3 + (loop(\(x,i).2x,x,loop(\(x,i).(x + (if x <= 0 then 1 else ((x + 3) + ((x2 + 3x + 2) div 2)))),1,(x + 1))) div 2))
A048507: 1 10 35 101 269 685 1693 4093 9725 22781 52733 120829 274429 618493 1384445 3080189
(3 + (2 * loop(\(x,i).(x2 + 2x),1,compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1)))))
A184417: 33 73 289 649 1801 3529 7201 10369 20809 23329 38089 45001 64801 73729 78409 103969
(3 * (loop(\(x,i).(x2 + x),1,(2 + loop(\(x,i).(x2 + x),1,(1 + loop(\(x,i).x3,x2,2x))))) div 2))
A250435: 30 12834 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3))
A035116: 1 4 4 9 4 16 4 16 9 16 4 36 4 16 16 25
loop(\(x,i).(x * i),x,((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3))
A318249: 1 2 4 18 48 480 1440 20160 120960 1451520 7257600 239500800 958003200 24908083200 348713164800 6538371840000
(3 + (2 * ((3x + 1) + (loop(\(x,i).(x + loop(\(x,i).(2 * (2x - (x div (if i <= 0 then 1 else i)))),i,x)),x,1) div 2))))
A129924: 5 13 37 463
((x + 3) + ((1 + ((1 + compr(\x.loop(\(x,i).((if x <= 0 then 2 else loop(\(x,i).(x div (2 - (x mod 2))),x,x)) div 2),2,x),(x + 1))) div 2)) div 2))
A179242: 4 6 7 9 10 11 14 15 16 18 22 23 24 26 29 35
((if (x mod 3) <= 0 then ((1 + (if (x mod 2) <= 0 then 22 else 1)) * (if x <= 0 then 1 else 2)) else 1) * (1 + (x mod 2)))
A040521: 23 2 1 8 1 2 46 2 1 8 1 2 46 2 1 8
(1 + compr(\x.(~1 + loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(6x2 + 12x + 3))),x))
A187102: 1 2 3 4 6 7 9 11
A143831: 1 2 3 4 6 7 9 11 13 14 15 17 20 22 24 25
loop(\(x,i).(36x + loop(\(x,i).(4x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A163927: 1 49 1897 69553 2515513 90663937 3264855049 117543378001 4231639039705 152339702576545 5484235568128681 197432536935184369 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(8x + 1),i,1)),i,1)),x,1)
A024114: 1 27 487 7407 102943 1357119 17315839 216369279 2667080575 32582253951 395677903231 4786097041791 57739474264447 695339842109823 8363901349806463 100525966375567743
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A022448: 1 24 391 5466 71017 888660 10902187 132353502 1597893853 19235078616 231195264703 2776650139458 33333948627409 400093791131292 4801651568584339 57623013420037734
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A020758: 1 28 532 8560 125776 1747648 23401792 305401600 3912299776 49432480768 618099069952 7666644643840 94496470552576 1158938055589888 14157139120832512 172384964172513280
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).7x,i,1)),i,1)),x,1)
A020577: 1 25 427 6229 83779 1076341 13459699 165601573 2017494787 24431946517 294797887891 3549239159557 42674698231075 512696237681653 6156632228705203 73909998565124581
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A020972: 1 28 529 8428 122257 1673980 22067473 283450636 3574941073 44501447452 548719235857 6718924954924 81849587868049 993294339107644 12020103854584081 145151139884150092
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(4x + 1),i,1)),i,1)),x,1)
A021894: 1 24 393 5536 72513 914088 11282041 137597232 1666743345 20110305592 242090763369 2910464426688 34963222353697 419822302356936 5039713424985177 60489483108391504
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021629: 1 23 366 5062 65555 820701 10087792 122732444 1484551749 17896987459 215340503378 2588122883346 31085733296983 373226612833097 4480104054056724 53770941570620968
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).5x,i,1)),i,1)),x,1)
A020341: 1 24 397 5652 74665 946992 11736613 143526444 1741517569 21034565640 253379036989 3047347017156 36615998359513 439728040092768 5279095003079125 63365680208288988
loop(\(x,i).(12x + loop(\(x,i).(9x + loop(\(x,i).(4x + 1),i,1)),i,1)),x,1)
A021974: 1 26 459 6916 96005 1270542 16318303 205487672 2552951769 31419668098 384095637107 4672689817068 56644179720493 684877363365494 8264853578776071 99595171342479904
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A022725: 1 26 455 6760 92301 1200966 15177955 188364020 2310685001 28133195506 340850357055 4116281407680 49604299052101 596924491783646 7176484756065755 86224982057057740
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A020980: 1 30 604 10200 156016 2241120 30844864 411749760 5373888256 68949788160 873102490624 10942870149120 136039563882496 1680275743334400 20645716733968384 252607863319265280
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).7x,i,1)),i,1)),x,1)
A020969: 1 27 493 7611 107293 1432011 18457741 232505307 2883927805 35398400235 431393410669 5231599117563 63232056214237 762504498009099 9180490786688077 110414131486397979
loop(\(x,i).(12x + loop(\(x,i).(9x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021704: 1 25 430 6370 87451 1148875 14682760 184262740 2283789301 28059228925 342594651490 4164091223110 50445694121551 609637726848175 7354257305858620 88598528944951480
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A021994: 1 27 495 7735 111111 1517607 20059495 259217895 3295741671 41400518887 515323813095 6369067214055 78280643507431 957886180955367 11679819118040295 142009680313898215
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A019752: 1 27 505 8115 120241 1695387 23126185 308127555 4034342881 52117311147 666165944665 8442335850195 106239836635921 1329127977509307 16546285315207945 205119670292296035
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A020568: 1 27 499 7863 113731 1561647 20724139 268611543 3422947891 43073421567 536871293179 6642406690023 81708636139651 1000502412972687 12206022852156619 148472243708301303
loop(\(x,i).(12x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A020983: 1 31 643 11155 174811 2566291 36012523 489103555 6481822171 84295081651 1080159920203 13679489505955 171612008243131 2136467306462611 26431716545456683 325327578356628355
loop(\(x,i).(12x + loop(\(x,i).(10x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021724: 1 26 465 7150 101621 1378026 18123145 233349350 2958918141 37094306626 461004657425 5690785933950 69876732453061 854393804284826 10411455807073305 126524771262956950
loop(\(x,i).(12x + loop(\(x,i).(2x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021334: 1 26 473 7462 109221 1527162 20707681 274691534 3584491901 46184032258 589079813049 7452543446166 93649963947541 1170213435915914 14553113785023377 180253443514702558
loop(\(x,i).(12x + loop(\(x,i).(3x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A018208: 1 26 475 7520 110341 1545446 20980975 278565740 3637529881 46892529266 598374287875 7572794935160 95188878040621 1189735265087486 14798979200433175 183331466632763780
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A022033: 1 19 236 2426 22407 193305 1591402 12667072 98321333 748601711 5614533288 41608696038 305407826179 2224262385637 16095911708294 115865978983724
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A020572: 1 23 357 4675 55781 628803 6831637 72401555 754291461 7764923683 79263766517 804302170035 8126850016741 81868359076163 822960967286997 8260021493532115
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(9x + 1),i,1)),i,1)),x,1)
A023954: 1 24 379 4974 58825 651228 6891463 70602378 706070629 6931922712 67078160227 641665645062 6081300568513 57197856053076 534603948966271 4970585718586626
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A023955: 1 25 413 5693 70989 831693 9347341 102052621 1091175437 11489041421 119581270029 1233774903309 12644058796045 128906738896909 1308890633457677 13248056512466957
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(7x + 1),i,1)),i,1)),x,1)
A023949: 1 22 317 3782 40533 405534 3869149 35663254 320292005 2819331086 24426173421 208945416966 1768927681717 14848644708478 123763757447933 1025496480025718
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A020593: 1 25 423 6053 79079 977613 11662351 135834661 1556251287 17625401981 197992990559 2211194243349 24591484236775 272666167778029 3016684939110447 33322861263616517
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021834: 1 22 329 4226 50469 580422 6541681 72922570 808020125 8923802030 98376704361 1083438632562 11925616635349 131228622530326 1443796242996449 15883448475593882
loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).(9x + 1),i,1)),i,1)),x,1)
A022291: 1 21 292 3402 36043 360843 3485854 32899944 305751325 2812114305 25683350056 233457113526 2115260975647 19123756383207 172639882457698 1556953539144948
loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A022343: 1 22 323 4004 45465 491106 5149327 53020528 539857109 5458923470 54963556011 551942523132 5533572185233 55422129454714 554747369555975 5550668292585416
loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A019854: 1 22 333 4334 52325 606606 6874477 76908238 854115189 9445967630 104219612861 1148348383182 12643672205893 139152654913294 1531118871452685 16844976107996366
loop(\(x,i).(6x + loop(\(x,i).(3x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021524: 1 21 304 3822 45031 513639 5760910 64038576 708445573 7817058249 86132670988 948329828082 10436851589347 114836710756971 1263391885146058 13898439159046260
loop(\(x,i).(7x + loop(\(x,i).(9x + loop(\(x,i).(4x + 1),i,1)),i,1)),x,1)
A021864: 1 21 294 3466 37275 379407 3727648 35761572 337430709 3146261833 29083452762 267126341118 2441786303503 22239710844099 202003194298836 1830950757258904
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A022452: 1 21 290 3330 34491 334791 3109900 27997860 246301781 2129087961 18155626710 153166509990 1281087729871 10640517267531 87874475534720 722286313011720
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A020838: 1 25 419 5885 74811 892605 10199659 113009005 1223954171 13030808285 136920690699 1424085096525 14693717768731 150657001125565 1537006821834539 15618310264486445
loop(\(x,i).(7x + loop(\(x,i).(9x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021594: 1 20 270 3100 32711 328440 3195340 30437000 285695421 2653625260 24459281210 224170373700 2045792060131 18609941810480 168874176353880 1529560509125200
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A021874: 1 22 325 4070 46781 511742 5430405 56516790 580744461 5916830062 59935396885 604729235110 6084941584541 61113049957982 612976296281765 6142684971387030
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A019623: 1 22 335 4400 53661 628122 7178395 80862100 902846921 10025125022 110934086055 1224883116600 13505988249781 148791855626722 1638292574483315 18032294531183900
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A019958: 1 22 329 4178 48621 537222 5744929 60136378 620564021 6341995022 64384199529 650640568578 6554239839421 65878458172822 661143103694129 6627971208280778
loop(\(x,i).(7x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A020970: 1 26 453 6610 87221 1079106 12770773 146348690 1637020341 17972357986 194425446293 2078548587570 22007974284661 231179027537666 2412362060669013 25033514235831250
loop(\(x,i).(7x + loop(\(x,i).(10x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021604: 1 21 300 3670 41511 449151 4730890 48987840 501640821 5098774681 51564400680 519680849610 5225067192931 52448485198611 525869552045670 5268388442396980
loop(\(x,i).(7x + loop(\(x,i).(2x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021244: 1 21 308 3942 47271 547407 6213586 69694464 776054741 8602512633 95089014384 1049208790266 11563904125411 127361197423299 1402080935995502 15430644646390548
loop(\(x,i).(7x + loop(\(x,i).(3x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A018054: 1 21 310 3990 48031 557571 6338620 71164380 792891661 8792412321 97210822930 1072779241170 11824793506891 130242283148271 1433852001421240 15780680237514360
(1 + (if x <= 0 then 2 else (1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))))
A230847: 3 2 3 3 5 3 5 3 5 7 3 7 5 3 5 7
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021924: 1 24 389 5364 68025 821808 9633613 110741388 1256415809 14127007752 157849954197 1755978039972 19472809159753 215457395996256 2380083675784541 26261340423891516
loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).(9x + 1),i,1)),i,1)),x,1)
A022469: 1 23 350 4450 51231 554433 5756260 58034900 572630861 5558653243 53279890170 505596134550 4759287370891 44506489496453 413949260130080 3832708325439400
loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A022565: 1 24 383 5130 62481 718164 7948003 85708590 907402661 9479002104 98042032023 1006497443250 10273896592441 104411869082844 1057509545490443 10682260439173110
loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A020447: 1 24 393 5480 70161 853944 10066393 116192520 1322205921 14898923864 166735197993 1856912289960 20608880226481 228161663489784 2521496249891193 27830232878409800
loop(\(x,i).(8x + loop(\(x,i).(3x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021664: 1 23 362 4894 61251 733461 8546764 97847228 1106991941 12422320339 138608884206 1540404875802 17070111627271 188776494239057 2084583574516688 22994756444303416
loop(\(x,i).(9x + loop(\(x,i).(4x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A021954: 1 24 387 5278 65793 776412 8835919 98027226 1067371965 11457966520 121639285131 1279935023094 13371252146617 138859728185748 1434922500247623 14766153399643282
loop(\(x,i).(9x + loop(\(x,i).(10x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1)
A021684: 1 23 360 4810 59111 690573 7801990 86089520 933531621 9989073523 105774639620 1110701801430 11583617458531 120125571974873 1239860303429250 12746044308940540
loop(\(x,i).(9x + loop(\(x,i).(2x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021294: 1 23 368 5098 65559 806541 9640606 112964816 1304876837 14914020979 169097614764 1905464222454 21368620595635 238731453906137 2659135639187642 29548298847110812
loop(\(x,i).(9x + loop(\(x,i).(3x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A018091: 1 23 370 5150 66451 819413 9810340 115087100 1330524901 15216894803 172615989910 1945847389850 21827965327351 243920416546193 2717439768299080 30200674142257400
loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021784: 1 21 302 3762 43923 497223 5545264 61398804 677478725 7463074905 82149266706 903924739926 9944608539607 109397965416267 1203414334895828 13237742692094328
loop(\(x,i).(4x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A019742: 1 25 431 6365 86511 1117605 13957591 170189245 2038704671 24092243285 281680643751 3265150951725 37583315950831 430083097386565 4897580558961911 55540052099419805
loop(\(x,i).(5x + loop(\(x,i).(3x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021474: 1 20 278 3388 39039 438648 4872316 53834696 593387597 6533322796 71896935474 791018479524 8701965018475 95725426313264 1052998752170552 11583081609022672
loop(\(x,i).(10x + loop(\(x,i).(2x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021314: 1 24 401 5796 77637 992880 12310537 149304732 1781240813 20982537576 244696801713 2830553706708 32524979660629 371663665151712 4227189205549529 47887970149917324
loop(\(x,i).(11x + loop(\(x,i).(6x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A020606: 1 26 457 6782 91693 1170218 14373409 171896534 2016642805 23325176930 266916367081 3029497622606 34167408893437 383440973924762 4286324362209073 47766301010614598
loop(\(x,i).(11x + loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A020499: 1 25 426 6170 81851 1029315 12498676 148149460 1726010901 19855374605 226242178526 2559210312750 28786474721551 322368894171895 3597522989519976 40035969784960040
loop(\(x,i).4x,(compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1)
A140299: 4 16 16 256 16 256 16 256 4096 16 4096 256 16 256 4096 4096
loop(\(x,i).(3x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A018206: 1 24 403 5850 78601 1007364 12509263 151886670 1813607701 21378247704 249446413723 2886767617890 33183014997601 379298878576044 4315144805143783 48895164279003510
loop(\(x,i).(loop(\(x,i).4x,x,1) - loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(3x + 1))),1,(x + 1))
A138156: 0 2 14 74 352 1588 6946 29786 126008 527900 2195580 9080772 37392864 153434536 627778954 2562441466
((x + 1) * (if loop(\(x,i).(12x + 1),2x,1) <= 0 then 1 else loop(\(x,i).(10x + 1),x,1)))
A000461: 1 22 333 4444 55555 666666 7777777 88888888 999999999 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((if x <= 0 then 1 else (2 * (1 + ((1 + ((loop(\(x,i).3x,(x div 2),1) div (if (x mod 3) <= 0 then 1 else 2)) div 2)) div 2)))) div (x + 1))
A319773: 1 1 0 1 0 0 2 1 2 4 5
(if x <= 0 then 1 else loop(\(x,i).(1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)),(if x <= 0 then 0 else 1),(x + ~1)))
A193515: 1 1 1 1 1 2 1 1 3 3 1 1 4 5 4 1
loop(\(x,i).(if x <= 0 then 1 else (x - ((1 - (loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) div 3)) div 3))),1,(x + ~1))
A001646: 1 1 1 2 3 5 10 21 55
loop(\(x,i).(11x + loop(\(x,i).(8x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A020977: 1 28 525 8240 116921 1555428 19795525 244020280 2937425841 34724726828 404763120125 4666104381120 53319258206761 604990586218228 6825603208406325 76653180504610760
((1 + (loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),2),1,i)),x,1) div 2)) div 2)
A193494: 0 1 2 4 5 7 9 13 14 16 18 22 24 28 32 40
((if x <= 0 then 3 else (if (x + ~1) <= 0 then x else (1 + (2 * (loop(\(x,i).(x - (((~x + ~1) + (x mod 2)) div 5)),x,1) div 2))))) div 2)
A058703: 1 0 1 2 2 3 4 5 6 8 10 12 15 18 22 27
(3 + (2 * compr(\x.(2 - (x mod loop(\(x,i).4x,(1 - loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x)),1))),x)))
A001132: 7 17 23 31 41 47 71 73 79 89 97 103 113 127 137 151
(2 * (1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(9x + 5)),x)))
A024908: 2 4 8 12 16 18 22 24 26 32 38 42 46 52 56 64
(2 * loop(\(x,i).(4x + loop(\(x,i).(4x + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),i,1)),i,1)),x,1))
A000184: 2 22 164 1030 5868 31388 160648 795846 3845020 18211380 84876152 390331292 1775032504 7995075960 35715205136 158401506118
(2 + (3 * (if (x mod 2) <= 0 then (15 * (2 + (if x <= 0 then 0 else 2))) else 1)) - ((if x <= 0 then 1 else 2) + (x mod 2)))
A283896: 91 2 180 2 180 2 180 2 180 2 180 2 180 2 180 2
(((compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)) div 2) + (if x <= 0 then 1 else 2))
A231407: 1 4 6
A162735: 1 4 6 9 12 15 18 21 26 30 34 39 42 45 50 56
(2 * (1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(17x + 16)),x)))
A124127: 6 8 14 18 24 26 36 38 54 56 60 66 74 78 80 84
((1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(13x + 4)),x)) div 2)
A067570: 0 1 2 3 4 5 7
A191848: 0 1 2 3 4 5 7 8 9 11 13 14 18 20 21 22
(2 * (1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(11x + 8)),x)))
A107992: 2 4 10 14 16 22 26 32 46 50 52 56 64 74 80 92
(((5 * (1 + ((if ((if x <= 0 then 1 else (x div ((if (x mod 2) <= 0 then 2 else x) mod 4))) mod 2) <= 0 then x else 1) div 3))) div 2) div 2)
A271187-A157694: 1 1 1 1 2 1 1 3 3 1 1 1 6 1 1 1
(2 * (if x <= 0 then 1 else loop(\(x,i).2x,((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3),2)))
A338506: 2 4 4 8 4 16 4 16 8 16 4 64 4 16 16 32
(~2 + (2 * (1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(2x2 + 6x + 5)),x))))
A129412: 0 2 4 10 12 14 24 30 32 34 42 44 54 62 64 70
(4 + ((1 + (loop(\(x,i).((x + 1) + loop(\(x,i).(x - (loop(\(x,i).(~x2 + 1),2,4) mod (x + 1))),2,x)),x,1) div 2)) div 2))
A158650: 4 5 6 8 12 20 28 36
((2 + (loop(\(x,i).x2,1,(1 + (2 * compr(\x.(2 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),x,(x2 + x + 1))),x)))) div 2)) div 2)
A002383: 3 7 13 31 43 73 157 211 241 307 421 463 601 757 1123 1483
(4 + (compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A283623: 4 6 9 13 18 22 27 31 38 45 50 58 63 67 74 83
(loop(\(x,i).(x2 + x),1,((x + 2) + loop(\(x,i).(~1 + loop(\(x,i).(x div (2 - ((x * (x div 2)) mod 2))),x,x)),(x + 1),(x + 1)))) div 2)
A245541: 1 1 3 1 1 3 6 1 1 1 3 3 3 6 10 1
((~4x + 1) + loop(\(x,i).(x + (if x <= 0 then 1 else x3)),x,loop(\(x,i).40x,x,1)))
A051833: 2 64037 4611686018427387903
((x + 2) + loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).3x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1),1,i)),x,1))
A151923: 3 7 11 21 25 35 45 73 77 87 97 125 135 163 191 273
(x - (loop(\(x,i).(x - (if x <= 0 then 0 else (if (x mod 3) <= 0 then 1 else ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)))),2,x) div 2))
A086155: 0 1 1 2 3 3 4 5 5 6 5 6 7 8 7 8
(1 - (2 * (compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))
A062234: 1 1 3 3 9 9 15 15 17 27 25 33 39 39 41 47
(loop(\(x,i).(2x + 2),loop(\(x,i).(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1,(x + (x div 4))),x) div (x + 2))
A103901: 3 7 31 127
A057612: 3 7 31 127 8191 131071 524287 8388607
(2x + ((1 + (2 * (if x <= 0 then 1 else (2 * ((x + ~1) + loop(\(x,i).(x + (if (~2 + (x div 4)) <= 0 then 1 else 2)),2,x)))))) div 3))
A315410: 1 6 11 15 20 25 29 34 39 43 48 54 60 65 69 74
(2x + (if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + loop(\(x,i).(loop(\(x,i).(x div (2 - (x mod 2))),x,x) div 2),2,(x + 1))) div 2)) div 2)))))
A231407: 1 4 6
A020645: 1 4 6 8 10 12 16 16 18 20 24 24 28 30 32 32
(2 * compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(23x + 4)),x))
A102768: 0 4 6 10 16 24 30 36 42 46 64 70 72 76 90 100
compr(\x.(1 - (x mod (1 + (2 * ((loop(\(x,i).(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x)),1,(x + ~2)) div 2) mod 2))))),x)
A173977: 5 8 11 13 14 17 20 23 25 26 28 29 32 35 38 41
compr(\x.(1 - loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,((3x + 20) div 2))),x)
A199595: 1 4 9 11 14 18 21 23 24 31 32 33 34 37 40 41
loop(\(x,i).6x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165827: 1 6 6 36 6 36 6 216 36 36 6 216 6 36 36 1296
loop(\(x,i).8x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165829: 1 8 8 64 8 64 8 512 64 64 8 512 8 64 64 4096
loop(\(x,i).5x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A256693-A165826: 1 5 5 25 5 25 5 125 25 25 5 125 5 25 25 625
(1 + (9 * (1 + loop(\(x,i).(10x + 1),x,loop(\(x,i).10x,x,1)))))
A171226: 19 919 90109 9001009 900010009 90000100009 9000001000009 900000010000009 90000000100000009 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((2 * (1 + (((1 + (((x + 1) * (1 + (if (if (x mod 2) <= 0 then x else 0) <= 0 then (x mod 4) else 2))) div 2)) div 2) div 2))) div 3))
A248222: 1 1 2 3 3 2 3 4 3 3 4 5 5 3 5 7
(1 + ((2 * (1 + (((loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) + (if (x mod 8) <= 0 then x else 1)) div 2) div 2))) div 3))
A072084: 1 1 2 1 2 2 3 1 4 2 3 2 3 3 4 1
(1 + ((2 * (1 + (x * (1 + ((1 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),x,2x)) mod 3))))) div 3))
A026207-A026199-A026183: 1 2 5 3 4 11 13 6 17 7 8 23 9 10 29 31
(1 + ((2 * (compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 3))
A087458: 1 2 2 3 2 3 2 3 5 2 5 3 2 3 5 5
(1 + loop(\(x,i).(x10 + x9 + x8 + x7 + x6 + x5 + x4 + x3 + x2 + x),1,loop(\(x,i).2x,x,1)))
A020519: 11 2047 1398101 1227133513 1172812402961 1162219258676257 1171221845949812801 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).(2 * i),((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3),1) mod (x + 1)))
A342086: 1 2 2 3 2 5 2 5 3 5 2 9 2 5 5 7
((x + 1) div (1 + loop(\(x,i).((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3),1,(x + 1))))
A131755: 1 2 1 4 1 6 2 4 3 10 2 12 4 4 3 16
(1 + ((x + 1) * ((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3)))
A083271: 2 5 7 13 11 25 15 33 28 41 23 73 27 57 61 81
(1 + compr(\x.(loop(\(x,i).(2x + 2),x,(x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))) mod (x + 1)),(x + 1)))
A193063-A165132: 2 3 5 7 11 13
A020625: 2 3 5 7 11 13 17
A247142: 2 3 5 7 11 13 17 19 23 29 31 35 37 41 43 47
(~1 + loop(\(x,i).(if (x + ~1) <= 0 then 1 else (2 * ((x + 1) - (((x + 1) mod (1 + (2 * ((1 + (x div 4)) div 2)))) div 2)))),1,(x + ~1)))
A159482: 0 0 0 5 7 7 11 13 13 17 19 19 23 23 23 29
loop(\(x,i).4x,(2 * ((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1))),1)
A165837: 1 16 16 256 16 256 16 4096 256 256 16 4096 16 256 256 65536
loop(\(x,i).3x,(2 * ((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1))),1)
A165830: 1 9 9 81 9 81 9 729 81 81 9 729 9 81 81 6561
(1 + (2 * (~1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(7x + ~3))),x)))))
A111517: 3 15 19 31 39 43 51 55 75 79 99 111 123 139 159 163
(1 + (2 * (1 + (2 * compr(\x.(1 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(8x2 + 8x))),x)))))
A071696: 7 19 31 43 103 139 151 199 271 283 463 523 571 619 643 811
(if x <= 0 then 0 else (1 + (((~1 + loop(\(x,i).2x,x,(1 + (2 * (((2x + 1) mod (2 + (x div 4))) div 2))))) mod (x + 1)) div 2)))
A334033: 0 1 1 2 1 3 1 4 2 3 1 6 1 3 3 8
(if x <= 0 then 0 else (1 + (((1 + (loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) mod 13)) div 2) div 2)))
A317905: 0 1 1 2 1 2 1 1 1 1 1 1 4 1 1 2
(~1 + (4 * (1 + (4 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,8x)),x)))))
A091968: 3 19 67 83 131 163 179 211 227 307 419 467 499 547 563 643
(1 + (((~1 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) div 2) div 2))
A160830: 1 1 2 4 5 7 8 10 12 14 16 19 20 22 24 27
((((x * loop(\(x,i).(x * loop(\(x,i).((x2 + ~x) div 2),2,(x + ~2))),1,(x + ~1))) div 2) div 3) div 15)
A000579: 0 0 0 0 0 0 1 7 28 84 210 462 924 1716 3003 5005
((2 * (if x <= 0 then 2 else (1 + (19 * loop(\(x,i).10x,x,1))))) div 5)
A136962: 0 76 760 7600 76000 760000 7600000 76000000 760000000 7600000000 76000000000 760000000000 7600000000000 76000000000000 760000000000000
(loop(\(x,i).(x6 + ~x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 5)
A138444: 12 144 3120 23520 354288 965328 4827456 9409104 29607072 118964496 177500544 513145008 950020512 1264272240 2155842624 4432871664
(loop(\(x,i).(x2 * (x4 div 2)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 5)
A138446: 6 72 1560 11760 177144 482664 2413728 4704552 14803536 59482248 88750272 256572504 475010256 632136120 1077921312 2216435832
loop(\(x,i).i,(~2 + (((x + 1) + ((1 + (2 * ((x + ((x + loop(\(x,i).2x,x,1)) div (x + 1))) div 2))) div (2x + 1))) div 2)),1)
A005860: 1 1 1 1 1 1 2 2 3 4 6 7 11 16 24
((1 + ((((x + 1) * (1 + loop(\(x,i).(loop(\(x,i).(4x + ~1),x,2) div 3),1,(x + 1)))) div 2) div 3)) mod 3)
A115382-A115381: 1 1 1 0 2 0 1 1 1 1 0 1 2 1 0 0
(((x + 1) * (if x <= 0 then 1 else (2 * (1 + ((1 + ((loop(\(x,i).((3x + 1) - (i mod 2)),x,1) div 2) div 2)) div 2))))) mod 3)
A112607: 1 1 0 1 0 0 1 0 0 0 1 0 1 1 0 2
((2 + ((2 + (loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) + (3 * loop(\(x,i).(2x + 2),x,2)))) mod (x + 1))) div 3)
A161064: 0 1 1 1 1 2 1 2 3 2 3 4 3 5 5 5
((x - ((if x <= 0 then 1 else (2 * (1 + (((1 + (x mod (2 + (if (x mod (2 + (x mod 2))) <= 0 then 2 else 0)))) mod (x + 1)) div 2)))) div 2)) mod 3)
A283319: 0 0 1 2 0 0 1 2 1 1 2 0 2 2 0 0
(((x + 2) - ((if x <= 0 then 1 else (loop(\(x,i).x5,1,11) mod (x + 1))) div 2)) div 3)
A283190: 0 1 1 1 2 1 2 2 2 3 4 2 3 3 3 4
(((loop(\(x,i).(x3 * (x2 div 2)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 2) div 3)
A138438: 1 9 125 686 6655 15379 58956 102885 267674 853615 1191640 2887221 4824470 6122039 9551716 17418609
((loop(\(x,i).(x6 + ~x4),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 3)
A138456: 8 108 2500 19208 292820 799708 4009008 7819260 24626008 99019340 147763360 427308708 791213080 1052990708 1795722608 3692745108
((loop(\(x,i).(x2 * (x4 div 2)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 3)
A138447: 5 60 1300 9800 147620 402220 2011440 3920460 12336280 49568540 73958560 213810420 395841880 526780100 898267760 1847029860
(x div (1 + ((~1 + loop(\(x,i).2x,x,((x5 + ~1) + loop(\(x,i).8x,x,1)))) mod (x + 2))))
A096863: 0 1 0 1 1 1 0 1 1 1 2 0 1 1 0 1
(0 + ((x + 1) div (if x <= 0 then 1 else (2 * (1 + ((if (x mod (2 + (x mod 2))) <= 0 then 1 else x) mod (1 + (x div 4))))))) - (x mod 2))
A112219: 1 0 1 1 1 0 1 1 2 1 2 1 3 2 3 3
(if x <= 0 then 0 else ((x + 1) + (((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (x mod 2))))
A295220: 0 3 3 6 5 9 7 11 10 13 11 17 13 17 17 20
(1 + compr(\x.((x + 1) mod (~1 + loop(\(x,i).2x,(1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))),1))),x))
A325327: 1 2 3 5 6 7 11 13 17 19 21 23 29 30 31 37
(1 + compr(\x.(1 - ((2 * (1 + (((((if x <= 0 then 1 else x) mod 2) - loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))) div 2) div 2))) mod 3)),x))
A345917: 1 2 4 5 7 8 9 11 14 16 17 18 19 21 22 23
((x + 1) + loop(\(x,i).(0 - (x div (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))))),1,(x + 1)))
A076563: 0 0 2 0 3 0 6 6 5 0 9 0 7 10 14 0
((~x + 1) + (2 * (((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1))))
A134156: 1 2 1 2 ~1 2 ~3 0 ~3 ~2 ~7 0 ~9 ~6 ~7 ~6
((2 * ((1 + loop(\(x,i).10x,(2x + 1),1)) div 3)) + loop(\(x,i).10x,x,1))
A332167: 7 676 66766 6667666 666676666 66666766666 6666667666666 666666676666666 66666666766666666 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).4x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),(x + 1))
A166625: 1 8 12 64 20 96 28 512 144 160 44 768 52 224 240 4096
loop(\(x,i).3x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),(x + 1))
A166624: 1 6 9 36 15 54 21 216 81 90 33 324 39 126 135 1296
((x + 1) * (~1 + loop(\(x,i).2x,(1 + (((4x + ~4) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))) mod 4)),2)))
A328567: 3 6 21 12 75 42 105 24 279 150 341 84 403 210 465 48
((x + 1) * (if (x mod 3) <= 0 then 1 else (2 + (((1 + (x mod (1 + (2 * ((if (x mod 2) <= 0 then 1 else x) mod 3))))) mod (x + 1)) div 2))))
A231407: 1 4 6
A143174: 1 4 6 4 15 12 7 24 27 10 33 36 13 42 45 16
(2 + (if ((x div ~2) mod 2) <= 0 then (1 - ((2 * (1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 8))) mod 3)) else 0))
A136165-A134193: 1 2 2 1 2 2 2 1 1 2 2 3 2 2 2 1
((1 + ((if x <= 0 then 2 else (1 + (loop(\(x,i).(1 + ((1 + ((x2 + (x div 2)) div 3)) div 3)),2,x) div 3))) div 2)) div 2)
A017842: 1 0 0 0 0 1 1 1 1 1 2 3 3 4 5 7
((1 + (loop(\(x,i).(x + loop(\(x,i).(x - ((x - (((x + 1) * (2 - ((x div 2) mod 2))) mod 3)) div 2)),2,x)),(x + 1),1) div 2)) div 2)
A052337: 1 1 1 2 2 3 5 6 8 10 13 17 21 27 34 42
((x + 1) div (if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + loop(\(x,i).(x div (2 - ((x - (x div 8)) mod 2))),x,x)) div 2)) div 2)))))
A345138: 1 0 0 1 1 1 1 1 1 2 1 2 1 3 1 2
(if x <= 0 then 1 else (2 * (1 + ((3 * ((1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))) div 2)) div 2))))
A328721: 1 2 2 4 2 4 2 8 4 4 2 8 2 4 4 14
(2 + ((x + 1) div (1 + ((loop(\(x,i).2x,x,(2 - (((2 + loop(\(x,i).(x div (~2 + (x mod 2))),x,x)) div 2) mod 2))) mod (x + 1)) div 2))))
A182258: 3 4 5 6 7 4 5 10 5 5 13
((1 + (((3 * (1 + (if (2x mod (4 + (x div 4))) <= 0 then (2 + (if x <= 0 then 0 else (x + 2))) else 0))) div 2) div 2)) div 2)
A133109: 1 0 3 0 0 4 0 0 0 5 0 0 0 0 7 0
(((loop(\(x,i).(x2 + x),1,(~2 + loop(\(x,i).10x,(x + 1),2))) div 2) div 15) div 2)
A332165: 5 656 66566 6665666 666656666 66666566666 6666665666666 666666656666666 66666666566666666 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~2 + (5 * (1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (2 + i)) <= 0 then 0 else x)),x,10x)),x)))))
A030431: 3 13 23 43 53 73 83 103 113 163 173 193 223 233 263 283
((5 * loop(\(x,i).(10x + 1),x,loop(\(x,i).(10x + 19),x,1))) div 2)
A332172: 2 727 77277 7772777 777727777 77777277777 7777772777777 777777727777777 77777777277777777 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(loop(\(x,i).7x,(4x + 3),1) mod (~2 + loop(\(x,i).x2,(3x + 2),3)))
A132661: 27 823543 4611686018427387903
(((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3) mod 6)
A084302: 1 2 2 3 2 4 2 4 3 4 2 0 2 4 4 5
(x - ((1 + (x div (2 + ((1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)) mod (x + 1))))) * ((x mod 3) div 2)))
A101684: 0 1 0 3 4 3 6 7 6 9 10 8 12 13 11 15
(loop(\(x,i).(1 + ((2 * (1 + (x div (1 + (loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)))))) + (x mod 2))),1,(x + 1)) div 2)
A126594: 2 3 2 5 2 7 2 3 3 11 2 13 4 4 2 17
((2x + 2) + ((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3))
A140482: 3 6 8 11 12 16 16 20 21 24 24 30 28 32 34 37
((1 + (loop(\(x,i).3x,2x,1) div (x5 + loop(\(x,i).7x,x,1)))) div 2)
A175773: 1 1 1 1 1 1 2 3 4 5 6 8 10 13 17 22
((2 + (((x + ~1) - ((1 + (if x <= 0 then 1 else (2 * ((1 + (if (x mod 3) <= 0 then 0 else x)) div 3)))) div 2)) mod 5)) div 2)
A225332: 2 1 1 2 2 2 1 3 3 2 1 1 1 2 2 3
((((1 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x)) * (1 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) div 2) div 2)
A087427: 2 6 15 30 48 72 99 154 210 270 360 420 483 598 754 870
(4 * ((x + 2) - ((x + 1) div (if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 2)))))))
A274919: 4 8 12 16 16 24 20 32 32 40 28 48 32 52 52 64
((loop(\(x,i).(10x + 1),(2x + 1),1) + loop(\(x,i).10x,x,8)) div 2)
A332159: 9 595 55955 5559555 555595555 55555955555 5555559555555 555555595555555 55555555955555555 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(((loop(\(x,i).(x6 + ~x4),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 2) div 2)
A138457: 6 81 1875 14406 219615 599781 3006756 5864445 18469506 74264505 110822520 320481531 593409810 789743031 1346791956 2769558831
(2 + (2 * compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))
A210497: 4 7 9 15 15 21 21 27 35 33 43 45 45 51 59 65
((5 * (if (x mod 2) <= 0 then ((~1 + (9 * (2 - ((x div 2) mod 2)))) * (if x <= 0 then 1 else 2)) else 1)) div 4)
A040460: 21 1 20 1 42 1 20 1 42 1 20 1 42 1 20 1
(324 * (1 + loop(\(x,i).3x,x,1) - loop(\(x,i).2x,x,2)))
A337313: 0 0 648 3888 16200 58320 195048 625968 1960200 6045840 18468648 56068848 169533000 511252560 1539065448 4627812528
(2 * (2 + compr(\x.((~x + 1) + (23 * loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x))),x)))
A242058: 6 8 12 14 18 20 24 30 32 38 42 44 48 52 54 58
(((x + 2) + ((x + ((3 * (2 + compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,(x + 2)),x))) div 2)) div 2)) div 2)
A196276: 5 7 11 13 15 18 21 23 24 29 30 31 32 33 36 38
(if x <= 0 then 1 else (2 * (2x + (((x + 1) + (2 * ((1 + (if (~2 + (x div 2)) <= 0 then x else (x + 4))) div 3))) div 3))))
A310505: 1 4 10 16 20 26 32 38 42 48 54 58 62 68 74 78
((x * (1 + (2 * loop(\(x,i).x5,1,loop(\(x,i).(14x + 1),(x + 2),1))))) div 2)
A054213: 0 225313610074846875 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(((x + 1) + (2 * ((2 + ((1 + (((x + 1) * (1 + (if (x mod 2) <= 0 then (if x <= 0 then 0 else (2x + 1)) else 0))) div 2)) div 2)) div 2))) div 2)
A137442: 1 2 4 3 9 5 16 6 25 7 36 8 49 10 64 11
(4x div ((x + 2) + loop(\(x,i).((1 + (x * loop(\(x,i).(8x + 2),2,2x))) mod (x + 1)),1,(x + 1))))
A060502: 0 1 1 2 1 1 1 2 2 3 2 2 1 2 1 2
((~1 + (((~2x + 2) mod (4 + (x div 4))) + (if x <= 0 then 1 else (~1 + (x div (if (x mod 2) <= 0 then 4 else 1)))))) div (x + 2))
A218171: 1 ~1 0 0 0 0 ~1 0 0 0 0 1 0 1 0 0
compr(\x.loop(\(x,i).(x2 + x),1,(2 - (3 * ((1 + (((1 + loop(\(x,i).((x * (x mod 2)) + (x div 2)),x,x)) div 2) div 2)) div 2)))),x)
A039501: 5 7 9 10 13 14 18 19 20 26 27 28 35 36 38 40
(x + loop(\(x,i).((x + 2) - ((~x + 1) div (1 + loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),2)))),x,1))
A311312: 1 4 8 12 16 21 26 31 36 40 44 48 52 56 60 64
(1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x)))
A128139: 1 1 2 1 3 3 1 4 5 4 1 5 7 7 5 1
((2x + 2) + loop(\(x,i).((2x + 1) + (loop(\(x,i).(1 + (4 * (x + (x mod 2)))),x,0) + (x mod 2))),(x + ~1),(x mod 2)))
A062621: 2 5 7 701
loop(\(x,i).(~1 + ((2 * ((x + 3) + ((4 * (x + ((x div 2) div 7))) div 3))) div 3)),x,0)
A202278: 0 1 2 3 5 8 13 21 34 55 89
A132636: 0 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987
(1 + (if ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) <= 0 then (2 * ((2x + 1) div (3 + (x div 4)))) else 0))
A131843: 1 3 3 5 1 5 7 1 1 7 9 1 1 1 9 11
(1 + (x mod (1 + (x mod (1 + ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod (1 + (x mod 12))))))))
A084310: 1 2 3 4 1 2 1 4 3 10 1 2 1 2 3 2
(1 + (x mod (1 + (x mod (1 + (x mod (1 + ((1 + (14 * (if (x mod 4) <= 0 then 0 else 2))) mod (x + 1)))))))))
A079893: 1 2 3 2 1 6 1 2 1 10 1 6 1 2 15 2
(~1 + loop(\(x,i).(2 * (x - (x div 5))),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1))
A299904: 0 0 0 0 1 0 0 3 3 0 0 7 13 7 0 0
(1 + (if x <= 0 then 0 else (1 + ((2 * (1 + ((((1 + ((x - (x div 3)) div 3)) * (1 + (x div 2))) div 2) div 2))) div 3))))
A039730: 1 2 2 2 3 3 4 4 4 4 5 5 6 7 8 8
((((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4))) + (if x <= 0 then 0 else 1)) mod (1 + (x mod 11)))
A328919-A267115: 0 1 1 2 1 1 1 3 2 1 1 0 1 1 1 4
(1 + (x mod (1 + ((~1 + (((x + 1) * (~1 + ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 2))) div 2)) mod (x + 1)))))
A340079-A323072-A055032: 1 1 1 4 1 3 1 8 9 5 1 12 1 7 15 16
loop(\(x,i).i,((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + ((1 + (x div 3)) div 2))),1)
A154218: 1 1 1 1 2 1 1 4 4 1 1 9 12 9 1 1
(1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) div (if ((x + 2) mod 5) <= 0 then 2 else 1)))
A112739: 1 1 1 1 2 1 1 3 2 1 1 4 5 2 1 1
(1 + ((1 + (x div (1 + (x mod (1 + ((~1 + loop(\(x,i).2x,x,(((~x + 1) mod 3) - (x mod 2)))) mod (x + 1))))))) div 3))
A319522: 1 1 2 1 1 2 3 1 4 1 1 2 5 3 2 1
(1 + (loop(\(x,i).(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)),1,(x + 1)) div 3))
A275420: 1 1 1 1 1 1 2 2 1 1 2 3 2 1 1 5
loop(\(x,i).40x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A176644: 1 1 1 1 40 1 1 1600 1600 1 1 64000 2560000 64000 1 1
loop(\(x,i).21x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A176643: 1 1 1 1 21 1 1 441 441 1 1 9261 194481 9261 1 1
loop(\(x,i).(2 + (2x mod 7)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A261790: 1 1 1 1 4 1 1 3 3 1 1 8 4 8 1 1
loop(\(x,i).(2 * (x - ((2 - (i mod 4)) div 2))),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A333157: 1 1 1 1 2 1 1 4 4 1 1 10 18 10 1 1
loop(\(x,i).28x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A176641: 1 1 1 1 28 1 1 784 784 1 1 21952 614656 21952 1 1
loop(\(x,i).(2 * (x + (2 mod (1 + (x div 4))))),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A155971: 1 1 1 1 2 1 1 4 4 1 1 8 20 8 1 1
(1 + ((2 * (1 + (loop(\(x,i).x2,1,(1 + (x mod (1 + ((4 + (x div 2)) mod (1 + (x div 3))))))) div 2))) div 3))
A069290: 1 1 1 3 1 1 1 3 4 1 1 3 1 1 1 7
(if x <= 0 then 2 else (1 + ((2 * (1 + ((1 + ((2 + ((3 * (2 + (x mod 4))) mod (x + 1))) div 3)) div 2))) div 3)))
A194822: 2 2 1 2 2 2 2 3 2 3 2 2 2 3 3 3
(1 + ((2 * (1 + ((1 + (((~1 + loop(\(x,i).(3x + ((x2 + 2x) div 3)),x,1)) div 2) div 2)) div 2))) div 3))
A326973: 1 1 3 19 1243
(if x <= 0 then 0 else (1 + ((2 * (1 + ((((x mod ((x + ~1) - (x mod 12))) * (1 + (x div 2))) div 2) div 2))) div 3)))
A218027: 0 1 1 1 1 1 1 1 1 1 1 1 2 3 5 7
(if x <= 0 then 1 else (~1 + ((2 * (2 + (((2 - (((~2x + 2) mod (4 + (x div 4))) div 2)) div 2) mod (x + 1)))) div 3)))
A265117: 1 1 0 1 0 0 1 0 0 0 1 0 8 0 0 1
(~1 + ((2 * ((x + 2) + (if x <= 0 then 1 else (2 * (4x - ((x + ((x div 3) mod 3)) div 3)))))) div 3))
A315696: 1 6 12 17 23 27 33 38 44 50 56 62 67 73 77 83
(~1 + ((2 * ((x + 2) + (if x <= 0 then 1 else (8x - ((x - ((x + (x div 3)) div 3)) div 2))))) div 3))
A315548: 1 6 11 17 23 29 35 41 47 53 58 64 70 75 81 87
(~1 + ((2 * ((x + 2) + (if x <= 0 then 1 else (2 * (4x - ((x - ((x + (x div 3)) div 3)) div 2)))))) div 3))
A315539: 1 6 11 17 23 29 33 39 45 51 56 62 68 73 79 85
loop(\(x,i).x2,1,(1 - (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((2 * ((~x + 2) div 2)) div 3)))))
A189150: 1 1 1 1 1 1 1 4 4 1 1 16 49 16 1 1
(~1 + ((2 * ((2x + 2) + (if x <= 0 then 1 else (6x + (((x + 1) + (x mod 2)) div 5))))) div 3))
A314210: 1 5 11 17 22 27 33 38 43 49 55 60 65 71 77 82
(1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~1) - (if x <= 0 then 1 else (2 - (x mod 5))))) div 2))
A249488: 1 1 1 1 3 1 1 4 5 1 1 5 12 7 1 1
(1 + (x2 div (1 + (2 * (1 + ((1 + loop(\(x,i).(x - (x div ~3)),x,1)) div 3))) - (x div ~3))))
A341166: 1 1 1 2 2 3 3 4 4 4 4 4 3 3 3 3
(1 + (loop(\(x,i).(x + (5 * i)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2))
A177944: 1 1 1 1 4 1 1 9 9 1 1 16 26 16 1 1
(1 + ((x + 1) div (2 * (1 + ((1 + ((x + 1) div (1 + (if (x mod (1 + ((x2 + ~x) mod 8))) <= 0 then 2 else 0)))) div 2)))))
A071891: 1 2 1 1 1 2 1 1 2 2 1 1 1 1 2 3
(1 + ((1 + ((1 + ((1 + ((1 + (((x + ~1) * (~1 + loop(\(x,i).(1 + (x * ((1 + i) div 2))),x,0))) div 2)) div 2)) div 2)) div 2)) div 2))
A006249: 1 1 1 2 2 6 17 79
(5 - ((loop(\(x,i).(2x + 2),x,(12 * (x div 7))) mod 5) div 2))
A305394: 5 4 5 3 5 4 5 5 4 5 3 5 4 5 4 5
(1 - ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) div (if ((x + 2) mod 5) <= 0 then 2 else 1)))
A336201: 1 1 1 1 0 1 1 ~1 0 1 1 ~2 ~3 0 1 1
loop(\(x,i).i,(2 * ((2 * (1 + (2 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))) div 3)),1)
A143188-A141540-A132046: 1 1 1 1 4 1 1 6 6 1 1 8 12 8 1 1
((~1 + (22 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))) div 7)
A097426: 6 9 15 21 34 40 53 59 72 91 97 116 128 135 147 166
(1 + (((loop(\(x,i).4x,((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2),1) div 3) * (1 + (x div 2))) div 2))
A137896: 1 1 1 1 2 1 1 3 3 1 1 4 18 4 1 1
(1 + (((loop(\(x,i).x3,1,((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) * (1 + (x div 3))) div 2) div 2))
A298444: 1 1 1 1 1 1 1 1 1 1 1 2 11 2 1 1
(1 + (4 * ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (if (x mod 3) <= 0 then 2 else 1))))
A081578: 1 1 1 1 5 1 1 9 9 1 1 13 33 13 1 1
(1 + (((1 + (((x + 1) * (x - (((0 - loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1)) div 2) div 2))) div 2)) div 2) div 2))
A002877: 1 1 2 3 6 13 35 116
(if x <= 0 then 0 else (1 + ((((1 + ((2x + 1) mod (1 + (2x mod (2 + (x div 4)))))) * (1 + (x div 4))) div 2) div 2)))
A209062: 0 1 1 1 1 2 1 1 1 2 1 3 2 3 3 2
loop(\(x,i).i,(2 * ((3 * ((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~1) div 2))) div 2)) div 2)),1)
A283795: 1 1 1 1 2 1 1 6 6 1 1 8 14 8 1 1
((2x + 1) mod (if (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) <= 0 then (2 + (x div 4)) else 1))
A145677: 1 1 1 1 0 2 1 0 0 3 1 0 0 0 4 1
(if x <= 0 then 0 else (1 + (~2 mod (1 - (2 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2))))))
A128966-A055907: 0 1 1 1 2 1 1 4 4 1 1 6 10 6 1 1
(((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)) mod (1 + ((x + 1) mod 4)))
A344478: 0 1 1 0 1 2 1 0 0 2 1 0 1 2 2 0
((1 + (((~1 + (6 * (1 + (2 * loop(\(x,i).((4x * i) - (x mod 2)),x,1))))) div 2) div 2)) div 5)
A245896: 1 2 14 165 2639
loop(\(x,i).10x,(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)),1)
A178166: 10 10 10 10 100 10 10 1000 1000 10 10 10000 1000000 10000 10 10
(2 - ((1 + ((if x <= 0 then 2 else (1 + ((1 + ((x + 1) div 2)) mod ((1 + ((x mod 3) div 2)) * (1 + (x mod 2)))))) div 2)) mod 3))
A316771: 0 1 1 0 1 1 1 0 0 1 1 2 1 1 1 0
((1 + (x mod (2 + ((1 + ((if ((x * (x mod 3)) mod 5) <= 0 then 1 else 2) * (1 + (x mod 2)))) mod (x + 1))))) div 3)
A319662: 0 0 0 1 1 0 1 0 1 1 1 1 0 2 1 0
((1 + (((3 * (1 + (loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,x2) div 3))) div 2) div 2)) mod 3)
A287146: 1 1 0 1 0 0 1 1 0 0 0 1 1 2 1 1
((1 + (2 * (if x <= 0 then 1 else (2 * (3x + ((2 * (x - (2x div ~7))) div 3)))))) div 3)
A137002: 1 5 11 15
A314040: 1 5 11 15 21 25 31 36 41 47 51 57 61 67 72 77
((1 + ((x * (1 + (2x * (1 + loop(\(x,i).(45x + 1),x,0))))) div 2)) div 3)
A296782: 0 1 63 6216
(((2x + 1) * (1 + (2 * ((~1 + loop(\(x,i).(24x + 1),2,x2)) div (x + 1))))) mod 3)
A116852: 1 0 1 1 0 0 0 0 2 1 0 1 0 0 0 0
((if x <= 0 then 1 else 6x) - (((x + 1) div 3) + (((x + 1) + (2 * ((x + ((x div 2) mod 2)) div 2))) div 3)))
A315260: 1 6 10 15 20 25 30 35 40 45 50 54 60 66 70 75
(((x + ((x - ((1 - (x div 2)) div 3)) mod 3)) div 3) + (if x <= 0 then 1 else 4x) + ((x + 1) div 3))
A310393: 1 4 10 14 19 23 28 33 37 42 46 52 56 60 66 70
(((x + ((x + ((2 - (x div 2)) mod 6)) div 3)) div 2) + (if x <= 0 then 1 else 4x) + ((x + 1) div 3))
A313707: 1 5 10 15 19 25 30 35 41 45 50 55 60 65 70 75
((2 * (1 + ((1 + (x div (1 + (x mod (1 + ((~1 + loop(\(x,i).2x,x,(x div (2 - (x mod 2))))) mod (x + 1))))))) div 2))) div 3)
A335904: 0 0 1 0 2 1 2 0 2 2 4 1 4 2 3 0
((2 * (1 + ((1 + ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod (2 * (1 + (x div 4))))) div 2))) div 3)
A255337: 0 1 1 1 2 1 1 2 2 2 1 1 1 2 3 2
((2 * (1 + ((1 + ((loop(\(x,i).(2x + ~2),x,(1 + (2x mod (2 + (x div 4))))) mod (x + 1)) div 2)) div 2))) div 3)
A279792: 0 0 0 1 1 1 0 1 2 1 0 2 1 1 2 1
(1 - ((2 * (1 + ((1 + ((x - (2 * loop(\(x,i).(x - (((~x + ~1) + (x div 3)) div 3)),x,1))) div 2)) div 2))) div 3))
A018120: 1 1 1 1 2 3 3 4 5 7 9 11 13 17 21 27
(((1 + (((1 + ((((x + 1) * (~1 + loop(\(x,i).(8x + 4),(x + 1),0))) div 2) div 2)) div 2) div 2)) div 2) mod 3)
A026610: 0 2 0 2 1 1 1 0 1 2 1 1 1 0 2 0
(((1 + (((1 + ((x * ((x + 2) + ((2 * loop(\(x,i).(x div (2 - (x mod 2))),x,x)) mod (x + 1)))) div 2)) div 2) div 2)) div 2) mod 3)
A105700: 0 0 1 1 2 1 2 1 0 2 2 1 0 1 2 2
(~3 + loop(\(x,i).x2,1,(2 * (1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))))
A141596: 1 1 1 1 13 1 1 33 33 1 1 61 141 61 1 1
(6 * ((x + 3) + ((loop(\(x,i).(x2 + x),1,(18x + 8)) div 2) div 3)))
A304165: 90 726 2010 3942 6522 9750 13626 18150 23322 29142 35610 42726 50490 58902 67962 77670
((2 * ((2x + 1) + ((2 * ((2x + 2) + ((~1 + loop(\(x,i).2x,x,(x + 2))) div 3))) div 3))) mod 3)
A025883: 1 0 0 0 0 1 0 1 0 1 1 0 1 0 2 1
(((3x + 3) + (((1 + (loop(\(x,i).((x + 1) + (x div (1 + (x mod 4)))),x,0) div 2)) div 2) div 2)) div 3)
A141340: 1 2 3 4 5 6 7 8 10 12 14 16 18 24 30 36
(if x <= 0 then (x + 1) else ((2x + ~2) + (2 * (((x + 1) + (3 * ((x mod (1 + (x div 2))) div 3))) div 2))))
A222011: 1 2 4 8
A226872: 1 2 4 8 10 14 16 22 26 28 32 34 38 44 46 50
(1 + ((x + ((((~x + 1) + (2 * ((1 + (((1 + (loop(\(x,i).4x,(x + ~2),x) div 2)) div 2) div 2)) div 2))) div 2) div 2)) div 2))
A318895: 1 1 1 2 3 8 27 115
(1 - ((1 + (((x + 1) * (1 + ((x - ((1 + ((loop(\(x,i).(x + (x div 2)),x,2) div 2) div 2)) div 2)) div 2))) div 2)) div (2x + 1)))
A218026: 0 1 1 1 1 1 1 1 1 1 1 2 3 5 7 11
(0 + (((2 * (1 + ((1 + (x div (1 + (loop(\(x,i).(2x + 1),x,(x mod 2)) mod (x + 1))))) div 2))) div 3) + (x mod 2)))
A071338: 0 1 1 1 2 2 2 1 1 2 4 2 4 3 2 1
(1 + compr(\x.(1 - (x mod (1 + ((~1 + loop(\(x,i).2x,x,(1 + (x mod (2 * (1 + (x mod 2)))))) - (x mod 2)) mod (2x + 1))))),x))
A028741: 2 3 5 6 7 10 11 12 13 14 15 17 18 19 20 22
(1 + compr(\x.((x + ((1 + (((x + loop(\(x,i).((3x + 1) - ((x + 1) div 5)),x,1)) div 2) div 2)) div 2)) mod 2),x))
A227194: 1 2 3 4 6 7 9 10 11 12 14 15 16 23 24 25
((1 + (x mod (1 + (x mod (1 + (x mod (1 + (x div (1 + (2 * (if ((x + 1) mod (2 + ((x div 2) mod 2))) <= 0 then x else 1))))))))))) mod (x + 1))
A304495: 0 1 1 2 1 1 1 2 3 1 1 1 1 1 1 4
((x + 1) * (1 + (x mod (1 + ((~1 + loop(\(x,i).2x,x,(1 + (x mod (2 * (1 + (x mod 2)))))) - (x mod 2)) mod (2x + 1))))))
A197863-A087321-A087320: 1 4 9 4 25 36 49 8 9 100 121 36 169 196 225 16
((if x <= 0 then 2 else (1 + ((((x + 1) + (2 * (x mod ((x + ~1) - (x mod 12))))) mod (1 + (x div 2))) div 2))) mod (x + 1))
A072625: 0 1 1 1 2 1 2 1 3 1 3 1 1 3 3 1
((2 * ((6x + 6) mod (3 * (1 + ((6 * (2 + (if x <= 0 then 0 else 2))) + (x mod 2)))))) mod (x + 1))
A084342: 0 0 0 0 0 0 0 0 0 0 0 0 6 12 0 4
((2 * ((x + 1) + ((1 + loop(\(x,i).((x + 1) * ((x2 + 3x + 2) div 2)),1,(x2 + 2x + 1))) div (x + 1)))) div (x + 1))
A197903: 16 40 124 327 732 1447 2604 4359 6892 10407 15132 21319 29244 39207 51532 66567
(2 * (~1 + loop(\(x,i).(3 * ((x + 1) div 2)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)))
A272626: 0 0 0 0 4 0 0 10 10 0 0 16 28 16 0 0
((1 + loop(\(x,i).(x * (x + (x div 2))),1,(1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))) div 2)
A146769: 1 1 1 1 3 1 1 6 6 1 1 12 18 12 1 1
((1 + ((x + 1) mod (1 + ((~1 + (2 * (loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) + ((x + ~1) mod 4)))) mod (x + 1))))) div 2)
A278522: 0 0 1 0 0 0 1 1 2 0 1 1 1 0 1 2
(loop(\(x,i).(2 * (x + ((x + ~1) mod 3))),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2)
A221768: 0 0 0 0 1 0 0 3 3 0 0 8 16 8 0 0
(if x <= 0 then 1 else (2 * (1 + (x div (2 + (x mod (1 + ((x + 1) div (1 + (((2x div (1 + (x div 4))) mod 2) + (x mod 2)))))))))))
A322327: 1 2 2 4 2 4 2 6 4 4 2 8 2 4 4 8
((x + 1) div (if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + (x div (1 + ((x + 1) mod (2 * (1 + (x mod (2 + (x mod 2))))))))) div 2)) div 2)))))
A178526: 1 1 0 1 1 1 1 1 2 1 1 1 2 3 2 1
((1 + ((1 + ((1 + ((loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(x + ~2),x) * ((x + ~1) div 2)) div 2)) div 2)) div 2)) div 2)
A282742: 0 0 0 1 1 4 11 56 198
(if (x + ~1) <= 0 then 1 else (2 * (1 + (((x + 1) mod (1 + (2 * (x div (3 * (1 + ((x2 + 2x) mod 6))))))) div 2))))
A248913: 1 1 2 2 4 2 4 2 2 2 6 2 6 4 2 2
((1 + ((1 + ((((x + 1) * (6 + loop(\(x,i).((x + 1) - (((~x + 2) div 2) div 3)),x,1))) div 2) div 2)) div 2)) div 2)
A233693: 1 1 2 3 4 6 8 11 14 18 24 30 38 48 60 75
(((1 + (((x + 1) div (2 * (1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 8)))) div 2)) * (1 + (2 * (x mod 2)))) div 2)
A318315: 0 1 0 3 0 1 0 4 1 1 0 3 0 1 0 7
(loop(\(x,i).2x,(1 + ((x div (2 + ((x div 2) div (1 + (x mod (2 + ((x mod 3) div 2))))))) + (x mod 2))),1) div 6)
A319164: 0 0 0 1 0 2 0 2 1 2 0 5 0 2 2 5
(6 + (((x + 2) * loop(\(x,i).4x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),2)) div 3))
A100599: 7 14 16 59
(if x <= 0 then 1 else (2 + ((1 + (2 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))) mod (1 + (x div 2)))))
A242285: 1 2 3 3 2 3 3 3 2 3 3 3 4 2 3 3
((2 + ((1 + (((x + (if (x mod 2) <= 0 then x else 1)) div 3) * (1 + (x div 5)))) div 3) - (x mod 2)) div 2)
A029196: 1 0 1 0 1 1 2 1 2 1 4 2 5 2 5 4
(2 + ((1 + (loop(\(x,i).(x * (1 + ((1 - (2x mod (4 + (x div 4)))) mod (x + 1)))),(x + 1),1) div 3)) div 2))
A098463: 2 3 5 7 167
(((7 * (1 + ((1 + (x div (1 + (if ((x * (x div 2)) mod 2) <= 0 then x else (x mod 3))))) div 3))) div 2) div 2)
A091842: 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 10
(((7 * (if x <= 0 then 1 else (x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))))) div 2) div 2)
A216677: 1 0 0 1 0 1 0 3 1 1 0 3 0 1 1 5
(((3 * ((x + 1) - (2 * (~2 - (if x <= 0 then 1 else (2 * (2x + ((x + ((x div 2) mod 2)) div 2)))))))) div 2) div 2)
A027884: 5 10 20 30 36 43
(((3 * ((2 + ((2 * (loop(\(x,i).5x,x,4) div 3)) div 3)) div 2)) div 2) div 2)
A276508: 0 2 9 42 208 1041 5208 26042 130209 651042 3255208 16276041 81380208 406901042 2034505209 10172526042
(((3 * ((5x + 5) - ((((x div 2) mod 2) - (if (~x + 2) <= 0 then x else 0)) div 2))) div 2) div 2)
A189361: 3 7 12 15 20 24 28 32 36 41 45 48 53 57 61 65
(2 + ((((x2 + ~1) - ((2 * (1 + ((1 + ((1 + loop(\(x,i).(x + (i * i)),(x + ~1),x)) div 2)) div 2))) div 3)) div 2) div 2))
A341159: 1 1 2 3 4 6 8 9 11 13 14 15 16 16 15 15
(((loop(\(x,i).x2,1,(1 + (2 * (1 + ((2x + 1) mod (1 + (2x mod (3 + (x div 4))))))))) div 2) div 2) div 2)
A115017: 1 1 3 1 1 6 1 1 3 10 1 6 1 1 15 1
(((((1 + (((x + 1) * (1 + (if (~1 + ((2x + 1) mod (2 + (x div 4)))) <= 0 then x else 0))) div 3)) div 2) div 2) div 2) div 2)
A322841: 0 0 0 0 0 0 1 1 1 0 2 0 3 0 0 5
(2 - ((if x <= 0 then 1 else ((x + 2) - ((x mod 2) + (2 * ((2 - (x mod (~1 + (2 * (x div 5))))) div 2))))) mod 4))
A194947: 1 2 0 0 2 2 0 0 2 2 2 2 2 0 2 0
(((1 - (x mod (~1 + (4 * (1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 8)))))) mod (2x + 2)) mod 4)
A091959: 1 0 1 1 3 0 1 0 1 0 1 1 3 0 1 1
(4x * (3 + (x2 * (1 + (3 * ((x2 + 2) + (if x <= 0 then (3x + 7) else 1)))))))
A008513: 0 64 728 4032 14896 42560 102024 215488 413792 737856 1240120 1985984 3055248 4543552 6563816 9247680
((((x2 + x) * ((2 * (4 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3)) div 2) div 2)
A088110: 0 1 3 9
A308084: 0 1 3 9 10 30 21 56 54 90 55 198 78 182 210 300
(((if x <= 0 then 1 else (2 * (1 + ((1 + ((~x + 2) mod (1 + ((((x + 1) + (x2 div 4)) div 2) div 2)))) div 2)))) - (x mod 2)) div 2)
A185216: 0 0 1 1 2 1 2 1 2 1 2 1 3 2 4 3
(if x <= 0 then 1 else (2 * ((x + ~1) + ((2 * ((3x + 2) - ((x - ((x + (x div 3)) div 3)) div 2))) div 3))))
A315345: 1 6 10 16 22 28 34 40 46 52 56 62 68 72 78 84
(if x <= 0 then 1 else (2 * (2x + (((2 * (2x div (4 + (x div 8)))) div 3) + ((x + 1) div 3)))))
A310421: 1 4 10 14 20 26 32 36 42 46 50 56 60 66 72 78
(2 + compr(\x.(((loop(\(x,i).(x4 mod 27),2,(2x + 1)) div 2) div 2) div 3),x))
A175904: 2 3 6 8 9 10 12 14 15 16 18 20 21 22 24 27
(((x + 2) + ((1 + (2 * ((x + 1) + (x mod (1 + (loop(\(x,i).2x,x,(1 + (x mod 2))) mod (2x + 1))))))) mod (x + 1))) div 2)
A097246: 1 2 3 3 5 6 7 6 5 10 11 9 13 14 15 9
((if (x + ~1) <= 0 then 1 else (2 * ((x + 1) + (((x + 1) * ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2)) div 3)))) mod (x + 2))
A047994: 1 1 2 3 4 2 6 7 8 4 10 6 12 6 8 15
(2x + ((1 + (2 * (if x <= 0 then 1 else (2 * ((2 * (4x - (x div 7))) div 3))))) div 3))
A314193: 1 5 11 17 21 27 33 38 43 49 55 59 65 71 76 81
(2x + ((1 + (2 * (if x <= 0 then 1 else (2 * (2x + ((2x + ((x div 3) mod 3)) div 3)))))) div 3))
A314231: 1 5 11 17 23 27 33 39 45 50 55 61 67 73 77 83
(1 + (((x + 1) div (if (1 + ((x div (1 + (2x mod 3))) mod 2) - (x mod 2)) <= 0 then (3x + 3) else 1)) + (x div 2)))
A026221-A026214: 2 1 5 6 8 3 11 4 14 15 17 18 20 7 23 24
(1 + (((2 * (1 + (((2x + 1) - (x div 4)) div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))) div 3) + (x mod 2)))
A228367: 2 4 2 7 2 4 2 12 2 4 2 7 2 4 2 21
(1 + ((2 * (1 + ((((if ((x + 2) mod (1 + (x mod 4))) <= 0 then 1 else 2) * (1 + (x div 2))) div 2) div 2))) div 3) - (x mod 2))
A106348: 1 0 2 1 1 1 3 2 2 2 2 2 2 2 4 3
(1 + (((x + (2 * ((2 + ((loop(\(x,i).2x,(x div 2),~2) mod (x + 1)) div 2)) div 2))) div 3) + (x mod 2)))
A125748: 1 3 2 3 3 5 4 5 5 7 5 7 5 9 8 7
((~x + 1) + (((2x + 1) + (2 * ((1 + ((1 + ((x * (x + (if (~2 + (x div 2)) <= 0 then 2 else 1))) div 2)) div 2)) div 2))) div 3))
A327719: 1 1 1 1 2 3 3 3 4 6 7 9 10 12 14 16
((~x + 1) + ((9 * loop(\(x,i).(x3 mod 47),2,x)) div (x + 1)))
A068891: 1 4 125 81
(x + ((2 + ((2x + 2) * (~1 + (3 * (1 + loop(\(x,i).2x,(2 + (x mod 2)),(x div 2))))))) div (1 + ((x div 2) mod 2))))
A242488: 6 11 45 108
compr(\x.(((~x + ~1) + (((2 + ((1 + ((3 * (x + (if (~2 + (x div 4)) <= 0 then 1 else 2))) div 2)) div 2)) div 2) div 2)) mod 3),x)
A190685: 3 6 7 10 14 18 21 22 25 29 33 36 40 44 47 48
((2x + 4) - (x mod (1 + (((x + (if (x mod 3) <= 0 then 7 else (x div 2))) div 3) mod 3))))
A272475: 4 6 8 10 11 12 16 18 20 22 23 24 28 30 32 33
((2x + 1) - ((2 * (1 + ((1 + (x div (1 + (loop(\(x,i).(5x + ~2),x,1) mod (x + 1))))) div 2))) div 3))
A184823: 1 3 4 7 8 10 11 15 16 18 19 22 23 25 28 30
((2x + 1) + (((x + 1) + (((x + 1) + (loop(\(x,i).(x + ((x * (1 + i)) div (2 + (x div 4)))),x,1) div 2)) div 2)) div 2))
A134918: 1 4 7 11 15 20 26 32 39 47 55 63 72 82 92 102
(2x + (if x <= 0 then 1 else (2 * (x + (((x + 1) - ((((x + 1) + ((2x + ~1) mod 7)) div 2) div 2)) div 2)))))
A315202: 1 6 10 14 20 24 28 32 38 42 46 52 58 62 66 72
(1 + (x div (1 + (x mod (1 + (x mod (1 + (((x + 1) - (9 * (x mod 10))) mod (x + 1)))))))))
A078268: 1 1 3 2 1 3 7 4 9 1 11 3 13 7 3 4
(1 + (x mod (1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + ((x mod 3) mod 2))))))
A192650: 1 1 1 1 2 1 1 3 3 1 1 4 3 7 1 1
(1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) mod (1 + (x mod (1 + (x mod 8))))))
A207974: 1 1 1 1 2 1 1 3 1 1 1 4 2 2 1 1
(1 + ((1 + (2 * (2x div 3))) mod (1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))))
A111604: 1 1 1 1 2 1 1 1 3 1 1 4 3 2 1 1
(1 + ((1 + (x div 2)) mod (1 + ((2 * (1 + ((1 + ((40 mod (x + 1)) div 2)) div 2))) div 3))))
A256972: 1 1 1 1 1 2 1 1 2 1 1 1 1 2 3 3
(1 + (3 * ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + (((x + 1) div 2) div 2)))))
A176284: 1 1 1 1 7 1 1 19 19 1 1 37 49 37 1 1
(1 + ((1 + (((6x4 + 15x3 + 14x2 + 6x + 1) div 2) div 3)) mod 9))
A097881: 2 9 4 3 9 4 2 7
(1 + (x mod (1 + ((x * ((3 * ((2x + 1) mod (1 + (2x mod (2 + (x div 4)))))) div 2)) mod 8))))
A344877: 1 1 1 1 1 6 1 1 1 2 1 2 1 2 1 1
(3 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((2x2 + 4) div 3))) mod 3))
A337265: 3 3 3 3 2 3 3 1 3 3 3 1 2 2 3 3
(1 + ((7 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)) div 3))
A056152: 1 1 1 1 3 1 1 5 5 1 1 8 17 8 1 1
(1 + (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + ((x + ~1) mod 4))) div 3))
A067049: 1 1 1 1 2 1 1 3 3 1 1 4 6 2 1 1
(~1 + ((1 - ((2 * (1 + (x div (3 * (1 + (x mod (2 * (1 + (x mod (3 + (x mod 2))))))))))) mod 3)) mod 3))
A089509: 1 1 1 1 ~1 1 0 1 1 ~1 ~1 1 ~1 0 ~1 1
(~1 + ((2 * (1 + ((4 + ((x + (((x div 2) * (x div 2)) div 2)) div 2) - ((x mod 2) + (x div 2))) div 2))) div 3))
A213424: 1 0 1 0 1 1 1 1 2 1 3 2 3 3 5 4
(1 + (6 * ((((~x2 + 2) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))) * (1 + (x div 2))) div 2)))
A081580: 1 1 1 1 7 1 1 13 13 1 1 19 61 19 1 1
(~1 + ((2 * ((2x + 2) + ((2 * ((x + 2) + (2 * ((x div 3) div (1 + (x div 4)))))) div 3))) div 3))
A183988: 1 3 4 7 8 9 12 14 15 17 19 21 23 25 27 28
(1 + (((2x + 1) div (2 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4))) - (x mod 2))) mod (x + 1)))
A279513-A000026: 1 2 3 4 5 6 7 6 6 10 11 12 13 14 15 8
(1 + ((1 + ((((3x + 1) - (((x mod 2) - ((x - ((x2 + 2x) div 3)) div 2)) div 2)) div 2) div 2)) mod (x + 1)))
A240676: 1 1 3 4 5 5 6 6 7 7 8 8 8 8 9 9
(~1 + (2 * (1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((~1 + ((x + ~1) div 3)) mod 3))))))
A277930: 1 1 1 1 3 1 1 5 5 1 1 7 13 3 1 1
(1 + ((((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2) * (1 + (x mod 5))) div 2))
A124234: 1 1 1 1 3 1 1 4 5 1 1 4 11 7 1 1
(1 + ((1 + (((1 + ((~1 + (((x + 1) - ((x3 div 8) mod 2)) mod 3)) mod (x + 1))) div 2) div 2)) div 2))
A143421: 1 1 1 2 1 1 2 1 2 2 1 3 1 1 1 3
(1 + ((1 + (((1 + (((x + 2) * ((3x + 1) + (((x2 + 3x + 2) div 2) div 3))) div 2)) div 2) div 2)) div 2))
A071424: 1 2 3 5 8 11 15 20 26 33 41 50 60 71 84 98
(1 + ((1 + (((3 * (x mod (1 + ((~1 + ((~2x + 2) mod (4 + (x div 4)))) mod (x + 1))))) div 2) div 2)) div 2))
A195825: 1 1 1 2 1 1 3 1 1 1 5 2 1 1 1 7
(1 + (((1 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 2)) div 2) * ((1 + (((x + 1) div 2) div 2)) div 2)))
A171246: 1 1 1 1 2 1 1 3 3 1 1 7 13 7 1 1
(1 + ((3 * (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (~1 + (3 * (((x + 1) div 2) div 2))))) div 2))
A132789: 1 1 1 1 4 1 1 8 8 1 1 13 25 13 1 1
compr(\x.((x div 7) mod 2),(1 + (2 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))))
A176700: 1 1 1 1 3 1 1 5 5 1 1 14 16 14 1 1
(1 + ((3 * ((5 * ((2 + (x div 3)) mod (~1 + (2x mod (4 + (x div 4)))))) div 2)) div 2))
A298575: 1 1 1 1 4 1 1 4 4 1 1 8 1 8 1 1
(1 + ((1 + (((x + 1) - (((x + 1) mod (2 + ((1 - (2x mod (4 + (x div 4)))) mod (x + 1)))) div 2)) div 2)) div 2))
A182210: 1 1 2 2 2 3 2 3 3 4 3 4 4 4 5 3
(1 + (((13 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) div 2) div 2))
A157172: 1 1 1 1 4 1 1 7 7 1 1 10 14 10 1 1
(1 + (((((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2) * (1 + (x div 3))) div 2) div 2))
A124976: 1 1 1 1 1 1 1 2 2 1 1 4 9 4 1 1
(1 + (2 * ((1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * ((1 + (x div 2)) div 2))) div 2)))
A176481: 1 1 1 1 3 1 1 5 5 1 1 11 13 11 1 1
(1 + (((1 + (((1 + (((x + 1) * (1 + ((x2 + 4x + 4) div 2) - (x mod 2))) div 5)) div 2) div 2)) div 2) div 2))
A199120: 1 1 1 1 2 3 4 5 7 8 11 13 17 20 25 30
(1 + (((17 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) div 2) div 2))
A296128-A183450-A157174: 1 1 1 1 5 1 1 9 9 1 1 13 18 13 1 1
(1 + (((1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (x - (x div 4)))) div 2) div 2))
A306326-A156006: 1 1 1 1 2 1 1 4 4 1 1 8 10 8 1 1
(1 + (((3 * (1 + (((x + 1) mod ((x + 3) - (2x mod (4 + (x div 4))))) div 3))) div 2) div 2))
A334215: 1 1 2 1 1 3 1 1 1 4 1 1 1 2 5 1
(1 + (((3 * (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (x - (2 * (((x + 1) div 2) div 2))))) div 2) div 2))
A175105: 1 1 1 1 2 1 1 3 4 1 1 4 10 6 1 1
(1 + ((((1 + (3 * ((1 - ((2x + ~1) mod (4 + (x div 4)))) mod (x + 3)))) mod (x + 1)) div 2) div 2))
A202084: 1 1 1 1 2 2 1 1 1 2 1 1 2 4 2 1
(~1 + (8 * ((3 * compr(\x.(1 - (x mod (2 + ((1 + ((x - ((x div 2) mod 2)) div 2)) mod 5)))),x)) div 2)))
A141175-A007522: 7 23 31 47 71 79 103 127 151 167 191 199 223 239 263 271
(1 - ((x div 15) + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))
A216219-A180181: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 0
(18 * (1 + (2 * ((1 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4)))) * (x mod 2)))))
A059137: 18 54 18 90 18 54 18 126 18 54 18 90 18 54 18 162
((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + ((2x + 1) div (3 + (x div 4))))
A059036: 0 1 1 2 3 2 3 5 5 3 4 7 8 7 4 5
((1 - (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((x - (x mod 5)) div 2)))) mod 5)
A283798: 1 1 1 1 0 1 1 3 3 1 1 0 4 0 1 1
(1 + (((1 + ((1 + (((2x + 2) * ((1 + (x div 4)) div 2)) div 3)) div 3)) div 2) + (x div 5)))
A120506: 1 1 1 1 2 3 3 3 3 3 4 5 6 6 7 8
(1 + (((1 + ((1 + ((1 + ((((x + ~1) * (x2 div 4)) div 2) div 3)) div 2)) div 2)) div 2) + (x div 5)))
A304885: 1 1 1 1 2 3 3 4 5 6 8 10 12 14 17 21
((1 + ((2 * (1 + (2 * (1 + (x mod (2 + (35 mod (x + 1)))))))) div 3)) div 3)
A113924: 1 1 1 2 1 3 1 1 4 1 1 5 1 2 1 1
(1 - ((2 * (1 + ((1 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) mod 8)) div 2))) div 3))
A110503: 1 1 1 1 ~1 1 1 ~2 1 1 1 ~1 1 ~1 1 1
(1 - (((((~1 + ((~2x + 2) mod (4 + (x div 4)))) mod (1 + (x2 div 4))) mod (x + 1)) div 2) mod 3))
A128190: 1 1 1 0 0 1 0 0 0 1 0 0 ~1 0 1 0
((2 * (2 + (7 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))) div 3)
A144395: 1 1 1 1 6 1 1 10 10 1 1 15 20 15 1 1
((8 * (1 + ((12x + 116) div 7))) div 3)
A295493: 45 50 56 58
((x + ~3) - (2 * (4 + (((x + 4) + ((x + 1) div (1 + (x div (2 + (x mod (2 + (x mod 2)))))))) div 2))))
A291575: ~15 ~16 ~15 ~16 ~15 ~18 ~15 ~16 ~15 ~16 ~15 ~18 ~15 ~16 ~15 ~16
(((x + 2) - (((~x + ~1) + (2 * ((x - ((x div (0 - (2 * (2 + (2x mod 5))))) mod 2)) mod 2))) div 2)) mod 3)
A287438: 0 1 2 1 2 0 2 1 0 1 2 0 2 1 0 0
((2 * (x + ((1 + (((1 + (((x + 1) * (1 + (2 * ((1 + ((x2 + x) div 2)) div 2)))) div 2)) div 2) div 2)) div 2))) mod 3)
A084934: 0 1 0 1 1 0 2 2 1 0 2 2 2 1 0 2
(1 - ((2 * ((x + 5) + ((1 + (20 div (x + 1))) mod 10))) mod 3))
A016242-A015780-A015472-A015318-A011642: 1 ~1 0 0 0 0 0 1 ~1 0 0 1 ~1 0 1 ~1
(((2x + 1) + (2 * ((1 + (((x + 2) * (1 + (3 * ((x2 + 2x) div 2)))) div 3)) div 3))) mod 3)
A258124: 1 2 2 1 2 1 2 2 0 0 2 2 1 2 0 0
(~1 + (2 * ((x + 1) + ((2 * (1 + (x2 div ((x + 1) + (6 * (1 + (x div 8))))))) div 3))))
A111622: 1 3 5 7 11 15 17 19 21 23 27 31 33 35 39 43
(1 + (((x + 1) + (((x + 1) + (((1 + ((((x + (x2 div 3)) * (2 + (x div 2))) div 2) div 2)) div 2) div 2)) div 2)) div 2))
A229769: 1 2 3 4 5 6 7 8 10 11 14 15 18 20 23 25
((2x + 1) - compr(\x.(~1 + (((1 - (2 * ((2x + 2) + ((x - (x div 4)) div 2)))) mod (x + 1)) mod 3)),x))
A071754: 1 2 2 3 4 5 6 7 7 7 7 7 8 9 10 10
(1 + compr(\x.(~1 + ((1 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) mod 9)) mod (x + 1))),x))
A198323: 1 2 3 4 5 6 7 8 9 10 11 15 16 19 22 25
((x + 1) + ((2 * ((x + 1) + (2 * ((31x + 31) div 9)))) div 3))
A190365: 5 11 18 24 31 36 43 49 56 62 67 74 80 87 93 100
compr(\x.(~1 + ((1 + (x mod (2 + (x div (1 + (x mod (1 + (x mod (1 + (x div (2 + (x div 5)))))))))))) mod (x + 1))),(x + 1))
A230374: 1 2 3 4 6 8 10 12 15 16 18 20 24 28 30 36
((1 + (2 * ((1 + ((((2x4 + 11x3 + 21x2 + 15x + 3) div 2) div 3) div 2)) div 2))) div (x + 1))
A227016: 1 2 7 14 27 45 69 101 141 191 252 323 408 506 618 746
((1 + ((((1 + (x mod (2 * (1 + (x mod (2 * (1 + (x mod (1 + (x div 3)))))))))) mod (x + 1)) div 2) + (x mod 2))) mod (x + 1))
A182850: 0 0 1 2 1 3 1 2 2 3 1 4 1 3 3 2
(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (2 * (x div (~1 - (x mod 5)))))) div 2))
A214986: 1 1 1 1 2 1 1 4 3 1 1 7 8 5 1 1
(3 - (2 * (1 + ((1 + ((x + 1) div (2 + ((x + 1) div (1 + ((x - (((x + ~1) div 2) div 3)) mod 3)))))) div 2))))
A123271: 1 1 ~1 1 ~1 ~1 1 1 ~1 ~1 1 ~1 ~1 ~1 1 ~1
(2 * (1 + ((1 + ((1 + (((x + 1) * (1 + ((1 + ((((x + 1) div (2 - (x mod 2))) div 2) div 2)) mod 2))) div 3)) div 2)) div 2)))
A049111: 2 4 4 4 4 4 4 6 4 6 4 4 4 4 6 8
(x - ((1 + ((3 * (x2 - ((14x3 + ~12x2 + ~2x) div 3))) div 2)) div 2))
A307253: 0 0 14 62 166 346 624 1020 1556 2252 3130 4210 5514 7062 8876 10976
((1 + ((x + 1) div (2 + ((~1 + (3 * (7 + ((x div 7) mod 2)))) mod (x + 1))))) div 2)
A125184: 0 1 0 1 1 1 0 0 1 1 2 0 1 1 1 1
((1 + (((3 * (1 + ((19x + 19) mod 11))) div 2) div 2)) div 2)
A190698: 3 2 1 4 3 2 1 4 3 2 0 3 2 1 4 3
(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (((x * (2 - (x mod 5))) div 2) div 2))) div 2))
A327785: 1 1 1 1 2 1 1 1 2 1 1 0 0 3 1 1
((1 + (x div 3)) div ((3 * (1 + ((x div 2) div (1 + (x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4)))))))))) div 2))
A113503: 1 1 0 2 0 0 0 3 1 1 0 1 0 0 0 6
((3 * (1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((x - (x mod 5)) div 2))))) div 2)
A056241: 1 1 1 1 3 1 1 6 6 1 1 10 19 10 1 1
((3 * (1 - (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (x div (~1 - (x mod 5)))))) div 2)
A162430: 1 1 1 1 3 1 1 6 4 1 1 10 13 7 1 1
((3 * ((x + 1) div (1 + (2 * ((2x + 1) div (3 + ((~2x + 2) mod (4 + (x div 4))))))))) div 2)
A343875-A343874: 1 0 1 0 1 1 0 1 1 1 0 1 3 3 1 0
((3 * (1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * ((1 + (x div 2)) div 2)))) div 2)
A063394: 1 1 1 1 3 1 1 7 7 1 1 15 19 15 1 1
((3 * (1 + (x div (2 + (x mod (2 + (x div (1 + ((((x + ~2) mod (2 - (x div ~3))) mod 2) + (x mod 2)))))))))) div 2)
A333752: 1 1 1 3 1 3 1 3 4 3 1 6 1 3 4 3
((3 * ((1 + (2 * (1 - (x mod (1 - ((2 - (2x mod (4 + (x div 4)))) mod (x + 1))))))) div 3)) div 2)
A180979-A174032: 1 1 1 1 3 1 1 4 4 1 1 7 10 7 1 1
(2 + (3 * (1 + ((3 * (1 + (2 * (1 + (2 * (1 + (2 * ((2x + 2) - (x mod 2))))))))) div 2) - (x mod 2))))
A039555: 107 140 251 284 395 428 539 572 683 716 827 860 971 1004 1115 1148
(x mod ((3 * (6 + ((1 + (2 * (2 + (23 mod (x + 1))))) div (x + 1)))) div 2))
A103303: 0 1 2 3 4 5 6 7 8 9
A047813: 0 1 2 3 4 5 6 7 8 9 1 11 2 3 4 5
((2 + ((2 * (1 + ((1 + (x2 mod (~1 + (4 * (2x div 3))))) div 2))) div 3) - (x mod 2)) div 2)
A029170: 1 0 1 1 1 1 2 1 2 2 2 3 4 3 5 5
((((x + ~1) + ((x mod 2) + ((2 * (2 + ((~1 + (x2 div (3 + (x div 4)))) div 2))) div 3))) mod (x + 1)) div 2)
A238209: 0 0 1 0 0 0 1 1 1 2 2 3 3 4 4 6
((2x + 2) + ((2 * (x + ((2 * ((2x + 2) - ((x - (x div 5)) div 3))) div 3))) div 3))
A189395: 2 6 10 12 16 20 23 26 30 34 37 40 44 47 50 54
(2 + (((x + 1) - (((3 * (1 + (2 * (2 + ((4x + (x2 div 4)) div (x + 2)))))) div 2) div 2)) div 2))
A029278: 1 0 0 1 0 1 1 1 2 1 2 2 2 3 3 4
(((5 * (1 + (2 * (((0 - (x mod (1 + (2 * (x div (2 * (2 + (x mod 2)))))))) mod (x + 1)) div 3)))) div 2) div 2)
A109647: 1 1 1 1 3 1 1 6 6 1 1 8 6 8 1 1
((2 + (5 * ((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~1) div 2))) div 3))) div 2)
A157636: 1 1 1 1 1 1 1 3 3 1 1 6 8 6 1 1
(1 - (((1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (x - (x div 4)))) div 2) div 2))
A176224: 1 1 1 1 0 1 1 ~2 ~2 1 1 ~6 ~8 ~6 1 1
(~2 + ((3 * (1 + ((2 * ((2x + 3) - ((~x + ((x div 3) mod 3)) div 3))) div 3))) div 2))
A286693: 2 5 7 8 11 14 16 17 20 23 26 28 29 32 35 37
(~2 + ((3 * ((x + 1) + ((2 * (1 + ((1 + ((((x + 2) * (2 + (x div 4))) div 2) div 2)) div 2))) div 3))) div 2))
A191535-A100598: 1 2 4 5 8 10
A138007: 1 2 4 5 8 10 11 13 17 19 20 23 26 28 31 34
(1 - (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 - (2 * ((1 + (x div 2)) div 2)))) div 2))
A176480: 1 1 1 1 2 1 1 4 4 1 1 9 11 9 1 1
(((((x + 1) * (6 + ((3 * ((12x + 12) div 5)) div 2))) div 2) div 2) div 2)
A007187: 1 3 6 9 15 20 26 34 41
((x + 12) + ((64x + 62) div (2x + 3)))
A345491: 32 38 41 43 44 46 47 49 50 51 52 53 54 55 56 57
(3 - (2 * (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) - ((2x + ~1) div (4 + (x div 4))))))
A204022: 1 3 3 5 3 5 7 5 5 7 9 7 5 7 9 11
((1 + (3 * (1 + ((19x + 19) mod 11)))) div 8)
A190704: 3 2 1 4 3 2 0 3 2 1 0 3 2 1 4 3
(((x * (1 + ((((x - ((x - (((x div 3) * (x div 2)) div 2)) div 2)) div 2) mod 2) + (2 * (x mod 2))))) div 3) div 4)
A037281: 0 0 0 1 0 1 0 1 1 2 0
A114325: 0 0 0 1 0 1 0 1 1 2 0 2 1 3 2 3
((x div (2 + (x mod (1 + ((x + 1) div (1 + (((2x div (1 + ((x + 1) div 5))) mod 2) + (x mod 2)))))))) + (x mod 2))
A318979: 0 1 0 2 0 2 0 3 0 2 0 4 0 2 1 4
((x + 1) + ((2 * (1 + (((x + 1) * ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4)))) div 3))) div 3))
A333645: 1 2 3 5 5 6 7 12 11 10 11 15 13 14 15 27
compr(\x.(x2 mod (1 + ((2 * (1 + (((((1 + (x mod 8)) mod (x + 1)) * (1 + (x div 2))) div 2) div 2))) div 3))),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A075905: 0 1 2 3 4 5 6 7 8 9 10 18 20 24 25 30
((x + 1) + (compr(\x.(2 - (((2 * ((1 + (x div 3)) * (1 + (x div 3)))) div 3) mod 5)),x) div 3))
A284681: 2 3 4 9 10 11 13 14 15 17 18 19 21 22 23 28
(x + ((2 * ((x + 2) + (2 * (x + ((x + (((3 * (x + (x div 7))) div 2) div 2)) div 2))))) div 3))
A058759: 1 4 8 13
A311848: 1 4 8 13 17 21 26 30 34 39 43 47 50 55 60 63
((3x + 1) + ((x + ((x + ((x + ((x + ((x2 + (x2 div 4)) div 3)) div 2)) div 2)) div 2)) div 2))
A058759: 1 4 8 13
A311808: 1 4 8 13 17 21 25 29 34 38 42 47 52 56 61 65
compr(\x.(1 - ((((2 * (1 + ((1 + (((2x3 + 5x2 + ~3x) div 2) div 3)) div 2))) mod (x + 1)) div 2) div 2)),x)
A132858: 4 6 8 9 10 14 15 16 18 20 21 22 25 26 27 28
compr(\x.(x - (2 * ((x + ((3 * ((~2 + ((2 * ((x2 + x) mod 9)) mod (x + 1))) div 2)) div 2)) div 2))),x)
A191920: 4 6 7 10 12 13 14 15 16 19 20 21 22 23 24 25
(1 + compr(\x.(~1 + loop(\(x,i).(if x <= 0 then 1 else loop(\(x,i).(if (x mod 2) <= 0 then 2 else loop(\(x,i).(~1 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)),x,x)),2,x)),2,x)),x))
A222011: 1 2 4 8
A074202: 1 2 4 8 14 16 22 26 28 32 38 42 44 50 52 56
loop(\(x,i).(x + (if x <= 0 then 1 else loop(\(x,i).(x - (if x <= 0 then 1 else (x - ((if x <= 0 then 2 else loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 2)))),x,x))),1,(x + ~1))
A008687: 0 1 1 2 1 3 2 2 1 4 3 3 2 3 2 2
(1 + (2 * compr(\x.loop(\(x,i).(if x <= 0 then 1 else (~2 + (if x <= 0 then 2 else (loop(\(x,i).(1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),2,x) mod (x + 1))))),x,x),x)))
A043725: 1 3 7 15 21 31 37 41 43 45 53 63 69 73 75 77
(loop(\(x,i).2x,x,1) div loop(\(x,i).(x + (loop(\(x,i).((if x <= 0 then 2 else loop(\(x,i).(x div (2 - (x mod 2))),x,x)) div 2),2,x) + ((x + 1) div 2))),x,1))
A225482: 1 0 0 1 1 1 1 2 2 3 4 4 6 8 10 12
loop(\(x,i).(x + loop(\(x,i).(x + loop(\(x,i).(x + loop(\(x,i).(x + (if x <= 0 then 1 else (1 + (11 * i)))),i,1)),i,1)),i,1)),x,1)
A056118: 1 16 81 266 686 1512 2982 5412 9207 14872 23023 34398 49868 70448 97308 131784
(2 * compr(\x.loop(\(x,i).(if x <= 0 then 1 else (~2 + (if x <= 0 then 2 else (loop(\(x,i).(1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),2,x) mod (x + 1))))),2,x),(x + 1)))
A043767-A043758-A043750-A043743-A043737-A043732-A043724-A043571: 10 18 20 22 26 34 36 38 40 44 46 50 52 54 58 66
(1 + loop(\(x,i).2x,x,(if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + loop(\(x,i).(1 + loop(\(x,i).(1 + (x2 * i)),x,2)),x,0)) div 2)) div 2))))))
A325624: 2 9 15625 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(1 + (2 * (1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(x2 + 3x)),x)))))
A109367: 9 25 49 121 169 361 529 625 841 961 1369 1681 2209 3025 4225 4489
(~1 + ((loop(\(x,i).(2x + 2),x,(1 + loop(\(x,i).2x,x,1))) div 2) + loop(\(x,i).2x,x,2)) - loop(\(x,i).(3x + 1),x,1))
A134045: 1 3 7 18 61 258 1177 5358 23821 103338 439297 1838598 7605781 31191618 127100617 515462238
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025929: 1 21 307 3969 48979 593817 7152139 85937313 1031713507 12382483113 148597656571 1783203843057 21398575559635 256783429254009 3081403255517803 36976847527073601
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025938: 1 19 237 2471 23429 210063 1818349 15380167 128060757 1054660607 8618507261 70035919863 566816115685 4573706232751 36824728021773 296008336113959
loop(\(x,i).2x,x,loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1))
A028019: 1 32 668 11536 179088 2599296 36043456 483836672 6341561600 81632911360 1036368313344 13015606775808 162070777434112 2004417298202624 24654551330373632 301916965980012544
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025958: 1 17 185 1645 13041 96117 674185 4565165 30122081 194911717 1242462585 7828123485 48869031121 302849847317 1865814241385 11440608686605
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A025967: 1 21 289 3321 34705 343257 3282913 30740457 283960369 2599944633 23667405697 214622461833 1941330570193 17530479823449 158125883415841 1425244488222249
loop(\(x,i).2x,x,loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1))
A028003: 1 30 592 9744 145264 2038176 27478144 360357888 4633015552 58698511872 735496093696 9137636831232 112771744215040 1384481544019968 16926102208872448 206237168590258176
loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025930: 1 16 165 1400 10661 75936 517525 3421000 22124421 140796656 885205685 5513890200 34098207781 209668346176 1283419890645 7827611393000
loop(\(x,i).(6x + loop(\(x,i).(2x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A025939: 1 20 265 2960 30301 295340 2795905 25996520 238988101 2181067460 19810829545 179385327680 1620996705901 14628147660380 131888407103185 1188406175868440
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025445: 1 16 167 1454 11529 86772 633739 4547818 32300477 228024368 1604029791 11260172742 78950652145 553177103404 3874344193523 27128870214626
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025960: 1 19 235 2415 22491 197799 1679875 13959055 114403531 929407479 7508252115 60439364895 485415209371 3892957335559 31192373841955 249784713973935
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A025976: 1 23 347 4363 49683 532491 5483299 54909371 538792595 5206523179 49719923331 470377414299 4416615113587 41215417310987 382666342963043 3537819931431547
loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025932: 1 18 213 2114 19173 165354 1384741 11393778 92748645 750039290 6040740069 48528576642 389243479717 3119026937226 24977625311397 199948094540306
loop(\(x,i).(8x + loop(\(x,i).(2x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A025948: 1 22 321 3938 44045 465894 4751017 47229226 460842789 4433881166 42195474113 398084143314 3729357886333 34737030515638 322015765266009 2973201855377402
loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A025961: 1 20 263 2902 29289 281472 2630731 24196634 220500797 1998686404 18061169919 162923877246 1468215185425 13223572329416 119060866122227 1071793518338338
loop(\(x,i).(4x + loop(\(x,i).(10x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025927: 1 19 245 2735 28701 293079 2957125 29682895 297294701 2974868039 29756539605 297597360255 2976103045501 29761552993399 297617634403685 2976184804896815
loop(\(x,i).7x,x,loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1))
A075923: 1 70 3185 120050 4084101 130590390 4012419145 120031392250 3525181576301 102196720335710 2935410756419505 83751552660170850 2377917929557166101 4611686018427387903 4611686018427387903
loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(5x + loop(\(x,i).(3x + 1),i,1)),i,1)),i,1)),x,1)
A000481: 1 15 140 1050 6951 42525 246730 1379400 7508501 40075035 210766920 1096190550 5652751651 28958095545 147589284710 749206090500
loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A025933: 1 19 240 2570 25391 240489 2226310 20352640 184772181 1670999759 15079423580 135917468310 1224272081371 11023527831829 99237160300050 893261534749580
loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).2x,((((1 + (8 mod (1 + (x div 2)))) div 2) + (if x <= 0 then 0 else 1)) - (x mod 2)),2),1,i)),x,1)
A064194: 1 3 7 9 17 21 25 27 43 51 59 63 71 75 79 81
((1 + ((loop(\(x,i).2x,(1 + loop(\(x,i).(x + (loop(\(x,i).(x * i),x,2) div (x + 1))),x,1)),1) div 2) * (1 + loop(\(x,i).2x,x,2)))) div 2)
A104603: 3 10 36 544 4611686018427387903
(2 * (1 + loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))))
A072056: 2 2 2 4 2 4 4 4 2 2 6 6 2 4 4 2
(if (x mod 2) <= 0 then ((1 + (2 * (if (x mod 2) <= 0 then (if (x mod 4) <= 0 then 13 else 2) else (x div 2)))) * (if x <= 0 then 1 else 2)) else 2)
A040727: 27 2 10 2 54 2 10 2 54 2 10 2 54 2 10 2
(((2 * ((x + loop(\(x,i).(if x <= 0 then 1 else (x - (if x <= 0 then 1 else (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))),2,x)) div 2)) div 3) * (x mod 2))
A336120: 0 0 0 1 0 2 0 2 0 4 0 4 0 8 0 5
(x + (if (x mod 2) <= 0 then (1 + loop(\(x,i).((x + 1) - (if x <= 0 then 1 else (if (x mod (1 + ((x + ~1) mod 9))) <= 0 then 2 else 0))),x,x)) else 1))
A257738: 1 2 3 4 5 6 7 8 9 10 11 12 25 14 33 16
loop(\(x,i).(1 + loop(\(x,i).(loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1)),1,12x)),1,x2)
A081508: 3 244672067 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).(x + 1),(if x <= 0 then 1 else ((2x + 1) - loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),2))),0)
A267445: 1 0 1 0 5 3 5 0 13 11 13 7 17 11 13 0
loop(\(x,i).(x2 + x),1,(((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1)))
A337524: 0 2 2 6 2 12 2 12 6 12 2 30 2 12 12 20
(loop(\(x,i).(2x + 1),x,0) mod loop(\(x,i).(~1 + (2 * (~1 + (2 * loop(\(x,i).x2,1,(11x + 5)))))),1,1))
A222010: 0 1 3 7
A305493: 0 1 3 7 15 31 63 127 255 511 2 5 11 23 47 95
(~1 + loop(\(x,i).2x,(1 + (2 * loop(\(x,i).(x * (1 + ((~1 + loop(\(x,i).12x,(x + 1),1)) mod (x + 1)))),x,1))),1))
A139314: 7 31 8191 2305843009213693951
(1 + (2 * (1 + (2 * (1 + (2 * compr(\x.(x - loop(\(x,i).loop(\(x,i).(if (x mod (2 + i)) <= 0 then 0 else x),x,(2x + 1)),2,(2x + 1))),x)))))))
A101789: 7 23 47 167 263 359 383 479 503 719 839 863 887 983 1319 1367
(1 + ((1 + (((loop(\(x,i).5x,x,1) - (loop(\(x,i).2x,x,2) + loop(\(x,i).3x,x,1))) mod (x + 1)) div 2)) div 2))
A235122: 1 1 2 2 2 2 2 2 3 3 3 4 4 4 3 2
(1 + ((1 + ((x * (1 + (2 * (((loop(\(x,i).(x2 + ~x),1,(loop(\(x,i).loop(\(x,i).2x,x,x),x,1) div 2)) div 2) div 2) div 2)))) div 2)) div 2))
A250495: 1 1 3 196418 4611686018427387903
(~1 + (2 * (if x <= 0 then 1 else loop(\(x,i).2x,((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3),2))))
A100587: 1 3 3 7 3 15 3 15 7 15 3 63 3 15 15 31
(5 * ((1 + (loop(\(x,i).(x * i),x,(loop(\(x,i).7x,x,1) + loop(\(x,i).3x,x,1))) div 2)) div 2))
A245648: 5 15 145 2775
(loop(\(x,i).x2,2,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div loop(\(x,i).3x,(x + 1),(x + 5)))
A034188: 1 1 3 3 6 3 3 1 1 0 0 0 0 0 0 0
((loop(\(x,i).10x,(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1))),1) div 3) div 3)
A038713: 1 11 1 111 1 11 1 1111 1 11 1 111 1 11 1 11111
(3 + (2 * (1 + compr(\x.(loop(\(x,i).(~2x + 4),(1 + loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x)),1) mod (x + 1)),x))))
A144742: 5 7 11 17 23 29 37 41 47 53 59 67 71 79 83 89
loop(\(x,i).x3,1,((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3))
A319089: 1 8 8 27 8 64 8 64 27 64 8 216 8 64 64 125
(~1 + (2 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) - compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x))))
A124115: 3 3 5 5 11 11 17 17 19 29 27 35 41 41 43 49
loop(\(x,i).(20x + loop(\(x,i).(4x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A080250: 1 35 871 19215 402591 8236095 166570111 3349906175 67183250431 1345516627455 26928850135551 538762184167935 10777095520297471 215560428864815615 4311393762242888191 4611686018427387903
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(9x + 1),i,1)),i,1)),x,1)
A024347: 1 28 523 8218 117649 1592416 20790631 264958246 3320750557 41132364364 505211150899 6167574174034 74958865496425 908053837462072 10973667150086527 132377759927894782
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A024435: 1 29 561 9121 134897 1882545 25284337 330685937 4242985713 53675466481 671774536433 8338419180273 102834889732849 1261772945322737 15418912066155249 187803876238668529
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(7x + 1),i,1)),i,1)),x,1)
A023953: 1 26 453 6682 90461 1166802 14626501 180228074 2197722861 26629669378 321427557269 3870666716826 46545364947901 559241602629554 6715873831334757 80625872396459338
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A020766: 1 29 571 9521 144907 2083865 28847827 388709777 5134091323 66784487561 858403625443 10928093824193 138039056180299 1732402968047417 21624191213455219 268679676312195569
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(5x + 1),i,1)),i,1)),x,1)
A022456: 1 25 422 6074 80739 1027731 12764344 156290788 1897808357 22932373997 276311410986 3323658428142 39939656787655 479667696880423 5758762699959548 69124442908248536
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).10x,i,1)),i,1)),x,1)
A020974: 1 29 567 9337 139775 1971417 26715823 352001609 4543901439 57765992185 725866130639 9039113138601 111770394659743 1374351994892633 16823974751541615 205209952708309513
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(9x + 1),i,1)),i,1)),x,1)
A024778: 1 30 595 9840 147061 2063010 27740215 362136180 4628090521 58232585190 724277646235 8930528438520 109397647960381 1333481828166570 16193198750646655 196081347032548860
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A025007: 1 31 635 10835 166851 2407971 33252835 445002595 5818890851 74768679011 947871169635 11890741318755 147930305201251 1828206048535651 22473922782504035 275081786101769315
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(7x + 1),i,1)),i,1)),x,1)
A024440: 1 28 521 8132 115425 1547436 20005177 252510484 3136438289 38534838524 469928249193 5701527366756 68933583580993 831438081590092 10011928868278169 120426060354676148
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A020981: 1 31 645 11255 177821 2636991 37440565 515147335 6923011341 91364030351 1188608942885 15286543614615 194762842152061 2462271368182111 30927944350627605 386358083836485095
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A022000: 1 28 533 8648 128889 1824276 24950461 333078016 4367420897 56484732044 722650676709 9164986526904 115404823162825 1444532800672132 17990818115880077 223110488408176112
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).(9x + 1),i,1)),i,1)),x,1)
A023772: 1 27 490 7530 105991 1416477 18318520 231807060 2890036381 35658042927 436707179350 5319843165390 64552636279171 781063825879377 9430663254710980 113689073300930520
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A023947: 1 28 527 8390 122121 1683768 22407907 291019450 3713967341 46787388908 583658682087 7226065372110 88934701511761 1089437114484448 13295459966641067 161767703674942370
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).13x,i,1)),i,1)),x,1)
A124099: 1 30 619 10920 177061 2726130 40547359 588485820 8387148121 117876868230 1638536364499 22574666496720 308755233696781 4197234089634330 56765041887676039 764357559726523620
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A020569: 1 28 537 8780 131681 1872828 25708777 344166700 4522666161 58593270428 750663052217 9530987332620 120125429898241 1504795780456828 18753752307454857 232703290568738540
loop(\(x,i).(12x + loop(\(x,i).(3x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021734: 1 27 502 8022 118363 1663809 22644784 301210524 3938740405 50831269671 649205557546 8222000492706 103410878533327 1293146143620813 16092125344053988 199423591976817768
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(9x + 1),i,1)),i,1)),x,1)
A023950: 1 23 348 4378 49679 528381 5380306 53132816 513181317 4875626899 45752166824 425305531014 3925114125115 36023250380777 329183853207102 2998041099306172
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A023951: 1 24 381 5056 60837 689640 7521277 79922832 834214293 8599137976 87862904493 892165074528 9019015091269 90887374167432 913848341454429 9173869834986544
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A020573: 1 24 391 5406 68497 824460 9612667 109824522 1238345653 13843811256 153896453503 1704525493398 18833608743769 207769555090212 2289742482517699 25217579128356834
loop(\(x,i).(6x + loop(\(x,i).(9x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A024170: 1 26 447 6412 83153 1012158 11803219 133502864 1476280245 16046160130 172084379831 1825884161556 19206817023577 200615621740742 2083177317949083 21525527306347288
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A023956: 1 26 449 6502 85581 1063194 12725545 148560206 1704811493 19330213474 217323204033 2428517447382 27020001684157 299686169462186 3316371108572633 36639232372189150
loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A022412: 1 23 356 4690 57015 663621 7538098 84446336 938561525 10384529155 114604142016 1262952525198 13906624731091 153059279644385 1684178151097070 18529154259093436
loop(\(x,i).(6x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A020726: 1 27 493 7599 106645 1411431 17955757 222093423 2690508229 32080473975 377794514461 4405195463487 50953884924853 585473143132359 6690087028209805 76090252032830991
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(9x + 1),i,1)),i,1)),x,1)
A024437: 1 25 410 5570 67971 774075 8402620 88071940 898959941 8988218525 88404153630 858025759110 8237487011911 78372461725375 740024044725440 6943130337867080
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A024438: 1 26 445 6330 81141 973746 11173405 124182410 1348136581 14378944866 151299635565 1575384732090 16269102500821 166926103626386 1703932925460925 17322243189947370
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A020968: 1 26 455 6700 89661 1130766 13712035 161844800 1874156921 21406992706 242089527615 2717862993300 30349359729781 337562780465846 3743627395703195 41428143398876200
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021884: 1 23 358 4758 58419 686541 7864936 88727036 991573957 11016698979 121950785034 1346833901634 14852822151415 163644677778137 1801937252261452 19834231783445352
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).(9x + 1),i,1)),i,1)),x,1)
A022453: 1 22 320 3890 42861 444612 4433080 43016380 409466321 3843870602 35717758440 329381322270 3020187550381 27573503381992 250911867832400 2277497319225560
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A022454: 1 23 352 4530 53151 590373 6335302 66471680 687035701 7029030723 71413230252 722053798830 7276293638251 73154751811073 734297855505202 7362269063785980
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A020000: 1 23 362 4870 60411 715533 8243572 93366380 1046230421 11644889443 129058033182 1426436938290 15738640474831 173461105001753 1910430676985192 21031277618176600
loop(\(x,i).(7x + loop(\(x,i).(3x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021614: 1 22 332 4322 52353 609924 6948544 78112924 871004585 9663416906 106874239836 1179653481006 13004446987897 143246730136168 1577098731557408 17357778969071768
(if x <= 0 then 3 else ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))))
A125266: 3 1 2 2 4 2 4 2 4 6 2 6 4 2 4 6
(1 + compr(\x.(loop(\(x,i).(x2 + x),1,(~1 + (loop(\(x,i).(2x + 2),x,2) mod loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))) mod (x + 1)),x))
A241071: 1 2 4 6 8 10 12
A267817: 1 2 4 6 8 10 12 16 18 20 24 30 32 36 40 42
loop(\(x,i).(8x + loop(\(x,i).(9x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A024771: 1 28 515 7850 107481 1373088 16714975 196403350 2246489861 25160397548 277090599435 3010102678050 32332333478641 344033387428408 3631750686931895 38080468894107950
loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A022628: 1 25 418 5898 76059 930003 10996396 127188916 1449394837 16348318701 183083516694 2039995806654 22648876033135 250810539522919 2772306789414112 30602539667823912
loop(\(x,i).(8x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A020979: 1 29 563 9145 134211 1845249 24249163 308352185 3824765171 46535545969 557596038363 6599196683625 77316285612931 898280118486689 10363489117309163 118857642802045465
loop(\(x,i).(9x + loop(\(x,i).(4x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021964: 1 25 422 6050 79563 993675 12002224 141692500 1645717205 18887136125 214818117306 2426541462150 27263857999327 305049644712175 3401871310224068 37837512809631800
loop(\(x,i).(9x + loop(\(x,i).(5x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A022845: 1 25 416 5810 73731 881895 10139746 113382280 1242174461 13399350965 142804173876 1507398751950 15788505813991 164317248669235 1701069830850806 17531812552906820
loop(\(x,i).(9x + loop(\(x,i).(3x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021694: 1 24 394 5544 71995 891408 10701748 125788848 1456313749 16673208552 189289198462 2135136588312 23963101915663 267883518461856 2985323286760936 33185997429018336
loop(\(x,i).(4x + loop(\(x,i).(10x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021984: 1 26 457 6822 93333 1210938 15168529 185357774 2224062445 26316305730 307996949481 3573147901206 41156463852037 471239561238602 5368820120200513 60908872219620318
loop(\(x,i).(5x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A020567: 1 26 461 6946 95781 1250466 15739501 193056386 2323229621 27553572706 323079534141 3753826047426 43291842381061 496209045488546 5658293396858381 64241196847864066
loop(\(x,i).(11x + loop(\(x,i).(7x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A020971: 1 27 490 7470 103291 1343097 16753780 202932540 2405791381 28065859767 323426323870 3691983687210 41834308968271 471276683342037 5284615302054760 59040661951743480
loop(\(x,i).(11x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),x,1)
A020982: 1 30 601 10050 151501 2135070 28702801 372684090 4712104501 58346365110 710428956601 8532288986130 101313313019101 1191569650755150 13901375026212001 161062105099480170
loop(\(x,i).(3x + loop(\(x,i).(10x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A021714: 1 25 428 6278 84879 1092243 13601506 165488176 1979095877 23357343581 272803757304 3159571375194 36342586372795 415641464948839 4730786270092622 53625950549096132
((x + 2) + compr(\x.(~1 + ((2 * (1 + loop(\(x,i).loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1,(3x + 3)))) mod 3)),x))
A185871: 5 12 14 23 25 27 38 40 42 44 57 59 61 63 65 80
((1 + (x mod 2) - (loop(\(x,i).2x,x,1) + loop(\(x,i).2x,(x - (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))),1))) mod (x + 1))
A141564: 0 1 2 1 4 2 6 1 2 4 10 2 12 6 8 1
(2 * loop(\(x,i).(x + loop(\(x,i).(loop(\(x,i).3x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1) div 3),1,i)),x,0))
A160716: 0 2 4 10 12 18 24 42 44 50 56 74 80 98 116 170
(loop(\(x,i).2x,x,(1 + ((1 + ((loop(\(x,i).x3,1,(1 + loop(\(x,i).(x * i),x,1))) div 3) div 3)) div 3))) div 2)
A327145: 0 1 4 56 4640
((1 + ((loop(\(x,i).7x,x,1) + loop(\(x,i).6x,x,1)) div loop(\(x,i).5x,x,1))) div 2)
A136422: 1 1 2 2 3 4 5 7 10 13 18 24 33 45 62 85
((1 + (3 * (if (x mod 2) <= 0 then (3 * (if (x mod 4) <= 0 then (3 * (2 + (if x <= 0 then 0 else 2))) else 1)) else 1)) - (x mod 2)) div 2)
A040748: 27 1 5 1 54 1 5 1 54 1 5 1 54 1 5 1
(2 * (1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(11x + 9)),x)))
A107960: 4 10 12 18 22 24 28 34 40 42 52 54 60 70 78 88
((1 + (if x <= 0 then 0 else (2 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))))) div 2)
A162800: 0 2 4 6 9 12 15 18 21 26 30 34 39 42 45 50
(((compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) + loop(\(x,i).2x,x,1)) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) div 2)
A018251: 1 2 3 6 9 18
A085431: 1 2 3 6 9 18 33 66 131 257 515 1026 2049 4098 8195 16387
(loop(\(x,i).(loop(\(x,i).4x,x,1) - loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,(3x + 1))),1,(x + 1)) div 2)
A006419: 0 1 7 37 176 794 3473 14893 63004 263950 1097790 4540386 18696432 76717268 313889477 1281220733
(((2 * (1 + ((x mod (1 + loop(\(x,i).(1 + (((x + ~1) + loop(\(x,i).(x - (if x <= 0 then 0 else i)),x,x)) mod (x + 1))),2,x))) div 2))) mod (x + 1)) div 2)
A229878: 0 0 1 0 1 2
A051010: 0 0 1 0 1 2 0 1 1 2 0 1 2 3 2 0
(2 * (1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(21x + 20)),x)))
A124198: 2 6 10 16 18 20 22 26 30 32 36 42 46 48 50 52
(2 * (1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(17x + 12)),x)))
A138628: 4 10 12 22 24 30 34 40 48 52 54 60 72 78 88 90
(x - (((~1 + (2 * compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(2x div 3)),(x + 1)))) div 2) div 2))
A112310: 0 1 1 2 2 2 3 2 3 3 3 4 3 3 4 3
(~2 + loop(\(x,i).(x + i),((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3),2))
A184389: 1 3 3 6 3 10 3 10 6 10 3 21 3 10 10 15
((2 + (loop(\(x,i).(~1 + (3 * (1 + (x div (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))))),2,x) div 3)) div 2)
A143773: 1 1 1 2 1 2 1 3 2 3 1 5 1 4 3 6
(~2 + (2 * (1 + compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(11x + 8)),x))))
A108725: 0 2 8 12 14 20 24 30 44 48 50 54 62 72 78 90
(loop(\(x,i).((x + 1) * (1 + (2 * ((loop(\(x,i).6x,(x + 1),1) + loop(\(x,i).(2x + 2),x,2)) mod (x + 1))))),2,x) div 2)
A081618: 1 7 232 430
(~2 + loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) - compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))
A062235: 1 4 18 38 108 152 270 338 500 810 924 1328 1638 1802 2156 2750
(loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) * (2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)))
A251720: 12 45 175 539 1573 2873 5491 8303 15341 26071 35557 56129 72283 86903 117077 165731
(loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) mod (2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)))
A167770: 1 4 4 5 4 16 4 16 7 4 36 16 4 16 36 36
loop(\(x,i).x2,1,((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))))
A166329: 36 225 1225 5929 20449 48841 104329 190969 444889 808201 1315609 2301289 3108169 4084441 6205081 9778129
(loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x))) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))
A179397: 1 1 1 1 3 10 2 5 18 6 7 36 36 14 3 11
((~x + 1) - loop(\(x,i).(loop(\(x,i).6x,x,1) - loop(\(x,i).7x,x,1)),x,8x))
A307846: 1 4085185
(2x + (if x <= 0 then 1 else loop(\(x,i).(x - ((if x <= 0 then 1 else (2 * (2 + ((x + ~1) div 13)))) div 2)),1,(x + ~1))))
A145441: 1 2 3 6 9 12 15 18 21 24
A308012: 1 2 3 6 9 12 15 18 21 24 27 30 33 36 39 41
loop(\(x,i).12x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165833: 1 12 12 144 12 144 12 1728 144 144 12 1728 12 144 144 20736
loop(\(x,i).10x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165831: 1 10 10 100 10 100 10 1000 100 100 10 1000 10 100 100 10000
loop(\(x,i).7x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165828: 1 7 7 49 7 49 7 343 49 49 7 343 7 49 49 2401
(1 + (x div (1 + (x mod (1 + ((~1 + (2 * loop(\(x,i).x2,1,loop(\(x,i).((2 * (x - (2x * i))) div (1 + i)),x,1)))) mod (x + 1)))))))
A093527: 1 1 3 2 5 1 7 4 9 5 11 3 13 7 1 8
(1 + (x mod (1 + ((~1 + loop(\(x,i).x2,1,(1 + (x mod (1 + (loop(\(x,i).2x,x,(1 + (x mod 2))) mod (2x + 1))))))) mod (x + 1)))))
A071975: 1 2 3 1 5 6 7 4 1 10 11 3 13 14 15 1
(1 + (x div (if (x mod 2) <= 0 then 1 else (1 + ((1 - ((1 + ((2 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 3)) mod 3)) mod (x + 1))))))
A237517: 1 2 3 4 5 1 7 8 9 5 11 1 13 7 15 16
(x div (1 + ((x + 1) div (~1 + (2 * (1 + (((~1 + loop(\(x,i).2x,x,(if ((x + (x div 2)) mod 4) <= 0 then 2 else 1))) mod (x + 1)) div 2)))))))
A086798: 0 0 0 1 0 0 0 3 4 0 0 2 0 0 2 7
(~1 + loop(\(x,i).(10x + ~1),(2x + 1),1) - loop(\(x,i).10x,x,7))
A332181: 1 818 88188 8881888 888818888 88888188888 8888881888888 888888818888888 88888888188888888 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (5 * (loop(\(x,i).(10x + 3),2x,1) - loop(\(x,i).10x,x,1))))
A332161: 1 616 66166 6661666 666616666 66666166666 6666661666666 666666616666666 66666666166666666 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + ((((2 * (4 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1)) mod 3))
A210826: 1 ~1 ~1 0 ~1 1 ~1 1 0 1 ~1 0 ~1 1 1 ~1
(~1 + ((1 + ((compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x) - compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)) div 2)) mod 3))
A341952: 1 1 ~1 1 ~1 1 ~1 0 1 0 ~1 1 ~1 0 0 1
(if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (((~1 + loop(\(x,i).2x,(x - (x div 8)),2)) mod (x + 1)) div 2)) div 2))) div 3)))
A284257: 0 1 1 2 1 2 1 3 2 1 1 3 1 1 2 4
(1 + ((2 * (1 + ((1 + (((1 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),x,(2x + 1))) div 2) div 2)) div 2))) div 3))
A274515: 1 1 2 2 1 3 3 2 3 3 2 3 3 1 4 4
(~1 + (6 * (1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(6x + 1))),x)))))
A068230-A040117: 5 17 29 41 53 89 101 113 137 149 173 197 233 257 269 281
(1 + (6 * (1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(6x + 2))),x)))))
A068229: 7 19 31 43 67 79 103 127 139 151 163 199 211 223 271 283
((x + 1) - ((x + 1) mod ((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3)))
A161654: 1 2 2 3 4 4 6 8 9 8 10 12 12 12 12 15
loop(\(x,i).6x,(2 * ((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1))),1)
A165857: 1 36 36 1296 36 1296 36 46656 1296 1296 36 46656 36 1296 1296 1679616
loop(\(x,i).5x,(2 * ((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1))),1)
A165846: 1 25 25 625 25 625 25 15625 625 625 25 15625 25 625 625 390625
(1 + (2 * (1 + compr(\x.(loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x) + ((3x + 2) mod 7)),x))))
A045471: 11 53 67 109 137 151 179 193 263 277 347 389 431 487 557 571
(3 + (((1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (1 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) div 2))
A201498: 4 7 15 33 63 99 147 201 311 423 543 723 843 969 1199 1511
(loop(\(x,i).(x5 + ~x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 15)
A138429: 2 16 208 1120 10736 24752 94656 165072 429088 1367408 1908608 4622928 7723744 9800560 15289664 27879696
(loop(\(x,i).(x * (x4 div 2)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 15)
A138430: 1 8 104 560 5368 12376 47328 82536 214544 683704 954304 2311464 3861872 4900280 7644832 13939848
((6 * (if (x mod 2) <= 0 then ((~1 + (9 * (2 - ((x div 2) mod 2)))) * (if x <= 0 then 1 else 2)) else 1)) div 5)
A040418: 20 1 19 1 40 1 19 1 40 1 19 1 40 1 19 1
((loop(\(x,i).(x2 * (x4 div 2)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 5)
A122220: 3 36 780 5880 88572 241332 1206864 2352276 7401768 29741124 44375136 128286252 237505128 316068060 538960656 1108217916
(1 + (((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3) + (2 * (x mod 2))))
A037852: 2 5 3 6 3 7 3 7 4 7 3 9 3 7 5 8
((1 + ((1 + (2 * (if (x mod (1 + (2 * (x mod 4)))) <= 0 then 1 else loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))) div 3)) div 3)
A245536: 0 0 1 0 0 1 2 0 0 0 0 1 0 2 3 0
((1 + (loop(\(x,i).(2x + 2),(if x <= 0 then 1 else (2 * (1 + (x div (2 + (x div (1 + (x mod (2 * (1 + (x mod 2))))))))))),1) div 2)) div 3)
A174354: 1 2 2 8 2 8 2 32 2 8 2 32 2 8 2 128
((2 * (1 + ((loop(\(x,i).2x,x,(3 + (2 * (2 + loop(\(x,i).4x,x,2))) - (x mod 2))) div 2) div 3))) div 3)
A243693: 1 5 32 233 1833
((2 * (1 + ((1 + ((x + (((~1 + ((x + 1) * (if (x div 2) <= 0 then 1 else ((if (x mod 2) <= 0 then 2 else x) div 2)))) div 2) div 2)) div 2)) div 2))) mod 3)
A004578: 2 2 1 1 1 0 0 2 2 0 2 2 1 0 1 0
(((1 + (((1 + ((loop(\(x,i).2x,x,(loop(\(x,i).((x2 + ~x) div 2),2,(x + 1)) div 3)) div 2) div 2)) div 2) div 2)) div 2) mod 3)
A093315: 0 0 0 1 2 2 2 0 0 0 0 1 1 0 1 1
(if x <= 0 then 1 else (6x - ((2 * ((2x + 2) + (x div (1 + (2 * (if (~4 + (x div 2)) <= 0 then 2 else 1)))))) div 3)))
A058759: 1 4 8 13
A312077: 1 4 8 13 18 22 26 31 36 40 44 48 52 57 62 66
((2 * (2 + ((1 + ((1 + (((x + 1) * loop(\(x,i).(2x + 1),x,loop(\(x,i).2x,x,1))) div 3)) div 3)) div 2))) mod 3)
A242086: 1 0 1 0 1 0 0 1 0 1 0 2 0 1 0 0
(((loop(\(x,i).(x6 + ~x4),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 2) div 3)
A138459: 4 54 1250 9604 146410 399854 2004504 3909630 12313004 49509670 73881680 213654354 395606540 526495354 897861304 1846372554
(((loop(\(x,i).(x4 * (x2 div 2)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 2) div 3)
A138458: 2 27 625 4802 73205 199927 1002252 1954815 6156502 24754835 36940840 106827177 197803270 263247677 448930652 923186277
(~1 + ((if x <= 0 then 1 else 4x) + ((2 * ((x + 2) + ((2 * ((x + (if (~2 + (x div 2)) <= 0 then 1 else 0)) div 2)) div 3))) div 3)))
A315032: 1 5 9 15 19 25 29 34 39 43 49 53 59 63 68 73
(1 + (2 * (((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1))) - (x mod 2))
A086369: 1 2 3 4 3 6 3 6 5 6 3 10 3 6 7 8
(x mod (x - (if x <= 0 then 1 else (1 + (if (x mod 5) <= 0 then 1 else ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) - (x mod 2)))))
A076473: 0 0 0 0 0 1 1 1 2 0 2 1 3 1 1 1
(1 + compr(\x.(loop(\(x,i).(18 * (~1 + ((x + 1) * loop(\(x,i).x2,2,4)))),2,5) mod (x + 1)),x))
A343238: 1 2 3 5 6 7 9 10 14 15 18 21 23 27 29 30
((x2 + 2x + 1) * ((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3))
A034714: 1 8 18 48 50 144 98 256 243 400 242 864 338 784 900 1280
loop(\(x,i).6x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),(x + 1))
A166627: 1 12 18 144 30 216 42 1728 324 360 66 2592 78 504 540 20736
loop(\(x,i).8x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),(x + 1))
A166629: 1 16 24 256 40 384 56 4096 576 640 88 6144 104 896 960 65536
loop(\(x,i).5x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),(x + 1))
A166626: 1 10 15 100 25 150 35 1000 225 250 55 1500 65 350 375 10000
((2 - (x mod (if (x mod 2) <= 0 then (1 - ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 9)) else 1))) mod (x + 1))
A325273: 0 0 1 2 2 2 3 2 2 2 4 2 2 2 2 2
(loop(\(x,i).(3x + 2),(x div (2 + (x div (1 + (((if (x mod 2) <= 0 then 1 else x) mod 4) + ((x mod 3) div 2)))))),1) div (x + 1))
A260649: 1 0 1 1 1 0 0 2 1 0 0 1 0 0 1 3
((1 + (2 * ((x + 1) - loop(\(x,i).(1 + (((2 + ((x2 div 2) div 5)) div 3) + (if x <= 0 then 0 else 1))),2,x)))) mod (x + 1))
A341019: 0 1 0 1 2 3 4 3 4 5 6 7 6 7 6 5
((4x + 4) * ((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3))
A145229: 4 16 24 48 40 96 56 128 108 160 88 288 104 224 240 320
((2 + compr(\x.(~1 + ((1 + (if (x mod 3) <= 0 then 0 else (if ((1 + (x div 3)) mod 5) <= 0 then 2 else 1))) mod 3)),x)) mod (x + 1))
A260644: 0 1 2 3 4 3 2 1 2 3 4 5 4 3 2 3
((x + 1) + loop(\(x,i).x2,1,((if (x + ~1) <= 0 then 1 else (2 * (((x2 mod (x - ((~x + 2) div 2))) div (x + 1)) + (x mod 2)))) - (x mod 2))))
A056896: 2 2 3 5 5 7 7 17 13 11 11 13 13 23 19 17
loop(\(x,i).(x + loop(\(x,i).(2 * (1 + (((1 + (x mod ((1 + (x mod (1 + (x div 4)))) * (1 + (x mod 2))))) mod (x + 1)) div 2))),1,i)),x,1)
A101114: 1 3 5 9 11 15 17 23 27 31 33 41 43 47 51 61
((if x <= 0 then 2 else (1 + ((x + 1) mod (1 + ((1 + (x mod (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))) mod (x + 1)))))) div 2)
A331416: 1 0 0 1 0 0 0 1 1 0 0 0 0 0 2 1
(if x <= 0 then 1 else (2 * ((2x + 1) - ((2 * ((2x + 2) + (x div (1 + (2 * (if (~4 + (x div 2)) <= 0 then 2 else 1)))))) div 3))))
A045999: 1 2 2 4 6 6 6 8 10 10 10 10 10 12 14 14
((x + 1) div (if x <= 0 then 1 else (2 * (1 + ((1 + (loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) mod (2x + 3))) div 2)))))
A029396: 1 0 0 0 0 1 0 1 1 0 1 0 2 1 1 2
((x + 1) div (2 * (1 + ((1 + (loop(\(x,i).(2 + (x div (1 + (2 * (x mod 2))))),1,(1 + (if (~1 + (x mod 3)) <= 0 then x else 2))) div 2)) div 2))))
A293909: 0 0 0 0 1 1 1 1 2 1 2 3 2 1 3 1
((1 + ((1 + (((1 + (2 * (1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) + (((x + 1) div 2) div 2))))) mod (x + 1)) div 2)) div 2)) div 2)
A333365: 0 0 1 0 1 1 1 0 1 1 1 2 0 0 1 2
((1 + ((if x <= 0 then 2 else (1 + loop(\(x,i).(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) - (i div 3)),2,x))) div 2)) div 2)
A221833: 1 0 1 0 1 1 0 0 2 1 0 0 3 3 1 0
(if x <= 0 then 1 else (2 * (1 + (((~1 + loop(\(x,i).2x,x,(1 + (2 * (((2x + 1) mod (2 + (x div 4))) div 2))))) mod (x + 1)) div 2))))
A284011-A278524-A278523-A278237-A275468-A083260-A071364-A046523: 1 2 2 4 2 6 2 8 4 6 2 12 2 6 6 16
(2 + (5 * (1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(5x + 2))),x)))))
A030432: 7 17 37 47 67 97 107 127 137 157 167 197 227 257 277 307
((if (x mod 7) <= 0 then loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) else 17) mod 10)
A083947: 1 7 7 7 7 7 7 1 7 7 7 7 7 7 5 7
(2 + (3 * (2 + (loop(\(x,i).(10x + 3),2x,2) + loop(\(x,i).10x,x,1)))))
A171766: 17 737 70307 7003007 700030007 70000300007 7000003000007 700000030000007 70000000300000007 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 1 else (2 * (4x - ((2 * ((2x + 2) + (x div (1 + (2 * (if (~4 + (x div 2)) <= 0 then 2 else 1)))))) div 3))))
A312658: 1 4 8 14 20 24 28 34 40 44 48 52 56 62 68 72
((1 + (if x <= 0 then 1 else (2 * (1 + compr(\x.(~1 + (loop(\(x,i).(2x + 1),(x div (1 + (x mod 2))),1) mod (x + 1))),(x + 1))))) - (x mod 2)) div 2)
A176175: 1 3 5 6 7 10 11 13 14 17 19 22 23 26 29 31
(2 * ((2 * ((1 + (loop(\(x,i).2x,((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3),1) div 2)) div 2)) mod (x + 1)))
A345450: 0 0 0 4 0 4 0 4 4 4 0 8 0 4 4 0
(((1 + (((1 + loop(\(x,i).2x,x,1) - (2 * ((1 - loop(\(x,i).((x2 + ~x) div (1 + i)),2,(x + ~1))) div 2))) div 2) div 2)) div 2) div 2)
A261667: 0 0 0 0 1 2 6 12 25 48 90
(2 * ((1 + (((((x + ~1) * (1 + (loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),x,(1 + (x div 2))) div 2))) div 2) div 2) div 2)) div 2))
A086973: 0 0 0 0 0 0 2 2 2 4 2 2 6 6 8 8
(8 * ((x + 2) - ((x + 1) div (if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 2)))))))
A244371: 8 16 24 32 32 48 40 64 64 80 56 96 64 104 104 128
(((1 + ((2 * (2 + compr(\x.(loop(\(x,i).((x + 2) * loop(\(x,i).x2,2,(x + 2))),2,1) mod (x + 1)),x))) div 3)) div 2) mod 8)
A274913: 1 2 3 1 4 1 2 3 2 3 1 4 1 4 1 2
(1 - (2 * ((~2 + (x mod (~1 - (if (x mod 5) <= 0 then 2 else 0))) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) div 2)))
A261033: 3 5 7 9 13
A157048: 3 5 7 9 13 15 19 21 25 31 35 39 43 45 49 55
(4x + (if x <= 0 then 1 else (((2x + ~1) + (2 * ((4 * (x + (if (~2 + (x div 2)) <= 0 then 1 else 2))) div 3))) div 3)))
A314221: 1 5 11 17 22 28 34 40 45 51 57 62 67 73 79 84
(((x + 1) + ((2 * (1 + (if x <= 0 then 0 else (if x <= 0 then 1 else (2 * compr(\x.(1 - (x mod (1 + (2x mod (1 + (x div 2)))))),x)))))) div 3)) div 2)
A167376: 0 4 6 8 9 10 12 13 14 16 17 18 19 20 21 23
(if x <= 0 then 1 else ((2x + ~1) + ((2 * (2x + loop(\(x,i).((x + 1) + (((2x + ~4) div (2 + (x div 2))) mod 2)),x,1))) div 3)))
A058759: 1 4 8 13
A311795: 1 4 8 13 17 21 25 29 33 37 41 45 49 53 58 63
((2x + ~1) + (2 * (1 + (x div (3 * (2 + ((1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)) mod (x + 1))))))))
A165704: 1 3 5 7 9 11 15 15 17 19 23 23 29 29 29 33
(2x + ((1 + (2 * (if x <= 0 then 1 else (2 * (2x + ((2 * (x + (if (~2 + (x div 4)) <= 0 then 1 else 2))) div 3)))))) div 3))
A315702: 1 6 12 17 23 29 33 39 45 50 56 62 68 74 79 85
(if (x div 5) <= 0 then (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) else (36 + (x div 2)))
A195337: 2 3 5 7 11 38 39
((if (x mod 4) <= 0 then 1 else (if x <= 0 then 0 else (1 + (x div (1 + (2 * (1 + (((x2 + ~x + 2) mod (x + 4)) div 2)))))))) + (x mod 2))
A036989: 1 2 1 3 1 2 2 4 1 2 1 3 1 3 3 5
(~x + ((1 + ((1 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))) div 2)) div 2))
A024683: 0 0 0 0 0 1 1 2 2 4 5 6 7 8 8 10
(2x + (if x <= 0 then 1 else ((2x + ~1) + ((2 * (2 + (((x + 1) + (if (x mod 4) <= 0 then 2x else (x div 2))) div 2))) div 3))))
A314776: 1 5 9 13 20 23 27 31 40 41 45 49 60 59 63 67
(1 + (x div (1 + (x mod (1 + (x mod (1 + (x div (2 + (if x <= 0 then 0 else (1 + ((x div (1 + (2x mod 3))) mod 2) - (x mod 2))))))))))))
A280697: 1 2 3 2 5 2 7 2 3 5 11 3 13 2 5 4
(1 + (x mod (1 + (x mod (1 + ((~1 + loop(\(x,i).(x2 + ~x),1,(~1 + ((~2x + 2) mod (4 + (x div 4)))))) mod (x + 1)))))))
A324646: 1 2 3 2 1 6 1 2 3 10 1 6 1 2 15 2
(if x <= 0 then 2 else (1 + ((x + 1) mod (1 + ((1 + (x mod (1 + (2 * (x div (1 + (2 * (x mod (2 + (x mod (2 + (x mod 2)))))))))))) mod (x + 1))))))
A162154: 2 1 1 1 1 3 1 1 1 3 1 1 1 3 1 5
(1 + ((2 * loop(\(x,i).x2,1,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))) mod 7))
A338878: 1 1 1 1 3 1 1 2 2 1 1 5 5 5 1 1
(2 div (1 + (if x <= 0 then 0 else (1 + ((((2 * ((x div (4 + (8 mod (1 + (x div 2))))) + (x mod 2))) mod (x + 1)) div 2) mod 2)))))
A145679: 2 1 1 0 1 0 0 1 0 1 0 1 1 0 0 1
(1 + ((1 + ((((x + 1) * loop(\(x,i).x2,2,((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2))) div 2) div 3)) div 3))
A299521: 1 1 1 1 1 1 1 1 1 1 1 2 12 2 1 1
(if (x + ~1) <= 0 then x else (~1 + ((1 + ((1 + (x mod (2 * (1 + (x mod (2 * (1 + (x mod (1 + (x div 3)))))))))) mod (x + 1))) mod 3)))
A294079: 0 1 1 0 1 ~1 1 0 0 ~1 1 1 1 ~1 ~1 0
(~1 + ((~1 + ((loop(\(x,i).(2x + 2),x,(12 * (x div 7))) mod 5) div 2)) mod 3))
A317193: 1 ~1 1 0 1 ~1 1 1 ~1 1 0 1 ~1 1 ~1 1
loop(\(x,i).(5x + (x div 5)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A172342: 1 1 1 1 5 1 1 26 26 1 1 135 702 135 1 1
loop(\(x,i).(x * (~1 + ((~1 + (((x + 1) div 2) div 2)) div 2))),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A156609: 1 1 1 1 ~2 1 1 4 4 1 1 ~4 8 ~4 1 1
(1 + ((2 * (1 + (((2x + 8) * ((if x <= 0 then 1 else 4x) - ((x + (x div 2)) div 4))) div 3))) mod 3))
A335620: 1 2 1 3 1 3 1 2 2 2 3 2 2 2 3 3
(1 + ((2 * (1 + ((1 + (x div (1 + (loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) mod (1 + (x mod 8)))))) div 2))) div 3))
A050430: 1 1 2 2 3 2 3 3 4 3 3 2 3 3 4 4
(~1 + ((2 * (1 + (((((8x + 5) * loop(\(x,i).2x,(x mod 5),1)) div 2) div 2) div 2))) mod 3))
A011633: 1 1 0 ~1 ~1 ~1 0 1 1
A014339: 1 1 0 ~1 ~1 ~1 0 1 1 0 0 ~1 ~1 0 1 1
(x - ((x + 1) mod (1 + ((4 * (1 + (2 * (0 - ((2 * (x + (if (x + ~4) <= 0 then 1 else x))) div (x + 2)))))) div 3))))
A171592: 0 1 2 3 4 5 11 11 11 11 11 11 17 17 17 17
((x + 1) mod (~1 + ((2 * ((x + 3) + ((1 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))) div 3))) div 3)))
A093489: 0 0 0 1 1 1 1 3 2 3 2 4 2 3 4 5
(1 + ((1 + (x mod (1 + ((1 + (x mod (2 + (x div (1 + ((x * loop(\(x,i).(x2 div 3),2,x)) mod 3)))))) mod (x + 1))))) div 2))
A105535: 1 1 1 1 2 1 1 3 1 1 1 4 1 4 2 1
(x div (1 + (2 * (1 + ((2 * ((2x + 1) + (2 * (loop(\(x,i).10x,(x + 1),1) div (x + 1))))) mod 3)))))
A308028: 0 0 0 1 0 0 2 1 1 3 3 3 1 2 2 5
(1 + ((1 + ((x mod (1 + ((2 - ((x + 1) mod (1 + (2 * (1 + (loop(\(x,i).(~x + 1),x,(x + 2)) mod 3)))))) mod (x + 1)))) div 2)) div 2))
A055893: 1 1 2 1 1 2 1 3 1 3 1 2 2 1 2 1
(~1 + (2 * (1 + ((1 + ((1 + ((((2x + 3) * (if x <= 0 then 1 else (6x2 + 2))) div 2) div 2)) div 2)) div 2))))
A299262: 1 7 25 65 137 249 411 631 919 1283 1733 2277 2925 3685 4567 5579
(1 + (((x + 1) div ((if (2 * ((2x + 1) mod (1 + (2x mod (2 + (x div 4)))))) <= 0 then (x + 1) else 0) + (x div 3))) div 2))
A073802: 1 1 1 1 1 4 1 1 1 2 1 3 1 2 2 1
(1 + (2 * (((loop(\(x,i).4x,((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2),1) div 3) * (1 + (x div 2))) div 2)))
A137897: 1 1 1 1 3 1 1 5 5 1 1 7 35 7 1 1
(1 + (((2 + (((x + ~1) + ((x mod 2) + ((if x <= 0 then 1 else (~2 + ((x2 div 4) mod (x + 1)))) mod 3))) mod (x + 1))) div 2) div 2))
A027199: 1 1 1 2 1 1 2 1 1 1 4 1 1 1 1 5
(4x + ((if x <= 0 then 1 else ((2 * (x - (2x div ~7))) div 3)) + ((2x + 2) div 5)))
A137002: 1 5 11 15
A314065: 1 5 11 15 22 26 31 37 42 48 52 58 63 68 74 79
(~1 + (((x + 2) * loop(\(x,i).2x,((x + 1) + ((3 * (x div (4 - ((x * (x div 2)) mod 2)))) div 2) - (x div 2)),1)) div 2))
A147760: 1 5 7 39 47 111 127 1151 1279 2815 3071 13311 14335 30719 32767 557055
(if x <= 0 then 0 else (2 - ((1 + ((2 + ((2x mod (~1 + (2 * (((~x + 2) div 2) mod 4)))) div 2)) mod (1 + (x div 3)))) mod 3)))
A226456: 0 1 1 1 0 1 2 2 2 2 2 1 0 1 2 2
(4x + ((if x <= 0 then 1 else ((2 * (2x div (4 + (x div 8)))) div 3)) + ((2x + 1) div 3)))
A314945: 1 5 9 14 20 24 30 35 39 44 49 53 58 64 68 74
(if ((1 + (x div 2)) mod (1 + (x div 5))) <= 0 then 1 else (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))
A215703: 1 1 1 1 1 0 1 1 2 0 1 1 4 3 0 1
loop(\(x,i).(x div (1 + (3 * (1 - (x mod 3))))),1,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))
A343316: 0 0 0 0 1 0 0 ~1 ~1 0 0 0 4 0 0 0
compr(\x.(if x <= 0 then 1 else (~1 + (x mod (4 + (x div 3))))),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))
A050178: 1 1 1 1 5 1 1 6 6 1 1 7 20 7 1 1
((if x <= 0 then 1 else 6x) - (((x + 1) div 3) + ((x + ((x - ((1 - (x div 2)) div 3)) mod 3)) div 3)))
A315322: 1 6 10 16 21 27 32 37 43 48 54 58 64 70 74 80
(x + (((2 * (2x div (4 + (x div 8)))) div 3) + (if x <= 0 then 1 else 4x) + ((x + 1) div 3)))
A314163: 1 5 11 16 22 28 34 39 45 50 55 61 66 72 78 84
((((2 * (1 + ((x - (((x div 2) div 3) mod 2)) div 2))) div 3) + (if x <= 0 then 1 else 5x)) - ((x + 1) div 3))
A313769: 1 5 10 15 21 25 30 35 39 45 50 55 60 65 70 75
(x + ((if x <= 0 then 1 else 4x) + ((x + 1) div 3)) - ((2 * (2x div (4 + (x div 8)))) div 3))
A314099: 1 5 11 16 20 26 30 35 41 46 51 57 62 66 72 76
(x + (if x <= 0 then 1 else 4x) - (((x + 1) div 3) + ((2 * (2x div (4 + (x div 8)))) div 3)))
A314828: 1 5 9 14 18 22 26 31 35 40 45 49 54 58 62 66
((2 * (1 + ((1 + ((((x + 1) * (4 + (x div (3 * (if (x + ~6) <= 0 then 1 else 2))))) div 2) div 2)) div 2))) div 3)
A055748: 1 1 2 2 2 3 4 4 4 4 5 6 7 8 8 8
((2 * (1 + (((1 + (((1 + ((loop(\(x,i).((~2x + 4) + (x div 2)),(x + 1),3) div 2) div 2)) div 2) div 2)) div 2) div 2))) div 3)
A246579: 0 0 0 0 0 0 0 0 0 1 ~1 2 ~3 5 ~7 11
((2 * (2 + ((1 + ((((x2 + 2x + 1) * loop(\(x,i).(5x + 8),x,1)) div 2) div 3)) div 3))) mod 3)
A175083: 1 1 1 0 1 2 1 0 0 2 1 2 1 1 1 0
((2x + ~1) + ((2 * (2 + (if x <= 0 then 1 else (2 * (2x + ((x - ((x div 2) mod ~4)) div 5)))))) div 3))
A137002: 1 5 11 15
A314025: 1 5 11 15 20 25 29 34 39 43 49 54 59 65 69 74
((2x + ~1) + ((2 * (2 + (if x <= 0 then 1 else (2 * (3x - ((2 * (x - ((x div 2) div 3))) div 3)))))) div 3))
A315426: 1 6 11 15 21 26 32 37 43 47 52 58 64 69 73 79
(((x + 1) + ((2 * (1 + ((1 + ((x + loop(\(x,i).((x + 2) + (2x div 5)),x,2)) div 2)) div 2))) div 3)) div 3)
A005140: 0 1 1 2 3 4 5 6 7 10 13 16 22
(((2x + 2) + ((~1 + (6 * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))) div 5)) div 3)
A061979: 1 2 3 5 7 9 11 12 15 18 19 22 25 26 28 31
(1 + ((x + ((1 + (((((x + ~1) * (1 + (2 * (1 + (2 * (loop(\(x,i).(x * (2 + i)),x,1) div 3)))))) div 2) div 2) div 2)) div 2)) div 2))
A330474: 1 1 2 7 48 424
(2x + ((2 * ((3x + 4) + loop(\(x,i).(x - ((~1 + (x div 4)) div 2)),2,(x + ~1)))) div 3))
A190374: 3 8 12 17 21 25 30 34 39 44 48 53 58 62 66 70
((x + 1) div (2 + ((((1 + (((x + 1) * (1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))) div 2)) div 2) div 2) + (x mod 2))))
A055941: 0 0 1 0 2 1 2 0 3 2 3 1 4 2 3 0
(0 + ((((3 * ((3 * (1 + ((2 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 3))) div 2)) div 2) div 2) + (x mod 2)))
A300510: 0 1 2 1 3 3 3 1 4 4 5 3 5 4 6 1
(1 + ((4 * ((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3)) div 3) - (x mod 2))
A345182: 1 0 1 1 1 2 1 2 2 2 1 5 1 2 3 4
(if (x + ~1) <= 0 then x else (1 + ((((1 + (x mod (2 * (1 + (x mod (2 * (1 + (x mod (1 + (x div 3)))))))))) mod (x + 1)) div 2) + (x mod 2))))
A323014-A293227: 0 1 1 2 1 3 1 2 2 3 1 4 1 3 3 2
(1 + compr(\x.(~1 + ((1 + (((1 + (2x mod (2 + (x div 3)))) div 2) * (loop(\(x,i).(2x + 2),x,0) mod (x + 1)))) mod (x + 1))),x))
A081998: 1 2 3 4 5 7 9 11 13 17 19 21 23 26 29 31
(1 + (x * (1 + (x * (1 + ((x2 + x) * loop(\(x,i).(x7 + x6 + x5 + x4 + x3 + x2 + x + 1),1,x2)))))))
A269446: 1 19 524287 581130733 91625968981 4768371582031 121871948002099 1899815864228857 20587884010836553 168856464709124011 1111111111111111111 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.(~2 + ((1 + (9 * ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3))) mod (x + 1))),x))
A066050: 1 2 3 4 5 7 9 10 11 13 17 19 23 29 31 37
((1 + ((x + 1) div (~1 + (2 * (1 + ((x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))) + (x mod 2))))))) mod (x + 1))
A317840: 0 1 1 1 1 2 1 1 2 3 1 2 1 3 4 1
((4x + ((loop(\(x,i).3x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),3) div 2) div 2)) div (x + 1))
A267592: 0 3 3 4 3 4 4 6 3 4 4 5 4 5 5 7
(2 * (1 + (if x <= 0 then 0 else (1 + ((2 * (1 + ((((1 + ((x - (x div 3)) div 3)) * (1 + (x div 2))) div 2) div 2))) div 3)))))
A050829: 2 4 4 4 6 6 8 8 8 8 10 10 12 14 16 16
(2 * (1 + ((1 + ((1 + ((x + 1) div (1 + ((1 + (if ((x mod (~1 + (2 * (x div 3)))) mod 2) <= 0 then 1 else x)) mod 3)))) div 2)) div 2)))
A283207: 2 2 4 4 4 4 4 4 4 4 4 8 6 4 6 6
((x + 1) div (if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + ((x5 mod 17) div 2)) div 2)) div 2)))))
A128764: 1 1 0 1 1 1 1 1 2 2 2 2 3 2 2 4
((1 + ((1 + (((1 + (((x + 1) * (if x <= 0 then 1 else (2 * (1 + (~x2 mod 6))))) div 3)) div 2) div 2)) div 2)) div 2)
A178771: 0 1 1 1 1 2 1 2 1 2 2 3 1 4 2 3
(2 + ((~1 + ((6x + 6) * ((2 + (if x <= 0 then 0 else 2)) * (1 + (((x + 1) div 2) mod 3))))) mod 7))
A255823: 6 6 5 2 4 5 8 7
(1 + (x div 4) - ((1 + (((if (x + ~1) <= 0 then 1 else ((1 + (((x + 1) * (2 + (x mod 2))) div 2)) div 2)) + (x mod 3)) div 2)) mod 2))
A317192: 0 1 0 1 1 2 1 2 3 2 3 3 4 3 4 3
((if ((x + 1) mod 4) <= 0 then 1 else (1 + (2 * (3 div (4 - (((~2x + 2) mod (4 + (x div 4))) div 2)))))) div 2)
A321609: 1 0 1 0 1 1 0 0 1 1 0 0 3 1 1 0
(1 - (2 * (1 + ((~2 + (3 * (x div 15)) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) div 2))))
A093893: 1 3 5 7 11 13 17 19 23 29 31 37 41 43 47 49
((3 * (loop(\(x,i).6x,(((x + ~1) div 2) - ((3 * (x div 4)) div 2)),1) div 9)) div 2)
A173066: 0 0 0 0 0 0 0 6 0 0 0 6 0 6 6 36
(3 - ((2 * (1 + ((1 + (x div (1 + (loop(\(x,i).3x,(((x + ~1) div 2) mod 4),1) mod (x + 1))))) div 2))) mod 3))
A008335: 1 1 2 1 2 2 2 2 2 3 1 2 3 2 2 2
(2 * ((2 * (1 + ((1 + ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod (2 * (1 + (x div 4))))) div 2))) div 3))
A255336: 0 2 2 2 4 2 2 4 4 4 2 2 2 4 6 4
(((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)) mod (2 + (6 mod (x + 1))))
A173438: 0 1 1 2 1 0 1 3 2 2 1 3 1 2 2 4
((2 - (((x + 1) - (3 * (1 + ((x - (2 * ((x + (if (x mod 3) <= 0 then 1 else 2)) div 4))) * (x div 3))))) div 2)) div 2)
A036500: 1 1 1 1 2 2 6 4 5 10
(x - (((((1 + (((x + 1) * (1 + (if (~1 + ((2x + 1) mod (2 + (x div 4)))) <= 0 then x else 0))) div 3)) div 2) div 2) div 2) div 2))
A330292: 0 1 2 3 4 5 5 6 7 9 8 11 9 13 14 10
(4 * ((x + 3) + ((((4x + 2) + loop(\(x,i).2x,((x + 2) + (x div 4)),2)) div 2) div 2)))
A308664: 20 36 60 100 300
((((x + 2) + (((2x + 1) + (4 * ((1 + (loop(\(x,i).(2x + 2),(x div 2),(x mod 2)) div 2)) div 2))) div 3)) div 2) div 2)
A241651: 0 1 1 2 2 3 4 5 6 8 10 13 16 22 27 38
loop(\(x,i).(x * (1 + (2 * (x div 4)))),1,(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))
A141542: 1 1 1 1 2 1 1 3 3 1 1 12 18 12 1 1
((x + 2) + ((~1 + (((2 * ((2x + 2) + (if x <= 0 then 1 else (2 * (x + ((x div 2) div 5)))))) div 3) + (x mod 2))) div 2))
A284657: 2 5 6 9 11 14 16 19 20 23 26 29 30 33 35 38
(if x <= 0 then 1 else (2 * (x + (((x + 1) + (((x + 1) + (((3 * ((2x + 1) - (x mod 5))) div 2) div 2)) div 2)) div 2))))
A311347: 1 4 8 12 16 22 26 30 34 38 44 48 52 56 58 64
((3 * (if x <= 0 then 1 else (2 * (x mod (1 + ((((1 + (8 mod (1 + (x div 2)))) div 2) - (x mod 2)) mod (x + 1))))))) div (x + 2))
A080024: 1 2 0 3 0 0 0 4 1 0 0 0 0 0 0 5
(1 + (((2 * (1 + ((1 + (x div (1 + (x mod (1 + (loop(\(x,i).(3x + 3),x,0) mod (x + 1))))))) div 2))) div 3) + (x mod 2)))
A127971: 1 2 2 2 3 3 3 2 4 4 5 3 5 4 4 2
(1 + (((2 * (1 + ((1 + (x div (1 + (loop(\(x,i).(1 + (2 * (x - (x div ~2)))),x,0) mod (x + 1))))) div 2))) div 3) + (x mod 2)))
A035191: 1 2 1 3 2 2 2 4 1 4 2 3 2 4 2 5
(if x <= 0 then 1 else (3x + ((x + (((3 * (x + (2 * ((x - (x div ~4)) div 2)))) div 2) div 2)) div 2)))
A058759: 1 4 8 13
A311851: 1 4 8 13 17 21 26 30 34 39 43 47 51 56 61 64
compr(\x.(1 - ((2 * (2 + compr(\x.((x + 1) mod (1 + (x mod (2 * (2 + (loop(\(x,i).(3x + 2),x,0) mod (x + 1))))))),x))) mod 3)),x)
A228082: 0 2 3 5 7 8 9 10 11 12 14 16 17 19 20 22
(1 + (x mod (1 + (x mod (1 + ((~1 + (2 * (1 + ((1 + ((1 + (((x + 1) * (x div (2 - (x mod 2)))) div 2)) div 2)) div 2)))) mod (x + 1)))))))
A295310: 1 2 1 2 1 2 1 8 3 2 1 12 1 2 1 2
(1 + (5 mod (1 + ((2 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)) mod (x + 1)))))
A146531: 1 1 1 1 3 1 1 1 1 1 1 6 2 6 1 1
(1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + ((2x + 1) div (3 + (x div 4)))))
A003991: 1 2 2 3 4 3 4 6 6 4 5 8 9 8 5 6
(1 + (3 * ((1 + ((1 + (((0 - ((~2x + 2) mod (4 + (x div 4)))) mod (x + 1)) div 3)) mod 3)) mod 2)))
A145079: 1 1 1 1 1 4 1 4 4 4 1 4 4 1 4 1
(1 + ((2 * (1 + ((1 + (((~1 + ((1 + ((32 mod (x + 1)) div 2)) div 2)) mod (x + 1)) div 2)) div 2))) div 3))
A138904: 1 1 1 2 1 1 1 3 1 1 2 1 1 1 1 4
(1 + ((2 + (7 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2))) div 3))
A144480: 1 1 1 1 4 1 1 6 6 1 1 8 18 8 1 1
(1 + ((4 * (x div (2 + (x mod (1 + ((x + 1) div (1 + (((2x div (1 + (x div 4))) mod 2) + (x mod 2))))))))) div 3))
A299201: 1 1 1 2 1 2 1 3 2 2 1 5 1 2 2 5
(1 + ((2 * ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 - (2 * ((x div 2) mod 2))))) div 3))
A133815: 1 1 1 1 1 1 1 ~1 2 1 1 ~1 3 3 1 1
(1 + (2x mod (1 + compr(\x.(((((1 - (2 * ((x mod (1 + (((x + 1) div 2) div 2))) mod 2))) * (1 + (x div 2))) div 2) mod 2) - (x mod 2)),x))))
A200262: 1 1 1 1 2 3 4 5 5 5 6 7 7 7 7 8
(1 + (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + (x div (3 + ((x div 2) mod 2))))) div 2))
A160449: 1 1 1 1 2 1 1 3 4 1 1 5 11 8 1 1
(1 + ((1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + (x div (2 * (2 + (x mod 2))))))) div 2))
A104559: 1 1 1 1 2 1 1 3 4 1 1 4 9 6 1 1
(1 + ((1 + (((2x + 1) * (1 + (((1 + ((3x2 + ~5x + 2) div 2)) div 2) div 5))) div 3)) div 2))
A029866: 1 2 2 2 4 7 12 16
(1 + ((1 + ((1 + ((1 + (x div (1 + ((~1 + ((x2 + ~x) mod (3 + ((x div 2) div 3)))) mod (x + 1))))) div 2)) div 2)) div 2))
A096492: 1 1 2 1 1 2 2 2 1 1 2 2 2 3 2 1
(1 + ((1 + (x div (2 + ((~1 + (4 * ((2 * ((1 + (x mod (2 + (x div 4)))) mod 2)) - (x mod 3)))) mod (x + 1))))) div 2))
A255191: 1 1 1 1 2 1 3 2 1 1 2 2 2 2 1 2
(1 + (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + (x div (2 * (2 + ((x div 2) mod 2)))))) div 2))
A080853-A071922: 1 1 1 1 2 1 1 3 4 1 1 4 9 7 1 1
(1 + ((5 * ((x * ((~x2 + 2) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))) div 5)) div 2))
A174116: 1 1 1 1 1 1 1 3 3 1 1 6 18 6 1 1
(1 + ((3 * ((4 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)) div 3)) div 2))
A296990: 1 1 1 1 2 1 1 4 4 1 1 7 14 7 1 1
((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 - (2 * ((((x + 1) div 2) div 2) div 2))))) mod 7)
A204244: 1 1 1 1 2 1 1 0 0 1 1 0 6 0 1 1
(1 - ((x + 1) div (1 + (2 * ((x + 1) div (1 - (2 * ((x div 2) div (1 + (x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4)))))))))))))))
A290103-A225395-A156061: 1 1 2 1 3 2 4 1 2 3 5 2 6 4 6 1
(~1 + (((5 * (1 + (x div (1 + (x mod (2 + (x div (1 + (2 * ((x mod (~1 + (2 * (x div 3)))) mod 2)))))))))) div 2) div 2))
A284075: 0 0 0 0 0 0 0 1 0 0 0 6 15 0 0 0
((1 + (((3 * ((3 * (~2 + (2 * (x2 mod 19)))) div 2)) div 2) div 2)) mod 3)
A290320: 1 1 1 1 1 0 1 2 2 1 1 2 2 1 0 1
(2 - ((1 + ((x mod (2 + ((1 + (2 * ((2 * (1 + (x mod (2 + (x mod 4))))) mod (1 + (x div 2))))) mod (x + 1)))) div 2)) mod 3))
A157045: 1 1 0 1 1 0 1 1 1 0 1 1 2 0 0 1
((5 * (1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (2 * (x div 5)))))) div 3)
A114176: 1 1 1 1 3 1 1 6 6 1 1 10 18 10 1 1
((1 + (2 * ((x + 1) + (((x + 1) + (((x + 1) + ((4x + 1) div (2 + (x div 8)))) div 2)) div 2)))) mod 3)
A049321: 0 0 1 2 0 0 1 2 1 2 0 1 2 0 0 1
((2 * (1 + (((2 * (2 + ((2x + 1) mod (1 + (2x mod (2 + (x div 4))))))) + (x mod 3)) div 3))) mod 3)
A152815: 1 1 0 1 1 0 1 1 0 0 1 2 1 0 0 1
((2 * (1 + ((1 + ((((2x + 3) * ((8x + 2) + (x div 3))) div 2) div 3)) div 2))) mod 3)
A219494: 1 1 0 0 0 0 0 1 2 2 1 0 0 0 0 1
((2 * (1 + ((1 + (x div (2 + ((2 * (((1 + (8 mod (1 + (x div 2)))) div 2) - (x mod 2))) mod (x + 1))))) div 2))) div 3)
A124737: 0 0 1 0 1 1 2 0 1 1 1 2 2 2 3 0
((2 * ((x + 2) + ((1 + (((1 + (((x + 1) * ((x + 1) - ((~2x + 2) div 5))) div 2)) div 2) div 2)) div 2))) div 3)
A260317: 1 2 3 4 5 6 8 10 11 13 14 16 19 21 24 26
(6 * (((3x + 2) - (x2 div (6 + ((x2 + ~x) div 11)))) div 2))
A188158: 6 12 24 30 36 42 48 54 60 66 72 84 90 96 108 114
(1 + (((x + 1) + ((3 * ((x + (((((x + 2) * ((x + 2) + (x div 7))) div 2) div 2) div 2)) div 2)) div 2)) div 2))
A026480: 1 2 4 5 6 7 9 11 13 15 17 19 21 23 27 29
(0 + (((2 * (1 + ((1 + ((x mod (2 + ((2 - (2x mod (2 + (x div 2)))) mod (x + 1)))) div 2)) div 2))) div 3) + (x mod 2)))
A244417: 0 1 1 2 0 1 0 3 2 1 0 2 0 1 1 4
(1 + ((x div (2 + (x mod (1 + ((x + 1) div (1 + (((2x div (1 + ((x + 1) div 5))) mod 2) + (x mod 2)))))))) + (x mod 2)))
A327530-A327513: 1 2 1 3 1 3 1 4 1 3 1 5 1 3 2 5
((1 + ((2 * (1 + ((1 + ((x + 1) mod (1 + (2 * ((x div 2) div (1 + ((((x + 1) div 2) div 2) div 2))))))) div 2))) div 3)) mod (x + 1))
A061394: 0 1 1 2 1 2 1 2 3 1 2 2 3 1 2 2
(3 + (11 * ((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~1) div 2))) div 2)))
A153491: 3 3 3 3 14 3 3 25 25 3 3 36 58 36 3 3
(1 - ((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (2 * (2 + (x mod (~5 + (x mod 2)))))))) div 2))
A265313: 1 1 1 1 ~1 1 1 ~1 0 1 1 ~1 2 1 1 1
(3 + ((1 + ((1 + ((3 * ((x + 1) + ((24x + 12) div (x + 4)))) div 2)) div 2)) div 2))
A213443: 5 7 8 9 10 11 12 12 13 13 14 15 15 16 16 16
((x + 2) div (2 * (1 + ((1 + ((1 + (((x + 1) * (1 + (2 * ((x + 2) mod (1 + (2 * (2x mod 3))))))) div 2)) div 2)) div 2))))
A216266: 1 0 1 1 1 0 2 0 1 1 0 1 2 2 1 2
((1 + ((1 + (((3 * (1 + ((11x + 10) mod 15))) div 2) div 2)) div 2)) div 2)
A190683: 2 2 1 3 2 1 1 3 2 1 0 3 2 1 3 2
((1 + (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + (x div (2 * (2 - (x mod 2)))))) div 2)) div 2)
A298719-A298133-A298070-A297866: 0 0 0 0 1 0 0 2 2 0 0 5 4 5 0 0
(3 + (((1 + compr(\x.((1 + ((4 * (1 + ((x + 1) div (2 + (x div 8))))) div 3)) mod 3),x)) div 2) div 2))
A011375: 3 3 4 4 5 5 5 6 7 8 8 8 8 9 9 9
(((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + (4 * ((1 + (x div 3)) div 2)))) div 2)
A278177: 0 0 0 0 2 0 0 5 5 0 0 13 18 13 0 0
(((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div (2 - ((x div 2) mod 2)))))) mod 9) div 2)
A173541: 0 0 0 0 2 0 0 0 3 0 0 2 3 4 0 0
((3 * (1 + (((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2) * (((x + 1) div 2) div 2)))) div 2)
A046802: 1 1 1 1 3 1 1 7 7 1 1 15 33 15 1 1
(1 - ((3 * ((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((3 * ((~x + 2) div 2)) div 2))) div 2)) div 2))
A173076: 1 1 1 1 3 1 1 4 4 1 1 7 13 7 1 1
(1 + (((x - ((3 - ((1 + ((~2x + 2) mod (4 + (x div 4)))) mod 5)) div 2)) mod 2) + ((x + 1) div 2)))
A327982: 1 2 2 3 4 5 5 5 6 7 7 7 7 8 8 9
(((1 + ((((x + 1) * (8 + ((3 * (x - (x div 11))) div 2))) div 2) div 2)) div 2) div 2)
A067570: 0 1 2 3 4 5 7
A089237: 0 1 2 3 4 5 7 9 11 13 16 17 19 23 25 29
(((5 * (1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (x - (2 * (((x + 1) div 2) div 2)))))) div 2) div 2)
A271942: 1 1 1 1 3 1 1 5 6 1 1 7 16 10 1 1
(~2 + ((3 * (((x + 1) * (7 + ((5 * (1 + (x div 4))) mod (x + 1)))) div 3)) div 2))
A251965: 1 5 11 13 14 31
(((3 * ((~1 + (6 * (1 + ((x + 2) mod (1 + (((1 + (x * (x div 2))) div 3) mod 3)))))) div 2)) div 2) div 2)
A295931: 1 1 1 3 1 1 1 3 3 1 1 1 1 1 1 6
(((3 * (2 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * ((x + 1) mod 4)))) div 2) div 2)
A326153: 1 1 1 1 2 1 1 1 3 1 1 1 4 6 1 1
((2 + ((1 + (2 * ((1 + ((x * (1 - ((x3 div 8) mod 2))) mod 5)) mod 3))) mod (x + 1))) div 2)
A254123: 1 1 1 2 1 2 2 1 2 2 2 3 1 2 2 2
((2 + ((2 * (2 + (2x div (1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))))) mod (x + 1))) div 2)
A155582: 1 1 1 1 2 1 1 3 3 1 1 2 7 2 1 1
(1 - (2 * (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 - (2 * (x div 5)))) div 2)))
A176344: 1 1 1 1 1 1 1 3 3 1 1 11 13 11 1 1
((((x + 2) + ((2 * ((x + 1) mod (1 + (2 * (1 + (x mod (1 + (8 * (x mod (2 + (x mod 2))))))))))) mod (x + 1))) div 2) div 2)
A322141: 0 0 1 1 2 1 2 2 2 3 4 3 4 5 4 4
((x + 1) - ((2 * (1 + ((2 * ((x + 2) + ((1 + ((x * (x div 7)) div 2)) div 2))) div 3))) div 3))
A225633: 0 0 1 2 2 3 3 3 3 4 4 5 5 6 5 5
((x + 1) + ((2 * (1 + ((1 + (((3 * ((x + 1) + (2 * (x + (((x div 2) div 3) mod 2))))) div 2) div 2)) div 2))) div 3))
A191771: 1 4 5 7 9 10 13 14 16 18 19 22 23 24 26 28
((x + 1) + ((2 * ((x + 1) + (((2x + 1) + (2 * (x + ((3 * ((1 + (x div 2)) div 2)) div 2)))) div 3))) div 3))
A178598: 1 4 7 10 12 14 18 20 23 26 29 31 34 36 40 42
(5 + ((2 * (1 + ((x + (3 * (2 - ((~x + 2) div (2 - (x div ~4)))))) div 2))) div 3))
A168679: 6 7 8 9 9 10 10 11 12 12 13 13 13 13 14 15
(x + ((x + (((3 * (1 + (((1 + ((x * ((x + 1) + (2 * ((x + (x div 2)) div 4)))) div 2)) div 2) div 2))) div 2) div 2)) div 2))
A186705: 0 1 3 5 7 9 12 14 18 20 23 27 30 33
(((if x <= 0 then 0 else 1) + loop(\(x,i).2x,x,(loop(\(x,i).3x,x,1) - loop(\(x,i).(2x + 1),x,0)))) - loop(\(x,i).5x,x,1))
A178690: 0 0 0 36 432 3660 27000 185556 1223712 7862940 49653000 309776676 1915868592 11772890220 71992229400 438593697396
(loop(\(x,i).11x,x,1) div loop(\(x,i).3x,x,(loop(\(x,i).3x,x,1) + loop(\(x,i).(2x + 1),x,0))))
A280127: 1 0 1 1 1 2 3 3 4 5 7 8 11 13 16 20
loop(\(x,i).(((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1)),1,(x - (if x <= 0 then 0 else 1)))
A032741: 0 0 1 1 2 1 3 1 3 2 3 1 5 1 3 3
(1 - (if x <= 0 then 0 else (1 + ((if (x mod 2) <= 0 then (if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).2x,x,(1 + (x div 4))) mod (x + 1)) div 2)))) else 1) div 2))))
A181587: 1 0 ~1 0 ~2 0 ~2 0 ~2 0 ~2 0 ~3 0 ~1 0
(1 + (2 * (1 + loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))))
A097524-A073703: 3 5 3 3 7 3 3 3 7 3 5 5 7 3 3 3
((2 * (2 + (loop(\(x,i).((x + 1) + loop(\(x,i).((if x <= 0 then 2 else loop(\(x,i).(x div (2 - (x mod 2))),x,x)) div 2),2,x) - (x mod 2)),x,1) div 2))) div 3)
A028825: 1 2 2 3 3 4 4 4 5 6 6 7 7 8 10 11
(1 + (2 * ((x + 1) + (loop(\(x,i).((x + ~1) + loop(\(x,i).(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1))),2,x)),x,x) div 2))))
A284795: 3 5 11 13 15 17 21 23 27 29 35 37 39 41 47 49
((x + (loop(\(x,i).(x - (if x <= 0 then 1 else (x - ((if x <= 0 then 2 else loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 2)))),x,(x + 1)) + (x mod 2))) div (1 + (x mod 2)))
A066030: 1 1 1 2 2 1 1 2 3 2 2 2 2 1 1 3
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025942: 1 23 361 4907 62545 773171 9415897 113824139 1370909089 16481083619 197954225833 2376538571771 28524991618033 342339076723667 4108303998843769 49301058498065003
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025951: 1 25 423 6125 82103 1054725 13214671 163046125 1992333255 24194295125 292622085119 3529789897725 42504079369207 511221761969125 6144043634254767 73803583579040525
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025964: 1 23 359 4843 61287 753315 9137263 110167211 1324737623 15911030707 191005360767 2292437677179 27511152416359 330143464656899 3961770291040271 47541489215721547
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A025982: 1 27 487 7431 103951 1382439 17812639 224794647 2797053391 34460823111 421597615231 5131789410423 62235068724271 752703321093543 9085382857597663 109501083478899159
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025936: 1 22 333 4406 55133 673566 8144701 98052262 1178225565 14146756910 169801508669 2037820760118 24454863987997 293463446955454 3521586773279037 42259168371397574
loop(\(x,i).(12x + loop(\(x,i).(2x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A025954: 1 26 457 6854 94789 1251002 16035889 201651758 2502830077 30781099778 376097622121 4573691815862 55428986530165 670050005786954 8084719590584353 97413710820261566
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025937: 1 18 211 2052 18025 148806 1179487 9089784 68647909 510709914 3756191803 27381204396 198197187553 1426557620142 10220981500759 72957382445088
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025987: 1 21 285 3185 31941 299481 2685565 23352945 198684981 1663903241 13774041645 113050606305 921961387621 7483064823801 60518933442525 488128819261265
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028033: 1 21 283 3129 31003 287217 2547091 21931833 185027755 1538650113 12663786499 103454051337 840560481307 6802315926609 54886579262707 441905197121241
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A026561: 1 25 405 5405 64661 721725 7683685 79078285 793624821 7813101725 75772440965 726132366765 6891899656981 64900354798525 607206802510245 5650395374640845
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(7x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025965: 1 19 233 2351 21273 179823 1452361 11360767 86821625 652052687 4832272809 35441720223 257820455257 1863247878511 13394300154377 95871638560319
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028025: 1 18 205 1890 15421 116298 830845 5709330 38119741 249026778 1599719485 10142356770 63639854461 396031348458 2448208592125 15053605980210
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028034: 1 22 313 3682 39109 391174 3769921 35484394 328932637 3018821806 27523981849 249859595986 2261664434485 20432811986518 184363359728497 1662082800576058
loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A025988: 1 22 315 3740 40121 405042 3935095 37284280 347419941 3201202862 29273641475 266321046420 2414445954961 21837387317482 197190900709455 1778695458106160
loop(\(x,i).2x,x,loop(\(x,i).(6x + loop(\(x,i).(10x + loop(\(x,i).(3x + 1),i,1)),i,1)),x,1))
A071952: 1 40 1092 25664 561104 11807616 243248704 4950550528 100040447232 2013177300992 40412056994816 810023815790592 16221871691714560 324694197936160768 4611686018427387903 4611686018427387903
loop(\(x,i).(6x + loop(\(x,i).(10x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025940: 1 21 295 3525 38911 411741 4255255 43385925 438878671 4418961261 44370835015 444796211925 4454490876031 44584086067581 446075938835575 4462169900295525
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025943: 1 20 263 2890 28833 271320 2457211 21670550 187473605 1598611300 13480822719 112690635330 935435043817 7720854845360 63428474542787 519059289782830
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025959: 1 18 209 1998 17157 137970 1063273 7962966 58471853 423482202 3037367697 21634921854 153344743189 1083048862914 7630057197881 53656123623462
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A025972: 1 22 317 3806 41421 424974 4198189 40430302 382529741 3573890606 33084972141 304212832638 2783085627661 25364095795918 230491675046573 2089930913053214
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).8x,i,1)),i,1)),i,1)),x,1)
A025971: 1 21 287 3249 33159 317457 2913079 25951233 226266887 1941258033 16450020951 138048250977 1149556141735 9512774280849 78317007130103 642041894674881
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025931: 1 17 188 1726 14343 112371 848506 6255392 45386165 325753285 2320698744 16447547298 116147697667 818112983159 5752200695702 40392496919044
loop(\(x,i).(7x + loop(\(x,i).(2x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A025944: 1 21 292 3414 36439 368607 3604114 34449888 324158197 3016246233 27838148416 255387389322 2332396465075 21228942680499 192722119904398 1746130572580116
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028027: 1 20 257 2716 25809 230244 1975009 16524332 136058417 1108775668 8975764161 72350153148 581586939025 4666887733892 37407122372513 299621333407564
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028043: 1 24 373 4788 55321 599088 6215581 62589516 616742401 5979165192 57244372549 542670685284 5103872340841 47693804106336 443316920660077 4102438007485692
loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A025997: 1 24 375 4850 56481 616164 6434155 65146950 644889861 6275802104 60272841135 572861926650 5399415089641 50546032304844 470534835243315 4359828735795950
loop(\(x,i).(8x + loop(\(x,i).(10x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025949: 1 23 353 4579 54393 613419 6692161 71391683 749696585 7783261915 80123162769 819556503987 8342165636377 84594465902411 855327149649377 8628331464477091
loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A025962: 1 21 293 3465 37821 396081 4058293 41102985 413760941 4151788641 41590878693 416282134905 4164721639261 41656852053201 416617235689493 4166418080133225
loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A025980: 1 25 413 5717 71949 854517 9768541 108728389 1186801517 12764197589 135709713789 1429715165541 14950747454605 155389970948341 1606842713958557 16544916327312773
loop(\(x,i).(4x + loop(\(x,i).(3x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025928: 1 20 275 3310 37761 421440 4662175 51395570 565817021 6225908260 68492850075 753453315030 8288115908281 91169797529480 1002869877293975 11031577111093690
loop(\(x,i).(5x + loop(\(x,i).(4x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028028: 1 21 286 3234 33187 322455 3035152 28040628 256229413 2326373049 21042916258 189930286182 1712158289479 15423616827003 138884571944404 1250325501927096
loop(\(x,i).(5x + loop(\(x,i).(10x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025934: 1 20 269 3100 33261 344580 3507709 35392940 355527821 3563328340 35673709149 356939747580 3570412342381 35709202523300 357117435046589 3571301442515020
((loop(\(x,i).3x,x,1) + loop(\(x,i).7x,x,1)) - (loop(\(x,i).5x,x,1) + loop(\(x,i).2x,x,1)))
A135163: 0 3 29 237 1841 13893 102689 747477 5380481 38419653 272767649 1928673717 13597673921 95669893413 672124323809 4717058247957
((loop(\(x,i).3x,x,1) + loop(\(x,i).2x,x,1) + loop(\(x,i).7x,x,1)) - loop(\(x,i).5x,x,1))
A135164: 2 7 37 253 1873 13957 102817 747733 5380993 38420677 272769697 1928677813 13597682113 95669909797 672124356577 4717058313493
(loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1) + loop(\(x,i).7x,x,1) + loop(\(x,i).2x,x,1))
A135168: 4 17 87 503 3123 20207 134067 903983 6162243 42326927 292300947 2026334063 14085963363 98111316047 684331387827 4778093469743
((loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1) + loop(\(x,i).7x,x,1)) - loop(\(x,i).2x,x,1))
A135167: 2 13 79 487 3091 20143 133939 903727 6161731 42325903 292298899 2026329967 14085955171 98111299663 684331355059 4778093404207
((loop(\(x,i).5x,x,1) + loop(\(x,i).7x,x,1)) - (loop(\(x,i).3x,x,1) + loop(\(x,i).2x,x,1)))
A135165: 0 7 61 433 2929 19657 132481 899353 6148609 42286537 292180801 2025975673 14084892289 98108111017 684321789121 4778064706393
((loop(\(x,i).5x,x,1) + loop(\(x,i).2x,x,1) + loop(\(x,i).7x,x,1)) - loop(\(x,i).3x,x,1))
A135166: 2 11 69 449 2961 19721 132609 899609 6149121 42287561 292182849 2025979769 14084900481 98108127401 684321821889 4778064771929
((loop(\(x,i).7x,x,1) + loop(\(x,i).2x,x,1)) - (loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1)))
A135162: 0 1 19 199 1711 13471 101359 743359 5367871 38381311 272651599 1928323519 13596619231 95666721151 672114790639 4717029615679
(loop(\(x,i).7x,x,1) - (loop(\(x,i).2x,x,1) + loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1)))
A135161: ~2 ~3 11 183 1679 13407 101231 743103 5367359 38380287 272649551 1928319423 13596611039 95666704767 672114757871 4717029550143
loop(\(x,i).(3x + loop(\(x,i).(2x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A025952: 1 24 385 5220 64741 760944 8633305 95554140 1038550381 11132642664 118050851425 1241028864660 12954973386421 134451901289184 1388638534032745 14283461073576780
compr(\x.(~1 + ((x + loop(\(x,i).(x - (if x <= 0 then 1 else (x - ((if x <= 0 then 2 else loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 2)))),(x + ~1),x)) mod 3)),(x + 1))
A143070: 2 4 5 6 9 10 11 12 13 14 16 19 21 22 23 25
loop(\(x,i).(x * loop(\(x,i).(2 * (1 + ((loop(\(x,i).7x,x,1) - loop(\(x,i).(3x + 2),x,0)) div (x + 1)))),1,i)),x,1)
A198176: 1 6 168 26880
((x + 1) div (2 + ((x div 2) div (1 + (loop(\(x,i).loop(\(x,i).((if x <= 0 then 2 else loop(\(x,i).(x div (2 - (x mod 2))),x,x)) div 2),2,x),1,(x + 1)) mod 3)))))
A083415: 0 1 1 2 1 1 2 2 1 1 3 1 2 2 1 3
(2 * (1 + loop(\(x,i).compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))))
A073123: 4 6 12 18 36 42 60 70 88 112 130 162 180 192 222 250
(loop(\(x,i).2x,(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))),1) div 2)
A077748: 1 2 4 2 2
A058384: 1 2 4 2 2 4 16 2 2 4 2 4 8 2 2 4
(loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).2x,((((1 + (8 mod (1 + (x div 2)))) div 2) + (if x <= 0 then 0 else 1)) - (x mod 2)),2),1,i)),x,1) div 2)
A268514: 0 1 3 4 8 10 12 13 21 25 29 31 35 37 39 40
((2x + 4) + loop(\(x,i).(x + loop(\(x,i).compr(\x.(1 - loop(\(x,i).(if (x mod (1 + i)) <= 0 then 0 else x),(x div 2),(x2 + 2x))),(x + 1)),1,i)),x,1))
A086168: 5 12 25 44 75 118 179 252 355 464 603 754 935 1128 1327 1556
compr(\x.((x + 1) + loop(\(x,i).(x + loop(\(x,i).(x - (if x <= 0 then 1 else (if (x mod 2) <= 0 then (x div 2) else 19))),x,(x + 1))),2,x)),x)
A101373: 1 2 3 4 5 6 7 8 9 10 11 13 15 19 20 22
loop(\(x,i).(x div (2 - (x mod 2))),1,(((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1)))
A296082: 0 1 1 1 1 3 1 3 1 3 1 5 1 3 3 2
loop(\(x,i).(x * loop(\(x,i).(x2 + 2),2,2)),((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165859: 1 38 38 1444 38 1444 38 54872 1444 1444 38 54872 38 1444 1444 2085136
(1 + (6 * (~1 + (6 * loop(\(x,i).loop(\(x,i).x3,4,2),(x + ~2),loop(\(x,i).6x,x,1))))))
A290008: 31 211 1291 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + ((x * loop(\(x,i).(2x + 2),x,0)) mod loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))) div 2))) div 3)))
A329322: 0 1 1 1 1 2 1 1 3 3 1 2 1 3 5 1
(1 + ((2 * loop(\(x,i).(1 + (loop(\(x,i).(x * (2 + i)),compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x),1) div 3)),1,(x + 1))) div 3))
A139089: 561 4435201 691891201 39520825344001 13516122267648001 4611686018427387903 4611686018427387903 4611686018427387903
(~1 + ((2 * loop(\(x,i).(1 + (loop(\(x,i).(x * (2 + i)),compr(\x.(loop(\(x,i).(~2x + 1),x,1) mod (x + 2)),x),1) div 3)),1,(x + 1))) div 3))
A139197: 559 4435199 691891199 39520825343999 13516122267647999 4611686018427387903 4611686018427387903 4611686018427387903
((~3x + ~4) + compr(\x.(~1 + loop(\(x,i).(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1))),2,x)),(x + 1)))
A095774: 1 0 ~1 0 1 2 1 0 1 0 ~1 0 ~1 ~2 ~1 0
loop(\(x,i).(x * (1 + (3 * loop(\(x,i).(2 * (loop(\(x,i).(32x + 1),(x + 1),1) div 2)),1,1)))),(2x + 1),1)
A155484: 3169 31824875809 319603256629306849 4611686018427387903 4611686018427387903 4611686018427387903
(1 + compr(\x.(~1 + ((~1 + (2 * (if x <= 0 then 1 else (2 * ((loop(\(x,i).2x,x,(if (x mod 4) <= 0 then 0 else 1)) mod (x + 1)) div 2))))) mod 3)),(x + 1)))
A273157: 6 10 12 14 15 18 20 22 24 26 28 30 34 35 36 38
(((x + 1) * (loop(\(x,i).4x,x,1) - loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1))) mod loop(\(x,i).4x,(x + ~1),1))
A094780: 0 0 2 12 58 4 100 664 3514 16916 77388 343144 1490148 6376616 26992264 113317936
(1 + loop(\(x,i).((x + 1) + ((x + loop(\(x,i).(x2 div 2),(x + ~2),loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1))) div 3)),x,1))
A089678: 2 3 5 1608
(~1 + ((if x <= 0 then 2 else (1 + ((2 * (1 + ((1 + (x div (1 + ((~1 + loop(\(x,i).(if x <= 0 then i else (x div 2)),x,2)) mod (x + 1))))) div 2))) div 3))) div 2))
A057094: 0 0 ~1 0 0 ~1 0 0 1 ~1 0 0 0 2 ~1 0
(1 + ((1 + (if x <= 0 then 1 else (compr(\x.(loop(\(x,i).(~2x + 2),x,2) mod (x + 2)),x) mod (1 + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))))) div 2))
A162345: 2 2 2 3 3 3 3 3 5 4 4 5 3 3 5 6
loop(\(x,i).2x,1,(~1 + (2 * (1 + ((1 + (((1 + (loop(\(x,i).(x2 + 2x),1,loop(\(x,i).(1 + (x * (2 + i))),x,1)) div 2)) div 2) div 2)) div 2)))))
A111265: 2 10 82 1894
(loop(\(x,i).2x,x,1) div (1 + (((1 + (((2 + (loop(\(x,i).2x,(x mod 4),1) + loop(\(x,i).2x,x,1))) div 3) div 2)) div 2) div 2)))
A290128: 1 2 4 4 8 16 16 18
(~1 + (8 * (1 + (2 * compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(8x + 2)),x)))))
A141194: 7 23 71 103 151 167 199 263 311 359 439 487 503 599 631 647
((2 * (1 + (7 * (if (x mod 2) <= 0 then (3 * (if (x mod 4) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1)) else 1)))) div 5)
A040282: 17 3 8 3 34 3 8 3 34 3 8 3 34 3 8 3
(if x <= 0 then 0 else ((1 + (((1 + (loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else 2x),x,(2x + 12)) div 3)) div 2) div 2)) mod 3))
A235644: 0 1 1 2 1 2 1 2 1 2 1 2 2 2 2 0
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A024436: 1 30 601 10122 155029 2238894 31086721 419796498 5553887821 72338375382 930742000825 11858835825018 149897892005317 1882300860052734 23506492073507953 292186168385703522
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(9x + 1),i,1)),i,1)),x,1)
A024443: 1 29 558 8986 131243 1805223 23872696 307323332 3882264405 48383711857 597102947714 7316027902638 89165615770687 1082459954878331 13102563809462412 158253703693612504
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A024445: 1 30 597 9934 149709 2121126 28836949 380838558 4924739997 62690732182 788556862821 9827670001422 121598064661165 1495950059553798 18319924811095413 223529877519404926
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A020975: 1 30 607 10344 160189 2335746 32694859 444486828 5913240457 77372622822 999305059831 12772807490352 161880145667605 2037329650638858 25491080959642723 317372095748963316
loop(\(x,i).(12x + loop(\(x,i).(9x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A025031: 1 32 675 11830 186641 2752932 38765455 527869010 7009691181 91304772832 1171464693035 14850954198990 186462962442121 2322930268904732 28754646814361415 354082225170989770
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A025008: 1 32 677 11932 189753 2826744 40267309 555414644 7478425985 98842456336 1287451399221 16573995013836 211336837165897 2673608205348008 33601552555975613 419959636392460708
loop(\(x,i).(12x + loop(\(x,i).(9x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A020984: 1 32 685 12260 198121 2997512 43322245 605523020 8251539841 110243798192 1449890883805 18826690025780 241910703467161 3081364962170072 38962058064701365 489593051613776540
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A023948: 1 29 566 9346 141027 2013855 27722632 371889332 4894555493 63487825921 814150878138 10345138210758 130470568108999 1635266348565827 20389018656020684 253092309224759224
loop(\(x,i).(12x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A021021: 1 33 727 13365 221431 3428733 50631967 721942485 10021257511 136192514733 1819621847407 23973890545605 312209398691191 4026262617877533 51492399583946047 653858524870924725
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A023952: 1 25 416 5822 74319 898779 10511446 120335968 1358681621 15202492877 169098946380 1873624439778 20707233183547 228476788273759 2518219270791458 27735798399148292
loop(\(x,i).(6x + loop(\(x,i).(10x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A024434: 1 28 521 8120 114765 1526196 19481953 241575376 2932083605 35012557580 412807072041 4818002535528 55771887460381 641245030592740 7331332058802545 83421584091633536
loop(\(x,i).(7x + loop(\(x,i).(9x + loop(\(x,i).(10x + 1),i,1)),i,1)),x,1)
A024441: 1 27 480 7090 94311 1173417 13944190 160292880 1797313221 19769671207 214195117500 2292743705070 24300717989731 255479745527397 2667841806196410 27701356042027660
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A024439: 1 27 482 7182 96843 1227609 14939644 176784444 2050941365 23457934071 265547461686 2983410454986 33332770184767 370895550650613 4114522946353808 45542666345230008
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A022455: 1 24 386 5256 65667 781200 9024772 102391152 1148621573 12793511016 141851544198 1568288482488 17306928957319 190768033959072 2101198710944264 23132476329120864
loop(\(x,i).(7x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),x,1)
A020973: 1 28 527 8330 119361 1607088 20736787 259516390 3174562421 38159361548 452427201447 5305418786850 61660643651881 711374339146408 8156868543440507 93047809667655710
loop(\(x,i).(8x + loop(\(x,i).(9x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A024772: 1 29 554 8794 125715 1681143 21476668 265496948 3202922789 37927649617 442690769742 5108795150862 58428053357623 663418639575851 7489021847982176 84142202352592936
loop(\(x,i).(8x + loop(\(x,i).(10x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A024999: 1 30 593 9738 143949 1989198 26238361 334590546 4159355717 50694901686 608290940049 7207487623674 84523773236605 982803891723294 11346293009032457 130203935811077922
loop(\(x,i).(9x + loop(\(x,i).(6x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A024346: 1 27 484 7266 98959 1269177 15642586 187539120 2204181925 25529358855 292445725936 3321943348542 37489352241979 420930326166741 4707254688375814 52473555698990412
loop(\(x,i).(9x + loop(\(x,i).(5x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A023540: 1 26 452 6622 88473 1117788 13616464 161765924 1887776825 21743151430 247985329956 2807195642706 31593670364257 353962564536152 3951485554056128 43987455339016168
loop(\(x,i).(5x + loop(\(x,i).(10x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A023946: 1 27 488 7434 103215 1353681 17093182 210149568 2533379189 30086951895 353166486036 4106992533462 47398834914523 543607880403069 6201901277261450 70443098125125516
loop(\(x,i).(0 - (((loop(\(x,i).loop(\(x,i).x2,2,x3),1,(10x + 1)) div 2) div 2) div 3)),x2,1)
A015418: 1 ~261535698060 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 mod ((x + 2) div (if x <= 0 then 1 else (x - loop(\(x,i).2x,((((1 + (8 mod (1 + (x div 2)))) div 2) + (if x <= 0 then 0 else 1)) - (x mod 2)),2)))))
A151758: 0 ~1 0 2 0 2 2 0 0 2 2 0 2 0 0 0
((1 + ((1 + ((1 + ((((x + 5) * loop(\(x,i).2x,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1)) div 2) div 2)) div 2)) div 2)) div 2)
A267998: 1 1 1 1 1 2 1 1 2 4 1 1 3 5 10 1
((2 + (if (x mod 2) <= 0 then (3 * (if (x mod 2) <= 0 then ((~1 + (9 * (2 - ((x div 2) mod 2)))) * (if x <= 0 then 1 else 2)) else 1)) else 1)) div 2)
A040700: 26 1 25 1 52 1 25 1 52 1 25 1 52 1 25 1
((loop(\(x,i).x2,1,((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3)) div 2) div 2)
A337175: 0 1 1 2 1 4 1 4 2 4 1 9 1 4 4 6
(if x <= 0 then 0 else (7 + (loop(\(x,i).((x2 + x) div 2),1,loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1)) div 3)))
A343298: 0 7 8 12 42
((loop(\(x,i).(1 + ((2 * (1 + (if x <= 0 then 0 else ((x + 5) + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2))))) div 3)),2,x) div 2) div 2)
A318781: 1 2 2 2 3 3 3 3 3 4 3 3 4 3 4 3
loop(\(x,i).(1 + (4 * (~1 + (2 * loop(\(x,i).4x,x,(1 + (2 * loop(\(x,i).(5x + ~4),x,8)))))))),x,2)
A290047: 2 45181 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x3,1,((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))))
A152241: 216 3375 42875 456533 2924207 10793861 33698267 83453453 296740963 726572699 1509003523 3491055413 5479701947 8254655261 15456856771 30576209383
((~2x + 3) + loop(\(x,i).(x + 2),(x + ~1),(loop(\(x,i).x3,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)))
A110496: 7 14 63 172 666 1099 2457 3430 6084 12195 14896 25327 34461 39754 51912 74439
(~x + ((3x + 3) * (1 + (4 * loop(\(x,i).(2 * (2 + ((if x <= 0 then 2 else (~2 + loop(\(x,i).4x,(x + 1),2))) div 2))),x,2)))))
A132645: 27 3125 4611686018427387903
compr(\x.((if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),x,2x)) div 3))) div 3))) mod 2),x)
A328727: 0 1 2 3 6 9 10 11 18 19 20 27 28 29 30 33
(~1 + ((x mod 2) + (if (x mod (2 + ((1 + (2 * ((x + loop(\(x,i).2x,(2 - (x mod 2)),(x div 2))) mod 5))) mod (x + 1)))) <= 0 then 2 else 0)))
A123739: 1 0 1 2 1 2 1 0 1 0 ~1 0 ~1 0 1 0
((x mod 9) - (((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1)))
A075491: 0 0 1 1 3 2 5 4 6 ~3 0 ~3 2 1 2 2
loop(\(x,i).20x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165841: 1 20 20 400 20 400 20 8000 400 400 20 8000 20 400 400 160000
loop(\(x,i).15x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165836: 1 15 15 225 15 225 15 3375 225 225 15 3375 15 225 225 50625
loop(\(x,i).18x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165839: 1 18 18 324 18 324 18 5832 324 324 18 5832 18 324 324 104976
loop(\(x,i).24x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165845: 1 24 24 576 24 576 24 13824 576 576 24 13824 24 576 576 331776
loop(\(x,i).32x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165853: 1 32 32 1024 32 1024 32 32768 1024 1024 32 32768 32 1024 1024 1048576
loop(\(x,i).14x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165835: 1 14 14 196 14 196 14 2744 196 196 14 2744 14 196 196 38416
loop(\(x,i).13x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165834: 1 13 13 169 13 169 13 2197 169 169 13 2197 13 169 169 28561
loop(\(x,i).11x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165832: 1 11 11 121 11 121 11 1331 121 121 11 1331 11 121 121 14641
loop(\(x,i).17x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165838: 1 17 17 289 17 289 17 4913 289 289 17 4913 17 289 289 83521
(1 + (x mod (1 + (x mod (1 + ((1 + (loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) + loop(\(x,i).4x,x,1))) mod (x + 1)))))))
A344704-A325975-A325813-A325640-A325633-A325632-A324544-A323166-A323160-A009194: 1 1 1 1 1 6 1 1 1 2 1 4 1 2 3 1
(1 + (if x <= 0 then 0 else (1 + ((1 + ((2 * (2 + (x div (1 + ((x div 2) mod (1 + (if (x mod 2) <= 0 then 6 else 1))))))) div 3)) mod 3))))
A322483-A061389: 1 2 2 2 2 4 2 3 2 4 2 4 2 4 4 3
(1 + (14 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(7x + ~1))),x)))
A140444-A042969-A042967: 29 43 71 113 127 197 211 239 281 337 379 421 449 463 491 547
(~1 + ((1 + ((if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2)))) div (2 + (x mod 2)))) mod 5))
A105307: 0 0 1 1 1 2 1 2 2 2 1 ~1 1 2 3 3
(1 + ((1 + ((1 + (2 * (if (x mod (1 + (2 * (x mod 4)))) <= 0 then 1 else loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))) div 3)) div 3))
A144790: 1 1 2 1 1 2 3 1 1 1 1 2 1 3 4 1
(1 + ((2 * (1 + ((1 + ((1 + (loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x) * (3 + (((x + 1) div 2) div 2)))) div 2)) div 2))) div 3))
A036995: 1 1 2 1 2 3 1 3 3 4 1 3 3 5 5 1
(if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + ((x mod (1 + ((~1 + loop(\(x,i).2x,(x div (2 + (x mod 2))),2)) mod (x + 1)))) div 2)) div 2))) div 3)))
A062842: 0 1 1 2 1 1 1 3 2 2 1 2 1 1 1 4
(if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (x div (2 + (loop(\(x,i).2x,(2 - ((~x + 2) div 5)),1) mod (x + 1))))) div 2))) div 3)))
A274036-A086342: 0 1 1 2 1 2 2 3 1 2 2 2 2 2 3 4
(if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (x div (2 + (loop(\(x,i).2x,(1 + (((1 + (x div 2)) div 2) div 2)),2) mod (x + 1))))) div 2))) div 3)))
A124769: 0 1 1 2 1 1 2 3 1 1 2 2 2 2 3 4
(~1 + (3 * (2 + (2 * (1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(6x + 4))),x)))))))
A068231: 11 23 47 59 71 83 107 131 167 179 191 227 239 251 263 311
loop(\(x,i).7x,(2 * ((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1))),1)
A165870: 1 49 49 2401 49 2401 49 117649 2401 2401 49 117649 49 2401 2401 5764801
(~1 + (2 * (1 + (if x <= 0 then 0 else (if (x mod (2 + ((1 + (2 * (1 + ((((2x + 2) mod (2 + (x div 2))) div 2) div 2)))) mod (x + 1)))) <= 0 then 2 else 1)))))
A112755: 1 3 5 3 3 5 3 3 3 3 5 3 3 3 3 3
(~1 + ((1 + ((1 + ((1 + ((loop(\(x,i).x2,1,(8 + loop(\(x,i).2x,x,1) - (x mod 2))) div 2) div 2)) div 3)) div 2)) div 2))
A056323: 1 1 2 4 11 31 107 379 1451 5611 22187 87979 350891 1400491 5597867 22379179
(~1 + (2 * (~1 + (4 * (1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(8x + 1))),x)))))))
A127589: 5 37 53 101 149 181 197 229 277 293 373 389 421 613 661 677
(~1 + (4 * (1 + (2 * (1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(8x + 4))),x)))))))
A141195: 11 43 59 107 139 251 283 331 347 379 443 491 523 571 587 619
(~1 + (2 * ((3 * ((x + 1) - ((x - loop(\(x,i).(x - (x2 div (x + 16))),2,(if x <= 0 then 1 else x))) mod (x + 1)))) div 2)))
A054500: 1 5 7 11 13 13 13 13 17 17 17 17 17 19 19 19
(1 + ((x mod (2 + ((if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + (loop(\(x,i).(3 * (2 + (x div 2))),x,0) div 2)) div 2)) div 2)))) mod (x + 1)))) div 2))
A002784: 1 1 1 2 3 1 1 4 5 1 3 1 3 1 1 8
(loop(\(x,i).(x6 + ~x2),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 15)
A138448: 4 48 1040 7840 118096 321776 1609152 3136368 9869024 39654832 59166848 171048336 316673504 421424080 718614208 1477623888
(((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3) + (x div 9))
A134681: 1 2 2 3 2 4 2 4 3 5 3 7 3 5 5 6
((loop(\(x,i).(x2 * (x4 div 2)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 3) div 5)
A138450: 2 24 520 3920 59048 160888 804576 1568184 4934512 19827416 29583424 85524168 158336752 210712040 359307104 738811944
((2 * (1 + (loop(\(x,i).2x,((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3),1) div 2))) div 3)
A070288: 0 0 0 1 0 2 0 2 1 2 0 6 0 2 2 3
(~3 + (4 * (1 + (4 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(8x + ~1))),x)))))
A131204-A094407: 17 97 113 193 241 257 337 353 401 433 449 577 593 641 673 769
(~3 + (2 * (2 + compr(\x.((~x + 1) + (23 * loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x))),x))))
A160771: 3 5 9 11 15 17 21 27 29 35 39 41 45 49 51 55
loop(\(x,i).9x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),(x + 1))
A166630: 1 18 27 324 45 486 63 5832 729 810 99 8748 117 1134 1215 104976
loop(\(x,i).10x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),(x + 1))
A166631: 1 20 30 400 50 600 70 8000 900 1000 110 12000 130 1400 1500 160000
loop(\(x,i).7x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),(x + 1))
A166628: 1 14 21 196 35 294 49 2744 441 490 77 4116 91 686 735 38416
(1 - ((1 + ((1 + ((1 + ((1 + ((1 + (loop(\(x,i).(2x + loop(\(x,i).(2 * (x - (i mod 2))),i,1)),x,1) div 2)) div 2)) div 2)) div 2)) div 2)) div 2))
A319762: 1 0 0 0 0 0 1 1 4 9 24
(((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (2 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) mod 10)
A137727: 6 5 5 7 3 1 3 7 7 9 7 7 3 1 1 7
(~2 + (3 * loop(\(x,i).(1 + (2 * (~1 + ((3x + 3) * (3 + loop(\(x,i).(2x2 + x),3,x)))))),(x + 1),1)))
A172700: 32611 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(2 - (2 * (1 + loop(\(x,i).(x - (if x <= 0 then 0 else (1 + i))),x,x) - (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))))
A338896: 0 2 0 4 4 0 6 8 6 0 8 12 12 8 0 10
(((3x + 3) * ((1 + ((x + 1) * loop(\(x,i).x3,1,loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1)))) div 2)) div 2)
A323325: 1 3 54 1500 51450 2000376 84523824 3789772272 177645575250 8619977394600 429995817814992 21940447761898848 1140809521021467024 4611686018427387903 4611686018427387903 4611686018427387903
(((x2 + 3x + 2) * ((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3)) div 2)
A143272: 1 6 12 30 30 84 56 144 135 220 132 468 182 420 480 680
loop(\(x,i).(1 + (2 * (if x <= 0 then 2 else ((x + 1) - ((1 - (((x + 1) mod (1 + (2 * ((1 + (x div 4)) div 2)))) div 2)) mod 2))))),1,((x + 1) div 2))
A270753: 5 3 3 5 5 7 7 11 11 11 11 13 13 17 17 17
(((3 * ((~1 + (6 * (1 + (x div (3 + ((~1 + loop(\(x,i).(if x <= 0 then i else (x div 2)),x,2)) mod (x + 1))))))) div 2)) div 2) div 2)
A209563: 1 1 1 1 3 1 1 3 6 1 1 3 8 10 1 1
(1 + (if x <= 0 then 0 else (1 + (((x + 1) + (((x + 1) + ((loop(\(x,i).(2x + (i mod 2)),x,(1 + (x mod 2))) div 2) div 2)) div 2)) div 2))) - (x mod 2))
A123120: 1 2 4 5 7 10 13
A223729: 1 2 4 5 7 10 13 28
(x + (if x <= 0 then 1 else (6x - ((2 * ((2x + 2) + (x div (1 + (2 * (if (~4 + (x div 2)) <= 0 then 2 else 1)))))) div 3))))
A313916: 1 5 10 16 22 27 32 38 44 49 54 59 64 70 76 81
(3x + (if x <= 0 then 1 else ((2x + ~1) + ((2 * (2 + (((x + 1) + (if (x mod 4) <= 0 then 2x else (x div 2))) div 2))) div 3))))
A315505: 1 6 11 16 24 28 33 38 48 50 55 60 72 72 77 82
(2 div (1 + ((x + 1) div (1 + (2 * ((2 * (1 + (x div 5))) div (1 + (if (2x mod (4 + (x div 4))) <= 0 then 2 else 0))))))))
A133696: 1 2 0 2 1 0 2 2 1 0 2 2 1 1 0 2
loop(\(x,i).(1 + (3 * (1 + (2 * ((1 + (x div 2)) div 2))))),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)
A142595: 1 1 1 1 4 1 1 10 10 1 1 22 40 22 1 1
(((if ((x div 5) mod 2) <= 0 then 1 else x) mod 4) div (1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))
A153659: 1 1 1 1 0 1 2 1 0 1 1 0 0 0 1 3
(1 + ((2 * (1 + ((1 + ((x mod (2 + ((~1 + (2 * (if (~2 + (((x + 1) div 2) mod 4)) <= 0 then 1 else 0))) mod (x + 1)))) div 2)) div 2))) div 3))
A161789: 1 1 2 1 1 2 3 1 2 1 1 2 1 3 4 1
(1 + (((2 * loop(\(x,i).4x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)) div 3) div (x + 1)))
A331315: 1 1 1 1 1 1 1 2 2 1 1 4 14 4 1 1
((2x + 1) - ((x + ((2x + 1) * loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1))) div (x + 1)))
A071050: 0 0 1 0 5 3 5 0 13 11 13 7 17 11 13 0
(1 + ((9 * (loop(\(x,i).2x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2)) div 2))
A173046: 1 1 1 1 5 1 1 10 10 1 1 19 37 19 1 1
(1 + (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + (if (x + ~2) <= 0 then 1 else 2) + (x div 5)) div 2))
A143901: 1 1 1 2 2 2 2 3 3 2 3 4 5 4 3 3
(loop(\(x,i).3x,((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~1) div 2))) div 2),1) mod 7)
A143214: 1 1 1 1 3 1 1 2 2 1 1 6 5 6 1 1
((loop(\(x,i).5x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2) div 7)
A282189: 0 0 0 0 0 0 0 1 1 0 0 8 44 8 0 0
(~1 + ((2 + ((2 * (1 + (loop(\(x,i).((x + 1) + (3 * (x div 5))),x,1) div (x + 1)))) div 3) - (x mod 2)) div 2))
A308992: 0 0 0 0 0 0 0 0 1 1 2 3 5 7 12 17
(~1 + ((2 + ((2 * (1 + ((1 + (loop(\(x,i).((x + 1) + (2 * ((x div 2) div 3))),x,1) div 2)) div 2))) div 3) - (x mod 2)) div 2))
A035562: 0 0 0 0 0 0 1 0 1 1 2 3 4 5 8 10
(1 + (2 * (loop(\(x,i).(x * (2 + (x div 5))),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2)))
A171229: 1 1 1 1 3 1 1 5 5 1 1 9 25 9 1 1
((1 + (((3x + 9) * ((x + 1) + loop(\(x,i).x3,1,(4x + 4)))) div 3)) mod 9)
A171677: 7 5 7 4 2 4 1 8 1 7 5 7 4 2 4 1
((loop(\(x,i).5x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2) div 9)
A283232: 0 0 0 0 0 0 0 1 1 0 0 6 34 6 0 0
((x + 2) - ((2x + 1) mod (if (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) <= 0 then (2 + (x div 4)) else 1)))
A194970: 1 2 3 4 6 5 7 9 10 8 11 13 14 15 12 16
(x - ((1 - ((x div 3) + (2 * (if x <= 0 then 1 else (2 * (3x + ((x + ((x div 3) mod 3)) div 3))))))) div 3))
A313979: 1 5 10 17 22 28 33 40 45 50 55 60 67 72 78 83
((2 * ((1 + ((x * ((x + 1) + (2 * ((1 + ((x * loop(\(x,i).(10x + 1),x,1)) div 2)) div 2)))) div 2)) div 2)) mod 3)
A217522: 0 1 2 1 0 2 1 2 0 1 0 2 0 1 2 0
((2 * ((x + 2) + ((loop(\(x,i).((6x + 4) - ((2x + 4) div 5)),x,3) div 2) div 3))) mod 3)
A035203: 1 0 1 1 2 0 1 0 1 0 0 1 0 0 2 1
(~3 + (2 * (x + ((2 * ((x + 2) + (if x <= 0 then 1 else ((16x + 8) mod 17)))) div 3))))
A337254: 1 11 13 15 17 19 21 23 25 51 53 55 57 59 61 63
((x + ((2 + ((1 + ((((((x + 1) * loop(\(x,i).((x2 + ~x) div 2),2,(x + 4))) div 3) div 2) div 2) div 2)) div 2)) div 2)) mod 3)
A321457: 1 0 0 1 0 0 1 0 0 2 0 1 2 0 2 2
compr(\x.((((2 * (1 + ((1 + ((x2 + ~x) div (3 * (if ((x + ~2) mod (2 + (x mod 2))) <= 0 then 1 else 2)))) div 2))) mod (x + 1)) div 2) div 2),(x + 1))
A090467: 1 2 3 4 5 7 8 11 13 14 17 19 20 23 26 29
((1 + ((2 * (1 + ((loop(\(x,i).2x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),2) - (x mod 3)) div 2))) div 3)) div 2)
A140191: 1 1 1 2 1 1 2 3 1 2 1 3 2 3 3 6
(2 * (1 + compr(\x.(~1 + (((1 + ((((x + 1) * (2 + ((if (x mod 2) <= 0 then (x + 3) else x) mod (x + 1)))) div 2) div 2)) div 2) mod 3)),(x + 1))))
A242483: 4 8 10 14 16 22 26 32 34 36 38 44 46 48 50 52
(2 * (1 + ((1 + (x div (2 + (loop(\(x,i).2x,(1 + ((1 + (8 mod (1 + (x div 2)))) div 2) - (x mod 2)),1) mod (x + 1))))) div 2)))
A066012: 2 2 2 4 2 4 4 4 2 4 4 4 4 6 6 8
(if x <= 0 then 1 else (2 * (1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (~1 + (8 * ((1 + (x div 2)) div 2)))) div 2))))
A055921: 1 2 2 2 8 2 2 16 16 2 2 24 48 24 2 2
(x div (2 * (1 + (x div (2 + ((0 + (2 * (1 + ((loop(\(x,i).2x,x,2) mod (2 + (x div 4))) div 2))) - (x mod 2)) mod (x + 1)))))))
A081387: 0 0 1 0 2 1 1 1 1 1 1 1 2 3 2 1
(~2 + (3 * (1 + (loop(\(x,i).x2,1,(1 + ((x mod (1 + (31 mod (x + 1)))) div 3))) div 3))))
A127707: 1 1 1 4 1 1 1 10 4 1 1 4 1 1 1 37
(2 * ((1 + (loop(\(x,i).(4x + ~2),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2)) div 3))
A230592-A230275: 0 0 0 0 0 0 0 2 2 0 0 8 28 8 0 0
((3 * (1 + ((loop(\(x,i).(2x + 4),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2) div 2))) div 2)
A157152: 1 1 1 1 3 1 1 7 7 1 1 15 30 15 1 1
((3 * (loop(\(x,i).(x2 + x),1,(1 + (((x * (1 - ((x3 div 8) mod 2))) + (x mod 2)) div 3))) div 2)) div 2)
A146955: 1 1 1 1 4 1 1 9 9 1 1 22 22 22 1 1
(((1 + (3 * loop(\(x,i).(2x + 2),(~1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)),1))) div 2) div 2)
A196809-A196646-A196601-A196578: 1 1 1 1 1 1 1 3 3 1 1 7 16 7 1 1
((loop(\(x,i).((8x + 8) div 3),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2) div 2)
A290448: 0 0 0 0 1 0 0 4 4 0 0 11 30 11 0 0
(((3 * ((3 * (1 + (((3 * (1 + ((2 + loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 3))) div 2) div 2))) div 2)) div 2) div 2)
A334861: 0 0 2 0 3 2 3 0 4 3 4 2 4 3 5 0
(((3x + 6) mod (2 + (9 * (if x <= 0 then 1 else 2)) - ((x mod 2) + (x mod 7)))) div 8)
A091430: 0 1 1 1 0 0 1 1 1 2 0 1 1 0 1 1
(2 + (((x + 2) + (if x <= 0 then 1 else (2 * (1 + (x div (3 * (2 + ((1 + (2x mod (1 + ((x div 2) div 3)))) mod (x + 1))))))))) div 2))
A037038: 3 4 5 5 6 6 7 7 8 9 10 10 11 10 12 12
(1 - ((loop(\(x,i).3x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 3) mod (x + 4)))
A176602: 1 1 1 1 0 1 1 ~2 ~2 1 1 ~8 ~10 ~8 1 1
((~1 + (4 * (1 + (((1 + (((2x + 1) * (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2)) div 2) div 2)))) div (x + 2))
A098389: 1 2 3 5 8 10 13 15 19 25 27 32 36 38 42 48
(1 + (((2 * (1 + ((1 + (((~1 + loop(\(x,i).2x,2x,(1 + (x div (2 + (x mod 2)))))) mod (x + 1)) div 2)) div 2))) div 3) + (x mod 2)))
A177062: 1 2 1 3 2 2 2 4 3 3 2 3 3 3 3 5
((x + 1) + ((2 * (1 + ((1 + (((1 + ((x * (loop(\(x,i).2x,x,(2 + (x div 4))) div 3)) div 2)) div 2) div 2)) div 2))) div 3))
A125730: 1 2 3 5 8 13 23 46 123
compr(\x.(~1 + (((3 * (1 + (((5 * (if x <= 0 then 1 else 2)) + (x div 7)) mod 9))) div 2) div 2)),x)
A028428: 1 2 3 4 5 6 56 57 58 59 60 61 62 63 64 65
compr(\x.(1 - (x mod (2 + ((2 * ((2x + 2) + (if x <= 0 then 1 else (4x + ((x - ((~x + 1) div 3)) div 3))))) mod 3)))),x)
A266114: 1 3 5 6 7 8 9 11 13 14 17 18 19 20 22 23
((x + 2) + (((x2 + ~1) - (2 * (2 - (((x + 1) + (if (x mod 2) <= 0 then (1 + (2 * (x - ((1 + (x mod 4)) div 2)))) else 2)) div 2)))) div 2))
A266617: 0 3 6 10 18 21 32 36 52 55 74 78 102 105 132 136
((2x + 2) + (((1 + ((((x + 1) * (1 + loop(\(x,i).(x2 + ~2x),2,8))) div 2) div 3)) div 2) div 9))
A038153: 22 44 67 89 112 134 157 179 202 224 247 269 291 314 336 359
(1 + (x mod (1 + (x mod (1 + ((1 + ((x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) mod 9)) mod (x + 1)))))))
A100387: 1 2 1 2 1 2 1 1 1 2 1 4 3 2 1 2
(1 + (x div (~1 + (6 * (1 + ((1 + (((2 * (1 + (x div (4 * (2 + (x mod 4)))))) - (x mod 3)) div 2)) div 2))))))
A224076: 1 1 1 1 1 2 1 2 1 1 3 3 2 2 3 2
(1 + ((2 * (1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + ((x + 1) mod 4))))) div 3))
A125127: 1 1 1 1 3 1 1 3 4 1 1 3 7 7 1 1
(1 + ((2 * (1 + ((1 + (x mod (1 + ((((1 + (8 mod (1 + (x div 2)))) div 2) - (x mod 2)) mod (1 + (x div 2)))))) div 2))) div 3))
A331183: 1 1 1 2 1 1 1 3 2 2 1 1 1 1 1 4
(1 + ((2 * (1 + ((1 + (x div (2 + ((2 * (((1 + (8 mod (1 + (x div 2)))) div 2) - (x mod 2))) mod (x + 1))))) div 2))) div 3))
A124736: 1 1 2 1 2 2 3 1 2 2 2 3 3 3 4 1
(~1 + ((1 + ((2 * (2 + ((3x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 2))) mod 7)) div 2))
A124961: 1 1 1 1 0 1 1 1 ~1 1 1 0 2 ~1 1 1
(1 + ((1 + ((1 + (4 * ((3 * ((1 + (x div 2)) div 2)) div 2))) * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2))) div 2))
A141541: 1 1 1 1 4 1 1 8 8 1 1 10 18 10 1 1
(~3 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) - ((2x + 1) div (3 + (x div 4))))
A201006: ~3 ~4 ~4 ~5 ~4 ~5 ~6 ~4 ~4 ~6 ~7 ~4 ~3 ~4 ~7 ~8
(1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + (2 * ((2x + 1) div (3 + (x div 4))))))
A204250: 1 3 3 5 6 5 7 9 9 7 9 12 13 12 9 11
(1 + ((1 + (9 mod (1 - (2 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2))))) div 2))
A214281: 1 1 1 1 1 1 1 3 3 1 1 2 6 2 1 1
(1 + ((3 * (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (~1 + (((2 - ((x div 2) mod 2)) * (x div 2)) div 3)))) div 2))
A229243: 1 1 1 1 1 1 1 1 2 1 1 1 10 5 1 1
(~1 + ((3 * ((1 + (2 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (~3 + (x div 2))) div 2))) div 3)) div 2))
A172972: ~1 ~1 ~1 ~1 ~3 ~1 ~1 ~1 ~1 ~1 ~1 0 2 0 ~1 ~1
(1 + ((3 * ((8 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)) div 3)) div 2))
A319251: 1 1 1 1 4 1 1 8 8 1 1 13 28 13 1 1
(1 + (4 * (1 + (2 * (~1 + ((3 * compr(\x.(1 - (x mod (2 + ((1 + ((x - ((x div 2) mod 2)) div 2)) mod 5)))),x)) div 2))))))
A186304: 5 21 29 45 69 77 101 125 149 165 189 197 221 237 261 269
(1 + (((1 + ((((x + 1) * ((x + 3) + ((1 + ((x * (x div 2)) div 4)) div 5) - (x mod 2))) div 2) div 2)) div 2) div 2))
A029017: 1 1 2 2 3 3 5 6 8 9 11 12 15 17 21 23
(1 + ((((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + (2 * (2 + ((x div 3) mod 2))))) div 2) div 2))
A285522: 1 1 1 1 2 1 1 3 3 1 1 6 6 4 1 1
(1 + ((((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + (2 * (2 + ((x + 1) mod 4))))) div 2) div 2))
A092422-A089899: 1 1 1 1 2 1 1 3 4 1 1 4 8 7 1 1
(1 + (((3 * (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((x * (1 + ((x div 2) mod 2))) div 3)))) div 2) div 2))
A210764-A138155-A091186: 1 1 1 1 2 1 1 4 3 1 1 7 8 4 1 1
(1 + (2 * ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * ((1 + (x div 2)) div 2) * (((x + 1) div 2) div 2))))
A176293: 1 1 1 1 3 1 1 17 17 1 1 55 73 55 1 1
(1 + (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + ((2x + ~1) div (4 + (x div 4)))) div 2))
A143902: 0 1 1 1 2 1 2 3 3 2 2 4 4 4 2 3
(((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 - (2 * (x div 7)))) mod 5)
A298930-A298895-A298259: 0 0 0 0 1 0 0 3 3 0 0 2 1 2 0 0
((1 + (16 * ((1 + ((((5x3 + 2x2 + ~3x) div 2) div 3) div 2)) div 2))) mod 3)
A067742: 1 1 0 1 0 2 0 1 1 0 0 2 0 0 2 1
((2 * (1 + ((1 + (((1 + (((x + 1) * ((x + 1) + (2 * (1 + (x div 3) - (2 * (x mod 2)))))) div 2)) div 2) div 2)) div 2))) div 3)
A340282: 0 0 1 1 2 2 4 4 6 6 9 8 13 12 16 16
(((5 * (1 + (((1 + (x mod ((1 + (x mod (1 + (x div 4)))) * (1 + (x mod 2))))) mod (x + 1)) + (x mod 2)))) div 2) div 3)
A309891: 0 1 1 3 1 3 1 5 3 3 1 6 1 3 3 8
((((x2 + 5x + 6) * ((x2 + 2x + 2) + ((5x2 + 19x + 12) div 2))) div 2) div 3)
A190048: 8 46 150 370 770 1428 2436 3900 5940 8690 12298 16926 22750 29960 38760 49368
((4 * (1 + compr(\x.(~1 + (((x + 1) * (1 + (x mod (2 * (2 + ((x2 + x) mod 8)))))) mod 3)),(x + 1)))) div 3)
A285035: 2 4 5 6 8 9 12 14 16 17 18 20 21 24 25 26
((4 * (1 + (((1 + (((1 + (((x + 1) * (1 + (2 * (x - (x mod 10))))) div 2)) div 2) div 2)) div 2) div 2))) div 3)
A098732: 1 1 1 1 1 1 1 1 1 1 10 12 12 13 14 14
((2 * ((4x + 3) + ((x - ((x - (3 * (1 - (((x + 1) div 2) mod 5)))) div 2)) div 2))) div 3)
A190521: 2 4 7 10 12 15 18 20 23 28 30 33 36 38 41 43
(x div (2 + ((((x + 1) + (2 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))) div 2) div 2) - (x mod 2)))
A207822: 0 1 1 1 1 2 2 1 1 3 2 2 1 2 2 3
((1 + (x div (1 + (x div (2 + ((((x + 1) div 2) div (1 + ((x div 2) mod (1 + (x mod (1 + ((~x + 2) mod 4))))))) + (x mod 2))))))) div 2)
A303639: 0 1 1 2 1 3 2 2 1 2 3 3 3 3 4 2
((1 + ((1 + (((1 + (((x + 1) * (1 + (2 * (((x - (2 * (2 + (x div 8)))) mod (x + 1)) div 2)))) div 2)) div 2) div 2)) div 2)) div 2)
A238217: 0 0 0 1 0 1 1 1 1 1 2 2 3 3 5 5
((1 + (((~1 + (2 * (~1 + (6 * (1 + (((x + 1) mod (1 + (2 * ((1 + (x div 4)) div 2)))) div 2)))))) mod (x + 1)) div 2)) div 2)
A152197: 0 0 0 0 0 1 1 1 0 2 3 2 2 1 2 2
((1 + ((((x + 1) * ((5x + 6) + (((x + (x2 div 4)) div 2) div 3))) div 2) div 2)) div 2)
A083462: 1 3 6 11
A023601: 1 3 6 11 17 24 33 44 56 69 84 101 120 140 161 184
((3 * ((x + 1) div (1 + ((2 * (1 + (x div (1 + (x mod (1 + (x mod (1 + (x div (2 + (x div 5))))))))))) div 3)))) div 2)
A066839: 1 1 1 3 1 3 1 3 4 3 1 6 1 3 4 7
((3 * (1 + ((3 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~1) - ((x div 2) mod 2))) div 2)) div 2))) div 2)
A008278: 1 1 1 1 3 1 1 6 7 1 1 10 25 15 1 1
((3 * (1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (x + (x div (1 + (2 * (2 - ((x div 2) mod 2))))))) div 2))) div 2)
A146986: 1 1 1 1 4 1 1 7 7 1 1 12 22 12 1 1
(((2 * ((2x + 1) div (3 + (x div 4)))) - (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) div 2)
A231205: 0 1 1 2 1 2 3 2 2 3 4 2
A341839: 0 1 1 2 1 2 3 2 2 3 4 2 2 2 4 5
(2 + (((2x + 1) + (2 * ((1 + (((26x2 + 65x + 26) div 2) div 3)) div 2))) div 3))
A100967: 3 9 18 29 44 61 81 104 130 159 191 225 263 303 347 393
(~2 + (3 * ((2x + 1) + (2 * ((2 + (((x + 1) + (2 * ((x div 2) mod (1 + (x2 mod (2 * (2 + (x mod 2)))))))) div 2)) div 2)))))
A129904: 7 13 19 31 37 43 49 61 67 73 79 91 97 103 109 127
(((1 + (2 * (((~1 + (6 * (1 + (x div (4 + (x div (1 + ((x + ~1) mod 5)))))))) div 2) div 2))) mod (x + 1)) div 2)
A055255: 0 0 0 1 1 2 1 2 2 2 2 1 2 2 4 4
(~2 + (2 * (1 + (2 * ((((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (3 + (x div 2))) div 2) div 2)))))
A049207: 0 0 0 0 4 0 0 12 12 0 0 24 36 24 0 0
((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + (2 * (2 + ((2x + 1) div (3 + (x div 4))))))
A173395: 4 6 6 8 9 8 10 12 12 10 12 15 16 15 12 14
(1 - ((1 - (((x mod (3 + (x div 4))) - (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) div 2)) div 2))
A301367: 1 1 1 1 0 1 1 1 1 2 1 0 0 0 1 1
(2 + ((3 * ((x + 1) + ((x - ((~x + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) div 2)) div 2))) div 2))
A342744: 3 6 8 11 14 17 18 21 23 27 29 30 33 36 39 42
(x mod (4 + (((2x + 1) + (2 * (1 - (x mod (1 + (((x + 1) - (2 * (x div (2 * (2 - (x mod 2)))))) mod (x + 1))))))) div 3)))
A103303: 0 1 2 3 4 5 6 7 8 9
A093691: 0 1 2 3 4 5 6 7 8 9 0 0 2 0 3 0
(2 * (((4 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)) div 3) * (((x + 1) div 2) div 2)))
A058347: 0 0 0 0 2 0 0 8 8 0 0 24 54 24 0 0
(((~1 + (6 * (1 + (x div (3 * (1 + (x mod (2 * (1 + (x mod (3 + (x mod 2)))))))))))) div 3) mod 8)
A339903: 1 1 1 1 3 1 5 1 1 3 3 1 1 5 3 1
((2x + ~1) + (2 * (1 + ((1 + ((1 + ((1 + (((x + 1) * (1 + (2 * ((x + 1) div 7)))) div 2)) div 2)) div 2)) div 2))))
A005763: 1 5 7 9 11 13 17
A336366: 1 5 7 9 11 13 17 19 21 23 25 29 31 37 39 41
((~2x + 1) + (2 * (x + (2 * ((((x + 1) + ((((3 * ((x * (x mod 4)) div 2)) mod (x + 1)) div 2) div 2)) div 2) div 3)))))
A241154: 1 1 1 1 1 5 5 5 5 5 9 9 9 9 13 9
(1 + ((2 * (1 + ((1 + (((1 + ((((x + ~1) * ((x + 1) + (x2 div 4))) div 2) div 2)) div 2) div 2)) div 2))) div 3) - (x mod 2))
A035937: 1 0 1 1 2 2 3 3 5 6 8 9 13 14 19 22
((x + 1) + ((2 * (1 + ((1 + (((1 + (((x + 1) * (x - ((x + 1) mod 13))) div 2)) div 2) div 2)) div 2))) div 3))
A277861: 1 2 3 4 5 6 7 8 9 10 11 12 20 22 23 24
((~x + 1) + ((2 * (1 + ((x + ((x + (2 * ((((x + 3) * ((x + 1) - ((~x + 1) div 3))) div 2) div 2))) div 2)) div 2))) div 3))
A109950: 1 1 2 2 3 4 5 6 8 10 11 14 16 18 23 25
((~x + ~1) + ((2 * ((x + 3) + ((2 * (1 + ((x - ((((~x + 1) div 3) * (1 + (x div 2))) div 2)) div 2))) div 3))) div 3))
A264401: 1 0 1 1 1 1 1 1 2 2 1 2 3 2 4 4
compr(\x.(2 - (((2x + 1) + (2 * (((x + 1) + (2 * (20 mod (1 + (x div 2))))) div 2))) mod 7)),x)
A225647: 1 3 4 6 7
A066650: 1 3 4 6 7 8 11 13 14 15 16 18 19 20 21 22
compr(\x.(1 - ((1 + ((1 + ((1 + ((1 + ((1 + (((x div (~2 + (x mod 2))) + (x mod 3)) div 2)) mod (x + 1))) div 2)) div 2)) div 2)) mod 3)),x)
A103303: 0 1 2 3 4 5 6 7 8 9
A336668: 0 1 2 3 4 5 6 7 8 9 11 20 22 24 26 28
compr(\x.(((1 + (((1 + (((x + 1) * (1 + ((1 + (x div (2 * (2 - ((x * (x div 2)) mod 2))))) div 3))) div 2)) div 2) div 2)) mod 3) div 2),x)
A171551: 0 1 2 3 4 7 8 9 10 12 13 15 18 20 21 22
compr(\x.((2 + ((2 * (1 + ((1 + ((x + 1) div (1 + (x div (1 + (2 * (1 + (x mod 3)))))))) div 2))) div 3) - (x mod 2)) mod 2),x)
A079279: 1 2 3 4 8 9 10 14 15 16 21 22 26 27 28 32
((4x + 5) + ((((33x + 480) div 2) div 2) div 2))
A282113: 65 73 81 89 97 105 113 121 130 138 146 154 162 170 178 186
(~x + (((x + ~1) + ((2 * ((x + 2) + ((2 * (1 + (2 * (x - ((~2x2 + 4x) div 5))))) div 3))) div 3)) div 2))
A211536: 0 0 0 2 3 4 6 8 11 14 17 21 24 29 34 39
((4x + 1) + (((x + 1) + ((x + ((1 + (((x + 1) * (x + ((x + (x mod 2)) div 5))) div 2)) div 2)) div 2)) div 2))
A085813: 1 6 11 16 21 27 33 38 44 51 57 63 70 76 83 90
loop(\(x,i).2x,x,loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1))
A028138: 1 30 580 9240 132496 1784160 23095360 291434880 3616450816 44380976640 540619555840 6552897361920 79164966670336 954260234526720 11485602445803520 138104474808975360
loop(\(x,i).2x,x,loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1))
A028136: 1 28 500 7280 94416 1138368 13069120 144981760 1569049856 16674065408 174788490240 1813347594240 18663674269696 190917377179648 1943653403279360 19713779492126720
(~2 + loop(\(x,i).(if x <= 0 then 1 else (2 * (1 + loop(\(x,i).2x,x,(loop(\(x,i).10x,x,1) - loop(\(x,i).4x,x,1)))))),1,(x + 1)))
A291066: 24 672 14976 311808 6334464 127475712 2555805696 51166445568 1023731564544 20477852516352 409582820130816 8191862561046528 163838900488372224 3276791203906977792 4611686018427387903 4611686018427387903
(1 + (loop(\(x,i).(x2 + x),1,loop(\(x,i).3x,x,1)) + loop(\(x,i).5x,x,1) + loop(\(x,i).7x,x,1)))
A134007: 5 25 165 1225 9669 79225 665445 5686825 49208709 429746905 3779084325 33407391625 296515495749 2639977136185 23561123826405 210669225531625
(1 + (2 * (1 + loop(\(x,i).compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),x),1,(1 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))))
A117249-A072677: 5 7 13 19 37 43 61 71 89 113 131 163 181 193 223 251
(1 + (((1 + (3 * (x + loop(\(x,i).(x - (if x <= 0 then 1 else (x - ((if x <= 0 then 2 else loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 2)))),x,(x + 2))))) div 2) div 2))
A207666: 2 2 3 2 2 2 4 3 3 2 3 2 2 2 5 4
((compr(\x.(1 - loop(\(x,i).(x + loop(\(x,i).(x - (if x <= 0 then 1 else (if (x mod 2) <= 0 then (x div 2) else (2x + ~1)))),x,(x + 1))),1,(2x + ~1))),x) div 2) mod 3)
A309011: 0 1 2 0 1 0 2 0 1 2 0 2 1 0 1 2
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025991: 1 25 417 5909 77369 972381 11958289 145367893 1756276137 21149737037 254259660161 3053974195077 36665246878105 440090336260093 5281738449973233 63384838751399861
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028037: 1 25 415 5845 76111 952525 11679655 141710965 1710104671 20579684125 247310795095 2969873300485 35651407676431 427894724193325 5135204742169735 61625269469056405
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028001: 1 29 553 8801 127033 1728833 22655881 289479377 3634751065 45081115937 554241018409 6770845059953 82332981442297 997760934850241 12061135182324937 145526363142458129
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025947: 1 24 391 5478 71449 898044 11063179 134771010 1631361325 19675158360 236793832639 2846370045246 34190350504129 410521580544372 4927920602312371 59146678721188986
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A026006: 1 27 483 7271 100083 1308831 16594651 206375367 2535071715 30892653935 374502469419 4524435989463 54536889623347 656393971978239 7892348208238587 94833193717469159
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028046: 1 27 481 7203 98665 1285179 16245937 201600531 2472643129 30100201131 364634299393 4403082925059 53056831273993 638440928326683 7675363823623249 92216951605023987
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028017: 1 31 627 10499 158219 2232387 30141979 394679923 5055314187 63715123043 793475307131 9793201406547 120053522334955 1464191224876099 17788099372232283 215464347026366771
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).(7x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025975: 1 25 419 5981 78939 999453 12366859 151048909 1831243931 22106050109 266192557995 3200758779309 38454275485627 461767630974493 5543426384577227 66536622452560781
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028031: 1 24 385 5280 67441 833064 10129825 122282160 1471249681 17675304504 212209212865 2547054594240 30567440844721 366823482358344 4401953808801505 52823810060045520
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028049: 1 28 517 8008 113113 1513876 19589389 247937536 3091276705 38140546444 467097608341 5689887004984 69041150918377 835356636400132 10086046124610973 121588456137536752
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A026108: 1 28 519 8078 114617 1539720 19981483 253451506 3165132333 39098271212 479245678847 5841627343734 70916047801249 858343285202704 10366285999237011 124990982044693562
loop(\(x,i).(12x + loop(\(x,i).(10x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025956: 1 27 493 7671 109813 1496031 19737181 254700567 3234969925 40605328335 505121007469 6240023291463 76665993102037 937849058035839 11432760118860157 138978835693603959
loop(\(x,i).(6x + loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A174515: 1 25 397 5125 58813 626725 6356749 62315125 596370205 5610245125 52128987181 480061573525 4392455087677 40002549209125 363080219023693 3287474035532725
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A026326: 1 24 373 4776 54853 588408 6028741 59809992 579668485 5521782552 51920105029 483393574248 4466595742597 41031327740856 375223258308037 3419303762715144
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(7x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A026324: 1 23 341 4147 45045 455091 4373797 40541699 365712149 3230463379 28067769093 240654781731 2041291828213 17162300683187 143239714105829 1188212150789443
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028135: 1 27 463 6447 79639 910959 9884071 103247199 1048457047 10419680271 101824958599 981887319231 9367184200375 88585292286063 831747262057447 7762970817850143
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).5x,i,1)),i,1)),i,1)),x,1)
A028110: 1 23 335 3955 41391 401163 3691255 32746835 282966431 2398399003 20039831175 165661847715 1358507565871 11073172312043 89845493043095 726472924548595
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028054: 1 22 309 3542 36197 344190 3119173 27339334 233997093 1968524558 16351808837 134557949526 1099534023589 8937744119326 72366036152901 584189060834918
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028079: 1 26 433 5894 71533 807002 8661241 89694638 904552165 8939508578 86964763249 835481774582 7946080247197 74954796226154 702270481591657 6542793214395326
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025969: 1 23 353 4603 55449 640851 7242961 80866811 896831177 9909444259 109271790849 1203605509899 13249389022585 145801783940147 1604171188346417 17647994609290267
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(7x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028032: 1 20 255 2650 24521 210840 1725235 13631750 104995341 793395460 5908353815 43502236050 317443722961 2299938136880 16567618807995 118785894675550
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028111: 1 24 367 4578 50953 528612 5239459 50371926 474339085 4403719320 40486113031 369718215594 3360676724497 30451202305548 275320935296683 2485597397873982
loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).(7x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025986: 1 20 257 2704 25389 221676 1841449 14758568 115171397 880623172 6627177921 49248518592 362296167325 2643446894108 19158543110873 138087153497176
loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A025989: 1 23 347 4375 50211 546063 5750347 59371895 605580371 6130227103 61765086747 620509140615 6222647943331 62333853156143 623992946413547 6243906815856535
loop(\(x,i).(6x + loop(\(x,i).(10x + loop(\(x,i).(4x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028035: 1 23 345 4315 49121 530403 5553385 57088955 580462641 5863054483 58985130425 591995063595 5932878706561 59406619141763 594534243267465 5948154995694235
loop(\(x,i).(6x + loop(\(x,i).(2x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A026795: 1 27 475 6915 90571 1110147 13011355 147722355 1638222091 17846324067 191730867835 2037261517395 21455455896811 224319716510787 2331201129229915 24104752246858035
loop(\(x,i).(6x + loop(\(x,i).(3x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025941: 1 22 327 4172 49553 567714 6382699 71043064 786493125 8681598926 95678810591 1053554778276 11595631317817 127591121803258 1403737417995603 15442522109891408
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025992: 1 22 313 3666 38493 377286 3529681 31947322 282198565 2447183310 20920905369 176852694018 1481626607917 12322682753494 101879323774177 838170485025354
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028038: 1 22 311 3608 37485 363594 3368947 30231916 265060169 2283904766 19419219183 163405866624 1363677239653 11304693716338 93205539717419 765024499566932
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028005: 1 26 437 6034 74469 855042 9338629 98346578 1007581157 10104420898 99624776901 968871159282 9317203571365 88769381856194 839190346712453 7881486986566546
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028026: 1 19 230 2270 19971 163569 1278040 9670540 71557541 521211119 3754036650 26822296410 190541788711 1347984742669 9507913700060 66919750327880
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A025973: 1 23 349 4443 51597 568155 6054973 63196331 650620333 6637326267 67293219357 679380276939 6838972903309 68706054180059 689275354683901 6908259384473067
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028039: 1 23 342 4198 46403 481341 4792264 46410716 440901285 4131534979 38331795866 353038275954 3233774790247 29499248911337 268261230188748 2433731253526312
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A025993: 1 23 344 4258 47487 496725 4981918 48547136 463544213 4361492707 40596873252 374857310334 3440520848779 31434357529169 286207079508746 2598999610410652
loop(\(x,i).(7x + loop(\(x,i).(10x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A025945: 1 22 323 4016 45873 499386 5280511 54817972 562288925 5721711710 57909049419 583934547768 5873255438857 58969928883394 591360924613847 5925240739579004
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025978: 1 25 415 5805 74271 902325 10616455 122340685 1390355791 15651303525 175025553495 1948179192765 21613189505311 239210965847125 2643048211482535 29167353171072045
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028120: 1 26 431 5824 70077 783510 8335867 85622108 857084393 8414359954 81378676743 777830951352 7365015041749 69207262292558 646271819803859 6003846344524756
loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A025998: 1 25 409 5565 68481 792645 8815129 95390845 1012475761 10596550965 109756131849 1127967674925 11523334499041 117184641488485 1187466959384569 11999684812451805
loop(\(x,i).(8x + loop(\(x,i).(10x + loop(\(x,i).(4x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028044: 1 25 407 5501 67239 773589 8559679 92246077 975897527 10187458853 105306474351 1080536075853 11025196931815 112010922356917 1134181907272223 11454404794267229
loop(\(x,i).(8x + loop(\(x,i).(2x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028015: 1 29 545 8425 116481 1498569 18339025 216366425 2482819361 27879546409 307689294705 3348390668025 36019012136641 383739078223049 4055195455949585 42559109119075225
loop(\(x,i).(8x + loop(\(x,i).(3x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025950: 1 24 387 5306 66969 806148 9425599 108151662 1225448037 13766224472 153719012811 1709234017218 18948174785905 209602732183596 2315012544644823 25540197959076374
loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025963: 1 22 325 4110 48381 550062 6148165 68149870 752379661 8290355502 91266902805 1004309278830 11049302357341 121551961591342 1337120292662245 14708568942522990
loop(\(x,i).(4x + loop(\(x,i).(3x + loop(\(x,i).(5x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028029: 1 22 317 3830 42381 447582 4608877 46813030 471994061 4740248942 47508048237 475624522230 4759030936141 47604501583102 476117036332397 4761534717751430
loop(\(x,i).(4x + loop(\(x,i).(3x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028047: 1 26 441 6214 79157 948090 10903777 121902638 1335052653 14395752514 153368576153 1618401466422 16946521522789 176328040607498 1825046893884369 18806371581048766
loop(\(x,i).(5x + loop(\(x,i).(8x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028064: 1 25 402 5306 62699 691299 7275724 74105812 736913397 7196762573 69311524646 660250818318 6234443691295 58450533199447 544794370231968 5053142176005224
loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A026024: 1 26 443 6280 80481 969126 11196103 125634740 1380061661 14917299826 159239422563 1683073423200 17647253908441 183823250672126 1904399083525823 19639540889107660
loop(\(x,i).(3x + loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028055: 1 23 340 4130 45031 459893 4504690 42928160 401635861 3711270563 34005047440 309788905790 2811170579491 25442007146033 229842147512590 2073840099225020
loop(\(x,i).(3x + loop(\(x,i).(5x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025935: 1 21 300 3710 43071 485751 5405170 59772720 659098341 7258131881 79879876440 878881296930 9668709132811 106360879560411 1169995084978110 12870073026808340
((if x <= 0 then 1 else ((2x + ~1) * (if (((x + 1) div 2) div 2) <= 0 then 1 else (if x <= 0 then 1 else (if ((x + 1) mod 9) <= 0 then (x + 1) else 0))))) div (x + 1))
A287285: 1 0 1 0 0 0 0 0 15 0 0 0 0 0 0 0
compr(\x.(x + loop(\(x,i).(x - (if x <= 0 then 1 else (if (x mod 2) <= 0 then (x div 2) else (1 + (9 * loop(\(x,i).(x div (1 + (x mod 2))),x,x)))))),x,x)),(x + 1))
A094695: 5 9 10 11 13 17 18 19 20 21 22 25 26 27 29 33
(2 * loop(\(x,i).(((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1)),1,(x - (if x <= 0 then 0 else 1))))
A319410: 0 0 2 2 4 2 6 2 6 4 6 2 10 2 6 6
(((loop(\(x,i).4x,x,1) + loop(\(x,i).6x,x,1)) - (loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1))) div 2)
A083328: 0 1 9 64 423 2716 17199 108004 673983 4183516 25845039 158993044 974443743 5952752716 36262150479 220363399684
((~x + 1) + loop(\(x,i).(if x <= 0 then 1 else (x * ((loop(\(x,i).((x * ((x * loop(\(x,i).((x2 + ~x) div 2),2,(x + 2))) div (x + 1))) div 2),x,2) div 2) div 2))),x,0))
A259329: 1 1 1 4872 4611686018427387903 4611686018427387903
(x * loop(\(x,i).(((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1)),(if x <= 0 then 0 else 1),(x + ~1)))
A168014: 0 0 2 3 8 5 18 7 24 18 30 11 60 13 42 45
(2 + loop(\(x,i).(x - (if x <= 0 then 1 else loop(\(x,i).(x - (if x <= 0 then 1 else (~1 + ((2x + 1) mod (2 - ((~x + 2) div 5)))))),x,x))),2,x))
A293439-A144095: 0 1 1 1 1 2 1 0 1 2 1 2 1 2 2 1
(~1 + ((2 * ((2x + 2) + (if x <= 0 then 1 else (2 * ((4x + 1) - loop(\(x,i).(x + (if (~2 + (x div 4)) <= 0 then 1 else 2)),2,x)))))) div 3))
A313259: 1 4 9 15 20 25 31 36 41 47 52 56 60 65 71 76
(1 + (loop(\(x,i).(x2 + 2),1,(compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 3))
A082910: 2 3 3 7 3 7 3 7 13 3 13 7 3 7 13 13
((x + 1) mod loop(\(x,i).2x,((~1 + loop(\(x,i).x2,1,(1 + (x mod (1 + (x div (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))))))) mod (x + 1)),1))
A286875: 0 0 0 4 0 0 0 8 9 0 0 4 0 0 0 16
(1 + ((3 * (((if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).2x,x,2) mod loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))) div 2)))) - (x mod 2)) div 2)) div 2))
A244971: 1 1 4 1 4 1 4 1 8 4 4 1 4 4 8 1
(1 + (((3 * (1 + ((1 + (5 * (loop(\(x,i).2x,loop(\(x,i).(x - (if (~x + i) <= 0 then i else 0)),x,x),1) div 2))) div 3))) div 2) div 2))
A104765: 1 1 3 1 3 4 1 3 4 7 1 3 4 7 11 1
(4 + loop(\(x,i).x2,1,(1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(2x2 + 2x + 1))),x)))))
A005473: 5 13 29 53 173 229 293 733 1093 1229 1373 2029 2213 3253 4229 4493
(9x * loop(\(x,i).(((1 + loop(\(x,i).4x,x,2) - loop(\(x,i).3x,x,3)) div 2) div 2),1,3x))
A216592: 0 108 27018
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A024446: 1 31 638 10982 171171 2506917 35201776 479688604 6392929061 83765551883 1083070611714 13855878102066 175736023769671 2213065674408529 27704146634051252 345076242383014568
loop(\(x,i).(12x + loop(\(x,i).(9x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A025130: 1 33 718 12978 211099 3208611 46530856 652053876 8903593717 119147391909 1569038275714 20395728301494 262306431768655 3343671393938727 42305729458640092 531898781072416632
loop(\(x,i).(12x + loop(\(x,i).(10x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A025190: 1 34 761 14126 235557 3664290 54296257 776238742 10797496253 146990010986 1966611858393 25940502403998 338149901095189 4364412518972722 55856812102918769 709715336973843494
loop(\(x,i).(7x + loop(\(x,i).(9x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A024442: 1 28 518 7988 111279 1454376 18208156 221140696 2626932077 30692791844 354119115714 4046102802924 45880411771195 517157095113232 5801772397167992 64842434348911472
loop(\(x,i).(7x + loop(\(x,i).(10x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A024444: 1 29 556 8886 128247 1735335 22472122 281988512 3456550933 41615912481 494043113928 5799461900778 67460105552659 778834444699067 8935702988139574 101983512655795284
loop(\(x,i).(9x + loop(\(x,i).(10x + loop(\(x,i).(11x + 1),i,1)),i,1)),x,1)
A025009: 1 31 632 10682 162183 2297253 31000054 403684144 5115788645 63462153755 773891110356 9306180096486 110619493115587 1302189143870737 15203564170082738 176265669269562908
(x div (if (x + ~1) <= 0 then 1 else (2 * (1 + (x div (2 + ((if x <= 0 then 1 else (2 * (1 + ((1 + ((loop(\(x,i).2x,x,2) mod (x + 1)) div 2)) div 2)))) mod (x + 1))))))))
A206483-A198337: 0 1 1 1 2 2 1 1 2 2 2 2 2 2 3 1
((loop(\(x,i).x2,1,(((2 * (4 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1))) div 2) div 2)
A337174: 1 2 2 4 2 6 2 6 4 6 2 12 2 6 6 9
(2 + (2 * (~1 + (2 * loop(\(x,i).10x,1,((loop(\(x,i).x2,1,(~1 + loop(\(x,i).10x,x,1))) div 2) div 2))))))
A093220: 0 800 98000 9980000 999800000 99998000000 9999980000000 999999800000000 99999998000000000 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((if x <= 0 then 1 else (2 + ((((loop(\(x,i).(2x + 2),x,0) mod (x + 1)) - loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))) mod (x + 1)) div 2) - (x mod 2))) div 2)
A227083: 0 0 1 0 1 1 1 1 2 2 1 3 1 2 2 3
((2x - loop(\(x,i).(x - (if x <= 0 then 1 else (1 - (((x2 + 1) div (1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))) mod 3)))),x,x)) div 2)
A280242: 0 0 0 0 1 2 3 4 3 4 5 6 6 6 5 6
((x + 1) + ((x * loop(\(x,i).(if x <= 0 then 1 else (2 * (1 + ((1 + (((1 + loop(\(x,i).(x * i),(x + ~1),1)) div 2) div 2)) div 2)))),1,(x + ~1))) div 5))
A335597: 1 2 3 5 6 10 16 52
(~x + ((2 * (2 + compr(\x.(~1 + loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,18x)),x))) div 3))
A031231: 1 1 1 1 2 1 2 3 4 4 5 5 6 6 6 5
(if ((5x mod 33) mod 2) <= 0 then 1 else (x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,(x + 1))))
A265578: 1 2 1 3 1 2 1 1 1 1 1 1 1 1 1 5
(2x + (if x <= 0 then 1 else (2 * (x + (((x + 1) + ((3 * ((x + 1) - loop(\(x,i).(x + (if (~2 + (x div 4)) <= 0 then 1 else 2)),2,x))) div 2)) div 2)))))
A312556: 1 4 8 14 18 24 28 34 38 44 48 52 56 60 66 70
(2 + ((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)) - (if ((x + 1) mod 8) <= 0 then 1 else 2))
A257089: 0 1 1 2 1 2 1 4 2 2 1 3 1 2 2 5
loop(\(x,i).30x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165851: 1 30 30 900 30 900 30 27000 900 900 30 27000 30 900 900 810000
loop(\(x,i).40x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165861: 1 40 40 1600 40 1600 40 64000 1600 1600 40 64000 40 1600 1600 2560000
loop(\(x,i).27x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165848: 1 27 27 729 27 729 27 19683 729 729 27 19683 27 729 729 531441
loop(\(x,i).48x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165869: 1 48 48 2304 48 2304 48 110592 2304 2304 48 110592 48 2304 2304 5308416
loop(\(x,i).21x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165842: 1 21 21 441 21 441 21 9261 441 441 21 9261 21 441 441 194481
loop(\(x,i).28x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165849: 1 28 28 784 28 784 28 21952 784 784 28 21952 28 784 784 614656
loop(\(x,i).26x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165847: 1 26 26 676 26 676 26 17576 676 676 26 17576 26 676 676 456976
loop(\(x,i).22x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165843: 1 22 22 484 22 484 22 10648 484 484 22 10648 22 484 484 234256
loop(\(x,i).34x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165855: 1 34 34 1156 34 1156 34 39304 1156 1156 34 39304 34 1156 1156 1336336
loop(\(x,i).19x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165840: 1 19 19 361 19 361 19 6859 361 361 19 6859 19 361 361 130321
loop(\(x,i).23x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165844: 1 23 23 529 23 529 23 12167 529 529 23 12167 23 529 529 279841
loop(\(x,i).33x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165854: 1 33 33 1089 33 1089 33 35937 1089 1089 33 35937 33 1089 1089 1185921
loop(\(x,i).31x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165852: 1 31 31 961 31 961 31 29791 961 961 31 29791 31 961 961 923521
(if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (x div (1 + (x mod (1 + ((~1 + loop(\(x,i).2x,((x + 1) + (x div 2)),2)) mod (x + 1))))))) div 2))) div 3)))
A333766: 0 1 2 1 3 2 2 1 4 3 2 2 3 2 2 1
(if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (x mod (1 + (x mod (1 + (x div (2 + ((x div 2) mod (1 + (if (x mod 3) <= 0 then 0 else 2)))))))))) div 2))) div 3)))
A173442: 0 1 1 2 1 2 1 3 2 3 1 2 1 3 3 4
(~1 + ((2 * (1 + ((1 + ((x + 1) div (1 + ((1 - (2 * (if x <= 0 then 2 else (loop(\(x,i).(2x + i),x,0) div (x + 1))))) mod (x + 1))))) div 2))) div 3))
A249422: 0 0 0 0 0 1 0 0 0 0 0 0 0 2 5 0
(if x <= 0 then 0 else (1 + ((2 * (1 + ((((~1 + (2 * (1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 8)))) mod (x + 1)) div 2) div 2))) div 3)))
A053821: 0 1 1 1 2 2 2 1 1 3 2 2 3 3 3 1
(1 + (loop(\(x,i).2x,(0 + ((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) - (x mod 2)),1) div 2))
A011776: 1 1 1 1 1 2 1 2 2 2 1 5 1 2 3 3
(((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)) * (if ((x + 1) mod 12) <= 0 then 2 else 1))
A066921: 0 1 1 2 1 2 1 3 2 2 1 6 1 2 2 4
(1 + ((((2 * (1 + ((1 + (((loop(\(x,i).(x + (if x <= 0 then 1 else ((x * (x mod 2)) + (x div 2)))),x,1) div 2) div 2) + (x mod 2))) div 2))) mod (x + 1)) div 2) div 2))
A201080: 1 1 1 1 1 1 2 1 1 1 1 3 3 4 3 3
(((loop(\(x,i).(x2 * (x4 div 2)),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 3) div 5)
A138451: 1 12 260 1960 29524 80444 402288 784092 2467256 9913708 14791712 42762084 79168376 105356020 179653552 369405972
((10x + 10) + ((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3))
A065998: 11 22 32 43 52 64 72 84 93 104 112 126 132 144 154 165
(1 - ((1 + (2 * (((x mod 2) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) - compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)))) div 3))
A143117: 2 2 2 3 2 3 2 3 5 2 5 3 2 3 5 4
(~3 + (2 * loop(\(x,i).2x,(1 + (((x + 1) + (((x + 1) + ((3 * (1 + (if x <= 0 then 0 else (2 * (1 - (x div 2)))))) div 2)) div 2)) div 2)),1)))
A151994: 5 13 13 29 29 61 61 61 61
((2 + ((10 * (if (x mod 2) <= 0 then ((~1 + (5 * (2 - ((x div 2) mod 2)))) * (if x <= 0 then 1 else 2)) else 1)) div 3)) div 3)
A010184: 10 1 9 1 20 1 9 1 20 1 9 1 20 1 9 1
((2x + 1) + (3 * ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * loop(\(x,i).x5,2x,3))))
A211378: 19 7625597484990 4611686018427387903
(1 + compr(\x.(1 - ((((loop(\(x,i).(x * (4 + (x div 4))),1,loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))) div 2) div 2) div 3) mod 3)),x))
A184987: 3 5 6 7 9 10 11 12 13 14 15 17 18 20 22 23
compr(\x.(x mod 2),(1 + compr(\x.(1 - ((2 * (2 + (if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 2)))))) mod 3)),x)))
A181794: 4 6 10 12 14 16 20 22 24 26 28 34 36 38 44 46
((2 * (x + (((3x + 1) + (if x <= 0 then 1 else (x + ((x + 1) div 2) - (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))))) div 2))) div (x + 1))
A082090: 2 3 4 4 5 5 5 5 5 5 6 5 6 6 6 5
((1 + (if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (x div (1 + ((1 + ((loop(\(x,i).(x + (x div 2)),x,2) div 2) div 2)) mod (x + 1))))) div 2))) div 3)))) div 2)
A080345: 0 1 1 1 1 1 1 2 1 1 2 3 2 1 1 2
((if x <= 0 then 2 else (1 + ((2 * (1 + ((1 + ((loop(\(x,i).(x div (2 - (x mod 2))),x,(1 + ((x2 + x) div 2))) div 2) div 3)) div 2))) div 3))) div 2)
A029271: 1 0 0 1 1 0 1 1 1 1 1 2 3 1 2 4
(~1 - (if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (((~1 + loop(\(x,i).2x,(x - (x div 8)),2)) mod (x + 1)) div 2)) div 2))) div 3))))
A299990: ~1 ~2 ~2 ~3 ~2 ~3 ~2 ~4 ~3 ~2 ~2 ~4 ~2 ~2 ~3 ~5
((1 + ((1 + ((3 * (1 + ((loop(\(x,i).((2x + 1) - (x div (2 + (if (x mod 2) <= 0 then 1 else 8)))),x,1) div 2) div 2))) div 2)) div 2)) div 2)
A306006: 1 1 1 2 3 5 10 16 30 57
((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) - ((x div 7) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))) div 2)
A331366: 1 1 1 1 2 1 2 1 2 3 1 3 2 1 1 2
(((1 + (2 * (if x <= 0 then 1 else (2 + ((1 + (4 * (if (x mod 2) <= 0 then (14x + 28) else 2))) mod (x + 1)))))) div 3) div 2)
A035456: 0 1 0 1 1 1 1 1 1 3 1 3 2 3 4 3
(2 + (if x <= 0 then 0 else (1 + compr(\x.(~1 + ((2 * ((x + 2) + (if x <= 0 then 1 else (4x + ((x + (2 * (x mod 2))) div 5))))) mod 3)),x))))
A308395: 2 5 6 9 10 13 14 17 18 20 21 22 24 25 26 27
((3 + (if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + ((x * (1 + (if ((x + (x div 2)) mod 5) <= 0 then 2 else 1))) div 2)) div 2))) div 3)))) div 2)
A285717: 1 2 2 3 3 3 3 4 3 4 5 4 4 4 4 5
(((3 * ((~1 + (3 * ((1 + ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3)) * (if x <= 0 then 1 else 2)))) div 2)) div 2) div 2)
A066637: 0 1 1 3 1 3 1 6 3 3 1 8 1 3 3 12
(2 * (2 + loop(\(x,i).(2 * (1 + (6 * (~1 + (6 * (~2 + loop(\(x,i).10x,(x + 1),(x + 1)))))))),x,1)))
A134728: 6 28496 4611686018427387903 4611686018427387903
(~2 + loop(\(x,i).(1 + ((4 * loop(\(x,i).2x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),2)) div 3)),2,x))
A205545: 1 1 1 1 1 1 1 20 20 1 1 84 1 84 1 1
(2x + (if x <= 0 then 1 else (2 * ((2x + 1) - ((2 * ((x + 2) + ((2 * ((x + (if (~2 + (x div 2)) <= 0 then 1 else 0)) div 2)) div 3))) div 3)))))
A310341: 1 4 10 12 18 20 26 30 34 40 42 48 50 56 60 64
(1 + ((x + ~1) mod (1 + (x mod (2 + ((1 + (2 * ((1 + (if x <= 0 then 2 else (1 - ((4 * (x div 3)) div 3)))) mod (x + 1)))) mod (x + 1)))))))
A332937: 1 1 2 3 4 1 1 1 2 1 1 1 3 1 2 5
(1 + ((~2 + loop(\(x,i).2x,(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)),1)) mod 9))
A146900: 1 1 1 1 3 1 1 7 7 1 1 6 9 6 1 1
(1 + ((2 * (1 + ((1 + (x div (1 + (x mod (1 + ((~1 + loop(\(x,i).2x,x,23)) mod (x + 1))))))) div 2))) div 3))
A336470: 1 1 2 1 2 2 3 1 4 2 5 2 3 3 6 1
(if x <= 0 then 1 else (1 + ((4 * ((3 * (1 + (x mod (1 + (2 * ((x + ~1) mod (1 + (x div (2 + ((x div 2) mod 3)))))))))) div 2)) div 3)))
A115281: 1 2 2 2 5 2 2 6 6 2 2 6 9 6 2 2
(if 2x <= 0 then 1 else (~1 + ((2 * ((x + 2) + ((2 * ((x + 1) + (2 * (4x + ((x mod (1 + (x div 2))) div 2))))) div 3))) div 3)))
A314913: 1 5 9 14 19 25 29 34 39 44 49 53 58 63 68 73
(~1 + ((2 * ((4x + 2) + (if x <= 0 then 1 else ((2 * (4x - (3x div 5))) div 3)))) div 3))
A058759: 1 4 8 13
A311799: 1 4 8 13 17 21 25 29 33 37 41 46 50 55 59 63
(1 + ((1 + (x mod (2 * (1 + (x mod (2 * (1 + ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 10)))))))) mod (x + 1)))
A080388: 1 1 1 1 2 1 1 1 2 1 6 1 2 3 1 1
(1 + ((1 + ((loop(\(x,i).(3x + 5),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2) div 2)) div 2))
A187617: 1 1 1 1 2 1 1 5 5 1 1 13 36 13 1 1
(if x <= 0 then 2 else (1 + ((3 * ((4 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)) div 3)) div 2)))
A154844: 2 1 1 1 2 1 1 4 4 1 1 7 14 7 1 1
(~1 + (((2 * (1 + ((1 + ((1 + (loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) mod (2 * (2 + (x mod 4))))) div 2)) div 2))) + (x mod 3)) div 2))
A199596: 1 1 2 1 1 2 2 1 2 2 1 2 1 1 3 1
((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + loop(\(x,i).x2,1,((2x + 1) div (3 + (x div 4)))))
A281385: 0 1 1 4 5 4 9 11 11 9 16 19 20 19 16 25
(0 + ((1 + (loop(\(x,i).3x,(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1) div 3)) mod 3) - (2 * (x mod 2)))
A081729: 1 0 2 ~1 2 ~1 1 ~1 2 ~1 1 ~1 1 ~1 1 ~1
((1 + (((loop(\(x,i).x2,1,(1 - (2 * ((2x + 1) - (x mod (1 + ((x2 + ~x) mod 8))))))) div 2) div 2) div 3)) mod 3)
A135341: 1 0 0 2 1 1 0 1 1 1 1 1 1 2 1 2
((1 + (4 * loop(\(x,i).((2x + 1) - (x mod 2)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1))) div 3)
A176331: 1 1 1 1 3 1 1 7 7 1 1 13 28 13 1 1
(2 - ((1 + ((x mod (2 + ((5 * (1 + (if (x + ~4) <= 0 then 0 else (1 + (x mod (1 + (x mod 4))))))) mod (x + 1)))) div 2)) mod 3))
A053692: 1 1 0 1 1 1 1 1 0 0 2 0 1 1 1 2
(loop(\(x,i).x2,1,((2x + 1) div (3 + (x div 4)))) - (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))
A073254: 0 1 1 4 3 4 9 7 7 9 16 13 12 13 16 25
(((1 + (2 * (if x <= 0 then 1 else (2 * (4x - ((x + ((x + (x div 3)) mod 3)) div 3)))))) div 3) + ((x + 1) div 3))
A313846: 1 5 10 16 20 27 31 37 42 47 52 57 63 67 74 78
(x + (((1 + (2 * (if x <= 0 then 1 else (2 * (2x + ((2x + ((x div 3) mod 3)) div 3)))))) div 3) + ((x + 1) div 3)))
A310454: 1 4 10 15 20 24 29 34 40 44 48 54 59 64 68 73
((2 * ((x + 1) + ((4 * (4x - ((2 * ((((x div 2) div 3) mod 2) - (if x <= 0 then 1 else x))) div 3))) div 3))) div 3)
A313619: 1 5 10 14 20 25 29 33 38 44 48 53 58 63 68 72
(((2x + 2) + (if x <= 0 then 1 else (2 * (((x + 2) + (((x + 1) div (2 * (1 + (x mod (2 + (x mod 2)))))) div 2) - (x mod 2)) div 2)))) mod 3)
A138363: 0 0 1 0 1 0 1 0 0 2 0 0 0 0 0 1
((~1 + (2 * ((x + 1) + ((2 * ((4 * (x + (if (~4 + (x div 2)) <= 0 then 1 else 2))) div 3)) div 3)))) div (2 - ((~x + 1) div 3)))
A293771: 0 2 3 4 5 5 6 6 6 7 8 7 8 8 8 8
(((2x + 1) + (2 * ((1 + (((x + 1) * loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),(2x + ~1),1)) div 2)) div 3))) mod 3)
A008626: 1 0 0 0 0 0 0 1 1 0 1 2 1 0 0 2
(1 + compr(\x.(~1 + (x mod (1 + ((~1 + (((2x + 2) * (1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) mod 8))) mod 3)) mod (x + 1))))),x))
A343108: 1 2 4 5 7 8 10 13 14 16 17 20 23 25 26 28
((x + 2) + ((2 * (1 + ((1 + ((((1 + (4 * (if (~2 + (x div 3)) <= 0 then 0 else 2))) * (1 + (x div 2))) div 2) div 2)) div 2))) div 3))
A194125-A073726: 2 3 4 5 6 7 9 10 11 15 17 18 20 21 22 23
((2 - ((1 + ((1 + loop(\(x,i).((2 - (2x mod (4 + (x div 4)))) mod (x + 1)),3,x)) div 3)) mod 5)) mod (x + 1))
A054070: 0 1 0 1 0 0 1 1 1 0 1 1 2 1 0 1
((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((loop(\(x,i).(x2 + ~2x),2,(x + ~2)) div 2) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 3)) div 2)
A308929: 0 0 0 0 0 0 0 1 1 2 3 5 8 13 19 27
((~1 + ((x div 2) + (x mod (1 + ((1 + (2 * ((1 + (x * ((1 + loop(\(x,i).((x * (x mod 2)) + (x div 2)),x,x)) mod 2))) mod (x + 1)))) mod (x + 1)))))) div 2)
A051631: ~1 0 0 1 0 1 2 1 1 2 3 3 2 3 3 4
((1 + ((1 + ((1 + (((((x + 1) * (if x <= 0 then 1 else (2 * (1 + (((x + 2) div (1 + ((x + 1) mod 3))) div 2))))) div 2) div 2) div 2)) div 2)) div 2)) div 2)
A161039: 0 0 1 1 1 1 1 1 2 1 1 3 2 2 5 3
((1 + ((2 + ((x + ((1 + (((x + 1) * (loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1))) div 2)) div 2)) div 2) - (x mod 2)) div 2)) div 2)
A304714: 1 1 1 1 1 2 1 2 2 3 2 5 2 5 5 6
((1 + (((loop(\(x,i).(5x + 2),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2) div 2) div 2)) div 2)
A283494: 0 0 0 0 0 0 0 2 2 0 0 12 59 12 0 0
((3 * loop(\(x,i).i,(2 * ((2 * (1 + (2 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))) div 3)),1)) div 2)
A132047: 1 1 1 1 6 1 1 9 9 1 1 12 18 12 1 1
(((2 * (x - ((2 * ((~2x + ~2) + ((2x + 1) div (1 + (x div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))))) div 3))) div 3) div 2)
A045747: 0 1 1 2 1 3 2 5 3 5 3 8 4 7 5 12
(1 - (((loop(\(x,i).(1 + ((1 + ((x + 1) mod (1 + (x div (2 + (x mod (2 + (x mod 2)))))))) mod (x + 1))),2,x) div 2) div 2) + ((x div 3) mod 2)))
A187036: 1 1 1 0 ~1 0 1 0 0 0 ~1 0 0 0 1 0
(2 - ((1 + loop(\(x,i).(1 - (x mod (1 + ((1 + (x mod ((1 + (x mod 5)) * (1 + (x mod 5))))) mod (x + 1))))),1,2x)) div 2))
A319135: 1 1 1 2 1 1 2 1 1 2 1 3 1 2 1 1
(2 + ((1 + (2 * ((4 * ((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3)) div 3))) mod (x + 1)))
A105555: 2 3 3 5 3 7 3 7 5 7 3 13 3 7 7 11
((if x <= 0 then 1 else x) div (((~1 + (6 * (1 + ((x div 2) div (1 + (x mod (2 * (1 + (x mod (1 + ((2 - (x div 2)) mod 4))))))))))) div 2) div 2))
A078897: 1 1 1 3 1 2 1 7 4 2 1 5 1 2 3 15
(((5 * loop(\(x,i).(3 * (1 + (x div 2))),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1)) div 2) div 2)
A328300: 1 1 1 1 3 1 1 7 7 1 1 15 26 15 1 1
(if x <= 0 then 1 else (2 * (x + ((2 * ((x + 1) + (((x + 1) + ((3 * (x + ((3 * ((x div 2) div 3)) div 2))) div 2)) div 2))) div 3))))
A315638: 1 6 12 16 20 26 32 38 42 46 52 58 64 70 74 78
(((3x + 1) + (if (x mod 7) <= 0 then 1 else (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))) div 2)
A256133: 1 2 3 5 7 8 9 11 13 14 15 18 20 21 22 23
((if x <= 0 then 1 else (2 * (1 + (((1 + (x mod (2 + (x div (1 + ((x div 2) mod (1 + (x mod (1 + (2x mod 3)))))))))) mod (x + 1)) div 2)))) - (x mod 2))
A060272: 1 1 2 1 2 1 2 3 2 1 6 5 2 1 2 1
((x + 1) + ((2 * (1 + ((1 + (((2x + 1) + (compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x) + (2 * (x mod 2)))) div 2)) div 2))) div 3))
A223133: 1 4 5 6 8 10 11 14 15 18 19 22 23 26 27 30
compr(\x.((1 + ((1 + ((1 + ((1 + (x div (1 + ((x div 2) mod (1 + (x mod (2 + (if (x mod 5) <= 0 then 2 else 0)))))))) div 2)) div 2)) div 2)) mod 3),x)
A295486: 9 12 13 14 16 19 23
(x + (2 * (2 + (if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (x div (1 + (x mod (1 + (x mod (2 + (x div (2 * (2 - (x mod 2))))))))))) div 2))) div 3))))))
A090384: 4 7 10 13 14 13 16 17 20 19 20
(1 + (x div (1 + (x mod (1 + (x mod (1 + ((~1 + (2 * (1 + ((1 + ((1 + (((x + 1) * (x div (2 - (x mod 2)))) div 2)) div 2)) div 2)))) mod (x + 1)))))))))
A295311: 1 1 3 2 5 3 7 1 3 5 11 1 13 7 15 8
((~1 + (2 * ((1 + (x div (1 + (x div 5)))) mod 2))) div (1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))
A155076: 1 ~1 1 ~1 0 1 ~1 ~1 0 1 ~1 ~1 0 0 1 ~1
(x div (1 + ((2 * (1 + ((1 + ((((2x + 1) * (1 + ((1 + ((x * (x mod 3)) div 3)) div 3))) div 2) div 2)) div 2))) div 3)))
A233867: 0 1 1 1 2 1 2 1 1 3 2 1 4 2 1 3
(1 + (((5 * (1 + (((1 + (x mod ((1 + (x mod (1 + (x div 4)))) * (1 + (x mod 2))))) mod (x + 1)) + (x mod 2)))) div 2) div 3))
A169594: 1 2 2 4 2 4 2 6 4 4 2 7 2 4 4 9
(1 + ((2 * ((x + 1) + ((2 * ((x + 2) + ((2 * ((x + 1) + (2 * (x + ((x + ((x div 2) mod 2)) div 2))))) div 3))) div 3))) div 3))
A043000: 2 4 7 9 11 13 16 19 21 23 25 27 29 31 35 37
(~1 + ((2 + ((1 + ((2 * (1 + ((1 + (x mod (1 + (x mod (1 + (x div (2 + (x mod 5)))))))) div 2))) div 3)) mod (x + 1))) mod 3))
A344864: 1 ~1 ~1 ~1 ~1 0 ~1 0 ~1 0 ~1 1 ~1 0 0 ~1
(x div (1 + (x div (2 + (((2 * (1 + ((1 + ((x mod (2 + ((~1 + (2 * (x mod 4))) mod (x + 1)))) div 2)) div 2))) div 3) + (x mod 2))))))
A279346: 0 1 1 1 2 2 1 2 2 2 1 3 3 2 2 2
(1 + (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + (x div (1 + (2 * (1 + (2 * ((x div 2) mod 2)))))))) div 2))
A271465-A124834: 1 1 1 1 2 1 1 3 4 1 1 4 11 8 1 1
(2 div (1 + (((1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) * (1 + ((2 - (x div 3)) mod 3))) div 2)))
A167230-A093658: 1 1 1 1 0 1 2 1 1 1 1 0 0 0 1 2
(1 + ((1 + ((1 + ((1 + (((x + 1) * (1 + (((x + 1) * ((x mod (2 - (x div (1 + ((x div 2) mod 2))))) mod 2)) div 3))) div 2)) div 2)) div 2)) div 2))
A305976: 1 2 2 2 2 3 2 2 2 4 2 5 2 6 7 2
(1 + ((3 * (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + ((1 + (x div 2)) div 2))) div 3)) div 2))
A046539: 1 1 1 1 1 1 1 4 4 1 1 7 8 7 1 1
(1 + (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + (2 * ((2x + 1) div (3 + (x div 4))))) div 2))
A135646: 1 2 2 3 3 3 4 5 5 4 5 6 7 6 5 6
((1 + (2 * (1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (~1 + (8 * ((1 + (x div 2)) div 2)))) div 2)))) div 3)
A296541: 1 1 1 1 3 1 1 5 5 1 1 8 16 8 1 1
((~1 + compr(\x.((1 + ((1 + ((1 + ((1 + ((((x + 1) * (1 + (x mod (1 + (x mod 4))))) div 2) div 2)) div 2)) div 2)) div 2)) mod 3),x)) mod 3)
A333451: 1 1 2 1 2 0 0 1 1 2 2 0 2 1 2 1
((2 * (1 + (x div (1 + ((1 + ((((1 + (x mod (1 + (x mod (2 * (2 + ((x div 2) mod 2))))))) mod (x + 1)) div 2) + (x mod 2))) mod (x + 1)))))) div 3)
A304574: 0 1 1 1 2 1 2 1 3 2 4 1 4 2 3 2
(1 - ((2 * (1 + (2 * (((1 + (2 * ((1 + (x mod (2 + ((2 - (2x mod 5)) mod (x + 1))))) div 2))) mod (x + 1)) div 2)))) div 3))
A238882: 1 1 1 1 1 ~1 1 1 ~1 1 ~1 ~1 1 ~1 1 ~2
((2 * ((~x + 2) + ((2 * (1 + ((15x3 + 30x2 + 16x + 1) div 3))) div 3))) mod 3)
A039978: 1 0 2 2 1 1 0 1 1 2 1 0 0 2 2 1
((4 * (1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 3) - (x mod (2 - ((x div 2) mod 2))))))) div 3)
A147566: 1 1 1 1 4 1 1 5 5 1 1 6 14 6 1 1
((4 * (1 + ((8 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)) div 3))) div 3)
A334552: 1 1 1 1 4 1 1 8 8 1 1 12 25 12 1 1
((3x + 2) + (((2 * (2 + ((1 + (5 * ((x + ((x div 2) mod 2)) div 2))) div 3))) div 3) + (x div 2)))
A225521: 3 6 11 15 19 22 27 32 36 39 43 48 52
((2x + 4) + (5 * ((2 * (~1 + (6 * ((x + 1) + (5 * (1 + (x div 2))))))) div 3)))
A039557: 119 141 263 285 407 429 551 573 695 717 839 861 983 1005 1127 1149
(~x + ((1 + (2 * (x + ((1 + (((1 + ((((3x3 + 3x2 + ~2x) div 2) div 2) div 2)) div 2) div 2)) div 2)))) div 3))
A173645: 0 0 0 0 1 3 6 10 15 22 31 42 55 70 87 107
compr(\x.(1 - ((2 * (1 + ((1 + ((x + 1) div (1 + ((1 + ((x2 mod (2 + (x mod 8))) mod 2)) mod (x + 1))))) div 2))) mod 3)),(x + 1))
A084368: 1 2 3 4 9 10 12 14 15 16 17 19 21 22 23 24
((1 + (2 * (x + (((2x + 1) + (2 * (x + ((x4 + 2x3 + 2x2) div (x + 1))))) div 3)))) div (x + 1))
A328363: 1 4 9 16 26 38 53 70 90 113 138 166 197 230 266 305
((2 - ((x + 1) mod (~1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (2 - (2 * (1 + (x div (1 + (x mod 5)))))))))) div 2)
A332700-A256268-A213275-A069777: 1 1 1 1 1 1 1 2 1 1 1 6 3 1 1 1
((1 + ((1 + ((1 + ((~1 + ((~2x + 2) mod (4 + (x div 4))) - ((x div (2 + (x mod 2))) mod 3)) mod (x + 1))) div 2)) div 2)) div 2)
A108339: 0 1 0 1 1 0 1 0 1 1 1 1 1 1 0 2
((1 + ((1 + ((x mod (2 + ((6 * (1 + (((x2 + 2x) div 2) mod (1 + ((1 + (x div 2)) div 3))))) mod (x + 1)))) div 2)) div 2)) div 2)
A248639: 0 0 0 1 0 0 1 0 0 0 1 1 1 2 0 0
((1 + (((~1 + (6 * (1 + (((3x + ~6) * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2)) div 2)))) div 2) div 2)) div 2)
A339231: 1 1 1 1 3 1 1 6 7 1 1 10 23 13 1 1
(3 mod (2 * (1 + (2 * ((1 + (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * ((~x + 2) div 2)) div 2)) div 2)))))
A174952: 1 1 1 1 1 1 1 ~1 ~1 1 1 ~11 ~15 ~11 1 1
((1 + (x2 div (4 + (((x + 2) + (2 * ((1 + ((1 + ((32 mod (x + 1)) div 2)) div 2)) div 2))) div 3)))) div 2)
A325106: 0 0 0 1 1 2 3 4 4 5 6 7 8 9 10 13
(4 * (1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + ((2x + 1) div (3 + (x div 4))))))
A098352: 4 8 8 12 16 12 16 24 24 16 20 32 36 32 20 24
(((5 * (1 - (((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2) * (x div 5)))) div 2) div 2)
A340934: 1 1 1 1 1 1 1 3 3 1 1 8 13 8 1 1
(~2 + ((3 * (1 + ((3 * (1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (~1 + (x div ~2))) div 2))) div 2))) div 2))
A054110: 1 1 1 1 5 1 1 8 8 1 1 10 17 10 1 1
(~2 + ((3 * (2 + ((0 - (x mod 5)) mod (1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))))) div 2))
A219585: 1 1 1 1 1 1 1 2 1 1 1 5 5 2 1 1
((3x + 4) + ((2 * (x + ((2 * (1 + (2 * (2x - ((2x + 1) div 7))))) div 3))) div 3))
A189388: 4 9 15 19 25 30 36 40 46 51 56 61 66 72 76 82
((~x + 3) + (2 * (x - ((2 * ((x + 1) - (((x - ((2 - ((x + 1) div (2 * (2 - ((x div 4) mod 2))))) div 2)) div 2) div 2))) div 3))))
A285200: 1 2 1 2 3 2 1 2 3 2 1 2 3 4 3 2
(1 + ((2 * (1 + ((1 + (((1 + (((x + 1) * (1 - ((x - (x2 div 3)) div 3))) div 2)) div 2) div 2)) div 2))) div 3) - (x mod 2))
A225044: 1 0 1 0 2 1 2 2 4 4 5 6 9 10 13 14
((~x + 1) + ((2 * (x + ((((2x + 3) * ((9x + 9) - (x mod 5))) div 2) div 3))) div 3))
A234940: 3 10 19 32 49 77
((x + 8) + ((2 * (1 + ((x2 + 2x + 2) div (~x + 25)))) div 3))
A120209: 8 9 10 11 13 14 16 17 19 21 24 26 29 32 36 40
compr(\x.(2 * (1 + ((1 + ((1 + (((((x + 1) * (1 + (2 mod (1 + (x mod 3))) - (x mod 7))) div 2) div 2) div 2)) div 2)) div 2))),x)
A297135: 6 12 13 18 19 20 24 25 26 27 30 31 32 33 34 37
((x + 2) + (((4x + 2) + (((3 * (1 + ((13x2 + 13x) div 2))) div 2) div 2)) div 3))
A034972: 2 8 17 29 44 63 85 110 138 170 205 243 284 329 376 427
compr(\x.(2 - (x mod (4 + ((x + 1) mod (1 + (((2 * (1 + ((1 + ((x + 1) div (2 + (x mod (2 * (2 - (x mod 2))))))) div 2))) mod 3) div 2)))))),x)
A307414: 2 3 6 7 10 11 12 14 15 18 19 22 23 24 27 30
((3x + 3) + (((x + 1) + (((x + 1) + (((2x + 1) + ((2x2 + 8x + 8) div 3)) div 3)) div 2)) div 2))
A190952: 4 8 12 16 21 26 30 35 40 45 51 56 61 67 72 78
(x + (x * ((x + 1) + ((2 * (1 + (((x + ~1) * ((x8 + x6 + x4 + x2) div 2)) div 3))) div 3))))
A217524: 0 3 84 4935
loop(\(x,i).2x,x,loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1))
A028159: 1 34 740 13160 208656 3075744 43147840 584341120 7711252736 99794799104 1272281687040 16031996897280 200167551471616 2480945949220864 30569500530851840 374885865442672640
loop(\(x,i).2x,x,loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1))
A028143: 1 32 660 11200 170576 2429952 33121600 437888000 5663851776 72087887872 906450621440 11292447129600 139666259070976 1717603091873792 21027551488327680 256495170125824000
loop(\(x,i).2x,x,loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(5x + loop(\(x,i).(3x + 1),i,1)),i,1)),i,1)),x,1))
A075510: 1 30 560 8400 111216 1360800 15790720 176563200 1922176256 20518417920 215825326080 2244998246400 23153670762496 237224718704640 2418102840688640 24549985173504000
((1 + ((1 + (loop(\(x,i).2x,x,(if x <= 0 then 1 else (2 * ((if x <= 0 then 2 else (loop(\(x,i).2x,(x + ~2),x) - ((x + ~1) * (if x <= 0 then 1 else x)))) div 2)))) div 2)) div 2)) div 2)
A159710: 0 0 0 0 8 80 528 2912 14592 69120 316160 1413632 6223872 27103232 117067776 502456320
(2 + (loop(\(x,i).3x,x,(1 + loop(\(x,i).2x,x,1))) + loop(\(x,i).5x,x,1) + loop(\(x,i).(2x + 1),x,loop(\(x,i).2x,x,1))))
A001553: 6 21 91 441 2275 12201 67171 376761 2142595 12313161 71340451 415998681 2438235715 14350108521 84740914531 501790686201
(1 + (loop(\(x,i).2x,((1 + (((~1 + loop(\(x,i).2x,x,(if x <= 0 then 1 else (2 * (if (~2 + (x div 3)) <= 0 then 0 else 2))))) mod (x + 1)) div 2)) div 2),1) div 3))
A232800: 1 1 1 1 1 1 2 2 2 2 1 2 1 2 1 6
(1 + loop(\(x,i).((x + 1) + loop(\(x,i).(2 + (compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + compr(\x.(loop(\(x,i).(2x + 2),x,0) mod (x + 1)),x))),1,i)),x,1))
A061802: 2 7 15 27 45 69 99 135 177 229 289 357 435 519 609 709
(~1 + (2 * (1 + loop(\(x,i).(if x <= 0 then 1 else (2x * ((x + 1) + (2 * loop(\(x,i).(2 * (1 + loop(\(x,i).(2x * (2 + i)),4x,1))),x,1))))),2,x))))
A116134-A116122-A116097: 92185 4611686018427387903 4611686018427387903 4611686018427387903
(1 + (((1 + loop(\(x,i).(2x + 2),(x + ~1),(if x <= 0 then 1 else ((2 + (loop(\(x,i).3x,(x + ~1),1) + loop(\(x,i).2x,x,1))) div 2)))) div 2) div 2))
A233162: 1 1 3 11 48 236 1248 6896 39168 226496 1325568 7821056 46399488 276294656 1649369088 9862639616
loop(\(x,i).(~1 + loop(\(x,i).x2,1,(if x <= 0 then 1 else (2 * (1 + ((1 + ((loop(\(x,i).(20x + ~21),x,1) div 2) div 2)) div 2)))))),x,1)
A135760: 1 3 43263 4611686018427387903 4611686018427387903
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A026543: 1 27 481 7191 98161 1272663 16005025 197611623 2412718033 29257382583 353312653057 4255864465671 51186427162417 615069092006487 7386770412718177 88683539390560935
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028082: 1 29 547 8561 121219 1617833 20812219 261490097 3235181587 39620718137 481957803691 5836292549633 70462254871555 848987132460041 10215522905076763 122808633740991569
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028141: 1 31 619 10171 150115 2075227 27499123 354164107 4472448739 55701408763 686884421587 8409900709483 102430894160323 1242818548606939 15036887507052211 181551642806017099
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).5x,i,1)),i,1)),i,1)),x,1)
A028114: 1 27 475 6975 93451 1191447 14779315 180568575 2187814651 26388443367 317513959555 3815510712975 45819341339851 550037207863287 6601706608906195 79228188287078175
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028058: 1 26 445 6410 84781 1071986 13229485 161139770 1948959661 23484063746 282412377325 3392692006730 40735374508141 488965966028306 5868455675537965 70426728878067290
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028011: 1 30 589 9606 141469 1956918 25981309 335413254 4245767581 52992982614 654705201085 8028335357094 97906258582237 1189106856272118 14398317567128317 173947775018406726
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(7x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A028008: 1 29 551 8713 124719 1681449 21820639 276146585 3436220975 42270842185 515935095039 6263469307641 75758994829519 914022487668137 11008535762024351 132431203010446681
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028157: 1 33 697 12033 185353 2657361 36306649 479622561 6184444585 78342273009 979414153081 12123907404609 148962749140297 1819935176767377 22139457629549593 268445978800100577
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).5x,i,1)),i,1)),i,1)),x,1)
A028123: 1 29 545 8485 119481 1586589 20323345 254479445 3140238761 38383465549 466251023745 5640435145605 68049758226841 819519225638909 9857637166837745 118479045968342965
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028067: 1 28 513 7844 109073 1435884 18284641 228039988 2806440945 34241833340 415442661569 5021759035332 60553294750417 728980076982796 8766500495230497 105347998786683476
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(3x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028101: 1 32 661 11228 170905 2428664 32963197 433285556 5565811009 70301927696 876950844133 10837103324684 132978429495913 1623019468693928 19728775328561869 239074474267587812
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025985: 1 29 563 9241 138723 1972833 27071851 362271257 4758885395 61635081937 789436108539 10021208067273 126282252770467 1581692483050241 19709670281308427 244539010854912889
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).(7x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028042: 1 26 447 6484 86429 1100862 13670539 167326808 2031126537 24536941858 295591283351 3555147513372 42718200467125 513013681404614 6158932166842083 73926566183932576
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028126: 1 30 583 9372 135949 1854282 24319171 310765224 3901290217 48373167414 594541806079 7261303210356 88278005955205 1069623213421026 12928092282515707 155970779176282368
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).(7x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025996: 1 26 449 6550 87765 1122522 13981657 171489758 2084497085 25203559810 303786156609 3654919330374 43925837020261 527579714133290 6334254431345705 76034189070980398
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A026241: 1 29 557 8977 131685 1825017 24374173 317359889 4057667669 51188756905 639248806989 7920904304001 97550444747653 1195603302467993 14597229457092605 177666702622486513
loop(\(x,i).(12x + loop(\(x,i).(10x + loop(\(x,i).(4x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028051: 1 29 555 8905 130091 1796769 23932195 310954985 3969388731 50012943409 623962124435 7725629774265 95088465616171 1164870934296449 14216545739974275 172979498415780745
loop(\(x,i).(12x + loop(\(x,i).(2x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028022: 1 33 709 12573 199957 2966205 41944933 572993421 7627809013 99550699677 1279261319557 16238012145069 204088032533269 2544643371529149 31521003288514981 388369584933658317
loop(\(x,i).(12x + loop(\(x,i).(3x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025957: 1 28 531 8582 127505 1800456 24581887 327729514 4292988909 55478507084 709331302043 8991457539246 113171793119113 1416078851325712 17631136903084599 218593740438932978
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028074: 1 24 367 4566 50449 516348 5012659 46832082 425124997 3774414072 32930084551 283309497198 2409910756345 20309449295796 169843460626843 1411263104458314
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).5x,i,1)),i,1)),i,1)),x,1)
A028109: 1 22 305 3410 33621 305382 2619625 21554170 171870941
A003468: 1 22 305 3410 33621 305382 2619625 21554170 171870941 1337764142 10216988145 76862115330 571247591461 4203844925302 30687029023865 222518183370890
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(2x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A026391: 1 25 407 5489 66759 762321 8356279 89114113 932519687 9629963057 98523692631 1001349555297 10129549127335 102127457330833 1027215881948663 10314453257429441
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A026727: 1 27 477 7007 93093 1163799 13989949 163814559 1883880405 21393162791 240779316141 2692752875631 29976989988037 332620147754103 3681925234618653 40686711732853823
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(7x + loop(\(x,i).4x,i,1)),i,1)),i,1)),x,1)
A028130: 1 25 395 5045 56931 592725 5834515 55132165 505157411 4519668725 39685517235 343261312485 2933027514691 24811827085525 208162421081555 1734382406904005
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028170: 1 28 495 7070 89201 1038408 11432275 120872290 1239829701 12425000588 122271240455 1185943687110 11369353359001 107963322279568 1017222704311035 9522095291175530
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028112: 1 25 401 5285 62601 696045 7442401 77640805 797399801 8108665565 81939294801 824736146325 8280574247401 83010854259085 831368657137601 8321395551579845
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028139: 1 29 537 8113 109193 1365777 16254169 186716321 2089642665 22928450545 247752021881 2644807869249 27960164339017 293249462073233 3055559544501273 31664588166403297
loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025990: 1 24 381 5096 62517 731640 8337757 93583752 1041282693 11528533016 127276678893 1402901740968 15449475687829 170051606288952 1871222084030589 20587420276057544
loop(\(x,i).(6x + loop(\(x,i).(3x + loop(\(x,i).(8x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028080: 1 27 469 6687 85357 1016775 11565973 127403199 1371332413 14511863223 151627818277 1569077088111 16117515157069 164615225572071 1673829571276981 16960654592840223
loop(\(x,i).(6x + loop(\(x,i).(3x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028036: 1 24 379 5034 61345 713988 8103223 90690558 1007169229 11137289592 122864771107 1353656241522 14903146727353 164012446077036 1804604958697231 19853467108689126
loop(\(x,i).(6x + loop(\(x,i).(3x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028083: 1 28 505 7480 99181 1226548 14470705 165111760 1838112661 20084217868 216290873305 2302672401640 24288950066941 254275654917988 2645388660962305 27378515971285120
loop(\(x,i).(7x + loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028131: 1 26 429 5746 68285 751842 7859293 79189682 776807229 7469674498 70755237917 662574315858 6150105857533 56698559685794 519954841569501 4748676612377074
loop(\(x,i).(7x + loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028053: 1 21 280 3030 29071 258111 2172430 17592960 138433141 1065579801 8062670980 60182175690 444345657211 3251891531091 23627323915930 170652039023220
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028145: 1 28 497 7148 90993 1070076 11908849 127304716 1320106865 13369686044 132894679281 1301200322604 12584262543217 120472024886332 1143539682545393 10777265023323212
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).5x,i,1)),i,1)),i,1)),x,1)
A028115: 1 24 365 4500 49161 496944 4762885 43939500 394061921 3459033864 29862674205 254461580100 2145767540281 17942499698784 149003957062325 1230427665726300
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028059: 1 23 338 4054 43323 430269 4065916 37085708 329561045 2871469315 24640946694 208933723362 1754722389967 14623596707561 121104748389872 997726082646616
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(2x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028006: 1 27 473 6831 88473 1069551 12338761 137686527 1499327225 16029462735 168979616169 1762044328863 18217806426457 187092613978479 1911192049791497 19440694364069439
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025974: 1 24 383 5166 63993 756108 8690611 98243322 1099333565 12223792152 135381670359 1495646457318 16497281164417 181786417955556 2001865410394427 22036025351972754
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028116: 1 25 398 5162 59619 640227 6549376 64780804 625573157 5936696909 55620675474 516146265726 4755391291015 43574880995671 397637888433092 3617137005125528
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A025994: 1 24 377 4932 58485 654192 7053313 74243004 769050029 7880095080 80144389689 810929347956 8176098535333 82230655243488 825604414181105 8279180036642988
loop(\(x,i).(7x + loop(\(x,i).(10x + loop(\(x,i).(4x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028040: 1 24 375 4870 57321 636924 6829435 71574690 738951741 7552940824 76677389295 774826006110 7804690367761 78442179476724 787189784753955 7891278029367130
loop(\(x,i).(7x + loop(\(x,i).(2x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028009: 1 28 509 7628 102477 1284060 15338893 177026476 1991073293 21954504572 238334455437 2555217498444 27118409281549 285415846100764 2983193752870541 30999901741572332
loop(\(x,i).x3,1,loop(\(x,i).(1 + (x * (if (1 + ((1 + ((1 + loop(\(x,i).(x * ((1 + (4 * i)) * i)),x,1)) div 2)) div 2)) <= 0 then 1 else (x * i)))),x,1))
A068895: 1 8 729 14526784 4611686018427387903
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028121: 1 27 467 6615 83811 990927 11193547 122534775 1311833171 13818932127 143838758427 1483810444935 15202640928931 154948536206127 1572891821232107 15916318178611095
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028155: 1 31 611 9779 138747 1820595 22624267 270185443 3130828283 35437220819 393679085163 4307728419267 46553144477659 497913631860403 5279371826945099 55566205514956451
loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025999: 1 26 445 6370 82901 1019746 12105885 140404290 1603014501 18104952866 202945103725 2262802497410 25134485221301 278430633932386 3078357517755965 33986947913921730
loop(\(x,i).(8x + loop(\(x,i).(3x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028045: 1 26 443 6304 81573 998502 11807311 136529708 1555263545 17536382578 196332094179 2187124368312 24278204224717 268819199510654 2971083878320247 32794508383067716
loop(\(x,i).(8x + loop(\(x,i).(3x + loop(\(x,i).(5x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028065: 1 26 437 6058 75525 882258 9876613 107390426 1143865349 12003195490 124572616389 1282173260394 13113918930373 133479729281522 1353536864252165 13685361486439162
loop(\(x,i).(8x + loop(\(x,i).(3x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028099: 1 30 577 9066 126829 1646094 20280169 240528882 2771673157 31228927158 345616983361 3769863028698 40631819886685 433596513609822 4588506840332953 48214238728174914
loop(\(x,i).(9x + loop(\(x,i).(4x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025981: 1 26 449 6526 86565 1087242 13183033 156056342 1816137389 20873693698 237678368577 2687080081998 30211476701173 338208740115194 3773239145742281 41982119790892294
loop(\(x,i).(4x + loop(\(x,i).(4x + loop(\(x,i).(4x + loop(\(x,i).((2x div (1 + i)) * (1 + (2 * i))),i,1)),i,1)),i,1)),x,1)
A045724: 1 15 142 1083 7266 44758 259356 1435347 7663898 39761282 201483204 1001098462 4891910100 23565178380 112118316088 527674017411
loop(\(x,i).(4x + loop(\(x,i).(4x + loop(\(x,i).(4x + loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),i,1)),i,1)),i,1)),x,1)
A041001: 1 14 125 906 5810 34364 191901 1026610 5312230 26767940 131990066 639210404 3048892740 14354652152 66828135005 308078809794
loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028124: 1 28 503 7406 97545 1198344 14051227 159447442 1766581949 19223504300 206298840111 2189789938518 23040266816113 240689810119696 2499511822660355 25828790012697434
loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A025983: 1 27 485 7335 101181 1319967 16597525 203384295 2445473261 28983189807 339647023365 3944444998455 45472205947741 521027509282047 5939635577526005 67419323254471815
loop(\(x,i).(5x + loop(\(x,i).(3x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028068: 1 27 472 6810 88351 1073217 12477502 140675040 1550817301 16809628407 179833708132 1904095702470 19993394169451 208508925363597 2162279358272362 22317580796873100
loop(\(x,i).(3x + loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028056: 1 24 373 4800 55861 613224 6497893 67364880 688931221 6985860024 70462212613 708365604960 7106726476981 71208736700424 712951450202533 7134775273637040
loop(\(x,i).(3x + loop(\(x,i).(7x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025946: 1 23 356 4702 57435 672441 7683502 86531384 965954429 10724321179 118659465288 1310098171746 14444989850383 159132262849037 1752116527119314 19284913291752988
loop(\(x,i).(3x + loop(\(x,i).(7x + loop(\(x,i).(6x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028075: 1 25 400 5230 60991 661675 6836950 68263360 664838581 6356961325 59947423900 559395635890 5177995501771 47632122760975 436056971109250 3977028159426820
loop(\(x,i).(3x + loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028089: 1 27 466 6558 82075 952329 10485532 111125916 1144265749 11522055831 113982102598 1111567913274 10714164992623 102277469691333 968483992074064 9108558269363832
loop(\(x,i).(3x + loop(\(x,i).(9x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025953: 1 25 420 5990 78431 976275 11762890 138612880 1607750661 18432396125 209480782160 2364808954170 26557583235691 297035583017575 3311510934334230 36823696010925860
loop(\(x,i).(3x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028030: 1 23 350 4510 53691 614373 6891160 76527020 845660981 9322579123 102653929170 1129737260730 12429895581871 136743043622273 1504245500346380 16547064858237640
loop(\(x,i).(3x + loop(\(x,i).(5x + loop(\(x,i).(12x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028070: 1 29 550 8690 124531 1684079 21954280 279351380 3496283461 43256856929 530819707210 6475595107670 78659578436791 952489924910579 11507069203563340 138779617656909560
loop(\(x,i).(3x + loop(\(x,i).(2x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A025955: 1 26 455 6760 92121 1191606 14892475 181671620 2176950941 25732149586 300910712895 3488589043680 40160193084961 459619264745966 5234383334635715 59363930948274940
(loop(\(x,i).(2 * ((x + 2) + (if (x + ~1) <= 0 then 1 else (2 * loop(\(x,i).x2,1,loop(\(x,i).((2 * (x - (2x * i))) div (1 + i)),x,1)))))),1,(x + ~1)) mod (x + 1))
A074644: 0 0 2 0 0 4 0 0 0 0 0 4 0 0 10 0
loop(\(x,i).(11x + loop(\(x,i).(5x + loop(\(x,i).(2x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A026028: 1 27 480 7130 96111 1221537 14941750 178032960 2082076821 24019528247 274281235020 3107772782790 35002020287131 392372934746157 4382268859012290 48800507502984620
loop(\(x,i).(3x + loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028060: 1 24 370 4680 53011 560784 5670820 55595760 533237221 5034115944 46976235670 434592270840 3994583040631 36537064953504 332949559310920 3025434129325920
(2 + loop(\(x,i).((x + 1) + loop(\(x,i).((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3),1,i)),x,0))
A156745: 2 5 8 12 15 20 23 28 32 37 40 47 50 55 60 66
(2 * (1 + (((x + 1) * (~1 + loop(\(x,i).(x + loop(\(x,i).(x - (if x <= 0 then 1 else (if ((x mod 3) div 2) <= 0 then x else ((x + 1) div 2)))),x,(x + 1))),2,x))) div 3)))
A038674: 2 2 4 4 2 6 6 2 8 8 16
((1 + ((1 + ((loop(\(x,i).(6x + 1),x,0) - (loop(\(x,i).2x,x,1) + loop(\(x,i).2x,x,1) + loop(\(x,i).2x,x,1))) div 2)) div 2)) div 2)
A241271: 0 0 0 3 27 183 1143 6951 41895 251751 1511271 9069159 54418023 326514279 1959097959 11754612327
(2 + loop(\(x,i).((x + 1) + ((((x * (x2 - (if x <= 0 then 1 else ((x + 1) - loop(\(x,i).loop(\(x,i).(x + (i * i)),(x + ~1),1),2,x))))) div 2) div 3) mod 2)),x,1))
A325439: 3 4 6 7 9 10 11 13 14 15 16 17 19 21 23 24
((1 + (5 * ((3 * (if (x mod 2) <= 0 then (3 * (if (x mod 4) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1)) else 1)) - (if x <= 0 then 1 else 2)))) div 4)
A040458: 21 1 9 1 42 1 9 1 42 1 9 1 42 1 9 1
(~x + (if x <= 0 then 1 else (2 * (x + ((x + (((loop(\(x,i).8x,x,1) + loop(\(x,i).2x,x,1)) - loop(\(x,i).(3x + 2),x,0)) div 2)) div 2)))))
A080503: 1 5 34 253 2024
(1 + (10 * (1 + (2 * compr(\x.loop(\(x,i).loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 0 else 1)),x,x),1,(10x + 4)),x)))))
A141884: 11 31 71 131 151 191 211 251 271 311 331 431 491 571 631 691
(1 + (loop(\(x,i).(x2 + 2x),1,(((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1))) div 3))
A342530-A328706: 1 2 2 3 2 6 2 6 3 6 2 12 2 6 6 9
(loop(\(x,i).2x,x,1) div (1 + ((2 * (1 + ((1 + (if (x + ~1) <= 0 then x else loop(\(x,i).((2x * (1 + (2 * i))) div (2 + i)),(x + ~2),1))) div 2))) div 3)))
A034214: 1 1 2 4 5 5 4 2 1 1 0 0 0 0 0 0
loop(\(x,i).~x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),(if ((x + 1) mod 8) <= 0 then 2 else 1))
A307428: 1 ~1 ~1 1 ~1 1 ~1 ~2 1 1 ~1 ~1 ~1 1 1 2
(loop(\(x,i).(if x <= 0 then 1 else ((x mod 5) + (x div 3))),(1 + (x mod 3)),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) mod 3)
A089679: 2 2 1 1 2 2 1 0 1 1 1 2 2 1 1 2
(1 + compr(\x.(~1 + ((1 + (((x + 1) * (1 - (loop(\(x,i).x2,2,(1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1))) mod (x + 1)))) div 2)) div 2)),x))
A116998: 1 2 3 4 5 6 10 12 14 15 18 20 21 22 24 26
(1 + compr(\x.(1 - ((1 + (((x + 1) * (~1 + loop(\(x,i).2x,x,loop(\(x,i).(3x + (if (i mod 3) <= 0 then 1 else 2)),x,1)))) div 3)) mod 3)),x))
A050078: 1 2 3 4 6 8 9 10 11 12 14 17 18 20 21 22
((loop(\(x,i).(10x + 1),(x + 1),loop(\(x,i).(10x + 10),x,0)) div 2) + loop(\(x,i).10x,x,1))
A332151: 1 515 55155 5551555 555515555 55555155555 5555551555555 555555515555555 55555555155555555 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((1 + ((1 + ((x + 1) div (~1 + (3 * (1 + (if (x mod 3) <= 0 then (2 * (if (x mod 2) <= 0 then (2 + (if x <= 0 then 0 else 2)) else 1)) else 1) - (x mod 2)))))) div 2)) div 2)
A191225: 0 1 0 0 1 1 0 1 1 1 1 2 0 2 1 1
(if x <= 0 then 1 else (2 * (1 + ((1 + ((x mod (1 + (loop(\(x,i).(2x + 2),(loop(\(x,i).(~3x2 + x),2,2) mod (x + 1)),1) mod (x + 1)))) div 2)) div 2))))
A260123: 1 2 2 2 2 2 4 2 4 2 4 2 2 4 4 2
loop(\(x,i).x2,1,(if x <= 0 then 1 else (2 * (1 + (((~1 + loop(\(x,i).2x,x,(1 + (2 * (((2x + 1) mod (2 + (x div 4))) div 2))))) mod (x + 1)) div 2)))))
A278254: 1 4 4 16 4 36 4 64 16 36 4 144 4 36 36 256
((if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + ((1 + ((1 + ((1 + loop(\(x,i).(if (x + ~2) <= 0 then i else 2x),x,1)) div 2)) div 2)) div 2)) div 2)) div 2)))) div (2x + 2))
A251766: 0 1 0 0 0 0 0 0 0 0 1 2 3 6 12 24
((loop(\(x,i).(10x + 1),(x + 1),loop(\(x,i).(10x + 10),x,0)) div 2) + loop(\(x,i).10x,x,2))
A332152: 2 525 55255 5552555 555525555 55555255555 5555552555555 555555525555555 55555555255555555 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).35x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165856: 1 35 35 1225 35 1225 35 42875 1225 1225 35 42875 35 1225 1225 1500625
loop(\(x,i).45x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165866: 1 45 45 2025 45 2025 45 91125 2025 2025 45 91125 45 2025 2025 4100625
loop(\(x,i).39x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165860: 1 39 39 1521 39 1521 39 59319 1521 1521 39 59319 39 1521 1521 2313441
loop(\(x,i).29x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165850: 1 29 29 841 29 841 29 24389 841 841 29 24389 29 841 841 707281
loop(\(x,i).44x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165865: 1 44 44 1936 44 1936 44 85184 1936 1936 44 85184 44 1936 1936 3748096
loop(\(x,i).46x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165867: 1 46 46 2116 46 2116 46 97336 2116 2116 46 97336 46 2116 2116 4477456
loop(\(x,i).37x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165858: 1 37 37 1369 37 1369 37 50653 1369 1369 37 50653 37 1369 1369 1874161
loop(\(x,i).47x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1)
A165868: 1 47 47 2209 47 2209 47 103823 2209 2209 47 103823 47 2209 2209 4879681
(1 + (x div (1 + (x mod (1 + (x mod (1 + ((1 + (loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) + loop(\(x,i).4x,x,1))) mod (x + 1)))))))))
A332883-A017666: 1 2 3 4 5 1 7 8 9 5 11 3 13 7 5 16
(3 mod (1 + (if x <= 0 then 0 else (1 + ((1 + ((2 * (2 + (x div (1 + ((x div 2) mod (1 + (if (x mod 2) <= 0 then 6 else 1))))))) div 3)) mod 3)))))
A304326: 0 1 1 1 1 3 1 0 1 3 1 3 1 3 3 0
(1 + ((2 * (1 + ((1 + (((~1 + loop(\(x,i).2x,x,(1 + (if ((x mod 7) mod 3) <= 0 then 2 else 0)))) mod (x + 1)) div 2)) div 2))) div 3))
A005793: 1 1 1 2 1 1 2 3 2 1 2 3 1 2 3 4
(x div (1 + (((x + 2) + (((x + 1) * (loop(\(x,i).(2x + 2),x,0) mod (x + 1))) mod (2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)))) div 3)))
A339210: 0 0 1 1 1 0 2 1 1 0 2 0 2 0 0 1
(1 + ((x mod (2 + ((1 + (2 * (if x <= 0 then 0 else (1 + compr(\x.(~1 + ((1 + (x * loop(\(x,i).(~x2 + 1),2,4x))) mod (x + 1))),x))))) mod (x + 1)))) div 2))
A030336: 1 1 2 1 1 1 1 2 1 1 1 1 3 2 2 1
((if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + (((x + 1) * (1 + ((x + 1) mod (1 + ((x + (if (x mod 2) <= 0 then x else 2)) mod 3))))) div 2)) div 2)) div 2)))) mod 3)
A301366: 1 1 1 1 0 1 1 1 2 2 1 0 0 0 1 1
((2 * (((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3) + (x div 5))) div 3)
A070956: 0 1 1 2 1 3 2 3 2 3 2 5 2 4 4 5
(1 + (((x + 1) + ((x + ((x + ((if x <= 0 then 2 else (1 + ((x + loop(\(x,i).(1 + (x * i) - (2 * (x mod 2))),(x + ~2),1)) div 3))) div 2)) div 2)) div 2)) div 2))
A085904: 1 2 3 4 5 6 7 8 14 48
(1 + compr(\x.(~1 + (x mod (1 + ((~1 + ((1 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),(1 + (2 * (x mod 2))),(x + ~1))) mod 3)) mod (x + 1))))),x))
A026168: 1 2 3 5 6 9 11 12 14 15 18 21 23 24 27 29
loop(\(x,i).((6x + 1) - ((2 * (2 + (if x <= 0 then 1 else (6x + (((x + 1) + (x mod 2)) div 5))))) div 3)),x,1)
A059633: 1 2 4 7 13 24 45 84 157 293 547 1021 1906 3558 6642 12399
(1 + compr(\x.((x + 1) - ((2 * ((x + 2) + (if x <= 0 then 1 else (2 * (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))))))) div 3)),x))
A337800: 1 2 3 4 5 6 8 9 10 12 16 18 20 24 25 27
(1 + compr(\x.(loop(\(x,i).(24 * (1 + (((x + 1) * (1 + ((x + 1) * loop(\(x,i).x2,2,3)))) div 3))),2,x) mod (x + 1)),x))
A097755: 1 2 3 4 6 8 9 12 16 18 21 24 27 32 36 42
((1 + (((1 + loop(\(x,i).x2,1,(1 + ((2 * (1 + (((1 + (loop(\(x,i).2x,(x + ~8),1) div 2)) div 2) div 2))) div 3)))) div 2) div 2)) div 2)
A144557: 0 0 0 0 0 0 0 0 0 0 0 1 1 2 6 18
(5 - ((1 + (if x <= 0 then 2 else (1 + (2 * (1 + (if (~x + 2) <= 0 then (1 - (2 * ((x mod (1 + (((x + 1) div 2) div 2))) mod 2))) else 0)))))) mod 5))
A093779: 2 1 4 3 4 3 4 3 4 4 3 3 4 3 4 4
((loop(\(x,i).2x,(if (x mod 2) <= 0 then (1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2) - (x mod 2)) else 1),1) div 2) div 2)
A218881: 0 0 0 0 1 0 0 0 2 0 0 0 64 0 0 0
(4 + ((4 * (if ((2 + (loop(\(x,i).4x,x,(2 - ((2x + 2) mod 5))) div 3)) div 3) <= 0 then 1 else 2)) div (x + 1)))
A121948: 8 6 6 5 5 4 4 5 4 4 4 4 4 4 4 4
(1 + ((((1 + (2 * ((x + 1) + (((x + 2) + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)) div 3)))) mod (x + 1)) div 2) div 2) - (x mod 2))
A319820-A319819-A319818-A319817-A319799: 1 0 1 0 1 1 1 1 1 2 2 2 2 2 4 3
((2x + ~1) + (2 * ((1 + (((x + 1) * (x + (if x <= 0 then 2 else (~1 + (2 * (if x <= 0 then 1 else (4x + (2 div (~2 + (x mod 2)))))))))) div 2)) div 2)))
A298041: 1 5 25 49 89 129 189 245
compr(\x.(((x + 1) mod (1 + (2 * (((1 + (x * (2 + (loop(\(x,i).(1 + loop(\(x,i).(x div (2 - (x mod 2))),x,x)),2,x) mod (x + 1))))) div (x + 1)) mod 3)))) mod 2),x)
A175413: 1 2 3 4 6 7 8 11 12 13 14 15 16 19 23 24
(if (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) <= 0 then (1 + (3 * ((2x + 1) div (3 + (x div 4))))) else 1)
A131844: 1 4 4 7 1 7 10 1 1 10 13 1 1 1 13 16
(1 + ((1 + (7 * (loop(\(x,i).2x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2))) div 3))
A162747-A162745-A001263: 1 1 1 1 3 1 1 6 6 1 1 10 20 10 1 1
(1 + ((1 + ((loop(\(x,i).2x,((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2),1) - (x mod 2)) div 3)) div 3))
A299321: 1 1 1 1 1 1 1 1 1 1 1 2 15 2 1 1
((x + 2) div (1 + ((2 * (1 + ((1 + (x div (1 + (x mod (1 + ((1 + (if ((x + ~1) mod 3) <= 0 then 1 else x) - (x mod 2)) mod (x + 1))))))) div 2))) div 3)))
A218993: 2 3 2 5 3 7 2 3 2 11 4 13 2 5 2 17
((x + 1) mod (1 + ((1 + (2 * (((x + 1) + (2 * ((1 + ((loop(\(x,i).x2,1,(5x + 1)) div 3) div 2)) div 2))) div 2))) mod (x + 1))))
A160826: 0 0 0 0 0 0 0 0 1 2 5 4 3 0 0 0
((x + 1) div (1 + (2 * (1 + (if (x mod 3) <= 0 then 0 else (1 + (2 * ((~1 + (x2 div 2)) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))))))))))
A263390: 0 0 0 1 0 1 2 0 1 3 2 0 4 1 3 5
(1 + ((loop(\(x,i).(2 * ((x + 3) - ((~x + 1) div 3))),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2) div 2))
A034801: 1 1 1 1 3 1 1 8 8 1 1 21 56 21 1 1
(1 + ((loop(\(x,i).3x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 3) div (4 - ((x div 2) mod 2))))
A331572: 1 1 1 1 1 1 1 2 1 1 1 4 7 3 1 1
(((1 + (loop(\(x,i).3x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 4)) div 2) * (x div 5))
A282377-A281936: 0 0 0 0 0 0 0 1 1 0 0 6 20 6 0 0
(((1 + (2 * ((4 * ((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3)) div 3))) mod (x + 1)) mod 3)
A193347: 0 1 1 0 1 2 1 2 0 2 1 2 1 2 2 0
((1 + ((2 * (if x <= 0 then 0 else (1 + ((x div (2 + (x div (1 + ((x mod (1 + ((2 - (x mod 4)) mod (x + 1)))) div 2))))) + (x mod 2))))) + (x mod 2))) mod 3)
A197881: 1 0 0 2 0 0 0 1 2 0 0 0 0 0 0 1
(((2x + 1) + (2 * ((1 - (x mod (1 + ((if (x mod 2) <= 0 then (x div 2) else (6x + 6)) mod 7)))) mod (x + 1)))) mod 3)
A165414: 1 0 1 2 0 2 1 2 1 0 1 0 1 2 1 2
(2 div (2 + ((x + 1) mod (1 + (2 * ((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1))))) - (x mod 2)))
A330733: 1 0 1 0 0 1 0 1 0 2 0 0 0 0 1 0
((1 + (if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (x div (1 + (x mod (1 + (x div (2 + ((~2x + 1) mod (2 + (x div 4)))))))))) div 2))) div 3)))) div 2)
A007895: 0 1 1 1 2 1 2 2 1 2 2 2 3 1 2 2
((1 + ((if x <= 0 then 2 else (1 + ((2 * (1 + ((1 + (x div (1 + ((~1 + ((1 + (x div (2 - (x mod 2)))) mod 3)) mod (x + 1))))) div 2))) div 3))) div 2)) div 2)
A333179: 1 0 1 1 0 0 1 1 1 1 0 0 1 1 1 2
((1 + ((2 + ((2 * (1 + (((x + 1) * (if x <= 0 then 1 else (2 * ((x mod (1 + (x div 2))) div 2)))) div 5))) div 3) - (x mod 2)) div 2)) div 2)
A124789: 1 0 1 0 1 1 1 1 1 2 2 2 2 3 4 4
(x div (2 * (1 + ((0 + (2 * (1 + (x mod (2 + (x div (2 + (if ((x + 1) mod 5) <= 0 then 0 else 2))) - (x mod 2))))) - (x mod 2)) div 2))))
A235330: 0 0 0 1 1 1 1 1 2 0 1 1 1 3 1 1
((1 + (((5 * loop(\(x,i).x2,1,(~1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))) div 2) div 2)) div 2)
A180959: 1 1 1 1 3 1 1 6 6 1 1 10 23 10 1 1
(2 * ((loop(\(x,i).3x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2) mod 21))
A230910: 0 0 0 0 2 0 0 8 8 0 0 26 38 26 0 0
(((1 + ((2 * (1 + (((x + 1) mod (2 + ((~1 + (2 * (if (16 mod (x + 1)) <= 0 then 0 else 2))) mod (x + 1)))) div 2))) div 3)) mod (x + 1)) div 2)
A179229: 0 0 0 1 0 0 1 2 1 0 0 1 1 1 0 3
(((~1 + (6 * (1 + ((2 * (2 + ((1 + (2 * (loop(\(x,i).(x * (~1 + (2 * i))),x,~2) mod (x + 1)))) * (x mod 2)))) div 3)))) div 2) div 2)
A094756: 2 4 2 7 2 4 2 7 2 4 2 16 2 4 2 7
(6 + ((3 * (1 - ((loop(\(x,i).(2x + 2),x,(12 * (x div 7))) mod 5) div 2))) div 2))
A276792: 7 6 7 4 7 6 7 7 6 7 4 7 6 7 6 7
(2x + (((2x + 2) + (if x <= 0 then 1 else (2 * (2x + ((x + ((2x - ((x + 2) mod 4)) div 3)) div 2))))) div 3))
A313031: 1 4 9 14 18 22 28 32 36 41 46 50 54 59 64 68
((6x + 3) - ((2 * (2 + (if x <= 0 then 1 else (2 * (4x - ((~x + ((x div 2) mod 2)) div 3)))))) div 3))
A128622: 1 1 2 3 2 3 3 4 3 4 5 4 5 4 5 5
(1 + ((1 + ((1 + ((x mod (2 + ((6 * (1 + (((x2 + 2x) div 2) mod (1 + ((1 + (x div 2)) div 3))))) mod (x + 1)))) div 2)) div 2)) div 2))
A322286-A282934-A248641: 1 1 1 2 1 1 2 1 1 1 2 2 2 3 1 1
(2 div (1 + (((2 * (1 + ((1 + ((1 + ((x2 + 2x) mod (1 + (2 * (2 + (x div 8)))))) div 2)) div 2))) - (x div 7)) div 2)))
A178687: 1 0 0 1 0 1 0 1 1 1 1 1 2 0 2 1
(1 + (2 * ((5 * ((4 * ((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~1) div 2))) div 2)) div 3)) div 2)))
A296974-A296039: 1 1 1 1 5 1 1 11 11 1 1 21 31 21 1 1
(~1 + (((5 * ((x + 1) div (1 + (((1 + (x mod ((1 + (x mod (1 + (x div 4)))) * (1 + (x mod 2))))) mod (x + 1)) + (x mod 2))))) div 2) div 2))
A322838: 0 0 0 0 1 0 2 0 1 1 5 0 6 2 2 0
(1 + (((3 * (1 + ((((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2) * (1 + (x div 4))) div 2))) div 2) div 2))
A093541: 1 1 1 1 2 1 1 3 4 1 1 4 12 6 1 1
(~1 + ((1 + (((3 * (1 + (((1 + (x mod ((1 + (x mod (1 + (x div 4)))) * (1 + (x mod 2))))) mod (x + 1)) + (x mod 2)))) div 2) div 2)) mod 4))
A299202: 0 1 1 ~1 1 ~1 1 0 ~1 ~1 1 2 1 ~1 ~1 ~1
(2 - ((1 + ((1 + (x mod 9)) mod (1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))) mod 5))
A279006: 1 1 1 1 0 1 1 ~1 1 1 1 ~2 2 0 1 1
((5 * compr(\x.((x mod 4) * (x div 3)),(1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))) div 3)
A189610: 1 1 1 1 3 1 1 6 6 1 1 13 20 13 1 1
(((2 + ((1 + ((((x + 1) * (6 + ((x + 1) div (5 * (1 + (x mod 3)))))) div 2) div 2)) div 2)) mod 5) mod 3)
A277937: 0 1 1 0 1 2 0 0 1 2 2 1 0 1 0 0
((2 * (1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + ((2x + 1) div (3 + (x div 4)))))) div 3)
A143979: 0 1 1 2 2 2 2 4 4 2 3 5 6 5 3 4
(1 + compr(\x.(1 - ((2 * ((x + 2) + ((x + ((3 * ((3 * (x + (x div 4))) - (x mod 2))) div 7)) div 2))) mod 3)),x))
A285279: 1 4 5 6 8 9 10 12 13 14 16 17 18 19 22 23
compr(\x.(~1 + ((1 + (2 * (1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 - (x div (~1 + ((~x + 1) div 3)))))))) mod 3)),(x + 1))
A141820: 1 2 3 4 5 6 8 9 10 12 14 15 16 18 21 24
compr(\x.(1 - ((2 * (1 + ((1 + (x div (1 + (x mod (1 + ((1 - ((2x + ~1) mod (4 + (x div 4)))) mod 3)))))) div 2))) mod 3)),(x + 1))
A249053: 1 2 4 5 6 8 11 12 13 14 17 18 20 23 24 25
(2 * (1 + ((1 + (((2 + (((x + ~1) + ((1 + (x * ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2))) mod 3)) mod (x + 1))) div 2) div 2)) div 2)))
A060267: 2 2 4 4 2 4 4 2 4 4 6 6 6 2 6 6
((1 + (((1 + (((x + 1) * (3 + (2 * (1 + ((2 * ((2x + 4) - ((~x + 2) div (2 + (x div 4))))) div 3))))) div 2)) div 2) div 2)) div 2)
A193622: 1 2 3 5 7 10
A225645: 1 2 3 5 7 10 13 16 19 23 27 32 37 43 48 53
((1 + (((9 * (1 + ((((((x + 1) * (~1 + ((~2x + 2) mod (4 + (x div 4))))) div 2) div 2) div 2) div 2))) div 2) div 2)) div 2)
A065177-A064044: 1 0 1 0 1 1 0 2 2 1 0 3 6 3 1 0
(x - (2 * ((6x mod (1 + compr(\x.((((x + 1) div (1 + (2 * (x mod (3 * (1 + (x mod 4))))))) mod 2) - (x mod 2)),x))) div 3)))
A163530: 0 1 2 3 2 1 2 3 4 5 6 7 6 5 4 3
((3 * ((3 * (1 + (7 mod (1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))))) div 2)) div 2)
A183374: 1 1 1 1 4 1 1 4 4 1 1 9 6 9 1 1
((3 * ((3 * (1 + (((~1 + ((~2x + 2) mod (4 + (x div 4)))) * (1 + (4 * (x mod 2)))) div (x + 4)))) div 2)) div 2)
A103524: 1 0 1 0 1 1 0 1 1 1 0 4 1 1 1 0
((x + 3) + ((2 * ((2x + 2) + ((2 * ((x + 2) + ((3 * (x + (6x div (x + 1)))) div 2))) div 3))) div 3))
A275537: 5 10 14 18 21 25 29 32 35 39 42 46 49 53 56 60
(((1 + (2 * ((3 * (2 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2))) mod 5))) mod (x + 1)) div 2)
A140885: 0 0 0 1 2 1 1 2 2 1 1 0 2 0 1 1
(4 + (7 * ((3 * (1 + (2 * ((1 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4)))) * (x mod 2))))) div 2)))
A059134: 11 32 11 53 11 32 11 74 11 32 11 53 11 32 11 95
(((2x + 5) + compr(\x.(1 - (x mod (1 + ((1 + (x mod (1 + (2 * (2 + ((2x + 2) mod 9)))))) mod (x + 1))))),x)) div 2)
A184113: 6 8 11 12 14 16 18 20 21 23 24 26 27 29 31 32
((1 + (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + (3 * ((1 + (x div 2)) div 2)))) div 2)) mod 8)
A204181: 1 1 1 1 3 1 1 0 0 1 1 0 5 0 1 1
(1 + ((2 * (1 + ((1 + (((1 + (((x + 1) * (1 + (2 * (1 + ((1 + (x div (2 + (x mod 2)))) div 2))))) div 2)) div 2) div 2)) div 2))) div 3) - (x div 2))
A122433: 1 2 1 1 1 1 0 0 0 1 0 0 0 ~1 1 0
((x + 1) + ((((x + 1) + (2 * (((x + 1) + (2 * ((1 + (((x + 1) * (1 + ((2x mod (2 + (x div 3))) mod 2))) div 2)) div 2))) div 2))) div 2) div 2))
A225647: 1 3 4 6 7
A341292: 1 3 4 6 7 10 11 13 14 17 17 19 20 23 24 26
compr(\x.(1 - ((1 - ((2 * (1 + ((1 + (((2 - (2x mod (4 + (x div 3)))) mod (2x + 5)) div 2)) div 2))) mod 3)) mod 3)),x)
A097044: 1 3 4 7 8 9 10 11 13 14 15 16 17 18 19 23
((3x + 2) + (((2 * (((x + 4) + ((2 * (2x - ((x div 2) div ~5))) div 5)) div 2)) mod 3) div 2))
A287409: 2 5 9 12 14 17 21 23 26 30 32 35 39 41 44 47
loop(\(x,i).2x,x,loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1))
A028214: 1 36 820 15120 246736 3721536 53174080 730794240 9758653696 127501710336 1638112752640 20771546664960 260668843872256 3244288806567936 40111449573376000 493276560759521280
loop(\(x,i).4x,x,loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(5x + loop(\(x,i).(3x + 1),i,1)),i,1)),i,1)),x,1))
A075908: 1 60 2240 67200 1779456 43545600 1010606080 22600089600 492077121536 10505429975040 221005133905920 4597756408627200 94837435443183616 1943344895628410880 4611686018427387903
((2 + (if x <= 0 then 1 else (2 * (1 + (x div (2 + (x div (1 + ((loop(\(x,i).(x2 + x),1,loop(\(x,i).(if x <= 0 then i else (x div 2)),x,0)) mod (x + 1)) mod 3))))))))) mod 3)
A093997: 0 1 1 1 0 1 1 0 2 1 1 1 1 2 1 1
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A028004: 1 31 633 10787 166481 2416827 33681481 456072739 6046236801 78876961163 1016157547769 12960408919731 163959874019761 2060322716086939 25744836645629097 320169349603453763
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).4x,i,1)),i,1)),i,1)),x,1)
A028134: 1 29 543 8401 117383 1545873 19643191 244174337 2994192135 36408715057 440432748119 5310970152033 63918578839207 768370553038481 9230114440859127 110830456328561089
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028078: 1 28 511 7762 107065 1397536 17652307 218558494 2673170269 32451457324 392152259863 4725695939146 56851786048513 683251595827192 8206387016186779 98529159613684918
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028212: 1 35 775 13895 220591 3239495 45114175 605081015 7896440431 100983137255 1271943884575 15837914099735 195494604120271 2397051804927815 29242027752046975 355340314794184055
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).5x,i,1)),i,1)),i,1)),x,1)
A028173: 1 31 615 9995 145511 1981731 25867375 328390315 4092662871 50378487731 614988087935 7465359578235 90280175113831 1089001243414531 13113567724769295 157729903649607755
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028176: 1 32 655 10970 164281 2296172 30679075 397562990 5043607261 63029650112 779227037095 9558498208610 116583782365441 1416013883792852 17145682731588715 207132506435751830
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028092: 1 30 583 9360 135373 1838130 23972131 304421700 3797192905 46789978950 571763347519 6946889160120 84072723694597 1014722669092890 12224658793966747 147088107868298220
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).5x,i,1)),i,1)),i,1)),x,1)
A028119: 1 28 509 7688 105417 1368660 17211253 212371456 2591003393 31398579212 378973353837 4563240432504 54868960089529 659203880450884 7915910524882661 95029322307819632
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(2x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028013: 1 31 629 10595 160965 2293347 31302517 414606643 5373114725 68512221635 862890573909 10764894286419 133300183232581 1640952361357795 20105879474257205 245421711656823923
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A028020: 1 33 711 12677 203175 3043341 43527247 602201829 8127414999 107618860349 1403846663583 18094236941781 230951316035623 2924174000253357 36776292351134319 459910668538753733
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(7x + loop(\(x,i).4x,i,1)),i,1)),i,1)),x,1)
A028148: 1 31 617 10079 147609 2022447 26547529 338695423 4238709497 52353238223 640806363561 7794824571807 94411354501465 1140149916014959 13741090450747913 165378493289389631
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028192: 1 34 735 12920 201821 2925054 40302475 535908340 6945496041 88331974874 1107704935415 13744775469360 169190996868661 2070039164549494 25209912745227555 305937712008039980
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028128: 1 31 623 10355 155151 2182251 29453143 386424115 4968644351 62947998971 788663289063 9797059846275 120896875524751 1484089915071691 18142382512443383 221041773758074835
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028162: 1 35 783 14287 231959 3494127 49989031 689059679 9238060887 121247325199 1565149220999 19940086389951 251372353802935 3141956721674351 38999543432154087 481325752085244703
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A026308: 1 30 597 9974 151629 2176086 30060949 404288598 5331243357 69255757142 889174566501 11309336465622 142744102829485 1790283986115798 22334320279686453 277371931128111446
loop(\(x,i).(12x + loop(\(x,i).(3x + loop(\(x,i).(8x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028103: 1 33 703 12309 192943 2819949 39304711 529663893 6962879935 89838427965 1142617774519 14370723472677 179151734300527 2217730946235981 27298909572676327 334504592037294261
loop(\(x,i).(12x + loop(\(x,i).(3x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028052: 1 30 595 9900 149941 2145210 29561815 396813000 5224781881 67791656790 869540915035 11050958595300 139392712421821 1747306114774770 21788203659532255 270484281270892800
loop(\(x,i).(12x + loop(\(x,i).(3x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028106: 1 34 745 13390 214981 3211234 45646225 626042230 8359948861 109374928234 1408284704905 17904343620670 225325039105141 2812442423778034 34869043816790785 429934709807000710
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A026542: 1 26 443 6292 81081 986622 11585911 132996344 1504338341 16852487938 187601429379 2079728352156 22993065448081 253755685986374 2797253854490447 30812086837337728
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028200: 1 30 565 8550 113701 1388310 15958405 175419750 1863406501 19269697590 195034120645 1939826329350 19018419228901 184245490086870 1767124523521285 16805853434269350
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).5x,i,1)),i,1)),i,1)),x,1)
A028165: 1 26 425 5590 64701 688506 6906145 66324830 616252901 5580303586 49508360265 432061044870 3720287489101 31681154472266 267320885100785 2238337148081710
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028132: 1 27 465 6535 81921 956487 10657585 115031895 1214419041 12622599847 129754165905 1323318833655 13420125351361 135548860481607 1365156409213425 13720647130385815
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028137: 1 29 539 8209 111915 1425273 17363443 205288433 2377405019 27135022057 306533078787 3437326558497 38340790470763 426029329661081 4720802257754771 52206070294635601
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028171: 1 29 533 7945 105021 1285809 14944693 167428745 1826266541 19529198689 205738222053 2142884743545 22124707610461 226886218153169 2314414985326613 23511240805642345
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028210: 1 33 685 11445 168301 2275413 28994365 353654565 4172013901 47945991093 539606148445 5970648969285 65146124616301 702577801647573 7503184109388925 79467822863509605
loop(\(x,i).(6x + loop(\(x,i).(9x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A028000: 1 28 513 7808 107309 1384836 17143081 206182696 2429008197 28183193324 323282753729 3676063130064 41519535153565 466480044231892 5219284450672857 58204869911960312
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028113: 1 26 437 6082 76653 913218 10527349 119017634 1330185725 14766710530 163286454981 1801494203106 19849649018317 218551250986562 2405323875398933 26466271609592098
loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028174: 1 30 571 8820 120841 1533210 18457111 213985200 2412703381 26633396790 289205203651 3099825799980 32880061861921 345809114026770 3611607266342191 37500386320109160
loop(\(x,i).(6x + loop(\(x,i).(2x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028002: 1 29 551 8701 124047 1659525 21274807 264643037 3219794303 38520062581 454834639623 5314864742733 61583614410319 708640371952997 8107367772115799 92304987577062589
loop(\(x,i).(6x + loop(\(x,i).(3x + loop(\(x,i).(7x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028076: 1 26 435 5980 73721 849966 9381535 100546160 1055929941 10932713506 112061907035 1140487891140 11548313690161 116513300146646 1172500867726935 11777524096712920
loop(\(x,i).(6x + loop(\(x,i).(3x + loop(\(x,i).(8x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028081: 1 28 507 7574 101801 1283016 15511399 182368858 2103357861 23935475564 269799417251 3020592495102 33653261722081 373625952944272 4137562797943263 45735549657446306
loop(\(x,i).(7x + loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028151: 1 32 657 11056 166481 2339904 31427089 409158992 5211577041 65347755616 810110258321 9959365988208 121687051820881 1480042546391168 17940274040148753 216912236044745104
loop(\(x,i).(7x + loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1)
A028063: 1 27 478 7086 95923 1234761 15440896 189849132 2311064965 27967760535 337282318594 4059193972938 48793580278327 586108780927749 7037421345862372 84477944245876104
loop(\(x,i).(7x + loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028166: 1 27 460 6330 76951 863457 9169210 93598560 928041301 9002652087 85889800360 809002365990 7544820424051 69822238375917 642271794705910 5880216219628620
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A028007: 1 28 511 7722 105105 1340976 16393987 194632774 2263422469 25933837644 293957202903 3305777399106 36960914527993 411484609521832 4566596614746859 50561336628369918
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028146: 1 29 535 8025 106911 1320249 15480655 174931625 1923680671 20725530969 219822814575 2303376354825 23907223188031 246285893877689 2522150397345295 25706911853867625
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028180: 1 29 530 7810 101451 1213359 13695340 148146020 1551618101 15847349089 158652680550 1562885008230 15193886293951 146104406183219 1392173613916160 13163974362722440
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028117: 1 26 433 5910 72261 826266 9049993 96336350 1005909421 10365632706 105846730353 1074027489990 10850349799381 109279857370346 1098262533175513 11021021340982830
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028149: 1 30 573 8902 122829 1570422 19052461 222558534 2527254477 28081375894 306750949869 3305552387046 35230183832845 372099762869046 3900761112145197 40636558684412038
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A025995: 1 25 412 5694 71799 859131 9961834 113290048 1272810517 14190510477 157439054136 1741315046562 19221270567955 211903646137663 2334237969260518 25699753556697636
loop(\(x,i).(7x + loop(\(x,i).(3x + loop(\(x,i).(8x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028090: 1 28 503 7394 96993 1183584 13750411 154260238 1686734885 18091012940 191193729519 1997666285082 20686716623977 212717150997496 2175158274827027 22143785088967526
loop(\(x,i).(8x + loop(\(x,i).(9x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A028016: 1 30 585 9410 135741 1826910 23449345 290918970 3519263781 41763254390 488289628905 5642683638930 64604625484621 734199837187470 8294002882781265 93241186270173290
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028122: 1 28 505 7500 100161 1254588 15084745 176531500 2028331921 23012251548 258784204185 2892049106700 32177076653281 356869970102908 3948976130302825 43626137399621100
loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028190: 1 32 647 10570 152481 2028012 25481947 307098110 3585577061 40841792992 456139166847 5013707912850 54390770364841 583654905773972 6205991828373347 65478677349042790
loop(\(x,i).(8x + loop(\(x,i).(2x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028018: 1 31 625 10395 155001 2155251 28559665 365471515 4555708201 55646962371 668889963105 7936976609835 93190238832601 1084660596151891 12532810309612945 143923263421271355
loop(\(x,i).(9x + loop(\(x,i).(3x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028048: 1 27 478 7062 94699 1198209 14603176 173499804 2024524117 23314991271 265875954994 3009351209826 33865370166655 379381897212813 4234967357150332 47140543570858728
loop(\(x,i).(4x + loop(\(x,i).(3x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028050: 1 28 515 7910 110241 1448328 18302575 225096970 2713995581 32234230028 378383333835 4400300953230 50784218810521 582435753818128 6644887820416295 75474715560668690
loop(\(x,i).(5x + loop(\(x,i).(3x + loop(\(x,i).(8x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028066: 1 27 474 6902 90867 1126545 13446028 156530604 1791797733 20274317063 227558149182 2539586737506 28227640438999 312844584806781 3460030004311536 38210322891344408
loop(\(x,i).(3x + loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028087: 1 31 625 10435 157081 2218891 30058465 395576995 5099030761 64729573051 812287789105 10103508011155 124806994586041 1533359039348011 18757216238876545 228656612889142915
loop(\(x,i).(3x + loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028072: 1 30 589 9630 142621 1989510 26692669 348689550 4469016541 56480471190 706312706749 8761344810270 107992670570461 1324480424684070 16179464126208829 197010636086927790
loop(\(x,i).(3x + loop(\(x,i).(7x + loop(\(x,i).(12x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028095: 1 31 622 10294 153139 2133397 28467664 368853628 4681501957 58545953323 724357095826 8891996242402 108525576595255 1318871068893409 15976717061264308 193081291067943016
loop(\(x,i).(3x + loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028041: 1 25 410 5630 70551 839775 9697720 109955260 1232712701 13723263125 152103875430 1681194742890 18549572478451 204440573062075 2251614293669540 24787137412192520
loop(\(x,i).(3x + loop(\(x,i).(5x + loop(\(x,i).(6x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028057: 1 25 408 5558 68999 813603 9315286 104854096 1168677477 12952000061 143075613044 1577575222314 17376397872835 191281848531799 2104964417048082 23159869359140612
loop(\(x,i).(3x + loop(\(x,i).(5x + loop(\(x,i).(7x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028061: 1 25 404 5390 64791 731595 7939714 83955520 872430581 8959286765 91262059824 924426748050 9327520083571 93861018423535 942726158964734 9456149685174980
loop(\(x,i).(3x + loop(\(x,i).(7x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028093: 1 29 540 8230 111911 1414839 17015290 197394560 2229204021 24659970049 268405356440 2883764656890 30659268255331 323156832303659 3381832557579990 35179011908571220
((x + 1) - loop(\(x,i).(x - loop(\(x,i).(~1 + (((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1))),1,i)),x,1))
A233524: 0 1 2 4 5 8
A002541: 0 1 2 4 5 8 9 12 14 17 18 23 24 27 30 34
(~1 + (loop(\(x,i).(x2 + x),1,(((2 * (4 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1))) div 3))
A248955: 1 3 3 5 3 9 3 9 5 9 3 17 3 9 9 13
(if x <= 0 then 0 else (1 + ((2 * (1 + (loop(\(x,i).2x,((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3),1) div 2))) div 3)))
A344462: 0 1 1 2 1 3 1 3 2 3 1 7 1 3 3 4
(~1 + (2 * (1 + (4 * (1 + (2 * compr(\x.loop(\(x,i).(2 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(4x + ~1))),1,(2x + 1)),x)))))))
A105126: 41 73 89 137 233 281 313 409 457 521 569 601 617 761 809 857
(if x <= 0 then 1 else (1 - ((1 + (loop(\(x,i).2x,(if (x + ~2) <= 0 then 1 else (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)),1) div 2)) mod 3)))
A178904: 1 ~1 ~1 0 ~1 0 0 1 1 0 0 ~1 1 ~1 0 0
(loop(\(x,i).(2x + 1),(x + ~1),(if x <= 0 then 1 else (2 * (1 + ((1 + (((1 + (((x + ~1) * loop(\(x,i).(x * i),(x + ~1),(x + 1))) div 2)) div 2) div 2)) div 2))))) div 3)
A280006: 0 0 1 6 39 399
(3 + (loop(\(x,i).(x + loop(\(x,i).(4 * ((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1))),1,i)),x,0) div 2))
A123567: 3 5 7 11 13 17 19 25 29 33 35 41 43 47 51 59
(if 2x <= 0 then x else (if x <= 0 then 1 else (2 * (1 + ((1 + (((1 + ((x * ((2x + 4) + loop(\(x,i).(2x - ((~1 + i) div 2)),x,1))) div 2)) div 2) div 2)) div 2)))))
A000937: 0 4 6 8 14 26 48 96
((1 + ((x + (loop(\(x,i).2x,x,loop(\(x,i).2x,((((1 + (8 mod (1 + (x div 2)))) div 2) + (if x <= 0 then 0 else 1)) - (x mod 2)),1)) mod (x + 1))) div 2)) div 2)
A113757: 0 0 1 1 2 2 2 2 3 4 4 4 4 4 6 4
(2 + loop(\(x,i).(~1 + (10 * loop(\(x,i).(5x + 2),(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),2))),1,(x2 + 1)))
A181285: 3121 78121 30517578121 4611686018427387903 4611686018427387903
(2 * (if x <= 0 then 1 else (2 * (1 + ((1 + ((x mod (1 + (loop(\(x,i).(2x + 2),(loop(\(x,i).(~3x2 + x),2,2) mod (x + 1)),1) mod (x + 1)))) div 2)) div 2)))))
A260085: 2 4 4 4 4 4 8 4 8 4 8 4 4 8 8 4
(((loop(\(x,i).(10x + 10),(2x + 1),0) + loop(\(x,i).10x,x,2)) div 2) + loop(\(x,i).10x,x,2))
A332158: 8 585 55855 5558555 555585555 55555855555 5555558555555 555555585555555 55555555855555555 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
((x + 1) mod (~1 + (2 * (1 + (if x <= 0 then 0 else (1 + (((x + 1) - ((1 + (x div (1 + (x mod (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))) mod (x + 1))) div 2)))))))
A140523: 0 2 3 4 5 1 7 8 9 3 11 1 13 5 2 16
(1 + ((1 + (((3 * (1 + (x div (1 + (x mod (1 + (loop(\(x,i).(x2 + 2x),1,(loop(\(x,i).(2x + 1),x,0) mod (x + 1))) mod (x + 1)))))))) div 2) div 2)) div 2))
A336472: 1 1 2 1 3 2 4 1 3 3 5 2 6 4 7 1
((1 + (2 * ((2 * (1 + ((compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)) div 2))) div 3))) div 3)
A057165: 0 1 2 3 5 6 7 9 11 13 15 17 18 19 21 24
((loop(\(x,i).(2x + 2),1,(x div (2 + (x div (1 + (loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1) mod 9)))))) mod (x + 1)) mod 3)
A237348: 0 0 1 0 1 0 1 0 1 1 0 2 2 2 2 2
((2 * (1 + ((4 * ((2 * (2 + (if x <= 0 then 0 else (2 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))))) div 3)) div 3))) div 3)
A252505: 1 2 2 3 2 4 2 4 3 4 2 6 2 4 4 4
((2 * (1 + ((1 + ((x + ((x + ((1 + ((loop(\(x,i).(3x + 1),x,0) - loop(\(x,i).3x,(x div 2),1)) div 2)) div 2)) div 2)) div 2)) div 2))) mod 3)
A306863: 2 2 1 0 2 0 1 2 1 0 1 0 2 0 1 2
(1 + compr(\x.(~1 + (loop(\(x,i).8x,((x div (2 + (x div (1 + (((x2 + 2x) div 2) mod (3 + (x mod 2))))))) + (if x <= 0 then 0 else 1)),1) div (x + 1))),x))
A322271: 1 5 7 11 13 17 19 23
A067291: 1 5 7 11 13 17 19 23 25 29 31 33 34 35 37 38
((~1 + (2 * ((3 * ((~1 + (2 * (if x <= 0 then 1 else (2 * (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))))))) div 2)) div 2))) div (x + 1))
A280827: ~1 0 0 1 0 1 0 2 1 0 0 1 0 0 0 2
((1 + ((3x + 2) * loop(\(x,i).4x,((1 + loop(\(x,i).34x,2,(2x + 1))) mod (x + 1)),x))) mod (x + 1))
A337224: 0 1 2 1 2 5 2 1 2 5 2 5 4 5 2 1
((2x + 1) div (if x <= 0 then 1 else (2 * (1 + (((loop(\(x,i).2x,x,(1 + (x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4)))))))) - (x mod 2)) mod (x + 1)) div 2)))))
A345046: 1 1 2 1 4 2 6 1 4 4 10 2 12 6 4 1
(((2 + ((2 * (1 + compr(\x.(loop(\(x,i).(2x + 2),x,(loop(\(x,i).(2 * (x - i)),x,2) mod (x + 1))) mod (x + 1)),x))) div 3) - (x mod 2)) mod (x + 1)) div 2)
A240866: 0 0 0 0 0 0 1 0 2 1 3 2 4 3 5 6
(~2 + (((x + 1) * (6 + (if x <= 0 then 1 else ((x + 1) + ((2 * (4 + (if x <= 0 then 2 else ((x + 2) + (2 * (2 - (x mod 2))))))) div 3))))) div 2))
A029756: 1 12 23 32 48
(2 + (2 * ((x + 6) + (((1 + ((((loop(\(x,i).x2,1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))) div 2) div 2) div 2) div 2)) div 2) div 2))))
A053425: 14 16 18 22 26 28 34 38 46 58
((3x + 1) + (((x + 1) + (((x + 1) + ((5 * compr(\x.loop(\(x,i).(x - (if (x mod (1 + (2 * i))) <= 0 then 2 else 1)),x,(x + 2)),x)) div 2)) div 2)) div 2))
A134445: 8 14 23 28 34 42 49
(1 + loop(\(x,i).(~3 + ((2 * ((1 + ((x div 2) mod 2)) * (x div 3))) div 2)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1))
A177227: 2 2 2 2 ~2 2 2 ~3 ~3 2 2 ~4 ~6 ~4 2 2
(1 + (if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (((1 + (((x + 1) * (1 + (3 * ((x div 3) mod 2)) - (x mod 2))) div 2)) div 2) div 2)) div 2))) div 3))))
A338687-A338686: 1 2 2 3 3 3 3 2 3 4 4 4 3 2 3 4
(1 + ((x + 1) div (1 + (2 * (1 + (if (x mod 3) <= 0 then 0 else (1 + (2 * ((~1 + (x2 div 2)) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))))))))))
A163491: 1 1 1 2 1 2 3 1 2 4 3 1 5 2 4 6
loop(\(x,i).4x,(~1 + (((3 * (1 + ((3 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) div 2))) div 2) div 2)),1)
A173778: 1 1 1 1 1 1 1 16 16 1 1 16 256 16 1 1
(1 + ((1 + (if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (x div (1 + (x mod (1 + (x div (2 + ((~2x + 1) mod (2 + (x div 4)))))))))) div 2))) div 3)))) div 2))
A143299: 1 2 2 2 3 2 3 3 2 3 3 3 4 2 3 3
(1 + ((1 + (((1 + (((x + 2) * (if (x mod 3) <= 0 then 1 else (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))) div 2)) div 2) div 2)) div 2))
A108461: 1 1 1 1 2 1 2 2 2 2 1 4 2 4 1 2
(1 + (((loop(\(x,i).3x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 5) + (x div 5)) div 2))
A215959: 1 1 1 1 1 1 1 2 2 1 2 4 10 4 2 2
(1 + (2 * ((1 + (7 * (loop(\(x,i).2x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2))) div 3)))
A132787: 1 1 1 1 5 1 1 11 11 1 1 19 39 19 1 1
(~1 + (4 * (~1 + (2 * (~1 + (4 * (1 + (36 * (1 + ((x + 1) * (1 + loop(\(x,i).(x * (x + i)),2,4))))))))))))
A076337: 509203
((x + 2) div (1 + (2 * ((2 + ((~1 + (2 * ((if (x mod 3) <= 0 then 1 else (((x + 1) div 2) - ((3 * (x div 4)) div 2))) + (x mod 2)))) mod (x + 1))) div 2))))
A277692: 0 1 1 1 2 1 2 1 3 2 2 1 4 1 2 3
((2 * (1 + ((1 + ((x + 1) div (1 + (2 * (((1 + (2 * (1 + (if x <= 0 then 0 else (1 + (((x + 1) div (2 + (x mod 2))) div 2)))))) mod (x + 1)) div 2))))) div 2))) div 3)
A264744: 1 1 1 2 1 2 3 1 4 1 1 1 1
(~3 + (4 * (1 + (loop(\(x,i).(x * (1 + (x mod 5))),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2))))
A143007: 1 1 1 1 5 1 1 13 13 1 1 25 73 25 1 1
((2 * (2 + (((x + 1) * (1 + ((~1 + (loop(\(x,i).13x,x,1) mod 31)) mod (x + 1)))) div 2))) mod 3)
A255318: 1 0 1 1 1 1 0 1 0 1 1 1 0 2 1 0
((2 * ((3x + 2) + ((2 * (2x + (if x <= 0 then 1 else (2 * (x + ((x + (2 * ((x2 div 8) mod 2))) div 2)))))) div 3))) mod 3)
A122856: 1 2 1 0 0 2 2 0 2 2 1 0 0 2 0 0
loop(\(x,i).2x,((x + ((1 + ((1 + ((((x + 1) * ((x + 2) + ((2 * (2x + ((x2 + 2x) div 4))) div 3))) div 2) div 2)) div 2)) div 2)) div 2),1)
A222011: 1 2 4 8
A074700: 1 2 4 8 16 64 256 1024 8192 131072 1048576
(x - ((1 + (if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (x div (1 + (x mod (1 + (x div (2 + ((~2x + 1) mod (2 + (x div 4)))))))))) div 2))) div 3)))) div 2))
A219641: 0 0 1 2 2 4 4 5 7 7 8 9 9 12 12 13
((x + ~1) mod (2 * (1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((x * (1 + (2 * loop(\(x,i).(1 + (2 * (x mod (1 + i)))),x,1)))) div 2)) div 2)) div 2)) div 2)) div 2)) div 2))))
A332845: 1 0 1 2 3 0 5 6 7 0 9 2 11 0 3 14
((1 + ((1 + ((1 + (x mod (2 + ((1 + (2 * (1 + ((if x <= 0 then 0 else (1 + ((2x mod (2 + (x div 3))) mod 2))) + (x mod 2))))) mod (x + 1))))) div 2)) div 2)) div 2)
A258045: 0 1 1 1 0 0 1 1 1 2 1 1 1 1 0 1
((1 + ((2 + ((2 * (1 + ((2 * ((1 + ((x * ((x + (if (x mod 2) <= 0 then 2 else x)) div 2)) div 2)) div 3)) div 3))) div 3) - (x mod 2)) div 2)) div 2)
A029209: 1 0 1 0 1 1 1 1 1 2 2 3 2 3 3 4
(~2 + (3 * (1 + ((1 + ((3 * (loop(\(x,i).(x * i),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2)) div 2)) div 2))))
A172347: 1 1 1 1 1 1 1 4 4 1 1 7 28 7 1 1
(4 * ((3 * ((1 + (2 * (loop(\(x,i).2x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2))) div 3)) div 2))
A203285: 0 0 0 0 4 0 0 4 4 0 0 16 28 16 0 0
(((1 + (((2 * (1 + ((1 + ((1 + loop(\(x,i).((x + 1) + (2 * ((x + (x div 2)) div 4))),((x + 1) div 2),1)) div 2)) div 2))) div 3) + (x mod 2))) div 2) div 2)
A034394: 0 0 0 0 0 1 0 1 0 1 1 2 1 3 3 5
(1 + (if x <= 0 then 0 else (1 + (x div (2 + (((2 * (1 + ((1 + ((32 mod (x + 1)) div 2)) div 2))) div 3) + (x mod 2)))))) - (x mod 2))
A318881: 1 1 2 2 3 2 4 3 4 3 4 3 5 4 6 6
compr(\x.((2 + (((x + 4) + ((2 + (((2x + 4) + (if x <= 0 then 1 else ((x + 4) + (x div (4 + (x div 2)))))) div 2)) div 2)) div 2)) mod 3),x)
A190778: 1 4 5 8 11 15 18 21 22 25 28 32 35 39 42 45
(x + ((x + ((x + (((x * (~1 + ((2 * ((x + ~1) + (2 * ((4 * (x + (if (~2 + (x div 2)) <= 0 then 1 else 2))) div 3)))) div 3))) div 2) div 2)) div 2)) div 2))
A185595: 0 1 4 6 9 12 16 20 24 28 33 38 43 49 55 60
(1 + (((2 * (1 + (~2 mod (1 - (2 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))))) - (x div 3)) div 3))
A216201: 1 1 1 1 2 1 1 3 3 0 0 4 6 3 0 0
(1 + ((2 * (1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + ((2x + 1) div (3 + (x div 4)))))) div 3))
A143997: 1 2 2 3 3 3 3 5 5 3 4 6 7 6 4 5
(~1 + ((4 * (2 + (((x + 1) div (1 + (x mod (2 + (x div (1 + ((x div 2) mod (1 + (x mod (1 + ((~x + 2) mod 4))))))))))) div 3))) div 3))
A295920: 1 1 1 3 1 1 1 3 3 1 1 1 1 1 1 8
((x + 3) div (1 + (x div (2 + (((2 * (1 + (((1 + (x div (2 + (x mod (2 + (x mod (2 + (x mod 2)))))))) mod (x + 1)) div 2))) div 3) + (x mod 2))))))
A187824: 3 4 5 6 3 4 4 5 3 6 4 4 3 5 5 4
(1 + (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + (((1 + ((x + 2) div (1 + (2 * ((x div 2) mod 2))))) div 2) div 2))) div 2))
A138028-A009999: 1 1 1 1 2 1 1 3 4 1 1 4 9 8 1 1
(1 + (((2 * (1 + (((~1 + (6 * (1 + ((2 + ((~3x + 5) mod (1 + (x div 2)))) div 3)))) div 2) div 2))) + (x mod 3)) div 2))
A216199: 3 3 5 3 4 5 4 3 5 4 6 5 6 4 5 3
(1 + (((3 * ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (2 + (x div 4) - (x div 5)))) div 2) div 2))
A104730: 1 1 1 1 3 1 1 4 5 1 1 5 10 7 1 1
((2 * (1 + (((3 * (1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2))) - (x div 5)) div 2))) div 3)
A216210: 1 1 1 1 2 1 1 3 3 1 0 4 6 4 0 0
((2 * (1 + ((2 + ((2 * (1 + ((1 + ((((x + 1) * (1 + (2x mod (1 + (x div 2))))) div 2) div 2)) div 2))) div 3) - (x mod 2)) div 2))) div 3)
A341974: 1 0 1 1 2 1 1 1 2 2 2 2 2 3 3 4
((x + 3) - (2 * (1 + (((3 * (1 + ((1 + ((1 + ((((x + 2) * (1 + (2 * ((1 + (x div 4)) div 2)))) div 2) div 2)) div 2)) div 2))) div 2) div 2))))
A076827: 1 2 1 2 3 2 3 4 5 6 5 6 5 6 7 6
((2 + (2 * (1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + ((2x + 1) div (3 + (x div 4))))))) div 3)
A143976: 1 2 2 2 3 2 3 4 4 3 4 6 6 6 4 4
((x + 3) - (2 * ((2 + (((x + 2) + ((2 * (1 + ((x + (2 * (4 - ((~x + 1) div (2 + (x div 4)))))) div 3))) mod (x + 1))) div 2)) div 2)))
A030307: 1 2 1 2 3 4 3 2 3 2 3 4 5 4 5 6
((x + (2 * ((2x + 2) + ((1 + (2 * (2 + (2 * (x - (((x div 2) - ((~1 + (x div 4)) div 2)) mod 2))) - (x mod 2)))) div 3)))) div 3)
A190366: 1 3 7 9 12 14 16 19 22 25 26 29 32 34 38 40
(((1 + (((x + 1) * (1 + (4 * (2 + ((1 + ((19x2 + 19x) div 2)) div 2))))) div 3)) div 3) div (x + 1))
A202821: 1 5 14 26 43 64 89 119 153 191 233 279 330 385 444 507
((~x + 1) + (2 * (((2x + 1) + (2 * ((x + 1) + (((x + 1) + (((x + 1) + ((2 * (x3 div (x + 2))) div 3)) div 2)) div 2)))) div 3)))
A123581: 3 6 9 12 15 20 25 30 35 42 49 56 63 70 77 88
((1 + ((1 + ((1 + (((x + 1) * (1 + (((x mod ((x + ~1) - (x mod (2 * (1 + (x mod (1 + ((~x + 2) mod 4)))))))) div 2) + (x mod 2)))) div 2)) div 2)) div 2)) div 2)
A344174: 0 1 1 1 1 2 1 1 2 2 1 3 1 3 1 2
((3 * (1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (x mod (1 + (2 * ((1 + (((x + 1) div 2) div 2)) div 2))))))) div 2)
A263950: 1 1 1 1 3 1 1 4 7 1 1 6 13 15 1 1
((3 * (1 + ((5 * ((4 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)) div 3)) div 2))) div 2)
A124216: 1 1 1 1 4 1 1 9 9 1 1 16 34 16 1 1
(((~1 + (6 * (1 + ((1 + (x div (3 + ((x mod (1 + (x div (2 + ((x + 1) mod 5))))) div 2)))) div (1 + (x div 4)))))) div 2) div 2)
A337539: 2 2 2 4 2 2 2 2 2 1 2 2 2 2 1 2
(((5 * ((3 * (1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) div (1 + ((x div 2) mod 2))))) div 2)) div 2) div 2)
A116445: 1 1 1 1 3 1 1 3 5 1 1 3 8 7 1 1
(((3 * (1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + ((2x + 1) div (3 + (x div 4)))))) div 2) div 2)
A143998: 0 1 1 2 3 2 3 4 4 3 3 6 6 6 3 4
(((~2 + (7 * (~1 + (2 * (1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (x + ((~x + 1) mod 4))) div 2)))))) div 2) div 2)
A157170: 1 1 1 1 8 1 1 15 15 1 1 22 46 22 1 1
(4 * (2 + (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + (2 * ((2x + 1) div (3 + (x div 4))))) div 2)))
A295782: 8 12 12 16 16 16 20 24 24 20 24 28 32 28 24 28
(((1 + (((2 * (1 + ((1 + ((x + 1) div (1 + ((6x + 1) mod (4 + (x div 4)))))) div 2))) div 3) + (x mod 2))) div 2) mod 4)
A125029: 0 1 1 1 1 2 1 1 1 2 1 2 1 2 2 0
(loop(\(x,i).2x,(x + loop(\(x,i).(x - (if x <= 0 then 1 else (if (x mod 2) <= 0 then (x div 2) else ((x + ~1) + loop(\(x,i).x2,2,loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))))))),x,x)),1) div 2)
A341509: 0 1 2 1 4 0 2 1 8 0 0 0 4 0 2 1
(1 + (loop(\(x,i).(x + loop(\(x,i).loop(\(x,i).2x,(compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x) - compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)),1),1,i)),x,1) div 2))
A086769: 1 3 5 13 15 23 25 33 65 67 99 107 109 117 149 181
(1 + ((((2 * (x + (if x <= 0 then 1 else (x - loop(\(x,i).loop(\(x,i).((x + ~1) - (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)),x,x),1,2x))))) mod (x + 1)) div 2) div 2))
A151552: 1 1 1 1 2 2 1 1 2 2 2 3 4 3 1 1
loop(\(x,i).(x * i),(~x + (3 * (2 + (if (1 + ((x + 1) * loop(\(x,i).(x * (1 - loop(\(x,i).3x,x,loop(\(x,i).(3x + ~6),x,0)))),x,1))) <= 0 then x else 2)))),1)
A072232: 479001600 39916800 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).2x,x,loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).3x,i,1)),i,1)),i,1)),x,1))
A001241: 1 50 1660 46760 1217776 30480800 747497920 18139003520 437786795776 10536798272000 253246254177280 6082300519393280 146028165842661376 3505313580591718400 4611686018427387903 4611686018427387903
loop(\(x,i).8x,x,loop(\(x,i).(4x + loop(\(x,i).(2x + loop(\(x,i).(5x + loop(\(x,i).(3x + 1),i,1)),i,1)),i,1)),x,1))
A076005: 1 120 8960 537600 28471296 1393459200 64678789120 2892811468800 125971743113216 5378780147220480 226309257119662080 4611686018427387903 4611686018427387903 4611686018427387903
loop(\(x,i).x2,1,(~1 + (2 * ((x + 1) + ((2 * (1 + (((loop(\(x,i).(x2 + x),1,loop(\(x,i).(x * i),x,1)) - loop(\(x,i).3x,x,1)) div 2) div 2))) div 3)))))
A227078: 1 9 25 121 32761
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).7x,i,1)),i,1)),i,1)),x,1)
A028203: 1 33 691 11757 177835 2499021 33451867 433216509 5483226859 68297761389 841179979003 10278678991581 124904130163723 1511929278991437 18252066460636699 219926530250218173
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028144: 1 33 703 12333 194239 2860821 40291111 549874221 7333588207 96118840389 1242878986999 15899609772189 201637495269055 2538952949123637 31780003009949767 395799688351994637
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028178: 1 33 697 12045 186001 2677653 36790057 489351885 6359059201 81227776773 1024237953817 12787834412925 158435642617201 1951116268675893 23912720464211977 291948566493573165
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028217: 1 37 865 16345 272881 4203577 61233985 856507465 11620866961 154020283417 2004281620705 25705179230185 325843083624241 4091525808208057 50980871394705025 631212806724858505
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A028014: 1 32 671 11686 183561 2702868 38100595 520688018 6954616493 91281855808 1181868771447 15136545033246 192153235734097 2421636122107052 30334353203856827 378040802156676970
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(6x + loop(\(x,i).5x,i,1)),i,1)),i,1)),x,1)
A028169: 1 30 577 9114 129349 1723086 22075129 275977218 3397380877 41418850902 501892142401 6058699871562 72968197588885 877537225626078 10544318356835593 126631590349302546
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028221: 1 36 817 14964 241969 3609732 50945329 691013268 9103047217 117325825188 1487325837361 18617531653812 230789841098545 2839613067896004 34737008397752113 423047207066166996
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).5x,i,1)),i,1)),i,1)),x,1)
A028183: 1 32 653 10876 161673 2240376 29659621 380803412 4787944865 59338124560 728084033469 8872019284908 107592152638777 1300465261202984 15682817092702997 188828216949912964
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028153: 1 33 699 12133 188307 2724645 37614403 502459221 6553738323 83980945477 1061789912547 13286272788789 164915485814899 2034013938152229 24960030504150531 305050074724911637
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028160: 1 35 785 14395 235401 3578595 51754945 722167115 9811679801 130610749555 1711051941105 22130751379035 283285847668201 3595414758854915 45309603386047265 567596497380674155
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028194: 1 35 779 14095 226491 3373575 47712739 650313455 8625455531 112077065815 1433487819699 18110309247615 226591110120571 2813231293937255 34711873203654659 426167229337538575
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A016091: 1 39 955 18795 325171 5167659 77353795 1107933915 15345293491 207057429579 2736619356835 35572444360635 456191563128211 5785999811488299 72719715037363075 907085298655532955
loop(\(x,i).(12x + loop(\(x,i).(9x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A028023: 1 34 753 13766 225653 3448818 50219881 705962782 9663465405 129570729002 1709032341809 22244754709398 286400212885957 3654165387941986 46270388840585337 582133829294947214
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028129: 1 32 665 11440 177441 2582592 36039145 488323280 6475959281 84497107552 1088651482425 13885593262320 175667802947521 2207466992246912 27583620276442505 343037771674508560
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028197: 1 36 823 15270 251161 3822096 55123003 764718570 10305415021 135822156756 1759270703983 22475843025870 283991223372481 3556423423325016 44213833662081763 546396746667037170
loop(\(x,i).(12x + loop(\(x,i).(2x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028024: 1 35 797 14959 251349 3931431 58494829 838932143 11699121797 159590758327 2138803364061 28251497273727 368712393238645 4763687404354823 61019774392655693 775898073656236111
loop(\(x,i).(12x + loop(\(x,i).(3x + loop(\(x,i).(6x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028088: 1 32 667 11522 179473 2622284 36714679 498853814 6630652765 86676445856 1118432963011 14283392713226 180889234319977 2275070671007348 28449403226477263 354027885991627358
loop(\(x,i).(12x + loop(\(x,i).(3x + loop(\(x,i).(7x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028097: 1 32 663 11326 173753 2492676 34193851 454583162 5907650925 75488944960 952332965519 11896112035158 147458730765217 1816728187188284 22274159313106467 272032430647628914
loop(\(x,i).(12x + loop(\(x,i).(3x + loop(\(x,i).(8x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028104: 1 34 747 13496 218309 3291918 47316319 657096292 8894300217 118046931002 1542749735891 19914792822288 254507220618925 3225793030038886 40605323440744263 508174054158717884
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028201: 1 31 605 9515 131901 1684011 20303725 234831355 2632942301 28828462091 309891463245 3283433875995 34394321024701 357022927273771 3679144385477165 37693176577349435
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028133: 1 28 503 7418 98169 1217136 14481211 167749366 1909343117 21481183724 239821188399 2663810246994 29488849731745 325724954017192 3592642298586467 39588148322702702
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028204: 1 32 645 10480 150101 1979712 24649045 294242960 3402478101 38387226592 424748805845 4627041422640 49770222820501 529800364460672 5591164247433045 58580499720429520
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028172: 1 30 573 8918 123669 1595958 19642141 234045366 2726478117 31257792566 354281953389 3982604010294 44504504288245 495188689219254 5492628385206717 60786003189650102
loop(\(x,i).(6x + loop(\(x,i).(9x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028140: 1 30 577 9090 128053 1682430 21103129 256309050 3041879005 35492692950 408887138881 4665046178130 52827593605957 594751348348590 6665329755603433 74427620033028330
loop(\(x,i).(6x + loop(\(x,i).(4x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028142: 1 31 617 10067 146913 1999083 25952089 325901779 3994115345 48056935355 570022255881 6685284487011 77695022872897 896253234623947 10275099966705593 117190651899653363
loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).(7x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028167: 1 28 497 7160 91581 1086708 12265177 133727440 1422928661 14879566988 153661601457 1572610177320 15989900903341 161817863592868 1632050285251337 16420272919788800
loop(\(x,i).(6x + loop(\(x,i).(3x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028086: 1 30 583 9348 134689 1815498 23402251 292300176 3567408757 42782700246 506142615199 5923623309084 68724754852105 791647407688674 9065029251275827 103285339786658472
loop(\(x,i).(7x + loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028206: 1 34 733 12826 199213 2869258 39283021 519148762 6689833645 84640449322 1056561931789 13058296545658 160199367141997 1954490541959626 23747047106341837 287633422522201114
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028147: 1 30 575 9000 125661 1633410 20245675 242827500 2845466921 32788860390 373244969175 4210842870000 47192731209781 526333705304970 5848962216923075 64823992266568500
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028181: 1 30 569 8730 118461 1484910 17624209 201130050 2229604421 24178830390 257814842649 2713159309770 28259514317581 291954572713470 2996779685401889 30602208691495890
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A016109: 1 34 725 12410 186501 2571114 33339685 413066170 4941549701 57504755594 654463491045 7314256515930 80522026412101 875355238834474 9415203971344805 100355146006589690
loop(\(x,i).(7x + loop(\(x,i).(9x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A028010: 1 29 548 8566 120423 1583943 19921666 242775872 2891343125 33848546017 391123415904 4474230519018 50782770006307 572842223354651 6430299748764062 71901261449271604
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028118: 1 27 470 6750 87411 1065177 12504280 143383500 1619764421 18123947127 201553821690 2232652225050 24669249375031 272138102501877 2998983086992700 33027209966147400
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).(12x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028186: 1 33 694 11898 181747 2582715 34981048 458355876 5866720453 73835049717 917894484442 11308397377134 138391574753719 1685252212876239 20446364918965276 247382964478976472
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028184: 1 31 608 9650 135471 1756461 21553078 254114080 2907590741 32510311691 356977004748 3863433611310 41325142341211 437804739243721 4601385756887618 48040443020269340
loop(\(x,i).(7x + loop(\(x,i).(2x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028012: 1 30 587 9504 138369 1883826 24504439 308525268 3791612957 45742587462 543912376371 6393243539592 74447130731065 860268600608538 9877405744657583 112802621156970876
loop(\(x,i).(7x + loop(\(x,i).(3x + loop(\(x,i).(6x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028077: 1 27 472 6822 88963 1091349 12886714 148484664 1683799645 18895210191 210582084076 2336271745626 25842423980647 285296827032153 3145632963614158 34654478019199308
loop(\(x,i).(7x + loop(\(x,i).(3x + loop(\(x,i).(8x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028091: 1 29 542 8326 114639 1474683 18136084 216253052 2522916077 28975740937 329016750426 3704913244578 41464099463515 461955078856391 5129492632272368 56816621295693304
loop(\(x,i).(8x + loop(\(x,i).(9x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028156: 1 32 653 10852 160329 2196744 28582501 358350284 4370826977 52208034736 613595259069 7120485417396 81801199876345 932195385723608 10554384751300757 118870719509813788
loop(\(x,i).(8x + loop(\(x,i).(4x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028158: 1 33 695 11925 181911 2572893 34540735 446515125 5610825671 68978848653 833511432975 9933242415525 117049255275031 1366477139586813 15829397675656415 182175233504671125
loop(\(x,i).(8x + loop(\(x,i).(3x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028102: 1 32 659 11122 167577 2347980 31293103 402231494 5031459653 61629924928 742485813147 8826654123066 103796247982129 1209668862433076 13992495704608391 160835129915870638
loop(\(x,i).(9x + loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028125: 1 29 542 8338 115203 1490127 18459184 221986196 2613955685 30311197345 347486967906 3949158184374 44583107459047 500701324008083 5600328285552308 62437282927169272
loop(\(x,i).(9x + loop(\(x,i).(2x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028021: 1 32 665 11380 174261 2483592 33669985 440024060 5592152621 69530670352 849490297305 10231269580740 121775852180581 1435121355116312 16771617736444625 194605340572369420
loop(\(x,i).(9x + loop(\(x,i).(3x + loop(\(x,i).(8x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028100: 1 31 618 10094 147203 1997037 25786636 321380188 3901566405 46429426043 544051398254 6298258575882 72214033934407 821632688021449 9290501272470672 104524684322022776
loop(\(x,i).(4x + loop(\(x,i).(5x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028127: 1 30 581 9270 132861 1781910 22867141 284524950 3461329421 41398890390 488675095701 5708526430230 66125948101981 760712837896470 8701144748444261 99045775841641110
loop(\(x,i).(5x + loop(\(x,i).(3x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028071: 1 29 548 8590 121551 1615119 20584858 254810960 3087662501 36816560209 433529214768 5054413691730 58455083456251 671574295857299 7673016284430278 87260245701154900
loop(\(x,i).(3x + loop(\(x,i).(9x + loop(\(x,i).(6x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028084: 1 29 544 8414 116935 1521023 18936478 228705968 2702760709 31433459057 361216744252 4113147855362 46506852459523 522961531303331 5855208956119066 65331927878971796
loop(\(x,i).(3x + loop(\(x,i).(5x + loop(\(x,i).(12x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028073: 1 31 630 10670 163691 2363901 32800480 442568140 5850370581 76144382171 979096198730 12468275928810 157530257684671 1977386553510841 24685911967987380 306761026472700680
((x + 1) + (if x <= 0 then 1 else (2 * (1 + ((1 + (loop(\(x,i).(2 * ((1 + (((loop(\(x,i).4x,x,2) - loop(\(x,i).3x,x,1)) div 2) div 2)) div 2)),x,1) div 2)) div 2)))))
A333185: 2 6 9 940
loop(\(x,i).(10x + loop(\(x,i).(5x + loop(\(x,i).(11x + loop(\(x,i).2x,i,1)),i,1)),i,1)),x,1)
A026149: 1 28 517 7980 111741 1473948 18687397 230431180 2784091981 33121756668 389323047477 4532472142380 52356786665821 600922618820188 6860138634498757 77961474116861580
(if x <= 0 then 1 else (6x - (if x <= 0 then 1 else (2 * (((2x + 1) + (2 * ((x + 1) - loop(\(x,i).(x + (if (~2 + (x div 4)) <= 0 then 1 else 2)),2,x)))) div 3)))))
A315305: 1 6 10 16 20 24 30 34 38 44 48 54 60 64 70 74
((3 * (1 + ((3 * (if (x mod 2) <= 0 then (3 * (if (x mod 4) <= 0 then (2 * (2 + (if x <= 0 then 0 else 2))) else 1)) else 1)) + (if x <= 0 then 1 else 2) + (x mod 2)))) div 4)
A040766: 28 5 9 5 56 5 9 5 56 5 9 5 56 5 9 5
((x + 2) - loop(\(x,i).2x,(1 + ((2 * (1 + ((1 + (((~1 + loop(\(x,i).2x,x,(if (x mod 4) <= 0 then 2 else (x mod 2)))) mod (x + 1)) div 2)) div 2))) div 3)),1))
A075424: 0 1 0 1 4 5 0 1 2 9 4 5 12 13 0 1
(1 + (if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (x div (1 + ((loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) - loop(\(x,i).4x,x,1)) mod (x + 1))))) div 2))) div 3))))
A329612: 1 2 2 3 2 2 2 4 3 4 2 2 2 4 2 5
((if x <= 0 then 2 else (1 + ((1 + (if (x + ~2) <= 0 then x else (if ((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) <= 0 then (2 * (1 + (x div 5))) else 1))) div 3))) div 2)
A304871: 1 0 1 1 0 1 1 0 0 1 1 0 0 0 1 2
((1 + ((1 + (((2 * (1 + (((loop(\(x,i).(2x + (i mod 2)),x,2) div 3) + loop(\(x,i).2x,x,1)) div 3))) div 3) + loop(\(x,i).2x,x,1))) div 2)) div 2)
A164363: 1 1 2 3 6 12 23 46 91 182 364 727 1454 2908 5816 11631
((1 + ((1 + (((2 * (1 + ((1 + ((x + loop(\(x,i).3x,x,3) - loop(\(x,i).2x,x,2)) div 2)) div 2))) div 3) + loop(\(x,i).2x,x,1))) div 2)) div 2)
A279196: 1 1 2 5 13 36 102 295 864
(((if x <= 0 then 1 else (2 * (1 + ((1 + (((~1 + (6 * (1 + loop(\(x,i).(if x <= 0 then 2 else (2 * (2x - (x div (1 + i))))),x,0)))) div 2) div 2)) div 2)))) div (x + 1)) div 2)
A192225: 0 1 2 5
A058495: 0 1 2 5 15 47 149 489
((2x + ~1) + (3 * loop(\(x,i).x2,1,(3 * (if x <= 0 then 4 else (2 + ((1 + loop(\(x,i).11x,x,3)) div (x + 1))))))))
A179173: 431 9748
(1 + ((2 * (1 + ((1 + (((~1 + loop(\(x,i).2x,x,(2 - (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))) mod (x + 1)) div 2)) div 2))) div 3) - (x mod 2))
A112329: 1 0 2 1 2 0 2 2 3 0 2 2 2 0 4 3
(1 + (if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + ((9 * ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3)) div 2)) div 2))) div 3))))
A294337: 1 2 2 4 2 4 2 6 4 4 2 7 2 4 4 10
(1 + (10 * (2 + loop(\(x,i).(2 + (3 * ((~1 + (6 * (~1 + loop(\(x,i).11x,x,4)))) div 2))),x,1))))
A177465: 31 3881 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903 4611686018427387903
(1 + ((1 + (if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (x div (1 + ((~1 + (if (x mod (3 + ((x div 2) div 3))) <= 0 then 1 else 0)) mod (x + 1))))) div 2))) div 3)))) div 2))
A329614-A071187: 1 2 2 3 2 2 2 2 3 2 2 2 2 2 2 5
loop(\(x,i).i,(2 * ((1 + (7 * (loop(\(x,i).2x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2))) div 3)),1)
A174043: 1 1 1 1 4 1 1 10 10 1 1 18 38 18 1 1
(1 + (((x + 1) div 2) div (2 * ((2 - (x mod (~1 - loop(\(x,i).2x,((((1 + (8 mod (1 + (x div 2)))) div 2) + (if x <= 0 then 0 else 1)) - (x mod 2)),2)))) div 2))))
A320012: 1 1 1 2 1 2 1 2 1 3 1 2 1 2 4 5
((1 + (((x + 1) * (~1 + loop(\(x,i).(~x5 + x2 + 2x),1,(2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x))))) div 3)) mod 3)
A276729-A257629: 1 1 0 0 1 0 1 0 1 1 2 2 1 1 2 1
((if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + (loop(\(x,i).(2 * ((~1 + (((x2 + x) * (1 - (2 * (x mod 2)))) div 2)) div 2)),1,(x + 1)) div 2)) div 2)) div 2)))) div (2x + 1))
A306216: 1 1 0 0 ~1 0 ~1 0 ~1 0 ~1 0 ~1 1 ~1 1
(if x <= 0 then 1 else (2 + ((2 * (1 + ((1 + (((~1 + loop(\(x,i).2x,x,(1 + (x mod (1 + ((x + 1) mod 3)))))) mod (x + 1)) div 2)) div 2))) div 3) - (x mod 2)))
A056691: 1 1 2 2 2 1 2 3 3 2 2 3 2 2 3 4
((x + 2) + ((2 * (x + ((1 + (2 * (if x <= 0 then 1 else (1 + compr(\x.(~1 + (x mod ((x + 1) - (loop(\(x,i).2x,x,1) mod (x + 1))))),(x + 1)))))) div 3))) div 3))
A187344: 2 5 7 9 12 15 16 19 21 24 26 29 32 33 36 39
((1 + ((1 + ((1 + ((1 + ((1 + (((1 + ((((x + 1) * loop(\(x,i).(x + ((if (i mod 2) <= 0 then 2 else i) * i)),x,0)) div 2) div 3)) div 2) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)
A027194: 0 0 0 1 1 1 1 2 2 3 4 6 7 10 12 17
(2 * (1 + (x div (2 + ((6 * (1 + ((x mod (1 + (loop(\(x,i).(2x + 2),(loop(\(x,i).x2,4,2) mod (x + 1)),1) mod (x + 1)))) div 2))) mod (x + 1))))))
A175462: 2 2 4 2 2 6 2 2 4 4 4 4 2 2 6 4
(loop(\(x,i).(2 * (1 + ((1 + ((1 + ((1 + (((x + 1) * ((loop(\(x,i).(2x + 1),x,(2 * (x mod 2))) mod (x + 1)) div 3)) div 2)) div 2)) div 2)) div 2))),1,(x + 1)) div 2)
A295635: 1 1 2 1 2 1 2 2 2 1 4 1 2 2 6 1
(((x + 1) * (2 + (x * (1 + loop(\(x,i).(2 * (~1 + (54 * loop(\(x,i).x2,1,(9x + 4))))),1,0))))) div 2)
A130859: 1 1729 5184 10366 17275 25911 36274 48364 62181 77725 94996 113994 134719 157171 181350 207256
(~2 + (if x <= 0 then 3 else (2 * (1 + ((1 + ((1 + ((loop(\(x,i).(3x + ~1),(((x + 1) div 2) - ((3 * (x div 4)) div 2)),1) div 2) div 2)) div 2)) div 2)))))
A102395: 1 0 0 2 0 2 2 2 0 2 2 2 2 2 2 6
(~2 + (2 * (1 + compr(\x.(2 - (x mod (~1 + ((~1 + (6 * (1 + (loop(\(x,i).(if (x mod (1 + i)) <= 0 then 1 else x),x,(2x + 1)) div (x + 1))))) div 2)))),x))))
A263458: 4 6 12 22 28 30 36 46 52 60 70 78 100 102 108 126
((3x + ~2) + ((2 * ((x + 5) + compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,7x)),x))) div 3))
A313698: 1 5 10 15 19 24 30 36 41 45 50 55 60 65 70 75
(x + (if x <= 0 then 1 else (2 * ((4x + 1) - ((2 * ((2x + 2) + (if x <= 0 then 1 else (2 * (2x + ((x + (x div 3)) div 5)))))) div 3)))))
A034697: 1 1 2 3 2 3 4 5 2 3 4 5 4 5 6 5
(1 + (x div (1 + ((x + 1) div (2 * (1 + ((1 + (x mod (1 + (if x <= 0 then 0 else (1 + (x div (1 + (2 * (1 + (((x2 + ~x + 2) mod (x + 4)) div 2)))))))))) div 2)))))))
A302791: 1 2 2 2 2 3 2 4 2 4 2 3 2 4 4 2
(1 + ((1 + ((loop(\(x,i).x2,2,(~1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2))) div 2) div 3)) div 7))
A197529-A197373: 1 1 1 1 1 1 1 3 3 1 1 7 32 7 1 1
(1 + (loop(\(x,i).(2 * ((3 * (1 + (2 * (1 + (x div 5))))) div 2)),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2))
A132048: 1 1 1 1 5 1 1 8 8 1 1 11 17 11 1 1
(~1 + (2 * (1 + ((1 + (x div (1 + (x mod (1 + ((~1 + (2 * ((x + 1) + ((1 + (x div (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))) div 2)))) mod (x + 1))))))) div 2))))
A331736: 1 1 1 3 1 1 1 3 9 1 1 3 1 1 1 5
(if x <= 0 then 1 else (1 + (((5 * ((3 * (1 + (((1 + (x mod ((1 + (x mod (1 + (x div 4)))) * (1 + (x mod 2))))) mod (x + 1)) div 2))) div 2)) div 2) div 2)))
A124315: 1 2 2 4 2 4 2 6 4 4 2 8 2 4 4 9
(1 + ((if x <= 0 then 0 else (1 + ((2 * (1 + (((2 + (x mod (2 * (1 + (x mod (2 * (1 + (x mod (1 + (x div 3)))))))))) mod (x + 1)) div 2))) div 3))) + (x div 3)))
A321211: 1 2 3 3 4 4 5 4 6 6 6 7 7 7 8 7
(2 div (2 + ((2 * (1 + ((x + 1) mod (1 + (2 * (((2x + 1) mod (1 + (2x mod (2 + (x div 4))))) + (if x <= 0 then 0 else 1))))))) div 3) - (x mod 2)))
A307666: 1 0 1 1 0 1 0 0 1 2 0 0 0 0 1 1
((1 + ((1 + (x div (3 * (1 - ((2 + (loop(\(x,i).8x,((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2),1) div 2)) div 3))))) div 2)) div 2)
A108063: 0 0 0 1 0 1 1 0 0 1 1 ~1 0 ~1 1 2
((x + 1) div (2 * (1 + ((2 + ((2 * ((3 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 2)) div 3) - (x mod 2)) div 2))))
A109967: 0 1 0 1 1 1 1 2 1 2 2 1 3 2 2 2
((x + 2) div (2 * (1 + (x mod (2 * ((~1 + (6 * (1 + ((1 + (x mod (1 + (2 * (if (16 mod (x + 1)) <= 0 then 1 else 2))))) div 3)))) div 2))))))
A029380: 1 0 0 0 0 1 1 1 0 0 2 1 2 1 1 2
(2 + ((2 * (~1 + ((loop(\(x,i).2x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2) * (2 + (x div 5))))) div 3))
A008518: 1 1 1 1 2 1 1 5 5 1 1 12 22 12 1 1
(1 - (x2 div (2 * (1 + (((x + 1) + (((x + 1) + (((1 + ((1 + ((x * (1 + (loop(\(x,i).3x,(x div 2),1) div 2))) div 2)) div 2)) div 2) div 2)) div 2)) div 2)))))
A016004-A015794-A011650: 1 1 1 0 0 ~1 ~1 ~2 ~1 ~1 0 0 1 1 1 1
(((7 * (1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) div (if ((x + 2) mod 5) <= 0 then 2 else 1)))) div 2) div 2)
A134836: 1 1 1 1 3 1 1 5 3 1 1 7 8 3 1 1
(((if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + ((1 + ((1 + (((1 + ((x * (1 + ((x * (x div 2)) div 3))) div 2)) div 2) div 2)) div 2)) div 2)) div 2)) div 2)))) - (x mod 2)) div 2)
A185215: 0 0 1 1 2 1 2 1 2 1 3 2 4 3 5 5
(1 + (x div (1 + (2 * (1 + ((3 * (((1 + (x2 mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))) * (1 + (x div 3))) div 3)) div 2))))))
A143786: 1 1 1 2 1 2 2 1 1 2 3 2 1 2 3 2
(1 + ((4 * ((1 + (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + (x div (2 * (2 - (x mod 2)))))) div 2)) div 2)) div 3))
A124975: 1 1 1 1 2 1 1 3 3 1 1 7 6 7 1 1
(~1 + (2 * (1 + ((1 + (x div (1 + (x div (1 + (2 * (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((x - (x mod 5)) div 2))))))))) div 2))))
A108553: 1 1 1 1 3 1 1 5 5 1 1 13 13 7 1 1
(~1 + (2 * (1 + (2 * (2 + (3 * (1 + (2 * (~1 + ((3 * compr(\x.(1 - (x mod (2 + ((1 + ((x - ((x div 2) mod 2)) div 2)) mod 5)))),x)) div 2))))))))))
A178389: 21 69 93 141 213 237 309 381 453 501 573 597 669 717 789 813
(1 + (((3 * ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (2 + (x div (1 + (2 * (1 + (2 * ((x div 2) mod 2))))))))) div 2) div 2))
A247285: 1 1 1 1 3 1 1 5 7 1 1 7 19 14 1 1
(1 + (((3 * ((3 * (1 + (2 * ((((~x2 + 2) mod (~1 + ((~2x + 2) mod (4 + (x div 4))))) * (1 + (x div 2))) div 2)))) div 2)) div 2) div 2))
A144463: 1 1 1 1 4 1 1 6 6 1 1 8 24 8 1 1
((2 * (1 + ((1 + (x div (1 + ((1 - ((2 * (1 + ((1 + (x mod (1 + (x div 4)))) div (1 + ((x + 1) mod 4))))) mod 3)) mod (x + 1))))) div 2))) div 3)
A175070: 0 0 0 2 0 0 0 2 3 0 0 0 0 0 0 6
(x div (2 + ((2 * (1 + (((x + 1) div (2 + ((x * (x div 3)) mod (1 + ((2 - (x div 2)) mod 4))) - (x mod 2))) div 2))) div 3) - (x mod 2)))
A098236: 0 0 1 1 1 1 2 3 2 1 2 3 3 2 3 5
(1 + compr(\x.(~1 + ((1 + (x mod (2 + (x mod ((x + 1) - ((x - (((x + ~1) + ((x + 1) mod (~1 + (2 * (x - (x mod 10)))))) div 2)) div 2)))))) mod (x + 1))),x))
A193622: 1 2 3 5 7 10
A267521: 1 2 3 5 7 10 11 12 13 14 15 16 17 18 19 21
(~1 + compr(\x.(((x + 1) + (((x + ~1) + ((2 * ((x + 3) + compr(\x.(1 - (x mod (1 + (2 * (x div (2 + ((x div 2) div 3))))))),x))) div 3)) div 2)) mod 3),x))
A003664: 2 5 6 9 10 13 17 20 21 24 28 32 35 36 39 43
(1 - (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + ((1 + ((4x + 2) mod (3 + (x div 4)))) div 2))) div 2))
A307884: 1 1 1 1 0 1 1 ~1 ~2 1 1 ~2 ~3 0 1 1
((3 * (1 + ((8 * ((4 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)) div 3)) div 3))) div 2)
A259333: 1 1 1 1 4 1 1 9 9 1 1 16 37 16 1 1
(2 + (((2x + 1) + (2 * ((2x + 2) + (((5 * ((2x + 1) - ((~x + ((x + ~2) div 3)) div 3))) div 2) div 3)))) div 3))
A191404: 4 7 11 13 17 20 23 27 29 33 37 39 43 46 49 53
((1 + ((x + ((1 + (((x + 1) * ((2x + 3) + ((~x + (2 * (x - (((x2 + ~x) div 2) div 7)))) div 3))) div 2)) div 2)) div 2)) div 2)
A219643: 0 1 2 3 5 7 8 10 13 15 18 21 23 26 29 32
(~2 + (2 * (1 + ((((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + (2 * (1 + (2 * ((((x + 1) div 2) div 2) mod 2)))))) div 2) div 2))))
A230899: 0 0 0 0 2 0 0 2 2 0 0 10 14 10 0 0
((((x + 1) + (2 * (((2x + 1) + (2 * ((3 * (1 + ((4 * ((2x + 1) - ((x div 2) div 3))) div 3))) div 2))) div 3))) div 2) div 2)
A286340: 1 3 4 7 8 10 12 13 15 18 19 21 22 25 26 28
((x + ((x + (((x + 2) + ((1 + (((1 + (((x + 1) * (1 + (((x3 + 3x2 + ~x + ~3) div 2) div 3))) div 3)) div 2) div 2)) div 2)) div 2)) div 2)) div 2)
A067570: 0 1 2 3 4 5 7
A318156: 0 1 2 3 4 5 7 9 12 16 21 27 35 44 55 69
loop(\(x,i).(1 + loop(\(x,i).(if x <= 0 then 1 else (~1 + loop(\(x,i).(x2 + x),1,(1 + loop(\(x,i).3x,x,(2 * (1 + loop(\(x,i).(x2 + ~x),1,loop(\(x,i).x2,x,2))))))))),x,0)),x,0)
A196750: 0 1 2 6320
(~1 + loop(\(x,i).6x,x,1) - (loop(\(x,i).2x,x,1) + loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1) + loop(\(x,i).4x,x,1)))
A147977: ~4 ~9 ~19 ~9 317 3351 26141 183111 1216637 7842231 49591901 309595431 1915328957 11771279511 71987413661 438579282951
((loop(\(x,i).2x,x,3) + loop(\(x,i).6x,x,1)) - (loop(\(x,i).4x,x,1) + loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1)))
A081685: 1 0 ~2 24 382 3480 26398 183624 1217662 7844280 49595998 309603624 1915345342 11771312280 71987479198 438579414024
(((1 + (((x + 1) * loop(\(x,i).(x * (x + loop(\(x,i).loop(\(x,i).loop(\(x,i).x2,1,loop(\(x,i).((2 * (x - (2x * i))) div (1 + i)),x,1)),1,(x + ~1)),1,i))),x,1)) div 2)) div 2) div 2)
A030249: 0 0 2 30 3187
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028208: 1 35 777 13999 223769 3314031 46600009 631601663 8333511417 107767060687 1372468494761 17273924107167 215413939302745 2666835630709103 32824988535796233 402159883923086911
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028215: 1 37 867 16457 276563 4296369 63218779 894460009 12289771395 165102658721 2179224895211 28361892985881 364934200067347 4651876568586193 58839203762144763 739393306409353673
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028223: 1 37 863 16241 269703 4129041 59748151 829986817 11183795975 147236359985 1903757010519 24269169222753 305923748441767 3821741982426769 47397910610955767 584393237595955649
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028154: 1 34 743 13316 213453 3189558 45453091 626299192 8418437225 111046371722 1443490546719 18546769677228 236067224376517 2981598548144926 37417475152222427 467041996357853024
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(10x + loop(\(x,i).3x,(2 * i),1)),i,1)),i,1)),x,1)
A028226: 1 38 909 17518 297437 4648350 68550973 968960366 13264544733 177146894782 2320188183677 29920806791694 381057655784989 4803870896957534 60058812824159421 745739268125744302
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028195: 1 36 825 15380 254721 3910596 56993545 800115060 10923586641 145981963556 1918518760665 24879137417940 319158529241761 4058064014390916 51218264422582185 642449405949396020
loop(\(x,i).(12x + loop(\(x,i).(9x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028163: 1 36 829 15576 260425 4039212 59479093 843439392 11625297409 156744987828 2076870835117 27134173366248 350447396932153 4483154549898684 56894676264296101 717171756670960944
loop(\(x,i).(12x + loop(\(x,i).(4x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028164: 1 37 875 16865 288891 4584297 68969155 997819105 14012533931 192242650457 2588592449235 34328260342545 449522440061371 5824352378123017 74789809096438115 953017761256677185
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).(6x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028179: 1 34 741 13226 211037 3139050 44543077 611425162 8191217133 107740573226 1397106491573 17913626282058 227607187590589 2870438906000362 35976385743457029 448561605029480714
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).(7x + loop(\(x,i).10x,i,1)),i,1)),i,1)),x,1)
A028188: 1 34 737 13022 204885 2995842 41695033 560476774 7346285309 94497418730 1198353224289 15030879260046 186924790959973 2308975949692498 28368854500004105 347054225208330038
loop(\(x,i).(12x + loop(\(x,i).(3x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028108: 1 36 835 15870 269041 4235856 63339535 911961090 12757140781 174463937076 2343013658635 31002931521510 405218193255721 5241917197644696 67218151176880135 855512978401565130
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028202: 1 32 647 10582 153153 2049684 26010139 317905634 3781590725 44096537056 506668749951 5757875493006 64896612687817 726942456592748 8105282135259683 90059836210434298
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(9x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028211: 1 34 729 12614 192605 2711058 36061873 460391518 5699774949 68923376522 818303379257 9575924656662 110774806146733 1269639423098626 14443439746998081 163313818986599246
loop(\(x,i).(6x + loop(\(x,i).(8x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028213: 1 35 773 13783 216909 3146703 43129381 567128471 7227535997 89900761951 1097000610069 13181200344039 156403487677165 1836701044549679 21383695384607237 247159815109688887
loop(\(x,i).(6x + loop(\(x,i).(5x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028177: 1 32 653 10864 160965 2216256 29037037 367278608 4526901269 54714980320 651369416061 7662042543792 89264097643813 1031793631351424 11849055184966925 135335527957665616
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028182: 1 31 610 9750 138411 1822821 22826140 275975500 3254034421 37677164811 430475351670 4870239751650 54700558488031 611065572906001 6798955260233200 75422919700042200
loop(\(x,i).(7x + loop(\(x,i).(9x + loop(\(x,i).(4x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028150: 1 31 614 9926 142995 1915077 24414088 300588892 3608146949 42498447563 493420114122 5665664143698 64496965543063 729264545514289 8201673484111916 91847355888191144
loop(\(x,i).(7x + loop(\(x,i).(4x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028152: 1 32 655 10950 163161 2259732 29775715 378619250 4689039421 56915519232 680089278375 8025775900350 93763747253281 1086429328159532 12502585856078635 143058153091970250
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).(6x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028168: 1 29 536 8086 108927 1369095 16458142 192115232 2198921813 24838420321 278088555108 3094968268938 34308450088459 379311805532507 4186301510180234 46149086679258004
loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028193: 1 34 733 12810 198261 2836554 38431933 500511850 6327324421 78172168074 948456878733 11341481077290 134023690999381 1568398573483594 18205481984727133 209885052725681130
loop(\(x,i).(9x + loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028191: 1 33 690 11690 175371 2432283 31956940 403804980 4956450741 59506980533 702298022790 8177594495070 94207230682111 1076026739628783 12205736906550240 137681865037361960
loop(\(x,i).(9x + loop(\(x,i).(4x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028161: 1 34 737 12998 203493 2949042 40498969 534679966 6850824365 85749662570 1053427606881 12745999413654 152297310673717 1800758893450018 21104410600012073 245479747499528462
loop(\(x,i).(9x + loop(\(x,i).(5x + loop(\(x,i).(6x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028175: 1 31 612 9842 140903 1874733 23747074 290631904 3469802325 40674188555 470287309856 5380934171886 61072079752867 688801372689097 7730331225654558 86417957138887388
((loop(\(x,i).3x,2x,1) + loop(\(x,i).(9x + loop(\(x,i).10x,i,1)),x,1)) - loop(\(x,i).10x,x,1))
A088924: 1 18 252 3168 37512 427608 4748472 51736248 555626232 5900636088 62105724792 648951523128 6740563708152 69665073373368 716985660360312 7352870943242808
loop(\(x,i).(3x + loop(\(x,i).(7x + loop(\(x,i).(12x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028098: 1 33 706 12462 197575 2928471 41480272 568927644 7620023389 100232692989 1300003138798 16672816906746 211898596387843 2673025439802387 33510157279049884 417902567586112968
loop(\(x,i).(3x + loop(\(x,i).(7x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028096: 1 31 620 10190 149931 2056881 26907430 340238680 4195278461 50745196931 604662792240 7119407163570 83018865142591 960430934574181 11038161347163050 126162293709144860
loop(\(x,i).(3x + loop(\(x,i).(9x + loop(\(x,i).(12x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028107: 1 35 790 14630 242011 3723545 54492880 769001660 10558544821 141919432655 1875649181770 24453637571090 315271616180431 4027179810711365 51043597496835460 642723844104282920
loop(\(x,i).(3x + loop(\(x,i).(9x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028105: 1 33 700 12150 187951 2698923 36799570 483082800 6161352901 76830423813 940920228040 11355049670250 135378462029851 1597705036844703 18694490136746110 217145575509718500
(1 + ((2 * (1 + ((1 + ((x + 1) div (1 + ((1 + (2 * (1 + (if x <= 0 then 0 else (1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))))) mod (x + 1))))) div 2))) div 3))
A141242: 2 2 3 2 2 3 2 2 5 2 2 2 3 2 2 2
(~1 + (2 * loop(\(x,i).(1 + (18 * (~2 + loop(\(x,i).x3,1,(10x + 5)) - loop(\(x,i).2x,(x + ~1),1)))),x,1)))
A068136: 1 121393 4611686018427387903
((x + (if x <= 0 then 1 else (2 * ((1 + ((loop(\(x,i).2x,x,(1 + compr(\x.(loop(\(x,i).(2x2 + 12x + 16),2,(x2 + 2x)) mod (x + 1)),x))) div 2) div 2)) div 2)))) div (x + 1))
A245899: 1 1 2 3 7 14 37 80
(if x <= 0 then 1 else (2 * (1 + (((compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)) mod 5) mod (1 + (x div 4))))))
A270438: 1 2 2 2 2 4 2 4 2 4 4 4 2 4 4 8
loop(\(x,i).(x2 + x),1,(1 - ((2 + ((2 * (1 + ((if x <= 0 then 0 else ((2x + 1) - (if (x mod 4) <= 0 then (x div 4) else 0))) div 2))) div 3) - (x mod 2)) div 2)))
A116564: 0 0 0 0 0 0 2 2 2 2 6 6 12 12 20 12
((if x <= 0 then 1 else (2 * (1 + ((1 + ((loop(\(x,i).2x,x,(1 + ((2 * (1 + ((1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2)) div 2))) div 3))) mod (x + 1)) div 2)) div 2)))) div 2)
A193523: 0 1 2 1 2 2 2 1 2 2 2 2 2 3 1 1
(1 + ((1 + ((1 + ((1 + (((1 + ((loop(\(x,i).7x2,1,loop(\(x,i).(~1 + (2 * (x + (i mod 2)))),x,0)) div 2) div 3)) div 2) div 2)) div 2)) div 2)) div 2))
A006250: 1 1 1 2 2 6 17 69
(1 + ((loop(\(x,i).(2x + 2),x,(1 + ((2 * (1 + ((1 + ((compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + ((x + ~1) div 3)) div 2)) div 2))) div 3))) div 2) div 2))
A222011: 1 2 4 8
A014225: 1 2 4 8 20
A236397: 1 2 4 8 20 40 96 224
((2 + ((1 + (2 * ((3 * (x - (2 * ((if (x mod 3) <= 0 then (5 * (if x <= 0 then 1 else 2)) else 1) * (2 - (x mod 2)))))) div 2))) mod 7)) div 4)
A109066: 1 1 1 1 0 1 1 0 2 1 1 2 0 1 1 2
(((x + 2) + ((2 * (1 + ((1 + (x div (1 + (x mod (1 + ((1 + loop(\(x,i).(x - (if (x mod (1 + i)) <= 0 then 1 else 0)),x,x)) mod (x + 1))))))) div 2))) div 3) - (x mod 2)) div 2)
A071693: 1 1 2 2 4 3 5 4 6 6 7 6 9 7 10 9
(1 + ((2 * (1 + (2 * ((1 + (loop(\(x,i).(4x + ~2),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2)) div 3)))) div 3))
A196904-A196746: 1 1 1 1 1 1 1 3 3 1 1 7 20 7 1 1
(~1 + ((2 * ((3x + 2) + (((1 + (2 * (if x <= 0 then 1 else (2 * (4x - ((x + ((x div 2) mod 2)) div 2)))))) div 3) + ((x + 1) div 3)))) div 3))
A137002: 1 5 11 15
A314060: 1 5 11 15 21 27 32 37 43 49 53 59 64 69 75 79
(~1 + ((2 * ((2x + 2) + (if x <= 0 then 1 else (2 * ((x + ~1) + ((2 * ((3x + 2) - ((x - ((x + (x div 3)) div 3)) div 2))) div 3)))))) div 3))
A315062: 1 5 9 15 20 25 31 36 41 47 51 56 61 65 71 76
((2 * (~1 + (24 * (2 + loop(\(x,i).x2,1,((23x + 23) + (x div 9))))))) mod 5)
A112085: 1 2 2 1 4 1 2 2 1 2 2 1 4 1 2 2
((1 + (((x + 1) * (~1 + (2 * (1 + ((1 + ((1 + ((1 + (loop(\(x,i).(3 * ((2x div (1 + i)) * (~1 + (2 * i)))),x,1) div 2)) div 2)) div 2)) div 2))))) div 2)) mod 3)
A199322: 1 1 2 0 1 1 1 1 2 0 2 1 2 1 2 1
((4 * (1 + ((~2 + loop(\(x,i).2x,(1 - ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)),1)) mod 9))) div 3)
A152237: 1 1 1 1 4 1 1 9 9 1 1 8 12 8 1 1
((4 * ((1 + (4 * (1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (if (x mod 3) <= 0 then 2 else 1))))) div 3)) div 3)
A204621: 1 1 1 1 4 1 1 5 5 1 1 6 16 6 1 1
((x + 4) + (((x + 1) - (((1 + (((1 + (((x + 1) * (1 + (2 * (x - (x div (2 + (if (~2 + (x div 4)) <= 0 then 1 else 2))))))) div 2)) div 2) div 2)) div 2) div 2)) div 2))
A225871: 4 6 7 9 10 11 12 13 15 16 17 18 18 19 20 21
((2x + 2) - ((1 + (if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (x div (1 + (x mod (1 + (x div (2 + ((~2x + 1) mod (2 + (x div 4)))))))))) div 2))) div 3)))) div 2))
A288625: 2 3 5 7 8 11 12 14 17 18 20 22 23 27 28 30
((1 + ((1 + ((1 + (((x + 1) * (1 + ((if x <= 0 then 1 else (((2x + 1) + ((3x2 + 6x + 3) div 5)) div 2)) + (x mod 2)))) div 2)) div 2)) div 2)) div 2)
A062426: 1 1 2 3 4 7 10 14 19 26 33 42 52 65 78 94
(if x <= 0 then 1 else (2 * (1 + (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + (((2x + 1) mod (3 + (x div 4))) div 2))) div 2))))
A140818-A139813: 1 2 2 2 2 2 2 6 6 2 2 8 6 8 2 2
(((~1 + (6 * (1 + ((1 + (x mod (2 + ((1 + ((if ((x * (x mod 3)) mod 5) <= 0 then 1 else 2) * (1 + (x mod 2)))) mod (x + 1))))) div 3)))) div 2) div 2)
A003643: 1 1 1 2 2 1 2 1 2 2 2 2 1 4 2 1
(x div (4 + ((x + 1) mod (4 + ((6 + ((1 + ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 7)) div 2)) mod (x + 1))))))
A036848: 0 0 0 0 0 0 1 1 0 0 0 2 3 1 2 1
((4x + 1) + ((1 + ((1 + ((1 + ((1 + ((1 + (((1 + ((x * loop(\(x,i).(x + (x2 div 3)),1,(x + ~1))) div 2)) div 2) div 2)) div 2)) div 2)) div 2)) div 2)) div 2))
A314825: 1 5 9 14 18 22 26 30 34 38 43 47 52 57 61 66
(((x + 2) + (((1 + (2 * ((1 + ((5 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) mod 19)) div 2))) mod (x + 1)) div 2)) div 2)
A226142: 1 1 2 3 3 4 4
A084242: 1 1 2 3 3 4 4 5 5 6 7 7 8 9 11 9
(3x + (((3x + 2) + ((3x + (((3x + 2) - (loop(\(x,i).2x,x,1) mod 9)) div 2)) div 2)) div 2))
A315692: 1 6 12 17 22 28 34 40 45 50 56 62 68 74 79 84
(1 + ((2 * ((5x + 6) + ((x + ((1 + ((((3x2 + 17x) div 2) div 2) div 2)) div 2)) div 2))) div 3))
A190951: 5 9 13 17 21 26 31 36 41 46 51 56 62 67 73 79
(1 + ((1 + (2 * ((3 * ((3 * (1 + ((3 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) div 2))) div 2)) div 2))) div (x + 1)))
A123402: 4 2 2 1 2 1 1 3 3 1 1 2 3 2 1 1
((x + 1) div (1 + (2 * (1 + ((1 + ((1 + ((1 + ((1 + ((((x + 1) * (~1 + ((~2x + 2) mod (4 + (x div 4))))) div 2) div 2)) div 2)) div 2)) div 2)) mod 3)))))
A330601: 0 0 0 0 0 0 1 1 1 1 2 4 4 4 2 3
(~1 + (2 * ((~1 + (6 * (1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((x + 1) div (2 + (x mod 5)))))))) div 5)))
A108625: 1 1 1 1 3 1 1 7 5 1 1 13 19 7 1 1
(1 + ((((3 * ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (2 + (x div (1 + (2 * (1 + (2 * ((x div 2) mod 2))))))))) div 2) div 2) div 2))
A162717-A122175: 1 1 1 1 2 1 1 3 4 1 1 4 10 7 1 1
((1 + (2 * (1 + ((8 * ((4 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)) div 3)) div 3)))) div 3)
A202979: 1 1 1 1 2 1 1 4 4 1 1 7 17 7 1 1
((((2x + 1) + (2 * ((x + 1) + (((3 * ((2x + 1) + (2 * ((3 * (x + ((x div 2) div 5))) div 2)))) div 2) div 2)))) div 3) mod 3)
A303942: 1 1 0 0 1 1 0 0 1 2 1 0 0 1 1 0
(0 + (x div (1 + ((x + 1) div (1 + ((x div (2 + (x mod (1 + ((x + 1) div (1 + (((2x div (1 + (x div 4))) mod 2) + (x mod 2)))))))) + (x mod 2)))))) - (x mod 2))
A085122: 0 ~1 0 0 0 0 0 1 1 1 0 2 0 1 1 2
((1 + ((1 + ((1 + ((1 + ((1 + ((((x + 1) * (6 + (((x + 1) * ((x + 1) + (x mod 2))) div (1 + (x div 3))))) div 2) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)
A226591: 1 1 1 1 1 2 2 2 3 3 4 5 4 6 6 7
((1 + ((1 + (((1 + (((1 + (((x + 1) * ((((~x + 1) + (2 * ((x3 + ~3x2 + 2x) div 9))) div 2) div 2)) div 2)) div 2) div 2)) div 2) div 2)) div 2)) div 2)
A035547: 0 0 0 0 0 0 1 1 1 2 4 5 7 10 14 19
(((~1 + (6 * (1 + ((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (2 * (x mod (2 * (2 + (x div 5)))))))) div 2)))) div 2) div 2)
A192404: 1 1 1 1 2 1 1 4 5 1 1 7 14 10 1 1
(2 * (2 + ((2 * (1 + ((2 * (1 + (x mod (1 + (2 * (x div 4)))))) mod (1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))))) mod (x + 1))))
A333167: 4 4 8 8 8 8 8 12 16 8 8 8 16 16 8 8
((x + 1) + (((2x + 1) + ((2 * ((4x + 1) + (((x + 1) + (((x + 1) + (((x2 + ~x) div 2) + (x div 3))) div 2)) div 2))) div 3)) div 2))
A281582: 1 5 9 13 16 20 24 28 33 37 41 46 50 55 60 64
compr(\x.(if x <= 0 then 1 else loop(\(x,i).(x - (if x <= 0 then 1 else (x - loop(\(x,i).(if x <= 0 then 1 else loop(\(x,i).(x - (if x <= 0 then 1 else (x - (if x <= 0 then 1 else ((2x * (~1 + (2 * i))) div (2 + i)))))),1,x)),2,x)))),x,x)),x)
A342792: 2 5 6 7 12 13 14 15 16 17 27 28 29 30 31 32
((2 + (loop(\(x,i).((x + 1) + ((if x <= 0 then 0 else loop(\(x,i).2x,(~1 + loop(\(x,i).(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x div (2 - (x mod 2))))),x,x)),2,x)),1)) + ((x + 1) div 2))),x,1) div 2)) div 2)
A081226: 1 2 3 5 8 12 18 27 41 62 93 139 209 314 472 708
(1 + ((1 + loop(\(x,i).2x,x,(if x <= 0 then 1 else (2 * (1 + ((1 + ((loop(\(x,i).2x,x,(~x3 + loop(\(x,i).5x,(x + 1),1))) div 2) div 2)) div 2)))))) div 3))
A234283: 1 10 161 3196
((2 + loop(\(x,i).2x,(x + ~1),(if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + (((x * (~1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).(x * i),x,1)))) div 2) div 3)) div 2)) div 2)))))) div 3)
A297118: 1 1 3 16 539
loop(\(x,i).(12x + loop(\(x,i).(6x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028219: 1 39 961 19131 336217 5446035 83308177 1221791547 17352006793 240304555491 3261449180353 43542585627723 573464912457529 7467052092622707 96294712139682289 1231626797709018459
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(6x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028209: 1 36 823 15282 251881 3847032 55777051 779149134 10588135261 140901434388 1844713666159 23841089487306 304926682591441 3866889746187504 48692419436767747 609526612369569798
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028224: 1 38 911 17632 301245 4745706 70660507 1009770884 13991407529 189303883054 2513736124263 32882696484456 424941717543253 5436863390984882 68985988087521779 869260000449137548
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(9x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A016092: 1 40 1005 20300 360521 5881680 90375685 1328528500 18879767841 261281940920 3540146411165 47147861315100 619093593987961 8034113714073760 103234967777291445 1315472793832108100
loop(\(x,i).(12x + loop(\(x,i).(8x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A016093: 1 41 1055 21805 395871 6595701 103397575 1549123085 22414242191 315506452261 4343673465495 58723278269565 781995624847711 10282227616659221 133750220517219815 1723860289008683245
loop(\(x,i).(12x + loop(\(x,i).(9x + loop(\(x,i).(6x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028218: 1 38 913 17738 304549 4824806 72271081 1039149506 14486436877 197162419454 2632865400529 34623882428954 449653998040885 5779288950415382 73637791767193657 931419802216938482
loop(\(x,i).(12x + loop(\(x,i).(5x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028199: 1 38 917 17950 311181 4984638 75555157 1099718270 15519848861 213791759038 2888580642597 38416793758590 504293367484141 6547729455298238 84231046860437237 1075013759173110910
loop(\(x,i).(6x + loop(\(x,i).(7x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028207: 1 34 731 12716 195657 2781030 37422967 484054192 6078887573 74632686986 900223323363 10706758727028 125901196014049 1466781515230702 16957557634824719 194793155476604024
loop(\(x,i).(6x + loop(\(x,i).(9x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028216: 1 36 817 14952 241213 3582348 50196889 673865424 8755297045 110878147380 1375697840881 16786476031416 202032169207597 2403762666000732 28323951022216393 331005811232778528
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(9x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028220: 1 35 770 13630 212331 3041745 41087740 531634460 6658867061 81336796255 974120693910 11484949238490 133713902876191 1540987906351565 17612518552867280 199940810374681720
loop(\(x,i).(7x + loop(\(x,i).(8x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028222: 1 36 815 14850 238161 3512376 48835795 650202750 8376184421 105168836916 1293777896775 15655641961050 186905779340281 2206620573868656 25809833134389755 299526474742773750
loop(\(x,i).(7x + loop(\(x,i).(9x + loop(\(x,i).(6x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028205: 1 33 688 11598 172879 2380371 31036006 389148576 4740682837 56509956789 662486064604 7666900074834 87835709417275 998290939845687 11274360941128882 126686827598516772
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).(12x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028189: 1 35 782 14254 231459 3493041 50160064 695287148 9389676197 124321003807 1620910078866 20877357884682 266266935091015 3368664326093933 42334402590112388 529044108699525256
loop(\(x,i).(7x + loop(\(x,i).(5x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028187: 1 33 692 11790 178311 2498643 33230002 425666400 5302894421 64673833653 775796369712 9184400635410 107582646828931 1249287573291063 14403306409895822 165064341717134820
loop(\(x,i).(8x + loop(\(x,i).(9x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A016075: 1 38 905 17290 289821 4453638 64331905 887339330 11810819141 152832918238 1933092302505 23997027406170 293289532268461 3537885908902838 42204462297434705 498697803478957810
loop(\(x,i).(9x + loop(\(x,i).(5x + loop(\(x,i).(12x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028198: 1 37 870 16610 281171 4403367 65339080 932218420 12912631941 174806957897 2323925673290 30446318392230 394142295428311 5052076439311627 64222440261259500 810705252920074040
loop(\(x,i).(9x + loop(\(x,i).(5x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028196: 1 35 776 13930 221151 3240825 44906926 597218720 7698198101 96837355615 1194615734676 14505367659510 173840151316651 2060770407338405 24205227062904026 282088240414000300
(x + loop(\(x,i).(if x <= 0 then 1 else (2 * (1 + ((1 + (((1 + ((x + 1) * (1 + loop(\(x,i).(x2 + x),1,loop(\(x,i).(2 * (2x - (x div (1 + i)))),x,1))))) div 2) div 2)) div 2)))),1,(x + ~1)))
A245894: 1 2 14 163 2558
(if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + ((x + 1) div (if x <= 0 then 1 else (2 * (1 + ((1 + ((loop(\(x,i).2x,x,(1 + (x div 8))) mod (x + 1)) div 2)) div 2)))))) div 2))) div 3)))
A196067: 0 2 2 2 2 2 3 3 2 2 2 3 3 3 2 4
(((loop(\(x,i).x2,1,(~1 + (2 * ((x + 1) + ((2 * (1 + (((1 + (loop(\(x,i).(2x + 1),x,loop(\(x,i).3x,x,1)) div 3)) div 2) div 2))) div 3))))) div 2) div 2) div 2)
A138496: 0 1 10 120 3003
(1 + (x mod (1 + (x mod (1 + (x mod (1 + ((1 + ((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (x - (if (x mod 15) <= 0 then 2 else 0)))) mod (x + 1)))))))))
A180173: 1 1 3 1 1 1 1 1 3 1 1 1 13 1 15 1
(1 + ((1 + (((1 + (((x + 1) * (1 + (((x + 1) + (((x + 1) + loop(\(x,i).(if x <= 0 then 1 else (2 * (x - ((3 * (x div 4)) div 2)))),x,0)) div 2)) div 2))) div 2)) div 2) div 2)) div 2))
A318053: 1 1 2 2 3 4 5 7 9 12 15 19 24 31 39 50
(1 + compr(\x.(~1 + (((~1 + (2 * (1 + ((1 + (((loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)) + (loop(\(x,i).(2x + 2),x,0) mod (x + 1))) div 2) div 2)) div 2)))) mod (x + 1)) mod 3)),x))
A028826: 1 2 3 4 5 6 7 8 10 11 12 14 15 21 23
loop(\(x,i).(2 * (1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + loop(\(x,i).2x,(1 + (2 * (2x mod 5))),(x div 2))) div 3)) div 2)) div 2)) div 2)) div 2)) div 2))),x,1)
A328217: 1 2 14 22 120
((x + ~1) + ((2 * (1 + ((2 * (1 + compr(\x.(1 - (x mod (2 + ((1 + (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)) mod (x + 1))))),(x + 1)))) div 3))) div 3))
A304452: 1 3 5 6 7 10 11 13 14 16 18 20 22 24 25 26
(~1 + ((2 * (1 + ((2 + ((2 * (1 + ((1 + ((2 + (loop(\(x,i).(x - (x div (~2 + (x mod ~2)))),x,1) div 2)) div 3)) div 2))) div 3) - (x mod 2)) div 2))) div 3))
A332286: 0 0 0 0 0 0 0 0 1 0 1 1 2 3 5 5
(~1 + loop(\(x,i).((x + 1) + ((1 + ((1 + ((1 + (((((x + 1) * ((x + 1) + (2 * (((((x + 1) * (4 + (x div 2))) div 2) div 2) div 2)))) div 2) div 2) div 2)) div 2)) div 2)) mod 2)),x,1))
A155498: 0 1 2 3 5 7 9 11 12 13 15 17 18 19 20 22
(1 + ((1 + ((1 + (2 * (1 + ((1 + (x mod (1 + (if x <= 0 then 0 else (1 + (x div (1 + (2 * (1 + (((x2 + ~x + 2) mod (x + 4)) div 2)))))))))) div 2)))) mod 3)) mod (x + 1)))
A173439: 1 2 2 2 2 4 2 3 2 4 2 4 2 4 4 2
(~1 + (((2 * (1 + ((1 + ((1 + ((1 + (((x + 1) * (1 + (((x + (if ((x div 2) mod (1 + (2 * (x mod 2)))) <= 0 then 2 else 0)) div 2) mod 2))) div 2)) div 2)) div 2)) div 2))) - (x mod 3)) div 2))
A138468: 1 0 0 1 0 0 1 0 1 1 0 1 2 1 0 2
((((~1 + (6 * (1 + ((1 + (((loop(\(x,i).11x,x,(1 + (x mod 2))) div 2) div 2) div 2)) div 2)))) * (1 + (x mod 2))) div 3) div 5)
A152435: 0 1 3 133 366 16105 44289 1948717 5358972 235794769 648435615 28531167061 78460709418 3452271214393 9493745839581 417724816941565
((2 * (1 + ((1 + (((1 + (((2x + 2) * (1 + ((1 + ((1 + ((1 + loop(\(x,i).((x + 2) + (x div 2)),(x div 2),(x mod 2))) div 2)) div 2)) div 2))) div 2)) div 2) div 2)) div 2))) div 3)
A274759: 0 1 1 1 1 2 2 2 3 4 4 6 7 8 12 14
loop(\(x,i).((x + 4) + ((1 + ((x + (3 * (1 + (2 * ((((x + 2) + ((3 * ((x + 2) + (2x div 7))) div 2)) div 2) div 2))))) div 2)) mod 2)),x,1)
A313689: 1 5 10 15 19 24 28 33 37 42 47 52 57 62 67 71
((1 + ((2 * ((x + 3) + ((2 * (1 + ((1 + (x div (1 + (x mod (1 + (x div (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))))))) div 2))) div 3))) mod 3)) mod (x + 1))
A171899: 0 0 1 3 1 3 2 2 1 3 2 1 3 1 3 2
((1 + ((2 + ((2 * (1 + ((1 + ((1 + (((1 + loop(\(x,i).2x,(1 + (x div 2) - (2 * (x mod 2))),2)) div 3) div 2)) div 2)) div 2))) div 3) - (x mod 2)) div 2)) div 2)
A029234: 1 0 1 0 1 0 1 1 1 1 2 1 3 1 4 1
(3 - ((2 * (1 + ((1 + (((~1 + loop(\(x,i).2x,x,(1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))) mod (x + 1)) div 2)) div 2))) mod 3))
A222580: 1 1 1 2 1 1 1 3 2 1 1 3 2 3 2 2
(~2 + ((4 * ((1 + (4 * (1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (if (x mod 3) <= 0 then 2 else 1))))) div 3)) div 3))
A143199: ~1 ~1 ~1 ~1 2 ~1 ~1 3 3 ~1 ~1 4 14 4 ~1 ~1
((1 + (if (x mod 2) <= 0 then (1 + ((2 * (1 + ((1 + (((1 + (((x + 1) * (1 + (2 * (((x div 3) * (x div 2)) div 2)))) div 2)) div 2) div 2)) div 2))) div 3)) else 0) - (x mod 2)) div 2)
A046767: 1 0 1 0 1 0 2 0 3 0 4 0 8 0 10 0
(((~1 + (6 * ((1 + (loop(\(x,i).3x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 3)) mod (x + 4)))) div 2) div 2)
A306344: 1 1 1 1 2 1 1 5 5 1 1 14 17 14 1 1
(4 + (3 * (5 + (3 * (4 + (((3 * (1 + ((2 - (x mod 2)) mod (1 + (if (~1 + (x mod 3)) <= 0 then 2 else 0))))) mod 5) div 2))))))
A153646: 73 55 64 55 73
(((2 + (((x + 1) + (2 * ((1 + (2 * (((1 + (2 * ((x + 1) + (loop(\(x,i).(4 * (2x - (x mod 2))),x,1) div 3)))) mod (x + 1)) div 2))) mod (x + 1)))) div 2)) div 2) div 2)
A078641: 0 1 1 1 1 2 1 2 2 2 2 2 2 3 4 5
((x + 3) - ((((~1 + (6 * (1 + (((~1 + (6 * (1 + ((1 + (if ((x + 1) mod (3 - (x mod 2))) <= 0 then x else 1)) div 2)))) div 2) div 2)))) div 2) div 2) div 2))
A062854: 1 2 3 3 5 4 7 5 6 6 11 6 13 8 9 8
((5x + 1) + ((1 + ((1 + ((1 + ((1 + ((1 + (((1 + ((x * loop(\(x,i).(x + (x2 div 3)),1,(x + ~1))) div 2)) div 2) div 2)) div 2)) div 2)) div 2)) div 2)) div 2))
A315517: 1 6 11 17 22 27 32 37 42 47 53 58 64 70 75 81
(~1 + ((1 + (((18 * (1 + (~2 mod (1 - (2 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((~x + 2) div 2)) div 2)))))) div 2) div 2)) div 2))
A177947: 1 1 1 1 4 1 1 8 8 1 1 13 22 13 1 1
(1 + ((1 + (((3 * ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (2 + (x div (1 + (2 * (1 + (2 * ((x div 2) mod 2))))))))) div 2) div 2)) div 2))
A137153-A073165: 1 1 1 1 2 1 1 3 4 1 1 4 10 8 1 1
((2 * (1 + ((1 + ((3 * (1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (~1 + (2 * (2 + (x div (1 + (x mod 5))))))))) div 2)) div 2))) div 3)
A062715: 1 1 1 1 2 1 1 4 4 1 1 8 12 6 1 1
(((x + 2) + (((2x + 1) + (2 * (((2x + 1) + (2 * (1 + (((10x2 + 27x + 14) div 2) div 2)))) div 3))) div 3)) div 3)
A184015: 1 3 6 9 14 19 25 31 38 46 55 64 75 86 97 110
(x div (2 + (((2 * (1 + ((1 + ((1 + ((1 + ((((x + 1) * (1 + (3 * ((2x + 2) mod 5)))) div 2) div 2)) div 2)) div 2)) div 2))) div 3) + (x mod 2))))
A230243: 0 0 0 0 1 1 1 1 2 2 2 1 3 1 4 2
(x div (2 + ((1 + (2 * ((2 * (1 + ((1 + (x div (2 + ((5 * (1 + (x mod 5))) mod (x + 1))))) div 2))) div (1 + (x mod (1 + (x div 3))))))) mod (x + 1))))
A035459: 0 0 1 1 0 1 1 1 1 1 2 3 1 2 4 3
(1 - (((2 * (1 + ((1 + ((1 - ((1 + ((1 + (x mod (2 * (1 + (x mod (2 * (1 + (x mod (1 + (x div 3)))))))))) mod (x + 1))) mod 3)) mod (x + 1))) div 2))) mod (x + 1)) div 2))
A157657: 1 1 1 0 1 ~1 1 0 0 ~1 1 0 1 ~1 ~1 0
(1 - ((1 - ((((8 * ((2x + 1) div (3 + (x div 4)))) - (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) div 2) div 2)) div 2))
A244580: 1 2 2 3 2 3 4 3 3 4 5 4 4 4 5 6
((x + 5) + ((2 * (1 + ((1 + ((1 + ((1 + ((1 + ((1 + (((x + 1) * (1 + (((x2 + ~x) div 2) div 3))) div 2)) div 2)) div 2)) div 2)) div 2)) div 2))) div 3))
A191846: 5 7 8 9 10 11 12 13 15 16 17 19 21 22 25 26
((x + 1) + ((2 * (1 + ((1 + (x div (1 + ((1 - ((2 * (1 + ((1 + (x mod (1 + (x div 4)))) div (1 + ((x + 1) mod 4))))) mod 3)) mod (x + 1))))) div 2))) div 3))
A175067: 1 2 3 6 5 6 7 10 12 10 11 12 13 14 15 22
(x div (1 + ((x + 1) div (1 + ((1 + (((3 * (x + loop(\(x,i).(x - (if x <= 0 then 1 else (x - ((if x <= 0 then 2 else loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 2)))),x,(x + 1)))) div 2) div 2)) mod 3)))))
A188921: 0 1 1 0 2 1 1 1 0 0 2 0 2 2 1 1
((if x <= 0 then 1 else (2 * (1 + ((1 + (((loop(\(x,i).2x,x,1) + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) - compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x)) div 2)) div 2)))) mod 3)
A194852: 1 2 1 1 1 1 1 1 2 0 2 1 1 1 2 1
loop(\(x,i).(12x + loop(\(x,i).(7x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028228: 1 40 1007 20414 364329 5979036 92485219 1369339018 19606630637 273438929192 3733694351751 50109751007862 662977655746225 8667106208101108 112162143040653803 1438993526155501346
loop(\(x,i).(12x + loop(\(x,i).(9x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A016094: 1 42 1105 23310 431221 7309722 116419465 1769717670 25948716541 369730963602 5147200519825 70298695224030 944897655707461 12530341519244682 164265473257148185 2132247784185258390
loop(\(x,i).(7x + loop(\(x,i).(9x + loop(\(x,i).(12x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028227: 1 39 958 18966 330883 5313693 80518096 1169149692 16435587685 225292911987 3026941267714 40015278899778 522017655765607 6735488552529321 86110477932406612 1092366397140622824
loop(\(x,i).(7x + loop(\(x,i).(9x + loop(\(x,i).(10x + loop(\(x,i).11x,i,1)),i,1)),i,1)),x,1)
A028225: 1 37 860 16070 263991 3983007 56583850 768771040 10093501781 129000877577 1613435099640 19826334683610 240097655804371 2872253241385747 34007147715912230 399112139110865780
(2 + ((1 + (((x + 1) * (if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + (((loop(\(x,i).x2,1,(1 + compr(\x.(loop(\(x,i).(~2x + 4),x,1) mod (x + 1)),x))) div 2) div 2) div 2)) div 2)) div 2))))) div 2)) div 2))
A146747: 2 3 5 6 7 20 30
(~2 + (2 * (2 + ((2 * (1 + ((1 + (((~1 + loop(\(x,i).2x,x,(2 - (if (x mod 2) <= 0 then (if (~1 + (x mod 3)) <= 0 then x else 2) else 1)))) mod (x + 1)) div 2)) div 2))) div 3) - (x mod 2))))
A094572: 2 0 4 2 4 0 4 4 6 0 4 4 4 0 8 6
(1 - (if (x + ~1) <= 0 then 0 else (1 + ((((2 * (1 + (((~1 + (6 * (1 + ((1 + ((x mod (1 + (x div (if (x mod 2) <= 0 then 4 else 1)))) div 2)) div 2)))) div 2) div 2))) mod (x + 1)) div 2) mod 2))))
A113681: 1 1 0 ~1 0 0 0 ~1 ~1 0 0 0 0 0 ~1 0
((1 + (((~1 + (6 * (1 + (if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (x div (1 + (x mod ((x + 1) - (loop(\(x,i).2x,x,2) mod (x + 1))))))) div 2))) div 3)))))) div 2) div 2)) div 2)
A336471: 1 1 2 1 2 2 3 1 4 2 3 2 3 3 5 1
(~2 + (((~1 + (6 * (~1 + (6 * (1 + (2 * compr(\x.(0 - loop(\(x,i).(~1 + (if (x mod (1 + (2 * i))) <= 0 then 0 else x)),x,(9x + 1))),x))))))) div 2) div 2))
A061240: 5 23 41 59 113 131 149 167 239 257 293 311 347 383 401 419
compr(\x.(2 * (x - (x * ((loop(\(x,i).2x,x,(~1 + ((2 * (1 + ((((x + 1) * (if (x mod 2) <= 0 then 1 else (2 * (1 + (8 * (x mod 2)))))) div 2) div 2))) mod 3))) mod (x + 1)) div 2)))),x)
A165991: 0 5 8 9 10 11 13 14 17 19 20 21 22 23 24 25
(if x <= 0 then 0 else (1 + ((2 * (1 + (((21 * ((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((x + ~1) div 2))) div 2)) div 2) div 2))) div 3)))
A141398: 0 1 1 1 5 1 1 8 8 1 1 11 19 11 1 1
(~1 + ((2 * ((3x + 1) + (((2 * ((2x + 2) + (if x <= 0 then 1 else (2 * (2x + ((x + ((x div 2) mod 2)) div 2)))))) div 3) + ((x + 1) div 3)))) div 3))
A314189: 1 5 11 17 21 27 32 37 43 47 53 59 64 69 75 81
(1 + (2 * ((5 * (((3 * (1 + (loop(\(x,i).3x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 3))) div 2) div 2)) div 2)))
A056940: 1 1 1 1 5 1 1 15 15 1 1 35 105 35 1 1
((2 * ((x + 3) + (((x + 1) + (((1 + (((1 + (((2x + 5) * compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) div 3)) div 2) div 2)) div 2) div 2)) div 2))) div 3)
A075471: 2 3 4 5 6 8 10 11 13 15 17 20 22 24 26 29
((1 + (2 * ((1 + (3 * ((loop(\(x,i).2x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2) * (1 + (x div 5))))) div 2))) div (x + 1))
A327693: 1 0 0 0 1 0 0 1 1 0 0 3 5 2 0 0
((3 * (1 + ((((5 * (1 + (loop(\(x,i).3x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 3))) div 2) div 2) div 2))) div 2)
A171145: 1 1 1 1 3 1 1 4 4 1 1 10 27 10 1 1
(2 * ((2 * ((3 * (1 + ((2 * (1 + (loop(\(x,i).(x * i),(1 + (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)),1) div 2))) div 3))) div 2)) div 3))
A204301: 0 0 0 0 4 0 0 4 4 0 0 16 80 16 0 0
(1 + (2 * ((x + 1) + ((2 * ((1 + (((x + 1) * ((x + 3) + ((2 * (1 + (((x * ((x + 2) + (2 * (x mod 2)))) div 2) + (x mod 2)))) div 3))) div 2)) div 2)) + (x div 3)))))
A319304: 7 17 31 67 89
(1 + (2 * ((1 + (((3 * ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (2 + (x div (1 + (2 * (1 + (2 * ((x div 2) mod 2))))))))) div 2) div 2)) div 2)))
A047969: 1 1 1 1 3 1 1 5 7 1 1 7 19 15 1 1
(~1 + (((5 * (1 + ((3 * (1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * ((1 + (((x + 1) div 2) div 2)) div 2)))) div 2))) div 2) div 2))
A174037: 1 1 1 1 4 1 1 5 5 1 1 12 16 12 1 1
((1 + (2 * (1 + (x div 5))) - ((3 * ((1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * ((3 * ((~x + 2) div 2)) div 2))) div 2)) div 2)) div 3)
A294783: 1 1 1 1 1 1 1 2 2 1 2 4 6 4 2 3
((3 * (1 + (((3 * ((3 * ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + (2 * ((1 + (x div 2)) div 2))))) div 2)) div 2) div 2))) div 2)
A157632: 1 1 1 1 6 1 1 18 18 1 1 36 48 36 1 1
(7 mod (2 + ((1 + ((3 * ((3 * (1 + ((3 * (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)) div 2))) div 2)) div 2)) div 2)))
A204242: 1 1 1 1 3 1 1 0 0 1 1 0 7 0 1 1
(((3 * (1 + (((~1 + (6 * (1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (2 * ((x div 2) mod 2))) * (x div 4))))) div 2) div 2))) div 2) div 2)
A167630-A137743-A099239-A055587: 1 1 1 1 2 1 1 4 3 1 1 8 8 4 1 1
(1 + ((((3 * (1 + ((x + 1) div (2 + ((x + 1) div (1 + (((1 + (x mod ((1 + (x mod (1 + (x div 4)))) * (1 + (x mod 2))))) mod (x + 1)) + (x mod 2)))))))) div 2) div 2) + (x mod 2)))
A286605: 1 2 2 3 2 4 2 4 3 4 2 5 2 4 4 6
((~x + 1) + (((x + 1) + (((1 + (((1 + (((x + 1) * ((2x + 1) - (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3))) div 2)) div 2) div 2)) div 2) div 2)) div 2))
A016338: 1 1 0 0 0 0 0 ~1 ~1 0 0 ~1 ~1 0 1 1
(1 + compr(\x.(1 - (((1 + ((loop(\(x,i).2x,(x + loop(\(x,i).(x - (if x <= 0 then 1 else (x - ((if x <= 0 then 2 else loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 2)))),x,(x + 1))),1) div 2) div 3)) div 2) mod 3)),x))
A144754: 4 8 9 10 12 17 18 19 20 21 22 24 25 26 28 32
(loop(\(x,i).2x,x,(if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + ((compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x) + ((~1 + loop(\(x,i).2x,x,2)) div (x + 3))) div 2)) div 2)) div 2))))) mod 3)
A281491: 1 1 1 2 0 1 1 1 2 0 2 0 1 2 1 1
(2 * (2 + loop(\(x,i).2x,x,(1 + loop(\(x,i).(if (x mod 2) <= 0 then (x div 2) else (1 + (9 * (~1 + (5 * loop(\(x,i).7x,x,2)))))),x,3)))))
A069048: 12 123456 4611686018427387903 4611686018427387903 4611686018427387903
((2 * ((2x + 2) + (if x <= 0 then 1 else ((2x + ~1) + ((2 * (3x + (if x <= 0 then 1 else 5x) - ((~2x + 2) div 9))) div 3))))) div 3)
A277690: 2 6 13 19 26 32 38 44 51 57 63 70 76 82 88 95
(1 + ((2 * (1 + ((1 + (x div (1 + (x mod (1 + ((~1 + loop(\(x,i).2x,(1 + (x div (2 + ((x div 2) div (1 + (x mod (1 + (x mod (3 + (x mod 2)))))))))),1)) mod (x + 1))))))) div 2))) div 3))
A336390: 1 1 2 1 3 2 2 1 4 3 3 2 5 2 6 1
(~1 + ((2 * (1 + (((3 * ((2x + 1) + ((2 * ((2x + 2) + (if x <= 0 then 1 else (2 * (4x + ((x + ((x div 2) mod 2)) div 2)))))) div 3))) div 2) div 2))) div 3))
A315018: 1 5 9 15 19 23 28 33 37 41 47 51 56 61 65 71
(~1 + ((2 * ((2x + 2) + (if x <= 0 then 1 else ((2x + ~1) + ((2 * ((x + 2) + ((2 * ((x + 1) + (2 * (2x + (2x div 5))))) div 3))) div 3))))) div 3))
A315030: 1 5 9 15 19 25 29 33 39 43 49 53 58 63 67 73
((2 * (1 + ((1 + (((5 * (1 + (loop(\(x,i).(3x + 3),(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 2))) div 2) div 2)) div 2))) div 3)
A060854: 1 1 1 1 2 1 1 5 5 1 1 14 42 14 1 1
((4 * loop(\(x,i).((2x + ~1) + ((2 * ((2x + 2) + (((2x + 1) + (2 * ((x + 1) + (5 * (x + (x div 4)))))) div 3))) div 3)),x,1)) div 3)
A037540: 1 9 64 449 3145 22016 154113 1078793 7551552 52860865 370026057 2590182400 18131276801 126918937609 888432563264 6219027942849
(if x <= 0 then 1 else (2 + ((2x + 2) mod (1 + (((x + 1) * (1 + (((1 + (x mod ((1 + (x mod (1 + (x div 4)))) * (1 + (x mod 2))))) mod (x + 1)) + (x mod 2)))) mod 3))) - (x mod 2)))
A067005: 1 1 2 1 2 1 4 1 2 1 2 1 4 2 2 1
((1 + (2 * ((1 + (((x * (1 + (x mod (1 + (x mod (1 + ((~1 + (2 * ((1 + (((x2 + x) * (if (x mod 2) <= 0 then 4 else 1)) div 2)) div 3))) mod (x + 1)))))))) div 2) div 2)) div 2))) div (x + 1))
A029324: 1 0 0 1 0 0 1 0 0 2 0 1 3 0 1 3
(x - (((if x <= 0 then 1 else (x + ((x + ((x - ((x - ((x + (2 * ((1 + ((x * (x - ((1 + (((x * (x + (2 * (x mod 2)))) div 2) div 2)) div 2))) div 2)) div 2))) div 2)) div 2)) div 2)) div 2))) - (x mod 2)) div 2))
A127685: 0 1 1 1 1 2 1 2 2 3 2 4 3 5 5 7
((2 * (1 + ((1 + (4 * (1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + ((2x + 1) div (3 + (x div 4))))))) div 3))) div 3)
A319840: 1 2 2 3 4 3 4 6 6 4 5 8 8 8 5 6
((1 + ((x + 1) mod (1 + ((1 - (6 * (2 + ((1 + (((x + 1) * (1 + (2 * (37 div (x + 1))))) div 2)) div 2)))) mod 9)))) div 2)
A296559: 1 0 1 0 1 1 1 0 2 1 1 2 1 3 1 1
(~1 + (2 * (1 + (2 * loop(\(x,i).(if x <= 0 then 1 else (2x * ((x + ~1) + (3 * (1 + loop(\(x,i).loop(\(x,i).5x,x,1),(i - (x mod 3)),loop(\(x,i).5x,x,1))))))),x,0)))))
A145232: 1 5 75025 4611686018427387903 4611686018427387903
((2x + 1) div (if x <= 0 then 1 else (2 * (1 + ((1 + (loop(\(x,i).(2x + 2),(((2 * (1 + ((loop(\(x,i).(x + ((1 + (2 * i)) * i)),x,0) mod (x + 1)) div 2))) div 3) + (if x <= 0 then 0 else 1)),1) div 2)) div 2)))))
A279507: 1 0 1 0 2 0 3 1 2 1 5 0 6 1 2 1
((1 + (((if x <= 0 then 1 else (2 * (1 + ((loop(\(x,i).2x,x,loop(\(x,i).2x,((((1 + (8 mod (1 + (x div 2)))) div 2) + (if x <= 0 then 0 else 1)) - (x mod 2)),1)) mod (x + 1)) div 2)))) - (x mod 2)) div 2)) div 2)
A331410: 0 0 1 0 2 1 1 0 2 2 2 1 2 1 3 0
(2 + ((1 + ((1 + (((x + 1) * (~1 + loop(\(x,i).2x,x,loop(\(x,i).(8x + loop(\(x,i).(5x + loop(\(x,i).3x,i,1)),i,1)),x,1)))) div 3)) div 3)) div 2))
A180058: 2 6 120 3003
((if x <= 0 then 1 else (x - (2 * ((if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + (((loop(\(x,i).x2,1,(~1 + (9 * (x mod 5)))) div 2) div 2) div 2)) div 2)) div 2)))) mod (x + 1))))) mod 3)
A220354: 1 1 1 0 1 1 0 2 1 0 0 2 1 0 1 2
((~1 + (6 * (1 + (((~1 + (6 * (1 + ((loop(\(x,i).(8x + 10),x,loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1))) div 2) div 3)))) div 2) div 2)))) div 3)
A100459: 3 11 143 623
loop(\(x,i).((2x + ~1) + ((2 * ((4x + 1) + ((2 * (2 + (if x <= 0 then 1 else (2 * (3x + ((x - (x div 12)) div 2)))))) div 3))) div 3)),x,1)
A243670: 1 7 54 418 3236
(x div (2 * (1 + (((2 * (1 + ((1 + (((1 + (((x + 1) * (if x <= 0 then 1 else (2 * ((if ((x + 1) mod (1 + (x div 4))) <= 0 then 1 else 2) + ((x mod 3) div 2))))) div 2)) div 2) div 2)) div 2))) mod (x + 1)) div 2))))
A054845: 0 0 1 1 0 2 0 1 1 0 1 1 1 1 0 1
(2 + loop(\(x,i).(2x + (((1 + (((3 * ((2x + 1) + (2 * (((2x + 1) + (2 * ((8x + 1) div (1 + (if x <= 0 then 0 else 2))))) div 3)))) div 2) div 2)) div 2) mod 2)),x,1))
A282390: 3 5 8 14 27 53 104 206 410 818 1635 3269 6536 13070 26139 52277
(~1 + ((2 * ((2x + 2) + (if x <= 0 then 1 else (2 * (x + ((x + (((2x + 1) + (((x + 1) + (4 * (2x - (2x div 7)))) div 3)) div 2)) div 2)))))) div 3))
A315049: 1 5 9 15 20 24 29 33 39 44 49 53 59 64 68 73
(loop(\(x,i).(2x + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + (((((2x + 3) * (1 + (x2 div 4))) div 2) div 2) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) mod 2)),x,1) div 2)
A329355: 0 1 3 6 12 25 50 101 203 406 813 1627 3254 6508 13017 26034
(~1 + ((2 * (1 + ((1 + (((3 * (1 + (6 * (1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (x div (2 - ((x div 2) mod 2)))) div 2))))) div 2) div 2)) div 2))) div 3))
A320435: 1 1 1 1 3 1 1 5 4 1 1 9 10 5 1 1
(~3 + (2 * (2 + ((((3 * ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (2 + (x div (1 + (2 * (1 + (2 * ((x div 2) mod 2))))))))) div 2) div 2) div 2))))
A099608: 1 1 1 1 3 1 1 5 7 1 1 7 19 13 1 1
(((~1 + (6 * (1 + (2 * ((3 * (1 + ((4 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)) div 3))) div 2))))) div 5) div 2)
A171142: 1 1 1 1 4 1 1 5 5 1 1 8 18 8 1 1
(~2 + (3 * ((3 * (1 + (((3 * (1 - (((~1 + (6 * (1 + ((~2 + (x mod 2)) mod (~1 + ((~2x + 2) mod (4 + (x div 4)))))))) div 2) div 2))) div 2) div 2))) div 2)))
A176261: 1 1 1 1 ~2 1 1 ~2 ~2 1 1 ~11 ~11 ~11 1 1
(1 + (loop(\(x,i).(1 + ((x + ((1 + ((((x + 1) * (x + (if x <= 0 then 1 else loop(\(x,i).(x - (if x <= 0 then 1 else (x - ((if x <= 0 then 2 else loop(\(x,i).(x div (1 + (x mod 2))),x,x)) div 2)))),x,x)))) div 2) div 2)) div 2)) div 2)),1,(x + 1)) div 2))
A048688: 1 2 2 3 3 3 3 4 4 5 5 5 5 6 5 8
(((1 + (loop(\(x,i).2x,x,(if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + ((loop(\(x,i).(2x2 + ~x),1,loop(\(x,i).((2x * (~1 + (2 * i))) div (1 + i)),x,1)) div 2) div 2)) div 2)) div 2))))) div 2)) div 2) mod 3)
A141747: 0 1 1 1 2 0 1 0 1 1 2 0 1 0 0 0
((2 * (1 + (((3 * ((~1 + (6 * (1 + ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (3 + (x div (1 + (x mod 5))))) div 2)))) div 2)) div 2) div 2))) div 3)
A104382: 1 1 1 1 2 1 1 4 4 1 1 7 12 6 1 1
(((~1 + (6 * (1 + (((3 * ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (2 + (x div (1 + (2 * (1 + (2 * ((x div 2) mod 2))))))))) div 2) div 2)))) div 2) div 2)
A193636: 1 1 1 1 4 1 1 7 10 1 1 10 28 20 1 1
(~2 + loop(\(x,i).7x,x,1) - (loop(\(x,i).3x,x,(1 + loop(\(x,i).2x,x,1))) + loop(\(x,i).5x,x,1) + loop(\(x,i).(2x + 1),x,loop(\(x,i).2x,x,1))))
A147978: ~5 ~14 ~42 ~98 126 4606 50478 446782 3622206 28040446 211134798 1561328062 11403051486 82538901886 593482158318 4245770823742
(1 + ((loop(\(x,i).(2x + 2),x,(if x <= 0 then 1 else (2 * (1 + ((1 + ((x + ((1 + (((loop(\(x,i).3x,(x + ~1),loop(\(x,i).(x2 + x),1,loop(\(x,i).(x * i),x,1))) div 2) div 2) div 2)) div 2)) div 2)) div 2))))) div 2) div 2))
A275904: 1 2 6 36 2048
(1 + ((2 * (1 + ((1 + (x div (1 + (x mod (1 + (x div (if x <= 0 then 1 else (2 * ((~1 + (2 * (if x <= 0 then 1 else (2 * (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))))))) div 2))))))))) div 2))) div 3))
A329345-A329045: 1 2 2 3 2 3 2 4 4 3 2 5 2 3 6 7
(1 + ((loop(\(x,i).2x,x,(1 - ((1 + (((3 * (1 + (loop(\(x,i).3x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 3))) div 2) div 2)) div 2))) mod (x + 1)) div 2))
A184441: 1 1 1 1 1 2 1 1 3 2 1 1 2 5 3 1
((2x + 3) + (2 * ((x + 1) + (((x + 1) + (((2x + 1) + (2 * (((x + 1) + (2 * ((1 + (loop(\(x,i).((x + 1) + loop(\(x,i).2x,x,1) - (x mod 2)),x,1) div 2)) div 2))) div 2))) div 3)) div 2))))
A087714: 5 13 19 367
((1 + ((1 + ((x + 1) div (1 + ((2 * (1 + ((1 + (x mod (1 + (2 * (if (x mod 5) <= 0 then 1 else (((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3)))))) div 2))) div 3)))) div 2)) div 2)
A171850: 1 1 1 1 1 1 2 1 1 3 2 1 1 1 4 4
(((3 * (1 + (((~1 + (6 * (1 + (((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + (if (x + ~2) <= 0 then 1 else 2) + (x div 5)) div 2)))) div 2) div 2))) div 2) div 2)
A115263: 1 1 1 2 2 2 2 3 3 2 3 4 6 4 3 3
((2 * (1 + (((7 * (1 + ((4 * ((8 * ((((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div 2))) div 2)) div 3)) div 3))) div 2) div 2))) div 3)
A100754: 1 1 1 1 4 1 1 8 8 1 1 13 29 13 1 1
((1 + (((~1 + (6 * (1 + ((2 * (1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) + ((2x + 1) div (3 + (x div 4)))))) div 3)))) div 2) div 2)) div 2)
A179004: 1 1 1 2 2 2 2 4 4 2 3 4 5 4 3 4
(1 + (loop(\(x,i).5x,x,1) + loop(\(x,i).3x,x,1) + loop(\(x,i).4x,x,1) + loop(\(x,i).6x,x,1) + loop(\(x,i).7x,x,1) + loop(\(x,i).2x,x,1)))
A001554: 7 28 140 784 4676 29008 184820 1200304 7907396 52666768 353815700 2393325424 16279522916 111239118928 762963987380 5249352196144
(1 + (((1 + (((x + 1) * ((2x + 1) + (((x + 1) + (((x + 1) + (((3x + 1) + (if (x + ~1) <= 0 then 1 else (2 * ((x + 1) - (((~x2 + x) div 2) div 5))))) div 2)) div 2)) div 2))) div 2)) div 2) div 2))
A293239: 1 2 4 7 11 15 21 28 35 43 53 64 76 88 102 117
(1 + compr(\x.(~1 + ((2 * ((3 * (3 + (((~1 + (6 * (1 + (((~1 + (6 * (1 + ((1 + ((loop(\(x,i).2x,x,2) mod (x + 1)) div 2)) div 2)))) div 2) div 2)))) div 2) div 2))) div 2)) mod 3)),x))
A333312: 9 15 20 21 24 25 27 28 33 35 36 39 40 44 45 48
(3 + (loop(\(x,i).(2 * (((x + ~1) + ((2 * (3 + (((~1 + (6 * (1 + ((1 + (x div (1 + (x mod (1 + (x mod (1 + (x div (2 * (2 - (x mod 2))))))))))) div 2)))) div 2) div 2))) div 3)) div 2)),x,1) div 2))
A130788: 3 4 5 6 8 11 15 21 26 30
(1 + (((3 * ((3 * ((3 * (1 + ((((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + (4 * (1 + (x div 5))))) div 2) div 2))) div 2)) div 2)) div 2) div 2))
A296405: 1 1 1 1 4 1 1 8 8 1 1 17 24 17 1 1
(((~1 + (6 * (1 + (((3 * (1 + ((((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + (4 * (1 + ((1 + (x div 2)) div 2))))) div 2) div 2))) div 2) div 2)))) div 2) div 2)
A332307: 1 1 1 1 4 1 1 8 8 1 1 14 20 14 1 1
((x - (((x + ~2) - (((2x + 3) + (2 * ((1 + (((2x + 2) * (1 + (((1 + (((x + 1) * (1 + ((x + (x mod 4)) * (1 + (x div 4))))) div 2)) div 2) div 2))) div 2)) div 2))) div 3)) div 2)) div 2)
A328085: 1 1 2 3 5 8 12 18 26 38 52
(1 + ((2 * (1 + ((1 + (((5 * (2 + ((1 + loop(\(x,i).2x,((((1 + (8 mod (1 + (x div 2)))) div 2) + (if x <= 0 then 0 else 1)) - (x mod 2)),2)) div 3) - (x mod 2))) div 2) div 2)) div 2))) mod 3))
A089280: 1 2 1 2 3 2 1 2 2 3 3 2 3 2 1 2
((1 + ((1 + (((x + 1) * (1 + (((1 + (if x <= 0 then 0 else ((x + 2) + (((3 * ((3 * (1 + ((1 + (x div (1 + ((if (x mod 2) <= 0 then 3 else ~2) mod (x + 1))))) div 2))) div 2)) div 2) div 2)))) div 2) div 2))) div 2)) div 2)) div 2)
A264396: 0 1 1 2 2 3 3 4 5 5 6 8 8 9 12 12
(((x + 2) + (((3 * ((3 * (1 + (((1 + (((2 * (1 + ((1 + ((1 + loop(\(x,i).(x div (1 + (if (x mod 3) <= 0 then 2 else 0))),2,(2x + 1))) div 2)) div 2))) div 3) + (x mod 2))) div 2) div 2))) div 2)) div 2) div 2)) div 2)
A302779: 1 1 2 3 3 4 5 5 6 6 6 7 8 7 9 10
((1 + (if x <= 0 then 0 else (1 + ((2 * (1 + ((1 + (x div (1 + (x mod (1 + ((~1 + (2 * ((3 * (1 + (((1 + (x mod (1 + (x mod (2 * (2 + ((x div 2) mod 2))))))) mod (x + 1)) div 2))) div 2))) mod (x + 1))))))) div 2))) div 3)))) div 2)
A067148: 0 1 1 1 2 1 2 2 2 1 3 1 3 2 2 1
(((3 * ((~1 + (6 * (1 + ((1 + (((3 * (1 + (loop(\(x,i).3x,(((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3),1) div 3))) div 2) div 2)) div 2)))) div 2)) div 2) div 2)
A131235: 1 1 1 1 3 1 1 6 6 1 1 10 26 10 1 1
(1 + ((2 * (1 + ((1 + (x div (2 + (loop(\(x,i).2x,x,(~1 + (x mod 2) - ((1 + loop(\(x,i).2x,((((1 + (8 mod (1 + (x div 2)))) div 2) + (if x <= 0 then 0 else 1)) - (x mod 2)),2)) div 3))) mod (x + 1))))) div 2))) div 3))
A343068: 1 1 1 2 2 1 1 3 2 2 2 2 2 1 2 4
(x + (if x <= 0 then 1 else ((2x + ~1) + ((2 * (3 + ((4 * (1 + ((((2 + compr(\x.(loop(\(x,i).(2x + 2),x,2) mod (x + 2)),x)) * (1 + compr(\x.((~1 + loop(\(x,i).2x,x,2)) mod (x + 2)),x))) div 2) div 2))) div 3))) div 3))))
A225227: 1 7 13
A337433: 1 7 13 26 43 62
(1 + ((1 + ((1 + ((((x + 1) * (0 + (((2 * (1 + ((1 + (x div (1 + ((~1 + loop(\(x,i).2x,x,(1 + (x mod (2 * (1 + (x mod 2)))))) - (x mod 2)) mod (2x + 1))))) div 2))) div 3) + (x mod 2)))) div 2) div 2)) div 2)) div 2))
A331175: 1 1 1 2 1 2 1 3 3 2 1 4 1 2 1 4
(((~1 + (6 * (1 + ((1 + ((1 + ((((x + 1) * (0 + (((2 * (1 + ((1 + (x div (1 + (x mod (1 + (loop(\(x,i).2x,x,2) mod (2x + 1))))))) div 2))) div 3) + (x mod 2)))) div 2) div 2)) div 2)) div 2)))) div 2) div 2)
A077191: 1 1 1 2 1 2 1 4 2 2 1 5 1 2 1 11
(~3 + (2 * (1 + ((1 + (((~1 + (6 * (1 + (((~1 + (6 * (1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + (x div (1 + (x mod 5)))))))) div 2) div 2)))) div 2) div 2)) div 2))))
A344527: 1 1 1 1 3 1 1 7 7 1 1 15 25 11 1 1
((2 * ((3x + 4) + (if x <= 0 then 1 else ((2x + ~1) + ((2 * ((4x + ~1) + ((2 * ((2x + 2) + (if x <= 0 then 1 else (2 * (2x + ((x - (x div 4)) div 2)))))) div 3))) div 3))))) mod 3)
A218907: 1 2 0 2 0 1 2 0 2 1 2 0 2 2 1 2
(1 - ((1 + ((1 + ((1 + ((1 + ((1 + ((((x + 1) * (if x <= 0 then 1 else (2 * (1 + ((1 + (((1 + (((x + 1) * (x - loop(\(x,i).(1 + ((2x2 + ~x) div (x + 3))),2,x))) div 2)) div 2) div 2)) div 2))))) div 2) div 2)) div 2)) div 2)) div 2)) div 2)) div 2))
A017899-A017846: 1 0 0 0 0 1 1 1 1 1 2 3 4 5 6 8
(~1 + ((2 * ((2x + 3) + ((2 * ((x + 2) + (((2x + 1) + (2 * ((x + 1) + ((2 * (1 + ((2 * (1 + (2 * (2x - (2x div 7))))) div 3))) div 3)))) div 3))) div 3))) div 3))
A191406: 2 5 7 11 13 16 19 21 25 27 30 33 35 39 41 45
(1 + compr(\x.(1 - ((2 * (1 + ((2 + ((2 * (1 + ((2 * (1 + ((((2 - (2x mod (4 + (x div 4)))) mod (x + 1)) div 3) * (1 + ((1 + (x div 2)) div 2))))) div 3))) div 3) - (x mod 2)) div 2))) mod 3)),(x + 1)))
A287531: 2 3 4 6 7 10 11 12 14 15 16 17 18 20 21 23
(1 - ((1 + ((1 + ((1 + (x mod (2 + ((1 + (2 * (1 + (((1 + (x div 3)) div (2 * (1 + (((((x + ~2) * (x div 3)) mod (1 + (x div 2))) div 2) * (1 + ((x - (x mod 5)) div 2)))))) + (x mod 2))))) mod (x + 1))))) div 2)) div 2)) div 2))
A291955: 1 0 1 0 0 0 0 1 0 ~1 0 0 0 0 0 0
(1 + ((2 * ((((if x <= 0 then 1 else (2 * (1 + ((1 + ((x mod (2 + ((1 + (2 * (((if x <= 0 then 1 else (2 * (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1))))))))) - (x mod 2)) div 2))) mod (x + 1)))) div 2)) div 2)))) - (x mod 2)) div 2) mod 2)) + (x mod 2)))
A171171: 1 2 3 4 1 2 3 2 3 4 3 4 1 4 1 2
((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + (((1 + loop(\(x,i).x2,1,(1 + ((~1 + loop(\(x,i).((x + 1) + (((1 + i) * i) div 2)),x,1)) div 2)))) div 2) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)
A218025: 0 1 1 1 1 1 1 1 1 1 2 3 5 7 11 15
(2 + ((((3 * (1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + (loop(\(x,i).(2 * (x + (i mod 2))),(x + ~2),1) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2))) div 2) + (x mod 3)) div 2))
A295569: 2 3 3 3 4 4 3 4 4 3 4 4 3 4 5 5
(1 + compr(\x.(1 - ((2 * (1 + ((1 + (x div (1 + ((~1 + (2 * ((x + 1) + ((2 * (1 + ((1 + (x div (1 + ((~1 + (2 * ((x + 1) + (2 div (1 + (3 div (1 + (loop(\(x,i).(x div (1 + (x mod 2))),x,x) div 2)))))))) mod (x + 1))))) div 2))) div 3)))) mod (x + 1))))) div 2))) mod 3)),(x + 1)))
A087721: 2 3 4 5 6 8 10 11 12 16 20 21 22 23 24 25
(if x <= 0 then 0 else (1 + ((2 * (1 + ((2 + ((2 * (1 + ((2 + ((2 * (1 + ((2 + ((2 * (1 + ((1 + (x2 div loop(\(x,i).(x div (2 - (x mod 2))),x,(x + 1)))) div 2))) div 3) - (x mod 2)) div 2))) div 3) - (x mod 2)) div 2))) div 3) - (x mod 2)) div 2))) div 3)))
A318490: 0 2 2 2 3 2 3 2 3 2 3 2 3 2 3 5
((1 + (((~1 + (6 * (1 + ((1 + (((~1 + (6 * (1 + (((~1 + (6 * (1 + ((1 + (((1 + (((x + 1) * (1 + (x div (2 + (x div (1 + (loop(\(x,i).(2x + 1),x,0) mod (x + 1)))))))) div 2)) div 2) div 2)) div 2)))) div 2) div 2)))) div 2) div 2)) div 2)))) div 2) div 2)) div 2)
A163373: 1 1 1 2 1 2 2 4 4 2 2 4 2 4 4 8
((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + (if x <= 0 then 0 else (x + (loop(\(x,i).(x * i),x,1) div (x + 1))))) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)
A213002: 0 1 1 1 1 1 1 1 1 1 1 1 1 1 3 39
((x * ((1 + (((x + 1) * (if x <= 0 then 1 else (2 * (1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + ((1 + (loop(\(x,i).(2x + ~1),(x + ~1),loop(\(x,i).2x,x,1)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2)) div 2))))) div 2)) div 2)) div 2)
A069693: 0 1 3 6 10 15 21 28 36 45 55 66 78 91 105 300