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listlengths 1
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8
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2.35k
| offset_a
int64 -14,827
666,262,453B
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635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
listlengths 1
3
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231
⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-14 02:38:35
| filename
stringlengths 29
29
| hash
stringlengths 32
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A384575 | G.f. A(x) satisfies A(x) = 1 + x * A(x*A(x)^5). | [
"1",
"1",
"1",
"6",
"31",
"236",
"2166",
"22722",
"269889",
"3567412",
"51765431",
"816476196",
"13892821878",
"253442895075",
"4930644856063",
"101830536332051",
"2223767436058566",
"51172807259226084",
"1237092039069090235",
"31332521053777095784",
"829389782837272248191",
"22894754438382163120136"
]
| [
"nonn"
]
| 12 | 0 | 4 | [
"A087949",
"A143500",
"A143501",
"A384574",
"A384575",
"A384579",
"A384583"
]
| null | Seiichi Manyama, Jun 04 2025 | 2025-06-04T09:53:13 | oeisdata/seq/A384/A384575.seq | a4ed8468ed2de3313ac307678a8bb403 |
A384576 | G.f. A(x) satisfies A(x) = ( 1 + x * A(x*A(x))^(1/2) )^2. | [
"1",
"2",
"3",
"8",
"27",
"118",
"609",
"3602",
"23866",
"174186",
"1383868",
"11860702",
"108889022",
"1064691402",
"11034753421",
"120739899232",
"1389891203976",
"16781698952902",
"211959646629376",
"2793804347189762",
"38347179124969391",
"547046497259184494",
"8096627908313404104"
]
| [
"nonn"
]
| 13 | 0 | 2 | [
"A143500",
"A384576",
"A384580"
]
| null | Seiichi Manyama, Jun 04 2025 | 2025-06-04T09:52:47 | oeisdata/seq/A384/A384576.seq | 9bb9e050efd752ed47121d1e71d16020 |
A384577 | G.f. A(x) satisfies A(x) = ( 1 + x * A(x*A(x))^(1/3) )^3. | [
"1",
"3",
"6",
"19",
"78",
"411",
"2617",
"19251",
"160254",
"1482400",
"15035622",
"165545253",
"1963006576",
"24908182305",
"336397711074",
"4813816122917",
"72704962269990",
"1155070280657286",
"19245587072017468",
"335418172582313610",
"6100293082529588802",
"115532044092709366555",
"2274095852526512246841"
]
| [
"nonn"
]
| 12 | 0 | 2 | [
"A384577",
"A384581"
]
| null | Seiichi Manyama, Jun 04 2025 | 2025-06-04T09:53:52 | oeisdata/seq/A384/A384577.seq | 2bd8a187e92da6e21601011d97890411 |
A384578 | G.f. A(x) satisfies A(x) = ( 1 + x * A(x*A(x))^(1/4) )^4. | [
"1",
"4",
"10",
"36",
"171",
"1032",
"7656",
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"651065",
"7170044",
"87058242",
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"16497960553",
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"1335030266607501",
"25927404824529616",
"528984983237731754",
"11306375975258492540",
"252529515598101796399",
"5880779189553142120704"
]
| [
"nonn"
]
| 12 | 0 | 2 | [
"A384574",
"A384578",
"A384582"
]
| null | Seiichi Manyama, Jun 04 2025 | 2025-06-04T09:53:08 | oeisdata/seq/A384/A384578.seq | 0362aba1561bd05fbab9de3445a530f6 |
A384579 | G.f. A(x) satisfies A(x) = ( 1 + x * A(x*A(x))^(1/5) )^5. | [
"1",
"5",
"15",
"60",
"320",
"2151",
"17985",
"176610",
"1985755",
"25116455",
"351852746",
"5393800690",
"89651625560",
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"30688985052200",
"624900202917151",
"13480450499067220",
"306905745410816990",
"7349620218635161140",
"184589745041317074895",
"4849519725067777296866"
]
| [
"nonn"
]
| 10 | 0 | 2 | [
"A384575",
"A384579",
"A384583"
]
| null | Seiichi Manyama, Jun 04 2025 | 2025-06-04T09:54:04 | oeisdata/seq/A384/A384579.seq | 21b33c10a86bd41b90655a1e3bdba516 |
A384580 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A143500. | [
"1",
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"6597",
"23866",
"74400",
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]
| [
"nonn",
"tabl"
]
| 12 | 0 | 8 | [
"A000007",
"A143500",
"A381566",
"A384576",
"A384580",
"A384581",
"A384582",
"A384583"
]
| null | Seiichi Manyama, Jun 04 2025 | 2025-06-04T09:52:51 | oeisdata/seq/A384/A384580.seq | f2d55d930b07e7e244fa2c34f091b48c |
A384581 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A143501. | [
"1",
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"19251",
"93234",
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]
| [
"nonn",
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]
| 10 | 0 | 8 | [
"A000007",
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"A381566",
"A384580",
"A384581",
"A384582",
"A384583"
]
| null | Seiichi Manyama, Jun 04 2025 | 2025-06-04T09:53:56 | oeisdata/seq/A384/A384581.seq | 5b83768f405dbdc7da61e33ce5e4f6d0 |
A384582 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A384574. | [
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"43587",
"259789",
"1329433",
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]
| [
"nonn",
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]
| 12 | 0 | 8 | [
"A000007",
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"A384574",
"A384580",
"A384581",
"A384582",
"A384583"
]
| null | Seiichi Manyama, Jun 04 2025 | 2025-06-04T09:54:00 | oeisdata/seq/A384/A384582.seq | 13a1ad26026b927d5f91863d4a2dcc8d |
A384583 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A384575. | [
"1",
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"2151",
"12634",
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]
| [
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]
| 11 | 0 | 8 | [
"A000007",
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"A384575",
"A384580",
"A384581",
"A384582",
"A384583"
]
| null | Seiichi Manyama, Jun 04 2025 | 2025-06-04T09:54:09 | oeisdata/seq/A384/A384583.seq | c8ca3fdedc61528305d833c293cf1bc1 |
A384584 | Numbers k such that A383844(k) = 2. | [
"4",
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"62",
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"200",
"247",
"305",
"522",
"707",
"900",
"1235",
"1504",
"1532",
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"2396",
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"6419",
"9066",
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"14292",
"17914",
"22696",
"33924",
"35933",
"38951",
"80602"
]
| [
"nonn",
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]
| 6 | 1 | 1 | [
"A024934",
"A383844",
"A384584"
]
| null | Miles Englezou, Jun 04 2025 | 2025-06-09T23:27:45 | oeisdata/seq/A384/A384584.seq | c6a50a2cd2b0e6fb7472ca97457e465c |
A384585 | a(n) = 6 * (4*n)! / ((n+1)! * (3*n+1)!). | [
"6",
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"33",
"168",
"969",
"6072",
"40365",
"280488",
"2017356",
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"16558857808956320",
"139428557033056785",
"1180350813375438840",
"10041660963789578955"
]
| [
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]
| 19 | 0 | 1 | [
"A000260",
"A002293",
"A384585"
]
| null | Karol A. Penson, Jun 04 2025 | 2025-06-22T00:51:29 | oeisdata/seq/A384/A384585.seq | 4d9dec9fdc264acadab84becf9faccf5 |
A384586 | Decimal expansion of the second largest zero of the Laguerre polynomial of degree 4. | [
"4",
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]
| [
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| 14 | 1 | 1 | [
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"A384277",
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"A384280",
"A384281",
"A384463",
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"A384465",
"A384466",
"A384467",
"A384586",
"A384587",
"A384588",
"A384589"
]
| null | A.H.M. Smeets, Jun 04 2025 | 2025-06-18T12:24:13 | oeisdata/seq/A384/A384586.seq | 1d251b1c142f13704ad4924bb658e598 |
A384587 | Decimal expansion of the largest zero of the Laguerre polynomial of degree 4. | [
"9",
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"0",
"7",
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| [
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| 11 | 1 | 1 | [
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"A384589"
]
| null | A.H.M. Smeets, Jun 07 2025 | 2025-06-18T12:23:13 | oeisdata/seq/A384/A384587.seq | 073c55b48cb78fe41b7845dcd069ed0f |
A384588 | Decimal expansion of the weight factor for Laguerre-Gauss quadrature corresponding to abscissa A384586. | [
"0",
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| [
"nonn",
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]
| 11 | 0 | 2 | [
"A014176",
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"A384586",
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"A384589"
]
| null | A.H.M. Smeets, Jun 07 2025 | 2025-06-26T08:00:59 | oeisdata/seq/A384/A384588.seq | 6be59330ee6dd0a854f0bdaa71d2acb1 |
A384589 | Decimal expansion of the weight factor for Laguerre-Gauss quadrature corresponding to abscissa A384587. | [
"0",
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"5",
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"9",
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]
| [
"nonn",
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]
| 11 | 0 | 4 | [
"A014176",
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"A384466",
"A384467",
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"A384588",
"A384589",
"A384590"
]
| null | A.H.M. Smeets, Jun 14 2025 | 2025-06-26T08:00:09 | oeisdata/seq/A384/A384589.seq | 6170486aae828172b95b065cd9d06e83 |
A384590 | a(n) = floor(X(n,n)), where X(n,n) is the largest zero of the Laguerre polynomial of degree n. | [
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]
| [
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]
| 25 | 1 | 2 | [
"A014176",
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"A384590"
]
| null | A.H.M. Smeets, Jun 14 2025 | 2025-07-08T22:25:00 | oeisdata/seq/A384/A384590.seq | 2ce13df091e3204eee322ff794501456 |
A384591 | a(n) = permanent of the n X n circulant matrix with (row 1) = (F(1), F(2), ..., F(n)), where F = A000045 (Fibonacci numbers). | [
"1",
"1",
"2",
"16",
"265",
"12552",
"1431040",
"426749895",
"323397418338",
"635720375415040",
"3236089602490212389",
"42921641465456435652532",
"1485502760348227071906663424",
"134453761950835461349077548216607",
"31856917244136936392984483908703780290"
]
| [
"nonn",
"new"
]
| 7 | 0 | 3 | [
"A000045",
"A123744",
"A384080",
"A384313",
"A384591"
]
| null | Clark Kimberling, Jun 27 2025 | 2025-07-02T17:20:54 | oeisdata/seq/A384/A384591.seq | d7997a87ac49c10b2b1945c1d6c88124 |
A384592 | a(n) = neg(M(n)), where M(n) is the n X n circulant matrix with (row 1) = (F(1), F(2), ..., F(n)), where F = A000045 (Fibonacci numbers), and neg(M(n)) is the negative part of the determinant of M(n); see A380661. | [
"0",
"-1",
"-6",
"-150",
"-5370",
"-800640",
"-190224111",
"-176905217601",
"-291774510700416",
"-1732081174959242854",
"-20169113574187183899414",
"-780617739418078727245260288",
"-64339950490716309261029142530799",
"-16501635484912814610105139633118406681"
]
| [
"sign",
"new"
]
| 4 | 1 | 3 | [
"A000045",
"A123745",
"A380661",
"A384591",
"A384592",
"A384593"
]
| null | Clark Kimberling, Jul 02 2025 | 2025-07-03T16:21:11 | oeisdata/seq/A384/A384592.seq | 009007698fed6e7f722c62ce8a6eb0b8 |
A384593 | a(n) = pos(M(n)), where M(n) is the n X n circulant matrix with (row 1) = (F(1), F(2), ..., F(n)), where F = A000045 (Fibonacci numbers), and neg(M(n)) is the negative part of the determinant of M(n); see A380661. | [
"1",
"1",
"10",
"115",
"7182",
"630400",
"236525784",
"146492200737",
"343945864714624",
"1504008427530969535",
"22752527891269251753118",
"704885020930148344661403136",
"70113811460119152088048405685808",
"15355281759224121782879344275585373609"
]
| [
"nonn",
"new"
]
| 4 | 1 | 3 | [
"A000045",
"A123745",
"A380661",
"A384591",
"A384592",
"A384593"
]
| null | Clark Kimberling, Jul 02 2025 | 2025-07-03T16:22:01 | oeisdata/seq/A384/A384593.seq | b93a0e62132f1061016a1f134d5ca0f6 |
A384597 | Integers k such that k + 1 has a divisor that is an anagram of k, which must have the same number of digits as k. | [
"1",
"41",
"73",
"631",
"793",
"6031",
"6391",
"6733",
"7412",
"7520",
"7993",
"8627",
"9710",
"25147",
"37112",
"43916",
"49316",
"51427",
"60031",
"60391",
"60733",
"62314",
"63214",
"63991",
"66331",
"67393",
"67933",
"70211",
"71132",
"72101",
"74102",
"74912",
"75020",
"75290",
"78260",
"79993",
"81103",
"85712",
"86927",
"89627"
]
| [
"nonn",
"base"
]
| 9 | 1 | 2 | [
"A100412",
"A384597"
]
| null | Gonzalo Martínez, Jun 04 2025 | 2025-06-16T21:50:47 | oeisdata/seq/A384/A384597.seq | 16e6f7c934454d3263e8a13c5174c1e5 |
A384598 | Expansion of (1-3*x^2) / (1-x-4*x^2+2*x^3+2*x^4). | [
"1",
"1",
"2",
"4",
"8",
"18",
"38",
"86",
"186",
"418",
"914",
"2042",
"4490",
"9994",
"22042",
"48954",
"108154",
"239898",
"530522",
"1175898",
"2601882",
"5764634",
"12759322",
"28262298",
"62566554",
"138567834",
"306790810",
"679404442",
"1504298906",
"3331199386",
"7376004506",
"16333395354",
"36166416794"
]
| [
"nonn",
"walk",
"easy"
]
| 16 | 0 | 3 | [
"A062112",
"A382683",
"A384598",
"A384599",
"A384600"
]
| null | Sean A. Irvine, Jun 04 2025 | 2025-06-04T18:03:01 | oeisdata/seq/A384/A384598.seq | 30dc89b6add3571acf3fdd13aa940f8a |
A384599 | Expansion of (1+3*x+2*x^2) / (1-4*x^2-2*x^3). | [
"1",
"3",
"6",
"14",
"30",
"68",
"148",
"332",
"728",
"1624",
"3576",
"7952",
"17552",
"38960",
"86112",
"190944",
"422368",
"936000",
"2071360",
"4588736",
"10157440",
"22497664",
"49807232",
"110305536",
"244224256",
"540836608",
"1197508096",
"2651794944",
"5871705600",
"13002195968",
"28790412288",
"63752195072"
]
| [
"nonn",
"walk",
"easy"
]
| 12 | 0 | 2 | [
"A062112",
"A382683",
"A384598",
"A384599",
"A384600"
]
| null | Sean A. Irvine, Jun 04 2025 | 2025-06-04T17:46:12 | oeisdata/seq/A384/A384599.seq | c087cc9b3535d0eaafbff9707d7361ec |
A384600 | Expansion of (1+x-x^2) / (1-x-4*x^2+2*x^3+2*x^4). | [
"1",
"2",
"5",
"11",
"25",
"55",
"123",
"271",
"603",
"1331",
"2955",
"6531",
"14483",
"32035",
"70995",
"157107",
"348051",
"770419",
"1706419",
"3777779",
"8366515",
"18523955",
"41021619",
"90828851",
"201134387",
"445358643",
"986195251",
"2183703347",
"4835498291",
"10707203891",
"23709399859",
"52499812147"
]
| [
"nonn",
"walk",
"easy"
]
| 12 | 0 | 2 | [
"A062112",
"A382683",
"A384598",
"A384599",
"A384600"
]
| null | Sean A. Irvine, Jun 04 2025 | 2025-06-04T17:46:06 | oeisdata/seq/A384/A384600.seq | 094007cc1b1fb2a10d4e53694cdd4422 |
A384601 | Numbers k such that T(k, 1) mod 3 = 1 and T(k, 2) mod 3 = 1, where T is the Wythoff array (A035513). | [
"2",
"8",
"17",
"26",
"32",
"41",
"56",
"65",
"71",
"80",
"89",
"95",
"104",
"110",
"119",
"128",
"134",
"143",
"158",
"167",
"173",
"182",
"191",
"197",
"206",
"221",
"230",
"236",
"245",
"260",
"269",
"275",
"284",
"293",
"299",
"308",
"323",
"332",
"338",
"347",
"356",
"362",
"371",
"377",
"386",
"395",
"401",
"410",
"425",
"434",
"440",
"449",
"458",
"464"
]
| [
"nonn"
]
| 15 | 1 | 1 | [
"A035513",
"A384601",
"A384602"
]
| null | Clark Kimberling, Jun 05 2025 | 2025-06-26T01:20:57 | oeisdata/seq/A384/A384601.seq | b348a5fedc4986b18a83c08f542244d3 |
A384602 | Numbers k such that T(k, 1) mod 3 = 1 and T(k, 2) mod 3 = 2, where T is the Wythoff array (A035513). | [
"1",
"10",
"16",
"25",
"34",
"40",
"49",
"55",
"64",
"73",
"79",
"88",
"103",
"112",
"118",
"127",
"136",
"142",
"151",
"166",
"175",
"181",
"190",
"205",
"214",
"220",
"229",
"238",
"244",
"253",
"268",
"277",
"283",
"292",
"301",
"307",
"316",
"331",
"340",
"346",
"355",
"370",
"379",
"385",
"394",
"403",
"409",
"418",
"433",
"442",
"448",
"457",
"466",
"472"
]
| [
"nonn"
]
| 11 | 1 | 2 | [
"A035513",
"A384601",
"A384602"
]
| null | Clark Kimberling, Jun 06 2025 | 2025-06-26T01:20:49 | oeisdata/seq/A384/A384602.seq | ea50a51fd2e24227c93080eb7f7c67ec |
A384603 | Primes preceded and followed by gaps whose quotient (value greater or equal to 1) is less than 2. | [
"5",
"23",
"37",
"47",
"53",
"67",
"79",
"83",
"89",
"131",
"157",
"163",
"167",
"173",
"211",
"233",
"251",
"257",
"263",
"277",
"293",
"337",
"353",
"359",
"367",
"373",
"379",
"383",
"389",
"409",
"439",
"443",
"449",
"479",
"503",
"547",
"557",
"563",
"577",
"587",
"593",
"607",
"613",
"631",
"647",
"653",
"677",
"683",
"691",
"701",
"709",
"719",
"727",
"733",
"739",
"751",
"757",
"787",
"797"
]
| [
"nonn"
]
| 10 | 1 | 1 | [
"A383215",
"A384603"
]
| null | Alain Rocchelli, Jun 04 2025 | 2025-06-11T03:19:59 | oeisdata/seq/A384/A384603.seq | 97b673a1d0e3602d429d552241b42b74 |
A384604 | Expansion of (1-x^2) / (1-x-4*x^2+2*x^3). | [
"1",
"1",
"4",
"6",
"20",
"36",
"104",
"208",
"552",
"1176",
"2968",
"6568",
"16088",
"36424",
"87640",
"201160",
"478872",
"1108232",
"2621400",
"6096584",
"14365720",
"33509256",
"78778968",
"184084552",
"432181912",
"1010962184",
"2371520728",
"5551005640",
"13015164184",
"30476145288",
"71434790744",
"167309043528"
]
| [
"nonn",
"easy",
"walk"
]
| 7 | 0 | 3 | [
"A213173",
"A382683",
"A384604",
"A384605"
]
| null | Sean A. Irvine, Jun 04 2025 | 2025-06-04T23:22:04 | oeisdata/seq/A384/A384604.seq | ac9abb64b53b0505bfd96ed2977ac769 |
A384605 | Expansion of (1+x) / (1-x-4*x^2+2*x^3). | [
"1",
"2",
"6",
"12",
"32",
"68",
"172",
"380",
"932",
"2108",
"5076",
"11644",
"27732",
"64156",
"151796",
"352956",
"831828",
"1940060",
"4561460",
"10658044",
"25023764",
"58533020",
"137311988",
"321396540",
"753578452",
"1764540636",
"4136061364",
"9687067004",
"22702231188",
"53178376476",
"124613167220"
]
| [
"nonn",
"easy",
"walk"
]
| 7 | 0 | 2 | [
"A213173",
"A382683",
"A384604",
"A384605"
]
| null | Sean A. Irvine, Jun 04 2025 | 2025-06-04T23:21:59 | oeisdata/seq/A384/A384605.seq | 6842e1669192b23bed1fa3f9bca88df7 |
A384606 | Possible values for the number of groups of order equal to a prime power, in order of first appearance. | [
"1",
"2",
"5",
"14",
"51",
"267",
"15",
"2328",
"67",
"56092",
"10494213",
"504",
"49487367289"
]
| [
"nonn",
"more",
"hard"
]
| 10 | 1 | 2 | [
"A098885",
"A384606",
"A384607"
]
| null | Robin Jones, Jun 04 2025 | 2025-06-16T18:38:35 | oeisdata/seq/A384/A384606.seq | 65c995453490e41f0778ba9305c081c2 |
A384607 | Possible values for the number of groups of order equal to a prime power, in order of size. | [
"1",
"2",
"5",
"14",
"15",
"51",
"67",
"77",
"83",
"87",
"97",
"101",
"107",
"111",
"125",
"131",
"145",
"149",
"155",
"159",
"173",
"183",
"193",
"203",
"207",
"217",
"227",
"231",
"245",
"265",
"267",
"269",
"275",
"279",
"289",
"293",
"323",
"327",
"341",
"347",
"365",
"371",
"385",
"395",
"399",
"413",
"423",
"433",
"447",
"457",
"461",
"467",
"491",
"504",
"515"
]
| [
"nonn"
]
| 14 | 1 | 2 | [
"A000001",
"A098885",
"A384606",
"A384607"
]
| null | Robin Jones, Jun 04 2025 | 2025-06-16T18:44:01 | oeisdata/seq/A384/A384607.seq | 39ccaebe1a7b8c9a7698e0dabd018960 |
A384608 | Consecutive states of the linear congruential pseudo-random number generator (129*s+27098671125) mod 2^35 when started at s=1. | [
"1",
"27098671254",
"18133949355",
"29915928896",
"3603063125",
"10857477098",
"18963943679",
"33905981588",
"2923784873",
"26309797694",
"19448475219",
"27691073512",
"25834363901",
"26836992658",
"18737148839",
"4649447228",
"8402072913",
"11454449126",
"27253858555",
"3793372816",
"1047688869"
]
| [
"nonn",
"easy"
]
| 16 | 1 | 2 | [
"A096550",
"A096561",
"A384387",
"A384565",
"A384608"
]
| null | Sean A. Irvine, Jun 04 2025 | 2025-06-12T05:56:53 | oeisdata/seq/A384/A384608.seq | 2d82e49a96f44cd4f068f24d1e586376 |
A384609 | Possible values for the number of nilpotent groups of a finite order, ordered by size. | [
"1",
"2",
"4",
"5",
"8",
"10",
"14",
"15",
"16",
"20",
"25",
"28",
"30",
"32",
"40",
"50",
"51",
"56",
"60",
"64",
"67",
"70",
"75",
"77",
"80",
"83",
"87",
"97",
"100",
"101",
"102",
"107",
"111",
"112",
"120",
"125",
"128",
"131",
"134",
"140",
"145",
"149",
"150",
"154",
"155",
"159",
"160",
"166",
"173",
"174",
"183",
"193",
"194",
"196",
"200",
"202",
"203",
"204",
"207"
]
| [
"nonn"
]
| 15 | 1 | 2 | [
"A066060",
"A384607",
"A384609"
]
| null | Robin Jones, Jun 04 2025 | 2025-06-11T00:02:17 | oeisdata/seq/A384/A384609.seq | eb00ab8998405f959b01acc4fd27d27d |
A384610 | Consecutive states of the linear congruential pseudo-random number generator (262145*s+3) mod 2^35 when started at s=1. | [
"1",
"262148",
"1310727",
"3145738",
"5767181",
"9175056",
"13369363",
"18350102",
"24117273",
"30670876",
"38010911",
"46137378",
"55050277",
"64749608",
"75235371",
"86507566",
"98566193",
"111411252",
"125042743",
"139460666",
"154665021",
"170655808",
"187433027",
"204996678",
"223346761",
"242483276"
]
| [
"nonn",
"easy"
]
| 11 | 1 | 2 | [
"A096550",
"A096561",
"A384160",
"A384387",
"A384565",
"A384608",
"A384610"
]
| null | Sean A. Irvine, Jun 04 2025 | 2025-06-12T05:58:44 | oeisdata/seq/A384/A384610.seq | 20916aef23fc8506ffdf0afd924290b3 |
A384611 | Expansion of (1+2*x-x^3) / (1-5*x^2+2*x^4). | [
"1",
"2",
"5",
"9",
"23",
"41",
"105",
"187",
"479",
"853",
"2185",
"3891",
"9967",
"17749",
"45465",
"80963",
"207391",
"369317",
"946025",
"1684659",
"4315343",
"7684661",
"19684665",
"35053987",
"89792639",
"159900613",
"409593865",
"729395091",
"1868384047",
"3327174229",
"8522732505",
"15177080963",
"38876894431"
]
| [
"nonn",
"easy",
"walk"
]
| 6 | 0 | 2 | [
"A000079",
"A005824",
"A079162",
"A384611"
]
| null | Sean A. Irvine, Jun 04 2025 | 2025-06-04T23:20:58 | oeisdata/seq/A384/A384611.seq | e97af8c0ba01f110fb853751d3778178 |
A384612 | a(n) is the smallest integer k such that k^n is an abelian square; or -1 if no such k exists. | [
"11",
"836",
"11",
"207",
"624",
"818222",
"1001",
"2776",
"100001",
"32323107",
"100001",
"85692627",
"10000001",
"501249084",
"10000001",
"27962757",
"41695607",
"70983559",
"72768046",
"977688137",
"219873071",
"112562383",
"2338280974",
"2435385853",
"1231380445",
"4557057314",
"361499019",
"8096434047",
"5278552513"
]
| [
"nonn",
"base",
"changed"
]
| 52 | 1 | 1 | [
"A001597",
"A001700",
"A075786",
"A272655",
"A342942",
"A384612"
]
| null | Gonzalo Martínez, Jun 04 2025 | 2025-07-12T08:36:08 | oeisdata/seq/A384/A384612.seq | 3f4c08249786b1ba6f27fbd37f99d07c |
A384613 | Number of rooted ordered trees with n non-root nodes such that all leaf nodes can be k different colors where k is the degree of their parent node. | [
"1",
"1",
"5",
"36",
"340",
"4019",
"57696",
"982146",
"19419042",
"438068191",
"11106513798",
"312555754796",
"9663786464541",
"325515760762637",
"11861723942987878",
"464834173383876612",
"19490387161582849600",
"870582781070074780946",
"41266849779858887379029",
"2068827708558025551348644"
]
| [
"nonn"
]
| 6 | 0 | 3 | [
"A000108",
"A002212",
"A007318",
"A102407",
"A258173",
"A384613"
]
| null | John Tyler Rascoe, Jun 04 2025 | 2025-06-05T09:56:05 | oeisdata/seq/A384/A384613.seq | 01a6b2f3133931ed87a732b03b01a248 |
A384614 | Expansion of (1+x+x^2) / (1-x-3*x^2). | [
"1",
"2",
"6",
"12",
"30",
"66",
"156",
"354",
"822",
"1884",
"4350",
"10002",
"23052",
"53058",
"122214",
"281388",
"648030",
"1492194",
"3436284",
"7912866",
"18221718",
"41960316",
"96625470",
"222506418",
"512382828",
"1179902082",
"2717050566",
"6256756812",
"14407908510",
"33178178946",
"76401904476",
"175936441314"
]
| [
"nonn",
"easy",
"walk"
]
| 5 | 0 | 2 | [
"A105476",
"A382683",
"A384614"
]
| null | Sean A. Irvine, Jun 04 2025 | 2025-06-04T23:20:44 | oeisdata/seq/A384/A384614.seq | 732058d57b549a5c55fbc33cc5bf3022 |
A384615 | Consecutive states of the linear congruential pseudo-random number generator for GLIM3 when started at 1. | [
"1",
"8404998",
"360890399",
"5017796764",
"15125873421",
"33338412866",
"27454835787",
"8568995192",
"3575673689",
"25551208638",
"18220712887",
"6754914964",
"4760804581",
"21551239290",
"20533449315",
"8548686832",
"11051010993",
"29945330294",
"1980032079",
"24405357964",
"9609153469",
"4583291570"
]
| [
"nonn",
"easy"
]
| 10 | 1 | 2 | [
"A096550",
"A096561",
"A384615"
]
| null | Sean A. Irvine, Jun 04 2025 | 2025-06-12T12:59:11 | oeisdata/seq/A384/A384615.seq | 367a252334eebd7f3317ed6af02872f4 |
A384616 | A(m,n) is the maximum sum of absolute differences of the labels of adjacent vertices of the grid graph P_m X P_n where the m*n labels are exactly 1, 2, ..., m*n. | [
"0",
"1",
"8",
"3",
"23",
"58",
"7",
"44",
"115"
]
| [
"nonn",
"tabl",
"more",
"changed"
]
| 43 | 1 | 3 | [
"A047838",
"A067725",
"A384616"
]
| null | Sela Fried, Jun 07 2025 | 2025-06-30T17:21:00 | oeisdata/seq/A384/A384616.seq | 56e7689aadef13d98f60ee6d0d81d6f7 |
A384617 | E.g.f. A(x) satisfies A(x) = exp( x/A(-x*A(x))^2 ). | [
"1",
"1",
"5",
"13",
"-63",
"-2279",
"-51167",
"-423387",
"13717889",
"885044593",
"37051519041",
"779965433149",
"-14179999608959",
"-2798466635425239",
"-224720509492366495",
"-11148988922254048619",
"-300176114650473574143",
"18804123010954180467937",
"4351564646569010083711105"
]
| [
"sign"
]
| 22 | 0 | 3 | [
"A052750",
"A213108",
"A213110",
"A213111",
"A384617",
"A384808",
"A384809",
"A384810"
]
| null | Seiichi Manyama, Jun 10 2025 | 2025-06-10T13:57:25 | oeisdata/seq/A384/A384617.seq | 3c439b10d252fd0fb8f437e32622adc8 |
A384618 | Primes preceded and followed by gaps whose quotient (value greater or equal to 1) is greater than 2. | [
"29",
"31",
"59",
"61",
"73",
"113",
"127",
"137",
"139",
"149",
"151",
"179",
"181",
"191",
"199",
"223",
"239",
"241",
"269",
"271",
"283",
"307",
"317",
"331",
"347",
"419",
"421",
"431",
"433",
"467",
"521",
"523",
"541",
"569",
"571",
"599",
"601",
"619",
"641",
"659",
"661",
"673",
"773",
"809",
"811",
"821",
"829",
"853",
"863",
"877",
"887",
"907",
"953",
"967"
]
| [
"nonn"
]
| 12 | 1 | 1 | [
"A384603",
"A384618"
]
| null | Alain Rocchelli, Jun 04 2025 | 2025-06-11T03:05:14 | oeisdata/seq/A384/A384618.seq | 1c283e4a672ce1d219fe6791becd2d99 |
A384619 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of (B(x)/x)^k, where B(x) is the g.f. of A213591. | [
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"2",
"4",
"0",
"1",
"3",
"9",
"24",
"0",
"1",
"4",
"15",
"56",
"178",
"0",
"1",
"5",
"22",
"97",
"420",
"1512",
"0",
"1",
"6",
"30",
"148",
"738",
"3572",
"14152",
"0",
"1",
"7",
"39",
"210",
"1145",
"6300",
"33328",
"142705",
"0",
"1",
"8",
"49",
"284",
"1655",
"9832",
"58702",
"334354",
"1528212",
"0",
"1",
"9",
"60",
"371",
"2283",
"14321",
"91640",
"586635",
"3559310",
"17211564",
"0"
]
| [
"nonn",
"tabl"
]
| 12 | 0 | 8 | [
"A000007",
"A213591",
"A379599",
"A384619",
"A384620",
"A384621",
"A384623"
]
| null | Seiichi Manyama, Jun 04 2025 | 2025-06-05T09:55:37 | oeisdata/seq/A384/A384619.seq | 16f449a48955c08afe8d96ef70d70a9b |
A384620 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of (B(x)/x)^k, where B(x) is the g.f. of A213639. | [
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"2",
"5",
"0",
"1",
"3",
"11",
"38",
"0",
"1",
"4",
"18",
"86",
"357",
"0",
"1",
"5",
"26",
"145",
"815",
"3832",
"0",
"1",
"6",
"35",
"216",
"1389",
"8758",
"45189",
"0",
"1",
"7",
"45",
"300",
"2095",
"14967",
"103056",
"572378",
"0",
"1",
"8",
"56",
"398",
"2950",
"22668",
"175937",
"1300586",
"7676653",
"0",
"1",
"9",
"68",
"511",
"3972",
"32091",
"266470",
"2214012",
"17368633",
"107971691",
"0"
]
| [
"nonn",
"tabl"
]
| 11 | 0 | 8 | [
"A000007",
"A213639",
"A379599",
"A384619",
"A384620",
"A384621",
"A384623"
]
| null | Seiichi Manyama, Jun 05 2025 | 2025-06-05T09:55:30 | oeisdata/seq/A384/A384620.seq | 6914c1016d9ba9997db5831de7495007 |
A384621 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of (B(x)/x)^k, where B(x) is the g.f. of A376176. | [
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"2",
"6",
"0",
"1",
"3",
"13",
"55",
"0",
"1",
"4",
"21",
"122",
"622",
"0",
"1",
"5",
"30",
"202",
"1390",
"8015",
"0",
"1",
"6",
"40",
"296",
"2322",
"17934",
"113164",
"0",
"1",
"7",
"51",
"405",
"3437",
"30030",
"252847",
"1711898",
"0",
"1",
"8",
"63",
"530",
"4755",
"44600",
"423111",
"3814724",
"27357970",
"0",
"1",
"9",
"76",
"672",
"6297",
"61966",
"628454",
"6369930",
"60766238",
"457507917",
"0"
]
| [
"nonn",
"tabl"
]
| 11 | 0 | 8 | [
"A000007",
"A376176",
"A379599",
"A384619",
"A384620",
"A384621",
"A384623"
]
| null | Seiichi Manyama, Jun 05 2025 | 2025-06-05T09:55:26 | oeisdata/seq/A384/A384621.seq | f335c11e1fd42368ce866582da680e76 |
A384622 | G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x) * A(x*A(x))^5 ). | [
"1",
"1",
"7",
"75",
"989",
"14822",
"242833",
"4253818",
"78573475",
"1516124048",
"30358711661",
"627789264431",
"13357722853019",
"291611321803145",
"6517101781199460",
"148833150175812360",
"3468184751644757228",
"82363850033966966043",
"1991430772785525516280",
"48980124394583747435367"
]
| [
"nonn"
]
| 10 | 0 | 3 | [
"A088714",
"A213591",
"A213639",
"A376176",
"A384622",
"A384623"
]
| null | Seiichi Manyama, Jun 05 2025 | 2025-06-05T04:50:29 | oeisdata/seq/A384/A384622.seq | 459862da81b56c27af3d87ef085ecf27 |
A384623 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A384622. | [
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"2",
"7",
"0",
"1",
"3",
"15",
"75",
"0",
"1",
"4",
"24",
"164",
"989",
"0",
"1",
"5",
"34",
"268",
"2177",
"14822",
"0",
"1",
"6",
"45",
"388",
"3585",
"32672",
"242833",
"0",
"1",
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"57",
"525",
"5235",
"53922",
"534781",
"4253818",
"0",
"1",
"8",
"70",
"680",
"7150",
"78972",
"882304",
"9349160",
"78573475",
"0",
"1",
"9",
"84",
"854",
"9354",
"108251",
"1292456",
"15399930",
"172255669",
"1516124048",
"0"
]
| [
"nonn",
"tabl"
]
| 10 | 0 | 8 | [
"A000007",
"A379599",
"A384619",
"A384620",
"A384621",
"A384622",
"A384623"
]
| null | Seiichi Manyama, Jun 05 2025 | 2025-06-05T09:55:23 | oeisdata/seq/A384/A384623.seq | 1a2fd76d6b8089ed3f531d50fa251c5f |
A384624 | Decimal expansion of the volume of a pentagonal orthobicupola with unit edge. | [
"4",
"6",
"4",
"8",
"0",
"9",
"0",
"6",
"3",
"6",
"6",
"6",
"6",
"3",
"8",
"6",
"2",
"6",
"1",
"8",
"7",
"8",
"8",
"9",
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"2",
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"4",
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"0",
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"4",
"8",
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"9",
"6",
"5",
"6",
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"4",
"5",
"2",
"9",
"6",
"6",
"0",
"5",
"4",
"7",
"3",
"6",
"1",
"2",
"3",
"4",
"1",
"8",
"3",
"7",
"3",
"9",
"8",
"6",
"5",
"8",
"8",
"5",
"8",
"8",
"5",
"8",
"7"
]
| [
"nonn",
"cons",
"easy"
]
| 10 | 1 | 1 | [
"A010532",
"A384287",
"A384624",
"A384625"
]
| null | Paolo Xausa, Jun 05 2025 | 2025-06-09T10:37:45 | oeisdata/seq/A384/A384624.seq | 049b54b73d964a75b2c86e759da65698 |
A384625 | Decimal expansion of the surface area of a pentagonal orthobicupola with unit edge. | [
"1",
"7",
"7",
"7",
"1",
"0",
"8",
"1",
"8",
"2",
"0",
"1",
"0",
"0",
"1",
"2",
"7",
"0",
"7",
"9",
"3",
"3",
"6",
"6",
"3",
"9",
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"0",
"8",
"5",
"4",
"1",
"9",
"0",
"0",
"1",
"1",
"6",
"1",
"7",
"1",
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"6",
"1",
"4",
"7",
"4",
"5",
"4",
"6",
"3",
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"8",
"2",
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"3",
"7",
"0",
"6",
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"6",
"2",
"6",
"7",
"7",
"5",
"7",
"0",
"5",
"2",
"6",
"6",
"8",
"9",
"9",
"3",
"2",
"5",
"5",
"5",
"3",
"6",
"7",
"7",
"4",
"7",
"9"
]
| [
"nonn",
"cons",
"easy"
]
| 13 | 2 | 2 | [
"A002163",
"A384284",
"A384286",
"A384624",
"A384625",
"A384872"
]
| null | Paolo Xausa, Jun 05 2025 | 2025-06-12T12:59:31 | oeisdata/seq/A384/A384625.seq | d6d05765ce2a80bf56af60962df3868b |
A384626 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A143426. | [
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"2",
"2",
"0",
"1",
"3",
"5",
"7",
"0",
"1",
"4",
"9",
"18",
"32",
"0",
"1",
"5",
"14",
"34",
"82",
"175",
"0",
"1",
"6",
"20",
"56",
"156",
"442",
"1086",
"0",
"1",
"7",
"27",
"85",
"261",
"834",
"2699",
"7429",
"0",
"1",
"8",
"35",
"122",
"405",
"1392",
"5027",
"18178",
"54994",
"0",
"1",
"9",
"44",
"168",
"597",
"2166",
"8310",
"33387",
"132664",
"435120",
"0"
]
| [
"nonn",
"tabl"
]
| 10 | 0 | 8 | [
"A000007",
"A143426",
"A384626"
]
| null | Seiichi Manyama, Jun 05 2025 | 2025-06-05T09:52:15 | oeisdata/seq/A384/A384626.seq | 5a99e3a414a122884e04c321084b8e39 |
A384627 | Decimal expansion of 1/998001. | [
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"2",
"0",
"0",
"3",
"0",
"0",
"4",
"0",
"0",
"5",
"0",
"0",
"6",
"0",
"0",
"7",
"0",
"0",
"8",
"0",
"0",
"9",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"2",
"0",
"1",
"3",
"0",
"1",
"4",
"0",
"1",
"5",
"0",
"1",
"6",
"0",
"1",
"7",
"0",
"1",
"8",
"0",
"1",
"9",
"0",
"2",
"0",
"0",
"2",
"1",
"0",
"2",
"2",
"0",
"2",
"3",
"0",
"2",
"4",
"0",
"2",
"5",
"0",
"2",
"6",
"0",
"2",
"7",
"0",
"2",
"8",
"0",
"2",
"9"
]
| [
"nonn",
"cons",
"easy"
]
| 10 | 0 | 9 | [
"A021085",
"A034948",
"A384627"
]
| null | Paolo Xausa, Jun 05 2025 | 2025-06-05T09:52:26 | oeisdata/seq/A384/A384627.seq | 8ea9939ea2883d8cb0277cd4ec84193b |
A384628 | a(n) = Sum_{k = 1..n} gcd(n, floor(n / k)). | [
"1",
"3",
"5",
"8",
"9",
"14",
"13",
"20",
"19",
"25",
"21",
"35",
"25",
"37",
"37",
"44",
"33",
"56",
"37",
"60",
"51",
"58",
"45",
"84",
"53",
"71",
"69",
"85",
"57",
"103",
"61",
"99",
"83",
"93",
"83",
"130",
"73",
"104",
"101",
"136",
"81",
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"85",
"140",
"129",
"124",
"93",
"188",
"103",
"155",
"131",
"163",
"105",
"191",
"127",
"185",
"145",
"159",
"117",
"251",
"121"
]
| [
"nonn"
]
| 35 | 1 | 2 | [
"A000040",
"A000203",
"A005408",
"A018804",
"A384628"
]
| null | Ctibor O. Zizka, Jun 05 2025 | 2025-06-17T13:59:30 | oeisdata/seq/A384/A384628.seq | 0cb03855be1df4de821e49e59186e515 |
A384629 | Maximum number of steps that an n-instruction Turing machine (allowing any number of states and symbols) can take on an initially blank tape before eventually halting. | [
"0",
"1",
"3",
"5",
"16",
"37"
]
| [
"hard",
"more",
"nonn"
]
| 16 | 0 | 3 | [
"A060843",
"A384629"
]
| null | Brian Galebach, Jun 05 2025 | 2025-06-09T00:27:53 | oeisdata/seq/A384/A384629.seq | 286c136f0d47e2e0b1ca7b05ba1e3483 |
A384630 | Number of self-inverse double cosets in Z_n\S_n/Z_n. | [
"1",
"1",
"2",
"3",
"6",
"14",
"34",
"98",
"294",
"952",
"3246",
"11698",
"43732",
"170752",
"689996",
"2888034",
"12458784",
"55406422",
"253142182",
"1187934740",
"5712033368",
"28131119956",
"141645386202",
"728841303696",
"3827217750492",
"20499431084644",
"111876916526070",
"621831335167486",
"3516904353610572"
]
| [
"nonn"
]
| 13 | 1 | 3 | [
"A000142",
"A002619",
"A384630",
"A384631"
]
| null | Ludovic Schwob, Jun 05 2025 | 2025-06-17T19:28:37 | oeisdata/seq/A384/A384630.seq | 53b203e55da56641efc119f8d60c297d |
A384631 | Number of self-inverse double cosets in D_n\S_n/D_n. | [
"1",
"2",
"4",
"8",
"17",
"52",
"153",
"482",
"1623",
"5879",
"21926",
"85436",
"344998",
"1444437",
"6230232",
"27704051",
"126571091",
"593974930",
"2856031804",
"14065575098",
"70822693101",
"364420818168",
"1913609207886",
"10249715874962",
"55938458263035",
"310915671908063",
"1758452185453926",
"10115287840489764"
]
| [
"nonn"
]
| 15 | 3 | 2 | [
"A000940",
"A001710",
"A384630",
"A384631"
]
| null | Ludovic Schwob, Jun 05 2025 | 2025-06-22T19:35:43 | oeisdata/seq/A384/A384631.seq | 2a03a614f4fb767714a8e51b3a0d765b |
A384632 | a(0)=0. For each digit d in the sequence, let a(n) equal the smallest unused integer which has at least d divisors. | [
"0",
"1",
"2",
"3",
"4",
"6",
"12",
"5",
"7",
"16",
"24",
"8",
"18",
"9",
"10",
"30",
"11",
"36",
"48",
"13",
"14",
"15",
"17",
"19",
"20",
"21",
"28",
"22",
"40",
"23",
"25",
"26",
"27",
"29",
"32",
"31",
"42",
"33",
"60",
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"35",
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"38",
"39",
"54",
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"43",
"44",
"45",
"46",
"49",
"47",
"50",
"51",
"52",
"53",
"56",
"55",
"72",
"57",
"58",
"62",
"59",
"63",
"61",
"64",
"65"
]
| [
"nonn",
"base"
]
| 13 | 0 | 3 | [
"A000005",
"A362371",
"A362551",
"A384632"
]
| null | Gavin Lupo, Jun 05 2025 | 2025-06-17T18:00:47 | oeisdata/seq/A384/A384632.seq | f55e6c479fb72ee456c3abacb925b72f |
A384633 | Expansion of (1+x-2*x^2-2*x^3) / (1-6*x^2-4*x^3+2*x^4). | [
"1",
"1",
"4",
"8",
"26",
"62",
"180",
"460",
"1276",
"3356",
"9136",
"24320",
"65688",
"175752",
"473136",
"1268624",
"3410448",
"9152784",
"24590912",
"66021248",
"177335712",
"476185568",
"1278917440",
"3434413760",
"9223575488",
"24769781184",
"66521273088",
"178644161536",
"479759612288",
"1288410499200"
]
| [
"nonn",
"easy",
"walk",
"changed"
]
| 8 | 0 | 3 | [
"A005824",
"A105476",
"A384633",
"A384634",
"A384635"
]
| null | Sean A. Irvine, Jun 05 2025 | 2025-07-08T11:48:04 | oeisdata/seq/A384/A384633.seq | cd4545d5827ba60e25379e94608506d6 |
A384634 | Expansion of (1+2*x+x^2) / (1-6*x^2-4*x^3+2*x^4). | [
"1",
"2",
"7",
"16",
"48",
"120",
"338",
"880",
"2412",
"6392",
"17316",
"46240",
"124640",
"333920",
"898168",
"2409600",
"6475408",
"17382432",
"46694512",
"125377024",
"336745984",
"904275328",
"2428594976",
"6521881856",
"17515179200",
"47037120384",
"126321412672",
"339239675392",
"911046599168",
"2446649462272"
]
| [
"nonn",
"easy",
"walk",
"changed"
]
| 7 | 0 | 2 | [
"A005824",
"A105476",
"A384633",
"A384634",
"A384635"
]
| null | Sean A. Irvine, Jun 05 2025 | 2025-07-08T11:49:43 | oeisdata/seq/A384/A384634.seq | df5baf6a68f236ebf777a3d01119fc41 |
A384635 | Expansion of (1+3*x+2*x^2) / (1-6*x^2-4*x^3+2*x^4). | [
"1",
"3",
"8",
"22",
"58",
"158",
"420",
"1136",
"3036",
"8180",
"21920",
"58952",
"158168",
"425032",
"1140976",
"3064960",
"8229648",
"22103600",
"59355776",
"159410272",
"428089760",
"1149677536",
"3087468096",
"8291603712",
"22267339200",
"59800139584",
"160595513856",
"431286986880",
"1158238963072"
]
| [
"nonn",
"easy",
"walk",
"changed"
]
| 6 | 0 | 2 | [
"A005824",
"A105476",
"A384633",
"A384634",
"A384635"
]
| null | Sean A. Irvine, Jun 05 2025 | 2025-07-08T11:50:39 | oeisdata/seq/A384/A384635.seq | 2e58d33e3bb0bcdbe64f124411e4215b |
A384636 | Triprimes that are the concatenation of three consecutive primes in reverse order. | [
"1175",
"231917",
"434137",
"534743",
"595347",
"10310197",
"107103101",
"137131127",
"149139137",
"163157151",
"167163157",
"179173167",
"223211199",
"239233229",
"251241239",
"269263257",
"281277271",
"293283281",
"311307293",
"349347337",
"383379373",
"401397389",
"419409401",
"421419409",
"449443439",
"457449443",
"487479467",
"491487479"
]
| [
"nonn",
"base"
]
| 13 | 1 | 1 | [
"A014612",
"A383114",
"A384636",
"A384638"
]
| null | Will Gosnell and Robert Israel, Jun 05 2025 | 2025-06-09T11:13:00 | oeisdata/seq/A384/A384636.seq | 323a216a38d5fb14ee2c88e4cdff747f |
A384637 | Consecutive states of the linear congruential pseudo-random number generator 5^13*s mod 2^35 when started at s=1. | [
"1",
"1220703125",
"30903841977",
"6589172397",
"2335288753",
"33236884229",
"14113929449",
"5184031389",
"9287939169",
"11535683445",
"23833284121",
"2547937165",
"6466389009",
"29109403877",
"12213593161",
"31057406333",
"2513210561",
"12977872725",
"17811893113",
"2710136941",
"28076457585"
]
| [
"nonn",
"easy"
]
| 20 | 1 | 2 | [
"A096550",
"A096561",
"A384637"
]
| null | Sean A. Irvine, Jun 05 2025 | 2025-06-19T20:14:25 | oeisdata/seq/A384/A384637.seq | 3f2398635ad388f322556337c06b1b94 |
A384638 | Primes p such that the concatenations of three consecutive primes starting with p, in both forward and backwards orders, are triprimes. | [
"43",
"47",
"97",
"101",
"151",
"157",
"167",
"199",
"281",
"293",
"487",
"601",
"607",
"809",
"839",
"967",
"1013",
"1069",
"1129",
"1223",
"1249",
"1259",
"1289",
"1361",
"1367",
"1543",
"1571",
"1663",
"1753",
"1861",
"1871",
"1873",
"1997",
"2141",
"2281",
"2551",
"2593",
"2909",
"3121",
"3271",
"3313",
"3361",
"3371",
"3461",
"3823",
"3881",
"3907",
"4019",
"4211",
"4289",
"4327",
"4349",
"4451",
"4513"
]
| [
"nonn",
"base"
]
| 29 | 1 | 1 | [
"A014612",
"A383114",
"A384636",
"A384638"
]
| null | Will Gosnell and Robert Israel, Jun 05 2025 | 2025-06-20T15:41:36 | oeisdata/seq/A384/A384638.seq | 47ffdad9585c6cdc52562f551349afe0 |
A384640 | Expansion of (1-3*x^2) / (1-x-5*x^2+x^3+2*x^4). | [
"1",
"1",
"3",
"7",
"19",
"49",
"131",
"343",
"911",
"2397",
"6347",
"16735",
"44251",
"116785",
"308611",
"814815",
"2152583",
"5684477",
"15015355",
"39655527",
"104742659",
"276635985",
"730663043",
"1929789255",
"5096983167",
"13461994429",
"35555794923",
"93909205391",
"248032219243",
"655098462417",
"1730238763395"
]
| [
"nonn",
"easy",
"walk",
"changed"
]
| 7 | 0 | 3 | [
"A005824",
"A026597",
"A384640",
"A384641",
"A384642"
]
| null | Sean A. Irvine, Jun 05 2025 | 2025-07-08T11:52:09 | oeisdata/seq/A384/A384640.seq | 6909e846e0853c6583bdafac2fb77171 |
A384641 | Expansion of (1+2*x-x^3) / (1-x-5*x^2+x^3+2*x^4). | [
"1",
"3",
"8",
"21",
"56",
"147",
"390",
"1027",
"2718",
"7169",
"18952",
"50025",
"132180",
"349015",
"921986",
"2434831",
"6431386",
"16985525",
"44863652",
"118490229",
"312960192",
"826576635",
"2183160062",
"5766102587",
"15229405878",
"40223605481",
"106238212160",
"280594628513",
"741103272076",
"1957390991519"
]
| [
"nonn",
"easy",
"walk",
"changed"
]
| 6 | 0 | 2 | [
"A005824",
"A026597",
"A384640",
"A384641",
"A384642"
]
| null | Sean A. Irvine, Jun 05 2025 | 2025-07-08T11:54:18 | oeisdata/seq/A384/A384641.seq | 4e36563b56636150427a9ed0c4733570 |
A384642 | Expansion of (1+x-x^2+x^3) / (1-x-5*x^2+x^3+2*x^4). | [
"1",
"2",
"6",
"16",
"42",
"112",
"294",
"780",
"2054",
"5436",
"14338",
"37904",
"100050",
"264360",
"698030",
"1843972",
"4869662",
"12862772",
"33971050",
"89727304",
"236980458",
"625920384",
"1653153270",
"4366320124",
"11532205174",
"30458811756",
"80447210962",
"212476424320",
"561189257026",
"1482206544152"
]
| [
"nonn",
"easy",
"walk",
"changed"
]
| 6 | 0 | 2 | [
"A005824",
"A026597",
"A384640",
"A384641",
"A384642"
]
| null | Sean A. Irvine, Jun 05 2025 | 2025-07-08T11:55:01 | oeisdata/seq/A384/A384642.seq | acdcef094586784ae9b01aadeb2bceff |
A384643 | Consecutive states of the linear congruential pseudo-random number generator for Simula on the UNIVAC when started at 1. | [
"1",
"30517578125",
"4728272809",
"14042552597",
"5475208593",
"22652899805",
"14780701625",
"12079957477",
"33211157537",
"21459834669",
"11626649801",
"22641538997",
"32099503025",
"31057406333",
"28470525657",
"2272198277",
"31308848193",
"23703460045",
"6636903913",
"5151124053",
"2502905297"
]
| [
"nonn",
"easy"
]
| 9 | 1 | 2 | [
"A096550",
"A096561",
"A384643"
]
| null | Sean A. Irvine, Jun 05 2025 | 2025-06-12T05:59:56 | oeisdata/seq/A384/A384643.seq | 4b6458ddf8dac960334dfacd43c5d479 |
A384644 | a(n) is the least k such that {A007504(1), A007504(2), ..., A007504(k)} mod n = {0,...,n-1}. | [
"1",
"2",
"10",
"20",
"10",
"57",
"18",
"24",
"20",
"35",
"25",
"97",
"49",
"27",
"67",
"43",
"115",
"113",
"60",
"62",
"97",
"50",
"107",
"187",
"98",
"92",
"72",
"94",
"66",
"230",
"125",
"132",
"191",
"130",
"180",
"168",
"91",
"113",
"142",
"199",
"157",
"305",
"184",
"224",
"242",
"229",
"119",
"297",
"200",
"292",
"179",
"133",
"198",
"341",
"357",
"286",
"324",
"329"
]
| [
"nonn"
]
| 14 | 1 | 2 | [
"A007504",
"A384644"
]
| null | Charles L. Hohn, Jun 05 2025 | 2025-06-12T19:27:32 | oeisdata/seq/A384/A384644.seq | a523fb617b2bd0342b4d6dd8a62aa392 |
A384645 | Consecutive states of the linear congruential pseudo-random number generator HSRPUN when started at 1. | [
"1",
"3418906842",
"8274876767",
"11636484000",
"6772886125",
"17960856150",
"33658810027",
"33635241596",
"6134001049",
"12062168466",
"17176042167",
"27491204376",
"18560177541",
"31970401934",
"4441762179",
"1351356276",
"30265814577",
"5092081994",
"21499143951",
"17730019728",
"16438010781"
]
| [
"nonn",
"easy"
]
| 11 | 1 | 2 | [
"A384643",
"A384645"
]
| null | Sean A. Irvine, Jun 05 2025 | 2025-06-12T12:59:42 | oeisdata/seq/A384/A384645.seq | d6293ad76c084a52c097394036262076 |
A384646 | Expansion of (1+x) / (1-x-5*x^2-2*x^3). | [
"1",
"2",
"7",
"19",
"58",
"167",
"495",
"1446",
"4255",
"12475",
"36642",
"107527",
"315687",
"926606",
"2720095",
"7984499",
"23438186",
"68800871",
"201960799",
"592841526",
"1740247263",
"5108376491",
"14995295858",
"44017672839",
"129210905111",
"379289861022",
"1113379732255",
"3268250847587",
"9593729230906"
]
| [
"nonn",
"easy",
"walk",
"changed"
]
| 10 | 0 | 2 | [
"A077937",
"A384646",
"A384647",
"A384648"
]
| null | Sean A. Irvine, Jun 05 2025 | 2025-07-08T11:56:10 | oeisdata/seq/A384/A384646.seq | 0d4e4bee31fe54097d8e5fed1eda7d80 |
A384647 | Expansion of (1+3*x+x^2) / (1-x-5*x^2-2*x^3). | [
"1",
"4",
"10",
"32",
"90",
"270",
"784",
"2314",
"6774",
"19912",
"58410",
"171518",
"503392",
"1477802",
"4337798",
"12733592",
"37378186",
"109721742",
"322079856",
"945444938",
"2775287702",
"8146672104",
"23914000490",
"70197936414",
"206061283072",
"604878966122",
"1775581254310",
"5212098651064"
]
| [
"nonn",
"easy",
"walk",
"changed"
]
| 6 | 0 | 2 | [
"A077937",
"A384646",
"A384647",
"A384648"
]
| null | Sean A. Irvine, Jun 05 2025 | 2025-07-08T11:57:04 | oeisdata/seq/A384/A384647.seq | 7aa2ca27528a6ecc7ea64114438a9eda |
A384648 | Expansion of (1+2*x+x^2) / (1-x-5*x^2-2*x^3). | [
"1",
"3",
"9",
"26",
"77",
"225",
"662",
"1941",
"5701",
"16730",
"49117",
"144169",
"423214",
"1242293",
"3646701",
"10704594",
"31422685",
"92239057",
"270761670",
"794802325",
"2333088789",
"6848623754",
"20103672349",
"59012968697",
"173228577950",
"508500766133",
"1492669593277",
"4381630579842"
]
| [
"nonn",
"easy",
"walk",
"changed"
]
| 7 | 0 | 2 | [
"A077937",
"A384646",
"A384647",
"A384648"
]
| null | Sean A. Irvine, Jun 05 2025 | 2025-07-08T11:57:59 | oeisdata/seq/A384/A384648.seq | cd04fdf5e19817a657e1835f7cf36f78 |
A384649 | G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x*A(x)^4) ). | [
"1",
"1",
"2",
"9",
"56",
"432",
"3935",
"40820",
"471633",
"5980210",
"82329140",
"1220547845",
"19359684220",
"326799737576",
"5844913732057",
"110341722975077",
"2191461358459051",
"45656013573862832",
"995196646595460516",
"22644288881875546322",
"536706817952488705651",
"13225669497771610891404"
]
| [
"nonn"
]
| 9 | 0 | 3 | [
"A110447",
"A162661",
"A384145",
"A384649",
"A384650",
"A384653"
]
| null | Seiichi Manyama, Jun 06 2025 | 2025-06-06T08:35:57 | oeisdata/seq/A384/A384649.seq | 7f64cfb15a93f0f3915d6493a0cab19e |
A384650 | G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x*A(x)^5) ). | [
"1",
"1",
"2",
"10",
"69",
"592",
"6052",
"70870",
"928497",
"13404514",
"210892157",
"3584892350",
"65390514877",
"1272723903336",
"26307949481077",
"575201364472316",
"13255835789428863",
"320999903683710948",
"8145524458876305526",
"216062918679078474529",
"5977572987203090333399"
]
| [
"nonn"
]
| 10 | 0 | 3 | [
"A110447",
"A162661",
"A384145",
"A384649",
"A384650",
"A384654"
]
| null | Seiichi Manyama, Jun 06 2025 | 2025-06-06T08:35:53 | oeisdata/seq/A384/A384650.seq | 14a739c8c6f5ce665befd896d4239f43 |
A384651 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A162661. | [
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"2",
"2",
"0",
"1",
"3",
"5",
"7",
"0",
"1",
"4",
"9",
"18",
"33",
"0",
"1",
"5",
"14",
"34",
"84",
"189",
"0",
"1",
"6",
"20",
"56",
"159",
"472",
"1249",
"0",
"1",
"7",
"27",
"85",
"265",
"882",
"3057",
"9237",
"0",
"1",
"8",
"35",
"122",
"410",
"1460",
"5615",
"22190",
"74972",
"0",
"1",
"9",
"44",
"168",
"603",
"2256",
"9166",
"40053",
"177149",
"659042",
"0"
]
| [
"nonn",
"tabl"
]
| 11 | 0 | 8 | [
"A000007",
"A162661",
"A379598",
"A384651",
"A384652",
"A384653",
"A384654"
]
| null | Seiichi Manyama, Jun 06 2025 | 2025-06-06T08:35:41 | oeisdata/seq/A384/A384651.seq | 87b7caeeaad5292617dfc3a8bb8e4b31 |
A384652 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A384145. | [
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"2",
"2",
"0",
"1",
"3",
"5",
"8",
"0",
"1",
"4",
"9",
"20",
"44",
"0",
"1",
"5",
"14",
"37",
"108",
"298",
"0",
"1",
"6",
"20",
"60",
"198",
"716",
"2359",
"0",
"1",
"7",
"27",
"90",
"321",
"1290",
"5554",
"21112",
"0",
"1",
"8",
"35",
"128",
"485",
"2064",
"9821",
"48838",
"209175",
"0",
"1",
"9",
"44",
"175",
"699",
"3091",
"15452",
"84888",
"476714",
"2262121",
"0"
]
| [
"nonn",
"tabl"
]
| 11 | 0 | 8 | [
"A000007",
"A379598",
"A384145",
"A384651",
"A384652",
"A384653",
"A384654"
]
| null | Seiichi Manyama, Jun 06 2025 | 2025-06-06T08:35:45 | oeisdata/seq/A384/A384652.seq | 5b933cfb4fb6a8c030c781694be9c557 |
A384653 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A384649. | [
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"2",
"2",
"0",
"1",
"3",
"5",
"9",
"0",
"1",
"4",
"9",
"22",
"56",
"0",
"1",
"5",
"14",
"40",
"134",
"432",
"0",
"1",
"6",
"20",
"64",
"240",
"1012",
"3935",
"0",
"1",
"7",
"27",
"95",
"381",
"1779",
"9039",
"40820",
"0",
"1",
"8",
"35",
"134",
"565",
"2780",
"15596",
"92246",
"471633",
"0",
"1",
"9",
"44",
"182",
"801",
"4071",
"23950",
"156597",
"1051558",
"5980210",
"0"
]
| [
"nonn",
"tabl"
]
| 11 | 0 | 8 | [
"A000007",
"A379598",
"A384649",
"A384651",
"A384652",
"A384653",
"A384654"
]
| null | Seiichi Manyama, Jun 06 2025 | 2025-06-06T08:35:48 | oeisdata/seq/A384/A384653.seq | bc343b3cffff4bb274944d50d70802f5 |
A384654 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A384650. | [
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"2",
"2",
"0",
"1",
"3",
"5",
"10",
"0",
"1",
"4",
"9",
"24",
"69",
"0",
"1",
"5",
"14",
"43",
"162",
"592",
"0",
"1",
"6",
"20",
"68",
"285",
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"1",
"7",
"27",
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"2352",
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"70870",
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"8",
"35",
"140",
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"23171",
"157592",
"928497",
"0",
"1",
"9",
"44",
"189",
"909",
"5201",
"34972",
"263190",
"2039543",
"13404514",
"0"
]
| [
"nonn",
"tabl"
]
| 12 | 0 | 8 | [
"A000007",
"A379598",
"A384650",
"A384651",
"A384652",
"A384653",
"A384654"
]
| null | Seiichi Manyama, Jun 06 2025 | 2025-06-06T08:35:37 | oeisdata/seq/A384/A384654.seq | 428e773d244b119b1209f864a0668081 |
A384655 | a(n) = Sum_{k=1..n} A051903(gcd(n,k)). | [
"0",
"1",
"1",
"3",
"1",
"4",
"1",
"7",
"4",
"6",
"1",
"11",
"1",
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"63",
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"46",
"1",
"53",
"25",
"46",
"1",
"81",
"1",
"38"
]
| [
"nonn"
]
| 8 | 1 | 4 | [
"A000010",
"A005117",
"A033150",
"A050873",
"A051903",
"A051953",
"A063659",
"A067259",
"A254926",
"A357310",
"A383156",
"A384655",
"A384656"
]
| null | Amiram Eldar, Jun 06 2025 | 2025-06-07T08:18:30 | oeisdata/seq/A384/A384655.seq | 58bd7abc4f7e1bf26fee055ea0cc0da5 |
A384656 | a(n) = Sum_{k=1..n} A051903(ugcd(n,k)), where ugcd(n,k) is the greatest divisor of k that is a unitary divisor of n. | [
"0",
"1",
"1",
"2",
"1",
"4",
"1",
"3",
"2",
"6",
"1",
"9",
"1",
"8",
"7",
"4",
"1",
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"1",
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"1",
"37",
"25",
"46",
"1",
"41",
"1",
"38",
"30"
]
| [
"nonn"
]
| 8 | 1 | 4 | [
"A000961",
"A002110",
"A005117",
"A047994",
"A051953",
"A088860",
"A097250",
"A383159",
"A384046",
"A384048",
"A384049",
"A384655",
"A384656"
]
| null | Amiram Eldar, Jun 06 2025 | 2025-06-07T08:18:42 | oeisdata/seq/A384/A384656.seq | a74af3839340148d9783c19abc0df412 |
A384657 | Numbers k such that A384655(k) > k. | [
"24",
"48",
"72",
"80",
"96",
"108",
"112",
"120",
"144",
"160",
"168",
"180",
"192",
"200",
"216",
"224",
"240",
"252",
"264",
"280",
"288",
"300",
"312",
"320",
"324",
"336",
"352",
"360",
"384",
"396",
"400",
"408",
"416",
"420",
"432",
"440",
"448",
"456",
"468",
"480",
"504",
"520",
"528",
"540",
"552",
"560",
"576",
"600",
"612",
"624",
"640",
"648",
"660",
"672",
"684",
"696"
]
| [
"nonn"
]
| 8 | 1 | 1 | [
"A005117",
"A013929",
"A051953",
"A384655",
"A384657",
"A384658"
]
| null | Amiram Eldar, Jun 06 2025 | 2025-06-07T08:18:47 | oeisdata/seq/A384/A384657.seq | 1f6db9aabc3609751254560d70c73647 |
A384658 | Primitive terms in A384657: numbers k such that A384655(k) > k and A384655(d) <= d for every proper divisor d of k. | [
"24",
"80",
"108",
"112",
"180",
"200",
"252",
"280",
"300",
"352",
"396",
"416",
"420",
"440",
"468",
"520",
"612",
"660",
"684",
"780",
"828",
"1044",
"1088",
"1116",
"1216",
"1332",
"1472",
"1476",
"1548",
"1692",
"1856",
"1908",
"1984",
"2124",
"2196",
"2288",
"2412",
"2556",
"2628",
"2844",
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"2992",
"3204",
"3344",
"3492",
"3536",
"3636",
"3708",
"3852",
"3924",
"3952"
]
| [
"nonn"
]
| 7 | 1 | 1 | [
"A013929",
"A384655",
"A384657",
"A384658"
]
| null | Amiram Eldar, Jun 06 2025 | 2025-06-07T08:18:53 | oeisdata/seq/A384/A384658.seq | 0903cb1a696b805904d6c0c46971433c |
A384659 | Numbers k such that A384655(k)/k > A384655(m)/m for all m < k. | [
"1",
"2",
"4",
"8",
"12",
"16",
"24",
"48",
"72",
"96",
"144",
"288",
"432",
"576",
"720",
"1440",
"2160",
"2880",
"4320",
"8640",
"17280",
"21600",
"25920",
"30240",
"43200",
"60480",
"120960",
"151200",
"181440",
"241920",
"302400",
"604800",
"907200",
"1209600",
"1814400",
"3326400",
"3628800",
"5443200",
"6350400",
"6652800",
"9979200"
]
| [
"nonn"
]
| 7 | 1 | 2 | [
"A013929",
"A025487",
"A033150",
"A384655",
"A384659"
]
| null | Amiram Eldar, Jun 06 2025 | 2025-06-07T08:18:58 | oeisdata/seq/A384/A384659.seq | 7ca8df30b882a12ec9aa499959a40b70 |
A384660 | a(1) = 1. Thereafter a(n) = a(a(n-1)) if a(n-1) is a novel term, or n - S(n) if a(n-1) is a repeat term. S(n) is the sum of distinct terms in multiset {a(1),a(2),..a(n-1)}. | [
"1",
"1",
"2",
"1",
"2",
"3",
"2",
"2",
"3",
"4",
"1",
"2",
"3",
"4",
"5",
"2",
"2",
"3",
"4",
"5",
"6",
"3",
"2",
"3",
"4",
"5",
"6",
"7",
"2",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"2",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"3",
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"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"4",
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"4",
"5",
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"8",
"9",
"10",
"11",
"1",
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"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"2",
"2",
"3",
"4",
"5",
"6",
"7"
]
| [
"nonn",
"easy"
]
| 12 | 1 | 3 | [
"A002260",
"A384660"
]
| null | David James Sycamore, Jun 06 2025 | 2025-06-07T08:22:27 | oeisdata/seq/A384/A384660.seq | 387a0ef9375a55c86200aa6cbf4c670e |
A384661 | Solution of the complementary equation b(n)=a(a(n))+a(n)+2 with a(1)=1; this is the sequence a(n). | [
"1",
"2",
"3",
"5",
"7",
"9",
"10",
"11",
"12",
"13",
"15",
"16",
"17",
"18",
"20",
"21",
"22",
"24",
"26",
"27",
"29",
"31",
"33",
"34",
"35",
"36",
"38",
"40",
"42",
"43",
"45",
"46",
"47",
"48",
"50",
"51",
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"54",
"56",
"57",
"58",
"59",
"61",
"62",
"63",
"65",
"66",
"68",
"69",
"70",
"71",
"72",
"74",
"75",
"76",
"77",
"79",
"80",
"81",
"83",
"85",
"86",
"88",
"90",
"91",
"92"
]
| [
"nonn"
]
| 8 | 1 | 2 | [
"A136497",
"A136499",
"A136500",
"A384661",
"A384662",
"A384663",
"A384664"
]
| null | Clark Kimberling, Jun 06 2025 | 2025-06-16T00:00:14 | oeisdata/seq/A384/A384661.seq | f59e32fbb332cb44daaafd9ffab275e6 |
A384662 | Solution of the complementary equation b(n)=a(a(n))+a(n)+2 with a(1)=1; this is the sequence b. | [
"4",
"6",
"8",
"14",
"19",
"23",
"25",
"28",
"30",
"32",
"37",
"39",
"41",
"44",
"49",
"52",
"55",
"60",
"64",
"67",
"73",
"78",
"82",
"84",
"87",
"89",
"94",
"99",
"103",
"106",
"110",
"113",
"115",
"118",
"122",
"124",
"129",
"131",
"135",
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"140",
"142",
"148",
"150",
"153",
"158",
"160",
"165",
"167",
"169",
"171",
"174",
"178",
"181",
"183",
"186",
"190",
"193"
]
| [
"nonn"
]
| 7 | 1 | 1 | [
"A136498",
"A136499",
"A136500",
"A384661",
"A384662",
"A384663",
"A384664"
]
| null | Clark Kimberling, Jun 09 2025 | 2025-06-16T00:00:27 | oeisdata/seq/A384/A384662.seq | 756e08cf0aa44f6c9cbf71e678a3fb03 |
A384663 | Solution of the complementary equation b(n)=a(a(n))+a(n)+3 with a(1)=1; this is the sequence a. Sequence b is A384664. | [
"1",
"2",
"3",
"4",
"6",
"8",
"10",
"12",
"13",
"14",
"15",
"16",
"18",
"19",
"20",
"21",
"22",
"24",
"25",
"26",
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"32",
"33",
"35",
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"39",
"41",
"42",
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"80",
"81",
"83",
"84",
"85",
"86",
"87",
"89",
"90",
"91",
"92"
]
| [
"nonn"
]
| 7 | 1 | 2 | [
"A136499",
"A136500",
"A384661",
"A384662",
"A384663",
"A384664"
]
| null | Clark Kimberling, Jun 11 2025 | 2025-06-22T18:24:50 | oeisdata/seq/A384/A384663.seq | d402205bb5519b1c04bbba8e9cc8f53f |
A384664 | Solution of the complementary equation b(n)=a(a(n))+a(n)+3 with a(1)=1; this is the sequence b. Sequence a is A384663. | [
"5",
"7",
"9",
"11",
"17",
"23",
"27",
"31",
"34",
"36",
"38",
"40",
"45",
"47",
"49",
"52",
"54",
"59",
"61",
"64",
"70",
"73",
"75",
"79",
"82",
"88",
"93",
"98",
"102",
"105",
"108",
"110",
"115",
"119",
"124",
"126",
"132",
"136",
"139",
"141",
"144",
"148",
"152",
"155",
"159",
"161",
"164",
"166",
"168",
"173",
"175",
"180",
"185",
"187",
"190",
"195",
"197",
"202"
]
| [
"nonn"
]
| 5 | 1 | 1 | [
"A136499",
"A136500",
"A384661",
"A384662",
"A384663",
"A384664"
]
| null | Clark Kimberling, Jun 16 2025 | 2025-06-22T18:25:07 | oeisdata/seq/A384/A384664.seq | 1e43494dc6ea5c8835189945b9e7534c |
A384665 | Smallest odd multiplier k such that k*n is abundant. | [
"945",
"9",
"315",
"3",
"189",
"3",
"135",
"3",
"105",
"3",
"315",
"1",
"315",
"3",
"63",
"3",
"315",
"1",
"315",
"1",
"45",
"3",
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"1",
"63",
"3",
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"3",
"315",
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"3",
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"3",
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"1",
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"1",
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"3",
"21",
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"1",
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"3",
"105",
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"1",
"63",
"1",
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"3",
"315",
"1",
"315",
"3",
"15",
"3",
"63",
"1",
"315",
"3"
]
| [
"nonn",
"changed"
]
| 25 | 1 | 1 | [
"A005101",
"A005231",
"A023196",
"A254571",
"A384665"
]
| null | Sergio Pimentel, Jun 06 2025 | 2025-07-06T14:57:25 | oeisdata/seq/A384/A384665.seq | 9cbfe719970822415d6e30565ae57948 |
A384666 | Number of distinct values of the quadratic discriminant D=b^2-4*a*c, for a,b,c in the range [-n,n]. | [
"1",
"6",
"17",
"35",
"56",
"90",
"125",
"178",
"223",
"282",
"344",
"436",
"499",
"608",
"701",
"804",
"904",
"1062",
"1164",
"1339",
"1450",
"1604",
"1765",
"1988",
"2114",
"2335",
"2525",
"2735",
"2909",
"3194",
"3366",
"3679",
"3887",
"4137",
"4389",
"4661",
"4840",
"5237",
"5536",
"5835",
"6068",
"6507",
"6759",
"7195",
"7473",
"7773",
"8148",
"8645"
]
| [
"nonn"
]
| 8 | 0 | 2 | [
"A000217",
"A027384",
"A384666"
]
| null | Darío Clavijo, Jun 06 2025 | 2025-06-12T17:05:59 | oeisdata/seq/A384/A384666.seq | 08eeb14f900c20c27b0f42e66a562847 |
A384667 | Characteristic function of powers of squarefree numbers (A072774). | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"1",
"1",
"0",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"1",
"0",
"0",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"1"
]
| [
"nonn"
]
| 21 | 1 | null | [
"A005117",
"A059404",
"A059956",
"A072774",
"A382883",
"A384667"
]
| null | Friedjof Tellkamp, Jun 07 2025 | 2025-06-17T22:48:26 | oeisdata/seq/A384/A384667.seq | 9db3798eae228dfab38215d317a59ee3 |
A384668 | a(n) = 12 * (5*n+2)! / ((3*n+1)! * (2*n+2)!). | [
"12",
"105",
"1584",
"29172",
"596904",
"13037895",
"297748800",
"7023149820",
"169774618104",
"4183919862474",
"104722807600320",
"2654939113240050",
"68033328627480804",
"1759318006963275528",
"45853277234783179392",
"1203249937243079847660",
"31764232607604306053400",
"842982010030680328418706"
]
| [
"nonn"
]
| 13 | 0 | 1 | [
"A000260",
"A001450",
"A002293",
"A384585",
"A384668"
]
| null | Karol A. Penson, Jun 06 2025 | 2025-06-12T10:22:39 | oeisdata/seq/A384/A384668.seq | 281207cb9ddaf79d28d54c6af0c8bd87 |
A384669 | Positive integers setting a new record for the sum of the square roots of the prime exponents. | [
"1",
"2",
"4",
"6",
"12",
"24",
"30",
"60",
"120",
"180",
"210",
"360",
"420",
"840",
"1260",
"1680",
"2520",
"3360",
"4620",
"6720",
"7560",
"9240",
"13860",
"18480",
"27720",
"36960",
"55440",
"73920",
"83160",
"110880",
"120120",
"180180",
"221760",
"240240",
"360360",
"480480",
"720720",
"960960",
"1081080",
"1441440",
"2042040",
"2882880",
"4084080",
"5765760",
"6126120"
]
| [
"nonn",
"changed"
]
| 29 | 1 | 2 | [
"A000079",
"A001221",
"A001222",
"A002110",
"A002182",
"A007814",
"A025487",
"A029744",
"A046523",
"A051903",
"A056169",
"A095848",
"A168264",
"A384669"
]
| null | Hal M. Switkay, Jun 06 2025 | 2025-07-05T00:07:59 | oeisdata/seq/A384/A384669.seq | 1a66b618996cfda0a1e69d70ec6beb17 |
A384670 | Smallest denominator y for which there exists an integer x with round(100*x/y) = n. | [
"1",
"67",
"41",
"29",
"23",
"19",
"16",
"14",
"12",
"11",
"10",
"9",
"17",
"8",
"7",
"13",
"19",
"6",
"11",
"16",
"5",
"14",
"9",
"13",
"17",
"4",
"19",
"11",
"18",
"7",
"10",
"13",
"19",
"3",
"29",
"17",
"11",
"19",
"8",
"18",
"5",
"17",
"12",
"7",
"9",
"11",
"13",
"15",
"21",
"35",
"2",
"35",
"21",
"15",
"13",
"11",
"9",
"7",
"12",
"17",
"5",
"18",
"13",
"8",
"11",
"17",
"29",
"3",
"19",
"13",
"10",
"7",
"18",
"11",
"19",
"4",
"17",
"13",
"9",
"14",
"5",
"16",
"11",
"6",
"19",
"13",
"7",
"15",
"8",
"9",
"10",
"11",
"12",
"14",
"16",
"19",
"23",
"29",
"40",
"67",
"1"
]
| [
"nonn",
"easy"
]
| 20 | 0 | 2 | [
"A239525",
"A384670"
]
| null | James Beazley, Jun 06 2025 | 2025-06-28T20:19:37 | oeisdata/seq/A384/A384670.seq | 40b2eb946b10ce767c177e05664c6f2c |
A384671 | Expansion of (1-x^2) / (1-2*x-5*x^2+2*x^3). | [
"1",
"2",
"8",
"24",
"84",
"272",
"916",
"3024",
"10084",
"33456",
"111284",
"369680",
"1228868",
"4083568",
"13572116",
"45104336",
"149902116",
"498181680",
"1655665268",
"5502434704",
"18286832388",
"60774507760",
"201978308052",
"671255490128",
"2230853504996",
"7414027844528",
"24639812233780"
]
| [
"nonn",
"easy",
"walk"
]
| 7 | 0 | 2 | [
"A384646",
"A384671",
"A384672",
"A384673"
]
| null | Sean A. Irvine, Jun 05 2025 | 2025-06-07T09:02:17 | oeisdata/seq/A384/A384671.seq | 093b2b22a837f28fc20cbd0aa2661572 |
A384672 | Expansion of (1+2*x-x^2) / (1-2*x-5*x^2+2*x^3). | [
"1",
"4",
"12",
"42",
"136",
"458",
"1512",
"5042",
"16728",
"55642",
"184840",
"614434",
"2041784",
"6786058",
"22552168",
"74951058",
"249090840",
"827832634",
"2751217352",
"9143416194",
"30387253880",
"100989154026",
"335627745064",
"1115426752498",
"3707013922264",
"12319906116890",
"40944028340104"
]
| [
"nonn",
"easy",
"walk"
]
| 6 | 0 | 2 | [
"A384646",
"A384671",
"A384672",
"A384673"
]
| null | Sean A. Irvine, Jun 05 2025 | 2025-06-07T00:12:20 | oeisdata/seq/A384/A384672.seq | 262e736f564140848c816d9254f2a55b |
A384673 | Expansion of (1+x) / (1-2*x-5*x^2+2*x^3). | [
"1",
"3",
"11",
"35",
"119",
"391",
"1307",
"4331",
"14415",
"47871",
"159155",
"528835",
"1757703",
"5841271",
"19413387",
"64517723",
"214419839",
"712601519",
"2368266787",
"7870701491",
"26157533879",
"86932041639",
"288910349691",
"960165839819",
"3191019344815",
"10605047189343",
"35244859423123"
]
| [
"nonn",
"easy",
"walk"
]
| 4 | 0 | 2 | [
"A384646",
"A384671",
"A384672",
"A384673"
]
| null | Sean A. Irvine, Jun 05 2025 | 2025-06-07T00:12:03 | oeisdata/seq/A384/A384673.seq | b11a5c2a6c0df7af9e6d4945ef15cf55 |
A384674 | Lexicographically smallest sequence of distinct primes whose inverse binomial transform consists only of primes. | [
"2",
"5",
"11",
"23",
"47",
"97",
"211",
"491",
"1187",
"2857",
"6659",
"14879",
"31891",
"65929",
"132469",
"261059",
"510031",
"999721",
"1988797",
"4048339",
"8450557",
"18014701",
"38902439",
"84347189",
"182269327",
"390630769",
"828123239",
"1735146097",
"3594509969",
"7369765889",
"14975024861",
"30200498591",
"60537295711"
]
| [
"nonn"
]
| 22 | 0 | 1 | [
"A000040",
"A007442",
"A111107",
"A384674"
]
| null | Alexander R. Povolotsky, Jun 06 2025 | 2025-06-08T21:29:49 | oeisdata/seq/A384/A384674.seq | a969f5da1caf59219592fc2c25c935cc |
A384675 | Consecutive states of the linear congruential pseudo-random number generator 7^13*s mod 10^11 when started at 1. | [
"1",
"96889010407",
"47754305649",
"5019889143",
"18113311201",
"58918668807",
"8009274449",
"41680190743",
"64272062401",
"49842407207",
"88954803249",
"44998412343",
"99404253601",
"47356225607",
"72862892049",
"19678553943",
"78037884801",
"24356124007",
"88405540849",
"55224615543",
"68300956001"
]
| [
"nonn",
"easy"
]
| 10 | 1 | 2 | [
"A096550",
"A096561",
"A384675"
]
| null | Sean A. Irvine, Jun 06 2025 | 2025-06-12T10:17:16 | oeisdata/seq/A384/A384675.seq | 749252671c48d8624501bfce1339d559 |
A384676 | Binomial transform of A111107. | [
"2",
"5",
"13",
"37",
"101",
"271",
"727",
"1931",
"5003",
"12547",
"30449",
"71761",
"165037",
"372149",
"826303",
"1813219",
"3944921",
"8533073",
"18393821",
"39588071",
"85192381",
"183479291",
"395667617",
"854417989",
"1847225579",
"3996807053",
"8650687127",
"18721431499",
"40496966207",
"87538925959",
"189076973699"
]
| [
"nonn"
]
| 9 | 0 | 1 | [
"A000040",
"A111107",
"A384676"
]
| null | Alois P. Heinz, Jun 06 2025 | 2025-06-06T18:17:01 | oeisdata/seq/A384/A384676.seq | 453b4e050fbe5aee44e606dec3ee4cc5 |
A384677 | Expansion of (1-x-2*x^2) / (1-2*x-4*x^2+2*x^3). | [
"1",
"1",
"4",
"10",
"34",
"100",
"316",
"964",
"2992",
"9208",
"28456",
"87760",
"270928",
"835984",
"2580160",
"7962400",
"24573472",
"75836224",
"234041536",
"722281024",
"2229055744",
"6879152512",
"21229965952",
"65518430464",
"202198419712",
"624010629376",
"1925778076672",
"5943201831424",
"18341494710784"
]
| [
"nonn",
"easy",
"walk",
"changed"
]
| 11 | 0 | 3 | [
"A000244",
"A384633",
"A384640",
"A384677",
"A384678"
]
| null | Sean A. Irvine, Jun 05 2025 | 2025-07-08T11:46:15 | oeisdata/seq/A384/A384677.seq | 049750a61b793052f67002b149092a57 |
A384678 | Expansion of (1+x) / (1-2*x-4*x^2+2*x^3). | [
"1",
"3",
"10",
"30",
"94",
"288",
"892",
"2748",
"8488",
"26184",
"80824",
"249408",
"769744",
"2375472",
"7331104",
"22624608",
"69822688",
"215481600",
"665004736",
"2052290496",
"6333636736",
"19546425984",
"60322817920",
"186164066304",
"574526552320",
"1773063734016",
"5471905544704",
"16887012920832"
]
| [
"nonn",
"easy",
"walk",
"changed"
]
| 9 | 0 | 2 | [
"A000244",
"A384633",
"A384640",
"A384677",
"A384678"
]
| null | Sean A. Irvine, Jun 05 2025 | 2025-07-07T18:40:50 | oeisdata/seq/A384/A384678.seq | c64c0d1b50116a81e9584021d73c4a4b |
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