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| offset_a
int64 -14,827
666,262,453B
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635M
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listlengths 1
128
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listlengths 1
3
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⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-19 00:40:46
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A364601 | Numbers m such that, if k is the number of digits of m, then for some r > 1, the sum of the k-th powers of the digits of m^r is equal to m. | [
"1",
"7",
"8",
"9",
"180",
"205",
"38998",
"45994",
"89080",
"726191",
"5540343",
"7491889",
"8690141",
"167535050",
"749387107",
"9945245922"
]
| [
"nonn",
"base",
"fini",
"more"
]
| 58 | 1 | 2 | [
"A005188",
"A065999",
"A066003",
"A066004",
"A364601"
]
| null | René-Louis Clerc, Jul 29 2023 | 2024-04-24T14:54:17 | oeisdata/seq/A364/A364601.seq | a297892007b92d6c054b2de3d42086d7 |
A364602 | Triangle T(n,k) with rows of length 2*n-1, generated by T(1,1)=0, T(n,1)=T(n-1,1)+2, T(n,2)=4*(n-1)-1, and for k>=3, T(n,k)=4*T(n-1,k-2)+1. | [
"0",
"2",
"3",
"1",
"4",
"7",
"9",
"13",
"5",
"6",
"11",
"17",
"29",
"37",
"53",
"21",
"8",
"15",
"25",
"45",
"69",
"117",
"149",
"213",
"85",
"10",
"19",
"33",
"61",
"101",
"181",
"277",
"469",
"597",
"853",
"341",
"12",
"23",
"41",
"77",
"133",
"245",
"405",
"725",
"1109",
"1877",
"2389",
"3413",
"1365",
"14",
"27",
"49",
"93",
"165",
"309",
"533",
"981",
"1621",
"2901"
]
| [
"nonn",
"tabf"
]
| 82 | 1 | 2 | [
"A002450",
"A007310",
"A071797",
"A087445",
"A096773",
"A255138",
"A257480",
"A364602"
]
| null | Ruud H.G. van Tol, Jul 29 2023 | 2023-09-06T21:09:40 | oeisdata/seq/A364/A364602.seq | f12f8790229ba4f64c3fd947b86a3be4 |
A364603 | Lexicographically earliest sequence where after the m-th appearance of term z, it is banned from re-appearing in the next m*z terms. | [
"1",
"2",
"1",
"3",
"2",
"1",
"4",
"3",
"5",
"1",
"2",
"4",
"6",
"7",
"1",
"3",
"5",
"2",
"8",
"6",
"1",
"4",
"7",
"9",
"10",
"3",
"2",
"1",
"5",
"8",
"11",
"12",
"6",
"9",
"4",
"1",
"10",
"2",
"3",
"7",
"13",
"14",
"11",
"15",
"1",
"5",
"8",
"12",
"16",
"17",
"2",
"4",
"6",
"9",
"1",
"3",
"13",
"10",
"14",
"15",
"18",
"7",
"19",
"20",
"21",
"1",
"2",
"5",
"11",
"16",
"17",
"8",
"4",
"12",
"3",
"22",
"23",
"1",
"6",
"18",
"24",
"9",
"19",
"2",
"13",
"20",
"21",
"14"
]
| [
"nonn",
"look"
]
| 24 | 1 | 2 | [
"A364448",
"A364449",
"A364603",
"A364604"
]
| null | Rok Cestnik, Jul 29 2023 | 2023-08-14T02:01:03 | oeisdata/seq/A364/A364603.seq | da3b6fa516069f0dfd97575432047d06 |
A364604 | Lexicographically earliest sequence, where after every appearance, a term is banned from re-appearing for twice as long as last time; first appearance bans it for 1 term. | [
"1",
"2",
"1",
"2",
"3",
"1",
"2",
"3",
"4",
"5",
"1",
"2",
"3",
"4",
"5",
"6",
"4",
"3",
"5",
"1",
"2",
"4",
"6",
"5",
"7",
"6",
"3",
"7",
"8",
"9",
"4",
"6",
"5",
"7",
"8",
"9",
"1",
"2",
"7",
"8",
"6",
"9",
"10",
"3",
"8",
"10",
"9",
"4",
"7",
"5",
"10",
"11",
"12",
"8",
"11",
"9",
"10",
"6",
"11",
"12",
"13",
"14",
"12",
"11",
"13",
"7",
"10",
"12",
"13",
"1",
"2",
"8",
"9",
"11",
"13",
"14",
"3",
"12",
"14",
"15",
"4",
"15",
"5",
"10",
"13",
"14",
"15",
"16"
]
| [
"nonn"
]
| 15 | 1 | 2 | [
"A364448",
"A364449",
"A364603",
"A364604"
]
| null | Rok Cestnik, Jul 29 2023 | 2023-08-10T07:11:43 | oeisdata/seq/A364/A364604.seq | 7451930278f28c672d2c275b0db3783e |
A364605 | Number of 6-cycles in the n-Lucas cube graph. | [
"0",
"0",
"0",
"0",
"5",
"44",
"147",
"464",
"1236",
"3100",
"7293",
"16472",
"35919",
"76216",
"158040",
"321472",
"643229",
"1268868",
"2472147",
"4764120",
"9092300",
"17202636",
"32294277",
"60199088",
"111498175",
"205306192",
"376014960",
"685273120",
"1243205205",
"2245893340",
"4041415347",
"7245914176",
"12947137412"
]
| [
"nonn",
"easy"
]
| 32 | 1 | 5 | [
"A245961",
"A364605"
]
| null | Eric W. Weisstein, Jul 30 2023 | 2025-06-21T01:57:00 | oeisdata/seq/A364/A364605.seq | 07d8876b7e9cf03f634d154efd87ac9e |
A364606 | Numbers k such that the average digit of 2^k is an integer. | [
"0",
"1",
"2",
"3",
"6",
"13",
"16",
"26",
"46",
"51",
"56",
"73",
"122",
"141",
"166",
"313",
"383"
]
| [
"nonn",
"base"
]
| 17 | 1 | 3 | [
"A000079",
"A001370",
"A034887",
"A061383",
"A364606"
]
| null | Jon E. Schoenfield, Jul 29 2023 | 2023-07-31T10:43:14 | oeisdata/seq/A364/A364606.seq | 72bef69ffbe6c829ddbe80308576d866 |
A364607 | Denominations of a 4-coin system that returns the fewest coins in change on average. | [
"1",
"5",
"18",
"25"
]
| [
"nonn",
"full",
"fini"
]
| 41 | 1 | 2 | [
"A208953",
"A339333",
"A364607",
"A366013"
]
| null | Thomas Young, Aug 06 2023 | 2023-10-03T03:49:10 | oeisdata/seq/A364/A364607.seq | cb478b2c685da551fae72bcd10d1542b |
A364608 | Smallest k such that there are as many 0's as 1's in the binary representation of (2*n+1)^k, or -1 if no such k exists. | [
"2",
"4",
"2",
"1",
"4",
"2",
"2",
"21",
"8",
"5",
"10",
"2",
"4",
"2",
"2",
"61",
"1",
"1",
"34",
"1",
"18",
"12",
"6",
"1",
"63",
"11",
"49",
"2",
"496",
"2",
"2",
"58",
"24",
"12",
"11",
"40",
"7",
"43",
"59",
"3",
"3",
"53",
"31",
"54",
"15",
"7",
"59",
"30",
"5",
"185",
"2",
"5",
"97",
"28",
"10",
"2",
"6",
"4",
"42",
"2",
"27",
"2",
"2",
"15",
"3",
"72",
"1",
"7",
"1",
"1",
"15",
"37",
"1",
"1",
"129"
]
| [
"nonn",
"base"
]
| 42 | 1 | 1 | [
"A031443",
"A364608"
]
| null | Pontus von Brömssen, Jul 30 2023 | 2023-08-02T13:45:21 | oeisdata/seq/A364/A364608.seq | 2eba7aec55d6c1756eda67c5bfeff26b |
A364609 | a(n) = greatest integer k such that 1/n + 1/(n + 1) + ... + 1/k < sqrt(2). | [
"1",
"5",
"9",
"13",
"18",
"22",
"26",
"30",
"34",
"38",
"42",
"46",
"50",
"55",
"59",
"63",
"67",
"71",
"75",
"79",
"83",
"87",
"92",
"96",
"100",
"104",
"108",
"112",
"116",
"120",
"124",
"129",
"133",
"137",
"141",
"145",
"149",
"153",
"157",
"161",
"166",
"170",
"174",
"178",
"182",
"186",
"190",
"194",
"198",
"203",
"207",
"211",
"215",
"219",
"223",
"227",
"231"
]
| [
"nonn"
]
| 19 | 1 | 2 | [
"A001620",
"A136616",
"A357923",
"A363993",
"A364609"
]
| null | Clark Kimberling, Sep 06 2023 | 2023-09-08T07:09:22 | oeisdata/seq/A364/A364609.seq | 83136e458140dd79384f716e4bf5c4b4 |
A364610 | Centered pentagonal numbers which are products of three distinct primes. | [
"1266",
"1626",
"2806",
"3706",
"4731",
"6126",
"7426",
"7701",
"9766",
"10726",
"13506",
"15801",
"18706",
"19581",
"25251",
"26266",
"26781",
"31641",
"35106",
"36906",
"40006",
"50766",
"52926",
"56626",
"57381",
"62806",
"69306",
"71826",
"74391",
"76126",
"85101",
"90726",
"93606",
"95551",
"96531",
"99501",
"106606",
"108681",
"109726",
"117181",
"121551",
"123766"
]
| [
"nonn"
]
| 23 | 1 | 1 | [
"A005891",
"A007304",
"A364610"
]
| null | Massimo Kofler, Sep 07 2023 | 2025-03-10T12:26:22 | oeisdata/seq/A364/A364610.seq | 3df4b1585f13d2068203d23dbf02621c |
A364611 | For p = 5 and n > 0, write n = p^m + k, m >= 0, with maximal p^m <= n, with 0 <= k < p^(m+1) - p^m, then for n such that k=0, a(n)=n, and for n such that k > 0, a(n) is the smallest q*a(k), prime q != p, that is not already a term. | [
"1",
"2",
"4",
"8",
"5",
"3",
"6",
"12",
"16",
"10",
"9",
"18",
"24",
"32",
"20",
"27",
"36",
"48",
"64",
"40",
"54",
"72",
"96",
"128",
"25",
"7",
"14",
"28",
"56",
"15",
"21",
"42",
"84",
"112",
"30",
"63",
"126",
"168",
"224",
"60",
"81",
"108",
"144",
"192",
"80",
"162",
"216",
"288",
"256",
"50",
"49",
"98",
"196",
"392",
"45",
"147",
"294",
"252",
"336",
"90",
"189",
"378",
"504"
]
| [
"nonn"
]
| 37 | 1 | 2 | [
"A005940",
"A356867",
"A364611",
"A364628"
]
| null | Michael De Vlieger, Sep 16 2023 | 2023-09-17T01:36:11 | oeisdata/seq/A364/A364611.seq | 1e19ab415a0a03c2c5ec606c300b224b |
A364612 | a(n) = number of partitions of n whose difference multiset has at least one duplicate; see Comments. | [
"0",
"0",
"0",
"1",
"2",
"4",
"7",
"10",
"15",
"24",
"32",
"45",
"66",
"86",
"117",
"158",
"206",
"268",
"357",
"452",
"583",
"745",
"948",
"1188",
"1507",
"1874",
"2348",
"2908",
"3604",
"4428",
"5472",
"6675",
"8169",
"9939",
"12096",
"14622",
"17713",
"21322",
"25687",
"30808",
"36924",
"44107",
"52701",
"62697",
"74572",
"88457",
"104850",
"123934"
]
| [
"nonn"
]
| 10 | 0 | 5 | [
"A000041",
"A363994",
"A364612"
]
| null | Clark Kimberling, Sep 08 2023 | 2023-09-18T02:08:37 | oeisdata/seq/A364/A364612.seq | 789f474ea090ab5bf2628a8c275563d7 |
A364613 | a(n) = number of partitions of n whose sum multiset is free of duplicates; see Comments. | [
"1",
"1",
"2",
"2",
"3",
"3",
"5",
"5",
"7",
"8",
"10",
"12",
"15",
"18",
"20",
"26",
"29",
"36",
"38",
"50",
"53",
"67",
"69",
"89",
"95",
"115",
"122",
"151",
"161",
"195",
"201",
"247",
"266",
"312",
"330",
"386",
"419",
"487",
"520",
"600",
"641",
"742",
"793",
"901",
"979",
"1088",
"1186",
"1331",
"1454",
"1605",
"1730",
"1925",
"2102",
"2311",
"2525",
"2741",
"3001"
]
| [
"nonn"
]
| 17 | 0 | 3 | [
"A000041",
"A236912",
"A325877",
"A363994",
"A364613"
]
| null | Clark Kimberling, Sep 17 2023 | 2023-09-22T05:23:12 | oeisdata/seq/A364/A364613.seq | 040171f51a1d442f85037bc618a5a158 |
A364614 | Numbers not divisible by any prime of the form 3*k - 1. | [
"1",
"3",
"7",
"9",
"13",
"19",
"21",
"27",
"31",
"37",
"39",
"43",
"49",
"57",
"61",
"63",
"67",
"73",
"79",
"81",
"91",
"93",
"97",
"103",
"109",
"111",
"117",
"127",
"129",
"133",
"139",
"147",
"151",
"157",
"163",
"169",
"171",
"181",
"183",
"189",
"193",
"199",
"201",
"211",
"217",
"219",
"223",
"229",
"237",
"241",
"243",
"247",
"259",
"271",
"273",
"277",
"279"
]
| [
"nonn"
]
| 7 | 1 | 2 | [
"A003627",
"A215800",
"A364614",
"A364832"
]
| null | Clark Kimberling, Aug 09 2023 | 2023-09-13T22:50:27 | oeisdata/seq/A364/A364614.seq | 5c4d8b7da2c7db28651886a72bd63f85 |
A364615 | Numbers k such that the average of the decimal digits of 2^k is closer to 9/2 (the expected average for random digits) than for any smaller power of 2. | [
"0",
"1",
"2",
"8",
"14",
"20",
"29",
"47",
"62",
"80",
"113",
"134",
"182",
"206",
"281",
"287",
"299",
"326",
"419",
"500",
"560",
"620",
"638",
"674",
"833",
"911",
"1271",
"1289",
"1376",
"1418",
"1583",
"1670",
"1814",
"2273",
"2753",
"3365",
"3794",
"4127",
"4160",
"4202",
"4280",
"4292",
"4538",
"4553",
"4646",
"4805",
"4952",
"4979",
"5105",
"5276"
]
| [
"nonn",
"base"
]
| 7 | 1 | 3 | [
"A000079",
"A001370",
"A034887",
"A364606",
"A364615"
]
| null | Pontus von Brömssen and Jon E. Schoenfield, Jul 29 2023 | 2023-08-02T13:46:22 | oeisdata/seq/A364/A364615.seq | 3e561abb03e561bef675d5f33f18adb5 |
A364616 | Number of tilings of a 6 X n rectangle using dominoes and trominoes (of any shape). | [
"1",
"2",
"108",
"3540",
"115958",
"3927233",
"128441094",
"4263997124",
"141186107223",
"4671227129777",
"154679198549385",
"5119908497703914",
"169488865440883593",
"5610718094136694973",
"185732776135043052107",
"6148417237267189975927",
"203533740825252409802705",
"6737670699036802296758849"
]
| [
"nonn"
]
| 12 | 0 | 2 | [
"A364457",
"A364616"
]
| null | Alois P. Heinz, Jul 29 2023 | 2025-04-05T09:19:09 | oeisdata/seq/A364/A364616.seq | 59e2b13d9aa16085011d0b647fd67e55 |
A364617 | Number of tilings of a 7 X n rectangle using dominoes and trominoes (of any shape). | [
"1",
"3",
"280",
"17300",
"1075397",
"68846551",
"4263997124",
"267855152858",
"16785795917908",
"1051116421516975",
"65871551452359237",
"4126577980480405170",
"258538236543240798654",
"16197912784372244064693",
"1014813990592495583029006",
"63579642939479330198729573",
"3983348112669764700919476270"
]
| [
"nonn"
]
| 15 | 0 | 2 | [
"A364457",
"A364617"
]
| null | Alois P. Heinz, Jul 29 2023 | 2025-04-07T07:46:23 | oeisdata/seq/A364/A364617.seq | 9af7652c9d189867945ea4703f8ce015 |
A364618 | Decimal expansion of Sum_{k>=0} erfc(k), where erfc(x) is the complementary error function. | [
"1",
"1",
"6",
"1",
"9",
"9",
"9",
"0",
"4",
"7",
"9",
"4",
"7",
"1",
"2",
"6",
"3",
"6",
"3",
"5",
"3",
"2",
"3",
"0",
"8",
"3",
"2",
"2",
"4",
"5",
"5",
"7",
"9",
"7",
"1",
"7",
"1",
"1",
"6",
"6",
"3",
"4",
"3",
"5",
"0",
"6",
"2",
"2",
"5",
"8",
"6",
"8",
"0",
"3",
"1",
"2",
"1",
"6",
"8",
"2",
"6",
"3",
"3",
"2",
"4",
"1",
"5",
"9",
"4",
"1",
"7",
"5",
"5",
"0",
"4",
"9",
"4",
"0",
"0",
"2",
"3",
"8",
"6",
"4",
"7",
"8",
"1",
"3",
"2",
"8",
"3",
"6",
"2",
"6",
"2",
"8",
"9",
"3",
"3",
"5",
"1",
"8",
"4",
"4",
"7"
]
| [
"nonn",
"cons"
]
| 17 | 1 | 3 | [
"A099287",
"A364618"
]
| null | Amiram Eldar, Jul 30 2023 | 2024-10-11T07:09:48 | oeisdata/seq/A364/A364618.seq | aab1621d3e8f4914ca3cf6baa3853ee8 |
A364619 | Number of 4-cycles in the n-Pell graph. | [
"0",
"0",
"1",
"8",
"40",
"164",
"601",
"2048",
"6632",
"20680",
"62633",
"185352",
"538272",
"1538892",
"4341905",
"12112960",
"33464240",
"91666192",
"249215921",
"673049800",
"1806888568",
"4824913652",
"12821690281",
"33922774464",
"89391291480",
"234694621656",
"614106591769",
"1601882815304",
"4166439039664"
]
| [
"nonn"
]
| 14 | 0 | 4 | null | null | Eric W. Weisstein, Jul 30 2023 | 2025-02-16T08:34:06 | oeisdata/seq/A364/A364619.seq | 4c7ed390587826663c1c481244627a42 |
A364620 | G.f. satisfies A(x) = 1/(1-x)^2 + x*A(x)^3. | [
"1",
"3",
"12",
"67",
"449",
"3315",
"25963",
"211685",
"1777410",
"15263446",
"133427406",
"1183336278",
"10620959908",
"96292118665",
"880540044576",
"8112042293581",
"75218203558241",
"701439747294225",
"6574348389693202",
"61897799517155325",
"585138783209680944",
"5551797662571097495"
]
| [
"nonn"
]
| 7 | 0 | 2 | [
"A086616",
"A364620",
"A364621"
]
| null | Seiichi Manyama, Jul 30 2023 | 2023-07-30T09:20:00 | oeisdata/seq/A364/A364620.seq | 69173f17b64150b89b0330b2e8b1cc7d |
A364621 | G.f. satisfies A(x) = 1/(1-x)^2 + x*A(x)^4. | [
"1",
"3",
"15",
"118",
"1125",
"11805",
"131431",
"1524090",
"18208749",
"222570985",
"2770129627",
"34985756752",
"447243818573",
"5775955923428",
"75245253495035",
"987627627396792",
"13048147674230169",
"173382031819242855",
"2315662483861709467",
"31068798980975635130",
"418552735866147739185"
]
| [
"nonn"
]
| 7 | 0 | 2 | [
"A086616",
"A364620",
"A364621"
]
| null | Seiichi Manyama, Jul 30 2023 | 2023-07-30T09:22:00 | oeisdata/seq/A364/A364621.seq | 225eb2a663bd1cbed1bac7320e4c11e5 |
A364622 | G.f. satisfies A(x) = 1/(1-x)^2 + x^2*A(x)^4. | [
"1",
"2",
"4",
"12",
"45",
"182",
"779",
"3480",
"16005",
"75234",
"359893",
"1746268",
"8573477",
"42511646",
"212587561",
"1070897000",
"5429174465",
"27679933778",
"141829437174",
"729972918876",
"3772160853821",
"19563615260102",
"101797930474515",
"531293155760840",
"2780515192595481",
"14588670579665882"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A086615",
"A086631",
"A364622"
]
| null | Seiichi Manyama, Jul 30 2023 | 2024-01-20T14:44:56 | oeisdata/seq/A364/A364622.seq | 9561d4a7dca553c12425731e11f64517 |
A364623 | G.f. satisfies A(x) = 1/(1-x)^3 + x*A(x)^3. | [
"1",
"4",
"18",
"112",
"847",
"7086",
"62974",
"583002",
"5560323",
"54249583",
"538873135",
"5431177821",
"55402340842",
"570899082760",
"5933922697380",
"62138800690564",
"654949976467593",
"6942859160218698",
"73972792893687427",
"791722414873487767",
"8508265804914763731"
]
| [
"nonn"
]
| 13 | 0 | 2 | [
"A001764",
"A162481",
"A199475",
"A364620",
"A364623",
"A364624",
"A364629"
]
| null | Seiichi Manyama, Jul 30 2023 | 2023-10-03T09:00:04 | oeisdata/seq/A364/A364623.seq | deff0b2dc1f448fe2ec117c18644b002 |
A364624 | G.f. satisfies A(x) = 1/(1-x)^3 + x*A(x)^4. | [
"1",
"4",
"22",
"194",
"2103",
"25129",
"318816",
"4214724",
"57419725",
"800461033",
"11363418314",
"163708299724",
"2387365301187",
"35173224652637",
"522752043513952",
"7827979832083872",
"117992516684761733",
"1788819120580964014",
"27258417705055812586",
"417270970443908301926"
]
| [
"nonn"
]
| 7 | 0 | 2 | [
"A162481",
"A364623",
"A364624"
]
| null | Seiichi Manyama, Jul 30 2023 | 2023-07-30T09:56:51 | oeisdata/seq/A364/A364624.seq | b8e8fe6107b20a7eedb760c081a5564a |
A364625 | G.f. satisfies A(x) = 1/(1-x)^3 + x^2*A(x)^2. | [
"1",
"3",
"7",
"16",
"38",
"95",
"249",
"678",
"1901",
"5451",
"15906",
"47066",
"140868",
"425657",
"1296665",
"3977684",
"12276617",
"38094013",
"118768915",
"371875752",
"1168843808",
"3686549845",
"11664123048",
"37011249678",
"117750111763",
"375529083267",
"1200327617200",
"3844662925222",
"12338289374046"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A000108",
"A086615",
"A162481",
"A360045",
"A364625",
"A364626",
"A364627"
]
| null | Seiichi Manyama, Jul 30 2023 | 2023-07-30T09:56:39 | oeisdata/seq/A364/A364625.seq | ac89fd60f85e1abe959bd746578099aa |
A364626 | G.f. satisfies A(x) = 1/(1-x)^3 + x^2*A(x)^3. | [
"1",
"3",
"7",
"19",
"63",
"231",
"895",
"3615",
"15055",
"64111",
"277791",
"1220767",
"5427775",
"24371199",
"110350335",
"503289727",
"2309992959",
"10661634303",
"49452179455",
"230391918591",
"1077644520703",
"5058766156543",
"23824929459711",
"112541456498175",
"533063457631231",
"2531252417738751"
]
| [
"nonn"
]
| 8 | 0 | 2 | [
"A086631",
"A364625",
"A364626",
"A364627"
]
| null | Seiichi Manyama, Jul 30 2023 | 2023-07-30T09:56:36 | oeisdata/seq/A364/A364626.seq | 7e74954990491d069dd393bc05e7a2be |
A364627 | G.f. satisfies A(x) = 1/(1-x)^3 + x^2*A(x)^4. | [
"1",
"3",
"7",
"22",
"97",
"469",
"2339",
"12148",
"65295",
"358979",
"2006977",
"11380702",
"65311575",
"378574425",
"2213092750",
"13032826536",
"77244242937",
"460413902079",
"2758088752351",
"16596379614234",
"100269075879881",
"607996092039949",
"3698873710967989",
"22570809986322440"
]
| [
"nonn"
]
| 8 | 0 | 2 | [
"A364622",
"A364625",
"A364626",
"A364627"
]
| null | Seiichi Manyama, Jul 30 2023 | 2023-07-30T09:56:32 | oeisdata/seq/A364/A364627.seq | bd7c79f30a3a71cb087523019406245d |
A364628 | For p = 7 and n > 0, write n = p^m + k, m >= 0, with maximal p^m <= n, with 0 <= k < p^(m+1) - p^m, then for n such that k=0, a(n)=n, and for n such that k > 0, a(n) is the smallest q*a(k), prime q != p, that is not already a term. | [
"1",
"2",
"4",
"8",
"16",
"32",
"7",
"3",
"6",
"12",
"24",
"48",
"64",
"14",
"9",
"18",
"36",
"72",
"96",
"128",
"28",
"27",
"54",
"108",
"144",
"192",
"256",
"56",
"81",
"162",
"216",
"288",
"384",
"512",
"112",
"243",
"324",
"432",
"576",
"768",
"1024",
"224",
"486",
"648",
"864",
"1152",
"1536",
"2048",
"49",
"5",
"10",
"20",
"40",
"80",
"160",
"21",
"15",
"30",
"60",
"120"
]
| [
"nonn"
]
| 25 | 1 | 2 | [
"A005940",
"A356867",
"A364611",
"A364628"
]
| null | Michael De Vlieger, Sep 16 2023 | 2023-09-17T01:36:22 | oeisdata/seq/A364/A364628.seq | d50ddda1b463387e8479cdce898c75a3 |
A364629 | G.f. satisfies A(x) = (1+x*A(x)^3)/(1-x)^2. | [
"1",
"3",
"14",
"94",
"735",
"6239",
"55888",
"520028",
"4977321",
"48689260",
"484623552",
"4892304686",
"49971163021",
"515496741918",
"5363023614620",
"56204877993184",
"592811175777029",
"6287909183751105",
"67029933733468729",
"717749621979800340",
"7716543390041275964"
]
| [
"nonn"
]
| 7 | 0 | 2 | [
"A162477",
"A364620",
"A364629",
"A364630"
]
| null | Seiichi Manyama, Jul 30 2023 | 2023-07-30T09:20:12 | oeisdata/seq/A364/A364629.seq | 246510b92fe253847d2262cd2fc15355 |
A364630 | G.f. satisfies A(x) = (1+x*A(x)^4)/(1-x)^2. | [
"1",
"3",
"17",
"153",
"1621",
"18732",
"229103",
"2915498",
"38204497",
"512027945",
"6985933889",
"96705749625",
"1354868839933",
"19175008086962",
"273731258980839",
"3936883123412972",
"56991044183321197",
"829750943505927435",
"12142121554514962205",
"178488780583916045949"
]
| [
"nonn"
]
| 8 | 0 | 2 | [
"A162477",
"A364629",
"A364630"
]
| null | Seiichi Manyama, Jul 30 2023 | 2023-07-30T09:20:08 | oeisdata/seq/A364/A364630.seq | 1557cdb1036011a566ae49534c7c80e4 |
A364631 | a(n) is the number of iterations of phi(psi(x)) starting at x = n and terminating when psi(phi(x)) = x (n is counted), -1 otherwise. | [
"1",
"1",
"2",
"2",
"2",
"3",
"3",
"3",
"3",
"4",
"3",
"4",
"4",
"4",
"4",
"4",
"4",
"5",
"4",
"5",
"5",
"5",
"4",
"5",
"4",
"5",
"5",
"5",
"4",
"6",
"5",
"5",
"5",
"6",
"5",
"6",
"6",
"5",
"6",
"6",
"5",
"6",
"6",
"6",
"6",
"6",
"5",
"6",
"6",
"6",
"6",
"6",
"6",
"7",
"6",
"6",
"6",
"6",
"5",
"7",
"7",
"6",
"6",
"6",
"6",
"7",
"6",
"7",
"6",
"7",
"6",
"7",
"7",
"7",
"6",
"6",
"6",
"7",
"6",
"7",
"7",
"7",
"6",
"7",
"7",
"7",
"6",
"7"
]
| [
"nonn"
]
| 49 | 1 | 3 | [
"A000010",
"A001615",
"A003434",
"A364631"
]
| null | Torlach Rush, Jul 30 2023 | 2023-08-14T14:17:34 | oeisdata/seq/A364/A364631.seq | 16d33eb82d9d872333b8d5144a8f2350 |
A364632 | Number of tilings of an 8 X n rectangle using dominoes and trominoes (of any shape). | [
"1",
"4",
"727",
"84479",
"9935791",
"1204757533",
"141186107223",
"16785795917908",
"1990875917805852",
"235938457227641114",
"27983642750014402471",
"3317789294005871444981",
"393402890773982287366724",
"46647231741875687157655718",
"5531042470843072944881265311",
"655831959035571795593459804091"
]
| [
"nonn"
]
| 18 | 0 | 2 | [
"A364457",
"A364632"
]
| null | Alois P. Heinz, Jul 30 2023 | 2025-04-06T20:46:46 | oeisdata/seq/A364/A364632.seq | 1deb697ad85a629b305a3508d4075517 |
A364633 | a(n) is the smallest nonnegative number k such that prime(n) + k is divisible by n + 1. | [
"0",
"0",
"3",
"3",
"1",
"1",
"7",
"8",
"7",
"4",
"5",
"2",
"1",
"2",
"1",
"15",
"13",
"15",
"13",
"13",
"15",
"13",
"13",
"11",
"7",
"7",
"9",
"9",
"11",
"11",
"1",
"1",
"33",
"1",
"31",
"34",
"33",
"32",
"33",
"32",
"31",
"34",
"29",
"32",
"33",
"36",
"29",
"22",
"23",
"26",
"27",
"26",
"29",
"24",
"23",
"22",
"21",
"24",
"23",
"24",
"27",
"22",
"13",
"14",
"17",
"18",
"9",
"8",
"3",
"6",
"7",
"6",
"3",
"2",
"1",
"2",
"1"
]
| [
"nonn",
"look"
]
| 39 | 1 | 3 | [
"A068901",
"A364633"
]
| null | Andres Cicuttin, Jul 30 2023 | 2023-09-05T12:21:50 | oeisdata/seq/A364/A364633.seq | 668b82f13cf9fae5b124263346c8b475 |
A364634 | a(n) = n * LegendreP(n, 3). | [
"0",
"3",
"26",
"189",
"1284",
"8415",
"53934",
"340473",
"2125832",
"13163067",
"80974530",
"495513909",
"3019151628",
"18329137047",
"110933875542",
"669635727345",
"4032883785744",
"24239190315123",
"145427707041642",
"871139168383917",
"5210876275948820",
"31129900498786383",
"185755111545655806"
]
| [
"nonn"
]
| 4 | 0 | 2 | [
"A364361",
"A364634"
]
| null | Peter Luschny, Jul 30 2023 | 2023-07-30T16:34:49 | oeisdata/seq/A364/A364634.seq | 246e608dafa9641303bad4ebf61bd729 |
A364635 | a(n) is the largest prime p such that p/PrimePi(p) < n. | [
"7",
"31",
"113",
"359",
"1129",
"3089",
"8467",
"24281",
"64717",
"175141",
"481447",
"1304713",
"3524621",
"9560081",
"25874773",
"70119967",
"189969349",
"514282961",
"1394199299",
"3779856617",
"10246936393",
"27788573801",
"75370126379",
"204475055189",
"554805820519",
"1505578026059",
"4086199303001",
"11091501632977"
]
| [
"nonn"
]
| 14 | 2 | 1 | [
"A000720",
"A038625",
"A062743",
"A102281",
"A364635"
]
| null | Jon E. Schoenfield, Sep 09 2023 | 2023-09-10T15:29:56 | oeisdata/seq/A364/A364635.seq | 440039e559db75ebe51e295c9e6bb8cf |
A364636 | a(n) = ((1 - sqrt(2))^n + (1 + sqrt(2))^n)*n/2. | [
"0",
"1",
"6",
"21",
"68",
"205",
"594",
"1673",
"4616",
"12537",
"33630",
"89309",
"235212",
"615173",
"1599402",
"4137105",
"10653712",
"27327857",
"69856182",
"178017061",
"452390740",
"1146776253",
"2900399106",
"7320463897",
"18441561624",
"46376946025",
"116442406158",
"291929022189",
"730881930716",
"1827523107829"
]
| [
"nonn",
"easy"
]
| 14 | 0 | 3 | [
"A093967",
"A364553",
"A364636"
]
| null | Peter Luschny, Jul 30 2023 | 2023-07-31T08:06:28 | oeisdata/seq/A364/A364636.seq | d7f2f1734c5720938e09bcf4a92906b1 |
A364637 | a(n) is the least k > 1 that can be represented as a sum of one or more distinct positive m-th powers for 1 <= m <= n. | [
"2",
"4",
"9",
"881",
"7809",
"134067",
"12939267",
"2029992385",
"122120396036"
]
| [
"nonn",
"more",
"hard"
]
| 13 | 1 | 1 | [
"A001661",
"A030052",
"A364637"
]
| null | David A. Corneth and Peter Munn, Jul 30 2023 | 2023-08-01T11:15:55 | oeisdata/seq/A364/A364637.seq | 8ef0681874cbe1a9464733d803348474 |
A364638 | Number of tilings of a 9 X n rectangle using dominoes and trominoes (of any shape). | [
"1",
"5",
"1875",
"411963",
"91795006",
"21062468900",
"4671227129777",
"1051116421516975",
"235938457227641114",
"52918918728713551244",
"11878705076408687696978",
"2665431732701413911595239",
"598150296697458294727127430",
"134230850702665615645367175811",
"30122246289517237819939951946581"
]
| [
"nonn"
]
| 15 | 0 | 2 | [
"A364457",
"A364638"
]
| null | Alois P. Heinz, Jul 30 2023 | 2025-04-06T20:26:18 | oeisdata/seq/A364/A364638.seq | c9df6039c16e131bb4909179f9341d26 |
A364639 | Irregular triangle read by rows: T(n,k) = A237591(n,k) - A237591(n-1,k). | [
"1",
"1",
"0",
"1",
"1",
"0",
"0",
"1",
"1",
"-1",
"1",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"-1",
"1",
"0",
"1",
"0",
"0",
"1",
"-1",
"1",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"-1",
"1",
"0",
"0",
"1",
"-1",
"1",
"1",
"0",
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"1",
"0",
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"1",
"-1",
"0",
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"0",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"-1",
"1",
"0",
"0",
"1",
"0",
"-1",
"1",
"1",
"0",
"-1",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"-1",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"-1",
"1",
"0"
]
| [
"sign",
"tabf"
]
| 77 | 1 | null | [
"A000012",
"A000079",
"A000217",
"A000396",
"A002378",
"A003056",
"A008588",
"A063221",
"A065091",
"A091999",
"A097806",
"A100484",
"A135528",
"A196020",
"A235791",
"A236104",
"A237048",
"A237591",
"A237593",
"A245092",
"A249351",
"A262626",
"A286000",
"A286001",
"A299765",
"A347529",
"A360022",
"A362866",
"A364414",
"A364639",
"A364746",
"A365081"
]
| null | Omar E. Pol, Jul 30 2023 | 2024-09-06T20:19:24 | oeisdata/seq/A364/A364639.seq | f2ba7f8dcabcca6fd01d3d068e8d66e0 |
A364640 | Number of tilings of a 10 X n rectangle using dominoes and trominoes (of any shape). | [
"1",
"7",
"4832",
"2011408",
"848550447",
"368521437132",
"154679198549385",
"65871551452359237",
"27983642750014402471",
"11878705076408687696978",
"5046393600526600826576990",
"2143056706386201138428021036",
"910185960619655990533522509279",
"386568166093787098350944666459955"
]
| [
"nonn"
]
| 16 | 0 | 2 | [
"A364457",
"A364640"
]
| null | Alois P. Heinz, Jul 30 2023 | 2025-04-05T17:07:25 | oeisdata/seq/A364/A364640.seq | 3ae0431c4d11a144b7ac5415465656a9 |
A364641 | G.f. satisfies A(x) = 1/(1 - 2*x) - x*A(x)^3. | [
"1",
"1",
"1",
"2",
"3",
"5",
"10",
"16",
"31",
"59",
"101",
"206",
"376",
"692",
"1408",
"2528",
"4943",
"9767",
"17755",
"35950",
"68659",
"129029",
"262758",
"490832",
"958948",
"1920580",
"3581020",
"7203080",
"14054600",
"26665160",
"54195040",
"103450560",
"201749935",
"406617695",
"769870535",
"1539785150",
"3042812185"
]
| [
"nonn"
]
| 22 | 0 | 4 | [
"A001405",
"A349253",
"A349255",
"A349533",
"A364641",
"A364645",
"A364646",
"A364647"
]
| null | Seiichi Manyama, Jul 31 2023 | 2023-08-01T09:33:28 | oeisdata/seq/A364/A364641.seq | f417dc7ecb3d77b3ea2a40829dcb229a |
A364642 | a(n) is the number of iterations of psi(phi(x)) starting at x = n and terminating when psi(phi(x)) = x (n is counted), -1 otherwise. | [
"1",
"2",
"1",
"2",
"3",
"2",
"4",
"3",
"4",
"3",
"5",
"3",
"5",
"4",
"4",
"4",
"5",
"4",
"6",
"4",
"5",
"5",
"6",
"4",
"6",
"5",
"6",
"5",
"6",
"4",
"7",
"5",
"6",
"5",
"6",
"5",
"7",
"6",
"6",
"5",
"7",
"5",
"7",
"6",
"6",
"6",
"7",
"5",
"7",
"6",
"6",
"6",
"7",
"6",
"7",
"6",
"7",
"6",
"7",
"5",
"8",
"7",
"7",
"6",
"7",
"6",
"8",
"6",
"7",
"6",
"8",
"6",
"8",
"7",
"7",
"7",
"8",
"6",
"8",
"6",
"8",
"7",
"8",
"6",
"7",
"7",
"7",
"7"
]
| [
"nonn"
]
| 34 | 1 | 2 | [
"A000010",
"A001615",
"A003434",
"A364631",
"A364642"
]
| null | Torlach Rush, Jul 30 2023 | 2023-09-13T23:13:42 | oeisdata/seq/A364/A364642.seq | 5d7a7bdedfa7b56a1751b92a505c3a54 |
A364643 | Number of separable elements of the Weyl group of type D_n. | [
"1",
"2",
"4",
"22",
"102",
"474",
"2250",
"10910",
"53886",
"270322",
"1373970",
"7061542",
"36639702",
"191677386",
"1009942362",
"5354887470",
"28550730222",
"152979375842",
"823329316386",
"4448856020534",
"24126427982406",
"131270003806906",
"716377546590186",
"3920251765198782",
"21507301494123102",
"118269635529457874"
]
| [
"nonn"
]
| 29 | 0 | 2 | [
"A006318",
"A364643"
]
| null | Fern Gossow, Jul 30 2023 | 2024-03-25T10:27:14 | oeisdata/seq/A364/A364643.seq | a3572050ecbe9116712777add1a922b7 |
A364644 | Numbers k such that floor(10^k/7) is prime. | [
"7",
"25",
"355",
"823"
]
| [
"nonn",
"more",
"hard"
]
| 13 | 1 | 1 | [
"A090519",
"A364644"
]
| null | Robert Israel, Jul 31 2023 | 2024-01-27T15:56:58 | oeisdata/seq/A364/A364644.seq | 78831ad2dccb1ee33bc9ade6a90778b1 |
A364645 | G.f. satisfies A(x) = 1/(1 - 3*x) - x*A(x)^3. | [
"1",
"2",
"3",
"6",
"19",
"51",
"114",
"312",
"981",
"2616",
"6564",
"19647",
"59922",
"159056",
"430302",
"1329996",
"3926217",
"10498968",
"30052851",
"93244764",
"267690168",
"729649143",
"2173840338",
"6663260223",
"18768583674",
"52570016676",
"160362713250",
"481809941520",
"1346473504182",
"3886164785178"
]
| [
"nonn"
]
| 15 | 0 | 2 | [
"A005773",
"A349254",
"A349256",
"A349534",
"A364641",
"A364645",
"A364646",
"A364647"
]
| null | Seiichi Manyama, Jul 31 2023 | 2023-08-02T09:38:58 | oeisdata/seq/A364/A364645.seq | d4a32be42239ea5515e0d71c93108a38 |
A364646 | G.f. satisfies A(x) = 1/(1 - 4*x) - x*A(x)^3. | [
"1",
"3",
"7",
"16",
"55",
"235",
"856",
"2664",
"9055",
"37417",
"151431",
"533452",
"1825972",
"7141860",
"29778280",
"113688592",
"400940751",
"1499506693",
"6185139781",
"24862774872",
"91529003839",
"334939413067",
"1338383383444",
"5510330536000",
"21217042841668",
"77850045234108",
"300471644949940"
]
| [
"nonn"
]
| 8 | 0 | 2 | [
"A001700",
"A349535",
"A364641",
"A364645",
"A364646",
"A364647"
]
| null | Seiichi Manyama, Jul 31 2023 | 2023-07-31T10:08:20 | oeisdata/seq/A364/A364646.seq | 04d4097f119519eb3842ff63abd4b63e |
A364647 | G.f. satisfies A(x) = 1/(1 - 5*x) - x*A(x)^3. | [
"1",
"4",
"13",
"38",
"135",
"677",
"3538",
"15868",
"63313",
"268430",
"1348190",
"7038185",
"33328258",
"144159428",
"642323050",
"3213846836",
"16700677289",
"80935833050",
"363843867265",
"1660048399600",
"8276473557820",
"42830085070355",
"210286731046320",
"967456811687945",
"4476690297795850"
]
| [
"nonn"
]
| 8 | 0 | 2 | [
"A026378",
"A364641",
"A364645",
"A364646",
"A364647"
]
| null | Seiichi Manyama, Jul 31 2023 | 2023-07-31T10:08:24 | oeisdata/seq/A364/A364647.seq | 6f6271814e925a5558d80c4d0039a16b |
A364648 | Starting position of the first occurrence of the longest monochromatic arithmetic progression of difference n in the Fibonacci infinite word (A003849). | [
"2",
"3",
"20",
"16",
"11",
"20",
"0",
"143",
"2",
"11",
"54",
"8",
"32",
"2",
"11",
"7",
"70",
"3",
"7",
"0",
"986",
"10",
"3",
"7",
"16",
"11",
"2",
"87",
"376",
"2",
"3",
"2",
"21",
"87",
"2",
"3",
"7",
"16",
"3",
"7",
"0",
"20",
"23",
"11",
"20",
"8",
"11",
"2",
"11",
"20",
"36",
"11",
"7",
"0",
"6764",
"31",
"3",
"376",
"84",
"11",
"54",
"0",
"20",
"2",
"3",
"2",
"42",
"87",
"2",
"3",
"54",
"304"
]
| [
"nonn"
]
| 44 | 1 | 1 | [
"A003849",
"A339949",
"A364648"
]
| null | Gandhar Joshi, Jul 31 2023 | 2025-02-07T16:08:51 | oeisdata/seq/A364/A364648.seq | 1aaf441db25392335681b148839a7e20 |
A364649 | Maximal number of pairwise non-orthogonal 1-dimensional subspaces over F_3^n. | [
"1",
"2",
"5",
"7",
"11",
"18",
"28",
"45",
"82"
]
| [
"nonn",
"more"
]
| 10 | 1 | 2 | null | null | Benjamin Sambale, Jul 31 2023 | 2023-09-01T04:46:26 | oeisdata/seq/A364/A364649.seq | 2c826dcc2c187833b0209497bfaa3a5e |
A364650 | Number of powers of 3 whose binary representation contains exactly n 1's. | [
"1",
"2",
"1",
"1",
"1",
"3",
"0",
"1",
"1",
"1",
"2",
"0",
"1",
"3",
"1",
"1",
"2",
"1",
"1",
"1",
"0",
"1"
]
| [
"nonn",
"base",
"more"
]
| 4 | 1 | 2 | [
"A011754",
"A364650"
]
| null | Pontus von Brömssen, Jul 31 2023 | 2023-08-02T13:50:36 | oeisdata/seq/A364/A364650.seq | ee8940d8aeaac7e0323213b247987835 |
A364651 | Number of 6-cycles in the n-Pell graph. | [
"0",
"0",
"0",
"20",
"206",
"1282",
"6302",
"26942",
"104948",
"382444",
"1325444",
"4417024",
"14263474",
"44884286",
"138222194",
"417923290",
"1243857480",
"3651728760",
"10592838440",
"30403009612",
"86440264694",
"243689593114",
"681776739174",
"1894276352726",
"5230101132028",
"14357448589988"
]
| [
"nonn",
"easy"
]
| 20 | 0 | 4 | [
"A290031",
"A364619",
"A364651"
]
| null | Eric W. Weisstein, Jul 31 2023 | 2025-06-12T21:38:10 | oeisdata/seq/A364/A364651.seq | f22b824390967c151287ad2e5c7a9873 |
A364652 | Lower independence number of the n-Lucas cube graph. | [
"1",
"1",
"1",
"3",
"4",
"5",
"8",
"11",
"17",
"24",
"35"
]
| [
"nonn",
"more",
"hard"
]
| 11 | 1 | 4 | null | null | Eric W. Weisstein, Jul 31 2023 | 2025-02-16T08:34:06 | oeisdata/seq/A364/A364652.seq | 25dfce1e70eece5fb3d7f5f05e073689 |
A364653 | Domination number of the n-Lucas cube graph. | [
"1",
"1",
"1",
"3",
"4",
"5",
"7",
"11",
"16",
"23",
"35"
]
| [
"nonn",
"more",
"hard"
]
| 5 | 1 | 4 | null | null | Eric W. Weisstein, Jul 31 2023 | 2025-02-16T08:34:06 | oeisdata/seq/A364/A364653.seq | 1fd7f15bdadc2818ed97583cb923d6ef |
A364654 | Numbers which are the sum or difference of two seventh powers. | [
"0",
"1",
"2",
"127",
"128",
"129",
"256",
"2059",
"2186",
"2187",
"2188",
"2315",
"4374",
"14197",
"16256",
"16383",
"16384",
"16385",
"16512",
"18571",
"32768",
"61741",
"75938",
"77997",
"78124",
"78125",
"78126",
"78253",
"80312",
"94509",
"156250",
"201811",
"263552",
"277749",
"279808",
"279935",
"279936",
"279937",
"280064",
"282123",
"296320"
]
| [
"nonn"
]
| 15 | 1 | 3 | [
"A001015",
"A247099",
"A364654"
]
| null | Geoffrey Caveney, Jul 31 2023 | 2023-09-03T10:25:04 | oeisdata/seq/A364/A364654.seq | 0ca58c318a16941245ecdf734e9bb8e3 |
A364655 | Circuit rank and corank of the n-Pell graph. | [
"0",
"0",
"1",
"7",
"30",
"106",
"339",
"1021",
"2956",
"8324",
"22965",
"62371",
"167306",
"444302",
"1170151",
"3060409",
"7956824",
"20581576",
"53000873",
"135952639",
"347525686",
"885612402",
"2250586811",
"5705067061",
"14429119332",
"36418383564",
"91744440541",
"230719450651",
"579286267938",
"1452310024726"
]
| [
"nonn"
]
| 9 | 0 | 4 | null | null | Eric W. Weisstein, Jul 31 2023 | 2025-02-16T08:34:06 | oeisdata/seq/A364/A364655.seq | 37b47c6181ccd2d7f459dd2371372009 |
A364656 | Number of strict interval closure operators on a set of n elements. | [
"1",
"1",
"4",
"45",
"2062",
"589602",
"1553173541"
]
| [
"nonn",
"hard",
"more"
]
| 32 | 0 | 3 | [
"A334255",
"A356544",
"A358144",
"A358152",
"A364656"
]
| null | Tian Vlasic, Jul 31 2023 | 2024-05-14T07:06:22 | oeisdata/seq/A364/A364656.seq | 51654311e1f50145793a3d8f403133be |
A364657 | Numbers k such that sigma(k) > sigma(k+1) > sigma(k+2). | [
"44",
"45",
"104",
"105",
"116",
"117",
"164",
"165",
"224",
"225",
"272",
"273",
"296",
"297",
"315",
"344",
"345",
"356",
"357",
"405",
"464",
"465",
"512",
"513",
"525",
"560",
"561",
"584",
"585",
"620",
"621",
"693",
"704",
"705",
"765",
"776",
"777",
"824",
"825",
"836",
"837",
"860",
"861",
"884",
"885",
"945",
"1004",
"1005",
"1112",
"1113",
"1125",
"1155"
]
| [
"nonn",
"easy"
]
| 12 | 1 | 1 | [
"A050944",
"A053226",
"A364657",
"A364659"
]
| null | Seiichi Manyama, Aug 01 2023 | 2023-08-01T11:16:04 | oeisdata/seq/A364/A364657.seq | 7c86e8709cadaa411e30ea953ae9bda0 |
A364658 | Numerators of coefficients in expansion of (1 + x)^(2/3). | [
"1",
"2",
"-1",
"4",
"-7",
"14",
"-91",
"208",
"-494",
"10868",
"-27170",
"69160",
"-535990",
"1401820",
"-3704810",
"29638480",
"-79653415",
"215532770",
"-5280552865",
"14452039420",
"-39743108405",
"329300041070",
"-913059204785",
"2540686482880",
"-21278249294120",
"59579098023536",
"-167279775219928",
"12713262916714528"
]
| [
"sign",
"frac"
]
| 10 | 0 | 2 | [
"A002596",
"A067622",
"A067623",
"A127974",
"A161200",
"A364658",
"A364661"
]
| null | Ilya Gutkovskiy, Aug 01 2023 | 2023-08-02T07:05:56 | oeisdata/seq/A364/A364658.seq | a22e0dd00c1a5d7c1cbe7c370334ee1e |
A364659 | Numbers k such that sigma(k) < sigma(k+1) < sigma(k+2). | [
"1",
"2",
"61",
"62",
"73",
"74",
"133",
"134",
"145",
"146",
"193",
"194",
"253",
"254",
"313",
"397",
"398",
"403",
"457",
"458",
"481",
"482",
"493",
"494",
"523",
"553",
"554",
"565",
"566",
"613",
"614",
"625",
"626",
"661",
"662",
"673",
"674",
"691",
"733",
"734",
"757",
"758",
"763",
"793",
"794",
"817",
"818",
"853",
"854",
"913",
"914",
"943",
"973",
"974",
"997",
"998"
]
| [
"nonn",
"easy"
]
| 11 | 1 | 2 | [
"A053224",
"A364657",
"A364659",
"A364662"
]
| null | Seiichi Manyama, Aug 01 2023 | 2023-08-01T11:16:09 | oeisdata/seq/A364/A364659.seq | aa7c33212618005abf7347609c8b34b0 |
A364660 | Numerators of coefficients in expansion of (1 + x)^(1/4). | [
"1",
"1",
"-3",
"7",
"-77",
"231",
"-1463",
"4807",
"-129789",
"447051",
"-3129357",
"11094993",
"-159028233",
"574948227",
"-4188908511",
"15359331207",
"-906200541213",
"3358272593907",
"-25000473754641",
"93422822977869",
"-1401342344668035",
"5271716439465465",
"-39777496770512145",
"150462705175415505",
"-4564035390320936985"
]
| [
"sign",
"frac"
]
| 13 | 0 | 3 | [
"A002596",
"A004130",
"A008545",
"A067622",
"A088802",
"A123854",
"A364660",
"A364661"
]
| null | Ilya Gutkovskiy, Aug 01 2023 | 2023-08-02T07:07:12 | oeisdata/seq/A364/A364660.seq | 89aadbeee20892268f648d8e1de69509 |
A364661 | Numerators of coefficients in expansion of (1 + x)^(3/4). | [
"1",
"3",
"-3",
"5",
"-45",
"117",
"-663",
"1989",
"-49725",
"160225",
"-1057485",
"3556995",
"-48612265",
"168273225",
"-1177912575",
"4161957765",
"-237231592605",
"851242773465",
"-6147864475025",
"22326455198775",
"-325966245902115",
"1195209568307755",
"-8801088639357105",
"32525762362841475",
"-964930950097630425"
]
| [
"sign",
"frac"
]
| 9 | 0 | 2 | [
"A002596",
"A067002",
"A088802",
"A123854",
"A364658",
"A364660",
"A364661"
]
| null | Ilya Gutkovskiy, Aug 01 2023 | 2023-08-02T07:05:25 | oeisdata/seq/A364/A364661.seq | 25349c8bdbe80afb48be025d018de766 |
A364662 | Numbers k such that sigma(k) < sigma(k+1) < sigma(k+2) < sigma(k+3). | [
"1",
"61",
"73",
"133",
"145",
"193",
"253",
"397",
"457",
"481",
"493",
"553",
"565",
"613",
"625",
"661",
"673",
"733",
"757",
"793",
"817",
"853",
"913",
"973",
"997",
"1033",
"1093",
"1213",
"1237",
"1285",
"1321",
"1453",
"1513",
"1537",
"1645",
"1657",
"1681",
"1813",
"1825",
"1873",
"1933",
"2077",
"2113",
"2173",
"2233",
"2245",
"2293",
"2413",
"2497",
"2533",
"2581",
"2593",
"2653",
"2713"
]
| [
"nonn",
"easy"
]
| 13 | 1 | 2 | [
"A050944",
"A053224",
"A364659",
"A364662"
]
| null | Seiichi Manyama, Aug 01 2023 | 2023-08-01T11:16:00 | oeisdata/seq/A364/A364662.seq | c4bee40c67eefd5ba760d4aaa2141db4 |
A364663 | a(n+1) = a(|n-a(n)*a(n-1)|)+1; a(0) = 0. | [
"0",
"1",
"2",
"1",
"2",
"3",
"2",
"1",
"4",
"3",
"2",
"3",
"4",
"1",
"4",
"3",
"2",
"3",
"4",
"3",
"2",
"5",
"4",
"3",
"4",
"5",
"4",
"3",
"4",
"3",
"4",
"5",
"4",
"5",
"2",
"5",
"6",
"3",
"4",
"5",
"4",
"3",
"4",
"5",
"4",
"5",
"6",
"3",
"4",
"7",
"6",
"5",
"6",
"5",
"4",
"3",
"6",
"5",
"4",
"5",
"6",
"5",
"6",
"5",
"6",
"3",
"4",
"5",
"4",
"5",
"8",
"5",
"6",
"5",
"6",
"5",
"6",
"7",
"6",
"7",
"4",
"7",
"6",
"5",
"6",
"5",
"4",
"5",
"6",
"5",
"6",
"7",
"8",
"7",
"4",
"5",
"6"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A003056",
"A004001",
"A005185",
"A007660",
"A339929",
"A340134",
"A340224",
"A364197",
"A364663"
]
| null | Rok Cestnik, Aug 01 2023 | 2023-08-11T10:03:10 | oeisdata/seq/A364/A364663.seq | 4f77ac183887cb432ba805c70310e5ed |
A364664 | Lexicographically earliest permutation of the positive integers such that the successive cumulative sums reproduce the sequence itself, digit by digit. | [
"91",
"10",
"1",
"102",
"20",
"4",
"2",
"24",
"22",
"8",
"230",
"25",
"42",
"7",
"6",
"28",
"45",
"14",
"5",
"3",
"9",
"58",
"15",
"88",
"59",
"46",
"226",
"67",
"68",
"16",
"86",
"689",
"69",
"87",
"56",
"77",
"18",
"599",
"189",
"64",
"11",
"90",
"12",
"57",
"13",
"251",
"34",
"114",
"27",
"21",
"162",
"185",
"227",
"223",
"282",
"40",
"52",
"423",
"30",
"2232",
"113",
"275",
"32",
"863",
"37",
"63",
"38",
"83",
"44",
"53"
]
| [
"base",
"nonn"
]
| 26 | 1 | 1 | [
"A309151",
"A364664"
]
| null | Eric Angelini, Aug 01 2023 | 2023-08-05T13:01:36 | oeisdata/seq/A364/A364664.seq | efa69936712793f277fbcba00d20d7db |
A364665 | Lower independence number of the n-triangular honeycomb obtuse knight graph. | [
"1",
"3",
"6",
"4",
"5",
"5",
"6",
"7",
"9",
"12",
"13",
"14",
"15",
"16",
"19",
"22",
"24",
"26",
"28",
"30",
"32",
"34",
"38",
"41",
"44"
]
| [
"nonn",
"more"
]
| 32 | 1 | 2 | null | null | Eric W. Weisstein, Aug 01 2023 | 2025-02-16T08:34:06 | oeisdata/seq/A364/A364665.seq | ded453aefd3bc8967259be7069f086e1 |
A364666 | Lower independence number of the n X n X n grid graph. | [
"1",
"2",
"6",
"16",
"26",
"43",
"66"
]
| [
"nonn",
"more"
]
| 14 | 1 | 2 | null | null | Eric W. Weisstein, Aug 01 2023 | 2025-02-16T08:34:06 | oeisdata/seq/A364/A364666.seq | 057f1c216ed52420677406fa96e47b79 |
A364667 | Lower independence number of the n-diagonal intersection graph. | [
"1",
"1",
"2",
"4",
"10",
"12",
"30",
"36",
"74",
"60"
]
| [
"nonn",
"more"
]
| 13 | 3 | 3 | null | null | Eric W. Weisstein, Aug 01 2023 | 2025-02-16T08:34:06 | oeisdata/seq/A364/A364667.seq | 5a49cc8602583919c1931cb035b3bf4c |
A364668 | Domination and lower independence number of the n-Goldberg graph. | [
"0",
"3",
"5",
"7",
"9",
"11",
"14",
"16",
"18",
"20",
"22",
"25",
"27",
"29",
"31",
"33",
"36",
"38",
"40",
"42",
"44",
"47",
"49",
"51",
"53",
"55",
"58",
"60",
"62",
"64",
"66",
"69",
"71",
"73",
"75",
"77",
"80",
"82",
"84",
"86",
"88",
"91",
"93",
"95",
"97",
"99",
"102",
"104",
"106",
"108",
"110",
"113",
"115",
"117",
"119",
"121",
"124",
"126",
"128",
"130",
"132"
]
| [
"nonn",
"easy"
]
| 13 | 0 | 2 | [
"A364668",
"A382431"
]
| null | Eric W. Weisstein, Aug 01 2023 | 2025-05-25T16:06:44 | oeisdata/seq/A364/A364668.seq | 14b045ebed7a569e3a5d9d4591c22fae |
A364669 | Lower independence number of the hypercube graph Q_n. | [
"1",
"1",
"2",
"2",
"4",
"8",
"12",
"16",
"32"
]
| [
"nonn",
"more"
]
| 5 | 0 | 3 | null | null | Eric W. Weisstein, Aug 01 2023 | 2025-02-16T08:34:06 | oeisdata/seq/A364/A364669.seq | 8fec539bee483c92d40cbd5ed062eb68 |
A364670 | Number of strict integer partitions of n with a part equal to the sum of two distinct others. A variation of sum-full strict partitions. | [
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"3",
"1",
"4",
"3",
"7",
"6",
"10",
"10",
"14",
"16",
"24",
"25",
"34",
"39",
"48",
"59",
"71",
"81",
"103",
"120",
"136",
"166",
"194",
"226",
"260",
"312",
"353",
"419",
"473",
"557",
"636",
"742",
"824",
"974",
"1097",
"1266",
"1418",
"1646",
"1837",
"2124",
"2356",
"2717",
"3029",
"3469",
"3830",
"4383",
"4884",
"5547"
]
| [
"nonn"
]
| 8 | 0 | 11 | [
"A000009",
"A000041",
"A007865",
"A008284",
"A008289",
"A025065",
"A085489",
"A088809",
"A093971",
"A108917",
"A111133",
"A151897",
"A236912",
"A237113",
"A237667",
"A237668",
"A240861",
"A275972",
"A299702",
"A320340",
"A323092",
"A325862",
"A363225",
"A363226",
"A364272",
"A364346",
"A364349",
"A364350",
"A364532",
"A364533",
"A364534",
"A364670"
]
| null | Gus Wiseman, Aug 03 2023 | 2023-08-05T06:24:01 | oeisdata/seq/A364/A364670.seq | 5dd5cae37612c1870c4c73e77a1443c1 |
A364671 | Number of subsets of {1..n} containing all of their own first differences. | [
"1",
"2",
"4",
"6",
"10",
"14",
"23",
"34",
"58",
"96",
"171",
"302",
"565",
"1041",
"1969",
"3719",
"7105",
"13544",
"25999",
"49852",
"95949",
"184658",
"356129",
"687068",
"1327540",
"2566295",
"4966449",
"9617306",
"18640098",
"36150918",
"70166056",
"136272548",
"264844111",
"515036040",
"1002211421",
"1951345157",
"3801569113"
]
| [
"nonn"
]
| 12 | 0 | 2 | [
"A007862",
"A054519",
"A151897",
"A196723",
"A237667",
"A237668",
"A325325",
"A326083",
"A363225",
"A363260",
"A364345",
"A364463",
"A364464",
"A364466",
"A364467",
"A364536",
"A364537",
"A364671",
"A364672",
"A364673",
"A364674",
"A364675",
"A364752",
"A364753"
]
| null | Gus Wiseman, Aug 04 2023 | 2023-09-06T20:30:49 | oeisdata/seq/A364/A364671.seq | 6934149eb4df0daad1b603ffc4f5b098 |
A364672 | Number of subsets of {1..n} not containing all of their own first differences. | [
"0",
"0",
"0",
"2",
"6",
"18",
"41",
"94",
"198",
"416",
"853",
"1746",
"3531",
"7151",
"14415",
"29049",
"58431",
"117528",
"236145",
"474436",
"952627",
"1912494",
"3838175",
"7701540",
"15449676",
"30988137",
"62142415",
"124600422",
"249795358",
"500719994",
"1003575768",
"2011211100",
"4030123185",
"8074898552",
"16177657763",
"32408393211",
"64917907623"
]
| [
"nonn"
]
| 12 | 0 | 4 | [
"A007862",
"A054519",
"A151897",
"A237667",
"A325325",
"A326083",
"A363225",
"A363260",
"A364345",
"A364463",
"A364464",
"A364466",
"A364467",
"A364536",
"A364537",
"A364671",
"A364672",
"A364673",
"A364674",
"A364675",
"A364752",
"A364753"
]
| null | Gus Wiseman, Aug 05 2023 | 2024-01-28T02:41:12 | oeisdata/seq/A364/A364672.seq | 8c58932c3cb6f49d31dcf6729b5fb69f |
A364673 | Number of (necessarily strict) integer partitions of n containing all of their own first differences. | [
"1",
"1",
"1",
"2",
"1",
"1",
"3",
"2",
"1",
"2",
"2",
"2",
"5",
"2",
"2",
"4",
"2",
"3",
"6",
"4",
"4",
"8",
"4",
"4",
"10",
"8",
"7",
"8",
"13",
"9",
"15",
"12",
"13",
"17",
"20",
"15",
"31",
"24",
"27",
"32",
"33",
"32",
"50",
"42",
"45",
"53",
"61",
"61",
"85",
"76",
"86",
"101",
"108",
"118",
"137",
"141",
"147",
"179",
"184",
"196",
"222",
"244",
"257",
"295",
"324",
"348",
"380",
"433"
]
| [
"nonn"
]
| 15 | 0 | 4 | [
"A000009",
"A000041",
"A002865",
"A007862",
"A008284",
"A008289",
"A025065",
"A196723",
"A229816",
"A236912",
"A237113",
"A237667",
"A320347",
"A325325",
"A363225",
"A363260",
"A364272",
"A364345",
"A364463",
"A364464",
"A364467",
"A364536",
"A364537",
"A364671",
"A364672",
"A364673",
"A364674",
"A364675",
"A370386"
]
| null | Gus Wiseman, Aug 03 2023 | 2024-03-09T19:18:48 | oeisdata/seq/A364/A364673.seq | 6e48ef7b8fc262c0b07e77bb5bdeac3b |
A364674 | Number of integer partitions of n containing all of their own nonzero first differences. | [
"1",
"1",
"2",
"3",
"4",
"4",
"8",
"7",
"11",
"13",
"17",
"18",
"32",
"30",
"44",
"54",
"70",
"78",
"114",
"125",
"171",
"205",
"257",
"302",
"408",
"464",
"592",
"711",
"892",
"1042",
"1330",
"1543",
"1925",
"2279",
"2787",
"3291",
"4061",
"4727",
"5753",
"6792",
"8197",
"9583",
"11593",
"13505",
"16198",
"18965",
"22548",
"26290",
"31340",
"36363",
"43046"
]
| [
"nonn"
]
| 9 | 0 | 3 | [
"A000009",
"A000041",
"A002865",
"A007862",
"A008284",
"A008289",
"A025065",
"A229816",
"A236912",
"A237113",
"A237667",
"A320347",
"A325325",
"A326083",
"A363225",
"A363260",
"A364272",
"A364463",
"A364464",
"A364466",
"A364467",
"A364536",
"A364537",
"A364671",
"A364672",
"A364673",
"A364674",
"A364675"
]
| null | Gus Wiseman, Aug 04 2023 | 2023-08-06T08:17:52 | oeisdata/seq/A364/A364674.seq | 91920b119f2940369b8a1661c4d7869c |
A364675 | Number of integer partitions of n whose nonzero first differences are a submultiset of the parts. | [
"1",
"1",
"2",
"3",
"4",
"4",
"7",
"7",
"10",
"12",
"15",
"15",
"26",
"25",
"35",
"45",
"55",
"60",
"86",
"94",
"126",
"150",
"186",
"216",
"288",
"328",
"407",
"493",
"610",
"699",
"896",
"1030",
"1269",
"1500",
"1816",
"2130",
"2620",
"3029",
"3654",
"4300",
"5165",
"5984",
"7222",
"8368",
"9976",
"11637",
"13771",
"15960",
"18978",
"21896",
"25815",
"29915"
]
| [
"nonn"
]
| 8 | 0 | 3 | [
"A000009",
"A000041",
"A002865",
"A007862",
"A008284",
"A008289",
"A101925",
"A108917",
"A154402",
"A229816",
"A236912",
"A237113",
"A237667",
"A237668",
"A320347",
"A325325",
"A342337",
"A363225",
"A363260",
"A364272",
"A364345",
"A364463",
"A364464",
"A364466",
"A364467",
"A364536",
"A364537",
"A364671",
"A364672",
"A364673",
"A364675"
]
| null | Gus Wiseman, Aug 04 2023 | 2023-08-10T07:11:48 | oeisdata/seq/A364/A364675.seq | 3b9cb9366ec4f9c1faf46ffebe8c493f |
A364676 | Lower independence number of the n-cube connected cycle graph. | [
"6",
"16",
"47",
"96",
"224",
"512",
"1152",
"2560"
]
| [
"nonn",
"more"
]
| 13 | 3 | 1 | null | null | Eric W. Weisstein, Aug 01 2023 | 2025-02-16T08:34:06 | oeisdata/seq/A364/A364676.seq | 89185e385e3962e7793b139b9e3ae439 |
A364677 | Domination and lower independence number of the n-middle layer graph. | [
"2",
"6",
"14",
"50",
"132"
]
| [
"nonn",
"more"
]
| 9 | 1 | 1 | null | null | Eric W. Weisstein, Aug 02 2023 | 2025-03-10T11:02:49 | oeisdata/seq/A364/A364677.seq | 00fe31a6667481e0603cd4fbb997cb33 |
A364678 | Maximum number of primes between consecutive multiples of n, as permitted by divisibility considerations. | [
"0",
"1",
"1",
"2",
"2",
"2",
"2",
"3",
"3",
"4",
"4",
"4",
"4",
"4",
"4",
"5",
"5",
"6",
"6",
"6",
"5",
"7",
"7",
"6",
"7",
"7",
"7",
"7",
"8",
"7",
"8",
"9",
"8",
"10",
"8",
"10",
"10",
"10",
"11",
"11",
"11",
"10",
"11",
"11",
"11",
"12",
"12",
"12",
"12",
"13",
"12",
"13",
"14",
"13",
"13",
"14",
"14",
"15",
"15",
"14",
"15",
"15",
"15",
"16",
"15",
"15",
"16",
"16",
"17",
"16",
"17",
"18",
"18",
"18",
"18",
"18",
"17",
"19",
"19",
"19",
"19",
"20",
"20",
"19",
"19",
"20",
"21",
"21"
]
| [
"nonn"
]
| 47 | 1 | 4 | [
"A000010",
"A005097",
"A007811",
"A023193",
"A056956",
"A123985",
"A123986",
"A144769",
"A309871",
"A364678"
]
| null | Brian Kehrig, Aug 24 2023 | 2025-04-27T03:23:30 | oeisdata/seq/A364/A364678.seq | 1807f9e564bdcb632aa407e2e07b2026 |
A364679 | Least increasing sequence of semiprimes with alternating parity such that a(n-1) + a(n) is a semiprime, with a(1)=4. | [
"4",
"21",
"34",
"35",
"58",
"65",
"94",
"111",
"142",
"145",
"146",
"155",
"166",
"169",
"202",
"205",
"206",
"209",
"218",
"219",
"226",
"247",
"254",
"265",
"278",
"287",
"302",
"309",
"314",
"319",
"362",
"391",
"394",
"395",
"398",
"415",
"454",
"469",
"482",
"497",
"514",
"527",
"554",
"565",
"626",
"629",
"634",
"679",
"706",
"731",
"734",
"763",
"766",
"771",
"794",
"849",
"862",
"865",
"866",
"869",
"926"
]
| [
"nonn"
]
| 60 | 1 | 1 | [
"A001358",
"A254923",
"A364679"
]
| null | Zak Seidov and Robert Israel, Sep 04 2023 | 2023-09-05T19:14:54 | oeisdata/seq/A364/A364679.seq | 1de1d5be62396f9a551095f477e4fe4a |
A364680 | Smallest initial number k of n consecutive numbers satisfying sigma(k) > sigma(k+1) > ... > sigma(k+n-1). | [
"1",
"4",
"44",
"44",
"20021154",
"20021154"
]
| [
"nonn",
"more"
]
| 10 | 1 | 2 | [
"A000203",
"A050944",
"A050945",
"A053226",
"A075029",
"A364657",
"A364680"
]
| null | Seiichi Manyama, Aug 02 2023 | 2023-08-02T11:45:35 | oeisdata/seq/A364/A364680.seq | a7be8fa4973b147b2df062d6fcb3948f |
A364681 | a(n) is the number of isogeny classes of elliptic curves over GF(q), where q = A246655(n) is the n-th prime power > 1. | [
"5",
"7",
"9",
"9",
"11",
"9",
"13",
"13",
"15",
"13",
"17",
"17",
"19",
"20",
"17",
"21",
"23",
"15",
"25",
"25",
"27",
"27",
"27",
"29",
"31",
"31",
"21",
"33",
"33",
"35",
"35",
"29",
"37",
"37",
"39",
"41",
"41",
"41",
"41",
"43",
"45",
"37",
"45",
"25",
"45",
"47",
"47",
"49",
"49",
"51",
"51",
"51",
"50",
"53",
"53",
"53",
"55",
"55",
"57",
"57",
"59",
"59",
"61",
"61",
"61",
"61",
"63",
"45",
"63",
"37",
"65",
"65"
]
| [
"nonn"
]
| 14 | 1 | 1 | [
"A005523",
"A362570",
"A364681"
]
| null | Robin Visser, Aug 02 2023 | 2023-08-04T15:47:55 | oeisdata/seq/A364/A364681.seq | 6410e3af343f73d51a00ba806adbc720 |
A364682 | Number of iterations of the "x -> sum of squares of digits of x" map (A003132) for n to converge to either 0, 1 or the 8-cycle (37,58,89,145,42,20,4,16). | [
"1",
"1",
"2",
"6",
"1",
"5",
"10",
"6",
"6",
"5",
"2",
"3",
"6",
"3",
"7",
"4",
"1",
"6",
"4",
"5",
"1",
"6",
"7",
"4",
"2",
"4",
"3",
"7",
"4",
"3",
"6",
"3",
"4",
"5",
"5",
"6",
"9",
"1",
"3",
"6",
"2",
"7",
"1",
"5",
"5",
"8",
"5",
"4",
"7",
"5",
"5",
"4",
"4",
"6",
"8",
"6",
"3",
"5",
"1",
"3",
"10",
"2",
"3",
"9",
"5",
"3",
"8",
"3",
"3",
"6",
"6",
"6",
"7",
"2",
"4",
"5",
"3",
"3",
"5",
"4",
"6",
"4",
"4",
"3",
"7",
"2"
]
| [
"nonn"
]
| 15 | 0 | 3 | [
"A003132",
"A007770",
"A039943",
"A099645",
"A193995",
"A364682"
]
| null | Chai Wah Wu, Aug 02 2023 | 2023-08-03T04:18:33 | oeisdata/seq/A364/A364682.seq | 3f457e7b07cc41d73bc3ed125a1e442c |
A364683 | a(n) is the least k such that 1 + 2^k + 3^k is divisible by n, or -1 if there is no such k. | [
"0",
"1",
"0",
"3",
"-1",
"1",
"2",
"-1",
"3",
"-1",
"9",
"3",
"-1",
"2",
"-1",
"-1",
"9",
"3",
"-1",
"-1",
"-1",
"9",
"5",
"-1",
"-1",
"-1",
"9",
"-1",
"-1",
"-1",
"16",
"-1",
"9",
"9",
"-1",
"3",
"12",
"-1",
"-1",
"-1",
"18",
"-1",
"-1",
"9",
"-1",
"5",
"-1",
"-1",
"4",
"-1",
"9",
"-1",
"-1",
"9",
"-1",
"-1",
"-1",
"-1",
"-1",
"-1",
"-1",
"16",
"-1",
"-1",
"-1",
"9",
"-1",
"9",
"5",
"-1",
"-1",
"-1",
"19",
"12",
"-1",
"-1",
"-1",
"-1",
"33",
"-1",
"27"
]
| [
"sign",
"look"
]
| 6 | 1 | 4 | [
"A001550",
"A364683"
]
| null | Robert Israel, Aug 02 2023 | 2023-08-02T13:48:40 | oeisdata/seq/A364/A364683.seq | dad0688b49e21f155de7b7bdc7a5952d |
A364684 | Number of achiral triangular polyominoes with 6n cells and sixfold rotational symmetry. | [
"1",
"1",
"1",
"1",
"3",
"4",
"7",
"9",
"16",
"22",
"46",
"63",
"121",
"167",
"455",
"912",
"1263",
"2535",
"3514",
"7099",
"9873",
"20043",
"27956",
"56807",
"79397",
"161736",
"226559",
"462482",
"649100",
"1327165",
"1865833",
"3820605",
"5379507",
"11028753",
"15550459",
"31913892",
"45057416",
"92557088",
"130837407",
"268988726"
]
| [
"nonn"
]
| 10 | 1 | 5 | [
"A000577",
"A001420",
"A006534",
"A030223",
"A030224",
"A364684"
]
| null | Robert A. Russell, Aug 02 2023 | 2023-08-04T02:58:43 | oeisdata/seq/A364/A364684.seq | 0c9a88dcae9a1547b7d8280fd7bab484 |
A364685 | The number of binary sequences of length n for which all patterns {0,1},{0,0},{1,0},{1,1} appear for the first time. In particular, three of the patterns will have appeared at least once before the (n-1)st digit in the sequence and the remaining pattern appears for the first and only time at positions {n-1,n} in the sequence. | [
"4",
"10",
"18",
"30",
"48",
"76",
"120",
"190",
"302",
"482",
"772",
"1240",
"1996",
"3218",
"5194",
"8390",
"13560",
"21924",
"35456",
"57350",
"92774",
"150090",
"242828",
"392880",
"635668",
"1028506",
"1664130",
"2692590",
"4356672",
"7049212",
"11405832",
"18454990",
"29860766",
"48315698",
"78176404",
"126492040",
"204668380"
]
| [
"nonn",
"easy"
]
| 26 | 5 | 1 | [
"A000045",
"A242206",
"A364685"
]
| null | Evan Fisher and Ruiqi (Violet) Cai, Aug 02 2023 | 2023-08-05T21:27:47 | oeisdata/seq/A364/A364685.seq | 7b9fc7dbea4e42ea001759959fbe6838 |
A364686 | a(n) is the number of parity self-conjugate partitions of n. | [
"1",
"0",
"1",
"1",
"1",
"1",
"1",
"4",
"2",
"2",
"2",
"7",
"5",
"3",
"4",
"11",
"11",
"5",
"10",
"17",
"18",
"8",
"17",
"29",
"30",
"16",
"28",
"46",
"45",
"28",
"42",
"77",
"69",
"48",
"65",
"119",
"103",
"77",
"97",
"182",
"157",
"118",
"149",
"267",
"236",
"176",
"222",
"389",
"353",
"258",
"335",
"551",
"515",
"373",
"494",
"785",
"746",
"534",
"718",
"1099",
"1061",
"764",
"1021",
"1538",
"1494"
]
| [
"nonn"
]
| 20 | 1 | 8 | [
"A000700",
"A110654",
"A364686"
]
| null | Eric Gottlieb, Aug 02 2023 | 2024-01-18T20:21:39 | oeisdata/seq/A364/A364686.seq | 9ae88605005bc2ecd2aebd36a5d0069d |
A364687 | Number of chordless cycles (of length >= 4) in the n-folded cube graph. | [
"0",
"0",
"0",
"252",
"1920",
"16240",
"103936",
"584640",
"3056640",
"15265536"
]
| [
"nonn",
"more"
]
| 42 | 2 | 4 | null | null | Eric W. Weisstein, Aug 16 2023 | 2025-02-16T08:34:06 | oeisdata/seq/A364/A364687.seq | 67a20ed896000c676f6a619cfb7bd3e2 |
A364688 | Number of 8-cycles in the hypercube graph Q_n. | [
"0",
"0",
"0",
"6",
"696",
"6720",
"39840",
"184800",
"736512",
"2644992",
"8801280",
"27624960",
"82790400",
"238977024",
"668688384",
"1822679040",
"4858183680",
"12700876800",
"32647938048",
"82682707968",
"206650736640",
"510425825280",
"1247438438400",
"3019527684096",
"7245593051136",
"17248655769600"
]
| [
"nonn"
]
| 8 | 0 | 4 | [
"A001788",
"A290031",
"A364688"
]
| null | Eric W. Weisstein, Aug 02 2023 | 2025-02-16T08:34:06 | oeisdata/seq/A364/A364688.seq | 4bd1dcaed3dd4adb015ee0008f52c901 |
A364689 | Prime numbers that are the exact average of ten consecutive odd semiprimes. | [
"43",
"53",
"73",
"83",
"113",
"373",
"449",
"577",
"971",
"1259",
"1327",
"1381",
"1499",
"1543",
"1847",
"2239",
"2311",
"2339",
"2351",
"2383",
"2953",
"3109",
"3257",
"3389",
"4021",
"4297",
"4919",
"5101",
"5227",
"5591",
"5701",
"5737",
"5927",
"6733",
"6907",
"7109",
"7253",
"7823",
"8011",
"9137",
"9403",
"9613",
"10177",
"11471",
"11621",
"11677",
"12251",
"12479",
"12671",
"12781"
]
| [
"nonn"
]
| 32 | 1 | 1 | [
"A000040",
"A046315",
"A363074",
"A363187",
"A363188",
"A364147",
"A364148",
"A364149",
"A364320",
"A364321",
"A364689"
]
| null | Elmo R. Oliveira, Sep 25 2023 | 2023-10-09T18:38:06 | oeisdata/seq/A364/A364689.seq | 86ef59fe313d4a9ed815b3b375fd90b3 |
A364690 | Prime powers q such that there does not exist an elliptic curve E over GF(q) with cardinality q + 1 + floor(2*sqrt(q)). | [
"128",
"2048",
"2187",
"16807",
"32768",
"131072",
"524288",
"1953125",
"2097152",
"8388608",
"14348907",
"48828125",
"134217728",
"536870912",
"30517578125",
"549755813888",
"847288609443",
"2199023255552",
"19073486328125",
"140737488355328",
"562949953421312",
"36028797018963968",
"144115188075855872",
"450283905890997363"
]
| [
"nonn"
]
| 23 | 1 | 1 | [
"A005523",
"A246547",
"A246655",
"A364690"
]
| null | Robin Visser, Aug 02 2023 | 2025-02-04T01:30:17 | oeisdata/seq/A364/A364690.seq | 0dfe5afe31114f2e5ee46aeb9bae8a0e |
A364691 | Pentagonal numbers which are the sum of the first k primes, for some k >= 0. | [
"0",
"5",
"13490",
"3299391550",
"22042432252064127",
"2387505511919644051",
"680588297594638712735"
]
| [
"nonn",
"hard",
"more"
]
| 26 | 1 | 2 | [
"A000326",
"A007504",
"A061890",
"A066527",
"A364691",
"A364694",
"A364696",
"A366269"
]
| null | Paolo Xausa, Aug 03 2023 | 2023-10-07T07:01:03 | oeisdata/seq/A364/A364691.seq | 09a984386ae81f3abe417c741a652102 |
A364692 | Largest number that is the sum of n distinct primes in exactly n ways; 0 if no solution exists. | [
"68",
"130",
"42",
"59",
"76",
"0",
"0",
"161",
"192",
"233",
"227",
"276",
"0",
"425",
"480",
"0",
"0",
"0",
"752"
]
| [
"nonn",
"more"
]
| 15 | 2 | 1 | [
"A344989",
"A364692"
]
| null | Dmitry Kamenetsky, Aug 03 2023 | 2023-08-06T02:37:30 | oeisdata/seq/A364/A364692.seq | db7d1795c69a921a73f66efda56ee69d |
A364693 | Characteristic function of polygonal numbers of order greater than 2 (A090466): a(n) = 1 if n is in A090466, 0 otherwise. | [
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"1",
"1",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"1",
"1",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1"
]
| [
"nonn"
]
| 19 | 0 | null | [
"A010052",
"A010054",
"A090466",
"A255849",
"A364693"
]
| null | Paolo Xausa, Aug 03 2023 | 2023-08-07T09:48:19 | oeisdata/seq/A364/A364693.seq | 2b089881a26249ce8393cad61d6910dc |
A364694 | Polygonal numbers of order greater than 2 (A090466) which are the sum of the first k primes, for some k > 0. | [
"10",
"28",
"58",
"100",
"129",
"160",
"238",
"328",
"381",
"501",
"568",
"639",
"712",
"874",
"963",
"1060",
"1161",
"1264",
"1371",
"1480",
"1593",
"1720",
"1851",
"2127",
"2276",
"2427",
"2584",
"2914",
"3087",
"3447",
"3831",
"4227",
"4438",
"4888",
"5350",
"5589",
"5830",
"6081",
"6601",
"6870",
"8275",
"10191",
"10887",
"11599",
"12339",
"12718"
]
| [
"nonn"
]
| 16 | 1 | 1 | [
"A007504",
"A061890",
"A066527",
"A090466",
"A364691",
"A364694",
"A364695"
]
| null | Paolo Xausa, Aug 03 2023 | 2023-08-07T08:32:27 | oeisdata/seq/A364/A364694.seq | 08e3c66ac564094f7988bd56d760c6de |
A364695 | Positive integers k such that the sum of the first k primes is a polygonal number of order greater than 2 (A090466). | [
"3",
"5",
"7",
"9",
"10",
"11",
"13",
"15",
"16",
"18",
"19",
"20",
"21",
"23",
"24",
"25",
"26",
"27",
"28",
"29",
"30",
"31",
"32",
"34",
"35",
"36",
"37",
"39",
"40",
"42",
"44",
"46",
"47",
"49",
"51",
"52",
"53",
"54",
"56",
"57",
"62",
"68",
"70",
"72",
"74",
"75",
"76",
"77",
"78",
"79",
"80",
"82",
"83",
"84",
"85",
"86",
"87",
"88",
"90",
"91",
"92",
"97",
"99",
"103",
"105",
"106"
]
| [
"nonn"
]
| 21 | 1 | 1 | [
"A007504",
"A033997",
"A090466",
"A175133",
"A364693",
"A364694",
"A364695",
"A364696"
]
| null | Paolo Xausa, Aug 03 2023 | 2023-08-07T10:07:21 | oeisdata/seq/A364/A364695.seq | 831e470ca605f20b3128c216edc369e5 |
A364696 | Nonnegative integers k such that the sum of the first k primes is a pentagonal number. | [
"0",
"2",
"77",
"24587",
"48070640",
"471412484",
"7471587112"
]
| [
"nonn",
"hard",
"more"
]
| 18 | 1 | 2 | [
"A000326",
"A007504",
"A033997",
"A175133",
"A364691",
"A364695",
"A364696",
"A366270"
]
| null | Paolo Xausa, Aug 03 2023 | 2023-10-07T07:01:26 | oeisdata/seq/A364/A364696.seq | 0c871eb9476b79003fb62fe948a9f358 |
A364697 | Lexicographically earliest permutation of the positive integers such that the successive cumulative products reproduce the sequence itself, digit by digit. | [
"1",
"11",
"2",
"25",
"50",
"27",
"500",
"7",
"4",
"2500",
"3",
"71",
"250000",
"259",
"8",
"750000",
"10",
"39",
"5000000",
"2598",
"7500000000",
"77",
"9",
"6",
"2500000000",
"5",
"53",
"533",
"75000000001",
"38",
"383",
"43",
"75000000000000",
"35",
"84",
"13",
"103",
"12",
"5000000000000",
"28",
"67",
"30",
"48",
"25000000000000000",
"21",
"504",
"78",
"61",
"87"
]
| [
"base",
"nonn"
]
| 15 | 1 | 2 | [
"A309151",
"A364664",
"A364697"
]
| null | Eric Angelini, Aug 03 2023 | 2023-08-05T12:59:47 | oeisdata/seq/A364/A364697.seq | 5eddbde3fe9b35b48caef13dbc66baf0 |
A364698 | Numbers k such that k! + k^2 + k - 1 is prime. | [
"1",
"2",
"3",
"4",
"5",
"6",
"9",
"11",
"13",
"1045"
]
| [
"nonn",
"more"
]
| 87 | 1 | 2 | [
"A066143",
"A079649",
"A364698"
]
| null | Saish S. Kambali, Aug 03 2023 | 2024-07-06T01:30:59 | oeisdata/seq/A364/A364698.seq | 478c686ea78cc1313e13fc8077f1a717 |
A364699 | Numbers k such that 1 + 2^k + 3^k is divisible by 2*k-1. | [
"1",
"4",
"9",
"16",
"21",
"40",
"45",
"52",
"57",
"64",
"69",
"76",
"100",
"112",
"117",
"129",
"136",
"141",
"177",
"184",
"201",
"220",
"225",
"232",
"244",
"261",
"285",
"297",
"304",
"309",
"316",
"321",
"364",
"376",
"381",
"405",
"412",
"429",
"441",
"460",
"465",
"477",
"484",
"489",
"496",
"520",
"525",
"532",
"544",
"549",
"597",
"609",
"616",
"640",
"645",
"652",
"664",
"681",
"700",
"705",
"712",
"717"
]
| [
"nonn"
]
| 11 | 1 | 2 | [
"A001550",
"A290402",
"A364683",
"A364699"
]
| null | Robert Israel, Aug 02 2023 | 2025-06-02T15:27:01 | oeisdata/seq/A364/A364699.seq | 6facf09a434167390844a102e2e6d0ec |
A364700 | Numerators of coefficients in expansion of sqrt( Sum_{j>=1} x^prime(j) ). | [
"1",
"1",
"-1",
"9",
"-37",
"183",
"-565",
"1081",
"-25453",
"96427",
"-404927",
"1279359",
"-12561457",
"33077619",
"-194103389",
"577222425",
"-25302548477",
"74326953907",
"-423955653883",
"1225808143651",
"-14456976876619",
"42661352483945",
"-250437691682371",
"741244373831663",
"-17624677238323753",
"52507307961906687",
"-314022434935401067"
]
| [
"sign",
"frac"
]
| 10 | 1 | 4 | [
"A000040",
"A001790",
"A010051",
"A046161",
"A073749",
"A364700"
]
| null | Ilya Gutkovskiy, Aug 03 2023 | 2023-08-05T21:24:59 | oeisdata/seq/A364/A364700.seq | fe21745fc4cfa0613ad5bd5a635f0046 |
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