sequence_id
stringlengths 7
7
| sequence_name
stringlengths 4
573
| sequence
listlengths 1
348
| keywords
listlengths 1
8
| score
int64 1
2.35k
| offset_a
int64 -14,827
666,262,453B
| offset_b
int64 0
635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
listlengths 1
3
⌀ | author
stringlengths 7
231
⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-14 02:38:35
| filename
stringlengths 29
29
| hash
stringlengths 32
32
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A381815 | Smallest k>1 such that 10*k^(3*2^n)+1 is prime. | [
"3",
"2",
"2",
"2",
"138",
"24",
"695",
"107",
"250",
"404",
"4657",
"2185",
"27931"
]
| [
"nonn",
"base",
"more",
"hard"
]
| 25 | 0 | 1 | [
"A002254",
"A007283",
"A089319",
"A381793",
"A381815"
]
| null | Jakub Buczak, Mar 07 2025 | 2025-04-15T07:39:58 | oeisdata/seq/A381/A381815.seq | c29de8da4204e93bdc3ed4a4141fbfa9 |
A381816 | a(n) = (4*n^2 - (-1)^n - 2*n - 7)/4. | [
"-1",
"1",
"6",
"12",
"21",
"31",
"44",
"58",
"75",
"93",
"114",
"136",
"161",
"187",
"216",
"246",
"279",
"313",
"350",
"388",
"429",
"471",
"516",
"562",
"611",
"661",
"714",
"768",
"825",
"883",
"944",
"1006",
"1071",
"1137",
"1206",
"1276",
"1349",
"1423",
"1500",
"1578",
"1659",
"1741",
"1826",
"1912",
"2001",
"2091",
"2184",
"2278",
"2375",
"2473"
]
| [
"sign",
"easy"
]
| 8 | 1 | 3 | null | null | Eric W. Weisstein, Mar 07 2025 | 2025-03-08T01:34:27 | oeisdata/seq/A381/A381816.seq | 035224066a0b72793d0f8227307d688f |
A381817 | Expansion of (1/x) * Series_Reversion( x * (1-x) / C(x) ), where C(x) is the g.f. of A000108. | [
"1",
"2",
"8",
"41",
"239",
"1507",
"10016",
"69123",
"490676",
"3560150",
"26285896",
"196862679",
"1491921261",
"11420072162",
"88166571504",
"685724643699",
"5367842153463",
"42259058503891",
"334373741310812",
"2657683458672907",
"21209720057079565",
"169886023881795700",
"1365290865904393560"
]
| [
"nonn"
]
| 11 | 0 | 2 | [
"A000108",
"A381817",
"A381818",
"A381819",
"A381820"
]
| null | Seiichi Manyama, Mar 07 2025 | 2025-03-10T11:02:14 | oeisdata/seq/A381/A381817.seq | 0abc16636d99e4326f3821e9cfc22bb9 |
A381818 | Expansion of ( (1/x) * Series_Reversion( x * ((1-x) / C(x))^2 ) )^(1/2), where C(x) is the g.f. of A000108. | [
"1",
"2",
"12",
"97",
"903",
"9129",
"97419",
"1080058",
"12319200",
"143630575",
"1704099034",
"20507897766",
"249734145622",
"3071587654688",
"38102046141882",
"476138815310364",
"5988435287060671",
"75745116484532586",
"962898676577135634",
"12295850972794555196",
"157649023155654522723",
"2028662477759375282902"
]
| [
"nonn"
]
| 13 | 0 | 2 | [
"A000108",
"A364592",
"A381772",
"A381817",
"A381818",
"A381819",
"A381820",
"A381830",
"A381831"
]
| null | Seiichi Manyama, Mar 07 2025 | 2025-03-08T09:40:20 | oeisdata/seq/A381/A381818.seq | 4e092cb37e59f6969a0aad9caed0fc70 |
A381819 | Expansion of ( (1/x) * Series_Reversion( x * ((1-x) / C(x))^3 ) )^(1/3), where C(x) is the g.f. of A000108. | [
"1",
"2",
"16",
"177",
"2271",
"31731",
"468614",
"7195295",
"113712012",
"1837457589",
"30220139048",
"504212998955",
"8513461623355",
"145197727340337",
"2497695979786842",
"43285207907364178",
"755005614380697735",
"13244500528948104210",
"233515959911770430972",
"4135792046643993604967"
]
| [
"nonn"
]
| 13 | 0 | 2 | [
"A000108",
"A381773",
"A381817",
"A381818",
"A381819",
"A381820"
]
| null | Seiichi Manyama, Mar 07 2025 | 2025-03-08T09:40:06 | oeisdata/seq/A381/A381819.seq | df951a6414923f47e25237f6b65c72fb |
A381820 | Expansion of ( (1/x) * Series_Reversion( x * ((1-x) / C(x))^4 ) )^(1/4), where C(x) is the g.f. of A000108. | [
"1",
"2",
"20",
"281",
"4599",
"82113",
"1550993",
"30473930",
"616463800",
"12753523628",
"268586285058",
"5738804673016",
"124098812744140",
"2710824280371114",
"59728504549831296",
"1325862161472193292",
"29623682752417138511",
"665679666998856945540",
"15034747192791290846435"
]
| [
"nonn"
]
| 10 | 0 | 2 | [
"A000108",
"A381774",
"A381817",
"A381818",
"A381819",
"A381820"
]
| null | Seiichi Manyama, Mar 07 2025 | 2025-03-08T09:40:02 | oeisdata/seq/A381/A381820.seq | 271540bd63e30cb960c3487ebdfe23e7 |
A381821 | Fixed points of A381419. | [
"1",
"81",
"91",
"93",
"110",
"122",
"129",
"156",
"159",
"163",
"165",
"172",
"185",
"188",
"201",
"205",
"213",
"216",
"232",
"254",
"281",
"286",
"292",
"356",
"481",
"507",
"548",
"3553",
"3698",
"3776",
"3796",
"3808",
"3909",
"4132",
"4199",
"4250",
"4318",
"4414",
"4712",
"4713",
"4805",
"4898",
"4912",
"4976",
"5005",
"5182",
"5193",
"5354",
"5361",
"5445",
"5577",
"5658",
"5696"
]
| [
"nonn"
]
| 8 | 1 | 2 | [
"A381419",
"A381420",
"A381821"
]
| null | Scott R. Shannon, Mar 07 2025 | 2025-03-08T09:40:54 | oeisdata/seq/A381/A381821.seq | 37fab8a94b34d59d190ff12f7e43d220 |
A381822 | Odd cubefree numbers: odd numbers that are not divisible by any cube greater than 1. | [
"1",
"3",
"5",
"7",
"9",
"11",
"13",
"15",
"17",
"19",
"21",
"23",
"25",
"29",
"31",
"33",
"35",
"37",
"39",
"41",
"43",
"45",
"47",
"49",
"51",
"53",
"55",
"57",
"59",
"61",
"63",
"65",
"67",
"69",
"71",
"73",
"75",
"77",
"79",
"83",
"85",
"87",
"89",
"91",
"93",
"95",
"97",
"99",
"101",
"103",
"105",
"107",
"109",
"111",
"113",
"115",
"117",
"119",
"121",
"123",
"127",
"129",
"131"
]
| [
"nonn",
"easy"
]
| 10 | 1 | 2 | [
"A002117",
"A004709",
"A005408",
"A056911",
"A233091",
"A381822"
]
| null | Amiram Eldar, Mar 08 2025 | 2025-03-09T12:27:55 | oeisdata/seq/A381/A381822.seq | 08777f9dd27573e7c38471cee71c36fc |
A381823 | Odd cubefree numbers that are not squarefree. | [
"9",
"25",
"45",
"49",
"63",
"75",
"99",
"117",
"121",
"147",
"153",
"169",
"171",
"175",
"207",
"225",
"245",
"261",
"275",
"279",
"289",
"315",
"325",
"333",
"361",
"363",
"369",
"387",
"423",
"425",
"441",
"475",
"477",
"495",
"507",
"525",
"529",
"531",
"539",
"549",
"575",
"585",
"603",
"605",
"637",
"639",
"657",
"693",
"711",
"725",
"735",
"747",
"765",
"775"
]
| [
"nonn",
"easy"
]
| 8 | 1 | 1 | [
"A002117",
"A005408",
"A013661",
"A048103",
"A051903",
"A056911",
"A067259",
"A375039",
"A381822",
"A381823"
]
| null | Amiram Eldar, Mar 08 2025 | 2025-03-09T12:27:44 | oeisdata/seq/A381/A381823.seq | 7a2bad35adcbafc77eba4bf9068e5a1f |
A381824 | Odd cubefull numbers: odd numbers that are divisible by the cube of any of their prime factors. | [
"1",
"27",
"81",
"125",
"243",
"343",
"625",
"729",
"1331",
"2187",
"2197",
"2401",
"3125",
"3375",
"4913",
"6561",
"6859",
"9261",
"10125",
"12167",
"14641",
"15625",
"16807",
"16875",
"19683",
"24389",
"27783",
"28561",
"29791",
"30375",
"35937",
"42875",
"50625",
"50653",
"59049",
"59319",
"64827",
"68921",
"78125",
"79507",
"83349",
"83521",
"84375",
"91125"
]
| [
"nonn",
"easy"
]
| 7 | 1 | 2 | [
"A005408",
"A016755",
"A020639",
"A036966",
"A051904",
"A065483",
"A381824",
"A381825"
]
| null | Amiram Eldar, Mar 08 2025 | 2025-03-09T12:27:52 | oeisdata/seq/A381/A381824.seq | aaae56988d68ffc05d9cc6f19b8eb15e |
A381825 | Odd cubefull exponentially odd numbers: numbers whose prime factorization has only odd primes and odd exponents that are larger than 1 (except for 1 whose prime factorization is empty). | [
"1",
"27",
"125",
"243",
"343",
"1331",
"2187",
"2197",
"3125",
"3375",
"4913",
"6859",
"9261",
"12167",
"16807",
"19683",
"24389",
"29791",
"30375",
"35937",
"42875",
"50653",
"59319",
"68921",
"78125",
"79507",
"83349",
"84375",
"103823",
"132651",
"148877",
"161051",
"166375",
"177147",
"185193",
"205379",
"226981",
"273375",
"274625"
]
| [
"nonn",
"easy"
]
| 8 | 1 | 2 | [
"A005408",
"A036966",
"A065487",
"A335988",
"A369118",
"A376218",
"A381824",
"A381825"
]
| null | Amiram Eldar, Mar 08 2025 | 2025-03-09T12:27:48 | oeisdata/seq/A381/A381825.seq | 64b227483c25e6b0fc026102e44c2325 |
A381826 | G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x)^2), where C(x) is the g.f. of A000108. | [
"1",
"2",
"8",
"41",
"241",
"1545",
"10503",
"74429",
"543833",
"4067510",
"30985633",
"239560975",
"1874831287",
"14823253892",
"118222204539",
"949963236834",
"7683289712433",
"62499664522578",
"510992689465500",
"4196824203859773",
"34609480384100715",
"286461380785102398",
"2378954616256505177"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A000108",
"A014137",
"A129442",
"A381826",
"A381827"
]
| null | Seiichi Manyama, Mar 08 2025 | 2025-03-10T10:41:50 | oeisdata/seq/A381/A381826.seq | da003e48824d2bcdf4508ee595d21033 |
A381827 | G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x)^3), where C(x) is the g.f. of A000108. | [
"1",
"2",
"10",
"69",
"562",
"5042",
"48100",
"478547",
"4908338",
"51522174",
"550758208",
"5974753990",
"65608248500",
"727835313461",
"8144965594184",
"91834891588099",
"1042244963201914",
"11896871741939462",
"136493661712053752",
"1573151972820654218",
"18205626549920314728",
"211468167403628323318"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A000108",
"A014137",
"A129442",
"A381782",
"A381826",
"A381827"
]
| null | Seiichi Manyama, Mar 08 2025 | 2025-03-08T09:39:48 | oeisdata/seq/A381/A381827.seq | 7a881996845db48b5d4e7445f3366132 |
A381828 | Expansion of ( (1/x) * Series_Reversion( x * ((1-x) * (1-x+x^2))^2 ) )^(1/2). | [
"1",
"2",
"10",
"65",
"480",
"3824",
"32039",
"278256",
"2482578",
"22617830",
"209540672",
"1968031520",
"18696064179",
"179332892186",
"1734451272240",
"16895744042472",
"165621305486976",
"1632518433458400",
"16170959983623314",
"160888256475481560",
"1607061512154585046",
"16110030923830784248"
]
| [
"nonn"
]
| 13 | 0 | 2 | [
"A000108",
"A129442",
"A188687",
"A368975",
"A381817",
"A381828",
"A381829",
"A381831"
]
| null | Seiichi Manyama, Mar 08 2025 | 2025-03-10T10:50:02 | oeisdata/seq/A381/A381828.seq | 791b91ac9943c2214c05f26515ac533e |
A381829 | G.f. A(x) satisfies A(x) = C(x*A(x)) / (1 - x*A(x)^3), where C(x) is the g.f. of A000108. | [
"1",
"2",
"12",
"97",
"905",
"9187",
"98578",
"1099980",
"12636101",
"148449436",
"1775331503",
"21541303494",
"264533752068",
"3281596216087",
"41062196808517",
"517655936768189",
"6568539787903369",
"83827401412072474",
"1075254139150601581",
"13855040994605807348",
"179256835556387995412",
"2327788724156294034612"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A000108",
"A188687",
"A381783",
"A381817",
"A381828",
"A381829"
]
| null | Seiichi Manyama, Mar 08 2025 | 2025-03-08T09:39:40 | oeisdata/seq/A381/A381829.seq | c16aaaae78e637d98dba00014402004e |
A381830 | G.f. A(x) satisfies A(x) = C(x*A(x)^2) / (1 - x*A(x)), where C(x) is the g.f. of A000108. | [
"1",
"2",
"10",
"69",
"558",
"4946",
"46506",
"455587",
"4599494",
"47517909",
"499933964",
"5337957532",
"57694565830",
"630010984557",
"6939976239376",
"77027050722166",
"860564349616694",
"9670164031087137",
"109221767288604000",
"1239281689627682221",
"14119315749935075540",
"161460732437631678114"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A000108",
"A364592",
"A381778",
"A381818",
"A381830",
"A381831"
]
| null | Seiichi Manyama, Mar 08 2025 | 2025-03-08T09:39:53 | oeisdata/seq/A381/A381830.seq | a1276355fd9cfac85a59847c3c398334 |
A381831 | Expansion of ( (1/x) * Series_Reversion( x * ((1-x) * (1-x+x^2))^3 ) )^(1/3). | [
"1",
"2",
"14",
"133",
"1456",
"17306",
"217066",
"2827896",
"37895130",
"519000037",
"7232429952",
"102220846756",
"1461817707558",
"21112968248198",
"307527937374182",
"4512344039147420",
"66634574697351360",
"989569163283434676",
"14769533757869187052",
"221426909287107012800",
"3333042591222552282784",
"50353576994047154278451"
]
| [
"nonn"
]
| 11 | 0 | 2 | [
"A000108",
"A129442",
"A364592",
"A381818",
"A381828",
"A381830",
"A381831"
]
| null | Seiichi Manyama, Mar 08 2025 | 2025-03-08T09:39:36 | oeisdata/seq/A381/A381831.seq | c5d83828e8f7dbba52bfb5f606ea30c3 |
A381832 | G.f. A(x) satisfies A(x) = C(x*A(x)^3) / (1 - x), where C(x) is the g.f. of A000108. | [
"1",
"2",
"10",
"81",
"796",
"8616",
"98973",
"1184324",
"14602486",
"184219731",
"2366543116",
"30851212416",
"407106050261",
"5427274340091",
"72986372975716",
"988937692146346",
"13487903251385562",
"185022817888443780",
"2551096865411701371",
"35335463473311506321",
"491444773227779518956",
"6860346682881319595632"
]
| [
"nonn"
]
| 10 | 0 | 2 | [
"A000108",
"A014137",
"A188687",
"A364592",
"A381786",
"A381832"
]
| null | Seiichi Manyama, Mar 08 2025 | 2025-03-08T09:39:31 | oeisdata/seq/A381/A381832.seq | c5a134246c9fdd9d0c9f7f0628dc5f85 |
A381833 | k/25 is in this list if k > 5 and A053824(k) = A112765(k), i.e. if digitsum(k, 5) = valuation(k, 5). | [
"2",
"6",
"15",
"26",
"35",
"55",
"100",
"126",
"135",
"155",
"200",
"255",
"300",
"400",
"626",
"635",
"655",
"700",
"755",
"800",
"900",
"1125",
"1255",
"1300",
"1400",
"1625",
"1900",
"2125",
"2625",
"3126",
"3135",
"3155",
"3200",
"3255",
"3300",
"3400",
"3625",
"3755",
"3800",
"3900",
"4125",
"4400",
"4625",
"5125",
"6255",
"6300",
"6400",
"6625",
"6900",
"7125"
]
| [
"nonn",
"base"
]
| 6 | 1 | 1 | [
"A053824",
"A112765",
"A381833",
"A381834",
"A381835",
"A381836"
]
| null | Peter Luschny, Mar 09 2025 | 2025-03-09T12:57:22 | oeisdata/seq/A381/A381833.seq | 460a8c2c0322eef4a1673bcbe4e3719d |
A381834 | k/16 is in this list if k > 4 and A053737(k) = A235127(k), i.e. if digitsum(k, 4) = valuation(k, 4). | [
"2",
"5",
"12",
"17",
"24",
"36",
"65",
"72",
"84",
"112",
"132",
"160",
"208",
"257",
"264",
"276",
"304",
"324",
"352",
"400",
"516",
"544",
"592",
"704",
"784",
"896",
"1025",
"1032",
"1044",
"1072",
"1092",
"1120",
"1168",
"1284",
"1312",
"1360",
"1472",
"1552",
"1664",
"1856",
"2052",
"2080",
"2128",
"2240",
"2320",
"2432",
"2624",
"3088",
"3200",
"3392"
]
| [
"nonn",
"base"
]
| 5 | 1 | 1 | [
"A053737",
"A235127",
"A381833",
"A381834",
"A381835",
"A381837"
]
| null | Peter Luschny, Mar 09 2025 | 2025-03-09T12:57:29 | oeisdata/seq/A381/A381834.seq | 1e9867f46fc735091908d8b130b9d3b7 |
A381835 | k/9 is in this list if k > 3 and A053735(k) = A007949(k), i.e. if digitsum(k, 3) = valuation(k, 3). | [
"2",
"4",
"10",
"15",
"21",
"28",
"33",
"39",
"57",
"72",
"82",
"87",
"93",
"111",
"126",
"144",
"165",
"180",
"198",
"244",
"249",
"255",
"273",
"288",
"306",
"327",
"342",
"360",
"414",
"459",
"489",
"504",
"522",
"576",
"621",
"675",
"730",
"735",
"741",
"759",
"774",
"792",
"813",
"828",
"846",
"900",
"945",
"975",
"990",
"1008",
"1062",
"1107",
"1161",
"1224",
"1269",
"1323"
]
| [
"nonn",
"base"
]
| 6 | 0 | 1 | [
"A007949",
"A053735",
"A381833",
"A381834",
"A381835",
"A381838"
]
| null | Peter Luschny, Mar 09 2025 | 2025-03-09T12:57:40 | oeisdata/seq/A381/A381835.seq | 2ac8cfe36a18765e9e59c16499f00e9d |
A381836 | k/25 is in this list if A053824(k) < A112765(k), i.e. if digitsum(k, 5) < valuation(k, 5). | [
"1",
"5",
"10",
"25",
"30",
"50",
"75",
"125",
"130",
"150",
"175",
"250",
"275",
"375",
"500",
"625",
"630",
"650",
"675",
"750",
"775",
"875",
"1000",
"1250",
"1275",
"1375",
"1500",
"1875",
"2000",
"2500",
"3125",
"3130",
"3150",
"3175",
"3250",
"3275",
"3375",
"3500",
"3750",
"3775",
"3875",
"4000",
"4375",
"4500",
"5000",
"5625",
"6250",
"6275",
"6375"
]
| [
"nonn",
"base"
]
| 10 | 1 | 2 | [
"A053824",
"A112765",
"A371176",
"A381836",
"A381837",
"A381838"
]
| null | Peter Luschny, Mar 08 2025 | 2025-03-09T12:57:47 | oeisdata/seq/A381/A381836.seq | c6454c1c1e37d143c26d7e5ad19ad393 |
A381837 | k/16 is in this list if A053737(k) < A235127(k), i.e. if digitsum(k, 4) < valuation(k, 4). | [
"1",
"4",
"8",
"16",
"20",
"32",
"48",
"64",
"68",
"80",
"96",
"128",
"144",
"192",
"256",
"260",
"272",
"288",
"320",
"336",
"384",
"448",
"512",
"528",
"576",
"640",
"768",
"832",
"1024",
"1028",
"1040",
"1056",
"1088",
"1104",
"1152",
"1216",
"1280",
"1296",
"1344",
"1408",
"1536",
"1600",
"1792",
"2048",
"2064",
"2112",
"2176",
"2304",
"2368",
"2560",
"2816"
]
| [
"nonn",
"base"
]
| 10 | 1 | 2 | [
"A053737",
"A235127",
"A371176",
"A381836",
"A381837",
"A381838"
]
| null | Peter Luschny, Mar 08 2025 | 2025-03-09T12:57:56 | oeisdata/seq/A381/A381837.seq | bf639f5098a9ec19c6f130a9cb154444 |
A381838 | k/9 is in this list if A053735(k) < A007949(k), i.e. if digitsum(k, 3) < valuation(k, 3). | [
"1",
"3",
"6",
"9",
"12",
"18",
"27",
"30",
"36",
"45",
"54",
"63",
"81",
"84",
"90",
"99",
"108",
"117",
"135",
"162",
"171",
"189",
"216",
"243",
"246",
"252",
"261",
"270",
"279",
"297",
"324",
"333",
"351",
"378",
"405",
"432",
"486",
"495",
"513",
"540",
"567",
"594",
"648",
"729",
"732",
"738",
"747",
"756",
"765",
"783",
"810",
"819",
"837",
"864",
"891",
"918",
"972",
"981",
"999"
]
| [
"nonn",
"base"
]
| 11 | 1 | 2 | [
"A007949",
"A053735",
"A371176",
"A381836",
"A381837",
"A381838"
]
| null | Peter Luschny, Mar 08 2025 | 2025-03-09T12:58:26 | oeisdata/seq/A381/A381838.seq | b3725485dfeade84769faf92bc824503 |
A381839 | In the binary expansion of n (without leading zeros): complement the bits strictly between the leftmost and the rightmost 0's, if any. | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"10",
"9",
"8",
"11",
"12",
"13",
"14",
"15",
"22",
"21",
"20",
"19",
"18",
"17",
"16",
"23",
"26",
"25",
"24",
"27",
"28",
"29",
"30",
"31",
"46",
"45",
"44",
"43",
"42",
"41",
"40",
"39",
"38",
"37",
"36",
"35",
"34",
"33",
"32",
"47",
"54",
"53",
"52",
"51",
"50",
"49",
"48",
"55",
"58",
"57",
"56",
"59",
"60",
"61",
"62",
"63",
"94",
"93",
"92",
"91"
]
| [
"nonn",
"base",
"easy"
]
| 14 | 0 | 3 | [
"A000225",
"A030130",
"A122155",
"A381839",
"A381852"
]
| null | Rémy Sigrist, Mar 08 2025 | 2025-03-10T11:11:50 | oeisdata/seq/A381/A381839.seq | 9ec0e945aeb3809568901ce60d16cd77 |
A381840 | G.f. A(x) satisfies A(x) = 1 + x*A(x)^4 - x^2*A(x)^7. | [
"1",
"1",
"3",
"11",
"42",
"153",
"469",
"690",
"-5967",
"-82708",
"-700876",
"-4989894",
"-32082336",
"-190742496",
"-1053280998",
"-5347579160",
"-24162468390",
"-88249158963",
"-157067396045",
"1334548659436",
"20996875910808",
"194476989681546",
"1491599102987040",
"10232074769143770",
"64440205192609155"
]
| [
"sign"
]
| 7 | 0 | 3 | [
"A103779",
"A367027",
"A368971",
"A381840"
]
| null | Seiichi Manyama, Mar 08 2025 | 2025-03-08T09:39:24 | oeisdata/seq/A381/A381840.seq | f97a792f5a360777436332c0f6a097f3 |
A381841 | Position of the n-th occurrence of the digit 3 in A105083(n-1) for n>=1. | [
"3",
"9",
"12",
"16",
"22",
"28",
"31",
"37",
"40",
"44",
"50",
"53",
"57",
"63",
"69",
"72",
"76",
"82",
"88",
"91",
"97",
"100",
"104",
"110",
"116",
"119",
"125",
"128",
"132",
"138",
"141",
"145",
"151",
"157",
"160",
"166",
"169",
"173",
"179",
"182",
"186",
"192",
"198",
"201",
"205",
"211",
"217",
"220",
"226",
"229",
"233",
"239",
"242",
"246",
"252",
"258"
]
| [
"nonn"
]
| 11 | 1 | 1 | [
"A064105",
"A105083",
"A136495",
"A136496",
"A202342",
"A381841"
]
| null | Jeffrey Shallit, Mar 08 2025 | 2025-03-09T12:51:57 | oeisdata/seq/A381/A381841.seq | f9497f9c3e0b36b380354f856e78a2af |
A381842 | Triangle read by rows: T(n,k) is the number of non-equivalent subsets of size k in S_n, 0 <= k <= n!. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"2",
"1",
"1",
"1",
"1",
"4",
"10",
"41",
"103",
"309",
"691",
"1458",
"2448",
"3703",
"4587",
"5050",
"4587",
"3703",
"2448",
"1458",
"691",
"309",
"103",
"41",
"10",
"4",
"1",
"1",
"1",
"1",
"6",
"37",
"715",
"13710",
"256751",
"4140666",
"58402198",
"726296995",
"8060937770",
"80604620206",
"732149722382"
]
| [
"nonn",
"tabf"
]
| 65 | 0 | 10 | [
"A000041",
"A362763",
"A381842"
]
| null | Raghavendra Tripathi, Mar 09 2025 | 2025-04-09T11:21:13 | oeisdata/seq/A381/A381842.seq | 4bc45806876495e1cfb2cefdd21b6054 |
A381843 | Decimal expansion of (40320*e^9 - 322560*e^8 + 987840*e^7 - 1451520*e^6 + 1050000*e^5 - 344064*e^4 + 40824*e^3 - 1024*e^2 + e) / 40320. | [
"1",
"8",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"5",
"2",
"7",
"0",
"3",
"2",
"1",
"3",
"4",
"8",
"9",
"5",
"5",
"5",
"2",
"1",
"7",
"2",
"2",
"9",
"4",
"8",
"5",
"6",
"9",
"6",
"1",
"0",
"0",
"2",
"7",
"8",
"4",
"8",
"3",
"5",
"6",
"2",
"1",
"5",
"5",
"0",
"7",
"6",
"9",
"8",
"4",
"1",
"6",
"0",
"8",
"4",
"6",
"7",
"9",
"9",
"2",
"7",
"1",
"6",
"2",
"2",
"2",
"5",
"3",
"5",
"9",
"5",
"2",
"6",
"2",
"6",
"5",
"8",
"1",
"1",
"3"
]
| [
"nonn",
"cons",
"easy"
]
| 30 | 2 | 2 | [
"A001113",
"A089087",
"A089139",
"A090142",
"A090143",
"A090611",
"A379601",
"A381673",
"A381843",
"A382020",
"A382026"
]
| null | Daniel Mondot, Mar 12 2025 | 2025-03-23T05:29:15 | oeisdata/seq/A381/A381843.seq | ccd79adce917fd403f73ac8549b2a80a |
A381844 | Quotients of A380487. | [
"1",
"3",
"5",
"7",
"11",
"19",
"23",
"34",
"91",
"105",
"209",
"221",
"231",
"385",
"399",
"429",
"481",
"609",
"665",
"715",
"805",
"897",
"1001",
"1105",
"1430",
"1729",
"1870",
"2046",
"2233",
"2261",
"3094",
"3230",
"3553",
"3565",
"3774",
"4278",
"4862",
"4921",
"4945",
"5270",
"5358",
"5365",
"6409",
"6670",
"7429",
"7462",
"7657",
"7990",
"8041",
"8569"
]
| [
"nonn"
]
| 39 | 1 | 2 | [
"A007947",
"A008472",
"A380487",
"A381844"
]
| null | Torlach Rush, Mar 10 2025 | 2025-05-02T04:22:20 | oeisdata/seq/A381/A381844.seq | a0157b53d8a263c2a01b30a48b0a464f |
A381845 | a(n) = denominator( (e/Pi)*Integral_{x=-oo..+oo} cos(x)/(1 + x^2)^n dx ). | [
"1",
"1",
"8",
"48",
"192",
"3840",
"46080",
"322560",
"10321920",
"26542080",
"1857945600",
"11678515200",
"1961990553600",
"25505877196800",
"1428329123020800",
"42849873690624000",
"8903869857792000",
"46620662575398912000",
"2634762720116736000",
"31888533201572855808000",
"196237127394294497280000"
]
| [
"nonn",
"frac"
]
| 13 | 1 | 3 | [
"A061360",
"A061382",
"A143991",
"A381845"
]
| null | Stefano Spezia, Mar 12 2025 | 2025-03-13T08:56:32 | oeisdata/seq/A381/A381845.seq | ec27e632c5efe083f98d5501ae894dbe |
A381846 | Area of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000108(n) and its long leg and hypotenuse are consecutive natural numbers. | [
"0",
"0",
"6",
"180",
"4914",
"142926",
"4547796",
"157355484",
"5842280730",
"229795151586",
"9475645552620",
"406294220860710",
"18000809380947036",
"820011973477512900",
"38258534425043501640",
"1822437060664227775020",
"88405827105467677196970",
"4358079981772447955690490",
"217935769988152202470568700"
]
| [
"nonn",
"easy"
]
| 14 | 0 | 3 | [
"A000108",
"A131428",
"A381846",
"A383615",
"A383616"
]
| null | Miguel-Ángel Pérez García-Ortega, May 06 2025 | 2025-05-11T18:00:27 | oeisdata/seq/A381/A381846.seq | da8a7faf5987b618c291a92afacf4f8d |
A381847 | a(n) is the number of ways to partition an n X n X n cube into 3 cuboids of different dimensions. | [
"0",
"0",
"2",
"3",
"8",
"11",
"19",
"23",
"35",
"40",
"55",
"62",
"80",
"88",
"110",
"119",
"144",
"155",
"183",
"195",
"227",
"240",
"275",
"290",
"328",
"344",
"386",
"403",
"448",
"467",
"515",
"535",
"587",
"608",
"663",
"686",
"744",
"768",
"830",
"855",
"920",
"947",
"1015",
"1043",
"1115",
"1144",
"1219",
"1250",
"1328",
"1360",
"1442",
"1475",
"1560"
]
| [
"nonn"
]
| 29 | 1 | 3 | [
"A381847",
"A381848",
"A381849"
]
| null | Janaka Rodrigo, May 06 2025 | 2025-05-15T19:03:56 | oeisdata/seq/A381/A381847.seq | 3058571ba625888ee4760687d08b3b8a |
A381848 | Sequence obtained by replacing 3-term subwords of A010060 by 0,1,2,3,4,5 as described in Comments. | [
"2",
"5",
"4",
"1",
"3",
"0",
"2",
"5",
"3",
"0",
"1",
"4",
"2",
"5",
"4",
"1",
"3",
"0",
"1",
"4",
"2",
"5",
"3",
"0",
"2",
"5",
"4",
"1",
"3",
"0",
"2",
"5",
"3",
"0",
"1",
"4",
"2",
"5",
"3",
"0",
"2",
"5",
"4",
"1",
"3",
"0",
"1",
"4",
"2",
"5",
"4",
"1",
"3",
"0",
"2",
"5",
"3",
"0",
"1",
"4",
"2",
"5",
"4",
"1",
"3",
"0",
"1",
"4",
"2",
"5",
"3",
"0",
"2",
"5",
"4",
"1",
"3",
"0",
"1",
"4",
"2",
"5",
"4",
"1",
"3",
"0"
]
| [
"nonn"
]
| 47 | 1 | 1 | [
"A010060",
"A157970",
"A157971",
"A248057",
"A248104",
"A248105",
"A248956",
"A381848",
"A383999"
]
| null | Clark Kimberling, May 28 2025 | 2025-06-01T17:38:28 | oeisdata/seq/A381/A381848.seq | 490606365d4d3d545ac77f3ab37fb331 |
A381849 | Intersection of A025487 and A242298. | [
"1",
"2",
"4",
"6",
"12",
"24",
"36",
"48",
"60",
"120",
"180",
"240",
"360",
"420",
"840",
"1680",
"2520",
"5040",
"7560",
"10080",
"12600",
"15120",
"20160",
"25200",
"27720",
"55440",
"83160",
"110880",
"138600",
"166320",
"221760",
"277200",
"332640",
"360360",
"720720",
"1441440",
"2162160",
"2882880",
"3603600",
"4324320",
"5765760",
"6486480",
"7207200",
"8648640"
]
| [
"nonn"
]
| 28 | 1 | 2 | [
"A025487",
"A095848",
"A242298",
"A381849"
]
| null | Hal M. Switkay, May 18 2025 | 2025-05-22T21:31:06 | oeisdata/seq/A381/A381849.seq | 38ab7e0d903c34022bfe229633f83d09 |
A381850 | Primes p preceded and followed by primes whose difference is less than 2*log(p). | [
"41",
"43",
"59",
"61",
"71",
"73",
"101",
"103",
"107",
"109",
"137",
"151",
"163",
"167",
"179",
"193",
"197",
"227",
"229",
"233",
"239",
"269",
"271",
"277",
"281",
"311",
"313",
"349",
"353",
"379",
"383",
"419",
"421",
"431",
"433",
"439",
"443",
"457",
"461",
"463",
"487",
"491",
"499",
"503",
"563",
"569",
"571",
"593",
"599",
"601",
"607",
"613",
"617",
"641",
"643",
"647",
"653"
]
| [
"nonn"
]
| 40 | 1 | 1 | [
"A000040",
"A031131",
"A288907",
"A381850",
"A383652"
]
| null | Alain Rocchelli, May 06 2025 | 2025-06-06T19:26:29 | oeisdata/seq/A381/A381850.seq | c79c12e0b9833928426ec1b94b2ac215 |
A381851 | a(n) is the least number k such that both k and k - s have n prime divisors, counted with multiplicity, where s is the sum of the decimal digits of k. | [
"10",
"20",
"40",
"80",
"224",
"448",
"2176",
"24640",
"98816",
"287744",
"3771392",
"5637632",
"6508544",
"323903488",
"1126252544",
"7698939904",
"20511260672",
"249460531200",
"857557762048",
"582799458304",
"11797582053376",
"24614476447744",
"591901367468032",
"1314105503776768",
"5988418763882496"
]
| [
"nonn",
"base",
"hard"
]
| 27 | 2 | 1 | [
"A001222",
"A007953",
"A066568",
"A381851",
"A382996",
"A383665"
]
| null | Robert Israel, May 06 2025 | 2025-05-29T00:54:24 | oeisdata/seq/A381/A381851.seq | ed4c74087026d21edd2e8e096742b2a3 |
A381852 | In the binary expansion of n (without leading zeros): complement the bits strictly to the right of the leftmost zero digit, if any. | [
"0",
"1",
"2",
"3",
"5",
"4",
"6",
"7",
"11",
"10",
"9",
"8",
"13",
"12",
"14",
"15",
"23",
"22",
"21",
"20",
"19",
"18",
"17",
"16",
"27",
"26",
"25",
"24",
"29",
"28",
"30",
"31",
"47",
"46",
"45",
"44",
"43",
"42",
"41",
"40",
"39",
"38",
"37",
"36",
"35",
"34",
"33",
"32",
"55",
"54",
"53",
"52",
"51",
"50",
"49",
"48",
"59",
"58",
"57",
"56",
"61",
"60",
"62",
"63",
"95",
"94",
"93",
"92"
]
| [
"nonn",
"base",
"easy"
]
| 14 | 0 | 3 | [
"A054429",
"A063250",
"A075427",
"A381839",
"A381852"
]
| null | Rémy Sigrist, Mar 08 2025 | 2025-03-10T11:11:53 | oeisdata/seq/A381/A381852.seq | 0f6d827355c1baa0419de32d6fbe372f |
A381853 | Expansion of 1/( Product_{k=0..3} (1 + (-1)^k * (2*k+1) * x) ). | [
"1",
"4",
"50",
"260",
"2331",
"13944",
"110020",
"709720",
"5275061",
"35405084",
"255481590",
"1750273980",
"12442802191",
"86146389424",
"607794442760",
"4230723277040",
"29734284335721",
"207543980222964",
"1455788202761530",
"10175616585022900",
"71303822881787651",
"498754234084641704"
]
| [
"nonn",
"easy"
]
| 96 | 0 | 2 | [
"A381853",
"A383624"
]
| null | Seiichi Manyama, May 03 2025 | 2025-05-04T14:44:05 | oeisdata/seq/A381/A381853.seq | a047fa6964ff6f505ae2ba184dba3c0b |
A381854 | Triangle read by rows: T(n, k) is the number of invertible n X n matrices over GF(2) that can be optimally row-reduced in k steps, n >= 0, k >= 0. | [
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"6",
"24",
"51",
"60",
"24",
"2",
"1",
"12",
"96",
"542",
"2058",
"5316",
"7530",
"4058",
"541",
"6",
"1",
"20",
"260",
"2570",
"19680",
"117860",
"540470",
"1769710",
"3571175",
"3225310",
"736540",
"15740",
"24",
"1",
"30",
"570",
"8415",
"101610",
"1026852",
"8747890",
"61978340",
"355193925",
"1561232840",
"4753747050",
"8111988473",
"4866461728",
"437272014",
"949902",
"120"
]
| [
"nonn",
"tabf",
"hard"
]
| 40 | 0 | 4 | [
"A002378",
"A002884",
"A172225",
"A381854"
]
| null | Søren Fuglede Jørgensen, Mar 08 2025 | 2025-03-09T16:21:26 | oeisdata/seq/A381/A381854.seq | 47368eb92436352616bc28167fbfc254 |
A381855 | Starting from prime(n), a(n) is the minimum number > 1 of consecutive primes whose sum is the lesser of a twin prime pair. | [
"2",
"95",
"317",
"23",
"3",
"5",
"3",
"3",
"277",
"7",
"7",
"25",
"35",
"237",
"7",
"5",
"17",
"41",
"15",
"33",
"23",
"7",
"3",
"111",
"257",
"3",
"7",
"57",
"5",
"11",
"57",
"13",
"11",
"79",
"45",
"67",
"29",
"97",
"11",
"15",
"15",
"21",
"113",
"19",
"35",
"15",
"9",
"5",
"123",
"29",
"59",
"27",
"19",
"227",
"223",
"37",
"279",
"53",
"41",
"3",
"135",
"53",
"143",
"81",
"41",
"29",
"39",
"63"
]
| [
"nonn"
]
| 27 | 1 | 1 | [
"A001359",
"A381855"
]
| null | Abhiram R Devesh, Mar 08 2025 | 2025-03-23T16:46:05 | oeisdata/seq/A381/A381855.seq | 48a1d07111f1e246c24ddcc7a35ca26b |
A381856 | Lexicographically earliest sequence of positive integers such that for any value k, no two sets of two or more indices at which k occurs have the same standard deviation. | [
"1",
"1",
"2",
"1",
"2",
"2",
"3",
"1",
"3",
"2",
"4",
"3",
"3",
"4",
"4",
"1",
"5",
"2",
"5",
"3",
"4",
"5",
"4",
"6",
"1",
"5",
"6",
"6",
"2",
"3",
"7",
"5",
"6",
"4",
"6",
"1",
"7",
"7",
"8",
"5",
"7",
"8",
"8",
"9",
"6",
"9",
"2",
"8",
"3",
"7",
"4",
"5",
"9",
"9",
"8",
"10",
"9",
"10",
"10",
"11",
"7",
"1",
"8",
"10",
"11",
"11",
"6",
"11",
"9",
"12",
"10",
"2",
"12",
"8",
"11",
"13",
"12",
"12",
"3",
"10",
"13",
"13"
]
| [
"nonn"
]
| 18 | 1 | 3 | [
"A337226",
"A380751",
"A380783",
"A380968",
"A381856",
"A382381"
]
| null | Neal Gersh Tolunsky, Mar 08 2025 | 2025-03-29T15:44:30 | oeisdata/seq/A381/A381856.seq | e6e9276fc24943a72d0eadca9a90270a |
A381857 | Number of n X n binary matrices with at least 2 adjacent 1's. | [
"0",
"0",
"9",
"449",
"64302",
"33498985",
"68713877875",
"562948673292362",
"18446743413061588661",
"2417851638458709952150645",
"1267650600226199352445557225326",
"2658455991569819662405962686908743173",
"22300745198530622979053904922855772969397419"
]
| [
"nonn"
]
| 17 | 0 | 3 | [
"A002416",
"A006506",
"A381857"
]
| null | Benjamin Ghitterman, Mar 08 2025 | 2025-03-15T23:29:40 | oeisdata/seq/A381/A381857.seq | 0b575347fa772d2f7a447b5ea38d2cb5 |
A381858 | a(n) is the number of permutations of [n] that avoid 312 and 4321 and whose square avoids 231. | [
"1",
"1",
"2",
"5",
"12",
"26",
"56",
"125",
"279",
"618",
"1367",
"3030",
"6720",
"14896",
"33013",
"73173",
"162198",
"359525",
"796900",
"1766366",
"3915256",
"8678393",
"19236131",
"42637934",
"94509351",
"209485238",
"464335636",
"1029225640",
"2281335673",
"5056707001",
"11208471338",
"24844197877",
"55068541516"
]
| [
"nonn",
"easy"
]
| 26 | 0 | 3 | null | null | Kassie Archer, Mar 10 2025 | 2025-05-13T09:53:28 | oeisdata/seq/A381/A381858.seq | c2356ed4ec46a1d5ab646611fc85bb88 |
A381859 | a(n) is the number of permutations that avoid 312 and 4321 and whose square avoids 321. | [
"1",
"1",
"2",
"5",
"11",
"23",
"50",
"109",
"236",
"511",
"1108",
"2402",
"5206",
"11284",
"24459",
"53016",
"114914",
"249081",
"539894",
"1170243",
"2536551",
"5498082",
"11917326",
"25831309",
"55990457",
"121361689",
"263056605",
"570186341",
"1235903062",
"2678872272",
"5806569196",
"12585984849",
"27280655629"
]
| [
"nonn",
"easy"
]
| 23 | 0 | 3 | [
"A001590",
"A381859"
]
| null | Kassie Archer, Mar 10 2025 | 2025-05-13T09:46:53 | oeisdata/seq/A381/A381859.seq | 3632ad139cf7674faca5c60805fddb37 |
A381860 | G.f. A(x) satisfies A(x) = (1 + x)^3 * C(x*A(x)), where C(x) is the g.f. of A000108. | [
"1",
"4",
"12",
"55",
"327",
"2157",
"15141",
"110853",
"836790",
"6465309",
"50876776",
"406335099",
"3285202335",
"26835060422",
"221128733649",
"1835973630276",
"15344202894457",
"128983332603009",
"1089803313492966",
"9250137181234430",
"78837133437062307",
"674408139329393187",
"5788618956395607745"
]
| [
"nonn"
]
| 10 | 0 | 2 | [
"A000108",
"A367640",
"A381787",
"A381860",
"A381882"
]
| null | Seiichi Manyama, Mar 08 2025 | 2025-03-10T10:37:18 | oeisdata/seq/A381/A381860.seq | b8a01bfe5ff059299dd69f9de8e0de3a |
A381861 | G.f. A(x) satisfies A(x) = (1 + x*A(x))^4 * C(x), where C(x) is the g.f. of A000108. | [
"1",
"5",
"32",
"231",
"1797",
"14715",
"125064",
"1093194",
"9766783",
"88793815",
"818832674",
"7640868924",
"72014955566",
"684551660324",
"6555290711728",
"63179148757584",
"612376024087047",
"5965515657187437",
"58375460484257734",
"573545171374958628",
"5655759227878768987",
"55957005428512022905"
]
| [
"nonn"
]
| 14 | 0 | 2 | [
"A000108",
"A127632",
"A153299",
"A381861",
"A381877"
]
| null | Seiichi Manyama, Mar 08 2025 | 2025-03-09T09:55:26 | oeisdata/seq/A381/A381861.seq | 33494d2fbe6f2d5846d4caf71bee7203 |
A381862 | Number of pairs of triangles that are pairwise edge-disjoint in the complete graph K_n. | [
"15",
"100",
"385",
"1120",
"2730",
"5880",
"11550",
"21120",
"36465",
"60060",
"95095",
"145600",
"216580",
"314160",
"445740",
"620160",
"847875",
"1141140",
"1514205",
"1983520",
"2567950",
"3289000",
"4171050",
"5241600",
"6531525",
"8075340",
"9911475",
"12082560",
"14635720",
"17622880",
"21101080",
"25132800",
"29786295"
]
| [
"nonn",
"easy"
]
| 45 | 5 | 1 | [
"A054647",
"A381862",
"A381863"
]
| null | Julian Allagan, Mar 08 2025 | 2025-03-28T08:35:45 | oeisdata/seq/A381/A381862.seq | 3a9110344adc8ef6fae5165a0de47200 |
A381863 | Number of triples of triangles that are pairwise edge-disjoint in the complete graph K_n. | [
"120",
"1575",
"10080",
"44380",
"154000",
"451990",
"1170400",
"2748460",
"5965960",
"12137125",
"23383360",
"43006600",
"75988640",
"129645740",
"214472000",
"345209480",
"542187800",
"832980995",
"1254434720",
"1855122500",
"2698295600",
"3865397250",
"5460218400",
"7613778900",
"10490025000"
]
| [
"nonn",
"easy"
]
| 42 | 6 | 1 | [
"A054647",
"A381862",
"A381863"
]
| null | Julian Allagan, Mar 08 2025 | 2025-03-28T08:55:52 | oeisdata/seq/A381/A381863.seq | 4efbf9bd047621fcf2055659a40a156d |
A381864 | Numbers k in A024619 such that p^(m+1) == r (mod k) where r is also in A024619 for all p | n. | [
"15",
"33",
"35",
"44",
"45",
"51",
"63",
"65",
"66",
"69",
"70",
"75",
"76",
"77",
"80",
"85",
"87",
"88",
"90",
"91",
"92",
"95",
"99",
"102",
"104",
"105",
"115",
"119",
"123",
"130",
"133",
"135",
"138",
"140",
"141",
"143",
"144",
"145",
"152",
"153",
"154",
"159",
"160",
"161",
"170",
"172",
"174",
"175",
"176",
"177",
"180",
"184",
"185",
"187",
"188",
"189",
"190"
]
| [
"nonn"
]
| 78 | 1 | 1 | [
"A000961",
"A024619",
"A381750",
"A381864",
"A382120"
]
| null | Michael De Vlieger, Apr 06 2025 | 2025-05-30T23:15:38 | oeisdata/seq/A381/A381864.seq | a0dff8562fc6a8f64e6aee8ac44aa212 |
A381865 | Number of sequences in which the matches of a fully symmetric single-elimination tournament with 3^n players can be played if arbitrarily many matches can occur simultaneously and each match involves 3 players. | [
"1",
"1",
"13",
"308682013",
"20447648974223714249697186722386536049691073"
]
| [
"nonn",
"more"
]
| 9 | 0 | 3 | [
"A273723",
"A379758",
"A381865"
]
| null | Noah A Rosenberg, Mar 08 2025 | 2025-03-19T10:25:12 | oeisdata/seq/A381/A381865.seq | d85ffb704327ad24c4fe3de2833fba5f |
A381866 | Number of labeled histories for rooted 5-furcating trees with 4n+1 leaves if simultaneous 5-furcations are not allowed. | [
"1",
"1",
"126",
"162162",
"1003458456",
"20419376121144",
"1084881453316380720",
"128835096988586792403600",
"30577206578883234961900809600",
"13328512616115465470187677202211200",
"9988360697491697592427704919982668857600",
"12203369577406758958826880335333105520792518400"
]
| [
"nonn"
]
| 14 | 0 | 3 | [
"A006472",
"A007696",
"A339411",
"A381533",
"A381536",
"A381866"
]
| null | Noah A Rosenberg, Mar 08 2025 | 2025-03-12T13:13:01 | oeisdata/seq/A381/A381866.seq | 5519293914efac175fe6c5c93b7284bd |
A381867 | G.f. A(x) satisfies A(x) = C(x*A(x)) / (1 - x)^2, where C(x) is the g.f. of A000108. | [
"1",
"3",
"10",
"44",
"239",
"1464",
"9610",
"65946",
"466951",
"3385259",
"24999475",
"187385168",
"1421901090",
"10901237530",
"84312106160",
"657031204068",
"5153954345309",
"40663760712441",
"322478148002872",
"2569086552458460",
"20551321340065924",
"165009872444132477",
"1329352163579556971",
"10742386009423170696"
]
| [
"nonn"
]
| 10 | 0 | 2 | [
"A000108",
"A188687",
"A366034",
"A381867"
]
| null | Seiichi Manyama, Mar 08 2025 | 2025-03-09T09:55:33 | oeisdata/seq/A381/A381867.seq | 0625bd2f87db20c8783ef85d71e348f9 |
A381868 | Starting from the n-th prime, a(n) is the minimum number > 1 of consecutive primes whose sum is the greater of a twin prime pair. | [
"2",
"137",
"95",
"3",
"339",
"93",
"51",
"5",
"49",
"5",
"3",
"115",
"91",
"35",
"331",
"7",
"11",
"3",
"19",
"29",
"5",
"187",
"515",
"15",
"13",
"79",
"203",
"11",
"3",
"69",
"9",
"93",
"7",
"13",
"13",
"5",
"189",
"71",
"289",
"419",
"35",
"239",
"11",
"9",
"9",
"33",
"3",
"129",
"57",
"75",
"71",
"53",
"23",
"121",
"523",
"13",
"11",
"3",
"9",
"11",
"3",
"193",
"87",
"5",
"23",
"181",
"115",
"3"
]
| [
"nonn"
]
| 24 | 1 | 1 | [
"A006512",
"A381766",
"A381855",
"A381868"
]
| null | Abhiram R Devesh, Mar 08 2025 | 2025-05-12T14:38:25 | oeisdata/seq/A381/A381868.seq | 52bcf2dc9dbeb133578a27beb68d1dda |
A381869 | Smallest starting prime for which the sum of 2*n consecutive primes is 0 modulo 10, or -1 if no such prime exists. | [
"13",
"11",
"7",
"7",
"13",
"17",
"7",
"17",
"37",
"3",
"7",
"41",
"7",
"7",
"11",
"11",
"11",
"11",
"11",
"13",
"11",
"13",
"11",
"7",
"7",
"17",
"7",
"43",
"41",
"3",
"3",
"13",
"11",
"7",
"13",
"19",
"7",
"11",
"11",
"29",
"7",
"43",
"3",
"7",
"11",
"13",
"23",
"29",
"3",
"7",
"7",
"11",
"11",
"11",
"19",
"13",
"5",
"5",
"13",
"37",
"17",
"3",
"3",
"7",
"17",
"17",
"3",
"11",
"19",
"13",
"3",
"7",
"23"
]
| [
"nonn"
]
| 26 | 1 | 1 | [
"A007652",
"A111324",
"A381869"
]
| null | Jean-Marc Rebert, Mar 09 2025 | 2025-05-11T11:53:36 | oeisdata/seq/A381/A381869.seq | 1e169edde1edbdc543a639f4319a2164 |
A381870 | Numbers whose prime indices have a unique multiset partition into sets with distinct sums. | [
"1",
"2",
"3",
"5",
"7",
"11",
"12",
"13",
"17",
"18",
"19",
"20",
"23",
"28",
"29",
"31",
"36",
"37",
"41",
"43",
"44",
"45",
"47",
"50",
"52",
"53",
"59",
"61",
"63",
"67",
"68",
"71",
"73",
"75",
"76",
"79",
"83",
"89",
"92",
"97",
"98",
"99",
"100",
"101",
"103",
"107",
"109",
"113",
"116",
"117",
"120",
"124",
"127",
"131",
"137",
"139",
"147",
"148",
"149",
"151",
"153"
]
| [
"nonn"
]
| 7 | 1 | 2 | [
"A000720",
"A000961",
"A001055",
"A001222",
"A003963",
"A005117",
"A045778",
"A050320",
"A050326",
"A055396",
"A056239",
"A061395",
"A066328",
"A089259",
"A112798",
"A116540",
"A122111",
"A166684",
"A265947",
"A270995",
"A279785",
"A293243",
"A293511",
"A296119",
"A299202",
"A300383",
"A300385",
"A317141",
"A318360",
"A321469",
"A381633",
"A381634",
"A381635",
"A381718",
"A381806",
"A381870",
"A381990",
"A381991"
]
| null | Gus Wiseman, Mar 12 2025 | 2025-03-13T08:55:19 | oeisdata/seq/A381/A381870.seq | 30d6bef107752c89309da348a253cd7e |
A381871 | Numbers whose prime indices cannot be partitioned into constant blocks having a common sum. | [
"6",
"10",
"14",
"15",
"18",
"20",
"21",
"22",
"24",
"26",
"28",
"30",
"33",
"34",
"35",
"38",
"39",
"42",
"44",
"45",
"46",
"50",
"51",
"52",
"54",
"55",
"56",
"57",
"58",
"60",
"62",
"65",
"66",
"68",
"69",
"70",
"72",
"74",
"75",
"76",
"77",
"78",
"80",
"82",
"84",
"85",
"86",
"87",
"88",
"90",
"91",
"92",
"93",
"94",
"95",
"96",
"98",
"99",
"100",
"102",
"104",
"105",
"106",
"110"
]
| [
"nonn"
]
| 9 | 1 | 1 | [
"A000688",
"A000720",
"A000961",
"A001055",
"A001222",
"A006171",
"A045778",
"A050361",
"A055396",
"A056239",
"A061395",
"A112798",
"A265947",
"A279784",
"A295935",
"A300383",
"A317141",
"A321469",
"A381453",
"A381455",
"A381633",
"A381635",
"A381636",
"A381715",
"A381716",
"A381717",
"A381719",
"A381806",
"A381871",
"A381993",
"A381995",
"A383093"
]
| null | Gus Wiseman, Mar 13 2025 | 2025-04-27T09:09:27 | oeisdata/seq/A381/A381871.seq | c1db315b30e92fe8495230feff094f36 |
A381872 | Number of multisets that can be obtained by taking the sum of each block of a multiset partition of the prime indices of n into blocks having a common sum. | [
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"3",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"4",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"3",
"1",
"1",
"2",
"1",
"1",
"1"
]
| [
"nonn"
]
| 6 | 1 | 4 | [
"A000005",
"A000009",
"A000041",
"A000688",
"A000720",
"A000961",
"A001055",
"A001222",
"A050361",
"A055396",
"A056239",
"A061395",
"A089723",
"A112798",
"A265947",
"A279787",
"A279789",
"A300383",
"A305551",
"A306017",
"A317141",
"A321451",
"A321452",
"A321453",
"A321454",
"A321455",
"A321469",
"A381453",
"A381455",
"A381635",
"A381636",
"A381637",
"A381715",
"A381716",
"A381872"
]
| null | Gus Wiseman, Mar 14 2025 | 2025-03-14T17:10:14 | oeisdata/seq/A381/A381872.seq | e3df823b187e051baac475e33436c256 |
A381873 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused positive number that shares a factor with a(n-1) while containing at most two distinct prime factors. | [
"1",
"2",
"4",
"6",
"3",
"9",
"12",
"8",
"10",
"5",
"15",
"18",
"14",
"7",
"21",
"24",
"16",
"20",
"22",
"11",
"33",
"27",
"36",
"26",
"13",
"39",
"45",
"25",
"35",
"28",
"32",
"34",
"17",
"51",
"48",
"38",
"19",
"57",
"54",
"40",
"44",
"46",
"23",
"69",
"63",
"49",
"56",
"50",
"52",
"58",
"29",
"87",
"72",
"62",
"31",
"93",
"75",
"55",
"65",
"80",
"64",
"68",
"74",
"37",
"111",
"81"
]
| [
"nonn",
"look"
]
| 21 | 1 | 2 | [
"A000977",
"A027748",
"A064413",
"A070915",
"A381873"
]
| null | Scott R. Shannon, Mar 09 2025 | 2025-05-25T16:07:07 | oeisdata/seq/A381/A381873.seq | cbea84b171d5232e72ff74bc3364d3d6 |
A381874 | Numbers whose set of divisors can be partitioned: a) into two disjoint subsets with equal sums and cardinalities, and b) into two disjoint subsets with equal products and cardinalities. | [
"24",
"30",
"42",
"54",
"60",
"66",
"78",
"84",
"90",
"96",
"102",
"108",
"114",
"120",
"126",
"132",
"138",
"140",
"150",
"156",
"160",
"168",
"174",
"186",
"198",
"204",
"210",
"216",
"220",
"222",
"224",
"228",
"240",
"246",
"258",
"260",
"264",
"270",
"276",
"280",
"282",
"306",
"308",
"312",
"318",
"330",
"336",
"340",
"342",
"348",
"352",
"354",
"360",
"364",
"366",
"372",
"378",
"380",
"384",
"390",
"402"
]
| [
"nonn"
]
| 4 | 1 | 1 | [
"A083207",
"A347063",
"A381874"
]
| null | Ivan N. Ianakiev, Mar 09 2025 | 2025-03-12T08:40:15 | oeisdata/seq/A381/A381874.seq | 26b71edcad384dea766fb408eb1752a4 |
A381875 | G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^2, where C(x) is the g.f. of A000108. | [
"1",
"3",
"13",
"66",
"368",
"2185",
"13570",
"87147",
"574241",
"3861286",
"26390591",
"182798850",
"1280387583",
"9053335674",
"64534088960",
"463249047099",
"3345832486407",
"24296575830677",
"177286818019264",
"1299208549351640",
"9557974679439901",
"70563100013789595",
"522608148884843970"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A000108",
"A129442",
"A381875",
"A381876",
"A381877"
]
| null | Seiichi Manyama, Mar 09 2025 | 2025-03-09T09:55:38 | oeisdata/seq/A381/A381875.seq | 86b19ed4e2b2462f087da811a7ddfff0 |
A381876 | G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^3, where C(x) is the g.f. of A000108. | [
"1",
"4",
"23",
"156",
"1167",
"9311",
"77710",
"670294",
"5928183",
"53467931",
"489904745",
"4547296624",
"42667426369",
"404044679434",
"3856480309376",
"37062228265769",
"358330619946164",
"3482936427997599",
"34014454418349579",
"333598711996924548",
"3284326412065118717",
"32446900771699499147"
]
| [
"nonn"
]
| 10 | 0 | 2 | [
"A000108",
"A129442",
"A381875",
"A381876",
"A381877",
"A381880"
]
| null | Seiichi Manyama, Mar 09 2025 | 2025-03-09T09:55:42 | oeisdata/seq/A381/A381876.seq | 2582e5ec137d434fbe586cbe68b3a165 |
A381877 | G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^4, where C(x) is the g.f. of A000108. | [
"1",
"5",
"36",
"307",
"2891",
"29029",
"304716",
"3303712",
"36708842",
"415818822",
"4783832314",
"55743318579",
"656528284027",
"7802975428711",
"93467830304056",
"1127239608233884",
"13676060532043690",
"166800618473750824",
"2043978275887704674",
"25152767272402722288",
"310703538187552229521"
]
| [
"nonn"
]
| 10 | 0 | 2 | [
"A000108",
"A129442",
"A381861",
"A381875",
"A381876",
"A381877"
]
| null | Seiichi Manyama, Mar 09 2025 | 2025-03-09T12:26:15 | oeisdata/seq/A381/A381877.seq | effab6b95e3e0b6138641dbc45b833e3 |
A381878 | Prime numbers p such that the sum of the d_i-th prime numbers, where (d_i) are the nonzero digits of p, is also a prime. | [
"2",
"3",
"5",
"7",
"13",
"17",
"31",
"71",
"103",
"107",
"181",
"211",
"223",
"227",
"229",
"233",
"239",
"257",
"277",
"293",
"347",
"383",
"389",
"433",
"443",
"449",
"467",
"479",
"487",
"499",
"523",
"563",
"569",
"587",
"647",
"653",
"659",
"677",
"683",
"701",
"727",
"743",
"769",
"787",
"811",
"839",
"857",
"859",
"863",
"877",
"883",
"947",
"967",
"983"
]
| [
"nonn",
"base",
"less"
]
| 15 | 1 | 1 | [
"A046704",
"A052034",
"A381878"
]
| null | Jean-Marc Rebert, Mar 09 2025 | 2025-03-19T10:30:26 | oeisdata/seq/A381/A381878.seq | b710a5b654768f5311afcc55eaa97534 |
A381879 | Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / C(x) ), where C(x) is the g.f. of A000108. | [
"1",
"3",
"16",
"106",
"788",
"6292",
"52743",
"457946",
"4083328",
"37174786",
"344142192",
"3229827900",
"30661272627",
"293907951057",
"2840826401664",
"27657352868946",
"270968414904700",
"2669604470832568",
"26431802684789970",
"262864480970961882",
"2624640191306617088",
"26301183967687772360"
]
| [
"nonn"
]
| 10 | 0 | 2 | [
"A000108",
"A381817",
"A381879",
"A381880",
"A381881"
]
| null | Seiichi Manyama, Mar 09 2025 | 2025-03-09T12:29:03 | oeisdata/seq/A381/A381879.seq | 27ba4e3d6094948586ba8bd94c7c35c6 |
A381880 | Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / C(x) ), where C(x) is the g.f. of A000108. | [
"1",
"4",
"27",
"223",
"2052",
"20199",
"208205",
"2219149",
"24261279",
"270581313",
"3066581130",
"35216499786",
"408919039968",
"4792955710138",
"56633333886618",
"673881539636365",
"8067939162382594",
"97117925556632184",
"1174721577627568371",
"14270877151754826473",
"174044527062280321368"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A000108",
"A381817",
"A381879",
"A381880",
"A381882"
]
| null | Seiichi Manyama, Mar 09 2025 | 2025-03-09T12:29:00 | oeisdata/seq/A381/A381880.seq | 6d31ff055a1d3342103a6444a8e5771d |
A381881 | Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * C(x)) ), where C(x) is the g.f. of A000108. | [
"1",
"3",
"14",
"82",
"547",
"3958",
"30249",
"240362",
"1966235",
"16449495",
"140093989",
"1210575512",
"10587490383",
"93540456103",
"833619150838",
"7484887130882",
"67645312129491",
"614872423359187",
"5617522739173495",
"51556112664387720",
"475105557839611760",
"4394434006611790855"
]
| [
"nonn"
]
| 11 | 0 | 2 | [
"A000108",
"A054727",
"A381879",
"A381881",
"A381882"
]
| null | Seiichi Manyama, Mar 09 2025 | 2025-03-09T12:26:20 | oeisdata/seq/A381/A381881.seq | a5c0d6f28310195a5eb67388520b6ae0 |
A381882 | Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 * C(x)) ), where C(x) is the g.f. of A000108. | [
"1",
"4",
"24",
"175",
"1428",
"12525",
"115468",
"1103777",
"10844715",
"108860766",
"1111722956",
"11514401451",
"120666441067",
"1277161022725",
"13633269293868",
"146606818816257",
"1586739194404521",
"17271207134469417",
"188942438655850740",
"2076317084779878706",
"22909617070555385010"
]
| [
"nonn"
]
| 10 | 0 | 2 | [
"A000108",
"A054727",
"A381880",
"A381881",
"A381882"
]
| null | Seiichi Manyama, Mar 09 2025 | 2025-03-09T12:26:24 | oeisdata/seq/A381/A381882.seq | 4e46a69e01d6912c9eb0478c4c5ec684 |
A381883 | Triangle read by rows: T(n, k) = binomial(2*n - 1, k). | [
"1",
"1",
"1",
"1",
"3",
"3",
"1",
"5",
"10",
"10",
"1",
"7",
"21",
"35",
"35",
"1",
"9",
"36",
"84",
"126",
"126",
"1",
"11",
"55",
"165",
"330",
"462",
"462",
"1",
"13",
"78",
"286",
"715",
"1287",
"1716",
"1716",
"1",
"15",
"105",
"455",
"1365",
"3003",
"5005",
"6435",
"6435",
"1",
"17",
"136",
"680",
"2380",
"6188",
"12376",
"19448",
"24310",
"24310"
]
| [
"nonn",
"tabl",
"easy"
]
| 10 | 0 | 5 | [
"A007318",
"A088218",
"A114121",
"A262977",
"A381883"
]
| null | Peter Luschny, Mar 15 2025 | 2025-04-03T09:58:47 | oeisdata/seq/A381/A381883.seq | adf858376f6e0855245e6fd59fb87b77 |
A381884 | Triangle read by rows: T(n, k) = 0 if n = 0 or k is not a quadratic residue modulo n, otherwise T(n, k) = k. | [
"0",
"0",
"1",
"0",
"1",
"2",
"0",
"1",
"0",
"3",
"0",
"1",
"0",
"0",
"4",
"0",
"1",
"0",
"0",
"4",
"5",
"0",
"1",
"0",
"3",
"4",
"0",
"6",
"0",
"1",
"2",
"0",
"4",
"0",
"0",
"7",
"0",
"1",
"0",
"0",
"4",
"0",
"0",
"0",
"8",
"0",
"1",
"0",
"0",
"4",
"0",
"0",
"7",
"0",
"9",
"0",
"1",
"0",
"0",
"4",
"5",
"6",
"0",
"0",
"9",
"10",
"0",
"1",
"0",
"3",
"4",
"5",
"0",
"0",
"0",
"9",
"0",
"11",
"0",
"1",
"0",
"0",
"4",
"0",
"0",
"0",
"0",
"9",
"0",
"0",
"12"
]
| [
"nonn",
"tabl"
]
| 15 | 0 | 6 | [
"A057125",
"A057126",
"A057762",
"A262931",
"A262932",
"A381884"
]
| null | Peter Luschny, Mar 17 2025 | 2025-03-18T12:23:15 | oeisdata/seq/A381/A381884.seq | 6896fbdd5d9505609c22aee035659e47 |
A381885 | a(n) = Product_{k=2..n-1} k^ord(n, k) where ord(n, k) = 0 if k does not divide n, otherwise is the exponent of the highest power of k that divides n. | [
"1",
"1",
"1",
"4",
"1",
"6",
"1",
"32",
"9",
"10",
"1",
"288",
"1",
"14",
"15",
"2048",
"1",
"972",
"1",
"800",
"21",
"22",
"1",
"55296",
"25",
"26",
"243",
"1568",
"1",
"27000",
"1",
"65536",
"33",
"34",
"35",
"10077696",
"1",
"38",
"39",
"256000",
"1",
"74088",
"1",
"3872",
"6075",
"46",
"1",
"169869312",
"49",
"12500",
"51",
"5408",
"1",
"1417176",
"55",
"702464",
"57"
]
| [
"nonn"
]
| 13 | 1 | 4 | [
"A005451",
"A364813",
"A381885"
]
| null | Peter Luschny, Apr 01 2025 | 2025-04-01T08:55:35 | oeisdata/seq/A381/A381885.seq | 27edb8677fdb23ac57634eae0438d0d9 |
A381886 | Triangle read by rows: T(n, k) = Sum_{j=1..floor(log[k](n))} floor(n / k^j) if k >= 2, T(n, 1) = n, T(n, 0) = 0^n. | [
"1",
"0",
"1",
"0",
"2",
"1",
"0",
"3",
"1",
"1",
"0",
"4",
"3",
"1",
"1",
"0",
"5",
"3",
"1",
"1",
"1",
"0",
"6",
"4",
"2",
"1",
"1",
"1",
"0",
"7",
"4",
"2",
"1",
"1",
"1",
"1",
"0",
"8",
"7",
"2",
"2",
"1",
"1",
"1",
"1",
"0",
"9",
"7",
"4",
"2",
"1",
"1",
"1",
"1",
"1",
"0",
"10",
"8",
"4",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"0",
"11",
"8",
"4",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"0",
"12",
"10",
"5",
"3",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"1"
]
| [
"nonn",
"tabl"
]
| 21 | 0 | 5 | [
"A011371",
"A027868",
"A054861",
"A054893",
"A054895",
"A054896",
"A054897",
"A054898",
"A078567",
"A078632",
"A078651",
"A153216",
"A366471",
"A381886"
]
| null | Peter Luschny, Apr 03 2025 | 2025-04-04T13:56:16 | oeisdata/seq/A381/A381886.seq | e84f35c3cb2e25c335fb0da513864068 |
A381887 | a(n) = 1 if n != p^m*(p-1) for any prime p and any m >= 0, otherwise Product_{p in W} p, where W are the primes such that n = p^m*(p-1) for some m >= 0. | [
"2",
"6",
"1",
"10",
"1",
"21",
"1",
"2",
"1",
"11",
"1",
"13",
"1",
"1",
"1",
"34",
"1",
"57",
"1",
"5",
"1",
"23",
"1",
"1",
"1",
"1",
"1",
"29",
"1",
"31",
"1",
"2",
"1",
"1",
"1",
"37",
"1",
"1",
"1",
"41",
"1",
"301",
"1",
"1",
"1",
"47",
"1",
"1",
"1",
"1",
"1",
"53",
"1",
"3",
"1",
"1",
"1",
"59",
"1",
"61",
"1",
"1",
"1",
"2",
"1",
"67",
"1",
"1",
"1",
"71",
"1",
"73",
"1",
"1",
"1",
"1",
"1",
"79",
"1"
]
| [
"nonn"
]
| 9 | 1 | 1 | [
"A155457",
"A381887"
]
| null | Peter Luschny, Apr 05 2025 | 2025-04-06T14:58:11 | oeisdata/seq/A381/A381887.seq | 2c70a75a03173f9450a51bc1b7435cb6 |
A381888 | Triangle read by rows: T(n, k) = (n + 1) * Sum_{j=k..n} binomial(n, j) * Eulerian1(j, j - k). | [
"1",
"2",
"2",
"3",
"9",
"3",
"4",
"28",
"28",
"4",
"5",
"75",
"165",
"75",
"5",
"6",
"186",
"786",
"786",
"186",
"6",
"7",
"441",
"3311",
"6181",
"3311",
"441",
"7",
"8",
"1016",
"12888",
"40888",
"40888",
"12888",
"1016",
"8",
"9",
"2295",
"47529",
"241191",
"404361",
"241191",
"47529",
"2295",
"9",
"10",
"5110",
"168670",
"1312750",
"3445510",
"3445510",
"1312750",
"168670",
"5110",
"10"
]
| [
"nonn",
"tabl"
]
| 20 | 0 | 2 | [
"A007526",
"A046802",
"A058877",
"A122045",
"A173018",
"A381706",
"A381888"
]
| null | Peter Luschny, Mar 11 2025 | 2025-03-15T09:30:06 | oeisdata/seq/A381/A381888.seq | c35ad7bd457c9353ef39b42c7e4e63f0 |
A381889 | Expansion of e.g.f.: (BesselI(0, 2*x) + BesselI(1, 2*x))^2*exp(2*x). | [
"1",
"4",
"18",
"86",
"428",
"2192",
"11468",
"60986",
"328532",
"1788368",
"9819128",
"54302712",
"302157424",
"1690193728",
"9497996152",
"53588976802",
"303434431108",
"1723578967056",
"9818195961512",
"56071829010968",
"320970950634288",
"1841213871449152",
"10582333064327824",
"60929582362628968",
"351385363433883472"
]
| [
"nonn"
]
| 14 | 0 | 2 | [
"A001405",
"A001700",
"A005566",
"A151093",
"A381889"
]
| null | Mélika Tebni, Mar 09 2025 | 2025-03-19T10:16:56 | oeisdata/seq/A381/A381889.seq | fc53d4126d5cf30a946dfce43c5f4a11 |
A381890 | Expansion of Product_{k>=1} (1 + k*x)^((1/12) * (3/4)^k). | [
"1",
"1",
"-3",
"21",
"-225",
"3207",
"-56821",
"1202099",
"-29558466",
"828401462",
"-26068940938",
"910286433318",
"-34930741605414",
"1461245816594058",
"-66187658069563710",
"3227353484661602866",
"-168557942284281821933",
"9388117645333487820387",
"-555463036269652132509113"
]
| [
"sign"
]
| 21 | 0 | 3 | [
"A050352",
"A090353",
"A381890",
"A384343",
"A384344",
"A384345"
]
| null | Seiichi Manyama, May 26 2025 | 2025-05-27T10:10:29 | oeisdata/seq/A381/A381890.seq | 33373852a4237f2da1fca537df64a040 |
A381891 | Triangle read by rows: T(n,k) is the number of partitions of a 2-colored set of n objects into at most k parts with 0 <= k <= n. | [
"1",
"0",
"2",
"0",
"3",
"6",
"0",
"4",
"10",
"14",
"0",
"5",
"19",
"28",
"33",
"0",
"6",
"28",
"52",
"64",
"70",
"0",
"7",
"44",
"93",
"127",
"142",
"149",
"0",
"8",
"60",
"152",
"228",
"272",
"290",
"298",
"0",
"9",
"85",
"242",
"404",
"507",
"561",
"582",
"591",
"0",
"10",
"110",
"370",
"672",
"904",
"1034",
"1098",
"1122",
"1132",
"0",
"11",
"146",
"546",
"1100",
"1568",
"1870",
"2027",
"2101",
"2128",
"2139"
]
| [
"nonn",
"tabl"
]
| 30 | 0 | 3 | [
"A005380",
"A026820",
"A381891"
]
| null | Peter Dolland, Mar 09 2025 | 2025-03-26T15:27:10 | oeisdata/seq/A381/A381891.seq | c20069787367360591492f10a6e4f77d |
A381892 | Numbers k such that A381781(k) is negative. | [
"99",
"260515",
"18997153",
"37362253",
"50601157",
"122925461",
"534483448"
]
| [
"nonn",
"hard",
"more"
]
| 6 | 1 | 1 | [
"A381781",
"A381892",
"A381893"
]
| null | Simcha Z. Katzoff, Mar 09 2025 | 2025-03-19T10:38:26 | oeisdata/seq/A381/A381892.seq | 93d8e660acd8c00aff0b09668fc26ebc |
A381893 | Negative values of A381781. | [
"-810",
"-39184",
"-4396135",
"-124970",
"-61325522",
"-64927344",
"-439288021"
]
| [
"sign",
"hard",
"more"
]
| 19 | 1 | 1 | [
"A381781",
"A381892",
"A381893"
]
| null | Simcha Z. Katzoff, Mar 09 2025 | 2025-03-19T10:38:38 | oeisdata/seq/A381/A381893.seq | 789cd674d375e4b12212dbc0659834ef |
A381894 | Lexicographically earliest sequence of positive integers such that a(n) is the length of the n-th run of consecutive, equal terms and no two runs have the same sum. | [
"1",
"2",
"2",
"1",
"1",
"3",
"5",
"2",
"2",
"2",
"3",
"3",
"3",
"3",
"3",
"4",
"4",
"5",
"5",
"6",
"6",
"3",
"3",
"3",
"6",
"6",
"6",
"7",
"7",
"7",
"8",
"8",
"8",
"9",
"9",
"9",
"4",
"4",
"4",
"4",
"5",
"5",
"5",
"5",
"6",
"6",
"6",
"6",
"6",
"5",
"5",
"5",
"5",
"5",
"6",
"6",
"6",
"6",
"6",
"6",
"7",
"7",
"7",
"7",
"7",
"7",
"11",
"11",
"11",
"13",
"13",
"13",
"15",
"15",
"15",
"8",
"8",
"8",
"8",
"8",
"8",
"9",
"9",
"9",
"9",
"9",
"9"
]
| [
"nonn"
]
| 15 | 1 | 2 | [
"A000002",
"A331910",
"A381894",
"A382028"
]
| null | Neal Gersh Tolunsky, Mar 09 2025 | 2025-03-21T17:10:57 | oeisdata/seq/A381/A381894.seq | 8b0bf551403c6a13c39643b9c821c465 |
A381895 | Triangle read by rows: T(n, k) is the number of partitions of n with at most k parts where 0 <= k <= n, and each part is one of two kinds. | [
"1",
"0",
"2",
"0",
"2",
"5",
"0",
"2",
"6",
"10",
"0",
"2",
"9",
"15",
"20",
"0",
"2",
"10",
"22",
"30",
"36",
"0",
"2",
"13",
"31",
"48",
"58",
"65",
"0",
"2",
"14",
"40",
"68",
"90",
"102",
"110",
"0",
"2",
"17",
"51",
"97",
"135",
"162",
"176",
"185",
"0",
"2",
"18",
"64",
"128",
"194",
"242",
"274",
"290",
"300",
"0",
"2",
"21",
"77",
"171",
"271",
"357",
"415",
"452",
"470",
"481"
]
| [
"nonn",
"tabl"
]
| 29 | 0 | 3 | [
"A000712",
"A026820",
"A381895"
]
| null | Peter Dolland, Mar 09 2025 | 2025-03-20T06:01:39 | oeisdata/seq/A381/A381895.seq | 7c010cc406174b16a8a0f87d5a33b595 |
A381896 | Number of n X n Erdős matrices up to equivalence. | [
"1",
"2",
"6",
"41"
]
| [
"nonn",
"hard",
"more"
]
| 39 | 1 | 2 | [
"A000041",
"A381896"
]
| null | Raghavendra Tripathi, Mar 09 2025 | 2025-03-25T21:10:56 | oeisdata/seq/A381/A381896.seq | 4009d867b5d301f60063c4cebc2d9dd1 |
A381897 | a(n) = least integer m >= 2 such that prime(n) is a sum of the form Sum_{k>=0} floor(h/m^k) for some integer h >= 1. | [
"3",
"2",
"3",
"2",
"2",
"3",
"3",
"2",
"2",
"4",
"2",
"4",
"2",
"4",
"2",
"2",
"3",
"3",
"2",
"2",
"2",
"2",
"5",
"2",
"2",
"2",
"3",
"3",
"2",
"2",
"2",
"2",
"2",
"3",
"2",
"3",
"3",
"3",
"3",
"2",
"3",
"2",
"2",
"2",
"2",
"4",
"3",
"3",
"3",
"2",
"3",
"2",
"4",
"3",
"3",
"2",
"3",
"2",
"2",
"2",
"3",
"2",
"4",
"2",
"3",
"3",
"3",
"2",
"4",
"2",
"2",
"2",
"2",
"3",
"3",
"2",
"2",
"2",
"2",
"3",
"3",
"2",
"2",
"4",
"2",
"4"
]
| [
"nonn"
]
| 14 | 1 | 1 | [
"A000040",
"A381239",
"A381897",
"A382278"
]
| null | Clark Kimberling, Mar 09 2025 | 2025-03-22T18:50:42 | oeisdata/seq/A381/A381897.seq | cdec63b0e095283b3e72de07ff65bfd2 |
A381898 | Decimal expansion of exp(Sum_{k>=2} log_2(k)/(k * 2^k)). | [
"1",
"2",
"8",
"3",
"3",
"0",
"3",
"1",
"7",
"1",
"1",
"8",
"7",
"4",
"0",
"6",
"8",
"1",
"9",
"3",
"9",
"2",
"7",
"9",
"8",
"8",
"5",
"0",
"8",
"1",
"6",
"1",
"7",
"3",
"9",
"2",
"0",
"7",
"7",
"4",
"1",
"3",
"2",
"4",
"0",
"1",
"8",
"8",
"3",
"0",
"2",
"5",
"4",
"6",
"1",
"6",
"0",
"5",
"9",
"1",
"0",
"8",
"2",
"3",
"0",
"8",
"4",
"4",
"0",
"4",
"3",
"2",
"1",
"7",
"6",
"6",
"1",
"1",
"0",
"1",
"3",
"3",
"5",
"2",
"6",
"9",
"4",
"7",
"9",
"9",
"2",
"8",
"4",
"0",
"8",
"1",
"5",
"5",
"6",
"3",
"9",
"3",
"7",
"1",
"0",
"9",
"7",
"6",
"6",
"1",
"5",
"3",
"8",
"0",
"7",
"7",
"9",
"6",
"4",
"4"
]
| [
"nonn",
"cons"
]
| 43 | 1 | 2 | [
"A381456",
"A381898",
"A381900"
]
| null | Jwalin Bhatt, Mar 09 2025 | 2025-06-02T01:56:07 | oeisdata/seq/A381/A381898.seq | ea35d9de1f84ef38af9efb52720b8604 |
A381899 | Irregular triangular array read by rows. T(n,k) is the number of length n words x on {0,1} such that I(x) + W(x)*(n-W(x)) = k, where I(x) is the number of inversions in x and W(x) is the number of 1's in x, n >= 0, 0 <= k <= floor(n^2/2). | [
"1",
"2",
"2",
"1",
"1",
"2",
"0",
"2",
"2",
"2",
"2",
"0",
"0",
"2",
"3",
"3",
"4",
"1",
"1",
"2",
"0",
"0",
"0",
"2",
"2",
"4",
"4",
"6",
"4",
"4",
"2",
"2",
"2",
"0",
"0",
"0",
"0",
"2",
"2",
"2",
"4",
"5",
"7",
"6",
"9",
"7",
"7",
"5",
"4",
"1",
"1",
"2",
"0",
"0",
"0",
"0",
"0",
"2",
"2",
"2",
"2",
"4",
"4",
"8",
"6",
"10",
"12",
"14",
"12",
"14",
"10",
"10",
"6",
"4",
"2",
"2"
]
| [
"nonn",
"tabf"
]
| 29 | 0 | 2 | [
"A000079",
"A001788",
"A053846",
"A060546",
"A083906",
"A132186",
"A226622",
"A226635",
"A381899"
]
| null | Geoffrey Critzer, Mar 09 2025 | 2025-03-12T15:55:04 | oeisdata/seq/A381/A381899.seq | 314113b300b75ed244c19a3575950b82 |
A381900 | Sequence where k is appended after every (2^(k-1))*k occurrences of 1, with multiple values following a 1 listed in order. | [
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"3",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"3",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"4",
"1",
"1",
"1",
"1",
"2",
"3",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"3",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"3",
"1",
"1",
"1",
"1",
"2",
"4",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"3",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"5"
]
| [
"nonn"
]
| 13 | 1 | 5 | [
"A381522",
"A381898",
"A381900"
]
| null | Jwalin Bhatt, Mar 09 2025 | 2025-05-25T09:22:31 | oeisdata/seq/A381/A381900.seq | 4f1850b9492aa377943b2a2c7aaf8e5a |
A381901 | Partition the natural numbers by letting a(1)=1 (denoting the set {1}) and for n>1 define a(n) to be the least integer such that the product of the set of integers {a(n-1)+1,...,a(n)} is an integer multiple of the previous partition's product. | [
"1",
"2",
"4",
"8",
"14",
"26",
"46",
"86",
"166",
"326",
"634",
"1262",
"2518",
"5006",
"10006",
"19946",
"39874",
"79738",
"159398",
"318778",
"637502",
"1274998",
"2549978",
"5099902",
"10199786",
"20399534",
"40799062",
"81598082",
"163196134",
"326392258",
"652784498",
"1305568942",
"2611137838",
"5222275634",
"10444551254"
]
| [
"nonn"
]
| 17 | 1 | 2 | [
"A006992",
"A090905",
"A113117",
"A113118",
"A381901"
]
| null | Andy Niedermaier, Mar 09 2025 | 2025-04-13T17:42:14 | oeisdata/seq/A381/A381901.seq | 9504b8c6bdc5a781bf663d48e65195a5 |
A381902 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused positive number such that a(n) shares a factor with a(n-1), while the total number of prime factors, counted with multiplicity, of the form 4*k+1 and 4*k+3 for all terms a(1)..a(n) never differs by more than 1. | [
"1",
"2",
"4",
"6",
"8",
"10",
"5",
"15",
"3",
"12",
"16",
"20",
"14",
"26",
"13",
"39",
"9",
"30",
"25",
"35",
"7",
"28",
"32",
"34",
"17",
"51",
"18",
"40",
"22",
"50",
"24",
"38",
"52",
"44",
"55",
"60",
"58",
"29",
"87",
"21",
"70",
"64",
"68",
"46",
"74",
"37",
"111",
"33",
"75",
"45",
"65",
"78",
"36",
"80",
"48",
"82",
"41",
"123",
"42",
"91",
"104",
"56",
"100",
"62",
"31"
]
| [
"nonn"
]
| 10 | 1 | 2 | [
"A007350",
"A027748",
"A038698",
"A064413",
"A381902",
"A382091"
]
| null | Scott R. Shannon, Mar 09 2025 | 2025-04-01T08:53:43 | oeisdata/seq/A381/A381902.seq | e7277018c8f5c9f88cc956021db1e1ac |
A381903 | Primes prime(k) such that (prime(k) - k)^k == k (mod prime(k)). | [
"2",
"5",
"7",
"97",
"877",
"12979",
"203659",
"364717",
"1681853",
"189961939",
"189962137",
"466446781",
"1511085889"
]
| [
"nonn",
"more"
]
| 42 | 1 | 1 | [
"A014689",
"A381903"
]
| null | Juri-Stepan Gerasimov, May 12 2025 | 2025-05-17T23:22:28 | oeisdata/seq/A381/A381903.seq | ff6831810de95bd3df9ecbc464a7092b |
A381904 | Number of minimum total dominating sets in the n X n zebra graph. | [
"0",
"0",
"0",
"0",
"0",
"144",
"11616",
"30976"
]
| [
"nonn",
"more"
]
| 10 | 1 | 6 | null | null | Eric W. Weisstein, May 11 2025 | 2025-05-11T09:23:57 | oeisdata/seq/A381/A381904.seq | 96c3e4cc66f43ce882dc45b8c0a57ac8 |
A381905 | Expansion of (1/x) * Series_Reversion( x / ((1+x) * B(x)) ), where B(x) is the g.f. of A001764. | [
"1",
"2",
"8",
"47",
"331",
"2570",
"21204",
"182383",
"1617163",
"14675783",
"135643839",
"1272434069",
"12083390801",
"115934171020",
"1122129142754",
"10943574296787",
"107433077283767",
"1060800046515405",
"10528321010319417",
"104972259713887665",
"1050936451974803973",
"10560662821468607719"
]
| [
"nonn"
]
| 8 | 0 | 2 | [
"A001764",
"A381905",
"A381906",
"A381907",
"A381911"
]
| null | Seiichi Manyama, Mar 10 2025 | 2025-03-10T06:57:16 | oeisdata/seq/A381/A381905.seq | ad8885ab3b1692f92ce5d8a54ad334e1 |
A381906 | Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * B(x)) ), where B(x) is the g.f. of A001764. | [
"1",
"3",
"15",
"100",
"787",
"6848",
"63583",
"617350",
"6191888",
"63650430",
"667043379",
"7099806346",
"76538663840",
"833975952491",
"9169925032189",
"101616966476850",
"1133736002540882",
"12724529836447420",
"143567856744995568",
"1627454706916166076",
"18526192807286106198",
"211694470334287787868"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A001764",
"A381881",
"A381905",
"A381906",
"A381907"
]
| null | Seiichi Manyama, Mar 10 2025 | 2025-03-10T06:58:10 | oeisdata/seq/A381/A381906.seq | 5657ab2036798af68ffce569e03e05c7 |
A381907 | Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 * B(x)) ), where B(x) is the g.f. of A001764. | [
"1",
"4",
"25",
"197",
"1783",
"17646",
"185622",
"2039617",
"23149542",
"269367631",
"3196544816",
"38539697456",
"470773651286",
"5813914938293",
"72470441063067",
"910587733474165",
"11521140613913305",
"146659482494039073",
"1876975898990490298",
"24137070792680577688",
"311724732112458291945"
]
| [
"nonn"
]
| 10 | 0 | 2 | [
"A001764",
"A381882",
"A381905",
"A381906",
"A381907"
]
| null | Seiichi Manyama, Mar 10 2025 | 2025-03-10T06:59:29 | oeisdata/seq/A381/A381907.seq | af1ae9e26c7b37a2495f50f00071679d |
A381908 | Expansion of (1/x) * Series_Reversion( x / ((1+x) * B(x)) ), where B(x) is the g.f. of A002293. | [
"1",
"2",
"9",
"64",
"556",
"5351",
"54818",
"585941",
"6459430",
"72902748",
"838174008",
"9781930978",
"115579403512",
"1379879992445",
"16620303073607",
"201717610488447",
"2464502123154530",
"30286289207099652",
"374115157763376043",
"4642636869759251879",
"57852132860181652189",
"723592983110972398779"
]
| [
"nonn"
]
| 10 | 0 | 2 | [
"A002293",
"A381908",
"A381909",
"A381910"
]
| null | Seiichi Manyama, Mar 10 2025 | 2025-03-10T07:02:32 | oeisdata/seq/A381/A381908.seq | 078e8cb4d2060da2b70a4a8fc933ae08 |
A381909 | Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * B(x)) ), where B(x) is the g.f. of A002293. | [
"1",
"3",
"16",
"121",
"1117",
"11569",
"128648",
"1500054",
"18091859",
"223794730",
"2823369749",
"36185653049",
"469808971400",
"6165903108879",
"81667617713170",
"1090234962290114",
"14654059445570507",
"198151602861222385",
"2693625234657193038",
"36789566028850640226",
"504600217464088999466"
]
| [
"nonn"
]
| 12 | 0 | 2 | [
"A002293",
"A381908",
"A381909",
"A381910"
]
| null | Seiichi Manyama, Mar 10 2025 | 2025-03-10T07:01:08 | oeisdata/seq/A381/A381909.seq | 0ec9bf92078c6ed75176642c41a31756 |
A381910 | Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 * B(x)) ), where B(x) is the g.f. of A002293. | [
"1",
"4",
"26",
"222",
"2243",
"25243",
"305217",
"3878731",
"51097713",
"691596081",
"9558970897",
"134347855874",
"1914131985782",
"27582542400252",
"401284140631911",
"5886072268606617",
"86951528919335670",
"1292467847124221832",
"19316795168721092789",
"290107272994659617741",
"4375905051887803660504"
]
| [
"nonn"
]
| 12 | 0 | 2 | [
"A002293",
"A381908",
"A381909",
"A381910"
]
| null | Seiichi Manyama, Mar 10 2025 | 2025-03-10T07:03:49 | oeisdata/seq/A381/A381910.seq | d93f88d5d2d2fddc53224750df10b571 |
A381911 | Expansion of (1/x) * Series_Reversion( x * (1-x) / B(x) ), where B(x) is the g.f. of A001764. | [
"1",
"2",
"9",
"55",
"394",
"3102",
"25969",
"226891",
"2045342",
"18883205",
"177640462",
"1696658418",
"16408796013",
"160366113609",
"1581329919636",
"15713344659359",
"157187582466527",
"1581676730708500",
"15998326150898211",
"162571286470135097",
"1658893916098102321",
"16991130941208846890"
]
| [
"nonn"
]
| 15 | 0 | 2 | [
"A001764",
"A381817",
"A381911",
"A381912",
"A381913",
"A381914"
]
| null | Seiichi Manyama, Mar 10 2025 | 2025-03-22T10:16:32 | oeisdata/seq/A381/A381911.seq | 0b9e2170e8c165e000e2418c9a05ceb6 |
A381912 | Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / B(x) ), where B(x) is the g.f. of A001764. | [
"1",
"3",
"17",
"124",
"1038",
"9470",
"91586",
"923542",
"9608323",
"102403921",
"1112500651",
"12275235274",
"137193964646",
"1549964417407",
"17672282336488",
"203092563108610",
"2350061579393077",
"27357919380212638",
"320186582453226290",
"3765185566095185740",
"44465070300433434901",
"527131055014319691537"
]
| [
"nonn"
]
| 12 | 0 | 2 | [
"A001764",
"A381879",
"A381911",
"A381912",
"A381913",
"A381915"
]
| null | Seiichi Manyama, Mar 10 2025 | 2025-03-10T09:42:46 | oeisdata/seq/A381/A381912.seq | d80ffcde8ecac2081fa1b6c8fc8cfe5d |
A381913 | Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / B(x) ), where B(x) is the g.f. of A001764. | [
"1",
"4",
"28",
"245",
"2422",
"25860",
"291106",
"3405405",
"41014131",
"505344113",
"6341182427",
"80768735045",
"1041645452650",
"13575670575944",
"178528253213469",
"2366073408348545",
"31571528771106126",
"423794981085407622",
"5718929869862880055",
"77539914280883389432",
"1055790501909183080512"
]
| [
"nonn"
]
| 13 | 0 | 2 | [
"A001764",
"A381880",
"A381911",
"A381912",
"A381913",
"A381916"
]
| null | Seiichi Manyama, Mar 10 2025 | 2025-03-10T09:42:50 | oeisdata/seq/A381/A381913.seq | b2cbee32ede105ab07abdfce8bce6df0 |
A381914 | Expansion of (1/x) * Series_Reversion( x * (1-x) / B(x) ), where B(x) is the g.f. of A002293. | [
"1",
"2",
"10",
"72",
"624",
"6009",
"61809",
"664813",
"7384613",
"84045565",
"974913510",
"11483316680",
"136974177209",
"1651166320547",
"20083352214058",
"246168280262403",
"3037682020219285",
"37706043912831337",
"470482875049515074",
"5897864081341146065",
"74243055437832292562",
"938101296155866961124"
]
| [
"nonn"
]
| 13 | 0 | 2 | [
"A002293",
"A381817",
"A381911",
"A381914",
"A381915",
"A381916"
]
| null | Seiichi Manyama, Mar 10 2025 | 2025-03-10T09:42:53 | oeisdata/seq/A381/A381914.seq | c114bd55dd4d0fb3c35814adabb53f2f |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.