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⌀ | cross_references
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timestamp[us]date 1999-12-11 03:00:00
2025-07-19 00:40:46
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A356701 | Records values in A081119. | [
"5",
"7",
"10",
"16",
"26",
"32"
]
| [
"nonn",
"hard",
"more"
]
| 6 | 1 | 1 | [
"A081119",
"A081120",
"A356699",
"A356700",
"A356701",
"A356702"
]
| null | Jianing Song, Aug 23 2022 | 2022-08-23T21:25:23 | oeisdata/seq/A356/A356701.seq | 143558c0047c77e083c38547587d6ab3 |
A356702 | Records values in A081120. | [
"1",
"2",
"4",
"6",
"8",
"14",
"18",
"20",
"22"
]
| [
"nonn",
"hard",
"more"
]
| 6 | 1 | 2 | [
"A081119",
"A081120",
"A356699",
"A356700",
"A356701",
"A356702"
]
| null | Jianing Song, Aug 23 2022 | 2022-08-23T21:25:18 | oeisdata/seq/A356/A356702.seq | 6dca73f91fd6f9657697cdf251f50408 |
A356703 | Numbers k such that Mordell elliptic curve y^2 = x^3 + k has a number of integral points that is both odd and > 1. | [
"1",
"8",
"64",
"343",
"512",
"729",
"1000",
"1331",
"2744",
"4096",
"5832",
"9261",
"10648",
"12167",
"15625",
"17576",
"21952",
"32768",
"35937",
"39304",
"42875",
"46656",
"50653",
"54872",
"64000",
"85184",
"97336",
"117649",
"125000",
"175616",
"185193",
"250047",
"262144",
"274625",
"343000",
"357911",
"373248",
"405224",
"474552",
"531441",
"592704",
"636056"
]
| [
"nonn"
]
| 28 | 1 | 2 | [
"A081119",
"A179145",
"A179147",
"A179149",
"A179151",
"A179163",
"A179419",
"A228948",
"A356703",
"A356709",
"A356713",
"A356720"
]
| null | Jianing Song, Aug 23 2022 | 2022-09-24T12:33:01 | oeisdata/seq/A356/A356703.seq | 3e0b651eb05ffcedb64a36acb399b598 |
A356704 | a(n) is the least k such that Mordell's equation y^2 = x^3 + k^3 has exactly 2*n+1 integral solutions. | [
"3",
"7",
"1",
"2",
"8",
"329",
"217",
"506",
"65",
"260",
"585"
]
| [
"nonn",
"hard",
"more"
]
| 9 | 0 | 1 | [
"A081119",
"A081120",
"A179162",
"A179175",
"A356704",
"A356705",
"A356706",
"A356707",
"A356708"
]
| null | Jianing Song, Aug 23 2022 | 2022-08-24T09:03:41 | oeisdata/seq/A356/A356704.seq | 8faf4628bbda6f994542ae75b25fc22a |
A356705 | a(n) is the least k such that Mordell's equation y^2 = x^3 - k^3 has exactly 2*n+1 integral solutions. | [
"1",
"11",
"6",
"38",
"7",
"63",
"416",
"2600",
"10400",
"93600"
]
| [
"nonn",
"hard",
"more"
]
| 16 | 0 | 2 | [
"A081119",
"A081120",
"A179162",
"A179175",
"A356704",
"A356705"
]
| null | Jianing Song, Aug 23 2022 | 2024-08-05T12:46:35 | oeisdata/seq/A356/A356705.seq | 7ff6b429cfa107bf741e6f5d57e0c86b |
A356706 | Number of integral solutions to Mordell's equation y^2 = x^3 + n^3. | [
"5",
"7",
"1",
"5",
"1",
"1",
"3",
"9",
"5",
"5",
"3",
"1",
"1",
"5",
"1",
"5",
"1",
"7",
"1",
"1",
"3",
"3",
"3",
"1",
"5",
"3",
"1",
"5",
"1",
"1",
"1",
"9",
"5",
"3",
"3",
"5",
"5",
"3",
"1",
"5",
"1",
"1",
"1",
"3",
"1",
"3",
"1",
"1",
"5",
"7",
"1",
"1",
"1",
"1",
"1",
"7",
"7",
"1",
"1",
"1",
"1",
"1",
"3",
"5",
"17",
"1",
"1",
"1",
"1",
"5",
"3",
"9",
"1",
"3",
"1",
"1",
"1",
"9",
"1",
"1",
"5",
"1",
"1",
"5",
"1",
"3",
"1",
"5",
"1",
"5",
"5",
"3",
"1",
"1",
"3",
"1",
"1"
]
| [
"nonn",
"hard"
]
| 29 | 1 | 1 | [
"A081119",
"A356706",
"A356707",
"A356708",
"A356709",
"A356710",
"A356711",
"A356712"
]
| null | Jianing Song, Aug 23 2022 | 2023-06-02T01:56:49 | oeisdata/seq/A356/A356706.seq | f40818b7d5d8203dee5d5d39cdb963d9 |
A356707 | Number of integral solutions to Mordell's equation y^2 = x^3 + n^3 with y positive. | [
"2",
"3",
"0",
"2",
"0",
"0",
"1",
"4",
"2",
"2",
"1",
"0",
"0",
"2",
"0",
"2",
"0",
"3",
"0",
"0",
"1",
"1",
"1",
"0",
"2",
"1",
"0",
"2",
"0",
"0",
"0",
"4",
"2",
"1",
"1",
"2",
"2",
"1",
"0",
"2",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"2",
"3",
"0",
"0",
"0",
"0",
"0",
"3",
"3",
"0",
"0",
"0",
"0",
"0",
"1",
"2",
"8",
"0",
"0",
"0",
"0",
"2",
"1",
"4",
"0",
"1",
"0",
"0",
"0",
"4",
"0",
"0",
"2",
"0",
"0",
"2",
"0",
"1",
"0",
"2",
"0",
"2",
"2",
"1",
"0",
"0",
"1",
"0",
"0",
"3",
"1",
"2"
]
| [
"nonn",
"hard"
]
| 25 | 1 | 1 | [
"A081119",
"A356706",
"A356707",
"A356708",
"A356709",
"A356710",
"A356711",
"A356712"
]
| null | Jianing Song, Aug 23 2022 | 2023-06-06T15:36:10 | oeisdata/seq/A356/A356707.seq | 594807f922483ebfec0d6b901b79abc6 |
A356708 | Number of integral solutions to Mordell's equation y^2 = x^3 + n^3 with y nonnegative. | [
"3",
"4",
"1",
"3",
"1",
"1",
"2",
"5",
"3",
"3",
"2",
"1",
"1",
"3",
"1",
"3",
"1",
"4",
"1",
"1",
"2",
"2",
"2",
"1",
"3",
"2",
"1",
"3",
"1",
"1",
"1",
"5",
"3",
"2",
"2",
"3",
"3",
"2",
"1",
"3",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"3",
"4",
"1",
"1",
"1",
"1",
"1",
"4",
"4",
"1",
"1",
"1",
"1",
"1",
"2",
"3",
"9",
"1",
"1",
"1",
"1",
"3",
"2",
"5",
"1",
"2",
"1",
"1",
"1",
"5",
"1",
"1",
"3",
"1",
"1",
"3",
"1",
"2",
"1",
"3",
"1",
"3",
"3",
"2",
"1",
"1",
"2",
"1",
"1",
"4",
"2",
"3"
]
| [
"nonn",
"hard"
]
| 21 | 1 | 1 | [
"A081119",
"A134108",
"A356706",
"A356707",
"A356708",
"A356709",
"A356710",
"A356711",
"A356712"
]
| null | Jianing Song, Aug 23 2022 | 2023-06-02T01:56:41 | oeisdata/seq/A356/A356708.seq | a62d6a719c0401226d0101107938ef9e |
A356709 | Numbers k such that Mordell's equation y^2 = x^3 + k^3 has exactly 1 integral solution. | [
"3",
"5",
"6",
"12",
"13",
"15",
"17",
"19",
"20",
"24",
"27",
"29",
"30",
"31",
"39",
"41",
"42",
"43",
"45",
"47",
"48",
"51",
"52",
"53",
"54",
"55",
"58",
"59",
"60",
"61",
"62",
"66",
"67",
"68",
"69",
"73",
"75",
"76",
"77",
"79",
"80",
"82",
"83",
"85",
"87",
"89",
"93",
"94",
"96",
"97",
"101",
"102",
"103",
"106",
"107",
"108",
"109",
"111",
"113",
"115",
"116",
"117",
"118",
"119"
]
| [
"nonn"
]
| 19 | 1 | 1 | [
"A081119",
"A179145",
"A179147",
"A179149",
"A179151",
"A228948",
"A356706",
"A356707",
"A356708",
"A356709",
"A356710",
"A356711",
"A356712",
"A356713",
"A356720"
]
| null | Jianing Song, Aug 23 2022 | 2022-09-24T12:33:48 | oeisdata/seq/A356/A356709.seq | af0f0851488f1ad2fbf56c4595884230 |
A356710 | Numbers k such that Mordell's equation y^2 = x^3 + k^3 has exactly 3 integral solutions. | [
"7",
"11",
"21",
"22",
"23",
"26",
"34",
"35",
"38",
"44",
"46",
"63",
"71",
"74",
"86",
"92",
"95",
"99",
"110",
"122",
"129",
"136",
"152",
"155",
"158",
"170",
"175",
"177",
"183",
"189",
"190",
"198",
"201",
"203",
"207",
"211"
]
| [
"nonn",
"hard",
"more"
]
| 10 | 1 | 1 | [
"A081119",
"A179145",
"A179147",
"A179149",
"A179151",
"A356706",
"A356707",
"A356708",
"A356709",
"A356710",
"A356711",
"A356712"
]
| null | Jianing Song, Aug 23 2022 | 2023-06-02T01:57:00 | oeisdata/seq/A356/A356710.seq | 5c01f4e6259cd87e284a65849acca5d3 |
A356711 | Numbers k such that Mordell's equation y^2 = x^3 + k^3 has exactly 5 integral solutions. | [
"1",
"4",
"9",
"10",
"14",
"16",
"25",
"28",
"33",
"36",
"37",
"40",
"49",
"64",
"70",
"81",
"84",
"88",
"90",
"91",
"100",
"104",
"121",
"126",
"130",
"132",
"140",
"144",
"154",
"160",
"169",
"176",
"184",
"193",
"196"
]
| [
"nonn",
"hard",
"more"
]
| 16 | 1 | 2 | [
"A081119",
"A179145",
"A179147",
"A179149",
"A179151",
"A356706",
"A356707",
"A356708",
"A356709",
"A356710",
"A356711",
"A356712"
]
| null | Jianing Song, Aug 23 2022 | 2023-06-06T17:40:44 | oeisdata/seq/A356/A356711.seq | 0adb3c92c9e6e2b2ad263f886b8d5f37 |
A356712 | Numbers k such that Mordell's equation y^2 = x^3 + k^3 has exactly 7 integral solutions. | [
"2",
"18",
"50",
"56",
"57",
"98",
"112",
"114",
"148",
"162",
"224",
"228",
"273",
"280",
"330",
"336",
"338",
"364",
"448",
"504",
"513",
"578"
]
| [
"nonn",
"hard",
"more"
]
| 6 | 1 | 1 | [
"A081119",
"A179145",
"A179147",
"A179149",
"A179151",
"A356706",
"A356707",
"A356708",
"A356709",
"A356710",
"A356711",
"A356712"
]
| null | Jianing Song, Aug 23 2022 | 2022-08-24T09:03:09 | oeisdata/seq/A356/A356712.seq | 6ff5189b75971c1a7cb59270b678eb32 |
A356713 | Numbers k such that Mordell's equation y^2 = x^3 - k^3 has exactly 1 integral solution. | [
"1",
"2",
"3",
"4",
"5",
"8",
"9",
"10",
"12",
"13",
"14",
"15",
"16",
"17",
"18",
"19",
"20",
"21",
"22",
"25",
"27",
"29",
"30",
"32",
"33",
"34",
"35",
"36",
"37",
"39",
"40",
"41",
"43",
"45",
"46",
"48",
"49",
"50",
"51",
"52",
"53",
"56",
"57",
"58",
"59",
"60",
"62",
"64",
"65",
"66",
"67",
"68",
"69",
"70",
"71",
"72",
"73",
"74",
"75",
"76",
"77",
"78",
"79",
"80",
"81",
"82",
"83",
"85",
"86",
"87",
"88"
]
| [
"nonn"
]
| 16 | 1 | 2 | [
"A081120",
"A179163",
"A228948",
"A356709",
"A356713",
"A356720"
]
| null | Jianing Song, Aug 23 2022 | 2022-09-24T12:34:10 | oeisdata/seq/A356/A356713.seq | 81ac744c9b6ec42f3d02fe8236642c6e |
A356714 | Cardinality of the set{a_1+a_2+a_3+a_4: -floor((n-1)/2) <= a_1,a_2,a_3,a_4 <= floor(n/2), and a_1^2,a_2^2,a_3^2,a_4^2 are pairwise distinct}. | [
"0",
"0",
"0",
"0",
"0",
"4",
"7",
"15",
"21",
"25",
"29",
"33",
"37",
"41",
"45",
"49",
"53",
"57",
"61",
"65",
"69",
"73",
"77",
"81",
"85",
"89",
"93",
"97",
"101",
"105",
"109",
"113",
"117",
"121",
"125",
"129",
"133",
"137",
"141",
"145",
"149",
"153",
"157",
"161",
"165",
"169",
"173",
"177",
"181",
"185"
]
| [
"nonn"
]
| 45 | 1 | 6 | [
"A000290",
"A004546",
"A356714"
]
| null | Zhi-Wei Sun, Sep 26 2022 | 2022-09-28T05:37:10 | oeisdata/seq/A356/A356714.seq | dbfd7e35d2a13dba439ea718bcf21e70 |
A356715 | Total number of distinct numbers that can be obtained by starting with 1 and applying the "Choix de Bruxelles", version 2 operation at most n times in ternary (base 3). | [
"1",
"2",
"3",
"6",
"11",
"26",
"68",
"177",
"492",
"1403",
"4113",
"12149",
"36225",
"108268",
"324529",
"973163",
"2920533",
"8764041",
"26303715",
"78935398",
"236878491",
"710783343"
]
| [
"nonn",
"base",
"more"
]
| 26 | 0 | 2 | [
"A323289",
"A356511",
"A356715"
]
| null | J. Conrad, Aug 24 2022 | 2025-01-09T13:05:51 | oeisdata/seq/A356/A356715.seq | 4ee5bd8af30208b221bd062f9801e434 |
A356716 | a(n) is the integer w such that (c(n)^2, -d(n)^2, -w) is a primitive solution to the Diophantine equation 2*x^3 + 2*y^3 + z^3 = 11^3, where c(n) = F(n+2) + (-1)^n * F(n-3), d(n) = F(n+1) + (-1)^n * F(n-4) and F(n) is the n-th Fibonacci number (A000045). | [
"5",
"19",
"31",
"101",
"179",
"655",
"1189",
"4451",
"8111",
"30469",
"55555",
"208799",
"380741",
"1431091",
"2609599",
"9808805",
"17886419",
"67230511",
"122595301",
"460804739",
"840280655",
"3158402629",
"5759369251",
"21648013631",
"39475304069",
"148377692755",
"270567759199",
"1016995835621",
"1854499010291"
]
| [
"nonn",
"easy"
]
| 42 | 1 | 1 | [
"A000045",
"A081016",
"A089270",
"A206351",
"A228208",
"A237132",
"A337928",
"A354336",
"A356716",
"A356717"
]
| null | XU Pingya, Aug 24 2022 | 2024-08-03T19:22:10 | oeisdata/seq/A356/A356716.seq | 96f9741bf37673b6643ca2aac1605eb7 |
A356717 | a(n) is the integer w such that (c(n)^2, -d(n)^2, w) is a primitive solution to the Diophantine equation 2*x^3 + 2*y^3 + z^3 = 11^3, where c(n) = F(n+2) + (-1)^n * F(n-3), d(n) = F(n+3) + (-1)^n * F(n-2) and F(n) is the n-th Fibonacci number (A000045). | [
"1",
"29",
"59",
"241",
"445",
"1691",
"3089",
"11629",
"21211",
"79745",
"145421",
"546619",
"996769",
"3746621",
"6831995",
"25679761",
"46827229",
"176011739",
"320958641",
"1206402445",
"2199883291",
"8268805409",
"15078224429",
"56675235451",
"103347687745",
"388457842781",
"708355589819",
"2662529664049"
]
| [
"nonn",
"easy"
]
| 18 | 1 | 2 | [
"A000045",
"A081016",
"A081018",
"A089270",
"A228208",
"A237132",
"A337929",
"A354337",
"A356716",
"A356717"
]
| null | XU Pingya, Aug 24 2022 | 2022-10-02T00:22:02 | oeisdata/seq/A356/A356717.seq | 9d71c35e61d8fa89b0ad05b571020790 |
A356718 | T(n,k) is the total number of prime factors, counted with multiplicity, of k!*(n-k)!, for 0 <= k <= n. Triangle read by rows. | [
"0",
"0",
"0",
"1",
"0",
"1",
"2",
"1",
"1",
"2",
"4",
"2",
"2",
"2",
"4",
"5",
"4",
"3",
"3",
"4",
"5",
"7",
"5",
"5",
"4",
"5",
"5",
"7",
"8",
"7",
"6",
"6",
"6",
"6",
"7",
"8",
"11",
"8",
"8",
"7",
"8",
"7",
"8",
"8",
"11",
"13",
"11",
"9",
"9",
"9",
"9",
"9",
"9",
"11",
"13",
"15",
"13",
"12",
"10",
"11",
"10",
"11",
"10",
"12",
"13",
"15",
"16",
"15",
"14",
"13",
"12",
"12",
"12"
]
| [
"nonn",
"tabl",
"easy",
"look"
]
| 89 | 0 | 7 | [
"A001222",
"A007318",
"A022559",
"A132896",
"A303279",
"A356718"
]
| null | Dario T. de Castro, Aug 24 2022 | 2025-03-04T23:15:23 | oeisdata/seq/A356/A356718.seq | 9a52d90a08520d12e517c5efd23ba2f7 |
A356719 | a(n) = Sum_{k=0..n} k^binomial(n,k). | [
"0",
"1",
"3",
"12",
"150",
"61103",
"4560574625",
"1180642129099670883352",
"1395184353688945915375285901200638422723404",
"11754943508230112085264929216560108802852371298464244215700837207032911162905441549473573"
]
| [
"nonn",
"easy"
]
| 6 | 0 | 3 | [
"A001315",
"A064405",
"A087314",
"A356719"
]
| null | Seiichi Manyama, Aug 24 2022 | 2022-08-24T12:09:55 | oeisdata/seq/A356/A356719.seq | e37bb70fc4c1aa8be231b0b82a96efb8 |
A356720 | Numbers k such that Mordell's equation y^2 = x^3 + k^3 has more than 1 integral solution. | [
"1",
"2",
"4",
"7",
"8",
"9",
"10",
"11",
"14",
"16",
"18",
"21",
"22",
"23",
"25",
"26",
"28",
"32",
"33",
"34",
"35",
"36",
"37",
"38",
"40",
"44",
"46",
"49",
"50",
"56",
"57",
"63",
"64",
"65",
"70",
"71",
"72",
"74",
"78",
"81",
"84",
"86",
"88",
"90",
"91",
"92",
"95",
"98",
"99",
"100",
"104",
"105",
"110",
"112",
"114",
"121",
"122",
"126",
"128",
"129",
"130",
"132",
"136",
"140",
"144",
"148"
]
| [
"nonn"
]
| 18 | 1 | 2 | [
"A081119",
"A103254",
"A228948",
"A356703",
"A356709",
"A356710",
"A356711",
"A356712",
"A356713",
"A356720"
]
| null | Jianing Song, Aug 24 2022 | 2022-09-24T12:34:25 | oeisdata/seq/A356/A356720.seq | 0e7d2ead4c6ab4fd8d14950929e19962 |
A356721 | Numbers written using exactly two distinct Roman numerals. | [
"4",
"6",
"7",
"8",
"9",
"11",
"12",
"13",
"15",
"19",
"21",
"22",
"23",
"25",
"29",
"31",
"32",
"33",
"35",
"39",
"40",
"51",
"52",
"53",
"55",
"60",
"70",
"80",
"90",
"101",
"102",
"103",
"105",
"110",
"120",
"130",
"150",
"190",
"201",
"202",
"203",
"205",
"210",
"220",
"230",
"250",
"290",
"301",
"302",
"303",
"305",
"310",
"320",
"330",
"350",
"390",
"400",
"501",
"502"
]
| [
"nonn",
"base",
"fini",
"easy"
]
| 14 | 1 | 1 | null | null | Alain Cousquer and Pierre-Hugues Villaume, Aug 24 2022 | 2022-10-05T05:10:20 | oeisdata/seq/A356/A356721.seq | 8b0d46beaa8c0fde6a6b7336df2bbe2d |
A356722 | Number of n X n tables where each row represents a permutation of { 1, 2, ..., n } and the column sums are equal. | [
"1",
"2",
"12",
"2520",
"7015680",
"1395793843200",
"20278935204394809600",
"33190120270913939567661168000"
]
| [
"nonn",
"more"
]
| 17 | 1 | 2 | [
"A356722",
"A356723",
"A356724",
"A356725"
]
| null | Max Alekseyev, Aug 24 2022 | 2023-10-30T09:44:39 | oeisdata/seq/A356/A356722.seq | ed29c2ce9d25c87472978c1c9fb35d5c |
A356723 | Number of n X n tables where each row represents a permutation of { 1, 2, ..., n } and the column sums are equal, with the first row being the identity permutation. | [
"1",
"1",
"2",
"105",
"58464",
"1938602560",
"4023598254840240",
"823167665449254453563025"
]
| [
"nonn",
"more"
]
| 5 | 1 | 3 | [
"A356722",
"A356723",
"A356724",
"A356725"
]
| null | Max Alekseyev, Aug 25 2022 | 2022-08-25T08:34:08 | oeisdata/seq/A356/A356723.seq | bc6221c02c8a711207fd75078976627d |
A356724 | Number of n X n tables where each row represents a permutation of { 1, 2, ..., n } and the column sums are equal, up to permutation of rows. | [
"1",
"1",
"2",
"114",
"60024",
"1951262760",
"4029043460476320",
"823357371521186302202640"
]
| [
"nonn",
"hard",
"more"
]
| 13 | 1 | 3 | [
"A356722",
"A356723",
"A356724",
"A356725"
]
| null | Max Alekseyev, Aug 25 2022 | 2022-10-11T20:11:02 | oeisdata/seq/A356/A356724.seq | 1fee290a6870b80432a09572dc967337 |
A356725 | Number of n X n tables where each row represents a permutation of { 1, 2, ..., n } and the column sums are equal, up to permutation of rows and columns. | [
"1",
"1",
"1",
"10",
"505",
"2712342",
"799413385118",
"20420569739290737009"
]
| [
"hard",
"more",
"nonn"
]
| 9 | 1 | 4 | [
"A356722",
"A356723",
"A356724",
"A356725",
"A357766",
"A357767",
"A357768"
]
| null | Max Alekseyev, Oct 11 2022 | 2022-10-18T06:23:57 | oeisdata/seq/A356/A356725.seq | d764de377fab4dace5aa5922e5a34724 |
A356726 | Integers which have in Roman numerals more distinct symbols than any smaller number. | [
"1",
"4",
"14",
"44",
"144",
"444",
"1444"
]
| [
"nonn",
"fini",
"full",
"easy"
]
| 26 | 1 | 2 | [
"A038378",
"A057226",
"A356726"
]
| null | Alain Cousquer, Aug 24 2022 | 2022-09-11T00:51:50 | oeisdata/seq/A356/A356726.seq | 8f940b572bb7e0841fbc5f6517672a1e |
A356727 | Primes of the form 4*k^2 + 84*k + 43. | [
"43",
"131",
"227",
"331",
"443",
"563",
"691",
"827",
"971",
"1123",
"1283",
"1451",
"1627",
"1811",
"2003",
"2203",
"2411",
"2851",
"3083",
"3323",
"3571",
"4091",
"4363",
"4643",
"4931",
"5227",
"5531",
"5843",
"6163",
"6491",
"6827",
"7523",
"7883",
"8627",
"9011",
"9403",
"9803",
"10211",
"10627",
"11483",
"11923",
"13291",
"13763",
"14243",
"14731",
"15227",
"15731"
]
| [
"nonn",
"less"
]
| 22 | 1 | 1 | [
"A005846",
"A221712",
"A331940",
"A356727"
]
| null | Charles Delaporte, Aug 24 2022 | 2023-05-07T18:52:58 | oeisdata/seq/A356/A356727.seq | eea5173c010c864a052215e59cb8386a |
A356728 | The number of 3-permutations that avoid the patterns 132 and 213. | [
"1",
"4",
"12",
"28",
"58",
"114",
"220",
"424",
"822",
"1606",
"3160",
"6252",
"12418",
"24730",
"49332",
"98512",
"196846",
"393486",
"786736",
"1573204",
"3146106",
"6291874",
"12583372",
"25166328",
"50332198",
"100663894",
"201327240",
"402653884",
"805307122",
"1610613546",
"3221226340"
]
| [
"nonn",
"easy"
]
| 18 | 1 | 2 | [
"A308580",
"A356728"
]
| null | Nathan Sun, Aug 24 2022 | 2022-12-09T23:04:19 | oeisdata/seq/A356/A356728.seq | e4bd7d9f9b14e402a5573250dbb85558 |
A356729 | Numbers having at least 4 distinct partitions into exactly 3 parts with the same product. | [
"118",
"130",
"133",
"135",
"137",
"140",
"148",
"149",
"153",
"155",
"161",
"167",
"169",
"174",
"175",
"182",
"183",
"185",
"189",
"190",
"194",
"195",
"200",
"202",
"205",
"206",
"208",
"209",
"210",
"213",
"214",
"215",
"216",
"217",
"220",
"221",
"222",
"223",
"224",
"225",
"228",
"229",
"231",
"234",
"235",
"236",
"239",
"240",
"243",
"244",
"245",
"247",
"248",
"249",
"250",
"251",
"253",
"254"
]
| [
"nonn"
]
| 15 | 1 | 1 | [
"A119028",
"A356729"
]
| null | Tanya Khovanova, Sep 09 2022 | 2022-09-11T00:24:37 | oeisdata/seq/A356/A356729.seq | e9e58ffada62c51b94f76b34e47e0d6e |
A356730 | Conductor of the elliptic curve y^2 = x^3 + n. | [
"36",
"1728",
"3888",
"108",
"2700",
"15552",
"21168",
"576",
"972",
"14400",
"52272",
"3888",
"18252",
"84672",
"97200",
"27",
"10404",
"15552",
"51984",
"2700",
"47628",
"209088",
"228528",
"15552",
"2700",
"97344",
"144",
"7056",
"90828",
"388800",
"415152",
"1728",
"117612",
"499392",
"176400",
"972",
"49284",
"623808",
"657072",
"43200",
"181548"
]
| [
"nonn"
]
| 11 | 1 | 1 | [
"A060950",
"A356730",
"A356731"
]
| null | Jianing Song, Aug 24 2022 | 2022-08-25T09:54:35 | oeisdata/seq/A356/A356730.seq | 7340205da910de2aebd97deeac6c90d5 |
A356731 | Conductor of the elliptic curve y^2 = x^3 - n. | [
"144",
"1728",
"972",
"432",
"10800",
"15552",
"5292",
"576",
"3888",
"14400",
"13068",
"972",
"73008",
"84672",
"24300",
"432",
"41616",
"15552",
"12996",
"10800",
"190512",
"209088",
"57132",
"15552",
"10800",
"97344",
"36",
"1764",
"363312",
"388800",
"103788",
"1728",
"470448",
"499392",
"44100",
"3888",
"197136",
"623808",
"164268",
"43200",
"726192"
]
| [
"nonn"
]
| 11 | 1 | 1 | [
"A060951",
"A356730",
"A356731"
]
| null | Jianing Song, Aug 24 2022 | 2022-08-25T09:54:39 | oeisdata/seq/A356/A356731.seq | 6b44ba41ebd16d6726660fa29f7681b4 |
A356732 | Let u defined by u(1) = p and for 1 < i, u(i) = u(i-1) + primorial(i), such that all u(i) are primes for 1 <= i <= k, and u(k+1) is not prime. Let m the length of the longest run of primes obtained when u is repeatedly applied to an n-digit p. Triangle read by rows: for 1 <= n, 1 <= k <= m, T(n,k) is the least n-digit prime p beginning a run of only k primes when applied u, or -1 if no such prime p exists. | [
"2",
"-1",
"7",
"5",
"19",
"13",
"53",
"11",
"37",
"23",
"-1",
"-1",
"-1",
"61",
"109",
"107",
"131",
"257",
"103",
"101",
"331",
"-1",
"193",
"1009",
"1063",
"1087",
"1013",
"1601",
"1543",
"1447",
"9397",
"1741",
"10007",
"10061",
"10133",
"10847",
"11251",
"10253",
"17203",
"10267",
"47563",
"100003",
"100043",
"100357",
"101833",
"101113",
"109583",
"115657",
"101287",
"106747",
"895667",
"306847"
]
| [
"sign",
"tabf",
"base"
]
| 67 | 1 | 1 | [
"A002110",
"A356732"
]
| null | Jean-Marc Rebert, Aug 24 2022 | 2025-05-06T11:24:43 | oeisdata/seq/A356/A356732.seq | aeed89287f968fea4b887fc7570da92f |
A356733 | Number of neighborless parts in the integer partition with Heinz number n. | [
"0",
"1",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"2",
"1",
"0",
"1",
"2",
"0",
"1",
"1",
"0",
"1",
"2",
"2",
"2",
"1",
"0",
"1",
"2",
"1",
"2",
"1",
"0",
"1",
"1",
"2",
"2",
"0",
"0",
"1",
"2",
"2",
"2",
"1",
"1",
"1",
"2",
"0",
"2",
"1",
"0",
"1",
"2",
"2",
"2",
"1",
"0",
"2",
"2",
"2",
"2",
"1",
"0",
"1",
"2",
"2",
"1",
"2",
"1",
"1",
"2",
"2",
"1",
"1",
"0",
"1",
"2",
"0",
"2",
"0",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"2",
"2",
"2",
"2",
"1",
"0",
"2",
"2",
"2",
"2",
"2",
"0",
"1",
"2",
"2",
"2",
"1",
"1",
"1",
"2",
"0"
]
| [
"nonn"
]
| 12 | 1 | 10 | [
"A000005",
"A001221",
"A001222",
"A001414",
"A003963",
"A007690",
"A056239",
"A066205",
"A066312",
"A073491",
"A073492",
"A112798",
"A132747",
"A132881",
"A183558",
"A286470",
"A287170",
"A289508",
"A325160",
"A328166",
"A328335",
"A355393",
"A355394",
"A356069",
"A356224",
"A356225",
"A356231",
"A356233",
"A356234",
"A356235",
"A356236",
"A356237",
"A356606",
"A356607",
"A356733",
"A356734",
"A356735"
]
| null | Gus Wiseman, Aug 26 2022 | 2025-01-28T16:55:06 | oeisdata/seq/A356/A356733.seq | 1d0d3fd7561482c346bebf30fd186275 |
A356734 | Heinz numbers of integer partitions with at least one neighborless part. | [
"2",
"3",
"4",
"5",
"7",
"8",
"9",
"10",
"11",
"13",
"14",
"16",
"17",
"19",
"20",
"21",
"22",
"23",
"25",
"26",
"27",
"28",
"29",
"31",
"32",
"33",
"34",
"37",
"38",
"39",
"40",
"41",
"42",
"43",
"44",
"46",
"47",
"49",
"50",
"51",
"52",
"53",
"55",
"56",
"57",
"58",
"59",
"61",
"62",
"63",
"64",
"65",
"66",
"67",
"68",
"69",
"70",
"71",
"73",
"74",
"76",
"78",
"79",
"80",
"81",
"82",
"83"
]
| [
"nonn"
]
| 7 | 1 | 1 | [
"A000005",
"A001221",
"A001222",
"A001414",
"A003963",
"A007690",
"A056239",
"A066205",
"A073491",
"A073492",
"A112798",
"A132747",
"A132881",
"A183558",
"A286470",
"A287170",
"A289508",
"A325160",
"A328166",
"A328335",
"A355393",
"A355394",
"A356069",
"A356224",
"A356225",
"A356231",
"A356233",
"A356234",
"A356235",
"A356236",
"A356237",
"A356606",
"A356607",
"A356734",
"A356736"
]
| null | Gus Wiseman, Aug 26 2022 | 2022-08-30T09:41:50 | oeisdata/seq/A356/A356734.seq | 9cc14999b449e87b718cd301544fe157 |
A356735 | Number of distinct parts that have neighbors in the integer partition with Heinz number n. | [
"0",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"2",
"0",
"0",
"2",
"0",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"0",
"0",
"0",
"3",
"0",
"0",
"0",
"0",
"2",
"2",
"0",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"2",
"0",
"0",
"2",
"0",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"0",
"0",
"0",
"3",
"0",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"0",
"2",
"0",
"2",
"0",
"0",
"2",
"0",
"2",
"2",
"0",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"0",
"0",
"0",
"3",
"0",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"3"
]
| [
"nonn"
]
| 13 | 1 | 6 | [
"A000005",
"A001221",
"A001222",
"A001414",
"A002110",
"A007690",
"A056239",
"A066205",
"A066312",
"A073491",
"A073492",
"A112798",
"A183558",
"A231209",
"A286470",
"A287170",
"A289508",
"A325160",
"A328166",
"A328335",
"A355393",
"A355394",
"A356226",
"A356227",
"A356228",
"A356229",
"A356230",
"A356231",
"A356232",
"A356233",
"A356234",
"A356235",
"A356236",
"A356237",
"A356733",
"A356734",
"A356735",
"A356736"
]
| null | Gus Wiseman, Aug 31 2022 | 2025-01-28T16:54:54 | oeisdata/seq/A356/A356735.seq | 98bc5a7f4982bae2a0e5ce83badf606e |
A356736 | Heinz numbers of integer partitions with no neighborless parts. | [
"1",
"6",
"12",
"15",
"18",
"24",
"30",
"35",
"36",
"45",
"48",
"54",
"60",
"72",
"75",
"77",
"90",
"96",
"105",
"108",
"120",
"135",
"143",
"144",
"150",
"162",
"175",
"180",
"192",
"210",
"216",
"221",
"225",
"240",
"245",
"270",
"288",
"300",
"315",
"323",
"324",
"360",
"375",
"384",
"385",
"405",
"420",
"432",
"437",
"450",
"462",
"480",
"486",
"525",
"539",
"540"
]
| [
"nonn"
]
| 10 | 1 | 2 | [
"A000009",
"A000041",
"A001221",
"A001222",
"A001414",
"A003963",
"A007690",
"A056239",
"A066205",
"A066312",
"A073491",
"A073492",
"A112798",
"A183558",
"A286470",
"A287170",
"A328171",
"A328187",
"A328221",
"A328335",
"A355393",
"A355394",
"A356231",
"A356234",
"A356235",
"A356236",
"A356237",
"A356606",
"A356607",
"A356734",
"A356736"
]
| null | Gus Wiseman, Aug 31 2022 | 2022-09-01T09:33:46 | oeisdata/seq/A356/A356736.seq | 317e263d3f818d429079a4ed8168bc29 |
A356737 | Number of integer partitions of n into odd parts covering an interval of odd numbers. | [
"1",
"1",
"1",
"2",
"2",
"3",
"3",
"4",
"4",
"6",
"6",
"7",
"8",
"9",
"10",
"13",
"13",
"15",
"17",
"19",
"21",
"25",
"26",
"29",
"33",
"37",
"40",
"46",
"49",
"54",
"61",
"66",
"72",
"81",
"87",
"97",
"106",
"115",
"125",
"139",
"150",
"163",
"179",
"193",
"210",
"232",
"248",
"269",
"293",
"317",
"343",
"373",
"401",
"433",
"470",
"507",
"545",
"590",
"633",
"682",
"737",
"790"
]
| [
"nonn"
]
| 6 | 0 | 4 | [
"A000009",
"A000041",
"A001227",
"A011782",
"A034178",
"A053251",
"A055932",
"A060142",
"A066205",
"A066208",
"A073491",
"A107428",
"A107429",
"A332032",
"A333217",
"A356224",
"A356232",
"A356603",
"A356604",
"A356605",
"A356737",
"A356841",
"A356846"
]
| null | Gus Wiseman, Sep 03 2022 | 2022-09-03T12:19:54 | oeisdata/seq/A356/A356737.seq | cc114523e3dc370487a8d99a4426640e |
A356738 | Smallest positive integer whose American English name consists of n words. | [
"1",
"21",
"101",
"121",
"1101",
"1121",
"21121",
"101121",
"121121",
"1101121",
"1121121",
"21121121",
"101121121",
"121121121",
"1101121121",
"1121121121",
"21121121121",
"121121121121",
"1101121121121",
"1121121121121",
"21121121121121",
"101121121121121",
"121121121121121",
"1101121121121121"
]
| [
"nonn",
"word",
"fini"
]
| 6 | 1 | 2 | [
"A080777",
"A356738"
]
| null | Ivan N. Ianakiev, Aug 25 2022 | 2022-09-04T12:39:27 | oeisdata/seq/A356/A356738.seq | 7b05fdd5a5b06107cafbc3e28382ec68 |
A356739 | a(n) is the smallest k such that k! has at least n consecutive zeros immediately after the leading digit in base 10. | [
"7",
"153",
"197",
"7399",
"24434",
"24434",
"9242360",
"238861211",
"238861211"
]
| [
"nonn",
"base",
"more"
]
| 17 | 1 | 1 | [
"A000142",
"A027869",
"A356739"
]
| null | Christian Perfect, Aug 25 2022 | 2022-10-02T00:23:54 | oeisdata/seq/A356/A356739.seq | 25f6f2e33a356cf3dfc16d4a8996984c |
A356740 | a(n) is the least emirp that begins a sequence of exactly n emirps under the map p -> (p*R(p)) mod (p+R(p)), where R(p) is the digit reversal of p. | [
"13",
"389",
"15013",
"7149589",
"1471573153"
]
| [
"nonn",
"base",
"more",
"less"
]
| 53 | 1 | 1 | [
"A004086",
"A006567",
"A355651",
"A356740"
]
| null | J. M. Bergot and Robert Israel, Sep 04 2022 | 2022-09-09T10:03:31 | oeisdata/seq/A356/A356740.seq | c6729c15c5fcc44c4c7d2d365308d89e |
A356741 | a(n) is the least prime(m) such that prime(n) + prime(m)# is prime, where prime(m)# denotes the product of the first m primes, or -1 if no such prime(m) exists. | [
"2",
"2",
"3",
"2",
"3",
"2",
"7",
"3",
"2",
"3",
"3",
"2",
"5",
"3",
"3",
"2",
"3",
"3",
"2",
"3",
"5",
"3",
"11",
"3",
"2",
"3",
"2",
"5",
"11",
"5",
"3",
"2",
"7",
"2",
"3",
"3",
"5",
"3",
"3",
"2",
"5",
"2",
"3",
"2",
"5",
"5",
"3",
"2",
"7",
"3",
"2",
"5",
"3",
"3",
"3",
"2",
"3",
"3",
"2",
"5",
"7",
"3",
"2",
"7",
"5",
"3",
"5",
"2",
"5",
"3",
"5",
"3",
"3",
"5",
"3",
"5",
"7",
"5",
"5",
"2",
"7",
"2",
"3",
"11",
"3",
"5",
"3"
]
| [
"nonn"
]
| 59 | 2 | 1 | [
"A002110",
"A100380",
"A356741"
]
| null | Alain Rocchelli, Sep 04 2022 | 2022-10-18T11:21:08 | oeisdata/seq/A356/A356741.seq | 709982c3f00a58b553c4a5c82de58ef7 |
A356742 | Numbers k such that k and k+2 both have exactly 4 divisors. | [
"6",
"8",
"33",
"55",
"85",
"91",
"93",
"123",
"141",
"143",
"159",
"183",
"185",
"201",
"203",
"213",
"215",
"217",
"219",
"235",
"247",
"265",
"299",
"301",
"303",
"319",
"321",
"327",
"339",
"341",
"391",
"393",
"411",
"413",
"415",
"445",
"451",
"469",
"471",
"515",
"517",
"533",
"535",
"543",
"551",
"579",
"581",
"589",
"633",
"667",
"669",
"679",
"685",
"687",
"695",
"697"
]
| [
"nonn"
]
| 10 | 1 | 1 | [
"A001359",
"A039832",
"A356742",
"A356743",
"A356744"
]
| null | Jianing Song, Aug 25 2022 | 2022-10-07T11:56:53 | oeisdata/seq/A356/A356742.seq | 68127168767547cd299f63e791915120 |
A356743 | Numbers k such that k and k+2 both have exactly 6 divisors. | [
"18",
"50",
"242",
"243",
"423",
"475",
"603",
"637",
"722",
"845",
"925",
"1682",
"1773",
"2007",
"2523",
"2525",
"2527",
"3123",
"3175",
"3177",
"4203",
"4475",
"4525",
"4923",
"5823",
"6725",
"6811",
"6962",
"7299",
"7442",
"7675",
"8425",
"8957",
"8973",
"9457",
"9925",
"10051",
"10082",
"10467",
"11673",
"11709",
"12427",
"12482",
"12591",
"13023",
"13075"
]
| [
"nonn"
]
| 10 | 1 | 1 | [
"A001359",
"A048161",
"A049103",
"A356742",
"A356743",
"A356744"
]
| null | Jianing Song, Aug 25 2022 | 2022-08-25T09:13:32 | oeisdata/seq/A356/A356743.seq | d6ad97b95fe5ea71eaa136e743aa996f |
A356744 | Numbers k such that both k and k+2 have exactly 8 divisors. | [
"40",
"54",
"102",
"128",
"136",
"152",
"182",
"184",
"230",
"246",
"248",
"374",
"424",
"470",
"472",
"534",
"582",
"663",
"710",
"806",
"822",
"824",
"854",
"872",
"902",
"904",
"999",
"1105",
"1192",
"1256",
"1309",
"1334",
"1336",
"1432",
"1446",
"1526",
"1542",
"1545",
"1576",
"1593",
"1645",
"1686",
"1784",
"1832",
"1864",
"1885",
"1910",
"1928",
"2006",
"2013"
]
| [
"nonn"
]
| 8 | 1 | 1 | [
"A001359",
"A274357",
"A356742",
"A356744"
]
| null | Jianing Song, Aug 25 2022 | 2022-08-25T09:13:22 | oeisdata/seq/A356/A356744.seq | 5930b20b8530a48b12fc538511c5fbed |
A356745 | a(n) is the first prime that starts a string of exactly n consecutive primes where the prime + the next prime + 1 is prime. | [
"37",
"5",
"283",
"929",
"13",
"696607",
"531901",
"408079937",
"17028422981"
]
| [
"nonn",
"more"
]
| 30 | 1 | 1 | [
"A177017",
"A356745"
]
| null | J. M. Bergot and Robert Israel, Sep 17 2022 | 2022-09-19T20:24:00 | oeisdata/seq/A356/A356745.seq | c9203d2c05cc9115fd67a8d8c7c1a444 |
A356746 | Number of 2-colored labeled directed acyclic graphs on n nodes such that all black nodes are sources. | [
"1",
"2",
"8",
"74",
"1664",
"90722",
"11756288",
"3544044674",
"2439773425664",
"3777981938265602",
"12999312305021800448",
"98399334883456516073474",
"1625096032161083727093530624",
"58150966795467956854830216929282"
]
| [
"nonn"
]
| 39 | 0 | 2 | [
"A003024",
"A356746"
]
| null | Geoffrey Critzer, Oct 08 2022 | 2022-10-08T22:17:01 | oeisdata/seq/A356/A356746.seq | 7259a35fe15995d1d78c59a353f91345 |
A356747 | Numbers m that divide A306070(m) = Sum_{k=1..m} bphi(k), where bphi is the bi-unitary totient function (A116550). | [
"1",
"2",
"141",
"1035",
"2388",
"3973",
"5157",
"14160",
"37023",
"68861",
"99889",
"116106",
"117939",
"627400",
"1561944",
"1626983",
"5901444",
"10054091",
"12260525",
"32619981",
"49775099"
]
| [
"nonn",
"more"
]
| 8 | 1 | 2 | [
"A048290",
"A116550",
"A306070",
"A306950",
"A356747"
]
| null | Amiram Eldar, Aug 25 2022 | 2022-08-26T07:30:06 | oeisdata/seq/A356/A356747.seq | d4a84f4e4221577802211b1f573ca2a2 |
A356748 | Numbers k such that k and k+1 are both products of 2 triangular numbers. | [
"0",
"9",
"90",
"135",
"945",
"1710",
"1890",
"4959",
"5670",
"8910",
"10584",
"11025",
"11934",
"13860",
"19305",
"21735",
"26334",
"32130",
"36855",
"44550",
"49140",
"65340",
"107415",
"138600",
"172080",
"239085",
"305370",
"351540",
"366795",
"459360",
"849555",
"873180",
"933660",
"1100385",
"1413720",
"1516410",
"1904175",
"2297295"
]
| [
"nonn"
]
| 16 | 1 | 2 | [
"A085780",
"A356748"
]
| null | Amiram Eldar, Aug 25 2022 | 2023-04-05T16:40:38 | oeisdata/seq/A356/A356748.seq | 40946041ad43b5762dfa0408188b93ed |
A356749 | a(n) is the number of trailing 1's in the dual Zeckendorf representation of n (A104326). | [
"0",
"1",
"0",
"2",
"1",
"0",
"3",
"0",
"2",
"1",
"0",
"4",
"1",
"0",
"3",
"0",
"2",
"1",
"0",
"5",
"0",
"2",
"1",
"0",
"4",
"1",
"0",
"3",
"0",
"2",
"1",
"0",
"6",
"1",
"0",
"3",
"0",
"2",
"1",
"0",
"5",
"0",
"2",
"1",
"0",
"4",
"1",
"0",
"3",
"0",
"2",
"1",
"0",
"7",
"0",
"2",
"1",
"0",
"4",
"1",
"0",
"3",
"0",
"2",
"1",
"0",
"6",
"1",
"0",
"3",
"0",
"2",
"1",
"0",
"5",
"0",
"2",
"1",
"0",
"4",
"1",
"0",
"3",
"0",
"2",
"1",
"0"
]
| [
"nonn",
"base"
]
| 11 | 0 | 4 | [
"A001622",
"A003849",
"A035614",
"A104326",
"A276084",
"A278045",
"A356749"
]
| null | Amiram Eldar, Aug 25 2022 | 2022-08-26T07:28:39 | oeisdata/seq/A356/A356749.seq | a591f142817f3a42562c79766a9dc1b3 |
A356750 | Palindromic odd numbers with an odd number of distinct prime factors. | [
"3",
"5",
"7",
"9",
"11",
"101",
"121",
"131",
"151",
"181",
"191",
"313",
"343",
"353",
"373",
"383",
"525",
"555",
"585",
"595",
"727",
"757",
"777",
"787",
"797",
"919",
"929",
"969",
"1001",
"1221",
"1331",
"1551",
"1771",
"1881",
"3333",
"3553",
"3663",
"5225",
"5335",
"5445",
"5555",
"5665",
"5885",
"5995",
"7007",
"7227",
"7337",
"7557",
"7667",
"7777",
"7887",
"9339",
"9669",
"9779",
"9889",
"9999",
"10201",
"10301"
]
| [
"nonn",
"base"
]
| 24 | 1 | 1 | null | null | Tanya Khovanova, Aug 25 2022 | 2022-09-14T08:25:41 | oeisdata/seq/A356/A356750.seq | dddaa456d18756f765227137d182cddc |
A356751 | Positive integers m such that x^2 - x + m contains more than m/2 prime numbers for x = 1, 2, ..., m. | [
"3",
"5",
"7",
"11",
"17",
"41",
"47",
"59",
"67",
"101",
"107",
"161",
"221",
"227",
"347",
"377"
]
| [
"nonn",
"more"
]
| 63 | 1 | 1 | [
"A005846",
"A007635",
"A007641",
"A014556",
"A057604",
"A188424",
"A331940",
"A356751",
"A356756"
]
| null | Marco Ripà, Aug 25 2022 | 2024-06-20T16:26:36 | oeisdata/seq/A356/A356751.seq | 9befcf42b80381a0c6cbd4e814cd8209 |
A356752 | E.g.f. satisfies A(x) = 1/(1 - x)^(x^2/2 * A(x)). | [
"1",
"0",
"0",
"3",
"6",
"20",
"360",
"2394",
"17220",
"260280",
"3076920",
"35980560",
"595686960",
"9760411440",
"159321570408",
"3093987619800",
"63314740616400",
"1318245318411840",
"30240056863978560",
"736919729169603840",
"18522487833889334400",
"495842871278901363840",
"14014346231616983128800"
]
| [
"nonn"
]
| 27 | 0 | 4 | [
"A351492",
"A355842",
"A356752",
"A356753",
"A356912"
]
| null | Seiichi Manyama, Sep 03 2022 | 2025-02-16T08:34:03 | oeisdata/seq/A356/A356752.seq | ffc1baf02a759830b2e182904d0f6350 |
A356753 | E.g.f. satisfies A(x) = 1/(1 - x)^(x^3/6 * A(x)). | [
"1",
"0",
"0",
"0",
"4",
"10",
"40",
"210",
"3024",
"25200",
"225000",
"2217600",
"29974560",
"400720320",
"5558957040",
"81340459200",
"1344965825280",
"23566775232000",
"432681781459200",
"8309927446329600",
"170258024427580800",
"3679448236206220800",
"83235946152090547200",
"1962840630226968307200"
]
| [
"nonn"
]
| 27 | 0 | 5 | [
"A351493",
"A355842",
"A356752",
"A356753",
"A356913"
]
| null | Seiichi Manyama, Sep 03 2022 | 2025-02-16T08:34:03 | oeisdata/seq/A356/A356753.seq | 96043729727e46b5913ace9005b02a5f |
A356754 | Triangle read by rows: T(n,k) = ((n-1)*(n+2))/2 + 2*k. | [
"2",
"4",
"6",
"7",
"9",
"11",
"11",
"13",
"15",
"17",
"16",
"18",
"20",
"22",
"24",
"22",
"24",
"26",
"28",
"30",
"32",
"29",
"31",
"33",
"35",
"37",
"39",
"41",
"37",
"39",
"41",
"43",
"45",
"47",
"49",
"51",
"46",
"48",
"50",
"52",
"54",
"56",
"58",
"60",
"62",
"56",
"58",
"60",
"62",
"64",
"66",
"68",
"70",
"72",
"74",
"67",
"69",
"71",
"73",
"75",
"77",
"79",
"81",
"83",
"85",
"87"
]
| [
"nonn",
"tabl",
"easy"
]
| 48 | 1 | 1 | [
"A000124",
"A004120",
"A046691",
"A051938",
"A055999",
"A056000",
"A155212",
"A167487",
"A167499",
"A167614",
"A246172",
"A334563",
"A356288",
"A356754"
]
| null | Torlach Rush, Aug 25 2022 | 2023-05-26T14:10:04 | oeisdata/seq/A356/A356754.seq | 19d46a31efd45aa483889c4b8389abcb |
A356755 | Semiprimes k such that k is congruent to 2 modulo k's index in the sequence of semiprimes. | [
"4",
"6",
"10",
"119",
"155",
"158",
"215",
"27682",
"3066887",
"3066907",
"3067027",
"3067167",
"3067187",
"3067247",
"3067277",
"3067682",
"3067687",
"3067742",
"3067787",
"3067847",
"3067907",
"3067917",
"3067937",
"3067942",
"3068042",
"3068067",
"348933302",
"348933422",
"44690978131",
"44690978257",
"44690978537",
"44690978719",
"44690978971"
]
| [
"nonn",
"hard"
]
| 45 | 1 | 1 | [
"A001358",
"A106127",
"A356755"
]
| null | Lucas A. Brown, Oct 13 2022 | 2022-10-15T16:29:04 | oeisdata/seq/A356/A356755.seq | 94802ad702f1d69399f2a428e4dbcdf6 |
A356756 | Positive integers m such that x^2 + x + m contains at least m/2 prime numbers for x = 1, 2, ..., m. | [
"1",
"5",
"11",
"17",
"41",
"47",
"59",
"67",
"101",
"107",
"161",
"221",
"227",
"347",
"377"
]
| [
"nonn",
"more"
]
| 35 | 1 | 2 | [
"A005846",
"A007635",
"A007641",
"A057604",
"A188424",
"A331940",
"A356751",
"A356756"
]
| null | Marco Ripà, Aug 26 2022 | 2022-09-05T22:22:39 | oeisdata/seq/A356/A356756.seq | 82ab91d716b5c09cd92dc7ac6951b059 |
A356757 | Omit zero digits from factorial numbers. | [
"1",
"1",
"2",
"6",
"24",
"12",
"72",
"54",
"432",
"36288",
"36288",
"399168",
"47916",
"622728",
"871782912",
"137674368",
"2922789888",
"35568742896",
"64237375728",
"121645148832",
"243292817664",
"5199421717944",
"11247277776768",
"258521673888497664",
"624484173323943936",
"15511214333985984",
"4329146112665635584"
]
| [
"nonn",
"base"
]
| 11 | 0 | 3 | [
"A000142",
"A004154",
"A004719",
"A027869",
"A243657",
"A321475",
"A356757",
"A356758"
]
| null | Stefano Spezia, Aug 26 2022 | 2022-08-30T13:57:35 | oeisdata/seq/A356/A356757.seq | 7d010c32b83716e014e6552b6519497b |
A356758 | a(n) is the number of nonzero digits in n!. | [
"1",
"1",
"1",
"1",
"2",
"2",
"2",
"2",
"3",
"5",
"5",
"6",
"5",
"6",
"9",
"9",
"10",
"11",
"11",
"12",
"12",
"13",
"14",
"18",
"18",
"17",
"19",
"20",
"20",
"24",
"24",
"27",
"26",
"29",
"28",
"32",
"32",
"32",
"29",
"35",
"39",
"35",
"39",
"40",
"43",
"44",
"42",
"49",
"48",
"49",
"46",
"49",
"50",
"53",
"54",
"56",
"58",
"57",
"62",
"62",
"63",
"58",
"66",
"67",
"70",
"71",
"70",
"73",
"72",
"78",
"81"
]
| [
"easy",
"base",
"nonn"
]
| 19 | 0 | 5 | [
"A000142",
"A027869",
"A034886",
"A356757",
"A356758"
]
| null | Stefano Spezia, Aug 26 2022 | 2024-08-10T21:39:05 | oeisdata/seq/A356/A356758.seq | 82d859888c47793fab8072eb5e134915 |
A356759 | Bit-reverse the odd part of the dual Zeckendorf representation of n: a(n) = A022290(A057889(A003754(n+1))). | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"9",
"8",
"10",
"11",
"12",
"15",
"17",
"13",
"16",
"14",
"18",
"19",
"20",
"25",
"22",
"28",
"30",
"21",
"26",
"29",
"23",
"27",
"24",
"31",
"32",
"33",
"41",
"46",
"36",
"43",
"38",
"49",
"51",
"34",
"42",
"37",
"47",
"50",
"35",
"44",
"48",
"39",
"45",
"40",
"52",
"53",
"54",
"67",
"59",
"75",
"80",
"56",
"70",
"77",
"62",
"72",
"64",
"83",
"85",
"55"
]
| [
"nonn",
"base",
"look"
]
| 20 | 0 | 3 | [
"A000045",
"A003714",
"A003754",
"A022290",
"A057889",
"A104326",
"A345201",
"A356331",
"A356759"
]
| null | Rémy Sigrist, Aug 26 2022 | 2022-08-29T10:28:41 | oeisdata/seq/A356/A356759.seq | 69b4ae615c98a2ffdf0e4e05fffffc02 |
A356760 | a(n) = L(2*F(n)) + L(2*F(n+1)), where L(n) is the n-th Lucas number (A000032), and F(n) is the n-th Fibonacci number (A000045). | [
"5",
"6",
"10",
"25",
"141",
"2330",
"273650",
"599346021",
"162615199748425",
"97418273437938007563970",
"15841633607002514292104722681296528726",
"1543264591854508694059707631430587191184612139118583889182925"
]
| [
"nonn"
]
| 13 | 0 | 1 | [
"A000032",
"A000045",
"A316275",
"A356760",
"A356761"
]
| null | Amiram Eldar, Aug 26 2022 | 2025-01-05T19:51:42 | oeisdata/seq/A356/A356760.seq | f65e2265733f68667fcaa756d108426f |
A356761 | a(n) = L(2*L(n)) + L(2*L(n+1)), where L(n) is the n-th Lucas number (A000032). | [
"10",
"21",
"65",
"890",
"40446",
"33424885",
"1322190707485",
"44140596372269298846",
"58360810951947188228658239895890",
"2576080923024092500207469693559464507701547824744865",
"150342171745412969401059031474740559845525757221446054521410222913066501974929718621"
]
| [
"nonn"
]
| 12 | 0 | 1 | [
"A000032",
"A356760",
"A356761"
]
| null | Amiram Eldar, Aug 26 2022 | 2025-01-05T19:51:42 | oeisdata/seq/A356/A356761.seq | 5aacf583e06d5dcf7789f7a0c22645e8 |
A356762 | Primes p such that, if q is the next prime, p*q+p+q, p*q-p-q, p*q+2*(p+q) and p*q-2*(p+q) are all prime. | [
"5",
"50929",
"74759",
"127541",
"349849",
"1287731",
"1294753",
"3941711",
"4190023",
"6130739",
"6310061",
"6593329",
"6816973",
"7347709",
"7573849",
"8690351",
"9813409",
"10985959",
"11703187",
"12130553",
"12504001",
"18032059",
"18468763",
"20207471",
"21357191",
"23635603",
"24301309",
"25078181",
"28509521",
"28729567",
"28855459",
"30200411",
"31304239"
]
| [
"nonn"
]
| 16 | 1 | 1 | [
"A356762",
"A356765"
]
| null | J. M. Bergot and Robert Israel, Aug 26 2022 | 2022-09-05T09:10:37 | oeisdata/seq/A356/A356762.seq | 0d4cf3b08587258aa7372801fffa3621 |
A356763 | Triprime gaps (A114403) in the order of first occurrence. | [
"4",
"6",
"2",
"7",
"1",
"12",
"5",
"11",
"3",
"14",
"8",
"9",
"10",
"18",
"13",
"15",
"16",
"21",
"17",
"19",
"22",
"32",
"24",
"20",
"23",
"29",
"28",
"25",
"26",
"33",
"34",
"27",
"30",
"31",
"37",
"40",
"35",
"36",
"46",
"39",
"41",
"44",
"45",
"42",
"38",
"50",
"58",
"43",
"51",
"54",
"49",
"52",
"48",
"47",
"56",
"55",
"53",
"60",
"57",
"59",
"63",
"61",
"65",
"66",
"69",
"64",
"62",
"67",
"68",
"70",
"83",
"71",
"73",
"78",
"72"
]
| [
"nonn"
]
| 13 | 1 | 1 | [
"A014320",
"A014612",
"A114403",
"A356763",
"A356769"
]
| null | Zak Seidov, Aug 26 2022 | 2022-08-28T21:12:22 | oeisdata/seq/A356/A356763.seq | 3a66c6167efe2da449c6bfbd278a168b |
A356764 | Semiprimes divisible by their indices in the sequence of semiprimes, divided by those indices. | [
"4",
"3",
"3",
"3",
"3",
"3",
"3",
"5",
"5",
"5",
"5",
"5",
"5",
"7",
"7",
"7",
"7"
]
| [
"nonn",
"hard",
"more"
]
| 37 | 1 | 1 | [
"A001358",
"A106125",
"A356764",
"A357741"
]
| null | Lucas A. Brown, Oct 13 2022 | 2022-10-16T03:23:06 | oeisdata/seq/A356/A356764.seq | 051e4a6a6a50d3841d707a5eb4895b42 |
A356765 | Semiprimes p*q such that p*q+p+q, p*q-(p+q), p*q+2*(p+q) and p*q-2*(p+q) are all primes. | [
"33",
"35",
"65",
"111",
"209",
"321",
"371",
"395",
"545",
"815",
"1385",
"1841",
"1865",
"4101",
"5241",
"6119",
"6905",
"8735",
"10361",
"13061",
"14811",
"15321",
"16145",
"18689",
"22235",
"25079",
"32405",
"36095",
"38789",
"39395",
"43739",
"43829",
"43881",
"49745",
"50811",
"52331",
"57701",
"59195",
"60035",
"62765",
"65561",
"71931",
"72329",
"76019",
"77135",
"79751",
"81311",
"84395"
]
| [
"nonn"
]
| 10 | 1 | 1 | [
"A356762",
"A356765"
]
| null | J. M. Bergot and Robert Israel, Aug 26 2022 | 2022-09-05T09:10:27 | oeisdata/seq/A356/A356765.seq | d324d386b9f7932b7a1eb8cfeb9c4634 |
A356766 | Least number k such that k and k+2 both have exactly 2n divisors, or -1 if no such number exists. | [
"3",
"6",
"18",
"40",
"127251",
"198",
"26890623",
"918",
"17298",
"6640",
"25269208984375",
"3400",
"3900566650390623",
"640062",
"8418573",
"18088",
"1164385682220458984373",
"41650",
"69528379848480224609373",
"128464",
"34084859373",
"12164094",
"150509919493198394775390625",
"90270",
"418514293125",
"64505245696"
]
| [
"nonn"
]
| 29 | 1 | 1 | [
"A000005",
"A001359",
"A003680",
"A005238",
"A006558",
"A006601",
"A062832",
"A067888",
"A067889",
"A075036",
"A356742",
"A356743",
"A356744",
"A356766"
]
| null | Jean-Marc Rebert, Aug 26 2022 | 2023-07-01T11:00:08 | oeisdata/seq/A356/A356766.seq | cd018c9b94b236b5f479da29f9d5c7b7 |
A356767 | Tetraprimes (products of four distinct primes) whose reversals are different tetraprimes. | [
"1518",
"2046",
"2226",
"2262",
"2418",
"2478",
"2618",
"2622",
"2814",
"2838",
"2886",
"3135",
"3927",
"4170",
"4182",
"4386",
"4389",
"4746",
"4785",
"4935",
"5313",
"5394",
"5406",
"5478",
"5565",
"5655",
"5838",
"5874",
"6018",
"6045",
"6222",
"6402",
"6438",
"6474",
"6486",
"6690",
"6699",
"6834",
"6846",
"6882",
"7293",
"7458",
"8106",
"8142"
]
| [
"nonn",
"base"
]
| 11 | 1 | 1 | [
"A046394",
"A270175",
"A356767"
]
| null | Tanya Khovanova, Aug 26 2022 | 2022-08-28T10:37:38 | oeisdata/seq/A356/A356767.seq | 3c7165a365c7272f4b656ef3041ef9e3 |
A356768 | a(n) = (n^2+n+1)*(n^2+n)*n^2. | [
"0",
"6",
"168",
"1404",
"6720",
"23250",
"65016",
"156408",
"336384",
"663390",
"1221000",
"2124276",
"3526848",
"5628714",
"8684760",
"13014000",
"19009536",
"27149238",
"38007144",
"52265580",
"70728000",
"94332546",
"124166328",
"161480424",
"207705600",
"264468750",
"333610056",
"417200868",
"517562304"
]
| [
"nonn",
"easy"
]
| 33 | 0 | 2 | [
"A169938",
"A356768"
]
| null | R. J. Mathar, Aug 29 2022 | 2025-04-19T19:36:48 | oeisdata/seq/A356/A356768.seq | 830494ec80164faa6d66303122ad73a2 |
A356769 | Semiprime gaps (A065516) in the order of first occurrences. | [
"2",
"3",
"1",
"4",
"6",
"7",
"5",
"11",
"9",
"8",
"10",
"14",
"13",
"12",
"19",
"15",
"17",
"20",
"16",
"18",
"24",
"22",
"21",
"25",
"28",
"27",
"30",
"32",
"38",
"23",
"31",
"26",
"36",
"35",
"34",
"29",
"47",
"33",
"40",
"41",
"54",
"50",
"43",
"55",
"39",
"48",
"37",
"42",
"45",
"44",
"53",
"70",
"46",
"56",
"74",
"52",
"62",
"51",
"66",
"49",
"58",
"68",
"59",
"63",
"67",
"60",
"57",
"61",
"72",
"64",
"65",
"76",
"69",
"73",
"75",
"82",
"85"
]
| [
"nonn"
]
| 20 | 1 | 1 | [
"A001358",
"A065516",
"A356769"
]
| null | Zak Seidov, Aug 27 2022 | 2022-08-30T17:14:51 | oeisdata/seq/A356/A356769.seq | 814b33d39c7afabdc7750b45cfd4eb46 |
A356770 | a(n) is the number of equations in the set {x+2y=n, 2x+3y=n, ..., k*x+(k+1)*y=n, ..., n*x+(n+1)*y=n} which admit at least one nonnegative integer solution. | [
"1",
"2",
"3",
"4",
"4",
"5",
"5",
"6",
"6",
"7",
"6",
"8",
"7",
"8",
"8",
"9",
"8",
"10",
"8",
"10",
"10",
"10",
"9",
"12",
"10",
"11",
"11",
"12",
"10",
"13",
"11",
"13",
"12",
"12",
"12",
"15",
"12",
"13",
"13",
"15",
"12",
"15",
"13",
"15",
"15",
"14",
"13",
"17",
"14",
"16",
"15",
"16",
"14",
"17",
"15",
"17",
"16",
"16",
"15",
"20",
"15",
"16",
"17",
"18",
"17",
"19",
"16",
"18",
"17",
"19",
"16",
"21",
"17",
"18",
"19",
"19"
]
| [
"nonn"
]
| 32 | 1 | 2 | [
"A000005",
"A356770"
]
| null | Luca Onnis, Aug 27 2022 | 2022-10-01T01:16:57 | oeisdata/seq/A356/A356770.seq | 7ba7499462544a5d309e7e34e9f8d603 |
A356771 | a(n) is the sum of the Fibonacci numbers in common in the Zeckendorf and dual Zeckendorf representations of n. | [
"0",
"1",
"2",
"0",
"4",
"0",
"1",
"7",
"0",
"1",
"2",
"3",
"12",
"0",
"1",
"2",
"0",
"4",
"5",
"6",
"20",
"0",
"1",
"2",
"3",
"4",
"0",
"1",
"7",
"8",
"9",
"10",
"11",
"33",
"0",
"1",
"2",
"0",
"4",
"5",
"6",
"7",
"0",
"1",
"2",
"3",
"12",
"13",
"14",
"15",
"13",
"17",
"18",
"19",
"54",
"0",
"1",
"2",
"3",
"4",
"0",
"1",
"7",
"8",
"9",
"10",
"11",
"12",
"0",
"1",
"2",
"0",
"4",
"5",
"6",
"20",
"21",
"22",
"23",
"24"
]
| [
"nonn",
"base"
]
| 22 | 0 | 3 | [
"A000071",
"A003714",
"A003754",
"A022290",
"A035517",
"A112309",
"A331467",
"A356326",
"A356771"
]
| null | Rémy Sigrist, Aug 27 2022 | 2022-09-06T10:29:15 | oeisdata/seq/A356/A356771.seq | 907929286cce86061340276d3a7185b4 |
A356772 | E.g.f. A(x) satisfies: A(x) = Sum_{n>=0} ( x^n + x*A(x) )^n / n!. | [
"1",
"2",
"5",
"34",
"329",
"3716",
"55777",
"1010206",
"21187049",
"511352272",
"13929248861",
"422450642054",
"14129873671069",
"516664310959720",
"20503766568423881",
"877759284120870526",
"40321132468408643153",
"1978363648482263649728",
"103262474042895179595061",
"5713315282015940379009862"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A108459",
"A326009",
"A326090",
"A326091",
"A326261",
"A356772",
"A356773"
]
| null | Paul D. Hanna, Aug 27 2022 | 2025-07-03T12:59:02 | oeisdata/seq/A356/A356772.seq | 40f543c7a573b612424d152fa3427a4b |
A356773 | E.g.f. A(x) satisfies: A(x) = Sum_{n>=0} ( x^n + A(x) )^n * x^n / n!. | [
"1",
"1",
"5",
"22",
"197",
"2076",
"29527",
"477394",
"9248745",
"204340600",
"5111234891",
"142148945214",
"4362830874877",
"146338813894612",
"5328688224075231",
"209295914833477546",
"8821420994034588113",
"397128156446044087536",
"19019218255697847951955",
"965527468715744517674998"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A108459",
"A326009",
"A326090",
"A326091",
"A326261",
"A356772",
"A356773"
]
| null | Paul D. Hanna, Aug 27 2022 | 2025-07-03T13:02:00 | oeisdata/seq/A356/A356773.seq | 4e3bb1874cd95c29dbe4759567f1d6a7 |
A356774 | Coefficients in the power series expansion of A(x) = Sum_{n=-oo..+oo} n * x^n * (1 - x^n)^(n-2). | [
"1",
"4",
"7",
"11",
"16",
"17",
"29",
"21",
"46",
"21",
"67",
"22",
"92",
"1",
"151",
"-23",
"154",
"22",
"191",
"-118",
"407",
"-175",
"277",
"23",
"326",
"-363",
"946",
"-643",
"436",
"282",
"497",
"-1199",
"1948",
"-1019",
"701",
"-47",
"704",
"-1519",
"3641",
"-3127",
"862",
"1759",
"947",
"-5301",
"7036",
"-2943",
"1129",
"-1187",
"1226",
"-2149",
"10252"
]
| [
"sign"
]
| 20 | 1 | 2 | [
"A291937",
"A356774",
"A356775",
"A357156",
"A357157"
]
| null | Paul D. Hanna, Sep 22 2022 | 2022-12-25T07:26:47 | oeisdata/seq/A356/A356774.seq | bed8b0874b34a3d426cace053d37f728 |
A356775 | Coefficients in the power series expansion of A(x) = Sum_{n=-oo..+oo} n*(n+1)/2 * x^(2*n) * (1 - x^n)^(n-2). | [
"1",
"1",
"5",
"1",
"11",
"1",
"21",
"-8",
"36",
"1",
"22",
"1",
"85",
"-89",
"137",
"1",
"-23",
"1",
"302",
"-349",
"287",
"1",
"23",
"-24",
"456",
"-944",
"1177",
"1",
"-903",
"1",
"2113",
"-2078",
"970",
"-559",
"709",
"1",
"1331",
"-4003",
"4293",
"1",
"-3323",
"1",
"9153",
"-10694",
"2301",
"1",
"5869",
"-48",
"-4774",
"-11474",
"20294",
"1",
"-7334",
"-14783"
]
| [
"sign"
]
| 9 | 2 | 3 | [
"A291937",
"A356774",
"A356775",
"A357156",
"A357157"
]
| null | Paul D. Hanna, Sep 22 2022 | 2022-09-23T03:11:06 | oeisdata/seq/A356/A356775.seq | e352b243255526c356643a93d1a71a92 |
A356776 | a(n) = coefficient in the power series expansion of A(x) = Sum_{n=-oo..+oo} x^n * (1-x)^n * ((1-x)^n + x^n)^n. | [
"2",
"1",
"1",
"-3",
"7",
"15",
"-39",
"-307",
"917",
"2540",
"-16939",
"-25016",
"441962",
"-498346",
"-10210949",
"42714405",
"195220459",
"-2142879945",
"532985665",
"83535107090",
"-365902332521",
"-2233273290797",
"28143121253695",
"-20874136499710",
"-1436795595314700",
"8862053852144592",
"38496064560804831"
]
| [
"sign"
]
| 11 | 0 | 1 | [
"A319016",
"A356776"
]
| null | Paul D. Hanna, Sep 04 2022 | 2022-12-03T12:05:42 | oeisdata/seq/A356/A356776.seq | faf098c94811410e5e9de9f41b05e633 |
A356777 | G.f.: Sum_{n=-oo..+oo} x^(n^2) * C(x)^(2*n-1), where C(x) = 1 + x*C(x)^2 is a g.f. of the Catalan numbers (A000108). | [
"1",
"1",
"-3",
"0",
"1",
"-5",
"5",
"0",
"0",
"1",
"-7",
"14",
"-7",
"0",
"0",
"0",
"1",
"-9",
"27",
"-30",
"9",
"0",
"0",
"0",
"0",
"1",
"-11",
"44",
"-77",
"55",
"-11",
"0",
"0",
"0",
"0",
"0",
"1",
"-13",
"65",
"-156",
"182",
"-91",
"13",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"-15",
"90",
"-275",
"450",
"-378",
"140",
"-15",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"-17",
"119",
"-442",
"935",
"-1122",
"714",
"-204",
"17",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"-19",
"152",
"-665",
"1729",
"-2717",
"2508",
"-1254",
"285",
"-19"
]
| [
"sign"
]
| 8 | 0 | 3 | [
"A000108",
"A082985",
"A355341",
"A355342",
"A355345",
"A356777",
"A356778"
]
| null | Paul D. Hanna, Sep 08 2022 | 2022-09-13T04:42:16 | oeisdata/seq/A356/A356777.seq | 832d93edf4a710dab971e7ebd026c589 |
A356778 | G.f.: Sum_{n=-oo..+oo} x^(n^2) * C(x)^(4*n-4), where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108). | [
"1",
"-2",
"-6",
"20",
"-15",
"-10",
"54",
"-112",
"105",
"-35",
"-14",
"104",
"-352",
"660",
"-672",
"336",
"-63",
"-18",
"170",
"-800",
"2275",
"-4004",
"4290",
"-2640",
"825",
"-99",
"-22",
"252",
"-1520",
"5814",
"-14688",
"24752",
"-27456",
"19305",
"-8008",
"1716",
"-143",
"-26",
"350",
"-2576",
"12397",
"-40964",
"94962",
"-155040",
"176358",
"-136136",
"68068",
"-20384",
"3185"
]
| [
"sign"
]
| 12 | 0 | 2 | [
"A000108",
"A034807",
"A355341",
"A355345",
"A356777",
"A356778"
]
| null | Paul D. Hanna, Sep 08 2022 | 2022-09-13T04:43:13 | oeisdata/seq/A356/A356778.seq | 852bbc2d58eae7d73dfcedd152f2aa83 |
A356779 | G.f.: Sum_{n=-oo..+oo} x^(n^2) * C(x)^(6*n-9), where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108). | [
"1",
"-7",
"9",
"60",
"-265",
"429",
"-189",
"-812",
"2925",
"-5732",
"6980",
"-4824",
"-198",
"10010",
"-32298",
"69768",
"-104651",
"107373",
"-72435",
"26422",
"19656",
"-115011",
"361763",
"-834900",
"1427679",
"-1797817",
"1641447",
"-1057446",
"454155",
"-69564",
"-298980",
"1307448",
"-4102104",
"9924525",
"-18599295"
]
| [
"sign"
]
| 9 | 0 | 2 | [
"A000108",
"A034807",
"A355341",
"A355345",
"A356777",
"A356778",
"A356779"
]
| null | Paul D. Hanna, Sep 08 2022 | 2022-09-13T04:44:15 | oeisdata/seq/A356/A356779.seq | 8d4f17194894384d2d8c7e9eee6b853f |
A356780 | Coefficients in the odd function A(x) such that: A(x) = A( x^2 + 2*x^2*A(x)^2 )^(1/2), with A(0)=0, A'(0)=1. | [
"1",
"1",
"2",
"6",
"21",
"78",
"303",
"1223",
"5085",
"21623",
"93585",
"410894",
"1825682",
"8193544",
"37087449",
"169114547",
"776110247",
"3581944258",
"16614576945",
"77410877233",
"362126147797",
"1700179143293",
"8008689767674",
"37838553977426",
"179268540549758",
"851478474635404",
"4053760582437106"
]
| [
"nonn"
]
| 11 | 1 | 3 | [
"A000108",
"A271931",
"A271932",
"A271933",
"A356780",
"A356781"
]
| null | Paul D. Hanna, Aug 27 2022 | 2022-09-02T18:55:35 | oeisdata/seq/A356/A356780.seq | 221058729b75b2639591e64a56ee1d97 |
A356781 | Expansion of g.f. A(x) satisfying A(x) = A( x^2 + 2*x^2*A(x) )^(1/2), with A(0)=0, A'(0)=1. | [
"1",
"1",
"1",
"2",
"4",
"7",
"14",
"32",
"74",
"172",
"408",
"978",
"2349",
"5662",
"13737",
"33568",
"82596",
"204618",
"510208",
"1279544",
"3224828",
"8162144",
"20735397",
"52848816",
"135088609",
"346214873",
"889451320",
"2290164276",
"5908894762",
"15274778235",
"39555942836",
"102603159040",
"266545251022"
]
| [
"nonn"
]
| 27 | 1 | 4 | [
"A000108",
"A356781",
"A370540"
]
| null | Paul D. Hanna, Aug 27 2022 | 2024-03-14T08:00:17 | oeisdata/seq/A356/A356781.seq | e16bcb458d52beb0d29e25aafe692cb0 |
A356782 | Expansion of g.f. A(x) satisfies A(x) = x * Product_{n>=0} (1 + 2*A(x)^(2^n)). | [
"1",
"2",
"6",
"24",
"106",
"496",
"2428",
"12288",
"63762",
"337392",
"1813628",
"9876096",
"54365876",
"302037408",
"1691327224",
"9536234496",
"54093070626",
"308474110000",
"1767481876540",
"10170367611008",
"58746459504884",
"340513035730944",
"1979964903739992",
"11546094361266176",
"67509252360531940"
]
| [
"nonn"
]
| 22 | 1 | 2 | [
"A000120",
"A001316",
"A356782",
"A372534"
]
| null | Paul D. Hanna, Sep 01 2022 | 2024-05-30T06:59:30 | oeisdata/seq/A356/A356782.seq | ec0406977fb19622644d9733200b70fa |
A356783 | Coefficients in the power series A(x) such that: 1 = Sum_{n=-oo..+oo} x^(2*n+1) * (1 - x^n)^(n+1) * A(x)^n. | [
"1",
"1",
"2",
"6",
"17",
"50",
"163",
"525",
"1770",
"6066",
"21154",
"74787",
"267371",
"965233",
"3513029",
"12877687",
"47499333",
"176167086",
"656568385",
"2457710598",
"9236079055",
"34832753818",
"131792634266",
"500121476517",
"1902979982421",
"7258942377746",
"27752992782498",
"106333425162358",
"408213503595652"
]
| [
"nonn"
]
| 24 | 0 | 3 | [
"A356783",
"A357151",
"A357152",
"A357153",
"A357154",
"A357155",
"A357200",
"A357400",
"A357402",
"A357403",
"A357404",
"A357405"
]
| null | Paul D. Hanna, Sep 15 2022 | 2025-03-22T09:37:46 | oeisdata/seq/A356/A356783.seq | 0ff2a1bf0de8f66043164e45ec5944e5 |
A356784 | Inventory of positions as an irregular table; row 0 contains 0, subsequent rows contain the 0-based positions of 0's, followed by the position of 1's, of 2's, etc. in prior rows flattened. | [
"0",
"0",
"0",
"1",
"0",
"1",
"2",
"3",
"0",
"1",
"2",
"4",
"3",
"5",
"6",
"7",
"0",
"1",
"2",
"4",
"8",
"3",
"5",
"9",
"6",
"10",
"7",
"12",
"11",
"13",
"14",
"15",
"0",
"1",
"2",
"4",
"8",
"16",
"3",
"5",
"9",
"17",
"6",
"10",
"18",
"7",
"12",
"21",
"11",
"19",
"13",
"22",
"14",
"24",
"15",
"26",
"20",
"23",
"25",
"28",
"27",
"29",
"30",
"31",
"0",
"1",
"2",
"4",
"8",
"16",
"32",
"3",
"5",
"9",
"17",
"33"
]
| [
"nonn",
"tabf"
]
| 73 | 0 | 7 | [
"A000051",
"A005126",
"A011782",
"A052548",
"A131577",
"A342585",
"A356784",
"A357317",
"A357491"
]
| null | Rémy Sigrist, Oct 01 2022 | 2022-11-01T10:26:19 | oeisdata/seq/A356/A356784.seq | 7de651a58e3860645f28618e5e114ac9 |
A356785 | E.g.f. satisfies log(A(x)) = x * (exp(x*A(x)) - 1) * A(x). | [
"1",
"0",
"2",
"3",
"64",
"365",
"7356",
"85687",
"1920752",
"34821369",
"905128300",
"22172123171",
"672107454888",
"20552960420005",
"721088019634724",
"26257726364294895",
"1053711696230404576",
"44336326818388565105",
"2010106841636689325532",
"95747319823049127621019"
]
| [
"nonn"
]
| 23 | 0 | 3 | [
"A184949",
"A349557",
"A349560",
"A355843",
"A356785",
"A356788",
"A356789"
]
| null | Seiichi Manyama, Aug 27 2022 | 2024-09-21T13:25:23 | oeisdata/seq/A356/A356785.seq | 8431d011a5524289fd684dccc4e6917d |
A356786 | E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(x * A(x)^2). | [
"1",
"0",
"2",
"3",
"92",
"510",
"15114",
"174300",
"5558944",
"103712616",
"3672530280",
"96397602840",
"3830335035240",
"129817630491120",
"5796134828193696",
"239906921239210680",
"11996259216566469120",
"584024600798956215360",
"32523678395272329425856"
]
| [
"nonn"
]
| 14 | 0 | 3 | [
"A184949",
"A349559",
"A355766",
"A356786",
"A356787"
]
| null | Seiichi Manyama, Aug 27 2022 | 2022-08-28T04:24:55 | oeisdata/seq/A356/A356786.seq | 23a122d90b1db4b37db71f145614ba50 |
A356787 | E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(x * A(x)^3). | [
"1",
"0",
"2",
"3",
"116",
"630",
"24054",
"273000",
"11105072",
"207213552",
"9175467960",
"245785969440",
"11954556125544",
"421832039016960",
"22609694372667024",
"991695134898861120",
"58565049582761702400",
"3065736317041568378880",
"199024242549235933723200"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A184949",
"A349559",
"A356786",
"A356787"
]
| null | Seiichi Manyama, Aug 27 2022 | 2022-08-28T04:24:51 | oeisdata/seq/A356/A356787.seq | 40285da47e970c4452dfc2f8b3a597d1 |
A356788 | E.g.f. satisfies log(A(x)) = x * (exp(x*A(x)) - 1) * A(x)^2. | [
"1",
"0",
"2",
"3",
"88",
"485",
"13896",
"158767",
"4919664",
"90698841",
"3130084360",
"81025744811",
"3144372342552",
"104942286748741",
"4582896912897408",
"186591555463556895",
"9135453970592830816",
"437146665470130792497",
"23852990622867670807704",
"1307029600226135900982835"
]
| [
"nonn"
]
| 12 | 0 | 3 | [
"A349560",
"A355762",
"A356785",
"A356788",
"A356789"
]
| null | Seiichi Manyama, Aug 27 2022 | 2022-08-28T04:24:32 | oeisdata/seq/A356/A356788.seq | 7b89b03abe03047163b54d416759969b |
A356789 | E.g.f. satisfies log(A(x)) = x * (exp(x*A(x)) - 1) * A(x)^3. | [
"1",
"0",
"2",
"3",
"112",
"605",
"22596",
"254527",
"10166416",
"188035353",
"8190917380",
"217293592571",
"10408915205976",
"363500829796117",
"19203682103461324",
"833182131498018135",
"48525371633295259936",
"2511705297938365594289",
"160874324235464440678164"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A349560",
"A356785",
"A356788",
"A356789"
]
| null | Seiichi Manyama, Aug 27 2022 | 2022-08-28T04:24:29 | oeisdata/seq/A356/A356789.seq | d28f5e179084c2a4f5f45f0e6d092d64 |
A356790 | Table read by antidiagonals: T(n,k) (n >= 1, k >= 1) is the number of regions formed by straight line segments when connecting the k-1 points along the top side of a rectangle to each of the k-1 points along the bottom side that divide these sides into k equal parts, along with straight lines that directly connect the n-1 points along the left side to the diametrically opposite point on the right side that divide these sides into n equal parts. | [
"1",
"2",
"2",
"6",
"4",
"3",
"18",
"10",
"6",
"4",
"48",
"24",
"16",
"8",
"5",
"106",
"56",
"34",
"20",
"10",
"6",
"216",
"116",
"70",
"44",
"26",
"12",
"7",
"382",
"228",
"134",
"84",
"58",
"30",
"14",
"8",
"650",
"396",
"250",
"152",
"112",
"60",
"36",
"16",
"9",
"1030",
"666",
"422",
"272",
"190",
"112",
"78",
"40",
"18",
"10",
"1564",
"1048",
"696",
"448",
"320",
"196",
"150",
"84",
"46",
"20",
"11"
]
| [
"nonn",
"tabl"
]
| 32 | 1 | 2 | [
"A146951",
"A290131",
"A306302",
"A331452",
"A355798",
"A355902",
"A356790"
]
| null | Scott R. Shannon and N. J. A. Sloane, Sep 04 2022 | 2022-09-08T15:20:50 | oeisdata/seq/A356/A356790.seq | f2e79fa529722aaedb78df8f19b64aba |
A356791 | Emirps p such that R(p) > p and R(p) mod p is prime, where R(p) is the reversal of p. | [
"13",
"17",
"107",
"149",
"337",
"1009",
"1069",
"1109",
"1409",
"1499",
"1559",
"3257",
"3347",
"3407",
"3467",
"3527",
"3697",
"3767",
"10009",
"10429",
"10739",
"10859",
"10939",
"11057",
"11149",
"11159",
"11257",
"11497",
"11657",
"11677",
"11717",
"11897",
"11959",
"13759",
"13829",
"14029",
"14479",
"14549",
"15149",
"15299",
"15649",
"30367",
"30557",
"31267",
"31307",
"32257"
]
| [
"nonn",
"base"
]
| 55 | 1 | 1 | [
"A004086",
"A006567",
"A109308",
"A356791"
]
| null | J. M. Bergot and Robert Israel, Sep 18 2022 | 2022-09-24T21:51:04 | oeisdata/seq/A356/A356791.seq | 4f0504c0908a78f3e1470ff848bc0266 |
A356792 | Smallest number k with A355915(k) = n. | [
"1",
"11",
"49",
"103",
"179",
"313",
"545",
"601",
"959",
"1087",
"1675",
"1931",
"2813",
"2909",
"3133",
"4565",
"4673",
"6049",
"5089",
"8837",
"8095",
"9463",
"10883",
"14771",
"12023",
"9911",
"15587",
"16883",
"17891",
"18179",
"17315",
"16739",
"26461",
"17635",
"29221",
"30437",
"28709",
"33161",
"39193",
"39401",
"30757",
"40165",
"55625"
]
| [
"nonn"
]
| 31 | 1 | 2 | [
"A355915",
"A356792"
]
| null | Michael S. Branicky and N. J. A. Sloane, Sep 21 2022 | 2022-09-21T19:04:36 | oeisdata/seq/A356/A356792.seq | 5dc86d94dff667505bbe102fa87e86de |
A356793 | Decimal expansion of sum of squares of reciprocals of lesser twin primes, Sum_{j>=1} 1/(A001359(j))^2. | [
"1",
"6",
"5",
"6",
"1",
"8",
"4",
"6",
"5",
"3",
"9",
"5"
]
| [
"nonn",
"cons",
"hard",
"more"
]
| 65 | 0 | 2 | [
"A006512",
"A065421",
"A077800",
"A078437",
"A085548",
"A096247",
"A160910",
"A194098",
"A209328",
"A209329",
"A242301",
"A242302",
"A242303",
"A242304",
"A306539",
"A342714",
"A347278",
"A356793"
]
| null | Artur Jasinski, Sep 04 2022 | 2022-09-29T22:05:29 | oeisdata/seq/A356/A356793.seq | bcc9a6eebe02a7a49c3877f999da637f |
A356794 | Odd numbers that have at least one prime factor congruent to 1 (mod 4) and at least one prime factor congruent to 3 (mod 4). | [
"15",
"35",
"39",
"45",
"51",
"55",
"75",
"87",
"91",
"95",
"105",
"111",
"115",
"117",
"119",
"123",
"135",
"143",
"153",
"155",
"159",
"165",
"175",
"183",
"187",
"195",
"203",
"215",
"219",
"225",
"235",
"245",
"247",
"255",
"259",
"261",
"267",
"273",
"275",
"285",
"287",
"291",
"295",
"299",
"303",
"315",
"319",
"323",
"327",
"333",
"335",
"339",
"345",
"351"
]
| [
"nonn"
]
| 10 | 1 | 1 | [
"A004613",
"A004614",
"A356794"
]
| null | Jon E. Schoenfield, Aug 27 2022 | 2022-08-29T10:30:05 | oeisdata/seq/A356/A356794.seq | 7dbf1164ade59f24d474ec1f51697183 |
A356795 | E.g.f. satisfies A(x) = 1/(1 - x)^(x * A(x)^2). | [
"1",
"0",
"2",
"3",
"68",
"330",
"7674",
"73080",
"1883440",
"28281960",
"818625960",
"17120406600",
"557507325000",
"15014517495120",
"548643259812816",
"18056683281775320",
"736892260092195840",
"28579282973977498560",
"1295028345251832359616",
"57666859088090317591680"
]
| [
"nonn"
]
| 21 | 0 | 3 | [
"A066166",
"A355842",
"A356786",
"A356795",
"A356796"
]
| null | Seiichi Manyama, Aug 28 2022 | 2025-02-16T08:34:03 | oeisdata/seq/A356/A356795.seq | c1e89040dd77d887ea65c03ed2f69f7d |
A356796 | E.g.f. satisfies A(x) = 1/(1 - x)^(x * A(x)^3). | [
"1",
"0",
"2",
"3",
"92",
"450",
"14454",
"141540",
"4980128",
"78711696",
"3048567480",
"68677353360",
"2930551701384",
"86832573553440",
"4079649847428960",
"150444517302424800",
"7768028697749806080",
"342721736137376184960",
"19392702029822685015360",
"994397473912386435004800"
]
| [
"nonn"
]
| 24 | 0 | 3 | [
"A066166",
"A355842",
"A356787",
"A356795",
"A356796"
]
| null | Seiichi Manyama, Aug 28 2022 | 2025-02-16T08:34:03 | oeisdata/seq/A356/A356796.seq | 69c99241537f21aea26f2758f12f9cda |
A356797 | E.g.f. satisfies log(A(x)) = x * (exp(x) - 1) * A(x)^2. | [
"1",
"0",
"2",
"3",
"64",
"305",
"6936",
"64897",
"1645008",
"24290289",
"692240680",
"14243244521",
"456748635432",
"12105737521033",
"435619742434800",
"14112089558682585",
"567134312211275296",
"21653262317886286817",
"966207399513747354072",
"42358800314758614030505"
]
| [
"nonn"
]
| 33 | 0 | 3 | [
"A052506",
"A355843",
"A356788",
"A356797",
"A356798"
]
| null | Seiichi Manyama, Aug 28 2022 | 2025-02-16T08:34:03 | oeisdata/seq/A356/A356797.seq | e813ec420b54b92ce90e388c0b378d1b |
A356798 | E.g.f. satisfies log(A(x)) = x * (exp(x) - 1) * A(x)^3. | [
"1",
"0",
"2",
"3",
"88",
"425",
"13476",
"130417",
"4543120",
"71005041",
"2723297860",
"60685651961",
"2564091428856",
"75166650583609",
"3496499475113932",
"127585829832674865",
"6521845096842043936",
"284745004488498858209",
"15950013722559213419412",
"809403234909367349670409"
]
| [
"nonn"
]
| 23 | 0 | 3 | [
"A052506",
"A355843",
"A356789",
"A356797",
"A356798"
]
| null | Seiichi Manyama, Aug 28 2022 | 2025-02-16T08:34:03 | oeisdata/seq/A356/A356798.seq | 4f31c3f792fbd2d13512184ec7a335f6 |
A356799 | Table read by antidiagonals: T(n,k) (n >= 2, k >= 1) is the number of regions formed in a regular 2n-gon by straight line segments when connecting the k+1 points that divide each side into k equal parts to the equivalent point on the side diagonally opposite. | [
"1",
"4",
"13",
"9",
"24",
"25",
"16",
"55",
"48",
"41",
"25",
"66",
"105",
"70",
"61",
"36",
"121",
"144",
"171",
"108",
"85",
"49",
"126",
"233",
"220",
"253",
"140",
"113",
"64",
"211",
"288",
"381",
"312",
"351",
"192",
"145",
"81",
"204",
"409",
"450",
"565",
"448",
"465",
"234",
"181",
"100",
"325",
"480",
"671",
"636",
"785",
"608",
"595",
"300",
"221",
"121",
"300",
"633",
"760",
"997",
"924",
"1041",
"738",
"741",
"352",
"265"
]
| [
"nonn",
"tabl"
]
| 48 | 2 | 2 | [
"A000096",
"A000217",
"A000290",
"A001105",
"A001844",
"A005563",
"A051890",
"A249127",
"A265225",
"A356044",
"A356799"
]
| null | Scott R. Shannon, Aug 28 2022 | 2022-08-30T09:41:12 | oeisdata/seq/A356/A356799.seq | ec7ebb610e84ea26c40046e8c2b776f0 |
A356800 | Numbers m for which Sum_{k=1..m} 1/k^s has no zero in the half-plane Re(s)>1. | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"13",
"14",
"15",
"16",
"17",
"18",
"20",
"21",
"28"
]
| [
"nonn",
"fini",
"full"
]
| 10 | 1 | 2 | null | null | Benoit Cloitre, Aug 28 2022 | 2022-08-28T08:22:31 | oeisdata/seq/A356/A356800.seq | 23334974ebc693df3ee578e8dc657917 |
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