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2025-04-28 00:58:08
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A357301 | a(n) is the number of distinct radii of circles passing through at least three points in a square grid of n X n points. | [
"0",
"1",
"7",
"19",
"48",
"112",
"212",
"383",
"641",
"988",
"1523",
"2250",
"3103",
"4364",
"5831",
"7696",
"9985",
"12945",
"16164",
"20246",
"24946",
"30145",
"36385",
"43839",
"51752",
"61610",
"72475",
"84273",
"97231",
"112733"
] | [
"nonn",
"more"
] | 10 | 1 | 3 | [
"A192493",
"A192494",
"A355884",
"A357301"
] | null | Hugo Pfoertner, Sep 23 2022, following a suggestion by Ed Pegg Jr, Jan 09 2013 | 2022-09-23T11:52:40 | oeisdata/seq/A357/A357301.seq | af82d5f6b3af46883bc631559215dd1c |
A357302 | Numbers k such that k^2 can be represented as x^2 + x*y + y^2 in more ways than for any smaller k. | [
"1",
"7",
"49",
"91",
"637",
"1729",
"12103",
"53599",
"375193",
"1983163",
"13882141",
"85276009",
"596932063",
"4178524441",
"5201836549",
"36412855843",
"254889990901",
"348523048783",
"2439661341481",
"17077629390367",
"25442182561159",
"178095277928113",
"1246666945496791",
"2009932422331561",
"14069526956320927"
] | [
"nonn"
] | 29 | 1 | 2 | [
"A002324",
"A003136",
"A004016",
"A050931",
"A087503",
"A088534",
"A230655",
"A246360",
"A357302",
"A357303"
] | null | Hugo Pfoertner, Sep 25 2022 | 2022-10-02T18:12:13 | oeisdata/seq/A357/A357302.seq | 26fb7a0a97a2759b0111e6770baa7f98 |
A357303 | Records in the numbers of representations of k^2 as x^2 - x*y + y^2, x > 2*y >= 0, corresponding to the numbers of grid points with squared radius A357302(n)^2 in an angular sector 0 <= phi < Pi/6 of the triangular lattice. | [
"1",
"2",
"3",
"5",
"8",
"14",
"23",
"41",
"68",
"122",
"203",
"365",
"608",
"851",
"1094",
"1823",
"2552",
"3281",
"5468",
"7655",
"9842",
"16403",
"22964",
"29525",
"49208",
"68891",
"82013",
"88574",
"114818",
"147623",
"206672",
"246038",
"265721"
] | [
"nonn",
"more"
] | 9 | 1 | 2 | [
"A002324",
"A003136",
"A004016",
"A087503",
"A230655",
"A246360",
"A357302",
"A357303"
] | null | Hugo Pfoertner, Sep 25 2022 | 2022-09-27T19:17:34 | oeisdata/seq/A357/A357303.seq | 2ce6fa61b014bdd00a2c13e1e8545034 |
A357304 | Records of the Hamming weight of squares. | [
"0",
"1",
"2",
"3",
"5",
"6",
"7",
"8",
"9",
"10",
"13",
"14",
"15",
"16",
"17",
"18",
"19",
"20",
"21",
"22",
"23",
"24",
"25",
"26",
"27",
"28",
"29",
"30",
"31",
"33",
"34",
"35",
"37",
"38",
"39",
"40",
"41",
"42",
"44",
"45",
"46",
"47",
"48",
"49",
"50",
"51",
"52",
"53",
"54",
"55",
"56",
"57",
"58",
"59",
"60",
"62",
"63",
"64",
"65",
"66",
"67",
"68",
"69",
"70",
"72",
"73",
"74",
"75",
"76",
"77",
"78",
"79",
"80",
"81",
"82",
"83",
"85",
"87",
"88",
"89"
] | [
"nonn",
"hard"
] | 21 | 1 | 3 | [
"A000120",
"A000290",
"A159918",
"A230097",
"A357304",
"A357658"
] | null | Hugo Pfoertner, Oct 01 2022 | 2022-11-30T10:59:12 | oeisdata/seq/A357/A357304.seq | 8d603802b1dbdbbd7076c4c6239f3dfe |
A357305 | Numbers k > 1 such that the ratio (numbers of zeros)/(total length) in the binary representation of k^2 is a new minimum. | [
"2",
"3",
"5",
"11",
"45",
"181",
"48589783221",
"66537313397",
"398064946368587",
"796095014224053"
] | [
"nonn",
"base",
"hard",
"more"
] | 14 | 1 | 1 | [
"A000120",
"A000290",
"A070939",
"A159918",
"A230097",
"A357305"
] | null | Hugo Pfoertner, Oct 01 2022 | 2022-11-30T14:55:23 | oeisdata/seq/A357/A357305.seq | 53522f3c0f93eeee8bf3ae9db0697d74 |
A357306 | Number of compositions (ordered partitions) of n into distinct Lucas numbers (beginning at 2). | [
"1",
"1",
"1",
"3",
"3",
"4",
"8",
"9",
"8",
"8",
"32",
"9",
"14",
"32",
"38",
"32",
"36",
"150",
"33",
"32",
"32",
"158",
"38",
"60",
"174",
"176",
"150",
"150",
"870",
"33",
"56",
"152",
"182",
"158",
"180",
"894",
"182",
"174",
"174",
"1014",
"176",
"294",
"990",
"1014",
"870",
"888",
"5904",
"153",
"152",
"152",
"902",
"182",
"300",
"1014",
"1022",
"894",
"894"
] | [
"nonn"
] | 5 | 0 | 4 | [
"A000032",
"A003263",
"A067593",
"A067595",
"A218396",
"A288039",
"A331922",
"A357306"
] | null | Ilya Gutkovskiy, Sep 23 2022 | 2022-09-25T11:03:40 | oeisdata/seq/A357/A357306.seq | 8d9f256dadad909c93086aeb74e8e687 |
A357307 | a(0) = 1, a(1) = 0, a(2) = 1; a(n) = a(n-1) + Sum_{k=0..n-3} a(k) * a(n-k-3). | [
"1",
"0",
"1",
"2",
"2",
"4",
"8",
"13",
"25",
"49",
"91",
"177",
"349",
"681",
"1349",
"2693",
"5377",
"10806",
"21820",
"44163",
"89721",
"182868",
"373616",
"765341",
"1571551",
"3233690",
"6667242",
"13772469",
"28498419",
"59065838",
"122606998",
"254865837",
"530507839",
"1105663034",
"2307131590",
"4819623077",
"10079039819",
"21099213611",
"44211213545"
] | [
"nonn"
] | 6 | 0 | 4 | [
"A000245",
"A023426",
"A023431",
"A090345",
"A346503",
"A346504",
"A357307",
"A357308"
] | null | Ilya Gutkovskiy, Sep 23 2022 | 2022-09-24T15:00:00 | oeisdata/seq/A357/A357307.seq | 9051a23ba9d63a49beeb925ac8424e4e |
A357308 | a(0) = a(1) = 0, a(2) = 1; a(n) = a(n-1) + Sum_{k=0..n-3} a(k) * a(n-k-3). | [
"0",
"0",
"1",
"1",
"1",
"1",
"1",
"2",
"4",
"7",
"11",
"16",
"24",
"39",
"67",
"116",
"196",
"324",
"534",
"892",
"1516",
"2601",
"4463",
"7630",
"13022",
"22276",
"38286",
"66084",
"114328",
"197929",
"342783",
"594218",
"1031794",
"1794944",
"3127450",
"5455272",
"9523812",
"16640542",
"29102938",
"50951070",
"89289998",
"156616648",
"274923328",
"482945930",
"848972814"
] | [
"nonn"
] | 5 | 0 | 8 | [
"A006318",
"A023426",
"A023431",
"A025246",
"A346503",
"A346504",
"A357307",
"A357308"
] | null | Ilya Gutkovskiy, Sep 23 2022 | 2022-09-24T14:59:47 | oeisdata/seq/A357/A357308.seq | 87c8e762fef6cd28b1b4713560b2db13 |
A357309 | Number of ascent sequences of length 2n with n zeros. | [
"1",
"1",
"6",
"54",
"660",
"10255",
"193732",
"4312980",
"110598510",
"3210608808",
"104085718451",
"3727491264497",
"146140031249576",
"6225801069767760",
"286376011804522536",
"14145748008085964988",
"746808042116142422388",
"41964968782188114180606",
"2500755433211714966201145"
] | [
"nonn"
] | 8 | 0 | 3 | [
"A175579",
"A357309"
] | null | Alois P. Heinz, Sep 23 2022 | 2022-09-23T12:12:42 | oeisdata/seq/A357/A357309.seq | 306a563b3165b85db77c2019359e0012 |
A357310 | a(n) is the number of j in the range 1 <= j <= n with the same maximal exponent in prime factorization as n. | [
"1",
"1",
"2",
"1",
"3",
"4",
"5",
"1",
"2",
"6",
"7",
"3",
"8",
"9",
"10",
"1",
"11",
"4",
"12",
"5",
"13",
"14",
"15",
"2",
"6",
"16",
"3",
"7",
"17",
"18",
"19",
"1",
"20",
"21",
"22",
"8",
"23",
"24",
"25",
"4",
"26",
"27",
"28",
"9",
"10",
"29",
"30",
"2",
"11",
"12",
"31",
"13",
"32",
"5",
"33",
"6",
"34",
"35",
"36",
"14",
"37",
"38",
"15",
"1",
"39",
"40",
"41",
"16",
"42",
"43",
"44",
"7",
"45",
"46",
"17",
"18",
"47",
"48",
"49",
"3"
] | [
"nonn"
] | 14 | 1 | 3 | [
"A000079",
"A051903",
"A058933",
"A289023",
"A357310"
] | null | Ilya Gutkovskiy, Sep 23 2022 | 2024-01-05T02:51:01 | oeisdata/seq/A357/A357310.seq | 007eb500c5be1757c5491da0aefd48e1 |
A357311 | Number of partitions of n into divisors of n that are smaller than sqrt(n). | [
"1",
"0",
"1",
"1",
"1",
"1",
"4",
"1",
"5",
"1",
"6",
"1",
"19",
"1",
"8",
"6",
"9",
"1",
"37",
"1",
"36",
"8",
"12",
"1",
"169",
"1",
"14",
"10",
"64",
"1",
"247",
"1",
"81",
"12",
"18",
"8",
"478",
"1",
"20",
"14",
"405",
"1",
"512",
"1",
"144",
"82",
"24",
"1",
"2825",
"1",
"146",
"18",
"196",
"1",
"1000",
"12",
"743",
"20",
"30",
"1",
"19858",
"1",
"32",
"112",
"289",
"14",
"1728",
"1",
"324",
"24",
"1105"
] | [
"nonn"
] | 10 | 0 | 7 | [
"A018818",
"A210442",
"A293813",
"A327642",
"A357311",
"A357312"
] | null | Ilya Gutkovskiy, Sep 23 2022 | 2022-09-24T13:45:44 | oeisdata/seq/A357/A357311.seq | f3eb095bb2a582eb5bdba374b14e8e35 |
A357312 | Number of compositions (ordered partitions) of n into divisors of n that are smaller than sqrt(n). | [
"1",
"0",
"1",
"1",
"1",
"1",
"13",
"1",
"34",
"1",
"89",
"1",
"927",
"1",
"610",
"189",
"1597",
"1",
"35890",
"1",
"46754",
"1873",
"28657",
"1",
"3919944",
"1",
"196418",
"18560",
"4205249",
"1",
"110187694",
"1",
"39882198",
"183916",
"9227465",
"9496",
"10312882481",
"1",
"63245986",
"1822473",
"11969319436",
"1",
"141930520462",
"1",
"34020543362",
"339200673"
] | [
"nonn",
"look"
] | 10 | 0 | 7 | [
"A100346",
"A294137",
"A294138",
"A327766",
"A357311",
"A357312"
] | null | Ilya Gutkovskiy, Sep 23 2022 | 2022-09-24T13:29:04 | oeisdata/seq/A357/A357312.seq | c5ba4d39940a896fb9f9bc0ed68c818f |
A357313 | a(n) is the unique number m such that A001065(m) = A057709(n). | [
"4",
"9",
"8",
"15",
"14",
"21",
"121",
"289",
"529",
"46",
"28",
"841",
"62",
"24",
"1369",
"217",
"2209",
"106",
"68",
"3481",
"54",
"4489",
"134",
"5041",
"66",
"6241",
"158",
"6889",
"166",
"116",
"9409",
"10201",
"218",
"226",
"148",
"130",
"114",
"16129",
"17161",
"18769",
"278",
"90",
"24649",
"314",
"26569",
"27889",
"108",
"29929",
"225",
"32041",
"244"
] | [
"nonn"
] | 9 | 1 | 1 | [
"A001065",
"A057709",
"A357313"
] | null | Amiram Eldar, Sep 23 2022 | 2022-09-28T03:53:22 | oeisdata/seq/A357/A357313.seq | 70beac7adafdbe2f320bf13c7f6048c0 |
A357314 | a(1) = 1; a(n) is the second smallest number k such that k > a(n-1) and concatenation of a(1), ..., a(n-1), k is a palindrome. | [
"1",
"21",
"1121",
"1211121",
"2111211211121",
"112112111212111211211121",
"12111212111211211121112112111212111211211121",
"211121121112111211211121211121121112112111212111211211121112112111212111211211121"
] | [
"nonn",
"base"
] | 22 | 1 | 2 | [
"A000073",
"A002275",
"A055642",
"A083122",
"A305393",
"A357314"
] | null | Gleb Ivanov, Sep 23 2022 | 2023-03-21T06:12:31 | oeisdata/seq/A357/A357314.seq | 7677831e64122692d4215feaa4ecf81a |
A357315 | Numbers m such that for all k < m, at least one of m*k - 1 and m*k + 1 is squarefree. | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"12",
"14",
"15",
"16",
"18",
"20",
"21",
"22",
"24",
"30",
"32",
"36",
"42",
"44",
"48",
"50",
"52",
"54",
"56",
"62",
"64",
"66",
"70",
"72",
"78",
"84",
"90",
"96",
"126",
"132",
"140",
"144",
"150",
"156",
"168",
"180",
"198",
"210",
"216",
"228",
"240",
"246",
"264",
"270",
"360",
"378",
"390",
"414",
"420",
"450",
"510",
"546",
"630",
"780",
"840",
"1230",
"1470",
"1680",
"5250"
] | [
"nonn"
] | 65 | 1 | 2 | [
"A005117",
"A013929",
"A257771",
"A281192",
"A357315"
] | null | Juri-Stepan Gerasimov, Oct 17 2022 | 2023-01-04T15:53:02 | oeisdata/seq/A357/A357315.seq | 1493799e0eb3f1322cd881a354ba7caf |
A357316 | A distension of the Wythoff array by inclusion of intermediate rows. Square array A(n,k), n >= 0, k >= 0, read by descending antidiagonals. If S is the set such that Sum_{i in S} F_i is the Zeckendorf representation of n then A(n,k) = Sum_{i in S} F_{i+k-2}. | [
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"2",
"2",
"2",
"1",
"0",
"3",
"3",
"3",
"3",
"2",
"0",
"5",
"5",
"5",
"4",
"3",
"2",
"0",
"8",
"8",
"8",
"7",
"5",
"4",
"3",
"0",
"13",
"13",
"13",
"11",
"8",
"6",
"4",
"3",
"0",
"21",
"21",
"21",
"18",
"13",
"10",
"7",
"5",
"3",
"0",
"34",
"34",
"34",
"29",
"21",
"16",
"11",
"8",
"6",
"4",
"0",
"55",
"55",
"55",
"47",
"34",
"26",
"18",
"13",
"9",
"6",
"4"
] | [
"nonn",
"tabl"
] | 8 | 0 | 12 | [
"A000045",
"A000204",
"A003622",
"A003714",
"A005206",
"A022342",
"A026274",
"A035336",
"A035337",
"A035338",
"A035513",
"A054582",
"A101345",
"A101642",
"A130128",
"A135090",
"A287869",
"A287870",
"A356874",
"A357316"
] | null | Peter Munn, Sep 23 2022 | 2022-09-30T14:38:34 | oeisdata/seq/A357/A357316.seq | da9e5679f00b36a8bd57977ff89827b3 |
A357317 | Inventory count sequence: record what you see and where it is located. | [
"0",
"1",
"0",
"0",
"3",
"0",
"0",
"2",
"3",
"1",
"1",
"1",
"5",
"0",
"0",
"2",
"3",
"5",
"6",
"4",
"1",
"1",
"9",
"10",
"11",
"1",
"2",
"7",
"2",
"3",
"4",
"8",
"7",
"0",
"0",
"2",
"3",
"5",
"6",
"13",
"14",
"7",
"1",
"1",
"9",
"10",
"11",
"20",
"21",
"25",
"4",
"2",
"7",
"15",
"26",
"28",
"4",
"3",
"4",
"8",
"16",
"29",
"2",
"4",
"19",
"30",
"2",
"5",
"12",
"17",
"1",
"6",
"18",
"1",
"7",
"27",
"1",
"8",
"31",
"1",
"9",
"22",
"1",
"10",
"23",
"1",
"11",
"24",
"9",
"0",
"0",
"2",
"3"
] | [
"nonn",
"look"
] | 40 | 0 | 5 | [
"A342585",
"A357317"
] | null | Ctibor O. Zizka, Sep 29 2022 | 2022-10-31T06:00:26 | oeisdata/seq/A357/A357317.seq | 69fe59ed51e9006414f1f00c8803cb37 |
A357318 | Decimal expansion of 1/(2*L), where L is the conjectured Landau's constant A081760. | [
"9",
"2",
"0",
"3",
"7",
"1",
"3",
"7",
"3",
"3",
"1",
"7",
"9",
"4",
"2",
"4",
"9",
"7",
"6",
"5",
"5",
"5",
"1",
"8",
"5",
"6",
"4",
"5",
"4",
"3",
"1",
"7",
"2",
"9",
"9",
"4",
"7",
"2",
"6",
"2",
"4",
"5",
"7",
"9",
"1",
"9",
"4",
"9",
"8",
"9",
"4",
"3",
"3",
"8",
"3",
"4",
"3",
"3",
"0",
"0",
"1",
"9",
"9",
"7",
"7",
"3",
"1",
"0",
"1",
"8",
"0",
"8",
"0",
"8",
"0",
"5",
"6",
"8",
"5",
"6",
"3",
"9",
"3",
"6",
"3",
"3",
"8",
"5"
] | [
"nonn",
"cons"
] | 30 | 0 | 1 | [
"A004117",
"A073005",
"A081760",
"A175379",
"A203145",
"A357318"
] | null | Stefano Spezia, Sep 23 2022 | 2023-07-27T12:18:41 | oeisdata/seq/A357/A357318.seq | e031623cb4a5711159b3764992551f27 |
A357319 | Decimal expansion of 6*Pi*Gamma(2/3)^2/(sqrt(3)*Gamma(1/3)^4). | [
"3",
"8",
"7",
"4",
"3",
"8",
"2",
"3",
"8",
"7",
"8",
"4",
"8",
"8",
"5",
"4",
"2",
"0",
"5",
"6",
"9",
"5",
"6",
"4",
"8",
"8",
"4",
"7",
"5",
"4",
"0",
"1",
"8",
"9",
"4",
"8",
"0",
"4",
"9",
"6",
"0",
"3",
"8",
"8",
"3",
"3",
"6",
"3",
"6",
"8",
"4",
"8",
"9",
"0",
"4",
"3",
"9",
"4",
"6",
"4",
"4",
"5",
"7",
"5",
"5",
"8",
"7",
"6",
"5",
"4",
"3",
"9",
"0",
"4",
"2",
"8",
"9",
"6",
"0",
"6",
"0",
"3",
"4",
"0",
"6",
"6",
"2",
"8",
"6",
"1"
] | [
"nonn",
"cons"
] | 9 | 0 | 1 | [
"A000796",
"A002194",
"A073005",
"A073006",
"A212003",
"A357319"
] | null | Stefano Spezia, Sep 23 2022 | 2022-09-25T02:14:58 | oeisdata/seq/A357/A357319.seq | 7ed3bb623842e8abadda71017aeca24d |
A357320 | The total number of fixed points among all strict partitions of n, when parts are written in increasing order. | [
"0",
"1",
"0",
"2",
"1",
"1",
"4",
"3",
"4",
"4",
"9",
"8",
"11",
"12",
"15",
"21",
"24",
"28",
"34",
"40",
"46",
"60",
"67",
"80",
"93",
"110",
"125",
"148",
"174",
"200",
"231",
"268",
"306",
"354",
"404",
"461",
"534",
"606",
"690",
"786",
"895",
"1012",
"1150",
"1298",
"1467",
"1662",
"1872",
"2104",
"2374",
"2664",
"2990",
"3355",
"3759",
"4202",
"4702",
"5256"
] | [
"nonn"
] | 25 | 0 | 4 | [
"A352829",
"A357320",
"A357459"
] | null | Jeremy Lovejoy, Sep 29 2022 | 2022-09-30T03:50:31 | oeisdata/seq/A357/A357320.seq | b9dc3516761f2b072cb00bd04a4d92bd |
A357321 | Expansion of e.g.f. -LambertW(log(1 - 2*x)/2). | [
"0",
"1",
"4",
"29",
"308",
"4349",
"77094",
"1650893",
"41532280",
"1201865049",
"39351776970",
"1438731784137",
"58107225611412",
"2569486856423733",
"123475320944016846",
"6407225728624769925",
"357061085760608504304",
"21268522319028809507889",
"1348496822257863921774738"
] | [
"nonn"
] | 19 | 0 | 3 | [
"A052807",
"A357321",
"A357322",
"A357333"
] | null | Seiichi Manyama, Sep 24 2022 | 2025-02-16T08:34:04 | oeisdata/seq/A357/A357321.seq | fc36c5e485c56c071a382c4a5cfe89b0 |
A357322 | Expansion of e.g.f. -LambertW(log(1 - 3*x)/3). | [
"0",
"1",
"5",
"45",
"586",
"10024",
"213084",
"5428072",
"161475320",
"5501761488",
"211466328400",
"9057714349672",
"428022643010544",
"22127292215218072",
"1242503403120434168",
"75319473068729478360",
"4902798528238919060224",
"341102498012848479889408"
] | [
"nonn"
] | 20 | 0 | 3 | [
"A052807",
"A357321",
"A357322",
"A357334"
] | null | Seiichi Manyama, Sep 24 2022 | 2025-02-16T08:34:04 | oeisdata/seq/A357/A357322.seq | 2c186d8893406ac1fdad5c1df1135910 |
A357323 | Numbers k such that k and k+2 are both unitary untouchable numbers (A063948). | [
"2",
"3",
"5",
"30756",
"34182",
"46128",
"51816",
"56352",
"72522",
"86640",
"88896",
"119796",
"133062",
"133618",
"149682",
"164290",
"207282",
"207642",
"213636",
"245708",
"257820",
"261156",
"279730",
"283050",
"286356",
"286858",
"310842",
"318060",
"327300",
"339402",
"339612",
"349030",
"360390",
"371820",
"377940",
"384576",
"396090"
] | [
"nonn"
] | 10 | 1 | 1 | [
"A063948",
"A231964",
"A357323"
] | null | Amiram Eldar, Sep 24 2022 | 2022-09-28T03:53:26 | oeisdata/seq/A357/A357323.seq | 64e7049191854a093e341a6ad8ced3d8 |
A357324 | Numbers k such that there is a unique m for which the sum of the aliquot unitary divisors of m (A034460) is k. | [
"6",
"9",
"11",
"13",
"128",
"150",
"164",
"222",
"224",
"332",
"338",
"390",
"404",
"416",
"420",
"458",
"510",
"548",
"558",
"570",
"576",
"582",
"584",
"598",
"660",
"668",
"750",
"788",
"800",
"810",
"818",
"822",
"836",
"852",
"878",
"884",
"926",
"930",
"1046",
"1118",
"1200",
"1202",
"1230",
"1244",
"1250",
"1260",
"1284",
"1298",
"1304",
"1382",
"1422",
"1472",
"1478"
] | [
"nonn"
] | 15 | 1 | 1 | [
"A034460",
"A057709",
"A063948",
"A324938",
"A357324",
"A357325"
] | null | Amiram Eldar, Sep 24 2022 | 2022-09-28T03:53:19 | oeisdata/seq/A357/A357324.seq | 93b8dc187585611650927f95a3c2cbb4 |
A357325 | a(n) is the unique number m such that A034460(m) = A357324(n). | [
"6",
"15",
"21",
"35",
"250",
"138",
"4192",
"10048",
"6112",
"748",
"20736",
"5968",
"802",
"12256",
"41728",
"3592",
"498",
"53632",
"8656",
"80128",
"2284",
"2308",
"36352",
"2372",
"10288",
"5272",
"11728",
"84352",
"1594",
"630",
"6472",
"48448",
"6616",
"50368",
"1426",
"1762",
"102016",
"172288",
"32416",
"8872",
"2328",
"9544",
"19408"
] | [
"nonn"
] | 11 | 1 | 1 | [
"A034460",
"A057709",
"A357313",
"A357324",
"A357325"
] | null | Amiram Eldar, Sep 24 2022 | 2022-09-28T03:53:16 | oeisdata/seq/A357/A357325.seq | 979b434660230ec584d5a7dcbc22e828 |
A357326 | Weird untouchable numbers. | [
"836",
"7192",
"7912",
"12670",
"13510",
"16030",
"16310",
"16870",
"17272",
"18830",
"21910",
"24290",
"24430",
"26530",
"26810",
"29470",
"31430",
"34930",
"35210",
"35630",
"37870",
"42910",
"43330",
"46130",
"46270",
"48370",
"52990",
"53830",
"57890",
"61810",
"70910",
"73430",
"74270",
"74410",
"76790",
"77630",
"79030",
"82670"
] | [
"nonn"
] | 13 | 1 | 1 | [
"A001065",
"A005101",
"A005114",
"A006037",
"A357326"
] | null | Amiram Eldar, Sep 24 2022 | 2022-09-28T03:53:13 | oeisdata/seq/A357/A357326.seq | d8acdc2999db9bbd7e342a52cc348f1b |
A357327 | a(n) is the unique nonnegative integer k <= A058084(n)/2 such that binomial(A058084(n),k) = n. | [
"0",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"3",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"3",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"3",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"3",
"1",
"1",
"1"
] | [
"nonn"
] | 15 | 1 | 6 | [
"A007318",
"A058084",
"A357327"
] | null | Pontus von Brömssen, Sep 24 2022 | 2022-09-24T16:41:12 | oeisdata/seq/A357/A357327.seq | 6e0cd6b0c4c11f2356b09c6b38473467 |
A357328 | Number of permutations p of [n] such that p(i) divides p(j) if i divides j for 1 <= i <= j <= n. | [
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"2",
"2",
"2",
"1",
"2",
"2",
"6",
"4",
"2",
"2",
"6",
"6",
"24",
"24",
"24",
"6",
"24",
"24",
"24",
"12",
"12",
"12",
"48",
"48",
"240",
"240",
"120",
"48",
"48",
"48",
"240",
"144",
"96",
"96",
"480",
"480",
"2880",
"1440",
"1440",
"720",
"4320",
"4320",
"4320",
"4320",
"2880",
"2880",
"20160",
"20160",
"10080",
"10080",
"10080",
"2880",
"20160",
"20160",
"161280",
"60480",
"60480",
"60480",
"120960"
] | [
"nonn"
] | 42 | 0 | 4 | [
"A320843",
"A357328"
] | null | Seiichi Manyama, Oct 01 2022 | 2022-10-02T10:30:09 | oeisdata/seq/A357/A357328.seq | e7ce28d81c22863bb96386242f998ccd |
A357329 | Triangular array read by rows: T(n, k) = number of occurrences of 2k as a sum |1 - p(1)| + |2 - p(2)| + ... + |n - p(n)|, where (p(1), p(2), ..., p(n)) ranges through the permutations of (1,2,...,n), for n >= 1, 0 <= k <= n-1. | [
"1",
"1",
"1",
"1",
"2",
"3",
"1",
"3",
"7",
"9",
"1",
"4",
"12",
"24",
"35",
"1",
"5",
"18",
"46",
"93",
"137",
"1",
"6",
"25",
"76",
"187",
"366",
"591",
"1",
"7",
"33",
"115",
"327",
"765",
"1523",
"2553",
"1",
"8",
"42",
"164",
"524",
"1400",
"3226",
"6436",
"11323",
"1",
"9",
"52",
"224",
"790",
"2350",
"6072",
"13768",
"27821",
"50461",
"1",
"10",
"63",
"296",
"1138",
"3708",
"10538",
"26480",
"59673",
"121626",
"226787"
] | [
"nonn",
"tabl"
] | 38 | 1 | 5 | [
"A000142",
"A062869",
"A072948",
"A263898",
"A357329"
] | null | Clark Kimberling, Sep 24 2022 | 2024-07-05T08:20:23 | oeisdata/seq/A357/A357329.seq | d58fc48f210b913268c61b141ca738f2 |
A357330 | Decimal expansion of sigma(N) / (N * log(log(N))) for N = 5040, where sigma = A000203. | [
"1",
"7",
"9",
"0",
"9",
"7",
"3",
"3",
"6",
"6",
"5",
"3",
"4",
"8",
"8",
"1",
"1",
"3",
"3",
"3",
"6",
"1",
"9",
"0",
"1",
"3",
"5",
"0",
"5",
"9",
"1",
"0",
"9",
"5",
"1",
"7",
"4",
"0",
"9",
"0",
"9",
"5",
"3",
"9",
"0",
"7",
"9",
"8",
"7",
"5",
"7",
"3",
"5",
"7",
"7",
"9",
"1",
"7",
"4",
"6",
"5",
"3",
"5",
"2",
"3",
"5",
"6",
"6",
"7",
"0",
"4",
"6",
"9",
"5",
"5",
"7",
"6",
"9",
"5",
"2",
"2",
"9",
"7",
"7",
"9",
"3",
"4",
"2",
"3",
"5"
] | [
"nonn",
"cons"
] | 13 | 1 | 2 | [
"A000203",
"A001620",
"A067698",
"A073004",
"A357330",
"A357331"
] | null | Jianing Song, Sep 24 2022 | 2025-02-16T08:34:04 | oeisdata/seq/A357/A357330.seq | 28ce1be0631212f4b8d89a86aa03807f |
A357331 | Decimal expansion of sigma(N) / (exp(gamma) * N * log(log(N))) for N = 5040, where sigma = A000203 and gamma = A001620 is the Euler-Mascheroni constant. | [
"1",
"0",
"0",
"5",
"5",
"5",
"8",
"9",
"8",
"1",
"4",
"5",
"6",
"7",
"2",
"0",
"1",
"0",
"3",
"6",
"4",
"2",
"4",
"7",
"0",
"7",
"6",
"7",
"7",
"8",
"1",
"5",
"5",
"4",
"4",
"3",
"1",
"6",
"9",
"8",
"4",
"4",
"3",
"0",
"1",
"4",
"6",
"7",
"4",
"1",
"5",
"2",
"7",
"9",
"7",
"3",
"6",
"8",
"0",
"2",
"5",
"8",
"3",
"2",
"2",
"5",
"7",
"4",
"6",
"5",
"9",
"5",
"4",
"9",
"5",
"5",
"8",
"5",
"2",
"2",
"7",
"8",
"7",
"7",
"1",
"4",
"6",
"2",
"3",
"9"
] | [
"nonn",
"cons"
] | 15 | 1 | 4 | [
"A000203",
"A001620",
"A067698",
"A073004",
"A357330",
"A357331"
] | null | Jianing Song, Sep 24 2022 | 2025-02-16T08:34:04 | oeisdata/seq/A357/A357331.seq | a28f21e24e8d02b9ed82f10e9da6466d |
A357332 | 2-adic valuation of A000793(n). | [
"0",
"1",
"0",
"2",
"1",
"1",
"2",
"0",
"2",
"1",
"1",
"2",
"2",
"2",
"0",
"2",
"1",
"1",
"2",
"2",
"2",
"2",
"3",
"3",
"2",
"2",
"2",
"1",
"3",
"2",
"2",
"2",
"2",
"3",
"3",
"2",
"2",
"2",
"2",
"3",
"1",
"3",
"2",
"2",
"2",
"2",
"3",
"3",
"2",
"2",
"2",
"2",
"3",
"3",
"3",
"3",
"3",
"1",
"3",
"2",
"2",
"2",
"2",
"3",
"3",
"2",
"2",
"2",
"2",
"3",
"3",
"3",
"3",
"3",
"3",
"3",
"1",
"4",
"2",
"2",
"2",
"2",
"3",
"3",
"2",
"2",
"2",
"2",
"3",
"3",
"3"
] | [
"nonn"
] | 12 | 1 | 4 | [
"A000793",
"A357332"
] | null | Jianing Song, Sep 24 2022 | 2022-09-25T04:25:25 | oeisdata/seq/A357/A357332.seq | acca2fb7f6951380727d0f9d0a17ba9a |
A357333 | E.g.f. satisfies A(x) = -log(1 - x) * exp(2 * A(x)). | [
"0",
"1",
"5",
"50",
"778",
"16604",
"451668",
"14947568",
"582982160",
"26187136128",
"1331445995520",
"75589772147328",
"4739901861071232",
"325353447339098112",
"24264683011603485696",
"1953776475810372817920",
"168924939633683095452672",
"15609228287753846217412608"
] | [
"nonn"
] | 21 | 0 | 3 | [
"A052807",
"A264407",
"A357321",
"A357333",
"A357334"
] | null | Seiichi Manyama, Sep 24 2022 | 2025-02-16T08:34:04 | oeisdata/seq/A357/A357333.seq | 3520ca3c51604c958a14533d9a0fe248 |
A357334 | E.g.f. satisfies A(x) = -log(1 - x) * exp(3 * A(x)). | [
"0",
"1",
"7",
"101",
"2286",
"71064",
"2815812",
"135719352",
"7708432680",
"504204903504",
"37327594368240",
"3085620116373288",
"281715917686701264",
"28154794766366676888",
"3057177180272007475368",
"358397769923628731936280",
"45115415964514707860498688",
"6069465245766845367272738304"
] | [
"nonn"
] | 22 | 0 | 3 | [
"A052807",
"A264408",
"A357322",
"A357333",
"A357334"
] | null | Seiichi Manyama, Sep 24 2022 | 2025-02-16T08:34:04 | oeisdata/seq/A357/A357334.seq | 30e77528ebeedf30e356b40cdb0f2fdb |
A357335 | E.g.f. satisfies A(x) = (exp(x) - 1) * exp(2 * A(x)). | [
"0",
"1",
"5",
"49",
"757",
"16081",
"435477",
"14345297",
"556857973",
"24894290257",
"1259621627349",
"71165987957329",
"4440821632449077",
"303338709537825105",
"22512353926895739797",
"1803812930088064925265",
"155195078834104237961717",
"14270228623788585753803089"
] | [
"nonn"
] | 20 | 0 | 3 | [
"A048802",
"A349524",
"A356000",
"A357335",
"A357336",
"A357347"
] | null | Seiichi Manyama, Sep 24 2022 | 2025-02-16T08:34:04 | oeisdata/seq/A357/A357335.seq | ea028538a2cd5a0d6c74854b55836fbe |
A357336 | E.g.f. satisfies A(x) = (exp(x) - 1) * exp(3 * A(x)). | [
"0",
"1",
"7",
"100",
"2257",
"70021",
"2768740",
"133164109",
"7546722487",
"492531820066",
"36381833190223",
"3000677194970137",
"273342303933512362",
"27256107730344331879",
"2952882035628632383975",
"345384835617231362018764",
"43378466647737203462409829",
"5822506028894124326533926193"
] | [
"nonn"
] | 20 | 0 | 3 | [
"A048802",
"A349525",
"A356001",
"A357335",
"A357336"
] | null | Seiichi Manyama, Sep 24 2022 | 2025-02-16T08:34:04 | oeisdata/seq/A357/A357336.seq | b105e8bc98bf3b6d1d524e2a2bab1c68 |
A357337 | E.g.f. satisfies A(x) = log(1 + x) * exp(2 * A(x)). | [
"0",
"1",
"3",
"26",
"334",
"5964",
"135228",
"3729872",
"121172560",
"4532603904",
"191869653120",
"9067948437888",
"473297792213376",
"27039987154142208",
"1678363256057198592",
"112467293224249912320",
"8092242817059530284032",
"622253112192770288799744"
] | [
"nonn"
] | 24 | 0 | 3 | [
"A277489",
"A349504",
"A357337",
"A357338"
] | null | Seiichi Manyama, Sep 24 2022 | 2025-02-16T08:34:04 | oeisdata/seq/A357/A357337.seq | 59945e58c3e6d517379578c862aeedfd |
A357338 | E.g.f. satisfies A(x) = log(1 + x) * exp(3 * A(x)). | [
"0",
"1",
"5",
"65",
"1302",
"35904",
"1260372",
"53796168",
"2704942440",
"156602951568",
"10260496538640",
"750563024381928",
"60636437884772208",
"5362045857366832152",
"515154874732515894744",
"53432840588453561773080",
"5950904875941534263739648",
"708296073287989866587094528"
] | [
"nonn"
] | 26 | 0 | 3 | [
"A277489",
"A349505",
"A357337",
"A357338"
] | null | Seiichi Manyama, Sep 24 2022 | 2025-02-16T08:34:04 | oeisdata/seq/A357/A357338.seq | b969bccc37eaae35b2480c9a1aa9ce26 |
A357339 | Triangle read by rows. T(n, k) = Sum_{j=0..n-k} binomial(-n, j) * A268437(n - k, j). | [
"1",
"-1",
"1",
"10",
"-2",
"1",
"-270",
"24",
"-3",
"1",
"14056",
"-720",
"44",
"-4",
"1",
"-1197000",
"40320",
"-1500",
"70",
"-5",
"1",
"151169040",
"-3628800",
"92064",
"-2700",
"102",
"-6",
"1",
"-26521775280",
"479001600",
"-8890560",
"181888",
"-4410",
"140",
"-7",
"1",
"6169461217920",
"-87178291200",
"1241982720",
"-18910080",
"324912",
"-6720",
"184",
"-8",
"1"
] | [
"sign",
"tabl"
] | 12 | 0 | 4 | [
"A268437",
"A357339",
"A357340",
"A357342"
] | null | Peter Luschny, Sep 25 2022 | 2023-12-10T09:23:51 | oeisdata/seq/A357/A357339.seq | 1b4636c02fac013696e07b708e2332c6 |
A357340 | Triangle read by rows. T(n, k) = Sum_{j=0..n-k} binomial(-n, j) * A268438(n - k, j). | [
"1",
"-1",
"1",
"2",
"-2",
"1",
"0",
"12",
"-3",
"1",
"-56",
"-120",
"28",
"-4",
"1",
"0",
"1680",
"-450",
"50",
"-5",
"1",
"15840",
"-30240",
"10416",
"-1080",
"78",
"-6",
"1",
"0",
"665280",
"-317520",
"33712",
"-2100",
"112",
"-7",
"1",
"-17297280",
"-17297280",
"12070080",
"-1391040",
"81648",
"-3600",
"152",
"-8",
"1"
] | [
"sign",
"tabl"
] | 13 | 0 | 4 | [
"A264437",
"A268438",
"A357339",
"A357340",
"A357341"
] | null | Peter Luschny, Sep 25 2022 | 2023-12-10T09:23:38 | oeisdata/seq/A357/A357340.seq | f06b3359f0733de45b5b6b650d3f35e1 |
A357341 | a(n) = Sum_{k=0..n} (-1)^(n - k) * A357340(n, k). | [
"1",
"2",
"5",
"16",
"97",
"2186",
"57661",
"1018732",
"13546529",
"1146511702",
"102660872221",
"2825817094376",
"-145181157396863",
"13773236811700354",
"5271279146947177757",
"116514699193035121156",
"-76433013927946696971839",
"1553218338489700863557582",
"3403068210845899797768538429"
] | [
"sign"
] | 6 | 0 | 2 | [
"A357340",
"A357341"
] | null | Peter Luschny, Sep 25 2022 | 2022-10-01T08:38:28 | oeisdata/seq/A357/A357341.seq | dab895aeb8a6510ad3433d2a7333725c |
A357342 | a(n) = Sum_{k=0..n} ((-1)^(n - k) * A357339(n, k)). | [
"1",
"2",
"13",
"298",
"14825",
"1238896",
"154892713",
"27009853886",
"6257900733745",
"1858486623941620",
"688135964728698641",
"310726469248576739458",
"168049914540105868641241",
"107234597681651999462375720",
"79717829408115648827783288185",
"68293032241442657676784109954086"
] | [
"nonn"
] | 4 | 0 | 2 | [
"A357339",
"A357342"
] | null | Peter Luschny, Sep 25 2022 | 2022-10-01T08:38:25 | oeisdata/seq/A357/A357342.seq | be32f0347615840f7f4534b92e4db370 |
A357343 | E.g.f. satisfies A(x) = -log(1 - x * exp(A(x))) * exp(A(x)). | [
"0",
"1",
"5",
"53",
"878",
"19904",
"573984",
"20112770",
"829953368",
"39425517072",
"2119169565120",
"127163052628512",
"8426599011632592",
"611181716437826832",
"48159349246147915944",
"4096752391897622411880",
"374189567290578072309504",
"36525100459236757201316352"
] | [
"nonn"
] | 18 | 0 | 3 | [
"A006963",
"A052807",
"A349556",
"A357343",
"A357344",
"A357345",
"A357422"
] | null | Seiichi Manyama, Sep 25 2022 | 2024-09-09T09:33:51 | oeisdata/seq/A357/A357343.seq | 8fef4121f7dc9c8b4ac7925a49e1ebce |
A357344 | E.g.f. satisfies A(x) = -log(1 - x * exp(A(x))) * exp(2 * A(x)). | [
"0",
"1",
"7",
"104",
"2422",
"77304",
"3141108",
"155155580",
"9027723248",
"604793361744",
"45851401106880",
"3880989671623008",
"362790690552990720",
"37120807927059003744",
"4126551430278515989632",
"495243629308215934662720",
"63819561948443247132306432",
"8789113187481077533462305024"
] | [
"nonn"
] | 17 | 0 | 3 | [
"A006963",
"A355766",
"A357343",
"A357344",
"A357345",
"A357422"
] | null | Seiichi Manyama, Sep 25 2022 | 2024-09-09T09:33:54 | oeisdata/seq/A357/A357344.seq | 13044f9d273d87602723bdcbd94c55bc |
A357345 | E.g.f. satisfies A(x) = -log(1 - x * exp(A(x))) * exp(3 * A(x)). | [
"0",
"1",
"9",
"173",
"5226",
"216564",
"11429592",
"733443990",
"55447217928",
"4826605609584",
"475490102407200",
"52299789903627408",
"6353202640983827472",
"844774875973448667792",
"122040471544637793494760",
"19034141943046836097099080",
"3187643959565686909679931648"
] | [
"nonn"
] | 15 | 0 | 3 | [
"A006963",
"A357334",
"A357343",
"A357344",
"A357345",
"A375422"
] | null | Seiichi Manyama, Sep 25 2022 | 2024-09-09T09:33:57 | oeisdata/seq/A357/A357345.seq | cfd0d63b6f9c98c6b1b2808d2104ac69 |
A357346 | E.g.f. satisfies A(x) = (exp(x * exp(A(x))) - 1) * exp(A(x)). | [
"0",
"1",
"5",
"52",
"849",
"18996",
"540986",
"18726247",
"763480675",
"35837071558",
"1903538106065",
"112880374866172",
"7392418912962210",
"529898419942327801",
"41266682731537698181",
"3469461853041348996044",
"313200848521114144611273",
"30215925892728362737156556"
] | [
"nonn"
] | 16 | 0 | 3 | [
"A048802",
"A052888",
"A349557",
"A357346",
"A357347",
"A357348",
"A357424"
] | null | Seiichi Manyama, Sep 25 2022 | 2024-09-09T09:34:01 | oeisdata/seq/A357/A357346.seq | a6af7a50321e7e1be31b6994a1f6376f |
A357347 | E.g.f. satisfies A(x) = (exp(x * exp(A(x))) - 1) * exp(2 * A(x)). | [
"0",
"1",
"7",
"103",
"2385",
"75756",
"3064239",
"150689953",
"8729691693",
"582299930167",
"43956280309659",
"3704637865439380",
"344825037782332457",
"35131983926187957173",
"3888817094785288023367",
"464724955485177444101895",
"59631976064836824117227621",
"8177487264101392841050876136"
] | [
"nonn"
] | 14 | 0 | 3 | [
"A052888",
"A355762",
"A357346",
"A357347",
"A357348",
"A357424"
] | null | Seiichi Manyama, Sep 25 2022 | 2024-09-09T09:34:04 | oeisdata/seq/A357/A357347.seq | aa36e25dd795fc6d8b2d2b5762681746 |
A357348 | E.g.f. satisfies A(x) = (exp(x * exp(A(x))) - 1) * exp(3 * A(x)). | [
"0",
"1",
"9",
"172",
"5181",
"214196",
"11279542",
"722242795",
"54482959375",
"4732518179422",
"465226448603533",
"51061919634063284",
"6189640391474229790",
"821277806639279795053",
"118394082630978607655201",
"18426248367244130561233924",
"3079294928622816257125500821"
] | [
"nonn"
] | 14 | 0 | 3 | [
"A052888",
"A357345",
"A357346",
"A357347",
"A357348",
"A357424"
] | null | Seiichi Manyama, Sep 25 2022 | 2024-09-09T09:34:07 | oeisdata/seq/A357/A357348.seq | 5e048c21a9c0a1e879b16f8e0bb04804 |
A357349 | E.g.f. satisfies A(x) = log(1 + x * exp(A(x))) * exp(A(x)). | [
"0",
"1",
"3",
"23",
"278",
"4624",
"98064",
"2530142",
"76931224",
"2694025872",
"106782582720",
"4726084696992",
"231030209532528",
"12362764041338736",
"718779255989466840",
"45118706229328822680",
"3041140847160686156544",
"219071239142209684437504",
"16796070771249534388114176"
] | [
"nonn"
] | 18 | 0 | 3 | [
"A162655",
"A357349",
"A357350",
"A357351",
"A357423"
] | null | Seiichi Manyama, Sep 25 2022 | 2024-09-10T04:15:14 | oeisdata/seq/A357/A357349.seq | 9076521792fa2067b677c1adc8a8bfa8 |
A357350 | E.g.f. satisfies A(x) = log(1 + x * exp(A(x))) * exp(2 * A(x)). | [
"0",
"1",
"5",
"62",
"1210",
"32464",
"1109988",
"46159364",
"2261784880",
"127625290704",
"8150589862080",
"581192861530368",
"45772039038334464",
"3945903751253912928",
"369585982325018567808",
"37372951572516507717120",
"4057994343926975346772992",
"470900282395259211311765760"
] | [
"nonn"
] | 18 | 0 | 3 | [
"A162656",
"A357349",
"A357350",
"A357351",
"A357423"
] | null | Seiichi Manyama, Sep 25 2022 | 2024-09-10T04:16:48 | oeisdata/seq/A357/A357350.seq | 5cb9f3431803d7348eaafcddb6d3ca04 |
A357351 | E.g.f. satisfies A(x) = log(1 + x * exp(A(x))) * exp(3 * A(x)). | [
"0",
"1",
"7",
"119",
"3186",
"117204",
"5493672",
"313159146",
"21032534856",
"1626654909168",
"142381874412000",
"13915051276560048",
"1501957674420194736",
"177456652252068578544",
"22779601954164759020184",
"3156967397734735846493880",
"469790199951668305705905408"
] | [
"nonn"
] | 16 | 0 | 3 | [
"A357349",
"A357350",
"A357351",
"A357423"
] | null | Seiichi Manyama, Sep 25 2022 | 2024-09-10T04:18:34 | oeisdata/seq/A357/A357351.seq | 8ed6e6de474598e28b54b38e898311ba |
A357352 | Number of partitions of n into distinct positive triangular numbers such that the number of parts is a triangular number. | [
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"2",
"0",
"0",
"0",
"1",
"1",
"0",
"1",
"0",
"2",
"0",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"3",
"0",
"1",
"1",
"2",
"0",
"1",
"1",
"1",
"3",
"0",
"2",
"1",
"1",
"1",
"1",
"2",
"2",
"2",
"1",
"0",
"3",
"1",
"0",
"4",
"1",
"2",
"2",
"2",
"1",
"2",
"2",
"1",
"3",
"1",
"3",
"2",
"1",
"3",
"3",
"1",
"2",
"3",
"3",
"2",
"2",
"3",
"1",
"3",
"3",
"2",
"4",
"2",
"2",
"6",
"2",
"4",
"2",
"4"
] | [
"nonn",
"changed"
] | 16 | 0 | 11 | [
"A000217",
"A024940",
"A045450",
"A178927",
"A357352",
"A357354"
] | null | Ilya Gutkovskiy, Sep 25 2022 | 2025-04-23T13:30:20 | oeisdata/seq/A357/A357352.seq | 8b2af895fcfd6efca1ff35b6987f0e85 |
A357353 | Frobenius number of (n, n+1, n+prime(1), n+prime(2), n+prime(3), ...). | [
"1",
"2",
"3",
"9",
"10",
"13",
"14",
"17",
"19",
"21",
"22",
"25",
"26",
"29",
"31",
"33",
"34",
"37",
"38",
"41",
"43",
"45",
"46",
"49",
"51",
"53",
"83",
"85",
"87",
"89",
"62",
"93",
"67",
"97",
"99",
"109",
"103",
"113",
"115",
"117",
"119",
"121",
"86",
"125",
"127",
"129",
"123",
"133",
"135",
"137",
"139",
"157",
"159",
"161",
"147",
"165",
"173",
"175",
"177",
"179",
"181"
] | [
"nonn"
] | 44 | 2 | 2 | [
"A000040",
"A357353",
"A357995"
] | null | Michel Marcus, Oct 26 2022 | 2025-01-31T04:30:25 | oeisdata/seq/A357/A357353.seq | 92f97a162a7dc0311546fe08702afd49 |
A357354 | Number of partitions of n into distinct positive squares such that the number of parts is a square. | [
"1",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"1",
"1",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"1",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"3",
"1",
"0",
"2",
"0",
"0",
"1",
"1",
"1"
] | [
"nonn",
"changed"
] | 19 | 0 | 79 | [
"A000290",
"A033461",
"A045450",
"A089333",
"A357352",
"A357354"
] | null | Ilya Gutkovskiy, Sep 25 2022 | 2025-04-24T06:48:58 | oeisdata/seq/A357/A357354.seq | e3f0dd883d28444a1e6160414ffff41e |
A357355 | Number of nonempty subsets of {1..n} whose elements have an odd average. | [
"1",
"1",
"2",
"4",
"9",
"13",
"20",
"38",
"71",
"119",
"206",
"384",
"713",
"1285",
"2356",
"4428",
"8331",
"15569",
"29270",
"55582",
"105717",
"200847",
"382808",
"732744",
"1404667",
"2694391",
"5178186",
"9973416",
"19233457",
"37125547",
"71754692",
"138871244",
"269038123",
"521666967",
"1012485750",
"1966957674",
"3824314685"
] | [
"nonn"
] | 12 | 1 | 3 | [
"A051293",
"A309160",
"A357355",
"A357356"
] | null | Ilya Gutkovskiy, Sep 25 2022 | 2022-09-25T11:03:55 | oeisdata/seq/A357/A357355.seq | 86f9b28511948e25cfe83a440f4d5b75 |
A357356 | Number of nonempty subsets of {1..n} whose elements have an even average. | [
"0",
"1",
"3",
"4",
"6",
"13",
"25",
"38",
"64",
"119",
"219",
"384",
"686",
"1285",
"2405",
"4428",
"8236",
"15569",
"29463",
"55582",
"105326",
"200847",
"383609",
"732744",
"1403004",
"2694391",
"5181663",
"9973416",
"19226166",
"37125547",
"71770069",
"138871244",
"269005540",
"521666967",
"1012555015",
"1966957674",
"3824166974"
] | [
"nonn"
] | 10 | 1 | 3 | [
"A051293",
"A309160",
"A357355",
"A357356"
] | null | Ilya Gutkovskiy, Sep 25 2022 | 2022-09-25T11:04:09 | oeisdata/seq/A357/A357356.seq | c60691e237deef4df1116b43fdb95154 |
A357357 | Length of the longest induced cycle in the n X n grid graph. | [
"0",
"4",
"8",
"12",
"16",
"20",
"32",
"40",
"50",
"62",
"76",
"90",
"104",
"120",
"140",
"160",
"180"
] | [
"nonn",
"more"
] | 39 | 1 | 2 | [
"A000937",
"A297664",
"A331968",
"A357357",
"A357358",
"A360914",
"A360915"
] | null | Pontus von Brömssen, Sep 25 2022 | 2025-02-16T08:34:04 | oeisdata/seq/A357/A357357.seq | 183c816fc9cd619b5160ea5d73971074 |
A357358 | Length of the longest induced cycle in the n X n torus grid graph. | [
"6",
"8",
"15",
"20",
"28",
"40",
"48",
"58",
"73",
"88",
"104",
"126"
] | [
"nonn",
"more"
] | 18 | 3 | 1 | [
"A000937",
"A297669",
"A357357",
"A357358",
"A357359"
] | null | Pontus von Brömssen, Sep 25 2022 | 2022-12-14T09:49:45 | oeisdata/seq/A357/A357358.seq | 063904afd383ecca2b2fd6eccd14ff02 |
A357359 | Maximum number of nodes in an induced path (or chordless path or snake path) in the n X n torus grid graph. | [
"5",
"8",
"14",
"21",
"28",
"39",
"50"
] | [
"nonn",
"more"
] | 9 | 3 | 1 | [
"A331968",
"A357234",
"A357358",
"A357359"
] | null | Pontus von Brömssen, Sep 25 2022 | 2022-10-01T10:25:29 | oeisdata/seq/A357/A357359.seq | 191fed7fc1e510230e5a70d43962f69e |
A357360 | Maximum length of an induced path (or chordless path or snake path) between two antipodal nodes of the n-dimensional hypercube. | [
"0",
"1",
"2",
"3",
"4",
"11",
"24"
] | [
"nonn",
"more"
] | 8 | 0 | 3 | [
"A099155",
"A357234",
"A357360",
"A357499"
] | null | Pontus von Brömssen, Sep 25 2022 | 2022-10-02T08:34:01 | oeisdata/seq/A357/A357360.seq | d3f3f98ef2e324c3703f5ec2f38f5263 |
A357361 | Smallest number k such that A345112(k) = n. | [
"1",
"5",
"19",
"118",
"89",
"123",
"102",
"145",
"104",
"777",
"1133",
"1012",
"858",
"942",
"651",
"150",
"453",
"132",
"39",
"112551",
"39782",
"23244",
"81914",
"43810",
"40346"
] | [
"nonn",
"base",
"more"
] | 4 | 1 | 2 | [
"A345112",
"A357361"
] | null | Felix Fröhlich, Sep 25 2022 | 2022-09-26T20:21:27 | oeisdata/seq/A357/A357361.seq | 9e141bac9bb534b638fdec2539634e39 |
A357362 | Primes q such that either p^(q-1) == 1 (mod q^2) or q^(p-1) == 1 (mod p^2), where p = A151799(q). | [
"7",
"53",
"59",
"151057",
"240733",
"911135857"
] | [
"nonn",
"hard",
"more"
] | 12 | 1 | 1 | [
"A151799",
"A151800",
"A357362",
"A357363",
"A357364",
"A357365"
] | null | Felix Fröhlich, Sep 25 2022 | 2023-03-25T15:30:59 | oeisdata/seq/A357/A357362.seq | 6de7d61ae36332592e6190075b69d90a |
A357363 | Primes p such that either p^(q-1) == 1 (mod q^2) or q^(p-1) == 1 (mod p^2), where q = A151800(A151800(p)). | [
"5",
"19",
"263",
"1667"
] | [
"nonn",
"hard",
"more"
] | 4 | 1 | 1 | [
"A151800",
"A357362",
"A357363",
"A357364",
"A357365"
] | null | Felix Fröhlich, Sep 25 2022 | 2022-10-01T19:35:19 | oeisdata/seq/A357/A357363.seq | b530604989b2e892a1d1e0daa474f8f5 |
A357364 | Primes p such that either p^(q-1) == 1 (mod q^2) or q^(p-1) == 1 (mod p^2), where q = A151800(A151800(A151800(p))). | [
"11",
"23",
"41",
"107",
"389",
"1987673",
"35603983"
] | [
"nonn",
"hard",
"more"
] | 4 | 1 | 1 | [
"A151800",
"A357362",
"A357363",
"A357364",
"A357365"
] | null | Felix Fröhlich, Sep 25 2022 | 2022-10-01T19:35:28 | oeisdata/seq/A357/A357364.seq | 86db81ad3cd9c3e821f6a8c6979a4e27 |
A357365 | Primes q such that either p^(q-1) == 1 (mod q^2) or q^(p-1) == 1 (mod p^2), where p = A151799(A151799(A151799(A151799(q)))). | [
"19",
"67",
"349",
"2011",
"22307",
"13699249",
"2018905087",
"9809844767"
] | [
"nonn",
"hard",
"more"
] | 9 | 1 | 1 | [
"A151799",
"A151800",
"A357362",
"A357363",
"A357364",
"A357365"
] | null | Felix Fröhlich, Sep 25 2022 | 2023-03-25T15:31:28 | oeisdata/seq/A357/A357365.seq | 122ede2c4a708f60588f845c887b0062 |
A357366 | Expansion of Product_{k>=0} 1 / (1 - x^(2^k) - x^(2^(k+1)))^(2^k). | [
"1",
"1",
"4",
"5",
"18",
"23",
"59",
"82",
"203",
"285",
"610",
"895",
"1838",
"2733",
"5217",
"7950",
"14763",
"22713",
"40526",
"63239",
"110652",
"173891",
"297529",
"471420",
"796706",
"1268126",
"2116508",
"3384634",
"5606444",
"8991078",
"14791302",
"23782380",
"38955441",
"62737821",
"102388280",
"165126101",
"268844542",
"433970643"
] | [
"nonn"
] | 14 | 0 | 3 | [
"A073709",
"A084782",
"A173285",
"A237651",
"A357366"
] | null | Ilya Gutkovskiy, Sep 25 2022 | 2022-10-08T06:49:53 | oeisdata/seq/A357/A357366.seq | 791356cc13a7d82acc314972714b45dc |
A357367 | Triangle read by rows. T(n, k) = Sum_{m=0..k} (-1)^(m + k) * binomial(n + k, n + m) * L(n + m, m), where L denotes the unsigned Lah numbers A271703. | [
"1",
"0",
"2",
"0",
"6",
"12",
"0",
"24",
"120",
"120",
"0",
"120",
"1080",
"2520",
"1680",
"0",
"720",
"10080",
"40320",
"60480",
"30240",
"0",
"5040",
"100800",
"604800",
"1512000",
"1663200",
"665280",
"0",
"40320",
"1088640",
"9072000",
"33264000",
"59875200",
"51891840",
"17297280"
] | [
"nonn",
"tabl"
] | 11 | 0 | 3 | [
"A032037",
"A271703",
"A357367"
] | null | Peter Luschny, Sep 26 2022 | 2023-12-10T09:23:20 | oeisdata/seq/A357/A357367.seq | cce9b073ca1db621438e2d8f77dd11ac |
A357368 | Triangle read by rows. Convolution triangle of the prime indicator sequence A089026. | [
"1",
"0",
"1",
"0",
"2",
"1",
"0",
"3",
"4",
"1",
"0",
"1",
"10",
"6",
"1",
"0",
"5",
"14",
"21",
"8",
"1",
"0",
"1",
"23",
"47",
"36",
"10",
"1",
"0",
"7",
"28",
"90",
"108",
"55",
"12",
"1",
"0",
"1",
"49",
"147",
"258",
"205",
"78",
"14",
"1",
"0",
"1",
"46",
"249",
"520",
"595",
"346",
"105",
"16",
"1",
"0",
"1",
"75",
"360",
"978",
"1437",
"1185",
"539",
"136",
"18",
"1"
] | [
"nonn",
"tabl"
] | 24 | 0 | 5 | [
"A089026",
"A340991",
"A357368",
"A357588"
] | null | Peter Luschny, Oct 03 2022 | 2023-01-30T03:32:36 | oeisdata/seq/A357/A357368.seq | 853b18ff8c5b51c7fd972f3739ee00ae |
A357369 | a(n) is the first prime p such that (p+q)/(2*n) is prime, where q is the next prime after p. | [
"3",
"5",
"11",
"13",
"11",
"19",
"53",
"17",
"29",
"467",
"59",
"23",
"41",
"29",
"173",
"31",
"197",
"4877",
"59",
"41",
"151",
"67",
"71",
"47",
"751",
"79",
"53",
"661",
"59",
"89",
"61",
"97",
"101",
"103",
"71",
"109",
"73",
"193",
"113",
"199",
"461",
"83",
"1361",
"223",
"137",
"3331",
"139",
"2297",
"149",
"101",
"257",
"1531",
"107",
"163",
"1621",
"397",
"751",
"997",
"113",
"7741",
"181",
"313",
"191",
"193"
] | [
"nonn"
] | 10 | 2 | 1 | [
"A357369",
"A357373"
] | null | Robert Israel, Sep 25 2022 | 2022-10-03T08:45:15 | oeisdata/seq/A357/A357369.seq | 8b0ff21705ff7ac079ace7460956226b |
A357370 | Positions of 0's in A355917. | [
"1",
"3",
"7",
"13",
"21",
"33",
"47",
"64",
"82",
"102",
"125",
"149",
"176",
"204",
"234",
"267",
"302",
"339",
"378",
"419",
"462",
"507",
"554",
"603",
"654",
"707",
"763",
"820",
"880",
"943",
"1008",
"1075",
"1143",
"1215",
"1288",
"1362",
"1437",
"1513",
"1592",
"1674",
"1757",
"1842",
"1928",
"2017",
"2107",
"2199",
"2293",
"2389",
"2487",
"2587",
"2690"
] | [
"nonn"
] | 16 | 1 | 2 | [
"A355916",
"A355917",
"A357370",
"A357371"
] | null | Michael De Vlieger, Sep 25 2022 | 2022-10-06T04:30:29 | oeisdata/seq/A357/A357370.seq | 3a996ca85542f8d5a79f67fe0a0e2d28 |
A357371 | a(1) = 1, thereafter, first differences of A357370. | [
"1",
"2",
"4",
"6",
"8",
"12",
"14",
"17",
"18",
"20",
"23",
"24",
"27",
"28",
"30",
"33",
"35",
"37",
"39",
"41",
"43",
"45",
"47",
"49",
"51",
"53",
"56",
"57",
"60",
"63",
"65",
"67",
"68",
"72",
"73",
"74",
"75",
"76",
"79",
"82",
"83",
"85",
"86",
"89",
"90",
"92",
"94",
"96",
"98",
"100",
"103",
"104",
"107",
"109",
"110",
"112",
"114",
"116",
"118",
"120",
"122",
"124",
"126"
] | [
"nonn"
] | 9 | 1 | 2 | [
"A355916",
"A355917",
"A357370",
"A357371"
] | null | Michael De Vlieger, Sep 25 2022 | 2022-09-27T12:43:51 | oeisdata/seq/A357/A357371.seq | 61f06a8586f4d4a9b594de6496d7f6bd |
A357372 | Square array A(n, k), n, k > 0, read by antidiagonals; A(n, k) is the numerator of 1/n + 1/k. | [
"2",
"3",
"3",
"4",
"1",
"4",
"5",
"5",
"5",
"5",
"6",
"3",
"2",
"3",
"6",
"7",
"7",
"7",
"7",
"7",
"7",
"8",
"2",
"8",
"1",
"8",
"2",
"8",
"9",
"9",
"1",
"9",
"9",
"1",
"9",
"9",
"10",
"5",
"10",
"5",
"2",
"5",
"10",
"5",
"10",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"11",
"12",
"3",
"4",
"3",
"12",
"1",
"12",
"3",
"4",
"3",
"12",
"13",
"13",
"13",
"13",
"13",
"13",
"13",
"13",
"13",
"13",
"13",
"13"
] | [
"nonn",
"tabl",
"easy",
"frac"
] | 8 | 1 | 1 | [
"A000034",
"A257522",
"A357372"
] | null | Rémy Sigrist, Sep 25 2022 | 2022-09-26T10:39:11 | oeisdata/seq/A357/A357372.seq | c1525f8dba74aa995f9c60770ab60b45 |
A357373 | a(n) is the first prime p such that (p+q)/(2*n) is the square of a prime, where q is the next prime after p. | [
"3",
"17",
"11",
"47521",
"43",
"149",
"26041",
"71",
"79",
"3607",
"97",
"107",
"6871",
"53",
"59",
"61",
"31397",
"71",
"73",
"179",
"2539",
"197",
"2777",
"599",
"223",
"647",
"107",
"61843",
"1520777",
"113",
"277",
"283",
"823",
"5743",
"313",
"139",
"254887",
"337",
"349",
"157",
"75797",
"1049",
"5197",
"173",
"179",
"409",
"2297",
"191",
"439",
"6047",
"457",
"892357",
"8951",
"242399",
"491"
] | [
"nonn"
] | 13 | 1 | 1 | [
"A357369",
"A357373"
] | null | Robert Israel, Sep 25 2022 | 2022-10-16T16:34:44 | oeisdata/seq/A357/A357373.seq | 2cf6511f22b843ae17bf20f5476865ed |
A357374 | Number of ordered factorizations of n into numbers > 1 with an even number of prime divisors (prime factors counted with multiplicity). | [
"1",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"1",
"1",
"2",
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"3",
"1",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"1",
"4",
"0",
"1",
"1",
"3",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"3",
"1",
"3",
"1",
"1",
"0",
"5",
"0",
"1",
"0",
"4",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"2",
"1",
"0",
"5",
"1",
"1",
"1",
"3",
"0",
"5"
] | [
"nonn"
] | 5 | 1 | 16 | [
"A028260",
"A050334",
"A065043",
"A074206",
"A308063",
"A353337",
"A357374",
"A357375"
] | null | Ilya Gutkovskiy, Sep 25 2022 | 2022-09-26T20:17:16 | oeisdata/seq/A357/A357374.seq | 227e45ef23bb68e8857e6d9197b74e9c |
A357375 | Number of ordered factorizations of n into numbers > 1 with an even number of distinct prime divisors. | [
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"1",
"1",
"2",
"0",
"1",
"1",
"1",
"0",
"0",
"0",
"1",
"1",
"1",
"0",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"1",
"1",
"0",
"2",
"0",
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"3",
"0",
"1",
"1",
"1",
"1",
"0",
"0",
"1",
"0",
"1",
"0",
"2",
"1",
"1",
"1",
"1",
"0",
"2"
] | [
"nonn"
] | 4 | 1 | 36 | [
"A030231",
"A050334",
"A074206",
"A308063",
"A357374",
"A357375"
] | null | Ilya Gutkovskiy, Sep 25 2022 | 2022-09-26T20:17:24 | oeisdata/seq/A357/A357375.seq | e9571b839697e585c35880b065034e38 |
A357376 | The lowest number on Ulam Spiral for which all numbers in the square which is centered at a(n) and spans n-1 spaces in each cardinal direction are nonprime. | [
"1",
"26",
"1016",
"5136",
"39639",
"203100",
"2729736",
"32264250",
"42119062",
"1065799391",
"12444190246"
] | [
"nonn",
"more"
] | 37 | 1 | 2 | [
"A000040",
"A115258",
"A136626",
"A225073",
"A357376"
] | null | Samuel Harkness, Sep 26 2022 | 2022-11-06T09:05:24 | oeisdata/seq/A357/A357376.seq | ff2f54e2d85fd17ae77f3b46a87059a1 |
A357377 | a(0) = 0; for n > 0, a(n) is the smallest positive number not occurring earlier such that |a(n) - a(n-1)| does not appear in the string concatenation of a(0)..a(n-1). | [
"0",
"1",
"3",
"5",
"7",
"9",
"11",
"13",
"15",
"17",
"19",
"21",
"25",
"2",
"6",
"10",
"14",
"22",
"4",
"12",
"20",
"28",
"44",
"8",
"24",
"40",
"56",
"18",
"34",
"50",
"23",
"39",
"55",
"26",
"42",
"58",
"29",
"45",
"61",
"31",
"47",
"63",
"27",
"43",
"59",
"75",
"37",
"53",
"69",
"85",
"36",
"52",
"68",
"30",
"46",
"62",
"78",
"94",
"110",
"33",
"49",
"65",
"81",
"97",
"113",
"41",
"57",
"73",
"35",
"51",
"67",
"105",
"143",
"16",
"54"
] | [
"nonn",
"base",
"look"
] | 12 | 0 | 3 | [
"A007088",
"A030302",
"A118248",
"A341766",
"A355611",
"A357082",
"A357377"
] | null | Scott R. Shannon, Sep 26 2022 | 2023-01-16T09:10:46 | oeisdata/seq/A357/A357377.seq | 90048db4502288bfeedae828a7f8597f |
A357378 | Lexicographically earliest sequence of positive integers such that the values a(floor(n/2)) * a(n) are all distinct. | [
"1",
"2",
"2",
"3",
"4",
"5",
"1",
"3",
"3",
"4",
"1",
"3",
"7",
"11",
"6",
"7",
"8",
"9",
"5",
"7",
"13",
"14",
"10",
"11",
"5",
"6",
"2",
"4",
"6",
"8",
"7",
"8",
"4",
"5",
"5",
"6",
"5",
"10",
"9",
"10",
"2",
"3",
"6",
"7",
"6",
"8",
"5",
"6",
"13",
"15",
"12",
"13",
"17",
"19",
"13",
"16",
"15",
"16",
"11",
"13",
"11",
"13",
"14",
"15",
"17",
"19",
"17",
"19",
"20",
"21",
"17",
"18",
"22",
"23",
"13"
] | [
"nonn"
] | 15 | 0 | 2 | [
"A050292",
"A357378",
"A357379"
] | null | Rémy Sigrist, Sep 26 2022 | 2022-09-29T03:25:47 | oeisdata/seq/A357/A357378.seq | cd8e8b06d2542bb54628ccb3df214661 |
A357379 | a(n) = A357378(floor(n/2)) * A357378(n). | [
"1",
"2",
"4",
"6",
"8",
"10",
"3",
"9",
"12",
"16",
"5",
"15",
"7",
"11",
"18",
"21",
"24",
"27",
"20",
"28",
"13",
"14",
"30",
"33",
"35",
"42",
"22",
"44",
"36",
"48",
"49",
"56",
"32",
"40",
"45",
"54",
"25",
"50",
"63",
"70",
"26",
"39",
"84",
"98",
"60",
"80",
"55",
"66",
"65",
"75",
"72",
"78",
"34",
"38",
"52",
"64",
"90",
"96",
"88",
"104",
"77",
"91",
"112",
"120",
"68",
"76",
"85"
] | [
"nonn"
] | 16 | 0 | 2 | [
"A357378",
"A357379",
"A357396"
] | null | Rémy Sigrist, Sep 26 2022 | 2022-09-29T03:25:44 | oeisdata/seq/A357/A357379.seq | f30a6afb4ac3285fef5671c903ef5cec |
A357380 | Expansion of Product_{k>=1} (1 - x^Fibonacci(k)). | [
"1",
"-2",
"0",
"1",
"1",
"-1",
"0",
"1",
"-2",
"1",
"0",
"1",
"-2",
"0",
"2",
"-1",
"0",
"0",
"1",
"-2",
"0",
"1",
"1",
"0",
"-2",
"1",
"0",
"0",
"0",
"1",
"-2",
"0",
"1",
"1",
"-1",
"0",
"1",
"-1",
"-1",
"0",
"2",
"-1",
"0",
"0",
"0",
"0",
"0",
"1",
"-2",
"0",
"1",
"1",
"-1",
"0",
"1",
"-2",
"1",
"0",
"1",
"-2",
"1",
"0",
"-1",
"1",
"1",
"0",
"-2",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"-2",
"0",
"1",
"1",
"-1",
"0",
"1",
"-2",
"1",
"0",
"1",
"-2",
"0",
"2",
"-1",
"0",
"0",
"1",
"-2",
"0",
"2",
"-1",
"0",
"-1"
] | [
"sign"
] | 5 | 0 | 2 | [
"A000045",
"A007000",
"A093996",
"A357380",
"A357381"
] | null | Ilya Gutkovskiy, Sep 26 2022 | 2022-09-26T20:17:37 | oeisdata/seq/A357/A357380.seq | 1d9d8dfceadc165aa660aa9a69fc88cc |
A357381 | Expansion of Product_{k>=1} 1 / (1 + x^Fibonacci(k)). | [
"1",
"-2",
"2",
"-3",
"5",
"-7",
"9",
"-11",
"13",
"-16",
"20",
"-23",
"26",
"-31",
"36",
"-41",
"48",
"-55",
"62",
"-71",
"81",
"-92",
"104",
"-116",
"129",
"-145",
"163",
"-180",
"198",
"-219",
"242",
"-267",
"293",
"-320",
"349",
"-381",
"416",
"-452",
"489",
"-529",
"572",
"-618",
"668",
"-719",
"771",
"-829",
"892",
"-956",
"1023",
"-1094",
"1167",
"-1246",
"1331",
"-1416",
"1504"
] | [
"sign"
] | 4 | 0 | 2 | [
"A000045",
"A000121",
"A298949",
"A357380",
"A357381"
] | null | Ilya Gutkovskiy, Sep 26 2022 | 2022-09-26T20:17:50 | oeisdata/seq/A357/A357381.seq | 4fc4b3e6c4261d3df179f397cc48bbb5 |
A357382 | Expansion of Product_{k>=1} (1 - x^Lucas(k)). | [
"1",
"-1",
"0",
"-1",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"-1",
"0",
"0",
"0",
"1",
"-1",
"0",
"-1",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"-1",
"0",
"-1",
"0",
"1",
"0",
"1",
"-1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"-1",
"0",
"-1",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"-1",
"0",
"-1",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"-1",
"0",
"-1",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"-1",
"0",
"0",
"0",
"1",
"-1",
"0",
"0",
"0",
"0",
"-1",
"0",
"1",
"0",
"1",
"-1"
] | [
"sign"
] | 5 | 0 | null | [
"A000204",
"A067592",
"A357382",
"A357383"
] | null | Ilya Gutkovskiy, Sep 26 2022 | 2022-09-26T20:18:01 | oeisdata/seq/A357/A357382.seq | 6b69942344c6640633f285bfbd43182b |
A357383 | Expansion of Product_{k>=1} 1 / (1 + x^Lucas(k)). | [
"1",
"-1",
"1",
"-2",
"1",
"-1",
"2",
"-2",
"3",
"-4",
"4",
"-5",
"5",
"-5",
"7",
"-7",
"8",
"-10",
"9",
"-10",
"11",
"-11",
"14",
"-15",
"16",
"-18",
"17",
"-18",
"20",
"-21",
"24",
"-26",
"27",
"-29",
"29",
"-31",
"35",
"-36",
"40",
"-43",
"43",
"-46",
"48",
"-51",
"56",
"-59",
"63",
"-67",
"68",
"-72",
"77",
"-80",
"86",
"-91",
"94",
"-99",
"103",
"-108",
"116",
"-121",
"127",
"-134",
"137",
"-143",
"151"
] | [
"sign"
] | 4 | 0 | 4 | [
"A000204",
"A003263",
"A357382",
"A357383"
] | null | Ilya Gutkovskiy, Sep 26 2022 | 2022-09-26T20:18:09 | oeisdata/seq/A357/A357383.seq | 9b565835b8759dfff527c1e0be62b1ab |
A357384 | Expansion of 1 / (1 + Sum_{k>=1}(-x)^Lucas(k)). | [
"1",
"1",
"1",
"2",
"2",
"2",
"3",
"4",
"5",
"7",
"10",
"14",
"19",
"26",
"36",
"48",
"64",
"87",
"116",
"155",
"210",
"283",
"382",
"518",
"701",
"948",
"1282",
"1732",
"2339",
"3158",
"4263",
"5756",
"7772",
"10495",
"14176",
"19148",
"25865",
"34941",
"47198",
"63753",
"86114",
"116311",
"157095",
"212181",
"286580",
"387070",
"522805",
"706142",
"953777",
"1288260",
"1740044"
] | [
"nonn"
] | 4 | 0 | 4 | [
"A000204",
"A080889",
"A288039",
"A357384"
] | null | Ilya Gutkovskiy, Sep 26 2022 | 2022-09-26T20:18:17 | oeisdata/seq/A357/A357384.seq | 98dd1f4196693fbb7300a2f01c3924c2 |
A357385 | a(n) = A071626(n+1) - A071626(n). | [
"1",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"-1",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0"
] | [
"sign"
] | 10 | 1 | null | [
"A071626",
"A357385"
] | null | Amiram Eldar, Sep 26 2022 | 2022-09-28T03:53:10 | oeisdata/seq/A357/A357385.seq | f36348066a9292d0febd33856a0c4ed6 |
A357386 | a(n) is the start of the least run of exactly n consecutive positive integers with the same value of A071626, or -1 if no such run exists. | [
"1",
"2",
"116",
"6",
"10",
"290",
"15",
"333",
"136",
"55",
"22",
"102",
"410",
"119",
"477",
"232",
"68",
"261",
"451",
"2343",
"153",
"348",
"708",
"492",
"1037",
"377",
"976",
"826",
"174",
"615",
"1940",
"656",
"1422",
"8642",
"1711",
"7712",
"10382",
"3232",
"5921",
"9089",
"3434",
"2286",
"2556",
"1988",
"5617",
"6040",
"6576",
"17025",
"12939",
"6194",
"19694"
] | [
"nonn"
] | 9 | 1 | 2 | [
"A071626",
"A357385",
"A357386",
"A357387"
] | null | Amiram Eldar, Sep 26 2022 | 2022-09-28T03:53:07 | oeisdata/seq/A357/A357386.seq | 65bba235bc38f089828ddbca28e0e1af |
A357387 | Starts of record-length runs of consecutive positive integers with the same value of A071626. | [
"1",
"2",
"6",
"10",
"15",
"22",
"68",
"153",
"174",
"615",
"656",
"1422",
"1711",
"1846",
"2425",
"7164",
"8791",
"13988",
"42755",
"48290",
"186108",
"221131",
"3860731"
] | [
"nonn",
"more"
] | 5 | 1 | 2 | [
"A071626",
"A357385",
"A357386",
"A357387"
] | null | Amiram Eldar, Sep 26 2022 | 2022-09-26T20:15:28 | oeisdata/seq/A357/A357387.seq | 32e08170ea74dec3d6be02eb67ecc7ae |
A357388 | Numbers k such that A071626(k) < A071626(k+1). | [
"1",
"3",
"5",
"9",
"14",
"21",
"32",
"43",
"54",
"65",
"67",
"84",
"101",
"115",
"118",
"135",
"144",
"152",
"173",
"202",
"221",
"231",
"258",
"260",
"289",
"295",
"318",
"332",
"347",
"369",
"376",
"405",
"409",
"423",
"434",
"450",
"476",
"491",
"530",
"532",
"573",
"589",
"614",
"648",
"655",
"696",
"707",
"736",
"737",
"766",
"778",
"803",
"819",
"825",
"860",
"870"
] | [
"nonn"
] | 8 | 1 | 2 | [
"A071626",
"A342091",
"A357385",
"A357388",
"A357390"
] | null | Amiram Eldar, Sep 26 2022 | 2022-09-28T03:53:04 | oeisdata/seq/A357/A357388.seq | 0d4b82c3a462fea9dc18a4c2640e4d0e |
A357389 | a(n) is the start of the least run of exactly n consecutive positive integers with strictly increasing values of A071626, or -1 if no such run exists. | [
"7",
"1",
"736",
"26048",
"991434"
] | [
"nonn",
"hard",
"more"
] | 6 | 1 | 1 | [
"A071626",
"A342091",
"A357388",
"A357389",
"A357391"
] | null | Amiram Eldar, Sep 26 2022 | 2022-09-26T20:16:08 | oeisdata/seq/A357/A357389.seq | c63cafce854cd1fcff0a3cf69f4ff9e5 |
A357390 | Numbers k such that A071626(k) > A071626(k+1). | [
"64",
"113",
"132",
"151",
"216",
"247",
"278",
"309",
"340",
"371",
"402",
"422",
"433",
"469",
"515",
"558",
"601",
"644",
"687",
"730",
"731",
"773",
"792",
"816",
"853",
"859",
"914",
"975",
"1021",
"1036",
"1094",
"1097",
"1129",
"1156",
"1158",
"1167",
"1219",
"1240",
"1242",
"1244",
"1280",
"1313",
"1327",
"1341",
"1355",
"1386",
"1402",
"1410",
"1459"
] | [
"nonn"
] | 10 | 1 | 1 | [
"A071626",
"A342091",
"A357385",
"A357388",
"A357390"
] | null | Amiram Eldar, Sep 26 2022 | 2022-09-28T03:53:01 | oeisdata/seq/A357/A357390.seq | 42b739ef854c264aba230ad8fd484dde |
A357391 | a(n) is the start of the least run of exactly n consecutive positive integers with strictly decreasing values of A071626, or -1 if no such run exists. | [
"1",
"64",
"730",
"8755",
"12734",
"8419585"
] | [
"nonn",
"hard",
"more"
] | 7 | 1 | 2 | [
"A071626",
"A342091",
"A357389",
"A357390",
"A357391"
] | null | Amiram Eldar, Sep 26 2022 | 2022-09-26T20:16:36 | oeisdata/seq/A357/A357391.seq | da278d1aa5a3c626aceaf7374f4cdfdf |
A357392 | E.g.f. satisfies A(x) = -log(1 - x * exp(2 * A(x))). | [
"0",
"1",
"5",
"56",
"990",
"24024",
"742560",
"27907200",
"1235591280",
"62990928000",
"3634245014400",
"234102016512000",
"16654322805120000",
"1296884927852236800",
"109720581991308288000",
"10021650950985427353600",
"982869376029609100032000",
"103017324974226408345600000"
] | [
"nonn"
] | 16 | 0 | 3 | [
"A006963",
"A357333",
"A357338",
"A357392",
"A357393"
] | null | Seiichi Manyama, Sep 26 2022 | 2024-09-10T04:20:07 | oeisdata/seq/A357/A357392.seq | c709f209b431c42a0feb33edbb16987f |
A357393 | E.g.f. satisfies A(x) = -log(1 - x * exp(3 * A(x))). | [
"0",
"1",
"7",
"110",
"2730",
"93024",
"4037880",
"213127200",
"13253058000",
"948964262400",
"76899763100160",
"6957624460550400",
"695236239163065600",
"76043127767523840000",
"9036546669251861760000",
"1159342449440429270016000",
"159708538424128885551360000",
"23512778013219939149561856000"
] | [
"nonn"
] | 17 | 0 | 3 | [
"A006963",
"A357334",
"A357392",
"A357393"
] | null | Seiichi Manyama, Sep 26 2022 | 2024-09-10T04:21:51 | oeisdata/seq/A357/A357393.seq | ebc4117ba4691080e50a3f39143061fe |
A357394 | E.g.f. satisfies A(x) = exp(x * exp(2 * A(x))) - 1. | [
"0",
"1",
"5",
"55",
"953",
"22651",
"685525",
"25222359",
"1093148145",
"54549313651",
"3080446982221",
"194213549023407",
"13522789698386281",
"1030619149263349387",
"85336828127587240261",
"7628421633465044832391",
"732208108150442899232737",
"75108533335473988089786147"
] | [
"nonn"
] | 18 | 0 | 3 | [
"A052888",
"A357335",
"A357394",
"A357395"
] | null | Seiichi Manyama, Sep 26 2022 | 2024-09-10T04:23:48 | oeisdata/seq/A357/A357394.seq | 4af54a6f026685d9baa8eaf31d6d04ad |
A357395 | E.g.f. satisfies A(x) = exp(x * exp(3 * A(x))) - 1. | [
"0",
"1",
"7",
"109",
"2677",
"90226",
"3873007",
"202134997",
"12427851625",
"879806921041",
"70486590597331",
"6304879010400202",
"622838214328334077",
"67347956304168803173",
"7911963620634266270071",
"1003477119181096373029261",
"136658009168055564212000209",
"19889317400287888238121299854"
] | [
"nonn"
] | 16 | 0 | 3 | [
"A052888",
"A357336",
"A357394",
"A357395"
] | null | Seiichi Manyama, Sep 26 2022 | 2024-09-10T04:25:26 | oeisdata/seq/A357/A357395.seq | 276baa413c4f6cb89584edd59812c5b5 |
A357396 | Inverse of A357379. | [
"0",
"1",
"6",
"2",
"10",
"3",
"12",
"4",
"7",
"5",
"13",
"8",
"20",
"21",
"11",
"9",
"104",
"14",
"106",
"18",
"15",
"26",
"146",
"16",
"36",
"40",
"17",
"19",
"162",
"22",
"208",
"32",
"23",
"52",
"24",
"28",
"209",
"53",
"41",
"33",
"212",
"25",
"213",
"27",
"34",
"80",
"292",
"29",
"30",
"37",
"82",
"54",
"293",
"35",
"46",
"31",
"83",
"81",
"324",
"44",
"325",
"386",
"38",
"55"
] | [
"nonn"
] | 24 | 1 | 3 | [
"A357379",
"A357396"
] | null | Rémy Sigrist, Sep 26 2022 | 2022-09-29T03:29:25 | oeisdata/seq/A357/A357396.seq | fb6935cb99d73367456a05fa123b725c |
A357397 | a(n) = coefficient of x^n, n >= 0, in A(x) such that: 0 = Sum_{n>=1} ((1+x)^n - A(x))^n / (1+x)^(n^2). | [
"1",
"1",
"1",
"5",
"37",
"367",
"4463",
"63797",
"1043961",
"19208815",
"392278493",
"8802891869",
"215335062049",
"5704017709585",
"162695460126735",
"4972552233126827",
"162156046298476305",
"5620675413587870585",
"206382551428754263839",
"8003189847508668434429"
] | [
"nonn"
] | 13 | 0 | 4 | [
"A357397",
"A357398"
] | null | Paul D. Hanna, Oct 20 2022 | 2022-12-03T12:05:10 | oeisdata/seq/A357/A357397.seq | af9b4cde5ff75f85fac75590c76aa616 |
A357398 | a(n) = coefficient of x^n/n!, n >= 0, in A(x) such that: 0 = Sum_{n>=1} exp(-n^2*x) * (exp(n*x) - A(x))^n. | [
"1",
"1",
"3",
"37",
"1083",
"53701",
"3934443",
"395502997",
"51998075643",
"8643190760101",
"1770707733052683",
"438247927304923957",
"128926370847248904603",
"44477192002157773868101",
"17787359321176954021105323",
"8164879801560415752441320917",
"4264616618784184682736855291963"
] | [
"nonn"
] | 13 | 0 | 3 | [
"A357397",
"A357398"
] | null | Paul D. Hanna, Oct 20 2022 | 2022-12-03T12:05:27 | oeisdata/seq/A357/A357398.seq | 6099635d746457bd320bd27160b8fcbf |
A357399 | Coefficients of x^n, n >= 0, in A(x) such that: x = Sum_{n=-oo..+oo} (-x)^n * (1 - (-x)^n)^n * A(x)^n. | [
"1",
"1",
"3",
"10",
"37",
"143",
"564",
"2270",
"9305",
"38755",
"163569",
"698186",
"3009129",
"13077850",
"57250728",
"252221229",
"1117409653",
"4975095073",
"22249463540",
"99901607730",
"450187852401",
"2035353779794",
"9229671434155",
"41968536407303",
"191318458136066",
"874179701912764",
"4002949886221529"
] | [
"nonn"
] | 17 | 0 | 3 | [
"A357399",
"A357791"
] | null | Paul D. Hanna, Nov 07 2022 | 2022-12-24T13:51:41 | oeisdata/seq/A357/A357399.seq | 91974c10c1cab2109f04a6e93c963db0 |
A357400 | Coefficients T(n,k) of x^n*y^k in the function A(x,y) that satisfies: y = Sum_{n=-oo..+oo} x^(2*n+1) * (1 - x^n)^(n+1) * A(x,y)^n, as a triangle read by rows with k = 0..n for each row index n >= 0. | [
"1",
"0",
"1",
"0",
"0",
"2",
"0",
"1",
"0",
"5",
"0",
"0",
"3",
"0",
"14",
"0",
"-2",
"0",
"10",
"0",
"42",
"0",
"8",
"-12",
"0",
"35",
"0",
"132",
"0",
"-14",
"36",
"-52",
"0",
"126",
"0",
"429",
"0",
"16",
"-76",
"148",
"-210",
"0",
"462",
"0",
"1430",
"0",
"-7",
"84",
"-354",
"590",
"-825",
"0",
"1716",
"0",
"4862",
"0",
"-24",
"-27",
"416",
"-1565",
"2322",
"-3199",
"0",
"6435",
"0",
"16796",
"0",
"103",
"-276",
"-120",
"1950",
"-6732",
"9086",
"-12320",
"0",
"24310",
"0",
"58786",
"0",
"-232",
"987",
"-1752",
"-560",
"8832",
"-28490",
"35464",
"-47268",
"0",
"92378",
"0",
"208012"
] | [
"sign",
"tabl"
] | 16 | 0 | 6 | [
"A000108",
"A001700",
"A356783",
"A357151",
"A357400",
"A357401",
"A357402",
"A357403",
"A357404",
"A357405"
] | null | Paul D. Hanna, Sep 26 2022 | 2022-10-08T00:26:10 | oeisdata/seq/A357/A357400.seq | 3d5243b033cefa895625ef9e3833116a |
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